LMFDB - Embedded newform 270.3.q.a.103.7

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			103.7
Character	$\chi$	$=$	270.103
Dual form			270.3.q.a.97.7

$q$-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} +(-1.44746 - 2.62771i) q^{3} +(-1.96962 - 0.347296i) q^{4} +(2.62607 + 4.25485i) q^{5} +(-3.88041 + 1.71535i) q^{6} +(4.27007 + 2.98993i) q^{7} +(-0.732051 + 2.73205i) q^{8} +(-4.80969 + 7.60703i) q^{9} +(6.31805 - 3.17526i) q^{10} +(15.1478 + 5.51335i) q^{11} +(1.93835 + 5.67827i) q^{12} +(1.55269 + 17.7473i) q^{13} +(4.73863 - 5.64727i) q^{14} +(7.37935 - 13.0593i) q^{15} +(3.75877 + 1.36808i) q^{16} +(-4.75767 - 17.7559i) q^{17} +(10.1242 + 7.71367i) q^{18} +(13.8079 - 7.97198i) q^{19} +(-3.69466 - 9.29244i) q^{20} +(1.67590 - 15.5483i) q^{21} +(9.63445 - 20.6611i) q^{22} +(-28.1579 + 19.7163i) q^{23} +(8.23865 - 2.03093i) q^{24} +(-11.2075 + 22.3471i) q^{25} +25.1943 q^{26} +(26.9509 + 1.62757i) q^{27} +(-7.37199 - 7.37199i) q^{28} +(21.3277 + 25.4174i) q^{29} +(-17.4888 - 12.0059i) q^{30} +(9.37711 - 53.1802i) q^{31} +(2.39069 - 5.12685i) q^{32} +(-7.43843 - 47.7843i) q^{33} +(-25.6014 + 4.51422i) q^{34} +(-1.50821 + 26.0203i) q^{35} +(12.1151 - 13.3125i) q^{36} +(-9.82224 - 36.6571i) q^{37} +(-9.52926 - 20.4356i) q^{38} +(44.3872 - 29.7686i) q^{39} +(-13.5469 + 4.05980i) q^{40} +(23.6451 + 19.8406i) q^{41} +(-21.6984 - 4.27750i) q^{42} +(5.99495 + 12.8562i) q^{43} +(-27.9206 - 16.1199i) q^{44} +(-44.9974 - 0.487922i) q^{45} +(24.3064 + 42.0999i) q^{46} +(40.5758 + 28.4115i) q^{47} +(-1.84577 - 11.8572i) q^{48} +(-7.46522 - 20.5105i) q^{49} +(30.1019 + 18.5439i) q^{50} +(-39.7706 + 38.2027i) q^{51} +(3.10537 - 35.4946i) q^{52} +(-4.96152 - 4.96152i) q^{53} +(5.61486 - 37.7687i) q^{54} +(16.3207 + 78.9300i) q^{55} +(-11.2945 + 9.47725i) q^{56} +(-40.9344 - 24.7439i) q^{57} +(38.4376 - 26.9143i) q^{58} +(34.7007 + 95.3395i) q^{59} +(-19.0699 + 23.1590i) q^{60} +(-0.982624 - 5.57274i) q^{61} +(-73.7662 - 19.7656i) q^{62} +(-43.2822 + 18.1018i) q^{63} +(-6.92820 - 4.00000i) q^{64} +(-71.4345 + 53.2121i) q^{65} +(-68.2370 + 4.58975i) q^{66} +(-4.32587 + 0.378465i) q^{67} +(3.20423 + 36.6245i) q^{68} +(92.5663 + 45.4519i) q^{69} +(36.4723 + 5.33199i) q^{70} +(-30.5433 + 52.9025i) q^{71} +(-17.2618 - 18.7091i) q^{72} +(29.5458 - 110.267i) q^{73} +(-52.8543 + 9.31965i) q^{74} +(74.9440 - 2.89661i) q^{75} +(-29.9648 + 10.9063i) q^{76} +(48.1975 + 68.8332i) q^{77} +(-36.4679 - 66.2033i) q^{78} +(51.8225 + 61.7596i) q^{79} +(4.04983 + 19.5857i) q^{80} +(-34.7337 - 73.1749i) q^{81} +(30.8665 - 30.8665i) q^{82} +(-96.3552 - 8.42999i) q^{83} +(-8.70075 + 30.0421i) q^{84} +(63.0545 - 66.8713i) q^{85} +(18.8512 - 6.86126i) q^{86} +(35.9183 - 92.8337i) q^{87} +(-26.1517 + 37.3485i) q^{88} +(-16.9858 + 9.80676i) q^{89} +(-6.23363 + 63.3336i) q^{90} +(-46.4331 + 80.4244i) q^{91} +(62.3076 - 29.0545i) q^{92} +(-153.315 + 52.3362i) q^{93} +(45.0283 - 53.6626i) q^{94} +(70.1800 + 37.8154i) q^{95} +(-16.9323 + 1.13890i) q^{96} +(-105.578 + 49.2318i) q^{97} +(-29.8160 + 7.98918i) q^{98} +(-114.796 + 88.7122i) 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
$3$	−1.44746	−	2.62771i	−0.482488	−	0.875903i
$3$	−1.44746	−	2.62771i	−0.482488	−	0.875903i
$4$	−1.96962	−	0.347296i	−0.492404	−	0.0868241i
$5$	2.62607	+	4.25485i	0.525215	+	0.850970i
$5$	2.62607	+	4.25485i	0.525215	+	0.850970i
$6$	−3.88041	+	1.71535i	−0.646735	+	0.285892i
$7$	4.27007	+	2.98993i	0.610009	+	0.427133i	0.837338	−	0.546685i	$-0.184110\pi$
$7$	4.27007	+	2.98993i	0.610009	+	0.427133i	−0.227329	+	0.973818i	$0.572999\pi$
$8$	−0.732051	+	2.73205i	−0.0915064	+	0.341506i
$9$	−4.80969	+	7.60703i	−0.534410	+	0.845225i
$10$	6.31805	−	3.17526i	0.631805	−	0.317526i
$11$	15.1478	+	5.51335i	1.37707	+	0.501213i	0.921289	−	0.388878i	$-0.127137\pi$
$11$	15.1478	+	5.51335i	1.37707	+	0.501213i	0.455783	+	0.890091i	$0.349359\pi$
$12$	1.93835	+	5.67827i	0.161530	+	0.473189i
$13$	1.55269	+	17.7473i	0.119437	+	1.36518i	0.785307	+	0.619107i	$0.212505\pi$
$13$	1.55269	+	17.7473i	0.119437	+	1.36518i	−0.665869	+	0.746068i	$0.731939\pi$
$14$	4.73863	−	5.64727i	0.338473	−	0.403377i
$15$	7.37935	−	13.0593i	0.491957	−	0.870620i
$16$	3.75877	+	1.36808i	0.234923	+	0.0855050i
$17$	−4.75767	−	17.7559i	−0.279863	−	1.04446i	−0.952512	−	0.304501i	$-0.901510\pi$
$17$	−4.75767	−	17.7559i	−0.279863	−	1.04446i	0.672649	−	0.739961i	$-0.265156\pi$
$18$	10.1242	+	7.71367i	0.562455	+	0.428537i
$19$	13.8079	−	7.97198i	0.726730	−	0.419578i	−0.0904946	−	0.995897i	$-0.528845\pi$
$19$	13.8079	−	7.97198i	0.726730	−	0.419578i	0.817225	+	0.576319i	$0.195511\pi$
$20$	−3.69466	−	9.29244i	−0.184733	−	0.464622i
$21$	1.67590	−	15.5483i	0.0798047	−	0.740395i
$22$	9.63445	−	20.6611i	0.437929	−	0.939143i
$23$	−28.1579	+	19.7163i	−1.22425	+	0.857232i	−0.993281	−	0.115728i	$-0.963080\pi$
$23$	−28.1579	+	19.7163i	−1.22425	+	0.857232i	−0.230973	+	0.972960i	$0.574191\pi$
$24$	8.23865	−	2.03093i	0.343277	−	0.0846221i
$25$	−11.2075	+	22.3471i	−0.448299	+	0.893883i
$26$	25.1943			0.969012
$27$	26.9509	+	1.62757i	0.998181	+	0.0602804i
$28$	−7.37199	−	7.37199i	−0.263285	−	0.263285i
$29$	21.3277	+	25.4174i	0.735438	+	0.876461i	0.996033	−	0.0889873i	$-0.0283630\pi$
$29$	21.3277	+	25.4174i	0.735438	+	0.876461i	−0.260595	+	0.965448i	$0.583919\pi$
$30$	−17.4888	−	12.0059i	−0.582960	−	0.400197i
$31$	9.37711	−	53.1802i	0.302487	−	1.71549i	−0.332615	−	0.943063i	$-0.607931\pi$
$31$	9.37711	−	53.1802i	0.302487	−	1.71549i	0.635102	−	0.772428i	$-0.280958\pi$
$32$	2.39069	−	5.12685i	0.0747091	−	0.160214i
$33$	−7.43843	−	47.7843i	−0.225407	−	1.44801i
$34$	−25.6014	+	4.51422i	−0.752983	+	0.132771i
$35$	−1.50821	+	26.0203i	−0.0430917	+	0.743436i
$36$	12.1151	−	13.3125i	0.336532	−	0.369792i
$37$	−9.82224	−	36.6571i	−0.265466	−	0.990732i	−0.961965	−	0.273174i	$-0.911926\pi$
$37$	−9.82224	−	36.6571i	−0.265466	−	0.990732i	0.696499	−	0.717558i	$-0.254740\pi$
$38$	−9.52926	−	20.4356i	−0.250770	−	0.537778i
$39$	44.3872	−	29.7686i	1.13813	−	0.763296i
$40$	−13.5469	+	4.05980i	−0.338672	+	0.101495i
$41$	23.6451	+	19.8406i	0.576710	+	0.483917i	0.883865	−	0.467742i	$-0.154933\pi$
$41$	23.6451	+	19.8406i	0.576710	+	0.483917i	−0.307155	+	0.951660i	$0.599377\pi$
$42$	−21.6984	−	4.27750i	−0.516628	−	0.101845i
$43$	5.99495	+	12.8562i	0.139417	+	0.298982i	0.963603	−	0.267339i	$-0.0861442\pi$
$43$	5.99495	+	12.8562i	0.139417	+	0.298982i	−0.824185	+	0.566320i	$0.808366\pi$
$44$	−27.9206	−	16.1199i	−0.634558	−	0.366362i
$45$	−44.9974	−	0.487922i	−0.999941	−	0.0108427i
$46$	24.3064	+	42.0999i	0.528399	+	0.915214i
$47$	40.5758	+	28.4115i	0.863316	+	0.604500i	0.919136	−	0.393941i	$-0.128888\pi$
$47$	40.5758	+	28.4115i	0.863316	+	0.604500i	−0.0558202	+	0.998441i	$0.517777\pi$
$48$	−1.84577	−	11.8572i	−0.0384536	−	0.247025i
$49$	−7.46522	−	20.5105i	−0.152351	−	0.418582i
$50$	30.1019	+	18.5439i	0.602038	+	0.370878i
$51$	−39.7706	+	38.2027i	−0.779816	+	0.749073i
$52$	3.10537	−	35.4946i	0.0597187	−	0.682588i
$53$	−4.96152	−	4.96152i	−0.0936135	−	0.0936135i	0.658749	−	0.752363i	$-0.271086\pi$
$53$	−4.96152	−	4.96152i	−0.0936135	−	0.0936135i	−0.752363	+	0.658749i	$0.771086\pi$
$54$	5.61486	−	37.7687i	0.103979	−	0.699420i
$55$	16.3207	+	78.9300i	0.296741	+	1.43509i
$56$	−11.2945	+	9.47725i	−0.201688	+	0.169237i
$57$	−40.9344	−	24.7439i	−0.718148	−	0.434103i
$58$	38.4376	−	26.9143i	0.662717	−	0.464040i
$59$	34.7007	+	95.3395i	0.588148	+	1.61592i	0.773886	+	0.633325i	$0.218310\pi$
$59$	34.7007	+	95.3395i	0.588148	+	1.61592i	−0.185738	+	0.982599i	$0.559468\pi$
$60$	−19.0699	+	23.1590i	−0.317832	+	0.385983i
$61$	−0.982624	−	5.57274i	−0.0161086	−	0.0913564i	0.975694	−	0.219139i	$-0.0703250\pi$
$61$	−0.982624	−	5.57274i	−0.0161086	−	0.0913564i	−0.991802	+	0.127783i	$0.959214\pi$
$62$	−73.7662	−	19.7656i	−1.18978	−	0.318800i
$63$	−43.2822	+	18.1018i	−0.687019	+	0.287331i
$64$	−6.92820	−	4.00000i	−0.108253	−	0.0625000i
$65$	−71.4345	+	53.2121i	−1.09899	+	0.818647i
$66$	−68.2370	+	4.58975i	−1.03389	+	0.0695417i
$67$	−4.32587	+	0.378465i	−0.0645652	+	0.00564873i	−0.119393	−	0.992847i	$-0.538095\pi$
$67$	−4.32587	+	0.378465i	−0.0645652	+	0.00564873i	0.0548274	+	0.998496i	$0.482539\pi$
$68$	3.20423	+	36.6245i	0.0471210	+	0.538596i
$69$	92.5663	+	45.4519i	1.34154	+	0.658723i
$70$	36.4723	+	5.33199i	0.521033	+	0.0761713i
$71$	−30.5433	+	52.9025i	−0.430187	+	0.745106i	−0.996889	−	0.0788169i	$-0.974886\pi$
$71$	−30.5433	+	52.9025i	−0.430187	+	0.745106i	0.566702	+	0.823923i	$0.308219\pi$
$72$	−17.2618	−	18.7091i	−0.239748	−	0.259848i
$73$	29.5458	−	110.267i	0.404738	−	1.51050i	−0.399802	−	0.916602i	$-0.630921\pi$
$73$	29.5458	−	110.267i	0.404738	−	1.51050i	0.804539	−	0.593900i	$-0.202412\pi$
$74$	−52.8543	+	9.31965i	−0.714248	+	0.125941i
$75$	74.9440	−	2.89661i	0.999254	−	0.0386215i
$76$	−29.9648	+	10.9063i	−0.394274	+	0.143504i
$77$	48.1975	+	68.8332i	0.625942	+	0.893938i
$78$	−36.4679	−	66.2033i	−0.467537	−	0.848760i
$79$	51.8225	+	61.7596i	0.655981	+	0.781768i	0.986803	−	0.161926i	$-0.0517704\pi$
$79$	51.8225	+	61.7596i	0.655981	+	0.781768i	−0.330822	+	0.943693i	$0.607326\pi$
$80$	4.04983	+	19.5857i	0.0506228	+	0.244821i
$81$	−34.7337	−	73.1749i	−0.428811	−	0.903394i
$82$	30.8665	−	30.8665i	0.376421	−	0.376421i
$83$	−96.3552	−	8.42999i	−1.16091	−	0.101566i	−0.509621	−	0.860399i	$-0.670214\pi$
$83$	−96.3552	−	8.42999i	−1.16091	−	0.101566i	−0.651286	+	0.758833i	$0.725770\pi$
$84$	−8.70075	+	30.0421i	−0.103580	+	0.357645i
$85$	63.0545	−	66.8713i	0.741818	−	0.786721i
$86$	18.8512	−	6.86126i	0.219200	−	0.0797821i
$87$	35.9183	−	92.8337i	0.412854	−	1.06705i
$88$	−26.1517	+	37.3485i	−0.297178	+	0.424415i
$89$	−16.9858	+	9.80676i	−0.190852	+	0.110188i	−0.592381	−	0.805658i	$-0.701812\pi$
$89$	−16.9858	+	9.80676i	−0.190852	+	0.110188i	0.401529	+	0.915846i	$0.368479\pi$
$90$	−6.23363	+	63.3336i	−0.0692626	+	0.703706i
$91$	−46.4331	+	80.4244i	−0.510254	+	0.883785i
$92$	62.3076	−	29.0545i	0.677256	−	0.315810i
$93$	−153.315	+	52.3362i	−1.64855	+	0.562754i
$94$	45.0283	−	53.6626i	0.479024	−	0.570879i
$95$	70.1800	+	37.8154i	0.738737	+	0.398057i
$96$	−16.9323	+	1.13890i	−0.176378	+	0.0118635i
$97$	−105.578	+	49.2318i	−1.08843	+	0.507545i	−0.882160	−	0.470950i	$-0.843911\pi$
$97$	−105.578	+	49.2318i	−1.08843	+	0.507545i	−0.206273	+	0.978494i	$0.566134\pi$
$98$	−29.8160	+	7.98918i	−0.304245	+	0.0815223i
$99$	−114.796	+	88.7122i	−1.15956	+	0.896082i
$100$	29.8355	−	40.1228i	0.298355	−	0.401228i
$101$	6.61040	+	37.4894i	0.0654495	+	0.371183i	0.999887	+	0.0150545i	$0.00479218\pi$
$101$	6.61040	+	37.4894i	0.0654495	+	0.371183i	−0.934437	+	0.356128i	$0.884097\pi$
$102$	48.9192	+	60.7389i	0.479600	+	0.595479i
$103$	62.2028	+	29.0057i	0.603911	+	0.281608i	0.700428	−	0.713723i	$-0.252992\pi$
$103$	62.2028	+	29.0057i	0.603911	+	0.281608i	−0.0965171	+	0.995331i	$0.530770\pi$
$104$	−49.6231	−	8.74989i	−0.477145	−	0.0841336i
$105$	70.5567	−	33.7003i	0.671969	−	0.320955i
$106$	−7.60148	+	6.37840i	−0.0717121	+	0.0601736i
$107$	112.517	−	112.517i	1.05156	−	1.05156i	0.0529635	−	0.998596i	$-0.483133\pi$
$107$	112.517	−	112.517i	1.05156	−	1.05156i	0.998596	−	0.0529635i	$-0.0168667\pi$
$108$	−52.5177	−	12.5656i	−0.486275	−	0.116349i
$109$		−	124.089i		−	1.13843i	−0.822188	−	0.569215i	$-0.807247\pi$
$109$		−	124.089i		−	1.13843i	0.822188	−	0.569215i	$-0.192753\pi$
$110$	113.211	−	13.2645i	1.02919	−	0.120587i
$111$	−82.1068	+	78.8698i	−0.739701	+	0.710539i
$112$	11.9597	+	17.0803i	0.106783	+	0.152502i
$113$	−136.570	−	63.6838i	−1.20859	−	0.563573i	−0.289329	−	0.957230i	$-0.593432\pi$
$113$	−136.570	−	63.6838i	−1.20859	−	0.563573i	−0.919258	+	0.393656i	$0.871210\pi$
$114$	−39.9054	+	54.6199i	−0.350048	+	0.479122i
$115$	−157.835	−	68.0309i	−1.37247	−	0.591573i
$116$	−33.1800	−	57.4695i	−0.286035	−	0.495427i
$117$	−142.472	−	73.5477i	−1.21771	−	0.628612i
$118$	138.594	−	37.1363i	1.17453	−	0.314714i
$119$	32.7732	−	90.0438i	0.275405	−	0.756670i
$120$	30.2766	+	29.7208i	0.252305	+	0.247674i
$121$	106.367	+	89.2528i	0.879069	+	0.737626i
$122$	−7.97217	+	0.697475i	−0.0653457	+	0.00571700i
$123$	17.9098	−	90.8510i	0.145609	−	0.738626i
$124$	−36.9386	+	101.488i	−0.297892	+	0.818451i
$125$	−124.515	+	10.9989i	−0.996121	+	0.0879912i
$126$	20.1676	+	63.2085i	0.160061	+	0.501655i
$127$	−52.5085	−	14.0696i	−0.413453	−	0.110784i	0.0460957	−	0.998937i	$-0.485322\pi$
$127$	−52.5085	−	14.0696i	−0.413453	−	0.110784i	−0.459548	+	0.888153i	$0.651989\pi$
$128$	−6.48928	+	9.26765i	−0.0506975	+	0.0724035i
$129$	25.1049	−	34.3619i	0.194612	−	0.266371i
$130$	66.1621	+	107.198i	0.508939	+	0.824600i
$131$	26.8116	−	152.056i	0.204669	−	1.16073i	−0.693292	−	0.720657i	$-0.743840\pi$
$131$	26.8116	−	152.056i	0.204669	−	1.16073i	0.897960	−	0.440077i	$-0.145049\pi$
$132$	−1.94448	+	96.7001i	−0.0147309	+	0.732577i
$133$	82.7962	+	7.24373i	0.622528	+	0.0544641i
$134$			6.14107i			0.0458289i
$135$	63.8499	+	118.946i	0.472963	+	0.881083i
$136$	51.9928			0.382300
$137$	−1.53357	+	17.5288i	−0.0111939	+	0.127947i	−0.999735	−	0.0230022i	$-0.992678\pi$
$137$	−1.53357	+	17.5288i	−0.0111939	+	0.127947i	0.988541	+	0.150950i	$0.0482331\pi$
$138$	75.4435	−	124.808i	0.546692	−	0.904406i
$139$	54.3175	+	9.57763i	0.390773	+	0.0689038i	0.365583	−	0.930779i	$-0.380870\pi$
$139$	54.3175	+	9.57763i	0.390773	+	0.0689038i	0.0251903	+	0.999683i	$0.491981\pi$
$140$	12.0073	−	50.7261i	0.0857667	−	0.362329i
$141$	15.9251	−	147.746i	0.112944	−	1.04784i
$142$	70.7661	+	49.5510i	0.498353	+	0.348950i
$143$	−74.3271	+	277.393i	−0.519770	+	1.93981i
$144$	−28.4856	+	22.0130i	−0.197816	+	0.152868i
$145$	−52.1390	+	157.494i	−0.359579	+	1.08617i
$146$	−151.705	−	55.2162i	−1.03908	−	0.378193i
$147$	−43.0900	+	49.3047i	−0.293130	+	0.335406i
$148$	6.61516	+	75.6116i	0.0446970	+	0.510889i
$149$	18.5330	−	22.0868i	0.124383	−	0.148234i	−0.700259	−	0.713889i	$-0.746932\pi$
$149$	18.5330	−	22.0868i	0.124383	−	0.148234i	0.824642	+	0.565655i	$0.191377\pi$
$150$	5.15652	−	105.941i	0.0343768	−	0.706271i
$151$	−0.0631467	−	0.0229835i	−0.000418190	−	0.000152209i	0.341811	−	0.939769i	$-0.388960\pi$
$151$	−0.0631467	−	0.0229835i	−0.000418190	−	0.000152209i	−0.342229	+	0.939616i	$0.611182\pi$
$152$	11.6718	+	43.5597i	0.0767881	+	0.286577i
$153$	157.952	+	49.2085i	1.03237	+	0.321624i
$154$	102.915	−	59.4181i	0.668280	−	0.385832i
$155$	250.899	−	99.7569i	1.61870	−	0.643593i
$156$	−97.7642	+	43.2171i	−0.626694	+	0.277033i
$157$	20.1025	−	43.1099i	0.128041	−	0.274585i	−0.831828	−	0.555034i	$-0.812705\pi$
$157$	20.1025	−	43.1099i	0.128041	−	0.274585i	0.959869	+	0.280448i	$0.0904831\pi$
$158$	93.3964	−	65.3969i	0.591117	−	0.413904i
$159$	−5.85580	+	20.2190i	−0.0368289	+	0.127164i
$160$	28.0921	−	3.29146i	0.175576	−	0.0205716i
$161$	−179.186			−1.11296
$162$	−107.372	+	39.9146i	−0.662792	+	0.246387i
$163$	−220.421	−	220.421i	−1.35228	−	1.35228i	−0.883110	−	0.469166i	$-0.844555\pi$
$163$	−220.421	−	220.421i	−1.35228	−	1.35228i	−0.469166	−	0.883110i	$-0.655445\pi$
$164$	−39.6812	−	47.2902i	−0.241959	−	0.288355i
$165$	183.781	−	157.135i	1.11383	−	0.952331i
$166$	−23.7529	+	134.709i	−0.143090	+	0.811502i
$167$	−1.03414	+	2.21773i	−0.00619248	+	0.0132798i	−0.909380	−	0.415967i	$-0.863443\pi$
$167$	−1.03414	+	2.21773i	−0.00619248	+	0.0132798i	0.903187	+	0.429247i	$0.141221\pi$
$168$	41.2519	+	15.9608i	0.245547	+	0.0950047i
$169$	−146.122	+	25.7653i	−0.864630	+	0.152458i
$170$	−86.4386	−	97.0756i	−0.508462	−	0.571033i
$171$	−5.76859	+	143.380i	−0.0337345	+	0.838477i
$172$	−7.34283	−	27.4038i	−0.0426909	−	0.159325i
$173$	46.1309	+	98.9280i	0.266652	+	0.571838i	0.993352	−	0.115118i	$-0.0367245\pi$
$173$	46.1309	+	98.9280i	0.266652	+	0.571838i	−0.726699	+	0.686956i	$0.758947\pi$
$174$	−126.360	−	62.0453i	−0.726206	−	0.356582i
$175$	−114.673	+	61.9139i	−0.655274	+	0.353794i
$176$	49.3944	+	41.4468i	0.280650	+	0.235493i
$177$	200.296	−	229.184i	1.13162	−	1.29482i
$178$	11.7225	+	25.1389i	0.0658565	+	0.141230i
$179$	−206.170	−	119.032i	−1.15179	−	0.664983i	−0.202464	−	0.979290i	$-0.564895\pi$
$179$	−206.170	−	119.032i	−1.15179	−	0.664983i	−0.949322	+	0.314306i	$0.898228\pi$
$180$	88.4580	+	16.5884i	0.491434	+	0.0921580i
$181$	−117.770	−	203.984i	−0.650666	−	1.12699i	−0.982962	−	0.183811i	$-0.941157\pi$
$181$	−117.770	−	203.984i	−0.650666	−	1.12699i	0.332296	−	0.943175i	$-0.392177\pi$
$182$	107.581	+	75.3293i	0.591106	+	0.413897i
$183$	−13.2212	+	10.6484i	−0.0722471	+	0.0581879i
$184$	−33.2531	−	91.3620i	−0.180723	−	0.496533i
$185$	130.176	−	138.056i	0.703657	−	0.746250i
$186$	54.8357	+	222.446i	0.294816	+	1.19595i
$187$	25.8260	−	295.193i	0.138107	−	1.57857i
$188$	−70.0516	−	70.0516i	−0.372615	−	0.372615i
$189$	110.216	+	87.5312i	0.583152	+	0.463128i
$190$	61.9258	−	94.2109i	0.325925	−	0.495847i
$191$	115.883	−	97.2376i	0.606719	−	0.509097i	−0.286879	−	0.957967i	$-0.592618\pi$
$191$	115.883	−	97.2376i	0.606719	−	0.509097i	0.893597	+	0.448869i	$0.148173\pi$
$192$	−0.482503	+	23.9951i	−0.00251304	+	0.124975i
$193$	220.915	−	154.686i	1.14464	−	0.801482i	0.161956	−	0.986798i	$-0.448220\pi$
$193$	220.915	−	154.686i	1.14464	−	0.801482i	0.982679	+	0.185316i	$0.0593308\pi$
$194$	56.3462	+	154.810i	0.290444	+	0.797989i
$195$	243.225	+	110.686i	1.24731	+	0.567623i
$196$	7.58039	+	42.9905i	0.0386754	+	0.219339i
$197$	110.325	+	29.5616i	0.560027	+	0.150059i	0.527719	−	0.849419i	$-0.323047\pi$
$197$	110.325	+	29.5616i	0.560027	+	0.150059i	0.0323084	+	0.999478i	$0.489714\pi$
$198$	110.831	+	172.663i	0.559753	+	0.872037i
$199$	151.282	+	87.3426i	0.760210	+	0.438908i	0.829371	−	0.558698i	$-0.188699\pi$
$199$	151.282	+	87.3426i	0.760210	+	0.438908i	−0.0691610	+	0.997606i	$0.522032\pi$
$200$	−52.8489	−	46.9786i	−0.264245	−	0.234893i
$201$	7.25604	+	10.8193i	0.0360997	+	0.0538274i
$202$	53.6311	−	4.69211i	0.265500	−	0.0232283i
$203$	15.0745	+	172.302i	0.0742586	+	0.848779i
$204$	91.6005	−	61.4325i	0.449022	−	0.301140i
$205$	−22.3250	+	152.709i	−0.108902	+	0.744923i
$206$	48.5310	−	84.0582i	0.235587	−	0.408049i
$207$	−14.5521	−	309.027i	−0.0702998	−	1.49288i
$208$	−18.4435	+	68.8321i	−0.0886707	+	0.330924i
$209$	253.111	−	44.6303i	1.21106	−	0.213542i
$210$	−38.7814	−	103.556i	−0.184673	−	0.493125i
$211$	−124.232	+	45.2168i	−0.588778	+	0.214298i	−0.619192	−	0.785240i	$-0.712540\pi$
$211$	−124.232	+	45.2168i	−0.588778	+	0.214298i	0.0304138	+	0.999537i	$0.490317\pi$
$212$	8.04916	+	11.4954i	0.0379677	+	0.0542236i
$213$	183.223	+	3.68431i	0.860200	+	0.0172972i
$214$	−144.649	−	172.386i	−0.675930	−	0.805542i
$215$	−38.9581	+	59.2690i	−0.181200	+	0.275670i
$216$	−24.1760	+	72.4398i	−0.111926	+	0.335369i
$217$	199.046	−	199.046i	0.917263	−	0.917263i
$218$	−174.820	−	15.2948i	−0.801929	−	0.0701597i
$219$	−332.515	+	81.9691i	−1.51833	+	0.374288i
$220$	−4.73349	−	161.130i	−0.0215159	−	0.732409i
$221$	307.731	−	112.005i	1.39245	−	0.506809i
$222$	100.994	+	125.396i	0.454928	+	0.564846i
$223$	−43.0492	+	61.4806i	−0.193046	+	0.275698i	−0.903993	−	0.427548i	$-0.859378\pi$
$223$	−43.0492	+	61.4806i	−0.193046	+	0.275698i	0.710947	+	0.703246i	$0.248267\pi$
$224$	25.5373	−	14.7440i	0.114006	−	0.0658214i
$225$	−116.090	−	192.738i	−0.515957	−	0.856615i
$226$	−106.553	+	184.555i	−0.471473	+	0.816616i
$227$	−113.386	+	52.8727i	−0.499497	+	0.232919i	−0.656004	−	0.754758i	$-0.727754\pi$
$227$	−113.386	+	52.8727i	−0.499497	+	0.232919i	0.156507	+	0.987677i	$0.449977\pi$
$228$	72.0316	+	62.9523i	0.315928	+	0.276107i
$229$	−6.30753	+	7.51702i	−0.0275438	+	0.0328254i	−0.779640	−	0.626227i	$-0.784598\pi$
$229$	−6.30753	+	7.51702i	−0.0275438	+	0.0328254i	0.752097	+	0.659053i	$0.229043\pi$
$230$	−115.298	+	213.977i	−0.501297	+	0.930336i
$231$	111.109	−	226.283i	0.480993	−	0.979579i
$232$	−85.0545	+	39.6616i	−0.366614	+	0.170955i
$233$	−214.972	+	57.6015i	−0.922626	+	0.247217i	−0.688708	−	0.725039i	$-0.741822\pi$
$233$	−214.972	+	57.6015i	−0.922626	+	0.247217i	−0.233919	+	0.972256i	$0.575155\pi$
$234$	−121.177	+	191.654i	−0.517850	+	0.819033i
$235$	−14.3316	+	247.255i	−0.0609855	+	1.05215i
$236$	−35.2361	−	199.834i	−0.149305	−	0.846753i
$237$	87.2751	−	225.569i	0.368249	−	0.951769i
$238$	−122.817	−	57.2705i	−0.516038	−	0.240632i
$239$	322.885	+	56.9333i	1.35098	+	0.238215i	0.801853	−	0.597522i	$-0.203848\pi$
$239$	322.885	+	56.9333i	1.35098	+	0.238215i	0.549130	+	0.835737i	$0.314959\pi$
$240$	45.6035	−	38.9913i	0.190014	−	0.162464i
$241$	−268.887	+	225.623i	−1.11571	+	0.936194i	−0.998380	−	0.0568989i	$-0.981879\pi$
$241$	−268.887	+	225.623i	−1.11571	+	0.936194i	−0.117332	+	0.993093i	$0.537434\pi$
$242$	138.853	−	138.853i	0.573771	−	0.573771i
$243$	−142.007	+	197.188i	−0.584389	+	0.811474i
$244$			11.3174i			0.0463829i
$245$	67.6650	−	85.6255i	0.276184	−	0.349492i
$246$	−125.786	−	36.4300i	−0.511326	−	0.148089i
$247$	162.920	+	232.674i	0.659596	+	0.942001i
$248$	138.427	+	64.5493i	0.558171	+	0.260280i
$249$	117.319	+	265.396i	0.471162	+	1.06585i
$250$	0.148262	+	176.777i	0.000593047	+	0.707107i
$251$	8.84668	+	15.3229i	0.0352457	+	0.0610474i	0.883110	−	0.469166i	$-0.155445\pi$
$251$	8.84668	+	15.3229i	0.0352457	+	0.0610474i	−0.847864	+	0.530213i	$0.822112\pi$
$252$	91.5360	−	20.6219i	0.363238	−	0.0818330i
$253$	−535.232	+	143.415i	−2.11554	+	0.566858i
$254$	−26.2937	+	72.2415i	−0.103519	+	0.284415i
$255$	−266.987	−	68.8950i	−1.04701	−	0.270176i
$256$	12.2567	+	10.2846i	0.0478778	+	0.0401742i
$257$	−465.800	+	40.7522i	−1.81245	+	0.158569i	−0.942421	−	0.334429i	$-0.891457\pi$
$257$	−465.800	+	40.7522i	−1.81245	+	0.158569i	−0.870031	+	0.492998i	$0.835901\pi$
$258$	−45.3158	−	39.6039i	−0.175643	−	0.153504i
$259$	67.6606	−	185.896i	0.261238	−	0.717745i
$260$	159.179	−	79.9984i	0.612227	−	0.307686i
$261$	−295.930	+	39.9906i	−1.13383	+	0.153221i
$262$	−210.917	−	56.5150i	−0.805026	−	0.215706i
$263$	197.107	−	281.498i	0.749457	−	1.07034i	−0.245437	−	0.969413i	$-0.578931\pi$
$263$	197.107	−	281.498i	0.749457	−	1.07034i	0.994894	−	0.100923i	$-0.0321796\pi$
$264$	135.995	+	14.6584i	0.515131	+	0.0555242i
$265$	8.08120	−	34.1398i	0.0304951	−	0.128829i
$266$	20.4104	−	115.753i	0.0767308	−	0.435162i
$267$	50.3557	+	30.4388i	0.188598	+	0.114003i
$268$	8.65174	+	0.756929i	0.0322826	+	0.00282436i
$269$			127.519i			0.474050i	0.971504	+	0.237025i	$0.0761723\pi$
$269$			127.519i			0.474050i	−0.971504	+	0.237025i	$0.923828\pi$
$270$	175.445	−	75.2929i	0.649797	−	0.278863i
$271$	309.350			1.14151			0.570756	−	0.821120i	$-0.306650\pi$
$271$	309.350			1.14151			0.570756	+	0.821120i	$0.306650\pi$
$272$	6.40846	−	73.2491i	0.0235605	−	0.269298i
$273$	278.542	+	5.60103i	1.02030	+	0.0205166i
$274$	24.5061	+	4.32109i	0.0894383	+	0.0157704i
$275$	−292.976	+	276.718i	−1.06537	+	1.00625i
$276$	−166.535	−	121.671i	−0.603386	−	0.440836i
$277$	−136.147	−	95.3308i	−0.491504	−	0.344155i	0.301404	−	0.953497i	$-0.402545\pi$
$277$	−136.147	−	95.3308i	−0.491504	−	0.344155i	−0.792908	+	0.609342i	$0.791434\pi$
$278$	20.1883	−	75.3437i	0.0726197	−	0.271020i
$279$	359.442	+	327.112i	1.28832	+	1.17245i
$280$	−69.9846	−	23.1687i	−0.249945	−	0.0827452i
$281$	−122.307	−	44.5162i	−0.435257	−	0.158420i	0.115093	−	0.993355i	$-0.463283\pi$
$281$	−122.307	−	44.5162i	−0.435257	−	0.158420i	−0.550350	+	0.834934i	$0.685506\pi$
$282$	−206.187	−	40.6464i	−0.731158	−	0.144136i
$283$	2.42060	+	27.6676i	0.00855336	+	0.0977653i	0.999271	−	0.0381681i	$-0.0121522\pi$
$283$	2.42060	+	27.6676i	0.00855336	+	0.0977653i	−0.990718	+	0.135933i	$0.956597\pi$
$284$	78.5314	−	93.5901i	0.276519	−	0.329542i
$285$	−2.21524	−	239.149i	−0.00777276	−	0.839120i
$286$	381.638	+	138.905i	1.33440	+	0.485682i
$287$	41.6441	+	155.418i	0.145101	+	0.541526i
$288$	27.5016	+	42.8446i	0.0954917	+	0.148766i
$289$	−42.3536	+	24.4529i	−0.146552	+	0.0846121i
$290$	215.456	+	92.8673i	0.742952	+	0.320232i
$291$	282.187	+	206.167i	0.969716	+	0.708477i
$292$	−96.4891	+	206.922i	−0.330442	+	0.708636i
$293$	−136.187	+	95.3595i	−0.464804	+	0.325459i	−0.782410	−	0.622764i	$-0.786010\pi$
$293$	−136.187	+	95.3595i	−0.464804	+	0.325459i	0.317606	+	0.948223i	$0.397121\pi$
$294$	64.1509	+	66.7838i	0.218200	+	0.227156i
$295$	−314.529	+	398.015i	−1.06620	+	1.34920i
$296$	107.339			0.362633
$297$	399.273	+	173.244i	1.34435	+	0.583312i
$298$	−28.8323	−	28.8323i	−0.0967526	−	0.0967526i
$299$	−393.632	−	469.112i	−1.31649	−	1.56894i
$300$	−148.617	−	20.3226i	−0.495390	−	0.0677419i
$301$	−12.8404	+	72.8214i	−0.0426590	+	0.241931i
$302$	−0.0401632	+	0.0861302i	−0.000132991	+	0.000285199i
$303$	88.9430	−	71.6348i	0.293541	−	0.236419i
$304$	62.8069	−	11.0746i	0.206602	−	0.0364295i
$305$	21.1307	−	18.8153i	0.0692811	−	0.0616896i
$306$	88.7952	−	216.463i	0.290181	−	0.707395i
$307$	44.6680	+	166.703i	0.145498	+	0.543007i	0.999733	+	0.0231190i	$0.00735967\pi$
$307$	44.6680	+	166.703i	0.145498	+	0.543007i	−0.854234	+	0.519888i	$0.825974\pi$
$308$	−71.0251	−	152.314i	−0.230601	−	0.494525i
$309$	−13.8180	−	205.435i	−0.0447184	−	0.664840i
$310$	−109.616	−	365.770i	−0.353599	−	1.17990i
$311$	−288.924	−	242.436i	−0.929017	−	0.779538i	0.0466240	−	0.998913i	$-0.485154\pi$
$311$	−288.924	−	242.436i	−0.929017	−	0.779538i	−0.975641	+	0.219375i	$0.929598\pi$
$312$	48.8355	+	143.060i	0.156524	+	0.458526i
$313$	−65.8309	−	141.175i	−0.210322	−	0.451037i	0.772640	−	0.634844i	$-0.218936\pi$
$313$	−65.8309	−	141.175i	−0.210322	−	0.451037i	−0.982962	+	0.183807i	$0.941158\pi$
$314$	−58.2569	−	33.6346i	−0.185531	−	0.107117i
$315$	−190.683	−	136.622i	−0.605342	−	0.433722i
$316$	−80.6215	−	139.641i	−0.255131	−	0.441900i
$317$	117.836	+	82.5096i	0.371722	+	0.260283i	0.744478	−	0.667647i	$-0.232698\pi$
$317$	117.836	+	82.5096i	0.371722	+	0.260283i	−0.372756	+	0.927929i	$0.621587\pi$
$318$	27.7635	+	10.7420i	0.0873065	+	0.0337798i
$319$	182.933	+	502.604i	0.573457	+	1.57556i
$320$	−1.17457	−	39.9828i	−0.00367052	−	0.124946i
$321$	−458.526	−	132.797i	−1.42843	−	0.413699i
$322$	−22.0859	+	252.444i	−0.0685899	+	0.783986i
$323$	−207.243	−	207.243i	−0.641618	−	0.641618i
$324$	42.9986	+	156.189i	0.132712	+	0.482066i
$325$	−414.002	−	164.204i	−1.27385	−	0.505244i
$326$	−337.705	+	283.368i	−1.03590	+	0.869226i
$327$	−326.069	+	179.614i	−0.997154	+	0.549279i
$328$	−71.5149	+	50.0753i	−0.218033	+	0.152669i
$329$	88.3130	+	242.638i	0.268429	+	0.737501i
$330$	−198.724	−	278.285i	−0.602194	−	0.843288i
$331$	−30.8906	−	175.190i	−0.0933252	−	0.529274i	−0.995248	−	0.0973756i	$-0.968955\pi$
$331$	−30.8906	−	175.190i	−0.0933252	−	0.529274i	0.901923	−	0.431898i	$-0.142156\pi$
$332$	186.855	+	50.0677i	0.562817	+	0.150806i
$333$	326.093	+	101.591i	0.979260	+	0.305079i
$334$	2.99694	+	1.73029i	0.00897288	+	0.00518050i
$335$	−12.9704	−	17.4121i	−0.0387175	−	0.0519763i
$336$	27.5707	−	56.1497i	0.0820555	−	0.167112i
$337$	−418.489	+	36.6130i	−1.24181	+	0.108644i	−0.689059	−	0.724705i	$-0.741976\pi$
$337$	−418.489	+	36.6130i	−1.24181	+	0.108644i	−0.552747	+	0.833349i	$0.686420\pi$
$338$	18.2884	+	209.038i	0.0541078	+	0.618455i
$339$	30.3383	+	451.047i	0.0894935	+	1.33052i
$340$	−147.417	+	109.812i	−0.433580	+	0.322977i
$341$	435.243	−	753.864i	1.27637	−	2.21074i
$342$	201.287	+	25.7995i	0.588558	+	0.0754371i
$343$	95.5574	−	356.625i	0.278593	−	1.03972i
$344$	−39.5124	+	6.96711i	−0.114862	+	0.0202532i
$345$	49.6947	+	513.215i	0.144043	+	1.48758i
$346$	145.059	−	52.7971i	0.419245	−	0.152593i
$347$	69.5273	+	99.2952i	0.200367	+	0.286153i	0.906743	−	0.421683i	$-0.138560\pi$
$347$	69.5273	+	99.2952i	0.200367	+	0.286153i	−0.706377	+	0.707836i	$0.749672\pi$
$348$	−102.986	+	170.372i	−0.295937	+	0.489576i
$349$	−438.094	−	522.100i	−1.25528	−	1.49599i	−0.792956	−	0.609279i	$-0.791459\pi$
$349$	−438.094	−	522.100i	−1.25528	−	1.49599i	−0.462327	−	0.886709i	$-0.652985\pi$
$350$	73.0920	+	169.186i	0.208834	+	0.483389i
$351$	12.9613	+	480.832i	0.0369268	+	1.36989i
$352$	64.4798	−	64.4798i	0.183181	−	0.183181i
$353$	560.545	+	49.0413i	1.58795	+	0.138927i	0.846612	−	0.532210i	$-0.178638\pi$
$353$	560.545	+	49.0413i	1.58795	+	0.138927i	0.741333	+	0.671138i	$0.234194\pi$
$354$	−298.194	−	310.432i	−0.842355	−	0.876927i
$355$	−305.301	+	8.96878i	−0.860003	+	0.0252642i
$356$	36.8614	−	13.4164i	0.103543	−	0.0376866i
$357$	−284.047	+	44.2166i	−0.795649	+	0.123856i
$358$	−193.108	+	275.787i	−0.539408	+	0.770354i
$359$	−155.812	+	89.9578i	−0.434015	+	0.250579i	−0.701056	−	0.713106i	$-0.747288\pi$
$359$	−155.812	+	89.9578i	−0.434015	+	0.250579i	0.267040	+	0.963685i	$0.413954\pi$
$360$	34.2734	−	122.578i	0.0952038	−	0.340494i
$361$	−53.3951	+	92.4830i	−0.147909	+	0.256186i
$362$	−301.896	+	140.776i	−0.833966	+	0.388885i
$363$	80.5673	−	408.692i	0.221948	−	1.12587i
$364$	119.386	−	142.279i	0.327985	−	0.390877i
$365$	546.757	−	163.855i	1.49797	−	0.448918i
$366$	13.3722	+	19.9390i	0.0365360	+	0.0544780i
$367$	−96.9202	+	45.1946i	−0.264088	+	0.123146i	−0.550153	−	0.835064i	$-0.685430\pi$
$367$	−96.9202	+	45.1946i	−0.264088	+	0.123146i	0.286065	+	0.958210i	$0.407653\pi$
$368$	−132.812	+	35.5870i	−0.360903	+	0.0967038i
$369$	−264.654	+	84.4417i	−0.717219	+	0.228839i
$370$	−178.453	−	200.413i	−0.482306	−	0.541657i
$371$	−6.35140	−	36.0206i	−0.0171197	−	0.0970905i
$372$	320.148	−	49.8364i	0.860613	−	0.133969i
$373$	142.256	+	66.3349i	0.381383	+	0.177842i	0.603849	−	0.797099i	$-0.293633\pi$
$373$	142.256	+	66.3349i	0.381383	+	0.177842i	−0.222466	+	0.974940i	$0.571411\pi$
$374$	−412.694	−	72.7690i	−1.10346	−	0.194570i
$375$	209.133	+	311.269i	0.557688	+	0.830050i
$376$	−107.325	+	90.0566i	−0.285439	+	0.239512i
$377$	−417.974	+	417.974i	−1.10868	+	1.10868i
$378$	136.902	−	144.487i	0.362174	−	0.382240i
$379$		−	121.521i		−	0.320635i	−0.987065	−	0.160318i	$-0.948748\pi$
$379$		−	121.521i		−	0.320635i	0.987065	−	0.160318i	$-0.0512519\pi$
$380$	−125.095	−	98.8551i	−0.329196	−	0.260145i
$381$	39.0334	+	158.342i	0.102450	+	0.415596i
$382$	−122.708	−	175.245i	−0.321225	−	0.458757i
$383$	−173.366	−	80.8418i	−0.452652	−	0.211075i	0.182902	−	0.983131i	$-0.441451\pi$
$383$	−173.366	−	80.8418i	−0.452652	−	0.211075i	−0.635555	+	0.772056i	$0.719229\pi$
$384$	33.7457	+	3.63733i	0.0878793	+	0.00947222i
$385$	−166.305	+	385.834i	−0.431960	+	1.00217i
$386$	−190.697	−	330.298i	−0.494035	−	0.855694i
$387$	−126.631	−	16.2307i	−0.327213	−	0.0419398i
$388$	225.046	−	60.3009i	0.580016	−	0.155415i
$389$	−38.3638	+	105.404i	−0.0986216	+	0.270961i	−0.979186	−	0.202966i	$-0.934942\pi$
$389$	−38.3638	+	105.404i	−0.0986216	+	0.270961i	0.880564	+	0.473927i	$0.157164\pi$
$390$	185.918	−	329.020i	0.476712	−	0.843641i
$391$	484.046	+	406.163i	1.23797	+	1.03878i
$392$	61.5007	−	5.38062i	0.156890	−	0.0137261i
$393$	−438.368	+	149.643i	−1.11544	+	0.380770i
$394$	55.2457	−	151.786i	0.140217	−	0.385244i
$395$	−126.688	+	382.682i	−0.320730	+	0.968816i
$396$	256.914	−	134.860i	0.648773	−	0.340557i
$397$	−87.6170	−	23.4769i	−0.220698	−	0.0591358i	0.146776	−	0.989170i	$-0.453110\pi$
$397$	−87.6170	−	23.4769i	−0.220698	−	0.0591358i	−0.367473	+	0.930034i	$0.619777\pi$
$398$	141.698	−	202.365i	0.356024	−	0.508455i
$399$	−100.810	−	228.049i	−0.252657	−	0.571552i
$400$	−72.6990	+	68.6648i	−0.181747	+	0.171662i
$401$	5.33556	−	30.2595i	0.0133056	−	0.0754601i	−0.977432	−	0.211251i	$-0.932246\pi$
$401$	5.33556	−	30.2595i	0.0133056	−	0.0754601i	0.990738	+	0.135791i	$0.0433575\pi$
$402$	16.1369	−	8.88898i	0.0401417	−	0.0221119i
$403$	958.364	+	83.8460i	2.37807	+	0.208054i
$404$		−	76.1355i		−	0.188454i
$405$	220.135	−	339.949i	0.543544	−	0.839381i
$406$	244.603			0.602470
$407$	53.3180	−	609.427i	0.131002	−	1.49736i
$408$	−75.2577	−	136.622i	−0.184455	−	0.334857i
$409$	258.118	+	45.5131i	0.631095	+	0.111279i	0.480040	−	0.877246i	$-0.340622\pi$
$409$	258.118	+	45.5131i	0.631095	+	0.111279i	0.151054	+	0.988525i	$0.451733\pi$
$410$	212.390	+	50.2746i	0.518024	+	0.122621i
$411$	48.2803	−	21.3425i	0.117470	−	0.0519283i
$412$	−112.442	−	78.7328i	−0.272918	−	0.191099i
$413$	−136.884	+	510.859i	−0.331439	+	1.23695i
$414$	−437.161	−	17.5883i	−1.05594	−	0.0424838i
$415$	−217.168	−	432.115i	−0.523295	−	1.04124i
$416$	94.6996	+	34.4678i	0.227643	+	0.0828554i
$417$	−53.4554	−	156.594i	−0.128190	−	0.375524i
$418$	−31.6789	−	362.092i	−0.0757870	−	0.866249i
$419$	250.534	−	298.575i	0.597934	−	0.712590i	−0.379176	−	0.925325i	$-0.623793\pi$
$419$	250.534	−	298.575i	0.597934	−	0.712590i	0.977110	+	0.212735i	$0.0682370\pi$
$420$	−150.674	+	41.8725i	−0.358747	+	0.0996964i
$421$	141.713	+	51.5793i	0.336610	+	0.122516i	0.504795	−	0.863239i	$-0.331568\pi$
$421$	141.713	+	51.5793i	0.336610	+	0.122516i	−0.168184	+	0.985756i	$0.553790\pi$
$422$	48.3904	+	180.596i	0.114669	+	0.427952i
$423$	−411.284	+	172.011i	−0.972304	+	0.406645i
$424$	17.1872	−	9.92303i	0.0405358	−	0.0234034i
$425$	450.113	+	92.6785i	1.05909	+	0.218067i
$426$	27.7740	−	257.676i	0.0651972	−	0.604873i
$427$	12.4662	−	26.7339i	0.0291949	−	0.0626088i
$428$	−260.692	+	182.538i	−0.609093	+	0.426491i
$429$	836.492	−	206.206i	1.94987	−	0.480667i
$430$	78.6982	+	62.1907i	0.183019	+	0.144630i
$431$	388.292			0.900910			0.450455	−	0.892799i	$-0.351262\pi$
$431$	388.292			0.900910			0.450455	+	0.892799i	$0.351262\pi$
$432$	99.0756	+	42.9887i	0.229342	+	0.0995108i
$433$	−22.2797	−	22.2797i	−0.0514543	−	0.0514543i	0.680911	−	0.732366i	$-0.261584\pi$
$433$	−22.2797	−	22.2797i	−0.0514543	−	0.0514543i	−0.732366	+	0.680911i	$0.761584\pi$
$434$	−255.889	−	304.956i	−0.589605	−	0.702664i
$435$	489.318	−	90.9610i	1.12487	−	0.209106i
$436$	−43.0956	+	244.408i	−0.0988432	+	0.560568i
$437$	−231.622	+	496.715i	−0.530027	+	1.13665i
$438$	74.4960	+	478.561i	0.170082	+	1.09260i
$439$	757.803	−	133.621i	1.72620	−	0.304376i	0.779480	−	0.626428i	$-0.215484\pi$
$439$	757.803	−	133.621i	1.72620	−	0.304376i	0.946722	+	0.322052i	$0.104372\pi$
$440$	−227.588	−	13.1917i	−0.517247	−	0.0299811i
$441$	191.930	+	41.8612i	0.435214	+	0.0949234i
$442$	−119.866	−	447.347i	−0.271190	−	1.01210i
$443$	−163.361	−	350.328i	−0.368760	−	0.790808i	−0.999886	−	0.0151278i	$-0.995185\pi$
$443$	−163.361	−	350.328i	−0.368760	−	0.790808i	0.631126	−	0.775681i	$-0.282593\pi$
$444$	189.110	−	126.828i	0.425923	−	0.285648i
$445$	−86.3323	−	46.5188i	−0.194005	−	0.104537i
$446$	81.3098	+	68.2270i	0.182309	+	0.152975i
$447$	−84.8636	−	16.7295i	−0.189851	−	0.0374262i
$448$	−17.6242	−	37.7951i	−0.0393396	−	0.0843641i
$449$	152.938	+	88.2986i	0.340618	+	0.196656i	0.660545	−	0.750786i	$-0.270325\pi$
$449$	152.938	+	88.2986i	0.340618	+	0.196656i	−0.319927	+	0.947442i	$0.603658\pi$
$450$	−285.845	+	139.795i	−0.635211	+	0.310656i
$451$	248.783	+	430.905i	0.551625	+	0.955443i
$452$	246.874	+	172.863i	0.546181	+	0.382440i
$453$	0.0310086	+	0.199199i	6.84517e−5	+	0.000439733i
$454$	60.5131	+	166.258i	0.133289	+	0.366208i
$455$	−464.131	+	13.6347i	−1.02007	+	0.0299663i
$456$	97.5677	−	93.7212i	0.213964	−	0.205529i
$457$	0.222898	−	2.54773i	0.000487742	−	0.00557491i	−0.995947	−	0.0899429i	$-0.971332\pi$
$457$	0.222898	−	2.54773i	0.000487742	−	0.00557491i	0.996435	+	0.0843679i	$0.0268871\pi$
$458$	9.81277	+	9.81277i	0.0214253	+	0.0214253i
$459$	−99.3245	−	486.280i	−0.216393	−	1.05943i
$460$	287.247	+	188.810i	0.624449	+	0.410457i
$461$	489.473	−	410.717i	1.06176	−	0.890926i	0.0674834	−	0.997720i	$-0.478503\pi$
$461$	489.473	−	410.717i	1.06176	−	0.890926i	0.994281	+	0.106794i	$0.0340586\pi$
$462$	−305.099	−	184.425i	−0.660388	−	0.399189i
$463$	249.262	−	174.535i	0.538362	−	0.376965i	−0.272542	−	0.962144i	$-0.587864\pi$
$463$	249.262	−	174.535i	0.538362	−	0.376965i	0.810904	+	0.585179i	$0.198976\pi$
$464$	45.3929	+	124.716i	0.0978296	+	0.268785i
$465$	−625.299	−	514.894i	−1.34473	−	1.10730i
$466$	54.6542	+	309.959i	0.117284	+	0.665148i
$467$	739.883	+	198.251i	1.58433	+	0.424521i	0.940264	−	0.340447i	$-0.110578\pi$
$467$	739.883	+	198.251i	1.58433	+	0.424521i	0.644069	+	0.764967i	$0.277245\pi$
$468$	255.072	+	194.341i	0.545026	+	0.415258i
$469$	−19.6033	−	11.3180i	−0.0417982	−	0.0241322i
$470$	346.574	+	50.6666i	0.737391	+	0.107801i
$471$	−142.378	+	9.57662i	−0.302288	+	0.0203325i
$472$	−285.875	+	25.0108i	−0.605668	+	0.0529891i
$473$	19.9295	+	227.796i	0.0421343	+	0.481597i
$474$	−307.032	−	150.759i	−0.647747	−	0.318057i
$475$	23.3990	+	397.912i	0.0492610	+	0.837709i
$476$	−95.8226	+	165.970i	−0.201308	+	0.348676i
$477$	61.6058	−	13.8790i	0.129153	−	0.0290964i
$478$	120.007	−	447.873i	0.251061	−	0.936973i
$479$	−454.918	+	80.2144i	−0.949725	+	0.167462i	−0.626990	−	0.779027i	$-0.715713\pi$
$479$	−454.918	+	80.2144i	−0.949725	+	0.167462i	−0.322735	+	0.946489i	$0.604602\pi$
$480$	−49.3113	−	69.0536i	−0.102732	−	0.143862i
$481$	635.313	−	231.235i	1.32082	−	0.480738i
$482$	284.722	+	406.626i	0.590710	+	0.843622i
$483$	259.366	+	470.849i	0.536989	+	0.974843i
$484$	−178.506	−	212.735i	−0.368813	−	0.439534i
$485$	−486.730	−	319.932i	−1.00357	−	0.659654i
$486$	260.302	+	224.368i	0.535600	+	0.461663i
$487$	−106.860	+	106.860i	−0.219426	+	0.219426i	−0.808257	−	0.588831i	$-0.799589\pi$
$487$	−106.860	+	106.860i	−0.219426	+	0.219426i	0.588831	+	0.808257i	$0.299589\pi$
$488$	15.9443	+	1.39495i	0.0326728	+	0.00285850i
$489$	−260.150	+	898.253i	−0.532005	+	1.83692i
$490$	−112.292	−	105.883i	−0.229167	−	0.216087i
$491$	389.402	−	141.731i	0.793079	−	0.288657i	0.0864639	−	0.996255i	$-0.472443\pi$
$491$	389.402	−	141.731i	0.793079	−	0.288657i	0.706616	+	0.707598i	$0.250221\pi$
$492$	−66.8277	+	172.721i	−0.135829	+	0.351060i
$493$	349.837	−	499.619i	0.709609	−	1.01343i
$494$	347.880	−	200.849i	0.704210	−	0.406576i
$495$	−678.921	−	255.477i	−1.37156	−	0.516115i
$496$	108.001	−	187.064i	0.217744	−	0.377144i
$497$	−288.597	+	134.575i	−0.580678	+	0.270774i
$498$	388.358	−	132.571i	0.779836	−	0.266207i
$499$	150.013	−	178.778i	0.300626	−	0.358273i	−0.594492	−	0.804102i	$-0.702647\pi$
$499$	150.013	−	178.778i	0.300626	−	0.358273i	0.895118	+	0.445829i	$0.147091\pi$
$500$	249.067	+	21.5801i	0.498134	+	0.0431601i
$501$	7.32443	−	0.492656i	0.0146196	−	0.000983345i
$502$	22.6778	−	10.5748i	0.0451749	−	0.0210654i
$503$	−286.809	+	76.8502i	−0.570197	+	0.152784i	−0.532387	−	0.846501i	$-0.678705\pi$
$503$	−286.809	+	76.8502i	−0.570197	+	0.152784i	−0.0378099	+	0.999285i	$0.512038\pi$
$504$	−17.7704	−	131.501i	−0.0352587	−	0.260914i
$505$	−142.153	+	126.576i	−0.281490	+	0.250646i
$506$	136.077	+	771.729i	0.268926	+	1.52516i
$507$	279.211	+	346.673i	0.550712	+	0.683773i
$508$	98.5352	+	45.9477i	0.193967	+	0.0904483i
$509$	−705.434	−	124.387i	−1.38592	−	0.244375i	−0.569576	−	0.821939i	$-0.692892\pi$
$509$	−705.434	−	124.387i	−1.38592	−	0.244375i	−0.816346	+	0.577564i	$0.804004\pi$
$510$	−129.969	+	367.649i	−0.254842	+	0.720880i
$511$	455.852	−	382.505i	0.892079	−	0.748543i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	385.110	−	192.379i	0.750701	−	0.375007i
$514$			661.257i			1.28649i
$515$	39.9344	+	340.835i	0.0775426	+	0.661815i
$516$	−61.3808	+	58.9609i	−0.118955	+	0.114265i
$517$	457.992	+	654.080i	0.885864	+	1.26515i
$518$	−253.557	−	118.235i	−0.489492	−	0.228254i
$519$	193.181	−	264.413i	0.372218	−	0.509466i
$520$	−93.0844	−	234.117i	−0.179008	−	0.450224i
$521$	172.850	+	299.384i	0.331765	+	0.574634i	0.982858	−	0.184364i	$-0.0590226\pi$
$521$	172.850	+	299.384i	0.331765	+	0.574634i	−0.651093	+	0.758998i	$0.725689\pi$
$522$	19.8647	+	421.845i	0.0380549	+	0.808133i
$523$	−118.195	+	31.6704i	−0.225995	+	0.0605552i	−0.370039	−	0.929016i	$-0.620656\pi$
$523$	−118.195	+	31.6704i	−0.225995	+	0.0605552i	0.144044	+	0.989571i	$0.453989\pi$
$524$	−105.617	+	290.181i	−0.201559	+	0.553780i
$525$	328.677	+	211.709i	0.626051	+	0.403255i
$526$	−372.289	−	312.388i	−0.707774	−	0.593893i
$527$	−988.873	+	86.5152i	−1.87642	+	0.164165i
$528$	37.4135	−	189.787i	0.0708589	−	0.359445i
$529$	223.202	−	613.242i	0.421932	−	1.15925i
$530$	−47.1012	−	15.5930i	−0.0888702	−	0.0294208i
$531$	−892.150	−	194.584i	−1.68013	−	0.366449i
$532$	−160.561	−	43.0222i	−0.301806	−	0.0808687i
$533$	−315.403	+	450.442i	−0.591751	+	0.845108i
$534$	49.0898	−	67.1909i	0.0919285	−	0.125826i
$535$	774.220	+	183.265i	1.44714	+	0.342551i
$536$	2.13277	−	12.0956i	0.00397905	−	0.0225663i
$537$	−14.3583	+	714.048i	−0.0267381	+	1.32970i
$538$	179.653	+	15.7176i	0.333928	+	0.0292149i
$539$		−	351.848i		−	0.652779i
$540$	−84.4503	−	256.453i	−0.156389	−	0.474913i
$541$	228.458			0.422288			0.211144	−	0.977455i	$-0.432281\pi$
$541$	228.458			0.422288			0.211144	+	0.977455i	$0.432281\pi$
$542$	38.1295	−	435.822i	0.0703496	−	0.804099i
$543$	−365.543	+	604.727i	−0.673191	+	1.11368i
$544$	−102.406	−	18.0569i	−0.188246	−	0.0331928i
$545$	527.980	−	325.867i	0.968770	−	0.597920i
$546$	42.2231	−	391.729i	0.0773317	−	0.717452i
$547$	315.351	+	220.811i	0.576510	+	0.403677i	0.825145	−	0.564920i	$-0.191093\pi$
$547$	315.351	+	220.811i	0.576510	+	0.403677i	−0.248635	+	0.968597i	$0.579982\pi$
$548$	9.10823	−	33.9924i	0.0166209	−	0.0620299i
$549$	47.1181	+	19.3283i	0.0858253	+	0.0352064i
$550$	353.738	+	446.861i	0.643161	+	0.812475i
$551$	497.117	+	180.936i	0.902209	+	0.328377i
$552$	−191.940	+	219.623i	−0.347718	+	0.397867i
$553$	36.6283	+	418.663i	0.0662356	+	0.757077i
$554$	−151.086	+	180.057i	−0.272719	+	0.325013i
$555$	−551.197	−	142.234i	−0.993149	−	0.256278i
$556$	−103.658	−	37.7285i	−0.186436	−	0.0678570i
$557$	−87.5631	−	326.790i	−0.157205	−	0.586697i	−0.998906	−	0.0467536i	$-0.985112\pi$
$557$	−87.5631	−	326.790i	−0.157205	−	0.586697i	0.841702	−	0.539943i	$-0.181554\pi$
$558$	505.150	−	466.075i	0.905287	−	0.835260i
$559$	−218.855	+	126.356i	−0.391511	+	0.226039i
$560$	−41.2668	+	95.7408i	−0.0736908	+	0.170966i
$561$	−813.062	+	359.418i	−1.44931	+	0.640673i
$562$	−77.7910	+	166.823i	−0.138418	+	0.296839i
$563$	655.548	−	459.020i	1.16438	−	0.815311i	0.178699	−	0.983904i	$-0.442811\pi$
$563$	655.548	−	459.020i	1.16438	−	0.815311i	0.985686	+	0.168593i	$0.0539224\pi$
$564$	−82.6779	+	285.472i	−0.146592	+	0.506156i
$565$	−87.6787	−	748.325i	−0.155183	−	1.32447i
$566$	39.2773			0.0693946
$567$	70.4730	−	416.313i	0.124291	−	0.734238i
$568$	−122.173	−	122.173i	−0.215094	−	0.215094i
$569$	−676.021	−	805.651i	−1.18809	−	1.41591i	−0.886663	−	0.462416i	$-0.846983\pi$
$569$	−676.021	−	805.651i	−1.18809	−	1.41591i	−0.301423	−	0.953490i	$-0.597462\pi$
$570$	−337.194	−	26.3559i	−0.591568	−	0.0462384i
$571$	81.4821	−	462.108i	0.142701	−	0.809296i	−0.826484	−	0.562960i	$-0.809662\pi$
$571$	81.4821	−	462.108i	0.142701	−	0.809296i	0.969185	−	0.246335i	$-0.0792265\pi$
$572$	242.733	−	520.543i	0.424359	−	0.910041i
$573$	−423.249	−	163.759i	−0.738654	−	0.285793i
$574$	224.091	−	39.5132i	0.390402	−	0.0688384i
$575$	−125.024	−	850.217i	−0.217433	−	1.47864i
$576$	63.7506	−	33.4642i	0.110678	−	0.0580976i
$577$	212.476	+	792.972i	0.368243	+	1.37430i	0.862971	+	0.505253i	$0.168601\pi$
$577$	212.476	+	792.972i	0.368243	+	1.37430i	−0.494728	+	0.869048i	$0.664732\pi$
$578$	29.2296	+	62.6832i	0.0505703	+	0.108448i
$579$	−726.236	−	356.596i	−1.25429	−	0.615883i
$580$	157.391	−	292.095i	0.271364	−	0.503612i
$581$	−386.238	−	324.092i	−0.664782	−	0.557818i
$582$	325.236	−	372.143i	0.558825	−	0.639421i
$583$	−47.8015	−	102.511i	−0.0819922	−	0.175833i
$584$	279.625	+	161.441i	0.478810	+	0.276441i
$585$	−61.2074	−	799.338i	−0.104628	−	1.36639i
$586$	117.559	+	203.619i	0.200613	+	0.347473i
$587$	296.995	+	207.958i	0.505955	+	0.354273i	0.798516	−	0.601973i	$-0.205619\pi$
$587$	296.995	+	207.958i	0.505955	+	0.354273i	−0.292561	+	0.956247i	$0.594508\pi$
$588$	101.994	−	82.1463i	0.173459	−	0.139705i
$589$	−294.474	−	809.060i	−0.499955	−	1.37362i
$590$	521.968	+	492.176i	0.884692	+	0.834197i
$591$	−82.0128	−	332.692i	−0.138770	−	0.562931i
$592$	13.2303	−	151.223i	0.0223485	−	0.255445i
$593$	696.858	+	696.858i	1.17514	+	1.17514i	0.980967	+	0.194173i	$0.0622024\pi$
$593$	696.858	+	696.858i	1.17514	+	1.17514i	0.194173	+	0.980967i	$0.437798\pi$
$594$	293.285	−	541.156i	0.493745	−	0.911036i
$595$	469.188	−	97.0162i	0.788550	−	0.163052i
$596$	−44.1736	+	37.0661i	−0.0741168	+	0.0621914i
$597$	10.5358	−	523.950i	0.0176479	−	0.877638i
$598$	−709.418	+	496.740i	−1.18632	+	0.830668i
$599$	−267.879	−	735.992i	−0.447210	−	1.22870i	−0.934658	−	0.355548i	$-0.884294\pi$
$599$	−267.879	−	735.992i	−0.447210	−	1.22870i	0.487447	−	0.873152i	$-0.337928\pi$
$600$	−46.9492	+	206.871i	−0.0782486	+	0.344786i
$601$	−74.2983	−	421.367i	−0.123624	−	0.701109i	−0.982115	−	0.188280i	$-0.939709\pi$
$601$	−74.2983	−	421.367i	−0.123624	−	0.701109i	0.858491	−	0.512829i	$-0.171402\pi$
$602$	101.010	+	27.0657i	0.167791	+	0.0449596i
$603$	17.9271	−	34.7273i	0.0297299	−	0.0575909i
$604$	0.116393	+	0.0671993i	0.000192703	+	0.000111257i
$605$	−100.429	+	686.961i	−0.165998	+	1.13547i
$606$	−89.9586	−	134.135i	−0.148447	−	0.221345i
$607$	591.627	−	51.7607i	0.974674	−	0.0852729i	0.411322	−	0.911490i	$-0.365067\pi$
$607$	591.627	−	51.7607i	0.974674	−	0.0852729i	0.563352	+	0.826217i	$0.309512\pi$
$608$	−7.86081	−	89.8494i	−0.0129290	−	0.147779i
$609$	430.940	−	289.013i	0.707619	−	0.474569i
$610$	−23.9031	−	32.0888i	−0.0391855	−	0.0526045i
$611$	−441.225	+	764.225i	−0.722136	+	1.25078i
$612$	−294.015	−	151.778i	−0.480417	−	0.248003i
$613$	90.3151	−	337.061i	0.147333	−	0.549854i	−0.852307	−	0.523041i	$-0.824797\pi$
$613$	90.3151	−	337.061i	0.147333	−	0.549854i	0.999640	−	0.0268131i	$-0.00853591\pi$
$614$	240.362	−	42.3824i	0.391470	−	0.0690267i
$615$	433.590	−	162.378i	0.705024	−	0.264029i
$616$	−223.339	+	81.2887i	−0.362563	+	0.131962i
$617$	−8.84321	−	12.6294i	−0.0143326	−	0.0204691i	0.811922	−	0.583766i	$-0.198422\pi$
$617$	−8.84321	−	12.6294i	−0.0143326	−	0.0204691i	−0.826254	+	0.563297i	$0.809533\pi$
$618$	−291.127	−	5.85409i	−0.471080	−	0.00947264i
$619$	490.574	+	584.643i	0.792526	+	0.944496i	0.999426	−	0.0338665i	$-0.0107821\pi$
$619$	490.574	+	584.643i	0.792526	+	0.944496i	−0.206901	+	0.978362i	$0.566338\pi$
$620$	−528.819	+	109.347i	−0.852934	+	0.176365i
$621$	−790.969	+	485.544i	−1.27370	+	0.781875i
$622$	−377.164	+	377.164i	−0.606373	+	0.606373i
$623$	−101.852	−	8.91090i	−0.163486	−	0.0143032i
$624$	207.567	−	51.1679i	0.332640	−	0.0819998i
$625$	−373.785	−	500.909i	−0.598055	−	0.801455i
$626$	−207.006	+	75.3439i	−0.330680	+	0.120358i
$627$	−483.645	−	600.501i	−0.771363	−	0.957737i
$628$	−54.5661	+	77.9284i	−0.0868887	+	0.124090i
$629$	−604.147	+	348.804i	−0.960488	+	0.554538i
$630$	−215.981	+	251.800i	−0.342827	+	0.399683i
$631$	205.499	−	355.934i	0.325671	−	0.564079i	−0.655977	−	0.754781i	$-0.727743\pi$
$631$	205.499	−	355.934i	0.325671	−	0.564079i	0.981648	+	0.190702i	$0.0610764\pi$
$632$	−206.667	+	96.3705i	−0.327005	+	0.152485i
$633$	298.638	+	260.996i	0.471782	+	0.412316i
$634$	130.766	−	155.841i	0.206256	−	0.245806i
$635$	−78.0271	−	260.364i	−0.122877	−	0.410021i
$636$	18.5557	−	37.7900i	0.0291756	−	0.0594183i
$637$	352.415	−	164.334i	0.553242	−	0.257981i
$638$	730.633	−	195.772i	1.14519	−	0.306853i
$639$	−255.527	−	486.789i	−0.399886	−	0.761797i
$640$	−56.4738	−	3.27338i	−0.0882402	−	0.00511466i
$641$	57.2108	+	324.459i	0.0892524	+	0.506176i	0.996358	+	0.0852719i	$0.0271759\pi$
$641$	57.2108	+	324.459i	0.0892524	+	0.506176i	−0.907105	+	0.420904i	$0.861713\pi$
$642$	−243.606	+	629.618i	−0.379448	+	0.980713i
$643$	−893.056	−	416.439i	−1.38889	−	0.647650i	−0.422887	−	0.906183i	$-0.638983\pi$
$643$	−893.056	−	416.439i	−1.38889	−	0.647650i	−0.966002	+	0.258533i	$0.916761\pi$
$644$	352.928	+	62.2308i	0.548025	+	0.0966316i
$645$	212.132	+	16.5807i	0.328887	+	0.0257066i
$646$	−317.514	+	266.426i	−0.491508	+	0.412424i
$647$	393.575	−	393.575i	0.608308	−	0.608308i	−0.334196	−	0.942504i	$-0.608465\pi$
$647$	393.575	−	393.575i	0.608308	−	0.608308i	0.942504	+	0.334196i	$0.108465\pi$
$648$	225.344	−	41.3264i	0.347754	−	0.0637753i
$649$			1635.50i			2.52003i
$650$	−282.365	+	563.019i	−0.434408	+	0.866184i
$651$	−811.147	−	234.923i	−1.24600	−	0.360864i
$652$	357.593	+	510.696i	0.548456	+	0.783276i
$653$	−865.695	−	403.680i	−1.32572	−	0.618193i	−0.374649	−	0.927167i	$-0.622237\pi$
$653$	−865.695	−	403.680i	−1.32572	−	0.618193i	−0.951071	+	0.308974i	$0.900015\pi$
$654$	212.856	+	481.516i	0.325468	+	0.736263i
$655$	717.385	−	285.231i	1.09524	−	0.435467i
$656$	61.7330	+	106.925i	0.0941052	+	0.162995i
$657$	696.694	+	755.105i	1.06042	+	1.14932i
$658$	352.721	−	94.5114i	0.536051	−	0.143634i
$659$	−289.749	+	796.079i	−0.439680	+	1.20801i	0.500021	+	0.866013i	$0.333326\pi$
$659$	−289.749	+	796.079i	−0.439680	+	1.20801i	−0.939701	+	0.341997i	$0.888897\pi$
$660$	−416.551	+	245.668i	−0.631138	+	0.372224i
$661$	259.827	+	218.021i	0.393082	+	0.329835i	0.817812	−	0.575485i	$-0.195187\pi$
$661$	259.827	+	218.021i	0.393082	+	0.329835i	−0.424731	+	0.905320i	$0.639631\pi$
$662$	−250.620	+	21.9264i	−0.378580	+	0.0331215i
$663$	−739.746	−	646.504i	−1.11576	−	0.975119i
$664$	93.5681	−	257.076i	0.140916	−	0.387163i
$665$	186.608	+	371.308i	0.280613	+	0.558358i
$666$	183.318	−	446.889i	0.275253	−	0.671005i
$667$	−1101.68	−	295.194i	−1.65169	−	0.442570i
$668$	2.80708	−	4.00892i	0.00420221	−	0.00600138i
$669$	223.865	+	24.1297i	0.334627	+	0.0360683i
$670$	−26.1293	+	16.1269i	−0.0389990	+	0.0240700i
$671$	15.8399	−	89.8323i	0.0236063	−	0.133878i
$672$	−75.7073	−	45.7633i	−0.112660	−	0.0681001i
$673$	267.923	+	23.4402i	0.398103	+	0.0348295i	0.284450	−	0.958691i	$-0.408189\pi$
$673$	267.923	+	23.4402i	0.398103	+	0.0348295i	0.113653	+	0.993520i	$0.463745\pi$
$674$			594.093i			0.881444i
$675$	−338.423	+	584.033i	−0.501368	+	0.865234i
$676$	296.753			0.438984
$677$	−31.9916	+	365.665i	−0.0472549	+	0.540126i	0.935263	+	0.353955i	$0.115163\pi$
$677$	−31.9916	+	365.665i	−0.0472549	+	0.540126i	−0.982517	+	0.186171i	$0.940392\pi$
$678$	639.189	+	12.8530i	0.942756	+	0.0189573i
$679$	−598.025	−	105.448i	−0.880744	−	0.155299i
$680$	136.537	+	221.221i	0.200789	+	0.325325i
$681$	303.056	+	221.413i	0.445016	+	0.325130i
$682$	−1008.42	−	706.104i	−1.47862	−	1.03534i
$683$	74.2591	−	277.139i	0.108725	−	0.405767i	−0.890016	−	0.455929i	$-0.849307\pi$
$683$	74.2591	−	277.139i	0.108725	−	0.405767i	0.998741	+	0.0501622i	$0.0159738\pi$
$684$	61.1571	−	280.399i	0.0894110	−	0.409941i
$685$	−78.6096	+	39.5068i	−0.114759	+	0.0576741i
$686$	−490.647	−	178.581i	−0.715228	−	0.260322i
$687$	28.8824	+	5.69372i	0.0420414	+	0.00828780i
$688$	4.94531	+	56.5251i	0.00718795	+	0.0821586i
$689$	80.3497	−	95.7571i	0.116618	−	0.138980i
$690$	729.160	−	6.75420i	1.05675	−	0.00978869i
$691$	−1028.15	−	374.217i	−1.48792	−	0.541559i	−0.535020	−	0.844839i	$-0.679696\pi$
$691$	−1028.15	−	374.217i	−1.48792	−	0.541559i	−0.952901	+	0.303280i	$0.901918\pi$
$692$	−56.5027	−	210.871i	−0.0816514	−	0.304727i
$693$	−755.431	+	35.5732i	−1.09009	+	0.0513322i
$694$	148.460	−	85.7134i	0.213919	−	0.123506i
$695$	101.890	+	256.264i	0.146605	+	0.368725i
$696$	227.332	+	166.090i	0.326627	+	0.238635i
$697$	239.791	−	514.234i	0.344033	−	0.737782i
$698$	−789.549	+	552.848i	−1.13116	+	0.792046i
$699$	462.524	+	481.507i	0.661694	+	0.688851i
$700$	247.364	−	82.1211i	0.353377	−	0.117316i
$701$	534.326			0.762233			0.381117	−	0.924527i	$-0.375540\pi$
$701$	534.326			0.762233			0.381117	+	0.924527i	$0.375540\pi$
$702$	679.009	+	41.0055i	0.967250	+	0.0584124i
$703$	−427.854	−	427.854i	−0.608611	−	0.608611i
$704$	−82.8936	−	98.7888i	−0.117747	−	0.140325i
$705$	670.458	−	320.233i	0.951004	−	0.454231i
$706$	138.182	−	783.669i	0.195725	−	1.11001i
$707$	−83.8640	+	179.847i	−0.118620	+	0.254380i
$708$	−474.101	+	381.842i	−0.669635	+	0.539325i
$709$	−1193.74	+	210.488i	−1.68369	+	0.296880i	−0.931952	−	0.362582i	$-0.881895\pi$
$709$	−1193.74	+	210.488i	−1.68369	+	0.296880i	−0.751738	+	0.659462i	$0.770784\pi$
$710$	−24.9949	+	431.224i	−0.0352042	+	0.607357i
$711$	−719.057	+	97.1701i	−1.01133	+	0.136667i
$712$	−14.3581	−	53.5851i	−0.0201659	−	0.0752600i
$713$	784.480	+	1682.32i	1.10025	+	2.35950i
$714$	27.2831	+	405.624i	0.0382116	+	0.568101i
$715$	−1375.45	+	412.202i	−1.92371	+	0.576507i
$716$	364.735	+	306.049i	0.509407	+	0.427443i
$717$	−317.760	−	930.856i	−0.443180	−	1.29827i
$718$	107.531	+	230.600i	0.149764	+	0.321170i
$719$	533.707	+	308.136i	0.742290	+	0.428561i	0.822901	−	0.568184i	$-0.192354\pi$
$719$	533.707	+	308.136i	0.742290	+	0.428561i	−0.0806112	+	0.996746i	$0.525687\pi$
$720$	−168.467	−	63.3940i	−0.233982	−	0.0880472i
$721$	178.885	+	309.838i	0.248107	+	0.429734i
$722$	123.712	+	86.6239i	0.171346	+	0.119978i
$723$	982.074	+	379.975i	1.35833	+	0.525553i
$724$	161.120	+	442.672i	0.222541	+	0.611426i
$725$	−807.034	+	191.747i	−1.11315	+	0.264479i
$726$	−565.848	−	163.880i	−0.779406	−	0.225730i
$727$	−54.0589	+	617.896i	−0.0743588	+	0.849925i	0.863826	+	0.503790i	$0.168062\pi$
$727$	−54.0589	+	617.896i	−0.0743588	+	0.849925i	−0.938185	+	0.346135i	$0.887494\pi$
$728$	−185.732	−	185.732i	−0.255127	−	0.255127i
$729$	723.702	+	87.7290i	0.992733	+	0.120342i
$730$	−163.453	−	790.485i	−0.223908	−	1.08286i
$731$	199.751	−	167.611i	0.273257	−	0.229290i
$732$	29.7389	−	16.3816i	0.0406269	−	0.0223792i
$733$	−1168.76	+	818.372i	−1.59448	+	1.11647i	−0.665471	+	0.746424i	$0.731769\pi$
$733$	−1168.76	+	818.372i	−1.59448	+	1.11647i	−0.929014	+	0.370046i	$0.879342\pi$
$734$	51.7256	+	142.115i	0.0704708	+	0.193617i
$735$	−322.942	−	53.8639i	−0.439376	−	0.0732843i
$736$	33.7660	+	191.497i	0.0458778	+	0.260186i
$737$	−67.6140	−	18.1171i	−0.0917422	−	0.0245822i
$738$	86.3438	+	383.261i	0.116997	+	0.519323i
$739$	74.7205	+	43.1399i	0.101110	+	0.0583761i	0.549702	−	0.835361i	$-0.314741\pi$
$739$	74.7205	+	43.1399i	0.101110	+	0.0583761i	−0.448592	+	0.893737i	$0.648074\pi$
$740$	−304.344	+	226.708i	−0.411276	+	0.306362i
$741$	375.578	−	764.894i	0.506854	−	1.03225i
$742$	−51.5298	+	4.50827i	−0.0694472	+	0.00607584i
$743$	−68.7336	−	785.629i	−0.0925082	−	1.05737i	−0.890585	−	0.454818i	$-0.849704\pi$
$743$	−68.7336	−	785.629i	−0.0925082	−	1.05737i	0.798076	−	0.602556i	$-0.205851\pi$
$744$	−30.7506	−	457.177i	−0.0413315	−	0.614486i
$745$	142.645	+	20.8537i	0.191470	+	0.0279915i
$746$	110.989	−	192.238i	0.148779	−	0.257692i
$747$	527.566	−	692.431i	0.706247	−	0.926949i
$748$	−153.387	+	572.447i	−0.205062	+	0.765303i
$749$	816.872	−	144.037i	1.09062	−	0.192305i
$750$	464.303	−	256.267i	0.619070	−	0.341690i
$751$	−525.648	+	191.320i	−0.699930	+	0.254754i	−0.667381	−	0.744716i	$-0.732585\pi$
$751$	−525.648	+	191.320i	−0.699930	+	0.254754i	−0.0325492	+	0.999470i	$0.510363\pi$
$752$	113.646	+	162.303i	0.151125	+	0.215829i
$753$	27.4589	−	45.4259i	0.0364659	−	0.0603265i
$754$	537.337	+	640.373i	0.712648	+	0.849301i
$755$	−0.0680364	−	0.329036i	−9.01144e−5	−	0.000435809i
$756$	−186.683	−	210.680i	−0.246936	−	0.278678i
$757$	587.650	−	587.650i	0.776288	−	0.776288i	−0.202909	−	0.979198i	$-0.565040\pi$
$757$	587.650	−	587.650i	0.776288	−	0.776288i	0.979198	+	0.202909i	$0.0650397\pi$
$758$	−171.202	−	14.9783i	−0.225861	−	0.0197603i
$759$	1151.58	+	1198.85i	1.51724	+	1.57951i
$760$	−154.689	+	164.053i	−0.203538	+	0.215859i
$761$	−429.081	+	156.173i	−0.563838	+	0.205220i	−0.608184	−	0.793796i	$-0.708102\pi$
$761$	−429.081	+	156.173i	−0.563838	+	0.205220i	0.0443460	+	0.999016i	$0.485880\pi$
$762$	227.889	−	35.4747i	0.299067	−	0.0465547i
$763$	371.017	−	529.868i	0.486261	−	0.694453i
$764$	−262.016	+	151.275i	−0.342953	+	0.198004i
$765$	205.419	+	801.288i	0.268521	+	1.04744i
$766$	−135.261	+	234.279i	−0.176581	+	0.305847i
$767$	−1638.14	+	763.876i	−2.13577	+	0.995927i
$768$	9.28377	−	47.0936i	0.0120882	−	0.0613199i
$769$	−216.817	+	258.392i	−0.281946	+	0.336010i	−0.888367	−	0.459133i	$-0.848160\pi$
$769$	−216.817	+	258.392i	−0.281946	+	0.336010i	0.606421	+	0.795143i	$0.292604\pi$
$770$	523.078	+	281.852i	0.679321	+	0.366042i
$771$	781.314	+	1165.00i	1.01338	+	1.51102i
$772$	−488.839	+	227.949i	−0.633211	+	0.295271i
$773$	28.3348	−	7.59230i	0.0366557	−	0.00982186i	−0.240445	−	0.970663i	$-0.577293\pi$
$773$	28.3348	−	7.59230i	0.0366557	−	0.00982186i	0.277100	+	0.960841i	$0.410627\pi$
$774$	−38.4745	+	176.402i	−0.0497087	+	0.227909i
$775$	1083.33	+	805.568i	1.39784	+	1.03944i
$776$	−57.2154	−	324.485i	−0.0737312	−	0.418150i
$777$	−586.417	+	91.2855i	−0.754719	+	0.117485i
$778$	143.768	+	67.0399i	0.184791	+	0.0861695i
$779$	484.657	+	85.4582i	0.622153	+	0.109702i
$780$	−440.618	−	302.481i	−0.564895	−	0.387796i
$781$	−754.333	+	632.961i	−0.965856	+	0.810449i
$782$	631.877	−	631.877i	0.808027	−	0.808027i
$783$	533.432	+	719.733i	0.681267	+	0.919200i
$784$		−	87.3074i		−	0.111361i
$785$	236.217	−	27.6767i	0.300913	−	0.0352570i
$786$	156.790	+	636.031i	0.199478	+	0.809200i
$787$	102.127	+	145.853i	0.129768	+	0.185328i	0.878778	−	0.477231i	$-0.158359\pi$
$787$	102.127	+	145.853i	0.129768	+	0.185328i	−0.749010	+	0.662559i	$0.769471\pi$
$788$	−207.032	−	96.5406i	−0.262731	−	0.122513i
$789$	−1025.00	−	110.481i	−1.29911	−	0.140027i
$790$	523.520	+	225.651i	0.662683	+	0.285634i
$791$	−392.754	−	680.270i	−0.496529	−	0.860013i
$792$	−158.329	−	378.571i	−0.199911	−	0.477994i
$793$	97.3753	−	26.0916i	0.122794	−	0.0329024i
$794$	−43.8744	+	120.544i	−0.0552574	+	0.151819i
$795$	−101.407	+	28.1811i	−0.127556	+	0.0354479i
$796$	−267.633	−	224.571i	−0.336223	−	0.282124i
$797$	1114.42	−	97.4990i	1.39827	−	0.122333i	0.637047	−	0.770825i	$-0.280156\pi$
$797$	1114.42	−	97.4990i	1.39827	−	0.122333i	0.761221	+	0.648493i	$0.224600\pi$
$798$	−333.709	+	113.916i	−0.418181	+	0.142752i
$799$	311.424	−	855.631i	0.389768	−	1.07088i
$800$	87.7766	+	110.884i	0.109721	+	0.138605i
$801$	7.09626	−	176.379i	0.00885925	−	0.220199i
$802$	−41.9729	−	11.2466i	−0.0523353	−	0.0140232i
$803$	1055.49	−	1507.40i	1.31444	−	1.87721i
$804$	−10.5341	−	23.8299i	−0.0131021	−	0.0296391i
$805$	−470.556	−	762.411i	−0.584542	−	0.947094i
$806$	236.250	−	1339.84i	0.293114	−	1.66233i
$807$	335.084	−	184.580i	0.415221	−	0.228723i
$808$	−107.262	−	9.38423i	−0.132750	−	0.0116141i
$809$			219.364i			0.271155i	0.990767	+	0.135578i	$0.0432890\pi$
$809$			219.364i			0.271155i	−0.990767	+	0.135578i	$0.956711\pi$
$810$	−451.798	−	352.035i	−0.557776	−	0.434611i
$811$	913.840			1.12681			0.563403	−	0.826182i	$-0.309492\pi$
$811$	913.840			1.12681			0.563403	+	0.826182i	$0.309492\pi$
$812$	30.1490	−	344.604i	0.0371293	−	0.424390i
$813$	−447.773	−	812.880i	−0.550766	−	0.999853i
$814$	−852.009	−	150.232i	−1.04669	−	0.184560i
$815$	359.017	−	1516.70i	0.440511	−	1.86098i
$816$	−201.753	+	89.1858i	−0.247246	+	0.109296i
$817$	185.267	+	129.725i	0.226765	+	0.158783i
$818$	95.9351	−	358.035i	0.117280	−	0.437695i
$819$	−388.462	−	740.035i	−0.474313	−	0.903583i
$820$	97.0070	−	293.025i	0.118301	−	0.357348i
$821$	−1042.56	−	379.460i	−1.26986	−	0.462192i	−0.382795	−	0.923833i	$-0.625038\pi$
$821$	−1042.56	−	379.460i	−1.26986	−	0.462192i	−0.887067	+	0.461641i	$0.847261\pi$
$822$	−24.1172	−	70.6495i	−0.0293396	−	0.0859483i
$823$	16.6220	+	189.990i	0.0201968	+	0.230851i	0.999584	+	0.0288567i	$0.00918665\pi$
$823$	16.6220	+	189.990i	0.0201968	+	0.230851i	−0.979387	+	0.201994i	$0.935258\pi$
$824$	−124.781	+	148.708i	−0.151433	+	0.180470i
$825$	1151.21	+	369.315i	1.39540	+	0.447655i
$826$	702.842	+	255.814i	0.850899	+	0.309702i
$827$	−39.9541	−	149.111i	−0.0483121	−	0.180303i	0.937554	−	0.347841i	$-0.113085\pi$
$827$	−39.9541	−	149.111i	−0.0483121	−	0.180303i	−0.985866	+	0.167538i	$0.946418\pi$
$828$	−78.6620	+	613.718i	−0.0950024	+	0.741206i
$829$	−636.204	+	367.312i	−0.767435	+	0.443079i	−0.831959	−	0.554837i	$-0.812781\pi$
$829$	−636.204	+	367.312i	−0.767435	+	0.443079i	0.0645236	+	0.997916i	$0.479447\pi$
$830$	−635.545	+	252.691i	−0.765716	+	0.304448i
$831$	−53.4343	+	495.741i	−0.0643012	+	0.596560i
$832$	60.2318	−	129.167i	0.0723940	−	0.155249i
$833$	−328.665	+	230.134i	−0.394556	+	0.276271i
$834$	−227.203	+	56.0084i	−0.272426	+	0.0671564i
$835$	−12.1518	+	1.42379i	−0.0145531	+	0.00170514i
$836$	−514.031			−0.614870
$837$	339.276	−	1417.99i	0.405348	−	1.69414i
$838$	−389.762	−	389.762i	−0.465110	−	0.465110i
$839$	−559.077	−	666.282i	−0.666361	−	0.794138i	0.321923	−	0.946766i	$-0.395671\pi$
$839$	−559.077	−	666.282i	−0.666361	−	0.794138i	−0.988284	+	0.152628i	$0.951226\pi$
$840$	40.4197	+	217.435i	0.0481187	+	0.258851i
$841$	−45.1336	+	255.965i	−0.0536665	+	0.304358i
$842$	90.1336	−	193.292i	0.107047	−	0.229563i
$843$	60.0598	+	385.823i	0.0712453	+	0.457678i
$844$	260.393	−	45.9144i	0.308523	−	0.0544009i
$845$	−493.356	−	554.067i	−0.583853	−	0.655701i
$846$	191.641	+	600.632i	0.226526	+	0.709967i
$847$	187.336	+	699.146i	0.221175	+	0.825438i
$848$	−11.8614	−	25.4370i	−0.0139876	−	0.0299964i
$849$	69.1986	−	46.4085i	0.0815060	−	0.0546625i
$850$	186.048	−	622.711i	0.218880	−	0.732601i
$851$	999.317	+	838.526i	1.17429	+	0.985342i
$852$	−359.599	−	70.8892i	−0.422064	−	0.0832033i
$853$	461.125	+	988.887i	0.540593	+	1.15930i	0.967001	+	0.254774i	$0.0820009\pi$
$853$	461.125	+	988.887i	0.540593	+	1.15930i	−0.426408	+	0.904531i	$0.640221\pi$
$854$	−36.1271	−	20.8580i	−0.0423034	−	0.0244239i
$855$	−625.207	+	351.981i	−0.731237	+	0.411673i
$856$	225.034	+	389.770i	0.262890	+	0.455339i
$857$	−483.534	−	338.574i	−0.564217	−	0.395069i	0.256380	−	0.966576i	$-0.417470\pi$
$857$	−483.534	−	338.574i	−0.564217	−	0.395069i	−0.820597	+	0.571507i	$0.806359\pi$
$858$	−187.406	−	1203.89i	−0.218422	−	1.40314i
$859$	−207.579	−	570.319i	−0.241652	−	0.663934i	−0.999928	−	0.0119999i	$-0.996180\pi$
$859$	−207.579	−	570.319i	−0.241652	−	0.663934i	0.758276	−	0.651934i	$-0.226042\pi$
$860$	97.3163	−	103.207i	0.113159	−	0.120008i
$861$	348.114	−	334.390i	0.404314	−	0.388374i
$862$	47.8597	−	547.038i	0.0555216	−	0.634615i
$863$	515.588	+	515.588i	0.597436	+	0.597436i	0.939630	−	0.342193i	$-0.111170\pi$
$863$	515.588	+	515.588i	0.597436	+	0.597436i	−0.342193	+	0.939630i	$0.611170\pi$
$864$	72.7756	−	134.282i	0.0842310	−	0.155419i
$865$	−299.781	+	456.072i	−0.346567	+	0.527251i
$866$	−34.1345	+	28.6423i	−0.0394163	+	0.0330742i
$867$	125.560	+	75.8983i	0.144822	+	0.0875413i
$868$	−461.172	+	322.916i	−0.531304	+	0.372023i
$869$	444.494	+	1221.24i	0.511501	+	1.40534i
$870$	−67.8370	−	700.578i	−0.0779736	−	0.805262i
$871$	−13.4334	−	76.1848i	−0.0154230	−	0.0874682i
$872$	339.017	+	90.8394i	0.388781	+	0.104174i
$873$	133.290	−	1039.92i	0.152681	−	1.19121i
$874$	671.238	+	387.540i	0.768007	+	0.443409i
$875$	−564.574	−	325.326i	−0.645227	−	0.371801i
$876$	683.394	−	45.9664i	0.780130	−	0.0524731i
$877$	1463.81	−	128.067i	1.66911	−	0.146029i	0.786965	−	0.616998i	$-0.211651\pi$
$877$	1463.81	−	128.067i	1.66911	−	0.146029i	0.882150	+	0.470969i	$0.156096\pi$
$878$	−94.8453	−	1084.09i	−0.108024	−	1.23472i
$879$	447.703	+	219.831i	0.509333	+	0.250093i
$880$	−46.6367	+	319.008i	−0.0529962	+	0.362509i
$881$	−16.9394	+	29.3398i	−0.0192274	+	0.0333029i	−0.875479	−	0.483256i	$-0.839454\pi$
$881$	−16.9394	+	29.3398i	−0.0192274	+	0.0333029i	0.856252	+	0.516559i	$0.172787\pi$
$882$	82.6321	−	265.237i	0.0936872	−	0.300722i
$883$	163.363	−	609.680i	0.185009	−	0.690464i	−0.809619	−	0.586955i	$-0.800326\pi$
$883$	163.363	−	609.680i	0.185009	−	0.690464i	0.994629	−	0.103509i	$-0.0330070\pi$
$884$	−645.010	+	113.733i	−0.729650	+	0.128657i
$885$	1501.14	+	250.377i	1.69620	+	0.282912i
$886$	−513.689	+	186.967i	−0.579784	+	0.211024i
$887$	−90.5425	−	129.308i	−0.102077	−	0.145781i	0.764864	−	0.644192i	$-0.222806\pi$
$887$	−90.5425	−	129.308i	−0.102077	−	0.145781i	−0.866941	+	0.498410i	$0.833917\pi$
$888$	−155.370	−	282.057i	−0.174966	−	0.317631i
$889$	−182.148	−	217.075i	−0.204890	−	0.244179i
$890$	−76.1782	+	115.894i	−0.0855935	+	0.130218i
$891$	−122.700	−	1299.94i	−0.137710	−	1.45896i
$892$	106.142	−	106.142i	0.118994	−	0.118994i
$893$	786.762	+	68.8327i	0.881032	+	0.0770803i
$894$	−34.0291	+	117.496i	−0.0380639	+	0.131428i
$895$	−34.9528	−	1189.81i	−0.0390534	−	1.32939i
$896$	−55.4193	+	20.1710i	−0.0618519	+	0.0225122i
$897$	−662.921	+	1713.37i	−0.739043	+	1.91011i
$898$	143.249	−	204.580i	0.159520	−	0.227817i
$899$	1551.69	−	895.871i	1.72602	−	0.996519i
$900$	161.716	+	419.938i	0.179684	+	0.466598i
$901$	−64.4907	+	111.701i	−0.0715768	+	0.123975i
$902$	637.737	−	297.382i	0.707025	−	0.329691i
$903$	209.939	−	71.6656i	0.232491	−	0.0793639i
$904$	273.964	−	326.497i	0.303057	−	0.361170i
$905$	558.649	−	1036.77i	0.617292	−	1.14561i
$906$	0.284460	−	0.0191333i	0.000313973	−	2.11185e-5i
$907$	−554.562	+	258.597i	−0.611425	+	0.285112i	−0.703561	−	0.710634i	$-0.748408\pi$
$907$	−554.562	+	258.597i	−0.611425	+	0.285112i	0.0921369	+	0.995746i	$0.470630\pi$
$908$	241.689	−	64.7603i	0.266177	−	0.0713220i
$909$	−316.977	−	130.027i	−0.348710	−	0.143044i
$910$	−37.9983	+	655.563i	−0.0417564	+	0.720398i
$911$	248.791	+	1410.96i	0.273097	+	1.54881i	0.744943	+	0.667128i	$0.232476\pi$
$911$	248.791	+	1410.96i	0.273097	+	1.54881i	−0.471847	+	0.881681i	$0.656412\pi$
$912$	−120.011	−	149.008i	−0.131592	−	0.163386i
$913$	−1413.09	−	658.936i	−1.54775	−	0.721726i
$914$	−3.56186	−	0.628051i	−0.00389700	−	0.000687146i
$915$	−80.0272	−	28.2908i	−0.0874614	−	0.0309190i
$916$	15.0340	−	12.6151i	0.0164127	−	0.0137719i
$917$	569.125	−	569.125i	0.620638	−	0.620638i
$918$	−697.329	+	79.9942i	−0.759617	+	0.0871397i
$919$			588.105i			0.639940i	0.947428	+	0.319970i	$0.103673\pi$
$919$			588.105i			0.639940i	−0.947428	+	0.319970i	$0.896327\pi$
$920$	301.407	−	381.410i	0.327616	−	0.414576i
$921$	373.392	−	358.671i	0.405420	−	0.389437i
$922$	−518.300	−	740.210i	−0.562148	−	0.802830i
$923$	−986.300	−	459.919i	−1.06858	−	0.498287i
$924$	−297.430	+	407.102i	−0.321894	+	0.440587i
$925$	929.262	+	191.335i	1.00461	+	0.206849i
$926$	−215.167	−	372.680i	−0.232362	−	0.402463i
$927$	−519.823	+	333.670i	−0.560759	+	0.359946i
$928$	181.299	−	48.5789i	0.195365	−	0.0523480i
$929$	−526.710	+	1447.12i	−0.566964	+	1.55772i	0.242254	+	0.970213i	$0.422113\pi$
$929$	−526.710	+	1447.12i	−0.566964	+	1.55772i	−0.809218	+	0.587508i	$0.800109\pi$
$930$	−802.472	+	817.477i	−0.862873	+	0.879008i
$931$	−266.588	−	223.694i	−0.286346	−	0.240273i
$932$	443.417	−	38.7939i	0.475769	−	0.0416244i
$933$	−218.844	+	1110.13i	−0.234559	+	1.18985i
$934$	370.498	−	1017.94i	0.396679	−	1.08987i
$935$	1323.82	−	665.312i	1.41585	−	0.711563i
$936$	305.233	−	335.400i	0.326103	−	0.358333i
$937$	24.8288	+	6.65285i	0.0264982	+	0.00710016i	0.272044	−	0.962285i	$-0.412300\pi$
$937$	24.8288	+	6.65285i	0.0264982	+	0.00710016i	−0.245546	+	0.969385i	$0.578967\pi$
$938$	−18.3614	+	26.2228i	−0.0195750	+	0.0279561i
$939$	−275.678	+	377.330i	−0.293587	+	0.401842i
$940$	114.098	−	482.019i	0.121381	−	0.512787i
$941$	−71.0509	+	402.950i	−0.0755057	+	0.428214i	0.923499	+	0.383602i	$0.125316\pi$
$941$	−71.0509	+	402.950i	−0.0755057	+	0.428214i	−0.999004	+	0.0446126i	$0.985795\pi$
$942$	−4.05720	+	201.767i	−0.00430701	+	0.214190i
$943$	−1056.98	−	92.4737i	−1.12087	−	0.0980633i
$944$			405.833i			0.429908i
$945$	−82.9974	+	698.815i	−0.0878279	+	0.739486i
$946$	323.382			0.341842
$947$	132.920	−	1519.28i	0.140359	−	1.60431i	−0.520543	−	0.853835i	$-0.674271\pi$
$947$	132.920	−	1519.28i	0.140359	−	1.60431i	0.660902	−	0.750472i	$-0.270174\pi$
$948$	−250.238	+	413.974i	−0.263964	+	0.436682i
$949$	2002.81	+	353.149i	2.11044	+	0.372127i
$950$	563.475	+	16.0801i	0.593131	+	0.0169264i
$951$	46.2478	−	429.068i	0.0486307	−	0.451175i
$952$	222.012	+	155.455i	0.233206	+	0.163293i
$953$	−121.730	+	454.301i	−0.127733	+	0.476706i	−0.999922	−	0.0124622i	$-0.996033\pi$
$953$	−121.730	+	454.301i	−0.127733	+	0.476706i	0.872189	+	0.489169i	$0.162700\pi$
$954$	−11.9599	−	88.5028i	−0.0125365	−	0.0927703i
$955$	718.049	+	237.713i	0.751884	+	0.248914i
$956$	−616.187	−	224.274i	−0.644547	−	0.234596i
$957$	1055.91	−	1208.20i	1.10335	−	1.26248i
$958$	56.9368	+	650.791i	0.0594330	+	0.679322i
$959$	−58.9583	+	70.2638i	−0.0614790	+	0.0732678i
$960$	−103.363	+	60.9600i	−0.107670	+	0.0635000i
$961$	−1837.16	−	668.672i	−1.91172	−	0.695808i
$962$	−247.465	−	923.550i	−0.257240	−	0.960031i
$963$	314.747	+	1397.09i	0.326840	+	1.45077i
$964$	607.961	−	351.007i	0.630665	−	0.364115i
$965$	1238.30	+	533.742i	1.28322	+	0.553100i
$966$	695.316	−	307.368i	0.719789	−	0.318186i
$967$	171.669	−	368.146i	0.177528	−	0.380709i	−0.797328	−	0.603546i	$-0.793754\pi$
$967$	171.669	−	368.146i	0.177528	−	0.380709i	0.974856	+	0.222837i	$0.0715317\pi$
$968$	−321.709	+	225.263i	−0.332344	+	0.232710i
$969$	−244.597	+	844.549i	−0.252422	+	0.871568i
$970$	−510.723	+	646.286i	−0.526519	+	0.666275i
$971$	−410.358			−0.422613			−0.211307	−	0.977420i	$-0.567772\pi$
$971$	−410.358			−0.422613			−0.211307	+	0.977420i	$0.567772\pi$
$972$	348.181	−	339.066i	0.358211	−	0.348834i
$973$	203.303	+	203.303i	0.208944	+	0.208944i
$974$	137.377	+	163.720i	0.141044	+	0.168090i
$975$	167.772	+	1325.56i	0.172073	+	1.35954i
$976$	3.93050	−	22.2910i	0.00402715	−	0.0228391i
$977$	404.042	−	866.472i	0.413554	−	0.886870i	−0.583640	−	0.812012i	$-0.698372\pi$
$977$	404.042	−	866.472i	0.413554	−	0.886870i	0.997194	−	0.0748573i	$-0.0238501\pi$
$978$	1233.42	+	477.224i	1.26117	+	0.487959i
$979$	−311.366	+	54.9022i	−0.318045	+	0.0560798i
$980$	−163.011	+	145.150i	−0.166338	+	0.148112i
$981$	943.948	+	596.830i	0.962230	+	0.608389i
$982$	−151.678	−	566.071i	−0.154459	−	0.576447i
$983$	89.0268	+	190.918i	0.0905664	+	0.194220i	0.946373	−	0.323075i	$-0.104717\pi$
$983$	89.0268	+	190.918i	0.0905664	+	0.194220i	−0.855807	+	0.517295i	$0.826939\pi$
$984$	235.099	+	115.438i	0.238921	+	0.117315i
$985$	163.942	+	547.049i	0.166439	+	0.555379i
$986$	−660.760	−	554.443i	−0.670141	−	0.562315i
$987$	509.752	−	583.270i	0.516466	−	0.590953i
$988$	−240.083	−	514.860i	−0.242999	−	0.521114i
$989$	−422.282	−	243.805i	−0.426979	−	0.246517i
$990$	−443.606	+	924.996i	−0.448087	+	0.934339i
$991$	−41.8212	−	72.4365i	−0.0422010	−	0.0730943i	0.844153	−	0.536102i	$-0.180104\pi$
$991$	−41.8212	−	72.4365i	−0.0422010	−	0.0730943i	−0.886354	+	0.463007i	$0.846770\pi$
$992$	−250.229	−	175.212i	−0.252247	−	0.176625i
$993$	−415.634	+	334.752i	−0.418564	+	0.337112i
$994$	154.022	+	423.172i	0.154952	+	0.425726i
$995$	25.6474	+	873.049i	0.0257763	+	0.877437i
$996$	−138.903	−	563.472i	−0.139461	−	0.565735i
$997$	114.747	−	1311.57i	0.115092	−	1.31551i	−0.690625	−	0.723213i	$-0.742665\pi$
$997$	114.747	−	1311.57i	0.115092	−	1.31551i	0.805718	−	0.592300i	$-0.201780\pi$
$998$	−233.378	−	233.378i	−0.233846	−	0.233846i
$999$	−205.056	−	1003.93i	−0.205261	−	1.00493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.q.a.103.7	yes	216
5.2	odd	4	inner	270.3.q.a.157.4	yes	216
27.16	even	9	inner	270.3.q.a.43.4	✓	216
135.97	odd	36	inner	270.3.q.a.97.7	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.q.a.43.4	✓	216	27.16	even	9	inner
270.3.q.a.97.7	yes	216	135.97	odd	36	inner
270.3.q.a.103.7	yes	216	1.1	even	1	trivial
270.3.q.a.157.4	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} +(-1.44746 - 2.62771i) q^{3} +(-1.96962 - 0.347296i) q^{4} +(2.62607 + 4.25485i) q^{5} +(-3.88041 + 1.71535i) q^{6} +(4.27007 + 2.98993i) q^{7} +(-0.732051 + 2.73205i) q^{8} +(-4.80969 + 7.60703i) q^{9} +(6.31805 - 3.17526i) q^{10} +(15.1478 + 5.51335i) q^{11} +(1.93835 + 5.67827i) q^{12} +(1.55269 + 17.7473i) q^{13} +(4.73863 - 5.64727i) q^{14} +(7.37935 - 13.0593i) q^{15} +(3.75877 + 1.36808i) q^{16} +(-4.75767 - 17.7559i) q^{17} +(10.1242 + 7.71367i) q^{18} +(13.8079 - 7.97198i) q^{19} +(-3.69466 - 9.29244i) q^{20} +(1.67590 - 15.5483i) q^{21} +(9.63445 - 20.6611i) q^{22} +(-28.1579 + 19.7163i) q^{23} +(8.23865 - 2.03093i) q^{24} +(-11.2075 + 22.3471i) q^{25} +25.1943 q^{26} +(26.9509 + 1.62757i) q^{27} +(-7.37199 - 7.37199i) q^{28} +(21.3277 + 25.4174i) q^{29} +(-17.4888 - 12.0059i) q^{30} +(9.37711 - 53.1802i) q^{31} +(2.39069 - 5.12685i) q^{32} +(-7.43843 - 47.7843i) q^{33} +(-25.6014 + 4.51422i) q^{34} +(-1.50821 + 26.0203i) q^{35} +(12.1151 - 13.3125i) q^{36} +(-9.82224 - 36.6571i) q^{37} +(-9.52926 - 20.4356i) q^{38} +(44.3872 - 29.7686i) q^{39} +(-13.5469 + 4.05980i) q^{40} +(23.6451 + 19.8406i) q^{41} +(-21.6984 - 4.27750i) q^{42} +(5.99495 + 12.8562i) q^{43} +(-27.9206 - 16.1199i) q^{44} +(-44.9974 - 0.487922i) q^{45} +(24.3064 + 42.0999i) q^{46} +(40.5758 + 28.4115i) q^{47} +(-1.84577 - 11.8572i) q^{48} +(-7.46522 - 20.5105i) q^{49} +(30.1019 + 18.5439i) q^{50} +(-39.7706 + 38.2027i) q^{51} +(3.10537 - 35.4946i) q^{52} +(-4.96152 - 4.96152i) q^{53} +(5.61486 - 37.7687i) q^{54} +(16.3207 + 78.9300i) q^{55} +(-11.2945 + 9.47725i) q^{56} +(-40.9344 - 24.7439i) q^{57} +(38.4376 - 26.9143i) q^{58} +(34.7007 + 95.3395i) q^{59} +(-19.0699 + 23.1590i) q^{60} +(-0.982624 - 5.57274i) q^{61} +(-73.7662 - 19.7656i) q^{62} +(-43.2822 + 18.1018i) q^{63} +(-6.92820 - 4.00000i) q^{64} +(-71.4345 + 53.2121i) q^{65} +(-68.2370 + 4.58975i) q^{66} +(-4.32587 + 0.378465i) q^{67} +(3.20423 + 36.6245i) q^{68} +(92.5663 + 45.4519i) q^{69} +(36.4723 + 5.33199i) q^{70} +(-30.5433 + 52.9025i) q^{71} +(-17.2618 - 18.7091i) q^{72} +(29.5458 - 110.267i) q^{73} +(-52.8543 + 9.31965i) q^{74} +(74.9440 - 2.89661i) q^{75} +(-29.9648 + 10.9063i) q^{76} +(48.1975 + 68.8332i) q^{77} +(-36.4679 - 66.2033i) q^{78} +(51.8225 + 61.7596i) q^{79} +(4.04983 + 19.5857i) q^{80} +(-34.7337 - 73.1749i) q^{81} +(30.8665 - 30.8665i) q^{82} +(-96.3552 - 8.42999i) q^{83} +(-8.70075 + 30.0421i) q^{84} +(63.0545 - 66.8713i) q^{85} +(18.8512 - 6.86126i) q^{86} +(35.9183 - 92.8337i) q^{87} +(-26.1517 + 37.3485i) q^{88} +(-16.9858 + 9.80676i) q^{89} +(-6.23363 + 63.3336i) q^{90} +(-46.4331 + 80.4244i) q^{91} +(62.3076 - 29.0545i) q^{92} +(-153.315 + 52.3362i) q^{93} +(45.0283 - 53.6626i) q^{94} +(70.1800 + 37.8154i) q^{95} +(-16.9323 + 1.13890i) q^{96} +(-105.578 + 49.2318i) q^{97} +(-29.8160 + 7.98918i) q^{98} +(-114.796 + 88.7122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 36 q^{6} + 18 q^{7} + 216 q^{8} + 36 q^{11} - 18 q^{15} + 72 q^{20} + 288 q^{21} + 36 q^{22} + 108 q^{23} + 54 q^{25} - 162 q^{27} - 120 q^{30} - 432 q^{31} + 114 q^{33} - 162 q^{35} + 48 q^{36}+ \cdots + 756 q^{98}+O(q^{100}) \) 216 * q - 36 * q^6 + 18 * q^7 + 216 * q^8 + 36 * q^11 - 18 * q^15 + 72 * q^20 + 288 * q^21 + 36 * q^22 + 108 * q^23 + 54 * q^25 - 162 * q^27 - 120 * q^30 - 432 * q^31 + 114 * q^33 - 162 * q^35 + 48 * q^36 + 108 * q^38 - 36 * q^40 + 216 * q^41 - 48 * q^42 - 216 * q^43 + 18 * q^45 + 108 * q^46 - 144 * q^47 - 72 * q^48 - 162 * q^50 + 60 * q^51 - 540 * q^53 + 324 * q^55 - 72 * q^56 - 234 * q^57 + 72 * q^58 - 96 * q^60 + 504 * q^61 - 24 * q^63 - 144 * q^66 + 72 * q^67 + 108 * q^68 + 72 * q^70 + 240 * q^72 - 216 * q^73 - 84 * q^75 + 216 * q^76 + 576 * q^77 + 168 * q^78 - 1068 * q^81 + 576 * q^83 + 576 * q^85 - 432 * q^86 - 324 * q^87 - 72 * q^88 - 606 * q^90 + 756 * q^91 - 324 * q^92 + 168 * q^93 - 468 * q^95 - 1332 * q^97 + 756 * q^98

Introduction

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