LMFDB - Embedded newform 588.4.k.d.521.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(509,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("588.509");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.k (of order $6$, 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:	$34.6931230834$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 94x^{12} - 128x^{10} + 2719x^{8} - 10368x^{6} - 616734x^{4} + 1062882x^{2} + 43046721 $ x^16 + 2x^14 - 94x^12 - 128x^10 + 2719x^8 - 10368x^6 - 616734x^4 + 1062882*x^2 + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{12} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.3
Root			$2.59507 - 1.50519i$ of defining polynomial
Character	$\chi$	$=$	588.521
Dual form			588.4.k.d.509.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60707 - 4.49480i) q^{3} +(-8.45479 - 14.6441i) q^{5} +(-13.4064 + 23.4365i) q^{9} +O(q^{10})$	\(q+(-2.60707 - 4.49480i) q^{3} +(-8.45479 - 14.6441i) q^{5} +(-13.4064 + 23.4365i) q^{9} +(-45.7714 - 26.4261i) q^{11} +49.8375i q^{13} +(-43.7802 + 76.1808i) q^{15} +(-0.687566 + 1.19090i) q^{17} +(62.9115 - 36.3220i) q^{19} +(-166.990 + 96.4117i) q^{23} +(-80.4669 + 139.373i) q^{25} +(140.294 - 0.841448i) q^{27} +34.2666i q^{29} +(81.2050 + 46.8837i) q^{31} +(0.549045 + 274.628i) q^{33} +(-150.121 - 260.017i) q^{37} +(224.010 - 129.930i) q^{39} -88.2653 q^{41} +136.747 q^{43} +(456.555 - 1.82553i) q^{45} +(-283.337 - 490.755i) q^{47} +(7.14538 - 0.0142853i) q^{51} +(395.847 + 228.542i) q^{53} +893.710i q^{55} +(-327.274 - 188.081i) q^{57} +(126.542 - 219.178i) q^{59} +(215.803 - 124.594i) q^{61} +(729.827 - 421.366i) q^{65} +(54.3074 - 94.0632i) q^{67} +(868.705 + 499.234i) q^{69} +21.4904i q^{71} +(310.185 + 179.085i) q^{73} +(836.235 - 1.67183i) q^{75} +(597.582 + 1035.04i) q^{79} +(-369.537 - 628.397i) q^{81} +834.327 q^{83} +23.2529 q^{85} +(154.021 - 89.3353i) q^{87} +(-114.929 - 199.063i) q^{89} +(-0.974085 - 487.229i) q^{93} +(-1063.81 - 614.189i) q^{95} +1140.39i q^{97} +(1232.97 - 718.441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{9}+O(q^{10}) $ 16 * q + 12 * q^9	$ 16 q + 12 q^{9} - 120 q^{15} - 320 q^{25} - 80 q^{37} + 732 q^{39} + 640 q^{43} - 552 q^{51} - 1560 q^{57} - 1840 q^{67} + 3176 q^{79} + 3456 q^{81} + 1920 q^{85} - 3960 q^{93} + 1152 q^{99}+O(q^{100}) $ 16 * q + 12 * q^9 - 120 * q^15 - 320 * q^25 - 80 * q^37 + 732 * q^39 + 640 * q^43 - 552 * q^51 - 1560 * q^57 - 1840 * q^67 + 3176 * q^79 + 3456 * q^81 + 1920 * q^85 - 3960 * q^93 + 1152 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−2.60707	−	4.49480i	−0.501730	−	0.865024i
$3$	−2.60707	−	4.49480i	−0.501730	−	0.865024i
$4$		0			0
$5$	−8.45479	−	14.6441i	−0.756219	−	1.30981i	−0.944766	−	0.327746i	$-0.893711\pi$
$5$	−8.45479	−	14.6441i	−0.756219	−	1.30981i	0.188546	−	0.982064i	$-0.439622\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−13.4064	+	23.4365i	−0.496533	+	0.868018i
$10$		0			0
$11$	−45.7714	−	26.4261i	−1.25460	−	0.724344i	−0.282580	−	0.959244i	$-0.591190\pi$
$11$	−45.7714	−	26.4261i	−1.25460	−	0.724344i	−0.972020	+	0.234900i	$0.924524\pi$
$12$		0			0
$13$			49.8375i			1.06326i	0.846975	+	0.531632i	$0.178421\pi$
$13$			49.8375i			1.06326i	−0.846975	+	0.531632i	$0.821579\pi$
$14$		0			0
$15$	−43.7802	+	76.1808i	−0.753599	+	1.31132i
$16$		0			0
$17$	−0.687566	+	1.19090i	−0.00980937	+	0.0169903i	−0.870888	−	0.491481i	$-0.836456\pi$
$17$	−0.687566	+	1.19090i	−0.00980937	+	0.0169903i	0.861079	+	0.508471i	$0.169789\pi$
$18$		0			0
$19$	62.9115	−	36.3220i	0.759626	−	0.438570i	−0.0695358	−	0.997579i	$-0.522152\pi$
$19$	62.9115	−	36.3220i	0.759626	−	0.438570i	0.829161	+	0.559009i	$0.188818\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−166.990	+	96.4117i	−1.51390	+	0.874053i	−0.514037	+	0.857768i	$0.671851\pi$
$23$	−166.990	+	96.4117i	−1.51390	+	0.874053i	−0.999867	+	0.0162856i	$0.994816\pi$
$24$		0			0
$25$	−80.4669	+	139.373i	−0.643735	+	1.11498i
$26$		0			0
$27$	140.294	−	0.841448i	0.999982	−	0.00599766i
$28$		0			0
$29$			34.2666i			0.219419i	0.993964	+	0.109709i	$0.0349920\pi$
$29$			34.2666i			0.219419i	−0.993964	+	0.109709i	$0.965008\pi$
$30$		0			0
$31$	81.2050	+	46.8837i	0.470479	+	0.271631i	0.716440	−	0.697649i	$-0.245770\pi$
$31$	81.2050	+	46.8837i	0.470479	+	0.271631i	−0.245961	+	0.969280i	$0.579104\pi$
$32$		0			0
$33$	0.549045	+	274.628i	0.00289626	+	1.44868i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−150.121	−	260.017i	−0.667018	−	1.15531i	−0.978734	−	0.205134i	$-0.934237\pi$
$37$	−150.121	−	260.017i	−0.667018	−	1.15531i	0.311715	−	0.950176i	$-0.399096\pi$
$38$		0			0
$39$	224.010	−	129.930i	0.919750	−	0.533472i
$40$		0			0
$41$	−88.2653			−0.336213			−0.168106	−	0.985769i	$-0.553765\pi$
$41$	−88.2653			−0.336213			−0.168106	+	0.985769i	$0.553765\pi$
$42$		0			0
$43$	136.747			0.484971			0.242485	−	0.970155i	$-0.422037\pi$
$43$	136.747			0.484971			0.242485	+	0.970155i	$0.422037\pi$
$44$		0			0
$45$	456.555	−	1.82553i	1.51243	−	0.00604741i
$46$		0			0
$47$	−283.337	−	490.755i	−0.879341	−	1.52306i	−0.852066	−	0.523435i	$-0.824650\pi$
$47$	−283.337	−	490.755i	−0.879341	−	1.52306i	−0.0272750	−	0.999628i	$-0.508683\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	7.14538	−	0.0142853i	0.0196187	−	3.92224e-5i
$52$		0			0
$53$	395.847	+	228.542i	1.02592	+	0.592315i	0.915813	−	0.401605i	$-0.131547\pi$
$53$	395.847	+	228.542i	1.02592	+	0.592315i	0.110107	+	0.993920i	$0.464881\pi$
$54$		0			0
$55$			893.710i			2.19105i
$56$		0			0
$57$	−327.274	−	188.081i	−0.760501	−	0.437050i
$58$		0			0
$59$	126.542	−	219.178i	0.279227	−	0.483636i	−0.691966	−	0.721930i	$-0.743255\pi$
$59$	126.542	−	219.178i	0.279227	−	0.483636i	0.971193	+	0.238295i	$0.0765884\pi$
$60$		0			0
$61$	215.803	−	124.594i	0.452963	−	0.261518i	−0.256118	−	0.966646i	$-0.582444\pi$
$61$	215.803	−	124.594i	0.452963	−	0.261518i	0.709081	+	0.705127i	$0.249110\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	729.827	−	421.366i	1.39268	−	0.804061i
$66$		0			0
$67$	54.3074	−	94.0632i	0.0990255	−	0.171517i	−0.812256	−	0.583301i	$-0.801761\pi$
$67$	54.3074	−	94.0632i	0.0990255	−	0.171517i	0.911282	+	0.411784i	$0.135094\pi$
$68$		0			0
$69$	868.705	+	499.234i	1.51565	+	0.871025i
$70$		0			0
$71$			21.4904i			0.0359218i	0.999839	+	0.0179609i	$0.00571743\pi$
$71$			21.4904i			0.0359218i	−0.999839	+	0.0179609i	$0.994283\pi$
$72$		0			0
$73$	310.185	+	179.085i	0.497321	+	0.287128i	0.727607	−	0.685995i	$-0.240633\pi$
$73$	310.185	+	179.085i	0.497321	+	0.287128i	−0.230286	+	0.973123i	$0.573966\pi$
$74$		0			0
$75$	836.235	−	1.67183i	1.28747	−	0.00257395i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	597.582	+	1035.04i	0.851053	+	1.47407i	0.880259	+	0.474494i	$0.157369\pi$
$79$	597.582	+	1035.04i	0.851053	+	1.47407i	−0.0292056	+	0.999573i	$0.509298\pi$
$80$		0			0
$81$	−369.537	−	628.397i	−0.506909	−	0.861999i
$82$		0			0
$83$	834.327			1.10336			0.551682	−	0.834054i	$-0.313986\pi$
$83$	834.327			1.10336			0.551682	+	0.834054i	$0.313986\pi$
$84$		0			0
$85$	23.2529			0.0296721
$86$		0			0
$87$	154.021	−	89.3353i	0.189803	−	0.110089i
$88$		0			0
$89$	−114.929	−	199.063i	−0.136882	−	0.237086i	0.789433	−	0.613837i	$-0.210375\pi$
$89$	−114.929	−	199.063i	−0.136882	−	0.237086i	−0.926315	+	0.376751i	$0.877041\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.974085	−	487.229i	−0.00108611	−	0.543261i
$94$		0			0
$95$	−1063.81	−	614.189i	−1.14889	−	0.663310i
$96$		0			0
$97$			1140.39i			1.19370i	0.802352	+	0.596851i	$0.203582\pi$
$97$			1140.39i			1.19370i	−0.802352	+	0.596851i	$0.796418\pi$
$98$		0			0
$99$	1232.97	−	718.441i	1.25169	−	0.729354i
$100$		0			0
$101$	79.2514	−	137.267i	0.0780773	−	0.135234i	−0.824343	−	0.566091i	$-0.808455\pi$
$101$	79.2514	−	137.267i	0.0780773	−	0.135234i	0.902420	+	0.430857i	$0.141789\pi$
$102$		0			0
$103$	−215.773	+	124.576i	−0.206415	+	0.119174i	−0.599644	−	0.800267i	$-0.704691\pi$
$103$	−215.773	+	124.576i	−0.206415	+	0.119174i	0.393229	+	0.919440i	$0.371358\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−810.305	+	467.830i	−0.732104	+	0.422681i	−0.819192	−	0.573520i	$-0.805577\pi$
$107$	−810.305	+	467.830i	−0.732104	+	0.422681i	0.0870872	+	0.996201i	$0.472244\pi$
$108$		0			0
$109$	−772.055	+	1337.24i	−0.678435	+	1.17508i	0.297017	+	0.954872i	$0.404008\pi$
$109$	−772.055	+	1337.24i	−0.678435	+	1.17508i	−0.975452	+	0.220212i	$0.929325\pi$
$110$		0			0
$111$	−777.347	+	1352.64i	−0.664707	+	1.15664i
$112$		0			0
$113$		−	214.314i		−	0.178415i	−0.996013	−	0.0892077i	$-0.971566\pi$
$113$		−	214.314i		−	0.178415i	0.996013	−	0.0892077i	$-0.0284335\pi$
$114$		0			0
$115$	2823.73	+	1630.28i	2.28969	+	1.32195i
$116$		0			0
$117$	−1168.02	−	668.142i	−0.922933	−	0.527946i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	731.181	+	1266.44i	0.549347	+	0.951497i
$122$		0			0
$123$	230.114	+	396.735i	0.168688	+	0.290832i
$124$		0			0
$125$	607.627			0.434782
$126$		0			0
$127$	43.2529			0.0302211			0.0151105	−	0.999886i	$-0.495190\pi$
$127$	43.2529			0.0302211			0.0151105	+	0.999886i	$0.495190\pi$
$128$		0			0
$129$	−356.509	−	614.650i	−0.243324	−	0.419511i
$130$		0			0
$131$	641.264	+	1110.70i	0.427691	+	0.740783i	0.996668	−	0.0815711i	$-0.0259938\pi$
$131$	641.264	+	1110.70i	0.427691	+	0.740783i	−0.568976	+	0.822354i	$0.692660\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1198.48	−	2047.36i	−0.764062	−	1.30525i
$136$		0			0
$137$	544.226	+	314.209i	0.339389	+	0.195947i	0.660002	−	0.751264i	$-0.270555\pi$
$137$	544.226	+	314.209i	0.339389	+	0.195947i	−0.320613	+	0.947210i	$0.603889\pi$
$138$		0			0
$139$		−	1295.74i		−	0.790671i	−0.918537	−	0.395336i	$-0.870628\pi$
$139$		−	1295.74i		−	0.790671i	0.918537	−	0.395336i	$-0.129372\pi$
$140$		0			0
$141$	−1467.16	+	2552.98i	−0.876294	+	1.52482i
$142$		0			0
$143$	1317.01	−	2281.13i	0.770169	−	1.33397i
$144$		0			0
$145$	501.804	−	289.717i	0.287397	−	0.165929i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−24.6445	+	14.2285i	−0.0135501	+	0.00782313i	−0.506760	−	0.862087i	$-0.669157\pi$
$149$	−24.6445	+	14.2285i	−0.0135501	+	0.00782313i	0.493210	+	0.869910i	$0.335824\pi$
$150$		0			0
$151$	118.724	−	205.636i	0.0639842	−	0.110824i	−0.832259	−	0.554387i	$-0.812953\pi$
$151$	118.724	−	205.636i	0.0639842	−	0.110824i	0.896243	+	0.443564i	$0.146286\pi$
$152$		0			0
$153$	−18.6927	−	32.0798i	−0.00987723	−	0.0169510i
$154$		0			0
$155$		−	1585.57i		−	0.821651i
$156$		0			0
$157$	−2526.01	−	1458.39i	−1.28406	−	0.741352i	−0.306472	−	0.951880i	$-0.599149\pi$
$157$	−2526.01	−	1458.39i	−1.28406	−	0.741352i	−0.977588	+	0.210527i	$0.932482\pi$
$158$		0			0
$159$	−4.74833	−	2375.08i	−0.00236835	−	1.18463i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−488.284	−	845.733i	−0.234634	−	0.406398i	0.724532	−	0.689241i	$-0.242056\pi$
$163$	−488.284	−	845.733i	−0.234634	−	0.406398i	−0.959166	+	0.282843i	$0.908723\pi$
$164$		0			0
$165$	4017.04	−	2329.96i	1.89531	−	1.09932i
$166$		0			0
$167$	2802.61			1.29864			0.649318	−	0.760517i	$-0.275054\pi$
$167$	2802.61			1.29864			0.649318	+	0.760517i	$0.275054\pi$
$168$		0			0
$169$	−286.778			−0.130532
$170$		0			0
$171$	7.84251	+	1961.37i	0.00350720	+	0.877133i
$172$		0			0
$173$	1365.20	+	2364.59i	0.599965	+	1.03917i	0.992826	+	0.119571i	$0.0381520\pi$
$173$	1365.20	+	2364.59i	0.599965	+	1.03917i	−0.392861	+	0.919598i	$0.628515\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1315.06	+	2.62912i	−0.558453	+	0.00111648i
$178$		0			0
$179$	1354.53	+	782.039i	0.565600	+	0.326549i	0.755390	−	0.655275i	$-0.227447\pi$
$179$	1354.53	+	782.039i	0.565600	+	0.326549i	−0.189790	+	0.981825i	$0.560781\pi$
$180$		0			0
$181$			2818.69i			1.15752i	0.815498	+	0.578761i	$0.196463\pi$
$181$			2818.69i			1.15752i	−0.815498	+	0.578761i	$0.803537\pi$
$182$		0			0
$183$	−1122.64	−	645.165i	−0.453484	−	0.260612i
$184$		0			0
$185$	−2538.48	+	4396.77i	−1.00882	+	1.74734i
$186$		0			0
$187$	62.9417	−	36.3394i	0.0246137	−	0.0142107i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	696.633	−	402.202i	0.263909	−	0.152368i	−0.362207	−	0.932098i	$-0.617977\pi$
$191$	696.633	−	402.202i	0.263909	−	0.152368i	0.626116	+	0.779730i	$0.284643\pi$
$192$		0			0
$193$	−2101.70	+	3640.26i	−0.783854	+	1.35768i	0.145827	+	0.989310i	$0.453416\pi$
$193$	−2101.70	+	3640.26i	−0.783854	+	1.35768i	−0.929681	+	0.368365i	$0.879918\pi$
$194$		0			0
$195$	−3796.66	−	2181.89i	−1.39428	−	0.801275i
$196$		0			0
$197$			4885.06i			1.76673i	0.468686	+	0.883365i	$0.344728\pi$
$197$			4885.06i			1.76673i	−0.468686	+	0.883365i	$0.655272\pi$
$198$		0			0
$199$	−1750.52	−	1010.66i	−0.623572	−	0.360019i	0.154687	−	0.987964i	$-0.450563\pi$
$199$	−1750.52	−	1010.66i	−0.623572	−	0.360019i	−0.778258	+	0.627944i	$0.783897\pi$
$200$		0			0
$201$	−564.378	+	1.12832i	−0.198051	+	0.000395949i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	746.265	+	1292.57i	0.254251	+	0.440375i
$206$		0			0
$207$	−20.8169	−	5206.19i	−0.00698972	−	1.74809i
$208$		0			0
$209$	−3839.40			−1.27070
$210$		0			0
$211$	214.374			0.0699435			0.0349718	−	0.999388i	$-0.488866\pi$
$211$	214.374			0.0699435			0.0349718	+	0.999388i	$0.488866\pi$
$212$		0			0
$213$	96.5952	−	56.0270i	0.0310732	−	0.0180230i
$214$		0			0
$215$	−1156.17	−	2002.54i	−0.366744	−	0.635220i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.72079	−	1861.11i	−0.00114807	−	0.574256i
$220$		0			0
$221$	−59.3515	−	34.2666i	−0.0180652	−	0.0104300i
$222$		0			0
$223$		−	5589.50i		−	1.67848i	−0.543763	−	0.839239i	$-0.683001\pi$
$223$		−	5589.50i		−	1.67848i	0.543763	−	0.839239i	$-0.316999\pi$
$224$		0			0
$225$	−2187.64	−	3754.35i	−0.648189	−	1.11240i
$226$		0			0
$227$	1756.33	−	3042.05i	0.513532	−	0.889463i	−0.486345	−	0.873767i	$-0.661670\pi$
$227$	1756.33	−	3042.05i	0.513532	−	0.889463i	0.999877	−	0.0156961i	$-0.00499644\pi$
$228$		0			0
$229$	−3494.64	+	2017.63i	−1.00844	+	0.582222i	−0.910734	−	0.412994i	$-0.864483\pi$
$229$	−3494.64	+	2017.63i	−1.00844	+	0.582222i	−0.0977038	+	0.995216i	$0.531150\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4824.61	+	2785.49i	−1.35653	+	0.783191i	−0.989154	−	0.146883i	$-0.953076\pi$
$233$	−4824.61	+	2785.49i	−1.35653	+	0.783191i	−0.367372	+	0.930074i	$0.619743\pi$
$234$		0			0
$235$	−4791.12	+	8298.46i	−1.32995	+	2.30354i
$236$		0			0
$237$	3094.37	−	5384.43i	0.848104	−	1.47577i
$238$		0			0
$239$		−	398.423i		−	0.107832i	−0.998545	−	0.0539160i	$-0.982830\pi$
$239$		−	398.423i		−	0.107832i	0.998545	−	0.0539160i	$-0.0171703\pi$
$240$		0			0
$241$	−4288.39	−	2475.91i	−1.14622	−	0.661772i	−0.198259	−	0.980150i	$-0.563529\pi$
$241$	−4288.39	−	2475.91i	−1.14622	−	0.661772i	−0.947964	+	0.318377i	$0.896862\pi$
$242$		0			0
$243$	−1861.11	+	3299.27i	−0.491318	+	0.870980i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1810.20	+	3135.35i	0.466316	+	0.807683i
$248$		0			0
$249$	−2175.15	−	3750.13i	−0.553592	−	0.954437i
$250$		0			0
$251$	−4083.93			−1.02699			−0.513496	−	0.858092i	$-0.671650\pi$
$251$	−4083.93			−1.02699			−0.513496	+	0.858092i	$0.671650\pi$
$252$		0			0
$253$	10191.2			2.53246
$254$		0			0
$255$	−60.6219	−	104.517i	−0.0148874	−	0.0256671i
$256$		0			0
$257$	1730.25	+	2996.89i	0.419962	+	0.727396i	0.995935	−	0.0900727i	$-0.0287099\pi$
$257$	1730.25	+	2996.89i	0.419962	+	0.727396i	−0.575973	+	0.817469i	$0.695377\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−803.088	−	459.392i	−0.190459	−	0.108949i
$262$		0			0
$263$	−2442.98	−	1410.46i	−0.572778	−	0.330694i	0.185480	−	0.982648i	$-0.440616\pi$
$263$	−2442.98	−	1410.46i	−0.572778	−	0.330694i	−0.758258	+	0.651954i	$0.773949\pi$
$264$		0			0
$265$		−	7729.11i		−	1.79168i
$266$		0			0
$267$	−595.121	+	1035.55i	−0.136407	+	0.237359i
$268$		0			0
$269$	−1405.44	+	2434.29i	−0.318554	+	0.551751i	−0.980187	−	0.198077i	$-0.936531\pi$
$269$	−1405.44	+	2434.29i	−0.318554	+	0.551751i	0.661633	+	0.749828i	$0.269864\pi$
$270$		0			0
$271$	6714.72	−	3876.75i	1.50513	−	0.868988i	0.505148	−	0.863033i	$-0.331438\pi$
$271$	6714.72	−	3876.75i	1.50513	−	0.868988i	0.999982	−	0.00595501i	$-0.00189555\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7366.17	−	4252.86i	1.61526	−	0.932571i
$276$		0			0
$277$	−283.222	+	490.554i	−0.0614337	+	0.106406i	−0.895106	−	0.445852i	$-0.852901\pi$
$277$	−283.222	+	490.554i	−0.0614337	+	0.106406i	0.833673	+	0.552259i	$0.186234\pi$
$278$		0			0
$279$	−2187.46	+	1274.62i	−0.469389	+	0.273510i
$280$		0			0
$281$		−	5958.94i		−	1.26506i	−0.774538	−	0.632528i	$-0.782017\pi$
$281$		−	5958.94i		−	1.26506i	0.774538	−	0.632528i	$-0.217983\pi$
$282$		0			0
$283$	2591.09	+	1495.97i	0.544256	+	0.314226i	0.746802	−	0.665047i	$-0.231588\pi$
$283$	2591.09	+	1495.97i	0.544256	+	0.314226i	−0.202546	+	0.979273i	$0.564922\pi$
$284$		0			0
$285$	12.7608	+	6382.83i	0.00265222	+	1.32662i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2455.55	+	4253.15i	0.499808	+	0.865692i
$290$		0			0
$291$	5125.82	−	2973.07i	1.03258	−	0.598917i
$292$		0			0
$293$	−5247.58			−1.04630			−0.523151	−	0.852240i	$-0.675244\pi$
$293$	−5247.58			−1.04630			−0.523151	+	0.852240i	$0.675244\pi$
$294$		0			0
$295$	−4279.55			−0.844628
$296$		0			0
$297$	−6443.67	−	3668.90i	−1.25892	−	0.716806i
$298$		0			0
$299$	−4804.92	−	8322.36i	−0.929350	−	1.60968i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−823.603	+	1.64657i	−0.156154	+	0.000312189i
$304$		0			0
$305$	−3649.13	−	2106.83i	−0.685078	−	0.395530i
$306$		0			0
$307$			210.991i			0.0392243i	0.999808	+	0.0196122i	$0.00624315\pi$
$307$			210.991i			0.0392243i	−0.999808	+	0.0196122i	$0.993757\pi$
$308$		0			0
$309$	1122.48	+	645.075i	0.206652	+	0.118761i
$310$		0			0
$311$	−4628.03	+	8015.98i	−0.843831	+	1.46156i	0.0428024	+	0.999084i	$0.486371\pi$
$311$	−4628.03	+	8015.98i	−0.843831	+	1.46156i	−0.886633	+	0.462474i	$0.846962\pi$
$312$		0			0
$313$	−7305.05	+	4217.57i	−1.31919	+	0.761634i	−0.983598	−	0.180375i	$-0.942269\pi$
$313$	−7305.05	+	4217.57i	−1.31919	+	0.761634i	−0.335590	+	0.942008i	$0.608936\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5146.01	−	2971.05i	0.911763	−	0.526406i	0.0307648	−	0.999527i	$-0.490206\pi$
$317$	5146.01	−	2971.05i	0.911763	−	0.526406i	0.880998	+	0.473120i	$0.156872\pi$
$318$		0			0
$319$	905.533	−	1568.43i	0.158935	−	0.275283i
$320$		0			0
$321$	4215.32	+	2422.49i	0.732948	+	0.421216i
$322$		0			0
$323$			99.8950i			0.0172084i
$324$		0			0
$325$	−6946.00	−	4010.27i	−1.18552	−	0.684461i
$326$		0			0
$327$	8023.41	−	16.0407i	1.35687	−	0.00271269i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3110.61	+	5387.74i	0.516540	+	0.894673i	0.999816	+	0.0192049i	$0.00611349\pi$
$331$	3110.61	+	5387.74i	0.516540	+	0.894673i	−0.483276	+	0.875468i	$0.660553\pi$
$332$		0			0
$333$	8106.45	−	32.4135i	1.33403	−	0.00533408i
$334$		0			0
$335$	−1836.63			−0.299540
$336$		0			0
$337$	−7108.23			−1.14899			−0.574496	−	0.818508i	$-0.694802\pi$
$337$	−7108.23			−1.14899			−0.574496	+	0.818508i	$0.694802\pi$
$338$		0			0
$339$	−963.297	+	558.731i	−0.154334	+	0.0895165i
$340$		0			0
$341$	−2477.91	−	4291.87i	−0.393508	−	0.681577i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−33.8717	−	16942.3i	−0.00528577	−	2.64390i
$346$		0			0
$347$	9666.81	+	5581.13i	1.49551	+	0.863432i	0.999987	−	0.00516366i	$-0.00164365\pi$
$347$	9666.81	+	5581.13i	1.49551	+	0.863432i	0.495521	+	0.868596i	$0.334977\pi$
$348$		0			0
$349$		−	2438.46i		−	0.374006i	−0.982359	−	0.187003i	$-0.940123\pi$
$349$		−	2438.46i		−	0.374006i	0.982359	−	0.187003i	$-0.0598773\pi$
$350$		0			0
$351$	41.9357	+	6991.88i	0.00637710	+	1.06325i
$352$		0			0
$353$	−451.700	+	782.368i	−0.0681064	+	0.117964i	−0.898068	−	0.439857i	$-0.855029\pi$
$353$	−451.700	+	782.368i	−0.0681064	+	0.117964i	0.829961	+	0.557821i	$0.188362\pi$
$354$		0			0
$355$	314.709	−	181.697i	0.0470507	−	0.0271647i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6970.32	+	4024.32i	−1.02473	+	0.591630i	−0.915472	−	0.402382i	$-0.868182\pi$
$359$	−6970.32	+	4024.32i	−1.02473	+	0.591630i	−0.109262	+	0.994013i	$0.534849\pi$
$360$		0			0
$361$	−790.930	+	1369.93i	−0.115313	+	0.199727i
$362$		0			0
$363$	3786.16	−	6588.21i	0.547444	−	0.952593i
$364$		0			0
$365$		−	6056.52i		−	0.868528i
$366$		0			0
$367$	5858.89	+	3382.63i	0.833329	+	0.481122i	0.854991	−	0.518643i	$-0.173563\pi$
$367$	5858.89	+	3382.63i	0.833329	+	0.481122i	−0.0216624	+	0.999765i	$0.506896\pi$
$368$		0			0
$369$	1183.32	−	2068.63i	0.166941	−	0.291839i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1599.16	+	2769.82i	0.221987	+	0.384493i	0.955411	−	0.295278i	$-0.0954124\pi$
$373$	1599.16	+	2769.82i	0.221987	+	0.384493i	−0.733424	+	0.679771i	$0.762079\pi$
$374$		0			0
$375$	−1584.12	−	2731.16i	−0.218143	−	0.376097i
$376$		0			0
$377$	−1707.76			−0.233300
$378$		0			0
$379$	2066.41			0.280065			0.140032	−	0.990147i	$-0.455279\pi$
$379$	2066.41			0.280065			0.140032	+	0.990147i	$0.455279\pi$
$380$		0			0
$381$	−112.763	−	194.413i	−0.0151628	−	0.0261419i
$382$		0			0
$383$	4848.41	+	8397.69i	0.646846	+	1.12037i	0.983872	+	0.178875i	$0.0572459\pi$
$383$	4848.41	+	8397.69i	0.646846	+	1.12037i	−0.337025	+	0.941496i	$0.609421\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1833.29	+	3204.87i	−0.240804	+	0.420963i
$388$		0			0
$389$	−2518.43	−	1454.02i	−0.328250	−	0.189515i	0.326814	−	0.945089i	$-0.394025\pi$
$389$	−2518.43	−	1454.02i	−0.328250	−	0.189515i	−0.655064	+	0.755573i	$0.727358\pi$
$390$		0			0
$391$		−	265.158i		−	0.0342956i
$392$		0			0
$393$	3320.56	−	5778.03i	0.426209	−	0.741636i
$394$		0			0
$395$	10104.9	−	17502.1i	1.28717	−	2.22944i
$396$		0			0
$397$	−4666.67	+	2694.30i	−0.589958	+	0.340612i	−0.765081	−	0.643934i	$-0.777301\pi$
$397$	−4666.67	+	2694.30i	−0.589958	+	0.340612i	0.175123	+	0.984547i	$0.443968\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7221.31	+	4169.22i	−0.899289	+	0.519205i	−0.876969	−	0.480546i	$-0.840438\pi$
$401$	−7221.31	+	4169.22i	−0.899289	+	0.519205i	−0.0223196	+	0.999751i	$0.507105\pi$
$402$		0			0
$403$	−2336.57	+	4047.06i	−0.288816	+	0.500244i
$404$		0			0
$405$	−6077.97	+	10724.5i	−0.745721	+	1.31582i
$406$		0			0
$407$			15868.4i			1.93260i
$408$		0			0
$409$	3222.91	+	1860.75i	0.389640	+	0.224959i	0.682004	−	0.731348i	$-0.261109\pi$
$409$	3222.91	+	1860.75i	0.389640	+	0.224959i	−0.292364	+	0.956307i	$0.594442\pi$
$410$		0			0
$411$	−6.52819	−	3265.35i	−0.000783484	−	0.391892i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−7054.06	−	12218.0i	−0.834386	−	1.44520i
$416$		0			0
$417$	−5824.09	+	3378.08i	−0.683950	+	0.396704i
$418$		0			0
$419$	5794.95			0.675661			0.337831	−	0.941207i	$-0.390307\pi$
$419$	5794.95			0.675661			0.337831	+	0.941207i	$0.390307\pi$
$420$		0			0
$421$	3025.70			0.350269			0.175135	−	0.984544i	$-0.443964\pi$
$421$	3025.70			0.350269			0.175135	+	0.984544i	$0.443964\pi$
$422$		0			0
$423$	15300.1	−	61.1772i	1.75867	−	0.00703200i
$424$		0			0
$425$	−110.653	−	191.656i	−0.0126293	−	0.0218746i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−13686.8	+	27.3631i	−1.54033	+	0.00307949i
$430$		0			0
$431$	−1945.53	−	1123.25i	−0.217431	−	0.125534i	0.387329	−	0.921942i	$-0.373398\pi$
$431$	−1945.53	−	1123.25i	−0.217431	−	0.125534i	−0.604760	+	0.796408i	$0.706731\pi$
$432$		0			0
$433$			5546.43i			0.615576i	0.951455	+	0.307788i	$0.0995887\pi$
$433$			5546.43i			0.615576i	−0.951455	+	0.307788i	$0.900411\pi$
$434$		0			0
$435$	−2610.46	−	1500.20i	−0.287728	−	0.165354i
$436$		0			0
$437$	−7003.72	+	12130.8i	−0.766667	+	1.32791i
$438$		0			0
$439$	−0.592611	+	0.342144i	−6.44277e−5	+	3.71974e-5i	−0.500032	−	0.866007i	$-0.666679\pi$
$439$	−0.592611	+	0.342144i	−6.44277e−5	+	3.71974e-5i	0.499968	+	0.866044i	$0.333345\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8974.71	+	5181.55i	−0.962532	+	0.555718i	−0.896951	−	0.442129i	$-0.854223\pi$
$443$	−8974.71	+	5181.55i	−0.962532	+	0.555718i	−0.0655803	+	0.997847i	$0.520890\pi$
$444$		0			0
$445$	−1943.40	+	3366.08i	−0.207025	+	0.358578i
$446$		0			0
$447$	128.204	+	73.6775i	0.0135657	+	0.00779603i
$448$		0			0
$449$			737.618i			0.0775286i	0.999248	+	0.0387643i	$0.0123421\pi$
$449$			737.618i			0.0775286i	−0.999248	+	0.0387643i	$0.987658\pi$
$450$		0			0
$451$	4040.03	+	2332.51i	0.421812	+	0.243534i
$452$		0			0
$453$	−1233.81	+	2.46668i	−0.127968	+	0.000255838i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6091.92	+	10551.5i	0.623562	+	1.08004i	0.988817	+	0.149134i	$0.0476485\pi$
$457$	6091.92	+	10551.5i	0.623562	+	1.08004i	−0.365255	+	0.930907i	$0.619018\pi$
$458$		0			0
$459$	−95.4590	+	167.654i	−0.00970729	+	0.0170489i
$460$		0			0
$461$	16111.1			1.62770			0.813848	−	0.581078i	$-0.197369\pi$
$461$	16111.1			1.62770			0.813848	+	0.581078i	$0.197369\pi$
$462$		0			0
$463$	111.903			0.0112324			0.00561619	−	0.999984i	$-0.498212\pi$
$463$	111.903			0.0112324			0.00561619	+	0.999984i	$0.498212\pi$
$464$		0			0
$465$	−7126.81	+	4133.68i	−0.710748	+	0.412247i
$466$		0			0
$467$	−2468.01	−	4274.72i	−0.244552	−	0.423577i	0.717453	−	0.696607i	$-0.245308\pi$
$467$	−2468.01	−	4274.72i	−0.244552	−	0.423577i	−0.962006	+	0.273029i	$0.911974\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	30.3004	+	15156.0i	0.00296427	+	1.48270i
$472$		0			0
$473$	−6259.11	−	3613.70i	−0.608444	−	0.351285i
$474$		0			0
$475$			11690.9i			1.12929i
$476$		0			0
$477$	−10663.1	+	6213.33i	−1.02354	+	0.596413i
$478$		0			0
$479$	2203.81	−	3817.10i	0.210218	−	0.364108i	−0.741565	−	0.670881i	$-0.765916\pi$
$479$	2203.81	−	3817.10i	0.210218	−	0.364108i	0.951783	+	0.306773i	$0.0992493\pi$
$480$		0			0
$481$	12958.6	−	7481.64i	1.22840	−	0.709217i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16700.0	−	9641.76i	1.56352	−	0.902701i
$486$		0			0
$487$	−7376.21	+	12776.0i	−0.686341	+	1.18878i	0.286672	+	0.958029i	$0.407451\pi$
$487$	−7376.21	+	12776.0i	−0.686341	+	1.18878i	−0.973013	+	0.230749i	$0.925882\pi$
$488$		0			0
$489$	−2528.41	+	4399.62i	−0.233821	+	0.406867i
$490$		0			0
$491$			5995.54i			0.551069i	0.961291	+	0.275535i	$0.0888549\pi$
$491$			5995.54i			0.551069i	−0.961291	+	0.275535i	$0.911145\pi$
$492$		0			0
$493$	−40.8081	−	23.5605i	−0.00372800	−	0.00215236i
$494$		0			0
$495$	−20945.4	−	11981.4i	−1.90187	−	1.08793i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−192.202	−	332.904i	−0.0172428	−	0.0298654i	0.857275	−	0.514858i	$-0.172155\pi$
$499$	−192.202	−	332.904i	−0.0172428	−	0.0298654i	−0.874518	+	0.484993i	$0.838822\pi$
$500$		0			0
$501$	−7306.59	−	12597.2i	−0.651565	−	1.12335i
$502$		0			0
$503$	3491.74			0.309521			0.154761	−	0.987952i	$-0.450539\pi$
$503$	3491.74			0.309521			0.154761	+	0.987952i	$0.450539\pi$
$504$		0			0
$505$	−2680.21			−0.236174
$506$		0			0
$507$	747.651	+	1289.01i	0.0654918	+	0.112913i
$508$		0			0
$509$	11168.6	+	19344.5i	0.972571	+	1.68454i	0.687728	+	0.725968i	$0.258608\pi$
$509$	11168.6	+	19344.5i	0.972571	+	1.68454i	0.284842	+	0.958574i	$0.408059\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	8795.52	−	5148.68i	0.756981	−	0.443118i
$514$		0			0
$515$	3648.62	+	2106.53i	0.312189	+	0.180243i
$516$		0			0
$517$			29950.1i			2.54778i
$518$		0			0
$519$	7069.18	−	12300.9i	0.597886	−	1.04037i
$520$		0			0
$521$	9834.58	−	17034.0i	0.826988	−	1.43239i	−0.0734020	−	0.997302i	$-0.523386\pi$
$521$	9834.58	−	17034.0i	0.826988	−	1.43239i	0.900390	−	0.435083i	$-0.143281\pi$
$522$		0			0
$523$	14136.0	−	8161.42i	1.18188	−	0.682359i	0.225432	−	0.974259i	$-0.427621\pi$
$523$	14136.0	−	8161.42i	1.18188	−	0.682359i	0.956449	+	0.291900i	$0.0942874\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−111.668	+	64.4713i	−0.00923020	+	0.00532906i
$528$		0			0
$529$	12506.9	−	21662.6i	1.02794	−	1.78044i
$530$		0			0
$531$	3440.28	+	5904.09i	0.281159	+	0.482515i
$532$		0			0
$533$		−	4398.92i		−	0.357483i
$534$		0			0
$535$	13701.9	+	7910.81i	1.10726	+	0.639279i
$536$		0			0
$537$	−16.2481	−	8127.17i	−0.00130569	−	0.653097i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2872.09	−	4974.61i	−0.228246	−	0.395333i	0.729043	−	0.684468i	$-0.239966\pi$
$541$	−2872.09	−	4974.61i	−0.228246	−	0.395333i	−0.957288	+	0.289135i	$0.906632\pi$
$542$		0			0
$543$	12669.4	−	7348.51i	1.00128	−	0.580763i
$544$		0			0
$545$	26110.2			2.05218
$546$		0			0
$547$	8889.70			0.694874			0.347437	−	0.937703i	$-0.387052\pi$
$547$	8889.70			0.694874			0.347437	+	0.937703i	$0.387052\pi$
$548$		0			0
$549$	26.9018	+	6728.01i	0.00209133	+	0.523032i
$550$		0			0
$551$	1244.63	+	2155.76i	0.0962305	+	0.166676i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	26380.6	−	52.7409i	2.01764	−	0.00403374i
$556$		0			0
$557$	16872.5	+	9741.36i	1.28350	+	0.741032i	0.977487	−	0.210994i	$-0.0676701\pi$
$557$	16872.5	+	9741.36i	1.28350	+	0.741032i	0.306017	+	0.952026i	$0.401003\pi$
$558$		0			0
$559$			6815.14i			0.515652i
$560$		0			0
$561$	−327.432	−	188.171i	−0.0246420	−	0.0141615i
$562$		0			0
$563$	−5551.00	+	9614.61i	−0.415536	+	0.719729i	−0.995485	−	0.0949240i	$-0.969739\pi$
$563$	−5551.00	+	9614.61i	−0.415536	+	0.719729i	0.579949	+	0.814653i	$0.303073\pi$
$564$		0			0
$565$	−3138.44	+	1811.98i	−0.233690	+	0.134921i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2139.17	−	1235.05i	0.157607	−	0.0909947i	−0.419122	−	0.907930i	$-0.637662\pi$
$569$	2139.17	−	1235.05i	0.157607	−	0.0909947i	0.576729	+	0.816935i	$0.304329\pi$
$570$		0			0
$571$	1771.80	−	3068.85i	0.129856	−	0.224917i	−0.793765	−	0.608225i	$-0.791882\pi$
$571$	1771.80	−	3068.85i	0.129856	−	0.224917i	0.923621	+	0.383308i	$0.125215\pi$
$572$		0			0
$573$	−3623.98	−	2082.66i	−0.264213	−	0.151840i
$574$		0			0
$575$		−	31031.8i		−	2.25064i
$576$		0			0
$577$	−1071.07	−	618.385i	−0.0772780	−	0.0446164i	0.460863	−	0.887471i	$-0.347540\pi$
$577$	−1071.07	−	618.385i	−0.0772780	−	0.0446164i	−0.538141	+	0.842855i	$0.680873\pi$
$578$		0			0
$579$	21841.5	−	43.6662i	1.56771	−	0.00313421i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−12079.0	−	20921.4i	−0.858079	−	1.48624i
$584$		0			0
$585$	90.9798	+	22753.6i	0.00643000	+	1.60811i
$586$		0			0
$587$	−13251.5			−0.931772			−0.465886	−	0.884845i	$-0.654264\pi$
$587$	−13251.5			−0.931772			−0.465886	+	0.884845i	$0.654264\pi$
$588$		0			0
$589$	6811.64			0.476517
$590$		0			0
$591$	21957.3	−	12735.7i	1.52826	−	0.886422i
$592$		0			0
$593$	−7948.25	−	13766.8i	−0.550414	−	0.953345i	−0.998245	−	0.0592266i	$-0.981137\pi$
$593$	−7948.25	−	13766.8i	−0.550414	−	0.953345i	0.447831	−	0.894118i	$-0.352197\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	20.9981	+	10503.1i	0.00143952	+	0.720037i
$598$		0			0
$599$	−19294.9	−	11139.9i	−1.31614	−	0.759873i	−0.333034	−	0.942915i	$-0.608072\pi$
$599$	−19294.9	−	11139.9i	−1.31614	−	0.759873i	−0.983105	+	0.183042i	$0.941406\pi$
$600$		0			0
$601$		−	14741.7i		−	1.00055i	−0.865868	−	0.500273i	$-0.833233\pi$
$601$		−	14741.7i		−	1.00055i	0.865868	−	0.500273i	$-0.166767\pi$
$602$		0			0
$603$	1476.44	+	2533.82i	0.0997105	+	0.171120i
$604$		0			0
$605$	12364.0	−	21415.0i	0.830854	−	1.43908i
$606$		0			0
$607$	−10850.9	+	6264.76i	−0.725574	+	0.418911i	−0.816801	−	0.576920i	$-0.804255\pi$
$607$	−10850.9	+	6264.76i	−0.725574	+	0.418911i	0.0912266	+	0.995830i	$0.470921\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	24458.0	−	14120.8i	1.61942	−	0.934972i
$612$		0			0
$613$	763.731	−	1322.82i	0.0503211	−	0.0871586i	−0.839768	−	0.542946i	$-0.817309\pi$
$613$	763.731	−	1322.82i	0.0503211	−	0.0871586i	0.890089	+	0.455787i	$0.150642\pi$
$614$		0			0
$615$	3864.27	−	6724.12i	0.253370	−	0.440882i
$616$		0			0
$617$			12982.5i			0.847089i	0.905875	+	0.423545i	$0.139214\pi$
$617$			12982.5i			0.847089i	−0.905875	+	0.423545i	$0.860786\pi$
$618$		0			0
$619$	503.141	+	290.488i	0.0326703	+	0.0188622i	0.516246	−	0.856440i	$-0.327329\pi$
$619$	503.141	+	290.488i	0.0326703	+	0.0188622i	−0.483576	+	0.875302i	$0.660662\pi$
$620$		0			0
$621$	−23346.5	+	13666.5i	−1.50864	+	0.883118i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4921.01	+	8523.44i	0.314945	+	0.545500i
$626$		0			0
$627$	10009.6	+	17257.3i	0.637549	+	1.09919i
$628$		0			0
$629$	412.871			0.0261721
$630$		0			0
$631$	−9489.94			−0.598714			−0.299357	−	0.954141i	$-0.596772\pi$
$631$	−9489.94			−0.598714			−0.299357	+	0.954141i	$0.596772\pi$
$632$		0			0
$633$	−558.886	−	963.566i	−0.0350928	−	0.0605028i
$634$		0			0
$635$	−365.694	−	633.401i	−0.0228538	−	0.0395839i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−503.660	−	288.109i	−0.0311807	−	0.0178364i
$640$		0			0
$641$	14559.8	+	8406.12i	0.897158	+	0.517975i	0.876277	−	0.481807i	$-0.160019\pi$
$641$	14559.8	+	8406.12i	0.897158	+	0.517975i	0.0208812	+	0.999782i	$0.493353\pi$
$642$		0			0
$643$			7168.19i			0.439636i	0.975541	+	0.219818i	$0.0705463\pi$
$643$			7168.19i			0.439636i	−0.975541	+	0.219818i	$0.929454\pi$
$644$		0			0
$645$	−5986.81	+	10417.5i	−0.365473	+	0.635951i
$646$		0			0
$647$	−7911.81	+	13703.7i	−0.480750	+	0.832684i	−0.999756	−	0.0220870i	$-0.992969\pi$
$647$	−7911.81	+	13703.7i	−0.480750	+	0.832684i	0.519006	+	0.854771i	$0.326302\pi$
$648$		0			0
$649$	−11584.0	+	6688.05i	−0.700637	+	0.404513i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19470.9	+	11241.6i	−1.16686	+	0.673685i	−0.952937	−	0.303167i	$-0.901956\pi$
$653$	−19470.9	+	11241.6i	−1.16686	+	0.673685i	−0.213919	+	0.976851i	$0.568623\pi$
$654$		0			0
$655$	10843.5	−	18781.5i	0.646857	−	1.12039i
$656$		0			0
$657$	−8355.60	+	4868.76i	−0.496169	+	0.289115i
$658$		0			0
$659$		−	18754.4i		−	1.10860i	−0.832317	−	0.554300i	$-0.812986\pi$
$659$		−	18754.4i		−	1.10860i	0.832317	−	0.554300i	$-0.187014\pi$
$660$		0			0
$661$	5202.33	+	3003.56i	0.306123	+	0.176740i	0.645190	−	0.764022i	$-0.276778\pi$
$661$	5202.33	+	3003.56i	0.306123	+	0.176740i	−0.339067	+	0.940762i	$0.610112\pi$
$662$		0			0
$663$	0.711943	+	356.108i	4.17038e−5	+	0.0208599i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3303.70	−	5722.18i	−0.191784	−	0.332179i
$668$		0			0
$669$	−25123.7	+	14572.2i	−1.45192	+	0.842143i
$670$		0			0
$671$	−13170.1			−0.757716
$672$		0			0
$673$	13481.6			0.772178			0.386089	−	0.922461i	$-0.373826\pi$
$673$	13481.6			0.772178			0.386089	+	0.922461i	$0.373826\pi$
$674$		0			0
$675$	−11171.7	+	19620.8i	−0.637037	+	1.11882i
$676$		0			0
$677$	−1760.98	−	3050.10i	−0.0999702	−	0.173153i	0.811702	−	0.584072i	$-0.198541\pi$
$677$	−1760.98	−	3050.10i	−0.0999702	−	0.173153i	−0.911672	+	0.410918i	$0.865208\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−18252.3	+	36.4906i	−1.02706	+	0.00205334i
$682$		0			0
$683$	−25192.9	−	14545.1i	−1.41139	−	0.814866i	−0.415870	−	0.909424i	$-0.636523\pi$
$683$	−25192.9	−	14545.1i	−1.41139	−	0.814866i	−0.995519	+	0.0945581i	$0.969856\pi$
$684$		0			0
$685$		−	10626.3i		−	0.592714i
$686$		0			0
$687$	18179.6	+	10447.6i	1.00960	+	0.580204i
$688$		0			0
$689$	−11390.0	+	19728.0i	−0.629788	+	1.09082i
$690$		0			0
$691$	12510.8	−	7223.09i	0.688758	−	0.397655i	−0.114389	−	0.993436i	$-0.536491\pi$
$691$	12510.8	−	7223.09i	0.688758	−	0.397655i	0.803147	+	0.595781i	$0.203158\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18975.0	+	10955.2i	−1.03563	+	0.597921i
$696$		0			0
$697$	60.6882	−	105.115i	0.00329804	−	0.00571236i
$698$		0			0
$699$	25098.3	+	14423.7i	1.35809	+	0.780477i
$700$		0			0
$701$			14699.3i			0.791989i	0.918253	+	0.395994i	$0.129600\pi$
$701$			14699.3i			0.791989i	−0.918253	+	0.395994i	$0.870400\pi$
$702$		0			0
$703$	−18888.6	−	10905.4i	−1.01337	−	0.585069i
$704$		0			0
$705$	49790.6	−	99.5431i	2.65989	−	0.00531775i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	2510.97	+	4349.13i	0.133006	+	0.230374i	0.924834	−	0.380371i	$-0.124204\pi$
$709$	2510.97	+	4349.13i	0.133006	+	0.230374i	−0.791828	+	0.610745i	$0.790870\pi$
$710$		0			0
$711$	−32269.2	+	129.028i	−1.70209	+	0.00680579i
$712$		0			0
$713$	−18080.6			−0.949680
$714$		0			0
$715$	−44540.3			−2.32967
$716$		0			0
$717$	−1790.83	+	1038.72i	−0.0932772	+	0.0541026i
$718$		0			0
$719$	92.1486	+	159.606i	0.00477964	+	0.00827858i	0.868405	−	0.495855i	$-0.165145\pi$
$719$	92.1486	+	159.606i	0.00477964	+	0.00827858i	−0.863626	+	0.504134i	$0.831812\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	51.4409	+	25730.3i	0.00264607	+	1.32354i
$724$		0			0
$725$	−4775.83	−	2757.33i	−0.244648	−	0.141248i
$726$		0			0
$727$		−	11575.2i		−	0.590507i	−0.955419	−	0.295254i	$-0.904596\pi$
$727$		−	11575.2i		−	0.590507i	0.955419	−	0.295254i	$-0.0954041\pi$
$728$		0			0
$729$	19681.6	−	236.100i	0.999928	−	0.0119951i
$730$		0			0
$731$	−94.0227	+	162.852i	−0.00475726	+	0.00823981i
$732$		0			0
$733$	−2996.29	+	1729.91i	−0.150983	+	0.0871701i	−0.573588	−	0.819144i	$-0.694449\pi$
$733$	−2996.29	+	1729.91i	−0.150983	+	0.0871701i	0.422605	+	0.906314i	$0.361116\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4971.45	+	2870.27i	−0.248475	+	0.143457i
$738$		0			0
$739$	17933.4	−	31061.6i	0.892681	−	1.54617i	0.0560320	−	0.998429i	$-0.482155\pi$
$739$	17933.4	−	31061.6i	0.892681	−	1.54617i	0.836649	−	0.547740i	$-0.184512\pi$
$740$		0			0
$741$	9373.47	−	16310.5i	0.464700	−	0.808614i
$742$		0			0
$743$			21120.0i			1.04282i	0.853305	+	0.521412i	$0.174594\pi$
$743$			21120.0i			1.04282i	−0.853305	+	0.521412i	$0.825406\pi$
$744$		0			0
$745$	416.729	+	240.598i	0.0204936	+	0.0118320i
$746$		0			0
$747$	−11185.3	+	19553.7i	−0.547857	+	0.957740i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10074.1	−	17448.9i	−0.489493	−	0.847827i	0.510434	−	0.859917i	$-0.329485\pi$
$751$	−10074.1	−	17448.9i	−0.489493	−	0.847827i	−0.999927	+	0.0120899i	$0.996152\pi$
$752$		0			0
$753$	10647.1	+	18356.4i	0.515274	+	0.888374i
$754$		0			0
$755$	−4015.14			−0.193544
$756$		0			0
$757$	−24696.6			−1.18575			−0.592876	−	0.805293i	$-0.702008\pi$
$757$	−24696.6			−1.18575			−0.592876	+	0.805293i	$0.702008\pi$
$758$		0			0
$759$	−26569.0	−	45807.2i	−1.27061	−	2.19064i
$760$		0			0
$761$	−14444.6	−	25018.7i	−0.688061	−	1.19176i	−0.972464	−	0.233052i	$-0.925129\pi$
$761$	−14444.6	−	25018.7i	−0.688061	−	1.19176i	0.284403	−	0.958705i	$-0.408205\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−311.738	+	544.966i	−0.0147332	+	0.0257559i
$766$		0			0
$767$	10923.3	+	6306.55i	0.514233	+	0.296892i
$768$		0			0
$769$		−	29891.2i		−	1.40170i	−0.713311	−	0.700848i	$-0.752805\pi$
$769$		−	29891.2i		−	1.40170i	0.713311	−	0.700848i	$-0.247195\pi$
$770$		0			0
$771$	8959.52	−	15590.2i	0.418507	−	0.728234i
$772$		0			0
$773$	2656.64	−	4601.44i	0.123613	−	0.214104i	−0.797577	−	0.603217i	$-0.793885\pi$
$773$	2656.64	−	4601.44i	0.123613	−	0.214104i	0.921190	+	0.389113i	$0.127219\pi$
$774$		0			0
$775$	−13068.6	+	7545.18i	−0.605728	+	0.349717i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5552.90	+	3205.97i	−0.255396	+	0.147453i
$780$		0			0
$781$	567.909	−	983.648i	0.0260197	−	0.0450674i
$782$		0			0
$783$	28.8336	+	4807.38i	0.00131600	+	0.219415i
$784$		0			0
$785$			49321.6i			2.24250i
$786$		0			0
$787$	−25168.6	−	14531.1i	−1.13998	−	0.658167i	−0.193553	−	0.981090i	$-0.562001\pi$
$787$	−25168.6	−	14531.1i	−1.13998	−	0.658167i	−0.946425	+	0.322923i	$0.895334\pi$
$788$		0			0
$789$	29.3045	+	14657.9i	0.00132227	+	0.661386i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6209.45	+	10755.1i	0.278063	+	0.481619i
$794$		0			0
$795$	−34740.8	+	20150.3i	−1.54985	+	0.898941i
$796$		0			0
$797$	−16751.0			−0.744480			−0.372240	−	0.928137i	$-0.621410\pi$
$797$	−16751.0			−0.744480			−0.372240	+	0.928137i	$0.621410\pi$
$798$		0			0
$799$	779.253			0.0345031
$800$		0			0
$801$	6206.13	−	24.8151i	0.273761	−	0.00109463i
$802$		0			0
$803$	−9465.07	−	16394.0i	−0.415959	−	0.720462i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14605.7	−	29.2002i	0.637106	−	0.00127372i
$808$		0			0
$809$	12576.1	+	7260.80i	0.546540	+	0.315545i	0.747725	−	0.664008i	$-0.231146\pi$
$809$	12576.1	+	7260.80i	0.546540	+	0.315545i	−0.201185	+	0.979553i	$0.564479\pi$
$810$		0			0
$811$		−	39355.0i		−	1.70400i	−0.523545	−	0.851998i	$-0.675391\pi$
$811$		−	39355.0i		−	1.70400i	0.523545	−	0.851998i	$-0.324609\pi$
$812$		0			0
$813$	−34930.9	−	20074.4i	−1.50686	−	0.865977i
$814$		0			0
$815$	−8256.68	+	14301.0i	−0.354870	+	0.614652i
$816$		0			0
$817$	8602.96	−	4966.92i	0.368396	−	0.212694i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7358.13	+	4248.22i	−0.312790	+	0.180589i	−0.648174	−	0.761492i	$-0.724467\pi$
$821$	−7358.13	+	4248.22i	−0.312790	+	0.180589i	0.335384	+	0.942081i	$0.391134\pi$
$822$		0			0
$823$	7225.92	−	12515.7i	0.306051	−	0.530096i	−0.671444	−	0.741055i	$-0.734326\pi$
$823$	7225.92	−	12515.7i	0.306051	−	0.530096i	0.977495	+	0.210960i	$0.0676589\pi$
$824$		0			0
$825$	−38319.8	−	22021.9i	−1.61712	−	0.929340i
$826$		0			0
$827$			1062.24i			0.0446647i	0.999751	+	0.0223324i	$0.00710920\pi$
$827$			1062.24i			0.0446647i	−0.999751	+	0.0223324i	$0.992891\pi$
$828$		0			0
$829$	22209.8	+	12822.9i	0.930494	+	0.537221i	0.886968	−	0.461831i	$-0.152807\pi$
$829$	22209.8	+	12822.9i	0.930494	+	0.537221i	0.0435262	+	0.999052i	$0.486141\pi$
$830$		0			0
$831$	2943.32	−	5.88438i	0.122867	−	0.000245640i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−23695.5	−	41041.7i	−0.982054	−	1.70097i
$836$		0			0
$837$	11432.0	+	6509.16i	0.472100	+	0.268804i
$838$		0			0
$839$	−16815.2			−0.691924			−0.345962	−	0.938249i	$-0.612447\pi$
$839$	−16815.2			−0.691924			−0.345962	+	0.938249i	$0.612447\pi$
$840$		0			0
$841$	23214.8			0.951855
$842$		0			0
$843$	−26784.2	+	15535.4i	−1.09430	+	0.634717i
$844$		0			0
$845$	2424.65	+	4199.62i	0.0987107	+	0.170972i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−31.0811	−	15546.5i	−0.00125642	−	0.628451i
$850$		0			0
$851$	50137.3	+	28946.8i	2.01960	+	1.16602i
$852$		0			0
$853$			19156.1i			0.768924i	0.923141	+	0.384462i	$0.125613\pi$
$853$			19156.1i			0.768924i	−0.923141	+	0.384462i	$0.874387\pi$
$854$		0			0
$855$	28656.2	−	16697.8i	1.14623	−	0.667899i
$856$		0			0
$857$	−8028.58	+	13905.9i	−0.320013	+	0.554279i	−0.980490	−	0.196567i	$-0.937021\pi$
$857$	−8028.58	+	13905.9i	−0.320013	+	0.554279i	0.660477	+	0.750846i	$0.270354\pi$
$858$		0			0
$859$	−31157.6	+	17988.8i	−1.23758	+	0.714518i	−0.968599	−	0.248628i	$-0.920020\pi$
$859$	−31157.6	+	17988.8i	−1.23758	+	0.714518i	−0.268982	+	0.963145i	$0.586687\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	17212.5	−	9937.67i	0.678936	−	0.391984i	−0.120518	−	0.992711i	$-0.538456\pi$
$863$	17212.5	−	9937.67i	0.678936	−	0.391984i	0.799454	+	0.600727i	$0.205122\pi$
$864$		0			0
$865$	23084.9	−	39984.2i	0.907410	−	1.57168i
$866$		0			0
$867$	12715.2	−	22125.5i	0.498076	−	0.866690i
$868$		0			0
$869$		−	63167.1i		−	2.46582i
$870$		0			0
$871$	4687.88	+	2706.55i	0.182368	+	0.105290i
$872$		0			0
$873$	−26726.7	−	15288.5i	−1.03615	−	0.592713i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16566.3	−	28693.7i	−0.637862	−	1.10481i	−0.985901	−	0.167329i	$-0.946486\pi$
$877$	−16566.3	−	28693.7i	−0.637862	−	1.10481i	0.348040	−	0.937480i	$-0.386848\pi$
$878$		0			0
$879$	13680.8	+	23586.8i	0.524962	+	0.905077i
$880$		0			0
$881$	−35595.3			−1.36122			−0.680611	−	0.732645i	$-0.738285\pi$
$881$	−35595.3			−1.36122			−0.680611	+	0.732645i	$0.738285\pi$
$882$		0			0
$883$	134.531			0.00512719			0.00256360	−	0.999997i	$-0.499184\pi$
$883$	134.531			0.00512719			0.00256360	+	0.999997i	$0.499184\pi$
$884$		0			0
$885$	11157.1	+	19235.7i	0.423775	+	0.730623i
$886$		0			0
$887$	24466.1	+	42376.5i	0.926145	+	1.60413i	0.789709	+	0.613482i	$0.210232\pi$
$887$	24466.1	+	42376.5i	0.926145	+	1.60413i	0.136437	+	0.990649i	$0.456435\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	308.113	+	38528.1i	0.0115849	+	1.44864i
$892$		0			0
$893$	−35650.4	−	20582.7i	−1.33594	−	0.771305i
$894$		0			0
$895$		−	26447.9i		−	0.987772i
$896$		0			0
$897$	−24880.6	+	43294.1i	−0.926130	+	1.61154i
$898$		0			0
$899$	−1606.55	+	2782.62i	−0.0596010	+	0.103232i
$900$		0			0
$901$	−544.342	+	314.276i	−0.0201273	+	0.0116205i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	41277.2	−	23831.4i	1.51613	−	0.875340i
$906$		0			0
$907$	609.625	−	1055.90i	0.0223178	−	0.0386556i	−0.854651	−	0.519203i	$-0.826229\pi$
$907$	609.625	−	1055.90i	0.0223178	−	0.0386556i	0.876969	+	0.480548i	$0.159562\pi$
$908$		0			0
$909$	2154.59	+	3697.63i	0.0786174	+	0.134921i
$910$		0			0
$911$		−	19990.9i		−	0.727035i	−0.931587	−	0.363518i	$-0.881576\pi$
$911$		−	19990.9i		−	0.727035i	0.931587	−	0.363518i	$-0.118424\pi$
$912$		0			0
$913$	−38188.3	−	22048.0i	−1.38428	−	0.799215i
$914$		0			0
$915$	43.7727	+	21894.8i	0.00158151	+	0.791058i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	13171.5	+	22813.7i	0.472783	+	0.818884i	0.999515	−	0.0311478i	$-0.00991624\pi$
$919$	13171.5	+	22813.7i	0.472783	+	0.818884i	−0.526732	+	0.850031i	$0.676583\pi$
$920$		0			0
$921$	948.360	−	550.067i	0.0339300	−	0.0196800i
$922$		0			0
$923$	−1071.03			−0.0381944
$924$		0			0
$925$	48319.0			1.71753
$926$		0			0
$927$	−26.8981	−	6727.07i	−0.000953019	−	0.238345i
$928$		0			0
$929$	9954.66	+	17242.0i	0.351563	+	0.608924i	0.986523	−	0.163620i	$-0.0523171\pi$
$929$	9954.66	+	17242.0i	0.351563	+	0.608924i	−0.634961	+	0.772544i	$0.718984\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	48095.8	−	96.1547i	1.68766	−	0.00337402i
$934$		0			0
$935$	−1064.32	−	614.484i	−0.0372267	−	0.0214928i
$936$		0			0
$937$		−	25702.8i		−	0.896131i	−0.894001	−	0.448066i	$-0.852113\pi$
$937$		−	25702.8i		−	0.896131i	0.894001	−	0.448066i	$-0.147887\pi$
$938$		0			0
$939$	38001.9	+	21839.2i	1.32071	+	0.758995i
$940$		0			0
$941$	16597.4	−	28747.6i	0.574985	−	0.995904i	−0.421058	−	0.907034i	$-0.638341\pi$
$941$	16597.4	−	28747.6i	0.574985	−	0.995904i	0.996043	−	0.0888702i	$-0.0283256\pi$
$942$		0			0
$943$	14739.4	−	8509.81i	0.508994	−	0.293868i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13017.6	−	7515.74i	0.446691	−	0.257897i	−0.259740	−	0.965678i	$-0.583637\pi$
$947$	13017.6	−	7515.74i	0.446691	−	0.257897i	0.706432	+	0.707781i	$0.250304\pi$
$948$		0			0
$949$	−8925.18	+	15458.9i	−0.305293	+	0.528784i
$950$		0			0
$951$	−26770.3	−	15384.5i	−0.912813	−	0.524583i
$952$		0			0
$953$		−	36563.2i		−	1.24281i	−0.783489	−	0.621406i	$-0.786562\pi$
$953$		−	36563.2i		−	1.24281i	0.783489	−	0.621406i	$-0.213438\pi$
$954$		0			0
$955$	−11779.8	−	6801.06i	−0.399146	−	0.230447i
$956$		0			0
$957$	−9410.56	+	18.8139i	−0.317869	+	0.000635494i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−10499.3	−	18185.4i	−0.352433	−	0.610432i
$962$		0			0
$963$	−101.012	−	25262.6i	−0.00338014	−	0.845354i
$964$		0			0
$965$	71077.8			2.37106
$966$		0			0
$967$	−41795.4			−1.38992			−0.694959	−	0.719050i	$-0.744577\pi$
$967$	−41795.4			−1.38992			−0.694959	+	0.719050i	$0.744577\pi$
$968$		0			0
$969$	449.008	−	260.433i	0.0148857	−	0.00863397i
$970$		0			0
$971$	4765.36	+	8253.84i	0.157495	+	0.272789i	0.933965	−	0.357365i	$-0.116325\pi$
$971$	4765.36	+	8253.84i	0.157495	+	0.272789i	−0.776470	+	0.630155i	$0.782992\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	83.3198	+	41675.9i	0.00273679	+	1.36892i
$976$		0			0
$977$	−26449.9	−	15270.8i	−0.866127	−	0.500059i	−6.76530e−5	−	1.00000i	$-0.500022\pi$
$977$	−26449.9	−	15270.8i	−0.866127	−	0.500059i	−0.866059	+	0.499941i	$0.833355\pi$
$978$		0			0
$979$			12148.5i			0.396598i
$980$		0			0
$981$	−20989.7	−	36021.8i	−0.683128	−	1.17236i
$982$		0			0
$983$	−23005.9	+	39847.3i	−0.746463	+	1.29291i	0.203046	+	0.979169i	$0.434916\pi$
$983$	−23005.9	+	39847.3i	−0.746463	+	1.29291i	−0.949508	+	0.313742i	$0.898417\pi$
$984$		0			0
$985$	71537.4	−	41302.1i	2.31408	−	1.33604i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−22835.4	+	13184.0i	−0.734199	+	0.423890i
$990$		0			0
$991$	−9327.51	+	16155.7i	−0.298989	+	0.517864i	−0.975905	−	0.218196i	$-0.929983\pi$
$991$	−9327.51	+	16155.7i	−0.298989	+	0.517864i	0.676916	+	0.736060i	$0.263316\pi$
$992$		0			0
$993$	16107.2	−	28027.8i	0.514750	−	0.895704i
$994$		0			0
$995$			34179.7i			1.08901i
$996$		0			0
$997$	−41416.8	−	23912.0i	−1.31563	−	0.759579i	−0.332607	−	0.943065i	$-0.607928\pi$
$997$	−41416.8	−	23912.0i	−1.31563	−	0.759579i	−0.983022	+	0.183486i	$0.941262\pi$
$998$		0			0
$999$	−21279.8	−	36352.3i	−0.673936	−	1.15129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.d.521.3		16
3.2	odd	2	inner	588.4.k.d.521.1		16
7.2	even	3	inner	588.4.k.d.509.8		16
7.3	odd	6		84.4.f.a.41.5	yes	8
7.4	even	3		84.4.f.a.41.4	yes	8
7.5	odd	6	inner	588.4.k.d.509.1		16
7.6	odd	2	inner	588.4.k.d.521.6		16
21.2	odd	6	inner	588.4.k.d.509.6		16
21.5	even	6	inner	588.4.k.d.509.3		16
21.11	odd	6		84.4.f.a.41.6	yes	8
21.17	even	6		84.4.f.a.41.3	✓	8
21.20	even	2	inner	588.4.k.d.521.8		16
28.3	even	6		336.4.k.d.209.4		8
28.11	odd	6		336.4.k.d.209.5		8
84.11	even	6		336.4.k.d.209.3		8
84.59	odd	6		336.4.k.d.209.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.f.a.41.3	✓	8	21.17	even	6
84.4.f.a.41.4	yes	8	7.4	even	3
84.4.f.a.41.5	yes	8	7.3	odd	6
84.4.f.a.41.6	yes	8	21.11	odd	6
336.4.k.d.209.3		8	84.11	even	6
336.4.k.d.209.4		8	28.3	even	6
336.4.k.d.209.5		8	28.11	odd	6
336.4.k.d.209.6		8	84.59	odd	6
588.4.k.d.509.1		16	7.5	odd	6	inner
588.4.k.d.509.3		16	21.5	even	6	inner
588.4.k.d.509.6		16	21.2	odd	6	inner
588.4.k.d.509.8		16	7.2	even	3	inner
588.4.k.d.521.1		16	3.2	odd	2	inner
588.4.k.d.521.3		16	1.1	even	1	trivial
588.4.k.d.521.6		16	7.6	odd	2	inner
588.4.k.d.521.8		16	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.60707 - 4.49480i) q^{3} +(-8.45479 - 14.6441i) q^{5} +(-13.4064 + 23.4365i) q^{9} +O(q^{10})\)	\(q+(-2.60707 - 4.49480i) q^{3} +(-8.45479 - 14.6441i) q^{5} +(-13.4064 + 23.4365i) q^{9} +(-45.7714 - 26.4261i) q^{11} +49.8375i q^{13} +(-43.7802 + 76.1808i) q^{15} +(-0.687566 + 1.19090i) q^{17} +(62.9115 - 36.3220i) q^{19} +(-166.990 + 96.4117i) q^{23} +(-80.4669 + 139.373i) q^{25} +(140.294 - 0.841448i) q^{27} +34.2666i q^{29} +(81.2050 + 46.8837i) q^{31} +(0.549045 + 274.628i) q^{33} +(-150.121 - 260.017i) q^{37} +(224.010 - 129.930i) q^{39} -88.2653 q^{41} +136.747 q^{43} +(456.555 - 1.82553i) q^{45} +(-283.337 - 490.755i) q^{47} +(7.14538 - 0.0142853i) q^{51} +(395.847 + 228.542i) q^{53} +893.710i q^{55} +(-327.274 - 188.081i) q^{57} +(126.542 - 219.178i) q^{59} +(215.803 - 124.594i) q^{61} +(729.827 - 421.366i) q^{65} +(54.3074 - 94.0632i) q^{67} +(868.705 + 499.234i) q^{69} +21.4904i q^{71} +(310.185 + 179.085i) q^{73} +(836.235 - 1.67183i) q^{75} +(597.582 + 1035.04i) q^{79} +(-369.537 - 628.397i) q^{81} +834.327 q^{83} +23.2529 q^{85} +(154.021 - 89.3353i) q^{87} +(-114.929 - 199.063i) q^{89} +(-0.974085 - 487.229i) q^{93} +(-1063.81 - 614.189i) q^{95} +1140.39i q^{97} +(1232.97 - 718.441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{9}+O(q^{10}) \) 16 * q + 12 * q^9	\( 16 q + 12 q^{9} - 120 q^{15} - 320 q^{25} - 80 q^{37} + 732 q^{39} + 640 q^{43} - 552 q^{51} - 1560 q^{57} - 1840 q^{67} + 3176 q^{79} + 3456 q^{81} + 1920 q^{85} - 3960 q^{93} + 1152 q^{99}+O(q^{100}) \) 16 * q + 12 * q^9 - 120 * q^15 - 320 * q^25 - 80 * q^37 + 732 * q^39 + 640 * q^43 - 552 * q^51 - 1560 * q^57 - 1840 * q^67 + 3176 * q^79 + 3456 * q^81 + 1920 * q^85 - 3960 * q^93 + 1152 * q^99

Introduction

L-functions

Modular forms

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