LMFDB - Embedded newform 500.2.g.b.301.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [500,2,Mod(101,500)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("500.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(500, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 500 = 2^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	500.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.99252010106$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.4
Root			$0.917186 + 1.66637i$ of defining polynomial
Character	$\chi$	$=$	500.301
Dual form			500.2.g.b.201.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.713605 - 2.19625i) q^{3} -4.21139 q^{7} +(-1.88723 - 1.37116i) q^{9} +(0.451659 - 0.328150i) q^{11} +(-3.26033 - 2.36877i) q^{13} +(-1.22440 - 3.76832i) q^{17} +(-2.14177 - 6.59168i) q^{19} +(-3.00527 + 9.24926i) q^{21} +(0.308467 - 0.224115i) q^{23} +(1.24659 - 0.905698i) q^{27} +(-2.48680 + 7.65359i) q^{29} +(-0.0767462 - 0.236201i) q^{31} +(-0.398393 - 1.22613i) q^{33} +(5.80503 + 4.21760i) q^{37} +(-7.52900 + 5.47014i) q^{39} +(3.68773 + 2.67929i) q^{41} -0.207272 q^{43} +(2.86117 - 8.80576i) q^{47} +10.7358 q^{49} -9.14992 q^{51} +(-0.729597 + 2.24547i) q^{53} -16.0054 q^{57} +(-2.93557 - 2.13282i) q^{59} +(3.15785 - 2.29431i) q^{61} +(7.94787 + 5.77447i) q^{63} +(2.13234 + 6.56267i) q^{67} +(-0.272088 - 0.837401i) q^{69} +(4.44084 - 13.6675i) q^{71} +(-1.82346 + 1.32482i) q^{73} +(-1.90211 + 1.38197i) q^{77} +(2.35970 - 7.26242i) q^{79} +(-3.26215 - 10.0399i) q^{81} +(-2.34809 - 7.22667i) q^{83} +(15.0346 + 10.9233i) q^{87} +(12.9713 - 9.42417i) q^{89} +(13.7305 + 9.97581i) q^{91} -0.573522 q^{93} +(1.01080 - 3.11093i) q^{97} -1.30233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9} + 10 q^{11} + 16 q^{19} - 4 q^{21} + 16 q^{29} - 24 q^{31} - 44 q^{39} + 26 q^{41} - 28 q^{49} - 28 q^{51} - 18 q^{59} + 32 q^{61} + 28 q^{69} - 2 q^{71} + 48 q^{79} - 6 q^{81} + 74 q^{89}+ \cdots - 40 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 + 10 * q^11 + 16 * q^19 - 4 * q^21 + 16 * q^29 - 24 * q^31 - 44 * q^39 + 26 * q^41 - 28 * q^49 - 28 * q^51 - 18 * q^59 + 32 * q^61 + 28 * q^69 - 2 * q^71 + 48 * q^79 - 6 * q^81 + 74 * q^89 + 64 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

$n$	$251$	$377$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.713605	−	2.19625i	0.412000	−	1.26801i	−0.502907	−	0.864341i	$-0.667736\pi$
$3$	0.713605	−	2.19625i	0.412000	−	1.26801i	0.914907	−	0.403665i	$-0.132264\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.21139			−1.59175			−0.795877	−	0.605458i	$-0.792990\pi$
$7$	−4.21139			−1.59175			−0.795877	+	0.605458i	$0.792990\pi$
$8$		0			0
$9$	−1.88723	−	1.37116i	−0.629078	−	0.457052i
$10$		0			0
$11$	0.451659	−	0.328150i	0.136180	−	0.0989409i	−0.517610	−	0.855617i	$-0.673178\pi$
$11$	0.451659	−	0.328150i	0.136180	−	0.0989409i	0.653790	+	0.756676i	$0.273178\pi$
$12$		0			0
$13$	−3.26033	−	2.36877i	−0.904253	−	0.656978i	0.0353017	−	0.999377i	$-0.488761\pi$
$13$	−3.26033	−	2.36877i	−0.904253	−	0.656978i	−0.939555	+	0.342398i	$0.888761\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.22440	−	3.76832i	−0.296961	−	0.913953i	−0.982556	−	0.185969i	$-0.940458\pi$
$17$	−1.22440	−	3.76832i	−0.296961	−	0.913953i	0.685594	−	0.727984i	$-0.259542\pi$
$18$		0			0
$19$	−2.14177	−	6.59168i	−0.491355	−	1.51223i	−0.822561	−	0.568676i	$-0.807456\pi$
$19$	−2.14177	−	6.59168i	−0.491355	−	1.51223i	0.331207	−	0.943558i	$-0.392544\pi$
$20$		0			0
$21$	−3.00527	+	9.24926i	−0.655803	+	2.01835i
$22$		0			0
$23$	0.308467	−	0.224115i	0.0643199	−	0.0467311i	−0.555161	−	0.831743i	$-0.687343\pi$
$23$	0.308467	−	0.224115i	0.0643199	−	0.0467311i	0.619481	+	0.785012i	$0.287343\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.24659	−	0.905698i	0.239906	−	0.174302i
$28$		0			0
$29$	−2.48680	+	7.65359i	−0.461788	+	1.42124i	0.401190	+	0.915995i	$0.368597\pi$
$29$	−2.48680	+	7.65359i	−0.461788	+	1.42124i	−0.862978	+	0.505242i	$0.831403\pi$
$30$		0			0
$31$	−0.0767462	−	0.236201i	−0.0137840	−	0.0424229i	0.943928	−	0.330152i	$-0.107100\pi$
$31$	−0.0767462	−	0.236201i	−0.0137840	−	0.0424229i	−0.957712	+	0.287729i	$0.907100\pi$
$32$		0			0
$33$	−0.398393	−	1.22613i	−0.0693513	−	0.213441i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.80503	+	4.21760i	0.954342	+	0.693370i	0.951830	−	0.306627i	$-0.0992004\pi$
$37$	5.80503	+	4.21760i	0.954342	+	0.693370i	0.00251186	+	0.999997i	$0.499200\pi$
$38$		0			0
$39$	−7.52900	+	5.47014i	−1.20560	+	0.875923i
$40$		0			0
$41$	3.68773	+	2.67929i	0.575926	+	0.418435i	0.837253	−	0.546815i	$-0.184160\pi$
$41$	3.68773	+	2.67929i	0.575926	+	0.418435i	−0.261327	+	0.965250i	$0.584160\pi$
$42$		0			0
$43$	−0.207272			−0.0316086			−0.0158043	−	0.999875i	$-0.505031\pi$
$43$	−0.207272			−0.0316086			−0.0158043	+	0.999875i	$0.505031\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.86117	−	8.80576i	0.417344	−	1.28445i	−0.492794	−	0.870146i	$-0.664024\pi$
$47$	2.86117	−	8.80576i	0.417344	−	1.28445i	0.910138	−	0.414306i	$-0.135976\pi$
$48$		0			0
$49$	10.7358			1.53368
$50$		0			0
$51$	−9.14992			−1.28125
$52$		0			0
$53$	−0.729597	+	2.24547i	−0.100218	+	0.308439i	−0.988578	−	0.150708i	$-0.951845\pi$
$53$	−0.729597	+	2.24547i	−0.100218	+	0.308439i	0.888361	+	0.459147i	$0.151845\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−16.0054			−2.11996
$58$		0			0
$59$	−2.93557	−	2.13282i	−0.382179	−	0.277669i	0.380064	−	0.924960i	$-0.375902\pi$
$59$	−2.93557	−	2.13282i	−0.382179	−	0.277669i	−0.762243	+	0.647291i	$0.775902\pi$
$60$		0			0
$61$	3.15785	−	2.29431i	0.404321	−	0.293757i	−0.366977	−	0.930230i	$-0.619607\pi$
$61$	3.15785	−	2.29431i	0.404321	−	0.293757i	0.771299	+	0.636473i	$0.219607\pi$
$62$		0			0
$63$	7.94787	+	5.77447i	1.00134	+	0.727514i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.13234	+	6.56267i	0.260507	+	0.801758i	0.992695	+	0.120655i	$0.0384995\pi$
$67$	2.13234	+	6.56267i	0.260507	+	0.801758i	−0.732187	+	0.681103i	$0.761501\pi$
$68$		0			0
$69$	−0.272088	−	0.837401i	−0.0327556	−	0.100811i
$70$		0			0
$71$	4.44084	−	13.6675i	0.527031	−	1.62203i	−0.233233	−	0.972421i	$-0.574931\pi$
$71$	4.44084	−	13.6675i	0.527031	−	1.62203i	0.760264	−	0.649614i	$-0.225069\pi$
$72$		0			0
$73$	−1.82346	+	1.32482i	−0.213420	+	0.155058i	−0.689360	−	0.724419i	$-0.742108\pi$
$73$	−1.82346	+	1.32482i	−0.213420	+	0.155058i	0.475940	+	0.879478i	$0.342108\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.90211	+	1.38197i	−0.216766	+	0.157490i
$78$		0			0
$79$	2.35970	−	7.26242i	0.265487	−	0.817086i	−0.726093	−	0.687596i	$-0.758666\pi$
$79$	2.35970	−	7.26242i	0.265487	−	0.817086i	0.991581	−	0.129490i	$-0.0413341\pi$
$80$		0			0
$81$	−3.26215	−	10.0399i	−0.362461	−	1.11554i
$82$		0			0
$83$	−2.34809	−	7.22667i	−0.257736	−	0.793230i	−0.993278	−	0.115751i	$-0.963073\pi$
$83$	−2.34809	−	7.22667i	−0.257736	−	0.793230i	0.735542	−	0.677479i	$-0.236927\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	15.0346	+	10.9233i	1.61188	+	1.17110i
$88$		0			0
$89$	12.9713	−	9.42417i	1.37495	−	0.998960i	0.377619	−	0.925961i	$-0.376743\pi$
$89$	12.9713	−	9.42417i	1.37495	−	0.998960i	0.997332	−	0.0729990i	$-0.0232570\pi$
$90$		0			0
$91$	13.7305	+	9.97581i	1.43935	+	1.04575i
$92$		0			0
$93$	−0.573522			−0.0594715
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.01080	−	3.11093i	0.102631	−	0.315867i	−0.886536	−	0.462660i	$-0.846895\pi$
$97$	1.01080	−	3.11093i	0.102631	−	0.315867i	0.989167	+	0.146793i	$0.0468951\pi$
$98$		0			0
$99$	−1.30233			−0.130889
$100$		0			0
$101$	−9.34504			−0.929866			−0.464933	−	0.885346i	$-0.653922\pi$
$101$	−9.34504			−0.929866			−0.464933	+	0.885346i	$0.653922\pi$
$102$		0			0
$103$	−1.85114	+	5.69721i	−0.182398	+	0.561363i	−0.999894	−	0.0145714i	$-0.995362\pi$
$103$	−1.85114	+	5.69721i	−0.182398	+	0.561363i	0.817496	+	0.575934i	$0.195362\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.60078			0.541448			0.270724	−	0.962657i	$-0.412737\pi$
$107$	5.60078			0.541448			0.270724	+	0.962657i	$0.412737\pi$
$108$		0			0
$109$	11.1078	+	8.07030i	1.06394	+	0.772994i	0.974812	−	0.223026i	$-0.0715936\pi$
$109$	11.1078	+	8.07030i	1.06394	+	0.772994i	0.0891229	+	0.996021i	$0.471594\pi$
$110$		0			0
$111$	13.4054	−	9.73960i	1.27239	−	0.924442i
$112$		0			0
$113$	−3.28252	−	2.38489i	−0.308793	−	0.224351i	0.422585	−	0.906323i	$-0.361123\pi$
$113$	−3.28252	−	2.38489i	−0.308793	−	0.224351i	−0.731378	+	0.681972i	$0.761123\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.90506	+	8.94084i	0.268572	+	0.826581i
$118$		0			0
$119$	5.15643	+	15.8699i	0.472689	+	1.45479i
$120$		0			0
$121$	−3.30287	+	10.1652i	−0.300261	+	0.924109i
$122$		0			0
$123$	8.51598	−	6.18722i	0.767860	−	0.557883i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.34059	+	2.42708i	−0.296430	+	0.215369i	−0.726052	−	0.687640i	$-0.758647\pi$
$127$	−3.34059	+	2.42708i	−0.296430	+	0.215369i	0.429622	+	0.903009i	$0.358647\pi$
$128$		0			0
$129$	−0.147910	+	0.455220i	−0.0130228	+	0.0400799i
$130$		0			0
$131$	−4.07116	−	12.5298i	−0.355699	−	1.09473i	−0.955603	−	0.294657i	$-0.904794\pi$
$131$	−4.07116	−	12.5298i	−0.355699	−	1.09473i	0.599904	−	0.800072i	$-0.295206\pi$
$132$		0			0
$133$	9.01981	+	27.7601i	0.782116	+	2.40711i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.34201	+	0.975024i	0.114655	+	0.0833020i	0.643635	−	0.765332i	$-0.277425\pi$
$137$	1.34201	+	0.975024i	0.114655	+	0.0833020i	−0.528980	+	0.848634i	$0.677425\pi$
$138$		0			0
$139$	0.567399	−	0.412240i	0.0481262	−	0.0349657i	−0.563462	−	0.826142i	$-0.690531\pi$
$139$	0.567399	−	0.412240i	0.0481262	−	0.0349657i	0.611588	+	0.791176i	$0.290531\pi$
$140$		0			0
$141$	−17.2979	−	12.5677i	−1.45675	−	1.05839i
$142$		0			0
$143$	−2.24987			−0.188144
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.66111	−	23.5785i	0.631878	−	1.94472i
$148$		0			0
$149$	−18.3234			−1.50111			−0.750556	−	0.660807i	$-0.770214\pi$
$149$	−18.3234			−1.50111			−0.750556	+	0.660807i	$0.770214\pi$
$150$		0			0
$151$	0.0521578			0.00424454			0.00212227	−	0.999998i	$-0.499324\pi$
$151$	0.0521578			0.00424454			0.00212227	+	0.999998i	$0.499324\pi$
$152$		0			0
$153$	−2.85622	+	8.79055i	−0.230912	+	0.710674i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.18979			−0.254573			−0.127287	−	0.991866i	$-0.540627\pi$
$157$	−3.18979			−0.254573			−0.127287	+	0.991866i	$0.540627\pi$
$158$		0			0
$159$	4.41097	+	3.20475i	0.349812	+	0.254154i
$160$		0			0
$161$	−1.29908	+	0.943834i	−0.102382	+	0.0743845i
$162$		0			0
$163$	9.47378	+	6.88310i	0.742043	+	0.539126i	0.893350	−	0.449361i	$-0.148348\pi$
$163$	9.47378	+	6.88310i	0.742043	+	0.539126i	−0.151307	+	0.988487i	$0.548348\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.59596	+	17.2226i	0.433028	+	1.33272i	0.895094	+	0.445878i	$0.147109\pi$
$167$	5.59596	+	17.2226i	0.433028	+	1.33272i	−0.462065	+	0.886846i	$0.652891\pi$
$168$		0			0
$169$	1.00147	+	3.08221i	0.0770362	+	0.237093i
$170$		0			0
$171$	−4.99620	+	15.3767i	−0.382069	+	1.17589i
$172$		0			0
$173$	−13.9787	+	10.1561i	−1.06278	+	0.772154i	−0.974600	−	0.223951i	$-0.928104\pi$
$173$	−13.9787	+	10.1561i	−1.06278	+	0.772154i	−0.0881782	+	0.996105i	$0.528104\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.77905	+	4.92527i	−0.509544	+	0.370206i
$178$		0			0
$179$	1.23318	−	3.79534i	0.0921722	−	0.283677i	−0.894334	−	0.447399i	$-0.852350\pi$
$179$	1.23318	−	3.79534i	0.0921722	−	0.283677i	0.986506	+	0.163723i	$0.0523502\pi$
$180$		0			0
$181$	0.544543	+	1.67593i	0.0404756	+	0.124571i	0.969253	−	0.246068i	$-0.0791387\pi$
$181$	0.544543	+	1.67593i	0.0404756	+	0.124571i	−0.928777	+	0.370639i	$0.879139\pi$
$182$		0			0
$183$	−2.78543	−	8.57267i	−0.205905	−	0.633710i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.78959	−	1.30021i	−0.130868	−	0.0950809i
$188$		0			0
$189$	−5.24986	+	3.81425i	−0.381871	+	0.277446i
$190$		0			0
$191$	6.03752	+	4.38652i	0.436860	+	0.317397i	0.784386	−	0.620273i	$-0.212978\pi$
$191$	6.03752	+	4.38652i	0.436860	+	0.317397i	−0.347526	+	0.937670i	$0.612978\pi$
$192$		0			0
$193$	15.6167			1.12411			0.562057	−	0.827099i	$-0.310010\pi$
$193$	15.6167			1.12411			0.562057	+	0.827099i	$0.310010\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.67578	−	23.6236i	0.546876	−	1.68311i	−0.169610	−	0.985511i	$-0.554251\pi$
$197$	7.67578	−	23.6236i	0.546876	−	1.68311i	0.716486	−	0.697601i	$-0.245749\pi$
$198$		0			0
$199$	−4.27124			−0.302780			−0.151390	−	0.988474i	$-0.548375\pi$
$199$	−4.27124			−0.302780			−0.151390	+	0.988474i	$0.548375\pi$
$200$		0			0
$201$	15.9349			1.12396
$202$		0			0
$203$	10.4729	−	32.2322i	0.735053	−	2.26226i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.889446			−0.0618208
$208$		0			0
$209$	−3.13041	−	2.27437i	−0.216535	−	0.157322i
$210$		0			0
$211$	−6.77130	+	4.91963i	−0.466155	+	0.338682i	−0.795941	−	0.605374i	$-0.793023\pi$
$211$	−6.77130	+	4.91963i	−0.466155	+	0.338682i	0.329786	+	0.944056i	$0.393023\pi$
$212$		0			0
$213$	−26.8483	−	19.5064i	−1.83961	−	1.33656i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.323208	+	0.994732i	0.0219408	+	0.0675268i
$218$		0			0
$219$	1.60841	+	4.95017i	0.108686	+	0.334501i
$220$		0			0
$221$	−4.93433	+	15.1863i	−0.331919	+	1.02154i
$222$		0			0
$223$	−7.18669	+	5.22143i	−0.481256	+	0.349653i	−0.801812	−	0.597577i	$-0.796130\pi$
$223$	−7.18669	+	5.22143i	−0.481256	+	0.349653i	0.320556	+	0.947230i	$0.396130\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.17991	+	6.66960i	−0.609292	+	0.442677i	−0.849165	−	0.528128i	$-0.822894\pi$
$227$	−9.17991	+	6.66960i	−0.609292	+	0.442677i	0.239873	+	0.970804i	$0.422894\pi$
$228$		0			0
$229$	8.24697	−	25.3816i	0.544975	−	1.67726i	−0.176074	−	0.984377i	$-0.556340\pi$
$229$	8.24697	−	25.3816i	0.544975	−	1.67726i	0.721049	−	0.692884i	$-0.243660\pi$
$230$		0			0
$231$	1.67779	+	5.16369i	0.110390	+	0.339746i
$232$		0			0
$233$	−5.99693	−	18.4566i	−0.392872	−	1.20913i	−0.930607	−	0.366021i	$-0.880720\pi$
$233$	−5.99693	−	18.4566i	−0.392872	−	1.20913i	0.537735	−	0.843114i	$-0.319280\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−14.2662	−	10.3650i	−0.926690	−	0.673279i
$238$		0			0
$239$	3.88485	−	2.82251i	0.251290	−	0.182573i	−0.455008	−	0.890487i	$-0.650364\pi$
$239$	3.88485	−	2.82251i	0.251290	−	0.182573i	0.706298	+	0.707914i	$0.250364\pi$
$240$		0			0
$241$	16.3125	+	11.8517i	1.05078	+	0.763438i	0.972361	−	0.233482i	$-0.0750120\pi$
$241$	16.3125	+	11.8517i	1.05078	+	0.763438i	0.0784214	+	0.996920i	$0.475012\pi$
$242$		0			0
$243$	−19.7553			−1.26730
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.63130	+	26.5644i	−0.549196	+	1.69025i
$248$		0			0
$249$	−17.5472			−1.11201
$250$		0			0
$251$	−13.8723			−0.875614			−0.437807	−	0.899069i	$-0.644245\pi$
$251$	−13.8723			−0.875614			−0.437807	+	0.899069i	$0.644245\pi$
$252$		0			0
$253$	0.0657790	−	0.202447i	0.00413549	−	0.0127277i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.27079			−0.266405			−0.133202	−	0.991089i	$-0.542526\pi$
$257$	−4.27079			−0.266405			−0.133202	+	0.991089i	$0.542526\pi$
$258$		0			0
$259$	−24.4472	−	17.7620i	−1.51908	−	1.10367i
$260$		0			0
$261$	15.1874	−	11.0343i	0.940079	−	0.683008i
$262$		0			0
$263$	9.47939	+	6.88718i	0.584524	+	0.424682i	0.840352	−	0.542041i	$-0.182348\pi$
$263$	9.47939	+	6.88718i	0.584524	+	0.424682i	−0.255828	+	0.966722i	$0.582348\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−11.4415	−	35.2133i	−0.700208	−	2.15502i
$268$		0			0
$269$	−3.26685	−	10.0543i	−0.199184	−	0.613024i	−0.999902	−	0.0139833i	$-0.995549\pi$
$269$	−3.26685	−	10.0543i	−0.199184	−	0.613024i	0.800719	−	0.599041i	$-0.204451\pi$
$270$		0			0
$271$	4.02897	−	12.3999i	0.244742	−	0.753239i	−0.750936	−	0.660375i	$-0.770398\pi$
$271$	4.02897	−	12.3999i	0.244742	−	0.753239i	0.995679	−	0.0928649i	$-0.0296025\pi$
$272$		0			0
$273$	31.7075	−	23.0369i	1.91903	−	1.39426i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−10.1326	+	7.36175i	−0.608808	+	0.442325i	−0.848994	−	0.528402i	$-0.822791\pi$
$277$	−10.1326	+	7.36175i	−0.608808	+	0.442325i	0.240187	+	0.970727i	$0.422791\pi$
$278$		0			0
$279$	−0.179030	+	0.550997i	−0.0107182	+	0.0329873i
$280$		0			0
$281$	0.591748	+	1.82121i	0.0353007	+	0.108645i	0.967154	−	0.254190i	$-0.0818089\pi$
$281$	0.591748	+	1.82121i	0.0353007	+	0.108645i	−0.931853	+	0.362835i	$0.881809\pi$
$282$		0			0
$283$	−2.68131	−	8.25224i	−0.159388	−	0.490545i	0.839191	−	0.543836i	$-0.183029\pi$
$283$	−2.68131	−	8.25224i	−0.159388	−	0.490545i	−0.998579	+	0.0532916i	$0.983029\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−15.5304	−	11.2835i	−0.916733	−	0.666046i
$288$		0			0
$289$	1.05219	−	0.764461i	0.0618935	−	0.0449683i
$290$		0			0
$291$	−6.11107	−	4.43995i	−0.358237	−	0.260274i
$292$		0			0
$293$	18.1632			1.06110			0.530551	−	0.847653i	$-0.321985\pi$
$293$	18.1632			1.06110			0.530551	+	0.847653i	$0.321985\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.265828	−	0.818134i	0.0154249	−	0.0474730i
$298$		0			0
$299$	−1.53658			−0.0888628
$300$		0			0
$301$	0.872901			0.0503132
$302$		0			0
$303$	−6.66867	+	20.5240i	−0.383105	+	1.17908i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−23.4255			−1.33696			−0.668481	−	0.743729i	$-0.733055\pi$
$307$	−23.4255			−1.33696			−0.668481	+	0.743729i	$0.733055\pi$
$308$		0			0
$309$	11.1915	+	8.13112i	0.636664	+	0.462563i
$310$		0			0
$311$	−18.8884	+	13.7232i	−1.07106	+	0.778171i	−0.976103	−	0.217310i	$-0.930272\pi$
$311$	−18.8884	+	13.7232i	−1.07106	+	0.778171i	−0.0949585	+	0.995481i	$0.530272\pi$
$312$		0			0
$313$	−4.71689	−	3.42702i	−0.266614	−	0.193707i	0.446444	−	0.894812i	$-0.352690\pi$
$313$	−4.71689	−	3.42702i	−0.266614	−	0.193707i	−0.713058	+	0.701105i	$0.752690\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.31233	+	7.11662i	0.129873	+	0.399709i	0.994757	−	0.102263i	$-0.0326082\pi$
$317$	2.31233	+	7.11662i	0.129873	+	0.399709i	−0.864884	+	0.501972i	$0.832608\pi$
$318$		0			0
$319$	1.38834	+	4.27286i	0.0777319	+	0.239234i
$320$		0			0
$321$	3.99674	−	12.3007i	0.223077	−	0.686559i
$322$		0			0
$323$	−22.2172	+	16.1417i	−1.23620	+	0.898150i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	25.6510	−	18.6365i	1.41850	−	1.03060i
$328$		0			0
$329$	−12.0495	+	37.0845i	−0.664309	+	2.04453i
$330$		0			0
$331$	9.33063	+	28.7167i	0.512858	+	1.57841i	0.787146	+	0.616766i	$0.211558\pi$
$331$	9.33063	+	28.7167i	0.512858	+	1.57841i	−0.274288	+	0.961647i	$0.588442\pi$
$332$		0			0
$333$	−5.17246	−	15.9192i	−0.283449	−	0.872367i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	18.0708	+	13.1292i	0.984379	+	0.715193i	0.958683	−	0.284477i	$-0.0918199\pi$
$337$	18.0708	+	13.1292i	0.984379	+	0.715193i	0.0256956	+	0.999670i	$0.491820\pi$
$338$		0			0
$339$	−7.58023	+	5.50736i	−0.411702	+	0.299119i
$340$		0			0
$341$	−0.112172	−	0.0814980i	−0.00607447	−	0.00441336i
$342$		0			0
$343$	−15.7328			−0.849494
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.45054	+	10.6197i	−0.185235	+	0.570094i	−0.999952	−	0.00976387i	$-0.996892\pi$
$347$	−3.45054	+	10.6197i	−0.185235	+	0.570094i	0.814717	+	0.579858i	$0.196892\pi$
$348$		0			0
$349$	4.15360			0.222337			0.111168	−	0.993802i	$-0.464541\pi$
$349$	4.15360			0.222337			0.111168	+	0.993802i	$0.464541\pi$
$350$		0			0
$351$	−6.20967			−0.331448
$352$		0			0
$353$	−1.35856	+	4.18122i	−0.0723088	+	0.222544i	−0.980679	−	0.195623i	$-0.937327\pi$
$353$	−1.35856	+	4.18122i	−0.0723088	+	0.222544i	0.908370	+	0.418167i	$0.137327\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	38.5339			2.03943
$358$		0			0
$359$	0.385816	+	0.280311i	0.0203626	+	0.0147943i	0.597920	−	0.801556i	$-0.295994\pi$
$359$	0.385816	+	0.280311i	0.0203626	+	0.0147943i	−0.577557	+	0.816350i	$0.695994\pi$
$360$		0			0
$361$	−23.4917	+	17.0677i	−1.23641	+	0.898302i
$362$		0			0
$363$	19.9684	+	14.5079i	1.04807	+	0.761466i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.813414	+	2.50343i	0.0424599	+	0.130678i	0.970039	−	0.242948i	$-0.0781144\pi$
$367$	0.813414	+	2.50343i	0.0424599	+	0.130678i	−0.927579	+	0.373626i	$0.878114\pi$
$368$		0			0
$369$	−3.28588	−	10.1129i	−0.171056	−	0.526456i
$370$		0			0
$371$	3.07261	−	9.45653i	0.159522	−	0.490959i
$372$		0			0
$373$	20.2755	−	14.7310i	1.04983	−	0.762743i	0.0776460	−	0.996981i	$-0.475260\pi$
$373$	20.2755	−	14.7310i	1.04983	−	0.762743i	0.972179	+	0.234238i	$0.0752596\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	26.2374	−	19.0626i	1.35129	−	0.981773i
$378$		0			0
$379$	−0.674898	+	2.07712i	−0.0346672	+	0.106695i	−0.966893	−	0.255183i	$-0.917864\pi$
$379$	−0.674898	+	2.07712i	−0.0346672	+	0.106695i	0.932226	+	0.361878i	$0.117864\pi$
$380$		0			0
$381$	2.94662	+	9.06876i	0.150960	+	0.464607i
$382$		0			0
$383$	7.37534	+	22.6990i	0.376862	+	1.15986i	0.942214	+	0.335013i	$0.108741\pi$
$383$	7.37534	+	22.6990i	0.376862	+	1.15986i	−0.565351	+	0.824850i	$0.691259\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.391170	+	0.284202i	0.0198843	+	0.0144468i
$388$		0			0
$389$	−16.1638	+	11.7437i	−0.819537	+	0.595429i	−0.916580	−	0.399852i	$-0.869062\pi$
$389$	−16.1638	+	11.7437i	−0.819537	+	0.595429i	0.0970428	+	0.995280i	$0.469062\pi$
$390$		0			0
$391$	−1.22222	−	0.887998i	−0.0618106	−	0.0449080i
$392$		0			0
$393$	−30.4237			−1.53467
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.21244	+	16.0422i	−0.261605	+	0.805137i	0.730851	+	0.682537i	$0.239123\pi$
$397$	−5.21244	+	16.0422i	−0.261605	+	0.805137i	−0.992456	+	0.122600i	$0.960877\pi$
$398$		0			0
$399$	67.4047			3.37446
$400$		0			0
$401$	5.14817			0.257087			0.128544	−	0.991704i	$-0.458970\pi$
$401$	5.14817			0.257087			0.128544	+	0.991704i	$0.458970\pi$
$402$		0			0
$403$	−0.309287	+	0.951886i	−0.0154067	+	0.0474168i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.00590			0.198565
$408$		0			0
$409$	4.36350	+	3.17027i	0.215761	+	0.156760i	0.690417	−	0.723412i	$-0.257427\pi$
$409$	4.36350	+	3.17027i	0.215761	+	0.156760i	−0.474655	+	0.880172i	$0.657427\pi$
$410$		0			0
$411$	3.09906	−	2.25160i	0.152865	−	0.111063i
$412$		0			0
$413$	12.3628	+	8.98213i	0.608336	+	0.441982i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.500482	−	1.54033i	−0.0245087	−	0.0754301i
$418$		0			0
$419$	−7.67959	−	23.6354i	−0.375173	−	1.15466i	−0.943362	−	0.331765i	$-0.892356\pi$
$419$	−7.67959	−	23.6354i	−0.375173	−	1.15466i	0.568190	−	0.822898i	$-0.307644\pi$
$420$		0			0
$421$	10.4110	−	32.0418i	0.507401	−	1.56162i	−0.289295	−	0.957240i	$-0.593421\pi$
$421$	10.4110	−	32.0418i	0.507401	−	1.56162i	0.796696	−	0.604380i	$-0.206579\pi$
$422$		0			0
$423$	−17.4738	+	12.6954i	−0.849603	+	0.617273i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−13.2989	+	9.66224i	−0.643581	+	0.467589i
$428$		0			0
$429$	−1.60552	+	4.94128i	−0.0775152	+	0.238567i
$430$		0			0
$431$	−5.55833	−	17.1068i	−0.267736	−	0.824005i	−0.991051	−	0.133487i	$-0.957383\pi$
$431$	−5.55833	−	17.1068i	−0.267736	−	0.824005i	0.723315	−	0.690518i	$-0.242617\pi$
$432$		0			0
$433$	11.0707	+	34.0721i	0.532024	+	1.63740i	0.749994	+	0.661445i	$0.230057\pi$
$433$	11.0707	+	34.0721i	0.532024	+	1.63740i	−0.217970	+	0.975956i	$0.569943\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.13796	−	1.55332i	−0.102272	−	0.0743052i
$438$		0			0
$439$	3.34595	−	2.43097i	0.159693	−	0.116024i	−0.505069	−	0.863079i	$-0.668533\pi$
$439$	3.34595	−	2.43097i	0.159693	−	0.116024i	0.664762	+	0.747055i	$0.268533\pi$
$440$		0			0
$441$	−20.2609	−	14.7204i	−0.964806	−	0.700973i
$442$		0			0
$443$	24.8979			1.18293			0.591467	−	0.806329i	$-0.298549\pi$
$443$	24.8979			1.18293			0.591467	+	0.806329i	$0.298549\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.0757	+	40.2428i	−0.618458	+	1.90342i
$448$		0			0
$449$	−0.385885			−0.0182111			−0.00910553	−	0.999959i	$-0.502898\pi$
$449$	−0.385885			−0.0182111			−0.00910553	+	0.999959i	$0.502898\pi$
$450$		0			0
$451$	2.54481			0.119830
$452$		0			0
$453$	0.0372200	−	0.114552i	0.00174875	−	0.00538210i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	29.8819			1.39781			0.698907	−	0.715212i	$-0.253670\pi$
$457$	29.8819			1.39781			0.698907	+	0.715212i	$0.253670\pi$
$458$		0			0
$459$	−4.93929	−	3.58860i	−0.230546	−	0.167502i
$460$		0			0
$461$	16.1468	−	11.7313i	0.752029	−	0.546381i	−0.144426	−	0.989516i	$-0.546134\pi$
$461$	16.1468	−	11.7313i	0.752029	−	0.546381i	0.896455	+	0.443134i	$0.146134\pi$
$462$		0			0
$463$	−20.1865	−	14.6664i	−0.938146	−	0.681603i	0.00982748	−	0.999952i	$-0.496872\pi$
$463$	−20.1865	−	14.6664i	−0.938146	−	0.681603i	−0.947974	+	0.318349i	$0.896872\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.6896	−	35.9768i	−0.540928	−	1.66481i	−0.730479	−	0.682935i	$-0.760703\pi$
$467$	−11.6896	−	35.9768i	−0.540928	−	1.66481i	0.189551	−	0.981871i	$-0.439297\pi$
$468$		0			0
$469$	−8.98012	−	27.6380i	−0.414663	−	1.27620i
$470$		0			0
$471$	−2.27625	+	7.00558i	−0.104884	+	0.322800i
$472$		0			0
$473$	−0.0936162	+	0.0680161i	−0.00430448	+	0.00312739i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.45580	−	3.23733i	0.204017	−	0.148227i
$478$		0			0
$479$	−3.70950	+	11.4167i	−0.169491	+	0.521641i	−0.999339	−	0.0363490i	$-0.988427\pi$
$479$	−3.70950	+	11.4167i	−0.169491	+	0.521641i	0.829848	+	0.557990i	$0.188427\pi$
$480$		0			0
$481$	−8.93580	−	27.5016i	−0.407437	−	1.25396i
$482$		0			0
$483$	1.14587	+	3.52662i	0.0521388	+	0.160467i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−10.6428	−	7.73245i	−0.482271	−	0.350391i	0.319933	−	0.947440i	$-0.396340\pi$
$487$	−10.6428	−	7.73245i	−0.482271	−	0.350391i	−0.802204	+	0.597050i	$0.796340\pi$
$488$		0			0
$489$	21.8776	−	15.8950i	0.989337	−	0.718795i
$490$		0			0
$491$	−15.2130	−	11.0529i	−0.686554	−	0.498810i	0.188972	−	0.981983i	$-0.439485\pi$
$491$	−15.2130	−	11.0529i	−0.686554	−	0.498810i	−0.875525	+	0.483172i	$0.839485\pi$
$492$		0			0
$493$	31.8861			1.43608
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.7021	+	57.5592i	−0.838904	+	2.58188i
$498$		0			0
$499$	23.3350			1.04462			0.522309	−	0.852756i	$-0.325071\pi$
$499$	23.3350			1.04462			0.522309	+	0.852756i	$0.325071\pi$
$500$		0			0
$501$	41.8184			1.86831
$502$		0			0
$503$	6.20170	−	19.0869i	0.276520	−	0.851041i	−0.712293	−	0.701882i	$-0.752343\pi$
$503$	6.20170	−	19.0869i	0.276520	−	0.851041i	0.988813	−	0.149159i	$-0.0476566\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7.48396			0.332374
$508$		0			0
$509$	31.0184	+	22.5362i	1.37487	+	0.998899i	0.997339	+	0.0729009i	$0.0232257\pi$
$509$	31.0184	+	22.5362i	1.37487	+	0.998899i	0.377528	+	0.925998i	$0.376774\pi$
$510$		0			0
$511$	7.67929	−	5.57933i	0.339712	−	0.246815i
$512$		0			0
$513$	−8.63997	−	6.27730i	−0.381464	−	0.277150i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.59734	−	4.91610i	−0.0702508	−	0.216210i
$518$		0			0
$519$	12.3301	+	37.9481i	0.541231	+	1.66574i
$520$		0			0
$521$	7.81320	−	24.0466i	0.342303	−	1.05350i	−0.620709	−	0.784041i	$-0.713155\pi$
$521$	7.81320	−	24.0466i	0.342303	−	1.05350i	0.963012	−	0.269458i	$-0.0868446\pi$
$522$		0			0
$523$	1.32615	−	0.963505i	0.0579885	−	0.0421311i	−0.558413	−	0.829563i	$-0.688590\pi$
$523$	1.32615	−	0.963505i	0.0579885	−	0.0421311i	0.616402	+	0.787432i	$0.288590\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.796112	+	0.578409i	−0.0346792	+	0.0251959i
$528$		0			0
$529$	−7.06247	+	21.7360i	−0.307064	+	0.945045i
$530$		0			0
$531$	2.61569	+	8.05026i	0.113511	+	0.349351i
$532$		0			0
$533$	−5.67659	−	17.4708i	−0.245880	−	0.756742i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−7.45551	−	5.41674i	−0.321729	−	0.233750i
$538$		0			0
$539$	4.84892	−	3.52295i	0.208858	−	0.151744i
$540$		0			0
$541$	−9.24601	−	6.71762i	−0.397517	−	0.288813i	0.371012	−	0.928628i	$-0.379011\pi$
$541$	−9.24601	−	6.71762i	−0.397517	−	0.288813i	−0.768529	+	0.639815i	$0.779011\pi$
$542$		0			0
$543$	4.06936			0.174633
$544$		0			0
$545$		0			0
$546$		0			0
$547$	5.69840	−	17.5379i	0.243646	−	0.749866i	−0.752210	−	0.658924i	$-0.771012\pi$
$547$	5.69840	−	17.5379i	0.243646	−	0.749866i	0.995856	−	0.0909424i	$-0.0289879\pi$
$548$		0			0
$549$	−9.10546			−0.388612
$550$		0			0
$551$	55.7762			2.37614
$552$		0			0
$553$	−9.93763	+	30.5849i	−0.422591	+	1.30060i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.1154			−0.428603			−0.214301	−	0.976768i	$-0.568747\pi$
$557$	−10.1154			−0.428603			−0.214301	+	0.976768i	$0.568747\pi$
$558$		0			0
$559$	0.675774	+	0.490979i	0.0285822	+	0.0207662i
$560$		0			0
$561$	−4.13265	+	3.00255i	−0.174481	+	0.126768i
$562$		0			0
$563$	6.78049	+	4.92632i	0.285764	+	0.207619i	0.721427	−	0.692490i	$-0.243486\pi$
$563$	6.78049	+	4.92632i	0.285764	+	0.207619i	−0.435664	+	0.900109i	$0.643486\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	13.7382	+	42.2817i	0.576949	+	1.77567i
$568$		0			0
$569$	−7.45871	−	22.9556i	−0.312685	−	0.962347i	−0.976697	−	0.214624i	$-0.931147\pi$
$569$	−7.45871	−	22.9556i	−0.312685	−	0.962347i	0.664011	−	0.747723i	$-0.268853\pi$
$570$		0			0
$571$	−10.4189	+	32.0662i	−0.436019	+	1.34193i	0.456019	+	0.889970i	$0.349275\pi$
$571$	−10.4189	+	32.0662i	−0.436019	+	1.34193i	−0.892038	+	0.451960i	$0.850725\pi$
$572$		0			0
$573$	13.9423	−	10.1297i	0.582448	−	0.423173i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	36.6270	−	26.6111i	1.52480	−	1.10783i	0.565762	−	0.824569i	$-0.308582\pi$
$577$	36.6270	−	26.6111i	1.52480	−	1.10783i	0.959041	−	0.283266i	$-0.0914179\pi$
$578$		0			0
$579$	11.1441	−	34.2982i	0.463135	−	1.42538i
$580$		0			0
$581$	9.88870	+	30.4343i	0.410253	+	1.26263i
$582$		0			0
$583$	0.407321	+	1.25360i	0.0168695	+	0.0519190i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22.7642	+	16.5392i	0.939581	+	0.682645i	0.948320	−	0.317316i	$-0.102782\pi$
$587$	22.7642	+	16.5392i	0.939581	+	0.682645i	−0.00873900	+	0.999962i	$0.502782\pi$
$588$		0			0
$589$	−1.39259	+	1.01177i	−0.0573805	+	0.0416894i
$590$		0			0
$591$	−46.4059	−	33.7159i	−1.90888	−	1.38689i
$592$		0			0
$593$	−1.52944			−0.0628064			−0.0314032	−	0.999507i	$-0.509998\pi$
$593$	−1.52944			−0.0628064			−0.0314032	+	0.999507i	$0.509998\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.04798	+	9.38072i	−0.124746	+	0.383927i
$598$		0			0
$599$	−17.0156			−0.695240			−0.347620	−	0.937635i	$-0.613010\pi$
$599$	−17.0156			−0.695240			−0.347620	+	0.937635i	$0.613010\pi$
$600$		0			0
$601$	−30.8970			−1.26031			−0.630157	−	0.776468i	$-0.717009\pi$
$601$	−30.8970			−1.26031			−0.630157	+	0.776468i	$0.717009\pi$
$602$		0			0
$603$	4.97422	−	15.3091i	0.202566	−	0.623433i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	29.5437			1.19914			0.599570	−	0.800322i	$-0.295338\pi$
$607$	29.5437			1.19914			0.599570	+	0.800322i	$0.295338\pi$
$608$		0			0
$609$	−63.3166	−	46.0022i	−2.56572	−	1.86410i
$610$		0			0
$611$	−30.1872	+	21.9323i	−1.22124	+	0.887284i
$612$		0			0
$613$	−4.99633	−	3.63004i	−0.201800	−	0.146616i	0.482296	−	0.876008i	$-0.339803\pi$
$613$	−4.99633	−	3.63004i	−0.201800	−	0.146616i	−0.684096	+	0.729392i	$0.739803\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.4205	−	41.3041i	−0.540289	−	1.66284i	−0.731934	−	0.681376i	$-0.761382\pi$
$617$	−13.4205	−	41.3041i	−0.540289	−	1.66284i	0.191644	−	0.981464i	$-0.438618\pi$
$618$		0			0
$619$	15.2560	+	46.9531i	0.613191	+	1.88721i	0.425429	+	0.904992i	$0.360123\pi$
$619$	15.2560	+	46.9531i	0.613191	+	1.88721i	0.187761	+	0.982215i	$0.439877\pi$
$620$		0			0
$621$	0.181551	−	0.558757i	0.00728539	−	0.0224221i
$622$		0			0
$623$	−54.6270	+	39.6888i	−2.18858	+	1.59010i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.22897	+	5.25215i	−0.288697	+	0.209751i
$628$		0			0
$629$	8.78560	−	27.0393i	0.350305	−	1.07813i
$630$		0			0
$631$	4.09306	+	12.5971i	0.162942	+	0.501484i	0.998879	−	0.0473418i	$-0.0150750\pi$
$631$	4.09306	+	12.5971i	0.162942	+	0.501484i	−0.835937	+	0.548826i	$0.815075\pi$
$632$		0			0
$633$	5.97272	+	18.3821i	0.237394	+	0.730624i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−35.0022	−	25.4306i	−1.38684	−	1.00760i
$638$		0			0
$639$	−27.1212	+	19.7047i	−1.07290	+	0.779506i
$640$		0			0
$641$	11.9102	+	8.65325i	0.470424	+	0.341783i	0.797606	−	0.603178i	$-0.206099\pi$
$641$	11.9102	+	8.65325i	0.470424	+	0.341783i	−0.327183	+	0.944961i	$0.606099\pi$
$642$		0			0
$643$	−27.1451			−1.07050			−0.535249	−	0.844695i	$-0.679782\pi$
$643$	−27.1451			−1.07050			−0.535249	+	0.844695i	$0.679782\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.712513	+	2.19289i	−0.0280118	+	0.0862114i	−0.964085	−	0.265594i	$-0.914432\pi$
$647$	−0.712513	+	2.19289i	−0.0280118	+	0.0862114i	0.936073	+	0.351805i	$0.114432\pi$
$648$		0			0
$649$	−2.02576			−0.0795182
$650$		0			0
$651$	2.41532			0.0946640
$652$		0			0
$653$	−3.48548	+	10.7272i	−0.136397	+	0.419788i	−0.995805	−	0.0915034i	$-0.970833\pi$
$653$	−3.48548	+	10.7272i	−0.136397	+	0.419788i	0.859407	+	0.511292i	$0.170833\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	5.25783			0.205127
$658$		0			0
$659$	37.1885	+	27.0190i	1.44866	+	1.05251i	0.986142	+	0.165902i	$0.0530537\pi$
$659$	37.1885	+	27.0190i	1.44866	+	1.05251i	0.462517	+	0.886610i	$0.346946\pi$
$660$		0			0
$661$	−20.3520	+	14.7866i	−0.791600	+	0.575131i	−0.908438	−	0.418020i	$-0.862724\pi$
$661$	−20.3520	+	14.7866i	−0.791600	+	0.575131i	0.116838	+	0.993151i	$0.462724\pi$
$662$		0			0
$663$	29.8318	+	21.6741i	1.15857	+	0.841750i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.948185	+	2.91821i	0.0367139	+	0.112994i
$668$		0			0
$669$	6.33912	+	19.5098i	0.245085	+	0.754293i
$670$		0			0
$671$	0.673395	−	2.07250i	0.0259961	−	0.0800078i
$672$		0			0
$673$	0.666024	−	0.483895i	0.0256733	−	0.0186528i	−0.574875	−	0.818242i	$-0.694949\pi$
$673$	0.666024	−	0.483895i	0.0256733	−	0.0186528i	0.600548	+	0.799589i	$0.294949\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.4158	+	14.1064i	−0.746210	+	0.542153i	−0.894650	−	0.446768i	$-0.852575\pi$
$677$	−19.4158	+	14.1064i	−0.746210	+	0.542153i	0.148440	+	0.988921i	$0.452575\pi$
$678$		0			0
$679$	−4.25688	+	13.1013i	−0.163364	+	0.502783i
$680$		0			0
$681$	8.09728	+	24.9209i	0.310288	+	0.954969i
$682$		0			0
$683$	−10.0159	−	30.8259i	−0.383249	−	1.17952i	−0.937742	−	0.347332i	$-0.887088\pi$
$683$	−10.0159	−	30.8259i	−0.383249	−	1.17952i	0.554493	−	0.832188i	$-0.312912\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−49.8592	−	36.2248i	−1.90225	−	1.38206i
$688$		0			0
$689$	7.69772	−	5.59272i	0.293260	−	0.213066i
$690$		0			0
$691$	17.4077	+	12.6474i	0.662221	+	0.481131i	0.867412	−	0.497590i	$-0.165782\pi$
$691$	17.4077	+	12.6474i	0.662221	+	0.481131i	−0.205192	+	0.978722i	$0.565782\pi$
$692$		0			0
$693$	5.48462			0.208344
$694$		0			0
$695$		0			0
$696$		0			0
$697$	5.58117	−	17.1771i	0.211402	−	0.650628i
$698$		0			0
$699$	−44.8149			−1.69505
$700$		0			0
$701$	−42.0612			−1.58863			−0.794314	−	0.607507i	$-0.792170\pi$
$701$	−42.0612			−1.58863			−0.794314	+	0.607507i	$0.792170\pi$
$702$		0			0
$703$	15.3681	−	47.2980i	0.579617	−	1.78388i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	39.3556			1.48012
$708$		0			0
$709$	−5.55211	−	4.03384i	−0.208514	−	0.151494i	0.478627	−	0.878018i	$-0.341135\pi$
$709$	−5.55211	−	4.03384i	−0.208514	−	0.151494i	−0.687141	+	0.726524i	$0.741135\pi$
$710$		0			0
$711$	−14.4112	+	10.4704i	−0.540463	+	0.392669i
$712$		0			0
$713$	−0.0766097	−	0.0556602i	−0.00286906	−	0.00208449i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.42669	−	10.5463i	−0.127972	−	0.393858i
$718$		0			0
$719$	−11.8881	−	36.5879i	−0.443353	−	1.36450i	−0.884280	−	0.466957i	$-0.845350\pi$
$719$	−11.8881	−	36.5879i	−0.443353	−	1.36450i	0.440927	−	0.897543i	$-0.354650\pi$
$720$		0			0
$721$	7.79585	−	23.9932i	0.290333	−	0.893552i
$722$		0			0
$723$	37.6701	−	27.3689i	1.40097	−	1.01786i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	7.92289	−	5.75632i	0.293844	−	0.213490i	−0.431089	−	0.902309i	$-0.641871\pi$
$727$	7.92289	−	5.75632i	0.293844	−	0.213490i	0.724933	+	0.688819i	$0.241871\pi$
$728$		0			0
$729$	−4.31106	+	13.2681i	−0.159669	+	0.491410i
$730$		0			0
$731$	0.253784	+	0.781066i	0.00938654	+	0.0288888i
$732$		0			0
$733$	−9.34010	−	28.7459i	−0.344984	−	1.06175i	−0.961592	−	0.274482i	$-0.911494\pi$
$733$	−9.34010	−	28.7459i	−0.344984	−	1.06175i	0.616608	−	0.787270i	$-0.288506\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.11663	+	2.26437i	0.114803	+	0.0834090i
$738$		0			0
$739$	−21.4657	+	15.5958i	−0.789629	+	0.573699i	−0.907853	−	0.419288i	$-0.862280\pi$
$739$	−21.4657	+	15.5958i	−0.789629	+	0.573699i	0.118224	+	0.992987i	$0.462280\pi$
$740$		0			0
$741$	52.1827	+	37.9130i	1.91698	+	1.39277i
$742$		0			0
$743$	1.43832			0.0527669			0.0263835	−	0.999652i	$-0.491601\pi$
$743$	1.43832			0.0527669			0.0263835	+	0.999652i	$0.491601\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−5.47750	+	16.8580i	−0.200411	+	0.616802i
$748$		0			0
$749$	−23.5871			−0.861852
$750$		0			0
$751$	34.4429			1.25684			0.628420	−	0.777874i	$-0.283702\pi$
$751$	34.4429			1.25684			0.628420	+	0.777874i	$0.283702\pi$
$752$		0			0
$753$	−9.89937	+	30.4671i	−0.360753	+	1.11028i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	11.5191			0.418668			0.209334	−	0.977844i	$-0.432870\pi$
$757$	11.5191			0.418668			0.209334	+	0.977844i	$0.432870\pi$
$758$		0			0
$759$	−0.397684	−	0.288934i	−0.0144350	−	0.0104877i
$760$		0			0
$761$	6.90432	−	5.01628i	0.250281	−	0.181840i	−0.455570	−	0.890200i	$-0.650565\pi$
$761$	6.90432	−	5.01628i	0.250281	−	0.181840i	0.705851	+	0.708360i	$0.250565\pi$
$762$		0			0
$763$	−46.7793	−	33.9871i	−1.69352	−	1.23042i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.51879	+	13.9074i	0.163164	+	0.502167i
$768$		0			0
$769$	10.0753	+	31.0086i	0.363325	+	1.11820i	0.951023	+	0.309119i	$0.100034\pi$
$769$	10.0753	+	31.0086i	0.363325	+	1.11820i	−0.587698	+	0.809080i	$0.699966\pi$
$770$		0			0
$771$	−3.04766	+	9.37973i	−0.109759	+	0.337803i
$772$		0			0
$773$	24.1403	−	17.5389i	0.868265	−	0.630832i	−0.0618555	−	0.998085i	$-0.519702\pi$
$773$	24.1403	−	17.5389i	0.868265	−	0.630832i	0.930121	+	0.367253i	$0.119702\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−56.4554	+	41.0173i	−2.02533	+	1.47149i
$778$		0			0
$779$	9.76277	−	30.0467i	0.349788	−	1.07654i
$780$		0			0
$781$	−2.47924	−	7.63032i	−0.0887142	−	0.273034i
$782$		0			0
$783$	3.83183	+	11.7932i	0.136938	+	0.421453i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−42.8324	−	31.1195i	−1.52681	−	1.10929i	−0.957980	−	0.286836i	$-0.907397\pi$
$787$	−42.8324	−	31.1195i	−1.52681	−	1.10929i	−0.568829	−	0.822456i	$-0.692603\pi$
$788$		0			0
$789$	21.8905	−	15.9044i	0.779323	−	0.566211i
$790$		0			0
$791$	13.8239	+	10.0437i	0.491523	+	0.357112i
$792$		0			0
$793$	−15.7303			−0.558601
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.11472	−	12.6638i	0.145751	−	0.448575i	−0.851356	−	0.524588i	$-0.824219\pi$
$797$	4.11472	−	12.6638i	0.145751	−	0.448575i	0.997107	+	0.0760136i	$0.0242192\pi$
$798$		0			0
$799$	−36.6862			−1.29786
$800$		0			0
$801$	−37.4018			−1.32153
$802$		0			0
$803$	−0.388843	+	1.19673i	−0.0137220	+	0.0422319i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−24.4131			−0.859382
$808$		0			0
$809$	18.5016	+	13.4422i	0.650483	+	0.472604i	0.863436	−	0.504459i	$-0.168308\pi$
$809$	18.5016	+	13.4422i	0.650483	+	0.472604i	−0.212953	+	0.977063i	$0.568308\pi$
$810$		0			0
$811$	31.8550	−	23.1440i	1.11858	−	0.812695i	0.134586	−	0.990902i	$-0.457030\pi$
$811$	31.8550	−	23.1440i	1.11858	−	0.812695i	0.983993	+	0.178207i	$0.0570296\pi$
$812$		0			0
$813$	−24.3582	−	17.6972i	−0.854278	−	0.620669i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.443927	+	1.36627i	0.0155311	+	0.0477997i
$818$		0			0
$819$	−12.2343	−	37.6534i	−0.427502	−	1.31571i
$820$		0			0
$821$	9.98859	−	30.7417i	0.348604	−	1.07289i	−0.611022	−	0.791614i	$-0.709241\pi$
$821$	9.98859	−	30.7417i	0.348604	−	1.07289i	0.959626	−	0.281279i	$-0.0907588\pi$
$822$		0			0
$823$	36.4053	−	26.4500i	1.26901	−	0.921989i	0.269847	−	0.962903i	$-0.413027\pi$
$823$	36.4053	−	26.4500i	1.26901	−	0.921989i	0.999163	+	0.0409138i	$0.0130269\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.75110	+	1.99879i	−0.0956652	+	0.0695048i	−0.634590	−	0.772849i	$-0.718831\pi$
$827$	−2.75110	+	1.99879i	−0.0956652	+	0.0695048i	0.538924	+	0.842354i	$0.318831\pi$
$828$		0			0
$829$	5.67397	−	17.4627i	0.197065	−	0.606504i	−0.802881	−	0.596139i	$-0.796701\pi$
$829$	5.67397	−	17.4627i	0.197065	−	0.606504i	0.999946	−	0.0103649i	$-0.00329931\pi$
$830$		0			0
$831$	8.93759	+	27.5071i	0.310041	+	0.954209i
$832$		0			0
$833$	−13.1449	−	40.4559i	−0.455445	−	1.40171i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.309597	−	0.224936i	−0.0107012	−	0.00777491i
$838$		0			0
$839$	30.6714	−	22.2840i	1.05889	−	0.769331i	0.0850097	−	0.996380i	$-0.472908\pi$
$839$	30.6714	−	22.2840i	1.05889	−	0.769331i	0.973883	+	0.227049i	$0.0729079\pi$
$840$		0			0
$841$	−28.9318	−	21.0202i	−0.997648	−	0.724834i
$842$		0			0
$843$	4.42212			0.152306
$844$		0			0
$845$		0			0
$846$		0			0
$847$	13.9097	−	42.8096i	0.477942	−	1.47095i
$848$		0			0
$849$	−20.0374			−0.687681
$850$		0			0
$851$	2.73589			0.0937851
$852$		0			0
$853$	0.559493	−	1.72194i	0.0191567	−	0.0589582i	−0.941021	−	0.338348i	$-0.890132\pi$
$853$	0.559493	−	1.72194i	0.0191567	−	0.0589582i	0.960178	+	0.279389i	$0.0901320\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−42.3384			−1.44625			−0.723126	−	0.690717i	$-0.757295\pi$
$857$	−42.3384			−1.44625			−0.723126	+	0.690717i	$0.757295\pi$
$858$		0			0
$859$	−30.4965	−	22.1570i	−1.04053	−	0.755988i	−0.0701401	−	0.997537i	$-0.522345\pi$
$859$	−30.4965	−	22.1570i	−1.04053	−	0.755988i	−0.970389	+	0.241549i	$0.922345\pi$
$860$		0			0
$861$	−35.8641	+	26.0568i	−1.22224	+	0.888012i
$862$		0			0
$863$	44.3111	+	32.1939i	1.50837	+	1.09589i	0.966895	+	0.255175i	$0.0821330\pi$
$863$	44.3111	+	32.1939i	1.50837	+	1.09589i	0.541473	+	0.840718i	$0.317867\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.928099	−	2.85640i	−0.0315199	−	0.0970083i
$868$		0			0
$869$	−1.31738	−	4.05448i	−0.0446891	−	0.137539i
$870$		0			0
$871$	8.59332	−	26.4475i	0.291173	−	0.896140i
$872$		0			0
$873$	−6.17319	+	4.48508i	−0.208931	+	0.151797i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.52127	+	1.83181i	−0.0851371	+	0.0618558i	−0.629540	−	0.776968i	$-0.716756\pi$
$877$	−2.52127	+	1.83181i	−0.0851371	+	0.0618558i	0.544402	+	0.838824i	$0.316756\pi$
$878$		0			0
$879$	12.9613	−	39.8908i	0.437174	−	1.34548i
$880$		0			0
$881$	13.2528	+	40.7880i	0.446499	+	1.37418i	0.880832	+	0.473429i	$0.156984\pi$
$881$	13.2528	+	40.7880i	0.446499	+	1.37418i	−0.434333	+	0.900752i	$0.643016\pi$
$882$		0			0
$883$	1.91114	+	5.88188i	0.0643150	+	0.197941i	0.978050	−	0.208369i	$-0.0668154\pi$
$883$	1.91114	+	5.88188i	0.0643150	+	0.197941i	−0.913735	+	0.406310i	$0.866815\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.34803	+	4.61212i	0.213146	+	0.154860i	0.689236	−	0.724537i	$-0.257946\pi$
$887$	6.34803	+	4.61212i	0.213146	+	0.154860i	−0.476090	+	0.879397i	$0.657946\pi$
$888$		0			0
$889$	14.0685	−	10.2214i	0.471844	−	0.342814i
$890$		0			0
$891$	−4.76796	−	3.46412i	−0.159733	−	0.116052i
$892$		0			0
$893$	−64.1727			−2.14746
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1.09651	+	3.37472i	−0.0366115	+	0.112679i
$898$		0			0
$899$	1.99864			0.0666583
$900$		0			0
$901$	9.35497			0.311659
$902$		0			0
$903$	0.622907	−	1.91711i	0.0207290	−	0.0637974i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.385211			−0.0127907			−0.00639536	−	0.999980i	$-0.502036\pi$
$907$	−0.385211			−0.0127907			−0.00639536	+	0.999980i	$0.502036\pi$
$908$		0			0
$909$	17.6363	+	12.8135i	0.584958	+	0.424997i
$910$		0			0
$911$	0.507752	−	0.368903i	0.0168226	−	0.0122223i	−0.579342	−	0.815084i	$-0.696691\pi$
$911$	0.507752	−	0.368903i	0.0168226	−	0.0122223i	0.596165	+	0.802862i	$0.296691\pi$
$912$		0			0
$913$	−3.43197	−	2.49347i	−0.113581	−	0.0825218i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	17.1452	+	52.7677i	0.566186	+	1.74254i
$918$		0			0
$919$	8.88039	+	27.3310i	0.292937	+	0.901567i	0.983907	+	0.178683i	$0.0571838\pi$
$919$	8.88039	+	27.3310i	0.292937	+	0.901567i	−0.690970	+	0.722884i	$0.742816\pi$
$920$		0			0
$921$	−16.7165	+	51.4482i	−0.550828	+	1.69528i
$922$		0			0
$923$	−46.8538	+	34.0413i	−1.54221	+	1.12048i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	11.3053	−	8.21377i	0.371314	−	0.269776i
$928$		0			0
$929$	−8.86551	+	27.2852i	−0.290868	+	0.895200i	0.693710	+	0.720254i	$0.255975\pi$
$929$	−8.86551	+	27.2852i	−0.290868	+	0.895200i	−0.984578	+	0.174945i	$0.944025\pi$
$930$		0			0
$931$	−22.9935	−	70.7668i	−0.753583	−	2.31929i
$932$		0			0
$933$	16.6608	+	51.2765i	0.545449	+	1.67872i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	29.4169	+	21.3726i	0.961009	+	0.698214i	0.953385	−	0.301757i	$-0.0975732\pi$
$937$	29.4169	+	21.3726i	0.961009	+	0.698214i	0.00762389	+	0.999971i	$0.497573\pi$
$938$		0			0
$939$	−10.8926	+	7.91393i	−0.355466	+	0.258261i
$940$		0			0
$941$	12.2006	+	8.86422i	0.397727	+	0.288965i	0.768614	−	0.639712i	$-0.220947\pi$
$941$	12.2006	+	8.86422i	0.397727	+	0.288965i	−0.370888	+	0.928678i	$0.620947\pi$
$942$		0			0
$943$	1.73801			0.0565975
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.56648	−	7.89882i	0.0833995	−	0.256677i	−0.900658	−	0.434529i	$-0.856915\pi$
$947$	2.56648	−	7.89882i	0.0833995	−	0.256677i	0.984057	+	0.177852i	$0.0569148\pi$
$948$		0			0
$949$	9.08327			0.294855
$950$		0			0
$951$	17.2800			0.560341
$952$		0			0
$953$	9.49453	−	29.2212i	0.307558	−	0.946566i	−0.671152	−	0.741319i	$-0.734200\pi$
$953$	9.49453	−	29.2212i	0.307558	−	0.946566i	0.978710	−	0.205247i	$-0.0657996\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	10.3750			0.335376
$958$		0			0
$959$	−5.65171	−	4.10621i	−0.182503	−	0.132596i
$960$		0			0
$961$	25.0296	−	18.1851i	0.807407	−	0.586616i
$962$		0			0
$963$	−10.5700	−	7.67954i	−0.340613	−	0.247470i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−6.63081	−	20.4075i	−0.213232	−	0.656262i	−0.999274	−	0.0380888i	$-0.987873\pi$
$967$	−6.63081	−	20.4075i	−0.213232	−	0.656262i	0.786042	−	0.618173i	$-0.212127\pi$
$968$		0			0
$969$	19.5970	+	60.3133i	0.629546	+	1.93754i
$970$		0			0
$971$	−16.5763	+	51.0166i	−0.531959	+	1.63720i	0.218171	+	0.975911i	$0.429991\pi$
$971$	−16.5763	+	51.0166i	−0.531959	+	1.63720i	−0.750130	+	0.661291i	$0.770009\pi$
$972$		0			0
$973$	−2.38954	+	1.73610i	−0.0766050	+	0.0556568i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	44.0654	−	32.0154i	1.40978	−	1.02426i	0.416423	−	0.909171i	$-0.363283\pi$
$977$	44.0654	−	32.0154i	1.40978	−	1.02426i	0.993355	−	0.115093i	$-0.0367166\pi$
$978$		0			0
$979$	2.76605	−	8.51303i	0.0884034	−	0.272078i
$980$		0			0
$981$	−9.89740	−	30.4611i	−0.316000	−	0.972547i
$982$		0			0
$983$	0.761210	+	2.34276i	0.0242788	+	0.0747225i	0.962462	−	0.271417i	$-0.0874923\pi$
$983$	0.761210	+	2.34276i	0.0242788	+	0.0747225i	−0.938183	+	0.346140i	$0.887492\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	72.8482	+	52.9273i	2.31878	+	1.68470i
$988$		0			0
$989$	−0.0639365	+	0.0464526i	−0.00203306	+	0.00147711i
$990$		0			0
$991$	−39.3120	−	28.5618i	−1.24879	−	0.907296i	−0.250635	−	0.968082i	$-0.580639\pi$
$991$	−39.3120	−	28.5618i	−1.24879	−	0.907296i	−0.998151	+	0.0607857i	$0.980639\pi$
$992$		0			0
$993$	69.7275			2.21274
$994$		0			0
$995$		0			0
$996$		0			0
$997$	3.41611	−	10.5137i	0.108189	−	0.332972i	−0.882276	−	0.470732i	$-0.843990\pi$
$997$	3.41611	−	10.5137i	0.108189	−	0.332972i	0.990466	+	0.137759i	$0.0439900\pi$
$998$		0			0
$999$	11.0564			0.349807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.2.g.b.301.4		16
5.2	odd	4		100.2.i.a.89.1	yes	8
5.3	odd	4		500.2.i.a.449.2		8
5.4	even	2	inner	500.2.g.b.301.1		16
15.2	even	4		900.2.w.a.289.1		8
20.7	even	4		400.2.y.b.289.2		8
25.3	odd	20		2500.2.c.b.1249.8		8
25.4	even	10		2500.2.a.f.1.1		8
25.9	even	10	inner	500.2.g.b.201.1		16
25.12	odd	20		500.2.i.a.49.2		8
25.13	odd	20		100.2.i.a.9.1	✓	8
25.16	even	5	inner	500.2.g.b.201.4		16
25.21	even	5		2500.2.a.f.1.8		8
25.22	odd	20		2500.2.c.b.1249.1		8
75.38	even	20		900.2.w.a.109.1		8
100.63	even	20		400.2.y.b.209.2		8
100.71	odd	10		10000.2.a.bi.1.1		8
100.79	odd	10		10000.2.a.bi.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.i.a.9.1	✓	8	25.13	odd	20
100.2.i.a.89.1	yes	8	5.2	odd	4
400.2.y.b.209.2		8	100.63	even	20
400.2.y.b.289.2		8	20.7	even	4
500.2.g.b.201.1		16	25.9	even	10	inner
500.2.g.b.201.4		16	25.16	even	5	inner
500.2.g.b.301.1		16	5.4	even	2	inner
500.2.g.b.301.4		16	1.1	even	1	trivial
500.2.i.a.49.2		8	25.12	odd	20
500.2.i.a.449.2		8	5.3	odd	4
900.2.w.a.109.1		8	75.38	even	20
900.2.w.a.289.1		8	15.2	even	4
2500.2.a.f.1.1		8	25.4	even	10
2500.2.a.f.1.8		8	25.21	even	5
2500.2.c.b.1249.1		8	25.22	odd	20
2500.2.c.b.1249.8		8	25.3	odd	20
10000.2.a.bi.1.1		8	100.71	odd	10
10000.2.a.bi.1.8		8	100.79	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	500.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.713605 - 2.19625i) q^{3} -4.21139 q^{7} +(-1.88723 - 1.37116i) q^{9} +(0.451659 - 0.328150i) q^{11} +(-3.26033 - 2.36877i) q^{13} +(-1.22440 - 3.76832i) q^{17} +(-2.14177 - 6.59168i) q^{19} +(-3.00527 + 9.24926i) q^{21} +(0.308467 - 0.224115i) q^{23} +(1.24659 - 0.905698i) q^{27} +(-2.48680 + 7.65359i) q^{29} +(-0.0767462 - 0.236201i) q^{31} +(-0.398393 - 1.22613i) q^{33} +(5.80503 + 4.21760i) q^{37} +(-7.52900 + 5.47014i) q^{39} +(3.68773 + 2.67929i) q^{41} -0.207272 q^{43} +(2.86117 - 8.80576i) q^{47} +10.7358 q^{49} -9.14992 q^{51} +(-0.729597 + 2.24547i) q^{53} -16.0054 q^{57} +(-2.93557 - 2.13282i) q^{59} +(3.15785 - 2.29431i) q^{61} +(7.94787 + 5.77447i) q^{63} +(2.13234 + 6.56267i) q^{67} +(-0.272088 - 0.837401i) q^{69} +(4.44084 - 13.6675i) q^{71} +(-1.82346 + 1.32482i) q^{73} +(-1.90211 + 1.38197i) q^{77} +(2.35970 - 7.26242i) q^{79} +(-3.26215 - 10.0399i) q^{81} +(-2.34809 - 7.22667i) q^{83} +(15.0346 + 10.9233i) q^{87} +(12.9713 - 9.42417i) q^{89} +(13.7305 + 9.97581i) q^{91} -0.573522 q^{93} +(1.01080 - 3.11093i) q^{97} -1.30233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9} + 10 q^{11} + 16 q^{19} - 4 q^{21} + 16 q^{29} - 24 q^{31} - 44 q^{39} + 26 q^{41} - 28 q^{49} - 28 q^{51} - 18 q^{59} + 32 q^{61} + 28 q^{69} - 2 q^{71} + 48 q^{79} - 6 q^{81} + 74 q^{89}+ \cdots - 40 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 + 10 * q^11 + 16 * q^19 - 4 * q^21 + 16 * q^29 - 24 * q^31 - 44 * q^39 + 26 * q^41 - 28 * q^49 - 28 * q^51 - 18 * q^59 + 32 * q^61 + 28 * q^69 - 2 * q^71 + 48 * q^79 - 6 * q^81 + 74 * q^89 + 64 * q^91 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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