LMFDB - Embedded newform 560.2.bj.d.433.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(97,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("560.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bj (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.7
Character	$\chi$	$=$	560.433
Dual form			560.2.bj.d.97.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0703127 - 0.0703127i) q^{3} +(-2.16104 + 0.574360i) q^{5} +(2.58523 - 0.562657i) q^{7} +2.99011i q^{9} -0.777018 q^{11} +(-3.93876 + 3.93876i) q^{13} +(-0.111564 + 0.192334i) q^{15} +(0.982018 + 0.982018i) q^{17} +1.14872 q^{19} +(0.142213 - 0.221337i) q^{21} +(1.46167 + 1.46167i) q^{23} +(4.34022 - 2.48243i) q^{25} +(0.421181 + 0.421181i) q^{27} +4.69033i q^{29} +6.45186i q^{31} +(-0.0546342 + 0.0546342i) q^{33} +(-5.26363 + 2.70078i) q^{35} +(-1.30390 + 1.30390i) q^{37} +0.553890i q^{39} +9.81800i q^{41} +(7.13800 + 7.13800i) q^{43} +(-1.71740 - 6.46176i) q^{45} +(-7.34914 - 7.34914i) q^{47} +(6.36683 - 2.90920i) q^{49} +0.138097 q^{51} +(-2.08092 - 2.08092i) q^{53} +(1.67917 - 0.446288i) q^{55} +(0.0807696 - 0.0807696i) q^{57} -8.29508 q^{59} -5.88837i q^{61} +(1.68241 + 7.73013i) q^{63} +(6.24956 - 10.7741i) q^{65} +(6.30957 - 6.30957i) q^{67} +0.205548 q^{69} -12.3373 q^{71} +(7.23861 - 7.23861i) q^{73} +(0.130626 - 0.479719i) q^{75} +(-2.00877 + 0.437195i) q^{77} -2.83831i q^{79} -8.91111 q^{81} +(10.4188 - 10.4188i) q^{83} +(-2.68621 - 1.55815i) q^{85} +(0.329790 + 0.329790i) q^{87} +3.41911 q^{89} +(-7.96643 + 12.3988i) q^{91} +(0.453647 + 0.453647i) q^{93} +(-2.48243 + 0.659779i) q^{95} +(8.50258 + 8.50258i) q^{97} -2.32337i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7} - 8 q^{11} + 8 q^{15} + 16 q^{21} + 32 q^{23} + 8 q^{25} - 12 q^{35} - 8 q^{37} - 16 q^{43} + 24 q^{51} - 16 q^{53} - 20 q^{63} - 48 q^{65} + 32 q^{67} + 32 q^{71} - 40 q^{77} - 72 q^{81}+ \cdots + 24 q^{95}+O(q^{100}) $ 24 * q - 4 * q^7 - 8 * q^11 + 8 * q^15 + 16 * q^21 + 32 * q^23 + 8 * q^25 - 12 * q^35 - 8 * q^37 - 16 * q^43 + 24 * q^51 - 16 * q^53 - 20 * q^63 - 48 * q^65 + 32 * q^67 + 32 * q^71 - 40 * q^77 - 72 * q^81 + 16 * q^85 + 64 * q^91 + 72 * q^93 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.0703127	−	0.0703127i	0.0405951	−	0.0405951i	−0.686518	−	0.727113i	$-0.740862\pi$
$3$	0.0703127	−	0.0703127i	0.0405951	−	0.0405951i	0.727113	+	0.686518i	$0.240862\pi$
$4$		0			0
$5$	−2.16104	+	0.574360i	−0.966448	+	0.256862i
$5$	−2.16104	+	0.574360i	−0.966448	+	0.256862i
$6$		0			0
$7$	2.58523	−	0.562657i	0.977125	−	0.212664i
$7$	2.58523	−	0.562657i	0.977125	−	0.212664i
$8$		0			0
$9$			2.99011i			0.996704i
$10$		0			0
$11$	−0.777018			−0.234280			−0.117140	−	0.993115i	$-0.537373\pi$
$11$	−0.777018			−0.234280			−0.117140	+	0.993115i	$0.537373\pi$
$12$		0			0
$13$	−3.93876	+	3.93876i	−1.09241	+	1.09241i	−0.0971446	+	0.995270i	$0.530971\pi$
$13$	−3.93876	+	3.93876i	−1.09241	+	1.09241i	−0.995270	+	0.0971446i	$0.969029\pi$
$14$		0			0
$15$	−0.111564	+	0.192334i	−0.0288057	+	0.0496603i
$16$		0			0
$17$	0.982018	+	0.982018i	0.238174	+	0.238174i	0.816094	−	0.577920i	$-0.196135\pi$
$17$	0.982018	+	0.982018i	0.238174	+	0.238174i	−0.577920	+	0.816094i	$0.696135\pi$
$18$		0			0
$19$	1.14872			0.263534			0.131767	−	0.991281i	$-0.457935\pi$
$19$	1.14872			0.263534			0.131767	+	0.991281i	$0.457935\pi$
$20$		0			0
$21$	0.142213	−	0.221337i	0.0310333	−	0.0482996i
$22$		0			0
$23$	1.46167	+	1.46167i	0.304780	+	0.304780i	0.842881	−	0.538101i	$-0.180858\pi$
$23$	1.46167	+	1.46167i	0.304780	+	0.304780i	−0.538101	+	0.842881i	$0.680858\pi$
$24$		0			0
$25$	4.34022	−	2.48243i	0.868044	−	0.496487i
$26$		0			0
$27$	0.421181	+	0.421181i	0.0810563	+	0.0810563i
$28$		0			0
$29$			4.69033i			0.870973i	0.900195	+	0.435486i	$0.143424\pi$
$29$			4.69033i			0.870973i	−0.900195	+	0.435486i	$0.856576\pi$
$30$		0			0
$31$			6.45186i			1.15879i	0.815048	+	0.579394i	$0.196711\pi$
$31$			6.45186i			1.15879i	−0.815048	+	0.579394i	$0.803289\pi$
$32$		0			0
$33$	−0.0546342	+	0.0546342i	−0.00951060	+	0.00951060i
$34$		0			0
$35$	−5.26363	+	2.70078i	−0.889716	+	0.456515i
$36$		0			0
$37$	−1.30390	+	1.30390i	−0.214359	+	0.214359i	−0.806116	−	0.591757i	$-0.798435\pi$
$37$	−1.30390	+	1.30390i	−0.214359	+	0.214359i	0.591757	+	0.806116i	$0.298435\pi$
$38$		0			0
$39$			0.553890i			0.0886933i
$40$		0			0
$41$			9.81800i			1.53331i	0.642057	+	0.766657i	$0.278081\pi$
$41$			9.81800i			1.53331i	−0.642057	+	0.766657i	$0.721919\pi$
$42$		0			0
$43$	7.13800	+	7.13800i	1.08853	+	1.08853i	0.995680	+	0.0928552i	$0.0295994\pi$
$43$	7.13800	+	7.13800i	1.08853	+	1.08853i	0.0928552	+	0.995680i	$0.470401\pi$
$44$		0			0
$45$	−1.71740	−	6.46176i	−0.256015	−	0.963263i
$46$		0			0
$47$	−7.34914	−	7.34914i	−1.07198	−	1.07198i	−0.997200	−	0.0747825i	$-0.976174\pi$
$47$	−7.34914	−	7.34914i	−1.07198	−	1.07198i	−0.0747825	−	0.997200i	$-0.523826\pi$
$48$		0			0
$49$	6.36683	−	2.90920i	0.909548	−	0.415600i
$50$		0			0
$51$	0.138097			0.0193374
$52$		0			0
$53$	−2.08092	−	2.08092i	−0.285836	−	0.285836i	0.549595	−	0.835431i	$-0.314782\pi$
$53$	−2.08092	−	2.08092i	−0.285836	−	0.285836i	−0.835431	+	0.549595i	$0.814782\pi$
$54$		0			0
$55$	1.67917	−	0.446288i	0.226419	−	0.0601774i
$56$		0			0
$57$	0.0807696	−	0.0807696i	0.0106982	−	0.0106982i
$58$		0			0
$59$	−8.29508			−1.07993			−0.539964	−	0.841688i	$-0.681562\pi$
$59$	−8.29508			−1.07993			−0.539964	+	0.841688i	$0.681562\pi$
$60$		0			0
$61$		−	5.88837i		−	0.753929i	−0.926228	−	0.376965i	$-0.876968\pi$
$61$		−	5.88837i		−	0.753929i	0.926228	−	0.376965i	$-0.123032\pi$
$62$		0			0
$63$	1.68241	+	7.73013i	0.211963	+	0.973905i
$64$		0			0
$65$	6.24956	−	10.7741i	0.775163	−	1.33636i
$66$		0			0
$67$	6.30957	−	6.30957i	0.770837	−	0.770837i	−0.207416	−	0.978253i	$-0.566505\pi$
$67$	6.30957	−	6.30957i	0.770837	−	0.770837i	0.978253	+	0.207416i	$0.0665053\pi$
$68$		0			0
$69$	0.205548			0.0247451
$70$		0			0
$71$	−12.3373			−1.46417			−0.732084	−	0.681214i	$-0.761452\pi$
$71$	−12.3373			−1.46417			−0.732084	+	0.681214i	$0.761452\pi$
$72$		0			0
$73$	7.23861	−	7.23861i	0.847216	−	0.847216i	−0.142569	−	0.989785i	$-0.545536\pi$
$73$	7.23861	−	7.23861i	0.847216	−	0.847216i	0.989785	+	0.142569i	$0.0455364\pi$
$74$		0			0
$75$	0.130626	−	0.479719i	0.0150834	−	0.0553932i
$76$		0			0
$77$	−2.00877	+	0.437195i	−0.228921	+	0.0498229i
$78$		0			0
$79$		−	2.83831i		−	0.319335i	−0.987171	−	0.159668i	$-0.948958\pi$
$79$		−	2.83831i		−	0.319335i	0.987171	−	0.159668i	$-0.0510423\pi$
$80$		0			0
$81$	−8.91111			−0.990123
$82$		0			0
$83$	10.4188	−	10.4188i	1.14361	−	1.14361i	0.155823	−	0.987785i	$-0.450197\pi$
$83$	10.4188	−	10.4188i	1.14361	−	1.14361i	0.987785	−	0.155823i	$-0.0498029\pi$
$84$		0			0
$85$	−2.68621	−	1.55815i	−0.291361	−	0.169005i
$86$		0			0
$87$	0.329790	+	0.329790i	0.0353572	+	0.0353572i
$88$		0			0
$89$	3.41911			0.362425			0.181213	−	0.983444i	$-0.441998\pi$
$89$	3.41911			0.362425			0.181213	+	0.983444i	$0.441998\pi$
$90$		0			0
$91$	−7.96643	+	12.3988i	−0.835108	+	1.29974i
$92$		0			0
$93$	0.453647	+	0.453647i	0.0470411	+	0.0470411i
$94$		0			0
$95$	−2.48243	+	0.659779i	−0.254692	+	0.0676919i
$96$		0			0
$97$	8.50258	+	8.50258i	0.863306	+	0.863306i	0.991721	−	0.128414i	$-0.0409888\pi$
$97$	8.50258	+	8.50258i	0.863306	+	0.863306i	−0.128414	+	0.991721i	$0.540989\pi$
$98$		0			0
$99$		−	2.32337i		−	0.233507i
$100$		0			0
$101$		−	4.88126i		−	0.485703i	−0.970063	−	0.242852i	$-0.921917\pi$
$101$		−	4.88126i		−	0.485703i	0.970063	−	0.242852i	$-0.0780828\pi$
$102$		0			0
$103$	10.0443	−	10.0443i	0.989697	−	0.989697i	−0.0102503	−	0.999947i	$-0.503263\pi$
$103$	10.0443	−	10.0443i	0.989697	−	0.989697i	0.999947	+	0.0102503i	$0.00326282\pi$
$104$		0			0
$105$	−0.180201	+	0.559999i	−0.0175858	+	0.0546503i
$106$		0			0
$107$	−5.67065	+	5.67065i	−0.548203	+	0.548203i	−0.925921	−	0.377718i	$-0.876709\pi$
$107$	−5.67065	+	5.67065i	−0.548203	+	0.548203i	0.377718	+	0.925921i	$0.376709\pi$
$108$		0			0
$109$			11.9012i			1.13993i	0.821669	+	0.569965i	$0.193043\pi$
$109$			11.9012i			1.13993i	−0.821669	+	0.569965i	$0.806957\pi$
$110$		0			0
$111$			0.183361i			0.0174039i
$112$		0			0
$113$	−1.36519	−	1.36519i	−0.128427	−	0.128427i	0.639972	−	0.768398i	$-0.278946\pi$
$113$	−1.36519	−	1.36519i	−0.128427	−	0.128427i	−0.768398	+	0.639972i	$0.778946\pi$
$114$		0			0
$115$	−3.99827	−	2.31921i	−0.372840	−	0.216268i
$116$		0			0
$117$	−11.7773	−	11.7773i	−1.08881	−	1.08881i
$118$		0			0
$119$	3.09128	+	1.98620i	0.283377	+	0.182075i
$120$		0			0
$121$	−10.3962			−0.945113
$122$		0			0
$123$	0.690330	+	0.690330i	0.0622450	+	0.0622450i
$124$		0			0
$125$	−7.95360	+	7.85750i	−0.711391	+	0.702796i
$126$		0			0
$127$	9.49331	−	9.49331i	0.842395	−	0.842395i	−0.146775	−	0.989170i	$-0.546889\pi$
$127$	9.49331	−	9.49331i	0.842395	−	0.842395i	0.989170	+	0.146775i	$0.0468894\pi$
$128$		0			0
$129$	1.00378			0.0883783
$130$		0			0
$131$		−	19.4938i		−	1.70318i	−0.524206	−	0.851592i	$-0.675638\pi$
$131$		−	19.4938i		−	1.70318i	0.524206	−	0.851592i	$-0.324362\pi$
$132$		0			0
$133$	2.96971	−	0.646335i	0.257506	−	0.0560444i
$134$		0			0
$135$	−1.15210	−	0.668281i	−0.0991570	−	0.0575165i
$136$		0			0
$137$	5.77702	−	5.77702i	0.493564	−	0.493564i	−0.415863	−	0.909427i	$-0.636521\pi$
$137$	5.77702	−	5.77702i	0.493564	−	0.493564i	0.909427	+	0.415863i	$0.136521\pi$
$138$		0			0
$139$	15.2115			1.29023			0.645113	−	0.764087i	$-0.276810\pi$
$139$	15.2115			1.29023			0.645113	+	0.764087i	$0.276810\pi$
$140$		0			0
$141$	−1.03348			−0.0870344
$142$		0			0
$143$	3.06048	−	3.06048i	0.255931	−	0.255931i
$144$		0			0
$145$	−2.69394	−	10.1360i	−0.223719	−	0.841750i
$146$		0			0
$147$	0.243116	−	0.652223i	0.0200519	−	0.0537944i
$148$		0			0
$149$			16.5328i			1.35442i	0.735789	+	0.677211i	$0.236812\pi$
$149$			16.5328i			1.35442i	−0.735789	+	0.677211i	$0.763188\pi$
$150$		0			0
$151$	−12.4421			−1.01252			−0.506262	−	0.862380i	$-0.668973\pi$
$151$	−12.4421			−1.01252			−0.506262	+	0.862380i	$0.668973\pi$
$152$		0			0
$153$	−2.93634	+	2.93634i	−0.237389	+	0.237389i
$154$		0			0
$155$	−3.70569	−	13.9427i	−0.297648	−	1.11991i
$156$		0			0
$157$	−6.24218	−	6.24218i	−0.498180	−	0.498180i	0.412691	−	0.910871i	$-0.364589\pi$
$157$	−6.24218	−	6.24218i	−0.498180	−	0.498180i	−0.910871	+	0.412691i	$0.864589\pi$
$158$		0			0
$159$	−0.292630			−0.0232070
$160$		0			0
$161$	4.60118	+	2.95634i	0.362624	+	0.232992i
$162$		0			0
$163$	−9.47383	−	9.47383i	−0.742048	−	0.742048i	0.230924	−	0.972972i	$-0.425825\pi$
$163$	−9.47383	−	9.47383i	−0.742048	−	0.742048i	−0.972972	+	0.230924i	$0.925825\pi$
$164$		0			0
$165$	0.0866873	−	0.149447i	0.00674859	−	0.0116344i
$166$		0			0
$167$	0.725303	+	0.725303i	0.0561257	+	0.0561257i	0.734613	−	0.678487i	$-0.237364\pi$
$167$	0.725303	+	0.725303i	0.0561257	+	0.0561257i	−0.678487	+	0.734613i	$0.737364\pi$
$168$		0			0
$169$		−	18.0276i		−	1.38674i
$170$		0			0
$171$			3.43480i			0.262666i
$172$		0			0
$173$	3.12344	−	3.12344i	0.237471	−	0.237471i	−0.578331	−	0.815802i	$-0.696296\pi$
$173$	3.12344	−	3.12344i	0.237471	−	0.237471i	0.815802	+	0.578331i	$0.196296\pi$
$174$		0			0
$175$	9.82371	−	8.85972i	0.742603	−	0.669732i
$176$		0			0
$177$	−0.583250	+	0.583250i	−0.0438397	+	0.0438397i
$178$		0			0
$179$			9.18800i			0.686743i	0.939200	+	0.343372i	$0.111569\pi$
$179$			9.18800i			0.686743i	−0.939200	+	0.343372i	$0.888431\pi$
$180$		0			0
$181$			9.51164i			0.706995i	0.935435	+	0.353497i	$0.115008\pi$
$181$			9.51164i			0.706995i	−0.935435	+	0.353497i	$0.884992\pi$
$182$		0			0
$183$	−0.414028	−	0.414028i	−0.0306058	−	0.0306058i
$184$		0			0
$185$	2.06887	−	3.56669i	0.152107	−	0.262228i
$186$		0			0
$187$	−0.763045	−	0.763045i	−0.0557994	−	0.0557994i
$188$		0			0
$189$	1.32583	+	0.851870i	0.0964400	+	0.0619644i
$190$		0			0
$191$	21.2171			1.53522			0.767609	−	0.640918i	$-0.221446\pi$
$191$	21.2171			1.53522			0.767609	+	0.640918i	$0.221446\pi$
$192$		0			0
$193$	5.15371	+	5.15371i	0.370972	+	0.370972i	0.867831	−	0.496859i	$-0.165513\pi$
$193$	5.15371	+	5.15371i	0.370972	+	0.370972i	−0.496859	+	0.867831i	$0.665513\pi$
$194$		0			0
$195$	−0.318132	−	1.19698i	−0.0227819	−	0.0857175i
$196$		0			0
$197$	3.83269	−	3.83269i	0.273068	−	0.273068i	−0.557266	−	0.830334i	$-0.688150\pi$
$197$	3.83269	−	3.83269i	0.273068	−	0.273068i	0.830334	+	0.557266i	$0.188150\pi$
$198$		0			0
$199$	13.4648			0.954496			0.477248	−	0.878769i	$-0.341634\pi$
$199$	13.4648			0.954496			0.477248	+	0.878769i	$0.341634\pi$
$200$		0			0
$201$		−	0.887286i		−	0.0625844i
$202$		0			0
$203$	2.63905	+	12.1256i	0.185225	+	0.851049i
$204$		0			0
$205$	−5.63907	−	21.2171i	−0.393850	−	1.48187i
$206$		0			0
$207$	−4.37057	+	4.37057i	−0.303775	+	0.303775i
$208$		0			0
$209$	−0.892576			−0.0617408
$210$		0			0
$211$	−8.11050			−0.558350			−0.279175	−	0.960240i	$-0.590061\pi$
$211$	−8.11050			−0.558350			−0.279175	+	0.960240i	$0.590061\pi$
$212$		0			0
$213$	−0.867469	+	0.867469i	−0.0594380	+	0.0594380i
$214$		0			0
$215$	−19.5253	−	11.3257i	−1.33162	−	0.772410i
$216$		0			0
$217$	3.63018	+	16.6795i	0.246433	+	1.13228i
$218$		0			0
$219$		−	1.01793i		−	0.0687855i
$220$		0			0
$221$	−7.73586			−0.520370
$222$		0			0
$223$	−18.5407	+	18.5407i	−1.24157	+	1.24157i	−0.282226	+	0.959348i	$0.591073\pi$
$223$	−18.5407	+	18.5407i	−1.24157	+	1.24157i	−0.959348	+	0.282226i	$0.908927\pi$
$224$		0			0
$225$	7.42276	+	12.9777i	0.494850	+	0.865183i
$226$		0			0
$227$	−4.84230	−	4.84230i	−0.321395	−	0.321395i	0.527907	−	0.849302i	$-0.322977\pi$
$227$	−4.84230	−	4.84230i	−0.321395	−	0.321395i	−0.849302	+	0.527907i	$0.822977\pi$
$228$		0			0
$229$	−4.14288			−0.273769			−0.136884	−	0.990587i	$-0.543709\pi$
$229$	−4.14288			−0.273769			−0.136884	+	0.990587i	$0.543709\pi$
$230$		0			0
$231$	−0.110502	+	0.171982i	−0.00727048	+	0.0113156i
$232$		0			0
$233$	17.7734	+	17.7734i	1.16437	+	1.16437i	0.983508	+	0.180864i	$0.0578895\pi$
$233$	17.7734	+	17.7734i	1.16437	+	1.16437i	0.180864	+	0.983508i	$0.442110\pi$
$234$		0			0
$235$	20.1029	+	11.6608i	1.31137	+	0.760664i
$236$		0			0
$237$	−0.199570	−	0.199570i	−0.0129634	−	0.0129634i
$238$		0			0
$239$			24.8714i			1.60880i	0.594090	+	0.804399i	$0.297512\pi$
$239$			24.8714i			1.60880i	−0.594090	+	0.804399i	$0.702488\pi$
$240$		0			0
$241$			5.11385i			0.329412i	0.986343	+	0.164706i	$0.0526676\pi$
$241$			5.11385i			0.329412i	−0.986343	+	0.164706i	$0.947332\pi$
$242$		0			0
$243$	−1.89011	+	1.89011i	−0.121250	+	0.121250i
$244$		0			0
$245$	−12.0881	+	9.94376i	−0.772279	+	0.635283i
$246$		0			0
$247$	−4.52453	+	4.52453i	−0.287889	+	0.287889i
$248$		0			0
$249$		−	1.46514i		−	0.0928497i
$250$		0			0
$251$			21.4745i			1.35546i	0.735311	+	0.677729i	$0.237036\pi$
$251$			21.4745i			1.35546i	−0.735311	+	0.677729i	$0.762964\pi$
$252$		0			0
$253$	−1.13575	−	1.13575i	−0.0714037	−	0.0714037i
$254$		0			0
$255$	−0.298433	+	0.0793172i	−0.0186886	+	0.00496703i
$256$		0			0
$257$	−2.08456	−	2.08456i	−0.130031	−	0.130031i	0.639096	−	0.769127i	$-0.279309\pi$
$257$	−2.08456	−	2.08456i	−0.130031	−	0.130031i	−0.769127	+	0.639096i	$0.779309\pi$
$258$		0			0
$259$	−2.63723	+	4.10452i	−0.163869	+	0.255043i
$260$		0			0
$261$	−14.0246			−0.868102
$262$		0			0
$263$	−6.37087	−	6.37087i	−0.392845	−	0.392845i	0.482855	−	0.875700i	$-0.339600\pi$
$263$	−6.37087	−	6.37087i	−0.392845	−	0.392845i	−0.875700	+	0.482855i	$0.839600\pi$
$264$		0			0
$265$	5.69214	+	3.30176i	0.349666	+	0.202825i
$266$		0			0
$267$	0.240407	−	0.240407i	0.0147127	−	0.0147127i
$268$		0			0
$269$	9.57242			0.583641			0.291820	−	0.956473i	$-0.405739\pi$
$269$	9.57242			0.583641			0.291820	+	0.956473i	$0.405739\pi$
$270$		0			0
$271$			12.1076i			0.735486i	0.929927	+	0.367743i	$0.119869\pi$
$271$			12.1076i			0.735486i	−0.929927	+	0.367743i	$0.880131\pi$
$272$		0			0
$273$	0.311650	+	1.43193i	0.0188619	+	0.0866645i
$274$		0			0
$275$	−3.37243	+	1.92890i	−0.203365	+	0.116317i
$276$		0			0
$277$	16.2663	−	16.2663i	0.977345	−	0.977345i	−0.0224036	−	0.999749i	$-0.507132\pi$
$277$	16.2663	−	16.2663i	0.977345	−	0.977345i	0.999749	+	0.0224036i	$0.00713189\pi$
$278$		0			0
$279$	−19.2918			−1.15497
$280$		0			0
$281$	−0.910882			−0.0543387			−0.0271693	−	0.999631i	$-0.508649\pi$
$281$	−0.910882			−0.0543387			−0.0271693	+	0.999631i	$0.508649\pi$
$282$		0			0
$283$	−12.5625	+	12.5625i	−0.746766	+	0.746766i	−0.973870	−	0.227105i	$-0.927074\pi$
$283$	−12.5625	+	12.5625i	−0.746766	+	0.746766i	0.227105	+	0.973870i	$0.427074\pi$
$284$		0			0
$285$	−0.128156	+	0.220938i	−0.00759130	+	0.0130872i
$286$		0			0
$287$	5.52417	+	25.3818i	0.326081	+	1.49824i
$288$		0			0
$289$		−	15.0713i		−	0.886546i
$290$		0			0
$291$	1.19568			0.0700920
$292$		0			0
$293$	6.48178	−	6.48178i	0.378670	−	0.378670i	−0.491952	−	0.870622i	$-0.663717\pi$
$293$	6.48178	−	6.48178i	0.378670	−	0.378670i	0.870622	+	0.491952i	$0.163717\pi$
$294$		0			0
$295$	17.9260	−	4.76436i	1.04369	−	0.277392i
$296$		0			0
$297$	−0.327265	−	0.327265i	−0.0189899	−	0.0189899i
$298$		0			0
$299$	−11.5144			−0.665892
$300$		0			0
$301$	22.4696	+	14.4371i	1.29513	+	0.832142i
$302$		0			0
$303$	−0.343215	−	0.343215i	−0.0197172	−	0.0197172i
$304$		0			0
$305$	3.38205	+	12.7250i	0.193655	+	0.728633i
$306$		0			0
$307$	8.48970	+	8.48970i	0.484533	+	0.484533i	0.906576	−	0.422043i	$-0.138687\pi$
$307$	8.48970	+	8.48970i	0.484533	+	0.484533i	−0.422043	+	0.906576i	$0.638687\pi$
$308$		0			0
$309$		−	1.41249i		−	0.0803537i
$310$		0			0
$311$		−	25.9749i		−	1.47290i	−0.676490	−	0.736452i	$-0.736500\pi$
$311$		−	25.9749i		−	1.47290i	0.676490	−	0.736452i	$-0.263500\pi$
$312$		0			0
$313$	12.3142	−	12.3142i	0.696037	−	0.696037i	−0.267516	−	0.963553i	$-0.586203\pi$
$313$	12.3142	−	12.3142i	0.696037	−	0.696037i	0.963553	+	0.267516i	$0.0862029\pi$
$314$		0			0
$315$	−8.07563	−	15.7388i	−0.455010	−	0.886783i
$316$		0			0
$317$	14.4909	−	14.4909i	0.813888	−	0.813888i	−0.171327	−	0.985214i	$-0.554805\pi$
$317$	14.4909	−	14.4909i	0.813888	−	0.813888i	0.985214	+	0.171327i	$0.0548053\pi$
$318$		0			0
$319$		−	3.64447i		−	0.204051i
$320$		0			0
$321$			0.797438i			0.0445086i
$322$		0			0
$323$	1.12806	+	1.12806i	0.0627671	+	0.0627671i
$324$		0			0
$325$	−7.31737	+	26.8728i	−0.405895	+	1.49063i
$326$		0			0
$327$	0.836807	+	0.836807i	0.0462755	+	0.0462755i
$328$		0			0
$329$	−23.1343	−	14.8642i	−1.27543	−	0.819489i
$330$		0			0
$331$	27.4165			1.50695			0.753474	−	0.657477i	$-0.228376\pi$
$331$	27.4165			1.50695			0.753474	+	0.657477i	$0.228376\pi$
$332$		0			0
$333$	−3.89880	−	3.89880i	−0.213653	−	0.213653i
$334$		0			0
$335$	−10.0113	+	17.2592i	−0.546976	+	0.942972i
$336$		0			0
$337$	−11.1698	+	11.1698i	−0.608460	+	0.608460i	−0.942543	−	0.334084i	$-0.891573\pi$
$337$	−11.1698	+	11.1698i	−0.608460	+	0.608460i	0.334084	+	0.942543i	$0.391573\pi$
$338$		0			0
$339$	−0.191981			−0.0104270
$340$		0			0
$341$		−	5.01321i		−	0.271480i
$342$		0			0
$343$	14.8229	−	11.1033i	0.800359	−	0.599521i
$344$		0			0
$345$	−0.444199	+	0.118059i	−0.0239149	+	0.00635607i
$346$		0			0
$347$	11.4376	−	11.4376i	0.614004	−	0.614004i	−0.329983	−	0.943987i	$-0.607043\pi$
$347$	11.4376	−	11.4376i	0.614004	−	0.614004i	0.943987	+	0.329983i	$0.107043\pi$
$348$		0			0
$349$	17.1401			0.917487			0.458744	−	0.888569i	$-0.348300\pi$
$349$	17.1401			0.917487			0.458744	+	0.888569i	$0.348300\pi$
$350$		0			0
$351$	−3.31786			−0.177094
$352$		0			0
$353$	−11.1570	+	11.1570i	−0.593826	+	0.593826i	−0.938663	−	0.344837i	$-0.887934\pi$
$353$	−11.1570	+	11.1570i	−0.593826	+	0.593826i	0.344837	+	0.938663i	$0.387934\pi$
$354$		0			0
$355$	26.6614	−	7.08605i	1.41504	−	0.376088i
$356$		0			0
$357$	0.357012	−	0.0777011i	0.0188951	−	0.00411238i
$358$		0			0
$359$		−	20.9982i		−	1.10824i	−0.832437	−	0.554120i	$-0.813055\pi$
$359$		−	20.9982i		−	1.10824i	0.832437	−	0.554120i	$-0.186945\pi$
$360$		0			0
$361$	−17.6804			−0.930550
$362$		0			0
$363$	−0.730988	+	0.730988i	−0.0383669	+	0.0383669i
$364$		0			0
$365$	−11.4854	+	19.8005i	−0.601173	+	1.03641i
$366$		0			0
$367$	−2.32101	−	2.32101i	−0.121156	−	0.121156i	0.643929	−	0.765085i	$-0.277303\pi$
$367$	−2.32101	−	2.32101i	−0.121156	−	0.121156i	−0.765085	+	0.643929i	$0.777303\pi$
$368$		0			0
$369$	−29.3569			−1.52826
$370$		0			0
$371$	−6.55049	−	4.20880i	−0.340084	−	0.218510i
$372$		0			0
$373$	25.8674	+	25.8674i	1.33937	+	1.33937i	0.896674	+	0.442691i	$0.145976\pi$
$373$	25.8674	+	25.8674i	1.33937	+	1.33937i	0.442691	+	0.896674i	$0.354024\pi$
$374$		0			0
$375$	−0.00675707	+	1.11172i	−0.000348933	+	0.0574090i
$376$		0			0
$377$	−18.4741	−	18.4741i	−0.951463	−	0.951463i
$378$		0			0
$379$			13.1682i			0.676406i	0.941073	+	0.338203i	$0.109819\pi$
$379$			13.1682i			0.676406i	−0.941073	+	0.338203i	$0.890181\pi$
$380$		0			0
$381$		−	1.33500i		−	0.0683942i
$382$		0			0
$383$	−13.7289	+	13.7289i	−0.701514	+	0.701514i	−0.964736	−	0.263221i	$-0.915215\pi$
$383$	−13.7289	+	13.7289i	−0.701514	+	0.701514i	0.263221	+	0.964736i	$0.415215\pi$
$384$		0			0
$385$	4.08993	−	2.09855i	0.208442	−	0.106952i
$386$		0			0
$387$	−21.3434	+	21.3434i	−1.08495	+	1.08495i
$388$		0			0
$389$			13.4553i			0.682209i	0.940025	+	0.341104i	$0.110801\pi$
$389$			13.4553i			0.682209i	−0.940025	+	0.341104i	$0.889199\pi$
$390$		0			0
$391$			2.87078i			0.145181i
$392$		0			0
$393$	−1.37066	−	1.37066i	−0.0691408	−	0.0691408i
$394$		0			0
$395$	1.63021	+	6.13372i	0.0820250	+	0.308621i
$396$		0			0
$397$	9.78221	+	9.78221i	0.490955	+	0.490955i	0.908607	−	0.417652i	$-0.137147\pi$
$397$	9.78221	+	9.78221i	0.490955	+	0.490955i	−0.417652	+	0.908607i	$0.637147\pi$
$398$		0			0
$399$	0.163362	−	0.254254i	0.00817835	−	0.0127286i
$400$		0			0
$401$	−10.6960			−0.534134			−0.267067	−	0.963678i	$-0.586055\pi$
$401$	−10.6960			−0.534134			−0.267067	+	0.963678i	$0.586055\pi$
$402$		0			0
$403$	−25.4123	−	25.4123i	−1.26588	−	1.26588i
$404$		0			0
$405$	19.2573	−	5.11818i	0.956903	−	0.254325i
$406$		0			0
$407$	1.01315	−	1.01315i	0.0502201	−	0.0502201i
$408$		0			0
$409$	−30.2026			−1.49342			−0.746712	−	0.665148i	$-0.768369\pi$
$409$	−30.2026			−1.49342			−0.746712	+	0.665148i	$0.768369\pi$
$410$		0			0
$411$		−	0.812396i		−	0.0400725i
$412$		0			0
$413$	−21.4447	+	4.66729i	−1.05522	+	0.229662i
$414$		0			0
$415$	−16.5313	+	28.4995i	−0.811489	+	1.39899i
$416$		0			0
$417$	1.06957	−	1.06957i	0.0523768	−	0.0523768i
$418$		0			0
$419$	29.8749			1.45948			0.729742	−	0.683722i	$-0.239640\pi$
$419$	29.8749			1.45948			0.729742	+	0.683722i	$0.239640\pi$
$420$		0			0
$421$	35.1836			1.71474			0.857372	−	0.514697i	$-0.172096\pi$
$421$	35.1836			1.71474			0.857372	+	0.514697i	$0.172096\pi$
$422$		0			0
$423$	21.9748	−	21.9748i	1.06845	−	1.06845i
$424$		0			0
$425$	6.69997	+	1.82438i	0.324996	+	0.0884954i
$426$		0			0
$427$	−3.31314	−	15.2228i	−0.160334	−	0.736683i
$428$		0			0
$429$		−	0.430382i		−	0.0207790i
$430$		0			0
$431$	20.9552			1.00937			0.504687	−	0.863302i	$-0.331608\pi$
$431$	20.9552			1.00937			0.504687	+	0.863302i	$0.331608\pi$
$432$		0			0
$433$	12.5824	−	12.5824i	0.604670	−	0.604670i	−0.336878	−	0.941548i	$-0.609371\pi$
$433$	12.5824	−	12.5824i	0.604670	−	0.604670i	0.941548	+	0.336878i	$0.109371\pi$
$434$		0			0
$435$	−0.902109	−	0.523272i	−0.0432528	−	0.0250890i
$436$		0			0
$437$	1.67905	+	1.67905i	0.0803200	+	0.0803200i
$438$		0			0
$439$	7.23208			0.345168			0.172584	−	0.984995i	$-0.444788\pi$
$439$	7.23208			0.345168			0.172584	+	0.984995i	$0.444788\pi$
$440$		0			0
$441$	8.69882	+	19.0375i	0.414230	+	0.906550i
$442$		0			0
$443$	−3.46509	−	3.46509i	−0.164632	−	0.164632i	0.619983	−	0.784615i	$-0.287139\pi$
$443$	−3.46509	−	3.46509i	−0.164632	−	0.164632i	−0.784615	+	0.619983i	$0.787139\pi$
$444$		0			0
$445$	−7.38885	+	1.96380i	−0.350265	+	0.0930931i
$446$		0			0
$447$	1.16247	+	1.16247i	0.0549829	+	0.0549829i
$448$		0			0
$449$			6.08724i			0.287274i	0.989630	+	0.143637i	$0.0458798\pi$
$449$			6.08724i			0.287274i	−0.989630	+	0.143637i	$0.954120\pi$
$450$		0			0
$451$		−	7.62876i		−	0.359224i
$452$		0			0
$453$	−0.874838	+	0.874838i	−0.0411035	+	0.0411035i
$454$		0			0
$455$	10.0944	−	31.3699i	0.473235	−	1.47064i
$456$		0			0
$457$	−19.2746	+	19.2746i	−0.901630	+	0.901630i	−0.995577	−	0.0939472i	$-0.970052\pi$
$457$	−19.2746	+	19.2746i	−0.901630	+	0.901630i	0.0939472	+	0.995577i	$0.470052\pi$
$458$		0			0
$459$			0.827214i			0.0386111i
$460$		0			0
$461$		−	30.3964i		−	1.41570i	−0.706363	−	0.707850i	$-0.749665\pi$
$461$		−	30.3964i		−	1.41570i	0.706363	−	0.707850i	$-0.250335\pi$
$462$		0			0
$463$	−12.0768	−	12.0768i	−0.561259	−	0.561259i	0.368406	−	0.929665i	$-0.379904\pi$
$463$	−12.0768	−	12.0768i	−0.561259	−	0.561259i	−0.929665	+	0.368406i	$0.879904\pi$
$464$		0			0
$465$	−1.24091	−	0.719795i	−0.0575458	−	0.0333797i
$466$		0			0
$467$	−4.89096	−	4.89096i	−0.226327	−	0.226327i	0.584830	−	0.811156i	$-0.301161\pi$
$467$	−4.89096	−	4.89096i	−0.226327	−	0.226327i	−0.811156	+	0.584830i	$0.801161\pi$
$468$		0			0
$469$	12.7616	−	19.8618i	0.589275	−	0.917134i
$470$		0			0
$471$	−0.877809			−0.0404473
$472$		0			0
$473$	−5.54635	−	5.54635i	−0.255022	−	0.255022i
$474$		0			0
$475$	4.98570	−	2.85162i	0.228760	−	0.130841i
$476$		0			0
$477$	6.22217	−	6.22217i	0.284894	−	0.284894i
$478$		0			0
$479$	22.8349			1.04335			0.521676	−	0.853144i	$-0.325307\pi$
$479$	22.8349			1.04335			0.521676	+	0.853144i	$0.325307\pi$
$480$		0			0
$481$		−	10.2715i		−	0.468339i
$482$		0			0
$483$	0.531390	−	0.115653i	0.0241791	−	0.00526241i
$484$		0			0
$485$	−23.2580	−	13.4909i	−1.05609	−	0.612591i
$486$		0			0
$487$	11.1182	−	11.1182i	0.503812	−	0.503812i	−0.408808	−	0.912620i	$-0.634056\pi$
$487$	11.1182	−	11.1182i	0.503812	−	0.503812i	0.912620	+	0.408808i	$0.134056\pi$
$488$		0			0
$489$	−1.33226			−0.0602470
$490$		0			0
$491$	−4.45336			−0.200977			−0.100489	−	0.994938i	$-0.532041\pi$
$491$	−4.45336			−0.200977			−0.100489	+	0.994938i	$0.532041\pi$
$492$		0			0
$493$	−4.60599	+	4.60599i	−0.207443	+	0.207443i
$494$		0			0
$495$	1.33445	+	5.02091i	0.0599791	+	0.225673i
$496$		0			0
$497$	−31.8948	+	6.94167i	−1.43068	+	0.311376i
$498$		0			0
$499$		−	27.6446i		−	1.23754i	−0.785572	−	0.618770i	$-0.787631\pi$
$499$		−	27.6446i		−	1.23754i	0.785572	−	0.618770i	$-0.212369\pi$
$500$		0			0
$501$	0.101996			0.00455685
$502$		0			0
$503$	−16.9763	+	16.9763i	−0.756936	+	0.756936i	−0.975764	−	0.218828i	$-0.929777\pi$
$503$	−16.9763	+	16.9763i	−0.756936	+	0.756936i	0.218828	+	0.975764i	$0.429777\pi$
$504$		0			0
$505$	2.80360	+	10.5486i	0.124759	+	0.469407i
$506$		0			0
$507$	−1.26757	−	1.26757i	−0.0562948	−	0.0562948i
$508$		0			0
$509$	32.3762			1.43505			0.717525	−	0.696533i	$-0.245275\pi$
$509$	32.3762			1.43505			0.717525	+	0.696533i	$0.245275\pi$
$510$		0			0
$511$	14.6406	−	22.7863i	0.647663	−	1.00801i
$512$		0			0
$513$	0.483819	+	0.483819i	0.0213611	+	0.0213611i
$514$		0			0
$515$	−15.9372	+	27.4753i	−0.702276	+	1.21071i
$516$		0			0
$517$	5.71041	+	5.71041i	0.251144	+	0.251144i
$518$		0			0
$519$		−	0.439236i		−	0.0192803i
$520$		0			0
$521$		−	4.38603i		−	0.192156i	−0.995374	−	0.0960778i	$-0.969370\pi$
$521$		−	4.38603i		−	0.192156i	0.995374	−	0.0960778i	$-0.0306297\pi$
$522$		0			0
$523$	4.73788	−	4.73788i	0.207173	−	0.207173i	−0.595892	−	0.803065i	$-0.703201\pi$
$523$	4.73788	−	4.73788i	0.207173	−	0.207173i	0.803065	+	0.595892i	$0.203201\pi$
$524$		0			0
$525$	0.0677810	−	1.31368i	0.00295820	−	0.0573338i
$526$		0			0
$527$	−6.33583	+	6.33583i	−0.275993	+	0.275993i
$528$		0			0
$529$		−	18.7270i		−	0.814218i
$530$		0			0
$531$		−	24.8032i		−	1.07637i
$532$		0			0
$533$	−38.6707	−	38.6707i	−1.67502	−	1.67502i
$534$		0			0
$535$	8.99753	−	15.5115i	0.388997	−	0.670622i
$536$		0			0
$537$	0.646033	+	0.646033i	0.0278784	+	0.0278784i
$538$		0			0
$539$	−4.94714	+	2.26050i	−0.213089	+	0.0973665i
$540$		0			0
$541$	7.48796			0.321933			0.160966	−	0.986960i	$-0.448539\pi$
$541$	7.48796			0.321933			0.160966	+	0.986960i	$0.448539\pi$
$542$		0			0
$543$	0.668790	+	0.668790i	0.0287005	+	0.0287005i
$544$		0			0
$545$	−6.83558	−	25.7191i	−0.292804	−	1.10168i
$546$		0			0
$547$	−1.12562	+	1.12562i	−0.0481278	+	0.0481278i	−0.730761	−	0.682633i	$-0.760835\pi$
$547$	−1.12562	+	1.12562i	−0.0481278	+	0.0481278i	0.682633	+	0.730761i	$0.260835\pi$
$548$		0			0
$549$	17.6069			0.751444
$550$		0			0
$551$			5.38788i			0.229531i
$552$		0			0
$553$	−1.59700	−	7.33770i	−0.0679113	−	0.312031i
$554$		0			0
$555$	−0.105315	−	0.396252i	−0.00447039	−	0.0168199i
$556$		0			0
$557$	20.9130	−	20.9130i	0.886113	−	0.886113i	−0.108034	−	0.994147i	$-0.534456\pi$
$557$	20.9130	−	20.9130i	0.886113	−	0.886113i	0.994147	+	0.108034i	$0.0344557\pi$
$558$		0			0
$559$	−56.2297			−2.37826
$560$		0			0
$561$	−0.107304			−0.00453036
$562$		0			0
$563$	−5.94306	+	5.94306i	−0.250470	+	0.250470i	−0.821163	−	0.570693i	$-0.806675\pi$
$563$	−5.94306	+	5.94306i	−0.250470	+	0.250470i	0.570693	+	0.821163i	$0.306675\pi$
$564$		0			0
$565$	3.73436	+	2.16613i	0.157106	+	0.0911299i
$566$		0			0
$567$	−23.0373	+	5.01390i	−0.967474	+	0.210564i
$568$		0			0
$569$			6.64150i			0.278426i	0.990262	+	0.139213i	$0.0444573\pi$
$569$			6.64150i			0.278426i	−0.990262	+	0.139213i	$0.955543\pi$
$570$		0			0
$571$	−33.4643			−1.40044			−0.700218	−	0.713929i	$-0.746914\pi$
$571$	−33.4643			−1.40044			−0.700218	+	0.713929i	$0.746914\pi$
$572$		0			0
$573$	1.49183	−	1.49183i	0.0623223	−	0.0623223i
$574$		0			0
$575$	9.97249	+	2.71548i	0.415882	+	0.113243i
$576$		0			0
$577$	7.86048	+	7.86048i	0.327236	+	0.327236i	0.851535	−	0.524299i	$-0.175672\pi$
$577$	7.86048	+	7.86048i	0.327236	+	0.327236i	−0.524299	+	0.851535i	$0.675672\pi$
$578$		0			0
$579$	0.724743			0.0301193
$580$		0			0
$581$	21.0727	−	32.7971i	0.874244	−	1.36065i
$582$		0			0
$583$	1.61691	+	1.61691i	0.0669655	+	0.0669655i
$584$		0			0
$585$	32.2157	+	18.6869i	1.33196	+	0.772608i
$586$		0			0
$587$	7.65881	+	7.65881i	0.316113	+	0.316113i	0.847272	−	0.531159i	$-0.178243\pi$
$587$	7.65881	+	7.65881i	0.316113	+	0.316113i	−0.531159	+	0.847272i	$0.678243\pi$
$588$		0			0
$589$			7.41137i			0.305380i
$590$		0			0
$591$		−	0.538974i		−	0.0221704i
$592$		0			0
$593$	−8.24682	+	8.24682i	−0.338656	+	0.338656i	−0.855861	−	0.517205i	$-0.826972\pi$
$593$	−8.24682	+	8.24682i	−0.338656	+	0.338656i	0.517205	+	0.855861i	$0.326972\pi$
$594$		0			0
$595$	−7.82119	−	2.51676i	−0.320637	−	0.103177i
$596$		0			0
$597$	0.946748	−	0.946748i	0.0387478	−	0.0387478i
$598$		0			0
$599$			1.72554i			0.0705038i	0.999378	+	0.0352519i	$0.0112233\pi$
$599$			1.72554i			0.0705038i	−0.999378	+	0.0352519i	$0.988777\pi$
$600$		0			0
$601$		−	39.3868i		−	1.60662i	−0.595561	−	0.803310i	$-0.703070\pi$
$601$		−	39.3868i		−	1.60662i	0.595561	−	0.803310i	$-0.296930\pi$
$602$		0			0
$603$	18.8663	+	18.8663i	0.768296	+	0.768296i
$604$		0			0
$605$	22.4667	−	5.97119i	0.913403	−	0.242763i
$606$		0			0
$607$	13.0555	+	13.0555i	0.529905	+	0.529905i	0.920544	−	0.390639i	$-0.127746\pi$
$607$	13.0555	+	13.0555i	0.529905	+	0.529905i	−0.390639	+	0.920544i	$0.627746\pi$
$608$		0			0
$609$	1.03814	+	0.667024i	0.0420676	+	0.0270292i
$610$		0			0
$611$	57.8930			2.34210
$612$		0			0
$613$	−19.5565	−	19.5565i	−0.789878	−	0.789878i	0.191596	−	0.981474i	$-0.438634\pi$
$613$	−19.5565	−	19.5565i	−0.789878	−	0.789878i	−0.981474	+	0.191596i	$0.938634\pi$
$614$		0			0
$615$	−1.88833	−	1.09534i	−0.0761449	−	0.0441682i
$616$		0			0
$617$	−4.82431	+	4.82431i	−0.194219	+	0.194219i	−0.797517	−	0.603297i	$-0.793853\pi$
$617$	−4.82431	+	4.82431i	−0.194219	+	0.194219i	0.603297	+	0.797517i	$0.293853\pi$
$618$		0			0
$619$	−35.5806			−1.43011			−0.715053	−	0.699070i	$-0.753598\pi$
$619$	−35.5806			−1.43011			−0.715053	+	0.699070i	$0.753598\pi$
$620$		0			0
$621$			1.23126i			0.0494087i
$622$		0			0
$623$	8.83919	−	1.92379i	0.354135	−	0.0770749i
$624$		0			0
$625$	12.6750	−	21.5486i	0.507002	−	0.861945i
$626$		0			0
$627$	−0.0627594	+	0.0627594i	−0.00250637	+	0.00250637i
$628$		0			0
$629$	−2.56090			−0.102110
$630$		0			0
$631$	−28.6285			−1.13968			−0.569841	−	0.821755i	$-0.692995\pi$
$631$	−28.6285			−1.13968			−0.569841	+	0.821755i	$0.692995\pi$
$632$		0			0
$633$	−0.570271	+	0.570271i	−0.0226663	+	0.0226663i
$634$		0			0
$635$	−15.0629	+	25.9680i	−0.597752	+	1.03051i
$636$		0			0
$637$	−13.6188	+	36.5360i	−0.539596	+	1.44761i
$638$		0			0
$639$		−	36.8899i		−	1.45934i
$640$		0			0
$641$	−20.9369			−0.826956			−0.413478	−	0.910514i	$-0.635686\pi$
$641$	−20.9369			−0.826956			−0.413478	+	0.910514i	$0.635686\pi$
$642$		0			0
$643$	13.5706	−	13.5706i	0.535174	−	0.535174i	−0.386934	−	0.922108i	$-0.626466\pi$
$643$	13.5706	−	13.5706i	0.535174	−	0.535174i	0.922108	+	0.386934i	$0.126466\pi$
$644$		0			0
$645$	−2.16922	+	0.576534i	−0.0854130	+	0.0227010i
$646$		0			0
$647$	12.1526	+	12.1526i	0.477768	+	0.477768i	0.904417	−	0.426649i	$-0.140306\pi$
$647$	12.1526	+	12.1526i	0.477768	+	0.477768i	−0.426649	+	0.904417i	$0.640306\pi$
$648$		0			0
$649$	6.44543			0.253005
$650$		0			0
$651$	1.42803	+	0.917535i	0.0559690	+	0.0359610i
$652$		0			0
$653$	−16.3014	−	16.3014i	−0.637921	−	0.637921i	0.312121	−	0.950042i	$-0.398961\pi$
$653$	−16.3014	−	16.3014i	−0.637921	−	0.637921i	−0.950042	+	0.312121i	$0.898961\pi$
$654$		0			0
$655$	11.1965	+	42.1270i	0.437482	+	1.64604i
$656$		0			0
$657$	21.6443	+	21.6443i	0.844423	+	0.844423i
$658$		0			0
$659$		−	24.5415i		−	0.956001i	−0.878360	−	0.478000i	$-0.841362\pi$
$659$		−	24.5415i		−	0.956001i	0.878360	−	0.478000i	$-0.158638\pi$
$660$		0			0
$661$			22.1516i			0.861596i	0.902448	+	0.430798i	$0.141768\pi$
$661$			22.1516i			0.861596i	−0.902448	+	0.430798i	$0.858232\pi$
$662$		0			0
$663$	−0.543929	+	0.543929i	−0.0211245	+	0.0211245i
$664$		0			0
$665$	−6.04644	+	3.10244i	−0.234471	+	0.120307i
$666$		0			0
$667$	−6.85573	+	6.85573i	−0.265455	+	0.265455i
$668$		0			0
$669$			2.60729i			0.100804i
$670$		0			0
$671$			4.57537i			0.176630i
$672$		0			0
$673$	−9.43387	−	9.43387i	−0.363649	−	0.363649i	0.501505	−	0.865154i	$-0.332780\pi$
$673$	−9.43387	−	9.43387i	−0.363649	−	0.363649i	−0.865154	+	0.501505i	$0.832780\pi$
$674$		0			0
$675$	2.87357	+	0.782465i	0.110604	+	0.0301171i
$676$		0			0
$677$	10.4956	+	10.4956i	0.403378	+	0.403378i	0.879422	−	0.476044i	$-0.157930\pi$
$677$	10.4956	+	10.4956i	0.403378	+	0.403378i	−0.476044	+	0.879422i	$0.657930\pi$
$678$		0			0
$679$	26.7652	+	17.1971i	1.02715	+	0.659964i
$680$		0			0
$681$	−0.680951			−0.0260941
$682$		0			0
$683$	−7.11456	−	7.11456i	−0.272231	−	0.272231i	0.557767	−	0.829998i	$-0.311658\pi$
$683$	−7.11456	−	7.11456i	−0.272231	−	0.272231i	−0.829998	+	0.557767i	$0.811658\pi$
$684$		0			0
$685$	−9.16630	+	15.8025i	−0.350226	+	0.603782i
$686$		0			0
$687$	−0.291297	+	0.291297i	−0.0111137	+	0.0111137i
$688$		0			0
$689$	16.3924			0.624502
$690$		0			0
$691$			6.29829i			0.239598i	0.992798	+	0.119799i	$0.0382251\pi$
$691$			6.29829i			0.239598i	−0.992798	+	0.119799i	$0.961775\pi$
$692$		0			0
$693$	−1.30726	−	6.00645i	−0.0496587	−	0.228166i
$694$		0			0
$695$	−32.8728	+	8.73690i	−1.24694	+	0.331410i
$696$		0			0
$697$	−9.64145	+	9.64145i	−0.365196	+	0.365196i
$698$		0			0
$699$	2.49939			0.0945356
$700$		0			0
$701$	30.1579			1.13905			0.569523	−	0.821975i	$-0.307128\pi$
$701$	30.1579			1.13905			0.569523	+	0.821975i	$0.307128\pi$
$702$		0			0
$703$	−1.49781	+	1.49781i	−0.0564911	+	0.0564911i
$704$		0			0
$705$	2.23339	−	0.593587i	0.0841142	−	0.0223558i
$706$		0			0
$707$	−2.74648	−	12.6192i	−0.103292	−	0.474593i
$708$		0			0
$709$			1.75232i			0.0658099i	0.999458	+	0.0329049i	$0.0104759\pi$
$709$			1.75232i			0.0658099i	−0.999458	+	0.0329049i	$0.989524\pi$
$710$		0			0
$711$	8.48688			0.318283
$712$		0			0
$713$	−9.43050	+	9.43050i	−0.353175	+	0.353175i
$714$		0			0
$715$	−4.85602	+	8.37166i	−0.181605	+	0.313082i
$716$		0			0
$717$	1.74878	+	1.74878i	0.0653093	+	0.0653093i
$718$		0			0
$719$	−22.1398			−0.825675			−0.412837	−	0.910805i	$-0.635462\pi$
$719$	−22.1398			−0.825675			−0.412837	+	0.910805i	$0.635462\pi$
$720$		0			0
$721$	20.3154	−	31.6184i	0.756585	−	1.17753i
$722$		0			0
$723$	0.359569	+	0.359569i	0.0133725	+	0.0133725i
$724$		0			0
$725$	11.6434	+	20.3571i	0.432426	+	0.756043i
$726$		0			0
$727$	−36.3804	−	36.3804i	−1.34927	−	1.34927i	−0.886450	−	0.462825i	$-0.846836\pi$
$727$	−36.3804	−	36.3804i	−1.34927	−	1.34927i	−0.462825	−	0.886450i	$-0.653164\pi$
$728$		0			0
$729$		−	26.4675i		−	0.980279i
$730$		0			0
$731$			14.0193i			0.518522i
$732$		0			0
$733$	−26.3741	+	26.3741i	−0.974149	+	0.974149i	−0.999674	−	0.0255249i	$-0.991874\pi$
$733$	−26.3741	+	26.3741i	−0.974149	+	0.974149i	0.0255249	+	0.999674i	$0.491874\pi$
$734$		0			0
$735$	−0.150773	+	1.54912i	−0.00556136	+	0.0571401i
$736$		0			0
$737$	−4.90265	+	4.90265i	−0.180591	+	0.180591i
$738$		0			0
$739$		−	6.48932i		−	0.238714i	−0.992851	−	0.119357i	$-0.961917\pi$
$739$		−	6.48932i		−	0.238714i	0.992851	−	0.119357i	$-0.0380832\pi$
$740$		0			0
$741$			0.636264i			0.0233737i
$742$		0			0
$743$	−7.68617	−	7.68617i	−0.281978	−	0.281978i	0.551919	−	0.833897i	$-0.313896\pi$
$743$	−7.68617	−	7.68617i	−0.281978	−	0.281978i	−0.833897	+	0.551919i	$0.813896\pi$
$744$		0			0
$745$	−9.49580	−	35.7282i	−0.347899	−	1.30898i
$746$		0			0
$747$	31.1533	+	31.1533i	1.13984	+	1.13984i
$748$		0			0
$749$	−11.4693	+	17.8506i	−0.419079	+	0.652246i
$750$		0			0
$751$	2.05149			0.0748599			0.0374300	−	0.999299i	$-0.488083\pi$
$751$	2.05149			0.0748599			0.0374300	+	0.999299i	$0.488083\pi$
$752$		0			0
$753$	1.50993	+	1.50993i	0.0550249	+	0.0550249i
$754$		0			0
$755$	26.8879	−	7.14625i	0.978552	−	0.260079i
$756$		0			0
$757$	−4.22246	+	4.22246i	−0.153468	+	0.153468i	−0.779665	−	0.626197i	$-0.784611\pi$
$757$	−4.22246	+	4.22246i	−0.153468	+	0.153468i	0.626197	+	0.779665i	$0.284611\pi$
$758$		0			0
$759$	−0.159715			−0.00579728
$760$		0			0
$761$			46.0616i			1.66973i	0.550453	+	0.834866i	$0.314455\pi$
$761$			46.0616i			1.66973i	−0.550453	+	0.834866i	$0.685545\pi$
$762$		0			0
$763$	6.69631	+	30.7674i	0.242423	+	1.11385i
$764$		0			0
$765$	4.65905	−	8.03208i	0.168448	−	0.290401i
$766$		0			0
$767$	32.6723	−	32.6723i	1.17973	−	1.17973i
$768$		0			0
$769$	−44.8809			−1.61845			−0.809223	−	0.587501i	$-0.800112\pi$
$769$	−44.8809			−1.61845			−0.809223	+	0.587501i	$0.800112\pi$
$770$		0			0
$771$	−0.293143			−0.0105573
$772$		0			0
$773$	−4.22724	+	4.22724i	−0.152043	+	0.152043i	−0.779030	−	0.626987i	$-0.784288\pi$
$773$	−4.22724	+	4.22724i	−0.152043	+	0.152043i	0.626987	+	0.779030i	$0.284288\pi$
$774$		0			0
$775$	16.0163	+	28.0025i	0.575323	+	1.00588i
$776$		0			0
$777$	0.103169	+	0.474031i	0.00370118	+	0.0170058i
$778$		0			0
$779$			11.2781i			0.404081i
$780$		0			0
$781$	9.58630			0.343025
$782$		0			0
$783$	−1.97548	+	1.97548i	−0.0705978	+	0.0705978i
$784$		0			0
$785$	17.0749	+	9.90436i	0.609428	+	0.353502i
$786$		0			0
$787$	−2.71942	−	2.71942i	−0.0969367	−	0.0969367i	0.656975	−	0.753912i	$-0.271836\pi$
$787$	−2.71942	−	2.71942i	−0.0969367	−	0.0969367i	−0.753912	+	0.656975i	$0.771836\pi$
$788$		0			0
$789$	−0.895906			−0.0318951
$790$		0			0
$791$	−4.29748	−	2.76121i	−0.152801	−	0.0981772i
$792$		0			0
$793$	23.1929	+	23.1929i	0.823603	+	0.823603i
$794$		0			0
$795$	0.632386	−	0.168075i	0.0224284	−	0.00596100i
$796$		0			0
$797$	−28.8991	−	28.8991i	−1.02366	−	1.02366i	−0.999713	−	0.0239445i	$-0.992377\pi$
$797$	−28.8991	−	28.8991i	−1.02366	−	1.02366i	−0.0239445	−	0.999713i	$-0.507623\pi$
$798$		0			0
$799$		−	14.4340i		−	0.510637i
$800$		0			0
$801$			10.2235i			0.361231i
$802$		0			0
$803$	−5.62453	+	5.62453i	−0.198485	+	0.198485i
$804$		0			0
$805$	−11.6414	−	3.74605i	−0.410304	−	0.132031i
$806$		0			0
$807$	0.673063	−	0.673063i	0.0236929	−	0.0236929i
$808$		0			0
$809$			32.7627i			1.15187i	0.817494	+	0.575937i	$0.195363\pi$
$809$			32.7627i			1.15187i	−0.817494	+	0.575937i	$0.804637\pi$
$810$		0			0
$811$		−	24.6348i		−	0.865045i	−0.901623	−	0.432523i	$-0.857624\pi$
$811$		−	24.6348i		−	0.865045i	0.901623	−	0.432523i	$-0.142376\pi$
$812$		0			0
$813$	0.851321	+	0.851321i	0.0298571	+	0.0298571i
$814$		0			0
$815$	25.9148	+	15.0320i	0.907755	+	0.526547i
$816$		0			0
$817$	8.19956	+	8.19956i	0.286866	+	0.286866i
$818$		0			0
$819$	−37.0737	−	23.8205i	−1.29546	−	0.832356i
$820$		0			0
$821$	36.5320			1.27498			0.637488	−	0.770460i	$-0.279974\pi$
$821$	36.5320			1.27498			0.637488	+	0.770460i	$0.279974\pi$
$822$		0			0
$823$	14.6526	+	14.6526i	0.510758	+	0.510758i	0.914759	−	0.404001i	$-0.132381\pi$
$823$	14.6526	+	14.6526i	0.510758	+	0.510758i	−0.404001	+	0.914759i	$0.632381\pi$
$824$		0			0
$825$	−0.101499	+	0.372751i	−0.00353373	+	0.0129775i
$826$		0			0
$827$	22.1880	−	22.1880i	0.771552	−	0.771552i	−0.206826	−	0.978378i	$-0.566313\pi$
$827$	22.1880	−	22.1880i	0.771552	−	0.771552i	0.978378	+	0.206826i	$0.0663134\pi$
$828$		0			0
$829$	−46.4490			−1.61324			−0.806620	−	0.591070i	$-0.798706\pi$
$829$	−46.4490			−1.61324			−0.806620	+	0.591070i	$0.798706\pi$
$830$		0			0
$831$		−	2.28745i		−	0.0793508i
$832$		0			0
$833$	9.10922	+	3.39546i	0.315616	+	0.117646i
$834$		0			0
$835$	−1.98400	−	1.15083i	−0.0686591	−	0.0398260i
$836$		0			0
$837$	−2.71740	+	2.71740i	−0.0939271	+	0.0939271i
$838$		0			0
$839$	20.5166			0.708312			0.354156	−	0.935186i	$-0.384768\pi$
$839$	20.5166			0.708312			0.354156	+	0.935186i	$0.384768\pi$
$840$		0			0
$841$	7.00080			0.241407
$842$		0			0
$843$	−0.0640466	+	0.0640466i	−0.00220588	+	0.00220588i
$844$		0			0
$845$	10.3543	+	38.9585i	0.356200	+	1.34021i
$846$		0			0
$847$	−26.8767	+	5.84952i	−0.923494	+	0.200992i
$848$		0			0
$849$			1.76661i			0.0606300i
$850$		0			0
$851$	−3.81174			−0.130665
$852$		0			0
$853$	−17.5496	+	17.5496i	−0.600887	+	0.600887i	−0.940548	−	0.339661i	$-0.889688\pi$
$853$	−17.5496	+	17.5496i	−0.600887	+	0.600887i	0.339661	+	0.940548i	$0.389688\pi$
$854$		0			0
$855$	−1.97281	−	7.42276i	−0.0674688	−	0.253853i
$856$		0			0
$857$	11.1708	+	11.1708i	0.381588	+	0.381588i	0.871674	−	0.490086i	$-0.163035\pi$
$857$	11.1708	+	11.1708i	0.381588	+	0.381588i	−0.490086	+	0.871674i	$0.663035\pi$
$858$		0			0
$859$	42.5442			1.45159			0.725795	−	0.687911i	$-0.241472\pi$
$859$	42.5442			1.45159			0.725795	+	0.687911i	$0.241472\pi$
$860$		0			0
$861$	2.17308	+	1.39624i	0.0740585	+	0.0475839i
$862$		0			0
$863$	6.66647	+	6.66647i	0.226929	+	0.226929i	0.811409	−	0.584479i	$-0.198701\pi$
$863$	6.66647	+	6.66647i	0.226929	+	0.226929i	−0.584479	+	0.811409i	$0.698701\pi$
$864$		0			0
$865$	−4.95592	+	8.54388i	−0.168506	+	0.290501i
$866$		0			0
$867$	−1.05970	−	1.05970i	−0.0359894	−	0.0359894i
$868$		0			0
$869$			2.20542i			0.0748138i
$870$		0			0
$871$			49.7038i			1.68415i
$872$		0			0
$873$	−25.4237	+	25.4237i	−0.860461	+	0.860461i
$874$		0			0
$875$	−16.1408	+	24.7886i	−0.545659	+	0.838007i
$876$		0			0
$877$	−24.1080	+	24.1080i	−0.814069	+	0.814069i	−0.985241	−	0.171172i	$-0.945245\pi$
$877$	−24.1080	+	24.1080i	−0.814069	+	0.814069i	0.171172	+	0.985241i	$0.445245\pi$
$878$		0			0
$879$		−	0.911503i		−	0.0307442i
$880$		0			0
$881$			41.2812i			1.39080i	0.718623	+	0.695399i	$0.244773\pi$
$881$			41.2812i			1.39080i	−0.718623	+	0.695399i	$0.755227\pi$
$882$		0			0
$883$	7.58783	+	7.58783i	0.255351	+	0.255351i	0.823160	−	0.567809i	$-0.192209\pi$
$883$	7.58783	+	7.58783i	0.255351	+	0.255351i	−0.567809	+	0.823160i	$0.692209\pi$
$884$		0			0
$885$	0.925433	−	1.59542i	0.0311081	−	0.0536296i
$886$		0			0
$887$	−21.2247	−	21.2247i	−0.712657	−	0.712657i	0.254433	−	0.967090i	$-0.418111\pi$
$887$	−21.2247	−	21.2247i	−0.712657	−	0.712657i	−0.967090	+	0.254433i	$0.918111\pi$
$888$		0			0
$889$	19.2009	−	29.8839i	0.643978	−	1.00227i
$890$		0			0
$891$	6.92409			0.231966
$892$		0			0
$893$	−8.44210	−	8.44210i	−0.282504	−	0.282504i
$894$		0			0
$895$	−5.27722	−	19.8557i	−0.176398	−	0.663702i
$896$		0			0
$897$	−0.809606	+	0.809606i	−0.0270319	+	0.0270319i
$898$		0			0
$899$	−30.2613			−1.00927
$900$		0			0
$901$		−	4.08699i		−	0.136157i
$902$		0			0
$903$	2.59501	−	0.564786i	0.0863567	−	0.0187949i
$904$		0			0
$905$	−5.46311	−	20.5551i	−0.181600	−	0.683274i
$906$		0			0
$907$	2.69307	−	2.69307i	0.0894219	−	0.0894219i	−0.660981	−	0.750403i	$-0.729860\pi$
$907$	2.69307	−	2.69307i	0.0894219	−	0.0894219i	0.750403	+	0.660981i	$0.229860\pi$
$908$		0			0
$909$	14.5955			0.484103
$910$		0			0
$911$	41.2220			1.36575			0.682874	−	0.730536i	$-0.260730\pi$
$911$	41.2220			1.36575			0.682874	+	0.730536i	$0.260730\pi$
$912$		0			0
$913$	−8.09556	+	8.09556i	−0.267924	+	0.267924i
$914$		0			0
$915$	1.13253	+	0.656931i	0.0374404	+	0.0217175i
$916$		0			0
$917$	−10.9683	−	50.3960i	−0.362206	−	1.66422i
$918$		0			0
$919$			4.87087i			0.160675i	0.996768	+	0.0803376i	$0.0255998\pi$
$919$			4.87087i			0.160675i	−0.996768	+	0.0803376i	$0.974400\pi$
$920$		0			0
$921$	1.19387			0.0393393
$922$		0			0
$923$	48.5936	−	48.5936i	1.59948	−	1.59948i
$924$		0			0
$925$	−2.42236	+	8.89605i	−0.0796469	+	0.292500i
$926$		0			0
$927$	30.0337	+	30.0337i	0.986435	+	0.986435i
$928$		0			0
$929$	21.6087			0.708957			0.354479	−	0.935064i	$-0.384658\pi$
$929$	21.6087			0.708957			0.354479	+	0.935064i	$0.384658\pi$
$930$		0			0
$931$	7.31371	−	3.34185i	0.239697	−	0.109525i
$932$		0			0
$933$	−1.82637	−	1.82637i	−0.0597926	−	0.0597926i
$934$		0			0
$935$	2.08724	+	1.21071i	0.0682599	+	0.0395945i
$936$		0			0
$937$	5.78051	+	5.78051i	0.188841	+	0.188841i	0.795195	−	0.606354i	$-0.207369\pi$
$937$	5.78051	+	5.78051i	0.188841	+	0.188841i	−0.606354	+	0.795195i	$0.707369\pi$
$938$		0			0
$939$		−	1.73168i		−	0.0565113i
$940$		0			0
$941$		−	35.5016i		−	1.15732i	−0.815569	−	0.578660i	$-0.803576\pi$
$941$		−	35.5016i		−	1.15732i	0.815569	−	0.578660i	$-0.196424\pi$
$942$		0			0
$943$	−14.3507	+	14.3507i	−0.467323	+	0.467323i
$944$		0			0
$945$	−3.35446	−	1.07942i	−0.109121	−	0.0351137i
$946$		0			0
$947$	−29.6185	+	29.6185i	−0.962472	+	0.962472i	−0.999321	−	0.0368489i	$-0.988268\pi$
$947$	−29.6185	+	29.6185i	−0.962472	+	0.962472i	0.0368489	+	0.999321i	$0.488268\pi$
$948$		0			0
$949$			57.0223i			1.85102i
$950$		0			0
$951$		−	2.03778i		−	0.0660797i
$952$		0			0
$953$	−2.58171	−	2.58171i	−0.0836298	−	0.0836298i	0.664054	−	0.747684i	$-0.268834\pi$
$953$	−2.58171	−	2.58171i	−0.0836298	−	0.0836298i	−0.747684	+	0.664054i	$0.768834\pi$
$954$		0			0
$955$	−45.8512	+	12.1863i	−1.48371	+	0.394338i
$956$		0			0
$957$	−0.256253	−	0.256253i	−0.00828347	−	0.00828347i
$958$		0			0
$959$	11.6844	−	18.1854i	0.377310	−	0.587237i
$960$		0			0
$961$	−10.6264			−0.342788
$962$		0			0
$963$	−16.9559	−	16.9559i	−0.546396	−	0.546396i
$964$		0			0
$965$	−14.0975	−	8.17731i	−0.453814	−	0.263237i
$966$		0			0
$967$	15.8202	−	15.8202i	0.508744	−	0.508744i	−0.405397	−	0.914141i	$-0.632867\pi$
$967$	15.8202	−	15.8202i	0.508744	−	0.508744i	0.914141	+	0.405397i	$0.132867\pi$
$968$		0			0
$969$	0.158634			0.00509607
$970$		0			0
$971$			26.5709i			0.852701i	0.904558	+	0.426351i	$0.140201\pi$
$971$			26.5709i			0.852701i	−0.904558	+	0.426351i	$0.859799\pi$
$972$		0			0
$973$	39.3254	−	8.55889i	1.26071	−	0.274385i
$974$		0			0
$975$	1.37499	+	2.40400i	0.0440351	+	0.0769897i
$976$		0			0
$977$	40.8575	−	40.8575i	1.30715	−	1.30715i	0.383683	−	0.923465i	$-0.374656\pi$
$977$	40.8575	−	40.8575i	1.30715	−	1.30715i	0.923465	−	0.383683i	$-0.125344\pi$
$978$		0			0
$979$	−2.65671			−0.0849089
$980$		0			0
$981$	−35.5860			−1.13617
$982$		0			0
$983$	−4.75434	+	4.75434i	−0.151640	+	0.151640i	−0.778850	−	0.627210i	$-0.784197\pi$
$983$	−4.75434	+	4.75434i	−0.151640	+	0.151640i	0.627210	+	0.778850i	$0.284197\pi$
$984$		0			0
$985$	−6.08127	+	10.4840i	−0.193765	+	0.334046i
$986$		0			0
$987$	−2.67177	+	0.581493i	−0.0850435	+	0.0185091i
$988$		0			0
$989$			20.8668i			0.663527i
$990$		0			0
$991$	−27.2402			−0.865312			−0.432656	−	0.901559i	$-0.642424\pi$
$991$	−27.2402			−0.865312			−0.432656	+	0.901559i	$0.642424\pi$
$992$		0			0
$993$	1.92773	−	1.92773i	0.0611747	−	0.0611747i
$994$		0			0
$995$	−29.0981	+	7.73365i	−0.922471	+	0.245173i
$996$		0			0
$997$	6.58513	+	6.58513i	0.208553	+	0.208553i	0.803652	−	0.595099i	$-0.202887\pi$
$997$	6.58513	+	6.58513i	0.208553	+	0.208553i	−0.595099	+	0.803652i	$0.702887\pi$
$998$		0			0
$999$	−1.09835			−0.0347504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bj.d.433.7		24
4.3	odd	2		280.2.x.a.153.6	yes	24
5.2	odd	4	inner	560.2.bj.d.97.6		24
7.6	odd	2	inner	560.2.bj.d.433.6		24
20.3	even	4		1400.2.x.b.657.6		24
20.7	even	4		280.2.x.a.97.7	yes	24
20.19	odd	2		1400.2.x.b.993.7		24
28.27	even	2		280.2.x.a.153.7	yes	24
35.27	even	4	inner	560.2.bj.d.97.7		24
140.27	odd	4		280.2.x.a.97.6	✓	24
140.83	odd	4		1400.2.x.b.657.7		24
140.139	even	2		1400.2.x.b.993.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.6	✓	24	140.27	odd	4
280.2.x.a.97.7	yes	24	20.7	even	4
280.2.x.a.153.6	yes	24	4.3	odd	2
280.2.x.a.153.7	yes	24	28.27	even	2
560.2.bj.d.97.6		24	5.2	odd	4	inner
560.2.bj.d.97.7		24	35.27	even	4	inner
560.2.bj.d.433.6		24	7.6	odd	2	inner
560.2.bj.d.433.7		24	1.1	even	1	trivial
1400.2.x.b.657.6		24	20.3	even	4
1400.2.x.b.657.7		24	140.83	odd	4
1400.2.x.b.993.6		24	140.139	even	2
1400.2.x.b.993.7		24	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bj (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0703127 - 0.0703127i) q^{3} +(-2.16104 + 0.574360i) q^{5} +(2.58523 - 0.562657i) q^{7} +2.99011i q^{9} -0.777018 q^{11} +(-3.93876 + 3.93876i) q^{13} +(-0.111564 + 0.192334i) q^{15} +(0.982018 + 0.982018i) q^{17} +1.14872 q^{19} +(0.142213 - 0.221337i) q^{21} +(1.46167 + 1.46167i) q^{23} +(4.34022 - 2.48243i) q^{25} +(0.421181 + 0.421181i) q^{27} +4.69033i q^{29} +6.45186i q^{31} +(-0.0546342 + 0.0546342i) q^{33} +(-5.26363 + 2.70078i) q^{35} +(-1.30390 + 1.30390i) q^{37} +0.553890i q^{39} +9.81800i q^{41} +(7.13800 + 7.13800i) q^{43} +(-1.71740 - 6.46176i) q^{45} +(-7.34914 - 7.34914i) q^{47} +(6.36683 - 2.90920i) q^{49} +0.138097 q^{51} +(-2.08092 - 2.08092i) q^{53} +(1.67917 - 0.446288i) q^{55} +(0.0807696 - 0.0807696i) q^{57} -8.29508 q^{59} -5.88837i q^{61} +(1.68241 + 7.73013i) q^{63} +(6.24956 - 10.7741i) q^{65} +(6.30957 - 6.30957i) q^{67} +0.205548 q^{69} -12.3373 q^{71} +(7.23861 - 7.23861i) q^{73} +(0.130626 - 0.479719i) q^{75} +(-2.00877 + 0.437195i) q^{77} -2.83831i q^{79} -8.91111 q^{81} +(10.4188 - 10.4188i) q^{83} +(-2.68621 - 1.55815i) q^{85} +(0.329790 + 0.329790i) q^{87} +3.41911 q^{89} +(-7.96643 + 12.3988i) q^{91} +(0.453647 + 0.453647i) q^{93} +(-2.48243 + 0.659779i) q^{95} +(8.50258 + 8.50258i) q^{97} -2.32337i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7} - 8 q^{11} + 8 q^{15} + 16 q^{21} + 32 q^{23} + 8 q^{25} - 12 q^{35} - 8 q^{37} - 16 q^{43} + 24 q^{51} - 16 q^{53} - 20 q^{63} - 48 q^{65} + 32 q^{67} + 32 q^{71} - 40 q^{77} - 72 q^{81}+ \cdots + 24 q^{95}+O(q^{100}) \) 24 * q - 4 * q^7 - 8 * q^11 + 8 * q^15 + 16 * q^21 + 32 * q^23 + 8 * q^25 - 12 * q^35 - 8 * q^37 - 16 * q^43 + 24 * q^51 - 16 * q^53 - 20 * q^63 - 48 * q^65 + 32 * q^67 + 32 * q^71 - 40 * q^77 - 72 * q^81 + 16 * q^85 + 64 * q^91 + 72 * q^93 + 24 * q^95

Introduction

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