LMFDB - Embedded newform 55.6.e.b.32.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,6,Mod(32,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("55.32");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	55.e (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:	$8.82111008971$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.17
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.88475 - 2.88475i) q^{2} +(5.55436 - 5.55436i) q^{3} +15.3564i q^{4} +(-11.0950 + 54.7896i) q^{5} -32.0459i q^{6} +(-103.743 + 103.743i) q^{7} +(136.612 + 136.612i) q^{8} +181.298i q^{9} +(126.048 + 190.061i) q^{10} +(-271.739 - 295.311i) q^{11} +(85.2950 + 85.2950i) q^{12} +(40.9640 + 40.9640i) q^{13} +598.545i q^{14} +(242.696 + 365.947i) q^{15} +296.775 q^{16} +(752.091 - 752.091i) q^{17} +(523.000 + 523.000i) q^{18} +2333.79 q^{19} +(-841.372 - 170.379i) q^{20} +1152.45i q^{21} +(-1635.80 - 67.9994i) q^{22} +(-1568.23 + 1568.23i) q^{23} +1517.58 q^{24} +(-2878.80 - 1215.78i) q^{25} +236.342 q^{26} +(2356.70 + 2356.70i) q^{27} +(-1593.12 - 1593.12i) q^{28} -477.232 q^{29} +(1755.78 + 355.548i) q^{30} +8126.11 q^{31} +(-3515.44 + 3515.44i) q^{32} +(-3149.60 - 130.928i) q^{33} -4339.19i q^{34} +(-4533.01 - 6835.06i) q^{35} -2784.09 q^{36} +(-971.434 - 971.434i) q^{37} +(6732.40 - 6732.40i) q^{38} +455.058 q^{39} +(-9000.59 + 5969.19i) q^{40} -2223.10i q^{41} +(3324.53 + 3324.53i) q^{42} +(-10296.0 - 10296.0i) q^{43} +(4534.92 - 4172.94i) q^{44} +(-9933.26 - 2011.50i) q^{45} +9047.93i q^{46} +(3963.20 + 3963.20i) q^{47} +(1648.40 - 1648.40i) q^{48} -4718.17i q^{49} +(-11811.9 + 4797.42i) q^{50} -8354.77i q^{51} +(-629.061 + 629.061i) q^{52} +(11691.1 - 11691.1i) q^{53} +13597.0 q^{54} +(19194.9 - 11612.0i) q^{55} -28344.9 q^{56} +(12962.7 - 12962.7i) q^{57} +(-1376.69 + 1376.69i) q^{58} +2379.92i q^{59} +(-5619.63 + 3726.94i) q^{60} +34132.7i q^{61} +(23441.8 - 23441.8i) q^{62} +(-18808.4 - 18808.4i) q^{63} +29779.2i q^{64} +(-2698.90 + 1789.91i) q^{65} +(-9463.52 + 8708.13i) q^{66} +(31275.3 + 31275.3i) q^{67} +(11549.4 + 11549.4i) q^{68} +17421.1i q^{69} +(-32794.0 - 6640.83i) q^{70} +34239.7 q^{71} +(-24767.4 + 24767.4i) q^{72} +(6013.88 + 6013.88i) q^{73} -5604.69 q^{74} +(-22742.8 + 9237.05i) q^{75} +35838.6i q^{76} +(58827.5 + 2445.43i) q^{77} +(1312.73 - 1312.73i) q^{78} +97400.0 q^{79} +(-3292.71 + 16260.2i) q^{80} -17875.5 q^{81} +(-6413.09 - 6413.09i) q^{82} +(-58184.5 - 58184.5i) q^{83} -17697.5 q^{84} +(32862.4 + 49551.2i) q^{85} -59403.1 q^{86} +(-2650.72 + 2650.72i) q^{87} +(3220.21 - 77465.6i) q^{88} +109220. i q^{89} +(-34457.6 + 22852.3i) q^{90} -8499.46 q^{91} +(-24082.4 - 24082.4i) q^{92} +(45135.4 - 45135.4i) q^{93} +22865.7 q^{94} +(-25893.3 + 127867. i) q^{95} +39052.1i q^{96} +(-36525.4 - 36525.4i) q^{97} +(-13610.8 - 13610.8i) q^{98} +(53539.4 - 49265.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) $ 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	2.88475	−	2.88475i	0.509957	−	0.509957i	−0.404556	−	0.914513i	$-0.632574\pi$
$2$	2.88475	−	2.88475i	0.509957	−	0.509957i	0.914513	+	0.404556i	$0.132574\pi$
$3$	5.55436	−	5.55436i	0.356312	−	0.356312i	−0.506139	−	0.862452i	$-0.668928\pi$
$3$	5.55436	−	5.55436i	0.356312	−	0.356312i	0.862452	+	0.506139i	$0.168928\pi$
$4$			15.3564i			0.479888i
$5$	−11.0950	+	54.7896i	−0.198473	+	0.980106i
$5$	−11.0950	+	54.7896i	−0.198473	+	0.980106i
$6$		−	32.0459i		−	0.363408i
$7$	−103.743	+	103.743i	−0.800227	+	0.800227i	−0.983131	−	0.182904i	$-0.941450\pi$
$7$	−103.743	+	103.743i	−0.800227	+	0.800227i	0.182904	+	0.983131i	$0.441450\pi$
$8$	136.612	+	136.612i	0.754679	+	0.754679i
$9$			181.298i			0.746083i
$10$	126.048	+	190.061i	0.398599	+	0.601025i
$11$	−271.739	−	295.311i	−0.677128	−	0.735865i
$11$	−271.739	−	295.311i	−0.677128	−	0.735865i
$12$	85.2950	+	85.2950i	0.170990	+	0.170990i
$13$	40.9640	+	40.9640i	0.0672271	+	0.0672271i	0.739921	−	0.672694i	$-0.234863\pi$
$13$	40.9640	+	40.9640i	0.0672271	+	0.0672271i	−0.672694	+	0.739921i	$0.734863\pi$
$14$			598.545i			0.816163i
$15$	242.696	+	365.947i	0.278506	+	0.419942i
$16$	296.775			0.289820
$17$	752.091	−	752.091i	0.631173	−	0.631173i	−0.317190	−	0.948362i	$-0.602739\pi$
$17$	752.091	−	752.091i	0.631173	−	0.631173i	0.948362	+	0.317190i	$0.102739\pi$
$18$	523.000	+	523.000i	0.380470	+	0.380470i
$19$	2333.79			1.48312			0.741562	−	0.670884i	$-0.234085\pi$
$19$	2333.79			1.48312			0.741562	+	0.670884i	$0.234085\pi$
$20$	−841.372	−	170.379i	−0.470341	−	0.0952447i
$21$			1152.45i			0.570262i
$22$	−1635.80	−	67.9994i	−0.720566	−	0.0299536i
$23$	−1568.23	+	1568.23i	−0.618146	+	0.618146i	−0.945056	−	0.326910i	$-0.893993\pi$
$23$	−1568.23	+	1568.23i	−0.618146	+	0.618146i	0.326910	+	0.945056i	$0.393993\pi$
$24$	1517.58			0.537803
$25$	−2878.80	−	1215.78i	−0.921217	−	0.389049i
$26$	236.342			0.0685659
$27$	2356.70	+	2356.70i	0.622151	+	0.622151i
$28$	−1593.12	−	1593.12i	−0.384019	−	0.384019i
$29$	−477.232			−0.105374			−0.0526871	−	0.998611i	$-0.516779\pi$
$29$	−477.232			−0.105374			−0.0526871	+	0.998611i	$0.516779\pi$
$30$	1755.78	+	355.548i	0.356178	+	0.0721266i
$31$	8126.11			1.51872			0.759362	−	0.650669i	$-0.225511\pi$
$31$	8126.11			1.51872			0.759362	+	0.650669i	$0.225511\pi$
$32$	−3515.44	+	3515.44i	−0.606884	+	0.606884i
$33$	−3149.60	−	130.928i	−0.503467	−	0.0209289i
$34$		−	4339.19i		−	0.643742i
$35$	−4533.01	−	6835.06i	−0.625484	−	0.943131i
$36$	−2784.09			−0.358036
$37$	−971.434	−	971.434i	−0.116657	−	0.116657i	0.646369	−	0.763025i	$-0.276287\pi$
$37$	−971.434	−	971.434i	−0.116657	−	0.116657i	−0.763025	+	0.646369i	$0.776287\pi$
$38$	6732.40	−	6732.40i	0.756330	−	0.756330i
$39$	455.058			0.0479077
$40$	−9000.59	+	5969.19i	−0.889449	+	0.589883i
$41$		−	2223.10i		−	0.206538i	−0.994653	−	0.103269i	$-0.967070\pi$
$41$		−	2223.10i		−	0.206538i	0.994653	−	0.103269i	$-0.0329302\pi$
$42$	3324.53	+	3324.53i	0.290809	+	0.290809i
$43$	−10296.0	−	10296.0i	−0.849179	−	0.849179i	0.140852	−	0.990031i	$-0.455016\pi$
$43$	−10296.0	−	10296.0i	−0.849179	−	0.849179i	−0.990031	+	0.140852i	$0.955016\pi$
$44$	4534.92	−	4172.94i	0.353133	−	0.324945i
$45$	−9933.26	−	2011.50i	−0.731241	−	0.148077i
$46$			9047.93i			0.630456i
$47$	3963.20	+	3963.20i	0.261698	+	0.261698i	0.825744	−	0.564045i	$-0.190756\pi$
$47$	3963.20	+	3963.20i	0.261698	+	0.261698i	−0.564045	+	0.825744i	$0.690756\pi$
$48$	1648.40	−	1648.40i	0.103266	−	0.103266i
$49$		−	4718.17i		−	0.280727i
$50$	−11811.9	+	4797.42i	−0.668179	+	0.271383i
$51$		−	8354.77i		−	0.449789i
$52$	−629.061	+	629.061i	−0.0322615	+	0.0322615i
$53$	11691.1	−	11691.1i	0.571697	−	0.571697i	−0.360906	−	0.932602i	$-0.617532\pi$
$53$	11691.1	−	11691.1i	0.571697	−	0.571697i	0.932602	+	0.360906i	$0.117532\pi$
$54$	13597.0			0.634540
$55$	19194.9	−	11612.0i	0.855618	−	0.517608i
$56$	−28344.9			−1.20783
$57$	12962.7	−	12962.7i	0.528456	−	0.528456i
$58$	−1376.69	+	1376.69i	−0.0537363	+	0.0537363i
$59$			2379.92i			0.0890087i	0.999009	+	0.0445043i	$0.0141709\pi$
$59$			2379.92i			0.0890087i	−0.999009	+	0.0445043i	$0.985829\pi$
$60$	−5619.63	+	3726.94i	−0.201525	+	0.133652i
$61$			34132.7i			1.17448i	0.809413	+	0.587240i	$0.199786\pi$
$61$			34132.7i			1.17448i	−0.809413	+	0.587240i	$0.800214\pi$
$62$	23441.8	−	23441.8i	0.774484	−	0.774484i
$63$	−18808.4	−	18808.4i	−0.597036	−	0.597036i
$64$			29779.2i			0.908789i
$65$	−2698.90	+	1789.91i	−0.0792325	+	0.0525470i
$66$	−9463.52	+	8708.13i	−0.267419	+	0.246074i
$67$	31275.3	+	31275.3i	0.851167	+	0.851167i	0.990277	−	0.139110i	$-0.0444240\pi$
$67$	31275.3	+	31275.3i	0.851167	+	0.851167i	−0.139110	+	0.990277i	$0.544424\pi$
$68$	11549.4	+	11549.4i	0.302892	+	0.302892i
$69$			17421.1i			0.440506i
$70$	−32794.0	−	6640.83i	−0.799926	−	0.161986i
$71$	34239.7			0.806091			0.403046	−	0.915180i	$-0.367952\pi$
$71$	34239.7			0.806091			0.403046	+	0.915180i	$0.367952\pi$
$72$	−24767.4	+	24767.4i	−0.563053	+	0.563053i
$73$	6013.88	+	6013.88i	0.132083	+	0.132083i	0.770058	−	0.637974i	$-0.220227\pi$
$73$	6013.88	+	6013.88i	0.132083	+	0.132083i	−0.637974	+	0.770058i	$0.720227\pi$
$74$	−5604.69			−0.118980
$75$	−22742.8	+	9237.05i	−0.466864	+	0.189618i
$76$			35838.6i			0.711734i
$77$	58827.5	+	2445.43i	1.13072	+	0.0470033i
$78$	1312.73	−	1312.73i	0.0244309	−	0.0244309i
$79$	97400.0			1.75587			0.877933	−	0.478784i	$-0.158922\pi$
$79$	97400.0			1.75587			0.877933	+	0.478784i	$0.158922\pi$
$80$	−3292.71	+	16260.2i	−0.0575213	+	0.284054i
$81$	−17875.5			−0.302723
$82$	−6413.09	−	6413.09i	−0.105325	−	0.105325i
$83$	−58184.5	−	58184.5i	−0.927069	−	0.927069i	0.0704462	−	0.997516i	$-0.477558\pi$
$83$	−58184.5	−	58184.5i	−0.927069	−	0.927069i	−0.997516	+	0.0704462i	$0.977558\pi$
$84$	−17697.5			−0.273662
$85$	32862.4	+	49551.2i	0.493346	+	0.743887i
$86$	−59403.1			−0.866090
$87$	−2650.72	+	2650.72i	−0.0375461	+	0.0375461i
$88$	3220.21	−	77465.6i	0.0443279	−	1.06636i
$89$			109220.i			1.46159i	0.682596	+	0.730796i	$0.260851\pi$
$89$			109220.i			1.46159i	−0.682596	+	0.730796i	$0.739149\pi$
$90$	−34457.6	+	22852.3i	−0.448414	+	0.297388i
$91$	−8499.46			−0.107594
$92$	−24082.4	−	24082.4i	−0.296641	−	0.296641i
$93$	45135.4	−	45135.4i	0.541140	−	0.541140i
$94$	22865.7			0.266910
$95$	−25893.3	+	127867.i	−0.294360	+	1.45362i
$96$			39052.1i			0.432480i
$97$	−36525.4	−	36525.4i	−0.394154	−	0.394154i	0.482011	−	0.876165i	$-0.339906\pi$
$97$	−36525.4	−	36525.4i	−0.394154	−	0.394154i	−0.876165	+	0.482011i	$0.839906\pi$
$98$	−13610.8	−	13610.8i	−0.143158	−	0.143158i
$99$	53539.4	−	49265.8i	0.549017	−	0.505194i
$100$	18670.0	−	44208.1i	0.186700	−	0.442081i
$101$		−	152382.i		−	1.48638i	−0.669080	−	0.743190i	$-0.733312\pi$
$101$		−	152382.i		−	1.48638i	0.669080	−	0.743190i	$-0.266688\pi$
$102$	−24101.4	−	24101.4i	−0.229373	−	0.229373i
$103$	76493.8	−	76493.8i	0.710450	−	0.710450i	−0.256180	−	0.966629i	$-0.582464\pi$
$103$	76493.8	−	76493.8i	0.710450	−	0.710450i	0.966629	+	0.256180i	$0.0824639\pi$
$104$			11192.3i			0.101470i
$105$	−63142.3	−	12786.4i	−0.558917	−	0.113181i
$106$		−	67451.8i		−	0.583081i
$107$	160384.	−	160384.i	1.35426	−	1.35426i	0.473431	−	0.880831i	$-0.343015\pi$
$107$	160384.	−	160384.i	1.35426	−	1.35426i	0.880831	−	0.473431i	$-0.156985\pi$
$108$	−36190.5	+	36190.5i	−0.298563	+	0.298563i
$109$	−230522.			−1.85843			−0.929214	−	0.369543i	$-0.879514\pi$
$109$	−230522.			−1.85843			−0.929214	+	0.369543i	$0.879514\pi$
$110$	21874.8	−	88870.4i	0.172370	−	0.700286i
$111$	−10791.4			−0.0831323
$112$	−30788.3	+	30788.3i	−0.231922	+	0.231922i
$113$	117467.	−	117467.i	0.865409	−	0.865409i	−0.126551	−	0.991960i	$-0.540391\pi$
$113$	117467.	−	117467.i	0.865409	−	0.865409i	0.991960	+	0.126551i	$0.0403908\pi$
$114$		−	74788.4i		−	0.538979i
$115$	−68523.4	−	103322.i	−0.483164	−	0.728534i
$116$		−	7328.56i		−	0.0505678i
$117$	−7426.71	+	7426.71i	−0.0501570	+	0.0501570i
$118$	6865.48	+	6865.48i	0.0453906	+	0.0453906i
$119$			156048.i			1.01016i
$120$	−16837.5	+	83147.6i	−0.106739	+	0.527104i
$121$	−13366.5	+	160495.i	−0.0829956	+	0.996550i
$122$	98464.3	+	98464.3i	0.598934	+	0.598934i
$123$	−12347.9	−	12347.9i	−0.0735919	−	0.0735919i
$124$			124788.i			0.728817i
$125$	98552.2	−	144240.i	0.564146	−	0.825675i
$126$	−108515.			−0.608925
$127$	−131960.	+	131960.i	−0.725992	+	0.725992i	−0.969819	−	0.243827i	$-0.921597\pi$
$127$	−131960.	+	131960.i	−0.725992	+	0.725992i	0.243827	+	0.969819i	$0.421597\pi$
$128$	−26588.7	−	26588.7i	−0.143440	−	0.143440i
$129$	−114376.			−0.605146
$130$	−2622.21	+	12949.1i	−0.0136085	+	0.0672018i
$131$		−	5606.55i		−	0.0285442i	−0.999898	−	0.0142721i	$-0.995457\pi$
$131$		−	5606.55i		−	0.0285442i	0.999898	−	0.0142721i	$-0.00454310\pi$
$132$	2010.58	−	48366.6i	0.0100435	−	0.241608i
$133$	−242114.	+	242114.i	−1.18684	+	1.18684i
$134$	180443.			0.868117
$135$	−155270.	+	102975.i	−0.733254	+	0.486294i
$136$	205489.			0.952666
$137$	−51214.1	−	51214.1i	−0.233125	−	0.233125i	0.580871	−	0.813996i	$-0.302712\pi$
$137$	−51214.1	−	51214.1i	−0.233125	−	0.233125i	−0.813996	+	0.580871i	$0.802712\pi$
$138$	50255.4	+	50255.4i	0.224639	+	0.224639i
$139$	−29167.4			−0.128044			−0.0640222	−	0.997948i	$-0.520393\pi$
$139$	−29167.4			−0.128044			−0.0640222	+	0.997948i	$0.520393\pi$
$140$	104962.	−	69610.8i	0.452597	−	0.300162i
$141$	44026.0			0.186493
$142$	98773.1	−	98773.1i	0.411072	−	0.411072i
$143$	965.606	−	23228.7i	0.00394875	−	0.0949915i
$144$			53804.8i			0.216230i
$145$	5294.87	−	26147.3i	0.0209139	−	0.103278i
$146$	34697.1			0.134714
$147$	−26206.4	−	26206.4i	−0.100026	−	0.100026i
$148$	14917.7	−	14917.7i	0.0559821	−	0.0559821i
$149$	313510.			1.15687			0.578436	−	0.815728i	$-0.303663\pi$
$149$	313510.			1.15687			0.578436	+	0.815728i	$0.303663\pi$
$150$	−38960.7	+	92253.9i	−0.141383	+	0.334778i
$151$			173899.i			0.620662i	0.950629	+	0.310331i	$0.100440\pi$
$151$			173899.i			0.620662i	−0.950629	+	0.310331i	$0.899560\pi$
$152$	318823.	+	318823.i	1.11928	+	1.11928i
$153$	136353.	+	136353.i	0.470907	+	0.470907i
$154$	176757.	−	162648.i	0.600586	−	0.552646i
$155$	−90158.9	+	445227.i	−0.301425	+	1.48851i
$156$			6988.06i			0.0229903i
$157$	−161370.	−	161370.i	−0.522484	−	0.522484i	0.395837	−	0.918321i	$-0.370455\pi$
$157$	−161370.	−	161370.i	−0.522484	−	0.522484i	−0.918321	+	0.395837i	$0.870455\pi$
$158$	280975.	−	280975.i	0.895416	−	0.895416i
$159$		−	129873.i		−	0.407405i
$160$	−153606.	−	231614.i	−0.474361	−	0.715260i
$161$		−	325386.i		−	0.989314i
$162$	−51566.3	+	51566.3i	−0.154376	+	0.154376i
$163$	−442373.	+	442373.i	−1.30413	+	1.30413i	−0.378540	+	0.925585i	$0.623574\pi$
$163$	−442373.	+	442373.i	−1.30413	+	1.30413i	−0.925585	+	0.378540i	$0.876426\pi$
$164$	34138.8			0.0991149
$165$	42118.2	−	171113.i	0.120437	−	0.489297i
$166$	−335696.			−0.945531
$167$	−197052.	+	197052.i	−0.546751	+	0.546751i	−0.925500	−	0.378749i	$-0.876354\pi$
$167$	−197052.	+	197052.i	−0.546751	+	0.546751i	0.378749	+	0.925500i	$0.376354\pi$
$168$	−157438.	+	157438.i	−0.430364	+	0.430364i
$169$		−	367937.i		−	0.990961i
$170$	237743.	+	48143.2i	0.630935	+	0.127765i
$171$			423112.i			1.10653i
$172$	158110.	−	158110.i	0.407511	−	0.407511i
$173$	−38967.4	−	38967.4i	−0.0989888	−	0.0989888i	0.655878	−	0.754867i	$-0.272299\pi$
$173$	−38967.4	−	38967.4i	−0.0989888	−	0.0989888i	−0.754867	+	0.655878i	$0.772299\pi$
$174$			15293.3i			0.0382938i
$175$	424784.	−	172527.i	1.04851	−	0.425856i
$176$	−80645.5	−	87641.1i	−0.196245	−	0.213268i
$177$	13218.9	+	13218.9i	0.0317149	+	0.0317149i
$178$	315072.	+	315072.i	0.745349	+	0.745349i
$179$		−	334650.i		−	0.780653i	−0.920676	−	0.390327i	$-0.872362\pi$
$179$		−	334650.i		−	0.780653i	0.920676	−	0.390327i	$-0.127638\pi$
$180$	30889.4	−	152539.i	0.0710604	−	0.350914i
$181$	102496.			0.232547			0.116273	−	0.993217i	$-0.462905\pi$
$181$	102496.			0.232547			0.116273	+	0.993217i	$0.462905\pi$
$182$	−24518.8	+	24518.8i	−0.0548683	+	0.0548683i
$183$	189585.	+	189585.i	0.418482	+	0.418482i
$184$	−428477.			−0.933003
$185$	64002.5	−	42446.5i	0.137489	−	0.0911827i
$186$		−	260409.i		−	0.551916i
$187$	−426474.	−	17728.3i	−0.891843	−	0.0370735i
$188$	−60860.5	+	60860.5i	−0.125586	+	0.125586i
$189$	−488983.			−0.995724
$190$	294170.	+	443562.i	0.591173	+	0.891395i
$191$	565974.			1.12257			0.561284	−	0.827623i	$-0.310307\pi$
$191$	565974.			1.12257			0.561284	+	0.827623i	$0.310307\pi$
$192$	165404.	+	165404.i	0.323813	+	0.323813i
$193$	−364829.	−	364829.i	−0.705011	−	0.705011i	0.260471	−	0.965482i	$-0.416122\pi$
$193$	−364829.	−	364829.i	−0.705011	−	0.705011i	−0.965482	+	0.260471i	$0.916122\pi$
$194$	−210734.			−0.402003
$195$	−5048.85	+	24932.5i	−0.00950837	+	0.0469546i
$196$	72454.2			0.134717
$197$	−235641.	+	235641.i	−0.432598	+	0.432598i	−0.889511	−	0.456913i	$-0.848955\pi$
$197$	−235641.	+	235641.i	−0.432598	+	0.432598i	0.456913	+	0.889511i	$0.348955\pi$
$198$	12328.2	−	296568.i	0.0223479	−	0.537602i
$199$			767403.i			1.37370i	0.726801	+	0.686848i	$0.241006\pi$
$199$			767403.i			1.37370i	−0.726801	+	0.686848i	$0.758994\pi$
$200$	−227189.	−	559367.i	−0.401616	−	0.988830i
$201$	347429.			0.606563
$202$	−439584.	−	439584.i	−0.757990	−	0.757990i
$203$	49509.4	−	49509.4i	0.0843233	−	0.0843233i
$204$	128299.			0.215848
$205$	121803.	+	24665.2i	0.202429	+	0.0409921i
$206$		−	441331.i		−	0.724597i
$207$	−284318.	−	284318.i	−0.461188	−	0.461188i
$208$	12157.1	+	12157.1i	0.0194837	+	0.0194837i
$209$	−634182.	−	689195.i	−1.00427	−	1.09138i
$210$	−219036.	+	145264.i	−0.342741	+	0.227306i
$211$			218175.i			0.337364i	0.985671	+	0.168682i	$0.0539511\pi$
$211$			218175.i			0.337364i	−0.985671	+	0.168682i	$0.946049\pi$
$212$	179533.	+	179533.i	0.274350	+	0.274350i
$213$	190180.	−	190180.i	0.287220	−	0.287220i
$214$		−	925338.i		−	1.38123i
$215$	678351.	−	449882.i	1.00082	−	0.663747i
$216$			643906.i			0.939049i
$217$	−843027.	+	843027.i	−1.21532	+	1.21532i
$218$	−664998.	+	664998.i	−0.947718	+	0.947718i
$219$	66806.5			0.0941258
$220$	178319.	+	294765.i	0.248394	+	0.410601i
$221$	61617.4			0.0848638
$222$	−31130.5	+	31130.5i	−0.0423939	+	0.0423939i
$223$	34654.9	−	34654.9i	0.0466661	−	0.0466661i	−0.683389	−	0.730055i	$-0.739495\pi$
$223$	34654.9	−	34654.9i	0.0466661	−	0.0466661i	0.730055	+	0.683389i	$0.239495\pi$
$224$		−	729405.i		−	0.971289i
$225$	220418.	−	521922.i	0.290263	−	0.687304i
$226$		−	677729.i		−	0.882642i
$227$	136425.	−	136425.i	0.175724	−	0.175724i	−0.613765	−	0.789489i	$-0.710346\pi$
$227$	136425.	−	136425.i	0.175724	−	0.175724i	0.789489	+	0.613765i	$0.210346\pi$
$228$	199061.	+	199061.i	0.253600	+	0.253600i
$229$			582233.i			0.733682i	0.930284	+	0.366841i	$0.119561\pi$
$229$			582233.i			0.733682i	−0.930284	+	0.366841i	$0.880439\pi$
$230$	−495732.	−	100386.i	−0.617913	−	0.125128i
$231$	340332.	−	313166.i	0.419636	−	0.386140i
$232$	−65195.3	−	65195.3i	−0.0795237	−	0.0795237i
$233$	−283442.	−	283442.i	−0.342038	−	0.342038i	0.515095	−	0.857133i	$-0.327757\pi$
$233$	−283442.	−	283442.i	−0.342038	−	0.342038i	−0.857133	+	0.515095i	$0.827757\pi$
$234$			42848.4i			0.0511558i
$235$	−261113.	+	173170.i	−0.308432	+	0.204552i
$236$	−36547.0			−0.0427142
$237$	540995.	−	540995.i	0.625637	−	0.625637i
$238$	450160.	+	450160.i	0.515139	+	0.515139i
$239$	1.58918e6			1.79960			0.899802	−	0.436298i	$-0.143711\pi$
$239$	1.58918e6			1.79960			0.899802	+	0.436298i	$0.143711\pi$
$240$	72026.1	+	108604.i	0.0807164	+	0.121708i
$241$		−	519927.i		−	0.576633i	−0.957535	−	0.288317i	$-0.906904\pi$
$241$		−	519927.i		−	0.576633i	0.957535	−	0.288317i	$-0.0930956\pi$
$242$	424430.	+	501548.i	0.465873	+	0.550522i
$243$	−671966.	+	671966.i	−0.730015	+	0.730015i
$244$	−524156.			−0.563619
$245$	258507.	+	52347.9i	0.275142	+	0.0557166i
$246$	−71241.2			−0.0750574
$247$	95601.5	+	95601.5i	0.0997062	+	0.0997062i
$248$	1.11012e6	+	1.11012e6i	1.14615	+	1.14615i
$249$	−646356.			−0.660653
$250$	−131797.	−	700394.i	−0.133369	−	0.708749i
$251$	−70673.7			−0.0708066			−0.0354033	−	0.999373i	$-0.511272\pi$
$251$	−70673.7			−0.0708066			−0.0354033	+	0.999373i	$0.511272\pi$
$252$	288829.	−	288829.i	0.286510	−	0.286510i
$253$	889267.	+	36966.4i	0.873436	+	0.0363083i
$254$			761342.i			0.740449i
$255$	457755.	+	92695.9i	0.440841	+	0.0892709i
$256$	−1.10634e6			−1.05509
$257$	−1.20806e6	−	1.20806e6i	−1.14092	−	1.14092i	−0.988282	−	0.152640i	$-0.951223\pi$
$257$	−1.20806e6	−	1.20806e6i	−1.14092	−	1.14092i	−0.152640	−	0.988282i	$-0.548777\pi$
$258$	−329946.	+	329946.i	−0.308598	+	0.308598i
$259$	201559.			0.186703
$260$	−27486.6	−	41445.4i	−0.0252167	−	0.0380227i
$261$		−	86521.2i		−	0.0786179i
$262$	−16173.5	−	16173.5i	−0.0145563	−	0.0145563i
$263$	893794.	+	893794.i	0.796798	+	0.796798i	0.982589	−	0.185792i	$-0.0594849\pi$
$263$	893794.	+	893794.i	0.796798	+	0.796798i	−0.185792	+	0.982589i	$0.559485\pi$
$264$	−412386.	−	448158.i	−0.364161	−	0.395751i
$265$	510839.	+	770263.i	0.446857	+	0.673790i
$266$			1.39688e6i			1.21047i
$267$	606646.	+	606646.i	0.520784	+	0.520784i
$268$	−480277.	+	480277.i	−0.408465	+	0.408465i
$269$			969842.i			0.817184i	0.912717	+	0.408592i	$0.133980\pi$
$269$			969842.i			0.817184i	−0.912717	+	0.408592i	$0.866020\pi$
$270$	−150858.	+	744975.i	−0.125939	+	0.621917i
$271$		−	1.10341e6i		−	0.912669i	−0.889808	−	0.456334i	$-0.849162\pi$
$271$		−	1.10341e6i		−	0.912669i	0.889808	−	0.456334i	$-0.150838\pi$
$272$	223202.	−	223202.i	0.182926	−	0.182926i
$273$	−47209.0	+	47209.0i	−0.0383370	+	0.0383370i
$274$	−295480.			−0.237767
$275$	423251.	+	1.18052e6i	0.337494	+	0.941328i
$276$	−267525.			−0.211394
$277$	−170236.	+	170236.i	−0.133307	+	0.133307i	−0.770612	−	0.637305i	$-0.780049\pi$
$277$	−170236.	+	170236.i	−0.133307	+	0.133307i	0.637305	+	0.770612i	$0.280049\pi$
$278$	−84140.6	+	84140.6i	−0.0652971	+	0.0652971i
$279$			1.47325e6i			1.13309i
$280$	314486.	−	1.55301e6i	0.239721	−	1.18380i
$281$		−	14924.1i		−	0.0112751i	−0.999984	−	0.00563756i	$-0.998205\pi$
$281$		−	14924.1i		−	0.0112751i	0.999984	−	0.00563756i	$-0.00179450\pi$
$282$	127004.	−	127004.i	0.0951032	−	0.0951032i
$283$	−66100.1	−	66100.1i	−0.0490610	−	0.0490610i	0.682151	−	0.731212i	$-0.261045\pi$
$283$	−66100.1	−	66100.1i	−0.0490610	−	0.0490610i	−0.731212	+	0.682151i	$0.761045\pi$
$284$			525799.i			0.386833i
$285$	566401.	+	854043.i	0.413059	+	0.622827i
$286$	−64223.5	−	69794.5i	−0.0464279	−	0.0504552i
$287$	230631.	+	230631.i	0.165277	+	0.165277i
$288$	−637344.	−	637344.i	−0.452785	−	0.452785i
$289$			288575.i			0.203242i
$290$	−60154.2	−	90702.9i	−0.0420021	−	0.0633325i
$291$	−405751.			−0.280884
$292$	−92351.7	+	92351.7i	−0.0633852	+	0.0633852i
$293$	−1.59914e6	−	1.59914e6i	−1.08822	−	1.08822i	−0.995712	−	0.0925065i	$-0.970512\pi$
$293$	−1.59914e6	−	1.59914e6i	−1.08822	−	1.08822i	−0.0925065	−	0.995712i	$-0.529488\pi$
$294$	−151198.			−0.102018
$295$	−130395.	−	26405.1i	−0.0872380	−	0.0176658i
$296$		−	265418.i		−	0.176076i
$297$	55552.3	−	1.33637e6i	0.0365436	−	0.879095i
$298$	904398.	−	904398.i	0.589955	−	0.589955i
$299$	−128482.			−0.0831123
$300$	−141848.	−	349247.i	−0.0909955	−	0.224042i
$301$	2.13628e6			1.35907
$302$	501656.	+	501656.i	0.316511	+	0.316511i
$303$	−846384.	−	846384.i	−0.529616	−	0.529616i
$304$	692611.			0.429839
$305$	−1.87012e6	−	378701.i	−1.15112	−	0.233102i
$306$	786688.			0.480285
$307$	1.02898e6	−	1.02898e6i	0.623107	−	0.623107i	−0.323218	−	0.946325i	$-0.604765\pi$
$307$	1.02898e6	−	1.02898e6i	0.623107	−	0.623107i	0.946325	+	0.323218i	$0.104765\pi$
$308$	−37553.0	+	903379.i	−0.0225563	+	0.542617i
$309$		−	849748.i		−	0.506284i
$310$	1.02428e6	+	1.54445e6i	0.605362	+	0.912790i
$311$	−1.96307e6			−1.15089			−0.575446	−	0.817840i	$-0.695171\pi$
$311$	−1.96307e6			−1.15089			−0.575446	+	0.817840i	$0.695171\pi$
$312$	62166.2	+	62166.2i	0.0361549	+	0.0361549i
$313$	1.41211e6	−	1.41211e6i	0.814719	−	0.814719i	−0.170618	−	0.985337i	$-0.554576\pi$
$313$	1.41211e6	−	1.41211e6i	0.814719	−	0.814719i	0.985337	+	0.170618i	$0.0545764\pi$
$314$	−931023.			−0.532889
$315$	1.23918e6	−	821826.i	0.703654	−	0.466663i
$316$			1.49571e6i			0.842619i
$317$	−527387.	−	527387.i	−0.294769	−	0.294769i	0.544192	−	0.838961i	$-0.316836\pi$
$317$	−527387.	−	527387.i	−0.294769	−	0.294769i	−0.838961	+	0.544192i	$0.816836\pi$
$318$	−374652.	−	374652.i	−0.207759	−	0.207759i
$319$	129683.	+	140932.i	0.0713518	+	0.0775412i
$320$	−1.63159e6	−	330399.i	−0.890709	−	0.180370i
$321$		−	1.78167e6i		−	0.965081i
$322$	−938658.	−	938658.i	−0.504508	−	0.504508i
$323$	1.75522e6	−	1.75522e6i	0.936108	−	0.936108i
$324$		−	274503.i		−	0.145273i
$325$	−68124.3	−	167731.i	−0.0357761	−	0.0880854i
$326$			2.55227e6i			1.33010i
$327$	−1.28040e6	+	1.28040e6i	−0.662181	+	0.662181i
$328$	303701.	−	303701.i	0.155870	−	0.155870i
$329$	−822307.			−0.418836
$330$	−372118.	−	615119.i	−0.188103	−	0.310938i
$331$	103664.			0.0520067			0.0260034	−	0.999662i	$-0.491722\pi$
$331$	103664.			0.0520067			0.0260034	+	0.999662i	$0.491722\pi$
$332$	893506.	−	893506.i	0.444889	−	0.444889i
$333$	176119.	−	176119.i	0.0870355	−	0.0870355i
$334$			1.13689e6i			0.557639i
$335$	−2.06056e6	+	1.36656e6i	−1.00317	+	0.665301i
$336$			342019.i			0.165273i
$337$	−1.47688e6	+	1.47688e6i	−0.708387	+	0.708387i	−0.966196	−	0.257809i	$-0.916999\pi$
$337$	−1.47688e6	+	1.47688e6i	−0.708387	+	0.708387i	0.257809	+	0.966196i	$0.416999\pi$
$338$	−1.06141e6	−	1.06141e6i	−0.505347	−	0.505347i
$339$		−	1.30491e6i		−	0.616712i
$340$	−760929.	+	504648.i	−0.356982	+	0.236751i
$341$	−2.20818e6	−	2.39973e6i	−1.02837	−	1.11758i
$342$	1.22057e6	+	1.22057e6i	0.564285	+	0.564285i
$343$	−1.25413e6	−	1.25413e6i	−0.575582	−	0.575582i
$344$		−	2.81312e6i		−	1.28172i
$345$	−954493.	−	193286.i	−0.431743	−	0.0874284i
$346$	−224823.			−0.100960
$347$	−1.35556e6	+	1.35556e6i	−0.604358	+	0.604358i	−0.941466	−	0.337108i	$-0.890551\pi$
$347$	−1.35556e6	+	1.35556e6i	−0.604358	+	0.604358i	0.337108	+	0.941466i	$0.390551\pi$
$348$	−40705.5	−	40705.5i	−0.0180179	−	0.0180179i
$349$	3.89080e6			1.70992			0.854960	−	0.518695i	$-0.173582\pi$
$349$	3.89080e6			1.70992			0.854960	+	0.518695i	$0.173582\pi$
$350$	727697.	−	1.72309e6i	0.317527	−	0.751863i
$351$			193080.i			0.0836508i
$352$	1.99343e6	+	82866.2i	0.857522	+	0.0356468i
$353$	2.14991e6	−	2.14991e6i	0.918299	−	0.918299i	−0.0786071	−	0.996906i	$-0.525047\pi$
$353$	2.14991e6	−	2.14991e6i	0.918299	−	0.918299i	0.996906	+	0.0786071i	$0.0250473\pi$
$354$	76266.7			0.0323465
$355$	−379888.	+	1.87598e6i	−0.159987	+	0.790055i
$356$	−1.67722e6			−0.701401
$357$	866748.	+	866748.i	0.359933	+	0.359933i
$358$	−965382.	−	965382.i	−0.398100	−	0.398100i
$359$	2.36885e6			0.970067			0.485033	−	0.874496i	$-0.338807\pi$
$359$	2.36885e6			0.970067			0.485033	+	0.874496i	$0.338807\pi$
$360$	−1.08220e6	−	1.63179e6i	−0.440101	−	0.663603i
$361$	2.97048e6			1.19966
$362$	295675.	−	295675.i	0.118589	−	0.118589i
$363$	817206.	+	965692.i	0.325511	+	0.384655i
$364$		−	130521.i		−	0.0516330i
$365$	−396222.	+	262774.i	−0.155671	+	0.103241i
$366$	1.09381e6			0.426816
$367$	2.46073e6	+	2.46073e6i	0.953672	+	0.953672i	0.998973	−	0.0453010i	$-0.0144247\pi$
$367$	2.46073e6	+	2.46073e6i	0.953672	+	0.953672i	−0.0453010	+	0.998973i	$0.514425\pi$
$368$	−465413.	+	465413.i	−0.179151	+	0.179151i
$369$	403044.			0.154094
$370$	62183.9	−	307079.i	0.0236142	−	0.116613i
$371$			2.42574e6i			0.914974i
$372$	693117.	+	693117.i	0.259687	+	0.259687i
$373$	−2.21059e6	−	2.21059e6i	−0.822690	−	0.822690i	0.163803	−	0.986493i	$-0.447624\pi$
$373$	−2.21059e6	−	2.21059e6i	−0.822690	−	0.822690i	−0.986493	+	0.163803i	$0.947624\pi$
$374$	−1.28141e6	+	1.17913e6i	−0.473707	+	0.435895i
$375$	−253764.	−	1.34855e6i	−0.0931862	−	0.495210i
$376$			1.08284e6i			0.394996i
$377$	−19549.3	−	19549.3i	−0.00708400	−	0.00708400i
$378$	−1.41059e6	+	1.41059e6i	−0.507776	+	0.507776i
$379$			1.51410e6i			0.541447i	0.962657	+	0.270724i	$0.0872630\pi$
$379$			1.51410e6i			0.541447i	−0.962657	+	0.270724i	$0.912737\pi$
$380$	−1.96359e6	−	397628.i	−0.697575	−	0.141260i
$381$			1.46590e6i			0.517360i
$382$	1.63269e6	−	1.63269e6i	0.572462	−	0.572462i
$383$	−1.34885e6	+	1.34885e6i	−0.469857	+	0.469857i	−0.901868	−	0.432011i	$-0.857804\pi$
$383$	−1.34885e6	+	1.34885e6i	−0.469857	+	0.469857i	0.432011	+	0.901868i	$0.357804\pi$
$384$	−295366.			−0.102219
$385$	−786673.	+	3.19600e6i	−0.270484	+	1.09889i
$386$	−2.10488e6			−0.719050
$387$	1.86665e6	−	1.86665e6i	0.633558	−	0.633558i
$388$	560900.	−	560900.i	0.189150	−	0.189150i
$389$			1.61439e6i			0.540921i	0.962731	+	0.270461i	$0.0871760\pi$
$389$			1.61439e6i			0.540921i	−0.962731	+	0.270461i	$0.912824\pi$
$390$	57359.3	+	86488.6i	0.0190960	+	0.0287937i
$391$			2.35891e6i			0.780313i
$392$	644557.	−	644557.i	0.211859	−	0.211859i
$393$	−31140.8	−	31140.8i	−0.0101707	−	0.0101707i
$394$			1.35953e6i			0.441213i
$395$	−1.08065e6	+	5.33651e6i	−0.348491	+	1.72094i
$396$	756546.	+	822173.i	0.242436	+	0.263466i
$397$	−1.63341e6	−	1.63341e6i	−0.520137	−	0.520137i	0.397476	−	0.917613i	$-0.369886\pi$
$397$	−1.63341e6	−	1.63341e6i	−0.520137	−	0.520137i	−0.917613	+	0.397476i	$0.869886\pi$
$398$	2.21377e6	+	2.21377e6i	0.700526	+	0.700526i
$399$			2.68958e6i			0.845769i
$400$	−854358.	−	360813.i	−0.266987	−	0.112754i
$401$	−3.39398e6			−1.05402			−0.527010	−	0.849859i	$-0.676687\pi$
$401$	−3.39398e6			−1.05402			−0.527010	+	0.849859i	$0.676687\pi$
$402$	1.00225e6	−	1.00225e6i	0.309321	−	0.309321i
$403$	332879.	+	332879.i	0.102099	+	0.102099i
$404$	2.34004e6			0.713296
$405$	198328.	−	979391.i	0.0600822	−	0.296701i
$406$		−	285645.i		−	0.0860025i
$407$	−22898.7	+	550852.i	−0.00685211	+	0.164835i
$408$	1.14136e6	−	1.14136e6i	0.339446	−	0.339446i
$409$	4.46788e6			1.32067			0.660333	−	0.750973i	$-0.270415\pi$
$409$	4.46788e6			1.32067			0.660333	+	0.750973i	$0.270415\pi$
$410$	422524.	−	280218.i	0.124134	−	0.0823258i
$411$	−568923.			−0.166130
$412$	1.17467e6	+	1.17467e6i	0.340936	+	0.340936i
$413$	−246900.	−	246900.i	−0.0712271	−	0.0712271i
$414$	−1.64037e6			−0.470372
$415$	3.83346e6	−	2.54235e6i	1.09262	−	0.724629i
$416$	−288014.			−0.0815981
$417$	−162006.	+	162006.i	−0.0456238	+	0.0456238i
$418$	−3.81761e6	−	158696.i	−1.06869	−	0.0444249i
$419$		−	3.51858e6i		−	0.979112i	−0.871972	−	0.489556i	$-0.837159\pi$
$419$		−	3.51858e6i		−	0.979112i	0.871972	−	0.489556i	$-0.162841\pi$
$420$	196353.	−	969640.i	0.0543144	−	0.268218i
$421$	5.31362e6			1.46112			0.730559	−	0.682849i	$-0.239259\pi$
$421$	5.31362e6			1.46112			0.730559	+	0.682849i	$0.239259\pi$
$422$	629381.	+	629381.i	0.172041	+	0.172041i
$423$	−718520.	+	718520.i	−0.195249	+	0.195249i
$424$	3.19428e6			0.862895
$425$	−3.07950e6	+	1.25075e6i	−0.827004	+	0.335890i
$426$		−	1.09724e6i		−	0.292940i
$427$	−3.54102e6	−	3.54102e6i	−0.939851	−	0.939851i
$428$	2.46293e6	+	2.46293e6i	0.649894	+	0.649894i
$429$	−123657.	−	134384.i	−0.0324396	−	0.0352536i
$430$	659075.	−	3.25467e6i	0.171895	−	0.848860i
$431$		−	1.57613e6i		−	0.408694i	−0.978898	−	0.204347i	$-0.934493\pi$
$431$		−	1.57613e6i		−	0.408694i	0.978898	−	0.204347i	$-0.0655071\pi$
$432$	699412.	+	699412.i	0.180312	+	0.180312i
$433$	−3.29284e6	+	3.29284e6i	−0.844017	+	0.844017i	−0.989379	−	0.145361i	$-0.953566\pi$
$433$	−3.29284e6	+	3.29284e6i	−0.844017	+	0.844017i	0.145361	+	0.989379i	$0.453566\pi$
$434$			4.86385e6i			1.23953i
$435$	−115822.	−	174641.i	−0.0293473	−	0.0442511i
$436$		−	3.53999e6i		−	0.891837i
$437$	−3.65993e6	+	3.65993e6i	−0.916788	+	0.916788i
$438$	192720.	−	192720.i	0.0480001	−	0.0480001i
$439$	−4.51196e6			−1.11739			−0.558694	−	0.829374i	$-0.688698\pi$
$439$	−4.51196e6			−1.11739			−0.558694	+	0.829374i	$0.688698\pi$
$440$	4.20858e6	+	1.03591e6i	1.03634	+	0.255089i
$441$	855396.			0.209445
$442$	177751.	−	177751.i	0.0432769	−	0.0432769i
$443$	4.03065e6	−	4.03065e6i	0.975812	−	0.975812i	−0.0239020	−	0.999714i	$-0.507609\pi$
$443$	4.03065e6	−	4.03065e6i	0.975812	−	0.975812i	0.999714	+	0.0239020i	$0.00760897\pi$
$444$		−	165717.i		−	0.0398942i
$445$	−5.98411e6	−	1.21179e6i	−1.43252	−	0.290086i
$446$		−	199941.i		−	0.0475954i
$447$	1.74135e6	−	1.74135e6i	0.412208	−	0.412208i
$448$	−3.08938e6	−	3.08938e6i	−0.727237	−	0.727237i
$449$		−	7.25561e6i		−	1.69847i	−0.528014	−	0.849235i	$-0.677063\pi$
$449$		−	7.25561e6i		−	1.69847i	0.528014	−	0.849235i	$-0.322937\pi$
$450$	−869763.	−	2.14147e6i	−0.202474	−	0.498517i
$451$	−656506.	+	604103.i	−0.151984	+	0.139852i
$452$	1.80388e6	+	1.80388e6i	0.415299	+	0.415299i
$453$	965899.	+	965899.i	0.221150	+	0.221150i
$454$		−	787107.i		−	0.179223i
$455$	94301.2	−	465682.i	0.0213545	−	0.105453i
$456$	3.54171e6			0.797629
$457$	−3.32290e6	+	3.32290e6i	−0.744265	+	0.744265i	−0.973396	−	0.229131i	$-0.926412\pi$
$457$	−3.32290e6	+	3.32290e6i	−0.744265	+	0.744265i	0.229131	+	0.973396i	$0.426412\pi$
$458$	1.67960e6	+	1.67960e6i	0.374146	+	0.374146i
$459$	3.54491e6			0.785369
$460$	1.58666e6	−	1.05227e6i	0.349615	−	0.231864i
$461$		−	748252.i		−	0.163982i	−0.996633	−	0.0819909i	$-0.973872\pi$
$461$		−	748252.i		−	0.163982i	0.996633	−	0.0819909i	$-0.0261278\pi$
$462$	78366.0	−	1.88518e6i	0.0170814	−	0.410911i
$463$	4.39822e6	−	4.39822e6i	0.953509	−	0.953509i	−0.0454573	−	0.998966i	$-0.514475\pi$
$463$	4.39822e6	−	4.39822e6i	0.953509	−	0.953509i	0.998966	+	0.0454573i	$0.0144745\pi$
$464$	−141631.			−0.0305395
$465$	1.97217e6	+	2.97372e6i	0.422973	+	0.637776i
$466$	−1.63532e6			−0.348850
$467$	−694029.	−	694029.i	−0.147260	−	0.147260i	0.629633	−	0.776893i	$-0.283205\pi$
$467$	−694029.	−	694029.i	−0.147260	−	0.147260i	−0.776893	+	0.629633i	$0.783205\pi$
$468$	−114048.	−	114048.i	−0.0240697	−	0.0240697i
$469$	−6.48919e6			−1.36225
$470$	−253694.	+	1.25280e6i	−0.0529743	+	0.261600i
$471$	−1.79261e6			−0.372335
$472$	−325124.	+	325124.i	−0.0671730	+	0.0671730i
$473$	−242699.	+	5.83838e6i	−0.0498786	+	1.19988i
$474$		−	3.12127e6i		−	0.638095i
$475$	−6.71852e6	−	2.83737e6i	−1.36628	−	0.577008i
$476$	−2.39634e6			−0.484765
$477$	2.11958e6	+	2.11958e6i	0.426533	+	0.426533i
$478$	4.58438e6	−	4.58438e6i	0.917721	−	0.917721i
$479$	−4.12849e6			−0.822153			−0.411076	−	0.911601i	$-0.634847\pi$
$479$	−4.12849e6			−0.822153			−0.411076	+	0.911601i	$0.634847\pi$
$480$	−2.13965e6	−	433281.i	−0.423877	−	0.0858355i
$481$		−	79587.8i		−	0.0156850i
$482$	−1.49986e6	−	1.49986e6i	−0.294058	−	0.294058i
$483$	−1.80731e6	−	1.80731e6i	−0.352505	−	0.352505i
$484$	−2.46463e6	−	205262.i	−0.478232	−	0.0398286i
$485$	2.40646e6	−	1.59597e6i	0.464542	−	0.308084i
$486$			3.87691e6i			0.744552i
$487$	−2.14733e6	−	2.14733e6i	−0.410277	−	0.410277i	0.471558	−	0.881835i	$-0.343692\pi$
$487$	−2.14733e6	−	2.14733e6i	−0.410277	−	0.410277i	−0.881835	+	0.471558i	$0.843692\pi$
$488$	−4.66292e6	+	4.66292e6i	−0.886356	+	0.886356i
$489$			4.91419e6i			0.929352i
$490$	896739.	−	594717.i	0.168724	−	0.111897i
$491$		−	8.67245e6i		−	1.62345i	−0.584042	−	0.811723i	$-0.698530\pi$
$491$		−	8.67245e6i		−	1.62345i	0.584042	−	0.811723i	$-0.301470\pi$
$492$	189619.	−	189619.i	0.0353159	−	0.0353159i
$493$	−358922.	+	358922.i	−0.0665093	+	0.0665093i
$494$	551573.			0.101692
$495$	2.10524e6	+	3.48001e6i	0.386179	+	0.638362i
$496$	2.41163e6			0.440156
$497$	−3.55213e6	+	3.55213e6i	−0.645056	+	0.645056i
$498$	−1.86458e6	+	1.86458e6i	−0.336904	+	0.336904i
$499$			5.93754e6i			1.06747i	0.845652	+	0.533735i	$0.179212\pi$
$499$			5.93754e6i			1.06747i	−0.845652	+	0.533735i	$0.820788\pi$
$500$	2.21500e6	+	1.51341e6i	0.396232	+	0.270727i
$501$			2.18899e6i			0.389628i
$502$	−203876.	+	203876.i	−0.0361083	+	0.0361083i
$503$	−977755.	−	977755.i	−0.172310	−	0.172310i	0.615684	−	0.787993i	$-0.288880\pi$
$503$	−977755.	−	977755.i	−0.172310	−	0.172310i	−0.787993	+	0.615684i	$0.788880\pi$
$504$		−	5.13889e6i		−	0.901141i
$505$	8.34895e6	+	1.69067e6i	1.45681	+	0.295006i
$506$	2.67195e6	−	2.45868e6i	0.463930	−	0.426899i
$507$	−2.04365e6	−	2.04365e6i	−0.353092	−	0.353092i
$508$	−2.02643e6	−	2.02643e6i	−0.348395	−	0.348395i
$509$		−	5.91467e6i		−	1.01190i	−0.862564	−	0.505948i	$-0.831143\pi$
$509$		−	5.91467e6i		−	1.01190i	0.862564	−	0.505948i	$-0.168857\pi$
$510$	1.58791e6	−	1.05310e6i	0.270334	−	0.179286i
$511$	−1.24779e6			−0.211393
$512$	−2.34067e6	+	2.34067e6i	−0.394608	+	0.394608i
$513$	5.50005e6	+	5.50005e6i	0.922728	+	0.922728i
$514$	−6.96991e6			−1.16364
$515$	3.34237e6	+	5.03976e6i	0.555311	+	0.837321i
$516$		−	1.75640e6i		−	0.290402i
$517$	93420.6	−	2.24733e6i	0.0153715	−	0.369778i
$518$	581447.	−	581447.i	0.0952107	−	0.0952107i
$519$	−432878.			−0.0705419
$520$	−613223.	−	124178.i	−0.0994512	−	0.0201390i
$521$	−3.44763e6			−0.556451			−0.278225	−	0.960516i	$-0.589746\pi$
$521$	−3.44763e6			−0.556451			−0.278225	+	0.960516i	$0.589746\pi$
$522$	−249592.	−	249592.i	−0.0400917	−	0.0400917i
$523$	−179722.	−	179722.i	−0.0287308	−	0.0287308i	0.692595	−	0.721326i	$-0.256467\pi$
$523$	−179722.	−	179722.i	−0.0287308	−	0.0287308i	−0.721326	+	0.692595i	$0.756467\pi$
$524$	86096.6			0.0136980
$525$	1.40112e6	−	3.31768e6i	0.221860	−	0.525335i
$526$	5.15675e6			0.812665
$527$	6.11158e6	−	6.11158e6i	0.958577	−	0.958577i
$528$	−934725.	−	38856.1i	−0.145915	−	0.00606560i
$529$			1.51763e6i			0.235791i
$530$	3.69566e6	+	748376.i	0.571482	+	0.115726i
$531$	−431475.			−0.0664079
$532$	−3.71800e6	−	3.71800e6i	−0.569549	−	0.569549i
$533$	91067.1	−	91067.1i	0.0138849	−	0.0138849i
$534$	3.50005e6			0.531154
$535$	7.00794e6	+	1.05669e7i	1.05854	+	1.59610i
$536$			8.54514e6i			1.28472i
$537$	−1.85877e6	−	1.85877e6i	−0.278156	−	0.278156i
$538$	2.79775e6	+	2.79775e6i	0.416729	+	0.416729i
$539$	−1.39333e6	+	1.28211e6i	−0.206577	+	0.190088i
$540$	−1.58133e6	−	2.38440e6i	−0.233367	−	0.351880i
$541$		−	1.06366e7i		−	1.56247i	−0.624237	−	0.781235i	$-0.714590\pi$
$541$		−	1.06366e7i		−	1.56247i	0.624237	−	0.781235i	$-0.285410\pi$
$542$	−3.18306e6	−	3.18306e6i	−0.465422	−	0.465422i
$543$	569299.	−	569299.i	0.0828592	−	0.0828592i
$544$			5.28787e6i			0.766097i
$545$	2.55763e6	−	1.26302e7i	0.368847	−	1.82146i
$546$			272373.i			0.0391005i
$547$	−2.27156e6	+	2.27156e6i	−0.324606	+	0.324606i	−0.850531	−	0.525925i	$-0.823719\pi$
$547$	−2.27156e6	+	2.27156e6i	−0.324606	+	0.324606i	0.525925	+	0.850531i	$0.323719\pi$
$548$	786465.	−	786465.i	0.111874	−	0.111874i
$549$	−6.18819e6			−0.876260
$550$	4.62648e6	+	2.18453e6i	0.652144	+	0.307929i
$551$	−1.11376e6			−0.156283
$552$	−2.37992e6	+	2.37992e6i	−0.332441	+	0.332441i
$553$	−1.01046e7	+	1.01046e7i	−1.40509	+	1.40509i
$554$			982178.i			0.135962i
$555$	119730.	−	591256.i	0.0164995	−	0.0814785i
$556$		−	447906.i		−	0.0614469i
$557$	3.46671e6	−	3.46671e6i	0.473456	−	0.473456i	−0.429575	−	0.903031i	$-0.641337\pi$
$557$	3.46671e6	−	3.46671e6i	0.473456	−	0.473456i	0.903031	+	0.429575i	$0.141337\pi$
$558$	4.24996e6	+	4.24996e6i	0.577829	+	0.577829i
$559$		−	843535.i		−	0.114176i
$560$	−1.34529e6	−	2.02848e6i	−0.181278	−	0.273338i
$561$	−2.46726e6	+	2.27032e6i	−0.330984	+	0.304565i
$562$	−43052.2	−	43052.2i	−0.00574983	−	0.00574983i
$563$	3.54634e6	+	3.54634e6i	0.471530	+	0.471530i	0.902409	−	0.430880i	$-0.141797\pi$
$563$	3.54634e6	+	3.54634e6i	0.471530	+	0.471530i	−0.430880	+	0.902409i	$0.641797\pi$
$564$			676082.i			0.0894956i
$565$	5.13270e6	+	7.73929e6i	0.676433	+	1.01995i
$566$	−381365.			−0.0500379
$567$	1.85445e6	−	1.85445e6i	0.242247	−	0.242247i
$568$	4.67754e6	+	4.67754e6i	0.608340	+	0.608340i
$569$	−3.69527e6			−0.478482			−0.239241	−	0.970960i	$-0.576899\pi$
$569$	−3.69527e6			−0.478482			−0.239241	+	0.970960i	$0.576899\pi$
$570$	4.09763e6	+	829774.i	0.528257	+	0.106973i
$571$			57926.4i			0.00743509i	0.999993	+	0.00371754i	$0.00118333\pi$
$571$			57926.4i			0.00743509i	−0.999993	+	0.00371754i	$0.998817\pi$
$572$	356709.	+	14828.2i	0.0455853	+	0.00189496i
$573$	3.14362e6	−	3.14362e6i	0.399985	−	0.399985i
$574$	1.33062e6			0.168568
$575$	6.42126e6	−	2.60801e6i	0.809935	−	0.328958i
$576$	−5.39891e6			−0.678032
$577$	−4.07236e6	−	4.07236e6i	−0.509222	−	0.509222i	0.405066	−	0.914288i	$-0.367249\pi$
$577$	−4.07236e6	−	4.07236e6i	−0.509222	−	0.509222i	−0.914288	+	0.405066i	$0.867249\pi$
$578$	832467.	+	832467.i	0.103645	+	0.103645i
$579$	−4.05278e6			−0.502408
$580$	401529.	+	81310.2i	0.0495618	+	0.0100363i
$581$	1.20725e7			1.48373
$582$	−1.17049e6	+	1.17049e6i	−0.143239	+	0.143239i
$583$	−6.62945e6	−	275583.i	−0.807804	−	0.0335800i
$584$			1.64313e6i			0.199361i
$585$	−324507.	−	489305.i	−0.0392044	−	0.0591140i
$586$	−9.22622e6			−1.10989
$587$	9.28769e6	+	9.28769e6i	1.11253	+	1.11253i	0.992807	+	0.119725i	$0.0382013\pi$
$587$	9.28769e6	+	9.28769e6i	1.11253	+	1.11253i	0.119725	+	0.992807i	$0.461799\pi$
$588$	402437.	−	402437.i	0.0480014	−	0.0480014i
$589$	1.89646e7			2.25246
$590$	−452329.	+	299985.i	−0.0534964	+	0.0354788i
$591$			2.61767e6i			0.308280i
$592$	−288298.	−	288298.i	−0.0338094	−	0.0338094i
$593$	8.14113e6	+	8.14113e6i	0.950710	+	0.950710i	0.998841	−	0.0481307i	$-0.0153264\pi$
$593$	8.14113e6	+	8.14113e6i	0.950710	+	0.950710i	−0.0481307	+	0.998841i	$0.515326\pi$
$594$	−3.69484e6	−	4.01535e6i	−0.429665	−	0.466936i
$595$	−8.54982e6	−	1.73135e6i	−0.990067	−	0.200490i
$596$			4.81439e6i			0.555169i
$597$	4.26243e6	+	4.26243e6i	0.489465	+	0.489465i
$598$	−370640.	+	370640.i	−0.0423837	+	0.0423837i
$599$		−	9.35621e6i		−	1.06545i	−0.846288	−	0.532725i	$-0.821168\pi$
$599$		−	9.35621e6i		−	1.06545i	0.846288	−	0.532725i	$-0.178832\pi$
$600$	−4.36881e6	−	1.84504e6i	−0.495433	−	0.209232i
$601$		−	3.08695e6i		−	0.348612i	−0.984692	−	0.174306i	$-0.944232\pi$
$601$		−	3.08695e6i		−	0.348612i	0.984692	−	0.174306i	$-0.0557682\pi$
$602$	6.16265e6	−	6.16265e6i	0.693068	−	0.693068i
$603$	−5.67016e6	+	5.67016e6i	−0.635042	+	0.635042i
$604$	−2.67047e6			−0.297848
$605$	−8.64518e6	−	2.51304e6i	−0.960253	−	0.279133i
$606$	−4.88322e6			−0.540162
$607$	−8.54411e6	+	8.54411e6i	−0.941229	+	0.941229i	−0.998366	−	0.0571376i	$-0.981803\pi$
$607$	−8.54411e6	+	8.54411e6i	−0.941229	+	0.941229i	0.0571376	+	0.998366i	$0.481803\pi$
$608$	−8.20431e6	+	8.20431e6i	−0.900084	+	0.900084i
$609$		−	549986.i		−	0.0600908i
$610$	−6.48728e6	+	4.30236e6i	−0.705892	+	0.468147i
$611$			324697.i			0.0351864i
$612$	−2.09389e6	+	2.09389e6i	−0.225983	+	0.225983i
$613$	795336.	+	795336.i	0.0854868	+	0.0854868i	0.748557	−	0.663070i	$-0.230747\pi$
$613$	795336.	+	795336.i	0.0854868	+	0.0854868i	−0.663070	+	0.748557i	$0.730747\pi$
$614$		−	5.93673e6i		−	0.635516i
$615$	813536.	−	539537.i	0.0867339	−	0.0575219i
$616$	7.70243e6	+	8.37058e6i	0.817855	+	0.888800i
$617$	8.54656e6	+	8.54656e6i	0.903813	+	0.903813i	0.995764	−	0.0919506i	$-0.0293102\pi$
$617$	8.54656e6	+	8.54656e6i	0.903813	+	0.903813i	−0.0919506	+	0.995764i	$0.529310\pi$
$618$	−2.45131e6	−	2.45131e6i	−0.258183	−	0.258183i
$619$		−	1.12492e7i		−	1.18003i	−0.807392	−	0.590016i	$-0.799121\pi$
$619$		−	1.12492e7i		−	1.18003i	0.807392	−	0.590016i	$-0.200879\pi$
$620$	−6.83709e6	−	1.38452e6i	−0.714318	−	0.144650i
$621$	−7.39172e6			−0.769160
$622$	−5.66297e6	+	5.66297e6i	−0.586905	+	0.586905i
$623$	−1.13308e7	−	1.13308e7i	−1.16961	−	1.16961i
$624$	135050.			0.0138846
$625$	6.80940e6	+	6.99997e6i	0.697282	+	0.716797i
$626$		−	8.14718e6i		−	0.830944i
$627$	−7.35051e6	−	305557.i	−0.746704	−	0.0310402i
$628$	2.47806e6	−	2.47806e6i	0.250734	−	0.250734i
$629$	−1.46121e6			−0.147261
$630$	1.20397e6	−	5.94550e6i	0.120855	−	0.596811i
$631$	1.09646e7			1.09628			0.548139	−	0.836387i	$-0.315337\pi$
$631$	1.09646e7			1.09628			0.548139	+	0.836387i	$0.315337\pi$
$632$	1.33060e7	+	1.33060e7i	1.32512	+	1.32512i
$633$	1.21182e6	+	1.21182e6i	0.120207	+	0.120207i
$634$	−3.04276e6			−0.300639
$635$	−5.76593e6	−	8.69410e6i	−0.567460	−	0.855639i
$636$	1.99439e6			0.195509
$637$	193275.	−	193275.i	0.0188724	−	0.0188724i
$638$	780655.	+	32451.5i	0.0759290	+	0.00315633i
$639$			6.20760e6i			0.601411i
$640$	1.75178e6	−	1.16178e6i	0.169056	−	0.112118i
$641$	1.14621e7			1.10184			0.550922	−	0.834557i	$-0.314276\pi$
$641$	1.14621e7			1.10184			0.550922	+	0.834557i	$0.314276\pi$
$642$	−5.13966e6	−	5.13966e6i	−0.492149	−	0.492149i
$643$	1.26161e7	−	1.26161e7i	1.20337	−	1.20337i	0.230235	−	0.973135i	$-0.426050\pi$
$643$	1.26161e7	−	1.26161e7i	1.20337	−	1.20337i	0.973135	−	0.230235i	$-0.0739496\pi$
$644$	4.99676e6			0.474760
$645$	1.26900e6	−	6.26661e6i	0.120105	−	0.593108i
$646$		−	1.01268e7i		−	0.954749i
$647$	−1.04760e7	−	1.04760e7i	−0.983863	−	0.983863i	0.0160092	−	0.999872i	$-0.494904\pi$
$647$	−1.04760e7	−	1.04760e7i	−0.983863	−	0.983863i	−0.999872	+	0.0160092i	$0.994904\pi$
$648$	−2.44200e6	−	2.44200e6i	−0.228459	−	0.228459i
$649$	702817.	−	646718.i	0.0654984	−	0.0602703i
$650$	−680383.	−	287340.i	−0.0631640	−	0.0266755i
$651$			9.36495e6i			0.866070i
$652$	−6.79326e6	−	6.79326e6i	−0.625834	−	0.625834i
$653$	7.16606e6	−	7.16606e6i	0.657654	−	0.657654i	−0.297170	−	0.954824i	$-0.596043\pi$
$653$	7.16606e6	−	7.16606e6i	0.657654	−	0.657654i	0.954824	+	0.297170i	$0.0960429\pi$
$654$			7.38728e6i			0.675367i
$655$	307181.	+	62204.5i	0.0279764	+	0.00566524i
$656$		−	659761.i		−	0.0598587i
$657$	−1.09031e6	+	1.09031e6i	−0.0985451	+	0.0985451i
$658$	−2.37215e6	+	2.37215e6i	−0.213588	+	0.213588i
$659$	−3.23080e6			−0.289799			−0.144900	−	0.989446i	$-0.546286\pi$
$659$	−3.23080e6			−0.289799			−0.144900	+	0.989446i	$0.546286\pi$
$660$	2.62768e6	+	646784.i	0.234808	+	0.0577963i
$661$	−933367.			−0.0830900			−0.0415450	−	0.999137i	$-0.513228\pi$
$661$	−933367.			−0.0830900			−0.0415450	+	0.999137i	$0.513228\pi$
$662$	299046.	−	299046.i	0.0265212	−	0.0265212i
$663$	342245.	−	342245.i	0.0302380	−	0.0302380i
$664$		−	1.58973e7i		−	1.39928i
$665$	−1.05791e7	−	1.59516e7i	−0.927672	−	1.39878i
$666$		−	1.01612e6i		−	0.0887687i
$667$	748410.	−	748410.i	0.0651366	−	0.0651366i
$668$	−3.02601e6	−	3.02601e6i	−0.262379	−	0.262379i
$669$		−	384971.i		−	0.0332554i
$670$	−2.00201e6	+	9.88641e6i	−0.172298	+	0.850847i
$671$	1.00798e7	−	9.27519e6i	0.864260	−	0.795274i
$672$	−4.05138e6	−	4.05138e6i	−0.346082	−	0.346082i
$673$	−1.28117e6	−	1.28117e6i	−0.109036	−	0.109036i	0.650484	−	0.759520i	$-0.274566\pi$
$673$	−1.28117e6	−	1.28117e6i	−0.109036	−	0.109036i	−0.759520	+	0.650484i	$0.774566\pi$
$674$			8.52086e6i			0.722493i
$675$	−3.91926e6	−	9.64972e6i	−0.331089	−	0.815183i
$676$	5.65019e6			0.475550
$677$	9.10030e6	−	9.10030e6i	0.763105	−	0.763105i	−0.213778	−	0.976882i	$-0.568577\pi$
$677$	9.10030e6	−	9.10030e6i	0.763105	−	0.763105i	0.976882	+	0.213778i	$0.0685768\pi$
$678$	−3.76435e6	−	3.76435e6i	−0.314496	−	0.314496i
$679$	7.57851e6			0.630825
$680$	−2.27989e6	+	1.12586e7i	−0.189078	+	0.933714i
$681$		−	1.51551e6i		−	0.125225i
$682$	−1.32927e7	−	552571.i	−1.09434	−	0.0454912i
$683$	−2.56185e6	+	2.56185e6i	−0.210136	+	0.210136i	−0.804325	−	0.594189i	$-0.797473\pi$
$683$	−2.56185e6	+	2.56185e6i	−0.210136	+	0.210136i	0.594189	+	0.804325i	$0.297473\pi$
$684$	−6.49748e6			−0.531012
$685$	3.37422e6	−	2.23778e6i	0.274756	−	0.182218i
$686$	−7.23571e6			−0.587044
$687$	3.23393e6	+	3.23393e6i	0.261420	+	0.261420i
$688$	−3.05561e6	−	3.05561e6i	−0.246109	−	0.246109i
$689$	957829.			0.0768670
$690$	−3.31106e6	+	2.19589e6i	−0.264755	+	0.175585i
$691$	−1.42077e7			−1.13195			−0.565977	−	0.824421i	$-0.691501\pi$
$691$	−1.42077e7			−1.13195			−0.565977	+	0.824421i	$0.691501\pi$
$692$	598399.	−	598399.i	0.0475035	−	0.0475035i
$693$	−443352.	+	1.06653e7i	−0.0350684	+	0.843608i
$694$			7.82089e6i			0.616393i
$695$	323611.	−	1.59807e6i	0.0254133	−	0.125497i
$696$	−724237.			−0.0566705
$697$	−1.67197e6	−	1.67197e6i	−0.130361	−	0.130361i
$698$	1.12240e7	−	1.12240e7i	0.871985	−	0.871985i
$699$	−3.14868e6			−0.243745
$700$	2.64940e6	+	6.52315e6i	0.204363	+	0.503167i
$701$			5.09542e6i			0.391638i	0.980640	+	0.195819i	$0.0627365\pi$
$701$			5.09542e6i			0.391638i	−0.980640	+	0.195819i	$0.937264\pi$
$702$	556989.	+	556989.i	0.0426583	+	0.0426583i
$703$	−2.26712e6	−	2.26712e6i	−0.173016	−	0.173016i
$704$	8.79413e6	−	8.09217e6i	0.668746	−	0.615366i
$705$	−488467.	+	2.41217e6i	−0.0370137	+	0.182783i
$706$		−	1.24039e7i		−	0.936585i
$707$	1.58085e7	+	1.58085e7i	1.18944	+	1.18944i
$708$	−202995.	+	202995.i	−0.0152196	+	0.0152196i
$709$			1.06450e7i			0.795298i	0.917538	+	0.397649i	$0.130174\pi$
$709$			1.06450e7i			0.795298i	−0.917538	+	0.397649i	$0.869826\pi$
$710$	4.31586e6	+	6.50762e6i	0.321308	+	0.484481i
$711$			1.76584e7i			1.31002i
$712$	−1.49207e7	+	1.49207e7i	−1.10303	+	1.10303i
$713$	−1.27436e7	+	1.27436e7i	−0.938793	+	0.938793i
$714$	5.00071e6			0.367101
$715$	1.26198e6	+	310627.i	0.0923180	+	0.0227234i
$716$	5.13902e6			0.374626
$717$	8.82685e6	−	8.82685e6i	0.641221	−	0.641221i
$718$	6.83355e6	−	6.83355e6i	0.494692	−	0.494692i
$719$			1.91481e6i			0.138135i	0.997612	+	0.0690675i	$0.0220024\pi$
$719$			1.91481e6i			0.138135i	−0.997612	+	0.0690675i	$0.977998\pi$
$720$	−2.94795e6	−	596963.i	−0.211928	−	0.0429157i
$721$			1.58714e7i			1.13704i
$722$	8.56909e6	−	8.56909e6i	0.611775	−	0.611775i
$723$	−2.88786e6	−	2.88786e6i	−0.205462	−	0.205462i
$724$			1.57397e6i			0.111596i
$725$	1.37386e6	+	580207.i	0.0970725	+	0.0409957i
$726$	5.14322e6	+	428343.i	0.362154	+	0.0301613i
$727$	2.86558e6	+	2.86558e6i	0.201084	+	0.201084i	0.800464	−	0.599380i	$-0.204586\pi$
$727$	2.86558e6	+	2.86558e6i	0.201084	+	0.201084i	−0.599380	+	0.800464i	$0.704586\pi$
$728$	−1.16112e6	−	1.16112e6i	−0.0811989	−	0.0811989i
$729$			3.12094e6i			0.217504i
$730$	−384963.	+	1.90104e6i	−0.0267370	+	0.132034i
$731$	−1.54871e7			−1.07196
$732$	−2.91135e6	+	2.91135e6i	−0.200824	+	0.200824i
$733$	3.71404e6	+	3.71404e6i	0.255321	+	0.255321i	0.823148	−	0.567827i	$-0.192216\pi$
$733$	3.71404e6	+	3.71404e6i	0.255321	+	0.255321i	−0.567827	+	0.823148i	$0.692216\pi$
$734$	1.41972e7			0.972664
$735$	1.72660e6	−	1.14508e6i	0.117889	−	0.0781840i
$736$		−	1.10261e7i		−	0.750285i
$737$	737223.	−	1.77347e7i	0.0499954	−	1.20269i
$738$	1.16268e6	−	1.16268e6i	0.0785814	−	0.0785814i
$739$	361202.			0.0243298			0.0121649	−	0.999926i	$-0.496128\pi$
$739$	361202.			0.0243298			0.0121649	+	0.999926i	$0.496128\pi$
$740$	651826.	+	982849.i	0.0437575	+	0.0659793i
$741$	1.06201e6			0.0710531
$742$	6.99765e6	+	6.99765e6i	0.466597	+	0.466597i
$743$	−1.41219e7	−	1.41219e7i	−0.938471	−	0.938471i	0.0597430	−	0.998214i	$-0.480972\pi$
$743$	−1.41219e7	−	1.41219e7i	−0.938471	−	0.938471i	−0.998214	+	0.0597430i	$0.980972\pi$
$744$	1.23320e7			0.816774
$745$	−3.47838e6	+	1.71771e7i	−0.229608	+	1.13386i
$746$	−1.27540e7			−0.839073
$747$	1.05487e7	−	1.05487e7i	0.691671	−	0.691671i
$748$	272243.	−	6.54911e6i	0.0177911	−	0.427985i
$749$			3.32775e7i			2.16743i
$750$	−4.62229e6	−	3.15819e6i	−0.300057	−	0.205015i
$751$	1.69707e7			1.09800			0.548998	−	0.835824i	$-0.315009\pi$
$751$	1.69707e7			1.09800			0.548998	+	0.835824i	$0.315009\pi$
$752$	1.17618e6	+	1.17618e6i	0.0758453	+	0.0758453i
$753$	−392547.	+	392547.i	−0.0252293	+	0.0252293i
$754$	−112790.			−0.00722507
$755$	−9.52787e6	−	1.92941e6i	−0.608315	−	0.123184i
$756$		−	7.50902e6i		−	0.477836i
$757$	8.98692e6	+	8.98692e6i	0.569995	+	0.569995i	0.932127	−	0.362132i	$-0.117951\pi$
$757$	8.98692e6	+	8.98692e6i	0.569995	+	0.569995i	−0.362132	+	0.932127i	$0.617951\pi$
$758$	4.36780e6	+	4.36780e6i	0.276115	+	0.276115i
$759$	5.14464e6	−	4.73399e6i	0.324153	−	0.298279i
$760$	−2.10055e7	+	1.39308e7i	−1.31916	+	0.874870i
$761$			2.69339e7i			1.68592i	0.537973	+	0.842962i	$0.319190\pi$
$761$			2.69339e7i			1.68592i	−0.537973	+	0.842962i	$0.680810\pi$
$762$	4.22877e6	+	4.22877e6i	0.263831	+	0.263831i
$763$	2.39150e7	−	2.39150e7i	1.48716	−	1.48716i
$764$			8.69133e6i			0.538707i
$765$	−8.98354e6	+	5.95789e6i	−0.555001	+	0.368077i
$766$			7.78218e6i			0.479214i
$767$	−97491.2	+	97491.2i	−0.00598380	+	0.00598380i
$768$	−6.14500e6	+	6.14500e6i	−0.375940	+	0.375940i
$769$	202443.			0.0123449			0.00617243	−	0.999981i	$-0.498035\pi$
$769$	202443.			0.0123449			0.00617243	+	0.999981i	$0.498035\pi$
$770$	6.95032e6	+	1.14890e7i	0.422452	+	0.698323i
$771$	−1.34200e7			−0.813049
$772$	5.60246e6	−	5.60246e6i	0.338326	−	0.338326i
$773$	−1.15495e7	+	1.15495e7i	−0.695208	+	0.695208i	−0.963373	−	0.268165i	$-0.913583\pi$
$773$	−1.15495e7	+	1.15495e7i	−0.695208	+	0.695208i	0.268165	+	0.963373i	$0.413583\pi$
$774$		−	1.07697e7i		−	0.646175i
$775$	−2.33935e7	−	9.87955e6i	−1.39907	−	0.590858i
$776$		−	9.97959e6i		−	0.594920i
$777$	1.11953e6	−	1.11953e6i	0.0665247	−	0.0665247i
$778$	4.65711e6	+	4.65711e6i	0.275847	+	0.275847i
$779$		−	5.18825e6i		−	0.306321i
$780$	−382873.	−	77532.3i	−0.0225330	−	0.00456295i
$781$	−9.30427e6	−	1.01114e7i	−0.545827	−	0.593175i
$782$	6.80486e6	+	6.80486e6i	0.397926	+	0.397926i
$783$	−1.12469e6	−	1.12469e6i	−0.0655586	−	0.0655586i
$784$		−	1.40024e6i		−	0.0813601i
$785$	1.06318e7	−	7.05099e6i	0.615789	−	0.408391i
$786$	−179667.			−0.0103732
$787$	−4.00932e6	+	4.00932e6i	−0.230746	+	0.230746i	−0.813004	−	0.582258i	$-0.802169\pi$
$787$	−4.00932e6	+	4.00932e6i	−0.230746	+	0.230746i	0.582258	+	0.813004i	$0.302169\pi$
$788$	−3.61860e6	−	3.61860e6i	−0.207599	−	0.207599i
$789$	9.92891e6			0.567818
$790$	1.22771e7	+	1.85119e7i	0.699887	+	1.05532i
$791$			2.43728e7i			1.38505i
$792$	1.40444e7	+	583818.i	0.795590	+	0.0330723i
$793$	−1.39821e6	+	1.39821e6i	−0.0789569	+	0.0789569i
$794$	−9.42394e6			−0.530495
$795$	7.11570e6	+	1.44094e6i	0.399300	+	0.0808588i
$796$	−1.17846e7			−0.659220
$797$	−3.11217e6	−	3.11217e6i	−0.173547	−	0.173547i	0.614989	−	0.788536i	$-0.289160\pi$
$797$	−3.11217e6	−	3.11217e6i	−0.173547	−	0.173547i	−0.788536	+	0.614989i	$0.789160\pi$
$798$	7.75876e6	+	7.75876e6i	0.431306	+	0.431306i
$799$	5.96137e6			0.330354
$800$	1.43943e7	−	5.84628e6i	0.795179	−	0.322964i
$801$	−1.98014e7			−1.09047
$802$	−9.79080e6	+	9.79080e6i	−0.537505	+	0.537505i
$803$	141759.	−	3.41018e6i	0.00775824	−	0.186633i
$804$			5.33526e6i			0.291082i
$805$	1.78278e7	+	3.61015e6i	0.969633	+	0.196352i
$806$	1.92054e6			0.104133
$807$	5.38685e6	+	5.38685e6i	0.291173	+	0.291173i
$808$	2.08171e7	−	2.08171e7i	1.12174	−	1.12174i
$809$	−3.41033e7			−1.83200			−0.915998	−	0.401182i	$-0.868600\pi$
$809$	−3.41033e7			−1.83200			−0.915998	+	0.401182i	$0.868600\pi$
$810$	−2.25317e6	−	3.39743e6i	−0.120665	−	0.181944i
$811$		−	1.41485e7i		−	0.755367i	−0.925935	−	0.377683i	$-0.876721\pi$
$811$		−	1.41485e7i		−	0.755367i	0.925935	−	0.377683i	$-0.123279\pi$
$812$	760286.	+	760286.i	0.0404657	+	0.0404657i
$813$	−6.12873e6	−	6.12873e6i	−0.325195	−	0.325195i
$814$	1.52302e6	+	1.65513e6i	0.0805644	+	0.0875530i
$815$	−1.93293e7	−	2.91455e7i	−1.01935	−	1.53701i
$816$		−	2.47949e6i		−	0.130358i
$817$	−2.40288e7	−	2.40288e7i	−1.25944	−	1.25944i
$818$	1.28887e7	−	1.28887e7i	0.673483	−	0.673483i
$819$		−	1.54094e6i		−	0.0802740i
$820$	−378769.	+	1.87045e6i	−0.0196716	+	0.0971432i
$821$		−	426503.i		−	0.0220833i	−0.999939	−	0.0110416i	$-0.996485\pi$
$821$		−	426503.i		−	0.0220833i	0.999939	−	0.0110416i	$-0.00351474\pi$
$822$	−1.64120e6	+	1.64120e6i	−0.0847193	+	0.0847193i
$823$	−1.23191e7	+	1.23191e7i	−0.633985	+	0.633985i	−0.949065	−	0.315080i	$-0.897969\pi$
$823$	−1.23191e7	+	1.23191e7i	−0.633985	+	0.633985i	0.315080	+	0.949065i	$0.397969\pi$
$824$	2.08999e7			1.07232
$825$	8.90791e6	+	4.20613e6i	0.455660	+	0.215153i
$826$	−1.42449e6			−0.0726456
$827$	2.45123e7	−	2.45123e7i	1.24630	−	1.24630i	0.288951	−	0.957344i	$-0.406693\pi$
$827$	2.45123e7	−	2.45123e7i	1.24630	−	1.24630i	0.957344	−	0.288951i	$-0.0933066\pi$
$828$	4.36610e6	−	4.36610e6i	0.221319	−	0.221319i
$829$		−	3.31255e6i		−	0.167408i	−0.996491	−	0.0837039i	$-0.973325\pi$
$829$		−	3.31255e6i		−	0.167408i	0.996491	−	0.0837039i	$-0.0266750\pi$
$830$	3.72453e6	−	1.83926e7i	0.187662	−	0.926721i
$831$			1.89111e6i			0.0949978i
$832$	−1.21988e6	+	1.21988e6i	−0.0610952	+	0.0610952i
$833$	−3.54850e6	−	3.54850e6i	−0.177187	−	0.177187i
$834$			934695.i			0.0465323i
$835$	−8.61011e6	−	1.29827e7i	−0.427359	−	0.644389i
$836$	1.05836e7	−	9.73877e6i	0.523740	−	0.481935i
$837$	1.91509e7	+	1.91509e7i	0.944875	+	0.944875i
$838$	−1.01502e7	−	1.01502e7i	−0.499305	−	0.499305i
$839$			7.51942e6i			0.368790i	0.982852	+	0.184395i	$0.0590326\pi$
$839$			7.51942e6i			0.368790i	−0.982852	+	0.184395i	$0.940967\pi$
$840$	−6.87920e6	−	1.03727e7i	−0.336387	−	0.507219i
$841$	−2.02834e7			−0.988896
$842$	1.53285e7	−	1.53285e7i	0.745108	−	0.745108i
$843$	−82893.7	−	82893.7i	−0.00401747	−	0.00401747i
$844$	−3.35039e6			−0.161897
$845$	2.01591e7	+	4.08225e6i	0.971247	+	0.196679i
$846$			4.14550e6i			0.199137i
$847$	−1.52636e7	−	1.80369e7i	−0.731051	−	0.863882i
$848$	3.46963e6	−	3.46963e6i	0.165689	−	0.165689i
$849$	−734287.			−0.0349620
$850$	−5.27549e6	+	1.24917e7i	−0.250447	+	0.593026i
$851$	3.04687e6			0.144222
$852$	2.92048e6	+	2.92048e6i	0.137834	+	0.137834i
$853$	4.14004e6	+	4.14004e6i	0.194820	+	0.194820i	0.797775	−	0.602955i	$-0.206010\pi$
$853$	4.14004e6	+	4.14004e6i	0.194820	+	0.194820i	−0.602955	+	0.797775i	$0.706010\pi$
$854$	−2.04299e7			−0.958567
$855$	−2.31821e7	−	4.69441e6i	−1.08452	−	0.219617i
$856$	4.38207e7			2.04407
$857$	−2.93533e7	+	2.93533e7i	−1.36523	+	1.36523i	−0.498120	+	0.867108i	$0.665976\pi$
$857$	−2.93533e7	+	2.93533e7i	−1.36523	+	1.36523i	−0.867108	+	0.498120i	$0.834024\pi$
$858$	−744384.	−	30943.7i	−0.0345206	−	0.00143501i
$859$			3.26018e7i			1.50750i	0.657160	+	0.753751i	$0.271758\pi$
$859$			3.26018e7i			1.50750i	−0.657160	+	0.753751i	$0.728242\pi$
$860$	6.90858e6	+	1.04170e7i	0.318524	+	0.480284i
$861$	2.56201e6			0.117780
$862$	−4.54674e6	−	4.54674e6i	−0.208417	−	0.208417i
$863$	1.82172e7	−	1.82172e7i	0.832636	−	0.832636i	−0.155241	−	0.987877i	$-0.549615\pi$
$863$	1.82172e7	−	1.82172e7i	0.832636	−	0.832636i	0.987877	+	0.155241i	$0.0496153\pi$
$864$	−1.65697e7			−0.755146
$865$	2.56735e6	−	1.70267e6i	0.116666	−	0.0773730i
$866$			1.89981e7i			0.860825i
$867$	1.60285e6	+	1.60285e6i	0.0724177	+	0.0724177i
$868$	−1.29459e7	−	1.29459e7i	−0.583219	−	0.583219i
$869$	−2.64674e7	−	2.87633e7i	−1.18895	−	1.29208i
$870$	−837915.	−	169679.i	−0.0375320	−	0.00760028i
$871$			2.56233e6i			0.114443i
$872$	−3.14919e7	−	3.14919e7i	−1.40252	−	1.40252i
$873$	6.62199e6	−	6.62199e6i	0.294072	−	0.294072i
$874$			2.11160e7i			0.935044i
$875$	4.73974e6	+	2.51879e7i	0.209283	+	1.11217i
$876$			1.02591e6i			0.0451698i
$877$	2.48426e7	−	2.48426e7i	1.09068	−	1.09068i	0.0952252	−	0.995456i	$-0.469643\pi$
$877$	2.48426e7	−	2.48426e7i	1.09068	−	1.09068i	0.995456	−	0.0952252i	$-0.0303571\pi$
$878$	−1.30159e7	+	1.30159e7i	−0.569820	+	0.569820i
$879$	−1.77643e7			−0.775491
$880$	5.69658e6	−	3.44616e6i	0.247975	−	0.150013i
$881$	−2.11393e7			−0.917597			−0.458798	−	0.888540i	$-0.651720\pi$
$881$	−2.11393e7			−0.917597			−0.458798	+	0.888540i	$0.651720\pi$
$882$	2.46761e6	−	2.46761e6i	0.106808	−	0.106808i
$883$	−1.39827e7	+	1.39827e7i	−0.603516	+	0.603516i	−0.941244	−	0.337728i	$-0.890342\pi$
$883$	−1.39827e7	+	1.39827e7i	−0.603516	+	0.603516i	0.337728	+	0.941244i	$0.390342\pi$
$884$			946222.i			0.0407251i
$885$	−870924.	+	577597.i	−0.0373785	+	0.0247894i
$886$		−	2.32549e7i		−	0.995244i
$887$	−2.11639e7	+	2.11639e7i	−0.903205	+	0.903205i	−0.995712	−	0.0925066i	$-0.970512\pi$
$887$	−2.11639e7	+	2.11639e7i	−0.903205	+	0.903205i	0.0925066	+	0.995712i	$0.470512\pi$
$888$	−1.47423e6	−	1.47423e6i	−0.0627382	−	0.0627382i
$889$		−	2.73797e7i		−	1.16192i
$890$	−2.07584e7	+	1.37670e7i	−0.878453	+	0.582590i
$891$	4.85747e6	+	5.27883e6i	0.204982	+	0.222763i
$892$	532174.	+	532174.i	0.0223945	+	0.0223945i
$893$	9.24927e6	+	9.24927e6i	0.388131	+	0.388131i
$894$		−	1.00467e7i		−	0.420416i
$895$	1.83353e7	+	3.71293e6i	0.765123	+	0.154938i
$896$	5.51677e6			0.229570
$897$	−713637.	+	713637.i	−0.0296139	+	0.0296139i
$898$	−2.09306e7	−	2.09306e7i	−0.866147	−	0.866147i
$899$	−3.87804e6			−0.160034
$900$	8.01485e6	+	3.38483e6i	0.329829	+	0.139294i
$901$		−	1.75855e7i		−	0.721679i
$902$	−151170.	+	3.63655e6i	−0.00618654	+	0.148824i
$903$	1.18657e7	−	1.18657e7i	0.484254	−	0.484254i
$904$	3.20948e7			1.30621
$905$	−1.13719e6	+	5.61571e6i	−0.0461541	+	0.227920i
$906$	5.57276e6			0.225554
$907$	1.80897e7	+	1.80897e7i	0.730152	+	0.730152i	0.970650	−	0.240498i	$-0.0773107\pi$
$907$	1.80897e7	+	1.80897e7i	0.730152	+	0.730152i	−0.240498	+	0.970650i	$0.577311\pi$
$908$	2.09501e6	+	2.09501e6i	0.0843277	+	0.0843277i
$909$	2.76266e7			1.10896
$910$	−1.07134e6	−	1.61541e6i	−0.0428869	−	0.0646666i
$911$	−5.34182e6			−0.213252			−0.106626	−	0.994299i	$-0.534005\pi$
$911$	−5.34182e6			−0.213252			−0.106626	+	0.994299i	$0.534005\pi$
$912$	3.84701e6	−	3.84701e6i	0.153157	−	0.153157i
$913$	−1.37153e6	+	3.29936e7i	−0.0544537	+	1.30994i
$914$			1.91715e7i			0.759086i
$915$	−1.24907e7	+	8.28386e6i	−0.493214	+	0.327100i
$916$	−8.94101e6			−0.352085
$917$	581640.	+	581640.i	0.0228418	+	0.0228418i
$918$	1.02262e7	−	1.02262e7i	0.400504	−	0.400504i
$919$	2.14327e6			0.0837121			0.0418561	−	0.999124i	$-0.486673\pi$
$919$	2.14327e6			0.0837121			0.0418561	+	0.999124i	$0.486673\pi$
$920$	4.75394e6	−	2.34761e7i	0.185176	−	0.914443i
$921$		−	1.14307e7i		−	0.444042i
$922$	−2.15852e6	−	2.15852e6i	−0.0836237	−	0.0836237i
$923$	1.40260e6	+	1.40260e6i	0.0541912	+	0.0541912i
$924$	4.80911e6	+	5.22627e6i	0.185304	+	0.201378i
$925$	1.61552e6	+	3.97762e6i	0.0620809	+	0.152851i
$926$		−	2.53756e7i		−	0.972497i
$927$	1.38682e7	+	1.38682e7i	0.530054	+	0.530054i
$928$	1.67768e6	−	1.67768e6i	0.0639498	−	0.0639498i
$929$		−	1.07564e7i		−	0.408909i	−0.978876	−	0.204454i	$-0.934458\pi$
$929$		−	1.07564e7i		−	0.408909i	0.978876	−	0.204454i	$-0.0655420\pi$
$930$	1.42677e7	+	2.88922e6i	0.540937	+	0.109540i
$931$		−	1.10112e7i		−	0.416353i
$932$	4.35266e6	−	4.35266e6i	0.164140	−	0.164140i
$933$	−1.09036e7	+	1.09036e7i	−0.410077	+	0.410077i
$934$	−4.00420e6			−0.150193
$935$	5.70304e6	−	2.31696e7i	0.213342	−	0.866743i
$936$	−2.02915e6			−0.0757049
$937$	−2.67520e7	+	2.67520e7i	−0.995424	+	0.995424i	−0.999990	−	0.00456603i	$-0.998547\pi$
$937$	−2.67520e7	+	2.67520e7i	−0.995424	+	0.995424i	0.00456603	+	0.999990i	$0.498547\pi$
$938$	−1.87197e7	+	1.87197e7i	−0.694691	+	0.694691i
$939$		−	1.56867e7i		−	0.580589i
$940$	−2.65928e6	−	4.00977e6i	−0.0981621	−	0.148013i
$941$			1.84090e7i			0.677730i	0.940835	+	0.338865i	$0.110043\pi$
$941$			1.84090e7i			0.677730i	−0.940835	+	0.338865i	$0.889957\pi$
$942$	−5.17124e6	+	5.17124e6i	−0.189875	+	0.189875i
$943$	3.48634e6	+	3.48634e6i	0.127670	+	0.127670i
$944$			706302.i			0.0257965i
$945$	5.42524e6	−	2.67912e7i	0.197624	−	0.975916i
$946$	1.61421e7	+	1.75424e7i	0.586453	+	0.637325i
$947$	1.48200e7	+	1.48200e7i	0.537000	+	0.537000i	0.922646	−	0.385647i	$-0.126022\pi$
$947$	1.48200e7	+	1.48200e7i	0.537000	+	0.537000i	−0.385647	+	0.922646i	$0.626022\pi$
$948$	8.30774e6	+	8.30774e6i	0.300235	+	0.300235i
$949$			492706.i			0.0177592i
$950$	−2.75664e7	+	1.11962e7i	−0.990993	+	0.402495i
$951$	−5.85860e6			−0.210059
$952$	−2.13180e7	+	2.13180e7i	−0.762349	+	0.762349i
$953$	2.44828e7	+	2.44828e7i	0.873230	+	0.873230i	0.992823	−	0.119593i	$-0.0381591\pi$
$953$	2.44828e7	+	2.44828e7i	0.873230	+	0.873230i	−0.119593	+	0.992823i	$0.538159\pi$
$954$	1.22289e7			0.435027
$955$	−6.27946e6	+	3.10095e7i	−0.222799	+	1.10024i
$956$			2.44040e7i			0.863609i
$957$	1.50309e6	+	62482.7i	0.0530524	+	0.00220536i
$958$	−1.19097e7	+	1.19097e7i	−0.419262	+	0.419262i
$959$	1.06262e7			0.373105
$960$	−1.08976e7	+	7.22728e6i	−0.381639	+	0.253103i
$961$	3.74046e7			1.30652
$962$	−229591.	−	229591.i	−0.00799866	−	0.00799866i
$963$	2.90774e7	+	2.90774e7i	1.01039	+	1.01039i
$964$	7.98421e6			0.276719
$965$	2.40366e7	−	1.59411e7i	0.830911	−	0.551060i
$966$	−1.04273e7			−0.359525
$967$	1.53148e7	−	1.53148e7i	0.526679	−	0.526679i	−0.392901	−	0.919581i	$-0.628529\pi$
$967$	1.53148e7	−	1.53148e7i	0.526679	−	0.526679i	0.919581	+	0.392901i	$0.128529\pi$
$968$	−2.37515e7	+	2.00995e7i	−0.814710	+	0.689440i
$969$		−	1.94983e7i		−	0.667094i
$970$	2.33808e6	−	1.15460e7i	0.0797867	−	0.394006i
$971$	2.59371e7			0.882823			0.441412	−	0.897305i	$-0.354478\pi$
$971$	2.59371e7			0.882823			0.441412	+	0.897305i	$0.354478\pi$
$972$	−1.03190e7	−	1.03190e7i	−0.350325	−	0.350325i
$973$	3.02591e6	−	3.02591e6i	0.102465	−	0.102465i
$974$	−1.23891e7			−0.418447
$975$	−1.31002e6	−	553249.i	−0.0441334	−	0.0186384i
$976$			1.01297e7i			0.340388i
$977$	−2.89552e7	−	2.89552e7i	−0.970488	−	0.970488i	0.0290887	−	0.999577i	$-0.490739\pi$
$977$	−2.89552e7	−	2.89552e7i	−0.970488	−	0.970488i	−0.999577	+	0.0290887i	$0.990739\pi$
$978$	1.41762e7	+	1.41762e7i	0.473929	+	0.473929i
$979$	3.22538e7	−	2.96793e7i	1.07554	−	0.989685i
$980$	−803877.	+	3.96974e6i	−0.0267377	+	0.132037i
$981$		−	4.17932e7i		−	1.38654i
$982$	−2.50179e7	−	2.50179e7i	−0.827888	−	0.827888i
$983$	−3.40565e7	+	3.40565e7i	−1.12413	+	1.12413i	−0.133014	+	0.991114i	$0.542465\pi$
$983$	−3.40565e7	+	3.40565e7i	−1.12413	+	1.12413i	−0.991114	+	0.133014i	$0.957535\pi$
$984$		−	3.37373e6i		−	0.111077i
$985$	−1.02962e7	−	1.55251e7i	−0.338133	−	0.509851i
$986$			2.07080e6i			0.0678337i
$987$	−4.56739e6	+	4.56739e6i	−0.149236	+	0.149236i
$988$	−1.46810e6	+	1.46810e6i	−0.0478478	+	0.0478478i
$989$	3.22932e7			1.04983
$990$	1.61120e7	+	3.96586e6i	0.522472	+	0.128603i
$991$	−1.26497e7			−0.409162			−0.204581	−	0.978850i	$-0.565583\pi$
$991$	−1.26497e7			−0.409162			−0.204581	+	0.978850i	$0.565583\pi$
$992$	−2.85669e7	+	2.85669e7i	−0.921688	+	0.921688i
$993$	575789.	−	575789.i	0.0185306	−	0.0185306i
$994$			2.04940e7i			0.657902i
$995$	−4.20457e7	−	8.51430e6i	−1.34637	−	0.272641i
$996$		−	9.92570e6i		−	0.317039i
$997$	−1.08845e7	+	1.08845e7i	−0.346793	+	0.346793i	−0.858913	−	0.512121i	$-0.828860\pi$
$997$	−1.08845e7	+	1.08845e7i	−0.346793	+	0.346793i	0.512121	+	0.858913i	$0.328860\pi$
$998$	1.71283e7	+	1.71283e7i	0.544363	+	0.544363i
$999$		−	4.57877e6i		−	0.145156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.17	yes	52
5.3	odd	4	inner	55.6.e.b.43.10	yes	52
11.10	odd	2	inner	55.6.e.b.32.10	✓	52
55.43	even	4	inner	55.6.e.b.43.17	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.10	✓	52	11.10	odd	2	inner
55.6.e.b.32.17	yes	52	1.1	even	1	trivial
55.6.e.b.43.10	yes	52	5.3	odd	4	inner
55.6.e.b.43.17	yes	52	55.43	even	4	inner

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	55.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.88475 - 2.88475i) q^{2} +(5.55436 - 5.55436i) q^{3} +15.3564i q^{4} +(-11.0950 + 54.7896i) q^{5} -32.0459i q^{6} +(-103.743 + 103.743i) q^{7} +(136.612 + 136.612i) q^{8} +181.298i q^{9} +(126.048 + 190.061i) q^{10} +(-271.739 - 295.311i) q^{11} +(85.2950 + 85.2950i) q^{12} +(40.9640 + 40.9640i) q^{13} +598.545i q^{14} +(242.696 + 365.947i) q^{15} +296.775 q^{16} +(752.091 - 752.091i) q^{17} +(523.000 + 523.000i) q^{18} +2333.79 q^{19} +(-841.372 - 170.379i) q^{20} +1152.45i q^{21} +(-1635.80 - 67.9994i) q^{22} +(-1568.23 + 1568.23i) q^{23} +1517.58 q^{24} +(-2878.80 - 1215.78i) q^{25} +236.342 q^{26} +(2356.70 + 2356.70i) q^{27} +(-1593.12 - 1593.12i) q^{28} -477.232 q^{29} +(1755.78 + 355.548i) q^{30} +8126.11 q^{31} +(-3515.44 + 3515.44i) q^{32} +(-3149.60 - 130.928i) q^{33} -4339.19i q^{34} +(-4533.01 - 6835.06i) q^{35} -2784.09 q^{36} +(-971.434 - 971.434i) q^{37} +(6732.40 - 6732.40i) q^{38} +455.058 q^{39} +(-9000.59 + 5969.19i) q^{40} -2223.10i q^{41} +(3324.53 + 3324.53i) q^{42} +(-10296.0 - 10296.0i) q^{43} +(4534.92 - 4172.94i) q^{44} +(-9933.26 - 2011.50i) q^{45} +9047.93i q^{46} +(3963.20 + 3963.20i) q^{47} +(1648.40 - 1648.40i) q^{48} -4718.17i q^{49} +(-11811.9 + 4797.42i) q^{50} -8354.77i q^{51} +(-629.061 + 629.061i) q^{52} +(11691.1 - 11691.1i) q^{53} +13597.0 q^{54} +(19194.9 - 11612.0i) q^{55} -28344.9 q^{56} +(12962.7 - 12962.7i) q^{57} +(-1376.69 + 1376.69i) q^{58} +2379.92i q^{59} +(-5619.63 + 3726.94i) q^{60} +34132.7i q^{61} +(23441.8 - 23441.8i) q^{62} +(-18808.4 - 18808.4i) q^{63} +29779.2i q^{64} +(-2698.90 + 1789.91i) q^{65} +(-9463.52 + 8708.13i) q^{66} +(31275.3 + 31275.3i) q^{67} +(11549.4 + 11549.4i) q^{68} +17421.1i q^{69} +(-32794.0 - 6640.83i) q^{70} +34239.7 q^{71} +(-24767.4 + 24767.4i) q^{72} +(6013.88 + 6013.88i) q^{73} -5604.69 q^{74} +(-22742.8 + 9237.05i) q^{75} +35838.6i q^{76} +(58827.5 + 2445.43i) q^{77} +(1312.73 - 1312.73i) q^{78} +97400.0 q^{79} +(-3292.71 + 16260.2i) q^{80} -17875.5 q^{81} +(-6413.09 - 6413.09i) q^{82} +(-58184.5 - 58184.5i) q^{83} -17697.5 q^{84} +(32862.4 + 49551.2i) q^{85} -59403.1 q^{86} +(-2650.72 + 2650.72i) q^{87} +(3220.21 - 77465.6i) q^{88} +109220. i q^{89} +(-34457.6 + 22852.3i) q^{90} -8499.46 q^{91} +(-24082.4 - 24082.4i) q^{92} +(45135.4 - 45135.4i) q^{93} +22865.7 q^{94} +(-25893.3 + 127867. i) q^{95} +39052.1i q^{96} +(-36525.4 - 36525.4i) q^{97} +(-13610.8 - 13610.8i) q^{98} +(53539.4 - 49265.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) \) 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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