LMFDB - Embedded newform 600.3.p.b.499.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,3,Mod(499,600)] 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("600.499"); 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, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	600.p (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$16.3488158616$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			499.8
Character	$\chi$	$=$	600.499
Dual form			600.3.p.b.499.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24999 + 1.56126i) q^{2} -1.73205i q^{3} +(-0.875058 - 3.90311i) q^{4} +(2.70418 + 2.16504i) q^{6} +7.58970 q^{7} +(7.18758 + 3.51265i) q^{8} -3.00000 q^{9} +16.7055 q^{11} +(-6.76039 + 1.51564i) q^{12} +10.7512 q^{13} +(-9.48703 + 11.8495i) q^{14} +(-14.4685 + 6.83090i) q^{16} -8.61276i q^{17} +(3.74997 - 4.68378i) q^{18} -35.6616 q^{19} -13.1457i q^{21} +(-20.8817 + 26.0816i) q^{22} +11.2913 q^{23} +(6.08409 - 12.4493i) q^{24} +(-13.4388 + 16.7854i) q^{26} +5.19615i q^{27} +(-6.64142 - 29.6234i) q^{28} -0.589229i q^{29} +45.0411i q^{31} +(7.42072 - 31.1277i) q^{32} -28.9347i q^{33} +(13.4467 + 10.7658i) q^{34} +(2.62517 + 11.7093i) q^{36} +36.6203 q^{37} +(44.5766 - 55.6770i) q^{38} -18.6216i q^{39} -2.44967 q^{41} +(20.5239 + 16.4320i) q^{42} -7.91524i q^{43} +(-14.6183 - 65.2033i) q^{44} +(-14.1140 + 17.6286i) q^{46} +44.3755 q^{47} +(11.8315 + 25.0603i) q^{48} +8.60348 q^{49} -14.9177 q^{51} +(-9.40790 - 41.9630i) q^{52} +73.3176 q^{53} +(-8.11254 - 6.49513i) q^{54} +(54.5515 + 26.6600i) q^{56} +61.7677i q^{57} +(0.919939 + 0.736530i) q^{58} +89.7651 q^{59} -98.7987i q^{61} +(-70.3209 - 56.3009i) q^{62} -22.7691 q^{63} +(39.3226 + 50.4949i) q^{64} +(45.1746 + 36.1681i) q^{66} -89.5013i q^{67} +(-33.6165 + 7.53666i) q^{68} -19.5571i q^{69} -90.0121i q^{71} +(-21.5627 - 10.5380i) q^{72} +68.0795i q^{73} +(-45.7750 + 57.1738i) q^{74} +(31.2060 + 139.191i) q^{76} +126.790 q^{77} +(29.0731 + 23.2768i) q^{78} -36.2647i q^{79} +9.00000 q^{81} +(3.06206 - 3.82457i) q^{82} -95.5904i q^{83} +(-51.3093 + 11.5033i) q^{84} +(12.3577 + 9.89396i) q^{86} -1.02058 q^{87} +(120.072 + 58.6805i) q^{88} +7.89970 q^{89} +81.5982 q^{91} +(-9.88052 - 44.0711i) q^{92} +78.0135 q^{93} +(-55.4689 + 69.2817i) q^{94} +(-53.9147 - 12.8531i) q^{96} +137.133i q^{97} +(-10.7543 + 13.4323i) q^{98} -50.1164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{4} + 12 q^{6} - 96 q^{9} + 128 q^{11} + 40 q^{14} - 28 q^{16} + 64 q^{19} + 108 q^{24} + 72 q^{26} + 144 q^{34} + 84 q^{36} + 200 q^{44} + 424 q^{46} + 160 q^{49} + 192 q^{51} - 36 q^{54} - 232 q^{56}+ \cdots - 384 q^{99}+O(q^{100}) $ 32 * q - 28 * q^4 + 12 * q^6 - 96 * q^9 + 128 * q^11 + 40 * q^14 - 28 * q^16 + 64 * q^19 + 108 * q^24 + 72 * q^26 + 144 * q^34 + 84 * q^36 + 200 * q^44 + 424 * q^46 + 160 * q^49 + 192 * q^51 - 36 * q^54 - 232 * q^56 - 256 * q^59 - 28 * q^64 - 360 * q^66 - 600 * q^74 + 840 * q^76 + 288 * q^81 - 360 * q^84 + 624 * q^86 - 384 * q^91 - 920 * q^94 - 372 * q^96 - 384 * 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 $

$2$	−1.24999	+	1.56126i	−0.624994	+	0.780629i
$2$	−1.24999	+	1.56126i	−0.624994	+	0.780629i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−0.875058	−	3.90311i	−0.218764	−	0.975778i
$5$		0			0
$5$		0			0
$6$	2.70418	+	2.16504i	0.450697	+	0.360841i
$7$	7.58970			1.08424			0.542121	−	0.840300i	$-0.317621\pi$
$7$	7.58970			1.08424			0.542121	+	0.840300i	$0.317621\pi$
$8$	7.18758	+	3.51265i	0.898447	+	0.439081i
$9$	−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	$0.225522\pi$
$12$	−6.76039	+	1.51564i	−0.563366	+	0.126304i
$13$	10.7512			0.827014			0.413507	−	0.910501i	$-0.364304\pi$
$13$	10.7512			0.827014			0.413507	+	0.910501i	$0.364304\pi$
$14$	−9.48703	+	11.8495i	−0.677645	+	0.846391i
$15$		0			0
$16$	−14.4685	+	6.83090i	−0.904284	+	0.426931i
$17$		−	8.61276i		−	0.506633i	−0.967383	−	0.253316i	$-0.918479\pi$
$17$		−	8.61276i		−	0.506633i	0.967383	−	0.253316i	$-0.0815214\pi$
$18$	3.74997	−	4.68378i	0.208331	−	0.260210i
$19$	−35.6616			−1.87693			−0.938464	−	0.345378i	$-0.887751\pi$
$19$	−35.6616			−1.87693			−0.938464	+	0.345378i	$0.887751\pi$
$20$		0			0
$21$		−	13.1457i		−	0.625988i
$22$	−20.8817	+	26.0816i	−0.949166	+	1.18553i
$23$	11.2913			0.490925			0.245462	−	0.969406i	$-0.421060\pi$
$23$	11.2913			0.490925			0.245462	+	0.969406i	$0.421060\pi$
$24$	6.08409	−	12.4493i	0.253504	−	0.518719i
$25$		0			0
$26$	−13.4388	+	16.7854i	−0.516879	+	0.645591i
$27$			5.19615i			0.192450i
$28$	−6.64142	−	29.6234i	−0.237194	−	1.05798i
$29$		−	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	$0.258840\pi$
$31$			45.0411i			1.45294i	−0.687198	+	0.726470i	$0.741160\pi$
$32$	7.42072	−	31.1277i	0.231898	−	0.972740i
$33$		−	28.9347i		−	0.876810i
$34$	13.4467	+	10.7658i	0.395492	+	0.316643i
$35$		0			0
$36$	2.62517	+	11.7093i	0.0729215	+	0.325259i
$37$	36.6203			0.989738			0.494869	−	0.868968i	$-0.335216\pi$
$37$	36.6203			0.989738			0.494869	+	0.868968i	$0.335216\pi$
$38$	44.5766	−	55.6770i	1.17307	−	1.46518i
$39$		−	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	$0.509511\pi$
$42$	20.5239	+	16.4320i	0.488664	+	0.391239i
$43$		−	7.91524i		−	0.184075i	−0.995756	−	0.0920377i	$-0.970662\pi$
$43$		−	7.91524i		−	0.184075i	0.995756	−	0.0920377i	$-0.0293380\pi$
$44$	−14.6183	−	65.2033i	−0.332233	−	1.48189i
$45$		0			0
$46$	−14.1140	+	17.6286i	−0.306825	+	0.383230i
$47$	44.3755			0.944160			0.472080	−	0.881556i	$-0.343503\pi$
$47$	44.3755			0.944160			0.472080	+	0.881556i	$0.343503\pi$
$48$	11.8315	+	25.0603i	0.246489	+	0.522089i
$49$	8.60348			0.175581
$50$		0			0
$51$	−14.9177			−0.292505
$52$	−9.40790	−	41.9630i	−0.180921	−	0.806982i
$53$	73.3176			1.38335			0.691675	−	0.722209i	$-0.256873\pi$
$53$	73.3176			1.38335			0.691675	+	0.722209i	$0.256873\pi$
$54$	−8.11254	−	6.49513i	−0.150232	−	0.120280i
$55$		0			0
$56$	54.5515	+	26.6600i	0.974134	+	0.476071i
$57$			61.7677i			1.08364i
$58$	0.919939	+	0.736530i	0.0158610	+	0.0126988i
$59$	89.7651			1.52144			0.760721	−	0.649079i	$-0.224845\pi$
$59$	89.7651			1.52144			0.760721	+	0.649079i	$0.224845\pi$
$60$		0			0
$61$		−	98.7987i		−	1.61965i	−0.586671	−	0.809826i	$-0.699562\pi$
$61$		−	98.7987i		−	1.61965i	0.586671	−	0.809826i	$-0.300438\pi$
$62$	−70.3209	−	56.3009i	−1.13421	−	0.908079i
$63$	−22.7691			−0.361414
$64$	39.3226	+	50.4949i	0.614415	+	0.788983i
$65$		0			0
$66$	45.1746	+	36.1681i	0.684464	+	0.548001i
$67$		−	89.5013i		−	1.33584i	−0.744233	−	0.667920i	$-0.767185\pi$
$67$		−	89.5013i		−	1.33584i	0.744233	−	0.667920i	$-0.232815\pi$
$68$	−33.6165	+	7.53666i	−0.494361	+	0.110833i
$69$		−	19.5571i		−	0.283436i
$70$		0			0
$71$		−	90.0121i		−	1.26778i	−0.773425	−	0.633888i	$-0.781458\pi$
$71$		−	90.0121i		−	1.26778i	0.773425	−	0.633888i	$-0.218542\pi$
$72$	−21.5627	−	10.5380i	−0.299482	−	0.146360i
$73$			68.0795i			0.932596i	0.884628	+	0.466298i	$0.154412\pi$
$73$			68.0795i			0.932596i	−0.884628	+	0.466298i	$0.845588\pi$
$74$	−45.7750	+	57.1738i	−0.618580	+	0.772618i
$75$		0			0
$76$	31.2060	+	139.191i	0.410605	+	1.83146i
$77$	126.790			1.64662
$78$	29.0731	+	23.2768i	0.372732	+	0.298420i
$79$		−	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
$82$	3.06206	−	3.82457i	0.0373422	−	0.0466411i
$83$		−	95.5904i		−	1.15169i	−0.817558	−	0.575846i	$-0.804673\pi$
$83$		−	95.5904i		−	1.15169i	0.817558	−	0.575846i	$-0.195327\pi$
$84$	−51.3093	+	11.5033i	−0.610825	+	0.136944i
$85$		0			0
$86$	12.3577	+	9.89396i	0.143695	+	0.115046i
$87$	−1.02058			−0.0117307
$88$	120.072	+	58.6805i	1.36445	+	0.666824i
$89$	7.89970			0.0887607			0.0443803	−	0.999015i	$-0.485869\pi$
$89$	7.89970			0.0887607			0.0443803	+	0.999015i	$0.485869\pi$
$90$		0			0
$91$	81.5982			0.896683
$92$	−9.88052	−	44.0711i	−0.107397	−	0.479034i
$93$	78.0135			0.838855
$94$	−55.4689	+	69.2817i	−0.590095	+	0.737039i
$95$		0			0
$96$	−53.9147	−	12.8531i	−0.561612	−	0.133886i
$97$			137.133i			1.41375i	0.707341	+	0.706873i	$0.249895\pi$
$97$			137.133i			1.41375i	−0.707341	+	0.706873i	$0.750105\pi$
$98$	−10.7543	+	13.4323i	−0.109737	+	0.137064i
$99$	−50.1164			−0.506227
$100$		0			0
$101$			92.4295i			0.915144i	0.889173	+	0.457572i	$0.151281\pi$
$101$			92.4295i			0.915144i	−0.889173	+	0.457572i	$0.848719\pi$
$102$	18.6470	−	23.2904i	0.182814	−	0.228338i
$103$	−123.314			−1.19722			−0.598610	−	0.801040i	$-0.704280\pi$
$103$	−123.314			−1.19722			−0.598610	+	0.801040i	$0.704280\pi$
$104$	77.2749	+	37.7651i	0.743028	+	0.363126i
$105$		0			0
$106$	−91.6461	+	114.468i	−0.864586	+	1.07988i
$107$			0.240104i			0.00224396i	0.999999	+	0.00112198i	$0.000357137\pi$
$107$			0.240104i			0.00224396i	−0.999999	+	0.00112198i	$0.999643\pi$
$108$	20.2812	−	4.54693i	0.187789	−	0.0421012i
$109$			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
$112$	−109.812	+	51.8444i	−0.980463	+	0.462897i
$113$			41.1728i			0.364361i	0.983265	+	0.182180i	$0.0583155\pi$
$113$			41.1728i			0.364361i	−0.983265	+	0.182180i	$0.941685\pi$
$114$	−96.4354	−	77.2090i	−0.845925	−	0.677272i
$115$		0			0
$116$	−2.29983	+	0.515610i	−0.0198261	+	0.00444491i
$117$	−32.2535			−0.275671
$118$	−112.205	+	140.147i	−0.950893	+	1.18768i
$119$		−	65.3682i		−	0.549313i
$120$		0			0
$121$	158.073			1.30639
$122$	154.250	+	123.497i	1.26435	+	1.01227i
$123$			4.24295i			0.0344956i
$124$	175.800	−	39.4136i	1.41775	−	0.317852i
$125$		0			0
$126$	28.4611	−	35.5484i	0.225882	−	0.282130i
$127$	1.15264			0.00907591			0.00453795	−	0.999990i	$-0.498556\pi$
$127$	1.15264			0.00907591			0.00453795	+	0.999990i	$0.498556\pi$
$128$	−127.988	−	1.72536i	−0.999909	−	0.0134794i
$129$	−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	$0.761581\pi$
$132$	−112.935	+	25.3196i	−0.855572	+	0.191815i
$133$	−270.661			−2.03504
$134$	139.735	+	111.876i	1.04280	+	0.834892i
$135$		0			0
$136$	30.2536	−	61.9049i	0.222453	−	0.455183i
$137$		−	17.0127i		−	0.124180i	−0.998071	−	0.0620901i	$-0.980223\pi$
$137$		−	17.0127i		−	0.124180i	0.998071	−	0.0620901i	$-0.0197766\pi$
$138$	30.5336	+	24.4461i	0.221258	+	0.177146i
$139$	176.378			1.26890			0.634452	−	0.772963i	$-0.281226\pi$
$139$	176.378			1.26890			0.634452	+	0.772963i	$0.281226\pi$
$140$		0			0
$141$		−	76.8607i		−	0.545111i
$142$	140.532	+	112.514i	0.989663	+	0.792353i
$143$	179.604			1.25597
$144$	43.4056	−	20.4927i	0.301428	−	0.142310i
$145$		0			0
$146$	−106.290	−	85.0986i	−0.728011	−	0.582867i
$147$		−	14.9017i		−	0.101372i
$148$	−32.0449	−	142.933i	−0.216519	−	0.965764i
$149$		−	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	$-0.842555\pi$
$151$		−	143.361i		−	0.949408i	0.880146	−	0.474704i	$-0.157445\pi$
$152$	−256.321	−	125.267i	−1.68632	−	0.824124i
$153$			25.8383i			0.168878i
$154$	−158.485	+	197.951i	−1.02913	+	1.28540i
$155$		0			0
$156$	−72.6821	+	16.2950i	−0.465911	+	0.104455i
$157$	82.2710			0.524019			0.262009	−	0.965065i	$-0.415615\pi$
$157$	82.2710			0.524019			0.262009	+	0.965065i	$0.415615\pi$
$158$	56.6185	+	45.3304i	0.358345	+	0.286901i
$159$		−	126.990i		−	0.798678i
$160$		0			0
$161$	85.6973			0.532282
$162$	−11.2499	+	14.0513i	−0.0694438	+	0.0867366i
$163$			27.8115i			0.170623i	0.996354	+	0.0853113i	$0.0271885\pi$
$163$			27.8115i			0.170623i	−0.996354	+	0.0853113i	$0.972812\pi$
$164$	2.14360	+	9.56134i	0.0130708	+	0.0583008i
$165$		0			0
$166$	149.241	+	119.487i	0.899044	+	0.719800i
$167$	−207.819			−1.24443			−0.622214	−	0.782848i	$-0.713766\pi$
$167$	−207.819			−1.24443			−0.622214	+	0.782848i	$0.713766\pi$
$168$	46.1764	−	94.4860i	0.274860	−	0.562417i
$169$	−53.4122			−0.316048
$170$		0			0
$171$	106.985			0.625642
$172$	−30.8941	+	6.92629i	−0.179617	+	0.0402692i
$173$	45.7625			0.264523			0.132262	−	0.991215i	$-0.457776\pi$
$173$	45.7625			0.264523			0.132262	+	0.991215i	$0.457776\pi$
$174$	1.27571	−	1.59338i	0.00733165	−	0.00915737i
$175$		0			0
$176$	−241.704	+	114.113i	−1.37332	+	0.648372i
$177$		−	155.478i		−	0.878405i
$178$	−9.87453	+	12.3335i	−0.0554749	+	0.0692892i
$179$	33.0983			0.184907			0.0924533	−	0.995717i	$-0.470529\pi$
$179$	33.0983			0.184907			0.0924533	+	0.995717i	$0.470529\pi$
$180$		0			0
$181$		−	177.147i		−	0.978711i	−0.872084	−	0.489356i	$-0.837232\pi$
$181$		−	177.147i		−	0.978711i	0.872084	−	0.489356i	$-0.162768\pi$
$182$	−101.997	+	127.396i	−0.560422	+	0.699977i
$183$	−171.124			−0.935106
$184$	81.1569	+	39.6623i	0.441070	+	0.215556i
$185$		0			0
$186$	−97.5160	+	121.799i	−0.524280	+	0.654835i
$187$		−	143.880i		−	0.769413i
$188$	−38.8312	−	173.203i	−0.206549	−	0.921291i
$189$			39.4372i			0.208663i
$190$		0			0
$191$		−	28.8000i		−	0.150785i	−0.997154	−	0.0753927i	$-0.975979\pi$
$191$		−	28.8000i		−	0.150785i	0.997154	−	0.0753927i	$-0.0240210\pi$
$192$	87.4598	−	68.1087i	0.455520	−	0.354733i
$193$			87.7961i			0.454902i	0.973789	+	0.227451i	$0.0730392\pi$
$193$			87.7961i			0.454902i	−0.973789	+	0.227451i	$0.926961\pi$
$194$	−214.101	−	171.415i	−1.10361	−	0.883583i
$195$		0			0
$196$	−7.52855	−	33.5803i	−0.0384109	−	0.171328i
$197$	347.625			1.76459			0.882296	−	0.470696i	$-0.155997\pi$
$197$	347.625			1.76459			0.882296	+	0.470696i	$0.155997\pi$
$198$	62.6450	−	78.2447i	0.316389	−	0.395175i
$199$			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
$202$	−144.306	−	115.536i	−0.714388	−	0.571960i
$203$		−	4.47207i		−	0.0220299i
$204$	13.0539	+	58.2256i	0.0639896	+	0.285419i
$205$		0			0
$206$	154.141	−	192.525i	0.748256	−	0.934586i
$207$	−33.8738			−0.163642
$208$	−155.554	+	73.4402i	−0.747855	+	0.353078i
$209$	−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	$0.649089\pi$
$212$	−64.1571	−	286.167i	−0.302628	−	1.34984i
$213$	−155.905			−0.731951
$214$	−0.374864	−	0.300127i	−0.00175170	−	0.00140246i
$215$		0			0
$216$	−18.2523	+	37.3478i	−0.0845013	+	0.172906i
$217$			341.848i			1.57534i
$218$	−183.599	−	146.995i	−0.842197	−	0.674287i
$219$	117.917			0.538434
$220$		0			0
$221$		−	92.5973i		−	0.418992i
$222$	99.0279	+	79.2845i	0.446071	+	0.357138i
$223$	−211.437			−0.948149			−0.474075	−	0.880485i	$-0.657217\pi$
$223$	−211.437			−0.948149			−0.474075	+	0.880485i	$0.657217\pi$
$224$	56.3210	−	236.250i	0.251433	−	1.05469i
$225$		0			0
$226$	−64.2813	−	51.4655i	−0.284431	−	0.227723i
$227$		−	88.8880i		−	0.391577i	−0.980646	−	0.195788i	$-0.937273\pi$
$227$		−	88.8880i		−	0.391577i	0.980646	−	0.195788i	$-0.0627266\pi$
$228$	241.086	−	54.0503i	1.05740	−	0.237063i
$229$			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
$232$	2.06976	−	4.23513i	0.00892137	−	0.0182549i
$233$			188.417i			0.808656i	0.914614	+	0.404328i	$0.132495\pi$
$233$			188.417i			0.808656i	−0.914614	+	0.404328i	$0.867505\pi$
$234$	40.3165	−	50.3561i	0.172293	−	0.215197i
$235$		0			0
$236$	−78.5497	−	350.363i	−0.332838	−	1.48459i
$237$	−62.8122			−0.265030
$238$	102.057	+	81.7095i	0.428810	+	0.343317i
$239$		−	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	$0.685921\pi$
$242$	−197.590	+	246.793i	−0.816486	+	1.01981i
$243$		−	15.5885i		−	0.0641500i
$244$	−385.622	+	86.4546i	−1.58042	+	0.354322i
$245$		0			0
$246$	−6.62435	−	5.30364i	−0.0269283	−	0.0215595i
$247$	−383.404			−1.55224
$248$	−158.214	+	323.737i	−0.637959	+	1.30539i
$249$	−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	$0.400155\pi$
$252$	19.9243	+	88.8703i	0.0790646	+	0.352660i
$253$	188.626			0.745558
$254$	−1.44079	+	1.79957i	−0.00567239	+	0.00708492i
$255$		0			0
$256$	162.678	−	197.666i	0.635460	−	0.772134i
$257$			422.025i			1.64212i	0.570842	+	0.821060i	$0.306617\pi$
$257$			422.025i			1.64212i	−0.570842	+	0.821060i	$0.693383\pi$
$258$	17.1368	−	21.4042i	0.0664219	−	0.0829621i
$259$	277.937			1.07312
$260$		0			0
$261$			1.76769i			0.00677275i
$262$	239.845	−	299.571i	0.915440	−	1.14340i
$263$	118.083			0.448983			0.224492	−	0.974476i	$-0.427928\pi$
$263$	118.083			0.448983			0.224492	+	0.974476i	$0.427928\pi$
$264$	101.638	−	207.971i	0.384991	−	0.787768i
$265$		0			0
$266$	338.323	−	422.572i	1.27189	−	1.58862i
$267$		−	13.6827i		−	0.0512460i
$268$	−349.333	+	78.3188i	−1.30348	+	0.292234i
$269$			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	$0.233560\pi$
$271$			362.955i			1.33932i	−0.742669	+	0.669659i	$0.766440\pi$
$272$	58.8329	+	124.614i	0.216297	+	0.458140i
$273$		−	141.332i		−	0.517700i
$274$	26.5612	+	21.2657i	0.0969387	+	0.0776119i
$275$		0			0
$276$	−76.3334	+	17.1136i	−0.276570	+	0.0620056i
$277$	321.011			1.15888			0.579442	−	0.815013i	$-0.303270\pi$
$277$	321.011			1.15888			0.579442	+	0.815013i	$0.303270\pi$
$278$	−220.470	+	275.371i	−0.793057	+	0.990543i
$279$		−	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	$0.607252\pi$
$282$	119.999	+	96.0750i	0.425530	+	0.340691i
$283$		−	208.628i		−	0.737202i	−0.929588	−	0.368601i	$-0.879837\pi$
$283$		−	208.628i		−	0.737202i	0.929588	−	0.368601i	$-0.120163\pi$
$284$	−351.327	+	78.7658i	−1.23707	+	0.277344i
$285$		0			0
$286$	−224.502	+	280.408i	−0.784974	+	0.980447i
$287$	−18.5923			−0.0647814
$288$	−22.2622	+	93.3831i	−0.0772992	+	0.324247i
$289$	214.820			0.743323
$290$		0			0
$291$	237.522			0.816226
$292$	265.722	−	59.5735i	0.910006	−	0.204019i
$293$	306.925			1.04752			0.523762	−	0.851864i	$-0.324528\pi$
$293$	306.925			1.04752			0.523762	+	0.851864i	$0.324528\pi$
$294$	23.2654	+	18.6269i	0.0791339	+	0.0633568i
$295$		0			0
$296$	263.211	+	128.634i	0.889227	+	0.434576i
$297$			86.8042i			0.292270i
$298$	331.059	+	265.055i	1.11094	+	0.889448i
$299$	121.394			0.406002
$300$		0			0
$301$		−	60.0743i		−	0.199582i
$302$	223.823	+	179.199i	0.741136	+	0.593374i
$303$	160.093			0.528358
$304$	515.972	−	243.601i	1.69728	−	0.801318i
$305$		0			0
$306$	−40.3402	−	32.2975i	−0.131831	−	0.105548i
$307$		−	283.517i		−	0.923510i	−0.887008	−	0.461755i	$-0.847220\pi$
$307$		−	283.517i		−	0.923510i	0.887008	−	0.461755i	$-0.152780\pi$
$308$	−110.948	−	494.874i	−0.360221	−	1.60673i
$309$			213.586i			0.691216i
$310$		0			0
$311$			614.016i			1.97433i	0.159709	+	0.987164i	$0.448944\pi$
$311$			614.016i			1.97433i	−0.159709	+	0.987164i	$0.551056\pi$
$312$	65.4111	−	133.844i	0.209651	−	0.428988i
$313$		−	511.920i		−	1.63553i	−0.575555	−	0.817763i	$-0.695214\pi$
$313$		−	511.920i		−	1.63553i	0.575555	−	0.817763i	$-0.304786\pi$
$314$	−102.838	+	128.446i	−0.327509	+	0.409065i
$315$		0			0
$316$	−141.545	+	31.7337i	−0.447927	+	0.100423i
$317$	−429.605			−1.35522			−0.677611	−	0.735421i	$-0.736985\pi$
$317$	−429.605			−1.35522			−0.677611	+	0.735421i	$0.736985\pi$
$318$	198.264	+	158.736i	0.623471	+	0.499169i
$319$		−	9.84336i		−	0.0308569i
$320$		0			0
$321$	0.415872			0.00129555
$322$	−107.121	+	133.796i	−0.332673	+	0.415515i
$323$			307.145i			0.950913i
$324$	−7.87552	−	35.1280i	−0.0243072	−	0.108420i
$325$		0			0
$326$	−43.4209	−	34.7640i	−0.133193	−	0.106638i
$327$	203.684			0.622885
$328$	−17.6072	−	8.60484i	−0.0536805	−	0.0262343i
$329$	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	$0.801418\pi$
$332$	−373.100	+	83.6471i	−1.12379	+	0.251949i
$333$	−109.861			−0.329913
$334$	259.772	−	324.460i	0.777760	−	0.971436i
$335$		0			0
$336$	89.7972	+	190.200i	0.267253	+	0.566071i
$337$		−	158.578i		−	0.470559i	−0.971928	−	0.235279i	$-0.924400\pi$
$337$		−	158.578i		−	0.470559i	0.971928	−	0.235279i	$-0.0756005\pi$
$338$	66.7646	−	83.3902i	0.197528	−	0.246717i
$339$	71.3133			0.210364
$340$		0			0
$341$			752.434i			2.20655i
$342$	−133.730	+	167.031i	−0.391023	+	0.488395i
$343$	−306.597			−0.893870
$344$	27.8035	−	56.8914i	0.0808241	−	0.165382i
$345$		0			0
$346$	−57.2026	+	71.4472i	−0.165326	+	0.206495i
$347$		−	169.697i		−	0.489041i	−0.969644	−	0.244520i	$-0.921370\pi$
$347$		−	169.697i		−	0.489041i	0.969644	−	0.244520i	$-0.0786305\pi$
$348$	0.893062	+	3.98342i	0.00256627	+	0.0114466i
$349$			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
$352$	123.967	−	520.003i	0.352178	−	1.47728i
$353$			133.075i			0.376982i	0.982075	+	0.188491i	$0.0603596\pi$
$353$			133.075i			0.376982i	−0.982075	+	0.188491i	$0.939640\pi$
$354$	242.741	+	194.345i	0.685709	+	0.548998i
$355$		0			0
$356$	−6.91269	−	30.8334i	−0.0194177	−	0.0866107i
$357$	−113.221			−0.317146
$358$	−41.3725	+	51.6750i	−0.115566	+	0.144344i
$359$		−	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
$362$	276.572	+	221.431i	0.764011	+	0.611689i
$363$		−	273.791i		−	0.754244i
$364$	−71.4031	−	318.487i	−0.196162	−	0.874964i
$365$		0			0
$366$	213.904	−	267.169i	0.584436	−	0.729971i
$367$	−381.665			−1.03996			−0.519979	−	0.854179i	$-0.674060\pi$
$367$	−381.665			−1.03996			−0.519979	+	0.854179i	$0.674060\pi$
$368$	−163.368	+	77.1295i	−0.443936	+	0.209591i
$369$	7.34901			0.0199160
$370$		0			0
$371$	556.458			1.49989
$372$	−68.2663	−	304.495i	−0.183512	−	0.818536i
$373$	−42.2729			−0.113332			−0.0566661	−	0.998393i	$-0.518047\pi$
$373$	−42.2729			−0.113332			−0.0566661	+	0.998393i	$0.518047\pi$
$374$	224.634	+	179.849i	0.600626	+	0.480879i
$375$		0			0
$376$	318.953	+	155.876i	0.848278	+	0.414563i
$377$		−	6.33491i		−	0.0168035i
$378$	−61.5717	−	49.2961i	−0.162888	−	0.130413i
$379$	−412.302			−1.08787			−0.543934	−	0.839128i	$-0.683066\pi$
$379$	−412.302			−1.08787			−0.543934	+	0.839128i	$0.683066\pi$
$380$		0			0
$381$		−	1.99643i		−	0.00523998i
$382$	44.9643	+	35.9997i	0.117708	+	0.0942400i
$383$	403.711			1.05408			0.527038	−	0.849842i	$-0.323303\pi$
$383$	403.711			1.05408			0.527038	+	0.849842i	$0.323303\pi$
$384$	−2.98842	+	221.682i	−0.00778234	+	0.577298i
$385$		0			0
$386$	−137.072	−	109.744i	−0.355110	−	0.284311i
$387$			23.7457i			0.0613585i
$388$	535.246	−	120.000i	1.37950	−	0.309277i
$389$		−	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
$392$	61.8382	+	30.2210i	0.157751	+	0.0770945i
$393$			332.342i			0.845655i
$394$	−434.527	+	542.732i	−1.10286	+	1.37749i
$395$		0			0
$396$	43.8548	+	195.610i	0.110744	+	0.493965i
$397$	−323.080			−0.813803			−0.406902	−	0.913472i	$-0.633391\pi$
$397$	−323.080			−0.813803			−0.406902	+	0.913472i	$0.633391\pi$
$398$	−201.944	−	161.682i	−0.507397	−	0.406237i
$399$			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	$0.782149\pi$
$402$	193.774	−	242.027i	0.482025	−	0.602058i
$403$			484.245i			1.20160i
$404$	360.763	−	80.8812i	0.892977	−	0.200201i
$405$		0			0
$406$	6.98206	+	5.59004i	0.0171972	+	0.0137686i
$407$	611.760			1.50310
$408$	−107.222	−	52.4008i	−0.262800	−	0.128433i
$409$	−322.888			−0.789458			−0.394729	−	0.918798i	$-0.629161\pi$
$409$	−322.888			−0.789458			−0.394729	+	0.918798i	$0.629161\pi$
$410$		0			0
$411$	−29.4668			−0.0716954
$412$	107.907	+	481.307i	0.261909	+	1.16822i
$413$	681.290			1.64961
$414$	42.3419	−	52.8858i	0.102275	−	0.127743i
$415$		0			0
$416$	79.7815	−	334.659i	0.191782	−	0.804470i
$417$		−	305.495i		−	0.732602i
$418$	744.674	−	930.111i	1.78152	−	2.22515i
$419$	−19.2316			−0.0458988			−0.0229494	−	0.999737i	$-0.507306\pi$
$419$	−19.2316			−0.0458988			−0.0229494	+	0.999737i	$0.507306\pi$
$420$		0			0
$421$			312.791i			0.742970i	0.928439	+	0.371485i	$0.121151\pi$
$421$			312.791i			0.742970i	−0.928439	+	0.371485i	$0.878849\pi$
$422$	238.132	−	297.431i	0.564293	−	0.704813i
$423$	−133.127			−0.314720
$424$	526.976	+	257.539i	1.24287	+	0.607404i
$425$		0			0
$426$	194.880	−	243.409i	0.457465	−	0.571382i
$427$		−	749.852i		−	1.75609i
$428$	0.937151	−	0.210105i	0.00218961	−	0.000490899i
$429$		−	311.083i		−	0.725134i
$430$		0			0
$431$			417.415i			0.968479i	0.874935	+	0.484240i	$0.160904\pi$
$431$			417.415i			0.968479i	−0.874935	+	0.484240i	$0.839096\pi$
$432$	−35.4944	−	75.1808i	−0.0821629	−	0.174030i
$433$			279.474i			0.645436i	0.946495	+	0.322718i	$0.104596\pi$
$433$			279.474i			0.645436i	−0.946495	+	0.322718i	$0.895404\pi$
$434$	−533.714	−	427.307i	−1.22976	−	0.984577i
$435$		0			0
$436$	458.993	−	102.904i	1.05274	−	0.236018i
$437$	−402.665			−0.921430
$438$	−147.395	+	184.099i	−0.336518	+	0.420318i
$439$			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
$442$	144.568	+	115.746i	0.327078	+	0.261868i
$443$		−	56.2858i		−	0.127056i	−0.997980	−	0.0635279i	$-0.979765\pi$
$443$		−	56.2858i		−	0.127056i	0.997980	−	0.0635279i	$-0.0202352\pi$
$444$	−247.567	+	55.5034i	−0.557584	+	0.125008i
$445$		0			0
$446$	264.294	−	330.108i	0.592588	−	0.740153i
$447$	−367.275			−0.821644
$448$	298.446	+	383.241i	0.666175	+	0.855449i
$449$	283.497			0.631396			0.315698	−	0.948860i	$-0.397761\pi$
$449$	283.497			0.631396			0.315698	+	0.948860i	$0.397761\pi$
$450$		0			0
$451$	−40.9229			−0.0907382
$452$	160.702	−	36.0285i	0.355535	−	0.0797092i
$453$	−248.308			−0.548141
$454$	138.777	+	111.109i	0.305676	+	0.244733i
$455$		0			0
$456$	−216.969	+	443.960i	−0.475808	+	0.973597i
$457$			265.204i			0.580315i	0.956979	+	0.290158i	$0.0937078\pi$
$457$			265.204i			0.580315i	−0.956979	+	0.290158i	$0.906292\pi$
$458$	−238.673	−	191.089i	−0.521120	−	0.417224i
$459$	44.7532			0.0975015
$460$		0			0
$461$			709.643i			1.53936i	0.638432	+	0.769678i	$0.279583\pi$
$461$			709.643i			1.53936i	−0.638432	+	0.769678i	$0.720417\pi$
$462$	342.862	+	274.505i	0.742125	+	0.594166i
$463$	417.392			0.901495			0.450747	−	0.892652i	$-0.351157\pi$
$463$	417.392			0.901495			0.450747	+	0.892652i	$0.351157\pi$
$464$	4.02496	+	8.52529i	0.00867449	+	0.0183735i
$465$		0			0
$466$	−294.167	−	235.519i	−0.631260	−	0.505405i
$467$			679.287i			1.45458i	0.686332	+	0.727288i	$0.259220\pi$
$467$			679.287i			1.45458i	−0.686332	+	0.727288i	$0.740780\pi$
$468$	28.2237	+	125.889i	0.0603071	+	0.268994i
$469$		−	679.287i		−	1.44837i
$470$		0			0
$471$		−	142.498i		−	0.302543i
$472$	645.194	+	315.313i	1.36694	+	0.668037i
$473$		−	132.228i		−	0.279552i
$474$	78.5146	−	98.0661i	0.165643	−	0.206891i
$475$		0			0
$476$	−255.139	+	57.2010i	−0.536007	+	0.120170i
$477$	−219.953			−0.461117
$478$	355.934	+	284.971i	0.744633	+	0.596174i
$479$			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
$482$	332.239	−	414.973i	0.689292	−	0.860939i
$483$		−	148.432i		−	0.307313i
$484$	−138.323	−	616.977i	−0.285792	−	1.27475i
$485$		0			0
$486$	24.3376	+	19.4854i	0.0500774	+	0.0400934i
$487$	−736.646			−1.51262			−0.756311	−	0.654213i	$-0.773000\pi$
$487$	−736.646			−1.51262			−0.756311	+	0.654213i	$0.773000\pi$
$488$	347.045	−	710.123i	0.711159	−	1.45517i
$489$	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	$0.620317\pi$
$492$	16.5607	−	3.71283i	0.0336600	−	0.00754640i
$493$	−5.07489			−0.0102939
$494$	479.251	−	598.594i	0.970144	−	1.21173i
$495$		0			0
$496$	−307.671	−	651.680i	−0.620305	−	1.31387i
$497$		−	683.164i		−	1.37458i
$498$	206.957	−	258.494i	0.415577	−	0.519063i
$499$	−648.812			−1.30022			−0.650112	−	0.759838i	$-0.725278\pi$
$499$	−648.812			−1.30022			−0.650112	+	0.759838i	$0.725278\pi$
$500$		0			0
$501$			359.954i			0.718470i
$502$	−193.615	+	241.829i	−0.385687	+	0.481731i
$503$	−402.612			−0.800421			−0.400210	−	0.916423i	$-0.631063\pi$
$503$	−402.612			−0.800421			−0.400210	+	0.916423i	$0.631063\pi$
$504$	−163.655	−	79.9799i	−0.324711	−	0.158690i
$505$		0			0
$506$	−235.780	+	294.494i	−0.465969	+	0.582004i
$507$			92.5126i			0.182471i
$508$	−1.00863	−	4.49888i	−0.00198549	−	0.00885607i
$509$			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
$512$	105.263	+	501.063i	0.205592	+	0.978638i
$513$		−	185.303i		−	0.361215i
$514$	−658.890	−	527.526i	−1.28189	−	1.02632i
$515$		0			0
$516$	11.9967	+	53.5101i	0.0232494	+	0.103702i
$517$	741.315			1.43388
$518$	−347.418	+	433.931i	−0.670691	+	0.837706i
$519$		−	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	$0.547828\pi$
$522$	−2.75982	−	2.20959i	−0.00528701	−	0.00423293i
$523$		−	313.578i		−	0.599576i	−0.954006	−	0.299788i	$-0.903084\pi$
$523$		−	313.578i		−	0.599576i	0.954006	−	0.299788i	$-0.0969159\pi$
$524$	167.904	+	748.921i	0.320428	+	1.42924i
$525$		0			0
$526$	−147.602	+	184.357i	−0.280612	+	0.350489i
$527$	387.928			0.736107
$528$	197.650	+	418.644i	0.374338	+	0.792886i
$529$	−401.507			−0.758993
$530$		0			0
$531$	−269.295			−0.507147
$532$	236.844	+	1056.42i	0.445195	+	1.98575i
$533$	−26.3369			−0.0494125
$534$	21.3622	+	17.1032i	0.0400041	+	0.0320284i
$535$		0			0
$536$	314.387	−	643.297i	0.586542	−	1.20018i
$537$		−	57.3279i		−	0.106756i
$538$	−770.704	−	617.048i	−1.43254	−	1.14693i
$539$	143.725			0.266652
$540$		0			0
$541$		−	892.335i		−	1.64942i	−0.565557	−	0.824709i	$-0.691339\pi$
$541$		−	892.335i		−	1.64942i	0.565557	−	0.824709i	$-0.308661\pi$
$542$	−566.667	−	453.690i	−1.04551	−	0.837066i
$543$	−306.827			−0.565059
$544$	−268.095	−	63.9129i	−0.492822	−	0.117487i
$545$		0			0
$546$	220.656	+	176.664i	0.404132	+	0.323560i
$547$			671.435i			1.22749i	0.789506	+	0.613743i	$0.210337\pi$
$547$			671.435i			1.22749i	−0.789506	+	0.613743i	$0.789663\pi$
$548$	−66.4024	+	14.8871i	−0.121172	+	0.0271662i
$549$			296.396i			0.539884i
$550$		0			0
$551$			21.0129i			0.0381359i
$552$	68.6971	−	140.568i	0.124451	−	0.254652i
$553$		−	275.238i		−	0.497717i
$554$	−401.260	+	501.181i	−0.724296	+	0.904659i
$555$		0			0
$556$	−154.341	−	688.421i	−0.277591	−	1.23817i
$557$	−296.095			−0.531590			−0.265795	−	0.964030i	$-0.585634\pi$
$557$	−296.095			−0.531590			−0.265795	+	0.964030i	$0.585634\pi$
$558$	210.963	+	168.903i	0.378069	+	0.302693i
$559$		−	85.0982i		−	0.152233i
$560$		0			0
$561$	−249.208			−0.444221
$562$	232.247	−	290.080i	0.413250	−	0.516157i
$563$		−	707.222i		−	1.25617i	−0.778146	−	0.628084i	$-0.783839\pi$
$563$		−	707.222i		−	1.25617i	0.778146	−	0.628084i	$-0.216161\pi$
$564$	−299.996	+	67.2576i	−0.531907	+	0.119251i
$565$		0			0
$566$	325.722	+	260.783i	0.575481	+	0.460747i
$567$	68.3073			0.120471
$568$	316.181	−	646.969i	0.556657	−	1.13903i
$569$	−230.263			−0.404680			−0.202340	−	0.979315i	$-0.564855\pi$
$569$	−230.263			−0.404680			−0.202340	+	0.979315i	$0.564855\pi$
$570$		0			0
$571$	−439.428			−0.769575			−0.384788	−	0.923005i	$-0.625725\pi$
$571$	−439.428			−0.769575			−0.384788	+	0.923005i	$0.625725\pi$
$572$	−157.164	−	701.013i	−0.274761	−	1.22555i
$573$	−49.8831			−0.0870560
$574$	23.2401	−	29.0273i	0.0404880	−	0.0505703i
$575$		0			0
$576$	−117.968	−	151.485i	−0.204805	−	0.262994i
$577$			184.670i			0.320053i	0.987113	+	0.160026i	$0.0511579\pi$
$577$			184.670i			0.320053i	−0.987113	+	0.160026i	$0.948842\pi$
$578$	−268.523	+	335.390i	−0.464573	+	0.580260i
$579$	152.067			0.262638
$580$		0			0
$581$		−	725.502i		−	1.24871i
$582$	−296.900	+	370.833i	−0.510137	+	0.637170i
$583$	1224.81			2.10087
$584$	−239.139	+	489.327i	−0.409485	+	0.837888i
$585$		0			0
$586$	−383.652	+	479.189i	−0.654697	+	0.817729i
$587$		−	297.341i		−	0.506543i	−0.967395	−	0.253271i	$-0.918493\pi$
$587$		−	297.341i		−	0.506543i	0.967395	−	0.253271i	$-0.0815066\pi$
$588$	−58.1629	+	13.0398i	−0.0989164	+	0.0221766i
$589$		−	1606.24i		−	2.72706i
$590$		0			0
$591$		−	602.103i		−	1.01879i
$592$	−529.843	+	250.149i	−0.895004	+	0.422550i
$593$		−	607.065i		−	1.02372i	−0.859070	−	0.511859i	$-0.828957\pi$
$593$		−	607.065i		−	1.02372i	0.859070	−	0.511859i	$-0.171043\pi$
$594$	−135.524	−	108.504i	−0.228155	−	0.182667i
$595$		0			0
$596$	−827.640	+	185.553i	−1.38866	+	0.311330i
$597$	224.036			0.375269
$598$	−151.742	+	189.528i	−0.253749	+	0.316937i
$599$			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	$0.339542\pi$
$602$	93.7915	+	75.0921i	0.155800	+	0.124738i
$603$			268.504i			0.445280i
$604$	−559.552	+	125.449i	−0.926411	+	0.207697i
$605$		0			0
$606$	−200.114	+	249.946i	−0.330221	+	0.412452i
$607$	132.576			0.218413			0.109206	−	0.994019i	$-0.465169\pi$
$607$	132.576			0.218413			0.109206	+	0.994019i	$0.465169\pi$
$608$	−264.635	+	1110.06i	−0.435255	+	1.82576i
$609$	−7.74585			−0.0127190
$610$		0			0
$611$	477.089			0.780834
$612$	100.850	−	22.6100i	0.164787	−	0.0369444i
$613$	−175.738			−0.286685			−0.143343	−	0.989673i	$-0.545785\pi$
$613$	−175.738			−0.286685			−0.143343	+	0.989673i	$0.545785\pi$
$614$	442.644	+	354.393i	0.720919	+	0.577188i
$615$		0			0
$616$	911.310	+	445.367i	1.47940	+	0.722999i
$617$		−	283.254i		−	0.459082i	−0.973299	−	0.229541i	$-0.926277\pi$
$617$		−	283.254i		−	0.459082i	0.973299	−	0.229541i	$-0.0737226\pi$
$618$	−333.463	−	266.980i	−0.539583	−	0.432006i
$619$	80.2105			0.129581			0.0647904	−	0.997899i	$-0.479362\pi$
$619$	80.2105			0.129581			0.0647904	+	0.997899i	$0.479362\pi$
$620$		0			0
$621$			58.6712i			0.0944785i
$622$	−958.638	−	767.513i	−1.54122	−	1.23394i
$623$	59.9563			0.0962381
$624$	127.202	+	269.427i	0.203850	+	0.431775i
$625$		0			0
$626$	799.239	+	639.893i	1.27674	+	1.02219i
$627$			1031.86i			1.64571i
$628$	−71.9919	−	321.113i	−0.114637	−	0.511326i
$629$		−	315.402i		−	0.501434i
$630$		0			0
$631$			178.580i			0.283011i	0.989937	+	0.141505i	$0.0451942\pi$
$631$			178.580i			0.283011i	−0.989937	+	0.141505i	$0.954806\pi$
$632$	127.385	−	260.655i	0.201559	−	0.412429i
$633$			329.968i			0.521277i
$634$	537.002	−	670.725i	0.847006	−	1.05793i
$635$		0			0
$636$	−495.655	+	111.123i	−0.779332	+	0.174722i
$637$	92.4976			0.145208
$638$	15.3680	+	12.3041i	0.0240878	+	0.0192854i
$639$			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	$0.595709\pi$
$642$	−0.519835	+	0.649283i	−0.000809712	+	0.00101134i
$643$		−	847.921i		−	1.31869i	−0.751839	−	0.659347i	$-0.770833\pi$
$643$		−	847.921i		−	1.31869i	0.751839	−	0.659347i	$-0.229167\pi$
$644$	−74.9901	−	334.486i	−0.116444	−	0.519388i
$645$		0			0
$646$	−479.533	−	383.928i	−0.742311	−	0.594315i
$647$	−372.369			−0.575532			−0.287766	−	0.957701i	$-0.592913\pi$
$647$	−372.369			−0.575532			−0.287766	+	0.957701i	$0.592913\pi$
$648$	64.6882	+	31.6139i	0.0998275	+	0.0487868i
$649$	1499.57			2.31058
$650$		0			0
$651$	592.099			0.909522
$652$	108.551	−	24.3367i	0.166490	−	0.0373262i
$653$	−650.726			−0.996517			−0.498259	−	0.867028i	$-0.666027\pi$
$653$	−650.726			−0.996517			−0.498259	+	0.867028i	$0.666027\pi$
$654$	−254.602	+	318.003i	−0.389300	+	0.486243i
$655$		0			0
$656$	35.4432	−	16.7334i	0.0540292	−	0.0255083i
$657$		−	204.238i		−	0.310865i
$658$	−420.992	+	525.827i	−0.639806	+	0.799129i
$659$	−589.211			−0.894099			−0.447049	−	0.894509i	$-0.647525\pi$
$659$	−589.211			−0.894099			−0.447049	+	0.894509i	$0.647525\pi$
$660$		0			0
$661$		−	402.340i		−	0.608684i	−0.952563	−	0.304342i	$-0.901563\pi$
$661$		−	402.340i		−	0.608684i	0.952563	−	0.304342i	$-0.0984366\pi$
$662$	671.616	−	838.861i	1.01453	−	1.26716i
$663$	−160.383			−0.241905
$664$	335.776	−	687.063i	0.505686	−	1.03473i
$665$		0			0
$666$	137.325	−	171.521i	0.206193	−	0.257539i
$667$		−	6.65315i		−	0.00997473i
$668$	181.854	+	811.142i	0.272236	+	1.21428i
$669$			366.220i			0.547414i
$670$		0			0
$671$		−	1650.48i		−	2.45973i
$672$	−409.196	−	97.5509i	−0.608923	−	0.145165i
$673$			1237.67i			1.83903i	0.393056	+	0.919515i	$0.371418\pi$
$673$			1237.67i			1.83903i	−0.393056	+	0.919515i	$0.628582\pi$
$674$	247.582	+	198.221i	0.367332	+	0.294096i
$675$		0			0
$676$	46.7387	+	208.474i	0.0691401	+	0.308393i
$677$	163.462			0.241451			0.120725	−	0.992686i	$-0.461478\pi$
$677$	163.462			0.241451			0.120725	+	0.992686i	$0.461478\pi$
$678$	−89.1408	+	111.339i	−0.131476	+	0.164216i
$679$			1040.80i			1.53284i
$680$		0			0
$681$	−153.958			−0.226077
$682$	−1174.74	−	940.533i	−1.72250	−	1.37908i
$683$			992.033i			1.45246i	0.687449	+	0.726232i	$0.258730\pi$
$683$			992.033i			1.45246i	−0.687449	+	0.726232i	$0.741270\pi$
$684$	−93.6179	−	417.574i	−0.136868	−	0.610488i
$685$		0			0
$686$	383.243	−	478.678i	0.558663	−	0.697781i
$687$	264.783			0.385419
$688$	54.0682	+	114.522i	0.0785875	+	0.166456i
$689$	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	$0.609322\pi$
$692$	−40.0449	−	178.616i	−0.0578683	−	0.258116i
$693$	−380.369			−0.548872
$694$	264.941	+	212.119i	0.381759	+	0.305648i
$695$		0			0
$696$	−7.33546	−	3.58492i	−0.0105395	−	0.00515075i
$697$			21.0984i			0.0302703i
$698$	−462.710	−	370.459i	−0.662908	−	0.530743i
$699$	326.347			0.466878
$700$		0			0
$701$			261.352i			0.372827i	0.982471	+	0.186414i	$0.0596864\pi$
$701$			261.352i			0.372827i	−0.982471	+	0.186414i	$0.940314\pi$
$702$	−87.2194	−	69.8303i	−0.124244	−	0.0994734i
$703$	−1305.94			−1.85767
$704$	656.902	+	843.542i	0.933100	+	1.19821i
$705$		0			0
$706$	−207.764	−	166.342i	−0.294283	−	0.235611i
$707$			701.512i			0.992238i
$708$	−606.847	+	136.052i	−0.857128	+	0.192164i
$709$			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
$712$	56.7797	+	27.7489i	0.0797468	+	0.0389732i
$713$			508.572i			0.713284i
$714$	141.525	−	176.767i	0.198214	−	0.247573i
$715$		0			0
$716$	−28.9629	−	129.186i	−0.0404510	−	0.180428i
$717$	−394.871			−0.550727
$718$	371.728	+	297.616i	0.517727	+	0.414507i
$719$			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
$722$	−1138.43	+	1421.92i	−1.57677	+	1.96942i
$723$			460.368i			0.636747i
$724$	−691.423	+	155.014i	−0.955005	+	0.214107i
$725$		0			0
$726$	427.458	+	342.235i	0.588785	+	0.471398i
$727$	956.205			1.31527			0.657637	−	0.753335i	$-0.271556\pi$
$727$	956.205			1.31527			0.657637	+	0.753335i	$0.271556\pi$
$728$	586.493	+	286.626i	0.805623	+	0.393717i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−68.1721			−0.0932586
$732$	149.744	+	667.917i	0.204568	+	0.912456i
$733$	−398.986			−0.544320			−0.272160	−	0.962252i	$-0.587738\pi$
$733$	−398.986			−0.544320			−0.272160	+	0.962252i	$0.587738\pi$
$734$	477.076	−	595.877i	0.649968	−	0.811822i
$735$		0			0
$736$	83.7894	−	351.471i	0.113844	−	0.477542i
$737$		−	1495.16i		−	2.02871i
$738$	−9.18618	+	11.4737i	−0.0124474	+	0.0155470i
$739$	−1011.87			−1.36924			−0.684622	−	0.728899i	$-0.740033\pi$
$739$	−1011.87			−1.36924			−0.684622	+	0.728899i	$0.740033\pi$
$740$		0			0
$741$			664.076i			0.896189i
$742$	−695.566	+	868.775i	−0.937421	+	1.17086i
$743$	−346.145			−0.465875			−0.232938	−	0.972492i	$-0.574834\pi$
$743$	−346.145			−0.465875			−0.232938	+	0.972492i	$0.574834\pi$
$744$	560.728	+	274.034i	0.753667	+	0.368326i
$745$		0			0
$746$	52.8406	−	65.9989i	0.0708319	−	0.0884704i
$747$			286.771i			0.383897i
$748$	−561.581	+	125.904i	−0.750776	+	0.168320i
$749$			1.82231i			0.00243300i
$750$		0			0
$751$		−	71.2058i		−	0.0948146i	−0.998876	−	0.0474073i	$-0.984904\pi$
$751$		−	71.2058i		−	0.0948146i	0.998876	−	0.0474073i	$-0.0150959\pi$
$752$	−642.050	+	303.125i	−0.853789	+	0.403091i
$753$		−	268.283i		−	0.356286i
$754$	9.89043	+	7.91856i	0.0131173	+	0.0105021i
$755$		0			0
$756$	153.928	−	34.5098i	0.203608	−	0.0456479i
$757$	−1452.44			−1.91867			−0.959337	−	0.282264i	$-0.908915\pi$
$757$	−1452.44			−1.91867			−0.959337	+	0.282264i	$0.908915\pi$
$758$	515.373	−	643.710i	0.679912	−	0.849222i
$759$		−	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	$0.412221\pi$
$762$	3.11695	+	2.49552i	0.00409048	+	0.00327496i
$763$			892.523i			1.16976i
$764$	−112.410	+	25.2017i	−0.147133	+	0.0329865i
$765$		0			0
$766$	−504.634	+	630.297i	−0.658791	+	0.822842i
$767$	965.081			1.25825
$768$	−342.368	−	281.766i	−0.445792	−	0.366883i
$769$	132.780			0.172665			0.0863326	−	0.996266i	$-0.472485\pi$
$769$	132.780			0.172665			0.0863326	+	0.996266i	$0.472485\pi$
$770$		0			0
$771$	730.968			0.948078
$772$	342.678	−	76.8267i	0.443884	−	0.0995165i
$773$	135.449			0.175225			0.0876126	−	0.996155i	$-0.472076\pi$
$773$	135.449			0.175225			0.0876126	+	0.996155i	$0.472076\pi$
$774$	−37.0732	−	29.6819i	−0.0478982	−	0.0383487i
$775$		0			0
$776$	−481.702	+	985.656i	−0.620749	+	1.27018i
$777$		−	481.401i		−	0.619564i
$778$	122.567	+	98.1307i	0.157541	+	0.126132i
$779$	87.3592			0.112143
$780$		0			0
$781$		−	1503.70i		−	1.92535i
$782$	151.831	+	121.560i	0.194157	+	0.155448i
$783$	3.06173			0.00391025
$784$	−124.480	+	58.7695i	−0.158775	+	0.0749611i
$785$		0			0
$786$	−518.873	−	415.424i	−0.660143	−	0.528530i
$787$			370.900i			0.471283i	0.971840	+	0.235642i	$0.0757192\pi$
$787$			370.900i			0.471283i	−0.971840	+	0.235642i	$0.924281\pi$
$788$	−304.192	−	1356.82i	−0.386030	−	1.72185i
$789$		−	204.525i		−	0.259220i
$790$		0			0
$791$			312.489i			0.395055i
$792$	−360.216	−	176.042i	−0.454818	−	0.222275i
$793$		−	1062.20i		−	1.33947i
$794$	403.846	−	504.411i	0.508622	−	0.635279i
$795$		0			0
$796$	504.856	−	113.186i	0.634241	−	0.142194i
$797$	980.881			1.23072			0.615358	−	0.788247i	$-0.289011\pi$
$797$	980.881			1.23072			0.615358	+	0.788247i	$0.289011\pi$
$798$	−731.916	−	585.992i	−0.917187	−	0.734326i
$799$		−	382.196i		−	0.478343i
$800$		0			0
$801$	−23.6991			−0.0295869
$802$	776.729	−	970.149i	0.968490	−	1.20966i
$803$			1137.30i			1.41631i
$804$	135.652	+	605.063i	0.168722	+	0.752566i
$805$		0			0
$806$	−756.032	−	605.301i	−0.938005	−	0.750994i
$807$	855.014			1.05950
$808$	−324.673	+	664.344i	−0.401823	+	0.822208i
$809$	464.769			0.574498			0.287249	−	0.957856i	$-0.407259\pi$
$809$	464.769			0.574498			0.287249	+	0.957856i	$0.407259\pi$
$810$		0			0
$811$	−49.1816			−0.0606431			−0.0303216	−	0.999540i	$-0.509653\pi$
$811$	−49.1816			−0.0606431			−0.0303216	+	0.999540i	$0.509653\pi$
$812$	−17.4550	+	3.91332i	−0.0214963	+	0.00481936i
$813$	628.657			0.773255
$814$	−764.693	+	955.115i	−0.939426	+	1.17336i
$815$		0			0
$816$	215.838	−	101.901i	0.264507	−	0.124879i
$817$			282.270i			0.345496i
$818$	403.607	−	504.112i	0.493407	−	0.616274i
$819$	−244.795			−0.298894
$820$		0			0
$821$		−	911.027i		−	1.10965i	−0.831965	−	0.554827i	$-0.812784\pi$
$821$		−	911.027i		−	1.10965i	0.831965	−	0.554827i	$-0.187216\pi$
$822$	36.8332	−	46.0053i	0.0448092	−	0.0559676i
$823$	1278.02			1.55287			0.776437	−	0.630195i	$-0.217025\pi$
$823$	1278.02			1.55287			0.776437	+	0.630195i	$0.217025\pi$
$824$	−886.327	−	433.158i	−1.07564	−	0.525678i
$825$		0			0
$826$	−851.604	+	1063.67i	−1.03100	+	1.28774i
$827$			671.016i			0.811386i	0.914009	+	0.405693i	$0.132970\pi$
$827$			671.016i			0.811386i	−0.914009	+	0.405693i	$0.867030\pi$
$828$	29.6416	+	132.213i	0.0357990	+	0.159678i
$829$		−	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
$832$	422.764	+	542.880i	0.508130	+	0.652500i
$833$		−	74.0997i		−	0.0889552i
$834$	476.957	+	381.865i	0.571890	+	0.457872i
$835$		0			0
$836$	521.311	+	2325.26i	0.623578	+	2.78141i
$837$	−234.041			−0.279618
$838$	24.0393	−	30.0255i	0.0286865	−	0.0358299i
$839$		−	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
$842$	−488.347	−	390.985i	−0.579985	−	0.464352i
$843$			321.813i			0.381748i
$844$	166.705	+	743.570i	0.197518	+	0.881008i
$845$		0			0
$846$	166.407	−	207.845i	0.196698	−	0.245680i
$847$	1199.73			1.41644
$848$	−1060.80	+	500.825i	−1.25094	+	0.590595i
$849$	−361.354			−0.425623
$850$		0			0
$851$	413.490			0.485887
$852$	136.426	+	608.516i	0.160125	+	0.714221i
$853$	−512.714			−0.601072			−0.300536	−	0.953770i	$-0.597166\pi$
$853$	−512.714			−0.601072			−0.300536	+	0.953770i	$0.597166\pi$
$854$	1170.71	+	937.307i	1.37086	+	1.09755i
$855$		0			0
$856$	−0.843401	+	1.72576i	−0.000985281	+	0.00201608i
$857$			1620.81i			1.89126i	0.325243	+	0.945631i	$0.394554\pi$
$857$			1620.81i			1.89126i	−0.325243	+	0.945631i	$0.605446\pi$
$858$	485.680	+	388.850i	0.566061	+	0.453205i
$859$	−225.172			−0.262132			−0.131066	−	0.991374i	$-0.541840\pi$
$859$	−225.172			−0.262132			−0.131066	+	0.991374i	$0.541840\pi$
$860$		0			0
$861$			32.2027i			0.0374016i
$862$	−651.692	−	521.763i	−0.756023	−	0.605294i
$863$	−1029.21			−1.19260			−0.596299	−	0.802763i	$-0.703363\pi$
$863$	−1029.21			−1.19260			−0.596299	+	0.802763i	$0.703363\pi$
$864$	161.744	+	38.5592i	0.187204	+	0.0446287i
$865$		0			0
$866$	−436.331	−	349.339i	−0.503846	−	0.403394i
$867$		−	372.080i		−	0.429158i
$868$	1334.27	−	299.137i	1.53718	−	0.344628i
$869$		−	605.818i		−	0.697144i
$870$		0			0
$871$		−	962.244i		−	1.10476i
$872$	−413.076	+	845.236i	−0.473711	+	0.969307i
$873$		−	411.400i		−	0.471248i
$874$	503.327	−	628.664i	0.575889	−	0.719296i
$875$		0			0
$876$	−103.184	−	460.244i	−0.117790	−	0.525392i
$877$	570.056			0.650007			0.325003	−	0.945713i	$-0.394635\pi$
$877$	570.056			0.650007			0.325003	+	0.945713i	$0.394635\pi$
$878$	−47.0464	−	37.6667i	−0.0535836	−	0.0429005i
$879$		−	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	$0.390013\pi$
$882$	32.2628	−	40.2968i	0.0365791	−	0.0456880i
$883$			856.738i			0.970258i	0.874442	+	0.485129i	$0.161227\pi$
$883$			856.738i			0.970258i	−0.874442	+	0.485129i	$0.838773\pi$
$884$	−361.418	+	81.0280i	−0.408843	+	0.0916606i
$885$		0			0
$886$	87.8766	+	70.3565i	0.0991835	+	0.0794092i
$887$	1648.76			1.85880			0.929402	−	0.369068i	$-0.120323\pi$
$887$	1648.76			1.85880			0.929402	+	0.369068i	$0.120323\pi$
$888$	222.801	−	455.895i	0.250902	−	0.513396i
$889$	8.74819			0.00984048
$890$		0			0
$891$	150.349			0.168742
$892$	185.020	+	825.263i	0.207421	+	0.925183i
$893$	−1582.50			−1.77212
$894$	459.089	−	573.411i	0.513523	−	0.641400i
$895$		0			0
$896$	−971.393	−	13.0950i	−1.08414	−	0.0146149i
$897$		−	210.261i		−	0.234405i
$898$	−354.367	+	442.612i	−0.394619	+	0.492886i
$899$	26.5395			0.0295212
$900$		0			0
$901$		−	631.467i		−	0.700851i
$902$	51.1532	−	63.8913i	0.0567109	−	0.0708329i
$903$	−104.052			−0.115229
$904$	−144.626	+	295.932i	−0.159984	+	0.327359i
$905$		0			0
$906$	310.382	−	387.673i	0.342585	−	0.427895i
$907$		−	844.509i		−	0.931101i	−0.885021	−	0.465551i	$-0.845856\pi$
$907$		−	844.509i		−	0.931101i	0.885021	−	0.465551i	$-0.154144\pi$
$908$	−346.940	+	77.7821i	−0.382092	+	0.0856631i
$909$		−	277.289i		−	0.305048i
$910$		0			0
$911$		−	1074.78i		−	1.17978i	−0.807483	−	0.589891i	$-0.799171\pi$
$911$		−	1074.78i		−	1.17978i	0.807483	−	0.589891i	$-0.200829\pi$
$912$	−421.929	−	893.689i	−0.462641	−	0.979923i
$913$		−	1596.88i		−	1.74905i
$914$	−414.052	−	331.502i	−0.453011	−	0.362694i
$915$		0			0
$916$	596.677	−	133.772i	0.651395	−	0.146039i
$917$	−1456.30			−1.58811
$918$	−55.9410	+	69.8713i	−0.0609379	+	0.0761126i
$919$		−	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
$922$	−1107.94	−	887.046i	−1.20167	−	0.962089i
$923$		−	967.736i		−	1.04847i
$924$	−857.146	+	192.168i	−0.927647	+	0.207974i
$925$		0			0
$926$	−521.735	+	651.657i	−0.563429	+	0.703733i
$927$	369.941			0.399074
$928$	−18.3413	−	4.37251i	−0.0197644	−	0.00471175i
$929$	−415.953			−0.447742			−0.223871	−	0.974619i	$-0.571869\pi$
$929$	−415.953			−0.447742			−0.223871	+	0.974619i	$0.571869\pi$
$930$		0			0
$931$	−306.814			−0.329553
$932$	735.412	−	164.876i	0.789068	−	0.176905i
$933$	1063.51			1.13988
$934$	−1060.54	−	849.101i	−1.13549	−	0.909102i
$935$		0			0
$936$	−231.825	−	113.295i	−0.247676	−	0.121042i
$937$			846.979i			0.903927i	0.892037	+	0.451963i	$0.149276\pi$
$937$			846.979i			0.903927i	−0.892037	+	0.451963i	$0.850724\pi$
$938$	1060.54	+	849.101i	1.13064	+	0.905225i
$939$	−886.671			−0.944271
$940$		0			0
$941$			149.279i			0.158638i	0.996849	+	0.0793192i	$0.0252746\pi$
$941$			149.279i			0.158638i	−0.996849	+	0.0793192i	$0.974725\pi$
$942$	222.476	+	178.120i	0.236174	+	0.189087i
$943$	−27.6599			−0.0293318
$944$	−1298.77	+	613.176i	−1.37582	+	0.649551i
$945$		0			0
$946$	206.442	+	165.283i	0.218226	+	0.174718i
$947$		−	543.005i		−	0.573395i	−0.958021	−	0.286697i	$-0.907443\pi$
$947$		−	543.005i		−	0.573395i	0.958021	−	0.286697i	$-0.0925574\pi$
$948$	54.9643	+	245.163i	0.0579793	+	0.258611i
$949$			731.935i			0.771269i
$950$		0			0
$951$			744.098i			0.782438i
$952$	229.616	−	469.839i	0.241193	−	0.493529i
$953$		−	344.292i		−	0.361272i	−0.983550	−	0.180636i	$-0.942184\pi$
$953$		−	344.292i		−	0.361272i	0.983550	−	0.180636i	$-0.0578156\pi$
$954$	274.938	−	343.403i	0.288195	−	0.359961i
$955$		0			0
$956$	−889.828	+	199.495i	−0.930782	+	0.208677i
$957$	−17.0492			−0.0178153
$958$	−246.021	−	196.971i	−0.256807	−	0.205607i
$959$		−	129.121i		−	0.134641i
$960$		0			0
$961$	−1067.70			−1.11103
$962$	−492.135	+	614.685i	−0.511575	+	0.638966i
$963$		−	0.720311i		−	0.000747987i
$964$	232.585	+	1037.42i	0.241271	+	1.07616i
$965$		0			0
$966$	231.741	+	185.538i	0.239897	+	0.192069i
$967$	−1044.78			−1.08044			−0.540219	−	0.841524i	$-0.681659\pi$
$967$	−1044.78			−1.08044			−0.540219	+	0.841524i	$0.681659\pi$
$968$	1136.16	+	555.256i	1.17372	+	0.573611i
$969$	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	$0.449525\pi$
$972$	−60.8435	+	13.6408i	−0.0625962	+	0.0140337i
$973$	1338.65			1.37580
$974$	920.800	−	1150.10i	0.945379	−	1.18080i
$975$		0			0
$976$	674.884	+	1429.47i	0.691479	+	1.46462i
$977$		−	1753.81i		−	1.79509i	−0.440919	−	0.897547i	$-0.645347\pi$
$977$		−	1753.81i		−	1.79509i	0.440919	−	0.897547i	$-0.354653\pi$
$978$	−60.2131	+	75.2073i	−0.0615676	+	0.0768990i
$979$	131.968			0.134799
$980$		0			0
$981$		−	352.790i		−	0.359623i
$982$	453.005	−	565.812i	0.461309	−	0.576183i
$983$	951.541			0.967997			0.483999	−	0.875069i	$-0.339184\pi$
$983$	951.541			0.967997			0.483999	+	0.875069i	$0.339184\pi$
$984$	−14.9040	+	30.4966i	−0.0151464	+	0.0309924i
$985$		0			0
$986$	6.34355	−	7.92321i	0.00643362	−	0.00803571i
$987$		−	583.349i		−	0.591033i
$988$	335.501	+	1496.47i	0.339576	+	1.51465i
$989$		−	89.3731i		−	0.0903672i
$990$		0			0
$991$			1786.06i			1.80229i	0.433523	+	0.901143i	$0.357270\pi$
$991$			1786.06i			1.80229i	−0.433523	+	0.901143i	$0.642730\pi$
$992$	1402.03	+	334.238i	1.41333	+	0.336933i
$993$			930.627i			0.937187i
$994$	1066.60	+	853.947i	1.07303	+	0.859102i
$995$		0			0
$996$	144.881	+	646.228i	0.145463	+	0.648823i
$997$	1375.80			1.37994			0.689969	−	0.723839i	$-0.257624\pi$
$997$	1375.80			1.37994			0.689969	+	0.723839i	$0.257624\pi$
$998$	811.008	−	1012.96i	0.812633	−	1.01499i
$999$			190.285i			0.190475i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.g.a.91.5	✓	16	5.2	odd	4
120.3.g.a.91.6	yes	16	40.27	even	4
360.3.g.c.91.11		16	120.107	odd	4
360.3.g.c.91.12		16	15.2	even	4
480.3.g.a.271.9		16	20.7	even	4
480.3.g.a.271.16		16	40.37	odd	4
600.3.g.d.451.11		16	40.3	even	4
600.3.g.d.451.12		16	5.3	odd	4
600.3.p.b.499.7		32	40.19	odd	2	inner
600.3.p.b.499.8		32	1.1	even	1	trivial
600.3.p.b.499.25		32	5.4	even	2	inner
600.3.p.b.499.26		32	8.3	odd	2	inner
1440.3.g.c.271.7		16	120.77	even	4
1440.3.g.c.271.10		16	60.47	odd	4
2400.3.g.b.751.2		16	40.13	odd	4
2400.3.g.b.751.7		16	20.3	even	4
2400.3.p.b.1999.13		32	40.29	even	2
2400.3.p.b.1999.14		32	4.3	odd	2
2400.3.p.b.1999.31		32	20.19	odd	2
2400.3.p.b.1999.32		32	8.5	even	2

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.p (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.24999 + 1.56126i) q^{2} -1.73205i q^{3} +(-0.875058 - 3.90311i) q^{4} +(2.70418 + 2.16504i) q^{6} +7.58970 q^{7} +(7.18758 + 3.51265i) q^{8} -3.00000 q^{9} +16.7055 q^{11} +(-6.76039 + 1.51564i) q^{12} +10.7512 q^{13} +(-9.48703 + 11.8495i) q^{14} +(-14.4685 + 6.83090i) q^{16} -8.61276i q^{17} +(3.74997 - 4.68378i) q^{18} -35.6616 q^{19} -13.1457i q^{21} +(-20.8817 + 26.0816i) q^{22} +11.2913 q^{23} +(6.08409 - 12.4493i) q^{24} +(-13.4388 + 16.7854i) q^{26} +5.19615i q^{27} +(-6.64142 - 29.6234i) q^{28} -0.589229i q^{29} +45.0411i q^{31} +(7.42072 - 31.1277i) q^{32} -28.9347i q^{33} +(13.4467 + 10.7658i) q^{34} +(2.62517 + 11.7093i) q^{36} +36.6203 q^{37} +(44.5766 - 55.6770i) q^{38} -18.6216i q^{39} -2.44967 q^{41} +(20.5239 + 16.4320i) q^{42} -7.91524i q^{43} +(-14.6183 - 65.2033i) q^{44} +(-14.1140 + 17.6286i) q^{46} +44.3755 q^{47} +(11.8315 + 25.0603i) q^{48} +8.60348 q^{49} -14.9177 q^{51} +(-9.40790 - 41.9630i) q^{52} +73.3176 q^{53} +(-8.11254 - 6.49513i) q^{54} +(54.5515 + 26.6600i) q^{56} +61.7677i q^{57} +(0.919939 + 0.736530i) q^{58} +89.7651 q^{59} -98.7987i q^{61} +(-70.3209 - 56.3009i) q^{62} -22.7691 q^{63} +(39.3226 + 50.4949i) q^{64} +(45.1746 + 36.1681i) q^{66} -89.5013i q^{67} +(-33.6165 + 7.53666i) q^{68} -19.5571i q^{69} -90.0121i q^{71} +(-21.5627 - 10.5380i) q^{72} +68.0795i q^{73} +(-45.7750 + 57.1738i) q^{74} +(31.2060 + 139.191i) q^{76} +126.790 q^{77} +(29.0731 + 23.2768i) q^{78} -36.2647i q^{79} +9.00000 q^{81} +(3.06206 - 3.82457i) q^{82} -95.5904i q^{83} +(-51.3093 + 11.5033i) q^{84} +(12.3577 + 9.89396i) q^{86} -1.02058 q^{87} +(120.072 + 58.6805i) q^{88} +7.89970 q^{89} +81.5982 q^{91} +(-9.88052 - 44.0711i) q^{92} +78.0135 q^{93} +(-55.4689 + 69.2817i) q^{94} +(-53.9147 - 12.8531i) q^{96} +137.133i q^{97} +(-10.7543 + 13.4323i) q^{98} -50.1164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{4} + 12 q^{6} - 96 q^{9} + 128 q^{11} + 40 q^{14} - 28 q^{16} + 64 q^{19} + 108 q^{24} + 72 q^{26} + 144 q^{34} + 84 q^{36} + 200 q^{44} + 424 q^{46} + 160 q^{49} + 192 q^{51} - 36 q^{54} - 232 q^{56}+ \cdots - 384 q^{99}+O(q^{100}) \) 32 * q - 28 * q^4 + 12 * q^6 - 96 * q^9 + 128 * q^11 + 40 * q^14 - 28 * q^16 + 64 * q^19 + 108 * q^24 + 72 * q^26 + 144 * q^34 + 84 * q^36 + 200 * q^44 + 424 * q^46 + 160 * q^49 + 192 * q^51 - 36 * q^54 - 232 * q^56 - 256 * q^59 - 28 * q^64 - 360 * q^66 - 600 * q^74 + 840 * q^76 + 288 * q^81 - 360 * q^84 + 624 * q^86 - 384 * q^91 - 920 * q^94 - 372 * q^96 - 384 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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