LMFDB - Embedded newform 363.3.h.i.269.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8,0,4,-6,0,10,-26] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.i.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.303706 + 2.98459i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-6.29412 - 2.04508i) q^{5} +(-1.21113 - 2.74466i) q^{6} +(-7.16312 + 5.20431i) q^{7} +(4.11450 - 5.66312i) q^{8} +(-8.81553 + 1.81288i) q^{9} +6.61803 q^{10} +(-6.00000 - 6.70820i) q^{12} +(4.09017 + 12.5882i) q^{13} +(5.20431 - 7.16312i) q^{14} +(4.19217 - 19.4065i) q^{15} +(1.54508 - 4.75528i) q^{16} +(-5.70634 - 1.85410i) q^{17} +(7.82385 - 4.44829i) q^{18} +(7.38197 + 5.36331i) q^{19} +(18.8824 - 6.13525i) q^{20} +(-17.7082 - 19.7984i) q^{21} -17.5279i q^{23} +(18.1517 + 10.5602i) q^{24} +(15.2082 + 11.0494i) q^{25} +(-7.77997 - 10.7082i) q^{26} +(-8.08802 - 25.7601i) q^{27} +(8.20820 - 25.2623i) q^{28} +(15.5147 + 21.3541i) q^{29} +(2.00994 + 19.7521i) q^{30} +(-1.91641 - 5.89810i) q^{31} +33.0000i q^{32} +6.00000 q^{34} +(55.7288 - 18.1074i) q^{35} +(18.1990 - 19.9448i) q^{36} +(15.8541 - 11.5187i) q^{37} +(-8.67802 - 2.81966i) q^{38} +(-36.3285 + 16.0306i) q^{39} +(-37.4787 + 27.2299i) q^{40} +(-3.28969 + 4.52786i) q^{41} +(22.9595 + 13.3572i) q^{42} +26.2918 q^{43} +(59.1935 + 6.61803i) q^{45} +(5.41641 + 16.6700i) q^{46} +(-10.4086 + 14.3262i) q^{47} +(14.6618 + 3.16723i) q^{48} +(9.08359 - 27.9564i) q^{49} +(-17.8783 - 5.80902i) q^{50} +(3.80068 - 17.5942i) q^{51} +(-32.1246 - 23.3399i) q^{52} +(-21.1805 + 6.88197i) q^{53} +(15.6525 + 22.0000i) q^{54} +61.9787i q^{56} +(-13.7653 + 23.6610i) q^{57} +(-21.3541 - 15.5147i) q^{58} +(-12.8783 - 17.7254i) q^{59} +(24.0459 + 54.4928i) q^{60} +(28.8541 - 88.8038i) q^{61} +(3.64522 + 5.01722i) q^{62} +(53.7119 - 58.8646i) q^{63} +(-4.01722 - 12.3637i) q^{64} -87.5967i q^{65} -76.7902 q^{67} +(17.1190 - 5.56231i) q^{68} +(52.3134 - 5.32332i) q^{69} +(-47.4058 + 34.4423i) q^{70} +(-62.5982 - 20.3394i) q^{71} +(-26.0049 + 57.3824i) q^{72} +(12.1525 - 8.82929i) q^{73} +(-11.5187 + 15.8541i) q^{74} +(-28.3591 + 48.7460i) q^{75} -27.3738 q^{76} +(29.5967 - 26.4721i) q^{78} +(-36.4828 - 112.282i) q^{79} +(-19.4499 + 26.7705i) q^{80} +(74.4270 - 31.9629i) q^{81} +(1.72949 - 5.32282i) q^{82} +(105.744 + 34.3582i) q^{83} +(77.8903 + 16.8258i) q^{84} +(32.1246 + 23.3399i) q^{85} +(-25.0050 + 8.12461i) q^{86} +(-59.0213 + 52.7902i) q^{87} -97.6656i q^{89} +(-58.3414 + 11.9977i) q^{90} +(-94.8115 - 68.8846i) q^{91} +(30.9079 + 42.5410i) q^{92} +(17.0214 - 7.51098i) q^{93} +(5.47214 - 16.8415i) q^{94} +(-35.4946 - 48.8541i) q^{95} +(-98.4914 + 10.0223i) q^{96} +(-37.4483 - 115.254i) q^{97} +29.3951i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 6 q^{4} + 10 q^{6} - 26 q^{7} + 2 q^{9} + 44 q^{10} - 48 q^{12} - 12 q^{13} + 60 q^{15} - 10 q^{16} + 40 q^{18} + 68 q^{19} - 88 q^{21} + 70 q^{24} + 68 q^{25} - 44 q^{27} + 12 q^{28} + 32 q^{30}+ \cdots - 474 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 - 6 * q^4 + 10 * q^6 - 26 * q^7 + 2 * q^9 + 44 * q^10 - 48 * q^12 - 12 * q^13 + 60 * q^15 - 10 * q^16 + 40 * q^18 + 68 * q^19 - 88 * q^21 + 70 * q^24 + 68 * q^25 - 44 * q^27 + 12 * q^28 + 32 * q^30 + 92 * q^31 + 48 * q^34 + 6 * q^36 + 100 * q^37 + 24 * q^39 - 112 * q^40 + 40 * q^42 + 264 * q^43 + 80 * q^45 - 64 * q^46 + 20 * q^48 + 180 * q^49 + 60 * q^51 - 96 * q^52 + 224 * q^57 - 144 * q^58 - 150 * q^60 + 204 * q^61 + 26 * q^63 + 26 * q^64 - 24 * q^67 + 200 * q^69 - 178 * q^70 - 280 * q^72 - 28 * q^73 + 84 * q^75 + 264 * q^76 + 40 * q^78 - 350 * q^79 + 158 * q^81 + 148 * q^82 + 156 * q^84 + 96 * q^85 - 660 * q^87 + 6 * q^90 - 356 * q^91 - 184 * q^93 + 8 * q^94 - 330 * q^96 - 474 * q^97

Character values

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

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.475528	+	0.154508i	−0.536969	−	0.843602i	$-0.680431\pi$
$2$	−0.951057	+	0.309017i	−0.475528	+	0.154508i	0.0614403	+	0.998111i	$0.480431\pi$
$3$	0.303706	+	2.98459i	0.101235	+	0.994862i
$3$	0.303706	+	2.98459i	0.101235	+	0.994862i
$4$	−2.42705	+	1.76336i	−0.606763	+	0.440839i
$5$	−6.29412	−	2.04508i	−1.25882	−	0.409017i	−0.397749	−	0.917494i	$-0.630209\pi$
$5$	−6.29412	−	2.04508i	−1.25882	−	0.409017i	−0.861076	+	0.508477i	$0.830209\pi$
$6$	−1.21113	−	2.74466i	−0.201855	−	0.457444i
$7$	−7.16312	+	5.20431i	−1.02330	+	0.743473i	−0.966957	−	0.254938i	$-0.917945\pi$
$7$	−7.16312	+	5.20431i	−1.02330	+	0.743473i	−0.0563454	+	0.998411i	$0.517945\pi$
$8$	4.11450	−	5.66312i	0.514312	−	0.707890i
$9$	−8.81553	+	1.81288i	−0.979503	+	0.201431i
$10$	6.61803			0.661803
$11$		0			0
$11$		0			0
$12$	−6.00000	−	6.70820i	−0.500000	−	0.559017i
$13$	4.09017	+	12.5882i	0.314628	+	0.968327i	0.975907	+	0.218186i	$0.0700141\pi$
$13$	4.09017	+	12.5882i	0.314628	+	0.968327i	−0.661279	+	0.750140i	$0.729986\pi$
$14$	5.20431	−	7.16312i	0.371736	−	0.511651i
$15$	4.19217	−	19.4065i	0.279478	−	1.29376i
$16$	1.54508	−	4.75528i	0.0965678	−	0.297205i
$17$	−5.70634	−	1.85410i	−0.335667	−	0.109065i	0.136334	−	0.990663i	$-0.456468\pi$
$17$	−5.70634	−	1.85410i	−0.335667	−	0.109065i	−0.472001	+	0.881598i	$0.656468\pi$
$18$	7.82385	−	4.44829i	0.434659	−	0.247127i
$19$	7.38197	+	5.36331i	0.388525	+	0.282280i	0.764851	−	0.644208i	$-0.222813\pi$
$19$	7.38197	+	5.36331i	0.388525	+	0.282280i	−0.376326	+	0.926487i	$0.622813\pi$
$20$	18.8824	−	6.13525i	0.944119	−	0.306763i
$21$	−17.7082	−	19.7984i	−0.843248	−	0.942780i
$22$		0			0
$23$		−	17.5279i		−	0.762081i	−0.924558	−	0.381041i	$-0.875566\pi$
$23$		−	17.5279i		−	0.762081i	0.924558	−	0.381041i	$-0.124434\pi$
$24$	18.1517	+	10.5602i	0.756320	+	0.440006i
$25$	15.2082	+	11.0494i	0.608328	+	0.441976i
$26$	−7.77997	−	10.7082i	−0.299229	−	0.411854i
$27$	−8.08802	−	25.7601i	−0.299556	−	0.954079i
$28$	8.20820	−	25.2623i	0.293150	−	0.902223i
$29$	15.5147	+	21.3541i	0.534988	+	0.736348i	0.987880	−	0.155217i	$-0.0496077\pi$
$29$	15.5147	+	21.3541i	0.534988	+	0.736348i	−0.452892	+	0.891565i	$0.649608\pi$
$30$	2.00994	+	19.7521i	0.0669979	+	0.658403i
$31$	−1.91641	−	5.89810i	−0.0618196	−	0.190261i	0.915377	−	0.402598i	$-0.131893\pi$
$31$	−1.91641	−	5.89810i	−0.0618196	−	0.190261i	−0.977197	+	0.212337i	$0.931893\pi$
$32$			33.0000i			1.03125i
$33$		0			0
$34$	6.00000			0.176471
$35$	55.7288	−	18.1074i	1.59225	−	0.517354i
$36$	18.1990	−	19.9448i	0.505527	−	0.554024i
$37$	15.8541	−	11.5187i	0.428489	−	0.311316i	−0.352555	−	0.935791i	$-0.614687\pi$
$37$	15.8541	−	11.5187i	0.428489	−	0.311316i	0.781045	+	0.624475i	$0.214687\pi$
$38$	−8.67802	−	2.81966i	−0.228369	−	0.0742016i
$39$	−36.3285	+	16.0306i	−0.931501	+	0.411041i
$40$	−37.4787	+	27.2299i	−0.936968	+	0.680747i
$41$	−3.28969	+	4.52786i	−0.0802362	+	0.110436i	−0.847249	−	0.531197i	$-0.821743\pi$
$41$	−3.28969	+	4.52786i	−0.0802362	+	0.110436i	0.767012	+	0.641632i	$0.221743\pi$
$42$	22.9595	+	13.3572i	0.546656	+	0.318029i
$43$	26.2918			0.611437			0.305719	−	0.952122i	$-0.401103\pi$
$43$	26.2918			0.611437			0.305719	+	0.952122i	$0.401103\pi$
$44$		0			0
$45$	59.1935	+	6.61803i	1.31541	+	0.147067i
$46$	5.41641	+	16.6700i	0.117748	+	0.362391i
$47$	−10.4086	+	14.3262i	−0.221460	+	0.304814i	−0.905262	−	0.424854i	$-0.860325\pi$
$47$	−10.4086	+	14.3262i	−0.221460	+	0.304814i	0.683802	+	0.729668i	$0.260325\pi$
$48$	14.6618	+	3.16723i	0.305454	+	0.0659840i
$49$	9.08359	−	27.9564i	0.185379	−	0.570539i
$50$	−17.8783	−	5.80902i	−0.357566	−	0.116180i
$51$	3.80068	−	17.5942i	0.0745231	−	0.344984i
$52$	−32.1246	−	23.3399i	−0.617781	−	0.448844i
$53$	−21.1805	+	6.88197i	−0.399632	+	0.129848i	−0.501936	−	0.864905i	$-0.667379\pi$
$53$	−21.1805	+	6.88197i	−0.399632	+	0.129848i	0.102304	+	0.994753i	$0.467379\pi$
$54$	15.6525	+	22.0000i	0.289861	+	0.407407i
$55$		0			0
$56$			61.9787i			1.10676i
$57$	−13.7653	+	23.6610i	−0.241497	+	0.415105i
$58$	−21.3541	−	15.5147i	−0.368174	−	0.267494i
$59$	−12.8783	−	17.7254i	−0.218276	−	0.300431i	0.685811	−	0.727780i	$-0.259448\pi$
$59$	−12.8783	−	17.7254i	−0.218276	−	0.300431i	−0.904087	+	0.427349i	$0.859448\pi$
$60$	24.0459	+	54.4928i	0.400765	+	0.908213i
$61$	28.8541	−	88.8038i	0.473018	−	1.45580i	−0.375594	−	0.926784i	$-0.622561\pi$
$61$	28.8541	−	88.8038i	0.473018	−	1.45580i	0.848612	−	0.529016i	$-0.177439\pi$
$62$	3.64522	+	5.01722i	0.0587939	+	0.0809229i
$63$	53.7119	−	58.8646i	0.852570	−	0.934358i
$64$	−4.01722	−	12.3637i	−0.0627691	−	0.193183i
$65$		−	87.5967i		−	1.34764i
$66$		0			0
$67$	−76.7902			−1.14612			−0.573062	−	0.819512i	$-0.694244\pi$
$67$	−76.7902			−1.14612			−0.573062	+	0.819512i	$0.694244\pi$
$68$	17.1190	−	5.56231i	0.251750	−	0.0817986i
$69$	52.3134	−	5.32332i	0.758166	−	0.0771496i
$70$	−47.4058	+	34.4423i	−0.677225	+	0.492033i
$71$	−62.5982	−	20.3394i	−0.881665	−	0.286470i	−0.167017	−	0.985954i	$-0.553413\pi$
$71$	−62.5982	−	20.3394i	−0.881665	−	0.286470i	−0.714648	+	0.699484i	$0.753413\pi$
$72$	−26.0049	+	57.3824i	−0.361179	+	0.796978i
$73$	12.1525	−	8.82929i	0.166472	−	0.120949i	−0.501430	−	0.865198i	$-0.667192\pi$
$73$	12.1525	−	8.82929i	0.166472	−	0.120949i	0.667902	+	0.744249i	$0.267192\pi$
$74$	−11.5187	+	15.8541i	−0.155658	+	0.214245i
$75$	−28.3591	+	48.7460i	−0.378121	+	0.649947i
$76$	−27.3738			−0.360182
$77$		0			0
$78$	29.5967	−	26.4721i	0.379445	−	0.339386i
$79$	−36.4828	−	112.282i	−0.461807	−	1.42130i	−0.862954	−	0.505283i	$-0.831388\pi$
$79$	−36.4828	−	112.282i	−0.461807	−	1.42130i	0.401146	−	0.916014i	$-0.368612\pi$
$80$	−19.4499	+	26.7705i	−0.243124	+	0.334631i
$81$	74.4270	−	31.9629i	0.918851	−	0.394604i
$82$	1.72949	−	5.32282i	0.0210913	−	0.0649125i
$83$	105.744	+	34.3582i	1.27402	+	0.413954i	0.866470	−	0.499229i	$-0.166384\pi$
$83$	105.744	+	34.3582i	1.27402	+	0.413954i	0.407549	+	0.913183i	$0.366384\pi$
$84$	77.8903	+	16.8258i	0.927265	+	0.200307i
$85$	32.1246	+	23.3399i	0.377937	+	0.274587i
$86$	−25.0050	+	8.12461i	−0.290756	+	0.0944722i
$87$	−59.0213	+	52.7902i	−0.678406	+	0.606784i
$88$		0			0
$89$		−	97.6656i		−	1.09737i	−0.836030	−	0.548683i	$-0.815129\pi$
$89$		−	97.6656i		−	1.09737i	0.836030	−	0.548683i	$-0.184871\pi$
$90$	−58.3414	+	11.9977i	−0.648238	+	0.133307i
$91$	−94.8115	−	68.8846i	−1.04188	−	0.756974i
$92$	30.9079	+	42.5410i	0.335955	+	0.462402i
$93$	17.0214	−	7.51098i	0.183025	−	0.0807632i
$94$	5.47214	−	16.8415i	0.0582142	−	0.179165i
$95$	−35.4946	−	48.8541i	−0.373627	−	0.514254i
$96$	−98.4914	+	10.0223i	−1.02595	+	0.104399i
$97$	−37.4483	−	115.254i	−0.386065	−	1.18819i	−0.935705	−	0.352785i	$-0.885235\pi$
$97$	−37.4483	−	115.254i	−0.386065	−	1.18819i	0.549639	−	0.835402i	$-0.314765\pi$
$98$			29.3951i			0.299950i
$99$		0			0
$100$	−56.3951			−0.563951
$101$	−176.505	+	57.3500i	−1.74758	+	0.567822i	−0.995797	−	0.0915916i	$-0.970805\pi$
$101$	−176.505	+	57.3500i	−1.74758	+	0.567822i	−0.751780	+	0.659414i	$0.770805\pi$
$102$	1.82224	+	17.9075i	0.0178651	+	0.175564i
$103$	−139.627	+	101.445i	−1.35560	+	0.984903i	−0.356892	+	0.934146i	$0.616164\pi$
$103$	−139.627	+	101.445i	−1.35560	+	0.984903i	−0.998711	+	0.0507577i	$0.983836\pi$
$104$	88.1177	+	28.6312i	0.847286	+	0.275300i
$105$	70.9683	+	160.828i	0.675888	+	1.53170i
$106$	18.0172	−	13.0903i	0.169974	−	0.123493i
$107$	38.6658	−	53.2188i	0.361362	−	0.497372i	−0.589165	−	0.808012i	$-0.700543\pi$
$107$	38.6658	−	53.2188i	0.361362	−	0.497372i	0.950528	+	0.310640i	$0.100543\pi$
$108$	65.0543	+	48.2591i	0.602355	+	0.446843i
$109$	107.331			0.984690			0.492345	−	0.870400i	$-0.336140\pi$
$109$	107.331			0.984690			0.492345	+	0.870400i	$0.336140\pi$
$110$		0			0
$111$	39.1935	+	43.8197i	0.353095	+	0.394772i
$112$	13.6803	+	42.1038i	0.122146	+	0.375926i
$113$	−18.6126	+	25.6180i	−0.164713	+	0.226708i	−0.883393	−	0.468633i	$-0.844747\pi$
$113$	−18.6126	+	25.6180i	−0.164713	+	0.226708i	0.718680	+	0.695341i	$0.244747\pi$
$114$	5.77995	−	26.7567i	0.0507013	−	0.234708i
$115$	−35.8460	+	110.323i	−0.311704	+	0.959327i
$116$	−75.3098	−	24.4696i	−0.649222	−	0.210945i
$117$	−58.8779	−	103.557i	−0.503230	−	0.885103i
$118$	17.7254	+	12.8783i	0.150215	+	0.109138i
$119$	50.5245	−	16.4164i	0.424576	−	0.137953i
$120$	−92.6525	−	103.589i	−0.772104	−	0.863238i
$121$		0			0
$122$			93.3738i			0.765359i
$123$	−14.5129	−	8.44321i	−0.117991	−	0.0686440i
$124$	15.0517	+	10.9357i	0.121384	+	0.0881909i
$125$	24.1242	+	33.2041i	0.192994	+	0.265633i
$126$	−32.8929	+	72.5814i	−0.261055	+	0.576043i
$127$	−31.3394	+	96.4527i	−0.246767	+	0.759470i	0.748574	+	0.663051i	$0.230739\pi$
$127$	−31.3394	+	96.4527i	−0.246767	+	0.759470i	−0.995341	+	0.0964190i	$0.969261\pi$
$128$	−69.9464	−	96.2730i	−0.546457	−	0.752133i
$129$	7.98498	+	78.4702i	0.0618991	+	0.608296i
$130$	27.0689	+	83.3095i	0.208222	+	0.640842i
$131$			130.992i			0.999938i	0.866043	+	0.499969i	$0.166655\pi$
$131$			130.992i			0.999938i	−0.866043	+	0.499969i	$0.833345\pi$
$132$		0			0
$133$	−80.7902			−0.607445
$134$	73.0319	−	23.7295i	0.545014	−	0.177086i
$135$	−1.77467	+	178.678i	−0.0131457	+	1.32354i
$136$	−33.9787	+	24.6870i	−0.249843	+	0.181522i
$137$	198.531	+	64.5066i	1.44913	+	0.470851i	0.924731	−	0.380622i	$-0.124290\pi$
$137$	198.531	+	64.5066i	1.44913	+	0.470851i	0.524399	+	0.851472i	$0.324290\pi$
$138$	−48.1080	+	21.2285i	−0.348609	+	0.153830i
$139$	−66.0000	+	47.9518i	−0.474820	+	0.344977i	−0.799317	−	0.600910i	$-0.794805\pi$
$139$	−66.0000	+	47.9518i	−0.474820	+	0.344977i	0.324497	+	0.945887i	$0.394805\pi$
$140$	−103.327	+	142.217i	−0.738049	+	1.01584i
$141$	−45.9191	−	26.7145i	−0.325667	−	0.189464i
$142$	65.8197			0.463519
$143$		0			0
$144$	−5.00000	+	44.7214i	−0.0347222	+	0.310565i
$145$	−53.9803	−	166.134i	−0.372278	−	1.14575i
$146$	−8.82929	+	12.1525i	−0.0604746	+	0.0832361i
$147$	86.1971	+	18.6202i	0.586375	+	0.126668i
$148$	−18.1672	+	55.9128i	−0.122751	+	0.377789i
$149$	−6.64966	−	2.16061i	−0.0446286	−	0.0145007i	0.286618	−	0.958045i	$-0.407469\pi$
$149$	−6.64966	−	2.16061i	−0.0446286	−	0.0145007i	−0.331246	+	0.943544i	$0.607469\pi$
$150$	11.9078	−	55.1236i	0.0793851	−	0.367491i
$151$	−44.8607	−	32.5932i	−0.297091	−	0.215849i	0.429247	−	0.903187i	$-0.358779\pi$
$151$	−44.8607	−	32.5932i	−0.297091	−	0.215849i	−0.726337	+	0.687338i	$0.758779\pi$
$152$	60.7462	−	19.7376i	0.399646	−	0.129853i
$153$	53.6656	+	6.00000i	0.350756	+	0.0392157i
$154$		0			0
$155$			41.0426i			0.264791i
$156$	59.9035	−	102.967i	0.383997	−	0.660046i
$157$	−33.9787	−	24.6870i	−0.216425	−	0.157242i	0.474291	−	0.880368i	$-0.342704\pi$
$157$	−33.9787	−	24.6870i	−0.216425	−	0.157242i	−0.690716	+	0.723126i	$0.742704\pi$
$158$	69.3944	+	95.5132i	0.439205	+	0.604514i
$159$	−26.9725	−	61.1250i	−0.169638	−	0.384434i
$160$	67.4878	−	207.706i	0.421799	−	1.29816i
$161$	91.2204	+	125.554i	0.566587	+	0.779840i
$162$	−60.9072	+	53.3977i	−0.375970	+	0.329616i
$163$	−49.0689	−	151.018i	−0.301036	−	0.926494i	−0.981127	−	0.193366i	$-0.938060\pi$
$163$	−49.0689	−	151.018i	−0.301036	−	0.926494i	0.680091	−	0.733128i	$-0.261940\pi$
$164$		−	16.7902i		−	0.102380i
$165$		0			0
$166$	−111.185			−0.669791
$167$	−271.220	+	88.1246i	−1.62407	+	0.527692i	−0.972897	−	0.231237i	$-0.925723\pi$
$167$	−271.220	+	88.1246i	−1.62407	+	0.527692i	−0.651173	+	0.758930i	$0.725723\pi$
$168$	−184.981	+	18.8233i	−1.10108	+	0.112044i
$169$	−5.01064	+	3.64045i	−0.0296488	+	0.0215411i
$170$	−37.7647	−	12.2705i	−0.222146	−	0.0721795i
$171$	−74.7989	−	33.8978i	−0.437421	−	0.198233i
$172$	−63.8115	+	46.3618i	−0.370997	+	0.269545i
$173$	35.1486	−	48.3779i	0.203171	−	0.279641i	−0.695257	−	0.718761i	$-0.744710\pi$
$173$	35.1486	−	48.3779i	0.203171	−	0.279641i	0.898429	+	0.439120i	$0.144710\pi$
$174$	39.8195	−	68.4451i	0.228848	−	0.393363i
$175$	−166.443			−0.951101
$176$		0			0
$177$	48.9919	−	43.8197i	0.276790	−	0.247569i
$178$	30.1803	+	92.8855i	0.169552	+	0.521829i
$179$	155.080	−	213.449i	0.866369	−	1.19245i	−0.113644	−	0.993521i	$-0.536252\pi$
$179$	155.080	−	213.449i	0.866369	−	1.19245i	0.980013	−	0.198933i	$-0.0637475\pi$
$180$	−155.336	+	88.3169i	−0.862975	+	0.490649i
$181$	69.8278	−	214.908i	0.385789	−	1.18734i	−0.550117	−	0.835087i	$-0.685417\pi$
$181$	69.8278	−	214.908i	0.385789	−	1.18734i	0.935906	−	0.352249i	$-0.114583\pi$
$182$	111.458	+	36.2148i	0.612405	+	0.198982i
$183$	273.806	+	59.1473i	1.49621	+	0.323209i
$184$	−99.2624	−	72.1183i	−0.539469	−	0.391947i
$185$	−123.344	+	40.0770i	−0.666726	+	0.216633i
$186$	−13.8673	+	12.4033i	−0.0745551	+	0.0666842i
$187$		0			0
$188$		−	53.1246i		−	0.282578i
$189$	191.999	+	142.430i	1.01587	+	0.753599i
$190$	48.8541	+	35.4946i	0.257127	+	0.186814i
$191$	−35.3172	−	48.6099i	−0.184907	−	0.254502i	0.706493	−	0.707720i	$-0.250276\pi$
$191$	−35.3172	−	48.6099i	−0.184907	−	0.254502i	−0.891400	+	0.453218i	$0.850276\pi$
$192$	35.6806	−	15.7447i	0.185836	−	0.0820036i
$193$	−11.0279	+	33.9403i	−0.0571392	+	0.175856i	−0.975553	−	0.219765i	$-0.929471\pi$
$193$	−11.0279	+	33.9403i	−0.0571392	+	0.175856i	0.918414	+	0.395622i	$0.129471\pi$
$194$	71.2310	+	98.0410i	0.367170	+	0.505366i
$195$	261.440	−	26.6037i	1.34072	−	0.136429i
$196$	27.2508	+	83.8693i	0.139035	+	0.427904i
$197$		−	145.605i		−	0.739111i	−0.929209	−	0.369556i	$-0.879510\pi$
$197$		−	145.605i		−	0.739111i	0.929209	−	0.369556i	$-0.120490\pi$
$198$		0			0
$199$	241.185			1.21199			0.605993	−	0.795470i	$-0.292776\pi$
$199$	241.185			1.21199			0.605993	+	0.795470i	$0.292776\pi$
$200$	125.148	−	40.6631i	0.625741	−	0.203316i
$201$	−23.3217	−	229.187i	−0.116028	−	1.14023i
$202$	150.144	−	109.086i	0.743289	−	0.540031i
$203$	−222.267	−	72.2188i	−1.09491	−	0.355758i
$204$	21.8003	+	49.4039i	0.106864	+	0.242176i
$205$	29.9656	−	21.7713i	0.146173	−	0.106201i
$206$	101.445	−	139.627i	0.492452	−	0.677802i
$207$	31.7758	+	154.517i	0.153506	+	0.746461i
$208$	66.1803			0.318175
$209$		0			0
$210$	−117.193	−	131.026i	−0.558064	−	0.623935i
$211$	−13.2067	−	40.6459i	−0.0625908	−	0.192635i	0.914871	−	0.403745i	$-0.132292\pi$
$211$	−13.2067	−	40.6459i	−0.0625908	−	0.192635i	−0.977462	+	0.211111i	$0.932292\pi$
$212$	39.2708	−	54.0517i	0.185240	−	0.254961i
$213$	41.6932	−	193.007i	0.195743	−	0.906136i
$214$	−20.3278	+	62.5625i	−0.0949897	+	0.292348i
$215$	−165.484	−	53.7690i	−0.769692	−	0.250088i
$216$	−179.161	−	60.1866i	−0.829448	−	0.278641i
$217$	44.4230	+	32.2752i	0.204714	+	0.148734i
$218$	−102.078	+	33.1672i	−0.468248	+	0.152143i
$219$	30.0426	+	33.5886i	0.137181	+	0.153373i
$220$		0			0
$221$		−	79.4164i		−	0.359350i
$222$	−50.8162	−	29.5635i	−0.228902	−	0.133169i
$223$	134.290	+	97.5676i	0.602198	+	0.437523i	0.846659	−	0.532137i	$-0.178611\pi$
$223$	134.290	+	97.5676i	0.602198	+	0.437523i	−0.244460	+	0.969659i	$0.578611\pi$
$224$	−171.742	−	236.383i	−0.766706	−	1.05528i
$225$	−154.100	−	69.8357i	−0.684887	−	0.310381i
$226$	9.78522	−	30.1158i	0.0432974	−	0.133256i
$227$	−200.771	−	276.338i	−0.884455	−	1.21735i	−0.975167	−	0.221470i	$-0.928914\pi$
$227$	−200.771	−	276.338i	−0.884455	−	1.21735i	0.0907125	−	0.995877i	$-0.471086\pi$
$228$	−8.31360	−	81.6996i	−0.0364632	−	0.358332i
$229$	76.2574	+	234.696i	0.333002	+	1.02487i	0.967698	+	0.252112i	$0.0811251\pi$
$229$	76.2574	+	234.696i	0.333002	+	1.02487i	−0.634697	+	0.772761i	$0.718875\pi$
$230$		−	116.000i		−	0.504348i
$231$		0			0
$232$	184.766			0.796405
$233$	378.873	−	123.103i	1.62606	−	0.528340i	0.652703	−	0.757614i	$-0.273635\pi$
$233$	378.873	−	123.103i	1.62606	−	0.528340i	0.973362	+	0.229274i	$0.0736351\pi$
$234$	87.9971	+	80.2943i	0.376056	+	0.343138i
$235$	94.8115	−	68.8846i	0.403453	−	0.293126i
$236$	62.5125	+	20.3115i	0.264883	+	0.0860658i
$237$	324.037	−	142.987i	1.36724	−	0.603320i
$238$	−42.9787	+	31.2259i	−0.180583	+	0.131201i
$239$	94.7567	−	130.421i	0.396472	−	0.545696i	−0.563382	−	0.826196i	$-0.690500\pi$
$239$	94.7567	−	130.421i	0.396472	−	0.545696i	0.959854	+	0.280500i	$0.0905002\pi$
$240$	−85.8060	−	49.9196i	−0.357525	−	0.207998i
$241$	159.644			0.662425			0.331212	−	0.943556i	$-0.392542\pi$
$241$	159.644			0.662425			0.331212	+	0.943556i	$0.392542\pi$
$242$		0			0
$243$	118.000	+	212.426i	0.485597	+	0.874183i
$244$	86.5623	+	266.411i	0.354764	+	1.09185i
$245$	−114.347	+	157.384i	−0.466720	+	0.642386i
$246$	16.4117	+	3.54524i	0.0667142	+	0.0144115i
$247$	−37.3212	+	114.863i	−0.151098	+	0.465032i
$248$	−41.2867	−	13.4149i	−0.166479	−	0.0540922i
$249$	−70.4300	+	326.036i	−0.282851	+	1.30938i
$250$	−33.2041	−	24.1242i	−0.132817	−	0.0964969i
$251$	−46.4601	+	15.0958i	−0.185100	+	0.0601426i	−0.400100	−	0.916471i	$-0.631025\pi$
$251$	−46.4601	+	15.0958i	−0.185100	+	0.0601426i	0.215000	+	0.976614i	$0.431025\pi$
$252$	−26.5623	+	237.580i	−0.105406	+	0.942780i
$253$		0			0
$254$		−	101.416i		−	0.399277i
$255$	−59.9035	+	102.967i	−0.234916	+	0.403793i
$256$	138.342	+	100.511i	0.540398	+	0.392622i
$257$	−94.4196	−	129.957i	−0.367391	−	0.505671i	0.584798	−	0.811179i	$-0.301174\pi$
$257$	−94.4196	−	129.957i	−0.367391	−	0.505671i	−0.952190	+	0.305508i	$0.901174\pi$
$258$	−31.8428	−	72.1621i	−0.123422	−	0.279698i
$259$	−53.6180	+	165.019i	−0.207019	+	0.637140i
$260$	154.464	+	212.602i	0.594093	+	0.817699i
$261$	−175.482	−	160.121i	−0.672346	−	0.613492i
$262$	−40.4787	−	124.581i	−0.154499	−	0.475499i
$263$			140.420i			0.533914i	0.963708	+	0.266957i	$0.0860183\pi$
$263$			140.420i			0.533914i	−0.963708	+	0.266957i	$0.913982\pi$
$264$		0			0
$265$	147.387			0.556177
$266$	76.8361	−	24.9656i	0.288857	−	0.0938555i
$267$	291.492	−	29.6617i	1.09173	−	0.111092i
$268$	186.374	−	135.409i	0.695425	−	0.505256i
$269$	−393.494	−	127.854i	−1.46280	−	0.475294i	−0.533879	−	0.845561i	$-0.679266\pi$
$269$	−393.494	−	127.854i	−1.46280	−	0.475294i	−0.928925	+	0.370267i	$0.879266\pi$
$270$	−53.5268	−	170.481i	−0.198247	−	0.631413i
$271$	46.7426	−	33.9605i	0.172482	−	0.125316i	−0.498195	−	0.867065i	$-0.666004\pi$
$271$	46.7426	−	33.9605i	0.172482	−	0.125316i	0.670677	+	0.741749i	$0.266004\pi$
$272$	−17.6336	+	24.2705i	−0.0648293	+	0.0892298i
$273$	176.797	−	303.894i	0.647609	−	1.11316i
$274$	−208.748			−0.761853
$275$		0			0
$276$	−117.580	+	105.167i	−0.426016	+	0.381041i
$277$	101.708	+	313.026i	0.367178	+	1.13006i	0.948606	+	0.316459i	$0.102494\pi$
$277$	101.708	+	313.026i	0.367178	+	1.13006i	−0.581429	+	0.813597i	$0.697506\pi$
$278$	47.9518	−	66.0000i	0.172489	−	0.237410i
$279$	27.5867	+	48.5206i	0.0988769	+	0.173909i
$280$	126.752	−	390.102i	0.452685	−	1.39322i
$281$	−375.820	−	122.111i	−1.33744	−	0.434560i	−0.448991	−	0.893536i	$-0.648216\pi$
$281$	−375.820	−	122.111i	−1.33744	−	0.434560i	−0.888449	+	0.458976i	$0.848216\pi$
$282$	51.9269	+	11.2172i	0.184138	+	0.0397773i
$283$	232.254	+	168.743i	0.820686	+	0.596264i	0.916909	−	0.399096i	$-0.130676\pi$
$283$	232.254	+	168.743i	0.820686	+	0.596264i	−0.0962226	+	0.995360i	$0.530676\pi$
$284$	187.795	−	61.0182i	0.661249	−	0.214853i
$285$	135.029	−	120.774i	0.473787	−	0.423768i
$286$		0			0
$287$		−	49.5542i		−	0.172663i
$288$	−59.8249	−	290.912i	−0.207725	−	1.01011i
$289$	−204.681	−	148.710i	−0.708240	−	0.514566i
$290$	102.677	+	141.322i	0.354057	+	0.487318i
$291$	332.613	−	146.771i	1.14300	−	0.504369i
$292$	−13.9255	+	42.8583i	−0.0476901	+	0.146775i
$293$	42.1829	+	58.0598i	0.143969	+	0.198156i	0.874912	−	0.484283i	$-0.160919\pi$
$293$	42.1829	+	58.0598i	0.143969	+	0.198156i	−0.730943	+	0.682439i	$0.760919\pi$
$294$	−87.7323	+	8.92748i	−0.298409	+	0.0303656i
$295$	44.8075	+	137.903i	0.151890	+	0.467468i
$296$		−	137.177i		−	0.463437i
$297$		0			0
$298$	6.99187			0.0234626
$299$	220.645	−	71.6919i	0.737944	−	0.239772i
$300$	−17.1275	−	168.316i	−0.0570918	−	0.561054i
$301$	−188.331	+	136.831i	−0.625685	+	0.454587i
$302$	52.7369	+	17.1353i	0.174625	+	0.0567393i
$303$	−224.772	−	509.378i	−0.741822	−	1.68111i
$304$	36.9098	−	26.8166i	0.121414	−	0.0882124i
$305$	−363.223	+	499.933i	−1.19089	+	1.63912i
$306$	−52.8932	+	10.8773i	−0.172853	+	0.0355466i
$307$	−116.961			−0.380979			−0.190489	−	0.981689i	$-0.561008\pi$
$307$	−116.961			−0.380979			−0.190489	+	0.981689i	$0.561008\pi$
$308$		0			0
$309$	−345.177	−	385.920i	−1.11708	−	1.24893i
$310$	−12.6829	−	39.0338i	−0.0409124	−	0.125916i
$311$	−107.648	+	148.164i	−0.346133	+	0.476412i	−0.946220	−	0.323523i	$-0.895133\pi$
$311$	−107.648	+	148.164i	−0.346133	+	0.476412i	0.600087	+	0.799935i	$0.295133\pi$
$312$	−58.6904	+	271.691i	−0.188110	+	0.870803i
$313$	−23.1089	+	71.1220i	−0.0738305	+	0.227227i	−0.981161	−	0.193191i	$-0.938116\pi$
$313$	−23.1089	+	71.1220i	−0.0738305	+	0.227227i	0.907331	+	0.420418i	$0.138116\pi$
$314$	39.9444	+	12.9787i	0.127211	+	0.0413335i
$315$	−458.452	+	260.656i	−1.45540	+	0.827478i
$316$	286.539	+	208.183i	0.906770	+	0.658807i
$317$	−16.8069	+	5.46090i	−0.0530187	+	0.0172268i	−0.335406	−	0.942074i	$-0.608874\pi$
$317$	−16.8069	+	5.46090i	−0.0530187	+	0.0172268i	0.282388	+	0.959300i	$0.408874\pi$
$318$	44.5410	+	49.7984i	0.140066	+	0.156599i
$319$		0			0
$320$			86.0344i			0.268858i
$321$	170.579	+	99.2384i	0.531400	+	0.309154i
$322$	−125.554	−	91.2204i	−0.389920	−	0.283293i
$323$	−32.1799	−	44.2918i	−0.0996281	−	0.137126i
$324$	−124.276	+	208.817i	−0.383568	+	0.644496i
$325$	−76.8885	+	236.639i	−0.236580	+	0.728119i
$326$	93.3346	+	128.464i	0.286302	+	0.394061i
$327$	32.5972	+	320.340i	0.0996855	+	0.979632i
$328$	12.1064	+	37.2598i	0.0369099	+	0.113597i
$329$		−	156.790i		−	0.476566i
$330$		0			0
$331$	−395.580			−1.19511			−0.597554	−	0.801829i	$-0.703860\pi$
$331$	−395.580			−1.19511			−0.597554	+	0.801829i	$0.703860\pi$
$332$	−317.231	+	103.075i	−0.955514	+	0.310465i
$333$	−118.880	+	130.285i	−0.356998	+	0.391245i
$334$	230.713	−	167.623i	0.690758	−	0.501865i
$335$	483.327	+	157.043i	1.44277	+	0.468784i
$336$	−121.508	+	53.6173i	−0.361630	+	0.159575i
$337$	404.753	−	294.070i	1.20105	−	0.872611i	0.206659	−	0.978413i	$-0.433741\pi$
$337$	404.753	−	294.070i	1.20105	−	0.872611i	0.994387	+	0.105802i	$0.0337408\pi$
$338$	3.64045	−	5.01064i	0.0107705	−	0.0148244i
$339$	−82.1120	−	47.7706i	−0.242218	−	0.140916i
$340$	−119.125			−0.350367
$341$		0			0
$342$	81.6130	+	9.12461i	0.238635	+	0.0266802i
$343$	−53.6403	−	165.088i	−0.156386	−	0.481306i
$344$	108.178	−	148.894i	0.314470	−	0.432830i
$345$	−340.154	−	73.4798i	−0.985954	−	0.212985i
$346$	−18.4787	+	56.8716i	−0.0534067	+	0.164369i
$347$	586.779	+	190.656i	1.69100	+	0.549441i	0.986995	−	0.160750i	$-0.0513912\pi$
$347$	586.779	+	190.656i	1.69100	+	0.549441i	0.704010	+	0.710190i	$0.251391\pi$
$348$	50.1597	−	232.200i	0.144137	−	0.667242i
$349$	−250.957	−	182.331i	−0.719076	−	0.522439i	0.167013	−	0.985955i	$-0.446588\pi$
$349$	−250.957	−	182.331i	−0.719076	−	0.522439i	−0.886089	+	0.463516i	$0.846588\pi$
$350$	158.296	−	51.4336i	0.452276	−	0.146953i
$351$	291.193	−	207.177i	0.829611	−	0.590249i
$352$		0			0
$353$			308.577i			0.874157i	0.899423	+	0.437078i	$0.143987\pi$
$353$			308.577i			0.874157i	−0.899423	+	0.437078i	$0.856013\pi$
$354$	−33.0530	+	56.8143i	−0.0933701	+	0.160492i
$355$	352.405	+	256.037i	0.992691	+	0.721232i
$356$	172.219	+	237.039i	0.483762	+	0.665841i
$357$	64.3408	+	145.809i	0.180226	+	0.408429i
$358$	−81.5304	+	250.925i	−0.227738	+	0.700907i
$359$	−80.4033	−	110.666i	−0.223965	−	0.308261i	0.682217	−	0.731150i	$-0.261016\pi$
$359$	−80.4033	−	110.666i	−0.223965	−	0.308261i	−0.906181	+	0.422889i	$0.861016\pi$
$360$	281.030	−	307.990i	0.780639	−	0.855528i
$361$	−85.8268	−	264.148i	−0.237747	−	0.731711i
$362$			225.967i			0.624220i
$363$		0			0
$364$	351.580			0.965880
$365$	−94.5458	+	30.7198i	−0.259030	+	0.0841639i
$366$	−278.682	+	28.3582i	−0.761427	+	0.0774815i
$367$	101.956	−	74.0753i	0.277809	−	0.201840i	−0.440152	−	0.897923i	$-0.645076\pi$
$367$	101.956	−	74.0753i	0.277809	−	0.201840i	0.717961	+	0.696083i	$0.245076\pi$
$368$	−83.3499	−	27.0820i	−0.226494	−	0.0735925i
$369$	20.7919	−	45.8793i	0.0563465	−	0.124334i
$370$	104.923	−	76.2310i	0.283576	−	0.206030i
$371$	115.903	−	159.526i	0.312406	−	0.429990i
$372$	−28.0672	+	48.2442i	−0.0754494	+	0.129689i
$373$	−347.528			−0.931710			−0.465855	−	0.884861i	$-0.654253\pi$
$373$	−347.528			−0.931710			−0.465855	+	0.884861i	$0.654253\pi$
$374$		0			0
$375$	−91.7740	+	82.0851i	−0.244731	+	0.218894i
$376$	38.3050	+	117.891i	0.101875	+	0.313539i
$377$	−205.353	+	282.644i	−0.544703	+	0.749720i
$378$	−226.615	−	76.1283i	−0.599512	−	0.201398i
$379$	−146.584	+	451.138i	−0.386764	+	1.19034i	0.548428	+	0.836198i	$0.315226\pi$
$379$	−146.584	+	451.138i	−0.386764	+	1.19034i	−0.935192	+	0.354140i	$0.884774\pi$
$380$	172.294	+	55.9818i	0.453406	+	0.147321i
$381$	−297.390	−	64.2419i	−0.780550	−	0.168614i
$382$	48.6099	+	35.3172i	0.127251	+	0.0924533i
$383$	278.142	−	90.3738i	0.726219	−	0.235963i	0.0775019	−	0.996992i	$-0.475306\pi$
$383$	278.142	−	90.3738i	0.726219	−	0.235963i	0.648718	+	0.761029i	$0.275306\pi$
$384$	266.092	−	238.000i	0.692948	−	0.619792i
$385$		0			0
$386$		−	35.6869i		−	0.0924532i
$387$	−231.776	+	47.6638i	−0.598904	+	0.123162i
$388$	294.123	+	213.693i	0.758049	+	0.550755i
$389$	−46.1712	−	63.5492i	−0.118692	−	0.163365i	0.745537	−	0.666464i	$-0.232193\pi$
$389$	−46.1712	−	63.5492i	−0.118692	−	0.163365i	−0.864229	+	0.503099i	$0.832193\pi$
$390$	−240.423	+	106.091i	−0.616470	+	0.272028i
$391$	−32.4984	+	100.020i	−0.0831162	+	0.255805i
$392$	−120.946	−	166.468i	−0.308536	−	0.424663i
$393$	−390.957	+	39.7830i	−0.994801	+	0.101229i
$394$	44.9944	+	138.478i	0.114199	+	0.351468i
$395$			781.330i			1.97805i
$396$		0			0
$397$	166.741			0.420004			0.210002	−	0.977701i	$-0.432653\pi$
$397$	166.741			0.420004			0.210002	+	0.977701i	$0.432653\pi$
$398$	−229.381	+	74.5304i	−0.576334	+	0.187262i
$399$	−24.5365	−	241.126i	−0.0614950	−	0.604325i
$400$	76.0410	−	55.2470i	0.190103	−	0.138118i
$401$	−187.280	−	60.8510i	−0.467033	−	0.151748i	0.0660410	−	0.997817i	$-0.478963\pi$
$401$	−187.280	−	60.8510i	−0.467033	−	0.151748i	−0.533074	+	0.846069i	$0.678963\pi$
$402$	93.0030	+	210.763i	0.231351	+	0.524287i
$403$	66.4083	−	48.2484i	0.164785	−	0.119723i
$404$	327.259	−	450.433i	0.810046	−	1.11493i
$405$	−533.819	+	48.9690i	−1.31807	+	0.120911i
$406$	233.705			0.575628
$407$		0			0
$408$	−84.0000	−	93.9149i	−0.205882	−	0.230183i
$409$	−222.747	−	685.545i	−0.544614	−	1.67615i	−0.721906	−	0.691991i	$-0.756734\pi$
$409$	−222.747	−	685.545i	−0.544614	−	1.67615i	0.177292	−	0.984158i	$-0.443266\pi$
$410$	−21.7713	+	29.9656i	−0.0531006	+	0.0730867i
$411$	−132.230	+	612.124i	−0.321729	+	1.48935i
$412$	159.998	−	492.425i	0.388346	−	1.19521i
$413$	184.497	+	59.9468i	0.446725	+	0.145150i
$414$	−77.9691	−	137.135i	−0.188331	−	0.331245i
$415$	−595.298	−	432.509i	−1.43445	−	1.04219i
$416$	−415.412	+	134.976i	−0.998587	+	0.324461i
$417$	−163.161	−	182.420i	−0.391273	−	0.437457i
$418$		0			0
$419$		−	267.408i		−	0.638206i	−0.947720	−	0.319103i	$-0.896618\pi$
$419$		−	267.408i		−	0.638206i	0.947720	−	0.319103i	$-0.103382\pi$
$420$	−455.841	−	265.196i	−1.08534	−	0.631419i
$421$	−554.959	−	403.202i	−1.31819	−	0.957723i	−0.999953	−	0.00971339i	$-0.996908\pi$
$421$	−554.959	−	403.202i	−1.31819	−	0.957723i	−0.318240	−	0.948010i	$-0.603092\pi$
$422$	25.1205	+	34.5755i	0.0595274	+	0.0819324i
$423$	65.7858	−	145.163i	0.155522	−	0.343175i
$424$	−48.1738	+	148.264i	−0.113617	+	0.349678i
$425$	−66.2964	−	91.2492i	−0.155992	−	0.214704i
$426$	19.9898	+	196.445i	0.0469245	+	0.461137i
$427$	255.477	+	786.278i	0.598307	+	1.84140i
$428$			197.346i			0.461090i
$429$		0			0
$430$	174.000			0.404651
$431$	−525.351	+	170.697i	−1.21891	+	0.396049i	−0.846686	−	0.532093i	$-0.821406\pi$
$431$	−525.351	+	170.697i	−1.21891	+	0.396049i	−0.372227	+	0.928142i	$0.621406\pi$
$432$	−134.993	−	1.34078i	−0.312485	−	0.00310366i
$433$	230.263	−	167.296i	0.531786	−	0.386365i	−0.289239	−	0.957257i	$-0.593402\pi$
$433$	230.263	−	167.296i	0.531786	−	0.386365i	0.821025	+	0.570892i	$0.193402\pi$
$434$	−52.2224	−	16.9681i	−0.120328	−	0.0390969i
$435$	479.448	−	211.565i	1.10218	−	0.486356i
$436$	−260.498	+	189.263i	−0.597474	+	0.434090i
$437$	94.0074	−	129.390i	0.215120	−	0.296087i
$438$	−38.9516	−	22.6610i	−0.0889307	−	0.0517375i
$439$	−532.058			−1.21198			−0.605988	−	0.795474i	$-0.707222\pi$
$439$	−532.058			−1.21198			−0.605988	+	0.795474i	$0.707222\pi$
$440$		0			0
$441$	−29.3951	+	262.918i	−0.0666556	+	0.596186i
$442$	24.5410	+	75.5295i	0.0555227	+	0.170881i
$443$	70.7087	−	97.3222i	0.159613	−	0.219689i	−0.721719	−	0.692187i	$-0.756648\pi$
$443$	70.7087	−	97.3222i	0.159613	−	0.219689i	0.881332	+	0.472498i	$0.156648\pi$
$444$	−172.394	−	37.2405i	−0.388275	−	0.0838749i
$445$	−199.735	+	614.720i	−0.448842	+	1.38139i
$446$	−157.868	−	51.2943i	−0.353963	−	0.115010i
$447$	4.42898	−	20.5027i	0.00990822	−	0.0458673i
$448$	93.1205	+	67.6560i	0.207858	+	0.151018i
$449$	−65.3078	+	21.2198i	−0.145452	+	0.0472601i	−0.380838	−	0.924642i	$-0.624364\pi$
$449$	−65.3078	+	21.2198i	−0.145452	+	0.0472601i	0.235386	+	0.971902i	$0.424364\pi$
$450$	168.138	+	18.7984i	0.373639	+	0.0417742i
$451$		0			0
$452$		−	94.9969i		−	0.210170i
$453$	83.6528	−	143.789i	0.184664	−	0.317416i
$454$	276.338	+	200.771i	0.608674	+	0.442227i
$455$	455.881	+	627.466i	1.00194	+	1.37905i
$456$	77.3576	+	175.308i	0.169644	+	0.384447i
$457$	−214.924	+	661.467i	−0.470292	+	1.44741i	0.381911	+	0.924199i	$0.375266\pi$
$457$	−214.924	+	661.467i	−0.470292	+	1.44741i	−0.852203	+	0.523212i	$0.824734\pi$
$458$	−145.050	−	199.644i	−0.316703	−	0.435905i
$459$	−1.60894	+	161.992i	−0.00350531	+	0.352924i
$460$	−107.538	−	330.968i	−0.233778	−	0.719495i
$461$		−	824.322i		−	1.78812i	−0.447950	−	0.894059i	$-0.647846\pi$
$461$		−	824.322i		−	1.78812i	0.447950	−	0.894059i	$-0.352154\pi$
$462$		0			0
$463$	−158.137			−0.341548			−0.170774	−	0.985310i	$-0.554627\pi$
$463$	−158.137			−0.341548			−0.170774	+	0.985310i	$0.554627\pi$
$464$	125.516	−	40.7827i	0.270509	−	0.0878938i
$465$	−122.495	+	12.4649i	−0.263430	+	0.0268062i
$466$	−322.289	+	234.156i	−0.691607	+	0.502482i
$467$	725.951	+	235.876i	1.55450	+	0.505087i	0.955331	−	0.295537i	$-0.0954984\pi$
$467$	725.951	+	235.876i	1.55450	+	0.505087i	0.599167	+	0.800624i	$0.295498\pi$
$468$	325.508	+	147.516i	0.695529	+	0.315204i
$469$	550.058	−	399.640i	1.17283	−	0.852111i
$470$	−68.8846	+	94.8115i	−0.146563	+	0.201727i
$471$	63.3609	−	108.910i	0.134524	−	0.231231i
$472$	−153.369			−0.324934
$473$		0			0
$474$	−263.992	+	236.122i	−0.556945	+	0.498147i
$475$	53.0050	+	163.133i	0.111590	+	0.343437i
$476$	−93.6776	+	128.936i	−0.196802	+	0.270874i
$477$	174.241	−	99.0658i	0.365286	−	0.207685i
$478$	−49.8166	+	153.320i	−0.104219	+	0.320752i
$479$	−71.1607	−	23.1215i	−0.148561	−	0.0482704i	0.233793	−	0.972286i	$-0.424886\pi$
$479$	−71.1607	−	23.1215i	−0.148561	−	0.0482704i	−0.382353	+	0.924016i	$0.624886\pi$
$480$	640.414	+	138.342i	1.33419	+	0.288212i
$481$	209.846	+	152.462i	0.436270	+	0.316969i
$482$	−151.831	+	49.3328i	−0.315002	+	0.102350i
$483$	−347.023	+	310.387i	−0.718475	+	0.642623i
$484$		0			0
$485$			802.009i			1.65363i
$486$	−177.868	−	165.566i	−0.365984	−	0.340670i
$487$	−245.112	−	178.085i	−0.503311	−	0.365677i	0.306969	−	0.951719i	$-0.400685\pi$
$487$	−245.112	−	178.085i	−0.503311	−	0.365677i	−0.810280	+	0.586043i	$0.800685\pi$
$488$	−384.186	−	528.787i	−0.787267	−	1.08358i
$489$	435.825	−	192.316i	0.891258	−	0.393284i
$490$	60.1155	−	185.017i	0.122685	−	0.377585i
$491$	469.508	+	646.222i	0.956227	+	1.31613i	0.948705	+	0.316162i	$0.102394\pi$
$491$	469.508	+	646.222i	0.956227	+	1.31613i	0.00752206	+	0.999972i	$0.497606\pi$
$492$	50.1120	−	5.09930i	0.101854	−	0.0103644i
$493$	−48.9392	−	150.620i	−0.0992682	−	0.305516i
$494$		−	120.774i		−	0.244482i
$495$		0			0
$496$	−31.0081			−0.0625164
$497$	554.251	−	180.087i	1.11519	−	0.362348i
$498$	−33.7677	−	331.842i	−0.0678066	−	0.666350i
$499$	−473.066	+	343.702i	−0.948028	+	0.688782i	−0.950340	−	0.311215i	$-0.899264\pi$
$499$	−473.066	+	343.702i	−0.948028	+	0.688782i	0.00231194	+	0.999997i	$0.499264\pi$
$500$	−117.101	−	38.0486i	−0.234203	−	0.0760971i
$501$	−345.387	−	782.715i	−0.689395	−	1.56231i
$502$	39.5213	−	28.7139i	0.0787277	−	0.0571990i
$503$	−325.595	+	448.143i	−0.647306	+	0.890940i	−0.998979	−	0.0451830i	$-0.985613\pi$
$503$	−325.595	+	448.143i	−0.647306	+	0.890940i	0.351673	+	0.936123i	$0.385613\pi$
$504$	−112.360	−	546.375i	−0.222936	−	1.08408i
$505$	1228.23			2.43214
$506$		0			0
$507$	−12.3870	−	13.8491i	−0.0244319	−	0.0273157i
$508$	−94.0182	−	289.358i	−0.185075	−	0.569603i
$509$	−50.4847	+	69.4863i	−0.0991841	+	0.136515i	−0.855724	−	0.517432i	$-0.826888\pi$
$509$	−50.4847	+	69.4863i	−0.0991841	+	0.136515i	0.756540	+	0.653947i	$0.226888\pi$
$510$	25.1530	−	116.439i	0.0493197	−	0.228311i
$511$	−41.0993	+	126.491i	−0.0804291	+	0.247535i
$512$	290.072	+	94.2502i	0.566547	+	0.184082i
$513$	78.4541	−	233.539i	0.152932	−	0.455242i
$514$	129.957	+	94.4196i	0.252835	+	0.183696i
$515$	1086.29	−	352.958i	2.10931	−	0.685356i
$516$	−157.751	−	176.371i	−0.305719	−	0.341804i
$517$		0			0
$518$		−	173.512i		−	0.334964i
$519$	155.063	+	90.2114i	0.298772	+	0.173818i
$520$	−496.071	−	360.417i	−0.953982	−	0.693109i
$521$	431.206	+	593.503i	0.827650	+	1.13916i	0.988356	+	0.152160i	$0.0486229\pi$
$521$	431.206	+	593.503i	0.827650	+	1.13916i	−0.160706	+	0.987002i	$0.551377\pi$
$522$	216.374	+	98.0576i	0.414509	+	0.187850i
$523$	93.0151	−	286.271i	0.177849	−	0.547363i	−0.821903	−	0.569627i	$-0.807088\pi$
$523$	93.0151	−	286.271i	0.177849	−	0.547363i	0.999752	+	0.0222642i	$0.00708750\pi$
$524$	−230.985	−	317.924i	−0.440812	−	0.606725i
$525$	−50.5497	−	496.763i	−0.0962851	−	0.946215i
$526$	−43.3920	−	133.547i	−0.0824943	−	0.253891i
$527$			37.2098i			0.0706067i
$528$		0			0
$529$	221.774			0.419232
$530$	−140.173	+	45.5451i	−0.264478	+	0.0859341i
$531$	145.663	+	132.912i	0.274318	+	0.250305i
$532$	196.082	−	142.462i	0.368575	−	0.267786i
$533$	−70.4533	−	22.8916i	−0.132182	−	0.0429487i
$534$	−268.059	+	118.286i	−0.501983	+	0.221509i
$535$	−352.204	+	255.891i	−0.658325	+	0.478301i
$536$	−315.953	+	434.872i	−0.589465	+	0.811329i
$537$	684.157	+	398.024i	1.27404	+	0.741199i
$538$	413.745			0.769042
$539$		0			0
$540$	−310.766	−	436.790i	−0.575492	−	0.808871i
$541$	117.991	+	363.138i	0.218097	+	0.671235i	0.998919	+	0.0464809i	$0.0148007\pi$
$541$	117.991	+	363.138i	0.218097	+	0.671235i	−0.780822	+	0.624754i	$0.785199\pi$
$542$	−33.9605	+	46.7426i	−0.0626578	+	0.0862410i
$543$	662.618	+	143.138i	1.22029	+	0.263606i
$544$	61.1854	−	188.309i	0.112473	−	0.346157i
$545$	−675.556	−	219.502i	−1.23955	−	0.402755i
$546$	−74.2358	+	343.654i	−0.135963	+	0.629402i
$547$	−150.498	−	109.344i	−0.275134	−	0.199897i	0.441658	−	0.897183i	$-0.354390\pi$
$547$	−150.498	−	109.344i	−0.275134	−	0.199897i	−0.716792	+	0.697287i	$0.754390\pi$
$548$	−595.592	+	193.520i	−1.08685	+	0.353138i
$549$	−93.3738	+	835.161i	−0.170080	+	1.52124i
$550$		0			0
$551$			240.845i			0.437106i
$552$	185.097	−	318.160i	0.335320	−	0.576377i
$553$	845.683	+	614.425i	1.52926	+	1.11108i
$554$	−193.461	−	266.276i	−0.349207	−	0.480642i
$555$	−157.074	−	355.960i	−0.283016	−	0.641370i
$556$	75.6293	−	232.763i	0.136024	−	0.418638i
$557$	−256.630	−	353.221i	−0.460736	−	0.634149i	0.513925	−	0.857835i	$-0.328191\pi$
$557$	−256.630	−	353.221i	−0.460736	−	0.634149i	−0.974661	+	0.223686i	$0.928191\pi$
$558$	−41.2302	−	37.6211i	−0.0738892	−	0.0674213i
$559$	107.538	+	330.968i	0.192376	+	0.592071i
$560$		−	292.984i		−	0.523185i
$561$		0			0
$562$	395.161			0.703133
$563$	235.525	−	76.5267i	0.418339	−	0.135927i	−0.0922811	−	0.995733i	$-0.529416\pi$
$563$	235.525	−	76.5267i	0.418339	−	0.135927i	0.510620	+	0.859806i	$0.329416\pi$
$564$	158.555	−	16.1343i	0.281126	−	0.0286069i
$565$	169.541	−	123.179i	0.300073	−	0.218016i
$566$	−273.031	−	88.7132i	−0.482387	−	0.156737i
$567$	−366.784	+	616.295i	−0.646886	+	1.08694i
$568$	−372.745	+	270.815i	−0.656240	+	0.476787i
$569$	−163.177	+	224.594i	−0.286778	+	0.394716i	−0.927964	−	0.372669i	$-0.878443\pi$
$569$	−163.177	+	224.594i	−0.286778	+	0.394716i	0.641186	+	0.767385i	$0.278443\pi$
$570$	−91.0994	+	156.589i	−0.159823	+	0.274718i
$571$	−1010.88			−1.77037			−0.885187	−	0.465236i	$-0.845969\pi$
$571$	−1010.88			−1.77037			−0.885187	+	0.465236i	$0.845969\pi$
$572$		0			0
$573$	134.354	−	120.170i	0.234476	−	0.209721i
$574$	15.3131	+	47.1288i	0.0266778	+	0.0821060i
$575$	193.673	−	266.567i	0.336822	−	0.463595i
$576$	57.8278	+	101.710i	0.100396	+	0.176580i
$577$	80.4017	−	247.451i	0.139344	−	0.428858i	−0.856896	−	0.515489i	$-0.827610\pi$
$577$	80.4017	−	247.451i	0.139344	−	0.428858i	0.996240	+	0.0866313i	$0.0276102\pi$
$578$	240.617	+	78.1813i	0.416293	+	0.135262i
$579$	−104.647	−	22.6058i	−0.180737	−	0.0390428i
$580$	423.967	+	308.030i	0.730977	+	0.531086i
$581$	−936.264	+	304.211i	−1.61147	+	0.523598i
$582$	−270.979	+	242.371i	−0.465599	+	0.416445i
$583$		0			0
$584$		−	105.149i		−	0.180050i
$585$	158.802	+	772.211i	0.271456	+	1.32002i
$586$	−58.0598	−	42.1829i	−0.0990781	−	0.0719845i
$587$	−592.051	−	814.889i	−1.00861	−	1.38823i	−0.919893	−	0.392169i	$-0.871725\pi$
$587$	−592.051	−	814.889i	−1.00861	−	1.38823i	−0.0887124	−	0.996057i	$-0.528275\pi$
$588$	−242.039	+	106.804i	−0.411631	+	0.181639i
$589$	17.4865	−	53.8178i	0.0296884	−	0.0913716i
$590$	−85.2289	−	117.307i	−0.144456	−	0.198826i
$591$	434.570	−	44.2211i	0.735314	−	0.0748242i
$592$	−30.2786	−	93.1881i	−0.0511464	−	0.157412i
$593$		−	13.9837i		−	0.0235813i	−0.999930	−	0.0117907i	$-0.996247\pi$
$593$		−	13.9837i		−	0.0235813i	0.999930	−	0.0117907i	$-0.00375317\pi$
$594$		0			0
$595$	−351.580			−0.590892
$596$	19.9490	−	6.48182i	0.0334715	−	0.0108755i
$597$	73.2495	+	719.839i	0.122696	+	1.20576i
$598$	−187.692	+	136.366i	−0.313866	+	0.228037i
$599$	−164.882	−	53.5735i	−0.275263	−	0.0894383i	0.168133	−	0.985764i	$-0.446226\pi$
$599$	−164.882	−	53.5735i	−0.275263	−	0.0894383i	−0.443396	+	0.896326i	$0.646226\pi$
$600$	159.371	+	361.166i	0.265618	+	0.601944i
$601$	−635.183	+	461.488i	−1.05688	+	0.767866i	−0.973508	−	0.228652i	$-0.926568\pi$
$601$	−635.183	+	461.488i	−1.05688	+	0.767866i	−0.0833691	+	0.996519i	$0.526568\pi$
$602$	136.831	−	188.331i	0.227293	−	0.312843i
$603$	676.946	−	139.211i	1.12263	−	0.230864i
$604$	166.353			0.275418
$605$		0			0
$606$	371.177	+	414.989i	0.612504	+	0.684800i
$607$	−4.12343	−	12.6906i	−0.00679312	−	0.0209071i	0.947603	−	0.319452i	$-0.103499\pi$
$607$	−4.12343	−	12.6906i	−0.00679312	−	0.0209071i	−0.954396	+	0.298545i	$0.903499\pi$
$608$	−176.989	+	243.605i	−0.291101	+	0.400666i
$609$	148.040	−	685.308i	0.243086	−	1.12530i
$610$	190.957	−	587.707i	0.313045	−	0.963453i
$611$	−222.915	−	72.4296i	−0.364837	−	0.118543i
$612$	−140.829	+	80.0693i	−0.230113	+	0.130832i
$613$	−504.890	−	366.824i	−0.823639	−	0.598408i	0.0941138	−	0.995561i	$-0.469998\pi$
$613$	−504.890	−	366.824i	−0.823639	−	0.598408i	−0.917752	+	0.397153i	$0.869998\pi$
$614$	111.236	−	36.1428i	0.181166	−	0.0588645i
$615$	74.0789	+	82.8228i	0.120454	+	0.134671i
$616$		0			0
$617$		−	1103.25i		−	1.78808i	−0.447986	−	0.894041i	$-0.647859\pi$
$617$		−	1103.25i		−	1.78808i	0.447986	−	0.894041i	$-0.352141\pi$
$618$	447.539	+	260.366i	0.724173	+	0.421304i
$619$	148.220	+	107.688i	0.239450	+	0.173971i	0.701038	−	0.713124i	$-0.252720\pi$
$619$	148.220	+	107.688i	0.239450	+	0.173971i	−0.461588	+	0.887094i	$0.652720\pi$
$620$	−72.3727	−	99.6124i	−0.116730	−	0.160665i
$621$	−451.520	+	141.766i	−0.727085	+	0.228286i
$622$	56.5936	−	174.177i	0.0909866	−	0.280028i
$623$	508.282	+	699.591i	0.815862	+	1.12294i
$624$	20.0994	+	197.521i	0.0322105	+	0.316540i
$625$	−229.161	−	705.285i	−0.366658	−	1.12846i
$626$		−	74.7821i		−	0.119460i
$627$		0			0
$628$	126.000			0.200637
$629$	−111.826	+	36.3344i	−0.177783	+	0.0577653i
$630$	355.467	−	389.568i	0.564233	−	0.618362i
$631$	−225.579	+	163.893i	−0.357494	+	0.259735i	−0.752006	−	0.659156i	$-0.770914\pi$
$631$	−225.579	+	163.893i	−0.357494	+	0.259735i	0.394512	+	0.918891i	$0.370914\pi$
$632$	−785.977	−	255.379i	−1.24363	−	0.404081i
$633$	117.300	−	51.7608i	0.185309	−	0.0817706i
$634$	14.2968	−	10.3872i	0.0225502	−	0.0163837i
$635$	394.508	−	542.994i	0.621273	−	0.855108i
$636$	173.249	+	100.791i	0.272404	+	0.158477i
$637$	389.076			0.610794
$638$		0			0
$639$	588.709	+	65.8197i	0.921297	+	0.103004i
$640$	243.365	+	749.001i	0.380258	+	1.17031i
$641$	403.414	−	555.251i	0.629350	−	0.866226i	−0.368641	−	0.929572i	$-0.620177\pi$
$641$	403.414	−	555.251i	0.629350	−	0.866226i	0.997992	+	0.0633453i	$0.0201769\pi$
$642$	−192.897	−	41.6694i	−0.300463	−	0.0649057i
$643$	−41.7670	+	128.546i	−0.0649565	+	0.199916i	−0.978267	−	0.207348i	$-0.933517\pi$
$643$	−41.7670	+	128.546i	−0.0649565	+	0.199916i	0.913311	+	0.407263i	$0.133517\pi$
$644$	−442.793	−	143.872i	−0.687567	−	0.223404i
$645$	110.220	−	510.231i	0.170883	−	0.791056i
$646$	44.2918	+	32.1799i	0.0685632	+	0.0498140i
$647$	87.3625	−	28.3858i	0.135027	−	0.0438730i	−0.240724	−	0.970594i	$-0.577385\pi$
$647$	87.3625	−	28.3858i	0.135027	−	0.0438730i	0.375751	+	0.926721i	$0.377385\pi$
$648$	125.220	−	553.000i	0.193240	−	0.853395i
$649$		0			0
$650$		−	248.817i		−	0.382795i
$651$	−82.8366	+	142.386i	−0.127245	+	0.218720i
$652$	385.392	+	280.004i	0.591092	+	0.429454i
$653$	−463.947	−	638.568i	−0.710485	−	0.977898i	−0.999787	−	0.0206605i	$-0.993423\pi$
$653$	−463.947	−	638.568i	−0.710485	−	0.977898i	0.289302	−	0.957238i	$-0.406577\pi$
$654$	−129.992	−	294.588i	−0.198765	−	0.450440i
$655$	267.890	−	824.479i	0.408992	−	1.25875i
$656$	16.4484	+	22.6393i	0.0250738	+	0.0345112i
$657$	−91.1241	+	99.8658i	−0.138697	+	0.152003i
$658$	48.4508	+	149.116i	0.0736335	+	0.226621i
$659$			4.76585i			0.00723194i	0.999993	+	0.00361597i	$0.00115100\pi$
$659$			4.76585i			0.00723194i	−0.999993	+	0.00361597i	$0.998849\pi$
$660$		0			0
$661$	−1267.85			−1.91808			−0.959042	−	0.283264i	$-0.908583\pi$
$661$	−1267.85			−1.91808			−0.959042	+	0.283264i	$0.908583\pi$
$662$	376.219	−	122.241i	0.568307	−	0.184654i
$663$	237.025	−	24.1193i	0.357504	−	0.0363790i
$664$	629.656	−	457.472i	0.948277	−	0.688964i
$665$	508.504	+	165.223i	0.764667	+	0.248456i
$666$	72.8017	−	160.644i	0.109312	−	0.241207i
$667$	374.292	−	271.939i	0.561157	−	0.407705i
$668$	502.869	−	692.140i	0.752798	−	1.03614i
$669$	−250.414	+	430.433i	−0.374311	+	0.643397i
$670$	−508.200			−0.758508
$671$		0			0
$672$	653.346	−	584.371i	0.972242	−	0.869599i
$673$	56.6882	+	174.468i	0.0842322	+	0.259240i	0.984298	−	0.176514i	$-0.0564819\pi$
$673$	56.6882	+	174.468i	0.0842322	+	0.259240i	−0.900066	+	0.435753i	$0.856482\pi$
$674$	−294.070	+	404.753i	−0.436306	+	0.600523i
$675$	161.630	−	481.133i	0.239452	−	0.712790i
$676$	5.74169	−	17.6711i	0.00849362	−	0.0261407i
$677$	144.690	+	47.0128i	0.213723	+	0.0694428i	0.413922	−	0.910313i	$-0.364159\pi$
$677$	144.690	+	47.0128i	0.213723	+	0.0694428i	−0.200199	+	0.979755i	$0.564159\pi$
$678$	92.8551	+	20.0585i	0.136954	+	0.0295848i
$679$	868.065	+	630.686i	1.27845	+	0.928846i
$680$	264.353	−	85.8936i	0.388755	−	0.126314i
$681$	763.779	−	683.145i	1.12156	−	1.00315i
$682$		0			0
$683$		−	778.746i		−	1.14019i	−0.821580	−	0.570093i	$-0.806907\pi$
$683$		−	778.746i		−	1.14019i	0.821580	−	0.570093i	$-0.193093\pi$
$684$	241.315	−	49.6254i	0.352799	−	0.0725517i
$685$	−1117.66	−	812.025i	−1.63162	−	1.18544i
$686$	102.030	+	140.432i	0.148732	+	0.204711i
$687$	−677.311	+	298.875i	−0.985897	+	0.435044i
$688$	40.6231	−	125.025i	0.0590451	−	0.181722i
$689$	−173.264	−	238.477i	−0.251471	−	0.346121i
$690$	346.212	−	35.2299i	0.501757	−	0.0510579i
$691$	−139.925	−	430.645i	−0.202496	−	0.623219i	−0.999807	−	0.0196502i	$-0.993745\pi$
$691$	−139.925	−	430.645i	−0.202496	−	0.623219i	0.797311	−	0.603569i	$-0.206255\pi$
$692$			179.395i			0.259242i
$693$		0			0
$694$	−616.976			−0.889014
$695$	513.478	−	166.839i	0.738817	−	0.240056i
$696$	56.1145	+	551.450i	0.0806243	+	0.792313i
$697$	27.1672	−	19.7381i	0.0389773	−	0.0283187i
$698$	295.018	+	95.8572i	0.422662	+	0.137331i
$699$	482.479	+	1093.39i	0.690241	+	1.56422i
$700$	403.965	−	293.498i	0.577093	−	0.419282i
$701$	−31.2472	+	43.0081i	−0.0445752	+	0.0613525i	−0.830723	−	0.556686i	$-0.812073\pi$
$701$	−31.2472	+	43.0081i	−0.0445752	+	0.0613525i	0.786148	+	0.618039i	$0.212073\pi$
$702$	−212.920	+	287.021i	−0.303305	+	0.408862i
$703$	178.813			0.254357
$704$		0			0
$705$	234.387	+	262.053i	0.332464	+	0.371706i
$706$	−95.3557	−	293.475i	−0.135065	−	0.415686i
$707$	965.861	−	1329.39i	1.36614	−	1.88033i
$708$	−41.6361	+	192.743i	−0.0588081	+	0.272235i
$709$	333.942	−	1027.77i	0.471005	−	1.44960i	−0.380266	−	0.924877i	$-0.624168\pi$
$709$	333.942	−	1027.77i	0.471005	−	1.44960i	0.851271	−	0.524726i	$-0.175832\pi$
$710$	−414.277	−	134.607i	−0.583489	−	0.189587i
$711$	525.169	+	923.690i	0.738634	+	1.29914i
$712$	−553.092	−	401.845i	−0.776815	−	0.564389i
$713$	−103.381	+	33.5905i	−0.144994	+	0.0471116i
$714$	−106.249	−	118.790i	−0.148808	−	0.166373i
$715$		0			0
$716$			791.514i			1.10547i
$717$	418.032	+	243.200i	0.583030	+	0.339191i
$718$	110.666	+	80.4033i	0.154130	+	0.111982i
$719$	533.914	+	734.869i	0.742578	+	1.02207i	0.998466	+	0.0553647i	$0.0176322\pi$
$719$	533.914	+	734.869i	0.742578	+	1.02207i	−0.255888	+	0.966706i	$0.582368\pi$
$720$	122.930	−	271.256i	0.170736	−	0.376745i
$721$	472.214	−	1453.33i	0.654943	−	2.01571i
$722$	163.252	+	224.698i	0.226111	+	0.311215i
$723$	48.4850	+	476.473i	0.0670608	+	0.659021i
$724$	209.483	+	644.724i	0.289342	+	0.890502i
$725$			496.185i			0.684394i
$726$		0			0
$727$	−64.4195			−0.0886101			−0.0443050	−	0.999018i	$-0.514107\pi$
$727$	−64.4195			−0.0886101			−0.0443050	+	0.999018i	$0.514107\pi$
$728$	−780.203	+	253.503i	−1.07171	+	0.348219i
$729$	−598.168	+	416.697i	−0.820532	+	0.571600i
$730$	80.4255	−	58.4325i	0.110172	−	0.0800446i
$731$	−150.030	−	48.7477i	−0.205239	−	0.0666863i
$732$	−768.839	+	339.264i	−1.05033	+	0.463475i
$733$	−857.620	+	623.097i	−1.17001	+	0.850065i	−0.991011	−	0.133784i	$-0.957287\pi$
$733$	−857.620	+	623.097i	−1.17001	+	0.850065i	−0.179003	+	0.983849i	$0.557287\pi$
$734$	−74.0753	+	101.956i	−0.100920	+	0.138904i
$735$	−504.455	−	293.479i	−0.686334	−	0.399291i
$736$	578.420			0.785896
$737$		0			0
$738$	−5.59675	+	50.0588i	−0.00758367	+	0.0678304i
$739$	−49.4164	−	152.088i	−0.0668693	−	0.205803i	0.912039	−	0.410104i	$-0.134508\pi$
$739$	−49.4164	−	152.088i	−0.0668693	−	0.205803i	−0.978908	+	0.204302i	$0.934508\pi$
$740$	228.693	−	314.769i	0.309045	−	0.425363i
$741$	−354.153	−	76.5039i	−0.477939	−	0.103244i
$742$	−60.9336	+	187.534i	−0.0821208	+	0.252742i
$743$	−60.0542	−	19.5128i	−0.0808266	−	0.0262622i	0.268325	−	0.963329i	$-0.413530\pi$
$743$	−60.0542	−	19.5128i	−0.0808266	−	0.0262622i	−0.349151	+	0.937066i	$0.613530\pi$
$744$	27.4988	−	127.298i	0.0369607	−	0.171099i
$745$	37.4352	+	27.1983i	0.0502486	+	0.0365077i
$746$	330.519	−	107.392i	0.443054	−	0.143957i
$747$	−994.472	−	111.185i	−1.33129	−	0.148843i
$748$		0			0
$749$			582.442i			0.777626i
$750$	61.9165	−	106.427i	0.0825554	−	0.141903i
$751$	−132.939	−	96.5860i	−0.177016	−	0.128610i	0.495749	−	0.868466i	$-0.334894\pi$
$751$	−132.939	−	96.5860i	−0.177016	−	0.128610i	−0.672765	+	0.739856i	$0.734894\pi$
$752$	52.0431	+	71.6312i	0.0692063	+	0.0952542i
$753$	−59.1649	−	134.079i	−0.0785723	−	0.178060i
$754$	107.961	−	332.268i	0.143184	−	0.440674i
$755$	215.703	+	296.890i	0.285699	+	0.393231i
$756$	−717.147	−	7.12286i	−0.948607	−	0.00942177i
$757$	−280.054	−	861.917i	−0.369952	−	1.13860i	−0.946821	−	0.321759i	$-0.895726\pi$
$757$	−280.054	−	861.917i	−0.369952	−	1.13860i	0.576869	−	0.816836i	$-0.304274\pi$
$758$		−	474.354i		−	0.625797i
$759$		0			0
$760$	−422.709			−0.556196
$761$	−218.038	+	70.8448i	−0.286515	+	0.0930943i	−0.448749	−	0.893658i	$-0.648130\pi$
$761$	−218.038	+	70.8448i	−0.286515	+	0.0930943i	0.162234	+	0.986752i	$0.448130\pi$
$762$	302.686	−	30.8008i	0.397226	−	0.0404210i
$763$	−768.827	+	558.585i	−1.00764	+	0.732091i
$764$	171.433	+	55.7020i	0.224389	+	0.0729084i
$765$	−325.508	−	147.516i	−0.425500	−	0.192831i
$766$	−236.602	+	171.901i	−0.308880	+	0.224414i
$767$	170.458	−	234.615i	0.222240	−	0.305886i
$768$	−257.969	+	443.419i	−0.335898	+	0.577369i
$769$	−541.254			−0.703842			−0.351921	−	0.936030i	$-0.614471\pi$
$769$	−541.254			−0.703842			−0.351921	+	0.936030i	$0.614471\pi$
$770$		0			0
$771$	359.193	−	321.272i	0.465880	−	0.416696i
$772$	−33.0836	−	101.821i	−0.0428544	−	0.131892i
$773$	−440.204	+	605.889i	−0.569475	+	0.783815i	−0.992492	−	0.122307i	$-0.960971\pi$
$773$	−440.204	+	605.889i	−0.569475	+	0.783815i	0.423018	+	0.906122i	$0.360971\pi$
$774$	205.703	−	116.954i	0.265766	−	0.151103i
$775$	36.0254	−	110.875i	0.0464843	−	0.143064i
$776$	−806.779	−	262.138i	−1.03966	−	0.337807i
$777$	−508.799	−	109.910i	−0.654825	−	0.141455i
$778$	63.5492	+	46.1712i	0.0816827	+	0.0593460i
$779$	−48.5687	+	15.7809i	−0.0623475	+	0.0202579i
$780$	−587.617	+	525.580i	−0.753355	+	0.673821i
$781$		0			0
$782$		−	105.167i		−	0.134485i
$783$	424.601	−	572.372i	0.542275	−	0.730999i
$784$	−118.906	−	86.3901i	−0.151666	−	0.110191i
$785$	163.379	+	224.872i	0.208126	+	0.286462i
$786$	359.528	−	158.648i	0.457415	−	0.201842i
$787$	−76.0971	+	234.203i	−0.0966926	+	0.297589i	−0.987691	−	0.156417i	$-0.950006\pi$
$787$	−76.0971	+	234.203i	−0.0966926	+	0.297589i	0.890998	+	0.454006i	$0.150006\pi$
$788$	256.753	+	353.390i	0.325829	+	0.448465i
$789$	−419.094	+	42.6463i	−0.531172	+	0.0540510i
$790$	−241.444	−	743.089i	−0.305626	−	0.940619i
$791$		−	280.371i		−	0.354451i
$792$		0			0
$793$	1235.90			1.55852
$794$	−158.581	+	51.5259i	−0.199724	+	0.0648941i
$795$	44.7623	+	439.889i	0.0563048	+	0.553320i
$796$	−585.369	+	425.296i	−0.735388	+	0.534291i
$797$	−955.181	−	310.357i	−1.19847	−	0.389407i	−0.359273	−	0.933233i	$-0.616975\pi$
$797$	−955.181	−	310.357i	−1.19847	−	0.389407i	−0.839198	+	0.543826i	$0.816975\pi$
$798$	97.8475	+	221.742i	0.122616	+	0.277872i
$799$	85.9574	−	62.4517i	0.107581	−	0.0781624i
$800$	−364.630	+	501.871i	−0.455788	+	0.627338i
$801$	177.056	+	860.974i	0.221043	+	1.07487i
$802$	196.918			0.245534
$803$		0			0
$804$	460.741	+	515.125i	0.573062	+	0.640702i
$805$	−317.384	−	976.807i	−0.394266	−	1.21343i
$806$	−48.2484	+	66.4083i	−0.0598616	+	0.0823924i
$807$	262.085	−	1213.25i	0.324765	−	1.50341i
$808$	−401.450	+	1235.54i	−0.496844	+	1.52913i
$809$	1261.42	+	409.861i	1.55924	+	0.506627i	0.956604	−	0.291392i	$-0.0941183\pi$
$809$	1261.42	+	409.861i	1.55924	+	0.506627i	0.602633	+	0.798018i	$0.294118\pi$
$810$	492.560	−	211.532i	0.608099	−	0.261150i
$811$	−940.338	−	683.196i	−1.15948	−	0.842411i	−0.169768	−	0.985484i	$-0.554302\pi$
$811$	−940.338	−	683.196i	−1.15948	−	0.842411i	−0.989712	+	0.143073i	$0.954302\pi$
$812$	666.800	−	216.657i	0.821183	−	0.266818i
$813$	115.554	+	129.193i	0.142133	+	0.158910i
$814$		0			0
$815$			1050.88i			1.28942i
$816$	−77.7929	−	45.2578i	−0.0953344	−	0.0554630i
$817$	194.085	+	141.011i	0.237558	+	0.172596i
$818$	423.690	+	583.159i	0.517959	+	0.712909i
$819$	960.693	+	435.372i	1.17301	+	0.531590i
$820$	−34.3375	+	105.680i	−0.0418750	+	0.128878i
$821$	−557.320	−	767.085i	−0.678830	−	0.934330i	0.321089	−	0.947049i	$-0.395951\pi$
$821$	−557.320	−	767.085i	−0.678830	−	0.934330i	−0.999919	+	0.0127192i	$0.995951\pi$
$822$	−63.3980	−	623.026i	−0.0771265	−	0.757939i
$823$	456.674	+	1405.50i	0.554890	+	1.70778i	0.696234	+	0.717815i	$0.254858\pi$
$823$	456.674	+	1405.50i	0.554890	+	1.70778i	−0.141344	+	0.989961i	$0.545142\pi$
$824$			1208.12i			1.46617i
$825$		0			0
$826$	−193.992			−0.234857
$827$	152.775	−	49.6397i	0.184734	−	0.0600238i	−0.215189	−	0.976572i	$-0.569037\pi$
$827$	152.775	−	49.6397i	0.184734	−	0.0600238i	0.399923	+	0.916549i	$0.369037\pi$
$828$	−349.591	−	318.989i	−0.422211	−	0.385253i
$829$	−176.026	+	127.891i	−0.212336	+	0.154271i	−0.688870	−	0.724885i	$-0.741893\pi$
$829$	−176.026	+	127.891i	−0.212336	+	0.154271i	0.476534	+	0.879156i	$0.341893\pi$
$830$	699.815	+	227.384i	0.843150	+	0.273956i
$831$	−903.363	+	398.625i	−1.08708	+	0.479693i
$832$	139.207	−	101.140i	0.167316	−	0.121562i
$833$	−103.668	+	142.687i	−0.124452	+	0.171293i
$834$	211.546	+	123.072i	0.253652	+	0.147568i
$835$	1887.31			2.26025
$836$		0			0
$837$	−136.436	+	97.0708i	−0.163006	+	0.115975i
$838$	82.6337	+	254.320i	0.0986082	+	0.303485i
$839$	−322.053	+	443.267i	−0.383853	+	0.528328i	−0.956600	−	0.291404i	$-0.905878\pi$
$839$	−322.053	+	443.267i	−0.383853	+	0.528328i	0.572747	+	0.819732i	$0.305878\pi$
$840$	1202.79	+	259.825i	1.43189	+	0.309316i
$841$	44.5904	−	137.235i	0.0530207	−	0.163181i
$842$	652.394	+	211.976i	0.774815	+	0.251753i
$843$	250.313	−	1158.75i	0.296932	−	1.37456i
$844$	103.726	+	75.3616i	0.122899	+	0.0892910i
$845$	38.9826	−	12.6662i	0.0461333	−	0.0149896i
$846$	−17.7082	+	158.387i	−0.0209317	+	0.187219i
$847$		0			0
$848$			111.353i			0.131312i
$849$	−433.090	+	744.431i	−0.510118	+	0.876833i
$850$	91.2492	+	66.2964i	0.107352	+	0.0779958i
$851$	−201.898	−	277.889i	−0.237248	−	0.326544i
$852$	239.149	+	541.958i	0.280691	+	0.636101i
$853$	−226.029	+	695.647i	−0.264982	+	0.815530i	0.726716	+	0.686938i	$0.241046\pi$
$853$	−226.029	+	695.647i	−0.264982	+	0.815530i	−0.991698	+	0.128592i	$0.958954\pi$
$854$	−485.946	−	668.848i	−0.569024	−	0.783194i
$855$	401.470	+	366.327i	0.469555	+	0.428453i
$856$	−142.295	−	437.938i	−0.166232	−	0.511609i
$857$			333.112i			0.388696i	0.980933	+	0.194348i	$0.0622590\pi$
$857$			333.112i			0.388696i	−0.980933	+	0.194348i	$0.937741\pi$
$858$		0			0
$859$	146.468			0.170510			0.0852551	−	0.996359i	$-0.472829\pi$
$859$	146.468			0.170510			0.0852551	+	0.996359i	$0.472829\pi$
$860$	496.452	−	161.307i	0.577269	−	0.187566i
$861$	147.899	−	15.0499i	0.171776	−	0.0174796i
$862$	446.890	−	324.685i	0.518434	−	0.376665i
$863$	605.334	+	196.685i	0.701430	+	0.227908i	0.637954	−	0.770075i	$-0.279781\pi$
$863$	605.334	+	196.685i	0.701430	+	0.227908i	0.0634766	+	0.997983i	$0.479781\pi$
$864$	850.084	−	266.905i	0.983894	−	0.308917i
$865$	−320.167	+	232.615i	−0.370135	+	0.268919i
$866$	−167.296	+	230.263i	−0.193183	+	0.265893i
$867$	381.674	−	656.053i	0.440224	−	0.756694i
$868$	−164.729			−0.189781
$869$		0			0
$870$	−390.605	+	349.368i	−0.448971	+	0.401572i
$871$	−314.085	−	966.655i	−0.360603	−	1.10982i
$872$	441.614	−	607.830i	0.506438	−	0.697052i
$873$	539.068	+	948.137i	0.617489	+	1.08607i
$874$	−49.4226	+	152.107i	−0.0565476	+	0.174036i
$875$	−345.609	−	112.295i	−0.394982	−	0.128337i
$876$	−132.144	−	28.5455i	−0.150849	−	0.0325862i
$877$	1026.53	+	745.817i	1.17050	+	0.850418i	0.991069	−	0.133352i	$-0.0425742\pi$
$877$	1026.53	+	745.817i	1.17050	+	0.850418i	0.179431	+	0.983770i	$0.442574\pi$
$878$	506.017	−	164.415i	0.576329	−	0.187261i
$879$	−160.473	+	143.532i	−0.182564	+	0.163290i
$880$		0			0
$881$			425.862i			0.483385i	0.970353	+	0.241693i	$0.0777025\pi$
$881$			425.862i			0.483385i	−0.970353	+	0.241693i	$0.922297\pi$
$882$	−53.2897	−	259.133i	−0.0604192	−	0.293802i
$883$	−562.423	−	408.624i	−0.636946	−	0.462768i	0.221854	−	0.975080i	$-0.428789\pi$
$883$	−562.423	−	408.624i	−0.636946	−	0.462768i	−0.858800	+	0.512312i	$0.828789\pi$
$884$	140.039	+	192.748i	0.158416	+	0.218040i
$885$	−397.976	+	175.614i	−0.449690	+	0.198434i
$886$	−37.1738	+	114.409i	−0.0419568	+	0.129130i
$887$	−250.832	−	345.241i	−0.282787	−	0.389223i	0.643867	−	0.765137i	$-0.277329\pi$
$887$	−250.832	−	345.241i	−0.282787	−	0.389223i	−0.926655	+	0.375914i	$0.877329\pi$
$888$	409.417	−	41.6616i	0.461056	−	0.0469162i
$889$	−277.482	−	854.002i	−0.312128	−	0.960633i
$890$		−	646.354i		−	0.726241i
$891$		0			0
$892$	−497.976			−0.558269
$893$	−153.672	+	49.9311i	−0.172085	+	0.0559139i
$894$	2.12347	+	20.8678i	0.00237525	+	0.0233421i
$895$	−1412.61	+	1026.32i	−1.57834	+	1.14673i
$896$	1002.07	+	325.592i	1.11838	+	0.363384i
$897$	280.982	+	636.761i	0.313247	+	0.709879i
$898$	55.5542	−	40.3625i	0.0618643	−	0.0449471i
$899$	96.2161	−	132.430i	0.107026	−	0.147308i
$900$	497.153	−	102.237i	0.552392	−	0.113597i
$901$	133.623			0.148305
$902$		0			0
$903$	−465.580	−	520.535i	−0.515593	−	0.576451i
$904$	68.4965	+	210.811i	0.0757705	+	0.233198i
$905$	−879.010	+	1209.85i	−0.971281	+	1.33685i
$906$	−35.1251	+	162.602i	−0.0387695	+	0.179472i
$907$	−212.589	+	654.280i	−0.234387	+	0.721368i	0.762816	+	0.646616i	$0.223816\pi$
$907$	−212.589	+	654.280i	−0.234387	+	0.721368i	−0.997202	+	0.0747516i	$0.976184\pi$
$908$	974.564	+	316.655i	1.07331	+	0.348739i
$909$	1452.02	−	825.553i	1.59738	−	0.908199i
$910$	−627.466	−	455.881i	−0.689523	−	0.500968i
$911$	−1626.87	+	528.602i	−1.78581	+	0.580243i	−0.999303	−	0.0373428i	$-0.988111\pi$
$911$	−1626.87	+	528.602i	−1.78581	+	0.580243i	−0.786503	+	0.617586i	$0.788111\pi$
$912$	91.2461	+	102.016i	0.100051	+	0.111860i
$913$		0			0
$914$		−	695.507i		−	0.760949i
$915$	−1602.41	−	932.237i	−1.75126	−	1.01884i
$916$	−598.933	−	435.150i	−0.653857	−	0.475055i
$917$	−681.722	−	938.310i	−0.743427	−	1.02324i
$918$	−48.5281	−	154.561i	−0.0528628	−	0.168367i
$919$	−119.301	+	367.169i	−0.129816	+	0.399531i	−0.994748	−	0.102358i	$-0.967361\pi$
$919$	−119.301	+	367.169i	−0.129816	+	0.399531i	0.864932	+	0.501889i	$0.167361\pi$
$920$	477.282	+	656.922i	0.518784	+	0.714045i
$921$	−35.5216	−	349.079i	−0.0385686	−	0.379022i
$922$	254.729	+	783.977i	0.276279	+	0.850300i
$923$		−	871.193i		−	0.943872i
$924$		0			0
$925$	368.387			0.398256
$926$	150.397	−	48.8669i	0.162416	−	0.0527720i
$927$	1046.98	−	1147.42i	1.12943	−	1.23778i
$928$	−704.685	+	511.984i	−0.759359	+	0.551707i
$929$	71.0024	+	23.0701i	0.0764288	+	0.0248332i	0.346982	−	0.937872i	$-0.387207\pi$
$929$	71.0024	+	23.0701i	0.0764288	+	0.0248332i	−0.270553	+	0.962705i	$0.587207\pi$
$930$	112.648	−	49.7079i	0.121127	−	0.0534493i
$931$	216.994	−	157.655i	0.233076	−	0.169340i
$932$	−702.469	+	966.866i	−0.753722	+	1.03741i
$933$	−474.902	−	276.285i	−0.509005	−	0.296125i
$934$	−763.310			−0.817248
$935$		0			0
$936$	−828.709	−	92.6525i	−0.885373	−	0.0989877i
$937$	175.615	+	540.488i	0.187423	+	0.576828i	0.999982	−	0.00605080i	$-0.00192604\pi$
$937$	175.615	+	540.488i	0.187423	+	0.576828i	−0.812559	+	0.582879i	$0.801926\pi$
$938$	−399.640	+	550.058i	−0.426056	+	0.586415i
$939$	−219.288	−	47.3705i	−0.233534	−	0.0504478i
$940$	−108.644	+	334.373i	−0.115579	+	0.355716i
$941$	189.720	+	61.6436i	0.201615	+	0.0655086i	0.408084	−	0.912945i	$-0.366197\pi$
$941$	189.720	+	61.6436i	0.201615	+	0.0655086i	−0.206469	+	0.978453i	$0.566197\pi$
$942$	−26.6048	+	123.159i	−0.0282428	+	0.130742i
$943$	79.3638	+	57.6612i	0.0841610	+	0.0611465i
$944$	−104.187	+	33.8525i	−0.110368	+	0.0358608i
$945$	−917.184	−	1289.13i	−0.970565	−	1.36416i
$946$		0			0
$947$		−	984.860i		−	1.03998i	−0.854173	−	0.519990i	$-0.825936\pi$
$947$		−	984.860i		−	1.03998i	0.854173	−	0.519990i	$-0.174064\pi$
$948$	−534.317	+	918.429i	−0.563625	+	0.968807i
$949$	160.851	+	116.865i	0.169495	+	0.123146i
$950$	−100.822	−	138.769i	−0.106128	−	0.146073i
$951$	−21.4029	−	48.5032i	−0.0225057	−	0.0510023i
$952$	114.915	−	353.672i	0.120709	−	0.371504i
$953$	448.110	+	616.771i	0.470210	+	0.647189i	0.976587	−	0.215124i	$-0.0690155\pi$
$953$	448.110	+	616.771i	0.470210	+	0.647189i	−0.506377	+	0.862312i	$0.669015\pi$
$954$	−135.100	+	148.061i	−0.141614	+	0.155200i
$955$	122.879	+	378.183i	0.128669	+	0.396004i
$956$			483.629i			0.505888i
$957$		0			0
$958$	74.8228			0.0781031
$959$	−1757.81	+	571.148i	−1.83296	+	0.595566i
$960$	−256.777	+	26.1292i	−0.267476	+	0.0272179i
$961$	746.350	−	542.255i	0.776639	−	0.564262i
$962$	−246.689	−	80.1540i	−0.256433	−	0.0833202i
$963$	−244.380	+	539.248i	−0.253769	+	0.559967i
$964$	−387.465	+	281.510i	−0.401935	+	0.292023i
$965$	138.821	−	191.071i	0.143856	−	0.198001i
$966$	234.124	−	402.432i	0.242364	−	0.416596i
$967$	−1466.73			−1.51679			−0.758394	−	0.651797i	$-0.774015\pi$
$967$	−1466.73			−1.51679			−0.758394	+	0.651797i	$0.774015\pi$
$968$		0			0
$969$	122.420	−	109.495i	0.126336	−	0.112998i
$970$	−247.834	−	762.756i	−0.255499	−	0.786346i
$971$	−671.579	+	924.349i	−0.691637	+	0.951956i	0.308363	+	0.951269i	$0.400219\pi$
$971$	−671.579	+	924.349i	−0.691637	+	0.951956i	−1.00000		0.000687448i	$0.999781\pi$
$972$	−660.975	−	307.494i	−0.680016	−	0.316352i
$973$	223.210	−	686.969i	0.229404	−	0.706032i
$974$	288.147	+	93.6246i	0.295839	+	0.0961238i
$975$	−729.620	−	157.612i	−0.748328	−	0.161653i
$976$	−377.705	−	274.419i	−0.386993	−	0.281167i
$977$	−36.8048	+	11.9586i	−0.0376713	+	0.0122401i	−0.327792	−	0.944750i	$-0.606305\pi$
$977$	−36.8048	+	11.9586i	−0.0376713	+	0.0122401i	0.290121	+	0.956990i	$0.406305\pi$
$978$	−355.066	+	317.580i	−0.363053	+	0.324724i
$979$		0			0
$980$		−	583.614i		−	0.595524i
$981$	−946.181	+	194.578i	−0.964507	+	0.198347i
$982$	−646.222	−	469.508i	−0.658067	−	0.478114i
$983$	712.747	+	981.012i	0.725073	+	0.997978i	0.999340	+	0.0363240i	$0.0115648\pi$
$983$	712.747	+	981.012i	0.725073	+	0.997978i	−0.274267	+	0.961654i	$0.588435\pi$
$984$	−107.528	+	47.4487i	−0.109277	+	0.0482202i
$985$	−297.774	+	916.455i	−0.302309	+	0.930411i
$986$	93.0880	+	128.125i	0.0944097	+	0.129944i
$987$	467.954	−	47.6182i	0.474118	−	0.0482454i
$988$	−111.964	−	344.589i	−0.113324	−	0.348774i
$989$		−	460.839i		−	0.465965i
$990$		0			0
$991$	−1413.89			−1.42673			−0.713367	−	0.700790i	$-0.752831\pi$
$991$	−1413.89			−1.42673			−0.713367	+	0.700790i	$0.752831\pi$
$992$	194.637	−	63.2415i	0.196207	−	0.0637515i
$993$	−120.140	−	1180.64i	−0.120987	−	1.18897i
$994$	−471.474	+	342.546i	−0.474320	+	0.344614i
$995$	−1518.05	−	493.245i	−1.52568	−	0.495723i
$996$	−403.980	−	915.498i	−0.405602	−	0.919175i
$997$	762.909	−	554.286i	0.765204	−	0.555953i	−0.135298	−	0.990805i	$-0.543199\pi$
$997$	762.909	−	554.286i	0.765204	−	0.555953i	0.900502	+	0.434852i	$0.143199\pi$
$998$	343.702	−	473.066i	0.344391	−	0.474014i
$999$	−424.951	−	315.240i	−0.425376	−	0.315556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.i.269.1		8
3.2	odd	2	inner	363.3.h.i.269.2		8
11.2	odd	10		363.3.h.h.251.1		8
11.3	even	5		363.3.b.g.122.3		4
11.4	even	5		363.3.h.g.245.1		8
11.5	even	5		363.3.h.g.323.2		8
11.6	odd	10		33.3.h.a.26.1	yes	8
11.7	odd	10		33.3.h.a.14.2	yes	8
11.8	odd	10		363.3.b.f.122.1		4
11.9	even	5	inner	363.3.h.i.251.2		8
11.10	odd	2		363.3.h.h.269.2		8
33.2	even	10		363.3.h.h.251.2		8
33.5	odd	10		363.3.h.g.323.1		8
33.8	even	10		363.3.b.f.122.4		4
33.14	odd	10		363.3.b.g.122.2		4
33.17	even	10		33.3.h.a.26.2	yes	8
33.20	odd	10	inner	363.3.h.i.251.1		8
33.26	odd	10		363.3.h.g.245.2		8
33.29	even	10		33.3.h.a.14.1	✓	8
33.32	even	2		363.3.h.h.269.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.a.14.1	✓	8	33.29	even	10
33.3.h.a.14.2	yes	8	11.7	odd	10
33.3.h.a.26.1	yes	8	11.6	odd	10
33.3.h.a.26.2	yes	8	33.17	even	10
363.3.b.f.122.1		4	11.8	odd	10
363.3.b.f.122.4		4	33.8	even	10
363.3.b.g.122.2		4	33.14	odd	10
363.3.b.g.122.3		4	11.3	even	5
363.3.h.g.245.1		8	11.4	even	5
363.3.h.g.245.2		8	33.26	odd	10
363.3.h.g.323.1		8	33.5	odd	10
363.3.h.g.323.2		8	11.5	even	5
363.3.h.h.251.1		8	11.2	odd	10
363.3.h.h.251.2		8	33.2	even	10
363.3.h.h.269.1		8	33.32	even	2
363.3.h.h.269.2		8	11.10	odd	2
363.3.h.i.251.1		8	33.20	odd	10	inner
363.3.h.i.251.2		8	11.9	even	5	inner
363.3.h.i.269.1		8	1.1	even	1	trivial
363.3.h.i.269.2		8	3.2	odd	2	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 $\F_{q}$
Belyi maps

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+(-0.951057 + 0.309017i) q^{2} +(0.303706 + 2.98459i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-6.29412 - 2.04508i) q^{5} +(-1.21113 - 2.74466i) q^{6} +(-7.16312 + 5.20431i) q^{7} +(4.11450 - 5.66312i) q^{8} +(-8.81553 + 1.81288i) q^{9} +6.61803 q^{10} +(-6.00000 - 6.70820i) q^{12} +(4.09017 + 12.5882i) q^{13} +(5.20431 - 7.16312i) q^{14} +(4.19217 - 19.4065i) q^{15} +(1.54508 - 4.75528i) q^{16} +(-5.70634 - 1.85410i) q^{17} +(7.82385 - 4.44829i) q^{18} +(7.38197 + 5.36331i) q^{19} +(18.8824 - 6.13525i) q^{20} +(-17.7082 - 19.7984i) q^{21} -17.5279i q^{23} +(18.1517 + 10.5602i) q^{24} +(15.2082 + 11.0494i) q^{25} +(-7.77997 - 10.7082i) q^{26} +(-8.08802 - 25.7601i) q^{27} +(8.20820 - 25.2623i) q^{28} +(15.5147 + 21.3541i) q^{29} +(2.00994 + 19.7521i) q^{30} +(-1.91641 - 5.89810i) q^{31} +33.0000i q^{32} +6.00000 q^{34} +(55.7288 - 18.1074i) q^{35} +(18.1990 - 19.9448i) q^{36} +(15.8541 - 11.5187i) q^{37} +(-8.67802 - 2.81966i) q^{38} +(-36.3285 + 16.0306i) q^{39} +(-37.4787 + 27.2299i) q^{40} +(-3.28969 + 4.52786i) q^{41} +(22.9595 + 13.3572i) q^{42} +26.2918 q^{43} +(59.1935 + 6.61803i) q^{45} +(5.41641 + 16.6700i) q^{46} +(-10.4086 + 14.3262i) q^{47} +(14.6618 + 3.16723i) q^{48} +(9.08359 - 27.9564i) q^{49} +(-17.8783 - 5.80902i) q^{50} +(3.80068 - 17.5942i) q^{51} +(-32.1246 - 23.3399i) q^{52} +(-21.1805 + 6.88197i) q^{53} +(15.6525 + 22.0000i) q^{54} +61.9787i q^{56} +(-13.7653 + 23.6610i) q^{57} +(-21.3541 - 15.5147i) q^{58} +(-12.8783 - 17.7254i) q^{59} +(24.0459 + 54.4928i) q^{60} +(28.8541 - 88.8038i) q^{61} +(3.64522 + 5.01722i) q^{62} +(53.7119 - 58.8646i) q^{63} +(-4.01722 - 12.3637i) q^{64} -87.5967i q^{65} -76.7902 q^{67} +(17.1190 - 5.56231i) q^{68} +(52.3134 - 5.32332i) q^{69} +(-47.4058 + 34.4423i) q^{70} +(-62.5982 - 20.3394i) q^{71} +(-26.0049 + 57.3824i) q^{72} +(12.1525 - 8.82929i) q^{73} +(-11.5187 + 15.8541i) q^{74} +(-28.3591 + 48.7460i) q^{75} -27.3738 q^{76} +(29.5967 - 26.4721i) q^{78} +(-36.4828 - 112.282i) q^{79} +(-19.4499 + 26.7705i) q^{80} +(74.4270 - 31.9629i) q^{81} +(1.72949 - 5.32282i) q^{82} +(105.744 + 34.3582i) q^{83} +(77.8903 + 16.8258i) q^{84} +(32.1246 + 23.3399i) q^{85} +(-25.0050 + 8.12461i) q^{86} +(-59.0213 + 52.7902i) q^{87} -97.6656i q^{89} +(-58.3414 + 11.9977i) q^{90} +(-94.8115 - 68.8846i) q^{91} +(30.9079 + 42.5410i) q^{92} +(17.0214 - 7.51098i) q^{93} +(5.47214 - 16.8415i) q^{94} +(-35.4946 - 48.8541i) q^{95} +(-98.4914 + 10.0223i) q^{96} +(-37.4483 - 115.254i) q^{97} +29.3951i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 6 q^{4} + 10 q^{6} - 26 q^{7} + 2 q^{9} + 44 q^{10} - 48 q^{12} - 12 q^{13} + 60 q^{15} - 10 q^{16} + 40 q^{18} + 68 q^{19} - 88 q^{21} + 70 q^{24} + 68 q^{25} - 44 q^{27} + 12 q^{28} + 32 q^{30}+ \cdots - 474 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 - 6 * q^4 + 10 * q^6 - 26 * q^7 + 2 * q^9 + 44 * q^10 - 48 * q^12 - 12 * q^13 + 60 * q^15 - 10 * q^16 + 40 * q^18 + 68 * q^19 - 88 * q^21 + 70 * q^24 + 68 * q^25 - 44 * q^27 + 12 * q^28 + 32 * q^30 + 92 * q^31 + 48 * q^34 + 6 * q^36 + 100 * q^37 + 24 * q^39 - 112 * q^40 + 40 * q^42 + 264 * q^43 + 80 * q^45 - 64 * q^46 + 20 * q^48 + 180 * q^49 + 60 * q^51 - 96 * q^52 + 224 * q^57 - 144 * q^58 - 150 * q^60 + 204 * q^61 + 26 * q^63 + 26 * q^64 - 24 * q^67 + 200 * q^69 - 178 * q^70 - 280 * q^72 - 28 * q^73 + 84 * q^75 + 264 * q^76 + 40 * q^78 - 350 * q^79 + 158 * q^81 + 148 * q^82 + 156 * q^84 + 96 * q^85 - 660 * q^87 + 6 * q^90 - 356 * q^91 - 184 * q^93 + 8 * q^94 - 330 * q^96 - 474 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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