LMFDB - Embedded newform 270.3.q.a.103.18

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			103.18
Character	$\chi$	$=$	270.103
Dual form			270.3.q.a.97.18

$q$-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} +(2.87461 + 0.858266i) q^{3} +(-1.96962 - 0.347296i) q^{4} +(4.85982 + 1.17564i) q^{5} +(1.56347 - 3.94405i) q^{6} +(-0.652359 - 0.456787i) q^{7} +(-0.732051 + 2.73205i) q^{8} +(7.52676 + 4.93436i) q^{9} +(2.25528 - 6.70177i) q^{10} +(5.68724 + 2.06999i) q^{11} +(-5.36380 - 2.68880i) q^{12} +(-0.280399 - 3.20497i) q^{13} +(-0.723944 + 0.862763i) q^{14} +(12.9611 + 7.55052i) q^{15} +(3.75877 + 1.36808i) q^{16} +(0.588231 + 2.19531i) q^{17} +(7.87941 - 9.99574i) q^{18} +(3.13122 - 1.80781i) q^{19} +(-9.16369 - 4.00335i) q^{20} +(-1.48323 - 1.87298i) q^{21} +(3.61725 - 7.75723i) q^{22} +(0.925190 - 0.647825i) q^{23} +(-4.44919 + 7.22528i) q^{24} +(22.2357 + 11.4268i) q^{25} -4.54983 q^{26} +(17.4015 + 20.6443i) q^{27} +(1.12626 + 1.12626i) q^{28} +(-19.8287 - 23.6309i) q^{29} +(12.2350 - 17.3293i) q^{30} +(0.00905133 - 0.0513327i) q^{31} +(2.39069 - 5.12685i) q^{32} +(14.5720 + 10.8316i) q^{33} +(3.16532 - 0.558132i) q^{34} +(-2.63333 - 2.98684i) q^{35} +(-13.1111 - 12.3328i) q^{36} +(-4.78095 - 17.8427i) q^{37} +(-2.16096 - 4.63420i) q^{38} +(1.94468 - 9.45370i) q^{39} +(-6.76954 + 12.4167i) q^{40} +(-6.22209 - 5.22095i) q^{41} +(-2.82154 + 1.85877i) q^{42} +(19.8921 + 42.6587i) q^{43} +(-10.4828 - 6.05223i) q^{44} +(30.7777 + 32.8289i) q^{45} +(-0.798641 - 1.38329i) q^{46} +(-27.2749 - 19.0981i) q^{47} +(9.63082 + 7.15872i) q^{48} +(-16.5421 - 45.4490i) q^{49} +(18.8391 - 29.9180i) q^{50} +(-0.193225 + 6.81551i) q^{51} +(-0.560797 + 6.40994i) q^{52} +(-58.7394 - 58.7394i) q^{53} +(31.2292 - 21.9712i) q^{54} +(25.2054 + 16.7459i) q^{55} +(1.72553 - 1.44789i) q^{56} +(10.5526 - 2.50933i) q^{57} +(-35.7359 + 25.0226i) q^{58} +(-21.9317 - 60.2567i) q^{59} +(-22.9061 - 19.3730i) q^{60} +(9.89307 + 56.1064i) q^{61} +(-0.0712035 - 0.0190789i) q^{62} +(-2.65620 - 6.65710i) q^{63} +(-6.92820 - 4.00000i) q^{64} +(2.40520 - 15.9052i) q^{65} +(17.0560 - 19.1944i) q^{66} +(-58.3601 + 5.10585i) q^{67} +(-0.396166 - 4.52820i) q^{68} +(3.21557 - 1.06818i) q^{69} +(-4.53254 + 3.34178i) q^{70} +(-35.5365 + 61.5510i) q^{71} +(-18.9909 + 16.9513i) q^{72} +(-22.3272 + 83.3263i) q^{73} +(-25.7267 + 4.53631i) q^{74} +(54.1119 + 51.9317i) q^{75} +(-6.79516 + 2.47323i) q^{76} +(-2.76458 - 3.94823i) q^{77} +(-13.0790 - 3.90496i) q^{78} +(52.8171 + 62.9449i) q^{79} +(16.6586 + 11.0676i) q^{80} +(32.3042 + 74.2795i) q^{81} +(-8.12236 + 8.12236i) q^{82} +(-75.7516 - 6.62741i) q^{83} +(2.27092 + 4.20418i) q^{84} +(0.277810 + 11.3604i) q^{85} +(62.5507 - 22.7666i) q^{86} +(-36.7181 - 84.9478i) q^{87} +(-9.81865 + 14.0225i) q^{88} +(28.6318 - 16.5306i) q^{89} +(50.0439 - 39.3142i) q^{90} +(-1.28107 + 2.21888i) q^{91} +(-2.04726 + 0.954651i) q^{92} +(0.0700761 - 0.139793i) q^{93} +(-30.2678 + 36.0717i) q^{94} +(17.3425 - 5.10446i) q^{95} +(11.2725 - 12.6858i) q^{96} +(37.7569 - 17.6063i) q^{97} +(-66.0689 + 17.7031i) q^{98} +(32.5924 + 43.6432i) 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
$3$	2.87461	+	0.858266i	0.958203	+	0.286089i
$3$	2.87461	+	0.858266i	0.958203	+	0.286089i
$4$	−1.96962	−	0.347296i	−0.492404	−	0.0868241i
$5$	4.85982	+	1.17564i	0.971964	+	0.235128i
$5$	4.85982	+	1.17564i	0.971964	+	0.235128i
$6$	1.56347	−	3.94405i	0.260578	−	0.657342i
$7$	−0.652359	−	0.456787i	−0.0931942	−	0.0652553i	0.526051	−	0.850453i	$-0.323672\pi$
$7$	−0.652359	−	0.456787i	−0.0931942	−	0.0652553i	−0.619245	+	0.785198i	$0.712561\pi$
$8$	−0.732051	+	2.73205i	−0.0915064	+	0.341506i
$9$	7.52676	+	4.93436i	0.836306	+	0.548262i
$10$	2.25528	−	6.70177i	0.225528	−	0.670177i
$11$	5.68724	+	2.06999i	0.517022	+	0.188181i	0.587334	−	0.809344i	$-0.300177\pi$
$11$	5.68724	+	2.06999i	0.517022	+	0.188181i	−0.0703125	+	0.997525i	$0.522400\pi$
$12$	−5.36380	−	2.68880i	−0.446984	−	0.224066i
$13$	−0.280399	−	3.20497i	−0.0215691	−	0.246536i	−0.999323	−	0.0367822i	$-0.988289\pi$
$13$	−0.280399	−	3.20497i	−0.0215691	−	0.246536i	0.977754	−	0.209754i	$-0.0672663\pi$
$14$	−0.723944	+	0.862763i	−0.0517103	+	0.0616259i
$15$	12.9611	+	7.55052i	0.864072	+	0.503368i
$16$	3.75877	+	1.36808i	0.234923	+	0.0855050i
$17$	0.588231	+	2.19531i	0.0346018	+	0.129136i	0.981066	−	0.193672i	$-0.0620398\pi$
$17$	0.588231	+	2.19531i	0.0346018	+	0.129136i	−0.946464	+	0.322808i	$0.895373\pi$
$18$	7.87941	−	9.99574i	0.437745	−	0.555319i
$19$	3.13122	−	1.80781i	0.164801	−	0.0951481i	−0.415331	−	0.909670i	$-0.636334\pi$
$19$	3.13122	−	1.80781i	0.164801	−	0.0951481i	0.580132	+	0.814522i	$0.303001\pi$
$20$	−9.16369	−	4.00335i	−0.458184	−	0.200168i
$21$	−1.48323	−	1.87298i	−0.0706302	−	0.0891896i
$22$	3.61725	−	7.75723i	0.164421	−	0.352601i
$23$	0.925190	−	0.647825i	0.0402257	−	0.0281663i	−0.553291	−	0.832988i	$-0.686628\pi$
$23$	0.925190	−	0.647825i	0.0402257	−	0.0281663i	0.593516	+	0.804822i	$0.297739\pi$
$24$	−4.44919	+	7.22528i	−0.185383	+	0.301054i
$25$	22.2357	+	11.4268i	0.889430	+	0.457071i
$26$	−4.54983			−0.174993
$27$	17.4015	+	20.6443i	0.644500	+	0.764605i
$28$	1.12626	+	1.12626i	0.0402235	+	0.0402235i
$29$	−19.8287	−	23.6309i	−0.683747	−	0.814858i	0.306838	−	0.951762i	$-0.400729\pi$
$29$	−19.8287	−	23.6309i	−0.683747	−	0.814858i	−0.990584	+	0.136904i	$0.956285\pi$
$30$	12.2350	−	17.3293i	0.407832	−	0.577644i
$31$	0.00905133	−	0.0513327i	0.000291978	−	0.00165589i	−0.984661	−	0.174476i	$-0.944177\pi$
$31$	0.00905133	−	0.0513327i	0.000291978	−	0.00165589i	0.984953	+	0.172820i	$0.0552879\pi$
$32$	2.39069	−	5.12685i	0.0747091	−	0.160214i
$33$	14.5720	+	10.8316i	0.441576	+	0.328229i
$34$	3.16532	−	0.558132i	0.0930978	−	0.0164156i
$35$	−2.63333	−	2.98684i	−0.0752381	−	0.0853384i
$36$	−13.1111	−	12.3328i	−0.364198	−	0.342578i
$37$	−4.78095	−	17.8427i	−0.129215	−	0.482236i	0.870740	−	0.491744i	$-0.163640\pi$
$37$	−4.78095	−	17.8427i	−0.129215	−	0.482236i	−0.999955	+	0.00950747i	$0.996974\pi$
$38$	−2.16096	−	4.63420i	−0.0568674	−	0.121953i
$39$	1.94468	−	9.45370i	0.0498637	−	0.242403i
$40$	−6.76954	+	12.4167i	−0.169239	+	0.310416i
$41$	−6.22209	−	5.22095i	−0.151758	−	0.127340i	0.563747	−	0.825947i	$-0.309359\pi$
$41$	−6.22209	−	5.22095i	−0.151758	−	0.127340i	−0.715506	+	0.698607i	$0.753804\pi$
$42$	−2.82154	+	1.85877i	−0.0671794	+	0.0442564i
$43$	19.8921	+	42.6587i	0.462606	+	0.992062i	0.989819	+	0.142329i	$0.0454591\pi$
$43$	19.8921	+	42.6587i	0.462606	+	0.992062i	−0.527213	+	0.849733i	$0.676763\pi$
$44$	−10.4828	−	6.05223i	−0.238245	−	0.137551i
$45$	30.7777	+	32.8289i	0.683949	+	0.729530i
$46$	−0.798641	−	1.38329i	−0.0173618	−	0.0300715i
$47$	−27.2749	−	19.0981i	−0.580316	−	0.406342i	0.246229	−	0.969212i	$-0.420808\pi$
$47$	−27.2749	−	19.0981i	−0.580316	−	0.406342i	−0.826546	+	0.562870i	$0.809697\pi$
$48$	9.63082	+	7.15872i	0.200642	+	0.149140i
$49$	−16.5421	−	45.4490i	−0.337593	−	0.927530i
$50$	18.8391	−	29.9180i	0.376783	−	0.598360i
$51$	−0.193225	+	6.81551i	−0.00378872	+	0.133637i
$52$	−0.560797	+	6.40994i	−0.0107846	+	0.123268i
$53$	−58.7394	−	58.7394i	−1.10829	−	1.10829i	−0.993375	−	0.114915i	$-0.963340\pi$
$53$	−58.7394	−	58.7394i	−1.10829	−	1.10829i	−0.114915	−	0.993375i	$-0.536660\pi$
$54$	31.2292	−	21.9712i	0.578319	−	0.406875i
$55$	25.2054	+	16.7459i	0.458280	+	0.304471i
$56$	1.72553	−	1.44789i	0.0308130	−	0.0258551i
$57$	10.5526	−	2.50933i	0.185134	−	0.0440234i
$58$	−35.7359	+	25.0226i	−0.616137	+	0.431424i
$59$	−21.9317	−	60.2567i	−0.371723	−	1.02130i	−0.974695	−	0.223538i	$-0.928239\pi$
$59$	−21.9317	−	60.2567i	−0.371723	−	1.02130i	0.602972	−	0.797762i	$-0.293983\pi$
$60$	−22.9061	−	19.3730i	−0.381768	−	0.322883i
$61$	9.89307	+	56.1064i	0.162182	+	0.919777i	0.951923	+	0.306337i	$0.0991036\pi$
$61$	9.89307	+	56.1064i	0.162182	+	0.919777i	−0.789741	+	0.613440i	$0.789785\pi$
$62$	−0.0712035	−	0.0190789i	−0.00114844	−	0.000307724i
$63$	−2.65620	−	6.65710i	−0.0421619	−	0.105668i
$64$	−6.92820	−	4.00000i	−0.108253	−	0.0625000i
$65$	2.40520	−	15.9052i	0.0370031	−	0.244696i
$66$	17.0560	−	19.1944i	0.258424	−	0.290825i
$67$	−58.3601	+	5.10585i	−0.871046	+	0.0762067i	−0.513908	−	0.857845i	$-0.671803\pi$
$67$	−58.3601	+	5.10585i	−0.871046	+	0.0762067i	−0.357138	+	0.934052i	$0.616247\pi$
$68$	−0.396166	−	4.52820i	−0.00582598	−	0.0665912i
$69$	3.21557	−	1.06818i	0.0466024	−	0.0154809i
$70$	−4.53254	+	3.34178i	−0.0647505	+	0.0477397i
$71$	−35.5365	+	61.5510i	−0.500514	+	0.866915i	0.499486	+	0.866322i	$0.333522\pi$
$71$	−35.5365	+	61.5510i	−0.500514	+	0.866915i	−1.00000		0.000593321i	$0.999811\pi$
$72$	−18.9909	+	16.9513i	−0.263762	+	0.235434i
$73$	−22.3272	+	83.3263i	−0.305852	+	1.14146i	0.626357	+	0.779537i	$0.284545\pi$
$73$	−22.3272	+	83.3263i	−0.305852	+	1.14146i	−0.932209	+	0.361920i	$0.882121\pi$
$74$	−25.7267	+	4.53631i	−0.347658	+	0.0613015i
$75$	54.1119	+	51.9317i	0.721492	+	0.692423i
$76$	−6.79516	+	2.47323i	−0.0894099	+	0.0325426i
$77$	−2.76458	−	3.94823i	−0.0359037	−	0.0512757i
$78$	−13.0790	−	3.90496i	−0.167679	−	0.0500636i
$79$	52.8171	+	62.9449i	0.668571	+	0.796771i	0.988589	−	0.150640i	$-0.0481334\pi$
$79$	52.8171	+	62.9449i	0.668571	+	0.796771i	−0.320018	+	0.947411i	$0.603689\pi$
$80$	16.6586	+	11.0676i	0.208232	+	0.138345i
$81$	32.3042	+	74.2795i	0.398817	+	0.917031i
$82$	−8.12236	+	8.12236i	−0.0990532	+	0.0990532i
$83$	−75.7516	−	6.62741i	−0.912670	−	0.0798483i	−0.378861	−	0.925454i	$-0.623684\pi$
$83$	−75.7516	−	6.62741i	−0.912670	−	0.0798483i	−0.533809	+	0.845605i	$0.679240\pi$
$84$	2.27092	+	4.20418i	0.0270348	+	0.0500497i
$85$	0.277810	+	11.3604i	0.00326836	+	0.133651i
$86$	62.5507	−	22.7666i	0.727334	−	0.264728i
$87$	−36.7181	−	84.9478i	−0.422047	−	0.976411i
$88$	−9.81865	+	14.0225i	−0.111576	+	0.159347i
$89$	28.6318	−	16.5306i	0.321706	−	0.185737i	−0.330447	−	0.943825i	$-0.607199\pi$
$89$	28.6318	−	16.5306i	0.321706	−	0.185737i	0.652153	+	0.758088i	$0.273866\pi$
$90$	50.0439	−	39.3142i	0.556043	−	0.436825i
$91$	−1.28107	+	2.21888i	−0.0140777	+	0.0243833i
$92$	−2.04726	+	0.954651i	−0.0222528	+	0.0103766i
$93$	0.0700761	−	0.139793i	0.000753507	−	0.00150315i
$94$	−30.2678	+	36.0717i	−0.321998	+	0.383742i
$95$	17.3425	−	5.10446i	0.182553	−	0.0537312i
$96$	11.2725	−	12.6858i	0.117422	−	0.132144i
$97$	37.7569	−	17.6063i	0.389247	−	0.181509i	−0.218135	−	0.975919i	$-0.569997\pi$
$97$	37.7569	−	17.6063i	0.389247	−	0.181509i	0.607382	+	0.794410i	$0.292220\pi$
$98$	−66.0689	+	17.7031i	−0.674172	+	0.180644i
$99$	32.5924	+	43.6432i	0.329216	+	0.440840i
$100$	−39.8274	−	30.2288i	−0.398274	−	0.302288i
$101$	14.0944	+	79.9331i	0.139548	+	0.791417i	0.971584	+	0.236695i	$0.0760642\pi$
$101$	14.0944	+	79.9331i	0.139548	+	0.791417i	−0.832036	+	0.554722i	$0.812825\pi$
$102$	9.57810	+	1.11228i	0.0939029	+	0.0109047i
$103$	−5.58477	−	2.60422i	−0.0542211	−	0.0252837i	0.395319	−	0.918544i	$-0.370634\pi$
$103$	−5.58477	−	2.60422i	−0.0542211	−	0.0252837i	−0.449540	+	0.893260i	$0.648412\pi$
$104$	8.96141	+	1.58014i	0.0861674	+	0.0151936i
$105$	−5.00630	−	10.8461i	−0.0476791	−	0.103296i
$106$	−89.9940	+	75.5139i	−0.849000	+	0.712395i
$107$	−115.938	+	115.938i	−1.08353	+	1.08353i	−0.0873556	+	0.996177i	$0.527842\pi$
$107$	−115.938	+	115.938i	−1.08353	+	1.08353i	−0.996177	+	0.0873556i	$0.972158\pi$
$108$	−27.1046	−	46.7049i	−0.250968	−	0.432452i
$109$			86.5956i			0.794455i	0.917720	+	0.397227i	$0.130028\pi$
$109$			86.5956i			0.794455i	−0.917720	+	0.397227i	$0.869972\pi$
$110$	26.6989	−	33.4462i	0.242717	−	0.304056i
$111$	1.57047	−	55.3942i	0.0141483	−	0.499047i
$112$	−1.82715	−	2.60944i	−0.0163138	−	0.0232986i
$113$	−161.937	−	75.5125i	−1.43307	−	0.668252i	−0.457757	−	0.889077i	$-0.651347\pi$
$113$	−161.937	−	75.5125i	−1.43307	−	0.668252i	−0.975313	+	0.220825i	$0.929125\pi$
$114$	−2.23454	−	15.1762i	−0.0196013	−	0.133124i
$115$	5.25787	−	2.06063i	0.0457206	−	0.0179185i
$116$	30.8479	+	53.4302i	0.265930	+	0.460605i
$117$	13.7040	−	25.5066i	0.117128	−	0.218005i
$118$	−87.5948	+	23.4710i	−0.742329	+	0.198906i
$119$	0.619050	−	1.70083i	0.00520210	−	0.0142927i
$120$	−30.1166	+	29.8830i	−0.250972	+	0.249025i
$121$	−64.6315	−	54.2323i	−0.534145	−	0.448201i
$122$	80.2639	−	7.02218i	0.657901	−	0.0575589i
$123$	−13.4051	−	20.3484i	−0.108985	−	0.165434i
$124$	−0.0356553	+	0.0979621i	−0.000287543	+	0.000790017i
$125$	94.6280	+	81.6734i	0.757024	+	0.653387i
$126$	−9.70613	+	2.92161i	−0.0770328	+	0.0231873i
$127$	−217.376	−	58.2456i	−1.71162	−	0.458627i	−0.735798	−	0.677201i	$-0.763193\pi$
$127$	−217.376	−	58.2456i	−1.71162	−	0.458627i	−0.975820	+	0.218574i	$0.929860\pi$
$128$	−6.48928	+	9.26765i	−0.0506975	+	0.0724035i
$129$	20.5694	+	139.700i	0.159453	+	1.08294i
$130$	−22.1114	−	5.34895i	−0.170087	−	0.0411458i
$131$	−6.98428	+	39.6098i	−0.0533151	+	0.302365i	−0.999792	−	0.0204074i	$-0.993504\pi$
$131$	−6.98428	+	39.6098i	−0.0533151	+	0.302365i	0.946477	+	0.322772i	$0.104615\pi$
$132$	−24.9395	−	26.3948i	−0.188935	−	0.199961i
$133$	−2.86847	−	0.250959i	−0.0215674	−	0.00188691i
$134$			82.8489i			0.618275i
$135$	60.2979	+	120.786i	0.446651	+	0.894708i
$136$	−6.42831			−0.0472670
$137$	13.5498	−	154.875i	0.0989035	−	1.13047i	−0.770860	−	0.637004i	$-0.780173\pi$
$137$	13.5498	−	154.875i	0.0989035	−	1.13047i	0.869764	−	0.493468i	$-0.164271\pi$
$138$	−1.10855	−	4.66186i	−0.00803299	−	0.0337816i
$139$	133.547	+	23.5479i	0.960766	+	0.169409i	0.631971	−	0.774992i	$-0.282246\pi$
$139$	133.547	+	23.5479i	0.960766	+	0.169409i	0.328795	+	0.944401i	$0.393357\pi$
$140$	4.14934	+	6.79748i	0.0296381	+	0.0485534i
$141$	−62.0133	−	78.3086i	−0.439811	−	0.555380i
$142$	82.3349	+	57.6515i	0.579823	+	0.405997i
$143$	5.03955	−	18.8079i	0.0352416	−	0.131524i
$144$	21.5408	+	28.8443i	0.149589	+	0.200308i
$145$	−68.5824	−	138.153i	−0.472982	−	0.952780i
$146$	114.641	+	41.7258i	0.785211	+	0.285793i
$147$	−8.54467	−	144.846i	−0.0581270	−	0.985344i
$148$	3.21991	+	36.8037i	0.0217562	+	0.248674i
$149$	59.2589	−	70.6220i	0.397711	−	0.473973i	−0.529610	−	0.848241i	$-0.677662\pi$
$149$	59.2589	−	70.6220i	0.397711	−	0.473973i	0.927320	+	0.374268i	$0.122106\pi$
$150$	79.8328	−	69.8336i	0.532218	−	0.465557i
$151$	0.519781	+	0.189185i	0.00344226	+	0.00125288i	0.343741	−	0.939065i	$-0.388306\pi$
$151$	0.519781	+	0.189185i	0.00344226	+	0.00125288i	−0.340298	+	0.940317i	$0.610528\pi$
$152$	2.64682	+	9.87808i	0.0174133	+	0.0649873i
$153$	−6.40497	+	19.4261i	−0.0418625	+	0.126968i
$154$	−5.90315	+	3.40818i	−0.0383321	+	0.0221311i
$155$	0.104337	−	0.238827i	0.000673139	−	0.00154082i
$156$	−7.11351	+	17.9448i	−0.0455994	+	0.115031i
$157$	112.579	−	241.426i	0.717061	−	1.53774i	−0.121293	−	0.992617i	$-0.538704\pi$
$157$	112.579	−	241.426i	0.717061	−	1.53774i	0.838354	−	0.545126i	$-0.183518\pi$
$158$	95.1889	−	66.6520i	0.602462	−	0.421848i
$159$	−118.439	−	219.267i	−0.744898	−	1.37904i
$160$	17.6457	−	22.1050i	0.110285	−	0.138156i
$161$	−0.899475			−0.00558680
$162$	108.629	−	36.3557i	0.670549	−	0.224418i
$163$	228.749	+	228.749i	1.40337	+	1.40337i	0.789093	+	0.614274i	$0.210551\pi$
$163$	228.749	+	228.749i	1.40337	+	1.40337i	0.614274	+	0.789093i	$0.289449\pi$
$164$	10.4419	+	12.4442i	0.0636702	+	0.0758792i
$165$	58.0833	+	69.7709i	0.352020	+	0.422854i
$166$	−18.6738	+	105.904i	−0.112493	+	0.637978i
$167$	66.7035	−	143.046i	0.399422	−	0.856564i	−0.599018	−	0.800735i	$-0.704442\pi$
$167$	66.7035	−	143.046i	0.399422	−	0.856564i	0.998440	−	0.0558283i	$-0.0177799\pi$
$168$	6.20289	−	2.68115i	0.0369219	−	0.0159592i
$169$	156.239	−	27.5492i	0.924493	−	0.163013i
$170$	16.0391	+	1.00885i	0.0943475	+	0.00593443i
$171$	32.4884	+	1.84362i	0.189990	+	0.0107814i
$172$	−24.3645	−	90.9296i	−0.141654	−	0.528660i
$173$	−76.0505	−	163.091i	−0.439598	−	0.942722i	−0.993887	−	0.110398i	$-0.964788\pi$
$173$	−76.0505	−	163.091i	−0.439598	−	0.942722i	0.554289	−	0.832324i	$-0.312990\pi$
$174$	−124.203	+	41.2592i	−0.713810	+	0.237122i
$175$	−9.28609	−	17.6114i	−0.0530634	−	0.100636i
$176$	18.5451	+	15.5612i	0.105370	+	0.0884159i
$177$	−11.3286	−	192.038i	−0.0640035	−	1.08496i
$178$	−19.7598	−	42.3749i	−0.111010	−	0.238061i
$179$	305.867	+	176.593i	1.70876	+	0.986551i	0.936106	+	0.351719i	$0.114403\pi$
$179$	305.867	+	176.593i	1.70876	+	0.986551i	0.772650	+	0.634832i	$0.218931\pi$
$180$	−49.2189	−	75.3492i	−0.273438	−	0.418607i
$181$	−131.495	−	227.756i	−0.726490	−	1.25832i	−0.958358	−	0.285571i	$-0.907817\pi$
$181$	−131.495	−	227.756i	−0.726490	−	1.25832i	0.231867	−	0.972747i	$-0.425516\pi$
$182$	2.96812	+	2.07830i	0.0163084	+	0.0114192i
$183$	−19.7155	+	169.775i	−0.107735	+	0.927732i
$184$	1.09261	+	3.00191i	0.00593807	+	0.0163147i
$185$	−2.25795	−	92.3332i	−0.0122051	−	0.499098i
$186$	−0.188307	−	0.115956i	−0.00101240	−	0.000623419i
$187$	−1.19885	+	13.7029i	−0.00641094	+	0.0732774i
$188$	47.0883	+	47.0883i	0.250470	+	0.250470i
$189$	−1.92197	−	21.4163i	−0.0101692	−	0.113314i
$190$	−5.05375	−	25.0619i	−0.0265987	−	0.131905i
$191$	194.673	−	163.350i	1.01923	−	0.855235i	0.0296990	−	0.999559i	$-0.490545\pi$
$191$	194.673	−	163.350i	1.01923	−	0.855235i	0.989531	+	0.144324i	$0.0461007\pi$
$192$	−16.4828	−	17.4447i	−0.0858480	−	0.0908577i
$193$	148.925	−	104.279i	0.771634	−	0.540304i	−0.120155	−	0.992755i	$-0.538339\pi$
$193$	148.925	−	104.279i	0.771634	−	0.540304i	0.891789	+	0.452451i	$0.149450\pi$
$194$	−20.1506	−	55.3633i	−0.103869	−	0.285378i
$195$	20.5649	−	43.6571i	0.105461	−	0.223882i
$196$	16.7973	+	95.2620i	0.0857003	+	0.486030i
$197$	−288.693	−	77.3551i	−1.46545	−	0.392665i	−0.564080	−	0.825720i	$-0.690769\pi$
$197$	−288.693	−	77.3551i	−1.46545	−	0.392665i	−0.901368	+	0.433055i	$0.857436\pi$
$198$	65.5031	−	40.5379i	0.330824	−	0.204737i
$199$	70.9417	+	40.9582i	0.356491	+	0.205820i	0.667540	−	0.744574i	$-0.267347\pi$
$199$	70.9417	+	40.9582i	0.356491	+	0.205820i	−0.311049	+	0.950394i	$0.600680\pi$
$200$	−47.4963	+	52.3842i	−0.237481	+	0.261921i
$201$	−172.145	−	35.4112i	−0.856441	−	0.176175i
$202$	114.350	−	10.0043i	0.566087	−	0.0495262i
$203$	2.14114	+	24.4733i	0.0105475	+	0.120558i
$204$	2.74758	−	13.3568i	0.0134685	−	0.0654747i
$205$	−24.1003	−	32.6878i	−0.117562	−	0.159453i
$206$	−4.35727	+	7.54701i	−0.0211518	+	0.0366360i
$207$	10.1603	−	0.310801i	0.0490835	−	0.00150145i
$208$	3.33071	−	12.4304i	0.0160130	−	0.0597614i
$209$	21.5502	−	3.79988i	0.103111	−	0.0181812i
$210$	−15.8974	+	5.71618i	−0.0757019	+	0.0272199i
$211$	109.935	−	40.0131i	0.521020	−	0.189636i	−0.0681045	−	0.997678i	$-0.521695\pi$
$211$	109.935	−	40.0131i	0.521020	−	0.189636i	0.589124	+	0.808043i	$0.299473\pi$
$212$	95.2940	+	136.094i	0.449500	+	0.641953i
$213$	−154.981	+	146.435i	−0.727609	+	0.687490i
$214$	149.047	+	177.627i	0.696481	+	0.830034i
$215$	46.5207	+	230.699i	0.216375	+	1.07302i
$216$	−69.1401	+	32.4291i	−0.320093	+	0.150135i
$217$	−0.0293528	+	0.0293528i	−0.000135266	+	0.000135266i
$218$	121.999	+	10.6735i	0.559627	+	0.0489610i
$219$	−135.698	+	220.368i	−0.619627	+	1.00625i
$220$	−43.8292	−	41.7367i	−0.199224	−	0.189712i
$221$	6.87096	−	2.50083i	0.0310903	−	0.0113160i
$222$	−77.8476	−	9.04024i	−0.350665	−	0.0407218i
$223$	17.6738	−	25.2408i	0.0792548	−	0.113188i	−0.777567	−	0.628800i	$-0.783547\pi$
$223$	17.6738	−	25.2408i	0.0792548	−	0.113188i	0.856822	+	0.515612i	$0.172435\pi$
$224$	−3.90147	+	2.25251i	−0.0174173	+	0.0100559i
$225$	110.979	+	195.726i	0.493241	+	0.869893i
$226$	−126.344	+	218.835i	−0.559045	+	0.968295i
$227$	−366.696	+	170.993i	−1.61540	+	0.753275i	−0.999406	−	0.0344735i	$-0.989025\pi$
$227$	−366.696	+	170.993i	−1.61540	+	0.753275i	−0.615997	+	0.787748i	$0.711247\pi$
$228$	−21.6561	+	1.27753i	−0.0949830	+	0.00560320i
$229$	193.219	−	230.269i	0.843750	−	1.00554i	−0.156092	−	0.987743i	$-0.549890\pi$
$229$	193.219	−	230.269i	0.843750	−	1.00554i	0.999842	−	0.0177994i	$-0.00566603\pi$
$230$	−2.25501	−	7.66144i	−0.00980438	−	0.0333106i
$231$	−4.55846	−	13.7224i	−0.0197336	−	0.0594042i
$232$	79.0763	−	36.8739i	0.340846	−	0.158939i
$233$	179.838	−	48.1874i	0.771836	−	0.206813i	0.148654	−	0.988889i	$-0.452506\pi$
$233$	179.838	−	48.1874i	0.771836	−	0.206813i	0.623182	+	0.782077i	$0.285839\pi$
$234$	−34.2455	−	22.4505i	−0.146348	−	0.0959423i
$235$	−110.099	−	124.879i	−0.468505	−	0.531398i
$236$	22.2700	+	126.299i	0.0943643	+	0.535167i
$237$	97.8049	+	226.273i	0.412679	+	0.954739i
$238$	−2.31988	−	1.08178i	−0.00974738	−	0.00454528i
$239$	−1.82954	−	0.322597i	−0.00765498	−	0.00134978i	0.169819	−	0.985475i	$-0.445682\pi$
$239$	−1.82954	−	0.322597i	−0.00765498	−	0.00134978i	−0.177474	+	0.984125i	$0.556793\pi$
$240$	38.3880	+	46.1125i	0.159950	+	0.192135i
$241$	−250.023	+	209.794i	−1.03744	+	0.870514i	−0.991717	−	0.128440i	$-0.959003\pi$
$241$	−250.023	+	209.794i	−1.03744	+	0.870514i	−0.0457213	+	0.998954i	$0.514559\pi$
$242$	−84.3705	+	84.3705i	−0.348638	+	0.348638i
$243$	29.1103	+	241.250i	0.119795	+	0.992799i
$244$		−	113.944i		−	0.466983i
$245$	−26.9600	−	240.321i	−0.110041	−	0.980904i
$246$	−30.3198	+	16.3775i	−0.123251	+	0.0665751i
$247$	−6.67198	−	9.52858i	−0.0270121	−	0.0385772i
$248$	0.133617	+	0.0623068i	0.000538780	+	0.000251237i
$249$	−212.068	−	84.0662i	−0.851679	−	0.337615i
$250$	126.728	−	123.248i	0.506910	−	0.492993i
$251$	70.4335	+	121.994i	0.280612	+	0.486034i	0.971536	−	0.236894i	$-0.0761294\pi$
$251$	70.4335	+	121.994i	0.280612	+	0.486034i	−0.690924	+	0.722928i	$0.742796\pi$
$252$	2.91970	+	14.0344i	0.0115861	+	0.0556921i
$253$	6.60277	−	1.76921i	0.0260979	−	0.00699291i
$254$	−108.851	+	299.067i	−0.428548	+	1.17743i
$255$	−8.95161	+	32.8950i	−0.0351044	+	0.129000i
$256$	12.2567	+	10.2846i	0.0478778	+	0.0401742i
$257$	−35.1453	+	3.07481i	−0.136752	+	0.0119643i	−0.155326	−	0.987863i	$-0.549643\pi$
$257$	−35.1453	+	3.07481i	−0.136752	+	0.0119643i	0.0185742	+	0.999827i	$0.494087\pi$
$258$	199.349	−	11.7599i	0.772669	−	0.0455810i
$259$	−5.03144	+	13.8238i	−0.0194264	+	0.0533736i
$260$	−10.2612	+	30.4919i	−0.0394660	+	0.117277i
$261$	−32.6422	−	275.706i	−0.125066	−	1.05634i
$262$	54.9427	+	14.7218i	0.209705	+	0.0561903i
$263$	−134.056	+	191.452i	−0.509720	+	0.727955i	−0.988706	−	0.149867i	$-0.952115\pi$
$263$	−134.056	+	191.452i	−0.509720	+	0.727955i	0.478986	+	0.877822i	$0.341004\pi$
$264$	−40.2598	+	31.8822i	−0.152499	+	0.120766i
$265$	−216.407	−	354.519i	−0.816629	−	1.33781i
$266$	−0.707117	+	4.01026i	−0.00265833	+	0.0150762i
$267$	96.4929	−	22.9453i	0.361397	−	0.0859373i
$268$	116.720	+	10.2117i	0.435523	+	0.0381033i
$269$			28.0339i			0.104215i	0.998641	+	0.0521077i	$0.0165939\pi$
$269$			28.0339i			0.104215i	−0.998641	+	0.0521077i	$0.983406\pi$
$270$	177.599	−	70.0620i	0.657773	−	0.259489i
$271$	−107.555			−0.396883			−0.198441	−	0.980113i	$-0.563588\pi$
$271$	−107.555			−0.396883			−0.198441	+	0.980113i	$0.563588\pi$
$272$	−0.792333	+	9.05641i	−0.00291299	+	0.0332956i
$273$	−5.58696	+	5.27890i	−0.0204650	+	0.0193366i
$274$	−216.522	−	38.1787i	−0.790228	−	0.139338i
$275$	102.807	+	111.015i	0.373843	+	0.403689i
$276$	−6.70441	+	0.987159i	−0.0242913	+	0.00357666i
$277$	177.142	+	124.036i	0.639500	+	0.447783i	0.847824	−	0.530277i	$-0.177912\pi$
$277$	177.142	+	124.036i	0.639500	+	0.447783i	−0.208324	+	0.978060i	$0.566801\pi$
$278$	49.6355	−	185.242i	0.178545	−	0.666339i
$279$	0.321421	−	0.341706i	0.00115205	−	0.00122475i
$280$	10.0879	−	5.00788i	0.0360284	−	0.0178853i
$281$	−112.640	−	40.9977i	−0.400855	−	0.145899i	0.133722	−	0.991019i	$-0.457307\pi$
$281$	−112.640	−	40.9977i	−0.400855	−	0.145899i	−0.534577	+	0.845119i	$0.679529\pi$
$282$	−117.967	+	77.7143i	−0.418323	+	0.275583i
$283$	−3.43040	−	39.2096i	−0.0121216	−	0.138550i	0.987722	−	0.156220i	$-0.0499308\pi$
$283$	−3.43040	−	39.2096i	−0.0121216	−	0.138550i	−0.999844	+	0.0176698i	$0.994375\pi$
$284$	91.3696	−	108.890i	0.321724	−	0.383416i
$285$	54.2340	+	0.211168i	0.190295	+	0.000740940i
$286$	−25.8760	−	9.41808i	−0.0904754	−	0.0329303i
$287$	1.67418	+	6.24811i	0.00583337	+	0.0217704i
$288$	43.2919	−	26.7920i	0.150319	−	0.0930279i
$289$	245.808	−	141.917i	0.850547	−	0.491063i
$290$	−203.088	+	79.5927i	−0.700303	+	0.274458i
$291$	123.647	−	18.2059i	0.424905	−	0.0625631i
$292$	72.9150	−	156.367i	0.249709	−	0.535502i
$293$	30.8447	−	21.5977i	0.105272	−	0.0737123i	−0.519755	−	0.854315i	$-0.673977\pi$
$293$	30.8447	−	21.5977i	0.105272	−	0.0737123i	0.625027	+	0.780603i	$0.285088\pi$
$294$	−205.116	−	5.81519i	−0.697674	−	0.0197796i
$295$	−35.7438	−	318.621i	−0.121166	−	1.08007i
$296$	52.2472			0.176511
$297$	56.2330	+	153.430i	0.189337	+	0.516599i
$298$	−92.1905	−	92.1905i	−0.309364	−	0.309364i
$299$	−2.33568	−	2.78356i	−0.00781165	−	0.00930956i
$300$	−88.5439	−	121.078i	−0.295146	−	0.403595i
$301$	6.50915	−	36.9152i	0.0216251	−	0.122642i
$302$	0.330596	−	0.708966i	0.00109469	−	0.00234757i
$303$	−28.0881	+	241.873i	−0.0927000	+	0.798261i
$304$	14.2428	−	2.51139i	0.0468513	−	0.00826115i
$305$	−17.8823	+	284.298i	−0.0586304	+	0.932124i
$306$	26.5787	+	11.4179i	0.0868583	+	0.0373135i
$307$	71.8588	+	268.181i	0.234068	+	0.873553i	0.978567	+	0.205929i	$0.0660217\pi$
$307$	71.8588	+	268.181i	0.234068	+	0.873553i	−0.744499	+	0.667623i	$0.767312\pi$
$308$	4.07396	+	8.73663i	0.0132271	+	0.0283657i
$309$	−13.8189	−	12.2793i	−0.0447214	−	0.0397390i
$310$	−0.323606	−	0.176430i	−0.00104389	−	0.000569128i
$311$	313.411	+	262.983i	1.00775	+	0.845604i	0.988039	−	0.154202i	$-0.0492807\pi$
$311$	313.411	+	262.983i	1.00775	+	0.845604i	0.0197118	+	0.999806i	$0.493725\pi$
$312$	24.4044	+	12.2336i	0.0782192	+	0.0392101i
$313$	−124.718	−	267.459i	−0.398461	−	0.854502i	−0.998512	−	0.0545402i	$-0.982631\pi$
$313$	−124.718	−	267.459i	−0.398461	−	0.854502i	0.600051	−	0.799962i	$-0.295147\pi$
$314$	−326.252	−	188.362i	−1.03902	−	0.599878i
$315$	−5.08232	−	35.4751i	−0.0161343	−	0.112619i
$316$	−82.1688	−	142.321i	−0.260028	−	0.450381i
$317$	−28.4123	−	19.8945i	−0.0896286	−	0.0627586i	0.527903	−	0.849305i	$-0.322978\pi$
$317$	−28.4123	−	19.8945i	−0.0896286	−	0.0627586i	−0.617532	+	0.786546i	$0.711867\pi$
$318$	−323.509	+	139.834i	−1.01732	+	0.439730i
$319$	−63.8547	−	175.439i	−0.200172	−	0.549967i
$320$	−28.9673	−	27.5844i	−0.0905228	−	0.0862011i
$321$	−432.782	+	233.771i	−1.34823	+	0.728258i
$322$	−0.110866	+	1.26721i	−0.000344306	+	0.00393543i
$323$	5.81059	+	5.81059i	0.0179894	+	0.0179894i
$324$	−37.8298	−	157.521i	−0.116759	−	0.486176i
$325$	30.3877	−	74.4690i	0.0935005	−	0.229135i
$326$	350.463	−	294.074i	1.07504	−	0.902067i
$327$	−74.3221	+	248.928i	−0.227285	+	0.761249i
$328$	18.8188	−	13.1771i	0.0573744	−	0.0401740i
$329$	9.06927	+	24.9176i	0.0275662	+	0.0757374i
$330$	105.455	−	73.2299i	0.319559	−	0.221909i
$331$	17.6748	+	100.239i	0.0533983	+	0.302837i	0.999797	−	0.0201649i	$-0.00641912\pi$
$331$	17.6748	+	100.239i	0.0533983	+	0.302837i	−0.946398	+	0.323002i	$0.895308\pi$
$332$	146.900	+	39.3617i	0.442469	+	0.118559i
$333$	52.0575	−	157.889i	0.156329	−	0.474141i
$334$	−193.306	−	111.605i	−0.578761	−	0.334148i
$335$	−289.622	−	43.7969i	−0.864544	−	0.130737i
$336$	−3.01274	−	9.06929i	−0.00896650	−	0.0269919i
$337$	479.480	−	41.9491i	1.42279	−	0.124478i	0.650383	−	0.759606i	$-0.274608\pi$
$337$	479.480	−	41.9491i	1.42279	−	0.124478i	0.772407	+	0.635128i	$0.219053\pi$
$338$	−19.5546	−	223.511i	−0.0578540	−	0.661274i
$339$	−400.696	−	356.054i	−1.18199	−	1.05031i
$340$	3.39823	−	22.4720i	0.00999480	−	0.0660942i
$341$	0.157735	−	0.273205i	0.000462566	−	0.000801188i
$342$	6.60176	−	45.5434i	0.0193034	−	0.133168i
$343$	−20.0690	+	74.8984i	−0.0585101	+	0.218363i
$344$	−131.108	+	23.1178i	−0.381127	+	0.0672029i
$345$	16.8829	−	1.41084i	0.0489359	−	0.00408940i
$346$	−239.141	+	87.0404i	−0.691160	+	0.251562i
$347$	294.489	+	420.574i	0.848671	+	1.21203i	0.975477	+	0.220101i	$0.0706386\pi$
$347$	294.489	+	420.574i	0.848671	+	1.21203i	−0.126806	+	0.991928i	$0.540473\pi$
$348$	42.8184	+	180.067i	0.123041	+	0.517433i
$349$	110.903	+	132.169i	0.317774	+	0.378709i	0.901160	−	0.433486i	$-0.142717\pi$
$349$	110.903	+	132.169i	0.317774	+	0.378709i	−0.583386	+	0.812195i	$0.698272\pi$
$350$	−25.9560	+	10.9118i	−0.0741601	+	0.0311766i
$351$	61.2851	−	61.5599i	0.174601	−	0.175384i
$352$	24.2089	−	24.2089i	0.0687754	−	0.0687754i
$353$	−406.016	−	35.5218i	−1.15019	−	0.100628i	−0.503928	−	0.863746i	$-0.668112\pi$
$353$	−406.016	−	35.5218i	−1.15019	−	0.100628i	−0.646260	+	0.763117i	$0.723668\pi$
$354$	−271.945	−	7.70984i	−0.768207	−	0.0217792i
$355$	−245.063	+	257.349i	−0.690317	+	0.724926i
$356$	−62.1347	+	22.6152i	−0.174536	+	0.0635258i
$357$	3.23929	−	4.35790i	0.00907364	−	0.0122070i
$358$	286.490	−	409.149i	0.800250	−	1.14288i
$359$	329.355	−	190.153i	0.917425	−	0.529675i	0.0346122	−	0.999401i	$-0.488980\pi$
$359$	329.355	−	190.153i	0.917425	−	0.529675i	0.882813	+	0.469725i	$0.155647\pi$
$360$	−112.221	+	60.0538i	−0.311725	+	0.166816i
$361$	−173.964	+	301.314i	−0.481894	+	0.834664i
$362$	−337.077	+	157.182i	−0.931152	+	0.434203i
$363$	−139.245	−	211.368i	−0.383594	−	0.582280i
$364$	3.29382	−	3.92542i	0.00904896	−	0.0107841i
$365$	−206.468	+	378.702i	−0.565666	+	1.03754i
$366$	236.754	+	48.7018i	0.646870	+	0.133065i
$367$	−251.297	+	117.182i	−0.684733	+	0.319296i	−0.733670	−	0.679506i	$-0.762194\pi$
$367$	−251.297	+	117.182i	−0.684733	+	0.319296i	0.0489374	+	0.998802i	$0.484417\pi$
$368$	4.36386	−	1.16929i	0.0118583	−	0.00317742i
$369$	−21.0701	−	69.9989i	−0.0571005	−	0.189699i
$370$	−130.360	−	8.19963i	−0.352325	−	0.0221612i
$371$	11.4878	+	65.1506i	0.0309644	+	0.175608i
$372$	−0.186573	+	0.251001i	−0.000501539	+	0.000674734i
$373$	243.860	+	113.714i	0.653781	+	0.304863i	0.721062	−	0.692871i	$-0.243654\pi$
$373$	243.860	+	113.714i	0.653781	+	0.304863i	−0.0672803	+	0.997734i	$0.521432\pi$
$374$	19.1573	+	3.37795i	0.0512227	+	0.00903194i
$375$	201.921	+	315.995i	0.538456	+	0.842653i
$376$	72.1435	−	60.5355i	0.191871	−	0.160999i
$377$	−70.1763	+	70.1763i	−0.186144	+	0.186144i
$378$	−30.4089	+	0.0680286i	−0.0804467	+	0.000179970i
$379$			227.151i			0.599343i	0.954042	+	0.299672i	$0.0968771\pi$
$379$			227.151i			0.599343i	−0.954042	+	0.299672i	$0.903123\pi$
$380$	−35.9309	+	4.03084i	−0.0945550	+	0.0106075i
$381$	−574.880	−	354.000i	−1.50887	−	0.929133i
$382$	−206.138	−	294.395i	−0.539628	−	0.770668i
$383$	149.624	+	69.7709i	0.390664	+	0.182170i	0.608018	−	0.793923i	$-0.291965\pi$
$383$	149.624	+	69.7709i	0.390664	+	0.182170i	−0.217354	+	0.976093i	$0.569743\pi$
$384$	−26.6082	+	21.0713i	−0.0692923	+	0.0548733i
$385$	−8.79368	−	22.4379i	−0.0228407	−	0.0582801i
$386$	−128.555	−	222.664i	−0.333044	−	0.576850i
$387$	−60.7705	+	419.236i	−0.157030	+	1.08330i
$388$	−80.4813	+	21.5649i	−0.207426	+	0.0555796i
$389$	−31.6460	+	86.9467i	−0.0813522	+	0.223513i	−0.973700	−	0.227836i	$-0.926835\pi$
$389$	−31.6460	+	86.9467i	−0.0813522	+	0.223513i	0.892347	+	0.451349i	$0.149057\pi$
$390$	−58.9707	−	34.3536i	−0.151207	−	0.0880861i
$391$	1.96640	+	1.65001i	0.00502916	+	0.00421997i
$392$	136.279	−	11.9228i	0.347649	−	0.0304154i
$393$	−54.0728	+	107.868i	−0.137590	+	0.274474i
$394$	−144.564	+	397.186i	−0.366913	+	1.00809i
$395$	182.681	+	367.995i	0.462484	+	0.931633i
$396$	−49.0374	−	97.2795i	−0.123832	−	0.245655i
$397$	−102.854	−	27.5595i	−0.259077	−	0.0694195i	0.126943	−	0.991910i	$-0.459484\pi$
$397$	−102.854	−	27.5595i	−0.259077	−	0.0694195i	−0.386020	+	0.922491i	$0.626150\pi$
$398$	66.4473	−	94.8966i	0.166953	−	0.238434i
$399$	−8.03034	−	3.18332i	−0.0201262	−	0.00797824i
$400$	67.9463	+	73.3710i	0.169866	+	0.183427i
$401$	−10.3107	+	58.4750i	−0.0257125	+	0.145823i	−0.994961	−	0.100260i	$-0.968033\pi$
$401$	−10.3107	+	58.4750i	−0.0257125	+	0.145823i	0.969249	+	0.246083i	$0.0791436\pi$
$402$	−71.1064	+	238.158i	−0.176882	+	0.592433i
$403$	−0.167058	−	0.0146157i	−0.000414535	−	3.62671e-5i
$404$		−	162.332i		−	0.401813i
$405$	69.6667	+	398.963i	0.172017	+	0.985094i
$406$	34.7427			0.0855731
$407$	9.74383	−	111.372i	0.0239406	−	0.273642i
$408$	−18.4789	−	5.51720i	−0.0452914	−	0.0135226i
$409$	130.225	+	22.9622i	0.318398	+	0.0561422i	0.330563	−	0.943784i	$-0.392761\pi$
$409$	130.225	+	22.9622i	0.318398	+	0.0561422i	−0.0121651	+	0.999926i	$0.503872\pi$
$410$	−49.0222	+	29.9243i	−0.119566	+	0.0729861i
$411$	171.874	−	433.575i	0.418185	−	1.05493i
$412$	10.0954	+	7.06888i	0.0245034	+	0.0171575i
$413$	−13.2172	+	49.3271i	−0.0320028	+	0.119436i
$414$	0.814459	−	14.3524i	0.00196729	−	0.0346677i
$415$	−360.348	−	121.264i	−0.868308	−	0.292204i
$416$	−17.1018	−	6.22453i	−0.0411100	−	0.0149628i
$417$	363.684	+	182.309i	0.872143	+	0.437193i
$418$	−2.69718	−	30.8289i	−0.00645259	−	0.0737534i
$419$	348.421	−	415.232i	0.831553	−	0.991006i	−0.168433	−	0.985713i	$-0.553871\pi$
$419$	348.421	−	415.232i	0.831553	−	0.991006i	0.999986	−	0.00529323i	$-0.00168489\pi$
$420$	6.09368	+	23.1013i	0.0145088	+	0.0550032i
$421$	221.767	+	80.7167i	0.526763	+	0.191726i	0.591693	−	0.806164i	$-0.298460\pi$
$421$	221.767	+	80.7167i	0.526763	+	0.191726i	−0.0649292	+	0.997890i	$0.520682\pi$
$422$	−42.8215	−	159.812i	−0.101473	−	0.378702i
$423$	−111.055	−	278.330i	−0.262540	−	0.657992i
$424$	203.479	−	117.479i	0.479904	−	0.277073i
$425$	−12.0056	+	55.5359i	−0.0282484	+	0.130673i
$426$	187.200	+	236.391i	0.439437	+	0.554908i
$427$	19.1748	−	41.1206i	0.0449059	−	0.0963011i
$428$	268.618	−	188.088i	0.627612	−	0.439459i
$429$	30.6289	−	49.7400i	0.0713960	−	0.115944i
$430$	330.751	−	37.1046i	0.769188	−	0.0862898i
$431$	420.640			0.975963			0.487982	−	0.872854i	$-0.337733\pi$
$431$	420.640			0.975963			0.487982	+	0.872854i	$0.337733\pi$
$432$	37.1651	+	101.404i	0.0860304	+	0.234731i
$433$	574.468	+	574.468i	1.32672	+	1.32672i	0.908217	+	0.418501i	$0.137444\pi$
$433$	574.468	+	574.468i	1.32672	+	1.32672i	0.418501	+	0.908217i	$0.362556\pi$
$434$	0.0377352	+	0.0449711i	8.69476e−5	+	0.000103620i
$435$	−78.5754	−	455.998i	−0.180633	−	1.04827i
$436$	30.0743	−	170.560i	0.0689778	−	0.391193i
$437$	1.72583	−	3.70106i	0.00394927	−	0.00846924i
$438$	293.736	+	218.338i	0.670629	+	0.498488i
$439$	−792.973	+	139.823i	−1.80632	+	0.318502i	−0.972388	−	0.233371i	$-0.925024\pi$
$439$	−792.973	+	139.823i	−1.80632	+	0.318502i	−0.833928	+	0.551873i	$0.813913\pi$
$440$	−64.2023	+	56.6036i	−0.145914	+	0.128645i
$441$	99.7534	−	423.708i	0.226198	−	0.960789i
$442$	−2.67635	−	9.98827i	−0.00605509	−	0.0225979i
$443$	−321.687	−	689.861i	−0.726156	−	1.55725i	−0.826909	−	0.562336i	$-0.809903\pi$
$443$	−321.687	−	689.861i	−0.726156	−	1.55725i	0.100752	−	0.994912i	$-0.467875\pi$
$444$	−22.3314	+	108.560i	−0.0502960	+	0.244504i
$445$	158.580	−	46.6751i	0.356359	−	0.104888i
$446$	−33.3817	−	28.0105i	−0.0748468	−	0.0628039i
$447$	230.959	−	152.151i	0.516686	−	0.340382i
$448$	2.69253	+	5.77415i	0.00601011	+	0.0128887i
$449$	−104.196	−	60.1577i	−0.232063	−	0.133982i	0.379461	−	0.925208i	$-0.376110\pi$
$449$	−104.196	−	60.1577i	−0.232063	−	0.133982i	−0.611523	+	0.791226i	$0.709443\pi$
$450$	289.424	−	132.227i	0.643164	−	0.293837i
$451$	−24.5792	−	42.5725i	−0.0544994	−	0.0943957i
$452$	292.728	+	204.971i	0.647629	+	0.453475i
$453$	1.33180	+	0.989943i	0.00293995	+	0.00218530i
$454$	195.703	+	537.690i	0.431064	+	1.18434i
$455$	−8.83436	+	9.27727i	−0.0194162	+	0.0203896i
$456$	−0.869439	+	30.6673i	−0.00190667	+	0.0672528i
$457$	−18.3355	+	209.576i	−0.0401215	+	0.458591i	0.949386	+	0.314111i	$0.101707\pi$
$457$	−18.3355	+	209.576i	−0.0401215	+	0.458591i	−0.989508	+	0.144480i	$0.953849\pi$
$458$	−300.595	−	300.595i	−0.656321	−	0.656321i
$459$	−35.0846	+	50.3453i	−0.0764369	+	0.109685i
$460$	−11.0716	+	2.23260i	−0.0240688	+	0.00485349i
$461$	695.156	−	583.305i	1.50793	−	1.26530i	0.640269	−	0.768151i	$-0.278823\pi$
$461$	695.156	−	583.305i	1.50793	−	1.26530i	0.867662	−	0.497154i	$-0.165622\pi$
$462$	−19.8944	+	4.73073i	−0.0430614	+	0.0102397i
$463$	235.607	−	164.974i	0.508870	−	0.356315i	−0.290771	−	0.956793i	$-0.593912\pi$
$463$	235.607	−	164.974i	0.508870	−	0.356315i	0.799641	+	0.600478i	$0.205023\pi$
$464$	−42.2024	−	115.950i	−0.0909535	−	0.249893i
$465$	0.504903	−	0.596984i	0.00108581	−	0.00128384i
$466$	−45.7217	−	259.301i	−0.0981152	−	0.556439i
$467$	−306.450	−	82.1132i	−0.656211	−	0.175831i	−0.0846754	−	0.996409i	$-0.526985\pi$
$467$	−306.450	−	82.1132i	−0.656211	−	0.175831i	−0.571535	+	0.820577i	$0.693652\pi$
$468$	−35.8500	+	45.4789i	−0.0766025	+	0.0971772i
$469$	40.4040	+	23.3273i	0.0861494	+	0.0497384i
$470$	−189.503	+	139.718i	−0.403199	+	0.297273i
$471$	530.827	−	597.382i	1.12702	−	1.26833i
$472$	180.680	−	15.8074i	0.382796	−	0.0334903i
$473$	24.8281	+	283.786i	0.0524907	+	0.599971i
$474$	330.836	−	109.901i	0.697966	−	0.231859i
$475$	90.2826	−	4.41825i	0.190069	−	0.00930158i
$476$	−1.80998	+	3.13498i	−0.00380248	+	0.00658609i
$477$	−152.276	−	731.959i	−0.319237	−	1.53450i
$478$	−0.679989	+	2.53775i	−0.00142257	+	0.00530910i
$479$	533.976	−	94.1544i	1.11477	−	0.196564i	0.414228	−	0.910173i	$-0.364052\pi$
$479$	533.976	−	94.1544i	1.11477	−	0.196564i	0.700544	+	0.713609i	$0.252941\pi$
$480$	69.6963	−	48.3986i	0.145201	−	0.100830i
$481$	−55.8449	+	20.3259i	−0.116102	+	0.0422576i
$482$	264.747	+	378.099i	0.549269	+	0.784437i
$483$	−2.58564	−	0.771989i	−0.00535329	−	0.00159832i
$484$	108.465	+	129.263i	0.224100	+	0.267072i
$485$	204.191	−	41.1752i	0.421012	−	0.0848974i
$486$	343.469	−	11.2758i	0.706726	−	0.0232012i
$487$	−412.716	+	412.716i	−0.847467	+	0.847467i	−0.989816	−	0.142350i	$-0.954534\pi$
$487$	−412.716	+	412.716i	−0.847467	+	0.847467i	0.142350	+	0.989816i	$0.454534\pi$
$488$	−160.528	−	14.0444i	−0.328950	−	0.0287794i
$489$	461.236	+	853.891i	0.943223	+	1.74620i
$490$	−341.895	+	8.36083i	−0.697746	+	0.0170629i
$491$	155.990	−	56.7757i	0.317699	−	0.115633i	−0.178249	−	0.983985i	$-0.557043\pi$
$491$	155.990	−	56.7757i	0.317699	−	0.115633i	0.495947	+	0.868353i	$0.334821\pi$
$492$	19.3360	+	44.7341i	0.0393008	+	0.0909230i
$493$	40.2132	−	57.4304i	0.0815684	−	0.116492i
$494$	−14.2465	+	8.22524i	−0.0288391	+	0.0166503i
$495$	107.085	+	250.415i	0.216333	+	0.505889i
$496$	0.104249	−	0.180565i	0.000210180	−	0.000364042i
$497$	51.2982	−	23.9208i	0.103216	−	0.0481303i
$498$	−144.574	+	288.407i	−0.290309	+	0.579130i
$499$	−223.737	+	266.639i	−0.448371	+	0.534347i	−0.942128	−	0.335252i	$-0.891179\pi$
$499$	−223.737	+	266.639i	−0.448371	+	0.534347i	0.493758	+	0.869600i	$0.335623\pi$
$500$	−158.016	−	193.729i	−0.316032	−	0.387458i
$501$	314.518	−	353.952i	0.627781	−	0.706492i
$502$	180.551	−	84.1924i	0.359664	−	0.167714i
$503$	636.761	−	170.620i	1.26593	−	0.339204i	0.437458	−	0.899239i	$-0.355879\pi$
$503$	636.761	−	170.620i	1.26593	−	0.339204i	0.828469	+	0.560035i	$0.189212\pi$
$504$	20.1320	−	2.38354i	0.0399445	−	0.00472924i
$505$	−25.4763	+	405.031i	−0.0504482	+	0.802041i
$506$	−1.67868	−	9.52026i	−0.00331755	−	0.0188147i
$507$	472.771	+	54.9017i	0.932488	+	0.108287i
$508$	407.918	+	190.215i	0.802988	+	0.374439i
$509$	−919.472	−	162.128i	−1.80643	−	0.318522i	−0.834007	−	0.551754i	$-0.813959\pi$
$509$	−919.472	−	162.128i	−1.80643	−	0.318522i	−0.972421	+	0.233231i	$0.925070\pi$
$510$	45.2402	+	16.6659i	0.0887063	+	0.0326781i
$511$	52.6278	−	44.1599i	0.102990	−	0.0864187i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	91.8091	+	33.1834i	0.178965	+	0.0646849i
$514$			49.8928i			0.0970676i
$515$	−24.0794	−	19.2217i	−0.0467560	−	0.0373237i
$516$	8.00335	−	282.298i	0.0155104	−	0.547090i
$517$	−115.586	−	165.074i	−0.223570	−	0.319292i
$518$	18.8552	+	8.79232i	0.0364000	+	0.0169736i
$519$	−78.6401	−	534.094i	−0.151522	−	1.02908i
$520$	41.6932	+	18.2146i	0.0801792	+	0.0350280i
$521$	115.411	+	199.898i	0.221519	+	0.383682i	0.955269	−	0.295737i	$-0.0955652\pi$
$521$	115.411	+	199.898i	0.221519	+	0.383682i	−0.733750	+	0.679419i	$0.762232\pi$
$522$	−392.446	+	12.0048i	−0.751813	+	0.0229978i
$523$	−81.7206	+	21.8970i	−0.156253	+	0.0418680i	−0.336098	−	0.941827i	$-0.609107\pi$
$523$	−81.7206	+	21.8970i	−0.156253	+	0.0418680i	0.179844	+	0.983695i	$0.442441\pi$
$524$	27.5127	−	75.5904i	0.0525051	−	0.144257i
$525$	−11.5786	−	58.5958i	−0.0220546	−	0.111611i
$526$	253.201	+	212.461i	0.481370	+	0.403918i
$527$	0.118015	−	0.0103250i	0.000223938	−	1.95920e-5i
$528$	39.9543	+	60.6490i	0.0756711	+	0.114866i
$529$	−180.492	+	495.899i	−0.341195	+	0.937427i
$530$	−526.132	+	261.184i	−0.992701	+	0.492800i
$531$	132.254	−	561.756i	0.249066	−	1.05792i
$532$	5.56263	+	1.49050i	0.0104561	+	0.00280169i
$533$	−14.9883	+	21.4056i	−0.0281207	+	0.0401606i
$534$	−20.4326	−	138.771i	−0.0382633	−	0.259870i
$535$	−699.739	+	427.137i	−1.30792	+	0.798387i
$536$	28.7731	−	163.181i	0.0536812	−	0.304441i
$537$	727.686	+	770.150i	1.35509	+	1.43417i
$538$	39.4951	+	3.45537i	0.0734110	+	0.00642263i
$539$		−	292.721i		−	0.543082i
$540$	−76.8153	−	258.842i	−0.142251	−	0.479338i
$541$	141.371			0.261315			0.130657	−	0.991428i	$-0.458291\pi$
$541$	141.371			0.261315			0.130657	+	0.991428i	$0.458291\pi$
$542$	−13.2569	+	151.527i	−0.0244593	+	0.279571i
$543$	−182.521	−	767.566i	−0.336135	−	1.41356i
$544$	12.6613	+	2.23253i	0.0232744	+	0.00410391i
$545$	−101.805	+	420.839i	−0.186798	+	0.772182i
$546$	6.74846	+	8.52175i	0.0123598	+	0.0156076i
$547$	−472.814	−	331.068i	−0.864376	−	0.605243i	0.0550594	−	0.998483i	$-0.482465\pi$
$547$	−472.814	−	331.068i	−0.864376	−	0.605243i	−0.919436	+	0.393240i	$0.871354\pi$
$548$	−80.4753	+	300.338i	−0.146853	+	0.548062i
$549$	−202.387	+	471.115i	−0.368646	+	0.858134i
$550$	169.073	−	131.154i	0.307405	−	0.238462i
$551$	−104.808	−	38.1471i	−0.190214	−	0.0692324i
$552$	0.564377	+	9.56706i	0.00102242	+	0.0173316i
$553$	−5.70329	−	65.1889i	−0.0103134	−	0.117882i
$554$	196.580	−	234.274i	0.354837	−	0.422878i
$555$	72.7558	−	267.360i	0.131091	−	0.481729i
$556$	−254.857	−	92.7604i	−0.458376	−	0.166835i
$557$	−185.024	−	690.519i	−0.332180	−	1.23971i	−0.906895	−	0.421357i	$-0.861554\pi$
$557$	−185.024	−	690.519i	−0.332180	−	1.23971i	0.574715	−	0.818354i	$-0.305113\pi$
$558$	−0.441789	−	0.494946i	−0.000791736	−	0.000887000i
$559$	131.142	−	75.7149i	0.234601	−	0.135447i
$560$	−5.81186	−	14.8295i	−0.0103783	−	0.0264812i
$561$	−15.2069	+	38.3615i	−0.0271068	+	0.0683805i
$562$	−71.6426	+	153.638i	−0.127478	+	0.273377i
$563$	−553.136	+	387.310i	−0.982479	+	0.687939i	−0.950233	−	0.311541i	$-0.899155\pi$
$563$	−553.136	+	387.310i	−0.982479	+	0.687939i	−0.0322464	+	0.999480i	$0.510266\pi$
$564$	94.9462	+	175.775i	0.168344	+	0.311657i
$565$	−698.210	−	557.356i	−1.23577	−	0.986472i
$566$	−55.6626			−0.0983438
$567$	12.8560	−	63.2130i	0.0226737	−	0.111487i
$568$	−142.146	−	142.146i	−0.250257	−	0.250257i
$569$	108.701	+	129.545i	0.191039	+	0.227671i	0.853058	−	0.521815i	$-0.174745\pi$
$569$	108.701	+	129.545i	0.191039	+	0.227671i	−0.662020	+	0.749486i	$0.730301\pi$
$570$	6.98221	−	76.3806i	0.0122495	−	0.134001i
$571$	−10.7270	+	60.8361i	−0.0187864	+	0.106543i	−0.992759	−	0.120122i	$-0.961671\pi$
$571$	−10.7270	+	60.8361i	−0.0187864	+	0.106543i	0.973973	+	0.226665i	$0.0727824\pi$
$572$	−16.4579	+	35.2940i	−0.0287725	+	0.0617029i
$573$	699.806	−	302.486i	1.22130	−	0.527899i
$574$	9.00889	−	1.58851i	0.0156949	−	0.00276744i
$575$	27.9749	−	3.83293i	0.0486519	−	0.00666596i
$576$	−32.4095	−	64.2933i	−0.0562664	−	0.111620i
$577$	182.474	+	681.003i	0.316247	+	1.18025i	0.922823	+	0.385223i	$0.125876\pi$
$577$	182.474	+	681.003i	0.316247	+	1.18025i	−0.606577	+	0.795025i	$0.707458\pi$
$578$	−169.640	−	363.794i	−0.293495	−	0.629402i
$579$	517.601	−	171.943i	0.893957	−	0.296965i
$580$	87.1008	+	295.927i	0.150174	+	0.510219i
$581$	46.3900	+	38.9258i	0.0798450	+	0.0669979i
$582$	−10.4086	−	176.442i	−0.0178842	−	0.303166i
$583$	−212.475	−	455.655i	−0.364452	−	0.781569i
$584$	−211.307	−	121.998i	−0.361827	−	0.208901i
$585$	96.5856	−	107.847i	0.165104	−	0.184353i
$586$	−26.6257	−	46.1171i	−0.0454364	−	0.0786981i
$587$	655.287	+	458.837i	1.11633	+	0.781664i	0.977976	−	0.208719i	$-0.0669293\pi$
$587$	655.287	+	458.837i	1.11633	+	0.781664i	0.138356	+	0.990383i	$0.455818\pi$
$588$	−33.4746	+	288.257i	−0.0569296	+	0.490234i
$589$	−0.0644581	−	0.177097i	−0.000109437	−	0.000300674i
$590$	−453.289	+	11.0849i	−0.768286	+	0.0187879i
$591$	−763.489	−	470.141i	−1.29186	−	0.795501i
$592$	6.43982	−	73.6075i	0.0108781	−	0.124337i
$593$	199.640	+	199.640i	0.336662	+	0.336662i	0.855109	−	0.518448i	$-0.173490\pi$
$593$	199.640	+	199.640i	0.336662	+	0.336662i	−0.518448	+	0.855109i	$0.673490\pi$
$594$	223.088	−	60.3116i	0.375569	−	0.101535i
$595$	5.00803	−	7.53793i	0.00841686	−	0.0126688i
$596$	−141.244	+	118.518i	−0.236987	+	0.198855i
$597$	168.777	+	178.626i	0.282708	+	0.299206i
$598$	−4.20946	+	2.94749i	−0.00703923	+	0.00492892i
$599$	−266.831	−	733.112i	−0.445461	−	1.22389i	−0.935853	−	0.352391i	$-0.885369\pi$
$599$	−266.831	−	733.112i	−0.445461	−	1.22389i	0.490392	−	0.871502i	$-0.336853\pi$
$600$	−181.493	+	109.820i	−0.302488	+	0.183033i
$601$	50.5949	+	286.938i	0.0841845	+	0.477434i	0.997530	+	0.0702477i	$0.0223790\pi$
$601$	50.5949	+	286.938i	0.0841845	+	0.477434i	−0.913345	+	0.407186i	$0.866510\pi$
$602$	−51.2050	−	13.7203i	−0.0850582	−	0.0227913i
$603$	−464.456	−	249.539i	−0.770243	−	0.413830i
$604$	−0.958065	−	0.553139i	−0.00158620	−	0.000915793i
$605$	−250.340	−	339.543i	−0.413785	−	0.561227i
$606$	337.297	+	69.3839i	0.556595	+	0.114495i
$607$	−701.907	+	61.4089i	−1.15635	+	0.101168i	−0.649152	−	0.760659i	$-0.724876\pi$
$607$	−701.907	+	61.4089i	−1.15635	+	0.101168i	−0.507203	+	0.861827i	$0.669320\pi$
$608$	−1.78260	−	20.3752i	−0.00293191	−	0.0335119i
$609$	−14.8497	+	72.1888i	−0.0243837	+	0.118537i
$610$	398.324	+	60.2348i	0.652990	+	0.0987455i
$611$	−53.5609	+	92.7702i	−0.0876611	+	0.151833i
$612$	19.3619	−	36.0375i	0.0316372	−	0.0588848i
$613$	−142.210	+	530.735i	−0.231990	+	0.865800i	0.747492	+	0.664271i	$0.231258\pi$
$613$	−142.210	+	530.735i	−0.231990	+	0.865800i	−0.979482	+	0.201529i	$0.935409\pi$
$614$	386.679	−	68.1819i	0.629770	−	0.111045i
$615$	−41.2241	−	114.649i	−0.0670310	−	0.186422i
$616$	12.8106	−	4.66267i	0.0207964	−	0.00756927i
$617$	−350.277	−	500.247i	−0.567710	−	0.810774i	0.427954	−	0.903801i	$-0.359235\pi$
$617$	−350.277	−	500.247i	−0.567710	−	0.810774i	−0.995664	+	0.0930270i	$0.970346\pi$
$618$	−19.0028	+	17.9550i	−0.0307489	+	0.0290534i
$619$	−386.112	−	460.150i	−0.623768	−	0.743377i	0.357946	−	0.933742i	$-0.383477\pi$
$619$	−386.112	−	460.150i	−0.623768	−	0.743377i	−0.981713	+	0.190365i	$0.939033\pi$
$620$	−0.288446	+	0.434161i	−0.000465236	+	0.000700259i
$621$	29.4736	+	7.82680i	0.0474615	+	0.0126035i
$622$	409.128	−	409.128i	0.657763	−	0.657763i
$623$	−26.2292	−	2.29476i	−0.0421014	−	0.00368340i
$624$	20.2430	−	32.8738i	0.0324408	−	0.0526824i
$625$	363.857	+	508.166i	0.582171	+	0.813066i
$626$	−392.177	+	142.741i	−0.626482	+	0.228021i
$627$	65.2096	+	7.57263i	0.104003	+	0.0120776i
$628$	−305.583	+	436.418i	−0.486597	+	0.694932i
$629$	36.3580	−	20.9913i	0.0578029	−	0.0333725i
$630$	−50.6048	+	2.78758i	−0.0803251	+	0.00442474i
$631$	−73.5369	+	127.370i	−0.116540	+	0.201854i	−0.918394	−	0.395666i	$-0.870514\pi$
$631$	−73.5369	+	127.370i	−0.116540	+	0.201854i	0.801854	+	0.597520i	$0.203847\pi$
$632$	−210.634	+	98.2200i	−0.333281	+	0.155411i
$633$	350.363	−	20.6685i	0.553495	−	0.0326516i
$634$	−31.5300	+	37.5760i	−0.0497318	+	0.0592681i
$635$	−987.931	−	538.618i	−1.55580	−	0.848218i
$636$	157.128	+	473.005i	0.247057	+	0.743718i
$637$	−141.024	+	65.7607i	−0.221388	+	0.103235i
$638$	−255.035	+	68.3365i	−0.399742	+	0.107110i
$639$	−571.189	+	287.930i	−0.893880	+	0.450594i
$640$	−42.4321	+	37.4101i	−0.0663002	+	0.0584532i
$641$	186.524	+	1057.83i	0.290989	+	1.65028i	0.683071	+	0.730352i	$0.260644\pi$
$641$	186.524	+	1057.83i	0.290989	+	1.65028i	−0.392082	+	0.919930i	$0.628245\pi$
$642$	276.000	+	638.531i	0.429907	+	0.994597i
$643$	461.364	+	215.138i	0.717518	+	0.334584i	0.746856	−	0.664985i	$-0.231562\pi$
$643$	461.364	+	215.138i	0.717518	+	0.334584i	−0.0293384	+	0.999570i	$0.509340\pi$
$644$	1.77162	+	0.312384i	0.00275096	+	0.000485069i
$645$	−64.2726	+	703.098i	−0.0996474	+	1.09007i
$646$	8.90234	−	7.46995i	0.0137807	−	0.0115634i
$647$	256.439	−	256.439i	0.396351	−	0.396351i	−0.480593	−	0.876944i	$-0.659579\pi$
$647$	256.439	−	256.439i	0.396351	−	0.396351i	0.876944	+	0.480593i	$0.159579\pi$
$648$	−226.584	+	33.8803i	−0.349666	+	0.0522844i
$649$		−	388.093i		−	0.597986i
$650$	−101.169	−	51.9899i	−0.155644	−	0.0799845i
$651$	−0.109570	+	0.0591853i	−0.000168311	+	9.09145e-5i
$652$	−371.104	−	529.991i	−0.569177	−	0.812869i
$653$	249.711	+	116.442i	0.382406	+	0.178319i	0.604309	−	0.796750i	$-0.293449\pi$
$653$	249.711	+	116.442i	0.382406	+	0.178319i	−0.221903	+	0.975069i	$0.571227\pi$
$654$	341.538	+	135.389i	0.522229	+	0.207017i
$655$	−80.5091	+	184.286i	−0.122915	+	0.281352i
$656$	−16.2447	−	28.1367i	−0.0247633	−	0.0428913i
$657$	−579.214	+	517.007i	−0.881604	+	0.786920i
$658$	36.2226	−	9.70581i	0.0550495	−	0.0147505i
$659$	−106.155	+	291.658i	−0.161085	+	0.442577i	−0.993808	−	0.111113i	$-0.964558\pi$
$659$	−106.155	+	291.658i	−0.161085	+	0.442577i	0.832723	+	0.553690i	$0.186781\pi$
$660$	−90.1706	−	157.594i	−0.136622	−	0.238779i
$661$	−204.370	−	171.486i	−0.309182	−	0.259435i	0.474972	−	0.880001i	$-0.342458\pi$
$661$	−204.370	−	171.486i	−0.309182	−	0.259435i	−0.784154	+	0.620566i	$0.786903\pi$
$662$	143.398	−	12.5457i	0.216614	−	0.0189513i
$663$	21.8977	−	1.29178i	0.0330282	−	0.00194839i
$664$	73.5604	−	202.106i	0.110784	−	0.304376i
$665$	−13.6452	−	4.59190i	−0.0205191	−	0.00690511i
$666$	−216.023	−	92.8011i	−0.324358	−	0.139341i
$667$	−33.6540	−	9.01755i	−0.0504557	−	0.0135196i
$668$	−181.060	+	258.580i	−0.271047	+	0.387096i
$669$	72.4687	−	57.3887i	0.108324	−	0.0857828i
$670$	−97.4003	+	402.631i	−0.145374	+	0.600942i
$671$	−59.8752	+	339.569i	−0.0892328	+	0.506064i
$672$	−13.1485	+	3.12660i	−0.0195661	+	0.00465268i
$673$	42.9500	+	3.75764i	0.0638187	+	0.00558341i	0.119020	−	0.992892i	$-0.462025\pi$
$673$	42.9500	+	3.75764i	0.0638187	+	0.00558341i	−0.0552017	+	0.998475i	$0.517580\pi$
$674$		−	680.678i		−	1.00991i
$675$	151.037	+	657.885i	0.223758	+	0.974645i
$676$	−317.299			−0.469377
$677$	70.3437	−	804.032i	0.103905	−	1.18764i	−0.747911	−	0.663799i	$-0.768943\pi$
$677$	70.3437	−	804.032i	0.103905	−	1.18764i	0.851816	−	0.523841i	$-0.175501\pi$
$678$	−551.009	+	520.627i	−0.812697	+	0.767886i
$679$	−32.6734	−	5.76121i	−0.0481199	−	0.00848484i
$680$	−31.2404	−	7.55737i	−0.0459418	−	0.0111138i
$681$	−1200.87	+	176.816i	−1.76339	+	0.259642i
$682$	−0.365458	−	0.255896i	−0.000535862	−	0.000375215i
$683$	213.299	−	796.041i	0.312297	−	1.16551i	−0.614183	−	0.789163i	$-0.710514\pi$
$683$	213.299	−	796.041i	0.312297	−	1.16551i	0.926480	−	0.376344i	$-0.122819\pi$
$684$	−63.3493	−	14.9143i	−0.0926160	−	0.0218046i
$685$	247.926	−	736.734i	0.361936	−	1.07552i
$686$	103.046	+	37.5055i	0.150212	+	0.0546728i
$687$	753.061	−	496.101i	1.09616	−	0.722126i
$688$	16.4092	+	187.558i	0.0238506	+	0.272613i
$689$	−171.788	+	204.729i	−0.249329	+	0.297139i
$690$	0.0932880	−	23.9590i	0.000135200	−	0.0347233i
$691$	982.595	+	357.635i	1.42199	+	0.517562i	0.934624	−	0.355636i	$-0.115736\pi$
$691$	982.595	+	357.635i	1.42199	+	0.517562i	0.487365	+	0.873198i	$0.337958\pi$
$692$	93.1494	+	347.638i	0.134609	+	0.502368i
$693$	−1.32634	−	43.3588i	−0.00191391	−	0.0625669i
$694$	628.816	−	363.047i	0.906074	−	0.523122i
$695$	621.329	+	271.441i	0.893998	+	0.390562i
$696$	258.961	−	38.1295i	0.372071	−	0.0547838i
$697$	7.80158	−	16.7305i	0.0111931	−	0.0240036i
$698$	199.874	−	139.953i	0.286353	−	0.200506i
$699$	558.321	+	15.8288i	0.798742	+	0.0226449i
$700$	12.1737	+	37.9127i	0.0173910	+	0.0541609i
$701$	−623.558			−0.889526			−0.444763	−	0.895648i	$-0.646712\pi$
$701$	−623.558			−0.889526			−0.444763	+	0.895648i	$0.646712\pi$
$702$	−79.1738	−	93.9281i	−0.112783	−	0.133801i
$703$	−47.2266	−	47.2266i	−0.0671786	−	0.0671786i
$704$	−31.1224	−	37.0902i	−0.0442080	−	0.0526850i
$705$	−209.311	−	453.471i	−0.296895	−	0.643221i
$706$	−100.089	+	567.631i	−0.141769	+	0.804009i
$707$	27.3178	−	58.5832i	0.0386391	−	0.0828617i
$708$	−44.3810	+	382.175i	−0.0626850	+	0.539795i
$709$	−790.758	+	139.432i	−1.11531	+	0.196660i	−0.700783	−	0.713375i	$-0.747166\pi$
$709$	−790.758	+	139.432i	−1.11531	+	0.196660i	−0.414532	+	0.910035i	$0.636055\pi$
$710$	332.356	+	376.972i	0.468106	+	0.530947i
$711$	86.9483	+	734.390i	0.122290	+	1.03290i
$712$	24.2025	+	90.3248i	0.0339922	+	0.126861i
$713$	−0.0248804	−	0.0533562i	−3.48954e−5	−	7.48333e-5i
$714$	−5.74029	−	5.10076i	−0.00803962	−	0.00714392i
$715$	46.6026	−	85.4782i	0.0651784	−	0.119550i
$716$	−541.111	−	454.046i	−0.755742	−	0.634143i
$717$	−4.98234	−	2.49757i	−0.00694887	−	0.00348337i
$718$	−227.299	−	487.444i	−0.316572	−	0.678892i
$719$	−666.490	−	384.798i	−0.926968	−	0.535185i	−0.0411164	−	0.999154i	$-0.513091\pi$
$719$	−666.490	−	384.798i	−0.926968	−	0.535185i	−0.885851	+	0.463969i	$0.846425\pi$
$720$	70.7737	+	165.503i	0.0982968	+	0.229865i
$721$	2.45370	+	4.24994i	0.00340319	+	0.00589450i
$722$	403.058	+	282.225i	0.558253	+	0.390893i
$723$	−898.777	+	388.490i	−1.24312	+	0.537330i
$724$	179.895	+	494.259i	0.248474	+	0.682678i
$725$	−170.880	−	752.028i	−0.235697	−	1.03728i
$726$	−314.944	+	170.120i	−0.433808	+	0.234325i
$727$	5.68709	−	65.0038i	0.00782269	−	0.0894137i	−0.991280	−	0.131775i	$-0.957932\pi$
$727$	5.68709	−	65.0038i	0.00782269	−	0.0894137i	0.999102	+	0.0423611i	$0.0134880\pi$
$728$	−5.12427	−	5.12427i	−0.00703884	−	0.00703884i
$729$	−123.376	+	718.484i	−0.169240	+	0.985575i
$730$	508.080	+	337.556i	0.695999	+	0.462406i
$731$	−81.9478	+	68.7623i	−0.112104	+	0.0940661i
$732$	97.7942	−	327.544i	0.133599	−	0.447465i
$733$	542.827	−	380.092i	0.740556	−	0.518543i	−0.141355	−	0.989959i	$-0.545146\pi$
$733$	542.827	−	380.092i	0.740556	−	0.518543i	0.881911	+	0.471416i	$0.156257\pi$
$734$	134.115	+	368.479i	0.182718	+	0.502015i
$735$	128.760	−	713.969i	0.175184	−	0.971386i
$736$	−1.10946	−	6.29206i	−0.00150742	−	0.00854900i
$737$	−342.477	−	91.7664i	−0.464691	−	0.124513i
$738$	−101.214	+	21.0564i	−0.137146	+	0.0285317i
$739$	30.9505	+	17.8693i	0.0418816	+	0.0241803i	0.520795	−	0.853682i	$-0.325636\pi$
$739$	30.9505	+	17.8693i	0.0418816	+	0.0241803i	−0.478913	+	0.877862i	$0.658969\pi$
$740$	−27.6197	+	182.645i	−0.0373239	+	0.246818i
$741$	−11.0013	−	33.1173i	−0.0148465	−	0.0446927i
$742$	93.2022	−	8.15413i	0.125609	−	0.0109894i
$743$	87.8043	+	1003.61i	0.118175	+	1.35075i	0.791394	+	0.611307i	$0.209356\pi$
$743$	87.8043	+	1003.61i	0.118175	+	1.35075i	−0.673218	+	0.739444i	$0.735089\pi$
$744$	0.330622	+	0.293787i	0.000444384	+	0.000394875i
$745$	371.014	−	273.543i	0.498005	−	0.367172i
$746$	190.261	−	329.542i	0.255042	−	0.441746i
$747$	−537.462	−	423.669i	−0.719494	−	0.567160i
$748$	7.12022	−	26.5730i	0.00951902	−	0.0355254i
$749$	128.592	−	22.6743i	0.171685	−	0.0302727i
$750$	470.072	−	245.524i	0.626763	−	0.327366i
$751$	−336.078	+	122.322i	−0.447507	+	0.162879i	−0.555936	−	0.831225i	$-0.687640\pi$
$751$	−336.078	+	122.322i	−0.447507	+	0.162879i	0.108429	+	0.994104i	$0.465418\pi$
$752$	−76.3922	−	109.099i	−0.101585	−	0.145079i
$753$	97.7651	+	411.137i	0.129834	+	0.545999i
$754$	90.2170	+	107.516i	0.119651	+	0.142595i
$755$	2.30363	+	1.53048i	0.00305117	+	0.00202712i
$756$	−3.65226	+	42.8494i	−0.00483103	+	0.0566790i
$757$	845.879	−	845.879i	1.11741	−	1.11741i	0.125290	−	0.992120i	$-0.460014\pi$
$757$	845.879	−	845.879i	1.11741	−	1.11741i	0.992120	−	0.125290i	$-0.0399860\pi$
$758$	320.018	+	27.9979i	0.422187	+	0.0369366i
$759$	20.4988	+	0.581156i	0.0270077	+	0.000765687i
$760$	1.25004	+	51.1174i	0.00164479	+	0.0672597i
$761$	−976.441	+	355.396i	−1.28310	+	0.467011i	−0.891457	−	0.453105i	$-0.850316\pi$
$761$	−976.441	+	355.396i	−1.28310	+	0.467011i	−0.391646	+	0.920116i	$0.628094\pi$
$762$	−569.584	+	766.276i	−0.747485	+	1.00561i
$763$	39.5557	−	56.4914i	0.0518424	−	0.0740386i
$764$	−440.161	+	254.127i	−0.576128	+	0.332627i
$765$	−53.9651	+	86.8775i	−0.0705426	+	0.113565i
$766$	116.738	−	202.196i	0.152399	−	0.263963i
$767$	−186.971	+	87.1862i	−0.243770	+	0.113672i
$768$	26.4063	+	40.0837i	0.0343832	+	0.0521924i
$769$	−478.976	+	570.821i	−0.622856	+	0.742291i	−0.981559	−	0.191161i	$-0.938775\pi$
$769$	−478.976	+	570.821i	−0.622856	+	0.742291i	0.358703	+	0.933452i	$0.383219\pi$
$770$	−32.6950	+	9.62320i	−0.0424611	+	0.0124977i
$771$	−103.668	−	21.3251i	−0.134459	−	0.0276590i
$772$	−329.541	+	153.668i	−0.426867	+	0.199051i
$773$	164.355	−	44.0388i	0.212620	−	0.0569713i	−0.150937	−	0.988543i	$-0.548229\pi$
$773$	164.355	−	44.0388i	0.212620	−	0.0569713i	0.363557	+	0.931572i	$0.381562\pi$
$774$	583.143	+	137.289i	0.753414	+	0.177376i
$775$	0.787830	−	1.03799i	0.00101656	−	0.00133935i
$776$	20.4614	+	116.043i	0.0263678	+	0.149539i
$777$	−26.3279	+	35.4196i	−0.0338840	+	0.0455850i
$778$	118.593	+	55.3007i	0.152433	+	0.0710806i
$779$	−28.9213	−	5.09960i	−0.0371262	−	0.00654634i
$780$	−55.6670	+	78.8455i	−0.0713679	+	0.101084i
$781$	−329.514	+	276.495i	−0.421913	+	0.354027i
$782$	2.56696	−	2.56696i	0.00328255	−	0.00328255i
$783$	142.795	−	820.562i	0.182369	−	1.04797i
$784$		−	193.463i		−	0.246764i
$785$	830.941	−	1040.93i	1.05852	−	1.32603i
$786$	145.303	+	89.4750i	0.184864	+	0.113836i
$787$	327.527	+	467.757i	0.416171	+	0.594354i	0.971431	−	0.237323i	$-0.0762699\pi$
$787$	327.527	+	467.757i	0.416171	+	0.594354i	−0.555259	+	0.831677i	$0.687381\pi$
$788$	541.749	+	252.622i	0.687499	+	0.320586i
$789$	−549.676	+	435.294i	−0.696675	+	0.551704i
$790$	540.960	−	212.009i	0.684759	−	0.268366i
$791$	71.1480	+	123.232i	0.0899469	+	0.155793i
$792$	−143.095	+	57.0951i	−0.180675	+	0.0720898i
$793$	177.045	−	47.4392i	0.223260	−	0.0598224i
$794$	−51.5041	+	141.506i	−0.0648667	+	0.178220i
$795$	−317.813	−	1204.84i	−0.399765	−	1.51552i
$796$	−125.503	−	105.310i	−0.157667	−	0.132299i
$797$	−880.490	+	77.0329i	−1.10475	+	0.0966535i	−0.624908	−	0.780699i	$-0.714863\pi$
$797$	−880.490	+	77.0329i	−1.10475	+	0.0966535i	−0.479847	+	0.877352i	$0.659308\pi$
$798$	−5.47456	+	10.9210i	−0.00686035	+	0.0136855i
$799$	25.8822	−	71.1108i	0.0323933	−	0.0889997i
$800$	111.742	−	86.6815i	0.139678	−	0.108352i
$801$	297.073	+	16.8580i	0.370877	+	0.0210462i
$802$	81.1106	+	21.7335i	0.101135	+	0.0270992i
$803$	−299.465	+	427.680i	−0.372932	+	0.532602i
$804$	326.761	+	129.532i	0.406419	+	0.161109i
$805$	−4.37129	−	1.05746i	−0.00543017	−	0.00131361i
$806$	−0.0411820	+	0.233555i	−5.10943e−5	+	0.000289770i
$807$	−24.0606	+	80.5866i	−0.0298148	+	0.0998595i
$808$	−228.699	−	20.0086i	−0.283043	−	0.0247631i
$809$			97.2239i			0.120178i	0.998193	+	0.0600890i	$0.0191384\pi$
$809$			97.2239i			0.120178i	−0.998193	+	0.0600890i	$0.980862\pi$
$810$	570.659	−	48.9738i	0.704517	−	0.0604615i
$811$	−107.652			−0.132739			−0.0663696	−	0.997795i	$-0.521142\pi$
$811$	−107.652			−0.132739			−0.0663696	+	0.997795i	$0.521142\pi$
$812$	4.28227	−	48.9466i	0.00527373	−	0.0602790i
$813$	−309.179	−	92.3111i	−0.380294	−	0.113544i
$814$	−155.704	−	27.4548i	−0.191283	−	0.0337283i
$815$	842.753	+	1380.60i	1.03405	+	1.69399i
$816$	−10.0505	+	25.3536i	−0.0123167	+	0.0310706i
$817$	139.405	+	97.6127i	0.170631	+	0.119477i
$818$	48.4009	−	180.635i	0.0591699	−	0.220825i
$819$	−20.5910	+	10.3797i	−0.0251417	+	0.0126736i
$820$	36.1160	+	72.7524i	0.0440439	+	0.0887225i
$821$	−166.434	−	60.5771i	−0.202721	−	0.0737846i	0.238664	−	0.971102i	$-0.423291\pi$
$821$	−166.434	−	60.5771i	−0.202721	−	0.0737846i	−0.441385	+	0.897318i	$0.645513\pi$
$822$	−589.650	−	295.583i	−0.717335	−	0.359590i
$823$	−13.3632	−	152.742i	−0.0162372	−	0.185592i	−0.999982	−	0.00601921i	$-0.998084\pi$
$823$	−13.3632	−	152.742i	−0.0162372	−	0.185592i	0.983745	−	0.179573i	$-0.0574715\pi$
$824$	11.2032	−	13.3515i	0.0135961	−	0.0162032i
$825$	200.249	+	407.359i	0.242726	+	0.493769i
$826$	67.8645	+	24.7007i	0.0821605	+	0.0299040i
$827$	−258.188	−	963.571i	−0.312198	−	1.16514i	−0.926570	−	0.376123i	$-0.877257\pi$
$827$	−258.188	−	963.571i	−0.312198	−	1.16514i	0.614371	−	0.789017i	$-0.289410\pi$
$828$	−20.1198	−	2.91647i	−0.0242993	−	0.00352231i
$829$	1363.00	−	786.926i	1.64414	−	0.949247i	0.664807	−	0.747015i	$-0.268514\pi$
$829$	1363.00	−	786.926i	1.64414	−	0.949247i	0.979338	−	0.202232i	$-0.0648194\pi$
$830$	−215.257	+	492.723i	−0.259345	+	0.593642i
$831$	402.757	+	508.589i	0.484665	+	0.612021i
$832$	−10.8772	+	23.3263i	−0.0130736	+	0.0280364i
$833$	90.0439	−	63.0494i	0.108096	−	0.0756896i
$834$	301.670	−	489.898i	0.361714	−	0.587408i
$835$	492.338	−	616.760i	0.589626	−	0.738634i
$836$	−43.7652			−0.0523508
$837$	1.21723	−	0.706406i	0.00145428	−	0.000843974i
$838$	−542.046	−	542.046i	−0.646833	−	0.646833i
$839$	597.869	+	712.512i	0.712597	+	0.849240i	0.993889	−	0.110382i	$-0.0352076\pi$
$839$	597.869	+	712.512i	0.712597	+	0.849240i	−0.281292	+	0.959622i	$0.590763\pi$
$840$	33.2970	−	5.73757i	0.0396393	−	0.00683044i
$841$	−19.2044	+	108.913i	−0.0228352	+	0.129505i
$842$	141.051	−	302.484i	0.167519	−	0.359245i
$843$	−288.610	−	214.528i	−0.342361	−	0.254481i
$844$	−230.426	+	40.6304i	−0.273017	+	0.0481403i
$845$	791.683	+	49.7967i	0.936903	+	0.0589310i
$846$	−405.809	+	122.151i	−0.479680	+	0.144387i
$847$	17.3904	+	64.9018i	0.0205317	+	0.0766255i
$848$	−140.428	−	301.148i	−0.165599	−	0.355127i
$849$	23.7913	−	115.657i	0.0280227	−	0.136227i
$850$	76.7610	+	23.7590i	0.0903071	+	0.0279518i
$851$	−15.9823	−	13.4107i	−0.0187806	−	0.0157588i
$852$	356.109	−	234.597i	0.417968	−	0.275349i
$853$	−255.392	−	547.691i	−0.299405	−	0.642076i	0.697840	−	0.716254i	$-0.254145\pi$
$853$	−255.392	−	547.691i	−0.299405	−	0.642076i	−0.997245	+	0.0741776i	$0.976367\pi$
$854$	−55.5686	−	32.0825i	−0.0650686	−	0.0375674i
$855$	155.720	+	47.1542i	0.182129	+	0.0551512i
$856$	−231.876	−	401.621i	−0.270883	−	0.469183i
$857$	943.470	+	660.625i	1.10090	+	0.770858i	0.975225	−	0.221214i	$-0.0710019\pi$
$857$	943.470	+	660.625i	1.10090	+	0.770858i	0.125674	+	0.992072i	$0.459891\pi$
$858$	−66.3001	−	49.2818i	−0.0772728	−	0.0574380i
$859$	−220.689	−	606.337i	−0.256913	−	0.705864i	−0.999354	−	0.0359514i	$-0.988554\pi$
$859$	−220.689	−	606.337i	−0.256913	−	0.705864i	0.742440	−	0.669912i	$-0.233668\pi$
$860$	−11.5069	−	470.546i	−0.0133801	−	0.547146i
$861$	−0.549940	+	19.3978i	−0.000638723	+	0.0225293i
$862$	51.8468	−	592.611i	0.0601471	−	0.687484i
$863$	−12.8993	−	12.8993i	−0.0149470	−	0.0149470i	0.699594	−	0.714541i	$-0.253364\pi$
$863$	−12.8993	−	12.8993i	−0.0149470	−	0.0149470i	−0.714541	+	0.699594i	$0.753364\pi$
$864$	147.442	−	39.8607i	0.170650	−	0.0461351i
$865$	−177.856	−	882.001i	−0.205614	−	1.01965i
$866$	880.137	−	738.522i	1.01632	−	0.852797i
$867$	828.405	−	196.988i	0.955484	−	0.227207i
$868$	0.0680079	−	0.0476196i	7.83501e−5	−	5.48613e-5i
$869$	170.088	+	467.314i	0.195729	+	0.537760i
$870$	−652.110	+	54.4946i	−0.749552	+	0.0626375i
$871$	32.7282	+	185.611i	0.0375754	+	0.213101i
$872$	−236.584	−	63.3924i	−0.271311	−	0.0726977i
$873$	371.063	+	53.7876i	0.425044	+	0.0616124i
$874$	−5.00145	−	2.88759i	−0.00572248	−	0.00330388i
$875$	−24.4242	−	96.5052i	−0.0279133	−	0.110292i
$876$	343.806	−	386.913i	0.392473	−	0.441681i
$877$	−1524.69	+	133.393i	−1.73853	+	0.152102i	−0.911837	−	0.410553i	$-0.865336\pi$
$877$	−1524.69	+	133.393i	−1.73853	+	0.152102i	−0.826692	+	0.562654i	$0.809780\pi$
$878$	99.2471	+	1134.40i	0.113038	+	1.29203i
$879$	107.203	−	35.6120i	0.121960	−	0.0405142i
$880$	71.8316	+	97.4270i	0.0816269	+	0.110713i
$881$	−563.305	+	975.674i	−0.639393	+	1.10746i	0.346173	+	0.938171i	$0.387481\pi$
$881$	−563.305	+	975.674i	−0.639393	+	1.10746i	−0.985566	+	0.169291i	$0.945852\pi$
$882$	−584.638	−	192.761i	−0.662855	−	0.218550i
$883$	22.7162	−	84.7781i	0.0257262	−	0.0960114i	−0.951869	−	0.306505i	$-0.900840\pi$
$883$	22.7162	−	84.7781i	0.0257262	−	0.0960114i	0.977595	+	0.210493i	$0.0675071\pi$
$884$	−14.4017	+	2.53940i	−0.0162915	+	0.00287263i
$885$	170.712	−	946.588i	0.192895	−	1.06959i
$886$	−1011.55	+	368.173i	−1.14170	+	0.415546i
$887$	477.868	+	682.467i	0.538747	+	0.769410i	0.992569	−	0.121682i	$-0.0388288\pi$
$887$	477.868	+	682.467i	0.538747	+	0.769410i	−0.453822	+	0.891092i	$0.649940\pi$
$888$	150.190	+	44.8420i	0.169133	+	0.0504977i
$889$	115.201	+	137.291i	0.129585	+	0.154434i
$890$	−46.2113	−	229.165i	−0.0519228	−	0.257489i
$891$	29.9641	+	489.314i	0.0336297	+	0.549174i
$892$	−43.5767	+	43.5767i	−0.0488528	+	0.0488528i
$893$	−119.929	−	10.4925i	−0.134299	−	0.0117497i
$894$	−185.888	−	344.136i	−0.207928	−	0.384939i
$895$	1278.85	+	1217.80i	1.42888	+	1.36067i
$896$	8.46668	−	3.08162i	0.00944942	−	0.00343931i
$897$	−4.32514	−	10.0063i	−0.00482179	−	0.0111553i
$898$	−97.5950	+	139.380i	−0.108680	+	0.155212i
$899$	−1.39251	+	0.803967i	−0.00154896	+	0.000894290i
$900$	−150.612	−	424.047i	−0.167346	−	0.471164i
$901$	94.3987	−	163.503i	0.104771	−	0.181469i
$902$	−63.0070	+	29.3806i	−0.0698526	+	0.0325728i
$903$	50.3943	−	100.530i	0.0558077	−	0.111329i
$904$	324.850	−	387.141i	0.359347	−	0.428253i
$905$	−371.283	−	1261.44i	−0.410257	−	1.39386i
$906$	1.55882	−	1.75426i	0.00172055	−	0.00193627i
$907$	−832.554	+	388.226i	−0.917921	+	0.428034i	−0.823382	−	0.567488i	$-0.807915\pi$
$907$	−832.554	+	388.226i	−0.917921	+	0.428034i	−0.0945390	+	0.995521i	$0.530138\pi$
$908$	781.636	−	209.439i	0.860833	−	0.230660i
$909$	−288.334	+	671.184i	−0.317199	+	0.738376i
$910$	11.9812	+	13.5896i	0.0131662	+	0.0149336i
$911$	175.942	+	997.818i	0.193131	+	1.09530i	0.915056	+	0.403328i	$0.132147\pi$
$911$	175.942	+	997.818i	0.193131	+	1.09530i	−0.721925	+	0.691972i	$0.756742\pi$
$912$	43.0979	+	5.00485i	0.0472565	+	0.00548777i
$913$	−417.099	−	194.496i	−0.456844	−	0.213030i
$914$	292.998	+	51.6634i	0.320567	+	0.0565245i
$915$	−295.408	+	801.898i	−0.322850	+	0.876391i
$916$	−460.538	+	386.437i	−0.502771	+	0.421875i
$917$	22.6495	−	22.6495i	0.0246996	−	0.0246996i
$918$	66.6036	+	55.6336i	0.0725530	+	0.0606031i
$919$		−	220.261i		−	0.239675i	−0.992794	−	0.119837i	$-0.961763\pi$
$919$		−	220.261i		−	0.239675i	0.992794	−	0.119837i	$-0.0382373\pi$
$920$	1.78071	+	15.8732i	0.00193555	+	0.0172535i
$921$	−23.6045	+	832.589i	−0.0256292	+	0.904005i
$922$	−736.097	−	1051.25i	−0.798369	−	1.14019i
$923$	207.234	+	96.6346i	0.224522	+	0.104696i
$924$	4.21268	+	28.6109i	0.00455918	+	0.0309642i
$925$	97.5772	−	451.378i	0.105489	−	0.487976i
$926$	−203.380	−	352.265i	−0.219633	−	0.380415i
$927$	−29.1850	−	47.1586i	−0.0314833	−	0.0508723i
$928$	−168.556	+	45.1645i	−0.181634	+	0.0486686i
$929$	−434.218	+	1193.01i	−0.467404	+	1.28418i	0.452404	+	0.891813i	$0.350567\pi$
$929$	−434.218	+	1193.01i	−0.467404	+	1.28418i	−0.919808	+	0.392369i	$0.871656\pi$
$930$	−0.778818	−	0.784907i	−0.000837439	−	0.000843986i
$931$	−133.960	−	112.406i	−0.143888	−	0.120737i
$932$	−370.947	+	32.4536i	−0.398011	+	0.0348215i
$933$	675.224	+	1024.96i	0.723713	+	1.09857i
$934$	−153.456	+	421.616i	−0.164300	+	0.451409i
$935$	−21.9358	+	65.1841i	−0.0234607	+	0.0697156i
$936$	59.6534	+	56.1122i	0.0637323	+	0.0599489i
$937$	1546.75	+	414.451i	1.65075	+	0.442317i	0.959823	−	0.280606i	$-0.0905354\pi$
$937$	1546.75	+	414.451i	1.65075	+	0.442317i	0.690928	+	0.722923i	$0.257202\pi$
$938$	37.8443	−	54.0473i	0.0403457	−	0.0576197i
$939$	−128.965	−	875.882i	−0.137343	−	0.932782i
$940$	173.482	+	284.200i	0.184555	+	0.302340i
$941$	246.491	−	1397.92i	0.261946	−	1.48557i	−0.515646	−	0.856802i	$-0.672448\pi$
$941$	246.491	−	1397.92i	0.261946	−	1.48557i	0.777592	−	0.628769i	$-0.216441\pi$
$942$	−776.183	−	821.478i	−0.823973	−	0.872057i
$943$	−9.13889	−	0.799549i	−0.00969129	−	0.000847878i
$944$		−	256.495i		−	0.271711i
$945$	15.8374	−	106.339i	0.0167591	−	0.112528i
$946$	402.867			0.425864
$947$	15.5050	−	177.223i	0.0163728	−	0.187142i	−0.983604	−	0.180341i	$-0.942280\pi$
$947$	15.5050	−	177.223i	0.0163728	−	0.187142i	0.999977	−	0.00680044i	$-0.00216466\pi$
$948$	−114.054	−	479.639i	−0.120310	−	0.505948i
$949$	273.319	+	48.1935i	0.288007	+	0.0507835i
$950$	4.90338	−	127.738i	0.00516145	−	0.134461i
$951$	−64.5994	−	81.5741i	−0.0679279	−	0.0857772i
$952$	4.19357	+	2.93637i	0.00440501	+	0.00308442i
$953$	97.6401	−	364.398i	0.102456	−	0.382369i	−0.895589	−	0.444883i	$-0.853245\pi$
$953$	97.6401	−	364.398i	0.102456	−	0.382369i	0.998044	+	0.0625140i	$0.0199118\pi$
$954$	−1049.98	+	124.312i	−1.10060	+	0.130306i
$955$	1138.12	−	564.987i	1.19174	−	0.591609i
$956$	3.49145	+	1.27078i	0.00365215	+	0.00132927i
$957$	−32.9837	−	559.124i	−0.0344657	−	0.584247i
$958$	−66.8315	−	763.888i	−0.0697615	−	0.797378i
$959$	−79.5841	+	94.8446i	−0.0829865	+	0.0988995i
$960$	−59.5949	−	104.156i	−0.0620780	−	0.108496i
$961$	903.042	+	328.680i	0.939690	+	0.342019i
$962$	21.7525	+	81.1814i	0.0226117	+	0.0843881i
$963$	−1444.72	+	300.557i	−1.50023	+	0.312105i
$964$	565.309	−	326.381i	0.586420	−	0.338570i
$965$	846.345	−	331.694i	0.877042	−	0.343724i
$966$	−1.40630	+	3.54758i	−0.00145580	+	0.00367244i
$967$	297.044	−	637.012i	0.307181	−	0.658751i	−0.690747	−	0.723096i	$-0.742718\pi$
$967$	297.044	−	637.012i	0.307181	−	0.658751i	0.997928	+	0.0643456i	$0.0204960\pi$
$968$	195.479	−	136.876i	0.201941	−	0.141401i
$969$	11.7161	+	21.6902i	0.0120910	+	0.0223841i
$970$	−32.8411	−	292.746i	−0.0338568	−	0.301799i
$971$	189.252			0.194905			0.0974523	−	0.995240i	$-0.468931\pi$
$971$	189.252			0.194905			0.0974523	+	0.995240i	$0.468931\pi$
$972$	26.4492	−	485.280i	0.0272111	−	0.499259i
$973$	−76.3640	−	76.3640i	−0.0784830	−	0.0784830i
$974$	530.578	+	632.318i	0.544741	+	0.649197i
$975$	151.267	−	187.989i	0.155146	−	0.192809i
$976$	−39.5723	+	224.426i	−0.0405454	+	0.229944i
$977$	228.843	−	490.755i	0.234230	−	0.502308i	−0.753698	−	0.657221i	$-0.771732\pi$
$977$	228.843	−	490.755i	0.234230	−	0.502308i	0.987928	+	0.154913i	$0.0495097\pi$
$978$	1259.84	−	544.556i	1.28818	−	0.556806i
$979$	197.054	−	34.7460i	0.201281	−	0.0354913i
$980$	−30.3619	+	482.704i	−0.0309816	+	0.492555i
$981$	−427.294	+	651.784i	−0.435570	+	0.664408i
$982$	−60.7606	−	226.762i	−0.0618744	−	0.230918i
$983$	−100.045	−	214.547i	−0.101775	−	0.218258i	0.848826	−	0.528672i	$-0.177310\pi$
$983$	−100.045	−	214.547i	−0.101775	−	0.218258i	−0.950601	+	0.310414i	$0.899532\pi$
$984$	65.4061	−	21.7274i	0.0664696	−	0.0220807i
$985$	−1312.06	−	715.331i	−1.33204	−	0.726224i
$986$	−75.9533	−	63.7324i	−0.0770317	−	0.0646373i
$987$	4.68466	+	79.4122i	0.00474636	+	0.0804582i
$988$	9.83200	+	21.0848i	0.00995142	+	0.0213409i
$989$	46.0393	+	26.5808i	0.0465514	+	0.0268764i
$990$	365.992	−	119.999i	0.369688	−	0.121211i
$991$	−502.082	−	869.631i	−0.506642	−	0.877529i	−0.999970	−	0.00768622i	$-0.997553\pi$
$991$	−502.082	−	869.631i	−0.506642	−	0.877529i	0.493329	−	0.869843i	$-0.335780\pi$
$992$	−0.241536	−	0.169125i	−0.000243484	−	0.000170489i
$993$	−35.2235	+	303.318i	−0.0354718	+	0.305456i
$994$	−27.3775	−	75.2190i	−0.0275427	−	0.0756730i
$995$	296.612	+	282.451i	0.298103	+	0.283871i
$996$	388.497	+	239.229i	0.390057	+	0.240189i
$997$	−27.0761	+	309.482i	−0.0271576	+	0.310413i	0.970451	+	0.241298i	$0.0775731\pi$
$997$	−27.0761	+	309.482i	−0.0271576	+	0.310413i	−0.997609	+	0.0691150i	$0.977982\pi$
$998$	348.073	+	348.073i	0.348771	+	0.348771i
$999$	285.156	−	409.190i	0.285441	−	0.409599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.q.a.103.18	yes	216
5.2	odd	4	inner	270.3.q.a.157.11	yes	216
27.16	even	9	inner	270.3.q.a.43.11	✓	216
135.97	odd	36	inner	270.3.q.a.97.18	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.q.a.43.11	✓	216	27.16	even	9	inner
270.3.q.a.97.18	yes	216	135.97	odd	36	inner
270.3.q.a.103.18	yes	216	1.1	even	1	trivial
270.3.q.a.157.11	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} +(2.87461 + 0.858266i) q^{3} +(-1.96962 - 0.347296i) q^{4} +(4.85982 + 1.17564i) q^{5} +(1.56347 - 3.94405i) q^{6} +(-0.652359 - 0.456787i) q^{7} +(-0.732051 + 2.73205i) q^{8} +(7.52676 + 4.93436i) q^{9} +(2.25528 - 6.70177i) q^{10} +(5.68724 + 2.06999i) q^{11} +(-5.36380 - 2.68880i) q^{12} +(-0.280399 - 3.20497i) q^{13} +(-0.723944 + 0.862763i) q^{14} +(12.9611 + 7.55052i) q^{15} +(3.75877 + 1.36808i) q^{16} +(0.588231 + 2.19531i) q^{17} +(7.87941 - 9.99574i) q^{18} +(3.13122 - 1.80781i) q^{19} +(-9.16369 - 4.00335i) q^{20} +(-1.48323 - 1.87298i) q^{21} +(3.61725 - 7.75723i) q^{22} +(0.925190 - 0.647825i) q^{23} +(-4.44919 + 7.22528i) q^{24} +(22.2357 + 11.4268i) q^{25} -4.54983 q^{26} +(17.4015 + 20.6443i) q^{27} +(1.12626 + 1.12626i) q^{28} +(-19.8287 - 23.6309i) q^{29} +(12.2350 - 17.3293i) q^{30} +(0.00905133 - 0.0513327i) q^{31} +(2.39069 - 5.12685i) q^{32} +(14.5720 + 10.8316i) q^{33} +(3.16532 - 0.558132i) q^{34} +(-2.63333 - 2.98684i) q^{35} +(-13.1111 - 12.3328i) q^{36} +(-4.78095 - 17.8427i) q^{37} +(-2.16096 - 4.63420i) q^{38} +(1.94468 - 9.45370i) q^{39} +(-6.76954 + 12.4167i) q^{40} +(-6.22209 - 5.22095i) q^{41} +(-2.82154 + 1.85877i) q^{42} +(19.8921 + 42.6587i) q^{43} +(-10.4828 - 6.05223i) q^{44} +(30.7777 + 32.8289i) q^{45} +(-0.798641 - 1.38329i) q^{46} +(-27.2749 - 19.0981i) q^{47} +(9.63082 + 7.15872i) q^{48} +(-16.5421 - 45.4490i) q^{49} +(18.8391 - 29.9180i) q^{50} +(-0.193225 + 6.81551i) q^{51} +(-0.560797 + 6.40994i) q^{52} +(-58.7394 - 58.7394i) q^{53} +(31.2292 - 21.9712i) q^{54} +(25.2054 + 16.7459i) q^{55} +(1.72553 - 1.44789i) q^{56} +(10.5526 - 2.50933i) q^{57} +(-35.7359 + 25.0226i) q^{58} +(-21.9317 - 60.2567i) q^{59} +(-22.9061 - 19.3730i) q^{60} +(9.89307 + 56.1064i) q^{61} +(-0.0712035 - 0.0190789i) q^{62} +(-2.65620 - 6.65710i) q^{63} +(-6.92820 - 4.00000i) q^{64} +(2.40520 - 15.9052i) q^{65} +(17.0560 - 19.1944i) q^{66} +(-58.3601 + 5.10585i) q^{67} +(-0.396166 - 4.52820i) q^{68} +(3.21557 - 1.06818i) q^{69} +(-4.53254 + 3.34178i) q^{70} +(-35.5365 + 61.5510i) q^{71} +(-18.9909 + 16.9513i) q^{72} +(-22.3272 + 83.3263i) q^{73} +(-25.7267 + 4.53631i) q^{74} +(54.1119 + 51.9317i) q^{75} +(-6.79516 + 2.47323i) q^{76} +(-2.76458 - 3.94823i) q^{77} +(-13.0790 - 3.90496i) q^{78} +(52.8171 + 62.9449i) q^{79} +(16.6586 + 11.0676i) q^{80} +(32.3042 + 74.2795i) q^{81} +(-8.12236 + 8.12236i) q^{82} +(-75.7516 - 6.62741i) q^{83} +(2.27092 + 4.20418i) q^{84} +(0.277810 + 11.3604i) q^{85} +(62.5507 - 22.7666i) q^{86} +(-36.7181 - 84.9478i) q^{87} +(-9.81865 + 14.0225i) q^{88} +(28.6318 - 16.5306i) q^{89} +(50.0439 - 39.3142i) q^{90} +(-1.28107 + 2.21888i) q^{91} +(-2.04726 + 0.954651i) q^{92} +(0.0700761 - 0.139793i) q^{93} +(-30.2678 + 36.0717i) q^{94} +(17.3425 - 5.10446i) q^{95} +(11.2725 - 12.6858i) q^{96} +(37.7569 - 17.6063i) q^{97} +(-66.0689 + 17.7031i) q^{98} +(32.5924 + 43.6432i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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