LMFDB - Embedded newform 588.4.k.e.521.7

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			521.7
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.28059 + 4.02960i) q^{3} +(-1.01459 - 1.75732i) q^{5} +(-5.47539 - 26.4390i) q^{9} +O(q^{10})$	\(q+(-3.28059 + 4.02960i) q^{3} +(-1.01459 - 1.75732i) q^{5} +(-5.47539 - 26.4390i) q^{9} +(-25.2834 - 14.5974i) q^{11} +25.7266i q^{13} +(10.4097 + 1.67666i) q^{15} +(1.39964 - 2.42425i) q^{17} +(92.8920 - 53.6312i) q^{19} +(-70.3580 + 40.6212i) q^{23} +(60.4412 - 104.687i) q^{25} +(124.501 + 64.6720i) q^{27} +170.862i q^{29} +(22.4394 + 12.9554i) q^{31} +(141.766 - 53.9940i) q^{33} +(-90.6133 - 156.947i) q^{37} +(-103.668 - 84.3985i) q^{39} +257.354 q^{41} +239.983 q^{43} +(-40.9064 + 36.4467i) q^{45} +(186.576 + 323.160i) q^{47} +(5.17710 + 13.5930i) q^{51} +(-489.335 - 282.517i) q^{53} +59.2413i q^{55} +(-88.6285 + 550.260i) q^{57} +(-189.642 + 328.470i) q^{59} +(-194.113 + 112.071i) q^{61} +(45.2098 - 26.1019i) q^{65} +(-167.761 + 290.571i) q^{67} +(67.1288 - 416.777i) q^{69} +1029.35i q^{71} +(505.848 + 292.052i) q^{73} +(223.565 + 586.991i) q^{75} +(497.128 + 861.051i) q^{79} +(-669.040 + 289.528i) q^{81} +1281.20 q^{83} -5.68022 q^{85} +(-688.505 - 560.528i) q^{87} +(738.927 + 1279.86i) q^{89} +(-125.819 + 47.9204i) q^{93} +(-188.494 - 108.827i) q^{95} -1228.85i q^{97} +(-247.504 + 748.394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.28059	+	4.02960i	−0.631351	+	0.775497i
$3$	−3.28059	+	4.02960i	−0.631351	+	0.775497i
$4$		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
$9$	−5.47539	−	26.4390i	−0.202792	−	0.979222i
$10$		0			0
$11$	−25.2834	−	14.5974i	−0.693022	−	0.400116i	0.111721	−	0.993740i	$-0.464364\pi$
$11$	−25.2834	−	14.5974i	−0.693022	−	0.400116i	−0.804743	+	0.593623i	$0.797697\pi$
$12$		0			0
$13$			25.7266i			0.548867i	0.961606	+	0.274433i	$0.0884903\pi$
$13$			25.7266i			0.548867i	−0.961606	+	0.274433i	$0.911510\pi$
$14$		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	0.179810	−	0.983701i	$-0.442452\pi$
$19$	92.8920	−	53.6312i	1.12163	−	0.647571i	0.941815	+	0.336130i	$0.109118\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−70.3580	+	40.6212i	−0.637855	+	0.368266i	−0.783788	−	0.621029i	$-0.786715\pi$
$23$	−70.3580	+	40.6212i	−0.637855	+	0.368266i	0.145933	+	0.989295i	$0.453382\pi$
$24$		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	$0.184245\pi$
$29$			170.862i			1.09408i	−0.837107	+	0.547039i	$0.815755\pi$
$30$		0			0
$31$	22.4394	+	12.9554i	0.130007	+	0.0750598i	0.563593	−	0.826052i	$-0.309419\pi$
$31$	22.4394	+	12.9554i	0.130007	+	0.0750598i	−0.433586	+	0.901112i	$0.642752\pi$
$32$		0			0
$33$	141.766	−	53.9940i	0.747829	−	0.284823i
$34$		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
$39$	−103.668	−	84.3985i	−0.425645	−	0.346528i
$40$		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
$45$	−40.9064	+	36.4467i	−0.135510	+	0.120737i
$46$		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
$51$	5.17710	+	13.5930i	0.0142145	+	0.0373215i
$52$		0			0
$53$	−489.335	−	282.517i	−1.26821	−	0.732203i	−0.293563	−	0.955940i	$-0.594841\pi$
$53$	−489.335	−	282.517i	−1.26821	−	0.732203i	−0.974650	+	0.223737i	$0.928174\pi$
$54$		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	−0.689687	−	0.724107i	$-0.742252\pi$
$61$	−194.113	+	112.071i	−0.407436	+	0.235233i	0.282251	+	0.959340i	$0.408919\pi$
$62$		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	$0.329716\pi$
$71$			1029.35i			1.72057i	−0.509809	+	0.860287i	$0.670284\pi$
$72$		0			0
$73$	505.848	+	292.052i	0.811028	+	0.468247i	0.847313	−	0.531094i	$-0.178219\pi$
$73$	505.848	+	292.052i	0.811028	+	0.468247i	−0.0362846	+	0.999341i	$0.511552\pi$
$74$		0			0
$75$	223.565	+	586.991i	0.344201	+	0.903731i
$76$		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
$81$	−669.040	+	289.528i	−0.917751	+	0.397157i
$82$		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
$87$	−688.505	−	560.528i	−0.848454	−	0.690746i
$88$		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
$93$	−125.819	+	47.9204i	−0.140289	+	0.0534313i
$94$		0			0
$95$	−188.494	−	108.827i	−0.203569	−	0.117531i
$96$		0			0
$97$		−	1228.85i		−	1.28630i	−0.765742	−	0.643148i	$-0.777628\pi$
$97$		−	1228.85i		−	1.28630i	0.765742	−	0.643148i	$-0.222372\pi$
$98$		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	−0.884118	−	0.467264i	$-0.845240\pi$
$103$	−963.292	+	556.157i	−0.921514	+	0.532037i	−0.0373965	+	0.999301i	$0.511906\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−51.9337	+	29.9839i	−0.0469217	+	0.0270903i	−0.523277	−	0.852162i	$-0.675291\pi$
$107$	−51.9337	+	29.9839i	−0.0469217	+	0.0270903i	0.476356	+	0.879253i	$0.341957\pi$
$108$		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	$0.250569\pi$
$113$			1701.80i			1.41674i	−0.705841	+	0.708370i	$0.749431\pi$
$114$		0			0
$115$	142.769	+	82.4276i	0.115767	+	0.0668384i
$116$		0			0
$117$	680.185	−	140.863i	0.537462	−	0.111306i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−239.333	−	414.536i	−0.179814	−	0.311447i
$122$		0			0
$123$	−844.273	+	1037.03i	−0.618907	+	0.760212i
$124$		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
$129$	−787.288	+	967.037i	−0.537340	+	0.660022i
$130$		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
$135$	−12.6682	−	284.403i	−0.00807633	−	0.181315i
$136$		0			0
$137$	−2035.18	−	1175.01i	−1.26917	−	0.732758i	−0.294342	−	0.955700i	$-0.595101\pi$
$137$	−2035.18	−	1175.01i	−1.26917	−	0.732758i	−0.974832	+	0.222942i	$0.928434\pi$
$138$		0			0
$139$			1518.73i			0.926740i	0.886165	+	0.463370i	$0.153360\pi$
$139$			1518.73i			0.926740i	−0.886165	+	0.463370i	$0.846640\pi$
$140$		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	−0.534848	−	0.844948i	$-0.679631\pi$
$149$	−128.269	+	74.0563i	−0.0705250	+	0.0407176i	0.464323	+	0.885666i	$0.346298\pi$
$150$		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	0.980795	−	0.195039i	$-0.0624834\pi$
$157$	2561.86	+	1479.09i	1.30228	+	0.751874i	0.321489	+	0.946913i	$0.395817\pi$
$158$		0			0
$159$	2743.74	−	1045.00i	1.36851	−	0.521219i
$160$		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
$165$	−238.719	−	194.347i	−0.112632	−	0.0916962i
$166$		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
$171$	−1926.58	−	2162.32i	−0.861573	−	0.966998i
$172$		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
$177$	−701.465	−	1841.76i	−0.297883	−	0.782120i
$178$		0			0
$179$	2924.92	+	1688.71i	1.22134	+	0.705138i	0.965203	−	0.261503i	$-0.0842183\pi$
$179$	2924.92	+	1688.71i	1.22134	+	0.705138i	0.256133	+	0.966642i	$0.417552\pi$
$180$		0			0
$181$			1525.85i			0.626606i	0.949653	+	0.313303i	$0.101436\pi$
$181$			1525.85i			0.626606i	−0.949653	+	0.313303i	$0.898564\pi$
$182$		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	−0.727401	−	0.686212i	$-0.759272\pi$
$191$	−1311.45	+	757.169i	−0.496825	+	0.286842i	0.230577	+	0.973054i	$0.425939\pi$
$192$		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	$-0.825212\pi$
$197$		−	2886.30i		−	1.04386i	0.852989	−	0.521930i	$-0.174788\pi$
$198$		0			0
$199$	2555.15	+	1475.22i	0.910200	+	0.525504i	0.880495	−	0.474055i	$-0.157210\pi$
$199$	2555.15	+	1475.22i	0.910200	+	0.525504i	0.0297042	+	0.999559i	$0.490543\pi$
$200$		0			0
$201$	−620.530	−	1629.26i	−0.217755	−	0.571736i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−261.108	−	452.252i	−0.0889588	−	0.154081i
$206$		0			0
$207$	1459.22	+	1637.78i	0.489966	+	0.549920i
$208$		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
$213$	−4147.85	−	3376.87i	−1.33430	−	1.08629i
$214$		0			0
$215$	−243.484	−	421.727i	−0.0772347	−	0.133775i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−2836.34	+	1080.26i	−0.875168	+	0.333322i
$220$		0			0
$221$	62.3675	+	36.0079i	0.0189832	+	0.0109600i
$222$		0			0
$223$		−	575.704i		−	0.172879i	−0.996257	−	0.0864395i	$-0.972451\pi$
$223$		−	575.704i		−	0.172879i	0.996257	−	0.0864395i	$-0.0275489\pi$
$224$		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	−0.891202	−	0.453606i	$-0.850137\pi$
$229$	−3271.23	+	1888.65i	−0.943969	+	0.545001i	−0.0527668	+	0.998607i	$0.516804\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4879.34	−	2817.09i	1.37192	−	0.792076i	0.380746	−	0.924680i	$-0.375667\pi$
$233$	4879.34	−	2817.09i	1.37192	−	0.792076i	0.991169	+	0.132604i	$0.0423338\pi$
$234$		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	$-0.692233\pi$
$239$		−	6082.58i		−	1.64623i	0.567873	−	0.823116i	$-0.307767\pi$
$240$		0			0
$241$	2662.28	+	1537.07i	0.711587	+	0.410835i	0.811648	−	0.584146i	$-0.198571\pi$
$241$	2662.28	+	1537.07i	0.711587	+	0.410835i	−0.100061	+	0.994981i	$0.531904\pi$
$242$		0			0
$243$	1028.17	−	3645.79i	0.271428	−	0.962459i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1379.75	+	2389.79i	0.355430	+	0.615623i
$248$		0			0
$249$	−4203.11	+	5162.74i	−1.06972	+	1.31396i
$250$		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
$255$	18.6345	−	22.8890i	0.00457623	−	0.00562105i
$256$		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
$261$	4517.41	−	935.535i	1.07134	−	0.221870i
$262$		0			0
$263$	6041.88	+	3488.28i	1.41657	+	0.817858i	0.995996	−	0.0894000i	$-0.0284950\pi$
$263$	6041.88	+	3488.28i	1.41657	+	0.817858i	0.420575	+	0.907258i	$0.361828\pi$
$264$		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	$0.769465\pi$
$271$	−7572.04	+	4371.72i	−1.69730	+	0.979938i	−0.948303	+	0.317366i	$0.897202\pi$
$272$		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	$-0.841346\pi$
$281$		−	4503.57i		−	0.956087i	0.878336	−	0.478044i	$-0.158654\pi$
$282$		0			0
$283$	385.112	+	222.345i	0.0808924	+	0.0467032i	0.539901	−	0.841729i	$-0.318462\pi$
$283$	385.112	+	222.345i	0.0808924	+	0.0467032i	−0.459008	+	0.888432i	$0.651795\pi$
$284$		0			0
$285$	1056.90	−	402.539i	0.219669	−	0.0836643i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2452.58	+	4248.00i	0.499203	+	0.864644i
$290$		0			0
$291$	4951.77	+	4031.36i	0.997519	+	0.812104i
$292$		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
$297$	−2203.77	−	3452.52i	−0.430559	−	0.674530i
$298$		0			0
$299$	−1045.05	−	1810.07i	−0.202129	−	0.350097i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−812.672	−	2133.75i	−0.154082	−	0.404556i
$304$		0			0
$305$	393.889	+	227.412i	0.0739476	+	0.0426937i
$306$		0			0
$307$		−	7530.38i		−	1.39994i	−0.714172	−	0.699970i	$-0.753197\pi$
$307$		−	7530.38i		−	1.39994i	0.714172	−	0.699970i	$-0.246803\pi$
$308$		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	−0.774102	−	0.633061i	$-0.781798\pi$
$313$	−3393.99	+	1959.52i	−0.612906	+	0.353861i	0.161196	+	0.986922i	$0.448465\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	483.723	−	279.278i	0.0857054	−	0.0494820i	−0.456535	−	0.889706i	$-0.650910\pi$
$317$	483.723	−	279.278i	0.0857054	−	0.0494820i	0.542240	+	0.840224i	$0.317576\pi$
$318$		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
$327$	442.570	+	1162.01i	0.0748446	+	0.196511i
$328$		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
$333$	−3653.37	+	3255.07i	−0.601212	+	0.535666i
$334$		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
$339$	−6857.57	−	5582.91i	−1.09868	−	0.894460i
$340$		0			0
$341$	−378.229	−	655.112i	−0.0600652	−	0.104036i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−800.517	+	304.890i	−0.124923	+	0.0475789i
$346$		0			0
$347$	4113.91	+	2375.17i	0.636445	+	0.367452i	0.783244	−	0.621715i	$-0.213564\pi$
$347$	4113.91	+	2375.17i	0.636445	+	0.367452i	−0.146799	+	0.989166i	$0.546897\pi$
$348$		0			0
$349$			9257.25i			1.41985i	0.704275	+	0.709927i	$0.251272\pi$
$349$			9257.25i			1.41985i	−0.704275	+	0.709927i	$0.748728\pi$
$350$		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	−0.735453	−	0.677575i	$-0.763031\pi$
$359$	−3512.47	+	2027.93i	−0.516382	+	0.298133i	0.219071	+	0.975709i	$0.429697\pi$
$360$		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	$0.0920533\pi$
$367$	11844.5	+	6838.44i	1.68468	+	0.972653i	0.726210	+	0.687473i	$0.241280\pi$
$368$		0			0
$369$	−1409.11	−	6804.17i	−0.198795	−	0.959921i
$370$		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
$375$	1636.82	−	2010.52i	0.225399	−	0.276861i
$376$		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
$381$	−6062.66	+	7446.86i	−0.815222	+	1.00135i
$382$		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
$387$	−1314.00	−	6344.91i	−0.172596	−	0.833411i
$388$		0			0
$389$	−10631.5	−	6138.08i	−1.38570	−	0.800033i	−0.392871	−	0.919594i	$-0.628518\pi$
$389$	−10631.5	−	6138.08i	−1.38570	−	0.800033i	−0.992827	+	0.119561i	$0.961851\pi$
$390$		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	−0.00160665	−	0.999999i	$-0.500511\pi$
$397$	6831.34	−	3944.07i	0.863614	−	0.498608i	0.865221	+	0.501391i	$0.167178\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4883.77	−	2819.65i	0.608189	−	0.351138i	−0.164067	−	0.986449i	$-0.552461\pi$
$401$	4883.77	−	2819.65i	0.608189	−	0.351138i	0.772257	+	0.635311i	$0.219128\pi$
$402$		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	0.351665	−	0.936126i	$-0.385616\pi$
$409$	−2342.59	−	1352.49i	−0.283212	−	0.163512i	−0.634876	+	0.772614i	$0.718949\pi$
$410$		0			0
$411$	11411.4	−	4346.22i	1.36955	−	0.521614i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1299.89	−	2251.48i	−0.153757	−	0.266315i
$416$		0			0
$417$	−6119.87	−	4982.33i	−0.718684	−	0.585098i
$418$		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
$423$	7522.43	−	6702.31i	0.864665	−	0.770396i
$424$		0			0
$425$	−169.192	−	293.049i	−0.0193106	−	0.0334469i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1389.08	+	3647.16i	0.156330	+	0.410458i
$430$		0			0
$431$	−806.205	−	465.463i	−0.0901010	−	0.0520199i	0.454273	−	0.890863i	$-0.349899\pi$
$431$	−806.205	−	465.463i	−0.0901010	−	0.0520199i	−0.544374	+	0.838843i	$0.683233\pi$
$432$		0			0
$433$			10673.2i			1.18458i	0.805725	+	0.592290i	$0.201776\pi$
$433$			10673.2i			1.18458i	−0.805725	+	0.592290i	$0.798224\pi$
$434$		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	−0.647877	−	0.761745i	$-0.724343\pi$
$439$	−2870.95	+	1657.54i	−0.312125	+	0.180206i	0.335752	+	0.941950i	$0.391010\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3223.65	+	1861.18i	−0.345734	+	0.199610i	−0.662805	−	0.748792i	$-0.730634\pi$
$443$	−3223.65	+	1861.18i	−0.345734	+	0.199610i	0.317071	+	0.948402i	$0.397301\pi$
$444$		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	$0.148940\pi$
$449$			8582.14i			0.902041i	−0.892514	+	0.451021i	$0.851060\pi$
$450$		0			0
$451$	−6506.78	−	3756.69i	−0.679362	−	0.392230i
$452$		0			0
$453$	4608.89	+	12101.1i	0.478023	+	1.25509i
$454$		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
$459$	331.037	−	211.304i	0.0336634	−	0.0214876i
$460$		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
$465$	211.866	+	172.485i	0.0211292	+	0.0172017i
$466$		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
$471$	−14364.6	+	5470.98i	−1.40527	+	0.535222i
$472$		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	$0.221628\pi$
$491$			13955.7i			1.28271i	−0.767243	+	0.641357i	$0.778372\pi$
$492$		0			0
$493$	414.211	+	239.145i	0.0378400	+	0.0218469i
$494$		0			0
$495$	1566.28	−	324.370i	0.142220	−	0.0294532i
$496$		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
$501$	−4305.36	+	5288.33i	−0.383930	+	0.471587i
$502$		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
$507$	−5036.18	+	6186.02i	−0.441153	+	0.541875i
$508$		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
$513$	15033.6	−	669.642i	1.29386	−	0.0576324i
$514$		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	−0.635195	−	0.772352i	$-0.719080\pi$
$523$	−3395.81	+	1960.57i	−0.283917	+	0.163920i	0.351278	+	0.936271i	$0.385747\pi$
$524$		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
$537$	−16400.3	+	6246.32i	−1.31792	+	0.501953i
$538$		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
$543$	−6148.58	−	5005.70i	−0.485931	−	0.395608i
$544$		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
$549$	4025.89	+	4518.51i	0.312970	+	0.351267i
$550$		0			0
$551$	9163.53	+	15871.7i	0.708492	+	1.22714i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−680.115	−	1785.70i	−0.0520167	−	0.136575i
$556$		0			0
$557$	−18408.7	−	10628.3i	−1.40036	−	0.808501i	−0.405934	−	0.913902i	$-0.633054\pi$
$557$	−18408.7	−	10628.3i	−1.40036	−	0.808501i	−0.994430	+	0.105402i	$0.966387\pi$
$558$		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	0.199166	−	0.979966i	$-0.436177\pi$
$569$	15573.7	−	8991.49i	1.14742	−	0.662466i	0.948258	+	0.317500i	$0.102843\pi$
$570$		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	0.617618	−	0.786478i	$-0.288098\pi$
$577$	3400.09	+	1963.04i	0.245317	+	0.141634i	−0.372301	+	0.928112i	$0.621431\pi$
$578$		0			0
$579$	5501.03	+	14443.5i	0.394844	+	1.03670i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8248.03	+	14286.0i	0.585932	+	1.01486i
$584$		0			0
$585$	−937.648	−	1052.38i	−0.0662683	−	0.0743772i
$586$		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
$591$	11630.6	+	9468.78i	0.809510	+	0.659041i
$592$		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
$597$	−14326.9	+	5456.65i	−0.982182	+	0.374080i
$598$		0			0
$599$	1165.84	+	673.101i	0.0795244	+	0.0459134i	0.539235	−	0.842155i	$-0.318713\pi$
$599$	1165.84	+	673.101i	0.0795244	+	0.0459134i	−0.459711	+	0.888069i	$0.652047\pi$
$600$		0			0
$601$		−	15011.2i		−	1.01884i	−0.860519	−	0.509418i	$-0.829861\pi$
$601$		−	15011.2i		−	1.01884i	0.860519	−	0.509418i	$-0.170139\pi$
$602$		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	−0.776817	−	0.629727i	$-0.783167\pi$
$607$	−9270.02	+	5352.05i	−0.619866	+	0.357880i	0.156951	+	0.987606i	$0.449834\pi$
$608$		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	$0.165942\pi$
$617$			15265.5i			0.996056i	−0.867161	+	0.498028i	$0.834058\pi$
$618$		0			0
$619$	−19456.4	−	11233.2i	−1.26336	−	0.729402i	−0.289637	−	0.957136i	$-0.593535\pi$
$619$	−19456.4	−	11233.2i	−1.26336	−	0.729402i	−0.973723	+	0.227735i	$0.926868\pi$
$620$		0			0
$621$	−11386.7	+	507.199i	−0.735802	+	0.0327749i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7048.94	−	12209.1i	−0.451132	−	0.781383i
$626$		0			0
$627$	10273.2	−	12618.7i	0.654341	−	0.803737i
$628$		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
$633$	−2496.49	+	3066.48i	−0.156756	+	0.192546i
$634$		0			0
$635$	−1875.00	−	3247.59i	−0.117176	−	0.202955i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	27214.9	−	5636.07i	1.68482	−	0.348919i
$640$		0			0
$641$	10414.2	+	6012.64i	0.641710	+	0.370492i	0.785273	−	0.619150i	$-0.212523\pi$
$641$	10414.2	+	6012.64i	0.641710	+	0.370492i	−0.143563	+	0.989641i	$0.545856\pi$
$642$		0			0
$643$			12374.3i			0.758936i	0.925205	+	0.379468i	$0.123893\pi$
$643$			12374.3i			0.758936i	−0.925205	+	0.379468i	$0.876107\pi$
$644$		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	−0.947721	−	0.319099i	$-0.896620\pi$
$653$	−19110.1	+	11033.2i	−1.14523	+	0.661201i	−0.197513	+	0.980300i	$0.563286\pi$
$654$		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	$-0.975683\pi$
$659$		−	2582.20i		−	0.152638i	0.997083	−	0.0763190i	$-0.0243167\pi$
$660$		0			0
$661$	−8695.88	−	5020.57i	−0.511695	−	0.295427i	0.221835	−	0.975084i	$-0.428795\pi$
$661$	−8695.88	−	5020.57i	−0.511695	−	0.295427i	−0.733530	+	0.679657i	$0.762129\pi$
$662$		0			0
$663$	−349.700	+	133.189i	−0.0204845	+	0.00780186i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6940.62	−	12021.5i	−0.402911	−	0.697863i
$668$		0			0
$669$	2319.86	+	1888.65i	0.134067	+	0.109147i
$670$		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
$675$	14295.3	−	9124.83i	0.815152	−	0.520319i
$676$		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
$681$	5234.35	+	13743.3i	0.294538	+	0.773338i
$682$		0			0
$683$	−5897.72	−	3405.05i	−0.330410	−	0.190762i	0.325613	−	0.945503i	$-0.394429\pi$
$683$	−5897.72	−	3405.05i	−0.330410	−	0.190762i	−0.656023	+	0.754741i	$0.727763\pi$
$684$		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	−0.180893	−	0.983503i	$-0.557899\pi$
$691$	10542.5	−	6086.72i	0.580399	−	0.335094i	0.761292	+	0.648409i	$0.224565\pi$
$692$		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	$-0.670790\pi$
$701$		−	31903.7i		−	1.71895i	0.511176	−	0.859476i	$-0.329210\pi$
$702$		0			0
$703$	−16834.5	−	9719.41i	−0.903166	−	0.521443i
$704$		0			0
$705$	1400.38	+	3676.83i	0.0748105	+	0.196422i
$706$		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
$711$	20043.3	−	17858.2i	1.05722	−	0.941959i
$712$		0			0
$713$	−2105.05			−0.110568
$714$		0			0
$715$	−1524.08			−0.0797164
$716$		0			0
$717$	24510.4	+	19954.5i	1.27665	+	1.03935i
$718$		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
$723$	−14927.6	+	5685.43i	−0.767863	+	0.292453i
$724$		0			0
$725$	17887.1	+	10327.1i	0.916288	+	0.529019i
$726$		0			0
$727$		−	16192.1i		−	0.826040i	−0.910722	−	0.413020i	$-0.864474\pi$
$727$		−	16192.1i		−	0.826040i	0.910722	−	0.413020i	$-0.135526\pi$
$728$		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	$-0.303730\pi$
$733$	31235.2	−	18033.7i	1.57394	−	0.908716i	0.995679	−	0.0928663i	$-0.0296029\pi$
$734$		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	$-0.796009\pi$
$743$		−	24217.4i		−	1.19576i	0.801585	−	0.597881i	$-0.203991\pi$
$744$		0			0
$745$	260.281	+	150.273i	0.0127999	+	0.00739005i
$746$		0			0
$747$	−7015.10	−	33873.7i	−0.343600	−	1.65914i
$748$		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
$753$	8593.32	−	10555.3i	0.415880	−	0.510832i
$754$		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
$759$	−7781.10	+	9557.63i	−0.372116	+	0.457075i
$760$		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
$765$	31.1015	+	150.179i	0.00146990	+	0.00709771i
$766$		0			0
$767$	−8450.42	−	4878.85i	−0.397819	−	0.229681i
$768$		0			0
$769$			35637.1i			1.67114i	0.549383	+	0.835571i	$0.314863\pi$
$769$			35637.1i			1.67114i	−0.549383	+	0.835571i	$0.685137\pi$
$770$		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	0.275855	−	0.961199i	$-0.411039\pi$
$787$	−9242.80	−	5336.33i	−0.418641	−	0.241702i	−0.694496	+	0.719497i	$0.744372\pi$
$788$		0			0
$789$	−33877.3	+	12902.7i	−1.52860	+	0.582192i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2883.20	−	4993.86i	−0.129112	−	0.223628i
$794$		0			0
$795$	−4620.16	−	3761.38i	−0.206113	−	0.167802i
$796$		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
$801$	29792.2	−	26544.2i	1.31418	−	1.17090i
$802$		0			0
$803$	−8526.38	−	14768.1i	−0.374707	−	0.649011i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8633.63	−	22668.4i	−0.376602	−	0.988805i
$808$		0			0
$809$	18066.6	+	10430.7i	0.785150	+	0.453307i	0.838252	−	0.545282i	$-0.183578\pi$
$809$	18066.6	+	10430.7i	0.785150	+	0.453307i	−0.0531022	+	0.998589i	$0.516911\pi$
$810$		0			0
$811$			1052.96i			0.0455911i	0.999740	+	0.0227956i	$0.00725668\pi$
$811$			1052.96i			0.0455911i	−0.999740	+	0.0227956i	$0.992743\pi$
$812$		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	−0.970715	−	0.240233i	$-0.922776\pi$
$821$	−29358.8	+	16950.3i	−1.24803	+	0.720548i	−0.277310	+	0.960780i	$0.589443\pi$
$822$		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	$-0.815898\pi$
$827$		−	26002.1i		−	1.09333i	0.837353	−	0.546663i	$-0.184102\pi$
$828$		0			0
$829$	−18600.2	−	10738.8i	−0.779266	−	0.449910i	0.0569040	−	0.998380i	$-0.481877\pi$
$829$	−18600.2	−	10738.8i	−0.779266	−	0.449910i	−0.836170	+	0.548470i	$0.815210\pi$
$830$		0			0
$831$	1109.94	+	2914.24i	0.0463336	+	0.121653i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1331.52	−	2306.25i	−0.0551844	−	0.0955822i
$836$		0			0
$837$	1955.88	+	3064.15i	0.0807706	+	0.126538i
$838$		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
$843$	18147.6	+	14774.4i	0.741443	+	0.603626i
$844$		0			0
$845$	−1557.54	−	2697.73i	−0.0634094	−	0.109828i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2159.36	+	822.426i	−0.0872897	+	0.0332457i
$850$		0			0
$851$	12750.8	+	7361.65i	0.513620	+	0.296538i
$852$		0			0
$853$		−	10440.3i		−	0.419075i	−0.977801	−	0.209537i	$-0.932804\pi$
$853$		−	10440.3i		−	0.419075i	0.977801	−	0.209537i	$-0.0671958\pi$
$854$		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	−0.775805	−	0.630972i	$-0.782656\pi$
$859$	−15540.5	+	8972.31i	−0.617270	+	0.356381i	0.158535	+	0.987353i	$0.449323\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8043.37	−	4643.84i	0.317265	−	0.183173i	−0.332908	−	0.942959i	$-0.608030\pi$
$863$	8043.37	−	4643.84i	0.317265	−	0.183173i	0.650173	+	0.759786i	$0.274696\pi$
$864$		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
$873$	−32489.5	+	6728.43i	−1.25957	+	0.260851i
$874$		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
$879$	20674.3	−	25394.6i	0.793320	−	0.974446i
$880$		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
$885$	−2524.86	+	3101.32i	−0.0959009	+	0.117796i
$886$		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
$891$	21142.0	+	2445.99i	0.794930	+	0.0919682i
$892$		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	$-0.920257\pi$
$911$		−	13633.2i		−	0.495815i	0.968784	−	0.247908i	$-0.0797429\pi$
$912$		0			0
$913$	−32393.2	−	18702.2i	−1.17422	−	0.677934i
$914$		0			0
$915$	−2208.57	+	841.169i	−0.0797957	+	0.0303915i
$916$		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
$921$	30344.4	+	24704.1i	1.08565	+	0.883853i
$922$		0			0
$923$	−26481.5			−0.944367
$924$		0			0
$925$	−21907.1			−0.778705
$926$		0			0
$927$	19978.6	+	22423.3i	0.707858	+	0.794474i
$928$		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
$933$	17322.3	+	45481.2i	0.607830	+	1.59591i
$934$		0			0
$935$	143.615	+	82.9164i	0.00502324	+	0.00290017i
$936$		0			0
$937$		−	12018.0i		−	0.419010i	−0.977808	−	0.209505i	$-0.932815\pi$
$937$		−	12018.0i		−	0.419010i	0.977808	−	0.209505i	$-0.0671852\pi$
$938$		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	−0.216507	−	0.976281i	$-0.569467\pi$
$947$	15175.1	−	8761.35i	0.520723	−	0.300640i	0.737230	+	0.675641i	$0.236133\pi$
$948$		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	$0.172686\pi$
$953$			30378.0i			1.03257i	−0.856417	+	0.516285i	$0.827314\pi$
$954$		0			0
$955$	2661.17	+	1536.43i	0.0901712	+	0.0520604i
$956$		0			0
$957$	9225.51	+	24222.4i	0.311618	+	0.818182i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14559.8	−	25218.3i	−0.488732	−	0.846509i
$962$		0			0
$963$	1077.10	+	1208.90i	0.0360427	+	0.0404531i
$964$		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
$969$	1209.92	+	985.023i	0.0401116	+	0.0326558i
$970$		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
$975$	−15101.3	+	5751.56i	−0.496028	+	0.188920i
$976$		0			0
$977$	−14545.6	−	8397.90i	−0.476310	−	0.274998i	0.242568	−	0.970135i	$-0.422010\pi$
$977$	−14545.6	−	8397.90i	−0.476310	−	0.274998i	−0.718877	+	0.695137i	$0.755344\pi$
$978$		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	0.828345	−	0.560218i	$-0.189283\pi$
$997$	23841.9	+	13765.2i	0.757354	+	0.437259i	−0.0709909	+	0.997477i	$0.522616\pi$
$998$		0			0
$999$	−1131.40	−	25400.2i	−0.0358318	−	0.804432i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-3.28059 + 4.02960i) q^{3} +(-1.01459 - 1.75732i) q^{5} +(-5.47539 - 26.4390i) q^{9} +O(q^{10})\)	\(q+(-3.28059 + 4.02960i) q^{3} +(-1.01459 - 1.75732i) q^{5} +(-5.47539 - 26.4390i) q^{9} +(-25.2834 - 14.5974i) q^{11} +25.7266i q^{13} +(10.4097 + 1.67666i) q^{15} +(1.39964 - 2.42425i) q^{17} +(92.8920 - 53.6312i) q^{19} +(-70.3580 + 40.6212i) q^{23} +(60.4412 - 104.687i) q^{25} +(124.501 + 64.6720i) q^{27} +170.862i q^{29} +(22.4394 + 12.9554i) q^{31} +(141.766 - 53.9940i) q^{33} +(-90.6133 - 156.947i) q^{37} +(-103.668 - 84.3985i) q^{39} +257.354 q^{41} +239.983 q^{43} +(-40.9064 + 36.4467i) q^{45} +(186.576 + 323.160i) q^{47} +(5.17710 + 13.5930i) q^{51} +(-489.335 - 282.517i) q^{53} +59.2413i q^{55} +(-88.6285 + 550.260i) q^{57} +(-189.642 + 328.470i) q^{59} +(-194.113 + 112.071i) q^{61} +(45.2098 - 26.1019i) q^{65} +(-167.761 + 290.571i) q^{67} +(67.1288 - 416.777i) q^{69} +1029.35i q^{71} +(505.848 + 292.052i) q^{73} +(223.565 + 586.991i) q^{75} +(497.128 + 861.051i) q^{79} +(-669.040 + 289.528i) q^{81} +1281.20 q^{83} -5.68022 q^{85} +(-688.505 - 560.528i) q^{87} +(738.927 + 1279.86i) q^{89} +(-125.819 + 47.9204i) q^{93} +(-188.494 - 108.827i) q^{95} -1228.85i q^{97} +(-247.504 + 748.394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 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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