LMFDB - Embedded newform 10.6.b.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,6,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	10.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:	$1.60383819813$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.6.b.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000i q^{2} -14.0000i q^{3} -16.0000 q^{4} +(55.0000 - 10.0000i) q^{5} -56.0000 q^{6} +158.000i q^{7} +64.0000i q^{8} +47.0000 q^{9} +(-40.0000 - 220.000i) q^{10} -148.000 q^{11} +224.000i q^{12} -684.000i q^{13} +632.000 q^{14} +(-140.000 - 770.000i) q^{15} +256.000 q^{16} +2048.00i q^{17} -188.000i q^{18} -2220.00 q^{19} +(-880.000 + 160.000i) q^{20} +2212.00 q^{21} +592.000i q^{22} +1246.00i q^{23} +896.000 q^{24} +(2925.00 - 1100.00i) q^{25} -2736.00 q^{26} -4060.00i q^{27} -2528.00i q^{28} +270.000 q^{29} +(-3080.00 + 560.000i) q^{30} -2048.00 q^{31} -1024.00i q^{32} +2072.00i q^{33} +8192.00 q^{34} +(1580.00 + 8690.00i) q^{35} -752.000 q^{36} -4372.00i q^{37} +8880.00i q^{38} -9576.00 q^{39} +(640.000 + 3520.00i) q^{40} -2398.00 q^{41} -8848.00i q^{42} -2294.00i q^{43} +2368.00 q^{44} +(2585.00 - 470.000i) q^{45} +4984.00 q^{46} -10682.0i q^{47} -3584.00i q^{48} -8157.00 q^{49} +(-4400.00 - 11700.0i) q^{50} +28672.0 q^{51} +10944.0i q^{52} -2964.00i q^{53} -16240.0 q^{54} +(-8140.00 + 1480.00i) q^{55} -10112.0 q^{56} +31080.0i q^{57} -1080.00i q^{58} +39740.0 q^{59} +(2240.00 + 12320.0i) q^{60} -42298.0 q^{61} +8192.00i q^{62} +7426.00i q^{63} -4096.00 q^{64} +(-6840.00 - 37620.0i) q^{65} +8288.00 q^{66} +32098.0i q^{67} -32768.0i q^{68} +17444.0 q^{69} +(34760.0 - 6320.00i) q^{70} -4248.00 q^{71} +3008.00i q^{72} -30104.0i q^{73} -17488.0 q^{74} +(-15400.0 - 40950.0i) q^{75} +35520.0 q^{76} -23384.0i q^{77} +38304.0i q^{78} -35280.0 q^{79} +(14080.0 - 2560.00i) q^{80} -45419.0 q^{81} +9592.00i q^{82} +27826.0i q^{83} -35392.0 q^{84} +(20480.0 + 112640. i) q^{85} -9176.00 q^{86} -3780.00i q^{87} -9472.00i q^{88} +85210.0 q^{89} +(-1880.00 - 10340.0i) q^{90} +108072. q^{91} -19936.0i q^{92} +28672.0i q^{93} -42728.0 q^{94} +(-122100. + 22200.0i) q^{95} -14336.0 q^{96} -97232.0i q^{97} +32628.0i q^{98} -6956.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} + 110 q^{5} - 112 q^{6} + 94 q^{9} - 80 q^{10} - 296 q^{11} + 1264 q^{14} - 280 q^{15} + 512 q^{16} - 4440 q^{19} - 1760 q^{20} + 4424 q^{21} + 1792 q^{24} + 5850 q^{25} - 5472 q^{26} + 540 q^{29}+ \cdots - 13912 q^{99}+O(q^{100}) $ 2 * q - 32 * q^4 + 110 * q^5 - 112 * q^6 + 94 * q^9 - 80 * q^10 - 296 * q^11 + 1264 * q^14 - 280 * q^15 + 512 * q^16 - 4440 * q^19 - 1760 * q^20 + 4424 * q^21 + 1792 * q^24 + 5850 * q^25 - 5472 * q^26 + 540 * q^29 - 6160 * q^30 - 4096 * q^31 + 16384 * q^34 + 3160 * q^35 - 1504 * q^36 - 19152 * q^39 + 1280 * q^40 - 4796 * q^41 + 4736 * q^44 + 5170 * q^45 + 9968 * q^46 - 16314 * q^49 - 8800 * q^50 + 57344 * q^51 - 32480 * q^54 - 16280 * q^55 - 20224 * q^56 + 79480 * q^59 + 4480 * q^60 - 84596 * q^61 - 8192 * q^64 - 13680 * q^65 + 16576 * q^66 + 34888 * q^69 + 69520 * q^70 - 8496 * q^71 - 34976 * q^74 - 30800 * q^75 + 71040 * q^76 - 70560 * q^79 + 28160 * q^80 - 90838 * q^81 - 70784 * q^84 + 40960 * q^85 - 18352 * q^86 + 170420 * q^89 - 3760 * q^90 + 216144 * q^91 - 85456 * q^94 - 244200 * q^95 - 28672 * q^96 - 13912 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$-1$

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		−	14.0000i		−	0.898100i	−0.893507	−	0.449050i	$-0.851762\pi$
$3$		−	14.0000i		−	0.898100i	0.893507	−	0.449050i	$-0.148238\pi$
$4$	−16.0000			−0.500000
$5$	55.0000	−	10.0000i	0.983870	−	0.178885i
$5$	55.0000	−	10.0000i	0.983870	−	0.178885i
$6$	−56.0000			−0.635053
$7$			158.000i			1.21874i	0.792885	+	0.609371i	$0.208578\pi$
$7$			158.000i			1.21874i	−0.792885	+	0.609371i	$0.791422\pi$
$8$			64.0000i			0.353553i
$9$	47.0000			0.193416
$10$	−40.0000	−	220.000i	−0.126491	−	0.695701i
$11$	−148.000			−0.368791			−0.184395	−	0.982852i	$-0.559033\pi$
$11$	−148.000			−0.368791			−0.184395	+	0.982852i	$0.559033\pi$
$12$			224.000i			0.449050i
$13$		−	684.000i		−	1.12253i	−0.827636	−	0.561265i	$-0.810315\pi$
$13$		−	684.000i		−	1.12253i	0.827636	−	0.561265i	$-0.189685\pi$
$14$	632.000			0.861781
$15$	−140.000	−	770.000i	−0.160657	−	0.883614i
$16$	256.000			0.250000
$17$			2048.00i			1.71873i	0.511363	+	0.859365i	$0.329141\pi$
$17$			2048.00i			1.71873i	−0.511363	+	0.859365i	$0.670859\pi$
$18$		−	188.000i		−	0.136766i
$19$	−2220.00			−1.41081			−0.705406	−	0.708804i	$-0.749235\pi$
$19$	−2220.00			−1.41081			−0.705406	+	0.708804i	$0.749235\pi$
$20$	−880.000	+	160.000i	−0.491935	+	0.0894427i
$21$	2212.00			1.09455
$22$			592.000i			0.260774i
$23$			1246.00i			0.491132i	0.969380	+	0.245566i	$0.0789738\pi$
$23$			1246.00i			0.491132i	−0.969380	+	0.245566i	$0.921026\pi$
$24$	896.000			0.317526
$25$	2925.00	−	1100.00i	0.936000	−	0.352000i
$26$	−2736.00			−0.793748
$27$		−	4060.00i		−	1.07181i
$28$		−	2528.00i		−	0.609371i
$29$	270.000			0.0596168			0.0298084	−	0.999556i	$-0.490510\pi$
$29$	270.000			0.0596168			0.0298084	+	0.999556i	$0.490510\pi$
$30$	−3080.00	+	560.000i	−0.624809	+	0.113602i
$31$	−2048.00			−0.382759			−0.191380	−	0.981516i	$-0.561296\pi$
$31$	−2048.00			−0.382759			−0.191380	+	0.981516i	$0.561296\pi$
$32$		−	1024.00i		−	0.176777i
$33$			2072.00i			0.331211i
$34$	8192.00			1.21533
$35$	1580.00	+	8690.00i	0.218015	+	1.19908i
$36$	−752.000			−0.0967078
$37$		−	4372.00i		−	0.525020i	−0.964929	−	0.262510i	$-0.915450\pi$
$37$		−	4372.00i		−	0.525020i	0.964929	−	0.262510i	$-0.0845503\pi$
$38$			8880.00i			0.997594i
$39$	−9576.00			−1.00814
$40$	640.000	+	3520.00i	0.0632456	+	0.347851i
$41$	−2398.00			−0.222787			−0.111393	−	0.993776i	$-0.535531\pi$
$41$	−2398.00			−0.222787			−0.111393	+	0.993776i	$0.535531\pi$
$42$		−	8848.00i		−	0.773966i
$43$		−	2294.00i		−	0.189200i	−0.995515	−	0.0946002i	$-0.969843\pi$
$43$		−	2294.00i		−	0.189200i	0.995515	−	0.0946002i	$-0.0301573\pi$
$44$	2368.00			0.184395
$45$	2585.00	−	470.000i	0.190296	−	0.0345992i
$46$	4984.00			0.347283
$47$		−	10682.0i		−	0.705355i	−0.935745	−	0.352678i	$-0.885271\pi$
$47$		−	10682.0i		−	0.705355i	0.935745	−	0.352678i	$-0.114729\pi$
$48$		−	3584.00i		−	0.224525i
$49$	−8157.00			−0.485333
$50$	−4400.00	−	11700.0i	−0.248902	−	0.661852i
$51$	28672.0			1.54359
$52$			10944.0i			0.561265i
$53$		−	2964.00i		−	0.144940i	−0.997371	−	0.0724700i	$-0.976912\pi$
$53$		−	2964.00i		−	0.144940i	0.997371	−	0.0724700i	$-0.0230882\pi$
$54$	−16240.0			−0.757882
$55$	−8140.00	+	1480.00i	−0.362842	+	0.0659713i
$56$	−10112.0			−0.430891
$57$			31080.0i			1.26705i
$58$		−	1080.00i		−	0.0421555i
$59$	39740.0			1.48627			0.743135	−	0.669141i	$-0.233338\pi$
$59$	39740.0			1.48627			0.743135	+	0.669141i	$0.233338\pi$
$60$	2240.00	+	12320.0i	0.0803285	+	0.441807i
$61$	−42298.0			−1.45544			−0.727722	−	0.685873i	$-0.759421\pi$
$61$	−42298.0			−1.45544			−0.727722	+	0.685873i	$0.759421\pi$
$62$			8192.00i			0.270652i
$63$			7426.00i			0.235724i
$64$	−4096.00			−0.125000
$65$	−6840.00	−	37620.0i	−0.200804	−	1.10442i
$66$	8288.00			0.234202
$67$			32098.0i			0.873556i	0.899569	+	0.436778i	$0.143881\pi$
$67$			32098.0i			0.873556i	−0.899569	+	0.436778i	$0.856119\pi$
$68$		−	32768.0i		−	0.859365i
$69$	17444.0			0.441086
$70$	34760.0	−	6320.00i	0.847881	−	0.154160i
$71$	−4248.00			−0.100009			−0.0500044	−	0.998749i	$-0.515924\pi$
$71$	−4248.00			−0.100009			−0.0500044	+	0.998749i	$0.515924\pi$
$72$			3008.00i			0.0683828i
$73$		−	30104.0i		−	0.661176i	−0.943775	−	0.330588i	$-0.892753\pi$
$73$		−	30104.0i		−	0.661176i	0.943775	−	0.330588i	$-0.107247\pi$
$74$	−17488.0			−0.371245
$75$	−15400.0	−	40950.0i	−0.316131	−	0.840622i
$76$	35520.0			0.705406
$77$		−	23384.0i		−	0.449461i
$78$			38304.0i			0.712866i
$79$	−35280.0			−0.636005			−0.318003	−	0.948090i	$-0.603012\pi$
$79$	−35280.0			−0.636005			−0.318003	+	0.948090i	$0.603012\pi$
$80$	14080.0	−	2560.00i	0.245967	−	0.0447214i
$81$	−45419.0			−0.769175
$82$			9592.00i			0.157534i
$83$			27826.0i			0.443359i	0.975120	+	0.221680i	$0.0711539\pi$
$83$			27826.0i			0.443359i	−0.975120	+	0.221680i	$0.928846\pi$
$84$	−35392.0			−0.547277
$85$	20480.0	+	112640.i	0.307456	+	1.69101i
$86$	−9176.00			−0.133785
$87$		−	3780.00i		−	0.0535419i
$88$		−	9472.00i		−	0.130387i
$89$	85210.0			1.14029			0.570145	−	0.821544i	$-0.306887\pi$
$89$	85210.0			1.14029			0.570145	+	0.821544i	$0.306887\pi$
$90$	−1880.00	−	10340.0i	−0.0244654	−	0.134559i
$91$	108072.			1.36807
$92$		−	19936.0i		−	0.245566i
$93$			28672.0i			0.343756i
$94$	−42728.0			−0.498762
$95$	−122100.	+	22200.0i	−1.38805	+	0.252374i
$96$	−14336.0			−0.158763
$97$		−	97232.0i		−	1.04925i	−0.851333	−	0.524626i	$-0.824205\pi$
$97$		−	97232.0i		−	1.04925i	0.851333	−	0.524626i	$-0.175795\pi$
$98$			32628.0i			0.343183i
$99$	−6956.00			−0.0713299
$100$	−46800.0	+	17600.0i	−0.468000	+	0.176000i
$101$	−4298.00			−0.0419240			−0.0209620	−	0.999780i	$-0.506673\pi$
$101$	−4298.00			−0.0419240			−0.0209620	+	0.999780i	$0.506673\pi$
$102$		−	114688.i		−	1.09148i
$103$		−	124114.i		−	1.15273i	−0.817192	−	0.576365i	$-0.804471\pi$
$103$		−	124114.i		−	1.15273i	0.817192	−	0.576365i	$-0.195529\pi$
$104$	43776.0			0.396874
$105$	121660.	−	22120.0i	1.07690	−	0.195800i
$106$	−11856.0			−0.102488
$107$		−	42342.0i		−	0.357530i	−0.983892	−	0.178765i	$-0.942790\pi$
$107$		−	42342.0i		−	0.357530i	0.983892	−	0.178765i	$-0.0572101\pi$
$108$			64960.0i			0.535904i
$109$	35990.0			0.290145			0.145073	−	0.989421i	$-0.453658\pi$
$109$	35990.0			0.290145			0.145073	+	0.989421i	$0.453658\pi$
$110$	5920.00	+	32560.0i	0.0466487	+	0.256568i
$111$	−61208.0			−0.471521
$112$			40448.0i			0.304686i
$113$			228816.i			1.68574i	0.538118	+	0.842869i	$0.319135\pi$
$113$			228816.i			1.68574i	−0.538118	+	0.842869i	$0.680865\pi$
$114$	124320.			0.895940
$115$	12460.0	+	68530.0i	0.0878564	+	0.483210i
$116$	−4320.00			−0.0298084
$117$		−	32148.0i		−	0.217115i
$118$		−	158960.i		−	1.05095i
$119$	−323584.			−2.09469
$120$	49280.0	−	8960.00i	0.312405	−	0.0568009i
$121$	−139147.			−0.863993
$122$			169192.i			1.02915i
$123$			33572.0i			0.200085i
$124$	32768.0			0.191380
$125$	149875.	−	89750.0i	0.857935	−	0.513759i
$126$	29704.0			0.166682
$127$			175238.i			0.964093i	0.876146	+	0.482047i	$0.160106\pi$
$127$			175238.i			0.964093i	−0.876146	+	0.482047i	$0.839894\pi$
$128$			16384.0i			0.0883883i
$129$	−32116.0			−0.169921
$130$	−150480.	+	27360.0i	−0.780945	+	0.141990i
$131$	299652.			1.52559			0.762797	−	0.646638i	$-0.223826\pi$
$131$	299652.			1.52559			0.762797	+	0.646638i	$0.223826\pi$
$132$		−	33152.0i		−	0.165606i
$133$		−	350760.i		−	1.71942i
$134$	128392.			0.617698
$135$	−40600.0	−	223300.i	−0.191731	−	1.05452i
$136$	−131072.			−0.607663
$137$			107928.i			0.491284i	0.969361	+	0.245642i	$0.0789988\pi$
$137$			107928.i			0.491284i	−0.969361	+	0.245642i	$0.921001\pi$
$138$		−	69776.0i		−	0.311895i
$139$	196460.			0.862456			0.431228	−	0.902243i	$-0.358080\pi$
$139$	196460.			0.862456			0.431228	+	0.902243i	$0.358080\pi$
$140$	−25280.0	−	139040.i	−0.109008	−	0.599542i
$141$	−149548.			−0.633480
$142$			16992.0i			0.0707170i
$143$			101232.i			0.413978i
$144$	12032.0			0.0483539
$145$	14850.0	−	2700.00i	0.0586552	−	0.0106646i
$146$	−120416.			−0.467522
$147$			114198.i			0.435878i
$148$			69952.0i			0.262510i
$149$	−138850.			−0.512366			−0.256183	−	0.966628i	$-0.582465\pi$
$149$	−138850.			−0.512366			−0.256183	+	0.966628i	$0.582465\pi$
$150$	−163800.	+	61600.0i	−0.594410	+	0.223539i
$151$	416152.			1.48528			0.742642	−	0.669688i	$-0.233572\pi$
$151$	416152.			1.48528			0.742642	+	0.669688i	$0.233572\pi$
$152$		−	142080.i		−	0.498797i
$153$			96256.0i			0.332429i
$154$	−93536.0			−0.317817
$155$	−112640.	+	20480.0i	−0.376585	+	0.0684701i
$156$	153216.			0.504072
$157$			433108.i			1.40232i	0.713004	+	0.701160i	$0.247334\pi$
$157$			433108.i			1.40232i	−0.713004	+	0.701160i	$0.752666\pi$
$158$			141120.i			0.449724i
$159$	−41496.0			−0.130171
$160$	−10240.0	−	56320.0i	−0.0316228	−	0.173925i
$161$	−196868.			−0.598564
$162$			181676.i			0.543889i
$163$		−	149134.i		−	0.439651i	−0.975539	−	0.219825i	$-0.929451\pi$
$163$		−	149134.i		−	0.439651i	0.975539	−	0.219825i	$-0.0705487\pi$
$164$	38368.0			0.111393
$165$	20720.0	+	113960.i	0.0592488	+	0.325869i
$166$	111304.			0.313502
$167$		−	559602.i		−	1.55270i	−0.630301	−	0.776351i	$-0.717068\pi$
$167$		−	559602.i		−	1.55270i	0.630301	−	0.776351i	$-0.282932\pi$
$168$			141568.i			0.386983i
$169$	−96563.0			−0.260072
$170$	450560.	−	81920.0i	1.19572	−	0.217404i
$171$	−104340.			−0.272873
$172$			36704.0i			0.0946002i
$173$		−	343804.i		−	0.873365i	−0.899616	−	0.436682i	$-0.856153\pi$
$173$		−	343804.i		−	0.873365i	0.899616	−	0.436682i	$-0.143847\pi$
$174$	−15120.0			−0.0378598
$175$	173800.	+	462150.i	0.428997	+	1.14074i
$176$	−37888.0			−0.0921977
$177$		−	556360.i		−	1.33482i
$178$		−	340840.i		−	0.806307i
$179$	−23980.0			−0.0559392			−0.0279696	−	0.999609i	$-0.508904\pi$
$179$	−23980.0			−0.0559392			−0.0279696	+	0.999609i	$0.508904\pi$
$180$	−41360.0	+	7520.00i	−0.0951479	+	0.0172996i
$181$	−651898.			−1.47905			−0.739526	−	0.673128i	$-0.764950\pi$
$181$	−651898.			−1.47905			−0.739526	+	0.673128i	$0.764950\pi$
$182$		−	432288.i		−	0.967375i
$183$			592172.i			1.30713i
$184$	−79744.0			−0.173641
$185$	−43720.0	−	240460.i	−0.0939184	−	0.516551i
$186$	114688.			0.243072
$187$		−	303104.i		−	0.633852i
$188$			170912.i			0.352678i
$189$	641480.			1.30626
$190$	88800.0	+	488400.i	0.178455	+	0.981503i
$191$	202752.			0.402144			0.201072	−	0.979576i	$-0.435557\pi$
$191$	202752.			0.402144			0.201072	+	0.979576i	$0.435557\pi$
$192$			57344.0i			0.112263i
$193$			452656.i			0.874732i	0.899284	+	0.437366i	$0.144089\pi$
$193$			452656.i			0.874732i	−0.899284	+	0.437366i	$0.855911\pi$
$194$	−388928.			−0.741933
$195$	−526680.	+	95760.0i	−0.991883	+	0.180342i
$196$	130512.			0.242667
$197$			337468.i			0.619537i	0.950812	+	0.309768i	$0.100252\pi$
$197$			337468.i			0.619537i	−0.950812	+	0.309768i	$0.899748\pi$
$198$			27824.0i			0.0504379i
$199$	561000.			1.00422			0.502112	−	0.864803i	$-0.332557\pi$
$199$	561000.			1.00422			0.502112	+	0.864803i	$0.332557\pi$
$200$	70400.0	+	187200.i	0.124451	+	0.330926i
$201$	449372.			0.784541
$202$			17192.0i			0.0296448i
$203$			42660.0i			0.0726576i
$204$	−458752.			−0.771796
$205$	−131890.	+	23980.0i	−0.219193	+	0.0398533i
$206$	−496456.			−0.815103
$207$			58562.0i			0.0949927i
$208$		−	175104.i		−	0.280632i
$209$	328560.			0.520294
$210$	−88480.0	−	486640.i	−0.138451	−	0.761482i
$211$	−805548.			−1.24562			−0.622810	−	0.782373i	$-0.714009\pi$
$211$	−805548.			−1.24562			−0.622810	+	0.782373i	$0.714009\pi$
$212$			47424.0i			0.0724700i
$213$			59472.0i			0.0898180i
$214$	−169368.			−0.252812
$215$	−22940.0	−	126170.i	−0.0338452	−	0.186149i
$216$	259840.			0.378941
$217$		−	323584.i		−	0.466485i
$218$		−	143960.i		−	0.205164i
$219$	−421456.			−0.593802
$220$	130240.	−	23680.0i	0.181421	−	0.0329856i
$221$	1.40083e6			1.92932
$222$			244832.i			0.333415i
$223$		−	1.21855e6i		−	1.64090i	−0.571717	−	0.820451i	$-0.693722\pi$
$223$		−	1.21855e6i		−	1.64090i	0.571717	−	0.820451i	$-0.306278\pi$
$224$	161792.			0.215445
$225$	137475.	−	51700.0i	0.181037	−	0.0680823i
$226$	915264.			1.19200
$227$			564338.i			0.726900i	0.931614	+	0.363450i	$0.118401\pi$
$227$			564338.i			0.726900i	−0.931614	+	0.363450i	$0.881599\pi$
$228$		−	497280.i		−	0.633525i
$229$	−560330.			−0.706082			−0.353041	−	0.935608i	$-0.614852\pi$
$229$	−560330.			−0.706082			−0.353041	+	0.935608i	$0.614852\pi$
$230$	274120.	−	49840.0i	0.341681	−	0.0621239i
$231$	−327376.			−0.403661
$232$			17280.0i			0.0210777i
$233$			293576.i			0.354267i	0.984187	+	0.177134i	$0.0566824\pi$
$233$			293576.i			0.354267i	−0.984187	+	0.177134i	$0.943318\pi$
$234$	−128592.			−0.153523
$235$	−106820.	−	587510.i	−0.126178	−	0.693978i
$236$	−635840.			−0.743135
$237$			493920.i			0.571197i
$238$			1.29434e6i			1.48117i
$239$	−584240.			−0.661602			−0.330801	−	0.943701i	$-0.607319\pi$
$239$	−584240.			−0.661602			−0.330801	+	0.943701i	$0.607319\pi$
$240$	−35840.0	−	197120.i	−0.0401643	−	0.220903i
$241$	−563798.			−0.625289			−0.312645	−	0.949870i	$-0.601215\pi$
$241$	−563798.			−0.625289			−0.312645	+	0.949870i	$0.601215\pi$
$242$			556588.i			0.610936i
$243$		−	350714.i		−	0.381011i
$244$	676768.			0.727722
$245$	−448635.	+	81570.0i	−0.477505	+	0.0868191i
$246$	134288.			0.141481
$247$			1.51848e6i			1.58368i
$248$		−	131072.i		−	0.135326i
$249$	389564.			0.398181
$250$	−359000.	−	599500.i	−0.363282	−	0.606651i
$251$	−1.01975e6			−1.02167			−0.510833	−	0.859680i	$-0.670663\pi$
$251$	−1.01975e6			−1.02167			−0.510833	+	0.859680i	$0.670663\pi$
$252$		−	118816.i		−	0.117862i
$253$		−	184408.i		−	0.181125i
$254$	700952.			0.681717
$255$	1.57696e6	−	286720.i	1.51869	−	0.276126i
$256$	65536.0			0.0625000
$257$			657408.i			0.620872i	0.950594	+	0.310436i	$0.100475\pi$
$257$			657408.i			0.620872i	−0.950594	+	0.310436i	$0.899525\pi$
$258$			128464.i			0.120152i
$259$	690776.			0.639864
$260$	109440.	+	601920.i	0.100402	+	0.552211i
$261$	12690.0			0.0115308
$262$		−	1.19861e6i		−	1.07876i
$263$			562366.i			0.501337i	0.968073	+	0.250668i	$0.0806504\pi$
$263$			562366.i			0.501337i	−0.968073	+	0.250668i	$0.919350\pi$
$264$	−132608.			−0.117101
$265$	−29640.0	−	163020.i	−0.0259277	−	0.142602i
$266$	−1.40304e6			−1.21581
$267$		−	1.19294e6i		−	1.02410i
$268$		−	513568.i		−	0.436778i
$269$	−366570.			−0.308870			−0.154435	−	0.988003i	$-0.549356\pi$
$269$	−366570.			−0.308870			−0.154435	+	0.988003i	$0.549356\pi$
$270$	−893200.	+	162400.i	−0.745657	+	0.135574i
$271$	1.16075e6			0.960099			0.480050	−	0.877241i	$-0.340619\pi$
$271$	1.16075e6			0.960099			0.480050	+	0.877241i	$0.340619\pi$
$272$			524288.i			0.429682i
$273$		−	1.51301e6i		−	1.22867i
$274$	431712.			0.347390
$275$	−432900.	+	162800.i	−0.345188	+	0.129814i
$276$	−279104.			−0.220543
$277$		−	2.51501e6i		−	1.96943i	−0.174172	−	0.984715i	$-0.555725\pi$
$277$		−	2.51501e6i		−	1.96943i	0.174172	−	0.984715i	$-0.444275\pi$
$278$		−	785840.i		−	0.609849i
$279$	−96256.0			−0.0740316
$280$	−556160.	+	101120.i	−0.423940	+	0.0770800i
$281$	2.08600e6			1.57597			0.787987	−	0.615692i	$-0.211124\pi$
$281$	2.08600e6			1.57597			0.787987	+	0.615692i	$0.211124\pi$
$282$			598192.i			0.447938i
$283$			2.23803e6i			1.66111i	0.556935	+	0.830556i	$0.311977\pi$
$283$			2.23803e6i			1.66111i	−0.556935	+	0.830556i	$0.688023\pi$
$284$	67968.0			0.0500044
$285$	310800.	+	1.70940e6i	0.226657	+	1.24661i
$286$	404928.			0.292727
$287$		−	378884.i		−	0.271520i
$288$		−	48128.0i		−	0.0341914i
$289$	−2.77445e6			−1.95403
$290$	−10800.0	−	59400.0i	−0.00754100	−	0.0414755i
$291$	−1.36125e6			−0.942334
$292$			481664.i			0.330588i
$293$			975756.i			0.664006i	0.943278	+	0.332003i	$0.107724\pi$
$293$			975756.i			0.664006i	−0.943278	+	0.332003i	$0.892276\pi$
$294$	456792.			0.308212
$295$	2.18570e6	−	397400.i	1.46230	−	0.265872i
$296$	279808.			0.185623
$297$			600880.i			0.395273i
$298$			555400.i			0.362297i
$299$	852264.			0.551310
$300$	246400.	+	655200.i	0.158066	+	0.420311i
$301$	362452.			0.230587
$302$		−	1.66461e6i		−	1.05025i
$303$			60172.0i			0.0376520i
$304$	−568320.			−0.352703
$305$	−2.32639e6	+	422980.i	−1.43197	+	0.260358i
$306$	385024.			0.235063
$307$			87858.0i			0.0532029i	0.999646	+	0.0266015i	$0.00846850\pi$
$307$			87858.0i			0.0532029i	−0.999646	+	0.0266015i	$0.991531\pi$
$308$			374144.i			0.224730i
$309$	−1.73760e6			−1.03527
$310$	81920.0	+	450560.i	0.0484156	+	0.266286i
$311$	599352.			0.351383			0.175692	−	0.984445i	$-0.443784\pi$
$311$	599352.			0.351383			0.175692	+	0.984445i	$0.443784\pi$
$312$		−	612864.i		−	0.356433i
$313$			2.09342e6i			1.20780i	0.797060	+	0.603900i	$0.206387\pi$
$313$			2.09342e6i			1.20780i	−0.797060	+	0.603900i	$0.793613\pi$
$314$	1.73243e6			0.991590
$315$	74260.0	+	408430.i	0.0421676	+	0.231922i
$316$	564480.			0.318003
$317$		−	2.41625e6i		−	1.35050i	−0.737590	−	0.675249i	$-0.764036\pi$
$317$		−	2.41625e6i		−	1.35050i	0.737590	−	0.675249i	$-0.235964\pi$
$318$			165984.i			0.0920446i
$319$	−39960.0			−0.0219861
$320$	−225280.	+	40960.0i	−0.122984	+	0.0223607i
$321$	−592788.			−0.321097
$322$			787472.i			0.423249i
$323$		−	4.54656e6i		−	2.42480i
$324$	726704.			0.384587
$325$	−752400.	−	2.00070e6i	−0.395130	−	1.05069i
$326$	−596536.			−0.310880
$327$		−	503860.i		−	0.260580i
$328$		−	153472.i		−	0.0787670i
$329$	1.68776e6			0.859647
$330$	455840.	−	82880.0i	0.230424	−	0.0418953i
$331$	−1.64095e6			−0.823237			−0.411618	−	0.911356i	$-0.635036\pi$
$331$	−1.64095e6			−0.823237			−0.411618	+	0.911356i	$0.635036\pi$
$332$		−	445216.i		−	0.221680i
$333$		−	205484.i		−	0.101547i
$334$	−2.23841e6			−1.09793
$335$	320980.	+	1.76539e6i	0.156267	+	0.859466i
$336$	566272.			0.273638
$337$			2.18773e6i			1.04935i	0.851304	+	0.524673i	$0.175812\pi$
$337$			2.18773e6i			1.04935i	−0.851304	+	0.524673i	$0.824188\pi$
$338$			386252.i			0.183899i
$339$	3.20342e6			1.51396
$340$	−327680.	−	1.80224e6i	−0.153728	−	0.845503i
$341$	303104.			0.141158
$342$			417360.i			0.192950i
$343$			1.36670e6i			0.627246i
$344$	146816.			0.0668925
$345$	959420.	−	174440.i	0.433971	−	0.0789039i
$346$	−1.37522e6			−0.617562
$347$			2.74502e6i			1.22383i	0.790923	+	0.611916i	$0.209601\pi$
$347$			2.74502e6i			1.22383i	−0.790923	+	0.611916i	$0.790399\pi$
$348$			60480.0i			0.0267709i
$349$	2.65115e6			1.16512			0.582560	−	0.812788i	$-0.302051\pi$
$349$	2.65115e6			1.16512			0.582560	+	0.812788i	$0.302051\pi$
$350$	1.84860e6	−	695200.i	0.806627	−	0.303347i
$351$	−2.77704e6			−1.20313
$352$			151552.i			0.0651936i
$353$		−	3.05766e6i		−	1.30603i	−0.757345	−	0.653015i	$-0.773504\pi$
$353$		−	3.05766e6i		−	1.30603i	0.757345	−	0.653015i	$-0.226496\pi$
$354$	−2.22544e6			−0.943860
$355$	−233640.	+	42480.0i	−0.0983957	+	0.0178901i
$356$	−1.36336e6			−0.570145
$357$			4.53018e6i			1.88124i
$358$			95920.0i			0.0395550i
$359$	−3.79356e6			−1.55350			−0.776749	−	0.629810i	$-0.783133\pi$
$359$	−3.79356e6			−1.55350			−0.776749	+	0.629810i	$0.783133\pi$
$360$	30080.0	+	165440.i	0.0122327	+	0.0672797i
$361$	2.45230e6			0.990389
$362$			2.60759e6i			1.04585i
$363$			1.94806e6i			0.775953i
$364$	−1.72915e6			−0.684037
$365$	−301040.	−	1.65572e6i	−0.118275	−	0.650511i
$366$	2.36869e6			0.924283
$367$		−	3.11060e6i		−	1.20553i	−0.797917	−	0.602767i	$-0.794065\pi$
$367$		−	3.11060e6i		−	1.20553i	0.797917	−	0.602767i	$-0.205935\pi$
$368$			318976.i			0.122783i
$369$	−112706.			−0.0430905
$370$	−961840.	+	174880.i	−0.365257	+	0.0664104i
$371$	468312.			0.176645
$372$		−	458752.i		−	0.171878i
$373$			1.41520e6i			0.526677i	0.964703	+	0.263339i	$0.0848236\pi$
$373$			1.41520e6i			0.526677i	−0.964703	+	0.263339i	$0.915176\pi$
$374$	−1.21242e6			−0.448201
$375$	−1.25650e6	−	2.09825e6i	−0.461407	−	0.770511i
$376$	683648.			0.249381
$377$		−	184680.i		−	0.0669216i
$378$		−	2.56592e6i		−	0.923663i
$379$	3.90262e6			1.39559			0.697796	−	0.716297i	$-0.254164\pi$
$379$	3.90262e6			1.39559			0.697796	+	0.716297i	$0.254164\pi$
$380$	1.95360e6	−	355200.i	0.694027	−	0.126187i
$381$	2.45333e6			0.865852
$382$		−	811008.i		−	0.284359i
$383$		−	695674.i		−	0.242331i	−0.992632	−	0.121165i	$-0.961337\pi$
$383$		−	695674.i		−	0.242331i	0.992632	−	0.121165i	$-0.0386632\pi$
$384$	229376.			0.0793816
$385$	−233840.	−	1.28612e6i	−0.0804020	−	0.442211i
$386$	1.81062e6			0.618529
$387$		−	107818.i		−	0.0365943i
$388$			1.55571e6i			0.524626i
$389$	−498290.			−0.166958			−0.0834792	−	0.996510i	$-0.526603\pi$
$389$	−498290.			−0.166958			−0.0834792	+	0.996510i	$0.526603\pi$
$390$	383040.	+	2.10672e6i	0.127521	+	0.701367i
$391$	−2.55181e6			−0.844124
$392$		−	522048.i		−	0.171591i
$393$		−	4.19513e6i		−	1.37014i
$394$	1.34987e6			0.438079
$395$	−1.94040e6	+	352800.i	−0.625747	+	0.113772i
$396$	111296.			0.0356649
$397$			1.09567e6i			0.348901i	0.984666	+	0.174451i	$0.0558150\pi$
$397$			1.09567e6i			0.348901i	−0.984666	+	0.174451i	$0.944185\pi$
$398$		−	2.24400e6i		−	0.710093i
$399$	−4.91064e6			−1.54421
$400$	748800.	−	281600.i	0.234000	−	0.0880000i
$401$	−2.49160e6			−0.773779			−0.386890	−	0.922126i	$-0.626451\pi$
$401$	−2.49160e6			−0.773779			−0.386890	+	0.922126i	$0.626451\pi$
$402$		−	1.79749e6i		−	0.554755i
$403$			1.40083e6i			0.429659i
$404$	68768.0			0.0209620
$405$	−2.49804e6	+	454190.i	−0.756768	+	0.137594i
$406$	170640.			0.0513766
$407$			647056.i			0.193623i
$408$			1.83501e6i			0.545742i
$409$	3.63349e6			1.07403			0.537014	−	0.843573i	$-0.319552\pi$
$409$	3.63349e6			1.07403			0.537014	+	0.843573i	$0.319552\pi$
$410$	95920.0	+	527560.i	0.0281806	+	0.154993i
$411$	1.51099e6			0.441222
$412$			1.98582e6i			0.576365i
$413$			6.27892e6i			1.81138i
$414$	234248.			0.0671700
$415$	278260.	+	1.53043e6i	0.0793105	+	0.436208i
$416$	−700416.			−0.198437
$417$		−	2.75044e6i		−	0.774572i
$418$		−	1.31424e6i		−	0.367904i
$419$	3.64378e6			1.01395			0.506976	−	0.861960i	$-0.330763\pi$
$419$	3.64378e6			1.01395			0.506976	+	0.861960i	$0.330763\pi$
$420$	−1.94656e6	+	353920.i	−0.538449	+	0.0978998i
$421$	−1.82530e6			−0.501913			−0.250957	−	0.967998i	$-0.580745\pi$
$421$	−1.82530e6			−0.501913			−0.250957	+	0.967998i	$0.580745\pi$
$422$			3.22219e6i			0.880786i
$423$		−	502054.i		−	0.136427i
$424$	189696.			0.0512441
$425$	2.25280e6	+	5.99040e6i	0.604993	+	1.60873i
$426$	237888.			0.0635109
$427$		−	6.68308e6i		−	1.77381i
$428$			677472.i			0.178765i
$429$	1.41725e6			0.371794
$430$	−504680.	+	91760.0i	−0.131627	+	0.0239322i
$431$	2.85435e6			0.740141			0.370070	−	0.929004i	$-0.379334\pi$
$431$	2.85435e6			0.740141			0.370070	+	0.929004i	$0.379334\pi$
$432$		−	1.03936e6i		−	0.267952i
$433$			587776.i			0.150658i	0.997159	+	0.0753290i	$0.0240007\pi$
$433$			587776.i			0.150658i	−0.997159	+	0.0753290i	$0.975999\pi$
$434$	−1.29434e6			−0.329855
$435$	−37800.0	−	207900.i	−0.00957786	−	0.0526783i
$436$	−575840.			−0.145073
$437$		−	2.76612e6i		−	0.692895i
$438$			1.68582e6i			0.419882i
$439$	−6.11604e6			−1.51464			−0.757319	−	0.653045i	$-0.773491\pi$
$439$	−6.11604e6			−1.51464			−0.757319	+	0.653045i	$0.773491\pi$
$440$	−94720.0	−	520960.i	−0.0233244	−	0.128284i
$441$	−383379.			−0.0938711
$442$		−	5.60333e6i		−	1.36424i
$443$			2.35771e6i			0.570795i	0.958409	+	0.285398i	$0.0921257\pi$
$443$			2.35771e6i			0.570795i	−0.958409	+	0.285398i	$0.907874\pi$
$444$	979328.			0.235760
$445$	4.68655e6	−	852100.i	1.12190	−	0.203981i
$446$	−4.87422e6			−1.16029
$447$			1.94390e6i			0.460156i
$448$		−	647168.i		−	0.152343i
$449$	−5.49735e6			−1.28688			−0.643439	−	0.765497i	$-0.722493\pi$
$449$	−5.49735e6			−1.28688			−0.643439	+	0.765497i	$0.722493\pi$
$450$	−206800.	−	549900.i	−0.0481415	−	0.128013i
$451$	354904.			0.0821617
$452$		−	3.66106e6i		−	0.842869i
$453$		−	5.82613e6i		−	1.33393i
$454$	2.25735e6			0.513996
$455$	5.94396e6	−	1.08072e6i	1.34601	−	0.244729i
$456$	−1.98912e6			−0.447970
$457$		−	1.16039e6i		−	0.259905i	−0.991520	−	0.129952i	$-0.958518\pi$
$457$		−	1.16039e6i		−	0.259905i	0.991520	−	0.129952i	$-0.0414824\pi$
$458$			2.24132e6i			0.499275i
$459$	8.31488e6			1.84215
$460$	−199360.	−	1.09648e6i	−0.0439282	−	0.241605i
$461$	−2.30330e6			−0.504775			−0.252387	−	0.967626i	$-0.581216\pi$
$461$	−2.30330e6			−0.504775			−0.252387	+	0.967626i	$0.581216\pi$
$462$			1.30950e6i			0.285431i
$463$		−	2.71343e6i		−	0.588257i	−0.955766	−	0.294128i	$-0.904971\pi$
$463$		−	2.71343e6i		−	0.588257i	0.955766	−	0.294128i	$-0.0950293\pi$
$464$	69120.0			0.0149042
$465$	286720.	+	1.57696e6i	0.0614930	+	0.338211i
$466$	1.17430e6			0.250505
$467$			4.05050e6i			0.859441i	0.902962	+	0.429721i	$0.141388\pi$
$467$			4.05050e6i			0.859441i	−0.902962	+	0.429721i	$0.858612\pi$
$468$			514368.i			0.108557i
$469$	−5.07148e6			−1.06464
$470$	−2.35004e6	+	427280.i	−0.490716	+	0.0892212i
$471$	6.06351e6			1.25942
$472$			2.54336e6i			0.525476i
$473$			339512.i			0.0697754i
$474$	1.97568e6			0.403897
$475$	−6.49350e6	+	2.44200e6i	−1.32052	+	0.496606i
$476$	5.17734e6			1.04734
$477$		−	139308.i		−	0.0280337i
$478$			2.33696e6i			0.467823i
$479$	−5.60528e6			−1.11624			−0.558121	−	0.829759i	$-0.688478\pi$
$479$	−5.60528e6			−1.11624			−0.558121	+	0.829759i	$0.688478\pi$
$480$	−788480.	+	143360.i	−0.156202	+	0.0284004i
$481$	−2.99045e6			−0.589350
$482$			2.25519e6i			0.442146i
$483$			2.75615e6i			0.537570i
$484$	2.22635e6			0.431997
$485$	−972320.	−	5.34776e6i	−0.187696	−	1.03233i
$486$	−1.40286e6			−0.269415
$487$			7.13168e6i			1.36260i	0.732003	+	0.681301i	$0.238586\pi$
$487$			7.13168e6i			1.36260i	−0.732003	+	0.681301i	$0.761414\pi$
$488$		−	2.70707e6i		−	0.514577i
$489$	−2.08788e6			−0.394850
$490$	326280.	+	1.79454e6i	0.0613904	+	0.337647i
$491$	5.88145e6			1.10098			0.550492	−	0.834841i	$-0.314440\pi$
$491$	5.88145e6			1.10098			0.550492	+	0.834841i	$0.314440\pi$
$492$		−	537152.i		−	0.100042i
$493$			552960.i			0.102465i
$494$	6.07392e6			1.11983
$495$	−382580.	+	69560.0i	−0.0701793	+	0.0127599i
$496$	−524288.			−0.0956898
$497$		−	671184.i		−	0.121885i
$498$		−	1.55826e6i		−	0.281556i
$499$	−1.75710e6			−0.315897			−0.157948	−	0.987447i	$-0.550488\pi$
$499$	−1.75710e6			−0.315897			−0.157948	+	0.987447i	$0.550488\pi$
$500$	−2.39800e6	+	1.43600e6i	−0.428967	+	0.256879i
$501$	−7.83443e6			−1.39448
$502$			4.07899e6i			0.722426i
$503$		−	4.91411e6i		−	0.866015i	−0.901390	−	0.433007i	$-0.857452\pi$
$503$		−	4.91411e6i		−	0.866015i	0.901390	−	0.433007i	$-0.142548\pi$
$504$	−475264.			−0.0833410
$505$	−236390.	+	42980.0i	−0.0412478	+	0.00749960i
$506$	−737632.			−0.128075
$507$			1.35188e6i			0.233571i
$508$		−	2.80381e6i		−	0.482047i
$509$	5.75499e6			0.984578			0.492289	−	0.870432i	$-0.336160\pi$
$509$	5.75499e6			0.984578			0.492289	+	0.870432i	$0.336160\pi$
$510$	−1.14688e6	−	6.30784e6i	−0.195251	−	1.07388i
$511$	4.75643e6			0.805803
$512$		−	262144.i		−	0.0441942i
$513$			9.01320e6i			1.51212i
$514$	2.62963e6			0.439023
$515$	−1.24114e6	−	6.82627e6i	−0.206207	−	1.13414i
$516$	513856.			0.0849605
$517$			1.58094e6i			0.260128i
$518$		−	2.76310e6i		−	0.452452i
$519$	−4.81326e6			−0.784369
$520$	2.40768e6	−	437760.i	0.390472	−	0.0709950i
$521$	−1.61980e6			−0.261437			−0.130718	−	0.991420i	$-0.541728\pi$
$521$	−1.61980e6			−0.261437			−0.130718	+	0.991420i	$0.541728\pi$
$522$		−	50760.0i		−	0.00815352i
$523$		−	1.19117e7i		−	1.90422i	−0.305751	−	0.952112i	$-0.598907\pi$
$523$		−	1.19117e7i		−	1.90422i	0.305751	−	0.952112i	$-0.401093\pi$
$524$	−4.79443e6			−0.762797
$525$	6.47010e6	−	2.43320e6i	1.02450	−	0.385283i
$526$	2.24946e6			0.354499
$527$		−	4.19430e6i		−	0.657860i
$528$			530432.i			0.0828028i
$529$	4.88383e6			0.758789
$530$	−652080.	+	118560.i	−0.100835	+	0.0183336i
$531$	1.86778e6			0.287468
$532$			5.61216e6i			0.859708i
$533$			1.64023e6i			0.250085i
$534$	−4.77176e6			−0.724145
$535$	−423420.	−	2.32881e6i	−0.0639568	−	0.351763i
$536$	−2.05427e6			−0.308849
$537$			335720.i			0.0502391i
$538$			1.46628e6i			0.218404i
$539$	1.20724e6			0.178986
$540$	649600.	+	3.57280e6i	0.0958653	+	0.527259i
$541$	4.07630e6			0.598788			0.299394	−	0.954130i	$-0.403215\pi$
$541$	4.07630e6			0.598788			0.299394	+	0.954130i	$0.403215\pi$
$542$		−	4.64301e6i		−	0.678893i
$543$			9.12657e6i			1.32834i
$544$	2.09715e6			0.303831
$545$	1.97945e6	−	359900.i	0.285465	−	0.0519028i
$546$	−6.05203e6			−0.868800
$547$			1.23680e7i			1.76739i	0.468065	+	0.883694i	$0.344951\pi$
$547$			1.23680e7i			1.76739i	−0.468065	+	0.883694i	$0.655049\pi$
$548$		−	1.72685e6i		−	0.245642i
$549$	−1.98801e6			−0.281505
$550$	651200.	+	1.73160e6i	0.0917926	+	0.244085i
$551$	−599400.			−0.0841081
$552$			1.11642e6i			0.155947i
$553$		−	5.57424e6i		−	0.775127i
$554$	−1.00600e7			−1.39260
$555$	−3.36644e6	+	612080.i	−0.463915	+	0.0843482i
$556$	−3.14336e6			−0.431228
$557$			130308.i			0.0177964i	0.999960	+	0.00889822i	$0.00283243\pi$
$557$			130308.i			0.0177964i	−0.999960	+	0.00889822i	$0.997168\pi$
$558$			385024.i			0.0523483i
$559$	−1.56910e6			−0.212383
$560$	404480.	+	2.22464e6i	0.0545038	+	0.299771i
$561$	−4.24346e6			−0.569262
$562$		−	8.34401e6i		−	1.11438i
$563$			5.91687e6i			0.786721i	0.919384	+	0.393361i	$0.128688\pi$
$563$			5.91687e6i			0.786721i	−0.919384	+	0.393361i	$0.871312\pi$
$564$	2.39277e6			0.316740
$565$	2.28816e6	+	1.25849e7i	0.301554	+	1.65855i
$566$	8.95210e6			1.17458
$567$		−	7.17620e6i		−	0.937426i
$568$		−	271872.i		−	0.0353585i
$569$	9.03013e6			1.16927			0.584633	−	0.811298i	$-0.301239\pi$
$569$	9.03013e6			1.16927			0.584633	+	0.811298i	$0.301239\pi$
$570$	6.83760e6	−	1.24320e6i	0.881488	−	0.160271i
$571$	−1.07093e7			−1.37459			−0.687294	−	0.726379i	$-0.741202\pi$
$571$	−1.07093e7			−1.37459			−0.687294	+	0.726379i	$0.741202\pi$
$572$		−	1.61971e6i		−	0.206989i
$573$		−	2.83853e6i		−	0.361166i
$574$	−1.51554e6			−0.191994
$575$	1.37060e6	+	3.64455e6i	0.172879	+	0.459700i
$576$	−192512.			−0.0241770
$577$		−	1.22051e6i		−	0.152617i	−0.997084	−	0.0763084i	$-0.975687\pi$
$577$		−	1.22051e6i		−	0.152617i	0.997084	−	0.0763084i	$-0.0243134\pi$
$578$			1.10978e7i			1.38171i
$579$	6.33718e6			0.785597
$580$	−237600.	+	43200.0i	−0.0293276	+	0.00533229i
$581$	−4.39651e6			−0.540341
$582$			5.44499e6i			0.666331i
$583$			438672.i			0.0534526i
$584$	1.92666e6			0.233761
$585$	−321480.	−	1.76814e6i	−0.0388387	−	0.213613i
$586$	3.90302e6			0.469523
$587$		−	1.47104e7i		−	1.76210i	−0.473026	−	0.881049i	$-0.656838\pi$
$587$		−	1.47104e7i		−	1.76210i	0.473026	−	0.881049i	$-0.343162\pi$
$588$		−	1.82717e6i		−	0.217939i
$589$	4.54656e6			0.540001
$590$	−1.58960e6	−	8.74280e6i	−0.188000	−	1.03400i
$591$	4.72455e6			0.556406
$592$		−	1.11923e6i		−	0.131255i
$593$		−	8.52014e6i		−	0.994970i	−0.867472	−	0.497485i	$-0.834257\pi$
$593$		−	8.52014e6i		−	0.994970i	0.867472	−	0.497485i	$-0.165743\pi$
$594$	2.40352e6			0.279500
$595$	−1.77971e7	+	3.23584e6i	−2.06090	+	0.374709i
$596$	2.22160e6			0.256183
$597$		−	7.85400e6i		−	0.901893i
$598$		−	3.40906e6i		−	0.389835i
$599$	−2.90100e6			−0.330355			−0.165177	−	0.986264i	$-0.552820\pi$
$599$	−2.90100e6			−0.330355			−0.165177	+	0.986264i	$0.552820\pi$
$600$	2.62080e6	−	985600.i	0.297205	−	0.111769i
$601$	5.72760e6			0.646825			0.323412	−	0.946258i	$-0.395170\pi$
$601$	5.72760e6			0.646825			0.323412	+	0.946258i	$0.395170\pi$
$602$		−	1.44981e6i		−	0.163049i
$603$			1.50861e6i			0.168959i
$604$	−6.65843e6			−0.742642
$605$	−7.65308e6	+	1.39147e6i	−0.850057	+	0.154556i
$606$	240688.			0.0266240
$607$		−	8.79924e6i		−	0.969334i	−0.874699	−	0.484667i	$-0.838941\pi$
$607$		−	8.79924e6i		−	0.969334i	0.874699	−	0.484667i	$-0.161059\pi$
$608$			2.27328e6i			0.249399i
$609$	597240.			0.0652538
$610$	1.69192e6	+	9.30556e6i	0.184101	+	1.01255i
$611$	−7.30649e6			−0.791782
$612$		−	1.54010e6i		−	0.166215i
$613$		−	1.03408e6i		−	0.111149i	−0.998455	−	0.0555744i	$-0.982301\pi$
$613$		−	1.03408e6i		−	0.111149i	0.998455	−	0.0555744i	$-0.0176990\pi$
$614$	351432.			0.0376201
$615$	335720.	+	1.84646e6i	0.0357923	+	0.196858i
$616$	1.49658e6			0.158908
$617$			1.29854e7i			1.37323i	0.727020	+	0.686616i	$0.240905\pi$
$617$			1.29854e7i			1.37323i	−0.727020	+	0.686616i	$0.759095\pi$
$618$			6.95038e6i			0.732045i
$619$	−7.92002e6			−0.830806			−0.415403	−	0.909637i	$-0.636359\pi$
$619$	−7.92002e6			−0.830806			−0.415403	+	0.909637i	$0.636359\pi$
$620$	1.80224e6	−	327680.i	0.188293	−	0.0342350i
$621$	5.05876e6			0.526399
$622$		−	2.39741e6i		−	0.248465i
$623$			1.34632e7i			1.38972i
$624$	−2.45146e6			−0.252036
$625$	7.34562e6	−	6.43500e6i	0.752192	−	0.658944i
$626$	8.37366e6			0.854043
$627$		−	4.59984e6i		−	0.467276i
$628$		−	6.92973e6i		−	0.701160i
$629$	8.95386e6			0.902368
$630$	1.63372e6	−	297040.i	0.163993	−	0.0298170i
$631$	1.68218e7			1.68189			0.840945	−	0.541120i	$-0.181999\pi$
$631$	1.68218e7			1.68189			0.840945	+	0.541120i	$0.181999\pi$
$632$		−	2.25792e6i		−	0.224862i
$633$			1.12777e7i			1.11869i
$634$	−9.66501e6			−0.954947
$635$	1.75238e6	+	9.63809e6i	0.172462	+	0.948542i
$636$	663936.			0.0650854
$637$			5.57939e6i			0.544801i
$638$			159840.i			0.0155465i
$639$	−199656.			−0.0193433
$640$	163840.	+	901120.i	0.0158114	+	0.0869626i
$641$	−1.55154e7			−1.49148			−0.745741	−	0.666236i	$-0.767904\pi$
$641$	−1.55154e7			−1.49148			−0.745741	+	0.666236i	$0.767904\pi$
$642$			2.37115e6i			0.227050i
$643$		−	1.05801e7i		−	1.00916i	−0.863364	−	0.504582i	$-0.831646\pi$
$643$		−	1.05801e7i		−	1.00916i	0.863364	−	0.504582i	$-0.168354\pi$
$644$	3.14989e6			0.299282
$645$	−1.76638e6	+	321160.i	−0.167180	+	0.0303964i
$646$	−1.81862e7			−1.71460
$647$			1.37883e7i			1.29494i	0.762090	+	0.647471i	$0.224173\pi$
$647$			1.37883e7i			1.29494i	−0.762090	+	0.647471i	$0.775827\pi$
$648$		−	2.90682e6i		−	0.271944i
$649$	−5.88152e6			−0.548123
$650$	−8.00280e6	+	3.00960e6i	−0.742948	+	0.279399i
$651$	−4.53018e6			−0.418950
$652$			2.38614e6i			0.219825i
$653$			1.58924e6i			0.145850i	0.997337	+	0.0729248i	$0.0232333\pi$
$653$			1.58924e6i			0.145850i	−0.997337	+	0.0729248i	$0.976767\pi$
$654$	−2.01544e6			−0.184258
$655$	1.64809e7	−	2.99652e6i	1.50099	−	0.272907i
$656$	−613888.			−0.0556967
$657$		−	1.41489e6i		−	0.127882i
$658$		−	6.75102e6i		−	0.607862i
$659$	9.12434e6			0.818442			0.409221	−	0.912435i	$-0.365801\pi$
$659$	9.12434e6			0.818442			0.409221	+	0.912435i	$0.365801\pi$
$660$	−331520.	−	1.82336e6i	−0.0296244	−	0.162934i
$661$	6.50310e6			0.578918			0.289459	−	0.957190i	$-0.406525\pi$
$661$	6.50310e6			0.578918			0.289459	+	0.957190i	$0.406525\pi$
$662$			6.56379e6i			0.582116i
$663$		−	1.96116e7i		−	1.73273i
$664$	−1.78086e6			−0.156751
$665$	−3.50760e6	−	1.92918e7i	−0.307578	−	1.69168i
$666$	−821936.			−0.0718046
$667$			336420.i			0.0292797i
$668$			8.95363e6i			0.776351i
$669$	−1.70598e7			−1.47369
$670$	7.06156e6	−	1.28392e6i	0.607734	−	0.110497i
$671$	6.26010e6			0.536754
$672$		−	2.26509e6i		−	0.193492i
$673$			2.17810e6i			0.185370i	0.995695	+	0.0926850i	$0.0295449\pi$
$673$			2.17810e6i			0.185370i	−0.995695	+	0.0926850i	$0.970455\pi$
$674$	8.75091e6			0.741999
$675$	−4.46600e6	−	1.18755e7i	−0.377276	−	1.00321i
$676$	1.54501e6			0.130036
$677$			3.98419e6i			0.334094i	0.985949	+	0.167047i	$0.0534231\pi$
$677$			3.98419e6i			0.334094i	−0.985949	+	0.167047i	$0.946577\pi$
$678$		−	1.28137e7i		−	1.07053i
$679$	1.53627e7			1.27877
$680$	−7.20896e6	+	1.31072e6i	−0.597861	+	0.108702i
$681$	7.90073e6			0.652829
$682$		−	1.21242e6i		−	0.0998138i
$683$			5.91563e6i			0.485231i	0.970122	+	0.242616i	$0.0780054\pi$
$683$			5.91563e6i			0.485231i	−0.970122	+	0.242616i	$0.921995\pi$
$684$	1.66944e6			0.136436
$685$	1.07928e6	+	5.93604e6i	0.0878836	+	0.483360i
$686$	5.46680e6			0.443530
$687$			7.84462e6i			0.634133i
$688$		−	587264.i		−	0.0473001i
$689$	−2.02738e6			−0.162700
$690$	−697760.	−	3.83768e6i	−0.0557935	−	0.306864i
$691$	−1.55471e7			−1.23867			−0.619335	−	0.785127i	$-0.712598\pi$
$691$	−1.55471e7			−1.23867			−0.619335	+	0.785127i	$0.712598\pi$
$692$			5.50086e6i			0.436682i
$693$		−	1.09905e6i		−	0.0869328i
$694$	1.09801e7			0.865379
$695$	1.08053e7	−	1.96460e6i	0.848545	−	0.154281i
$696$	241920.			0.0189299
$697$		−	4.91110e6i		−	0.382910i
$698$		−	1.06046e7i		−	0.823864i
$699$	4.11006e6			0.318167
$700$	−2.78080e6	−	7.39440e6i	−0.214499	−	0.570372i
$701$	−2.27103e7			−1.74553			−0.872766	−	0.488139i	$-0.837676\pi$
$701$	−2.27103e7			−1.74553			−0.872766	+	0.488139i	$0.837676\pi$
$702$			1.11082e7i			0.850745i
$703$			9.70584e6i			0.740704i
$704$	606208.			0.0460988
$705$	−8.22514e6	+	1.49548e6i	−0.623262	+	0.113320i
$706$	−1.22307e7			−0.923502
$707$		−	679084.i		−	0.0510946i
$708$			8.90176e6i			0.667410i
$709$	−6.29841e6			−0.470560			−0.235280	−	0.971928i	$-0.575601\pi$
$709$	−6.29841e6			−0.470560			−0.235280	+	0.971928i	$0.575601\pi$
$710$	169920.	+	934560.i	0.0126502	+	0.0695763i
$711$	−1.65816e6			−0.123013
$712$			5.45344e6i			0.403154i
$713$		−	2.55181e6i		−	0.187985i
$714$	1.81207e7			1.33024
$715$	1.01232e6	+	5.56776e6i	0.0740547	+	0.407301i
$716$	383680.			0.0279696
$717$			8.17936e6i			0.594185i
$718$			1.51742e7i			1.09849i
$719$	−2.11911e7			−1.52873			−0.764367	−	0.644782i	$-0.776948\pi$
$719$	−2.11911e7			−1.52873			−0.764367	+	0.644782i	$0.776948\pi$
$720$	661760.	−	120320.i	0.0475740	−	0.00864981i
$721$	1.96100e7			1.40488
$722$		−	9.80920e6i		−	0.700311i
$723$			7.89317e6i			0.561572i
$724$	1.04304e7			0.739526
$725$	789750.	−	297000.i	0.0558013	−	0.0209851i
$726$	7.79223e6			0.548682
$727$			1.35610e7i			0.951605i	0.879552	+	0.475803i	$0.157842\pi$
$727$			1.35610e7i			0.951605i	−0.879552	+	0.475803i	$0.842158\pi$
$728$			6.91661e6i			0.483687i
$729$	−1.59468e7			−1.11136
$730$	−6.62288e6	+	1.20416e6i	−0.459981	+	0.0836329i
$731$	4.69811e6			0.325185
$732$		−	9.47475e6i		−	0.653567i
$733$		−	2.69413e7i		−	1.85208i	−0.377429	−	0.926038i	$-0.623192\pi$
$733$		−	2.69413e7i		−	1.85208i	0.377429	−	0.926038i	$-0.376808\pi$
$734$	−1.24424e7			−0.852441
$735$	1.14198e6	+	6.28089e6i	0.0779723	+	0.428847i
$736$	1.27590e6			0.0868207
$737$		−	4.75050e6i		−	0.322160i
$738$			450824.i			0.0304696i
$739$	−2.77414e6			−0.186860			−0.0934302	−	0.995626i	$-0.529783\pi$
$739$	−2.77414e6			−0.186860			−0.0934302	+	0.995626i	$0.529783\pi$
$740$	699520.	+	3.84736e6i	0.0469592	+	0.258276i
$741$	2.12587e7			1.42230
$742$		−	1.87325e6i		−	0.124907i
$743$		−	1.85538e7i		−	1.23299i	−0.787358	−	0.616497i	$-0.788551\pi$
$743$		−	1.85538e7i		−	1.23299i	0.787358	−	0.616497i	$-0.211449\pi$
$744$	−1.83501e6			−0.121536
$745$	−7.63675e6	+	1.38850e6i	−0.504101	+	0.0916548i
$746$	5.66078e6			0.372417
$747$			1.30782e6i			0.0857526i
$748$			4.84966e6i			0.316926i
$749$	6.69004e6			0.435736
$750$	−8.39300e6	+	5.02600e6i	−0.544834	+	0.326264i
$751$	−2.19285e6			−0.141876			−0.0709380	−	0.997481i	$-0.522599\pi$
$751$	−2.19285e6			−0.141876			−0.0709380	+	0.997481i	$0.522599\pi$
$752$		−	2.73459e6i		−	0.176339i
$753$			1.42765e7i			0.917558i
$754$	−738720.			−0.0473207
$755$	2.28884e7	−	4.16152e6i	1.46133	−	0.265696i
$756$	−1.02637e7			−0.653128
$757$		−	9.48749e6i		−	0.601744i	−0.953665	−	0.300872i	$-0.902722\pi$
$757$		−	9.48749e6i		−	0.601744i	0.953665	−	0.300872i	$-0.0972777\pi$
$758$		−	1.56105e7i		−	0.986832i
$759$	−2.58171e6			−0.162668
$760$	−1.42080e6	−	7.81440e6i	−0.0892275	−	0.490752i
$761$	9.69580e6			0.606907			0.303453	−	0.952846i	$-0.401860\pi$
$761$	9.69580e6			0.606907			0.303453	+	0.952846i	$0.401860\pi$
$762$		−	9.81333e6i		−	0.612250i
$763$			5.68642e6i			0.353612i
$764$	−3.24403e6			−0.201072
$765$	962560.	+	5.29408e6i	0.0594668	+	0.327067i
$766$	−2.78270e6			−0.171354
$767$		−	2.71822e7i		−	1.66838i
$768$		−	917504.i		−	0.0561313i
$769$	−9.32787e6			−0.568809			−0.284405	−	0.958704i	$-0.591796\pi$
$769$	−9.32787e6			−0.568809			−0.284405	+	0.958704i	$0.591796\pi$
$770$	−5.14448e6	+	935360.i	−0.312690	+	0.0568528i
$771$	9.20371e6			0.557606
$772$		−	7.24250e6i		−	0.437366i
$773$			9.68080e6i			0.582723i	0.956613	+	0.291362i	$0.0941083\pi$
$773$			9.68080e6i			0.582723i	−0.956613	+	0.291362i	$0.905892\pi$
$774$	−431272.			−0.0258761
$775$	−5.99040e6	+	2.25280e6i	−0.358263	+	0.134731i
$776$	6.22285e6			0.370967
$777$		−	9.67086e6i		−	0.574662i
$778$			1.99316e6i			0.118057i
$779$	5.32356e6			0.314310
$780$	8.42688e6	−	1.53216e6i	0.495941	−	0.0901712i
$781$	628704.			0.0368824
$782$			1.02072e7i			0.596886i
$783$		−	1.09620e6i		−	0.0638977i
$784$	−2.08819e6			−0.121333
$785$	4.33108e6	+	2.38209e7i	0.250855	+	1.37970i
$786$	−1.67805e7			−0.968833
$787$		−	5.52302e6i		−	0.317863i	−0.987290	−	0.158931i	$-0.949195\pi$
$787$		−	5.52302e6i		−	0.317863i	0.987290	−	0.158931i	$-0.0508049\pi$
$788$		−	5.39949e6i		−	0.309768i
$789$	7.87312e6			0.450251
$790$	1.41120e6	+	7.76160e6i	0.0804490	+	0.442470i
$791$	−3.61529e7			−2.05448
$792$		−	445184.i		−	0.0252189i
$793$			2.89318e7i			1.63378i
$794$	4.38267e6			0.246711
$795$	−2.28228e6	+	414960.i	−0.128071	+	0.0232857i
$796$	−8.97600e6			−0.502112
$797$		−	1.71119e7i		−	0.954230i	−0.878841	−	0.477115i	$-0.841682\pi$
$797$		−	1.71119e7i		−	0.954230i	0.878841	−	0.477115i	$-0.158318\pi$
$798$			1.96426e7i			1.09192i
$799$	2.18767e7			1.21232
$800$	−1.12640e6	−	2.99520e6i	−0.0622254	−	0.165463i
$801$	4.00487e6			0.220550
$802$			9.96639e6i			0.547145i
$803$			4.45539e6i			0.243836i
$804$	−7.18995e6			−0.392271
$805$	−1.08277e7	+	1.96868e6i	−0.588909	+	0.107074i
$806$	5.60333e6			0.303814
$807$			5.13198e6i			0.277397i
$808$		−	275072.i		−	0.0148224i
$809$	1.45309e7			0.780586			0.390293	−	0.920691i	$-0.372374\pi$
$809$	1.45309e7			0.780586			0.390293	+	0.920691i	$0.372374\pi$
$810$	1.81676e6	+	9.99218e6i	0.0972938	+	0.535116i
$811$	−2.13545e7			−1.14009			−0.570044	−	0.821614i	$-0.693074\pi$
$811$	−2.13545e7			−1.14009			−0.570044	+	0.821614i	$0.693074\pi$
$812$		−	682560.i		−	0.0363288i
$813$		−	1.62505e7i		−	0.862266i
$814$	2.58822e6			0.136912
$815$	−1.49134e6	−	8.20237e6i	−0.0786471	−	0.432559i
$816$	7.34003e6			0.385898
$817$			5.09268e6i			0.266926i
$818$		−	1.45340e7i		−	0.759453i
$819$	5.07938e6			0.264607
$820$	2.11024e6	−	383680.i	0.109597	−	0.0199267i
$821$	3.67967e7			1.90525			0.952623	−	0.304154i	$-0.0983737\pi$
$821$	3.67967e7			1.90525			0.952623	+	0.304154i	$0.0983737\pi$
$822$		−	6.04397e6i		−	0.311991i
$823$			3.30668e7i			1.70174i	0.525376	+	0.850870i	$0.323925\pi$
$823$			3.30668e7i			1.70174i	−0.525376	+	0.850870i	$0.676075\pi$
$824$	7.94330e6			0.407552
$825$	2.27920e6	+	6.06060e6i	0.116586	+	0.310014i
$826$	2.51157e7			1.28084
$827$			1.77309e7i			0.901505i	0.892649	+	0.450752i	$0.148844\pi$
$827$			1.77309e7i			0.901505i	−0.892649	+	0.450752i	$0.851156\pi$
$828$		−	936992.i		−	0.0474963i
$829$	−1.29375e7			−0.653830			−0.326915	−	0.945054i	$-0.606009\pi$
$829$	−1.29375e7			−0.653830			−0.326915	+	0.945054i	$0.606009\pi$
$830$	6.12172e6	−	1.11304e6i	0.308445	−	0.0560810i
$831$	−3.52102e7			−1.76875
$832$			2.80166e6i			0.140316i
$833$		−	1.67055e7i		−	0.834157i
$834$	−1.10018e7			−0.547705
$835$	−5.59602e6	−	3.07781e7i	−0.277756	−	1.52766i
$836$	−5.25696e6			−0.260147
$837$			8.31488e6i			0.410244i
$838$		−	1.45751e7i		−	0.716972i
$839$	−3.31812e7			−1.62738			−0.813688	−	0.581302i	$-0.802543\pi$
$839$	−3.31812e7			−1.62738			−0.813688	+	0.581302i	$0.802543\pi$
$840$	1.41568e6	+	7.78624e6i	0.0692256	+	0.380741i
$841$	−2.04382e7			−0.996446
$842$			7.30119e6i			0.354906i
$843$		−	2.92040e7i		−	1.41538i
$844$	1.28888e7			0.622810
$845$	−5.31096e6	+	965630.i	−0.255877	+	0.0465231i
$846$	−2.00822e6			−0.0964683
$847$		−	2.19852e7i		−	1.05299i
$848$		−	758784.i		−	0.0362350i
$849$	3.13324e7			1.49185
$850$	2.39616e7	−	9.01120e6i	1.13754	−	0.427795i
$851$	5.44751e6			0.257854
$852$		−	951552.i		−	0.0449090i
$853$			5.17224e6i			0.243392i	0.992567	+	0.121696i	$0.0388332\pi$
$853$			5.17224e6i			0.243392i	−0.992567	+	0.121696i	$0.961167\pi$
$854$	−2.67323e7			−1.25427
$855$	−5.73870e6	+	1.04340e6i	−0.268472	+	0.0488130i
$856$	2.70989e6			0.126406
$857$		−	1.05320e7i		−	0.489845i	−0.969543	−	0.244922i	$-0.921238\pi$
$857$		−	1.05320e7i		−	0.489845i	0.969543	−	0.244922i	$-0.0787625\pi$
$858$		−	5.66899e6i		−	0.262898i
$859$	1.14741e7			0.530563			0.265282	−	0.964171i	$-0.414535\pi$
$859$	1.14741e7			0.530563			0.265282	+	0.964171i	$0.414535\pi$
$860$	367040.	+	2.01872e6i	0.0169226	+	0.0930743i
$861$	−5.30438e6			−0.243852
$862$		−	1.14174e7i		−	0.523359i
$863$		−	1.92722e7i		−	0.880856i	−0.897788	−	0.440428i	$-0.854827\pi$
$863$		−	1.92722e7i		−	0.880856i	0.897788	−	0.440428i	$-0.145173\pi$
$864$	−4.15744e6			−0.189471
$865$	−3.43804e6	−	1.89092e7i	−0.156232	−	0.859277i
$866$	2.35110e6			0.106531
$867$			3.88423e7i			1.75492i
$868$			5.17734e6i			0.233243i
$869$	5.22144e6			0.234553
$870$	−831600.	+	151200.i	−0.0372491	+	0.00677257i
$871$	2.19550e7			0.980593
$872$			2.30336e6i			0.102582i
$873$		−	4.56990e6i		−	0.202942i
$874$	−1.10645e7			−0.489951
$875$	1.41805e7	+	2.36802e7i	0.626140	+	1.04560i
$876$	6.74330e6			0.296901
$877$			2.30524e7i			1.01208i	0.862509	+	0.506042i	$0.168892\pi$
$877$			2.30524e7i			1.01208i	−0.862509	+	0.506042i	$0.831108\pi$
$878$			2.44642e7i			1.07101i
$879$	1.36606e7			0.596344
$880$	−2.08384e6	+	378880.i	−0.0907105	+	0.0164928i
$881$	2.26690e7			0.983994			0.491997	−	0.870597i	$-0.336267\pi$
$881$	2.26690e7			0.983994			0.491997	+	0.870597i	$0.336267\pi$
$882$			1.53352e6i			0.0663769i
$883$		−	3.67337e6i		−	0.158549i	−0.996853	−	0.0792745i	$-0.974740\pi$
$883$		−	3.67337e6i		−	0.158549i	0.996853	−	0.0792745i	$-0.0252604\pi$
$884$	−2.24133e7			−0.964662
$885$	−5.56360e6	−	3.05998e7i	−0.238780	−	1.31329i
$886$	9.43082e6			0.403613
$887$			3.39649e7i			1.44951i	0.689007	+	0.724755i	$0.258047\pi$
$887$			3.39649e7i			1.44951i	−0.689007	+	0.724755i	$0.741953\pi$
$888$		−	3.91731e6i		−	0.166708i
$889$	−2.76876e7			−1.17498
$890$	−3.40840e6	−	1.87462e7i	−0.144237	−	0.793301i
$891$	6.72201e6			0.283665
$892$			1.94969e7i			0.820451i
$893$			2.37140e7i			0.995123i
$894$	7.77560e6			0.325379
$895$	−1.31890e6	+	239800.i	−0.0550369	+	0.0100067i
$896$	−2.58867e6			−0.107723
$897$		−	1.19317e7i		−	0.495132i
$898$			2.19894e7i			0.909960i
$899$	−552960.			−0.0228189
$900$	−2.19960e6	+	827200.i	−0.0905185	+	0.0340412i
$901$	6.07027e6			0.249113
$902$		−	1.41962e6i		−	0.0580971i
$903$		−	5.07433e6i		−	0.207090i
$904$	−1.46442e7			−0.595999
$905$	−3.58544e7	+	6.51898e6i	−1.45519	+	0.264581i
$906$	−2.33045e7			−0.943234
$907$		−	2.13327e7i		−	0.861050i	−0.902579	−	0.430525i	$-0.858328\pi$
$907$		−	2.13327e7i		−	0.861050i	0.902579	−	0.430525i	$-0.141672\pi$
$908$		−	9.02941e6i		−	0.363450i
$909$	−202006.			−0.00810876
$910$	−4.32288e6	−	2.37758e7i	−0.173049	−	0.951771i
$911$	−1.03512e7			−0.413235			−0.206617	−	0.978422i	$-0.566246\pi$
$911$	−1.03512e7			−0.413235			−0.206617	+	0.978422i	$0.566246\pi$
$912$			7.95648e6i			0.316763i
$913$		−	4.11825e6i		−	0.163507i
$914$	−4.64157e6			−0.183780
$915$	5.92172e6	+	3.25695e7i	0.233827	+	1.28605i
$916$	8.96528e6			0.353041
$917$			4.73450e7i			1.85931i
$918$		−	3.32595e7i		−	1.30259i
$919$	2.59019e7			1.01168			0.505839	−	0.862628i	$-0.331183\pi$
$919$	2.59019e7			1.01168			0.505839	+	0.862628i	$0.331183\pi$
$920$	−4.38592e6	+	797440.i	−0.170841	+	0.0310619i
$921$	1.23001e6			0.0477816
$922$			9.21319e6i			0.356930i
$923$			2.90563e6i			0.112263i
$924$	5.23802e6			0.201831
$925$	−4.80920e6	−	1.27881e7i	−0.184807	−	0.491419i
$926$	−1.08537e7			−0.415960
$927$		−	5.83336e6i		−	0.222956i
$928$		−	276480.i		−	0.0105389i
$929$	3.13230e7			1.19076			0.595379	−	0.803445i	$-0.297002\pi$
$929$	3.13230e7			1.19076			0.595379	+	0.803445i	$0.297002\pi$
$930$	6.30784e6	−	1.14688e6i	0.239152	−	0.0434821i
$931$	1.81085e7			0.684714
$932$		−	4.69722e6i		−	0.177134i
$933$		−	8.39093e6i		−	0.315577i
$934$	1.62020e7			0.607717
$935$	−3.03104e6	−	1.66707e7i	−0.113387	−	0.623628i
$936$	2.05747e6			0.0767617
$937$		−	2.08461e7i		−	0.775667i	−0.921729	−	0.387833i	$-0.873224\pi$
$937$		−	2.08461e7i		−	0.775667i	0.921729	−	0.387833i	$-0.126776\pi$
$938$			2.02859e7i			0.752814i
$939$	2.93078e7			1.08472
$940$	1.70912e6	+	9.40016e6i	0.0630889	+	0.346989i
$941$	−3.82929e7			−1.40976			−0.704878	−	0.709328i	$-0.748998\pi$
$941$	−3.82929e7			−1.40976			−0.704878	+	0.709328i	$0.748998\pi$
$942$		−	2.42540e7i		−	0.890547i
$943$		−	2.98791e6i		−	0.109418i
$944$	1.01734e7			0.371568
$945$	3.52814e7	−	6.41480e6i	1.28519	−	0.233670i
$946$	1.35805e6			0.0493387
$947$		−	4.25088e7i		−	1.54029i	−0.637866	−	0.770147i	$-0.720183\pi$
$947$		−	4.25088e7i		−	1.54029i	0.637866	−	0.770147i	$-0.279817\pi$
$948$		−	7.90272e6i		−	0.285598i
$949$	−2.05911e7			−0.742189
$950$	9.76800e6	+	2.59740e7i	0.351153	+	0.933748i
$951$	−3.38275e7			−1.21288
$952$		−	2.07094e7i		−	0.740585i
$953$		−	3.91855e7i		−	1.39763i	−0.715302	−	0.698816i	$-0.753711\pi$
$953$		−	3.91855e7i		−	1.39763i	0.715302	−	0.698816i	$-0.246289\pi$
$954$	−557232.			−0.0198228
$955$	1.11514e7	−	2.02752e6i	0.395658	−	0.0719377i
$956$	9.34784e6			0.330801
$957$			559440.i			0.0197458i
$958$			2.24211e7i			0.789303i
$959$	−1.70526e7			−0.598749
$960$	573440.	+	3.15392e6i	0.0200821	+	0.110452i
$961$	−2.44348e7			−0.853495
$962$			1.19618e7i			0.416734i
$963$		−	1.99007e6i		−	0.0691518i
$964$	9.02077e6			0.312645
$965$	4.52656e6	+	2.48961e7i	0.156477	+	0.860622i
$966$	1.10246e7			0.380120
$967$		−	1.84836e7i		−	0.635653i	−0.948149	−	0.317827i	$-0.897047\pi$
$967$		−	1.84836e7i		−	0.635653i	0.948149	−	0.317827i	$-0.102953\pi$
$968$		−	8.90541e6i		−	0.305468i
$969$	−6.36518e7			−2.17772
$970$	−2.13910e7	+	3.88928e6i	−0.729966	+	0.132721i
$971$	3.95031e7			1.34457			0.672284	−	0.740294i	$-0.265314\pi$
$971$	3.95031e7			1.34457			0.672284	+	0.740294i	$0.265314\pi$
$972$			5.61142e6i			0.190505i
$973$			3.10407e7i			1.05111i
$974$	2.85267e7			0.963506
$975$	−2.80098e7	+	1.05336e7i	−0.943623	+	0.354867i
$976$	−1.08283e7			−0.363861
$977$			3.29043e7i			1.10285i	0.834225	+	0.551425i	$0.185916\pi$
$977$			3.29043e7i			1.10285i	−0.834225	+	0.551425i	$0.814084\pi$
$978$			8.35150e6i			0.279201i
$979$	−1.26111e7			−0.420529
$980$	7.17816e6	−	1.30512e6i	0.238753	−	0.0434095i
$981$	1.69153e6			0.0561186
$982$		−	2.35258e7i		−	0.778513i
$983$			2.65797e7i			0.877338i	0.898649	+	0.438669i	$0.144550\pi$
$983$			2.65797e7i			0.877338i	−0.898649	+	0.438669i	$0.855450\pi$
$984$	−2.14861e6			−0.0707407
$985$	3.37468e6	+	1.85607e7i	0.110826	+	0.609544i
$986$	2.21184e6			0.0724538
$987$		−	2.36286e7i		−	0.772049i
$988$		−	2.42957e7i		−	0.791839i
$989$	2.85832e6			0.0929225
$990$	278240.	+	1.53032e6i	0.00902260	+	0.0496243i
$991$	1.92964e7			0.624153			0.312077	−	0.950057i	$-0.398975\pi$
$991$	1.92964e7			0.624153			0.312077	+	0.950057i	$0.398975\pi$
$992$			2.09715e6i			0.0676629i
$993$			2.29733e7i			0.739349i
$994$	−2.68474e6			−0.0861858
$995$	3.08550e7	−	5.61000e6i	0.988025	−	0.179641i
$996$	−6.23302e6			−0.199090
$997$		−	5.12017e7i		−	1.63135i	−0.578511	−	0.815674i	$-0.696366\pi$
$997$		−	5.12017e7i		−	1.63135i	0.578511	−	0.815674i	$-0.303634\pi$
$998$			7.02840e6i			0.223373i
$999$	−1.77503e7			−0.562720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.6.b.a.9.1	✓	2
3.2	odd	2		90.6.c.a.19.2		2
4.3	odd	2		80.6.c.c.49.2		2
5.2	odd	4		50.6.a.e.1.1		1
5.3	odd	4		50.6.a.c.1.1		1
5.4	even	2	inner	10.6.b.a.9.2	yes	2
8.3	odd	2		320.6.c.a.129.1		2
8.5	even	2		320.6.c.b.129.2		2
12.11	even	2		720.6.f.a.289.2		2
15.2	even	4		450.6.a.c.1.1		1
15.8	even	4		450.6.a.w.1.1		1
15.14	odd	2		90.6.c.a.19.1		2
20.3	even	4		400.6.a.c.1.1		1
20.7	even	4		400.6.a.k.1.1		1
20.19	odd	2		80.6.c.c.49.1		2
40.19	odd	2		320.6.c.a.129.2		2
40.29	even	2		320.6.c.b.129.1		2
60.59	even	2		720.6.f.a.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.6.b.a.9.1	✓	2	1.1	even	1	trivial
10.6.b.a.9.2	yes	2	5.4	even	2	inner
50.6.a.c.1.1		1	5.3	odd	4
50.6.a.e.1.1		1	5.2	odd	4
80.6.c.c.49.1		2	20.19	odd	2
80.6.c.c.49.2		2	4.3	odd	2
90.6.c.a.19.1		2	15.14	odd	2
90.6.c.a.19.2		2	3.2	odd	2
320.6.c.a.129.1		2	8.3	odd	2
320.6.c.a.129.2		2	40.19	odd	2
320.6.c.b.129.1		2	40.29	even	2
320.6.c.b.129.2		2	8.5	even	2
400.6.a.c.1.1		1	20.3	even	4
400.6.a.k.1.1		1	20.7	even	4
450.6.a.c.1.1		1	15.2	even	4
450.6.a.w.1.1		1	15.8	even	4
720.6.f.a.289.1		2	60.59	even	2
720.6.f.a.289.2		2	12.11	even	2

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -14.0000i q^{3} -16.0000 q^{4} +(55.0000 - 10.0000i) q^{5} -56.0000 q^{6} +158.000i q^{7} +64.0000i q^{8} +47.0000 q^{9} +(-40.0000 - 220.000i) q^{10} -148.000 q^{11} +224.000i q^{12} -684.000i q^{13} +632.000 q^{14} +(-140.000 - 770.000i) q^{15} +256.000 q^{16} +2048.00i q^{17} -188.000i q^{18} -2220.00 q^{19} +(-880.000 + 160.000i) q^{20} +2212.00 q^{21} +592.000i q^{22} +1246.00i q^{23} +896.000 q^{24} +(2925.00 - 1100.00i) q^{25} -2736.00 q^{26} -4060.00i q^{27} -2528.00i q^{28} +270.000 q^{29} +(-3080.00 + 560.000i) q^{30} -2048.00 q^{31} -1024.00i q^{32} +2072.00i q^{33} +8192.00 q^{34} +(1580.00 + 8690.00i) q^{35} -752.000 q^{36} -4372.00i q^{37} +8880.00i q^{38} -9576.00 q^{39} +(640.000 + 3520.00i) q^{40} -2398.00 q^{41} -8848.00i q^{42} -2294.00i q^{43} +2368.00 q^{44} +(2585.00 - 470.000i) q^{45} +4984.00 q^{46} -10682.0i q^{47} -3584.00i q^{48} -8157.00 q^{49} +(-4400.00 - 11700.0i) q^{50} +28672.0 q^{51} +10944.0i q^{52} -2964.00i q^{53} -16240.0 q^{54} +(-8140.00 + 1480.00i) q^{55} -10112.0 q^{56} +31080.0i q^{57} -1080.00i q^{58} +39740.0 q^{59} +(2240.00 + 12320.0i) q^{60} -42298.0 q^{61} +8192.00i q^{62} +7426.00i q^{63} -4096.00 q^{64} +(-6840.00 - 37620.0i) q^{65} +8288.00 q^{66} +32098.0i q^{67} -32768.0i q^{68} +17444.0 q^{69} +(34760.0 - 6320.00i) q^{70} -4248.00 q^{71} +3008.00i q^{72} -30104.0i q^{73} -17488.0 q^{74} +(-15400.0 - 40950.0i) q^{75} +35520.0 q^{76} -23384.0i q^{77} +38304.0i q^{78} -35280.0 q^{79} +(14080.0 - 2560.00i) q^{80} -45419.0 q^{81} +9592.00i q^{82} +27826.0i q^{83} -35392.0 q^{84} +(20480.0 + 112640. i) q^{85} -9176.00 q^{86} -3780.00i q^{87} -9472.00i q^{88} +85210.0 q^{89} +(-1880.00 - 10340.0i) q^{90} +108072. q^{91} -19936.0i q^{92} +28672.0i q^{93} -42728.0 q^{94} +(-122100. + 22200.0i) q^{95} -14336.0 q^{96} -97232.0i q^{97} +32628.0i q^{98} -6956.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} + 110 q^{5} - 112 q^{6} + 94 q^{9} - 80 q^{10} - 296 q^{11} + 1264 q^{14} - 280 q^{15} + 512 q^{16} - 4440 q^{19} - 1760 q^{20} + 4424 q^{21} + 1792 q^{24} + 5850 q^{25} - 5472 q^{26} + 540 q^{29}+ \cdots - 13912 q^{99}+O(q^{100}) \) 2 * q - 32 * q^4 + 110 * q^5 - 112 * q^6 + 94 * q^9 - 80 * q^10 - 296 * q^11 + 1264 * q^14 - 280 * q^15 + 512 * q^16 - 4440 * q^19 - 1760 * q^20 + 4424 * q^21 + 1792 * q^24 + 5850 * q^25 - 5472 * q^26 + 540 * q^29 - 6160 * q^30 - 4096 * q^31 + 16384 * q^34 + 3160 * q^35 - 1504 * q^36 - 19152 * q^39 + 1280 * q^40 - 4796 * q^41 + 4736 * q^44 + 5170 * q^45 + 9968 * q^46 - 16314 * q^49 - 8800 * q^50 + 57344 * q^51 - 32480 * q^54 - 16280 * q^55 - 20224 * q^56 + 79480 * q^59 + 4480 * q^60 - 84596 * q^61 - 8192 * q^64 - 13680 * q^65 + 16576 * q^66 + 34888 * q^69 + 69520 * q^70 - 8496 * q^71 - 34976 * q^74 - 30800 * q^75 + 71040 * q^76 - 70560 * q^79 + 28160 * q^80 - 90838 * q^81 - 70784 * q^84 + 40960 * q^85 - 18352 * q^86 + 170420 * q^89 - 3760 * q^90 + 216144 * q^91 - 85456 * q^94 - 244200 * q^95 - 28672 * q^96 - 13912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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