LMFDB - Embedded newform 65.6.b.a.14.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [65,6,Mod(14,65)] 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("65.14"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	65.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.4249482878$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.12
Character	$\chi$	$=$	65.14
Dual form			65.6.b.a.14.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.30124i q^{2} +24.0437i q^{3} +21.1018 q^{4} +(52.5959 + 18.9386i) q^{5} +79.3742 q^{6} +91.7264i q^{7} -175.302i q^{8} -335.101 q^{9} +(62.5210 - 173.632i) q^{10} -45.5406 q^{11} +507.366i q^{12} +169.000i q^{13} +302.811 q^{14} +(-455.356 + 1264.60i) q^{15} +96.5440 q^{16} +745.700i q^{17} +1106.25i q^{18} -306.010 q^{19} +(1109.87 + 399.639i) q^{20} -2205.45 q^{21} +150.340i q^{22} -704.422i q^{23} +4214.91 q^{24} +(2407.66 + 1992.19i) q^{25} +557.910 q^{26} -2214.45i q^{27} +1935.59i q^{28} +6802.33 q^{29} +(4174.76 + 1503.24i) q^{30} -7605.25 q^{31} -5928.38i q^{32} -1094.97i q^{33} +2461.74 q^{34} +(-1737.17 + 4824.43i) q^{35} -7071.24 q^{36} -109.012i q^{37} +1010.21i q^{38} -4063.39 q^{39} +(3319.98 - 9220.16i) q^{40} -13355.2 q^{41} +7280.71i q^{42} -4474.54i q^{43} -960.988 q^{44} +(-17624.9 - 6346.36i) q^{45} -2325.47 q^{46} +4860.59i q^{47} +2321.28i q^{48} +8393.26 q^{49} +(6576.70 - 7948.25i) q^{50} -17929.4 q^{51} +3566.21i q^{52} -40100.0i q^{53} -7310.45 q^{54} +(-2395.25 - 862.477i) q^{55} +16079.8 q^{56} -7357.62i q^{57} -22456.1i q^{58} +29655.8 q^{59} +(-9608.82 + 26685.4i) q^{60} +51545.6 q^{61} +25106.8i q^{62} -30737.6i q^{63} -16481.6 q^{64} +(-3200.63 + 8888.71i) q^{65} -3614.75 q^{66} -51877.6i q^{67} +15735.6i q^{68} +16936.9 q^{69} +(15926.6 + 5734.83i) q^{70} +42271.1 q^{71} +58743.9i q^{72} -45219.7i q^{73} -359.876 q^{74} +(-47899.7 + 57889.0i) q^{75} -6457.36 q^{76} -4177.27i q^{77} +13414.2i q^{78} -62532.7 q^{79} +(5077.82 + 1828.41i) q^{80} -28185.8 q^{81} +44088.9i q^{82} +46913.1i q^{83} -46538.9 q^{84} +(-14122.5 + 39220.8i) q^{85} -14771.5 q^{86} +163553. i q^{87} +7983.35i q^{88} +63387.4 q^{89} +(-20950.9 + 58184.2i) q^{90} -15501.8 q^{91} -14864.6i q^{92} -182859. i q^{93} +16046.0 q^{94} +(-16094.9 - 5795.41i) q^{95} +142540. q^{96} -132037. i q^{97} -27708.2i q^{98} +15260.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 500 q^{4} + 80 q^{5} - 404 q^{6} - 1926 q^{9} + 322 q^{10} - 652 q^{11} - 2668 q^{14} - 2064 q^{15} + 12092 q^{16} + 5248 q^{19} - 3460 q^{20} + 7060 q^{21} - 5480 q^{24} - 1178 q^{25} - 4056 q^{26}+ \cdots + 520976 q^{99}+O(q^{100}) $ 30 * q - 500 * q^4 + 80 * q^5 - 404 * q^6 - 1926 * q^9 + 322 * q^10 - 652 * q^11 - 2668 * q^14 - 2064 * q^15 + 12092 * q^16 + 5248 * q^19 - 3460 * q^20 + 7060 * q^21 - 5480 * q^24 - 1178 * q^25 - 4056 * q^26 + 6084 * q^29 + 19638 * q^30 - 22292 * q^31 - 46060 * q^34 - 272 * q^35 + 50344 * q^36 + 12168 * q^39 + 26166 * q^40 - 15856 * q^41 - 45516 * q^44 - 64644 * q^45 + 45396 * q^46 - 141086 * q^49 - 60544 * q^50 + 96168 * q^51 - 4964 * q^54 + 48544 * q^55 + 67156 * q^56 + 124624 * q^59 + 87348 * q^60 - 59060 * q^61 - 30132 * q^64 + 338 * q^65 - 2480 * q^66 - 398680 * q^69 + 297080 * q^70 - 45736 * q^71 + 517132 * q^74 + 249816 * q^75 - 278480 * q^76 - 259168 * q^79 + 100648 * q^80 + 115462 * q^81 + 30364 * q^84 - 108572 * q^85 - 483560 * q^86 + 335276 * q^89 - 501660 * q^90 - 103428 * q^91 - 208500 * q^94 + 217136 * q^95 - 92740 * q^96 + 520976 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.30124i		−	0.583583i	−0.956482	−	0.291791i	$-0.905749\pi$
$2$		−	3.30124i		−	0.583583i	0.956482	−	0.291791i	$-0.0942513\pi$
$3$			24.0437i			1.54241i	0.636589	+	0.771203i	$0.280345\pi$
$3$			24.0437i			1.54241i	−0.636589	+	0.771203i	$0.719655\pi$
$4$	21.1018			0.659431
$5$	52.5959	+	18.9386i	0.940864	+	0.338785i
$5$	52.5959	+	18.9386i	0.940864	+	0.338785i
$6$	79.3742			0.900121
$7$			91.7264i			0.707537i	0.935333	+	0.353769i	$0.115100\pi$
$7$			91.7264i			0.707537i	−0.935333	+	0.353769i	$0.884900\pi$
$8$		−	175.302i		−	0.968415i
$9$	−335.101			−1.37902
$10$	62.5210	−	173.632i	0.197709	−	0.549072i
$11$	−45.5406			−0.113479			−0.0567397	−	0.998389i	$-0.518071\pi$
$11$	−45.5406			−0.113479			−0.0567397	+	0.998389i	$0.518071\pi$
$12$			507.366i			1.01711i
$13$			169.000i			0.277350i
$13$			169.000i			0.277350i
$14$	302.811			0.412906
$15$	−455.356	+	1264.60i	−0.522544	+	1.45119i
$16$	96.5440			0.0942812
$17$			745.700i			0.625809i	0.949785	+	0.312905i	$0.101302\pi$
$17$			745.700i			0.625809i	−0.949785	+	0.312905i	$0.898698\pi$
$18$			1106.25i			0.804770i
$19$	−306.010			−0.194469			−0.0972347	−	0.995261i	$-0.531000\pi$
$19$	−306.010			−0.194469			−0.0972347	+	0.995261i	$0.531000\pi$
$20$	1109.87	+	399.639i	0.620435	+	0.223405i
$21$	−2205.45			−1.09131
$22$			150.340i			0.0662246i
$23$		−	704.422i		−	0.277660i	−0.990316	−	0.138830i	$-0.955666\pi$
$23$		−	704.422i		−	0.277660i	0.990316	−	0.138830i	$-0.0443342\pi$
$24$	4214.91			1.49369
$25$	2407.66	+	1992.19i	0.770450	+	0.637501i
$26$	557.910			0.161857
$27$		−	2214.45i		−	0.584598i
$28$			1935.59i			0.466572i
$29$	6802.33			1.50198			0.750988	−	0.660316i	$-0.229578\pi$
$29$	6802.33			1.50198			0.750988	+	0.660316i	$0.229578\pi$
$30$	4174.76	+	1503.24i	0.846892	+	0.304947i
$31$	−7605.25			−1.42138			−0.710689	−	0.703507i	$-0.751616\pi$
$31$	−7605.25			−1.42138			−0.710689	+	0.703507i	$0.751616\pi$
$32$		−	5928.38i		−	1.02344i
$33$		−	1094.97i		−	0.175031i
$34$	2461.74			0.365211
$35$	−1737.17	+	4824.43i	−0.239703	+	0.665696i
$36$	−7071.24			−0.909367
$37$		−	109.012i		−	0.0130909i	−0.999979	−	0.00654547i	$-0.997916\pi$
$37$		−	109.012i		−	0.0130909i	0.999979	−	0.00654547i	$-0.00208350\pi$
$38$			1010.21i			0.113489i
$39$	−4063.39			−0.427787
$40$	3319.98	−	9220.16i	0.328084	−	0.911147i
$41$	−13355.2			−1.24077			−0.620386	−	0.784296i	$-0.713024\pi$
$41$	−13355.2			−1.24077			−0.620386	+	0.784296i	$0.713024\pi$
$42$			7280.71i			0.636869i
$43$		−	4474.54i		−	0.369044i	−0.982828	−	0.184522i	$-0.940926\pi$
$43$		−	4474.54i		−	0.369044i	0.982828	−	0.184522i	$-0.0590736\pi$
$44$	−960.988			−0.0748319
$45$	−17624.9	−	6346.36i	−1.29747	−	0.467190i
$46$	−2325.47			−0.162038
$47$			4860.59i			0.320955i	0.987039	+	0.160478i	$0.0513035\pi$
$47$			4860.59i			0.320955i	−0.987039	+	0.160478i	$0.948697\pi$
$48$			2321.28i			0.145420i
$49$	8393.26			0.499391
$50$	6576.70	−	7948.25i	0.372034	−	0.449621i
$51$	−17929.4			−0.965252
$52$			3566.21i			0.182893i
$53$		−	40100.0i		−	1.96090i	−0.196777	−	0.980448i	$-0.563047\pi$
$53$		−	40100.0i		−	1.96090i	0.196777	−	0.980448i	$-0.436953\pi$
$54$	−7310.45			−0.341161
$55$	−2395.25	−	862.477i	−0.106769	−	0.0384451i
$56$	16079.8			0.685190
$57$		−	7357.62i		−	0.299951i
$58$		−	22456.1i		−	0.876526i
$59$	29655.8			1.10912			0.554561	−	0.832143i	$-0.312886\pi$
$59$	29655.8			1.10912			0.554561	+	0.832143i	$0.312886\pi$
$60$	−9608.82	+	26685.4i	−0.344582	+	0.956963i
$61$	51545.6			1.77365			0.886823	−	0.462109i	$-0.152907\pi$
$61$	51545.6			1.77365			0.886823	+	0.462109i	$0.152907\pi$
$62$			25106.8i			0.829491i
$63$		−	30737.6i		−	0.975706i
$64$	−16481.6			−0.502978
$65$	−3200.63	+	8888.71i	−0.0939620	+	0.260949i
$66$	−3614.75			−0.102145
$67$		−	51877.6i		−	1.41186i	−0.708280	−	0.705932i	$-0.750528\pi$
$67$		−	51877.6i		−	1.41186i	0.708280	−	0.705932i	$-0.249472\pi$
$68$			15735.6i			0.412678i
$69$	16936.9			0.428265
$70$	15926.6	+	5734.83i	0.388489	+	0.139886i
$71$	42271.1			0.995171			0.497585	−	0.867415i	$-0.334220\pi$
$71$	42271.1			0.995171			0.497585	+	0.867415i	$0.334220\pi$
$72$			58743.9i			1.33546i
$73$		−	45219.7i		−	0.993162i	−0.867990	−	0.496581i	$-0.834588\pi$
$73$		−	45219.7i		−	0.993162i	0.867990	−	0.496581i	$-0.165412\pi$
$74$	−359.876			−0.00763964
$75$	−47899.7	+	57889.0i	−0.983285	+	1.18835i
$76$	−6457.36			−0.128239
$77$		−	4177.27i		−	0.0802909i
$78$			13414.2i			0.249649i
$79$	−62532.7			−1.12730			−0.563650	−	0.826014i	$-0.690603\pi$
$79$	−62532.7			−1.12730			−0.563650	+	0.826014i	$0.690603\pi$
$80$	5077.82	+	1828.41i	0.0887058	+	0.0319410i
$81$	−28185.8			−0.477329
$82$			44088.9i			0.724093i
$83$			46913.1i			0.747479i	0.927534	+	0.373740i	$0.121925\pi$
$83$			46913.1i			0.747479i	−0.927534	+	0.373740i	$0.878075\pi$
$84$	−46538.9			−0.719644
$85$	−14122.5	+	39220.8i	−0.212015	+	0.588801i
$86$	−14771.5			−0.215367
$87$			163553.i			2.31666i
$88$			7983.35i			0.109895i
$89$	63387.4			0.848258			0.424129	−	0.905602i	$-0.360580\pi$
$89$	63387.4			0.848258			0.424129	+	0.905602i	$0.360580\pi$
$90$	−20950.9	+	58184.2i	−0.272644	+	0.757179i
$91$	−15501.8			−0.196236
$92$		−	14864.6i		−	0.183098i
$93$		−	182859.i		−	2.19234i
$94$	16046.0			0.187304
$95$	−16094.9	−	5795.41i	−0.182969	−	0.0658833i
$96$	142540.			1.57855
$97$		−	132037.i		−	1.42484i	−0.701752	−	0.712421i	$-0.747599\pi$
$97$		−	132037.i		−	1.42484i	0.701752	−	0.712421i	$-0.252401\pi$
$98$		−	27708.2i		−	0.291436i
$99$	15260.7			0.156490
$100$	50805.9	+	42038.8i	0.508059	+	0.420388i
$101$	174161.			1.69882			0.849408	−	0.527736i	$-0.176959\pi$
$101$	174161.			1.69882			0.849408	+	0.527736i	$0.176959\pi$
$102$			59189.3i			0.563304i
$103$			41504.6i			0.385481i	0.981250	+	0.192741i	$0.0617376\pi$
$103$			41504.6i			0.385481i	−0.981250	+	0.192741i	$0.938262\pi$
$104$	29626.0			0.268590
$105$	−115997.	−	41768.1i	−1.02677	−	0.369719i
$106$	−132380.			−1.14435
$107$			7340.14i			0.0619791i	0.999520	+	0.0309895i	$0.00986586\pi$
$107$			7340.14i			0.0619791i	−0.999520	+	0.0309895i	$0.990134\pi$
$108$		−	46729.0i		−	0.385502i
$109$	−51340.4			−0.413898			−0.206949	−	0.978352i	$-0.566353\pi$
$109$	−51340.4			−0.413898			−0.206949	+	0.978352i	$0.566353\pi$
$110$	−2847.24	+	7907.29i	−0.0224359	+	0.0623083i
$111$	2621.06			0.0201915
$112$			8855.63i			0.0667075i
$113$			145027.i			1.06845i	0.845344	+	0.534223i	$0.179396\pi$
$113$			145027.i			1.06845i	−0.845344	+	0.534223i	$0.820604\pi$
$114$	−24289.3			−0.175046
$115$	13340.8	−	37049.7i	0.0940669	−	0.261240i
$116$	143541.			0.990450
$117$		−	56632.1i		−	0.382470i
$118$		−	97900.9i		−	0.647264i
$119$	−68400.4			−0.442783
$120$	221687.	+	79824.7i	1.40536	+	0.506039i
$121$	−158977.			−0.987122
$122$		−	170164.i		−	1.03507i
$123$		−	321110.i		−	1.91378i
$124$	−160485.			−0.937301
$125$	88903.5	+	150379.i	0.508913	+	0.860818i
$126$	−101472.			−0.569405
$127$			69448.0i			0.382077i	0.981583	+	0.191038i	$0.0611855\pi$
$127$			69448.0i			0.382077i	−0.981583	+	0.191038i	$0.938814\pi$
$128$		−	135298.i		−	0.729907i
$129$	107585.			0.569215
$130$	29343.8	+	10566.1i	0.152285	+	0.0548346i
$131$	−264141.			−1.34480			−0.672400	−	0.740188i	$-0.734736\pi$
$131$	−264141.			−1.34480			−0.672400	+	0.740188i	$0.734736\pi$
$132$		−	23105.8i		−	0.115421i
$133$		−	28069.2i		−	0.137594i
$134$	−171260.			−0.823939
$135$	41938.8	−	116471.i	0.198053	−	0.550027i
$136$	130723.			0.606043
$137$		−	48840.0i		−	0.222318i	−0.993803	−	0.111159i	$-0.964544\pi$
$137$		−	48840.0i		−	0.222318i	0.993803	−	0.111159i	$-0.0354563\pi$
$138$		−	55912.9i		−	0.249928i
$139$	−193453.			−0.849255			−0.424627	−	0.905368i	$-0.639595\pi$
$139$	−193453.			−0.849255			−0.424627	+	0.905368i	$0.639595\pi$
$140$	−36657.5	+	101804.i	−0.158068	+	0.438981i
$141$	−116867.			−0.495043
$142$		−	139547.i		−	0.580764i
$143$		−	7696.36i		−	0.0314735i
$144$	−32352.0			−0.130015
$145$	357775.	+	128827.i	1.41315	+	0.508846i
$146$	−149281.			−0.579592
$147$			201805.i			0.770264i
$148$		−	2300.35i		−	0.00863258i
$149$	133014.			0.490830			0.245415	−	0.969418i	$-0.421076\pi$
$149$	133014.			0.490830			0.245415	+	0.969418i	$0.421076\pi$
$150$	191106.	+	158128.i	0.693498	+	0.573828i
$151$	−310303.			−1.10750			−0.553749	−	0.832684i	$-0.686803\pi$
$151$	−310303.			−1.10750			−0.553749	+	0.832684i	$0.686803\pi$
$152$			53644.1i			0.188327i
$153$		−	249885.i		−	0.863002i
$154$	−13790.2			−0.0468564
$155$	−400005.	−	144033.i	−1.33732	−	0.481541i
$156$	−85744.9			−0.282096
$157$		−	49697.8i		−	0.160912i	−0.996758	−	0.0804559i	$-0.974362\pi$
$157$		−	49697.8i		−	0.160912i	0.996758	−	0.0804559i	$-0.0256376\pi$
$158$			206436.i			0.657873i
$159$	964154.			3.02450
$160$	112275.	−	311808.i	0.346724	−	0.962914i
$161$	64614.1			0.196455
$162$			93048.2i			0.278561i
$163$		−	658943.i		−	1.94258i	−0.237899	−	0.971290i	$-0.576459\pi$
$163$		−	658943.i		−	1.94258i	0.237899	−	0.971290i	$-0.423541\pi$
$164$	−281820.			−0.818205
$165$	20737.2	−	57590.7i	0.0592979	−	0.164681i
$166$	154872.			0.436216
$167$			655469.i			1.81870i	0.416034	+	0.909349i	$0.363420\pi$
$167$			655469.i			1.81870i	−0.416034	+	0.909349i	$0.636580\pi$
$168$			386619.i			1.05684i
$169$	−28561.0			−0.0769231
$170$	129477.	+	46621.9i	0.343614	+	0.123728i
$171$	102544.			0.268177
$172$		−	94420.9i		−	0.243359i
$173$			280036.i			0.711376i	0.934605	+	0.355688i	$0.115753\pi$
$173$			280036.i			0.711376i	−0.934605	+	0.355688i	$0.884247\pi$
$174$	539929.			1.35196
$175$	−182736.	+	220846.i	−0.451055	+	0.545122i
$176$	−4396.67			−0.0106990
$177$			713036.i			1.71072i
$178$		−	209257.i		−	0.495028i
$179$	−261227.			−0.609377			−0.304689	−	0.952452i	$-0.598552\pi$
$179$	−261227.			−0.609377			−0.304689	+	0.952452i	$0.598552\pi$
$180$	−371918.	−	133920.i	−0.855591	−	0.308080i
$181$	−112896.			−0.256143			−0.128071	−	0.991765i	$-0.540879\pi$
$181$	−112896.			−0.256143			−0.128071	+	0.991765i	$0.540879\pi$
$182$			51175.1i			0.114520i
$183$			1.23935e6i			2.73568i
$184$	−123486.			−0.268890
$185$	2064.54	−	5733.59i	0.00443501	−	0.0123168i
$186$	−603660.			−1.27941
$187$		−	33959.6i		−	0.0710164i
$188$			102567.i			0.211648i
$189$	203124.			0.413625
$190$	−19132.0	+	53133.0i	−0.0384483	+	0.106778i
$191$	790161.			1.56723			0.783614	−	0.621247i	$-0.213374\pi$
$191$	790161.			1.56723			0.783614	+	0.621247i	$0.213374\pi$
$192$		−	396279.i		−	0.775797i
$193$		−	272267.i		−	0.526140i	−0.964777	−	0.263070i	$-0.915265\pi$
$193$		−	272267.i		−	0.526140i	0.964777	−	0.263070i	$-0.0847351\pi$
$194$	−435887.			−0.831513
$195$	−213718.	−	76955.1i	−0.402489	−	0.144928i
$196$	177113.			0.329314
$197$		−	304065.i		−	0.558215i	−0.960260	−	0.279107i	$-0.909961\pi$
$197$		−	304065.i		−	0.558215i	0.960260	−	0.279107i	$-0.0900385\pi$
$198$		−	50379.3i		−	0.0913248i
$199$	−291885.			−0.522492			−0.261246	−	0.965272i	$-0.584133\pi$
$199$	−291885.			−0.522492			−0.261246	+	0.965272i	$0.584133\pi$
$200$	349234.	−	422067.i	0.617365	−	0.746115i
$201$	1.24733e6			2.17767
$202$		−	574946.i		−	0.991400i
$203$			623953.i			1.06270i
$204$	−378343.			−0.636518
$205$	−702431.	−	252930.i	−1.16740	−	0.420355i
$206$	137017.			0.224960
$207$			236053.i			0.382898i
$208$			16315.9i			0.0261489i
$209$	13935.9			0.0220683
$210$	−137887.	+	382935.i	−0.215762	+	0.599207i
$211$	447521.			0.692003			0.346001	−	0.938234i	$-0.387539\pi$
$211$	447521.			0.692003			0.346001	+	0.938234i	$0.387539\pi$
$212$		−	846182.i		−	1.29308i
$213$			1.01635e6i			1.53496i
$214$	24231.6			0.0361699
$215$	84741.8	−	235343.i	0.125026	−	0.347220i
$216$	−388198.			−0.566134
$217$		−	697603.i		−	1.00568i
$218$			169487.i			0.241543i
$219$	1.08725e6			1.53186
$220$	−50544.0	−	18199.8i	−0.0704066	−	0.0253519i
$221$	−126023.			−0.173568
$222$		−	8652.75i		−	0.0117834i
$223$		−	158.327i		−	0.000213203i	−1.00000		0.000106602i	$-0.999966\pi$
$223$		−	158.327i		−	0.000213203i	1.00000		0.000106602i	$-3.39323e-5\pi$
$224$	543789.			0.724119
$225$	−806808.	−	667585.i	−1.06246	−	0.879124i
$226$	478769.			0.623526
$227$			1.13950e6i			1.46774i	0.679290	+	0.733870i	$0.262288\pi$
$227$			1.13950e6i			1.46774i	−0.679290	+	0.733870i	$0.737712\pi$
$228$		−	155259.i		−	0.197797i
$229$	−693287.			−0.873624			−0.436812	−	0.899553i	$-0.643892\pi$
$229$	−693287.			−0.873624			−0.436812	+	0.899553i	$0.643892\pi$
$230$	−122310.	−	44041.2i	−0.152455	−	0.0548958i
$231$	100437.			0.123841
$232$		−	1.19246e6i		−	1.45454i
$233$			399786.i			0.482434i	0.970471	+	0.241217i	$0.0775466\pi$
$233$			399786.i			0.482434i	−0.970471	+	0.241217i	$0.922453\pi$
$234$	−186956.			−0.223203
$235$	−92053.0	+	255647.i	−0.108735	+	0.301975i
$236$	625791.			0.731390
$237$		−	1.50352e6i		−	1.73876i
$238$			225806.i			0.258401i
$239$	−445444.			−0.504427			−0.252213	−	0.967672i	$-0.581158\pi$
$239$	−445444.			−0.504427			−0.252213	+	0.967672i	$0.581158\pi$
$240$	−43961.8	+	122090.i	−0.0492660	+	0.136820i
$241$	−1.23166e6			−1.36600			−0.682999	−	0.730420i	$-0.739324\pi$
$241$	−1.23166e6			−1.36600			−0.682999	+	0.730420i	$0.739324\pi$
$242$			524822.i			0.576067i
$243$		−	1.21580e6i		−	1.32083i
$244$	1.08771e6			1.16960
$245$	441451.	+	158957.i	0.469859	+	0.169186i
$246$	−1.06006e6			−1.11685
$247$		−	51715.7i		−	0.0539361i
$248$			1.33321e6i			1.37648i
$249$	−1.12797e6			−1.15292
$250$	496436.	−	293492.i	0.502358	−	0.296993i
$251$	615483.			0.616640			0.308320	−	0.951283i	$-0.400233\pi$
$251$	615483.			0.616640			0.308320	+	0.951283i	$0.400233\pi$
$252$		−	648619.i		−	0.643411i
$253$			32079.8i			0.0315087i
$254$	229265.			0.222973
$255$	−943014.	−	339559.i	−0.908171	−	0.327013i
$256$	−974063.			−0.928939
$257$		−	844218.i		−	0.797300i	−0.917103	−	0.398650i	$-0.869479\pi$
$257$		−	844218.i		−	0.797300i	0.917103	−	0.398650i	$-0.130521\pi$
$258$		−	355163.i		−	0.332184i
$259$	9999.30			0.00926233
$260$	−67539.1	+	187568.i	−0.0619615	+	0.172078i
$261$	−2.27947e6			−2.07125
$262$			871993.i			0.784802i
$263$		−	586640.i		−	0.522976i	−0.965207	−	0.261488i	$-0.915787\pi$
$263$		−	586640.i		−	0.522976i	0.965207	−	0.261488i	$-0.0842132\pi$
$264$	−191950.			−0.169503
$265$	759439.	−	2.10910e6i	0.664322	−	1.84494i
$266$	−92663.2			−0.0802977
$267$			1.52407e6i			1.30836i
$268$		−	1.09471e6i		−	0.931027i
$269$	−2.07403e6			−1.74757			−0.873786	−	0.486310i	$-0.838343\pi$
$269$	−2.07403e6			−1.74757			−0.873786	+	0.486310i	$0.838343\pi$
$270$	−384500.	−	138450.i	−0.320986	−	0.115580i
$271$	1.92221e6			1.58993			0.794963	−	0.606658i	$-0.207490\pi$
$271$	1.92221e6			1.58993			0.794963	+	0.606658i	$0.207490\pi$
$272$			71992.9i			0.0590021i
$273$		−	372720.i		−	0.302675i
$274$	−161233.			−0.129741
$275$	−109646.	−	90725.4i	−0.0874302	−	0.0723431i
$276$	357400.			0.282411
$277$			1.70508e6i			1.33520i	0.744521	+	0.667599i	$0.232678\pi$
$277$			1.70508e6i			1.33520i	−0.744521	+	0.667599i	$0.767322\pi$
$278$			638634.i			0.495610i
$279$	2.54853e6			1.96010
$280$	845732.	+	304530.i	0.644670	+	0.232132i
$281$	−961277.			−0.726244			−0.363122	−	0.931742i	$-0.618289\pi$
$281$	−961277.			−0.726244			−0.363122	+	0.931742i	$0.618289\pi$
$282$			385805.i			0.288899i
$283$			1.84545e6i			1.36973i	0.728668	+	0.684867i	$0.240140\pi$
$283$			1.84545e6i			1.36973i	−0.728668	+	0.684867i	$0.759860\pi$
$284$	891996.			0.656247
$285$	139343.	−	386981.i	0.101619	−	0.282213i
$286$	−25407.5			−0.0183674
$287$		−	1.22503e6i		−	0.877893i
$288$			1.98661e6i			1.41134i
$289$	863788.			0.608363
$290$	425289.	−	1.18110e6i	0.296954	−	0.824692i
$291$	3.17467e6			2.19769
$292$		−	954217.i		−	0.654923i
$293$		−	425094.i		−	0.289278i	−0.989484	−	0.144639i	$-0.953798\pi$
$293$		−	425094.i		−	0.289278i	0.989484	−	0.144639i	$-0.0462021\pi$
$294$	666208.			0.449512
$295$	1.55977e6	+	561640.i	1.04353	+	0.375754i
$296$	−19110.0			−0.0126775
$297$			100848.i			0.0663398i
$298$		−	439111.i		−	0.286440i
$299$	119047.			0.0770090
$300$	−1.01077e6	+	1.22156e6i	−0.648409	+	0.783633i
$301$	410434.			0.261112
$302$			1.02438e6i			0.646317i
$303$			4.18747e6i			2.62027i
$304$	−29543.4			−0.0183348
$305$	2.71109e6	+	976204.i	1.66876	+	0.600884i
$306$	−824931.			−0.503633
$307$		−	669386.i		−	0.405351i	−0.979246	−	0.202675i	$-0.935036\pi$
$307$		−	669386.i		−	0.405351i	0.979246	−	0.202675i	$-0.0649636\pi$
$308$		−	88148.0i		−	0.0529463i
$309$	−997926.			−0.594569
$310$	−475488.	+	1.32051e6i	−0.281019	+	0.780438i
$311$	−1.10103e6			−0.645506			−0.322753	−	0.946483i	$-0.604608\pi$
$311$	−1.10103e6			−0.645506			−0.322753	+	0.946483i	$0.604608\pi$
$312$			712320.i			0.414275i
$313$		−	698228.i		−	0.402844i	−0.979505	−	0.201422i	$-0.935444\pi$
$313$		−	698228.i		−	0.402844i	0.979505	−	0.201422i	$-0.0645562\pi$
$314$	−164064.			−0.0939053
$315$	582129.	−	1.61667e6i	0.330554	−	0.918007i
$316$	−1.31955e6			−0.743377
$317$		−	1.25102e6i		−	0.699226i	−0.936894	−	0.349613i	$-0.886313\pi$
$317$		−	1.25102e6i		−	0.699226i	0.936894	−	0.349613i	$-0.113687\pi$
$318$		−	3.18290e6i		−	1.76504i
$319$	−309782.			−0.170443
$320$	−866864.	−	312139.i	−0.473234	−	0.170401i
$321$	−176484.			−0.0955969
$322$		−	213307.i		−	0.114648i
$323$		−	228192.i		−	0.121701i
$324$	−594771.			−0.314766
$325$	−336680.	+	406894.i	−0.176811	+	0.213684i
$326$	−2.17533e6			−1.13366
$327$		−	1.23441e6i		−	0.638398i
$328$			2.34120e6i			1.20158i
$329$	−445845.			−0.227088
$330$	−190121.	−	68458.4i	−0.0961047	−	0.0346052i
$331$	−2.38101e6			−1.19452			−0.597258	−	0.802049i	$-0.703743\pi$
$331$	−2.38101e6			−1.19452			−0.597258	+	0.802049i	$0.703743\pi$
$332$			989952.i			0.492911i
$333$			36530.1i			0.0180526i
$334$	2.16386e6			1.06136
$335$	982491.	−	2.72855e6i	0.478318	−	1.32837i
$336$	−212923.			−0.102890
$337$			2.38010e6i			1.14161i	0.821084	+	0.570807i	$0.193370\pi$
$337$			2.38010e6i			1.14161i	−0.821084	+	0.570807i	$0.806630\pi$
$338$			94286.8i			0.0448910i
$339$	−3.48699e6			−1.64798
$340$	−298011.	+	827629.i	−0.139809	+	0.388274i
$341$	346348.			0.161297
$342$		−	338523.i		−	0.156503i
$343$			2.31153e6i			1.06088i
$344$	−784396.			−0.357387
$345$	890813.	+	320762.i	0.402939	+	0.145089i
$346$	924468.			0.415147
$347$			3.45043e6i			1.53833i	0.639049	+	0.769166i	$0.279328\pi$
$347$			3.45043e6i			1.53833i	−0.639049	+	0.769166i	$0.720672\pi$
$348$			3.45127e6i			1.52768i
$349$	−3.27121e6			−1.43762			−0.718811	−	0.695206i	$-0.755313\pi$
$349$	−3.27121e6			−1.43762			−0.718811	+	0.695206i	$0.755313\pi$
$350$	729065.	+	603257.i	0.318124	+	0.263228i
$351$	374243.			0.162138
$352$			269982.i			0.116139i
$353$		−	4.08960e6i		−	1.74680i	−0.487001	−	0.873401i	$-0.661909\pi$
$353$		−	4.08960e6i		−	1.74680i	0.487001	−	0.873401i	$-0.338091\pi$
$354$	2.35390e6			0.998345
$355$	2.22329e6	+	800557.i	0.936320	+	0.337149i
$356$	1.33759e6			0.559368
$357$		−	1.64460e6i		−	0.682952i
$358$			862375.i			0.355622i
$359$	−2.45540e6			−1.00551			−0.502754	−	0.864430i	$-0.667680\pi$
$359$	−2.45540e6			−1.00551			−0.502754	+	0.864430i	$0.667680\pi$
$360$	−1.11253e6	+	3.08969e6i	−0.452434	+	1.25649i
$361$	−2.38246e6			−0.962182
$362$			372697.i			0.149480i
$363$		−	3.82240e6i		−	1.52254i
$364$	−327115.			−0.129404
$365$	856399.	−	2.37837e6i	0.336468	−	0.934431i
$366$	4.09139e6			1.59650
$367$		−	328555.i		−	0.127333i	−0.997971	−	0.0636667i	$-0.979721\pi$
$367$		−	328555.i		−	0.127333i	0.997971	−	0.0636667i	$-0.0202795\pi$
$368$		−	68007.7i		−	0.0261781i
$369$	4.47536e6			1.71105
$370$	−18928.0	−	6815.55i	−0.00718787	−	0.00258819i
$371$	3.67823e6			1.38741
$372$		−	3.85865e6i		−	1.44570i
$373$		−	5.17656e6i		−	1.92650i	−0.268606	−	0.963250i	$-0.586563\pi$
$373$		−	5.17656e6i		−	1.92650i	0.268606	−	0.963250i	$-0.413437\pi$
$374$	−112109.			−0.0414439
$375$	−3.61567e6	+	2.13757e6i	−1.32773	+	0.784951i
$376$	852071.			0.310818
$377$			1.14959e6i			0.416573i
$378$		−	670561.i		−	0.241384i
$379$	−3.24314e6			−1.15976			−0.579880	−	0.814702i	$-0.696900\pi$
$379$	−3.24314e6			−1.15976			−0.579880	+	0.814702i	$0.696900\pi$
$380$	−339631.	−	122294.i	−0.120656	−	0.0434455i
$381$	−1.66979e6			−0.589318
$382$		−	2.60851e6i		−	0.914607i
$383$		−	4.53434e6i		−	1.57949i	−0.613435	−	0.789745i	$-0.710213\pi$
$383$		−	4.53434e6i		−	1.57949i	0.613435	−	0.789745i	$-0.289787\pi$
$384$	3.25308e6			1.12581
$385$	79111.9	−	219707.i	0.0272013	−	0.0755428i
$386$	−898819.			−0.307046
$387$			1.49942e6i			0.508917i
$388$		−	2.78622e6i		−	0.939586i
$389$	−1.77865e6			−0.595958			−0.297979	−	0.954572i	$-0.596313\pi$
$389$	−1.77865e6			−0.595958			−0.297979	+	0.954572i	$0.596313\pi$
$390$	−254047.	+	705534.i	−0.0845772	+	0.234885i
$391$	525288.			0.173762
$392$		−	1.47135e6i		−	0.483618i
$393$		−	6.35094e6i		−	2.07423i
$394$	−1.00379e6			−0.325764
$395$	−3.28897e6	−	1.18428e6i	−1.06064	−	0.381912i
$396$	322028.			0.103194
$397$			5.19763e6i			1.65512i	0.561378	+	0.827560i	$0.310271\pi$
$397$			5.19763e6i			1.65512i	−0.561378	+	0.827560i	$0.689729\pi$
$398$			963583.i			0.304917i
$399$	674888.			0.212226
$400$	232445.	+	192334.i	0.0726390	+	0.0601043i
$401$	4.03901e6			1.25434			0.627168	−	0.778884i	$-0.284214\pi$
$401$	4.03901e6			1.25434			0.627168	+	0.778884i	$0.284214\pi$
$402$		−	4.11774e6i		−	1.27085i
$403$		−	1.28529e6i		−	0.394219i
$404$	3.67510e6			1.12025
$405$	−1.48246e6	−	533801.i	−0.449102	−	0.161712i
$406$	2.05982e6			0.620175
$407$			4964.48i			0.00148555i
$408$			3.14306e6i			0.934765i
$409$	2.23547e6			0.660787			0.330393	−	0.943843i	$-0.392819\pi$
$409$	2.23547e6			0.660787			0.330393	+	0.943843i	$0.392819\pi$
$410$	−834984.	+	2.31890e6i	−0.245312	+	0.681273i
$411$	1.17430e6			0.342904
$412$			875823.i			0.254199i
$413$			2.72022e6i			0.784746i
$414$	779267.			0.223452
$415$	−888471.	+	2.46744e6i	−0.253234	+	0.703276i
$416$	1.00190e6			0.283850
$417$		−	4.65133e6i		−	1.30990i
$418$		−	46005.7i		−	0.0128787i
$419$	−1.52835e6			−0.425291			−0.212646	−	0.977129i	$-0.568208\pi$
$419$	−1.52835e6			−0.425291			−0.212646	+	0.977129i	$0.568208\pi$
$420$	−2.44775e6	−	881383.i	−0.677087	−	0.243804i
$421$	−2.80885e6			−0.772367			−0.386183	−	0.922422i	$-0.626207\pi$
$421$	−2.80885e6			−0.772367			−0.386183	+	0.922422i	$0.626207\pi$
$422$		−	1.47738e6i		−	0.403841i
$423$		−	1.62879e6i		−	0.442603i
$424$	−7.02961e6			−1.89896
$425$	−1.48558e6	+	1.79539e6i	−0.398954	+	0.482155i
$426$	3.35523e6			0.895774
$427$			4.72809e6i			1.25492i
$428$			154890.i			0.0408710i
$429$	185049.			0.0485449
$430$	−776923.	−	279753.i	−0.202631	−	0.0729632i
$431$	−2.64484e6			−0.685813			−0.342906	−	0.939370i	$-0.611411\pi$
$431$	−2.64484e6			−0.685813			−0.342906	+	0.939370i	$0.611411\pi$
$432$		−	213792.i		−	0.0551166i
$433$			6.38548e6i			1.63672i	0.574708	+	0.818359i	$0.305116\pi$
$433$			6.38548e6i			1.63672i	−0.574708	+	0.818359i	$0.694884\pi$
$434$	−2.30295e6			−0.586896
$435$	−3.09748e6	+	8.60224e6i	−0.784847	+	2.17966i
$436$	−1.08337e6			−0.272937
$437$			215560.i			0.0539964i
$438$		−	3.58927e6i		−	0.893967i
$439$	1.84296e6			0.456409			0.228205	−	0.973613i	$-0.426714\pi$
$439$	1.84296e6			0.456409			0.228205	+	0.973613i	$0.426714\pi$
$440$	−151194.	+	419891.i	−0.0372308	+	0.103396i
$441$	−2.81259e6			−0.688669
$442$			416033.i			0.101291i
$443$		−	610862.i		−	0.147888i	−0.997262	−	0.0739442i	$-0.976441\pi$
$443$		−	610862.i		−	0.147888i	0.997262	−	0.0739442i	$-0.0235587\pi$
$444$	55309.1			0.0133149
$445$	3.33392e6	+	1.20047e6i	0.798095	+	0.287377i
$446$	−522.676			−0.000124422
$447$			3.19815e6i			0.757059i
$448$		−	1.51180e6i		−	0.355876i
$449$	1.32831e6			0.310945			0.155473	−	0.987840i	$-0.450310\pi$
$449$	1.32831e6			0.310945			0.155473	+	0.987840i	$0.450310\pi$
$450$	−2.20386e6	+	2.66347e6i	−0.513041	+	0.620035i
$451$	608206.			0.140802
$452$			3.06033e6i			0.704567i
$453$		−	7.46083e6i		−	1.70821i
$454$	3.76176e6			0.856547
$455$	−815329.	−	293582.i	−0.184631	−	0.0664816i
$456$	−1.28980e6			−0.290477
$457$		−	1.05715e6i		−	0.236780i	−0.992967	−	0.118390i	$-0.962227\pi$
$457$		−	1.05715e6i		−	0.236780i	0.992967	−	0.118390i	$-0.0377733\pi$
$458$			2.28871e6i			0.509832i
$459$	1.65132e6			0.365847
$460$	281515.	−	781816.i	0.0620307	−	0.172270i
$461$	−88191.8			−0.0193275			−0.00966376	−	0.999953i	$-0.503076\pi$
$461$	−88191.8			−0.0193275			−0.00966376	+	0.999953i	$0.503076\pi$
$462$		−	331568.i		−	0.0722715i
$463$			5.10298e6i			1.10630i	0.833083	+	0.553148i	$0.186573\pi$
$463$			5.10298e6i			1.10630i	−0.833083	+	0.553148i	$0.813427\pi$
$464$	656724.			0.141608
$465$	3.46309e6	−	9.61761e6i	0.742731	−	2.06269i
$466$	1.31979e6			0.281540
$467$			4.32926e6i			0.918590i	0.888284	+	0.459295i	$0.151898\pi$
$467$			4.32926e6i			0.918590i	−0.888284	+	0.459295i	$0.848102\pi$
$468$		−	1.19504e6i		−	0.252213i
$469$	4.75855e6			0.998946
$470$	843953.	+	303889.i	0.176228	+	0.0634557i
$471$	1.19492e6			0.248191
$472$		−	5.19872e6i		−	1.07409i
$473$			203773.i			0.0418788i
$474$	−4.96348e6			−1.01471
$475$	−736766.	−	609629.i	−0.149829	−	0.123974i
$476$	−1.44337e6			−0.291985
$477$			1.34376e7i			2.70411i
$478$			1.47052e6i			0.294375i
$479$	−2.88997e6			−0.575513			−0.287756	−	0.957704i	$-0.592909\pi$
$479$	−2.88997e6			−0.575513			−0.287756	+	0.957704i	$0.592909\pi$
$480$	7.49703e6	+	2.69952e6i	1.48520	+	0.534790i
$481$	18423.1			0.00363077
$482$			4.06602e6i			0.797172i
$483$			1.55356e6i			0.303013i
$484$	−3.35470e6			−0.650940
$485$	2.50060e6	−	6.94461e6i	0.482715	−	1.34058i
$486$	−4.01366e6			−0.770815
$487$			3.37347e6i			0.644546i	0.946647	+	0.322273i	$0.104447\pi$
$487$			3.37347e6i			0.644546i	−0.946647	+	0.322273i	$0.895553\pi$
$488$		−	9.03604e6i		−	1.71763i
$489$	1.58434e7			2.99625
$490$	524755.	−	1.45734e6i	0.0987340	−	0.274201i
$491$	5.24844e6			0.982486			0.491243	−	0.871023i	$-0.336543\pi$
$491$	5.24844e6			0.982486			0.491243	+	0.871023i	$0.336543\pi$
$492$		−	6.77600e6i		−	1.26200i
$493$			5.07250e6i			0.939950i
$494$	−170726.			−0.0314762
$495$	802650.	+	289017.i	0.147236	+	0.0530164i
$496$	−734241.			−0.134009
$497$			3.87738e6i			0.704120i
$498$			3.72369e6i			0.672822i
$499$	3.51772e6			0.632427			0.316213	−	0.948688i	$-0.397588\pi$
$499$	3.51772e6			0.632427			0.316213	+	0.948688i	$0.397588\pi$
$500$	1.87602e6	+	3.17326e6i	0.335593	+	0.567650i
$501$	−1.57599e7			−2.80517
$502$		−	2.03186e6i		−	0.359860i
$503$		−	8.97569e6i		−	1.58179i	−0.611954	−	0.790893i	$-0.709616\pi$
$503$		−	8.97569e6i		−	1.58179i	0.611954	−	0.790893i	$-0.290384\pi$
$504$	−5.38836e6			−0.944889
$505$	9.16013e6	+	3.29836e6i	1.59836	+	0.575533i
$506$	105903.			0.0183879
$507$		−	686713.i		−	0.118647i
$508$			1.46548e6i			0.251953i
$509$	9.09941e6			1.55675			0.778375	−	0.627800i	$-0.216045\pi$
$509$	9.09941e6			1.55675			0.778375	+	0.627800i	$0.216045\pi$
$510$	−1.12097e6	+	3.11312e6i	−0.190839	+	0.529993i
$511$	4.14784e6			0.702700
$512$		−	1.11393e6i		−	0.187794i
$513$			677645.i			0.113686i
$514$	−2.78697e6			−0.465290
$515$	−786041.	+	2.18297e6i	−0.130595	+	0.362686i
$516$	2.27023e6			0.375358
$517$		−	221354.i		−	0.0364218i
$518$		−	33010.1i		−	0.00540533i
$519$	−6.73312e6			−1.09723
$520$	1.55821e6	+	561076.i	0.252707	+	0.0909942i
$521$	5.26898e6			0.850418			0.425209	−	0.905095i	$-0.360201\pi$
$521$	5.26898e6			0.850418			0.425209	+	0.905095i	$0.360201\pi$
$522$			7.52508e6i			1.20874i
$523$			4.16491e6i			0.665811i	0.942960	+	0.332906i	$0.108029\pi$
$523$			4.16491e6i			0.665811i	−0.942960	+	0.332906i	$0.891971\pi$
$524$	−5.57385e6			−0.886803
$525$	−5.30995e6	−	4.39366e6i	−0.840800	−	0.695711i
$526$	−1.93664e6			−0.305200
$527$		−	5.67124e6i		−	0.889511i
$528$		−	105712.i		−	0.0165022i
$529$	5.94013e6			0.922905
$530$	−6.96263e6	−	2.50709e6i	−1.07667	−	0.387687i
$531$	−9.93769e6			−1.52950
$532$		−	592311.i		−	0.0907341i
$533$		−	2.25704e6i		−	0.344129i
$534$	5.03132e6			0.763535
$535$	−139012.	+	386061.i	−0.0209976	+	0.0583139i
$536$	−9.09424e6			−1.36727
$537$		−	6.28088e6i		−	0.939907i
$538$			6.84689e6i			1.01985i
$539$	−382234.			−0.0566706
$540$	884984.	−	2.45775e6i	0.130602	−	0.362705i
$541$	−3.03221e6			−0.445416			−0.222708	−	0.974885i	$-0.571490\pi$
$541$	−3.03221e6			−0.445416			−0.222708	+	0.974885i	$0.571490\pi$
$542$		−	6.34567e6i		−	0.927853i
$543$		−	2.71444e6i		−	0.395076i
$544$	4.42079e6			0.640476
$545$	−2.70029e6	−	972317.i	−0.389421	−	0.140222i
$546$	−1.23044e6			−0.176636
$547$		−	3.32454e6i		−	0.475076i	−0.971378	−	0.237538i	$-0.923660\pi$
$547$		−	3.32454e6i		−	0.475076i	0.971378	−	0.237538i	$-0.0763404\pi$
$548$		−	1.03061e6i		−	0.146603i
$549$	−1.72730e7			−2.44589
$550$	−299507.	+	361968.i	−0.0422182	+	0.0510227i
$551$	−2.08158e6			−0.292088
$552$		−	2.96908e6i		−	0.414738i
$553$		−	5.73590e6i		−	0.797607i
$554$	5.62888e6			0.779198
$555$	137857.	+	49639.3i	0.0189975	+	0.00684059i
$556$	−4.08220e6			−0.560025
$557$			7.78685e6i			1.06347i	0.846912	+	0.531733i	$0.178459\pi$
$557$			7.78685e6i			1.06347i	−0.846912	+	0.531733i	$0.821541\pi$
$558$		−	8.41331e6i		−	1.14388i
$559$	756198.			0.102354
$560$	−167714.	+	465770.i	−0.0225995	+	0.0627627i
$561$	816516.			0.109536
$562$			3.17341e6i			0.423824i
$563$		−	4.68638e6i		−	0.623112i	−0.950228	−	0.311556i	$-0.899150\pi$
$563$		−	4.68638e6i		−	0.623112i	0.950228	−	0.311556i	$-0.100850\pi$
$564$	−2.46610e6			−0.326447
$565$	−2.74661e6	+	7.62782e6i	−0.361973	+	1.00526i
$566$	6.09227e6			0.799353
$567$		−	2.58538e6i		−	0.337728i
$568$		−	7.41020e6i		−	0.963738i
$569$	2.10415e6			0.272456			0.136228	−	0.990678i	$-0.456502\pi$
$569$	2.10415e6			0.272456			0.136228	+	0.990678i	$0.456502\pi$
$570$	−1.27752e6	−	460006.i	−0.164695	−	0.0593029i
$571$	1.20728e7			1.54959			0.774796	−	0.632211i	$-0.217852\pi$
$571$	1.20728e7			1.54959			0.774796	+	0.632211i	$0.217852\pi$
$572$		−	162407.i		−	0.0207546i
$573$			1.89984e7i			2.41730i
$574$	−4.04412e6			−0.512323
$575$	1.40334e6	−	1.69601e6i	0.177008	−	0.213923i
$576$	5.52300e6			0.693615
$577$		−	1.02267e7i		−	1.27878i	−0.768883	−	0.639390i	$-0.779187\pi$
$577$		−	1.02267e7i		−	1.27878i	0.768883	−	0.639390i	$-0.220813\pi$
$578$		−	2.85157e6i		−	0.355030i
$579$	6.54631e6			0.811522
$580$	7.54969e6	+	2.71848e6i	0.931878	+	0.335549i
$581$	−4.30317e6			−0.528869
$582$		−	1.04803e7i		−	1.28253i
$583$			1.82618e6i			0.222521i
$584$	−7.92709e6			−0.961794
$585$	1.07253e6	−	2.97862e6i	0.129575	−	0.359853i
$586$	−1.40334e6			−0.168818
$587$		−	2.24352e6i		−	0.268741i	−0.990931	−	0.134371i	$-0.957099\pi$
$587$		−	2.24352e6i		−	0.268741i	0.990931	−	0.134371i	$-0.0429013\pi$
$588$			4.25846e6i			0.507936i
$589$	2.32728e6			0.276414
$590$	1.85411e6	−	5.14919e6i	0.219283	−	0.608988i
$591$	7.31086e6			0.860994
$592$		−	10524.5i		−	0.00123423i
$593$		−	590374.i		−	0.0689430i	−0.999406	−	0.0344715i	$-0.989025\pi$
$593$		−	590374.i		−	0.0689430i	0.999406	−	0.0344715i	$-0.0109748\pi$
$594$	332922.			0.0387148
$595$	−3.59758e6	−	1.29541e6i	−0.416599	−	0.150008i
$596$	2.80683e6			0.323669
$597$		−	7.01801e6i		−	0.805894i
$598$		−	393004.i		−	0.0449411i
$599$	−2.71185e6			−0.308815			−0.154407	−	0.988007i	$-0.549347\pi$
$599$	−2.71185e6			−0.308815			−0.154407	+	0.988007i	$0.549347\pi$
$600$	1.01481e7	+	8.39690e6i	1.15081	+	0.952228i
$601$	−9.99011e6			−1.12820			−0.564098	−	0.825708i	$-0.690776\pi$
$601$	−9.99011e6			−1.12820			−0.564098	+	0.825708i	$0.690776\pi$
$602$		−	1.35494e6i		−	0.152380i
$603$			1.73842e7i			1.94698i
$604$	−6.54795e6			−0.730319
$605$	−8.36154e6	−	3.01081e6i	−0.928748	−	0.334422i
$606$	1.38239e7			1.52914
$607$		−	4.27804e6i		−	0.471273i	−0.971841	−	0.235637i	$-0.924282\pi$
$607$		−	4.27804e6i		−	0.471273i	0.971841	−	0.235637i	$-0.0757175\pi$
$608$			1.81414e6i			0.199027i
$609$	−1.50022e7			−1.63912
$610$	3.22268e6	−	8.94995e6i	0.350666	−	0.973859i
$611$	−821440.			−0.0890170
$612$		−	5.27302e6i		−	0.569090i
$613$			645645.i			0.0693973i	0.999398	+	0.0346986i	$0.0110471\pi$
$613$			645645.i			0.0693973i	−0.999398	+	0.0346986i	$0.988953\pi$
$614$	−2.20981e6			−0.236556
$615$	6.08139e6	−	1.68891e7i	0.648358	−	1.80060i
$616$	−732284.			−0.0777549
$617$			2.65549e6i			0.280822i	0.990093	+	0.140411i	$0.0448424\pi$
$617$			2.65549e6i			0.280822i	−0.990093	+	0.140411i	$0.955158\pi$
$618$			3.29440e6i			0.346980i
$619$	1.11716e7			1.17190			0.585948	−	0.810349i	$-0.300722\pi$
$619$	1.11716e7			1.17190			0.585948	+	0.810349i	$0.300722\pi$
$620$	−8.44083e6	−	3.03936e6i	−0.881873	−	0.317543i
$621$	−1.55991e6			−0.162320
$622$			3.63478e6i			0.376706i
$623$			5.81430e6i			0.600174i
$624$	−392296.			−0.0403322
$625$	1.82799e6	+	9.59301e6i	0.187186	+	0.982324i
$626$	−2.30502e6			−0.235092
$627$			335070.i			0.0340382i
$628$		−	1.04871e6i		−	0.106110i
$629$	81290.4			0.00819243
$630$	−5.33703e6	−	1.92175e6i	−0.535733	−	0.192906i
$631$	−1.49550e6			−0.149525			−0.0747624	−	0.997201i	$-0.523820\pi$
$631$	−1.49550e6			−0.149525			−0.0747624	+	0.997201i	$0.523820\pi$
$632$			1.09621e7i			1.09169i
$633$			1.07601e7i			1.06735i
$634$	−4.12993e6			−0.408056
$635$	−1.31525e6	+	3.65268e6i	−0.129442	+	0.359482i
$636$	2.03454e7			1.99445
$637$			1.41846e6i			0.138506i
$638$			1.02267e6i			0.0994676i
$639$	−1.41651e7			−1.37236
$640$	2.56237e6	−	7.11613e6i	0.247281	−	0.686743i
$641$	9.23788e6			0.888030			0.444015	−	0.896019i	$-0.353554\pi$
$641$	9.23788e6			0.888030			0.444015	+	0.896019i	$0.353554\pi$
$642$			582618.i			0.0557887i
$643$			3.69634e6i			0.352569i	0.984339	+	0.176285i	$0.0564079\pi$
$643$			3.69634e6i			0.352569i	−0.984339	+	0.176285i	$0.943592\pi$
$644$	1.36347e6			0.129548
$645$	5.65852e6	+	2.03751e6i	0.535554	+	0.192841i
$646$	−753316.			−0.0710225
$647$			1.94037e7i			1.82232i	0.412055	+	0.911159i	$0.364811\pi$
$647$			1.94037e7i			1.82232i	−0.412055	+	0.911159i	$0.635189\pi$
$648$			4.94103e6i			0.462253i
$649$	−1.35054e6			−0.125862
$650$	1.34325e6	+	1.11146e6i	0.124702	+	0.103184i
$651$	1.67730e7			1.55116
$652$		−	1.39049e7i		−	1.28100i
$653$			6.16635e6i			0.565907i	0.959134	+	0.282953i	$0.0913142\pi$
$653$			6.16635e6i			0.565907i	−0.959134	+	0.282953i	$0.908686\pi$
$654$	−4.07510e6			−0.372558
$655$	−1.38927e7	−	5.00247e6i	−1.26527	−	0.455598i
$656$	−1.28937e6			−0.116982
$657$			1.51532e7i			1.36959i
$658$			1.47184e6i			0.132525i
$659$	−6.87190e6			−0.616401			−0.308200	−	0.951321i	$-0.599727\pi$
$659$	−6.87190e6			−0.616401			−0.308200	+	0.951321i	$0.599727\pi$
$660$	437591.	−	1.21527e6i	0.0391029	−	0.108596i
$661$	−3.87812e6			−0.345237			−0.172618	−	0.984989i	$-0.555223\pi$
$661$	−3.87812e6			−0.345237			−0.172618	+	0.984989i	$0.555223\pi$
$662$			7.86030e6i			0.697099i
$663$		−	3.03007e6i		−	0.267713i
$664$	8.22396e6			0.723870
$665$	531592.	−	1.47632e6i	0.0466149	−	0.129458i
$666$	120595.			0.0105352
$667$		−	4.79171e6i		−	0.417038i
$668$			1.38316e7i			1.19931i
$669$	3806.78			0.000328846
$670$	−9.00760e6	−	3.24344e6i	−0.775214	−	0.279138i
$671$	−2.34742e6			−0.201272
$672$			1.30747e7i			1.11689i
$673$			6.95400e6i			0.591830i	0.955214	+	0.295915i	$0.0956246\pi$
$673$			6.95400e6i			0.591830i	−0.955214	+	0.295915i	$0.904375\pi$
$674$	7.85727e6			0.666227
$675$	4.41161e6	−	5.33165e6i	0.372682	−	0.450404i
$676$	−602689.			−0.0507255
$677$		−	1.45095e7i		−	1.21669i	−0.793672	−	0.608345i	$-0.791834\pi$
$677$		−	1.45095e7i		−	1.21669i	0.793672	−	0.608345i	$-0.208166\pi$
$678$			1.15114e7i			0.961731i
$679$	1.21113e7			1.00813
$680$	6.87547e6	+	2.47571e6i	0.570204	+	0.205318i
$681$	−2.73978e7			−2.26385
$682$		−	1.14338e6i		−	0.0941301i
$683$		−	1.77058e7i		−	1.45232i	−0.687524	−	0.726162i	$-0.741302\pi$
$683$		−	1.77058e7i		−	1.45232i	0.687524	−	0.726162i	$-0.258698\pi$
$684$	2.16387e6			0.176844
$685$	924963.	−	2.56878e6i	0.0753179	−	0.209171i
$686$	7.63092e6			0.619108
$687$		−	1.66692e7i		−	1.34748i
$688$		−	431990.i		−	0.0347939i
$689$	6.77690e6			0.543855
$690$	1.05891e6	−	2.94079e6i	0.0846717	−	0.235148i
$691$	−8.82763e6			−0.703313			−0.351657	−	0.936129i	$-0.614382\pi$
$691$	−8.82763e6			−0.703313			−0.351657	+	0.936129i	$0.614382\pi$
$692$			5.90927e6i			0.469104i
$693$			1.39981e6i			0.110722i
$694$	1.13907e7			0.897744
$695$	−1.01748e7	−	3.66373e6i	−0.799033	−	0.287714i
$696$	2.86712e7			2.24348
$697$		−	9.95901e6i		−	0.776487i
$698$			1.07990e7i			0.838971i
$699$	−9.61236e6			−0.744110
$700$	−3.85607e6	+	4.66024e6i	−0.297440	+	0.359471i
$701$	1.38056e7			1.06111			0.530553	−	0.847652i	$-0.321984\pi$
$701$	1.38056e7			1.06111			0.530553	+	0.847652i	$0.321984\pi$
$702$		−	1.23547e6i		−	0.0946211i
$703$			33358.8i			0.00254579i
$704$	750581.			0.0570776
$705$	−6.14671e6	−	2.21330e6i	−0.465769	−	0.167713i
$706$	−1.35007e7			−1.01940
$707$			1.59751e7i			1.20198i
$708$			1.50463e7i			1.12810i
$709$	−2.05869e6			−0.153806			−0.0769032	−	0.997039i	$-0.524503\pi$
$709$	−2.05869e6			−0.153806			−0.0769032	+	0.997039i	$0.524503\pi$
$710$	2.64283e6	−	7.33960e6i	0.196754	−	0.546420i
$711$	2.09548e7			1.55457
$712$		−	1.11119e7i		−	0.821466i
$713$			5.35731e6i			0.394660i
$714$	−5.42923e6			−0.398559
$715$	145759.	−	404797.i	0.0106627	−	0.0296123i
$716$	−5.51237e6			−0.401842
$717$		−	1.07101e7i		−	0.778031i
$718$			8.10585e6i			0.586797i
$719$	7.96314e6			0.574463			0.287232	−	0.957861i	$-0.407265\pi$
$719$	7.96314e6			0.574463			0.287232	+	0.957861i	$0.407265\pi$
$720$	−1.70158e6	−	612703.i	−0.122327	−	0.0440472i
$721$	−3.80707e6			−0.272743
$722$			7.86507e6i			0.561512i
$723$		−	2.96138e7i		−	2.10692i
$724$	−2.38231e6			−0.168909
$725$	1.63777e7	+	1.35515e7i	1.15720	+	0.957510i
$726$	−1.26187e7			−0.888530
$727$		−	3.82952e6i		−	0.268725i	−0.990932	−	0.134363i	$-0.957101\pi$
$727$		−	3.82952e6i		−	0.268725i	0.990932	−	0.134363i	$-0.0428987\pi$
$728$			2.71749e6i			0.190037i
$729$	2.23833e7			1.55993
$730$	−7.85157e6	−	2.82718e6i	−0.545317	−	0.196357i
$731$	3.33667e6			0.230951
$732$			2.61525e7i			1.80400i
$733$		−	1.45934e7i		−	1.00322i	−0.865093	−	0.501611i	$-0.832741\pi$
$733$		−	1.45934e7i		−	1.00322i	0.865093	−	0.501611i	$-0.167259\pi$
$734$	−1.08464e6			−0.0743096
$735$	−3.82192e6	+	1.06141e7i	−0.260954	+	0.724713i
$736$	−4.17608e6			−0.284167
$737$			2.36254e6i			0.160217i
$738$		−	1.47742e7i		−	0.998537i
$739$	−1.03685e7			−0.698403			−0.349202	−	0.937048i	$-0.613547\pi$
$739$	−1.03685e7			−0.698403			−0.349202	+	0.937048i	$0.613547\pi$
$740$	43565.6	−	120989.i	0.00292458	−	0.00812208i
$741$	1.24344e6			0.0831914
$742$		−	1.21427e7i		−	0.809667i
$743$		−	5.40170e6i		−	0.358970i	−0.983761	−	0.179485i	$-0.942557\pi$
$743$		−	5.40170e6i		−	0.358970i	0.983761	−	0.179485i	$-0.0574432\pi$
$744$	−3.20555e7			−2.12310
$745$	6.99598e6	+	2.51910e6i	0.461804	+	0.166286i
$746$	−1.70891e7			−1.12427
$747$		−	1.57206e7i		−	1.03079i
$748$		−	716609.i		−	0.0468305i
$749$	−673285.			−0.0438525
$750$	7.05664e6	+	1.19362e7i	0.458084	+	0.774841i
$751$	−5.29620e6			−0.342661			−0.171330	−	0.985214i	$-0.554807\pi$
$751$	−5.29620e6			−0.342661			−0.171330	+	0.985214i	$0.554807\pi$
$752$			469261.i			0.0302601i
$753$			1.47985e7i			0.951109i
$754$	3.79509e6			0.243105
$755$	−1.63206e7	−	5.87671e6i	−1.04201	−	0.375203i
$756$	4.28628e6			0.272757
$757$		−	8.87136e6i		−	0.562665i	−0.959610	−	0.281333i	$-0.909224\pi$
$757$		−	8.87136e6i		−	0.562665i	0.959610	−	0.281333i	$-0.0907765\pi$
$758$			1.07064e7i			0.676815i
$759$	−771318.			−0.0485992
$760$	−1.01595e6	+	2.82146e6i	−0.0638024	+	0.177190i
$761$	−2.06961e7			−1.29547			−0.647734	−	0.761867i	$-0.724283\pi$
$761$	−2.06961e7			−1.29547			−0.647734	+	0.761867i	$0.724283\pi$
$762$			5.51238e6i			0.343916i
$763$		−	4.70927e6i		−	0.292848i
$764$	1.66738e7			1.03348
$765$	4.73248e6	−	1.31429e7i	0.292372	−	0.811967i
$766$	−1.49689e7			−0.921763
$767$			5.01183e6i			0.307615i
$768$		−	2.34201e7i		−	1.43280i
$769$	−5.78756e6			−0.352923			−0.176461	−	0.984308i	$-0.556465\pi$
$769$	−5.78756e6			−0.352923			−0.176461	+	0.984308i	$0.556465\pi$
$770$	−725307.	−	261167.i	−0.0440855	−	0.0158742i
$771$	2.02981e7			1.22976
$772$		−	5.74532e6i		−	0.346953i
$773$		−	1.74975e7i		−	1.05324i	−0.850101	−	0.526619i	$-0.823459\pi$
$773$		−	1.74975e7i		−	1.05324i	0.850101	−	0.526619i	$-0.176541\pi$
$774$	4.94996e6			0.296995
$775$	−1.83108e7	−	1.51511e7i	−1.09510	−	0.906129i
$776$	−2.31464e7			−1.37984
$777$			240420.i			0.0142863i
$778$			5.87175e6i			0.347791i
$779$	4.08684e6			0.241292
$780$	−4.50983e6	−	1.62389e6i	−0.265414	−	0.0955698i
$781$	−1.92505e6			−0.112931
$782$		−	1.73410e6i		−	0.101405i
$783$		−	1.50635e7i		−	0.878052i
$784$	810319.			0.0470832
$785$	941208.	−	2.61390e6i	0.0545144	−	0.151396i
$786$	−2.09660e7			−1.21048
$787$			1.50075e7i			0.863719i	0.901941	+	0.431860i	$0.142142\pi$
$787$			1.50075e7i			0.863719i	−0.901941	+	0.431860i	$0.857858\pi$
$788$		−	6.41633e6i		−	0.368104i
$789$	1.41050e7			0.806642
$790$	−3.90961e6	+	1.08577e7i	−0.222877	+	0.618969i
$791$	−1.33028e7			−0.755965
$792$		−	2.67523e6i		−	0.151547i
$793$			8.71121e6i			0.491921i
$794$	1.71586e7			0.965899
$795$	5.07105e7	+	1.82598e7i	2.84564	+	1.02465i
$796$	−6.15930e6			−0.344547
$797$			2.52578e7i			1.40848i	0.709962	+	0.704240i	$0.248712\pi$
$797$			2.52578e7i			1.40848i	−0.709962	+	0.704240i	$0.751288\pi$
$798$		−	2.22797e6i		−	0.123852i
$799$	−3.62455e6			−0.200857
$800$	1.18104e7	−	1.42735e7i	0.652441	−	0.788506i
$801$	−2.12412e7			−1.16976
$802$		−	1.33337e7i		−	0.732008i
$803$			2.05933e6i			0.112703i
$804$	2.63209e7			1.43602
$805$	3.39844e6	+	1.22370e6i	0.184837	+	0.0665559i
$806$	−4.24304e6			−0.230059
$807$		−	4.98675e7i		−	2.69547i
$808$		−	3.05307e7i		−	1.64516i
$809$	−4.92229e6			−0.264421			−0.132210	−	0.991222i	$-0.542207\pi$
$809$	−4.92229e6			−0.264421			−0.132210	+	0.991222i	$0.542207\pi$
$810$	−1.76221e6	+	4.89395e6i	−0.0943722	+	0.262088i
$811$	9.00480e6			0.480753			0.240376	−	0.970680i	$-0.422729\pi$
$811$	9.00480e6			0.480753			0.240376	+	0.970680i	$0.422729\pi$
$812$			1.31665e7i			0.700780i
$813$			4.62170e7i			2.45231i
$814$	16388.9			0.000866942
$815$	1.24795e7	−	3.46577e7i	0.658116	−	1.82770i
$816$	−1.73098e6			−0.0910052
$817$			1.36925e6i			0.0717677i
$818$		−	7.37984e6i		−	0.385624i
$819$	5.19466e6			0.270612
$820$	−1.48226e7	−	5.33728e6i	−0.769819	−	0.277195i
$821$	2.32720e7			1.20497			0.602486	−	0.798130i	$-0.294177\pi$
$821$	2.32720e7			1.20497			0.602486	+	0.798130i	$0.294177\pi$
$822$		−	3.87663e6i		−	0.200113i
$823$		−	2.00591e7i		−	1.03232i	−0.856493	−	0.516158i	$-0.827362\pi$
$823$		−	2.00591e7i		−	1.03232i	0.856493	−	0.516158i	$-0.172638\pi$
$824$	7.27584e6			0.373306
$825$	2.18138e6	−	2.63630e6i	0.111583	−	0.134853i
$826$	8.98010e6			0.457964
$827$		−	9.70394e6i		−	0.493383i	−0.969094	−	0.246692i	$-0.920657\pi$
$827$		−	9.70394e6i		−	0.493383i	0.969094	−	0.246692i	$-0.0793435\pi$
$828$			4.98114e6i			0.252495i
$829$	2.31044e7			1.16764			0.583819	−	0.811884i	$-0.301558\pi$
$829$	2.31044e7			1.16764			0.583819	+	0.811884i	$0.301558\pi$
$830$	8.14561e6	+	2.93306e6i	0.410420	+	0.147783i
$831$	−4.09965e7			−2.05942
$832$		−	2.78539e6i		−	0.139501i
$833$			6.25886e6i			0.312523i
$834$	−1.53552e7			−0.764432
$835$	−1.24137e7	+	3.44750e7i	−0.616147	+	1.71115i
$836$	294072.			0.0145525
$837$			1.68415e7i			0.830934i
$838$			5.04544e6i			0.248193i
$839$	−2.47020e6			−0.121151			−0.0605755	−	0.998164i	$-0.519294\pi$
$839$	−2.47020e6			−0.121151			−0.0605755	+	0.998164i	$0.519294\pi$
$840$	−7.32203e6	+	2.03346e7i	−0.358042	+	0.994344i
$841$	2.57605e7			1.25593
$842$			9.27270e6i			0.450740i
$843$		−	2.31127e7i		−	1.12016i
$844$	9.44351e6			0.456328
$845$	−1.50219e6	−	540906.i	−0.0723741	−	0.0260604i
$846$	−5.37703e6			−0.258295
$847$		−	1.45824e7i		−	0.698426i
$848$		−	3.87141e6i		−	0.184876i
$849$	−4.43715e7			−2.11269
$850$	5.92701e6	+	4.90424e6i	0.281377	+	0.232822i
$851$	−76790.6			−0.00363483
$852$			2.14469e7i			1.01220i
$853$			2.26066e7i			1.06381i	0.846805	+	0.531903i	$0.178523\pi$
$853$			2.26066e7i			1.06381i	−0.846805	+	0.531903i	$0.821477\pi$
$854$	1.56086e7			0.732350
$855$	5.39341e6	+	1.94205e6i	0.252318	+	0.0908541i
$856$	1.28674e6			0.0600215
$857$		−	352440.i		−	0.0163920i	−0.999966	−	0.00819602i	$-0.997391\pi$
$857$		−	352440.i		−	0.0163920i	0.999966	−	0.00819602i	$-0.00260890\pi$
$858$		−	610892.i		−	0.0283300i
$859$	−8.16362e6			−0.377485			−0.188743	−	0.982027i	$-0.560441\pi$
$859$	−8.16362e6			−0.377485			−0.188743	+	0.982027i	$0.560441\pi$
$860$	1.78820e6	−	4.96615e6i	0.0824463	−	0.228968i
$861$	2.94543e7			1.35407
$862$			8.73124e6i			0.400228i
$863$		−	2.20483e7i		−	1.00774i	−0.863780	−	0.503869i	$-0.831910\pi$
$863$		−	2.20483e7i		−	1.00774i	0.863780	−	0.503869i	$-0.168090\pi$
$864$	−1.31281e7			−0.598299
$865$	−5.30351e6	+	1.47288e7i	−0.241003	+	0.669308i
$866$	2.10800e7			0.955160
$867$			2.07687e7i			0.938343i
$868$		−	1.47207e7i		−	0.663175i
$869$	2.84778e6			0.127925
$870$	2.83981e7	+	1.02255e7i	1.27201	+	0.458023i
$871$	8.76731e6			0.391581
$872$			9.00007e6i			0.400825i
$873$			4.42458e7i			1.96488i
$874$	711616.			0.0315113
$875$	−1.37937e7	+	8.15480e6i	−0.609061	+	0.360075i
$876$	2.29429e7			1.01016
$877$		−	3.29930e7i		−	1.44852i	−0.689529	−	0.724258i	$-0.742182\pi$
$877$		−	3.29930e7i		−	1.44852i	0.689529	−	0.724258i	$-0.257818\pi$
$878$		−	6.08405e6i		−	0.266352i
$879$	1.02208e7			0.446185
$880$	−231247.	−	83266.9i	−0.0100663	−	0.00362465i
$881$	−2.33438e7			−1.01328			−0.506642	−	0.862156i	$-0.669114\pi$
$881$	−2.33438e7			−1.01328			−0.506642	+	0.862156i	$0.669114\pi$
$882$			9.28504e6i			0.401895i
$883$		−	3.71832e6i		−	0.160489i	−0.996775	−	0.0802444i	$-0.974430\pi$
$883$		−	3.71832e6i		−	0.160489i	0.996775	−	0.0802444i	$-0.0255701\pi$
$884$	−2.65932e6			−0.114456
$885$	−1.35039e7	+	3.75028e7i	−0.579565	+	1.60955i
$886$	−2.01660e6			−0.0863051
$887$			5.38193e6i			0.229683i	0.993384	+	0.114841i	$0.0366360\pi$
$887$			5.38193e6i			0.229683i	−0.993384	+	0.114841i	$0.963364\pi$
$888$		−	459477.i		−	0.0195538i
$889$	−6.37022e6			−0.270334
$890$	3.96304e6	−	1.10061e7i	0.167708	−	0.465754i
$891$	1.28360e6			0.0541670
$892$		−	3340.99i		−	0.000140593i
$893$		−	1.48739e6i		−	0.0624160i
$894$	1.05579e7			0.441807
$895$	−1.37395e7	−	4.94729e6i	−0.573341	−	0.206448i
$896$	1.24104e7			0.516436
$897$			2.86234e6i			0.118779i
$898$		−	4.38507e6i		−	0.181462i
$899$	−5.17334e7			−2.13487
$900$	−1.70251e7	−	1.40872e7i	−0.700622	−	0.579722i
$901$	2.99026e7			1.22715
$902$		−	2.00783e6i		−	0.0821697i
$903$			9.86836e6i			0.402741i
$904$	2.54235e7			1.03470
$905$	−5.93786e6	−	2.13810e6i	−0.240995	−	0.0867772i
$906$	−2.46300e7			−0.996883
$907$			2.68436e7i			1.08348i	0.840545	+	0.541742i	$0.182235\pi$
$907$			2.68436e7i			1.08348i	−0.840545	+	0.541742i	$0.817765\pi$
$908$			2.40455e7i			0.967873i
$909$	−5.83614e7			−2.34270
$910$	−969186.	+	2.69160e6i	−0.0387975	+	0.107747i
$911$	1.10032e7			0.439260			0.219630	−	0.975583i	$-0.429515\pi$
$911$	1.10032e7			0.439260			0.219630	+	0.975583i	$0.429515\pi$
$912$		−	710334.i		−	0.0282797i
$913$		−	2.13645e6i		−	0.0848235i
$914$	−3.48990e6			−0.138181
$915$	−2.34716e7	+	6.51847e7i	−0.926808	+	2.57391i
$916$	−1.46296e7			−0.576095
$917$		−	2.42287e7i		−	0.951496i
$918$		−	5.45140e6i		−	0.213502i
$919$	−4.98823e7			−1.94831			−0.974153	−	0.225887i	$-0.927472\pi$
$919$	−4.98823e7			−1.94831			−0.974153	+	0.225887i	$0.927472\pi$
$920$	−6.49488e6	−	2.33867e6i	−0.252989	−	0.0910959i
$921$	1.60945e7			0.625215
$922$			291143.i			0.0112792i
$923$			7.14381e6i			0.276011i
$924$	2.11941e6			0.0816647
$925$	217173.	−	262464.i	0.00834548	−	0.0100859i
$926$	1.68462e7			0.645615
$927$		−	1.39082e7i		−	0.531585i
$928$		−	4.03268e7i		−	1.53718i
$929$	4.09032e7			1.55495			0.777477	−	0.628911i	$-0.216499\pi$
$929$	4.09032e7			1.55495			0.777477	+	0.628911i	$0.216499\pi$
$930$	−3.17501e7	−	1.14325e7i	−1.20375	−	0.433445i
$931$	−2.56842e6			−0.0971163
$932$			8.43622e6i			0.318132i
$933$		−	2.64730e7i		−	0.995632i
$934$	1.42919e7			0.536073
$935$	643149.	−	1.78614e6i	0.0240593	−	0.0668168i
$936$	−9.92771e6			−0.370390
$937$			4.44775e7i			1.65498i	0.561483	+	0.827488i	$0.310231\pi$
$937$			4.44775e7i			1.65498i	−0.561483	+	0.827488i	$0.689769\pi$
$938$		−	1.57091e7i		−	0.582968i
$939$	1.67880e7			0.621348
$940$	−1.94248e6	+	5.39462e6i	−0.0717031	+	0.199132i
$941$	8.18280e6			0.301251			0.150625	−	0.988591i	$-0.451871\pi$
$941$	8.18280e6			0.301251			0.150625	+	0.988591i	$0.451871\pi$
$942$		−	3.94472e6i		−	0.144840i
$943$			9.40773e6i			0.344513i
$944$	2.86309e6			0.104569
$945$	1.06835e7	+	3.84689e6i	0.389165	+	0.140130i
$946$	672705.			0.0244397
$947$			3.72825e7i			1.35092i	0.737396	+	0.675461i	$0.236055\pi$
$947$			3.72825e7i			1.35092i	−0.737396	+	0.675461i	$0.763945\pi$
$948$		−	3.17270e7i		−	1.14659i
$949$	7.64213e6			0.275454
$950$	−2.01253e6	+	2.43224e6i	−0.0723493	+	0.0874376i
$951$	3.00793e7			1.07849
$952$			1.19907e7i			0.428798i
$953$		−	4.11870e7i		−	1.46902i	−0.678597	−	0.734511i	$-0.737412\pi$
$953$		−	4.11870e7i		−	1.46902i	0.678597	−	0.734511i	$-0.262588\pi$
$954$	4.43606e7			1.57807
$955$	4.15592e7	+	1.49646e7i	1.47455	+	0.530953i
$956$	−9.39967e6			−0.332635
$957$		−	7.44832e6i		−	0.262893i
$958$			9.54050e6i			0.335859i
$959$	4.47992e6			0.157298
$960$	7.50498e6	−	2.08426e7i	0.262828	−	0.729919i
$961$	2.92107e7			1.02031
$962$		−	60819.0i		−	0.00211886i
$963$		−	2.45969e6i		−	0.0854702i
$964$	−2.59903e7			−0.900781
$965$	5.15636e6	−	1.43201e7i	0.178248	−	0.495027i
$966$	5.12869e6			0.176833
$967$			2.42760e7i			0.834856i	0.908710	+	0.417428i	$0.137068\pi$
$967$			2.42760e7i			0.834856i	−0.908710	+	0.417428i	$0.862932\pi$
$968$			2.78690e7i			0.955944i
$969$	5.48658e6			0.187712
$970$	−2.29258e7	−	8.25510e6i	−0.782341	−	0.281704i
$971$	−2.85115e6			−0.0970446			−0.0485223	−	0.998822i	$-0.515451\pi$
$971$	−2.85115e6			−0.0970446			−0.0485223	+	0.998822i	$0.515451\pi$
$972$		−	2.56557e7i		−	0.870999i
$973$		−	1.77447e7i		−	0.600879i
$974$	1.11366e7			0.376146
$975$	−9.78325e6	−	8.09504e6i	−0.329588	−	0.272714i
$976$	4.97642e6			0.167222
$977$			3.23237e7i			1.08339i	0.840575	+	0.541695i	$0.182217\pi$
$977$			3.23237e7i			1.08339i	−0.840575	+	0.541695i	$0.817783\pi$
$978$		−	5.23031e7i		−	1.74856i
$979$	−2.88670e6			−0.0962597
$980$	9.31542e6	+	3.35428e6i	0.309840	+	0.111567i
$981$	1.72042e7			0.570772
$982$		−	1.73264e7i		−	0.573362i
$983$		−	1.56769e7i		−	0.517461i	−0.965950	−	0.258731i	$-0.916696\pi$
$983$		−	1.56769e7i		−	0.517461i	0.965950	−	0.258731i	$-0.0833042\pi$
$984$	−5.62912e7			−1.85333
$985$	5.75858e6	−	1.59926e7i	0.189115	−	0.525204i
$986$	1.67455e7			0.548538
$987$		−	1.07198e7i		−	0.350262i
$988$		−	1.09129e6i		−	0.0355672i
$989$	−3.15197e6			−0.102469
$990$	954114.	−	2.64974e6i	0.0309394	−	0.0859242i
$991$	5.10915e7			1.65259			0.826294	−	0.563239i	$-0.190445\pi$
$991$	5.10915e7			1.65259			0.826294	+	0.563239i	$0.190445\pi$
$992$			4.50868e7i			1.45469i
$993$		−	5.72485e7i		−	1.84243i
$994$	1.28002e7			0.410912
$995$	−1.53520e7	−	5.52791e6i	−0.491593	−	0.177012i
$996$	−2.38021e7			−0.760269
$997$		−	5.33407e7i		−	1.69950i	−0.527188	−	0.849749i	$-0.676753\pi$
$997$		−	5.33407e7i		−	1.69950i	0.527188	−	0.849749i	$-0.323247\pi$
$998$		−	1.16129e7i		−	0.369073i
$999$	−241403.			−0.00765294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.b.a.14.12	✓	30
5.2	odd	4		325.6.a.l.1.10		15
5.3	odd	4		325.6.a.m.1.6		15
5.4	even	2	inner	65.6.b.a.14.19	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.b.a.14.12	✓	30	1.1	even	1	trivial
65.6.b.a.14.19	yes	30	5.4	even	2	inner
325.6.a.l.1.10		15	5.2	odd	4
325.6.a.m.1.6		15	5.3	odd	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.30124i q^{2} +24.0437i q^{3} +21.1018 q^{4} +(52.5959 + 18.9386i) q^{5} +79.3742 q^{6} +91.7264i q^{7} -175.302i q^{8} -335.101 q^{9} +(62.5210 - 173.632i) q^{10} -45.5406 q^{11} +507.366i q^{12} +169.000i q^{13} +302.811 q^{14} +(-455.356 + 1264.60i) q^{15} +96.5440 q^{16} +745.700i q^{17} +1106.25i q^{18} -306.010 q^{19} +(1109.87 + 399.639i) q^{20} -2205.45 q^{21} +150.340i q^{22} -704.422i q^{23} +4214.91 q^{24} +(2407.66 + 1992.19i) q^{25} +557.910 q^{26} -2214.45i q^{27} +1935.59i q^{28} +6802.33 q^{29} +(4174.76 + 1503.24i) q^{30} -7605.25 q^{31} -5928.38i q^{32} -1094.97i q^{33} +2461.74 q^{34} +(-1737.17 + 4824.43i) q^{35} -7071.24 q^{36} -109.012i q^{37} +1010.21i q^{38} -4063.39 q^{39} +(3319.98 - 9220.16i) q^{40} -13355.2 q^{41} +7280.71i q^{42} -4474.54i q^{43} -960.988 q^{44} +(-17624.9 - 6346.36i) q^{45} -2325.47 q^{46} +4860.59i q^{47} +2321.28i q^{48} +8393.26 q^{49} +(6576.70 - 7948.25i) q^{50} -17929.4 q^{51} +3566.21i q^{52} -40100.0i q^{53} -7310.45 q^{54} +(-2395.25 - 862.477i) q^{55} +16079.8 q^{56} -7357.62i q^{57} -22456.1i q^{58} +29655.8 q^{59} +(-9608.82 + 26685.4i) q^{60} +51545.6 q^{61} +25106.8i q^{62} -30737.6i q^{63} -16481.6 q^{64} +(-3200.63 + 8888.71i) q^{65} -3614.75 q^{66} -51877.6i q^{67} +15735.6i q^{68} +16936.9 q^{69} +(15926.6 + 5734.83i) q^{70} +42271.1 q^{71} +58743.9i q^{72} -45219.7i q^{73} -359.876 q^{74} +(-47899.7 + 57889.0i) q^{75} -6457.36 q^{76} -4177.27i q^{77} +13414.2i q^{78} -62532.7 q^{79} +(5077.82 + 1828.41i) q^{80} -28185.8 q^{81} +44088.9i q^{82} +46913.1i q^{83} -46538.9 q^{84} +(-14122.5 + 39220.8i) q^{85} -14771.5 q^{86} +163553. i q^{87} +7983.35i q^{88} +63387.4 q^{89} +(-20950.9 + 58184.2i) q^{90} -15501.8 q^{91} -14864.6i q^{92} -182859. i q^{93} +16046.0 q^{94} +(-16094.9 - 5795.41i) q^{95} +142540. q^{96} -132037. i q^{97} -27708.2i q^{98} +15260.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 500 q^{4} + 80 q^{5} - 404 q^{6} - 1926 q^{9} + 322 q^{10} - 652 q^{11} - 2668 q^{14} - 2064 q^{15} + 12092 q^{16} + 5248 q^{19} - 3460 q^{20} + 7060 q^{21} - 5480 q^{24} - 1178 q^{25} - 4056 q^{26}+ \cdots + 520976 q^{99}+O(q^{100}) \) 30 * q - 500 * q^4 + 80 * q^5 - 404 * q^6 - 1926 * q^9 + 322 * q^10 - 652 * q^11 - 2668 * q^14 - 2064 * q^15 + 12092 * q^16 + 5248 * q^19 - 3460 * q^20 + 7060 * q^21 - 5480 * q^24 - 1178 * q^25 - 4056 * q^26 + 6084 * q^29 + 19638 * q^30 - 22292 * q^31 - 46060 * q^34 - 272 * q^35 + 50344 * q^36 + 12168 * q^39 + 26166 * q^40 - 15856 * q^41 - 45516 * q^44 - 64644 * q^45 + 45396 * q^46 - 141086 * q^49 - 60544 * q^50 + 96168 * q^51 - 4964 * q^54 + 48544 * q^55 + 67156 * q^56 + 124624 * q^59 + 87348 * q^60 - 59060 * q^61 - 30132 * q^64 + 338 * q^65 - 2480 * q^66 - 398680 * q^69 + 297080 * q^70 - 45736 * q^71 + 517132 * q^74 + 249816 * q^75 - 278480 * q^76 - 259168 * q^79 + 100648 * q^80 + 115462 * q^81 + 30364 * q^84 - 108572 * q^85 - 483560 * q^86 + 335276 * q^89 - 501660 * q^90 - 103428 * q^91 - 208500 * q^94 + 217136 * q^95 - 92740 * q^96 + 520976 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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