LMFDB - Embedded newform 560.4.q.p.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,4,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$33.0410696032$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 95 x^{10} - 258 x^{9} + 7289 x^{8} - 15564 x^{7} + 170984 x^{6} + 88720 x^{5} + \cdots + 6718464 $ x^12 - 2x^11 + 95x^10 - 258x^9 + 7289x^8 - 15564x^7 + 170984x^6 + 88720x^5 + 2094592x^4 - 681024x^3 + 5329728x^2 + 3297024*x + 6718464
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$3.54223 - 6.13533i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.4.q.p.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.04223 + 7.00136i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-18.4932 + 0.999858i) q^{7} +(-19.1793 - 33.2196i) q^{9} +(-19.1387 + 33.1492i) q^{11} -24.4727 q^{13} -40.4223 q^{15} +(24.5607 - 42.5405i) q^{17} +(-8.94558 - 15.4942i) q^{19} +(67.7537 - 133.519i) q^{21} +(-46.5837 - 80.6853i) q^{23} +(-12.5000 + 21.6506i) q^{25} +91.8286 q^{27} +122.266 q^{29} +(-102.755 + 177.977i) q^{31} +(-154.726 - 267.993i) q^{33} +(-50.5626 - 77.5785i) q^{35} +(-117.658 - 203.789i) q^{37} +(98.9244 - 171.342i) q^{39} -507.445 q^{41} +477.564 q^{43} +(95.8966 - 166.098i) q^{45} +(28.4095 + 49.2067i) q^{47} +(341.001 - 36.9812i) q^{49} +(198.561 + 343.917i) q^{51} +(-29.2152 + 50.6022i) q^{53} -191.387 q^{55} +144.640 q^{57} +(-0.720543 + 1.24802i) q^{59} +(415.848 + 720.270i) q^{61} +(387.903 + 595.161i) q^{63} +(-61.1817 - 105.970i) q^{65} +(79.1069 - 137.017i) q^{67} +753.209 q^{69} +202.622 q^{71} +(384.117 - 665.310i) q^{73} +(-101.056 - 175.034i) q^{75} +(320.792 - 632.172i) q^{77} +(-306.740 - 531.289i) q^{79} +(146.649 - 254.003i) q^{81} +623.021 q^{83} +245.607 q^{85} +(-494.227 + 856.025i) q^{87} +(800.544 + 1386.58i) q^{89} +(452.580 - 24.4692i) q^{91} +(-830.718 - 1438.85i) q^{93} +(44.7279 - 77.4710i) q^{95} +1371.59 q^{97} +1468.27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{3} + 30 q^{5} + 14 q^{7} - 34 q^{9} - 240 q^{13} - 80 q^{15} + 122 q^{17} - 2 q^{19} + 170 q^{21} + 30 q^{23} - 150 q^{25} + 64 q^{27} + 476 q^{29} - 122 q^{31} + 584 q^{33} - 100 q^{35} + 342 q^{37}+ \cdots + 216 q^{99}+O(q^{100}) $ 12 * q - 8 * q^3 + 30 * q^5 + 14 * q^7 - 34 * q^9 - 240 * q^13 - 80 * q^15 + 122 * q^17 - 2 * q^19 + 170 * q^21 + 30 * q^23 - 150 * q^25 + 64 * q^27 + 476 * q^29 - 122 * q^31 + 584 * q^33 - 100 * q^35 + 342 * q^37 - 126 * q^39 - 676 * q^41 - 1176 * q^43 + 170 * q^45 + 260 * q^47 - 368 * q^49 - 770 * q^51 - 680 * q^53 + 1380 * q^57 - 918 * q^59 + 1026 * q^61 + 1284 * q^63 - 600 * q^65 + 1532 * q^67 - 724 * q^69 + 300 * q^71 - 158 * q^73 - 200 * q^75 + 758 * q^77 + 222 * q^79 + 250 * q^81 - 704 * q^83 + 1220 * q^85 + 1306 * q^87 + 1684 * q^89 - 122 * q^91 - 2834 * q^93 + 10 * q^95 - 2600 * q^97 + 216 * q^99

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−4.04223	+	7.00136i	−0.777928	+	1.34741i	0.155205	+	0.987882i	$0.450396\pi$
$3$	−4.04223	+	7.00136i	−0.777928	+	1.34741i	−0.933134	+	0.359529i	$0.882937\pi$
$4$		0			0
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	−18.4932	+	0.999858i	−0.998542	+	0.0539872i
$7$	−18.4932	+	0.999858i	−0.998542	+	0.0539872i
$8$		0			0
$9$	−19.1793	−	33.2196i	−0.710345	−	1.23035i
$10$		0			0
$11$	−19.1387	+	33.1492i	−0.524594	+	0.908623i	0.474996	+	0.879988i	$0.342449\pi$
$11$	−19.1387	+	33.1492i	−0.524594	+	0.908623i	−0.999590	+	0.0286351i	$0.990884\pi$
$12$		0			0
$13$	−24.4727			−0.522116			−0.261058	−	0.965323i	$-0.584071\pi$
$13$	−24.4727			−0.522116			−0.261058	+	0.965323i	$0.584071\pi$
$14$		0			0
$15$	−40.4223			−0.695800
$16$		0			0
$17$	24.5607	−	42.5405i	0.350403	−	0.606916i	−0.635917	−	0.771758i	$-0.719378\pi$
$17$	24.5607	−	42.5405i	0.350403	−	0.606916i	0.986320	+	0.164841i	$0.0527112\pi$
$18$		0			0
$19$	−8.94558	−	15.4942i	−0.108013	−	0.187085i	0.806952	−	0.590617i	$-0.201116\pi$
$19$	−8.94558	−	15.4942i	−0.108013	−	0.187085i	−0.914965	+	0.403532i	$0.867782\pi$
$20$		0			0
$21$	67.7537	−	133.519i	0.704051	−	1.38744i
$22$		0			0
$23$	−46.5837	−	80.6853i	−0.422321	−	0.731481i	0.573845	−	0.818964i	$-0.305451\pi$
$23$	−46.5837	−	80.6853i	−0.422321	−	0.731481i	−0.996166	+	0.0874829i	$0.972118\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$	91.8286			0.654534
$28$		0			0
$29$	122.266			0.782902			0.391451	−	0.920199i	$-0.371973\pi$
$29$	122.266			0.782902			0.391451	+	0.920199i	$0.371973\pi$
$30$		0			0
$31$	−102.755	+	177.977i	−0.595333	+	1.03115i	0.398167	+	0.917313i	$0.369646\pi$
$31$	−102.755	+	177.977i	−0.595333	+	1.03115i	−0.993500	+	0.113833i	$0.963687\pi$
$32$		0			0
$33$	−154.726	−	267.993i	−0.816193	−	1.41369i
$34$		0			0
$35$	−50.5626	−	77.5785i	−0.244190	−	0.374662i
$36$		0			0
$37$	−117.658	−	203.789i	−0.522778	−	0.905478i	−0.999649	−	0.0265044i	$-0.991562\pi$
$37$	−117.658	−	203.789i	−0.522778	−	0.905478i	0.476871	−	0.878973i	$-0.341771\pi$
$38$		0			0
$39$	98.9244	−	171.342i	0.406169	−	0.703505i
$40$		0			0
$41$	−507.445			−1.93292			−0.966459	−	0.256821i	$-0.917325\pi$
$41$	−507.445			−1.93292			−0.966459	+	0.256821i	$0.917325\pi$
$42$		0			0
$43$	477.564			1.69367			0.846835	−	0.531856i	$-0.178505\pi$
$43$	477.564			1.69367			0.846835	+	0.531856i	$0.178505\pi$
$44$		0			0
$45$	95.8966	−	166.098i	0.317676	−	0.550231i
$46$		0			0
$47$	28.4095	+	49.2067i	0.0881691	+	0.152713i	0.906737	−	0.421696i	$-0.138565\pi$
$47$	28.4095	+	49.2067i	0.0881691	+	0.152713i	−0.818568	+	0.574409i	$0.805232\pi$
$48$		0			0
$49$	341.001	−	36.9812i	0.994171	−	0.107817i
$50$		0			0
$51$	198.561	+	343.917i	0.545177	+	0.944275i
$52$		0			0
$53$	−29.2152	+	50.6022i	−0.0757173	+	0.131146i	−0.901398	−	0.432992i	$-0.857458\pi$
$53$	−29.2152	+	50.6022i	−0.0757173	+	0.131146i	0.825681	+	0.564138i	$0.190791\pi$
$54$		0			0
$55$	−191.387			−0.469211
$56$		0			0
$57$	144.640			0.336107
$58$		0			0
$59$	−0.720543	+	1.24802i	−0.00158994	+	0.00275386i	−0.866819	−	0.498622i	$-0.833839\pi$
$59$	−0.720543	+	1.24802i	−0.00158994	+	0.00275386i	0.865229	+	0.501376i	$0.167173\pi$
$60$		0			0
$61$	415.848	+	720.270i	0.872851	+	1.51182i	0.859035	+	0.511918i	$0.171065\pi$
$61$	415.848	+	720.270i	0.872851	+	1.51182i	0.0138164	+	0.999905i	$0.495602\pi$
$62$		0			0
$63$	387.903	+	595.161i	0.775733	+	1.19021i
$64$		0			0
$65$	−61.1817	−	105.970i	−0.116749	−	0.202214i
$66$		0			0
$67$	79.1069	−	137.017i	0.144246	−	0.249841i	−0.784846	−	0.619691i	$-0.787258\pi$
$67$	79.1069	−	137.017i	0.144246	−	0.249841i	0.929091	+	0.369851i	$0.120591\pi$
$68$		0			0
$69$	753.209			1.31414
$70$		0			0
$71$	202.622			0.338687			0.169344	−	0.985557i	$-0.445835\pi$
$71$	202.622			0.338687			0.169344	+	0.985557i	$0.445835\pi$
$72$		0			0
$73$	384.117	−	665.310i	0.615856	−	1.06669i	−0.374378	−	0.927276i	$-0.622144\pi$
$73$	384.117	−	665.310i	0.615856	−	1.06669i	0.990234	−	0.139418i	$-0.0445231\pi$
$74$		0			0
$75$	−101.056	−	175.034i	−0.155586	−	0.269482i
$76$		0			0
$77$	320.792	−	632.172i	0.474775	−	0.935619i
$78$		0			0
$79$	−306.740	−	531.289i	−0.436847	−	0.756642i	0.560597	−	0.828089i	$-0.310572\pi$
$79$	−306.740	−	531.289i	−0.436847	−	0.756642i	−0.997444	+	0.0714470i	$0.977238\pi$
$80$		0			0
$81$	146.649	−	254.003i	0.201164	−	0.348427i
$82$		0			0
$83$	623.021			0.823921			0.411961	−	0.911202i	$-0.364844\pi$
$83$	623.021			0.823921			0.411961	+	0.911202i	$0.364844\pi$
$84$		0			0
$85$	245.607			0.313410
$86$		0			0
$87$	−494.227	+	856.025i	−0.609042	+	1.05489i
$88$		0			0
$89$	800.544	+	1386.58i	0.953455	+	1.65143i	0.737864	+	0.674949i	$0.235834\pi$
$89$	800.544	+	1386.58i	0.953455	+	1.65143i	0.215591	+	0.976484i	$0.430832\pi$
$90$		0			0
$91$	452.580	−	24.4692i	0.521354	−	0.0281876i
$92$		0			0
$93$	−830.718	−	1438.85i	−0.926252	−	1.60432i
$94$		0			0
$95$	44.7279	−	77.4710i	0.0483051	−	0.0836669i
$96$		0			0
$97$	1371.59			1.43571			0.717855	−	0.696192i	$-0.245124\pi$
$97$	1371.59			1.43571			0.717855	+	0.696192i	$0.245124\pi$
$98$		0			0
$99$	1468.27			1.49057
$100$		0			0
$101$	−280.619	+	486.046i	−0.276461	+	0.478845i	−0.970503	−	0.241090i	$-0.922495\pi$
$101$	−280.619	+	486.046i	−0.276461	+	0.478845i	0.694041	+	0.719935i	$0.255828\pi$
$102$		0			0
$103$	−964.125	−	1669.91i	−0.922311	−	1.59749i	−0.795830	−	0.605520i	$-0.792965\pi$
$103$	−964.125	−	1669.91i	−0.922311	−	1.59749i	−0.126481	−	0.991969i	$-0.540368\pi$
$104$		0			0
$105$	747.541	−	40.4166i	0.694786	−	0.0375643i
$106$		0			0
$107$	−407.537	−	705.875i	−0.368207	−	0.637753i	0.621079	−	0.783748i	$-0.286695\pi$
$107$	−407.537	−	705.875i	−0.368207	−	0.637753i	−0.989285	+	0.145996i	$0.953361\pi$
$108$		0			0
$109$	61.2225	−	106.040i	0.0537986	−	0.0931819i	−0.837872	−	0.545867i	$-0.816200\pi$
$109$	61.2225	−	106.040i	0.0537986	−	0.0931819i	0.891671	+	0.452685i	$0.149534\pi$
$110$		0			0
$111$	1902.40			1.62673
$112$		0			0
$113$	−6.21067			−0.00517036			−0.00258518	−	0.999997i	$-0.500823\pi$
$113$	−6.21067			−0.00517036			−0.00258518	+	0.999997i	$0.500823\pi$
$114$		0			0
$115$	232.919	−	403.427i	0.188868	−	0.327128i
$116$		0			0
$117$	469.370	+	812.972i	0.370882	+	0.642387i
$118$		0			0
$119$	−411.674	+	811.269i	−0.317127	+	0.624949i
$120$		0			0
$121$	−67.0785	−	116.183i	−0.0503971	−	0.0872903i
$122$		0			0
$123$	2051.21	−	3552.81i	1.50367	−	2.60444i
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−436.086			−0.304696			−0.152348	−	0.988327i	$-0.548683\pi$
$127$	−436.086			−0.304696			−0.152348	+	0.988327i	$0.548683\pi$
$128$		0			0
$129$	−1930.43	+	3343.60i	−1.31755	+	2.28207i
$130$		0			0
$131$	−848.858	−	1470.26i	−0.566145	−	0.980593i	−0.996942	−	0.0781437i	$-0.975101\pi$
$131$	−848.858	−	1470.26i	−0.566145	−	0.980593i	0.430797	−	0.902449i	$-0.358233\pi$
$132$		0			0
$133$	180.925	+	277.594i	0.117956	+	0.180981i
$134$		0			0
$135$	229.572	+	397.630i	0.146358	+	0.253500i
$136$		0			0
$137$	−417.686	+	723.454i	−0.260477	+	0.451159i	−0.966369	−	0.257160i	$-0.917213\pi$
$137$	−417.686	+	723.454i	−0.260477	+	0.451159i	0.705892	+	0.708320i	$0.250546\pi$
$138$		0			0
$139$	1937.72			1.18241			0.591207	−	0.806520i	$-0.298652\pi$
$139$	1937.72			1.18241			0.591207	+	0.806520i	$0.298652\pi$
$140$		0			0
$141$	−459.351			−0.274357
$142$		0			0
$143$	468.375	−	811.249i	0.273899	−	0.474406i
$144$		0			0
$145$	305.664	+	529.426i	0.175062	+	0.303217i
$146$		0			0
$147$	−1119.49	+	2536.95i	−0.628120	+	1.42343i
$148$		0			0
$149$	−1229.72	−	2129.95i	−0.676127	−	1.17109i	−0.976138	−	0.217151i	$-0.930324\pi$
$149$	−1229.72	−	2129.95i	−0.676127	−	1.17109i	0.300011	−	0.953936i	$-0.403010\pi$
$150$		0			0
$151$	−1361.19	+	2357.66i	−0.733592	+	1.27062i	0.221746	+	0.975104i	$0.428824\pi$
$151$	−1361.19	+	2357.66i	−0.733592	+	1.27062i	−0.955338	+	0.295514i	$0.904509\pi$
$152$		0			0
$153$	−1884.23			−0.995629
$154$		0			0
$155$	−1027.55			−0.532482
$156$		0			0
$157$	−206.900	+	358.361i	−0.105175	+	0.182168i	−0.913810	−	0.406143i	$-0.866873\pi$
$157$	−206.900	+	358.361i	−0.105175	+	0.182168i	0.808635	+	0.588311i	$0.200207\pi$
$158$		0			0
$159$	−236.189	−	409.092i	−0.117805	−	0.204045i
$160$		0			0
$161$	942.158	+	1445.56i	0.461195	+	0.707614i
$162$		0			0
$163$	−1287.48	−	2229.98i	−0.618669	−	1.07157i	−0.989729	−	0.142957i	$-0.954339\pi$
$163$	−1287.48	−	2229.98i	−0.618669	−	1.07157i	0.371060	−	0.928609i	$-0.378994\pi$
$164$		0			0
$165$	773.631	−	1339.97i	0.365012	−	0.632220i
$166$		0			0
$167$	−1814.53			−0.840794			−0.420397	−	0.907340i	$-0.638109\pi$
$167$	−1814.53			−0.840794			−0.420397	+	0.907340i	$0.638109\pi$
$168$		0			0
$169$	−1598.09			−0.727395
$170$		0			0
$171$	−343.140	+	594.336i	−0.153454	+	0.265790i
$172$		0			0
$173$	−939.835	−	1627.84i	−0.413031	−	0.715390i	0.582189	−	0.813054i	$-0.302196\pi$
$173$	−939.835	−	1627.84i	−0.413031	−	0.715390i	−0.995220	+	0.0976633i	$0.968863\pi$
$174$		0			0
$175$	209.518	−	412.889i	0.0905033	−	0.178351i
$176$		0			0
$177$	−5.82521	−	10.0896i	−0.00247373	−	0.00428462i
$178$		0			0
$179$	1798.83	−	3115.67i	0.751122	−	1.30098i	−0.196157	−	0.980573i	$-0.562846\pi$
$179$	1798.83	−	3115.67i	0.751122	−	1.30098i	0.947279	−	0.320409i	$-0.103820\pi$
$180$		0			0
$181$	923.641			0.379302			0.189651	−	0.981852i	$-0.439264\pi$
$181$	923.641			0.379302			0.189651	+	0.981852i	$0.439264\pi$
$182$		0			0
$183$	−6723.82			−2.71606
$184$		0			0
$185$	588.288	−	1018.94i	0.233793	−	0.404942i
$186$		0			0
$187$	940.121	+	1628.34i	0.367639	+	0.636769i
$188$		0			0
$189$	−1698.21	+	91.8156i	−0.653580	+	0.0353365i
$190$		0			0
$191$	−535.093	−	926.808i	−0.202712	−	0.351107i	0.746689	−	0.665173i	$-0.231642\pi$
$191$	−535.093	−	926.808i	−0.202712	−	0.351107i	−0.949401	+	0.314066i	$0.898309\pi$
$192$		0			0
$193$	81.3975	−	140.985i	0.0303582	−	0.0525819i	−0.850447	−	0.526060i	$-0.823669\pi$
$193$	81.3975	−	140.985i	0.0303582	−	0.0525819i	0.880805	+	0.473479i	$0.157002\pi$
$194$		0			0
$195$	989.244			0.363288
$196$		0			0
$197$	558.652			0.202042			0.101021	−	0.994884i	$-0.467789\pi$
$197$	558.652			0.202042			0.101021	+	0.994884i	$0.467789\pi$
$198$		0			0
$199$	230.435	−	399.125i	0.0820859	−	0.142177i	−0.822060	−	0.569401i	$-0.807175\pi$
$199$	230.435	−	399.125i	0.0820859	−	0.142177i	0.904146	+	0.427224i	$0.140508\pi$
$200$		0			0
$201$	639.538	+	1107.71i	0.224425	+	0.388716i
$202$		0			0
$203$	−2261.09	+	122.248i	−0.781760	+	0.0422667i
$204$		0			0
$205$	−1268.61	−	2197.30i	−0.432214	−	0.748616i
$206$		0			0
$207$	−1786.89	+	3094.98i	−0.599987	+	1.03921i
$208$		0			0
$209$	684.826			0.226653
$210$		0			0
$211$	−6051.16			−1.97431			−0.987154	−	0.159770i	$-0.948925\pi$
$211$	−6051.16			−1.97431			−0.987154	+	0.159770i	$0.948925\pi$
$212$		0			0
$213$	−819.045	+	1418.63i	−0.263475	+	0.456351i
$214$		0			0
$215$	1193.91	+	2067.91i	0.378716	+	0.655956i
$216$		0			0
$217$	1722.32	−	3394.11i	0.538796	−	1.06178i
$218$		0			0
$219$	3105.38	+	5378.68i	0.958184	+	1.65962i
$220$		0			0
$221$	−601.068	+	1041.08i	−0.182951	+	0.316880i
$222$		0			0
$223$	322.103			0.0967246			0.0483623	−	0.998830i	$-0.484600\pi$
$223$	322.103			0.0967246			0.0483623	+	0.998830i	$0.484600\pi$
$224$		0			0
$225$	958.966			0.284138
$226$		0			0
$227$	319.611	−	553.582i	0.0934507	−	0.161861i	−0.815510	−	0.578743i	$-0.803544\pi$
$227$	319.611	−	553.582i	0.0934507	−	0.161861i	0.908961	+	0.416881i	$0.136877\pi$
$228$		0			0
$229$	−3094.58	−	5359.98i	−0.892995	−	1.54671i	−0.836266	−	0.548324i	$-0.815266\pi$
$229$	−3094.58	−	5359.98i	−0.892995	−	1.54671i	−0.0567290	−	0.998390i	$-0.518067\pi$
$230$		0			0
$231$	3129.34	+	4801.37i	0.891323	+	1.36756i
$232$		0			0
$233$	−1825.98	−	3162.68i	−0.513406	−	0.889246i	−0.999879	−	0.0155502i	$-0.995050\pi$
$233$	−1825.98	−	3162.68i	−0.513406	−	0.889246i	0.486473	−	0.873696i	$-0.338283\pi$
$234$		0			0
$235$	−142.047	+	246.033i	−0.0394304	+	0.0682955i
$236$		0			0
$237$	4959.66			1.35934
$238$		0			0
$239$	4653.34			1.25941			0.629706	−	0.776833i	$-0.283175\pi$
$239$	4653.34			1.25941			0.629706	+	0.776833i	$0.283175\pi$
$240$		0			0
$241$	−2502.09	+	4333.75i	−0.668772	+	1.15835i	0.309476	+	0.950907i	$0.399846\pi$
$241$	−2502.09	+	4333.75i	−0.668772	+	1.15835i	−0.978248	+	0.207439i	$0.933487\pi$
$242$		0			0
$243$	2425.26	+	4200.68i	0.640250	+	1.10895i
$244$		0			0
$245$	1012.63	+	1384.12i	0.264061	+	0.360932i
$246$		0			0
$247$	218.922	+	379.185i	0.0563955	+	0.0976799i
$248$		0			0
$249$	−2518.40	+	4361.99i	−0.640952	+	1.11016i
$250$		0			0
$251$	3335.76			0.838849			0.419425	−	0.907790i	$-0.362232\pi$
$251$	3335.76			0.838849			0.419425	+	0.907790i	$0.362232\pi$
$252$		0			0
$253$	3566.20			0.886187
$254$		0			0
$255$	−992.803	+	1719.59i	−0.243811	+	0.422293i
$256$		0			0
$257$	1992.62	+	3451.32i	0.483643	+	0.837694i	0.999824	−	0.0187856i	$-0.00597999\pi$
$257$	1992.62	+	3451.32i	0.483643	+	0.837694i	−0.516181	+	0.856480i	$0.672647\pi$
$258$		0			0
$259$	2379.63	+	3651.08i	0.570900	+	0.875934i
$260$		0			0
$261$	−2344.97	−	4061.61i	−0.556131	−	0.963247i
$262$		0			0
$263$	948.952	−	1643.63i	0.222490	−	0.385364i	−0.733073	−	0.680150i	$-0.761915\pi$
$263$	948.952	−	1643.63i	0.222490	−	0.385364i	0.955564	+	0.294785i	$0.0952481\pi$
$264$		0			0
$265$	−292.152			−0.0677236
$266$		0			0
$267$	−12943.9			−2.96688
$268$		0			0
$269$	−2929.03	+	5073.23i	−0.663890	+	1.14989i	0.315695	+	0.948861i	$0.397762\pi$
$269$	−2929.03	+	5073.23i	−0.663890	+	1.14989i	−0.979585	+	0.201030i	$0.935571\pi$
$270$		0			0
$271$	−4127.73	−	7149.44i	−0.925246	−	1.60257i	−0.791164	−	0.611604i	$-0.790525\pi$
$271$	−4127.73	−	7149.44i	−0.925246	−	1.60257i	−0.134082	−	0.990970i	$-0.542809\pi$
$272$		0			0
$273$	−1658.12	+	3267.58i	−0.367596	+	0.724407i
$274$		0			0
$275$	−478.467	−	828.729i	−0.104919	−	0.181725i
$276$		0			0
$277$	3761.81	−	6515.64i	0.815975	−	1.41331i	−0.0926506	−	0.995699i	$-0.529534\pi$
$277$	3761.81	−	6515.64i	0.815975	−	1.41331i	0.908626	−	0.417612i	$-0.137133\pi$
$278$		0			0
$279$	7883.07			1.69157
$280$		0			0
$281$	−3588.95			−0.761917			−0.380958	−	0.924592i	$-0.624406\pi$
$281$	−3588.95			−0.761917			−0.380958	+	0.924592i	$0.624406\pi$
$282$		0			0
$283$	−98.6675	+	170.897i	−0.0207250	+	0.0358967i	−0.876202	−	0.481944i	$-0.839931\pi$
$283$	−98.6675	+	170.897i	−0.0207250	+	0.0358967i	0.855477	+	0.517841i	$0.173264\pi$
$284$		0			0
$285$	361.601	+	626.312i	0.0751558	+	0.130174i
$286$		0			0
$287$	9384.31	−	507.373i	1.93010	−	0.104353i
$288$		0			0
$289$	1250.04	+	2165.13i	0.254435	+	0.440694i
$290$		0			0
$291$	−5544.29	+	9602.99i	−1.11688	+	1.93449i
$292$		0			0
$293$	−3779.52			−0.753590			−0.376795	−	0.926297i	$-0.622974\pi$
$293$	−3779.52			−0.753590			−0.376795	+	0.926297i	$0.622974\pi$
$294$		0			0
$295$	−7.20543			−0.00142209
$296$		0			0
$297$	−1757.48	+	3044.04i	−0.343365	+	0.594725i
$298$		0			0
$299$	1140.03	+	1974.59i	0.220500	+	0.381918i
$300$		0			0
$301$	−8831.71	+	477.496i	−1.69120	+	0.0914366i
$302$		0			0
$303$	−2268.65	−	3929.42i	−0.430134	−	0.745014i
$304$		0			0
$305$	−2079.24	+	3601.35i	−0.390351	+	0.676107i
$306$		0			0
$307$	−4494.68			−0.835585			−0.417793	−	0.908542i	$-0.637196\pi$
$307$	−4494.68			−0.835585			−0.417793	+	0.908542i	$0.637196\pi$
$308$		0			0
$309$	15588.9			2.86997
$310$		0			0
$311$	4871.50	−	8437.69i	0.888224	−	1.53845i	0.0462507	−	0.998930i	$-0.485273\pi$
$311$	4871.50	−	8437.69i	0.888224	−	1.53845i	0.841973	−	0.539519i	$-0.181394\pi$
$312$		0			0
$313$	−2283.13	−	3954.50i	−0.412301	−	0.714126i	0.582840	−	0.812587i	$-0.301941\pi$
$313$	−2283.13	−	3954.50i	−0.412301	−	0.714126i	−0.995141	+	0.0984609i	$0.968608\pi$
$314$		0			0
$315$	−1607.37	+	3167.57i	−0.287507	+	0.566579i
$316$		0			0
$317$	−4634.53	−	8027.25i	−0.821140	−	1.42226i	−0.904834	−	0.425765i	$-0.860005\pi$
$317$	−4634.53	−	8027.25i	−0.821140	−	1.42226i	0.0836938	−	0.996492i	$-0.473328\pi$
$318$		0			0
$319$	−2340.00	+	4053.01i	−0.410706	+	0.711363i
$320$		0			0
$321$	6589.45			1.14575
$322$		0			0
$323$	−878.840			−0.151393
$324$		0			0
$325$	305.909	−	529.849i	0.0522116	−	0.0904331i
$326$		0			0
$327$	494.951	+	857.280i	0.0837029	+	0.144978i
$328$		0			0
$329$	−574.583	−	881.586i	−0.0962851	−	0.147731i
$330$		0			0
$331$	−490.867	−	850.206i	−0.0815120	−	0.141183i	0.822388	−	0.568928i	$-0.192642\pi$
$331$	−490.867	−	850.206i	−0.0815120	−	0.141183i	−0.903900	+	0.427745i	$0.859308\pi$
$332$		0			0
$333$	−4513.18	+	7817.06i	−0.742706	+	1.28640i
$334$		0			0
$335$	791.069			0.129017
$336$		0			0
$337$	84.2571			0.0136195			0.00680975	−	0.999977i	$-0.497832\pi$
$337$	84.2571			0.0136195			0.00680975	+	0.999977i	$0.497832\pi$
$338$		0			0
$339$	25.1050	−	43.4831i	0.00402217	−	0.00696660i
$340$		0			0
$341$	−3933.18	−	6812.47i	−0.624615	−	1.08187i
$342$		0			0
$343$	−6269.23	+	1024.86i	−0.986900	+	0.161332i
$344$		0			0
$345$	1883.02	+	3261.49i	0.293851	+	0.508965i
$346$		0			0
$347$	−4111.38	+	7121.11i	−0.636053	+	1.10168i	0.350238	+	0.936661i	$0.386101\pi$
$347$	−4111.38	+	7121.11i	−0.636053	+	1.10168i	−0.986291	+	0.165015i	$0.947233\pi$
$348$		0			0
$349$	315.862			0.0484461			0.0242231	−	0.999707i	$-0.492289\pi$
$349$	315.862			0.0484461			0.0242231	+	0.999707i	$0.492289\pi$
$350$		0			0
$351$	−2247.29			−0.341743
$352$		0			0
$353$	−5591.22	+	9684.28i	−0.843033	+	1.46018i	0.0442851	+	0.999019i	$0.485899\pi$
$353$	−5591.22	+	9684.28i	−0.843033	+	1.46018i	−0.887318	+	0.461157i	$0.847434\pi$
$354$		0			0
$355$	506.555	+	877.379i	0.0757328	+	0.131173i
$356$		0			0
$357$	−4015.90	−	6161.61i	−0.595361	−	0.913465i
$358$		0			0
$359$	−5526.16	−	9571.59i	−0.812422	−	1.40716i	−0.911164	−	0.412044i	$-0.864815\pi$
$359$	−5526.16	−	9571.59i	−0.812422	−	1.40716i	0.0987415	−	0.995113i	$-0.468518\pi$
$360$		0			0
$361$	3269.45	−	5662.86i	0.476666	−	0.825610i
$362$		0			0
$363$	1084.59			0.156821
$364$		0			0
$365$	3841.17			0.550838
$366$		0			0
$367$	1062.42	−	1840.16i	0.151111	−	0.261732i	−0.780525	−	0.625124i	$-0.785048\pi$
$367$	1062.42	−	1840.16i	0.151111	−	0.261732i	0.931636	+	0.363392i	$0.118382\pi$
$368$		0			0
$369$	9732.46	+	16857.1i	1.37304	+	2.37817i
$370$		0			0
$371$	489.689	−	965.010i	0.0685266	−	0.135043i
$372$		0			0
$373$	−4354.21	−	7541.71i	−0.604430	−	1.04690i	−0.992141	−	0.125122i	$-0.960068\pi$
$373$	−4354.21	−	7541.71i	−0.604430	−	1.04690i	0.387712	−	0.921781i	$-0.373266\pi$
$374$		0			0
$375$	505.279	−	875.169i	0.0695800	−	0.120516i
$376$		0			0
$377$	−2992.17			−0.408765
$378$		0			0
$379$	724.535			0.0981976			0.0490988	−	0.998794i	$-0.484365\pi$
$379$	724.535			0.0981976			0.0490988	+	0.998794i	$0.484365\pi$
$380$		0			0
$381$	1762.76	−	3053.19i	0.237032	−	0.410551i
$382$		0			0
$383$	4702.82	+	8145.52i	0.627422	+	1.08673i	0.988067	+	0.154024i	$0.0492233\pi$
$383$	4702.82	+	8145.52i	0.627422	+	1.08673i	−0.360645	+	0.932703i	$0.617443\pi$
$384$		0			0
$385$	3539.36	−	191.360i	0.468527	−	0.0253314i
$386$		0			0
$387$	−9159.35	−	15864.5i	−1.20309	−	2.08381i
$388$		0			0
$389$	1220.99	−	2114.81i	0.159143	−	0.275643i	−0.775417	−	0.631449i	$-0.782460\pi$
$389$	1220.99	−	2114.81i	0.159143	−	0.275643i	0.934560	+	0.355806i	$0.115794\pi$
$390$		0			0
$391$	−4576.52			−0.591930
$392$		0			0
$393$	13725.1			1.76168
$394$		0			0
$395$	1533.70	−	2656.45i	0.195364	−	0.338380i
$396$		0			0
$397$	2593.54	+	4492.14i	0.327874	+	0.567894i	0.982090	−	0.188414i	$-0.0603346\pi$
$397$	2593.54	+	4492.14i	0.327874	+	0.567894i	−0.654216	+	0.756308i	$0.727001\pi$
$398$		0			0
$399$	−2674.87	+	144.620i	−0.335617	+	0.0181455i
$400$		0			0
$401$	−220.116	−	381.252i	−0.0274116	−	0.0474783i	0.851994	−	0.523551i	$-0.175393\pi$
$401$	−220.116	−	381.252i	−0.0274116	−	0.0474783i	−0.879406	+	0.476073i	$0.842060\pi$
$402$		0			0
$403$	2514.69	−	4355.57i	0.310832	−	0.538378i
$404$		0			0
$405$	1466.49			0.179927
$406$		0			0
$407$	9007.24			1.09698
$408$		0			0
$409$	2097.39	−	3632.79i	0.253568	−	0.439193i	−0.710938	−	0.703255i	$-0.751729\pi$
$409$	2097.39	−	3632.79i	0.253568	−	0.439193i	0.964506	+	0.264062i	$0.0850625\pi$
$410$		0			0
$411$	−3376.77	−	5848.74i	−0.405265	−	0.701939i
$412$		0			0
$413$	12.0773	−	23.8003i	0.00143895	−	0.00283568i
$414$		0			0
$415$	1557.55	+	2697.76i	0.184234	+	0.319103i
$416$		0			0
$417$	−7832.73	+	13566.7i	−0.919833	+	1.59320i
$418$		0			0
$419$	9420.34			1.09836			0.549181	−	0.835703i	$-0.314940\pi$
$419$	9420.34			1.09836			0.549181	+	0.835703i	$0.314940\pi$
$420$		0			0
$421$	−4037.44			−0.467394			−0.233697	−	0.972309i	$-0.575082\pi$
$421$	−4037.44			−0.467394			−0.233697	+	0.972309i	$0.575082\pi$
$422$		0			0
$423$	1089.75	−	1887.50i	0.125261	−	0.216958i
$424$		0			0
$425$	614.019	+	1063.51i	0.0700807	+	0.121383i
$426$		0			0
$427$	−8410.55	−	12904.3i	−0.953197	−	1.46249i
$428$		0			0
$429$	3786.56	+	6558.52i	0.426147	+	0.738108i
$430$		0			0
$431$	7442.50	−	12890.8i	0.831769	−	1.44067i	−0.0648645	−	0.997894i	$-0.520662\pi$
$431$	7442.50	−	12890.8i	0.831769	−	1.44067i	0.896634	−	0.442773i	$-0.146005\pi$
$432$		0			0
$433$	−15136.6			−1.67995			−0.839977	−	0.542621i	$-0.817432\pi$
$433$	−15136.6			−1.67995			−0.839977	+	0.542621i	$0.817432\pi$
$434$		0			0
$435$	−4942.27			−0.544744
$436$		0			0
$437$	−833.436	+	1443.55i	−0.0912326	+	0.158020i
$438$		0			0
$439$	−6789.29	−	11759.4i	−0.738121	−	1.27846i	−0.953341	−	0.301897i	$-0.902380\pi$
$439$	−6789.29	−	11759.4i	−0.738121	−	1.27846i	0.215220	−	0.976566i	$-0.430953\pi$
$440$		0			0
$441$	−7768.66	−	10618.6i	−0.838858	−	1.14659i
$442$		0			0
$443$	6181.24	+	10706.2i	0.662933	+	1.14823i	0.979841	+	0.199778i	$0.0640220\pi$
$443$	6181.24	+	10706.2i	0.662933	+	1.14823i	−0.316908	+	0.948456i	$0.602645\pi$
$444$		0			0
$445$	−4002.72	+	6932.92i	−0.426398	+	0.738543i
$446$		0			0
$447$	19883.3			2.10391
$448$		0			0
$449$	2631.38			0.276575			0.138288	−	0.990392i	$-0.455840\pi$
$449$	2631.38			0.276575			0.138288	+	0.990392i	$0.455840\pi$
$450$		0			0
$451$	9711.84	−	16821.4i	1.01400	−	1.75629i
$452$		0			0
$453$	−11004.5	−	19060.4i	−1.14136	−	1.97690i
$454$		0			0
$455$	1237.40	+	1898.55i	0.127495	+	0.195617i
$456$		0			0
$457$	−8780.85	−	15208.9i	−0.898799	−	1.55677i	−0.829031	−	0.559202i	$-0.811108\pi$
$457$	−8780.85	−	15208.9i	−0.898799	−	1.55677i	−0.0697674	−	0.997563i	$-0.522226\pi$
$458$		0			0
$459$	2255.38	−	3906.43i	0.229351	−	0.397248i
$460$		0			0
$461$	13957.4			1.41011			0.705056	−	0.709152i	$-0.250922\pi$
$461$	13957.4			1.41011			0.705056	+	0.709152i	$0.250922\pi$
$462$		0			0
$463$	−8495.00			−0.852691			−0.426346	−	0.904560i	$-0.640199\pi$
$463$	−8495.00			−0.852691			−0.426346	+	0.904560i	$0.640199\pi$
$464$		0			0
$465$	4153.59	−	7194.23i	0.414233	−	0.717472i
$466$		0			0
$467$	−1386.60	−	2401.66i	−0.137396	−	0.237978i	0.789114	−	0.614247i	$-0.210540\pi$
$467$	−1386.60	−	2401.66i	−0.137396	−	0.237978i	−0.926510	+	0.376269i	$0.877207\pi$
$468$		0			0
$469$	−1325.95	+	2612.99i	−0.130547	+	0.257264i
$470$		0			0
$471$	−1672.68	−	2897.16i	−0.163637	−	0.283427i
$472$		0			0
$473$	−9139.95	+	15830.9i	−0.888489	+	1.53891i
$474$		0			0
$475$	447.279			0.0432054
$476$		0			0
$477$	2241.31			0.215142
$478$		0			0
$479$	−4405.45	+	7630.47i	−0.420230	+	0.727860i	−0.995962	−	0.0897787i	$-0.971384\pi$
$479$	−4405.45	+	7630.47i	−0.420230	+	0.727860i	0.575731	+	0.817639i	$0.304717\pi$
$480$		0			0
$481$	2879.40	+	4987.26i	0.272950	+	0.472764i
$482$		0			0
$483$	−13929.3	+	753.102i	−1.31222	+	0.0709469i
$484$		0			0
$485$	3428.98	+	5939.16i	0.321035	+	0.556048i
$486$		0			0
$487$	−2959.47	+	5125.96i	−0.275373	+	0.476960i	−0.970229	−	0.242189i	$-0.922135\pi$
$487$	−2959.47	+	5125.96i	−0.275373	+	0.476960i	0.694856	+	0.719149i	$0.255468\pi$
$488$		0			0
$489$	20817.1			1.92512
$490$		0			0
$491$	13182.5			1.21165			0.605823	−	0.795600i	$-0.292844\pi$
$491$	13182.5			1.21165			0.605823	+	0.795600i	$0.292844\pi$
$492$		0			0
$493$	3002.94	−	5201.24i	0.274332	−	0.475156i
$494$		0			0
$495$	3670.67	+	6357.79i	0.333302	+	0.577296i
$496$		0			0
$497$	−3747.14	+	202.593i	−0.338193	+	0.0182848i
$498$		0			0
$499$	9824.53	+	17016.6i	0.881376	+	1.52659i	0.849812	+	0.527086i	$0.176715\pi$
$499$	9824.53	+	17016.6i	0.881376	+	1.52659i	0.0315639	+	0.999502i	$0.489951\pi$
$500$		0			0
$501$	7334.76	−	12704.2i	0.654077	−	1.13290i
$502$		0			0
$503$	2208.83			0.195799			0.0978993	−	0.995196i	$-0.468788\pi$
$503$	2208.83			0.195799			0.0978993	+	0.995196i	$0.468788\pi$
$504$		0			0
$505$	−2806.19			−0.247275
$506$		0			0
$507$	6459.84	−	11188.8i	0.565861	−	0.980101i
$508$		0			0
$509$	8126.90	+	14076.2i	0.707698	+	1.22577i	0.965709	+	0.259627i	$0.0835998\pi$
$509$	8126.90	+	14076.2i	0.707698	+	1.22577i	−0.258010	+	0.966142i	$0.583067\pi$
$510$		0			0
$511$	−6438.36	+	12687.8i	−0.557370	+	1.09839i
$512$		0			0
$513$	−821.460	−	1422.81i	−0.0706985	−	0.122453i
$514$		0			0
$515$	4820.62	−	8349.56i	0.412470	−	0.714419i
$516$		0			0
$517$	−2174.88			−0.185012
$518$		0			0
$519$	15196.1			1.28523
$520$		0			0
$521$	4661.14	−	8073.33i	0.391955	−	0.678885i	−0.600753	−	0.799435i	$-0.705132\pi$
$521$	4661.14	−	8073.33i	0.391955	−	0.678885i	0.992707	+	0.120550i	$0.0384657\pi$
$522$		0			0
$523$	6068.10	+	10510.3i	0.507341	+	0.878740i	0.999964	+	0.00849740i	$0.00270484\pi$
$523$	6068.10	+	10510.3i	0.507341	+	0.878740i	−0.492623	+	0.870243i	$0.663962\pi$
$524$		0			0
$525$	2043.86	+	3135.90i	0.169907	+	0.260690i
$526$		0			0
$527$	5047.47	+	8742.48i	0.417213	+	0.722634i
$528$		0			0
$529$	1743.42	−	3019.69i	0.143291	−	0.248187i
$530$		0			0
$531$	55.2781			0.00451764
$532$		0			0
$533$	12418.6			1.00921
$534$		0			0
$535$	2037.69	−	3529.38i	0.164667	−	0.285212i
$536$		0			0
$537$	14542.6	+	25188.5i	1.16864	+	2.02414i
$538$		0			0
$539$	−5300.40	+	12011.7i	−0.423571	+	0.959886i
$540$		0			0
$541$	3680.89	+	6375.49i	0.292521	+	0.506661i	0.974405	−	0.224799i	$-0.0721725\pi$
$541$	3680.89	+	6375.49i	0.292521	+	0.506661i	−0.681884	+	0.731460i	$0.738839\pi$
$542$		0			0
$543$	−3733.57	+	6466.74i	−0.295070	+	0.511076i
$544$		0			0
$545$	612.225			0.0481189
$546$		0			0
$547$	18758.5			1.46628			0.733140	−	0.680077i	$-0.238054\pi$
$547$	18758.5			1.46628			0.733140	+	0.680077i	$0.238054\pi$
$548$		0			0
$549$	15951.4	−	27628.6i	1.24005	−	2.14783i
$550$		0			0
$551$	−1093.74	−	1894.41i	−0.0845640	−	0.146469i
$552$		0			0
$553$	6203.83	+	9518.56i	0.477059	+	0.731954i
$554$		0			0
$555$	4755.99	+	8237.62i	0.363749	+	0.630032i
$556$		0			0
$557$	6764.63	−	11716.7i	0.514590	−	0.891296i	−0.485266	−	0.874366i	$-0.661277\pi$
$557$	6764.63	−	11716.7i	0.514590	−	0.891296i	0.999857	−	0.0169301i	$-0.00538926\pi$
$558$		0			0
$559$	−11687.3			−0.884292
$560$		0			0
$561$	−15200.8			−1.14399
$562$		0			0
$563$	1145.80	−	1984.58i	0.0857722	−	0.148562i	−0.819948	−	0.572438i	$-0.805998\pi$
$563$	1145.80	−	1984.58i	0.0857722	−	0.148562i	0.905720	+	0.423876i	$0.139331\pi$
$564$		0			0
$565$	−15.5267	−	26.8930i	−0.00115613	−	0.00200247i
$566$		0			0
$567$	−2458.05	+	4843.98i	−0.182060	+	0.358779i
$568$		0			0
$569$	−11906.9	−	20623.3i	−0.877261	−	1.51946i	−0.854334	−	0.519724i	$-0.826035\pi$
$569$	−11906.9	−	20623.3i	−0.877261	−	1.51946i	−0.0229269	−	0.999737i	$-0.507299\pi$
$570$		0			0
$571$	−6374.66	+	11041.2i	−0.467200	+	0.809215i	−0.999298	−	0.0374685i	$-0.988071\pi$
$571$	−6374.66	+	11041.2i	−0.467200	+	0.809215i	0.532098	+	0.846683i	$0.321404\pi$
$572$		0			0
$573$	8651.88			0.630781
$574$		0			0
$575$	2329.19			0.168928
$576$		0			0
$577$	8245.45	−	14281.5i	0.594909	−	1.03041i	−0.398650	−	0.917103i	$-0.630521\pi$
$577$	8245.45	−	14281.5i	0.594909	−	1.03041i	0.993560	−	0.113310i	$-0.0361454\pi$
$578$		0			0
$579$	658.056	+	1139.79i	0.0472329	+	0.0818099i
$580$		0			0
$581$	−11521.7	+	622.933i	−0.822719	+	0.0444812i
$582$		0			0
$583$	−1118.28	−	1936.92i	−0.0794416	−	0.137597i
$584$		0			0
$585$	−2346.85	+	4064.86i	−0.165864	+	0.287284i
$586$		0			0
$587$	755.669			0.0531342			0.0265671	−	0.999647i	$-0.491542\pi$
$587$	755.669			0.0531342			0.0265671	+	0.999647i	$0.491542\pi$
$588$		0			0
$589$	3676.80			0.257216
$590$		0			0
$591$	−2258.20	+	3911.32i	−0.157174	+	0.272234i
$592$		0			0
$593$	9058.20	+	15689.3i	0.627278	+	1.08648i	0.988096	+	0.153841i	$0.0491643\pi$
$593$	9058.20	+	15689.3i	0.627278	+	1.08648i	−0.360818	+	0.932636i	$0.617502\pi$
$594$		0			0
$595$	−4542.08	+	245.573i	−0.312953	+	0.0169202i
$596$		0			0
$597$	1862.94	+	3226.71i	0.127714	+	0.221207i
$598$		0			0
$599$	−6681.20	+	11572.2i	−0.455737	+	0.789360i	−0.998730	−	0.0503774i	$-0.983958\pi$
$599$	−6681.20	+	11572.2i	−0.455737	+	0.789360i	0.542993	+	0.839737i	$0.317291\pi$
$600$		0			0
$601$	7760.63			0.526726			0.263363	−	0.964697i	$-0.415168\pi$
$601$	7760.63			0.526726			0.263363	+	0.964697i	$0.415168\pi$
$602$		0			0
$603$	−6068.87			−0.409857
$604$		0			0
$605$	335.393	−	580.917i	0.0225383	−	0.0390374i
$606$		0			0
$607$	6318.17	+	10943.4i	0.422482	+	0.731760i	0.996182	−	0.0873055i	$-0.0278256\pi$
$607$	6318.17	+	10943.4i	0.422482	+	0.731760i	−0.573700	+	0.819066i	$0.694492\pi$
$608$		0			0
$609$	8283.95	−	16324.8i	0.551203	−	1.08623i
$610$		0			0
$611$	−695.256	−	1204.22i	−0.0460345	−	0.0797340i
$612$		0			0
$613$	2495.30	−	4321.98i	0.164411	−	0.284769i	−0.772035	−	0.635580i	$-0.780761\pi$
$613$	2495.30	−	4321.98i	0.164411	−	0.284769i	0.936446	+	0.350812i	$0.114094\pi$
$614$		0			0
$615$	20512.1			1.34493
$616$		0			0
$617$	3065.36			0.200011			0.100006	−	0.994987i	$-0.468114\pi$
$617$	3065.36			0.200011			0.100006	+	0.994987i	$0.468114\pi$
$618$		0			0
$619$	3049.52	−	5281.93i	0.198014	−	0.342970i	−0.749870	−	0.661585i	$-0.769884\pi$
$619$	3049.52	−	5281.93i	0.198014	−	0.342970i	0.947884	+	0.318614i	$0.103218\pi$
$620$		0			0
$621$	−4277.72	−	7409.22i	−0.276423	−	0.478779i
$622$		0			0
$623$	−16191.0	−	24842.0i	−1.04122	−	1.59755i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−2768.23	+	4794.71i	−0.176320	+	0.305394i
$628$		0			0
$629$	−11559.0			−0.732732
$630$		0			0
$631$	−14367.3			−0.906425			−0.453212	−	0.891403i	$-0.649722\pi$
$631$	−14367.3			−0.906425			−0.453212	+	0.891403i	$0.649722\pi$
$632$		0			0
$633$	24460.2	−	42366.3i	1.53587	−	2.66021i
$634$		0			0
$635$	−1090.22	−	1888.31i	−0.0681321	−	0.118008i
$636$		0			0
$637$	−8345.20	+	905.030i	−0.519072	+	0.0562930i
$638$		0			0
$639$	−3886.15	−	6731.01i	−0.240585	−	0.416705i
$640$		0			0
$641$	422.426	−	731.663i	0.0260294	−	0.0450842i	−0.852717	−	0.522373i	$-0.825047\pi$
$641$	422.426	−	731.663i	0.0260294	−	0.0450842i	0.878747	+	0.477289i	$0.158380\pi$
$642$		0			0
$643$	−10319.6			−0.632918			−0.316459	−	0.948606i	$-0.602494\pi$
$643$	−10319.6			−0.632918			−0.316459	+	0.948606i	$0.602494\pi$
$644$		0			0
$645$	−19304.3			−1.17846
$646$		0			0
$647$	4185.35	−	7249.23i	0.254317	−	0.440490i	−0.710393	−	0.703805i	$-0.751483\pi$
$647$	4185.35	−	7249.23i	0.254317	−	0.440490i	0.964710	+	0.263316i	$0.0848161\pi$
$648$		0			0
$649$	−27.5805	−	47.7708i	−0.00166815	−	0.00288932i
$650$		0			0
$651$	16801.3	+	25778.3i	1.01151	+	1.55197i
$652$		0			0
$653$	2690.14	+	4659.46i	0.161215	+	0.279233i	0.935305	−	0.353843i	$-0.115125\pi$
$653$	2690.14	+	4659.46i	0.161215	+	0.279233i	−0.774090	+	0.633076i	$0.781792\pi$
$654$		0			0
$655$	4244.29	−	7351.32i	0.253188	−	0.438534i
$656$		0			0
$657$	−29468.4			−1.74988
$658$		0			0
$659$	26587.2			1.57161			0.785804	−	0.618475i	$-0.212249\pi$
$659$	26587.2			1.57161			0.785804	+	0.618475i	$0.212249\pi$
$660$		0			0
$661$	−5452.15	+	9443.40i	−0.320823	+	0.555682i	−0.980658	−	0.195729i	$-0.937293\pi$
$661$	−5452.15	+	9443.40i	−0.320823	+	0.555682i	0.659835	+	0.751411i	$0.270626\pi$
$662$		0			0
$663$	−4859.31	−	8416.58i	−0.284646	−	0.493021i
$664$		0			0
$665$	−749.704	+	1477.41i	−0.0437177	+	0.0861527i
$666$		0			0
$667$	−5695.59	−	9865.05i	−0.330636	−	0.572678i
$668$		0			0
$669$	−1302.01	+	2255.16i	−0.0752448	+	0.130328i
$670$		0			0
$671$	−31835.2			−1.83157
$672$		0			0
$673$	−17375.9			−0.995233			−0.497616	−	0.867397i	$-0.665791\pi$
$673$	−17375.9			−0.995233			−0.497616	+	0.867397i	$0.665791\pi$
$674$		0			0
$675$	−1147.86	+	1988.15i	−0.0654534	+	0.113369i
$676$		0			0
$677$	−6861.25	−	11884.0i	−0.389512	−	0.674654i	0.602872	−	0.797838i	$-0.294023\pi$
$677$	−6861.25	−	11884.0i	−0.389512	−	0.674654i	−0.992384	+	0.123184i	$0.960690\pi$
$678$		0			0
$679$	−25365.2	+	1371.40i	−1.43362	+	0.0775101i
$680$		0			0
$681$	2583.88	+	4475.42i	0.145396	+	0.251833i
$682$		0			0
$683$	−308.676	+	534.643i	−0.0172931	+	0.0299525i	−0.874542	−	0.484949i	$-0.838838\pi$
$683$	−308.676	+	534.643i	−0.0172931	+	0.0299525i	0.857249	+	0.514901i	$0.172171\pi$
$684$		0			0
$685$	−4176.86			−0.232978
$686$		0			0
$687$	50036.2			2.77875
$688$		0			0
$689$	714.975	−	1238.37i	0.0395332	−	0.0684735i
$690$		0			0
$691$	−10294.4	−	17830.3i	−0.566738	−	0.981618i	−0.996886	−	0.0788599i	$-0.974872\pi$
$691$	−10294.4	−	17830.3i	−0.566738	−	0.981618i	0.430148	−	0.902758i	$-0.358461\pi$
$692$		0			0
$693$	−27153.0	+	1468.06i	−1.48840	+	0.0804718i
$694$		0			0
$695$	4844.31	+	8390.58i	0.264396	+	0.457947i
$696$		0			0
$697$	−12463.2	+	21587.0i	−0.677301	+	1.17312i
$698$		0			0
$699$	29524.1			1.59757
$700$		0			0
$701$	−33857.2			−1.82421			−0.912104	−	0.409958i	$-0.865543\pi$
$701$	−33857.2			−1.82421			−0.912104	+	0.409958i	$0.865543\pi$
$702$		0			0
$703$	−2105.03	+	3646.02i	−0.112934	+	0.195608i
$704$		0			0
$705$	−1148.38	−	1989.05i	−0.0613481	−	0.106258i
$706$		0			0
$707$	4703.57	−	9269.14i	0.250207	−	0.493072i
$708$		0			0
$709$	1208.81	+	2093.72i	0.0640309	+	0.110905i	0.896264	−	0.443522i	$-0.146271\pi$
$709$	1208.81	+	2093.72i	0.0640309	+	0.110905i	−0.832233	+	0.554426i	$0.812938\pi$
$710$		0			0
$711$	−11766.1	+	20379.5i	−0.620625	+	1.07495i
$712$		0			0
$713$	19146.8			1.00568
$714$		0			0
$715$	4683.75			0.244982
$716$		0			0
$717$	−18809.9	+	32579.7i	−0.979733	+	1.69695i
$718$		0			0
$719$	8909.26	+	15431.3i	0.462113	+	0.800403i	0.999066	−	0.0432089i	$-0.0137581\pi$
$719$	8909.26	+	15431.3i	0.462113	+	0.800403i	−0.536953	+	0.843612i	$0.680425\pi$
$720$		0			0
$721$	19499.5	+	29918.1i	1.00721	+	1.54537i
$722$		0			0
$723$	−20228.1	−	35036.1i	−1.04051	−	1.80222i
$724$		0			0
$725$	−1528.32	+	2647.13i	−0.0782902	+	0.135603i
$726$		0			0
$727$	−24410.7			−1.24531			−0.622657	−	0.782495i	$-0.713947\pi$
$727$	−24410.7			−1.24531			−0.622657	+	0.782495i	$0.713947\pi$
$728$		0			0
$729$	−31294.9			−1.58995
$730$		0			0
$731$	11729.3	−	20315.8i	0.593468	−	1.02792i
$732$		0			0
$733$	−15856.2	−	27463.7i	−0.798991	−	1.38389i	−0.920274	−	0.391276i	$-0.872034\pi$
$733$	−15856.2	−	27463.7i	−0.798991	−	1.38389i	0.121282	−	0.992618i	$-0.461299\pi$
$734$		0			0
$735$	−13784.0	+	1494.87i	−0.691744	+	0.0750191i
$736$		0			0
$737$	3028.01	+	5244.66i	0.151341	+	0.262130i
$738$		0			0
$739$	−12105.7	+	20967.7i	−0.602593	+	1.04372i	0.389834	+	0.920885i	$0.372532\pi$
$739$	−12105.7	+	20967.7i	−0.602593	+	1.04372i	−0.992427	+	0.122836i	$0.960801\pi$
$740$		0			0
$741$	−3539.74			−0.175487
$742$		0			0
$743$	−32221.1			−1.59095			−0.795477	−	0.605983i	$-0.792780\pi$
$743$	−32221.1			−1.59095			−0.795477	+	0.605983i	$0.792780\pi$
$744$		0			0
$745$	6148.62	−	10649.7i	0.302373	−	0.523726i
$746$		0			0
$747$	−11949.1	−	20696.5i	−0.585268	−	1.01371i
$748$		0			0
$749$	8242.46	+	12646.4i	0.402100	+	0.616944i
$750$		0			0
$751$	−11742.2	−	20338.1i	−0.570545	−	0.988212i	−0.996510	−	0.0834728i	$-0.973399\pi$
$751$	−11742.2	−	20338.1i	−0.570545	−	0.988212i	0.425965	−	0.904739i	$-0.359935\pi$
$752$		0			0
$753$	−13483.9	+	23354.8i	−0.652565	+	1.13028i
$754$		0			0
$755$	−13611.9			−0.656145
$756$		0			0
$757$	25506.7			1.22465			0.612323	−	0.790608i	$-0.290235\pi$
$757$	25506.7			1.22465			0.612323	+	0.790608i	$0.290235\pi$
$758$		0			0
$759$	−14415.4	+	24968.3i	−0.689390	+	1.19406i
$760$		0			0
$761$	14956.4	+	25905.2i	0.712442	+	1.23399i	0.963938	+	0.266127i	$0.0857441\pi$
$761$	14956.4	+	25905.2i	0.712442	+	1.23399i	−0.251496	+	0.967858i	$0.580923\pi$
$762$		0			0
$763$	−1026.18	+	2022.25i	−0.0486895	+	0.0959505i
$764$		0			0
$765$	−4710.59	−	8158.97i	−0.222630	−	0.385606i
$766$		0			0
$767$	17.6336	−	30.5423i	0.000830135	−	0.00143784i
$768$		0			0
$769$	−615.472			−0.0288615			−0.0144307	−	0.999896i	$-0.504594\pi$
$769$	−615.472			−0.0288615			−0.0144307	+	0.999896i	$0.504594\pi$
$770$		0			0
$771$	−32218.6			−1.50496
$772$		0			0
$773$	−926.195	+	1604.22i	−0.0430956	+	0.0746438i	−0.886769	−	0.462214i	$-0.847055\pi$
$773$	−926.195	+	1604.22i	−0.0430956	+	0.0746438i	0.843673	+	0.536857i	$0.180389\pi$
$774$		0			0
$775$	−2568.87	−	4449.41i	−0.119067	−	0.206229i
$776$		0			0
$777$	−35181.5	+	1902.13i	−1.62436	+	0.0878229i
$778$		0			0
$779$	4539.39	+	7862.45i	0.208781	+	0.361620i
$780$		0			0
$781$	−3877.92	+	6716.75i	−0.177673	+	0.307739i
$782$		0			0
$783$	11227.5			0.512436
$784$		0			0
$785$	−2069.00			−0.0940711
$786$		0			0
$787$	−10608.8	+	18375.0i	−0.480512	+	0.832271i	−0.999750	−	0.0223587i	$-0.992882\pi$
$787$	−10608.8	+	18375.0i	−0.480512	+	0.832271i	0.519238	+	0.854630i	$0.326216\pi$
$788$		0			0
$789$	7671.78	+	13287.9i	0.346163	+	0.599572i
$790$		0			0
$791$	114.855	−	6.20979i	0.00516282	−	0.000279133i
$792$		0			0
$793$	−10176.9	−	17626.9i	−0.455729	−	0.789346i
$794$		0			0
$795$	1180.95	−	2045.46i	0.0526841	−	0.0912516i
$796$		0			0
$797$	16797.7			0.746557			0.373278	−	0.927719i	$-0.378234\pi$
$797$	16797.7			0.746557			0.373278	+	0.927719i	$0.378234\pi$
$798$		0			0
$799$	2791.03			0.123579
$800$		0			0
$801$	30707.8	−	53187.4i	1.35456	−	2.34617i
$802$		0			0
$803$	14703.0	+	25466.3i	0.646148	+	1.11916i
$804$		0			0
$805$	−3904.05	+	7693.56i	−0.170931	+	0.336848i
$806$		0			0
$807$	−23679.7	−	41014.4i	−1.03292	−	1.78907i
$808$		0			0
$809$	−11103.0	+	19230.9i	−0.482521	+	0.835751i	−0.999799	−	0.0200667i	$-0.993612\pi$
$809$	−11103.0	+	19230.9i	−0.482521	+	0.835751i	0.517278	+	0.855818i	$0.326945\pi$
$810$		0			0
$811$	35024.7			1.51650			0.758250	−	0.651964i	$-0.226054\pi$
$811$	35024.7			1.51650			0.758250	+	0.651964i	$0.226054\pi$
$812$		0			0
$813$	66741.0			2.87910
$814$		0			0
$815$	6437.39	−	11149.9i	0.276677	−	0.479219i
$816$		0			0
$817$	−4272.08	−	7399.47i	−0.182939	−	0.316860i
$818$		0			0
$819$	−9493.03	−	14565.2i	−0.405022	−	0.621427i
$820$		0			0
$821$	13885.1	+	24049.7i	0.590247	+	1.02234i	0.994199	+	0.107557i	$0.0343028\pi$
$821$	13885.1	+	24049.7i	0.590247	+	1.02234i	−0.403952	+	0.914780i	$0.632364\pi$
$822$		0			0
$823$	1705.89	−	2954.69i	0.0722523	−	0.125145i	−0.827636	−	0.561265i	$-0.810315\pi$
$823$	1705.89	−	2954.69i	0.0722523	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$824$		0			0
$825$	7736.31			0.326477
$826$		0			0
$827$	9664.20			0.406357			0.203178	−	0.979142i	$-0.434873\pi$
$827$	9664.20			0.406357			0.203178	+	0.979142i	$0.434873\pi$
$828$		0			0
$829$	−5668.61	+	9818.31i	−0.237489	+	0.411344i	−0.959993	−	0.280023i	$-0.909658\pi$
$829$	−5668.61	+	9818.31i	−0.237489	+	0.411344i	0.722504	+	0.691367i	$0.242991\pi$
$830$		0			0
$831$	30412.2	+	52675.5i	1.26954	+	2.19891i
$832$		0			0
$833$	6802.03	−	15414.6i	0.282925	−	0.641158i
$834$		0			0
$835$	−4536.32	−	7857.15i	−0.188007	−	0.325638i
$836$		0			0
$837$	−9435.83	+	16343.3i	−0.389666	+	0.674921i
$838$		0			0
$839$	−44881.4			−1.84682			−0.923408	−	0.383819i	$-0.874609\pi$
$839$	−44881.4			−1.84682			−0.923408	+	0.383819i	$0.874609\pi$
$840$		0			0
$841$	−9440.11			−0.387064
$842$		0			0
$843$	14507.4	−	25127.5i	0.592717	−	1.02662i
$844$		0			0
$845$	−3995.22	−	6919.92i	−0.162651	−	0.281719i
$846$		0			0
$847$	1356.67	+	2081.54i	0.0550362	+	0.0844422i
$848$		0			0
$849$	−797.674	−	1381.61i	−0.0322451	−	0.0558502i
$850$		0			0
$851$	−10961.8	+	18986.5i	−0.441560	+	0.764804i
$852$		0			0
$853$	−21817.2			−0.875741			−0.437871	−	0.899038i	$-0.644267\pi$
$853$	−21817.2			−0.875741			−0.437871	+	0.899038i	$0.644267\pi$
$854$		0			0
$855$	−3431.40			−0.137253
$856$		0			0
$857$	−11194.0	+	19388.6i	−0.446184	+	0.772814i	−0.998134	−	0.0610636i	$-0.980551\pi$
$857$	−11194.0	+	19388.6i	−0.446184	+	0.772814i	0.551950	+	0.833877i	$0.313884\pi$
$858$		0			0
$859$	−2960.29	−	5127.38i	−0.117583	−	0.203660i	0.801226	−	0.598362i	$-0.204181\pi$
$859$	−2960.29	−	5127.38i	−0.117583	−	0.203660i	−0.918809	+	0.394702i	$0.870848\pi$
$860$		0			0
$861$	−34381.3	+	67753.8i	−1.36087	+	2.68182i
$862$		0			0
$863$	−1347.96	−	2334.73i	−0.0531692	−	0.0920917i	0.838216	−	0.545339i	$-0.183599\pi$
$863$	−1347.96	−	2334.73i	−0.0531692	−	0.0920917i	−0.891385	+	0.453247i	$0.850266\pi$
$864$		0			0
$865$	4699.17	−	8139.21i	0.184713	−	0.319932i
$866$		0			0
$867$	−20211.8			−0.791729
$868$		0			0
$869$	23482.4			0.916669
$870$		0			0
$871$	−1935.96	+	3353.18i	−0.0753128	+	0.130446i
$872$		0			0
$873$	−26306.2	−	45563.6i	−1.01985	−	1.76643i
$874$		0			0
$875$	2311.66	−	124.982i	0.0893123	−	0.00482877i
$876$		0			0
$877$	−3933.82	−	6813.58i	−0.151466	−	0.262347i	0.780301	−	0.625405i	$-0.215066\pi$
$877$	−3933.82	−	6813.58i	−0.151466	−	0.262347i	−0.931767	+	0.363058i	$0.881733\pi$
$878$		0			0
$879$	15277.7	−	26461.7i	0.586239	−	1.01540i
$880$		0			0
$881$	17182.7			0.657092			0.328546	−	0.944488i	$-0.393441\pi$
$881$	17182.7			0.657092			0.328546	+	0.944488i	$0.393441\pi$
$882$		0			0
$883$	7732.99			0.294718			0.147359	−	0.989083i	$-0.452923\pi$
$883$	7732.99			0.294718			0.147359	+	0.989083i	$0.452923\pi$
$884$		0			0
$885$	29.1260	−	50.4478i	0.00110628	−	0.00191614i
$886$		0			0
$887$	19140.5	+	33152.2i	0.724547	+	1.25495i	0.959160	+	0.282864i	$0.0912845\pi$
$887$	19140.5	+	33152.2i	0.724547	+	1.25495i	−0.234613	+	0.972089i	$0.575382\pi$
$888$		0			0
$889$	8064.65	−	436.024i	0.304252	−	0.0164497i
$890$		0			0
$891$	5613.33	+	9722.58i	0.211059	+	0.365565i
$892$		0			0
$893$	508.278	−	880.364i	0.0190469	−	0.0329902i
$894$		0			0
$895$	17988.3			0.671824
$896$		0			0
$897$	−18433.1			−0.686133
$898$		0			0
$899$	−12563.4	+	21760.4i	−0.466087	+	0.807287i
$900$		0			0
$901$	1435.09	+	2485.66i	0.0530632	+	0.0919081i
$902$		0			0
$903$	32356.7	−	63764.1i	1.19243	−	2.34987i
$904$		0			0
$905$	2309.10	+	3999.48i	0.0848146	+	0.146903i
$906$		0			0
$907$	1761.13	−	3050.36i	0.0644733	−	0.111671i	−0.831987	−	0.554795i	$-0.812797\pi$
$907$	1761.13	−	3050.36i	0.0644733	−	0.111671i	0.896460	+	0.443124i	$0.146130\pi$
$908$		0			0
$909$	21528.3			0.785532
$910$		0			0
$911$	−7101.21			−0.258259			−0.129129	−	0.991628i	$-0.541218\pi$
$911$	−7101.21			−0.258259			−0.129129	+	0.991628i	$0.541218\pi$
$912$		0			0
$913$	−11923.8	+	20652.6i	−0.432224	+	0.748634i
$914$		0			0
$915$	−16809.6	−	29115.0i	−0.607330	−	1.05193i
$916$		0			0
$917$	17168.2	+	26341.2i	0.618259	+	0.948598i
$918$		0			0
$919$	−16853.0	−	29190.2i	−0.604928	−	1.04777i	−0.992063	−	0.125743i	$-0.959869\pi$
$919$	−16853.0	−	29190.2i	−0.604928	−	1.04777i	0.387135	−	0.922023i	$-0.373465\pi$
$920$		0			0
$921$	18168.5	−	31468.8i	0.650026	−	1.12588i
$922$		0			0
$923$	−4958.70			−0.176834
$924$		0			0
$925$	5882.88			0.209111
$926$		0			0
$927$	−36982.5	+	64055.6i	−1.31032	+	2.26954i
$928$		0			0
$929$	17970.7	+	31126.2i	0.634661	+	1.09927i	0.986587	+	0.163237i	$0.0521936\pi$
$929$	17970.7	+	31126.2i	0.634661	+	1.09927i	−0.351926	+	0.936028i	$0.614473\pi$
$930$		0			0
$931$	−3623.44	−	4952.71i	−0.127555	−	0.174349i
$932$		0			0
$933$	39383.5	+	68214.3i	1.38195	+	2.39361i
$934$		0			0
$935$	−4700.60	+	8141.69i	−0.164413	+	0.284772i
$936$		0			0
$937$	−2167.66			−0.0755757			−0.0377878	−	0.999286i	$-0.512031\pi$
$937$	−2167.66			−0.0755757			−0.0377878	+	0.999286i	$0.512031\pi$
$938$		0			0
$939$	36915.8			1.28296
$940$		0			0
$941$	−9998.15	+	17317.3i	−0.346366	+	0.599924i	−0.985601	−	0.169088i	$-0.945918\pi$
$941$	−9998.15	+	17317.3i	−0.346366	+	0.599924i	0.639235	+	0.769011i	$0.279251\pi$
$942$		0			0
$943$	23638.7	+	40943.4i	0.816311	+	1.41389i
$944$		0			0
$945$	−4643.10	−	7123.92i	−0.159831	−	0.245229i
$946$		0			0
$947$	6864.50	+	11889.7i	0.235550	+	0.407985i	0.959433	−	0.281938i	$-0.0909774\pi$
$947$	6864.50	+	11889.7i	0.235550	+	0.407985i	−0.723882	+	0.689924i	$0.757644\pi$
$948$		0			0
$949$	−9400.38	+	16281.9i	−0.321548	+	0.556938i
$950$		0			0
$951$	74935.5			2.55515
$952$		0			0
$953$	−10076.1			−0.342495			−0.171248	−	0.985228i	$-0.554780\pi$
$953$	−10076.1			−0.342495			−0.171248	+	0.985228i	$0.554780\pi$
$954$		0			0
$955$	2675.46	−	4634.04i	0.0906555	−	0.157020i
$956$		0			0
$957$	−18917.7	−	32766.4i	−0.638999	−	1.10678i
$958$		0			0
$959$	7001.02	−	13796.6i	0.235740	−	0.464564i
$960$		0			0
$961$	−6221.61	−	10776.1i	−0.208842	−	0.361725i
$962$		0			0
$963$	−15632.6	+	27076.4i	−0.523108	+	0.906049i
$964$		0			0
$965$	813.975			0.0271532
$966$		0			0
$967$	24434.2			0.812566			0.406283	−	0.913747i	$-0.366825\pi$
$967$	24434.2			0.812566			0.406283	+	0.913747i	$0.366825\pi$
$968$		0			0
$969$	3552.48	−	6153.07i	0.117773	−	0.203989i
$970$		0			0
$971$	9328.53	+	16157.5i	0.308308	+	0.534004i	0.977992	−	0.208641i	$-0.0669041\pi$
$971$	9328.53	+	16157.5i	0.308308	+	0.534004i	−0.669685	+	0.742646i	$0.733571\pi$
$972$		0			0
$973$	−35834.8	+	1937.45i	−1.18069	+	0.0638353i
$974$		0			0
$975$	2473.11	+	4283.55i	0.0812337	+	0.140701i
$976$		0			0
$977$	26037.2	−	45097.7i	0.852614	−	1.47677i	−0.0262279	−	0.999656i	$-0.508350\pi$
$977$	26037.2	−	45097.7i	0.852614	−	1.47677i	0.878841	−	0.477114i	$-0.158317\pi$
$978$		0			0
$979$	−61285.4			−2.00071
$980$		0			0
$981$	−4696.82			−0.152862
$982$		0			0
$983$	−4602.58	+	7971.90i	−0.149338	+	0.258662i	−0.930983	−	0.365062i	$-0.881048\pi$
$983$	−4602.58	+	7971.90i	−0.149338	+	0.258662i	0.781645	+	0.623724i	$0.214381\pi$
$984$		0			0
$985$	1396.63	+	2419.03i	0.0451780	+	0.0782506i
$986$		0			0
$987$	8494.89	−	459.286i	0.273957	−	0.0148118i
$988$		0			0
$989$	−22246.7	−	38532.4i	−0.715272	−	1.23889i
$990$		0			0
$991$	10542.3	−	18259.8i	0.337929	−	0.585311i	−0.646114	−	0.763241i	$-0.723607\pi$
$991$	10542.3	−	18259.8i	0.337929	−	0.585311i	0.984043	+	0.177930i	$0.0569402\pi$
$992$		0			0
$993$	7936.79			0.253642
$994$		0			0
$995$	2304.35			0.0734199
$996$		0			0
$997$	−26388.0	+	45705.3i	−0.838231	+	1.45186i	0.0531416	+	0.998587i	$0.483077\pi$
$997$	−26388.0	+	45705.3i	−0.838231	+	1.45186i	−0.891373	+	0.453271i	$0.850257\pi$
$998$		0			0
$999$	−10804.3	−	18713.6i	−0.342176	−	0.592666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.4.q.p.81.1		12
4.3	odd	2		280.4.q.e.81.6	✓	12
7.2	even	3	inner	560.4.q.p.401.1		12
28.3	even	6		1960.4.a.bb.1.6		6
28.11	odd	6		1960.4.a.w.1.1		6
28.23	odd	6		280.4.q.e.121.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.4.q.e.81.6	✓	12	4.3	odd	2
280.4.q.e.121.6	yes	12	28.23	odd	6
560.4.q.p.81.1		12	1.1	even	1	trivial
560.4.q.p.401.1		12	7.2	even	3	inner
1960.4.a.w.1.1		6	28.11	odd	6
1960.4.a.bb.1.6		6	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.04223 + 7.00136i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-18.4932 + 0.999858i) q^{7} +(-19.1793 - 33.2196i) q^{9} +(-19.1387 + 33.1492i) q^{11} -24.4727 q^{13} -40.4223 q^{15} +(24.5607 - 42.5405i) q^{17} +(-8.94558 - 15.4942i) q^{19} +(67.7537 - 133.519i) q^{21} +(-46.5837 - 80.6853i) q^{23} +(-12.5000 + 21.6506i) q^{25} +91.8286 q^{27} +122.266 q^{29} +(-102.755 + 177.977i) q^{31} +(-154.726 - 267.993i) q^{33} +(-50.5626 - 77.5785i) q^{35} +(-117.658 - 203.789i) q^{37} +(98.9244 - 171.342i) q^{39} -507.445 q^{41} +477.564 q^{43} +(95.8966 - 166.098i) q^{45} +(28.4095 + 49.2067i) q^{47} +(341.001 - 36.9812i) q^{49} +(198.561 + 343.917i) q^{51} +(-29.2152 + 50.6022i) q^{53} -191.387 q^{55} +144.640 q^{57} +(-0.720543 + 1.24802i) q^{59} +(415.848 + 720.270i) q^{61} +(387.903 + 595.161i) q^{63} +(-61.1817 - 105.970i) q^{65} +(79.1069 - 137.017i) q^{67} +753.209 q^{69} +202.622 q^{71} +(384.117 - 665.310i) q^{73} +(-101.056 - 175.034i) q^{75} +(320.792 - 632.172i) q^{77} +(-306.740 - 531.289i) q^{79} +(146.649 - 254.003i) q^{81} +623.021 q^{83} +245.607 q^{85} +(-494.227 + 856.025i) q^{87} +(800.544 + 1386.58i) q^{89} +(452.580 - 24.4692i) q^{91} +(-830.718 - 1438.85i) q^{93} +(44.7279 - 77.4710i) q^{95} +1371.59 q^{97} +1468.27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{3} + 30 q^{5} + 14 q^{7} - 34 q^{9} - 240 q^{13} - 80 q^{15} + 122 q^{17} - 2 q^{19} + 170 q^{21} + 30 q^{23} - 150 q^{25} + 64 q^{27} + 476 q^{29} - 122 q^{31} + 584 q^{33} - 100 q^{35} + 342 q^{37}+ \cdots + 216 q^{99}+O(q^{100}) \) 12 * q - 8 * q^3 + 30 * q^5 + 14 * q^7 - 34 * q^9 - 240 * q^13 - 80 * q^15 + 122 * q^17 - 2 * q^19 + 170 * q^21 + 30 * q^23 - 150 * q^25 + 64 * q^27 + 476 * q^29 - 122 * q^31 + 584 * q^33 - 100 * q^35 + 342 * q^37 - 126 * q^39 - 676 * q^41 - 1176 * q^43 + 170 * q^45 + 260 * q^47 - 368 * q^49 - 770 * q^51 - 680 * q^53 + 1380 * q^57 - 918 * q^59 + 1026 * q^61 + 1284 * q^63 - 600 * q^65 + 1532 * q^67 - 724 * q^69 + 300 * q^71 - 158 * q^73 - 200 * q^75 + 758 * q^77 + 222 * q^79 + 250 * q^81 - 704 * q^83 + 1220 * q^85 + 1306 * q^87 + 1684 * q^89 - 122 * q^91 - 2834 * q^93 + 10 * q^95 - 2600 * q^97 + 216 * q^99

Introduction

L-functions

Modular forms

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