LMFDB - Embedded newform 224.3.n.a.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(17,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("224.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	224.17
Dual form			224.3.n.a.145.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70138 - 2.94687i) q^{3} +(2.15858 + 3.73877i) q^{5} +(1.43197 + 6.85197i) q^{7} +(-1.28938 - 2.23327i) q^{9} +O(q^{10})$	\(q+(1.70138 - 2.94687i) q^{3} +(2.15858 + 3.73877i) q^{5} +(1.43197 + 6.85197i) q^{7} +(-1.28938 - 2.23327i) q^{9} +(15.4899 + 8.94308i) q^{11} +3.25607 q^{13} +14.6903 q^{15} +(-13.6263 - 7.86717i) q^{17} +(-0.778522 - 1.34844i) q^{19} +(22.6282 + 7.43796i) q^{21} +(-20.7069 - 35.8655i) q^{23} +(3.18105 - 5.50975i) q^{25} +21.8499 q^{27} -3.74374i q^{29} +(0.0145172 + 0.00838150i) q^{31} +(52.7082 - 30.4311i) q^{33} +(-22.5269 + 20.1443i) q^{35} +(-1.16774 + 0.674194i) q^{37} +(5.53981 - 9.59523i) q^{39} +70.3018i q^{41} -13.0380i q^{43} +(5.56646 - 9.64139i) q^{45} +(-30.9797 + 17.8862i) q^{47} +(-44.8989 + 19.6236i) q^{49} +(-46.3671 + 26.7701i) q^{51} +(39.7989 + 22.9779i) q^{53} +77.2174i q^{55} -5.29824 q^{57} +(34.3509 - 59.4974i) q^{59} +(-48.0386 - 83.2052i) q^{61} +(13.4559 - 12.0328i) q^{63} +(7.02849 + 12.1737i) q^{65} +(-12.0808 - 6.97484i) q^{67} -140.921 q^{69} +75.7095 q^{71} +(-46.0282 - 26.5744i) q^{73} +(-10.8244 - 18.7483i) q^{75} +(-39.0967 + 118.942i) q^{77} +(-11.6744 - 20.2206i) q^{79} +(48.7794 - 84.4884i) q^{81} -102.487 q^{83} -67.9277i q^{85} +(-11.0323 - 6.36952i) q^{87} +(-76.6985 + 44.2819i) q^{89} +(4.66259 + 22.3105i) q^{91} +(0.0493984 - 0.0285202i) q^{93} +(3.36100 - 5.82143i) q^{95} -140.869i q^{97} -46.1241i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) $ 28 * q + 4 * q^7 - 32 * q^9	$ 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) $ 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	1.70138	−	2.94687i	0.567126	−	0.982291i	−0.429722	−	0.902961i	$-0.641388\pi$
$3$	1.70138	−	2.94687i	0.567126	−	0.982291i	0.996848	−	0.0793303i	$-0.0252782\pi$
$4$		0			0
$5$	2.15858	+	3.73877i	0.431716	+	0.747754i	0.997021	−	0.0771275i	$-0.0245748\pi$
$5$	2.15858	+	3.73877i	0.431716	+	0.747754i	−0.565305	+	0.824882i	$0.691242\pi$
$6$		0			0
$7$	1.43197	+	6.85197i	0.204567	+	0.978853i
$7$	1.43197	+	6.85197i	0.204567	+	0.978853i
$8$		0			0
$9$	−1.28938	−	2.23327i	−0.143264	−	0.248141i
$10$		0			0
$11$	15.4899	+	8.94308i	1.40817	+	0.813007i	0.995212	−	0.0977432i	$-0.0311624\pi$
$11$	15.4899	+	8.94308i	1.40817	+	0.813007i	0.412958	+	0.910750i	$0.364496\pi$
$12$		0			0
$13$	3.25607			0.250467			0.125233	−	0.992127i	$-0.460032\pi$
$13$	3.25607			0.250467			0.125233	+	0.992127i	$0.460032\pi$
$14$		0			0
$15$	14.6903			0.979350
$16$		0			0
$17$	−13.6263	−	7.86717i	−0.801550	−	0.462775i	0.0424631	−	0.999098i	$-0.486479\pi$
$17$	−13.6263	−	7.86717i	−0.801550	−	0.462775i	−0.844013	+	0.536323i	$0.819813\pi$
$18$		0			0
$19$	−0.778522	−	1.34844i	−0.0409748	−	0.0709705i	0.844811	−	0.535065i	$-0.179713\pi$
$19$	−0.778522	−	1.34844i	−0.0409748	−	0.0709705i	−0.885786	+	0.464095i	$0.846380\pi$
$20$		0			0
$21$	22.6282	+	7.43796i	1.07753	+	0.354188i
$22$		0			0
$23$	−20.7069	−	35.8655i	−0.900301	−	1.55937i	−0.827103	−	0.562050i	$-0.810013\pi$
$23$	−20.7069	−	35.8655i	−0.900301	−	1.55937i	−0.0731984	−	0.997317i	$-0.523321\pi$
$24$		0			0
$25$	3.18105	−	5.50975i	0.127242	−	0.220390i
$26$		0			0
$27$	21.8499			0.809257
$28$		0			0
$29$		−	3.74374i		−	0.129095i	−0.997915	−	0.0645473i	$-0.979440\pi$
$29$		−	3.74374i		−	0.129095i	0.997915	−	0.0645473i	$-0.0205603\pi$
$30$		0			0
$31$	0.0145172	+	0.00838150i	0.000468296	+	0.000270371i	0.500234	−	0.865890i	$-0.333247\pi$
$31$	0.0145172	+	0.00838150i	0.000468296	+	0.000270371i	−0.499766	+	0.866161i	$0.666581\pi$
$32$		0			0
$33$	52.7082	−	30.4311i	1.59722	−	0.922155i
$34$		0			0
$35$	−22.5269	+	20.1443i	−0.643626	+	0.575553i
$36$		0			0
$37$	−1.16774	+	0.674194i	−0.0315605	+	0.0182215i	−0.515697	−	0.856771i	$-0.672467\pi$
$37$	−1.16774	+	0.674194i	−0.0315605	+	0.0182215i	0.484137	+	0.874992i	$0.339134\pi$
$38$		0			0
$39$	5.53981	−	9.59523i	0.142046	−	0.246031i
$40$		0			0
$41$			70.3018i			1.71468i	0.514753	+	0.857339i	$0.327884\pi$
$41$			70.3018i			1.71468i	−0.514753	+	0.857339i	$0.672116\pi$
$42$		0			0
$43$		−	13.0380i		−	0.303210i	−0.988441	−	0.151605i	$-0.951556\pi$
$43$		−	13.0380i		−	0.303210i	0.988441	−	0.151605i	$-0.0484442\pi$
$44$		0			0
$45$	5.56646	−	9.64139i	0.123699	−	0.214253i
$46$		0			0
$47$	−30.9797	+	17.8862i	−0.659144	+	0.380557i	−0.791951	−	0.610585i	$-0.790934\pi$
$47$	−30.9797	+	17.8862i	−0.659144	+	0.380557i	0.132807	+	0.991142i	$0.457601\pi$
$48$		0			0
$49$	−44.8989	+	19.6236i	−0.916305	+	0.400482i
$50$		0			0
$51$	−46.3671	+	26.7701i	−0.909160	+	0.524904i
$52$		0			0
$53$	39.7989	+	22.9779i	0.750923	+	0.433546i	0.826027	−	0.563630i	$-0.190596\pi$
$53$	39.7989	+	22.9779i	0.750923	+	0.433546i	−0.0751042	+	0.997176i	$0.523929\pi$
$54$		0			0
$55$			77.2174i			1.40395i
$56$		0			0
$57$	−5.29824			−0.0929516
$58$		0			0
$59$	34.3509	−	59.4974i	0.582218	−	1.00843i	−0.412998	−	0.910732i	$-0.635518\pi$
$59$	34.3509	−	59.4974i	0.582218	−	1.00843i	0.995216	−	0.0976993i	$-0.0311484\pi$
$60$		0			0
$61$	−48.0386	−	83.2052i	−0.787517	−	1.36402i	−0.927484	−	0.373864i	$-0.878033\pi$
$61$	−48.0386	−	83.2052i	−0.787517	−	1.36402i	0.139966	−	0.990156i	$-0.455301\pi$
$62$		0			0
$63$	13.4559	−	12.0328i	0.213586	−	0.190996i
$64$		0			0
$65$	7.02849	+	12.1737i	0.108131	+	0.187288i
$66$		0			0
$67$	−12.0808	−	6.97484i	−0.180310	−	0.104102i	0.407128	−	0.913371i	$-0.366530\pi$
$67$	−12.0808	−	6.97484i	−0.180310	−	0.104102i	−0.587438	+	0.809269i	$0.699864\pi$
$68$		0			0
$69$	−140.921			−2.04234
$70$		0			0
$71$	75.7095			1.06633			0.533166	−	0.846011i	$-0.321002\pi$
$71$	75.7095			1.06633			0.533166	+	0.846011i	$0.321002\pi$
$72$		0			0
$73$	−46.0282	−	26.5744i	−0.630523	−	0.364033i	0.150432	−	0.988620i	$-0.451934\pi$
$73$	−46.0282	−	26.5744i	−0.630523	−	0.364033i	−0.780955	+	0.624588i	$0.785267\pi$
$74$		0			0
$75$	−10.8244	−	18.7483i	−0.144325	−	0.249978i
$76$		0			0
$77$	−39.0967	+	118.942i	−0.507749	+	1.54470i
$78$		0			0
$79$	−11.6744	−	20.2206i	−0.147777	−	0.255957i	0.782628	−	0.622489i	$-0.213878\pi$
$79$	−11.6744	−	20.2206i	−0.147777	−	0.255957i	−0.930406	+	0.366532i	$0.880545\pi$
$80$		0			0
$81$	48.7794	−	84.4884i	0.602215	−	1.04307i
$82$		0			0
$83$	−102.487			−1.23479			−0.617393	−	0.786655i	$-0.711811\pi$
$83$	−102.487			−1.23479			−0.617393	+	0.786655i	$0.711811\pi$
$84$		0			0
$85$		−	67.9277i		−	0.799150i
$86$		0			0
$87$	−11.0323	−	6.36952i	−0.126808	−	0.0732129i
$88$		0			0
$89$	−76.6985	+	44.2819i	−0.861781	+	0.497549i	−0.864608	−	0.502447i	$-0.832433\pi$
$89$	−76.6985	+	44.2819i	−0.861781	+	0.497549i	0.00282755	+	0.999996i	$0.499100\pi$
$90$		0			0
$91$	4.66259	+	22.3105i	0.0512373	+	0.245170i
$92$		0			0
$93$	0.0493984	−	0.0285202i	0.000531166	−	0.000306669i
$94$		0			0
$95$	3.36100	−	5.82143i	0.0353790	−	0.0612782i
$96$		0			0
$97$		−	140.869i		−	1.45226i	−0.687558	−	0.726130i	$-0.741317\pi$
$97$		−	140.869i		−	1.45226i	0.687558	−	0.726130i	$-0.258683\pi$
$98$		0			0
$99$		−	46.1241i		−	0.465900i
$100$		0			0
$101$	17.6988	−	30.6553i	0.175236	−	0.303518i	−0.765007	−	0.644022i	$-0.777265\pi$
$101$	17.6988	−	30.6553i	0.175236	−	0.303518i	0.940243	+	0.340504i	$0.110598\pi$
$102$		0			0
$103$	−87.1651	+	50.3248i	−0.846263	+	0.488590i	−0.859388	−	0.511324i	$-0.829155\pi$
$103$	−87.1651	+	50.3248i	−0.846263	+	0.488590i	0.0131250	+	0.999914i	$0.495822\pi$
$104$		0			0
$105$	21.0360	+	100.657i	0.200343	+	0.958640i
$106$		0			0
$107$	−92.6215	+	53.4751i	−0.865622	+	0.499767i	−0.865891	−	0.500233i	$-0.833248\pi$
$107$	−92.6215	+	53.4751i	−0.865622	+	0.499767i	0.000269099		1.00000i	$0.499914\pi$
$108$		0			0
$109$	45.5799	+	26.3156i	0.418165	+	0.241427i	0.694292	−	0.719694i	$-0.255718\pi$
$109$	45.5799	+	26.3156i	0.418165	+	0.241427i	−0.276127	+	0.961121i	$0.589051\pi$
$110$		0			0
$111$			4.58824i			0.0413355i
$112$		0			0
$113$	45.4346			0.402076			0.201038	−	0.979583i	$-0.435568\pi$
$113$	45.4346			0.402076			0.201038	+	0.979583i	$0.435568\pi$
$114$		0			0
$115$	89.3952	−	154.837i	0.777350	−	1.34641i
$116$		0			0
$117$	−4.19831	−	7.27168i	−0.0358830	−	0.0621511i
$118$		0			0
$119$	34.3931	−	104.633i	0.289018	−	0.879267i
$120$		0			0
$121$	99.4572	+	172.265i	0.821961	+	1.42368i
$122$		0			0
$123$	207.171	+	119.610i	1.68431	+	0.972439i
$124$		0			0
$125$	135.395			1.08316
$126$		0			0
$127$	−125.695			−0.989723			−0.494861	−	0.868972i	$-0.664781\pi$
$127$	−125.695			−0.989723			−0.494861	+	0.868972i	$0.664781\pi$
$128$		0			0
$129$	−38.4215	−	22.1827i	−0.297841	−	0.171959i
$130$		0			0
$131$	56.6504	+	98.1214i	0.432446	+	0.749018i	0.997083	−	0.0763210i	$-0.0243174\pi$
$131$	56.6504	+	98.1214i	0.432446	+	0.749018i	−0.564638	+	0.825339i	$0.690984\pi$
$132$		0			0
$133$	8.12464	−	7.26533i	0.0610875	−	0.0546265i
$134$		0			0
$135$	47.1648	+	81.6919i	0.349369	+	0.605125i
$136$		0			0
$137$	−39.1679	+	67.8408i	−0.285897	+	0.495188i	−0.972826	−	0.231536i	$-0.925625\pi$
$137$	−39.1679	+	67.8408i	−0.285897	+	0.495188i	0.686929	+	0.726724i	$0.258958\pi$
$138$		0			0
$139$	−149.038			−1.07222			−0.536109	−	0.844149i	$-0.680106\pi$
$139$	−149.038			−1.07222			−0.536109	+	0.844149i	$0.680106\pi$
$140$		0			0
$141$			121.725i			0.863295i
$142$		0			0
$143$	50.4361	+	29.1193i	0.352700	+	0.203631i
$144$		0			0
$145$	13.9970	−	8.08117i	0.0965310	−	0.0557322i
$146$		0			0
$147$	−18.5617	+	165.699i	−0.126270	+	1.12720i
$148$		0			0
$149$	73.8369	−	42.6298i	0.495550	−	0.286106i	−0.231324	−	0.972877i	$-0.574306\pi$
$149$	73.8369	−	42.6298i	0.495550	−	0.286106i	0.726874	+	0.686771i	$0.240972\pi$
$150$		0			0
$151$	65.9012	−	114.144i	0.436432	−	0.755922i	−0.560979	−	0.827830i	$-0.689575\pi$
$151$	65.9012	−	114.144i	0.436432	−	0.755922i	0.997411	+	0.0719076i	$0.0229087\pi$
$152$		0			0
$153$			40.5751i			0.265197i
$154$		0			0
$155$			0.0723686i			0.000466894i
$156$		0			0
$157$	122.552	−	212.267i	0.780589	−	1.35202i	−0.151010	−	0.988532i	$-0.548253\pi$
$157$	122.552	−	212.267i	0.780589	−	1.35202i	0.931599	−	0.363487i	$-0.118414\pi$
$158$		0			0
$159$	135.426	−	78.1883i	0.851737	−	0.491750i
$160$		0			0
$161$	216.097	−	193.241i	1.34222	−	1.20026i
$162$		0			0
$163$	208.089	−	120.140i	1.27662	−	0.737057i	0.300395	−	0.953815i	$-0.402882\pi$
$163$	208.089	−	120.140i	1.27662	−	0.737057i	0.976225	+	0.216758i	$0.0695482\pi$
$164$		0			0
$165$	227.550	+	131.376i	1.37909	+	0.796219i
$166$		0			0
$167$		−	73.1965i		−	0.438302i	−0.975691	−	0.219151i	$-0.929671\pi$
$167$		−	73.1965i		−	0.438302i	0.975691	−	0.219151i	$-0.0703288\pi$
$168$		0			0
$169$	−158.398			−0.937266
$170$		0			0
$171$	−2.00762	+	3.47730i	−0.0117405	+	0.0203351i
$172$		0			0
$173$	−18.5246	−	32.0855i	−0.107078	−	0.185465i	0.807507	−	0.589858i	$-0.200816\pi$
$173$	−18.5246	−	32.0855i	−0.107078	−	0.185465i	−0.914585	+	0.404393i	$0.867483\pi$
$174$		0			0
$175$	42.3078	+	13.9067i	0.241759	+	0.0794668i
$176$		0			0
$177$	−116.888	−	202.455i	−0.660382	−	1.14382i
$178$		0			0
$179$	205.982	+	118.924i	1.15074	+	0.664379i	0.949067	−	0.315074i	$-0.102029\pi$
$179$	205.982	+	118.924i	1.15074	+	0.664379i	0.201672	+	0.979453i	$0.435363\pi$
$180$		0			0
$181$	−292.553			−1.61631			−0.808157	−	0.588966i	$-0.799535\pi$
$181$	−292.553			−1.61631			−0.808157	+	0.588966i	$0.799535\pi$
$182$		0			0
$183$	−326.927			−1.78649
$184$		0			0
$185$	−5.04132	−	2.91061i	−0.0272504	−	0.0157330i
$186$		0			0
$187$	−140.713	−	243.723i	−0.752478	−	1.30333i
$188$		0			0
$189$	31.2884	+	149.715i	0.165547	+	0.792143i
$190$		0			0
$191$	70.6135	+	122.306i	0.369704	+	0.640346i	0.989519	−	0.144402i	$-0.0461257\pi$
$191$	70.6135	+	122.306i	0.369704	+	0.640346i	−0.619815	+	0.784748i	$0.712792\pi$
$192$		0			0
$193$	32.9799	−	57.1229i	0.170880	−	0.295973i	−0.767848	−	0.640633i	$-0.778672\pi$
$193$	32.9799	−	57.1229i	0.170880	−	0.295973i	0.938728	+	0.344659i	$0.112006\pi$
$194$		0			0
$195$	47.8325			0.245295
$196$		0			0
$197$			199.421i			1.01229i	0.862448	+	0.506145i	$0.168930\pi$
$197$			199.421i			1.01229i	−0.862448	+	0.506145i	$0.831070\pi$
$198$		0			0
$199$	−58.6230	−	33.8460i	−0.294588	−	0.170080i	0.345421	−	0.938448i	$-0.387736\pi$
$199$	−58.6230	−	33.8460i	−0.294588	−	0.170080i	−0.640009	+	0.768367i	$0.721069\pi$
$200$		0			0
$201$	−41.1079	+	23.7337i	−0.204517	+	0.118078i
$202$		0			0
$203$	25.6520	−	5.36092i	0.126365	−	0.0264085i
$204$		0			0
$205$	−262.842	+	151.752i	−1.28216	+	0.740254i
$206$		0			0
$207$	−53.3982	+	92.4884i	−0.257962	+	0.446804i
$208$		0			0
$209$		−	27.8495i		−	0.133251i
$210$		0			0
$211$		−	62.1464i		−	0.294533i	−0.989097	−	0.147266i	$-0.952953\pi$
$211$		−	62.1464i		−	0.294533i	0.989097	−	0.147266i	$-0.0470475\pi$
$212$		0			0
$213$	128.811	−	223.106i	0.604744	−	1.04745i
$214$		0			0
$215$	48.7463	−	28.1437i	0.226727	−	0.130901i
$216$		0			0
$217$	−0.0366416	+	0.111473i	−0.000168855	+	0.000513702i
$218$		0			0
$219$	−156.623	+	90.4261i	−0.715172	+	0.412905i
$220$		0			0
$221$	−44.3683	−	25.6161i	−0.200762	−	0.115910i
$222$		0			0
$223$		−	115.525i		−	0.518050i	−0.965871	−	0.259025i	$-0.916599\pi$
$223$		−	115.525i		−	0.518050i	0.965871	−	0.259025i	$-0.0834012\pi$
$224$		0			0
$225$	−16.4063			−0.0729171
$226$		0			0
$227$	−28.2532	+	48.9360i	−0.124463	+	0.215577i	−0.921523	−	0.388324i	$-0.873054\pi$
$227$	−28.2532	+	48.9360i	−0.124463	+	0.215577i	0.797060	+	0.603901i	$0.206388\pi$
$228$		0			0
$229$	59.1696	+	102.485i	0.258383	+	0.447532i	0.965809	−	0.259255i	$-0.0834771\pi$
$229$	59.1696	+	102.485i	0.258383	+	0.447532i	−0.707426	+	0.706787i	$0.750144\pi$
$230$		0			0
$231$	283.990	+	317.579i	1.22939	+	1.37480i
$232$		0			0
$233$	12.3403	+	21.3740i	0.0529625	+	0.0917337i	0.891291	−	0.453431i	$-0.149800\pi$
$233$	12.3403	+	21.3740i	0.0529625	+	0.0917337i	−0.838329	+	0.545165i	$0.816467\pi$
$234$		0			0
$235$	−133.745	−	77.2175i	−0.569126	−	0.328585i
$236$		0			0
$237$	−79.4503			−0.335233
$238$		0			0
$239$	251.189			1.05100			0.525499	−	0.850794i	$-0.323879\pi$
$239$	251.189			1.05100			0.525499	+	0.850794i	$0.323879\pi$
$240$		0			0
$241$	97.3782	+	56.2213i	0.404059	+	0.233283i	0.688234	−	0.725489i	$-0.258386\pi$
$241$	97.3782	+	56.2213i	0.404059	+	0.233283i	−0.284175	+	0.958772i	$0.591720\pi$
$242$		0			0
$243$	−67.6598	−	117.190i	−0.278436	−	0.482265i
$244$		0			0
$245$	−170.286	−	125.508i	−0.695046	−	0.512276i
$246$		0			0
$247$	−2.53492	−	4.39061i	−0.0102628	−	0.0177758i
$248$		0			0
$249$	−174.370	+	302.017i	−0.700280	+	1.21292i
$250$		0			0
$251$	−121.248			−0.483059			−0.241529	−	0.970394i	$-0.577649\pi$
$251$	−121.248			−0.483059			−0.241529	+	0.970394i	$0.577649\pi$
$252$		0			0
$253$		−	740.735i		−	2.92781i
$254$		0			0
$255$	−200.174	−	115.571i	−0.784998	−	0.453219i
$256$		0			0
$257$	−90.7377	+	52.3874i	−0.353065	+	0.203842i	−0.666034	−	0.745921i	$-0.732010\pi$
$257$	−90.7377	+	52.3874i	−0.353065	+	0.203842i	0.312969	+	0.949763i	$0.398676\pi$
$258$		0			0
$259$	−6.29172	−	7.03588i	−0.0242924	−	0.0271656i
$260$		0			0
$261$	−8.36079	+	4.82710i	−0.0320337	+	0.0184946i
$262$		0			0
$263$	−52.3392	+	90.6542i	−0.199008	+	0.344693i	−0.948207	−	0.317653i	$-0.897105\pi$
$263$	−52.3392	+	90.6542i	−0.199008	+	0.344693i	0.749199	+	0.662345i	$0.230439\pi$
$264$		0			0
$265$			198.399i			0.748675i
$266$		0			0
$267$			301.361i			1.12869i
$268$		0			0
$269$	−152.466	+	264.079i	−0.566789	+	0.981707i	0.430092	+	0.902785i	$0.358481\pi$
$269$	−152.466	+	264.079i	−0.566789	+	0.981707i	−0.996881	+	0.0789222i	$0.974852\pi$
$270$		0			0
$271$	−88.8942	+	51.3231i	−0.328023	+	0.189384i	−0.654963	−	0.755661i	$-0.727316\pi$
$271$	−88.8942	+	51.3231i	−0.328023	+	0.189384i	0.326940	+	0.945045i	$0.393982\pi$
$272$		0			0
$273$	73.6790	+	24.2185i	0.269886	+	0.0887125i
$274$		0			0
$275$	98.5482	−	56.8968i	0.358357	−	0.206898i
$276$		0			0
$277$	14.4235	+	8.32739i	0.0520703	+	0.0300628i	0.525809	−	0.850603i	$-0.323763\pi$
$277$	14.4235	+	8.32739i	0.0520703	+	0.0300628i	−0.473739	+	0.880665i	$0.657096\pi$
$278$		0			0
$279$		−	0.0432277i		−	0.000154938i
$280$		0			0
$281$	75.8291			0.269855			0.134927	−	0.990856i	$-0.456920\pi$
$281$	75.8291			0.269855			0.134927	+	0.990856i	$0.456920\pi$
$282$		0			0
$283$	−43.6656	+	75.6311i	−0.154296	+	0.267248i	−0.932802	−	0.360389i	$-0.882644\pi$
$283$	−43.6656	+	75.6311i	−0.154296	+	0.267248i	0.778507	+	0.627636i	$0.215977\pi$
$284$		0			0
$285$	−11.4367	−	19.8089i	−0.0401287	−	0.0695050i
$286$		0			0
$287$	−481.706	+	100.670i	−1.67842	+	0.350767i
$288$		0			0
$289$	−20.7152	−	35.8798i	−0.0716789	−	0.124151i
$290$		0			0
$291$	−415.124	−	239.672i	−1.42654	−	0.823614i
$292$		0			0
$293$	27.5057			0.0938760			0.0469380	−	0.998898i	$-0.485054\pi$
$293$	27.5057			0.0938760			0.0469380	+	0.998898i	$0.485054\pi$
$294$		0			0
$295$	296.597			1.00541
$296$		0			0
$297$	338.452	+	195.406i	1.13957	+	0.657931i
$298$		0			0
$299$	−67.4232	−	116.780i	−0.225496	−	0.390570i
$300$		0			0
$301$	89.3363	−	18.6701i	0.296798	−	0.0620269i
$302$		0			0
$303$	−60.2248	−	104.312i	−0.198762	−	0.344266i
$304$		0			0
$305$	207.390	−	359.211i	0.679968	−	1.17774i
$306$		0			0
$307$	−247.996			−0.807805			−0.403902	−	0.914802i	$-0.632346\pi$
$307$	−247.996			−0.807805			−0.403902	+	0.914802i	$0.632346\pi$
$308$		0			0
$309$			342.486i			1.10837i
$310$		0			0
$311$	−378.484	−	218.518i	−1.21699	−	0.702630i	−0.252717	−	0.967540i	$-0.581324\pi$
$311$	−378.484	−	218.518i	−1.21699	−	0.702630i	−0.964273	+	0.264910i	$0.914658\pi$
$312$		0			0
$313$	−71.7330	+	41.4151i	−0.229179	+	0.132317i	−0.610193	−	0.792253i	$-0.708908\pi$
$313$	−71.7330	+	41.4151i	−0.229179	+	0.132317i	0.381014	+	0.924569i	$0.375575\pi$
$314$		0			0
$315$	74.0335	+	24.3350i	0.235027	+	0.0772540i
$316$		0			0
$317$	−211.775	+	122.268i	−0.668059	+	0.385704i	−0.795341	−	0.606162i	$-0.792708\pi$
$317$	−211.775	+	122.268i	−0.668059	+	0.385704i	0.127282	+	0.991867i	$0.459375\pi$
$318$		0			0
$319$	33.4806	−	57.9900i	0.104955	−	0.181787i
$320$		0			0
$321$			363.925i			1.13372i
$322$		0			0
$323$			24.4991i			0.0758485i
$324$		0			0
$325$	10.3577	−	17.9401i	0.0318699	−	0.0552004i
$326$		0			0
$327$	155.097	−	89.5456i	0.474304	−	0.273840i
$328$		0			0
$329$	−166.917	−	186.660i	−0.507348	−	0.567355i
$330$		0			0
$331$	66.2919	−	38.2736i	0.200278	−	0.115630i	−0.396507	−	0.918032i	$-0.629778\pi$
$331$	66.2919	−	38.2736i	0.200278	−	0.115630i	0.596785	+	0.802401i	$0.296445\pi$
$332$		0			0
$333$	3.01132	+	1.73858i	0.00904299	+	0.00522097i
$334$		0			0
$335$		−	60.2230i		−	0.179770i
$336$		0			0
$337$	−38.2520			−0.113507			−0.0567537	−	0.998388i	$-0.518075\pi$
$337$	−38.2520			−0.113507			−0.0567537	+	0.998388i	$0.518075\pi$
$338$		0			0
$339$	77.3015	−	133.890i	0.228028	−	0.394956i
$340$		0			0
$341$	0.149913	+	0.259656i	0.000439627	+	0.000761456i
$342$		0			0
$343$	−198.754	−	279.546i	−0.579459	−	0.815002i
$344$		0			0
$345$	−304.190	−	526.873i	−0.881711	−	1.52717i
$346$		0			0
$347$	208.395	+	120.317i	0.600561	+	0.346734i	0.769262	−	0.638933i	$-0.220624\pi$
$347$	208.395	+	120.317i	0.600561	+	0.346734i	−0.168701	+	0.985667i	$0.553957\pi$
$348$		0			0
$349$	430.367			1.23314			0.616572	−	0.787298i	$-0.288521\pi$
$349$	430.367			1.23314			0.616572	+	0.787298i	$0.288521\pi$
$350$		0			0
$351$	71.1449			0.202692
$352$		0			0
$353$	−265.950	−	153.546i	−0.753399	−	0.434975i	0.0735214	−	0.997294i	$-0.476576\pi$
$353$	−265.950	−	153.546i	−0.753399	−	0.434975i	−0.826921	+	0.562318i	$0.809910\pi$
$354$		0			0
$355$	163.425	+	283.061i	0.460353	+	0.797354i
$356$		0			0
$357$	−249.824	−	279.372i	−0.699787	−	0.782555i
$358$		0			0
$359$	230.880	+	399.896i	0.643120	+	1.11392i	0.984732	+	0.174075i	$0.0556935\pi$
$359$	230.880	+	399.896i	0.643120	+	1.11392i	−0.341613	+	0.939841i	$0.610973\pi$
$360$		0			0
$361$	179.288	−	310.536i	0.496642	−	0.860209i
$362$		0			0
$363$	676.858			1.86462
$364$		0			0
$365$		−	229.452i		−	0.628635i
$366$		0			0
$367$	542.949	+	313.471i	1.47942	+	0.854146i	0.999729	−	0.0232895i	$-0.00741394\pi$
$367$	542.949	+	313.471i	1.47942	+	0.854146i	0.479695	+	0.877435i	$0.340747\pi$
$368$		0			0
$369$	157.003	−	90.6457i	0.425482	−	0.245652i
$370$		0			0
$371$	−100.453	+	305.605i	−0.270763	+	0.823732i
$372$		0			0
$373$	357.317	−	206.297i	0.957953	−	0.553075i	0.0624108	−	0.998051i	$-0.480121\pi$
$373$	357.317	−	206.297i	0.957953	−	0.553075i	0.895543	+	0.444976i	$0.146788\pi$
$374$		0			0
$375$	230.359	−	398.993i	0.614290	−	1.06398i
$376$		0			0
$377$		−	12.1899i		−	0.0323339i
$378$		0			0
$379$		−	327.118i		−	0.863107i	−0.902087	−	0.431554i	$-0.857966\pi$
$379$		−	327.118i		−	0.863107i	0.902087	−	0.431554i	$-0.142034\pi$
$380$		0			0
$381$	−213.854	+	370.407i	−0.561298	+	0.972196i
$382$		0			0
$383$	215.523	−	124.432i	0.562724	−	0.324889i	−0.191514	−	0.981490i	$-0.561340\pi$
$383$	215.523	−	124.432i	0.562724	−	0.324889i	0.754238	+	0.656601i	$0.228006\pi$
$384$		0			0
$385$	−529.091	+	110.573i	−1.37426	+	0.287203i
$386$		0			0
$387$	−29.1175	+	16.8110i	−0.0752390	+	0.0434392i
$388$		0			0
$389$	−326.728	−	188.637i	−0.839918	−	0.484927i	0.0173181	−	0.999850i	$-0.494487\pi$
$389$	−326.728	−	188.637i	−0.839918	−	0.484927i	−0.857236	+	0.514923i	$0.827821\pi$
$390$		0			0
$391$			651.620i			1.66655i
$392$		0			0
$393$	385.535			0.981005
$394$		0			0
$395$	50.4003	−	87.2958i	0.127596	−	0.221002i
$396$		0			0
$397$	335.874	+	581.752i	0.846031	+	1.46537i	0.884723	+	0.466118i	$0.154348\pi$
$397$	335.874	+	581.752i	0.846031	+	1.46537i	−0.0386913	+	0.999251i	$0.512319\pi$
$398$		0			0
$399$	−7.58692	−	36.3034i	−0.0190148	−	0.0909859i
$400$		0			0
$401$	235.200	+	407.378i	0.586534	+	1.01591i	0.994682	+	0.102991i	$0.0328411\pi$
$401$	235.200	+	407.378i	0.586534	+	1.01591i	−0.408149	+	0.912915i	$0.633826\pi$
$402$		0			0
$403$	0.0472689	+	0.0272907i	0.000117293	+	6.77189e-5i
$404$		0			0
$405$	421.177			1.03994
$406$		0			0
$407$	−24.1175			−0.0592567
$408$		0			0
$409$	−57.7400	−	33.3362i	−0.141174	−	0.0815067i	0.427750	−	0.903897i	$-0.359307\pi$
$409$	−57.7400	−	33.3362i	−0.141174	−	0.0815067i	−0.568923	+	0.822391i	$0.692640\pi$
$410$		0			0
$411$	133.279	+	230.846i	0.324279	+	0.561669i
$412$		0			0
$413$	456.864	+	150.172i	1.10621	+	0.363614i
$414$		0			0
$415$	−221.227	−	383.177i	−0.533077	−	0.923317i
$416$		0			0
$417$	−253.571	+	439.197i	−0.608083	+	1.05323i
$418$		0			0
$419$	437.380			1.04387			0.521933	−	0.852986i	$-0.325211\pi$
$419$	437.380			1.04387			0.521933	+	0.852986i	$0.325211\pi$
$420$		0			0
$421$			703.800i			1.67173i	0.548933	+	0.835867i	$0.315034\pi$
$421$			703.800i			1.67173i	−0.548933	+	0.835867i	$0.684966\pi$
$422$		0			0
$423$	79.8893	+	46.1241i	0.188864	+	0.109040i
$424$		0			0
$425$	−86.6923	+	50.0518i	−0.203982	+	0.117769i
$426$		0			0
$427$	501.330	−	448.306i	1.17407	−	1.04990i
$428$		0			0
$429$	171.622	−	99.0858i	0.400051	−	0.230969i
$430$		0			0
$431$	−274.869	+	476.087i	−0.637747	+	1.10461i	0.348178	+	0.937428i	$0.386800\pi$
$431$	−274.869	+	476.087i	−0.637747	+	1.10461i	−0.985926	+	0.167183i	$0.946533\pi$
$432$		0			0
$433$		−	355.012i		−	0.819890i	−0.912110	−	0.409945i	$-0.865548\pi$
$433$		−	355.012i		−	0.819890i	0.912110	−	0.409945i	$-0.134452\pi$
$434$		0			0
$435$		−	54.9965i		−	0.126429i
$436$		0			0
$437$	−32.2416	+	55.8441i	−0.0737794	+	0.127790i
$438$		0			0
$439$	−477.032	+	275.415i	−1.08663	+	0.627369i	−0.932678	−	0.360709i	$-0.882535\pi$
$439$	−477.032	+	275.415i	−1.08663	+	0.627369i	−0.153956	+	0.988078i	$0.549201\pi$
$440$		0			0
$441$	101.717	+	74.9692i	0.230650	+	0.169998i
$442$		0			0
$443$	234.027	−	135.116i	0.528278	−	0.305001i	−0.212037	−	0.977262i	$-0.568010\pi$
$443$	234.027	−	135.116i	0.528278	−	0.305001i	0.740315	+	0.672260i	$0.234676\pi$
$444$		0			0
$445$	−331.120	−	191.172i	−0.744089	−	0.429600i
$446$		0			0
$447$		−	290.117i		−	0.649032i
$448$		0			0
$449$	455.397			1.01425			0.507124	−	0.861873i	$-0.330709\pi$
$449$	455.397			1.01425			0.507124	+	0.861873i	$0.330709\pi$
$450$		0			0
$451$	−628.714	+	1088.96i	−1.39404	+	2.41456i
$452$		0			0
$453$	−224.246	−	388.405i	−0.495024	−	0.857406i
$454$		0			0
$455$	−73.3492	+	65.5914i	−0.161207	+	0.144157i
$456$		0			0
$457$	84.3172	+	146.042i	0.184501	+	0.319566i	0.943408	−	0.331633i	$-0.107600\pi$
$457$	84.3172	+	146.042i	0.184501	+	0.319566i	−0.758907	+	0.651199i	$0.774266\pi$
$458$		0			0
$459$	−297.735	−	171.897i	−0.648659	−	0.374504i
$460$		0			0
$461$	265.062			0.574971			0.287485	−	0.957785i	$-0.407181\pi$
$461$	265.062			0.574971			0.287485	+	0.957785i	$0.407181\pi$
$462$		0			0
$463$	−97.4735			−0.210526			−0.105263	−	0.994444i	$-0.533568\pi$
$463$	−97.4735			−0.210526			−0.105263	+	0.994444i	$0.533568\pi$
$464$		0			0
$465$	0.213261	+	0.123126i	0.000458626	+	0.000264788i
$466$		0			0
$467$	37.0997	+	64.2586i	0.0794427	+	0.137599i	0.903010	−	0.429620i	$-0.141353\pi$
$467$	37.0997	+	64.2586i	0.0794427	+	0.137599i	−0.823567	+	0.567219i	$0.808019\pi$
$468$		0			0
$469$	30.4921	−	92.7648i	0.0650150	−	0.197793i
$470$		0			0
$471$	−417.016	−	722.293i	−0.885385	−	1.53353i
$472$		0			0
$473$	116.600	−	201.958i	0.246512	−	0.426972i
$474$		0			0
$475$	−9.90608			−0.0208549
$476$		0			0
$477$		−	118.509i		−	0.248447i
$478$		0			0
$479$	475.220	+	274.368i	0.992108	+	0.572794i	0.905904	−	0.423484i	$-0.139193\pi$
$479$	475.220	+	274.368i	0.992108	+	0.572794i	0.0862043	+	0.996277i	$0.472526\pi$
$480$		0			0
$481$	−3.80224	+	2.19522i	−0.00790486	+	0.00456387i
$482$		0			0
$483$	−201.795	−	965.588i	−0.417795	−	1.99915i
$484$		0			0
$485$	526.678	−	304.078i	1.08593	−	0.626964i
$486$		0			0
$487$	283.938	−	491.795i	0.583034	−	1.00985i	−0.412083	−	0.911146i	$-0.635199\pi$
$487$	283.938	−	491.795i	0.583034	−	1.00985i	0.995117	−	0.0986990i	$-0.0314681\pi$
$488$		0			0
$489$		−	817.617i		−	1.67202i
$490$		0			0
$491$			78.8005i			0.160490i	0.996775	+	0.0802449i	$0.0255702\pi$
$491$			78.8005i			0.160490i	−0.996775	+	0.0802449i	$0.974430\pi$
$492$		0			0
$493$	−29.4527	+	51.0135i	−0.0597417	+	0.103476i
$494$		0			0
$495$	172.447	−	99.5626i	0.348379	−	0.201136i
$496$		0			0
$497$	108.414	+	518.759i	0.218136	+	1.04378i
$498$		0			0
$499$	−290.932	+	167.970i	−0.583030	+	0.336612i	−0.762337	−	0.647181i	$-0.775948\pi$
$499$	−290.932	+	167.970i	−0.583030	+	0.336612i	0.179307	+	0.983793i	$0.442615\pi$
$500$		0			0
$501$	−215.701	−	124.535i	−0.430541	−	0.248573i
$502$		0			0
$503$		−	274.052i		−	0.544836i	−0.962179	−	0.272418i	$-0.912177\pi$
$503$		−	274.052i		−	0.544836i	0.962179	−	0.272418i	$-0.0878233\pi$
$504$		0			0
$505$	152.817			0.302609
$506$		0			0
$507$	−269.495	+	466.779i	−0.531548	+	0.920669i
$508$		0			0
$509$	−168.009	−	291.000i	−0.330076	−	0.571709i	0.652450	−	0.757831i	$-0.273741\pi$
$509$	−168.009	−	291.000i	−0.330076	−	0.571709i	−0.982526	+	0.186123i	$0.940408\pi$
$510$		0			0
$511$	116.176	−	353.437i	0.227350	−	0.691658i
$512$		0			0
$513$	−17.0106	−	29.4633i	−0.0331591	−	0.0574333i
$514$		0			0
$515$	−376.306	−	217.260i	−0.730691	−	0.421865i
$516$		0			0
$517$	−639.829			−1.23758
$518$		0			0
$519$	−126.069			−0.242908
$520$		0			0
$521$	−547.572	−	316.141i	−1.05100	−	0.606796i	−0.128072	−	0.991765i	$-0.540879\pi$
$521$	−547.572	−	316.141i	−1.05100	−	0.606796i	−0.922930	+	0.384969i	$0.874212\pi$
$522$		0			0
$523$	389.623	+	674.847i	0.744977	+	1.29034i	0.950206	+	0.311624i	$0.100873\pi$
$523$	389.623	+	674.847i	0.744977	+	1.29034i	−0.205229	+	0.978714i	$0.565794\pi$
$524$		0			0
$525$	112.963	−	101.015i	0.215167	−	0.192410i
$526$		0			0
$527$	−0.131877	−	0.228418i	−0.000250242	−	0.000433431i
$528$		0			0
$529$	−593.054	+	1027.20i	−1.12109	+	1.94178i
$530$		0			0
$531$	−177.165			−0.333644
$532$		0			0
$533$			228.907i			0.429470i
$534$		0			0
$535$	−399.862	−	230.861i	−0.747406	−	0.431515i
$536$		0			0
$537$	700.908	−	404.669i	1.30523	−	0.753574i
$538$		0			0
$539$	−870.974	−	97.5673i	−1.61591	−	0.181015i
$540$		0			0
$541$	−583.617	+	336.952i	−1.07878	+	0.622831i	−0.930566	−	0.366125i	$-0.880684\pi$
$541$	−583.617	+	336.952i	−1.07878	+	0.622831i	−0.148209	+	0.988956i	$0.547351\pi$
$542$		0			0
$543$	−497.743	+	862.117i	−0.916655	+	1.58769i
$544$		0			0
$545$			227.217i			0.416913i
$546$		0			0
$547$		−	52.5329i		−	0.0960382i	−0.998846	−	0.0480191i	$-0.984709\pi$
$547$		−	52.5329i		−	0.0960382i	0.998846	−	0.0480191i	$-0.0152908\pi$
$548$		0			0
$549$	−123.880	+	214.566i	−0.225646	+	0.390831i
$550$		0			0
$551$	−5.04821	+	2.91458i	−0.00916190	+	0.00528963i
$552$		0			0
$553$	121.834	−	108.948i	0.220314	−	0.197012i
$554$		0			0
$555$	−17.1544	+	9.90409i	−0.0309088	+	0.0178452i
$556$		0			0
$557$	−678.123	−	391.515i	−1.21746	−	0.702899i	−0.253083	−	0.967445i	$-0.581445\pi$
$557$	−678.123	−	391.515i	−1.21746	−	0.702899i	−0.964373	+	0.264546i	$0.914778\pi$
$558$		0			0
$559$		−	42.4528i		−	0.0759441i
$560$		0			0
$561$	−957.628			−1.70700
$562$		0			0
$563$	446.202	−	772.844i	0.792543	−	1.37272i	−0.131845	−	0.991270i	$-0.542090\pi$
$563$	446.202	−	772.844i	0.792543	−	1.37272i	0.924388	−	0.381454i	$-0.124577\pi$
$564$		0			0
$565$	98.0743	+	169.870i	0.173583	+	0.300654i
$566$		0			0
$567$	648.763	+	213.250i	1.14420	+	0.376102i
$568$		0			0
$569$	148.722	+	257.593i	0.261373	+	0.452712i	0.966607	−	0.256263i	$-0.0824912\pi$
$569$	148.722	+	257.593i	0.261373	+	0.452712i	−0.705234	+	0.708975i	$0.749158\pi$
$570$		0			0
$571$	−218.885	−	126.373i	−0.383335	−	0.221319i	0.295933	−	0.955209i	$-0.404369\pi$
$571$	−218.885	−	126.373i	−0.383335	−	0.221319i	−0.679268	+	0.733890i	$0.737703\pi$
$572$		0			0
$573$	480.561			0.838676
$574$		0			0
$575$	−263.479			−0.458225
$576$		0			0
$577$	764.454	+	441.358i	1.32488	+	0.764918i	0.984502	−	0.175371i	$-0.0561126\pi$
$577$	764.454	+	441.358i	1.32488	+	0.764918i	0.340375	+	0.940290i	$0.389446\pi$
$578$		0			0
$579$	−112.223	−	194.375i	−0.193821	−	0.335709i
$580$		0			0
$581$	−146.759	−	702.239i	−0.252597	−	1.20867i
$582$		0			0
$583$	410.987	+	711.850i	0.704951	+	1.22101i
$584$		0			0
$585$	18.1248	−	31.3930i	0.0309825	−	0.0536633i
$586$		0			0
$587$	−66.7814			−0.113767			−0.0568836	−	0.998381i	$-0.518116\pi$
$587$	−66.7814			−0.113767			−0.0568836	+	0.998381i	$0.518116\pi$
$588$		0			0
$589$		−	0.0261007i		−	4.43136e-5i
$590$		0			0
$591$	587.670	+	339.291i	0.994365	+	0.574097i
$592$		0			0
$593$	−311.911	+	180.082i	−0.525989	+	0.303680i	−0.739381	−	0.673287i	$-0.764882\pi$
$593$	−311.911	+	180.082i	−0.525989	+	0.303680i	0.213393	+	0.976967i	$0.431549\pi$
$594$		0			0
$595$	465.439	−	97.2704i	0.782250	−	0.163480i
$596$		0			0
$597$	−199.480	+	115.170i	−0.334137	+	0.192914i
$598$		0			0
$599$	−99.0219	+	171.511i	−0.165312	+	0.286329i	−0.936766	−	0.349956i	$-0.886196\pi$
$599$	−99.0219	+	171.511i	−0.165312	+	0.286329i	0.771454	+	0.636285i	$0.219530\pi$
$600$		0			0
$601$		−	373.907i		−	0.622141i	−0.950387	−	0.311071i	$-0.899312\pi$
$601$		−	373.907i		−	0.622141i	0.950387	−	0.311071i	$-0.100688\pi$
$602$		0			0
$603$			35.9728i			0.0596565i
$604$		0			0
$605$	−429.373	+	743.696i	−0.709708	+	1.22925i
$606$		0			0
$607$	−200.164	+	115.565i	−0.329760	+	0.190387i	−0.655735	−	0.754992i	$-0.727641\pi$
$607$	−200.164	+	115.565i	−0.329760	+	0.190387i	0.325975	+	0.945379i	$0.394308\pi$
$608$		0			0
$609$	27.8458	−	84.7142i	0.0457238	−	0.139104i
$610$		0			0
$611$	−100.872	+	58.2386i	−0.165094	+	0.0953168i
$612$		0			0
$613$	444.718	+	256.758i	0.725479	+	0.418855i	0.816766	−	0.576969i	$-0.195765\pi$
$613$	444.718	+	256.758i	0.725479	+	0.418855i	−0.0912873	+	0.995825i	$0.529098\pi$
$614$		0			0
$615$			1032.75i			1.67927i
$616$		0			0
$617$	−1119.01			−1.81363			−0.906815	−	0.421529i	$-0.861493\pi$
$617$	−1119.01			−1.81363			−0.906815	+	0.421529i	$0.861493\pi$
$618$		0			0
$619$	64.1019	−	111.028i	0.103557	−	0.179366i	−0.809591	−	0.586995i	$-0.800311\pi$
$619$	64.1019	−	111.028i	0.103557	−	0.179366i	0.913148	+	0.407629i	$0.133644\pi$
$620$		0			0
$621$	−452.445	−	783.658i	−0.728575	−	1.26193i
$622$		0			0
$623$	−413.248	−	462.125i	−0.663319	−	0.741774i
$624$		0			0
$625$	212.735	+	368.469i	0.340377	+	0.589550i
$626$		0			0
$627$	−82.0690	−	47.3826i	−0.130892	−	0.0755703i
$628$		0			0
$629$	21.2160			0.0337297
$630$		0			0
$631$	−313.995			−0.497615			−0.248808	−	0.968553i	$-0.580039\pi$
$631$	−313.995			−0.497615			−0.248808	+	0.968553i	$0.580039\pi$
$632$		0			0
$633$	−183.138	−	105.735i	−0.289317	−	0.167037i
$634$		0			0
$635$	−271.322	−	469.944i	−0.427279	−	0.740070i
$636$		0			0
$637$	−146.194	+	63.8959i	−0.229504	+	0.100307i
$638$		0			0
$639$	−97.6183	−	169.080i	−0.152767	−	0.264601i
$640$		0			0
$641$	115.594	−	200.215i	0.180334	−	0.312348i	−0.761660	−	0.647977i	$-0.775615\pi$
$641$	115.594	−	200.215i	0.180334	−	0.312348i	0.941994	+	0.335629i	$0.108949\pi$
$642$		0			0
$643$	637.869			0.992020			0.496010	−	0.868317i	$-0.334798\pi$
$643$	637.869			0.992020			0.496010	+	0.868317i	$0.334798\pi$
$644$		0			0
$645$		−	191.532i		−	0.296949i
$646$		0			0
$647$	586.461	+	338.594i	0.906432	+	0.523329i	0.879281	−	0.476303i	$-0.158023\pi$
$647$	586.461	+	338.594i	0.906432	+	0.523329i	0.0271505	+	0.999631i	$0.491357\pi$
$648$		0			0
$649$	1064.18	−	614.405i	1.63972	−	0.946695i
$650$		0			0
$651$	0.266157	+	0.297636i	0.000408843	+	0.000457199i
$652$		0			0
$653$	916.022	−	528.865i	1.40279	−	0.809901i	0.408112	−	0.912932i	$-0.366187\pi$
$653$	916.022	−	528.865i	1.40279	−	0.809901i	0.994678	+	0.103031i	$0.0328541\pi$
$654$		0			0
$655$	−244.569	+	423.606i	−0.373388	+	0.646726i
$656$		0			0
$657$			137.058i			0.208612i
$658$		0			0
$659$			644.502i			0.978000i	0.872284	+	0.489000i	$0.162638\pi$
$659$			644.502i			0.978000i	−0.872284	+	0.489000i	$0.837362\pi$
$660$		0			0
$661$	−560.069	+	970.068i	−0.847306	+	1.46758i	0.0362979	+	0.999341i	$0.488443\pi$
$661$	−560.069	+	970.068i	−0.847306	+	1.46758i	−0.883604	+	0.468236i	$0.844890\pi$
$662$		0			0
$663$	−150.975	+	87.1652i	−0.227714	+	0.131471i
$664$		0			0
$665$	44.7011	+	14.6934i	0.0672197	+	0.0220953i
$666$		0			0
$667$	−134.271	+	77.5214i	−0.201306	+	0.116224i
$668$		0			0
$669$	−340.438	−	196.552i	−0.508876	−	0.293800i
$670$		0			0
$671$		−	1718.45i		−	2.56103i
$672$		0			0
$673$	−307.811			−0.457371			−0.228686	−	0.973500i	$-0.573443\pi$
$673$	−307.811			−0.457371			−0.228686	+	0.973500i	$0.573443\pi$
$674$		0			0
$675$	69.5058	−	120.388i	0.102972	−	0.178352i
$676$		0			0
$677$	507.773	+	879.488i	0.750033	+	1.29910i	0.947806	+	0.318848i	$0.103296\pi$
$677$	507.773	+	879.488i	0.750033	+	1.29910i	−0.197773	+	0.980248i	$0.563371\pi$
$678$		0			0
$679$	965.231	−	201.720i	1.42155	−	0.297084i
$680$		0			0
$681$	96.1388	+	166.517i	0.141173	+	0.244519i
$682$		0			0
$683$	−840.220	−	485.102i	−1.23019	−	0.710251i	−0.263121	−	0.964763i	$-0.584752\pi$
$683$	−840.220	−	485.102i	−1.23019	−	0.710251i	−0.967070	+	0.254512i	$0.918085\pi$
$684$		0			0
$685$	−338.188			−0.493706
$686$		0			0
$687$	402.680			0.586143
$688$		0			0
$689$	129.588	+	74.8177i	0.188081	+	0.108589i
$690$		0			0
$691$	274.581	+	475.588i	0.397367	+	0.688260i	0.993400	−	0.114700i	$-0.0365906\pi$
$691$	274.581	+	475.588i	0.397367	+	0.688260i	−0.596033	+	0.802960i	$0.703257\pi$
$692$		0			0
$693$	316.041	−	66.0483i	0.456047	−	0.0953078i
$694$		0			0
$695$	−321.711	−	557.221i	−0.462894	−	0.801756i
$696$		0			0
$697$	553.076	−	957.956i	0.793510	−	1.37440i
$698$		0			0
$699$	83.9818			0.120146
$700$		0			0
$701$			452.665i			0.645742i	0.946443	+	0.322871i	$0.104648\pi$
$701$			452.665i			0.645742i	−0.946443	+	0.322871i	$0.895352\pi$
$702$		0			0
$703$	1.81822	+	1.04975i	0.00258637	+	0.00149324i
$704$		0			0
$705$	−455.100	+	262.752i	−0.645533	+	0.372698i
$706$		0			0
$707$	235.393	+	77.3744i	0.332946	+	0.109440i
$708$		0			0
$709$	609.174	−	351.707i	0.859202	−	0.496060i	−0.00454321	−	0.999990i	$-0.501446\pi$
$709$	609.174	−	351.707i	0.859202	−	0.496060i	0.863745	+	0.503929i	$0.168113\pi$
$710$		0			0
$711$	−30.1054	+	52.1442i	−0.0423424	+	0.0733392i
$712$		0			0
$713$		−	0.694220i		−	0.000973661i
$714$		0			0
$715$			251.425i			0.351644i
$716$		0			0
$717$	427.367	−	740.221i	0.596049	−	1.03239i
$718$		0			0
$719$	−54.1160	+	31.2439i	−0.0752656	+	0.0434546i	−0.537161	−	0.843480i	$-0.680503\pi$
$719$	−54.1160	+	31.2439i	−0.0752656	+	0.0434546i	0.461895	+	0.886935i	$0.347170\pi$
$720$		0			0
$721$	−469.642	−	525.189i	−0.651376	−	0.728417i
$722$		0			0
$723$	331.354	−	191.307i	0.458305	−	0.264602i
$724$		0			0
$725$	−20.6271	−	11.9090i	−0.0284511	−	0.0164263i
$726$		0			0
$727$		−	889.995i		−	1.22420i	−0.790779	−	0.612101i	$-0.790324\pi$
$727$		−	889.995i		−	1.22420i	0.790779	−	0.612101i	$-0.209676\pi$
$728$		0			0
$729$	417.569			0.572797
$730$		0			0
$731$	−102.573	+	177.661i	−0.140318	+	0.243038i
$732$		0			0
$733$	456.127	+	790.035i	0.622274	+	1.07781i	0.989061	+	0.147505i	$0.0471243\pi$
$733$	456.127	+	790.035i	0.622274	+	1.07781i	−0.366787	+	0.930305i	$0.619542\pi$
$734$		0			0
$735$	−659.577	+	288.276i	−0.897383	+	0.392212i
$736$		0			0
$737$	−124.753	−	216.079i	−0.169271	−	0.293187i
$738$		0			0
$739$	1081.52	+	624.415i	1.46349	+	0.844946i	0.999171	−	0.0407224i	$-0.0129659\pi$
$739$	1081.52	+	624.415i	1.46349	+	0.844946i	0.464319	+	0.885668i	$0.346299\pi$
$740$		0			0
$741$	−17.2514			−0.0232813
$742$		0			0
$743$	305.880			0.411682			0.205841	−	0.978585i	$-0.434007\pi$
$743$	305.880			0.411682			0.205841	+	0.978585i	$0.434007\pi$
$744$		0			0
$745$	318.766	+	184.040i	0.427874	+	0.247033i
$746$		0			0
$747$	132.145	+	228.882i	0.176901	+	0.306401i
$748$		0			0
$749$	−499.041	−	558.065i	−0.666276	−	0.745080i
$750$		0			0
$751$	258.895	+	448.420i	0.344734	+	0.597097i	0.985305	−	0.170802i	$-0.0546358\pi$
$751$	258.895	+	448.420i	0.344734	+	0.597097i	−0.640571	+	0.767899i	$0.721302\pi$
$752$		0			0
$753$	−206.288	+	357.302i	−0.273955	+	0.474504i
$754$		0			0
$755$	569.012			0.753659
$756$		0			0
$757$		−	939.898i		−	1.24161i	−0.783965	−	0.620804i	$-0.786806\pi$
$757$		−	939.898i		−	1.24161i	0.783965	−	0.620804i	$-0.213194\pi$
$758$		0			0
$759$	−2182.85	−	1260.27i	−2.87596	−	1.66044i
$760$		0			0
$761$	−976.757	+	563.931i	−1.28352	+	0.741039i	−0.977490	−	0.210983i	$-0.932334\pi$
$761$	−976.757	+	563.931i	−1.28352	+	0.741039i	−0.306028	+	0.952022i	$0.599000\pi$
$762$		0			0
$763$	−115.044	+	349.995i	−0.150779	+	0.458710i
$764$		0			0
$765$	−151.701	+	87.5846i	−0.198302	+	0.114490i
$766$		0			0
$767$	111.849	−	193.728i	0.145826	−	0.252579i
$768$		0			0
$769$			300.115i			0.390267i	0.980777	+	0.195133i	$0.0625139\pi$
$769$			300.115i			0.390267i	−0.980777	+	0.195133i	$0.937486\pi$
$770$		0			0
$771$			356.524i			0.462417i
$772$		0			0
$773$	375.120	−	649.727i	0.485278	−	0.840527i	−0.514579	−	0.857443i	$-0.672052\pi$
$773$	375.120	−	649.727i	0.485278	−	0.840527i	0.999857	+	0.0169165i	$0.00538495\pi$
$774$		0			0
$775$	0.0923598	−	0.0533240i	0.000119174	−	6.88051e-5i
$776$		0			0
$777$	−31.4385	+	6.57022i	−0.0404613	+	0.00845588i
$778$		0			0
$779$	94.7977	−	54.7315i	0.121691	−	0.0702586i
$780$		0			0
$781$	1172.73	+	677.076i	1.50158	+	0.866935i
$782$		0			0
$783$		−	81.8005i		−	0.104471i
$784$		0			0
$785$	1058.16			1.34797
$786$		0			0
$787$	−144.776	+	250.760i	−0.183960	+	0.318627i	−0.943225	−	0.332153i	$-0.892225\pi$
$787$	−144.776	+	250.760i	−0.183960	+	0.318627i	0.759266	+	0.650781i	$0.225558\pi$
$788$		0			0
$789$	178.098	+	308.474i	0.225726	+	0.390969i
$790$		0			0
$791$	65.0610	+	311.316i	0.0822516	+	0.393573i
$792$		0			0
$793$	−156.417	−	270.922i	−0.197247	−	0.341642i
$794$		0			0
$795$	584.657	+	337.552i	0.735417	+	0.424593i
$796$		0			0
$797$	1086.57			1.36332			0.681659	−	0.731670i	$-0.261259\pi$
$797$	1086.57			1.36332			0.681659	+	0.731670i	$0.261259\pi$
$798$		0			0
$799$	562.854			0.704448
$800$		0			0
$801$	197.787	+	114.192i	0.246925	+	0.142562i
$802$		0			0
$803$	−475.313	−	823.267i	−0.591922	−	1.02524i
$804$		0			0
$805$	1188.95	+	390.811i	1.47696	+	0.485480i
$806$		0			0
$807$	518.806	+	898.598i	0.642882	+	1.11350i
$808$		0			0
$809$	−90.9745	+	157.572i	−0.112453	+	0.194774i	−0.916759	−	0.399441i	$-0.869204\pi$
$809$	−90.9745	+	157.572i	−0.112453	+	0.194774i	0.804306	+	0.594216i	$0.202537\pi$
$810$		0			0
$811$	−1005.31			−1.23960			−0.619799	−	0.784760i	$-0.712786\pi$
$811$	−1005.31			−1.23960			−0.619799	+	0.784760i	$0.712786\pi$
$812$		0			0
$813$			349.280i			0.429619i
$814$		0			0
$815$	898.355	+	518.665i	1.10228	+	0.636399i
$816$		0			0
$817$	−17.5810	+	10.1504i	−0.0215190	+	0.0124240i
$818$		0			0
$819$	43.8135	−	39.1795i	0.0534963	−	0.0478382i
$820$		0			0
$821$	−851.009	+	491.330i	−1.03655	+	0.598453i	−0.918855	−	0.394596i	$-0.870885\pi$
$821$	−851.009	+	491.330i	−1.03655	+	0.598453i	−0.117697	+	0.993050i	$0.537551\pi$
$822$		0			0
$823$	742.505	−	1286.06i	0.902194	−	1.56265i	0.0775532	−	0.996988i	$-0.475289\pi$
$823$	742.505	−	1286.06i	0.902194	−	1.56265i	0.824641	−	0.565657i	$-0.191377\pi$
$824$		0			0
$825$		−	387.212i		−	0.469348i
$826$		0			0
$827$		−	708.113i		−	0.856243i	−0.903721	−	0.428121i	$-0.859176\pi$
$827$		−	708.113i		−	0.856243i	0.903721	−	0.428121i	$-0.140824\pi$
$828$		0			0
$829$	75.0164	−	129.932i	0.0904902	−	0.156734i	−0.817227	−	0.576316i	$-0.804490\pi$
$829$	75.0164	−	129.932i	0.0904902	−	0.156734i	0.907718	+	0.419582i	$0.137823\pi$
$830$		0			0
$831$	49.0796	−	28.3361i	0.0590609	−	0.0340988i
$832$		0			0
$833$	766.191	+	85.8294i	0.919797	+	0.103037i
$834$		0			0
$835$	273.665	−	158.001i	0.327743	−	0.189222i
$836$		0			0
$837$	0.317199	+	0.183135i	0.000378972	+	0.000218799i
$838$		0			0
$839$			1106.41i			1.31873i	0.751824	+	0.659364i	$0.229174\pi$
$839$			1106.41i			1.31873i	−0.751824	+	0.659364i	$0.770826\pi$
$840$		0			0
$841$	826.984			0.983335
$842$		0			0
$843$	129.014	−	223.459i	0.153042	−	0.265076i
$844$		0			0
$845$	−341.915	−	592.214i	−0.404633	−	0.700845i
$846$		0			0
$847$	−1037.93	+	928.156i	−1.22542	+	1.09582i
$848$		0			0
$849$	148.584	+	257.354i	0.175010	+	0.303126i
$850$		0			0
$851$	48.3606	+	27.9210i	0.0568279	+	0.0328096i
$852$		0			0
$853$	−1243.82			−1.45817			−0.729086	−	0.684423i	$-0.760054\pi$
$853$	−1243.82			−1.45817			−0.729086	+	0.684423i	$0.760054\pi$
$854$		0			0
$855$	−17.3344			−0.0202742
$856$		0			0
$857$	245.650	+	141.826i	0.286639	+	0.165491i	0.636425	−	0.771339i	$-0.280412\pi$
$857$	245.650	+	141.826i	0.286639	+	0.165491i	−0.349786	+	0.936830i	$0.613746\pi$
$858$		0			0
$859$	455.900	+	789.641i	0.530733	+	0.919256i	0.999357	+	0.0358586i	$0.0114166\pi$
$859$	455.900	+	789.641i	0.530733	+	0.919256i	−0.468624	+	0.883398i	$0.655250\pi$
$860$		0			0
$861$	−522.902	+	1590.80i	−0.607319	+	1.84762i
$862$		0			0
$863$	−436.908	−	756.747i	−0.506266	−	0.876879i	−0.999974	−	0.00725099i	$-0.997692\pi$
$863$	−436.908	−	756.747i	−0.506266	−	0.876879i	0.493707	−	0.869628i	$-0.335641\pi$
$864$		0			0
$865$	79.9735	−	138.518i	0.0924550	−	0.160137i
$866$		0			0
$867$	−140.978			−0.162604
$868$		0			0
$869$		−	417.620i		−	0.480575i
$870$		0			0
$871$	−39.3358	−	22.7105i	−0.0451617	−	0.0260741i
$872$		0			0
$873$	−314.599	+	181.634i	−0.360365	+	0.208057i
$874$		0			0
$875$	193.882	+	927.724i	0.221579	+	1.06026i
$876$		0			0
$877$	−549.476	+	317.240i	−0.626540	+	0.361733i	−0.779411	−	0.626513i	$-0.784482\pi$
$877$	−549.476	+	317.240i	−0.626540	+	0.361733i	0.152871	+	0.988246i	$0.451148\pi$
$878$		0			0
$879$	46.7975	−	81.0557i	0.0532395	−	0.0922136i
$880$		0			0
$881$			670.044i			0.760549i	0.924874	+	0.380274i	$0.124170\pi$
$881$			670.044i			0.760549i	−0.924874	+	0.380274i	$0.875830\pi$
$882$		0			0
$883$		−	875.514i		−	0.991522i	−0.868459	−	0.495761i	$-0.834889\pi$
$883$		−	875.514i		−	0.991522i	0.868459	−	0.495761i	$-0.165111\pi$
$884$		0			0
$885$	504.623	−	874.033i	0.570196	−	0.987608i
$886$		0			0
$887$	−854.152	+	493.145i	−0.962967	+	0.555969i	−0.897085	−	0.441858i	$-0.854319\pi$
$887$	−854.152	+	493.145i	−0.962967	+	0.555969i	−0.0658820	+	0.997827i	$0.520986\pi$
$888$		0			0
$889$	−179.991	−	861.257i	−0.202465	−	0.968793i
$890$		0			0
$891$	1511.17	−	872.476i	1.69604	−	0.979210i
$892$		0			0
$893$	48.2368	+	27.8495i	0.0540166	+	0.0311865i
$894$		0			0
$895$			1026.83i			1.14729i
$896$		0			0
$897$	−458.850			−0.511538
$898$		0			0
$899$	0.0313782	−	0.0543486i	3.49034e−5	−	6.04545e-5i
$900$		0			0
$901$	−361.543	−	626.210i	−0.401268	−	0.695017i
$902$		0			0
$903$	96.9764	−	295.028i	0.107394	−	0.326719i
$904$		0			0
$905$	−631.499	−	1093.79i	−0.697789	−	1.20861i
$906$		0			0
$907$	−750.592	−	433.355i	−0.827555	−	0.477789i	0.0254599	−	0.999676i	$-0.491895\pi$
$907$	−750.592	−	433.355i	−0.827555	−	0.477789i	−0.853015	+	0.521887i	$0.825228\pi$
$908$		0			0
$909$	−91.2820			−0.100420
$910$		0			0
$911$	128.713			0.141288			0.0706438	−	0.997502i	$-0.477495\pi$
$911$	128.713			0.141288			0.0706438	+	0.997502i	$0.477495\pi$
$912$		0			0
$913$	−1587.51	−	916.552i	−1.73879	−	1.00389i
$914$		0			0
$915$	−705.699	−	1222.31i	−0.771256	−	1.33585i
$916$		0			0
$917$	−591.203	+	528.673i	−0.644714	+	0.576525i
$918$		0			0
$919$	430.087	+	744.933i	0.467995	+	0.810591i	0.999331	−	0.0365701i	$-0.0116432\pi$
$919$	430.087	+	744.933i	0.467995	+	0.810591i	−0.531336	+	0.847161i	$0.678310\pi$
$920$		0			0
$921$	−421.935	+	730.813i	−0.458127	+	0.793500i
$922$		0			0
$923$	246.515			0.267081
$924$		0			0
$925$			8.57859i			0.00927415i
$926$		0			0
$927$	224.778	+	129.776i	0.242479	+	0.139995i
$928$		0			0
$929$	202.025	−	116.639i	0.217465	−	0.125554i	−0.387311	−	0.921949i	$-0.626596\pi$
$929$	202.025	−	116.639i	0.217465	−	0.125554i	0.604776	+	0.796396i	$0.293263\pi$
$930$		0			0
$931$	61.4160	+	45.2661i	0.0659678	+	0.0486209i
$932$		0			0
$933$	−1287.89	+	743.563i	−1.38037	+	0.796960i
$934$		0			0
$935$	607.483	−	1052.19i	0.649714	−	1.12534i
$936$		0			0
$937$			1426.29i			1.52219i	0.648641	+	0.761095i	$0.275338\pi$
$937$			1426.29i			1.52219i	−0.648641	+	0.761095i	$0.724662\pi$
$938$		0			0
$939$			281.851i			0.300161i
$940$		0			0
$941$	635.425	−	1100.59i	0.675265	−	1.16959i	−0.301126	−	0.953584i	$-0.597362\pi$
$941$	635.425	−	1100.59i	0.675265	−	1.16959i	0.976391	−	0.216010i	$-0.0693043\pi$
$942$		0			0
$943$	2521.41	−	1455.73i	2.67381	−	1.54373i
$944$		0			0
$945$	−492.212	+	440.152i	−0.520859	+	0.465770i
$946$		0			0
$947$	−1413.50	+	816.086i	−1.49261	+	0.861759i	−0.999964	−	0.00847064i	$-0.997304\pi$
$947$	−1413.50	+	816.086i	−1.49261	+	0.861759i	−0.492646	+	0.870230i	$0.663970\pi$
$948$		0			0
$949$	−149.871	−	86.5280i	−0.157925	−	0.0911781i
$950$		0			0
$951$			832.098i			0.874972i
$952$		0			0
$953$	95.9158			0.100646			0.0503231	−	0.998733i	$-0.483975\pi$
$953$	95.9158			0.100646			0.0503231	+	0.998733i	$0.483975\pi$
$954$		0			0
$955$	−304.850	+	528.015i	−0.319215	+	0.552896i
$956$		0			0
$957$	−113.926	−	197.326i	−0.119045	−	0.206192i
$958$		0			0
$959$	−520.930	−	171.231i	−0.543201	−	0.178552i
$960$		0			0
$961$	−480.500	−	832.250i	−0.500000	−	0.866025i
$962$		0			0
$963$	238.849	+	137.899i	0.248025	+	0.143198i
$964$		0			0
$965$	284.759			0.295087
$966$		0			0
$967$	−1419.97			−1.46843			−0.734216	−	0.678916i	$-0.762450\pi$
$967$	−1419.97			−1.46843			−0.734216	+	0.678916i	$0.762450\pi$
$968$		0			0
$969$	72.1956	+	41.6822i	0.0745053	+	0.0430157i
$970$		0			0
$971$	−329.817	−	571.261i	−0.339668	−	0.588322i	0.644702	−	0.764434i	$-0.276981\pi$
$971$	−329.817	−	571.261i	−0.339668	−	0.588322i	−0.984370	+	0.176112i	$0.943648\pi$
$972$		0			0
$973$	−213.418	−	1021.21i	−0.219341	−	1.04954i
$974$		0			0
$975$	−35.2448	−	61.0459i	−0.0361486	−	0.0626111i
$976$		0			0
$977$	957.151	−	1657.83i	0.979683	−	1.69686i	0.316160	−	0.948706i	$-0.397606\pi$
$977$	957.151	−	1657.83i	0.979683	−	1.69686i	0.663523	−	0.748156i	$-0.269060\pi$
$978$		0			0
$979$	−1584.07			−1.61804
$980$		0			0
$981$		−	135.723i		−	0.138352i
$982$		0			0
$983$	−193.655	−	111.806i	−0.197004	−	0.113740i	0.398253	−	0.917275i	$-0.369616\pi$
$983$	−193.655	−	111.806i	−0.197004	−	0.113740i	−0.595257	+	0.803535i	$0.702950\pi$
$984$		0			0
$985$	−745.591	+	430.467i	−0.756945	+	0.437022i
$986$		0			0
$987$	−834.053	+	174.306i	−0.845038	+	0.176602i
$988$		0			0
$989$	−467.616	+	269.978i	−0.472816	+	0.272981i
$990$		0			0
$991$	−736.371	+	1275.43i	−0.743058	+	1.28701i	0.208038	+	0.978121i	$0.433292\pi$
$991$	−736.371	+	1275.43i	−0.743058	+	1.28701i	−0.951096	+	0.308894i	$0.900041\pi$
$992$		0			0
$993$		−	260.472i		−	0.262308i
$994$		0			0
$995$		−	292.237i		−	0.293706i
$996$		0			0
$997$	53.4480	−	92.5746i	0.0536088	−	0.0928532i	−0.837976	−	0.545708i	$-0.816261\pi$
$997$	53.4480	−	92.5746i	0.0536088	−	0.0928532i	0.891584	+	0.452854i	$0.149594\pi$
$998$		0			0
$999$	−25.5150	+	14.7311i	−0.0255405	+	0.0147458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.n.a.17.11		28
4.3	odd	2		56.3.j.a.45.14	yes	28
7.3	odd	6		1568.3.h.a.881.21		28
7.4	even	3		1568.3.h.a.881.7		28
7.5	odd	6	inner	224.3.n.a.145.4		28
8.3	odd	2		56.3.j.a.45.5	yes	28
8.5	even	2	inner	224.3.n.a.17.4		28
28.3	even	6		392.3.h.a.293.11		28
28.11	odd	6		392.3.h.a.293.12		28
28.19	even	6		56.3.j.a.5.5	✓	28
28.23	odd	6		392.3.j.e.117.5		28
28.27	even	2		392.3.j.e.325.14		28
56.3	even	6		392.3.h.a.293.10		28
56.5	odd	6	inner	224.3.n.a.145.11		28
56.11	odd	6		392.3.h.a.293.9		28
56.19	even	6		56.3.j.a.5.14	yes	28
56.27	even	2		392.3.j.e.325.5		28
56.45	odd	6		1568.3.h.a.881.8		28
56.51	odd	6		392.3.j.e.117.14		28
56.53	even	6		1568.3.h.a.881.22		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.5	✓	28	28.19	even	6
56.3.j.a.5.14	yes	28	56.19	even	6
56.3.j.a.45.5	yes	28	8.3	odd	2
56.3.j.a.45.14	yes	28	4.3	odd	2
224.3.n.a.17.4		28	8.5	even	2	inner
224.3.n.a.17.11		28	1.1	even	1	trivial
224.3.n.a.145.4		28	7.5	odd	6	inner
224.3.n.a.145.11		28	56.5	odd	6	inner
392.3.h.a.293.9		28	56.11	odd	6
392.3.h.a.293.10		28	56.3	even	6
392.3.h.a.293.11		28	28.3	even	6
392.3.h.a.293.12		28	28.11	odd	6
392.3.j.e.117.5		28	28.23	odd	6
392.3.j.e.117.14		28	56.51	odd	6
392.3.j.e.325.5		28	56.27	even	2
392.3.j.e.325.14		28	28.27	even	2
1568.3.h.a.881.7		28	7.4	even	3
1568.3.h.a.881.8		28	56.45	odd	6
1568.3.h.a.881.21		28	7.3	odd	6
1568.3.h.a.881.22		28	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70138 - 2.94687i) q^{3} +(2.15858 + 3.73877i) q^{5} +(1.43197 + 6.85197i) q^{7} +(-1.28938 - 2.23327i) q^{9} +O(q^{10})\)	\(q+(1.70138 - 2.94687i) q^{3} +(2.15858 + 3.73877i) q^{5} +(1.43197 + 6.85197i) q^{7} +(-1.28938 - 2.23327i) q^{9} +(15.4899 + 8.94308i) q^{11} +3.25607 q^{13} +14.6903 q^{15} +(-13.6263 - 7.86717i) q^{17} +(-0.778522 - 1.34844i) q^{19} +(22.6282 + 7.43796i) q^{21} +(-20.7069 - 35.8655i) q^{23} +(3.18105 - 5.50975i) q^{25} +21.8499 q^{27} -3.74374i q^{29} +(0.0145172 + 0.00838150i) q^{31} +(52.7082 - 30.4311i) q^{33} +(-22.5269 + 20.1443i) q^{35} +(-1.16774 + 0.674194i) q^{37} +(5.53981 - 9.59523i) q^{39} +70.3018i q^{41} -13.0380i q^{43} +(5.56646 - 9.64139i) q^{45} +(-30.9797 + 17.8862i) q^{47} +(-44.8989 + 19.6236i) q^{49} +(-46.3671 + 26.7701i) q^{51} +(39.7989 + 22.9779i) q^{53} +77.2174i q^{55} -5.29824 q^{57} +(34.3509 - 59.4974i) q^{59} +(-48.0386 - 83.2052i) q^{61} +(13.4559 - 12.0328i) q^{63} +(7.02849 + 12.1737i) q^{65} +(-12.0808 - 6.97484i) q^{67} -140.921 q^{69} +75.7095 q^{71} +(-46.0282 - 26.5744i) q^{73} +(-10.8244 - 18.7483i) q^{75} +(-39.0967 + 118.942i) q^{77} +(-11.6744 - 20.2206i) q^{79} +(48.7794 - 84.4884i) q^{81} -102.487 q^{83} -67.9277i q^{85} +(-11.0323 - 6.36952i) q^{87} +(-76.6985 + 44.2819i) q^{89} +(4.66259 + 22.3105i) q^{91} +(0.0493984 - 0.0285202i) q^{93} +(3.36100 - 5.82143i) q^{95} -140.869i q^{97} -46.1241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) \) 28 * q + 4 * q^7 - 32 * q^9	\( 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) \) 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Introduction

L-functions

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