LMFDB - Embedded newform 2548.2.u.c.1765.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(589,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2548.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.u (of order $6$, degree $2$, 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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1765.6
Root			$1.75101i$ of defining polynomial
Character	$\chi$	$=$	2548.1765
Dual form			2548.2.u.c.589.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.875503 + 1.51642i) q^{3} +1.38536i q^{5} +(-0.0330100 + 0.0571750i) q^{9} +(0.998442 - 0.576451i) q^{11} +(1.65348 + 3.20406i) q^{13} +(-2.10079 + 1.21289i) q^{15} +(0.781246 - 1.35316i) q^{17} +(7.26523 + 4.19458i) q^{19} +(-1.11067 - 1.92374i) q^{23} +3.08077 q^{25} +5.13741 q^{27} +(-1.43491 - 2.48533i) q^{29} -6.65024i q^{31} +(1.74828 + 1.00937i) q^{33} +(3.01436 - 1.74034i) q^{37} +(-3.41106 + 5.31253i) q^{39} +(-10.8758 + 6.27917i) q^{41} +(-3.07841 + 5.33196i) q^{43} +(-0.0792081 - 0.0457308i) q^{45} +7.40432i q^{47} +2.73593 q^{51} +11.2301 q^{53} +(0.798593 + 1.38320i) q^{55} +14.6895i q^{57} +(-6.97634 - 4.02779i) q^{59} +(0.829207 - 1.43623i) q^{61} +(-4.43879 + 2.29067i) q^{65} +(-3.21406 + 1.85564i) q^{67} +(1.94479 - 3.36848i) q^{69} +(8.60538 + 4.96832i) q^{71} +3.30200i q^{73} +(2.69722 + 4.67173i) q^{75} +4.64811 q^{79} +(4.59685 + 7.96198i) q^{81} -1.82551i q^{83} +(1.87462 + 1.08231i) q^{85} +(2.51253 - 4.35183i) q^{87} +(-2.05837 + 1.18840i) q^{89} +(10.0845 - 5.82230i) q^{93} +(-5.81102 + 10.0650i) q^{95} +(6.53519 + 3.77309i) q^{97} +0.0761145i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} + 6 q^{11} - 10 q^{13} + 6 q^{15} - 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} - 42 q^{33} + 12 q^{37} + 24 q^{39} - 36 q^{41} + 6 q^{43} + 30 q^{45} - 4 q^{51} + 8 q^{53} - 2 q^{55} + 18 q^{59}+ \cdots + 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 + 6 * q^11 - 10 * q^13 + 6 * q^15 - 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 - 42 * q^33 + 12 * q^37 + 24 * q^39 - 36 * q^41 + 6 * q^43 + 30 * q^45 - 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 - 4 * q^61 - 30 * q^65 + 24 * q^67 + 52 * q^69 + 36 * q^71 + 10 * q^75 + 8 * q^79 + 42 * q^85 - 26 * q^87 + 36 * q^89 - 42 * q^93 - 30 * q^95 + 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.875503	+	1.51642i	0.505472	+	0.875503i	0.999980	+	0.00632977i	$0.00201484\pi$
$3$	0.875503	+	1.51642i	0.505472	+	0.875503i	−0.494508	+	0.869173i	$0.664652\pi$
$4$		0			0
$5$			1.38536i			0.619553i	0.950809	+	0.309777i	$0.100254\pi$
$5$			1.38536i			0.619553i	−0.950809	+	0.309777i	$0.899746\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.0330100	+	0.0571750i	−0.0110033	+	0.0190583i
$10$		0			0
$11$	0.998442	−	0.576451i	0.301042	−	0.173806i	−0.341869	−	0.939748i	$-0.611060\pi$
$11$	0.998442	−	0.576451i	0.301042	−	0.173806i	0.642911	+	0.765941i	$0.277727\pi$
$12$		0			0
$13$	1.65348	+	3.20406i	0.458593	+	0.888647i
$13$	1.65348	+	3.20406i	0.458593	+	0.888647i
$14$		0			0
$15$	−2.10079	+	1.21289i	−0.542420	+	0.313167i
$16$		0			0
$17$	0.781246	−	1.35316i	0.189480	−	0.328189i	−0.755597	−	0.655037i	$-0.772653\pi$
$17$	0.781246	−	1.35316i	0.189480	−	0.328189i	0.945077	+	0.326848i	$0.105986\pi$
$18$		0			0
$19$	7.26523	+	4.19458i	1.66676	+	0.962303i	0.969368	+	0.245612i	$0.0789888\pi$
$19$	7.26523	+	4.19458i	1.66676	+	0.962303i	0.697390	+	0.716692i	$0.254345\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.11067	−	1.92374i	−0.231591	−	0.401127i	0.726685	−	0.686970i	$-0.241060\pi$
$23$	−1.11067	−	1.92374i	−0.231591	−	0.401127i	−0.958276	+	0.285843i	$0.907726\pi$
$24$		0			0
$25$	3.08077			0.616154
$26$		0			0
$27$	5.13741			0.988696
$28$		0			0
$29$	−1.43491	−	2.48533i	−0.266455	−	0.461514i	0.701489	−	0.712681i	$-0.252519\pi$
$29$	−1.43491	−	2.48533i	−0.266455	−	0.461514i	−0.967944	+	0.251167i	$0.919186\pi$
$30$		0			0
$31$		−	6.65024i		−	1.19442i	−0.802086	−	0.597209i	$-0.796276\pi$
$31$		−	6.65024i		−	1.19442i	0.802086	−	0.597209i	$-0.203724\pi$
$32$		0			0
$33$	1.74828	+	1.00937i	0.304336	+	0.175708i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.01436	−	1.74034i	0.495557	−	0.286110i	−0.231320	−	0.972878i	$-0.574304\pi$
$37$	3.01436	−	1.74034i	0.495557	−	0.286110i	0.726877	+	0.686768i	$0.240971\pi$
$38$		0			0
$39$	−3.41106	+	5.31253i	−0.546207	+	0.850685i
$40$		0			0
$41$	−10.8758	+	6.27917i	−1.69852	+	0.980641i	−0.751353	+	0.659901i	$0.770598\pi$
$41$	−10.8758	+	6.27917i	−1.69852	+	0.980641i	−0.947167	+	0.320740i	$0.896068\pi$
$42$		0			0
$43$	−3.07841	+	5.33196i	−0.469453	+	0.813116i	−0.999390	−	0.0349208i	$-0.988882\pi$
$43$	−3.07841	+	5.33196i	−0.469453	+	0.813116i	0.529937	+	0.848037i	$0.322215\pi$
$44$		0			0
$45$	−0.0792081	−	0.0457308i	−0.0118076	−	0.00681715i
$46$		0			0
$47$			7.40432i			1.08003i	0.841655	+	0.540015i	$0.181582\pi$
$47$			7.40432i			1.08003i	−0.841655	+	0.540015i	$0.818418\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.73593			0.383107
$52$		0			0
$53$	11.2301			1.54257			0.771285	−	0.636490i	$-0.219614\pi$
$53$	11.2301			1.54257			0.771285	+	0.636490i	$0.219614\pi$
$54$		0			0
$55$	0.798593	+	1.38320i	0.107682	+	0.186511i
$56$		0			0
$57$			14.6895i			1.94567i
$58$		0			0
$59$	−6.97634	−	4.02779i	−0.908243	−	0.524374i	−0.0283773	−	0.999597i	$-0.509034\pi$
$59$	−6.97634	−	4.02779i	−0.908243	−	0.524374i	−0.879865	+	0.475223i	$0.842367\pi$
$60$		0			0
$61$	0.829207	−	1.43623i	0.106169	−	0.183890i	−0.808046	−	0.589119i	$-0.799475\pi$
$61$	0.829207	−	1.43623i	0.106169	−	0.183890i	0.914215	+	0.405229i	$0.132808\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.43879	+	2.29067i	−0.550564	+	0.284123i
$66$		0			0
$67$	−3.21406	+	1.85564i	−0.392660	+	0.226702i	−0.683312	−	0.730126i	$-0.739461\pi$
$67$	−3.21406	+	1.85564i	−0.392660	+	0.226702i	0.290652	+	0.956829i	$0.406128\pi$
$68$		0			0
$69$	1.94479	−	3.36848i	0.234125	−	0.405517i
$70$		0			0
$71$	8.60538	+	4.96832i	1.02127	+	0.589631i	0.914472	−	0.404650i	$-0.132607\pi$
$71$	8.60538	+	4.96832i	1.02127	+	0.589631i	0.106799	+	0.994281i	$0.465940\pi$
$72$		0			0
$73$			3.30200i			0.386470i	0.981153	+	0.193235i	$0.0618979\pi$
$73$			3.30200i			0.386470i	−0.981153	+	0.193235i	$0.938102\pi$
$74$		0			0
$75$	2.69722	+	4.67173i	0.311448	+	0.539444i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.64811			0.522953			0.261477	−	0.965210i	$-0.415791\pi$
$79$	4.64811			0.522953			0.261477	+	0.965210i	$0.415791\pi$
$80$		0			0
$81$	4.59685	+	7.96198i	0.510761	+	0.884664i
$82$		0			0
$83$		−	1.82551i		−	0.200376i	−0.994969	−	0.100188i	$-0.968056\pi$
$83$		−	1.82551i		−	0.200376i	0.994969	−	0.100188i	$-0.0319445\pi$
$84$		0			0
$85$	1.87462	+	1.08231i	0.203331	+	0.117393i
$86$		0			0
$87$	2.51253	−	4.35183i	0.269371	−	0.466565i
$88$		0			0
$89$	−2.05837	+	1.18840i	−0.218187	+	0.125970i	−0.605111	−	0.796141i	$-0.706871\pi$
$89$	−2.05837	+	1.18840i	−0.218187	+	0.125970i	0.386923	+	0.922112i	$0.373538\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	10.0845	−	5.82230i	1.04572	−	0.603744i
$94$		0			0
$95$	−5.81102	+	10.0650i	−0.596198	+	1.03265i
$96$		0			0
$97$	6.53519	+	3.77309i	0.663548	+	0.383099i	0.793627	−	0.608404i	$-0.208190\pi$
$97$	6.53519	+	3.77309i	0.663548	+	0.383099i	−0.130080	+	0.991504i	$0.541523\pi$
$98$		0			0
$99$			0.0761145i			0.00764980i
$100$		0			0
$101$	−6.60026	−	11.4320i	−0.656751	−	1.13753i	−0.981452	−	0.191709i	$-0.938597\pi$
$101$	−6.60026	−	11.4320i	−0.656751	−	1.13753i	0.324701	−	0.945817i	$-0.394736\pi$
$102$		0			0
$103$	−5.90120			−0.581463			−0.290731	−	0.956805i	$-0.593899\pi$
$103$	−5.90120			−0.581463			−0.290731	+	0.956805i	$0.593899\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.09634	−	8.82712i	−0.492682	−	0.853350i	0.507283	−	0.861780i	$-0.330650\pi$
$107$	−5.09634	−	8.82712i	−0.492682	−	0.853350i	−0.999964	+	0.00842995i	$0.997317\pi$
$108$		0			0
$109$		−	6.14856i		−	0.588925i	−0.955663	−	0.294463i	$-0.904859\pi$
$109$		−	6.14856i		−	0.588925i	0.955663	−	0.294463i	$-0.0951407\pi$
$110$		0			0
$111$	5.27816	+	3.04734i	0.500980	+	0.289241i
$112$		0			0
$113$	−7.29876	+	12.6418i	−0.686609	+	1.18924i	0.286319	+	0.958134i	$0.407568\pi$
$113$	−7.29876	+	12.6418i	−0.686609	+	1.18924i	−0.972928	+	0.231108i	$0.925765\pi$
$114$		0			0
$115$	2.66508	−	1.53868i	0.248520	−	0.143483i
$116$		0			0
$117$	−0.237773	−	0.0112283i	−0.0219822	−	0.00103806i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.83541	+	8.37517i	−0.439583	+	0.761380i
$122$		0			0
$123$	−19.0436	−	10.9949i	−1.71711	−	0.991373i
$124$		0			0
$125$			11.1948i			1.00129i
$126$		0			0
$127$	4.36114	+	7.55372i	0.386989	+	0.670284i	0.992043	−	0.125900i	$-0.0401818\pi$
$127$	4.36114	+	7.55372i	0.386989	+	0.670284i	−0.605054	+	0.796184i	$0.706849\pi$
$128$		0			0
$129$	−10.7806			−0.949180
$130$		0			0
$131$	−19.4433			−1.69877			−0.849385	−	0.527773i	$-0.823027\pi$
$131$	−19.4433			−1.69877			−0.849385	+	0.527773i	$0.823027\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$			7.11718i			0.612550i
$136$		0			0
$137$	2.90516	+	1.67730i	0.248205	+	0.143301i	0.618942	−	0.785437i	$-0.287562\pi$
$137$	2.90516	+	1.67730i	0.248205	+	0.143301i	−0.370737	+	0.928738i	$0.620895\pi$
$138$		0			0
$139$	−3.95629	+	6.85250i	−0.335568	+	0.581222i	−0.983594	−	0.180397i	$-0.942262\pi$
$139$	−3.95629	+	6.85250i	−0.335568	+	0.581222i	0.648025	+	0.761619i	$0.275595\pi$
$140$		0			0
$141$	−11.2280	+	6.48250i	−0.945570	+	0.545925i
$142$		0			0
$143$	3.49789	+	2.24592i	0.292508	+	0.187813i
$144$		0			0
$145$	3.44308	−	1.98787i	0.285933	−	0.165083i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.04756	+	1.18216i	0.167743	+	0.0968464i	0.581521	−	0.813531i	$-0.302458\pi$
$149$	2.04756	+	1.18216i	0.167743	+	0.0968464i	−0.413778	+	0.910378i	$0.635791\pi$
$150$		0			0
$151$		−	11.5883i		−	0.943041i	−0.881855	−	0.471520i	$-0.843705\pi$
$151$		−	11.5883i		−	0.943041i	0.881855	−	0.471520i	$-0.156295\pi$
$152$		0			0
$153$	0.0515779	+	0.0893355i	0.00416982	+	0.00722235i
$154$		0			0
$155$	9.21299			0.740005
$156$		0			0
$157$	9.03642			0.721184			0.360592	−	0.932724i	$-0.382575\pi$
$157$	9.03642			0.721184			0.360592	+	0.932724i	$0.382575\pi$
$158$		0			0
$159$	9.83196	+	17.0295i	0.779725	+	1.35052i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−18.4945	−	10.6778i	−1.44860	−	0.836351i	−0.450203	−	0.892926i	$-0.648648\pi$
$163$	−18.4945	−	10.6778i	−1.44860	−	0.836351i	−0.998398	+	0.0565755i	$0.981982\pi$
$164$		0			0
$165$	−1.39834	+	2.42200i	−0.108861	+	0.188552i
$166$		0			0
$167$	2.75508	−	1.59065i	0.213194	−	0.123088i	−0.389601	−	0.920984i	$-0.627387\pi$
$167$	2.75508	−	1.59065i	0.213194	−	0.123088i	0.602795	+	0.797896i	$0.294054\pi$
$168$		0			0
$169$	−7.53201	+	10.5957i	−0.579385	+	0.815054i
$170$		0			0
$171$	−0.479650	+	0.276926i	−0.0366798	+	0.0211771i
$172$		0			0
$173$	−2.66952	+	4.62374i	−0.202960	+	0.351537i	−0.949481	−	0.313825i	$-0.898389\pi$
$173$	−2.66952	+	4.62374i	−0.202960	+	0.351537i	0.746521	+	0.665362i	$0.231723\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	14.1054i		−	1.06023i
$178$		0			0
$179$	4.92279	+	8.52652i	0.367947	+	0.637302i	0.989244	−	0.146272i	$-0.0467276\pi$
$179$	4.92279	+	8.52652i	0.367947	+	0.637302i	−0.621298	+	0.783575i	$0.713394\pi$
$180$		0			0
$181$	−15.1253			−1.12425			−0.562127	−	0.827051i	$-0.690017\pi$
$181$	−15.1253			−1.12425			−0.562127	+	0.827051i	$0.690017\pi$
$182$		0			0
$183$	2.90389			0.214662
$184$		0			0
$185$	2.41100	+	4.17598i	0.177260	+	0.307024i
$186$		0			0
$187$		−	1.80140i		−	0.131731i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0900	−	19.2084i	0.802443	−	1.38987i	−0.115561	−	0.993300i	$-0.536867\pi$
$191$	11.0900	−	19.2084i	0.802443	−	1.38987i	0.918004	−	0.396571i	$-0.129800\pi$
$192$		0			0
$193$	−6.03781	+	3.48593i	−0.434611	+	0.250923i	−0.701309	−	0.712857i	$-0.747401\pi$
$193$	−6.03781	+	3.48593i	−0.434611	+	0.250923i	0.266698	+	0.963780i	$0.414067\pi$
$194$		0			0
$195$	−7.35978	−	4.72556i	−0.527045	−	0.338404i
$196$		0			0
$197$	17.0895	−	9.86660i	1.21757	−	0.702966i	0.253175	−	0.967421i	$-0.418525\pi$
$197$	17.0895	−	9.86660i	1.21757	−	0.702966i	0.964398	+	0.264455i	$0.0851919\pi$
$198$		0			0
$199$	6.90193	−	11.9545i	0.489265	−	0.847431i	−0.510659	−	0.859783i	$-0.670599\pi$
$199$	6.90193	−	11.9545i	0.489265	−	0.847431i	0.999924	+	0.0123521i	$0.00393191\pi$
$200$		0			0
$201$	−5.62784	−	3.24923i	−0.396957	−	0.229183i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−8.69892	−	15.0670i	−0.607559	−	1.05232i
$206$		0			0
$207$	0.146653			0.0101931
$208$		0			0
$209$	9.67188			0.669018
$210$		0			0
$211$	4.73718	+	8.20504i	0.326121	+	0.564859i	0.981739	−	0.190235i	$-0.0609249\pi$
$211$	4.73718	+	8.20504i	0.326121	+	0.564859i	−0.655617	+	0.755093i	$0.727592\pi$
$212$		0			0
$213$			17.3991i			1.19217i
$214$		0			0
$215$	−7.38670	−	4.26471i	−0.503769	−	0.290851i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−5.00720	+	2.89091i	−0.338355	+	0.195350i
$220$		0			0
$221$	5.62738	+	0.265740i	0.378538	+	0.0178756i
$222$		0			0
$223$	−12.6335	+	7.29395i	−0.846001	+	0.488439i	−0.859300	−	0.511473i	$-0.829100\pi$
$223$	−12.6335	+	7.29395i	−0.846001	+	0.488439i	0.0132984	+	0.999912i	$0.495767\pi$
$224$		0			0
$225$	−0.101696	+	0.176143i	−0.00677974	+	0.0117429i
$226$		0			0
$227$	6.20380	+	3.58176i	0.411760	+	0.237730i	0.691546	−	0.722333i	$-0.256930\pi$
$227$	6.20380	+	3.58176i	0.411760	+	0.237730i	−0.279785	+	0.960063i	$0.590263\pi$
$228$		0			0
$229$			12.3005i			0.812839i	0.913687	+	0.406420i	$0.133223\pi$
$229$			12.3005i			0.812839i	−0.913687	+	0.406420i	$0.866777\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.8037			−1.23187			−0.615936	−	0.787796i	$-0.711222\pi$
$233$	−18.8037			−1.23187			−0.615936	+	0.787796i	$0.711222\pi$
$234$		0			0
$235$	−10.2577			−0.669136
$236$		0			0
$237$	4.06943	+	7.04846i	0.264338	+	0.457847i
$238$		0			0
$239$		−	1.60295i		−	0.103686i	−0.998655	−	0.0518432i	$-0.983490\pi$
$239$		−	1.60295i		−	0.103686i	0.998655	−	0.0518432i	$-0.0165096\pi$
$240$		0			0
$241$	15.9051	+	9.18284i	1.02454	+	0.591519i	0.915416	−	0.402509i	$-0.131862\pi$
$241$	15.9051	+	9.18284i	1.02454	+	0.591519i	0.109125	+	0.994028i	$0.465195\pi$
$242$		0			0
$243$	−0.342988	+	0.594073i	−0.0220027	+	0.0381098i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.42679	+	30.2139i	−0.0907842	+	1.92246i
$248$		0			0
$249$	2.76824	−	1.59824i	0.175430	−	0.101285i
$250$		0			0
$251$	7.18228	−	12.4401i	0.453341	−	0.785210i	−0.545250	−	0.838274i	$-0.683565\pi$
$251$	7.18228	−	12.4401i	0.453341	−	0.785210i	0.998591	+	0.0530634i	$0.0168986\pi$
$252$		0			0
$253$	−2.21788	−	1.28049i	−0.139437	−	0.0805040i
$254$		0			0
$255$			3.79026i			0.237355i
$256$		0			0
$257$	−8.68283	−	15.0391i	−0.541620	−	0.938113i	−0.998811	−	0.0487448i	$-0.984478\pi$
$257$	−8.68283	−	15.0391i	−0.541620	−	0.938113i	0.457191	−	0.889368i	$-0.348855\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.189465			0.0117276
$262$		0			0
$263$	−8.37095	−	14.4989i	−0.516175	−	0.894042i	−0.999824	−	0.0187793i	$-0.994022\pi$
$263$	−8.37095	−	14.4989i	−0.516175	−	0.894042i	0.483648	−	0.875262i	$-0.339311\pi$
$264$		0			0
$265$			15.5577i			0.955704i
$266$		0			0
$267$	−3.60422	−	2.08090i	−0.220575	−	0.127349i
$268$		0			0
$269$	12.3957	−	21.4700i	0.755781	−	1.30905i	−0.189204	−	0.981938i	$-0.560591\pi$
$269$	12.3957	−	21.4700i	0.755781	−	1.30905i	0.944985	−	0.327114i	$-0.106076\pi$
$270$		0			0
$271$	17.5211	−	10.1158i	1.06433	−	0.614493i	0.137706	−	0.990473i	$-0.456027\pi$
$271$	17.5211	−	10.1158i	1.06433	−	0.614493i	0.926628	+	0.375980i	$0.122694\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.07597	−	1.77591i	0.185488	−	0.107091i
$276$		0			0
$277$	5.52664	−	9.57242i	0.332064	−	0.575151i	−0.650853	−	0.759204i	$-0.725588\pi$
$277$	5.52664	−	9.57242i	0.332064	−	0.575151i	0.982916	+	0.184053i	$0.0589218\pi$
$278$		0			0
$279$	0.380227	+	0.219524i	0.0227636	+	0.0131426i
$280$		0			0
$281$			3.18955i			0.190273i	0.995464	+	0.0951363i	$0.0303287\pi$
$281$			3.18955i			0.190273i	−0.995464	+	0.0951363i	$0.969671\pi$
$282$		0			0
$283$	−8.96481	−	15.5275i	−0.532903	−	0.923015i	−0.999262	−	0.0384190i	$-0.987768\pi$
$283$	−8.96481	−	15.5275i	−0.532903	−	0.923015i	0.466359	−	0.884596i	$-0.345565\pi$
$284$		0			0
$285$	−20.3503			−1.20545
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.27931	+	12.6081i	0.428195	+	0.741655i
$290$		0			0
$291$			13.2134i			0.774584i
$292$		0			0
$293$	14.6945	+	8.48385i	0.858460	+	0.495632i	0.863496	−	0.504355i	$-0.168270\pi$
$293$	14.6945	+	8.48385i	0.858460	+	0.495632i	−0.00503646	+	0.999987i	$0.501603\pi$
$294$		0			0
$295$	5.57996	−	9.66477i	0.324878	−	0.562705i
$296$		0			0
$297$	5.12941	−	2.96147i	0.297639	−	0.171842i
$298$		0			0
$299$	4.32730	−	6.73952i	0.250255	−	0.389757i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	11.5571	−	20.0175i	0.663938	−	1.14997i
$304$		0			0
$305$	1.98970	+	1.14875i	0.113930	+	0.0657774i
$306$		0			0
$307$		−	26.9884i		−	1.54031i	−0.637857	−	0.770155i	$-0.720179\pi$
$307$		−	26.9884i		−	1.54031i	0.637857	−	0.770155i	$-0.279821\pi$
$308$		0			0
$309$	−5.16652	−	8.94868i	−0.293913	−	0.509072i
$310$		0			0
$311$	−28.3781			−1.60918			−0.804588	−	0.593834i	$-0.797614\pi$
$311$	−28.3781			−1.60918			−0.804588	+	0.593834i	$0.797614\pi$
$312$		0			0
$313$	16.6674			0.942095			0.471047	−	0.882108i	$-0.343876\pi$
$313$	16.6674			0.942095			0.471047	+	0.882108i	$0.343876\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			28.7427i			1.61435i	0.590312	+	0.807175i	$0.299005\pi$
$317$			28.7427i			1.61435i	−0.590312	+	0.807175i	$0.700995\pi$
$318$		0			0
$319$	−2.86534	−	1.65430i	−0.160428	−	0.0926233i
$320$		0			0
$321$	8.92372	−	15.4563i	0.498073	−	0.862688i
$322$		0			0
$323$	11.3519	−	6.55401i	0.631635	−	0.364675i
$324$		0			0
$325$	5.09399	+	9.87097i	0.282564	+	0.547543i
$326$		0			0
$327$	9.32377	−	5.38308i	0.515606	−	0.297685i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	22.6827	+	13.0959i	1.24675	+	0.719814i	0.970461	−	0.241260i	$-0.0775606\pi$
$331$	22.6827	+	13.0959i	1.24675	+	0.719814i	0.276293	+	0.961073i	$0.410894\pi$
$332$		0			0
$333$			0.229794i			0.0125927i
$334$		0			0
$335$	−2.57073	−	4.45264i	−0.140454	−	0.243274i
$336$		0			0
$337$	4.47831			0.243949			0.121975	−	0.992533i	$-0.461077\pi$
$337$	4.47831			0.243949			0.121975	+	0.992533i	$0.461077\pi$
$338$		0			0
$339$	−25.5603			−1.38825
$340$		0			0
$341$	−3.83353	−	6.63988i	−0.207597	−	0.359569i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.66657	+	2.69424i	0.251239	+	0.145053i
$346$		0			0
$347$	13.4606	−	23.3144i	0.722602	−	1.25158i	−0.237351	−	0.971424i	$-0.576279\pi$
$347$	13.4606	−	23.3144i	0.722602	−	1.25158i	0.959953	−	0.280160i	$-0.0903874\pi$
$348$		0			0
$349$	−17.9560	+	10.3669i	−0.961164	+	0.554928i	−0.896531	−	0.442981i	$-0.853921\pi$
$349$	−17.9560	+	10.3669i	−0.961164	+	0.554928i	−0.0646328	+	0.997909i	$0.520588\pi$
$350$		0			0
$351$	8.49461	+	16.4606i	0.453409	+	0.878601i
$352$		0			0
$353$	9.78961	−	5.65204i	0.521049	−	0.300828i	−0.216315	−	0.976324i	$-0.569404\pi$
$353$	9.78961	−	5.65204i	0.521049	−	0.300828i	0.737364	+	0.675496i	$0.236070\pi$
$354$		0			0
$355$	−6.88292	+	11.9216i	−0.365308	+	0.632731i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	17.7453i		−	0.936559i	−0.883580	−	0.468279i	$-0.844874\pi$
$359$		−	17.7453i		−	0.936559i	0.883580	−	0.468279i	$-0.155126\pi$
$360$		0			0
$361$	25.6891	+	44.4948i	1.35206	+	2.34183i
$362$		0			0
$363$	−16.9337			−0.888786
$364$		0			0
$365$	−4.57447			−0.239439
$366$		0			0
$367$	4.78155	+	8.28189i	0.249595	+	0.432311i	0.963413	−	0.268020i	$-0.0863692\pi$
$367$	4.78155	+	8.28189i	0.249595	+	0.432311i	−0.713819	+	0.700331i	$0.753036\pi$
$368$		0			0
$369$		−	0.829101i		−	0.0431613i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.94176	+	10.2914i	−0.307653	+	0.532870i	−0.977848	−	0.209314i	$-0.932877\pi$
$373$	−5.94176	+	10.2914i	−0.307653	+	0.532870i	0.670196	+	0.742184i	$0.266210\pi$
$374$		0			0
$375$	−16.9760	+	9.80108i	−0.876635	+	0.506125i
$376$		0			0
$377$	5.59056	−	8.70697i	0.287928	−	0.448432i
$378$		0			0
$379$	−14.9391	+	8.62512i	−0.767372	+	0.443042i	−0.831936	−	0.554871i	$-0.812768\pi$
$379$	−14.9391	+	8.62512i	−0.767372	+	0.443042i	0.0645643	+	0.997914i	$0.479434\pi$
$380$		0			0
$381$	−7.63639	+	13.2266i	−0.391224	+	0.677620i
$382$		0			0
$383$	11.2843	+	6.51499i	0.576600	+	0.332900i	0.759781	−	0.650179i	$-0.225306\pi$
$383$	11.2843	+	6.51499i	0.576600	+	0.332900i	−0.183181	+	0.983079i	$0.558639\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.203236	−	0.352016i	−0.0103311	−	0.0178940i
$388$		0			0
$389$	24.1585			1.22488			0.612442	−	0.790516i	$-0.290187\pi$
$389$	24.1585			1.22488			0.612442	+	0.790516i	$0.290187\pi$
$390$		0			0
$391$	−3.47083			−0.175528
$392$		0			0
$393$	−17.0227	−	29.4841i	−0.858680	−	1.48728i
$394$		0			0
$395$			6.43932i			0.323997i
$396$		0			0
$397$	−4.17021	−	2.40767i	−0.209297	−	0.120838i	0.391688	−	0.920098i	$-0.371891\pi$
$397$	−4.17021	−	2.40767i	−0.209297	−	0.120838i	−0.600985	+	0.799261i	$0.705225\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.94702	+	4.01086i	−0.346918	+	0.200293i	−0.663327	−	0.748330i	$-0.730856\pi$
$401$	−6.94702	+	4.01086i	−0.346918	+	0.200293i	0.316409	+	0.948623i	$0.397523\pi$
$402$		0			0
$403$	21.3078	−	10.9960i	1.06142	−	0.547751i
$404$		0			0
$405$	−11.0302	+	6.36831i	−0.548097	+	0.316444i
$406$		0			0
$407$	2.00644	−	3.47526i	0.0994555	−	0.172262i
$408$		0			0
$409$	8.63206	+	4.98372i	0.426828	+	0.246429i	0.697994	−	0.716103i	$-0.254076\pi$
$409$	8.63206	+	4.98372i	0.426828	+	0.246429i	−0.271166	+	0.962532i	$0.587409\pi$
$410$		0			0
$411$			5.87391i			0.289739i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.52900			0.124144
$416$		0			0
$417$	−13.8550			−0.678481
$418$		0			0
$419$	−14.8442	−	25.7109i	−0.725187	−	1.25606i	−0.958897	−	0.283754i	$-0.908420\pi$
$419$	−14.8442	−	25.7109i	−0.725187	−	1.25606i	0.233710	−	0.972306i	$-0.424913\pi$
$420$		0			0
$421$		−	13.1380i		−	0.640305i	−0.947366	−	0.320152i	$-0.896266\pi$
$421$		−	13.1380i		−	0.640305i	0.947366	−	0.320152i	$-0.103734\pi$
$422$		0			0
$423$	−0.423342	−	0.244416i	−0.0205836	−	0.0118839i
$424$		0			0
$425$	2.40684	−	4.16877i	0.116749	−	0.202215i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.343336	+	7.27056i	−0.0165764	+	0.351026i
$430$		0			0
$431$	−12.4729	+	7.20126i	−0.600800	+	0.346872i	−0.769356	−	0.638820i	$-0.779423\pi$
$431$	−12.4729	+	7.20126i	−0.600800	+	0.346872i	0.168556	+	0.985692i	$0.446090\pi$
$432$		0			0
$433$	18.1596	−	31.4534i	0.872695	−	1.51155i	0.0134964	−	0.999909i	$-0.495704\pi$
$433$	18.1596	−	31.4534i	0.872695	−	1.51155i	0.859198	−	0.511643i	$-0.170963\pi$
$434$		0			0
$435$	6.02886	+	3.48076i	0.289062	+	0.166890i
$436$		0			0
$437$		−	18.6352i		−	0.891443i
$438$		0			0
$439$	−10.2722	−	17.7920i	−0.490266	−	0.849166i	0.509671	−	0.860369i	$-0.329767\pi$
$439$	−10.2722	−	17.7920i	−0.490266	−	0.849166i	−0.999937	+	0.0112036i	$0.996434\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−25.3211			−1.20304			−0.601521	−	0.798857i	$-0.705439\pi$
$443$	−25.3211			−1.20304			−0.601521	+	0.798857i	$0.705439\pi$
$444$		0			0
$445$	−1.64637	−	2.85160i	−0.0780454	−	0.135179i
$446$		0			0
$447$			4.13994i			0.195812i
$448$		0			0
$449$	−29.0997	−	16.8007i	−1.37330	−	0.792876i	−0.381959	−	0.924179i	$-0.624751\pi$
$449$	−29.0997	−	16.8007i	−1.37330	−	0.792876i	−0.991342	+	0.131303i	$0.958084\pi$
$450$		0			0
$451$	−7.23926	+	12.5388i	−0.340883	+	0.590427i
$452$		0			0
$453$	17.5726	−	10.1456i	0.825635	−	0.476680i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	32.9050	−	18.9977i	1.53923	−	0.888677i	0.540350	−	0.841441i	$-0.318292\pi$
$457$	32.9050	−	18.9977i	1.53923	−	0.888677i	0.998884	−	0.0472361i	$-0.0150413\pi$
$458$		0			0
$459$	4.01359	−	6.95174i	0.187338	−	0.324479i
$460$		0			0
$461$	31.4812	+	18.1757i	1.46623	+	0.846525i	0.999287	−	0.0377645i	$-0.0120237\pi$
$461$	31.4812	+	18.1757i	1.46623	+	0.846525i	0.466938	+	0.884290i	$0.345357\pi$
$462$		0			0
$463$		−	35.3400i		−	1.64239i	−0.570649	−	0.821194i	$-0.693308\pi$
$463$		−	35.3400i		−	1.64239i	0.570649	−	0.821194i	$-0.306692\pi$
$464$		0			0
$465$	8.06600	+	13.9707i	0.374052	+	0.647877i
$466$		0			0
$467$	29.5717			1.36842			0.684208	−	0.729287i	$-0.260148\pi$
$467$	29.5717			1.36842			0.684208	+	0.729287i	$0.260148\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.91141	+	13.7030i	0.364538	+	0.631399i
$472$		0			0
$473$			7.09820i			0.326376i
$474$		0			0
$475$	22.3825	+	12.9225i	1.02698	+	0.592927i
$476$		0			0
$477$	−0.370705	+	0.642079i	−0.0169734	+	0.0293988i
$478$		0			0
$479$	−18.8339	+	10.8738i	−0.860545	+	0.496836i	−0.864195	−	0.503157i	$-0.832172\pi$
$479$	−18.8339	+	10.8738i	−0.860545	+	0.496836i	0.00364974	+	0.999993i	$0.498838\pi$
$480$		0			0
$481$	10.5603	+	6.78057i	0.481510	+	0.309167i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.22710	+	9.05361i	−0.237350	+	0.411103i
$486$		0			0
$487$	−26.0217	−	15.0236i	−1.17916	−	0.680786i	−0.223337	−	0.974741i	$-0.571695\pi$
$487$	−26.0217	−	15.0236i	−1.17916	−	0.680786i	−0.955819	+	0.293955i	$0.905028\pi$
$488$		0			0
$489$		−	37.3938i		−	1.69101i
$490$		0			0
$491$	−20.0899	−	34.7967i	−0.906643	−	1.57035i	−0.818696	−	0.574227i	$-0.805303\pi$
$491$	−20.0899	−	34.7967i	−0.906643	−	1.57035i	−0.0879471	−	0.996125i	$-0.528031\pi$
$492$		0			0
$493$	−4.48406			−0.201952
$494$		0			0
$495$	−0.105446			−0.00473946
$496$		0			0
$497$		0			0
$498$		0			0
$499$			11.7400i			0.525554i	0.964857	+	0.262777i	$0.0846383\pi$
$499$			11.7400i			0.525554i	−0.964857	+	0.262777i	$0.915362\pi$
$500$		0			0
$501$	4.82416	+	2.78523i	0.215528	+	0.124435i
$502$		0			0
$503$	−16.6965	+	28.9191i	−0.744459	+	1.28944i	0.205989	+	0.978554i	$0.433959\pi$
$503$	−16.6965	+	28.9191i	−0.744459	+	1.28944i	−0.950447	+	0.310886i	$0.899374\pi$
$504$		0			0
$505$	15.8375	−	9.14376i	0.704758	−	0.406892i
$506$		0			0
$507$	−22.6618	−	2.14509i	−1.00644	−	0.0952667i
$508$		0			0
$509$	17.9983	−	10.3913i	0.797759	−	0.460586i	−0.0449282	−	0.998990i	$-0.514306\pi$
$509$	17.9983	−	10.3913i	0.797759	−	0.460586i	0.842687	+	0.538404i	$0.180973\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	37.3245	+	21.5493i	1.64792	+	0.951425i
$514$		0			0
$515$		−	8.17531i		−	0.360247i
$516$		0			0
$517$	4.26822	+	7.39278i	0.187716	+	0.325134i
$518$		0			0
$519$	−9.34869			−0.410362
$520$		0			0
$521$	−7.50239			−0.328686			−0.164343	−	0.986403i	$-0.552550\pi$
$521$	−7.50239			−0.328686			−0.164343	+	0.986403i	$0.552550\pi$
$522$		0			0
$523$	3.66289	+	6.34431i	0.160167	+	0.277417i	0.934928	−	0.354836i	$-0.115463\pi$
$523$	3.66289	+	6.34431i	0.160167	+	0.277417i	−0.774762	+	0.632254i	$0.782130\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.99882	−	5.19547i	−0.391995	−	0.226318i
$528$		0			0
$529$	9.03282	−	15.6453i	0.392731	−	0.680230i
$530$		0			0
$531$	0.460578	−	0.265915i	0.0199874	−	0.0115397i
$532$		0			0
$533$	−38.1018	−	24.4644i	−1.65037	−	1.05967i
$534$		0			0
$535$	12.2288	−	7.06028i	0.528696	−	0.305243i
$536$		0			0
$537$	−8.61983	+	14.9300i	−0.371973	+	0.644277i
$538$		0			0
$539$		0			0
$540$		0			0
$541$			11.6924i			0.502698i	0.967897	+	0.251349i	$0.0808741\pi$
$541$			11.6924i			0.502698i	−0.967897	+	0.251349i	$0.919126\pi$
$542$		0			0
$543$	−13.2422	−	22.9362i	−0.568278	−	0.984287i
$544$		0			0
$545$	8.51799			0.364871
$546$		0			0
$547$	5.10513			0.218280			0.109140	−	0.994026i	$-0.465190\pi$
$547$	5.10513			0.218280			0.109140	+	0.994026i	$0.465190\pi$
$548$		0			0
$549$	0.0547442	+	0.0948197i	0.00233643	+	0.00404681i
$550$		0			0
$551$		−	24.0753i		−	1.02564i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.22168	+	7.31216i	−0.179200	+	0.310384i
$556$		0			0
$557$	10.8544	−	6.26679i	0.459916	−	0.265532i	−0.252093	−	0.967703i	$-0.581119\pi$
$557$	10.8544	−	6.26679i	0.459916	−	0.265532i	0.712009	+	0.702171i	$0.247786\pi$
$558$		0			0
$559$	−22.1740	−	1.04712i	−0.937860	−	0.0442884i
$560$		0			0
$561$	2.73167	−	1.57713i	0.115331	−	0.0665865i
$562$		0			0
$563$	−1.95315	+	3.38296i	−0.0823155	+	0.142575i	−0.904244	−	0.427016i	$-0.859565\pi$
$563$	−1.95315	+	3.38296i	−0.0823155	+	0.142575i	0.821929	+	0.569590i	$0.192898\pi$
$564$		0			0
$565$	−17.5135	−	10.1114i	−0.736799	−	0.425391i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.0664	−	39.9523i	−0.966996	−	1.67489i	−0.704155	−	0.710046i	$-0.748674\pi$
$569$	−23.0664	−	39.9523i	−0.966996	−	1.67489i	−0.262841	−	0.964839i	$-0.584659\pi$
$570$		0			0
$571$	−30.1160			−1.26031			−0.630157	−	0.776467i	$-0.717010\pi$
$571$	−30.1160			−1.26031			−0.630157	+	0.776467i	$0.717010\pi$
$572$		0			0
$573$	38.8372			1.62245
$574$		0			0
$575$	−3.42172	−	5.92660i	−0.142696	−	0.247156i
$576$		0			0
$577$			25.6300i			1.06699i	0.845803	+	0.533496i	$0.179122\pi$
$577$			25.6300i			1.06699i	−0.845803	+	0.533496i	$0.820878\pi$
$578$		0			0
$579$	−10.5722	−	6.10388i	−0.439367	−	0.253669i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	11.2126	−	6.47358i	0.464377	−	0.268108i
$584$		0			0
$585$	0.0155553	−	0.329403i	0.000643133	−	0.0136191i
$586$		0			0
$587$	−11.4147	+	6.59025i	−0.471133	+	0.272009i	−0.716714	−	0.697367i	$-0.754355\pi$
$587$	−11.4147	+	6.59025i	−0.471133	+	0.272009i	0.245581	+	0.969376i	$0.421021\pi$
$588$		0			0
$589$	27.8950	−	48.3155i	1.14939	−	1.99081i
$590$		0			0
$591$	29.9237	+	17.2765i	1.23090	+	0.710659i
$592$		0			0
$593$			6.53704i			0.268444i	0.990951	+	0.134222i	$0.0428536\pi$
$593$			6.53704i			0.268444i	−0.990951	+	0.134222i	$0.957146\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	24.1706			0.989238
$598$		0			0
$599$	12.4244			0.507649			0.253824	−	0.967250i	$-0.418311\pi$
$599$	12.4244			0.507649			0.253824	+	0.967250i	$0.418311\pi$
$600$		0			0
$601$	−9.27019	−	16.0564i	−0.378139	−	0.654956i	0.612653	−	0.790352i	$-0.290102\pi$
$601$	−9.27019	−	16.0564i	−0.378139	−	0.654956i	−0.990791	+	0.135397i	$0.956769\pi$
$602$		0			0
$603$		−	0.245018i		−	0.00997792i
$604$		0			0
$605$	−11.6027	−	6.69880i	−0.471715	−	0.272345i
$606$		0			0
$607$	7.87226	−	13.6351i	0.319525	−	0.553434i	−0.660864	−	0.750506i	$-0.729810\pi$
$607$	7.87226	−	13.6351i	0.319525	−	0.553434i	0.980389	+	0.197072i	$0.0631433\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−23.7239	+	12.2429i	−0.959766	+	0.495294i
$612$		0			0
$613$	16.6796	−	9.62996i	0.673682	−	0.388950i	−0.123788	−	0.992309i	$-0.539504\pi$
$613$	16.6796	−	9.62996i	0.673682	−	0.388950i	0.797470	+	0.603358i	$0.206171\pi$
$614$		0			0
$615$	15.2319	−	26.3824i	0.614208	−	1.06384i
$616$		0			0
$617$	37.5872	+	21.7010i	1.51320	+	0.873649i	0.999881	+	0.0154532i	$0.00491911\pi$
$617$	37.5872	+	21.7010i	1.51320	+	0.873649i	0.513323	+	0.858195i	$0.328414\pi$
$618$		0			0
$619$			13.3880i			0.538109i	0.963125	+	0.269054i	$0.0867111\pi$
$619$			13.3880i			0.538109i	−0.963125	+	0.269054i	$0.913289\pi$
$620$		0			0
$621$	−5.70598	−	9.88305i	−0.228973	−	0.396593i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.105015			−0.00420059
$626$		0			0
$627$	8.46776	+	14.6666i	0.338170	+	0.585727i
$628$		0			0
$629$		−	5.43854i		−	0.216849i
$630$		0			0
$631$	13.1568	+	7.59606i	0.523762	+	0.302394i	0.738473	−	0.674283i	$-0.235547\pi$
$631$	13.1568	+	7.59606i	0.523762	+	0.302394i	−0.214710	+	0.976678i	$0.568881\pi$
$632$		0			0
$633$	−8.29484	+	14.3671i	−0.329690	+	0.571040i
$634$		0			0
$635$	−10.4646	+	6.04177i	−0.415277	+	0.239760i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.568127	+	0.328008i	−0.0224747	+	0.0129758i
$640$		0			0
$641$	−17.9671	+	31.1199i	−0.709658	+	1.22916i	0.255326	+	0.966855i	$0.417817\pi$
$641$	−17.9671	+	31.1199i	−0.709658	+	1.22916i	−0.964984	+	0.262309i	$0.915516\pi$
$642$		0			0
$643$	−7.72476	−	4.45989i	−0.304635	−	0.175881i	0.339888	−	0.940466i	$-0.389611\pi$
$643$	−7.72476	−	4.45989i	−0.304635	−	0.175881i	−0.644523	+	0.764585i	$0.722944\pi$
$644$		0			0
$645$		−	14.9351i		−	0.588068i
$646$		0			0
$647$	−4.88360	−	8.45865i	−0.191994	−	0.332544i	0.753917	−	0.656970i	$-0.228162\pi$
$647$	−4.88360	−	8.45865i	−0.191994	−	0.332544i	−0.945911	+	0.324426i	$0.894829\pi$
$648$		0			0
$649$	−9.28730			−0.364558
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.26858	−	14.3216i	−0.323575	−	0.560448i	0.657648	−	0.753325i	$-0.271551\pi$
$653$	−8.26858	−	14.3216i	−0.323575	−	0.560448i	−0.981223	+	0.192877i	$0.938218\pi$
$654$		0			0
$655$		−	26.9361i		−	1.05248i
$656$		0			0
$657$	−0.188792	−	0.108999i	−0.00736547	−	0.00425245i
$658$		0			0
$659$	−7.82010	+	13.5448i	−0.304628	+	0.527631i	−0.977178	−	0.212420i	$-0.931865\pi$
$659$	−7.82010	+	13.5448i	−0.304628	+	0.527631i	0.672550	+	0.740051i	$0.265199\pi$
$660$		0			0
$661$	21.9320	−	12.6624i	0.853056	−	0.492512i	−0.00862494	−	0.999963i	$-0.502745\pi$
$661$	21.9320	−	12.6624i	0.853056	−	0.492512i	0.861681	+	0.507451i	$0.169412\pi$
$662$		0			0
$663$	4.52381	+	8.76610i	0.175690	+	0.340447i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.18742	+	5.52077i	−0.123417	+	0.213765i
$668$		0			0
$669$	−22.1213	−	12.7717i	−0.855259	−	0.493784i
$670$		0			0
$671$		−	1.91199i		−	0.0738114i
$672$		0			0
$673$	−4.08919	−	7.08268i	−0.157627	−	0.273017i	0.776386	−	0.630258i	$-0.217051\pi$
$673$	−4.08919	−	7.08268i	−0.157627	−	0.273017i	−0.934012	+	0.357241i	$0.883718\pi$
$674$		0			0
$675$	15.8272			0.609189
$676$		0			0
$677$	−44.9616			−1.72801			−0.864007	−	0.503480i	$-0.832053\pi$
$677$	−44.9616			−1.72801			−0.864007	+	0.503480i	$0.832053\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			12.5434i			0.480663i
$682$		0			0
$683$	17.7090	+	10.2243i	0.677616	+	0.391222i	0.798956	−	0.601389i	$-0.205386\pi$
$683$	17.7090	+	10.2243i	0.677616	+	0.391222i	−0.121340	+	0.992611i	$0.538719\pi$
$684$		0			0
$685$	−2.32367	+	4.02471i	−0.0887827	+	0.153776i
$686$		0			0
$687$	−18.6526	+	10.7691i	−0.711643	+	0.410867i
$688$		0			0
$689$	18.5687	+	35.9818i	0.707411	+	1.37080i
$690$		0			0
$691$	29.1943	−	16.8554i	1.11061	−	0.641208i	0.171619	−	0.985163i	$-0.445100\pi$
$691$	29.1943	−	16.8554i	1.11061	−	0.641208i	0.938986	+	0.343955i	$0.111767\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.49320	−	5.48090i	−0.360098	−	0.207902i
$696$		0			0
$697$			19.6223i			0.743248i
$698$		0			0
$699$	−16.4627	−	28.5142i	−0.622676	−	1.07851i
$700$		0			0
$701$	−29.6172			−1.11862			−0.559312	−	0.828957i	$-0.688935\pi$
$701$	−29.6172			−1.11862			−0.559312	+	0.828957i	$0.688935\pi$
$702$		0			0
$703$	29.2000			1.10130
$704$		0			0
$705$	−8.98062	−	15.5549i	−0.338230	−	0.585831i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	8.59653	+	4.96321i	0.322849	+	0.186397i	0.652662	−	0.757649i	$-0.273652\pi$
$709$	8.59653	+	4.96321i	0.322849	+	0.186397i	−0.329813	+	0.944046i	$0.606986\pi$
$710$		0			0
$711$	−0.153434	+	0.265756i	−0.00575423	+	0.00996661i
$712$		0			0
$713$	−12.7933	+	7.38623i	−0.479114	+	0.276616i
$714$		0			0
$715$	−3.11141	+	4.84584i	−0.116360	+	0.181224i
$716$		0			0
$717$	2.43074	−	1.40339i	0.0907778	−	0.0524106i
$718$		0			0
$719$	10.3425	−	17.9138i	0.385711	−	0.668071i	−0.606157	−	0.795345i	$-0.707290\pi$
$719$	10.3425	−	17.9138i	0.385711	−	0.668071i	0.991868	+	0.127274i	$0.0406229\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$			32.1584i			1.19598i
$724$		0			0
$725$	−4.42061	−	7.65673i	−0.164177	−	0.284364i
$726$		0			0
$727$	−4.83449			−0.179301			−0.0896506	−	0.995973i	$-0.528575\pi$
$727$	−4.83449			−0.179301			−0.0896506	+	0.995973i	$0.528575\pi$
$728$		0			0
$729$	26.3800			0.977035
$730$		0			0
$731$	4.80999	+	8.33115i	0.177904	+	0.308139i
$732$		0			0
$733$			12.7037i			0.469223i	0.972089	+	0.234612i	$0.0753819\pi$
$733$			12.7037i			0.469223i	−0.972089	+	0.234612i	$0.924618\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.13937	+	3.70549i	−0.0788046	+	0.136494i
$738$		0			0
$739$	−2.23852	+	1.29241i	−0.0823451	+	0.0475420i	−0.540607	−	0.841275i	$-0.681805\pi$
$739$	−2.23852	+	1.29241i	−0.0823451	+	0.0475420i	0.458262	+	0.888817i	$0.348472\pi$
$740$		0			0
$741$	−47.0660	+	24.2888i	−1.72901	+	0.892270i
$742$		0			0
$743$	9.98318	−	5.76379i	0.366247	−	0.211453i	−0.305570	−	0.952169i	$-0.598847\pi$
$743$	9.98318	−	5.76379i	0.366247	−	0.211453i	0.671818	+	0.740717i	$0.265514\pi$
$744$		0			0
$745$	−1.63772	+	2.83662i	−0.0600015	+	0.103926i
$746$		0			0
$747$	0.104374	+	0.0602602i	0.00381884	+	0.00220481i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.50269	−	6.06684i	−0.127815	−	0.221382i	0.795015	−	0.606590i	$-0.207463\pi$
$751$	−3.50269	−	6.06684i	−0.127815	−	0.221382i	−0.922830	+	0.385208i	$0.874130\pi$
$752$		0			0
$753$	25.1524			0.916605
$754$		0			0
$755$	16.0540			0.584264
$756$		0			0
$757$	8.60091	+	14.8972i	0.312605	+	0.541449i	0.978926	−	0.204217i	$-0.0654649\pi$
$757$	8.60091	+	14.8972i	0.312605	+	0.541449i	−0.666320	+	0.745666i	$0.732132\pi$
$758$		0			0
$759$		−	4.48431i		−	0.162770i
$760$		0			0
$761$	−29.9238	−	17.2765i	−1.08474	−	0.626274i	−0.152567	−	0.988293i	$-0.548754\pi$
$761$	−29.9238	−	17.2765i	−1.08474	−	0.626274i	−0.932170	+	0.362020i	$0.882087\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.123762	+	0.0714541i	−0.00447463	+	0.00258343i
$766$		0			0
$767$	1.37005	−	29.0125i	0.0494697	−	1.04758i
$768$		0			0
$769$	−9.48253	+	5.47474i	−0.341949	+	0.197424i	−0.661133	−	0.750268i	$-0.729924\pi$
$769$	−9.48253	+	5.47474i	−0.341949	+	0.197424i	0.319185	+	0.947693i	$0.396591\pi$
$770$		0			0
$771$	15.2037	−	26.3335i	0.547547	−	0.948379i
$772$		0			0
$773$	−19.0556	−	11.0018i	−0.685384	−	0.395707i	0.116496	−	0.993191i	$-0.462834\pi$
$773$	−19.0556	−	11.0018i	−0.685384	−	0.395707i	−0.801880	+	0.597484i	$0.796167\pi$
$774$		0			0
$775$		−	20.4878i		−	0.735945i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−105.354			−3.77470
$780$		0			0
$781$	11.4560			0.409926
$782$		0			0
$783$	−7.37171	−	12.7682i	−0.263443	−	0.456297i
$784$		0			0
$785$			12.5187i			0.446812i
$786$		0			0
$787$	−34.0548	−	19.6616i	−1.21392	−	0.700859i	−0.250312	−	0.968165i	$-0.580533\pi$
$787$	−34.0548	−	19.6616i	−1.21392	−	0.700859i	−0.963612	+	0.267306i	$0.913866\pi$
$788$		0			0
$789$	14.6576	−	25.3877i	0.521824	−	0.903826i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	5.97284	+	0.282054i	0.212102	+	0.0100160i
$794$		0			0
$795$	−23.5920	+	13.6208i	−0.836721	+	0.483081i
$796$		0			0
$797$	27.2620	−	47.2192i	0.965669	−	1.67259i	0.257863	−	0.966181i	$-0.416982\pi$
$797$	27.2620	−	47.2192i	0.965669	−	1.67259i	0.707806	−	0.706407i	$-0.249685\pi$
$798$		0			0
$799$	10.0192	+	5.78460i	0.354454	+	0.204644i
$800$		0			0
$801$		−	0.156917i		−	0.00554438i
$802$		0			0
$803$	1.90344	+	3.29685i	0.0671709	+	0.116343i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	43.4100			1.52810
$808$		0			0
$809$	−1.56318	−	2.70751i	−0.0549586	−	0.0951911i	0.837237	−	0.546840i	$-0.184169\pi$
$809$	−1.56318	−	2.70751i	−0.0549586	−	0.0951911i	−0.892196	+	0.451649i	$0.850836\pi$
$810$		0			0
$811$		−	4.48741i		−	0.157574i	−0.996891	−	0.0787872i	$-0.974895\pi$
$811$		−	4.48741i		−	0.157574i	0.996891	−	0.0787872i	$-0.0251048\pi$
$812$		0			0
$813$	30.6796	+	17.7129i	1.07598	+	0.621218i
$814$		0			0
$815$	14.7926	−	25.6216i	0.518164	−	0.897486i
$816$		0			0
$817$	−44.7307	+	25.8253i	−1.56493	+	0.903512i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−21.3797	+	12.3436i	−0.746158	+	0.430795i	−0.824304	−	0.566147i	$-0.808433\pi$
$821$	−21.3797	+	12.3436i	−0.746158	+	0.430795i	0.0781459	+	0.996942i	$0.475100\pi$
$822$		0			0
$823$	−5.50672	+	9.53791i	−0.191952	+	0.332471i	−0.945897	−	0.324467i	$-0.894815\pi$
$823$	−5.50672	+	9.53791i	−0.191952	+	0.332471i	0.753945	+	0.656938i	$0.228148\pi$
$824$		0			0
$825$	5.38604	+	3.10963i	0.187518	+	0.108263i
$826$		0			0
$827$		−	23.8575i		−	0.829605i	−0.909911	−	0.414803i	$-0.863851\pi$
$827$		−	23.8575i		−	0.829605i	0.909911	−	0.414803i	$-0.136149\pi$
$828$		0			0
$829$	−10.2157	−	17.6941i	−0.354806	−	0.614541i	0.632279	−	0.774741i	$-0.282120\pi$
$829$	−10.2157	−	17.6941i	−0.354806	−	0.614541i	−0.987085	+	0.160199i	$0.948786\pi$
$830$		0			0
$831$	19.3544			0.671395
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.20362	+	3.81679i	0.0762595	+	0.132085i
$836$		0			0
$837$		−	34.1650i		−	1.18092i
$838$		0			0
$839$	−21.0080	−	12.1290i	−0.725276	−	0.418738i	0.0914153	−	0.995813i	$-0.470861\pi$
$839$	−21.0080	−	12.1290i	−0.725276	−	0.418738i	−0.816692	+	0.577074i	$0.804194\pi$
$840$		0			0
$841$	10.3821	−	17.9823i	0.358003	−	0.620080i
$842$		0			0
$843$	−4.83668	+	2.79246i	−0.166584	+	0.0961775i
$844$		0			0
$845$	−14.6789	−	10.4346i	−0.504969	−	0.358960i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	15.6974	−	27.1888i	0.538734	−	0.933115i
$850$		0			0
$851$	−6.69592	−	3.86589i	−0.229533	−	0.132521i
$852$		0			0
$853$		−	51.8470i		−	1.77521i	−0.460608	−	0.887604i	$-0.652369\pi$
$853$		−	51.8470i		−	1.77521i	0.460608	−	0.887604i	$-0.347631\pi$
$854$		0			0
$855$	−0.383643	−	0.664490i	−0.0131203	−	0.0227251i
$856$		0			0
$857$	26.9054			0.919071			0.459536	−	0.888159i	$-0.348016\pi$
$857$	26.9054			0.919071			0.459536	+	0.888159i	$0.348016\pi$
$858$		0			0
$859$	−33.4509			−1.14133			−0.570665	−	0.821183i	$-0.693315\pi$
$859$	−33.4509			−1.14133			−0.570665	+	0.821183i	$0.693315\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			5.94352i			0.202320i	0.994870	+	0.101160i	$0.0322554\pi$
$863$			5.94352i			0.202320i	−0.994870	+	0.101160i	$0.967745\pi$
$864$		0			0
$865$	−6.40557	−	3.69825i	−0.217796	−	0.125744i
$866$		0			0
$867$	−12.7461	+	22.0769i	−0.432881	+	0.749771i
$868$		0			0
$869$	4.64087	−	2.67941i	0.157431	−	0.0908926i
$870$		0			0
$871$	−11.2600	−	7.22978i	−0.381529	−	0.244972i
$872$		0			0
$873$	−0.431453	+	0.249099i	−0.0146025	+	0.00843074i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	43.0073	+	24.8303i	1.45225	+	0.838458i	0.998609	−	0.0527255i	$-0.0167908\pi$
$877$	43.0073	+	24.8303i	1.45225	+	0.838458i	0.453643	+	0.891184i	$0.350124\pi$
$878$		0			0
$879$			29.7105i			1.00211i
$880$		0			0
$881$	10.6452	+	18.4381i	0.358647	+	0.621195i	0.987735	−	0.156139i	$-0.0499049\pi$
$881$	10.6452	+	18.4381i	0.358647	+	0.621195i	−0.629088	+	0.777334i	$0.716572\pi$
$882$		0			0
$883$	−32.8053			−1.10399			−0.551993	−	0.833848i	$-0.686133\pi$
$883$	−32.8053			−1.10399			−0.551993	+	0.833848i	$0.686133\pi$
$884$		0			0
$885$	19.5411			0.656866
$886$		0			0
$887$	−8.61790	−	14.9266i	−0.289361	−	0.501187i	0.684297	−	0.729204i	$-0.260109\pi$
$887$	−8.61790	−	14.9266i	−0.289361	−	0.501187i	−0.973657	+	0.228016i	$0.926776\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	9.17938	+	5.29972i	0.307521	+	0.177547i
$892$		0			0
$893$	−31.0580	+	53.7941i	−1.03932	+	1.80015i
$894$		0			0
$895$	−11.8123	+	6.81985i	−0.394843	+	0.227963i
$896$		0			0
$897$	14.0085	+	0.661520i	0.467730	+	0.0220875i
$898$		0			0
$899$	−16.5280	+	9.54247i	−0.551241	+	0.318259i
$900$		0			0
$901$	8.77345	−	15.1961i	0.292286	−	0.506254i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	20.9540i		−	0.696535i
$906$		0			0
$907$	−17.3178	−	29.9953i	−0.575028	−	0.995978i	−0.996039	−	0.0889223i	$-0.971658\pi$
$907$	−17.3178	−	29.9953i	−0.575028	−	0.995978i	0.421010	−	0.907056i	$-0.361676\pi$
$908$		0			0
$909$	0.871499			0.0289058
$910$		0			0
$911$	−7.85153			−0.260133			−0.130066	−	0.991505i	$-0.541519\pi$
$911$	−7.85153			−0.260133			−0.130066	+	0.991505i	$0.541519\pi$
$912$		0			0
$913$	−1.05232	−	1.82267i	−0.0348267	−	0.0603216i
$914$		0			0
$915$			4.02294i			0.132994i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.3659	−	31.8106i	0.605834	−	1.04934i	−0.386085	−	0.922463i	$-0.626173\pi$
$919$	18.3659	−	31.8106i	0.605834	−	1.04934i	0.991919	−	0.126872i	$-0.0404937\pi$
$920$		0			0
$921$	40.9256	−	23.6284i	1.34854	−	0.778583i
$922$		0			0
$923$	−1.68997	+	35.7872i	−0.0556260	+	1.17795i
$924$		0			0
$925$	9.28654	−	5.36159i	0.305339	−	0.176288i
$926$		0			0
$927$	0.194799	−	0.337401i	0.00639803	−	0.0110817i
$928$		0			0
$929$	−28.6355	−	16.5327i	−0.939501	−	0.542421i	−0.0496975	−	0.998764i	$-0.515826\pi$
$929$	−28.6355	−	16.5327i	−0.939501	−	0.542421i	−0.889804	+	0.456343i	$0.849159\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−24.8451	−	43.0330i	−0.813393	−	1.40884i
$934$		0			0
$935$	2.49559			0.0816146
$936$		0			0
$937$	45.8626			1.49826			0.749132	−	0.662421i	$-0.230471\pi$
$937$	45.8626			1.49826			0.749132	+	0.662421i	$0.230471\pi$
$938$		0			0
$939$	14.5923	+	25.2746i	0.476202	+	0.824806i
$940$		0			0
$941$		−	5.77729i		−	0.188334i	−0.995556	−	0.0941671i	$-0.969981\pi$
$941$		−	5.77729i		−	0.188334i	0.995556	−	0.0941671i	$-0.0300188\pi$
$942$		0			0
$943$	24.1590	+	13.9482i	0.786724	+	0.454215i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.0487521	+	0.0281471i	−0.00158423	+	0.000914656i	−0.500792	−	0.865568i	$-0.666958\pi$
$947$	−0.0487521	+	0.0281471i	−0.00158423	+	0.000914656i	0.499208	+	0.866482i	$0.333624\pi$
$948$		0			0
$949$	−10.5798	+	5.45979i	−0.343435	+	0.177232i
$950$		0			0
$951$	−43.5858	+	25.1643i	−1.41337	+	0.816008i
$952$		0			0
$953$	−20.0778	+	34.7758i	−0.650385	+	1.12650i	0.332645	+	0.943052i	$0.392059\pi$
$953$	−20.0778	+	34.7758i	−0.650385	+	1.12650i	−0.983030	+	0.183447i	$0.941274\pi$
$954$		0			0
$955$	26.6106	+	15.3636i	0.861099	+	0.497156i
$956$		0			0
$957$		−	5.79339i		−	0.187274i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−13.2257			−0.426634
$962$		0			0
$963$	0.672920			0.0216846
$964$		0			0
$965$	−4.82928	−	8.36456i	−0.155460	−	0.269265i
$966$		0			0
$967$			32.3647i			1.04078i	0.853929	+	0.520390i	$0.174213\pi$
$967$			32.3647i			1.04078i	−0.853929	+	0.520390i	$0.825787\pi$
$968$		0			0
$969$	19.8772	+	11.4761i	0.638547	+	0.368665i
$970$		0			0
$971$	−15.3459	+	26.5799i	−0.492473	+	0.852989i	−0.999962	−	0.00866935i	$-0.997240\pi$
$971$	−15.3459	+	26.5799i	−0.492473	+	0.852989i	0.507489	+	0.861658i	$0.330574\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−10.5087	+	16.3667i	−0.336547	+	0.524153i
$976$		0			0
$977$	4.87565	−	2.81496i	0.155986	−	0.0900585i	−0.419975	−	0.907536i	$-0.637961\pi$
$977$	4.87565	−	2.81496i	0.155986	−	0.0900585i	0.575961	+	0.817477i	$0.304628\pi$
$978$		0			0
$979$	−1.37011	+	2.37310i	−0.0437890	+	0.0758447i
$980$		0			0
$981$	0.351544	+	0.202964i	0.0112239	+	0.00648014i
$982$		0			0
$983$		−	6.66363i		−	0.212537i	−0.994337	−	0.106268i	$-0.966110\pi$
$983$		−	6.66363i		−	0.212537i	0.994337	−	0.106268i	$-0.0338903\pi$
$984$		0			0
$985$	13.6688	+	23.6751i	0.435525	+	0.754351i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	13.6764			0.434884
$990$		0			0
$991$	26.4156	+	45.7532i	0.839120	+	1.45340i	0.890631	+	0.454726i	$0.150263\pi$
$991$	26.4156	+	45.7532i	0.839120	+	1.45340i	−0.0515115	+	0.998672i	$0.516404\pi$
$992$		0			0
$993$			45.8618i			1.45538i
$994$		0			0
$995$	16.5613	+	9.56167i	0.525029	+	0.303125i
$996$		0			0
$997$	−7.31833	+	12.6757i	−0.231774	+	0.401444i	−0.958330	−	0.285663i	$-0.907786\pi$
$997$	−7.31833	+	12.6757i	−0.231774	+	0.401444i	0.726556	+	0.687107i	$0.241120\pi$
$998$		0			0
$999$	15.4860	−	8.94085i	0.489955	−	0.282876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.u.c.1765.6		16
7.2	even	3		2548.2.bq.c.361.3		16
7.3	odd	6		2548.2.bb.d.569.3		16
7.4	even	3		2548.2.bb.c.569.6		16
7.5	odd	6		2548.2.bq.e.361.6		16
7.6	odd	2		364.2.u.a.309.3	yes	16
13.4	even	6	inner	2548.2.u.c.589.6		16
21.20	even	2		3276.2.cf.c.1765.6		16
28.27	even	2		1456.2.cc.f.673.6		16
91.4	even	6		2548.2.bq.c.1941.3		16
91.17	odd	6		2548.2.bq.e.1941.6		16
91.30	even	6		2548.2.bb.c.1733.6		16
91.41	even	12		4732.2.a.t.1.6		8
91.55	odd	6		4732.2.g.k.337.11		16
91.62	odd	6		4732.2.g.k.337.12		16
91.69	odd	6		364.2.u.a.225.3	✓	16
91.76	even	12		4732.2.a.s.1.6		8
91.82	odd	6		2548.2.bb.d.1733.3		16
273.251	even	6		3276.2.cf.c.2773.3		16
364.251	even	6		1456.2.cc.f.225.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.3	✓	16	91.69	odd	6
364.2.u.a.309.3	yes	16	7.6	odd	2
1456.2.cc.f.225.6		16	364.251	even	6
1456.2.cc.f.673.6		16	28.27	even	2
2548.2.u.c.589.6		16	13.4	even	6	inner
2548.2.u.c.1765.6		16	1.1	even	1	trivial
2548.2.bb.c.569.6		16	7.4	even	3
2548.2.bb.c.1733.6		16	91.30	even	6
2548.2.bb.d.569.3		16	7.3	odd	6
2548.2.bb.d.1733.3		16	91.82	odd	6
2548.2.bq.c.361.3		16	7.2	even	3
2548.2.bq.c.1941.3		16	91.4	even	6
2548.2.bq.e.361.6		16	7.5	odd	6
2548.2.bq.e.1941.6		16	91.17	odd	6
3276.2.cf.c.1765.6		16	21.20	even	2
3276.2.cf.c.2773.3		16	273.251	even	6
4732.2.a.s.1.6		8	91.76	even	12
4732.2.a.t.1.6		8	91.41	even	12
4732.2.g.k.337.11		16	91.55	odd	6
4732.2.g.k.337.12		16	91.62	odd	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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.875503 + 1.51642i) q^{3} +1.38536i q^{5} +(-0.0330100 + 0.0571750i) q^{9} +(0.998442 - 0.576451i) q^{11} +(1.65348 + 3.20406i) q^{13} +(-2.10079 + 1.21289i) q^{15} +(0.781246 - 1.35316i) q^{17} +(7.26523 + 4.19458i) q^{19} +(-1.11067 - 1.92374i) q^{23} +3.08077 q^{25} +5.13741 q^{27} +(-1.43491 - 2.48533i) q^{29} -6.65024i q^{31} +(1.74828 + 1.00937i) q^{33} +(3.01436 - 1.74034i) q^{37} +(-3.41106 + 5.31253i) q^{39} +(-10.8758 + 6.27917i) q^{41} +(-3.07841 + 5.33196i) q^{43} +(-0.0792081 - 0.0457308i) q^{45} +7.40432i q^{47} +2.73593 q^{51} +11.2301 q^{53} +(0.798593 + 1.38320i) q^{55} +14.6895i q^{57} +(-6.97634 - 4.02779i) q^{59} +(0.829207 - 1.43623i) q^{61} +(-4.43879 + 2.29067i) q^{65} +(-3.21406 + 1.85564i) q^{67} +(1.94479 - 3.36848i) q^{69} +(8.60538 + 4.96832i) q^{71} +3.30200i q^{73} +(2.69722 + 4.67173i) q^{75} +4.64811 q^{79} +(4.59685 + 7.96198i) q^{81} -1.82551i q^{83} +(1.87462 + 1.08231i) q^{85} +(2.51253 - 4.35183i) q^{87} +(-2.05837 + 1.18840i) q^{89} +(10.0845 - 5.82230i) q^{93} +(-5.81102 + 10.0650i) q^{95} +(6.53519 + 3.77309i) q^{97} +0.0761145i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} + 6 q^{11} - 10 q^{13} + 6 q^{15} - 2 q^{17} - 44 q^{25} + 12 q^{27} - 22 q^{29} - 42 q^{33} + 12 q^{37} + 24 q^{39} - 36 q^{41} + 6 q^{43} + 30 q^{45} - 4 q^{51} + 8 q^{53} - 2 q^{55} + 18 q^{59}+ \cdots + 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 + 6 * q^11 - 10 * q^13 + 6 * q^15 - 2 * q^17 - 44 * q^25 + 12 * q^27 - 22 * q^29 - 42 * q^33 + 12 * q^37 + 24 * q^39 - 36 * q^41 + 6 * q^43 + 30 * q^45 - 4 * q^51 + 8 * q^53 - 2 * q^55 + 18 * q^59 - 4 * q^61 - 30 * q^65 + 24 * q^67 + 52 * q^69 + 36 * q^71 + 10 * q^75 + 8 * q^79 + 42 * q^85 - 26 * q^87 + 36 * q^89 - 42 * q^93 - 30 * q^95 + 42 * q^97

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