LMFDB - Embedded newform 588.4.k.e.521.11

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			521.11
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84944 + 4.85588i) q^{3} +(-1.01459 - 1.75732i) q^{5} +(-20.1591 - 17.9613i) q^{9} +O(q^{10})$	\(q+(-1.84944 + 4.85588i) q^{3} +(-1.01459 - 1.75732i) q^{5} +(-20.1591 - 17.9613i) q^{9} +(25.2834 + 14.5974i) q^{11} -25.7266i q^{13} +(10.4097 - 1.67666i) q^{15} +(1.39964 - 2.42425i) q^{17} +(-92.8920 + 53.6312i) q^{19} +(70.3580 - 40.6212i) q^{23} +(60.4412 - 104.687i) q^{25} +(124.501 - 64.6720i) q^{27} -170.862i q^{29} +(-22.4394 - 12.9554i) q^{31} +(-117.643 + 95.7762i) q^{33} +(-90.6133 - 156.947i) q^{37} +(124.925 + 47.5798i) q^{39} +257.354 q^{41} +239.983 q^{43} +(-11.1105 + 53.6493i) q^{45} +(186.576 + 323.160i) q^{47} +(9.18329 + 11.2800i) q^{51} +(489.335 + 282.517i) q^{53} -59.2413i q^{55} +(-88.6285 - 550.260i) q^{57} +(-189.642 + 328.470i) q^{59} +(194.113 - 112.071i) q^{61} +(-45.2098 + 26.1019i) q^{65} +(-167.761 + 290.571i) q^{67} +(67.1288 + 416.777i) q^{69} -1029.35i q^{71} +(-505.848 - 292.052i) q^{73} +(396.566 + 487.108i) q^{75} +(497.128 + 861.051i) q^{79} +(83.7817 + 724.170i) q^{81} +1281.20 q^{83} -5.68022 q^{85} +(829.684 + 315.999i) q^{87} +(738.927 + 1279.86i) q^{89} +(104.410 - 85.0026i) q^{93} +(188.494 + 108.827i) q^{95} +1228.85i q^{97} +(-247.504 - 748.394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.84944	+	4.85588i	−0.355925	+	0.934515i
$3$	−1.84944	+	4.85588i	−0.355925	+	0.934515i
$4$		0			0
$5$	−1.01459	−	1.75732i	−0.0907475	−	0.157179i	0.817078	−	0.576527i	$-0.195592\pi$
$5$	−1.01459	−	1.75732i	−0.0907475	−	0.157179i	−0.907826	+	0.419347i	$0.862259\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−20.1591	−	17.9613i	−0.746635	−	0.665234i
$10$		0			0
$11$	25.2834	+	14.5974i	0.693022	+	0.400116i	0.804743	−	0.593623i	$-0.202303\pi$
$11$	25.2834	+	14.5974i	0.693022	+	0.400116i	−0.111721	+	0.993740i	$0.535636\pi$
$12$		0			0
$13$		−	25.7266i		−	0.548867i	−0.961606	−	0.274433i	$-0.911510\pi$
$13$		−	25.7266i		−	0.548867i	0.961606	−	0.274433i	$-0.0884903\pi$
$14$		0			0
$15$	10.4097	−	1.67666i	0.179186	−	0.0288608i
$16$		0			0
$17$	1.39964	−	2.42425i	0.0199684	−	0.0345862i	−0.855869	−	0.517193i	$-0.826977\pi$
$17$	1.39964	−	2.42425i	0.0199684	−	0.0345862i	0.875837	+	0.482607i	$0.160310\pi$
$18$		0			0
$19$	−92.8920	+	53.6312i	−1.12163	+	0.647571i	−0.941815	−	0.336130i	$-0.890882\pi$
$19$	−92.8920	+	53.6312i	−1.12163	+	0.647571i	−0.179810	+	0.983701i	$0.557548\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	70.3580	−	40.6212i	0.637855	−	0.368266i	−0.145933	−	0.989295i	$-0.546618\pi$
$23$	70.3580	−	40.6212i	0.637855	−	0.368266i	0.783788	+	0.621029i	$0.213285\pi$
$24$		0			0
$25$	60.4412	−	104.687i	0.483530	−	0.837498i
$26$		0			0
$27$	124.501	−	64.6720i	0.887417	−	0.460968i
$28$		0			0
$29$		−	170.862i		−	1.09408i	−0.837107	−	0.547039i	$-0.815755\pi$
$29$		−	170.862i		−	1.09408i	0.837107	−	0.547039i	$-0.184245\pi$
$30$		0			0
$31$	−22.4394	−	12.9554i	−0.130007	−	0.0750598i	0.433586	−	0.901112i	$-0.357248\pi$
$31$	−22.4394	−	12.9554i	−0.130007	−	0.0750598i	−0.563593	+	0.826052i	$0.690581\pi$
$32$		0			0
$33$	−117.643	+	95.7762i	−0.620578	+	0.505227i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−90.6133	−	156.947i	−0.402615	−	0.697349i	0.591426	−	0.806359i	$-0.298565\pi$
$37$	−90.6133	−	156.947i	−0.402615	−	0.697349i	−0.994041	+	0.109010i	$0.965232\pi$
$38$		0			0
$39$	124.925	+	47.5798i	0.512924	+	0.195355i
$40$		0			0
$41$	257.354			0.980289			0.490145	−	0.871641i	$-0.336944\pi$
$41$	257.354			0.980289			0.490145	+	0.871641i	$0.336944\pi$
$42$		0			0
$43$	239.983			0.851095			0.425548	−	0.904936i	$-0.360082\pi$
$43$	239.983			0.851095			0.425548	+	0.904936i	$0.360082\pi$
$44$		0			0
$45$	−11.1105	+	53.6493i	−0.0368058	+	0.177724i
$46$		0			0
$47$	186.576	+	323.160i	0.579041	+	1.00293i	0.995590	+	0.0938154i	$0.0299063\pi$
$47$	186.576	+	323.160i	0.579041	+	1.00293i	−0.416548	+	0.909114i	$0.636760\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	9.18329	+	11.2800i	0.0252141	+	0.0309708i
$52$		0			0
$53$	489.335	+	282.517i	1.26821	+	0.732203i	0.974650	−	0.223737i	$-0.0718256\pi$
$53$	489.335	+	282.517i	1.26821	+	0.732203i	0.293563	+	0.955940i	$0.405159\pi$
$54$		0			0
$55$		−	59.2413i		−	0.145238i
$56$		0			0
$57$	−88.6285	−	550.260i	−0.205950	−	1.27866i
$58$		0			0
$59$	−189.642	+	328.470i	−0.418463	+	0.724800i	−0.995785	−	0.0917170i	$-0.970764\pi$
$59$	−189.642	+	328.470i	−0.418463	+	0.724800i	0.577322	+	0.816517i	$0.304098\pi$
$60$		0			0
$61$	194.113	−	112.071i	0.407436	−	0.235233i	−0.282251	−	0.959340i	$-0.591081\pi$
$61$	194.113	−	112.071i	0.407436	−	0.235233i	0.689687	+	0.724107i	$0.257748\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−45.2098	+	26.1019i	−0.0862705	+	0.0498083i
$66$		0			0
$67$	−167.761	+	290.571i	−0.305900	+	0.529835i	−0.977461	−	0.211114i	$-0.932291\pi$
$67$	−167.761	+	290.571i	−0.305900	+	0.529835i	0.671561	+	0.740949i	$0.265624\pi$
$68$		0			0
$69$	67.1288	+	416.777i	0.117121	+	0.727160i
$70$		0			0
$71$		−	1029.35i		−	1.72057i	−0.509809	−	0.860287i	$-0.670284\pi$
$71$		−	1029.35i		−	1.72057i	0.509809	−	0.860287i	$-0.329716\pi$
$72$		0			0
$73$	−505.848	−	292.052i	−0.811028	−	0.468247i	0.0362846	−	0.999341i	$-0.488448\pi$
$73$	−505.848	−	292.052i	−0.811028	−	0.468247i	−0.847313	+	0.531094i	$0.821781\pi$
$74$		0			0
$75$	396.566	+	487.108i	0.610554	+	0.749952i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	497.128	+	861.051i	0.707991	+	1.22628i	0.965601	+	0.260027i	$0.0837316\pi$
$79$	497.128	+	861.051i	0.707991	+	1.22628i	−0.257610	+	0.966249i	$0.582935\pi$
$80$		0			0
$81$	83.7817	+	724.170i	0.114927	+	0.993374i
$82$		0			0
$83$	1281.20			1.69434			0.847171	−	0.531320i	$-0.178304\pi$
$83$	1281.20			1.69434			0.847171	+	0.531320i	$0.178304\pi$
$84$		0			0
$85$	−5.68022			−0.00724832
$86$		0			0
$87$	829.684	+	315.999i	1.02243	+	0.389409i
$88$		0			0
$89$	738.927	+	1279.86i	0.880068	+	1.52432i	0.851264	+	0.524737i	$0.175836\pi$
$89$	738.927	+	1279.86i	0.880068	+	1.52432i	0.0288039	+	0.999585i	$0.490830\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	104.410	−	85.0026i	0.116417	−	0.0947781i
$94$		0			0
$95$	188.494	+	108.827i	0.203569	+	0.117531i
$96$		0			0
$97$			1228.85i			1.28630i	0.765742	+	0.643148i	$0.222372\pi$
$97$			1228.85i			1.28630i	−0.765742	+	0.643148i	$0.777628\pi$
$98$		0			0
$99$	−247.504	−	748.394i	−0.251263	−	0.759762i
$100$		0			0
$101$	−219.708	+	380.545i	−0.216453	+	0.374907i	−0.953721	−	0.300693i	$-0.902782\pi$
$101$	−219.708	+	380.545i	−0.216453	+	0.374907i	0.737268	+	0.675600i	$0.236115\pi$
$102$		0			0
$103$	963.292	−	556.157i	0.921514	−	0.532037i	0.0373965	−	0.999301i	$-0.488094\pi$
$103$	963.292	−	556.157i	0.921514	−	0.532037i	0.884118	+	0.467264i	$0.154760\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	51.9337	−	29.9839i	0.0469217	−	0.0270903i	−0.476356	−	0.879253i	$-0.658043\pi$
$107$	51.9337	−	29.9839i	0.0469217	−	0.0270903i	0.523277	+	0.852162i	$0.324709\pi$
$108$		0			0
$109$	119.650	−	207.239i	0.105141	−	0.182109i	−0.808655	−	0.588283i	$-0.799804\pi$
$109$	119.650	−	207.239i	0.105141	−	0.182109i	0.913796	+	0.406174i	$0.133137\pi$
$110$		0			0
$111$	929.699	−	149.744i	0.794983	−	0.128045i
$112$		0			0
$113$		−	1701.80i		−	1.41674i	−0.705841	−	0.708370i	$-0.749431\pi$
$113$		−	1701.80i		−	1.41674i	0.705841	−	0.708370i	$-0.250569\pi$
$114$		0			0
$115$	−142.769	−	82.4276i	−0.115767	−	0.0668384i
$116$		0			0
$117$	−462.083	+	518.626i	−0.365125	+	0.409803i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−239.333	−	414.536i	−0.179814	−	0.311447i
$122$		0			0
$123$	−475.960	+	1249.68i	−0.348910	+	0.916095i
$124$		0			0
$125$	−498.939			−0.357011
$126$		0			0
$127$	1848.04			1.29124			0.645618	−	0.763661i	$-0.276600\pi$
$127$	1848.04			1.29124			0.645618	+	0.763661i	$0.276600\pi$
$128$		0			0
$129$	−443.835	+	1165.33i	−0.302926	+	0.795361i
$130$		0			0
$131$	149.935	+	259.695i	0.0999991	+	0.173203i	0.911684	−	0.410892i	$-0.134783\pi$
$131$	149.935	+	259.695i	0.0999991	+	0.173203i	−0.811685	+	0.584095i	$0.801449\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−239.967	−	153.173i	−0.152985	−	0.0976519i
$136$		0			0
$137$	2035.18	+	1175.01i	1.26917	+	0.732758i	0.974832	−	0.222942i	$-0.0715660\pi$
$137$	2035.18	+	1175.01i	1.26917	+	0.732758i	0.294342	+	0.955700i	$0.404899\pi$
$138$		0			0
$139$		−	1518.73i		−	0.926740i	−0.886165	−	0.463370i	$-0.846640\pi$
$139$		−	1518.73i		−	0.926740i	0.886165	−	0.463370i	$-0.153360\pi$
$140$		0			0
$141$	−1914.29	+	308.327i	−1.14335	+	0.184155i
$142$		0			0
$143$	375.541	−	650.456i	0.219610	−	0.380377i
$144$		0			0
$145$	−300.258	+	173.354i	−0.171966	+	0.0992847i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	128.269	−	74.0563i	0.0705250	−	0.0407176i	−0.464323	−	0.885666i	$-0.653702\pi$
$149$	128.269	−	74.0563i	0.0705250	−	0.0407176i	0.534848	+	0.844948i	$0.320369\pi$
$150$		0			0
$151$	1246.02	−	2158.17i	0.671522	−	1.16311i	−0.305950	−	0.952048i	$-0.598974\pi$
$151$	1246.02	−	2158.17i	0.671522	−	1.16311i	0.977472	−	0.211063i	$-0.0676926\pi$
$152$		0			0
$153$	−71.7582	+	23.7313i	−0.0379170	+	0.0125396i
$154$		0			0
$155$			52.5774i			0.0272459i
$156$		0			0
$157$	−2561.86	−	1479.09i	−1.30228	−	0.751874i	−0.321489	−	0.946913i	$-0.604183\pi$
$157$	−2561.86	−	1479.09i	−1.30228	−	0.751874i	−0.980795	+	0.195039i	$0.937517\pi$
$158$		0			0
$159$	−2276.87	+	1853.65i	−1.13564	+	0.924554i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	76.2823	+	132.125i	0.0366558	+	0.0634897i	0.883771	−	0.467919i	$-0.154996\pi$
$163$	76.2823	+	132.125i	0.0366558	+	0.0634897i	−0.847115	+	0.531409i	$0.821663\pi$
$164$		0			0
$165$	287.669	+	109.563i	0.135727	+	0.0516939i
$166$		0			0
$167$	1312.37			0.608110			0.304055	−	0.952655i	$-0.401659\pi$
$167$	1312.37			0.608110			0.304055	+	0.952655i	$0.401659\pi$
$168$		0			0
$169$	1535.14			0.698745
$170$		0			0
$171$	2835.91	+	587.304i	1.26823	+	0.262645i
$172$		0			0
$173$	−1296.27	−	2245.20i	−0.569673	−	0.986703i	−0.996598	−	0.0824156i	$-0.973737\pi$
$173$	−1296.27	−	2245.20i	−0.569673	−	0.986703i	0.426925	−	0.904287i	$-0.359597\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1244.28	−	1528.37i	−0.528394	−	0.649034i
$178$		0			0
$179$	−2924.92	−	1688.71i	−1.22134	−	0.705138i	−0.256133	−	0.966642i	$-0.582448\pi$
$179$	−2924.92	−	1688.71i	−1.22134	−	0.705138i	−0.965203	+	0.261503i	$0.915782\pi$
$180$		0			0
$181$		−	1525.85i		−	0.626606i	−0.949653	−	0.313303i	$-0.898564\pi$
$181$		−	1525.85i		−	0.626606i	0.949653	−	0.313303i	$-0.101436\pi$
$182$		0			0
$183$	185.204	+	1149.86i	0.0748122	+	0.464480i
$184$		0			0
$185$	−183.870	+	318.473i	−0.0730725	+	0.126565i
$186$		0			0
$187$	70.7753	−	40.8621i	0.0276770	−	0.0159793i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1311.45	−	757.169i	0.496825	−	0.286842i	−0.230577	−	0.973054i	$-0.574061\pi$
$191$	1311.45	−	757.169i	0.496825	−	0.286842i	0.727401	+	0.686212i	$0.240728\pi$
$192$		0			0
$193$	1487.21	−	2575.93i	0.554674	−	0.960723i	−0.443255	−	0.896395i	$-0.646176\pi$
$193$	1487.21	−	2575.93i	0.554674	−	0.960723i	0.997929	−	0.0643273i	$-0.0204902\pi$
$194$		0			0
$195$	−43.1348	−	267.807i	−0.0158407	−	0.0983490i
$196$		0			0
$197$			2886.30i			1.04386i	0.852989	+	0.521930i	$0.174788\pi$
$197$			2886.30i			1.04386i	−0.852989	+	0.521930i	$0.825212\pi$
$198$		0			0
$199$	−2555.15	−	1475.22i	−0.910200	−	0.525504i	−0.0297042	−	0.999559i	$-0.509457\pi$
$199$	−2555.15	−	1475.22i	−0.910200	−	0.525504i	−0.880495	+	0.474055i	$0.842790\pi$
$200$		0			0
$201$	−1100.71	−	1352.02i	−0.386261	−	0.474450i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−261.108	−	452.252i	−0.0889588	−	0.154081i
$206$		0			0
$207$	−2147.97	−	444.834i	−0.721228	−	0.149363i
$208$		0			0
$209$	−3131.50			−1.03641
$210$		0			0
$211$	760.988			0.248287			0.124144	−	0.992264i	$-0.460382\pi$
$211$	760.988			0.248287			0.124144	+	0.992264i	$0.460382\pi$
$212$		0			0
$213$	4998.38	+	1903.71i	1.60790	+	0.612396i
$214$		0			0
$215$	−243.484	−	421.727i	−0.0772347	−	0.133775i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2353.70	−	1916.21i	0.726249	−	0.591257i
$220$		0			0
$221$	−62.3675	−	36.0079i	−0.0189832	−	0.0109600i
$222$		0			0
$223$			575.704i			0.172879i	0.996257	+	0.0864395i	$0.0275489\pi$
$223$			575.704i			0.172879i	−0.996257	+	0.0864395i	$0.972451\pi$
$224$		0			0
$225$	−3098.76	+	1024.80i	−0.918153	+	0.303645i
$226$		0			0
$227$	1415.12	−	2451.05i	0.413765	−	0.716662i	−0.581533	−	0.813523i	$-0.697547\pi$
$227$	1415.12	−	2451.05i	0.413765	−	0.716662i	0.995298	+	0.0968611i	$0.0308803\pi$
$228$		0			0
$229$	3271.23	−	1888.65i	0.943969	−	0.545001i	0.0527668	−	0.998607i	$-0.483196\pi$
$229$	3271.23	−	1888.65i	0.943969	−	0.545001i	0.891202	+	0.453606i	$0.149863\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4879.34	+	2817.09i	−1.37192	+	0.792076i	−0.991169	−	0.132604i	$-0.957666\pi$
$233$	−4879.34	+	2817.09i	−1.37192	+	0.792076i	−0.380746	+	0.924680i	$0.624333\pi$
$234$		0			0
$235$	378.596	−	655.747i	0.105093	−	0.182027i
$236$		0			0
$237$	−5100.57	+	821.531i	−1.39796	+	0.225165i
$238$		0			0
$239$			6082.58i			1.64623i	0.567873	+	0.823116i	$0.307767\pi$
$239$			6082.58i			1.64623i	−0.567873	+	0.823116i	$0.692233\pi$
$240$		0			0
$241$	−2662.28	−	1537.07i	−0.711587	−	0.410835i	0.100061	−	0.994981i	$-0.468096\pi$
$241$	−2662.28	−	1537.07i	−0.711587	−	0.410835i	−0.811648	+	0.584146i	$0.801429\pi$
$242$		0			0
$243$	−3671.43	−	932.475i	−0.969228	−	0.246166i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1379.75	+	2389.79i	0.355430	+	0.615623i
$248$		0			0
$249$	−2369.51	+	6221.37i	−0.603059	+	1.58339i
$250$		0			0
$251$	−2619.44			−0.658715			−0.329357	−	0.944205i	$-0.606832\pi$
$251$	−2619.44			−0.658715			−0.329357	+	0.944205i	$0.606832\pi$
$252$		0			0
$253$	2371.86			0.589396
$254$		0			0
$255$	10.5052	−	27.5825i	0.00257986	−	0.00677366i
$256$		0			0
$257$	−2128.61	−	3686.86i	−0.516650	−	0.894864i	−0.999813	−	0.0193338i	$-0.993845\pi$
$257$	−2128.61	−	3686.86i	−0.516650	−	0.894864i	0.483163	−	0.875530i	$-0.339488\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3068.90	+	3444.43i	−0.727818	+	0.816876i
$262$		0			0
$263$	−6041.88	−	3488.28i	−1.41657	−	0.817858i	−0.420575	−	0.907258i	$-0.638172\pi$
$263$	−6041.88	−	3488.28i	−1.41657	−	0.817858i	−0.995996	+	0.0894000i	$0.971505\pi$
$264$		0			0
$265$		−	1146.55i		−	0.265782i
$266$		0			0
$267$	−7581.44	+	1221.12i	−1.73774	+	0.279892i
$268$		0			0
$269$	−2334.12	+	4042.81i	−0.529047	+	0.916337i	0.470379	+	0.882465i	$0.344117\pi$
$269$	−2334.12	+	4042.81i	−0.529047	+	0.916337i	−0.999426	+	0.0338722i	$0.989216\pi$
$270$		0			0
$271$	7572.04	−	4371.72i	1.69730	−	0.979938i	0.748998	−	0.662572i	$-0.230535\pi$
$271$	7572.04	−	4371.72i	1.69730	−	0.979938i	0.948303	−	0.317366i	$-0.102798\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3056.32	−	1764.57i	0.670193	−	0.386936i
$276$		0			0
$277$	300.073	−	519.742i	0.0650890	−	0.112737i	−0.831644	−	0.555308i	$-0.812600\pi$
$277$	300.073	−	519.742i	0.0650890	−	0.112737i	0.896733	+	0.442571i	$0.145934\pi$
$278$		0			0
$279$	219.662	+	664.209i	0.0471357	+	0.142528i
$280$		0			0
$281$			4503.57i			0.956087i	0.878336	+	0.478044i	$0.158654\pi$
$281$			4503.57i			0.956087i	−0.878336	+	0.478044i	$0.841346\pi$
$282$		0			0
$283$	−385.112	−	222.345i	−0.0808924	−	0.0467032i	0.459008	−	0.888432i	$-0.348205\pi$
$283$	−385.112	−	222.345i	−0.0808924	−	0.0467032i	−0.539901	+	0.841729i	$0.681538\pi$
$284$		0			0
$285$	−877.060	+	714.036i	−0.182290	+	0.148406i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2452.58	+	4248.00i	0.499203	+	0.864644i
$290$		0			0
$291$	−5967.14	−	2272.68i	−1.20206	−	0.457825i
$292$		0			0
$293$	−6302.01			−1.25654			−0.628272	−	0.777994i	$-0.716237\pi$
$293$	−6302.01			−1.25654			−0.628272	+	0.777994i	$0.716237\pi$
$294$		0			0
$295$	769.635			0.151898
$296$		0			0
$297$	4091.86	+	182.264i	0.799440	+	0.0356095i
$298$		0			0
$299$	−1045.05	−	1810.07i	−0.202129	−	0.350097i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1441.54	−	1770.67i	−0.273315	−	0.335717i
$304$		0			0
$305$	−393.889	−	227.412i	−0.0739476	−	0.0426937i
$306$		0			0
$307$			7530.38i			1.39994i	0.714172	+	0.699970i	$0.246803\pi$
$307$			7530.38i			1.39994i	−0.714172	+	0.699970i	$0.753197\pi$
$308$		0			0
$309$	919.080	+	5706.21i	0.169206	+	1.05053i
$310$		0			0
$311$	4683.11	−	8111.38i	0.853873	−	1.47895i	−0.0238130	−	0.999716i	$-0.507581\pi$
$311$	4683.11	−	8111.38i	0.853873	−	1.47895i	0.877686	−	0.479236i	$-0.159086\pi$
$312$		0			0
$313$	3393.99	−	1959.52i	0.612906	−	0.353861i	−0.161196	−	0.986922i	$-0.551535\pi$
$313$	3393.99	−	1959.52i	0.612906	−	0.353861i	0.774102	+	0.633061i	$0.218202\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−483.723	+	279.278i	−0.0857054	+	0.0494820i	−0.542240	−	0.840224i	$-0.682424\pi$
$317$	−483.723	+	279.278i	−0.0857054	+	0.0494820i	0.456535	+	0.889706i	$0.349090\pi$
$318$		0			0
$319$	2494.14	−	4319.97i	0.437758	−	0.758219i
$320$		0			0
$321$	49.5501	+	307.637i	0.00861563	+	0.0534911i
$322$		0			0
$323$			300.257i			0.0517237i
$324$		0			0
$325$	−2693.25	−	1554.95i	−0.459675	−	0.265393i
$326$		0			0
$327$	785.044	+	964.281i	0.132762	+	0.163073i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−549.892	−	952.441i	−0.0913136	−	0.158160i	0.816751	−	0.576991i	$-0.195773\pi$
$331$	−549.892	−	952.441i	−0.0913136	−	0.158160i	−0.908064	+	0.418831i	$0.862440\pi$
$332$		0			0
$333$	−992.287	+	4791.45i	−0.163294	+	0.788498i
$334$		0			0
$335$	680.835			0.111039
$336$		0			0
$337$	3838.95			0.620537			0.310268	−	0.950649i	$-0.399581\pi$
$337$	3838.95			0.620537			0.310268	+	0.950649i	$0.399581\pi$
$338$		0			0
$339$	8263.72	+	3147.37i	1.32396	+	0.504253i
$340$		0			0
$341$	−378.229	−	655.112i	−0.0600652	−	0.104036i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	664.301	−	540.823i	0.103666	−	0.0843969i
$346$		0			0
$347$	−4113.91	−	2375.17i	−0.636445	−	0.367452i	0.146799	−	0.989166i	$-0.453103\pi$
$347$	−4113.91	−	2375.17i	−0.636445	−	0.367452i	−0.783244	+	0.621715i	$0.786436\pi$
$348$		0			0
$349$		−	9257.25i		−	1.41985i	−0.704275	−	0.709927i	$-0.748728\pi$
$349$		−	9257.25i		−	1.41985i	0.704275	−	0.709927i	$-0.251272\pi$
$350$		0			0
$351$	−1663.79	−	3202.99i	−0.253010	−	0.487074i
$352$		0			0
$353$	−2270.09	+	3931.92i	−0.342280	+	0.592847i	−0.984856	−	0.173376i	$-0.944533\pi$
$353$	−2270.09	+	3931.92i	−0.342280	+	0.592847i	0.642576	+	0.766222i	$0.277866\pi$
$354$		0			0
$355$	−1808.89	+	1044.36i	−0.270439	+	0.156138i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3512.47	−	2027.93i	0.516382	−	0.298133i	−0.219071	−	0.975709i	$-0.570303\pi$
$359$	3512.47	−	2027.93i	0.516382	−	0.298133i	0.735453	+	0.677575i	$0.236969\pi$
$360$		0			0
$361$	2323.12	−	4023.76i	0.338696	−	0.586639i
$362$		0			0
$363$	2455.57	−	395.510i	0.355052	−	0.0571870i
$364$		0			0
$365$			1185.25i			0.169969i
$366$		0			0
$367$	−11844.5	−	6838.44i	−1.68468	−	0.972653i	−0.958474	−	0.285180i	$-0.907947\pi$
$367$	−11844.5	−	6838.44i	−1.68468	−	0.972653i	−0.726210	−	0.687473i	$-0.758720\pi$
$368$		0			0
$369$	−5188.03	−	4622.41i	−0.731918	−	0.652122i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−84.0879	−	145.645i	−0.0116727	−	0.0202177i	0.860130	−	0.510075i	$-0.170382\pi$
$373$	−84.0879	−	145.645i	−0.0116727	−	0.0202177i	−0.871803	+	0.489857i	$0.837049\pi$
$374$		0			0
$375$	922.757	−	2422.79i	0.127069	−	0.333632i
$376$		0			0
$377$	−4395.69			−0.600503
$378$		0			0
$379$	−398.381			−0.0539933			−0.0269966	−	0.999636i	$-0.508594\pi$
$379$	−398.381			−0.0539933			−0.0269966	+	0.999636i	$0.508594\pi$
$380$		0			0
$381$	−3417.84	+	8973.85i	−0.459583	+	1.20668i
$382$		0			0
$383$	1531.44	+	2652.54i	0.204316	+	0.353886i	0.949915	−	0.312510i	$-0.101170\pi$
$383$	1531.44	+	2652.54i	0.204316	+	0.353886i	−0.745599	+	0.666395i	$0.767836\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4837.85	−	4310.42i	−0.635457	−	0.566178i
$388$		0			0
$389$	10631.5	+	6138.08i	1.38570	+	0.800033i	0.992827	−	0.119561i	$-0.0381487\pi$
$389$	10631.5	+	6138.08i	1.38570	+	0.800033i	0.392871	+	0.919594i	$0.371482\pi$
$390$		0			0
$391$		−	227.420i		−	0.0294147i
$392$		0			0
$393$	−1538.34	+	247.776i	−0.197453	+	0.0318031i
$394$		0			0
$395$	1008.76	−	1747.22i	0.128497	−	0.222563i
$396$		0			0
$397$	−6831.34	+	3944.07i	−0.863614	+	0.498608i	−0.865221	−	0.501391i	$-0.832822\pi$
$397$	−6831.34	+	3944.07i	−0.863614	+	0.498608i	0.00160665	+	0.999999i	$0.499489\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4883.77	+	2819.65i	−0.608189	+	0.351138i	−0.772257	−	0.635311i	$-0.780872\pi$
$401$	−4883.77	+	2819.65i	−0.608189	+	0.351138i	0.164067	+	0.986449i	$0.447539\pi$
$402$		0			0
$403$	−333.297	+	577.288i	−0.0411978	+	0.0713567i
$404$		0			0
$405$	1187.59	−	881.965i	0.145708	−	0.108210i
$406$		0			0
$407$		−	5290.87i		−	0.644371i
$408$		0			0
$409$	2342.59	+	1352.49i	0.283212	+	0.163512i	0.634876	−	0.772614i	$-0.281051\pi$
$409$	2342.59	+	1352.49i	0.283212	+	0.163512i	−0.351665	+	0.936126i	$0.614384\pi$
$410$		0			0
$411$	−9469.64	+	7709.46i	−1.13650	+	0.925255i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1299.89	−	2251.48i	−0.153757	−	0.266315i
$416$		0			0
$417$	7374.76	+	2808.80i	0.866052	+	0.329850i
$418$		0			0
$419$	13118.4			1.52953			0.764766	−	0.644309i	$-0.222855\pi$
$419$	13118.4			1.52953			0.764766	+	0.644309i	$0.222855\pi$
$420$		0			0
$421$	5668.08			0.656165			0.328082	−	0.944649i	$-0.393598\pi$
$421$	5668.08			0.656165			0.328082	+	0.944649i	$0.393598\pi$
$422$		0			0
$423$	2043.16	−	9865.77i	0.234850	−	1.13402i
$424$		0			0
$425$	−169.192	−	293.049i	−0.0193106	−	0.0334469i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	2463.99	+	3026.56i	0.277303	+	0.340615i
$430$		0			0
$431$	806.205	+	465.463i	0.0901010	+	0.0520199i	0.544374	−	0.838843i	$-0.316767\pi$
$431$	806.205	+	465.463i	0.0901010	+	0.0520199i	−0.454273	+	0.890863i	$0.650101\pi$
$432$		0			0
$433$		−	10673.2i		−	1.18458i	−0.805725	−	0.592290i	$-0.798224\pi$
$433$		−	10673.2i		−	1.18458i	0.805725	−	0.592290i	$-0.201776\pi$
$434$		0			0
$435$	−286.477	−	1778.63i	−0.0315760	−	0.196043i
$436$		0			0
$437$	−4357.13	+	7546.78i	−0.476956	+	0.826113i
$438$		0			0
$439$	2870.95	−	1657.54i	0.312125	−	0.180206i	−0.335752	−	0.941950i	$-0.608990\pi$
$439$	2870.95	−	1657.54i	0.312125	−	0.180206i	0.647877	+	0.761745i	$0.275657\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3223.65	−	1861.18i	0.345734	−	0.199610i	−0.317071	−	0.948402i	$-0.602699\pi$
$443$	3223.65	−	1861.18i	0.345734	−	0.199610i	0.662805	+	0.748792i	$0.269366\pi$
$444$		0			0
$445$	1499.41	−	2597.06i	0.159728	−	0.276657i
$446$		0			0
$447$	122.382	+	759.823i	0.0129496	+	0.0803991i
$448$		0			0
$449$		−	8582.14i		−	0.902041i	−0.892514	−	0.451021i	$-0.851060\pi$
$449$		−	8582.14i		−	0.902041i	0.892514	−	0.451021i	$-0.148940\pi$
$450$		0			0
$451$	6506.78	+	3756.69i	0.679362	+	0.392230i
$452$		0			0
$453$	8175.39	+	10042.0i	0.847932	+	1.04153i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6516.79	−	11287.4i	−0.667052	−	1.15537i	−0.978725	−	0.205178i	$-0.934223\pi$
$457$	−6516.79	−	11287.4i	−0.667052	−	1.15537i	0.311673	−	0.950189i	$-0.399111\pi$
$458$		0			0
$459$	17.4760	−	392.339i	0.00177714	−	0.0398972i
$460$		0			0
$461$	9125.03			0.921898			0.460949	−	0.887427i	$-0.347509\pi$
$461$	9125.03			0.921898			0.460949	+	0.887427i	$0.347509\pi$
$462$		0			0
$463$	6710.20			0.673541			0.336770	−	0.941587i	$-0.390665\pi$
$463$	6710.20			0.673541			0.336770	+	0.941587i	$0.390665\pi$
$464$		0			0
$465$	−255.310	−	97.2388i	−0.0254617	−	0.00969751i
$466$		0			0
$467$	2451.93	+	4246.87i	0.242959	+	0.420818i	0.961556	−	0.274610i	$-0.0885486\pi$
$467$	2451.93	+	4246.87i	0.242959	+	0.420818i	−0.718597	+	0.695427i	$0.755215\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	11920.3	−	9704.59i	1.16615	−	0.949393i
$472$		0			0
$473$	6067.59	+	3503.13i	0.589827	+	0.340537i
$474$		0			0
$475$			12966.1i			1.25248i
$476$		0			0
$477$	−4790.18	−	14484.4i	−0.459805	−	1.39035i
$478$		0			0
$479$	−704.962	+	1221.03i	−0.0672454	+	0.116472i	−0.897688	−	0.440632i	$-0.854754\pi$
$479$	−704.962	+	1221.03i	−0.0672454	+	0.116472i	0.830442	+	0.557104i	$0.188088\pi$
$480$		0			0
$481$	−4037.71	+	2331.17i	−0.382752	+	0.220982i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2159.48	−	1246.77i	0.202179	−	0.116728i
$486$		0			0
$487$	1007.21	−	1744.54i	0.0937186	−	0.162325i	−0.815355	−	0.578962i	$-0.803458\pi$
$487$	1007.21	−	1744.54i	0.0937186	−	0.162325i	0.909073	+	0.416637i	$0.136791\pi$
$488$		0			0
$489$	−782.662	+	126.061i	−0.0723788	+	0.0116578i
$490$		0			0
$491$		−	13955.7i		−	1.28271i	−0.767243	−	0.641357i	$-0.778372\pi$
$491$		−	13955.7i		−	1.28271i	0.767243	−	0.641357i	$-0.221628\pi$
$492$		0			0
$493$	−414.211	−	239.145i	−0.0378400	−	0.0218469i
$494$		0			0
$495$	−1064.05	+	1194.25i	−0.0966174	+	0.108440i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6464.30	+	11196.5i	0.579923	+	1.00446i	0.995487	+	0.0948930i	$0.0302509\pi$
$499$	6464.30	+	11196.5i	0.579923	+	1.00446i	−0.415564	+	0.909564i	$0.636416\pi$
$500$		0			0
$501$	−2427.15	+	6372.72i	−0.216441	+	0.568287i
$502$		0			0
$503$	13733.1			1.21735			0.608676	−	0.793419i	$-0.291701\pi$
$503$	13733.1			1.21735			0.608676	+	0.793419i	$0.291701\pi$
$504$		0			0
$505$	891.651			0.0785702
$506$		0			0
$507$	−2839.16	+	7454.47i	−0.248701	+	0.652988i
$508$		0			0
$509$	6588.20	+	11411.1i	0.573707	+	0.993690i	0.996181	+	0.0873148i	$0.0278286\pi$
$509$	6588.20	+	11411.1i	0.573707	+	0.993690i	−0.422474	+	0.906375i	$0.638838\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−8096.73	+	12684.7i	−0.696841	+	1.09170i
$514$		0			0
$515$	−1954.69	−	1128.54i	−0.167250	−	0.0965620i
$516$		0			0
$517$			10894.1i			0.926735i
$518$		0			0
$519$	13299.8	−	2142.15i	1.12485	−	0.181176i
$520$		0			0
$521$	2649.64	−	4589.31i	0.222808	−	0.385914i	−0.732852	−	0.680388i	$-0.761811\pi$
$521$	2649.64	−	4589.31i	0.222808	−	0.385914i	0.955659	+	0.294474i	$0.0951445\pi$
$522$		0			0
$523$	3395.81	−	1960.57i	0.283917	−	0.163920i	−0.351278	−	0.936271i	$-0.614253\pi$
$523$	3395.81	−	1960.57i	0.283917	−	0.163920i	0.635195	+	0.772352i	$0.280920\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−62.8140	+	36.2657i	−0.00519207	+	0.00299764i
$528$		0			0
$529$	−2783.33	+	4820.87i	−0.228761	+	0.396225i
$530$		0			0
$531$	9722.79	−	3215.45i	0.794601	−	0.262785i
$532$		0			0
$533$		−	6620.83i		−	0.538048i
$534$		0			0
$535$	−105.383	−	60.8427i	−0.00851605	−	0.00491675i
$536$		0			0
$537$	13609.6	−	11079.9i	1.09367	−	0.890379i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2550.35	+	4417.33i	0.202676	+	0.351046i	0.949390	−	0.314100i	$-0.101703\pi$
$541$	2550.35	+	4417.33i	0.202676	+	0.351046i	−0.746714	+	0.665146i	$0.768369\pi$
$542$		0			0
$543$	7409.35	+	2821.97i	0.585572	+	0.223025i
$544$		0			0
$545$	−485.580			−0.0381651
$546$		0			0
$547$	−23173.5			−1.81138			−0.905691	−	0.423939i	$-0.860647\pi$
$547$	−23173.5			−1.81138			−0.905691	+	0.423939i	$0.860647\pi$
$548$		0			0
$549$	−5926.09	−	1227.27i	−0.460691	−	0.0954070i
$550$		0			0
$551$	9163.53	+	15871.7i	0.708492	+	1.22714i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1206.41	−	1481.85i	−0.0922688	−	0.113335i
$556$		0			0
$557$	18408.7	+	10628.3i	1.40036	+	0.808501i	0.994430	−	0.105402i	$-0.0336129\pi$
$557$	18408.7	+	10628.3i	1.40036	+	0.808501i	0.405934	+	0.913902i	$0.366946\pi$
$558$		0			0
$559$		−	6173.95i		−	0.467138i
$560$		0			0
$561$	67.5269	+	419.248i	0.00508198	+	0.0315520i
$562$		0			0
$563$	−4931.19	+	8541.07i	−0.369138	+	0.639366i	−0.989431	−	0.145004i	$-0.953680\pi$
$563$	−4931.19	+	8541.07i	−0.369138	+	0.639366i	0.620293	+	0.784370i	$0.287014\pi$
$564$		0			0
$565$	−2990.60	+	1726.62i	−0.222682	+	0.128566i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15573.7	+	8991.49i	−1.14742	+	0.662466i	−0.948258	−	0.317500i	$-0.897157\pi$
$569$	−15573.7	+	8991.49i	−1.14742	+	0.662466i	−0.199166	+	0.979966i	$0.563823\pi$
$570$		0			0
$571$	−13285.5	+	23011.2i	−0.973699	+	1.68650i	−0.289537	+	0.957167i	$0.593501\pi$
$571$	−13285.5	+	23011.2i	−0.973699	+	1.68650i	−0.684163	+	0.729330i	$0.739832\pi$
$572$		0			0
$573$	1251.26	+	7768.60i	0.0912255	+	0.566384i
$574$		0			0
$575$		−	9820.79i		−	0.712270i
$576$		0			0
$577$	−3400.09	−	1963.04i	−0.245317	−	0.141634i	0.372301	−	0.928112i	$-0.378569\pi$
$577$	−3400.09	−	1963.04i	−0.245317	−	0.141634i	−0.617618	+	0.786478i	$0.711902\pi$
$578$		0			0
$579$	9757.89	+	11985.8i	0.700387	+	0.860296i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8248.03	+	14286.0i	0.585932	+	1.01486i
$584$		0			0
$585$	1380.21	+	285.836i	0.0975467	+	0.0202015i
$586$		0			0
$587$	−9284.76			−0.652850			−0.326425	−	0.945223i	$-0.605844\pi$
$587$	−9284.76			−0.652850			−0.326425	+	0.945223i	$0.605844\pi$
$588$		0			0
$589$	2779.25			0.194426
$590$		0			0
$591$	−14015.5	−	5338.04i	−0.975502	−	0.371536i
$592$		0			0
$593$	−2701.61	−	4679.32i	−0.187085	−	0.324041i	0.757192	−	0.653193i	$-0.226571\pi$
$593$	−2701.61	−	4679.32i	−0.187085	−	0.324041i	−0.944277	+	0.329151i	$0.893237\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11889.1	−	9679.17i	0.815054	−	0.663555i
$598$		0			0
$599$	−1165.84	−	673.101i	−0.0795244	−	0.0459134i	0.459711	−	0.888069i	$-0.347953\pi$
$599$	−1165.84	−	673.101i	−0.0795244	−	0.0459134i	−0.539235	+	0.842155i	$0.681287\pi$
$600$		0			0
$601$			15011.2i			1.01884i	0.860519	+	0.509418i	$0.170139\pi$
$601$			15011.2i			1.01884i	−0.860519	+	0.509418i	$0.829861\pi$
$602$		0			0
$603$	8600.97	−	2844.45i	0.580860	−	0.192098i
$604$		0			0
$605$	−485.648	+	841.167i	−0.0326354	+	0.0565261i
$606$		0			0
$607$	9270.02	−	5352.05i	0.619866	−	0.357880i	−0.156951	−	0.987606i	$-0.550166\pi$
$607$	9270.02	−	5352.05i	0.619866	−	0.357880i	0.776817	+	0.629727i	$0.216833\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8313.79	−	4799.97i	0.550474	−	0.317817i
$612$		0			0
$613$	−1496.91	+	2592.72i	−0.0986290	+	0.170830i	−0.911117	−	0.412147i	$-0.864779\pi$
$613$	−1496.91	+	2592.72i	−0.0986290	+	0.170830i	0.812488	+	0.582977i	$0.198112\pi$
$614$		0			0
$615$	2678.98	−	431.495i	0.175654	−	0.0282920i
$616$		0			0
$617$		−	15265.5i		−	0.996056i	−0.867161	−	0.498028i	$-0.834058\pi$
$617$		−	15265.5i		−	0.996056i	0.867161	−	0.498028i	$-0.165942\pi$
$618$		0			0
$619$	19456.4	+	11233.2i	1.26336	+	0.729402i	0.973723	−	0.227735i	$-0.0731320\pi$
$619$	19456.4	+	11233.2i	1.26336	+	0.729402i	0.289637	+	0.957136i	$0.406465\pi$
$620$		0			0
$621$	6132.60	−	9607.58i	0.396285	−	0.620836i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7048.94	−	12209.1i	−0.451132	−	0.781383i
$626$		0			0
$627$	5791.53	−	15206.2i	0.368886	−	0.968544i
$628$		0			0
$629$	−507.304			−0.0321582
$630$		0			0
$631$	6614.90			0.417330			0.208665	−	0.977987i	$-0.433088\pi$
$631$	6614.90			0.417330			0.208665	+	0.977987i	$0.433088\pi$
$632$		0			0
$633$	−1407.40	+	3695.27i	−0.0883716	+	0.232028i
$634$		0			0
$635$	−1875.00	−	3247.59i	−0.117176	−	0.202955i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−18488.4	+	20750.7i	−1.14459	+	1.28464i
$640$		0			0
$641$	−10414.2	−	6012.64i	−0.641710	−	0.370492i	0.143563	−	0.989641i	$-0.454144\pi$
$641$	−10414.2	−	6012.64i	−0.641710	−	0.370492i	−0.785273	+	0.619150i	$0.787477\pi$
$642$		0			0
$643$		−	12374.3i		−	0.758936i	−0.925205	−	0.379468i	$-0.876107\pi$
$643$		−	12374.3i		−	0.758936i	0.925205	−	0.379468i	$-0.123893\pi$
$644$		0			0
$645$	2498.16	−	402.371i	0.152504	−	0.0245633i
$646$		0			0
$647$	860.863	−	1491.06i	0.0523091	−	0.0906021i	−0.838685	−	0.544617i	$-0.816675\pi$
$647$	860.863	−	1491.06i	0.0523091	−	0.0906021i	0.890994	+	0.454014i	$0.150009\pi$
$648$		0			0
$649$	−9589.62	+	5536.57i	−0.580008	+	0.334868i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19110.1	−	11033.2i	1.14523	−	0.661201i	0.197513	−	0.980300i	$-0.436714\pi$
$653$	19110.1	−	11033.2i	1.14523	−	0.661201i	0.947721	+	0.319099i	$0.103380\pi$
$654$		0			0
$655$	304.244	−	526.967i	0.0181493	−	0.0314356i
$656$		0			0
$657$	4951.83	+	14973.2i	0.294048	+	0.889134i
$658$		0			0
$659$			2582.20i			0.152638i	0.997083	+	0.0763190i	$0.0243167\pi$
$659$			2582.20i			0.152638i	−0.997083	+	0.0763190i	$0.975683\pi$
$660$		0			0
$661$	8695.88	+	5020.57i	0.511695	+	0.295427i	0.733530	−	0.679657i	$-0.237871\pi$
$661$	8695.88	+	5020.57i	0.511695	+	0.295427i	−0.221835	+	0.975084i	$0.571205\pi$
$662$		0			0
$663$	290.195	−	236.255i	0.0169989	−	0.0138392i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6940.62	−	12021.5i	−0.402911	−	0.697863i
$668$		0			0
$669$	−2795.55	−	1064.73i	−0.161558	−	0.0615319i
$670$		0			0
$671$	6543.78			0.376483
$672$		0			0
$673$	−15931.2			−0.912488			−0.456244	−	0.889855i	$-0.650806\pi$
$673$	−15931.2			−0.912488			−0.456244	+	0.889855i	$0.650806\pi$
$674$		0			0
$675$	754.672	−	16942.5i	0.0430331	−	0.966102i
$676$		0			0
$677$	3485.21	+	6036.57i	0.197855	+	0.342694i	0.947833	−	0.318768i	$-0.103269\pi$
$677$	3485.21	+	6036.57i	0.197855	+	0.342694i	−0.749978	+	0.661463i	$0.769936\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	9284.85	+	11404.7i	0.522461	+	0.641747i
$682$		0			0
$683$	5897.72	+	3405.05i	0.330410	+	0.190762i	0.656023	−	0.754741i	$-0.272237\pi$
$683$	5897.72	+	3405.05i	0.330410	+	0.190762i	−0.325613	+	0.945503i	$0.605571\pi$
$684$		0			0
$685$		−	4768.60i		−	0.265984i
$686$		0			0
$687$	3121.09	+	19377.6i	0.173329	+	1.07613i
$688$		0			0
$689$	7268.21	−	12588.9i	0.401882	−	0.696080i
$690$		0			0
$691$	−10542.5	+	6086.72i	−0.580399	+	0.335094i	−0.761292	−	0.648409i	$-0.775435\pi$
$691$	−10542.5	+	6086.72i	−0.580399	+	0.335094i	0.180893	+	0.983503i	$0.442101\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2668.89	+	1540.88i	−0.145664	+	0.0840993i
$696$		0			0
$697$	360.202	−	623.888i	0.0195748	−	0.0339045i
$698$		0			0
$699$	−4655.39	−	28903.5i	−0.251907	−	1.56399i
$700$		0			0
$701$			31903.7i			1.71895i	0.511176	+	0.859476i	$0.329210\pi$
$701$			31903.7i			1.71895i	−0.511176	+	0.859476i	$0.670790\pi$
$702$		0			0
$703$	16834.5	+	9719.41i	0.903166	+	0.521443i
$704$		0			0
$705$	2484.04	+	3051.18i	0.132701	+	0.162999i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−11558.0	−	20019.0i	−0.612228	−	1.06041i	−0.990864	−	0.134865i	$-0.956940\pi$
$709$	−11558.0	−	20019.0i	−0.612228	−	1.06041i	0.378636	−	0.925546i	$-0.376393\pi$
$710$		0			0
$711$	5443.94	−	26287.1i	0.287150	−	1.38656i
$712$		0			0
$713$	−2105.05			−0.110568
$714$		0			0
$715$	−1524.08			−0.0797164
$716$		0			0
$717$	−29536.3	−	11249.4i	−1.53843	−	0.585935i
$718$		0			0
$719$	−11738.3	−	20331.3i	−0.608852	−	1.05456i	−0.991430	−	0.130639i	$-0.958297\pi$
$719$	−11738.3	−	20331.3i	−0.608852	−	1.05456i	0.382578	−	0.923923i	$-0.375036\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	12387.5	−	10085.0i	0.637203	−	0.518762i
$724$		0			0
$725$	−17887.1	−	10327.1i	−0.916288	−	0.529019i
$726$		0			0
$727$			16192.1i			0.826040i	0.910722	+	0.413020i	$0.135526\pi$
$727$			16192.1i			0.826040i	−0.910722	+	0.413020i	$0.864474\pi$
$728$		0			0
$729$	11318.1	−	16103.5i	0.575018	−	0.818141i
$730$		0			0
$731$	335.890	−	581.778i	0.0169950	−	0.0294362i
$732$		0			0
$733$	−31235.2	+	18033.7i	−1.57394	+	0.908716i	−0.578264	+	0.815850i	$0.696270\pi$
$733$	−31235.2	+	18033.7i	−1.57394	+	0.908716i	−0.995679	+	0.0928663i	$0.970397\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8483.16	+	4897.76i	−0.423991	+	0.244791i
$738$		0			0
$739$	−10083.4	+	17464.9i	−0.501925	+	0.869360i	0.498072	+	0.867136i	$0.334041\pi$
$739$	−10083.4	+	17464.9i	−0.501925	+	0.869360i	−0.999998	+	0.00222472i	$0.999292\pi$
$740$		0			0
$741$	−14156.3	+	2280.11i	−0.701815	+	0.113039i
$742$		0			0
$743$			24217.4i			1.19576i	0.801585	+	0.597881i	$0.203991\pi$
$743$			24217.4i			1.19576i	−0.801585	+	0.597881i	$0.796009\pi$
$744$		0			0
$745$	−260.281	−	150.273i	−0.0127999	−	0.00739005i
$746$		0			0
$747$	−25828.0	−	23012.1i	−1.26505	−	1.12713i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	3037.56	+	5261.20i	0.147592	+	0.255638i	0.930337	−	0.366705i	$-0.119514\pi$
$751$	3037.56	+	5261.20i	0.147592	+	0.255638i	−0.782745	+	0.622343i	$0.786181\pi$
$752$		0			0
$753$	4844.50	−	12719.7i	0.234453	−	0.615579i
$754$		0			0
$755$	−5056.80			−0.243756
$756$		0			0
$757$	−34408.2			−1.65203			−0.826015	−	0.563648i	$-0.809397\pi$
$757$	−34408.2			−1.65203			−0.826015	+	0.563648i	$0.809397\pi$
$758$		0			0
$759$	−4386.61	+	11517.4i	−0.209781	+	0.550799i
$760$		0			0
$761$	−7900.11	−	13683.4i	−0.376319	−	0.651804i	0.614204	−	0.789147i	$-0.289477\pi$
$761$	−7900.11	−	13683.4i	−0.376319	−	0.651804i	−0.990524	+	0.137343i	$0.956144\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	114.508	+	102.024i	0.00541184	+	0.00482183i
$766$		0			0
$767$	8450.42	+	4878.85i	0.397819	+	0.229681i
$768$		0			0
$769$		−	35637.1i		−	1.67114i	−0.549383	−	0.835571i	$-0.685137\pi$
$769$		−	35637.1i		−	1.67114i	0.549383	−	0.835571i	$-0.314863\pi$
$770$		0			0
$771$	21839.7	−	3517.65i	1.02015	−	0.164312i
$772$		0			0
$773$	−8586.42	+	14872.1i	−0.399524	+	0.691996i	−0.993667	−	0.112364i	$-0.964158\pi$
$773$	−8586.42	+	14872.1i	−0.399524	+	0.691996i	0.594143	+	0.804359i	$0.297491\pi$
$774$		0			0
$775$	−2712.52	+	1566.08i	−0.125725	+	0.0725873i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−23906.1	+	13802.2i	−1.09952	+	0.634807i
$780$		0			0
$781$	15025.8	−	26025.4i	0.688430	−	1.19240i
$782$		0			0
$783$	−11050.0	−	21272.5i	−0.504334	−	0.970903i
$784$		0			0
$785$			6002.67i			0.272923i
$786$		0			0
$787$	9242.80	+	5336.33i	0.418641	+	0.241702i	0.694496	−	0.719497i	$-0.255628\pi$
$787$	9242.80	+	5336.33i	0.418641	+	0.241702i	−0.275855	+	0.961199i	$0.588961\pi$
$788$		0			0
$789$	28112.8	−	22887.3i	1.26849	−	1.03271i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2883.20	−	4993.86i	−0.129112	−	0.223628i
$794$		0			0
$795$	5567.53	+	2120.49i	0.248377	+	0.0945986i
$796$		0			0
$797$	−30569.6			−1.35863			−0.679317	−	0.733845i	$-0.737724\pi$
$797$	−30569.6			−1.35863			−0.679317	+	0.733845i	$0.737724\pi$
$798$		0			0
$799$	1044.56			0.0462500
$800$		0			0
$801$	8091.83	−	39072.9i	0.356942	−	1.72356i
$802$		0			0
$803$	−8526.38	−	14768.1i	−0.374707	−	0.649011i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−15314.6	−	18811.1i	−0.668029	−	0.820550i
$808$		0			0
$809$	−18066.6	−	10430.7i	−0.785150	−	0.453307i	0.0531022	−	0.998589i	$-0.483089\pi$
$809$	−18066.6	−	10430.7i	−0.785150	−	0.453307i	−0.838252	+	0.545282i	$0.816422\pi$
$810$		0			0
$811$		−	1052.96i		−	0.0455911i	−0.999740	−	0.0227956i	$-0.992743\pi$
$811$		−	1052.96i		−	0.0455911i	0.999740	−	0.0227956i	$-0.00725668\pi$
$812$		0			0
$813$	7224.51	+	44854.2i	0.311654	+	1.93494i
$814$		0			0
$815$	154.790	−	268.105i	0.00665284	−	0.0115231i
$816$		0			0
$817$	−22292.5	+	12870.6i	−0.954610	+	0.551144i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	29358.8	−	16950.3i	1.24803	−	0.720548i	0.277310	−	0.960780i	$-0.410557\pi$
$821$	29358.8	−	16950.3i	1.24803	−	0.720548i	0.970715	+	0.240233i	$0.0772237\pi$
$822$		0			0
$823$	−11801.0	+	20439.9i	−0.499826	+	0.865725i	−1.00000		0.000200564i	$-0.999936\pi$
$823$	−11801.0	+	20439.9i	−0.499826	+	0.865725i	0.500174	+	0.865925i	$0.333269\pi$
$824$		0			0
$825$	2916.04	+	18104.6i	0.123059	+	0.764025i
$826$		0			0
$827$			26002.1i			1.09333i	0.837353	+	0.546663i	$0.184102\pi$
$827$			26002.1i			1.09333i	−0.837353	+	0.546663i	$0.815898\pi$
$828$		0			0
$829$	18600.2	+	10738.8i	0.779266	+	0.449910i	0.836170	−	0.548470i	$-0.184790\pi$
$829$	18600.2	+	10738.8i	0.779266	+	0.449910i	−0.0569040	+	0.998380i	$0.518123\pi$
$830$		0			0
$831$	1968.84	+	2418.35i	0.0821880	+	0.100953i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1331.52	−	2306.25i	−0.0551844	−	0.0955822i
$836$		0			0
$837$	−3631.57	−	161.761i	−0.149971	−	0.00668016i
$838$		0			0
$839$	−26619.1			−1.09534			−0.547671	−	0.836694i	$-0.684485\pi$
$839$	−26619.1			−1.09534			−0.547671	+	0.836694i	$0.684485\pi$
$840$		0			0
$841$	−4804.75			−0.197005
$842$		0			0
$843$	−21868.8	−	8329.09i	−0.893477	−	0.340295i
$844$		0			0
$845$	−1557.54	−	2697.73i	−0.0634094	−	0.109828i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1791.92	−	1458.85i	0.0724365	−	0.0589723i
$850$		0			0
$851$	−12750.8	−	7361.65i	−0.513620	−	0.296538i
$852$		0			0
$853$			10440.3i			0.419075i	0.977801	+	0.209537i	$0.0671958\pi$
$853$			10440.3i			0.419075i	−0.977801	+	0.209537i	$0.932804\pi$
$854$		0			0
$855$	−1845.20	−	5579.47i	−0.0738065	−	0.223174i
$856$		0			0
$857$	13344.9	−	23114.1i	0.531918	−	0.921310i	−0.467387	−	0.884053i	$-0.654805\pi$
$857$	13344.9	−	23114.1i	0.531918	−	0.921310i	0.999306	−	0.0372570i	$-0.0118620\pi$
$858$		0			0
$859$	15540.5	−	8972.31i	0.617270	−	0.356381i	−0.158535	−	0.987353i	$-0.550677\pi$
$859$	15540.5	−	8972.31i	0.617270	−	0.356381i	0.775805	+	0.630972i	$0.217344\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8043.37	+	4643.84i	−0.317265	+	0.183173i	−0.650173	−	0.759786i	$-0.725304\pi$
$863$	−8043.37	+	4643.84i	−0.317265	+	0.183173i	0.332908	+	0.942959i	$0.391970\pi$
$864$		0			0
$865$	−2630.36	+	4555.91i	−0.103393	+	0.179082i
$866$		0			0
$867$	−25163.7	+	4053.03i	−0.985701	+	0.158764i
$868$		0			0
$869$			29027.1i			1.13311i
$870$		0			0
$871$	7475.40	+	4315.93i	0.290809	+	0.167898i
$872$		0			0
$873$	22071.8	−	24772.5i	0.855688	−	0.960393i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1716.56	+	2973.16i	0.0660935	+	0.114477i	0.897179	−	0.441668i	$-0.145613\pi$
$877$	1716.56	+	2973.16i	0.0660935	+	0.114477i	−0.831085	+	0.556145i	$0.812280\pi$
$878$		0			0
$879$	11655.2	−	30601.8i	0.447235	−	1.17426i
$880$		0			0
$881$	30222.9			1.15577			0.577885	−	0.816118i	$-0.303878\pi$
$881$	30222.9			1.15577			0.577885	+	0.816118i	$0.303878\pi$
$882$		0			0
$883$	−8445.55			−0.321875			−0.160937	−	0.986965i	$-0.551452\pi$
$883$	−8445.55			−0.321875			−0.160937	+	0.986965i	$0.551452\pi$
$884$		0			0
$885$	−1423.39	+	3737.26i	−0.0540643	+	0.141951i
$886$		0			0
$887$	−3758.68	−	6510.22i	−0.142282	−	0.246439i	0.786074	−	0.618133i	$-0.212111\pi$
$887$	−3758.68	−	6510.22i	−0.142282	−	0.246439i	−0.928356	+	0.371693i	$0.878777\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−8452.70	+	19532.5i	−0.317818	+	0.734414i
$892$		0			0
$893$	−34662.9	−	20012.6i	−1.29894	−	0.749941i
$894$		0			0
$895$			6853.36i			0.255958i
$896$		0			0
$897$	10722.2	−	1726.99i	0.399114	−	0.0642839i
$898$		0			0
$899$	−2213.58	+	3834.03i	−0.0821212	+	0.142238i
$900$		0			0
$901$	1369.78	−	790.845i	0.0506483	−	0.0292418i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2681.41	+	1548.11i	−0.0984894	+	0.0568629i
$906$		0			0
$907$	−4833.51	+	8371.88i	−0.176950	+	0.306487i	−0.940834	−	0.338866i	$-0.889957\pi$
$907$	−4833.51	+	8371.88i	−0.176950	+	0.306487i	0.763884	+	0.645353i	$0.223290\pi$
$908$		0			0
$909$	11264.2	−	3725.21i	0.411012	−	0.135927i
$910$		0			0
$911$			13633.2i			0.495815i	0.968784	+	0.247908i	$0.0797429\pi$
$911$			13633.2i			0.495815i	−0.968784	+	0.247908i	$0.920257\pi$
$912$		0			0
$913$	32393.2	+	18702.2i	1.17422	+	0.677934i
$914$		0			0
$915$	1832.76	−	1492.09i	0.0662176	−	0.0539093i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	15801.4	+	27368.9i	0.567183	+	0.982389i	0.996843	+	0.0793984i	$0.0252999\pi$
$919$	15801.4	+	27368.9i	0.567183	+	0.982389i	−0.429660	+	0.902991i	$0.641367\pi$
$920$		0			0
$921$	−36566.6	−	13927.0i	−1.30826	−	0.498274i
$922$		0			0
$923$	−26481.5			−0.944367
$924$		0			0
$925$	−21907.1			−0.778705
$926$		0			0
$927$	−29408.5	−	6090.36i	−1.04196	−	0.215786i
$928$		0			0
$929$	−15455.3	−	26769.3i	−0.545825	−	0.945396i	−0.998555	−	0.0537486i	$-0.982883\pi$
$929$	−15455.3	−	26769.3i	−0.545825	−	0.945396i	0.452730	−	0.891648i	$-0.350450\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	30726.8	+	37742.1i	1.07819	+	1.32435i
$934$		0			0
$935$	−143.615	−	82.9164i	−0.00502324	−	0.00290017i
$936$		0			0
$937$			12018.0i			0.419010i	0.977808	+	0.209505i	$0.0671852\pi$
$937$			12018.0i			0.419010i	−0.977808	+	0.209505i	$0.932815\pi$
$938$		0			0
$939$	3238.21	+	20104.8i	0.112540	+	0.698718i
$940$		0			0
$941$	11957.3	−	20710.7i	0.414237	−	0.717479i	−0.581111	−	0.813824i	$-0.697382\pi$
$941$	11957.3	−	20710.7i	0.414237	−	0.717479i	0.995348	+	0.0963449i	$0.0307152\pi$
$942$		0			0
$943$	18106.9	−	10454.0i	0.625283	−	0.361007i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15175.1	+	8761.35i	−0.520723	+	0.300640i	−0.737230	−	0.675641i	$-0.763867\pi$
$947$	−15175.1	+	8761.35i	−0.520723	+	0.300640i	0.216507	+	0.976281i	$0.430533\pi$
$948$		0			0
$949$	−7513.49	+	13013.7i	−0.257005	+	0.445147i
$950$		0			0
$951$	−461.522	−	2865.41i	−0.0157370	−	0.0977048i
$952$		0			0
$953$		−	30378.0i		−	1.03257i	−0.856417	−	0.516285i	$-0.827314\pi$
$953$		−	30378.0i		−	1.03257i	0.856417	−	0.516285i	$-0.172686\pi$
$954$		0			0
$955$	−2661.17	−	1536.43i	−0.0901712	−	0.0520604i
$956$		0			0
$957$	16364.5	+	20100.8i	0.552758	+	0.678960i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14559.8	−	25218.3i	−0.488732	−	0.846509i
$962$		0			0
$963$	−1585.49	−	328.348i	−0.0530547	−	0.0109874i
$964$		0			0
$965$	−6035.64			−0.201341
$966$		0			0
$967$	−39792.1			−1.32330			−0.661648	−	0.749814i	$-0.730143\pi$
$967$	−39792.1			−1.32330			−0.661648	+	0.749814i	$0.730143\pi$
$968$		0			0
$969$	−1458.01	−	555.308i	−0.0483366	−	0.0184098i
$970$		0			0
$971$	7925.17	+	13726.8i	0.261927	+	0.453670i	0.966754	−	0.255709i	$-0.0823088\pi$
$971$	7925.17	+	13726.8i	0.261927	+	0.453670i	−0.704827	+	0.709379i	$0.748976\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	12531.6	−	10202.3i	0.411624	−	0.335113i
$976$		0			0
$977$	14545.6	+	8397.90i	0.476310	+	0.274998i	0.718877	−	0.695137i	$-0.244656\pi$
$977$	14545.6	+	8397.90i	0.476310	+	0.274998i	−0.242568	+	0.970135i	$0.577990\pi$
$978$		0			0
$979$			43145.6i			1.40852i
$980$		0			0
$981$	−6134.33	+	2028.70i	−0.199647	+	0.0660259i
$982$		0			0
$983$	−7308.50	+	12658.7i	−0.237136	+	0.410732i	−0.959891	−	0.280372i	$-0.909542\pi$
$983$	−7308.50	+	12658.7i	−0.237136	+	0.410732i	0.722755	+	0.691104i	$0.242875\pi$
$984$		0			0
$985$	5072.14	−	2928.40i	0.164073	−	0.0947276i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	16884.7	−	9748.41i	0.542875	−	0.313429i
$990$		0			0
$991$	−24857.9	+	43055.2i	−0.796809	+	1.38011i	0.124875	+	0.992172i	$0.460147\pi$
$991$	−24857.9	+	43055.2i	−0.796809	+	1.38011i	−0.921684	+	0.387941i	$0.873186\pi$
$992$		0			0
$993$	5641.93	−	908.727i	0.180303	−	0.0290409i
$994$		0			0
$995$			5986.94i			0.190753i
$996$		0			0
$997$	−23841.9	−	13765.2i	−0.757354	−	0.437259i	0.0709909	−	0.997477i	$-0.477384\pi$
$997$	−23841.9	−	13765.2i	−0.757354	−	0.437259i	−0.828345	+	0.560218i	$0.810717\pi$
$998$		0			0
$999$	−21431.5	−	13679.9i	−0.678742	−	0.433247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.e.521.11		48
3.2	odd	2	inner	588.4.k.e.521.18		48
7.2	even	3	inner	588.4.k.e.509.7		48
7.3	odd	6		588.4.f.d.293.2	yes	24
7.4	even	3		588.4.f.d.293.23	yes	24
7.5	odd	6	inner	588.4.k.e.509.18		48
7.6	odd	2	inner	588.4.k.e.521.14		48
21.2	odd	6	inner	588.4.k.e.509.14		48
21.5	even	6	inner	588.4.k.e.509.11		48
21.11	odd	6		588.4.f.d.293.1	✓	24
21.17	even	6		588.4.f.d.293.24	yes	24
21.20	even	2	inner	588.4.k.e.521.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.f.d.293.1	✓	24	21.11	odd	6
588.4.f.d.293.2	yes	24	7.3	odd	6
588.4.f.d.293.23	yes	24	7.4	even	3
588.4.f.d.293.24	yes	24	21.17	even	6
588.4.k.e.509.7		48	7.2	even	3	inner
588.4.k.e.509.11		48	21.5	even	6	inner
588.4.k.e.509.14		48	21.2	odd	6	inner
588.4.k.e.509.18		48	7.5	odd	6	inner
588.4.k.e.521.7		48	21.20	even	2	inner
588.4.k.e.521.11		48	1.1	even	1	trivial
588.4.k.e.521.14		48	7.6	odd	2	inner
588.4.k.e.521.18		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)

\(f(q)\)	\(=\)	\(q+(-1.84944 + 4.85588i) q^{3} +(-1.01459 - 1.75732i) q^{5} +(-20.1591 - 17.9613i) q^{9} +O(q^{10})\)	\(q+(-1.84944 + 4.85588i) q^{3} +(-1.01459 - 1.75732i) q^{5} +(-20.1591 - 17.9613i) q^{9} +(25.2834 + 14.5974i) q^{11} -25.7266i q^{13} +(10.4097 - 1.67666i) q^{15} +(1.39964 - 2.42425i) q^{17} +(-92.8920 + 53.6312i) q^{19} +(70.3580 - 40.6212i) q^{23} +(60.4412 - 104.687i) q^{25} +(124.501 - 64.6720i) q^{27} -170.862i q^{29} +(-22.4394 - 12.9554i) q^{31} +(-117.643 + 95.7762i) q^{33} +(-90.6133 - 156.947i) q^{37} +(124.925 + 47.5798i) q^{39} +257.354 q^{41} +239.983 q^{43} +(-11.1105 + 53.6493i) q^{45} +(186.576 + 323.160i) q^{47} +(9.18329 + 11.2800i) q^{51} +(489.335 + 282.517i) q^{53} -59.2413i q^{55} +(-88.6285 - 550.260i) q^{57} +(-189.642 + 328.470i) q^{59} +(194.113 - 112.071i) q^{61} +(-45.2098 + 26.1019i) q^{65} +(-167.761 + 290.571i) q^{67} +(67.1288 + 416.777i) q^{69} -1029.35i q^{71} +(-505.848 - 292.052i) q^{73} +(396.566 + 487.108i) q^{75} +(497.128 + 861.051i) q^{79} +(83.7817 + 724.170i) q^{81} +1281.20 q^{83} -5.68022 q^{85} +(829.684 + 315.999i) q^{87} +(738.927 + 1279.86i) q^{89} +(104.410 - 85.0026i) q^{93} +(188.494 + 108.827i) q^{95} +1228.85i q^{97} +(-247.504 - 748.394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 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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