LMFDB - Embedded newform 560.2.x.b.127.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(127,560)]

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([2, 0, 1, 0]))

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

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

chi := DirichletCharacter("560.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.x (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.11
Character	$\chi$	$=$	560.127
Dual form			560.2.x.b.463.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.77851 + 1.77851i) q^{3} +(-2.23308 + 0.115477i) q^{5} +(0.707107 - 0.707107i) q^{7} +3.32619i q^{9} +O(q^{10})$	\(q+(1.77851 + 1.77851i) q^{3} +(-2.23308 + 0.115477i) q^{5} +(0.707107 - 0.707107i) q^{7} +3.32619i q^{9} +3.79417i q^{11} +(-3.76091 + 3.76091i) q^{13} +(-4.17694 - 3.76618i) q^{15} +(4.22420 + 4.22420i) q^{17} -2.26616 q^{19} +2.51519 q^{21} +(0.265314 + 0.265314i) q^{23} +(4.97333 - 0.515739i) q^{25} +(-0.580128 + 0.580128i) q^{27} +1.40991i q^{29} +0.0693289i q^{31} +(-6.74797 + 6.74797i) q^{33} +(-1.49737 + 1.66068i) q^{35} +(2.58089 + 2.58089i) q^{37} -13.3776 q^{39} +4.82470 q^{41} +(-8.35042 - 8.35042i) q^{43} +(-0.384098 - 7.42766i) q^{45} +(6.39117 - 6.39117i) q^{47} -1.00000i q^{49} +15.0255i q^{51} +(5.32704 - 5.32704i) q^{53} +(-0.438139 - 8.47270i) q^{55} +(-4.03038 - 4.03038i) q^{57} -3.71731 q^{59} -12.2508 q^{61} +(2.35197 + 2.35197i) q^{63} +(7.96413 - 8.83273i) q^{65} +(8.67249 - 8.67249i) q^{67} +0.943726i q^{69} -3.80010i q^{71} +(-7.40559 + 7.40559i) q^{73} +(9.76236 + 7.92786i) q^{75} +(2.68288 + 2.68288i) q^{77} +14.0309 q^{79} +7.91504 q^{81} +(9.62491 + 9.62491i) q^{83} +(-9.92078 - 8.94519i) q^{85} +(-2.50754 + 2.50754i) q^{87} +14.3390i q^{89} +5.31873i q^{91} +(-0.123302 + 0.123302i) q^{93} +(5.06052 - 0.261689i) q^{95} +(-7.58508 - 7.58508i) q^{97} -12.6201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{13} + 8 q^{17} - 8 q^{21} + 32 q^{25} + 24 q^{33} - 16 q^{37} + 32 q^{41} - 24 q^{45} + 8 q^{53} + 40 q^{57} + 16 q^{61} - 16 q^{73} + 16 q^{77} - 104 q^{81} - 8 q^{85} - 8 q^{93} - 24 q^{97}+O(q^{100}) $ 24 * q - 8 * q^13 + 8 * q^17 - 8 * q^21 + 32 * q^25 + 24 * q^33 - 16 * q^37 + 32 * q^41 - 24 * q^45 + 8 * q^53 + 40 * q^57 + 16 * q^61 - 16 * q^73 + 16 * q^77 - 104 * q^81 - 8 * q^85 - 8 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.77851	+	1.77851i	1.02682	+	1.02682i	0.999630	+	0.0271924i	$0.00865666\pi$
$3$	1.77851	+	1.77851i	1.02682	+	1.02682i	0.0271924	+	0.999630i	$0.491343\pi$
$4$		0			0
$5$	−2.23308	+	0.115477i	−0.998666	+	0.0516428i
$5$	−2.23308	+	0.115477i	−0.998666	+	0.0516428i
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$			3.32619i			1.10873i
$10$		0			0
$11$			3.79417i			1.14399i	0.820259	+	0.571993i	$0.193829\pi$
$11$			3.79417i			1.14399i	−0.820259	+	0.571993i	$0.806171\pi$
$12$		0			0
$13$	−3.76091	+	3.76091i	−1.04309	+	1.04309i	−0.0440602	+	0.999029i	$0.514029\pi$
$13$	−3.76091	+	3.76091i	−1.04309	+	1.04309i	−0.999029	+	0.0440602i	$0.985971\pi$
$14$		0			0
$15$	−4.17694	−	3.76618i	−1.07848	−	0.972424i
$16$		0			0
$17$	4.22420	+	4.22420i	1.02452	+	1.02452i	0.999692	+	0.0248265i	$0.00790332\pi$
$17$	4.22420	+	4.22420i	1.02452	+	1.02452i	0.0248265	+	0.999692i	$0.492097\pi$
$18$		0			0
$19$	−2.26616			−0.519892			−0.259946	−	0.965623i	$-0.583705\pi$
$19$	−2.26616			−0.519892			−0.259946	+	0.965623i	$0.583705\pi$
$20$		0			0
$21$	2.51519			0.548860
$22$		0			0
$23$	0.265314	+	0.265314i	0.0553218	+	0.0553218i	0.734226	−	0.678905i	$-0.237545\pi$
$23$	0.265314	+	0.265314i	0.0553218	+	0.0553218i	−0.678905	+	0.734226i	$0.737545\pi$
$24$		0			0
$25$	4.97333	−	0.515739i	0.994666	−	0.103148i
$26$		0			0
$27$	−0.580128	+	0.580128i	−0.111646	+	0.111646i
$28$		0			0
$29$			1.40991i			0.261814i	0.991395	+	0.130907i	$0.0417889\pi$
$29$			1.40991i			0.261814i	−0.991395	+	0.130907i	$0.958211\pi$
$30$		0			0
$31$			0.0693289i			0.0124518i	0.999981	+	0.00622592i	$0.00198179\pi$
$31$			0.0693289i			0.0124518i	−0.999981	+	0.00622592i	$0.998018\pi$
$32$		0			0
$33$	−6.74797	+	6.74797i	−1.17467	+	1.17467i
$34$		0			0
$35$	−1.49737	+	1.66068i	−0.253102	+	0.280707i
$36$		0			0
$37$	2.58089	+	2.58089i	0.424296	+	0.424296i	0.886680	−	0.462384i	$-0.153006\pi$
$37$	2.58089	+	2.58089i	0.424296	+	0.424296i	−0.462384	+	0.886680i	$0.653006\pi$
$38$		0			0
$39$	−13.3776			−2.14213
$40$		0			0
$41$	4.82470			0.753492			0.376746	−	0.926317i	$-0.377043\pi$
$41$	4.82470			0.753492			0.376746	+	0.926317i	$0.377043\pi$
$42$		0			0
$43$	−8.35042	−	8.35042i	−1.27343	−	1.27343i	−0.944278	−	0.329150i	$-0.893238\pi$
$43$	−8.35042	−	8.35042i	−1.27343	−	1.27343i	−0.329150	−	0.944278i	$-0.606762\pi$
$44$		0			0
$45$	−0.384098	−	7.42766i	−0.0572579	−	1.10725i
$46$		0			0
$47$	6.39117	−	6.39117i	0.932248	−	0.932248i	−0.0655977	−	0.997846i	$-0.520895\pi$
$47$	6.39117	−	6.39117i	0.932248	−	0.932248i	0.997846	+	0.0655977i	$0.0208954\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$			15.0255i			2.10400i
$52$		0			0
$53$	5.32704	−	5.32704i	0.731725	−	0.731725i	−0.239236	−	0.970961i	$-0.576897\pi$
$53$	5.32704	−	5.32704i	0.731725	−	0.731725i	0.970961	+	0.239236i	$0.0768971\pi$
$54$		0			0
$55$	−0.438139	−	8.47270i	−0.0590787	−	1.14246i
$56$		0			0
$57$	−4.03038	−	4.03038i	−0.533837	−	0.533837i
$58$		0			0
$59$	−3.71731			−0.483953			−0.241977	−	0.970282i	$-0.577796\pi$
$59$	−3.71731			−0.483953			−0.241977	+	0.970282i	$0.577796\pi$
$60$		0			0
$61$	−12.2508			−1.56855			−0.784277	−	0.620411i	$-0.786966\pi$
$61$	−12.2508			−1.56855			−0.784277	+	0.620411i	$0.786966\pi$
$62$		0			0
$63$	2.35197	+	2.35197i	0.296320	+	0.296320i
$64$		0			0
$65$	7.96413	−	8.83273i	0.987829	−	1.09557i
$66$		0			0
$67$	8.67249	−	8.67249i	1.05951	−	1.05951i	0.0613995	−	0.998113i	$-0.480444\pi$
$67$	8.67249	−	8.67249i	1.05951	−	1.05951i	0.998113	−	0.0613995i	$-0.0195564\pi$
$68$		0			0
$69$			0.943726i			0.113611i
$70$		0			0
$71$		−	3.80010i		−	0.450989i	−0.974244	−	0.225494i	$-0.927600\pi$
$71$		−	3.80010i		−	0.450989i	0.974244	−	0.225494i	$-0.0723997\pi$
$72$		0			0
$73$	−7.40559	+	7.40559i	−0.866759	+	0.866759i	−0.992112	−	0.125353i	$-0.959994\pi$
$73$	−7.40559	+	7.40559i	−0.866759	+	0.866759i	0.125353	+	0.992112i	$0.459994\pi$
$74$		0			0
$75$	9.76236	+	7.92786i	1.12726	+	0.915431i
$76$		0			0
$77$	2.68288	+	2.68288i	0.305743	+	0.305743i
$78$		0			0
$79$	14.0309			1.57860			0.789298	−	0.614011i	$-0.210445\pi$
$79$	14.0309			1.57860			0.789298	+	0.614011i	$0.210445\pi$
$80$		0			0
$81$	7.91504			0.879449
$82$		0			0
$83$	9.62491	+	9.62491i	1.05647	+	1.05647i	0.998307	+	0.0581646i	$0.0185248\pi$
$83$	9.62491	+	9.62491i	1.05647	+	1.05647i	0.0581646	+	0.998307i	$0.481475\pi$
$84$		0			0
$85$	−9.92078	−	8.94519i	−1.07606	−	0.970242i
$86$		0			0
$87$	−2.50754	+	2.50754i	−0.268836	+	0.268836i
$88$		0			0
$89$			14.3390i			1.51993i	0.649962	+	0.759967i	$0.274785\pi$
$89$			14.3390i			1.51993i	−0.649962	+	0.759967i	$0.725215\pi$
$90$		0			0
$91$			5.31873i			0.557555i
$92$		0			0
$93$	−0.123302	+	0.123302i	−0.0127858	+	0.0127858i
$94$		0			0
$95$	5.06052	−	0.261689i	0.519199	−	0.0268487i
$96$		0			0
$97$	−7.58508	−	7.58508i	−0.770149	−	0.770149i	0.207984	−	0.978132i	$-0.433310\pi$
$97$	−7.58508	−	7.58508i	−0.770149	−	0.770149i	−0.978132	+	0.207984i	$0.933310\pi$
$98$		0			0
$99$	−12.6201			−1.26837
$100$		0			0
$101$	17.2224			1.71369			0.856844	−	0.515575i	$-0.172422\pi$
$101$	17.2224			1.71369			0.856844	+	0.515575i	$0.172422\pi$
$102$		0			0
$103$	−4.29289	−	4.29289i	−0.422991	−	0.422991i	0.463241	−	0.886232i	$-0.346686\pi$
$103$	−4.29289	−	4.29289i	−0.422991	−	0.422991i	−0.886232	+	0.463241i	$0.846686\pi$
$104$		0			0
$105$	−5.61663	+	0.290447i	−0.548127	+	0.0283447i
$106$		0			0
$107$	3.67887	−	3.67887i	0.355650	−	0.355650i	−0.506557	−	0.862207i	$-0.669082\pi$
$107$	3.67887	−	3.67887i	0.355650	−	0.355650i	0.862207	+	0.506557i	$0.169082\pi$
$108$		0			0
$109$			11.9090i			1.14067i	0.821411	+	0.570337i	$0.193187\pi$
$109$			11.9090i			1.14067i	−0.821411	+	0.570337i	$0.806813\pi$
$110$		0			0
$111$			9.18028i			0.871354i
$112$		0			0
$113$	7.31997	−	7.31997i	0.688604	−	0.688604i	−0.273319	−	0.961923i	$-0.588121\pi$
$113$	7.31997	−	7.31997i	0.688604	−	0.688604i	0.961923	+	0.273319i	$0.0881215\pi$
$114$		0			0
$115$	−0.623106	−	0.561831i	−0.0581049	−	0.0523910i
$116$		0			0
$117$	−12.5095	−	12.5095i	−1.15650	−	1.15650i
$118$		0			0
$119$	5.97392			0.547628
$120$		0			0
$121$	−3.39573			−0.308703
$122$		0			0
$123$	8.58077	+	8.58077i	0.773702	+	0.773702i
$124$		0			0
$125$	−11.0463	+	1.72599i	−0.988012	+	0.154378i
$126$		0			0
$127$	0.864802	−	0.864802i	0.0767388	−	0.0767388i	−0.667696	−	0.744434i	$-0.732719\pi$
$127$	0.864802	−	0.864802i	0.0767388	−	0.0767388i	0.744434	+	0.667696i	$0.232719\pi$
$128$		0			0
$129$		−	29.7026i		−	2.61517i
$130$		0			0
$131$		−	5.96786i		−	0.521414i	−0.965418	−	0.260707i	$-0.916044\pi$
$131$		−	5.96786i		−	0.521414i	0.965418	−	0.260707i	$-0.0839557\pi$
$132$		0			0
$133$	−1.60242	+	1.60242i	−0.138947	+	0.138947i
$134$		0			0
$135$	1.22848	−	1.36247i	0.105731	−	0.117262i
$136$		0			0
$137$	−12.2699	−	12.2699i	−1.04829	−	1.04829i	−0.998774	−	0.0495125i	$-0.984233\pi$
$137$	−12.2699	−	12.2699i	−1.04829	−	1.04829i	−0.0495125	−	0.998774i	$-0.515767\pi$
$138$		0			0
$139$	17.7077			1.50195			0.750975	−	0.660331i	$-0.229584\pi$
$139$	17.7077			1.50195			0.750975	+	0.660331i	$0.229584\pi$
$140$		0			0
$141$	22.7335			1.91451
$142$		0			0
$143$	−14.2695	−	14.2695i	−1.19328	−	1.19328i
$144$		0			0
$145$	−0.162812	−	3.14845i	−0.0135208	−	0.261464i
$146$		0			0
$147$	1.77851	−	1.77851i	0.146689	−	0.146689i
$148$		0			0
$149$			9.87712i			0.809165i	0.914501	+	0.404583i	$0.132583\pi$
$149$			9.87712i			0.809165i	−0.914501	+	0.404583i	$0.867417\pi$
$150$		0			0
$151$		−	5.60156i		−	0.455848i	−0.973679	−	0.227924i	$-0.926806\pi$
$151$		−	5.60156i		−	0.455848i	0.973679	−	0.227924i	$-0.0731938\pi$
$152$		0			0
$153$	−14.0505	+	14.0505i	−1.13591	+	1.13591i
$154$		0			0
$155$	−0.00800589	−	0.154817i	−0.000643048	−	0.0124352i
$156$		0			0
$157$	3.85712	+	3.85712i	0.307832	+	0.307832i	0.844068	−	0.536236i	$-0.180154\pi$
$157$	3.85712	+	3.85712i	0.307832	+	0.307832i	−0.536236	+	0.844068i	$0.680154\pi$
$158$		0			0
$159$	18.9484			1.50270
$160$		0			0
$161$	0.375211			0.0295707
$162$		0			0
$163$	−4.10185	−	4.10185i	−0.321282	−	0.321282i	0.527977	−	0.849259i	$-0.322951\pi$
$163$	−4.10185	−	4.10185i	−0.321282	−	0.321282i	−0.849259	+	0.527977i	$0.822951\pi$
$164$		0			0
$165$	14.2895	−	15.8480i	1.11244	−	1.23377i
$166$		0			0
$167$	−14.2817	+	14.2817i	−1.10515	+	1.10515i	−0.111370	+	0.993779i	$0.535524\pi$
$167$	−14.2817	+	14.2817i	−1.10515	+	1.10515i	−0.993779	+	0.111370i	$0.964476\pi$
$168$		0			0
$169$		−	15.2889i		−	1.17607i
$170$		0			0
$171$		−	7.53767i		−	0.576420i
$172$		0			0
$173$	8.32513	−	8.32513i	0.632948	−	0.632948i	−0.315859	−	0.948806i	$-0.602293\pi$
$173$	8.32513	−	8.32513i	0.632948	−	0.632948i	0.948806	+	0.315859i	$0.102293\pi$
$174$		0			0
$175$	3.15199	−	3.88136i	0.238268	−	0.293403i
$176$		0			0
$177$	−6.61128	−	6.61128i	−0.496934	−	0.496934i
$178$		0			0
$179$	−14.3035			−1.06909			−0.534547	−	0.845139i	$-0.679518\pi$
$179$	−14.3035			−1.06909			−0.534547	+	0.845139i	$0.679518\pi$
$180$		0			0
$181$	12.5727			0.934524			0.467262	−	0.884119i	$-0.345240\pi$
$181$	12.5727			0.934524			0.467262	+	0.884119i	$0.345240\pi$
$182$		0			0
$183$	−21.7882	−	21.7882i	−1.61063	−	1.61063i
$184$		0			0
$185$	−6.06138	−	5.46532i	−0.445642	−	0.401818i
$186$		0			0
$187$	−16.0273	+	16.0273i	−1.17203	+	1.17203i
$188$		0			0
$189$			0.820424i			0.0596771i
$190$		0			0
$191$		−	8.62462i		−	0.624055i	−0.950073	−	0.312028i	$-0.898992\pi$
$191$		−	8.62462i		−	0.624055i	0.950073	−	0.312028i	$-0.101008\pi$
$192$		0			0
$193$	−4.57601	+	4.57601i	−0.329389	+	0.329389i	−0.852354	−	0.522965i	$-0.824826\pi$
$193$	−4.57601	+	4.57601i	−0.329389	+	0.329389i	0.522965	+	0.852354i	$0.324826\pi$
$194$		0			0
$195$	29.8734	−	1.54481i	2.13928	−	0.110626i
$196$		0			0
$197$	0.0500512	+	0.0500512i	0.00356600	+	0.00356600i	0.708888	−	0.705322i	$-0.249197\pi$
$197$	0.0500512	+	0.0500512i	0.00356600	+	0.00356600i	−0.705322	+	0.708888i	$0.749197\pi$
$198$		0			0
$199$	−14.7487			−1.04551			−0.522754	−	0.852484i	$-0.675095\pi$
$199$	−14.7487			−1.04551			−0.522754	+	0.852484i	$0.675095\pi$
$200$		0			0
$201$	30.8482			2.17586
$202$		0			0
$203$	0.996957	+	0.996957i	0.0699727	+	0.0699727i
$204$		0			0
$205$	−10.7740	+	0.557141i	−0.752486	+	0.0389124i
$206$		0			0
$207$	−0.882484	+	0.882484i	−0.0613369	+	0.0613369i
$208$		0			0
$209$		−	8.59819i		−	0.594749i
$210$		0			0
$211$		−	6.41376i		−	0.441541i	−0.975326	−	0.220771i	$-0.929143\pi$
$211$		−	6.41376i		−	0.441541i	0.975326	−	0.220771i	$-0.0708572\pi$
$212$		0			0
$213$	6.75851	−	6.75851i	0.463085	−	0.463085i
$214$		0			0
$215$	19.6115	+	17.6829i	1.33749	+	1.20596i
$216$		0			0
$217$	0.0490230	+	0.0490230i	0.00332789	+	0.00332789i
$218$		0			0
$219$	−26.3418			−1.78002
$220$		0			0
$221$	−31.7737			−2.13733
$222$		0			0
$223$	−7.44183	−	7.44183i	−0.498342	−	0.498342i	0.412580	−	0.910921i	$-0.364628\pi$
$223$	−7.44183	−	7.44183i	−0.498342	−	0.498342i	−0.910921	+	0.412580i	$0.864628\pi$
$224$		0			0
$225$	1.71545	+	16.5422i	0.114363	+	1.10282i
$226$		0			0
$227$	0.301817	−	0.301817i	0.0200323	−	0.0200323i	−0.697020	−	0.717052i	$-0.745491\pi$
$227$	0.301817	−	0.301817i	0.0200323	−	0.0200323i	0.717052	+	0.697020i	$0.245491\pi$
$228$		0			0
$229$			23.4954i			1.55262i	0.630351	+	0.776310i	$0.282911\pi$
$229$			23.4954i			1.55262i	−0.630351	+	0.776310i	$0.717089\pi$
$230$		0			0
$231$			9.54306i			0.627888i
$232$		0			0
$233$	−9.34225	+	9.34225i	−0.612031	+	0.612031i	−0.943475	−	0.331444i	$-0.892464\pi$
$233$	−9.34225	+	9.34225i	−0.612031	+	0.612031i	0.331444	+	0.943475i	$0.392464\pi$
$234$		0			0
$235$	−13.5340	+	15.0101i	−0.882861	+	0.979148i
$236$		0			0
$237$	24.9540	+	24.9540i	1.62094	+	1.62094i
$238$		0			0
$239$	13.9658			0.903371			0.451686	−	0.892177i	$-0.350823\pi$
$239$	13.9658			0.903371			0.451686	+	0.892177i	$0.350823\pi$
$240$		0			0
$241$	−6.55433			−0.422201			−0.211101	−	0.977464i	$-0.567705\pi$
$241$	−6.55433			−0.422201			−0.211101	+	0.977464i	$0.567705\pi$
$242$		0			0
$243$	15.8173	+	15.8173i	1.01468	+	1.01468i
$244$		0			0
$245$	0.115477	+	2.23308i	0.00737755	+	0.142667i
$246$		0			0
$247$	8.52282	−	8.52282i	0.542294	−	0.542294i
$248$		0			0
$249$			34.2360i			2.16962i
$250$		0			0
$251$			7.91448i			0.499558i	0.968303	+	0.249779i	$0.0803579\pi$
$251$			7.91448i			0.499558i	−0.968303	+	0.249779i	$0.919642\pi$
$252$		0			0
$253$	−1.00665	+	1.00665i	−0.0632873	+	0.0632873i
$254$		0			0
$255$	−1.73510	−	33.5533i	−0.108656	−	2.10119i
$256$		0			0
$257$	2.64378	+	2.64378i	0.164915	+	0.164915i	0.784740	−	0.619825i	$-0.212797\pi$
$257$	2.64378	+	2.64378i	0.164915	+	0.164915i	−0.619825	+	0.784740i	$0.712797\pi$
$258$		0			0
$259$	3.64993			0.226796
$260$		0			0
$261$	−4.68963			−0.290281
$262$		0			0
$263$	−4.93627	−	4.93627i	−0.304383	−	0.304383i	0.538343	−	0.842726i	$-0.319051\pi$
$263$	−4.93627	−	4.93627i	−0.304383	−	0.304383i	−0.842726	+	0.538343i	$0.819051\pi$
$264$		0			0
$265$	−11.2806	+	12.5109i	−0.692960	+	0.768537i
$266$		0			0
$267$	−25.5021	+	25.5021i	−1.56070	+	1.56070i
$268$		0			0
$269$			26.0276i			1.58693i	0.608615	+	0.793466i	$0.291725\pi$
$269$			26.0276i			1.58693i	−0.608615	+	0.793466i	$0.708275\pi$
$270$		0			0
$271$			10.4328i			0.633746i	0.948468	+	0.316873i	$0.102633\pi$
$271$			10.4328i			0.633746i	−0.948468	+	0.316873i	$0.897367\pi$
$272$		0			0
$273$	−9.45941	+	9.45941i	−0.572510	+	0.572510i
$274$		0			0
$275$	1.95680	+	18.8697i	0.118000	+	1.13788i
$276$		0			0
$277$	−20.5322	−	20.5322i	−1.23366	−	1.23366i	−0.962547	−	0.271115i	$-0.912608\pi$
$277$	−20.5322	−	20.5322i	−1.23366	−	1.23366i	−0.271115	−	0.962547i	$-0.587392\pi$
$278$		0			0
$279$	−0.230601			−0.0138057
$280$		0			0
$281$	13.3739			0.797818			0.398909	−	0.916990i	$-0.369389\pi$
$281$	13.3739			0.797818			0.398909	+	0.916990i	$0.369389\pi$
$282$		0			0
$283$	−10.5130	−	10.5130i	−0.624935	−	0.624935i	0.321855	−	0.946789i	$-0.395694\pi$
$283$	−10.5130	−	10.5130i	−0.624935	−	0.624935i	−0.946789	+	0.321855i	$0.895694\pi$
$284$		0			0
$285$	9.46560	+	8.53477i	0.560694	+	0.505556i
$286$		0			0
$287$	3.41158	−	3.41158i	0.201379	−	0.201379i
$288$		0			0
$289$			18.6877i			1.09928i
$290$		0			0
$291$		−	26.9803i		−	1.58161i
$292$		0			0
$293$	9.93750	−	9.93750i	0.580555	−	0.580555i	−0.354501	−	0.935056i	$-0.615349\pi$
$293$	9.93750	−	9.93750i	0.580555	−	0.580555i	0.935056	+	0.354501i	$0.115349\pi$
$294$		0			0
$295$	8.30107	−	0.429264i	0.483307	−	0.0249927i
$296$		0			0
$297$	−2.20110	−	2.20110i	−0.127721	−	0.127721i
$298$		0			0
$299$	−1.99564			−0.115411
$300$		0			0
$301$	−11.8093			−0.680676
$302$		0			0
$303$	30.6301	+	30.6301i	1.75965	+	1.75965i
$304$		0			0
$305$	27.3571	−	1.41468i	1.56646	−	0.0810046i
$306$		0			0
$307$	15.5905	−	15.5905i	0.889798	−	0.889798i	−0.104705	−	0.994503i	$-0.533390\pi$
$307$	15.5905	−	15.5905i	0.889798	−	0.889798i	0.994503	+	0.104705i	$0.0333898\pi$
$308$		0			0
$309$		−	15.2699i		−	0.868673i
$310$		0			0
$311$			33.3463i			1.89089i	0.325777	+	0.945446i	$0.394374\pi$
$311$			33.3463i			1.89089i	−0.325777	+	0.945446i	$0.605626\pi$
$312$		0			0
$313$	14.8374	−	14.8374i	0.838661	−	0.838661i	−0.150022	−	0.988683i	$-0.547934\pi$
$313$	14.8374	−	14.8374i	0.838661	−	0.838661i	0.988683	+	0.150022i	$0.0479345\pi$
$314$		0			0
$315$	−5.52374	−	4.98055i	−0.311228	−	0.280622i
$316$		0			0
$317$	0.337577	+	0.337577i	0.0189602	+	0.0189602i	0.716523	−	0.697563i	$-0.245732\pi$
$317$	0.337577	+	0.337577i	0.0189602	+	0.0189602i	−0.697563	+	0.716523i	$0.745732\pi$
$318$		0			0
$319$	−5.34944			−0.299511
$320$		0			0
$321$	13.0858			0.730378
$322$		0			0
$323$	−9.57270	−	9.57270i	−0.532639	−	0.532639i
$324$		0			0
$325$	−16.7646	+	20.6439i	−0.929933	+	1.14512i
$326$		0			0
$327$	−21.1802	+	21.1802i	−1.17127	+	1.17127i
$328$		0			0
$329$		−	9.03848i		−	0.498308i
$330$		0			0
$331$		−	9.56951i		−	0.525988i	−0.964798	−	0.262994i	$-0.915290\pi$
$331$		−	9.56951i		−	0.525988i	0.964798	−	0.262994i	$-0.0847099\pi$
$332$		0			0
$333$	−8.58453	+	8.58453i	−0.470430	+	0.470430i
$334$		0			0
$335$	−18.3649	+	20.3679i	−1.00338	+	1.11282i
$336$		0			0
$337$	7.20161	+	7.20161i	0.392297	+	0.392297i	0.875505	−	0.483209i	$-0.160529\pi$
$337$	7.20161	+	7.20161i	0.392297	+	0.392297i	−0.483209	+	0.875505i	$0.660529\pi$
$338$		0			0
$339$	26.0372			1.41415
$340$		0			0
$341$	−0.263046			−0.0142447
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	−0.108979	−	2.10742i	−0.00586721	−	0.113460i
$346$		0			0
$347$	23.6744	−	23.6744i	1.27091	−	1.27091i	0.325300	−	0.945611i	$-0.394535\pi$
$347$	23.6744	−	23.6744i	1.27091	−	1.27091i	0.945611	−	0.325300i	$-0.105465\pi$
$348$		0			0
$349$		−	17.3048i		−	0.926303i	−0.886279	−	0.463151i	$-0.846719\pi$
$349$		−	17.3048i		−	0.926303i	0.886279	−	0.463151i	$-0.153281\pi$
$350$		0			0
$351$		−	4.36362i		−	0.232913i
$352$		0			0
$353$	−6.63874	+	6.63874i	−0.353345	+	0.353345i	−0.861352	−	0.508008i	$-0.830382\pi$
$353$	−6.63874	+	6.63874i	−0.353345	+	0.353345i	0.508008	+	0.861352i	$0.330382\pi$
$354$		0			0
$355$	0.438823	+	8.48594i	0.0232903	+	0.450387i
$356$		0			0
$357$	10.6247	+	10.6247i	0.562317	+	0.562317i
$358$		0			0
$359$	−6.91215			−0.364810			−0.182405	−	0.983224i	$-0.558388\pi$
$359$	−6.91215			−0.364810			−0.182405	+	0.983224i	$0.558388\pi$
$360$		0			0
$361$	−13.8645			−0.729712
$362$		0			0
$363$	−6.03934	−	6.03934i	−0.316983	−	0.316983i
$364$		0			0
$365$	15.6821	−	17.3925i	0.820841	−	0.910364i
$366$		0			0
$367$	−0.407780	+	0.407780i	−0.0212859	+	0.0212859i	−0.717670	−	0.696384i	$-0.754791\pi$
$367$	−0.407780	+	0.407780i	−0.0212859	+	0.0212859i	0.696384	+	0.717670i	$0.254791\pi$
$368$		0			0
$369$			16.0479i			0.835418i
$370$		0			0
$371$		−	7.53357i		−	0.391123i
$372$		0			0
$373$	−8.58302	+	8.58302i	−0.444412	+	0.444412i	−0.893492	−	0.449080i	$-0.851752\pi$
$373$	−8.58302	+	8.58302i	−0.444412	+	0.444412i	0.449080	+	0.893492i	$0.351752\pi$
$374$		0			0
$375$	−22.7157	−	16.5763i	−1.17303	−	0.855995i
$376$		0			0
$377$	−5.30255	−	5.30255i	−0.273095	−	0.273095i
$378$		0			0
$379$	−28.1144			−1.44414			−0.722069	−	0.691821i	$-0.756809\pi$
$379$	−28.1144			−1.44414			−0.722069	+	0.691821i	$0.756809\pi$
$380$		0			0
$381$	3.07612			0.157594
$382$		0			0
$383$	−8.83610	−	8.83610i	−0.451504	−	0.451504i	0.444350	−	0.895853i	$-0.353435\pi$
$383$	−8.83610	−	8.83610i	−0.451504	−	0.451504i	−0.895853	+	0.444350i	$0.853435\pi$
$384$		0			0
$385$	−6.30092	−	5.68129i	−0.321124	−	0.289546i
$386$		0			0
$387$	27.7751	−	27.7751i	1.41189	−	1.41189i
$388$		0			0
$389$			8.90601i			0.451553i	0.974179	+	0.225776i	$0.0724919\pi$
$389$			8.90601i			0.451553i	−0.974179	+	0.225776i	$0.927508\pi$
$390$		0			0
$391$			2.24148i			0.113356i
$392$		0			0
$393$	10.6139	−	10.6139i	0.535400	−	0.535400i
$394$		0			0
$395$	−31.3321	+	1.62024i	−1.57649	+	0.0815232i
$396$		0			0
$397$	−17.8195	−	17.8195i	−0.894337	−	0.894337i	0.100591	−	0.994928i	$-0.467927\pi$
$397$	−17.8195	−	17.8195i	−0.894337	−	0.894337i	−0.994928	+	0.100591i	$0.967927\pi$
$398$		0			0
$399$	−5.69982			−0.285348
$400$		0			0
$401$	−16.5480			−0.826365			−0.413183	−	0.910648i	$-0.635583\pi$
$401$	−16.5480			−0.826365			−0.413183	+	0.910648i	$0.635583\pi$
$402$		0			0
$403$	−0.260740	−	0.260740i	−0.0129884	−	0.0129884i
$404$		0			0
$405$	−17.6749	+	0.914004i	−0.878275	+	0.0454172i
$406$		0			0
$407$	−9.79235	+	9.79235i	−0.485389	+	0.485389i
$408$		0			0
$409$		−	21.7095i		−	1.07347i	−0.843752	−	0.536734i	$-0.819658\pi$
$409$		−	21.7095i		−	1.07347i	0.843752	−	0.536734i	$-0.180342\pi$
$410$		0			0
$411$		−	43.6442i		−	2.15281i
$412$		0			0
$413$	−2.62854	+	2.62854i	−0.129342	+	0.129342i
$414$		0			0
$415$	−22.6047	−	20.3818i	−1.10962	−	1.00050i
$416$		0			0
$417$	31.4934	+	31.4934i	1.54224	+	1.54224i
$418$		0			0
$419$	0.714490			0.0349051			0.0174526	−	0.999848i	$-0.494444\pi$
$419$	0.714490			0.0349051			0.0174526	+	0.999848i	$0.494444\pi$
$420$		0			0
$421$	8.29124			0.404090			0.202045	−	0.979376i	$-0.435241\pi$
$421$	8.29124			0.404090			0.202045	+	0.979376i	$0.435241\pi$
$422$		0			0
$423$	21.2582	+	21.2582i	1.03361	+	1.03361i
$424$		0			0
$425$	23.1869	+	18.8297i	1.12473	+	0.913377i
$426$		0			0
$427$	−8.66262	+	8.66262i	−0.419214	+	0.419214i
$428$		0			0
$429$		−	50.7570i		−	2.45057i
$430$		0			0
$431$			26.6946i			1.28583i	0.765936	+	0.642917i	$0.222276\pi$
$431$			26.6946i			1.28583i	−0.765936	+	0.642917i	$0.777724\pi$
$432$		0			0
$433$	−3.21300	+	3.21300i	−0.154407	+	0.154407i	−0.780083	−	0.625676i	$-0.784823\pi$
$433$	−3.21300	+	3.21300i	−0.154407	+	0.154407i	0.625676	+	0.780083i	$0.284823\pi$
$434$		0			0
$435$	5.30998	−	5.88911i	0.254594	−	0.282361i
$436$		0			0
$437$	−0.601243	−	0.601243i	−0.0287614	−	0.0287614i
$438$		0			0
$439$	22.5953			1.07841			0.539207	−	0.842173i	$-0.318724\pi$
$439$	22.5953			1.07841			0.539207	+	0.842173i	$0.318724\pi$
$440$		0			0
$441$	3.32619			0.158390
$442$		0			0
$443$	0.290202	+	0.290202i	0.0137879	+	0.0137879i	0.713967	−	0.700179i	$-0.246897\pi$
$443$	0.290202	+	0.290202i	0.0137879	+	0.0137879i	−0.700179	+	0.713967i	$0.746897\pi$
$444$		0			0
$445$	−1.65583	−	32.0203i	−0.0784937	−	1.51791i
$446$		0			0
$447$	−17.5665	+	17.5665i	−0.830869	+	0.830869i
$448$		0			0
$449$		−	8.60505i		−	0.406098i	−0.979169	−	0.203049i	$-0.934915\pi$
$449$		−	8.60505i		−	0.406098i	0.979169	−	0.203049i	$-0.0650850\pi$
$450$		0			0
$451$			18.3057i			0.861983i
$452$		0			0
$453$	9.96242	−	9.96242i	0.468075	−	0.468075i
$454$		0			0
$455$	−0.614191	−	11.8772i	−0.0287937	−	0.556811i
$456$		0			0
$457$	20.4957	+	20.4957i	0.958748	+	0.958748i	0.999182	−	0.0404345i	$-0.0128742\pi$
$457$	20.4957	+	20.4957i	0.958748	+	0.958748i	−0.0404345	+	0.999182i	$0.512874\pi$
$458$		0			0
$459$	−4.90115			−0.228766
$460$		0			0
$461$	−22.2173			−1.03476			−0.517380	−	0.855756i	$-0.673093\pi$
$461$	−22.2173			−1.03476			−0.517380	+	0.855756i	$0.673093\pi$
$462$		0			0
$463$	18.1752	+	18.1752i	0.844675	+	0.844675i	0.989463	−	0.144788i	$-0.0462499\pi$
$463$	18.1752	+	18.1752i	0.844675	+	0.844675i	−0.144788	+	0.989463i	$0.546250\pi$
$464$		0			0
$465$	0.261105	−	0.289583i	0.0121085	−	0.0134291i
$466$		0			0
$467$	3.27771	−	3.27771i	0.151675	−	0.151675i	−0.627191	−	0.778866i	$-0.715795\pi$
$467$	3.27771	−	3.27771i	0.151675	−	0.151675i	0.778866	+	0.627191i	$0.215795\pi$
$468$		0			0
$469$		−	12.2647i		−	0.566333i
$470$		0			0
$471$			13.7198i			0.632177i
$472$		0			0
$473$	31.6829	−	31.6829i	1.45678	−	1.45678i
$474$		0			0
$475$	−11.2704	+	1.16875i	−0.517119	+	0.0536258i
$476$		0			0
$477$	17.7187	+	17.7187i	0.811285	+	0.811285i
$478$		0			0
$479$	19.9252			0.910406			0.455203	−	0.890388i	$-0.349567\pi$
$479$	19.9252			0.910406			0.455203	+	0.890388i	$0.349567\pi$
$480$		0			0
$481$	−19.4130			−0.885157
$482$		0			0
$483$	0.667315	+	0.667315i	0.0303639	+	0.0303639i
$484$		0			0
$485$	17.8140	+	16.0622i	0.808894	+	0.729348i
$486$		0			0
$487$	13.6543	−	13.6543i	0.618736	−	0.618736i	−0.326471	−	0.945207i	$-0.605860\pi$
$487$	13.6543	−	13.6543i	0.618736	−	0.618736i	0.945207	+	0.326471i	$0.105860\pi$
$488$		0			0
$489$		−	14.5904i		−	0.659799i
$490$		0			0
$491$		−	22.8174i		−	1.02973i	−0.857270	−	0.514867i	$-0.827841\pi$
$491$		−	22.8174i		−	1.02973i	0.857270	−	0.514867i	$-0.172159\pi$
$492$		0			0
$493$	−5.95574	+	5.95574i	−0.268233	+	0.268233i
$494$		0			0
$495$	28.1818	−	1.45733i	1.26668	−	0.0655022i
$496$		0			0
$497$	−2.68707	−	2.68707i	−0.120532	−	0.120532i
$498$		0			0
$499$	−24.5799			−1.10035			−0.550174	−	0.835050i	$-0.685439\pi$
$499$	−24.5799			−1.10035			−0.550174	+	0.835050i	$0.685439\pi$
$500$		0			0
$501$	−50.8002			−2.26958
$502$		0			0
$503$	−2.82725	−	2.82725i	−0.126061	−	0.126061i	0.641261	−	0.767322i	$-0.278411\pi$
$503$	−2.82725	−	2.82725i	−0.126061	−	0.126061i	−0.767322	+	0.641261i	$0.778411\pi$
$504$		0			0
$505$	−38.4590	+	1.98878i	−1.71140	+	0.0884997i
$506$		0			0
$507$	27.1915	−	27.1915i	1.20762	−	1.20762i
$508$		0			0
$509$		−	14.5774i		−	0.646132i	−0.946376	−	0.323066i	$-0.895286\pi$
$509$		−	14.5774i		−	0.646132i	0.946376	−	0.323066i	$-0.104714\pi$
$510$		0			0
$511$			10.4731i			0.463302i
$512$		0			0
$513$	1.31466	−	1.31466i	0.0580437	−	0.0580437i
$514$		0			0
$515$	10.0821	+	9.09065i	0.444271	+	0.400582i
$516$		0			0
$517$	24.2492	+	24.2492i	1.06648	+	1.06648i
$518$		0			0
$519$	29.6126			1.29985
$520$		0			0
$521$	−13.9497			−0.611147			−0.305574	−	0.952168i	$-0.598848\pi$
$521$	−13.9497			−0.611147			−0.305574	+	0.952168i	$0.598848\pi$
$522$		0			0
$523$	−2.74325	−	2.74325i	−0.119954	−	0.119954i	0.644582	−	0.764535i	$-0.277032\pi$
$523$	−2.74325	−	2.74325i	−0.119954	−	0.119954i	−0.764535	+	0.644582i	$0.777032\pi$
$524$		0			0
$525$	12.5089	−	1.29718i	0.545932	−	0.0566137i
$526$		0			0
$527$	−0.292859	+	0.292859i	−0.0127571	+	0.0127571i
$528$		0			0
$529$		−	22.8592i		−	0.993879i
$530$		0			0
$531$		−	12.3645i		−	0.536573i
$532$		0			0
$533$	−18.1453	+	18.1453i	−0.785959	+	0.785959i
$534$		0			0
$535$	−7.79040	+	8.64005i	−0.336808	+	0.373542i
$536$		0			0
$537$	−25.4389	−	25.4389i	−1.09777	−	1.09777i
$538$		0			0
$539$	3.79417			0.163426
$540$		0			0
$541$	−0.897490			−0.0385861			−0.0192931	−	0.999814i	$-0.506142\pi$
$541$	−0.897490			−0.0385861			−0.0192931	+	0.999814i	$0.506142\pi$
$542$		0			0
$543$	22.3607	+	22.3607i	0.959590	+	0.959590i
$544$		0			0
$545$	−1.37521	−	26.5938i	−0.0589076	−	1.13915i
$546$		0			0
$547$	19.7720	−	19.7720i	0.845388	−	0.845388i	−0.144166	−	0.989554i	$-0.546050\pi$
$547$	19.7720	−	19.7720i	0.845388	−	0.845388i	0.989554	+	0.144166i	$0.0460499\pi$
$548$		0			0
$549$		−	40.7485i		−	1.73910i
$550$		0			0
$551$		−	3.19508i		−	0.136115i
$552$		0			0
$553$	9.92132	−	9.92132i	0.421897	−	0.421897i
$554$		0			0
$555$	−1.06011	−	20.5003i	−0.0449992	−	0.870191i
$556$		0			0
$557$	1.02182	+	1.02182i	0.0432959	+	0.0432959i	0.728423	−	0.685127i	$-0.240253\pi$
$557$	1.02182	+	1.02182i	0.0432959	+	0.0432959i	−0.685127	+	0.728423i	$0.740253\pi$
$558$		0			0
$559$	62.8104			2.65660
$560$		0			0
$561$	−57.0095			−2.40694
$562$		0			0
$563$	29.1607	+	29.1607i	1.22898	+	1.22898i	0.964351	+	0.264625i	$0.0852482\pi$
$563$	29.1607	+	29.1607i	1.22898	+	1.22898i	0.264625	+	0.964351i	$0.414752\pi$
$564$		0			0
$565$	−15.5008	+	17.1914i	−0.652124	+	0.723247i
$566$		0			0
$567$	5.59678	−	5.59678i	0.235043	−	0.235043i
$568$		0			0
$569$			3.11064i			0.130405i	0.997872	+	0.0652024i	$0.0207693\pi$
$569$			3.11064i			0.130405i	−0.997872	+	0.0652024i	$0.979231\pi$
$570$		0			0
$571$			19.0258i			0.796205i	0.917341	+	0.398102i	$0.130331\pi$
$571$			19.0258i			0.796205i	−0.917341	+	0.398102i	$0.869669\pi$
$572$		0			0
$573$	15.3390	−	15.3390i	0.640794	−	0.640794i
$574$		0			0
$575$	1.45633	+	1.18266i	0.0607330	+	0.0493204i
$576$		0			0
$577$	17.9230	+	17.9230i	0.746146	+	0.746146i	0.973753	−	0.227607i	$-0.0730902\pi$
$577$	17.9230	+	17.9230i	0.746146	+	0.746146i	−0.227607	+	0.973753i	$0.573090\pi$
$578$		0			0
$579$	−16.2770			−0.676447
$580$		0			0
$581$	13.6117			0.564708
$582$		0			0
$583$	20.2117	+	20.2117i	0.837083	+	0.837083i
$584$		0			0
$585$	29.3793	+	26.4902i	1.21469	+	1.09524i
$586$		0			0
$587$	−0.599519	+	0.599519i	−0.0247448	+	0.0247448i	−0.719371	−	0.694626i	$-0.755570\pi$
$587$	−0.599519	+	0.599519i	−0.0247448	+	0.0247448i	0.694626	+	0.719371i	$0.255570\pi$
$588$		0			0
$589$		−	0.157110i		−	0.00647362i
$590$		0			0
$591$			0.178033i			0.00732330i
$592$		0			0
$593$	6.58918	−	6.58918i	0.270585	−	0.270585i	−0.558751	−	0.829336i	$-0.688719\pi$
$593$	6.58918	−	6.58918i	0.270585	−	0.270585i	0.829336	+	0.558751i	$0.188719\pi$
$594$		0			0
$595$	−13.3403	+	0.689849i	−0.546897	+	0.0282811i
$596$		0			0
$597$	−26.2307	−	26.2307i	−1.07355	−	1.07355i
$598$		0			0
$599$	−28.7172			−1.17335			−0.586677	−	0.809821i	$-0.699564\pi$
$599$	−28.7172			−1.17335			−0.586677	+	0.809821i	$0.699564\pi$
$600$		0			0
$601$	−11.1115			−0.453247			−0.226623	−	0.973982i	$-0.572769\pi$
$601$	−11.1115			−0.453247			−0.226623	+	0.973982i	$0.572769\pi$
$602$		0			0
$603$	28.8463	+	28.8463i	1.17471	+	1.17471i
$604$		0			0
$605$	7.58295	−	0.392128i	0.308291	−	0.0159423i
$606$		0			0
$607$	−17.7343	+	17.7343i	−0.719814	+	0.719814i	−0.968567	−	0.248753i	$-0.919979\pi$
$607$	−17.7343	+	17.7343i	−0.719814	+	0.719814i	0.248753	+	0.968567i	$0.419979\pi$
$608$		0			0
$609$			3.54619i			0.143699i
$610$		0			0
$611$			48.0733i			1.94484i
$612$		0			0
$613$	3.49661	−	3.49661i	0.141227	−	0.141227i	−0.632959	−	0.774185i	$-0.718160\pi$
$613$	3.49661	−	3.49661i	0.141227	−	0.141227i	0.774185	+	0.632959i	$0.218160\pi$
$614$		0			0
$615$	−20.1525	−	18.1707i	−0.812626	−	0.732714i
$616$		0			0
$617$	−30.6264	−	30.6264i	−1.23297	−	1.23297i	−0.962816	−	0.270157i	$-0.912924\pi$
$617$	−30.6264	−	30.6264i	−1.23297	−	1.23297i	−0.270157	−	0.962816i	$-0.587076\pi$
$618$		0			0
$619$	−25.1748			−1.01186			−0.505930	−	0.862575i	$-0.668850\pi$
$619$	−25.1748			−1.01186			−0.505930	+	0.862575i	$0.668850\pi$
$620$		0			0
$621$	−0.307832			−0.0123529
$622$		0			0
$623$	10.1392	+	10.1392i	0.406219	+	0.406219i
$624$		0			0
$625$	24.4680	−	5.12988i	0.978721	−	0.205195i
$626$		0			0
$627$	15.2920	−	15.2920i	0.610702	−	0.610702i
$628$		0			0
$629$			21.8044i			0.869398i
$630$		0			0
$631$		−	13.3443i		−	0.531226i	−0.964080	−	0.265613i	$-0.914426\pi$
$631$		−	13.3443i		−	0.531226i	0.964080	−	0.265613i	$-0.0855744\pi$
$632$		0			0
$633$	11.4069	−	11.4069i	0.453384	−	0.453384i
$634$		0			0
$635$	−1.83131	+	2.03104i	−0.0726734	+	0.0805994i
$636$		0			0
$637$	3.76091	+	3.76091i	0.149013	+	0.149013i
$638$		0			0
$639$	12.6398			0.500024
$640$		0			0
$641$	4.86135			0.192012			0.0960059	−	0.995381i	$-0.469393\pi$
$641$	4.86135			0.192012			0.0960059	+	0.995381i	$0.469393\pi$
$642$		0			0
$643$	−33.6560	−	33.6560i	−1.32726	−	1.32726i	−0.907747	−	0.419517i	$-0.862199\pi$
$643$	−33.6560	−	33.6560i	−1.32726	−	1.32726i	−0.419517	−	0.907747i	$-0.637801\pi$
$644$		0			0
$645$	3.42996	+	66.3284i	0.135055	+	2.61168i
$646$		0			0
$647$	8.53015	−	8.53015i	0.335355	−	0.335355i	−0.519261	−	0.854616i	$-0.673793\pi$
$647$	8.53015	−	8.53015i	0.335355	−	0.335355i	0.854616	+	0.519261i	$0.173793\pi$
$648$		0			0
$649$		−	14.1041i		−	0.553635i
$650$		0			0
$651$			0.174376i			0.00683432i
$652$		0			0
$653$	21.6815	−	21.6815i	0.848461	−	0.848461i	−0.141480	−	0.989941i	$-0.545186\pi$
$653$	21.6815	−	21.6815i	0.848461	−	0.848461i	0.989941	+	0.141480i	$0.0451862\pi$
$654$		0			0
$655$	0.689150	+	13.3267i	0.0269273	+	0.520719i
$656$		0			0
$657$	−24.6324	−	24.6324i	−0.961001	−	0.961001i
$658$		0			0
$659$	35.9123			1.39894			0.699472	−	0.714660i	$-0.253418\pi$
$659$	35.9123			1.39894			0.699472	+	0.714660i	$0.253418\pi$
$660$		0			0
$661$	25.0070			0.972659			0.486329	−	0.873776i	$-0.338335\pi$
$661$	25.0070			0.972659			0.486329	+	0.873776i	$0.338335\pi$
$662$		0			0
$663$	−56.5097	−	56.5097i	−2.19466	−	2.19466i
$664$		0			0
$665$	3.39329	−	3.76337i	0.131586	−	0.145937i
$666$		0			0
$667$	−0.374069	+	0.374069i	−0.0144840	+	0.0144840i
$668$		0			0
$669$		−	26.4707i		−	1.02342i
$670$		0			0
$671$		−	46.4816i		−	1.79440i
$672$		0			0
$673$	1.96689	−	1.96689i	0.0758180	−	0.0758180i	−0.668181	−	0.743999i	$-0.732927\pi$
$673$	1.96689	−	1.96689i	0.0758180	−	0.0758180i	0.743999	+	0.668181i	$0.232927\pi$
$674$		0			0
$675$	−2.58597	+	3.18436i	−0.0995341	+	0.122566i
$676$		0			0
$677$	−14.3489	−	14.3489i	−0.551472	−	0.551472i	0.375394	−	0.926865i	$-0.377507\pi$
$677$	−14.3489	−	14.3489i	−0.551472	−	0.551472i	−0.926865	+	0.375394i	$0.877507\pi$
$678$		0			0
$679$	−10.7269			−0.411662
$680$		0			0
$681$	1.07357			0.0411393
$682$		0			0
$683$	18.7583	+	18.7583i	0.717768	+	0.717768i	0.968148	−	0.250380i	$-0.0805556\pi$
$683$	18.7583	+	18.7583i	0.717768	+	0.717768i	−0.250380	+	0.968148i	$0.580556\pi$
$684$		0			0
$685$	28.8165	+	25.9828i	1.10102	+	0.992751i
$686$		0			0
$687$	−41.7868	+	41.7868i	−1.59427	+	1.59427i
$688$		0			0
$689$			40.0690i			1.52651i
$690$		0			0
$691$		−	50.2795i		−	1.91272i	−0.292189	−	0.956361i	$-0.594384\pi$
$691$		−	50.2795i		−	1.91272i	0.292189	−	0.956361i	$-0.405616\pi$
$692$		0			0
$693$	−8.92377	+	8.92377i	−0.338986	+	0.338986i
$694$		0			0
$695$	−39.5428	+	2.04483i	−1.49995	+	0.0775650i
$696$		0			0
$697$	20.3805	+	20.3805i	0.771966	+	0.771966i
$698$		0			0
$699$	−33.2305			−1.25689
$700$		0			0
$701$	1.57290			0.0594076			0.0297038	−	0.999559i	$-0.490544\pi$
$701$	1.57290			0.0594076			0.0297038	+	0.999559i	$0.490544\pi$
$702$		0			0
$703$	−5.84871	−	5.84871i	−0.220588	−	0.220588i
$704$		0			0
$705$	−50.7659	+	2.62520i	−1.91195	+	0.0988706i
$706$		0			0
$707$	12.1780	−	12.1780i	0.458002	−	0.458002i
$708$		0			0
$709$			21.0275i			0.789704i	0.918745	+	0.394852i	$0.129204\pi$
$709$			21.0275i			0.789704i	−0.918745	+	0.394852i	$0.870796\pi$
$710$		0			0
$711$			46.6693i			1.75023i
$712$		0			0
$713$	−0.0183939	+	0.0183939i	−0.000688858	+	0.000688858i
$714$		0			0
$715$	33.5129	+	30.2173i	1.25331	+	1.13006i
$716$		0			0
$717$	24.8383	+	24.8383i	0.927602	+	0.927602i
$718$		0			0
$719$	−28.4334			−1.06039			−0.530193	−	0.847877i	$-0.677881\pi$
$719$	−28.4334			−1.06039			−0.530193	+	0.847877i	$0.677881\pi$
$720$		0			0
$721$	−6.07106			−0.226098
$722$		0			0
$723$	−11.6569	−	11.6569i	−0.433526	−	0.433526i
$724$		0			0
$725$	0.727146	+	7.01195i	0.0270055	+	0.260417i
$726$		0			0
$727$	3.50732	−	3.50732i	0.130079	−	0.130079i	−0.639070	−	0.769149i	$-0.720680\pi$
$727$	3.50732	−	3.50732i	0.130079	−	0.130079i	0.769149	+	0.639070i	$0.220680\pi$
$728$		0			0
$729$			32.5175i			1.20435i
$730$		0			0
$731$		−	70.5477i		−	2.60930i
$732$		0			0
$733$	−20.2898	+	20.2898i	−0.749420	+	0.749420i	−0.974370	−	0.224950i	$-0.927778\pi$
$733$	−20.2898	+	20.2898i	−0.749420	+	0.749420i	0.224950	+	0.974370i	$0.427778\pi$
$734$		0			0
$735$	−3.76618	+	4.17694i	−0.138918	+	0.154069i
$736$		0			0
$737$	32.9049	+	32.9049i	1.21207	+	1.21207i
$738$		0			0
$739$	9.65136			0.355031			0.177515	−	0.984118i	$-0.443194\pi$
$739$	9.65136			0.355031			0.177515	+	0.984118i	$0.443194\pi$
$740$		0			0
$741$	30.3158			1.11368
$742$		0			0
$743$	8.63967	+	8.63967i	0.316959	+	0.316959i	0.847598	−	0.530639i	$-0.178048\pi$
$743$	8.63967	+	8.63967i	0.316959	+	0.316959i	−0.530639	+	0.847598i	$0.678048\pi$
$744$		0			0
$745$	−1.14058	−	22.0564i	−0.0417876	−	0.808085i
$746$		0			0
$747$	−32.0143	+	32.0143i	−1.17134	+	1.17134i
$748$		0			0
$749$		−	5.20271i		−	0.190103i
$750$		0			0
$751$		−	52.6925i		−	1.92278i	−0.275197	−	0.961388i	$-0.588743\pi$
$751$		−	52.6925i		−	1.92278i	0.275197	−	0.961388i	$-0.411257\pi$
$752$		0			0
$753$	−14.0760	+	14.0760i	−0.512957	+	0.512957i
$754$		0			0
$755$	0.646850	+	12.5087i	0.0235413	+	0.455240i
$756$		0			0
$757$	−2.23225	−	2.23225i	−0.0811324	−	0.0811324i	0.665376	−	0.746508i	$-0.268271\pi$
$757$	−2.23225	−	2.23225i	−0.0811324	−	0.0811324i	−0.746508	+	0.665376i	$0.768271\pi$
$758$		0			0
$759$	−3.58066			−0.129970
$760$		0			0
$761$	−31.0440			−1.12535			−0.562673	−	0.826680i	$-0.690227\pi$
$761$	−31.0440			−1.12535			−0.562673	+	0.826680i	$0.690227\pi$
$762$		0			0
$763$	8.42092	+	8.42092i	0.304858	+	0.304858i
$764$		0			0
$765$	29.7534	−	32.9984i	1.07574	−	1.19306i
$766$		0			0
$767$	13.9805	−	13.9805i	0.504806	−	0.504806i
$768$		0			0
$769$		−	29.9865i		−	1.08134i	−0.841235	−	0.540670i	$-0.818171\pi$
$769$		−	29.9865i		−	1.08134i	0.841235	−	0.540670i	$-0.181829\pi$
$770$		0			0
$771$			9.40398i			0.338676i
$772$		0			0
$773$	16.2363	−	16.2363i	0.583979	−	0.583979i	−0.352015	−	0.935994i	$-0.614504\pi$
$773$	16.2363	−	16.2363i	0.583979	−	0.583979i	0.935994	+	0.352015i	$0.114504\pi$
$774$		0			0
$775$	0.0357556	+	0.344796i	0.00128438	+	0.0123854i
$776$		0			0
$777$	6.49144	+	6.49144i	0.232879	+	0.232879i
$778$		0			0
$779$	−10.9335			−0.391735
$780$		0			0
$781$	14.4182			0.515924
$782$		0			0
$783$	−0.817928	−	0.817928i	−0.0292304	−	0.0292304i
$784$		0			0
$785$	−9.05869	−	8.16787i	−0.323318	−	0.291524i
$786$		0			0
$787$	−34.6951	+	34.6951i	−1.23675	+	1.23675i	−0.275426	+	0.961322i	$0.588819\pi$
$787$	−34.6951	+	34.6951i	−1.23675	+	1.23675i	−0.961322	+	0.275426i	$0.911181\pi$
$788$		0			0
$789$		−	17.5584i		−	0.625096i
$790$		0			0
$791$		−	10.3520i		−	0.368075i
$792$		0			0
$793$	46.0742	−	46.0742i	1.63614	−	1.63614i
$794$		0			0
$795$	−42.3133	+	2.18810i	−1.50070	+	0.0776039i
$796$		0			0
$797$	−17.9512	−	17.9512i	−0.635864	−	0.635864i	0.313669	−	0.949533i	$-0.398442\pi$
$797$	−17.9512	−	17.9512i	−0.635864	−	0.635864i	−0.949533	+	0.313669i	$0.898442\pi$
$798$		0			0
$799$	53.9951			1.91021
$800$		0			0
$801$	−47.6943			−1.68519
$802$		0			0
$803$	−28.0981	−	28.0981i	−0.991560	−	0.991560i
$804$		0			0
$805$	−0.837877	+	0.0433282i	−0.0295313	+	0.00152712i
$806$		0			0
$807$	−46.2903	+	46.2903i	−1.62950	+	1.62950i
$808$		0			0
$809$			36.6292i			1.28782i	0.765103	+	0.643908i	$0.222688\pi$
$809$			36.6292i			1.28782i	−0.765103	+	0.643908i	$0.777312\pi$
$810$		0			0
$811$			11.1915i			0.392986i	0.980505	+	0.196493i	$0.0629553\pi$
$811$			11.1915i			0.392986i	−0.980505	+	0.196493i	$0.937045\pi$
$812$		0			0
$813$	−18.5548	+	18.5548i	−0.650745	+	0.650745i
$814$		0			0
$815$	9.63346	+	8.68612i	0.337445	+	0.304261i
$816$		0			0
$817$	18.9234	+	18.9234i	0.662045	+	0.662045i
$818$		0			0
$819$	−17.6911			−0.618177
$820$		0			0
$821$	−32.6945			−1.14105			−0.570524	−	0.821281i	$-0.693260\pi$
$821$	−32.6945			−1.14105			−0.570524	+	0.821281i	$0.693260\pi$
$822$		0			0
$823$	8.54839	+	8.54839i	0.297978	+	0.297978i	0.840221	−	0.542243i	$-0.182425\pi$
$823$	8.54839	+	8.54839i	0.297978	+	0.297978i	−0.542243	+	0.840221i	$0.682425\pi$
$824$		0			0
$825$	−30.0797	+	37.0401i	−1.04724	+	1.28957i
$826$		0			0
$827$	8.85815	−	8.85815i	0.308028	−	0.308028i	−0.536116	−	0.844144i	$-0.680109\pi$
$827$	8.85815	−	8.85815i	0.308028	−	0.308028i	0.844144	+	0.536116i	$0.180109\pi$
$828$		0			0
$829$			7.53521i			0.261709i	0.991402	+	0.130854i	$0.0417720\pi$
$829$			7.53521i			0.261709i	−0.991402	+	0.130854i	$0.958228\pi$
$830$		0			0
$831$		−	73.0335i		−	2.53350i
$832$		0			0
$833$	4.22420	−	4.22420i	0.146360	−	0.146360i
$834$		0			0
$835$	30.2430	−	33.5414i	1.04660	−	1.16075i
$836$		0			0
$837$	−0.0402196	−	0.0402196i	−0.00139019	−	0.00139019i
$838$		0			0
$839$	−10.0436			−0.346744			−0.173372	−	0.984856i	$-0.555466\pi$
$839$	−10.0436			−0.346744			−0.173372	+	0.984856i	$0.555466\pi$
$840$		0			0
$841$	27.0122			0.931454
$842$		0			0
$843$	23.7855	+	23.7855i	0.819218	+	0.819218i
$844$		0			0
$845$	1.76552	+	34.1414i	0.0607356	+	1.17450i
$846$		0			0
$847$	−2.40114	+	2.40114i	−0.0825043	+	0.0825043i
$848$		0			0
$849$		−	37.3950i		−	1.28339i
$850$		0			0
$851$			1.36949i			0.0469456i
$852$		0			0
$853$	16.3992	−	16.3992i	0.561499	−	0.561499i	−0.368234	−	0.929733i	$-0.620037\pi$
$853$	16.3992	−	16.3992i	0.561499	−	0.561499i	0.929733	+	0.368234i	$0.120037\pi$
$854$		0			0
$855$	0.870427	+	16.8322i	0.0297680	+	0.575651i
$856$		0			0
$857$	10.9702	+	10.9702i	0.374736	+	0.374736i	0.869199	−	0.494463i	$-0.164635\pi$
$857$	10.9702	+	10.9702i	0.374736	+	0.374736i	−0.494463	+	0.869199i	$0.664635\pi$
$858$		0			0
$859$	18.7738			0.640554			0.320277	−	0.947324i	$-0.396224\pi$
$859$	18.7738			0.640554			0.320277	+	0.947324i	$0.396224\pi$
$860$		0			0
$861$	12.1350			0.413561
$862$		0			0
$863$	−27.0121	−	27.0121i	−0.919503	−	0.919503i	0.0774906	−	0.996993i	$-0.475309\pi$
$863$	−27.0121	−	27.0121i	−0.919503	−	0.919503i	−0.996993	+	0.0774906i	$0.975309\pi$
$864$		0			0
$865$	−17.6293	+	19.5521i	−0.599416	+	0.664790i
$866$		0			0
$867$	−33.2362	+	33.2362i	−1.12876	+	1.12876i
$868$		0			0
$869$			53.2355i			1.80589i
$870$		0			0
$871$			65.2329i			2.21033i
$872$		0			0
$873$	25.2294	−	25.2294i	0.853886	−	0.853886i
$874$		0			0
$875$	−6.59046	+	9.03138i	−0.222798	+	0.305316i
$876$		0			0
$877$	18.2791	+	18.2791i	0.617243	+	0.617243i	0.944823	−	0.327580i	$-0.106233\pi$
$877$	18.2791	+	18.2791i	0.617243	+	0.617243i	−0.327580	+	0.944823i	$0.606233\pi$
$878$		0			0
$879$	35.3479			1.19225
$880$		0			0
$881$	−23.7320			−0.799550			−0.399775	−	0.916613i	$-0.630912\pi$
$881$	−23.7320			−0.799550			−0.399775	+	0.916613i	$0.630912\pi$
$882$		0			0
$883$	−18.6049	−	18.6049i	−0.626104	−	0.626104i	0.320982	−	0.947085i	$-0.395987\pi$
$883$	−18.6049	−	18.6049i	−0.626104	−	0.626104i	−0.947085	+	0.320982i	$0.895987\pi$
$884$		0			0
$885$	15.5270	+	14.0001i	0.521934	+	0.470608i
$886$		0			0
$887$	−2.81236	+	2.81236i	−0.0944297	+	0.0944297i	−0.752744	−	0.658314i	$-0.771270\pi$
$887$	−2.81236	+	2.81236i	−0.0944297	+	0.0944297i	0.658314	+	0.752744i	$0.271270\pi$
$888$		0			0
$889$		−	1.22302i		−	0.0410186i
$890$		0			0
$891$			30.0310i			1.00608i
$892$		0			0
$893$	−14.4834	+	14.4834i	−0.484669	+	0.484669i
$894$		0			0
$895$	31.9409	−	1.65172i	1.06767	−	0.0552111i
$896$		0			0
$897$	−3.54927	−	3.54927i	−0.118507	−	0.118507i
$898$		0			0
$899$	−0.0977475			−0.00326006
$900$		0			0
$901$	45.0049			1.49933
$902$		0			0
$903$	−21.0029	−	21.0029i	−0.698933	−	0.698933i
$904$		0			0
$905$	−28.0760	+	1.45186i	−0.933277	+	0.0482615i
$906$		0			0
$907$	−27.9579	+	27.9579i	−0.928326	+	0.928326i	−0.997598	−	0.0692715i	$-0.977933\pi$
$907$	−27.9579	+	27.9579i	−0.928326	+	0.928326i	0.0692715	+	0.997598i	$0.477933\pi$
$908$		0			0
$909$			57.2848i			1.90002i
$910$		0			0
$911$			40.5095i			1.34214i	0.741394	+	0.671070i	$0.234165\pi$
$911$			40.5095i			1.34214i	−0.741394	+	0.671070i	$0.765835\pi$
$912$		0			0
$913$	−36.5186	+	36.5186i	−1.20859	+	1.20859i
$914$		0			0
$915$	51.1708	+	46.1388i	1.69165	+	1.52530i
$916$		0			0
$917$	−4.21991	−	4.21991i	−0.139354	−	0.139354i
$918$		0			0
$919$	49.0259			1.61722			0.808608	−	0.588347i	$-0.200221\pi$
$919$	49.0259			1.61722			0.808608	+	0.588347i	$0.200221\pi$
$920$		0			0
$921$	55.4558			1.82733
$922$		0			0
$923$	14.2918	+	14.2918i	0.470421	+	0.470421i
$924$		0			0
$925$	14.1667	+	11.5046i	0.465798	+	0.378268i
$926$		0			0
$927$	14.2789	−	14.2789i	0.468982	−	0.468982i
$928$		0			0
$929$			42.2155i			1.38505i	0.721396	+	0.692523i	$0.243501\pi$
$929$			42.2155i			1.38505i	−0.721396	+	0.692523i	$0.756499\pi$
$930$		0			0
$931$			2.26616i			0.0742703i
$932$		0			0
$933$	−59.3066	+	59.3066i	−1.94161	+	1.94161i
$934$		0			0
$935$	33.9396	−	37.6411i	1.10994	−	1.23100i
$936$		0			0
$937$	−15.3451	−	15.3451i	−0.501304	−	0.501304i	0.410539	−	0.911843i	$-0.365340\pi$
$937$	−15.3451	−	15.3451i	−0.501304	−	0.501304i	−0.911843	+	0.410539i	$0.865340\pi$
$938$		0			0
$939$	52.7770			1.72231
$940$		0			0
$941$	−27.0507			−0.881828			−0.440914	−	0.897549i	$-0.645346\pi$
$941$	−27.0507			−0.881828			−0.440914	+	0.897549i	$0.645346\pi$
$942$		0			0
$943$	1.28006	+	1.28006i	0.0416845	+	0.0416845i
$944$		0			0
$945$	−0.0947401	−	1.83208i	−0.00308189	−	0.0595975i
$946$		0			0
$947$	20.1551	−	20.1551i	0.654954	−	0.654954i	−0.299228	−	0.954182i	$-0.596729\pi$
$947$	20.1551	−	20.1551i	0.654954	−	0.654954i	0.954182	+	0.299228i	$0.0967290\pi$
$948$		0			0
$949$		−	55.7036i		−	1.80821i
$950$		0			0
$951$			1.20077i			0.0389376i
$952$		0			0
$953$	−9.41415	+	9.41415i	−0.304954	+	0.304954i	−0.842949	−	0.537994i	$-0.819182\pi$
$953$	−9.41415	+	9.41415i	−0.304954	+	0.304954i	0.537994	+	0.842949i	$0.319182\pi$
$954$		0			0
$955$	0.995944	+	19.2595i	0.0322280	+	0.623223i
$956$		0			0
$957$	−9.51402	−	9.51402i	−0.307545	−	0.307545i
$958$		0			0
$959$	−17.3522			−0.560332
$960$		0			0
$961$	30.9952			0.999845
$962$		0			0
$963$	12.2366	+	12.2366i	0.394319	+	0.394319i
$964$		0			0
$965$	9.69020	−	10.7470i	0.311939	−	0.345960i
$966$		0			0
$967$	4.53775	−	4.53775i	0.145924	−	0.145924i	−0.630370	−	0.776295i	$-0.717097\pi$
$967$	4.53775	−	4.53775i	0.145924	−	0.145924i	0.776295	+	0.630370i	$0.217097\pi$
$968$		0			0
$969$		−	34.0503i		−	1.09385i
$970$		0			0
$971$		−	57.5718i		−	1.84757i	−0.382917	−	0.923783i	$-0.625080\pi$
$971$		−	57.5718i		−	1.84757i	0.382917	−	0.923783i	$-0.374920\pi$
$972$		0			0
$973$	12.5213	−	12.5213i	0.401413	−	0.401413i
$974$		0			0
$975$	−66.5314	+	6.89937i	−2.13071	+	0.220957i
$976$		0			0
$977$	21.9593	+	21.9593i	0.702539	+	0.702539i	0.964955	−	0.262416i	$-0.0845193\pi$
$977$	21.9593	+	21.9593i	0.702539	+	0.702539i	−0.262416	+	0.964955i	$0.584519\pi$
$978$		0			0
$979$	−54.4047			−1.73878
$980$		0			0
$981$	−39.6115			−1.26470
$982$		0			0
$983$	−29.0558	−	29.0558i	−0.926735	−	0.926735i	0.0707581	−	0.997494i	$-0.477458\pi$
$983$	−29.0558	−	29.0558i	−0.926735	−	0.926735i	−0.997494	+	0.0707581i	$0.977458\pi$
$984$		0			0
$985$	−0.117548	−	0.105989i	−0.00374540	−	0.00337708i
$986$		0			0
$987$	16.0750	−	16.0750i	0.511674	−	0.511674i
$988$		0			0
$989$		−	4.43097i		−	0.140897i
$990$		0			0
$991$		−	10.7249i		−	0.340686i	−0.985385	−	0.170343i	$-0.945512\pi$
$991$		−	10.7249i		−	0.340686i	0.985385	−	0.170343i	$-0.0544876\pi$
$992$		0			0
$993$	17.0195	−	17.0195i	0.540096	−	0.540096i
$994$		0			0
$995$	32.9351	−	1.70313i	1.04411	−	0.0539930i
$996$		0			0
$997$	−1.18125	−	1.18125i	−0.0374107	−	0.0374107i	0.688154	−	0.725565i	$-0.258421\pi$
$997$	−1.18125	−	1.18125i	−0.0374107	−	0.0374107i	−0.725565	+	0.688154i	$0.758421\pi$
$998$		0			0
$999$	−2.99449			−0.0947416

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.x.b.127.11	yes	24
4.3	odd	2	inner	560.2.x.b.127.2	✓	24
5.3	odd	4	inner	560.2.x.b.463.2	yes	24
20.3	even	4	inner	560.2.x.b.463.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.x.b.127.2	✓	24	4.3	odd	2	inner
560.2.x.b.127.11	yes	24	1.1	even	1	trivial
560.2.x.b.463.2	yes	24	5.3	odd	4	inner
560.2.x.b.463.11	yes	24	20.3	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.77851 + 1.77851i) q^{3} +(-2.23308 + 0.115477i) q^{5} +(0.707107 - 0.707107i) q^{7} +3.32619i q^{9} +O(q^{10})\)	\(q+(1.77851 + 1.77851i) q^{3} +(-2.23308 + 0.115477i) q^{5} +(0.707107 - 0.707107i) q^{7} +3.32619i q^{9} +3.79417i q^{11} +(-3.76091 + 3.76091i) q^{13} +(-4.17694 - 3.76618i) q^{15} +(4.22420 + 4.22420i) q^{17} -2.26616 q^{19} +2.51519 q^{21} +(0.265314 + 0.265314i) q^{23} +(4.97333 - 0.515739i) q^{25} +(-0.580128 + 0.580128i) q^{27} +1.40991i q^{29} +0.0693289i q^{31} +(-6.74797 + 6.74797i) q^{33} +(-1.49737 + 1.66068i) q^{35} +(2.58089 + 2.58089i) q^{37} -13.3776 q^{39} +4.82470 q^{41} +(-8.35042 - 8.35042i) q^{43} +(-0.384098 - 7.42766i) q^{45} +(6.39117 - 6.39117i) q^{47} -1.00000i q^{49} +15.0255i q^{51} +(5.32704 - 5.32704i) q^{53} +(-0.438139 - 8.47270i) q^{55} +(-4.03038 - 4.03038i) q^{57} -3.71731 q^{59} -12.2508 q^{61} +(2.35197 + 2.35197i) q^{63} +(7.96413 - 8.83273i) q^{65} +(8.67249 - 8.67249i) q^{67} +0.943726i q^{69} -3.80010i q^{71} +(-7.40559 + 7.40559i) q^{73} +(9.76236 + 7.92786i) q^{75} +(2.68288 + 2.68288i) q^{77} +14.0309 q^{79} +7.91504 q^{81} +(9.62491 + 9.62491i) q^{83} +(-9.92078 - 8.94519i) q^{85} +(-2.50754 + 2.50754i) q^{87} +14.3390i q^{89} +5.31873i q^{91} +(-0.123302 + 0.123302i) q^{93} +(5.06052 - 0.261689i) q^{95} +(-7.58508 - 7.58508i) q^{97} -12.6201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{13} + 8 q^{17} - 8 q^{21} + 32 q^{25} + 24 q^{33} - 16 q^{37} + 32 q^{41} - 24 q^{45} + 8 q^{53} + 40 q^{57} + 16 q^{61} - 16 q^{73} + 16 q^{77} - 104 q^{81} - 8 q^{85} - 8 q^{93} - 24 q^{97}+O(q^{100}) \) 24 * q - 8 * q^13 + 8 * q^17 - 8 * q^21 + 32 * q^25 + 24 * q^33 - 16 * q^37 + 32 * q^41 - 24 * q^45 + 8 * q^53 + 40 * q^57 + 16 * q^61 - 16 * q^73 + 16 * q^77 - 104 * q^81 - 8 * q^85 - 8 * q^93 - 24 * q^97

Introduction

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