LMFDB - Embedded newform 588.4.k.e.521.9

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			521.9
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.69298 - 4.44386i) q^{3} +(-4.87287 - 8.44005i) q^{5} +(-12.4957 + 23.9344i) q^{9} +O(q^{10})$	\(q+(-2.69298 - 4.44386i) q^{3} +(-4.87287 - 8.44005i) q^{5} +(-12.4957 + 23.9344i) q^{9} +(42.9817 + 24.8155i) q^{11} +2.47499i q^{13} +(-24.3838 + 44.3832i) q^{15} +(24.7602 - 42.8858i) q^{17} +(96.0631 - 55.4620i) q^{19} +(149.767 - 86.4683i) q^{23} +(15.0103 - 25.9987i) q^{25} +(140.012 - 8.92575i) q^{27} +134.538i q^{29} +(2.18514 + 1.26159i) q^{31} +(-5.47234 - 257.832i) q^{33} +(58.5515 + 101.414i) q^{37} +(10.9985 - 6.66509i) q^{39} -160.696 q^{41} -442.678 q^{43} +(262.898 - 11.1648i) q^{45} +(-155.814 - 269.879i) q^{47} +(-257.257 + 5.46014i) q^{51} +(-248.907 - 143.706i) q^{53} -483.690i q^{55} +(-505.161 - 277.532i) q^{57} +(-276.360 + 478.670i) q^{59} +(504.937 - 291.525i) q^{61} +(20.8890 - 12.0603i) q^{65} +(450.723 - 780.675i) q^{67} +(-787.573 - 432.688i) q^{69} +984.717i q^{71} +(178.030 + 102.786i) q^{73} +(-155.957 + 3.31010i) q^{75} +(-321.643 - 557.103i) q^{79} +(-416.714 - 598.156i) q^{81} -351.902 q^{83} -482.612 q^{85} +(597.869 - 362.309i) q^{87} +(544.376 + 942.887i) q^{89} +(-0.278207 - 13.1079i) q^{93} +(-936.205 - 540.518i) q^{95} -1365.09i q^{97} +(-1131.03 + 718.654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.69298	−	4.44386i	−0.518264	−	0.855221i
$3$	−2.69298	−	4.44386i	−0.518264	−	0.855221i
$4$		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
$9$	−12.4957	+	23.9344i	−0.462804	+	0.886460i
$10$		0			0
$11$	42.9817	+	24.8155i	1.17813	+	0.680195i	0.955582	−	0.294726i	$-0.0952284\pi$
$11$	42.9817	+	24.8155i	1.17813	+	0.680195i	0.222551	+	0.974921i	$0.428562\pi$
$12$		0			0
$13$			2.47499i			0.0528029i	0.999651	+	0.0264015i	$0.00840482\pi$
$13$			2.47499i			0.0528029i	−0.999651	+	0.0264015i	$0.991595\pi$
$14$		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	0.208631	−	0.977994i	$-0.433099\pi$
$19$	96.0631	−	55.4620i	1.15991	−	0.669677i	0.951284	+	0.308317i	$0.0997658\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	149.767	−	86.4683i	1.35777	−	0.783908i	0.368446	−	0.929649i	$-0.379890\pi$
$23$	149.767	−	86.4683i	1.35777	−	0.783908i	0.989323	+	0.145741i	$0.0465567\pi$
$24$		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	$0.141749\pi$
$29$			134.538i			0.861488i	−0.902474	+	0.430744i	$0.858251\pi$
$30$		0			0
$31$	2.18514	+	1.26159i	0.0126601	+	0.00730929i	0.506317	−	0.862348i	$-0.331007\pi$
$31$	2.18514	+	1.26159i	0.0126601	+	0.00730929i	−0.493657	+	0.869657i	$0.664340\pi$
$32$		0			0
$33$	−5.47234	−	257.832i	−0.0288670	−	1.36008i
$34$		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
$39$	10.9985	−	6.66509i	0.0451582	−	0.0273659i
$40$		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
$45$	262.898	−	11.1648i	0.870900	−	0.0369854i
$46$		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
$51$	−257.257	+	5.46014i	−0.706337	+	0.0149916i
$52$		0			0
$53$	−248.907	−	143.706i	−0.645093	−	0.372445i	0.141480	−	0.989941i	$-0.454814\pi$
$53$	−248.907	−	143.706i	−0.645093	−	0.372445i	−0.786574	+	0.617496i	$0.788147\pi$
$54$		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	0.134455	−	0.990920i	$-0.457072\pi$
$61$	504.937	−	291.525i	1.05984	−	0.611901i	0.925389	+	0.379018i	$0.123738\pi$
$62$		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	$0.307695\pi$
$71$			984.717i			1.64598i	−0.568058	+	0.822988i	$0.692305\pi$
$72$		0			0
$73$	178.030	+	102.786i	0.285436	+	0.164797i	0.635882	−	0.771786i	$-0.280637\pi$
$73$	178.030	+	102.786i	0.285436	+	0.164797i	−0.350446	+	0.936583i	$0.613970\pi$
$74$		0			0
$75$	−155.957	+	3.31010i	−0.240111	+	0.00509623i
$76$		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
$81$	−416.714	−	598.156i	−0.571624	−	0.820516i
$82$		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
$87$	597.869	−	362.309i	0.736762	−	0.446478i
$88$		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
$93$	−0.278207	−	13.1079i	−0.000310202	−	0.0146153i
$94$		0			0
$95$	−936.205	−	540.518i	−1.01108	−	0.583747i
$96$		0			0
$97$		−	1365.09i		−	1.42891i	−0.699683	−	0.714454i	$-0.746675\pi$
$97$		−	1365.09i		−	1.42891i	0.699683	−	0.714454i	$-0.253325\pi$
$98$		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	0.125027	−	0.992153i	$-0.460098\pi$
$103$	1094.23	−	631.752i	1.04677	−	0.604354i	0.921744	+	0.387800i	$0.126765\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1267.25	+	731.647i	−1.14495	+	0.661037i	−0.947652	−	0.319306i	$-0.896550\pi$
$107$	−1267.25	+	731.647i	−1.14495	+	0.661037i	−0.197299	+	0.980343i	$0.563217\pi$
$108$		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	$-0.962636\pi$
$113$		−	281.355i		−	0.234227i	0.993119	−	0.117114i	$-0.0373642\pi$
$114$		0			0
$115$	−1459.59	−	842.697i	−1.18355	−	0.683321i
$116$		0			0
$117$	−59.2374	−	30.9268i	−0.0468077	−	0.0244374i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	566.115	+	980.541i	0.425331	+	0.736695i
$122$		0			0
$123$	432.752	+	714.111i	0.317235	+	0.523490i
$124$		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
$129$	1192.12	+	1967.20i	0.813647	+	1.34265i
$130$		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
$135$	−757.593	−	1138.21i	−0.482987	−	0.725643i
$136$		0			0
$137$	892.802	+	515.459i	0.556768	+	0.321450i	0.751847	−	0.659337i	$-0.229163\pi$
$137$	892.802	+	515.459i	0.556768	+	0.321450i	−0.195079	+	0.980787i	$0.562496\pi$
$138$		0			0
$139$		−	234.497i		−	0.143092i	−0.997437	−	0.0715460i	$-0.977207\pi$
$139$		−	234.497i		−	0.143092i	0.997437	−	0.0715460i	$-0.0227933\pi$
$140$		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	0.169830	−	0.985473i	$-0.445678\pi$
$149$	2015.55	−	1163.68i	1.10819	−	0.639814i	0.938360	+	0.345660i	$0.112345\pi$
$150$		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	0.490211	−	0.871604i	$-0.336920\pi$
$157$	−38.3884	−	22.1635i	−0.0195142	−	0.0112665i	−0.509725	+	0.860337i	$0.670253\pi$
$158$		0			0
$159$	31.6903	+	1493.10i	0.0158063	+	0.744722i
$160$		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
$165$	−2149.45	+	1302.57i	−1.01415	+	0.614574i
$166$		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
$171$	127.075	+	2992.25i	0.0568285	+	1.33815i
$172$		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
$177$	2871.37	−	60.9433i	1.21935	−	0.0258801i
$178$		0			0
$179$	372.577	+	215.108i	0.155574	+	0.0898206i	0.575766	−	0.817615i	$-0.304704\pi$
$179$	372.577	+	215.108i	0.155574	+	0.0898206i	−0.420192	+	0.907435i	$0.638037\pi$
$180$		0			0
$181$			2230.49i			0.915971i	0.888960	+	0.457986i	$0.151429\pi$
$181$			2230.49i			0.915971i	−0.888960	+	0.457986i	$0.848571\pi$
$182$		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	−0.677855	−	0.735195i	$-0.737090\pi$
$191$	−1003.30	+	579.256i	−0.380086	+	0.219442i	0.297770	+	0.954638i	$0.403757\pi$
$192$		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	$-0.797863\pi$
$197$		−	3280.44i		−	1.18641i	0.805053	−	0.593203i	$-0.202137\pi$
$198$		0			0
$199$	−3818.10	−	2204.38i	−1.36009	−	0.785248i	−0.370454	−	0.928851i	$-0.620798\pi$
$199$	−3818.10	−	2204.38i	−1.36009	−	0.785248i	−0.989635	+	0.143603i	$0.954131\pi$
$200$		0			0
$201$	−4683.00	+	99.3940i	−1.64335	+	0.0348792i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	783.051	+	1356.28i	0.266784	+	0.462083i
$206$		0			0
$207$	198.117	+	4665.08i	0.0665221	+	1.56640i
$208$		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
$213$	4375.94	−	2651.82i	1.40767	−	0.853051i
$214$		0			0
$215$	2157.11	+	3736.22i	0.684249	+	1.18515i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−22.6664	−	1067.94i	−0.00699386	−	0.329519i
$220$		0			0
$221$	106.142	+	61.2811i	0.0323072	+	0.0186525i
$222$		0			0
$223$			1134.63i			0.340718i	0.985382	+	0.170359i	$0.0544928\pi$
$223$			1134.63i			0.340718i	−0.985382	+	0.170359i	$0.945507\pi$
$224$		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	−0.793662	−	0.608359i	$-0.791828\pi$
$229$	−2299.77	+	1327.77i	−0.663638	+	0.383152i	0.130023	+	0.991511i	$0.458495\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2734.14	+	1578.56i	−0.768754	+	0.443840i	−0.832430	−	0.554130i	$-0.813051\pi$
$233$	−2734.14	+	1578.56i	−0.768754	+	0.443840i	0.0636761	+	0.997971i	$0.479718\pi$
$234$		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	$0.0890351\pi$
$239$			2040.14i			0.552157i	−0.961135	+	0.276079i	$0.910965\pi$
$240$		0			0
$241$	−3958.64	−	2285.52i	−1.05809	−	0.610886i	−0.133184	−	0.991091i	$-0.542520\pi$
$241$	−3958.64	−	2285.52i	−1.05809	−	0.610886i	−0.924902	+	0.380205i	$0.875853\pi$
$242$		0			0
$243$	−1535.92	+	3462.64i	−0.405470	+	0.914109i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	137.268	+	237.755i	0.0353609	+	0.0612469i
$248$		0			0
$249$	947.664	+	1563.80i	0.241188	+	0.397999i
$250$		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
$255$	1299.66	+	2144.66i	0.319169	+	0.526681i
$256$		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
$261$	−3220.10	−	1681.15i	−0.763675	−	0.398700i
$262$		0			0
$263$	4077.64	+	2354.23i	0.956038	+	0.551969i	0.894951	−	0.446164i	$-0.147210\pi$
$263$	4077.64	+	2354.23i	0.956038	+	0.551969i	0.0610865	+	0.998132i	$0.480543\pi$
$264$		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	−0.576484	−	0.817109i	$-0.695576\pi$
$271$	−700.809	+	404.612i	−0.157089	+	0.0906953i	0.419395	+	0.907804i	$0.362242\pi$
$272$		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	$-0.956280\pi$
$281$		−	1289.89i		−	0.273837i	0.990582	−	0.136919i	$-0.0437198\pi$
$282$		0			0
$283$	−7466.08	−	4310.54i	−1.56824	−	0.905424i	−0.996374	−	0.0850780i	$-0.972886\pi$
$283$	−7466.08	−	4310.54i	−1.56824	−	0.905424i	−0.571867	−	0.820346i	$-0.693781\pi$
$284$		0			0
$285$	119.196	+	5615.97i	0.0247739	+	1.16723i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1230.37	+	2131.06i	0.250431	+	0.433760i
$290$		0			0
$291$	−6066.27	+	3676.16i	−1.22203	+	0.740551i
$292$		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
$297$	6239.44	+	3090.82i	1.21902	+	0.603863i
$298$		0			0
$299$	214.008	+	370.673i	0.0413926	+	0.0716941i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6773.49	+	143.764i	−1.28425	+	0.0272574i
$304$		0			0
$305$	−4920.98	−	2841.13i	−0.923850	−	0.533385i
$306$		0			0
$307$		−	3785.51i		−	0.703747i	−0.936048	−	0.351873i	$-0.885545\pi$
$307$		−	3785.51i		−	0.703747i	0.936048	−	0.351873i	$-0.114455\pi$
$308$		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	−0.875861	−	0.482563i	$-0.839706\pi$
$313$	−4960.97	+	2864.22i	−0.895881	+	0.517237i	−0.0200193	+	0.999800i	$0.506373\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5818.71	−	3359.43i	1.03095	−	0.595219i	0.113693	−	0.993516i	$-0.463732\pi$
$317$	5818.71	−	3359.43i	1.03095	−	0.595219i	0.917257	+	0.398297i	$0.130398\pi$
$318$		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
$327$	−11635.6	+	246.960i	−1.96774	+	0.0417643i
$328$		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
$333$	−3158.93	+	134.154i	−0.519845	+	0.0220768i
$334$		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
$339$	−1250.30	+	757.684i	−0.200316	+	0.121392i
$340$		0			0
$341$	62.6139	+	108.450i	0.00994349	+	0.0172226i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	185.833	+	8755.59i	0.0289997	+	1.36633i
$346$		0			0
$347$	1092.59	+	630.806i	0.169029	+	0.0975891i	0.582128	−	0.813097i	$-0.302220\pi$
$347$	1092.59	+	630.806i	0.169029	+	0.0975891i	−0.413099	+	0.910686i	$0.635554\pi$
$348$		0			0
$349$			10981.9i			1.68438i	0.539179	+	0.842191i	$0.318735\pi$
$349$			10981.9i			1.68438i	−0.539179	+	0.842191i	$0.681265\pi$
$350$		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	−0.467885	−	0.883789i	$-0.654984\pi$
$359$	432.312	−	249.595i	0.0635559	−	0.0366940i	0.531441	+	0.847095i	$0.321651\pi$
$360$		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	0.479746	−	0.877408i	$-0.340729\pi$
$367$	−282.908	−	163.337i	−0.0402390	−	0.0232320i	−0.519985	+	0.854176i	$0.674062\pi$
$368$		0			0
$369$	2008.01	−	3846.17i	0.283287	−	0.542612i
$370$		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
$375$	4068.53	+	6713.73i	0.560261	+	0.924522i
$376$		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
$381$	1551.41	+	2560.08i	0.208612	+	0.344244i
$382$		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
$387$	5531.57	−	10595.2i	0.726578	−	1.39170i
$388$		0			0
$389$	1558.98	+	900.077i	0.203196	+	0.117315i	0.598146	−	0.801388i	$-0.295904\pi$
$389$	1558.98	+	900.077i	0.203196	+	0.117315i	−0.394949	+	0.918703i	$0.629238\pi$
$390$		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	−0.102249	−	0.994759i	$-0.532604\pi$
$397$	5601.29	−	3233.91i	0.708113	−	0.408829i	0.810362	+	0.585930i	$0.199271\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2974.16	−	1717.13i	0.370381	−	0.213839i	−0.303244	−	0.952913i	$-0.598070\pi$
$401$	2974.16	−	1717.13i	0.370381	−	0.213839i	0.673625	+	0.739074i	$0.264736\pi$
$402$		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	0.449786	−	0.893136i	$-0.351500\pi$
$409$	−817.228	−	471.827i	−0.0988003	−	0.0570424i	−0.548586	+	0.836094i	$0.684834\pi$
$410$		0			0
$411$	−113.670	−	5355.61i	−0.0136421	−	0.642756i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1714.77	+	2970.07i	0.202831	+	0.351313i
$416$		0			0
$417$	−1042.07	+	631.496i	−0.122375	+	0.0741594i
$418$		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
$423$	8406.41	−	357.004i	0.966273	−	0.0410357i
$424$		0			0
$425$	−743.317	−	1287.46i	−0.0848381	−	0.146944i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	638.131	−	13.5440i	0.0718164	−	0.00152426i
$430$		0			0
$431$	14439.3	+	8336.51i	1.61372	+	0.931684i	0.988497	+	0.151241i	$0.0483268\pi$
$431$	14439.3	+	8336.51i	1.61372	+	0.931684i	0.625227	+	0.780443i	$0.285007\pi$
$432$		0			0
$433$		−	2848.46i		−	0.316140i	−0.987428	−	0.158070i	$-0.949473\pi$
$433$		−	2848.46i		−	0.316140i	0.987428	−	0.158070i	$-0.0505271\pi$
$434$		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	0.00556785	−	0.999984i	$-0.498228\pi$
$439$	8042.46	−	4643.32i	0.874364	−	0.504814i	0.868796	+	0.495170i	$0.164894\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4281.76	+	2472.08i	−0.459216	+	0.265128i	−0.711714	−	0.702469i	$-0.752081\pi$
$443$	−4281.76	+	2472.08i	−0.459216	+	0.265128i	0.252499	+	0.967597i	$0.418748\pi$
$444$		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	$0.316858\pi$
$449$			15964.7i			1.67799i	−0.544136	+	0.838997i	$0.683142\pi$
$450$		0			0
$451$	−6906.99	−	3987.75i	−0.721147	−	0.416355i
$452$		0			0
$453$	5481.44	−	116.341i	0.568522	−	0.0120666i
$454$		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
$459$	3083.93	−	6225.53i	0.313607	−	0.633078i
$460$		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
$465$	−109.275	+	66.2210i	−0.0108979	+	0.00660414i
$466$		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
$471$	4.88753	+	230.278i	0.000478144	+	0.0225280i
$472$		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	$-0.980901\pi$
$491$		−	1304.86i		−	0.119933i	0.998200	−	0.0599667i	$-0.0190995\pi$
$492$		0			0
$493$	5769.79	+	3331.19i	0.527096	+	0.304319i
$494$		0			0
$495$	11576.8	+	6044.05i	1.05119	+	0.548808i
$496$		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
$501$	−4463.21	−	7365.03i	−0.398007	−	0.656777i
$502$		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
$507$	−5899.98	−	9735.93i	−0.516819	−	0.852836i
$508$		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
$513$	12954.9	−	8622.78i	1.11496	−	0.742115i
$514$		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	−0.237574	−	0.971369i	$-0.576352\pi$
$523$	5799.32	−	3348.24i	0.484869	−	0.279940i	0.722444	+	0.691430i	$0.243019\pi$
$524$		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
$537$	−47.4358	−	2234.96i	−0.00381193	−	0.179601i
$538$		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
$543$	9911.96	−	6006.66i	0.783357	−	0.474715i
$544$		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
$549$	667.945	+	15728.2i	0.0519257	+	1.22270i
$550$		0			0
$551$	7461.77	+	12924.2i	0.576918	+	0.999252i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−5928.79	+	125.835i	−0.453447	+	0.00962417i
$556$		0			0
$557$	6062.22	+	3500.02i	0.461157	+	0.266249i	0.712531	−	0.701641i	$-0.247549\pi$
$557$	6062.22	+	3500.02i	0.461157	+	0.266249i	−0.251374	+	0.967890i	$0.580882\pi$
$558$		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	−0.782239	−	0.622979i	$-0.785922\pi$
$569$	−8603.00	+	4966.94i	−0.633843	+	0.365949i	0.148396	+	0.988928i	$0.452589\pi$
$570$		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	0.937006	−	0.349313i	$-0.113585\pi$
$577$	15287.5	+	8826.26i	1.10300	+	0.636815i	0.165989	+	0.986128i	$0.446918\pi$
$578$		0			0
$579$	−11718.2	+	248.713i	−0.841093	+	0.0178517i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−7132.28	−	12353.5i	−0.506670	−	0.877579i
$584$		0			0
$585$	27.6326	+	650.669i	0.00195294	+	0.0459861i
$586$		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
$591$	−14577.8	+	8834.16i	−1.01464	+	0.614871i
$592$		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
$597$	486.113	+	22903.4i	0.0333254	+	1.57014i
$598$		0			0
$599$	−23961.5	−	13834.2i	−1.63446	−	0.943655i	−0.982695	−	0.185233i	$-0.940696\pi$
$599$	−23961.5	−	13834.2i	−1.63446	−	0.943655i	−0.651764	−	0.758422i	$-0.725971\pi$
$600$		0			0
$601$		−	11624.0i		−	0.788937i	−0.918909	−	0.394469i	$-0.870929\pi$
$601$		−	11624.0i		−	0.788937i	0.918909	−	0.394469i	$-0.129071\pi$
$602$		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	−0.586793	−	0.809737i	$-0.699610\pi$
$607$	−2675.97	+	1544.97i	−0.178936	+	0.103309i	0.407857	+	0.913046i	$0.366276\pi$
$608$		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	$-0.886639\pi$
$617$		−	10686.9i		−	0.697307i	0.937252	−	0.348654i	$-0.113361\pi$
$618$		0			0
$619$	−4946.00	−	2855.58i	−0.321158	−	0.185420i	0.330751	−	0.943718i	$-0.392698\pi$
$619$	−4946.00	−	2855.58i	−0.321158	−	0.185420i	−0.651908	+	0.758298i	$0.726031\pi$
$620$		0			0
$621$	20197.4	−	13443.4i	1.30514	−	0.868702i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	5485.59	+	9501.31i	0.351077	+	0.608084i
$626$		0			0
$627$	−14825.6	−	24464.6i	−0.944300	−	1.55825i
$628$		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
$633$	−15135.8	−	24976.5i	−0.950385	−	1.56829i
$634$		0			0
$635$	2807.23	+	4862.27i	0.175436	+	0.303864i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−23568.6	−	12304.7i	−1.45909	−	0.761765i
$640$		0			0
$641$	14083.3	+	8131.00i	0.867796	+	0.501022i	0.866615	−	0.498977i	$-0.166291\pi$
$641$	14083.3	+	8131.00i	0.867796	+	0.501022i	0.00118054	+	0.999999i	$0.499624\pi$
$642$		0			0
$643$			13805.8i			0.846729i	0.905959	+	0.423365i	$0.139151\pi$
$643$			13805.8i			0.846729i	−0.905959	+	0.423365i	$0.860849\pi$
$644$		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	0.0756247	−	0.997136i	$-0.475905\pi$
$653$	16302.6	−	9412.30i	0.976983	−	0.564061i	0.901358	+	0.433075i	$0.142572\pi$
$654$		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	$-0.967273\pi$
$659$		−	3472.55i		−	0.205268i	0.994719	−	0.102634i	$-0.0327270\pi$
$660$		0			0
$661$	11328.2	+	6540.36i	0.666592	+	0.384857i	0.794784	−	0.606892i	$-0.207584\pi$
$661$	11328.2	+	6540.36i	0.666592	+	0.384857i	−0.128192	+	0.991749i	$0.540917\pi$
$662$		0			0
$663$	−13.5138	−	636.708i	−0.000791602	−	0.0372967i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11633.3	+	20149.5i	0.675327	+	1.16970i
$668$		0			0
$669$	5042.11	−	3055.52i	0.291389	−	0.176582i
$670$		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
$675$	1869.57	−	3774.10i	0.106607	−	0.215208i
$676$		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
$681$	11030.0	−	234.106i	0.620661	−	0.0131732i
$682$		0			0
$683$	22216.3	+	12826.6i	1.24463	+	0.718589i	0.970034	−	0.242970i	$-0.0781218\pi$
$683$	22216.3	+	12826.6i	1.24463	+	0.718589i	0.274598	+	0.961559i	$0.411455\pi$
$684$		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	−0.290335	−	0.956925i	$-0.593767\pi$
$691$	7142.53	−	4123.74i	0.393219	−	0.227025i	0.683554	+	0.729900i	$0.260433\pi$
$692$		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	$0.239463\pi$
$701$			25364.7i			1.36663i	−0.730122	+	0.683317i	$0.760537\pi$
$702$		0			0
$703$	11249.3	+	6494.77i	0.603519	+	0.348442i
$704$		0			0
$705$	15777.4	−	334.867i	0.842855	−	0.0178891i
$706$		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
$711$	17353.1	−	736.952i	0.915320	−	0.0388718i
$712$		0			0
$713$	436.350			0.0229193
$714$		0			0
$715$	1197.13			0.0626154
$716$		0			0
$717$	9066.09	−	5494.05i	0.472216	−	0.286163i
$718$		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
$723$	504.007	+	23746.5i	0.0259256	+	1.22150i
$724$		0			0
$725$	3497.82	+	2019.47i	0.179180	+	0.103450i
$726$		0			0
$727$			35634.9i			1.81792i	0.416887	+	0.908958i	$0.363121\pi$
$727$			35634.9i			1.81792i	−0.416887	+	0.908958i	$0.636879\pi$
$728$		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	−0.747427	−	0.664344i	$-0.768711\pi$
$733$	−10831.6	+	6253.60i	−0.545802	+	0.315119i	0.201625	+	0.979463i	$0.435378\pi$
$734$		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	$0.0971866\pi$
$743$			12175.9i			0.601198i	−0.953751	+	0.300599i	$0.902813\pi$
$744$		0			0
$745$	−19643.0	−	11340.9i	−0.965992	−	0.557716i
$746$		0			0
$747$	4397.27	−	8422.57i	0.215378	−	0.412538i
$748$		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
$753$	15749.7	+	25989.6i	0.762220	+	1.25779i
$754$		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
$759$	−23113.9	−	38141.6i	−1.10538	−	1.82405i
$760$		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
$765$	6030.58	−	11551.0i	0.285015	−	0.545920i
$766$		0			0
$767$	−1184.70	−	683.988i	−0.0557720	−	0.0322000i
$768$		0			0
$769$			5932.67i			0.278202i	0.990278	+	0.139101i	$0.0444213\pi$
$769$			5932.67i			0.278202i	−0.990278	+	0.139101i	$0.955579\pi$
$770$		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	0.999704	−	0.0243259i	$-0.00774392\pi$
$787$	32642.3	+	18846.0i	1.47849	+	0.853606i	0.478785	+	0.877932i	$0.341077\pi$
$788$		0			0
$789$	−519.157	−	24460.3i	−0.0234252	−	1.10369i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	721.521	+	1249.71i	0.0323102	+	0.0559629i
$794$		0			0
$795$	12447.4	−	7543.16i	0.555303	−	0.336514i
$796$		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
$801$	−29369.8	+	1247.28i	−1.29555	+	0.0550193i
$802$		0			0
$803$	5101.35	+	8835.80i	0.224188	+	0.388305i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	21344.0	−	453.015i	0.931034	−	0.0197607i
$808$		0			0
$809$	10538.2	+	6084.21i	0.457975	+	0.264412i	0.711193	−	0.702997i	$-0.248155\pi$
$809$	10538.2	+	6084.21i	0.457975	+	0.264412i	−0.253217	+	0.967409i	$0.581489\pi$
$810$		0			0
$811$			24850.5i			1.07598i	0.842952	+	0.537989i	$0.180816\pi$
$811$			24850.5i			1.07598i	−0.842952	+	0.537989i	$0.819184\pi$
$812$		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	−0.997606	−	0.0691595i	$-0.977968\pi$
$821$	−33792.8	+	19510.3i	−1.43651	+	0.829372i	−0.438909	+	0.898532i	$0.644635\pi$
$822$		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	$-0.852527\pi$
$827$		−	21256.9i		−	0.893805i	0.894583	−	0.446902i	$-0.147473\pi$
$828$		0			0
$829$	25539.6	+	14745.3i	1.07000	+	0.617763i	0.928181	−	0.372130i	$-0.121372\pi$
$829$	25539.6	+	14745.3i	1.07000	+	0.617763i	0.141817	+	0.989893i	$0.454706\pi$
$830$		0			0
$831$	−38727.9	+	821.978i	−1.61667	+	0.0343130i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−8076.05	−	13988.1i	−0.334711	−	0.579736i
$836$		0			0
$837$	317.206	+	157.134i	0.0130994	+	0.00648904i
$838$		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
$843$	−5732.07	+	3473.64i	−0.234191	+	0.141920i
$844$		0			0
$845$	−10675.8	−	18491.1i	−0.434627	−	0.752796i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	950.566	+	44786.4i	0.0384256	+	1.81044i
$850$		0			0
$851$	17538.2	+	10125.7i	0.706465	+	0.407878i
$852$		0			0
$853$			12458.2i			0.500072i	0.968237	+	0.250036i	$0.0804424\pi$
$853$			12458.2i			0.500072i	−0.968237	+	0.250036i	$0.919558\pi$
$854$		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	−0.806755	−	0.590886i	$-0.798778\pi$
$859$	−17583.3	+	10151.7i	−0.698410	+	0.403227i	0.108345	+	0.994113i	$0.465445\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15233.4	−	8795.00i	0.600870	−	0.346912i	−0.168514	−	0.985699i	$-0.553897\pi$
$863$	15233.4	−	8795.00i	0.600870	−	0.346912i	0.769384	+	0.638787i	$0.220563\pi$
$864$		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
$873$	32672.7	+	17057.8i	1.26667	+	0.661305i
$874$		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
$879$	−16663.4	−	27497.3i	−0.639412	−	1.05513i
$880$		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
$885$	−14506.2	−	23937.6i	−0.550983	−	0.909212i
$886$		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
$891$	−3067.54	−	36050.7i	−0.115338	−	1.35549i
$892$		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	$-0.885215\pi$
$911$		−	19404.0i		−	0.705688i	0.935682	−	0.352844i	$-0.114785\pi$
$912$		0			0
$913$	−15125.3	−	8732.61i	−0.548275	−	0.316547i
$914$		0			0
$915$	626.529	+	29519.2i	0.0226365	+	1.06653i
$916$		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
$921$	−16822.2	+	10194.3i	−0.601859	+	0.364727i
$922$		0			0
$923$	−2437.16			−0.0869124
$924$		0			0
$925$	3515.51			0.124961
$926$		0			0
$927$	1447.48	+	34083.9i	0.0512852	+	1.20762i
$928$		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
$933$	−31157.0	+	661.290i	−1.09328	+	0.0232044i
$934$		0			0
$935$	−20743.5	−	11976.2i	−0.725544	−	0.418893i
$936$		0			0
$937$		−	18758.1i		−	0.654004i	−0.945024	−	0.327002i	$-0.893962\pi$
$937$		−	18758.1i		−	0.654004i	0.945024	−	0.327002i	$-0.106038\pi$
$938$		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	0.0433905	−	0.999058i	$-0.486184\pi$
$947$	27111.0	−	15652.6i	0.930296	−	0.537106i	0.886905	+	0.461952i	$0.152851\pi$
$948$		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	$-0.804744\pi$
$953$		−	33871.8i		−	1.15133i	0.817687	−	0.575663i	$-0.195256\pi$
$954$		0			0
$955$	9777.91	+	5645.28i	0.331315	+	0.191285i
$956$		0			0
$957$	34688.3	−	736.240i	1.17170	−	0.0248686i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14892.3	−	25794.2i	−0.499893	−	0.865840i
$962$		0			0
$963$	−1676.36	−	39473.4i	−0.0560954	−	1.32088i
$964$		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
$969$	−24410.1	+	14792.5i	−0.809252	+	0.490407i
$970$		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
$975$	−8.19246	−	385.992i	−0.000269096	−	0.0126786i
$976$		0			0
$977$	33448.2	+	19311.4i	1.09530	+	0.632369i	0.934981	−	0.354697i	$-0.115416\pi$
$977$	33448.2	+	19311.4i	1.09530	+	0.632369i	0.160314	+	0.987066i	$0.448749\pi$
$978$		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	0.531380	−	0.847134i	$-0.321674\pi$
$997$	1996.82	+	1152.87i	0.0634303	+	0.0366215i	−0.467949	+	0.883755i	$0.655007\pi$
$998$		0			0
$999$	9103.10	+	13676.6i	0.288298	+	0.433140i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-2.69298 - 4.44386i) q^{3} +(-4.87287 - 8.44005i) q^{5} +(-12.4957 + 23.9344i) q^{9} +O(q^{10})\)	\(q+(-2.69298 - 4.44386i) q^{3} +(-4.87287 - 8.44005i) q^{5} +(-12.4957 + 23.9344i) q^{9} +(42.9817 + 24.8155i) q^{11} +2.47499i q^{13} +(-24.3838 + 44.3832i) q^{15} +(24.7602 - 42.8858i) q^{17} +(96.0631 - 55.4620i) q^{19} +(149.767 - 86.4683i) q^{23} +(15.0103 - 25.9987i) q^{25} +(140.012 - 8.92575i) q^{27} +134.538i q^{29} +(2.18514 + 1.26159i) q^{31} +(-5.47234 - 257.832i) q^{33} +(58.5515 + 101.414i) q^{37} +(10.9985 - 6.66509i) q^{39} -160.696 q^{41} -442.678 q^{43} +(262.898 - 11.1648i) q^{45} +(-155.814 - 269.879i) q^{47} +(-257.257 + 5.46014i) q^{51} +(-248.907 - 143.706i) q^{53} -483.690i q^{55} +(-505.161 - 277.532i) q^{57} +(-276.360 + 478.670i) q^{59} +(504.937 - 291.525i) q^{61} +(20.8890 - 12.0603i) q^{65} +(450.723 - 780.675i) q^{67} +(-787.573 - 432.688i) q^{69} +984.717i q^{71} +(178.030 + 102.786i) q^{73} +(-155.957 + 3.31010i) q^{75} +(-321.643 - 557.103i) q^{79} +(-416.714 - 598.156i) q^{81} -351.902 q^{83} -482.612 q^{85} +(597.869 - 362.309i) q^{87} +(544.376 + 942.887i) q^{89} +(-0.278207 - 13.1079i) q^{93} +(-936.205 - 540.518i) q^{95} -1365.09i q^{97} +(-1131.03 + 718.654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 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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