LMFDB - Embedded newform 588.4.k.e.521.5

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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.5
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.40550 - 2.75527i) q^{3} +(9.23835 + 16.0013i) q^{5} +(11.8169 + 24.2767i) q^{9} +O(q^{10})$	\(q+(-4.40550 - 2.75527i) q^{3} +(9.23835 + 16.0013i) q^{5} +(11.8169 + 24.2767i) q^{9} +(-36.0100 - 20.7904i) q^{11} -43.5225i q^{13} +(3.38832 - 95.9479i) q^{15} +(62.7713 - 108.723i) q^{17} +(-59.2370 + 34.2005i) q^{19} +(77.2203 - 44.5831i) q^{23} +(-108.194 + 187.398i) q^{25} +(14.8294 - 139.510i) q^{27} +133.876i q^{29} +(75.4755 + 43.5758i) q^{31} +(101.359 + 190.810i) q^{33} +(114.216 + 197.828i) q^{37} +(-119.916 + 191.739i) q^{39} -37.0648 q^{41} +412.216 q^{43} +(-279.290 + 413.363i) q^{45} +(-303.043 - 524.886i) q^{47} +(-576.101 + 306.028i) q^{51} +(417.740 + 241.182i) q^{53} -768.275i q^{55} +(355.200 + 12.5436i) q^{57} +(-43.6046 + 75.5255i) q^{59} +(655.420 - 378.407i) q^{61} +(696.417 - 402.077i) q^{65} +(17.3248 - 30.0075i) q^{67} +(-463.033 - 16.3516i) q^{69} +481.981i q^{71} +(496.651 + 286.741i) q^{73} +(992.982 - 527.478i) q^{75} +(-227.051 - 393.264i) q^{79} +(-449.719 + 573.754i) q^{81} +866.824 q^{83} +2319.61 q^{85} +(368.866 - 589.793i) q^{87} +(309.454 + 535.991i) q^{89} +(-212.445 - 399.929i) q^{93} +(-1094.50 - 631.912i) q^{95} +593.517i q^{97} +(79.1943 - 1119.88i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 64 q^{9}+O(q^{10}) $ 48 * q + 64 * q^9	$ 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) $ 48 * q + 64 * q^9 - 192 * q^15 - 456 * q^25 + 432 * q^37 - 688 * q^39 + 1248 * q^43 + 1536 * q^51 - 2720 * q^57 + 528 * q^67 - 3744 * q^79 - 3408 * q^81 + 13824 * q^85 + 5088 * q^93 - 15472 * 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
$3$	−4.40550	−	2.75527i	−0.847840	−	0.530252i
$3$	−4.40550	−	2.75527i	−0.847840	−	0.530252i
$4$		0			0
$5$	9.23835	+	16.0013i	0.826303	+	1.43120i	0.900919	+	0.433987i	$0.142894\pi$
$5$	9.23835	+	16.0013i	0.826303	+	1.43120i	−0.0746162	+	0.997212i	$0.523773\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	11.8169	+	24.2767i	0.437665	+	0.899138i
$10$		0			0
$11$	−36.0100	−	20.7904i	−0.987039	−	0.569867i	−0.0826509	−	0.996579i	$-0.526339\pi$
$11$	−36.0100	−	20.7904i	−0.987039	−	0.569867i	−0.904388	+	0.426712i	$0.859672\pi$
$12$		0			0
$13$		−	43.5225i		−	0.928537i	−0.885694	−	0.464269i	$-0.846317\pi$
$13$		−	43.5225i		−	0.928537i	0.885694	−	0.464269i	$-0.153683\pi$
$14$		0			0
$15$	3.38832	−	95.9479i	0.0583240	−	1.65158i
$16$		0			0
$17$	62.7713	−	108.723i	0.895546	−	1.55113i	0.0624189	−	0.998050i	$-0.480119\pi$
$17$	62.7713	−	108.723i	0.895546	−	1.55113i	0.833127	−	0.553081i	$-0.186548\pi$
$18$		0			0
$19$	−59.2370	+	34.2005i	−0.715258	+	0.412954i	−0.813005	−	0.582257i	$-0.802170\pi$
$19$	−59.2370	+	34.2005i	−0.715258	+	0.412954i	0.0977471	+	0.995211i	$0.468836\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	77.2203	−	44.5831i	0.700067	−	0.404184i	−0.107306	−	0.994226i	$-0.534222\pi$
$23$	77.2203	−	44.5831i	0.700067	−	0.404184i	0.807372	+	0.590042i	$0.200889\pi$
$24$		0			0
$25$	−108.194	+	187.398i	−0.865554	+	1.49918i
$26$		0			0
$27$	14.8294	−	139.510i	0.105701	−	0.994398i
$28$		0			0
$29$			133.876i			0.857248i	0.903483	+	0.428624i	$0.141002\pi$
$29$			133.876i			0.857248i	−0.903483	+	0.428624i	$0.858998\pi$
$30$		0			0
$31$	75.4755	+	43.5758i	0.437284	+	0.252466i	0.702445	−	0.711738i	$-0.252092\pi$
$31$	75.4755	+	43.5758i	0.437284	+	0.252466i	−0.265161	+	0.964204i	$0.585425\pi$
$32$		0			0
$33$	101.359	+	190.810i	0.534677	+	1.00654i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	114.216	+	197.828i	0.507487	+	0.878994i	0.999962	+	0.00866731i	$0.00275893\pi$
$37$	114.216	+	197.828i	0.507487	+	0.878994i	−0.492475	+	0.870327i	$0.663908\pi$
$38$		0			0
$39$	−119.916	+	191.739i	−0.492359	+	0.787251i
$40$		0			0
$41$	−37.0648			−0.141184			−0.0705921	−	0.997505i	$-0.522489\pi$
$41$	−37.0648			−0.141184			−0.0705921	+	0.997505i	$0.522489\pi$
$42$		0			0
$43$	412.216			1.46192			0.730958	−	0.682423i	$-0.239074\pi$
$43$	412.216			1.46192			0.730958	+	0.682423i	$0.239074\pi$
$44$		0			0
$45$	−279.290	+	413.363i	−0.925202	+	1.36935i
$46$		0			0
$47$	−303.043	−	524.886i	−0.940497	−	1.62899i	−0.764525	−	0.644594i	$-0.777027\pi$
$47$	−303.043	−	524.886i	−0.940497	−	1.62899i	−0.175972	−	0.984395i	$-0.556307\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−576.101	+	306.028i	−1.58177	+	0.840245i
$52$		0			0
$53$	417.740	+	241.182i	1.08266	+	0.625074i	0.931613	−	0.363453i	$-0.118402\pi$
$53$	417.740	+	241.182i	1.08266	+	0.625074i	0.151047	+	0.988527i	$0.451735\pi$
$54$		0			0
$55$		−	768.275i		−	1.88353i
$56$		0			0
$57$	355.200	+	12.5436i	0.825394	+	0.0291481i
$58$		0			0
$59$	−43.6046	+	75.5255i	−0.0962176	+	0.166654i	−0.910116	−	0.414353i	$-0.864008\pi$
$59$	−43.6046	+	75.5255i	−0.0962176	+	0.166654i	0.813898	+	0.581007i	$0.197341\pi$
$60$		0			0
$61$	655.420	−	378.407i	1.37570	−	0.794263i	0.384064	−	0.923306i	$-0.374524\pi$
$61$	655.420	−	378.407i	1.37570	−	0.794263i	0.991639	+	0.129044i	$0.0411907\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	696.417	−	402.077i	1.32892	−	0.767253i
$66$		0			0
$67$	17.3248	−	30.0075i	0.0315905	−	0.0547164i	−0.849798	−	0.527109i	$-0.823276\pi$
$67$	17.3248	−	30.0075i	0.0315905	−	0.0547164i	0.881388	+	0.472392i	$0.156609\pi$
$68$		0			0
$69$	−463.033	−	16.3516i	−0.807864	−	0.0285290i
$70$		0			0
$71$			481.981i			0.805643i	0.915279	+	0.402821i	$0.131970\pi$
$71$			481.981i			0.805643i	−0.915279	+	0.402821i	$0.868030\pi$
$72$		0			0
$73$	496.651	+	286.741i	0.796282	+	0.459733i	0.842169	−	0.539213i	$-0.181278\pi$
$73$	496.651	+	286.741i	0.796282	+	0.459733i	−0.0458876	+	0.998947i	$0.514612\pi$
$74$		0			0
$75$	992.982	−	527.478i	1.52880	−	0.812105i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−227.051	−	393.264i	−0.323357	−	0.560071i	0.657821	−	0.753174i	$-0.271478\pi$
$79$	−227.051	−	393.264i	−0.323357	−	0.560071i	−0.981179	+	0.193103i	$0.938145\pi$
$80$		0			0
$81$	−449.719	+	573.754i	−0.616899	+	0.787042i
$82$		0			0
$83$	866.824			1.14634			0.573170	−	0.819436i	$-0.305713\pi$
$83$	866.824			1.14634			0.573170	+	0.819436i	$0.305713\pi$
$84$		0			0
$85$	2319.61			2.95997
$86$		0			0
$87$	368.866	−	589.793i	0.454558	−	0.726809i
$88$		0			0
$89$	309.454	+	535.991i	0.368563	+	0.638370i	0.989341	−	0.145617i	$-0.0465166\pi$
$89$	309.454	+	535.991i	0.368563	+	0.638370i	−0.620778	+	0.783986i	$0.713183\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−212.445	−	399.929i	−0.236876	−	0.445922i
$94$		0			0
$95$	−1094.50	−	631.912i	−1.18204	−	0.682451i
$96$		0			0
$97$			593.517i			0.621263i	0.950530	+	0.310632i	$0.100541\pi$
$97$			593.517i			0.621263i	−0.950530	+	0.310632i	$0.899459\pi$
$98$		0			0
$99$	79.1943	−	1119.88i	0.0803972	−	1.13689i
$100$		0			0
$101$	527.552	−	913.747i	0.519736	−	0.900210i	−0.480000	−	0.877268i	$-0.659363\pi$
$101$	527.552	−	913.747i	0.519736	−	0.900210i	0.999737	−	0.0229416i	$-0.00730318\pi$
$102$		0			0
$103$	1270.00	−	733.237i	1.21492	−	0.701437i	0.251096	−	0.967962i	$-0.419209\pi$
$103$	1270.00	−	733.237i	1.21492	−	0.701437i	0.963828	+	0.266525i	$0.0858756\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−710.060	+	409.953i	−0.641533	+	0.370390i	−0.785205	−	0.619236i	$-0.787442\pi$
$107$	−710.060	+	409.953i	−0.641533	+	0.370390i	0.143672	+	0.989625i	$0.454109\pi$
$108$		0			0
$109$	−428.204	+	741.671i	−0.376280	+	0.651735i	−0.990518	−	0.137385i	$-0.956130\pi$
$109$	−428.204	+	741.671i	−0.376280	+	0.651735i	0.614238	+	0.789121i	$0.289463\pi$
$110$		0			0
$111$	41.8907	−	1186.23i	0.0358206	−	1.01434i
$112$		0			0
$113$		−	1907.54i		−	1.58802i	−0.607906	−	0.794009i	$-0.707990\pi$
$113$		−	1907.54i		−	1.58802i	0.607906	−	0.794009i	$-0.292010\pi$
$114$		0			0
$115$	1426.78	+	823.749i	1.15693	+	0.667957i
$116$		0			0
$117$	1056.59	−	514.304i	0.834883	−	0.406388i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	198.980	+	344.644i	0.149497	+	0.258936i
$122$		0			0
$123$	163.289	+	102.124i	0.119702	+	0.0748633i
$124$		0			0
$125$	−1688.56			−1.20823
$126$		0			0
$127$	1137.79			0.794982			0.397491	−	0.917606i	$-0.369881\pi$
$127$	1137.79			0.794982			0.397491	+	0.917606i	$0.369881\pi$
$128$		0			0
$129$	−1816.02	−	1135.77i	−1.23947	−	0.775184i
$130$		0			0
$131$	499.355	+	864.909i	0.333045	+	0.576851i	0.983107	−	0.183030i	$-0.0585906\pi$
$131$	499.355	+	864.909i	0.333045	+	0.576851i	−0.650062	+	0.759881i	$0.725257\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2369.34	−	1051.55i	1.51052	−	0.670396i
$136$		0			0
$137$	717.658	+	414.340i	0.447545	+	0.258390i	0.706793	−	0.707421i	$-0.250141\pi$
$137$	717.658	+	414.340i	0.447545	+	0.258390i	−0.259248	+	0.965811i	$0.583475\pi$
$138$		0			0
$139$		−	2907.84i		−	1.77439i	−0.461399	−	0.887193i	$-0.652652\pi$
$139$		−	2907.84i		−	1.77439i	0.461399	−	0.887193i	$-0.347348\pi$
$140$		0			0
$141$	−111.146	+	3147.35i	−0.0663844	+	1.87982i
$142$		0			0
$143$	−904.851	+	1567.25i	−0.529143	+	0.916502i
$144$		0			0
$145$	−2142.19	+	1236.80i	−1.22689	+	0.708347i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2003.31	+	1156.61i	−1.10146	+	0.635928i	−0.936604	−	0.350390i	$-0.886049\pi$
$149$	−2003.31	+	1156.61i	−1.10146	+	0.635928i	−0.164855	+	0.986318i	$0.552716\pi$
$150$		0			0
$151$	692.341	−	1199.17i	0.373125	−	0.646271i	−0.616920	−	0.787026i	$-0.711620\pi$
$151$	692.341	−	1199.17i	0.373125	−	0.646271i	0.990044	+	0.140755i	$0.0449529\pi$
$152$		0			0
$153$	3381.21	+	239.107i	1.78663	+	0.126344i
$154$		0			0
$155$			1610.27i			0.834454i
$156$		0			0
$157$	1809.09	+	1044.48i	0.919625	+	0.530946i	0.883515	−	0.468402i	$-0.155170\pi$
$157$	1809.09	+	1044.48i	0.919625	+	0.530946i	0.0361096	+	0.999348i	$0.488503\pi$
$158$		0			0
$159$	−1175.83	−	2213.52i	−0.586475	−	1.10405i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1287.07	+	2229.28i	0.618475	+	1.07123i	0.989764	+	0.142712i	$0.0455823\pi$
$163$	1287.07	+	2229.28i	0.618475	+	1.07123i	−0.371290	+	0.928517i	$0.621084\pi$
$164$		0			0
$165$	−2116.81	+	3384.64i	−0.998747	+	1.59693i
$166$		0			0
$167$	−1570.77			−0.727842			−0.363921	−	0.931430i	$-0.618562\pi$
$167$	−1570.77			−0.727842			−0.363921	+	0.931430i	$0.618562\pi$
$168$		0			0
$169$	302.788			0.137819
$170$		0			0
$171$	−1530.28	−	1033.93i	−0.684346	−	0.462380i
$172$		0			0
$173$	−1245.44	−	2157.17i	−0.547337	−	0.948015i	−0.998456	−	0.0555511i	$-0.982308\pi$
$173$	−1245.44	−	2157.17i	−0.547337	−	0.948015i	0.451119	−	0.892464i	$-0.351025\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	400.194	−	212.585i	0.169946	−	0.0902761i
$178$		0			0
$179$	2356.54	+	1360.55i	0.984002	+	0.568114i	0.903476	−	0.428639i	$-0.141007\pi$
$179$	2356.54	+	1360.55i	0.984002	+	0.568114i	0.0805259	+	0.996753i	$0.474340\pi$
$180$		0			0
$181$			2661.91i			1.09314i	0.837413	+	0.546570i	$0.184067\pi$
$181$			2661.91i			1.09314i	−0.837413	+	0.546570i	$0.815933\pi$
$182$		0			0
$183$	−3930.07	−	138.787i	−1.58754	−	0.0560625i
$184$		0			0
$185$	−2110.34	+	3655.21i	−0.838677	+	1.45263i
$186$		0			0
$187$	−4520.79	+	2610.08i	−1.76788	+	1.02068i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1261.77	+	728.485i	−0.478004	+	0.275976i	−0.719584	−	0.694405i	$-0.755668\pi$
$191$	−1261.77	+	728.485i	−0.478004	+	0.275976i	0.241580	+	0.970381i	$0.422334\pi$
$192$		0			0
$193$	202.837	−	351.324i	0.0756504	−	0.131030i	−0.825719	−	0.564082i	$-0.809230\pi$
$193$	202.837	−	351.324i	0.0756504	−	0.131030i	0.901369	+	0.433052i	$0.142563\pi$
$194$		0			0
$195$	−4175.90	−	147.468i	−1.53355	−	0.0541560i
$196$		0			0
$197$		−	2047.00i		−	0.740318i	−0.928968	−	0.370159i	$-0.879303\pi$
$197$		−	2047.00i		−	0.740318i	0.928968	−	0.370159i	$-0.120697\pi$
$198$		0			0
$199$	−547.780	−	316.261i	−0.195131	−	0.112659i	0.399251	−	0.916842i	$-0.369270\pi$
$199$	−547.780	−	316.261i	−0.195131	−	0.112659i	−0.594382	+	0.804183i	$0.702603\pi$
$200$		0			0
$201$	−159.003	+	84.4635i	−0.0557972	+	0.0296398i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−342.418	−	593.085i	−0.116661	−	0.202063i
$206$		0			0
$207$	1994.84	+	1347.82i	0.669812	+	0.452560i
$208$		0			0
$209$	2844.17			0.941316
$210$		0			0
$211$	−223.172			−0.0728141			−0.0364071	−	0.999337i	$-0.511591\pi$
$211$	−223.172			−0.0728141			−0.0364071	+	0.999337i	$0.511591\pi$
$212$		0			0
$213$	1327.99	−	2123.37i	0.427194	−	0.683056i
$214$		0			0
$215$	3808.20	+	6595.99i	1.20799	+	2.09229i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1397.95	−	2631.65i	−0.431345	−	0.812011i
$220$		0			0
$221$	−4731.91	−	2731.97i	−1.44028	−	0.831548i
$222$		0			0
$223$			628.099i			0.188613i	0.995543	+	0.0943064i	$0.0300633\pi$
$223$			628.099i			0.188613i	−0.995543	+	0.0943064i	$0.969937\pi$
$224$		0			0
$225$	−5827.93	−	412.131i	−1.72680	−	0.122113i
$226$		0			0
$227$	1819.34	−	3151.20i	0.531956	−	0.921375i	−0.467348	−	0.884074i	$-0.654790\pi$
$227$	1819.34	−	3151.20i	0.531956	−	0.921375i	0.999304	−	0.0373018i	$-0.0118763\pi$
$228$		0			0
$229$	−3213.66	+	1855.41i	−0.927356	+	0.535409i	−0.885974	−	0.463734i	$-0.846509\pi$
$229$	−3213.66	+	1855.41i	−0.927356	+	0.535409i	−0.0413813	+	0.999143i	$0.513176\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1975.85	−	1140.76i	0.555546	−	0.320745i	−0.195810	−	0.980642i	$-0.562734\pi$
$233$	1975.85	−	1140.76i	0.555546	−	0.320745i	0.751356	+	0.659897i	$0.229400\pi$
$234$		0			0
$235$	5599.23	−	9698.16i	1.55427	−	2.69208i
$236$		0			0
$237$	−83.2748	+	2358.11i	−0.0228240	+	0.646312i
$238$		0			0
$239$			151.501i			0.0410034i	0.999790	+	0.0205017i	$0.00652635\pi$
$239$			151.501i			0.0410034i	−0.999790	+	0.0205017i	$0.993474\pi$
$240$		0			0
$241$	4350.51	+	2511.77i	1.16283	+	0.671358i	0.951980	−	0.306161i	$-0.0990445\pi$
$241$	4350.51	+	2511.77i	1.16283	+	0.671358i	0.210847	+	0.977519i	$0.432378\pi$
$242$		0			0
$243$	3562.09	−	1288.58i	0.940363	−	0.340173i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1488.49	+	2578.14i	0.383443	+	0.664143i
$248$		0			0
$249$	−3818.80	−	2388.34i	−0.971913	−	0.607850i
$250$		0			0
$251$	4859.29			1.22197			0.610987	−	0.791641i	$-0.290773\pi$
$251$	4859.29			1.22197			0.610987	+	0.791641i	$0.290773\pi$
$252$		0			0
$253$	−3707.60			−0.921324
$254$		0			0
$255$	−10219.1	−	6391.17i	−2.50958	−	1.56953i
$256$		0			0
$257$	−2927.17	−	5070.01i	−0.710474	−	1.23058i	−0.964679	−	0.263427i	$-0.915147\pi$
$257$	−2927.17	−	5070.01i	−0.710474	−	1.23058i	0.254205	−	0.967150i	$-0.418186\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3250.08	+	1582.01i	−0.770785	+	0.375187i
$262$		0			0
$263$	−2236.46	−	1291.22i	−0.524358	−	0.302738i	0.214358	−	0.976755i	$-0.431234\pi$
$263$	−2236.46	−	1291.22i	−0.524358	−	0.302738i	−0.738716	+	0.674017i	$0.764567\pi$
$264$		0			0
$265$			8912.50i			2.06600i
$266$		0			0
$267$	113.498	−	3213.94i	0.0260148	−	0.736667i
$268$		0			0
$269$	4045.25	−	7006.57i	0.916889	−	1.58810i	0.112776	−	0.993620i	$-0.464026\pi$
$269$	4045.25	−	7006.57i	0.916889	−	1.58810i	0.804113	−	0.594477i	$-0.202641\pi$
$270$		0			0
$271$	−939.407	+	542.367i	−0.210572	+	0.121574i	−0.601577	−	0.798815i	$-0.705461\pi$
$271$	−939.407	+	542.367i	−0.210572	+	0.121574i	0.391005	+	0.920388i	$0.372127\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7792.15	−	4498.80i	1.70867	−	0.986501i
$276$		0			0
$277$	2293.96	−	3973.26i	0.497584	−	0.861841i	−0.502412	−	0.864628i	$-0.667554\pi$
$277$	2293.96	−	3973.26i	0.497584	−	0.861841i	0.999996	+	0.00278763i	$0.000887331\pi$
$278$		0			0
$279$	−165.988	+	2347.23i	−0.0356181	+	0.503674i
$280$		0			0
$281$		−	1160.57i		−	0.246383i	−0.992383	−	0.123191i	$-0.960687\pi$
$281$		−	1160.57i		−	0.246383i	0.992383	−	0.123191i	$-0.0393129\pi$
$282$		0			0
$283$	1408.01	+	812.914i	0.295751	+	0.170752i	0.640532	−	0.767931i	$-0.278714\pi$
$283$	1408.01	+	812.914i	0.295751	+	0.170752i	−0.344782	+	0.938683i	$0.612047\pi$
$284$		0			0
$285$	3080.75	+	5799.55i	0.640309	+	1.20539i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5423.98	−	9394.61i	−1.10401	−	1.91219i
$290$		0			0
$291$	1635.30	−	2614.74i	0.329426	−	0.526732i
$292$		0			0
$293$	−7814.04			−1.55802			−0.779012	−	0.627009i	$-0.784279\pi$
$293$	−7814.04			−1.55802			−0.779012	+	0.627009i	$0.784279\pi$
$294$		0			0
$295$	−1611.34			−0.318020
$296$		0			0
$297$	−3434.48	+	4715.45i	−0.671005	+	0.921274i
$298$		0			0
$299$	−1940.37	−	3360.82i	−0.375300	−	0.650038i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4841.75	+	2571.97i	−0.917992	+	0.487642i
$304$		0			0
$305$	12110.0	+	6991.71i	2.27350	+	1.31260i
$306$		0			0
$307$			6885.55i			1.28006i	0.768349	+	0.640031i	$0.221078\pi$
$307$			6885.55i			1.28006i	−0.768349	+	0.640031i	$0.778922\pi$
$308$		0			0
$309$	−7615.28	−	268.927i	−1.40200	−	0.0495104i
$310$		0			0
$311$	−2535.23	+	4391.14i	−0.462249	+	0.800639i	−0.999073	−	0.0430555i	$-0.986291\pi$
$311$	−2535.23	+	4391.14i	−0.462249	+	0.800639i	0.536823	+	0.843695i	$0.319624\pi$
$312$		0			0
$313$	−3854.07	+	2225.15i	−0.695991	+	0.401831i	−0.805852	−	0.592116i	$-0.798293\pi$
$313$	−3854.07	+	2225.15i	−0.695991	+	0.401831i	0.109862	+	0.993947i	$0.464959\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4139.57	+	2389.98i	−0.733443	+	0.423453i	−0.819680	−	0.572821i	$-0.805849\pi$
$317$	−4139.57	+	2389.98i	−0.733443	+	0.423453i	0.0862375	+	0.996275i	$0.472516\pi$
$318$		0			0
$319$	2783.34	−	4820.89i	0.488518	−	0.846137i
$320$		0			0
$321$	4257.71	+	150.357i	0.740318	+	0.0261437i
$322$		0			0
$323$			8587.24i			1.47928i
$324$		0			0
$325$	8156.03	+	4708.89i	1.39205	+	0.803699i
$326$		0			0
$327$	3929.96	−	2087.62i	0.664609	−	0.353044i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4476.90	+	7754.23i	0.743423	+	1.28765i	0.950928	+	0.309412i	$0.100132\pi$
$331$	4476.90	+	7754.23i	0.743423	+	1.28765i	−0.207505	+	0.978234i	$0.566534\pi$
$332$		0			0
$333$	−3452.94	+	5110.52i	−0.568228	+	0.841006i
$334$		0			0
$335$	640.211			0.104413
$336$		0			0
$337$	2981.42			0.481924			0.240962	−	0.970535i	$-0.422537\pi$
$337$	2981.42			0.481924			0.240962	+	0.970535i	$0.422537\pi$
$338$		0			0
$339$	−5255.79	+	8403.67i	−0.842051	+	1.34639i
$340$		0			0
$341$	−1811.92	−	3138.33i	−0.287744	−	0.498388i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−4016.01	−	7560.19i	−0.626710	−	1.17979i
$346$		0			0
$347$	−9110.07	−	5259.70i	−1.40938	−	0.813705i	−0.414050	−	0.910254i	$-0.635886\pi$
$347$	−9110.07	−	5259.70i	−1.40938	−	0.813705i	−0.995328	+	0.0965491i	$0.969220\pi$
$348$		0			0
$349$		−	2261.34i		−	0.346839i	−0.984848	−	0.173419i	$-0.944518\pi$
$349$		−	2261.34i		−	0.346839i	0.984848	−	0.173419i	$-0.0554816\pi$
$350$		0			0
$351$	−6071.84	−	645.413i	−0.923335	−	0.0981470i
$352$		0			0
$353$	−1048.41	+	1815.90i	−0.158077	+	0.273798i	−0.934175	−	0.356815i	$-0.883863\pi$
$353$	−1048.41	+	1815.90i	−0.158077	+	0.273798i	0.776098	+	0.630612i	$0.217196\pi$
$354$		0			0
$355$	−7712.32	+	4452.71i	−1.15303	+	0.665705i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3108.29	+	1794.57i	−0.456962	+	0.263827i	−0.710766	−	0.703429i	$-0.751651\pi$
$359$	−3108.29	+	1794.57i	−0.456962	+	0.263827i	0.253804	+	0.967256i	$0.418318\pi$
$360$		0			0
$361$	−1090.15	+	1888.20i	−0.158938	+	0.275288i
$362$		0			0
$363$	72.9794	−	2066.58i	0.0105521	−	0.298808i
$364$		0			0
$365$			10596.1i			1.51952i
$366$		0			0
$367$	−8433.16	−	4868.88i	−1.19947	−	0.692517i	−0.239036	−	0.971011i	$-0.576832\pi$
$367$	−8433.16	−	4868.88i	−1.19947	−	0.692517i	−0.960438	+	0.278494i	$0.910165\pi$
$368$		0			0
$369$	−437.993	−	899.813i	−0.0617914	−	0.126944i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−302.085	−	523.226i	−0.0419339	−	0.0726317i	0.844297	−	0.535876i	$-0.180019\pi$
$373$	−302.085	−	523.226i	−0.0419339	−	0.0726317i	−0.886231	+	0.463244i	$0.846685\pi$
$374$		0			0
$375$	7438.94	+	4652.43i	1.02439	+	0.640668i
$376$		0			0
$377$	5826.64			0.795987
$378$		0			0
$379$	7261.70			0.984191			0.492095	−	0.870541i	$-0.336231\pi$
$379$	7261.70			0.984191			0.492095	+	0.870541i	$0.336231\pi$
$380$		0			0
$381$	−5012.55	−	3134.93i	−0.674017	−	0.421541i
$382$		0			0
$383$	−4689.57	−	8122.57i	−0.625654	−	1.08366i	−0.988414	−	0.151782i	$-0.951499\pi$
$383$	−4689.57	−	8122.57i	−0.625654	−	1.08366i	0.362760	−	0.931883i	$-0.381835\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4871.14	+	10007.3i	0.639829	+	1.31446i
$388$		0			0
$389$	3643.44	+	2103.54i	0.474884	+	0.274174i	0.718282	−	0.695752i	$-0.244929\pi$
$389$	3643.44	+	2103.54i	0.474884	+	0.274174i	−0.243398	+	0.969926i	$0.578262\pi$
$390$		0			0
$391$		−	11194.2i		−	1.44786i
$392$		0			0
$393$	183.147	−	5186.22i	0.0235077	−	0.665675i
$394$		0			0
$395$	4195.15	−	7266.22i	0.534382	−	0.925578i
$396$		0			0
$397$	−830.923	+	479.734i	−0.105045	+	0.0606477i	−0.551602	−	0.834107i	$-0.685983\pi$
$397$	−830.923	+	479.734i	−0.105045	+	0.0606477i	0.446557	+	0.894755i	$0.352650\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12670.8	−	7315.49i	1.57793	−	0.911018i	0.582781	−	0.812630i	$-0.301965\pi$
$401$	12670.8	−	7315.49i	1.57793	−	0.911018i	0.995148	−	0.0983880i	$-0.0313686\pi$
$402$		0			0
$403$	1896.53	−	3284.89i	0.234424	−	0.406034i
$404$		0			0
$405$	−13335.5	−	1895.55i	−1.63616	−	0.232570i
$406$		0			0
$407$		−	9498.40i		−	1.15680i
$408$		0			0
$409$	7310.28	+	4220.59i	0.883790	+	0.510257i	0.871906	−	0.489673i	$-0.162884\pi$
$409$	7310.28	+	4220.59i	0.883790	+	0.510257i	0.0118840	+	0.999929i	$0.496217\pi$
$410$		0			0
$411$	−2020.03	−	3802.72i	−0.242435	−	0.456385i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	8008.02	+	13870.3i	0.947225	+	1.64064i
$416$		0			0
$417$	−8011.88	+	12810.5i	−0.940872	+	1.50439i
$418$		0			0
$419$	−3570.61			−0.416314			−0.208157	−	0.978095i	$-0.566747\pi$
$419$	−3570.61			−0.416314			−0.208157	+	0.978095i	$0.566747\pi$
$420$		0			0
$421$	−1420.00			−0.164386			−0.0821932	−	0.996616i	$-0.526192\pi$
$421$	−1420.00			−0.164386			−0.0821932	+	0.996616i	$0.526192\pi$
$422$		0			0
$423$	9161.47	−	13559.4i	1.05306	−	1.55859i
$424$		0			0
$425$	13583.0	+	23526.4i	1.55029	+	2.68517i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	8304.52	−	4411.41i	0.934606	−	0.496468i
$430$		0			0
$431$	−1806.39	−	1042.92i	−0.201881	−	0.116556i	0.395652	−	0.918401i	$-0.370519\pi$
$431$	−1806.39	−	1042.92i	−0.201881	−	0.116556i	−0.597532	+	0.801845i	$0.703852\pi$
$432$		0			0
$433$		−	7904.10i		−	0.877244i	−0.898672	−	0.438622i	$-0.855467\pi$
$433$		−	7904.10i		−	0.877244i	0.898672	−	0.438622i	$-0.144533\pi$
$434$		0			0
$435$	12845.2	+	453.616i	1.41581	+	0.0499982i
$436$		0			0
$437$	−3049.53	+	5281.94i	−0.333819	+	0.578191i
$438$		0			0
$439$	3772.77	−	2178.21i	0.410169	−	0.236811i	−0.280693	−	0.959798i	$-0.590564\pi$
$439$	3772.77	−	2178.21i	0.410169	−	0.236811i	0.690862	+	0.722986i	$0.257231\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11892.9	+	6866.38i	−1.27551	+	0.736415i	−0.976019	−	0.217685i	$-0.930149\pi$
$443$	−11892.9	+	6866.38i	−1.27551	+	0.736415i	−0.299488	+	0.954100i	$0.596816\pi$
$444$		0			0
$445$	−5717.69	+	9903.34i	−0.609089	+	1.05497i
$446$		0			0
$447$	12012.4	+	424.207i	1.27106	+	0.0448865i
$448$		0			0
$449$		−	10838.5i		−	1.13920i	−0.821923	−	0.569598i	$-0.807099\pi$
$449$		−	10838.5i		−	1.13920i	0.821923	−	0.569598i	$-0.192901\pi$
$450$		0			0
$451$	1334.71	+	770.592i	0.139354	+	0.0804563i
$452$		0			0
$453$	−6354.15	+	3375.36i	−0.659037	+	0.350084i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4628.16	−	8016.21i	−0.473734	−	0.820531i	0.525814	−	0.850599i	$-0.323761\pi$
$457$	−4628.16	−	8016.21i	−0.473734	−	0.820531i	−0.999548	+	0.0300687i	$0.990427\pi$
$458$		0			0
$459$	−14237.1	−	10369.5i	−1.44778	−	1.05448i
$460$		0			0
$461$	3115.89			0.314797			0.157399	−	0.987535i	$-0.449689\pi$
$461$	3115.89			0.314797			0.157399	+	0.987535i	$0.449689\pi$
$462$		0			0
$463$	7214.41			0.724151			0.362075	−	0.932149i	$-0.382068\pi$
$463$	7214.41			0.724151			0.362075	+	0.932149i	$0.382068\pi$
$464$		0			0
$465$	4436.74	−	7094.07i	0.442471	−	0.707483i
$466$		0			0
$467$	1263.72	+	2188.83i	0.125221	+	0.216888i	0.921819	−	0.387620i	$-0.126703\pi$
$467$	1263.72	+	2188.83i	0.125221	+	0.216888i	−0.796599	+	0.604509i	$0.793369\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−5092.13	−	9585.99i	−0.498159	−	0.937790i
$472$		0			0
$473$	−14843.9	−	8570.13i	−1.44297	−	0.833098i
$474$		0			0
$475$		−	14801.2i		−	1.42974i
$476$		0			0
$477$	−918.706	+	12991.4i	−0.0881859	+	1.24703i
$478$		0			0
$479$	−2375.51	+	4114.51i	−0.226597	+	0.392478i	−0.956797	−	0.290755i	$-0.906093\pi$
$479$	−2375.51	+	4114.51i	−0.226597	+	0.392478i	0.730200	+	0.683233i	$0.239427\pi$
$480$		0			0
$481$	8609.99	−	4970.98i	0.816178	−	0.471221i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−9497.04	+	5483.12i	−0.889151	+	0.513352i
$486$		0			0
$487$	−10535.3	+	18247.7i	−0.980291	+	1.69791i	−0.319056	+	0.947736i	$0.603366\pi$
$487$	−10535.3	+	18247.7i	−0.980291	+	1.69791i	−0.661235	+	0.750179i	$0.729967\pi$
$488$		0			0
$489$	472.056	−	13367.3i	0.0436546	−	1.23618i
$490$		0			0
$491$		−	20752.0i		−	1.90738i	−0.300785	−	0.953692i	$-0.597249\pi$
$491$		−	20752.0i		−	1.90738i	0.300785	−	0.953692i	$-0.402751\pi$
$492$		0			0
$493$	14555.5	+	8403.59i	1.32970	+	0.767706i
$494$		0			0
$495$	18651.2	−	9078.67i	1.69356	−	0.824355i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1097.80	−	1901.45i	−0.0984859	−	0.170583i	0.812572	−	0.582861i	$-0.198067\pi$
$499$	−1097.80	−	1901.45i	−0.0984859	−	0.170583i	−0.911058	+	0.412278i	$0.864733\pi$
$500$		0			0
$501$	6920.03	+	4327.89i	0.617094	+	0.385940i
$502$		0			0
$503$	−86.6754			−0.00768323			−0.00384161	−	0.999993i	$-0.501223\pi$
$503$	−86.6754			−0.00768323			−0.00384161	+	0.999993i	$0.501223\pi$
$504$		0			0
$505$	19494.8			1.71784
$506$		0			0
$507$	−1333.93	−	834.263i	−0.116848	−	0.0730788i
$508$		0			0
$509$	−1065.21	−	1844.99i	−0.0927592	−	0.160664i	0.815912	−	0.578176i	$-0.196235\pi$
$509$	−1065.21	−	1844.99i	−0.0927592	−	0.160664i	−0.908671	+	0.417512i	$0.862902\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	3892.87	+	8771.33i	0.335038	+	0.754900i
$514$		0			0
$515$	23465.5	+	13547.8i	2.00779	+	1.15920i
$516$		0			0
$517$			25201.5i			2.14383i
$518$		0			0
$519$	−456.787	+	12935.0i	−0.0386334	+	1.09399i
$520$		0			0
$521$	1029.25	−	1782.71i	0.0865493	−	0.149908i	−0.819501	−	0.573078i	$-0.805749\pi$
$521$	1029.25	−	1782.71i	0.0865493	−	0.149908i	0.906050	+	0.423170i	$0.139083\pi$
$522$		0			0
$523$	6816.53	−	3935.53i	0.569916	−	0.329041i	−0.187200	−	0.982322i	$-0.559941\pi$
$523$	6816.53	−	3935.53i	0.569916	−	0.329041i	0.757116	+	0.653281i	$0.226608\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9475.40	−	5470.62i	0.783216	−	0.452190i
$528$		0			0
$529$	−2108.19	+	3651.49i	−0.173271	+	0.300114i
$530$		0			0
$531$	−2348.79	−	166.098i	−0.191956	−	0.0135745i
$532$		0			0
$533$			1613.16i			0.131095i
$534$		0			0
$535$	−13119.6	−	7574.58i	−1.06020	−	0.612108i
$536$		0			0
$537$	−6633.08	−	12486.8i	−0.533032	−	1.00344i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1088.16	+	1884.75i	0.0864763	+	0.149781i	0.906019	−	0.423236i	$-0.139106\pi$
$541$	1088.16	+	1884.75i	0.0864763	+	0.149781i	−0.819543	+	0.573018i	$0.805773\pi$
$542$		0			0
$543$	7334.29	−	11727.1i	0.579640	−	0.926807i
$544$		0			0
$545$	−15823.6			−1.24368
$546$		0			0
$547$	16504.4			1.29009			0.645043	−	0.764146i	$-0.276840\pi$
$547$	16504.4			1.29009			0.645043	+	0.764146i	$0.276840\pi$
$548$		0			0
$549$	16931.5	+	11439.8i	1.31625	+	0.889327i
$550$		0			0
$551$	−4578.63	−	7930.43i	−0.354004	−	0.613153i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	19368.2	−	10288.5i	1.48132	−	0.786888i
$556$		0			0
$557$	114.281	+	65.9801i	0.00869343	+	0.00501915i	0.504340	−	0.863505i	$-0.331736\pi$
$557$	114.281	+	65.9801i	0.00869343	+	0.00501915i	−0.495647	+	0.868524i	$0.665069\pi$
$558$		0			0
$559$		−	17940.7i		−	1.35744i
$560$		0			0
$561$	27107.9	+	957.291i	2.04010	+	0.0720443i
$562$		0			0
$563$	−10253.5	+	17759.6i	−0.767554	+	1.32944i	0.171332	+	0.985213i	$0.445193\pi$
$563$	−10253.5	+	17759.6i	−0.767554	+	1.32944i	−0.938886	+	0.344229i	$0.888140\pi$
$564$		0			0
$565$	30523.1	−	17622.5i	2.27277	−	1.31218i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13228.4	+	7637.41i	−0.974627	+	0.562701i	−0.900644	−	0.434558i	$-0.856904\pi$
$569$	−13228.4	+	7637.41i	−0.974627	+	0.562701i	−0.0739832	+	0.997259i	$0.523571\pi$
$570$		0			0
$571$	6499.02	−	11256.6i	0.476315	−	0.825001i	−0.523317	−	0.852138i	$-0.675306\pi$
$571$	6499.02	−	11256.6i	0.476315	−	0.825001i	0.999632	+	0.0271369i	$0.00863900\pi$
$572$		0			0
$573$	7565.93	+	267.184i	0.551608	+	0.0194796i
$574$		0			0
$575$			19294.5i			1.39937i
$576$		0			0
$577$	−15259.5	−	8810.08i	−1.10097	−	0.635647i	−0.164497	−	0.986378i	$-0.552600\pi$
$577$	−15259.5	−	8810.08i	−1.10097	−	0.635647i	−0.936477	+	0.350730i	$0.885933\pi$
$578$		0			0
$579$	−1861.59	+	988.888i	−0.133619	+	0.0709789i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−10028.5	−	17369.9i	−0.712418	−	1.23394i
$584$		0			0
$585$	17990.6	+	12155.4i	1.27149	+	0.859084i
$586$		0			0
$587$	−2139.84			−0.150461			−0.0752306	−	0.997166i	$-0.523969\pi$
$587$	−2139.84			−0.150461			−0.0752306	+	0.997166i	$0.523969\pi$
$588$		0			0
$589$	−5961.26			−0.417028
$590$		0			0
$591$	−5640.04	+	9018.07i	−0.392556	+	0.627671i
$592$		0			0
$593$	−6770.91	−	11727.6i	−0.468883	−	0.812130i	0.530484	−	0.847695i	$-0.322010\pi$
$593$	−6770.91	−	11727.6i	−0.468883	−	0.812130i	−0.999367	+	0.0355652i	$0.988677\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1541.86	+	2902.57i	0.105702	+	0.198986i
$598$		0			0
$599$	−7883.37	−	4551.46i	−0.537739	−	0.310464i	0.206423	−	0.978463i	$-0.433818\pi$
$599$	−7883.37	−	4551.46i	−0.537739	−	0.310464i	−0.744162	+	0.667999i	$0.767151\pi$
$600$		0			0
$601$		−	7463.40i		−	0.506553i	−0.967394	−	0.253276i	$-0.918492\pi$
$601$		−	7463.40i		−	0.506553i	0.967394	−	0.253276i	$-0.0815082\pi$
$602$		0			0
$603$	933.210	+	65.9933i	0.0630236	+	0.00445681i
$604$		0			0
$605$	−3676.50	+	6367.89i	−0.247060	+	0.427920i
$606$		0			0
$607$	4625.36	−	2670.45i	0.309287	−	0.178567i	−0.337320	−	0.941390i	$-0.609521\pi$
$607$	4625.36	−	2670.45i	0.309287	−	0.178567i	0.646608	+	0.762823i	$0.276187\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−22844.4	+	13189.2i	−1.51258	+	0.873287i
$612$		0			0
$613$	−1691.43	+	2929.65i	−0.111446	+	0.193030i	−0.916353	−	0.400370i	$-0.868881\pi$
$613$	−1691.43	+	2929.65i	−0.111446	+	0.193030i	0.804908	+	0.593400i	$0.202215\pi$
$614$		0			0
$615$	−125.588	+	3556.29i	−0.00823444	+	0.233177i
$616$		0			0
$617$			17592.6i			1.14789i	0.818893	+	0.573946i	$0.194588\pi$
$617$			17592.6i			1.14789i	−0.818893	+	0.573946i	$0.805412\pi$
$618$		0			0
$619$	18463.5	+	10659.9i	1.19889	+	0.692177i	0.960307	−	0.278946i	$-0.0899849\pi$
$619$	18463.5	+	10659.9i	1.19889	+	0.692177i	0.238579	+	0.971123i	$0.423318\pi$
$620$		0			0
$621$	−5074.67	−	11434.2i	−0.327922	−	0.738867i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2075.20	−	3594.35i	−0.132813	−	0.230038i
$626$		0			0
$627$	−12530.0	−	7836.45i	−0.798085	−	0.499135i
$628$		0			0
$629$	28678.0			1.81791
$630$		0			0
$631$	−16069.1			−1.01379			−0.506895	−	0.862008i	$-0.669207\pi$
$631$	−16069.1			−1.01379			−0.506895	+	0.862008i	$0.669207\pi$
$632$		0			0
$633$	983.185	+	614.899i	0.0617347	+	0.0386099i
$634$		0			0
$635$	10511.3	+	18206.1i	0.656896	+	1.13778i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−11700.9	+	5695.54i	−0.724384	+	0.352601i
$640$		0			0
$641$	−11898.6	−	6869.67i	−0.733178	−	0.423300i	0.0864059	−	0.996260i	$-0.472462\pi$
$641$	−11898.6	−	6869.67i	−0.733178	−	0.423300i	−0.819584	+	0.572960i	$0.805795\pi$
$642$		0			0
$643$		−	8719.09i		−	0.534755i	−0.963592	−	0.267377i	$-0.913843\pi$
$643$		−	8719.09i		−	0.534755i	0.963592	−	0.267377i	$-0.0861570\pi$
$644$		0			0
$645$	1396.72	−	39551.3i	0.0852648	−	2.41447i
$646$		0			0
$647$	7183.36	−	12441.9i	0.436487	−	0.756017i	−0.560929	−	0.827864i	$-0.689556\pi$
$647$	7183.36	−	12441.9i	0.436487	−	0.756017i	0.997416	+	0.0718466i	$0.0228892\pi$
$648$		0			0
$649$	3140.41	−	1813.11i	0.189941	−	0.109663i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	15240.3	−	8798.97i	0.913319	−	0.527305i	0.0318217	−	0.999494i	$-0.489869\pi$
$653$	15240.3	−	8798.97i	0.913319	−	0.527305i	0.881498	+	0.472188i	$0.156536\pi$
$654$		0			0
$655$	−9226.44	+	15980.7i	−0.550392	+	0.953307i
$656$		0			0
$657$	−1092.25	+	15445.5i	−0.0648595	+	0.917176i
$658$		0			0
$659$			4716.29i			0.278787i	0.990237	+	0.139393i	$0.0445153\pi$
$659$			4716.29i			0.278787i	−0.990237	+	0.139393i	$0.955485\pi$
$660$		0			0
$661$	−19548.4	−	11286.3i	−1.15029	−	0.664121i	−0.201334	−	0.979523i	$-0.564528\pi$
$661$	−19548.4	−	11286.3i	−1.15029	−	0.664121i	−0.948958	+	0.315401i	$0.897861\pi$
$662$		0			0
$663$	13319.1	+	25073.4i	0.780199	+	1.46873i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5968.63	+	10338.0i	0.346486	+	0.600131i
$668$		0			0
$669$	1730.58	−	2767.09i	0.100012	−	0.159913i
$670$		0			0
$671$	−31468.9			−1.81050
$672$		0			0
$673$	−5006.92			−0.286780			−0.143390	−	0.989666i	$-0.545800\pi$
$673$	−5006.92			−0.286780			−0.143390	+	0.989666i	$0.545800\pi$
$674$		0			0
$675$	24539.5	+	17873.2i	1.39929	+	1.01917i
$676$		0			0
$677$	2759.17	+	4779.02i	0.156637	+	0.271304i	0.933654	−	0.358176i	$-0.116601\pi$
$677$	2759.17	+	4779.02i	0.156637	+	0.271304i	−0.777017	+	0.629480i	$0.783268\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−16697.5	+	8869.82i	−0.939575	+	0.499108i
$682$		0			0
$683$	21451.9	+	12385.3i	1.20181	+	0.693864i	0.960957	−	0.276698i	$-0.0892402\pi$
$683$	21451.9	+	12385.3i	1.20181	+	0.693864i	0.240851	+	0.970562i	$0.422574\pi$
$684$		0			0
$685$			15311.3i			0.854035i
$686$		0			0
$687$	19269.9	+	680.501i	1.07015	+	0.0377915i
$688$		0			0
$689$	10496.9	−	18181.1i	0.580404	−	1.00529i
$690$		0			0
$691$	−13161.4	+	7598.71i	−0.724575	+	0.418334i	−0.816434	−	0.577438i	$-0.804052\pi$
$691$	−13161.4	+	7598.71i	−0.724575	+	0.418334i	0.0918589	+	0.995772i	$0.470719\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	46529.1	−	26863.6i	2.53950	−	1.46618i
$696$		0			0
$697$	−2326.61	+	4029.81i	−0.126437	+	0.218995i
$698$		0			0
$699$	−11847.7	−	418.392i	−0.641090	−	0.0226395i
$700$		0			0
$701$		−	18885.5i		−	1.01754i	−0.860902	−	0.508770i	$-0.830100\pi$
$701$		−	18885.5i		−	1.01754i	0.860902	−	0.508770i	$-0.169900\pi$
$702$		0			0
$703$	−13531.6	−	7812.50i	−0.725968	−	0.419138i
$704$		0			0
$705$	−51388.5	+	27297.9i	−2.74525	+	1.45829i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	2761.09	+	4782.35i	0.146255	+	0.253322i	0.929841	−	0.367963i	$-0.119945\pi$
$709$	2761.09	+	4782.35i	0.146255	+	0.253322i	−0.783585	+	0.621284i	$0.786611\pi$
$710$		0			0
$711$	6864.11	−	10159.2i	0.362060	−	0.535867i
$712$		0			0
$713$	7770.99			0.408171
$714$		0			0
$715$	−33437.3			−1.74893
$716$		0			0
$717$	417.427	−	667.440i	0.0217421	−	0.0347643i
$718$		0			0
$719$	−6929.83	−	12002.8i	−0.359443	−	0.622573i	0.628425	−	0.777870i	$-0.283700\pi$
$719$	−6929.83	−	12002.8i	−0.359443	−	0.622573i	−0.987868	+	0.155297i	$0.950366\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−12245.6	−	23052.5i	−0.629902	−	1.18580i
$724$		0			0
$725$	−25088.1	−	14484.6i	−1.28517	−	0.741995i
$726$		0			0
$727$			4460.45i			0.227550i	0.993507	+	0.113775i	$0.0362943\pi$
$727$			4460.45i			0.227550i	−0.993507	+	0.113775i	$0.963706\pi$
$728$		0			0
$729$	−19243.2	−	4137.70i	−0.977655	−	0.210217i
$730$		0			0
$731$	25875.4	−	44817.4i	1.30921	−	2.26762i
$732$		0			0
$733$	−1017.43	+	587.412i	−0.0512682	+	0.0295997i	−0.525415	−	0.850846i	$-0.676090\pi$
$733$	−1017.43	+	587.412i	−0.0512682	+	0.0295997i	0.474147	+	0.880446i	$0.342757\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1247.73	+	720.380i	−0.0623621	+	0.0360048i
$738$		0			0
$739$	−9262.91	+	16043.8i	−0.461085	+	0.798622i	−0.999015	−	0.0443669i	$-0.985873\pi$
$739$	−9262.91	+	16043.8i	−0.461085	+	0.798622i	0.537930	+	0.842989i	$0.319206\pi$
$740$		0			0
$741$	545.930	−	15459.2i	0.0270651	−	0.766409i
$742$		0			0
$743$		−	25777.5i		−	1.27279i	−0.771361	−	0.636397i	$-0.780424\pi$
$743$		−	25777.5i		−	1.27279i	0.771361	−	0.636397i	$-0.219576\pi$
$744$		0			0
$745$	−37014.5	−	21370.3i	−1.82028	−	1.05094i
$746$		0			0
$747$	10243.2	+	21043.6i	0.501713	+	1.03072i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	12464.8	+	21589.7i	0.605655	+	1.04902i	0.991948	+	0.126649i	$0.0404221\pi$
$751$	12464.8	+	21589.7i	0.605655	+	1.04902i	−0.386293	+	0.922376i	$0.626245\pi$
$752$		0			0
$753$	−21407.6	−	13388.7i	−1.03604	−	0.647955i
$754$		0			0
$755$	25584.3			1.23326
$756$		0			0
$757$	−8650.66			−0.415342			−0.207671	−	0.978199i	$-0.566588\pi$
$757$	−8650.66			−0.415342			−0.207671	+	0.978199i	$0.566588\pi$
$758$		0			0
$759$	16333.9	+	10215.5i	0.781135	+	0.488534i
$760$		0			0
$761$	−5193.55	−	8995.49i	−0.247393	−	0.428497i	0.715409	−	0.698706i	$-0.246240\pi$
$761$	−5193.55	−	8995.49i	−0.247393	−	0.428497i	−0.962802	+	0.270209i	$0.912907\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	27410.8	+	56312.7i	1.29547	+	2.66142i
$766$		0			0
$767$	3287.06	+	1897.79i	0.154744	+	0.0893417i
$768$		0			0
$769$			6275.09i			0.294259i	0.989117	+	0.147130i	$0.0470034\pi$
$769$			6275.09i			0.294259i	−0.989117	+	0.147130i	$0.952997\pi$
$770$		0			0
$771$	−1073.59	+	30401.1i	−0.0501483	+	1.42006i
$772$		0			0
$773$	−4517.01	+	7823.69i	−0.210175	+	0.364034i	−0.951769	−	0.306815i	$-0.900737\pi$
$773$	−4517.01	+	7823.69i	−0.210175	+	0.364034i	0.741594	+	0.670849i	$0.234070\pi$
$774$		0			0
$775$	−16332.0	+	9429.30i	−0.756986	+	0.437046i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2195.61	−	1267.64i	0.100983	−	0.0583026i
$780$		0			0
$781$	10020.6	−	17356.1i	0.459109	−	0.795200i
$782$		0			0
$783$	18677.1	+	1985.30i	0.852446	+	0.0906117i
$784$		0			0
$785$			38597.0i			1.75489i
$786$		0			0
$787$	−10295.3	−	5943.99i	−0.466312	−	0.269225i	0.248383	−	0.968662i	$-0.420101\pi$
$787$	−10295.3	−	5943.99i	−0.466312	−	0.269225i	−0.714695	+	0.699437i	$0.753434\pi$
$788$		0			0
$789$	6295.08	+	11850.5i	0.284044	+	0.534716i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−16469.2	−	28525.5i	−0.737502	−	1.27739i
$794$		0			0
$795$	24556.4	−	39264.1i	1.09550	−	1.75164i
$796$		0			0
$797$	14167.3			0.629650			0.314825	−	0.949150i	$-0.398054\pi$
$797$	14167.3			0.629650			0.314825	+	0.949150i	$0.398054\pi$
$798$		0			0
$799$	−76089.7			−3.36903
$800$		0			0
$801$	−9355.30	+	13846.3i	−0.412676	+	0.610781i
$802$		0			0
$803$	−11922.9	−	20651.1i	−0.523974	−	0.907549i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−37126.4	+	19721.7i	−1.61947	+	0.860270i
$808$		0			0
$809$	12835.1	+	7410.33i	0.557796	+	0.322044i	0.752260	−	0.658866i	$-0.228964\pi$
$809$	12835.1	+	7410.33i	0.557796	+	0.322044i	−0.194465	+	0.980910i	$0.562297\pi$
$810$		0			0
$811$		−	510.470i		−	0.0221024i	−0.999939	−	0.0110512i	$-0.996482\pi$
$811$		−	510.470i		−	0.0221024i	0.999939	−	0.0110512i	$-0.00351778\pi$
$812$		0			0
$813$	5632.93	+	198.922i	0.242996	+	0.00858119i
$814$		0			0
$815$	−23780.9	+	41189.7i	−1.02209	+	1.77032i
$816$		0			0
$817$	−24418.4	+	14098.0i	−1.04565	+	0.603704i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16503.7	−	9528.41i	0.701563	−	0.405047i	−0.106366	−	0.994327i	$-0.533922\pi$
$821$	16503.7	−	9528.41i	0.701563	−	0.405047i	0.807929	+	0.589280i	$0.200588\pi$
$822$		0			0
$823$	−10746.9	+	18614.1i	−0.455179	+	0.788393i	−0.998698	−	0.0510034i	$-0.983758\pi$
$823$	−10746.9	+	18614.1i	−0.455179	+	0.788393i	0.543520	+	0.839397i	$0.317091\pi$
$824$		0			0
$825$	−46723.8	−	1650.01i	−1.97177	−	0.0696315i
$826$		0			0
$827$		−	7914.71i		−	0.332795i	−0.986059	−	0.166397i	$-0.946787\pi$
$827$		−	7914.71i		−	0.332795i	0.986059	−	0.166397i	$-0.0532135\pi$
$828$		0			0
$829$	1403.46	+	810.285i	0.0587986	+	0.0339474i	0.529111	−	0.848553i	$-0.322525\pi$
$829$	1403.46	+	810.285i	0.0587986	+	0.0339474i	−0.470313	+	0.882500i	$0.655859\pi$
$830$		0			0
$831$	−21053.5	+	11183.7i	−0.878865	+	0.466858i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−14511.3	−	25134.3i	−0.601418	−	1.04169i
$836$		0			0
$837$	7198.53	−	9883.40i	0.297273	−	0.408149i
$838$		0			0
$839$	−19995.8			−0.822801			−0.411400	−	0.911455i	$-0.634960\pi$
$839$	−19995.8			−0.822801			−0.411400	+	0.911455i	$0.634960\pi$
$840$		0			0
$841$	6466.14			0.265125
$842$		0			0
$843$	−3197.67	+	5112.88i	−0.130645	+	0.208893i
$844$		0			0
$845$	2797.26	+	4845.00i	0.113880	+	0.197246i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3963.19	−	7460.74i	−0.160208	−	0.301593i
$850$		0			0
$851$	17639.6	+	10184.2i	0.710550	+	0.410236i
$852$		0			0
$853$		−	3374.92i		−	0.135469i	−0.997703	−	0.0677345i	$-0.978423\pi$
$853$		−	3374.92i		−	0.135469i	0.997703	−	0.0677345i	$-0.0215771\pi$
$854$		0			0
$855$	2407.07	−	34038.2i	0.0962806	−	1.36150i
$856$		0			0
$857$	−7692.89	+	13324.5i	−0.306633	+	0.531103i	−0.977623	−	0.210362i	$-0.932536\pi$
$857$	−7692.89	+	13324.5i	−0.306633	+	0.531103i	0.670991	+	0.741466i	$0.265869\pi$
$858$		0			0
$859$	−11531.4	+	6657.65i	−0.458028	+	0.264443i	−0.711215	−	0.702975i	$-0.751855\pi$
$859$	−11531.4	+	6657.65i	−0.458028	+	0.264443i	0.253187	+	0.967417i	$0.418521\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8083.25	+	4666.86i	−0.318838	+	0.184081i	−0.650874	−	0.759185i	$-0.725598\pi$
$863$	−8083.25	+	4666.86i	−0.318838	+	0.184081i	0.332037	+	0.943266i	$0.392264\pi$
$864$		0			0
$865$	23011.7	−	39857.4i	0.904532	−	1.56670i
$866$		0			0
$867$	−1989.34	+	56332.5i	−0.0779255	+	2.20664i
$868$		0			0
$869$			18881.9i			0.737083i
$870$		0			0
$871$	−1306.00	−	754.020i	−0.0508062	−	0.0293330i
$872$		0			0
$873$	−14408.7	+	7013.56i	−0.558602	+	0.271905i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7658.69	+	13265.2i	0.294887	+	0.510759i	0.974959	−	0.222387i	$-0.0713847\pi$
$877$	7658.69	+	13265.2i	0.294887	+	0.510759i	−0.680072	+	0.733146i	$0.738051\pi$
$878$		0			0
$879$	34424.8	+	21529.8i	1.32096	+	0.826146i
$880$		0			0
$881$	−16622.6			−0.635675			−0.317837	−	0.948145i	$-0.602957\pi$
$881$	−16622.6			−0.635675			−0.317837	+	0.948145i	$0.602957\pi$
$882$		0			0
$883$	−28971.2			−1.10414			−0.552072	−	0.833797i	$-0.686163\pi$
$883$	−28971.2			−1.10414			−0.552072	+	0.833797i	$0.686163\pi$
$884$		0			0
$885$	7098.77	+	4439.68i	0.269630	+	0.168631i
$886$		0			0
$887$	−1738.97	−	3011.98i	−0.0658274	−	0.114016i	0.831233	−	0.555924i	$-0.187635\pi$
$887$	−1738.97	−	3011.98i	−0.0658274	−	0.114016i	−0.897061	+	0.441907i	$0.854302\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	28123.0	−	11311.0i	1.05741	−	0.425291i
$892$		0			0
$893$	35902.7	+	20728.4i	1.34540	+	0.776764i
$894$		0			0
$895$			50277.0i			1.87774i
$896$		0			0
$897$	−711.664	+	20152.4i	−0.0264903	+	0.750132i
$898$		0			0
$899$	−5833.77	+	10104.4i	−0.216426	+	0.374861i
$900$		0			0
$901$	52444.2	−	30278.7i	1.93914	−	1.11957i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−42594.0	+	24591.7i	−1.56450	+	0.903265i
$906$		0			0
$907$	−22438.4	+	38864.4i	−0.821448	+	1.42279i	0.0831551	+	0.996537i	$0.473500\pi$
$907$	−22438.4	+	38864.4i	−0.821448	+	1.42279i	−0.904604	+	0.426254i	$0.859833\pi$
$908$		0			0
$909$	28416.8	+	2009.54i	1.03688	+	0.0733248i
$910$		0			0
$911$			25614.1i			0.931542i	0.884905	+	0.465771i	$0.154223\pi$
$911$			25614.1i			0.931542i	−0.884905	+	0.465771i	$0.845777\pi$
$912$		0			0
$913$	−31214.3	−	18021.6i	−1.13148	−	0.653262i
$914$		0			0
$915$	−34086.6	−	64168.3i	−1.23155	−	2.31840i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−11188.0	−	19378.2i	−0.401587	−	0.695570i	0.592330	−	0.805695i	$-0.298208\pi$
$919$	−11188.0	−	19378.2i	−0.401587	−	0.695570i	−0.993918	+	0.110126i	$0.964875\pi$
$920$		0			0
$921$	18971.6	−	30334.3i	0.678756	−	1.08529i
$922$		0			0
$923$	20977.0			0.748069
$924$		0			0
$925$	−49430.1			−1.75703
$926$		0			0
$927$	32808.2	+	22166.9i	1.16242	+	0.785391i
$928$		0			0
$929$	5485.50	+	9501.16i	0.193728	+	0.335547i	0.946483	−	0.322754i	$-0.104609\pi$
$929$	5485.50	+	9501.16i	0.193728	+	0.335547i	−0.752755	+	0.658301i	$0.771275\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	23267.7	−	12360.0i	0.816454	−	0.433705i
$934$		0			0
$935$	−83529.3	−	48225.7i	−2.92161	−	1.68679i
$936$		0			0
$937$			56712.6i			1.97729i	0.150272	+	0.988645i	$0.451985\pi$
$937$			56712.6i			1.97729i	−0.150272	+	0.988645i	$0.548015\pi$
$938$		0			0
$939$	23110.0	+	816.112i	0.803160	+	0.0283629i
$940$		0			0
$941$	1614.07	−	2795.65i	0.0559162	−	0.0968497i	−0.836712	−	0.547643i	$-0.815525\pi$
$941$	1614.07	−	2795.65i	0.0559162	−	0.0968497i	0.892629	+	0.450793i	$0.148859\pi$
$942$		0			0
$943$	−2862.16	+	1652.47i	−0.0988384	+	0.0570644i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15905.6	+	9183.11i	−0.545790	+	0.315112i	−0.747422	−	0.664349i	$-0.768709\pi$
$947$	−15905.6	+	9183.11i	−0.545790	+	0.315112i	0.201632	+	0.979461i	$0.435375\pi$
$948$		0			0
$949$	12479.7	−	21615.5i	0.426880	−	0.739377i
$950$		0			0
$951$	24821.9	+	876.566i	0.846379	+	0.0298892i
$952$		0			0
$953$		−	3326.89i		−	0.113083i	−0.998400	−	0.0565417i	$-0.981993\pi$
$953$		−	3326.89i		−	0.113083i	0.998400	−	0.0565417i	$-0.0180074\pi$
$954$		0			0
$955$	−23313.4	−	13460.0i	−0.789952	−	0.456079i
$956$		0			0
$957$	−25544.9	+	13569.6i	−0.862851	+	0.458351i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−11097.8	−	19221.9i	−0.372522	−	0.645227i
$962$		0			0
$963$	−18343.1	−	12393.5i	−0.613808	−	0.414721i
$964$		0			0
$965$	7495.51			0.250041
$966$		0			0
$967$	49692.0			1.65252			0.826260	−	0.563289i	$-0.190464\pi$
$967$	49692.0			1.65252			0.826260	+	0.563289i	$0.190464\pi$
$968$		0			0
$969$	23660.2	−	37831.1i	0.784391	−	1.25419i
$970$		0			0
$971$	19155.1	+	33177.6i	0.633076	+	1.09652i	0.986919	+	0.161215i	$0.0515414\pi$
$971$	19155.1	+	33177.6i	0.633076	+	1.09652i	−0.353843	+	0.935305i	$0.615125\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−22957.2	−	43217.1i	−0.754070	−	1.41954i
$976$		0			0
$977$	22737.3	+	13127.4i	0.744554	+	0.429869i	0.823723	−	0.566993i	$-0.191893\pi$
$977$	22737.3	+	13127.4i	0.744554	+	0.429869i	−0.0791685	+	0.996861i	$0.525227\pi$
$978$		0			0
$979$		−	25734.7i		−	0.840127i
$980$		0			0
$981$	−23065.4	−	1631.10i	−0.750685	−	0.0530858i
$982$		0			0
$983$	13534.0	−	23441.6i	0.439133	−	0.760600i	−0.558490	−	0.829511i	$-0.688619\pi$
$983$	13534.0	−	23441.6i	0.439133	−	0.760600i	0.997623	+	0.0689112i	$0.0219525\pi$
$984$		0			0
$985$	32754.6	−	18910.9i	1.05954	−	0.611727i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	31831.4	−	18377.9i	1.02344	−	0.590883i
$990$		0			0
$991$	14969.4	−	25927.8i	0.479839	−	0.831105i	−0.519894	−	0.854231i	$-0.674029\pi$
$991$	14969.4	−	25927.8i	0.479839	−	0.831105i	0.999733	+	0.0231261i	$0.00736191\pi$
$992$		0			0
$993$	1641.98	−	46496.4i	0.0524740	−	1.48592i
$994$		0			0
$995$		−	11686.9i		−	0.372362i
$996$		0			0
$997$	18875.9	+	10898.0i	0.599604	+	0.346181i	0.768886	−	0.639386i	$-0.220812\pi$
$997$	18875.9	+	10898.0i	0.599604	+	0.346181i	−0.169282	+	0.985568i	$0.554145\pi$
$998$		0			0
$999$	29292.8	−	13000.7i	0.927711	−	0.411734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.e.521.5		48
3.2	odd	2	inner	588.4.k.e.521.4		48
7.2	even	3	inner	588.4.k.e.509.21		48
7.3	odd	6		588.4.f.d.293.13	yes	24
7.4	even	3		588.4.f.d.293.12	yes	24
7.5	odd	6	inner	588.4.k.e.509.4		48
7.6	odd	2	inner	588.4.k.e.521.20		48
21.2	odd	6	inner	588.4.k.e.509.20		48
21.5	even	6	inner	588.4.k.e.509.5		48
21.11	odd	6		588.4.f.d.293.14	yes	24
21.17	even	6		588.4.f.d.293.11	✓	24
21.20	even	2	inner	588.4.k.e.521.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.f.d.293.11	✓	24	21.17	even	6
588.4.f.d.293.12	yes	24	7.4	even	3
588.4.f.d.293.13	yes	24	7.3	odd	6
588.4.f.d.293.14	yes	24	21.11	odd	6
588.4.k.e.509.4		48	7.5	odd	6	inner
588.4.k.e.509.5		48	21.5	even	6	inner
588.4.k.e.509.20		48	21.2	odd	6	inner
588.4.k.e.509.21		48	7.2	even	3	inner
588.4.k.e.521.4		48	3.2	odd	2	inner
588.4.k.e.521.5		48	1.1	even	1	trivial
588.4.k.e.521.20		48	7.6	odd	2	inner
588.4.k.e.521.21		48	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)

\(f(q)\)	\(=\)	\(q+(-4.40550 - 2.75527i) q^{3} +(9.23835 + 16.0013i) q^{5} +(11.8169 + 24.2767i) q^{9} +O(q^{10})\)	\(q+(-4.40550 - 2.75527i) q^{3} +(9.23835 + 16.0013i) q^{5} +(11.8169 + 24.2767i) q^{9} +(-36.0100 - 20.7904i) q^{11} -43.5225i q^{13} +(3.38832 - 95.9479i) q^{15} +(62.7713 - 108.723i) q^{17} +(-59.2370 + 34.2005i) q^{19} +(77.2203 - 44.5831i) q^{23} +(-108.194 + 187.398i) q^{25} +(14.8294 - 139.510i) q^{27} +133.876i q^{29} +(75.4755 + 43.5758i) q^{31} +(101.359 + 190.810i) q^{33} +(114.216 + 197.828i) q^{37} +(-119.916 + 191.739i) q^{39} -37.0648 q^{41} +412.216 q^{43} +(-279.290 + 413.363i) q^{45} +(-303.043 - 524.886i) q^{47} +(-576.101 + 306.028i) q^{51} +(417.740 + 241.182i) q^{53} -768.275i q^{55} +(355.200 + 12.5436i) q^{57} +(-43.6046 + 75.5255i) q^{59} +(655.420 - 378.407i) q^{61} +(696.417 - 402.077i) q^{65} +(17.3248 - 30.0075i) q^{67} +(-463.033 - 16.3516i) q^{69} +481.981i q^{71} +(496.651 + 286.741i) q^{73} +(992.982 - 527.478i) q^{75} +(-227.051 - 393.264i) q^{79} +(-449.719 + 573.754i) q^{81} +866.824 q^{83} +2319.61 q^{85} +(368.866 - 589.793i) q^{87} +(309.454 + 535.991i) q^{89} +(-212.445 - 399.929i) q^{93} +(-1094.50 - 631.912i) q^{95} +593.517i q^{97} +(79.1943 - 1119.88i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 48 * q + 64 * q^9	\( 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) \) 48 * q + 64 * q^9 - 192 * q^15 - 456 * q^25 + 432 * q^37 - 688 * q^39 + 1248 * q^43 + 1536 * q^51 - 2720 * q^57 + 528 * q^67 - 3744 * q^79 - 3408 * q^81 + 13824 * q^85 + 5088 * q^93 - 15472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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