LMFDB - Embedded newform 38.9.d.a.27.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,9,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, 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:	$15.4803871823$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.4
Character	$\chi$	$=$	38.27
Dual form			38.9.d.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.79796 - 5.65685i) q^{2} +(58.9458 + 34.0324i) q^{3} +(64.0000 + 110.851i) q^{4} +(-530.398 + 918.676i) q^{5} +(-385.033 - 666.896i) q^{6} -2153.04 q^{7} -1448.15i q^{8} +(-964.092 - 1669.86i) q^{9} +O(q^{10})$	\(q+(-9.79796 - 5.65685i) q^{2} +(58.9458 + 34.0324i) q^{3} +(64.0000 + 110.851i) q^{4} +(-530.398 + 918.676i) q^{5} +(-385.033 - 666.896i) q^{6} -2153.04 q^{7} -1448.15i q^{8} +(-964.092 - 1669.86i) q^{9} +(10393.6 - 6000.77i) q^{10} -9213.72 q^{11} +8712.29i q^{12} +(43154.6 - 24915.3i) q^{13} +(21095.4 + 12179.4i) q^{14} +(-62529.5 + 36101.4i) q^{15} +(-8192.00 + 14189.0i) q^{16} +(25345.4 - 43899.4i) q^{17} +21814.9i q^{18} +(-25153.1 - 127871. i) q^{19} -135782. q^{20} +(-126913. - 73273.2i) q^{21} +(90275.6 + 52120.7i) q^{22} +(-70168.5 - 121535. i) q^{23} +(49284.2 - 85362.7i) q^{24} +(-367332. - 636237. i) q^{25} -563770. q^{26} -577815. i q^{27} +(-137795. - 238667. i) q^{28} +(-1.06258e6 + 613479. i) q^{29} +816882. q^{30} +1.50687e6i q^{31} +(160530. - 92681.9i) q^{32} +(-543110. - 313565. i) q^{33} +(-496665. + 286750. i) q^{34} +(1.14197e6 - 1.97795e6i) q^{35} +(123404. - 213742. i) q^{36} -1.62845e6i q^{37} +(-476897. + 1.39516e6i) q^{38} +3.39171e6 q^{39} +(1.33039e6 + 768098. i) q^{40} +(1.18030e6 + 681445. i) q^{41} +(828991. + 1.43586e6i) q^{42} +(-1.29015e6 + 2.23461e6i) q^{43} +(-589678. - 1.02135e6i) q^{44} +2.04541e6 q^{45} +1.58773e6i q^{46} +(-1.02116e6 - 1.76871e6i) q^{47} +(-965769. + 557587. i) q^{48} -1.12921e6 q^{49} +8.31177e6i q^{50} +(2.98801e6 - 1.72513e6i) q^{51} +(5.52379e6 + 3.18916e6i) q^{52} +(-9.98477e6 + 5.76471e6i) q^{53} +(-3.26861e6 + 5.66140e6i) q^{54} +(4.88694e6 - 8.46442e6i) q^{55} +3.11794e6i q^{56} +(2.86907e6 - 8.39346e6i) q^{57} +1.38814e7 q^{58} +(-6.40032e6 - 3.69523e6i) q^{59} +(-8.00378e6 - 4.62098e6i) q^{60} +(-8.47005e6 - 1.46706e7i) q^{61} +(8.52414e6 - 1.47642e7i) q^{62} +(2.07573e6 + 3.59527e6i) q^{63} -2.09715e6 q^{64} +5.28602e7i q^{65} +(3.54758e6 + 6.14459e6i) q^{66} +(6.43570e6 - 3.71565e6i) q^{67} +6.48841e6 q^{68} -9.55200e6i q^{69} +(-2.23779e7 + 1.29199e7i) q^{70} +(8.60933e6 + 4.97060e6i) q^{71} +(-2.41821e6 + 1.39615e6i) q^{72} +(7.57665e6 - 1.31231e7i) q^{73} +(-9.21190e6 + 1.59555e7i) q^{74} -5.00047e7i q^{75} +(1.25648e7 - 1.09720e7i) q^{76} +1.98375e7 q^{77} +(-3.32319e7 - 1.91864e7i) q^{78} +(-3.65375e7 - 2.10949e7i) q^{79} +(-8.69004e6 - 1.50516e7i) q^{80} +(1.33390e7 - 2.31038e7i) q^{81} +(-7.70967e6 - 1.33535e7i) q^{82} -3.31238e7 q^{83} -1.87579e7i q^{84} +(2.68863e7 + 4.65684e7i) q^{85} +(2.52817e7 - 1.45964e7i) q^{86} -8.35126e7 q^{87} +1.33429e7i q^{88} +(7.84432e7 - 4.52892e7i) q^{89} +(-2.00409e7 - 1.15706e7i) q^{90} +(-9.29137e7 + 5.36438e7i) q^{91} +(8.98156e6 - 1.55565e7i) q^{92} +(-5.12823e7 + 8.88236e7i) q^{93} +2.31063e7i q^{94} +(1.30813e8 + 4.47148e7i) q^{95} +1.26167e7 q^{96} +(-1.15844e8 - 6.68824e7i) q^{97} +(1.10640e7 + 6.38778e6i) q^{98} +(8.88287e6 + 1.53856e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9}+O(q^{10}) $ 24 * q + 168 * q^3 + 1536 * q^4 - 558 * q^5 + 896 * q^6 + 11992 * q^7 + 18448 * q^9	\( 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9} + 33516 q^{11} + 60870 q^{13} - 71424 q^{14} - 351930 q^{15} - 196608 q^{16} + 3546 q^{17} - 727738 q^{19} - 142848 q^{20} - 674568 q^{21} - 681600 q^{22} + 726 q^{23} - 114688 q^{24} - 277874 q^{25} - 960000 q^{26} + 767488 q^{28} - 254286 q^{29} - 71168 q^{30} - 2796150 q^{33} - 2740224 q^{34} - 690672 q^{35} - 2361344 q^{36} - 6829056 q^{38} - 1599924 q^{39} - 5153976 q^{41} + 4153600 q^{42} + 5692338 q^{43} + 2145024 q^{44} + 42653840 q^{45} + 11113938 q^{47} - 2752512 q^{48} + 17359944 q^{49} + 62169786 q^{51} + 7791360 q^{52} + 10399050 q^{53} - 24215680 q^{54} + 40181572 q^{55} - 27798558 q^{57} - 10126848 q^{58} - 58809492 q^{59} - 45047040 q^{60} - 45012614 q^{61} + 5892096 q^{62} + 62488724 q^{63} - 50331648 q^{64} + 45107968 q^{66} - 93677268 q^{67} + 907776 q^{68} - 291840 q^{70} + 5993046 q^{71} + 11698176 q^{72} + 23359860 q^{73} - 31474944 q^{74} - 1303552 q^{76} + 35611680 q^{77} + 94099200 q^{78} - 93221166 q^{79} - 9142272 q^{80} - 115510580 q^{81} + 6074880 q^{82} - 194283156 q^{83} - 15300674 q^{85} + 58611456 q^{86} + 89779380 q^{87} - 49833126 q^{89} - 63377664 q^{90} - 101275308 q^{91} - 92928 q^{92} - 157549992 q^{93} - 87570126 q^{95} - 29360128 q^{96} - 178814556 q^{97} - 88409088 q^{98} - 54444376 q^{99}+O(q^{100}) \) 24 * q + 168 * q^3 + 1536 * q^4 - 558 * q^5 + 896 * q^6 + 11992 * q^7 + 18448 * q^9 + 33516 * q^11 + 60870 * q^13 - 71424 * q^14 - 351930 * q^15 - 196608 * q^16 + 3546 * q^17 - 727738 * q^19 - 142848 * q^20 - 674568 * q^21 - 681600 * q^22 + 726 * q^23 - 114688 * q^24 - 277874 * q^25 - 960000 * q^26 + 767488 * q^28 - 254286 * q^29 - 71168 * q^30 - 2796150 * q^33 - 2740224 * q^34 - 690672 * q^35 - 2361344 * q^36 - 6829056 * q^38 - 1599924 * q^39 - 5153976 * q^41 + 4153600 * q^42 + 5692338 * q^43 + 2145024 * q^44 + 42653840 * q^45 + 11113938 * q^47 - 2752512 * q^48 + 17359944 * q^49 + 62169786 * q^51 + 7791360 * q^52 + 10399050 * q^53 - 24215680 * q^54 + 40181572 * q^55 - 27798558 * q^57 - 10126848 * q^58 - 58809492 * q^59 - 45047040 * q^60 - 45012614 * q^61 + 5892096 * q^62 + 62488724 * q^63 - 50331648 * q^64 + 45107968 * q^66 - 93677268 * q^67 + 907776 * q^68 - 291840 * q^70 + 5993046 * q^71 + 11698176 * q^72 + 23359860 * q^73 - 31474944 * q^74 - 1303552 * q^76 + 35611680 * q^77 + 94099200 * q^78 - 93221166 * q^79 - 9142272 * q^80 - 115510580 * q^81 + 6074880 * q^82 - 194283156 * q^83 - 15300674 * q^85 + 58611456 * q^86 + 89779380 * q^87 - 49833126 * q^89 - 63377664 * q^90 - 101275308 * q^91 - 92928 * q^92 - 157549992 * q^93 - 87570126 * q^95 - 29360128 * q^96 - 178814556 * q^97 - 88409088 * q^98 - 54444376 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−9.79796	−	5.65685i	−0.612372	−	0.353553i
$2$	−9.79796	−	5.65685i	−0.612372	−	0.353553i
$3$	58.9458	+	34.0324i	0.727726	+	0.420153i	0.817590	−	0.575801i	$-0.195310\pi$
$3$	58.9458	+	34.0324i	0.727726	+	0.420153i	−0.0898635	+	0.995954i	$0.528643\pi$
$4$	64.0000	+	110.851i	0.250000	+	0.433013i
$5$	−530.398	+	918.676i	−0.848637	+	1.46988i	0.0337880	+	0.999429i	$0.489243\pi$
$5$	−530.398	+	918.676i	−0.848637	+	1.46988i	−0.882425	+	0.470453i	$0.844090\pi$
$6$	−385.033	−	666.896i	−0.297093	−	0.514580i
$7$	−2153.04			−0.896727			−0.448364	−	0.893851i	$-0.647993\pi$
$7$	−2153.04			−0.896727			−0.448364	+	0.893851i	$0.647993\pi$
$8$		−	1448.15i		−	0.353553i
$9$	−964.092	−	1669.86i	−0.146943	−	0.254513i
$10$	10393.6	−	6000.77i	1.03936	−	0.600077i
$11$	−9213.72			−0.629309			−0.314655	−	0.949206i	$-0.601889\pi$
$11$	−9213.72			−0.629309			−0.314655	+	0.949206i	$0.601889\pi$
$12$			8712.29i			0.420153i
$13$	43154.6	−	24915.3i	1.51096	−	0.872355i	0.511046	−	0.859554i	$-0.329258\pi$
$13$	43154.6	−	24915.3i	1.51096	−	0.872355i	0.999918	−	0.0128016i	$-0.00407499\pi$
$14$	21095.4	+	12179.4i	0.549131	+	0.317041i
$15$	−62529.5	+	36101.4i	−1.23515	+	0.713115i
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	25345.4	−	43899.4i	0.303461	−	0.525610i	−0.673457	−	0.739227i	$-0.735191\pi$
$17$	25345.4	−	43899.4i	0.303461	−	0.525610i	0.976917	+	0.213617i	$0.0685245\pi$
$18$			21814.9i			0.207809i
$19$	−25153.1	−	127871.i	−0.193008	−	0.981197i
$19$	−25153.1	−	127871.i	−0.193008	−	0.981197i
$20$	−135782.			−0.848637
$21$	−126913.	−	73273.2i	−0.652572	−	0.376763i
$22$	90275.6	+	52120.7i	0.385372	+	0.222494i
$23$	−70168.5	−	121535.i	−0.250744	−	0.434301i	0.712987	−	0.701177i	$-0.247342\pi$
$23$	−70168.5	−	121535.i	−0.250744	−	0.434301i	−0.963731	+	0.266876i	$0.914009\pi$
$24$	49284.2	−	85362.7i	0.148547	−	0.257290i
$25$	−367332.	−	636237.i	−0.940369	−	1.62877i
$26$	−563770.			−1.23370
$27$		−	577815.i		−	1.08726i
$28$	−137795.	−	238667.i	−0.224182	−	0.388294i
$29$	−1.06258e6	+	613479.i	−1.50234	+	0.867376i	−0.502344	+	0.864668i	$0.667529\pi$
$29$	−1.06258e6	+	613479.i	−1.50234	+	0.867376i	−0.999996	+	0.00270820i	$0.999138\pi$
$30$	816882.			1.00850
$31$			1.50687e6i			1.63166i	0.578295	+	0.815828i	$0.303718\pi$
$31$			1.50687e6i			1.63166i	−0.578295	+	0.815828i	$0.696282\pi$
$32$	160530.	−	92681.9i	0.153093	−	0.0883883i
$33$	−543110.	−	313565.i	−0.457965	−	0.264406i
$34$	−496665.	+	286750.i	−0.371662	+	0.214579i
$35$	1.14197e6	−	1.97795e6i	0.760996	−	1.31808i
$36$	123404.	−	213742.i	0.0734715	−	0.127256i
$37$		−	1.62845e6i		−	0.868895i	−0.900697	−	0.434447i	$-0.856944\pi$
$37$		−	1.62845e6i		−	0.868895i	0.900697	−	0.434447i	$-0.143056\pi$
$38$	−476897.	+	1.39516e6i	−0.228713	+	0.669097i
$39$	3.39171e6			1.46609
$40$	1.33039e6	+	768098.i	0.519682	+	0.300038i
$41$	1.18030e6	+	681445.i	0.417692	+	0.241154i	0.694089	−	0.719889i	$-0.255807\pi$
$41$	1.18030e6	+	681445.i	0.417692	+	0.241154i	−0.276397	+	0.961043i	$0.589141\pi$
$42$	828991.	+	1.43586e6i	0.266411	+	0.461438i
$43$	−1.29015e6	+	2.23461e6i	−0.377369	+	0.653622i	−0.990679	−	0.136220i	$-0.956505\pi$
$43$	−1.29015e6	+	2.23461e6i	−0.377369	+	0.653622i	0.613309	+	0.789843i	$0.289838\pi$
$44$	−589678.	−	1.02135e6i	−0.157327	−	0.272499i
$45$	2.04541e6			0.498805
$46$			1.58773e6i			0.354606i
$47$	−1.02116e6	−	1.76871e6i	−0.209268	−	0.362463i	0.742216	−	0.670161i	$-0.233775\pi$
$47$	−1.02116e6	−	1.76871e6i	−0.209268	−	0.362463i	−0.951484	+	0.307697i	$0.900442\pi$
$48$	−965769.	+	557587.i	−0.181932	+	0.105038i
$49$	−1.12921e6			−0.195880
$50$			8.31177e6i			1.32988i
$51$	2.98801e6	−	1.72513e6i	0.441673	−	0.255000i
$52$	5.52379e6	+	3.18916e6i	0.755482	+	0.436178i
$53$	−9.98477e6	+	5.76471e6i	−1.26542	+	0.730591i	−0.974118	−	0.226041i	$-0.927422\pi$
$53$	−9.98477e6	+	5.76471e6i	−1.26542	+	0.730591i	−0.291302	+	0.956631i	$0.594088\pi$
$54$	−3.26861e6	+	5.66140e6i	−0.384404	+	0.665808i
$55$	4.88694e6	−	8.46442e6i	0.534055	−	0.925011i
$56$			3.11794e6i			0.317041i
$57$	2.86907e6	−	8.39346e6i	0.271796	−	0.795136i
$58$	1.38814e7			1.22666
$59$	−6.40032e6	−	3.69523e6i	−0.528194	−	0.304953i	0.212087	−	0.977251i	$-0.431974\pi$
$59$	−6.40032e6	−	3.69523e6i	−0.528194	−	0.304953i	−0.740281	+	0.672298i	$0.765307\pi$
$60$	−8.00378e6	−	4.62098e6i	−0.617575	−	0.356557i
$61$	−8.47005e6	−	1.46706e7i	−0.611740	−	1.05956i	−0.990947	−	0.134253i	$-0.957137\pi$
$61$	−8.47005e6	−	1.46706e7i	−0.611740	−	1.05956i	0.379207	−	0.925312i	$-0.376197\pi$
$62$	8.52414e6	−	1.47642e7i	0.576878	−	0.999181i
$63$	2.07573e6	+	3.59527e6i	0.131768	+	0.228228i
$64$	−2.09715e6			−0.125000
$65$			5.28602e7i			2.96125i
$66$	3.54758e6	+	6.14459e6i	0.186963	+	0.323830i
$67$	6.43570e6	−	3.71565e6i	0.319372	−	0.184389i	−0.331741	−	0.943371i	$-0.607636\pi$
$67$	6.43570e6	−	3.71565e6i	0.319372	−	0.184389i	0.651113	+	0.758981i	$0.274303\pi$
$68$	6.48841e6			0.303461
$69$		−	9.55200e6i		−	0.421403i
$70$	−2.23779e7	+	1.29199e7i	−0.932026	+	0.538105i
$71$	8.60933e6	+	4.97060e6i	0.338794	+	0.195603i	0.659739	−	0.751495i	$-0.270667\pi$
$71$	8.60933e6	+	4.97060e6i	0.338794	+	0.195603i	−0.320944	+	0.947098i	$0.604000\pi$
$72$	−2.41821e6	+	1.39615e6i	−0.0899838	+	0.0519522i
$73$	7.57665e6	−	1.31231e7i	0.266800	−	0.462111i	−0.701234	−	0.712932i	$-0.747367\pi$
$73$	7.57665e6	−	1.31231e7i	0.266800	−	0.462111i	0.968034	+	0.250820i	$0.0807003\pi$
$74$	−9.21190e6	+	1.59555e7i	−0.307201	+	0.532087i
$75$		−	5.00047e7i		−	1.58040i
$76$	1.25648e7	−	1.09720e7i	0.376619	−	0.328874i
$77$	1.98375e7			0.564319
$78$	−3.32319e7	−	1.91864e7i	−0.897794	−	0.518341i
$79$	−3.65375e7	−	2.10949e7i	−0.938059	−	0.541589i	−0.0487079	−	0.998813i	$-0.515510\pi$
$79$	−3.65375e7	−	2.10949e7i	−0.938059	−	0.541589i	−0.889351	+	0.457224i	$0.848844\pi$
$80$	−8.69004e6	−	1.50516e7i	−0.212159	−	0.367471i
$81$	1.33390e7	−	2.31038e7i	0.309873	−	0.536715i
$82$	−7.70967e6	−	1.33535e7i	−0.170522	−	0.295353i
$83$	−3.31238e7			−0.697955			−0.348977	−	0.937131i	$-0.613471\pi$
$83$	−3.31238e7			−0.697955			−0.348977	+	0.937131i	$0.613471\pi$
$84$		−	1.87579e7i		−	0.376763i
$85$	2.68863e7	+	4.65684e7i	0.515056	+	0.892103i
$86$	2.52817e7	−	1.45964e7i	0.462181	−	0.266840i
$87$	−8.35126e7			−1.45772
$88$			1.33429e7i			0.222494i
$89$	7.84432e7	−	4.52892e7i	1.25025	−	0.721830i	0.279088	−	0.960266i	$-0.409968\pi$
$89$	7.84432e7	−	4.52892e7i	1.25025	−	0.721830i	0.971158	+	0.238436i	$0.0766346\pi$
$90$	−2.00409e7	−	1.15706e7i	−0.305454	−	0.176354i
$91$	−9.29137e7	+	5.36438e7i	−1.35492	+	0.782265i
$92$	8.98156e6	−	1.55565e7i	0.125372	−	0.217151i
$93$	−5.12823e7	+	8.88236e7i	−0.685545	+	1.18740i
$94$			2.31063e7i			0.295950i
$95$	1.30813e8	+	4.47148e7i	1.60604	+	0.548980i
$96$	1.26167e7			0.148547
$97$	−1.15844e8	−	6.68824e7i	−1.30854	−	0.755483i	−0.326684	−	0.945134i	$-0.605931\pi$
$97$	−1.15844e8	−	6.68824e7i	−1.30854	−	0.755483i	−0.981852	+	0.189650i	$0.939265\pi$
$98$	1.10640e7	+	6.38778e6i	0.119952	+	0.0692542i
$99$	8.88287e6	+	1.53856e7i	0.0924725	+	0.160167i
$100$	4.70185e7	−	8.14384e7i	0.470185	−	0.814384i
$101$	2.37747e7	+	4.11789e7i	0.228470	+	0.395722i	0.957355	−	0.288915i	$-0.0932944\pi$
$101$	2.37747e7	+	4.11789e7i	0.228470	+	0.395722i	−0.728885	+	0.684636i	$0.759961\pi$
$102$	−3.90351e7			−0.360624
$103$			4.41796e7i			0.392530i	0.980551	+	0.196265i	$0.0628813\pi$
$103$			4.41796e7i			0.392530i	−0.980551	+	0.196265i	$0.937119\pi$
$104$	−3.60813e7	−	6.24946e7i	−0.308424	−	0.534206i
$105$	1.34629e8	−	7.77279e7i	1.10759	−	0.639469i
$106$	1.30441e8			1.03321
$107$			2.25354e8i			1.71922i	0.510953	+	0.859608i	$0.329292\pi$
$107$			2.25354e8i			1.71922i	−0.510953	+	0.859608i	$0.670708\pi$
$108$	6.40515e7	−	3.69801e7i	0.470797	−	0.271815i
$109$	9.05110e7	+	5.22565e7i	0.641203	+	0.370199i	0.785078	−	0.619397i	$-0.212623\pi$
$109$	9.05110e7	+	5.22565e7i	0.641203	+	0.370199i	−0.143875	+	0.989596i	$0.545956\pi$
$110$	−9.57640e7	+	5.52894e7i	−0.654081	+	0.377634i
$111$	5.54200e7	−	9.59903e7i	0.365069	−	0.632318i
$112$	1.76377e7	−	3.05494e7i	0.112091	−	0.194147i
$113$			1.13413e7i			0.0695585i	0.999395	+	0.0347792i	$0.0110728\pi$
$113$			1.13413e7i			0.0695585i	−0.999395	+	0.0347792i	$0.988927\pi$
$114$	−7.55916e7	+	6.60088e7i	−0.447563	+	0.390825i
$115$	1.48869e8			0.851162
$116$	−1.36010e8	−	7.85253e7i	−0.751170	−	0.433688i
$117$	−8.32101e7	−	4.80414e7i	−0.444051	−	0.256373i
$118$	4.18067e7	+	7.24113e7i	0.215634	+	0.373490i
$119$	−5.45696e7	+	9.45173e7i	−0.272122	+	0.471328i
$120$	5.22805e7	+	9.05524e7i	0.252124	+	0.436692i
$121$	−1.29466e8			−0.603970
$122$			1.91655e8i			0.865131i
$123$	4.63824e7	+	8.03367e7i	0.202644	+	0.350989i
$124$	−1.67038e8	+	9.64396e7i	−0.706528	+	0.407914i
$125$	3.64955e8			1.49485
$126$		−	4.69684e7i		−	0.186348i
$127$	1.14188e8	−	6.59265e7i	0.438940	−	0.253422i	−0.264208	−	0.964466i	$-0.585110\pi$
$127$	1.14188e8	−	6.59265e7i	0.438940	−	0.253422i	0.703148	+	0.711043i	$0.251777\pi$
$128$	2.05478e7	+	1.18633e7i	0.0765466	+	0.0441942i
$129$	−1.52098e8	+	8.78138e7i	−0.549243	+	0.317106i
$130$	2.99022e8	−	5.17922e8i	1.04696	−	1.81339i
$131$	−1.59695e8	+	2.76600e8i	−0.542258	+	0.939218i	0.456516	+	0.889715i	$0.349097\pi$
$131$	−1.59695e8	+	2.76600e8i	−0.542258	+	0.939218i	−0.998774	+	0.0495028i	$0.984236\pi$
$132$		−	8.02726e7i		−	0.264406i
$133$	5.41556e7	+	2.75311e8i	0.173076	+	0.879866i
$134$	−8.40756e7			−0.260766
$135$	5.30825e8	+	3.06472e8i	1.59814	+	0.922689i
$136$	−6.35732e7	−	3.67040e7i	−0.185831	−	0.107290i
$137$	−3.24197e8	−	5.61525e8i	−0.920293	−	1.59399i	−0.798962	−	0.601382i	$-0.794617\pi$
$137$	−3.24197e8	−	5.61525e8i	−0.920293	−	1.59399i	−0.121331	−	0.992612i	$-0.538716\pi$
$138$	−5.40343e7	+	9.35901e7i	−0.148989	+	0.258056i
$139$	−2.51048e8	−	4.34829e8i	−0.672509	−	1.16482i	−0.977190	−	0.212366i	$-0.931883\pi$
$139$	−2.51048e8	−	4.34829e8i	−0.672509	−	1.16482i	0.304681	−	0.952454i	$-0.401450\pi$
$140$	2.92344e8			0.760996
$141$		−	1.39010e8i		−	0.351699i
$142$	−5.62359e7	−	9.74034e7i	−0.138312	−	0.239564i
$143$	−3.97615e8	+	2.29563e8i	−0.950863	+	0.548981i
$144$	3.15914e7			0.0734715
$145$		−	1.30155e9i		−	2.94435i
$146$	−1.48471e8	+	8.57200e7i	−0.326762	+	0.188656i
$147$	−6.65623e7	−	3.84298e7i	−0.142547	−	0.0822997i
$148$	1.80516e8	−	1.04221e8i	0.376243	−	0.217224i
$149$	−2.41592e8	+	4.18450e8i	−0.490160	+	0.848982i	−0.999936	−	0.0113254i	$-0.996395\pi$
$149$	−2.41592e8	+	4.18450e8i	−0.490160	+	0.848982i	0.509776	+	0.860307i	$0.329728\pi$
$150$	−2.82869e8	+	4.89944e8i	−0.558754	+	0.967791i
$151$			1.94882e8i			0.374856i	0.982278	+	0.187428i	$0.0600152\pi$
$151$			1.94882e8i			0.374856i	−0.982278	+	0.187428i	$0.939985\pi$
$152$	−1.85176e8	+	3.64255e7i	−0.346906	+	0.0682388i
$153$	−9.77410e7			−0.178366
$154$	−1.94367e8	−	1.12218e8i	−0.345573	−	0.199517i
$155$	−1.38432e9	−	7.99240e8i	−2.39834	−	1.38468i
$156$	2.17070e8	+	3.75976e8i	0.366523	+	0.634836i
$157$	2.61403e8	−	4.52763e8i	0.430241	−	0.745199i	−0.566653	−	0.823956i	$-0.691762\pi$
$157$	2.61403e8	−	4.52763e8i	0.430241	−	0.745199i	0.996894	+	0.0787578i	$0.0250954\pi$
$158$	2.38662e8	+	4.13375e8i	0.382961	+	0.663308i
$159$	−7.84748e8			−1.22784
$160$			1.96633e8i			0.300038i
$161$	1.51076e8	+	2.61671e8i	0.224849	+	0.389450i
$162$	−2.61390e8	+	1.50914e8i	−0.379515	+	0.219113i
$163$	−2.11044e8			−0.298966			−0.149483	−	0.988764i	$-0.547761\pi$
$163$	−2.11044e8			−0.298966			−0.149483	+	0.988764i	$0.547761\pi$
$164$			1.74450e8i			0.241154i
$165$	5.76129e8	−	3.32628e8i	0.777292	−	0.448770i
$166$	3.24545e8	+	1.87376e8i	0.427408	+	0.246764i
$167$	5.44367e8	−	3.14290e8i	0.699884	−	0.404078i	−0.107420	−	0.994214i	$-0.534259\pi$
$167$	5.44367e8	−	3.14290e8i	0.699884	−	0.404078i	0.807304	+	0.590136i	$0.200926\pi$
$168$	−1.06111e8	+	1.83789e8i	−0.133206	+	0.230719i
$169$	8.33683e8	−	1.44398e9i	1.02201	−	1.77017i
$170$		−	6.08366e8i		−	0.728399i
$171$	−1.89276e8	+	1.65281e8i	−0.221366	+	0.193303i
$172$	−3.30278e8			−0.377369
$173$	7.24817e8	+	4.18473e8i	0.809178	+	0.467179i	0.846670	−	0.532118i	$-0.178604\pi$
$173$	7.24817e8	+	4.18473e8i	0.809178	+	0.467179i	−0.0374925	+	0.999297i	$0.511937\pi$
$174$	8.18253e8	+	4.72419e8i	0.892669	+	0.515383i
$175$	7.90881e8	+	1.36985e9i	0.843255	+	1.46056i
$176$	7.54788e7	−	1.30733e8i	0.0786637	−	0.136249i
$177$	−2.51515e8	−	4.35636e8i	−0.256254	−	0.443845i
$178$	−1.02478e9			−1.02082
$179$			8.02978e8i			0.782152i	0.920358	+	0.391076i	$0.127897\pi$
$179$			8.02978e8i			0.782152i	−0.920358	+	0.391076i	$0.872103\pi$
$180$	1.30906e8	+	2.26736e8i	0.124701	+	0.215989i
$181$	2.02552e8	−	1.16944e8i	0.188722	−	0.108959i	−0.402662	−	0.915349i	$-0.631915\pi$
$181$	2.02552e8	−	1.16944e8i	0.188722	−	0.108959i	0.591384	+	0.806390i	$0.298582\pi$
$182$	1.21382e9			1.10629
$183$		−	1.15302e9i		−	1.02810i
$184$	−1.76002e8	+	1.01615e8i	−0.153549	+	0.0886514i
$185$	1.49602e9	+	8.63726e8i	1.27717	+	0.737376i
$186$	1.00492e9	−	5.80194e8i	0.839618	−	0.484754i
$187$	−2.33525e8	+	4.04477e8i	−0.190971	+	0.330771i
$188$	1.30709e8	−	2.26394e8i	0.104634	−	0.181232i
$189$			1.24406e9i			0.974976i
$190$	−1.02875e9	−	1.17810e9i	−0.789400	−	0.904001i
$191$	−1.44614e9			−1.08662			−0.543310	−	0.839532i	$-0.682829\pi$
$191$	−1.44614e9			−1.08662			−0.543310	+	0.839532i	$0.682829\pi$
$192$	−1.23618e8	−	7.13711e7i	−0.0909658	−	0.0525191i
$193$	8.07271e8	+	4.66078e8i	0.581822	+	0.335915i	0.761857	−	0.647745i	$-0.224288\pi$
$193$	8.07271e8	+	4.66078e8i	0.581822	+	0.335915i	−0.180035	+	0.983660i	$0.557621\pi$
$194$	7.56688e8	+	1.31062e9i	0.534207	+	0.925275i
$195$	−1.79896e9	+	3.11589e9i	−1.24418	+	2.15498i
$196$	−7.22695e7	−	1.25174e8i	−0.0489701	−	0.0848187i
$197$	4.24646e8			0.281944			0.140972	−	0.990014i	$-0.454977\pi$
$197$	4.24646e8			0.281944			0.140972	+	0.990014i	$0.454977\pi$
$198$		−	2.00996e8i		−	0.130776i
$199$	−3.62865e7	−	6.28500e7i	−0.0231384	−	0.0400768i	0.854224	−	0.519905i	$-0.174032\pi$
$199$	−3.62865e7	−	6.28500e7i	−0.0231384	−	0.0400768i	−0.877363	+	0.479828i	$0.840699\pi$
$200$	−9.21370e8	+	5.31953e8i	−0.575856	+	0.332471i
$201$	5.05810e8			0.309887
$202$		−	5.37959e8i		−	0.323105i
$203$	2.28777e9	−	1.32085e9i	1.34719	−	0.777800i
$204$	3.82465e8	+	2.20816e8i	0.220836	+	0.127500i
$205$	−1.25205e9	+	7.22874e8i	−0.708937	+	0.409305i
$206$	2.49917e8	−	4.32870e8i	0.138780	−	0.240374i
$207$	−1.35298e8	+	2.34343e8i	−0.0736901	+	0.127635i
$208$			8.16426e8i			0.436178i
$209$	2.31753e8	+	1.17816e9i	0.121462	+	0.617476i
$210$	−1.75878e9			−0.904346
$211$	−1.81101e9	−	1.04559e9i	−0.913672	−	0.527509i	−0.0320614	−	0.999486i	$-0.510207\pi$
$211$	−1.81101e9	−	1.04559e9i	−0.913672	−	0.527509i	−0.881611	+	0.471977i	$0.843541\pi$
$212$	−1.27805e9	−	7.37883e8i	−0.632710	−	0.365295i
$213$	3.38323e8	+	5.85992e8i	0.164366	+	0.284691i
$214$	1.27480e9	−	2.20801e9i	0.607835	−	1.05280i
$215$	−1.36859e9	−	2.37046e9i	−0.640499	−	1.10938i
$216$	−8.36765e8			−0.384404
$217$		−	3.24435e9i		−	1.46315i
$218$	−5.91215e8	−	1.02402e9i	−0.261770	−	0.453399i
$219$	8.93224e8	−	5.15703e8i	0.388315	−	0.224194i
$220$	1.25106e9			0.534055
$221$		−	2.52595e9i		−	1.05890i
$222$	−1.08601e9	+	6.27006e8i	−0.447116	+	0.258143i
$223$	3.11439e9	+	1.79809e9i	1.25937	+	0.727097i	0.972952	−	0.231008i	$-0.0742022\pi$
$223$	3.11439e9	+	1.79809e9i	1.25937	+	0.727097i	0.286418	+	0.958105i	$0.407536\pi$
$224$	−3.45627e8	+	1.99548e8i	−0.137283	+	0.0792602i
$225$	−7.08283e8	+	1.22678e9i	−0.276361	+	0.478672i
$226$	6.41562e7	−	1.11122e8i	0.0245926	−	0.0425957i
$227$			4.05417e9i			1.52686i	0.645893	+	0.763428i	$0.276485\pi$
$227$			4.05417e9i			1.52686i	−0.645893	+	0.763428i	$0.723515\pi$
$228$	1.11405e9	−	2.19141e8i	0.412253	−	0.0810931i
$229$	9.31035e8			0.338551			0.169275	−	0.985569i	$-0.445857\pi$
$229$	9.31035e8			0.338551			0.169275	+	0.985569i	$0.445857\pi$
$230$	−1.45861e9	−	8.42129e8i	−0.521228	−	0.300931i
$231$	1.16934e9	+	6.75118e8i	0.410670	+	0.237100i
$232$	8.88412e8	+	1.53878e9i	0.306664	+	0.531157i
$233$	−2.50440e9	+	4.33774e9i	−0.849728	+	1.47177i	0.0317239	+	0.999497i	$0.489900\pi$
$233$	−2.50440e9	+	4.33774e9i	−0.849728	+	1.47177i	−0.881451	+	0.472275i	$0.843433\pi$
$234$	5.43526e8	+	9.41415e8i	0.181283	+	0.313991i
$235$	2.16649e9			0.710371
$236$		−	9.45978e8i		−	0.304953i
$237$	−1.43582e9	−	2.48692e9i	−0.455100	−	0.788257i
$238$	1.06934e9	−	6.17385e8i	0.333279	−	0.192419i
$239$	−5.59166e8			−0.171376			−0.0856879	−	0.996322i	$-0.527309\pi$
$239$	−5.59166e8			−0.171376			−0.0856879	+	0.996322i	$0.527309\pi$
$240$		−	1.18297e9i		−	0.356557i
$241$	3.16179e8	−	1.82546e8i	0.0937271	−	0.0541134i	−0.452404	−	0.891813i	$-0.649433\pi$
$241$	3.16179e8	−	1.82546e8i	0.0937271	−	0.0541134i	0.546131	+	0.837700i	$0.316100\pi$
$242$	1.26851e9	+	7.32372e8i	0.369854	+	0.213536i
$243$	−1.71058e9	+	9.87604e8i	−0.490590	+	0.283242i
$244$	1.08417e9	−	1.87783e9i	0.305870	−	0.529782i
$245$	5.98931e8	−	1.03738e9i	0.166231	−	0.287921i
$246$		−	1.04951e9i		−	0.286581i
$247$	−4.27141e9	−	4.89151e9i	−1.14758	−	1.31418i
$248$	2.18218e9			0.576878
$249$	−1.95251e9	−	1.12728e9i	−0.507920	−	0.293248i
$250$	−3.57581e9	−	2.06450e9i	−0.915408	−	0.528511i
$251$	−2.66383e9	−	4.61388e9i	−0.671137	−	1.16244i	−0.977582	−	0.210555i	$-0.932473\pi$
$251$	−2.66383e9	−	4.61388e9i	−0.671137	−	1.16244i	0.306445	−	0.951888i	$-0.400860\pi$
$252$	−2.65694e8	+	4.60195e8i	−0.0658838	+	0.114114i
$253$	6.46512e8	+	1.11979e9i	0.157796	+	0.273310i
$254$	−1.49175e9			−0.358393
$255$			3.66001e9i			0.865610i
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	6.86444e8	−	3.96318e8i	0.157352	−	0.0908472i	−0.419256	−	0.907868i	$-0.637709\pi$
$257$	6.86444e8	−	3.96318e8i	0.157352	−	0.0908472i	0.576608	+	0.817021i	$0.304376\pi$
$258$	1.98700e9			0.448455
$259$			3.50612e9i			0.779162i
$260$	−5.85962e9	+	3.38305e9i	−1.28226	+	0.740313i
$261$	2.04884e9	+	1.18290e9i	0.441516	+	0.254910i
$262$	3.12937e9	−	1.80674e9i	0.664127	−	0.383434i
$263$	−2.13900e9	+	3.70486e9i	−0.447083	+	0.774370i	−0.998195	−	0.0600615i	$-0.980870\pi$
$263$	−2.13900e9	+	3.70486e9i	−0.447083	+	0.774370i	0.551112	+	0.834431i	$0.314204\pi$
$264$	−4.54090e8	+	7.86508e8i	−0.0934817	+	0.161915i
$265$		−	1.22304e10i		−	2.48002i
$266$	1.02678e9	−	3.00383e9i	0.205093	−	0.599997i
$267$	6.16520e9			1.21312
$268$	8.23770e8	+	4.75604e8i	0.159686	+	0.0921947i
$269$	−2.21536e9	−	1.27904e9i	−0.423093	−	0.244273i	0.273307	−	0.961927i	$-0.411883\pi$
$269$	−2.21536e9	−	1.27904e9i	−0.423093	−	0.244273i	−0.696400	+	0.717654i	$0.745216\pi$
$270$	−3.46733e9	−	6.00559e9i	−0.652440	−	1.13006i
$271$	−1.39118e9	+	2.40959e9i	−0.257932	+	0.446752i	−0.965688	−	0.259705i	$-0.916375\pi$
$271$	−1.39118e9	+	2.40959e9i	−0.257932	+	0.446752i	0.707755	+	0.706457i	$0.249708\pi$
$272$	4.15258e8	+	7.19248e8i	0.0758652	+	0.131402i
$273$	−7.30250e9			−1.31468
$274$			7.33573e9i			1.30149i
$275$	3.38449e9	+	5.86211e9i	0.591783	+	1.02500i
$276$	1.05885e9	−	6.11328e8i	0.182473	−	0.105351i
$277$	6.49454e9			1.10314			0.551568	−	0.834130i	$-0.314030\pi$
$277$	6.49454e9			1.10314			0.551568	+	0.834130i	$0.314030\pi$
$278$			5.68058e9i			0.951072i
$279$	2.51626e9	−	1.45276e9i	0.415277	−	0.239760i
$280$	−2.86438e9	−	1.65375e9i	−0.466013	−	0.269053i
$281$	5.56437e9	−	3.21259e9i	0.892463	−	0.515264i	0.0177159	−	0.999843i	$-0.494361\pi$
$281$	5.56437e9	−	3.21259e9i	0.892463	−	0.515264i	0.874747	+	0.484579i	$0.161027\pi$
$282$	−7.86362e8	+	1.36202e9i	−0.124344	+	0.215371i
$283$	−5.24372e9	+	9.08239e9i	−0.817511	+	1.41597i	0.0899998	+	0.995942i	$0.471313\pi$
$283$	−5.24372e9	+	9.08239e9i	−0.817511	+	1.41597i	−0.907511	+	0.420029i	$0.862020\pi$
$284$			1.27247e9i			0.195603i
$285$	6.18912e9	+	7.08762e9i	0.938101	+	1.07429i
$286$	5.19441e9			0.776377
$287$	−2.54123e9	−	1.46718e9i	−0.374556	−	0.216250i
$288$	−3.09531e8	−	1.78708e8i	−0.0449919	−	0.0259761i
$289$	2.20311e9	+	3.81589e9i	0.315823	+	0.547022i
$290$	−7.36269e9	+	1.27526e10i	−1.04099	+	1.80304i
$291$	−4.55234e9	−	7.88488e9i	−0.634837	−	1.09957i
$292$	1.93962e9			0.266800
$293$		−	5.53405e9i		−	0.750883i	−0.926846	−	0.375442i	$-0.877491\pi$
$293$		−	5.53405e9i		−	0.750883i	0.926846	−	0.375442i	$-0.122509\pi$
$294$	4.34783e8	+	7.53066e8i	0.0581947	+	0.100796i
$295$	6.78943e9	−	3.91988e9i	0.896490	−	0.517589i
$296$	−2.35825e9			−0.307201
$297$			5.32382e9i			0.684223i
$298$	4.73422e9	−	2.73330e9i	0.600321	−	0.346595i
$299$	−6.05619e9	−	3.49654e9i	−0.757730	−	0.437476i
$300$	5.54309e9	−	3.20030e9i	0.684332	−	0.395099i
$301$	2.77775e9	−	4.81120e9i	0.338397	−	0.586121i
$302$	1.10242e9	−	1.90945e9i	0.132532	−	0.229552i
$303$			3.23644e9i			0.383969i
$304$	2.02040e9	+	6.90620e8i	0.236561	+	0.0808621i
$305$	1.79700e10			2.07658
$306$	9.57663e8	+	5.52907e8i	0.109226	+	0.0630618i
$307$	−1.37986e10	−	7.96665e9i	−1.55340	−	0.896855i	−0.997862	−	0.0653636i	$-0.979179\pi$
$307$	−1.37986e10	−	7.96665e9i	−1.55340	−	0.896855i	−0.555537	−	0.831492i	$-0.687487\pi$
$308$	1.26960e9	+	2.19901e9i	0.141080	+	0.244357i
$309$	−1.50354e9	+	2.60420e9i	−0.164923	+	0.285654i
$310$	9.04237e9	+	1.56618e10i	0.979119	+	1.69588i
$311$	7.55913e9			0.808035			0.404018	−	0.914751i	$-0.367613\pi$
$311$	7.55913e9			0.808035			0.404018	+	0.914751i	$0.367613\pi$
$312$		−	4.91173e9i		−	0.518341i
$313$	3.22379e9	+	5.58377e9i	0.335884	+	0.581768i	0.983654	−	0.180068i	$-0.0576317\pi$
$313$	3.22379e9	+	5.58377e9i	0.335884	+	0.581768i	−0.647770	+	0.761836i	$0.724298\pi$
$314$	−5.12242e9	+	2.95743e9i	−0.526935	+	0.304226i
$315$	−4.40386e9			−0.447292
$316$		−	5.40030e9i		−	0.541589i
$317$	3.19053e9	−	1.84205e9i	0.315955	−	0.182417i	−0.333633	−	0.942703i	$-0.608275\pi$
$317$	3.19053e9	−	1.84205e9i	0.315955	−	0.182417i	0.649588	+	0.760286i	$0.274941\pi$
$318$	7.68893e9	+	4.43920e9i	0.751895	+	0.434107i
$319$	9.79028e9	−	5.65242e9i	0.945436	−	0.545848i
$320$	1.11233e9	−	1.92660e9i	0.106080	−	0.183735i
$321$	−7.66935e9	+	1.32837e10i	−0.722334	+	1.25112i
$322$		−	3.41845e9i		−	0.317984i
$323$	−6.25096e9	−	2.13672e9i	−0.574297	−	0.196308i
$324$	3.41478e9			0.309873
$325$	−3.17041e10	−	1.83044e10i	−2.84173	−	1.64067i
$326$	2.06780e9	+	1.19384e9i	0.183079	+	0.105701i
$327$	3.55683e9	+	6.16061e9i	0.311080	+	0.538807i
$328$	9.86838e8	−	1.70925e9i	0.0852610	−	0.147676i
$329$	2.19861e9	+	3.80810e9i	0.187657	+	0.325031i
$330$	−7.52652e9			−0.634656
$331$		−	1.84789e9i		−	0.153944i	−0.997033	−	0.0769722i	$-0.975475\pi$
$331$		−	1.84789e9i		−	0.153944i	0.997033	−	0.0769722i	$-0.0245253\pi$
$332$	−2.11992e9	−	3.67181e9i	−0.174489	−	0.302223i
$333$	−2.71928e9	+	1.56998e9i	−0.221145	+	0.127678i
$334$	−7.11158e9			−0.571453
$335$			7.88310e9i			0.625919i
$336$	2.07934e9	−	1.20051e9i	0.163143	−	0.0941907i
$337$	−1.90933e10	−	1.10235e10i	−1.48034	−	0.854673i	−0.480585	−	0.876948i	$-0.659576\pi$
$337$	−1.90933e10	−	1.10235e10i	−1.48034	−	0.854673i	−0.999752	+	0.0222751i	$0.992909\pi$
$338$	−1.63368e10	+	9.43204e9i	−1.25170	+	0.722668i
$339$	−3.85972e8	+	6.68524e8i	−0.0292252	+	0.0506195i
$340$	−3.44144e9	+	5.96075e9i	−0.257528	+	0.446052i
$341$		−	1.38839e10i		−	1.02682i
$342$	2.78949e9	−	5.48712e8i	0.203901	−	0.0401088i
$343$	1.48431e10			1.07238
$344$	3.23605e9	+	1.86834e9i	0.231090	+	0.133420i
$345$	8.77520e9	+	5.06636e9i	0.619413	+	0.357618i
$346$	−4.73448e9	−	8.20037e9i	−0.330345	−	0.572175i
$347$	4.38818e7	−	7.60055e7i	0.00302668	−	0.00524236i	−0.864508	−	0.502619i	$-0.832370\pi$
$347$	4.38818e7	−	7.60055e7i	0.00302668	−	0.00524236i	0.867535	+	0.497377i	$0.165703\pi$
$348$	−5.34481e9	−	9.25748e9i	−0.364431	−	0.631213i
$349$	6.26240e9			0.422123			0.211062	−	0.977473i	$-0.432308\pi$
$349$	6.26240e9			0.422123			0.211062	+	0.977473i	$0.432308\pi$
$350$		−	1.78956e10i		−	1.19254i
$351$	−1.43964e10	−	2.49354e10i	−0.948477	−	1.64281i
$352$	−1.47908e9	+	8.53945e8i	−0.0963429	+	0.0556236i
$353$	8.52586e9			0.549085			0.274542	−	0.961575i	$-0.411474\pi$
$353$	8.52586e9			0.549085			0.274542	+	0.961575i	$0.411474\pi$
$354$			5.69113e9i			0.362398i
$355$	−9.13274e9	+	5.27279e9i	−0.575027	+	0.331992i
$356$	1.00407e10	+	5.79702e9i	0.625123	+	0.360915i
$357$	−6.43330e9	+	3.71427e9i	−0.396060	+	0.228665i
$358$	4.54233e9	−	7.86754e9i	0.276533	−	0.478968i
$359$	1.48789e10	−	2.57711e10i	0.895766	−	1.55151i	0.0629114	−	0.998019i	$-0.479961\pi$
$359$	1.48789e10	−	2.57711e10i	0.895766	−	1.55151i	0.832854	−	0.553492i	$-0.186705\pi$
$360$		−	2.96207e9i		−	0.176354i
$361$	−1.57182e10	+	6.43267e9i	−0.925495	+	0.378759i
$362$	−2.64613e9			−0.154091
$363$	−7.63150e9	−	4.40605e9i	−0.439525	−	0.253760i
$364$	−1.18930e10	−	6.86640e9i	−0.677461	−	0.391132i
$365$	8.03728e9	+	1.39210e10i	0.452833	+	0.784329i
$366$	−6.52249e9	+	1.12973e10i	−0.363487	+	0.629578i
$367$	1.44434e10	+	2.50168e10i	0.796171	+	1.37901i	0.922093	+	0.386968i	$0.126478\pi$
$367$	1.44434e10	+	2.50168e10i	0.796171	+	1.37901i	−0.125923	+	0.992040i	$0.540189\pi$
$368$	2.29928e9			0.125372
$369$		−	2.62790e9i		−	0.141744i
$370$	−9.77195e9	−	1.69255e10i	−0.521404	−	0.903098i
$371$	2.14976e10	−	1.24117e10i	1.13474	−	0.655140i
$372$	−1.31283e10			−0.685545
$373$		−	7.29345e9i		−	0.376788i	−0.982093	−	0.188394i	$-0.939672\pi$
$373$		−	7.29345e9i		−	0.376788i	0.982093	−	0.188394i	$-0.0603282\pi$
$374$	4.57613e9	−	2.64203e9i	0.233890	−	0.135037i
$375$	2.15126e10	+	1.24203e10i	1.08785	+	0.628068i
$376$	−2.56136e9	+	1.47880e9i	−0.128150	+	0.0739875i
$377$	−3.05701e10	+	5.29489e10i	−1.51332	+	2.62115i
$378$	7.03746e9	−	1.21892e10i	0.344706	−	0.597048i
$379$			5.86823e9i			0.284414i	0.989837	+	0.142207i	$0.0454198\pi$
$379$			5.86823e9i			0.284414i	−0.989837	+	0.142207i	$0.954580\pi$
$380$	3.41533e9	+	1.73625e10i	0.163794	+	0.832680i
$381$	8.97454e9			0.425905
$382$	1.41692e10	+	8.18061e9i	0.665416	+	0.384178i
$383$	−1.76231e10	−	1.01747e10i	−0.819005	−	0.472853i	0.0310684	−	0.999517i	$-0.490109\pi$
$383$	−1.76231e10	−	1.01747e10i	−0.819005	−	0.472853i	−0.850073	+	0.526665i	$0.823442\pi$
$384$	8.07472e8	+	1.39858e9i	0.0371366	+	0.0643225i
$385$	−1.05218e10	+	1.82243e10i	−0.478902	+	0.829482i
$386$	−5.27307e9	−	9.13322e9i	−0.237528	−	0.411410i
$387$	4.97529e9			0.221807
$388$		−	1.71219e10i		−	0.755483i
$389$	−1.23411e10	−	2.13753e10i	−0.538957	−	0.933500i	−0.998961	−	0.0455835i	$-0.985485\pi$
$389$	−1.23411e10	−	2.13753e10i	−0.538957	−	0.933500i	0.460004	−	0.887917i	$-0.347848\pi$
$390$	3.52522e10	−	2.03529e10i	1.52380	−	0.879767i
$391$	−7.11378e9			−0.304364
$392$			1.63527e9i			0.0692542i
$393$	−1.88267e10	+	1.08696e10i	−0.789230	+	0.455662i
$394$	−4.16066e9	−	2.40216e9i	−0.172654	−	0.0996821i
$395$	3.87588e10	−	2.23774e10i	1.59214	−	0.919225i
$396$	−1.13701e9	+	1.96936e9i	−0.0462363	+	0.0800836i
$397$	−3.73868e9	+	6.47558e9i	−0.150507	+	0.260685i	−0.931414	−	0.363962i	$-0.881424\pi$
$397$	−3.73868e9	+	6.47558e9i	−0.150507	+	0.260685i	0.780907	+	0.624647i	$0.214757\pi$
$398$			8.21069e8i			0.0327226i
$399$	−6.17724e9	+	1.80715e10i	−0.243726	+	0.713020i
$400$	1.20367e10			0.470185
$401$	1.55904e10	+	9.00113e9i	0.602949	+	0.348113i	0.770201	−	0.637802i	$-0.220156\pi$
$401$	1.55904e10	+	9.00113e9i	0.602949	+	0.348113i	−0.167252	+	0.985914i	$0.553489\pi$
$402$	−4.95591e9	−	2.86130e9i	−0.189766	−	0.109562i
$403$	3.75441e10	+	6.50284e10i	1.42338	+	2.46537i
$404$	−3.04316e9	+	5.27091e9i	−0.114235	+	0.197861i
$405$	1.41500e10	+	2.45085e10i	0.525939	+	0.910953i
$406$	−2.98873e10			−1.09998
$407$			1.50041e10i			0.546804i
$408$	−2.49825e9	−	4.32709e9i	−0.0901561	−	0.156155i
$409$	6.19571e9	−	3.57709e9i	0.221410	−	0.127831i	−0.385193	−	0.922836i	$-0.625865\pi$
$409$	6.19571e9	−	3.57709e9i	0.221410	−	0.127831i	0.606603	+	0.795005i	$0.292532\pi$
$410$	1.63568e10			0.578845
$411$		−	4.41327e10i		−	1.54666i
$412$	−4.89736e9	+	2.82749e9i	−0.169970	+	0.0981325i
$413$	1.37802e10	+	7.95598e9i	0.473646	+	0.273460i
$414$	2.65128e9	−	1.53072e9i	0.0902516	−	0.0521068i
$415$	1.75688e10	−	3.04300e10i	0.592310	−	1.02591i
$416$	4.61840e9	−	7.99931e9i	0.154212	−	0.267103i
$417$		−	3.41751e10i		−	1.13023i
$418$	4.39399e9	−	1.28546e10i	0.143931	−	0.421069i
$419$	−3.98349e10			−1.29243			−0.646216	−	0.763154i	$-0.723650\pi$
$419$	−3.98349e10			−1.29243			−0.646216	+	0.763154i	$0.723650\pi$
$420$	1.72325e10	+	9.94917e9i	0.553797	+	0.319735i
$421$	1.10602e10	+	6.38563e9i	0.352076	+	0.203271i	0.665599	−	0.746309i	$-0.268176\pi$
$421$	1.10602e10	+	6.38563e9i	0.352076	+	0.203271i	−0.313523	+	0.949581i	$0.601509\pi$
$422$	1.18295e10	+	2.04892e10i	0.373005	+	0.646064i
$423$	−1.96899e9	+	3.41039e9i	−0.0615010	+	0.106523i
$424$	8.34819e9	+	1.44595e10i	0.258303	+	0.447394i
$425$	−3.72406e10			−1.14146
$426$		−	7.65537e9i		−	0.232449i
$427$	1.82364e10	+	3.15863e10i	0.548564	+	0.950140i
$428$	−2.49808e10	+	1.44227e10i	−0.744443	+	0.429804i
$429$	−3.12503e10			−0.922624
$430$			3.09676e10i			0.905802i
$431$	7.12357e9	−	4.11279e9i	0.206438	−	0.119187i	−0.393217	−	0.919446i	$-0.628638\pi$
$431$	7.12357e9	−	4.11279e9i	0.206438	−	0.119187i	0.599655	+	0.800259i	$0.295305\pi$
$432$	8.19859e9	+	4.73346e9i	0.235399	+	0.135908i
$433$	3.28948e10	−	1.89918e10i	0.935784	−	0.540275i	0.0471478	−	0.998888i	$-0.484987\pi$
$433$	3.28948e10	−	1.89918e10i	0.935784	−	0.540275i	0.888636	+	0.458613i	$0.151653\pi$
$434$	−1.83528e10	+	3.17880e10i	−0.517302	+	0.895993i
$435$	4.42949e10	−	7.67211e10i	1.23708	−	2.14268i
$436$			1.33777e10i			0.370199i
$437$	−1.37758e10	+	1.20295e10i	−0.377740	+	0.329853i
$438$	−1.16690e10			−0.317058
$439$	5.59379e9	+	3.22957e9i	0.150608	+	0.0869535i	0.573410	−	0.819268i	$-0.305620\pi$
$439$	5.59379e9	+	3.22957e9i	0.150608	+	0.0869535i	−0.422802	+	0.906222i	$0.638953\pi$
$440$	−1.22578e10	−	7.07704e9i	−0.327041	−	0.188817i
$441$	1.08866e9	+	1.88562e9i	0.0287832	+	0.0498540i
$442$	−1.42889e10	+	2.47492e10i	−0.374379	+	0.648443i
$443$	−5.77143e9	−	9.99641e9i	−0.149854	−	0.259555i	0.781319	−	0.624131i	$-0.214547\pi$
$443$	−5.77143e9	−	9.99641e9i	−0.149854	−	0.259555i	−0.931173	+	0.364577i	$0.881214\pi$
$444$	1.41875e10			0.365069
$445$			9.60853e10i			2.45029i
$446$	−2.03431e10	−	3.52353e10i	−0.514135	−	0.890509i
$447$	−2.84817e10	+	1.64439e10i	−0.713404	+	0.411884i
$448$	4.51526e9			0.112091
$449$			1.91704e10i			0.471678i	0.971792	+	0.235839i	$0.0757838\pi$
$449$			1.91704e10i			0.471678i	−0.971792	+	0.235839i	$0.924216\pi$
$450$	1.38795e10	−	8.01331e9i	0.338472	−	0.195417i
$451$	−1.08749e10	−	6.27864e9i	−0.262857	−	0.151761i
$452$	−1.25720e9	+	7.25845e8i	−0.0301197	+	0.0173896i
$453$	−6.63231e9	+	1.14875e10i	−0.157497	+	0.272793i
$454$	2.29338e10	−	3.97226e10i	0.539825	−	0.935005i
$455$		−	1.13810e11i		−	2.65543i
$456$	−1.21550e10	−	4.15486e9i	−0.281123	−	0.0960943i
$457$	1.13746e10			0.260779			0.130389	−	0.991463i	$-0.458377\pi$
$457$	1.13746e10			0.260779			0.130389	+	0.991463i	$0.458377\pi$
$458$	−9.12224e9	−	5.26673e9i	−0.207319	−	0.119696i
$459$	−2.53657e10	−	1.46449e10i	−0.571474	−	0.329941i
$460$	9.52761e9	+	1.65023e10i	0.212791	+	0.368564i
$461$	−8.30895e9	+	1.43915e10i	−0.183968	+	0.318642i	−0.943228	−	0.332145i	$-0.892228\pi$
$461$	−8.30895e9	+	1.43915e10i	−0.183968	+	0.318642i	0.759260	+	0.650787i	$0.225561\pi$
$462$	−7.63809e9	−	1.32296e10i	−0.167655	−	0.290387i
$463$	−8.13908e10			−1.77113			−0.885567	−	0.464512i	$-0.846230\pi$
$463$	−8.13908e10			−1.77113			−0.885567	+	0.464512i	$0.846230\pi$
$464$		−	2.01025e10i		−	0.433688i
$465$	−5.44001e10	−	9.42238e10i	−1.16356	−	2.01534i
$466$	4.90760e10	−	2.83340e10i	1.04070	−	0.600848i
$467$	5.38028e10			1.13119			0.565597	−	0.824682i	$-0.308646\pi$
$467$	5.38028e10			1.13119			0.565597	+	0.824682i	$0.308646\pi$
$468$		−	1.22986e10i		−	0.256373i
$469$	−1.38563e10	+	7.99996e9i	−0.286389	+	0.165347i
$470$	−2.12272e10	−	1.22555e10i	−0.435012	−	0.251154i
$471$	3.08172e10	−	1.77923e10i	0.626195	−	0.361534i
$472$	−5.35126e9	+	9.26865e9i	−0.107817	+	0.186745i
$473$	1.18871e10	−	2.05890e10i	0.237482	−	0.411331i
$474$			3.24889e10i			0.643609i
$475$	−7.21165e10	+	6.29742e10i	−1.41664	+	1.23705i
$476$	−1.39698e10			−0.272122
$477$	1.92525e10	+	1.11154e10i	0.371889	+	0.214710i
$478$	5.47869e9	+	3.16312e9i	0.104946	+	0.0605905i
$479$	−2.04687e10	−	3.54529e10i	−0.388820	−	0.673456i	0.603471	−	0.797385i	$-0.293784\pi$
$479$	−2.04687e10	−	3.54529e10i	−0.388820	−	0.673456i	−0.992291	+	0.123929i	$0.960451\pi$
$480$	−6.69190e9	+	1.15907e10i	−0.126062	+	0.218346i
$481$	−4.05734e10	−	7.02751e10i	−0.757985	−	1.31287i
$482$	−4.13055e9			−0.0765279
$483$			2.05659e10i			0.377884i
$484$	−8.28584e9	−	1.43515e10i	−0.150992	−	0.261527i
$485$	1.22887e11	−	7.09486e10i	2.22094	−	1.28226i
$486$	2.23469e10			0.400565
$487$			8.98508e10i			1.59737i	0.601748	+	0.798686i	$0.294471\pi$
$487$			8.98508e10i			1.59737i	−0.601748	+	0.798686i	$0.705529\pi$
$488$	−2.12452e10	+	1.22659e10i	−0.374613	+	0.216283i
$489$	−1.24401e10	−	7.18232e9i	−0.217566	−	0.125612i
$490$	−1.17366e10	+	6.77614e9i	−0.203591	+	0.117543i
$491$	8.14601e9	−	1.41093e10i	0.140158	−	0.242762i	−0.787398	−	0.616445i	$-0.788572\pi$
$491$	8.14601e9	−	1.41093e10i	0.140158	−	0.242762i	0.927556	+	0.373684i	$0.121905\pi$
$492$	−5.93695e9	+	1.02831e10i	−0.101322	+	0.175494i
$493$			6.21953e10i			1.05286i
$494$	1.41805e10	+	7.20896e10i	0.238114	+	1.21050i
$495$	−1.88458e10			−0.313902
$496$	−2.13809e10	−	1.23443e10i	−0.353264	−	0.203957i
$497$	−1.85362e10	−	1.07019e10i	−0.303806	−	0.175402i
$498$	1.27537e10	+	2.20901e10i	0.207358	+	0.359154i
$499$	−8.91926e9	+	1.54486e10i	−0.143856	+	0.249165i	−0.928945	−	0.370217i	$-0.879283\pi$
$499$	−8.91926e9	+	1.54486e10i	−0.143856	+	0.249165i	0.785090	+	0.619382i	$0.212617\pi$
$500$	2.33571e10	+	4.04557e10i	0.373714	+	0.647291i
$501$	4.27842e10			0.679098
$502$			6.02755e10i			0.949131i
$503$	−1.25051e10	−	2.16595e10i	−0.195351	−	0.338358i	0.751664	−	0.659546i	$-0.229251\pi$
$503$	−1.25051e10	−	2.16595e10i	−0.195351	−	0.338358i	−0.947016	+	0.321188i	$0.895918\pi$
$504$	5.20651e9	−	3.00598e9i	0.0806909	−	0.0465869i
$505$	−5.04402e10			−0.775552
$506$		−	1.46289e10i		−	0.223157i
$507$	9.82843e10	−	5.67444e10i	1.48748	−	0.858799i
$508$	1.46161e10	+	8.43859e9i	0.219470	+	0.126711i
$509$	6.59173e10	−	3.80574e10i	0.982038	−	0.566980i	0.0791535	−	0.996862i	$-0.474778\pi$
$509$	6.59173e10	−	3.80574e10i	0.982038	−	0.566980i	0.902885	+	0.429882i	$0.141445\pi$
$510$	2.07042e10	−	3.58607e10i	0.306039	−	0.530075i
$511$	−1.63128e10	+	2.82547e10i	−0.239247	+	0.414388i
$512$			3.03700e9i			0.0441942i
$513$	−7.38855e10	+	1.45338e10i	−1.06682	+	0.209850i
$514$	−8.96766e9			−0.128477
$515$	−4.05867e10	−	2.34328e10i	−0.576973	−	0.333115i
$516$	−1.94685e10	−	1.12402e10i	−0.274621	−	0.158553i
$517$	9.40870e9	+	1.62963e10i	0.131694	+	0.228102i
$518$	1.98336e10	−	3.43528e10i	0.275475	−	0.477137i
$519$	2.84833e10	+	4.93345e10i	0.392573	+	0.679957i
$520$	7.65497e10			1.04696
$521$		−	1.40614e11i		−	1.90843i	−0.299121	−	0.954215i	$-0.596693\pi$
$521$		−	1.40614e11i		−	1.90843i	0.299121	−	0.954215i	$-0.403307\pi$
$522$	−1.33830e10	−	2.31800e10i	−0.180248	−	0.312199i
$523$	9.07519e10	−	5.23956e10i	1.21297	−	0.700307i	0.249562	−	0.968359i	$-0.419713\pi$
$523$	9.07519e10	−	5.23956e10i	1.21297	−	0.700307i	0.963404	+	0.268052i	$0.0863799\pi$
$524$	−4.08819e10			−0.542258
$525$			1.07662e11i			1.41718i
$526$	4.19157e10	−	2.42000e10i	0.547562	−	0.316135i
$527$	6.61507e10	+	3.81921e10i	0.857614	+	0.495144i
$528$	8.89832e9	−	5.13745e9i	0.114491	−	0.0661015i
$529$	2.93083e10	−	5.07634e10i	0.374255	−	0.648228i
$530$	−6.91854e10	+	1.19833e11i	−0.876821	+	1.51870i
$531$			1.42502e10i			0.179243i
$532$	−2.70526e10	+	2.36231e10i	−0.337724	+	0.294911i
$533$	6.79137e10			0.841490
$534$	−6.04064e10	−	3.48757e10i	−0.742879	−	0.428901i
$535$	−2.07028e11	−	1.19527e11i	−2.52705	−	1.45899i
$536$	−5.38084e9	−	9.31989e9i	−0.0651915	−	0.112915i
$537$	−2.73272e10	+	4.73322e10i	−0.328624	+	0.569193i
$538$	1.44707e10	+	2.50640e10i	0.172727	+	0.299172i
$539$	1.04042e10			0.123269
$540$			7.84568e10i			0.922689i
$541$	−3.67637e10	−	6.36766e10i	−0.429171	−	0.743346i	0.567629	−	0.823285i	$-0.307861\pi$
$541$	−3.67637e10	−	6.36766e10i	−0.429171	−	0.743346i	−0.996800	+	0.0799385i	$0.974528\pi$
$542$	2.72614e10	−	1.57394e10i	0.315901	−	0.182386i
$543$	1.59195e10			0.183118
$544$		−	9.39622e9i		−	0.107290i
$545$	−9.60137e10	+	5.54335e10i	−1.08830	+	0.628328i
$546$	7.15496e10	+	4.13092e10i	0.805076	+	0.464811i
$547$	−1.33127e11	+	7.68608e10i	−1.48702	+	0.858530i	−0.999890	−	0.0148001i	$-0.995289\pi$
$547$	−1.33127e11	+	7.68608e10i	−1.48702	+	0.858530i	−0.487128	+	0.873331i	$0.661955\pi$
$548$	4.14972e10	−	7.18752e10i	0.460146	−	0.796997i
$549$	−1.63318e10	+	2.82876e10i	−0.179782	+	0.311391i
$550$		−	7.65823e10i		−	0.836908i
$551$	1.05173e11	+	1.20441e11i	1.14103	+	1.30668i
$552$	−1.38328e10			−0.148989
$553$	7.86667e10	+	4.54183e10i	0.841183	+	0.485657i
$554$	−6.36332e10	−	3.67387e10i	−0.675530	−	0.390018i
$555$	5.87893e10	+	1.01826e11i	0.619622	+	1.07322i
$556$	3.21342e10	−	5.56581e10i	0.336255	−	0.582410i
$557$	1.93015e10	+	3.34312e10i	0.200526	+	0.347322i	0.948698	−	0.316183i	$-0.102401\pi$
$557$	1.93015e10	+	3.34312e10i	0.200526	+	0.347322i	−0.748172	+	0.663505i	$0.769068\pi$
$558$	−3.28722e10			−0.339072
$559$			1.28578e11i			1.31680i
$560$	1.87100e10	+	3.24067e10i	0.190249	+	0.329521i
$561$	−2.75306e10	+	1.58948e10i	−0.277949	+	0.160474i
$562$	−7.26926e10			−0.728693
$563$			9.88137e10i			0.983521i	0.870731	+	0.491760i	$0.163646\pi$
$563$			9.88137e10i			0.983521i	−0.870731	+	0.491760i	$0.836354\pi$
$564$	1.54095e10	−	8.89667e9i	0.152290	−	0.0879247i
$565$	−1.04190e10	−	6.01542e9i	−0.102243	−	0.0590299i
$566$	1.02755e11	−	5.93259e10i	1.00124	−	0.578068i
$567$	−2.87194e10	+	4.97435e10i	−0.277871	+	0.481287i
$568$	7.19820e9	−	1.24676e10i	0.0691561	−	0.119782i
$569$		−	4.37360e10i		−	0.417244i	−0.977996	−	0.208622i	$-0.933102\pi$
$569$		−	4.37360e10i		−	0.417244i	0.977996	−	0.208622i	$-0.0668979\pi$
$570$	−2.05471e10	−	1.04455e11i	−0.194648	−	0.989534i
$571$	1.45714e11			1.37075			0.685373	−	0.728192i	$-0.259639\pi$
$571$	1.45714e11			1.37075			0.685373	+	0.728192i	$0.259639\pi$
$572$	−5.08947e10	−	2.93840e10i	−0.475432	−	0.274491i
$573$	−8.52440e10	−	4.92157e10i	−0.790761	−	0.456546i
$574$	1.65992e10	+	2.87507e10i	0.152912	+	0.264851i
$575$	−5.15502e10	+	8.92876e10i	−0.471584	+	0.816807i
$576$	2.02185e9	+	3.50194e9i	0.0183679	+	0.0318141i
$577$	6.77475e9			0.0611210			0.0305605	−	0.999533i	$-0.490271\pi$
$577$	6.77475e9			0.0611210			0.0305605	+	0.999533i	$0.490271\pi$
$578$		−	4.98506e10i		−	0.446641i
$579$	3.17235e10	+	5.49467e10i	0.282271	+	0.488908i
$580$	1.44279e11	−	8.32993e10i	1.27494	−	0.736088i
$581$	7.13168e10			0.625875
$582$			1.03008e11i			0.897796i
$583$	9.19969e10	−	5.31144e10i	0.796341	−	0.459767i
$584$	−1.90043e10	−	1.09722e10i	−0.163381	−	0.0943281i
$585$	8.82690e10	−	5.09621e10i	0.753676	−	0.435135i
$586$	−3.13053e10	+	5.42224e10i	−0.265477	+	0.459820i
$587$	7.71731e10	−	1.33668e11i	0.650000	−	1.12583i	−0.333122	−	0.942884i	$-0.608102\pi$
$587$	7.71731e10	−	1.33668e11i	0.650000	−	1.12583i	0.983122	−	0.182949i	$-0.0585644\pi$
$588$		−	9.83802e9i		−	0.0822997i
$589$	1.92684e11	−	3.79023e10i	1.60098	−	0.314923i
$590$	−8.86968e10			−0.731981
$591$	2.50311e10	+	1.44517e10i	0.205178	+	0.118459i
$592$	2.31060e10	+	1.33403e10i	0.188121	+	0.108612i
$593$	−3.94683e10	−	6.83611e10i	−0.319176	−	0.552828i	0.661141	−	0.750262i	$-0.270073\pi$
$593$	−3.94683e10	−	6.83611e10i	−0.319176	−	0.552828i	−0.980316	+	0.197434i	$0.936739\pi$
$594$	3.01161e10	−	5.21626e10i	0.241909	−	0.418999i
$595$	−5.78872e10	−	1.00264e11i	−0.461865	−	0.799973i
$596$	−6.18476e10			−0.490160
$597$		−	4.93966e9i		−	0.0388866i
$598$	3.95589e10	+	6.85179e10i	0.309342	+	0.535796i
$599$	−5.34310e10	+	3.08484e10i	−0.415036	+	0.239621i	−0.692951	−	0.720984i	$-0.743690\pi$
$599$	−5.34310e10	+	3.08484e10i	−0.415036	+	0.239621i	0.277915	+	0.960606i	$0.410357\pi$
$600$	−7.24146e10			−0.558754
$601$			7.68648e10i			0.589155i	0.955628	+	0.294578i	$0.0951790\pi$
$601$			7.68648e10i			0.589155i	−0.955628	+	0.294578i	$0.904821\pi$
$602$	−5.44325e10	+	3.14266e10i	−0.414450	+	0.239283i
$603$	−1.24092e10	−	7.16447e9i	−0.0938588	−	0.0541894i
$604$	−2.16029e10	+	1.24725e10i	−0.162317	+	0.0937140i
$605$	6.86687e10	−	1.18938e11i	0.512551	−	0.887765i
$606$	1.83080e10	−	3.17105e10i	0.135754	−	0.235132i
$607$		−	7.35845e10i		−	0.542041i	−0.962574	−	0.271020i	$-0.912639\pi$
$607$		−	7.35845e10i		−	0.542041i	0.962574	−	0.271020i	$-0.0873611\pi$
$608$	−1.58891e10	−	1.81958e10i	−0.116275	−	0.133155i
$609$	1.79806e11			1.30718
$610$	−1.76069e11	−	1.01654e11i	−1.27164	−	0.734182i
$611$	−8.81358e10	−	5.08852e10i	−0.632394	−	0.365113i
$612$	−6.25543e9	−	1.08347e10i	−0.0445914	−	0.0772346i
$613$	−1.33165e11	+	2.30648e11i	−0.943079	+	1.63346i	−0.183526	+	0.983015i	$0.558751\pi$
$613$	−1.33165e11	+	2.30648e11i	−0.943079	+	1.63346i	−0.759553	+	0.650445i	$0.774582\pi$
$614$	9.01324e10	+	1.56114e11i	0.634172	+	1.09842i
$615$	−9.84046e10			−0.687883
$616$		−	2.87278e10i		−	0.199517i
$617$	9.51933e9	+	1.64880e10i	0.0656850	+	0.113770i	0.896998	−	0.442035i	$-0.145743\pi$
$617$	9.51933e9	+	1.64880e10i	0.0656850	+	0.113770i	−0.831313	+	0.555805i	$0.812410\pi$
$618$	2.94632e10	−	1.70106e10i	0.201988	−	0.116618i
$619$	−1.04794e11			−0.713797			−0.356898	−	0.934143i	$-0.616166\pi$
$619$	−1.04794e11			−0.713797			−0.356898	+	0.934143i	$0.616166\pi$
$620$		−	2.04606e11i		−	1.38468i
$621$	−7.02249e10	+	4.05444e10i	−0.472199	+	0.272624i
$622$	−7.40641e10	−	4.27609e10i	−0.494819	−	0.285684i
$623$	−1.68892e11	+	9.75096e10i	−1.12113	+	0.647285i
$624$	−2.77849e10	+	4.81249e10i	−0.183261	+	0.317418i
$625$	−5.00823e10	+	8.67451e10i	−0.328220	+	0.568493i
$626$		−	7.29460e10i		−	0.475012i
$627$	−2.64348e10	+	7.73349e10i	−0.171043	+	0.500386i
$628$	6.69191e10			0.430241
$629$	−7.14880e10	−	4.12736e10i	−0.456699	−	0.263676i
$630$	4.31488e10	+	2.49120e10i	0.273909	+	0.158142i
$631$	−1.22980e11	−	2.13007e11i	−0.775740	−	1.34362i	−0.934377	−	0.356285i	$-0.884043\pi$
$631$	−1.22980e11	−	2.13007e11i	−0.775740	−	1.34362i	0.158637	−	0.987337i	$-0.449290\pi$
$632$	−3.05487e10	+	5.29119e10i	−0.191481	+	0.331654i
$633$	−7.11676e10	−	1.23266e11i	−0.443269	−	0.767764i
$634$	−4.16809e10			−0.257976
$635$			1.39869e11i			0.860254i
$636$	−5.02239e10	−	8.69903e10i	−0.306960	−	0.531670i
$637$	−4.87307e10	+	2.81347e10i	−0.295968	+	0.170877i
$638$	−1.27900e11			−0.771946
$639$		−	1.91685e10i		−	0.114970i
$640$	−2.17970e10	+	1.25845e10i	−0.129920	+	0.0750096i
$641$	−4.32821e9	−	2.49889e9i	−0.0256375	−	0.0148018i	0.487126	−	0.873331i	$-0.338045\pi$
$641$	−4.32821e9	−	2.49889e9i	−0.0256375	−	0.0148018i	−0.512764	+	0.858530i	$0.671378\pi$
$642$	1.50288e11	−	8.67687e10i	0.884675	−	0.510767i
$643$	5.49334e10	−	9.51474e10i	0.321360	−	0.556613i	−0.659409	−	0.751785i	$-0.729193\pi$
$643$	5.49334e10	−	9.51474e10i	0.321360	−	0.556613i	0.980769	+	0.195172i	$0.0625266\pi$
$644$	−1.93377e10	+	3.34938e10i	−0.112424	+	0.194725i
$645$		−	1.86305e11i		−	1.07643i
$646$	4.91595e10	+	5.62963e10i	0.282278	+	0.323258i
$647$	−1.92677e11			−1.09955			−0.549773	−	0.835314i	$-0.685286\pi$
$647$	−1.92677e11			−1.09955			−0.549773	+	0.835314i	$0.685286\pi$
$648$	−3.34579e10	−	1.93169e10i	−0.189757	−	0.109557i
$649$	5.89707e10	+	3.40468e10i	0.332397	+	0.191910i
$650$	2.07091e11	+	3.58691e11i	1.16013	+	2.00940i
$651$	1.10413e11	−	1.91241e11i	0.614747	−	1.06477i
$652$	−1.35068e10	−	2.33945e10i	−0.0747415	−	0.129456i
$653$	1.16573e11			0.641129			0.320565	−	0.947227i	$-0.396127\pi$
$653$	1.16573e11			0.641129			0.320565	+	0.947227i	$0.396127\pi$
$654$		−	8.04819e10i		−	0.439934i
$655$	−1.69404e11	−	2.93416e11i	−0.920360	−	1.59411i
$656$	−1.93380e10	+	1.11648e10i	−0.104423	+	0.0602886i
$657$	−2.92184e10			−0.156817
$658$		−	4.97488e10i		−	0.265386i
$659$	−1.56409e11	+	9.03026e10i	−0.829314	+	0.478805i	−0.853618	−	0.520900i	$-0.825596\pi$
$659$	−1.56409e11	+	9.03026e10i	−0.829314	+	0.478805i	0.0243036	+	0.999705i	$0.492263\pi$
$660$	7.37445e10	+	4.25764e10i	0.388646	+	0.224385i
$661$	2.49257e11	−	1.43908e11i	1.30569	−	0.753842i	0.324318	−	0.945948i	$-0.394865\pi$
$661$	2.49257e11	−	1.43908e11i	1.30569	−	0.753842i	0.981374	+	0.192106i	$0.0615318\pi$
$662$	−1.04532e10	+	1.81055e10i	−0.0544276	+	0.0942713i
$663$	8.59642e10	−	1.48894e11i	0.444901	−	0.770591i
$664$			4.79683e10i			0.246764i
$665$	−2.81646e11	−	9.62728e10i	−1.44018	−	0.492286i
$666$	3.55245e10			0.180564
$667$	1.49119e11	+	8.60937e10i	0.753405	+	0.434979i
$668$	6.96790e10	+	4.02292e10i	0.349942	+	0.202039i
$669$	1.22387e11	+	2.11980e11i	0.610984	+	1.05826i
$670$	4.45936e10	−	7.72383e10i	0.221296	−	0.383295i
$671$	7.80407e10	+	1.35170e11i	0.384974	+	0.666794i
$672$	−2.71644e10			−0.133206
$673$		−	3.60612e11i		−	1.75784i	−0.476968	−	0.878921i	$-0.658264\pi$
$673$		−	3.60612e11i		−	1.75784i	0.476968	−	0.878921i	$-0.341736\pi$
$674$	1.24717e11	+	2.16016e11i	0.604345	+	1.04676i
$675$	−3.67627e11	+	2.12250e11i	−1.77089	+	1.02243i
$676$	2.13423e11			1.02201
$677$			1.32859e10i			0.0632466i	0.999500	+	0.0316233i	$0.0100677\pi$
$677$			1.32859e10i			0.0632466i	−0.999500	+	0.0316233i	$0.989932\pi$
$678$	7.56348e9	−	4.36678e9i	0.0357934	−	0.0206653i
$679$	2.49416e11	+	1.44001e11i	1.17340	+	0.677463i
$680$	6.74382e10	−	3.89355e10i	0.315406	−	0.182100i
$681$	−1.37973e11	+	2.38976e11i	−0.641513	+	1.11113i
$682$	−7.85390e10	+	1.36034e11i	−0.363034	+	0.628794i
$683$			4.20400e9i			0.0193188i	0.999953	+	0.00965940i	$0.00307473\pi$
$683$			4.20400e9i			0.0193188i	−0.999953	+	0.00965940i	$0.996925\pi$
$684$	−3.04353e10	−	1.04035e10i	−0.139044	−	0.0475284i
$685$	6.87813e11			3.12398
$686$	−1.45432e11	−	8.39652e10i	−0.656695	−	0.379143i
$687$	5.48806e10	+	3.16853e10i	0.246372	+	0.142243i
$688$	−2.11378e10	−	3.66118e10i	−0.0943423	−	0.163406i
$689$	−2.87259e11	+	4.97548e11i	−1.27467	+	2.20779i
$690$	−5.73194e10	−	9.92800e10i	−0.252874	−	0.437991i
$691$	1.45427e11			0.637870			0.318935	−	0.947777i	$-0.396675\pi$
$691$	1.45427e11			0.637870			0.318935	+	0.947777i	$0.396675\pi$
$692$			1.07129e11i			0.467179i
$693$	−1.91252e10	−	3.31258e10i	−0.0829226	−	0.143626i
$694$	−8.59904e8	+	4.96466e8i	−0.00370691	+	0.00214019i
$695$	5.32622e11			2.28287
$696$			1.20939e11i			0.515383i
$697$	5.98301e10	−	3.45429e10i	0.253506	−	0.146362i
$698$	−6.13588e10	−	3.54255e10i	−0.258497	−	0.149243i
$699$	−2.95248e11	+	1.70461e11i	−1.23674	+	0.714031i
$700$	−1.01233e11	+	1.75340e11i	−0.421627	+	0.730280i
$701$	1.88615e11	−	3.26691e11i	0.781096	−	1.35290i	−0.150207	−	0.988654i	$-0.547994\pi$
$701$	1.88615e11	−	3.26691e11i	0.781096	−	1.35290i	0.931304	−	0.364244i	$-0.118672\pi$
$702$			3.25754e11i			1.34135i
$703$	−2.08231e11	+	4.09605e10i	−0.852557	+	0.167704i
$704$	1.93226e10			0.0786637
$705$	1.27706e11	+	7.37309e10i	0.516956	+	0.298465i
$706$	−8.35360e10	−	4.82295e10i	−0.336244	−	0.194131i
$707$	−5.11879e10	−	8.86600e10i	−0.204875	−	0.354854i
$708$	3.21939e10	−	5.57615e10i	0.128127	−	0.221922i
$709$	−1.09110e11	−	1.88984e11i	−0.431797	−	0.747894i	0.565231	−	0.824932i	$-0.308787\pi$
$709$	−1.09110e11	−	1.88984e11i	−0.431797	−	0.747894i	−0.997028	+	0.0770386i	$0.975454\pi$
$710$	1.19310e11			0.469507
$711$			8.13498e10i			0.318331i
$712$	−6.55858e10	−	1.13598e11i	−0.255205	−	0.442029i
$713$	1.83138e11	−	1.05735e11i	0.708630	−	0.409128i
$714$	8.40443e10			0.323382
$715$		−	4.87039e11i		−	1.86354i
$716$	−8.90111e10	+	5.13906e10i	−0.338682	+	0.195538i
$717$	−3.29605e10	−	1.90298e10i	−0.124715	−	0.0720040i
$718$	−2.91567e11	+	1.68336e11i	−1.09708	+	0.633402i
$719$	−1.51549e11	+	2.62491e11i	−0.567072	+	0.982198i	0.429781	+	0.902933i	$0.358591\pi$
$719$	−1.51549e11	+	2.62491e11i	−0.567072	+	0.982198i	−0.996854	+	0.0792651i	$0.974743\pi$
$720$	−1.67560e10	+	2.90223e10i	−0.0623506	+	0.107994i
$721$		−	9.51205e10i		−	0.351992i
$722$	1.90395e11	+	2.58886e10i	0.700659	+	0.0952707i
$723$	2.48499e10			0.0909436
$724$	2.59267e10	+	1.49688e10i	0.0943611	+	0.0544794i
$725$	7.80636e11	+	4.50700e11i	2.82551	+	1.63131i
$726$	4.98487e10	+	8.63406e10i	0.179435	+	0.310791i
$727$	4.63344e8	−	8.02536e8i	0.00165869	−	0.00287294i	−0.865195	−	0.501436i	$-0.832805\pi$
$727$	4.63344e8	−	8.02536e8i	0.00165869	−	0.00287294i	0.866854	+	0.498563i	$0.166139\pi$
$728$	7.76845e10	+	1.34553e11i	0.276572	+	0.479037i
$729$	−3.09477e11			−1.09577
$730$		−	1.81863e11i		−	0.640402i
$731$	6.53986e10	+	1.13274e11i	0.229033	+	0.396698i
$732$	1.27814e11	−	7.37936e10i	0.445179	−	0.257024i
$733$	−5.66784e10			−0.196337			−0.0981684	−	0.995170i	$-0.531298\pi$
$733$	−5.66784e10			−0.196337			−0.0981684	+	0.995170i	$0.531298\pi$
$734$		−	3.26818e11i		−	1.12596i
$735$	7.06090e10	−	4.07661e10i	0.241942	−	0.139685i
$736$	−2.25282e10	−	1.30067e10i	−0.0767744	−	0.0443257i
$737$	−5.92967e10	+	3.42350e10i	−0.200984	+	0.116038i
$738$	−1.48657e10	+	2.57481e10i	−0.0501140	+	0.0868000i
$739$	−1.93337e11	+	3.34869e11i	−0.648241	+	1.12279i	0.335301	+	0.942111i	$0.391162\pi$
$739$	−1.93337e11	+	3.34869e11i	−0.648241	+	1.12279i	−0.983543	+	0.180676i	$0.942171\pi$
$740$			2.21114e11i			0.737376i
$741$	−8.53120e10	−	4.33701e11i	−0.282968	−	1.43852i
$742$	−2.80844e11			−0.926509
$743$	1.60545e11	+	9.26906e10i	0.526794	+	0.304145i	0.739710	−	0.672926i	$-0.234963\pi$
$743$	1.60545e11	+	9.26906e10i	0.526794	+	0.304145i	−0.212916	+	0.977071i	$0.568296\pi$
$744$	1.28630e11	+	7.42648e10i	0.419809	+	0.242377i
$745$	−2.56280e11	−	4.43890e11i	−0.831935	−	1.44095i
$746$	−4.12580e10	+	7.14609e10i	−0.133215	+	0.230735i
$747$	3.19344e10	+	5.53119e10i	0.102559	+	0.177638i
$748$	−5.97824e10			−0.190971
$749$		−	4.85197e11i		−	1.54167i
$750$	−1.40519e11	−	2.43387e11i	−0.444111	−	0.769223i
$751$	−2.98600e11	+	1.72397e11i	−0.938708	+	0.541963i	−0.889555	−	0.456828i	$-0.848985\pi$
$751$	−2.98600e11	+	1.72397e11i	−0.938708	+	0.541963i	−0.0491528	+	0.998791i	$0.515652\pi$
$752$	3.34615e10			0.104634
$753$		−	3.62625e11i		−	1.12792i
$754$	5.99048e11	−	3.45861e11i	1.85343	−	1.07008i
$755$	−1.79034e11	−	1.03365e11i	−0.550994	−	0.318117i
$756$	−1.37905e11	+	7.96198e10i	−0.422177	+	0.243744i
$757$	−2.31359e11	+	4.00725e11i	−0.704534	+	1.22029i	0.262325	+	0.964979i	$0.415511\pi$
$757$	−2.31359e11	+	4.00725e11i	−0.704534	+	1.22029i	−0.966859	+	0.255309i	$0.917823\pi$
$758$	3.31957e10	−	5.74967e10i	0.100555	−	0.174167i
$759$			8.80094e10i			0.265193i
$760$	6.47539e10	−	1.89437e11i	0.194094	−	0.567820i
$761$	−6.19793e11			−1.84802			−0.924012	−	0.382363i	$-0.875111\pi$
$761$	−6.19793e11			−1.84802			−0.924012	+	0.382363i	$0.875111\pi$
$762$	−8.79322e10	−	5.07677e10i	−0.260812	−	0.150580i
$763$	−1.94874e11	−	1.12511e11i	−0.574984	−	0.331967i
$764$	−9.25531e10	−	1.60307e11i	−0.271655	−	0.470520i
$765$	5.18417e10	−	8.97924e10i	0.151368	−	0.262177i
$766$	1.15113e11	+	1.99382e11i	0.334357	+	0.579124i
$767$	−3.68271e11			−1.06411
$768$		−	1.82710e10i		−	0.0525191i
$769$	2.61975e11	+	4.53754e11i	0.749125	+	1.29752i	0.948242	+	0.317547i	$0.102859\pi$
$769$	2.61975e11	+	4.53754e11i	0.749125	+	1.29752i	−0.199117	+	0.979976i	$0.563807\pi$
$770$	2.06184e11	−	1.19040e11i	0.586532	−	0.338635i
$771$	5.39507e10			0.152679
$772$			1.19316e11i			0.335915i
$773$	−3.51016e11	+	2.02659e11i	−0.983124	+	0.567607i	−0.903212	−	0.429195i	$-0.858797\pi$
$773$	−3.51016e11	+	2.02659e11i	−0.983124	+	0.567607i	−0.0799124	+	0.996802i	$0.525464\pi$
$774$	−4.87477e10	−	2.81445e10i	−0.135828	−	0.0784206i
$775$	9.58726e11	−	5.53521e11i	2.65759	−	1.53436i
$776$	−9.68561e10	+	1.67760e11i	−0.267104	+	0.462637i
$777$	−1.19322e11	+	2.06671e11i	−0.327367	+	0.567016i
$778$			2.79246e11i			0.762200i
$779$	5.74487e10	−	1.68066e11i	0.156002	−	0.456383i
$780$	−4.60533e11			−1.24418
$781$	−7.93239e10	−	4.57977e10i	−0.213206	−	0.123095i
$782$	6.97005e10	+	4.02416e10i	0.186384	+	0.107609i
$783$	3.54477e11	+	6.13972e11i	0.943064	+	1.63343i
$784$	9.25050e9	−	1.60223e10i	0.0244850	−	0.0424093i
$785$	2.77295e11	+	4.80289e11i	0.730236	+	1.26481i
$786$	2.45951e11			0.644404
$787$			3.63751e11i			0.948210i	0.880468	+	0.474105i	$0.157228\pi$
$787$			3.63751e11i			0.948210i	−0.880468	+	0.474105i	$0.842772\pi$
$788$	2.71773e10	+	4.70725e10i	0.0704859	+	0.122085i
$789$	−2.52170e11	+	1.45591e11i	−0.650707	+	0.375686i
$790$	−5.06343e11			−1.29998
$791$		−	2.44183e10i		−	0.0623750i
$792$	2.22807e10	−	1.28638e10i	0.0566276	−	0.0326940i
$793$	−7.31044e11	−	4.22068e11i	−1.84863	−	1.06731i
$794$	7.32628e10	−	4.22983e10i	0.184332	−	0.106424i
$795$	4.16229e11	−	7.20929e11i	1.04199	−	1.80478i
$796$	4.64467e9	−	8.04480e9i	0.0115692	−	0.0200384i
$797$		−	4.24845e11i		−	1.05293i	−0.850198	−	0.526463i	$-0.823518\pi$
$797$		−	4.24845e11i		−	1.05293i	0.850198	−	0.526463i	$-0.176482\pi$
$798$	1.62752e11	−	1.42120e11i	0.401342	−	0.350464i
$799$	−1.03527e11			−0.254019
$800$	−1.17935e11	−	6.80900e10i	−0.287928	−	0.166235i
$801$	−1.51253e11	−	8.73260e10i	−0.367430	−	0.212136i
$802$	−1.01836e11	−	1.76385e11i	−0.246153	−	0.426349i
$803$	−6.98091e10	+	1.20913e11i	−0.167900	+	0.290811i
$804$	3.23719e10	+	5.60697e10i	0.0774718	+	0.134185i
$805$	−3.20521e11			−0.763261
$806$		−	8.49527e11i		−	2.01297i
$807$	−8.70576e10	−	1.50788e11i	−0.205264	−	0.355528i
$808$	5.96335e10	−	3.44294e10i	0.139909	−	0.0807763i
$809$	3.88068e11			0.905970			0.452985	−	0.891518i	$-0.350359\pi$
$809$	3.88068e11			0.905970			0.452985	+	0.891518i	$0.350359\pi$
$810$		−	3.20177e11i		−	0.743790i
$811$	5.44170e11	−	3.14177e11i	1.25791	−	0.726257i	0.285246	−	0.958454i	$-0.407925\pi$
$811$	5.44170e11	−	3.14177e11i	1.25791	−	0.726257i	0.972669	+	0.232197i	$0.0745914\pi$
$812$	2.92835e11	+	1.69068e11i	0.673595	+	0.388900i
$813$	−1.64008e11	+	9.46903e10i	−0.375408	+	0.216742i
$814$	8.48758e10	−	1.47009e11i	0.193324	−	0.334847i
$815$	1.11937e11	−	1.93881e11i	0.253714	−	0.439445i
$816$			5.65289e10i			0.127500i
$817$	3.18191e11	+	1.08765e11i	0.714168	+	0.244119i
$818$	−8.09404e10			−0.180781
$819$	1.79155e11	+	1.03435e11i	0.398192	+	0.229896i
$820$	−1.60263e11	−	9.25279e10i	−0.354469	−	0.204653i
$821$	−3.34048e11	−	5.78588e11i	−0.735252	−	1.27349i	−0.954613	−	0.297850i	$-0.903731\pi$
$821$	−3.34048e11	−	5.78588e11i	−0.735252	−	1.27349i	0.219361	−	0.975644i	$-0.429603\pi$
$822$	−2.49652e11	+	4.32411e11i	−0.546825	+	0.947129i
$823$	−1.96025e11	−	3.39525e11i	−0.427279	−	0.740069i	0.569351	−	0.822094i	$-0.307194\pi$
$823$	−1.96025e11	−	3.39525e11i	−0.427279	−	0.740069i	−0.996630	+	0.0820255i	$0.973861\pi$
$824$	6.39789e10			0.138780
$825$			4.60729e11i			0.994558i
$826$	−9.00116e10	−	1.55905e11i	−0.193365	−	0.334918i
$827$	−5.73484e11	+	3.31101e11i	−1.22602	+	0.707845i	−0.966196	−	0.257809i	$-0.916999\pi$
$827$	−5.73484e11	+	3.31101e11i	−1.22602	+	0.707845i	−0.259829	+	0.965655i	$0.583666\pi$
$828$	−3.46362e10			−0.0736901
$829$			4.86594e11i			1.03026i	0.857111	+	0.515132i	$0.172257\pi$
$829$			4.86594e11i			1.03026i	−0.857111	+	0.515132i	$0.827743\pi$
$830$	−3.44276e11	+	1.98768e11i	−0.725429	+	0.418827i
$831$	3.82826e11	+	2.21025e11i	0.802781	+	0.463486i
$832$	−9.05018e10	+	5.22513e10i	−0.188870	+	0.109044i
$833$	−2.86203e10	+	4.95717e10i	−0.0594420	+	0.102957i
$834$	−1.93324e11	+	3.34846e11i	−0.399596	+	0.692120i
$835$			6.66796e11i			1.37166i
$836$	−1.15769e11	+	1.01093e11i	−0.237010	+	0.206964i
$837$	8.70691e11			1.77403
$838$	3.90301e11	+	2.25340e11i	0.791450	+	0.456944i
$839$	−6.08753e11	−	3.51464e11i	−1.22855	−	0.709304i	−0.261824	−	0.965116i	$-0.584324\pi$
$839$	−6.08753e11	−	3.51464e11i	−1.22855	−	0.709304i	−0.966727	+	0.255812i	$0.917657\pi$
$840$	−1.12562e11	−	1.94963e11i	−0.226087	−	0.391593i
$841$	5.02589e11	−	8.70510e11i	1.00468	−	1.74016i
$842$	−7.22452e10	−	1.25132e11i	−0.143734	−	0.248955i
$843$	4.37328e11			0.865959
$844$		−	2.67670e11i		−	0.527509i
$845$	8.84368e11	+	1.53177e12i	1.73463	+	3.00446i
$846$	3.85842e10	−	2.22766e10i	0.0753230	−	0.0434878i
$847$	2.78746e11			0.541596
$848$		−	1.88898e11i		−	0.365295i
$849$	−6.18191e11	+	3.56913e11i	−1.18985	+	0.686959i
$850$	3.64882e11	+	2.10665e11i	0.698999	+	0.403567i
$851$	−1.97914e11	+	1.14266e11i	−0.377362	+	0.217870i
$852$	−4.33053e10	+	7.50070e10i	−0.0821832	+	0.142345i
$853$	2.40694e10	−	4.16895e10i	0.0454642	−	0.0787464i	−0.842398	−	0.538856i	$-0.818857\pi$
$853$	2.40694e10	−	4.16895e10i	0.0454642	−	0.0787464i	0.887862	+	0.460110i	$0.152190\pi$
$854$		−	4.12642e11i		−	0.775786i
$855$	−5.14483e10	−	2.61548e11i	−0.0962735	−	0.489426i
$856$	3.26348e11			0.607835
$857$	−2.58162e11	−	1.49050e11i	−0.478595	−	0.276317i	0.241236	−	0.970467i	$-0.422447\pi$
$857$	−2.58162e11	−	1.49050e11i	−0.478595	−	0.276317i	−0.719831	+	0.694149i	$0.755781\pi$
$858$	3.06189e11	+	1.76778e11i	0.564990	+	0.326197i
$859$	−1.39351e11	−	2.41363e11i	−0.255940	−	0.443301i	0.709211	−	0.704997i	$-0.249052\pi$
$859$	−1.39351e11	−	2.41363e11i	−0.255940	−	0.443301i	−0.965150	+	0.261696i	$0.915718\pi$
$860$	1.75179e11	−	3.03419e11i	0.320249	−	0.554688i
$861$	−9.98633e10	−	1.72968e11i	−0.181716	−	0.314741i
$862$	−9.30619e10			−0.168556
$863$			1.00492e12i			1.81171i	0.423585	+	0.905857i	$0.360772\pi$
$863$			1.00492e12i			1.81171i	−0.423585	+	0.905857i	$0.639228\pi$
$864$	−5.35530e10	−	9.27564e10i	−0.0961011	−	0.166452i
$865$	−7.68883e11	+	4.43915e11i	−1.37340	+	0.792931i
$866$	−4.29736e11			−0.764064
$867$			2.99908e11i			0.530776i
$868$	3.59640e11	−	2.07639e11i	0.633563	−	0.365788i
$869$	3.36646e11	+	1.94363e11i	0.590329	+	0.340827i
$870$	−8.68000e11	+	5.01140e11i	−1.51510	+	0.874746i
$871$	1.85154e11	−	3.20695e11i	0.321706	−	0.557211i
$872$	7.56756e10	−	1.31074e11i	0.130885	−	0.226699i
$873$			2.57923e11i			0.444052i
$874$	2.03024e11	−	3.99363e10i	0.347938	−	0.0684419i
$875$	−7.85763e11			−1.34048
$876$	1.14333e11	+	6.60100e10i	0.194157	+	0.112097i
$877$	8.18175e11	+	4.72373e11i	1.38308	+	0.798522i	0.992523	−	0.122056i	$-0.0389488\pi$
$877$	8.18175e11	+	4.72373e11i	1.38308	+	0.798522i	0.390558	+	0.920578i	$0.372282\pi$
$878$	−3.65385e10	−	6.32865e10i	−0.0614854	−	0.106496i
$879$	1.88337e11	−	3.26209e11i	0.315486	−	0.546438i
$880$	8.00676e10	+	1.38681e11i	0.133514	+	0.231253i
$881$	7.10781e11			1.17987			0.589933	−	0.807452i	$-0.299154\pi$
$881$	7.10781e11			1.17987			0.589933	+	0.807452i	$0.299154\pi$
$882$		−	2.46337e10i		−	0.0407056i
$883$	2.88352e11	+	4.99440e11i	0.474330	+	0.821563i	0.999568	−	0.0293921i	$-0.00935715\pi$
$883$	2.88352e11	+	4.99440e11i	0.474330	+	0.821563i	−0.525238	+	0.850955i	$0.676024\pi$
$884$	2.80005e11	−	1.61661e11i	0.458518	−	0.264726i
$885$	5.33612e11			0.869866
$886$			1.30593e11i			0.211926i
$887$	1.65998e11	−	9.58390e10i	0.268169	−	0.154827i	−0.359886	−	0.932996i	$-0.617185\pi$
$887$	1.65998e11	−	9.58390e10i	0.268169	−	0.154827i	0.628055	+	0.778169i	$0.283851\pi$
$888$	−1.39009e11	−	8.02568e10i	−0.223558	−	0.129071i
$889$	−2.45852e11	+	1.41942e11i	−0.393610	+	0.227251i
$890$	5.43540e11	−	9.41440e11i	0.866307	−	1.50049i
$891$	−1.22902e11	+	2.12872e11i	−0.195006	+	0.337760i
$892$			4.60312e11i			0.727097i
$893$	−2.00480e11	+	1.75065e11i	−0.315257	+	0.275292i
$894$	3.72083e11			0.582492
$895$	−7.37677e11	−	4.25898e11i	−1.14967	−	0.663763i
$896$	−4.42403e10	−	2.55421e10i	−0.0686414	−	0.0396301i
$897$	−2.37991e11	−	4.12213e11i	−0.367613	−	0.636725i
$898$	1.08444e11	−	1.87831e11i	0.166763	−	0.288843i
$899$	−9.24432e11	−	1.60116e12i	−1.41526	−	2.45130i
$900$	−1.81321e11			−0.276361
$901$			5.84435e11i			0.886822i
$902$	7.10347e10	+	1.23036e11i	0.107311	+	0.185868i
$903$	3.27473e11	−	1.89067e11i	0.492521	−	0.284357i
$904$	1.64240e10			0.0245926
$905$			2.48107e11i			0.369866i
$906$	1.29966e11	−	7.50360e10i	0.192894	−	0.111367i
$907$	−3.71873e11	−	2.14701e11i	−0.549498	−	0.317253i	0.199422	−	0.979914i	$-0.436094\pi$
$907$	−3.71873e11	−	2.14701e11i	−0.549498	−	0.317253i	−0.748919	+	0.662661i	$0.769427\pi$
$908$	−4.49409e11	+	2.59467e11i	−0.661148	+	0.381714i
$909$	4.58420e10	−	7.94006e10i	0.0671441	−	0.116297i
$910$	−6.43808e11	+	1.11511e12i	−0.938838	+	1.62612i
$911$		−	8.01686e11i		−	1.16394i	−0.813210	−	0.581971i	$-0.802282\pi$
$911$		−	8.01686e11i		−	1.16394i	0.813210	−	0.581971i	$-0.197718\pi$
$912$	9.55910e10	+	1.09468e11i	0.138178	+	0.158237i
$913$	3.05193e11			0.439229
$914$	−1.11448e11	−	6.43446e10i	−0.159694	−	0.0921993i
$915$	1.05926e12	+	6.11562e11i	1.51118	+	0.872481i
$916$	5.95862e10	+	1.03206e11i	0.0846377	+	0.146597i
$917$	3.43830e11	−	5.95531e11i	0.486257	−	0.842222i
$918$	1.65688e11	+	2.86981e11i	0.233303	+	0.404093i
$919$	9.36742e11			1.31328			0.656641	−	0.754203i	$-0.271977\pi$
$919$	9.36742e11			1.31328			0.656641	+	0.754203i	$0.271977\pi$
$920$		−	2.15585e11i		−	0.300931i
$921$	−5.42248e11	−	9.39202e11i	−0.753633	−	1.30533i
$922$	1.62821e11	−	9.40050e10i	0.225314	−	0.130085i
$923$	4.95377e11			0.682541
$924$			1.72830e11i			0.237100i
$925$	−1.03608e12	+	5.98181e11i	−1.41523	+	0.817082i
$926$	7.97464e11	+	4.60416e11i	1.08459	+	0.626190i
$927$	7.37736e10	−	4.25932e10i	0.0999038	−	0.0576795i
$928$	−1.13717e11	+	1.96963e11i	−0.153332	+	0.265579i
$929$	−3.46016e11	+	5.99317e11i	−0.464551	+	0.804626i	−0.999181	−	0.0404603i	$-0.987118\pi$
$929$	−3.46016e11	+	5.99317e11i	−0.464551	+	0.804626i	0.534630	+	0.845086i	$0.320451\pi$
$930$			1.23093e12i			1.64552i
$931$	2.84031e10	+	1.44393e11i	0.0378066	+	0.192197i
$932$	−6.41126e11			−0.849728
$933$	4.45579e11	+	2.57255e11i	0.588029	+	0.339498i
$934$	−5.27157e11	−	3.04355e11i	−0.692712	−	0.399938i
$935$	−2.47722e11	−	4.29068e11i	−0.324130	−	0.561409i
$936$	−6.95713e10	+	1.20501e11i	−0.0906415	+	0.156996i
$937$	−1.20278e11	−	2.08328e11i	−0.156037	−	0.270264i	0.777399	−	0.629008i	$-0.216539\pi$
$937$	−1.20278e11	−	2.08328e11i	−0.156037	−	0.270264i	−0.933436	+	0.358743i	$0.883205\pi$
$938$	1.81018e11			0.233836
$939$			4.38853e11i			0.564491i
$940$	1.38655e11	+	2.40158e11i	0.177593	+	0.307600i
$941$	−1.03630e12	+	5.98311e11i	−1.32169	+	0.763077i	−0.983998	−	0.178181i	$-0.942979\pi$
$941$	−1.03630e12	+	5.98311e11i	−1.32169	+	0.763077i	−0.337690	+	0.941257i	$0.609645\pi$
$942$	−4.02594e11			−0.511286
$943$		−	1.91264e11i		−	0.241872i
$944$	1.04863e11	−	6.05426e10i	0.132049	−	0.0762383i
$945$	−1.14289e12	−	6.59847e11i	−1.43310	−	0.827400i
$946$	−2.32938e11	+	1.34487e11i	−0.290855	+	0.167925i
$947$	6.48439e11	−	1.12313e12i	0.806249	−	1.39646i	−0.109196	−	0.994020i	$-0.534828\pi$
$947$	6.48439e11	−	1.12313e12i	0.806249	−	1.39646i	0.915445	−	0.402444i	$-0.131839\pi$
$948$	1.83785e11	−	3.18325e11i	0.227550	−	0.394128i
$949$		−	7.55099e11i		−	0.930978i
$950$	1.06283e12	−	2.09066e11i	1.30488	−	0.256679i
$951$	2.50758e11			0.306572
$952$	1.36876e11	+	7.90252e10i	0.166640	+	0.0962095i
$953$	−1.15542e12	−	6.67080e11i	−1.40077	−	0.808735i	−0.406299	−	0.913740i	$-0.633181\pi$
$953$	−1.15542e12	−	6.67080e11i	−1.40077	−	0.808735i	−0.994472	+	0.105005i	$0.966514\pi$
$954$	−1.25757e11	−	2.17817e11i	−0.151823	−	0.262965i
$955$	7.67031e11	−	1.32854e12i	0.922145	−	1.59720i
$956$	−3.57866e10	−	6.19843e10i	−0.0428439	−	0.0742079i
$957$	7.69462e11			0.917359
$958$			4.63154e11i			0.549875i
$959$	6.98009e11	+	1.20899e12i	0.825252	+	1.42938i
$960$	1.31134e11	−	7.57102e10i	0.154394	−	0.0891393i
$961$	−1.41776e12			−1.66230
$962$			9.18070e11i			1.07195i
$963$	3.76309e11	−	2.17262e11i	0.437562	−	0.252627i
$964$	4.04710e10	+	2.33659e10i	0.0468636	+	0.0270567i
$965$	−8.56350e11	+	4.94414e11i	−0.987511	+	0.570140i
$966$	1.16338e11	−	2.01503e11i	0.133602	−	0.231406i
$967$	3.70910e11	−	6.42435e11i	0.424192	−	0.734722i	−0.572153	−	0.820147i	$-0.693892\pi$
$967$	3.70910e11	−	6.42435e11i	0.424192	−	0.734722i	0.996345	+	0.0854251i	$0.0272248\pi$
$968$			1.87487e11i			0.213536i
$969$	−2.95750e11	−	3.38686e11i	−0.335452	−	0.384151i
$970$	−1.60538e12			−1.81339
$971$	8.36122e11	+	4.82735e11i	0.940574	+	0.543040i	0.890140	−	0.455687i	$-0.150606\pi$
$971$	8.36122e11	+	4.82735e11i	0.940574	+	0.543040i	0.0504335	+	0.998727i	$0.483940\pi$
$972$	−2.18954e11	−	1.26413e11i	−0.245295	−	0.141621i
$973$	5.40518e11	+	9.36204e11i	0.603057	+	1.04453i
$974$	5.08273e11	−	8.80354e11i	0.564756	−	0.978187i
$975$	−1.24588e12	−	2.15794e12i	−1.37867	−	2.38792i
$976$	2.77547e11			0.305870
$977$		−	8.26011e11i		−	0.906583i	−0.891362	−	0.453292i	$-0.850250\pi$
$977$		−	8.26011e11i		−	0.906583i	0.891362	−	0.453292i	$-0.149750\pi$
$978$	8.12587e10	+	1.40744e11i	0.0888208	+	0.153842i
$979$	−7.22754e11	+	4.17282e11i	−0.786792	+	0.454254i
$980$	1.53326e11			0.166231
$981$		−	2.01521e11i		−	0.217592i
$982$	−1.59629e11	+	9.21616e10i	−0.171658	+	0.0991070i
$983$	−8.55836e11	−	4.94117e11i	−0.916593	−	0.529195i	−0.0340461	−	0.999420i	$-0.510839\pi$
$983$	−8.55836e11	−	4.94117e11i	−0.916593	−	0.529195i	−0.882546	+	0.470225i	$0.844173\pi$
$984$	1.16340e11	−	6.71689e10i	0.124093	−	0.0716453i
$985$	−2.25231e11	+	3.90112e11i	−0.239268	+	0.414424i
$986$	3.51830e11	−	6.09387e11i	0.372242	−	0.644742i
$987$			2.99295e11i			0.315378i
$988$	2.68860e11	−	7.86548e11i	0.282162	−	0.825463i
$989$	3.62111e11			0.378492
$990$	1.84651e11	+	1.06608e11i	0.192225	+	0.110981i
$991$	6.46773e11	+	3.73414e11i	0.670590	+	0.387165i	0.796300	−	0.604902i	$-0.206788\pi$
$991$	6.46773e11	+	3.73414e11i	0.670590	+	0.387165i	−0.125710	+	0.992067i	$0.540121\pi$
$992$	1.39659e11	+	2.41897e11i	0.144219	+	0.249795i
$993$	6.28881e10	−	1.08925e11i	0.0646802	−	0.112029i
$994$	1.21078e11	+	2.09714e11i	0.124028	+	0.214823i
$995$	7.69851e10			0.0785443
$996$		−	2.88584e11i		−	0.293248i
$997$	1.44718e11	+	2.50659e11i	0.146468	+	0.253689i	0.929920	−	0.367763i	$-0.119876\pi$
$997$	1.44718e11	+	2.50659e11i	0.146468	+	0.253689i	−0.783452	+	0.621452i	$0.786543\pi$
$998$	1.74781e11	−	1.00910e11i	0.176186	−	0.101721i
$999$	−9.40941e11			−0.944715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.9.d.a.27.4	✓	24
19.12	odd	6	inner	38.9.d.a.31.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.9.d.a.27.4	✓	24	1.1	even	1	trivial
38.9.d.a.31.4	yes	24	19.12	odd	6	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.79796 - 5.65685i) q^{2} +(58.9458 + 34.0324i) q^{3} +(64.0000 + 110.851i) q^{4} +(-530.398 + 918.676i) q^{5} +(-385.033 - 666.896i) q^{6} -2153.04 q^{7} -1448.15i q^{8} +(-964.092 - 1669.86i) q^{9} +O(q^{10})\)	\(q+(-9.79796 - 5.65685i) q^{2} +(58.9458 + 34.0324i) q^{3} +(64.0000 + 110.851i) q^{4} +(-530.398 + 918.676i) q^{5} +(-385.033 - 666.896i) q^{6} -2153.04 q^{7} -1448.15i q^{8} +(-964.092 - 1669.86i) q^{9} +(10393.6 - 6000.77i) q^{10} -9213.72 q^{11} +8712.29i q^{12} +(43154.6 - 24915.3i) q^{13} +(21095.4 + 12179.4i) q^{14} +(-62529.5 + 36101.4i) q^{15} +(-8192.00 + 14189.0i) q^{16} +(25345.4 - 43899.4i) q^{17} +21814.9i q^{18} +(-25153.1 - 127871. i) q^{19} -135782. q^{20} +(-126913. - 73273.2i) q^{21} +(90275.6 + 52120.7i) q^{22} +(-70168.5 - 121535. i) q^{23} +(49284.2 - 85362.7i) q^{24} +(-367332. - 636237. i) q^{25} -563770. q^{26} -577815. i q^{27} +(-137795. - 238667. i) q^{28} +(-1.06258e6 + 613479. i) q^{29} +816882. q^{30} +1.50687e6i q^{31} +(160530. - 92681.9i) q^{32} +(-543110. - 313565. i) q^{33} +(-496665. + 286750. i) q^{34} +(1.14197e6 - 1.97795e6i) q^{35} +(123404. - 213742. i) q^{36} -1.62845e6i q^{37} +(-476897. + 1.39516e6i) q^{38} +3.39171e6 q^{39} +(1.33039e6 + 768098. i) q^{40} +(1.18030e6 + 681445. i) q^{41} +(828991. + 1.43586e6i) q^{42} +(-1.29015e6 + 2.23461e6i) q^{43} +(-589678. - 1.02135e6i) q^{44} +2.04541e6 q^{45} +1.58773e6i q^{46} +(-1.02116e6 - 1.76871e6i) q^{47} +(-965769. + 557587. i) q^{48} -1.12921e6 q^{49} +8.31177e6i q^{50} +(2.98801e6 - 1.72513e6i) q^{51} +(5.52379e6 + 3.18916e6i) q^{52} +(-9.98477e6 + 5.76471e6i) q^{53} +(-3.26861e6 + 5.66140e6i) q^{54} +(4.88694e6 - 8.46442e6i) q^{55} +3.11794e6i q^{56} +(2.86907e6 - 8.39346e6i) q^{57} +1.38814e7 q^{58} +(-6.40032e6 - 3.69523e6i) q^{59} +(-8.00378e6 - 4.62098e6i) q^{60} +(-8.47005e6 - 1.46706e7i) q^{61} +(8.52414e6 - 1.47642e7i) q^{62} +(2.07573e6 + 3.59527e6i) q^{63} -2.09715e6 q^{64} +5.28602e7i q^{65} +(3.54758e6 + 6.14459e6i) q^{66} +(6.43570e6 - 3.71565e6i) q^{67} +6.48841e6 q^{68} -9.55200e6i q^{69} +(-2.23779e7 + 1.29199e7i) q^{70} +(8.60933e6 + 4.97060e6i) q^{71} +(-2.41821e6 + 1.39615e6i) q^{72} +(7.57665e6 - 1.31231e7i) q^{73} +(-9.21190e6 + 1.59555e7i) q^{74} -5.00047e7i q^{75} +(1.25648e7 - 1.09720e7i) q^{76} +1.98375e7 q^{77} +(-3.32319e7 - 1.91864e7i) q^{78} +(-3.65375e7 - 2.10949e7i) q^{79} +(-8.69004e6 - 1.50516e7i) q^{80} +(1.33390e7 - 2.31038e7i) q^{81} +(-7.70967e6 - 1.33535e7i) q^{82} -3.31238e7 q^{83} -1.87579e7i q^{84} +(2.68863e7 + 4.65684e7i) q^{85} +(2.52817e7 - 1.45964e7i) q^{86} -8.35126e7 q^{87} +1.33429e7i q^{88} +(7.84432e7 - 4.52892e7i) q^{89} +(-2.00409e7 - 1.15706e7i) q^{90} +(-9.29137e7 + 5.36438e7i) q^{91} +(8.98156e6 - 1.55565e7i) q^{92} +(-5.12823e7 + 8.88236e7i) q^{93} +2.31063e7i q^{94} +(1.30813e8 + 4.47148e7i) q^{95} +1.26167e7 q^{96} +(-1.15844e8 - 6.68824e7i) q^{97} +(1.10640e7 + 6.38778e6i) q^{98} +(8.88287e6 + 1.53856e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9}+O(q^{10}) \) 24 * q + 168 * q^3 + 1536 * q^4 - 558 * q^5 + 896 * q^6 + 11992 * q^7 + 18448 * q^9	\( 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9} + 33516 q^{11} + 60870 q^{13} - 71424 q^{14} - 351930 q^{15} - 196608 q^{16} + 3546 q^{17} - 727738 q^{19} - 142848 q^{20} - 674568 q^{21} - 681600 q^{22} + 726 q^{23} - 114688 q^{24} - 277874 q^{25} - 960000 q^{26} + 767488 q^{28} - 254286 q^{29} - 71168 q^{30} - 2796150 q^{33} - 2740224 q^{34} - 690672 q^{35} - 2361344 q^{36} - 6829056 q^{38} - 1599924 q^{39} - 5153976 q^{41} + 4153600 q^{42} + 5692338 q^{43} + 2145024 q^{44} + 42653840 q^{45} + 11113938 q^{47} - 2752512 q^{48} + 17359944 q^{49} + 62169786 q^{51} + 7791360 q^{52} + 10399050 q^{53} - 24215680 q^{54} + 40181572 q^{55} - 27798558 q^{57} - 10126848 q^{58} - 58809492 q^{59} - 45047040 q^{60} - 45012614 q^{61} + 5892096 q^{62} + 62488724 q^{63} - 50331648 q^{64} + 45107968 q^{66} - 93677268 q^{67} + 907776 q^{68} - 291840 q^{70} + 5993046 q^{71} + 11698176 q^{72} + 23359860 q^{73} - 31474944 q^{74} - 1303552 q^{76} + 35611680 q^{77} + 94099200 q^{78} - 93221166 q^{79} - 9142272 q^{80} - 115510580 q^{81} + 6074880 q^{82} - 194283156 q^{83} - 15300674 q^{85} + 58611456 q^{86} + 89779380 q^{87} - 49833126 q^{89} - 63377664 q^{90} - 101275308 q^{91} - 92928 q^{92} - 157549992 q^{93} - 87570126 q^{95} - 29360128 q^{96} - 178814556 q^{97} - 88409088 q^{98} - 54444376 q^{99}+O(q^{100}) \) 24 * q + 168 * q^3 + 1536 * q^4 - 558 * q^5 + 896 * q^6 + 11992 * q^7 + 18448 * q^9 + 33516 * q^11 + 60870 * q^13 - 71424 * q^14 - 351930 * q^15 - 196608 * q^16 + 3546 * q^17 - 727738 * q^19 - 142848 * q^20 - 674568 * q^21 - 681600 * q^22 + 726 * q^23 - 114688 * q^24 - 277874 * q^25 - 960000 * q^26 + 767488 * q^28 - 254286 * q^29 - 71168 * q^30 - 2796150 * q^33 - 2740224 * q^34 - 690672 * q^35 - 2361344 * q^36 - 6829056 * q^38 - 1599924 * q^39 - 5153976 * q^41 + 4153600 * q^42 + 5692338 * q^43 + 2145024 * q^44 + 42653840 * q^45 + 11113938 * q^47 - 2752512 * q^48 + 17359944 * q^49 + 62169786 * q^51 + 7791360 * q^52 + 10399050 * q^53 - 24215680 * q^54 + 40181572 * q^55 - 27798558 * q^57 - 10126848 * q^58 - 58809492 * q^59 - 45047040 * q^60 - 45012614 * q^61 + 5892096 * q^62 + 62488724 * q^63 - 50331648 * q^64 + 45107968 * q^66 - 93677268 * q^67 + 907776 * q^68 - 291840 * q^70 + 5993046 * q^71 + 11698176 * q^72 + 23359860 * q^73 - 31474944 * q^74 - 1303552 * q^76 + 35611680 * q^77 + 94099200 * q^78 - 93221166 * q^79 - 9142272 * q^80 - 115510580 * q^81 + 6074880 * q^82 - 194283156 * q^83 - 15300674 * q^85 + 58611456 * q^86 + 89779380 * q^87 - 49833126 * q^89 - 63377664 * q^90 - 101275308 * q^91 - 92928 * q^92 - 157549992 * q^93 - 87570126 * q^95 - 29360128 * q^96 - 178814556 * q^97 - 88409088 * q^98 - 54444376 * q^99

Introduction

L-functions

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