LMFDB - Embedded newform 270.3.o.a.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(11,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13, 0]))

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

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

chi := DirichletCharacter("270.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.o (of order $18$, degree $6$, 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:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	270.11
Dual form			270.3.o.a.221.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.909039 - 1.08335i) q^{2} +(-1.68760 - 2.48032i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(-4.22115 - 0.426446i) q^{6} +(-2.08160 + 11.8053i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-3.30400 + 8.37159i) q^{9} +(1.58114 + 2.73861i) q^{10} +(0.641461 + 1.76240i) q^{11} +(-4.29918 + 4.18533i) q^{12} +(-3.66205 + 3.07282i) q^{13} +(10.8970 + 12.9866i) q^{14} +(6.50234 - 1.64911i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-7.02615 + 4.05655i) q^{17} +(6.06590 + 11.1895i) q^{18} +(-6.69415 + 11.5946i) q^{19} +(4.40419 + 0.776578i) q^{20} +(32.7939 - 14.7596i) q^{21} +(2.49241 + 0.907162i) q^{22} +(10.9185 - 1.92523i) q^{23} +(0.626056 + 8.46215i) q^{24} +(-3.83022 - 3.21394i) q^{25} +6.76060i q^{26} +(26.3401 - 5.93292i) q^{27} +23.9749 q^{28} +(-5.41796 + 6.45687i) q^{29} +(4.12431 - 8.54342i) q^{30} +(-5.64651 - 32.0229i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(3.28879 - 4.56526i) q^{33} +(-1.99238 + 11.2993i) q^{34} +(-23.2136 - 13.4024i) q^{35} +(17.6363 + 3.60019i) q^{36} +(21.8945 + 37.9224i) q^{37} +(6.47578 + 17.7921i) q^{38} +(13.8017 + 3.89736i) q^{39} +(4.84489 - 4.06535i) q^{40} +(27.5924 + 32.8833i) q^{41} +(13.8211 - 48.9444i) q^{42} +(-63.9448 + 23.2740i) q^{43} +(3.24847 - 1.87551i) q^{44} +(-15.0637 - 13.3449i) q^{45} +(7.83966 - 13.5787i) q^{46} +(-40.5756 - 7.15456i) q^{47} +(9.73659 + 7.01419i) q^{48} +(-88.9876 - 32.3888i) q^{49} +(-6.96364 + 1.22788i) q^{50} +(21.9189 + 10.5813i) q^{51} +(7.32410 + 6.14565i) q^{52} +75.3378i q^{53} +(17.5167 - 33.9288i) q^{54} -4.19376 q^{55} +(21.7941 - 25.9732i) q^{56} +(40.0554 - 2.96342i) q^{57} +(2.06992 + 11.7391i) q^{58} +(20.6518 - 56.7402i) q^{59} +(-5.50636 - 12.2344i) q^{60} +(-1.88736 + 10.7037i) q^{61} +(-39.8250 - 22.9929i) q^{62} +(-91.9517 - 56.4311i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-3.65601 - 10.0448i) q^{65} +(-1.95614 - 7.71291i) q^{66} +(-77.1798 + 64.7615i) q^{67} +(10.4300 + 12.4300i) q^{68} +(-23.2013 - 23.8324i) q^{69} +(-35.6215 + 12.9652i) q^{70} +(102.710 - 59.2994i) q^{71} +(19.9323 - 15.8336i) q^{72} +(-29.4831 + 51.0663i) q^{73} +(60.9863 + 10.7535i) q^{74} +(-1.50772 + 14.9240i) q^{75} +(25.1618 + 9.15814i) q^{76} +(-22.1409 + 3.90405i) q^{77} +(16.7685 - 11.4092i) q^{78} +(-109.039 - 91.4948i) q^{79} -8.94427i q^{80} +(-59.1671 - 55.3195i) q^{81} +60.7068 q^{82} +(52.8064 - 62.9322i) q^{83} +(-40.4600 - 59.4654i) q^{84} +(-3.15023 - 17.8658i) q^{85} +(-32.9144 + 90.4317i) q^{86} +(25.1585 + 2.54166i) q^{87} +(0.921157 - 5.22414i) q^{88} +(38.9210 + 22.4710i) q^{89} +(-28.1506 + 4.18827i) q^{90} +(-28.6528 - 49.6280i) q^{91} +(-7.58393 - 20.8367i) q^{92} +(-69.8982 + 68.0471i) q^{93} +(-44.6357 + 37.4538i) q^{94} +(-19.2432 - 22.9332i) q^{95} +(16.4498 - 4.17197i) q^{96} +(124.808 - 45.4263i) q^{97} +(-115.982 + 66.9621i) q^{98} +(-16.8735 - 0.452923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{6} + 12 q^{9} + 24 q^{12} + 36 q^{14} + 96 q^{18} + 96 q^{21} - 72 q^{22} + 216 q^{23} - 12 q^{27} - 252 q^{29} - 516 q^{33} + 144 q^{34} - 48 q^{36} - 144 q^{38} + 48 q^{39} + 108 q^{41}+ \cdots - 444 q^{99}+O(q^{100}) $ 144 * q - 12 * q^6 + 12 * q^9 + 24 * q^12 + 36 * q^14 + 96 * q^18 + 96 * q^21 - 72 * q^22 + 216 * q^23 - 12 * q^27 - 252 * q^29 - 516 * q^33 + 144 * q^34 - 48 * q^36 - 144 * q^38 + 48 * q^39 + 108 * q^41 - 180 * q^43 + 60 * q^45 + 432 * q^47 - 72 * q^49 - 204 * q^51 - 288 * q^54 + 72 * q^56 - 612 * q^57 - 252 * q^59 + 144 * q^61 - 720 * q^63 + 576 * q^64 + 360 * q^65 + 864 * q^66 + 252 * q^67 + 144 * q^68 + 708 * q^69 + 360 * q^70 + 1296 * q^71 - 252 * q^73 + 720 * q^74 + 144 * q^76 + 684 * q^77 + 192 * q^78 + 72 * q^79 - 492 * q^81 - 828 * q^83 - 216 * q^84 - 360 * q^85 - 648 * q^86 - 660 * q^87 - 288 * q^88 + 324 * q^89 - 480 * q^90 + 396 * q^91 - 216 * q^92 - 1548 * q^93 - 504 * q^94 - 720 * q^95 - 192 * q^96 - 180 * q^97 - 1296 * q^98 - 444 * q^99

Character values

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

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$3$	−1.68760	−	2.48032i	−0.562534	−	0.826774i
$3$	−1.68760	−	2.48032i	−0.562534	−	0.826774i
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	−0.764780	+	2.10122i	−0.152956	+	0.420243i
$5$	−0.764780	+	2.10122i	−0.152956	+	0.420243i
$6$	−4.22115	−	0.426446i	−0.703526	−	0.0710744i
$7$	−2.08160	+	11.8053i	−0.297371	+	1.68647i	0.360036	+	0.932938i	$0.382764\pi$
$7$	−2.08160	+	11.8053i	−0.297371	+	1.68647i	−0.657407	+	0.753536i	$0.728347\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$	−3.30400	+	8.37159i	−0.367111	+	0.930177i
$10$	1.58114	+	2.73861i	0.158114	+	0.273861i
$11$	0.641461	+	1.76240i	0.0583146	+	0.160218i	0.965429	−	0.260666i	$-0.0839421\pi$
$11$	0.641461	+	1.76240i	0.0583146	+	0.160218i	−0.907114	+	0.420884i	$0.861720\pi$
$12$	−4.29918	+	4.18533i	−0.358265	+	0.348778i
$13$	−3.66205	+	3.07282i	−0.281696	+	0.236371i	−0.772677	−	0.634799i	$-0.781083\pi$
$13$	−3.66205	+	3.07282i	−0.281696	+	0.236371i	0.490981	+	0.871170i	$0.336638\pi$
$14$	10.8970	+	12.9866i	0.778361	+	0.927614i
$15$	6.50234	−	1.64911i	0.433489	−	0.109941i
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	−7.02615	+	4.05655i	−0.413303	+	0.238621i	−0.692208	−	0.721698i	$-0.743362\pi$
$17$	−7.02615	+	4.05655i	−0.413303	+	0.238621i	0.278905	+	0.960319i	$0.410029\pi$
$18$	6.06590	+	11.1895i	0.336995	+	0.621639i
$19$	−6.69415	+	11.5946i	−0.352324	+	0.610243i	−0.986656	−	0.162818i	$-0.947942\pi$
$19$	−6.69415	+	11.5946i	−0.352324	+	0.610243i	0.634332	+	0.773060i	$0.281275\pi$
$20$	4.40419	+	0.776578i	0.220210	+	0.0388289i
$21$	32.7939	−	14.7596i	1.56161	−	0.702840i
$22$	2.49241	+	0.907162i	0.113291	+	0.0412347i
$23$	10.9185	−	1.92523i	0.474718	−	0.0837056i	0.0688301	−	0.997628i	$-0.478073\pi$
$23$	10.9185	−	1.92523i	0.474718	−	0.0837056i	0.405888	+	0.913923i	$0.366962\pi$
$24$	0.626056	+	8.46215i	0.0260857	+	0.352590i
$25$	−3.83022	−	3.21394i	−0.153209	−	0.128558i
$26$			6.76060i			0.260023i
$27$	26.3401	−	5.93292i	0.975559	−	0.219738i
$28$	23.9749			0.856245
$29$	−5.41796	+	6.45687i	−0.186826	+	0.222651i	−0.851325	−	0.524638i	$-0.824201\pi$
$29$	−5.41796	+	6.45687i	−0.186826	+	0.222651i	0.664499	+	0.747289i	$0.268645\pi$
$30$	4.12431	−	8.54342i	0.137477	−	0.284781i
$31$	−5.64651	−	32.0229i	−0.182145	−	1.03300i	−0.929568	−	0.368650i	$-0.879820\pi$
$31$	−5.64651	−	32.0229i	−0.182145	−	1.03300i	0.747423	−	0.664348i	$-0.231291\pi$
$32$	−1.93476	+	5.31570i	−0.0604612	+	0.166116i
$33$	3.28879	−	4.56526i	0.0996602	−	0.138341i
$34$	−1.99238	+	11.2993i	−0.0585994	+	0.332334i
$35$	−23.2136	−	13.4024i	−0.663245	−	0.382925i
$36$	17.6363	+	3.60019i	0.489897	+	0.100005i
$37$	21.8945	+	37.9224i	0.591744	+	1.02493i	0.993998	+	0.109402i	$0.0348937\pi$
$37$	21.8945	+	37.9224i	0.591744	+	1.02493i	−0.402253	+	0.915528i	$0.631773\pi$
$38$	6.47578	+	17.7921i	0.170415	+	0.468212i
$39$	13.8017	+	3.89736i	0.353889	+	0.0999323i
$40$	4.84489	−	4.06535i	0.121122	−	0.101634i
$41$	27.5924	+	32.8833i	0.672986	+	0.802033i	0.989187	−	0.146659i	$-0.0468520\pi$
$41$	27.5924	+	32.8833i	0.672986	+	0.802033i	−0.316202	+	0.948692i	$0.602408\pi$
$42$	13.8211	−	48.9444i	0.329073	−	1.16534i
$43$	−63.9448	+	23.2740i	−1.48709	+	0.541256i	−0.952681	−	0.303971i	$-0.901688\pi$
$43$	−63.9448	+	23.2740i	−1.48709	+	0.541256i	−0.534408	+	0.845227i	$0.679465\pi$
$44$	3.24847	−	1.87551i	0.0738289	−	0.0426251i
$45$	−15.0637	−	13.3449i	−0.334749	−	0.296552i
$46$	7.83966	−	13.5787i	0.170427	−	0.295189i
$47$	−40.5756	−	7.15456i	−0.863310	−	0.152225i	−0.275576	−	0.961279i	$-0.588869\pi$
$47$	−40.5756	−	7.15456i	−0.863310	−	0.152225i	−0.587734	+	0.809055i	$0.699980\pi$
$48$	9.73659	+	7.01419i	0.202846	+	0.146129i
$49$	−88.9876	−	32.3888i	−1.81607	−	0.660997i
$50$	−6.96364	+	1.22788i	−0.139273	+	0.0245576i
$51$	21.9189	+	10.5813i	0.429782	+	0.207476i
$52$	7.32410	+	6.14565i	0.140848	+	0.118186i
$53$			75.3378i			1.42147i	0.703461	+	0.710734i	$0.251637\pi$
$53$			75.3378i			1.42147i	−0.703461	+	0.710734i	$0.748363\pi$
$54$	17.5167	−	33.9288i	0.324384	−	0.628311i
$55$	−4.19376			−0.0762501
$56$	21.7941	−	25.9732i	0.389180	−	0.463807i
$57$	40.0554	−	2.96342i	0.702727	−	0.0519899i
$58$	2.06992	+	11.7391i	0.0356883	+	0.202398i
$59$	20.6518	−	56.7402i	0.350030	−	0.961699i	−0.632330	−	0.774699i	$-0.717901\pi$
$59$	20.6518	−	56.7402i	0.350030	−	0.961699i	0.982360	−	0.187000i	$-0.0598764\pi$
$60$	−5.50636	−	12.2344i	−0.0917727	−	0.203906i
$61$	−1.88736	+	10.7037i	−0.0309403	+	0.175471i	−0.996362	−	0.0852221i	$-0.972840\pi$
$61$	−1.88736	+	10.7037i	−0.0309403	+	0.175471i	0.965422	+	0.260693i	$0.0839511\pi$
$62$	−39.8250	−	22.9929i	−0.642338	−	0.370854i
$63$	−91.9517	−	56.4311i	−1.45955	−	0.895732i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−3.65601	−	10.0448i	−0.0562462	−	0.154535i
$66$	−1.95614	−	7.71291i	−0.0296384	−	0.116862i
$67$	−77.1798	+	64.7615i	−1.15194	+	0.966590i	−0.999763	−	0.0217634i	$-0.993072\pi$
$67$	−77.1798	+	64.7615i	−1.15194	+	0.966590i	−0.152174	+	0.988354i	$0.548627\pi$
$68$	10.4300	+	12.4300i	0.153382	+	0.182794i
$69$	−23.2013	−	23.8324i	−0.336251	−	0.345398i
$70$	−35.6215	+	12.9652i	−0.508879	+	0.185217i
$71$	102.710	−	59.2994i	1.44661	−	0.835203i	0.448337	−	0.893865i	$-0.352016\pi$
$71$	102.710	−	59.2994i	1.44661	−	0.835203i	0.998278	+	0.0586611i	$0.0186831\pi$
$72$	19.9323	−	15.8336i	0.276838	−	0.219911i
$73$	−29.4831	+	51.0663i	−0.403878	+	0.699538i	−0.994190	−	0.107637i	$-0.965671\pi$
$73$	−29.4831	+	51.0663i	−0.403878	+	0.699538i	0.590312	+	0.807175i	$0.299005\pi$
$74$	60.9863	+	10.7535i	0.824139	+	0.145318i
$75$	−1.50772	+	14.9240i	−0.0201029	+	0.198987i
$76$	25.1618	+	9.15814i	0.331076	+	0.120502i
$77$	−22.1409	+	3.90405i	−0.287545	+	0.0507019i
$78$	16.7685	−	11.4092i	0.214980	−	0.146272i
$79$	−109.039	−	91.4948i	−1.38024	−	1.15816i	−0.969122	−	0.246581i	$-0.920693\pi$
$79$	−109.039	−	91.4948i	−1.38024	−	1.15816i	−0.411121	−	0.911581i	$-0.634863\pi$
$80$		−	8.94427i		−	0.111803i
$81$	−59.1671	−	55.3195i	−0.730458	−	0.682957i
$82$	60.7068			0.740326
$83$	52.8064	−	62.9322i	0.636222	−	0.758220i	−0.347547	−	0.937663i	$-0.612985\pi$
$83$	52.8064	−	62.9322i	0.636222	−	0.758220i	0.983768	+	0.179443i	$0.0574296\pi$
$84$	−40.4600	−	59.4654i	−0.481667	−	0.707922i
$85$	−3.15023	−	17.8658i	−0.0370615	−	0.210186i
$86$	−32.9144	+	90.4317i	−0.382726	+	1.05153i
$87$	25.1585	+	2.54166i	0.289178	+	0.0292145i
$88$	0.921157	−	5.22414i	0.0104677	−	0.0593652i
$89$	38.9210	+	22.4710i	0.437314	+	0.252484i	0.702458	−	0.711725i	$-0.252086\pi$
$89$	38.9210	+	22.4710i	0.437314	+	0.252484i	−0.265143	+	0.964209i	$0.585419\pi$
$90$	−28.1506	+	4.18827i	−0.312785	+	0.0465363i
$91$	−28.6528	−	49.6280i	−0.314866	−	0.545363i
$92$	−7.58393	−	20.8367i	−0.0824340	−	0.226485i
$93$	−69.8982	+	68.0471i	−0.751593	+	0.731689i
$94$	−44.6357	+	37.4538i	−0.474847	+	0.398444i
$95$	−19.2432	−	22.9332i	−0.202560	−	0.241402i
$96$	16.4498	−	4.17197i	0.171352	−	0.0434580i
$97$	124.808	−	45.4263i	1.28668	−	0.468312i	0.394042	−	0.919092i	$-0.371076\pi$
$97$	124.808	−	45.4263i	1.28668	−	0.468312i	0.892635	+	0.450780i	$0.148854\pi$
$98$	−115.982	+	66.9621i	−1.18349	+	0.683286i
$99$	−16.8735	−	0.452923i	−0.170439	−	0.00457498i
$100$	−5.00000	+	8.66025i	−0.0500000	+	0.0866025i
$101$	141.132	+	24.8854i	1.39735	+	0.246390i	0.821053	−	0.570852i	$-0.193387\pi$
$101$	141.132	+	24.8854i	1.39735	+	0.246390i	0.576295	+	0.817242i	$0.304498\pi$
$102$	31.3884	−	14.1270i	0.307729	−	0.138500i
$103$	−89.9634	−	32.7440i	−0.873431	−	0.317903i	−0.133875	−	0.990998i	$-0.542742\pi$
$103$	−89.9634	−	32.7440i	−0.873431	−	0.317903i	−0.739556	+	0.673095i	$0.764964\pi$
$104$	13.3158	−	2.34793i	0.128036	−	0.0225763i
$105$	5.93307	+	80.1950i	0.0565054	+	0.763762i
$106$	81.6172	+	68.4850i	0.769974	+	0.646085i
$107$			181.817i			1.69923i	0.527406	+	0.849613i	$0.323165\pi$
$107$			181.817i			1.69923i	−0.527406	+	0.849613i	$0.676835\pi$
$108$	−20.8334	−	49.8194i	−0.192902	−	0.461291i
$109$	31.2020			0.286257			0.143128	−	0.989704i	$-0.454284\pi$
$109$	31.2020			0.286257			0.143128	+	0.989704i	$0.454284\pi$
$110$	−3.81229	+	4.54331i	−0.0346572	+	0.0413028i
$111$	57.1107	−	118.303i	0.514510	−	1.06580i
$112$	−8.32639	−	47.2213i	−0.0743427	−	0.421619i
$113$	−29.5486	+	81.1840i	−0.261492	+	0.718443i	0.737576	+	0.675265i	$0.235971\pi$
$113$	−29.5486	+	81.1840i	−0.261492	+	0.718443i	−0.999067	+	0.0431782i	$0.986252\pi$
$114$	33.2015	−	46.0880i	0.291242	−	0.404280i
$115$	−4.30494	+	24.4146i	−0.0374343	+	0.212300i
$116$	14.5992	+	8.42885i	0.125855	+	0.0726625i
$117$	−13.6250	−	40.8098i	−0.116453	−	0.348802i
$118$	−42.6963	−	73.9522i	−0.361833	−	0.626713i
$119$	−33.2633	−	91.3900i	−0.279523	−	0.767983i
$120$	−18.2596	−	5.15621i	−0.152163	−	0.0429684i
$121$	89.9968	−	75.5163i	0.743775	−	0.624102i
$122$	9.88022	+	11.7748i	0.0809854	+	0.0965146i
$123$	34.9963	−	123.932i	0.284523	−	1.00758i
$124$	−61.1119	+	22.2429i	−0.492838	+	0.179378i
$125$	9.68246	−	5.59017i	0.0774597	−	0.0447214i
$126$	−144.722	+	48.3179i	−1.14859	+	0.383475i
$127$	35.2713	−	61.0916i	0.277726	−	0.481036i	−0.693093	−	0.720848i	$-0.743752\pi$
$127$	35.2713	−	61.0916i	0.277726	−	0.481036i	0.970819	+	0.239812i	$0.0770858\pi$
$128$	11.1418	+	1.96460i	0.0870455	+	0.0153485i
$129$	165.640	+	119.327i	1.28403	+	0.925012i
$130$	−14.2055	−	5.17037i	−0.109273	−	0.0397721i
$131$	−133.134	+	23.4751i	−1.01629	+	0.179199i	−0.656891	−	0.753985i	$-0.728129\pi$
$131$	−133.134	+	23.4751i	−1.01629	+	0.179199i	−0.359398	+	0.933184i	$0.617018\pi$
$132$	−10.1340	−	4.89215i	−0.0767726	−	0.0370617i
$133$	−122.944	−	103.162i	−0.924388	−	0.775654i
$134$			142.484i			1.06331i
$135$	−7.67804	+	59.8836i	−0.0568744	+	0.443582i
$136$	22.9473			0.168730
$137$	101.020	−	120.391i	0.737374	−	0.878768i	−0.258820	−	0.965925i	$-0.583334\pi$
$137$	101.020	−	120.391i	0.737374	−	0.878768i	0.996195	+	0.0871572i	$0.0277782\pi$
$138$	−46.9098	+	3.47053i	−0.339926	+	0.0251488i
$139$	12.3842	+	70.2343i	0.0890949	+	0.505282i	0.996398	+	0.0848044i	$0.0270265\pi$
$139$	12.3842	+	70.2343i	0.0890949	+	0.505282i	−0.907303	+	0.420478i	$0.861862\pi$
$140$	−18.3355	+	50.3764i	−0.130968	+	0.359831i
$141$	50.7297	+	112.715i	0.359785	+	0.799394i
$142$	29.1250	−	165.176i	0.205106	−	1.16321i
$143$	−7.76460	−	4.48289i	−0.0542979	−	0.0313489i
$144$	0.965976	−	35.9870i	0.00670816	−	0.249910i
$145$	−9.42374	−	16.3224i	−0.0649913	−	0.112568i
$146$	28.5214	+	78.3618i	0.195352	+	0.536725i
$147$	69.8408	+	275.377i	0.475108	+	1.87332i
$148$	67.0887	−	56.2941i	0.453302	−	0.380366i
$149$	−18.3920	−	21.9188i	−0.123436	−	0.147106i	0.700787	−	0.713371i	$-0.252832\pi$
$149$	−18.3920	−	21.9188i	−0.123436	−	0.147106i	−0.824223	+	0.566265i	$0.808388\pi$
$150$	14.7974	+	15.1999i	0.0986492	+	0.101333i
$151$	−86.2830	+	31.4044i	−0.571411	+	0.207976i	−0.611534	−	0.791218i	$-0.709447\pi$
$151$	−86.2830	+	31.4044i	−0.571411	+	0.207976i	0.0401233	+	0.999195i	$0.487225\pi$
$152$	32.7945	−	18.9339i	0.215753	−	0.124565i
$153$	−10.7454	−	72.2229i	−0.0702311	−	0.472045i
$154$	−15.8975	+	27.5353i	−0.103231	+	0.178801i
$155$	71.6055	+	12.6260i	0.461971	+	0.0814579i
$156$	2.88303	−	28.5375i	0.0184810	−	0.182933i
$157$	−179.167	−	65.2115i	−1.14119	−	0.415360i	−0.298848	−	0.954301i	$-0.596602\pi$
$157$	−179.167	−	65.2115i	−1.14119	−	0.415360i	−0.842344	+	0.538941i	$0.818825\pi$
$158$	−198.242	+	34.9554i	−1.25469	+	0.221237i
$159$	186.862	−	127.140i	1.17523	−	0.799623i
$160$	−9.68978	−	8.13069i	−0.0605611	−	0.0508168i
$161$			132.904i			0.825492i
$162$	−113.716	+	13.8111i	−0.701949	+	0.0852538i
$163$	245.130			1.50386			0.751931	−	0.659242i	$-0.229123\pi$
$163$	245.130			1.50386			0.751931	+	0.659242i	$0.229123\pi$
$164$	55.1848	−	65.7667i	0.336493	−	0.401016i
$165$	7.07739	+	10.4019i	0.0428933	+	0.0630417i
$166$	−20.1746	−	114.416i	−0.121534	−	0.689251i
$167$	90.7245	−	249.263i	0.543260	−	1.49260i	−0.299388	−	0.954131i	$-0.596783\pi$
$167$	90.7245	−	249.263i	0.543260	−	1.49260i	0.842648	−	0.538464i	$-0.180995\pi$
$168$	−101.202	−	10.2240i	−0.602391	−	0.0608571i
$169$	−25.3782	+	143.927i	−0.150167	+	0.851638i
$170$	−22.2186	−	12.8279i	−0.130698	−	0.0754584i
$171$	−74.9479	−	94.3494i	−0.438292	−	0.551751i
$172$	68.0487	+	117.864i	0.395632	+	0.685254i
$173$	57.6650	+	158.433i	0.333324	+	0.915800i	0.987241	+	0.159234i	$0.0509023\pi$
$173$	57.6650	+	158.433i	0.333324	+	0.915800i	−0.653917	+	0.756566i	$0.726875\pi$
$174$	25.6236	−	24.9450i	0.147262	−	0.143362i
$175$	45.9145	−	38.5269i	0.262369	−	0.220154i
$176$	−4.82221	−	5.74688i	−0.0273989	−	0.0326527i
$177$	−175.586	+	44.5319i	−0.992012	+	0.251593i
$178$	59.7247	−	21.7380i	0.335532	−	0.122124i
$179$	45.4398	−	26.2347i	0.253853	−	0.146562i	−0.367674	−	0.929955i	$-0.619846\pi$
$179$	45.4398	−	26.2347i	0.253853	−	0.146562i	0.621527	+	0.783392i	$0.286512\pi$
$180$	−21.0527	+	34.3043i	−0.116959	+	0.190579i
$181$	16.2816	−	28.2006i	0.0899538	−	0.155805i	−0.817538	−	0.575875i	$-0.804661\pi$
$181$	16.2816	−	28.2006i	0.0899538	−	0.155805i	0.907491	+	0.420071i	$0.137995\pi$
$182$	−79.8110	−	14.0728i	−0.438522	−	0.0773233i
$183$	29.7338	−	13.3824i	0.162480	−	0.0731278i
$184$	−29.4675	−	10.7253i	−0.160149	−	0.0582896i
$185$	−96.4278	+	17.0028i	−0.521231	+	0.0919071i
$186$	10.1787	+	137.582i	0.0547243	+	0.739686i
$187$	−11.6563	−	9.78076i	−0.0623329	−	0.0523035i
$188$			82.4030i			0.438314i
$189$	15.2105	+	323.303i	0.0804791	+	1.71060i
$190$	−42.3375			−0.222829
$191$	141.170	−	168.240i	0.739110	−	0.880837i	−0.257227	−	0.966351i	$-0.582809\pi$
$191$	141.170	−	168.240i	0.739110	−	0.880837i	0.996337	+	0.0855143i	$0.0272533\pi$
$192$	10.4338	−	21.6133i	0.0543426	−	0.112569i
$193$	49.7483	+	282.137i	0.257763	+	1.46185i	0.788879	+	0.614549i	$0.210662\pi$
$193$	49.7483	+	282.137i	0.257763	+	1.46185i	−0.531116	+	0.847299i	$0.678227\pi$
$194$	64.2425	−	176.505i	0.331147	−	0.909818i
$195$	−18.7444	+	26.0197i	−0.0961254	+	0.133434i
$196$	−32.8885	+	186.520i	−0.167798	+	0.951632i
$197$	−0.147107	−	0.0849323i	−0.000746736	−	0.000431128i	0.499627	−	0.866241i	$-0.333471\pi$
$197$	−0.147107	−	0.0849323i	−0.000746736	−	0.000431128i	−0.500373	+	0.865810i	$0.666804\pi$
$198$	−15.8293	+	17.8682i	−0.0799461	+	0.0902432i
$199$	56.4065	+	97.6990i	0.283450	+	0.490950i	0.972232	−	0.234019i	$-0.0751877\pi$
$199$	56.4065	+	97.6990i	0.283450	+	0.490950i	−0.688782	+	0.724968i	$0.741854\pi$
$200$	4.83690	+	13.2893i	0.0241845	+	0.0664463i
$201$	290.878	+	82.1392i	1.44716	+	0.408653i
$202$	155.254	−	130.274i	0.768585	−	0.644920i
$203$	−64.9475	−	77.4014i	−0.319938	−	0.381288i
$204$	13.2287	−	46.8466i	0.0648466	−	0.229640i
$205$	−90.1972	+	32.8291i	−0.439986	+	0.160142i
$206$	−117.253	+	67.6963i	−0.569191	+	0.328623i
$207$	−19.9576	+	97.7664i	−0.0964135	+	0.472301i
$208$	9.56093	−	16.5600i	0.0459660	−	0.0796155i
$209$	−24.7284	−	4.36028i	−0.118318	−	0.0208626i
$210$	92.2727	+	66.4728i	0.439394	+	0.316537i
$211$	256.252	+	93.2681i	1.21446	+	0.442029i	0.868250	−	0.496127i	$-0.165245\pi$
$211$	256.252	+	93.2681i	1.21446	+	0.442029i	0.346214	+	0.938156i	$0.387467\pi$
$212$	148.386	−	26.1645i	0.699936	−	0.123418i
$213$	−320.415	−	154.679i	−1.50429	−	0.726194i
$214$	196.972	+	165.279i	0.920429	+	0.772332i
$215$		−	152.161i		−	0.707728i
$216$	−72.9102	−	22.7179i	−0.337547	−	0.105175i
$217$	389.795			1.79629
$218$	28.3638	−	33.8027i	0.130109	−	0.155058i
$219$	176.417	−	13.0518i	0.805555	−	0.0595975i
$220$	1.45648	+	8.26009i	0.00662035	+	0.0375459i
$221$	13.2650	−	36.4454i	0.0600228	−	0.164911i
$222$	−76.2483	−	169.413i	−0.343461	−	0.763123i
$223$	−41.5724	+	235.769i	−0.186423	+	1.05726i	0.737690	+	0.675140i	$0.235917\pi$
$223$	−41.5724	+	235.769i	−0.186423	+	1.05726i	−0.924113	+	0.382119i	$0.875194\pi$
$224$	−58.7262	−	33.9056i	−0.262171	−	0.151364i
$225$	39.5608	−	21.4462i	0.175826	−	0.0953164i
$226$	61.0899	+	105.811i	0.270310	+	0.468190i
$227$	59.1807	+	162.598i	0.260708	+	0.716289i	0.999120	+	0.0419392i	$0.0133536\pi$
$227$	59.1807	+	162.598i	0.260708	+	0.716289i	−0.738412	+	0.674349i	$0.764424\pi$
$228$	−19.7479	−	77.8646i	−0.0866137	−	0.341512i
$229$	−104.198	+	87.4322i	−0.455011	+	0.381800i	−0.841292	−	0.540582i	$-0.818204\pi$
$229$	−104.198	+	87.4322i	−0.455011	+	0.381800i	0.386280	+	0.922381i	$0.373760\pi$
$230$	22.5362	+	26.8575i	0.0979833	+	0.116772i
$231$	47.0484	+	48.3282i	0.203673	+	0.209213i
$232$	22.4026	−	8.15389i	0.0965631	−	0.0351461i
$233$	−96.8200	+	55.8991i	−0.415537	+	0.239910i	−0.693166	−	0.720778i	$-0.743785\pi$
$233$	−96.8200	+	55.8991i	−0.415537	+	0.239910i	0.277629	+	0.960688i	$0.410451\pi$
$234$	−56.5970	−	22.3370i	−0.241867	−	0.0954574i
$235$	46.0647	−	79.7864i	0.196020	−	0.339516i
$236$	−118.929	−	20.9703i	−0.503935	−	0.0888574i
$237$	−42.9218	+	424.859i	−0.181105	+	1.79265i
$238$	−129.245	−	47.0413i	−0.543046	−	0.197653i
$239$	195.009	−	34.3853i	0.815935	−	0.143871i	0.249920	−	0.968266i	$-0.419596\pi$
$239$	195.009	−	34.3853i	0.815935	−	0.143871i	0.566015	+	0.824395i	$0.308484\pi$
$240$	−22.1847	+	15.0944i	−0.0924362	+	0.0628932i
$241$	−116.739	−	97.9553i	−0.484392	−	0.406454i	0.367619	−	0.929976i	$-0.380173\pi$
$241$	−116.739	−	97.9553i	−0.484392	−	0.406454i	−0.852012	+	0.523523i	$0.824617\pi$
$242$		−	166.145i		−	0.686551i
$243$	−37.3598	+	240.111i	−0.153744	+	0.988111i
$244$	21.7377			0.0890890
$245$	136.112	−	162.212i	0.555559	−	0.662089i
$246$	−102.449	−	150.572i	−0.416459	−	0.612083i
$247$	−11.1139	−	63.0300i	−0.0449955	−	0.255182i
$248$	−31.4562	+	86.4252i	−0.126840	+	0.348489i
$249$	−245.208	−	24.7724i	−0.984773	−	0.0994877i
$250$	2.74562	−	15.5712i	0.0109825	−	0.0622847i
$251$	28.1150	+	16.2322i	0.112012	+	0.0646700i	0.554959	−	0.831878i	$-0.312734\pi$
$251$	28.1150	+	16.2322i	0.112012	+	0.0646700i	−0.442947	+	0.896548i	$0.646067\pi$
$252$	−79.2131	+	200.708i	−0.314338	+	0.796460i
$253$	10.3968	+	18.0078i	0.0410942	+	0.0711772i
$254$	−34.1207	−	93.7458i	−0.134333	−	0.369078i
$255$	−38.9967	+	37.9640i	−0.152928	+	0.148878i
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	−187.262	−	223.170i	−0.728645	−	0.868365i	0.266795	−	0.963753i	$-0.414035\pi$
$257$	−187.262	−	223.170i	−0.728645	−	0.868365i	−0.995440	+	0.0953879i	$0.969591\pi$
$258$	279.846	−	70.9742i	1.08467	−	0.275094i
$259$	−493.262	+	179.533i	−1.90449	+	0.693177i
$260$	−18.5147	+	10.6894i	−0.0712102	+	0.0411132i
$261$	−36.1534	−	66.6905i	−0.138519	−	0.255519i
$262$	−95.5921	+	165.570i	−0.364855	+	0.631948i
$263$	−340.756	−	60.0844i	−1.29565	−	0.228458i	−0.517037	−	0.855963i	$-0.672965\pi$
$263$	−340.756	−	60.0844i	−1.29565	−	0.228458i	−0.778612	+	0.627505i	$0.784076\pi$
$264$	−14.5121	+	6.53150i	−0.0549701	+	0.0247405i
$265$	−158.301	−	57.6168i	−0.597362	−	0.217422i
$266$	−223.521	+	39.4128i	−0.840305	+	0.148168i
$267$	−9.94767	−	134.459i	−0.0372572	−	0.503591i
$268$	154.360	+	129.523i	0.575969	+	0.483295i
$269$		−	149.195i		−	0.554628i	−0.960779	−	0.277314i	$-0.910556\pi$
$269$		−	149.195i		−	0.554628i	0.960779	−	0.277314i	$-0.0894442\pi$
$270$	57.8953	+	62.7545i	0.214427	+	0.232424i
$271$	421.844			1.55662			0.778310	−	0.627880i	$-0.216077\pi$
$271$	421.844			1.55662			0.778310	+	0.627880i	$0.216077\pi$
$272$	20.8600	−	24.8600i	0.0766912	−	0.0913970i
$273$	−74.7391	+	154.820i	−0.273770	+	0.567108i
$274$	−38.5946	−	218.881i	−0.140856	−	0.798835i
$275$	3.20730	−	8.81199i	0.0116629	−	0.0320436i
$276$	−38.8830	+	53.9746i	−0.140880	+	0.195560i
$277$	35.9170	−	203.695i	0.129664	−	0.735362i	−0.848764	−	0.528772i	$-0.822652\pi$
$277$	35.9170	−	203.695i	0.129664	−	0.735362i	0.978428	−	0.206589i	$-0.0662364\pi$
$278$	87.3460	+	50.4293i	0.314194	+	0.181400i
$279$	286.739	+	58.5336i	1.02774	+	0.209798i
$280$	37.9076	+	65.6579i	0.135384	+	0.234492i
$281$	58.0904	+	159.602i	0.206727	+	0.567979i	0.999116	−	0.0420377i	$-0.0133849\pi$
$281$	58.0904	+	159.602i	0.206727	+	0.567979i	−0.792389	+	0.610017i	$0.791163\pi$
$282$	168.225	+	47.5038i	0.596541	+	0.168453i
$283$	370.679	−	311.036i	1.30982	−	1.09907i	0.321460	−	0.946923i	$-0.395826\pi$
$283$	370.679	−	311.036i	1.30982	−	1.09907i	0.988358	−	0.152145i	$-0.0486180\pi$
$284$	−152.468	−	181.704i	−0.536858	−	0.639803i
$285$	−24.4068	+	86.4315i	−0.0856380	+	0.303269i
$286$	−11.9149	+	4.33666i	−0.0416604	+	0.0151631i
$287$	−445.635	+	257.287i	−1.55273	+	0.896472i
$288$	−38.1085	−	33.7601i	−0.132321	−	0.117223i
$289$	−111.589	+	193.278i	−0.386121	+	0.668780i
$290$	−26.2494	−	4.62848i	−0.0905153	−	0.0159603i
$291$	−323.298	−	232.902i	−1.11099	−	0.800350i
$292$	110.820	+	40.3353i	0.379522	+	0.138135i
$293$	−5.14044	+	0.906398i	−0.0175442	+	0.00309351i	−0.182413	−	0.983222i	$-0.558391\pi$
$293$	−5.14044	+	0.906398i	−0.0175442	+	0.00309351i	0.164869	+	0.986315i	$0.447280\pi$
$294$	361.818	+	174.667i	1.23067	+	0.594105i
$295$	103.429	+	86.7876i	0.350608	+	0.294195i
$296$		−	123.854i		−	0.418426i
$297$	27.3523	+	42.6160i	0.0920953	+	0.143488i
$298$	−40.4648			−0.135788
$299$	−34.0683	+	40.6010i	−0.113941	+	0.135789i
$300$	29.9182	−	2.21344i	0.0997274	−	0.00737814i
$301$	−141.650	−	803.336i	−0.470598	−	2.66889i
$302$	−44.4126	+	122.023i	−0.147062	+	0.404048i
$303$	−176.451	−	392.050i	−0.582347	−	1.29389i
$304$	9.29942	−	52.7396i	0.0305902	−	0.173486i
$305$	−21.0475	−	12.1518i	−0.0690081	−	0.0398418i
$306$	−88.0107	−	54.0124i	−0.287617	−	0.176511i
$307$	−112.081	−	194.131i	−0.365086	−	0.632347i	0.623704	−	0.781660i	$-0.285627\pi$
$307$	−112.081	−	194.131i	−0.365086	−	0.632347i	−0.988790	+	0.149313i	$0.952294\pi$
$308$	15.3789	+	42.2533i	0.0499316	+	0.137186i
$309$	70.6066	+	278.397i	0.228500	+	0.900961i
$310$	78.7705	−	66.0963i	0.254098	−	0.213214i
$311$	−308.452	−	367.599i	−0.991807	−	1.18199i	−0.983294	−	0.182026i	$-0.941735\pi$
$311$	−308.452	−	367.599i	−0.991807	−	1.18199i	−0.00851297	−	0.999964i	$-0.502710\pi$
$312$	−28.2954	−	29.0651i	−0.0906902	−	0.0931572i
$313$	215.924	−	78.5899i	0.689853	−	0.251086i	0.0267807	−	0.999641i	$-0.491474\pi$
$313$	215.924	−	78.5899i	0.689853	−	0.251086i	0.663072	+	0.748555i	$0.269252\pi$
$314$	−233.517	+	134.821i	−0.743684	+	0.429366i
$315$	188.897	−	150.053i	0.599672	−	0.476359i
$316$	−142.341	+	246.541i	−0.450445	+	0.780193i
$317$	115.448	+	20.3566i	0.364190	+	0.0642165i	0.352749	−	0.935718i	$-0.385247\pi$
$317$	115.448	+	20.3566i	0.364190	+	0.0642165i	0.0114411	+	0.999935i	$0.496358\pi$
$318$	32.1275	−	318.012i	0.101030	−	1.00004i
$319$	−14.8550	−	5.40678i	−0.0465674	−	0.0169491i
$320$	−17.6168	+	3.10631i	−0.0550524	+	0.00970723i
$321$	450.966	−	306.835i	1.40488	−	0.955873i
$322$	143.982	+	120.815i	0.447149	+	0.375202i
$323$		−	108.621i		−	0.336287i
$324$	−88.4097	+	135.749i	−0.272869	+	0.418978i
$325$	23.9023			0.0735456
$326$	222.832	−	265.561i	0.683535	−	0.814605i
$327$	−52.6565	−	77.3910i	−0.161029	−	0.236670i
$328$	−21.0832	−	119.569i	−0.0642782	−	0.364540i
$329$	168.924	−	464.115i	0.513446	−	1.41068i
$330$	17.7025	+	1.78841i	0.0536439	+	0.00541943i
$331$	−36.7879	+	208.635i	−0.111142	+	0.630316i	0.877447	+	0.479674i	$0.159245\pi$
$331$	−36.7879	+	208.635i	−0.111142	+	0.630316i	−0.988588	+	0.150642i	$0.951866\pi$
$332$	−142.292	−	82.1522i	−0.428590	−	0.247446i
$333$	−389.811	+	57.9962i	−1.17060	+	0.174163i
$334$	−187.568	−	324.877i	−0.561580	−	0.972684i
$335$	−77.0524	−	211.700i	−0.230007	−	0.631940i
$336$	−103.072	+	100.343i	−0.306763	+	0.298639i
$337$	−318.750	+	267.463i	−0.945845	+	0.793658i	−0.978593	−	0.205806i	$-0.934018\pi$
$337$	−318.750	+	267.463i	−0.945845	+	0.793658i	0.0327483	+	0.999464i	$0.489574\pi$
$338$	132.853	+	158.329i	0.393058	+	0.468428i
$339$	251.229	−	63.7163i	0.741088	−	0.187954i
$340$	−34.0947	+	12.4095i	−0.100279	+	0.0364985i
$341$	52.8152	−	30.4929i	0.154883	−	0.0894219i
$342$	−170.344	−	4.57243i	−0.498082	−	0.0133697i
$343$	273.905	−	474.417i	0.798556	−	1.38314i
$344$	189.547	+	33.4222i	0.551008	+	0.0971575i
$345$	67.8210	−	30.5244i	0.196583	−	0.0884765i
$346$	224.059	+	81.5507i	0.647568	+	0.235696i
$347$	−619.212	+	109.184i	−1.78447	+	0.314651i	−0.965737	−	0.259521i	$-0.916435\pi$
$347$	−619.212	+	109.184i	−1.78447	+	0.314651i	−0.818735	+	0.574172i	$0.805324\pi$
$348$	−3.73136	−	50.4353i	−0.0107223	−	0.144929i
$349$	−153.156	−	128.514i	−0.438844	−	0.368234i	0.396433	−	0.918064i	$-0.370248\pi$
$349$	−153.156	−	128.514i	−0.438844	−	0.368234i	−0.835276	+	0.549830i	$0.814692\pi$
$350$		−	84.7640i		−	0.242183i
$351$	−78.2279	+	102.665i	−0.222871	+	0.292493i
$352$	−10.6095			−0.0301405
$353$	171.408	−	204.276i	0.485576	−	0.578686i	−0.466511	−	0.884515i	$-0.654489\pi$
$353$	171.408	−	204.276i	0.485576	−	0.578686i	0.952086	+	0.305829i	$0.0989336\pi$
$354$	−111.371	+	230.702i	−0.314607	+	0.651702i
$355$	46.0507	+	261.166i	0.129720	+	0.735680i
$356$	30.7422	−	84.4635i	0.0863545	−	0.237257i
$357$	−170.542	+	236.734i	−0.477708	+	0.663119i
$358$	12.8852	−	73.0755i	0.0359921	−	0.204122i
$359$	512.176	+	295.705i	1.42668	+	0.823691i	0.996857	−	0.0792241i	$-0.0252443\pi$
$359$	512.176	+	295.705i	1.42668	+	0.823691i	0.429818	+	0.902915i	$0.358578\pi$
$360$	18.0259	+	53.9914i	0.0500719	+	0.149976i
$361$	90.8766	+	157.403i	0.251736	+	0.436019i
$362$	−15.7505	−	43.2742i	−0.0435097	−	0.119542i
$363$	−339.183	−	95.7797i	−0.934390	−	0.263856i
$364$	−87.7972	+	73.6706i	−0.241201	+	0.202392i
$365$	−84.7532	−	101.005i	−0.232201	−	0.276726i
$366$	12.5314	−	44.3773i	0.0342388	−	0.121249i
$367$	231.034	−	84.0896i	0.629522	−	0.229127i	−0.00750151	−	0.999972i	$-0.502388\pi$
$367$	231.034	−	84.0896i	0.629522	−	0.229127i	0.637023	+	0.770845i	$0.280166\pi$
$368$	−38.4063	+	22.1739i	−0.104365	+	0.0602552i
$369$	−366.451	+	122.346i	−0.993093	+	0.331560i
$370$	−69.2366	+	119.921i	−0.187126	+	0.324112i
$371$	−889.386	−	156.823i	−2.39727	−	0.422703i
$372$	158.302	+	114.040i	0.425543	+	0.306559i
$373$	245.993	+	89.5340i	0.659498	+	0.240038i	0.650020	−	0.759917i	$-0.274761\pi$
$373$	245.993	+	89.5340i	0.659498	+	0.240038i	0.00947842	+	0.999955i	$0.496983\pi$
$374$	−21.1920	+	3.73672i	−0.0566630	+	0.00999122i
$375$	−30.2056	−	14.5816i	−0.0805482	−	0.0388844i
$376$	89.2713	+	74.9075i	0.237424	+	0.199222i
$377$		−	40.2938i		−	0.106880i
$378$	364.078	+	277.417i	0.963168	+	0.733907i
$379$	−349.974			−0.923415			−0.461707	−	0.887032i	$-0.652763\pi$
$379$	−349.974			−0.923415			−0.461707	+	0.887032i	$0.652763\pi$
$380$	−38.4865	+	45.8664i	−0.101280	+	0.120701i
$381$	−211.051	+	15.6142i	−0.553939	+	0.0409821i
$382$	−53.9337	−	305.873i	−0.141188	−	0.800715i
$383$	18.7009	−	51.3803i	0.0488274	−	0.134152i	−0.912882	−	0.408224i	$-0.866148\pi$
$383$	18.7009	−	51.3803i	0.0488274	−	0.134152i	0.961709	+	0.274072i	$0.0883705\pi$
$384$	−13.9301	−	30.9508i	−0.0362763	−	0.0806010i
$385$	8.72971	−	49.5087i	0.0226746	−	0.128594i
$386$	350.876	+	202.578i	0.909005	+	0.524814i
$387$	16.4333	−	612.218i	0.0424634	−	1.58196i
$388$	−132.818	−	230.047i	−0.342313	−	0.592904i
$389$	−27.6471	−	75.9598i	−0.0710723	−	0.195270i	0.899071	−	0.437804i	$-0.144244\pi$
$389$	−27.6471	−	75.9598i	−0.0710723	−	0.195270i	−0.970143	+	0.242534i	$0.922021\pi$
$390$	11.1490	+	43.9597i	0.0285872	+	0.112717i
$391$	−68.9054	+	57.8185i	−0.176229	+	0.147873i
$392$	172.170	+	205.184i	0.439208	+	0.523428i
$393$	282.903	+	290.598i	0.719854	+	0.739436i
$394$	−0.225737	+	0.0821617i	−0.000572938	+	0.000208532i
$395$	275.641	−	159.142i	0.697826	−	0.402890i
$396$	4.96801	+	33.3916i	0.0125455	+	0.0843221i
$397$	−237.051	+	410.585i	−0.597107	+	1.03422i	0.396139	+	0.918191i	$0.370350\pi$
$397$	−237.051	+	410.585i	−0.597107	+	1.03422i	−0.993246	+	0.116029i	$0.962983\pi$
$398$	157.118	+	27.7041i	0.394769	+	0.0696084i
$399$	−48.3951	+	479.036i	−0.121291	+	1.20059i
$400$	18.7939	+	6.84040i	0.0469846	+	0.0171010i
$401$	−200.401	+	35.3361i	−0.499753	+	0.0881199i	−0.417842	−	0.908520i	$-0.637213\pi$
$401$	−200.401	+	35.3361i	−0.499753	+	0.0881199i	−0.0819110	+	0.996640i	$0.526102\pi$
$402$	353.405	−	240.455i	0.879117	−	0.598148i
$403$	119.079	+	99.9188i	0.295480	+	0.247938i
$404$		−	286.619i		−	0.709452i
$405$	161.488	−	82.0157i	0.398736	−	0.202508i
$406$	−142.893			−0.351952
$407$	−52.7900	+	62.9126i	−0.129705	+	0.154577i
$408$	−38.7259	−	56.9167i	−0.0949164	−	0.139502i
$409$	11.2630	+	63.8758i	0.0275380	+	0.156176i	0.995476	−	0.0950137i	$-0.0302895\pi$
$409$	11.2630	+	63.8758i	0.0275380	+	0.156176i	−0.967938	+	0.251189i	$0.919178\pi$
$410$	−46.4273	+	127.558i	−0.113237	+	0.311117i
$411$	−469.091	−	47.3904i	−1.14134	−	0.115305i
$412$	−33.2491	+	188.565i	−0.0807017	+	0.457682i
$413$	626.848	+	361.911i	1.51779	+	0.876298i
$414$	87.7730	+	110.495i	0.212012	+	0.266895i
$415$	91.8489	+	159.087i	0.221323	+	0.383342i
$416$	−9.24904	−	25.4115i	−0.0222333	−	0.0610854i
$417$	153.304	−	149.244i	0.367636	−	0.357900i
$418$	−27.2028	+	22.8258i	−0.0650784	+	0.0546072i
$419$	−85.9874	−	102.476i	−0.205220	−	0.244572i	0.653611	−	0.756831i	$-0.273253\pi$
$419$	−85.9874	−	102.476i	−0.205220	−	0.244572i	−0.858831	+	0.512259i	$0.828809\pi$
$420$	155.893	−	39.5373i	0.371173	−	0.0941364i
$421$	0.510743	−	0.185895i	0.00121317	−	0.000441557i	−0.341413	−	0.939913i	$-0.610906\pi$
$421$	0.510743	−	0.185895i	0.00121317	−	0.000441557i	0.342627	+	0.939472i	$0.388683\pi$
$422$	333.985	−	192.826i	0.791434	−	0.456934i
$423$	193.957	−	316.043i	0.458527	−	0.747147i
$424$	106.544	−	184.539i	0.251282	−	0.435234i
$425$	39.9492	+	7.04412i	0.0939981	+	0.0165744i
$426$	−458.841	+	206.512i	−1.07709	+	0.484770i
$427$	−122.432	−	44.5617i	−0.286727	−	0.104360i
$428$	358.110	−	63.1445i	0.836706	−	0.147534i
$429$	1.98453	+	26.8241i	0.00462593	+	0.0625269i
$430$	−164.844	−	138.321i	−0.383359	−	0.321676i
$431$			751.424i			1.74344i	0.490002	+	0.871722i	$0.336996\pi$
$431$			751.424i			1.74344i	−0.490002	+	0.871722i	$0.663004\pi$
$432$	−90.8897	+	58.3358i	−0.210393	+	0.135037i
$433$	756.647			1.74745			0.873726	−	0.486419i	$-0.161697\pi$
$433$	756.647			1.74745			0.873726	+	0.486419i	$0.161697\pi$
$434$	354.339	−	422.284i	0.816448	−	0.973005i
$435$	−24.5813	+	50.9196i	−0.0565087	+	0.117057i
$436$	−10.8363	−	61.4559i	−0.0248540	−	0.140954i
$437$	−50.7680	+	139.484i	−0.116174	+	0.319185i
$438$	146.230	−	202.986i	0.333858	−	0.463438i
$439$	−34.4598	+	195.431i	−0.0784961	+	0.445174i	0.920075	+	0.391741i	$0.128127\pi$
$439$	−34.4598	+	195.431i	−0.0784961	+	0.445174i	−0.998571	+	0.0534323i	$0.982984\pi$
$440$	10.2726	+	5.93087i	0.0233467	+	0.0134792i
$441$	565.162	−	637.955i	1.28155	−	1.44661i
$442$	−27.4247	−	47.5010i	−0.0620468	−	0.107468i
$443$	266.470	+	732.121i	0.601513	+	1.65264i	0.748209	+	0.663463i	$0.230914\pi$
$443$	266.470	+	732.121i	0.601513	+	1.65264i	−0.146696	+	0.989182i	$0.546864\pi$
$444$	−252.847	−	71.3997i	−0.569474	−	0.160810i
$445$	−76.9825	+	64.5960i	−0.172994	+	0.145160i
$446$	217.629	+	259.360i	0.487958	+	0.581526i
$447$	−23.3272	+	82.6083i	−0.0521861	+	0.184806i
$448$	−90.1160	+	32.7996i	−0.201152	+	0.0732133i
$449$	244.029	−	140.890i	0.543493	−	0.313786i	−0.203000	−	0.979179i	$-0.565069\pi$
$449$	244.029	−	140.890i	0.543493	−	0.313786i	0.746494	+	0.665393i	$0.231736\pi$
$450$	12.7286	−	62.3537i	0.0282858	−	0.138564i
$451$	−40.2541	+	69.7222i	−0.0892553	+	0.154595i
$452$	170.163	+	30.0044i	0.376468	+	0.0663814i
$453$	223.504	+	161.011i	0.493387	+	0.355434i
$454$	229.948	+	83.6941i	0.506492	+	0.184348i
$455$	126.192	−	22.2511i	0.277346	−	0.0489035i
$456$	−102.306	−	49.3881i	−0.224356	−	0.108307i
$457$	560.171	+	470.039i	1.22576	+	1.02853i	0.998503	+	0.0546965i	$0.0174191\pi$
$457$	560.171	+	470.039i	1.22576	+	1.02853i	0.227254	+	0.973836i	$0.427025\pi$
$458$			192.362i			0.420004i
$459$	−161.002	+	148.535i	−0.350767	+	0.323607i
$460$	49.5824			0.107788
$461$	−459.220	+	547.278i	−0.996140	+	1.18715i	−0.0138272	+	0.999904i	$0.504401\pi$
$461$	−459.220	+	547.278i	−0.996140	+	1.18715i	−0.982313	+	0.187249i	$0.940043\pi$
$462$	95.1252	−	7.03765i	0.205899	−	0.0152330i
$463$	136.457	+	773.888i	0.294724	+	1.67147i	0.668320	+	0.743874i	$0.267014\pi$
$463$	136.457	+	773.888i	0.294724	+	1.67147i	−0.373596	+	0.927592i	$0.621875\pi$
$464$	11.5313	−	31.6821i	0.0248520	−	0.0682804i
$465$	−89.5250	−	198.912i	−0.192527	−	0.427768i
$466$	−27.4549	+	155.704i	−0.0589161	+	0.334130i
$467$	−307.906	−	177.770i	−0.659328	−	0.380663i	0.132693	−	0.991157i	$-0.457638\pi$
$467$	−307.906	−	177.770i	−0.659328	−	0.380663i	−0.792021	+	0.610494i	$0.790971\pi$
$468$	−75.6477	+	41.0091i	−0.161640	+	0.0876263i
$469$	−603.874	−	1045.94i	−1.28758	−	2.23015i
$470$	−44.5620	−	122.433i	−0.0948128	−	0.260496i
$471$	140.617	+	554.443i	0.298550	+	1.17716i
$472$	−130.829	+	109.779i	−0.277180	+	0.232582i
$473$	−82.0362	−	97.7669i	−0.173438	−	0.206695i
$474$	421.254	+	432.713i	0.888721	+	0.912896i
$475$	62.9045	−	22.8954i	0.132430	−	0.0482007i
$476$	−168.451	+	97.2552i	−0.353889	+	0.204318i
$477$	−630.697	−	248.916i	−1.32222	−	0.521837i
$478$	140.019	−	242.520i	0.292927	−	0.507364i
$479$	−752.891	−	132.755i	−1.57180	−	0.277150i	−0.681253	−	0.732048i	$-0.738565\pi$
$479$	−752.891	−	132.755i	−1.57180	−	0.277150i	−0.890544	+	0.454897i	$0.849676\pi$
$480$	−3.81425	+	37.7552i	−0.00794636	+	0.0786566i
$481$	−196.708	−	71.5958i	−0.408956	−	0.148848i
$482$	−212.240	+	37.4236i	−0.440332	+	0.0776423i
$483$	329.645	−	224.289i	0.682495	−	0.464367i
$484$	−179.994	−	151.033i	−0.371888	−	0.312051i
$485$			296.989i			0.612349i
$486$	226.163	+	258.744i	0.465355	+	0.532395i
$487$	−248.950			−0.511191			−0.255596	−	0.966784i	$-0.582272\pi$
$487$	−248.950			−0.511191			−0.255596	+	0.966784i	$0.582272\pi$
$488$	19.7604	−	23.5496i	0.0404927	−	0.0482573i
$489$	−413.681	−	608.000i	−0.845973	−	1.24335i
$490$	−52.0013	−	294.914i	−0.106125	−	0.601865i
$491$	−160.577	+	441.182i	−0.327041	+	0.898537i	0.661816	+	0.749666i	$0.269786\pi$
$491$	−160.577	+	441.182i	−0.327041	+	0.898537i	−0.988857	+	0.148871i	$0.952436\pi$
$492$	−256.253	−	25.8882i	−0.520839	−	0.0526183i
$493$	11.8748	−	67.3452i	0.0240868	−	0.136603i
$494$	−78.3865	−	45.2565i	−0.158677	−	0.0916123i
$495$	13.8562	−	35.1084i	0.0279923	−	0.0709261i
$496$	65.0339	+	112.642i	0.131117	+	0.227101i
$497$	486.249	+	1335.96i	0.978368	+	2.68804i
$498$	−249.741	+	243.128i	−0.501488	+	0.488208i
$499$	−112.078	+	94.0449i	−0.224606	+	0.188467i	−0.748146	−	0.663534i	$-0.769056\pi$
$499$	−112.078	+	94.0449i	−0.224606	+	0.188467i	0.523540	+	0.852001i	$0.324611\pi$
$500$	−14.3732	−	17.1293i	−0.0287463	−	0.0342585i
$501$	−771.361	+	195.631i	−1.53964	+	0.390482i
$502$	43.1427	−	15.7027i	0.0859417	−	0.0312802i
$503$	11.1537	−	6.43957i	0.0221743	−	0.0128023i	−0.488872	−	0.872356i	$-0.662591\pi$
$503$	11.1537	−	6.43957i	0.0221743	−	0.0128023i	0.511046	+	0.859553i	$0.329258\pi$
$504$	145.429	+	268.267i	0.288550	+	0.532275i
$505$	−160.225	+	277.517i	−0.317277	+	0.549539i
$506$	28.9599	+	5.10641i	0.0572330	+	0.0100917i
$507$	399.813	−	179.945i	0.788586	−	0.354921i
$508$	−132.577	−	48.2539i	−0.260977	−	0.0949880i
$509$	287.870	−	50.7593i	0.565561	−	0.0997236i	0.116445	−	0.993197i	$-0.462850\pi$
$509$	287.870	−	50.7593i	0.565561	−	0.0997236i	0.449116	+	0.893474i	$0.351739\pi$
$510$	5.67878	+	76.7578i	0.0111349	+	0.150506i
$511$	−541.482	−	454.357i	−1.05965	−	0.889153i
$512$		−	22.6274i		−	0.0441942i
$513$	−107.535	+	345.119i	−0.209619	+	0.672747i
$514$	−411.999			−0.801555
$515$	137.604	−	163.991i	0.267193	−	0.318428i
$516$	177.501	−	367.690i	0.343994	−	0.712577i
$517$	−13.4184	−	76.0997i	−0.0259544	−	0.147195i
$518$	−253.898	+	697.578i	−0.490150	+	1.34668i
$519$	295.650	−	410.400i	0.569654	−	0.790752i
$520$	−5.25013	+	29.7750i	−0.0100964	+	0.0572596i
$521$	754.775	+	435.770i	1.44871	+	0.836410i	0.998404	−	0.0564668i	$-0.0179835\pi$
$521$	754.775	+	435.770i	1.44871	+	0.836410i	0.450301	+	0.892877i	$0.351317\pi$
$522$	−105.114	−	21.4575i	−0.201368	−	0.0411063i
$523$	185.321	+	320.985i	0.354342	+	0.613738i	0.987005	−	0.160689i	$-0.0513717\pi$
$523$	185.321	+	320.985i	0.354342	+	0.613738i	−0.632663	+	0.774427i	$0.718038\pi$
$524$	92.4738	+	254.070i	0.176477	+	0.484866i
$525$	−173.045	−	48.8649i	−0.329609	−	0.0930760i
$526$	−374.853	+	314.539i	−0.712648	+	0.597982i
$527$	169.576	+	202.093i	0.321776	+	0.383477i
$528$	−6.11616	+	21.6591i	−0.0115836	+	0.0410210i
$529$	−381.590	+	138.887i	−0.721342	+	0.262547i
$530$	−206.321	+	119.119i	−0.389285	+	0.224754i
$531$	406.773	+	360.358i	0.766050	+	0.678640i
$532$	−160.491	+	277.979i	−0.301676	+	0.522518i
$533$	−202.089	−	35.6338i	−0.379155	−	0.0668552i
$534$	−154.709	−	111.451i	−0.289717	−	0.208711i
$535$	−382.037	−	139.050i	−0.714089	−	0.259907i
$536$	280.638	−	49.4840i	0.523578	−	0.0923209i
$537$	−141.755	−	68.4316i	−0.263975	−	0.127433i
$538$	−161.630	−	135.624i	−0.300428	−	0.252089i
$539$		−	177.608i		−	0.329514i
$540$	120.614	−	5.67458i	0.223360	−	0.0105085i
$541$	−65.4031			−0.120893			−0.0604465	−	0.998171i	$-0.519252\pi$
$541$	−65.4031			−0.120893			−0.0604465	+	0.998171i	$0.519252\pi$
$542$	383.473	−	457.005i	0.707514	−	0.843183i
$543$	−97.4236	+	7.20770i	−0.179417	+	0.0132738i
$544$	−7.96952	−	45.1974i	−0.0146498	−	0.0830834i
$545$	−23.8627	+	65.5621i	−0.0437847	+	0.120297i
$546$	99.7840	+	221.706i	0.182755	+	0.406056i
$547$	8.97822	−	50.9180i	0.0164136	−	0.0930860i	−0.975501	−	0.219997i	$-0.929395\pi$
$547$	8.97822	−	50.9180i	0.0164136	−	0.0930860i	0.991914	+	0.126911i	$0.0405063\pi$
$548$	−272.208	−	157.160i	−0.496731	−	0.286788i
$549$	−83.3715	−	51.1654i	−0.151861	−	0.0931974i
$550$	−6.63091	−	11.4851i	−0.0120562	−	0.0208820i
$551$	−38.5963	−	106.042i	−0.0700477	−	0.192455i
$552$	23.1272	+	91.1889i	0.0418971	+	0.165197i
$553$	1307.10	−	1096.79i	2.36365	−	1.98334i
$554$	−188.023	−	224.078i	−0.339392	−	0.404472i
$555$	204.904	+	210.478i	0.369197	+	0.379240i
$556$	134.034	−	48.7842i	0.241067	−	0.0877414i
$557$	290.129	−	167.506i	0.520877	−	0.300728i	−0.216416	−	0.976301i	$-0.569437\pi$
$557$	290.129	−	167.506i	0.520877	−	0.300728i	0.737293	+	0.675573i	$0.236104\pi$
$558$	324.069	−	257.430i	0.580770	−	0.461343i
$559$	162.652	−	281.722i	0.290970	−	0.503975i
$560$	105.590	+	18.6184i	0.188554	+	0.0332471i
$561$	−4.58833	+	45.4173i	−0.00817884	+	0.0809577i
$562$	225.711	+	82.1523i	0.401622	+	0.146178i
$563$	777.450	−	137.085i	1.38091	−	0.243491i	0.566631	−	0.823971i	$-0.308246\pi$
$563$	777.450	−	137.085i	1.38091	−	0.243491i	0.814274	+	0.580480i	$0.197135\pi$
$564$	204.386	−	139.063i	0.362387	−	0.246566i
$565$	−147.987	−	124.176i	−0.261924	−	0.219780i
$566$		−	684.319i		−	1.20904i
$567$	776.227	−	583.334i	1.36901	−	1.02881i
$568$	−335.448			−0.590578
$569$	−172.119	+	205.124i	−0.302494	+	0.360499i	−0.895783	−	0.444491i	$-0.853385\pi$
$569$	−172.119	+	205.124i	−0.302494	+	0.360499i	0.593289	+	0.804989i	$0.297829\pi$
$570$	71.4489	+	105.011i	0.125349	+	0.184229i
$571$	−0.473414	−	2.68486i	−0.000829097	−	0.00470204i	0.984390	−	0.175999i	$-0.0563155\pi$
$571$	−0.473414	−	2.68486i	−0.000829097	−	0.00470204i	−0.985219	+	0.171297i	$0.945204\pi$
$572$	−6.13296	+	16.8502i	−0.0107220	+	0.0294583i
$573$	−655.528	−	66.2253i	−1.14403	−	0.115577i
$574$	−126.367	+	716.663i	−0.220152	+	1.24854i
$575$	−48.0079	−	27.7174i	−0.0834921	−	0.0482042i
$576$	−71.2161	+	10.5956i	−0.123639	+	0.0183951i
$577$	−445.361	−	771.387i	−0.771856	−	1.33689i	−0.936545	−	0.350548i	$-0.885995\pi$
$577$	−445.361	−	771.387i	−0.771856	−	1.33689i	0.164689	−	0.986346i	$-0.447338\pi$
$578$	107.949	+	296.587i	0.186762	+	0.513126i
$579$	615.835	−	599.526i	1.06362	−	1.03545i
$580$	−28.8760	+	24.2299i	−0.0497862	+	0.0417756i
$581$	633.013	+	754.396i	1.08952	+	1.29844i
$582$	−546.204	+	138.528i	−0.938496	+	0.238020i
$583$	−132.775	+	48.3262i	−0.227745	+	0.0828923i
$584$	144.437	−	83.3909i	0.247324	−	0.142793i
$585$	96.1704	+	2.58144i	0.164394	+	0.00441271i
$586$	−3.69091	+	6.39284i	−0.00629848	+	0.0109093i
$587$	752.843	+	132.747i	1.28253	+	0.226144i	0.773053	−	0.634342i	$-0.218729\pi$
$587$	752.843	+	132.747i	1.28253	+	0.226144i	0.509474	+	0.860486i	$0.329840\pi$
$588$	518.132	−	233.197i	0.881177	−	0.396594i
$589$	409.092	+	148.897i	0.694554	+	0.252797i
$590$	188.043	−	33.1570i	0.318717	−	0.0561984i
$591$	0.0375985	+	0.508205i	6.36185e−5	+	0.000859907i
$592$	−134.177	−	112.588i	−0.226651	−	0.190183i
$593$			407.377i			0.686976i	0.939157	+	0.343488i	$0.111609\pi$
$593$			407.377i			0.686976i	−0.939157	+	0.343488i	$0.888391\pi$
$594$	71.0324	+	9.10749i	0.119583	+	0.0153325i
$595$	217.469			0.365495
$596$	−36.7840	+	43.8375i	−0.0617182	+	0.0735529i
$597$	147.133	−	304.783i	0.246454	−	0.510525i
$598$	13.0157	+	73.8157i	0.0217654	+	0.123438i
$599$	87.3334	−	239.946i	0.145799	−	0.400578i	−0.845200	−	0.534450i	$-0.820519\pi$
$599$	87.3334	−	239.946i	0.145799	−	0.400578i	0.990999	+	0.133872i	$0.0427410\pi$
$600$	24.7989	−	34.4240i	0.0413315	−	0.0573734i
$601$	170.276	−	965.680i	0.283320	−	1.60679i	−0.427904	−	0.903824i	$-0.640748\pi$
$601$	170.276	−	965.680i	0.283320	−	1.60679i	0.711224	−	0.702965i	$-0.248141\pi$
$602$	−999.060	−	576.808i	−1.65957	−	0.958152i
$603$	−287.155	−	860.090i	−0.476211	−	1.42635i
$604$	91.8204	+	159.038i	0.152021	+	0.263307i
$605$	89.8483	+	246.856i	0.148510	+	0.408027i
$606$	−585.128	−	165.230i	−0.965558	−	0.272658i
$607$	−401.894	+	337.229i	−0.662099	+	0.555567i	−0.910715	−	0.413035i	$-0.864469\pi$
$607$	−401.894	+	337.229i	−0.662099	+	0.555567i	0.248616	+	0.968602i	$0.420024\pi$
$608$	−48.6820	−	58.0169i	−0.0800690	−	0.0954226i
$609$	−82.3750	+	291.713i	−0.135263	+	0.479004i
$610$	−32.2976	+	11.7554i	−0.0529468	+	0.0192711i
$611$	170.574	−	98.4812i	0.279172	−	0.161180i
$612$	−138.520	+	46.2470i	−0.226339	+	0.0755669i
$613$	−324.260	+	561.634i	−0.528972	+	0.916206i	0.470458	+	0.882423i	$0.344089\pi$
$613$	−324.260	+	561.634i	−0.528972	+	0.916206i	−0.999429	+	0.0337831i	$0.989244\pi$
$614$	−312.198	−	55.0489i	−0.508465	−	0.0896562i
$615$	233.644	+	168.316i	0.379908	+	0.273684i
$616$	59.7552	+	21.7491i	0.0970051	+	0.0353070i
$617$	539.451	−	95.1197i	0.874312	−	0.154165i	0.281554	−	0.959545i	$-0.409150\pi$
$617$	539.451	−	95.1197i	0.874312	−	0.154165i	0.592758	+	0.805381i	$0.298039\pi$
$618$	365.786	+	176.582i	0.591886	+	0.285731i
$619$	546.501	+	458.569i	0.882877	+	0.740822i	0.966769	−	0.255653i	$-0.0822904\pi$
$619$	546.501	+	458.569i	0.882877	+	0.740822i	−0.0838912	+	0.996475i	$0.526735\pi$
$620$		−	145.420i		−	0.234549i
$621$	276.173	−	115.489i	0.444722	−	0.185973i
$622$	−678.633			−1.09105
$623$	−346.296	+	412.699i	−0.555852	+	0.662438i
$624$	−57.2092	+	4.23251i	−0.0916815	+	0.00678287i
$625$	4.34120	+	24.6202i	0.00694593	+	0.0393923i
$626$	111.143	−	305.363i	0.177545	−	0.487800i
$627$	30.9167	+	68.6928i	0.0493090	+	0.109558i
$628$	−66.2175	+	375.538i	−0.105442	+	0.597991i
$629$	−307.668	−	177.632i	−0.489139	−	0.282405i
$630$	9.15446	−	341.046i	0.0145309	−	0.541342i
$631$	579.905	+	1004.42i	0.919025	+	1.59180i	0.800899	+	0.598799i	$0.204355\pi$
$631$	579.905	+	1004.42i	0.919025	+	1.59180i	0.118126	+	0.992999i	$0.462311\pi$
$632$	137.697	+	378.320i	0.217875	+	0.598608i
$633$	−201.116	−	792.987i	−0.317719	−	1.25274i
$634$	127.000	−	106.566i	0.200316	−	0.168085i
$635$	101.392	+	120.834i	0.159672	+	0.190290i
$636$	−315.314	−	323.891i	−0.495776	−	0.509263i
$637$	425.402	−	154.834i	0.667821	−	0.243067i
$638$	−19.3612	+	11.1782i	−0.0303467	+	0.0175207i
$639$	157.078	+	1055.77i	0.245818	+	1.65222i
$640$	−12.6491	+	21.9089i	−0.0197642	+	0.0342327i
$641$	−904.790	−	159.539i	−1.41153	−	0.248891i	−0.584657	−	0.811281i	$-0.698771\pi$
$641$	−904.790	−	159.539i	−1.41153	−	0.248891i	−0.826872	+	0.562390i	$0.809882\pi$
$642$	77.5353	−	767.479i	0.120772	−	1.19545i
$643$	−50.3224	−	18.3158i	−0.0782619	−	0.0284850i	0.302593	−	0.953120i	$-0.402148\pi$
$643$	−50.3224	−	18.3158i	−0.0782619	−	0.0284850i	−0.380854	+	0.924635i	$0.624370\pi$
$644$	261.770	−	46.1571i	0.406475	−	0.0716726i
$645$	−377.410	+	256.788i	−0.585131	+	0.398121i
$646$	−117.674	−	98.7404i	−0.182158	−	0.152849i
$647$		−	1161.93i		−	1.79587i	−0.440130	−	0.897934i	$-0.645068\pi$
$647$		−	1161.93i		−	1.79587i	0.440130	−	0.897934i	$-0.354932\pi$
$648$	66.6956	+	219.180i	0.102925	+	0.338240i
$649$	113.246			0.174493
$650$	21.7281	−	25.8946i	0.0334279	−	0.0398378i
$651$	−657.818	−	966.817i	−1.01047	−	1.48513i
$652$	−85.1326	−	482.811i	−0.130571	−	0.740508i
$653$	233.848	−	642.493i	0.358114	−	0.983910i	−0.621569	−	0.783359i	$-0.713505\pi$
$653$	233.848	−	642.493i	0.358114	−	0.983910i	0.979683	−	0.200551i	$-0.0642732\pi$
$654$	−131.708	−	13.3060i	−0.201389	−	0.0203455i
$655$	52.4919	−	297.696i	0.0801403	−	0.454498i
$656$	−148.701	−	85.8523i	−0.226678	−	0.130872i
$657$	−330.094	−	415.544i	−0.502426	−	0.632487i
$658$	−349.240	−	604.902i	−0.530760	−	0.919304i
$659$	201.917	+	554.762i	0.306399	+	0.841823i	0.993351	+	0.115121i	$0.0367257\pi$
$659$	201.917	+	554.762i	0.306399	+	0.841823i	−0.686953	+	0.726702i	$0.741052\pi$
$660$	18.0297	−	17.5523i	0.0273178	−	0.0265944i
$661$	−511.725	+	429.388i	−0.774168	+	0.649604i	−0.941773	−	0.336250i	$-0.890841\pi$
$661$	−511.725	+	429.388i	−0.774168	+	0.649604i	0.167605	+	0.985854i	$0.446397\pi$
$662$	192.583	+	229.511i	0.290911	+	0.346694i
$663$	−112.782	+	28.6037i	−0.170109	+	0.0431429i
$664$	−218.348	+	79.4723i	−0.328838	+	0.119687i
$665$	310.790	−	179.435i	0.467354	−	0.269827i
$666$	−291.523	+	475.023i	−0.437722	+	0.713247i
$667$	−46.7252	+	80.9303i	−0.0700527	+	0.121335i
$668$	−522.461	−	92.1241i	−0.782128	−	0.137910i
$669$	654.940	−	294.771i	0.978984	−	0.440614i
$670$	−299.389	−	108.969i	−0.446849	−	0.162640i
$671$	−20.0749	+	3.53975i	−0.0299179	+	0.00527534i
$672$	15.0096	+	202.879i	0.0223357	+	0.301903i
$673$	−281.308	−	236.045i	−0.417991	−	0.350736i	0.409407	−	0.912352i	$-0.365736\pi$
$673$	−281.308	−	236.045i	−0.417991	−	0.350736i	−0.827398	+	0.561616i	$0.810180\pi$
$674$			588.452i			0.873073i
$675$	−119.956	−	61.9310i	−0.177713	−	0.0917497i
$676$	292.294			0.432388
$677$	261.344	−	311.458i	0.386033	−	0.460056i	−0.537676	−	0.843152i	$-0.680698\pi$
$677$	261.344	−	311.458i	0.386033	−	0.460056i	0.923709	+	0.383095i	$0.125142\pi$
$678$	159.350	−	330.089i	0.235029	−	0.486858i
$679$	276.473	+	1567.95i	0.407176	+	2.30921i
$680$	−17.5496	+	48.2173i	−0.0258083	+	0.0709077i
$681$	303.421	−	421.187i	0.445552	−	0.618483i
$682$	14.9766	−	84.9365i	0.0219598	−	0.124540i
$683$	−1165.13	−	672.687i	−1.70590	−	0.984901i	−0.939508	−	0.342526i	$-0.888718\pi$
$683$	−1165.13	−	672.687i	−1.70590	−	0.984901i	−0.766390	−	0.642375i	$-0.777949\pi$
$684$	−159.803	+	180.386i	−0.233630	+	0.263722i
$685$	175.710	+	304.338i	0.256511	+	0.444289i
$686$	−264.970	−	727.998i	−0.386253	−	1.06122i
$687$	392.704	+	110.893i	0.571622	+	0.161416i
$688$	208.513	−	174.963i	0.303072	−	0.254307i
$689$	−231.500	−	275.891i	−0.335994	−	0.400422i
$690$	28.5833	−	101.222i	0.0414251	−	0.146698i
$691$	−699.338	+	254.538i	−1.01207	+	0.368362i	−0.794226	−	0.607623i	$-0.792123\pi$
$691$	−699.338	+	254.538i	−1.01207	+	0.368362i	−0.217840	+	0.975984i	$0.569901\pi$
$692$	292.026	−	168.601i	0.422003	−	0.243644i
$693$	40.4707	−	198.254i	0.0583992	−	0.286081i
$694$	−444.603	+	770.076i	−0.640639	+	1.10962i
$695$	−157.049	−	27.6919i	−0.225969	−	0.0398445i
$696$	−58.0310	−	41.8053i	−0.0833779	−	0.0600650i
$697$	−327.261	−	119.113i	−0.469528	−	0.170894i
$698$	−278.450	+	49.0983i	−0.398926	+	0.0703414i
$699$	302.041	+	145.810i	0.432105	+	0.208597i
$700$	−91.8291	−	77.0538i	−0.131184	−	0.110077i
$701$			782.894i			1.11682i	0.829564	+	0.558412i	$0.188589\pi$
$701$			782.894i			1.11682i	−0.829564	+	0.558412i	$0.811411\pi$
$702$	40.1101	+	178.075i	0.0571369	+	0.253668i
$703$	−586.261			−0.833942
$704$	−9.64441	+	11.4938i	−0.0136995	+	0.0163264i
$705$	−275.635	+	20.3923i	−0.390971	+	0.0289253i
$706$	−65.4861	−	371.390i	−0.0927565	−	0.526048i
$707$	−587.560	+	1614.31i	−0.831061	+	2.28332i
$708$	148.691	+	330.371i	0.210016	+	0.466626i
$709$	186.850	−	1059.68i	0.263540	−	1.49461i	−0.509621	−	0.860399i	$-0.670214\pi$
$709$	186.850	−	1059.68i	0.263540	−	1.49461i	0.773161	−	0.634210i	$-0.218675\pi$
$710$	324.796	+	187.521i	0.457460	+	0.264115i
$711$	1126.22	−	610.533i	1.58400	−	0.858696i
$712$	−63.5577	−	110.085i	−0.0892664	−	0.154614i
$713$	−123.303	−	338.772i	−0.172936	−	0.475136i
$714$	101.436	+	399.956i	0.142068	+	0.560163i
$715$	15.3577	−	12.8867i	0.0214794	−	0.0180233i
$716$	−67.4532	−	80.3876i	−0.0942084	−	0.112273i
$717$	−414.383	−	425.655i	−0.577940	−	0.593662i
$718$	785.941	−	286.059i	1.09462	−	0.398411i
$719$	84.5923	−	48.8394i	0.117653	−	0.0679268i	−0.440019	−	0.897989i	$-0.645028\pi$
$719$	84.5923	−	48.8394i	0.117653	−	0.0679268i	0.557672	+	0.830062i	$0.311695\pi$
$720$	74.8778	+	29.5519i	0.103997	+	0.0410443i
$721$	573.821	−	993.887i	0.795868	−	1.37848i
$722$	253.133	+	44.6342i	0.350600	+	0.0618202i
$723$	−45.9526	+	454.859i	−0.0635582	+	0.629127i
$724$	−61.1990	−	22.2746i	−0.0845290	−	0.0307660i
$725$	41.5040	−	7.31827i	0.0572469	−	0.0100942i
$726$	−412.094	+	280.387i	−0.567623	+	0.386208i
$727$	−837.807	−	703.004i	−1.15242	−	0.966993i	−0.152644	−	0.988281i	$-0.548779\pi$
$727$	−837.807	−	703.004i	−1.15242	−	0.966993i	−0.999773	+	0.0212887i	$0.993223\pi$
$728$			162.084i			0.222644i
$729$	658.601	−	312.547i	0.903431	−	0.428734i
$730$	−186.468			−0.255435
$731$	354.874	−	422.922i	0.485463	−	0.578553i
$732$	−36.6846	−	53.9166i	−0.0501156	−	0.0736565i
$733$	164.319	+	931.901i	0.224174	+	1.27135i	0.864258	+	0.503048i	$0.167788\pi$
$733$	164.319	+	931.901i	0.224174	+	1.27135i	−0.640085	+	0.768304i	$0.721101\pi$
$734$	118.921	−	326.732i	0.162017	−	0.445139i
$735$	−632.041	−	63.8525i	−0.859919	−	0.0868742i
$736$	−10.8907	+	61.7645i	−0.0147972	+	0.0839191i
$737$	−163.643	−	94.4796i	−0.222040	−	0.128195i
$738$	−200.575	+	508.212i	−0.271782	+	0.688635i
$739$	−320.838	−	555.708i	−0.434152	−	0.751973i	0.563074	−	0.826407i	$-0.309619\pi$
$739$	−320.838	−	555.708i	−0.434152	−	0.751973i	−0.997226	+	0.0744331i	$0.976285\pi$
$740$	66.9780	+	184.021i	0.0905108	+	0.248676i
$741$	−137.579	+	133.936i	−0.185667	+	0.180750i
$742$	−978.381	+	820.959i	−1.31857	+	1.10641i
$743$	−600.577	−	715.740i	−0.808313	−	0.963310i	0.191521	−	0.981488i	$-0.438658\pi$
$743$	−600.577	−	715.740i	−0.808313	−	0.963310i	−0.999835	+	0.0181780i	$0.994213\pi$
$744$	267.448	−	67.8298i	0.359473	−	0.0911690i
$745$	60.1219	−	21.8826i	0.0807006	−	0.0293726i
$746$	320.614	−	185.106i	0.429777	−	0.248132i
$747$	352.370	+	650.002i	0.471714	+	0.870150i
$748$	−15.2162	+	26.3552i	−0.0203425	+	0.0352342i
$749$	−2146.41	−	378.470i	−2.86570	−	0.505301i
$750$	−43.2551	+	19.4679i	−0.0576734	+	0.0259572i
$751$	552.984	+	201.270i	0.736331	+	0.268002i	0.682842	−	0.730566i	$-0.260744\pi$
$751$	552.984	+	201.270i	0.736331	+	0.268002i	0.0534887	+	0.998568i	$0.482966\pi$
$752$	162.302	−	28.6183i	0.215827	−	0.0380562i
$753$	−7.18580	−	97.1276i	−0.00954290	−	0.128988i
$754$	−43.6523	−	36.6287i	−0.0578943	−	0.0485791i
$755$		−	205.317i		−	0.271943i
$756$	631.500	−	142.241i	0.835318	−	0.188149i
$757$	−201.210			−0.265799			−0.132900	−	0.991130i	$-0.542429\pi$
$757$	−201.210			−0.265799			−0.132900	+	0.991130i	$0.542429\pi$
$758$	−318.140	+	379.145i	−0.419710	+	0.500191i
$759$	27.1195	−	56.1775i	0.0357306	−	0.0740152i
$760$	14.7037	+	83.3887i	0.0193469	+	0.109722i
$761$	167.677	−	460.690i	0.220338	−	0.605375i	−0.779439	−	0.626478i	$-0.784496\pi$
$761$	167.677	−	460.690i	0.220338	−	0.605375i	0.999777	+	0.0211036i	$0.00671797\pi$
$762$	−174.938	+	242.836i	−0.229577	+	0.318682i
$763$	−64.9499	+	368.349i	−0.0851244	+	0.482764i
$764$	−380.396	−	219.621i	−0.497900	−	0.287463i
$765$	159.974	+	32.6563i	0.209116	+	0.0426880i
$766$	−38.6630	−	66.9663i	−0.0504739	−	0.0874234i
$767$	98.7250	+	271.245i	0.128716	+	0.353644i
$768$	−46.1936	−	13.0443i	−0.0601479	−	0.0169848i
$769$	266.357	−	223.500i	0.346367	−	0.290637i	−0.452962	−	0.891530i	$-0.649633\pi$
$769$	266.357	−	223.500i	0.346367	−	0.290637i	0.799329	+	0.600893i	$0.205188\pi$
$770$	−45.6996	−	54.4626i	−0.0593501	−	0.0707307i
$771$	−237.510	+	841.092i	−0.308055	+	1.09091i
$772$	538.423	−	195.970i	0.697440	−	0.253847i
$773$	54.0624	−	31.2129i	0.0699384	−	0.0403790i	−0.464623	−	0.885509i	$-0.653810\pi$
$773$	54.0624	−	31.2129i	0.0699384	−	0.0403790i	0.534561	+	0.845130i	$0.320477\pi$
$774$	−648.308	−	574.333i	−0.837607	−	0.742032i
$775$	−81.2924	+	140.802i	−0.104893	+	0.181681i
$776$	−369.958	−	65.2335i	−0.476750	−	0.0840638i
$777$	1277.73	+	920.470i	1.64444	+	1.18465i
$778$	−107.423	−	39.0989i	−0.138076	−	0.0502557i
$779$	−565.978	+	99.7971i	−0.726544	+	0.128109i
$780$	57.7586	+	27.8828i	0.0740495	+	0.0357472i
$781$	170.393	+	142.977i	0.218173	+	0.183069i
$782$			127.208i			0.162670i
$783$	−104.401	+	202.219i	−0.133335	+	0.258262i
$784$	378.795			0.483156
$785$	274.047	−	326.597i	0.349105	−	0.416047i
$786$	571.989	−	42.3175i	0.727722	−	0.0538391i
$787$	127.446	+	722.781i	0.161939	+	0.918401i	0.952165	+	0.305585i	$0.0988520\pi$
$787$	127.446	+	722.781i	0.161939	+	0.918401i	−0.790226	+	0.612816i	$0.790037\pi$
$788$	−0.116194	+	0.319241i	−0.000147455	+	0.000405128i
$789$	426.031	+	946.583i	0.539963	+	1.19972i
$790$	78.1626	−	443.282i	0.0989400	−	0.561117i
$791$	−896.895	−	517.823i	−1.13388	−	0.654643i
$792$	40.6909	+	24.9721i	0.0513774	+	0.0315305i
$793$	−25.9791	−	44.9971i	−0.0327605	−	0.0567429i
$794$	229.319	+	630.048i	0.288814	+	0.793511i
$795$	124.241	+	489.872i	0.156277	+	0.616191i
$796$	172.840	−	145.030i	0.217135	−	0.182198i
$797$	558.865	+	666.029i	0.701211	+	0.835670i	0.992663	−	0.120915i	$-0.0385828\pi$
$797$	558.865	+	666.029i	0.701211	+	0.835670i	−0.291452	+	0.956585i	$0.594138\pi$
$798$	474.971	+	487.891i	0.595202	+	0.611393i
$799$	314.113	−	114.328i	0.393132	−	0.143088i
$800$	24.4949	−	14.1421i	0.0306186	−	0.0176777i
$801$	−316.713	+	251.586i	−0.395398	+	0.314090i
$802$	−143.891	+	249.226i	−0.179415	+	0.310756i
$803$	−108.911	−	19.2040i	−0.135631	−	0.0239153i
$804$	60.7616	−	601.445i	0.0755741	−	0.748066i
$805$	−279.261	−	101.643i	−0.346907	−	0.126264i
$806$	216.494	−	38.1738i	0.268603	−	0.0473620i
$807$	−370.052	+	251.782i	−0.458552	+	0.311997i
$808$	−310.509	−	260.548i	−0.384293	−	0.322460i
$809$			106.098i			0.131147i	0.997848	+	0.0655735i	$0.0208877\pi$
$809$			106.098i			0.131147i	−0.997848	+	0.0655735i	$0.979112\pi$
$810$	57.9473	−	249.504i	0.0715399	−	0.308029i
$811$	−949.215			−1.17042			−0.585212	−	0.810880i	$-0.698989\pi$
$811$	−949.215			−1.17042			−0.585212	+	0.810880i	$0.698989\pi$
$812$	−129.895	+	154.803i	−0.159969	+	0.190644i
$813$	−711.905	−	1046.31i	−0.875651	−	1.28697i
$814$	20.1683	+	114.380i	0.0247768	+	0.140516i
$815$	−187.470	+	515.070i	−0.230025	+	0.631988i
$816$	−96.8641	−	9.78579i	−0.118706	−	0.0119924i
$817$	158.203	−	897.216i	0.193639	−	1.09818i
$818$	79.4384	+	45.8638i	0.0971129	+	0.0560682i
$819$	510.135	−	75.8981i	0.622875	−	0.0926716i
$820$	95.9858	+	166.252i	0.117056	+	0.202747i
$821$	146.867	+	403.514i	0.178888	+	0.491491i	0.996434	−	0.0843717i	$-0.0268883\pi$
$821$	146.867	+	403.514i	0.178888	+	0.491491i	−0.817546	+	0.575863i	$0.804666\pi$
$822$	−477.763	+	465.110i	−0.581220	+	0.565828i
$823$	−1196.37	+	1003.87i	−1.45366	+	1.21977i	−0.523812	+	0.851834i	$0.675490\pi$
$823$	−1196.37	+	1003.87i	−1.45366	+	1.21977i	−0.929852	+	0.367935i	$0.880065\pi$
$824$	174.057	+	207.433i	0.211235	+	0.251740i
$825$	−27.2692	+	6.91598i	−0.0330536	+	0.00838301i
$826$	961.906	−	350.105i	1.16453	−	0.423856i
$827$	−635.340	+	366.814i	−0.768247	+	0.443548i	−0.832249	−	0.554402i	$-0.812947\pi$
$827$	−635.340	+	366.814i	−0.768247	+	0.443548i	0.0640018	+	0.997950i	$0.479614\pi$
$828$	199.493	+	5.35487i	0.240934	+	0.00646723i
$829$	460.822	−	798.168i	0.555878	−	0.962808i	−0.441957	−	0.897036i	$-0.645716\pi$
$829$	460.822	−	798.168i	0.555878	−	0.962808i	0.997835	−	0.0657719i	$-0.0209510\pi$
$830$	255.841	+	45.1117i	0.308242	+	0.0543515i
$831$	−565.843	+	254.671i	−0.680919	+	0.306463i
$832$	−35.9373	−	13.0801i	−0.0431939	−	0.0157213i
$833$	756.627	−	133.414i	0.908316	−	0.160161i
$834$	−22.3245	−	301.751i	−0.0267679	−	0.361812i
$835$	454.372	+	381.264i	0.544158	+	0.456603i
$836$			50.2197i			0.0600714i
$837$	−338.719	−	809.987i	−0.404682	−	0.967726i
$838$	−189.183			−0.225755
$839$	659.326	−	785.754i	0.785848	−	0.936537i	−0.213334	−	0.976979i	$-0.568432\pi$
$839$	659.326	−	785.754i	0.785848	−	0.936537i	0.999182	+	0.0404425i	$0.0128767\pi$
$840$	98.8799	−	204.827i	0.117714	−	0.243842i
$841$	133.701	+	758.257i	0.158979	+	0.901614i
$842$	0.262896	−	0.722300i	0.000312228	−	0.000857839i
$843$	297.831	−	413.428i	0.353299	−	0.490424i
$844$	94.7069	−	537.109i	0.112212	−	0.636386i
$845$	−283.013	−	163.397i	−0.334926	−	0.193370i
$846$	−166.071	−	497.419i	−0.196302	−	0.587966i
$847$	704.157	+	1219.64i	0.831354	+	1.43995i
$848$	−103.068	−	283.177i	−0.121543	−	0.333936i
$849$	−1397.03	−	394.497i	−1.64550	−	0.464661i
$850$	43.9466	−	36.8756i	0.0517019	−	0.0433831i
$851$	312.065	+	371.905i	0.366704	+	0.437021i
$852$	−193.380	+	684.813i	−0.226972	+	0.803772i
$853$	268.337	−	97.6667i	0.314580	−	0.114498i	−0.179905	−	0.983684i	$-0.557579\pi$
$853$	268.337	−	97.6667i	0.314580	−	0.114498i	0.494485	+	0.869186i	$0.335357\pi$
$854$	−159.572	+	92.1288i	−0.186852	+	0.107879i
$855$	255.567	−	85.3252i	0.298909	−	0.0997956i
$856$	257.128	−	445.360i	0.300384	−	0.520280i
$857$	−85.5805	−	15.0902i	−0.0998606	−	0.0176081i	0.123495	−	0.992345i	$-0.460590\pi$
$857$	−85.5805	−	15.0902i	−0.0998606	−	0.0176081i	−0.223355	+	0.974737i	$0.571701\pi$
$858$	30.8639	+	22.2342i	0.0359719	+	0.0259140i
$859$	1112.39	+	404.876i	1.29498	+	0.471334i	0.895358	−	0.445347i	$-0.146920\pi$
$859$	1112.39	+	404.876i	1.29498	+	0.471334i	0.399621	+	0.916681i	$0.369142\pi$
$860$	−299.700	+	52.8451i	−0.348488	+	0.0614478i
$861$	1390.21	+	671.120i	1.61465	+	0.779465i
$862$	814.055	+	683.074i	0.944380	+	0.792429i
$863$		−	458.946i		−	0.531803i	−0.964000	−	0.265901i	$-0.914330\pi$
$863$		−	458.946i		−	0.531803i	0.964000	−	0.265901i	$-0.0856695\pi$
$864$	−19.4241	+	151.495i	−0.0224816	+	0.175341i
$865$	−377.004			−0.435843
$866$	687.821	−	819.713i	0.794251	−	0.946551i
$867$	667.708	−	49.3991i	0.770136	−	0.0569770i
$868$	−135.374	−	767.746i	−0.155961	−	0.884500i
$869$	91.3059	−	250.861i	0.105070	−	0.288678i
$870$	32.8184	+	72.9181i	0.0377223	+	0.0838139i
$871$	83.6354	−	474.320i	0.0960223	−	0.544569i
$872$	−76.4289	−	44.1262i	−0.0876478	−	0.0506035i
$873$	−32.0746	+	1194.93i	−0.0367407	+	1.36876i
$874$	104.960	+	181.796i	0.120091	+	0.208004i
$875$	45.8388	+	125.941i	0.0523872	+	0.143933i
$876$	−86.9760	−	342.940i	−0.0992876	−	0.391484i
$877$	−15.3902	+	12.9139i	−0.0175487	+	0.0147251i	−0.651520	−	0.758632i	$-0.725868\pi$
$877$	−15.3902	+	12.9139i	−0.0175487	+	0.0147251i	0.633971	+	0.773357i	$0.281424\pi$
$878$	180.395	+	214.987i	0.205462	+	0.244860i
$879$	10.9232	+	11.2203i	0.0124268	+	0.0127649i
$880$	15.7634	−	5.73740i	0.0179129	−	0.00651977i
$881$	571.915	−	330.195i	0.649166	−	0.374796i	−0.138971	−	0.990297i	$-0.544379\pi$
$881$	571.915	−	330.195i	0.649166	−	0.374796i	0.788137	+	0.615500i	$0.211046\pi$
$882$	−177.375	−	1192.19i	−0.201106	−	1.35169i
$883$	39.4095	−	68.2592i	0.0446314	−	0.0773038i	−0.842847	−	0.538154i	$-0.819122\pi$
$883$	39.4095	−	68.2592i	0.0446314	−	0.0773038i	0.887478	+	0.460850i	$0.152455\pi$
$884$	−76.3903	−	13.4697i	−0.0864144	−	0.0152372i
$885$	40.7136	−	403.001i	0.0460041	−	0.455369i
$886$	1035.38	+	376.846i	1.16860	+	0.425334i
$887$	−156.446	+	27.5857i	−0.176377	+	0.0311000i	−0.261139	−	0.965301i	$-0.584098\pi$
$887$	−156.446	+	27.5857i	−0.176377	+	0.0311000i	0.0847621	+	0.996401i	$0.472987\pi$
$888$	−307.198	+	209.016i	−0.345944	+	0.235379i
$889$	647.786	+	543.557i	0.728668	+	0.611425i
$890$			142.119i			0.159685i
$891$	59.5417	−	139.761i	0.0668257	−	0.156859i
$892$	478.812			0.536784
$893$	354.573	−	422.564i	0.397059	−	0.473196i
$894$	68.2884	+	100.366i	0.0763852	+	0.112266i
$895$	20.3733	+	115.543i	0.0227634	+	0.129098i
$896$	−46.3856	+	127.443i	−0.0517696	+	0.142236i
$897$	158.197	+	15.9820i	0.176363	+	0.0178172i
$898$	69.1983	−	392.443i	0.0770582	−	0.437019i
$899$	237.361	+	137.040i	0.264027	+	0.152436i
$900$	−55.9801	−	70.4715i	−0.0622001	−	0.0783016i
$901$	−305.611	−	529.334i	−0.339191	−	0.587496i
$902$	38.9410	+	106.990i	0.0431718	+	0.118614i
$903$	−1753.49	+	1707.05i	−1.94184	+	1.89042i
$904$	187.190	−	157.071i	0.207069	−	0.173752i
$905$	46.8038	+	55.7786i	0.0517169	+	0.0616338i
$906$	377.606	−	95.7679i	0.416784	−	0.105704i
$907$	1551.72	−	564.780i	1.71083	−	0.622691i	0.713845	−	0.700304i	$-0.246952\pi$
$907$	1551.72	−	564.780i	1.71083	−	0.622691i	0.996984	+	0.0776128i	$0.0247298\pi$
$908$	299.701	−	173.033i	0.330068	−	0.190565i
$909$	−674.632	+	1099.28i	−0.742169	+	1.20933i
$910$	90.6080	−	156.938i	0.0995692	−	0.172459i
$911$	762.954	+	134.529i	0.837491	+	0.147672i	0.575914	−	0.817510i	$-0.304646\pi$
$911$	762.954	+	134.529i	0.837491	+	0.147672i	0.261577	+	0.965183i	$0.415757\pi$
$912$	−146.505	+	65.9379i	−0.160641	+	0.0723003i
$913$	144.785	+	52.6974i	0.158581	+	0.0577189i
$914$	1018.43	−	179.577i	1.11426	−	0.196474i
$915$	5.37944	+	72.7118i	0.00587917	+	0.0794665i
$916$	208.395	+	174.864i	0.227506	+	0.190900i
$917$		−	1620.55i		−	1.76723i
$918$	14.5586	+	309.446i	0.0158591	+	0.337087i
$919$	488.378			0.531423			0.265712	−	0.964053i	$-0.414393\pi$
$919$	488.378			0.531423			0.265712	+	0.964053i	$0.414393\pi$
$920$	45.0723	−	53.7151i	0.0489916	−	0.0583860i
$921$	−292.358	+	605.613i	−0.317435	+	0.657560i
$922$	175.444	+	994.993i	0.190287	+	1.07917i
$923$	−193.911	+	532.766i	−0.210088	+	0.577211i
$924$	78.8483	−	109.451i	0.0853336	−	0.118454i
$925$	38.0195	−	215.619i	0.0411021	−	0.233102i
$926$	962.437	+	555.664i	1.03935	+	0.600069i
$927$	571.359	−	644.950i	0.616352	−	0.695739i
$928$	−23.8404	−	41.2928i	−0.0256901	−	0.0444965i
$929$	−156.088	−	428.849i	−0.168017	−	0.461624i	0.826896	−	0.562354i	$-0.190104\pi$
$929$	−156.088	−	428.849i	−0.168017	−	0.461624i	−0.994914	+	0.100730i	$0.967882\pi$
$930$	−296.873	−	83.8321i	−0.319219	−	0.0901420i
$931$	971.233	−	814.961i	1.04321	−	0.875361i
$932$	143.725	+	171.285i	0.154211	+	0.183782i
$933$	−391.220	+	1385.42i	−0.419314	+	1.48491i
$934$	−472.486	+	171.971i	−0.505873	+	0.184123i
$935$	29.4660	−	17.0122i	0.0315144	−	0.0181948i
$936$	−24.3395	+	119.232i	−0.0260037	+	0.127384i
$937$	−526.313	+	911.601i	−0.561700	+	0.972894i	0.435648	+	0.900117i	$0.356519\pi$
$937$	−526.313	+	911.601i	−0.561700	+	0.972894i	−0.997348	+	0.0727765i	$0.976814\pi$
$938$	−1682.06	−	296.593i	−1.79325	−	0.316198i
$939$	−559.322	−	402.933i	−0.595657	−	0.429108i
$940$	−173.147	−	63.0202i	−0.184198	−	0.0670427i
$941$	−460.924	+	81.2733i	−0.489823	+	0.0863691i	−0.413104	−	0.910684i	$-0.635556\pi$
$941$	−460.924	+	81.2733i	−0.489823	+	0.0863691i	−0.0767190	+	0.997053i	$0.524444\pi$
$942$	728.483	+	351.673i	0.773337	+	0.373326i
$943$	364.576	+	305.916i	0.386613	+	0.324407i
$944$			241.527i			0.255855i
$945$	−690.963	−	215.295i	−0.731178	−	0.227826i
$946$	−180.490			−0.190793
$947$	761.695	−	907.752i	0.804324	−	0.958556i	−0.195430	−	0.980718i	$-0.562610\pi$
$947$	761.695	−	907.752i	0.804324	−	0.958556i	0.999754	+	0.0221616i	$0.00705484\pi$
$948$	851.716	−	63.0125i	0.898434	−	0.0664689i
$949$	−48.9490	−	277.604i	−0.0515796	−	0.292522i
$950$	32.3789	−	88.9603i	0.0340831	−	0.0936425i
$951$	−144.340	−	320.703i	−0.151777	−	0.337227i
$952$	−47.7670	+	270.900i	−0.0501755	+	0.284559i
$953$	1125.45	+	649.778i	1.18095	+	0.681824i	0.956235	−	0.292600i	$-0.0945203\pi$
$953$	1125.45	+	649.778i	1.18095	+	0.681824i	0.224719	+	0.974424i	$0.427854\pi$
$954$	−842.992	+	456.991i	−0.883639	+	0.479027i
$955$	245.544	+	425.295i	0.257114	+	0.445335i
$956$	−135.452	−	372.150i	−0.141686	−	0.389278i
$957$	11.6588	+	45.9697i	0.0121826	+	0.0480352i
$958$	−828.227	+	694.965i	−0.864538	+	0.725433i
$959$	1210.97	+	1443.18i	1.26275	+	1.50488i
$960$	37.4348	+	38.4531i	0.0389945	+	0.0400553i
$961$	−90.5407	+	32.9541i	−0.0942151	+	0.0342915i
$962$	−256.378	+	148.020i	−0.266506	+	0.153867i
$963$	−1522.10	−	600.725i	−1.58058	−	0.623806i
$964$	−152.391	+	263.950i	−0.158082	+	0.273807i
$965$	−630.877	−	111.241i	−0.653758	−	0.115275i
$966$	56.6765	−	561.009i	0.0586713	−	0.580755i
$967$	−939.599	−	341.986i	−0.971664	−	0.353657i	−0.193070	−	0.981185i	$-0.561844\pi$
$967$	−939.599	−	341.986i	−0.971664	−	0.353657i	−0.778594	+	0.627528i	$0.784067\pi$
$968$	−327.242	+	57.7017i	−0.338060	+	0.0596092i
$969$	−269.414	+	183.308i	−0.278033	+	0.189173i
$970$	321.743	+	269.975i	0.331694	+	0.278324i
$971$		−	352.638i		−	0.363170i	−0.983375	−	0.181585i	$-0.941877\pi$
$971$		−	352.638i		−	0.363170i	0.983375	−	0.181585i	$-0.0581228\pi$
$972$	485.901	−	9.80524i	0.499898	−	0.0100877i
$973$	−854.917			−0.878640
$974$	−226.305	+	269.700i	−0.232346	+	0.276900i
$975$	−40.3376	−	59.2855i	−0.0413719	−	0.0608056i
$976$	−7.54943	−	42.8150i	−0.00773507	−	0.0438678i
$977$	284.896	−	782.745i	0.291603	−	0.801172i	−0.704230	−	0.709972i	$-0.748708\pi$
$977$	284.896	−	782.745i	0.291603	−	0.801172i	0.995833	−	0.0912000i	$-0.0290703\pi$
$978$	−1034.73	−	104.535i	−1.05801	−	0.106886i
$979$	−14.6367	+	83.0086i	−0.0149506	+	0.0847892i
$980$	−366.766	−	211.753i	−0.374251	−	0.216074i
$981$	−103.091	+	261.210i	−0.105088	+	0.266269i
$982$	331.984	+	575.012i	0.338069	+	0.585552i
$983$	−429.415	−	1179.81i	−0.436841	−	1.20021i	−0.941536	−	0.336913i	$-0.890617\pi$
$983$	−429.415	−	1179.81i	−0.436841	−	1.20021i	0.504695	−	0.863298i	$-0.331605\pi$
$984$	−260.990	+	254.078i	−0.265233	+	0.258209i
$985$	0.290966	−	0.244149i	0.000295397	−	0.000247867i
$986$	−62.1638	−	74.0839i	−0.0630464	−	0.0751358i
$987$	−1436.23	+	364.255i	−1.45515	+	0.369052i
$988$	−120.285	+	43.7802i	−0.121746	+	0.0443119i
$989$	−653.375	+	377.226i	−0.660642	+	0.381422i
$990$	−25.4389	−	46.9260i	−0.0256959	−	0.0474000i
$991$	42.0546	−	72.8407i	0.0424365	−	0.0735023i	−0.844027	−	0.536301i	$-0.819821\pi$
$991$	42.0546	−	72.8407i	0.0424365	−	0.0735023i	0.886464	+	0.462798i	$0.153155\pi$
$992$	181.149	+	31.9415i	0.182610	+	0.0321991i
$993$	579.565	−	260.846i	0.583650	−	0.262685i
$994$	1889.33	+	687.660i	1.90073	+	0.691811i
$995$	−248.425	+	43.8041i	−0.249674	+	0.0440242i
$996$	36.3678	+	491.570i	0.0365139	+	0.493544i
$997$	−154.929	−	130.001i	−0.155395	−	0.130392i	0.561775	−	0.827290i	$-0.310119\pi$
$997$	−154.929	−	130.001i	−0.155395	−	0.130392i	−0.717170	+	0.696898i	$0.754563\pi$
$998$			206.911i			0.207325i
$999$	801.695	+	868.982i	0.802497	+	0.869852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.o.a.11.16	✓	144
27.5	odd	18	inner	270.3.o.a.221.16	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.o.a.11.16	✓	144	1.1	even	1	trivial
270.3.o.a.221.16	yes	144	27.5	odd	18	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.o (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.909039 - 1.08335i) q^{2} +(-1.68760 - 2.48032i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(-4.22115 - 0.426446i) q^{6} +(-2.08160 + 11.8053i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-3.30400 + 8.37159i) q^{9} +(1.58114 + 2.73861i) q^{10} +(0.641461 + 1.76240i) q^{11} +(-4.29918 + 4.18533i) q^{12} +(-3.66205 + 3.07282i) q^{13} +(10.8970 + 12.9866i) q^{14} +(6.50234 - 1.64911i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-7.02615 + 4.05655i) q^{17} +(6.06590 + 11.1895i) q^{18} +(-6.69415 + 11.5946i) q^{19} +(4.40419 + 0.776578i) q^{20} +(32.7939 - 14.7596i) q^{21} +(2.49241 + 0.907162i) q^{22} +(10.9185 - 1.92523i) q^{23} +(0.626056 + 8.46215i) q^{24} +(-3.83022 - 3.21394i) q^{25} +6.76060i q^{26} +(26.3401 - 5.93292i) q^{27} +23.9749 q^{28} +(-5.41796 + 6.45687i) q^{29} +(4.12431 - 8.54342i) q^{30} +(-5.64651 - 32.0229i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(3.28879 - 4.56526i) q^{33} +(-1.99238 + 11.2993i) q^{34} +(-23.2136 - 13.4024i) q^{35} +(17.6363 + 3.60019i) q^{36} +(21.8945 + 37.9224i) q^{37} +(6.47578 + 17.7921i) q^{38} +(13.8017 + 3.89736i) q^{39} +(4.84489 - 4.06535i) q^{40} +(27.5924 + 32.8833i) q^{41} +(13.8211 - 48.9444i) q^{42} +(-63.9448 + 23.2740i) q^{43} +(3.24847 - 1.87551i) q^{44} +(-15.0637 - 13.3449i) q^{45} +(7.83966 - 13.5787i) q^{46} +(-40.5756 - 7.15456i) q^{47} +(9.73659 + 7.01419i) q^{48} +(-88.9876 - 32.3888i) q^{49} +(-6.96364 + 1.22788i) q^{50} +(21.9189 + 10.5813i) q^{51} +(7.32410 + 6.14565i) q^{52} +75.3378i q^{53} +(17.5167 - 33.9288i) q^{54} -4.19376 q^{55} +(21.7941 - 25.9732i) q^{56} +(40.0554 - 2.96342i) q^{57} +(2.06992 + 11.7391i) q^{58} +(20.6518 - 56.7402i) q^{59} +(-5.50636 - 12.2344i) q^{60} +(-1.88736 + 10.7037i) q^{61} +(-39.8250 - 22.9929i) q^{62} +(-91.9517 - 56.4311i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-3.65601 - 10.0448i) q^{65} +(-1.95614 - 7.71291i) q^{66} +(-77.1798 + 64.7615i) q^{67} +(10.4300 + 12.4300i) q^{68} +(-23.2013 - 23.8324i) q^{69} +(-35.6215 + 12.9652i) q^{70} +(102.710 - 59.2994i) q^{71} +(19.9323 - 15.8336i) q^{72} +(-29.4831 + 51.0663i) q^{73} +(60.9863 + 10.7535i) q^{74} +(-1.50772 + 14.9240i) q^{75} +(25.1618 + 9.15814i) q^{76} +(-22.1409 + 3.90405i) q^{77} +(16.7685 - 11.4092i) q^{78} +(-109.039 - 91.4948i) q^{79} -8.94427i q^{80} +(-59.1671 - 55.3195i) q^{81} +60.7068 q^{82} +(52.8064 - 62.9322i) q^{83} +(-40.4600 - 59.4654i) q^{84} +(-3.15023 - 17.8658i) q^{85} +(-32.9144 + 90.4317i) q^{86} +(25.1585 + 2.54166i) q^{87} +(0.921157 - 5.22414i) q^{88} +(38.9210 + 22.4710i) q^{89} +(-28.1506 + 4.18827i) q^{90} +(-28.6528 - 49.6280i) q^{91} +(-7.58393 - 20.8367i) q^{92} +(-69.8982 + 68.0471i) q^{93} +(-44.6357 + 37.4538i) q^{94} +(-19.2432 - 22.9332i) q^{95} +(16.4498 - 4.17197i) q^{96} +(124.808 - 45.4263i) q^{97} +(-115.982 + 66.9621i) q^{98} +(-16.8735 - 0.452923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{6} + 12 q^{9} + 24 q^{12} + 36 q^{14} + 96 q^{18} + 96 q^{21} - 72 q^{22} + 216 q^{23} - 12 q^{27} - 252 q^{29} - 516 q^{33} + 144 q^{34} - 48 q^{36} - 144 q^{38} + 48 q^{39} + 108 q^{41}+ \cdots - 444 q^{99}+O(q^{100}) \) 144 * q - 12 * q^6 + 12 * q^9 + 24 * q^12 + 36 * q^14 + 96 * q^18 + 96 * q^21 - 72 * q^22 + 216 * q^23 - 12 * q^27 - 252 * q^29 - 516 * q^33 + 144 * q^34 - 48 * q^36 - 144 * q^38 + 48 * q^39 + 108 * q^41 - 180 * q^43 + 60 * q^45 + 432 * q^47 - 72 * q^49 - 204 * q^51 - 288 * q^54 + 72 * q^56 - 612 * q^57 - 252 * q^59 + 144 * q^61 - 720 * q^63 + 576 * q^64 + 360 * q^65 + 864 * q^66 + 252 * q^67 + 144 * q^68 + 708 * q^69 + 360 * q^70 + 1296 * q^71 - 252 * q^73 + 720 * q^74 + 144 * q^76 + 684 * q^77 + 192 * q^78 + 72 * q^79 - 492 * q^81 - 828 * q^83 - 216 * q^84 - 360 * q^85 - 648 * q^86 - 660 * q^87 - 288 * q^88 + 324 * q^89 - 480 * q^90 + 396 * q^91 - 216 * q^92 - 1548 * q^93 - 504 * q^94 - 720 * q^95 - 192 * q^96 - 180 * q^97 - 1296 * q^98 - 444 * q^99

Introduction

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