LMFDB - Embedded newform 784.2.bb.a.111.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.4
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.a.671.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.560590 - 0.702957i) q^{3} +(2.19080 - 1.74711i) q^{5} +(2.31112 + 1.28791i) q^{7} +(0.487675 - 2.13664i) q^{9} +O(q^{10})$	\(q+(-0.560590 - 0.702957i) q^{3} +(2.19080 - 1.74711i) q^{5} +(2.31112 + 1.28791i) q^{7} +(0.487675 - 2.13664i) q^{9} +(-0.0549517 + 0.0125424i) q^{11} +(0.507123 - 0.115747i) q^{13} +(-2.45628 - 0.560631i) q^{15} +(1.01960 - 2.11722i) q^{17} +0.578863 q^{19} +(-0.390248 - 2.34661i) q^{21} +(2.90194 + 6.02594i) q^{23} +(0.634629 - 2.78049i) q^{25} +(-4.20558 + 2.02530i) q^{27} +(-1.97138 - 0.949366i) q^{29} +0.487247 q^{31} +(0.0396221 + 0.0315976i) q^{33} +(7.31333 - 1.21623i) q^{35} +(-1.98964 - 0.958160i) q^{37} +(-0.365653 - 0.291599i) q^{39} +(2.98803 - 2.38288i) q^{41} +(-9.28042 - 7.40089i) q^{43} +(-2.66454 - 5.53298i) q^{45} +(-0.708665 - 3.10487i) q^{47} +(3.68259 + 5.95303i) q^{49} +(-2.05990 + 0.470158i) q^{51} +(7.43256 - 3.57933i) q^{53} +(-0.0984755 + 0.123484i) q^{55} +(-0.324505 - 0.406916i) q^{57} +(5.54338 - 6.95118i) q^{59} +(0.642889 - 1.33497i) q^{61} +(3.87888 - 4.30996i) q^{63} +(0.908783 - 1.13958i) q^{65} -1.50358i q^{67} +(2.60918 - 5.41802i) q^{69} +(-2.77845 - 5.76951i) q^{71} +(2.30514 + 0.526134i) q^{73} +(-2.31033 + 1.11260i) q^{75} +(-0.143154 - 0.0417858i) q^{77} +9.91121i q^{79} +(-2.14236 - 1.03170i) q^{81} +(-2.84261 + 12.4543i) q^{83} +(-1.46527 - 6.41977i) q^{85} +(0.437771 + 1.91800i) q^{87} +(5.82451 + 1.32941i) q^{89} +(1.32110 + 0.385621i) q^{91} +(-0.273145 - 0.342514i) q^{93} +(1.26817 - 1.01134i) q^{95} +17.7935i q^{97} +0.123529i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 14 q^{17} + 12 q^{25} + 28 q^{29} + 42 q^{37} + 28 q^{41} + 56 q^{49} - 38 q^{53} + 42 q^{57} + 84 q^{61} + 8 q^{65} + 56 q^{69} - 42 q^{73} - 42 q^{77} - 44 q^{81} - 12 q^{85} - 28 q^{89} + 98 q^{93}+O(q^{100}) $ 48 * q - 4 * q^9 + 14 * q^17 + 12 * q^25 + 28 * q^29 + 42 * q^37 + 28 * q^41 + 56 * q^49 - 38 * q^53 + 42 * q^57 + 84 * q^61 + 8 * q^65 + 56 * q^69 - 42 * q^73 - 42 * q^77 - 44 * q^81 - 12 * q^85 - 28 * q^89 + 98 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.560590	−	0.702957i	−0.323657	−	0.405853i	0.593209	−	0.805048i	$-0.297861\pi$
$3$	−0.560590	−	0.702957i	−0.323657	−	0.405853i	−0.916866	+	0.399196i	$0.869289\pi$
$4$		0			0
$5$	2.19080	−	1.74711i	0.979757	−	0.781330i	0.00395614	−	0.999992i	$-0.498741\pi$
$5$	2.19080	−	1.74711i	0.979757	−	0.781330i	0.975801	+	0.218662i	$0.0701693\pi$
$6$		0			0
$7$	2.31112	+	1.28791i	0.873523	+	0.486783i
$7$	2.31112	+	1.28791i	0.873523	+	0.486783i
$8$		0			0
$9$	0.487675	−	2.13664i	0.162558	−	0.712214i
$10$		0			0
$11$	−0.0549517	+	0.0125424i	−0.0165686	+	0.00378167i	−0.230797	−	0.973002i	$-0.574133\pi$
$11$	−0.0549517	+	0.0125424i	−0.0165686	+	0.00378167i	0.214229	+	0.976784i	$0.431276\pi$
$12$		0			0
$13$	0.507123	−	0.115747i	0.140651	−	0.0321026i	−0.151616	−	0.988439i	$-0.548448\pi$
$13$	0.507123	−	0.115747i	0.140651	−	0.0321026i	0.292267	+	0.956337i	$0.405591\pi$
$14$		0			0
$15$	−2.45628	−	0.560631i	−0.634210	−	0.144754i
$16$		0			0
$17$	1.01960	−	2.11722i	0.247290	−	0.513502i	−0.739966	−	0.672644i	$-0.765158\pi$
$17$	1.01960	−	2.11722i	0.247290	−	0.513502i	0.987256	+	0.159142i	$0.0508728\pi$
$18$		0			0
$19$	0.578863			0.132800			0.0664001	−	0.997793i	$-0.478849\pi$
$19$	0.578863			0.132800			0.0664001	+	0.997793i	$0.478849\pi$
$20$		0			0
$21$	−0.390248	−	2.34661i	−0.0851591	−	0.512072i
$22$		0			0
$23$	2.90194	+	6.02594i	0.605096	+	1.25650i	0.948342	+	0.317250i	$0.102759\pi$
$23$	2.90194	+	6.02594i	0.605096	+	1.25650i	−0.343246	+	0.939246i	$0.611526\pi$
$24$		0			0
$25$	0.634629	−	2.78049i	0.126926	−	0.556099i
$26$		0			0
$27$	−4.20558	+	2.02530i	−0.809364	+	0.389769i
$28$		0			0
$29$	−1.97138	−	0.949366i	−0.366076	−	0.176293i	0.241798	−	0.970327i	$-0.422263\pi$
$29$	−1.97138	−	0.949366i	−0.366076	−	0.176293i	−0.607873	+	0.794034i	$0.707977\pi$
$30$		0			0
$31$	0.487247			0.0875121			0.0437560	−	0.999042i	$-0.486068\pi$
$31$	0.487247			0.0875121			0.0437560	+	0.999042i	$0.486068\pi$
$32$		0			0
$33$	0.0396221	+	0.0315976i	0.00689732	+	0.00550043i
$34$		0			0
$35$	7.31333	−	1.21623i	1.23618	−	0.205580i
$36$		0			0
$37$	−1.98964	−	0.958160i	−0.327095	−	0.157520i	0.263128	−	0.964761i	$-0.415246\pi$
$37$	−1.98964	−	0.958160i	−0.327095	−	0.157520i	−0.590223	+	0.807240i	$0.700960\pi$
$38$		0			0
$39$	−0.365653	−	0.291599i	−0.0585514	−	0.0466932i
$40$		0			0
$41$	2.98803	−	2.38288i	0.466652	−	0.372143i	−0.361751	−	0.932275i	$-0.617821\pi$
$41$	2.98803	−	2.38288i	0.466652	−	0.372143i	0.828403	+	0.560132i	$0.189250\pi$
$42$		0			0
$43$	−9.28042	−	7.40089i	−1.41525	−	1.12863i	−0.972750	−	0.231857i	$-0.925520\pi$
$43$	−9.28042	−	7.40089i	−1.41525	−	1.12863i	−0.442501	−	0.896768i	$-0.645909\pi$
$44$		0			0
$45$	−2.66454	−	5.53298i	−0.397207	−	0.824808i
$46$		0			0
$47$	−0.708665	−	3.10487i	−0.103369	−	0.452891i	−0.999950	−	0.0100103i	$-0.996814\pi$
$47$	−0.708665	−	3.10487i	−0.103369	−	0.452891i	0.896580	−	0.442881i	$-0.146044\pi$
$48$		0			0
$49$	3.68259	+	5.95303i	0.526084	+	0.850433i
$50$		0			0
$51$	−2.05990	+	0.470158i	−0.288443	+	0.0658353i
$52$		0			0
$53$	7.43256	−	3.57933i	1.02094	−	0.491659i	0.152947	−	0.988234i	$-0.451124\pi$
$53$	7.43256	−	3.57933i	1.02094	−	0.491659i	0.867994	+	0.496575i	$0.165409\pi$
$54$		0			0
$55$	−0.0984755	+	0.123484i	−0.0132784	+	0.0166506i
$56$		0			0
$57$	−0.324505	−	0.406916i	−0.0429817	−	0.0538973i
$58$		0			0
$59$	5.54338	−	6.95118i	0.721687	−	0.904966i	−0.276746	−	0.960943i	$-0.589256\pi$
$59$	5.54338	−	6.95118i	0.721687	−	0.904966i	0.998432	+	0.0559769i	$0.0178273\pi$
$60$		0			0
$61$	0.642889	−	1.33497i	0.0823135	−	0.170926i	−0.855750	−	0.517390i	$-0.826904\pi$
$61$	0.642889	−	1.33497i	0.0823135	−	0.170926i	0.938063	+	0.346464i	$0.112618\pi$
$62$		0			0
$63$	3.87888	−	4.30996i	0.488692	−	0.543005i
$64$		0			0
$65$	0.908783	−	1.13958i	0.112721	−	0.141347i
$66$		0			0
$67$		−	1.50358i		−	0.183691i	−0.995773	−	0.0918455i	$-0.970723\pi$
$67$		−	1.50358i		−	0.183691i	0.995773	−	0.0918455i	$-0.0292766\pi$
$68$		0			0
$69$	2.60918	−	5.41802i	0.314108	−	0.652253i
$70$		0			0
$71$	−2.77845	−	5.76951i	−0.329741	−	0.684714i	0.668518	−	0.743696i	$-0.266929\pi$
$71$	−2.77845	−	5.76951i	−0.329741	−	0.684714i	−0.998259	+	0.0589816i	$0.981215\pi$
$72$		0			0
$73$	2.30514	+	0.526134i	0.269797	+	0.0615793i	0.355279	−	0.934760i	$-0.384386\pi$
$73$	2.30514	+	0.526134i	0.269797	+	0.0615793i	−0.0854822	+	0.996340i	$0.527243\pi$
$74$		0			0
$75$	−2.31033	+	1.11260i	−0.266774	+	0.128472i
$76$		0			0
$77$	−0.143154	−	0.0417858i	−0.0163139	−	0.00476193i
$78$		0			0
$79$			9.91121i			1.11510i	0.830144	+	0.557549i	$0.188258\pi$
$79$			9.91121i			1.11510i	−0.830144	+	0.557549i	$0.811742\pi$
$80$		0			0
$81$	−2.14236	−	1.03170i	−0.238040	−	0.114634i
$82$		0			0
$83$	−2.84261	+	12.4543i	−0.312017	+	1.36704i	0.539180	+	0.842190i	$0.318734\pi$
$83$	−2.84261	+	12.4543i	−0.312017	+	1.36704i	−0.851197	+	0.524846i	$0.824123\pi$
$84$		0			0
$85$	−1.46527	−	6.41977i	−0.158931	−	0.696322i
$86$		0			0
$87$	0.437771	+	1.91800i	0.0469340	+	0.205631i
$88$		0			0
$89$	5.82451	+	1.32941i	0.617397	+	0.140917i	0.519770	−	0.854306i	$-0.326018\pi$
$89$	5.82451	+	1.32941i	0.617397	+	0.140917i	0.0976269	+	0.995223i	$0.468875\pi$
$90$		0			0
$91$	1.32110	+	0.385621i	0.138488	+	0.0404240i
$92$		0			0
$93$	−0.273145	−	0.342514i	−0.0283239	−	0.0355170i
$94$		0			0
$95$	1.26817	−	1.01134i	0.130112	−	0.103761i
$96$		0			0
$97$			17.7935i			1.80665i	0.428955	+	0.903326i	$0.358882\pi$
$97$			17.7935i			1.80665i	−0.428955	+	0.903326i	$0.641118\pi$
$98$		0			0
$99$			0.123529i			0.0124151i
$100$		0			0
$101$	2.41978	−	1.92971i	0.240777	−	0.192013i	−0.495665	−	0.868514i	$-0.665076\pi$
$101$	2.41978	−	1.92971i	0.240777	−	0.192013i	0.736442	+	0.676500i	$0.236504\pi$
$102$		0			0
$103$	−6.05071	−	7.58735i	−0.596194	−	0.747604i	0.388585	−	0.921413i	$-0.372964\pi$
$103$	−6.05071	−	7.58735i	−0.596194	−	0.747604i	−0.984779	+	0.173809i	$0.944393\pi$
$104$		0			0
$105$	−4.95473	−	4.45915i	−0.483533	−	0.435169i
$106$		0			0
$107$	−3.33809	−	0.761897i	−0.322705	−	0.0736554i	0.0580997	−	0.998311i	$-0.481496\pi$
$107$	−3.33809	−	0.761897i	−0.322705	−	0.0736554i	−0.380805	+	0.924655i	$0.624353\pi$
$108$		0			0
$109$	−1.82745	−	8.00656i	−0.175038	−	0.766890i	−0.983875	−	0.178857i	$-0.942760\pi$
$109$	−1.82745	−	8.00656i	−0.175038	−	0.766890i	0.808837	−	0.588032i	$-0.200097\pi$
$110$		0			0
$111$	0.441826	+	1.93577i	0.0419363	+	0.183735i
$112$		0			0
$113$	−3.20477	+	14.0410i	−0.301479	+	1.32087i	0.566416	+	0.824119i	$0.308329\pi$
$113$	−3.20477	+	14.0410i	−0.301479	+	1.32087i	−0.867896	+	0.496747i	$0.834528\pi$
$114$		0			0
$115$	16.8855	+	8.13165i	1.57458	+	0.758280i
$116$		0			0
$117$		−	1.13999i		−	0.105392i
$118$		0			0
$119$	5.08321	−	3.58001i	0.465977	−	0.328179i
$120$		0			0
$121$	−9.90780	+	4.77134i	−0.900709	+	0.433758i
$122$		0			0
$123$	−3.35012	−	0.764643i	−0.302070	−	0.0689455i
$124$		0			0
$125$	2.61155	+	5.42294i	0.233584	+	0.485042i
$126$		0			0
$127$	1.37909	−	2.86372i	0.122375	−	0.254114i	−0.830778	−	0.556605i	$-0.812104\pi$
$127$	1.37909	−	2.86372i	0.122375	−	0.254114i	0.953152	+	0.302491i	$0.0978181\pi$
$128$		0			0
$129$			10.6726i			0.939670i
$130$		0			0
$131$	−7.87383	+	9.87347i	−0.687940	+	0.862649i	−0.996058	−	0.0886989i	$-0.971729\pi$
$131$	−7.87383	+	9.87347i	−0.687940	+	0.862649i	0.308119	+	0.951348i	$0.400301\pi$
$132$		0			0
$133$	1.33782	+	0.745522i	0.116004	+	0.0646449i
$134$		0			0
$135$	−5.67518	+	11.7846i	−0.488442	+	1.01426i
$136$		0			0
$137$	−10.9769	+	13.7646i	−0.937818	+	1.17599i	0.0463815	+	0.998924i	$0.485231\pi$
$137$	−10.9769	+	13.7646i	−0.937818	+	1.17599i	−0.984200	+	0.177063i	$0.943340\pi$
$138$		0			0
$139$	11.9311	+	14.9611i	1.01198	+	1.26898i	0.962806	+	0.270195i	$0.0870881\pi$
$139$	11.9311	+	14.9611i	1.01198	+	1.26898i	0.0491761	+	0.998790i	$0.484340\pi$
$140$		0			0
$141$	−1.78532	+	2.23872i	−0.150351	+	0.188534i
$142$		0			0
$143$	−0.0264155	+	0.0127210i	−0.00220898	+	0.00106379i
$144$		0			0
$145$	−5.97754	+	1.36434i	−0.496408	+	0.113302i
$146$		0			0
$147$	2.12031	−	5.92591i	0.174880	−	0.488761i
$148$		0			0
$149$	0.825097	+	3.61499i	0.0675946	+	0.296151i	0.997414	−	0.0718637i	$-0.0228947\pi$
$149$	0.825097	+	3.61499i	0.0675946	+	0.296151i	−0.929820	+	0.368015i	$0.880038\pi$
$150$		0			0
$151$	−6.49987	−	13.4971i	−0.528952	−	1.09838i	−0.978713	−	0.205232i	$-0.934205\pi$
$151$	−6.49987	−	13.4971i	−0.528952	−	1.09838i	0.449761	−	0.893149i	$-0.351509\pi$
$152$		0			0
$153$	−4.02652	−	3.21104i	−0.325524	−	0.259597i
$154$		0			0
$155$	1.06746	−	0.851272i	0.0857405	−	0.0683758i
$156$		0			0
$157$	−8.38528	−	6.68703i	−0.669218	−	0.533683i	0.228894	−	0.973451i	$-0.426489\pi$
$157$	−8.38528	−	6.68703i	−0.669218	−	0.533683i	−0.898111	+	0.439768i	$0.855061\pi$
$158$		0			0
$159$	−6.68274	−	3.21824i	−0.529976	−	0.255223i
$160$		0			0
$161$	−1.05411	+	17.6641i	−0.0830758	+	1.39213i
$162$		0			0
$163$	−10.7557	−	8.57741i	−0.842454	−	0.671834i	0.104034	−	0.994574i	$-0.466825\pi$
$163$	−10.7557	−	8.57741i	−0.842454	−	0.671834i	−0.946488	+	0.322739i	$0.895396\pi$
$164$		0			0
$165$	0.142009			0.0110553
$166$		0			0
$167$	10.8911	+	5.24488i	0.842779	+	0.405861i	0.804892	−	0.593421i	$-0.202223\pi$
$167$	10.8911	+	5.24488i	0.842779	+	0.405861i	0.0378871	+	0.999282i	$0.487937\pi$
$168$		0			0
$169$	−11.4688	+	5.52309i	−0.882217	+	0.424853i
$170$		0			0
$171$	0.282297	−	1.23682i	0.0215878	−	0.0945822i
$172$		0			0
$173$	4.22153	+	8.76610i	0.320957	+	0.666474i	0.997556	−	0.0698779i	$-0.0222610\pi$
$173$	4.22153	+	8.76610i	0.320957	+	0.666474i	−0.676598	+	0.736352i	$0.736547\pi$
$174$		0			0
$175$	5.04773	−	5.60872i	0.381572	−	0.423979i
$176$		0			0
$177$	−7.99394			−0.600862
$178$		0			0
$179$	10.2731	−	21.3324i	0.767850	−	1.59446i	−0.0358025	−	0.999359i	$-0.511399\pi$
$179$	10.2731	−	21.3324i	0.767850	−	1.59446i	0.803653	−	0.595099i	$-0.202887\pi$
$180$		0			0
$181$	−13.8785	−	3.16768i	−1.03158	−	0.235452i	−0.326963	−	0.945037i	$-0.606025\pi$
$181$	−13.8785	−	3.16768i	−1.03158	−	0.235452i	−0.704620	+	0.709585i	$0.748882\pi$
$182$		0			0
$183$	−1.29883	+	0.296449i	−0.0960120	+	0.0219141i
$184$		0			0
$185$	−6.03291	+	1.37697i	−0.443549	+	0.101237i
$186$		0			0
$187$	−0.0294738	+	0.129133i	−0.00215534	+	0.00944315i
$188$		0			0
$189$	−12.3280	−	0.735680i	−0.896731	−	0.0535128i
$190$		0			0
$191$	−15.7142	+	12.5316i	−1.13704	+	0.906756i	−0.996523	−	0.0833226i	$-0.973447\pi$
$191$	−15.7142	+	12.5316i	−1.13704	+	0.906756i	−0.140514	+	0.990079i	$0.544875\pi$
$192$		0			0
$193$	12.0772	+	15.1443i	0.869337	+	1.09011i	0.995180	+	0.0980639i	$0.0312650\pi$
$193$	12.0772	+	15.1443i	0.869337	+	1.09011i	−0.125843	+	0.992050i	$0.540164\pi$
$194$		0			0
$195$	−1.31053			−0.0938489
$196$		0			0
$197$	19.9897			1.42421			0.712105	−	0.702073i	$-0.247742\pi$
$197$	19.9897			1.42421			0.712105	+	0.702073i	$0.247742\pi$
$198$		0			0
$199$	16.0957	+	20.1834i	1.14099	+	1.43076i	0.885919	+	0.463840i	$0.153529\pi$
$199$	16.0957	+	20.1834i	1.14099	+	1.43076i	0.255075	+	0.966921i	$0.417900\pi$
$200$		0			0
$201$	−1.05695	+	0.842889i	−0.0745515	+	0.0594528i
$202$		0			0
$203$	−3.33340	−	4.73305i	−0.233959	−	0.332195i
$204$		0			0
$205$	2.38305	−	10.4408i	0.166439	−	0.729219i
$206$		0			0
$207$	14.2905	−	3.26171i	0.993257	−	0.226704i
$208$		0			0
$209$	−0.0318095	+	0.00726031i	−0.00220031	+	0.000502206i
$210$		0			0
$211$	−11.4060	−	2.60334i	−0.785219	−	0.179221i	−0.188930	−	0.981991i	$-0.560502\pi$
$211$	−11.4060	−	2.60334i	−0.785219	−	0.179221i	−0.596289	+	0.802769i	$0.703359\pi$
$212$		0			0
$213$	−2.49815	+	5.18746i	−0.171170	+	0.355439i
$214$		0			0
$215$	−33.2617			−2.26843
$216$		0			0
$217$	1.12609	+	0.627529i	0.0764438	+	0.0425994i
$218$		0			0
$219$	−0.922390	−	1.91536i	−0.0623293	−	0.129428i
$220$		0			0
$221$	0.272000	−	1.19171i	0.0182967	−	0.0801630i
$222$		0			0
$223$	20.1356	−	9.69678i	1.34838	−	0.649344i	0.386364	−	0.922346i	$-0.373731\pi$
$223$	20.1356	−	9.69678i	1.34838	−	0.649344i	0.962014	+	0.273002i	$0.0880165\pi$
$224$		0			0
$225$	−5.63143	−	2.71195i	−0.375428	−	0.180797i
$226$		0			0
$227$	10.6745			0.708495			0.354247	−	0.935152i	$-0.384737\pi$
$227$	10.6745			0.708495			0.354247	+	0.935152i	$0.384737\pi$
$228$		0			0
$229$	−4.81787	−	3.84212i	−0.318374	−	0.253895i	0.451242	−	0.892401i	$-0.350981\pi$
$229$	−4.81787	−	3.84212i	−0.318374	−	0.253895i	−0.769616	+	0.638507i	$0.779552\pi$
$230$		0			0
$231$	0.0508768	+	0.124056i	0.00334745	+	0.00816225i
$232$		0			0
$233$	18.5690	+	8.94237i	1.21650	+	0.585834i	0.928334	−	0.371748i	$-0.121241\pi$
$233$	18.5690	+	8.94237i	1.21650	+	0.585834i	0.288163	+	0.957581i	$0.406956\pi$
$234$		0			0
$235$	−6.97708	−	5.56403i	−0.455134	−	0.362958i
$236$		0			0
$237$	6.96716	−	5.55612i	0.452566	−	0.360909i
$238$		0			0
$239$	3.95182	+	3.15147i	0.255622	+	0.203852i	0.742913	−	0.669388i	$-0.233444\pi$
$239$	3.95182	+	3.15147i	0.255622	+	0.203852i	−0.487291	+	0.873240i	$0.662015\pi$
$240$		0			0
$241$	0.589430	+	1.22396i	0.0379685	+	0.0788424i	0.919090	−	0.394047i	$-0.128925\pi$
$241$	0.589430	+	1.22396i	0.0379685	+	0.0788424i	−0.881122	+	0.472889i	$0.843211\pi$
$242$		0			0
$243$	3.59182	+	15.7368i	0.230415	+	1.00951i
$244$		0			0
$245$	18.4684	+	6.60804i	1.17990	+	0.422172i
$246$		0			0
$247$	0.293554	−	0.0670019i	0.0186784	−	0.00426323i
$248$		0			0
$249$	10.3484	−	4.98351i	0.655802	−	0.315817i
$250$		0			0
$251$	−8.12860	+	10.1929i	−0.513073	+	0.643373i	−0.969122	−	0.246582i	$-0.920693\pi$
$251$	−8.12860	+	10.1929i	−0.513073	+	0.643373i	0.456049	+	0.889954i	$0.349264\pi$
$252$		0			0
$253$	−0.235046	−	0.294738i	−0.0147772	−	0.0185300i
$254$		0			0
$255$	−3.69141	+	4.62888i	−0.231165	+	0.289872i
$256$		0			0
$257$	−4.97938	+	10.3398i	−0.310605	+	0.644978i	−0.996579	−	0.0826481i	$-0.973662\pi$
$257$	−4.97938	+	10.3398i	−0.310605	+	0.644978i	0.685974	+	0.727626i	$0.259377\pi$
$258$		0			0
$259$	−3.36428	−	4.77690i	−0.209046	−	0.296822i
$260$		0			0
$261$	−2.98985	+	3.74915i	−0.185067	+	0.232066i
$262$		0			0
$263$		−	20.8260i		−	1.28419i	−0.766626	−	0.642094i	$-0.778066\pi$
$263$		−	20.8260i		−	1.28419i	0.766626	−	0.642094i	$-0.221934\pi$
$264$		0			0
$265$	10.0298	−	20.8271i	0.616126	−	1.27940i
$266$		0			0
$267$	−2.33064	−	4.83963i	−0.142633	−	0.296181i
$268$		0			0
$269$	9.43388	+	2.15322i	0.575194	+	0.131284i	0.500216	−	0.865901i	$-0.333254\pi$
$269$	9.43388	+	2.15322i	0.575194	+	0.131284i	0.0749783	+	0.997185i	$0.476111\pi$
$270$		0			0
$271$	−18.3974	+	8.85974i	−1.11756	+	0.538191i	−0.899139	−	0.437663i	$-0.855806\pi$
$271$	−18.3974	+	8.85974i	−1.11756	+	0.538191i	−0.218425	+	0.975854i	$0.570092\pi$
$272$		0			0
$273$	−0.469518	−	1.14485i	−0.0284165	−	0.0692894i
$274$		0			0
$275$			0.160753i			0.00969374i
$276$		0			0
$277$	−20.3057	−	9.77873i	−1.22005	−	0.587547i	−0.290727	−	0.956806i	$-0.593897\pi$
$277$	−20.3057	−	9.77873i	−1.22005	−	0.587547i	−0.929326	+	0.369259i	$0.879611\pi$
$278$		0			0
$279$	0.237618	−	1.04107i	0.0142258	−	0.0623273i
$280$		0			0
$281$	−2.99084	−	13.1037i	−0.178419	−	0.781703i	−0.982361	−	0.186996i	$-0.940125\pi$
$281$	−2.99084	−	13.1037i	−0.178419	−	0.781703i	0.803942	−	0.594708i	$-0.202732\pi$
$282$		0			0
$283$	5.50873	+	24.1353i	0.327460	+	1.43470i	0.823954	+	0.566656i	$0.191763\pi$
$283$	5.50873	+	24.1353i	0.327460	+	1.43470i	−0.496494	+	0.868040i	$0.665380\pi$
$284$		0			0
$285$	−1.42185	−	0.324528i	−0.0842232	−	0.0192234i
$286$		0			0
$287$	9.97464	−	1.65881i	0.588784	−	0.0979165i
$288$		0			0
$289$	7.15628	+	8.97369i	0.420958	+	0.527864i
$290$		0			0
$291$	12.5080	−	9.97483i	0.733234	−	0.584735i
$292$		0			0
$293$			32.2681i			1.88512i	0.334036	+	0.942560i	$0.391589\pi$
$293$			32.2681i			1.88512i	−0.334036	+	0.942560i	$0.608411\pi$
$294$		0			0
$295$		−	24.9135i		−	1.45052i
$296$		0			0
$297$	0.205702	−	0.164042i	0.0119360	−	0.00951866i
$298$		0			0
$299$	2.16913	+	2.72000i	0.125444	+	0.157302i
$300$		0			0
$301$	−11.9165	−	29.0567i	−0.686858	−	1.67480i
$302$		0			0
$303$	−2.71300	−	0.619225i	−0.155858	−	0.0355736i
$304$		0			0
$305$	−0.923897	−	4.04786i	−0.0529022	−	0.231780i
$306$		0			0
$307$	3.83620	+	16.8075i	0.218944	+	0.959255i	0.958260	+	0.285897i	$0.0922916\pi$
$307$	3.83620	+	16.8075i	0.218944	+	0.959255i	−0.739317	+	0.673358i	$0.764851\pi$
$308$		0			0
$309$	−1.94162	+	8.50678i	−0.110455	+	0.483934i
$310$		0			0
$311$	−6.72327	−	3.23775i	−0.381242	−	0.183596i	0.233441	−	0.972371i	$-0.425001\pi$
$311$	−6.72327	−	3.23775i	−0.381242	−	0.183596i	−0.614682	+	0.788775i	$0.710716\pi$
$312$		0			0
$313$		−	13.8301i		−	0.781723i	−0.920449	−	0.390862i	$-0.872177\pi$
$313$		−	13.8301i		−	0.781723i	0.920449	−	0.390862i	$-0.127823\pi$
$314$		0			0
$315$	0.967881	−	16.2191i	0.0545339	−	0.913842i
$316$		0			0
$317$	−6.64938	+	3.20217i	−0.373466	+	0.179852i	−0.611196	−	0.791480i	$-0.709311\pi$
$317$	−6.64938	+	3.20217i	−0.373466	+	0.179852i	0.237729	+	0.971331i	$0.423597\pi$
$318$		0			0
$319$	0.120238	+	0.0274435i	0.00673203	+	0.00153654i
$320$		0			0
$321$	1.33572	+	2.77365i	0.0745525	+	0.154810i
$322$		0			0
$323$	0.590209	−	1.22558i	0.0328401	−	0.0681932i
$324$		0			0
$325$		−	1.48351i		−	0.0822902i
$326$		0			0
$327$	−4.60382	+	5.77301i	−0.254592	+	0.319248i
$328$		0			0
$329$	2.36097	−	8.08843i	0.130164	−	0.445929i
$330$		0			0
$331$	5.44844	−	11.3138i	0.299473	−	0.621863i	−0.695879	−	0.718159i	$-0.744985\pi$
$331$	5.44844	−	11.3138i	0.299473	−	0.621863i	0.995353	+	0.0962959i	$0.0306995\pi$
$332$		0			0
$333$	−3.01754	+	3.78388i	−0.165360	+	0.207355i
$334$		0			0
$335$	−2.62691	−	3.29404i	−0.143523	−	0.179972i
$336$		0			0
$337$	12.1479	−	15.2330i	0.661739	−	0.829794i	−0.331792	−	0.943352i	$-0.607653\pi$
$337$	12.1479	−	15.2330i	0.661739	−	0.829794i	0.993531	+	0.113558i	$0.0362248\pi$
$338$		0			0
$339$	11.6668	−	5.61843i	0.633653	−	0.305151i
$340$		0			0
$341$	−0.0267750	+	0.00611122i	−0.00144995	+	0.000330941i
$342$		0			0
$343$	0.843958	+	18.5010i	0.0455695	+	0.998961i
$344$		0			0
$345$	−3.74966	−	16.4283i	−0.201875	−	0.884472i
$346$		0			0
$347$	−7.28755	−	15.1328i	−0.391216	−	0.812369i	−0.999821	−	0.0188956i	$-0.993985\pi$
$347$	−7.28755	−	15.1328i	−0.391216	−	0.812369i	0.608605	−	0.793473i	$-0.291729\pi$
$348$		0			0
$349$	−23.5747	−	18.8002i	−1.26192	−	1.00635i	−0.999139	−	0.0414974i	$-0.986787\pi$
$349$	−23.5747	−	18.8002i	−1.26192	−	1.00635i	−0.262786	−	0.964854i	$-0.584641\pi$
$350$		0			0
$351$	−1.89832	+	1.51386i	−0.101325	+	0.0808039i
$352$		0			0
$353$	15.9957	+	12.7561i	0.851364	+	0.678940i	0.948654	−	0.316316i	$-0.102446\pi$
$353$	15.9957	+	12.7561i	0.851364	+	0.678940i	−0.0972896	+	0.995256i	$0.531017\pi$
$354$		0			0
$355$	−16.1670	−	7.78560i	−0.858054	−	0.413217i
$356$		0			0
$357$	−5.36619	−	1.56636i	−0.284009	−	0.0829007i
$358$		0			0
$359$	2.72814	+	2.17562i	0.143986	+	0.114825i	0.692834	−	0.721097i	$-0.256362\pi$
$359$	2.72814	+	2.17562i	0.143986	+	0.114825i	−0.548848	+	0.835922i	$0.684933\pi$
$360$		0			0
$361$	−18.6649			−0.982364
$362$		0			0
$363$	8.90826	+	4.28999i	0.467562	+	0.225166i
$364$		0			0
$365$	5.96933	−	2.87468i	0.312449	−	0.150467i
$366$		0			0
$367$	2.52566	−	11.0657i	0.131839	−	0.577623i	−0.865248	−	0.501344i	$-0.832839\pi$
$367$	2.52566	−	11.0657i	0.131839	−	0.577623i	0.997087	−	0.0762785i	$-0.0243038\pi$
$368$		0			0
$369$	−3.63417	−	7.54642i	−0.189187	−	0.392851i
$370$		0			0
$371$	21.7874	+	1.30017i	1.13115	+	0.0675017i
$372$		0			0
$373$	3.48227			0.180305			0.0901526	−	0.995928i	$-0.471265\pi$
$373$	3.48227			0.180305			0.0901526	+	0.995928i	$0.471265\pi$
$374$		0			0
$375$	2.34809	−	4.87585i	0.121255	−	0.251788i
$376$		0			0
$377$	−1.10962	−	0.253263i	−0.0571482	−	0.0130437i
$378$		0			0
$379$	−27.8263	+	6.35117i	−1.42934	+	0.326238i	−0.866024	−	0.500003i	$-0.833332\pi$
$379$	−27.8263	+	6.35117i	−1.42934	+	0.326238i	−0.563317	+	0.826241i	$0.690475\pi$
$380$		0			0
$381$	−2.78618	+	0.635927i	−0.142740	+	0.0325795i
$382$		0			0
$383$	−3.71020	+	16.2555i	−0.189582	+	0.830615i	0.787254	+	0.616629i	$0.211502\pi$
$383$	−3.71020	+	16.2555i	−0.189582	+	0.830615i	−0.976837	+	0.213986i	$0.931355\pi$
$384$		0			0
$385$	−0.386625	+	0.158560i	−0.0197043	+	0.00808098i
$386$		0			0
$387$	−20.3389	+	16.2197i	−1.03388	+	0.824495i
$388$		0			0
$389$	18.1048	+	22.7027i	0.917949	+	1.15107i	0.988143	+	0.153538i	$0.0490669\pi$
$389$	18.1048	+	22.7027i	0.917949	+	1.15107i	−0.0701935	+	0.997533i	$0.522362\pi$
$390$		0			0
$391$	15.7171			0.794847
$392$		0			0
$393$	11.3546			0.572765
$394$		0			0
$395$	17.3159	+	21.7135i	0.871260	+	1.09253i
$396$		0			0
$397$	10.3116	−	8.22322i	0.517524	−	0.412712i	−0.329589	−	0.944125i	$-0.606910\pi$
$397$	10.3116	−	8.22322i	0.517524	−	0.412712i	0.847113	+	0.531413i	$0.178339\pi$
$398$		0			0
$399$	−0.225900	−	1.35836i	−0.0113091	−	0.0680033i
$400$		0			0
$401$	4.02067	−	17.6157i	0.200783	−	0.879686i	−0.769679	−	0.638431i	$-0.779584\pi$
$401$	4.02067	−	17.6157i	0.200783	−	0.879686i	0.970462	−	0.241255i	$-0.0775591\pi$
$402$		0			0
$403$	0.247094	−	0.0563975i	0.0123086	−	0.00280936i
$404$		0			0
$405$	−6.49598	+	1.48267i	−0.322788	+	0.0736742i
$406$		0			0
$407$	0.121352	+	0.0276977i	0.00601518	+	0.00137292i
$408$		0			0
$409$	10.6770	−	22.1710i	0.527944	−	1.09629i	−0.451069	−	0.892489i	$-0.648957\pi$
$409$	10.6770	−	22.1710i	0.527944	−	1.09629i	0.979013	−	0.203798i	$-0.0653286\pi$
$410$		0			0
$411$	15.8294			0.780808
$412$		0			0
$413$	21.7639	−	8.92567i	1.07093	−	0.439204i
$414$		0			0
$415$	15.5314	+	32.2512i	0.762405	+	1.58315i
$416$		0			0
$417$	3.82858	−	16.7741i	0.187486	−	0.821431i
$418$		0			0
$419$	−29.2647	+	14.0931i	−1.42967	+	0.688494i	−0.978937	−	0.204164i	$-0.934553\pi$
$419$	−29.2647	+	14.0931i	−1.42967	+	0.688494i	−0.450735	+	0.892658i	$0.648838\pi$
$420$		0			0
$421$	−3.94098	−	1.89787i	−0.192071	−	0.0924968i	0.335376	−	0.942084i	$-0.391137\pi$
$421$	−3.94098	−	1.89787i	−0.192071	−	0.0924968i	−0.527448	+	0.849588i	$0.676851\pi$
$422$		0			0
$423$	−6.97959			−0.339359
$424$		0			0
$425$	−5.23986	−	4.17865i	−0.254170	−	0.202694i
$426$		0			0
$427$	3.20512	−	2.25731i	0.155107	−	0.109239i
$428$		0			0
$429$	0.0237506	+	0.0114377i	0.00114669	+	0.000552217i
$430$		0			0
$431$	11.8056	+	9.41463i	0.568654	+	0.453487i	0.865126	−	0.501555i	$-0.167239\pi$
$431$	11.8056	+	9.41463i	0.568654	+	0.453487i	−0.296471	+	0.955042i	$0.595810\pi$
$432$		0			0
$433$	19.5472	−	15.5884i	0.939380	−	0.749131i	−0.0287476	−	0.999587i	$-0.509152\pi$
$433$	19.5472	−	15.5884i	0.939380	−	0.749131i	0.968128	+	0.250456i	$0.0805805\pi$
$434$		0			0
$435$	4.31002	+	3.43713i	0.206650	+	0.164798i
$436$		0			0
$437$	1.67982	+	3.48819i	0.0803569	+	0.166863i
$438$		0			0
$439$	−5.55204	−	24.3251i	−0.264984	−	1.16097i	−0.915768	−	0.401708i	$-0.868417\pi$
$439$	−5.55204	−	24.3251i	−0.264984	−	1.16097i	0.650784	−	0.759263i	$-0.274441\pi$
$440$		0			0
$441$	14.5154	−	4.96523i	0.691209	−	0.236439i
$442$		0			0
$443$	−0.651888	+	0.148789i	−0.0309721	+	0.00706918i	−0.237979	−	0.971270i	$-0.576485\pi$
$443$	−0.651888	+	0.148789i	−0.0309721	+	0.00706918i	0.207007	+	0.978340i	$0.433628\pi$
$444$		0			0
$445$	15.0830	−	7.26357i	0.715001	−	0.344326i
$446$		0			0
$447$	2.07864	−	2.60653i	0.0983163	−	0.123285i
$448$		0			0
$449$	8.69572	+	10.9041i	0.410377	+	0.514596i	0.943469	−	0.331461i	$-0.107542\pi$
$449$	8.69572	+	10.9041i	0.410377	+	0.514596i	−0.533092	+	0.846057i	$0.678970\pi$
$450$		0			0
$451$	−0.134311	+	0.168420i	−0.00632443	+	0.00793059i
$452$		0			0
$453$	−5.84414	+	12.1355i	−0.274582	+	0.570175i
$454$		0			0
$455$	3.56798	−	1.46328i	0.167269	−	0.0685994i
$456$		0			0
$457$	10.5751	−	13.2608i	0.494683	−	0.620313i	−0.470337	−	0.882487i	$-0.655868\pi$
$457$	10.5751	−	13.2608i	0.494683	−	0.620313i	0.965021	+	0.262173i	$0.0844392\pi$
$458$		0			0
$459$			10.9692i			0.511996i
$460$		0			0
$461$	12.7079	−	26.3882i	0.591864	−	1.22902i	−0.362948	−	0.931809i	$-0.618230\pi$
$461$	12.7079	−	26.3882i	0.591864	−	1.22902i	0.954812	−	0.297209i	$-0.0960560\pi$
$462$		0			0
$463$	−11.8538	−	24.6147i	−0.550893	−	1.14394i	−0.971575	−	0.236733i	$-0.923923\pi$
$463$	−11.8538	−	24.6147i	−0.550893	−	1.14394i	0.420681	−	0.907208i	$-0.361791\pi$
$464$		0			0
$465$	−1.19682	−	0.273165i	−0.0555010	−	0.0126677i
$466$		0			0
$467$	3.01253	−	1.45076i	0.139403	−	0.0671331i	−0.362882	−	0.931835i	$-0.618207\pi$
$467$	3.01253	−	1.45076i	0.139403	−	0.0671331i	0.502285	+	0.864702i	$0.332493\pi$
$468$		0			0
$469$	1.93647	−	3.47495i	0.0894177	−	0.160458i
$470$		0			0
$471$			9.64317i			0.444334i
$472$		0			0
$473$	0.602800	+	0.290293i	0.0277168	+	0.0133477i
$474$		0			0
$475$	0.367363	−	1.60952i	0.0168558	−	0.0738500i
$476$		0			0
$477$	−4.02308	−	17.6263i	−0.184204	−	0.807052i
$478$		0			0
$479$	−7.10775	−	31.1411i	−0.324761	−	1.42287i	−0.828971	−	0.559292i	$-0.811073\pi$
$479$	−7.10775	−	31.1411i	−0.324761	−	1.42287i	0.504209	−	0.863581i	$-0.331784\pi$
$480$		0			0
$481$	−1.11990	−	0.255609i	−0.0510628	−	0.0116548i
$482$		0			0
$483$	13.0080	−	9.16133i	0.591887	−	0.416855i
$484$		0			0
$485$	31.0871	+	38.9819i	1.41159	+	1.77008i
$486$		0			0
$487$	−13.4310	+	10.7109i	−0.608618	+	0.485357i	−0.878632	−	0.477500i	$-0.841543\pi$
$487$	−13.4310	+	10.7109i	−0.608618	+	0.485357i	0.270014	+	0.962857i	$0.412972\pi$
$488$		0			0
$489$			12.3692i			0.559356i
$490$		0			0
$491$			0.573616i			0.0258869i	0.999916	+	0.0129435i	$0.00412015\pi$
$491$			0.573616i			0.0258869i	−0.999916	+	0.0129435i	$0.995880\pi$
$492$		0			0
$493$	−4.02004	+	3.20587i	−0.181053	+	0.144385i
$494$		0			0
$495$	0.215818	+	0.270627i	0.00970029	+	0.0121638i
$496$		0			0
$497$	1.00926	−	16.9124i	0.0452713	−	0.758626i
$498$		0			0
$499$	−7.38119	−	1.68471i	−0.330428	−	0.0754180i	0.0540887	−	0.998536i	$-0.482775\pi$
$499$	−7.38119	−	1.68471i	−0.330428	−	0.0754180i	−0.384516	+	0.923118i	$0.625632\pi$
$500$		0			0
$501$	−2.41852	−	10.5962i	−0.108051	−	0.473404i
$502$		0			0
$503$	6.07104	+	26.5990i	0.270694	+	1.18599i	0.909196	+	0.416369i	$0.136698\pi$
$503$	6.07104	+	26.5990i	0.270694	+	1.18599i	−0.638501	+	0.769621i	$0.720445\pi$
$504$		0			0
$505$	1.92985	−	8.45522i	0.0858771	−	0.376252i
$506$		0			0
$507$	10.3118	+	4.96590i	0.457963	+	0.220543i
$508$		0			0
$509$		−	13.6450i		−	0.604803i	−0.953181	−	0.302401i	$-0.902212\pi$
$509$		−	13.6450i		−	0.604803i	0.953181	−	0.302401i	$-0.0977883\pi$
$510$		0			0
$511$	4.64986	+	4.18477i	0.205698	+	0.185123i
$512$		0			0
$513$	−2.43445	+	1.17237i	−0.107484	+	0.0517615i
$514$		0			0
$515$	−26.5118	−	6.05115i	−1.16825	−	0.266646i
$516$		0			0
$517$	0.0778847	+	0.161729i	0.00342537	+	0.00711285i
$518$		0			0
$519$	3.79565	−	7.88174i	0.166610	−	0.345970i
$520$		0			0
$521$		−	9.23329i		−	0.404518i	−0.979332	−	0.202259i	$-0.935172\pi$
$521$		−	9.23329i		−	0.404518i	0.979332	−	0.202259i	$-0.0648282\pi$
$522$		0			0
$523$	22.8239	−	28.6202i	0.998019	−	1.25148i	0.0302744	−	0.999542i	$-0.490362\pi$
$523$	22.8239	−	28.6202i	0.998019	−	1.25148i	0.967744	−	0.251934i	$-0.0810667\pi$
$524$		0			0
$525$	−6.77239	−	0.404146i	−0.295572	−	0.0176384i
$526$		0			0
$527$	0.496797	−	1.03161i	0.0216408	−	0.0449376i
$528$		0			0
$529$	−13.5504	+	16.9917i	−0.589149	+	0.738769i
$530$		0			0
$531$	−12.1488	−	15.2341i	−0.527214	−	0.661105i
$532$		0			0
$533$	1.23949	−	1.55427i	0.0536881	−	0.0673228i
$534$		0			0
$535$	−8.64421	+	4.16283i	−0.373722	+	0.179975i
$536$		0			0
$537$	−20.7548	+	4.73714i	−0.895635	+	0.204423i
$538$		0			0
$539$	−0.277029	−	0.280941i	−0.0119325	−	0.0121010i
$540$		0			0
$541$	−2.64689	−	11.5968i	−0.113799	−	0.498584i	−0.999416	−	0.0341688i	$-0.989122\pi$
$541$	−2.64689	−	11.5968i	−0.113799	−	0.498584i	0.885618	−	0.464415i	$-0.153736\pi$
$542$		0			0
$543$	5.55341	+	11.5318i	0.238320	+	0.494876i
$544$		0			0
$545$	−17.9919	−	14.3481i	−0.770688	−	0.614603i
$546$		0			0
$547$	−13.9855	+	11.1531i	−0.597977	+	0.476871i	−0.875086	−	0.483968i	$-0.839195\pi$
$547$	−13.9855	+	11.1531i	−0.597977	+	0.476871i	0.277108	+	0.960839i	$0.410624\pi$
$548$		0			0
$549$	−2.53884	−	2.02466i	−0.108355	−	0.0864103i
$550$		0			0
$551$	−1.14116	−	0.549552i	−0.0486149	−	0.0234117i
$552$		0			0
$553$	−12.7647	+	22.9060i	−0.542811	+	0.974064i
$554$		0			0
$555$	4.34994	+	3.46896i	0.184645	+	0.147249i
$556$		0			0
$557$	14.1512			0.599606			0.299803	−	0.954001i	$-0.403079\pi$
$557$	14.1512			0.599606			0.299803	+	0.954001i	$0.403079\pi$
$558$		0			0
$559$	−5.56295	−	2.67897i	−0.235288	−	0.113309i
$560$		0			0
$561$	0.107298	−	0.0516719i	0.00453012	−	0.00218159i
$562$		0			0
$563$	7.17814	−	31.4495i	0.302523	−	1.32544i	−0.563783	−	0.825923i	$-0.690655\pi$
$563$	7.17814	−	31.4495i	0.302523	−	1.32544i	0.866305	−	0.499515i	$-0.166488\pi$
$564$		0			0
$565$	17.5101	+	36.3601i	0.736656	+	1.52968i
$566$		0			0
$567$	−3.62251	−	5.14356i	−0.152131	−	0.216009i
$568$		0			0
$569$	−30.1929			−1.26575			−0.632877	−	0.774252i	$-0.718126\pi$
$569$	−30.1929			−1.26575			−0.632877	+	0.774252i	$0.718126\pi$
$570$		0			0
$571$	−4.85634	+	10.0843i	−0.203232	+	0.422015i	−0.977527	−	0.210809i	$-0.932390\pi$
$571$	−4.85634	+	10.0843i	−0.203232	+	0.422015i	0.774296	+	0.632824i	$0.218104\pi$
$572$		0			0
$573$	17.6184	+	4.02128i	0.736019	+	0.167991i
$574$		0			0
$575$	18.5967	−	4.24458i	0.775538	−	0.177011i
$576$		0			0
$577$	−17.6157	+	4.02066i	−0.733350	+	0.167382i	−0.572858	−	0.819655i	$-0.694165\pi$
$577$	−17.6157	+	4.02066i	−0.733350	+	0.167382i	−0.160492	+	0.987037i	$0.551308\pi$
$578$		0			0
$579$	3.87547	−	16.9795i	0.161059	−	0.705645i
$580$		0			0
$581$	−22.6096	+	25.1224i	−0.938005	+	1.04225i
$582$		0			0
$583$	−0.363539	+	0.289912i	−0.0150562	+	0.0120069i
$584$		0			0
$585$	−1.99168	−	2.49749i	−0.0823458	−	0.103258i
$586$		0			0
$587$	−13.4314			−0.554371			−0.277186	−	0.960816i	$-0.589402\pi$
$587$	−13.4314			−0.554371			−0.277186	+	0.960816i	$0.589402\pi$
$588$		0			0
$589$	0.282049			0.0116216
$590$		0			0
$591$	−11.2060	−	14.0519i	−0.460955	−	0.578020i
$592$		0			0
$593$	16.2891	−	12.9901i	0.668912	−	0.533440i	−0.229104	−	0.973402i	$-0.573580\pi$
$593$	16.2891	−	12.9901i	0.668912	−	0.533440i	0.898016	+	0.439962i	$0.145008\pi$
$594$		0			0
$595$	4.88165	−	16.7240i	0.200128	−	0.685618i
$596$		0			0
$597$	5.16496	−	22.6292i	0.211388	−	0.926151i
$598$		0			0
$599$	8.24257	−	1.88131i	0.336782	−	0.0768684i	−0.0507854	−	0.998710i	$-0.516172\pi$
$599$	8.24257	−	1.88131i	0.336782	−	0.0768684i	0.387568	+	0.921841i	$0.373315\pi$
$600$		0			0
$601$	−32.6666	+	7.45593i	−1.33250	+	0.304134i	−0.828703	−	0.559689i	$-0.810921\pi$
$601$	−32.6666	+	7.45593i	−1.33250	+	0.304134i	−0.503795	+	0.863823i	$0.668063\pi$
$602$		0			0
$603$	−3.21260	−	0.733256i	−0.130827	−	0.0298605i
$604$		0			0
$605$	−13.3700	+	27.7630i	−0.543567	+	1.12873i
$606$		0			0
$607$	20.2895			0.823526			0.411763	−	0.911291i	$-0.364913\pi$
$607$	20.2895			0.823526			0.411763	+	0.911291i	$0.364913\pi$
$608$		0			0
$609$	−1.45846	+	4.99654i	−0.0590999	+	0.202470i
$610$		0			0
$611$	−0.718761	−	1.49252i	−0.0290779	−	0.0603810i
$612$		0			0
$613$	−6.22301	+	27.2648i	−0.251345	+	1.10121i	0.678887	+	0.734242i	$0.262462\pi$
$613$	−6.22301	+	27.2648i	−0.251345	+	1.10121i	−0.930232	+	0.366971i	$0.880395\pi$
$614$		0			0
$615$	−8.67537	+	4.17784i	−0.349825	+	0.168467i
$616$		0			0
$617$	−21.9062	−	10.5495i	−0.881912	−	0.424706i	−0.0625892	−	0.998039i	$-0.519936\pi$
$617$	−21.9062	−	10.5495i	−0.881912	−	0.424706i	−0.819322	+	0.573333i	$0.805650\pi$
$618$		0			0
$619$	−7.85187			−0.315593			−0.157797	−	0.987472i	$-0.550439\pi$
$619$	−7.85187			−0.315593			−0.157797	+	0.987472i	$0.550439\pi$
$620$		0			0
$621$	−24.4087	−	19.4653i	−0.979487	−	0.781115i
$622$		0			0
$623$	11.7490	+	10.5739i	0.470714	+	0.423633i
$624$		0			0
$625$	28.0436	+	13.5051i	1.12175	+	0.540204i
$626$		0			0
$627$	0.0229358	+	0.0182907i	0.000915966	+	0.000730458i
$628$		0			0
$629$	−4.05728	+	3.23557i	−0.161774	+	0.129011i
$630$		0			0
$631$	−26.0516	−	20.7754i	−1.03710	−	0.827057i	−0.0519288	−	0.998651i	$-0.516537\pi$
$631$	−26.0516	−	20.7754i	−1.03710	−	0.827057i	−0.985168	+	0.171594i	$0.945108\pi$
$632$		0			0
$633$	4.56403	+	9.47731i	0.181404	+	0.376689i
$634$		0			0
$635$	−1.98190	−	8.68326i	−0.0786492	−	0.344585i
$636$		0			0
$637$	2.55657	+	2.59267i	0.101295	+	0.102725i
$638$		0			0
$639$	−13.6823	+	3.12291i	−0.541265	+	0.123540i
$640$		0			0
$641$	−6.90279	+	3.32421i	−0.272644	+	0.131298i	−0.565210	−	0.824947i	$-0.691205\pi$
$641$	−6.90279	+	3.32421i	−0.272644	+	0.131298i	0.292566	+	0.956245i	$0.405491\pi$
$642$		0			0
$643$	−8.06906	+	10.1183i	−0.318213	+	0.399026i	−0.915053	−	0.403334i	$-0.867851\pi$
$643$	−8.06906	+	10.1183i	−0.318213	+	0.399026i	0.596840	+	0.802360i	$0.296423\pi$
$644$		0			0
$645$	18.6462	+	23.3816i	0.734193	+	0.920648i
$646$		0			0
$647$	23.3193	−	29.2414i	0.916775	−	1.14960i	−0.0715802	−	0.997435i	$-0.522804\pi$
$647$	23.3193	−	29.2414i	0.916775	−	1.14960i	0.988355	−	0.152165i	$-0.0486244\pi$
$648$		0			0
$649$	−0.217434	+	0.451506i	−0.00853503	+	0.0177232i
$650$		0			0
$651$	−0.190147	−	1.14338i	−0.00745245	−	0.0448125i
$652$		0			0
$653$	−9.81971	+	12.3135i	−0.384275	+	0.481866i	−0.935920	−	0.352214i	$-0.885429\pi$
$653$	−9.81971	+	12.3135i	−0.384275	+	0.481866i	0.551645	+	0.834079i	$0.314000\pi$
$654$		0			0
$655$			35.3872i			1.38269i
$656$		0			0
$657$	2.24832	−	4.66868i	0.0877153	−	0.182143i
$658$		0			0
$659$	17.6014	+	36.5497i	0.685654	+	1.42377i	0.895060	+	0.445946i	$0.147133\pi$
$659$	17.6014	+	36.5497i	0.685654	+	1.42377i	−0.209406	+	0.977829i	$0.567153\pi$
$660$		0			0
$661$	−6.59869	−	1.50611i	−0.256659	−	0.0585808i	0.0922551	−	0.995735i	$-0.470592\pi$
$661$	−6.59869	−	1.50611i	−0.256659	−	0.0585808i	−0.348914	+	0.937155i	$0.613450\pi$
$662$		0			0
$663$	−0.990200	+	0.476855i	−0.0384562	+	0.0185195i
$664$		0			0
$665$	4.23341	−	0.704029i	0.164165	−	0.0273011i
$666$		0			0
$667$		−	14.6344i		−	0.566646i
$668$		0			0
$669$	−18.1042	−	8.71853i	−0.699950	−	0.337078i
$670$		0			0
$671$	−0.0185841	+	0.0814224i	−0.000717432	+	0.00314328i
$672$		0			0
$673$	6.94245	+	30.4169i	0.267612	+	1.17248i	0.912783	+	0.408446i	$0.133929\pi$
$673$	6.94245	+	30.4169i	0.267612	+	1.17248i	−0.645171	+	0.764038i	$0.723214\pi$
$674$		0			0
$675$	2.96235	+	12.9789i	0.114021	+	0.499558i
$676$		0			0
$677$	35.7142	+	8.15153i	1.37261	+	0.313289i	0.844348	−	0.535795i	$-0.179988\pi$
$677$	35.7142	+	8.15153i	1.37261	+	0.313289i	0.528259	+	0.849083i	$0.322845\pi$
$678$		0			0
$679$	−22.9163	+	41.1229i	−0.879448	+	1.57815i
$680$		0			0
$681$	−5.98404	−	7.50375i	−0.229309	−	0.287544i
$682$		0			0
$683$	−24.5925	+	19.6119i	−0.941005	+	0.750427i	−0.968453	−	0.249196i	$-0.919834\pi$
$683$	−24.5925	+	19.6119i	−0.941005	+	0.750427i	0.0274475	+	0.999623i	$0.491262\pi$
$684$		0			0
$685$			49.3332i			1.88493i
$686$		0			0
$687$			5.54061i			0.211388i
$688$		0			0
$689$	3.35492	−	2.67546i	0.127812	−	0.101927i
$690$		0			0
$691$	3.67133	+	4.60370i	0.139664	+	0.175133i	0.846744	−	0.532000i	$-0.178559\pi$
$691$	3.67133	+	4.60370i	0.139664	+	0.175133i	−0.707080	+	0.707133i	$0.749988\pi$
$692$		0			0
$693$	−0.159094	+	0.285490i	−0.00604347	+	0.0108449i
$694$		0			0
$695$	52.2773	+	11.9320i	1.98299	+	0.452605i
$696$		0			0
$697$	−1.99848	−	8.75591i	−0.0756978	−	0.331654i
$698$		0			0
$699$	−4.12350	−	18.0662i	−0.155965	−	0.683327i
$700$		0			0
$701$	−1.55630	+	6.81859i	−0.0587806	+	0.257535i	−0.995777	−	0.0918042i	$-0.970737\pi$
$701$	−1.55630	+	6.81859i	−0.0587806	+	0.257535i	0.936996	+	0.349339i	$0.113594\pi$
$702$		0			0
$703$	−1.15173	−	0.554643i	−0.0434382	−	0.0209188i
$704$		0			0
$705$			8.02373i			0.302191i
$706$		0			0
$707$	8.07769	−	1.34334i	0.303793	−	0.0505216i
$708$		0			0
$709$	−45.1941	+	21.7643i	−1.69730	+	0.817376i	−0.702947	+	0.711242i	$0.748133\pi$
$709$	−45.1941	+	21.7643i	−1.69730	+	0.817376i	−0.994352	+	0.106134i	$0.966153\pi$
$710$		0			0
$711$	21.1767	+	4.83345i	0.794189	+	0.181268i
$712$		0			0
$713$	1.41396	+	2.93612i	0.0529532	+	0.109958i
$714$		0			0
$715$	−0.0356461	+	0.0740200i	−0.00133309	+	0.00276819i
$716$		0			0
$717$		−	4.54464i		−	0.169723i
$718$		0			0
$719$	−16.2129	+	20.3304i	−0.604641	+	0.758196i	−0.986093	−	0.166193i	$-0.946853\pi$
$719$	−16.2129	+	20.3304i	−0.604641	+	0.758196i	0.381452	+	0.924388i	$0.375424\pi$
$720$		0			0
$721$	−4.21213	−	25.3281i	−0.156868	−	0.943267i
$722$		0			0
$723$	0.529966	−	1.10049i	0.0197096	−	0.0409275i
$724$		0			0
$725$	−3.89080	+	4.87891i	−0.144501	+	0.181198i
$726$		0			0
$727$	10.9125	+	13.6838i	0.404722	+	0.507505i	0.941868	−	0.335984i	$-0.109069\pi$
$727$	10.9125	+	13.6838i	0.404722	+	0.507505i	−0.537146	+	0.843489i	$0.680498\pi$
$728$		0			0
$729$	4.60108	−	5.76957i	0.170410	−	0.213688i
$730$		0			0
$731$	−25.1317	+	12.1028i	−0.929528	+	0.447637i
$732$		0			0
$733$	−17.3601	+	3.96233i	−0.641210	+	0.146352i	−0.530750	−	0.847528i	$-0.678090\pi$
$733$	−17.3601	+	3.96233i	−0.641210	+	0.146352i	−0.110460	+	0.993881i	$0.535233\pi$
$734$		0			0
$735$	−5.70802	−	16.6869i	−0.210544	−	0.615505i
$736$		0			0
$737$	0.0188584	+	0.0826240i	0.000694658	+	0.00304349i
$738$		0			0
$739$	0.414040	+	0.859763i	0.0152307	+	0.0316269i	0.908445	−	0.418003i	$-0.137270\pi$
$739$	0.414040	+	0.859763i	0.0152307	+	0.0316269i	−0.893215	+	0.449630i	$0.851556\pi$
$740$		0			0
$741$	−0.211663	−	0.168796i	−0.00777564	−	0.00620086i
$742$		0			0
$743$	20.7632	−	16.5581i	0.761728	−	0.607458i	−0.163643	−	0.986520i	$-0.552325\pi$
$743$	20.7632	−	16.5581i	0.761728	−	0.607458i	0.925371	+	0.379062i	$0.123753\pi$
$744$		0			0
$745$	8.12339	+	6.47819i	0.297618	+	0.237343i
$746$		0			0
$747$	25.2241	+	12.1473i	0.922901	+	0.444446i
$748$		0			0
$749$	−6.73348	−	6.05999i	−0.246036	−	0.221427i
$750$		0			0
$751$	−12.5240	−	9.98753i	−0.457006	−	0.364450i	0.367763	−	0.929919i	$-0.380124\pi$
$751$	−12.5240	−	9.98753i	−0.457006	−	0.364450i	−0.824769	+	0.565469i	$0.808695\pi$
$752$		0			0
$753$	11.7220			0.427174
$754$		0			0
$755$	−37.8209	−	18.2136i	−1.37644	−	0.662860i
$756$		0			0
$757$	−32.5972	+	15.6980i	−1.18476	+	0.570552i	−0.919296	−	0.393568i	$-0.871241\pi$
$757$	−32.5972	+	15.6980i	−1.18476	+	0.570552i	−0.265468	+	0.964120i	$0.585526\pi$
$758$		0			0
$759$	−0.0754241	+	0.330455i	−0.00273772	+	0.0119947i
$760$		0			0
$761$	−3.29821	−	6.84881i	−0.119560	−	0.248269i	0.832596	−	0.553880i	$-0.186853\pi$
$761$	−3.29821	−	6.84881i	−0.119560	−	0.248269i	−0.952156	+	0.305611i	$0.901139\pi$
$762$		0			0
$763$	6.08826	−	20.8577i	0.220410	−	0.755101i
$764$		0			0
$765$	−14.4313			−0.521766
$766$		0			0
$767$	2.00659	−	4.16673i	0.0724539	−	0.150452i
$768$		0			0
$769$	46.5547	+	10.6258i	1.67881	+	0.383176i	0.952582	−	0.304282i	$-0.0984165\pi$
$769$	46.5547	+	10.6258i	1.67881	+	0.383176i	0.726224	+	0.687458i	$0.241274\pi$
$770$		0			0
$771$	10.0598	−	2.29609i	0.362296	−	0.0826916i
$772$		0			0
$773$	43.3700	−	9.89892i	1.55991	−	0.356039i	0.646447	−	0.762959i	$-0.276254\pi$
$773$	43.3700	−	9.89892i	1.55991	−	0.356039i	0.913464	+	0.406920i	$0.133397\pi$
$774$		0			0
$775$	0.309221	−	1.35479i	0.0111075	−	0.0486653i
$776$		0			0
$777$	−1.47197	+	5.04283i	−0.0528068	+	0.180910i
$778$		0			0
$779$	1.72966	−	1.37936i	0.0619715	−	0.0494206i
$780$		0			0
$781$	0.225044	+	0.282196i	0.00805269	+	0.0100978i
$782$		0			0
$783$	10.2135			0.365002
$784$		0			0
$785$	−30.0534			−1.07265
$786$		0			0
$787$	3.43024	+	4.30138i	0.122275	+	0.153328i	0.839201	−	0.543821i	$-0.183023\pi$
$787$	3.43024	+	4.30138i	0.122275	+	0.153328i	−0.716926	+	0.697149i	$0.754452\pi$
$788$		0			0
$789$	−14.6398	+	11.6749i	−0.521191	+	0.415636i
$790$		0			0
$791$	−25.4901	+	28.3230i	−0.906324	+	1.00705i
$792$		0			0
$793$	0.171504	−	0.751408i	0.00609028	−	0.0266833i
$794$		0			0
$795$	−20.2632	+	4.62493i	−0.718660	+	0.164030i
$796$		0			0
$797$	−28.4246	+	6.48774i	−1.00685	+	0.229807i	−0.693985	−	0.719990i	$-0.744147\pi$
$797$	−28.4246	+	6.48774i	−1.00685	+	0.229807i	−0.312867	+	0.949797i	$0.601289\pi$
$798$		0			0
$799$	−7.29625	−	1.66532i	−0.258123	−	0.0589148i
$800$		0			0
$801$	5.68093	−	11.7966i	0.200726	−	0.416812i
$802$		0			0
$803$	−0.133270			−0.00470301
$804$		0			0
$805$	28.5518	+	40.5403i	1.00632	+	1.42886i
$806$		0			0
$807$	−3.77491	−	7.83869i	−0.132883	−	0.275935i
$808$		0			0
$809$	2.66773	−	11.6881i	0.0937922	−	0.410931i	−0.906135	−	0.422988i	$-0.860981\pi$
$809$	2.66773	−	11.6881i	0.0937922	−	0.410931i	0.999927	+	0.0120578i	$0.00383823\pi$
$810$		0			0
$811$	29.4020	−	14.1592i	1.03244	−	0.497198i	0.160618	−	0.987017i	$-0.448651\pi$
$811$	29.4020	−	14.1592i	1.03244	−	0.497198i	0.871825	+	0.489818i	$0.162937\pi$
$812$		0			0
$813$	16.5414	+	7.96593i	0.580133	+	0.279377i
$814$		0			0
$815$	−38.5493			−1.35032
$816$		0			0
$817$	−5.37209	−	4.28410i	−0.187946	−	0.149882i
$818$		0			0
$819$	1.46820	−	2.63465i	0.0513030	−	0.0920622i
$820$		0			0
$821$	3.85386	+	1.85592i	0.134501	+	0.0647721i	0.499924	−	0.866069i	$-0.333361\pi$
$821$	3.85386	+	1.85592i	0.134501	+	0.0647721i	−0.365423	+	0.930842i	$0.619076\pi$
$822$		0			0
$823$	20.0875	+	16.0193i	0.700208	+	0.558397i	0.907587	−	0.419863i	$-0.137922\pi$
$823$	20.0875	+	16.0193i	0.700208	+	0.558397i	−0.207379	+	0.978261i	$0.566493\pi$
$824$		0			0
$825$	0.113002	−	0.0901162i	0.00393423	−	0.00313744i
$826$		0			0
$827$	15.8890	+	12.6711i	0.552515	+	0.440616i	0.859527	−	0.511090i	$-0.170758\pi$
$827$	15.8890	+	12.6711i	0.552515	+	0.440616i	−0.307013	+	0.951705i	$0.599329\pi$
$828$		0			0
$829$	0.411011	+	0.853472i	0.0142750	+	0.0296423i	0.907984	−	0.419004i	$-0.137621\pi$
$829$	0.411011	+	0.853472i	0.0142750	+	0.0296423i	−0.893709	+	0.448646i	$0.851906\pi$
$830$		0			0
$831$	4.50916	+	19.7559i	0.156421	+	0.685325i
$832$		0			0
$833$	16.3587	−	1.72714i	0.566794	−	0.0598419i
$834$		0			0
$835$	33.0236	−	7.53743i	1.14283	−	0.260844i
$836$		0			0
$837$	−2.04915	+	0.986821i	−0.0708291	+	0.0341095i
$838$		0			0
$839$	9.60531	−	12.0447i	0.331612	−	0.415828i	−0.587873	−	0.808953i	$-0.700035\pi$
$839$	9.60531	−	12.0447i	0.331612	−	0.415828i	0.919485	+	0.393125i	$0.128606\pi$
$840$		0			0
$841$	−15.0962	−	18.9300i	−0.520558	−	0.652758i
$842$		0			0
$843$	−7.53473	+	9.44825i	−0.259510	+	0.325415i
$844$		0			0
$845$	−15.4765	+	32.1373i	−0.532407	+	1.10556i
$846$		0			0
$847$	−29.0432	−	1.73316i	−0.997936	−	0.0595522i
$848$		0			0
$849$	13.8780	−	17.4024i	0.476291	−	0.597249i
$850$		0			0
$851$		−	14.7700i		−	0.506308i
$852$		0			0
$853$	5.75716	−	11.9549i	0.197121	−	0.409327i	−0.778855	−	0.627204i	$-0.784199\pi$
$853$	5.75716	−	11.9549i	0.197121	−	0.409327i	0.975976	+	0.217878i	$0.0699134\pi$
$854$		0			0
$855$	−1.54240	−	3.20284i	−0.0527491	−	0.109535i
$856$		0			0
$857$	−32.0155	−	7.30733i	−1.09363	−	0.249614i	−0.362590	−	0.931949i	$-0.618107\pi$
$857$	−32.0155	−	7.30733i	−1.09363	−	0.249614i	−0.731040	+	0.682335i	$0.760965\pi$
$858$		0			0
$859$	40.9237	−	19.7078i	1.39630	−	0.672422i	0.423891	−	0.905713i	$-0.360664\pi$
$859$	40.9237	−	19.7078i	1.39630	−	0.672422i	0.972407	+	0.233291i	$0.0749496\pi$
$860$		0			0
$861$	−6.75775	−	6.08183i	−0.230304	−	0.207268i
$862$		0			0
$863$		−	39.2754i		−	1.33695i	−0.743735	−	0.668474i	$-0.766948\pi$
$863$		−	39.2754i		−	1.33695i	0.743735	−	0.668474i	$-0.233052\pi$
$864$		0			0
$865$	24.5639	+	11.8293i	0.835196	+	0.402209i
$866$		0			0
$867$	2.29638	−	10.0611i	0.0779893	−	0.341693i
$868$		0			0
$869$	−0.124310	−	0.544638i	−0.00421693	−	0.0184756i
$870$		0			0
$871$	−0.174035	−	0.762497i	−0.00589695	−	0.0258362i
$872$		0			0
$873$	38.0183	+	8.67742i	1.28672	+	0.293686i
$874$		0			0
$875$	−0.948631	+	15.8965i	−0.0320696	+	0.537400i
$876$		0			0
$877$	23.9121	+	29.9848i	0.807454	+	1.01251i	0.999515	+	0.0311319i	$0.00991118\pi$
$877$	23.9121	+	29.9848i	0.807454	+	1.01251i	−0.192062	+	0.981383i	$0.561517\pi$
$878$		0			0
$879$	22.6831	−	18.0892i	0.765081	−	0.610132i
$880$		0			0
$881$			15.4686i			0.521151i	0.965453	+	0.260576i	$0.0839123\pi$
$881$			15.4686i			0.521151i	−0.965453	+	0.260576i	$0.916088\pi$
$882$		0			0
$883$			56.2691i			1.89360i	0.321816	+	0.946802i	$0.395707\pi$
$883$			56.2691i			1.89360i	−0.321816	+	0.946802i	$0.604293\pi$
$884$		0			0
$885$	−17.5132	+	13.9663i	−0.588698	+	0.469471i
$886$		0			0
$887$	−9.25044	−	11.5997i	−0.310599	−	0.389479i	0.601891	−	0.798579i	$-0.294414\pi$
$887$	−9.25044	−	11.5997i	−0.310599	−	0.389479i	−0.912490	+	0.409099i	$0.865843\pi$
$888$		0			0
$889$	6.87546	−	4.84226i	0.230596	−	0.162404i
$890$		0			0
$891$	0.130666	+	0.0298237i	0.00437748	+	0.000999132i
$892$		0			0
$893$	−0.410220	−	1.79729i	−0.0137275	−	0.0601441i
$894$		0			0
$895$	−14.7635	−	64.6833i	−0.493491	−	2.16212i
$896$		0			0
$897$	0.696053	−	3.04961i	0.0232405	−	0.101823i
$898$		0			0
$899$	−0.960547	−	0.462575i	−0.0320360	−	0.0154277i
$900$		0			0
$901$		−	19.3859i		−	0.645838i
$902$		0			0
$903$	−13.7453	+	24.6657i	−0.457416	+	0.820823i
$904$		0			0
$905$	−35.9394	+	17.3075i	−1.19467	+	0.575321i
$906$		0			0
$907$	−10.0373	−	2.29096i	−0.333285	−	0.0760700i	0.0526039	−	0.998615i	$-0.483248\pi$
$907$	−10.0373	−	2.29096i	−0.333285	−	0.0760700i	−0.385889	+	0.922545i	$0.626105\pi$
$908$		0			0
$909$	−2.94303	−	6.11127i	−0.0976142	−	0.202698i
$910$		0			0
$911$	−7.71917	+	16.0290i	−0.255748	+	0.531065i	−0.988825	−	0.149080i	$-0.952369\pi$
$911$	−7.71917	+	16.0290i	−0.255748	+	0.531065i	0.733078	+	0.680145i	$0.238083\pi$
$912$		0			0
$913$		−	0.720037i		−	0.0238298i
$914$		0			0
$915$	−2.32754	+	2.91865i	−0.0769463	+	0.0964876i
$916$		0			0
$917$	−30.9135	+	12.6780i	−1.02085	+	0.418666i
$918$		0			0
$919$	6.22937	−	12.9354i	0.205488	−	0.426700i	−0.772600	−	0.634893i	$-0.781044\pi$
$919$	6.22937	−	12.9354i	0.205488	−	0.426700i	0.978088	+	0.208193i	$0.0667583\pi$
$920$		0			0
$921$	9.66442	−	12.1188i	0.318454	−	0.399328i
$922$		0			0
$923$	−2.07682	−	2.60425i	−0.0683593	−	0.0857199i
$924$		0			0
$925$	−3.92684	+	4.92410i	−0.129114	+	0.161903i
$926$		0			0
$927$	−19.1622	+	9.22805i	−0.629370	+	0.303089i
$928$		0			0
$929$	−10.9085	+	2.48980i	−0.357897	+	0.0816876i	−0.397689	−	0.917520i	$-0.630188\pi$
$929$	−10.9085	+	2.48980i	−0.357897	+	0.0816876i	0.0397919	+	0.999208i	$0.487330\pi$
$930$		0			0
$931$	2.13171	+	3.44599i	0.0698640	+	0.112938i
$932$		0			0
$933$	1.49299	+	6.54122i	0.0488783	+	0.214150i
$934$		0			0
$935$	0.161038	+	0.334399i	0.00526651	+	0.0109360i
$936$		0			0
$937$	−25.9611	−	20.7033i	−0.848112	−	0.676347i	0.0997550	−	0.995012i	$-0.468194\pi$
$937$	−25.9611	−	20.7033i	−0.848112	−	0.676347i	−0.947867	+	0.318665i	$0.896766\pi$
$938$		0			0
$939$	−9.72197	+	7.75301i	−0.317264	+	0.253010i
$940$		0			0
$941$	−31.6392	−	25.2314i	−1.03141	−	0.822521i	−0.0470847	−	0.998891i	$-0.514993\pi$
$941$	−31.6392	−	25.2314i	−1.03141	−	0.822521i	−0.984324	+	0.176370i	$0.943565\pi$
$942$		0			0
$943$	23.0302	+	11.0907i	0.749965	+	0.361164i
$944$		0			0
$945$	−28.2936	+	19.9266i	−0.920390	+	0.648214i
$946$		0			0
$947$	−24.0781	−	19.2017i	−0.782434	−	0.623970i	0.148602	−	0.988897i	$-0.452523\pi$
$947$	−24.0781	−	19.2017i	−0.782434	−	0.623970i	−0.931036	+	0.364927i	$0.881094\pi$
$948$		0			0
$949$	1.22989			0.0399239
$950$		0			0
$951$	5.97856	+	2.87912i	0.193868	+	0.0933620i
$952$		0			0
$953$	9.54627	−	4.59724i	0.309234	−	0.148919i	−0.272830	−	0.962062i	$-0.587960\pi$
$953$	9.54627	−	4.59724i	0.309234	−	0.148919i	0.582064	+	0.813143i	$0.302245\pi$
$954$		0			0
$955$	−12.5325	+	54.9086i	−0.405543	+	1.77680i
$956$		0			0
$957$	−0.0481125	−	0.0999066i	−0.00155526	−	0.00322952i
$958$		0			0
$959$	−43.0964	+	17.6744i	−1.39166	+	0.570737i
$960$		0			0
$961$	−30.7626			−0.992342
$962$		0			0
$963$	−3.25580	+	6.76074i	−0.104917	+	0.217862i
$964$		0			0
$965$	52.9176	+	12.0781i	1.70348	+	0.388808i
$966$		0			0
$967$	27.0508	−	6.17417i	0.869896	−	0.198548i	0.235799	−	0.971802i	$-0.424229\pi$
$967$	27.0508	−	6.17417i	0.869896	−	0.198548i	0.634097	+	0.773254i	$0.281372\pi$
$968$		0			0
$969$	−1.19240	+	0.272157i	−0.0383053	+	0.00874294i
$970$		0			0
$971$	−4.06007	+	17.7883i	−0.130294	+	0.570854i	0.867063	+	0.498198i	$0.166005\pi$
$971$	−4.06007	+	17.7883i	−0.130294	+	0.570854i	−0.997357	+	0.0726563i	$0.976852\pi$
$972$		0			0
$973$	8.30569	+	49.9431i	0.266268	+	1.60110i
$974$		0			0
$975$	−1.04284	+	0.831639i	−0.0333977	+	0.0266338i
$976$		0			0
$977$	−20.4875	−	25.6906i	−0.655454	−	0.821914i	0.337386	−	0.941367i	$-0.390457\pi$
$977$	−20.4875	−	25.6906i	−0.655454	−	0.821914i	−0.992840	+	0.119453i	$0.961886\pi$
$978$		0			0
$979$	−0.336741			−0.0107623
$980$		0			0
$981$	−17.9984			−0.574643
$982$		0			0
$983$	−31.3611	−	39.3256i	−1.00026	−	1.25429i	−0.966982	−	0.254846i	$-0.917975\pi$
$983$	−31.3611	−	39.3256i	−1.00026	−	1.25429i	−0.0332832	−	0.999446i	$-0.510596\pi$
$984$		0			0
$985$	43.7936	−	34.9242i	1.39538	−	1.11278i
$986$		0			0
$987$	−7.00935	+	2.87463i	−0.223110	+	0.0915004i
$988$		0			0
$989$	17.6661	−	77.4002i	0.561749	−	2.46118i
$990$		0			0
$991$	29.3601	−	6.70125i	0.932654	−	0.212872i	0.270912	−	0.962604i	$-0.412675\pi$
$991$	29.3601	−	6.70125i	0.932654	−	0.212872i	0.661742	+	0.749732i	$0.269817\pi$
$992$		0			0
$993$	−11.0075	+	2.51238i	−0.349311	+	0.0797280i
$994$		0			0
$995$	70.5250	+	16.0969i	2.23579	+	0.510305i
$996$		0			0
$997$	−10.7276	+	22.2760i	−0.339746	+	0.705489i	−0.998918	−	0.0465027i	$-0.985192\pi$
$997$	−10.7276	+	22.2760i	−0.339746	+	0.705489i	0.659173	+	0.751992i	$0.270907\pi$
$998$		0			0
$999$	10.3081			0.326135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.a.111.4	✓	48
4.3	odd	2	inner	784.2.bb.a.111.5	yes	48
49.34	odd	14	inner	784.2.bb.a.671.5	yes	48
196.83	even	14	inner	784.2.bb.a.671.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.a.111.4	✓	48	1.1	even	1	trivial
784.2.bb.a.111.5	yes	48	4.3	odd	2	inner
784.2.bb.a.671.4	yes	48	196.83	even	14	inner
784.2.bb.a.671.5	yes	48	49.34	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.560590 - 0.702957i) q^{3} +(2.19080 - 1.74711i) q^{5} +(2.31112 + 1.28791i) q^{7} +(0.487675 - 2.13664i) q^{9} +O(q^{10})\)	\(q+(-0.560590 - 0.702957i) q^{3} +(2.19080 - 1.74711i) q^{5} +(2.31112 + 1.28791i) q^{7} +(0.487675 - 2.13664i) q^{9} +(-0.0549517 + 0.0125424i) q^{11} +(0.507123 - 0.115747i) q^{13} +(-2.45628 - 0.560631i) q^{15} +(1.01960 - 2.11722i) q^{17} +0.578863 q^{19} +(-0.390248 - 2.34661i) q^{21} +(2.90194 + 6.02594i) q^{23} +(0.634629 - 2.78049i) q^{25} +(-4.20558 + 2.02530i) q^{27} +(-1.97138 - 0.949366i) q^{29} +0.487247 q^{31} +(0.0396221 + 0.0315976i) q^{33} +(7.31333 - 1.21623i) q^{35} +(-1.98964 - 0.958160i) q^{37} +(-0.365653 - 0.291599i) q^{39} +(2.98803 - 2.38288i) q^{41} +(-9.28042 - 7.40089i) q^{43} +(-2.66454 - 5.53298i) q^{45} +(-0.708665 - 3.10487i) q^{47} +(3.68259 + 5.95303i) q^{49} +(-2.05990 + 0.470158i) q^{51} +(7.43256 - 3.57933i) q^{53} +(-0.0984755 + 0.123484i) q^{55} +(-0.324505 - 0.406916i) q^{57} +(5.54338 - 6.95118i) q^{59} +(0.642889 - 1.33497i) q^{61} +(3.87888 - 4.30996i) q^{63} +(0.908783 - 1.13958i) q^{65} -1.50358i q^{67} +(2.60918 - 5.41802i) q^{69} +(-2.77845 - 5.76951i) q^{71} +(2.30514 + 0.526134i) q^{73} +(-2.31033 + 1.11260i) q^{75} +(-0.143154 - 0.0417858i) q^{77} +9.91121i q^{79} +(-2.14236 - 1.03170i) q^{81} +(-2.84261 + 12.4543i) q^{83} +(-1.46527 - 6.41977i) q^{85} +(0.437771 + 1.91800i) q^{87} +(5.82451 + 1.32941i) q^{89} +(1.32110 + 0.385621i) q^{91} +(-0.273145 - 0.342514i) q^{93} +(1.26817 - 1.01134i) q^{95} +17.7935i q^{97} +0.123529i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 14 q^{17} + 12 q^{25} + 28 q^{29} + 42 q^{37} + 28 q^{41} + 56 q^{49} - 38 q^{53} + 42 q^{57} + 84 q^{61} + 8 q^{65} + 56 q^{69} - 42 q^{73} - 42 q^{77} - 44 q^{81} - 12 q^{85} - 28 q^{89} + 98 q^{93}+O(q^{100}) \) 48 * q - 4 * q^9 + 14 * q^17 + 12 * q^25 + 28 * q^29 + 42 * q^37 + 28 * q^41 + 56 * q^49 - 38 * q^53 + 42 * q^57 + 84 * q^61 + 8 * q^65 + 56 * q^69 - 42 * q^73 - 42 * q^77 - 44 * q^81 - 12 * q^85 - 28 * q^89 + 98 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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