LMFDB - Embedded newform 288.5.t.b.79.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,5,Mod(79,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.79"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	288.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [88] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$29.7705493681$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.4
Character	$\chi$	$=$	288.79
Dual form			288.5.t.b.175.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.90483 - 1.30534i) q^{3} +(23.2381 - 13.4165i) q^{5} +(52.2165 + 30.1472i) q^{7} +(77.5922 + 23.2478i) q^{9} +(-92.8475 + 160.817i) q^{11} +(166.026 - 95.8552i) q^{13} +(-224.444 + 89.1381i) q^{15} -425.178 q^{17} +114.203 q^{19} +(-425.627 - 336.616i) q^{21} +(239.080 - 138.033i) q^{23} +(47.5051 - 82.2813i) q^{25} +(-660.599 - 308.302i) q^{27} +(757.999 + 437.631i) q^{29} +(-910.769 + 525.833i) q^{31} +(1036.71 - 1310.85i) q^{33} +1617.88 q^{35} +194.549i q^{37} +(-1603.56 + 636.853i) q^{39} +(1420.33 + 2460.08i) q^{41} +(449.077 - 777.825i) q^{43} +(2115.00 - 500.783i) q^{45} +(-348.382 - 201.138i) q^{47} +(617.208 + 1069.03i) q^{49} +(3786.14 + 555.004i) q^{51} +4662.79i q^{53} +4982.75i q^{55} +(-1016.96 - 149.074i) q^{57} +(1769.31 + 3064.53i) q^{59} +(1797.64 + 1037.87i) q^{61} +(3350.73 + 3553.10i) q^{63} +(2572.08 - 4454.98i) q^{65} +(-1465.53 - 2538.37i) q^{67} +(-2309.14 + 917.077i) q^{69} -3035.73i q^{71} +5570.78 q^{73} +(-530.431 + 670.691i) q^{75} +(-9696.34 + 5598.18i) q^{77} +(9323.76 + 5383.08i) q^{79} +(5480.08 + 3607.69i) q^{81} +(1407.36 - 2437.61i) q^{83} +(-9880.31 + 5704.40i) q^{85} +(-6178.59 - 4886.48i) q^{87} -1868.54 q^{89} +11559.1 q^{91} +(8796.64 - 3493.58i) q^{93} +(2653.85 - 1532.20i) q^{95} +(1255.93 - 2175.33i) q^{97} +(-10942.9 + 10319.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 18 q^{3} + 30 q^{9} - 44 q^{11} - 1156 q^{17} - 860 q^{19} + 5998 q^{25} - 504 q^{27} - 3204 q^{33} + 2508 q^{35} + 2348 q^{41} - 3500 q^{43} + 16462 q^{49} + 12378 q^{51} - 6522 q^{57} + 3508 q^{59}+ \cdots + 11742 q^{99}+O(q^{100}) $ 88 * q + 18 * q^3 + 30 * q^9 - 44 * q^11 - 1156 * q^17 - 860 * q^19 + 5998 * q^25 - 504 * q^27 - 3204 * q^33 + 2508 * q^35 + 2348 * q^41 - 3500 * q^43 + 16462 * q^49 + 12378 * q^51 - 6522 * q^57 + 3508 * q^59 - 2502 * q^65 - 5132 * q^67 + 19004 * q^73 + 39858 * q^75 - 11346 * q^81 - 17090 * q^83 - 8272 * q^89 + 9612 * q^91 + 9980 * q^97 + 11742 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	−8.90483	−	1.30534i	−0.989426	−	0.145038i
$3$	−8.90483	−	1.30534i	−0.989426	−	0.145038i
$4$		0			0
$5$	23.2381	−	13.4165i	0.929523	−	0.536660i	0.0428621	−	0.999081i	$-0.486352\pi$
$5$	23.2381	−	13.4165i	0.929523	−	0.536660i	0.886661	+	0.462421i	$0.153019\pi$
$6$		0			0
$7$	52.2165	+	30.1472i	1.06564	+	0.615249i	0.926988	−	0.375092i	$-0.122389\pi$
$7$	52.2165	+	30.1472i	1.06564	+	0.615249i	0.138655	+	0.990341i	$0.455722\pi$
$8$		0			0
$9$	77.5922	+	23.2478i	0.957928	+	0.287009i
$10$		0			0
$11$	−92.8475	+	160.817i	−0.767335	+	1.32906i	0.171669	+	0.985155i	$0.445084\pi$
$11$	−92.8475	+	160.817i	−0.767335	+	1.32906i	−0.939003	+	0.343908i	$0.888249\pi$
$12$		0			0
$13$	166.026	−	95.8552i	0.982402	−	0.567190i	0.0794078	−	0.996842i	$-0.474697\pi$
$13$	166.026	−	95.8552i	0.982402	−	0.567190i	0.902995	+	0.429652i	$0.141364\pi$
$14$		0			0
$15$	−224.444	+	89.1381i	−0.997530	+	0.396169i
$16$		0			0
$17$	−425.178			−1.47120			−0.735602	−	0.677414i	$-0.763101\pi$
$17$	−425.178			−1.47120			−0.735602	+	0.677414i	$0.763101\pi$
$18$		0			0
$19$	114.203			0.316351			0.158175	−	0.987411i	$-0.449439\pi$
$19$	114.203			0.316351			0.158175	+	0.987411i	$0.449439\pi$
$20$		0			0
$21$	−425.627	−	336.616i	−0.965140	−	0.763302i
$22$		0			0
$23$	239.080	−	138.033i	0.451946	−	0.260931i	−0.256705	−	0.966490i	$-0.582637\pi$
$23$	239.080	−	138.033i	0.451946	−	0.260931i	0.708652	+	0.705558i	$0.249304\pi$
$24$		0			0
$25$	47.5051	−	82.2813i	0.0760082	−	0.131650i
$26$		0			0
$27$	−660.599	−	308.302i	−0.906171	−	0.422911i
$28$		0			0
$29$	757.999	+	437.631i	0.901306	+	0.520369i	0.877624	−	0.479350i	$-0.159128\pi$
$29$	757.999	+	437.631i	0.901306	+	0.520369i	0.0236825	+	0.999720i	$0.492461\pi$
$30$		0			0
$31$	−910.769	+	525.833i	−0.947730	+	0.547172i	−0.892375	−	0.451294i	$-0.850962\pi$
$31$	−910.769	+	525.833i	−0.947730	+	0.547172i	−0.0553551	+	0.998467i	$0.517629\pi$
$32$		0			0
$33$	1036.71	−	1310.85i	0.951986	−	1.20372i
$34$		0			0
$35$	1617.88			1.32072
$36$		0			0
$37$			194.549i			0.142110i	0.997472	+	0.0710551i	$0.0226366\pi$
$37$			194.549i			0.142110i	−0.997472	+	0.0710551i	$0.977363\pi$
$38$		0			0
$39$	−1603.56	+	636.853i	−1.05428	+	0.418707i
$40$		0			0
$41$	1420.33	+	2460.08i	0.844930	+	1.46346i	0.885682	+	0.464292i	$0.153691\pi$
$41$	1420.33	+	2460.08i	0.844930	+	1.46346i	−0.0407524	+	0.999169i	$0.512975\pi$
$42$		0			0
$43$	449.077	−	777.825i	0.242876	−	0.420673i	−0.718656	−	0.695365i	$-0.755243\pi$
$43$	449.077	−	777.825i	0.242876	−	0.420673i	0.961532	+	0.274692i	$0.0885759\pi$
$44$		0			0
$45$	2115.00	−	500.783i	1.04444	−	0.247300i
$46$		0			0
$47$	−348.382	−	201.138i	−0.157710	−	0.0910540i	0.419068	−	0.907955i	$-0.362357\pi$
$47$	−348.382	−	201.138i	−0.157710	−	0.0910540i	−0.576778	+	0.816901i	$0.695690\pi$
$48$		0			0
$49$	617.208	+	1069.03i	0.257063	+	0.445246i
$50$		0			0
$51$	3786.14	+	555.004i	1.45565	+	0.213381i
$52$		0			0
$53$			4662.79i			1.65995i	0.557802	+	0.829974i	$0.311645\pi$
$53$			4662.79i			1.65995i	−0.557802	+	0.829974i	$0.688355\pi$
$54$		0			0
$55$			4982.75i			1.64719i
$56$		0			0
$57$	−1016.96	−	149.074i	−0.313006	−	0.0458830i
$58$		0			0
$59$	1769.31	+	3064.53i	0.508276	+	0.880359i	0.999954	+	0.00958239i	$0.00305022\pi$
$59$	1769.31	+	3064.53i	0.508276	+	0.880359i	−0.491678	+	0.870777i	$0.663616\pi$
$60$		0			0
$61$	1797.64	+	1037.87i	0.483107	+	0.278922i	0.721710	−	0.692195i	$-0.243356\pi$
$61$	1797.64	+	1037.87i	0.483107	+	0.278922i	−0.238604	+	0.971117i	$0.576690\pi$
$62$		0			0
$63$	3350.73	+	3553.10i	0.844226	+	0.895213i
$64$		0			0
$65$	2572.08	−	4454.98i	0.608777	−	1.05443i
$66$		0			0
$67$	−1465.53	−	2538.37i	−0.326471	−	0.565465i	0.655338	−	0.755336i	$-0.272526\pi$
$67$	−1465.53	−	2538.37i	−0.326471	−	0.565465i	−0.981809	+	0.189871i	$0.939193\pi$
$68$		0			0
$69$	−2309.14	+	917.077i	−0.485013	+	0.192623i
$70$		0			0
$71$		−	3035.73i		−	0.602208i	−0.953591	−	0.301104i	$-0.902645\pi$
$71$		−	3035.73i		−	0.602208i	0.953591	−	0.301104i	$-0.0973551\pi$
$72$		0			0
$73$	5570.78			1.04537			0.522685	−	0.852526i	$-0.324930\pi$
$73$	5570.78			1.04537			0.522685	+	0.852526i	$0.324930\pi$
$74$		0			0
$75$	−530.431	+	670.691i	−0.0942988	+	0.119234i
$76$		0			0
$77$	−9696.34	+	5598.18i	−1.63541	+	0.944204i
$78$		0			0
$79$	9323.76	+	5383.08i	1.49395	+	0.862535i	0.999976	−	0.00694001i	$-0.00220909\pi$
$79$	9323.76	+	5383.08i	1.49395	+	0.862535i	0.493978	+	0.869475i	$0.335542\pi$
$80$		0			0
$81$	5480.08	+	3607.69i	0.835251	+	0.549868i
$82$		0			0
$83$	1407.36	−	2437.61i	0.204291	−	0.353842i	−0.745616	−	0.666376i	$-0.767845\pi$
$83$	1407.36	−	2437.61i	0.204291	−	0.353842i	0.949906	+	0.312534i	$0.101178\pi$
$84$		0			0
$85$	−9880.31	+	5704.40i	−1.36752	+	0.789537i
$86$		0			0
$87$	−6178.59	−	4886.48i	−0.816302	−	0.645591i
$88$		0			0
$89$	−1868.54			−0.235897			−0.117949	−	0.993020i	$-0.537632\pi$
$89$	−1868.54			−0.235897			−0.117949	+	0.993020i	$0.537632\pi$
$90$		0			0
$91$	11559.1			1.39585
$92$		0			0
$93$	8796.64	−	3493.58i	1.01707	−	0.403929i
$94$		0			0
$95$	2653.85	−	1532.20i	0.294055	−	0.169773i
$96$		0			0
$97$	1255.93	−	2175.33i	0.133481	−	0.231197i	−0.791535	−	0.611124i	$-0.790718\pi$
$97$	1255.93	−	2175.33i	0.133481	−	0.231197i	0.925016	+	0.379927i	$0.124051\pi$
$98$		0			0
$99$	−10942.9	+	10319.6i	−1.11650	+	1.05291i
$100$		0			0
$101$	−4729.31	−	2730.47i	−0.463612	−	0.267667i	0.249950	−	0.968259i	$-0.419586\pi$
$101$	−4729.31	−	2730.47i	−0.463612	−	0.267667i	−0.713562	+	0.700592i	$0.752919\pi$
$102$		0			0
$103$	9762.25	−	5636.24i	0.920186	−	0.531270i	0.0364916	−	0.999334i	$-0.488382\pi$
$103$	9762.25	−	5636.24i	0.920186	−	0.531270i	0.883694	+	0.468064i	$0.155048\pi$
$104$		0			0
$105$	−14407.0	−	2111.89i	−1.30675	−	0.191555i
$106$		0			0
$107$	−4850.33			−0.423647			−0.211823	−	0.977308i	$-0.567940\pi$
$107$	−4850.33			−0.423647			−0.211823	+	0.977308i	$0.567940\pi$
$108$		0			0
$109$		−	17364.2i		−	1.46151i	−0.682639	−	0.730756i	$-0.739168\pi$
$109$		−	17364.2i		−	1.46151i	0.682639	−	0.730756i	$-0.260832\pi$
$110$		0			0
$111$	253.953	−	1732.43i	0.0206114	−	0.140608i
$112$		0			0
$113$	6670.25	+	11553.2i	0.522378	+	0.904786i	0.999661	+	0.0260362i	$0.00828850\pi$
$113$	6670.25	+	11553.2i	0.522378	+	0.904786i	−0.477283	+	0.878750i	$0.658378\pi$
$114$		0			0
$115$	3703.83	−	6415.23i	0.280063	−	0.485083i
$116$		0			0
$117$	15110.7	−	3577.88i	1.10386	−	0.261369i
$118$		0			0
$119$	−22201.3	−	12817.9i	−1.56778	−	0.905157i
$120$		0			0
$121$	−9920.81	−	17183.3i	−0.677605	−	1.17365i
$122$		0			0
$123$	−9436.53	−	23760.6i	−0.623738	−	1.57053i
$124$		0			0
$125$			14221.2i			0.910158i
$126$		0			0
$127$			1492.37i			0.0925269i	0.998929	+	0.0462634i	$0.0147314\pi$
$127$			1492.37i			0.0925269i	−0.998929	+	0.0462634i	$0.985269\pi$
$128$		0			0
$129$	−5014.29	+	6340.20i	−0.301321	+	0.380999i
$130$		0			0
$131$	3213.86	+	5566.56i	0.187277	+	0.324373i	0.944341	−	0.328967i	$-0.106701\pi$
$131$	3213.86	+	5566.56i	0.187277	+	0.324373i	−0.757065	+	0.653340i	$0.773367\pi$
$132$		0			0
$133$	5963.26	+	3442.89i	0.337117	+	0.194635i
$134$		0			0
$135$	−19487.4	+	1698.59i	−1.06927	+	0.0932010i
$136$		0			0
$137$	−10678.8	+	18496.2i	−0.568959	+	0.985466i	0.427710	+	0.903916i	$0.359320\pi$
$137$	−10678.8	+	18496.2i	−0.568959	+	0.985466i	−0.996669	+	0.0815500i	$0.974013\pi$
$138$		0			0
$139$	10328.6	+	17889.6i	0.534578	+	0.925916i	0.999184	+	0.0403986i	$0.0128628\pi$
$139$	10328.6	+	17889.6i	0.534578	+	0.925916i	−0.464606	+	0.885518i	$0.653804\pi$
$140$		0			0
$141$	2839.73	+	2245.86i	0.142836	+	0.112965i
$142$		0			0
$143$			35599.6i			1.74090i
$144$		0			0
$145$	23485.9			1.11705
$146$		0			0
$147$	−4100.67	−	10325.2i	−0.189767	−	0.477822i
$148$		0			0
$149$	4499.97	−	2598.06i	0.202692	−	0.117025i	−0.395218	−	0.918587i	$-0.629331\pi$
$149$	4499.97	−	2598.06i	0.202692	−	0.117025i	0.597911	+	0.801563i	$0.295998\pi$
$150$		0			0
$151$	17647.9	+	10189.0i	0.773998	+	0.446868i	0.834299	−	0.551313i	$-0.185873\pi$
$151$	17647.9	+	10189.0i	0.773998	+	0.446868i	−0.0603013	+	0.998180i	$0.519206\pi$
$152$		0			0
$153$	−32990.5	−	9884.43i	−1.40931	−	0.422249i
$154$		0			0
$155$	−14109.7	+	24438.7i	−0.587291	+	1.01722i
$156$		0			0
$157$	7737.56	−	4467.28i	0.313910	−	0.181236i	−0.334765	−	0.942302i	$-0.608657\pi$
$157$	7737.56	−	4467.28i	0.313910	−	0.181236i	0.648675	+	0.761066i	$0.275324\pi$
$158$		0			0
$159$	6086.55	−	41521.4i	0.240756	−	1.64240i
$160$		0			0
$161$	16645.2			0.642151
$162$		0			0
$163$	−38000.8			−1.43027			−0.715134	−	0.698987i	$-0.753634\pi$
$163$	−38000.8			−1.43027			−0.715134	+	0.698987i	$0.753634\pi$
$164$		0			0
$165$	6504.21	−	44370.6i	0.238906	−	1.62977i
$166$		0			0
$167$	11942.4	−	6894.97i	0.428213	−	0.247229i	−0.270372	−	0.962756i	$-0.587147\pi$
$167$	11942.4	−	6894.97i	0.428213	−	0.247229i	0.698585	+	0.715527i	$0.253813\pi$
$168$		0			0
$169$	4095.92	−	7094.35i	0.143410	−	0.248393i
$170$		0			0
$171$	8861.23	+	2654.96i	0.303041	+	0.0907956i
$172$		0			0
$173$	−9687.10	−	5592.85i	−0.323669	−	0.186871i	0.329358	−	0.944205i	$-0.393168\pi$
$173$	−9687.10	−	5592.85i	−0.323669	−	0.186871i	−0.653027	+	0.757335i	$0.726501\pi$
$174$		0			0
$175$	4961.10	−	2864.29i	0.161995	−	0.0935279i
$176$		0			0
$177$	−11755.1	−	29598.7i	−0.375215	−	0.944770i
$178$		0			0
$179$	−7133.34			−0.222632			−0.111316	−	0.993785i	$-0.535507\pi$
$179$	−7133.34			−0.222632			−0.111316	+	0.993785i	$0.535507\pi$
$180$		0			0
$181$			26104.7i			0.796822i	0.917207	+	0.398411i	$0.130438\pi$
$181$			26104.7i			0.796822i	−0.917207	+	0.398411i	$0.869562\pi$
$182$		0			0
$183$	−14652.9	−	11588.6i	−0.437544	−	0.346041i
$184$		0			0
$185$	2610.17	+	4520.94i	0.0762649	+	0.132095i
$186$		0			0
$187$	39476.7	−	68375.7i	1.12891	−	1.95532i
$188$		0			0
$189$	−25199.7	−	36013.7i	−0.705459	−	1.00819i
$190$		0			0
$191$	−39532.9	−	22824.3i	−1.08366	−	0.625649i	−0.151776	−	0.988415i	$-0.548499\pi$
$191$	−39532.9	−	22824.3i	−1.08366	−	0.625649i	−0.931880	+	0.362766i	$0.881832\pi$
$192$		0			0
$193$	−6039.50	−	10460.7i	−0.162139	−	0.280832i	0.773497	−	0.633800i	$-0.218506\pi$
$193$	−6039.50	−	10460.7i	−0.162139	−	0.280832i	−0.935635	+	0.352968i	$0.885173\pi$
$194$		0			0
$195$	−28719.2	+	36313.4i	−0.755273	+	0.954987i
$196$		0			0
$197$		−	70123.2i		−	1.80688i	−0.428714	−	0.903440i	$-0.641033\pi$
$197$		−	70123.2i		−	1.80688i	0.428714	−	0.903440i	$-0.358967\pi$
$198$		0			0
$199$			53477.1i			1.35040i	0.737636	+	0.675198i	$0.235942\pi$
$199$			53477.1i			1.35040i	−0.737636	+	0.675198i	$0.764058\pi$
$200$		0			0
$201$	9736.85	+	24516.8i	0.241005	+	0.606837i
$202$		0			0
$203$	26386.7	+	45703.1i	0.640314	+	1.10906i
$204$		0			0
$205$	66011.3	+	38111.6i	1.57076	+	0.906880i
$206$		0			0
$207$	21759.7	−	5152.19i	0.507822	−	0.120241i
$208$		0			0
$209$	−10603.4	+	18365.7i	−0.242747	+	0.420450i
$210$		0			0
$211$	−16582.5	−	28721.8i	−0.372465	−	0.645128i	0.617479	−	0.786587i	$-0.288154\pi$
$211$	−16582.5	−	28721.8i	−0.372465	−	0.645128i	−0.989944	+	0.141459i	$0.954821\pi$
$212$		0			0
$213$	−3962.67	+	27032.7i	−0.0873431	+	0.595840i
$214$		0			0
$215$		−	24100.2i		−	0.521367i
$216$		0			0
$217$	−63409.5			−1.34659
$218$		0			0
$219$	−49606.9	−	7271.79i	−1.03432	−	0.151619i
$220$		0			0
$221$	−70590.6	+	40755.5i	−1.44531	+	0.834453i
$222$		0			0
$223$	−53609.6	−	30951.5i	−1.07804	−	0.622404i	−0.147669	−	0.989037i	$-0.547177\pi$
$223$	−53609.6	−	30951.5i	−1.07804	−	0.622404i	−0.930366	+	0.366633i	$0.880510\pi$
$224$		0			0
$225$	5598.88	−	5280.00i	0.110595	−	0.104296i
$226$		0			0
$227$	121.231	−	209.978i	0.00235268	−	0.00407496i	−0.864847	−	0.502036i	$-0.832584\pi$
$227$	121.231	−	209.978i	0.00235268	−	0.00407496i	0.867199	+	0.497961i	$0.165918\pi$
$228$		0			0
$229$	10175.3	−	5874.70i	0.194033	−	0.112025i	−0.399836	−	0.916587i	$-0.630933\pi$
$229$	10175.3	−	5874.70i	0.194033	−	0.112025i	0.593869	+	0.804562i	$0.297600\pi$
$230$		0			0
$231$	93651.8	−	37193.8i	1.75506	−	0.697023i
$232$		0			0
$233$	−34752.2			−0.640134			−0.320067	−	0.947395i	$-0.603705\pi$
$233$	−34752.2			−0.640134			−0.320067	+	0.947395i	$0.603705\pi$
$234$		0			0
$235$	−10794.3			−0.195460
$236$		0			0
$237$	−75999.8	−	60106.1i	−1.35306	−	1.07009i
$238$		0			0
$239$	−41098.0	+	23728.0i	−0.719491	+	0.415398i	−0.814565	−	0.580072i	$-0.803024\pi$
$239$	−41098.0	+	23728.0i	−0.719491	+	0.415398i	0.0950746	+	0.995470i	$0.469691\pi$
$240$		0			0
$241$	34530.8	−	59809.0i	0.594527	−	1.02975i	−0.399086	−	0.916914i	$-0.630672\pi$
$241$	34530.8	−	59809.0i	0.594527	−	1.02975i	0.993613	−	0.112838i	$-0.0359942\pi$
$242$		0			0
$243$	−44090.0	−	39279.2i	−0.746667	−	0.665198i
$244$		0			0
$245$	28685.4	+	16561.5i	0.477891	+	0.275911i
$246$		0			0
$247$	18960.6	−	10946.9i	0.310784	−	0.179431i
$248$		0			0
$249$	−15714.2	+	19869.5i	−0.253451	+	0.320470i
$250$		0			0
$251$	59187.9			0.939475			0.469738	−	0.882806i	$-0.344348\pi$
$251$	59187.9			0.939475			0.469738	+	0.882806i	$0.344348\pi$
$252$		0			0
$253$			51263.9i			0.800887i
$254$		0			0
$255$	95428.8	−	37899.5i	1.46757	−	0.582846i
$256$		0			0
$257$	26280.3	+	45518.9i	0.397891	+	0.689168i	0.993466	−	0.114132i	$-0.0364087\pi$
$257$	26280.3	+	45518.9i	0.397891	+	0.689168i	−0.595574	+	0.803300i	$0.703075\pi$
$258$		0			0
$259$	−5865.11	+	10158.7i	−0.0874332	+	0.151439i
$260$		0			0
$261$	48640.8	+	51578.5i	0.714035	+	0.757160i
$262$		0			0
$263$	37110.2	+	21425.6i	0.536515	+	0.309757i	0.743665	−	0.668552i	$-0.233086\pi$
$263$	37110.2	+	21425.6i	0.536515	+	0.309757i	−0.207150	+	0.978309i	$0.566419\pi$
$264$		0			0
$265$	62558.4	+	108354.i	0.890828	+	1.54296i
$266$		0			0
$267$	16639.0	+	2439.09i	0.233403	+	0.0342141i
$268$		0			0
$269$		−	10584.0i		−	0.146267i	−0.997322	−	0.0731333i	$-0.976700\pi$
$269$		−	10584.0i		−	0.146267i	0.997322	−	0.0731333i	$-0.0232998\pi$
$270$		0			0
$271$		−	93339.2i		−	1.27094i	−0.772125	−	0.635471i	$-0.780806\pi$
$271$		−	93339.2i		−	1.27094i	0.772125	−	0.635471i	$-0.219194\pi$
$272$		0			0
$273$	−102932.	−	15088.6i	−1.38109	−	0.202452i
$274$		0			0
$275$	8821.46	+	15279.2i	0.116647	+	0.202039i
$276$		0			0
$277$	20273.5	+	11704.9i	0.264222	+	0.152549i	0.626259	−	0.779615i	$-0.284585\pi$
$277$	20273.5	+	11704.9i	0.264222	+	0.152549i	−0.362037	+	0.932164i	$0.617919\pi$
$278$		0			0
$279$	−82892.9	+	19627.2i	−1.06490	+	0.252144i
$280$		0			0
$281$	−3736.40	+	6471.63i	−0.0473195	+	0.0819598i	−0.888715	−	0.458460i	$-0.848401\pi$
$281$	−3736.40	+	6471.63i	−0.0473195	+	0.0819598i	0.841396	+	0.540420i	$0.181735\pi$
$282$		0			0
$283$	45059.8	+	78045.9i	0.562622	+	0.974490i	0.997267	+	0.0738877i	$0.0235407\pi$
$283$	45059.8	+	78045.9i	0.562622	+	0.974490i	−0.434645	+	0.900602i	$0.643126\pi$
$284$		0			0
$285$	−25632.1	+	10179.8i	−0.315569	+	0.125328i
$286$		0			0
$287$			171276.i			2.07937i
$288$		0			0
$289$	97255.3			1.16444
$290$		0			0
$291$	−14023.4	+	17731.5i	−0.165602	+	0.209392i
$292$		0			0
$293$	−118256.	+	68274.9i	−1.37748	+	0.795290i	−0.991856	−	0.127365i	$-0.959348\pi$
$293$	−118256.	+	68274.9i	−1.37748	+	0.795290i	−0.385627	+	0.922655i	$0.626015\pi$
$294$		0			0
$295$	82230.6	+	47475.8i	0.944907	+	0.545543i
$296$		0			0
$297$	110915.	−	77610.2i	1.25741	−	0.879844i
$298$		0			0
$299$	26462.3	−	45834.0i	0.295995	−	0.512679i
$300$		0			0
$301$	46898.5	−	27076.9i	0.517638	−	0.298858i
$302$		0			0
$303$	38549.5	+	30487.7i	0.419888	+	0.332078i
$304$		0			0
$305$	55698.2			0.598745
$306$		0			0
$307$	168794.			1.79094			0.895468	−	0.445126i	$-0.146841\pi$
$307$	168794.			1.79094			0.895468	+	0.445126i	$0.146841\pi$
$308$		0			0
$309$	−94288.5	+	37446.7i	−0.987510	+	0.392190i
$310$		0			0
$311$	−68907.1	+	39783.5i	−0.712431	+	0.411323i	−0.811961	−	0.583712i	$-0.801600\pi$
$311$	−68907.1	+	39783.5i	−0.712431	+	0.411323i	0.0995292	+	0.995035i	$0.468266\pi$
$312$		0			0
$313$	93373.0	−	161727.i	0.953087	−	1.65080i	0.214401	−	0.976746i	$-0.431220\pi$
$313$	93373.0	−	161727.i	0.953087	−	1.65080i	0.738686	−	0.674049i	$-0.235446\pi$
$314$		0			0
$315$	125535.	+	37612.1i	1.26515	+	0.379059i
$316$		0			0
$317$	95810.6	+	55316.3i	0.953443	+	0.550471i	0.894149	−	0.447770i	$-0.147782\pi$
$317$	95810.6	+	55316.3i	0.953443	+	0.550471i	0.0592945	+	0.998241i	$0.481115\pi$
$318$		0			0
$319$	−140757.	+	81265.8i	−1.38321	+	0.798595i
$320$		0			0
$321$	43191.4	+	6331.36i	0.419167	+	0.0614450i
$322$		0			0
$323$	−48556.4			−0.465417
$324$		0			0
$325$		−	18214.4i		−	0.172444i
$326$		0			0
$327$	−22666.3	+	154626.i	−0.211975	+	1.44606i
$328$		0			0
$329$	−12127.5	−	21005.5i	−0.112042	−	0.194062i
$330$		0			0
$331$	35525.1	−	61531.2i	0.324249	−	0.561616i	−0.657111	−	0.753794i	$-0.728222\pi$
$331$	35525.1	−	61531.2i	0.324249	−	0.561616i	0.981360	+	0.192178i	$0.0615550\pi$
$332$		0			0
$333$	−4522.83	+	15095.5i	−0.0407870	+	0.136131i
$334$		0			0
$335$	−68112.2	−	39324.6i	−0.606925	−	0.350408i
$336$		0			0
$337$	−3370.32	−	5837.57i	−0.0296764	−	0.0514011i	0.850806	−	0.525480i	$-0.176114\pi$
$337$	−3370.32	−	5837.57i	−0.0296764	−	0.0514011i	−0.880482	+	0.474079i	$0.842781\pi$
$338$		0			0
$339$	−44316.6	−	111586.i	−0.385626	−	0.970984i
$340$		0			0
$341$		−	195289.i		−	1.67946i
$342$		0			0
$343$		−	70338.5i		−	0.597868i
$344$		0			0
$345$	−41356.1	+	52291.7i	−0.347457	+	0.439334i
$346$		0			0
$347$	−43353.9	−	75091.2i	−0.360055	−	0.623634i	0.627914	−	0.778283i	$-0.283909\pi$
$347$	−43353.9	−	75091.2i	−0.360055	−	0.623634i	−0.987970	+	0.154648i	$0.950576\pi$
$348$		0			0
$349$	108745.	+	62783.7i	0.892805	+	0.515461i	0.874859	−	0.484378i	$-0.160954\pi$
$349$	108745.	+	62783.7i	0.892805	+	0.515461i	0.0179461	+	0.999839i	$0.494287\pi$
$350$		0			0
$351$	−139229.	+	12135.7i	−1.13010	+	0.0985031i
$352$		0			0
$353$	24176.0	−	41874.1i	0.194015	−	0.336044i	−0.752562	−	0.658521i	$-0.771182\pi$
$353$	24176.0	−	41874.1i	0.194015	−	0.336044i	0.946577	+	0.322477i	$0.104516\pi$
$354$		0			0
$355$	−40728.9	−	70544.5i	−0.323181	−	0.559766i
$356$		0			0
$357$	180967.	+	143122.i	1.41992	+	1.12297i
$358$		0			0
$359$			59745.2i			0.463568i	0.972767	+	0.231784i	$0.0744563\pi$
$359$			59745.2i			0.463568i	−0.972767	+	0.231784i	$0.925544\pi$
$360$		0			0
$361$	−117279.			−0.899922
$362$		0			0
$363$	65913.0	+	165965.i	0.500216	+	1.25951i
$364$		0			0
$365$	129454.	−	74740.4i	0.971696	−	0.561009i
$366$		0			0
$367$	145654.	+	84093.5i	1.08141	+	0.624353i	0.931277	−	0.364312i	$-0.118696\pi$
$367$	145654.	+	84093.5i	1.08141	+	0.624353i	0.150135	+	0.988666i	$0.452029\pi$
$368$		0			0
$369$	53014.9	+	223902.i	0.389355	+	1.64439i
$370$		0			0
$371$	−140570.	+	243475.i	−1.02128	+	1.76891i
$372$		0			0
$373$	−233844.	+	135010.i	−1.68077	+	0.970393i	−0.719620	+	0.694368i	$0.755684\pi$
$373$	−233844.	+	135010.i	−1.68077	+	0.970393i	−0.961150	+	0.276026i	$0.910983\pi$
$374$		0			0
$375$	18563.6	−	126638.i	0.132008	−	0.900534i
$376$		0			0
$377$	167797.			1.18059
$378$		0			0
$379$	−110475.			−0.769102			−0.384551	−	0.923104i	$-0.625644\pi$
$379$	−110475.			−0.769102			−0.384551	+	0.923104i	$0.625644\pi$
$380$		0			0
$381$	1948.05	−	13289.3i	0.0134199	−	0.0915485i
$382$		0			0
$383$	174715.	−	100872.i	1.19106	−	0.687659i	0.232513	−	0.972593i	$-0.425305\pi$
$383$	174715.	−	100872.i	1.19106	−	0.687659i	0.958547	+	0.284934i	$0.0919718\pi$
$384$		0			0
$385$	−150216.	+	260182.i	−1.01343	+	1.75532i
$386$		0			0
$387$	52927.6	−	49913.1i	0.353395	−	0.333267i
$388$		0			0
$389$	28286.6	+	16331.2i	0.186931	+	0.107925i	0.590545	−	0.807005i	$-0.298913\pi$
$389$	28286.6	+	16331.2i	0.186931	+	0.107925i	−0.403614	+	0.914929i	$0.632246\pi$
$390$		0			0
$391$	−101651.	+	58688.5i	−0.664905	+	0.383883i
$392$		0			0
$393$	−21352.6	−	53764.5i	−0.138250	−	0.348105i
$394$		0			0
$395$	288888.			1.85155
$396$		0			0
$397$		−	157999.i		−	1.00247i	−0.865310	−	0.501237i	$-0.832878\pi$
$397$		−	157999.i		−	1.00247i	0.865310	−	0.501237i	$-0.167122\pi$
$398$		0			0
$399$	−48607.7	−	38442.5i	−0.305323	−	0.241471i
$400$		0			0
$401$	−71882.8	−	124505.i	−0.447029	−	0.774277i	0.551162	−	0.834398i	$-0.314185\pi$
$401$	−71882.8	−	124505.i	−0.447029	−	0.774277i	−0.998191	+	0.0601210i	$0.980851\pi$
$402$		0			0
$403$	−100808.	+	174604.i	−0.620702	+	1.07509i
$404$		0			0
$405$	175749.	+	10312.1i	1.07148	+	0.0628690i
$406$		0			0
$407$	−31286.7	−	18063.4i	−0.188873	−	0.109046i
$408$		0			0
$409$	−6867.24	−	11894.4i	−0.0410521	−	0.0711044i	0.844769	−	0.535131i	$-0.179738\pi$
$409$	−6867.24	−	11894.4i	−0.0410521	−	0.0711044i	−0.885821	+	0.464026i	$0.846404\pi$
$410$		0			0
$411$	119237.	−	150766.i	0.705873	−	0.892525i
$412$		0			0
$413$			213359.i			1.25086i
$414$		0			0
$415$		−	75527.3i		−	0.438538i
$416$		0			0
$417$	−68622.2	−	172787.i	−0.394632	−	0.993660i
$418$		0			0
$419$	−135489.	−	234673.i	−0.771748	−	1.33671i	−0.936604	−	0.350389i	$-0.886049\pi$
$419$	−135489.	−	234673.i	−0.771748	−	1.33671i	0.164857	−	0.986318i	$-0.447284\pi$
$420$		0			0
$421$	−206716.	−	119347.i	−1.16630	−	0.673362i	−0.213493	−	0.976945i	$-0.568484\pi$
$421$	−206716.	−	119347.i	−1.16630	−	0.673362i	−0.952805	+	0.303582i	$0.901817\pi$
$422$		0			0
$423$	−22355.7	−	23705.8i	−0.124942	−	0.132487i
$424$		0			0
$425$	−20198.1	+	34984.2i	−0.111824	+	0.193684i
$426$		0			0
$427$	62577.6	+	108388.i	0.343213	+	0.594462i
$428$		0			0
$429$	46469.8	−	317009.i	0.252497	−	1.72249i
$430$		0			0
$431$		−	208255.i		−	1.12109i	−0.828124	−	0.560545i	$-0.810592\pi$
$431$		−	208255.i		−	1.12109i	0.828124	−	0.560545i	$-0.189408\pi$
$432$		0			0
$433$	−275527.			−1.46957			−0.734783	−	0.678303i	$-0.762716\pi$
$433$	−275527.			−1.46957			−0.734783	+	0.678303i	$0.762716\pi$
$434$		0			0
$435$	−209138.	−	30657.2i	−1.10523	−	0.162014i
$436$		0			0
$437$	27303.5	−	15763.7i	0.142974	−	0.0825458i
$438$		0			0
$439$	5755.89	+	3323.16i	0.0298664	+	0.0172434i	0.514859	−	0.857275i	$-0.327844\pi$
$439$	5755.89	+	3323.16i	0.0298664	+	0.0172434i	−0.484992	+	0.874518i	$0.661178\pi$
$440$		0			0
$441$	23037.8	+	97297.4i	0.118458	+	0.500293i
$442$		0			0
$443$	122953.	−	212960.i	0.626514	−	1.08515i	−0.361732	−	0.932282i	$-0.617814\pi$
$443$	122953.	−	212960.i	0.626514	−	1.08515i	0.988246	−	0.152872i	$-0.0488523\pi$
$444$		0			0
$445$	−43421.3	+	25069.3i	−0.219272	+	0.126597i
$446$		0			0
$447$	−43462.9	+	17261.3i	−0.217522	+	0.0863890i
$448$		0			0
$449$	−282931.			−1.40342			−0.701711	−	0.712462i	$-0.747580\pi$
$449$	−282931.			−1.40342			−0.701711	+	0.712462i	$0.747580\pi$
$450$		0			0
$451$	−527495.			−2.59338
$452$		0			0
$453$	−143852.	−	113768.i	−0.701000	−	0.554402i
$454$		0			0
$455$	268610.	−	155082.i	1.29748	−	0.749099i
$456$		0			0
$457$	108539.	−	187995.i	0.519702	−	0.900150i	−0.480036	−	0.877249i	$-0.659376\pi$
$457$	108539.	−	187995.i	0.519702	−	0.900150i	0.999738	−	0.0229008i	$-0.00729020\pi$
$458$		0			0
$459$	280872.	+	131083.i	1.33316	+	0.622188i
$460$		0			0
$461$	−86601.0	−	49999.1i	−0.407494	−	0.235267i	0.282219	−	0.959350i	$-0.408930\pi$
$461$	−86601.0	−	49999.1i	−0.407494	−	0.235267i	−0.689712	+	0.724084i	$0.742263\pi$
$462$		0			0
$463$	6135.09	−	3542.10i	0.0286193	−	0.0165234i	−0.485622	−	0.874169i	$-0.661407\pi$
$463$	6135.09	−	3542.10i	0.0286193	−	0.0165234i	0.514241	+	0.857645i	$0.328074\pi$
$464$		0			0
$465$	157545.	−	199204.i	0.728617	−	0.921282i
$466$		0			0
$467$	−429771.			−1.97062			−0.985312	−	0.170765i	$-0.945376\pi$
$467$	−429771.			−1.97062			−0.985312	+	0.170765i	$0.945376\pi$
$468$		0			0
$469$		−	176727.i		−	0.803445i
$470$		0			0
$471$	−74733.0	+	29680.2i	−0.336876	+	0.133790i
$472$		0			0
$473$	83391.4	+	144438.i	0.372734	+	0.645594i
$474$		0			0
$475$	5425.21	−	9396.74i	0.0240453	−	0.0416476i
$476$		0			0
$477$	−108399.	+	361796.i	−0.476420	+	1.59011i
$478$		0			0
$479$	49730.6	+	28712.0i	0.216747	+	0.125139i	0.604443	−	0.796648i	$-0.293396\pi$
$479$	49730.6	+	28712.0i	0.216747	+	0.125139i	−0.387696	+	0.921787i	$0.626729\pi$
$480$		0			0
$481$	18648.5	+	32300.2i	0.0806036	+	0.139609i
$482$		0			0
$483$	−148223.	−	21727.7i	−0.635361	−	0.0931365i
$484$		0			0
$485$		−	67400.6i		−	0.286537i
$486$		0			0
$487$		−	265572.i		−	1.11976i	−0.828574	−	0.559879i	$-0.810848\pi$
$487$		−	265572.i		−	1.11976i	0.828574	−	0.559879i	$-0.189152\pi$
$488$		0			0
$489$	338391.	+	49604.1i	1.41514	+	0.207444i
$490$		0			0
$491$	77229.5	+	133765.i	0.320347	+	0.554857i	0.980560	−	0.196222i	$-0.0628673\pi$
$491$	77229.5	+	133765.i	0.320347	+	0.554857i	−0.660213	+	0.751079i	$0.729534\pi$
$492$		0			0
$493$	−322284.	−	186071.i	−1.32601	−	0.765570i
$494$		0			0
$495$	−115838.	+	386623.i	−0.472759	+	1.57789i
$496$		0			0
$497$	91518.7	−	158515.i	0.370508	−	0.641738i
$498$		0			0
$499$	98724.4	+	170996.i	0.396482	+	0.686727i	0.993289	−	0.115658i	$-0.0368976\pi$
$499$	98724.4	+	170996.i	0.396482	+	0.686727i	−0.596807	+	0.802385i	$0.703564\pi$
$500$		0			0
$501$	−115346.	+	45809.6i	−0.459543	+	0.182507i
$502$		0			0
$503$		−	343592.i		−	1.35802i	−0.734127	−	0.679012i	$-0.762408\pi$
$503$		−	343592.i		−	1.35802i	0.734127	−	0.679012i	$-0.237592\pi$
$504$		0			0
$505$	−146533.			−0.574584
$506$		0			0
$507$	−45734.1	+	57827.4i	−0.177920	+	0.224966i
$508$		0			0
$509$	−73009.5	+	42152.1i	−0.281802	+	0.162698i	−0.634239	−	0.773137i	$-0.718686\pi$
$509$	−73009.5	+	42152.1i	−0.281802	+	0.162698i	0.352437	+	0.935836i	$0.385353\pi$
$510$		0			0
$511$	290887.	+	167943.i	1.11399	+	0.643163i
$512$		0			0
$513$	−75442.1	−	35208.9i	−0.286668	−	0.133788i
$514$		0			0
$515$	151237.	−	261951.i	0.570222	−	0.987654i
$516$		0			0
$517$	64692.7	−	37350.4i	0.242033	−	0.139738i
$518$		0			0
$519$	78961.4	+	62448.4i	0.293143	+	0.231839i
$520$		0			0
$521$	−397536.			−1.46454			−0.732270	−	0.681015i	$-0.761539\pi$
$521$	−397536.			−1.46454			−0.732270	+	0.681015i	$0.761539\pi$
$522$		0			0
$523$	286663.			1.04802			0.524008	−	0.851714i	$-0.324436\pi$
$523$	286663.			1.04802			0.524008	+	0.851714i	$0.324436\pi$
$524$		0			0
$525$	−47916.7	+	19030.1i	−0.173847	+	0.0690435i
$526$		0			0
$527$	387239.	−	223572.i	1.39430	−	0.805002i
$528$		0			0
$529$	−101814.	+	176348.i	−0.363830	+	0.630171i
$530$		0			0
$531$	66040.9	+	278916.i	0.234220	+	0.989200i
$532$		0			0
$533$	471622.	+	272291.i	1.66012	+	0.958472i
$534$		0			0
$535$	−112712.	+	65074.5i	−0.393789	+	0.227354i
$536$		0			0
$537$	63521.2	+	9311.47i	0.220278	+	0.0322901i
$538$		0			0
$539$	−229225.			−0.789012
$540$		0			0
$541$		−	412153.i		−	1.40820i	−0.710101	−	0.704100i	$-0.751351\pi$
$541$		−	412153.i		−	1.40820i	0.710101	−	0.704100i	$-0.248649\pi$
$542$		0			0
$543$	34075.6	−	232458.i	0.115570	−	0.788397i
$544$		0			0
$545$	−232967.	−	403511.i	−0.784335	−	1.35851i
$546$		0			0
$547$	168911.	−	292563.i	0.564527	−	0.977789i	−0.432567	−	0.901602i	$-0.642392\pi$
$547$	168911.	−	292563.i	0.564527	−	0.977789i	0.997094	−	0.0761869i	$-0.0242746\pi$
$548$		0			0
$549$	115355.	+	122322.i	0.382728	+	0.405843i
$550$		0			0
$551$	86565.4	+	49978.6i	0.285129	+	0.164619i
$552$		0			0
$553$	324569.	+	562171.i	1.06135	+	1.83831i
$554$		0			0
$555$	−17341.7	−	43665.4i	−0.0562997	−	0.141759i
$556$		0			0
$557$			251395.i			0.810302i	0.914250	+	0.405151i	$0.132781\pi$
$557$			251395.i			0.810302i	−0.914250	+	0.405151i	$0.867219\pi$
$558$		0			0
$559$		−	172186.i		−	0.551027i
$560$		0			0
$561$	−440787.	+	557343.i	−1.40057	+	1.77091i
$562$		0			0
$563$	32923.4	+	57025.0i	0.103870	+	0.179907i	0.913276	−	0.407342i	$-0.133544\pi$
$563$	32923.4	+	57025.0i	0.103870	+	0.179907i	−0.809406	+	0.587249i	$0.800211\pi$
$564$		0			0
$565$	310007.	+	178983.i	0.971125	+	0.560679i
$566$		0			0
$567$	177389.	+	353590.i	0.551773	+	1.09985i
$568$		0			0
$569$	59792.5	−	103564.i	0.184681	−	0.319877i	−0.758788	−	0.651338i	$-0.774208\pi$
$569$	59792.5	−	103564.i	0.184681	−	0.319877i	0.943469	+	0.331461i	$0.107541\pi$
$570$		0			0
$571$	−14325.3	−	24812.2i	−0.0439372	−	0.0761014i	0.843220	−	0.537568i	$-0.180657\pi$
$571$	−14325.3	−	24812.2i	−0.0439372	−	0.0761014i	−0.887158	+	0.461466i	$0.847323\pi$
$572$		0			0
$573$	322240.	+	254851.i	0.981454	+	0.776205i
$574$		0			0
$575$		−	26229.0i		−	0.0793317i
$576$		0			0
$577$	−101252.			−0.304126			−0.152063	−	0.988371i	$-0.548592\pi$
$577$	−101252.			−0.304126			−0.152063	+	0.988371i	$0.548592\pi$
$578$		0			0
$579$	40125.9	+	101035.i	0.119693	+	0.301379i
$580$		0			0
$581$	146975.	−	84855.8i	0.435401	−	0.251379i
$582$		0			0
$583$	−749854.	−	432929.i	−2.20617	−	1.27374i
$584$		0			0
$585$	303142.	−	285876.i	0.885796	−	0.835346i
$586$		0			0
$587$	36792.0	−	63725.7i	0.106777	−	0.184943i	−0.807686	−	0.589613i	$-0.799280\pi$
$587$	36792.0	−	63725.7i	0.106777	−	0.184943i	0.914463	+	0.404670i	$0.132614\pi$
$588$		0			0
$589$	−104012.	+	60051.5i	−0.299815	+	0.173098i
$590$		0			0
$591$	−91535.0	+	624436.i	−0.262067	+	1.78778i
$592$		0			0
$593$	295880.			0.841407			0.420704	−	0.907198i	$-0.361783\pi$
$593$	295880.			0.841407			0.420704	+	0.907198i	$0.361783\pi$
$594$		0			0
$595$	−687887.			−1.94305
$596$		0			0
$597$	69806.0	−	476204.i	0.195859	−	1.33612i
$598$		0			0
$599$	−528443.	+	305097.i	−1.47280	+	0.850323i	−0.999532	−	0.0305942i	$-0.990260\pi$
$599$	−528443.	+	305097.i	−1.47280	+	0.850323i	−0.473271	+	0.880917i	$0.656927\pi$
$600$		0			0
$601$	56375.3	−	97644.9i	0.156077	−	0.270334i	−0.777373	−	0.629039i	$-0.783448\pi$
$601$	56375.3	−	97644.9i	0.156077	−	0.270334i	0.933451	+	0.358705i	$0.116782\pi$
$602$		0			0
$603$	−54702.2	−	231028.i	−0.150442	−	0.635375i
$604$		0			0
$605$	−461081.	−	266205.i	−1.25970	−	0.727287i
$606$		0			0
$607$	−121995.	+	70434.1i	−0.331105	+	0.191164i	−0.656332	−	0.754472i	$-0.727893\pi$
$607$	−121995.	+	70434.1i	−0.331105	+	0.191164i	0.325226	+	0.945636i	$0.394560\pi$
$608$		0			0
$609$	−175311.	−	441422.i	−0.472687	−	1.19020i
$610$		0			0
$611$	−77120.6			−0.206580
$612$		0			0
$613$		−	471219.i		−	1.25401i	−0.779014	−	0.627006i	$-0.784280\pi$
$613$		−	471219.i		−	1.25401i	0.779014	−	0.627006i	$-0.215720\pi$
$614$		0			0
$615$	−538071.	−	425545.i	−1.42262	−	1.12511i
$616$		0			0
$617$	−189422.	−	328089.i	−0.497577	−	0.861828i	0.502419	−	0.864624i	$-0.332443\pi$
$617$	−189422.	−	328089.i	−0.497577	−	0.861828i	−0.999996	+	0.00279589i	$0.999110\pi$
$618$		0			0
$619$	−90319.8	+	156439.i	−0.235723	+	0.408284i	−0.959483	−	0.281768i	$-0.909079\pi$
$619$	−90319.8	+	156439.i	−0.235723	+	0.408284i	0.723760	+	0.690052i	$0.242412\pi$
$620$		0			0
$621$	−200491.	+	17475.5i	−0.519892	+	0.0453156i
$622$		0			0
$623$	−97568.6	−	56331.3i	−0.251382	−	0.145135i
$624$		0			0
$625$	220490.	+	381899.i	0.564454	+	0.977663i
$626$		0			0
$627$	118395.	−	149702.i	0.301161	−	0.380797i
$628$		0			0
$629$		−	82717.9i		−	0.209073i
$630$		0			0
$631$			115341.i			0.289685i	0.989455	+	0.144842i	$0.0462675\pi$
$631$			115341.i			0.289685i	−0.989455	+	0.144842i	$0.953733\pi$
$632$		0			0
$633$	110173.	+	277408.i	0.274958	+	0.692328i
$634$		0			0
$635$	20022.3	+	34679.7i	0.0496555	+	0.0860058i
$636$		0			0
$637$	204945.	+	118325.i	0.505078	+	0.291607i
$638$		0			0
$639$	70573.9	−	235549.i	0.172839	−	0.576871i
$640$		0			0
$641$	71144.9	−	123227.i	0.173152	−	0.299908i	−0.766368	−	0.642402i	$-0.777938\pi$
$641$	71144.9	−	123227.i	0.173152	−	0.299908i	0.939520	+	0.342493i	$0.111271\pi$
$642$		0			0
$643$	150535.	+	260734.i	0.364095	+	0.630631i	0.988630	−	0.150365i	$-0.0480450\pi$
$643$	150535.	+	260734.i	0.364095	+	0.630631i	−0.624535	+	0.780996i	$0.714712\pi$
$644$		0			0
$645$	−31459.1	+	214608.i	−0.0756182	+	0.515854i
$646$		0			0
$647$			562947.i			1.34480i	0.740186	+	0.672402i	$0.234737\pi$
$647$			562947.i			1.34480i	−0.740186	+	0.672402i	$0.765263\pi$
$648$		0			0
$649$	−657103.			−1.56007
$650$		0			0
$651$	564651.	+	82771.3i	1.33235	+	0.195307i
$652$		0			0
$653$	658714.	−	380308.i	1.54479	−	0.891887i	0.546267	−	0.837611i	$-0.316048\pi$
$653$	658714.	−	380308.i	1.54479	−	0.891887i	0.998526	−	0.0542753i	$-0.0172848\pi$
$654$		0			0
$655$	149368.	+	86237.4i	0.348156	+	0.201008i
$656$		0			0
$657$	432249.	+	129508.i	1.00139	+	0.300031i
$658$		0			0
$659$	207982.	−	360235.i	0.478911	−	0.829497i	−0.520797	−	0.853681i	$-0.674365\pi$
$659$	207982.	−	360235.i	0.478911	−	0.829497i	0.999708	+	0.0241831i	$0.00769847\pi$
$660$		0			0
$661$	−317798.	+	183481.i	−0.727358	+	0.419940i	−0.817455	−	0.575993i	$-0.804616\pi$
$661$	−317798.	+	183481.i	−0.727358	+	0.419940i	0.0900969	+	0.995933i	$0.471282\pi$
$662$		0			0
$663$	681798.	−	270776.i	1.55106	−	0.616003i
$664$		0			0
$665$	184766.			0.417810
$666$		0			0
$667$	241629.			0.543123
$668$		0			0
$669$	436982.	+	345597.i	0.976364	+	0.772179i
$670$		0			0
$671$	−333813.	+	192727.i	−0.741409	+	0.428053i
$672$		0			0
$673$	208572.	−	361257.i	0.460496	−	0.797602i	−0.538490	−	0.842632i	$-0.681005\pi$
$673$	208572.	−	361257.i	0.460496	−	0.797602i	0.998986	+	0.0450300i	$0.0143383\pi$
$674$		0			0
$675$	−56749.3	+	39709.0i	−0.124553	+	0.0871528i
$676$		0			0
$677$	−270633.	−	156250.i	−0.590477	−	0.340912i	0.174809	−	0.984602i	$-0.444069\pi$
$677$	−270633.	−	156250.i	−0.590477	−	0.340912i	−0.765286	+	0.643690i	$0.777403\pi$
$678$		0			0
$679$	131160.	−	75725.3i	0.284487	−	0.164249i
$680$		0			0
$681$	−1353.64	+	1711.57i	−0.00291882	+	0.00369064i
$682$		0			0
$683$	140348.			0.300860			0.150430	−	0.988621i	$-0.451934\pi$
$683$	140348.			0.300860			0.150430	+	0.988621i	$0.451934\pi$
$684$		0			0
$685$			573088.i			1.22135i
$686$		0			0
$687$	−98277.7	+	39031.0i	−0.208229	+	0.0826982i
$688$		0			0
$689$	446953.	+	774145.i	0.941506	+	1.63074i
$690$		0			0
$691$	−6583.82	+	11403.5i	−0.0137887	+	0.0238827i	−0.872837	−	0.488011i	$-0.837723\pi$
$691$	−6583.82	+	11403.5i	−0.0137887	+	0.0238827i	0.859049	+	0.511894i	$0.171056\pi$
$692$		0			0
$693$	−882505.	+	208957.i	−1.83760	+	0.435101i
$694$		0			0
$695$	480033.	+	277147.i	0.993805	+	0.573773i
$696$		0			0
$697$	−603892.	−	1.04597e6i	−1.24306	−	2.15305i
$698$		0			0
$699$	309463.	+	45363.6i	0.633365	+	0.0928439i
$700$		0			0
$701$		−	143500.i		−	0.292022i	−0.989283	−	0.146011i	$-0.953357\pi$
$701$		−	143500.i		−	0.292022i	0.989283	−	0.146011i	$-0.0466434\pi$
$702$		0			0
$703$			22218.0i			0.0449567i
$704$		0			0
$705$	96121.3	+	14090.3i	0.193393	+	0.0283492i
$706$		0			0
$707$	−164632.	−	285151.i	−0.329363	−	0.570474i
$708$		0			0
$709$	386361.	+	223066.i	0.768602	+	0.443752i	0.832376	−	0.554212i	$-0.186980\pi$
$709$	386361.	+	223066.i	0.768602	+	0.443752i	−0.0637739	+	0.997964i	$0.520314\pi$
$710$		0			0
$711$	598306.	+	634441.i	1.18354	+	1.25502i
$712$		0			0
$713$	−145164.	+	251432.i	−0.285549	+	0.494585i
$714$		0			0
$715$	477623.	+	827267.i	0.934271	+	1.61820i
$716$		0			0
$717$	396944.	−	157646.i	0.772131	−	0.306652i
$718$		0			0
$719$		−	316954.i		−	0.613110i	−0.951853	−	0.306555i	$-0.900824\pi$
$719$		−	316954.i		−	0.613110i	0.951853	−	0.306555i	$-0.0991763\pi$
$720$		0			0
$721$	679667.			1.30745
$722$		0			0
$723$	−385562.	+	487515.i	−0.737594	+	0.932634i
$724$		0			0
$725$	72017.6	−	41579.4i	0.137013	−	0.0791047i
$726$		0			0
$727$	429578.	+	248017.i	0.812779	+	0.469258i	0.847920	−	0.530124i	$-0.177855\pi$
$727$	429578.	+	248017.i	0.812779	+	0.469258i	−0.0351407	+	0.999382i	$0.511188\pi$
$728$		0			0
$729$	341341.	+	407328.i	0.642293	+	0.766459i
$730$		0			0
$731$	−190938.	+	330714.i	−0.357320	+	0.618896i
$732$		0			0
$733$	−607822.	+	350926.i	−1.13128	+	0.653143i	−0.944256	−	0.329213i	$-0.893217\pi$
$733$	−607822.	+	350926.i	−1.13128	+	0.653143i	−0.187021	+	0.982356i	$0.559883\pi$
$734$		0			0
$735$	−233820.	−	184922.i	−0.432820	−	0.342306i
$736$		0			0
$737$	544283.			1.00205
$738$		0			0
$739$	−591401.			−1.08291			−0.541456	−	0.840729i	$-0.682127\pi$
$739$	−591401.			−1.08291			−0.541456	+	0.840729i	$0.682127\pi$
$740$		0			0
$741$	−183131.	+	72730.3i	−0.333522	+	0.132458i
$742$		0			0
$743$	76816.9	−	44350.2i	0.139149	−	0.0803375i	−0.428810	−	0.903395i	$-0.641067\pi$
$743$	76816.9	−	44350.2i	0.139149	−	0.0803375i	0.567958	+	0.823057i	$0.307734\pi$
$744$		0			0
$745$	69713.8	−	120748.i	0.125605	−	0.217554i
$746$		0			0
$747$	165869.	−	156422.i	0.297251	−	0.280321i
$748$		0			0
$749$	−253267.	−	146224.i	−0.451456	−	0.260648i
$750$		0			0
$751$	−692048.	+	399554.i	−1.22703	+	0.708428i	−0.966408	−	0.257011i	$-0.917262\pi$
$751$	−692048.	+	399554.i	−1.22703	+	0.708428i	−0.260626	+	0.965440i	$0.583929\pi$
$752$		0			0
$753$	−527058.	−	77260.6i	−0.929541	−	0.136260i
$754$		0			0
$755$	546805.			0.959264
$756$		0			0
$757$			1.07119e6i			1.86927i	0.355603	+	0.934637i	$0.384275\pi$
$757$			1.07119e6i			1.86927i	−0.355603	+	0.934637i	$0.615725\pi$
$758$		0			0
$759$	66917.1	−	456497.i	0.116159	−	0.792418i
$760$		0			0
$761$	173781.	+	300998.i	0.300078	+	0.519750i	0.976153	−	0.217082i	$-0.0696540\pi$
$761$	173781.	+	300998.i	0.300078	+	0.519750i	−0.676075	+	0.736832i	$0.736321\pi$
$762$		0			0
$763$	523483.	−	906699.i	0.899194	−	1.55745i
$764$		0			0
$765$	−899249.	+	212922.i	−1.53659	+	0.363829i
$766$		0			0
$767$	587502.	+	339195.i	0.998662	+	0.576578i
$768$		0			0
$769$	307338.	+	532324.i	0.519712	+	0.900168i	0.999737	+	0.0229135i	$0.00729422\pi$
$769$	307338.	+	532324.i	0.519712	+	0.900168i	−0.480025	+	0.877255i	$0.659372\pi$
$770$		0			0
$771$	−174604.	−	439643.i	−0.293728	−	0.739590i
$772$		0			0
$773$			558543.i			0.934755i	0.884058	+	0.467378i	$0.154801\pi$
$773$			558543.i			0.934755i	−0.884058	+	0.467378i	$0.845199\pi$
$774$		0			0
$775$			99919.0i			0.166358i
$776$		0			0
$777$	65488.4	−	82805.2i	0.108473	−	0.137156i
$778$		0			0
$779$	162205.	+	280947.i	0.267294	+	0.462967i
$780$		0			0
$781$	488195.	+	281860.i	0.800371	+	0.462095i
$782$		0			0
$783$	−365811.	−	522791.i	−0.596668	−	0.852716i
$784$		0			0
$785$	119871.	−	207622.i	0.194524	−	0.336925i
$786$		0			0
$787$	−171055.	−	296276.i	−0.276176	−	0.478351i	0.694255	−	0.719729i	$-0.255734\pi$
$787$	−171055.	−	296276.i	−0.276176	−	0.478351i	−0.970431	+	0.241378i	$0.922401\pi$
$788$		0			0
$789$	−302492.	−	239233.i	−0.485915	−	0.384297i
$790$		0			0
$791$			804358.i			1.28557i
$792$		0			0
$793$	397940.			0.632807
$794$		0			0
$795$	−415632.	−	1.04654e6i	−0.657620	−	1.65585i
$796$		0			0
$797$	639205.	−	369045.i	1.00629	−	0.580982i	0.0961872	−	0.995363i	$-0.469335\pi$
$797$	639205.	−	369045.i	1.00629	−	0.580982i	0.910103	+	0.414381i	$0.136002\pi$
$798$		0			0
$799$	148124.	+	85519.6i	0.232024	+	0.133959i
$800$		0			0
$801$	−144984.	−	43439.4i	−0.225972	−	0.0677047i
$802$		0			0
$803$	−517233.	+	895874.i	−0.802149	+	1.38936i
$804$		0			0
$805$	386802.	−	223320.i	0.596894	−	0.344617i
$806$		0			0
$807$	−13815.8	+	94248.7i	−0.0212142	+	0.144720i
$808$		0			0
$809$	−869283.			−1.32820			−0.664101	−	0.747643i	$-0.731185\pi$
$809$	−869283.			−1.32820			−0.664101	+	0.747643i	$0.731185\pi$
$810$		0			0
$811$	524099.			0.796841			0.398420	−	0.917203i	$-0.369559\pi$
$811$	524099.			0.796841			0.398420	+	0.917203i	$0.369559\pi$
$812$		0			0
$813$	−121840.	+	831170.i	−0.184335	+	1.25750i
$814$		0			0
$815$	−883065.	+	509838.i	−1.32947	+	0.767568i
$816$		0			0
$817$	51285.8	−	88829.7i	0.0768340	−	0.133080i
$818$		0			0
$819$	896892.	+	268722.i	1.33713	+	0.400623i
$820$		0			0
$821$	−176424.	−	101858.i	−0.261741	−	0.151116i	0.363388	−	0.931638i	$-0.381620\pi$
$821$	−176424.	−	101858.i	−0.261741	−	0.151116i	−0.625128	+	0.780522i	$0.714953\pi$
$822$		0			0
$823$	840341.	−	485171.i	1.24067	−	0.716300i	0.271438	−	0.962456i	$-0.412501\pi$
$823$	840341.	−	485171.i	1.24067	−	0.716300i	0.969230	+	0.246156i	$0.0791675\pi$
$824$		0			0
$825$	−58609.0	−	147574.i	−0.0861106	−	0.216821i
$826$		0			0
$827$	876265.			1.28122			0.640611	−	0.767865i	$-0.278681\pi$
$827$	876265.			1.28122			0.640611	+	0.767865i	$0.278681\pi$
$828$		0			0
$829$		−	728747.i		−	1.06040i	−0.847874	−	0.530198i	$-0.822118\pi$
$829$		−	728747.i		−	1.06040i	0.847874	−	0.530198i	$-0.177882\pi$
$830$		0			0
$831$	−165253.	−	130694.i	−0.239303	−	0.189258i
$832$		0			0
$833$	−262423.	−	454530.i	−0.378192	−	0.655047i
$834$		0			0
$835$	185013.	−	320451.i	0.265356	−	0.459610i
$836$		0			0
$837$	763768.	−	66572.7i	1.09021	−	0.0950266i
$838$		0			0
$839$	−261880.	−	151197.i	−0.372031	−	0.214792i	0.302314	−	0.953208i	$-0.402241\pi$
$839$	−261880.	−	151197.i	−0.372031	−	0.214792i	−0.674345	+	0.738416i	$0.735574\pi$
$840$		0			0
$841$	29400.8	+	50923.6i	0.0415687	+	0.0719991i
$842$		0			0
$843$	41719.7	−	52751.5i	0.0587065	−	0.0742300i
$844$		0			0
$845$		−	219812.i		−	0.307849i
$846$		0			0
$847$		−	1.19634e6i		−	1.66758i
$848$		0			0
$849$	−299374.	−	753805.i	−0.415334	−	1.04579i
$850$		0			0
$851$	26854.1	+	46512.7i	0.0370810	+	0.0642262i
$852$		0			0
$853$	613667.	+	354301.i	0.843402	+	0.486938i	0.858419	−	0.512949i	$-0.171447\pi$
$853$	613667.	+	354301.i	0.843402	+	0.486938i	−0.0150171	+	0.999887i	$0.504780\pi$
$854$		0			0
$855$	241538.	−	57190.7i	0.330410	−	0.0782336i
$856$		0			0
$857$	−506749.	+	877715.i	−0.689972	+	1.19507i	0.281875	+	0.959451i	$0.409044\pi$
$857$	−506749.	+	877715.i	−0.689972	+	1.19507i	−0.971847	+	0.235615i	$0.924290\pi$
$858$		0			0
$859$	−187918.	−	325483.i	−0.254672	−	0.441105i	0.710134	−	0.704066i	$-0.248634\pi$
$859$	−187918.	−	325483.i	−0.254672	−	0.441105i	−0.964806	+	0.262961i	$0.915301\pi$
$860$		0			0
$861$	223574.	−	1.52518e6i	0.301588	−	2.05738i
$862$		0			0
$863$		−	771077.i		−	1.03532i	−0.855585	−	0.517662i	$-0.826802\pi$
$863$		−	771077.i		−	1.03532i	0.855585	−	0.517662i	$-0.173198\pi$
$864$		0			0
$865$	−300146.			−0.401144
$866$		0			0
$867$	−866042.	−	126952.i	−1.15213	−	0.168889i
$868$		0			0
$869$	−1.73138e6	+	999610.i	−2.29272	+	1.32371i
$870$		0			0
$871$	−486632.	−	280957.i	−0.641453	−	0.370343i
$872$		0			0
$873$	148022.	−	139591.i	0.194221	−	0.183159i
$874$		0			0
$875$	−428730.	+	742582.i	−0.559974	+	0.969903i
$876$		0			0
$877$	−121036.	+	69880.4i	−0.157368	+	0.0908566i	−0.576616	−	0.817015i	$-0.695627\pi$
$877$	−121036.	+	69880.4i	−0.157368	+	0.0908566i	0.419248	+	0.907872i	$0.362294\pi$
$878$		0			0
$879$	1.14217e6	−	453612.i	1.47827	−	0.587093i
$880$		0			0
$881$	764399.			0.984846			0.492423	−	0.870356i	$-0.336111\pi$
$881$	764399.			0.984846			0.492423	+	0.870356i	$0.336111\pi$
$882$		0			0
$883$	276974.			0.355237			0.177618	−	0.984099i	$-0.443161\pi$
$883$	276974.			0.355237			0.177618	+	0.984099i	$0.443161\pi$
$884$		0			0
$885$	−670277.	−	530104.i	−0.855791	−	0.676822i
$886$		0			0
$887$	−284311.	+	164147.i	−0.361365	+	0.208634i	−0.669679	−	0.742650i	$-0.733568\pi$
$887$	−284311.	+	164147.i	−0.361365	+	0.208634i	0.308314	+	0.951285i	$0.400235\pi$
$888$		0			0
$889$	−44990.7	+	77926.1i	−0.0569271	+	0.0986006i
$890$		0			0
$891$	−1.08899e6	+	546324.i	−1.37173	+	0.688168i
$892$		0			0
$893$	−39786.1	−	22970.5i	−0.0498917	−	0.0288050i
$894$		0			0
$895$	−165765.	+	95704.5i	−0.206941	+	0.119478i
$896$		0			0
$897$	−295472.	+	373602.i	−0.367224	+	0.464327i
$898$		0			0
$899$	−920482.			−1.13893
$900$		0			0
$901$		−	1.98252e6i		−	2.44212i
$902$		0			0
$903$	−452968.	+	179896.i	−0.555510	+	0.220621i
$904$		0			0
$905$	350234.	+	606623.i	0.427623	+	0.740664i
$906$		0			0
$907$	−2523.63	+	4371.06i	−0.00306769	+	0.00531339i	−0.867555	−	0.497341i	$-0.834310\pi$
$907$	−2523.63	+	4371.06i	−0.00306769	+	0.00531339i	0.864487	+	0.502654i	$0.167643\pi$
$908$		0			0
$909$	−303480.	−	321809.i	−0.367284	−	0.389466i
$910$		0			0
$911$	124609.	+	71943.0i	0.150145	+	0.0866865i	0.573191	−	0.819422i	$-0.305705\pi$
$911$	124609.	+	71943.0i	0.150145	+	0.0866865i	−0.423045	+	0.906109i	$0.639039\pi$
$912$		0			0
$913$	261339.	+	452653.i	0.313518	+	0.543030i
$914$		0			0
$915$	−495984.	−	72705.4i	−0.592414	−	0.0868409i
$916$		0			0
$917$			387555.i			0.460887i
$918$		0			0
$919$			1.50889e6i			1.78660i	0.449466	+	0.893298i	$0.351614\pi$
$919$			1.50889e6i			1.78660i	−0.449466	+	0.893298i	$0.648386\pi$
$920$		0			0
$921$	−1.50308e6	−	220334.i	−1.77200	−	0.259754i
$922$		0			0
$923$	−290990.	−	504010.i	−0.341566	−	0.591610i
$924$		0			0
$925$	16007.7	+	9242.07i	0.0187088	+	0.0108015i
$926$		0			0
$927$	888504.	−	210377.i	1.03395	−	0.244816i
$928$		0			0
$929$	489589.	−	847994.i	0.567284	−	0.982565i	−0.429549	−	0.903043i	$-0.641328\pi$
$929$	489589.	−	847994.i	0.567284	−	0.982565i	0.996833	−	0.0795211i	$-0.0253391\pi$
$930$		0			0
$931$	70486.7	+	122087.i	0.0813220	+	0.140854i
$932$		0			0
$933$	665537.	−	264318.i	0.764556	−	0.303643i
$934$		0			0
$935$		−	2.11856e6i		−	2.42335i
$936$		0			0
$937$	75553.9			0.0860553			0.0430276	−	0.999074i	$-0.486300\pi$
$937$	75553.9			0.0860553			0.0430276	+	0.999074i	$0.486300\pi$
$938$		0			0
$939$	−1.04258e6	+	1.31827e6i	−1.18244	+	1.49511i
$940$		0			0
$941$	33992.9	−	19625.8i	0.0383892	−	0.0221640i	−0.480683	−	0.876895i	$-0.659611\pi$
$941$	33992.9	−	19625.8i	0.0383892	−	0.0221640i	0.519072	+	0.854731i	$0.326278\pi$
$942$		0			0
$943$	679142.	+	392103.i	0.763726	+	0.440937i
$944$		0			0
$945$	−1.06877e6	−	498796.i	−1.19680	−	0.558546i
$946$		0			0
$947$	313680.	−	543310.i	0.349773	−	0.605825i	−0.636436	−	0.771330i	$-0.719592\pi$
$947$	313680.	−	543310.i	0.349773	−	0.605825i	0.986209	+	0.165504i	$0.0529252\pi$
$948$		0			0
$949$	924894.	−	533988.i	1.02697	−	0.592924i
$950$		0			0
$951$	−780971.	−	617648.i	−0.863522	−	0.682936i
$952$		0			0
$953$	−884152.			−0.973512			−0.486756	−	0.873538i	$-0.661820\pi$
$953$	−884152.			−0.973512			−0.486756	+	0.873538i	$0.661820\pi$
$954$		0			0
$955$	−1.22489e6			−1.34304
$956$		0			0
$957$	1.35949e6	−	539923.i	1.48441	−	0.589533i
$958$		0			0
$959$	−1.11522e6	+	643871.i	−1.21261	+	0.700103i
$960$		0			0
$961$	91239.2	−	158031.i	0.0987949	−	0.171118i
$962$		0			0
$963$	−376348.	−	112759.i	−0.405823	−	0.121591i
$964$		0			0
$965$	−280693.	−	162058.i	−0.301423	−	0.174027i
$966$		0			0
$967$	−415020.	+	239612.i	−0.443829	+	0.256245i	−0.705220	−	0.708988i	$-0.749152\pi$
$967$	−415020.	+	239612.i	−0.443829	+	0.256245i	0.261391	+	0.965233i	$0.415819\pi$
$968$		0			0
$969$	432387.	+	63382.9i	0.460495	+	0.0675032i
$970$		0			0
$971$	−37374.6			−0.0396404			−0.0198202	−	0.999804i	$-0.506309\pi$
$971$	−37374.6			−0.0396404			−0.0198202	+	0.999804i	$0.506309\pi$
$972$		0			0
$973$			1.24551e6i			1.31559i
$974$		0			0
$975$	−23776.1	+	162197.i	−0.0250110	+	0.170621i
$976$		0			0
$977$	−380919.	−	659770.i	−0.399064	−	0.691200i	0.594546	−	0.804061i	$-0.297332\pi$
$977$	−380919.	−	659770.i	−0.399064	−	0.691200i	−0.993611	+	0.112861i	$0.963998\pi$
$978$		0			0
$979$	173489.	−	300492.i	0.181012	−	0.313522i
$980$		0			0
$981$	403679.	−	1.34733e6i	0.419467	−	1.40002i
$982$		0			0
$983$	−958351.	−	553304.i	−0.991785	−	0.572607i	−0.0859774	−	0.996297i	$-0.527401\pi$
$983$	−958351.	−	553304.i	−0.991785	−	0.572607i	−0.905807	+	0.423690i	$0.860735\pi$
$984$		0			0
$985$	−940809.	−	1.62953e6i	−0.969681	−	1.67954i
$986$		0			0
$987$	80574.1	+	202881.i	0.0827106	+	0.208260i
$988$		0			0
$989$		−	247949.i		−	0.253496i
$990$		0			0
$991$		−	306890.i		−	0.312489i	−0.987718	−	0.156245i	$-0.950061\pi$
$991$		−	306890.i		−	0.312489i	0.987718	−	0.156245i	$-0.0499388\pi$
$992$		0			0
$993$	−396664.	+	501553.i	−0.402277	+	0.508649i
$994$		0			0
$995$	717475.	+	1.24270e6i	0.724704	+	1.25522i
$996$		0			0
$997$	−13764.4	−	7946.86i	−0.0138473	−	0.00799476i	0.493060	−	0.869995i	$-0.335878\pi$
$997$	−13764.4	−	7946.86i	−0.0138473	−	0.00799476i	−0.506908	+	0.862000i	$0.669212\pi$
$998$		0			0
$999$	59979.8	−	128519.i	0.0601000	−	0.128776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.5.t.b.79.4		88
3.2	odd	2		864.5.t.b.559.9		88
4.3	odd	2		72.5.p.b.43.18	✓	88
8.3	odd	2	inner	288.5.t.b.79.3		88
8.5	even	2		72.5.p.b.43.40	yes	88
9.4	even	3	inner	288.5.t.b.175.3		88
9.5	odd	6		864.5.t.b.847.36		88
12.11	even	2		216.5.p.b.19.27		88
24.5	odd	2		216.5.p.b.19.5		88
24.11	even	2		864.5.t.b.559.36		88
36.23	even	6		216.5.p.b.91.5		88
36.31	odd	6		72.5.p.b.67.40	yes	88
72.5	odd	6		216.5.p.b.91.27		88
72.13	even	6		72.5.p.b.67.18	yes	88
72.59	even	6		864.5.t.b.847.9		88
72.67	odd	6	inner	288.5.t.b.175.4		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.p.b.43.18	✓	88	4.3	odd	2
72.5.p.b.43.40	yes	88	8.5	even	2
72.5.p.b.67.18	yes	88	72.13	even	6
72.5.p.b.67.40	yes	88	36.31	odd	6
216.5.p.b.19.5		88	24.5	odd	2
216.5.p.b.19.27		88	12.11	even	2
216.5.p.b.91.5		88	36.23	even	6
216.5.p.b.91.27		88	72.5	odd	6
288.5.t.b.79.3		88	8.3	odd	2	inner
288.5.t.b.79.4		88	1.1	even	1	trivial
288.5.t.b.175.3		88	9.4	even	3	inner
288.5.t.b.175.4		88	72.67	odd	6	inner
864.5.t.b.559.9		88	3.2	odd	2
864.5.t.b.559.36		88	24.11	even	2
864.5.t.b.847.9		88	72.59	even	6
864.5.t.b.847.36		88	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	288.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.90483 - 1.30534i) q^{3} +(23.2381 - 13.4165i) q^{5} +(52.2165 + 30.1472i) q^{7} +(77.5922 + 23.2478i) q^{9} +(-92.8475 + 160.817i) q^{11} +(166.026 - 95.8552i) q^{13} +(-224.444 + 89.1381i) q^{15} -425.178 q^{17} +114.203 q^{19} +(-425.627 - 336.616i) q^{21} +(239.080 - 138.033i) q^{23} +(47.5051 - 82.2813i) q^{25} +(-660.599 - 308.302i) q^{27} +(757.999 + 437.631i) q^{29} +(-910.769 + 525.833i) q^{31} +(1036.71 - 1310.85i) q^{33} +1617.88 q^{35} +194.549i q^{37} +(-1603.56 + 636.853i) q^{39} +(1420.33 + 2460.08i) q^{41} +(449.077 - 777.825i) q^{43} +(2115.00 - 500.783i) q^{45} +(-348.382 - 201.138i) q^{47} +(617.208 + 1069.03i) q^{49} +(3786.14 + 555.004i) q^{51} +4662.79i q^{53} +4982.75i q^{55} +(-1016.96 - 149.074i) q^{57} +(1769.31 + 3064.53i) q^{59} +(1797.64 + 1037.87i) q^{61} +(3350.73 + 3553.10i) q^{63} +(2572.08 - 4454.98i) q^{65} +(-1465.53 - 2538.37i) q^{67} +(-2309.14 + 917.077i) q^{69} -3035.73i q^{71} +5570.78 q^{73} +(-530.431 + 670.691i) q^{75} +(-9696.34 + 5598.18i) q^{77} +(9323.76 + 5383.08i) q^{79} +(5480.08 + 3607.69i) q^{81} +(1407.36 - 2437.61i) q^{83} +(-9880.31 + 5704.40i) q^{85} +(-6178.59 - 4886.48i) q^{87} -1868.54 q^{89} +11559.1 q^{91} +(8796.64 - 3493.58i) q^{93} +(2653.85 - 1532.20i) q^{95} +(1255.93 - 2175.33i) q^{97} +(-10942.9 + 10319.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 18 q^{3} + 30 q^{9} - 44 q^{11} - 1156 q^{17} - 860 q^{19} + 5998 q^{25} - 504 q^{27} - 3204 q^{33} + 2508 q^{35} + 2348 q^{41} - 3500 q^{43} + 16462 q^{49} + 12378 q^{51} - 6522 q^{57} + 3508 q^{59}+ \cdots + 11742 q^{99}+O(q^{100}) \) 88 * q + 18 * q^3 + 30 * q^9 - 44 * q^11 - 1156 * q^17 - 860 * q^19 + 5998 * q^25 - 504 * q^27 - 3204 * q^33 + 2508 * q^35 + 2348 * q^41 - 3500 * q^43 + 16462 * q^49 + 12378 * q^51 - 6522 * q^57 + 3508 * q^59 - 2502 * q^65 - 5132 * q^67 + 19004 * q^73 + 39858 * q^75 - 11346 * q^81 - 17090 * q^83 - 8272 * q^89 + 9612 * q^91 + 9980 * q^97 + 11742 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more