LMFDB - Embedded newform 588.4.k.e.521.12

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			521.12
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68893 + 4.91401i) q^{3} +(6.50213 + 11.2620i) q^{5} +(-21.2951 - 16.5988i) q^{9} +O(q^{10})$	\(q+(-1.68893 + 4.91401i) q^{3} +(6.50213 + 11.2620i) q^{5} +(-21.2951 - 16.5988i) q^{9} +(4.49726 + 2.59650i) q^{11} -72.6603i q^{13} +(-66.3233 + 12.9308i) q^{15} +(44.7733 - 77.5496i) q^{17} +(113.080 - 65.2865i) q^{19} +(108.141 - 62.4354i) q^{23} +(-22.0553 + 38.2010i) q^{25} +(117.533 - 76.6101i) q^{27} -63.1418i q^{29} +(-91.6564 - 52.9179i) q^{31} +(-20.3548 + 17.7143i) q^{33} +(46.9184 + 81.2651i) q^{37} +(357.054 + 122.718i) q^{39} -320.640 q^{41} -351.830 q^{43} +(48.4728 - 347.753i) q^{45} +(102.656 + 177.805i) q^{47} +(305.461 + 350.992i) q^{51} +(68.9957 + 39.8347i) q^{53} +67.5310i q^{55} +(129.836 + 665.938i) q^{57} +(449.621 - 778.767i) q^{59} +(-489.428 + 282.571i) q^{61} +(818.302 - 472.447i) q^{65} +(41.1414 - 71.2591i) q^{67} +(124.166 + 636.856i) q^{69} +457.950i q^{71} +(769.098 + 444.039i) q^{73} +(-150.470 - 172.899i) q^{75} +(-247.926 - 429.421i) q^{79} +(177.959 + 706.945i) q^{81} -1022.84 q^{83} +1164.49 q^{85} +(310.280 + 106.642i) q^{87} +(65.5170 + 113.479i) q^{89} +(414.840 - 361.027i) q^{93} +(1470.51 + 849.002i) q^{95} -897.230i q^{97} +(-52.6707 - 129.942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.68893	+	4.91401i	−0.325034	+	0.945702i
$3$	−1.68893	+	4.91401i	−0.325034	+	0.945702i
$4$		0			0
$5$	6.50213	+	11.2620i	0.581568	+	1.00731i	0.995294	+	0.0969038i	$0.0308939\pi$
$5$	6.50213	+	11.2620i	0.581568	+	1.00731i	−0.413726	+	0.910402i	$0.635773\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−21.2951	−	16.5988i	−0.788706	−	0.614771i
$10$		0			0
$11$	4.49726	+	2.59650i	0.123271	+	0.0711703i	0.560367	−	0.828244i	$-0.310660\pi$
$11$	4.49726	+	2.59650i	0.123271	+	0.0711703i	−0.437097	+	0.899414i	$0.643993\pi$
$12$		0			0
$13$		−	72.6603i		−	1.55018i	−0.631850	−	0.775090i	$-0.717704\pi$
$13$		−	72.6603i		−	1.55018i	0.631850	−	0.775090i	$-0.282296\pi$
$14$		0			0
$15$	−66.3233	+	12.9308i	−1.14164	+	0.222582i
$16$		0			0
$17$	44.7733	−	77.5496i	0.638772	−	1.10639i	−0.346931	−	0.937891i	$-0.612776\pi$
$17$	44.7733	−	77.5496i	0.638772	−	1.10639i	0.985703	−	0.168495i	$-0.0538906\pi$
$18$		0			0
$19$	113.080	−	65.2865i	1.36538	−	0.788302i	0.375046	−	0.927006i	$-0.377627\pi$
$19$	113.080	−	65.2865i	1.36538	−	0.788302i	0.990334	+	0.138704i	$0.0442936\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	108.141	−	62.4354i	0.980392	−	0.566029i	0.0780033	−	0.996953i	$-0.475146\pi$
$23$	108.141	−	62.4354i	0.980392	−	0.566029i	0.902388	+	0.430924i	$0.141812\pi$
$24$		0			0
$25$	−22.0553	+	38.2010i	−0.176443	+	0.305608i
$26$		0			0
$27$	117.533	−	76.6101i	0.837746	−	0.546060i
$28$		0			0
$29$		−	63.1418i		−	0.404315i	−0.979353	−	0.202158i	$-0.935205\pi$
$29$		−	63.1418i		−	0.404315i	0.979353	−	0.202158i	$-0.0647953\pi$
$30$		0			0
$31$	−91.6564	−	52.9179i	−0.531032	−	0.306591i	0.210405	−	0.977614i	$-0.432522\pi$
$31$	−91.6564	−	52.9179i	−0.531032	−	0.306591i	−0.741436	+	0.671023i	$0.765855\pi$
$32$		0			0
$33$	−20.3548	+	17.7143i	−0.107373	+	0.0934445i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	46.9184	+	81.2651i	0.208469	+	0.361078i	0.951232	−	0.308475i	$-0.0998187\pi$
$37$	46.9184	+	81.2651i	0.208469	+	0.361078i	−0.742764	+	0.669554i	$0.766485\pi$
$38$		0			0
$39$	357.054	+	122.718i	1.46601	+	0.503861i
$40$		0			0
$41$	−320.640			−1.22136			−0.610678	−	0.791879i	$-0.709103\pi$
$41$	−320.640			−1.22136			−0.610678	+	0.791879i	$0.709103\pi$
$42$		0			0
$43$	−351.830			−1.24776			−0.623878	−	0.781522i	$-0.714444\pi$
$43$	−351.830			−1.24776			−0.623878	+	0.781522i	$0.714444\pi$
$44$		0			0
$45$	48.4728	−	347.753i	0.160576	−	1.15200i
$46$		0			0
$47$	102.656	+	177.805i	0.318593	+	0.551820i	0.980195	−	0.198036i	$-0.0634563\pi$
$47$	102.656	+	177.805i	0.318593	+	0.551820i	−0.661602	+	0.749856i	$0.730123\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	305.461	+	350.992i	0.838689	+	0.963701i
$52$		0			0
$53$	68.9957	+	39.8347i	0.178817	+	0.103240i	0.586737	−	0.809778i	$-0.300412\pi$
$53$	68.9957	+	39.8347i	0.178817	+	0.103240i	−0.407920	+	0.913018i	$0.633746\pi$
$54$		0			0
$55$			67.5310i			0.165561i
$56$		0			0
$57$	129.836	+	665.938i	0.301705	+	1.54747i
$58$		0			0
$59$	449.621	−	778.767i	0.992130	−	1.71842i	0.387629	−	0.921815i	$-0.373294\pi$
$59$	449.621	−	778.767i	0.992130	−	1.71842i	0.604501	−	0.796604i	$-0.293373\pi$
$60$		0			0
$61$	−489.428	+	282.571i	−1.02729	+	0.593107i	−0.916208	−	0.400703i	$-0.868766\pi$
$61$	−489.428	+	282.571i	−1.02729	+	0.593107i	−0.111084	+	0.993811i	$0.535432\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	818.302	−	472.447i	1.56151	−	0.901536i
$66$		0			0
$67$	41.1414	−	71.2591i	0.0750183	−	0.129936i	−0.826076	−	0.563559i	$-0.809432\pi$
$67$	41.1414	−	71.2591i	0.0750183	−	0.129936i	0.901094	+	0.433623i	$0.142765\pi$
$68$		0			0
$69$	124.166	+	636.856i	0.216635	+	1.11114i
$70$		0			0
$71$			457.950i			0.765474i	0.923857	+	0.382737i	$0.125018\pi$
$71$			457.950i			0.765474i	−0.923857	+	0.382737i	$0.874982\pi$
$72$		0			0
$73$	769.098	+	444.039i	1.23310	+	0.711929i	0.967674	−	0.252203i	$-0.0811551\pi$
$73$	769.098	+	444.039i	1.23310	+	0.711929i	0.265423	+	0.964132i	$0.414488\pi$
$74$		0			0
$75$	−150.470	−	172.899i	−0.231664	−	0.266195i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−247.926	−	429.421i	−0.353087	−	0.611565i	0.633701	−	0.773578i	$-0.281535\pi$
$79$	−247.926	−	429.421i	−0.353087	−	0.611565i	−0.986789	+	0.162013i	$0.948201\pi$
$80$		0			0
$81$	177.959	+	706.945i	0.244114	+	0.969747i
$82$		0			0
$83$	−1022.84			−1.35267			−0.676336	−	0.736594i	$-0.736433\pi$
$83$	−1022.84			−1.35267			−0.676336	+	0.736594i	$0.736433\pi$
$84$		0			0
$85$	1164.49			1.48596
$86$		0			0
$87$	310.280	+	106.642i	0.382362	+	0.131416i
$88$		0			0
$89$	65.5170	+	113.479i	0.0780313	+	0.135154i	0.902400	−	0.430898i	$-0.141803\pi$
$89$	65.5170	+	113.479i	0.0780313	+	0.135154i	−0.824369	+	0.566053i	$0.808470\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	414.840	−	361.027i	0.462547	−	0.402545i
$94$		0			0
$95$	1470.51	+	849.002i	1.58812	+	0.916903i
$96$		0			0
$97$		−	897.230i		−	0.939174i	−0.882886	−	0.469587i	$-0.844403\pi$
$97$		−	897.230i		−	0.939174i	0.882886	−	0.469587i	$-0.155597\pi$
$98$		0			0
$99$	−52.6707	−	129.942i	−0.0534708	−	0.131915i
$100$		0			0
$101$	574.855	−	995.677i	0.566338	−	0.980927i	−0.430585	−	0.902550i	$-0.641693\pi$
$101$	574.855	−	995.677i	0.566338	−	0.980927i	0.996924	−	0.0783770i	$-0.0249738\pi$
$102$		0			0
$103$	1425.92	−	823.254i	1.36408	−	0.787550i	0.373913	−	0.927464i	$-0.378016\pi$
$103$	1425.92	−	823.254i	1.36408	−	0.787550i	0.990164	+	0.139914i	$0.0446825\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1701.12	−	982.145i	1.53695	−	0.887360i	0.537938	−	0.842985i	$-0.319204\pi$
$107$	1701.12	−	982.145i	1.53695	−	0.887360i	0.999015	−	0.0443752i	$-0.0141297\pi$
$108$		0			0
$109$	−786.758	+	1362.70i	−0.691355	+	1.19746i	0.280039	+	0.959989i	$0.409653\pi$
$109$	−786.758	+	1362.70i	−0.691355	+	1.19746i	−0.971394	+	0.237474i	$0.923681\pi$
$110$		0			0
$111$	−478.580	+	93.3071i	−0.409232	+	0.0797866i
$112$		0			0
$113$			2002.30i			1.66691i	0.552590	+	0.833454i	$0.313640\pi$
$113$			2002.30i			1.66691i	−0.552590	+	0.833454i	$0.686360\pi$
$114$		0			0
$115$	1406.30	+	811.926i	1.14033	+	0.658369i
$116$		0			0
$117$	−1206.08	+	1547.31i	−0.953006	+	1.22264i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−652.016	−	1129.33i	−0.489870	−	0.848479i
$122$		0			0
$123$	541.537	−	1575.63i	0.396982	−	1.15504i
$124$		0			0
$125$	1051.91			0.752682
$126$		0			0
$127$	−166.537			−0.116361			−0.0581803	−	0.998306i	$-0.518530\pi$
$127$	−166.537			−0.116361			−0.0581803	+	0.998306i	$0.518530\pi$
$128$		0			0
$129$	594.214	−	1728.90i	0.405563	−	1.18001i
$130$		0			0
$131$	−157.967	−	273.606i	−0.105356	−	0.182482i	0.808528	−	0.588458i	$-0.200265\pi$
$131$	−157.967	−	273.606i	−0.105356	−	0.182482i	−0.913884	+	0.405976i	$0.866931\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1627.00	+	825.525i	1.03726	+	0.526295i
$136$		0			0
$137$	−345.158	−	199.277i	−0.215247	−	0.124273i	0.388501	−	0.921448i	$-0.372993\pi$
$137$	−345.158	−	199.277i	−0.215247	−	0.124273i	−0.603747	+	0.797176i	$0.706326\pi$
$138$		0			0
$139$		−	228.245i		−	0.139277i	−0.997572	−	0.0696384i	$-0.977815\pi$
$139$		−	228.245i		−	0.139277i	0.997572	−	0.0696384i	$-0.0221845\pi$
$140$		0			0
$141$	−1047.11	+	204.152i	−0.625411	+	0.121934i
$142$		0			0
$143$	188.662	−	326.773i	0.110327	−	0.191092i
$144$		0			0
$145$	711.104	−	410.556i	0.407269	−	0.235137i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3066.97	+	1770.71i	−1.68628	+	0.973574i	−0.728954	+	0.684563i	$0.759993\pi$
$149$	−3066.97	+	1770.71i	−1.68628	+	0.973574i	−0.957326	+	0.289011i	$0.906674\pi$
$150$		0			0
$151$	105.383	−	182.529i	0.0567945	−	0.0983710i	−0.836230	−	0.548378i	$-0.815245\pi$
$151$	105.383	−	182.529i	0.0567945	−	0.0983710i	0.893025	+	0.450007i	$0.148579\pi$
$152$		0			0
$153$	−2240.68	+	908.241i	−1.18398	+	0.479914i
$154$		0			0
$155$		−	1376.31i		−	0.713215i
$156$		0			0
$157$	−2462.26	−	1421.59i	−1.25166	−	0.722644i	−0.280218	−	0.959936i	$-0.590407\pi$
$157$	−2462.26	−	1421.59i	−1.25166	−	0.722644i	−0.971438	+	0.237292i	$0.923740\pi$
$158$		0			0
$159$	−312.277	+	271.768i	−0.155756	+	0.135551i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	228.833	+	396.350i	0.109961	+	0.190457i	0.915754	−	0.401739i	$-0.131594\pi$
$163$	228.833	+	396.350i	0.109961	+	0.190457i	−0.805794	+	0.592197i	$0.798261\pi$
$164$		0			0
$165$	−331.848	−	114.055i	−0.156572	−	0.0538131i
$166$		0			0
$167$	2108.64			0.977076			0.488538	−	0.872543i	$-0.337530\pi$
$167$	2108.64			0.977076			0.488538	+	0.872543i	$0.337530\pi$
$168$		0			0
$169$	−3082.52			−1.40306
$170$		0			0
$171$	−3491.71	−	486.705i	−1.56151	−	0.217657i
$172$		0			0
$173$	439.144	+	760.620i	0.192991	+	0.334271i	0.946240	−	0.323465i	$-0.104848\pi$
$173$	439.144	+	760.620i	0.192991	+	0.334271i	−0.753249	+	0.657736i	$0.771514\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3067.49	+	3524.72i	1.30264	+	1.49680i
$178$		0			0
$179$	2742.00	+	1583.09i	1.14495	+	0.661039i	0.947652	−	0.319304i	$-0.103449\pi$
$179$	2742.00	+	1583.09i	1.14495	+	0.661039i	0.197301	+	0.980343i	$0.436782\pi$
$180$		0			0
$181$		−	4000.19i		−	1.64272i	−0.570413	−	0.821358i	$-0.693217\pi$
$181$		−	4000.19i		−	1.64272i	0.570413	−	0.821358i	$-0.306783\pi$
$182$		0			0
$183$	−561.952	−	2882.30i	−0.226998	−	1.16429i
$184$		0			0
$185$	−610.139	+	1056.79i	−0.242478	+	0.419983i
$186$		0			0
$187$	402.715	−	232.507i	0.157483	−	0.0909231i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	861.175	−	497.200i	0.326243	−	0.188357i	−0.327929	−	0.944702i	$-0.606351\pi$
$191$	861.175	−	497.200i	0.326243	−	0.188357i	0.654172	+	0.756346i	$0.273017\pi$
$192$		0			0
$193$	1030.58	−	1785.02i	0.384367	−	0.665743i	−0.607314	−	0.794462i	$-0.707753\pi$
$193$	1030.58	−	1785.02i	0.384367	−	0.665743i	0.991681	+	0.128719i	$0.0410864\pi$
$194$		0			0
$195$	939.559	+	4819.07i	0.345042	+	1.76975i
$196$		0			0
$197$		−	399.812i		−	0.144596i	−0.997383	−	0.0722980i	$-0.976967\pi$
$197$		−	399.812i		−	0.144596i	0.997383	−	0.0722980i	$-0.0230333\pi$
$198$		0			0
$199$	2516.96	+	1453.17i	0.896597	+	0.517650i	0.876095	−	0.482139i	$-0.160140\pi$
$199$	2516.96	+	1453.17i	0.896597	+	0.517650i	0.0205024	+	0.999790i	$0.493473\pi$
$200$		0			0
$201$	280.683	+	322.521i	0.0984968	+	0.113178i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2084.84	−	3611.06i	−0.710301	−	1.23028i
$206$		0			0
$207$	−3339.23	−	465.451i	−1.12122	−	0.156285i
$208$		0			0
$209$	678.064			0.224415
$210$		0			0
$211$	2947.20			0.961582			0.480791	−	0.876835i	$-0.340350\pi$
$211$	2947.20			0.961582			0.480791	+	0.876835i	$0.340350\pi$
$212$		0			0
$213$	−2250.37	−	773.443i	−0.723910	−	0.248805i
$214$		0			0
$215$	−2287.64	−	3962.31i	−0.725655	−	1.25687i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3480.96	+	3029.41i	−1.07407	+	0.934742i
$220$		0			0
$221$	−5634.78	−	3253.24i	−1.71510	−	0.990212i
$222$		0			0
$223$		−	3481.59i		−	1.04549i	−0.852489	−	0.522745i	$-0.824908\pi$
$223$		−	3481.59i		−	1.04549i	0.852489	−	0.522745i	$-0.175092\pi$
$224$		0			0
$225$	1103.76	−	447.400i	0.327040	−	0.132563i
$226$		0			0
$227$	−1937.00	+	3354.98i	−0.566357	+	0.980959i	0.430565	+	0.902560i	$0.358314\pi$
$227$	−1937.00	+	3354.98i	−0.566357	+	0.980959i	−0.996922	+	0.0783996i	$0.975019\pi$
$228$		0			0
$229$	3472.34	−	2004.76i	1.00200	−	0.578507i	0.0931632	−	0.995651i	$-0.470302\pi$
$229$	3472.34	−	2004.76i	1.00200	−	0.578507i	0.908841	+	0.417144i	$0.136969\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4398.07	+	2539.23i	−1.23660	+	0.713949i	−0.968397	−	0.249414i	$-0.919762\pi$
$233$	−4398.07	+	2539.23i	−1.23660	+	0.713949i	−0.268200	+	0.963363i	$0.586429\pi$
$234$		0			0
$235$	−1334.96	+	2312.22i	−0.370567	+	0.641841i
$236$		0			0
$237$	2528.91	−	493.053i	0.693124	−	0.135136i
$238$		0			0
$239$		−	1081.25i		−	0.292636i	−0.989238	−	0.146318i	$-0.953258\pi$
$239$		−	1081.25i		−	0.292636i	0.989238	−	0.146318i	$-0.0467423\pi$
$240$		0			0
$241$	2854.95	+	1648.31i	0.763086	+	0.440568i	0.830403	−	0.557164i	$-0.188110\pi$
$241$	2854.95	+	1648.31i	0.763086	+	0.440568i	−0.0673168	+	0.997732i	$0.521444\pi$
$242$		0			0
$243$	−3774.50	−	319.484i	−0.996437	−	0.0843413i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4743.74	−	8216.40i	−1.22201	−	2.11659i
$248$		0			0
$249$	1727.51	−	5026.27i	0.439664	−	1.27922i
$250$		0			0
$251$	−690.705			−0.173693			−0.0868464	−	0.996222i	$-0.527679\pi$
$251$	−690.705			−0.173693			−0.0868464	+	0.996222i	$0.527679\pi$
$252$		0			0
$253$	648.453			0.161138
$254$		0			0
$255$	−1966.73	+	5722.31i	−0.482986	+	1.40527i
$256$		0			0
$257$	3948.33	+	6838.71i	0.958327	+	1.65987i	0.726563	+	0.687100i	$0.241117\pi$
$257$	3948.33	+	6838.71i	0.958327	+	1.65987i	0.231764	+	0.972772i	$0.425550\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1048.08	+	1344.61i	−0.248561	+	0.318886i
$262$		0			0
$263$	−2595.62	−	1498.58i	−0.608567	−	0.351356i	0.163838	−	0.986487i	$-0.447613\pi$
$263$	−2595.62	−	1498.58i	−0.608567	−	0.351356i	−0.772404	+	0.635131i	$0.780946\pi$
$264$		0			0
$265$			1036.04i			0.240164i
$266$		0			0
$267$	−668.289	+	130.294i	−0.153178	+	0.0298647i
$268$		0			0
$269$	−4041.71	+	7000.45i	−0.916087	+	1.58671i	−0.110785	+	0.993844i	$0.535337\pi$
$269$	−4041.71	+	7000.45i	−0.916087	+	1.58671i	−0.805302	+	0.592865i	$0.797997\pi$
$270$		0			0
$271$	2865.50	−	1654.40i	0.642313	−	0.370840i	−0.143192	−	0.989695i	$-0.545737\pi$
$271$	2865.50	−	1654.40i	0.642313	−	0.370840i	0.785505	+	0.618855i	$0.212403\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−198.377	+	114.533i	−0.0435004	+	0.0251150i
$276$		0			0
$277$	−2497.77	+	4326.26i	−0.541792	+	0.938411i	0.457009	+	0.889462i	$0.348921\pi$
$277$	−2497.77	+	4326.26i	−0.541792	+	0.938411i	−0.998801	+	0.0489494i	$0.984413\pi$
$278$		0			0
$279$	1073.46	+	2648.28i	0.230344	+	0.568273i
$280$		0			0
$281$		−	4123.67i		−	0.875436i	−0.899112	−	0.437718i	$-0.855787\pi$
$281$		−	4123.67i		−	0.875436i	0.899112	−	0.437718i	$-0.144213\pi$
$282$		0			0
$283$	1586.09	+	915.727i	0.333155	+	0.192347i	0.657241	−	0.753680i	$-0.271723\pi$
$283$	1586.09	+	915.727i	0.333155	+	0.192347i	−0.324086	+	0.946028i	$0.605057\pi$
$284$		0			0
$285$	−6655.60	+	5792.23i	−1.38331	+	1.20387i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1552.80	−	2689.52i	−0.316059	−	0.547430i
$290$		0			0
$291$	4409.00	+	1515.35i	0.888179	+	0.305263i
$292$		0			0
$293$	−2676.36			−0.533634			−0.266817	−	0.963747i	$-0.585972\pi$
$293$	−2676.36			−0.533634			−0.266817	+	0.963747i	$0.585972\pi$
$294$		0			0
$295$	11694.0			2.30796
$296$		0			0
$297$	727.492	−	39.3628i	0.142133	−	0.00769044i
$298$		0			0
$299$	−4536.58	−	7857.58i	−0.877448	−	1.51978i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	3921.89	+	4506.47i	0.743586	+	0.854422i
$304$		0			0
$305$	−6364.65	−	3674.63i	−1.19488	−	0.689865i
$306$		0			0
$307$			384.925i			0.0715597i	0.999360	+	0.0357798i	$0.0113915\pi$
$307$			384.925i			0.0715597i	−0.999360	+	0.0357798i	$0.988608\pi$
$308$		0			0
$309$	1637.21	+	8397.40i	0.301417	+	1.54599i
$310$		0			0
$311$	−1220.95	+	2114.75i	−0.222617	+	0.385584i	−0.955602	−	0.294661i	$-0.904793\pi$
$311$	−1220.95	+	2114.75i	−0.222617	+	0.385584i	0.732985	+	0.680245i	$0.238127\pi$
$312$		0			0
$313$	3573.75	−	2063.30i	0.645368	−	0.372603i	−0.141312	−	0.989965i	$-0.545132\pi$
$313$	3573.75	−	2063.30i	0.645368	−	0.372603i	0.786679	+	0.617362i	$0.211799\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5833.28	+	3367.85i	−1.03353	+	0.596710i	−0.917995	−	0.396593i	$-0.870192\pi$
$317$	−5833.28	+	3367.85i	−1.03353	+	0.596710i	−0.115538	+	0.993303i	$0.536859\pi$
$318$		0			0
$319$	163.947	−	283.965i	0.0287752	−	0.0498401i
$320$		0			0
$321$	1953.20	+	10018.1i	0.339617	+	1.74192i
$322$		0			0
$323$		−	11692.4i		−	2.01418i
$324$		0			0
$325$	2775.70	+	1602.55i	0.473747	+	0.273518i
$326$		0			0
$327$	−5367.57	−	6167.64i	−0.907729	−	1.04303i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2059.35	+	3566.90i	0.341970	+	0.592310i	0.984799	−	0.173700i	$-0.0555724\pi$
$331$	2059.35	+	3566.90i	0.341970	+	0.592310i	−0.642828	+	0.766010i	$0.722239\pi$
$332$		0			0
$333$	349.773	−	2509.34i	0.0575599	−	0.412945i
$334$		0			0
$335$	1070.03			0.174513
$336$		0			0
$337$	−4453.87			−0.719934			−0.359967	−	0.932965i	$-0.617212\pi$
$337$	−4453.87			−0.719934			−0.359967	+	0.932965i	$0.617212\pi$
$338$		0			0
$339$	−9839.33	−	3381.74i	−1.57640	−	0.541801i
$340$		0			0
$341$	−274.802	−	475.971i	−0.0436404	−	0.0755873i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−6364.94	+	5539.28i	−0.993267	+	0.864419i
$346$		0			0
$347$	−4468.22	−	2579.73i	−0.691258	−	0.399098i	0.112825	−	0.993615i	$-0.464010\pi$
$347$	−4468.22	−	2579.73i	−0.691258	−	0.399098i	−0.804083	+	0.594517i	$0.797343\pi$
$348$		0			0
$349$		−	2662.35i		−	0.408345i	−0.978935	−	0.204173i	$-0.934550\pi$
$349$		−	2662.35i		−	0.408345i	0.978935	−	0.204173i	$-0.0654504\pi$
$350$		0			0
$351$	−5566.51	−	8539.95i	−0.846491	−	1.29866i
$352$		0			0
$353$	294.789	−	510.590i	0.0444477	−	0.0769857i	−0.842946	−	0.537999i	$-0.819181\pi$
$353$	294.789	−	510.590i	0.0444477	−	0.0769857i	0.887393	+	0.461013i	$0.152514\pi$
$354$		0			0
$355$	−5157.44	+	2977.65i	−0.771066	+	0.445175i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7391.47	−	4267.47i	1.08665	−	0.627377i	0.153967	−	0.988076i	$-0.450795\pi$
$359$	7391.47	−	4267.47i	1.08665	−	0.627377i	0.932682	+	0.360699i	$0.117462\pi$
$360$		0			0
$361$	5095.15	−	8825.06i	0.742841	−	1.28664i
$362$		0			0
$363$	6650.73	−	1296.67i	0.961633	−	0.187486i
$364$		0			0
$365$			11548.8i			1.65614i
$366$		0			0
$367$	−6753.50	−	3899.13i	−0.960571	−	0.554586i	−0.0642224	−	0.997936i	$-0.520457\pi$
$367$	−6753.50	−	3899.13i	−0.960571	−	0.554586i	−0.896349	+	0.443350i	$0.853790\pi$
$368$		0			0
$369$	6828.05	+	5322.24i	0.963290	+	0.750854i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−602.802	−	1044.08i	−0.0836780	−	0.144934i	0.821149	−	0.570714i	$-0.193333\pi$
$373$	−602.802	−	1044.08i	−0.0836780	−	0.144934i	−0.904827	+	0.425779i	$0.860000\pi$
$374$		0			0
$375$	−1776.59	+	5169.08i	−0.244647	+	0.711813i
$376$		0			0
$377$	−4587.90			−0.626762
$378$		0			0
$379$	−8527.67			−1.15577			−0.577885	−	0.816118i	$-0.696122\pi$
$379$	−8527.67			−1.15577			−0.577885	+	0.816118i	$0.696122\pi$
$380$		0			0
$381$	281.269	−	818.366i	0.0378211	−	0.110042i
$382$		0			0
$383$	4723.71	+	8181.71i	0.630210	+	1.09156i	0.987509	+	0.157566i	$0.0503645\pi$
$383$	4723.71	+	8181.71i	0.630210	+	1.09156i	−0.357299	+	0.933990i	$0.616302\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7492.23	+	5839.95i	0.984113	+	0.767084i
$388$		0			0
$389$	8117.13	+	4686.42i	1.05798	+	0.610826i	0.924873	−	0.380276i	$-0.124171\pi$
$389$	8117.13	+	4686.42i	1.05798	+	0.610826i	0.133108	+	0.991102i	$0.457504\pi$
$390$		0			0
$391$		−	11181.8i		−	1.44625i
$392$		0			0
$393$	1611.30	−	314.150i	0.206818	−	0.0403225i
$394$		0			0
$395$	3224.10	−	5584.30i	0.410688	−	0.711333i
$396$		0			0
$397$	1236.96	−	714.160i	0.156376	−	0.0902837i	−0.419770	−	0.907630i	$-0.637889\pi$
$397$	1236.96	−	714.160i	0.156376	−	0.0902837i	0.576146	+	0.817347i	$0.304556\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2535.87	+	1464.08i	−0.315799	+	0.182326i	−0.649518	−	0.760346i	$-0.725029\pi$
$401$	−2535.87	+	1464.08i	−0.315799	+	0.182326i	0.333720	+	0.942672i	$0.391696\pi$
$402$		0			0
$403$	−3845.03	+	6659.79i	−0.475272	+	0.823195i
$404$		0			0
$405$	−6804.52	+	6600.83i	−0.834862	+	0.809871i
$406$		0			0
$407$			487.294i			0.0593471i
$408$		0			0
$409$	7106.97	+	4103.21i	0.859210	+	0.496065i	0.863748	−	0.503925i	$-0.168111\pi$
$409$	7106.97	+	4103.21i	0.859210	+	0.496065i	−0.00453767	+	0.999990i	$0.501444\pi$
$410$		0			0
$411$	1562.19	−	1359.55i	0.187488	−	0.163166i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6650.66	−	11519.3i	−0.786670	−	1.36255i
$416$		0			0
$417$	1121.60	+	385.489i	0.131714	+	0.0452697i
$418$		0			0
$419$	191.679			0.0223487			0.0111744	−	0.999938i	$-0.496443\pi$
$419$	191.679			0.0223487			0.0111744	+	0.999938i	$0.496443\pi$
$420$		0			0
$421$	−5722.17			−0.662427			−0.331213	−	0.943556i	$-0.607458\pi$
$421$	−5722.17			−0.662427			−0.331213	+	0.943556i	$0.607458\pi$
$422$		0			0
$423$	765.290	−	5490.33i	0.0879662	−	0.631085i
$424$		0			0
$425$	1974.98	+	3420.77i	0.225413	+	0.390427i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1287.13	+	1478.98i	0.144856	+	0.166448i
$430$		0			0
$431$	11254.2	+	6497.61i	1.25776	+	0.726169i	0.972639	−	0.232323i	$-0.0746325\pi$
$431$	11254.2	+	6497.61i	1.25776	+	0.726169i	0.285122	+	0.958491i	$0.407966\pi$
$432$		0			0
$433$		−	7022.02i		−	0.779346i	−0.920953	−	0.389673i	$-0.872588\pi$
$433$		−	7022.02i		−	0.779346i	0.920953	−	0.389673i	$-0.127412\pi$
$434$		0			0
$435$	816.476	+	4187.77i	0.0899932	+	0.461582i
$436$		0			0
$437$	8152.37	−	14120.3i	0.892405	−	1.54569i
$438$		0			0
$439$	10337.2	−	5968.16i	1.12384	−	0.648849i	0.181461	−	0.983398i	$-0.441917\pi$
$439$	10337.2	−	5968.16i	1.12384	−	0.648849i	0.942378	+	0.334549i	$0.108584\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6650.98	−	3839.94i	0.713313	−	0.411831i	−0.0989738	−	0.995090i	$-0.531556\pi$
$443$	6650.98	−	3839.94i	0.713313	−	0.411831i	0.812286	+	0.583259i	$0.198223\pi$
$444$		0			0
$445$	−851.999	+	1475.71i	−0.0907610	+	0.157203i
$446$		0			0
$447$	−3521.43	−	18061.7i	−0.372613	−	1.91116i
$448$		0			0
$449$			1268.09i			0.133285i	0.997777	+	0.0666425i	$0.0212287\pi$
$449$			1268.09i			0.133285i	−0.997777	+	0.0666425i	$0.978771\pi$
$450$		0			0
$451$	−1442.00	−	832.541i	−0.150557	−	0.0869242i
$452$		0			0
$453$	718.967	+	826.133i	0.0745695	+	0.0856846i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1900.21	−	3291.25i	−0.194503	−	0.336889i	0.752234	−	0.658896i	$-0.228976\pi$
$457$	−1900.21	−	3291.25i	−0.194503	−	0.336889i	−0.946738	+	0.322006i	$0.895643\pi$
$458$		0			0
$459$	−678.762	−	12544.7i	−0.0690237	−	1.27568i
$460$		0			0
$461$	11736.5			1.18573			0.592866	−	0.805301i	$-0.297996\pi$
$461$	11736.5			1.18573			0.592866	+	0.805301i	$0.297996\pi$
$462$		0			0
$463$	−5696.66			−0.571806			−0.285903	−	0.958259i	$-0.592294\pi$
$463$	−5696.66			−0.571806			−0.285903	+	0.958259i	$0.592294\pi$
$464$		0			0
$465$	6763.23	+	2324.49i	0.674489	+	0.231819i
$466$		0			0
$467$	−8339.06	−	14443.7i	−0.826307	−	1.43121i	−0.900916	−	0.433993i	$-0.857104\pi$
$467$	−8339.06	−	14443.7i	−0.826307	−	1.43121i	0.0746089	−	0.997213i	$-0.476229\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	11144.3	−	9698.64i	1.09024	−	0.948811i
$472$		0			0
$473$	−1582.27	−	913.524i	−0.153812	−	0.0888032i
$474$		0			0
$475$			5759.66i			0.556361i
$476$		0			0
$477$	−808.060	−	1993.53i	−0.0775650	−	0.191357i
$478$		0			0
$479$	−528.256	+	914.966i	−0.0503896	+	0.0872774i	−0.890120	−	0.455726i	$-0.849380\pi$
$479$	−528.256	+	914.966i	−0.0503896	+	0.0872774i	0.839730	+	0.543004i	$0.182713\pi$
$480$		0			0
$481$	5904.75	−	3409.11i	0.559737	−	0.323164i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10104.6	−	5833.90i	0.946035	−	0.546194i
$486$		0			0
$487$	−4919.83	+	8521.40i	−0.457780	+	0.792898i	−0.998843	−	0.0480836i	$-0.984689\pi$
$487$	−4919.83	+	8521.40i	−0.457780	+	0.792898i	0.541063	+	0.840982i	$0.318022\pi$
$488$		0			0
$489$	−2334.15	+	455.082i	−0.215857	+	0.0420849i
$490$		0			0
$491$			5838.19i			0.536606i	0.963335	+	0.268303i	$0.0864629\pi$
$491$			5838.19i			0.536606i	−0.963335	+	0.268303i	$0.913537\pi$
$492$		0			0
$493$	−4896.62	−	2827.07i	−0.447328	−	0.258265i
$494$		0			0
$495$	1120.93	−	1438.08i	0.101782	−	0.130579i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	9197.15	+	15929.9i	0.825092	+	1.42910i	0.901849	+	0.432052i	$0.142210\pi$
$499$	9197.15	+	15929.9i	0.825092	+	1.42910i	−0.0767565	+	0.997050i	$0.524456\pi$
$500$		0			0
$501$	−3561.34	+	10361.9i	−0.317583	+	0.924023i
$502$		0			0
$503$	5908.41			0.523743			0.261872	−	0.965103i	$-0.415660\pi$
$503$	5908.41			0.523743			0.261872	+	0.965103i	$0.415660\pi$
$504$		0			0
$505$	14951.1			1.31746
$506$		0			0
$507$	5206.16	−	15147.6i	0.456042	−	1.32688i
$508$		0			0
$509$	8348.77	+	14460.5i	0.727019	+	1.25923i	0.958138	+	0.286308i	$0.0924282\pi$
$509$	8348.77	+	14460.5i	0.727019	+	1.25923i	−0.231118	+	0.972926i	$0.574238\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	8288.92	−	16336.3i	0.713382	−	1.40598i
$514$		0			0
$515$	18543.0	+	10705.8i	1.58661	+	0.916028i
$516$		0			0
$517$			1066.18i			0.0906974i
$518$		0			0
$519$	−4479.38	+	873.330i	−0.378850	+	0.0738631i
$520$		0			0
$521$	3648.66	−	6319.67i	0.306815	−	0.531420i	−0.670849	−	0.741594i	$-0.734070\pi$
$521$	3648.66	−	6319.67i	0.306815	−	0.531420i	0.977664	+	0.210175i	$0.0674033\pi$
$522$		0			0
$523$	−5470.78	+	3158.56i	−0.457401	+	0.264080i	−0.710951	−	0.703242i	$-0.751735\pi$
$523$	−5470.78	+	3158.56i	−0.457401	+	0.264080i	0.253550	+	0.967322i	$0.418402\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8207.52	+	4738.61i	−0.678416	+	0.391684i
$528$		0			0
$529$	1712.85	−	2966.75i	0.140779	−	0.243836i
$530$		0			0
$531$	−22501.3	+	9120.71i	−1.83893	+	0.745395i
$532$		0			0
$533$			23297.8i			1.89332i
$534$		0			0
$535$	22121.9	+	12772.1i	1.78768	+	1.03212i
$536$		0			0
$537$	−12410.4	+	10800.5i	−0.997295	+	0.867925i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	6292.24	+	10898.5i	0.500045	+	0.866104i	1.00000		5.25096e-5i	$1.67143e-5\pi$
$541$	6292.24	+	10898.5i	0.500045	+	0.866104i	−0.499955	+	0.866052i	$0.666650\pi$
$542$		0			0
$543$	19657.0	+	6756.02i	1.55352	+	0.533938i
$544$		0			0
$545$	−20462.4			−1.60828
$546$		0			0
$547$	15886.3			1.24177			0.620887	−	0.783900i	$-0.286773\pi$
$547$	15886.3			1.24177			0.620887	+	0.783900i	$0.286773\pi$
$548$		0			0
$549$	15112.7	+	2106.55i	1.17486	+	0.163762i
$550$		0			0
$551$	−4122.31	−	7140.04i	−0.318723	−	0.552044i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4162.61	−	4783.08i	−0.318366	−	0.365820i
$556$		0			0
$557$	10421.1	+	6016.60i	0.792737	+	0.457687i	0.840925	−	0.541151i	$-0.182011\pi$
$557$	10421.1	+	6016.60i	0.792737	+	0.457687i	−0.0481881	+	0.998838i	$0.515345\pi$
$558$		0			0
$559$			25564.1i			1.93425i
$560$		0			0
$561$	462.389	+	2371.63i	0.0347987	+	0.178486i
$562$		0			0
$563$	1019.73	−	1766.23i	0.0763351	−	0.132216i	−0.825331	−	0.564649i	$-0.809011\pi$
$563$	1019.73	−	1766.23i	0.0763351	−	0.132216i	0.901666	+	0.432433i	$0.142345\pi$
$564$		0			0
$565$	−22549.9	+	13019.2i	−1.67908	+	0.969420i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11615.0	−	6705.91i	0.855756	−	0.494071i	−0.00683300	−	0.999977i	$-0.502175\pi$
$569$	11615.0	−	6705.91i	0.855756	−	0.494071i	0.862589	+	0.505906i	$0.168842\pi$
$570$		0			0
$571$	2317.42	−	4013.88i	0.169844	−	0.294178i	−0.768521	−	0.639825i	$-0.779007\pi$
$571$	2317.42	−	4013.88i	0.169844	−	0.294178i	0.938365	+	0.345646i	$0.112340\pi$
$572$		0			0
$573$	988.786	+	5071.56i	0.0720892	+	0.369751i
$574$		0			0
$575$			5508.13i			0.399487i
$576$		0			0
$577$	−18977.8	−	10956.9i	−1.36925	−	0.790538i	−0.378419	−	0.925634i	$-0.623532\pi$
$577$	−18977.8	−	10956.9i	−1.36925	−	0.790538i	−0.990832	+	0.135097i	$0.956865\pi$
$578$		0			0
$579$	7031.03	+	8079.05i	0.504662	+	0.579886i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	206.861	+	358.294i	0.0146952	+	0.0254529i
$584$		0			0
$585$	−25267.8	−	3522.05i	−1.78581	−	0.248921i
$586$		0			0
$587$	−3112.06			−0.218822			−0.109411	−	0.993997i	$-0.534896\pi$
$587$	−3112.06			−0.218822			−0.109411	+	0.993997i	$0.534896\pi$
$588$		0			0
$589$	−13819.3			−0.966746
$590$		0			0
$591$	1964.68	+	675.253i	0.136745	+	0.0469986i
$592$		0			0
$593$	−610.968	−	1058.23i	−0.0423094	−	0.0732820i	0.844095	−	0.536193i	$-0.180138\pi$
$593$	−610.968	−	1058.23i	−0.0423094	−	0.0732820i	−0.886405	+	0.462911i	$0.846805\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−11391.9	+	9914.10i	−0.780968	+	0.679660i
$598$		0			0
$599$	−7696.43	−	4443.53i	−0.524987	−	0.303102i	0.213985	−	0.976837i	$-0.431355\pi$
$599$	−7696.43	−	4443.53i	−0.524987	−	0.303102i	−0.738973	+	0.673735i	$0.764689\pi$
$600$		0			0
$601$		−	6820.42i		−	0.462913i	−0.972845	−	0.231457i	$-0.925651\pi$
$601$		−	6820.42i		−	0.462913i	0.972845	−	0.231457i	$-0.0743491\pi$
$602$		0			0
$603$	−2058.92	+	834.567i	−0.139048	+	0.0563619i
$604$		0			0
$605$	8478.99	−	14686.0i	0.569785	−	0.986897i
$606$		0			0
$607$	−11643.9	+	6722.61i	−0.778602	+	0.449526i	−0.835935	−	0.548829i	$-0.815074\pi$
$607$	−11643.9	+	6722.61i	−0.778602	+	0.449526i	0.0573326	+	0.998355i	$0.481740\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12919.4	−	7459.00i	0.855420	−	0.493877i
$612$		0			0
$613$	5472.47	−	9478.60i	0.360573	−	0.624530i	−0.627482	−	0.778631i	$-0.715915\pi$
$613$	5472.47	−	9478.60i	0.360573	−	0.624530i	0.988055	+	0.154100i	$0.0492479\pi$
$614$		0			0
$615$	21265.9	−	4146.15i	1.39435	−	0.271852i
$616$		0			0
$617$			14042.9i			0.916283i	0.888879	+	0.458141i	$0.151485\pi$
$617$			14042.9i			0.916283i	−0.888879	+	0.458141i	$0.848515\pi$
$618$		0			0
$619$	4108.96	+	2372.31i	0.266806	+	0.154041i	0.627435	−	0.778669i	$-0.284105\pi$
$619$	4108.96	+	2372.31i	0.266806	+	0.154041i	−0.360629	+	0.932709i	$0.617438\pi$
$620$		0			0
$621$	7926.94	−	15622.9i	0.512234	−	1.00954i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9596.54	+	16621.7i	0.614179	+	1.06379i
$626$		0			0
$627$	−1145.20	+	3332.02i	−0.0729424	+	0.212230i
$628$		0			0
$629$	8402.77			0.532656
$630$		0			0
$631$	10939.3			0.690151			0.345075	−	0.938575i	$-0.387853\pi$
$631$	10939.3			0.690151			0.345075	+	0.938575i	$0.387853\pi$
$632$		0			0
$633$	−4977.60	+	14482.6i	−0.312547	+	0.909370i
$634$		0			0
$635$	−1082.85	−	1875.54i	−0.0676716	−	0.117211i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	7601.42	−	9752.06i	0.470591	−	0.603734i
$640$		0			0
$641$	−3499.79	−	2020.61i	−0.215653	−	0.124507i	0.388283	−	0.921540i	$-0.373068\pi$
$641$	−3499.79	−	2020.61i	−0.215653	−	0.124507i	−0.603936	+	0.797033i	$0.706402\pi$
$642$		0			0
$643$			25370.2i			1.55599i	0.628268	+	0.777997i	$0.283764\pi$
$643$			25370.2i			1.55599i	−0.628268	+	0.777997i	$0.716236\pi$
$644$		0			0
$645$	23334.5	−	4549.45i	1.42449	−	0.277728i
$646$		0			0
$647$	−1094.96	+	1896.53i	−0.0665339	+	0.115240i	−0.897373	−	0.441272i	$-0.854527\pi$
$647$	−1094.96	+	1896.53i	−0.0665339	+	0.115240i	0.830839	+	0.556512i	$0.187861\pi$
$648$		0			0
$649$	4044.13	−	2334.88i	0.244601	−	0.141220i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8980.82	+	5185.08i	−0.538203	+	0.310732i	−0.744350	−	0.667789i	$-0.767241\pi$
$653$	−8980.82	+	5185.08i	−0.538203	+	0.310732i	0.206147	+	0.978521i	$0.433907\pi$
$654$		0			0
$655$	2054.24	−	3558.05i	0.122543	−	0.212251i
$656$		0			0
$657$	−9007.47	−	22221.9i	−0.534878	−	1.31957i
$658$		0			0
$659$		−	26192.1i		−	1.54825i	−0.633032	−	0.774126i	$-0.718190\pi$
$659$		−	26192.1i		−	1.54825i	0.633032	−	0.774126i	$-0.281810\pi$
$660$		0			0
$661$	−7399.81	−	4272.28i	−0.435430	−	0.251396i	0.266227	−	0.963910i	$-0.414223\pi$
$661$	−7399.81	−	4272.28i	−0.435430	−	0.251396i	−0.701657	+	0.712515i	$0.747556\pi$
$662$		0			0
$663$	25503.2	−	22194.9i	1.49391	−	1.30012i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3942.28	−	6828.23i	−0.228854	−	0.396387i
$668$		0			0
$669$	17108.6	+	5880.14i	0.988722	+	0.339820i
$670$		0			0
$671$	−2934.78			−0.168846
$672$		0			0
$673$	−32802.3			−1.87881			−0.939404	−	0.342813i	$-0.888620\pi$
$673$	−32802.3			−1.87881			−0.939404	+	0.342813i	$0.888620\pi$
$674$		0			0
$675$	334.358	+	6179.52i	0.0190659	+	0.352370i
$676$		0			0
$677$	−968.152	−	1676.89i	−0.0549617	−	0.0951965i	0.837236	−	0.546842i	$-0.184170\pi$
$677$	−968.152	−	1676.89i	−0.0549617	−	0.0951965i	−0.892197	+	0.451646i	$0.850837\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−13215.0	−	15184.7i	−0.743610	−	0.854450i
$682$		0			0
$683$	−1697.40	−	979.995i	−0.0950940	−	0.0549026i	0.451699	−	0.892170i	$-0.350818\pi$
$683$	−1697.40	−	979.995i	−0.0950940	−	0.0549026i	−0.546793	+	0.837268i	$0.684151\pi$
$684$		0			0
$685$		−	5182.89i		−	0.289092i
$686$		0			0
$687$	3986.88	+	20449.0i	0.221410	+	1.13563i
$688$		0			0
$689$	2894.40	−	5013.25i	0.160041	−	0.277198i
$690$		0			0
$691$	−17263.4	+	9967.05i	−0.950408	+	0.548718i	−0.893208	−	0.449645i	$-0.851551\pi$
$691$	−17263.4	+	9967.05i	−0.950408	+	0.548718i	−0.0572002	+	0.998363i	$0.518217\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2570.50	−	1484.08i	0.140294	−	0.0809989i
$696$		0			0
$697$	−14356.1	+	24865.5i	−0.780168	+	1.35129i
$698$		0			0
$699$	−5049.78	−	25900.7i	−0.273248	−	1.40151i
$700$		0			0
$701$		−	26738.5i		−	1.44065i	−0.693635	−	0.720327i	$-0.743992\pi$
$701$		−	26738.5i		−	1.44065i	0.693635	−	0.720327i	$-0.256008\pi$
$702$		0			0
$703$	10611.0	+	6126.28i	0.569278	+	0.328673i
$704$		0			0
$705$	−9107.64	−	10465.2i	−0.486544	−	0.559066i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−6441.45	−	11156.9i	−0.341204	−	0.590983i	0.643452	−	0.765486i	$-0.277501\pi$
$709$	−6441.45	−	11156.9i	−0.341204	−	0.590983i	−0.984657	+	0.174503i	$0.944168\pi$
$710$		0			0
$711$	−1848.27	+	13259.8i	−0.0974902	+	0.699413i
$712$		0			0
$713$	−13215.8			−0.694159
$714$		0			0
$715$	4906.82			0.256650
$716$		0			0
$717$	5313.26	+	1826.14i	0.276746	+	0.0951166i
$718$		0			0
$719$	13721.5	+	23766.3i	0.711717	+	1.23273i	0.964212	+	0.265131i	$0.0854153\pi$
$719$	13721.5	+	23766.3i	0.711717	+	1.23273i	−0.252496	+	0.967598i	$0.581251\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−12921.6	+	11245.4i	−0.664675	+	0.578453i
$724$		0			0
$725$	2412.08	+	1392.61i	0.123562	+	0.0713385i
$726$		0			0
$727$		−	10869.4i		−	0.554501i	−0.960798	−	0.277250i	$-0.910577\pi$
$727$		−	10869.4i		−	0.554501i	0.960798	−	0.277250i	$-0.0894231\pi$
$728$		0			0
$729$	7944.80	−	18008.4i	0.403638	−	0.914919i
$730$		0			0
$731$	−15752.6	+	27284.3i	−0.797032	+	1.38050i
$732$		0			0
$733$	28893.2	−	16681.5i	1.45593	−	0.840580i	0.457120	−	0.889405i	$-0.348881\pi$
$733$	28893.2	−	16681.5i	1.45593	−	0.840580i	0.998807	+	0.0488247i	$0.0155476\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	370.048	−	213.647i	0.0184951	−	0.0106781i
$738$		0			0
$739$	18226.4	−	31569.0i	0.907265	−	1.57143i	0.0894168	−	0.995994i	$-0.471500\pi$
$739$	18226.4	−	31569.0i	0.907265	−	1.57143i	0.817848	−	0.575434i	$-0.195167\pi$
$740$		0			0
$741$	48387.3	−	9433.91i	2.39886	−	0.467697i
$742$		0			0
$743$		−	139.301i		−	0.00687814i	−0.999994	−	0.00343907i	$-0.998905\pi$
$743$		−	139.301i		−	0.00687814i	0.999994	−	0.00343907i	$-0.00109469\pi$
$744$		0			0
$745$	−39883.6	−	23026.8i	−1.96137	−	1.13240i
$746$		0			0
$747$	21781.5	+	16978.0i	1.06686	+	0.831583i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	8485.28	+	14696.9i	0.412293	+	0.714113i	0.995140	−	0.0984692i	$-0.0313946\pi$
$751$	8485.28	+	14696.9i	0.412293	+	0.714113i	−0.582847	+	0.812582i	$0.698061\pi$
$752$		0			0
$753$	1166.55	−	3394.13i	0.0564560	−	0.164262i
$754$		0			0
$755$	2740.86			0.132120
$756$		0			0
$757$	−29233.1			−1.40356			−0.701781	−	0.712393i	$-0.747611\pi$
$757$	−29233.1			−1.40356			−0.701781	+	0.712393i	$0.747611\pi$
$758$		0			0
$759$	−1095.19	+	3186.51i	−0.0523753	+	0.152388i
$760$		0			0
$761$	−5497.11	−	9521.27i	−0.261853	−	0.453542i	0.704882	−	0.709325i	$-0.251000\pi$
$761$	−5497.11	−	9521.27i	−0.261853	−	0.453542i	−0.966734	+	0.255783i	$0.917667\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−24797.8	−	19329.1i	−1.17198	−	0.913523i
$766$		0			0
$767$	−56585.4	−	32669.6i	−2.66386	−	1.53798i
$768$		0			0
$769$		−	1694.37i		−	0.0794547i	−0.999211	−	0.0397273i	$-0.987351\pi$
$769$		−	1694.37i		−	0.0794547i	0.999211	−	0.0397273i	$-0.0126489\pi$
$770$		0			0
$771$	−40274.0	+	7852.08i	−1.88123	+	0.366778i
$772$		0			0
$773$	−16225.5	+	28103.4i	−0.754969	+	1.30764i	0.190421	+	0.981702i	$0.439015\pi$
$773$	−16225.5	+	28103.4i	−0.754969	+	1.30764i	−0.945390	+	0.325942i	$0.894319\pi$
$774$		0			0
$775$	4043.03	−	2334.24i	0.187393	−	0.108192i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−36257.8	+	20933.5i	−1.66761	+	0.962798i
$780$		0			0
$781$	−1189.06	+	2059.52i	−0.0544790	+	0.0943603i
$782$		0			0
$783$	−4837.30	−	7421.22i	−0.220780	−	0.338713i
$784$		0			0
$785$		−	36973.4i		−	1.68107i
$786$		0			0
$787$	−18152.9	−	10480.6i	−0.822212	−	0.474704i	0.0289667	−	0.999580i	$-0.490778\pi$
$787$	−18152.9	−	10480.6i	−0.822212	−	0.474704i	−0.851179	+	0.524876i	$0.824112\pi$
$788$		0			0
$789$	11747.9	−	10223.9i	0.530083	−	0.461320i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	20531.7	+	35562.0i	0.919424	+	1.59249i
$794$		0			0
$795$	−5091.12	−	1749.80i	−0.227124	−	0.0780615i
$796$		0			0
$797$	30873.3			1.37213			0.686066	−	0.727540i	$-0.259336\pi$
$797$	30873.3			1.37213			0.686066	+	0.727540i	$0.259336\pi$
$798$		0			0
$799$	18384.9			0.814033
$800$		0			0
$801$	488.424	−	3504.04i	0.0215451	−	0.154568i
$802$		0			0
$803$	2305.89	+	3993.92i	0.101336	+	0.175520i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−27574.1	−	31684.3i	−1.20280	−	1.38208i
$808$		0			0
$809$	−23921.2	−	13810.9i	−1.03958	−	0.600204i	−0.119869	−	0.992790i	$-0.538247\pi$
$809$	−23921.2	−	13810.9i	−1.03958	−	0.600204i	−0.919716	+	0.392585i	$0.871581\pi$
$810$		0			0
$811$			20022.9i			0.866954i	0.901165	+	0.433477i	$0.142713\pi$
$811$			20022.9i			0.866954i	−0.901165	+	0.433477i	$0.857287\pi$
$812$		0			0
$813$	3290.11	+	16875.3i	0.141930	+	0.727972i
$814$		0			0
$815$	−2975.80	+	5154.24i	−0.127899	+	0.221528i
$816$		0			0
$817$	−39784.7	+	22969.7i	−1.70366	+	0.983609i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6115.05	+	3530.52i	−0.259947	+	0.150081i	−0.624310	−	0.781176i	$-0.714620\pi$
$821$	−6115.05	+	3530.52i	−0.259947	+	0.150081i	0.364363	+	0.931257i	$0.381287\pi$
$822$		0			0
$823$	18834.7	−	32622.6i	0.797734	−	1.38172i	−0.123354	−	0.992363i	$-0.539365\pi$
$823$	18834.7	−	32622.6i	0.797734	−	1.38172i	0.921089	−	0.389353i	$-0.127301\pi$
$824$		0			0
$825$	−227.773	−	1168.27i	−0.00961217	−	0.0493016i
$826$		0			0
$827$			5566.45i			0.234056i	0.993129	+	0.117028i	$0.0373368\pi$
$827$			5566.45i			0.234056i	−0.993129	+	0.117028i	$0.962663\pi$
$828$		0			0
$829$	−9558.42	−	5518.56i	−0.400455	−	0.231203i	0.286225	−	0.958162i	$-0.407600\pi$
$829$	−9558.42	−	5518.56i	−0.400455	−	0.231203i	−0.686680	+	0.726959i	$0.740933\pi$
$830$		0			0
$831$	−17040.8	−	19580.8i	−0.711357	−	0.817390i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	13710.7	+	23747.6i	0.568236	+	0.984214i
$836$		0			0
$837$	−14826.7	+	802.233i	−0.612287	+	0.0331293i
$838$		0			0
$839$	−28936.3			−1.19069			−0.595347	−	0.803469i	$-0.702986\pi$
$839$	−28936.3			−1.19069			−0.595347	+	0.803469i	$0.702986\pi$
$840$		0			0
$841$	20402.1			0.836529
$842$		0			0
$843$	20263.8	+	6964.57i	0.827902	+	0.284546i
$844$		0			0
$845$	−20043.0	−	34715.4i	−0.815975	−	1.41331i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−7178.67	+	6247.45i	−0.290190	+	0.252546i
$850$		0			0
$851$	10147.6	+	5858.74i	0.408762	+	0.235999i
$852$		0			0
$853$			25646.9i			1.02946i	0.857351	+	0.514732i	$0.172109\pi$
$853$			25646.9i			1.02946i	−0.857351	+	0.514732i	$0.827891\pi$
$854$		0			0
$855$	−17222.3	−	42488.3i	−0.688877	−	1.69950i
$856$		0			0
$857$	−2745.33	+	4755.06i	−0.109427	+	0.189533i	−0.915538	−	0.402231i	$-0.868235\pi$
$857$	−2745.33	+	4755.06i	−0.109427	+	0.189533i	0.806111	+	0.591764i	$0.201568\pi$
$858$		0			0
$859$	−7955.53	+	4593.13i	−0.315994	+	0.182439i	−0.649606	−	0.760271i	$-0.725066\pi$
$859$	−7955.53	+	4593.13i	−0.315994	+	0.182439i	0.333611	+	0.942711i	$0.391733\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−38541.3	+	22251.9i	−1.52023	+	0.877708i	−0.520520	+	0.853850i	$0.674262\pi$
$863$	−38541.3	+	22251.9i	−1.52023	+	0.877708i	−0.999715	+	0.0238583i	$0.992405\pi$
$864$		0			0
$865$	−5710.74	+	9891.30i	−0.224475	+	0.388803i
$866$		0			0
$867$	15838.9	−	3088.06i	0.620436	−	0.120964i
$868$		0			0
$869$		−	2574.96i		−	0.100517i
$870$		0			0
$871$	−5177.71	−	2989.35i	−0.201424	−	0.116292i
$872$		0			0
$873$	−14892.9	+	19106.6i	−0.577377	+	0.740732i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9236.70	+	15998.4i	0.355645	+	0.615996i	0.987228	−	0.159312i	$-0.0509277\pi$
$877$	9236.70	+	15998.4i	0.355645	+	0.615996i	−0.631583	+	0.775308i	$0.717594\pi$
$878$		0			0
$879$	4520.18	−	13151.7i	0.173449	−	0.504659i
$880$		0			0
$881$	−9245.06			−0.353546			−0.176773	−	0.984252i	$-0.556566\pi$
$881$	−9245.06			−0.353546			−0.176773	+	0.984252i	$0.556566\pi$
$882$		0			0
$883$	14216.8			0.541827			0.270913	−	0.962604i	$-0.412674\pi$
$883$	14216.8			0.541827			0.270913	+	0.962604i	$0.412674\pi$
$884$		0			0
$885$	−19750.3	+	57464.4i	−0.750167	+	2.18265i
$886$		0			0
$887$	15492.2	+	26833.3i	0.586445	+	1.01575i	0.994694	+	0.102882i	$0.0328065\pi$
$887$	15492.2	+	26833.3i	0.586445	+	1.01575i	−0.408248	+	0.912871i	$0.633860\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1035.25	+	3641.39i	−0.0389251	+	0.136915i
$892$		0			0
$893$	23216.5	+	13404.1i	0.870001	+	0.502296i
$894$		0			0
$895$			41173.9i			1.53776i
$896$		0			0
$897$	46274.2	−	9021.93i	1.72246	−	0.335823i
$898$		0			0
$899$	−3341.33	+	5787.35i	−0.123959	+	0.214704i
$900$		0			0
$901$	6178.33	−	3567.06i	0.228446	−	0.131894i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	45050.2	−	26009.7i	1.65472	−	0.955351i
$906$		0			0
$907$	−22640.9	+	39215.3i	−0.828865	+	1.43564i	0.0700650	+	0.997542i	$0.477679\pi$
$907$	−22640.9	+	39215.3i	−0.828865	+	1.43564i	−0.898930	+	0.438093i	$0.855654\pi$
$908$		0			0
$909$	−28768.6	+	11661.1i	−1.04972	+	0.425495i
$910$		0			0
$911$			1202.70i			0.0437402i	0.999761	+	0.0218701i	$0.00696202\pi$
$911$			1202.70i			0.0437402i	−0.999761	+	0.0218701i	$0.993038\pi$
$912$		0			0
$913$	−4600.00	−	2655.81i	−0.166744	−	0.0962700i
$914$		0			0
$915$	28806.6	−	25069.8i	1.04078	−	0.905772i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	5398.13	+	9349.83i	0.193763	+	0.335607i	0.946494	−	0.322721i	$-0.104598\pi$
$919$	5398.13	+	9349.83i	0.193763	+	0.335607i	−0.752732	+	0.658328i	$0.771264\pi$
$920$		0			0
$921$	−1891.53	−	650.109i	−0.0676741	−	0.0232593i
$922$		0			0
$923$	33274.8			1.18662
$924$		0			0
$925$	−4139.21			−0.147131
$926$		0			0
$927$	−44030.1	−	6137.29i	−1.56002	−	0.217449i
$928$		0			0
$929$	−4138.39	−	7167.89i	−0.146153	−	0.253144i	0.783650	−	0.621203i	$-0.213356\pi$
$929$	−4138.39	−	7167.89i	−0.146153	−	0.253144i	−0.929802	+	0.368059i	$0.880022\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−8329.82	−	9571.44i	−0.292289	−	0.335857i
$934$		0			0
$935$	5237.00	+	3023.59i	0.183175	+	0.105756i
$936$		0			0
$937$			13731.8i			0.478760i	0.970926	+	0.239380i	$0.0769441\pi$
$937$			13731.8i			0.478760i	−0.970926	+	0.239380i	$0.923056\pi$
$938$		0			0
$939$	4103.31	+	21046.2i	0.142605	+	0.731434i
$940$		0			0
$941$	−24731.9	+	42837.0i	−0.856789	+	1.48400i	0.0181872	+	0.999835i	$0.494211\pi$
$941$	−24731.9	+	42837.0i	−0.856789	+	1.48400i	−0.874976	+	0.484167i	$0.839123\pi$
$942$		0			0
$943$	−34674.4	+	20019.3i	−1.19741	+	0.691323i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16333.6	+	9430.23i	−0.560477	+	0.323592i	−0.753337	−	0.657635i	$-0.771557\pi$
$947$	−16333.6	+	9430.23i	−0.560477	+	0.323592i	0.192860	+	0.981226i	$0.438224\pi$
$948$		0			0
$949$	32264.0	−	55882.9i	1.10362	−	1.91152i
$950$		0			0
$951$	−6697.67	−	34352.9i	−0.228377	−	1.17136i
$952$		0			0
$953$		−	26144.6i		−	0.888674i	−0.895860	−	0.444337i	$-0.853439\pi$
$953$		−	26144.6i		−	0.888674i	0.895860	−	0.444337i	$-0.146561\pi$
$954$		0			0
$955$	11198.9	+	6465.72i	0.379465	+	0.219084i
$956$		0			0
$957$	1118.51	+	1285.24i	0.0377810	+	0.0434125i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−9294.90	−	16099.2i	−0.312004	−	0.540406i
$962$		0			0
$963$	−52528.0	−	7321.81i	−1.75773	−	0.245007i
$964$		0			0
$965$	26803.9			0.894142
$966$		0			0
$967$	−12791.3			−0.425377			−0.212688	−	0.977120i	$-0.568222\pi$
$967$	−12791.3			−0.425377			−0.212688	+	0.977120i	$0.568222\pi$
$968$		0			0
$969$	57456.4	+	19747.5i	1.90482	+	0.654677i
$970$		0			0
$971$	−7487.53	−	12968.8i	−0.247463	−	0.428618i	0.715359	−	0.698758i	$-0.246263\pi$
$971$	−7487.53	−	12968.8i	−0.247463	−	0.428618i	−0.962821	+	0.270140i	$0.912930\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−12562.9	+	10933.2i	−0.412651	+	0.359121i
$976$		0			0
$977$	−26012.8	−	15018.5i	−0.851815	−	0.491796i	0.00944779	−	0.999955i	$-0.496993\pi$
$977$	−26012.8	−	15018.5i	−0.851815	−	0.491796i	−0.861263	+	0.508160i	$0.830326\pi$
$978$		0			0
$979$			680.458i			0.0222140i
$980$		0			0
$981$	39373.3	−	15959.6i	1.28144	−	0.519421i
$982$		0			0
$983$	8226.35	−	14248.5i	0.266918	−	0.462315i	−0.701147	−	0.713017i	$-0.747328\pi$
$983$	8226.35	−	14248.5i	0.266918	−	0.462315i	0.968064	+	0.250702i	$0.0806615\pi$
$984$		0			0
$985$	4502.69	−	2599.63i	0.145652	−	0.0840924i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−38047.3	+	21966.6i	−1.22329	+	0.706267i
$990$		0			0
$991$	−12196.1	+	21124.3i	−0.390941	+	0.677130i	−0.992574	−	0.121643i	$-0.961184\pi$
$991$	−12196.1	+	21124.3i	−0.390941	+	0.677130i	0.601633	+	0.798773i	$0.294517\pi$
$992$		0			0
$993$	−21005.9	+	4095.45i	−0.671301	+	0.130881i
$994$		0			0
$995$			37794.8i			1.20420i
$996$		0			0
$997$	15826.1	+	9137.19i	0.502725	+	0.290249i	0.729838	−	0.683620i	$-0.239595\pi$
$997$	15826.1	+	9137.19i	0.502725	+	0.290249i	−0.227113	+	0.973868i	$0.572929\pi$
$998$		0			0
$999$	11740.2	+	5956.87i	0.371814	+	0.188656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.e.521.12		48
3.2	odd	2	inner	588.4.k.e.521.19		48
7.2	even	3	inner	588.4.k.e.509.6		48
7.3	odd	6		588.4.f.d.293.4	yes	24
7.4	even	3		588.4.f.d.293.21	yes	24
7.5	odd	6	inner	588.4.k.e.509.19		48
7.6	odd	2	inner	588.4.k.e.521.13		48
21.2	odd	6	inner	588.4.k.e.509.13		48
21.5	even	6	inner	588.4.k.e.509.12		48
21.11	odd	6		588.4.f.d.293.3	✓	24
21.17	even	6		588.4.f.d.293.22	yes	24
21.20	even	2	inner	588.4.k.e.521.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.f.d.293.3	✓	24	21.11	odd	6
588.4.f.d.293.4	yes	24	7.3	odd	6
588.4.f.d.293.21	yes	24	7.4	even	3
588.4.f.d.293.22	yes	24	21.17	even	6
588.4.k.e.509.6		48	7.2	even	3	inner
588.4.k.e.509.12		48	21.5	even	6	inner
588.4.k.e.509.13		48	21.2	odd	6	inner
588.4.k.e.509.19		48	7.5	odd	6	inner
588.4.k.e.521.6		48	21.20	even	2	inner
588.4.k.e.521.12		48	1.1	even	1	trivial
588.4.k.e.521.13		48	7.6	odd	2	inner
588.4.k.e.521.19		48	3.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.68893 + 4.91401i) q^{3} +(6.50213 + 11.2620i) q^{5} +(-21.2951 - 16.5988i) q^{9} +O(q^{10})\)	\(q+(-1.68893 + 4.91401i) q^{3} +(6.50213 + 11.2620i) q^{5} +(-21.2951 - 16.5988i) q^{9} +(4.49726 + 2.59650i) q^{11} -72.6603i q^{13} +(-66.3233 + 12.9308i) q^{15} +(44.7733 - 77.5496i) q^{17} +(113.080 - 65.2865i) q^{19} +(108.141 - 62.4354i) q^{23} +(-22.0553 + 38.2010i) q^{25} +(117.533 - 76.6101i) q^{27} -63.1418i q^{29} +(-91.6564 - 52.9179i) q^{31} +(-20.3548 + 17.7143i) q^{33} +(46.9184 + 81.2651i) q^{37} +(357.054 + 122.718i) q^{39} -320.640 q^{41} -351.830 q^{43} +(48.4728 - 347.753i) q^{45} +(102.656 + 177.805i) q^{47} +(305.461 + 350.992i) q^{51} +(68.9957 + 39.8347i) q^{53} +67.5310i q^{55} +(129.836 + 665.938i) q^{57} +(449.621 - 778.767i) q^{59} +(-489.428 + 282.571i) q^{61} +(818.302 - 472.447i) q^{65} +(41.1414 - 71.2591i) q^{67} +(124.166 + 636.856i) q^{69} +457.950i q^{71} +(769.098 + 444.039i) q^{73} +(-150.470 - 172.899i) q^{75} +(-247.926 - 429.421i) q^{79} +(177.959 + 706.945i) q^{81} -1022.84 q^{83} +1164.49 q^{85} +(310.280 + 106.642i) q^{87} +(65.5170 + 113.479i) q^{89} +(414.840 - 361.027i) q^{93} +(1470.51 + 849.002i) q^{95} -897.230i q^{97} +(-52.6707 - 129.942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 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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