LMFDB - Embedded newform 588.4.k.e.521.24

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			521.24
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.19498 + 0.110261i) q^{3} +(-4.87287 - 8.44005i) q^{5} +(26.9757 + 1.14560i) q^{9} +O(q^{10})$	\(q+(5.19498 + 0.110261i) q^{3} +(-4.87287 - 8.44005i) q^{5} +(26.9757 + 1.14560i) q^{9} +(-42.9817 - 24.8155i) q^{11} -2.47499i q^{13} +(-24.3838 - 44.3832i) q^{15} +(24.7602 - 42.8858i) q^{17} +(-96.0631 + 55.4620i) q^{19} +(-149.767 + 86.4683i) q^{23} +(15.0103 - 25.9987i) q^{25} +(140.012 + 8.92575i) q^{27} -134.538i q^{29} +(-2.18514 - 1.26159i) q^{31} +(-220.553 - 133.655i) q^{33} +(58.5515 + 101.414i) q^{37} +(0.272894 - 12.8575i) q^{39} -160.696 q^{41} -442.678 q^{43} +(-121.780 - 233.259i) q^{45} +(-155.814 - 269.879i) q^{47} +(133.357 - 220.061i) q^{51} +(248.907 + 143.706i) q^{53} +483.690i q^{55} +(-505.161 + 277.532i) q^{57} +(-276.360 + 478.670i) q^{59} +(-504.937 + 291.525i) q^{61} +(-20.8890 + 12.0603i) q^{65} +(450.723 - 780.675i) q^{67} +(-787.573 + 432.688i) q^{69} -984.717i q^{71} +(-178.030 - 102.786i) q^{73} +(80.8451 - 133.408i) q^{75} +(-321.643 - 557.103i) q^{79} +(726.375 + 61.8069i) q^{81} -351.902 q^{83} -482.612 q^{85} +(14.8343 - 698.924i) q^{87} +(544.376 + 942.887i) q^{89} +(-11.2126 - 6.79487i) q^{93} +(936.205 + 540.518i) q^{95} +1365.09i q^{97} +(-1131.03 - 718.654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	5.19498	+	0.110261i	0.999775	+	0.0212197i
$3$	5.19498	+	0.110261i	0.999775	+	0.0212197i
$4$		0			0
$5$	−4.87287	−	8.44005i	−0.435842	−	0.754901i	0.561522	−	0.827462i	$-0.310216\pi$
$5$	−4.87287	−	8.44005i	−0.435842	−	0.754901i	−0.997364	+	0.0725609i	$0.976883\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	26.9757	+	1.14560i	0.999099	+	0.0424298i
$10$		0			0
$11$	−42.9817	−	24.8155i	−1.17813	−	0.680195i	−0.222551	−	0.974921i	$-0.571438\pi$
$11$	−42.9817	−	24.8155i	−1.17813	−	0.680195i	−0.955582	+	0.294726i	$0.904772\pi$
$12$		0			0
$13$		−	2.47499i		−	0.0528029i	−0.999651	−	0.0264015i	$-0.991595\pi$
$13$		−	2.47499i		−	0.0528029i	0.999651	−	0.0264015i	$-0.00840482\pi$
$14$		0			0
$15$	−24.3838	−	44.3832i	−0.419726	−	0.763980i
$16$		0			0
$17$	24.7602	−	42.8858i	0.353248	−	0.611844i	−0.633568	−	0.773687i	$-0.718410\pi$
$17$	24.7602	−	42.8858i	0.353248	−	0.611844i	0.986817	+	0.161843i	$0.0517438\pi$
$18$		0			0
$19$	−96.0631	+	55.4620i	−1.15991	+	0.669677i	−0.951284	−	0.308317i	$-0.900234\pi$
$19$	−96.0631	+	55.4620i	−1.15991	+	0.669677i	−0.208631	+	0.977994i	$0.566901\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−149.767	+	86.4683i	−1.35777	+	0.783908i	−0.989323	−	0.145741i	$-0.953443\pi$
$23$	−149.767	+	86.4683i	−1.35777	+	0.783908i	−0.368446	+	0.929649i	$0.620110\pi$
$24$		0			0
$25$	15.0103	−	25.9987i	0.120083	−	0.207989i
$26$		0			0
$27$	140.012	+	8.92575i	0.997974	+	0.0636208i
$28$		0			0
$29$		−	134.538i		−	0.861488i	−0.902474	−	0.430744i	$-0.858251\pi$
$29$		−	134.538i		−	0.861488i	0.902474	−	0.430744i	$-0.141749\pi$
$30$		0			0
$31$	−2.18514	−	1.26159i	−0.0126601	−	0.00730929i	0.493657	−	0.869657i	$-0.335660\pi$
$31$	−2.18514	−	1.26159i	−0.0126601	−	0.00730929i	−0.506317	+	0.862348i	$0.668993\pi$
$32$		0			0
$33$	−220.553	−	133.655i	−1.16343	−	0.705042i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	58.5515	+	101.414i	0.260157	+	0.450605i	0.966283	−	0.257481i	$-0.0828924\pi$
$37$	58.5515	+	101.414i	0.260157	+	0.450605i	−0.706127	+	0.708086i	$0.749559\pi$
$38$		0			0
$39$	0.272894	−	12.8575i	0.00112046	−	0.0527910i
$40$		0			0
$41$	−160.696			−0.612111			−0.306055	−	0.952014i	$-0.599009\pi$
$41$	−160.696			−0.612111			−0.306055	+	0.952014i	$0.599009\pi$
$42$		0			0
$43$	−442.678			−1.56995			−0.784973	−	0.619530i	$-0.787323\pi$
$43$	−442.678			−1.56995			−0.784973	+	0.619530i	$0.787323\pi$
$44$		0			0
$45$	−121.780	−	233.259i	−0.403420	−	0.772714i
$46$		0			0
$47$	−155.814	−	269.879i	−0.483572	−	0.837571i	0.516250	−	0.856438i	$-0.327327\pi$
$47$	−155.814	−	269.879i	−0.483572	−	0.837571i	−0.999822	+	0.0188668i	$0.993994\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	133.357	−	220.061i	0.366152	−	0.604210i
$52$		0			0
$53$	248.907	+	143.706i	0.645093	+	0.372445i	0.786574	−	0.617496i	$-0.211853\pi$
$53$	248.907	+	143.706i	0.645093	+	0.372445i	−0.141480	+	0.989941i	$0.545186\pi$
$54$		0			0
$55$			483.690i			1.18583i
$56$		0			0
$57$	−505.161	+	277.532i	−1.17386	+	0.644913i
$58$		0			0
$59$	−276.360	+	478.670i	−0.609814	+	1.05623i	0.381457	+	0.924387i	$0.375423\pi$
$59$	−276.360	+	478.670i	−0.609814	+	1.05623i	−0.991271	+	0.131842i	$0.957911\pi$
$60$		0			0
$61$	−504.937	+	291.525i	−1.05984	+	0.611901i	−0.925389	−	0.379018i	$-0.876262\pi$
$61$	−504.937	+	291.525i	−1.05984	+	0.611901i	−0.134455	+	0.990920i	$0.542928\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−20.8890	+	12.0603i	−0.0398610	+	0.0230138i
$66$		0			0
$67$	450.723	−	780.675i	0.821859	−	1.42350i	−0.0824369	−	0.996596i	$-0.526270\pi$
$67$	450.723	−	780.675i	0.821859	−	1.42350i	0.904296	−	0.426906i	$-0.140396\pi$
$68$		0			0
$69$	−787.573	+	432.688i	−1.37410	+	0.754920i
$70$		0			0
$71$		−	984.717i		−	1.64598i	−0.568058	−	0.822988i	$-0.692305\pi$
$71$		−	984.717i		−	1.64598i	0.568058	−	0.822988i	$-0.307695\pi$
$72$		0			0
$73$	−178.030	−	102.786i	−0.285436	−	0.164797i	0.350446	−	0.936583i	$-0.386030\pi$
$73$	−178.030	−	102.786i	−0.285436	−	0.164797i	−0.635882	+	0.771786i	$0.719363\pi$
$74$		0			0
$75$	80.8451	−	133.408i	0.124469	−	0.205394i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−321.643	−	557.103i	−0.458072	−	0.793405i	0.540787	−	0.841160i	$-0.318127\pi$
$79$	−321.643	−	557.103i	−0.458072	−	0.793405i	−0.998859	+	0.0477551i	$0.984793\pi$
$80$		0			0
$81$	726.375	+	61.8069i	0.996399	+	0.0847832i
$82$		0			0
$83$	−351.902			−0.465376			−0.232688	−	0.972551i	$-0.574752\pi$
$83$	−351.902			−0.465376			−0.232688	+	0.972551i	$0.574752\pi$
$84$		0			0
$85$	−482.612			−0.615842
$86$		0			0
$87$	14.8343	−	698.924i	0.0182805	−	0.861294i
$88$		0			0
$89$	544.376	+	942.887i	0.648357	+	1.12299i	0.983515	+	0.180825i	$0.0578767\pi$
$89$	544.376	+	942.887i	0.648357	+	1.12299i	−0.335159	+	0.942162i	$0.608790\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−11.2126	−	6.79487i	−0.0125021	−	0.00757629i
$94$		0			0
$95$	936.205	+	540.518i	1.01108	+	0.583747i
$96$		0			0
$97$			1365.09i			1.42891i	0.699683	+	0.714454i	$0.253325\pi$
$97$			1365.09i			1.42891i	−0.699683	+	0.714454i	$0.746675\pi$
$98$		0			0
$99$	−1131.03	−	718.654i	−1.14821	−	0.729571i
$100$		0			0
$101$	651.926	−	1129.17i	0.642268	−	1.11244i	−0.342658	−	0.939460i	$-0.611327\pi$
$101$	651.926	−	1129.17i	0.642268	−	1.11244i	0.984925	−	0.172980i	$-0.0553396\pi$
$102$		0			0
$103$	−1094.23	+	631.752i	−1.04677	+	0.604354i	−0.921744	−	0.387800i	$-0.873235\pi$
$103$	−1094.23	+	631.752i	−1.04677	+	0.604354i	−0.125027	+	0.992153i	$0.539902\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1267.25	−	731.647i	1.14495	−	0.661037i	0.197299	−	0.980343i	$-0.436783\pi$
$107$	1267.25	−	731.647i	1.14495	−	0.661037i	0.947652	+	0.319306i	$0.103450\pi$
$108$		0			0
$109$	1119.89	−	1939.71i	0.984093	−	1.70450i	0.338193	−	0.941077i	$-0.390184\pi$
$109$	1119.89	−	1939.71i	0.984093	−	1.70450i	0.645900	−	0.763422i	$-0.276482\pi$
$110$		0			0
$111$	292.992	+	533.300i	0.250536	+	0.456024i
$112$		0			0
$113$			281.355i			0.234227i	0.993119	+	0.117114i	$0.0373642\pi$
$113$			281.355i			0.234227i	−0.993119	+	0.117114i	$0.962636\pi$
$114$		0			0
$115$	1459.59	+	842.697i	1.18355	+	0.683321i
$116$		0			0
$117$	2.83536	−	66.7645i	0.00224042	−	0.0527554i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	566.115	+	980.541i	0.425331	+	0.736695i
$122$		0			0
$123$	−834.814	−	17.7185i	−0.611973	−	0.0129888i
$124$		0			0
$125$	−1510.79			−1.08103
$126$		0			0
$127$	−576.095			−0.402521			−0.201261	−	0.979538i	$-0.564504\pi$
$127$	−576.095			−0.402521			−0.201261	+	0.979538i	$0.564504\pi$
$128$		0			0
$129$	−2299.70	−	48.8099i	−1.56959	−	0.0333137i
$130$		0			0
$131$	−1142.71	−	1979.23i	−0.762130	−	1.32005i	−0.941750	−	0.336313i	$-0.890820\pi$
$131$	−1142.71	−	1979.23i	−0.762130	−	1.32005i	0.179620	−	0.983736i	$-0.442513\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−606.925	−	1225.20i	−0.386932	−	0.781101i
$136$		0			0
$137$	−892.802	−	515.459i	−0.556768	−	0.321450i	0.195079	−	0.980787i	$-0.437504\pi$
$137$	−892.802	−	515.459i	−0.556768	−	0.321450i	−0.751847	+	0.659337i	$0.770837\pi$
$138$		0			0
$139$			234.497i			0.143092i	0.997437	+	0.0715460i	$0.0227933\pi$
$139$			234.497i			0.143092i	−0.997437	+	0.0715460i	$0.977207\pi$
$140$		0			0
$141$	−779.697	−	1419.19i	−0.465690	−	0.847644i
$142$		0			0
$143$	−61.4180	+	106.379i	−0.0359163	+	0.0622088i
$144$		0			0
$145$	−1135.51	+	655.587i	−0.650338	+	0.375473i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2015.55	+	1163.68i	−1.10819	+	0.639814i	−0.938360	−	0.345660i	$-0.887655\pi$
$149$	−2015.55	+	1163.68i	−1.10819	+	0.639814i	−0.169830	+	0.985473i	$0.554322\pi$
$150$		0			0
$151$	−527.571	+	913.779i	−0.284325	+	0.492466i	−0.972445	−	0.233131i	$-0.925103\pi$
$151$	−527.571	+	913.779i	−0.284325	+	0.492466i	0.688120	+	0.725597i	$0.258436\pi$
$152$		0			0
$153$	717.052	−	1128.51i	0.378891	−	0.596305i
$154$		0			0
$155$			24.5902i			0.0127428i
$156$		0			0
$157$	38.3884	+	22.1635i	0.0195142	+	0.0112665i	0.509725	−	0.860337i	$-0.329747\pi$
$157$	38.3884	+	22.1635i	0.0195142	+	0.0112665i	−0.490211	+	0.871604i	$0.663080\pi$
$158$		0			0
$159$	1277.22	+	773.996i	0.637045	+	0.386050i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	126.057	+	218.337i	0.0605738	+	0.104917i	0.894722	−	0.446623i	$-0.147374\pi$
$163$	126.057	+	218.337i	0.0605738	+	0.104917i	−0.834148	+	0.551540i	$0.814040\pi$
$164$		0			0
$165$	−53.3320	+	2512.76i	−0.0251630	+	1.18556i
$166$		0			0
$167$	1657.35			0.767962			0.383981	−	0.923341i	$-0.374553\pi$
$167$	1657.35			0.767962			0.383981	+	0.923341i	$0.374553\pi$
$168$		0			0
$169$	2190.87			0.997212
$170$		0			0
$171$	−2654.90	+	1386.08i	−1.18728	+	0.619859i
$172$		0			0
$173$	−1663.55	−	2881.36i	−0.731084	−	1.26627i	−0.956420	−	0.291994i	$-0.905681\pi$
$173$	−1663.55	−	2881.36i	−0.731084	−	1.26627i	0.225336	−	0.974281i	$-0.427652\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1488.46	+	2456.21i	−0.632090	+	1.04305i
$178$		0			0
$179$	−372.577	−	215.108i	−0.155574	−	0.0898206i	0.420192	−	0.907435i	$-0.361963\pi$
$179$	−372.577	−	215.108i	−0.155574	−	0.0898206i	−0.575766	+	0.817615i	$0.695296\pi$
$180$		0			0
$181$		−	2230.49i		−	0.915971i	−0.888960	−	0.457986i	$-0.848571\pi$
$181$		−	2230.49i		−	0.915971i	0.888960	−	0.457986i	$-0.151429\pi$
$182$		0			0
$183$	−2655.28	+	1458.79i	−1.07259	+	0.589274i
$184$		0			0
$185$	570.627	−	988.355i	0.226775	−	0.392785i
$186$		0			0
$187$	−2128.47	+	1228.87i	−0.832346	+	0.480555i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1003.30	−	579.256i	0.380086	−	0.219442i	−0.297770	−	0.954638i	$-0.596243\pi$
$191$	1003.30	−	579.256i	0.380086	−	0.219442i	0.677855	+	0.735195i	$0.262910\pi$
$192$		0			0
$193$	1127.84	−	1953.48i	0.420641	−	0.728572i	−0.575361	−	0.817899i	$-0.695138\pi$
$193$	1127.84	−	1953.48i	0.420641	−	0.728572i	0.996002	+	0.0893276i	$0.0284718\pi$
$194$		0			0
$195$	−109.848	+	60.3497i	−0.0403404	+	0.0221627i
$196$		0			0
$197$			3280.44i			1.18641i	0.805053	+	0.593203i	$0.202137\pi$
$197$			3280.44i			1.18641i	−0.805053	+	0.593203i	$0.797863\pi$
$198$		0			0
$199$	3818.10	+	2204.38i	1.36009	+	0.785248i	0.989635	−	0.143603i	$-0.0458687\pi$
$199$	3818.10	+	2204.38i	1.36009	+	0.785248i	0.370454	+	0.928851i	$0.379202\pi$
$200$		0			0
$201$	2427.58	−	4005.90i	0.851880	−	1.40574i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	783.051	+	1356.28i	0.266784	+	0.462083i
$206$		0			0
$207$	−4139.14	+	2160.97i	−1.38981	+	0.725592i
$208$		0			0
$209$	5505.27			1.82204
$210$		0			0
$211$	5620.46			1.83378			0.916892	−	0.399135i	$-0.130689\pi$
$211$	5620.46			1.83378			0.916892	+	0.399135i	$0.130689\pi$
$212$		0			0
$213$	108.576	−	5115.59i	0.0349271	−	1.64561i
$214$		0			0
$215$	2157.11	+	3736.22i	0.684249	+	1.18515i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−913.530	−	553.600i	−0.281875	−	0.170816i
$220$		0			0
$221$	−106.142	−	61.2811i	−0.0323072	−	0.0186525i
$222$		0			0
$223$		−	1134.63i		−	0.340718i	−0.985382	−	0.170359i	$-0.945507\pi$
$223$		−	1134.63i		−	0.340718i	0.985382	−	0.170359i	$-0.0544928\pi$
$224$		0			0
$225$	434.699	−	684.136i	0.128800	−	0.202707i
$226$		0			0
$227$	−1061.60	+	1838.75i	−0.310400	+	0.537629i	−0.978449	−	0.206488i	$-0.933796\pi$
$227$	−1061.60	+	1838.75i	−0.310400	+	0.537629i	0.668049	+	0.744118i	$0.267130\pi$
$228$		0			0
$229$	2299.77	−	1327.77i	0.663638	−	0.383152i	−0.130023	−	0.991511i	$-0.541505\pi$
$229$	2299.77	−	1327.77i	0.663638	−	0.383152i	0.793662	+	0.608359i	$0.208172\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2734.14	−	1578.56i	0.768754	−	0.443840i	−0.0636761	−	0.997971i	$-0.520282\pi$
$233$	2734.14	−	1578.56i	0.768754	−	0.443840i	0.832430	+	0.554130i	$0.186949\pi$
$234$		0			0
$235$	−1518.53	+	2630.16i	−0.421522	+	0.730098i
$236$		0			0
$237$	−1609.51	−	2929.60i	−0.441133	−	0.802946i
$238$		0			0
$239$		−	2040.14i		−	0.552157i	−0.961135	−	0.276079i	$-0.910965\pi$
$239$		−	2040.14i		−	0.552157i	0.961135	−	0.276079i	$-0.0890351\pi$
$240$		0			0
$241$	3958.64	+	2285.52i	1.05809	+	0.610886i	0.924902	−	0.380205i	$-0.124147\pi$
$241$	3958.64	+	2285.52i	1.05809	+	0.610886i	0.133184	+	0.991091i	$0.457480\pi$
$242$		0			0
$243$	3766.69	+	401.177i	0.994376	+	0.105907i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	137.268	+	237.755i	0.0353609	+	0.0612469i
$248$		0			0
$249$	−1828.12	−	38.8009i	−0.465272	−	0.00987513i
$250$		0			0
$251$	−5848.44			−1.47072			−0.735359	−	0.677678i	$-0.762986\pi$
$251$	−5848.44			−1.47072			−0.735359	+	0.677678i	$0.762986\pi$
$252$		0			0
$253$	8583.01			2.13284
$254$		0			0
$255$	−2507.16	−	53.2131i	−0.615704	−	0.0130680i
$256$		0			0
$257$	3884.44	+	6728.05i	0.942820	+	1.63301i	0.760058	+	0.649855i	$0.225170\pi$
$257$	3884.44	+	6728.05i	0.942820	+	1.63301i	0.182762	+	0.983157i	$0.441496\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	154.128	−	3629.26i	0.0365527	−	0.860712i
$262$		0			0
$263$	−4077.64	−	2354.23i	−0.956038	−	0.551969i	−0.0610865	−	0.998132i	$-0.519457\pi$
$263$	−4077.64	−	2354.23i	−0.956038	−	0.551969i	−0.894951	+	0.446164i	$0.852790\pi$
$264$		0			0
$265$		−	2801.05i		−	0.649309i
$266$		0			0
$267$	2724.06	+	4958.30i	0.624381	+	1.13649i
$268$		0			0
$269$	−2054.29	+	3558.14i	−0.465622	+	0.806481i	−0.999229	−	0.0392514i	$-0.987503\pi$
$269$	−2054.29	+	3558.14i	−0.465622	+	0.806481i	0.533607	+	0.845732i	$0.320836\pi$
$270$		0			0
$271$	700.809	−	404.612i	0.157089	−	0.0906953i	−0.419395	−	0.907804i	$-0.637758\pi$
$271$	700.809	−	404.612i	0.157089	−	0.0906953i	0.576484	+	0.817109i	$0.304424\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1290.34	+	744.978i	−0.282947	+	0.163359i
$276$		0			0
$277$	3727.43	−	6456.10i	0.808518	−	1.40039i	−0.105372	−	0.994433i	$-0.533603\pi$
$277$	3727.43	−	6456.10i	0.808518	−	1.40039i	0.913890	−	0.405962i	$-0.133063\pi$
$278$		0			0
$279$	−57.5003	−	36.5355i	−0.0123385	−	0.00783988i
$280$		0			0
$281$			1289.89i			0.273837i	0.990582	+	0.136919i	$0.0437198\pi$
$281$			1289.89i			0.273837i	−0.990582	+	0.136919i	$0.956280\pi$
$282$		0			0
$283$	7466.08	+	4310.54i	1.56824	+	0.905424i	0.996374	+	0.0850780i	$0.0271139\pi$
$283$	7466.08	+	4310.54i	1.56824	+	0.905424i	0.571867	+	0.820346i	$0.306219\pi$
$284$		0			0
$285$	4803.97	+	2911.21i	0.998466	+	0.605071i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1230.37	+	2131.06i	0.250431	+	0.433760i
$290$		0			0
$291$	−150.516	+	7091.62i	−0.0303209	+	1.42859i
$292$		0			0
$293$	6187.72			1.23376			0.616878	−	0.787059i	$-0.288397\pi$
$293$	6187.72			1.23376			0.616878	+	0.787059i	$0.288397\pi$
$294$		0			0
$295$	5386.66			1.06313
$296$		0			0
$297$	−5796.45	−	3858.10i	−1.13247	−	0.753771i
$298$		0			0
$299$	214.008	+	370.673i	0.0413926	+	0.0716941i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	3511.25	−	5794.13i	0.665729	−	1.09856i
$304$		0			0
$305$	4920.98	+	2841.13i	0.923850	+	0.533385i
$306$		0			0
$307$			3785.51i			0.703747i	0.936048	+	0.351873i	$0.114455\pi$
$307$			3785.51i			0.703747i	−0.936048	+	0.351873i	$0.885545\pi$
$308$		0			0
$309$	−5754.15	+	3161.29i	−1.05936	+	0.582005i
$310$		0			0
$311$	2998.76	−	5194.00i	0.546765	−	0.947025i	−0.451728	−	0.892156i	$-0.649192\pi$
$311$	2998.76	−	5194.00i	0.546765	−	0.947025i	0.998494	−	0.0548698i	$-0.0174744\pi$
$312$		0			0
$313$	4960.97	−	2864.22i	0.895881	−	0.517237i	0.0200193	−	0.999800i	$-0.493627\pi$
$313$	4960.97	−	2864.22i	0.895881	−	0.517237i	0.875861	+	0.482563i	$0.160294\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5818.71	+	3359.43i	−1.03095	+	0.595219i	−0.917257	−	0.398297i	$-0.869602\pi$
$317$	−5818.71	+	3359.43i	−1.03095	+	0.595219i	−0.113693	+	0.993516i	$0.536268\pi$
$318$		0			0
$319$	−3338.63	+	5782.68i	−0.585980	+	1.01495i
$320$		0			0
$321$	6664.01	−	3661.17i	1.15872	−	0.636593i
$322$		0			0
$323$			5493.00i			0.946249i
$324$		0			0
$325$	−64.3464	−	37.1504i	−0.0109825	−	0.00634072i
$326$		0			0
$327$	6031.69	−	9953.27i	1.02004	−	1.68323i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−845.184	−	1463.90i	−0.140349	−	0.243092i	0.787279	−	0.616597i	$-0.211489\pi$
$331$	−845.184	−	1463.90i	−0.140349	−	0.243092i	−0.927628	+	0.373505i	$0.878156\pi$
$332$		0			0
$333$	1463.29	+	2802.79i	0.240803	+	0.461237i
$334$		0			0
$335$	−8785.25			−1.43280
$336$		0			0
$337$	4257.51			0.688194			0.344097	−	0.938934i	$-0.388185\pi$
$337$	4257.51			0.688194			0.344097	+	0.938934i	$0.388185\pi$
$338$		0			0
$339$	−31.0224	+	1461.64i	−0.00497023	+	0.234174i
$340$		0			0
$341$	62.6139	+	108.450i	0.00994349	+	0.0172226i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	7489.65	+	4538.73i	1.16878	+	0.708281i
$346$		0			0
$347$	−1092.59	−	630.806i	−0.169029	−	0.0975891i	0.413099	−	0.910686i	$-0.364446\pi$
$347$	−1092.59	−	630.806i	−0.169029	−	0.0975891i	−0.582128	+	0.813097i	$0.697780\pi$
$348$		0			0
$349$		−	10981.9i		−	1.68438i	−0.539179	−	0.842191i	$-0.681265\pi$
$349$		−	10981.9i		−	1.68438i	0.539179	−	0.842191i	$-0.318735\pi$
$350$		0			0
$351$	22.0911	−	346.528i	0.00335936	−	0.0526960i
$352$		0			0
$353$	−3677.09	+	6368.90i	−0.554424	+	0.960290i	0.443524	+	0.896262i	$0.353728\pi$
$353$	−3677.09	+	6368.90i	−0.554424	+	0.960290i	−0.997948	+	0.0640280i	$0.979605\pi$
$354$		0			0
$355$	−8311.06	+	4798.39i	−1.24255	+	0.717387i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−432.312	+	249.595i	−0.0635559	+	0.0366940i	−0.531441	−	0.847095i	$-0.678349\pi$
$359$	−432.312	+	249.595i	−0.0635559	+	0.0366940i	0.467885	+	0.883789i	$0.345016\pi$
$360$		0			0
$361$	2722.58	−	4715.64i	0.396935	−	0.687511i
$362$		0			0
$363$	2832.84	+	5156.31i	0.409603	+	0.745554i
$364$		0			0
$365$			2003.44i			0.287302i
$366$		0			0
$367$	282.908	+	163.337i	0.0402390	+	0.0232320i	0.519985	−	0.854176i	$-0.325938\pi$
$367$	282.908	+	163.337i	0.0402390	+	0.0232320i	−0.479746	+	0.877408i	$0.659271\pi$
$368$		0			0
$369$	−4334.89	−	184.094i	−0.611559	−	0.0259717i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	137.986	+	239.000i	0.0191546	+	0.0331767i	0.875444	−	0.483320i	$-0.160569\pi$
$373$	137.986	+	239.000i	0.0191546	+	0.0331767i	−0.856289	+	0.516497i	$0.827236\pi$
$374$		0			0
$375$	−7848.53	−	166.581i	−1.08079	−	0.0229392i
$376$		0			0
$377$	−332.981			−0.0454891
$378$		0			0
$379$	508.854			0.0689659			0.0344829	−	0.999405i	$-0.489022\pi$
$379$	508.854			0.0689659			0.0344829	+	0.999405i	$0.489022\pi$
$380$		0			0
$381$	−2992.80	−	63.5206i	−0.402430	−	0.00854137i
$382$		0			0
$383$	−2212.79	−	3832.66i	−0.295217	−	0.511331i	0.679818	−	0.733381i	$-0.262059\pi$
$383$	−2212.79	−	3832.66i	−0.295217	−	0.511331i	−0.975035	+	0.222049i	$0.928725\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−11941.5	−	507.133i	−1.56853	−	0.0666125i
$388$		0			0
$389$	−1558.98	−	900.077i	−0.203196	−	0.117315i	0.394949	−	0.918703i	$-0.370762\pi$
$389$	−1558.98	−	900.077i	−0.203196	−	0.117315i	−0.598146	+	0.801388i	$0.704096\pi$
$390$		0			0
$391$			8563.87i			1.10766i
$392$		0			0
$393$	−5718.13	−	10408.1i	−0.733948	−	1.33592i
$394$		0			0
$395$	−3134.65	+	5429.38i	−0.399295	+	0.691599i
$396$		0			0
$397$	−5601.29	+	3233.91i	−0.708113	+	0.408829i	−0.810362	−	0.585930i	$-0.800729\pi$
$397$	−5601.29	+	3233.91i	−0.708113	+	0.408829i	0.102249	+	0.994759i	$0.467396\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2974.16	+	1717.13i	−0.370381	+	0.213839i	−0.673625	−	0.739074i	$-0.735264\pi$
$401$	−2974.16	+	1717.13i	−0.370381	+	0.213839i	0.303244	+	0.952913i	$0.401930\pi$
$402$		0			0
$403$	−3.12242	+	5.40819i	−0.000385952	+	0.000668489i
$404$		0			0
$405$	−3017.88	−	6431.82i	−0.370270	−	0.789135i
$406$		0			0
$407$		−	5811.93i		−	0.707829i
$408$		0			0
$409$	817.228	+	471.827i	0.0988003	+	0.0570424i	0.548586	−	0.836094i	$-0.315166\pi$
$409$	817.228	+	471.827i	0.0988003	+	0.0570424i	−0.449786	+	0.893136i	$0.648500\pi$
$410$		0			0
$411$	−4581.26	−	2776.24i	−0.549822	−	0.333192i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1714.77	+	2970.07i	0.202831	+	0.351313i
$416$		0			0
$417$	−25.8558	+	1218.21i	−0.00303637	+	0.143060i
$418$		0			0
$419$	10148.4			1.18325			0.591626	−	0.806213i	$-0.298486\pi$
$419$	10148.4			1.18325			0.591626	+	0.806213i	$0.298486\pi$
$420$		0			0
$421$	−6775.40			−0.784354			−0.392177	−	0.919890i	$-0.628278\pi$
$421$	−6775.40			−0.784354			−0.392177	+	0.919890i	$0.628278\pi$
$422$		0			0
$423$	−3894.03	−	7458.66i	−0.447598	−	0.857335i
$424$		0			0
$425$	−743.317	−	1287.46i	−0.0848381	−	0.146944i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−330.795	+	545.865i	−0.0372283	+	0.0614327i
$430$		0			0
$431$	−14439.3	−	8336.51i	−1.61372	−	0.931684i	−0.988497	−	0.151241i	$-0.951673\pi$
$431$	−14439.3	−	8336.51i	−1.61372	−	0.931684i	−0.625227	−	0.780443i	$-0.714993\pi$
$432$		0			0
$433$			2848.46i			0.316140i	0.987428	+	0.158070i	$0.0505271\pi$
$433$			2848.46i			0.316140i	−0.987428	+	0.158070i	$0.949473\pi$
$434$		0			0
$435$	−5971.24	+	3280.56i	−0.658159	+	0.361588i
$436$		0			0
$437$	9591.41	−	16612.8i	1.04993	−	1.81853i
$438$		0			0
$439$	−8042.46	+	4643.32i	−0.874364	+	0.504814i	−0.868796	−	0.495170i	$-0.835106\pi$
$439$	−8042.46	+	4643.32i	−0.874364	+	0.504814i	−0.00556785	+	0.999984i	$0.501772\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4281.76	−	2472.08i	0.459216	−	0.265128i	−0.252499	−	0.967597i	$-0.581252\pi$
$443$	4281.76	−	2472.08i	0.459216	−	0.265128i	0.711714	+	0.702469i	$0.247919\pi$
$444$		0			0
$445$	5305.34	−	9189.12i	0.565163	−	0.978890i
$446$		0			0
$447$	−10599.1	+	5823.05i	−1.12152	+	0.616154i
$448$		0			0
$449$		−	15964.7i		−	1.67799i	−0.544136	−	0.838997i	$-0.683142\pi$
$449$		−	15964.7i		−	1.67799i	0.544136	−	0.838997i	$-0.316858\pi$
$450$		0			0
$451$	6906.99	+	3987.75i	0.721147	+	0.416355i
$452$		0			0
$453$	−2841.47	+	4688.90i	−0.294711	+	0.486321i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4133.41	+	7159.28i	0.423092	+	0.732816i	0.996240	−	0.0866354i	$-0.0276115\pi$
$457$	4133.41	+	7159.28i	0.423092	+	0.732816i	−0.573148	+	0.819452i	$0.694278\pi$
$458$		0			0
$459$	3849.50	−	5783.53i	0.391459	−	0.588130i
$460$		0			0
$461$	3468.42			0.350413			0.175207	−	0.984532i	$-0.443941\pi$
$461$	3468.42			0.350413			0.175207	+	0.984532i	$0.443941\pi$
$462$		0			0
$463$	−9918.45			−0.995572			−0.497786	−	0.867300i	$-0.665853\pi$
$463$	−9918.45			−0.995572			−0.497786	+	0.867300i	$0.665853\pi$
$464$		0			0
$465$	−2.71133	+	127.746i	−0.000270398	+	0.0127399i
$466$		0			0
$467$	−8430.55	−	14602.1i	−0.835373	−	1.44691i	−0.893726	−	0.448613i	$-0.851918\pi$
$467$	−8430.55	−	14602.1i	−0.835373	−	1.44691i	0.0583529	−	0.998296i	$-0.481415\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	196.983	+	119.372i	0.0192707	+	0.0116781i
$472$		0			0
$473$	19027.0	+	10985.3i	1.84960	+	1.06787i
$474$		0			0
$475$			3330.02i			0.321667i
$476$		0			0
$477$	6549.80	+	4161.72i	0.628710	+	0.399481i
$478$		0			0
$479$	1578.16	−	2733.46i	0.150539	−	0.260741i	−0.780887	−	0.624672i	$-0.785232\pi$
$479$	1578.16	−	2733.46i	0.150539	−	0.260741i	0.931426	+	0.363932i	$0.118566\pi$
$480$		0			0
$481$	250.999	−	144.914i	0.0237932	−	0.0137370i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	11521.4	−	6651.91i	1.07868	−	0.622778i
$486$		0			0
$487$	−1214.17	+	2103.01i	−0.112976	+	0.195681i	−0.916969	−	0.398958i	$-0.869372\pi$
$487$	−1214.17	+	2103.01i	−0.112976	+	0.195681i	0.803993	+	0.594639i	$0.202705\pi$
$488$		0			0
$489$	630.789	+	1148.15i	0.0583339	+	0.106179i
$490$		0			0
$491$			1304.86i			0.119933i	0.998200	+	0.0599667i	$0.0190995\pi$
$491$			1304.86i			0.119933i	−0.998200	+	0.0599667i	$0.980901\pi$
$492$		0			0
$493$	−5769.79	−	3331.19i	−0.527096	−	0.304319i
$494$		0			0
$495$	−554.117	+	13047.9i	−0.0503146	+	1.18476i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1272.72	−	2204.42i	−0.114178	−	0.197762i	0.803273	−	0.595611i	$-0.203090\pi$
$499$	−1272.72	−	2204.42i	−0.114178	−	0.197762i	−0.917451	+	0.397849i	$0.869757\pi$
$500$		0			0
$501$	8609.91	+	182.741i	0.767789	+	0.0162959i
$502$		0			0
$503$	787.994			0.0698507			0.0349253	−	0.999390i	$-0.488881\pi$
$503$	787.994			0.0698507			0.0349253	+	0.999390i	$0.488881\pi$
$504$		0			0
$505$	−12707.0			−1.11971
$506$		0			0
$507$	11381.6	+	241.567i	0.996987	+	0.0211605i
$508$		0			0
$509$	−1538.89	−	2665.44i	−0.134008	−	0.232109i	0.791210	−	0.611544i	$-0.209451\pi$
$509$	−1538.89	−	2665.44i	−0.134008	−	0.232109i	−0.925218	+	0.379436i	$0.876118\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−13945.0	+	6907.91i	−1.20017	+	0.594526i
$514$		0			0
$515$	10664.0	+	6156.89i	0.912454	+	0.526806i
$516$		0			0
$517$			15466.4i			1.31569i
$518$		0			0
$519$	−8324.43	−	15152.0i	−0.704050	−	1.28150i
$520$		0			0
$521$	663.114	−	1148.55i	0.0557611	−	0.0965811i	−0.836797	−	0.547513i	$-0.815575\pi$
$521$	663.114	−	1148.55i	0.0557611	−	0.0965811i	0.892559	+	0.450931i	$0.148908\pi$
$522$		0			0
$523$	−5799.32	+	3348.24i	−0.484869	+	0.279940i	−0.722444	−	0.691430i	$-0.756981\pi$
$523$	−5799.32	+	3348.24i	−0.484869	+	0.279940i	0.237574	+	0.971369i	$0.423648\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−108.209	+	62.4743i	−0.00894429	+	0.00516399i
$528$		0			0
$529$	8870.03	−	15363.3i	0.729023	−	1.26271i
$530$		0			0
$531$	−8003.37	+	12595.8i	−0.654080	+	1.02940i
$532$		0			0
$533$			397.721i			0.0323212i
$534$		0			0
$535$	−12350.3	−	7130.44i	−0.998036	−	0.576216i
$536$		0			0
$537$	−1911.81	−	1158.56i	−0.153633	−	0.0931016i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−9558.74	−	16556.2i	−0.759634	−	1.31573i	−0.943037	−	0.332687i	$-0.892045\pi$
$541$	−9558.74	−	16556.2i	−0.759634	−	1.31573i	0.183403	−	0.983038i	$-0.441289\pi$
$542$		0			0
$543$	245.935	−	11587.3i	0.0194366	−	0.915765i
$544$		0			0
$545$	−21828.3			−1.71564
$546$		0			0
$547$	−12400.5			−0.969297			−0.484649	−	0.874709i	$-0.661053\pi$
$547$	−12400.5			−0.969297			−0.484649	+	0.874709i	$0.661053\pi$
$548$		0			0
$549$	−13955.0	+	7285.64i	−1.08485	+	0.566381i
$550$		0			0
$551$	7461.77	+	12924.2i	0.576918	+	0.999252i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3073.37	−	5071.57i	0.235058	−	0.387885i
$556$		0			0
$557$	−6062.22	−	3500.02i	−0.461157	−	0.266249i	0.251374	−	0.967890i	$-0.419118\pi$
$557$	−6062.22	−	3500.02i	−0.461157	−	0.266249i	−0.712531	+	0.701641i	$0.752451\pi$
$558$		0			0
$559$			1095.62i			0.0828978i
$560$		0			0
$561$	−11192.8	+	6149.27i	−0.842356	+	0.462785i
$562$		0			0
$563$	−10239.9	+	17736.1i	−0.766538	+	1.32768i	0.172891	+	0.984941i	$0.444689\pi$
$563$	−10239.9	+	17736.1i	−0.766538	+	1.32768i	−0.939430	+	0.342742i	$0.888644\pi$
$564$		0			0
$565$	2374.65	−	1371.01i	0.176818	−	0.102086i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8603.00	−	4966.94i	0.633843	−	0.365949i	−0.148396	−	0.988928i	$-0.547411\pi$
$569$	8603.00	−	4966.94i	0.633843	−	0.365949i	0.782239	+	0.622979i	$0.214078\pi$
$570$		0			0
$571$	−2929.14	+	5073.42i	−0.214677	+	0.371832i	−0.953173	−	0.302427i	$-0.902203\pi$
$571$	−2929.14	+	5073.42i	−0.214677	+	0.371832i	0.738496	+	0.674258i	$0.235537\pi$
$572$		0			0
$573$	5276.00	−	2898.60i	0.384656	−	0.211328i
$574$		0			0
$575$			5191.68i			0.376535i
$576$		0			0
$577$	−15287.5	−	8826.26i	−1.10300	−	0.636815i	−0.165989	−	0.986128i	$-0.553082\pi$
$577$	−15287.5	−	8826.26i	−1.10300	−	0.636815i	−0.937006	+	0.349313i	$0.886415\pi$
$578$		0			0
$579$	6074.50	−	10023.9i	0.436006	−	0.719482i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−7132.28	−	12353.5i	−0.506670	−	0.877579i
$584$		0			0
$585$	−577.312	+	301.404i	−0.0408016	+	0.0213017i
$586$		0			0
$587$	−25424.1			−1.78768			−0.893838	−	0.448390i	$-0.851998\pi$
$587$	−25424.1			−1.78768			−0.893838	+	0.448390i	$0.851998\pi$
$588$		0			0
$589$	279.881			0.0195795
$590$		0			0
$591$	−361.704	+	17041.8i	−0.0251751	+	1.18614i
$592$		0			0
$593$	−3832.38	−	6637.89i	−0.265392	−	0.459672i	0.702275	−	0.711906i	$-0.252168\pi$
$593$	−3832.38	−	6637.89i	−0.265392	−	0.459672i	−0.967666	+	0.252235i	$0.918835\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	19591.9	+	11872.7i	1.34312	+	0.813932i
$598$		0			0
$599$	23961.5	+	13834.2i	1.63446	+	0.943655i	0.982695	+	0.185233i	$0.0593041\pi$
$599$	23961.5	+	13834.2i	1.63446	+	0.943655i	0.651764	+	0.758422i	$0.274029\pi$
$600$		0			0
$601$			11624.0i			0.788937i	0.918909	+	0.394469i	$0.129071\pi$
$601$			11624.0i			0.788937i	−0.918909	+	0.394469i	$0.870929\pi$
$602$		0			0
$603$	13052.9	−	20542.9i	0.881518	−	1.38735i
$604$		0			0
$605$	5517.21	−	9556.09i	0.370754	−	0.642166i
$606$		0			0
$607$	2675.97	−	1544.97i	0.178936	−	0.103309i	−0.407857	−	0.913046i	$-0.633724\pi$
$607$	2675.97	−	1544.97i	0.178936	−	0.103309i	0.586793	+	0.809737i	$0.300390\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−667.946	+	385.639i	−0.0442262	+	0.0255340i
$612$		0			0
$613$	1623.78	−	2812.47i	0.106989	−	0.185310i	−0.807560	−	0.589785i	$-0.799213\pi$
$613$	1623.78	−	2812.47i	0.106989	−	0.185310i	0.914549	+	0.404475i	$0.132546\pi$
$614$		0			0
$615$	3918.39	+	7132.21i	0.256918	+	0.467640i
$616$		0			0
$617$			10686.9i			0.697307i	0.937252	+	0.348654i	$0.113361\pi$
$617$			10686.9i			0.697307i	−0.937252	+	0.348654i	$0.886639\pi$
$618$		0			0
$619$	4946.00	+	2855.58i	0.321158	+	0.185420i	0.651908	−	0.758298i	$-0.273969\pi$
$619$	4946.00	+	2855.58i	0.321158	+	0.185420i	−0.330751	+	0.943718i	$0.607302\pi$
$620$		0			0
$621$	−21741.0	+	10769.8i	−1.40489	+	0.695938i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	5485.59	+	9501.31i	0.351077	+	0.608084i
$626$		0			0
$627$	28599.8	+	607.014i	1.82163	+	0.0386632i
$628$		0			0
$629$	5798.97			0.367600
$630$		0			0
$631$	−13708.4			−0.864854			−0.432427	−	0.901669i	$-0.642343\pi$
$631$	−13708.4			−0.864854			−0.432427	+	0.901669i	$0.642343\pi$
$632$		0			0
$633$	29198.2	+	619.716i	1.83337	+	0.0389123i
$634$		0			0
$635$	2807.23	+	4862.27i	0.175436	+	0.303864i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1128.10	−	26563.4i	0.0698385	−	1.64449i
$640$		0			0
$641$	−14083.3	−	8131.00i	−0.867796	−	0.501022i	−0.00118054	−	0.999999i	$-0.500376\pi$
$641$	−14083.3	−	8131.00i	−0.867796	−	0.501022i	−0.866615	+	0.498977i	$0.833709\pi$
$642$		0			0
$643$		−	13805.8i		−	0.846729i	−0.905959	−	0.423365i	$-0.860849\pi$
$643$		−	13805.8i		−	0.846729i	0.905959	−	0.423365i	$-0.139151\pi$
$644$		0			0
$645$	10794.2	+	19647.4i	0.658947	+	1.19941i
$646$		0			0
$647$	9180.08	−	15900.4i	0.557815	−	0.966163i	−0.439864	−	0.898064i	$-0.644973\pi$
$647$	9180.08	−	15900.4i	0.557815	−	0.966163i	0.997679	−	0.0680988i	$-0.0216933\pi$
$648$		0			0
$649$	23756.8	−	13716.0i	1.43688	−	0.829585i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16302.6	+	9412.30i	−0.976983	+	0.564061i	−0.901358	−	0.433075i	$-0.857428\pi$
$653$	−16302.6	+	9412.30i	−0.976983	+	0.564061i	−0.0756247	+	0.997136i	$0.524095\pi$
$654$		0			0
$655$	−11136.6	+	19289.1i	−0.664338	+	1.15067i
$656$		0			0
$657$	−4684.73	−	2976.67i	−0.278187	−	0.176759i
$658$		0			0
$659$			3472.55i			0.205268i	0.994719	+	0.102634i	$0.0327270\pi$
$659$			3472.55i			0.205268i	−0.994719	+	0.102634i	$0.967273\pi$
$660$		0			0
$661$	−11328.2	−	6540.36i	−0.666592	−	0.384857i	0.128192	−	0.991749i	$-0.459083\pi$
$661$	−11328.2	−	6540.36i	−0.666592	−	0.384857i	−0.794784	+	0.606892i	$0.792416\pi$
$662$		0			0
$663$	−544.649	−	330.057i	−0.0319041	−	0.0193339i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11633.3	+	20149.5i	0.675327	+	1.16970i
$668$		0			0
$669$	125.105	−	5894.36i	0.00722993	−	0.340641i
$670$		0			0
$671$	28937.3			1.66485
$672$		0			0
$673$	−13701.5			−0.784775			−0.392388	−	0.919800i	$-0.628351\pi$
$673$	−13701.5			−0.784775			−0.392388	+	0.919800i	$0.628351\pi$
$674$		0			0
$675$	2333.68	−	3506.15i	0.133072	−	0.199928i
$676$		0			0
$677$	−1975.54	−	3421.74i	−0.112151	−	0.194251i	0.804486	−	0.593971i	$-0.202441\pi$
$677$	−1975.54	−	3421.74i	−0.112151	−	0.194251i	−0.916637	+	0.399720i	$0.869107\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−5717.74	+	9435.20i	−0.321739	+	0.530922i
$682$		0			0
$683$	−22216.3	−	12826.6i	−1.24463	−	0.718589i	−0.274598	−	0.961559i	$-0.588545\pi$
$683$	−22216.3	−	12826.6i	−1.24463	−	0.718589i	−0.970034	+	0.242970i	$0.921878\pi$
$684$		0			0
$685$			10047.1i			0.560406i
$686$		0			0
$687$	12093.7	−	6644.19i	0.671619	−	0.368983i
$688$		0			0
$689$	355.671	−	616.041i	0.0196662	−	0.0340628i
$690$		0			0
$691$	−7142.53	+	4123.74i	−0.393219	+	0.227025i	−0.683554	−	0.729900i	$-0.739567\pi$
$691$	−7142.53	+	4123.74i	−0.393219	+	0.227025i	0.290335	+	0.956925i	$0.406233\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1979.17	−	1142.67i	0.108020	−	0.0623655i
$696$		0			0
$697$	−3978.86	+	6891.59i	−0.216227	+	0.374516i
$698$		0			0
$699$	14377.9	−	7899.11i	0.777999	−	0.427428i
$700$		0			0
$701$		−	25364.7i		−	1.36663i	−0.730122	−	0.683317i	$-0.760537\pi$
$701$		−	25364.7i		−	1.36663i	0.730122	−	0.683317i	$-0.239463\pi$
$702$		0			0
$703$	−11249.3	−	6494.77i	−0.603519	−	0.348442i
$704$		0			0
$705$	−8178.72	+	13496.2i	−0.436920	+	0.720989i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−14695.0	−	25452.5i	−0.778397	−	1.34822i	−0.932865	−	0.360225i	$-0.882700\pi$
$709$	−14695.0	−	25452.5i	−0.778397	−	1.34822i	0.154469	−	0.987998i	$-0.450633\pi$
$710$		0			0
$711$	−8038.33	−	15396.7i	−0.423996	−	0.812126i
$712$		0			0
$713$	436.350			0.0229193
$714$		0			0
$715$	1197.13			0.0626154
$716$		0			0
$717$	224.947	−	10598.5i	0.0117166	−	0.552033i
$718$		0			0
$719$	1802.02	+	3121.19i	0.0934687	+	0.161893i	0.908968	−	0.416865i	$-0.136871\pi$
$719$	1802.02	+	3121.19i	0.0934687	+	0.161893i	−0.815500	+	0.578757i	$0.803538\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	20313.1	+	12309.7i	1.04488	+	0.633201i
$724$		0			0
$725$	−3497.82	−	2019.47i	−0.179180	−	0.103450i
$726$		0			0
$727$		−	35634.9i		−	1.81792i	−0.416887	−	0.908958i	$-0.636879\pi$
$727$		−	35634.9i		−	1.81792i	0.416887	−	0.908958i	$-0.363121\pi$
$728$		0			0
$729$	19523.7	+	2499.42i	0.991905	+	0.126984i
$730$		0			0
$731$	−10960.8	+	18984.6i	−0.554581	+	0.960562i
$732$		0			0
$733$	10831.6	−	6253.60i	0.545802	−	0.315119i	−0.201625	−	0.979463i	$-0.564622\pi$
$733$	10831.6	−	6253.60i	0.545802	−	0.315119i	0.747427	+	0.664344i	$0.231289\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−38745.6	+	22369.8i	−1.93652	+	1.11805i
$738$		0			0
$739$	−4972.17	+	8612.05i	−0.247502	+	0.428687i	−0.962832	−	0.270100i	$-0.912943\pi$
$739$	−4972.17	+	8612.05i	−0.247502	+	0.428687i	0.715330	+	0.698787i	$0.246276\pi$
$740$		0			0
$741$	686.889	+	1250.27i	0.0340533	+	0.0619835i
$742$		0			0
$743$		−	12175.9i		−	0.601198i	−0.953751	−	0.300599i	$-0.902813\pi$
$743$		−	12175.9i		−	0.601198i	0.953751	−	0.300599i	$-0.0971866\pi$
$744$		0			0
$745$	19643.0	+	11340.9i	0.965992	+	0.557716i
$746$		0			0
$747$	−9492.79	−	403.140i	−0.464957	−	0.0197458i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7950.95	+	13771.4i	0.386331	+	0.669144i	0.991953	−	0.126608i	$-0.0404091\pi$
$751$	7950.95	+	13771.4i	0.386331	+	0.669144i	−0.605622	+	0.795752i	$0.707076\pi$
$752$		0			0
$753$	−30382.5	−	644.853i	−1.47039	−	0.0312081i
$754$		0			0
$755$	10283.1			0.495684
$756$		0			0
$757$	39209.6			1.88256			0.941279	−	0.337630i	$-0.109625\pi$
$757$	39209.6			1.88256			0.941279	+	0.337630i	$0.109625\pi$
$758$		0			0
$759$	44588.6	+	946.368i	2.13236	+	0.0452582i
$760$		0			0
$761$	5888.86	+	10199.8i	0.280514	+	0.485864i	0.971511	−	0.236993i	$-0.0761619\pi$
$761$	5888.86	+	10199.8i	0.280514	+	0.485864i	−0.690998	+	0.722857i	$0.742829\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−13018.8	−	552.882i	−0.615288	−	0.0261301i
$766$		0			0
$767$	1184.70	+	683.988i	0.0557720	+	0.0322000i
$768$		0			0
$769$		−	5932.67i		−	0.278202i	−0.990278	−	0.139101i	$-0.955579\pi$
$769$		−	5932.67i		−	0.278202i	0.990278	−	0.139101i	$-0.0444213\pi$
$770$		0			0
$771$	19437.8	+	35380.4i	0.907956	+	1.65265i
$772$		0			0
$773$	−12154.4	+	21052.1i	−0.565543	+	0.979550i	0.431456	+	0.902134i	$0.358000\pi$
$773$	−12154.4	+	21052.1i	−0.565543	+	0.979550i	−0.996999	+	0.0774157i	$0.975333\pi$
$774$		0			0
$775$	−65.5993	+	37.8738i	−0.00304051	+	0.00175544i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	15437.0	−	8912.54i	0.709996	−	0.409916i
$780$		0			0
$781$	−24436.2	+	42324.8i	−1.11959	+	1.93918i
$782$		0			0
$783$	1200.86	−	18837.0i	0.0548085	−	0.859742i
$784$		0			0
$785$		−	432.000i		−	0.0196417i
$786$		0			0
$787$	−32642.3	−	18846.0i	−1.47849	−	0.853606i	−0.478785	−	0.877932i	$-0.658923\pi$
$787$	−32642.3	−	18846.0i	−1.47849	−	0.853606i	−0.999704	+	0.0243259i	$0.992256\pi$
$788$		0			0
$789$	−20923.7	−	12679.8i	−0.944110	−	0.572131i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	721.521	+	1249.71i	0.0323102	+	0.0559629i
$794$		0			0
$795$	308.845	−	14551.4i	0.0137781	−	0.649163i
$796$		0			0
$797$	−5364.15			−0.238404			−0.119202	−	0.992870i	$-0.538034\pi$
$797$	−5364.15			−0.238404			−0.119202	+	0.992870i	$0.538034\pi$
$798$		0			0
$799$	−15432.0			−0.683284
$800$		0			0
$801$	13604.7	+	26058.7i	0.600125	+	1.14948i
$802$		0			0
$803$	5101.35	+	8835.80i	0.224188	+	0.388305i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11064.3	+	18257.9i	−0.482630	+	0.796419i
$808$		0			0
$809$	−10538.2	−	6084.21i	−0.457975	−	0.264412i	0.253217	−	0.967409i	$-0.418511\pi$
$809$	−10538.2	−	6084.21i	−0.457975	−	0.264412i	−0.711193	+	0.702997i	$0.751845\pi$
$810$		0			0
$811$		−	24850.5i		−	1.07598i	−0.842952	−	0.537989i	$-0.819184\pi$
$811$		−	24850.5i		−	1.07598i	0.842952	−	0.537989i	$-0.180816\pi$
$812$		0			0
$813$	3685.30	−	2024.68i	0.158978	−	0.0873415i
$814$		0			0
$815$	1228.52	−	2127.85i	0.0528013	−	0.0914545i
$816$		0			0
$817$	42525.0	−	24551.8i	1.82100	−	1.05136i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	33792.8	−	19510.3i	1.43651	−	0.829372i	0.438909	−	0.898532i	$-0.355365\pi$
$821$	33792.8	−	19510.3i	1.43651	−	0.829372i	0.997606	+	0.0691595i	$0.0220317\pi$
$822$		0			0
$823$	−7694.67	+	13327.6i	−0.325905	+	0.564483i	−0.981695	−	0.190460i	$-0.939002\pi$
$823$	−7694.67	+	13327.6i	−0.325905	+	0.564483i	0.655790	+	0.754943i	$0.272335\pi$
$824$		0			0
$825$	−6785.43	+	3727.87i	−0.286350	+	0.157319i
$826$		0			0
$827$			21256.9i			0.893805i	0.894583	+	0.446902i	$0.147473\pi$
$827$			21256.9i			0.893805i	−0.894583	+	0.446902i	$0.852527\pi$
$828$		0			0
$829$	−25539.6	−	14745.3i	−1.07000	−	0.617763i	−0.141817	−	0.989893i	$-0.545294\pi$
$829$	−25539.6	−	14745.3i	−1.07000	−	0.617763i	−0.928181	+	0.372130i	$0.878628\pi$
$830$		0			0
$831$	20075.8	−	33128.3i	0.838052	−	1.38292i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−8076.05	−	13988.1i	−0.334711	−	0.579736i
$836$		0			0
$837$	−294.685	−	196.142i	−0.0121694	−	0.00809993i
$838$		0			0
$839$	39336.9			1.61867			0.809333	−	0.587350i	$-0.199829\pi$
$839$	39336.9			1.61867			0.809333	+	0.587350i	$0.199829\pi$
$840$		0			0
$841$	6288.44			0.257839
$842$		0			0
$843$	−142.224	+	6700.94i	−0.00581073	+	0.273775i
$844$		0			0
$845$	−10675.8	−	18491.1i	−0.434627	−	0.752796i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	38310.9	+	23216.4i	1.54868	+	0.938498i
$850$		0			0
$851$	−17538.2	−	10125.7i	−0.706465	−	0.407878i
$852$		0			0
$853$		−	12458.2i		−	0.500072i	−0.968237	−	0.250036i	$-0.919558\pi$
$853$		−	12458.2i		−	0.500072i	0.968237	−	0.250036i	$-0.0804424\pi$
$854$		0			0
$855$	24635.6	+	15653.4i	0.985401	+	0.626122i
$856$		0			0
$857$	−1310.45	+	2269.77i	−0.0522337	+	0.0904714i	−0.890960	−	0.454082i	$-0.849967\pi$
$857$	−1310.45	+	2269.77i	−0.0522337	+	0.0904714i	0.838726	+	0.544553i	$0.183301\pi$
$858$		0			0
$859$	17583.3	−	10151.7i	0.698410	−	0.403227i	−0.108345	−	0.994113i	$-0.534555\pi$
$859$	17583.3	−	10151.7i	0.698410	−	0.403227i	0.806755	+	0.590886i	$0.201222\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15233.4	+	8795.00i	−0.600870	+	0.346912i	−0.769384	−	0.638787i	$-0.779437\pi$
$863$	−15233.4	+	8795.00i	−0.600870	+	0.346912i	0.168514	+	0.985699i	$0.446103\pi$
$864$		0			0
$865$	−16212.5	+	28080.9i	−0.637275	+	1.10379i
$866$		0			0
$867$	6156.77	+	11206.5i	0.241171	+	0.438976i
$868$		0			0
$869$			31926.9i			1.24631i
$870$		0			0
$871$	−1932.16	−	1115.53i	−0.0751651	−	0.0433966i
$872$		0			0
$873$	−1563.85	+	36824.3i	−0.0606282	+	1.42762i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9083.05	−	15732.3i	−0.349729	−	0.605749i	0.636472	−	0.771300i	$-0.280393\pi$
$877$	−9083.05	−	15732.3i	−0.349729	−	0.605749i	−0.986201	+	0.165551i	$0.947060\pi$
$878$		0			0
$879$	32145.1	+	682.262i	1.23348	+	0.0261799i
$880$		0			0
$881$	−7990.91			−0.305585			−0.152793	−	0.988258i	$-0.548827\pi$
$881$	−7990.91			−0.305585			−0.152793	+	0.988258i	$0.548827\pi$
$882$		0			0
$883$	2454.35			0.0935397			0.0467699	−	0.998906i	$-0.485107\pi$
$883$	2454.35			0.0935397			0.0467699	+	0.998906i	$0.485107\pi$
$884$		0			0
$885$	27983.6	+	593.937i	1.06289	+	0.0225593i
$886$		0			0
$887$	11813.7	+	20461.9i	0.447197	+	0.774568i	0.998202	−	0.0599335i	$-0.0190889\pi$
$887$	11813.7	+	20461.9i	0.447197	+	0.774568i	−0.551005	+	0.834502i	$0.685756\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−29687.0	−	20681.9i	−1.11622	−	0.777632i
$892$		0			0
$893$	29936.0	+	17283.6i	1.12180	+	0.647674i
$894$		0			0
$895$			4192.76i			0.156591i
$896$		0			0
$897$	1070.90	+	1949.23i	0.0398620	+	0.0725563i
$898$		0			0
$899$	−169.732	+	293.985i	−0.00629687	+	0.0109065i
$900$		0			0
$901$	12325.9	−	7116.38i	0.455756	−	0.263131i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18825.4	+	10868.9i	−0.691468	+	0.399219i
$906$		0			0
$907$	4609.53	−	7983.94i	0.168751	−	0.292285i	−0.769230	−	0.638972i	$-0.779360\pi$
$907$	4609.53	−	7983.94i	0.168751	−	0.292285i	0.937981	+	0.346687i	$0.112693\pi$
$908$		0			0
$909$	18879.7	−	29713.2i	0.688890	−	1.08419i
$910$		0			0
$911$			19404.0i			0.705688i	0.935682	+	0.352844i	$0.114785\pi$
$911$			19404.0i			0.705688i	−0.935682	+	0.352844i	$0.885215\pi$
$912$		0			0
$913$	15125.3	+	8732.61i	0.548275	+	0.316547i
$914$		0			0
$915$	25251.1	+	15302.2i	0.912324	+	0.552869i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	13656.8	+	23654.2i	0.490201	+	0.849053i	0.999936	−	0.0112781i	$-0.00359002\pi$
$919$	13656.8	+	23654.2i	0.490201	+	0.849053i	−0.509735	+	0.860331i	$0.670257\pi$
$920$		0			0
$921$	−417.392	+	19665.6i	−0.0149333	+	0.703588i
$922$		0			0
$923$	−2437.16			−0.0869124
$924$		0			0
$925$	3515.51			0.124961
$926$		0			0
$927$	−30241.3	+	15788.4i	−1.07147	+	0.559395i
$928$		0			0
$929$	8806.15	+	15252.7i	0.311002	+	0.538671i	0.978579	−	0.205869i	$-0.0660022\pi$
$929$	8806.15	+	15252.7i	0.311002	+	0.538671i	−0.667578	+	0.744540i	$0.732669\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	16151.2	−	26652.1i	0.566738	−	0.935210i
$934$		0			0
$935$	20743.5	+	11976.2i	0.725544	+	0.418893i
$936$		0			0
$937$			18758.1i			0.654004i	0.945024	+	0.327002i	$0.106038\pi$
$937$			18758.1i			0.654004i	−0.945024	+	0.327002i	$0.893962\pi$
$938$		0			0
$939$	26088.0	−	14332.6i	0.906655	−	0.498110i
$940$		0			0
$941$	−2123.19	+	3677.48i	−0.0735538	+	0.127399i	−0.900456	−	0.434946i	$-0.856767\pi$
$941$	−2123.19	+	3677.48i	−0.0735538	+	0.127399i	0.826903	+	0.562345i	$0.190101\pi$
$942$		0			0
$943$	24067.1	−	13895.1i	0.831104	−	0.479838i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27111.0	+	15652.6i	−0.930296	+	0.537106i	−0.886905	−	0.461952i	$-0.847149\pi$
$947$	−27111.0	+	15652.6i	−0.930296	+	0.537106i	−0.0433905	+	0.999058i	$0.513816\pi$
$948$		0			0
$949$	−254.393	+	440.622i	−0.00870175	+	0.0150719i
$950$		0			0
$951$	−30598.5	+	16810.6i	−1.04335	+	0.573209i
$952$		0			0
$953$			33871.8i			1.15133i	0.817687	+	0.575663i	$0.195256\pi$
$953$			33871.8i			1.15133i	−0.817687	+	0.575663i	$0.804744\pi$
$954$		0			0
$955$	−9777.91	−	5645.28i	−0.331315	−	0.191285i
$956$		0			0
$957$	−17981.7	+	29672.8i	−0.607385	+	1.00228i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14892.3	−	25794.2i	−0.499893	−	0.865840i
$962$		0			0
$963$	35023.1	−	18284.9i	1.17197	−	0.611862i
$964$		0			0
$965$	−21983.3			−0.733333
$966$		0			0
$967$	34214.9			1.13782			0.568912	−	0.822398i	$-0.307364\pi$
$967$	34214.9			1.13782			0.568912	+	0.822398i	$0.307364\pi$
$968$		0			0
$969$	−605.661	+	28536.0i	−0.0200791	+	0.946036i
$970$		0			0
$971$	6266.70	+	10854.2i	0.207114	+	0.358732i	0.950804	−	0.309792i	$-0.100260\pi$
$971$	6266.70	+	10854.2i	0.207114	+	0.358732i	−0.743690	+	0.668525i	$0.766926\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−330.182	−	200.091i	−0.0108454	−	0.00657234i
$976$		0			0
$977$	−33448.2	−	19311.4i	−1.09530	−	0.632369i	−0.160314	−	0.987066i	$-0.551251\pi$
$977$	−33448.2	−	19311.4i	−1.09530	−	0.632369i	−0.934981	+	0.354697i	$0.884584\pi$
$978$		0			0
$979$		−	54035.8i		−	1.76404i
$980$		0			0
$981$	32432.0	−	51042.0i	1.05553	−	1.66121i
$982$		0			0
$983$	17134.5	−	29677.9i	0.555958	−	0.962947i	−0.441870	−	0.897079i	$-0.645685\pi$
$983$	17134.5	−	29677.9i	0.555958	−	0.962947i	0.997828	−	0.0658685i	$-0.0209818\pi$
$984$		0			0
$985$	27687.1	−	15985.2i	0.895619	−	0.517086i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	66298.7	−	38277.6i	2.13162	−	1.23069i
$990$		0			0
$991$	−7547.62	+	13072.9i	−0.241935	+	0.419044i	−0.961266	−	0.275624i	$-0.911116\pi$
$991$	−7547.62	+	13072.9i	−0.241935	+	0.419044i	0.719330	+	0.694668i	$0.244449\pi$
$992$		0			0
$993$	−4229.31	−	7698.13i	−0.135159	−	0.246015i
$994$		0			0
$995$		−	42966.6i		−	1.36898i
$996$		0			0
$997$	−1996.82	−	1152.87i	−0.0634303	−	0.0366215i	0.467949	−	0.883755i	$-0.344993\pi$
$997$	−1996.82	−	1152.87i	−0.0634303	−	0.0366215i	−0.531380	+	0.847134i	$0.678326\pi$
$998$		0			0
$999$	7292.70	+	14721.8i	0.230962	+	0.466243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.e.521.24		48
3.2	odd	2	inner	588.4.k.e.521.16		48
7.2	even	3	inner	588.4.k.e.509.9		48
7.3	odd	6		588.4.f.d.293.18	yes	24
7.4	even	3		588.4.f.d.293.7	✓	24
7.5	odd	6	inner	588.4.k.e.509.16		48
7.6	odd	2	inner	588.4.k.e.521.1		48
21.2	odd	6	inner	588.4.k.e.509.1		48
21.5	even	6	inner	588.4.k.e.509.24		48
21.11	odd	6		588.4.f.d.293.17	yes	24
21.17	even	6		588.4.f.d.293.8	yes	24
21.20	even	2	inner	588.4.k.e.521.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.f.d.293.7	✓	24	7.4	even	3
588.4.f.d.293.8	yes	24	21.17	even	6
588.4.f.d.293.17	yes	24	21.11	odd	6
588.4.f.d.293.18	yes	24	7.3	odd	6
588.4.k.e.509.1		48	21.2	odd	6	inner
588.4.k.e.509.9		48	7.2	even	3	inner
588.4.k.e.509.16		48	7.5	odd	6	inner
588.4.k.e.509.24		48	21.5	even	6	inner
588.4.k.e.521.1		48	7.6	odd	2	inner
588.4.k.e.521.9		48	21.20	even	2	inner
588.4.k.e.521.16		48	3.2	odd	2	inner
588.4.k.e.521.24		48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.19498 + 0.110261i) q^{3} +(-4.87287 - 8.44005i) q^{5} +(26.9757 + 1.14560i) q^{9} +O(q^{10})\)	\(q+(5.19498 + 0.110261i) q^{3} +(-4.87287 - 8.44005i) q^{5} +(26.9757 + 1.14560i) q^{9} +(-42.9817 - 24.8155i) q^{11} -2.47499i q^{13} +(-24.3838 - 44.3832i) q^{15} +(24.7602 - 42.8858i) q^{17} +(-96.0631 + 55.4620i) q^{19} +(-149.767 + 86.4683i) q^{23} +(15.0103 - 25.9987i) q^{25} +(140.012 + 8.92575i) q^{27} -134.538i q^{29} +(-2.18514 - 1.26159i) q^{31} +(-220.553 - 133.655i) q^{33} +(58.5515 + 101.414i) q^{37} +(0.272894 - 12.8575i) q^{39} -160.696 q^{41} -442.678 q^{43} +(-121.780 - 233.259i) q^{45} +(-155.814 - 269.879i) q^{47} +(133.357 - 220.061i) q^{51} +(248.907 + 143.706i) q^{53} +483.690i q^{55} +(-505.161 + 277.532i) q^{57} +(-276.360 + 478.670i) q^{59} +(-504.937 + 291.525i) q^{61} +(-20.8890 + 12.0603i) q^{65} +(450.723 - 780.675i) q^{67} +(-787.573 + 432.688i) q^{69} -984.717i q^{71} +(-178.030 - 102.786i) q^{73} +(80.8451 - 133.408i) q^{75} +(-321.643 - 557.103i) q^{79} +(726.375 + 61.8069i) q^{81} -351.902 q^{83} -482.612 q^{85} +(14.8343 - 698.924i) q^{87} +(544.376 + 942.887i) q^{89} +(-11.2126 - 6.79487i) q^{93} +(936.205 + 540.518i) q^{95} +1365.09i q^{97} +(-1131.03 - 718.654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 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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