LMFDB - Embedded newform 600.3.g.d.451.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,3,Mod(451,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.451"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	600.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$16.3488158616$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + x^{14} + 24 x^{13} - 44 x^{12} - 32 x^{11} + 180 x^{10} - 64 x^{9} - 352 x^{8} + \cdots + 65536 $ x^16 - 4x^15 + x^14 + 24x^13 - 44x^12 - 32x^11 + 180x^10 - 64x^9 - 352x^8 - 256x^7 + 2880x^6 - 2048x^5 - 11264x^4 + 24576x^3 + 4096x^2 - 65536x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{19}\cdot 3 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.11
Root			$1.56126 + 1.24999i$ of defining polynomial
Character	$\chi$	$=$	600.451
Dual form			600.3.g.d.451.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.56126 - 1.24999i) q^{2} +1.73205 q^{3} +(0.875058 - 3.90311i) q^{4} +(2.70418 - 2.16504i) q^{6} +7.58970i q^{7} +(-3.51265 - 7.18758i) q^{8} +3.00000 q^{9} +16.7055 q^{11} +(1.51564 - 6.76039i) q^{12} -10.7512i q^{13} +(9.48703 + 11.8495i) q^{14} +(-14.4685 - 6.83090i) q^{16} -8.61276 q^{17} +(4.68378 - 3.74997i) q^{18} +35.6616 q^{19} +13.1457i q^{21} +(26.0816 - 20.8817i) q^{22} -11.2913i q^{23} +(-6.08409 - 12.4493i) q^{24} +(-13.4388 - 16.7854i) q^{26} +5.19615 q^{27} +(29.6234 + 6.64142i) q^{28} -0.589229i q^{29} -45.0411i q^{31} +(-31.1277 + 7.42072i) q^{32} +28.9347 q^{33} +(-13.4467 + 10.7658i) q^{34} +(2.62517 - 11.7093i) q^{36} +36.6203i q^{37} +(55.6770 - 44.5766i) q^{38} -18.6216i q^{39} -2.44967 q^{41} +(16.4320 + 20.5239i) q^{42} +7.91524 q^{43} +(14.6183 - 65.2033i) q^{44} +(-14.1140 - 17.6286i) q^{46} +44.3755i q^{47} +(-25.0603 - 11.8315i) q^{48} -8.60348 q^{49} -14.9177 q^{51} +(-41.9630 - 9.40790i) q^{52} -73.3176i q^{53} +(8.11254 - 6.49513i) q^{54} +(54.5515 - 26.6600i) q^{56} +61.7677 q^{57} +(-0.736530 - 0.919939i) q^{58} -89.7651 q^{59} +98.7987i q^{61} +(-56.3009 - 70.3209i) q^{62} +22.7691i q^{63} +(-39.3226 + 50.4949i) q^{64} +(45.1746 - 36.1681i) q^{66} -89.5013 q^{67} +(-7.53666 + 33.6165i) q^{68} -19.5571i q^{69} +90.0121i q^{71} +(-10.5380 - 21.5627i) q^{72} -68.0795 q^{73} +(45.7750 + 57.1738i) q^{74} +(31.2060 - 139.191i) q^{76} +126.790i q^{77} +(-23.2768 - 29.0731i) q^{78} -36.2647i q^{79} +9.00000 q^{81} +(-3.82457 + 3.06206i) q^{82} +95.5904 q^{83} +(51.3093 + 11.5033i) q^{84} +(12.3577 - 9.89396i) q^{86} -1.02058i q^{87} +(-58.6805 - 120.072i) q^{88} -7.89970 q^{89} +81.5982 q^{91} +(-44.0711 - 9.88052i) q^{92} -78.0135i q^{93} +(55.4689 + 69.2817i) q^{94} +(-53.9147 + 12.8531i) q^{96} +137.133 q^{97} +(-13.4323 + 10.7543i) q^{98} +50.1164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 14 q^{4} + 6 q^{6} - 20 q^{8} + 48 q^{9} + 64 q^{11} - 20 q^{14} - 14 q^{16} + 12 q^{18} - 32 q^{19} - 28 q^{22} - 54 q^{24} + 36 q^{26} + 28 q^{28} - 36 q^{32} - 72 q^{34} + 42 q^{36}+ \cdots + 192 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 14 * q^4 + 6 * q^6 - 20 * q^8 + 48 * q^9 + 64 * q^11 - 20 * q^14 - 14 * q^16 + 12 * q^18 - 32 * q^19 - 28 * q^22 - 54 * q^24 + 36 * q^26 + 28 * q^28 - 36 * q^32 - 72 * q^34 + 42 * q^36 + 240 * q^38 + 108 * q^42 + 192 * q^43 - 100 * q^44 + 212 * q^46 + 48 * q^48 - 80 * q^49 + 96 * q^51 - 232 * q^52 + 18 * q^54 - 116 * q^56 - 96 * q^57 - 140 * q^58 + 128 * q^59 - 104 * q^62 + 14 * q^64 - 180 * q^66 + 64 * q^67 + 576 * q^68 - 60 * q^72 + 160 * q^73 + 300 * q^74 + 420 * q^76 + 120 * q^78 + 144 * q^81 - 160 * q^82 + 180 * q^84 + 312 * q^86 - 604 * q^88 - 192 * q^91 - 216 * q^92 + 460 * q^94 - 186 * q^96 + 224 * q^97 - 428 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.56126	−	1.24999i	0.780629	−	0.624994i
$2$	1.56126	−	1.24999i	0.780629	−	0.624994i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	0.875058	−	3.90311i	0.218764	−	0.975778i
$5$		0			0
$5$		0			0
$6$	2.70418	−	2.16504i	0.450697	−	0.360841i
$7$			7.58970i			1.08424i	0.840300	+	0.542121i	$0.182379\pi$
$7$			7.58970i			1.08424i	−0.840300	+	0.542121i	$0.817621\pi$
$8$	−3.51265	−	7.18758i	−0.439081	−	0.898447i
$9$	3.00000			0.333333
$10$		0			0
$11$	16.7055			1.51868			0.759340	−	0.650694i	$-0.225522\pi$
$11$	16.7055			1.51868			0.759340	+	0.650694i	$0.225522\pi$
$12$	1.51564	−	6.76039i	0.126304	−	0.563366i
$13$		−	10.7512i		−	0.827014i	−0.910501	−	0.413507i	$-0.864304\pi$
$13$		−	10.7512i		−	0.827014i	0.910501	−	0.413507i	$-0.135696\pi$
$14$	9.48703	+	11.8495i	0.677645	+	0.846391i
$15$		0			0
$16$	−14.4685	−	6.83090i	−0.904284	−	0.426931i
$17$	−8.61276			−0.506633			−0.253316	−	0.967383i	$-0.581521\pi$
$17$	−8.61276			−0.506633			−0.253316	+	0.967383i	$0.581521\pi$
$18$	4.68378	−	3.74997i	0.260210	−	0.208331i
$19$	35.6616			1.87693			0.938464	−	0.345378i	$-0.112249\pi$
$19$	35.6616			1.87693			0.938464	+	0.345378i	$0.112249\pi$
$20$		0			0
$21$			13.1457i			0.625988i
$22$	26.0816	−	20.8817i	1.18553	−	0.949166i
$23$		−	11.2913i		−	0.490925i	−0.969406	−	0.245462i	$-0.921060\pi$
$23$		−	11.2913i		−	0.490925i	0.969406	−	0.245462i	$-0.0789398\pi$
$24$	−6.08409	−	12.4493i	−0.253504	−	0.518719i
$25$		0			0
$26$	−13.4388	−	16.7854i	−0.516879	−	0.645591i
$27$	5.19615			0.192450
$28$	29.6234	+	6.64142i	1.05798	+	0.237194i
$29$		−	0.589229i		−	0.0203183i	−0.999948	−	0.0101591i	$-0.996766\pi$
$29$		−	0.589229i		−	0.0203183i	0.999948	−	0.0101591i	$-0.00323381\pi$
$30$		0			0
$31$		−	45.0411i		−	1.45294i	−0.687198	−	0.726470i	$-0.741160\pi$
$31$		−	45.0411i		−	1.45294i	0.687198	−	0.726470i	$-0.258840\pi$
$32$	−31.1277	+	7.42072i	−0.972740	+	0.231898i
$33$	28.9347			0.876810
$34$	−13.4467	+	10.7658i	−0.395492	+	0.316643i
$35$		0			0
$36$	2.62517	−	11.7093i	0.0729215	−	0.325259i
$37$			36.6203i			0.989738i	0.868968	+	0.494869i	$0.164784\pi$
$37$			36.6203i			0.989738i	−0.868968	+	0.494869i	$0.835216\pi$
$38$	55.6770	−	44.5766i	1.46518	−	1.17307i
$39$		−	18.6216i		−	0.477477i
$40$		0			0
$41$	−2.44967			−0.0597481			−0.0298740	−	0.999554i	$-0.509511\pi$
$41$	−2.44967			−0.0597481			−0.0298740	+	0.999554i	$0.509511\pi$
$42$	16.4320	+	20.5239i	0.391239	+	0.488664i
$43$	7.91524			0.184075			0.0920377	−	0.995756i	$-0.470662\pi$
$43$	7.91524			0.184075			0.0920377	+	0.995756i	$0.470662\pi$
$44$	14.6183	−	65.2033i	0.332233	−	1.48189i
$45$		0			0
$46$	−14.1140	−	17.6286i	−0.306825	−	0.383230i
$47$			44.3755i			0.944160i	0.881556	+	0.472080i	$0.156497\pi$
$47$			44.3755i			0.944160i	−0.881556	+	0.472080i	$0.843503\pi$
$48$	−25.0603	−	11.8315i	−0.522089	−	0.246489i
$49$	−8.60348			−0.175581
$50$		0			0
$51$	−14.9177			−0.292505
$52$	−41.9630	−	9.40790i	−0.806982	−	0.180921i
$53$		−	73.3176i		−	1.38335i	−0.722209	−	0.691675i	$-0.756873\pi$
$53$		−	73.3176i		−	1.38335i	0.722209	−	0.691675i	$-0.243127\pi$
$54$	8.11254	−	6.49513i	0.150232	−	0.120280i
$55$		0			0
$56$	54.5515	−	26.6600i	0.974134	−	0.476071i
$57$	61.7677			1.08364
$58$	−0.736530	−	0.919939i	−0.0126988	−	0.0158610i
$59$	−89.7651			−1.52144			−0.760721	−	0.649079i	$-0.775155\pi$
$59$	−89.7651			−1.52144			−0.760721	+	0.649079i	$0.775155\pi$
$60$		0			0
$61$			98.7987i			1.61965i	0.586671	+	0.809826i	$0.300438\pi$
$61$			98.7987i			1.61965i	−0.586671	+	0.809826i	$0.699562\pi$
$62$	−56.3009	−	70.3209i	−0.908079	−	1.13421i
$63$			22.7691i			0.361414i
$64$	−39.3226	+	50.4949i	−0.614415	+	0.788983i
$65$		0			0
$66$	45.1746	−	36.1681i	0.684464	−	0.548001i
$67$	−89.5013			−1.33584			−0.667920	−	0.744233i	$-0.732815\pi$
$67$	−89.5013			−1.33584			−0.667920	+	0.744233i	$0.732815\pi$
$68$	−7.53666	+	33.6165i	−0.110833	+	0.494361i
$69$		−	19.5571i		−	0.283436i
$70$		0			0
$71$			90.0121i			1.26778i	0.773425	+	0.633888i	$0.218542\pi$
$71$			90.0121i			1.26778i	−0.773425	+	0.633888i	$0.781458\pi$
$72$	−10.5380	−	21.5627i	−0.146360	−	0.299482i
$73$	−68.0795			−0.932596			−0.466298	−	0.884628i	$-0.654412\pi$
$73$	−68.0795			−0.932596			−0.466298	+	0.884628i	$0.654412\pi$
$74$	45.7750	+	57.1738i	0.618580	+	0.772618i
$75$		0			0
$76$	31.2060	−	139.191i	0.410605	−	1.83146i
$77$			126.790i			1.64662i
$78$	−23.2768	−	29.0731i	−0.298420	−	0.372732i
$79$		−	36.2647i		−	0.459046i	−0.973303	−	0.229523i	$-0.926283\pi$
$79$		−	36.2647i		−	0.459046i	0.973303	−	0.229523i	$-0.0737167\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−3.82457	+	3.06206i	−0.0466411	+	0.0373422i
$83$	95.5904			1.15169			0.575846	−	0.817558i	$-0.304673\pi$
$83$	95.5904			1.15169			0.575846	+	0.817558i	$0.304673\pi$
$84$	51.3093	+	11.5033i	0.610825	+	0.136944i
$85$		0			0
$86$	12.3577	−	9.89396i	0.143695	−	0.115046i
$87$		−	1.02058i		−	0.0117307i
$88$	−58.6805	−	120.072i	−0.666824	−	1.36445i
$89$	−7.89970			−0.0887607			−0.0443803	−	0.999015i	$-0.514131\pi$
$89$	−7.89970			−0.0887607			−0.0443803	+	0.999015i	$0.514131\pi$
$90$		0			0
$91$	81.5982			0.896683
$92$	−44.0711	−	9.88052i	−0.479034	−	0.107397i
$93$		−	78.0135i		−	0.838855i
$94$	55.4689	+	69.2817i	0.590095	+	0.737039i
$95$		0			0
$96$	−53.9147	+	12.8531i	−0.561612	+	0.133886i
$97$	137.133			1.41375			0.706873	−	0.707341i	$-0.250105\pi$
$97$	137.133			1.41375			0.706873	+	0.707341i	$0.250105\pi$
$98$	−13.4323	+	10.7543i	−0.137064	+	0.109737i
$99$	50.1164			0.506227
$100$		0			0
$101$		−	92.4295i		−	0.915144i	−0.889173	−	0.457572i	$-0.848719\pi$
$101$		−	92.4295i		−	0.915144i	0.889173	−	0.457572i	$-0.151281\pi$
$102$	−23.2904	+	18.6470i	−0.228338	+	0.182814i
$103$			123.314i			1.19722i	0.801040	+	0.598610i	$0.204280\pi$
$103$			123.314i			1.19722i	−0.801040	+	0.598610i	$0.795720\pi$
$104$	−77.2749	+	37.7651i	−0.743028	+	0.363126i
$105$		0			0
$106$	−91.6461	−	114.468i	−0.864586	−	1.07988i
$107$	0.240104			0.00224396			0.00112198	−	0.999999i	$-0.499643\pi$
$107$	0.240104			0.00224396			0.00112198	+	0.999999i	$0.499643\pi$
$108$	4.54693	−	20.2812i	0.0421012	−	0.187789i
$109$			117.597i			1.07887i	0.842028	+	0.539435i	$0.181362\pi$
$109$			117.597i			1.07887i	−0.842028	+	0.539435i	$0.818638\pi$
$110$		0			0
$111$			63.4282i			0.571425i
$112$	51.8444	−	109.812i	0.462897	−	0.980463i
$113$	−41.1728			−0.364361			−0.182180	−	0.983265i	$-0.558315\pi$
$113$	−41.1728			−0.364361			−0.182180	+	0.983265i	$0.558315\pi$
$114$	96.4354	−	77.2090i	0.845925	−	0.677272i
$115$		0			0
$116$	−2.29983	−	0.515610i	−0.0198261	−	0.00444491i
$117$		−	32.2535i		−	0.275671i
$118$	−140.147	+	112.205i	−1.18768	+	0.950893i
$119$		−	65.3682i		−	0.549313i
$120$		0			0
$121$	158.073			1.30639
$122$	123.497	+	154.250i	1.01227	+	1.26435i
$123$	−4.24295			−0.0344956
$124$	−175.800	−	39.4136i	−1.41775	−	0.317852i
$125$		0			0
$126$	28.4611	+	35.5484i	0.225882	+	0.282130i
$127$			1.15264i			0.00907591i	0.999990	+	0.00453795i	$0.00144448\pi$
$127$			1.15264i			0.00907591i	−0.999990	+	0.00453795i	$0.998556\pi$
$128$	1.72536	+	127.988i	0.0134794	+	0.999909i
$129$	13.7096			0.106276
$130$		0			0
$131$	−191.878			−1.46472			−0.732359	−	0.680919i	$-0.761581\pi$
$131$	−191.878			−1.46472			−0.732359	+	0.680919i	$0.761581\pi$
$132$	25.3196	−	112.935i	0.191815	−	0.855572i
$133$			270.661i			2.03504i
$134$	−139.735	+	111.876i	−1.04280	+	0.834892i
$135$		0			0
$136$	30.2536	+	61.9049i	0.222453	+	0.455183i
$137$	−17.0127			−0.124180			−0.0620901	−	0.998071i	$-0.519777\pi$
$137$	−17.0127			−0.124180			−0.0620901	+	0.998071i	$0.519777\pi$
$138$	−24.4461	−	30.5336i	−0.177146	−	0.221258i
$139$	−176.378			−1.26890			−0.634452	−	0.772963i	$-0.718774\pi$
$139$	−176.378			−1.26890			−0.634452	+	0.772963i	$0.718774\pi$
$140$		0			0
$141$			76.8607i			0.545111i
$142$	112.514	+	140.532i	0.792353	+	0.989663i
$143$		−	179.604i		−	1.25597i
$144$	−43.4056	−	20.4927i	−0.301428	−	0.142310i
$145$		0			0
$146$	−106.290	+	85.0986i	−0.728011	+	0.582867i
$147$	−14.9017			−0.101372
$148$	142.933	+	32.0449i	0.965764	+	0.216519i
$149$		−	212.046i		−	1.42313i	−0.702620	−	0.711565i	$-0.747987\pi$
$149$		−	212.046i		−	1.42313i	0.702620	−	0.711565i	$-0.252013\pi$
$150$		0			0
$151$			143.361i			0.949408i	0.880146	+	0.474704i	$0.157445\pi$
$151$			143.361i			0.949408i	−0.880146	+	0.474704i	$0.842555\pi$
$152$	−125.267	−	256.321i	−0.824124	−	1.68632i
$153$	−25.8383			−0.168878
$154$	158.485	+	197.951i	1.02913	+	1.28540i
$155$		0			0
$156$	−72.6821	−	16.2950i	−0.465911	−	0.104455i
$157$			82.2710i			0.524019i	0.965065	+	0.262009i	$0.0843852\pi$
$157$			82.2710i			0.524019i	−0.965065	+	0.262009i	$0.915615\pi$
$158$	−45.3304	−	56.6185i	−0.286901	−	0.358345i
$159$		−	126.990i		−	0.798678i
$160$		0			0
$161$	85.6973			0.532282
$162$	14.0513	−	11.2499i	0.0867366	−	0.0694438i
$163$	−27.8115			−0.170623			−0.0853113	−	0.996354i	$-0.527188\pi$
$163$	−27.8115			−0.170623			−0.0853113	+	0.996354i	$0.527188\pi$
$164$	−2.14360	+	9.56134i	−0.0130708	+	0.0583008i
$165$		0			0
$166$	149.241	−	119.487i	0.899044	−	0.719800i
$167$		−	207.819i		−	1.24443i	−0.782848	−	0.622214i	$-0.786234\pi$
$167$		−	207.819i		−	1.24443i	0.782848	−	0.622214i	$-0.213766\pi$
$168$	94.4860	−	46.1764i	0.562417	−	0.274860i
$169$	53.4122			0.316048
$170$		0			0
$171$	106.985			0.625642
$172$	6.92629	−	30.8941i	0.0402692	−	0.179617i
$173$		−	45.7625i		−	0.264523i	−0.991215	−	0.132262i	$-0.957776\pi$
$173$		−	45.7625i		−	0.264523i	0.991215	−	0.132262i	$-0.0422239\pi$
$174$	−1.27571	−	1.59338i	−0.00733165	−	0.00915737i
$175$		0			0
$176$	−241.704	−	114.113i	−1.37332	−	0.648372i
$177$	−155.478			−0.878405
$178$	−12.3335	+	9.87453i	−0.0692892	+	0.0554749i
$179$	−33.0983			−0.184907			−0.0924533	−	0.995717i	$-0.529471\pi$
$179$	−33.0983			−0.184907			−0.0924533	+	0.995717i	$0.529471\pi$
$180$		0			0
$181$			177.147i			0.978711i	0.872084	+	0.489356i	$0.162768\pi$
$181$			177.147i			0.978711i	−0.872084	+	0.489356i	$0.837232\pi$
$182$	127.396	−	101.997i	0.699977	−	0.560422i
$183$			171.124i			0.935106i
$184$	−81.1569	+	39.6623i	−0.441070	+	0.215556i
$185$		0			0
$186$	−97.5160	−	121.799i	−0.524280	−	0.654835i
$187$	−143.880			−0.769413
$188$	173.203	+	38.8312i	0.921291	+	0.206549i
$189$			39.4372i			0.208663i
$190$		0			0
$191$			28.8000i			0.150785i	0.997154	+	0.0753927i	$0.0240210\pi$
$191$			28.8000i			0.150785i	−0.997154	+	0.0753927i	$0.975979\pi$
$192$	−68.1087	+	87.4598i	−0.354733	+	0.455520i
$193$	−87.7961			−0.454902			−0.227451	−	0.973789i	$-0.573039\pi$
$193$	−87.7961			−0.454902			−0.227451	+	0.973789i	$0.573039\pi$
$194$	214.101	−	171.415i	1.10361	−	0.883583i
$195$		0			0
$196$	−7.52855	+	33.5803i	−0.0384109	+	0.171328i
$197$			347.625i			1.76459i	0.470696	+	0.882296i	$0.344003\pi$
$197$			347.625i			1.76459i	−0.470696	+	0.882296i	$0.655997\pi$
$198$	78.2447	−	62.6450i	0.395175	−	0.316389i
$199$			129.347i			0.649985i	0.945717	+	0.324992i	$0.105362\pi$
$199$			129.347i			0.649985i	−0.945717	+	0.324992i	$0.894638\pi$
$200$		0			0
$201$	−155.021			−0.771247
$202$	−115.536	−	144.306i	−0.571960	−	0.714388i
$203$	4.47207			0.0220299
$204$	−13.0539	+	58.2256i	−0.0639896	+	0.285419i
$205$		0			0
$206$	154.141	+	192.525i	0.748256	+	0.934586i
$207$		−	33.8738i		−	0.163642i
$208$	−73.4402	+	155.554i	−0.353078	+	0.747855i
$209$	595.744			2.85045
$210$		0			0
$211$	−190.507			−0.902877			−0.451439	−	0.892302i	$-0.649089\pi$
$211$	−190.507			−0.902877			−0.451439	+	0.892302i	$0.649089\pi$
$212$	−286.167	−	64.1571i	−1.34984	−	0.302628i
$213$			155.905i			0.731951i
$214$	0.374864	−	0.300127i	0.00175170	−	0.00140246i
$215$		0			0
$216$	−18.2523	−	37.3478i	−0.0845013	−	0.172906i
$217$	341.848			1.57534
$218$	146.995	+	183.599i	0.674287	+	0.842197i
$219$	−117.917			−0.538434
$220$		0			0
$221$			92.5973i			0.418992i
$222$	79.2845	+	99.0279i	0.357138	+	0.446071i
$223$			211.437i			0.948149i	0.880485	+	0.474075i	$0.157217\pi$
$223$			211.437i			0.948149i	−0.880485	+	0.474075i	$0.842783\pi$
$224$	−56.3210	−	236.250i	−0.251433	−	1.05469i
$225$		0			0
$226$	−64.2813	+	51.4655i	−0.284431	+	0.227723i
$227$	−88.8880			−0.391577			−0.195788	−	0.980646i	$-0.562727\pi$
$227$	−88.8880			−0.391577			−0.195788	+	0.980646i	$0.562727\pi$
$228$	54.0503	−	241.086i	0.237063	−	1.05740i
$229$			152.872i			0.667565i	0.942650	+	0.333782i	$0.108325\pi$
$229$			152.872i			0.667565i	−0.942650	+	0.333782i	$0.891675\pi$
$230$		0			0
$231$			219.606i			0.950675i
$232$	−4.23513	+	2.06976i	−0.0182549	+	0.00892137i
$233$	−188.417			−0.808656			−0.404328	−	0.914614i	$-0.632495\pi$
$233$	−188.417			−0.808656			−0.404328	+	0.914614i	$0.632495\pi$
$234$	−40.3165	−	50.3561i	−0.172293	−	0.215197i
$235$		0			0
$236$	−78.5497	+	350.363i	−0.332838	+	1.48459i
$237$		−	62.8122i		−	0.265030i
$238$	−81.7095	−	102.057i	−0.343317	−	0.428810i
$239$		−	227.979i		−	0.953888i	−0.878934	−	0.476944i	$-0.841745\pi$
$239$		−	227.979i		−	0.953888i	0.878934	−	0.476944i	$-0.158255\pi$
$240$		0			0
$241$	−265.794			−1.10288			−0.551439	−	0.834215i	$-0.685921\pi$
$241$	−265.794			−1.10288			−0.551439	+	0.834215i	$0.685921\pi$
$242$	246.793	−	197.590i	1.01981	−	0.816486i
$243$	15.5885			0.0641500
$244$	385.622	+	86.4546i	1.58042	+	0.354322i
$245$		0			0
$246$	−6.62435	+	5.30364i	−0.0269283	+	0.0215595i
$247$		−	383.404i		−	1.55224i
$248$	−323.737	+	158.214i	−1.30539	+	0.637959i
$249$	165.567			0.664929
$250$		0			0
$251$	154.894			0.617106			0.308553	−	0.951207i	$-0.400155\pi$
$251$	154.894			0.617106			0.308553	+	0.951207i	$0.400155\pi$
$252$	88.8703	+	19.9243i	0.352660	+	0.0790646i
$253$		−	188.626i		−	0.745558i
$254$	1.44079	+	1.79957i	0.00567239	+	0.00708492i
$255$		0			0
$256$	162.678	+	197.666i	0.635460	+	0.772134i
$257$	422.025			1.64212			0.821060	−	0.570842i	$-0.193383\pi$
$257$	422.025			1.64212			0.821060	+	0.570842i	$0.193383\pi$
$258$	21.4042	−	17.1368i	0.0829621	−	0.0664219i
$259$	−277.937			−1.07312
$260$		0			0
$261$		−	1.76769i		−	0.00677275i
$262$	−299.571	+	239.845i	−1.14340	+	0.915440i
$263$		−	118.083i		−	0.448983i	−0.974476	−	0.224492i	$-0.927928\pi$
$263$		−	118.083i		−	0.448983i	0.974476	−	0.224492i	$-0.0720721\pi$
$264$	−101.638	−	207.971i	−0.384991	−	0.787768i
$265$		0			0
$266$	338.323	+	422.572i	1.27189	+	1.58862i
$267$	−13.6827			−0.0512460
$268$	−78.3188	+	349.333i	−0.292234	+	1.30348i
$269$			493.643i			1.83510i	0.397617	+	0.917551i	$0.369837\pi$
$269$			493.643i			1.83510i	−0.397617	+	0.917551i	$0.630163\pi$
$270$		0			0
$271$		−	362.955i		−	1.33932i	−0.742669	−	0.669659i	$-0.766440\pi$
$271$		−	362.955i		−	1.33932i	0.742669	−	0.669659i	$-0.233560\pi$
$272$	124.614	+	58.8329i	0.458140	+	0.216297i
$273$	141.332			0.517700
$274$	−26.5612	+	21.2657i	−0.0969387	+	0.0776119i
$275$		0			0
$276$	−76.3334	−	17.1136i	−0.276570	−	0.0620056i
$277$			321.011i			1.15888i	0.815013	+	0.579442i	$0.196730\pi$
$277$			321.011i			1.15888i	−0.815013	+	0.579442i	$0.803270\pi$
$278$	−275.371	+	220.470i	−0.990543	+	0.793057i
$279$		−	135.123i		−	0.484313i
$280$		0			0
$281$	−185.799			−0.661206			−0.330603	−	0.943770i	$-0.607252\pi$
$281$	−185.799			−0.661206			−0.330603	+	0.943770i	$0.607252\pi$
$282$	96.0750	+	119.999i	0.340691	+	0.425530i
$283$	208.628			0.737202			0.368601	−	0.929588i	$-0.379837\pi$
$283$	208.628			0.737202			0.368601	+	0.929588i	$0.379837\pi$
$284$	351.327	+	78.7658i	1.23707	+	0.277344i
$285$		0			0
$286$	−224.502	−	280.408i	−0.784974	−	0.980447i
$287$		−	18.5923i		−	0.0647814i
$288$	−93.3831	+	22.2622i	−0.324247	+	0.0772992i
$289$	−214.820			−0.743323
$290$		0			0
$291$	237.522			0.816226
$292$	−59.5735	+	265.722i	−0.204019	+	0.910006i
$293$		−	306.925i		−	1.04752i	−0.851864	−	0.523762i	$-0.824528\pi$
$293$		−	306.925i		−	1.04752i	0.851864	−	0.523762i	$-0.175472\pi$
$294$	−23.2654	+	18.6269i	−0.0791339	+	0.0633568i
$295$		0			0
$296$	263.211	−	128.634i	0.889227	−	0.434576i
$297$	86.8042			0.292270
$298$	−265.055	−	331.059i	−0.889448	−	1.11094i
$299$	−121.394			−0.406002
$300$		0			0
$301$			60.0743i			0.199582i
$302$	179.199	+	223.823i	0.593374	+	0.741136i
$303$		−	160.093i		−	0.528358i
$304$	−515.972	−	243.601i	−1.69728	−	0.801318i
$305$		0			0
$306$	−40.3402	+	32.2975i	−0.131831	+	0.105548i
$307$	−283.517			−0.923510			−0.461755	−	0.887008i	$-0.652780\pi$
$307$	−283.517			−0.923510			−0.461755	+	0.887008i	$0.652780\pi$
$308$	494.874	+	110.948i	1.60673	+	0.360221i
$309$			213.586i			0.691216i
$310$		0			0
$311$		−	614.016i		−	1.97433i	−0.159709	−	0.987164i	$-0.551056\pi$
$311$		−	614.016i		−	1.97433i	0.159709	−	0.987164i	$-0.448944\pi$
$312$	−133.844	+	65.4111i	−0.428988	+	0.209651i
$313$	511.920			1.63553			0.817763	−	0.575555i	$-0.195214\pi$
$313$	511.920			1.63553			0.817763	+	0.575555i	$0.195214\pi$
$314$	102.838	+	128.446i	0.327509	+	0.409065i
$315$		0			0
$316$	−141.545	−	31.7337i	−0.447927	−	0.100423i
$317$		−	429.605i		−	1.35522i	−0.735421	−	0.677611i	$-0.763015\pi$
$317$		−	429.605i		−	1.35522i	0.735421	−	0.677611i	$-0.236985\pi$
$318$	−158.736	−	198.264i	−0.499169	−	0.623471i
$319$		−	9.84336i		−	0.0308569i
$320$		0			0
$321$	0.415872			0.00129555
$322$	133.796	−	107.121i	0.415515	−	0.332673i
$323$	−307.145			−0.950913
$324$	7.87552	−	35.1280i	0.0243072	−	0.108420i
$325$		0			0
$326$	−43.4209	+	34.7640i	−0.133193	+	0.106638i
$327$			203.684i			0.622885i
$328$	8.60484	+	17.6072i	0.0262343	+	0.0536805i
$329$	−336.797			−1.02370
$330$		0			0
$331$	−537.298			−1.62326			−0.811628	−	0.584175i	$-0.801418\pi$
$331$	−537.298			−1.62326			−0.811628	+	0.584175i	$0.801418\pi$
$332$	83.6471	−	373.100i	0.251949	−	1.12379i
$333$			109.861i			0.329913i
$334$	−259.772	−	324.460i	−0.777760	−	0.971436i
$335$		0			0
$336$	89.7972	−	190.200i	0.267253	−	0.566071i
$337$	−158.578			−0.470559			−0.235279	−	0.971928i	$-0.575600\pi$
$337$	−158.578			−0.470559			−0.235279	+	0.971928i	$0.575600\pi$
$338$	83.3902	−	66.7646i	0.246717	−	0.197528i
$339$	−71.3133			−0.210364
$340$		0			0
$341$		−	752.434i		−	2.20655i
$342$	167.031	−	133.730i	0.488395	−	0.391023i
$343$			306.597i			0.893870i
$344$	−27.8035	−	56.8914i	−0.0808241	−	0.165382i
$345$		0			0
$346$	−57.2026	−	71.4472i	−0.165326	−	0.206495i
$347$	−169.697			−0.489041			−0.244520	−	0.969644i	$-0.578630\pi$
$347$	−169.697			−0.489041			−0.244520	+	0.969644i	$0.578630\pi$
$348$	−3.98342	−	0.893062i	−0.0114466	−	0.00256627i
$349$			296.370i			0.849196i	0.905382	+	0.424598i	$0.139585\pi$
$349$			296.370i			0.849196i	−0.905382	+	0.424598i	$0.860415\pi$
$350$		0			0
$351$		−	55.8648i		−	0.159159i
$352$	−520.003	+	123.967i	−1.47728	+	0.352178i
$353$	−133.075			−0.376982			−0.188491	−	0.982075i	$-0.560360\pi$
$353$	−133.075			−0.376982			−0.188491	+	0.982075i	$0.560360\pi$
$354$	−242.741	+	194.345i	−0.685709	+	0.548998i
$355$		0			0
$356$	−6.91269	+	30.8334i	−0.0194177	+	0.0866107i
$357$		−	113.221i		−	0.317146i
$358$	−51.6750	+	41.3725i	−0.144344	+	0.115566i
$359$		−	238.095i		−	0.663218i	−0.943417	−	0.331609i	$-0.892409\pi$
$359$		−	238.095i		−	0.663218i	0.943417	−	0.331609i	$-0.107591\pi$
$360$		0			0
$361$	910.751			2.52286
$362$	221.431	+	276.572i	0.611689	+	0.764011i
$363$	273.791			0.754244
$364$	71.4031	−	318.487i	0.196162	−	0.874964i
$365$		0			0
$366$	213.904	+	267.169i	0.584436	+	0.729971i
$367$		−	381.665i		−	1.03996i	−0.854179	−	0.519979i	$-0.825940\pi$
$367$		−	381.665i		−	1.03996i	0.854179	−	0.519979i	$-0.174060\pi$
$368$	−77.1295	+	163.368i	−0.209591	+	0.443936i
$369$	−7.34901			−0.0199160
$370$		0			0
$371$	556.458			1.49989
$372$	−304.495	−	68.2663i	−0.818536	−	0.183512i
$373$			42.2729i			0.113332i	0.998393	+	0.0566661i	$0.0180470\pi$
$373$			42.2729i			0.113332i	−0.998393	+	0.0566661i	$0.981953\pi$
$374$	−224.634	+	179.849i	−0.600626	+	0.480879i
$375$		0			0
$376$	318.953	−	155.876i	0.848278	−	0.414563i
$377$	−6.33491			−0.0168035
$378$	49.2961	+	61.5717i	0.130413	+	0.162888i
$379$	412.302			1.08787			0.543934	−	0.839128i	$-0.316934\pi$
$379$	412.302			1.08787			0.543934	+	0.839128i	$0.316934\pi$
$380$		0			0
$381$			1.99643i			0.00523998i
$382$	35.9997	+	44.9643i	0.0942400	+	0.117708i
$383$		−	403.711i		−	1.05408i	−0.849842	−	0.527038i	$-0.823303\pi$
$383$		−	403.711i		−	1.05408i	0.849842	−	0.527038i	$-0.176697\pi$
$384$	2.98842	+	221.682i	0.00778234	+	0.577298i
$385$		0			0
$386$	−137.072	+	109.744i	−0.355110	+	0.284311i
$387$	23.7457			0.0613585
$388$	120.000	−	535.246i	0.309277	−	1.37950i
$389$		−	78.5053i		−	0.201813i	−0.994896	−	0.100907i	$-0.967826\pi$
$389$		−	78.5053i		−	0.201813i	0.994896	−	0.100907i	$-0.0321743\pi$
$390$		0			0
$391$			97.2490i			0.248719i
$392$	30.2210	+	61.8382i	0.0770945	+	0.157751i
$393$	−332.342			−0.845655
$394$	434.527	+	542.732i	1.10286	+	1.37749i
$395$		0			0
$396$	43.8548	−	195.610i	0.110744	−	0.493965i
$397$		−	323.080i		−	0.813803i	−0.913472	−	0.406902i	$-0.866609\pi$
$397$		−	323.080i		−	0.813803i	0.913472	−	0.406902i	$-0.133391\pi$
$398$	161.682	+	201.944i	0.406237	+	0.507397i
$399$			468.798i			1.17493i
$400$		0			0
$401$	−621.389			−1.54960			−0.774799	−	0.632207i	$-0.782149\pi$
$401$	−621.389			−1.54960			−0.774799	+	0.632207i	$0.782149\pi$
$402$	−242.027	+	193.774i	−0.602058	+	0.482025i
$403$	−484.245			−1.20160
$404$	−360.763	−	80.8812i	−0.892977	−	0.200201i
$405$		0			0
$406$	6.98206	−	5.59004i	0.0171972	−	0.0137686i
$407$			611.760i			1.50310i
$408$	52.4008	+	107.222i	0.128433	+	0.262800i
$409$	322.888			0.789458			0.394729	−	0.918798i	$-0.370839\pi$
$409$	322.888			0.789458			0.394729	+	0.918798i	$0.370839\pi$
$410$		0			0
$411$	−29.4668			−0.0716954
$412$	481.307	+	107.907i	1.16822	+	0.261909i
$413$		−	681.290i		−	1.64961i
$414$	−42.3419	−	52.8858i	−0.102275	−	0.127743i
$415$		0			0
$416$	79.7815	+	334.659i	0.191782	+	0.804470i
$417$	−305.495			−0.732602
$418$	930.111	−	744.674i	2.22515	−	1.78152i
$419$	19.2316			0.0458988			0.0229494	−	0.999737i	$-0.492694\pi$
$419$	19.2316			0.0458988			0.0229494	+	0.999737i	$0.492694\pi$
$420$		0			0
$421$		−	312.791i		−	0.742970i	−0.928439	−	0.371485i	$-0.878849\pi$
$421$		−	312.791i		−	0.742970i	0.928439	−	0.371485i	$-0.121151\pi$
$422$	−297.431	+	238.132i	−0.704813	+	0.564293i
$423$			133.127i			0.314720i
$424$	−526.976	+	257.539i	−1.24287	+	0.607404i
$425$		0			0
$426$	194.880	+	243.409i	0.457465	+	0.571382i
$427$	−749.852			−1.75609
$428$	0.210105	−	0.937151i	0.000490899	−	0.00218961i
$429$		−	311.083i		−	0.725134i
$430$		0			0
$431$		−	417.415i		−	0.968479i	−0.874935	−	0.484240i	$-0.839096\pi$
$431$		−	417.415i		−	0.968479i	0.874935	−	0.484240i	$-0.160904\pi$
$432$	−75.1808	−	35.4944i	−0.174030	−	0.0821629i
$433$	−279.474			−0.645436			−0.322718	−	0.946495i	$-0.604596\pi$
$433$	−279.474			−0.645436			−0.322718	+	0.946495i	$0.604596\pi$
$434$	533.714	−	427.307i	1.22976	−	0.984577i
$435$		0			0
$436$	458.993	+	102.904i	1.05274	+	0.236018i
$437$		−	402.665i		−	0.921430i
$438$	−184.099	+	147.395i	−0.420318	+	0.336518i
$439$			30.1336i			0.0686415i	0.999411	+	0.0343207i	$0.0109268\pi$
$439$			30.1336i			0.0686415i	−0.999411	+	0.0343207i	$0.989073\pi$
$440$		0			0
$441$	−25.8104			−0.0585271
$442$	115.746	+	144.568i	0.261868	+	0.327078i
$443$	56.2858			0.127056			0.0635279	−	0.997980i	$-0.479765\pi$
$443$	56.2858			0.127056			0.0635279	+	0.997980i	$0.479765\pi$
$444$	247.567	+	55.5034i	0.557584	+	0.125008i
$445$		0			0
$446$	264.294	+	330.108i	0.592588	+	0.740153i
$447$		−	367.275i		−	0.821644i
$448$	−383.241	−	298.446i	−0.855449	−	0.666175i
$449$	−283.497			−0.631396			−0.315698	−	0.948860i	$-0.602239\pi$
$449$	−283.497			−0.631396			−0.315698	+	0.948860i	$0.602239\pi$
$450$		0			0
$451$	−40.9229			−0.0907382
$452$	−36.0285	+	160.702i	−0.0797092	+	0.355535i
$453$			248.308i			0.548141i
$454$	−138.777	+	111.109i	−0.305676	+	0.244733i
$455$		0			0
$456$	−216.969	−	443.960i	−0.475808	−	0.973597i
$457$	265.204			0.580315			0.290158	−	0.956979i	$-0.406292\pi$
$457$	265.204			0.580315			0.290158	+	0.956979i	$0.406292\pi$
$458$	191.089	+	238.673i	0.417224	+	0.521120i
$459$	−44.7532			−0.0975015
$460$		0			0
$461$		−	709.643i		−	1.53936i	−0.638432	−	0.769678i	$-0.720417\pi$
$461$		−	709.643i		−	1.53936i	0.638432	−	0.769678i	$-0.279583\pi$
$462$	274.505	+	342.862i	0.594166	+	0.742125i
$463$		−	417.392i		−	0.901495i	−0.892652	−	0.450747i	$-0.851157\pi$
$463$		−	417.392i		−	0.901495i	0.892652	−	0.450747i	$-0.148843\pi$
$464$	−4.02496	+	8.52529i	−0.00867449	+	0.0183735i
$465$		0			0
$466$	−294.167	+	235.519i	−0.631260	+	0.505405i
$467$	679.287			1.45458			0.727288	−	0.686332i	$-0.240780\pi$
$467$	679.287			1.45458			0.727288	+	0.686332i	$0.240780\pi$
$468$	−125.889	−	28.2237i	−0.268994	−	0.0603071i
$469$		−	679.287i		−	1.44837i
$470$		0			0
$471$			142.498i			0.302543i
$472$	315.313	+	645.194i	0.668037	+	1.36694i
$473$	132.228			0.279552
$474$	−78.5146	−	98.0661i	−0.165643	−	0.206891i
$475$		0			0
$476$	−255.139	−	57.2010i	−0.536007	−	0.120170i
$477$		−	219.953i		−	0.461117i
$478$	−284.971	−	355.934i	−0.596174	−	0.744633i
$479$			157.578i			0.328974i	0.986379	+	0.164487i	$0.0525968\pi$
$479$			157.578i			0.328974i	−0.986379	+	0.164487i	$0.947403\pi$
$480$		0			0
$481$	393.711			0.818527
$482$	−414.973	+	332.239i	−0.860939	+	0.689292i
$483$	148.432			0.307313
$484$	138.323	−	616.977i	0.285792	−	1.27475i
$485$		0			0
$486$	24.3376	−	19.4854i	0.0500774	−	0.0400934i
$487$		−	736.646i		−	1.51262i	−0.654213	−	0.756311i	$-0.727000\pi$
$487$		−	736.646i		−	1.51262i	0.654213	−	0.756311i	$-0.273000\pi$
$488$	710.123	−	347.045i	1.45517	−	0.711159i
$489$	−48.1709			−0.0985090
$490$		0			0
$491$	−362.408			−0.738101			−0.369050	−	0.929409i	$-0.620317\pi$
$491$	−362.408			−0.738101			−0.369050	+	0.929409i	$0.620317\pi$
$492$	−3.71283	+	16.5607i	−0.00754640	+	0.0336600i
$493$			5.07489i			0.0102939i
$494$	−479.251	−	598.594i	−0.970144	−	1.21173i
$495$		0			0
$496$	−307.671	+	651.680i	−0.620305	+	1.31387i
$497$	−683.164			−1.37458
$498$	258.494	−	206.957i	0.519063	−	0.415577i
$499$	648.812			1.30022			0.650112	−	0.759838i	$-0.274722\pi$
$499$	648.812			1.30022			0.650112	+	0.759838i	$0.274722\pi$
$500$		0			0
$501$		−	359.954i		−	0.718470i
$502$	241.829	−	193.615i	0.481731	−	0.385687i
$503$			402.612i			0.800421i	0.916423	+	0.400210i	$0.131063\pi$
$503$			402.612i			0.800421i	−0.916423	+	0.400210i	$0.868937\pi$
$504$	163.655	−	79.9799i	0.324711	−	0.158690i
$505$		0			0
$506$	−235.780	−	294.494i	−0.465969	−	0.582004i
$507$	92.5126			0.182471
$508$	4.49888	+	1.00863i	0.00885607	+	0.00198549i
$509$			470.175i			0.923724i	0.886952	+	0.461862i	$0.152818\pi$
$509$			470.175i			0.923724i	−0.886952	+	0.461862i	$0.847182\pi$
$510$		0			0
$511$		−	516.702i		−	1.01116i
$512$	501.063	+	105.263i	0.978638	+	0.205592i
$513$	185.303			0.361215
$514$	658.890	−	527.526i	1.28189	−	1.02632i
$515$		0			0
$516$	11.9967	−	53.5101i	0.0232494	−	0.103702i
$517$			741.315i			1.43388i
$518$	−433.931	+	347.418i	−0.837706	+	0.670691i
$519$		−	79.2630i		−	0.152723i
$520$		0			0
$521$	−155.978			−0.299382			−0.149691	−	0.988733i	$-0.547828\pi$
$521$	−155.978			−0.299382			−0.149691	+	0.988733i	$0.547828\pi$
$522$	−2.20959	−	2.75982i	−0.00423293	−	0.00528701i
$523$	313.578			0.599576			0.299788	−	0.954006i	$-0.403084\pi$
$523$	313.578			0.599576			0.299788	+	0.954006i	$0.403084\pi$
$524$	−167.904	+	748.921i	−0.320428	+	1.42924i
$525$		0			0
$526$	−147.602	−	184.357i	−0.280612	−	0.350489i
$527$			387.928i			0.736107i
$528$	−418.644	−	197.650i	−0.792886	−	0.374338i
$529$	401.507			0.758993
$530$		0			0
$531$	−269.295			−0.507147
$532$	1056.42	+	236.844i	1.98575	+	0.445195i
$533$			26.3369i			0.0494125i
$534$	−21.3622	+	17.1032i	−0.0400041	+	0.0320284i
$535$		0			0
$536$	314.387	+	643.297i	0.586542	+	1.20018i
$537$	−57.3279			−0.106756
$538$	617.048	+	770.704i	1.14693	+	1.43254i
$539$	−143.725			−0.266652
$540$		0			0
$541$			892.335i			1.64942i	0.565557	+	0.824709i	$0.308661\pi$
$541$			892.335i			1.64942i	−0.565557	+	0.824709i	$0.691339\pi$
$542$	−453.690	−	566.667i	−0.837066	−	1.04551i
$543$			306.827i			0.565059i
$544$	268.095	−	63.9129i	0.492822	−	0.117487i
$545$		0			0
$546$	220.656	−	176.664i	0.404132	−	0.323560i
$547$	671.435			1.22749			0.613743	−	0.789506i	$-0.289663\pi$
$547$	671.435			1.22749			0.613743	+	0.789506i	$0.289663\pi$
$548$	−14.8871	+	66.4024i	−0.0271662	+	0.121172i
$549$			296.396i			0.539884i
$550$		0			0
$551$		−	21.0129i		−	0.0381359i
$552$	−140.568	+	68.6971i	−0.254652	+	0.124451i
$553$	275.238			0.497717
$554$	401.260	+	501.181i	0.724296	+	0.904659i
$555$		0			0
$556$	−154.341	+	688.421i	−0.277591	+	1.23817i
$557$		−	296.095i		−	0.531590i	−0.964030	−	0.265795i	$-0.914366\pi$
$557$		−	296.095i		−	0.531590i	0.964030	−	0.265795i	$-0.0856344\pi$
$558$	−168.903	−	210.963i	−0.302693	−	0.378069i
$559$		−	85.0982i		−	0.152233i
$560$		0			0
$561$	−249.208			−0.444221
$562$	−290.080	+	232.247i	−0.516157	+	0.413250i
$563$	707.222			1.25617			0.628084	−	0.778146i	$-0.283839\pi$
$563$	707.222			1.25617			0.628084	+	0.778146i	$0.283839\pi$
$564$	299.996	+	67.2576i	0.531907	+	0.119251i
$565$		0			0
$566$	325.722	−	260.783i	0.575481	−	0.460747i
$567$			68.3073i			0.120471i
$568$	646.969	−	316.181i	1.13903	−	0.556657i
$569$	230.263			0.404680			0.202340	−	0.979315i	$-0.435145\pi$
$569$	230.263			0.404680			0.202340	+	0.979315i	$0.435145\pi$
$570$		0			0
$571$	−439.428			−0.769575			−0.384788	−	0.923005i	$-0.625725\pi$
$571$	−439.428			−0.769575			−0.384788	+	0.923005i	$0.625725\pi$
$572$	−701.013	−	157.164i	−1.22555	−	0.274761i
$573$			49.8831i			0.0870560i
$574$	−23.2401	−	29.0273i	−0.0404880	−	0.0505703i
$575$		0			0
$576$	−117.968	+	151.485i	−0.204805	+	0.262994i
$577$	184.670			0.320053			0.160026	−	0.987113i	$-0.448842\pi$
$577$	184.670			0.320053			0.160026	+	0.987113i	$0.448842\pi$
$578$	−335.390	+	268.523i	−0.580260	+	0.464573i
$579$	−152.067			−0.262638
$580$		0			0
$581$			725.502i			1.24871i
$582$	370.833	−	296.900i	0.637170	−	0.510137i
$583$		−	1224.81i		−	2.10087i
$584$	239.139	+	489.327i	0.409485	+	0.837888i
$585$		0			0
$586$	−383.652	−	479.189i	−0.654697	−	0.817729i
$587$	−297.341			−0.506543			−0.253271	−	0.967395i	$-0.581507\pi$
$587$	−297.341			−0.506543			−0.253271	+	0.967395i	$0.581507\pi$
$588$	−13.0398	+	58.1629i	−0.0221766	+	0.0989164i
$589$		−	1606.24i		−	2.72706i
$590$		0			0
$591$			602.103i			1.01879i
$592$	250.149	−	529.843i	0.422550	−	0.895004i
$593$	607.065			1.02372			0.511859	−	0.859070i	$-0.328957\pi$
$593$	607.065			1.02372			0.511859	+	0.859070i	$0.328957\pi$
$594$	135.524	−	108.504i	0.228155	−	0.182667i
$595$		0			0
$596$	−827.640	−	185.553i	−1.38866	−	0.311330i
$597$			224.036i			0.375269i
$598$	−189.528	+	151.742i	−0.316937	+	0.253749i
$599$			448.633i			0.748970i	0.927233	+	0.374485i	$0.122180\pi$
$599$			448.633i			0.748970i	−0.927233	+	0.374485i	$0.877820\pi$
$600$		0			0
$601$	580.584			0.966030			0.483015	−	0.875612i	$-0.339542\pi$
$601$	580.584			0.966030			0.483015	+	0.875612i	$0.339542\pi$
$602$	75.0921	+	93.7915i	0.124738	+	0.155800i
$603$	−268.504			−0.445280
$604$	559.552	+	125.449i	0.926411	+	0.207697i
$605$		0			0
$606$	−200.114	−	249.946i	−0.330221	−	0.412452i
$607$			132.576i			0.218413i	0.994019	+	0.109206i	$0.0348309\pi$
$607$			132.576i			0.218413i	−0.994019	+	0.109206i	$0.965169\pi$
$608$	−1110.06	+	264.635i	−1.82576	+	0.435255i
$609$	7.74585			0.0127190
$610$		0			0
$611$	477.089			0.780834
$612$	−22.6100	+	100.850i	−0.0369444	+	0.164787i
$613$			175.738i			0.286685i	0.989673	+	0.143343i	$0.0457851\pi$
$613$			175.738i			0.286685i	−0.989673	+	0.143343i	$0.954215\pi$
$614$	−442.644	+	354.393i	−0.720919	+	0.577188i
$615$		0			0
$616$	911.310	−	445.367i	1.47940	−	0.722999i
$617$	−283.254			−0.459082			−0.229541	−	0.973299i	$-0.573723\pi$
$617$	−283.254			−0.459082			−0.229541	+	0.973299i	$0.573723\pi$
$618$	266.980	+	333.463i	0.432006	+	0.539583i
$619$	−80.2105			−0.129581			−0.0647904	−	0.997899i	$-0.520638\pi$
$619$	−80.2105			−0.129581			−0.0647904	+	0.997899i	$0.520638\pi$
$620$		0			0
$621$		−	58.6712i		−	0.0944785i
$622$	−767.513	−	958.638i	−1.23394	−	1.54122i
$623$		−	59.9563i		−	0.0962381i
$624$	−127.202	+	269.427i	−0.203850	+	0.431775i
$625$		0			0
$626$	799.239	−	639.893i	1.27674	−	1.02219i
$627$	1031.86			1.64571
$628$	321.113	+	71.9919i	0.511326	+	0.114637i
$629$		−	315.402i		−	0.501434i
$630$		0			0
$631$		−	178.580i		−	0.283011i	−0.989937	−	0.141505i	$-0.954806\pi$
$631$		−	178.580i		−	0.283011i	0.989937	−	0.141505i	$-0.0451942\pi$
$632$	−260.655	+	127.385i	−0.412429	+	0.201559i
$633$	−329.968			−0.521277
$634$	−537.002	−	670.725i	−0.847006	−	1.05793i
$635$		0			0
$636$	−495.655	−	111.123i	−0.779332	−	0.174722i
$637$			92.4976i			0.145208i
$638$	−12.3041	−	15.3680i	−0.0192854	−	0.0240878i
$639$			270.036i			0.422592i
$640$		0			0
$641$	−379.689			−0.592339			−0.296169	−	0.955135i	$-0.595709\pi$
$641$	−379.689			−0.592339			−0.296169	+	0.955135i	$0.595709\pi$
$642$	0.649283	−	0.519835i	0.00101134	−	0.000809712i
$643$	847.921			1.31869			0.659347	−	0.751839i	$-0.270833\pi$
$643$	847.921			1.31869			0.659347	+	0.751839i	$0.270833\pi$
$644$	74.9901	−	334.486i	0.116444	−	0.519388i
$645$		0			0
$646$	−479.533	+	383.928i	−0.742311	+	0.594315i
$647$		−	372.369i		−	0.575532i	−0.957701	−	0.287766i	$-0.907087\pi$
$647$		−	372.369i		−	0.575532i	0.957701	−	0.287766i	$-0.0929126\pi$
$648$	−31.6139	−	64.6882i	−0.0487868	−	0.0998275i
$649$	−1499.57			−2.31058
$650$		0			0
$651$	592.099			0.909522
$652$	−24.3367	+	108.551i	−0.0373262	+	0.166490i
$653$			650.726i			0.996517i	0.867028	+	0.498259i	$0.166027\pi$
$653$			650.726i			0.996517i	−0.867028	+	0.498259i	$0.833973\pi$
$654$	254.602	+	318.003i	0.389300	+	0.486243i
$655$		0			0
$656$	35.4432	+	16.7334i	0.0540292	+	0.0255083i
$657$	−204.238			−0.310865
$658$	−525.827	+	420.992i	−0.799129	+	0.639806i
$659$	589.211			0.894099			0.447049	−	0.894509i	$-0.352475\pi$
$659$	589.211			0.894099			0.447049	+	0.894509i	$0.352475\pi$
$660$		0			0
$661$			402.340i			0.608684i	0.952563	+	0.304342i	$0.0984366\pi$
$661$			402.340i			0.608684i	−0.952563	+	0.304342i	$0.901563\pi$
$662$	−838.861	+	671.616i	−1.26716	+	1.01453i
$663$			160.383i			0.241905i
$664$	−335.776	−	687.063i	−0.505686	−	1.03473i
$665$		0			0
$666$	137.325	+	171.521i	0.206193	+	0.257539i
$667$	−6.65315			−0.00997473
$668$	−811.142	−	181.854i	−1.21428	−	0.272236i
$669$			366.220i			0.547414i
$670$		0			0
$671$			1650.48i			2.45973i
$672$	−97.5509	−	409.196i	−0.145165	−	0.608923i
$673$	−1237.67			−1.83903			−0.919515	−	0.393056i	$-0.871418\pi$
$673$	−1237.67			−1.83903			−0.919515	+	0.393056i	$0.871418\pi$
$674$	−247.582	+	198.221i	−0.367332	+	0.294096i
$675$		0			0
$676$	46.7387	−	208.474i	0.0691401	−	0.308393i
$677$			163.462i			0.241451i	0.992686	+	0.120725i	$0.0385221\pi$
$677$			163.462i			0.241451i	−0.992686	+	0.120725i	$0.961478\pi$
$678$	−111.339	+	89.1408i	−0.164216	+	0.131476i
$679$			1040.80i			1.53284i
$680$		0			0
$681$	−153.958			−0.226077
$682$	−940.533	−	1174.74i	−1.37908	−	1.72250i
$683$	−992.033			−1.45246			−0.726232	−	0.687449i	$-0.758730\pi$
$683$	−992.033			−1.45246			−0.726232	+	0.687449i	$0.758730\pi$
$684$	93.6179	−	417.574i	0.136868	−	0.610488i
$685$		0			0
$686$	383.243	+	478.678i	0.558663	+	0.697781i
$687$			264.783i			0.385419i
$688$	−114.522	−	54.0682i	−0.166456	−	0.0785875i
$689$	−788.250			−1.14405
$690$		0			0
$691$	−465.365			−0.673466			−0.336733	−	0.941600i	$-0.609322\pi$
$691$	−465.365			−0.673466			−0.336733	+	0.941600i	$0.609322\pi$
$692$	−178.616	−	40.0449i	−0.258116	−	0.0578683i
$693$			380.369i			0.548872i
$694$	−264.941	+	212.119i	−0.381759	+	0.305648i
$695$		0			0
$696$	−7.33546	+	3.58492i	−0.0105395	+	0.00515075i
$697$	21.0984			0.0302703
$698$	370.459	+	462.710i	0.530743	+	0.662908i
$699$	−326.347			−0.466878
$700$		0			0
$701$		−	261.352i		−	0.372827i	−0.982471	−	0.186414i	$-0.940314\pi$
$701$		−	261.352i		−	0.372827i	0.982471	−	0.186414i	$-0.0596864\pi$
$702$	−69.8303	−	87.2194i	−0.0994734	−	0.124244i
$703$			1305.94i			1.85767i
$704$	−656.902	+	843.542i	−0.933100	+	1.19821i
$705$		0			0
$706$	−207.764	+	166.342i	−0.294283	+	0.235611i
$707$	701.512			0.992238
$708$	−136.052	+	606.847i	−0.192164	+	0.857128i
$709$			186.604i			0.263194i	0.991303	+	0.131597i	$0.0420104\pi$
$709$			186.604i			0.263194i	−0.991303	+	0.131597i	$0.957990\pi$
$710$		0			0
$711$		−	108.794i		−	0.153015i
$712$	27.7489	+	56.7797i	0.0389732	+	0.0797468i
$713$	−508.572			−0.713284
$714$	−141.525	−	176.767i	−0.198214	−	0.247573i
$715$		0			0
$716$	−28.9629	+	129.186i	−0.0404510	+	0.180428i
$717$		−	394.871i		−	0.550727i
$718$	−297.616	−	371.728i	−0.414507	−	0.517727i
$719$			448.275i			0.623470i	0.950169	+	0.311735i	$0.100910\pi$
$719$			448.275i			0.623470i	−0.950169	+	0.311735i	$0.899090\pi$
$720$		0			0
$721$	−935.914			−1.29808
$722$	1421.92	−	1138.43i	1.96942	−	1.57677i
$723$	−460.368			−0.636747
$724$	691.423	+	155.014i	0.955005	+	0.214107i
$725$		0			0
$726$	427.458	−	342.235i	0.588785	−	0.471398i
$727$			956.205i			1.31527i	0.753335	+	0.657637i	$0.228444\pi$
$727$			956.205i			1.31527i	−0.753335	+	0.657637i	$0.771556\pi$
$728$	−286.626	−	586.493i	−0.393717	−	0.805623i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−68.1721			−0.0932586
$732$	667.917	+	149.744i	0.912456	+	0.204568i
$733$			398.986i			0.544320i	0.962252	+	0.272160i	$0.0877379\pi$
$733$			398.986i			0.544320i	−0.962252	+	0.272160i	$0.912262\pi$
$734$	−477.076	−	595.877i	−0.649968	−	0.811822i
$735$		0			0
$736$	83.7894	+	351.471i	0.113844	+	0.477542i
$737$	−1495.16			−2.02871
$738$	−11.4737	+	9.18618i	−0.0155470	+	0.0124474i
$739$	1011.87			1.36924			0.684622	−	0.728899i	$-0.259967\pi$
$739$	1011.87			1.36924			0.684622	+	0.728899i	$0.259967\pi$
$740$		0			0
$741$		−	664.076i		−	0.896189i
$742$	868.775	−	695.566i	1.17086	−	0.937421i
$743$			346.145i			0.465875i	0.972492	+	0.232938i	$0.0748338\pi$
$743$			346.145i			0.465875i	−0.972492	+	0.232938i	$0.925166\pi$
$744$	−560.728	+	274.034i	−0.753667	+	0.368326i
$745$		0			0
$746$	52.8406	+	65.9989i	0.0708319	+	0.0884704i
$747$	286.771			0.383897
$748$	−125.904	+	561.581i	−0.168320	+	0.750776i
$749$			1.82231i			0.00243300i
$750$		0			0
$751$			71.2058i			0.0948146i	0.998876	+	0.0474073i	$0.0150959\pi$
$751$			71.2058i			0.0948146i	−0.998876	+	0.0474073i	$0.984904\pi$
$752$	303.125	−	642.050i	0.403091	−	0.853789i
$753$	268.283			0.356286
$754$	−9.89043	+	7.91856i	−0.0131173	+	0.0105021i
$755$		0			0
$756$	153.928	+	34.5098i	0.203608	+	0.0456479i
$757$		−	1452.44i		−	1.91867i	−0.282264	−	0.959337i	$-0.591085\pi$
$757$		−	1452.44i		−	1.91867i	0.282264	−	0.959337i	$-0.408915\pi$
$758$	643.710	−	515.373i	0.849222	−	0.679912i
$759$		−	326.710i		−	0.430448i
$760$		0			0
$761$	414.416			0.544567			0.272284	−	0.962217i	$-0.412221\pi$
$761$	414.416			0.544567			0.272284	+	0.962217i	$0.412221\pi$
$762$	2.49552	+	3.11695i	0.00327496	+	0.00409048i
$763$	−892.523			−1.16976
$764$	112.410	+	25.2017i	0.147133	+	0.0329865i
$765$		0			0
$766$	−504.634	−	630.297i	−0.658791	−	0.822842i
$767$			965.081i			1.25825i
$768$	281.766	+	342.368i	0.366883	+	0.445792i
$769$	−132.780			−0.172665			−0.0863326	−	0.996266i	$-0.527515\pi$
$769$	−132.780			−0.172665			−0.0863326	+	0.996266i	$0.527515\pi$
$770$		0			0
$771$	730.968			0.948078
$772$	−76.8267	+	342.678i	−0.0995165	+	0.443884i
$773$		−	135.449i		−	0.175225i	−0.996155	−	0.0876126i	$-0.972076\pi$
$773$		−	135.449i		−	0.175225i	0.996155	−	0.0876126i	$-0.0279238\pi$
$774$	37.0732	−	29.6819i	0.0478982	−	0.0383487i
$775$		0			0
$776$	−481.702	−	985.656i	−0.620749	−	1.27018i
$777$	−481.401			−0.619564
$778$	−98.1307	−	122.567i	−0.126132	−	0.157541i
$779$	−87.3592			−0.112143
$780$		0			0
$781$			1503.70i			1.92535i
$782$	121.560	+	151.831i	0.155448	+	0.194157i
$783$		−	3.06173i		−	0.00391025i
$784$	124.480	+	58.7695i	0.158775	+	0.0749611i
$785$		0			0
$786$	−518.873	+	415.424i	−0.660143	+	0.528530i
$787$	370.900			0.471283			0.235642	−	0.971840i	$-0.424281\pi$
$787$	370.900			0.471283			0.235642	+	0.971840i	$0.424281\pi$
$788$	1356.82	+	304.192i	1.72185	+	0.386030i
$789$		−	204.525i		−	0.259220i
$790$		0			0
$791$		−	312.489i		−	0.395055i
$792$	−176.042	−	360.216i	−0.222275	−	0.454818i
$793$	1062.20			1.33947
$794$	−403.846	−	504.411i	−0.508622	−	0.635279i
$795$		0			0
$796$	504.856	+	113.186i	0.634241	+	0.142194i
$797$			980.881i			1.23072i	0.788247	+	0.615358i	$0.210989\pi$
$797$			980.881i			1.23072i	−0.788247	+	0.615358i	$0.789011\pi$
$798$	585.992	+	731.916i	0.734326	+	0.917187i
$799$		−	382.196i		−	0.478343i
$800$		0			0
$801$	−23.6991			−0.0295869
$802$	−970.149	+	776.729i	−1.20966	+	0.968490i
$803$	−1137.30			−1.41631
$804$	−135.652	+	605.063i	−0.168722	+	0.752566i
$805$		0			0
$806$	−756.032	+	605.301i	−0.938005	+	0.750994i
$807$			855.014i			1.05950i
$808$	−664.344	+	324.673i	−0.822208	+	0.401823i
$809$	−464.769			−0.574498			−0.287249	−	0.957856i	$-0.592741\pi$
$809$	−464.769			−0.574498			−0.287249	+	0.957856i	$0.592741\pi$
$810$		0			0
$811$	−49.1816			−0.0606431			−0.0303216	−	0.999540i	$-0.509653\pi$
$811$	−49.1816			−0.0606431			−0.0303216	+	0.999540i	$0.509653\pi$
$812$	3.91332	−	17.4550i	0.00481936	−	0.0214963i
$813$		−	628.657i		−	0.773255i
$814$	764.693	+	955.115i	0.939426	+	1.17336i
$815$		0			0
$816$	215.838	+	101.901i	0.264507	+	0.124879i
$817$	282.270			0.345496
$818$	504.112	−	403.607i	0.616274	−	0.493407i
$819$	244.795			0.298894
$820$		0			0
$821$			911.027i			1.10965i	0.831965	+	0.554827i	$0.187216\pi$
$821$			911.027i			1.10965i	−0.831965	+	0.554827i	$0.812784\pi$
$822$	−46.0053	+	36.8332i	−0.0559676	+	0.0448092i
$823$		−	1278.02i		−	1.55287i	−0.630195	−	0.776437i	$-0.717025\pi$
$823$		−	1278.02i		−	1.55287i	0.630195	−	0.776437i	$-0.282975\pi$
$824$	886.327	−	433.158i	1.07564	−	0.525678i
$825$		0			0
$826$	−851.604	−	1063.67i	−1.03100	−	1.28774i
$827$	671.016			0.811386			0.405693	−	0.914009i	$-0.367030\pi$
$827$	671.016			0.811386			0.405693	+	0.914009i	$0.367030\pi$
$828$	−132.213	−	29.6416i	−0.159678	−	0.0357990i
$829$		−	31.8486i		−	0.0384181i	−0.999815	−	0.0192091i	$-0.993885\pi$
$829$		−	31.8486i		−	0.0384181i	0.999815	−	0.0192091i	$-0.00611481\pi$
$830$		0			0
$831$			556.007i			0.669082i
$832$	542.880	+	422.764i	0.652500	+	0.508130i
$833$	74.0997			0.0889552
$834$	−476.957	+	381.865i	−0.571890	+	0.457872i
$835$		0			0
$836$	521.311	−	2325.26i	0.623578	−	2.78141i
$837$		−	234.041i		−	0.279618i
$838$	30.0255	−	24.0393i	0.0358299	−	0.0286865i
$839$		−	112.707i		−	0.134335i	−0.997742	−	0.0671674i	$-0.978604\pi$
$839$		−	112.707i		−	0.134335i	0.997742	−	0.0671674i	$-0.0213961\pi$
$840$		0			0
$841$	840.653			0.999587
$842$	−390.985	−	488.347i	−0.464352	−	0.579985i
$843$	−321.813			−0.381748
$844$	−166.705	+	743.570i	−0.197518	+	0.881008i
$845$		0			0
$846$	166.407	+	207.845i	0.196698	+	0.245680i
$847$			1199.73i			1.41644i
$848$	−500.825	+	1060.80i	−0.590595	+	1.25094i
$849$	361.354			0.425623
$850$		0			0
$851$	413.490			0.485887
$852$	608.516	+	136.426i	0.714221	+	0.160125i
$853$			512.714i			0.601072i	0.953770	+	0.300536i	$0.0971655\pi$
$853$			512.714i			0.601072i	−0.953770	+	0.300536i	$0.902834\pi$
$854$	−1170.71	+	937.307i	−1.37086	+	1.09755i
$855$		0			0
$856$	−0.843401	−	1.72576i	−0.000985281	−	0.00201608i
$857$	1620.81			1.89126			0.945631	−	0.325243i	$-0.105446\pi$
$857$	1620.81			1.89126			0.945631	+	0.325243i	$0.105446\pi$
$858$	−388.850	−	485.680i	−0.453205	−	0.566061i
$859$	225.172			0.262132			0.131066	−	0.991374i	$-0.458160\pi$
$859$	225.172			0.262132			0.131066	+	0.991374i	$0.458160\pi$
$860$		0			0
$861$		−	32.2027i		−	0.0374016i
$862$	−521.763	−	651.692i	−0.605294	−	0.756023i
$863$			1029.21i			1.19260i	0.802763	+	0.596299i	$0.203363\pi$
$863$			1029.21i			1.19260i	−0.802763	+	0.596299i	$0.796637\pi$
$864$	−161.744	+	38.5592i	−0.187204	+	0.0446287i
$865$		0			0
$866$	−436.331	+	349.339i	−0.503846	+	0.403394i
$867$	−372.080			−0.429158
$868$	299.137	−	1334.27i	0.344628	−	1.53718i
$869$		−	605.818i		−	0.697144i
$870$		0			0
$871$			962.244i			1.10476i
$872$	845.236	−	413.076i	0.969307	−	0.473711i
$873$	411.400			0.471248
$874$	−503.327	−	628.664i	−0.575889	−	0.719296i
$875$		0			0
$876$	−103.184	+	460.244i	−0.117790	+	0.525392i
$877$			570.056i			0.650007i	0.945713	+	0.325003i	$0.105365\pi$
$877$			570.056i			0.650007i	−0.945713	+	0.325003i	$0.894635\pi$
$878$	37.6667	+	47.0464i	0.0429005	+	0.0535836i
$879$		−	531.609i		−	0.604789i
$880$		0			0
$881$	596.788			0.677398			0.338699	−	0.940895i	$-0.390013\pi$
$881$	596.788			0.677398			0.338699	+	0.940895i	$0.390013\pi$
$882$	−40.2968	+	32.2628i	−0.0456880	+	0.0365791i
$883$	−856.738			−0.970258			−0.485129	−	0.874442i	$-0.661227\pi$
$883$	−856.738			−0.970258			−0.485129	+	0.874442i	$0.661227\pi$
$884$	361.418	+	81.0280i	0.408843	+	0.0916606i
$885$		0			0
$886$	87.8766	−	70.3565i	0.0991835	−	0.0794092i
$887$			1648.76i			1.85880i	0.369068	+	0.929402i	$0.379677\pi$
$887$			1648.76i			1.85880i	−0.369068	+	0.929402i	$0.620323\pi$
$888$	455.895	−	222.801i	0.513396	−	0.250902i
$889$	−8.74819			−0.00984048
$890$		0			0
$891$	150.349			0.168742
$892$	825.263	+	185.020i	0.925183	+	0.207421i
$893$			1582.50i			1.77212i
$894$	−459.089	−	573.411i	−0.513523	−	0.641400i
$895$		0			0
$896$	−971.393	+	13.0950i	−1.08414	+	0.0146149i
$897$	−210.261			−0.234405
$898$	−442.612	+	354.367i	−0.492886	+	0.394619i
$899$	−26.5395			−0.0295212
$900$		0			0
$901$			631.467i			0.700851i
$902$	−63.8913	+	51.1532i	−0.0708329	+	0.0567109i
$903$			104.052i			0.115229i
$904$	144.626	+	295.932i	0.159984	+	0.327359i
$905$		0			0
$906$	310.382	+	387.673i	0.342585	+	0.427895i
$907$	−844.509			−0.931101			−0.465551	−	0.885021i	$-0.654144\pi$
$907$	−844.509			−0.931101			−0.465551	+	0.885021i	$0.654144\pi$
$908$	−77.7821	+	346.940i	−0.0856631	+	0.382092i
$909$		−	277.289i		−	0.305048i
$910$		0			0
$911$			1074.78i			1.17978i	0.807483	+	0.589891i	$0.200829\pi$
$911$			1074.78i			1.17978i	−0.807483	+	0.589891i	$0.799171\pi$
$912$	−893.689	−	421.929i	−0.979923	−	0.462641i
$913$	1596.88			1.74905
$914$	414.052	−	331.502i	0.453011	−	0.362694i
$915$		0			0
$916$	596.677	+	133.772i	0.651395	+	0.146039i
$917$		−	1456.30i		−	1.58811i
$918$	−69.8713	+	55.9410i	−0.0761126	+	0.0609379i
$919$		−	1142.19i		−	1.24286i	−0.783471	−	0.621428i	$-0.786553\pi$
$919$		−	1142.19i		−	1.24286i	0.783471	−	0.621428i	$-0.213447\pi$
$920$		0			0
$921$	−491.067			−0.533188
$922$	−887.046	−	1107.94i	−0.962089	−	1.20167i
$923$	967.736			1.04847
$924$	857.146	+	192.168i	0.927647	+	0.207974i
$925$		0			0
$926$	−521.735	−	651.657i	−0.563429	−	0.703733i
$927$			369.941i			0.399074i
$928$	4.37251	+	18.3413i	0.00471175	+	0.0197644i
$929$	415.953			0.447742			0.223871	−	0.974619i	$-0.428131\pi$
$929$	415.953			0.447742			0.223871	+	0.974619i	$0.428131\pi$
$930$		0			0
$931$	−306.814			−0.329553
$932$	−164.876	+	735.412i	−0.176905	+	0.789068i
$933$		−	1063.51i		−	1.13988i
$934$	1060.54	−	849.101i	1.13549	−	0.909102i
$935$		0			0
$936$	−231.825	+	113.295i	−0.247676	+	0.121042i
$937$	846.979			0.903927			0.451963	−	0.892037i	$-0.350724\pi$
$937$	846.979			0.903927			0.451963	+	0.892037i	$0.350724\pi$
$938$	−849.101	−	1060.54i	−0.905225	−	1.13064i
$939$	886.671			0.944271
$940$		0			0
$941$		−	149.279i		−	0.158638i	−0.996849	−	0.0793192i	$-0.974725\pi$
$941$		−	149.279i		−	0.158638i	0.996849	−	0.0793192i	$-0.0252746\pi$
$942$	178.120	+	222.476i	0.189087	+	0.236174i
$943$			27.6599i			0.0293318i
$944$	1298.77	+	613.176i	1.37582	+	0.649551i
$945$		0			0
$946$	206.442	−	165.283i	0.218226	−	0.174718i
$947$	−543.005			−0.573395			−0.286697	−	0.958021i	$-0.592557\pi$
$947$	−543.005			−0.573395			−0.286697	+	0.958021i	$0.592557\pi$
$948$	−245.163	−	54.9643i	−0.258611	−	0.0579793i
$949$			731.935i			0.771269i
$950$		0			0
$951$		−	744.098i		−	0.782438i
$952$	−469.839	+	229.616i	−0.493529	+	0.241193i
$953$	344.292			0.361272			0.180636	−	0.983550i	$-0.442184\pi$
$953$	344.292			0.361272			0.180636	+	0.983550i	$0.442184\pi$
$954$	−274.938	−	343.403i	−0.288195	−	0.359961i
$955$		0			0
$956$	−889.828	−	199.495i	−0.930782	−	0.208677i
$957$		−	17.0492i		−	0.0178153i
$958$	196.971	+	246.021i	0.205607	+	0.256807i
$959$		−	129.121i		−	0.134641i
$960$		0			0
$961$	−1067.70			−1.11103
$962$	614.685	−	492.135i	0.638966	−	0.511575i
$963$	0.720311			0.000747987
$964$	−232.585	+	1037.42i	−0.241271	+	1.07616i
$965$		0			0
$966$	231.741	−	185.538i	0.239897	−	0.192069i
$967$		−	1044.78i		−	1.08044i	−0.841524	−	0.540219i	$-0.818341\pi$
$967$		−	1044.78i		−	1.08044i	0.841524	−	0.540219i	$-0.181659\pi$
$968$	−555.256	−	1136.16i	−0.573611	−	1.17372i
$969$	−531.991			−0.549010
$970$		0			0
$971$	306.656			0.315814			0.157907	−	0.987454i	$-0.449525\pi$
$971$	306.656			0.315814			0.157907	+	0.987454i	$0.449525\pi$
$972$	13.6408	−	60.8435i	0.0140337	−	0.0625962i
$973$		−	1338.65i		−	1.37580i
$974$	−920.800	−	1150.10i	−0.945379	−	1.18080i
$975$		0			0
$976$	674.884	−	1429.47i	0.691479	−	1.46462i
$977$	−1753.81			−1.79509			−0.897547	−	0.440919i	$-0.854653\pi$
$977$	−1753.81			−1.79509			−0.897547	+	0.440919i	$0.854653\pi$
$978$	−75.2073	+	60.2131i	−0.0768990	+	0.0615676i
$979$	−131.968			−0.134799
$980$		0			0
$981$			352.790i			0.359623i
$982$	−565.812	+	453.005i	−0.576183	+	0.461309i
$983$		−	951.541i		−	0.967997i	−0.875069	−	0.483999i	$-0.839184\pi$
$983$		−	951.541i		−	0.967997i	0.875069	−	0.483999i	$-0.160816\pi$
$984$	14.9040	+	30.4966i	0.0151464	+	0.0309924i
$985$		0			0
$986$	6.34355	+	7.92321i	0.00643362	+	0.00803571i
$987$	−583.349			−0.591033
$988$	−1496.47	−	335.501i	−1.51465	−	0.339576i
$989$		−	89.3731i		−	0.0903672i
$990$		0			0
$991$		−	1786.06i		−	1.80229i	−0.433523	−	0.901143i	$-0.642730\pi$
$991$		−	1786.06i		−	1.80229i	0.433523	−	0.901143i	$-0.357270\pi$
$992$	334.238	+	1402.03i	0.336933	+	1.41333i
$993$	−930.627			−0.937187
$994$	−1066.60	+	853.947i	−1.07303	+	0.859102i
$995$		0			0
$996$	144.881	−	646.228i	0.145463	−	0.648823i
$997$			1375.80i			1.37994i	0.723839	+	0.689969i	$0.242376\pi$
$997$			1375.80i			1.37994i	−0.723839	+	0.689969i	$0.757624\pi$
$998$	1012.96	−	811.008i	1.01499	−	0.812633i
$999$			190.285i			0.190475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.3.g.d.451.11		16
4.3	odd	2		2400.3.g.b.751.2		16
5.2	odd	4		600.3.p.b.499.26		32
5.3	odd	4		600.3.p.b.499.7		32
5.4	even	2		120.3.g.a.91.6	yes	16
8.3	odd	2	inner	600.3.g.d.451.12		16
8.5	even	2		2400.3.g.b.751.7		16
15.14	odd	2		360.3.g.c.91.11		16
20.3	even	4		2400.3.p.b.1999.13		32
20.7	even	4		2400.3.p.b.1999.32		32
20.19	odd	2		480.3.g.a.271.16		16
40.3	even	4		600.3.p.b.499.25		32
40.13	odd	4		2400.3.p.b.1999.31		32
40.19	odd	2		120.3.g.a.91.5	✓	16
40.27	even	4		600.3.p.b.499.8		32
40.29	even	2		480.3.g.a.271.9		16
40.37	odd	4		2400.3.p.b.1999.14		32
60.59	even	2		1440.3.g.c.271.7		16
120.29	odd	2		1440.3.g.c.271.10		16
120.59	even	2		360.3.g.c.91.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.g.a.91.5	✓	16	40.19	odd	2
120.3.g.a.91.6	yes	16	5.4	even	2
360.3.g.c.91.11		16	15.14	odd	2
360.3.g.c.91.12		16	120.59	even	2
480.3.g.a.271.9		16	40.29	even	2
480.3.g.a.271.16		16	20.19	odd	2
600.3.g.d.451.11		16	1.1	even	1	trivial
600.3.g.d.451.12		16	8.3	odd	2	inner
600.3.p.b.499.7		32	5.3	odd	4
600.3.p.b.499.8		32	40.27	even	4
600.3.p.b.499.25		32	40.3	even	4
600.3.p.b.499.26		32	5.2	odd	4
1440.3.g.c.271.7		16	60.59	even	2
1440.3.g.c.271.10		16	120.29	odd	2
2400.3.g.b.751.2		16	4.3	odd	2
2400.3.g.b.751.7		16	8.5	even	2
2400.3.p.b.1999.13		32	20.3	even	4
2400.3.p.b.1999.14		32	40.37	odd	4
2400.3.p.b.1999.31		32	40.13	odd	4
2400.3.p.b.1999.32		32	20.7	even	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	600.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56126 - 1.24999i) q^{2} +1.73205 q^{3} +(0.875058 - 3.90311i) q^{4} +(2.70418 - 2.16504i) q^{6} +7.58970i q^{7} +(-3.51265 - 7.18758i) q^{8} +3.00000 q^{9} +16.7055 q^{11} +(1.51564 - 6.76039i) q^{12} -10.7512i q^{13} +(9.48703 + 11.8495i) q^{14} +(-14.4685 - 6.83090i) q^{16} -8.61276 q^{17} +(4.68378 - 3.74997i) q^{18} +35.6616 q^{19} +13.1457i q^{21} +(26.0816 - 20.8817i) q^{22} -11.2913i q^{23} +(-6.08409 - 12.4493i) q^{24} +(-13.4388 - 16.7854i) q^{26} +5.19615 q^{27} +(29.6234 + 6.64142i) q^{28} -0.589229i q^{29} -45.0411i q^{31} +(-31.1277 + 7.42072i) q^{32} +28.9347 q^{33} +(-13.4467 + 10.7658i) q^{34} +(2.62517 - 11.7093i) q^{36} +36.6203i q^{37} +(55.6770 - 44.5766i) q^{38} -18.6216i q^{39} -2.44967 q^{41} +(16.4320 + 20.5239i) q^{42} +7.91524 q^{43} +(14.6183 - 65.2033i) q^{44} +(-14.1140 - 17.6286i) q^{46} +44.3755i q^{47} +(-25.0603 - 11.8315i) q^{48} -8.60348 q^{49} -14.9177 q^{51} +(-41.9630 - 9.40790i) q^{52} -73.3176i q^{53} +(8.11254 - 6.49513i) q^{54} +(54.5515 - 26.6600i) q^{56} +61.7677 q^{57} +(-0.736530 - 0.919939i) q^{58} -89.7651 q^{59} +98.7987i q^{61} +(-56.3009 - 70.3209i) q^{62} +22.7691i q^{63} +(-39.3226 + 50.4949i) q^{64} +(45.1746 - 36.1681i) q^{66} -89.5013 q^{67} +(-7.53666 + 33.6165i) q^{68} -19.5571i q^{69} +90.0121i q^{71} +(-10.5380 - 21.5627i) q^{72} -68.0795 q^{73} +(45.7750 + 57.1738i) q^{74} +(31.2060 - 139.191i) q^{76} +126.790i q^{77} +(-23.2768 - 29.0731i) q^{78} -36.2647i q^{79} +9.00000 q^{81} +(-3.82457 + 3.06206i) q^{82} +95.5904 q^{83} +(51.3093 + 11.5033i) q^{84} +(12.3577 - 9.89396i) q^{86} -1.02058i q^{87} +(-58.6805 - 120.072i) q^{88} -7.89970 q^{89} +81.5982 q^{91} +(-44.0711 - 9.88052i) q^{92} -78.0135i q^{93} +(55.4689 + 69.2817i) q^{94} +(-53.9147 + 12.8531i) q^{96} +137.133 q^{97} +(-13.4323 + 10.7543i) q^{98} +50.1164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 14 q^{4} + 6 q^{6} - 20 q^{8} + 48 q^{9} + 64 q^{11} - 20 q^{14} - 14 q^{16} + 12 q^{18} - 32 q^{19} - 28 q^{22} - 54 q^{24} + 36 q^{26} + 28 q^{28} - 36 q^{32} - 72 q^{34} + 42 q^{36}+ \cdots + 192 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 14 * q^4 + 6 * q^6 - 20 * q^8 + 48 * q^9 + 64 * q^11 - 20 * q^14 - 14 * q^16 + 12 * q^18 - 32 * q^19 - 28 * q^22 - 54 * q^24 + 36 * q^26 + 28 * q^28 - 36 * q^32 - 72 * q^34 + 42 * q^36 + 240 * q^38 + 108 * q^42 + 192 * q^43 - 100 * q^44 + 212 * q^46 + 48 * q^48 - 80 * q^49 + 96 * q^51 - 232 * q^52 + 18 * q^54 - 116 * q^56 - 96 * q^57 - 140 * q^58 + 128 * q^59 - 104 * q^62 + 14 * q^64 - 180 * q^66 + 64 * q^67 + 576 * q^68 - 60 * q^72 + 160 * q^73 + 300 * q^74 + 420 * q^76 + 120 * q^78 + 144 * q^81 - 160 * q^82 + 180 * q^84 + 312 * q^86 - 604 * q^88 - 192 * q^91 - 216 * q^92 + 460 * q^94 - 186 * q^96 + 224 * q^97 - 428 * q^98 + 192 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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