LMFDB - Embedded newform 363.3.h.l.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not 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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			323.1
Root			$-0.217724 + 1.71831i$ of defining polynomial
Character	$\chi$	$=$	363.323
Dual form			363.3.h.l.245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48377 + 2.04223i) q^{2} +(0.440460 + 2.96749i) q^{3} +(-0.733075 - 2.25617i) q^{4} +(-0.465695 - 0.640974i) q^{5} +(-6.71384 - 3.50355i) q^{6} +(-2.08418 - 6.41446i) q^{7} +(-3.90781 - 1.26972i) q^{8} +(-8.61199 + 2.61412i) q^{9} +O(q^{10})$	\(q+(-1.48377 + 2.04223i) q^{2} +(0.440460 + 2.96749i) q^{3} +(-0.733075 - 2.25617i) q^{4} +(-0.465695 - 0.640974i) q^{5} +(-6.71384 - 3.50355i) q^{6} +(-2.08418 - 6.41446i) q^{7} +(-3.90781 - 1.26972i) q^{8} +(-8.61199 + 2.61412i) q^{9} +2.00000 q^{10} +(6.37228 - 3.16915i) q^{12} +(7.67686 + 5.57757i) q^{13} +(16.1923 + 5.26119i) q^{14} +(1.69696 - 1.66427i) q^{15} +(16.0682 - 11.6742i) q^{16} +(-17.2206 - 23.7021i) q^{17} +(7.43955 - 21.4664i) q^{18} +(8.10666 - 24.9497i) q^{19} +(-1.10476 + 1.52057i) q^{20} +(18.1168 - 9.01011i) q^{21} +26.9205i q^{23} +(2.04666 - 12.1556i) q^{24} +(7.53145 - 23.1794i) q^{25} +(-22.7814 + 7.40212i) q^{26} +(-11.5506 - 24.4046i) q^{27} +(-12.9443 + 9.40456i) q^{28} +(-24.6733 + 8.01686i) q^{29} +(0.880920 + 5.93498i) q^{30} +(2.31493 + 1.68189i) q^{31} +33.7013i q^{32} +73.9565 q^{34} +(-3.14091 + 4.32309i) q^{35} +(12.2112 + 17.5138i) q^{36} +(-0.739796 - 2.27686i) q^{37} +(38.9247 + 53.5753i) q^{38} +(-13.1700 + 25.2377i) q^{39} +(1.00599 + 3.09610i) q^{40} +(16.7533 + 5.44348i) q^{41} +(-8.48047 + 50.3677i) q^{42} -12.5109 q^{43} +(5.68614 + 4.30268i) q^{45} +(-54.9780 - 39.9438i) q^{46} +(-39.6391 - 12.8795i) q^{47} +(41.7206 + 42.5402i) q^{48} +(2.84036 - 2.06364i) q^{49} +(36.1628 + 49.7739i) q^{50} +(62.7507 - 61.5417i) q^{51} +(6.95624 - 21.4091i) q^{52} +(52.6576 - 72.4770i) q^{53} +(66.9783 + 12.6217i) q^{54} +27.7128i q^{56} +(77.6087 + 13.0671i) q^{57} +(20.2373 - 62.2839i) q^{58} +(-14.0362 + 4.56063i) q^{59} +(-4.99888 - 2.60861i) q^{60} +(-51.3286 + 37.2924i) q^{61} +(-6.86963 + 2.23208i) q^{62} +(34.7172 + 49.7930i) q^{63} +(-4.55292 - 3.30789i) q^{64} -7.51811i q^{65} -63.3288 q^{67} +(-40.8520 + 56.2280i) q^{68} +(-79.8864 + 11.8574i) q^{69} +(-4.16837 - 12.8289i) q^{70} +(2.67521 + 3.68211i) q^{71} +(36.9732 + 0.719359i) q^{72} +(16.6147 + 51.1348i) q^{73} +(5.74756 + 1.86750i) q^{74} +(72.1020 + 12.1399i) q^{75} -62.2337 q^{76} +(-32.0000 - 64.3432i) q^{78} +(45.0455 + 32.7275i) q^{79} +(-14.9658 - 4.86267i) q^{80} +(67.3327 - 45.0256i) q^{81} +(-35.9749 + 26.1373i) q^{82} +(-38.4046 - 52.8594i) q^{83} +(-33.6094 - 34.2697i) q^{84} +(-7.17288 + 22.0759i) q^{85} +(18.5632 - 25.5501i) q^{86} +(-34.6576 - 69.6868i) q^{87} -14.1341i q^{89} +(-17.2240 + 5.22824i) q^{90} +(19.7771 - 60.8676i) q^{91} +(60.7374 - 19.7348i) q^{92} +(-3.97137 + 7.61033i) q^{93} +(85.1182 - 61.8420i) q^{94} +(-19.7673 + 6.42280i) q^{95} +(-100.008 + 14.8441i) q^{96} +(-120.774 - 87.7477i) q^{97} +8.86263i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9}+O(q^{10}) $ 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9	$ 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9} + 32 q^{10} + 56 q^{12} - 8 q^{13} - 13 q^{15} + 22 q^{16} + 38 q^{18} - 36 q^{19} + 152 q^{21} + 24 q^{24} - 86 q^{25} + 20 q^{27} - 64 q^{28} + 10 q^{30} - 46 q^{31} + 448 q^{34} + 86 q^{36} + 90 q^{37} - 56 q^{39} - 36 q^{40} + 68 q^{42} - 384 q^{43} + 68 q^{45} - 88 q^{46} - 110 q^{48} + 60 q^{49} + 214 q^{51} - 136 q^{52} + 704 q^{54} + 144 q^{57} - 216 q^{58} - 56 q^{60} - 24 q^{61} + 158 q^{63} - 34 q^{64} - 232 q^{67} + 253 q^{69} + 8 q^{70} + 72 q^{72} - 284 q^{73} + 124 q^{75} - 720 q^{76} - 512 q^{78} - 76 q^{79} - 113 q^{81} - 40 q^{82} + 80 q^{84} - 68 q^{85} + 1008 q^{87} + 14 q^{90} - 256 q^{91} - 25 q^{93} + 260 q^{94} + 272 q^{96} - 218 q^{97}+O(q^{100}) $ 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9 + 32 * q^10 + 56 * q^12 - 8 * q^13 - 13 * q^15 + 22 * q^16 + 38 * q^18 - 36 * q^19 + 152 * q^21 + 24 * q^24 - 86 * q^25 + 20 * q^27 - 64 * q^28 + 10 * q^30 - 46 * q^31 + 448 * q^34 + 86 * q^36 + 90 * q^37 - 56 * q^39 - 36 * q^40 + 68 * q^42 - 384 * q^43 + 68 * q^45 - 88 * q^46 - 110 * q^48 + 60 * q^49 + 214 * q^51 - 136 * q^52 + 704 * q^54 + 144 * q^57 - 216 * q^58 - 56 * q^60 - 24 * q^61 + 158 * q^63 - 34 * q^64 - 232 * q^67 + 253 * q^69 + 8 * q^70 + 72 * q^72 - 284 * q^73 + 124 * q^75 - 720 * q^76 - 512 * q^78 - 76 * q^79 - 113 * q^81 - 40 * q^82 + 80 * q^84 - 68 * q^85 + 1008 * q^87 + 14 * q^90 - 256 * q^91 - 25 * q^93 + 260 * q^94 + 272 * q^96 - 218 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.48377	+	2.04223i	−0.741884	+	1.02112i	0.256624	+	0.966511i	$0.417390\pi$
$2$	−1.48377	+	2.04223i	−0.741884	+	1.02112i	−0.998508	+	0.0546047i	$0.982610\pi$
$3$	0.440460	+	2.96749i	0.146820	+	0.989163i
$3$	0.440460	+	2.96749i	0.146820	+	0.989163i
$4$	−0.733075	−	2.25617i	−0.183269	−	0.564043i
$5$	−0.465695	−	0.640974i	−0.0931389	−	0.128195i	0.759904	−	0.650035i	$-0.225246\pi$
$5$	−0.465695	−	0.640974i	−0.0931389	−	0.128195i	−0.853043	+	0.521840i	$0.825246\pi$
$6$	−6.71384	−	3.50355i	−1.11897	−	0.583924i
$7$	−2.08418	−	6.41446i	−0.297741	−	0.916351i	−0.982287	−	0.187382i	$-0.940000\pi$
$7$	−2.08418	−	6.41446i	−0.297741	−	0.916351i	0.684546	−	0.728969i	$-0.260000\pi$
$8$	−3.90781	−	1.26972i	−0.488476	−	0.158715i
$9$	−8.61199	+	2.61412i	−0.956888	+	0.290458i
$10$	2.00000			0.200000
$11$		0			0
$11$		0			0
$12$	6.37228	−	3.16915i	0.531023	−	0.264096i
$13$	7.67686	+	5.57757i	0.590528	+	0.429044i	0.842504	−	0.538690i	$-0.181080\pi$
$13$	7.67686	+	5.57757i	0.590528	+	0.429044i	−0.251976	+	0.967733i	$0.581080\pi$
$14$	16.1923	+	5.26119i	1.15659	+	0.375799i
$15$	1.69696	−	1.66427i	0.113131	−	0.110951i
$16$	16.0682	−	11.6742i	1.00426	−	0.729640i
$17$	−17.2206	−	23.7021i	−1.01297	−	1.39424i	−0.917014	−	0.398855i	$-0.869408\pi$
$17$	−17.2206	−	23.7021i	−1.01297	−	1.39424i	−0.0959609	−	0.995385i	$-0.530592\pi$
$18$	7.43955	−	21.4664i	0.413309	−	1.19258i
$19$	8.10666	−	24.9497i	0.426666	−	1.31314i	−0.474724	−	0.880135i	$-0.657452\pi$
$19$	8.10666	−	24.9497i	0.426666	−	1.31314i	0.901390	−	0.433008i	$-0.142548\pi$
$20$	−1.10476	+	1.52057i	−0.0552379	+	0.0760285i
$21$	18.1168	−	9.01011i	0.862707	−	0.429053i
$22$		0			0
$23$			26.9205i			1.17046i	0.810868	+	0.585229i	$0.198995\pi$
$23$			26.9205i			1.17046i	−0.810868	+	0.585229i	$0.801005\pi$
$24$	2.04666	−	12.1556i	0.0852774	−	0.506485i
$25$	7.53145	−	23.1794i	0.301258	−	0.927177i
$26$	−22.7814	+	7.40212i	−0.876207	+	0.284697i
$27$	−11.5506	−	24.4046i	−0.427801	−	0.903873i
$28$	−12.9443	+	9.40456i	−0.462295	+	0.335877i
$29$	−24.6733	+	8.01686i	−0.850805	+	0.276443i	−0.701783	−	0.712391i	$-0.747612\pi$
$29$	−24.6733	+	8.01686i	−0.850805	+	0.276443i	−0.149022	+	0.988834i	$0.547612\pi$
$30$	0.880920	+	5.93498i	0.0293640	+	0.197833i
$31$	2.31493	+	1.68189i	0.0746751	+	0.0542546i	0.624496	−	0.781028i	$-0.285304\pi$
$31$	2.31493	+	1.68189i	0.0746751	+	0.0542546i	−0.549821	+	0.835282i	$0.685304\pi$
$32$			33.7013i			1.05316i
$33$		0			0
$34$	73.9565			2.17519
$35$	−3.14091	+	4.32309i	−0.0897402	+	0.123517i
$36$	12.2112	+	17.5138i	0.339199	+	0.486494i
$37$	−0.739796	−	2.27686i	−0.0199945	−	0.0615367i	0.940561	−	0.339624i	$-0.110300\pi$
$37$	−0.739796	−	2.27686i	−0.0199945	−	0.0615367i	−0.960556	+	0.278087i	$0.910300\pi$
$38$	38.9247	+	53.5753i	1.02433	+	1.40988i
$39$	−13.1700	+	25.2377i	−0.337693	+	0.647121i
$40$	1.00599	+	3.09610i	0.0251496	+	0.0774026i
$41$	16.7533	+	5.44348i	0.408617	+	0.132768i	0.506111	−	0.862468i	$-0.331083\pi$
$41$	16.7533	+	5.44348i	0.408617	+	0.132768i	−0.0974939	+	0.995236i	$0.531083\pi$
$42$	−8.48047	+	50.3677i	−0.201916	+	1.19923i
$43$	−12.5109			−0.290951			−0.145475	−	0.989362i	$-0.546471\pi$
$43$	−12.5109			−0.290951			−0.145475	+	0.989362i	$0.546471\pi$
$44$		0			0
$45$	5.68614	+	4.30268i	0.126359	+	0.0956150i
$46$	−54.9780	−	39.9438i	−1.19517	−	0.868344i
$47$	−39.6391	−	12.8795i	−0.843385	−	0.274032i	−0.144712	−	0.989474i	$-0.546226\pi$
$47$	−39.6391	−	12.8795i	−0.843385	−	0.274032i	−0.698673	+	0.715441i	$0.746226\pi$
$48$	41.7206	+	42.5402i	0.869179	+	0.886255i
$49$	2.84036	−	2.06364i	0.0579665	−	0.0421151i
$50$	36.1628	+	49.7739i	0.723256	+	0.995477i
$51$	62.7507	−	61.5417i	1.23041	−	1.20670i
$52$	6.95624	−	21.4091i	0.133774	−	0.411714i
$53$	52.6576	−	72.4770i	0.993541	−	1.36749i	0.0643348	−	0.997928i	$-0.479507\pi$
$53$	52.6576	−	72.4770i	0.993541	−	1.36749i	0.929206	−	0.369563i	$-0.120493\pi$
$54$	66.9783	+	12.6217i	1.24034	+	0.233735i
$55$		0			0
$56$			27.7128i			0.494872i
$57$	77.6087	+	13.0671i	1.36156	+	0.229247i
$58$	20.2373	−	62.2839i	0.348918	−	1.07386i
$59$	−14.0362	+	4.56063i	−0.237901	+	0.0772988i	−0.425541	−	0.904939i	$-0.639916\pi$
$59$	−14.0362	+	4.56063i	−0.237901	+	0.0772988i	0.187640	+	0.982238i	$0.439916\pi$
$60$	−4.99888	−	2.60861i	−0.0833146	−	0.0434768i
$61$	−51.3286	+	37.2924i	−0.841452	+	0.611351i	−0.922776	−	0.385337i	$-0.874085\pi$
$61$	−51.3286	+	37.2924i	−0.841452	+	0.611351i	0.0813237	+	0.996688i	$0.474085\pi$
$62$	−6.86963	+	2.23208i	−0.110800	+	0.0360013i
$63$	34.7172	+	49.7930i	0.551066	+	0.790364i
$64$	−4.55292	−	3.30789i	−0.0711394	−	0.0516858i
$65$		−	7.51811i		−	0.115663i
$66$		0			0
$67$	−63.3288			−0.945206			−0.472603	−	0.881276i	$-0.656685\pi$
$67$	−63.3288			−0.945206			−0.472603	+	0.881276i	$0.656685\pi$
$68$	−40.8520	+	56.2280i	−0.600765	+	0.826883i
$69$	−79.8864	+	11.8574i	−1.15777	+	0.171847i
$70$	−4.16837	−	12.8289i	−0.0595481	−	0.183270i
$71$	2.67521	+	3.68211i	0.0376790	+	0.0518607i	0.827441	−	0.561553i	$-0.189796\pi$
$71$	2.67521	+	3.68211i	0.0376790	+	0.0518607i	−0.789762	+	0.613414i	$0.789796\pi$
$72$	36.9732	+	0.719359i	0.513517	+	0.00999110i
$73$	16.6147	+	51.1348i	0.227599	+	0.700477i	0.998017	+	0.0629385i	$0.0200472\pi$
$73$	16.6147	+	51.1348i	0.227599	+	0.700477i	−0.770419	+	0.637538i	$0.779953\pi$
$74$	5.74756	+	1.86750i	0.0776697	+	0.0252364i
$75$	72.1020	+	12.1399i	0.961360	+	0.161865i
$76$	−62.2337			−0.818864
$77$		0			0
$78$	−32.0000	−	64.3432i	−0.410256	−	0.824912i
$79$	45.0455	+	32.7275i	0.570196	+	0.414272i	0.835177	−	0.549982i	$-0.185365\pi$
$79$	45.0455	+	32.7275i	0.570196	+	0.414272i	−0.264980	+	0.964254i	$0.585365\pi$
$80$	−14.9658	−	4.86267i	−0.187072	−	0.0607834i
$81$	67.3327	−	45.0256i	0.831268	−	0.555871i
$82$	−35.9749	+	26.1373i	−0.438718	+	0.318747i
$83$	−38.4046	−	52.8594i	−0.462706	−	0.636860i	0.512361	−	0.858770i	$-0.328771\pi$
$83$	−38.4046	−	52.8594i	−0.462706	−	0.636860i	−0.975067	+	0.221910i	$0.928771\pi$
$84$	−33.6094	−	34.2697i	−0.400112	−	0.407972i
$85$	−7.17288	+	22.0759i	−0.0843869	+	0.259716i
$86$	18.5632	−	25.5501i	0.215852	−	0.297094i
$87$	−34.6576	−	69.6868i	−0.398363	−	0.800998i
$88$		0			0
$89$		−	14.1341i		−	0.158810i	−0.996842	−	0.0794052i	$-0.974698\pi$
$89$		−	14.1341i		−	0.158810i	0.996842	−	0.0794052i	$-0.0253021\pi$
$90$	−17.2240	+	5.22824i	−0.191378	+	0.0580916i
$91$	19.7771	−	60.8676i	0.217331	−	0.668875i
$92$	60.7374	−	19.7348i	0.660189	−	0.214508i
$93$	−3.97137	+	7.61033i	−0.0427029	+	0.0818315i
$94$	85.1182	−	61.8420i	0.905513	−	0.657894i
$95$	−19.7673	+	6.42280i	−0.208077	+	0.0676084i
$96$	−100.008	+	14.8441i	−1.04175	+	0.154626i
$97$	−120.774	−	87.7477i	−1.24510	−	0.904615i	−0.247169	−	0.968972i	$-0.579500\pi$
$97$	−120.774	−	87.7477i	−1.24510	−	0.904615i	−0.997927	+	0.0643570i	$0.979500\pi$
$98$			8.86263i			0.0904350i
$99$		0			0
$100$	−57.8179			−0.578179
$101$	11.7613	−	16.1881i	0.116449	−	0.160278i	−0.746814	−	0.665033i	$-0.768417\pi$
$101$	11.7613	−	16.1881i	0.116449	−	0.160278i	0.863262	+	0.504755i	$0.168417\pi$
$102$	32.5749	+	219.465i	0.319362	+	2.15162i
$103$	−55.7540	−	171.593i	−0.541301	−	1.66595i	−0.729625	−	0.683847i	$-0.760305\pi$
$103$	−55.7540	−	171.593i	−0.541301	−	1.66595i	0.188324	−	0.982107i	$-0.439695\pi$
$104$	−22.9177	−	31.5436i	−0.220363	−	0.303303i
$105$	−14.2122	−	7.41646i	−0.135354	−	0.0706329i
$106$	69.8832	+	215.078i	0.659275	+	2.02904i
$107$	−61.3701	−	19.9403i	−0.573552	−	0.186358i	0.00785789	−	0.999969i	$-0.497499\pi$
$107$	−61.3701	−	19.9403i	−0.573552	−	0.186358i	−0.581410	+	0.813611i	$0.697499\pi$
$108$	−46.5935	+	43.9506i	−0.431421	+	0.406950i
$109$	−110.277			−1.01172			−0.505859	−	0.862616i	$-0.668824\pi$
$109$	−110.277			−1.01172			−0.505859	+	0.862616i	$0.668824\pi$
$110$		0			0
$111$	6.43070	−	3.19820i	0.0579343	−	0.0288126i
$112$	−108.373	−	78.7377i	−0.967617	−	0.703015i
$113$	119.110	+	38.7011i	1.05407	+	0.342488i	0.784264	−	0.620427i	$-0.213041\pi$
$113$	119.110	+	38.7011i	1.05407	+	0.342488i	0.269805	+	0.962915i	$0.413041\pi$
$114$	−141.839	+	139.106i	−1.24420	+	1.22023i
$115$	17.2553	−	12.5367i	0.150047	−	0.109015i
$116$	36.1748	+	49.7904i	0.311852	+	0.429228i
$117$	−80.6935	−	27.9657i	−0.689688	−	0.239023i
$118$	11.5126	−	35.4320i	0.0975641	−	0.300271i
$119$	−116.145	+	159.860i	−0.976010	+	1.34336i
$120$	−8.74456	+	4.34896i	−0.0728714	+	0.0362414i
$121$		0			0
$122$		−	160.158i		−	1.31277i
$123$	−8.77430	+	52.1129i	−0.0713358	+	0.423682i
$124$	2.09763	−	6.45583i	0.0169163	−	0.0520631i
$125$	−37.2025	+	12.0878i	−0.297620	+	0.0967026i
$126$	−153.201	−	2.98071i	−1.21588	−	0.0236565i
$127$	156.017	−	113.353i	1.22848	−	0.892544i	0.231706	−	0.972786i	$-0.425569\pi$
$127$	156.017	−	113.353i	1.22848	−	0.892544i	0.996775	+	0.0802421i	$0.0255693\pi$
$128$	−114.696	+	37.2671i	−0.896064	+	0.291149i
$129$	−5.51054	−	37.1259i	−0.0427174	−	0.287798i
$130$	15.3537	+	11.1551i	0.118106	+	0.0858087i
$131$		−	106.098i		−	0.809905i	−0.914338	−	0.404952i	$-0.867288\pi$
$131$		−	106.098i		−	0.809905i	0.914338	−	0.404952i	$-0.132712\pi$
$132$		0			0
$133$	−176.935			−1.33034
$134$	93.9653	−	129.332i	0.701233	−	0.965165i
$135$	−10.2636	+	18.7687i	−0.0760269	+	0.139028i
$136$	37.1996	+	114.489i	0.273526	+	0.841828i
$137$	−114.792	−	157.998i	−0.837901	−	1.15327i	−0.986401	−	0.164359i	$-0.947444\pi$
$137$	−114.792	−	157.998i	−0.837901	−	1.15327i	0.148500	−	0.988912i	$-0.452556\pi$
$138$	94.3173	−	180.740i	0.683459	−	1.30971i
$139$	−2.14296	−	6.59534i	−0.0154170	−	0.0474485i	0.943052	−	0.332645i	$-0.107941\pi$
$139$	−2.14296	−	6.59534i	−0.0154170	−	0.0474485i	−0.958469	+	0.285197i	$0.907941\pi$
$140$	12.0562	+	3.91728i	0.0861154	+	0.0279806i
$141$	20.7604	−	123.302i	0.147237	−	0.874479i
$142$	−11.4891			−0.0809093
$143$		0			0
$144$	−107.861	+	142.543i	−0.749038	+	0.989880i
$145$	16.6288	+	12.0816i	0.114682	+	0.0833211i
$146$	−129.082	−	41.9411i	−0.884120	−	0.287268i
$147$	7.37490	+	7.51978i	0.0501694	+	0.0511550i
$148$	−4.59466	+	3.33822i	−0.0310450	+	0.0225555i
$149$	−39.7916	−	54.7684i	−0.267058	−	0.367573i	0.654336	−	0.756204i	$-0.272948\pi$
$149$	−39.7916	−	54.7684i	−0.267058	−	0.367573i	−0.921394	+	0.388631i	$0.872948\pi$
$150$	−131.775	+	129.236i	−0.878501	+	0.861575i
$151$	−8.72469	+	26.8518i	−0.0577794	+	0.177827i	−0.975781	−	0.218750i	$-0.929802\pi$
$151$	−8.72469	+	26.8518i	−0.0577794	+	0.177827i	0.918001	+	0.396577i	$0.129802\pi$
$152$	−63.3585	+	87.2055i	−0.416832	+	0.573720i
$153$	210.264	+	159.105i	1.37427	+	1.03990i
$154$		0			0
$155$		−	2.26706i		−	0.0146262i
$156$	66.5953	+	11.2127i	0.426893	+	0.0718764i
$157$	−20.9502	+	64.4780i	−0.133441	+	0.410688i	−0.995344	−	0.0963843i	$-0.969272\pi$
$157$	−20.9502	+	64.4780i	−0.133441	+	0.410688i	0.861904	+	0.507072i	$0.169272\pi$
$158$	−133.674	+	43.4334i	−0.846039	+	0.274895i
$159$	238.268	+	124.338i	1.49854	+	0.781999i
$160$	21.6016	−	15.6945i	0.135010	−	0.0980906i
$161$	172.681	−	56.1073i	1.07255	−	0.348493i
$162$	−7.95348	+	204.317i	−0.0490955	+	1.26121i
$163$	54.9076	+	39.8927i	0.336856	+	0.244740i	0.743334	−	0.668920i	$-0.233243\pi$
$163$	54.9076	+	39.8927i	0.336856	+	0.244740i	−0.406478	+	0.913661i	$0.633243\pi$
$164$		−	41.7888i		−	0.254810i
$165$		0			0
$166$	164.935			0.993583
$167$	33.0542	−	45.4952i	0.197929	−	0.272426i	−0.698503	−	0.715607i	$-0.746150\pi$
$167$	33.0542	−	45.4952i	0.197929	−	0.272426i	0.896432	+	0.443181i	$0.146150\pi$
$168$	−82.2375	+	12.2064i	−0.489509	+	0.0726571i
$169$	−24.3989	−	75.0921i	−0.144372	−	0.444332i
$170$	−34.4411	−	47.4042i	−0.202595	−	0.278848i
$171$	−4.59281	+	236.059i	−0.0268585	+	1.38046i
$172$	9.17141	+	28.2267i	0.0533222	+	0.164109i
$173$	−213.546	−	69.3854i	−1.23437	−	0.401072i	−0.382075	−	0.924131i	$-0.624791\pi$
$173$	−213.546	−	69.3854i	−1.23437	−	0.401072i	−0.852296	+	0.523060i	$0.824791\pi$
$174$	193.740	+	32.6203i	1.11345	+	0.187473i
$175$	−164.380			−0.939316
$176$		0			0
$177$	−19.7160	−	39.6434i	−0.111390	−	0.223974i
$178$	28.8652	+	20.9718i	0.162164	+	0.117819i
$179$	133.586	+	43.4048i	0.746292	+	0.242485i	0.657385	−	0.753555i	$-0.271663\pi$
$179$	133.586	+	43.4048i	0.746292	+	0.242485i	0.0889068	+	0.996040i	$0.471663\pi$
$180$	5.53921	−	15.9831i	0.0307734	−	0.0887950i
$181$	−105.869	+	76.9184i	−0.584912	+	0.424964i	−0.840492	−	0.541824i	$-0.817734\pi$
$181$	−105.869	+	76.9184i	−0.584912	+	0.424964i	0.255579	+	0.966788i	$0.417734\pi$
$182$	94.9612	+	130.703i	0.521765	+	0.718148i
$183$	−133.273	−	135.891i	−0.728268	−	0.742575i
$184$	34.1816	−	105.200i	0.185770	−	0.571740i
$185$	−1.11489	+	1.53451i	−0.00602642	+	0.00829465i
$186$	−9.64947	−	19.4024i	−0.0518789	−	0.104314i
$187$		0			0
$188$			98.8744i			0.525928i
$189$	−132.469	+	124.955i	−0.700892	+	0.661136i
$190$	16.2133	−	49.8994i	0.0853332	−	0.262629i
$191$	334.202	−	108.589i	1.74975	−	0.568528i	0.753690	−	0.657230i	$-0.228272\pi$
$191$	334.202	−	108.589i	1.74975	−	0.568528i	0.996058	+	0.0887021i	$0.0282719\pi$
$192$	7.81075	−	14.9677i	0.0406810	−	0.0779570i
$193$	−198.618	+	144.304i	−1.02911	+	0.747691i	−0.968130	−	0.250448i	$-0.919422\pi$
$193$	−198.618	+	144.304i	−1.02911	+	0.747691i	−0.0609786	+	0.998139i	$0.519422\pi$
$194$	358.402	−	116.452i	1.84743	−	0.600268i
$195$	22.3099	−	3.31143i	0.114410	−	0.0169817i
$196$	−6.73813	−	4.89554i	−0.0343782	−	0.0249772i
$197$		−	6.15315i		−	0.0312343i	−0.999878	−	0.0156171i	$-0.995029\pi$
$197$		−	6.15315i		−	0.0312343i	0.999878	−	0.0156171i	$-0.00497129\pi$
$198$		0			0
$199$	193.272			0.971214			0.485607	−	0.874177i	$-0.338599\pi$
$199$	193.272			0.971214			0.485607	+	0.874177i	$0.338599\pi$
$200$	−58.8629	+	81.0178i	−0.294315	+	0.405089i
$201$	−27.8938	−	187.928i	−0.138775	−	0.934963i
$202$	15.6087	+	48.0387i	0.0772709	+	0.237815i
$203$	102.848	+	141.558i	0.506638	+	0.697328i
$204$	−184.850	−	96.4618i	−0.906126	−	0.472852i
$205$	−4.31280	−	13.2734i	−0.0210380	−	0.0647484i
$206$	433.159	+	140.742i	2.10272	+	0.683214i
$207$	−70.3735	−	231.839i	−0.339969	−	1.12000i
$208$	188.467			0.906093
$209$		0			0
$210$	36.2337	−	18.0202i	0.172541	−	0.0858106i
$211$	−86.3934	−	62.7684i	−0.409447	−	0.297481i	0.363931	−	0.931426i	$-0.381434\pi$
$211$	−86.3934	−	62.7684i	−0.409447	−	0.297481i	−0.773378	+	0.633945i	$0.781434\pi$
$212$	−202.123	−	65.6737i	−0.953409	−	0.309781i
$213$	−9.74831	+	9.56049i	−0.0457667	+	0.0448849i
$214$	131.782	−	95.7451i	0.615803	−	0.447407i
$215$	5.82625	+	8.01914i	0.0270988	+	0.0372983i
$216$	14.1505	+	110.034i	0.0655117	+	0.509419i
$217$	5.96370	−	18.3544i	0.0274825	−	0.0845824i
$218$	163.626	−	225.212i	0.750577	−	1.03308i
$219$	−144.424	+	71.8268i	−0.659470	+	0.327976i
$220$		0			0
$221$		−	278.007i		−	1.25795i
$222$	−3.01020	+	17.8784i	−0.0135595	+	0.0805333i
$223$	23.7112	−	72.9754i	0.106328	−	0.327244i	−0.883712	−	0.468031i	$-0.844963\pi$
$223$	23.7112	−	72.9754i	0.106328	−	0.327244i	0.990040	+	0.140787i	$0.0449634\pi$
$224$	216.175	−	70.2396i	0.965068	−	0.313570i
$225$	−4.26693	+	219.309i	−0.0189641	+	0.974707i
$226$	−255.768	+	185.826i	−1.13172	+	0.822241i
$227$	45.8822	−	14.9080i	0.202124	−	0.0656741i	−0.206205	−	0.978509i	$-0.566111\pi$
$227$	45.8822	−	14.9080i	0.202124	−	0.0656741i	0.408329	+	0.912835i	$0.366111\pi$
$228$	−27.4115	−	184.678i	−0.120226	−	0.809990i
$229$	12.4716	+	9.06117i	0.0544613	+	0.0395684i	0.614683	−	0.788774i	$-0.289284\pi$
$229$	12.4716	+	9.06117i	0.0544613	+	0.0395684i	−0.560222	+	0.828343i	$0.689284\pi$
$230$			53.8411i			0.234092i
$231$		0			0
$232$	106.598			0.459474
$233$	−101.807	+	140.126i	−0.436942	+	0.601399i	−0.969529	−	0.244976i	$-0.921220\pi$
$233$	−101.807	+	140.126i	−0.436942	+	0.601399i	0.532587	+	0.846375i	$0.321220\pi$
$234$	176.843	−	123.300i	0.755739	−	0.526924i
$235$	10.2043	+	31.4055i	0.0434225	+	0.133641i
$236$	20.5791	+	28.3247i	0.0871997	+	0.120020i
$237$	−77.2777	+	148.087i	−0.326066	+	0.624841i
$238$	−154.139	−	474.391i	−0.647643	−	1.99324i
$239$	281.890	+	91.5917i	1.17946	+	0.383229i	0.832165	−	0.554528i	$-0.187101\pi$
$239$	281.890	+	91.5917i	1.17946	+	0.383229i	0.347292	+	0.937757i	$0.387101\pi$
$240$	7.83810	−	46.5526i	0.0326588	−	0.193969i
$241$	−46.7011			−0.193780			−0.0968902	−	0.995295i	$-0.530890\pi$
$241$	−46.7011			−0.193780			−0.0968902	+	0.995295i	$0.530890\pi$
$242$		0			0
$243$	163.270	+	179.977i	0.671894	+	0.740647i
$244$	121.766	+	88.4681i	0.499040	+	0.362574i
$245$	−2.64548	−	0.859568i	−0.0107979	−	0.00350844i
$246$	−93.4076	−	95.2426i	−0.379706	−	0.387165i
$247$	201.392	−	146.320i	0.815354	−	0.592389i
$248$	−6.91075	−	9.51183i	−0.0278659	−	0.0383541i
$249$	139.944	−	137.248i	0.562024	−	0.551196i
$250$	30.5137	−	93.9117i	0.122055	−	0.375647i
$251$	−122.135	+	168.104i	−0.486592	+	0.669737i	−0.979755	−	0.200200i	$-0.935841\pi$
$251$	−122.135	+	168.104i	−0.486592	+	0.669737i	0.493163	+	0.869937i	$0.335841\pi$
$252$	86.8913	−	114.830i	0.344807	−	0.455674i
$253$		0			0
$254$			486.813i			1.91659i
$255$	−68.6693	−	11.5619i	−0.269291	−	0.0453408i
$256$	101.031	−	310.941i	0.394652	−	1.21461i
$257$	−189.962	+	61.7225i	−0.739153	+	0.240165i	−0.654307	−	0.756229i	$-0.727040\pi$
$257$	−189.962	+	61.7225i	−0.739153	+	0.240165i	−0.0848454	+	0.996394i	$0.527040\pi$
$258$	83.9961	+	43.8324i	0.325566	+	0.169893i
$259$	−13.0629	+	9.49079i	−0.0504361	+	0.0366440i
$260$	−16.9622	+	5.51134i	−0.0652391	+	0.0211975i
$261$	191.530	−	133.540i	0.733830	−	0.511648i
$262$	216.676	+	157.424i	0.827007	+	0.600856i
$263$			99.7592i			0.379313i	0.981851	+	0.189656i	$0.0607374\pi$
$263$			99.7592i			0.379313i	−0.981851	+	0.189656i	$0.939263\pi$
$264$		0			0
$265$	−70.9783			−0.267842
$266$	262.530	−	361.342i	0.986956	−	1.35843i
$267$	41.9429	−	6.22552i	0.157089	−	0.0233166i
$268$	46.4248	+	142.881i	0.173227	+	0.533137i
$269$	−29.6108	−	40.7558i	−0.110077	−	0.151509i	0.750424	−	0.660957i	$-0.229849\pi$
$269$	−29.6108	−	40.7558i	−0.110077	−	0.151509i	−0.860501	+	0.509448i	$0.829849\pi$
$270$	−23.1012	−	48.8091i	−0.0855601	−	0.180775i
$271$	38.4357	+	118.293i	0.141829	+	0.436505i	0.996590	−	0.0825177i	$-0.0262961\pi$
$271$	38.4357	+	118.293i	0.141829	+	0.436505i	−0.854761	+	0.519022i	$0.826296\pi$
$272$	−553.408	−	179.813i	−2.03459	−	0.661077i
$273$	189.335	+	31.8785i	0.693535	+	0.116771i
$274$	492.994			1.79925
$275$		0			0
$276$	85.3151	+	171.545i	0.309113	+	0.621540i
$277$	237.627	+	172.646i	0.857858	+	0.623271i	0.927301	−	0.374315i	$-0.122122\pi$
$277$	237.627	+	172.646i	0.857858	+	0.623271i	−0.0694432	+	0.997586i	$0.522122\pi$
$278$	16.6489	+	5.40955i	0.0598880	+	0.0194588i
$279$	−24.3328	−	8.43294i	−0.0872143	−	0.0302256i
$280$	17.7632	−	12.9057i	0.0634399	−	0.0460918i
$281$	−154.985	−	213.319i	−0.551549	−	0.759141i	0.438673	−	0.898647i	$-0.355449\pi$
$281$	−154.985	−	213.319i	−0.551549	−	0.759141i	−0.990221	+	0.139505i	$0.955449\pi$
$282$	221.007	+	225.349i	0.783712	+	0.799108i
$283$	−123.232	+	379.270i	−0.435450	+	1.34018i	0.457175	+	0.889377i	$0.348861\pi$
$283$	−123.232	+	379.270i	−0.435450	+	1.34018i	−0.892625	+	0.450800i	$0.851139\pi$
$284$	6.34636	−	8.73501i	0.0223463	−	0.0307571i
$285$	−27.7663	−	55.8304i	−0.0974257	−	0.195896i
$286$		0			0
$287$		−	118.809i		−	0.413967i
$288$	−88.0992	−	290.235i	−0.305900	−	1.00776i
$289$	−175.935	+	541.472i	−0.608771	+	1.87360i
$290$	−49.3467	+	16.0337i	−0.170161	+	0.0552887i
$291$	207.194	−	397.046i	0.712007	−	1.36442i
$292$	103.189	−	74.9713i	0.353388	−	0.256751i
$293$	−331.765	+	107.797i	−1.13230	+	0.367908i	−0.814451	−	0.580232i	$-0.802962\pi$
$293$	−331.765	+	107.797i	−1.13230	+	0.367908i	−0.317853	+	0.948140i	$0.602962\pi$
$294$	−26.2998	+	3.90364i	−0.0894550	+	0.0132777i
$295$	9.45981	+	6.87295i	0.0320671	+	0.0232981i
$296$			9.83686i			0.0332326i
$297$		0			0
$298$	170.891			0.573461
$299$	−150.151	+	206.665i	−0.502177	+	0.691188i
$300$	−25.4665	−	171.574i	−0.0848883	−	0.571913i
$301$	26.0750	+	80.2505i	0.0866278	+	0.266613i
$302$	−41.8923	−	57.6597i	−0.138716	−	0.190926i
$303$	53.2183	+	27.7714i	0.175638	+	0.0916548i
$304$	−161.010	−	495.537i	−0.529637	−	1.63005i
$305$	47.8069	+	15.5334i	0.156744	+	0.0509292i
$306$	−636.913	+	193.331i	−2.08141	+	0.631802i
$307$	398.527			1.29813			0.649067	−	0.760731i	$-0.275160\pi$
$307$	398.527			1.29813			0.649067	+	0.760731i	$0.275160\pi$
$308$		0			0
$309$	484.644	−	241.030i	1.56843	−	0.780031i
$310$	4.62985	+	3.36379i	0.0149350	+	0.0108509i
$311$	418.794	+	136.074i	1.34660	+	0.437538i	0.891548	−	0.452925i	$-0.149620\pi$
$311$	418.794	+	136.074i	1.34660	+	0.437538i	0.455055	+	0.890463i	$0.349620\pi$
$312$	83.5108	−	81.9018i	0.267663	−	0.262506i
$313$	−428.698	+	311.467i	−1.36964	+	0.995102i	−0.371876	+	0.928283i	$0.621285\pi$
$313$	−428.698	+	311.467i	−1.36964	+	0.995102i	−0.997765	+	0.0668198i	$0.978715\pi$
$314$	−100.594	−	138.455i	−0.320362	−	0.440941i
$315$	15.7484	−	45.4411i	0.0499948	−	0.144257i
$316$	40.8171	−	125.622i	0.129168	−	0.397539i
$317$	−216.556	+	298.063i	−0.683140	+	0.940262i	−0.999966	−	0.00822156i	$-0.997383\pi$
$317$	−216.556	+	298.063i	−0.683140	+	0.940262i	0.316826	+	0.948484i	$0.397383\pi$
$318$	−607.462	+	302.111i	−1.91026	+	0.950035i
$319$		0			0
$320$			4.45877i			0.0139337i
$321$	32.1417	−	190.898i	0.100130	−	0.594698i
$322$	−141.634	+	435.904i	−0.439857	+	1.35374i
$323$	−730.962	+	237.504i	−2.26304	+	0.735306i
$324$	−150.946	−	118.907i	−0.465881	−	0.366997i
$325$	187.103	−	135.938i	0.575701	−	0.418271i
$326$	−162.940	+	52.9425i	−0.499817	+	0.162400i
$327$	−48.5727	−	327.246i	−0.148540	−	1.00075i
$328$	−58.5570	−	42.5441i	−0.178527	−	0.129708i
$329$			281.107i			0.854428i
$330$		0			0
$331$	−115.649			−0.349394			−0.174697	−	0.984622i	$-0.555895\pi$
$331$	−115.649			−0.349394			−0.174697	+	0.984622i	$0.555895\pi$
$332$	−91.1065	+	125.397i	−0.274417	+	0.377703i
$333$	12.3231	+	17.6744i	0.0370063	+	0.0530762i
$334$	43.8670	+	135.009i	0.131338	+	0.404218i
$335$	29.4919	+	40.5921i	0.0880354	+	0.121170i
$336$	185.919	−	356.277i	0.553331	−	1.06035i
$337$	16.4618	+	50.6643i	0.0488482	+	0.150339i	0.972505	−	0.232881i	$-0.0748151\pi$
$337$	16.4618	+	50.6643i	0.0488482	+	0.150339i	−0.923657	+	0.383220i	$0.874815\pi$
$338$	189.558	+	61.5911i	0.560822	+	0.182222i
$339$	−62.3820	+	370.503i	−0.184018	+	1.09293i
$340$	55.0652			0.161957
$341$		0			0
$342$	−475.272	−	359.636i	−1.38968	−	1.05157i
$343$	−286.524	−	208.172i	−0.835346	−	0.606915i
$344$	48.8901	+	15.8854i	0.142122	+	0.0461784i
$345$	44.8030	+	45.6831i	0.129864	+	0.132415i
$346$	458.554	−	333.159i	1.32530	−	0.962888i
$347$	6.58804	+	9.06766i	0.0189857	+	0.0261316i	0.818404	−	0.574643i	$-0.194859\pi$
$347$	6.58804	+	9.06766i	0.0189857	+	0.0261316i	−0.799419	+	0.600774i	$0.794859\pi$
$348$	−131.819	+	129.279i	−0.378790	+	0.371492i
$349$	66.1346	−	203.541i	0.189498	−	0.583213i	−0.810499	−	0.585740i	$-0.800804\pi$
$349$	66.1346	−	203.541i	0.189498	−	0.583213i	0.999997	+	0.00252619i	$0.000804112\pi$
$350$	243.902	−	335.703i	0.696864	−	0.959151i
$351$	47.4456	−	251.775i	0.135173	−	0.717308i
$352$		0			0
$353$			531.528i			1.50574i	0.658167	+	0.752872i	$0.271332\pi$
$353$			531.528i			1.50574i	−0.658167	+	0.752872i	$0.728668\pi$
$354$	110.215	+	18.5570i	0.311342	+	0.0524209i
$355$	1.11431	−	3.42948i	0.00313889	−	0.00966051i
$356$	−31.8890	+	10.3614i	−0.0895760	+	0.0291050i
$357$	−525.541	−	274.248i	−1.47210	−	0.768201i
$358$	−286.854	+	208.411i	−0.801267	+	0.582155i
$359$	−166.620	+	54.1381i	−0.464122	+	0.150802i	−0.531738	−	0.846909i	$-0.678461\pi$
$359$	−166.620	+	54.1381i	−0.464122	+	0.150802i	0.0676158	+	0.997711i	$0.478461\pi$
$360$	−16.7571	−	24.0339i	−0.0465476	−	0.0667607i
$361$	−264.716	−	192.327i	−0.733284	−	0.532762i
$362$		−	330.338i		−	0.912537i
$363$		0			0
$364$	−151.826			−0.417104
$365$	25.0387	−	34.4628i	0.0685991	−	0.0944186i
$366$	475.268	−	70.5433i	1.29855	−	0.192741i
$367$	42.9643	+	132.231i	0.117069	+	0.360301i	0.992373	−	0.123272i	$-0.0393387\pi$
$367$	42.9643	+	132.231i	0.117069	+	0.360301i	−0.875304	+	0.483573i	$0.839339\pi$
$368$	314.277	+	432.565i	0.854013	+	1.17545i
$369$	−158.509	−	3.08399i	−0.429564	−	0.00835770i
$370$	−1.47959	−	4.55372i	−0.00399890	−	0.0123073i
$371$	−574.649	−	186.715i	−1.54892	−	0.503275i
$372$	20.0815	+	3.38115i	0.0539826	+	0.00908911i
$373$	−149.081			−0.399682			−0.199841	−	0.979828i	$-0.564043\pi$
$373$	−149.081			−0.399682			−0.199841	+	0.979828i	$0.564043\pi$
$374$		0			0
$375$	−52.2567	−	105.074i	−0.139351	−	0.280197i
$376$	138.549	+	100.661i	0.368480	+	0.267717i
$377$	−234.128	−	76.0730i	−0.621030	−	0.201785i
$378$	−58.6337	−	455.935i	−0.155116	−	1.20618i
$379$	−218.753	+	158.934i	−0.577186	+	0.419350i	−0.837708	−	0.546118i	$-0.816105\pi$
$379$	−218.753	+	158.934i	−0.577186	+	0.419350i	0.260523	+	0.965468i	$0.416105\pi$
$380$	28.9819	+	39.8902i	0.0762681	+	0.104974i
$381$	405.093	+	413.052i	1.06324	+	1.08413i
$382$	−274.115	+	843.639i	−0.717578	+	2.20848i
$383$	371.364	−	511.138i	0.969618	−	1.33456i	0.0273778	−	0.999625i	$-0.491284\pi$
$383$	371.364	−	511.138i	0.969618	−	1.33456i	0.942240	−	0.334939i	$-0.108716\pi$
$384$	−161.109	−	323.945i	−0.419554	−	0.843607i
$385$		0			0
$386$		−	619.738i		−	1.60554i
$387$	107.744	−	32.7050i	0.278407	−	0.0845089i
$388$	−109.437	+	336.814i	−0.282055	+	0.868076i
$389$	437.482	−	142.147i	1.12463	−	0.365415i	0.313098	−	0.949721i	$-0.398633\pi$
$389$	437.482	−	142.147i	1.12463	−	0.365415i	0.811534	+	0.584305i	$0.198633\pi$
$390$	−26.3400	+	50.4754i	−0.0675386	+	0.129424i
$391$	638.073	−	463.587i	1.63190	−	1.18564i
$392$	−13.7198	+	4.45784i	−0.0349995	+	0.0113720i
$393$	314.843	−	46.7317i	0.801128	−	0.118910i
$394$	12.5662	+	9.12985i	0.0318938	+	0.0231722i
$395$		−	44.1140i		−	0.111681i
$396$		0			0
$397$	−561.272			−1.41378			−0.706891	−	0.707322i	$-0.749903\pi$
$397$	−561.272			−1.41378			−0.706891	+	0.707322i	$0.749903\pi$
$398$	−286.770	+	394.706i	−0.720529	+	0.991722i
$399$	−77.9327	−	525.052i	−0.195320	−	1.31592i
$400$	−149.585	−	460.376i	−0.373963	−	1.15094i
$401$	−105.710	−	145.497i	−0.263616	−	0.362837i	0.656605	−	0.754234i	$-0.271992\pi$
$401$	−105.710	−	145.497i	−0.263616	−	0.362837i	−0.920222	+	0.391398i	$0.871992\pi$
$402$	425.180	+	221.875i	1.05766	+	0.551929i
$403$	8.39051	+	25.8233i	0.0208201	+	0.0640777i
$404$	−45.1450	−	14.6685i	−0.111745	−	0.0363082i
$405$	−60.2167	−	22.1903i	−0.148683	−	0.0547909i
$406$	−441.696			−1.08792
$407$		0			0
$408$	−323.359	+	160.817i	−0.792546	+	0.394159i
$409$	109.780	+	79.7598i	0.268411	+	0.195012i	0.713847	−	0.700302i	$-0.246951\pi$
$409$	109.780	+	79.7598i	0.268411	+	0.195012i	−0.445436	+	0.895314i	$0.646951\pi$
$410$	33.5066	+	10.8870i	0.0817234	+	0.0265535i
$411$	418.297	−	410.237i	1.01775	−	0.998144i
$412$	−346.272	+	251.582i	−0.840467	+	0.610635i
$413$	58.5079	+	80.5292i	0.141666	+	0.194986i
$414$	577.888	+	200.277i	1.39586	+	0.483760i
$415$	−15.9967	+	49.2327i	−0.0385462	+	0.118633i
$416$	−187.971	+	258.720i	−0.451853	+	0.621923i
$417$	18.6277	−	9.26419i	0.0446708	−	0.0222163i
$418$		0			0
$419$			50.3361i			0.120134i	0.998194	+	0.0600669i	$0.0191314\pi$
$419$			50.3361i			0.120134i	−0.998194	+	0.0600669i	$0.980869\pi$
$420$	−6.31424	+	37.5019i	−0.0150339	+	0.0892903i
$421$	−16.2805	+	50.1063i	−0.0386711	+	0.119017i	−0.968528	−	0.248903i	$-0.919930\pi$
$421$	−16.2805	+	50.1063i	−0.0386711	+	0.119017i	0.929857	+	0.367920i	$0.119930\pi$
$422$	256.375	−	83.3014i	0.607525	−	0.197397i
$423$	375.040	+	7.29687i	0.886620	+	0.0172503i
$424$	−297.802	+	216.366i	−0.702363	+	0.510296i
$425$	−679.096	+	220.652i	−1.59787	+	0.519181i
$426$	−5.06050	−	34.0939i	−0.0118791	−	0.0800325i
$427$	346.189	+	251.521i	0.810747	+	0.589042i
$428$			153.079i			0.357662i
$429$		0			0
$430$	−25.0217			−0.0581901
$431$	292.016	−	401.925i	0.677531	−	0.932541i	−0.322370	−	0.946614i	$-0.604480\pi$
$431$	292.016	−	401.925i	0.677531	−	0.932541i	0.999901	+	0.0140726i	$0.00447961\pi$
$432$	−470.503	−	257.293i	−1.08913	−	0.595586i
$433$	159.336	+	490.386i	0.367982	+	1.13253i	0.948093	+	0.317994i	$0.103009\pi$
$433$	159.336	+	490.386i	0.367982	+	1.13253i	−0.580111	+	0.814537i	$0.696991\pi$
$434$	28.6352	+	39.4129i	0.0659796	+	0.0908132i
$435$	−28.5276	+	54.6673i	−0.0655806	+	0.125672i
$436$	80.8415	+	248.804i	0.185416	+	0.570652i
$437$	671.660	+	218.235i	1.53698	+	0.499395i
$438$	67.6046	−	401.521i	0.154348	−	0.916716i
$439$	25.1087			0.0571953			0.0285977	−	0.999591i	$-0.490896\pi$
$439$	25.1087			0.0571953			0.0285977	+	0.999591i	$0.490896\pi$
$440$		0			0
$441$	−19.0665	+	25.1971i	−0.0432347	+	0.0571363i
$442$	567.754	+	412.497i	1.28451	+	0.933252i
$443$	−827.818	−	268.974i	−1.86866	−	0.607166i	−0.992029	−	0.126011i	$-0.959783\pi$
$443$	−827.818	−	268.974i	−1.86866	−	0.607166i	−0.876635	−	0.481155i	$-0.840217\pi$
$444$	−11.9299	−	12.1643i	−0.0268691	−	0.0273970i
$445$	−9.05960	+	6.58219i	−0.0203587	+	0.0147914i
$446$	113.851	+	156.702i	0.255271	+	0.351351i
$447$	144.998	−	142.204i	0.324380	−	0.318131i
$448$	−11.7292	+	36.0988i	−0.0261813	+	0.0805776i
$449$	338.354	−	465.704i	0.753572	−	1.03720i	−0.244150	−	0.969737i	$-0.578509\pi$
$449$	338.354	−	465.704i	0.753572	−	1.03720i	0.997722	−	0.0674648i	$-0.0214910\pi$
$450$	−441.549	−	334.118i	−0.981220	−	0.742484i
$451$		0			0
$452$		−	297.103i		−	0.657308i
$453$	−83.5254	−	14.0633i	−0.184383	−	0.0310447i
$454$	−37.6329	+	115.822i	−0.0828918	+	0.255115i
$455$	−48.2246	+	15.6691i	−0.105988	+	0.0344376i
$456$	−286.688	−	149.605i	−0.628702	−	0.328081i
$457$	20.7046	−	15.0428i	0.0453055	−	0.0329164i	−0.564902	−	0.825158i	$-0.691086\pi$
$457$	20.7046	−	15.0428i	0.0453055	−	0.0329164i	0.610208	+	0.792242i	$0.291086\pi$
$458$	−37.0100	+	12.0253i	−0.0808079	+	0.0262561i
$459$	−379.531	+	694.034i	−0.826865	+	1.51206i
$460$	−40.9345	−	29.7407i	−0.0889881	−	0.0646537i
$461$		−	289.365i		−	0.627691i	−0.949474	−	0.313845i	$-0.898383\pi$
$461$		−	289.365i		−	0.627691i	0.949474	−	0.313845i	$-0.101617\pi$
$462$		0			0
$463$	−201.052			−0.434237			−0.217118	−	0.976145i	$-0.569666\pi$
$463$	−201.052			−0.434237			−0.217118	+	0.976145i	$0.569666\pi$
$464$	−302.866	+	416.859i	−0.652728	+	0.898403i
$465$	6.72746	−	0.998548i	0.0144677	−	0.00214741i
$466$	−135.111	−	415.829i	−0.289938	−	0.892336i
$467$	64.8441	+	89.2503i	0.138853	+	0.191114i	0.872780	−	0.488114i	$-0.162315\pi$
$467$	64.8441	+	89.2503i	0.138853	+	0.191114i	−0.733928	+	0.679228i	$0.762315\pi$
$468$	−3.94105	+	202.560i	−0.00842104	+	0.432820i
$469$	131.989	+	406.220i	0.281426	+	0.866141i
$470$	−79.2782	−	25.7591i	−0.168677	−	0.0548065i
$471$	−200.565	−	33.7694i	−0.425829	−	0.0716973i
$472$	60.6414			0.128477
$473$		0			0
$474$	−187.766	−	377.546i	−0.396131	−	0.796511i
$475$	−517.265	−	375.815i	−1.08898	−	0.791190i
$476$	445.816	+	144.854i	0.936587	+	0.304316i
$477$	−264.023	+	761.825i	−0.553508	+	1.59712i
$478$	−605.312	+	439.785i	−1.26634	+	0.920052i
$479$	401.770	+	552.989i	0.838769	+	1.15447i	0.986227	+	0.165398i	$0.0528909\pi$
$479$	401.770	+	552.989i	0.838769	+	1.15447i	−0.147458	+	0.989068i	$0.547109\pi$
$480$	56.0879	+	57.1898i	0.116850	+	0.119145i
$481$	7.02002	−	21.6054i	0.0145946	−	0.0449177i
$482$	69.2936	−	95.3744i	0.143763	−	0.197872i
$483$	242.557	+	487.715i	0.502188	+	1.00976i
$484$		0			0
$485$			118.277i			0.243870i
$486$	−609.811	+	66.3915i	−1.25475	+	0.136608i
$487$	−40.2033	+	123.733i	−0.0825530	+	0.254072i	−0.983811	−	0.179212i	$-0.942645\pi$
$487$	−40.2033	+	123.733i	−0.0825530	+	0.254072i	0.901258	+	0.433284i	$0.142645\pi$
$488$	247.933	−	80.5584i	0.508060	−	0.165079i
$489$	−94.1965	+	180.509i	−0.192631	+	0.369139i
$490$	5.68071	−	4.12728i	0.0115933	−	0.00842302i
$491$	757.592	−	246.157i	1.54296	−	0.501338i	0.590767	−	0.806842i	$-0.298825\pi$
$491$	757.592	−	246.157i	1.54296	−	0.501338i	0.952191	+	0.305504i	$0.0988251\pi$
$492$	124.008	−	18.4063i	0.252049	−	0.0374112i
$493$	614.905	+	446.755i	1.24727	+	0.906196i
$494$			628.395i			1.27206i
$495$		0			0
$496$	56.8316			0.114580
$497$	18.0431	−	24.8342i	0.0363041	−	0.0499683i
$498$	72.6472	+	489.442i	0.145878	+	0.982816i
$499$	151.428	+	466.048i	0.303464	+	0.933965i	0.980246	+	0.197782i	$0.0633738\pi$
$499$	151.428	+	466.048i	0.303464	+	0.933965i	−0.676782	+	0.736183i	$0.736626\pi$
$500$	54.5445	+	75.0740i	0.109089	+	0.150148i
$501$	149.566	+	78.0491i	0.298534	+	0.155787i
$502$	−162.088	−	498.855i	−0.322884	−	0.993735i
$503$	−269.417	−	87.5387i	−0.535619	−	0.174033i	0.0287028	−	0.999588i	$-0.490862\pi$
$503$	−269.417	−	87.5387i	−0.535619	−	0.174033i	−0.564322	+	0.825555i	$0.690862\pi$
$504$	−72.4447	−	238.662i	−0.143739	−	0.473537i
$505$	−15.8533			−0.0313927
$506$		0			0
$507$	212.088	−	105.479i	0.418320	−	0.208045i
$508$	−370.116	−	268.905i	−0.728576	−	0.529341i
$509$	−231.725	−	75.2919i	−0.455255	−	0.147921i	0.0724082	−	0.997375i	$-0.476932\pi$
$509$	−231.725	−	75.2919i	−0.455255	−	0.147921i	−0.527663	+	0.849454i	$0.676932\pi$
$510$	125.501	−	123.083i	0.246081	−	0.241340i
$511$	293.374	−	213.149i	0.574118	−	0.417121i
$512$	201.563	+	277.427i	0.393677	+	0.541851i
$513$	−702.524	+	90.3453i	−1.36944	+	0.176112i
$514$	155.808	−	479.529i	0.303129	−	0.932935i
$515$	−84.0224	+	115.647i	−0.163150	+	0.224557i
$516$	−79.7228	+	39.6488i	−0.154502	+	0.0768388i
$517$		0			0
$518$		−	40.7597i		−	0.0786867i
$519$	111.842	−	664.258i	0.215495	−	1.27988i
$520$	−9.54592	+	29.3793i	−0.0183575	+	0.0564987i
$521$	−357.858	+	116.275i	−0.686867	+	0.223177i	−0.631599	−	0.775295i	$-0.717601\pi$
$521$	−357.858	+	116.275i	−0.686867	+	0.223177i	−0.0552676	+	0.998472i	$0.517601\pi$
$522$	−11.4654	+	589.291i	−0.0219643	+	1.12891i
$523$	449.686	−	326.716i	0.859820	−	0.624696i	−0.0680161	−	0.997684i	$-0.521667\pi$
$523$	449.686	−	326.716i	0.859820	−	0.624696i	0.927836	+	0.372989i	$0.121667\pi$
$524$	−239.374	+	77.7775i	−0.456821	+	0.148430i
$525$	−72.4030	−	487.797i	−0.137911	−	0.929137i
$526$	−203.732	−	148.020i	−0.387322	−	0.281406i
$527$		−	83.8317i		−	0.159074i
$528$		0			0
$529$	−195.715			−0.369971
$530$	105.315	−	144.954i	0.198708	−	0.273498i
$531$	108.957	−	75.9683i	0.205193	−	0.143067i
$532$	129.706	+	399.196i	0.243809	+	0.750368i
$533$	98.2514	+	135.231i	0.184337	+	0.253718i
$534$	−49.5196	+	94.8943i	−0.0927333	+	0.177705i
$535$	15.7985	+	48.6227i	0.0295299	+	0.0908836i
$536$	247.477	+	80.4100i	0.461710	+	0.150019i
$537$	−69.9638	+	415.534i	−0.130286	+	0.773806i
$538$	127.168			0.236373
$539$		0			0
$540$	49.8695	+	9.39764i	0.0923509	+	0.0174030i
$541$	754.171	+	547.937i	1.39403	+	1.01282i	0.995410	+	0.0957073i	$0.0305113\pi$
$541$	754.171	+	547.937i	1.39403	+	1.01282i	0.398622	+	0.917116i	$0.369489\pi$
$542$	−298.611	−	97.0246i	−0.550943	−	0.179012i
$543$	−274.886	−	280.286i	−0.506235	−	0.516180i
$544$	798.790	−	580.355i	1.46836	−	1.06683i
$545$	51.3555	+	70.6848i	0.0942303	+	0.129697i
$546$	−346.033	+	339.366i	−0.633760	+	0.621549i
$547$	−227.740	+	700.913i	−0.416344	+	1.28138i	0.494699	+	0.869065i	$0.335278\pi$
$547$	−227.740	+	700.913i	−0.416344	+	1.28138i	−0.911043	+	0.412312i	$0.864722\pi$
$548$	−272.320	+	374.816i	−0.496934	+	0.683971i
$549$	344.554	−	455.341i	0.627604	−	0.829401i
$550$		0			0
$551$			680.583i			1.23518i
$552$	327.236	+	55.0971i	0.592819	+	0.0998136i
$553$	116.046	−	357.153i	0.209848	−	0.645846i
$554$	−705.166	+	229.122i	−1.27286	+	0.413578i
$555$	−5.04471	−	2.63253i	−0.00908956	−	0.00474329i
$556$	−13.3093	+	9.66976i	−0.0239376	+	0.0173917i
$557$	604.548	−	196.430i	1.08536	−	0.352656i	0.288911	−	0.957356i	$-0.406707\pi$
$557$	604.548	−	196.430i	1.08536	−	0.352656i	0.796454	+	0.604700i	$0.206707\pi$
$558$	53.3263	−	37.1807i	0.0955668	−	0.0666321i
$559$	−96.0443	−	69.7803i	−0.171814	−	0.124831i
$560$			106.132i			0.189521i
$561$		0			0
$562$	665.609			1.18436
$563$	470.435	−	647.498i	0.835586	−	1.15009i	−0.151271	−	0.988492i	$-0.548337\pi$
$563$	470.435	−	647.498i	0.835586	−	1.15009i	0.986857	−	0.161593i	$-0.0516633\pi$
$564$	−293.409	+	43.5502i	−0.520228	+	0.0772167i
$565$	−30.6624	−	94.3691i	−0.0542697	−	0.167025i
$566$	−591.709	−	814.418i	−1.04542	−	1.43890i
$567$	−429.149	−	338.061i	−0.756876	−	0.596228i
$568$	−5.77895	−	17.7858i	−0.0101742	−	0.0313130i
$569$	−49.9733	−	16.2373i	−0.0878265	−	0.0285366i	0.264774	−	0.964310i	$-0.414703\pi$
$569$	−49.9733	−	16.2373i	−0.0878265	−	0.0285366i	−0.352601	+	0.935774i	$0.614703\pi$
$570$	155.217	+	26.1341i	0.272311	+	0.0458493i
$571$	−10.1143			−0.0177133			−0.00885666	−	0.999961i	$-0.502819\pi$
$571$	−10.1143			−0.0177133			−0.00885666	+	0.999961i	$0.502819\pi$
$572$		0			0
$573$	469.439	+	943.912i	0.819265	+	1.64732i
$574$	242.635	+	176.284i	0.422709	+	0.307116i
$575$	624.002	+	202.751i	1.08522	+	0.352610i
$576$	47.8569	+	16.5856i	0.0830849	+	0.0287945i
$577$	71.4329	−	51.8990i	0.123801	−	0.0899463i	−0.524162	−	0.851619i	$-0.675621\pi$
$577$	71.4329	−	51.8990i	0.123801	−	0.0899463i	0.647962	+	0.761672i	$0.275621\pi$
$578$	−844.764	−	1162.72i	−1.46153	−	2.01162i
$579$	−515.705	−	525.836i	−0.890682	−	0.908180i
$580$	15.0679	−	46.3742i	0.0259791	−	0.0799556i
$581$	−259.022	+	356.514i	−0.445822	+	0.613621i
$582$	503.432	+	1012.26i	0.865003	+	1.73928i
$583$		0			0
$584$		−	220.921i		−	0.378289i
$585$	19.6533	+	64.7459i	0.0335953	+	0.110677i
$586$	272.116	−	837.488i	0.464362	−	1.42916i
$587$	715.396	−	232.446i	1.21873	−	0.395990i	0.372112	−	0.928188i	$-0.378634\pi$
$587$	715.396	−	232.446i	1.21873	−	0.395990i	0.846620	+	0.532198i	$0.178634\pi$
$588$	11.5596	−	22.1516i	0.0196591	−	0.0376728i
$589$	60.7291	−	44.1222i	0.103105	−	0.0749104i
$590$	−28.0723	+	9.12125i	−0.0475802	+	0.0154598i
$591$	18.2594	−	2.71022i	0.0308958	−	0.00458582i
$592$	−38.4678	−	27.9485i	−0.0649794	−	0.0472103i
$593$		−	656.836i		−	1.10765i	−0.832633	−	0.553825i	$-0.813168\pi$
$593$		−	656.836i		−	1.10765i	0.832633	−	0.553825i	$-0.186832\pi$
$594$		0			0
$595$	156.554			0.263117
$596$	−94.3968	+	129.926i	−0.158384	+	0.217997i
$597$	85.1285	+	573.532i	0.142594	+	0.960689i
$598$	−199.269	−	613.287i	−0.333226	−	1.02556i
$599$	−237.419	−	326.780i	−0.396360	−	0.545542i	0.563466	−	0.826139i	$-0.309468\pi$
$599$	−237.419	−	326.780i	−0.396360	−	0.545542i	−0.959826	+	0.280597i	$0.909468\pi$
$600$	−266.346	−	138.990i	−0.443911	−	0.231650i
$601$	255.483	+	786.296i	0.425097	+	1.30831i	0.902902	+	0.429847i	$0.141433\pi$
$601$	255.483	+	786.296i	0.425097	+	1.30831i	−0.477805	+	0.878466i	$0.658567\pi$
$602$	−202.579	−	65.8220i	−0.336511	−	0.109339i
$603$	545.387	−	165.549i	0.904456	−	0.274543i
$604$	66.9783			0.110891
$605$		0			0
$606$	−135.679	+	67.4778i	−0.223893	+	0.111350i
$607$	−935.580	−	679.738i	−1.54132	−	1.11983i	−0.949503	−	0.313759i	$-0.898412\pi$
$607$	−935.580	−	679.738i	−1.54132	−	1.11983i	−0.591815	−	0.806074i	$-0.701588\pi$
$608$	840.837	+	273.204i	1.38296	+	0.449349i
$609$	−374.770	+	367.550i	−0.615387	+	0.603530i
$610$	−102.657	+	74.5848i	−0.168290	+	0.122270i
$611$	−232.468	−	319.964i	−0.380471	−	0.523673i
$612$	204.830	−	591.027i	0.334690	−	0.965731i
$613$	277.574	−	854.286i	0.452813	−	1.39362i	−0.420870	−	0.907121i	$-0.638275\pi$
$613$	277.574	−	854.286i	0.452813	−	1.39362i	0.873683	−	0.486495i	$-0.161725\pi$
$614$	−591.322	+	813.885i	−0.963065	+	1.32555i
$615$	37.4891	−	18.6446i	0.0609579	−	0.0303164i
$616$		0			0
$617$		−	713.002i		−	1.15560i	−0.816180	−	0.577798i	$-0.803912\pi$
$617$		−	713.002i		−	1.15560i	0.816180	−	0.577798i	$-0.196088\pi$
$618$	−226.861	+	1347.39i	−0.367089	+	2.18024i
$619$	−12.4874	+	38.4324i	−0.0201736	+	0.0620879i	−0.960637	−	0.277808i	$-0.910392\pi$
$619$	−12.4874	+	38.4324i	−0.0201736	+	0.0620879i	0.940463	+	0.339896i	$0.110392\pi$
$620$	−5.11487	+	1.66192i	−0.00824979	+	0.00268052i
$621$	656.984	−	310.949i	1.05795	−	0.500723i
$622$	−899.288	+	653.371i	−1.44580	+	1.05044i
$623$	−90.6628	+	29.4581i	−0.145526	+	0.0472843i
$624$	83.0124	+	559.275i	0.133033	+	0.896274i
$625$	−467.867	−	339.925i	−0.748587	−	0.543880i
$626$		−	1337.64i		−	2.13681i
$627$		0			0
$628$	160.832			0.256101
$629$	−41.2266	+	56.7435i	−0.0655431	+	0.0902123i
$630$	69.4343	+	99.5859i	0.110213	+	0.158073i
$631$	−231.300	−	711.868i	−0.366561	−	1.12816i	−0.948998	−	0.315283i	$-0.897901\pi$
$631$	−231.300	−	711.868i	−0.366561	−	1.12816i	0.582437	−	0.812876i	$-0.302099\pi$
$632$	−134.474	−	185.088i	−0.212776	−	0.292861i
$633$	148.212	−	284.018i	0.234142	−	0.448686i
$634$	−287.396	−	884.513i	−0.453306	−	1.39513i
$635$	−145.313	−	47.2149i	−0.228839	−	0.0743542i
$636$	105.859	−	628.724i	0.166445	−	0.988560i
$637$	33.3151			0.0523000
$638$		0			0
$639$	−32.6644	−	24.7170i	−0.0511180	−	0.0386807i
$640$	77.3006	+	56.1622i	0.120782	+	0.0877534i
$641$	116.317	+	37.7936i	0.181462	+	0.0589604i	0.398338	−	0.917239i	$-0.369587\pi$
$641$	116.317	+	37.7936i	0.181462	+	0.0589604i	−0.216877	+	0.976199i	$0.569587\pi$
$642$	342.167	+	348.889i	0.532971	+	0.543441i
$643$	509.125	−	369.901i	0.791796	−	0.575273i	−0.116700	−	0.993167i	$-0.537232\pi$
$643$	509.125	−	369.901i	0.791796	−	0.575273i	0.908496	+	0.417894i	$0.137232\pi$
$644$	−253.176	−	348.467i	−0.393130	−	0.541097i
$645$	−21.2305	+	20.8214i	−0.0329155	+	0.0322813i
$646$	599.540	−	1845.19i	0.928080	−	2.85634i
$647$	−109.228	+	150.340i	−0.168822	+	0.232364i	−0.885042	−	0.465510i	$-0.845871\pi$
$647$	−109.228	+	150.340i	−0.168822	+	0.232364i	0.716220	+	0.697875i	$0.245871\pi$
$648$	−320.293	+	90.4574i	−0.494280	+	0.139595i
$649$		0			0
$650$			583.808i			0.898166i
$651$	57.0932	+	9.61284i	0.0877008	+	0.0147663i
$652$	49.7535	−	153.125i	0.0763090	−	0.234855i
$653$	−192.509	+	62.5501i	−0.294808	+	0.0957888i	−0.452687	−	0.891670i	$-0.649534\pi$
$653$	−192.509	+	62.5501i	−0.294808	+	0.0957888i	0.157879	+	0.987458i	$0.449534\pi$
$654$	740.384	+	386.361i	1.13209	+	0.590766i
$655$	−68.0057	+	49.4090i	−0.103826	+	0.0754337i
$656$	332.744	−	108.115i	0.507232	−	0.164810i
$657$	−276.758	−	396.940i	−0.421245	−	0.604170i
$658$	−574.085	−	417.097i	−0.872470	−	0.633887i
$659$			1094.02i			1.66012i	0.557674	+	0.830060i	$0.311694\pi$
$659$			1094.02i			1.66012i	−0.557674	+	0.830060i	$0.688306\pi$
$660$		0			0
$661$	1024.53			1.54997			0.774985	−	0.631980i	$-0.217758\pi$
$661$	1024.53			1.54997			0.774985	+	0.631980i	$0.217758\pi$
$662$	171.597	−	236.183i	0.259210	−	0.356772i
$663$	824.982	−	122.451i	1.24432	−	0.184692i
$664$	82.9610	+	255.328i	0.124941	+	0.384530i
$665$	82.3976	+	113.411i	0.123906	+	0.170542i
$666$	−54.3798	−	1.05803i	−0.0816513	−	0.00158863i
$667$	−215.818	−	664.219i	−0.323565	−	0.995831i
$668$	−126.876	−	41.2246i	−0.189935	−	0.0617135i
$669$	226.998	+	38.2198i	0.339309	+	0.0571298i
$670$	−126.658			−0.189041
$671$		0			0
$672$	303.652	+	610.560i	0.451863	+	0.908572i
$673$	209.931	+	152.524i	0.311933	+	0.226633i	0.732726	−	0.680524i	$-0.238248\pi$
$673$	209.931	+	152.524i	0.311933	+	0.226633i	−0.420792	+	0.907157i	$0.638248\pi$
$674$	−127.894	−	41.5552i	−0.189754	−	0.0616547i
$675$	−652.677	+	83.9348i	−0.966928	+	0.124348i
$676$	−151.535	+	110.096i	−0.224164	+	0.162864i
$677$	−68.5153	−	94.3032i	−0.101204	−	0.139296i	0.755411	−	0.655251i	$-0.227437\pi$
$677$	−68.5153	−	94.3032i	−0.101204	−	0.139296i	−0.856616	+	0.515955i	$0.827437\pi$
$678$	−664.093	−	677.140i	−0.979489	−	0.998731i
$679$	−311.138	+	957.585i	−0.458230	+	1.41029i
$680$	56.0605	−	77.1606i	0.0824419	−	0.113472i
$681$	64.4486	+	129.588i	0.0946382	+	0.190291i
$682$		0			0
$683$		−	739.385i		−	1.08255i	−0.840844	−	0.541277i	$-0.817941\pi$
$683$		−	739.385i		−	1.08255i	0.840844	−	0.541277i	$-0.182059\pi$
$684$	535.956	−	162.686i	0.783561	−	0.237846i
$685$	−47.8145	+	147.158i	−0.0698022	+	0.214829i
$686$	850.270	−	276.269i	1.23946	−	0.402725i
$687$	−21.3957	+	41.0005i	−0.0311436	+	0.0596805i
$688$	−201.027	+	146.055i	−0.292191	+	0.212289i
$689$	808.491	−	262.695i	1.17343	−	0.381270i
$690$	−159.773	+	23.7148i	−0.231555	+	0.0343693i
$691$	−314.727	−	228.663i	−0.455466	−	0.330916i	0.336284	−	0.941761i	$-0.390830\pi$
$691$	−314.727	−	228.663i	−0.455466	−	0.330916i	−0.791750	+	0.610845i	$0.790830\pi$
$692$			532.662i			0.769743i
$693$		0			0
$694$	−28.2934			−0.0407686
$695$	−3.22948	+	4.44499i	−0.00464673	+	0.00639567i
$696$	46.9521	+	316.328i	0.0674599	+	0.454494i
$697$	−159.480	−	490.828i	−0.228809	−	0.704201i
$698$	317.550	+	437.071i	0.454943	+	0.626176i
$699$	−460.664	−	240.393i	−0.659033	−	0.343909i
$700$	120.503	+	370.871i	0.172147	+	0.529815i
$701$	1107.15	+	359.734i	1.57938	+	0.513172i	0.961897	−	0.273410i	$-0.0881517\pi$
$701$	1107.15	+	359.734i	1.57938	+	0.513172i	0.617485	+	0.786583i	$0.288152\pi$
$702$	443.785	+	470.471i	0.632172	+	0.670186i
$703$	−62.8043			−0.0893375
$704$		0			0
$705$	−88.7011	+	44.1140i	−0.125817	+	0.0625730i
$706$	−1085.50	−	788.664i	−1.53754	−	1.11709i
$707$	−128.350	−	41.7036i	−0.181542	−	0.0589867i
$708$	−74.9891	+	73.5443i	−0.105917	+	0.103876i
$709$	−1075.94	+	781.714i	−1.51754	+	1.10256i	−0.554853	+	0.831948i	$0.687226\pi$
$709$	−1075.94	+	781.714i	−1.51754	+	1.10256i	−0.962689	+	0.270611i	$0.912774\pi$
$710$	5.35042	+	7.36423i	0.00753581	+	0.0103721i
$711$	−473.485	−	164.094i	−0.665942	−	0.230794i
$712$	−17.9464	+	55.2335i	−0.0252057	+	0.0775751i
$713$	−45.2774	+	62.3190i	−0.0635027	+	0.0874040i
$714$	1339.86	−	666.356i	1.87655	−	0.933272i
$715$		0			0
$716$		−	333.213i		−	0.465381i
$717$	−147.636	+	876.849i	−0.205908	+	1.22294i
$718$	136.663	−	420.605i	0.190338	−	0.585800i
$719$	797.573	−	259.147i	1.10928	−	0.360427i	0.303614	−	0.952795i	$-0.401807\pi$
$719$	797.573	−	259.147i	1.10928	−	0.360427i	0.805668	+	0.592368i	$0.201807\pi$
$720$	141.597	+	2.75494i	0.196662	+	0.00382630i
$721$	−984.477	+	715.264i	−1.36543	+	0.992045i
$722$	785.553	−	255.242i	1.08802	−	0.353520i
$723$	−20.5700	−	138.585i	−0.0284508	−	0.191680i
$724$	251.151	+	182.472i	0.346894	+	0.252033i
$725$			632.292i			0.872127i
$726$		0			0
$727$	154.628			0.212693			0.106346	−	0.994329i	$-0.466085\pi$
$727$	154.628			0.212693			0.106346	+	0.994329i	$0.466085\pi$
$728$	−154.570	+	212.747i	−0.212322	+	0.292236i
$729$	−462.166	+	563.776i	−0.633973	+	0.773355i
$730$	33.2294	+	102.270i	0.0455197	+	0.140095i
$731$	215.444	+	296.534i	0.294726	+	0.405655i
$732$	−208.895	+	400.306i	−0.285376	+	0.546866i
$733$	−137.519	−	423.241i	−0.187612	−	0.577409i	0.812372	−	0.583140i	$-0.198176\pi$
$733$	−137.519	−	423.241i	−0.187612	−	0.577409i	−0.999984	+	0.00573049i	$0.998176\pi$
$734$	−333.795	−	108.456i	−0.454761	−	0.147761i
$735$	1.38553	−	8.22903i	0.00188508	−	0.0111960i
$736$	−907.255			−1.23268
$737$		0			0
$738$	241.489	−	319.137i	0.327221	−	0.432434i
$739$	49.6402	+	36.0657i	0.0671721	+	0.0488034i	0.620865	−	0.783918i	$-0.286782\pi$
$739$	49.6402	+	36.0657i	0.0671721	+	0.0488034i	−0.553692	+	0.832721i	$0.686782\pi$
$740$	4.27942	+	1.39047i	0.00578300	+	0.00187901i
$741$	522.909	+	533.182i	0.705680	+	0.719544i
$742$	1233.96	−	896.526i	1.66302	−	1.20826i
$743$	425.116	+	585.122i	0.572161	+	0.787512i	0.992809	−	0.119712i	$-0.0381970\pi$
$743$	425.116	+	585.122i	0.572161	+	0.787512i	−0.420647	+	0.907224i	$0.638197\pi$
$744$	25.1823	−	24.6972i	0.0338472	−	0.0331951i
$745$	−16.5744	+	51.0107i	−0.0222475	+	0.0684707i
$746$	221.202	−	304.459i	0.296518	−	0.408122i
$747$	468.921	+	354.830i	0.627739	+	0.475007i
$748$		0			0
$749$			435.215i			0.581062i
$750$	292.122	+	49.1849i	0.389496	+	0.0655798i
$751$	397.509	−	1223.41i	0.529306	−	1.62904i	−0.226333	−	0.974050i	$-0.572674\pi$
$751$	397.509	−	1223.41i	0.529306	−	1.62904i	0.755639	−	0.654988i	$-0.227326\pi$
$752$	−787.288	+	255.806i	−1.04693	+	0.340167i
$753$	−552.642	−	288.390i	−0.733921	−	0.382989i
$754$	502.751	−	365.270i	0.666779	−	0.484443i
$755$	21.2744	−	6.91246i	0.0281780	−	0.00915557i
$756$	379.029	+	207.271i	0.501361	+	0.274168i
$757$	220.633	+	160.299i	0.291457	+	0.211756i	0.723899	−	0.689906i	$-0.242348\pi$
$757$	220.633	+	160.299i	0.291457	+	0.211756i	−0.432442	+	0.901662i	$0.642348\pi$
$758$		−	682.566i		−	0.900483i
$759$		0			0
$760$	85.4021			0.112371
$761$	−280.158	+	385.605i	−0.368145	+	0.506708i	−0.952395	−	0.304865i	$-0.901389\pi$
$761$	−280.158	+	385.605i	−0.368145	+	0.506708i	0.584251	+	0.811573i	$0.301389\pi$
$762$	−1444.61	+	214.422i	−1.89582	+	0.281393i
$763$	229.838	+	707.369i	0.301229	+	0.927089i
$764$	−489.990	−	674.414i	−0.641349	−	0.882741i
$765$	4.06378	−	208.868i	0.00531214	−	0.273030i
$766$	492.845	+	1516.82i	0.643401	+	1.98018i
$767$	−133.191	−	43.2764i	−0.173652	−	0.0564229i
$768$	967.215	+	162.851i	1.25939	+	0.212045i
$769$	22.4401			0.0291808			0.0145904	−	0.999894i	$-0.495356\pi$
$769$	22.4401			0.0291808			0.0145904	+	0.999894i	$0.495356\pi$
$770$		0			0
$771$	−266.832	−	536.525i	−0.346085	−	0.695881i
$772$	471.178	+	342.331i	0.610334	+	0.443433i
$773$	−1167.70	−	379.407i	−1.51060	−	0.490825i	−0.567514	−	0.823364i	$-0.692095\pi$
$773$	−1167.70	−	379.407i	−1.51060	−	0.490825i	−0.943089	+	0.332539i	$0.892095\pi$
$774$	−93.0753	+	268.564i	−0.120252	+	0.346982i
$775$	56.4200	−	40.9916i	0.0728001	−	0.0528923i
$776$	360.548	+	496.251i	0.464623	+	0.639499i
$777$	−33.9175	−	34.5838i	−0.0436519	−	0.0445095i
$778$	−358.826	+	1104.35i	−0.461216	+	1.41948i
$779$	271.626	−	373.862i	0.348686	−	0.479925i
$780$	−23.8260	−	47.9075i	−0.0305462	−	0.0614199i
$781$		0			0
$782$			1990.95i			2.54597i
$783$	480.640	+	509.543i	0.613845	+	0.650757i
$784$	21.5480	−	66.3180i	0.0274847	−	0.0845893i
$785$	51.0851	−	16.5985i	0.0650765	−	0.0211446i
$786$	−371.718	+	712.322i	−0.472923	+	0.906262i
$787$	705.687	−	512.712i	0.896680	−	0.651476i	−0.0409312	−	0.999162i	$-0.513032\pi$
$787$	705.687	−	512.712i	0.896680	−	0.651476i	0.937611	+	0.347686i	$0.113032\pi$
$788$	−13.8826	+	4.51072i	−0.0176175	+	0.00572426i
$789$	−296.034	+	43.9400i	−0.375202	+	0.0556907i
$790$	90.0910	+	65.4550i	0.114039	+	0.0828544i
$791$		−	844.685i		−	1.06787i
$792$		0			0
$793$	−602.043			−0.759197
$794$	832.797	−	1146.25i	1.04886	−	1.44364i
$795$	−31.2631	−	210.627i	−0.0393247	−	0.264940i
$796$	−141.683	−	436.054i	−0.177993	−	0.547807i
$797$	32.7783	+	45.1155i	0.0411272	+	0.0566067i	0.829085	−	0.559122i	$-0.188862\pi$
$797$	32.7783	+	45.1155i	0.0411272	+	0.0566067i	−0.787958	+	0.615729i	$0.788862\pi$
$798$	1187.91	+	619.899i	1.48861	+	0.776816i
$799$	377.336	+	1161.32i	0.472261	+	1.45347i
$800$	781.175	+	253.819i	0.976469	+	0.317274i
$801$	36.9483	+	121.723i	0.0461278	+	0.151964i
$802$	453.989			0.566071
$803$		0			0
$804$	−403.549	+	200.698i	−0.501926	+	0.249625i
$805$	−116.380	−	84.5549i	−0.144571	−	0.105037i
$806$	−65.1868	−	21.1805i	−0.0808769	−	0.0262785i
$807$	107.900	−	105.821i	0.133705	−	0.131129i
$808$	−66.5153	+	48.3262i	−0.0823210	+	0.0598097i
$809$	778.882	+	1072.04i	0.962771	+	1.32514i	0.945615	+	0.325288i	$0.105461\pi$
$809$	778.882	+	1072.04i	0.962771	+	1.32514i	0.0171558	+	0.999853i	$0.494539\pi$
$810$	134.665	−	90.0512i	0.166254	−	0.111174i
$811$	317.710	−	977.810i	0.391751	−	1.20568i	−0.539713	−	0.841849i	$-0.681467\pi$
$811$	317.710	−	977.810i	0.391751	−	1.20568i	0.931463	−	0.363835i	$-0.118533\pi$
$812$	243.983	−	335.814i	0.300472	−	0.413565i
$813$	−334.103	+	166.161i	−0.410951	+	0.204380i
$814$		0			0
$815$		−	53.7721i		−	0.0659781i
$816$	289.839	−	1721.43i	0.355195	−	2.10960i
$817$	−101.421	+	312.143i	−0.124139	+	0.382060i
$818$	−325.776	+	105.851i	−0.398259	+	0.129402i
$819$	−11.2047	+	575.891i	−0.0136809	+	0.703164i
$820$	−26.7855	+	19.4608i	−0.0326653	+	0.0237327i
$821$	−848.423	+	275.669i	−1.03340	+	0.335773i	−0.776134	−	0.630568i	$-0.782822\pi$
$821$	−848.423	+	275.669i	−1.03340	+	0.335773i	−0.257268	+	0.966340i	$0.582822\pi$
$822$	217.144	+	1462.96i	0.264166	+	1.77975i
$823$	335.986	+	244.108i	0.408245	+	0.296608i	0.772891	−	0.634539i	$-0.218810\pi$
$823$	335.986	+	244.108i	0.408245	+	0.296608i	−0.364646	+	0.931146i	$0.618810\pi$
$824$			741.346i			0.899691i
$825$		0			0
$826$	−251.272			−0.304203
$827$	−273.061	+	375.837i	−0.330183	+	0.454458i	−0.941542	−	0.336895i	$-0.890623\pi$
$827$	−273.061	+	375.837i	−0.330183	+	0.454458i	0.611359	+	0.791353i	$0.290623\pi$
$828$	−471.481	+	328.731i	−0.569421	+	0.397018i
$829$	−273.849	−	842.819i	−0.330336	−	1.01667i	−0.968974	−	0.247163i	$-0.920502\pi$
$829$	−273.849	−	842.819i	−0.330336	−	1.01667i	0.638638	−	0.769507i	$-0.279498\pi$
$830$	−76.8092	−	105.719i	−0.0925412	−	0.127372i
$831$	−407.660	+	781.199i	−0.490565	+	0.940070i
$832$	−16.5022	−	50.7884i	−0.0198343	−	0.0610438i
$833$	−97.8252	−	31.7853i	−0.117437	−	0.0381576i
$834$	−8.71960	+	51.7880i	−0.0104552	+	0.0620960i
$835$	−44.5544			−0.0533585
$836$		0			0
$837$	14.3070	−	75.9217i	0.0170932	−	0.0907069i
$838$	−102.798	−	74.6871i	−0.122671	−	0.0891254i
$839$	155.481	+	50.5188i	0.185317	+	0.0602132i	0.400205	−	0.916425i	$-0.368939\pi$
$839$	155.481	+	50.5188i	0.185317	+	0.0602132i	−0.214888	+	0.976639i	$0.568939\pi$
$840$	46.1215	+	47.0276i	0.0549066	+	0.0559852i
$841$	−135.879	+	98.7221i	−0.161569	+	0.117387i
$842$	−78.1722	−	107.595i	−0.0928410	−	0.127785i
$843$	564.756	−	553.875i	0.669936	−	0.657029i
$844$	−78.2837	+	240.932i	−0.0927532	+	0.285465i
$845$	−36.7696	+	50.6090i	−0.0435143	+	0.0598924i
$846$	−571.375	+	755.092i	−0.675384	+	0.892544i
$847$		0			0
$848$		−	1779.31i		−	2.09825i
$849$	−1179.76	−	198.637i	−1.38959	−	0.233966i
$850$	557.000	−	1714.27i	0.655294	−	2.01679i
$851$	61.2942	−	19.9157i	0.0720261	−	0.0234027i
$852$	28.7164	+	14.9853i	0.0337047	+	0.0175884i
$853$	−365.390	+	265.471i	−0.428359	+	0.311221i	−0.780992	−	0.624541i	$-0.785286\pi$
$853$	−365.390	+	265.471i	−0.428359	+	0.311221i	0.352634	+	0.935762i	$0.385286\pi$
$854$	−1027.33	+	333.799i	−1.20296	+	0.390866i
$855$	153.446	−	106.987i	0.179469	−	0.125131i
$856$	214.504	+	155.846i	0.250588	+	0.182063i
$857$			233.720i			0.272719i	0.990659	+	0.136360i	$0.0435402\pi$
$857$			233.720i			0.272719i	−0.990659	+	0.136360i	$0.956460\pi$
$858$		0			0
$859$	−694.225			−0.808178			−0.404089	−	0.914720i	$-0.632411\pi$
$859$	−694.225			−0.808178			−0.404089	+	0.914720i	$0.632411\pi$
$860$	13.8215	−	19.0237i	0.0160715	−	0.0221205i
$861$	352.563	−	52.3305i	0.409481	−	0.0607787i
$862$	387.541	+	1192.73i	0.449583	+	1.38367i
$863$	672.067	+	925.021i	0.778756	+	1.07187i	0.995418	+	0.0956195i	$0.0304832\pi$
$863$	672.067	+	925.021i	0.778756	+	1.07187i	−0.216662	+	0.976247i	$0.569517\pi$
$864$	822.465	−	389.270i	0.951927	−	0.450544i
$865$	54.9731	+	169.190i	0.0635528	+	0.195595i
$866$	−1237.90	−	402.218i	−1.42945	−	0.464455i
$867$	−1684.30	−	283.588i	−1.94268	−	0.327091i
$868$	−45.7825			−0.0527448
$869$		0			0
$870$	−69.3151	−	139.374i	−0.0796726	−	0.160200i
$871$	−486.166	−	353.221i	−0.558170	−	0.405535i
$872$	430.942	+	140.022i	0.494200	+	0.160575i
$873$	1269.49	+	439.963i	1.45417	+	0.503967i
$874$	−1442.27	+	1047.87i	−1.65020	+	1.19894i
$875$	155.074	+	213.441i	0.177227	+	0.243932i
$876$	267.927	+	273.191i	0.305853	+	0.311862i
$877$	333.849	−	1027.48i	0.380672	−	1.17159i	−0.558900	−	0.829235i	$-0.688777\pi$
$877$	333.849	−	1027.48i	0.380672	−	1.17159i	0.939572	−	0.342352i	$-0.111223\pi$
$878$	−37.2556	+	51.2779i	−0.0424323	+	0.0584031i
$879$	−466.016	−	937.030i	−0.530166	−	1.06602i
$880$		0			0
$881$		−	638.008i		−	0.724186i	−0.932142	−	0.362093i	$-0.882062\pi$
$881$		−	638.008i		−	0.724186i	0.932142	−	0.362093i	$-0.117938\pi$
$882$	−23.1680	−	76.3249i	−0.0262676	−	0.0865362i
$883$	−300.425	+	924.613i	−0.340232	+	1.04713i	0.623855	+	0.781540i	$0.285566\pi$
$883$	−300.425	+	924.613i	−0.340232	+	1.04713i	−0.964087	+	0.265586i	$0.914434\pi$
$884$	−627.231	+	203.800i	−0.709537	+	0.230543i
$885$	−16.2287	+	31.0991i	−0.0183376	+	0.0351403i
$886$	1777.60	−	1291.50i	2.00632	−	1.45768i
$887$	−500.232	+	162.535i	−0.563960	+	0.183242i	−0.577102	−	0.816672i	$-0.695817\pi$
$887$	−500.232	+	162.535i	−0.563960	+	0.183242i	0.0131425	+	0.999914i	$0.495817\pi$
$888$	−29.1908	+	4.33275i	−0.0328725	+	0.00487922i
$889$	−1052.27	−	764.517i	−1.18365	−	0.859974i
$890$		−	28.2683i		−	0.0317621i
$891$		0			0
$892$	−182.027			−0.204066
$893$	−642.681	+	884.575i	−0.719688	+	0.990565i
$894$	75.2708	+	507.118i	0.0841955	+	0.567246i
$895$	−34.3890	−	105.839i	−0.0384235	−	0.118255i
$896$	478.096	+	658.043i	0.533589	+	0.734423i
$897$	−679.412	−	354.544i	−0.757427	−	0.395255i
$898$	449.037	+	1381.99i	0.500041	+	1.53897i
$899$	−70.6005	−	22.9395i	−0.0785322	−	0.0255167i
$900$	497.927	−	151.143i	0.553252	−	0.167937i
$901$	−2624.65			−2.91304
$902$		0			0
$903$	−226.658	+	112.724i	−0.251005	+	0.124833i
$904$	−416.318	−	302.473i	−0.460529	−	0.334594i
$905$	98.6053	+	32.0388i	0.108956	+	0.0354020i
$906$	152.653	−	149.712i	0.168491	−	0.165245i
$907$	464.947	−	337.804i	0.512621	−	0.372441i	−0.301196	−	0.953562i	$-0.597386\pi$
$907$	464.947	−	337.804i	0.512621	−	0.372441i	0.813817	+	0.581121i	$0.197386\pi$
$908$	−67.2701	−	92.5894i	−0.0740861	−	0.101971i
$909$	−58.9708	+	170.157i	−0.0648743	+	0.187191i
$910$	39.5542	−	121.735i	0.0434661	−	0.133775i
$911$	751.875	−	1034.87i	0.825329	−	1.13597i	−0.163445	−	0.986552i	$-0.552261\pi$
$911$	751.875	−	1034.87i	0.825329	−	1.13597i	0.988774	−	0.149416i	$-0.0477394\pi$
$912$	1399.58	−	696.058i	1.53463	−	0.763222i
$913$		0			0
$914$			64.6037i			0.0706823i
$915$	−25.0382	+	148.708i	−0.0273641	+	0.162523i
$916$	11.3009	−	34.7807i	0.0123373	−	0.0379702i
$917$	−680.558	+	221.127i	−0.742157	+	0.241142i
$918$	−854.243	−	1804.88i	−0.930548	−	1.96610i
$919$	−389.889	+	283.271i	−0.424253	+	0.308238i	−0.779347	−	0.626593i	$-0.784449\pi$
$919$	−389.889	+	283.271i	−0.424253	+	0.308238i	0.355094	+	0.934831i	$0.384449\pi$
$920$	−83.3488	+	27.0817i	−0.0905965	+	0.0294366i
$921$	175.535	+	1182.62i	0.190592	+	1.28407i
$922$	590.952	+	429.351i	0.640945	+	0.465674i
$923$			43.1883i			0.0467912i
$924$		0			0
$925$	−58.3480			−0.0630789
$926$	298.314	−	410.594i	0.322153	−	0.443406i
$927$	928.719	+	1332.01i	1.00185	+	1.43691i
$928$	−270.178	−	831.523i	−0.291140	−	0.896037i
$929$	−653.769	−	899.836i	−0.703734	−	0.968607i	−0.999909	−	0.0134736i	$-0.995711\pi$
$929$	−653.769	−	899.836i	−0.703734	−	0.968607i	0.296175	−	0.955134i	$-0.404289\pi$
$930$	−7.94273	+	15.2207i	−0.00854057	+	0.0163663i
$931$	−28.4615	−	87.5953i	−0.0305708	−	0.0940874i
$932$	390.781	+	126.972i	0.419293	+	0.136236i
$933$	−219.337	+	1302.70i	−0.235088	+	1.39625i
$934$	−278.484			−0.298162
$935$		0			0
$936$	279.826	+	211.743i	0.298959	+	0.226221i
$937$	1410.59	+	1024.85i	1.50543	+	1.09376i	0.968155	+	0.250350i	$0.0805457\pi$
$937$	1410.59	+	1024.85i	1.50543	+	1.09376i	0.537273	+	0.843408i	$0.319454\pi$
$938$	−1025.44	−	333.184i	−1.09322	−	0.355207i
$939$	−1113.10	−	1134.97i	−1.18541	−	1.20870i
$940$	63.3759	−	46.0453i	0.0674211	−	0.0489843i
$941$	−491.503	−	676.495i	−0.522319	−	0.718911i	0.463616	−	0.886036i	$-0.346552\pi$
$941$	−491.503	−	676.495i	−0.522319	−	0.718911i	−0.985936	+	0.167125i	$0.946552\pi$
$942$	366.558	−	359.495i	0.389127	−	0.381630i
$943$	−146.541	+	451.008i	−0.155399	+	0.478269i
$944$	−172.294	+	237.143i	−0.182515	+	0.251211i
$945$	141.783	+	26.7181i	0.150034	+	0.0282732i
$946$		0			0
$947$			114.725i			0.121145i	0.998164	+	0.0605726i	$0.0192927\pi$
$947$			114.725i			0.121145i	−0.998164	+	0.0605726i	$0.980707\pi$
$948$	390.761	+	65.7928i	0.412195	+	0.0694017i
$949$	−157.659	+	485.225i	−0.166132	+	0.511301i
$950$	1535.00	−	498.753i	1.61579	−	0.525003i
$951$	−979.883	−	511.341i	−1.03037	−	0.537688i
$952$	656.851	−	477.230i	0.689970	−	0.501293i
$953$	−311.052	+	101.067i	−0.326392	+	0.106051i	−0.467630	−	0.883924i	$-0.654892\pi$
$953$	−311.052	+	101.067i	−0.326392	+	0.106051i	0.141237	+	0.989976i	$0.454892\pi$
$954$	−1164.07	−	1669.57i	−1.22020	−	1.75007i
$955$	−225.239	−	163.645i	−0.235852	−	0.171356i
$956$		−	703.137i		−	0.735499i
$957$		0			0
$958$	−1725.47			−1.80111
$959$	−774.225	+	1065.63i	−0.807325	+	1.11119i
$960$	−13.2313	+	1.96391i	−0.0137827	+	0.00204574i
$961$	−294.435	−	906.178i	−0.306384	−	0.942954i
$962$	33.7072	+	46.3939i	0.0350386	+	0.0482265i
$963$	580.645	+	11.2972i	0.602954	+	0.0117312i
$964$	34.2354	+	105.366i	0.0355139	+	0.109301i
$965$	184.991	+	60.1071i	0.191700	+	0.0622872i
$966$	−1355.93	−	228.299i	−1.40365	−	0.236334i
$967$	−168.674			−0.174430			−0.0872150	−	0.996190i	$-0.527797\pi$
$967$	−168.674			−0.174430			−0.0872150	+	0.996190i	$0.527797\pi$
$968$		0			0
$969$	−1026.75	−	2064.51i	−1.05960	−	2.13056i
$970$	−241.549	−	175.495i	−0.249019	−	0.180923i
$971$	−77.7365	−	25.2581i	−0.0800582	−	0.0260125i	0.268714	−	0.963220i	$-0.413401\pi$
$971$	−77.7365	−	25.2581i	−0.0800582	−	0.0260125i	−0.348772	+	0.937208i	$0.613401\pi$
$972$	286.370	−	500.303i	0.294620	−	0.514715i
$973$	−37.8392	+	27.4918i	−0.0388892	+	0.0282547i
$974$	−193.039	−	265.696i	−0.198192	−	0.272788i
$975$	485.806	+	495.350i	0.498263	+	0.508051i
$976$	−389.398	+	1198.44i	−0.398974	+	1.22791i
$977$	−11.9651	+	16.4685i	−0.0122468	+	0.0168562i	−0.815096	−	0.579325i	$-0.803316\pi$
$977$	−11.9651	+	16.4685i	−0.0122468	+	0.0168562i	0.802850	+	0.596181i	$0.203316\pi$
$978$	−228.875	−	460.205i	−0.234024	−	0.470557i
$979$		0			0
$980$			6.59879i			0.00673346i
$981$	949.706	−	288.278i	0.968100	−	0.293861i
$982$	−621.383	+	1912.42i	−0.632773	+	1.94747i
$983$	−758.379	+	246.412i	−0.771494	+	0.250674i	−0.668204	−	0.743978i	$-0.732937\pi$
$983$	−758.379	+	246.412i	−0.771494	+	0.250674i	−0.103290	+	0.994651i	$0.532937\pi$
$984$	100.457	−	192.506i	0.102091	−	0.195636i
$985$	−3.94401	+	2.86549i	−0.00400407	+	0.00290912i
$986$	−1824.75	+	592.899i	−1.85066	+	0.601317i
$987$	−834.182	+	123.816i	−0.845169	+	0.125447i
$988$	−477.760	−	347.113i	−0.483562	−	0.351329i
$989$		−	336.799i		−	0.340545i
$990$		0			0
$991$	609.620			0.615156			0.307578	−	0.951523i	$-0.400481\pi$
$991$	609.620			0.615156			0.307578	+	0.951523i	$0.400481\pi$
$992$	−56.6819	+	78.0159i	−0.0571390	+	0.0786451i
$993$	−50.9390	−	343.189i	−0.0512981	−	0.345608i
$994$	23.9455	+	73.6965i	0.0240900	+	0.0741414i
$995$	−90.0056	−	123.882i	−0.0904578	−	0.124505i
$996$	−412.244	−	215.125i	−0.413900	−	0.215989i
$997$	−547.355	−	1684.58i	−0.549002	−	1.68965i	−0.711280	−	0.702908i	$-0.751884\pi$
$997$	−547.355	−	1684.58i	−0.549002	−	1.68965i	0.162279	−	0.986745i	$-0.448116\pi$
$998$	−1176.46	−	382.256i	−1.17882	−	0.383022i
$999$	−47.0207	+	44.3535i	−0.0470677	+	0.0443979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.l.323.1		16
3.2	odd	2	inner	363.3.h.l.323.4		16
11.2	odd	10		363.3.h.m.269.1		16
11.3	even	5	inner	363.3.h.l.245.4		16
11.4	even	5	inner	363.3.h.l.251.1		16
11.5	even	5		363.3.b.h.122.1		4
11.6	odd	10		33.3.b.b.23.4	yes	4
11.7	odd	10		363.3.h.m.251.4		16
11.8	odd	10		363.3.h.m.245.1		16
11.9	even	5	inner	363.3.h.l.269.4		16
11.10	odd	2		363.3.h.m.323.4		16
33.2	even	10		363.3.h.m.269.4		16
33.5	odd	10		363.3.b.h.122.4		4
33.8	even	10		363.3.h.m.245.4		16
33.14	odd	10	inner	363.3.h.l.245.1		16
33.17	even	10		33.3.b.b.23.1	✓	4
33.20	odd	10	inner	363.3.h.l.269.1		16
33.26	odd	10	inner	363.3.h.l.251.4		16
33.29	even	10		363.3.h.m.251.1		16
33.32	even	2		363.3.h.m.323.1		16
44.39	even	10		528.3.i.d.353.3		4
132.83	odd	10		528.3.i.d.353.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.b.23.1	✓	4	33.17	even	10
33.3.b.b.23.4	yes	4	11.6	odd	10
363.3.b.h.122.1		4	11.5	even	5
363.3.b.h.122.4		4	33.5	odd	10
363.3.h.l.245.1		16	33.14	odd	10	inner
363.3.h.l.245.4		16	11.3	even	5	inner
363.3.h.l.251.1		16	11.4	even	5	inner
363.3.h.l.251.4		16	33.26	odd	10	inner
363.3.h.l.269.1		16	33.20	odd	10	inner
363.3.h.l.269.4		16	11.9	even	5	inner
363.3.h.l.323.1		16	1.1	even	1	trivial
363.3.h.l.323.4		16	3.2	odd	2	inner
363.3.h.m.245.1		16	11.8	odd	10
363.3.h.m.245.4		16	33.8	even	10
363.3.h.m.251.1		16	33.29	even	10
363.3.h.m.251.4		16	11.7	odd	10
363.3.h.m.269.1		16	11.2	odd	10
363.3.h.m.269.4		16	33.2	even	10
363.3.h.m.323.1		16	33.32	even	2
363.3.h.m.323.4		16	11.10	odd	2
528.3.i.d.353.3		4	44.39	even	10
528.3.i.d.353.4		4	132.83	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.48377 + 2.04223i) q^{2} +(0.440460 + 2.96749i) q^{3} +(-0.733075 - 2.25617i) q^{4} +(-0.465695 - 0.640974i) q^{5} +(-6.71384 - 3.50355i) q^{6} +(-2.08418 - 6.41446i) q^{7} +(-3.90781 - 1.26972i) q^{8} +(-8.61199 + 2.61412i) q^{9} +O(q^{10})\)	\(q+(-1.48377 + 2.04223i) q^{2} +(0.440460 + 2.96749i) q^{3} +(-0.733075 - 2.25617i) q^{4} +(-0.465695 - 0.640974i) q^{5} +(-6.71384 - 3.50355i) q^{6} +(-2.08418 - 6.41446i) q^{7} +(-3.90781 - 1.26972i) q^{8} +(-8.61199 + 2.61412i) q^{9} +2.00000 q^{10} +(6.37228 - 3.16915i) q^{12} +(7.67686 + 5.57757i) q^{13} +(16.1923 + 5.26119i) q^{14} +(1.69696 - 1.66427i) q^{15} +(16.0682 - 11.6742i) q^{16} +(-17.2206 - 23.7021i) q^{17} +(7.43955 - 21.4664i) q^{18} +(8.10666 - 24.9497i) q^{19} +(-1.10476 + 1.52057i) q^{20} +(18.1168 - 9.01011i) q^{21} +26.9205i q^{23} +(2.04666 - 12.1556i) q^{24} +(7.53145 - 23.1794i) q^{25} +(-22.7814 + 7.40212i) q^{26} +(-11.5506 - 24.4046i) q^{27} +(-12.9443 + 9.40456i) q^{28} +(-24.6733 + 8.01686i) q^{29} +(0.880920 + 5.93498i) q^{30} +(2.31493 + 1.68189i) q^{31} +33.7013i q^{32} +73.9565 q^{34} +(-3.14091 + 4.32309i) q^{35} +(12.2112 + 17.5138i) q^{36} +(-0.739796 - 2.27686i) q^{37} +(38.9247 + 53.5753i) q^{38} +(-13.1700 + 25.2377i) q^{39} +(1.00599 + 3.09610i) q^{40} +(16.7533 + 5.44348i) q^{41} +(-8.48047 + 50.3677i) q^{42} -12.5109 q^{43} +(5.68614 + 4.30268i) q^{45} +(-54.9780 - 39.9438i) q^{46} +(-39.6391 - 12.8795i) q^{47} +(41.7206 + 42.5402i) q^{48} +(2.84036 - 2.06364i) q^{49} +(36.1628 + 49.7739i) q^{50} +(62.7507 - 61.5417i) q^{51} +(6.95624 - 21.4091i) q^{52} +(52.6576 - 72.4770i) q^{53} +(66.9783 + 12.6217i) q^{54} +27.7128i q^{56} +(77.6087 + 13.0671i) q^{57} +(20.2373 - 62.2839i) q^{58} +(-14.0362 + 4.56063i) q^{59} +(-4.99888 - 2.60861i) q^{60} +(-51.3286 + 37.2924i) q^{61} +(-6.86963 + 2.23208i) q^{62} +(34.7172 + 49.7930i) q^{63} +(-4.55292 - 3.30789i) q^{64} -7.51811i q^{65} -63.3288 q^{67} +(-40.8520 + 56.2280i) q^{68} +(-79.8864 + 11.8574i) q^{69} +(-4.16837 - 12.8289i) q^{70} +(2.67521 + 3.68211i) q^{71} +(36.9732 + 0.719359i) q^{72} +(16.6147 + 51.1348i) q^{73} +(5.74756 + 1.86750i) q^{74} +(72.1020 + 12.1399i) q^{75} -62.2337 q^{76} +(-32.0000 - 64.3432i) q^{78} +(45.0455 + 32.7275i) q^{79} +(-14.9658 - 4.86267i) q^{80} +(67.3327 - 45.0256i) q^{81} +(-35.9749 + 26.1373i) q^{82} +(-38.4046 - 52.8594i) q^{83} +(-33.6094 - 34.2697i) q^{84} +(-7.17288 + 22.0759i) q^{85} +(18.5632 - 25.5501i) q^{86} +(-34.6576 - 69.6868i) q^{87} -14.1341i q^{89} +(-17.2240 + 5.22824i) q^{90} +(19.7771 - 60.8676i) q^{91} +(60.7374 - 19.7348i) q^{92} +(-3.97137 + 7.61033i) q^{93} +(85.1182 - 61.8420i) q^{94} +(-19.7673 + 6.42280i) q^{95} +(-100.008 + 14.8441i) q^{96} +(-120.774 - 87.7477i) q^{97} +8.86263i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9}+O(q^{10}) \) 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9	\( 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9} + 32 q^{10} + 56 q^{12} - 8 q^{13} - 13 q^{15} + 22 q^{16} + 38 q^{18} - 36 q^{19} + 152 q^{21} + 24 q^{24} - 86 q^{25} + 20 q^{27} - 64 q^{28} + 10 q^{30} - 46 q^{31} + 448 q^{34} + 86 q^{36} + 90 q^{37} - 56 q^{39} - 36 q^{40} + 68 q^{42} - 384 q^{43} + 68 q^{45} - 88 q^{46} - 110 q^{48} + 60 q^{49} + 214 q^{51} - 136 q^{52} + 704 q^{54} + 144 q^{57} - 216 q^{58} - 56 q^{60} - 24 q^{61} + 158 q^{63} - 34 q^{64} - 232 q^{67} + 253 q^{69} + 8 q^{70} + 72 q^{72} - 284 q^{73} + 124 q^{75} - 720 q^{76} - 512 q^{78} - 76 q^{79} - 113 q^{81} - 40 q^{82} + 80 q^{84} - 68 q^{85} + 1008 q^{87} + 14 q^{90} - 256 q^{91} - 25 q^{93} + 260 q^{94} + 272 q^{96} - 218 q^{97}+O(q^{100}) \) 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9 + 32 * q^10 + 56 * q^12 - 8 * q^13 - 13 * q^15 + 22 * q^16 + 38 * q^18 - 36 * q^19 + 152 * q^21 + 24 * q^24 - 86 * q^25 + 20 * q^27 - 64 * q^28 + 10 * q^30 - 46 * q^31 + 448 * q^34 + 86 * q^36 + 90 * q^37 - 56 * q^39 - 36 * q^40 + 68 * q^42 - 384 * q^43 + 68 * q^45 - 88 * q^46 - 110 * q^48 + 60 * q^49 + 214 * q^51 - 136 * q^52 + 704 * q^54 + 144 * q^57 - 216 * q^58 - 56 * q^60 - 24 * q^61 + 158 * q^63 - 34 * q^64 - 232 * q^67 + 253 * q^69 + 8 * q^70 + 72 * q^72 - 284 * q^73 + 124 * q^75 - 720 * q^76 - 512 * q^78 - 76 * q^79 - 113 * q^81 - 40 * q^82 + 80 * q^84 - 68 * q^85 + 1008 * q^87 + 14 * q^90 - 256 * q^91 - 25 * q^93 + 260 * q^94 + 272 * q^96 - 218 * q^97

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