LMFDB - Embedded newform 115.6.b.a.24.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,6,Mod(24,115)] 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("115.24"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 6, names="a")

Level:	$N$	$=$	$115 = 5 \cdot 23$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	115.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:	$18.4441392785$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.10
Character	$\chi$	$=$	115.24
Dual form			115.6.b.a.24.45

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-7.77128i q^{2} +16.5107i q^{3} -28.3928 q^{4} +(38.9251 + 40.1228i) q^{5} +128.309 q^{6} -7.31009i q^{7} -28.0326i q^{8} -29.6034 q^{9} +(311.805 - 302.498i) q^{10} -512.382 q^{11} -468.785i q^{12} +603.915i q^{13} -56.8088 q^{14} +(-662.455 + 642.681i) q^{15} -1126.42 q^{16} +1547.97i q^{17} +230.056i q^{18} +2173.79 q^{19} +(-1105.19 - 1139.20i) q^{20} +120.695 q^{21} +3981.86i q^{22} +529.000i q^{23} +462.838 q^{24} +(-94.6706 + 3123.57i) q^{25} +4693.20 q^{26} +3523.33i q^{27} +207.554i q^{28} -2114.61 q^{29} +(4994.45 + 5148.12i) q^{30} -6354.77 q^{31} +7856.67i q^{32} -8459.79i q^{33} +12029.7 q^{34} +(293.301 - 284.546i) q^{35} +840.522 q^{36} -3404.46i q^{37} -16893.1i q^{38} -9971.07 q^{39} +(1124.75 - 1091.17i) q^{40} +8009.77 q^{41} -937.953i q^{42} +14626.7i q^{43} +14548.0 q^{44} +(-1152.31 - 1187.77i) q^{45} +4111.01 q^{46} +2294.90i q^{47} -18598.0i q^{48} +16753.6 q^{49} +(24274.1 + 735.712i) q^{50} -25558.1 q^{51} -17146.8i q^{52} +19770.6i q^{53} +27380.8 q^{54} +(-19944.5 - 20558.2i) q^{55} -204.921 q^{56} +35890.8i q^{57} +16433.2i q^{58} +48436.6 q^{59} +(18808.9 - 18247.5i) q^{60} -2261.14 q^{61} +49384.7i q^{62} +216.403i q^{63} +25011.0 q^{64} +(-24230.8 + 23507.5i) q^{65} -65743.4 q^{66} -47700.6i q^{67} -43951.2i q^{68} -8734.16 q^{69} +(-2211.29 - 2279.32i) q^{70} -59497.4 q^{71} +829.859i q^{72} -12040.2i q^{73} -26457.0 q^{74} +(-51572.3 - 1563.08i) q^{75} -61719.9 q^{76} +3745.56i q^{77} +77488.0i q^{78} -59066.2 q^{79} +(-43846.0 - 45195.0i) q^{80} -65366.3 q^{81} -62246.2i q^{82} +88291.8i q^{83} -3426.86 q^{84} +(-62108.8 + 60254.9i) q^{85} +113668. q^{86} -34913.6i q^{87} +14363.4i q^{88} +61494.9 q^{89} +(-9230.48 + 8954.96i) q^{90} +4414.68 q^{91} -15019.8i q^{92} -104922. i q^{93} +17834.3 q^{94} +(84614.9 + 87218.3i) q^{95} -129719. q^{96} -55907.6i q^{97} -130197. i q^{98} +15168.2 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$54 q - 832 q^{4} + 98 q^{5} - 144 q^{6} - 4270 q^{9} + 942 q^{10} - 380 q^{11} - 3988 q^{14} + 690 q^{15} + 16632 q^{16} - 2440 q^{19} - 2436 q^{20} + 4768 q^{21} - 17940 q^{24} - 9150 q^{25} - 15144 q^{26}+ \cdots - 14088 q^{99}+O(q^{100})$ 54 * q - 832 * q^4 + 98 * q^5 - 144 * q^6 - 4270 * q^9 + 942 * q^10 - 380 * q^11 - 3988 * q^14 + 690 * q^15 + 16632 * q^16 - 2440 * q^19 - 2436 * q^20 + 4768 * q^21 - 17940 * q^24 - 9150 * q^25 - 15144 * q^26 + 22958 * q^29 + 23034 * q^30 - 33970 * q^31 + 26120 * q^34 - 18694 * q^35 + 71560 * q^36 + 13416 * q^39 - 22230 * q^40 - 33842 * q^41 + 33908 * q^44 + 35260 * q^45 - 8464 * q^46 - 153772 * q^49 - 91728 * q^50 + 96576 * q^51 - 90500 * q^54 + 37344 * q^55 + 201796 * q^56 + 110106 * q^59 - 92484 * q^60 + 132924 * q^61 - 262108 * q^64 + 45090 * q^65 - 123288 * q^66 + 38088 * q^69 + 249664 * q^70 - 310814 * q^71 + 220660 * q^74 + 235776 * q^75 + 42220 * q^76 - 389348 * q^79 - 245138 * q^80 + 364422 * q^81 - 35836 * q^84 - 134118 * q^85 + 111980 * q^86 - 353788 * q^89 - 805800 * q^90 - 226632 * q^91 + 289804 * q^94 - 42676 * q^95 + 294416 * q^96 - 14088 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$ .

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$		−	7.77128i		−	1.37378i	−0.726761	−	0.686891i	$-0.758975\pi$
$2$		−	7.77128i		−	1.37378i	0.726761	−	0.686891i	$-0.241025\pi$
$3$			16.5107i			1.05916i	0.848259	+	0.529581i	$0.177651\pi$
$3$			16.5107i			1.05916i	−0.848259	+	0.529581i	$0.822349\pi$
$4$	−28.3928			−0.887275
$5$	38.9251	+	40.1228i	0.696314	+	0.717738i
$5$	38.9251	+	40.1228i	0.696314	+	0.717738i
$6$	128.309			1.45506
$7$		−	7.31009i		−	0.0563868i	−0.999602	−	0.0281934i	$-0.991025\pi$
$7$		−	7.31009i		−	0.0563868i	0.999602	−	0.0281934i	$-0.00897543\pi$
$8$		−	28.0326i		−	0.154860i
$9$	−29.6034			−0.121825
$10$	311.805	−	302.498i	0.986014	−	0.956583i
$11$	−512.382			−1.27677			−0.638384	−	0.769718i	$-0.720397\pi$
$11$	−512.382			−1.27677			−0.638384	+	0.769718i	$0.720397\pi$
$12$		−	468.785i		−	0.939768i
$13$			603.915i			0.991101i	0.868579	+	0.495550i	$0.165034\pi$
$13$			603.915i			0.991101i	−0.868579	+	0.495550i	$0.834966\pi$
$14$	−56.8088			−0.0774632
$15$	−662.455	+	642.681i	−0.760201	+	0.737509i
$16$	−1126.42			−1.10002
$17$			1547.97i			1.29909i	0.760322	+	0.649546i	$0.225041\pi$
$17$			1547.97i			1.29909i	−0.760322	+	0.649546i	$0.774959\pi$
$18$			230.056i			0.167360i
$19$	2173.79			1.38144			0.690722	−	0.723121i	$-0.257293\pi$
$19$	2173.79			1.38144			0.690722	+	0.723121i	$0.257293\pi$
$20$	−1105.19	−	1139.20i	−0.617822	−	0.636831i
$21$	120.695			0.0597228
$22$			3981.86i			1.75400i
$23$			529.000i			0.208514i
$23$			529.000i			0.208514i
$24$	462.838			0.164022
$25$	−94.6706	+	3123.57i	−0.0302946	+	0.999541i
$26$	4693.20			1.36156
$27$			3523.33i			0.930130i
$28$			207.554i			0.0500306i
$29$	−2114.61			−0.466911			−0.233456	−	0.972367i	$-0.575003\pi$
$29$	−2114.61			−0.466911			−0.233456	+	0.972367i	$0.575003\pi$
$30$	4994.45	+	5148.12i	1.01318	+	1.04435i
$31$	−6354.77			−1.18767			−0.593834	−	0.804587i	$-0.702387\pi$
$31$	−6354.77			−1.18767			−0.593834	+	0.804587i	$0.702387\pi$
$32$			7856.67i			1.35632i
$33$		−	8459.79i		−	1.35230i
$34$	12029.7			1.78467
$35$	293.301	−	284.546i	0.0404709	−	0.0392629i
$36$	840.522			0.108092
$37$		−	3404.46i		−	0.408831i	−0.978884	−	0.204415i	$-0.934471\pi$
$37$		−	3404.46i		−	0.408831i	0.978884	−	0.204415i	$-0.0655293\pi$
$38$		−	16893.1i		−	1.89780i
$39$	−9971.07			−1.04974
$40$	1124.75	−	1091.17i	0.111149	−	0.107831i
$41$	8009.77			0.744150			0.372075	−	0.928203i	$-0.378646\pi$
$41$	8009.77			0.744150			0.372075	+	0.928203i	$0.378646\pi$
$42$		−	937.953i		−	0.0820461i
$43$			14626.7i			1.20635i	0.797608	+	0.603176i	$0.206098\pi$
$43$			14626.7i			1.20635i	−0.797608	+	0.603176i	$0.793902\pi$
$44$	14548.0			1.13284
$45$	−1152.31	−	1187.77i	−0.0848281	−	0.0874381i
$46$	4111.01			0.286453
$47$			2294.90i			0.151537i	0.997125	+	0.0757685i	$0.0241410\pi$
$47$			2294.90i			0.151537i	−0.997125	+	0.0757685i	$0.975859\pi$
$48$		−	18598.0i		−	1.16510i
$49$	16753.6			0.996821
$50$	24274.1	+	735.712i	1.37315	+	0.0416181i
$51$	−25558.1			−1.37595
$52$		−	17146.8i		−	0.879379i
$53$			19770.6i			0.966785i	0.875404	+	0.483393i	$0.160596\pi$
$53$			19770.6i			0.966785i	−0.875404	+	0.483393i	$0.839404\pi$
$54$	27380.8			1.27780
$55$	−19944.5	−	20558.2i	−0.889031	−	0.916385i
$56$	−204.921			−0.00873205
$57$			35890.8i			1.46317i
$58$			16433.2i			0.641434i
$59$	48436.6			1.81152			0.905760	−	0.423791i	$-0.139301\pi$
$59$	48436.6			1.81152			0.905760	+	0.423791i	$0.139301\pi$
$60$	18808.9	−	18247.5i	0.674507	−	0.654373i
$61$	−2261.14			−0.0778041			−0.0389020	−	0.999243i	$-0.512386\pi$
$61$	−2261.14			−0.0778041			−0.0389020	+	0.999243i	$0.512386\pi$
$62$			49384.7i			1.63160i
$63$			216.403i			0.00686930i
$64$	25011.0			0.763275
$65$	−24230.8	+	23507.5i	−0.711350	+	0.690117i
$66$	−65743.4			−1.85777
$67$		−	47700.6i		−	1.29819i	−0.760709	−	0.649093i	$-0.775148\pi$
$67$		−	47700.6i		−	1.29819i	0.760709	−	0.649093i	$-0.224852\pi$
$68$		−	43951.2i		−	1.15265i
$69$	−8734.16			−0.220851
$70$	−2211.29	−	2279.32i	−0.0539387	−	0.0555982i
$71$	−59497.4			−1.40072			−0.700361	−	0.713789i	$-0.746978\pi$
$71$	−59497.4			−1.40072			−0.700361	+	0.713789i	$0.746978\pi$
$72$			829.859i			0.0188657i
$73$		−	12040.2i		−	0.264441i	−0.991220	−	0.132220i	$-0.957789\pi$
$73$		−	12040.2i		−	0.264441i	0.991220	−	0.132220i	$-0.0422106\pi$
$74$	−26457.0			−0.561644
$75$	−51572.3	−	1563.08i	−1.05868	−	0.0320869i
$76$	−61719.9			−1.22572
$77$			3745.56i			0.0719929i
$78$			77488.0i			1.44211i
$79$	−59066.2			−1.06481			−0.532404	−	0.846491i	$-0.678711\pi$
$79$	−59066.2			−1.06481			−0.532404	+	0.846491i	$0.678711\pi$
$80$	−43846.0	−	45195.0i	−0.765958	−	0.789524i
$81$	−65366.3			−1.10698
$82$		−	62246.2i		−	1.02230i
$83$			88291.8i			1.40678i	0.710806	+	0.703389i	$0.248331\pi$
$83$			88291.8i			1.40678i	−0.710806	+	0.703389i	$0.751669\pi$
$84$	−3426.86			−0.0529905
$85$	−62108.8	+	60254.9i	−0.932408	+	0.904576i
$86$	113668.			1.65726
$87$		−	34913.6i		−	0.494535i
$88$			14363.4i			0.197720i
$89$	61494.9			0.822932			0.411466	−	0.911425i	$-0.365017\pi$
$89$	61494.9			0.822932			0.411466	+	0.911425i	$0.365017\pi$
$90$	−9230.48	+	8954.96i	−0.120121	+	0.116535i
$91$	4414.68			0.0558850
$92$		−	15019.8i		−	0.185010i
$93$		−	104922.i		−	1.25793i
$94$	17834.3			0.208179
$95$	84614.9	+	87218.3i	0.961918	+	0.991514i
$96$	−129719.			−1.43657
$97$		−	55907.6i		−	0.603311i	−0.953417	−	0.301656i	$-0.902461\pi$
$97$		−	55907.6i		−	0.603311i	0.953417	−	0.301656i	$-0.0975393\pi$
$98$		−	130197.i		−	1.36941i
$99$	15168.2			0.155542
$100$	2687.96	−	88686.8i	0.0268796	−	0.886868i
$101$	−30742.8			−0.299875			−0.149937	−	0.988695i	$-0.547907\pi$
$101$	−30742.8			−0.299875			−0.149937	+	0.988695i	$0.547907\pi$
$102$			198619.i			1.89025i
$103$		−	161792.i		−	1.50267i	−0.659919	−	0.751337i	$-0.729409\pi$
$103$		−	161792.i		−	1.50267i	0.659919	−	0.751337i	$-0.270591\pi$
$104$	16929.3			0.153482
$105$	4698.06	+	4842.61i	0.0415858	+	0.0428653i
$106$	153643.			1.32815
$107$		−	165359.i		−	1.39627i	−0.715966	−	0.698135i	$-0.754014\pi$
$107$		−	165359.i		−	1.39627i	0.715966	−	0.698135i	$-0.245986\pi$
$108$		−	100037.i		−	0.825281i
$109$	128891.			1.03910			0.519549	−	0.854441i	$-0.326100\pi$
$109$	128891.			1.03910			0.519549	+	0.854441i	$0.326100\pi$
$110$	−159763.	+	154995.i	−1.25891	+	1.22133i
$111$	56210.0			0.433018
$112$			8234.22i			0.0620265i
$113$		−	44437.9i		−	0.327384i	−0.986511	−	0.163692i	$-0.947660\pi$
$113$		−	44437.9i		−	0.327384i	0.986511	−	0.163692i	$-0.0523404\pi$
$114$	278917.			2.01008
$115$	−21224.9	+	20591.4i	−0.149659	+	0.145191i
$116$	60039.5			0.414279
$117$		−	17877.9i		−	0.120740i
$118$		−	376414.i		−	2.48863i
$119$	11315.8			0.0732517
$120$	18016.0	+	18570.3i	0.114210	+	0.117724i
$121$	101484.			0.630138
$122$			17571.9i			0.106886i
$123$			132247.i			0.788175i
$124$	180430.			1.05379
$125$	−129011.	+	117787.i	−0.738503	+	0.674250i
$126$	1681.73			0.00943691
$127$		−	155427.i		−	0.855101i	−0.903991	−	0.427551i	$-0.859377\pi$
$127$		−	155427.i		−	0.855101i	0.903991	−	0.427551i	$-0.140623\pi$
$128$			57046.0i			0.307752i
$129$	−241496.			−1.27772
$130$	182683.	+	188304.i	0.948070	+	0.977240i
$131$	−181481.			−0.923961			−0.461981	−	0.886890i	$-0.652861\pi$
$131$	−181481.			−0.923961			−0.461981	+	0.886890i	$0.652861\pi$
$132$			240197.i			1.19987i
$133$		−	15890.6i		−	0.0778952i
$134$	−370695.			−1.78342
$135$	−141366.	+	137146.i	−0.667589	+	0.647662i
$136$	43393.6			0.201177
$137$		−	273627.i		−	1.24554i	−0.782406	−	0.622769i	$-0.786008\pi$
$137$		−	273627.i		−	1.24554i	0.782406	−	0.622769i	$-0.213992\pi$
$138$			67875.6i			0.303400i
$139$	435154.			1.91032			0.955160	−	0.296090i	$-0.0956829\pi$
$139$	435154.			1.91032			0.955160	+	0.296090i	$0.0956829\pi$
$140$	−8327.63	+	8079.06i	−0.0359089	+	0.0348370i
$141$	−37890.4			−0.160502
$142$			462371.i			1.92429i
$143$		−	309435.i		−	1.26541i
$144$	33345.8			0.134009
$145$	−82311.2	−	84843.8i	−0.325117	−	0.335120i
$146$	−93568.1			−0.363284
$147$			276613.i			1.05579i
$148$			96662.0i			0.362745i
$149$	−13438.2			−0.0495877			−0.0247939	−	0.999693i	$-0.507893\pi$
$149$	−13438.2			−0.0495877			−0.0247939	+	0.999693i	$0.507893\pi$
$150$	−12147.1	+	400783.i	−0.0440804	+	1.45439i
$151$	181022.			0.646083			0.323042	−	0.946385i	$-0.395295\pi$
$151$	181022.			0.646083			0.323042	+	0.946385i	$0.395295\pi$
$152$		−	60936.9i		−	0.213930i
$153$		−	45825.1i		−	0.158261i
$154$	29107.8			0.0989025
$155$	−247360.	−	254971.i	−0.826990	−	0.852435i
$156$	283107.			0.931405
$157$			419348.i			1.35777i	0.734245	+	0.678885i	$0.237536\pi$
$157$			419348.i			1.35777i	−0.734245	+	0.678885i	$0.762464\pi$
$158$			459020.i			1.46281i
$159$	−326426.			−1.02398
$160$	−315231.	+	305822.i	−0.973485	+	0.944427i
$161$	3867.04			0.0117575
$162$			507980.i			1.52075i
$163$		−	91209.3i		−	0.268887i	−0.990921	−	0.134444i	$-0.957075\pi$
$163$		−	91209.3i		−	0.268887i	0.990921	−	0.134444i	$-0.0429247\pi$
$164$	−227420.			−0.660265
$165$	339430.	−	329298.i	0.970600	−	0.941628i
$166$	686141.			1.93260
$167$		−	382602.i		−	1.06159i	−0.847501	−	0.530794i	$-0.821894\pi$
$167$		−	382602.i		−	1.06159i	0.847501	−	0.530794i	$-0.178106\pi$
$168$		−	3383.39i		−	0.00924866i
$169$	6579.14			0.0177195
$170$	468258.	+	482665.i	1.24269	+	1.28092i
$171$	−64351.4			−0.168294
$172$		−	415292.i		−	1.07037i
$173$		−	144391.i		−	0.366796i	−0.983039	−	0.183398i	$-0.941290\pi$
$173$		−	144391.i		−	0.366796i	0.983039	−	0.183398i	$-0.0587098\pi$
$174$	−271324.			−0.679382
$175$	22833.5	+	692.051i	0.0563609	+	0.00170822i
$176$	577157.			1.40447
$177$			799722.i			1.91869i
$178$		−	477894.i		−	1.13053i
$179$	−521036.			−1.21544			−0.607722	−	0.794150i	$-0.707916\pi$
$179$	−521036.			−1.21544			−0.607722	+	0.794150i	$0.707916\pi$
$180$	32717.4	+	33724.1i	0.0752658	+	0.0775816i
$181$	−103563.			−0.234967			−0.117483	−	0.993075i	$-0.537483\pi$
$181$	−103563.			−0.234967			−0.117483	+	0.993075i	$0.537483\pi$
$182$		−	34307.7i		−	0.0767738i
$183$		−	37333.0i		−	0.0824071i
$184$	14829.2			0.0322905
$185$	136596.	−	132519.i	0.293433	−	0.284674i
$186$	−815376.			−1.72813
$187$		−	793152.i		−	1.65864i
$188$		−	65158.5i		−	0.134455i
$189$	25755.9			0.0524471
$190$	677798.	−	657566.i	1.36212	−	1.32146i
$191$	886889.			1.75908			0.879540	−	0.475824i	$-0.157850\pi$
$191$	886889.			1.75908			0.879540	+	0.475824i	$0.157850\pi$
$192$			412949.i			0.808432i
$193$		−	175474.i		−	0.339094i	−0.985522	−	0.169547i	$-0.945769\pi$
$193$		−	175474.i		−	0.339094i	0.985522	−	0.169547i	$-0.0542305\pi$
$194$	−434473.			−0.828817
$195$	−388125.	−	400067.i	−0.730946	−	0.753435i
$196$	−475680.			−0.884454
$197$			878098.i			1.61205i	0.591885	+	0.806023i	$0.298384\pi$
$197$			878098.i			1.61205i	−0.591885	+	0.806023i	$0.701616\pi$
$198$		−	117877.i		−	0.213680i
$199$	621709.			1.11290			0.556448	−	0.830882i	$-0.312164\pi$
$199$	621709.			1.11290			0.556448	+	0.830882i	$0.312164\pi$
$200$	87561.7	+	2653.86i	0.154789	+	0.00469141i
$201$	787571.			1.37499
$202$			238911.i			0.411963i
$203$			15458.0i			0.0263276i
$204$	725665.			1.22085
$205$	311781.	+	321374.i	0.518162	+	0.534104i
$206$	−1.25733e6			−2.06434
$207$		−	15660.2i		−	0.0254022i
$208$		−	680262.i		−	1.09023i
$209$	−1.11381e6			−1.76378
$210$	37633.2	−	36509.9i	0.0588875	−	0.0571298i
$211$	531532.			0.821908			0.410954	−	0.911656i	$-0.365196\pi$
$211$	531532.			0.821908			0.410954	+	0.911656i	$0.365196\pi$
$212$		−	561342.i		−	0.857804i
$213$		−	982344.i		−	1.48359i
$214$	−1.28505e6			−1.91817
$215$	−586862.	+	569344.i	−0.865844	+	0.839999i
$216$	98768.1			0.144040
$217$			46453.9i			0.0669689i
$218$		−	1.00165e6i		−	1.42749i
$219$	198793.			0.280086
$220$	566281.	+	583704.i	0.788815	+	0.813085i
$221$	−934843.			−1.28753
$222$		−	436823.i		−	0.594872i
$223$		−	148971.i		−	0.200605i	−0.994957	−	0.100302i	$-0.968019\pi$
$223$		−	148971.i		−	0.200605i	0.994957	−	0.100302i	$-0.0319810\pi$
$224$	57433.0			0.0764788
$225$	2802.57	−	92468.0i	0.00369062	−	0.121769i
$226$	−345340.			−0.449754
$227$		−	912828.i		−	1.17577i	−0.808943	−	0.587887i	$-0.799960\pi$
$227$		−	912828.i		−	1.17577i	0.808943	−	0.587887i	$-0.200040\pi$
$228$		−	1.01904e6i		−	1.29824i
$229$	602691.			0.759462			0.379731	−	0.925097i	$-0.376017\pi$
$229$	602691.			0.759462			0.379731	+	0.925097i	$0.376017\pi$
$230$	160021.	+	164945.i	0.199461	+	0.205598i
$231$	−61841.8			−0.0762522
$232$			59277.9i			0.0723057i
$233$			1.08901e6i			1.31414i	0.753829	+	0.657070i	$0.228205\pi$
$233$			1.08901e6i			1.31414i	−0.753829	+	0.657070i	$0.771795\pi$
$234$	−138934.			−0.165871
$235$	−92077.6	+	89329.1i	−0.108764	+	0.105517i
$236$	−1.37525e6			−1.60732
$237$		−	975224.i		−	1.12780i
$238$		−	87938.2i		−	0.100632i
$239$	234332.			0.265361			0.132680	−	0.991159i	$-0.457642\pi$
$239$	234332.			0.265361			0.132680	+	0.991159i	$0.457642\pi$
$240$	746202.	−	723928.i	0.836234	−	0.811273i
$241$	−179624.			−0.199215			−0.0996076	−	0.995027i	$-0.531759\pi$
$241$	−179624.			−0.199215			−0.0996076	+	0.995027i	$0.531759\pi$
$242$		−	788663.i		−	0.865672i
$243$		−	223074.i		−	0.242345i
$244$	64200.0			0.0690336
$245$	652134.	+	672199.i	0.694100	+	0.715456i
$246$	1.02773e6			1.08278
$247$			1.31278e6i			1.36915i
$248$			178141.i			0.183922i
$249$	−1.45776e6			−1.49001
$250$	915354.	+	1.00258e6i	0.926273	+	1.01454i
$251$	−526227.			−0.527217			−0.263608	−	0.964630i	$-0.584913\pi$
$251$	−526227.			−0.527217			−0.263608	+	0.964630i	$0.584913\pi$
$252$		−	6144.29i		−	0.00609496i
$253$		−	271050.i		−	0.266225i
$254$	−1.20787e6			−1.17472
$255$	−994851.	−	1.02546e6i	−0.958093	−	0.987571i
$256$	1.24367e6			1.18606
$257$			1.81654e6i			1.71558i	0.513997	+	0.857792i	$0.328164\pi$
$257$			1.81654e6i			1.71558i	−0.513997	+	0.857792i	$0.671836\pi$
$258$			1.87674e6i			1.75531i
$259$	−24886.9			−0.0230527
$260$	687979.	−	667443.i	0.631163	−	0.612323i
$261$	62599.4			0.0568812
$262$			1.41034e6i			1.26932i
$263$		−	153539.i		−	0.136877i	−0.997655	−	0.0684385i	$-0.978198\pi$
$263$		−	153539.i		−	0.136877i	0.997655	−	0.0684385i	$-0.0218017\pi$
$264$	−237150.			−0.209418
$265$	−793250.	+	769572.i	−0.693898	+	0.673186i
$266$	−123490.			−0.107011
$267$			1.01532e6i			0.871619i
$268$			1.35435e6i			1.15185i
$269$	733721.			0.618230			0.309115	−	0.951025i	$-0.399967\pi$
$269$	733721.			0.618230			0.309115	+	0.951025i	$0.399967\pi$
$270$	1.06580e6	+	1.09859e6i	0.889746	+	0.917122i
$271$	595559.			0.492608			0.246304	−	0.969193i	$-0.420784\pi$
$271$	595559.			0.492608			0.246304	+	0.969193i	$0.420784\pi$
$272$		−	1.74366e6i		−	1.42903i
$273$			72889.4i			0.0591913i
$274$	−2.12643e6			−1.71110
$275$	48507.5	−	1.60046e6i	0.0386792	−	1.27618i
$276$	247987.			0.195955
$277$		−	1.32205e6i		−	1.03526i	−0.855605	−	0.517629i	$-0.826815\pi$
$277$		−	1.32205e6i		−	1.03526i	0.855605	−	0.517629i	$-0.173185\pi$
$278$		−	3.38170e6i		−	2.62436i
$279$	188122.			0.144687
$280$	−7976.57	−	8221.99i	−0.00608024	−	0.00626732i
$281$	−1.85236e6			−1.39946			−0.699729	−	0.714408i	$-0.746696\pi$
$281$	−1.85236e6			−1.39946			−0.699729	+	0.714408i	$0.746696\pi$
$282$			294457.i			0.220495i
$283$		−	840403.i		−	0.623766i	−0.950121	−	0.311883i	$-0.899040\pi$
$283$		−	840403.i		−	0.623766i	0.950121	−	0.311883i	$-0.100960\pi$
$284$	1.68930e6			1.24283
$285$	−1.44004e6	+	1.39705e6i	−1.05017	+	1.01883i
$286$	−2.40471e6			−1.73839
$287$		−	58552.1i		−	0.0419602i
$288$		−	232584.i		−	0.165234i
$289$	−976352.			−0.687641
$290$	−659345.	+	639664.i	−0.460381	+	0.446639i
$291$	923073.			0.639004
$292$			341856.i			0.234632i
$293$			130541.i			0.0888336i	0.999013	+	0.0444168i	$0.0141430\pi$
$293$			130541.i			0.0888336i	−0.999013	+	0.0444168i	$0.985857\pi$
$294$	2.14964e6			1.45043
$295$	1.88540e6	+	1.94341e6i	1.26139	+	1.30020i
$296$	−95435.8			−0.0633114
$297$		−	1.80529e6i		−	1.18756i
$298$			104432.i			0.0681227i
$299$	−319471.			−0.206659
$300$	1.46428e6	+	44380.2i	0.939337	+	0.0284699i
$301$	106922.			0.0680224
$302$		−	1.40677e6i		−	0.887577i
$303$		−	507585.i		−	0.317616i
$304$	−2.44859e6			−1.51961
$305$	−88015.0	−	90723.0i	−0.0541760	−	0.0558429i
$306$	−356120.			−0.217416
$307$			371862.i			0.225183i	0.993641	+	0.112591i	$0.0359151\pi$
$307$			371862.i			0.225183i	−0.993641	+	0.112591i	$0.964085\pi$
$308$		−	106347.i		−	0.0638775i
$309$	2.67130e6			1.59157
$310$	−1.98145e6	+	1.92230e6i	−1.17106	+	1.13610i
$311$	−1.29561e6			−0.759581			−0.379791	−	0.925073i	$-0.624004\pi$
$311$	−1.29561e6			−0.759581			−0.379791	+	0.925073i	$0.624004\pi$
$312$			279515.i			0.162562i
$313$		−	305809.i		−	0.176437i	−0.996101	−	0.0882183i	$-0.971883\pi$
$313$		−	305809.i		−	0.176437i	0.996101	−	0.0882183i	$-0.0281173\pi$
$314$	3.25887e6			1.86528
$315$	−8682.69	+	8423.52i	−0.00493035	+	0.00478319i
$316$	1.67705e6			0.944777
$317$			2.57648e6i			1.44005i	0.693946	+	0.720027i	$0.255871\pi$
$317$			2.57648e6i			1.44005i	−0.693946	+	0.720027i	$0.744129\pi$
$318$			2.53675e6i			1.40673i
$319$	1.08349e6			0.596138
$320$	973556.	+	1.00351e6i	0.531479	+	0.547831i
$321$	2.73020e6			1.47888
$322$		−	30051.8i		−	0.0161522i
$323$			3.36496e6i			1.79462i
$324$	1.85593e6			0.982198
$325$	−1.88637e6	−	57173.0i	−0.990646	−	0.0300250i
$326$	−708813.			−0.369392
$327$			2.12808e6i			1.10057i
$328$		−	224535.i		−	0.115239i
$329$	16775.9			0.00854469
$330$	−2.55907e6	−	2.63781e6i	−1.29359	−	1.33339i
$331$	2.22853e6			1.11801			0.559007	−	0.829163i	$-0.311182\pi$
$331$	2.22853e6			1.11801			0.559007	+	0.829163i	$0.311182\pi$
$332$		−	2.50685e6i		−	1.24820i
$333$			100783.i			0.0498056i
$334$	−2.97330e6			−1.45839
$335$	1.91388e6	−	1.85675e6i	0.931758	−	0.903945i
$336$	−135953.			−0.0656962
$337$			2.26386e6i			1.08586i	0.839777	+	0.542931i	$0.182686\pi$
$337$			2.26386e6i			1.08586i	−0.839777	+	0.542931i	$0.817314\pi$
$338$		−	51128.3i		−	0.0243428i
$339$	733702.			0.346753
$340$	1.76344e6	−	1.71080e6i	0.827302	−	0.802607i
$341$	3.25607e6			1.51638
$342$			500093.i			0.231199i
$343$		−	245331.i		−	0.112594i
$344$	410023.			0.186815
$345$	−339978.	−	350439.i	−0.153781	−	0.158513i
$346$	−1.12210e6			−0.503898
$347$		−	2.65136e6i		−	1.18207i	−0.806645	−	0.591037i	$-0.798719\pi$
$347$		−	2.65136e6i		−	1.18207i	0.806645	−	0.591037i	$-0.201281\pi$
$348$			991295.i			0.438788i
$349$	3.79224e6			1.66660			0.833301	−	0.552819i	$-0.186448\pi$
$349$	3.79224e6			1.66660			0.833301	+	0.552819i	$0.186448\pi$
$350$	5378.12	−	177446.i	0.00234672	−	0.0774276i
$351$	−2.12779e6			−0.921853
$352$		−	4.02562e6i		−	1.73171i
$353$			2.17078e6i			0.927213i	0.886041	+	0.463607i	$0.153445\pi$
$353$			2.17078e6i			0.927213i	−0.886041	+	0.463607i	$0.846555\pi$
$354$	6.21486e6			2.63587
$355$	−2.31594e6	−	2.38720e6i	−0.975342	−	1.00535i
$356$	−1.74601e6			−0.730167
$357$			186832.i			0.0775854i
$358$			4.04911e6i			1.66975i
$359$	−1.75257e6			−0.717695			−0.358847	−	0.933396i	$-0.616830\pi$
$359$	−1.75257e6			−0.717695			−0.358847	+	0.933396i	$0.616830\pi$
$360$	−33296.2	+	32302.4i	−0.0135406	+	0.0131365i
$361$	2.24925e6			0.908386
$362$			804814.i			0.322793i
$363$			1.67558e6i			0.667418i
$364$	−125345.			−0.0495854
$365$	483088.	−	468668.i	0.189799	−	0.184134i
$366$	−290125.			−0.113209
$367$			2.76408e6i			1.07124i	0.844460	+	0.535618i	$0.179921\pi$
$367$			2.76408e6i			1.07124i	−0.844460	+	0.535618i	$0.820079\pi$
$368$		−	595875.i		−	0.229370i
$369$	−237116.			−0.0906557
$370$	−1.02984e6	−	1.06153e6i	−0.391080	−	0.403113i
$371$	144525.			0.0545139
$372$			2.97902e6i			1.11613i
$373$			1.89476e6i			0.705151i	0.935783	+	0.352576i	$0.114694\pi$
$373$			1.89476e6i			0.705151i	−0.935783	+	0.352576i	$0.885306\pi$
$374$	−6.16380e6			−2.27861
$375$	−1.94474e6	−	2.13006e6i	−0.714141	−	0.782194i
$376$	64331.9			0.0234670
$377$		−	1.27704e6i		−	0.462756i
$378$		−	200156.i		−	0.0720508i
$379$	−209091.			−0.0747716			−0.0373858	−	0.999301i	$-0.511903\pi$
$379$	−209091.			−0.0747716			−0.0373858	+	0.999301i	$0.511903\pi$
$380$	−2.40245e6	−	2.47637e6i	−0.853486	−	0.879745i
$381$	2.56621e6			0.905691
$382$		−	6.89226e6i		−	2.41659i
$383$			3.11090e6i			1.08365i	0.840491	+	0.541825i	$0.182267\pi$
$383$			3.11090e6i			1.08365i	−0.840491	+	0.541825i	$0.817733\pi$
$384$	−941870.			−0.325959
$385$	−150282.	+	145796.i	−0.0516720	+	0.0501297i
$386$	−1.36366e6			−0.465842
$387$		−	432998.i		−	0.146963i
$388$			1.58737e6i			0.535303i
$389$	−1.50348e6			−0.503762			−0.251881	−	0.967758i	$-0.581049\pi$
$389$	−1.50348e6			−0.503762			−0.251881	+	0.967758i	$0.581049\pi$
$390$	−3.10903e6	+	3.01623e6i	−1.03506	+	1.00416i
$391$	−818876.			−0.270880
$392$		−	469646.i		−	0.154367i
$393$		−	2.99639e6i		−	0.978625i
$394$	6.82394e6			2.21460
$395$	−2.29916e6	−	2.36990e6i	−0.741440	−	0.764252i
$396$	−430668.			−0.138008
$397$			640908.i			0.204089i	0.994780	+	0.102044i	$0.0325384\pi$
$397$			640908.i			0.204089i	−0.994780	+	0.102044i	$0.967462\pi$
$398$		−	4.83148e6i		−	1.52888i
$399$	262365.			0.0825037
$400$	106639.	−	3.51844e6i	0.0333246	−	1.09951i
$401$	5.49966e6			1.70795			0.853975	−	0.520314i	$-0.174185\pi$
$401$	5.49966e6			1.70795			0.853975	+	0.520314i	$0.174185\pi$
$402$		−	6.12044e6i		−	1.88894i
$403$		−	3.83774e6i		−	1.17710i
$404$	872874.			0.266071
$405$	−2.54439e6	−	2.62267e6i	−0.770808	−	0.794524i
$406$	120128.			0.0361684
$407$			1.74438e6i			0.521982i
$408$			716459.i			0.213079i
$409$	−1.53891e6			−0.454888			−0.227444	−	0.973791i	$-0.573037\pi$
$409$	−1.53891e6			−0.454888			−0.227444	+	0.973791i	$0.573037\pi$
$410$	2.49749e6	−	2.42294e6i	0.733742	−	0.711841i
$411$	4.51777e6			1.31923
$412$			4.59373e6i			1.33328i
$413$		−	354076.i		−	0.102146i
$414$	−121700.			−0.0348970
$415$	−3.54251e6	+	3.43677e6i	−1.00970	+	0.979558i
$416$	−4.74477e6			−1.34425
$417$			7.18470e6i			2.02334i
$418$			8.65573e6i			2.42305i
$419$	−1.43328e6			−0.398837			−0.199419	−	0.979914i	$-0.563905\pi$
$419$	−1.43328e6			−0.398837			−0.199419	+	0.979914i	$0.563905\pi$
$420$	−133391.	−	137495.i	−0.0368980	−	0.0380333i
$421$	−4.41511e6			−1.21405			−0.607024	−	0.794683i	$-0.707637\pi$
$421$	−4.41511e6			−1.21405			−0.607024	+	0.794683i	$0.707637\pi$
$422$		−	4.13068e6i		−	1.12912i
$423$		−	67936.6i		−	0.0184609i
$424$	554221.			0.149716
$425$	−4.83518e6	−	146547.i	−1.29850	−	0.0393555i
$426$	−7.63407e6			−2.03813
$427$			16529.1i			0.00438712i
$428$			4.69501e6i			1.23888i
$429$	5.10900e6			1.34027
$430$	4.42453e6	+	4.56067e6i	1.15398	+	1.18948i
$431$	−323287.			−0.0838291			−0.0419146	−	0.999121i	$-0.513346\pi$
$431$	−323287.			−0.0838291			−0.0419146	+	0.999121i	$0.513346\pi$
$432$		−	3.96874e6i		−	1.02316i
$433$		−	408265.i		−	0.104646i	−0.998630	−	0.0523230i	$-0.983337\pi$
$433$		−	408265.i		−	0.104646i	0.998630	−	0.0523230i	$-0.0166625\pi$
$434$	361006.			0.0920006
$435$	1.40083e6	−	1.35902e6i	0.354946	−	0.344351i
$436$	−3.65958e6			−0.921966
$437$			1.14993e6i			0.288051i
$438$		−	1.54488e6i		−	0.384776i
$439$	−3.88258e6			−0.961521			−0.480761	−	0.876852i	$-0.659639\pi$
$439$	−3.88258e6			−0.961521			−0.480761	+	0.876852i	$0.659639\pi$
$440$	−576299.	+	559097.i	−0.141911	+	0.137675i
$441$	−495962.			−0.121437
$442$			7.26492e6i			1.76879i
$443$		−	2.35832e6i		−	0.570943i	−0.958387	−	0.285471i	$-0.907850\pi$
$443$		−	2.35832e6i		−	0.570943i	0.958387	−	0.285471i	$-0.0921502\pi$
$444$	−1.59596e6			−0.384206
$445$	2.39370e6	+	2.46734e6i	0.573019	+	0.590649i
$446$	−1.15770e6			−0.275587
$447$		−	221874.i		−	0.0525214i
$448$		−	182833.i		−	0.0430387i
$449$	6.47326e6			1.51533			0.757665	−	0.652644i	$-0.226340\pi$
$449$	6.47326e6			1.51533			0.757665	+	0.652644i	$0.226340\pi$
$450$	−718595.	−	21779.5i	−0.167283	−	0.00507011i
$451$	−4.10406e6			−0.950107
$452$			1.26172e6i			0.290480i
$453$			2.98880e6i			0.684307i
$454$	−7.09384e6			−1.61526
$455$	171842.	+	177129.i	0.0389135	+	0.0401108i
$456$	1.00611e6			0.226587
$457$		−	2.07856e6i		−	0.465557i	−0.972530	−	0.232779i	$-0.925218\pi$
$457$		−	2.07856e6i		−	0.465557i	0.972530	−	0.232779i	$-0.0747817\pi$
$458$		−	4.68368e6i		−	1.04333i
$459$	−5.45401e6			−1.20833
$460$	602635.	−	584647.i	0.132788	−	0.128825i
$461$	4.43220e6			0.971332			0.485666	−	0.874145i	$-0.338577\pi$
$461$	4.43220e6			0.971332			0.485666	+	0.874145i	$0.338577\pi$
$462$			480590.i			0.104754i
$463$		−	2.25296e6i		−	0.488428i	−0.969721	−	0.244214i	$-0.921470\pi$
$463$		−	2.25296e6i		−	0.488428i	0.969721	−	0.244214i	$-0.0785299\pi$
$464$	2.38193e6			0.513611
$465$	4.20975e6	−	4.08409e6i	0.902867	−	0.875917i
$466$	8.46300e6			1.80534
$467$		−	1.37928e6i		−	0.292658i	−0.989236	−	0.146329i	$-0.953254\pi$
$467$		−	1.37928e6i		−	0.292658i	0.989236	−	0.146329i	$-0.0467457\pi$
$468$			507604.i			0.107130i
$469$	−348696.			−0.0732006
$470$	694202.	+	715561.i	0.144958	+	0.149418i
$471$	−6.92374e6			−1.43810
$472$		−	1.35780e6i		−	0.280532i
$473$		−	7.49444e6i		−	1.54023i
$474$	−7.57874e6			−1.54936
$475$	−205794.	+	6.78997e6i	−0.0418503	+	1.38081i
$476$	−321287.			−0.0649944
$477$		−	585276.i		−	0.117778i
$478$		−	1.82106e6i		−	0.364548i
$479$	−9.86038e6			−1.96361			−0.981805	−	0.189894i	$-0.939185\pi$
$479$	−9.86038e6			−1.96361			−0.981805	+	0.189894i	$0.939185\pi$
$480$	−5.04933e6	−	5.20469e6i	−1.00030	−	1.03108i
$481$	2.05600e6			0.405192
$482$			1.39591e6i			0.273678i
$483$			63847.5i			0.0124531i
$484$	−2.88142e6			−0.559106
$485$	2.24317e6	−	2.17621e6i	0.433019	−	0.420094i
$486$	−1.73357e6			−0.332928
$487$		−	5.47539e6i		−	1.04615i	−0.852288	−	0.523073i	$-0.824786\pi$
$487$		−	5.47539e6i		−	1.04615i	0.852288	−	0.523073i	$-0.175214\pi$
$488$			63385.5i			0.0120487i
$489$	1.50593e6			0.284795
$490$	5.22385e6	−	5.06792e6i	0.982879	−	0.953541i
$491$	−5.62532e6			−1.05304			−0.526519	−	0.850164i	$-0.676503\pi$
$491$	−5.62532e6			−1.05304			−0.526519	+	0.850164i	$0.676503\pi$
$492$		−	3.75486e6i		−	0.699328i
$493$		−	3.27334e6i		−	0.606561i
$494$	1.02020e7			1.88091
$495$	590425.	+	608591.i	0.108306	+	0.111638i
$496$	7.15813e6			1.30646
$497$			434931.i			0.0789823i
$498$			1.13287e7i			2.04694i
$499$	9.22947e6			1.65930			0.829651	−	0.558282i	$-0.188539\pi$
$499$	9.22947e6			1.65930			0.829651	+	0.558282i	$0.188539\pi$
$500$	3.66299e6	−	3.34429e6i	0.655255	−	0.598245i
$501$	6.31702e6			1.12439
$502$			4.08946e6i			0.724280i
$503$			965448.i			0.170141i	0.996375	+	0.0850705i	$0.0271116\pi$
$503$			965448.i			0.170141i	−0.996375	+	0.0850705i	$0.972888\pi$
$504$	6066.35			0.00106378
$505$	−1.19667e6	−	1.23349e6i	−0.208807	−	0.215231i
$506$	−2.10641e6			−0.365734
$507$			108626.i			0.0187679i
$508$			4.41301e6i			0.758710i
$509$	3.27345e6			0.560030			0.280015	−	0.959996i	$-0.409661\pi$
$509$	3.27345e6			0.560030			0.280015	+	0.959996i	$0.409661\pi$
$510$	−7.96914e6	+	7.73126e6i	−1.35671	+	1.31621i
$511$	−88015.3			−0.0149110
$512$		−	7.83945e6i		−	1.32163i
$513$			7.65897e6i			1.28492i
$514$	1.41168e7			2.35684
$515$	6.49155e6	−	6.29778e6i	1.07853	−	1.04633i
$516$	6.85676e6			1.13369
$517$		−	1.17586e6i		−	0.193478i
$518$			193403.i			0.0316693i
$519$	2.38400e6			0.388497
$520$	658976.	+	679251.i	0.106871	+	0.110159i
$521$	−592762.			−0.0956723			−0.0478361	−	0.998855i	$-0.515233\pi$
$521$	−592762.			−0.0956723			−0.0478361	+	0.998855i	$0.515233\pi$
$522$		−	486478.i		−	0.0781424i
$523$			822001.i			0.131407i	0.997839	+	0.0657034i	$0.0209291\pi$
$523$			822001.i			0.131407i	−0.997839	+	0.0657034i	$0.979071\pi$
$524$	5.15276e6			0.819808
$525$	−11426.2	+	376998.i	−0.00180928	+	0.0596954i
$526$	−1.19320e6			−0.188039
$527$		−	9.83699e6i		−	1.54289i
$528$			9.52926e6i			1.48756i
$529$	−279841.			−0.0434783
$530$	5.98056e6	+	6.16457e6i	0.924810	+	0.953264i
$531$	−1.43388e6			−0.220688
$532$			451178.i			0.0691145i
$533$			4.83722e6i			0.737527i
$534$	7.89037e6			1.19741
$535$	6.63467e6	−	6.43663e6i	1.00216	−	0.972242i
$536$	−1.33717e6			−0.201037
$537$		−	8.60266e6i		−	1.28735i
$538$		−	5.70195e6i		−	0.849313i
$539$	−8.58422e6			−1.27271
$540$	4.01377e6	−	3.89396e6i	0.592335	−	0.574655i
$541$	6.54620e6			0.961604			0.480802	−	0.876829i	$-0.340346\pi$
$541$	6.54620e6			0.961604			0.480802	+	0.876829i	$0.340346\pi$
$542$		−	4.62826e6i		−	0.676736i
$543$		−	1.70989e6i		−	0.248868i
$544$	−1.21619e7			−1.76199
$545$	5.01710e6	+	5.17146e6i	0.723538	+	0.745800i
$546$	566444.			0.0813159
$547$			5.44281e6i			0.777776i	0.921285	+	0.388888i	$0.127141\pi$
$547$			5.44281e6i			0.777776i	−0.921285	+	0.388888i	$0.872859\pi$
$548$			7.76903e6i			1.10513i
$549$	66937.2			0.00947844
$550$	−1.24376e7	−	376966.i	−1.75320	−	0.0531367i
$551$	−4.59670e6			−0.645011
$552$			244841.i			0.0342009i
$553$			431779.i			0.0600411i
$554$	−1.02740e7			−1.42222
$555$	2.18798e6	+	2.25530e6i	0.301516	+	0.310793i
$556$	−1.23552e7			−1.69498
$557$		−	1.44274e6i		−	0.197037i	−0.995135	−	0.0985187i	$-0.968590\pi$
$557$		−	1.44274e6i		−	0.197037i	0.995135	−	0.0985187i	$-0.0314104\pi$
$558$		−	1.46195e6i		−	0.198769i
$559$	−8.83327e6			−1.19562
$560$	−330380.	+	320518.i	−0.0445188	+	0.0431899i
$561$	1.30955e7			1.75677
$562$			1.43952e7i			1.92255i
$563$			1.81146e6i			0.240857i	0.992722	+	0.120428i	$0.0384268\pi$
$563$			1.81146e6i			0.240857i	−0.992722	+	0.120428i	$0.961573\pi$
$564$	1.07581e6			0.142410
$565$	1.78297e6	−	1.72975e6i	0.234976	−	0.227962i
$566$	−6.53101e6			−0.856918
$567$			477833.i			0.0624193i
$568$			1.66787e6i			0.216915i
$569$	−9.21951e6			−1.19379			−0.596894	−	0.802320i	$-0.703599\pi$
$569$	−9.21951e6			−1.19379			−0.596894	+	0.802320i	$0.703599\pi$
$570$	1.08569e7	+	1.11909e7i	1.39965	+	1.44271i
$571$	1.07294e7			1.37716			0.688582	−	0.725158i	$-0.258234\pi$
$571$	1.07294e7			1.37716			0.688582	+	0.725158i	$0.258234\pi$
$572$			8.78574e6i			1.12276i
$573$			1.46432e7i			1.86315i
$574$	−455025.			−0.0576442
$575$	−1.65237e6	−	50080.8i	−0.208419	−	0.00631686i
$576$	−740410.			−0.0929856
$577$		−	9.83068e6i		−	1.22926i	−0.788815	−	0.614630i	$-0.789305\pi$
$577$		−	9.83068e6i		−	1.22926i	0.788815	−	0.614630i	$-0.210695\pi$
$578$			7.58751e6i			0.944669i
$579$	2.89721e6			0.359156
$580$	2.33705e6	+	2.40895e6i	0.288468	+	0.297343i
$581$	645421.			0.0793237
$582$		−	7.17346e6i		−	0.877852i
$583$		−	1.01301e7i		−	1.23436i
$584$	−337519.			−0.0409512
$585$	717312.	−	695900.i	0.0866599	−	0.0840732i
$586$	1.01447e6			0.122038
$587$			1.12085e7i			1.34262i	0.741177	+	0.671310i	$0.234268\pi$
$587$			1.12085e7i			1.34262i	−0.741177	+	0.671310i	$0.765732\pi$
$588$		−	7.85382e6i		−	0.936780i
$589$	−1.38139e7			−1.64070
$590$	1.51028e7	−	1.46520e7i	1.78619	−	1.73287i
$591$	−1.44980e7			−1.70742
$592$			3.83484e6i			0.449721i
$593$			1.38972e7i			1.62290i	0.584423	+	0.811449i	$0.301321\pi$
$593$			1.38972e7i			1.62290i	−0.584423	+	0.811449i	$0.698679\pi$
$594$	−1.40294e7			−1.63145
$595$	440469.	+	454021.i	0.0510062	+	0.0525755i
$596$	381547.			0.0439979
$597$			1.02649e7i			1.17874i
$598$			2.48270e6i			0.283904i
$599$	−5.10108e6			−0.580891			−0.290446	−	0.956892i	$-0.593804\pi$
$599$	−5.10108e6			−0.580891			−0.290446	+	0.956892i	$0.593804\pi$
$600$	−43817.2	+	1.44570e6i	−0.00496897	+	0.163946i
$601$	9.41211e6			1.06292			0.531461	−	0.847083i	$-0.321643\pi$
$601$	9.41211e6			1.06292			0.531461	+	0.847083i	$0.321643\pi$
$602$		−	830922.i		−	0.0934478i
$603$			1.41210e6i			0.158151i
$604$	−5.13972e6			−0.573254
$605$	3.95029e6	+	4.07183e6i	0.438774	+	0.452274i
$606$	−3.94459e6			−0.436335
$607$			1.61401e6i			0.177801i	0.996041	+	0.0889005i	$0.0283353\pi$
$607$			1.61401e6i			0.177801i	−0.996041	+	0.0889005i	$0.971665\pi$
$608$			1.70787e7i			1.87369i
$609$	−255222.			−0.0278852
$610$	−705034.	+	683989.i	−0.0767159	+	0.0744260i
$611$	−1.38592e6			−0.150188
$612$			1.30110e6i			0.140421i
$613$		−	1.39952e7i		−	1.50427i	−0.659007	−	0.752137i	$-0.729023\pi$
$613$		−	1.39952e7i		−	1.50427i	0.659007	−	0.752137i	$-0.270977\pi$
$614$	2.88984e6			0.309352
$615$	−5.30611e6	+	5.14773e6i	−0.565703	+	0.548817i
$616$	104998.			0.0111488
$617$			1.34927e7i			1.42687i	0.700720	+	0.713437i	$0.252862\pi$
$617$			1.34927e7i			1.42687i	−0.700720	+	0.713437i	$0.747138\pi$
$618$		−	2.07594e7i		−	2.18648i
$619$	−3.97835e6			−0.417327			−0.208664	−	0.977987i	$-0.566911\pi$
$619$	−3.97835e6			−0.417327			−0.208664	+	0.977987i	$0.566911\pi$
$620$	7.02324e6	+	7.23933e6i	0.733768	+	0.756344i
$621$	−1.86384e6			−0.193946
$622$			1.00686e7i			1.04350i
$623$		−	449533.i		−	0.0464025i
$624$	1.12316e7			1.15473
$625$	−9.74770e6	−	591420.i	−0.998164	−	0.0605614i
$626$	−2.37652e6			−0.242385
$627$		−	1.83898e7i		−	1.86813i
$628$		−	1.19065e7i		−	1.20471i
$629$	5.26999e6			0.531109
$630$	65461.6	+	67475.7i	0.00657105	+	0.00677323i
$631$	−1.37318e7			−1.37295			−0.686474	−	0.727155i	$-0.740842\pi$
$631$	−1.37318e7			−1.37295			−0.686474	+	0.727155i	$0.740842\pi$
$632$			1.65578e6i			0.164896i
$633$			8.77597e6i			0.870534i
$634$	2.00226e7			1.97832
$635$	6.23617e6	−	6.05002e6i	0.613738	−	0.595419i
$636$	9.26816e6			0.908554
$637$			1.01177e7i			0.987949i
$638$		−	8.42007e6i		−	0.818963i
$639$	1.76132e6			0.170642
$640$	−2.28884e6	+	2.22052e6i	−0.220885	+	0.214292i
$641$	−1.70708e7			−1.64100			−0.820499	−	0.571649i	$-0.806304\pi$
$641$	−1.70708e7			−1.64100			−0.820499	+	0.571649i	$0.806304\pi$
$642$		−	2.12171e7i		−	2.03165i
$643$		−	1.32344e7i		−	1.26234i	−0.775645	−	0.631169i	$-0.782576\pi$
$643$		−	1.32344e7i		−	1.26234i	0.775645	−	0.631169i	$-0.217424\pi$
$644$	−109796.			−0.0104321
$645$	−9.40028e6	−	9.68950e6i	−0.889695	−	0.917069i
$646$	2.61500e7			2.46542
$647$			6.34727e6i			0.596110i	0.954549	+	0.298055i	$0.0963378\pi$
$647$			6.34727e6i			0.596110i	−0.954549	+	0.298055i	$0.903662\pi$
$648$			1.83239e6i			0.171427i
$649$	−2.48180e7			−2.31289
$650$	−444308.	+	1.46595e7i	−0.0412478	+	1.36093i
$651$	−766987.			−0.0709309
$652$			2.58969e6i			0.238577i
$653$		−	1.60903e7i		−	1.47666i	−0.674437	−	0.738332i	$-0.735614\pi$
$653$		−	1.60903e7i		−	1.47666i	0.674437	−	0.738332i	$-0.264386\pi$
$654$	1.65379e7			1.51195
$655$	−7.06418e6	−	7.28153e6i	−0.643367	−	0.663162i
$656$	−9.02235e6			−0.818578
$657$			356432.i			0.0322154i
$658$		−	130370.i		−	0.0117385i
$659$	−2.11630e6			−0.189830			−0.0949148	−	0.995485i	$-0.530258\pi$
$659$	−2.11630e6			−0.189830			−0.0949148	+	0.995485i	$0.530258\pi$
$660$	−9.63737e6	+	9.34970e6i	−0.861189	+	0.835483i
$661$	5.77601e6			0.514191			0.257095	−	0.966386i	$-0.417235\pi$
$661$	5.77601e6			0.514191			0.257095	+	0.966386i	$0.417235\pi$
$662$		−	1.73185e7i		−	1.53591i
$663$		−	1.54349e7i		−	1.36370i
$664$	2.47505e6			0.217853
$665$	637574.	−	618543.i	0.0559083	−	0.0542395i
$666$	783216.			0.0684220
$667$		−	1.11863e6i		−	0.0973577i
$668$			1.08631e7i			0.941919i
$669$	2.45962e6			0.212473
$670$	−1.44293e7	−	1.48733e7i	−1.24182	−	1.28003i
$671$	1.15857e6			0.0993378
$672$			948259.i			0.0810035i
$673$		−	8.72533e6i		−	0.742582i	−0.928517	−	0.371291i	$-0.878915\pi$
$673$		−	8.72533e6i		−	0.742582i	0.928517	−	0.371291i	$-0.121085\pi$
$674$	1.75931e7			1.49174
$675$	−1.10053e7	−	333556.i	−0.929703	−	0.0281779i
$676$	−186800.			−0.0157221
$677$		−	2.64813e6i		−	0.222058i	−0.993817	−	0.111029i	$-0.964585\pi$
$677$		−	2.64813e6i		−	0.222058i	0.993817	−	0.111029i	$-0.0354147\pi$
$678$		−	5.70180e6i		−	0.476363i
$679$	−408689.			−0.0340188
$680$	1.68910e6	+	1.74107e6i	0.140082	+	0.144392i
$681$	1.50714e7			1.24534
$682$		−	2.53038e7i		−	2.08317i
$683$			2.03196e6i			0.166673i	0.996521	+	0.0833363i	$0.0265576\pi$
$683$			2.03196e6i			0.166673i	−0.996521	+	0.0833363i	$0.973442\pi$
$684$	1.82712e6			0.149323
$685$	1.09787e7	−	1.06510e7i	0.893970	−	0.867285i
$686$	−1.90653e6			−0.154680
$687$			9.95085e6i			0.804393i
$688$		−	1.64757e7i		−	1.32701i
$689$	−1.19398e7			−0.958181
$690$	−2.72336e6	+	2.64207e6i	−0.217762	+	0.211262i
$691$	1.68677e7			1.34388			0.671942	−	0.740604i	$-0.265460\pi$
$691$	1.68677e7			1.34388			0.671942	+	0.740604i	$0.265460\pi$
$692$			4.09967e6i			0.325449i
$693$		−	110881.i		−	0.00877051i
$694$	−2.06044e7			−1.62391
$695$	1.69384e7	+	1.74596e7i	1.33018	+	1.37111i
$696$	−978720.			−0.0765835
$697$			1.23989e7i			0.966719i
$698$		−	2.94705e7i		−	2.28955i
$699$	−1.79803e7			−1.39189
$700$	−648308.	−	19649.3i	−0.0500077	−	0.00151566i
$701$	−9.68545e6			−0.744431			−0.372216	−	0.928146i	$-0.621402\pi$
$701$	−9.68545e6			−0.744431			−0.372216	+	0.928146i	$0.621402\pi$
$702$			1.65357e7i			1.26642i
$703$		−	7.40057e6i		−	0.564776i
$704$	−1.28152e7			−0.974526
$705$	−1.47489e6	−	1.52027e6i	−0.111760	−	0.115198i
$706$	1.68698e7			1.27379
$707$			224733.i			0.0169090i
$708$		−	2.27063e7i		−	1.70241i
$709$	−6.35593e6			−0.474858			−0.237429	−	0.971405i	$-0.576305\pi$
$709$	−6.35593e6			−0.474858			−0.237429	+	0.971405i	$0.576305\pi$
$710$	−1.85516e7	+	1.79978e7i	−1.38113	+	1.33991i
$711$	1.74856e6			0.129720
$712$		−	1.72386e6i		−	0.127439i
$713$		−	3.36167e6i		−	0.247646i
$714$	1.45192e6			0.106585
$715$	1.24154e7	−	1.20448e7i	0.908230	−	0.881120i
$716$	1.47937e7			1.07843
$717$			3.86898e6i			0.281060i
$718$			1.36197e7i			0.985955i
$719$	2.63364e7			1.89991			0.949956	−	0.312384i	$-0.101128\pi$
$719$	2.63364e7			1.89991			0.949956	+	0.312384i	$0.101128\pi$
$720$	1.29799e6	+	1.33792e6i	0.0933124	+	0.0961835i
$721$	−1.18272e6			−0.0847310
$722$		−	1.74796e7i		−	1.24792i
$723$		−	2.96572e6i		−	0.211001i
$724$	2.94043e6			0.208480
$725$	200191.	−	6.60511e6i	0.0141449	−	0.466697i
$726$	1.30214e7			0.916887
$727$			1.98997e7i			1.39640i	0.715902	+	0.698200i	$0.246016\pi$
$727$			1.98997e7i			1.39640i	−0.715902	+	0.698200i	$0.753984\pi$
$728$		−	123755.i		−	0.00865434i
$729$	−1.22009e7			−0.850301
$730$	−3.64215e6	−	3.75421e6i	−0.252959	−	0.260742i
$731$	−2.26416e7			−1.56716
$732$			1.05999e6i			0.0731178i
$733$		−	1.47917e7i		−	1.01685i	−0.861106	−	0.508425i	$-0.830228\pi$
$733$		−	1.47917e7i		−	1.01685i	0.861106	−	0.508425i	$-0.169772\pi$
$734$	2.14804e7			1.47164
$735$	−1.10985e7	+	1.07672e7i	−0.757784	+	0.735164i
$736$	−4.15618e6			−0.282813
$737$			2.44410e7i			1.65748i
$738$			1.84270e6i			0.124541i
$739$	2.93771e7			1.97878			0.989391	−	0.145278i	$-0.0464075\pi$
$739$	2.93771e7			1.97878			0.989391	+	0.145278i	$0.0464075\pi$
$740$	−3.87835e6	+	3.76258e6i	−0.260356	+	0.252584i
$741$	−2.16750e7			−1.45015
$742$		−	1.12314e6i		−	0.0748902i
$743$		−	8.89487e6i		−	0.591109i	−0.955326	−	0.295555i	$-0.904496\pi$
$743$		−	8.89487e6i		−	0.591109i	0.955326	−	0.295555i	$-0.0955044\pi$
$744$	−2.94123e6			−0.194803
$745$	−523082.	−	539176.i	−0.0345286	−	0.0355910i
$746$	1.47247e7			0.968723
$747$		−	2.61374e6i		−	0.171380i
$748$			2.25198e7i			1.47167i
$749$	−1.20879e6			−0.0787312
$750$	−1.65533e7	+	1.51131e7i	−1.07456	+	0.981073i
$751$	−2.45791e7			−1.59025			−0.795125	−	0.606445i	$-0.792595\pi$
$751$	−2.45791e7			−1.59025			−0.795125	+	0.606445i	$0.792595\pi$
$752$		−	2.58501e6i		−	0.166693i
$753$		−	8.68838e6i		−	0.558408i
$754$	−9.92426e6			−0.635725
$755$	7.04630e6	+	7.26310e6i	0.449877	+	0.463718i
$756$	−731281.			−0.0465350
$757$			2.57709e7i			1.63452i	0.576268	+	0.817261i	$0.304508\pi$
$757$			2.57709e7i			1.63452i	−0.576268	+	0.817261i	$0.695492\pi$
$758$			1.62490e6i			0.102720i
$759$	4.47523e6			0.281975
$760$	2.44496e6	−	2.37198e6i	0.153546	−	0.148962i
$761$	1.91790e7			1.20051			0.600253	−	0.799810i	$-0.295067\pi$
$761$	1.91790e7			1.20051			0.600253	+	0.799810i	$0.295067\pi$
$762$		−	1.99428e7i		−	1.24422i
$763$		−	942205.i		−	0.0585915i
$764$	−2.51813e7			−1.56079
$765$	1.83863e6	−	1.78375e6i	0.113590	−	0.110200i
$766$	2.41757e7			1.48870
$767$			2.92516e7i			1.79540i
$768$			2.05339e7i			1.25623i
$769$	1.95840e7			1.19422			0.597111	−	0.802159i	$-0.296315\pi$
$769$	1.95840e7			1.19422			0.597111	+	0.802159i	$0.296315\pi$
$770$	1.13302e6	+	1.16788e6i	0.0688672	+	0.0709861i
$771$	−2.99923e7			−1.81708
$772$			4.98221e6i			0.300870i
$773$			1.93830e7i			1.16674i	0.812208	+	0.583368i	$0.198266\pi$
$773$			1.93830e7i			1.16674i	−0.812208	+	0.583368i	$0.801734\pi$
$774$	−3.36495e6			−0.201895
$775$	601610.	−	1.98495e7i	0.0359799	−	1.18712i
$776$	−1.56723e6			−0.0934286
$777$		−	410900.i		−	0.0244165i
$778$			1.16840e7i			0.692058i
$779$	1.74115e7			1.02800
$780$	1.10200e7	+	1.13590e7i	0.648550	+	0.668504i
$781$	3.04854e7			1.78840
$782$			6.36371e6i			0.372129i
$783$		−	7.45045e6i		−	0.434288i
$784$	−1.88715e7			−1.09652
$785$	−1.68254e7	+	1.63232e7i	−0.974522	+	0.945433i
$786$	−2.32858e7			−1.34442
$787$		−	2.91524e7i		−	1.67779i	−0.544294	−	0.838895i	$-0.683202\pi$
$787$		−	2.91524e7i		−	1.67779i	0.544294	−	0.838895i	$-0.316798\pi$
$788$		−	2.49316e7i		−	1.43033i
$789$	2.53504e6			0.144975
$790$	−1.84171e7	+	1.78674e7i	−1.04992	+	1.01858i
$791$	−324845.			−0.0184602
$792$		−	425205.i		−	0.0240871i
$793$		−	1.36554e6i		−	0.0771116i
$794$	4.98067e6			0.280373
$795$	−1.27062e7	−	1.30971e7i	−0.713013	−	0.734950i
$796$	−1.76521e7			−0.987445
$797$			1.26902e7i			0.707659i	0.935310	+	0.353829i	$0.115121\pi$
$797$			1.26902e7i			0.707659i	−0.935310	+	0.353829i	$0.884879\pi$
$798$		−	2.03891e6i		−	0.113342i
$799$	−3.55243e6			−0.196860
$800$	−2.45408e7	−	743796.i	−1.35570	−	0.0410893i
$801$	−1.82046e6			−0.100253
$802$		−	4.27394e7i		−	2.34635i
$803$			6.16921e6i			0.337630i
$804$	−2.23613e7			−1.21999
$805$	150525.	+	155156.i	0.00818688	+	0.00843878i
$806$	−2.98242e7			−1.61708
$807$			1.21143e7i			0.654806i
$808$			861801.i			0.0464385i
$809$	2.51445e7			1.35074			0.675369	−	0.737480i	$-0.263985\pi$
$809$	2.51445e7			1.35074			0.675369	+	0.737480i	$0.263985\pi$
$810$	−2.03815e7	+	1.97732e7i	−1.09150	+	1.05892i
$811$	−2.62629e7			−1.40214			−0.701069	−	0.713094i	$-0.747293\pi$
$811$	−2.62629e7			−1.40214			−0.701069	+	0.713094i	$0.747293\pi$
$812$		−	438895.i		−	0.0233599i
$813$			9.83310e6i			0.521752i
$814$	1.35561e7			0.717089
$815$	3.65957e6	−	3.55033e6i	0.192990	−	0.187230i
$816$	2.87891e7			1.51357
$817$			3.17953e7i			1.66651i
$818$			1.19593e7i			0.624917i
$819$	−130689.			−0.00680817
$820$	−8.85234e6	−	9.12470e6i	−0.459752	−	0.473897i
$821$	−3.02297e7			−1.56522			−0.782612	−	0.622510i	$-0.786113\pi$
$821$	−3.02297e7			−1.56522			−0.782612	+	0.622510i	$0.786113\pi$
$822$		−	3.51089e7i		−	1.81233i
$823$			5.41689e6i			0.278773i	0.990238	+	0.139386i	$0.0445130\pi$
$823$			5.41689e6i			0.278773i	−0.990238	+	0.139386i	$0.955487\pi$
$824$	−4.53546e6			−0.232704
$825$	2.64247e7	+	800893.i	1.35168	+	0.0409675i
$826$	−2.75162e6			−0.140326
$827$		−	1.84505e7i		−	0.938088i	−0.883175	−	0.469044i	$-0.844599\pi$
$827$		−	1.84505e7i		−	0.938088i	0.883175	−	0.469044i	$-0.155401\pi$
$828$			444636.i			0.0225387i
$829$	2.08062e7			1.05149			0.525747	−	0.850641i	$-0.323786\pi$
$829$	2.08062e7			1.05149			0.525747	+	0.850641i	$0.323786\pi$
$830$	2.67081e7	+	2.75298e7i	1.34570	+	1.38710i
$831$	2.18280e7			1.09651
$832$			1.51045e7i			0.756482i
$833$			2.59340e7i			1.29496i
$834$	5.58343e7			2.77962
$835$	1.53510e7	−	1.48928e7i	0.761941	−	0.739198i
$836$	3.16242e7			1.56496
$837$		−	2.23899e7i		−	1.10469i
$838$			1.11384e7i			0.547915i
$839$	3.38768e7			1.66149			0.830744	−	0.556655i	$-0.187915\pi$
$839$	3.38768e7			1.66149			0.830744	+	0.556655i	$0.187915\pi$
$840$	135751.	−	131699.i	0.00663811	−	0.00643997i
$841$	−1.60396e7			−0.781994
$842$			3.43110e7i			1.66784i
$843$		−	3.05838e7i		−	1.48225i
$844$	−1.50917e7			−0.729258
$845$	256094.	+	263973.i	0.0123384	+	0.0127180i
$846$	−527955.			−0.0253613
$847$		−	741860.i		−	0.0355315i
$848$		−	2.22700e7i		−	1.06348i
$849$	1.38756e7			0.660669
$850$	−1.13886e6	+	3.75756e7i	−0.0540658	+	1.78385i
$851$	1.80096e6			0.0852471
$852$			2.78915e7i			1.31635i
$853$			1.79175e7i			0.843150i	0.906793	+	0.421575i	$0.138523\pi$
$853$			1.79175e7i			0.843150i	−0.906793	+	0.421575i	$0.861477\pi$
$854$	128452.			0.00602695
$855$	−2.50489e6	−	2.58196e6i	−0.117185	−	0.120791i
$856$	−4.63545e6			−0.216226
$857$			730568.i			0.0339788i	0.999856	+	0.0169894i	$0.00540816\pi$
$857$			730568.i			0.0339788i	−0.999856	+	0.0169894i	$0.994592\pi$
$858$		−	3.97034e7i		−	1.84124i
$859$	2.57647e7			1.19136			0.595679	−	0.803223i	$-0.296883\pi$
$859$	2.57647e7			1.19136			0.595679	+	0.803223i	$0.296883\pi$
$860$	1.66626e7	−	1.61653e7i	0.768242	−	0.745310i
$861$	966737.			0.0444427
$862$			2.51235e6i			0.115163i
$863$			1.02389e7i			0.467980i	0.972239	+	0.233990i	$0.0751782\pi$
$863$			1.02389e7i			0.467980i	−0.972239	+	0.233990i	$0.924822\pi$
$864$	−2.76816e7			−1.26156
$865$	5.79337e6	−	5.62044e6i	0.263264	−	0.255405i
$866$	−3.17274e6			−0.143761
$867$		−	1.61203e7i		−	0.728324i
$868$		−	1.31896e6i		−	0.0594198i
$869$	3.02644e7			1.35951
$870$	−1.05613e7	−	1.08862e7i	−0.473063	−	0.487618i
$871$	2.88072e7			1.28663
$872$		−	3.61315e6i		−	0.160914i
$873$			1.65505e6i			0.0734981i
$874$	8.93646e6			0.395719
$875$	861032.	+	943083.i	0.0380188	+	0.0416418i
$876$	−5.64429e6			−0.248513
$877$		−	3.81971e7i		−	1.67699i	−0.544907	−	0.838497i	$-0.683435\pi$
$877$		−	3.81971e7i		−	1.67699i	0.544907	−	0.838497i	$-0.316565\pi$
$878$			3.01726e7i			1.32092i
$879$	−2.15532e6			−0.0940891
$880$	2.24659e7	+	2.31571e7i	0.977951	+	1.00804i
$881$	3.54313e7			1.53797			0.768983	−	0.639269i	$-0.220763\pi$
$881$	3.54313e7			1.53797			0.768983	+	0.639269i	$0.220763\pi$
$882$			3.85426e6i			0.166828i
$883$			1.38612e7i			0.598270i	0.954211	+	0.299135i	$0.0966982\pi$
$883$			1.38612e7i			0.598270i	−0.954211	+	0.299135i	$0.903302\pi$
$884$	2.65428e7			1.14239
$885$	−3.20870e7	+	3.11293e7i	−1.37712	+	1.33601i
$886$	−1.83271e7			−0.784351
$887$			1.95520e7i			0.834417i	0.908811	+	0.417208i	$0.136991\pi$
$887$			1.95520e7i			0.834417i	−0.908811	+	0.417208i	$0.863009\pi$
$888$		−	1.57571e6i		−	0.0670570i
$889$	−1.13619e6			−0.0482165
$890$	1.91744e7	−	1.86021e7i	0.811423	−	0.787202i
$891$	3.34925e7			1.41336
$892$			4.22971e6i			0.177991i
$893$			4.98862e6i			0.209340i
$894$	−1.72424e6			−0.0721530
$895$	−2.02814e7	−	2.09054e7i	−0.846330	−	0.872370i
$896$	417012.			0.0173531
$897$		−	5.27470e6i		−	0.218885i
$898$		−	5.03055e7i		−	2.08173i
$899$	1.34378e7			0.554536
$900$	−79572.7	+	2.62543e6i	−0.00327460	+	0.108042i
$901$	−3.06043e7			−1.25594
$902$			3.18938e7i			1.30524i
$903$			1.76536e6i			0.0720467i
$904$	−1.24571e6			−0.0506986
$905$	−4.03119e6	−	4.15522e6i	−0.163611	−	0.168645i
$906$	2.32268e7			0.940088
$907$		−	1.43934e7i		−	0.580960i	−0.956881	−	0.290480i	$-0.906185\pi$
$907$		−	1.43934e7i		−	0.580960i	0.956881	−	0.290480i	$-0.0938149\pi$
$908$			2.59177e7i			1.04324i
$909$	910091.			0.0365321
$910$	1.37652e6	−	1.33543e6i	0.0551034	−	0.0534586i
$911$	−1.75068e7			−0.698893			−0.349446	−	0.936956i	$-0.613630\pi$
$911$	−1.75068e7			−0.698893			−0.349446	+	0.936956i	$0.613630\pi$
$912$		−	4.04280e7i		−	1.60952i
$913$		−	4.52392e7i		−	1.79613i
$914$	−1.61531e7			−0.639573
$915$	1.49790e6	−	1.45319e6i	0.0591467	−	0.0573812i
$916$	−1.71121e7			−0.673851
$917$			1.32665e6i			0.0520993i
$918$			4.23846e7i			1.65997i
$919$	−3.61554e7			−1.41216			−0.706081	−	0.708131i	$-0.749539\pi$
$919$	−3.61554e7			−1.41216			−0.706081	+	0.708131i	$0.749539\pi$
$920$	577230.	+	594990.i	0.0224843	+	0.0231761i
$921$	−6.13970e6			−0.238505
$922$		−	3.44439e7i		−	1.33440i
$923$		−	3.59314e7i		−	1.38826i
$924$	1.75586e6			0.0676566
$925$	1.06340e7	+	322302.i	0.408643	+	0.0123854i
$926$	−1.75084e7			−0.670993
$927$			4.78959e6i			0.183062i
$928$		−	1.66138e7i		−	0.633283i
$929$	4.18440e6			0.159072			0.0795361	−	0.996832i	$-0.474656\pi$
$929$	4.18440e6			0.159072			0.0795361	+	0.996832i	$0.474656\pi$
$930$	−3.17386e7	−	3.27151e7i	−1.20332	−	1.24034i
$931$	3.64187e7			1.37705
$932$		−	3.09200e7i		−	1.16600i
$933$		−	2.13915e7i		−	0.804520i
$934$	−1.07188e7			−0.402047
$935$	3.18234e7	−	3.08735e7i	1.19047	−	1.15493i
$936$	−501165.			−0.0186978
$937$			2.01116e7i			0.748337i	0.927361	+	0.374168i	$0.122072\pi$
$937$			2.01116e7i			0.748337i	−0.927361	+	0.374168i	$0.877928\pi$
$938$			2.70981e6i			0.100562i
$939$	5.04911e6			0.186875
$940$	2.61434e6	−	2.53630e6i	0.0965033	−	0.0936228i
$941$	−2.16937e7			−0.798654			−0.399327	−	0.916808i	$-0.630756\pi$
$941$	−2.16937e7			−0.798654			−0.399327	+	0.916808i	$0.630756\pi$
$942$			5.38063e7i			1.97563i
$943$			4.23717e6i			0.155166i
$944$	−5.45598e7			−1.99271
$945$	1.00255e6	+	1.03340e6i	0.0365196	+	0.0376433i
$946$	−5.82414e7			−2.11594
$947$		−	3.88024e7i		−	1.40600i	−0.711192	−	0.702998i	$-0.751844\pi$
$947$		−	3.88024e7i		−	1.40600i	0.711192	−	0.702998i	$-0.248156\pi$
$948$			2.76893e7i			1.00067i
$949$	7.27129e6			0.262087
$950$	5.27667e7	+	1.59928e6i	1.89693	+	0.0574931i
$951$	−4.25395e7			−1.52525
$952$		−	317211.i		−	0.0113437i
$953$		−	4.09847e7i		−	1.46181i	−0.682481	−	0.730903i	$-0.739099\pi$
$953$		−	4.09847e7i		−	1.46181i	0.682481	−	0.730903i	$-0.260901\pi$
$954$	−4.54834e6			−0.161801
$955$	3.45222e7	+	3.55844e7i	1.22487	+	1.26256i
$956$	−6.65334e6			−0.235448
$957$			1.78891e7i			0.631406i
$958$			7.66278e7i			2.69757i
$959$	−2.00024e6			−0.0702320
$960$	−1.65687e7	+	1.60741e7i	−0.580242	+	0.562922i
$961$	1.17539e7			0.410558
$962$		−	1.59778e7i		−	0.556646i
$963$			4.89519e6i			0.170100i
$964$	5.10004e6			0.176759
$965$	7.04052e6	−	6.83036e6i	0.243381	−	0.236116i
$966$	496177.			0.0171078
$967$			3.06485e7i			1.05401i	0.849864	+	0.527003i	$0.176684\pi$
$967$			3.06485e7i			1.05401i	−0.849864	+	0.527003i	$0.823316\pi$
$968$		−	2.84487e6i		−	0.0975830i
$969$	−5.55578e7			−1.90080
$970$	−1.69119e7	−	1.74323e7i	−0.577117	−	0.594873i
$971$	−4.41972e7			−1.50434			−0.752172	−	0.658967i	$-0.770994\pi$
$971$	−4.41972e7			−1.50434			−0.752172	+	0.658967i	$0.770994\pi$
$972$			6.33370e6i			0.215026i
$973$		−	3.18102e6i		−	0.107717i
$974$	−4.25508e7			−1.43718
$975$	943967.	−	3.11453e7i	0.0318013	−	1.04925i
$976$	2.54699e6			0.0855859
$977$		−	2.11557e7i		−	0.709073i	−0.935042	−	0.354537i	$-0.884639\pi$
$977$		−	2.11557e7i		−	0.709073i	0.935042	−	0.354537i	$-0.115361\pi$
$978$		−	1.17030e7i		−	0.391246i
$979$	−3.15089e7			−1.05069
$980$	−1.85159e7	−	1.90856e7i	−0.615857	−	0.634806i
$981$	−3.81561e6			−0.126588
$982$			4.37160e7i			1.44664i
$983$			2.27966e7i			0.752466i	0.926525	+	0.376233i	$0.122781\pi$
$983$			2.27966e7i			0.752466i	−0.926525	+	0.376233i	$0.877219\pi$
$984$	3.70723e6			0.122057
$985$	−3.52317e7	+	3.41801e7i	−1.15703	+	1.12249i
$986$	−2.54381e7			−0.833282
$987$			276982.i			0.00905021i
$988$		−	3.72736e7i		−	1.21481i
$989$	−7.73750e6			−0.251542
$990$	4.72953e6	−	4.58836e6i	0.153366	−	0.148789i
$991$	3.93077e7			1.27143			0.635716	−	0.771923i	$-0.280705\pi$
$991$	3.93077e7			1.27143			0.635716	+	0.771923i	$0.280705\pi$
$992$		−	4.99273e7i		−	1.61086i
$993$			3.67945e7i			1.18416i
$994$	3.37997e6			0.108504
$995$	2.42001e7	+	2.49447e7i	0.774925	+	0.798767i
$996$	4.13899e7			1.32204
$997$			2.02220e7i			0.644298i	0.946689	+	0.322149i	$0.104405\pi$
$997$			2.02220e7i			0.644298i	−0.946689	+	0.322149i	$0.895595\pi$
$998$		−	7.17248e7i		−	2.27952i
$999$	1.19950e7			0.380266

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.6.b.a.24.10	✓	54
5.2	odd	4		575.6.a.l.1.22		27
5.3	odd	4		575.6.a.m.1.6		27
5.4	even	2	inner	115.6.b.a.24.45	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.6.b.a.24.10	✓	54	1.1	even	1	trivial
115.6.b.a.24.45	yes	54	5.4	even	2	inner
575.6.a.l.1.22		27	5.2	odd	4
575.6.a.m.1.6		27	5.3	odd	4

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	115.6.b.a.24.10

Level	$115$
Weight	$6$
Character	115.24
Analytic conductor	$18.444$
Analytic rank	$0$
Dimension	$54$
Inner twists	$2$