LMFDB - Embedded newform 65.6.b.a.14.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,6,Mod(14,65)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

$q$-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	$0.0942513\pi$
$2$			3.30124i			0.583583i	−0.956482	+	0.291791i	$0.905749\pi$
$3$		−	24.0437i		−	1.54241i	−0.636589	−	0.771203i	$-0.719655\pi$
$3$		−	24.0437i		−	1.54241i	0.636589	−	0.771203i	$-0.280345\pi$
$4$	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	$-0.884900\pi$
$7$		−	91.7264i		−	0.707537i	0.935333	−	0.353769i	$-0.115100\pi$
$8$			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	$-0.898698\pi$
$17$		−	745.700i		−	0.625809i	0.949785	−	0.312905i	$-0.101302\pi$
$18$		−	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	$0.0443342\pi$
$23$			704.422i			0.277660i	−0.990316	+	0.138830i	$0.955666\pi$
$24$	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	$0.00208350\pi$
$37$			109.012i			0.0130909i	−0.999979	+	0.00654547i	$0.997916\pi$
$38$		−	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	$0.0590736\pi$
$43$			4474.54i			0.369044i	−0.982828	+	0.184522i	$0.940926\pi$
$44$	−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	$-0.948697\pi$
$47$		−	4860.59i		−	0.320955i	0.987039	−	0.160478i	$-0.0513035\pi$
$48$		−	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	$0.436953\pi$
$53$			40100.0i			1.96090i	−0.196777	+	0.980448i	$0.563047\pi$
$54$	−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	$0.249472\pi$
$67$			51877.6i			1.41186i	−0.708280	+	0.705932i	$0.750528\pi$
$68$		−	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	$0.165412\pi$
$73$			45219.7i			0.993162i	−0.867990	+	0.496581i	$0.834588\pi$
$74$	−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	$-0.878075\pi$
$83$		−	46913.1i		−	0.747479i	0.927534	−	0.373740i	$-0.121925\pi$
$84$	−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	$0.252401\pi$
$97$			132037.i			1.42484i	−0.701752	+	0.712421i	$0.747599\pi$
$98$			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	$-0.938262\pi$
$103$		−	41504.6i		−	0.385481i	0.981250	−	0.192741i	$-0.0617376\pi$
$104$	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	$-0.990134\pi$
$107$		−	7340.14i		−	0.0619791i	0.999520	−	0.0309895i	$-0.00986586\pi$
$108$			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	$-0.820604\pi$
$113$		−	145027.i		−	1.06845i	0.845344	−	0.534223i	$-0.179396\pi$
$114$	−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	$-0.938814\pi$
$127$		−	69448.0i		−	0.382077i	0.981583	−	0.191038i	$-0.0611855\pi$
$128$			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	$0.0354563\pi$
$137$			48840.0i			0.222318i	−0.993803	+	0.111159i	$0.964544\pi$
$138$			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	$0.0256376\pi$
$157$			49697.8i			0.160912i	−0.996758	+	0.0804559i	$0.974362\pi$
$158$		−	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	$0.423541\pi$
$163$			658943.i			1.94258i	−0.237899	+	0.971290i	$0.576459\pi$
$164$	−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	$-0.636580\pi$
$167$		−	655469.i		−	1.81870i	0.416034	−	0.909349i	$-0.363420\pi$
$168$		−	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	$-0.884247\pi$
$173$		−	280036.i		−	0.711376i	0.934605	−	0.355688i	$-0.115753\pi$
$174$	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	$0.0847351\pi$
$193$			272267.i			0.526140i	−0.964777	+	0.263070i	$0.915265\pi$
$194$	−435887.			−0.831513
$195$	−213718.	+	76955.1i	−0.402489	+	0.144928i
$196$	177113.			0.329314
$197$			304065.i			0.558215i	0.960260	+	0.279107i	$0.0900385\pi$
$197$			304065.i			0.558215i	−0.960260	+	0.279107i	$0.909961\pi$
$198$			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	$3.39323e-5\pi$
$223$			158.327i			0.000213203i	−1.00000		0.000106602i	$0.999966\pi$
$224$	543789.			0.724119
$225$	−806808.	+	667585.i	−1.06246	+	0.879124i
$226$	478769.			0.623526
$227$		−	1.13950e6i		−	1.46774i	−0.679290	−	0.733870i	$-0.737712\pi$
$227$		−	1.13950e6i		−	1.46774i	0.679290	−	0.733870i	$-0.262288\pi$
$228$			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	$-0.922453\pi$
$233$		−	399786.i		−	0.482434i	0.970471	−	0.241217i	$-0.0775466\pi$
$234$	−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	$0.130521\pi$
$257$			844218.i			0.797300i	−0.917103	+	0.398650i	$0.869479\pi$
$258$			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	$0.0842132\pi$
$263$			586640.i			0.522976i	−0.965207	+	0.261488i	$0.915787\pi$
$264$	−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	$-0.767322\pi$
$277$		−	1.70508e6i		−	1.33520i	0.744521	−	0.667599i	$-0.232678\pi$
$278$		−	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	$-0.759860\pi$
$283$		−	1.84545e6i		−	1.36973i	0.728668	−	0.684867i	$-0.240140\pi$
$284$	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	$0.0462021\pi$
$293$			425094.i			0.289278i	−0.989484	+	0.144639i	$0.953798\pi$
$294$	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	$0.0649636\pi$
$307$			669386.i			0.405351i	−0.979246	+	0.202675i	$0.935036\pi$
$308$			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	$0.0645562\pi$
$313$			698228.i			0.402844i	−0.979505	+	0.201422i	$0.935444\pi$
$314$	−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	$0.113687\pi$
$317$			1.25102e6i			0.699226i	−0.936894	+	0.349613i	$0.886313\pi$
$318$			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	$-0.806630\pi$
$337$		−	2.38010e6i		−	1.14161i	0.821084	−	0.570807i	$-0.193370\pi$
$338$		−	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	$-0.720672\pi$
$347$		−	3.45043e6i		−	1.53833i	0.639049	−	0.769166i	$-0.279328\pi$
$348$		−	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	$0.338091\pi$
$353$			4.08960e6i			1.74680i	−0.487001	+	0.873401i	$0.661909\pi$
$354$	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	$0.0202795\pi$
$367$			328555.i			0.127333i	−0.997971	+	0.0636667i	$0.979721\pi$
$368$			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	$0.413437\pi$
$373$			5.17656e6i			1.92650i	−0.268606	+	0.963250i	$0.586563\pi$
$374$	−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	$0.289787\pi$
$383$			4.53434e6i			1.57949i	−0.613435	+	0.789745i	$0.710213\pi$
$384$	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	$-0.689729\pi$
$397$		−	5.19763e6i		−	1.65512i	0.561378	−	0.827560i	$-0.310271\pi$
$398$		−	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	$-0.694884\pi$
$433$		−	6.38548e6i		−	1.63672i	0.574708	−	0.818359i	$-0.305116\pi$
$434$	−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	$0.0235587\pi$
$443$			610862.i			0.147888i	−0.997262	+	0.0739442i	$0.976441\pi$
$444$	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	$0.0377733\pi$
$457$			1.05715e6i			0.236780i	−0.992967	+	0.118390i	$0.962227\pi$
$458$		−	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	$-0.813427\pi$
$463$		−	5.10298e6i		−	1.10630i	0.833083	−	0.553148i	$-0.186573\pi$
$464$	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	$-0.848102\pi$
$467$		−	4.32926e6i		−	0.918590i	0.888284	−	0.459295i	$-0.151898\pi$
$468$			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	$-0.895553\pi$
$487$		−	3.37347e6i		−	0.644546i	0.946647	−	0.322273i	$-0.104447\pi$
$488$			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	$0.290384\pi$
$503$			8.97569e6i			1.58179i	−0.611954	+	0.790893i	$0.709616\pi$
$504$	−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	$-0.891971\pi$
$523$		−	4.16491e6i		−	0.665811i	0.942960	−	0.332906i	$-0.108029\pi$
$524$	−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	$0.0763404\pi$
$547$			3.32454e6i			0.475076i	−0.971378	+	0.237538i	$0.923660\pi$
$548$			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	$-0.821541\pi$
$557$		−	7.78685e6i		−	1.06347i	0.846912	−	0.531733i	$-0.178459\pi$
$558$			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	$0.100850\pi$
$563$			4.68638e6i			0.623112i	−0.950228	+	0.311556i	$0.899150\pi$
$564$	−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	$0.220813\pi$
$577$			1.02267e7i			1.27878i	−0.768883	+	0.639390i	$0.779187\pi$
$578$			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	$0.0429013\pi$
$587$			2.24352e6i			0.268741i	−0.990931	+	0.134371i	$0.957099\pi$
$588$		−	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	$0.0109748\pi$
$593$			590374.i			0.0689430i	−0.999406	+	0.0344715i	$0.989025\pi$
$594$	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	$0.0757175\pi$
$607$			4.27804e6i			0.471273i	−0.971841	+	0.235637i	$0.924282\pi$
$608$		−	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	$-0.988953\pi$
$613$		−	645645.i		−	0.0693973i	0.999398	−	0.0346986i	$-0.0110471\pi$
$614$	−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	$-0.955158\pi$
$617$		−	2.65549e6i		−	0.280822i	0.990093	−	0.140411i	$-0.0448424\pi$
$618$		−	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	$-0.943592\pi$
$643$		−	3.69634e6i		−	0.352569i	0.984339	−	0.176285i	$-0.0564079\pi$
$644$	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	$-0.635189\pi$
$647$		−	1.94037e7i		−	1.82232i	0.412055	−	0.911159i	$-0.364811\pi$
$648$		−	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	$-0.908686\pi$
$653$		−	6.16635e6i		−	0.565907i	0.959134	−	0.282953i	$-0.0913142\pi$
$654$	−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	$-0.904375\pi$
$673$		−	6.95400e6i		−	0.591830i	0.955214	−	0.295915i	$-0.0956246\pi$
$674$	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	$0.208166\pi$
$677$			1.45095e7i			1.21669i	−0.793672	+	0.608345i	$0.791834\pi$
$678$		−	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	$0.258698\pi$
$683$			1.77058e7i			1.45232i	−0.687524	+	0.726162i	$0.741302\pi$
$684$	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	$0.0428987\pi$
$727$			3.82952e6i			0.268725i	−0.990932	+	0.134363i	$0.957101\pi$
$728$		−	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	$0.167259\pi$
$733$			1.45934e7i			1.00322i	−0.865093	+	0.501611i	$0.832741\pi$
$734$	−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	$0.0574432\pi$
$743$			5.40170e6i			0.358970i	−0.983761	+	0.179485i	$0.942557\pi$
$744$	−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	$0.0907765\pi$
$757$			8.87136e6i			0.562665i	−0.959610	+	0.281333i	$0.909224\pi$
$758$		−	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	$0.176541\pi$
$773$			1.74975e7i			1.05324i	−0.850101	+	0.526619i	$0.823459\pi$
$774$	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	$-0.857858\pi$
$787$		−	1.50075e7i		−	0.863719i	0.901941	−	0.431860i	$-0.142142\pi$
$788$			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	$-0.751288\pi$
$797$		−	2.52578e7i		−	1.40848i	0.709962	−	0.704240i	$-0.248712\pi$
$798$			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	$0.172638\pi$
$823$			2.00591e7i			1.03232i	−0.856493	+	0.516158i	$0.827362\pi$
$824$	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	$0.0793435\pi$
$827$			9.70394e6i			0.493383i	−0.969094	+	0.246692i	$0.920657\pi$
$828$		−	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	$-0.821477\pi$
$853$		−	2.26066e7i		−	1.06381i	0.846805	−	0.531903i	$-0.178523\pi$
$854$	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	$0.00260890\pi$
$857$			352440.i			0.0163920i	−0.999966	+	0.00819602i	$0.997391\pi$
$858$			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	$0.168090\pi$
$863$			2.20483e7i			1.00774i	−0.863780	+	0.503869i	$0.831910\pi$
$864$	−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	$0.257818\pi$
$877$			3.29930e7i			1.44852i	−0.689529	+	0.724258i	$0.742182\pi$
$878$			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	$0.0255701\pi$
$883$			3.71832e6i			0.160489i	−0.996775	+	0.0802444i	$0.974430\pi$
$884$	−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	$-0.963364\pi$
$887$		−	5.38193e6i		−	0.229683i	0.993384	−	0.114841i	$-0.0366360\pi$
$888$			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	$-0.817765\pi$
$907$		−	2.68436e7i		−	1.08348i	0.840545	−	0.541742i	$-0.182235\pi$
$908$		−	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	$-0.689769\pi$
$937$		−	4.44775e7i		−	1.65498i	0.561483	−	0.827488i	$-0.310231\pi$
$938$			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	$-0.763945\pi$
$947$		−	3.72825e7i		−	1.35092i	0.737396	−	0.675461i	$-0.236055\pi$
$948$			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	$0.262588\pi$
$953$			4.11870e7i			1.46902i	−0.678597	+	0.734511i	$0.737412\pi$
$954$	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	$-0.862932\pi$
$967$		−	2.42760e7i		−	0.834856i	0.908710	−	0.417428i	$-0.137068\pi$
$968$		−	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	$-0.817783\pi$
$977$		−	3.23237e7i		−	1.08339i	0.840575	−	0.541695i	$-0.182217\pi$
$978$			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	$0.0833042\pi$
$983$			1.56769e7i			0.517461i	−0.965950	+	0.258731i	$0.916696\pi$
$984$	−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	$0.323247\pi$
$997$			5.33407e7i			1.69950i	−0.527188	+	0.849749i	$0.676753\pi$
$998$			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.14.19	yes	30
5.2	odd	4		325.6.a.m.1.6		15
5.3	odd	4		325.6.a.l.1.10		15
5.4	even	2	inner	65.6.b.a.14.12	✓	30

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

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

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