LMFDB - Embedded newform 504.3.l.h.181.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(181,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.181"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,2,0,-6] 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:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.18
Character	$\chi$	$=$	504.181
Dual form			504.3.l.h.181.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.606108 - 1.90595i) q^{2} +(-3.26527 - 2.31042i) q^{4} +5.53884 q^{5} +(-5.95316 + 3.68238i) q^{7} +(-6.38264 + 4.82306i) q^{8} +(3.35714 - 10.5567i) q^{10} +16.1324i q^{11} -14.1524 q^{13} +(3.41016 + 13.5783i) q^{14} +(5.32392 + 15.0883i) q^{16} +7.47600i q^{17} -28.5884 q^{19} +(-18.0858 - 12.7970i) q^{20} +(30.7475 + 9.77800i) q^{22} -8.09656 q^{23} +5.67874 q^{25} +(-8.57789 + 26.9737i) q^{26} +(27.9465 + 1.73036i) q^{28} +5.91522i q^{29} +27.0356i q^{31} +(31.9843 - 1.00199i) q^{32} +(14.2488 + 4.53126i) q^{34} +(-32.9736 + 20.3961i) q^{35} -20.5381i q^{37} +(-17.3277 + 54.4879i) q^{38} +(-35.3524 + 26.7141i) q^{40} -49.1096i q^{41} +42.4974i q^{43} +(37.2727 - 52.6767i) q^{44} +(-4.90739 + 15.4316i) q^{46} -48.6891i q^{47} +(21.8802 - 43.8435i) q^{49} +(3.44193 - 10.8234i) q^{50} +(46.2114 + 32.6980i) q^{52} +77.1902i q^{53} +89.3549i q^{55} +(20.2366 - 52.2157i) q^{56} +(11.2741 + 3.58527i) q^{58} +40.7234 q^{59} +10.9064 q^{61} +(51.5284 + 16.3865i) q^{62} +(17.4762 - 61.5677i) q^{64} -78.3879 q^{65} +116.132i q^{67} +(17.2727 - 24.4111i) q^{68} +(18.8883 + 75.2081i) q^{70} +104.767 q^{71} -82.8647i q^{73} +(-39.1444 - 12.4483i) q^{74} +(93.3487 + 66.0512i) q^{76} +(-59.4057 - 96.0389i) q^{77} -44.7667 q^{79} +(29.4883 + 83.5715i) q^{80} +(-93.6002 - 29.7657i) q^{82} -65.8500 q^{83} +41.4083i q^{85} +(80.9977 + 25.7580i) q^{86} +(-77.8076 - 102.968i) q^{88} +134.189i q^{89} +(84.2515 - 52.1145i) q^{91} +(26.4374 + 18.7065i) q^{92} +(-92.7989 - 29.5109i) q^{94} -158.346 q^{95} +37.4629i q^{97} +(-70.3017 - 68.2764i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	0.606108	−	1.90595i	0.303054	−	0.952973i
$2$	0.606108	−	1.90595i	0.303054	−	0.952973i
$3$		0			0
$3$		0			0
$4$	−3.26527	−	2.31042i	−0.816316	−	0.577605i
$5$	5.53884			1.10777			0.553884	−	0.832594i	$-0.313145\pi$
$5$	5.53884			1.10777			0.553884	+	0.832594i	$0.313145\pi$
$6$		0			0
$7$	−5.95316	+	3.68238i	−0.850451	+	0.526054i
$7$	−5.95316	+	3.68238i	−0.850451	+	0.526054i
$8$	−6.38264	+	4.82306i	−0.797830	+	0.602882i
$9$		0			0
$10$	3.35714	−	10.5567i	0.335714	−	1.05567i
$11$			16.1324i			1.46658i	0.679914	+	0.733292i	$0.262017\pi$
$11$			16.1324i			1.46658i	−0.679914	+	0.733292i	$0.737983\pi$
$12$		0			0
$13$	−14.1524			−1.08865			−0.544323	−	0.838876i	$-0.683214\pi$
$13$	−14.1524			−1.08865			−0.544323	+	0.838876i	$0.683214\pi$
$14$	3.41016	+	13.5783i	0.243583	+	0.969880i
$15$		0			0
$16$	5.32392	+	15.0883i	0.332745	+	0.943017i
$17$			7.47600i			0.439764i	0.975526	+	0.219882i	$0.0705673\pi$
$17$			7.47600i			0.439764i	−0.975526	+	0.219882i	$0.929433\pi$
$18$		0			0
$19$	−28.5884			−1.50465			−0.752326	−	0.658791i	$-0.771068\pi$
$19$	−28.5884			−1.50465			−0.752326	+	0.658791i	$0.771068\pi$
$20$	−18.0858	−	12.7970i	−0.904289	−	0.639852i
$21$		0			0
$22$	30.7475	+	9.77800i	1.39762	+	0.444454i
$23$	−8.09656			−0.352024			−0.176012	−	0.984388i	$-0.556320\pi$
$23$	−8.09656			−0.352024			−0.176012	+	0.984388i	$0.556320\pi$
$24$		0			0
$25$	5.67874			0.227150
$26$	−8.57789	+	26.9737i	−0.329919	+	1.03745i
$27$		0			0
$28$	27.9465	+	1.73036i	0.998089	+	0.0617985i
$29$			5.91522i			0.203973i	0.994786	+	0.101987i	$0.0325199\pi$
$29$			5.91522i			0.203973i	−0.994786	+	0.101987i	$0.967480\pi$
$30$		0			0
$31$			27.0356i			0.872116i	0.899919	+	0.436058i	$0.143626\pi$
$31$			27.0356i			0.872116i	−0.899919	+	0.436058i	$0.856374\pi$
$32$	31.9843	−	1.00199i	0.999510	−	0.0313121i
$33$		0			0
$34$	14.2488	+	4.53126i	0.419084	+	0.133272i
$35$	−32.9736	+	20.3961i	−0.942103	+	0.582745i
$36$		0			0
$37$		−	20.5381i		−	0.555083i	−0.960714	−	0.277541i	$-0.910480\pi$
$37$		−	20.5381i		−	0.555083i	0.960714	−	0.277541i	$-0.0895196\pi$
$38$	−17.3277	+	54.4879i	−0.455991	+	1.43389i
$39$		0			0
$40$	−35.3524	+	26.7141i	−0.883811	+	0.667854i
$41$		−	49.1096i		−	1.19779i	−0.800826	−	0.598897i	$-0.795606\pi$
$41$		−	49.1096i		−	1.19779i	0.800826	−	0.598897i	$-0.204394\pi$
$42$		0			0
$43$			42.4974i			0.988311i	0.869374	+	0.494155i	$0.164523\pi$
$43$			42.4974i			0.988311i	−0.869374	+	0.494155i	$0.835477\pi$
$44$	37.2727	−	52.6767i	0.847106	−	1.19720i
$45$		0			0
$46$	−4.90739	+	15.4316i	−0.106682	+	0.335470i
$47$		−	48.6891i		−	1.03594i	−0.855399	−	0.517969i	$-0.826688\pi$
$47$		−	48.6891i		−	1.03594i	0.855399	−	0.517969i	$-0.173312\pi$
$48$		0			0
$49$	21.8802	−	43.8435i	0.446535	−	0.894766i
$50$	3.44193	−	10.8234i	0.0688386	−	0.216468i
$51$		0			0
$52$	46.2114	+	32.6980i	0.888680	+	0.628808i
$53$			77.1902i			1.45642i	0.685355	+	0.728209i	$0.259647\pi$
$53$			77.1902i			1.45642i	−0.685355	+	0.728209i	$0.740353\pi$
$54$		0			0
$55$			89.3549i			1.62464i
$56$	20.2366	−	52.2157i	0.361367	−	0.932424i
$57$		0			0
$58$	11.2741	+	3.58527i	0.194381	+	0.0618149i
$59$	40.7234			0.690228			0.345114	−	0.938561i	$-0.387840\pi$
$59$	40.7234			0.690228			0.345114	+	0.938561i	$0.387840\pi$
$60$		0			0
$61$	10.9064			0.178794			0.0893969	−	0.995996i	$-0.471506\pi$
$61$	10.9064			0.178794			0.0893969	+	0.995996i	$0.471506\pi$
$62$	51.5284	+	16.3865i	0.831103	+	0.264298i
$63$		0			0
$64$	17.4762	−	61.5677i	0.273066	−	0.961995i
$65$	−78.3879			−1.20597
$66$		0			0
$67$			116.132i			1.73331i	0.498909	+	0.866655i	$0.333734\pi$
$67$			116.132i			1.73331i	−0.498909	+	0.866655i	$0.666266\pi$
$68$	17.2727	−	24.4111i	0.254010	−	0.358987i
$69$		0			0
$70$	18.8883	+	75.2081i	0.269833	+	1.07440i
$71$	104.767			1.47560			0.737799	−	0.675021i	$-0.235865\pi$
$71$	104.767			1.47560			0.737799	+	0.675021i	$0.235865\pi$
$72$		0			0
$73$		−	82.8647i		−	1.13513i	−0.823328	−	0.567566i	$-0.807885\pi$
$73$		−	82.8647i		−	1.13513i	0.823328	−	0.567566i	$-0.192115\pi$
$74$	−39.1444	−	12.4483i	−0.528979	−	0.168220i
$75$		0			0
$76$	93.3487	+	66.0512i	1.22827	+	0.869094i
$77$	−59.4057	−	96.0389i	−0.771502	−	1.24726i
$78$		0			0
$79$	−44.7667			−0.566667			−0.283333	−	0.959022i	$-0.591440\pi$
$79$	−44.7667			−0.566667			−0.283333	+	0.959022i	$0.591440\pi$
$80$	29.4883	+	83.5715i	0.368604	+	1.04464i
$81$		0			0
$82$	−93.6002	−	29.7657i	−1.14147	−	0.362996i
$83$	−65.8500			−0.793374			−0.396687	−	0.917954i	$-0.629840\pi$
$83$	−65.8500			−0.793374			−0.396687	+	0.917954i	$0.629840\pi$
$84$		0			0
$85$			41.4083i			0.487157i
$86$	80.9977	+	25.7580i	0.941834	+	0.299512i
$87$		0			0
$88$	−77.8076	−	102.968i	−0.884178	−	1.17009i
$89$			134.189i			1.50774i	0.657025	+	0.753869i	$0.271815\pi$
$89$			134.189i			1.50774i	−0.657025	+	0.753869i	$0.728185\pi$
$90$		0			0
$91$	84.2515	−	52.1145i	0.925841	−	0.572687i
$92$	26.4374	+	18.7065i	0.287363	+	0.203331i
$93$		0			0
$94$	−92.7989	−	29.5109i	−0.987222	−	0.313945i
$95$	−158.346			−1.66680
$96$		0			0
$97$			37.4629i			0.386215i	0.981178	+	0.193107i	$0.0618566\pi$
$97$			37.4629i			0.386215i	−0.981178	+	0.193107i	$0.938143\pi$
$98$	−70.3017	−	68.2764i	−0.717364	−	0.696698i
$99$		0			0
$100$	−18.5426	−	13.1203i	−0.185426	−	0.131203i
$101$	140.538			1.39147			0.695734	−	0.718299i	$-0.255079\pi$
$101$	140.538			1.39147			0.695734	+	0.718299i	$0.255079\pi$
$102$		0			0
$103$		−	198.347i		−	1.92570i	−0.270033	−	0.962851i	$-0.587035\pi$
$103$		−	198.347i		−	1.92570i	0.270033	−	0.962851i	$-0.412965\pi$
$104$	90.3297	−	68.2579i	0.868555	−	0.656326i
$105$		0			0
$106$	147.120	+	46.7856i	1.38793	+	0.441374i
$107$			21.1655i			0.197809i	0.995097	+	0.0989044i	$0.0315338\pi$
$107$			21.1655i			0.197809i	−0.995097	+	0.0989044i	$0.968466\pi$
$108$		0			0
$109$		−	107.388i		−	0.985210i	−0.870253	−	0.492605i	$-0.836045\pi$
$109$		−	107.388i		−	0.985210i	0.870253	−	0.492605i	$-0.163955\pi$
$110$	170.306	+	54.1587i	1.54823	+	0.492352i
$111$		0			0
$112$	−87.2548	−	70.2182i	−0.779061	−	0.626948i
$113$	−112.913			−0.999234			−0.499617	−	0.866247i	$-0.666526\pi$
$113$	−112.913			−0.999234			−0.499617	+	0.866247i	$0.666526\pi$
$114$		0			0
$115$	−44.8455			−0.389961
$116$	13.6667	−	19.3148i	0.117816	−	0.166507i
$117$		0			0
$118$	24.6828	−	77.6167i	0.209176	−	0.657769i
$119$	−27.5294	−	44.5058i	−0.231340	−	0.373998i
$120$		0			0
$121$	−139.255			−1.15087
$122$	6.61047	−	20.7871i	0.0541842	−	0.170386i
$123$		0			0
$124$	62.4635	−	88.2784i	0.503738	−	0.711922i
$125$	−107.017			−0.856139
$126$		0			0
$127$	166.247			1.30903			0.654515	−	0.756049i	$-0.272873\pi$
$127$	166.247			1.30903			0.654515	+	0.756049i	$0.272873\pi$
$128$	−106.752	−	70.6254i	−0.834002	−	0.551761i
$129$		0			0
$130$	−47.5115	+	149.403i	−0.365473	+	1.14926i
$131$	−156.297			−1.19311			−0.596553	−	0.802574i	$-0.703464\pi$
$131$	−156.297			−1.19311			−0.596553	+	0.802574i	$0.703464\pi$
$132$		0			0
$133$	170.191	−	105.273i	1.27963	−	0.791528i
$134$	221.341	+	70.3884i	1.65180	+	0.525286i
$135$		0			0
$136$	−36.0572	−	47.7166i	−0.265126	−	0.350857i
$137$	−68.1911			−0.497746			−0.248873	−	0.968536i	$-0.580060\pi$
$137$	−68.1911			−0.497746			−0.248873	+	0.968536i	$0.580060\pi$
$138$		0			0
$139$	−190.458			−1.37020			−0.685101	−	0.728448i	$-0.740242\pi$
$139$	−190.458			−1.37020			−0.685101	+	0.728448i	$0.740242\pi$
$140$	154.791	+	9.58417i	1.10565	+	0.0684584i
$141$		0			0
$142$	63.5004	−	199.681i	0.447186	−	1.40621i
$143$		−	228.313i		−	1.59659i
$144$		0			0
$145$			32.7635i			0.225955i
$146$	−157.936	−	50.2250i	−1.08175	−	0.344007i
$147$		0			0
$148$	−47.4515	+	67.0622i	−0.320619	+	0.453123i
$149$		−	41.6094i		−	0.279257i	−0.990204	−	0.139629i	$-0.955409\pi$
$149$		−	41.6094i		−	0.279257i	0.990204	−	0.139629i	$-0.0445909\pi$
$150$		0			0
$151$	−149.930			−0.992914			−0.496457	−	0.868061i	$-0.665366\pi$
$151$	−149.930			−0.992914			−0.496457	+	0.868061i	$0.665366\pi$
$152$	182.469	−	137.883i	1.20046	−	0.907128i
$153$		0			0
$154$	−219.051	+	55.0141i	−1.42241	+	0.357234i
$155$			149.746i			0.966102i
$156$		0			0
$157$	−81.7752			−0.520861			−0.260431	−	0.965493i	$-0.583865\pi$
$157$	−81.7752			−0.520861			−0.260431	+	0.965493i	$0.583865\pi$
$158$	−27.1334	+	85.3229i	−0.171731	+	0.540018i
$159$		0			0
$160$	177.156	−	5.54985i	1.10722	−	0.0346866i
$161$	48.2001	−	29.8146i	0.299380	−	0.185184i
$162$		0			0
$163$			275.383i			1.68946i	0.535190	+	0.844732i	$0.320240\pi$
$163$			275.383i			1.68946i	−0.535190	+	0.844732i	$0.679760\pi$
$164$	−113.464	+	160.356i	−0.691852	+	0.977779i
$165$		0			0
$166$	−39.9122	+	125.507i	−0.240435	+	0.756064i
$167$			263.827i			1.57980i	0.613233	+	0.789902i	$0.289868\pi$
$167$			263.827i			1.57980i	−0.613233	+	0.789902i	$0.710132\pi$
$168$		0			0
$169$	31.2906			0.185152
$170$	78.9221	+	25.0979i	0.464248	+	0.147635i
$171$		0			0
$172$	98.1867	−	138.765i	0.570853	−	0.806774i
$173$	54.6502			0.315897			0.157949	−	0.987447i	$-0.449512\pi$
$173$	54.6502			0.315897			0.157949	+	0.987447i	$0.449512\pi$
$174$		0			0
$175$	−33.8064	+	20.9113i	−0.193180	+	0.119493i
$176$	−243.410	+	85.8878i	−1.38301	+	0.487999i
$177$		0			0
$178$	255.756	+	81.3328i	1.43683	+	0.456926i
$179$			105.555i			0.589691i	0.955545	+	0.294845i	$0.0952681\pi$
$179$			105.555i			0.589691i	−0.955545	+	0.294845i	$0.904732\pi$
$180$		0			0
$181$	135.753			0.750018			0.375009	−	0.927021i	$-0.377640\pi$
$181$	135.753			0.750018			0.375009	+	0.927021i	$0.377640\pi$
$182$	−48.2619	−	192.166i	−0.265175	−	1.05586i
$183$		0			0
$184$	51.6774	−	39.0502i	0.280856	−	0.212229i
$185$		−	113.757i		−	0.614903i
$186$		0			0
$187$	−120.606			−0.644952
$188$	−112.492	+	158.983i	−0.598363	+	0.845654i
$189$		0			0
$190$	−95.9751	+	301.800i	−0.505132	+	1.58842i
$191$	−21.5720			−0.112943			−0.0564713	−	0.998404i	$-0.517985\pi$
$191$	−21.5720			−0.112943			−0.0564713	+	0.998404i	$0.517985\pi$
$192$		0			0
$193$	−318.072			−1.64804			−0.824021	−	0.566560i	$-0.808274\pi$
$193$	−318.072			−1.64804			−0.824021	+	0.566560i	$0.808274\pi$
$194$	71.4022	+	22.7065i	0.368053	+	0.117044i
$195$		0			0
$196$	−172.742	+	92.6084i	−0.881335	+	0.472492i
$197$			0.244515i			0.00124119i	1.00000		0.000620597i	$0.000197542\pi$
$197$			0.244515i			0.00124119i	−1.00000		0.000620597i	$0.999802\pi$
$198$		0			0
$199$			236.282i			1.18735i	0.804706	+	0.593674i	$0.202323\pi$
$199$			236.282i			1.18735i	−0.804706	+	0.593674i	$0.797677\pi$
$200$	−36.2454	+	27.3889i	−0.181227	+	0.136944i
$201$		0			0
$202$	85.1814	−	267.859i	0.421690	−	1.32603i
$203$	−21.7821	−	35.2143i	−0.107301	−	0.173469i
$204$		0			0
$205$		−	272.010i		−	1.32688i
$206$	−378.039	−	120.220i	−1.83514	−	0.583592i
$207$		0			0
$208$	−75.3463	−	213.535i	−0.362242	−	1.02661i
$209$		−	461.200i		−	2.20670i
$210$		0			0
$211$			100.465i			0.476140i	0.971248	+	0.238070i	$0.0765147\pi$
$211$			100.465i			0.476140i	−0.971248	+	0.238070i	$0.923485\pi$
$212$	178.342	−	252.046i	0.841234	−	1.18890i
$213$		0			0
$214$	40.3404	+	12.8286i	0.188506	+	0.0599467i
$215$			235.386i			1.09482i
$216$		0			0
$217$	−99.5552	−	160.947i	−0.458780	−	0.741692i
$218$	−204.676	−	65.0887i	−0.938879	−	0.298572i
$219$		0			0
$220$	206.447	−	291.768i	0.938397	−	1.32622i
$221$		−	105.803i		−	0.478748i
$222$		0			0
$223$		−	378.232i		−	1.69611i	−0.529912	−	0.848053i	$-0.677775\pi$
$223$		−	378.232i		−	1.69611i	0.529912	−	0.848053i	$-0.322225\pi$
$224$	−186.718	+	123.743i	−0.833562	+	0.552425i
$225$		0			0
$226$	−68.4377	+	215.207i	−0.302822	+	0.952243i
$227$	56.6476			0.249549			0.124774	−	0.992185i	$-0.460179\pi$
$227$	56.6476			0.249549			0.124774	+	0.992185i	$0.460179\pi$
$228$		0			0
$229$	296.565			1.29504			0.647522	−	0.762047i	$-0.275805\pi$
$229$	296.565			1.29504			0.647522	+	0.762047i	$0.275805\pi$
$230$	−27.1813	+	85.4732i	−0.118179	+	0.371623i
$231$		0			0
$232$	−28.5295	−	37.7548i	−0.122972	−	0.162736i
$233$	112.373			0.482289			0.241145	−	0.970489i	$-0.422477\pi$
$233$	112.373			0.482289			0.241145	+	0.970489i	$0.422477\pi$
$234$		0			0
$235$		−	269.681i		−	1.14758i
$236$	−132.973	−	94.0883i	−0.563444	−	0.398679i
$237$		0			0
$238$	−101.511	+	25.4943i	−0.426519	+	0.107119i
$239$	94.4921			0.395364			0.197682	−	0.980266i	$-0.436659\pi$
$239$	94.4921			0.395364			0.197682	+	0.980266i	$0.436659\pi$
$240$		0			0
$241$			87.7294i			0.364022i	0.983296	+	0.182011i	$0.0582607\pi$
$241$			87.7294i			0.364022i	−0.983296	+	0.182011i	$0.941739\pi$
$242$	−84.4037	+	265.413i	−0.348776	+	1.09675i
$243$		0			0
$244$	−35.6124	−	25.1984i	−0.145952	−	0.103272i
$245$	121.191	−	242.842i	0.494657	−	0.991193i
$246$		0			0
$247$	404.594			1.63803
$248$	−130.394	−	172.558i	−0.525783	−	0.695800i
$249$		0			0
$250$	−64.8641	+	203.969i	−0.259456	+	0.815878i
$251$	344.939			1.37426			0.687130	−	0.726534i	$-0.258870\pi$
$251$	344.939			1.37426			0.687130	+	0.726534i	$0.258870\pi$
$252$		0			0
$253$		−	130.617i		−	0.516273i
$254$	100.764	−	316.858i	0.396707	−	1.24747i
$255$		0			0
$256$	−199.312	+	160.658i	−0.778561	+	0.627568i
$257$			75.7961i			0.294927i	0.989068	+	0.147463i	$0.0471108\pi$
$257$			75.7961i			0.294927i	−0.989068	+	0.147463i	$0.952889\pi$
$258$		0			0
$259$	75.6289	+	122.266i	0.292003	+	0.472071i
$260$	255.957	+	181.109i	0.984451	+	0.696573i
$261$		0			0
$262$	−94.7328	+	297.894i	−0.361576	+	1.13700i
$263$	19.8005			0.0752872			0.0376436	−	0.999291i	$-0.488015\pi$
$263$	19.8005			0.0752872			0.0376436	+	0.999291i	$0.488015\pi$
$264$		0			0
$265$			427.544i			1.61337i
$266$	−97.4908	−	388.182i	−0.366507	−	1.45933i
$267$		0			0
$268$	268.313	−	379.201i	1.00117	−	1.41493i
$269$	185.601			0.689966			0.344983	−	0.938609i	$-0.387885\pi$
$269$	185.601			0.689966			0.344983	+	0.938609i	$0.387885\pi$
$270$		0			0
$271$			138.260i			0.510185i	0.966917	+	0.255093i	$0.0821059\pi$
$271$			138.260i			0.510185i	−0.966917	+	0.255093i	$0.917894\pi$
$272$	−112.800	+	39.8016i	−0.414705	+	0.146329i
$273$		0			0
$274$	−41.3312	+	129.969i	−0.150844	+	0.474338i
$275$			91.6119i			0.333134i
$276$		0			0
$277$			110.650i			0.399457i	0.979851	+	0.199728i	$0.0640060\pi$
$277$			110.650i			0.399457i	−0.979851	+	0.199728i	$0.935994\pi$
$278$	−115.438	+	363.003i	−0.415245	+	1.30577i
$279$		0			0
$280$	112.087	−	289.214i	0.400311	−	1.03291i
$281$	531.686			1.89212			0.946061	−	0.323989i	$-0.105024\pi$
$281$	531.686			1.89212			0.946061	+	0.323989i	$0.105024\pi$
$282$		0			0
$283$	−439.139			−1.55173			−0.775864	−	0.630900i	$-0.782686\pi$
$283$	−439.139			−1.55173			−0.775864	+	0.630900i	$0.782686\pi$
$284$	−342.094	−	242.057i	−1.20455	−	0.852313i
$285$		0			0
$286$	−435.152	−	138.382i	−1.52151	−	0.483854i
$287$	180.840	+	292.357i	0.630104	+	1.01867i
$288$		0			0
$289$	233.109			0.806607
$290$	62.4454	+	19.8582i	0.215329	+	0.0684766i
$291$		0			0
$292$	−191.452	+	270.575i	−0.655658	+	0.926627i
$293$	122.938			0.419585			0.209793	−	0.977746i	$-0.432721\pi$
$293$	122.938			0.419585			0.209793	+	0.977746i	$0.432721\pi$
$294$		0			0
$295$	225.561			0.764612
$296$	99.0563	+	131.087i	0.334650	+	0.442862i
$297$		0			0
$298$	−79.3052	−	25.2198i	−0.266125	−	0.0846301i
$299$	114.586			0.383230
$300$		0			0
$301$	−156.491	−	252.994i	−0.519905	−	0.840510i
$302$	−90.8738	+	285.759i	−0.300907	+	0.946221i
$303$		0			0
$304$	−152.202	−	431.349i	−0.500666	−	1.41891i
$305$	60.4089			0.198062
$306$		0			0
$307$	5.82104			0.0189611			0.00948053	−	0.999955i	$-0.496982\pi$
$307$	5.82104			0.0189611			0.00948053	+	0.999955i	$0.496982\pi$
$308$	−27.9149	+	450.845i	−0.0906327	+	1.46378i
$309$		0			0
$310$	285.407	+	90.7621i	0.920669	+	0.292781i
$311$		−	208.552i		−	0.670585i	−0.942114	−	0.335293i	$-0.891165\pi$
$311$		−	208.552i		−	0.670585i	0.942114	−	0.335293i	$-0.108835\pi$
$312$		0			0
$313$			25.0482i			0.0800261i	0.999199	+	0.0400130i	$0.0127399\pi$
$313$			25.0482i			0.0800261i	−0.999199	+	0.0400130i	$0.987260\pi$
$314$	−49.5646	+	155.859i	−0.157849	+	0.496367i
$315$		0			0
$316$	146.175	+	103.430i	0.462579	+	0.327309i
$317$			172.733i			0.544899i	0.962170	+	0.272449i	$0.0878338\pi$
$317$			172.733i			0.544899i	−0.962170	+	0.272449i	$0.912166\pi$
$318$		0			0
$319$	−95.4269			−0.299144
$320$	96.7979	−	341.014i	0.302494	−	1.06567i
$321$		0			0
$322$	−27.6105	−	109.938i	−0.0857470	−	0.341421i
$323$		−	213.727i		−	0.661692i
$324$		0			0
$325$	−80.3678			−0.247286
$326$	524.865	+	166.912i	1.61001	+	0.511999i
$327$		0			0
$328$	236.858	+	313.449i	0.722129	+	0.955636i
$329$	179.292	+	289.854i	0.544959	+	0.881015i
$330$		0			0
$331$			285.098i			0.861323i	0.902513	+	0.430662i	$0.141720\pi$
$331$			285.098i			0.861323i	−0.902513	+	0.430662i	$0.858280\pi$
$332$	215.018	+	152.141i	0.647644	+	0.458257i
$333$		0			0
$334$	502.841	+	159.908i	1.50551	+	0.478766i
$335$			643.235i			1.92010i
$336$		0			0
$337$	507.150			1.50490			0.752448	−	0.658652i	$-0.228873\pi$
$337$	507.150			1.50490			0.752448	+	0.658652i	$0.228873\pi$
$338$	18.9655	−	59.6382i	0.0561109	−	0.176445i
$339$		0			0
$340$	95.6706	−	135.209i	0.281384	−	0.397674i
$341$	−436.150			−1.27903
$342$		0			0
$343$	31.1921	+	341.579i	0.0909391	+	0.995856i
$344$	−204.967	−	271.245i	−0.595835	−	0.788504i
$345$		0			0
$346$	33.1239	−	104.160i	0.0957339	−	0.301042i
$347$		−	4.14103i		−	0.0119338i	−0.999982	−	0.00596691i	$-0.998101\pi$
$347$		−	4.14103i		−	0.0119338i	0.999982	−	0.00596691i	$-0.00189934\pi$
$348$		0			0
$349$	−231.206			−0.662481			−0.331240	−	0.943546i	$-0.607467\pi$
$349$	−231.206			−0.662481			−0.331240	+	0.943546i	$0.607467\pi$
$350$	19.3654	+	77.1078i	0.0553297	+	0.220308i
$351$		0			0
$352$	16.1645	+	515.985i	0.0459219	+	1.46587i
$353$			543.259i			1.53898i	0.638660	+	0.769489i	$0.279489\pi$
$353$			543.259i			1.53898i	−0.638660	+	0.769489i	$0.720511\pi$
$354$		0			0
$355$	580.290			1.63462
$356$	310.032	−	438.162i	0.870877	−	1.23079i
$357$		0			0
$358$	201.182	+	63.9775i	0.561960	+	0.178708i
$359$	−270.411			−0.753235			−0.376618	−	0.926369i	$-0.622913\pi$
$359$	−270.411			−0.753235			−0.376618	+	0.926369i	$0.622913\pi$
$360$		0			0
$361$	456.296			1.26398
$362$	82.2811	−	258.738i	0.227296	−	0.714747i
$363$		0			0
$364$	−395.510	−	24.4887i	−1.08657	−	0.0672767i
$365$		−	458.974i		−	1.25746i
$366$		0			0
$367$			192.315i			0.524019i	0.965065	+	0.262010i	$0.0843852\pi$
$367$			192.315i			0.524019i	−0.965065	+	0.262010i	$0.915615\pi$
$368$	−43.1055	−	122.163i	−0.117134	−	0.331965i
$369$		0			0
$370$	−216.815	−	68.9491i	−0.585986	−	0.186349i
$371$	−284.243	−	459.525i	−0.766154	−	1.23861i
$372$		0			0
$373$			73.8655i			0.198031i	0.995086	+	0.0990155i	$0.0315693\pi$
$373$			73.8655i			0.198031i	−0.995086	+	0.0990155i	$0.968431\pi$
$374$	−73.1003	+	229.869i	−0.195455	+	0.614622i
$375$		0			0
$376$	234.830	+	310.765i	0.624549	+	0.826503i
$377$		−	83.7147i		−	0.222055i
$378$		0			0
$379$			10.9952i			0.0290111i	0.999895	+	0.0145056i	$0.00461742\pi$
$379$			10.9952i			0.0290111i	−0.999895	+	0.0145056i	$0.995383\pi$
$380$	517.043	+	365.847i	1.36064	+	0.962755i
$381$		0			0
$382$	−13.0750	+	41.1152i	−0.0342277	+	0.107631i
$383$		−	557.586i		−	1.45584i	−0.685663	−	0.727919i	$-0.740488\pi$
$383$		−	557.586i		−	1.45584i	0.685663	−	0.727919i	$-0.259512\pi$
$384$		0			0
$385$	−329.038	−	531.944i	−0.854645	−	1.38167i
$386$	−192.786	+	606.228i	−0.499446	+	1.57054i
$387$		0			0
$388$	86.5549	−	122.326i	0.223080	−	0.315274i
$389$		−	41.0393i		−	0.105499i	−0.998608	−	0.0527497i	$-0.983201\pi$
$389$		−	41.0393i		−	0.105499i	0.998608	−	0.0527497i	$-0.0167986\pi$
$390$		0			0
$391$		−	60.5299i		−	0.154808i
$392$	71.8065	+	385.367i	0.183180	+	0.983079i
$393$		0			0
$394$	0.466033	+	0.148203i	0.00118283	+	0.000376149i
$395$	−247.955			−0.627735
$396$		0			0
$397$	228.169			0.574733			0.287366	−	0.957821i	$-0.407220\pi$
$397$	228.169			0.574733			0.287366	+	0.957821i	$0.407220\pi$
$398$	450.341	+	143.212i	1.13151	+	0.359830i
$399$		0			0
$400$	30.2332	+	85.6823i	0.0755829	+	0.214206i
$401$	−582.508			−1.45264			−0.726319	−	0.687357i	$-0.758771\pi$
$401$	−582.508			−1.45264			−0.726319	+	0.687357i	$0.758771\pi$
$402$		0			0
$403$		−	382.619i		−	0.949426i
$404$	−458.895	−	324.702i	−1.13588	−	0.803719i
$405$		0			0
$406$	−80.3188	+	20.1718i	−0.197830	+	0.0496843i
$407$	331.329			0.814076
$408$		0			0
$409$			4.68899i			0.0114645i	0.999984	+	0.00573226i	$0.00182465\pi$
$409$			4.68899i			0.0114645i	−0.999984	+	0.00573226i	$0.998175\pi$
$410$	−518.437	−	164.867i	−1.26448	−	0.402116i
$411$		0			0
$412$	−458.265	+	647.657i	−1.11229	+	1.57198i
$413$	−242.433	+	149.959i	−0.587005	+	0.363097i
$414$		0			0
$415$	−364.733			−0.878874
$416$	−452.655	+	14.1806i	−1.08811	+	0.0340879i
$417$		0			0
$418$	−879.023	−	279.537i	−2.10293	−	0.668749i
$419$	105.256			0.251208			0.125604	−	0.992080i	$-0.459913\pi$
$419$	105.256			0.251208			0.125604	+	0.992080i	$0.459913\pi$
$420$		0			0
$421$			619.528i			1.47156i	0.677220	+	0.735781i	$0.263185\pi$
$421$			619.528i			1.47156i	−0.677220	+	0.735781i	$0.736815\pi$
$422$	191.482	+	60.8929i	0.453748	+	0.144296i
$423$		0			0
$424$	−372.293	−	492.677i	−0.878049	−	1.16197i
$425$			42.4542i			0.0998923i
$426$		0			0
$427$	−64.9277	+	40.1616i	−0.152055	+	0.0940552i
$428$	48.9013	−	69.1111i	0.114255	−	0.161475i
$429$		0			0
$430$	448.633	+	142.669i	1.04333	+	0.331789i
$431$	438.654			1.01776			0.508879	−	0.860838i	$-0.330060\pi$
$431$	438.654			1.01776			0.508879	+	0.860838i	$0.330060\pi$
$432$		0			0
$433$		−	43.0393i		−	0.0993979i	−0.998764	−	0.0496990i	$-0.984174\pi$
$433$		−	43.0393i		−	0.0993979i	0.998764	−	0.0496990i	$-0.0158262\pi$
$434$	−367.098	+	92.1956i	−0.845848	+	0.212432i
$435$		0			0
$436$	−248.111	+	350.650i	−0.569062	+	0.804243i
$437$	231.468			0.529674
$438$		0			0
$439$		−	206.214i		−	0.469736i	−0.972027	−	0.234868i	$-0.924534\pi$
$439$		−	206.214i		−	0.469736i	0.972027	−	0.234868i	$-0.0754658\pi$
$440$	−430.964	−	570.320i	−0.979464	−	1.29618i
$441$		0			0
$442$	−201.656	−	64.1283i	−0.456234	−	0.145087i
$443$			611.291i			1.37989i	0.723862	+	0.689945i	$0.242365\pi$
$443$			611.291i			1.37989i	−0.723862	+	0.689945i	$0.757635\pi$
$444$		0			0
$445$			743.249i			1.67022i
$446$	−720.889	−	229.249i	−1.61634	−	0.514012i
$447$		0			0
$448$	122.677	+	430.876i	0.273832	+	0.961778i
$449$	597.695			1.33117			0.665585	−	0.746322i	$-0.268182\pi$
$449$	597.695			1.33117			0.665585	+	0.746322i	$0.268182\pi$
$450$		0			0
$451$	792.257			1.75667
$452$	368.692	+	260.877i	0.815691	+	0.577162i
$453$		0			0
$454$	34.3345	−	107.967i	0.0756268	−	0.237813i
$455$	466.656	−	288.654i	1.02562	−	0.634404i
$456$		0			0
$457$	−350.459			−0.766868			−0.383434	−	0.923568i	$-0.625259\pi$
$457$	−350.459			−0.766868			−0.383434	+	0.923568i	$0.625259\pi$
$458$	179.750	−	565.237i	0.392468	−	1.23414i
$459$		0			0
$460$	146.433	+	103.612i	0.318332	+	0.225244i
$461$	−182.865			−0.396671			−0.198335	−	0.980134i	$-0.563553\pi$
$461$	−182.865			−0.396671			−0.198335	+	0.980134i	$0.563553\pi$
$462$		0			0
$463$	62.8699			0.135788			0.0678941	−	0.997693i	$-0.478372\pi$
$463$	62.8699			0.135788			0.0678941	+	0.997693i	$0.478372\pi$
$464$	−89.2505	+	31.4922i	−0.192350	+	0.0678711i
$465$		0			0
$466$	68.1104	−	214.178i	0.146160	−	0.459609i
$467$	−645.253			−1.38170			−0.690849	−	0.722999i	$-0.742763\pi$
$467$	−645.253			−1.38170			−0.690849	+	0.722999i	$0.742763\pi$
$468$		0			0
$469$	−427.641	−	691.350i	−0.911814	−	1.47409i
$470$	−513.998	−	163.456i	−1.09361	−	0.347779i
$471$		0			0
$472$	−259.923	+	196.412i	−0.550685	+	0.416126i
$473$	−685.586			−1.44944
$474$		0			0
$475$	−162.346			−0.341781
$476$	−12.9361	+	208.928i	−0.0271768	+	0.438924i
$477$		0			0
$478$	57.2724	−	180.097i	0.119817	−	0.376772i
$479$		−	437.654i		−	0.913684i	−0.889548	−	0.456842i	$-0.848981\pi$
$479$		−	437.654i		−	0.913684i	0.889548	−	0.456842i	$-0.151019\pi$
$480$		0			0
$481$			290.663i			0.604289i
$482$	167.208	+	53.1735i	0.346904	+	0.110318i
$483$		0			0
$484$	454.705	+	321.738i	0.939474	+	0.664748i
$485$			207.501i			0.427837i
$486$		0			0
$487$	−14.7391			−0.0302650			−0.0151325	−	0.999885i	$-0.504817\pi$
$487$	−14.7391			−0.0302650			−0.0151325	+	0.999885i	$0.504817\pi$
$488$	−69.6118	+	52.6023i	−0.142647	+	0.107792i
$489$		0			0
$490$	−389.390	−	378.172i	−0.794673	−	0.771780i
$491$		−	120.149i		−	0.244702i	−0.992487	−	0.122351i	$-0.960957\pi$
$491$		−	120.149i		−	0.244702i	0.992487	−	0.122351i	$-0.0390434\pi$
$492$		0			0
$493$	−44.2222			−0.0897002
$494$	245.228	−	771.135i	0.496413	−	1.56100i
$495$		0			0
$496$	−407.920	+	143.935i	−0.822420	+	0.290192i
$497$	−623.697	+	385.793i	−1.25492	+	0.776244i
$498$		0			0
$499$		−	4.70185i		−	0.00942254i	−0.999989	−	0.00471127i	$-0.998500\pi$
$499$		−	4.70185i		−	0.00942254i	0.999989	−	0.00471127i	$-0.00149965\pi$
$500$	349.440	+	247.255i	0.698880	+	0.494510i
$501$		0			0
$502$	209.071	−	657.436i	0.416475	−	1.30963i
$503$		−	112.427i		−	0.223512i	−0.993736	−	0.111756i	$-0.964352\pi$
$503$		−	112.427i		−	0.223512i	0.993736	−	0.111756i	$-0.0356475\pi$
$504$		0			0
$505$	778.419			1.54142
$506$	−248.949	−	79.1681i	−0.491995	−	0.156459i
$507$		0			0
$508$	−542.840	−	384.100i	−1.06858	−	0.756102i
$509$	764.966			1.50288			0.751440	−	0.659801i	$-0.229360\pi$
$509$	764.966			1.50288			0.751440	+	0.659801i	$0.229360\pi$
$510$		0			0
$511$	305.139	+	493.307i	0.597141	+	0.965375i
$512$	185.400	+	477.253i	0.362110	+	0.932135i
$513$		0			0
$514$	144.463	+	45.9406i	0.281057	+	0.0893787i
$515$		−	1098.61i		−	2.13323i
$516$		0			0
$517$	785.474			1.51929
$518$	278.872	−	70.0380i	0.538364	−	0.135208i
$519$		0			0
$520$	500.322	−	378.069i	0.962157	−	0.727057i
$521$			993.978i			1.90783i	0.300083	+	0.953913i	$0.402986\pi$
$521$			993.978i			1.90783i	−0.300083	+	0.953913i	$0.597014\pi$
$522$		0			0
$523$	−460.338			−0.880188			−0.440094	−	0.897952i	$-0.645055\pi$
$523$	−460.338			−0.880188			−0.440094	+	0.897952i	$0.645055\pi$
$524$	510.351	+	361.111i	0.973952	+	0.689144i
$525$		0			0
$526$	12.0013	−	37.7388i	0.0228161	−	0.0717467i
$527$	−202.118			−0.383525
$528$		0			0
$529$	−463.446			−0.876079
$530$	814.876	+	259.138i	1.53750	+	0.488939i
$531$		0			0
$532$	−798.945	−	49.4681i	−1.50178	−	0.0929852i
$533$			695.019i			1.30397i
$534$		0			0
$535$			117.232i			0.219126i
$536$	−560.110	−	741.227i	−1.04498	−	1.38289i
$537$		0			0
$538$	112.494	−	353.745i	0.209097	−	0.657519i
$539$	707.303	+	352.981i	1.31225	+	0.654881i
$540$		0			0
$541$			411.334i			0.760321i	0.924921	+	0.380160i	$0.124131\pi$
$541$			411.334i			0.760321i	−0.924921	+	0.380160i	$0.875869\pi$
$542$	263.516	+	83.8006i	0.486193	+	0.154614i
$543$		0			0
$544$	7.49086	+	239.115i	0.0137700	+	0.439549i
$545$		−	594.804i		−	1.09138i
$546$		0			0
$547$			30.2891i			0.0553732i	0.999617	+	0.0276866i	$0.00881404\pi$
$547$			30.2891i			0.0553732i	−0.999617	+	0.0276866i	$0.991186\pi$
$548$	222.662	+	157.550i	0.406318	+	0.287500i
$549$		0			0
$550$	174.607	+	55.5267i	0.317468	+	0.100958i
$551$		−	169.107i		−	0.306909i
$552$		0			0
$553$	266.503	−	164.848i	0.481922	−	0.298097i
$554$	210.892	+	67.0656i	0.380672	+	0.121057i
$555$		0			0
$556$	621.896	+	440.038i	1.11852	+	0.791435i
$557$			763.819i			1.37131i	0.727927	+	0.685655i	$0.240484\pi$
$557$			763.819i			1.37131i	−0.727927	+	0.685655i	$0.759516\pi$
$558$		0			0
$559$		−	601.440i		−	1.07592i
$560$	−483.291	−	388.927i	−0.863019	−	0.694513i
$561$		0			0
$562$	322.259	−	1013.37i	0.573415	−	1.80314i
$563$	−40.3472			−0.0716646			−0.0358323	−	0.999358i	$-0.511408\pi$
$563$	−40.3472			−0.0716646			−0.0358323	+	0.999358i	$0.511408\pi$
$564$		0			0
$565$	−625.409			−1.10692
$566$	−266.166	+	836.976i	−0.470258	+	1.47876i
$567$		0			0
$568$	−668.693	+	505.299i	−1.17728	+	0.889612i
$569$	−186.637			−0.328008			−0.164004	−	0.986460i	$-0.552441\pi$
$569$	−186.637			−0.328008			−0.164004	+	0.986460i	$0.552441\pi$
$570$		0			0
$571$		−	901.865i		−	1.57945i	−0.613462	−	0.789724i	$-0.710224\pi$
$571$		−	901.865i		−	1.57945i	0.613462	−	0.789724i	$-0.289776\pi$
$572$	−527.498	+	745.502i	−0.922200	+	1.30332i
$573$		0			0
$574$	666.826	−	167.471i	1.16172	−	0.291762i
$575$	−45.9783			−0.0799622
$576$		0			0
$577$		−	742.756i		−	1.28727i	−0.765332	−	0.643636i	$-0.777425\pi$
$577$		−	742.756i		−	1.28727i	0.765332	−	0.643636i	$-0.222575\pi$
$578$	141.290	−	444.294i	0.244446	−	0.768675i
$579$		0			0
$580$	75.6974	−	106.981i	0.130513	−	0.184451i
$581$	392.016	−	242.485i	0.674726	−	0.417357i
$582$		0			0
$583$	−1245.27			−2.13596
$584$	399.661	+	528.896i	0.684351	+	0.905643i
$585$		0			0
$586$	74.5140	−	234.314i	0.127157	−	0.399854i
$587$	514.288			0.876130			0.438065	−	0.898943i	$-0.355664\pi$
$587$	514.288			0.876130			0.438065	+	0.898943i	$0.355664\pi$
$588$		0			0
$589$		−	772.904i		−	1.31223i
$590$	136.714	−	429.907i	0.231719	−	0.728655i
$591$		0			0
$592$	309.884	−	109.343i	0.523452	−	0.184701i
$593$		−	466.087i		−	0.785982i	−0.919542	−	0.392991i	$-0.871440\pi$
$593$		−	466.087i		−	0.785982i	0.919542	−	0.392991i	$-0.128560\pi$
$594$		0			0
$595$	−152.481	−	246.510i	−0.256271	−	0.414303i
$596$	−96.1351	+	135.866i	−0.161300	+	0.227962i
$597$		0			0
$598$	69.4514	−	218.394i	0.116139	−	0.365208i
$599$	−947.796			−1.58230			−0.791149	−	0.611624i	$-0.790517\pi$
$599$	−947.796			−1.58230			−0.791149	+	0.611624i	$0.790517\pi$
$600$		0			0
$601$		−	153.107i		−	0.254754i	−0.991854	−	0.127377i	$-0.959344\pi$
$601$		−	153.107i		−	0.254754i	0.991854	−	0.127377i	$-0.0406559\pi$
$602$	−577.043	+	144.923i	−0.958543	+	0.240735i
$603$		0			0
$604$	489.561	+	346.401i	0.810532	+	0.573512i
$605$	−771.312			−1.27490
$606$		0			0
$607$		−	298.930i		−	0.492471i	−0.969210	−	0.246236i	$-0.920806\pi$
$607$		−	298.930i		−	0.492471i	0.969210	−	0.246236i	$-0.0791937\pi$
$608$	−914.380	+	28.6452i	−1.50391	+	0.0471139i
$609$		0			0
$610$	36.6143	−	115.136i	0.0600235	−	0.188748i
$611$			689.068i			1.12777i
$612$		0			0
$613$		−	291.497i		−	0.475525i	−0.971323	−	0.237762i	$-0.923586\pi$
$613$		−	291.497i		−	0.475525i	0.971323	−	0.237762i	$-0.0764140\pi$
$614$	3.52818	−	11.0946i	0.00574622	−	0.0180694i
$615$		0			0
$616$	842.366	+	326.465i	1.36748	+	0.529975i
$617$	359.433			0.582549			0.291275	−	0.956639i	$-0.405921\pi$
$617$	359.433			0.582549			0.291275	+	0.956639i	$0.405921\pi$
$618$		0			0
$619$	−57.2368			−0.0924666			−0.0462333	−	0.998931i	$-0.514722\pi$
$619$	−57.2368			−0.0924666			−0.0462333	+	0.998931i	$0.514722\pi$
$620$	345.976	−	488.960i	0.558025	−	0.788645i
$621$		0			0
$622$	−397.489	−	126.405i	−0.639050	−	0.203224i
$623$	−494.133	−	798.846i	−0.793151	−	1.28226i
$624$		0			0
$625$	−734.720			−1.17555
$626$	47.7405	+	15.1819i	0.0762627	+	0.0242522i
$627$		0			0
$628$	267.018	+	188.935i	0.425188	+	0.300852i
$629$	153.542			0.244106
$630$		0			0
$631$	−55.9357			−0.0886461			−0.0443230	−	0.999017i	$-0.514113\pi$
$631$	−55.9357			−0.0886461			−0.0443230	+	0.999017i	$0.514113\pi$
$632$	285.729	−	215.912i	0.452104	−	0.341633i
$633$		0			0
$634$	329.220	+	104.695i	0.519274	+	0.165134i
$635$	920.815			1.45010
$636$		0			0
$637$	−309.658	+	620.492i	−0.486119	+	0.974084i
$638$	−57.8390	+	181.879i	−0.0906568	+	0.285076i
$639$		0			0
$640$	−591.284	−	391.183i	−0.923881	−	0.611223i
$641$	459.772			0.717273			0.358636	−	0.933477i	$-0.383242\pi$
$641$	459.772			0.717273			0.358636	+	0.933477i	$0.383242\pi$
$642$		0			0
$643$	712.301			1.10778			0.553888	−	0.832591i	$-0.313143\pi$
$643$	712.301			1.10778			0.553888	+	0.832591i	$0.313143\pi$
$644$	−226.270	−	14.0099i	−0.351352	−	0.0217546i
$645$		0			0
$646$	−407.352	−	129.541i	−0.630575	−	0.200529i
$647$			10.9490i			0.0169228i	0.999964	+	0.00846139i	$0.00269338\pi$
$647$			10.9490i			0.0169228i	−0.999964	+	0.00846139i	$0.997307\pi$
$648$		0			0
$649$			656.968i			1.01228i
$650$	−48.7116	+	153.177i	−0.0749409	+	0.235657i
$651$		0			0
$652$	636.249	−	899.197i	0.975843	−	1.37914i
$653$		−	257.268i		−	0.393979i	−0.980406	−	0.196989i	$-0.936884\pi$
$653$		−	257.268i		−	0.393979i	0.980406	−	0.196989i	$-0.0631164\pi$
$654$		0			0
$655$	−865.704			−1.32168
$656$	740.978	−	261.455i	1.12954	−	0.398560i
$657$		0			0
$658$	661.116	−	166.037i	1.00474	−	0.252337i
$659$		−	1016.92i		−	1.54312i	−0.636157	−	0.771560i	$-0.719477\pi$
$659$		−	1016.92i		−	1.54312i	0.636157	−	0.771560i	$-0.280523\pi$
$660$		0			0
$661$	−740.204			−1.11982			−0.559912	−	0.828552i	$-0.689165\pi$
$661$	−740.204			−1.11982			−0.559912	+	0.828552i	$0.689165\pi$
$662$	543.382	+	172.800i	0.820818	+	0.261027i
$663$		0			0
$664$	420.297	−	317.599i	0.632978	−	0.478311i
$665$	942.662	−	583.091i	1.41754	−	0.876829i
$666$		0			0
$667$		−	47.8930i		−	0.0718036i
$668$	609.552	−	861.466i	0.912502	−	1.28962i
$669$		0			0
$670$	1225.97	+	389.870i	1.82981	+	0.581895i
$671$			175.947i			0.262216i
$672$		0			0
$673$	−1037.02			−1.54089			−0.770445	−	0.637506i	$-0.779966\pi$
$673$	−1037.02			−1.54089			−0.770445	+	0.637506i	$0.779966\pi$
$674$	307.388	−	966.601i	0.456065	−	1.43413i
$675$		0			0
$676$	−102.172	−	72.2945i	−0.151142	−	0.106944i
$677$	−809.104			−1.19513			−0.597566	−	0.801820i	$-0.703865\pi$
$677$	−809.104			−1.19513			−0.597566	+	0.801820i	$0.703865\pi$
$678$		0			0
$679$	−137.952	−	223.022i	−0.203170	−	0.328457i
$680$	−199.715	−	264.295i	−0.293698	−	0.388668i
$681$		0			0
$682$	−264.354	+	831.278i	−0.387616	+	1.21888i
$683$		−	306.279i		−	0.448432i	−0.974539	−	0.224216i	$-0.928018\pi$
$683$		−	306.279i		−	0.448432i	0.974539	−	0.224216i	$-0.0719822\pi$
$684$		0			0
$685$	−377.700			−0.551386
$686$	669.937	+	147.583i	0.976584	+	0.215136i
$687$		0			0
$688$	−641.212	+	226.253i	−0.931993	+	0.328856i
$689$		−	1092.43i		−	1.58553i
$690$		0			0
$691$	−77.2654			−0.111817			−0.0559084	−	0.998436i	$-0.517805\pi$
$691$	−77.2654			−0.111817			−0.0559084	+	0.998436i	$0.517805\pi$
$692$	−178.447	−	126.265i	−0.257872	−	0.182464i
$693$		0			0
$694$	−7.89259	−	2.50991i	−0.0113726	−	0.00361659i
$695$	−1054.92			−1.51787
$696$		0			0
$697$	367.143			0.526747
$698$	−140.136	+	440.666i	−0.200767	+	0.631326i
$699$		0			0
$700$	158.701	+	9.82625i	0.226715	+	0.0140375i
$701$		−	57.3914i		−	0.0818708i	−0.999162	−	0.0409354i	$-0.986966\pi$
$701$		−	57.3914i		−	0.0818708i	0.999162	−	0.0409354i	$-0.0130338\pi$
$702$		0			0
$703$			587.150i			0.835206i
$704$	993.237	+	281.934i	1.41085	+	0.400474i
$705$		0			0
$706$	1035.42	+	329.274i	1.46660	+	0.466393i
$707$	−836.647	+	517.515i	−1.18338	+	0.731987i
$708$		0			0
$709$			759.488i			1.07121i	0.844468	+	0.535605i	$0.179916\pi$
$709$			759.488i			1.07121i	−0.844468	+	0.535605i	$0.820084\pi$
$710$	351.718	−	1106.00i	0.495378	−	1.55775i
$711$		0			0
$712$	−647.200	−	856.478i	−0.908988	−	1.20292i
$713$		−	218.895i		−	0.307006i
$714$		0			0
$715$		−	1264.59i		−	1.76865i
$716$	243.876	−	344.664i	0.340608	−	0.481374i
$717$		0			0
$718$	−163.899	+	515.390i	−0.228271	+	0.717813i
$719$			1249.77i			1.73821i	0.494632	+	0.869103i	$0.335303\pi$
$719$			1249.77i			1.73821i	−0.494632	+	0.869103i	$0.664697\pi$
$720$		0			0
$721$	730.389	+	1180.79i	1.01302	+	1.63772i
$722$	276.565	−	869.676i	0.383053	−	1.20454i
$723$		0			0
$724$	−443.270	−	313.647i	−0.612252	−	0.433214i
$725$			33.5910i			0.0463324i
$726$		0			0
$727$		−	980.653i		−	1.34890i	−0.738319	−	0.674452i	$-0.764380\pi$
$727$		−	980.653i		−	1.34890i	0.738319	−	0.674452i	$-0.235620\pi$
$728$	−286.396	+	738.978i	−0.393401	+	1.01508i
$729$		0			0
$730$	−874.780	−	278.188i	−1.19833	−	0.381079i
$731$	−317.710			−0.434624
$732$		0			0
$733$	−532.385			−0.726309			−0.363155	−	0.931729i	$-0.618300\pi$
$733$	−532.385			−0.726309			−0.363155	+	0.931729i	$0.618300\pi$
$734$	366.542	+	116.564i	0.499376	+	0.158806i
$735$		0			0
$736$	−258.963	+	8.11266i	−0.351852	+	0.0110226i
$737$	−1873.49			−2.54204
$738$		0			0
$739$		−	1061.19i		−	1.43599i	−0.696049	−	0.717994i	$-0.745061\pi$
$739$		−	1061.19i		−	1.43599i	0.696049	−	0.717994i	$-0.254939\pi$
$740$	−262.826	+	371.447i	−0.355171	+	0.501955i
$741$		0			0
$742$	−1048.11	+	263.231i	−1.41255	+	0.354758i
$743$	237.425			0.319549			0.159774	−	0.987154i	$-0.448923\pi$
$743$	237.425			0.319549			0.159774	+	0.987154i	$0.448923\pi$
$744$		0			0
$745$		−	230.468i		−	0.309352i
$746$	140.784	+	44.7705i	0.188718	+	0.0600141i
$747$		0			0
$748$	393.811	+	278.650i	0.526485	+	0.372527i
$749$	−77.9395	−	126.002i	−0.104058	−	0.168227i
$750$		0			0
$751$	572.550			0.762384			0.381192	−	0.924496i	$-0.375514\pi$
$751$	572.550			0.762384			0.381192	+	0.924496i	$0.375514\pi$
$752$	734.634	−	259.217i	0.976908	−	0.344704i
$753$		0			0
$754$	−159.556	−	50.7401i	−0.211612	−	0.0672946i
$755$	−830.438			−1.09992
$756$		0			0
$757$			1232.38i			1.62798i	0.580876	+	0.813992i	$0.302710\pi$
$757$			1232.38i			1.62798i	−0.580876	+	0.813992i	$0.697290\pi$
$758$	20.9563	+	6.66428i	0.0276468	+	0.00879193i
$759$		0			0
$760$	1010.67	−	763.714i	1.32983	−	1.00489i
$761$		−	474.738i		−	0.623834i	−0.950109	−	0.311917i	$-0.899029\pi$
$761$		−	474.738i		−	0.623834i	0.950109	−	0.311917i	$-0.100971\pi$
$762$		0			0
$763$	395.443	+	639.297i	0.518273	+	0.837873i
$764$	70.4385	+	49.8405i	0.0921969	+	0.0652362i
$765$		0			0
$766$	−1062.73	−	337.957i	−1.38737	−	0.441198i
$767$	−576.335			−0.751414
$768$		0			0
$769$			812.878i			1.05706i	0.848915	+	0.528529i	$0.177256\pi$
$769$			812.878i			1.05706i	−0.848915	+	0.528529i	$0.822744\pi$
$770$	−1213.29	+	304.714i	−1.57570	+	0.395733i
$771$		0			0
$772$	1038.59	+	734.880i	1.34532	+	0.951917i
$773$	−864.876			−1.11886			−0.559428	−	0.828879i	$-0.688979\pi$
$773$	−864.876			−1.11886			−0.559428	+	0.828879i	$0.688979\pi$
$774$		0			0
$775$			153.528i			0.198101i
$776$	−180.686	−	239.112i	−0.232842	−	0.308134i
$777$		0			0
$778$	−78.2187	−	24.8742i	−0.100538	−	0.0319720i
$779$			1403.96i			1.80226i
$780$		0			0
$781$			1690.15i			2.16409i
$782$	−115.367	−	36.6876i	−0.147528	−	0.0469151i
$783$		0			0
$784$	778.012	+	96.7148i	0.992362	+	0.123361i
$785$	−452.940			−0.576993
$786$		0			0
$787$	1030.93			1.30995			0.654975	−	0.755651i	$-0.272679\pi$
$787$	1030.93			1.30995			0.654975	+	0.755651i	$0.272679\pi$
$788$	0.564933	−	0.798408i	0.000716920	−	0.00101321i
$789$		0			0
$790$	−150.288	+	472.590i	−0.190238	+	0.598215i
$791$	672.191	−	415.790i	0.849799	−	0.525651i
$792$		0			0
$793$	−154.352			−0.194643
$794$	138.295	−	434.878i	0.174175	−	0.547705i
$795$		0			0
$796$	545.911	−	771.524i	0.685818	−	0.969251i
$797$	−742.857			−0.932067			−0.466033	−	0.884767i	$-0.654317\pi$
$797$	−742.857			−0.932067			−0.466033	+	0.884767i	$0.654317\pi$
$798$		0			0
$799$	364.000			0.455569
$800$	181.631	−	5.69003i	0.227038	−	0.00711254i
$801$		0			0
$802$	−353.063	+	1110.23i	−0.440228	+	1.38433i
$803$	1336.81			1.66477
$804$		0			0
$805$	266.973	−	165.138i	0.331643	−	0.205141i
$806$	−729.251	−	231.908i	−0.904778	−	0.287727i
$807$		0			0
$808$	−897.006	+	677.825i	−1.11016	+	0.838892i
$809$	947.608			1.17133			0.585667	−	0.810552i	$-0.300833\pi$
$809$	947.608			1.17133			0.585667	+	0.810552i	$0.300833\pi$
$810$		0			0
$811$	580.571			0.715870			0.357935	−	0.933747i	$-0.383481\pi$
$811$	580.571			0.715870			0.357935	+	0.933747i	$0.383481\pi$
$812$	−10.2354	+	165.310i	−0.0126052	+	0.203583i
$813$		0			0
$814$	200.821	−	631.495i	0.246709	−	0.775792i
$815$			1525.30i			1.87153i
$816$		0			0
$817$		−	1214.93i		−	1.48706i
$818$	8.93697	+	2.84204i	0.0109254	+	0.00347437i
$819$		0			0
$820$	−628.457	+	888.185i	−0.766411	+	1.08315i
$821$			1364.03i			1.66143i	0.556700	+	0.830714i	$0.312067\pi$
$821$			1364.03i			1.66143i	−0.556700	+	0.830714i	$0.687933\pi$
$822$		0			0
$823$	−246.998			−0.300119			−0.150059	−	0.988677i	$-0.547947\pi$
$823$	−246.998			−0.300119			−0.150059	+	0.988677i	$0.547947\pi$
$824$	956.641	+	1265.98i	1.16097	+	1.53638i
$825$		0			0
$826$	138.873	+	552.956i	0.168127	+	0.669438i
$827$		−	737.549i		−	0.891837i	−0.895074	−	0.445918i	$-0.852877\pi$
$827$		−	737.549i		−	0.891837i	0.895074	−	0.445918i	$-0.147123\pi$
$828$		0			0
$829$	1260.35			1.52032			0.760162	−	0.649733i	$-0.225119\pi$
$829$	1260.35			1.52032			0.760162	+	0.649733i	$0.225119\pi$
$830$	−221.067	+	695.161i	−0.266346	+	0.837544i
$831$		0			0
$832$	−247.330	+	871.331i	−0.297272	+	1.04727i
$833$	327.774	+	163.576i	0.393486	+	0.196370i
$834$		0			0
$835$			1461.30i			1.75006i
$836$	−1065.57	+	1505.94i	−1.27460	+	1.80136i
$837$		0			0
$838$	63.7965	−	200.612i	0.0761295	−	0.239394i
$839$			272.430i			0.324708i	0.986733	+	0.162354i	$0.0519087\pi$
$839$			272.430i			0.324708i	−0.986733	+	0.162354i	$0.948091\pi$
$840$		0			0
$841$	806.010			0.958395
$842$	1180.79	+	375.501i	1.40236	+	0.445963i
$843$		0			0
$844$	232.117	−	328.046i	0.275021	−	0.388681i
$845$	173.314			0.205105
$846$		0			0
$847$	829.009	−	512.790i	0.978759	−	0.605419i
$848$	−1164.67	+	410.954i	−1.37343	+	0.484616i
$849$		0			0
$850$	80.9155	+	25.7319i	0.0951947	+	0.0302728i
$851$			166.288i			0.195403i
$852$		0			0
$853$	−167.153			−0.195959			−0.0979794	−	0.995188i	$-0.531238\pi$
$853$	−167.153			−0.195959			−0.0979794	+	0.995188i	$0.531238\pi$
$854$	37.1926	+	148.091i	0.0435511	+	0.173409i
$855$		0			0
$856$	−102.083	−	135.092i	−0.119255	−	0.157818i
$857$		−	13.0480i		−	0.0152252i	−0.999971	−	0.00761258i	$-0.997577\pi$
$857$		−	13.0480i		−	0.0152252i	0.999971	−	0.00761258i	$-0.00242318\pi$
$858$		0			0
$859$	−872.946			−1.01624			−0.508118	−	0.861288i	$-0.669658\pi$
$859$	−872.946			−1.01624			−0.508118	+	0.861288i	$0.669658\pi$
$860$	543.840	−	768.598i	0.632373	−	0.893719i
$861$		0			0
$862$	265.872	−	836.051i	0.308436	−	0.969896i
$863$	−560.236			−0.649173			−0.324587	−	0.945856i	$-0.605225\pi$
$863$	−560.236			−0.649173			−0.324587	+	0.945856i	$0.605225\pi$
$864$		0			0
$865$	302.699			0.349941
$866$	−82.0306	−	26.0865i	−0.0947236	−	0.0301230i
$867$		0			0
$868$	−46.7812	+	755.550i	−0.0538954	+	0.870449i
$869$		−	722.195i		−	0.831064i
$870$		0			0
$871$		−	1643.54i		−	1.88696i
$872$	517.938	+	685.418i	0.593966	+	0.786030i
$873$		0			0
$874$	140.294	−	441.165i	0.160520	−	0.504765i
$875$	637.091	−	394.078i	0.728104	−	0.450375i
$876$		0			0
$877$		−	819.789i		−	0.934766i	−0.884055	−	0.467383i	$-0.845197\pi$
$877$		−	819.789i		−	0.934766i	0.884055	−	0.467383i	$-0.154803\pi$
$878$	−393.033	−	124.988i	−0.447646	−	0.142356i
$879$		0			0
$880$	−1348.21	+	475.719i	−1.53206	+	0.540589i
$881$			930.214i			1.05586i	0.849287	+	0.527931i	$0.177032\pi$
$881$			930.214i			1.05586i	−0.849287	+	0.527931i	$0.822968\pi$
$882$		0			0
$883$		−	444.483i		−	0.503378i	−0.967808	−	0.251689i	$-0.919014\pi$
$883$		−	444.483i		−	0.503378i	0.967808	−	0.251689i	$-0.0809860\pi$
$884$	−244.450	+	345.476i	−0.276527	+	0.390810i
$885$		0			0
$886$	1165.09	+	370.508i	1.31500	+	0.418181i
$887$			159.932i			0.180307i	0.995928	+	0.0901536i	$0.0287358\pi$
$887$			159.932i			0.180307i	−0.995928	+	0.0901536i	$0.971264\pi$
$888$		0			0
$889$	−989.694	+	612.183i	−1.11327	+	0.688620i
$890$	1416.59	+	450.490i	1.59168	+	0.506168i
$891$		0			0
$892$	−873.874	+	1235.03i	−0.979679	+	1.38456i
$893$			1391.94i			1.55873i
$894$		0			0
$895$			584.650i			0.653240i
$896$	895.583	+	27.3422i	0.999534	+	0.0305159i
$897$		0			0
$898$	362.268	−	1139.18i	0.403417	−	1.26857i
$899$	−159.922			−0.177888
$900$		0			0
$901$	−577.073			−0.640481
$902$	480.193	−	1510.00i	0.532365	−	1.67406i
$903$		0			0
$904$	720.686	−	544.588i	0.797219	−	0.602420i
$905$	751.915			0.830845
$906$		0			0
$907$			66.5490i			0.0733727i	0.999327	+	0.0366863i	$0.0116802\pi$
$907$			66.5490i			0.0733727i	−0.999327	+	0.0366863i	$0.988320\pi$
$908$	−184.969	−	130.880i	−0.203711	−	0.144141i
$909$		0			0
$910$	−267.315	−	1064.38i	−0.293753	−	1.16964i
$911$	254.406			0.279260			0.139630	−	0.990204i	$-0.455409\pi$
$911$	254.406			0.279260			0.139630	+	0.990204i	$0.455409\pi$
$912$		0			0
$913$		−	1062.32i		−	1.16355i
$914$	−212.416	+	667.956i	−0.232403	+	0.730805i
$915$		0			0
$916$	−968.363	−	685.190i	−1.05717	−	0.748024i
$917$	930.460	−	575.544i	1.01468	−	0.627638i
$918$		0			0
$919$	1688.22			1.83702			0.918511	−	0.395395i	$-0.129392\pi$
$919$	1688.22			1.83702			0.918511	+	0.395395i	$0.129392\pi$
$920$	286.233	−	216.293i	0.311123	−	0.235101i
$921$		0			0
$922$	−110.836	+	348.531i	−0.120213	+	0.378016i
$923$	−1482.71			−1.60640
$924$		0			0
$925$		−	116.630i		−	0.126087i
$926$	38.1060	−	119.827i	0.0411512	−	0.129402i
$927$		0			0
$928$	5.92699	+	189.194i	0.00638684	+	0.203873i
$929$		−	905.524i		−	0.974730i	−0.873198	−	0.487365i	$-0.837958\pi$
$929$		−	905.524i		−	0.974730i	0.873198	−	0.487365i	$-0.162042\pi$
$930$		0			0
$931$	−625.520	+	1253.42i	−0.671879	+	1.34631i
$932$	−366.929	−	259.630i	−0.393701	−	0.278573i
$933$		0			0
$934$	−391.093	+	1229.82i	−0.418729	+	1.31672i
$935$	−668.017			−0.714457
$936$		0			0
$937$			1465.43i			1.56396i	0.623301	+	0.781982i	$0.285791\pi$
$937$			1465.43i			1.56396i	−0.623301	+	0.781982i	$0.714209\pi$
$938$	−1576.87	+	396.027i	−1.68110	+	0.422204i
$939$		0			0
$940$	−623.077	+	880.581i	−0.662848	+	0.936788i
$941$	250.000			0.265675			0.132837	−	0.991138i	$-0.457591\pi$
$941$	250.000			0.265675			0.132837	+	0.991138i	$0.457591\pi$
$942$		0			0
$943$			397.619i			0.421653i
$944$	216.808	+	614.446i	0.229670	+	0.650897i
$945$		0			0
$946$	−415.539	+	1306.69i	−0.439259	+	1.38128i
$947$		−	638.465i		−	0.674197i	−0.941469	−	0.337099i	$-0.890554\pi$
$947$		−	638.465i		−	0.674197i	0.941469	−	0.337099i	$-0.109446\pi$
$948$		0			0
$949$			1172.73i			1.23576i
$950$	−98.3992	+	309.423i	−0.103578	+	0.325708i
$951$		0			0
$952$	390.365	+	151.288i	0.410047	+	0.158916i
$953$	−436.356			−0.457876			−0.228938	−	0.973441i	$-0.573525\pi$
$953$	−436.356			−0.457876			−0.228938	+	0.973441i	$0.573525\pi$
$954$		0			0
$955$	−119.484			−0.125114
$956$	−308.542	−	218.316i	−0.322742	−	0.228364i
$957$		0			0
$958$	−834.146	−	265.266i	−0.870716	−	0.276896i
$959$	405.953	−	251.105i	0.423308	−	0.261841i
$960$		0			0
$961$	230.077			0.239414
$962$	553.988	+	176.173i	0.575871	+	0.183132i
$963$		0			0
$964$	202.692	−	286.460i	0.210261	−	0.297157i
$965$	−1761.75			−1.82565
$966$		0			0
$967$	−891.342			−0.921760			−0.460880	−	0.887463i	$-0.652466\pi$
$967$	−891.342			−0.921760			−0.460880	+	0.887463i	$0.652466\pi$
$968$	888.816	−	671.636i	0.918199	−	0.693839i
$969$		0			0
$970$	395.485	+	125.768i	0.407717	+	0.129658i
$971$	162.475			0.167327			0.0836635	−	0.996494i	$-0.473338\pi$
$971$	162.475			0.167327			0.0836635	+	0.996494i	$0.473338\pi$
$972$		0			0
$973$	1133.83	−	701.338i	1.16529	−	0.720800i
$974$	−8.93346	+	28.0918i	−0.00917193	+	0.0288417i
$975$		0			0
$976$	58.0650	+	164.559i	0.0594928	+	0.168606i
$977$	−499.904			−0.511673			−0.255836	−	0.966720i	$-0.582351\pi$
$977$	−499.904			−0.511673			−0.255836	+	0.966720i	$0.582351\pi$
$978$		0			0
$979$	−2164.79			−2.21122
$980$	−956.788	+	512.943i	−0.976315	+	0.523411i
$981$		0			0
$982$	−228.997	−	72.8232i	−0.233195	−	0.0741580i
$983$		−	544.456i		−	0.553872i	−0.960888	−	0.276936i	$-0.910681\pi$
$983$		−	544.456i		−	0.553872i	0.960888	−	0.276936i	$-0.0893190\pi$
$984$		0			0
$985$			1.35433i			0.00137496i
$986$	−26.8034	+	84.2851i	−0.0271840	+	0.0854819i
$987$		0			0
$988$	−1321.11	−	934.783i	−1.33715	−	0.946137i
$989$		−	344.082i		−	0.347909i
$990$		0			0
$991$	778.083			0.785149			0.392575	−	0.919720i	$-0.371585\pi$
$991$	778.083			0.785149			0.392575	+	0.919720i	$0.371585\pi$
$992$	27.0894	+	864.715i	0.0273078	+	0.871688i
$993$		0			0
$994$	357.273	+	1422.57i	0.359430	+	1.43115i
$995$			1308.73i			1.31530i
$996$		0			0
$997$	366.247			0.367349			0.183674	−	0.982987i	$-0.441201\pi$
$997$	366.247			0.367349			0.183674	+	0.982987i	$0.441201\pi$
$998$	−8.96147	−	2.84983i	−0.00897943	−	0.00285554i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.l.h.181.18		32
3.2	odd	2		168.3.l.a.13.16	yes	32
4.3	odd	2		2016.3.l.h.433.26		32
7.6	odd	2	inner	504.3.l.h.181.17		32
8.3	odd	2		2016.3.l.h.433.7		32
8.5	even	2	inner	504.3.l.h.181.19		32
12.11	even	2		672.3.l.a.433.14		32
21.20	even	2		168.3.l.a.13.15	yes	32
24.5	odd	2		168.3.l.a.13.13	✓	32
24.11	even	2		672.3.l.a.433.19		32
28.27	even	2		2016.3.l.h.433.8		32
56.13	odd	2	inner	504.3.l.h.181.20		32
56.27	even	2		2016.3.l.h.433.25		32
84.83	odd	2		672.3.l.a.433.30		32
168.83	odd	2		672.3.l.a.433.3		32
168.125	even	2		168.3.l.a.13.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.l.a.13.13	✓	32	24.5	odd	2
168.3.l.a.13.14	yes	32	168.125	even	2
168.3.l.a.13.15	yes	32	21.20	even	2
168.3.l.a.13.16	yes	32	3.2	odd	2
504.3.l.h.181.17		32	7.6	odd	2	inner
504.3.l.h.181.18		32	1.1	even	1	trivial
504.3.l.h.181.19		32	8.5	even	2	inner
504.3.l.h.181.20		32	56.13	odd	2	inner
672.3.l.a.433.3		32	168.83	odd	2
672.3.l.a.433.14		32	12.11	even	2
672.3.l.a.433.19		32	24.11	even	2
672.3.l.a.433.30		32	84.83	odd	2
2016.3.l.h.433.7		32	8.3	odd	2
2016.3.l.h.433.8		32	28.27	even	2
2016.3.l.h.433.25		32	56.27	even	2
2016.3.l.h.433.26		32	4.3	odd	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.606108 - 1.90595i) q^{2} +(-3.26527 - 2.31042i) q^{4} +5.53884 q^{5} +(-5.95316 + 3.68238i) q^{7} +(-6.38264 + 4.82306i) q^{8} +(3.35714 - 10.5567i) q^{10} +16.1324i q^{11} -14.1524 q^{13} +(3.41016 + 13.5783i) q^{14} +(5.32392 + 15.0883i) q^{16} +7.47600i q^{17} -28.5884 q^{19} +(-18.0858 - 12.7970i) q^{20} +(30.7475 + 9.77800i) q^{22} -8.09656 q^{23} +5.67874 q^{25} +(-8.57789 + 26.9737i) q^{26} +(27.9465 + 1.73036i) q^{28} +5.91522i q^{29} +27.0356i q^{31} +(31.9843 - 1.00199i) q^{32} +(14.2488 + 4.53126i) q^{34} +(-32.9736 + 20.3961i) q^{35} -20.5381i q^{37} +(-17.3277 + 54.4879i) q^{38} +(-35.3524 + 26.7141i) q^{40} -49.1096i q^{41} +42.4974i q^{43} +(37.2727 - 52.6767i) q^{44} +(-4.90739 + 15.4316i) q^{46} -48.6891i q^{47} +(21.8802 - 43.8435i) q^{49} +(3.44193 - 10.8234i) q^{50} +(46.2114 + 32.6980i) q^{52} +77.1902i q^{53} +89.3549i q^{55} +(20.2366 - 52.2157i) q^{56} +(11.2741 + 3.58527i) q^{58} +40.7234 q^{59} +10.9064 q^{61} +(51.5284 + 16.3865i) q^{62} +(17.4762 - 61.5677i) q^{64} -78.3879 q^{65} +116.132i q^{67} +(17.2727 - 24.4111i) q^{68} +(18.8883 + 75.2081i) q^{70} +104.767 q^{71} -82.8647i q^{73} +(-39.1444 - 12.4483i) q^{74} +(93.3487 + 66.0512i) q^{76} +(-59.4057 - 96.0389i) q^{77} -44.7667 q^{79} +(29.4883 + 83.5715i) q^{80} +(-93.6002 - 29.7657i) q^{82} -65.8500 q^{83} +41.4083i q^{85} +(80.9977 + 25.7580i) q^{86} +(-77.8076 - 102.968i) q^{88} +134.189i q^{89} +(84.2515 - 52.1145i) q^{91} +(26.4374 + 18.7065i) q^{92} +(-92.7989 - 29.5109i) q^{94} -158.346 q^{95} +37.4629i q^{97} +(-70.3017 - 68.2764i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Introduction

L-functions

Modular forms

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Database

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