LMFDB - Embedded newform 48.7.i.a.5.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, degree $2$, 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.20
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74289 + 7.80784i) q^{2} +(26.7985 - 3.29233i) q^{3} +(-57.9246 - 27.2165i) q^{4} +(59.2583 - 59.2583i) q^{5} +(-21.0010 + 214.977i) q^{6} -2.09133i q^{7} +(313.458 - 404.831i) q^{8} +(707.321 - 176.459i) q^{9} +O(q^{10})$	\(q+(-1.74289 + 7.80784i) q^{2} +(26.7985 - 3.29233i) q^{3} +(-57.9246 - 27.2165i) q^{4} +(59.2583 - 59.2583i) q^{5} +(-21.0010 + 214.977i) q^{6} -2.09133i q^{7} +(313.458 - 404.831i) q^{8} +(707.321 - 176.459i) q^{9} +(359.398 + 565.960i) q^{10} +(842.725 - 842.725i) q^{11} +(-1641.90 - 538.653i) q^{12} +(1366.40 - 1366.40i) q^{13} +(16.3287 + 3.64496i) q^{14} +(1392.94 - 1783.13i) q^{15} +(2614.53 + 3153.01i) q^{16} +3071.62i q^{17} +(144.980 + 5830.20i) q^{18} +(-1710.92 + 1710.92i) q^{19} +(-5045.31 + 1819.71i) q^{20} +(-6.88534 - 56.0445i) q^{21} +(5111.08 + 8048.64i) q^{22} +13903.8 q^{23} +(7067.38 - 11880.9i) q^{24} +8601.91i q^{25} +(8287.17 + 13050.2i) q^{26} +(18374.2 - 7057.58i) q^{27} +(-56.9185 + 121.139i) q^{28} +(5593.27 + 5593.27i) q^{29} +(11494.7 + 13983.6i) q^{30} -12523.8 q^{31} +(-29175.0 + 14918.5i) q^{32} +(19809.3 - 25358.3i) q^{33} +(-23982.7 - 5353.50i) q^{34} +(-123.928 - 123.928i) q^{35} +(-45773.9 - 9029.44i) q^{36} +(-66388.7 - 66388.7i) q^{37} +(-10376.6 - 16340.5i) q^{38} +(32119.0 - 41116.3i) q^{39} +(-5414.59 - 42564.6i) q^{40} +22700.4 q^{41} +(449.587 + 43.9199i) q^{42} +(-86617.3 - 86617.3i) q^{43} +(-71750.5 + 25878.6i) q^{44} +(31458.0 - 52371.3i) q^{45} +(-24232.9 + 108559. i) q^{46} +77853.7i q^{47} +(80446.3 + 75888.0i) q^{48} +117645. q^{49} +(-67162.3 - 14992.2i) q^{50} +(10112.8 + 82314.8i) q^{51} +(-116337. + 41959.8i) q^{52} +(123405. - 123405. i) q^{53} +(23080.2 + 155763. i) q^{54} -99876.9i q^{55} +(-846.634 - 655.544i) q^{56} +(-40217.2 + 51483.1i) q^{57} +(-53419.8 + 33922.9i) q^{58} +(-162615. + 162615. i) q^{59} +(-129216. + 65376.5i) q^{60} +(165494. - 165494. i) q^{61} +(21827.6 - 97783.7i) q^{62} +(-369.034 - 1479.24i) q^{63} +(-65632.0 - 253795. i) q^{64} -161942. i q^{65} +(163468. + 198864. i) q^{66} +(-385147. + 385147. i) q^{67} +(83598.5 - 177922. i) q^{68} +(372602. - 45776.1i) q^{69} +(1183.61 - 751.619i) q^{70} -190032. q^{71} +(150279. - 341658. i) q^{72} +358162. i q^{73} +(634061. - 402644. i) q^{74} +(28320.4 + 230519. i) q^{75} +(145670. - 52539.3i) q^{76} +(-1762.41 - 1762.41i) q^{77} +(265049. + 322441. i) q^{78} -493007. q^{79} +(341774. + 31909.3i) q^{80} +(469165. - 249627. i) q^{81} +(-39564.3 + 177241. i) q^{82} +(465981. + 465981. i) q^{83} +(-1126.50 + 3433.75i) q^{84} +(182019. + 182019. i) q^{85} +(827259. - 525329. i) q^{86} +(168306. + 131476. i) q^{87} +(-77002.1 - 605320. i) q^{88} -1.25673e6 q^{89} +(354079. + 336896. i) q^{90} +(-2857.60 - 2857.60i) q^{91} +(-805375. - 378413. i) q^{92} +(-335619. + 41232.5i) q^{93} +(-607869. - 135691. i) q^{94} +202772. i q^{95} +(-732731. + 495847. i) q^{96} +121446. q^{97} +(-205042. + 918550. i) q^{98} +(447371. - 744784. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.74289	+	7.80784i	−0.217862	+	0.975980i
$2$	−1.74289	+	7.80784i	−0.217862	+	0.975980i
$3$	26.7985	−	3.29233i	0.992538	−	0.121938i
$3$	26.7985	−	3.29233i	0.992538	−	0.121938i
$4$	−57.9246	−	27.2165i	−0.905073	−	0.425257i
$5$	59.2583	−	59.2583i	0.474066	−	0.474066i	−0.429162	−	0.903228i	$-0.641191\pi$
$5$	59.2583	−	59.2583i	0.474066	−	0.474066i	0.903228	+	0.429162i	$0.141191\pi$
$6$	−21.0010	+	214.977i	−0.0972267	+	0.995262i
$7$		−	2.09133i		−	0.00609716i	−0.999995	−	0.00304858i	$-0.999030\pi$
$7$		−	2.09133i		−	0.00609716i	0.999995	−	0.00304858i	$-0.000970395\pi$
$8$	313.458	−	404.831i	0.612223	−	0.790685i
$9$	707.321	−	176.459i	0.970262	−	0.242057i
$10$	359.398	+	565.960i	0.359398	+	0.565960i
$11$	842.725	−	842.725i	0.633152	−	0.633152i	−0.315705	−	0.948857i	$-0.602241\pi$
$11$	842.725	−	842.725i	0.633152	−	0.633152i	0.948857	+	0.315705i	$0.102241\pi$
$12$	−1641.90	−	538.653i	−0.950174	−	0.311721i
$13$	1366.40	−	1366.40i	0.621941	−	0.621941i	−0.324086	−	0.946027i	$-0.605057\pi$
$13$	1366.40	−	1366.40i	0.621941	−	0.621941i	0.946027	+	0.324086i	$0.105057\pi$
$14$	16.3287	+	3.64496i	0.00595071	+	0.00132834i
$15$	1392.94	−	1783.13i	0.412722	−	0.528335i
$16$	2614.53	+	3153.01i	0.638313	+	0.769777i
$17$			3071.62i			0.625202i	0.949885	+	0.312601i	$0.101200\pi$
$17$			3071.62i			0.625202i	−0.949885	+	0.312601i	$0.898800\pi$
$18$	144.980	+	5830.20i	0.0248593	+	0.999691i
$19$	−1710.92	+	1710.92i	−0.249442	+	0.249442i	−0.820741	−	0.571300i	$-0.806439\pi$
$19$	−1710.92	+	1710.92i	−0.249442	+	0.249442i	0.571300	+	0.820741i	$0.306439\pi$
$20$	−5045.31	+	1819.71i	−0.630664	+	0.227464i
$21$	−6.88534	−	56.0445i	−0.000743477	−	0.00605167i
$22$	5111.08	+	8048.64i	0.480004	+	0.755883i
$23$	13903.8			1.14275			0.571375	−	0.820689i	$-0.306410\pi$
$23$	13903.8			1.14275			0.571375	+	0.820689i	$0.306410\pi$
$24$	7067.38	−	11880.9i	0.511240	−	0.859438i
$25$			8601.91i			0.550522i
$26$	8287.17	+	13050.2i	0.471505	+	0.742499i
$27$	18374.2	−	7057.58i	0.933506	−	0.358562i
$28$	−56.9185	+	121.139i	−0.00259286	+	0.00551838i
$29$	5593.27	+	5593.27i	0.229336	+	0.229336i	0.812415	−	0.583079i	$-0.198152\pi$
$29$	5593.27	+	5593.27i	0.229336	+	0.229336i	−0.583079	+	0.812415i	$0.698152\pi$
$30$	11494.7	+	13983.6i	0.425728	+	0.517912i
$31$	−12523.8			−0.420388			−0.210194	−	0.977660i	$-0.567410\pi$
$31$	−12523.8			−0.420388			−0.210194	+	0.977660i	$0.567410\pi$
$32$	−29175.0	+	14918.5i	−0.890351	+	0.455275i
$33$	19809.3	−	25358.3i	0.551222	−	0.705632i
$34$	−23982.7	−	5353.50i	−0.610184	−	0.136208i
$35$	−123.928	−	123.928i	−0.00289046	−	0.00289046i
$36$	−45773.9	−	9029.44i	−0.981094	−	0.193532i
$37$	−66388.7	−	66388.7i	−1.31066	−	1.31066i	−0.920931	−	0.389726i	$-0.872570\pi$
$37$	−66388.7	−	66388.7i	−1.31066	−	1.31066i	−0.389726	−	0.920931i	$-0.627430\pi$
$38$	−10376.6	−	16340.5i	−0.189106	−	0.297794i
$39$	32119.0	−	41116.3i	0.541462	−	0.693138i
$40$	−5414.59	−	42564.6i	−0.0846030	−	0.665071i
$41$	22700.4			0.329368			0.164684	−	0.986346i	$-0.447340\pi$
$41$	22700.4			0.329368			0.164684	+	0.986346i	$0.447340\pi$
$42$	449.587	+	43.9199i	0.00606828	+	0.000592807i
$43$	−86617.3	−	86617.3i	−1.08943	−	1.08943i	−0.995587	−	0.0938429i	$-0.970085\pi$
$43$	−86617.3	−	86617.3i	−1.08943	−	1.08943i	−0.0938429	−	0.995587i	$-0.529915\pi$
$44$	−71750.5	+	25878.6i	−0.842301	+	0.303796i
$45$	31458.0	−	52371.3i	0.345218	−	0.574719i
$46$	−24232.9	+	108559.i	−0.248962	+	1.11530i
$47$			77853.7i			0.749869i	0.927051	+	0.374935i	$0.122335\pi$
$47$			77853.7i			0.749869i	−0.927051	+	0.374935i	$0.877665\pi$
$48$	80446.3	+	75888.0i	0.727415	+	0.686198i
$49$	117645.			0.999963
$50$	−67162.3	−	14992.2i	−0.537299	−	0.119938i
$51$	10112.8	+	82314.8i	0.0762360	+	0.620536i
$52$	−116337.	+	41959.8i	−0.827387	+	0.298417i
$53$	123405.	−	123405.i	0.828903	−	0.828903i	−0.158462	−	0.987365i	$-0.550654\pi$
$53$	123405.	−	123405.i	0.828903	−	0.828903i	0.987365	+	0.158462i	$0.0506536\pi$
$54$	23080.2	+	155763.i	0.146574	+	0.989200i
$55$		−	99876.9i		−	0.600312i
$56$	−846.634	−	655.544i	−0.00482094	−	0.00373282i
$57$	−40217.2	+	51483.1i	−0.217164	+	0.277997i
$58$	−53419.8	+	33922.9i	−0.273790	+	0.173863i
$59$	−162615.	+	162615.i	−0.791782	+	0.791782i	−0.981784	−	0.190002i	$-0.939151\pi$
$59$	−162615.	+	162615.i	−0.791782	+	0.791782i	0.190002	+	0.981784i	$0.439151\pi$
$60$	−129216.	+	65376.5i	−0.598222	+	0.302669i
$61$	165494.	−	165494.i	0.729108	−	0.729108i	−0.241334	−	0.970442i	$-0.577585\pi$
$61$	165494.	−	165494.i	0.729108	−	0.729108i	0.970442	+	0.241334i	$0.0775850\pi$
$62$	21827.6	−	97783.7i	0.0915865	−	0.410291i
$63$	−369.034	−	1479.24i	−0.00147586	−	0.00591585i
$64$	−65632.0	−	253795.i	−0.250366	−	0.968151i
$65$		−	161942.i		−	0.589682i
$66$	163468.	+	198864.i	0.568593	+	0.691711i
$67$	−385147.	+	385147.i	−1.28057	+	1.28057i	−0.340221	+	0.940345i	$0.610502\pi$
$67$	−385147.	+	385147.i	−1.28057	+	1.28057i	−0.940345	+	0.340221i	$0.889498\pi$
$68$	83598.5	−	177922.i	0.265872	−	0.565853i
$69$	372602.	−	45776.1i	1.13422	−	0.139345i
$70$	1183.61	−	751.619i	0.00345075	−	0.00219131i
$71$	−190032.			−0.530946			−0.265473	−	0.964118i	$-0.585528\pi$
$71$	−190032.			−0.530946			−0.265473	+	0.964118i	$0.585528\pi$
$72$	150279.	−	341658.i	0.402626	−	0.915364i
$73$			358162.i			0.920685i	0.887741	+	0.460343i	$0.152273\pi$
$73$			358162.i			0.920685i	−0.887741	+	0.460343i	$0.847727\pi$
$74$	634061.	−	402644.i	1.56472	−	0.993633i
$75$	28320.4	+	230519.i	0.0671297	+	0.546414i
$76$	145670.	−	52539.3i	0.331840	−	0.119686i
$77$	−1762.41	−	1762.41i	−0.00386043	−	0.00386043i
$78$	265049.	+	322441.i	0.558525	+	0.679464i
$79$	−493007.			−0.999935			−0.499968	−	0.866044i	$-0.666655\pi$
$79$	−493007.			−0.999935			−0.499968	+	0.866044i	$0.666655\pi$
$80$	341774.	+	31909.3i	0.667528	+	0.0623228i
$81$	469165.	−	249627.i	0.882817	−	0.469717i
$82$	−39564.3	+	177241.i	−0.0717567	+	0.321457i
$83$	465981.	+	465981.i	0.814956	+	0.814956i	0.985372	−	0.170416i	$-0.0545113\pi$
$83$	465981.	+	465981.i	0.814956	+	0.814956i	−0.170416	+	0.985372i	$0.554511\pi$
$84$	−1126.50	+	3433.75i	−0.00190061	+	0.00579337i
$85$	182019.	+	182019.i	0.296387	+	0.296387i
$86$	827259.	−	525329.i	1.30061	−	0.825916i
$87$	168306.	+	131476.i	0.255589	+	0.199660i
$88$	−77002.1	−	605320.i	−0.112994	−	0.888254i
$89$	−1.25673e6			−1.78267			−0.891336	−	0.453342i	$-0.850232\pi$
$89$	−1.25673e6			−1.78267			−0.891336	+	0.453342i	$0.850232\pi$
$90$	354079.	+	336896.i	0.485705	+	0.462135i
$91$	−2857.60	−	2857.60i	−0.00379208	−	0.00379208i
$92$	−805375.	−	378413.i	−1.03427	−	0.485963i
$93$	−335619.	+	41232.5i	−0.417251	+	0.0512614i
$94$	−607869.	−	135691.i	−0.731857	−	0.163368i
$95$			202772.i			0.236504i
$96$	−732731.	+	495847.i	−0.828191	+	0.560446i
$97$	121446.			0.133067			0.0665334	−	0.997784i	$-0.478806\pi$
$97$	121446.			0.133067			0.0665334	+	0.997784i	$0.478806\pi$
$98$	−205042.	+	918550.i	−0.217854	+	0.975943i
$99$	447371.	−	744784.i	0.461065	−	0.767582i
$100$	234114.	−	498263.i	0.234114	−	0.498263i
$101$	−767493.	+	767493.i	−0.744921	+	0.744921i	−0.973521	−	0.228599i	$-0.926585\pi$
$101$	−767493.	+	767493.i	−0.744921	+	0.744921i	0.228599	+	0.973521i	$0.426585\pi$
$102$	−660326.	−	64506.9i	−0.622240	−	0.0607863i
$103$			857827.i			0.785033i	0.919745	+	0.392516i	$0.128395\pi$
$103$			857827.i			0.785033i	−0.919745	+	0.392516i	$0.871605\pi$
$104$	−124852.	−	981473.i	−0.110993	−	0.872526i
$105$	−3729.11	−	2913.09i	−0.00322135	−	0.00251643i
$106$	748442.	+	1.17860e6i	0.628406	+	0.989579i
$107$	−1.37873e6	+	1.37873e6i	−1.12546	+	1.12546i	−0.134550	+	0.990907i	$0.542959\pi$
$107$	−1.37873e6	+	1.37873e6i	−1.12546	+	1.12546i	−0.990907	+	0.134550i	$0.957041\pi$
$108$	−1.25640e6	−	91272.6i	−0.997372	−	0.0724551i
$109$	1.47597e6	−	1.47597e6i	1.13972	−	1.13972i	0.151221	−	0.988500i	$-0.451679\pi$
$109$	1.47597e6	−	1.47597e6i	1.13972	−	1.13972i	0.988500	−	0.151221i	$-0.0483206\pi$
$110$	779822.	+	174075.i	0.585892	+	0.130785i
$111$	−1.99769e6	−	1.56055e6i	−1.46070	−	1.14106i
$112$	6593.97	−	5467.84i	0.00469346	−	0.00389190i
$113$			515901.i			0.357545i	0.983890	+	0.178772i	$0.0572126\pi$
$113$			515901.i			0.357545i	−0.983890	+	0.178772i	$0.942787\pi$
$114$	−331877.	−	403739.i	−0.224008	−	0.272512i
$115$	823918.	−	823918.i	0.541739	−	0.541739i
$116$	−171759.	−	476217.i	−0.110039	−	0.305092i
$117$	725372.	−	1.20760e6i	0.452901	−	0.753991i
$118$	−986253.	−	1.55310e6i	−0.600264	−	0.945262i
$119$	6423.76			0.00381196
$120$	−285240.	−	1.12284e6i	−0.165069	−	0.649792i
$121$			351190.i			0.198238i
$122$	1.00371e6	+	1.58058e6i	0.552750	+	0.870439i
$123$	608336.	−	74737.2i	0.326910	−	0.0401625i
$124$	725436.	+	340853.i	0.380482	+	0.178773i
$125$	1.43565e6	+	1.43565e6i	0.735050	+	0.735050i
$126$	12192.9	−	303.200i	0.00609528	−	0.000151571i
$127$	−2.29866e6			−1.12218			−0.561092	−	0.827753i	$-0.689619\pi$
$127$	−2.29866e6			−1.12218			−0.561092	+	0.827753i	$0.689619\pi$
$128$	2.09598e6	−	70106.5i	0.999441	−	0.0334294i
$129$	−2.60639e6	−	2.03604e6i	−1.21414	−	0.948457i
$130$	1.26441e6	+	282247.i	0.575518	+	0.128469i
$131$	1.03363e6	+	1.03363e6i	0.459780	+	0.459780i	0.898583	−	0.438803i	$-0.144597\pi$
$131$	1.03363e6	+	1.03363e6i	0.459780	+	0.459780i	−0.438803	+	0.898583i	$0.644597\pi$
$132$	−1.83761e6	+	929734.i	−0.798971	+	0.404238i
$133$	3578.10	+	3578.10i	0.00152089	+	0.00152089i
$134$	−2.33590e6	−	3.67844e6i	−0.970821	−	1.52879i
$135$	670603.	−	1.50704e6i	0.272561	−	0.612526i
$136$	1.24349e6	+	962823.i	0.494338	+	0.382763i
$137$	−1.24822e6			−0.485434			−0.242717	−	0.970097i	$-0.578039\pi$
$137$	−1.24822e6			−0.485434			−0.242717	+	0.970097i	$0.578039\pi$
$138$	−291994.	+	2.98900e6i	−0.111106	+	1.13734i
$139$	2.18517e6	+	2.18517e6i	0.813654	+	0.813654i	0.985180	−	0.171525i	$-0.0548696\pi$
$139$	2.18517e6	+	2.18517e6i	0.813654	+	0.813654i	−0.171525	+	0.985180i	$0.554870\pi$
$140$	3805.62	+	10551.4i	0.00138689	+	0.00384526i
$141$	256320.	+	2.08636e6i	0.0914377	+	0.744273i
$142$	331205.	−	1.48374e6i	0.115673	−	0.518193i
$143$		−	2.30301e6i		−	0.787566i
$144$	2.40569e6	+	1.76883e6i	0.805660	+	0.592378i
$145$	662895.			0.217441
$146$	−2.79647e6	−	624239.i	−0.898570	−	0.200582i
$147$	3.15270e6	−	387325.i	0.992501	−	0.121934i
$148$	2.03868e6	+	5.65241e6i	0.628874	+	1.74361i
$149$	2.91037e6	−	2.91037e6i	0.879811	−	0.879811i	−0.113704	−	0.993515i	$-0.536271\pi$
$149$	2.91037e6	−	2.91037e6i	0.879811	−	0.879811i	0.993515	+	0.113704i	$0.0362714\pi$
$150$	−1.84921e6	−	180649.i	−0.547914	−	0.0535255i
$151$			34436.8i			0.0100021i	0.999987	+	0.00500105i	$0.00159189\pi$
$151$			34436.8i			0.0100021i	−0.999987	+	0.00500105i	$0.998408\pi$
$152$	156331.	+	1.22894e6i	0.0445160	+	0.349944i
$153$	542015.	+	2.17262e6i	0.151334	+	0.606610i
$154$	16832.3	−	10688.9i	0.00460874	−	0.00292666i
$155$	−742138.	+	742138.i	−0.199292	+	0.199292i
$156$	−2.97952e6	+	1.50748e6i	−0.784824	+	0.397080i
$157$	1.60553e6	−	1.60553e6i	0.414876	−	0.414876i	−0.468557	−	0.883433i	$-0.655226\pi$
$157$	1.60553e6	−	1.60553e6i	0.414876	−	0.414876i	0.883433	+	0.468557i	$0.155226\pi$
$158$	859259.	−	3.84932e6i	0.217848	−	0.975917i
$159$	2.90077e6	−	3.71335e6i	0.721643	−	0.923792i
$160$	−844818.	+	2.61290e6i	−0.206254	+	0.637916i
$161$		−	29077.5i		−	0.00696754i
$162$	1.13134e6	+	4.09824e6i	0.266102	+	0.963945i
$163$	1.48327e6	−	1.48327e6i	0.342498	−	0.342498i	−0.514807	−	0.857306i	$-0.672137\pi$
$163$	1.48327e6	−	1.48327e6i	0.342498	−	0.342498i	0.857306	+	0.514807i	$0.172137\pi$
$164$	−1.31491e6	−	617824.i	−0.298102	−	0.140066i
$165$	−328828.	−	2.67655e6i	−0.0732009	−	0.595832i
$166$	−4.45046e6	+	2.82615e6i	−0.972928	+	0.617833i
$167$	761054.			0.163405			0.0817026	−	0.996657i	$-0.473964\pi$
$167$	761054.			0.163405			0.0817026	+	0.996657i	$0.473964\pi$
$168$	−24846.8	−	14780.2i	−0.00524014	−	0.00311711i
$169$			1.09269e6i			0.226379i
$170$	−1.73841e6	+	1.10393e6i	−0.353839	+	0.224696i
$171$	−908263.	+	1.51208e6i	−0.181645	+	0.302403i
$172$	2.65986e6	+	7.37469e6i	0.522725	+	1.44930i
$173$	5.57333e6	+	5.57333e6i	1.07641	+	1.07641i	0.996829	+	0.0795780i	$0.0253573\pi$
$173$	5.57333e6	+	5.57333e6i	1.07641	+	1.07641i	0.0795780	+	0.996829i	$0.474643\pi$
$174$	−1.31989e6	+	1.08496e6i	−0.250547	+	0.205952i
$175$	17989.4			0.00335663
$176$	4.86045e6	+	453789.i	0.891535	+	0.0832368i
$177$	−3.82247e6	+	4.89323e6i	−0.689325	+	0.882422i
$178$	2.19034e6	−	9.81234e6i	0.388376	−	1.73985i
$179$	326371.	+	326371.i	0.0569052	+	0.0569052i	0.734987	−	0.678082i	$-0.237188\pi$
$179$	326371.	+	326371.i	0.0569052	+	0.0569052i	−0.678082	+	0.734987i	$0.737188\pi$
$180$	−3.24755e6	+	2.17741e6i	−0.556851	+	0.373356i
$181$	−7.40642e6	−	7.40642e6i	−1.24903	−	1.24903i	−0.956149	−	0.292881i	$-0.905386\pi$
$181$	−7.40642e6	−	7.40642e6i	−1.24903	−	1.24903i	−0.292881	−	0.956149i	$-0.594614\pi$
$182$	27292.2	−	17331.2i	0.00452714	−	0.00287484i
$183$	3.89012e6	−	4.97984e6i	0.634761	−	0.812573i
$184$	4.35827e6	−	5.62871e6i	0.699618	−	0.903556i
$185$	−7.86816e6			−1.24268
$186$	263012.	−	2.69232e6i	0.0408730	−	0.418397i
$187$	2.58853e6	+	2.58853e6i	0.395848	+	0.395848i
$188$	2.11890e6	−	4.50965e6i	0.318887	−	0.678686i
$189$	−14759.7	−	38426.5i	−0.00218621	−	0.00569174i
$190$	−1.58321e6	−	353411.i	−0.230823	−	0.0515251i
$191$		−	1.06993e7i		−	1.53552i	−0.640735	−	0.767762i	$-0.721370\pi$
$191$		−	1.06993e7i		−	1.53552i	0.640735	−	0.767762i	$-0.278630\pi$
$192$	−2.59442e6	−	6.58525e6i	−0.366553	−	0.930397i
$193$	−1.97699e6			−0.275000			−0.137500	−	0.990502i	$-0.543907\pi$
$193$	−1.97699e6			−0.275000			−0.137500	+	0.990502i	$0.543907\pi$
$194$	−211668.	+	948234.i	−0.0289902	+	0.129870i
$195$	−533165.	−	4.33979e6i	−0.0719048	−	0.585282i
$196$	−6.81452e6	−	3.20187e6i	−0.905039	−	0.425241i
$197$	−4.06333e6	+	4.06333e6i	−0.531475	+	0.531475i	−0.921011	−	0.389536i	$-0.872635\pi$
$197$	−4.06333e6	+	4.06333e6i	−0.531475	+	0.531475i	0.389536	+	0.921011i	$0.372635\pi$
$198$	5.03543e6	+	4.79108e6i	0.648696	+	0.617216i
$199$			1.80797e6i			0.229421i	0.993399	+	0.114710i	$0.0365940\pi$
$199$			1.80797e6i			0.229421i	−0.993399	+	0.114710i	$0.963406\pi$
$200$	3.48232e6	+	2.69634e6i	0.435290	+	0.337042i
$201$	−9.05334e6	+	1.15894e7i	−1.11486	+	1.42716i
$202$	−4.65480e6	−	7.33012e6i	−0.564738	−	0.889318i
$203$	11697.4	−	11697.4i	0.00139830	−	0.00139830i
$204$	1.65454e6	−	5.04329e6i	0.194888	−	0.594050i
$205$	1.34519e6	−	1.34519e6i	0.156142	−	0.156142i
$206$	−6.69777e6	−	1.49510e6i	−0.766176	−	0.171029i
$207$	9.83448e6	−	2.45346e6i	1.10877	−	0.276610i
$208$	7.88079e6	+	735778.i	0.875749	+	0.0817630i
$209$			2.88367e6i			0.315869i
$210$	29244.3	−	24039.1i	0.00315780	−	0.00259574i
$211$	−9.24569e6	+	9.24569e6i	−0.984219	+	0.984219i	−0.999877	−	0.0156580i	$-0.995016\pi$
$211$	−9.24569e6	+	9.24569e6i	−0.984219	+	0.984219i	0.0156580	+	0.999877i	$0.495016\pi$
$212$	−1.05068e7	+	3.78953e6i	−1.10271	+	0.397721i
$213$	−5.09256e6	+	625647.i	−0.526984	+	0.0647427i
$214$	−8.36194e6	−	1.31679e7i	−0.853229	−	1.34362i
$215$	−1.02656e7			−1.03292
$216$	2.90241e6	−	9.65070e6i	0.288004	−	0.957629i
$217$			26191.3i			0.00256318i
$218$	8.95169e6	+	1.40966e7i	0.864043	+	1.36065i
$219$	1.17919e6	+	9.59822e6i	0.112267	+	0.913815i
$220$	−2.71829e6	+	5.78533e6i	−0.255287	+	0.543326i
$221$	4.19707e6	+	4.19707e6i	0.388839	+	0.388839i
$222$	1.56662e7	−	1.28778e7i	1.43188	−	1.17702i
$223$	−9.88905e6			−0.891743			−0.445872	−	0.895097i	$-0.647106\pi$
$223$	−9.88905e6			−0.891743			−0.445872	+	0.895097i	$0.647106\pi$
$224$	31199.4	+	61014.5i	0.00277589	+	0.00542861i
$225$	1.51789e6	+	6.08432e6i	0.133258	+	0.534151i
$226$	−4.02807e6	−	899160.i	−0.348957	−	0.0778953i
$227$	−1.84583e6	−	1.84583e6i	−0.157802	−	0.157802i	0.623790	−	0.781592i	$-0.285592\pi$
$227$	−1.84583e6	−	1.84583e6i	−0.157802	−	0.157802i	−0.781592	+	0.623790i	$0.785592\pi$
$228$	3.73075e6	−	1.88757e6i	0.314769	−	0.159257i
$229$	2.63596e6	+	2.63596e6i	0.219499	+	0.219499i	0.808287	−	0.588788i	$-0.200395\pi$
$229$	2.63596e6	+	2.63596e6i	0.219499	+	0.219499i	−0.588788	+	0.808287i	$0.700395\pi$
$230$	4.99702e6	+	7.86902e6i	0.410702	+	0.646751i
$231$	−53032.5	−	41427.6i	−0.00430236	−	0.00336089i
$232$	4.01758e6	−	511072.i	0.321737	−	0.0409278i
$233$	−5.01399e6			−0.396383			−0.198192	−	0.980163i	$-0.563507\pi$
$233$	−5.01399e6			−0.396383			−0.198192	+	0.980163i	$0.563507\pi$
$234$	8.16451e6	+	7.76831e6i	0.637210	+	0.606288i
$235$	4.61347e6	+	4.61347e6i	0.355488	+	0.355488i
$236$	1.38453e7	−	4.99362e6i	1.05333	−	0.379909i
$237$	−1.32119e7	+	1.62314e6i	−0.992474	+	0.121930i
$238$	−11195.9	+	50155.6i	−0.000830480	+	0.00372039i
$239$			1.42522e7i			1.04397i	0.852955	+	0.521984i	$0.174808\pi$
$239$			1.42522e7i			1.04397i	−0.852955	+	0.521984i	$0.825192\pi$
$240$	9.26410e6	−	270113.i	0.670146	−	0.0195395i
$241$	7.99472e6			0.571152			0.285576	−	0.958356i	$-0.407815\pi$
$241$	7.99472e6			0.571152			0.285576	+	0.958356i	$0.407815\pi$
$242$	−2.74203e6	−	612087.i	−0.193476	−	0.0431884i
$243$	1.17511e7	−	8.23427e6i	0.818953	−	0.573861i
$244$	−1.40903e7	+	5.08201e6i	−0.969954	+	0.349837i
$245$	6.97142e6	−	6.97142e6i	0.474049	−	0.474049i
$246$	−476730.	+	4.88005e6i	−0.0320234	+	0.327808i
$247$			4.67562e6i			0.310276i
$248$	−3.92568e6	+	5.07002e6i	−0.257371	+	0.332395i
$249$	1.40218e7	+	1.09534e7i	0.908248	+	0.709500i
$250$	−1.37115e7	+	8.70711e6i	−0.877533	+	0.557255i
$251$	8.90471e6	−	8.90471e6i	0.563117	−	0.563117i	−0.367075	−	0.930192i	$-0.619641\pi$
$251$	8.90471e6	−	8.90471e6i	0.563117	−	0.563117i	0.930192	+	0.367075i	$0.119641\pi$
$252$	−18883.5	+	95728.3i	−0.00118000	+	0.00598189i
$253$	1.17171e7	−	1.17171e7i	0.723535	−	0.723535i
$254$	4.00632e6	−	1.79476e7i	0.244481	−	1.09523i
$255$	5.47710e6	+	4.27857e6i	0.330316	+	0.258034i
$256$	−3.10569e6	+	1.64873e7i	−0.185113	+	0.982717i
$257$		−	2.87292e7i		−	1.69248i	−0.532798	−	0.846242i	$-0.678859\pi$
$257$		−	2.87292e7i		−	1.69248i	0.532798	−	0.846242i	$-0.321141\pi$
$258$	2.04397e7	−	1.68017e7i	1.19019	−	0.978347i
$259$	−138841.	+	138841.i	−0.00799129	+	0.00799129i
$260$	−4.40747e6	+	9.38041e6i	−0.250767	+	0.533705i
$261$	4.94322e6	+	2.96925e6i	0.278028	+	0.167004i
$262$	−9.87190e6	+	6.26890e6i	−0.548905	+	0.348568i
$263$	1.89544e7			1.04194			0.520970	−	0.853575i	$-0.325570\pi$
$263$	1.89544e7			1.04194			0.520970	+	0.853575i	$0.325570\pi$
$264$	−4.05646e6	−	1.59682e7i	−0.220463	−	0.867847i
$265$		−	1.46255e7i		−	0.785910i
$266$	−34173.4	+	21700.9i	−0.00181570	+	0.00115301i
$267$	−3.36785e7	+	4.13757e6i	−1.76937	+	0.217376i
$268$	3.27918e7	−	1.18272e7i	1.70358	−	0.614436i
$269$	−1.02772e7	−	1.02772e7i	−0.527980	−	0.527980i	0.391990	−	0.919970i	$-0.371787\pi$
$269$	−1.02772e7	−	1.02772e7i	−0.527980	−	0.527980i	−0.919970	+	0.391990i	$0.871787\pi$
$270$	1.05980e7	+	7.86257e6i	0.538432	+	0.399460i
$271$	−2.44749e7			−1.22974			−0.614868	−	0.788630i	$-0.710791\pi$
$271$	−2.44749e7			−1.22974			−0.614868	+	0.788630i	$0.710791\pi$
$272$	−9.68483e6	+	8.03083e6i	−0.481266	+	0.399074i
$273$	−85987.6	−	67171.3i	−0.00422618	−	0.00330138i
$274$	2.17552e6	−	9.74592e6i	0.105758	−	0.473774i
$275$	7.24905e6	+	7.24905e6i	0.348564	+	0.348564i
$276$	−2.28287e7	−	7.48936e6i	−1.08581	−	0.356219i
$277$	1.38988e7	+	1.38988e7i	0.653940	+	0.653940i	0.953939	−	0.300000i	$-0.0969866\pi$
$277$	1.38988e7	+	1.38988e7i	0.653940	+	0.653940i	−0.300000	+	0.953939i	$0.596987\pi$
$278$	−2.08699e7	+	1.32529e7i	−0.971374	+	0.616846i
$279$	−8.85834e6	+	2.20994e6i	−0.407887	+	0.101758i
$280$	−89016.4	+	11323.7i	−0.00405505	+	0.000515838i
$281$	2.20609e7			0.994270			0.497135	−	0.867673i	$-0.334385\pi$
$281$	2.20609e7			0.994270			0.497135	+	0.867673i	$0.334385\pi$
$282$	−1.67367e7	−	1.63500e6i	−0.746316	−	0.0729073i
$283$	−1.33701e7	−	1.33701e7i	−0.589895	−	0.589895i	0.347708	−	0.937603i	$-0.386960\pi$
$283$	−1.33701e7	−	1.33701e7i	−0.589895	−	0.589895i	−0.937603	+	0.347708i	$0.886960\pi$
$284$	1.10075e7	+	5.17199e6i	0.480545	+	0.225789i
$285$	667594.	+	5.43400e6i	0.0288388	+	0.234739i
$286$	1.79815e7	+	4.01389e6i	0.768649	+	0.171580i
$287$		−	47473.9i		−	0.00200821i
$288$	−1.80036e7	+	1.57003e7i	−0.753671	+	0.657252i
$289$	1.47027e7			0.609123
$290$	−1.15535e6	+	5.17577e6i	−0.0473720	+	0.212218i
$291$	3.25459e6	−	399842.i	0.132074	−	0.0162259i
$292$	9.74791e6	−	2.07464e7i	0.391528	−	0.833287i
$293$	8.22307e6	−	8.22307e6i	0.326912	−	0.326912i	−0.524499	−	0.851411i	$-0.675747\pi$
$293$	8.22307e6	−	8.22307e6i	0.326912	−	0.326912i	0.851411	+	0.524499i	$0.175747\pi$
$294$	−2.47065e6	+	2.52908e7i	−0.0972231	+	0.995225i
$295$			1.92726e7i			0.750714i
$296$	−4.76863e7	+	6.06612e6i	−1.83873	+	0.233903i
$297$	9.53679e6	−	2.14320e7i	0.364027	−	0.818075i
$298$	1.76512e7	+	2.77962e7i	0.667001	+	1.05035i
$299$	1.89983e7	−	1.89983e7i	0.710723	−	0.710723i
$300$	4.63345e6	−	1.41235e7i	0.171609	−	0.523092i
$301$	−181145.	+	181145.i	−0.00664243	+	0.00664243i
$302$	−268877.	−	60019.6i	−0.00976185	−	0.00217908i
$303$	−1.80408e7	+	2.30945e7i	−0.648528	+	0.830197i
$304$	−9.86780e6	−	921292.i	−0.351236	−	0.0327927i
$305$		−	1.96137e7i		−	0.691291i
$306$	−1.79081e7	+	445322.i	−0.625009	+	0.0155421i
$307$	−1.67447e7	+	1.67447e7i	−0.578710	+	0.578710i	−0.934548	−	0.355838i	$-0.884196\pi$
$307$	−1.67447e7	+	1.67447e7i	−0.578710	+	0.578710i	0.355838	+	0.934548i	$0.384196\pi$
$308$	54120.5	+	150054.i	0.00185229	+	0.00513565i
$309$	2.82425e6	+	2.29885e7i	0.0957255	+	0.779175i
$310$	−4.50103e6	−	7.08796e6i	−0.151087	−	0.237923i
$311$	−3.24545e7			−1.07893			−0.539466	−	0.842007i	$-0.681374\pi$
$311$	−3.24545e7			−1.07893			−0.539466	+	0.842007i	$0.681374\pi$
$312$	−6.57719e6	−	2.58910e7i	−0.216559	−	0.852481i
$313$		−	5.74828e7i		−	1.87458i	−0.348545	−	0.937292i	$-0.613324\pi$
$313$		−	5.74828e7i		−	1.87458i	0.348545	−	0.937292i	$-0.386676\pi$
$314$	9.73742e6	+	1.53339e7i	0.314525	+	0.495296i
$315$	−109526.	−	65788.9i	−0.00350416	−	0.00210485i
$316$	2.85573e7	+	1.34179e7i	0.905014	+	0.425230i
$317$	1.13421e6	+	1.13421e6i	0.0356055	+	0.0356055i	0.724685	−	0.689080i	$-0.241985\pi$
$317$	1.13421e6	+	1.13421e6i	0.0356055	+	0.0356055i	−0.689080	+	0.724685i	$0.741985\pi$
$318$	2.39375e7	+	2.91207e7i	0.744384	+	0.905567i
$319$	9.42717e6			0.290409
$320$	−1.89287e7	−	1.11502e7i	−0.577658	−	0.340278i
$321$	−3.24088e7	+	4.14873e7i	−0.979822	+	1.25429i
$322$	227032.	+	50679.0i	0.00680018	+	0.00151796i
$323$	−5.25529e6	−	5.25529e6i	−0.155951	−	0.155951i
$324$	−3.39702e7	+	1.69052e6i	−0.998764	+	0.0497033i
$325$	1.17537e7	+	1.17537e7i	0.342393	+	0.342393i
$326$	8.99597e6	+	1.41664e7i	0.259654	+	0.408889i
$327$	3.46945e7	−	4.44133e7i	0.992241	−	1.27019i
$328$	7.11562e6	−	9.18981e6i	0.201647	−	0.260426i
$329$	162817.			0.00457207
$330$	2.14712e7	+	2.09751e6i	0.597468	+	0.0583663i
$331$	−2.84976e7	−	2.84976e7i	−0.785823	−	0.785823i	0.194983	−	0.980807i	$-0.437535\pi$
$331$	−2.84976e7	−	2.84976e7i	−0.785823	−	0.785823i	−0.980807	+	0.194983i	$0.937535\pi$
$332$	−1.43094e7	−	3.96741e7i	−0.391028	−	1.08416i
$333$	−5.86730e7	−	3.52432e7i	−1.58893	−	0.954428i
$334$	−1.32644e6	+	5.94219e6i	−0.0355997	+	0.159480i
$335$			4.56463e7i			1.21415i
$336$	158707.	−	168239.i	0.00418386	−	0.00443517i
$337$	2.75455e7			0.719717			0.359858	−	0.933007i	$-0.382825\pi$
$337$	2.75455e7			0.719717			0.359858	+	0.933007i	$0.382825\pi$
$338$	−8.53152e6	−	1.90444e6i	−0.220941	−	0.0493192i
$339$	1.69852e6	+	1.38254e7i	0.0435984	+	0.354877i
$340$	−5.58947e6	−	1.54973e7i	−0.142211	−	0.394292i
$341$	−1.05541e7	+	1.05541e7i	−0.266170	+	0.266170i
$342$	−1.02231e7	−	9.72696e6i	−0.255566	−	0.243164i
$343$		−	492076.i		−	0.0121941i
$344$	−6.22163e7	+	7.91446e6i	−1.52837	+	0.194422i
$345$	1.93672e7	−	2.47924e7i	0.471638	−	0.603756i
$346$	−5.32294e7	+	3.38019e7i	−1.28506	+	0.816043i
$347$	5.37838e7	−	5.37838e7i	1.28725	−	1.28725i	0.350800	−	0.936450i	$-0.385910\pi$
$347$	5.37838e7	−	5.37838e7i	1.28725	−	1.28725i	0.936450	−	0.350800i	$-0.114090\pi$
$348$	−6.17075e6	−	1.21964e7i	−0.146420	−	0.289397i
$349$	1.17593e7	−	1.17593e7i	0.276633	−	0.276633i	−0.555130	−	0.831764i	$-0.687332\pi$
$349$	1.17593e7	−	1.17593e7i	0.276633	−	0.276633i	0.831764	+	0.555130i	$0.187332\pi$
$350$	−31353.6	+	140458.i	−0.000731280	+	0.00327600i
$351$	1.54631e7	−	3.47501e7i	0.357581	−	0.803590i
$352$	−1.20143e7	+	3.71587e7i	−0.275469	+	0.851986i
$353$		−	9.53350e6i		−	0.216735i	−0.994111	−	0.108367i	$-0.965438\pi$
$353$		−	9.53350e6i		−	0.216735i	0.994111	−	0.108367i	$-0.0345623\pi$
$354$	−3.15434e7	−	3.83736e7i	−0.711048	−	0.865013i
$355$	−1.12609e7	+	1.12609e7i	−0.251704	+	0.251704i
$356$	7.27956e7	+	3.42037e7i	1.61345	+	0.758094i
$357$	172147.	−	21149.1i	0.00378351	−	0.000464823i
$358$	−3.11708e6	+	1.97942e6i	−0.0679358	+	0.0431409i
$359$	−1.88519e7			−0.407447			−0.203724	−	0.979028i	$-0.565304\pi$
$359$	−1.88519e7			−0.407447			−0.203724	+	0.979028i	$0.565304\pi$
$360$	−1.13408e7	−	2.91514e7i	−0.243072	−	0.624815i
$361$			4.11914e7i			0.875558i
$362$	7.07368e7	−	4.49195e7i	1.49114	−	0.946912i
$363$	1.15623e6	+	9.41137e6i	0.0241727	+	0.196758i
$364$	87751.7	+	243299.i	0.00181950	+	0.00504471i
$365$	2.12241e7	+	2.12241e7i	0.436466	+	0.436466i
$366$	3.21017e7	+	3.90528e7i	0.654765	+	0.796542i
$367$	8.61904e7			1.74366			0.871828	−	0.489813i	$-0.162935\pi$
$367$	8.61904e7			1.74366			0.871828	+	0.489813i	$0.162935\pi$
$368$	3.63520e7	+	4.38389e7i	0.729432	+	0.879663i
$369$	1.60565e7	−	4.00569e6i	0.319573	−	0.0797257i
$370$	1.37134e7	−	6.14333e7i	0.270732	−	1.21283i
$371$	−258079.	−	258079.i	−0.00505396	−	0.00505396i
$372$	2.05628e7	+	6.74598e6i	0.399442	+	0.131044i
$373$	6.26031e6	+	6.26031e6i	0.120634	+	0.120634i	0.764846	−	0.644213i	$-0.222815\pi$
$373$	6.26031e6	+	6.26031e6i	0.120634	+	0.120634i	−0.644213	+	0.764846i	$0.722815\pi$
$374$	−2.47223e7	+	1.56993e7i	−0.472579	+	0.300099i
$375$	4.31998e7	+	3.37465e7i	0.819196	+	0.639934i
$376$	3.15176e7	+	2.44039e7i	0.592910	+	0.459087i
$377$	1.52853e7			0.285267
$378$	325752.	−	48268.2i	0.00603131	−	0.000893688i
$379$	1.43399e7	+	1.43399e7i	0.263407	+	0.263407i	0.826437	−	0.563030i	$-0.190364\pi$
$379$	1.43399e7	+	1.43399e7i	0.263407	+	0.263407i	−0.563030	+	0.826437i	$0.690364\pi$
$380$	5.51875e6	−	1.17455e7i	0.100575	−	0.214053i
$381$	−6.16008e7	+	7.56796e6i	−1.11381	+	0.136837i
$382$	8.35387e7	+	1.86478e7i	1.49864	+	0.334532i
$383$			7.36590e7i			1.31108i	0.755160	+	0.655540i	$0.227559\pi$
$383$			7.36590e7i			1.31108i	−0.755160	+	0.655540i	$0.772441\pi$
$384$	5.59383e7	−	8.77941e6i	0.987907	−	0.155050i
$385$	−208875.			−0.00366020
$386$	3.44569e6	−	1.54360e7i	0.0599120	−	0.268395i
$387$	−7.65507e7	−	4.59818e7i	−1.32074	−	0.793329i
$388$	−7.03474e6	−	3.30534e6i	−0.120435	−	0.0565876i
$389$	−6.48171e7	+	6.48171e7i	−1.10114	+	1.10114i	−0.106862	+	0.994274i	$0.534080\pi$
$389$	−6.48171e7	+	6.48171e7i	−1.10114	+	1.10114i	−0.994274	+	0.106862i	$0.965920\pi$
$390$	3.48136e7	+	3.40093e6i	0.586889	+	0.0573329i
$391$			4.27073e7i			0.714450i
$392$	3.68767e7	−	4.76262e7i	0.612200	−	0.790656i
$393$	3.11027e7	+	2.42967e7i	0.512414	+	0.400284i
$394$	−2.46439e7	−	3.88077e7i	−0.402921	−	0.634497i
$395$	−2.92148e7	+	2.92148e7i	−0.474036	+	0.474036i
$396$	−4.61842e7	+	3.09655e7i	−0.743717	+	0.498646i
$397$	−3.67219e7	+	3.67219e7i	−0.586886	+	0.586886i	−0.936787	−	0.349901i	$-0.886215\pi$
$397$	−3.67219e7	+	3.67219e7i	−0.586886	+	0.586886i	0.349901	+	0.936787i	$0.386215\pi$
$398$	−1.41164e7	−	3.15111e6i	−0.223910	−	0.0499820i
$399$	107668.	+	84107.4i	0.00169499	+	0.00132408i
$400$	−2.71219e7	+	2.24900e7i	−0.423780	+	0.351406i
$401$			6.94607e6i			0.107722i	0.998548	+	0.0538612i	$0.0171528\pi$
$401$			6.94607e6i			0.107722i	−0.998548	+	0.0538612i	$0.982847\pi$
$402$	−7.47092e7	−	9.08861e7i	−1.14999	−	1.39900i
$403$	−1.71126e7	+	1.71126e7i	−0.261457	+	0.261457i
$404$	6.53452e7	−	2.35683e7i	0.990991	−	0.357425i
$405$	1.30095e7	−	4.25944e7i	0.195837	−	0.641191i
$406$	70943.8	+	111718.i	0.00106007	+	0.00166935i
$407$	−1.11895e8			−1.65969
$408$	3.64935e7	+	2.17083e7i	0.537322	+	0.319628i
$409$			7.55926e7i			1.10487i	0.833557	+	0.552433i	$0.186300\pi$
$409$			7.55926e7i			1.10487i	−0.833557	+	0.552433i	$0.813700\pi$
$410$	8.15847e6	+	1.28475e7i	0.118374	+	0.186409i
$411$	−3.34505e7	+	4.10956e6i	−0.481812	+	0.0591930i
$412$	2.33470e7	−	4.96893e7i	0.333841	−	0.710512i
$413$	340082.	+	340082.i	0.00482762	+	0.00482762i
$414$	2.01577e6	+	8.10622e7i	0.0284080	+	1.14240i
$415$	5.52265e7			0.772686
$416$	−1.94802e7	+	6.02495e7i	−0.270591	+	0.836900i
$417$	6.57535e7	+	5.13649e7i	0.906798	+	0.708367i
$418$	−2.25152e7	−	5.02593e6i	−0.308282	−	0.0688157i
$419$	−7.39635e7	−	7.39635e7i	−1.00548	−	1.00548i	−0.999985	−	0.00549957i	$-0.998249\pi$
$419$	−7.39635e7	−	7.39635e7i	−1.00548	−	1.00548i	−0.00549957	−	0.999985i	$-0.501751\pi$
$420$	136724.	+	270233.i	0.00184542	+	0.00364746i
$421$	−6.58343e7	−	6.58343e7i	−0.882279	−	0.882279i	0.111487	−	0.993766i	$-0.464439\pi$
$421$	−6.58343e7	−	6.58343e7i	−0.882279	−	0.882279i	−0.993766	+	0.111487i	$0.964439\pi$
$422$	−5.60746e7	−	8.83031e7i	−0.746154	−	1.17500i
$423$	1.37380e7	+	5.50675e7i	0.181511	+	0.727570i
$424$	−1.12758e7	−	8.86402e7i	−0.147928	−	1.16287i
$425$	−2.64218e7			−0.344188
$426$	3.99085e6	−	4.08524e7i	0.0516222	−	0.528431i
$427$	−346101.	−	346101.i	−0.00444549	−	0.00444549i
$428$	1.17387e8	−	4.23384e7i	1.49723	−	0.540012i
$429$	−7.58226e6	−	6.17172e7i	−0.0960344	−	0.781689i
$430$	1.78918e7	−	8.01520e7i	0.225034	−	1.00811i
$431$			8.03753e7i			1.00390i	0.864896	+	0.501950i	$0.167384\pi$
$431$			8.03753e7i			1.00390i	−0.864896	+	0.501950i	$0.832616\pi$
$432$	7.02925e7	+	3.94817e7i	0.871882	+	0.489717i
$433$	−6.45783e7			−0.795469			−0.397734	−	0.917501i	$-0.630203\pi$
$433$	−6.45783e7			−0.795469			−0.397734	+	0.917501i	$0.630203\pi$
$434$	−204498.	−	45648.7i	−0.00250161	−	0.000558418i
$435$	1.77646e7	−	2.18247e6i	0.215818	−	0.0265143i
$436$	−1.25666e8	+	4.53244e7i	−1.51620	+	0.546856i
$437$	−2.37884e7	+	2.37884e7i	−0.285050	+	0.285050i
$438$	−7.69965e7	−	7.52176e6i	−0.916324	−	0.0895152i
$439$		−	1.39202e8i		−	1.64533i	−0.568529	−	0.822663i	$-0.692487\pi$
$439$		−	1.39202e8i		−	1.64533i	0.568529	−	0.822663i	$-0.307513\pi$
$440$	−4.04332e7	−	3.13072e7i	−0.474658	−	0.367525i
$441$	8.32125e7	−	2.07595e7i	0.970226	−	0.242048i
$442$	−4.00851e7	+	2.54550e7i	−0.464212	+	0.294786i
$443$	1.01408e8	−	1.01408e8i	1.16644	−	1.16644i	0.183404	−	0.983038i	$-0.441288\pi$
$443$	1.01408e8	−	1.01408e8i	1.16644	−	1.16644i	0.983038	−	0.183404i	$-0.0587117\pi$
$444$	7.32431e7	+	1.44764e8i	0.836793	+	1.65391i
$445$	−7.44716e7	+	7.44716e7i	−0.845105	+	0.845105i
$446$	1.72356e7	−	7.72121e7i	0.194277	−	0.870323i
$447$	6.84117e7	−	8.75755e7i	0.765963	−	0.980528i
$448$	−530769.	+	137258.i	−0.00590298	+	0.00152652i
$449$			1.29532e7i			0.143100i	0.997437	+	0.0715499i	$0.0227945\pi$
$449$			1.29532e7i			0.143100i	−0.997437	+	0.0715499i	$0.977205\pi$
$450$	−5.01509e7	+	1.24710e6i	−0.550352	+	0.0136856i
$451$	1.91302e7	−	1.91302e7i	0.208540	−	0.208540i
$452$	1.40410e7	−	2.98834e7i	0.152049	−	0.323604i
$453$	113377.	+	922854.i	0.00121964	+	0.00992747i
$454$	1.76290e7	−	1.11948e7i	0.188391	−	0.119633i
$455$	−338673.			−0.00359539
$456$	8.23551e6	+	3.24190e7i	0.0868553	+	0.341904i
$457$		−	1.29977e8i		−	1.36181i	−0.732370	−	0.680907i	$-0.761586\pi$
$457$		−	1.29977e8i		−	1.36181i	0.732370	−	0.680907i	$-0.238414\pi$
$458$	−2.51754e7	+	1.59870e7i	−0.262047	+	0.166406i
$459$	2.16782e7	+	5.64385e7i	0.224174	+	0.583630i
$460$	−7.01493e7	+	2.53010e7i	−0.720692	+	0.259935i
$461$	1.09839e8	+	1.09839e8i	1.12113	+	1.12113i	0.991573	+	0.129553i	$0.0413542\pi$
$461$	1.09839e8	+	1.09839e8i	1.12113	+	1.12113i	0.129553	+	0.991573i	$0.458646\pi$
$462$	415890.	−	341865.i	0.00421748	−	0.00346680i
$463$	−2.00196e7			−0.201703			−0.100851	−	0.994902i	$-0.532157\pi$
$463$	−2.00196e7			−0.201703			−0.100851	+	0.994902i	$0.532157\pi$
$464$	−3.01185e6	+	3.22594e7i	−0.0301494	+	0.322925i
$465$	−1.74448e7	+	2.23316e7i	−0.173503	+	0.222106i
$466$	8.73884e6	−	3.91484e7i	0.0863567	−	0.386862i
$467$	7.44018e7	+	7.44018e7i	0.730521	+	0.730521i	0.970723	−	0.240202i	$-0.0772136\pi$
$467$	7.44018e7	+	7.44018e7i	0.730521	+	0.730521i	−0.240202	+	0.970723i	$0.577214\pi$
$468$	−7.48835e7	+	5.02078e7i	−0.730548	+	0.489817i
$469$	805469.	+	805469.i	0.00780783	+	0.00780783i
$470$	−4.40620e7	+	2.79805e7i	−0.424396	+	0.269502i
$471$	3.77398e7	−	4.83116e7i	0.361191	−	0.462369i
$472$	1.48586e7	+	1.16805e8i	0.141303	+	1.11080i
$473$	−1.45989e8			−1.37955
$474$	1.03536e7	−	1.05985e8i	0.0972204	−	0.995198i
$475$	−1.47172e7	−	1.47172e7i	−0.137323	−	0.137323i
$476$	−372094.	−	174832.i	−0.00345010	−	0.00162106i
$477$	6.55108e7	−	1.09063e8i	0.603612	−	1.00489i
$478$	−1.11279e8	−	2.48400e7i	−1.01889	−	0.227441i
$479$		−	9.92388e7i		−	0.902974i	−0.892278	−	0.451487i	$-0.850894\pi$
$479$		−	9.92388e7i		−	0.902974i	0.892278	−	0.451487i	$-0.149106\pi$
$480$	−1.40373e7	+	7.28034e7i	−0.126929	+	0.658306i
$481$	−1.81428e8			−1.63030
$482$	−1.39339e7	+	6.24215e7i	−0.124432	+	0.557433i
$483$	−95732.8	−	779234.i	−0.000849609	−	0.00691554i
$484$	9.55815e6	−	2.03426e7i	0.0843019	−	0.179419i
$485$	7.19671e6	−	7.19671e6i	0.0630825	−	0.0630825i
$486$	4.38110e7	+	1.06102e8i	0.381658	+	0.924304i
$487$		−	4.97584e7i		−	0.430804i	−0.976525	−	0.215402i	$-0.930894\pi$
$487$		−	4.97584e7i		−	0.430804i	0.976525	−	0.215402i	$-0.0691062\pi$
$488$	−1.51216e7	−	1.18872e8i	−0.130118	−	1.02287i
$489$	3.48661e7	−	4.46330e7i	0.298179	−	0.381706i
$490$	4.22813e7	+	6.65821e7i	0.359385	+	0.565939i
$491$	−1.10583e7	+	1.10583e7i	−0.0934211	+	0.0934211i	−0.752273	−	0.658852i	$-0.771042\pi$
$491$	−1.10583e7	+	1.10583e7i	−0.0934211	+	0.0934211i	0.658852	+	0.752273i	$0.271042\pi$
$492$	−3.72718e7	−	1.22276e7i	−0.312957	−	0.102671i
$493$	−1.71804e7	+	1.71804e7i	−0.143381	+	0.143381i
$494$	−3.65065e7	−	8.14910e6i	−0.302823	−	0.0675973i
$495$	−1.76242e7	−	7.06450e7i	−0.145309	−	0.582460i
$496$	−3.27438e7	−	3.94876e7i	−0.268339	−	0.323605i
$497$			397418.i			0.00323727i
$498$	−1.09961e8	+	9.03890e7i	−0.890330	+	0.731859i
$499$	1.13840e8	−	1.13840e8i	0.916210	−	0.916210i	−0.0805412	−	0.996751i	$-0.525665\pi$
$499$	1.13840e8	−	1.13840e8i	0.916210	−	0.916210i	0.996751	+	0.0805412i	$0.0256649\pi$
$500$	−4.40861e7	−	1.22232e8i	−0.352689	−	0.977859i
$501$	2.03951e7	−	2.50564e6i	0.162186	−	0.0199253i
$502$	5.40066e7	+	8.50465e7i	0.426909	+	0.672272i
$503$	9.67006e6			0.0759846			0.0379923	−	0.999278i	$-0.487904\pi$
$503$	9.67006e6			0.0759846			0.0379923	+	0.999278i	$0.487904\pi$
$504$	−714519.	−	314283.i	−0.00558113	−	0.00245488i
$505$			9.09606e7i			0.706284i
$506$	7.10637e7	+	1.11907e8i	0.548525	+	0.863786i
$507$	3.59749e6	+	2.92824e7i	0.0276042	+	0.224689i
$508$	1.33149e8	+	6.25615e7i	1.01566	+	0.477217i
$509$	1.32353e7	+	1.32353e7i	0.100364	+	0.100364i	0.755506	−	0.655142i	$-0.227391\pi$
$509$	1.32353e7	+	1.32353e7i	0.100364	+	0.100364i	−0.655142	+	0.755506i	$0.727391\pi$
$510$	−4.29523e7	+	3.53072e7i	−0.323800	+	0.266166i
$511$	749035.			0.00561357
$512$	−1.23317e8	−	5.29842e7i	−0.918783	−	0.394763i
$513$	−1.93618e7	+	4.35118e7i	−0.143415	+	0.322296i
$514$	2.24313e8	+	5.00720e7i	1.65183	+	0.368728i
$515$	5.08333e7	+	5.08333e7i	0.372158	+	0.372158i
$516$	9.55603e7	+	1.88874e8i	0.695550	+	1.37475i
$517$	6.56092e7	+	6.56092e7i	0.474781	+	0.474781i
$518$	−842060.	−	1.32603e6i	−0.00605834	−	0.00954033i
$519$	1.67706e8	+	1.31008e8i	1.19963	+	0.937119i
$520$	−6.55589e7	−	5.07619e7i	−0.466253	−	0.361017i
$521$	1.04312e7			0.0737601			0.0368800	−	0.999320i	$-0.488258\pi$
$521$	1.04312e7			0.0737601			0.0368800	+	0.999320i	$0.488258\pi$
$522$	−3.17989e7	+	3.34208e7i	−0.223564	+	0.234966i
$523$	6.03081e7	+	6.03081e7i	0.421571	+	0.421571i	0.885744	−	0.464174i	$-0.153649\pi$
$523$	6.03081e7	+	6.03081e7i	0.421571	+	0.421571i	−0.464174	+	0.885744i	$0.653649\pi$
$524$	−3.17408e7	−	8.80042e7i	−0.220610	−	0.611659i
$525$	482090.	−	59227.1i	0.00333158	−	0.000409301i
$526$	−3.30355e7	+	1.47993e8i	−0.226999	+	1.01691i
$527$		−	3.84683e7i		−	0.262828i
$528$	1.31747e8	−	3.84134e6i	0.895032	−	0.0260964i
$529$	4.52811e7			0.305879
$530$	1.14193e8	+	2.54907e7i	0.767032	+	0.171220i
$531$	−8.63263e7	+	1.43716e8i	−0.576580	+	0.959892i
$532$	−109877.	−	304643.i	−0.000729745	−	0.00202328i
$533$	3.10179e7	−	3.10179e7i	0.204847	−	0.204847i
$534$	2.63925e7	−	2.70167e8i	0.173323	−	1.77423i
$535$			1.63403e8i			1.06708i
$536$	3.51919e7	+	2.76647e8i	0.228533	+	1.79652i
$537$	9.82077e6	+	7.67173e6i	0.0634195	+	0.0495417i
$538$	9.81547e7	−	6.23306e7i	0.630325	−	0.400271i
$539$	9.91421e7	−	9.91421e7i	0.633128	−	0.633128i
$540$	−7.98608e7	+	6.90435e7i	−0.507169	+	0.438472i
$541$	4.05355e6	−	4.05355e6i	0.0256002	−	0.0256002i	−0.694191	−	0.719791i	$-0.744238\pi$
$541$	4.05355e6	−	4.05355e6i	0.0256002	−	0.0256002i	0.719791	+	0.694191i	$0.244238\pi$
$542$	4.26571e7	−	1.91096e8i	0.267912	−	1.20020i
$543$	−2.22866e8	−	1.74097e8i	−1.39201	−	1.08740i
$544$	−4.58238e7	−	8.96144e7i	−0.284639	−	0.556649i
$545$		−	1.74927e8i		−	1.08061i
$546$	674329.	−	554305.i	0.00414280	−	0.00340542i
$547$	1.91385e8	−	1.91385e8i	1.16935	−	1.16935i	0.186991	−	0.982362i	$-0.440126\pi$
$547$	1.91385e8	−	1.91385e8i	1.16935	−	1.16935i	0.982362	−	0.186991i	$-0.0598735\pi$
$548$	7.23029e7	+	3.39722e7i	0.439353	+	0.206434i
$549$	8.78543e7	−	1.46260e8i	0.530940	−	0.883911i
$550$	−6.92337e7	+	4.39651e7i	−0.416130	+	0.264253i
$551$	−1.91393e7			−0.114412
$552$	9.82637e7	−	1.65190e8i	0.584219	−	0.982124i
$553$			1.03104e6i			0.00609677i
$554$	−1.32744e8	+	8.42954e7i	−0.780700	+	0.495763i
$555$	−2.10855e8	+	2.59046e7i	−1.23340	+	0.151530i
$556$	−6.71025e7	−	1.86047e8i	−0.390404	−	1.08243i
$557$	2.10252e8	+	2.10252e8i	1.21668	+	1.21668i	0.968789	+	0.247886i	$0.0797358\pi$
$557$	2.10252e8	+	2.10252e8i	1.21668	+	1.21668i	0.247886	+	0.968789i	$0.420264\pi$
$558$	−1.81569e6	−	7.30162e7i	−0.0104506	−	0.420258i
$559$	−2.36709e8			−1.35512
$560$	66732.7	−	714762.i	0.000379992	−	0.00407003i
$561$	7.78910e7	+	6.08464e7i	0.441163	+	0.344625i
$562$	−3.84498e7	+	1.72248e8i	−0.216613	+	0.970387i
$563$	7.56969e7	+	7.56969e7i	0.424183	+	0.424183i	0.886641	−	0.462458i	$-0.153033\pi$
$563$	7.56969e7	+	7.56969e7i	0.424183	+	0.424183i	−0.462458	+	0.886641i	$0.653033\pi$
$564$	4.19361e7	−	1.27828e8i	0.233750	−	0.712506i
$565$	3.05714e7	+	3.05714e7i	0.169500	+	0.169500i
$566$	1.27694e8	−	8.10888e7i	0.704241	−	0.447210i
$567$	−522051.	−	981178.i	−0.00286394	−	0.00538268i
$568$	−5.95669e7	+	7.69306e7i	−0.325058	+	0.419812i
$569$	−1.30415e8			−0.707929			−0.353964	−	0.935259i	$-0.615167\pi$
$569$	−1.30415e8			−0.707929			−0.353964	+	0.935259i	$0.615167\pi$
$570$	−4.35913e7	−	4.25842e6i	−0.235383	−	0.0229945i
$571$	6.99301e7	+	6.99301e7i	0.375626	+	0.375626i	0.869521	−	0.493895i	$-0.164427\pi$
$571$	6.99301e7	+	6.99301e7i	0.375626	+	0.375626i	−0.493895	+	0.869521i	$0.664427\pi$
$572$	−6.26797e7	+	1.33401e8i	−0.334918	+	0.712805i
$573$	−3.52258e7	−	2.86726e8i	−0.187239	−	1.52407i
$574$	370669.	+	82742.0i	0.00195997	+	0.000437512i
$575$			1.19600e8i			0.629110i
$576$	−9.12074e7	−	1.67933e8i	−0.477268	−	0.878758i
$577$	1.52115e8			0.791855			0.395927	−	0.918282i	$-0.370423\pi$
$577$	1.52115e8			0.791855			0.395927	+	0.918282i	$0.370423\pi$
$578$	−2.56253e7	+	1.14797e8i	−0.132704	+	0.594491i
$579$	−5.29804e7	+	6.50891e6i	−0.272948	+	0.0335330i
$580$	−3.83979e7	−	1.80416e7i	−0.196799	−	0.0924681i
$581$	974519.	−	974519.i	0.00496892	−	0.00496892i
$582$	−2.55049e6	+	2.61082e7i	−0.0129376	+	0.132436i
$583$		−	2.07992e8i		−	1.04964i
$584$	1.44995e8	+	1.12269e8i	0.727972	+	0.563665i
$585$	−2.85761e7	−	1.14545e8i	−0.142736	−	0.572147i
$586$	4.98725e7	+	7.85363e7i	0.247838	+	0.390281i
$587$	−1.66273e8	+	1.66273e8i	−0.822069	+	0.822069i	−0.986404	−	0.164336i	$-0.947452\pi$
$587$	−1.66273e8	+	1.66273e8i	−0.822069	+	0.822069i	0.164336	+	0.986404i	$0.447452\pi$
$588$	−1.93161e8	−	6.33697e7i	−0.950138	−	0.311709i
$589$	2.14272e7	−	2.14272e7i	0.104862	−	0.104862i
$590$	−1.50477e8	−	3.35901e7i	−0.732682	−	0.163552i
$591$	−9.55133e7	+	1.22269e8i	−0.462702	+	0.592316i
$592$	3.57488e7	−	3.82899e8i	0.172305	−	1.84552i
$593$		−	3.50914e8i		−	1.68282i	−0.540399	−	0.841409i	$-0.681727\pi$
$593$		−	3.50914e8i		−	1.68282i	0.540399	−	0.841409i	$-0.318273\pi$
$594$	1.50716e8	+	1.11815e8i	0.719117	+	0.533510i
$595$	380661.	−	380661.i	0.00180712	−	0.00180712i
$596$	−2.47792e8	+	8.93722e7i	−1.17044	+	0.422147i
$597$	5.95245e6	+	4.84510e7i	0.0279752	+	0.227709i
$598$	1.15223e8	+	1.81447e8i	0.538812	+	0.848491i
$599$	−3.78502e8			−1.76111			−0.880556	−	0.473941i	$-0.842831\pi$
$599$	−3.78502e8			−1.76111			−0.880556	+	0.473941i	$0.842831\pi$
$600$	1.02198e8	+	6.07930e7i	0.473140	+	0.281449i
$601$			2.83904e8i			1.30782i	0.756572	+	0.653911i	$0.226873\pi$
$601$			2.83904e8i			1.30782i	−0.756572	+	0.653911i	$0.773127\pi$
$602$	−1.09864e6	−	1.73007e6i	−0.00503575	−	0.00793001i
$603$	−2.04460e8	+	3.40385e8i	−0.932516	+	1.55245i
$604$	937246.	−	1.99474e6i	0.00425347	−	0.00905263i
$605$	2.08109e7	+	2.08109e7i	0.0939777	+	0.0939777i
$606$	−1.48875e8	−	1.81111e8i	−0.668966	−	0.813818i
$607$	−9.53399e7			−0.426294			−0.213147	−	0.977020i	$-0.568371\pi$
$607$	−9.53399e7			−0.426294			−0.213147	+	0.977020i	$0.568371\pi$
$608$	2.43918e7	−	7.54404e7i	0.108526	−	0.335655i
$609$	274960.	−	351983.i	0.00121736	−	0.00155837i
$610$	1.53141e8	+	3.41846e7i	0.674686	+	0.150606i
$611$	1.06380e8	+	1.06380e8i	0.466374	+	0.466374i
$612$	2.77350e7	−	1.40600e8i	0.120997	−	0.613382i
$613$	−6.06972e7	−	6.06972e7i	−0.263504	−	0.263504i	0.562972	−	0.826476i	$-0.309658\pi$
$613$	−6.06972e7	−	6.06972e7i	−0.263504	−	0.263504i	−0.826476	+	0.562972i	$0.809658\pi$
$614$	−1.01555e8	−	1.59924e8i	−0.438731	−	0.690888i
$615$	3.16202e7	−	4.04778e7i	0.135937	−	0.174017i
$616$	−1.26592e6	+	161037.i	−0.00541583	+	0.000688942i
$617$	−2.22851e8			−0.948767			−0.474383	−	0.880318i	$-0.657329\pi$
$617$	−2.22851e8			−0.948767			−0.474383	+	0.880318i	$0.657329\pi$
$618$	−1.84413e8	−	1.80152e7i	−0.781314	−	0.0763262i
$619$	−1.32795e7	−	1.32795e7i	−0.0559900	−	0.0559900i	0.678557	−	0.734547i	$-0.262605\pi$
$619$	−1.32795e7	−	1.32795e7i	−0.0559900	−	0.0559900i	−0.734547	+	0.678557i	$0.762605\pi$
$620$	6.31865e7	−	2.27897e7i	0.265124	−	0.0956234i
$621$	2.55472e8	−	9.81275e7i	1.06676	−	0.409747i
$622$	5.65648e7	−	2.53400e8i	0.235058	−	1.05302i
$623$			2.62823e6i			0.0108693i
$624$	2.13616e8	−	6.22840e6i	0.879184	−	0.0256344i
$625$	3.57428e7			0.146402
$626$	4.48816e8	+	1.00186e8i	1.82956	+	0.408400i
$627$	9.49400e6	+	7.72781e7i	0.0385165	+	0.313512i
$628$	−1.36696e8	+	4.93028e7i	−0.551922	+	0.199064i
$629$	2.03921e8	−	2.03921e8i	0.819425	−	0.819425i
$630$	704560.	−	740494.i	0.00281771	−	0.00296142i
$631$			376066.i			0.00149684i	1.00000		0.000748421i	$0.000238230\pi$
$631$			376066.i			0.00149684i	−1.00000		0.000748421i	$0.999762\pi$
$632$	−1.54537e8	+	1.99585e8i	−0.612183	+	0.790634i
$633$	−2.17331e8	+	2.78211e8i	−0.856861	+	1.09689i
$634$	−1.08326e7	+	6.87895e6i	−0.0425073	+	0.0269932i
$635$	−1.36215e8	+	1.36215e8i	−0.531990	+	0.531990i
$636$	−2.69090e8	+	1.36146e8i	−1.04599	+	0.529216i
$637$	1.60750e8	−	1.60750e8i	0.621918	−	0.621918i
$638$	−1.64306e7	+	7.36058e7i	−0.0632689	+	0.283433i
$639$	−1.34413e8	+	3.35328e7i	−0.515157	+	0.128519i
$640$	1.20050e8	−	1.28359e8i	0.457953	−	0.489649i
$641$			5.43123e7i			0.206217i	0.994670	+	0.103108i	$0.0328789\pi$
$641$			5.43123e7i			0.206217i	−0.994670	+	0.103108i	$0.967121\pi$
$642$	−2.67441e8	−	3.25350e8i	−1.01070	−	1.22955i
$643$	−1.77287e8	+	1.77287e8i	−0.666874	+	0.666874i	−0.956991	−	0.290117i	$-0.906306\pi$
$643$	−1.77287e8	+	1.77287e8i	−0.666874	+	0.666874i	0.290117	+	0.956991i	$0.406306\pi$
$644$	−791386.	+	1.68430e6i	−0.00296300	+	0.00630613i
$645$	−2.75102e8	+	3.37977e7i	−1.02522	+	0.125953i
$646$	5.01919e7	−	3.18731e7i	0.186181	−	0.118230i
$647$	2.03351e8			0.750815			0.375407	−	0.926860i	$-0.377503\pi$
$647$	2.03351e8			0.750815			0.375407	+	0.926860i	$0.377503\pi$
$648$	4.60071e7	−	2.68180e8i	0.169083	−	0.985602i
$649$			2.74080e8i			1.00264i
$650$	−1.12256e8	+	7.12855e7i	−0.408762	+	0.259574i
$651$	86230.6	+	701889.i	0.000312549	+	0.00254405i
$652$	−1.26288e8	+	4.55487e7i	−0.455636	+	0.164336i
$653$	−1.43067e8	−	1.43067e8i	−0.513807	−	0.513807i	0.401884	−	0.915691i	$-0.368356\pi$
$653$	−1.43067e8	−	1.43067e8i	−0.513807	−	0.513807i	−0.915691	+	0.401884i	$0.868356\pi$
$654$	2.86303e8	+	3.48296e8i	1.02351	+	1.24513i
$655$	1.22502e8			0.435933
$656$	5.93508e7	+	7.15744e7i	0.210240	+	0.253540i
$657$	6.32010e7	+	2.53336e8i	0.222858	+	0.893306i
$658$	−283773.	+	1.27125e6i	−0.000996080	+	0.00446225i
$659$	−1.57373e8	−	1.57373e8i	−0.549889	−	0.549889i	0.376520	−	0.926409i	$-0.377121\pi$
$659$	−1.57373e8	−	1.57373e8i	−0.549889	−	0.549889i	−0.926409	+	0.376520i	$0.877121\pi$
$660$	−5.37990e7	+	1.63988e8i	−0.187130	+	0.570400i
$661$	1.35146e8	+	1.35146e8i	0.467949	+	0.467949i	0.901250	−	0.433300i	$-0.142651\pi$
$661$	1.35146e8	+	1.35146e8i	0.467949	+	0.467949i	−0.433300	+	0.901250i	$0.642651\pi$
$662$	2.72173e8	−	1.72837e8i	0.938148	−	0.595747i
$663$	1.26293e8	+	9.86571e7i	0.433351	+	0.338523i
$664$	3.34709e8	−	4.25780e7i	1.14331	−	0.145439i
$665$	424064.			0.00144200
$666$	3.77434e8	−	3.96684e8i	1.27767	−	1.34283i
$667$	7.77679e7	+	7.77679e7i	0.262073	+	0.262073i
$668$	−4.40838e7	−	2.07132e7i	−0.147894	−	0.0694893i
$669$	−2.65012e8	+	3.25580e7i	−0.885089	+	0.108738i
$670$	−3.56399e8	−	7.95566e7i	−1.18498	−	0.264516i
$671$		−	2.78931e8i		−	0.923272i
$672$	1.03698e6	+	1.53238e6i	0.00341713	+	0.00504962i
$673$	3.17907e7			0.104293			0.0521465	−	0.998639i	$-0.483394\pi$
$673$	3.17907e7			0.104293			0.0521465	+	0.998639i	$0.483394\pi$
$674$	−4.80089e7	+	2.15071e8i	−0.156799	+	0.702429i
$675$	6.07087e7	+	1.58053e8i	0.197397	+	0.513916i
$676$	2.97391e7	−	6.32935e7i	0.0962692	−	0.204889i
$677$	1.63615e8	−	1.63615e8i	0.527300	−	0.527300i	−0.392467	−	0.919766i	$-0.628378\pi$
$677$	1.63615e8	−	1.63615e8i	0.527300	−	0.527300i	0.919766	+	0.392467i	$0.128378\pi$
$678$	−1.10907e8	−	1.08344e7i	−0.355851	−	0.0347629i
$679$		−	253984.i		−	0.000811330i
$680$	1.30742e8	−	1.66315e7i	0.415804	−	0.0528939i
$681$	−5.55425e7	−	4.33884e7i	−0.175867	−	0.137383i
$682$	−6.40101e7	−	1.00799e8i	−0.201788	−	0.317764i
$683$	3.14874e8	−	3.14874e8i	0.988269	−	0.988269i	−0.0116630	−	0.999932i	$-0.503713\pi$
$683$	3.14874e8	−	3.14874e8i	0.988269	−	0.988269i	0.999932	+	0.0116630i	$0.00371253\pi$
$684$	9.37642e7	−	6.28669e7i	0.293001	−	0.196451i
$685$	−7.39676e7	+	7.39676e7i	−0.230128	+	0.230128i
$686$	3.84205e6	+	857636.i	0.0119012	+	0.00265663i
$687$	7.93184e7	+	6.19615e7i	0.244627	+	0.191096i
$688$	4.66415e7	−	4.99568e8i	0.143221	−	1.53402i
$689$		−	3.37241e8i		−	1.03106i
$690$	1.59820e8	+	1.94426e8i	0.486501	+	0.591844i
$691$	−7.00333e7	+	7.00333e7i	−0.212261	+	0.212261i	−0.805227	−	0.592966i	$-0.797957\pi$
$691$	−7.00333e7	+	7.00333e7i	−0.212261	+	0.212261i	0.592966	+	0.805227i	$0.297957\pi$
$692$	−1.71147e8	−	4.74519e8i	−0.516477	−	1.43198i
$693$	−1.55759e6	−	935598.i	−0.00468007	−	0.00281119i
$694$	3.26196e8	+	5.13675e8i	0.975888	+	1.53677i
$695$	2.58978e8			0.771452
$696$	1.05983e8	−	2.69232e7i	0.314345	−	0.0798544i
$697$			6.97268e7i			0.205922i
$698$	7.13194e7	+	1.12310e8i	0.209721	+	0.330256i
$699$	−1.34367e8	+	1.65077e7i	−0.393425	+	0.0483343i
$700$	−1.04203e6	−	489608.i	−0.00303799	−	0.00142743i
$701$	2.84265e8	+	2.84265e8i	0.825220	+	0.825220i	0.986851	−	0.161631i	$-0.0516756\pi$
$701$	2.84265e8	+	2.84265e8i	0.825220	+	0.825220i	−0.161631	+	0.986851i	$0.551676\pi$
$702$	2.44373e8	+	1.81299e8i	0.706384	+	0.524063i
$703$	2.27172e8			0.653865
$704$	−2.69189e8	−	1.58570e8i	−0.771507	−	0.454467i
$705$	1.38823e8	+	1.08445e8i	0.396182	+	0.309487i
$706$	7.44360e7	+	1.66159e7i	0.211529	+	0.0472182i
$707$	1.60508e6	+	1.60508e6i	0.00454191	+	0.00454191i
$708$	3.54592e8	−	1.79405e8i	0.999145	−	0.505515i
$709$	−4.02163e8	−	4.02163e8i	−1.12840	−	1.12840i	−0.990437	−	0.137964i	$-0.955944\pi$
$709$	−4.02163e8	−	4.02163e8i	−1.12840	−	1.12840i	−0.137964	−	0.990437i	$-0.544056\pi$
$710$	−6.82970e7	−	1.07550e8i	−0.190821	−	0.300494i
$711$	−3.48714e8	+	8.69956e7i	−0.970199	+	0.242041i
$712$	−3.93932e8	+	5.08763e8i	−1.09139	+	1.40953i
$713$	−1.74129e8			−0.480399
$714$	−134905.	+	1.38096e6i	−0.000370624	+	0.00379390i
$715$	−1.36472e8	−	1.36472e8i	−0.373358	−	0.373358i
$716$	−1.00223e7	−	2.77876e7i	−0.0273040	−	0.0757027i
$717$	4.69229e7	+	3.81937e8i	0.127300	+	1.03618i
$718$	3.28568e7	−	1.47192e8i	0.0887671	−	0.397660i
$719$		−	3.10932e8i		−	0.836525i	−0.908326	−	0.418263i	$-0.862639\pi$
$719$		−	3.10932e8i		−	0.836525i	0.908326	−	0.418263i	$-0.137361\pi$
$720$	2.47375e8	−	3.77391e7i	0.662763	−	0.101110i
$721$	1.79400e6			0.00478647
$722$	−3.21616e8	−	7.17922e7i	−0.854526	−	0.190750i
$723$	2.14247e8	−	2.63213e7i	0.566890	−	0.0696453i
$724$	2.27438e8	+	6.30591e8i	0.599304	+	1.66162i
$725$	−4.81128e7	+	4.81128e7i	−0.126254	+	0.126254i
$726$	−7.54976e7	−	7.37533e6i	−0.197298	−	0.0192740i
$727$		−	1.78526e8i		−	0.464619i	−0.972642	−	0.232310i	$-0.925372\pi$
$727$		−	1.78526e8i		−	0.464619i	0.972642	−	0.232310i	$-0.0746283\pi$
$728$	−2.05258e6	+	261107.i	−0.00531994	+	0.000676743i
$729$	2.87802e8	−	2.59355e8i	0.742866	−	0.669440i
$730$	−2.02705e8	+	1.28723e8i	−0.521071	+	0.330893i
$731$	2.66055e8	−	2.66055e8i	0.681114	−	0.681114i
$732$	−3.60868e8	+	1.82580e8i	−0.920057	+	0.465501i
$733$	2.11702e8	−	2.11702e8i	0.537543	−	0.537543i	−0.385264	−	0.922807i	$-0.625890\pi$
$733$	2.11702e8	−	2.11702e8i	0.537543	−	0.537543i	0.922807	+	0.385264i	$0.125890\pi$
$734$	−1.50221e8	+	6.72961e8i	−0.379876	+	1.70177i
$735$	1.63871e8	−	2.09776e8i	0.412706	−	0.528316i
$736$	−4.05645e8	+	2.07424e8i	−1.01745	+	0.520266i
$737$			6.49146e8i			1.62159i
$738$	3.29109e6	+	1.32348e8i	0.00818786	+	0.329266i
$739$	−1.58704e8	+	1.58704e8i	−0.393237	+	0.393237i	−0.875840	−	0.482602i	$-0.839692\pi$
$739$	−1.58704e8	+	1.58704e8i	−0.393237	+	0.393237i	0.482602	+	0.875840i	$0.339692\pi$
$740$	4.55760e8	+	2.14143e8i	1.12471	+	0.528457i
$741$	1.53937e7	+	1.25300e8i	0.0378345	+	0.307961i
$742$	2.46485e6	−	1.56524e6i	0.00603362	−	0.00383150i
$743$	8.43384e7			0.205617			0.102809	−	0.994701i	$-0.467217\pi$
$743$	8.43384e7			0.205617			0.102809	+	0.994701i	$0.467217\pi$
$744$	−8.85103e7	+	1.48794e8i	−0.214919	+	0.361298i
$745$		−	3.44927e8i		−	0.834177i
$746$	−5.97905e7	+	3.79684e7i	−0.144018	+	0.0914547i
$747$	4.11825e8	+	2.47372e8i	0.987986	+	0.593455i
$748$	−7.94890e7	−	2.20390e8i	−0.189934	−	0.526608i
$749$	2.88338e6	+	2.88338e6i	0.00686210	+	0.00686210i
$750$	−3.38780e8	+	2.78480e8i	−0.803034	+	0.660101i
$751$	1.48005e8			0.349427			0.174714	−	0.984619i	$-0.444100\pi$
$751$	1.48005e8			0.349427			0.174714	+	0.984619i	$0.444100\pi$
$752$	−2.45473e8	+	2.03551e8i	−0.577232	+	0.478651i
$753$	2.09316e8	−	2.67950e8i	0.490249	−	0.627580i
$754$	−2.66407e7	+	1.19345e8i	−0.0621486	+	0.278414i
$755$	2.04066e6	+	2.04066e6i	0.00474166	+	0.00474166i
$756$	−190881.	+	2.62755e6i	−0.000441771	+	0.00608114i
$757$	−1.30940e7	−	1.30940e7i	−0.0301846	−	0.0301846i	0.691853	−	0.722038i	$-0.256794\pi$
$757$	−1.30940e7	−	1.30940e7i	−0.0301846	−	0.0301846i	−0.722038	+	0.691853i	$0.756794\pi$
$758$	−1.36956e8	+	8.69705e7i	−0.314466	+	0.199694i
$759$	2.75425e8	−	3.52578e8i	0.629909	−	0.806362i
$760$	8.20885e7	+	6.35607e7i	0.187000	+	0.144793i
$761$	4.37356e8			0.992388			0.496194	−	0.868212i	$-0.334731\pi$
$761$	4.37356e8			0.992388			0.496194	+	0.868212i	$0.334731\pi$
$762$	4.82742e7	−	4.94159e8i	0.109106	−	1.11687i
$763$	−3.08674e6	−	3.08674e6i	−0.00694907	−	0.00694907i
$764$	−2.91198e8	+	6.19755e8i	−0.652993	+	1.38976i
$765$	1.60865e8	+	9.66268e7i	0.359316	+	0.215831i
$766$	−5.75117e8	−	1.28380e8i	−1.27959	−	0.285634i
$767$			4.44397e8i			0.984883i
$768$	−2.89463e7	+	4.52059e8i	−0.0639014	+	0.997956i
$769$	−8.41289e8			−1.84998			−0.924988	−	0.379996i	$-0.875926\pi$
$769$	−8.41289e8			−1.84998			−0.924988	+	0.379996i	$0.875926\pi$
$770$	364047.	−	1.63086e6i	0.000797417	−	0.00357228i
$771$	−9.45862e7	−	7.69901e8i	−0.206379	−	1.67986i
$772$	1.14517e8	+	5.38067e7i	0.248895	+	0.116946i
$773$	−2.03252e8	+	2.03252e8i	−0.440044	+	0.440044i	−0.892027	−	0.451983i	$-0.850717\pi$
$773$	−2.03252e8	+	2.03252e8i	−0.440044	+	0.440044i	0.451983	+	0.892027i	$0.350717\pi$
$774$	4.92438e8	−	5.17554e8i	1.06201	−	1.11618i
$775$		−	1.07729e8i		−	0.231433i
$776$	3.80684e7	−	4.91653e7i	0.0814665	−	0.105214i
$777$	−3.26361e6	+	4.17783e6i	−0.00695721	+	0.00890610i
$778$	−3.93112e8	−	6.19051e8i	−0.834791	−	1.31458i
$779$	−3.88385e7	+	3.88385e7i	−0.0821581	+	0.0821581i
$780$	−8.72304e7	+	2.65892e8i	−0.183816	+	0.560301i
$781$	−1.60144e8	+	1.60144e8i	−0.336170	+	0.336170i
$782$	−3.33452e8	−	7.44342e7i	−0.697288	−	0.155651i
$783$	1.42247e8	+	6.32969e7i	0.296317	+	0.131855i
$784$	3.07585e8	+	3.70934e8i	0.638289	+	0.769748i
$785$		−	1.90281e8i		−	0.393357i
$786$	−2.43913e8	+	2.00499e8i	−0.502305	+	0.412899i
$787$	2.90888e8	−	2.90888e8i	0.596764	−	0.596764i	−0.342686	−	0.939450i	$-0.611337\pi$
$787$	2.90888e8	−	2.90888e8i	0.596764	−	0.596764i	0.939450	+	0.342686i	$0.111337\pi$
$788$	3.45956e8	−	1.24777e8i	0.707037	−	0.255010i
$789$	5.07950e8	−	6.24042e7i	1.03417	−	0.127052i
$790$	−1.77186e8	−	2.79022e8i	−0.359375	−	0.565923i
$791$	1.07892e6			0.00218001
$792$	−1.61279e8	−	4.14568e8i	−0.324641	−	0.834488i
$793$		−	4.52262e8i		−	0.906924i
$794$	−2.22716e8	−	3.50721e8i	−0.444929	−	0.700649i
$795$	−4.81519e7	−	3.91941e8i	−0.0958324	−	0.780045i
$796$	4.92067e7	−	1.04726e8i	0.0975629	−	0.207643i
$797$	−4.64579e8	−	4.64579e8i	−0.917667	−	0.917667i	0.0791926	−	0.996859i	$-0.474766\pi$
$797$	−4.64579e8	−	4.64579e8i	−0.917667	−	0.917667i	−0.996859	+	0.0791926i	$0.974766\pi$
$798$	−844350.	+	694063.i	−0.00166155	+	0.00136581i
$799$	−2.39137e8			−0.468819
$800$	−1.28327e8	−	2.50961e8i	−0.250639	−	0.490158i
$801$	−8.88911e8	+	2.21761e8i	−1.72966	+	0.431508i
$802$	−5.42338e7	−	1.21063e7i	−0.105135	−	0.0234686i
$803$	3.01832e8	+	3.01832e8i	0.582934	+	0.582934i
$804$	8.39834e8	−	4.24912e8i	1.61594	−	0.817582i
$805$	−1.72308e6	−	1.72308e6i	−0.00330307	−	0.00330307i
$806$	−1.03787e8	−	1.63437e8i	−0.198215	−	0.312138i
$807$	−3.09249e8	−	2.41578e8i	−0.588421	−	0.459659i
$808$	7.01279e7	+	5.51282e8i	0.132940	+	1.04506i
$809$	1.32003e8			0.249309			0.124654	−	0.992200i	$-0.460218\pi$
$809$	1.32003e8			0.249309			0.124654	+	0.992200i	$0.460218\pi$
$810$	3.09896e8	+	1.75813e8i	0.583124	+	0.330824i
$811$	−4.03500e8	−	4.03500e8i	−0.756452	−	0.756452i	0.219223	−	0.975675i	$-0.429648\pi$
$811$	−4.03500e8	−	4.03500e8i	−0.756452	−	0.756452i	−0.975675	+	0.219223i	$0.929648\pi$
$812$	−995926.	+	359205.i	−0.00186020	+	0.000670925i
$813$	−6.55890e8	+	8.05793e7i	−1.22056	+	0.149952i
$814$	1.95021e8	−	8.73657e8i	0.361583	−	1.61982i
$815$		−	1.75793e8i		−	0.324734i
$816$	−2.33099e8	+	2.47100e8i	−0.429012	+	0.454781i
$817$	2.96391e8			0.543499
$818$	−5.90215e8	−	1.31750e8i	−1.07833	−	0.240708i
$819$	−2.52549e6	−	1.51699e6i	−0.00459721	−	0.00276141i
$820$	−1.14531e8	+	4.13082e7i	−0.207721	+	0.0749195i
$821$	−3.26669e8	+	3.26669e8i	−0.590308	+	0.590308i	−0.937715	−	0.347406i	$-0.887062\pi$
$821$	−3.26669e8	+	3.26669e8i	−0.590308	+	0.590308i	0.347406	+	0.937715i	$0.387062\pi$
$822$	2.62139e7	−	2.68339e8i	0.0471972	−	0.483135i
$823$			7.37044e8i			1.32219i	0.750302	+	0.661095i	$0.229908\pi$
$823$			7.37044e8i			1.32219i	−0.750302	+	0.661095i	$0.770092\pi$
$824$	3.47275e8	+	2.68893e8i	0.620714	+	0.480615i
$825$	2.18130e8	+	1.70397e8i	0.388467	+	0.303460i
$826$	−3.24803e6	+	2.06258e6i	−0.00576342	+	0.00365991i
$827$	−1.90733e8	+	1.90733e8i	−0.337217	+	0.337217i	−0.855319	−	0.518102i	$-0.826639\pi$
$827$	−1.90733e8	+	1.90733e8i	−0.337217	+	0.337217i	0.518102	+	0.855319i	$0.326639\pi$
$828$	−6.36434e8	−	1.25544e8i	−1.12115	−	0.221159i
$829$	−2.73198e8	+	2.73198e8i	−0.479527	+	0.479527i	−0.904980	−	0.425453i	$-0.860115\pi$
$829$	−2.73198e8	+	2.73198e8i	−0.479527	+	0.479527i	0.425453	+	0.904980i	$0.360115\pi$
$830$	−9.62538e7	+	4.31199e8i	−0.168339	+	0.754126i
$831$	4.18226e8	+	3.26708e8i	0.728800	+	0.569320i
$832$	−4.36467e8	−	2.57107e8i	−0.757846	−	0.446420i
$833$			3.61359e8i			0.625179i
$834$	−5.15650e8	+	4.23869e8i	−0.888908	+	0.730690i
$835$	4.50987e7	−	4.50987e7i	0.0774649	−	0.0774649i
$836$	7.84833e7	−	1.67036e8i	0.134326	−	0.285884i
$837$	−2.30115e8	+	8.83877e7i	−0.392435	+	0.150735i
$838$	7.06405e8	−	4.48584e8i	1.20039	−	0.762276i
$839$	−4.77562e8			−0.808618			−0.404309	−	0.914622i	$-0.632488\pi$
$839$	−4.77562e8			−0.808618			−0.404309	+	0.914622i	$0.632488\pi$
$840$	−2.34823e6	+	596529.i	−0.00396189	+	0.00100645i
$841$		−	5.32254e8i		−	0.894810i
$842$	6.28766e8	−	3.99281e8i	1.05330	−	0.668872i
$843$	5.91199e8	−	7.26318e7i	0.986850	−	0.121239i
$844$	7.87188e8	−	2.83918e8i	1.30934	−	0.472244i
$845$	6.47507e7	+	6.47507e7i	0.107319	+	0.107319i
$846$	−4.53902e8	+	1.12872e7i	−0.749637	+	0.0186412i
$847$	734453.			0.00120869
$848$	7.11740e8	+	6.64506e7i	1.16717	+	0.108971i
$849$	−4.02317e8	−	3.14280e8i	−0.657424	−	0.513563i
$850$	4.60503e7	−	2.06297e8i	0.0749853	−	0.335920i
$851$	−9.23058e8	−	9.23058e8i	−1.49775	−	1.49775i
$852$	3.12013e8	+	1.02361e8i	0.504491	+	0.165507i
$853$	2.52178e8	+	2.52178e8i	0.406313	+	0.406313i	0.880451	−	0.474138i	$-0.157240\pi$
$853$	2.52178e8	+	2.52178e8i	0.406313	+	0.406313i	−0.474138	+	0.880451i	$0.657240\pi$
$854$	3.30552e6	−	2.09909e6i	0.00530721	−	0.00337021i
$855$	3.57811e7	+	1.43425e8i	0.0572473	+	0.229471i
$856$	1.25979e8	+	9.90329e8i	0.200852	+	1.57891i
$857$	1.22507e9			1.94633			0.973166	−	0.230102i	$-0.0739061\pi$
$857$	1.22507e9			1.94633			0.973166	+	0.230102i	$0.0739061\pi$
$858$	4.95093e8	+	4.83654e7i	0.783835	+	0.0765725i
$859$	5.29666e7	+	5.29666e7i	0.0835646	+	0.0835646i	0.747654	−	0.664089i	$-0.231180\pi$
$859$	5.29666e7	+	5.29666e7i	0.0835646	+	0.0835646i	−0.664089	+	0.747654i	$0.731180\pi$
$860$	5.94630e8	+	2.79393e8i	0.934871	+	0.439258i
$861$	−156300.	−	1.27223e6i	−0.000244878	−	0.00199323i
$862$	−6.27557e8	−	1.40086e8i	−0.979787	−	0.218711i
$863$			8.72616e8i			1.35766i	0.734296	+	0.678829i	$0.237512\pi$
$863$			8.72616e8i			1.35766i	−0.734296	+	0.678829i	$0.762488\pi$
$864$	−4.30779e8	+	4.80020e8i	−0.667903	+	0.744248i
$865$	6.60532e8			1.02058
$866$	1.12553e8	−	5.04217e8i	0.173302	−	0.776361i
$867$	3.94012e8	−	4.84063e7i	0.604577	−	0.0742753i
$868$	712836.	−	1.51712e6i	0.00109001	−	0.00231986i
$869$	−4.15469e8	+	4.15469e8i	−0.633111	+	0.633111i
$870$	−1.39214e7	+	1.42507e8i	−0.0211410	+	0.216410i
$871$			1.05253e9i			1.59287i
$872$	−1.34864e8	−	1.06017e9i	−0.203397	−	1.59892i
$873$	8.59017e7	−	2.14303e7i	0.129110	−	0.0322097i
$874$	−1.44275e8	−	2.27196e8i	−0.216101	−	0.340304i
$875$	3.00240e6	−	3.00240e6i	0.00448172	−	0.00448172i
$876$	1.92925e8	−	5.88067e8i	0.286997	−	0.874811i
$877$	−2.72026e8	+	2.72026e8i	−0.403284	+	0.403284i	−0.879389	−	0.476104i	$-0.842048\pi$
$877$	−2.72026e8	+	2.72026e8i	−0.403284	+	0.403284i	0.476104	+	0.879389i	$0.342048\pi$
$878$	1.08687e9	+	2.42614e8i	1.60581	+	0.358454i
$879$	1.93293e8	−	2.47439e8i	0.284610	−	0.364336i
$880$	3.14912e8	−	2.61131e8i	0.462106	−	0.383187i
$881$			4.93896e8i			0.722283i	0.932511	+	0.361142i	$0.117613\pi$
$881$			4.93896e8i			0.722283i	−0.932511	+	0.361142i	$0.882387\pi$
$882$	1.70561e7	+	6.85891e8i	0.0248584	+	0.999654i
$883$	−3.76502e8	+	3.76502e8i	−0.546871	+	0.546871i	−0.925534	−	0.378663i	$-0.876384\pi$
$883$	−3.76502e8	+	3.76502e8i	−0.546871	+	0.546871i	0.378663	+	0.925534i	$0.376384\pi$
$884$	−1.28884e8	−	3.57343e8i	−0.186571	−	0.517284i
$885$	6.34518e7	+	5.16477e8i	0.0915407	+	0.745112i
$886$	6.15037e8	+	9.68525e8i	0.884301	+	1.39255i
$887$	−1.68813e8			−0.241900			−0.120950	−	0.992659i	$-0.538594\pi$
$887$	−1.68813e8			−0.241900			−0.120950	+	0.992659i	$0.538594\pi$
$888$	−1.25795e9	+	3.19562e8i	−1.79649	+	0.456369i
$889$			4.80726e6i			0.00684214i
$890$	−4.51666e8	−	7.11258e8i	−0.640689	−	1.00892i
$891$	1.85011e8	−	6.05744e8i	0.261555	−	0.856359i
$892$	5.72819e8	+	2.69145e8i	0.807092	+	0.379220i
$893$	−1.33201e8	−	1.33201e8i	−0.187049	−	0.187049i
$894$	5.64541e8	+	6.86782e8i	0.790102	+	0.961184i
$895$	3.86803e7			0.0539537
$896$	−146616.	−	4.38338e6i	−0.000203824	−	0.00609376i
$897$	4.46577e8	−	5.71674e8i	0.618756	−	0.792084i
$898$	−1.01137e8	−	2.25761e7i	−0.139663	−	0.0311760i
$899$	−7.00489e7	−	7.00489e7i	−0.0964100	−	0.0964100i
$900$	7.76704e7	−	3.93743e8i	0.106544	−	0.540114i
$901$	3.79052e8	+	3.79052e8i	0.518232	+	0.518232i
$902$	1.16023e8	+	1.82707e8i	0.158098	+	0.248964i
$903$	−4.25803e6	+	5.45081e6i	−0.00578290	+	0.00740283i
$904$	2.08852e8	+	1.61713e8i	0.282706	+	0.218897i
$905$	−8.77784e8			−1.18425
$906$	−7.40310e6	−	723205.i	−0.00995472	−	0.000972472i
$907$	9.64059e8	+	9.64059e8i	1.29206	+	1.29206i	0.933513	+	0.358544i	$0.116727\pi$
$907$	9.64059e8	+	9.64059e8i	1.29206	+	1.29206i	0.358544	+	0.933513i	$0.383273\pi$
$908$	5.66821e7	+	1.57156e8i	0.0757161	+	0.209929i
$909$	−4.07433e8	+	6.78295e8i	−0.542456	+	0.903082i
$910$	590270.	−	2.64430e6i	0.000783298	−	0.00350903i
$911$		−	1.38420e8i		−	0.183081i	−0.995801	−	0.0915405i	$-0.970821\pi$
$911$		−	1.38420e8i		−	0.183081i	0.995801	−	0.0915405i	$-0.0291791\pi$
$912$	−2.67476e8	+	7.79879e6i	−0.352614	+	0.0102812i
$913$	7.85388e8			1.03198
$914$	1.01484e9	+	2.26536e8i	1.32910	+	0.296687i
$915$	−6.45749e7	−	5.25619e8i	−0.0842947	−	0.686132i
$916$	−8.09457e7	−	2.24429e8i	−0.105319	−	0.292006i
$917$	2.16165e6	−	2.16165e6i	0.00280336	−	0.00280336i
$918$	−4.78445e8	+	7.08935e7i	−0.618449	+	0.0916385i
$919$		−	4.74526e8i		−	0.611383i	−0.952131	−	0.305692i	$-0.901112\pi$
$919$		−	4.74526e8i		−	0.611383i	0.952131	−	0.305692i	$-0.0988877\pi$
$920$	−7.52836e7	−	5.91811e8i	−0.0966801	−	0.760011i
$921$	−3.93603e8	+	5.03861e8i	−0.503825	+	0.644959i
$922$	−1.04904e9	+	6.66168e8i	−1.33845	+	0.849945i
$923$	−2.59660e8	+	2.59660e8i	−0.330217	+	0.330217i
$924$	1.94438e6	+	3.84304e6i	0.00246470	+	0.00487146i
$925$	5.71070e8	−	5.71070e8i	0.721546	−	0.721546i
$926$	3.48920e7	−	1.56310e8i	0.0439433	−	0.196858i
$927$	1.51371e8	+	6.06759e8i	0.190022	+	0.761688i
$928$	−2.46627e8	−	7.97407e7i	−0.308600	−	0.0997783i
$929$			2.46290e8i			0.307185i	0.988134	+	0.153592i	$0.0490843\pi$
$929$			2.46290e8i			0.307185i	−0.988134	+	0.153592i	$0.950916\pi$
$930$	−1.43957e8	−	1.75128e8i	−0.178971	−	0.217724i
$931$	−2.01281e8	+	2.01281e8i	−0.249432	+	0.249432i
$932$	2.90433e8	+	1.36463e8i	0.358756	+	0.168565i
$933$	−8.69734e8	+	1.06851e8i	−1.07088	+	0.131563i
$934$	−7.10591e8	+	4.51243e8i	−0.872126	+	0.553821i
$935$	3.06783e8			0.375316
$936$	−2.61500e8	−	6.72185e8i	−0.318893	−	0.819712i
$937$		−	9.41204e8i		−	1.14410i	−0.820218	−	0.572051i	$-0.806148\pi$
$937$		−	9.41204e8i		−	1.14410i	0.820218	−	0.572051i	$-0.193852\pi$
$938$	−7.69281e6	+	4.88512e6i	−0.00932130	+	0.00591925i
$939$	−1.89252e8	−	1.54045e9i	−0.228583	−	1.86060i
$940$	−1.41671e8	−	3.92796e8i	−0.170568	−	0.472916i
$941$	−7.94957e8	−	7.94957e8i	−0.954058	−	0.954058i	0.0449320	−	0.998990i	$-0.485693\pi$
$941$	−7.94957e8	−	7.94957e8i	−0.954058	−	0.954058i	−0.998990	+	0.0449320i	$0.985693\pi$
$942$	3.11433e8	+	3.78868e8i	0.372573	+	0.453247i
$943$	3.15623e8			0.376386
$944$	−9.37890e8	−	8.75647e7i	−1.11490	−	0.104091i
$945$	−3.15172e6	−	1.40245e6i	−0.00373467	−	0.00166185i
$946$	2.54443e8	−	1.13986e9i	0.300551	−	1.34641i
$947$	2.17006e8	+	2.17006e8i	0.255518	+	0.255518i	0.823228	−	0.567710i	$-0.192171\pi$
$947$	2.17006e8	+	2.17006e8i	0.255518	+	0.255518i	−0.567710	+	0.823228i	$0.692171\pi$
$948$	8.09469e8	+	2.65560e8i	0.950112	+	0.311701i
$949$	4.89395e8	+	4.89395e8i	0.572612	+	0.572612i
$950$	1.40560e8	−	8.92589e7i	0.163942	−	0.104107i
$951$	3.41295e7	+	2.66611e7i	0.0396815	+	0.0309982i
$952$	2.01358e6	−	2.60053e6i	0.00233377	−	0.00301406i
$953$	7.01188e8			0.810132			0.405066	−	0.914287i	$-0.367249\pi$
$953$	7.01188e8			0.810132			0.405066	+	0.914287i	$0.367249\pi$
$954$	7.37364e8	+	7.01582e8i	0.849253	+	0.808041i
$955$	−6.34024e8	−	6.34024e8i	−0.727940	−	0.727940i
$956$	3.87894e8	−	8.25552e8i	0.443955	−	0.944868i
$957$	2.52634e8	−	3.10374e7i	0.288241	−	0.0354119i
$958$	7.74840e8	+	1.72963e8i	0.881284	+	0.196723i
$959$			2.61044e6i			0.00295977i
$960$	−5.43971e8	−	2.36490e8i	−0.614840	−	0.267300i
$961$	−7.30658e8			−0.823274
$962$	3.16209e8	−	1.41656e9i	0.355180	−	1.59114i
$963$	−7.31917e8	+	1.21850e9i	−0.819564	+	1.36441i
$964$	−4.63091e8	−	2.17588e8i	−0.516934	−	0.242887i
$965$	−1.17153e8	+	1.17153e8i	−0.130368	+	0.130368i
$966$	6.25098e6	+	610656.i	0.00693453	+	0.000677431i
$967$		−	3.42296e8i		−	0.378549i	−0.981924	−	0.189275i	$-0.939386\pi$
$967$		−	3.42296e8i		−	0.378549i	0.981924	−	0.189275i	$-0.0606136\pi$
$968$	1.42173e8	+	1.10083e8i	0.156744	+	0.121366i
$969$	−1.58136e8	−	1.23532e8i	−0.173804	−	0.135771i
$970$	4.36476e7	+	6.87338e7i	0.0478240	+	0.0753105i
$971$	−3.71472e8	+	3.71472e8i	−0.405759	+	0.405759i	−0.880257	−	0.474498i	$-0.842630\pi$
$971$	−3.71472e8	+	3.71472e8i	−0.405759	+	0.405759i	0.474498	+	0.880257i	$0.342630\pi$
$972$	−9.04785e8	+	1.57145e8i	−0.985250	+	0.171120i
$973$	4.56990e6	−	4.56990e6i	0.00496098	−	0.00496098i
$974$	3.88506e8	+	8.67236e7i	0.420456	+	0.0938557i
$975$	3.53679e8	+	2.76285e8i	0.381588	+	0.298087i
$976$	9.54490e8	+	8.91146e7i	1.02665	+	0.0958516i
$977$			8.89353e8i			0.953653i	0.878998	+	0.476826i	$0.158213\pi$
$977$			8.89353e8i			0.953653i	−0.878998	+	0.476826i	$0.841787\pi$
$978$	2.87719e8	+	3.50019e8i	0.307576	+	0.374176i
$979$	−1.05908e9	+	1.05908e9i	−1.12870	+	1.12870i
$980$	−5.93554e8	+	2.14080e8i	−0.630641	+	0.227456i
$981$	7.83537e8	−	1.30444e9i	0.829951	−	1.38171i
$982$	−6.70681e7	−	1.05615e8i	−0.0708242	−	0.111530i
$983$	1.25807e9			1.32448			0.662240	−	0.749292i	$-0.269606\pi$
$983$	1.25807e9			1.32448			0.662240	+	0.749292i	$0.269606\pi$
$984$	1.60432e8	−	2.69700e8i	0.168386	−	0.283072i
$985$			4.81572e8i			0.503909i
$986$	−1.04198e8	−	1.64085e8i	−0.108700	−	0.171174i
$987$	4.36327e6	−	536049.i	0.00453796	−	0.000557511i
$988$	1.27254e8	−	2.70834e8i	0.131947	−	0.280822i
$989$	−1.20431e9	−	1.20431e9i	−1.24495	−	1.24495i
$990$	5.82302e8	−	1.44801e7i	0.600126	−	0.0149233i
$991$	1.85726e8			0.190832			0.0954160	−	0.995437i	$-0.469582\pi$
$991$	1.85726e8			0.190832			0.0954160	+	0.995437i	$0.469582\pi$
$992$	3.65382e8	−	1.86836e8i	0.374293	−	0.191393i
$993$	−8.57518e8	−	6.69871e8i	−0.875781	−	0.684137i
$994$	−3.10298e6	−	692658.i	−0.00315951	−	0.000705277i
$995$	1.07137e8	+	1.07137e8i	0.108761	+	0.108761i
$996$	−5.14092e8	−	1.01610e9i	−0.520311	−	1.02839i
$997$	−1.24733e8	−	1.24733e8i	−0.125862	−	0.125862i	0.641370	−	0.767232i	$-0.278366\pi$
$997$	−1.24733e8	−	1.24733e8i	−0.125862	−	0.125862i	−0.767232	+	0.641370i	$0.778366\pi$
$998$	6.90436e8	+	1.08726e9i	0.694595	+	1.09381i
$999$	−1.68838e9	−	7.51295e8i	−1.69346	−	0.753554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.20	✓	92
3.2	odd	2	inner	48.7.i.a.5.27	yes	92
4.3	odd	2		192.7.i.a.113.2		92
12.11	even	2		192.7.i.a.113.21		92
16.3	odd	4		192.7.i.a.17.21		92
16.13	even	4	inner	48.7.i.a.29.27	yes	92
48.29	odd	4	inner	48.7.i.a.29.20	yes	92
48.35	even	4		192.7.i.a.17.2		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.20	✓	92	1.1	even	1	trivial
48.7.i.a.5.27	yes	92	3.2	odd	2	inner
48.7.i.a.29.20	yes	92	48.29	odd	4	inner
48.7.i.a.29.27	yes	92	16.13	even	4	inner
192.7.i.a.17.2		92	48.35	even	4
192.7.i.a.17.21		92	16.3	odd	4
192.7.i.a.113.2		92	4.3	odd	2
192.7.i.a.113.21		92	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.74289 + 7.80784i) q^{2} +(26.7985 - 3.29233i) q^{3} +(-57.9246 - 27.2165i) q^{4} +(59.2583 - 59.2583i) q^{5} +(-21.0010 + 214.977i) q^{6} -2.09133i q^{7} +(313.458 - 404.831i) q^{8} +(707.321 - 176.459i) q^{9} +O(q^{10})\)	\(q+(-1.74289 + 7.80784i) q^{2} +(26.7985 - 3.29233i) q^{3} +(-57.9246 - 27.2165i) q^{4} +(59.2583 - 59.2583i) q^{5} +(-21.0010 + 214.977i) q^{6} -2.09133i q^{7} +(313.458 - 404.831i) q^{8} +(707.321 - 176.459i) q^{9} +(359.398 + 565.960i) q^{10} +(842.725 - 842.725i) q^{11} +(-1641.90 - 538.653i) q^{12} +(1366.40 - 1366.40i) q^{13} +(16.3287 + 3.64496i) q^{14} +(1392.94 - 1783.13i) q^{15} +(2614.53 + 3153.01i) q^{16} +3071.62i q^{17} +(144.980 + 5830.20i) q^{18} +(-1710.92 + 1710.92i) q^{19} +(-5045.31 + 1819.71i) q^{20} +(-6.88534 - 56.0445i) q^{21} +(5111.08 + 8048.64i) q^{22} +13903.8 q^{23} +(7067.38 - 11880.9i) q^{24} +8601.91i q^{25} +(8287.17 + 13050.2i) q^{26} +(18374.2 - 7057.58i) q^{27} +(-56.9185 + 121.139i) q^{28} +(5593.27 + 5593.27i) q^{29} +(11494.7 + 13983.6i) q^{30} -12523.8 q^{31} +(-29175.0 + 14918.5i) q^{32} +(19809.3 - 25358.3i) q^{33} +(-23982.7 - 5353.50i) q^{34} +(-123.928 - 123.928i) q^{35} +(-45773.9 - 9029.44i) q^{36} +(-66388.7 - 66388.7i) q^{37} +(-10376.6 - 16340.5i) q^{38} +(32119.0 - 41116.3i) q^{39} +(-5414.59 - 42564.6i) q^{40} +22700.4 q^{41} +(449.587 + 43.9199i) q^{42} +(-86617.3 - 86617.3i) q^{43} +(-71750.5 + 25878.6i) q^{44} +(31458.0 - 52371.3i) q^{45} +(-24232.9 + 108559. i) q^{46} +77853.7i q^{47} +(80446.3 + 75888.0i) q^{48} +117645. q^{49} +(-67162.3 - 14992.2i) q^{50} +(10112.8 + 82314.8i) q^{51} +(-116337. + 41959.8i) q^{52} +(123405. - 123405. i) q^{53} +(23080.2 + 155763. i) q^{54} -99876.9i q^{55} +(-846.634 - 655.544i) q^{56} +(-40217.2 + 51483.1i) q^{57} +(-53419.8 + 33922.9i) q^{58} +(-162615. + 162615. i) q^{59} +(-129216. + 65376.5i) q^{60} +(165494. - 165494. i) q^{61} +(21827.6 - 97783.7i) q^{62} +(-369.034 - 1479.24i) q^{63} +(-65632.0 - 253795. i) q^{64} -161942. i q^{65} +(163468. + 198864. i) q^{66} +(-385147. + 385147. i) q^{67} +(83598.5 - 177922. i) q^{68} +(372602. - 45776.1i) q^{69} +(1183.61 - 751.619i) q^{70} -190032. q^{71} +(150279. - 341658. i) q^{72} +358162. i q^{73} +(634061. - 402644. i) q^{74} +(28320.4 + 230519. i) q^{75} +(145670. - 52539.3i) q^{76} +(-1762.41 - 1762.41i) q^{77} +(265049. + 322441. i) q^{78} -493007. q^{79} +(341774. + 31909.3i) q^{80} +(469165. - 249627. i) q^{81} +(-39564.3 + 177241. i) q^{82} +(465981. + 465981. i) q^{83} +(-1126.50 + 3433.75i) q^{84} +(182019. + 182019. i) q^{85} +(827259. - 525329. i) q^{86} +(168306. + 131476. i) q^{87} +(-77002.1 - 605320. i) q^{88} -1.25673e6 q^{89} +(354079. + 336896. i) q^{90} +(-2857.60 - 2857.60i) q^{91} +(-805375. - 378413. i) q^{92} +(-335619. + 41232.5i) q^{93} +(-607869. - 135691. i) q^{94} +202772. i q^{95} +(-732731. + 495847. i) q^{96} +121446. q^{97} +(-205042. + 918550. i) q^{98} +(447371. - 744784. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Introduction

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