LMFDB - Embedded newform 588.4.k.e.521.21

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			521.21
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.58889 + 2.43764i) q^{3} +(9.23835 + 16.0013i) q^{5} +(15.1158 + 22.3721i) q^{9} +O(q^{10})$	\(q+(4.58889 + 2.43764i) q^{3} +(9.23835 + 16.0013i) q^{5} +(15.1158 + 22.3721i) q^{9} +(36.0100 + 20.7904i) q^{11} +43.5225i q^{13} +(3.38832 + 95.9479i) q^{15} +(62.7713 - 108.723i) q^{17} +(59.2370 - 34.2005i) q^{19} +(-77.2203 + 44.5831i) q^{23} +(-108.194 + 187.398i) q^{25} +(14.8294 + 139.510i) q^{27} -133.876i q^{29} +(-75.4755 - 43.5758i) q^{31} +(114.566 + 183.184i) q^{33} +(114.216 + 197.828i) q^{37} +(-106.092 + 199.720i) q^{39} -37.0648 q^{41} +412.216 q^{43} +(-218.338 + 448.554i) q^{45} +(-303.043 - 524.886i) q^{47} +(553.079 - 345.904i) q^{51} +(-417.740 - 241.182i) q^{53} +768.275i q^{55} +(355.200 - 12.5436i) q^{57} +(-43.6046 + 75.5255i) q^{59} +(-655.420 + 378.407i) q^{61} +(-696.417 + 402.077i) q^{65} +(17.3248 - 30.0075i) q^{67} +(-463.033 + 16.3516i) q^{69} -481.981i q^{71} +(-496.651 - 286.741i) q^{73} +(-953.300 + 596.209i) q^{75} +(-227.051 - 393.264i) q^{79} +(-272.026 + 676.345i) q^{81} +866.824 q^{83} +2319.61 q^{85} +(326.343 - 614.343i) q^{87} +(309.454 + 535.991i) q^{89} +(-240.126 - 383.947i) q^{93} +(1094.50 + 631.912i) q^{95} -593.517i q^{97} +(79.1943 + 1119.88i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	4.58889	+	2.43764i	0.883132	+	0.469125i
$3$	4.58889	+	2.43764i	0.883132	+	0.469125i
$4$		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
$9$	15.1158	+	22.3721i	0.559844	+	0.828598i
$10$		0			0
$11$	36.0100	+	20.7904i	0.987039	+	0.569867i	0.904388	−	0.426712i	$-0.140328\pi$
$11$	36.0100	+	20.7904i	0.987039	+	0.569867i	0.0826509	+	0.996579i	$0.473661\pi$
$12$		0			0
$13$			43.5225i			0.928537i	0.885694	+	0.464269i	$0.153683\pi$
$13$			43.5225i			0.928537i	−0.885694	+	0.464269i	$0.846317\pi$
$14$		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	−0.0977471	−	0.995211i	$-0.531164\pi$
$19$	59.2370	−	34.2005i	0.715258	−	0.412954i	0.813005	+	0.582257i	$0.197830\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−77.2203	+	44.5831i	−0.700067	+	0.404184i	−0.807372	−	0.590042i	$-0.799111\pi$
$23$	−77.2203	+	44.5831i	−0.700067	+	0.404184i	0.107306	+	0.994226i	$0.465778\pi$
$24$		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	$-0.858998\pi$
$29$		−	133.876i		−	0.857248i	0.903483	−	0.428624i	$-0.141002\pi$
$30$		0			0
$31$	−75.4755	−	43.5758i	−0.437284	−	0.252466i	0.265161	−	0.964204i	$-0.414575\pi$
$31$	−75.4755	−	43.5758i	−0.437284	−	0.252466i	−0.702445	+	0.711738i	$0.747908\pi$
$32$		0			0
$33$	114.566	+	183.184i	0.604347	+	0.966312i
$34$		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
$39$	−106.092	+	199.720i	−0.435600	+	0.820021i
$40$		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
$45$	−218.338	+	448.554i	−0.723287	+	1.48592i
$46$		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
$51$	553.079	−	345.904i	1.51856	−	0.949731i
$52$		0			0
$53$	−417.740	−	241.182i	−1.08266	−	0.625074i	−0.151047	−	0.988527i	$-0.548265\pi$
$53$	−417.740	−	241.182i	−1.08266	−	0.625074i	−0.931613	+	0.363453i	$0.881598\pi$
$54$		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	−0.991639	−	0.129044i	$-0.958809\pi$
$61$	−655.420	+	378.407i	−1.37570	+	0.794263i	−0.384064	+	0.923306i	$0.625476\pi$
$62$		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	$-0.868030\pi$
$71$		−	481.981i		−	0.805643i	0.915279	−	0.402821i	$-0.131970\pi$
$72$		0			0
$73$	−496.651	−	286.741i	−0.796282	−	0.459733i	0.0458876	−	0.998947i	$-0.485388\pi$
$73$	−496.651	−	286.741i	−0.796282	−	0.459733i	−0.842169	+	0.539213i	$0.818722\pi$
$74$		0			0
$75$	−953.300	+	596.209i	−1.46770	+	0.917924i
$76$		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
$81$	−272.026	+	676.345i	−0.373149	+	0.927771i
$82$		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
$87$	326.343	−	614.343i	0.402156	−	0.757064i
$88$		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
$93$	−240.126	−	383.947i	−0.267741	−	0.428102i
$94$		0			0
$95$	1094.50	+	631.912i	1.18204	+	0.682451i
$96$		0			0
$97$		−	593.517i		−	0.621263i	−0.950530	−	0.310632i	$-0.899459\pi$
$97$		−	593.517i		−	0.621263i	0.950530	−	0.310632i	$-0.100541\pi$
$98$		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	−0.963828	−	0.266525i	$-0.914124\pi$
$103$	−1270.00	+	733.237i	−1.21492	+	0.701437i	−0.251096	+	0.967962i	$0.580791\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	710.060	−	409.953i	0.641533	−	0.370390i	−0.143672	−	0.989625i	$-0.545891\pi$
$107$	710.060	−	409.953i	0.641533	−	0.370390i	0.785205	+	0.619236i	$0.212558\pi$
$108$		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	$0.292010\pi$
$113$			1907.54i			1.58802i	−0.607906	+	0.794009i	$0.707990\pi$
$114$		0			0
$115$	−1426.78	−	823.749i	−1.15693	−	0.667957i
$116$		0			0
$117$	−973.693	+	657.878i	−0.769384	+	0.519836i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	198.980	+	344.644i	0.149497	+	0.258936i
$122$		0			0
$123$	−170.086	−	90.3508i	−0.124684	−	0.0662330i
$124$		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
$129$	1891.61	+	1004.84i	1.29106	+	0.685821i
$130$		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
$135$	−2095.34	+	1526.13i	−1.33584	+	0.972953i
$136$		0			0
$137$	−717.658	−	414.340i	−0.447545	−	0.258390i	0.259248	−	0.965811i	$-0.416525\pi$
$137$	−717.658	−	414.340i	−0.447545	−	0.258390i	−0.706793	+	0.707421i	$0.749859\pi$
$138$		0			0
$139$			2907.84i			1.77439i	0.461399	+	0.887193i	$0.347348\pi$
$139$			2907.84i			1.77439i	−0.461399	+	0.887193i	$0.652652\pi$
$140$		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	0.164855	−	0.986318i	$-0.447284\pi$
$149$	2003.31	−	1156.61i	1.10146	−	0.635928i	0.936604	+	0.350390i	$0.113951\pi$
$150$		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	−0.0361096	−	0.999348i	$-0.511497\pi$
$157$	−1809.09	−	1044.48i	−0.919625	−	0.530946i	−0.883515	+	0.468402i	$0.844830\pi$
$158$		0			0
$159$	−1329.05	−	2125.06i	−0.662894	−	1.05993i
$160$		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
$165$	−1872.78	+	3525.53i	−0.883611	+	1.66341i
$166$		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
$171$	1660.55	+	808.291i	0.742606	+	0.361471i
$172$		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
$177$	−384.201	+	240.285i	−0.163154	+	0.102039i
$178$		0			0
$179$	−2356.54	−	1360.55i	−0.984002	−	0.568114i	−0.0805259	−	0.996753i	$-0.525660\pi$
$179$	−2356.54	−	1360.55i	−0.984002	−	0.568114i	−0.903476	+	0.428639i	$0.858993\pi$
$180$		0			0
$181$		−	2661.91i		−	1.09314i	−0.837413	−	0.546570i	$-0.815933\pi$
$181$		−	2661.91i		−	1.09314i	0.837413	−	0.546570i	$-0.184067\pi$
$182$		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	−0.241580	−	0.970381i	$-0.577666\pi$
$191$	1261.77	−	728.485i	0.478004	−	0.275976i	0.719584	+	0.694405i	$0.244332\pi$
$192$		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	$0.120697\pi$
$197$			2047.00i			0.740318i	−0.928968	+	0.370159i	$0.879303\pi$
$198$		0			0
$199$	547.780	+	316.261i	0.195131	+	0.112659i	0.594382	−	0.804183i	$-0.297397\pi$
$199$	547.780	+	316.261i	0.195131	+	0.112659i	−0.399251	+	0.916842i	$0.630730\pi$
$200$		0			0
$201$	152.649	−	95.4692i	0.0535674	−	0.0335019i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−342.418	−	593.085i	−0.116661	−	0.202063i
$206$		0			0
$207$	−2164.67	−	1053.67i	−0.726834	−	0.353794i
$208$		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
$213$	1174.90	−	2211.76i	0.377947	−	0.711489i
$214$		0			0
$215$	3808.20	+	6595.99i	1.20799	+	2.09229i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1580.10	−	2526.48i	−0.487550	−	0.779561i
$220$		0			0
$221$	4731.91	+	2731.97i	1.44028	+	0.831548i
$222$		0			0
$223$		−	628.099i		−	0.188613i	−0.995543	−	0.0943064i	$-0.969937\pi$
$223$		−	628.099i		−	0.188613i	0.995543	−	0.0943064i	$-0.0300633\pi$
$224$		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	0.0413813	−	0.999143i	$-0.486824\pi$
$229$	3213.66	−	1855.41i	0.927356	−	0.535409i	0.885974	+	0.463734i	$0.153491\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1975.85	+	1140.76i	−0.555546	+	0.320745i	−0.751356	−	0.659897i	$-0.770600\pi$
$233$	−1975.85	+	1140.76i	−0.555546	+	0.320745i	0.195810	+	0.980642i	$0.437266\pi$
$234$		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	$-0.993474\pi$
$239$		−	151.501i		−	0.0410034i	0.999790	−	0.0205017i	$-0.00652635\pi$
$240$		0			0
$241$	−4350.51	−	2511.77i	−1.16283	−	0.671358i	−0.210847	−	0.977519i	$-0.567622\pi$
$241$	−4350.51	−	2511.77i	−1.16283	−	0.671358i	−0.951980	+	0.306161i	$0.900956\pi$
$242$		0			0
$243$	−2896.98	+	2440.57i	−0.764780	+	0.644291i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1488.49	+	2578.14i	0.383443	+	0.664143i
$248$		0			0
$249$	3977.76	+	2113.01i	1.01237	+	0.537776i
$250$		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
$255$	10644.4	+	5654.39i	2.61404	+	1.38859i
$256$		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
$261$	2995.10	−	2023.65i	0.710314	−	0.479926i
$262$		0			0
$263$	2236.46	+	1291.22i	0.524358	+	0.302738i	0.738716	−	0.674017i	$-0.235433\pi$
$263$	2236.46	+	1291.22i	0.524358	+	0.302738i	−0.214358	+	0.976755i	$0.568766\pi$
$264$		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	−0.391005	−	0.920388i	$-0.627873\pi$
$271$	939.407	−	542.367i	0.210572	−	0.121574i	0.601577	+	0.798815i	$0.294539\pi$
$272$		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	$0.0393129\pi$
$281$			1160.57i			0.246383i	−0.992383	+	0.123191i	$0.960687\pi$
$282$		0			0
$283$	−1408.01	−	812.914i	−0.295751	−	0.170752i	0.344782	−	0.938683i	$-0.387953\pi$
$283$	−1408.01	−	812.914i	−0.295751	−	0.170752i	−0.640532	+	0.767931i	$0.721286\pi$
$284$		0			0
$285$	3482.18	+	5567.78i	0.723742	+	1.15722i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5423.98	−	9394.61i	−1.10401	−	1.91219i
$290$		0			0
$291$	1446.78	−	2723.58i	0.291450	−	0.548657i
$292$		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
$297$	−2366.46	+	5332.07i	−0.462344	+	1.04174i
$298$		0			0
$299$	−1940.37	−	3360.82i	−0.375300	−	0.650038i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	4648.27	−	2907.10i	0.881306	−	0.551183i
$304$		0			0
$305$	−12110.0	−	6991.71i	−2.27350	−	1.31260i
$306$		0			0
$307$		−	6885.55i		−	1.28006i	−0.768349	−	0.640031i	$-0.778922\pi$
$307$		−	6885.55i		−	1.28006i	0.768349	−	0.640031i	$-0.221078\pi$
$308$		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	−0.109862	−	0.993947i	$-0.535041\pi$
$313$	3854.07	−	2225.15i	0.695991	−	0.401831i	0.805852	+	0.592116i	$0.201707\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4139.57	−	2389.98i	0.733443	−	0.423453i	−0.0862375	−	0.996275i	$-0.527484\pi$
$317$	4139.57	−	2389.98i	0.733443	−	0.423453i	0.819680	+	0.572821i	$0.194151\pi$
$318$		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
$327$	−3772.91	+	2359.64i	−0.638050	+	0.399046i
$328$		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
$333$	−2699.37	+	5545.59i	−0.444219	+	0.912603i
$334$		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
$339$	−4649.90	+	8753.48i	−0.744979	+	1.40243i
$340$		0			0
$341$	−1811.92	−	3138.33i	−0.287744	−	0.498388i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−4539.31	−	7258.06i	−0.708371	−	1.13264i
$346$		0			0
$347$	9110.07	+	5259.70i	1.40938	+	0.813705i	0.995328	−	0.0965491i	$-0.0307805\pi$
$347$	9110.07	+	5259.70i	1.40938	+	0.813705i	0.414050	+	0.910254i	$0.364114\pi$
$348$		0			0
$349$			2261.34i			0.346839i	0.984848	+	0.173419i	$0.0554816\pi$
$349$			2261.34i			0.346839i	−0.984848	+	0.173419i	$0.944518\pi$
$350$		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	−0.253804	−	0.967256i	$-0.581682\pi$
$359$	3108.29	−	1794.57i	0.456962	−	0.263827i	0.710766	+	0.703429i	$0.248349\pi$
$360$		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	0.960438	−	0.278494i	$-0.0898351\pi$
$367$	8433.16	+	4868.88i	1.19947	+	0.692517i	0.239036	+	0.971011i	$0.423168\pi$
$368$		0			0
$369$	−560.264	−	829.220i	−0.0790412	−	0.116985i
$370$		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
$375$	−7748.60	−	4116.10i	−1.06703	−	0.566812i
$376$		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
$381$	5221.20	+	2773.53i	0.702074	+	0.372945i
$382$		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
$387$	6230.97	+	9222.16i	0.818445	+	1.21134i
$388$		0			0
$389$	−3643.44	−	2103.54i	−0.474884	−	0.274174i	0.243398	−	0.969926i	$-0.421738\pi$
$389$	−3643.44	−	2103.54i	−0.474884	−	0.274174i	−0.718282	+	0.695752i	$0.755071\pi$
$390$		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	−0.446557	−	0.894755i	$-0.647350\pi$
$397$	830.923	−	479.734i	0.105045	−	0.0606477i	0.551602	+	0.834107i	$0.314017\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12670.8	+	7315.49i	−1.57793	+	0.911018i	−0.582781	+	0.812630i	$0.698035\pi$
$401$	−12670.8	+	7315.49i	−1.57793	+	0.911018i	−0.995148	+	0.0983880i	$0.968631\pi$
$402$		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	−0.0118840	−	0.999929i	$-0.503783\pi$
$409$	−7310.28	−	4220.59i	−0.883790	−	0.510257i	−0.871906	+	0.489673i	$0.837116\pi$
$410$		0			0
$411$	−2283.24	−	3650.76i	−0.274024	−	0.438147i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	8008.02	+	13870.3i	0.947225	+	1.64064i
$416$		0			0
$417$	−7088.27	+	13343.7i	−0.832408	+	1.56702i
$418$		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
$423$	7162.09	−	14713.8i	0.823245	−	1.69127i
$424$		0			0
$425$	13583.0	+	23526.4i	1.55029	+	2.68517i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−7972.65	+	4986.22i	−0.897257	+	0.561158i
$430$		0			0
$431$	1806.39	+	1042.92i	0.201881	+	0.116556i	0.597532	−	0.801845i	$-0.296148\pi$
$431$	1806.39	+	1042.92i	0.201881	+	0.116556i	−0.395652	+	0.918401i	$0.629481\pi$
$432$		0			0
$433$			7904.10i			0.877244i	0.898672	+	0.438622i	$0.144533\pi$
$433$			7904.10i			0.877244i	−0.898672	+	0.438622i	$0.855467\pi$
$434$		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	−0.690862	−	0.722986i	$-0.742769\pi$
$439$	−3772.77	+	2178.21i	−0.410169	+	0.236811i	0.280693	+	0.959798i	$0.409436\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11892.9	−	6866.38i	1.27551	−	0.736415i	0.299488	−	0.954100i	$-0.403184\pi$
$443$	11892.9	−	6866.38i	1.27551	−	0.736415i	0.976019	+	0.217685i	$0.0698507\pi$
$444$		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	$0.192901\pi$
$449$			10838.5i			1.13920i	−0.821923	+	0.569598i	$0.807099\pi$
$450$		0			0
$451$	−1334.71	−	770.592i	−0.139354	−	0.0804563i
$452$		0			0
$453$	6100.22	−	3815.17i	0.632700	−	0.395701i
$454$		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
$459$	16098.8	+	7144.94i	1.63710	+	0.726574i
$460$		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
$465$	3925.27	−	7389.37i	0.391463	−	0.736933i
$466$		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
$471$	−5755.65	−	9202.91i	−0.563071	−	0.900314i
$472$		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	$0.402751\pi$
$491$			20752.0i			1.90738i	−0.300785	+	0.953692i	$0.597249\pi$
$492$		0			0
$493$	−14555.5	−	8403.59i	−1.32970	−	0.767706i
$494$		0			0
$495$	−17188.0	+	11613.1i	−1.56069	+	1.05448i
$496$		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
$501$	−7208.08	−	3828.97i	−0.642781	−	0.341449i
$502$		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
$507$	1389.46	+	738.089i	0.121712	+	0.0646542i
$508$		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
$513$	5649.76	+	7756.99i	0.486244	+	0.667601i
$514$		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	−0.757116	−	0.653281i	$-0.773392\pi$
$523$	−6816.53	+	3935.53i	−0.569916	+	0.329041i	0.187200	+	0.982322i	$0.440059\pi$
$524$		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
$537$	−7497.38	−	11987.8i	−0.602487	−	0.963339i
$538$		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
$543$	6488.79	−	12215.2i	0.512819	−	0.965387i
$544$		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
$549$	−18373.0	−	8943.23i	−1.42830	−	0.695242i
$550$		0			0
$551$	−4578.63	−	7930.43i	−0.354004	−	0.613153i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−18594.2	+	11629.1i	−1.42213	+	0.889421i
$556$		0			0
$557$	−114.281	−	65.9801i	−0.00869343	−	0.00501915i	0.495647	−	0.868524i	$-0.334931\pi$
$557$	−114.281	−	65.9801i	−0.00869343	−	0.00501915i	−0.504340	+	0.863505i	$0.668264\pi$
$558$		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	0.0739832	−	0.997259i	$-0.476429\pi$
$569$	13228.4	−	7637.41i	0.974627	−	0.562701i	0.900644	+	0.434558i	$0.143096\pi$
$570$		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	0.936477	−	0.350730i	$-0.114067\pi$
$577$	15259.5	+	8810.08i	1.10097	+	0.635647i	0.164497	+	0.986378i	$0.447400\pi$
$578$		0			0
$579$	1787.20	−	1117.74i	0.128279	−	0.0802276i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−10028.5	−	17369.9i	−0.712418	−	1.23394i
$584$		0			0
$585$	−19522.2	−	9502.63i	−1.37973	−	0.671599i
$586$		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
$591$	−4989.85	+	9393.45i	−0.347301	+	0.653799i
$592$		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
$597$	1742.77	+	2786.58i	0.119475	+	0.191034i
$598$		0			0
$599$	7883.37	+	4551.46i	0.537739	+	0.310464i	0.744162	−	0.667999i	$-0.232849\pi$
$599$	7883.37	+	4551.46i	0.537739	+	0.310464i	−0.206423	+	0.978463i	$0.566182\pi$
$600$		0			0
$601$			7463.40i			0.506553i	0.967394	+	0.253276i	$0.0815082\pi$
$601$			7463.40i			0.506553i	−0.967394	+	0.253276i	$0.918492\pi$
$602$		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	−0.646608	−	0.762823i	$-0.723813\pi$
$607$	−4625.36	+	2670.45i	−0.309287	+	0.178567i	0.337320	+	0.941390i	$0.390479\pi$
$608$		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	$-0.805412\pi$
$617$		−	17592.6i		−	1.14789i	0.818893	−	0.573946i	$-0.194588\pi$
$618$		0			0
$619$	−18463.5	−	10659.9i	−1.19889	−	0.692177i	−0.238579	−	0.971123i	$-0.576682\pi$
$619$	−18463.5	−	10659.9i	−1.19889	−	0.692177i	−0.960307	+	0.278946i	$0.910015\pi$
$620$		0			0
$621$	−7364.93	−	10111.9i	−0.475917	−	0.653423i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2075.20	−	3594.35i	−0.132813	−	0.230038i
$626$		0			0
$627$	13051.6	+	6933.06i	0.831306	+	0.441594i
$628$		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
$633$	−1024.11	−	544.013i	−0.0643045	−	0.0341589i
$634$		0			0
$635$	10511.3	+	18206.1i	0.656896	+	1.13778i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	10782.9	−	7285.53i	0.667554	−	0.451034i
$640$		0			0
$641$	11898.6	+	6869.67i	0.733178	+	0.423300i	0.819584	−	0.572960i	$-0.194205\pi$
$641$	11898.6	+	6869.67i	0.733178	+	0.423300i	−0.0864059	+	0.996260i	$0.527538\pi$
$642$		0			0
$643$			8719.09i			0.534755i	0.963592	+	0.267377i	$0.0861570\pi$
$643$			8719.09i			0.534755i	−0.963592	+	0.267377i	$0.913843\pi$
$644$		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	−0.881498	−	0.472188i	$-0.843464\pi$
$653$	−15240.3	+	8798.97i	−0.913319	+	0.527305i	−0.0318217	+	0.999494i	$0.510131\pi$
$654$		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	$-0.955485\pi$
$659$		−	4716.29i		−	0.278787i	0.990237	−	0.139393i	$-0.0445153\pi$
$660$		0			0
$661$	19548.4	+	11286.3i	1.15029	+	0.664121i	0.948958	−	0.315401i	$-0.102139\pi$
$661$	19548.4	+	11286.3i	1.15029	+	0.664121i	0.201334	+	0.979523i	$0.435472\pi$
$662$		0			0
$663$	15054.6	+	24071.4i	0.881860	+	1.41004i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5968.63	+	10338.0i	0.346486	+	0.600131i
$668$		0			0
$669$	1531.08	−	2882.28i	0.0884829	−	0.166570i
$670$		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
$675$	−27748.4	−	12315.2i	−1.58227	−	0.702240i
$676$		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
$681$	16030.3	−	10025.6i	0.902028	−	0.564142i
$682$		0			0
$683$	−21451.9	−	12385.3i	−1.20181	−	0.693864i	−0.240851	−	0.970562i	$-0.577426\pi$
$683$	−21451.9	−	12385.3i	−1.20181	−	0.693864i	−0.960957	+	0.276698i	$0.910760\pi$
$684$		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	−0.0918589	−	0.995772i	$-0.529281\pi$
$691$	13161.4	−	7598.71i	0.724575	−	0.418334i	0.816434	+	0.577438i	$0.195948\pi$
$692$		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	$0.169900\pi$
$701$			18885.5i			1.01754i	−0.860902	+	0.508770i	$0.830100\pi$
$702$		0			0
$703$	13531.6	+	7812.50i	0.725968	+	0.419138i
$704$		0			0
$705$	49334.9	−	30854.8i	2.63555	−	1.64831i
$706$		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
$711$	5366.10	−	11024.1i	0.283044	−	0.581486i
$712$		0			0
$713$	7770.99			0.408171
$714$		0			0
$715$	−33437.3			−1.74893
$716$		0			0
$717$	369.306	−	695.223i	0.0192357	−	0.0362114i
$718$		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
$723$	−13841.2	−	22131.2i	−0.711979	−	1.13841i
$724$		0			0
$725$	25088.1	+	14484.6i	1.28517	+	0.741995i
$726$		0			0
$727$		−	4460.45i		−	0.227550i	−0.993507	−	0.113775i	$-0.963706\pi$
$727$		−	4460.45i		−	0.227550i	0.993507	−	0.113775i	$-0.0362943\pi$
$728$		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	−0.474147	−	0.880446i	$-0.657243\pi$
$733$	1017.43	−	587.412i	0.0512682	−	0.0295997i	0.525415	+	0.850846i	$0.323910\pi$
$734$		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	$0.219576\pi$
$743$			25777.5i			1.27279i	−0.771361	+	0.636397i	$0.780424\pi$
$744$		0			0
$745$	37014.5	+	21370.3i	1.82028	+	1.05094i
$746$		0			0
$747$	13102.7	+	19392.7i	0.641772	+	0.949855i
$748$		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
$753$	22298.7	+	11845.2i	1.07916	+	0.573258i
$754$		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
$759$	−17013.8	−	9037.81i	−0.813651	−	0.432216i
$760$		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
$765$	35062.8	+	51894.7i	1.65712	+	2.45263i
$766$		0			0
$767$	−3287.06	−	1897.79i	−0.154744	−	0.0893417i
$768$		0			0
$769$		−	6275.09i		−	0.294259i	−0.989117	−	0.147130i	$-0.952997\pi$
$769$		−	6275.09i		−	0.294259i	0.989117	−	0.147130i	$-0.0470034\pi$
$770$		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	0.714695	−	0.699437i	$-0.246566\pi$
$787$	10295.3	+	5943.99i	0.466312	+	0.269225i	−0.248383	+	0.968662i	$0.579899\pi$
$788$		0			0
$789$	7115.34	+	11377.0i	0.321055	+	0.513347i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−16469.2	−	28525.5i	−0.737502	−	1.27739i
$794$		0			0
$795$	21725.5	−	40898.5i	0.969213	−	1.82455i
$796$		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
$801$	−7313.61	+	15025.1i	−0.322614	+	0.662778i
$802$		0			0
$803$	−11922.9	−	20651.1i	−0.523974	−	0.907549i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	35642.7	−	22291.5i	1.55475	−	0.972365i
$808$		0			0
$809$	−12835.1	−	7410.33i	−0.557796	−	0.322044i	0.194465	−	0.980910i	$-0.437703\pi$
$809$	−12835.1	−	7410.33i	−0.557796	−	0.322044i	−0.752260	+	0.658866i	$0.771036\pi$
$810$		0			0
$811$			510.470i			0.0221024i	0.999939	+	0.0110512i	$0.00351778\pi$
$811$			510.470i			0.0221024i	−0.999939	+	0.0110512i	$0.996482\pi$
$812$		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	−0.807929	−	0.589280i	$-0.799412\pi$
$821$	−16503.7	+	9528.41i	−0.701563	+	0.405047i	0.106366	+	0.994327i	$0.466078\pi$
$822$		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	$0.0532135\pi$
$827$			7914.71i			0.332795i	−0.986059	+	0.166397i	$0.946787\pi$
$828$		0			0
$829$	−1403.46	−	810.285i	−0.0587986	−	0.0339474i	0.470313	−	0.882500i	$-0.344141\pi$
$829$	−1403.46	−	810.285i	−0.0587986	−	0.0339474i	−0.529111	+	0.848553i	$0.677475\pi$
$830$		0			0
$831$	20212.1	−	12641.0i	0.843743	−	0.527690i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−14511.3	−	25134.3i	−0.601418	−	1.04169i
$836$		0			0
$837$	4960.01	−	11175.8i	0.204831	−	0.461520i
$838$		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
$843$	−2829.04	+	5325.71i	−0.115584	+	0.217588i
$844$		0			0
$845$	2797.26	+	4845.00i	0.113880	+	0.197246i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4479.60	−	7162.59i	−0.181083	−	0.289540i
$850$		0			0
$851$	−17639.6	−	10184.2i	−0.710550	−	0.410236i
$852$		0			0
$853$			3374.92i			0.135469i	0.997703	+	0.0677345i	$0.0215771\pi$
$853$			3374.92i			0.135469i	−0.997703	+	0.0677345i	$0.978423\pi$
$854$		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	−0.253187	−	0.967417i	$-0.581479\pi$
$859$	11531.4	−	6657.65i	0.458028	−	0.264443i	0.711215	+	0.702975i	$0.248145\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8083.25	−	4666.86i	0.318838	−	0.184081i	−0.332037	−	0.943266i	$-0.607736\pi$
$863$	8083.25	−	4666.86i	0.318838	−	0.184081i	0.650874	+	0.759185i	$0.274402\pi$
$864$		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
$873$	13278.3	−	8971.48i	0.514777	−	0.347811i
$874$		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
$879$	−35857.8	−	19047.8i	−1.37594	−	0.730908i
$880$		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
$885$	−7394.26	−	3927.87i	−0.280853	−	0.149191i
$886$		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
$891$	−23857.1	+	18699.7i	−0.897019	+	0.703101i
$892$		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	$-0.845777\pi$
$911$		−	25614.1i		−	0.931542i	0.884905	−	0.465771i	$-0.154223\pi$
$912$		0			0
$913$	31214.3	+	18021.6i	1.13148	+	0.653262i
$914$		0			0
$915$	−38528.1	−	61604.0i	−1.39202	−	2.22576i
$916$		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
$921$	16784.5	−	31597.0i	0.600508	−	1.13046i
$922$		0			0
$923$	20977.0			0.748069
$924$		0			0
$925$	−49430.1			−1.75703
$926$		0			0
$927$	−35601.2	−	17329.2i	−1.26138	−	0.613988i
$928$		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
$933$	−22337.9	+	13970.5i	−0.783827	+	0.490218i
$934$		0			0
$935$	83529.3	+	48225.7i	2.92161	+	1.68679i
$936$		0			0
$937$		−	56712.6i		−	1.97729i	−0.150272	−	0.988645i	$-0.548015\pi$
$937$		−	56712.6i		−	1.97729i	0.150272	−	0.988645i	$-0.451985\pi$
$938$		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	−0.201632	−	0.979461i	$-0.564625\pi$
$947$	15905.6	−	9183.11i	0.545790	−	0.315112i	0.747422	+	0.664349i	$0.231291\pi$
$948$		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	$0.0180074\pi$
$953$			3326.89i			0.113083i	−0.998400	+	0.0565417i	$0.981993\pi$
$954$		0			0
$955$	23313.4	+	13460.0i	0.789952	+	0.456079i
$956$		0			0
$957$	24524.0	−	15337.7i	0.828369	−	0.518075i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−11097.8	−	19221.9i	−0.372522	−	0.645227i
$962$		0			0
$963$	19904.7	+	9688.79i	0.666063	+	0.324213i
$964$		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
$969$	20932.6	−	39405.9i	0.693966	−	1.30640i
$970$		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
$975$	−25948.5	−	41490.1i	−0.852326	−	1.36282i
$976$		0			0
$977$	−22737.3	−	13127.4i	−0.744554	−	0.429869i	0.0791685	−	0.996861i	$-0.474773\pi$
$977$	−22737.3	−	13127.4i	−0.744554	−	0.429869i	−0.823723	+	0.566993i	$0.808107\pi$
$978$		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	0.169282	−	0.985568i	$-0.445855\pi$
$997$	−18875.9	−	10898.0i	−0.599604	−	0.346181i	−0.768886	+	0.639386i	$0.779188\pi$
$998$		0			0
$999$	−25905.3	+	18868.0i	−0.820428	+	0.597555i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(4.58889 + 2.43764i) q^{3} +(9.23835 + 16.0013i) q^{5} +(15.1158 + 22.3721i) q^{9} +O(q^{10})\)	\(q+(4.58889 + 2.43764i) q^{3} +(9.23835 + 16.0013i) q^{5} +(15.1158 + 22.3721i) q^{9} +(36.0100 + 20.7904i) q^{11} +43.5225i q^{13} +(3.38832 + 95.9479i) q^{15} +(62.7713 - 108.723i) q^{17} +(59.2370 - 34.2005i) q^{19} +(-77.2203 + 44.5831i) q^{23} +(-108.194 + 187.398i) q^{25} +(14.8294 + 139.510i) q^{27} -133.876i q^{29} +(-75.4755 - 43.5758i) q^{31} +(114.566 + 183.184i) q^{33} +(114.216 + 197.828i) q^{37} +(-106.092 + 199.720i) q^{39} -37.0648 q^{41} +412.216 q^{43} +(-218.338 + 448.554i) q^{45} +(-303.043 - 524.886i) q^{47} +(553.079 - 345.904i) q^{51} +(-417.740 - 241.182i) q^{53} +768.275i q^{55} +(355.200 - 12.5436i) q^{57} +(-43.6046 + 75.5255i) q^{59} +(-655.420 + 378.407i) q^{61} +(-696.417 + 402.077i) q^{65} +(17.3248 - 30.0075i) q^{67} +(-463.033 + 16.3516i) q^{69} -481.981i q^{71} +(-496.651 - 286.741i) q^{73} +(-953.300 + 596.209i) q^{75} +(-227.051 - 393.264i) q^{79} +(-272.026 + 676.345i) q^{81} +866.824 q^{83} +2319.61 q^{85} +(326.343 - 614.343i) q^{87} +(309.454 + 535.991i) q^{89} +(-240.126 - 383.947i) q^{93} +(1094.50 + 631.912i) q^{95} -593.517i q^{97} +(79.1943 + 1119.88i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 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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