LMFDB - Embedded newform 16.12.e.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,12,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	16.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:	$12.2934908890$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	16.13
Dual form			16.12.e.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-33.6365 + 30.2752i) q^{2} +(-4.32776 - 4.32776i) q^{3} +(214.830 - 2036.70i) q^{4} +(2233.99 - 2233.99i) q^{5} +(276.594 + 14.5472i) q^{6} +71414.8i q^{7} +(54435.3 + 75011.5i) q^{8} -177110. i q^{9} +O(q^{10})$	\(q+(-33.6365 + 30.2752i) q^{2} +(-4.32776 - 4.32776i) q^{3} +(214.830 - 2036.70i) q^{4} +(2233.99 - 2233.99i) q^{5} +(276.594 + 14.5472i) q^{6} +71414.8i q^{7} +(54435.3 + 75011.5i) q^{8} -177110. i q^{9} +(-7509.26 + 142778. i) q^{10} +(-236433. + 236433. i) q^{11} +(-9744.08 + 7884.62i) q^{12} +(-282.811 - 282.811i) q^{13} +(-2.16209e6 - 2.40215e6i) q^{14} -19336.4 q^{15} +(-4.10200e6 - 875089. i) q^{16} -8.99999e6 q^{17} +(5.36202e6 + 5.95735e6i) q^{18} +(-1.07066e7 - 1.07066e7i) q^{19} +(-4.07005e6 - 5.02991e6i) q^{20} +(309066. - 309066. i) q^{21} +(794737. - 1.51108e7i) q^{22} +3.55394e7i q^{23} +(89049.0 - 560215. i) q^{24} +3.88467e7i q^{25} +(18074.9 + 950.630i) q^{26} +(-1.53314e6 + 1.53314e6i) q^{27} +(1.45451e8 + 1.53421e7i) q^{28} +(-4.42357e7 - 4.42357e7i) q^{29} +(650408. - 585412. i) q^{30} -1.07402e8 q^{31} +(1.64470e8 - 9.47537e7i) q^{32} +2.04645e6 q^{33} +(3.02728e8 - 2.72476e8i) q^{34} +(1.59540e8 + 1.59540e8i) q^{35} +(-3.60719e8 - 3.80485e7i) q^{36} +(-4.45048e8 + 4.45048e8i) q^{37} +(6.84274e8 + 3.59886e7i) q^{38} +2447.88i q^{39} +(2.89183e8 + 4.59672e7i) q^{40} -1.29648e8i q^{41} +(-1.03888e6 + 1.97529e7i) q^{42} +(-5.58350e8 + 5.58350e8i) q^{43} +(4.30751e8 + 5.32337e8i) q^{44} +(-3.95662e8 - 3.95662e8i) q^{45} +(-1.07596e9 - 1.19542e9i) q^{46} +4.62220e8 q^{47} +(1.39653e7 + 2.15396e7i) q^{48} -3.12275e9 q^{49} +(-1.17609e9 - 1.30667e9i) q^{50} +(3.89498e7 + 3.89498e7i) q^{51} +(-636758. + 515245. i) q^{52} +(1.27823e9 - 1.27823e9i) q^{53} +(5.15342e6 - 9.79853e7i) q^{54} +1.05638e9i q^{55} +(-5.35694e9 + 3.88749e9i) q^{56} +9.26709e7i q^{57} +(2.82717e9 + 1.48692e8i) q^{58} +(5.52124e9 - 5.52124e9i) q^{59} +(-4.15403e6 + 3.93824e7i) q^{60} +(-1.52419e9 - 1.52419e9i) q^{61} +(3.61261e9 - 3.25160e9i) q^{62} +1.26482e10 q^{63} +(-2.66353e9 + 8.16655e9i) q^{64} -1.26360e6 q^{65} +(-6.88355e7 + 6.19567e7i) q^{66} +(1.43834e10 + 1.43834e10i) q^{67} +(-1.93347e9 + 1.83303e10i) q^{68} +(1.53806e8 - 1.53806e8i) q^{69} +(-1.01965e10 - 5.36272e8i) q^{70} -7.48815e9i q^{71} +(1.32853e10 - 9.64101e9i) q^{72} -1.59325e10i q^{73} +(1.49597e9 - 2.84438e10i) q^{74} +(1.68119e8 - 1.68119e8i) q^{75} +(-2.41062e10 + 1.95060e10i) q^{76} +(-1.68848e10 - 1.68848e10i) q^{77} +(-74109.8 - 82338.0i) q^{78} +6.06745e9 q^{79} +(-1.11188e10 + 7.20890e9i) q^{80} -3.13612e10 q^{81} +(3.92511e9 + 4.36090e9i) q^{82} +(8.65455e9 + 8.65455e9i) q^{83} +(-5.63079e8 - 6.95872e8i) q^{84} +(-2.01059e10 + 2.01059e10i) q^{85} +(1.87682e9 - 3.56851e10i) q^{86} +3.82883e8i q^{87} +(-3.06056e10 - 4.86491e9i) q^{88} +5.51864e10i q^{89} +(2.52874e10 + 1.32996e9i) q^{90} +(2.01969e7 - 2.01969e7i) q^{91} +(7.23832e10 + 7.63493e9i) q^{92} +(4.64808e8 + 4.64808e8i) q^{93} +(-1.55475e10 + 1.39938e10i) q^{94} -4.78368e10 q^{95} +(-1.12186e9 - 3.01717e8i) q^{96} -1.47835e11 q^{97} +(1.05038e11 - 9.45417e10i) q^{98} +(4.18746e10 + 4.18746e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8}+O(q^{10}) $ 42 * q - 2 * q^2 - 2 * q^3 + 3080 * q^4 - 2 * q^5 + 30352 * q^6 + 74836 * q^8	\( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8} - 988948 q^{10} - 540846 q^{11} + 2300260 q^{12} - 2 q^{13} - 1829956 q^{14} - 6075004 q^{15} - 3721448 q^{16} - 4 q^{17} - 32219106 q^{18} - 11291290 q^{19} + 68655164 q^{20} + 354292 q^{21} - 85011388 q^{22} - 66180944 q^{24} + 305685384 q^{26} - 66463304 q^{27} - 322075880 q^{28} + 77673206 q^{29} + 290643636 q^{30} + 343549808 q^{31} + 404698568 q^{32} - 4 q^{33} - 882461836 q^{34} - 434731684 q^{35} + 1854387628 q^{36} - 522762058 q^{37} - 1276252832 q^{38} - 483241016 q^{40} + 2372079160 q^{42} + 3824193658 q^{43} - 2657283740 q^{44} + 97301954 q^{45} - 1032658964 q^{46} - 4586900144 q^{47} - 1058870552 q^{48} - 8474257474 q^{49} + 6515930886 q^{50} + 7074245796 q^{51} - 13915491564 q^{52} - 2100608058 q^{53} + 4385621536 q^{54} + 12910845976 q^{56} - 21491153128 q^{58} + 955824746 q^{59} + 25615752768 q^{60} + 2150827022 q^{61} - 15814519760 q^{62} + 27758037828 q^{63} + 9674332160 q^{64} - 1884965292 q^{65} + 10932459412 q^{66} - 3186519018 q^{67} + 13817664656 q^{68} - 16193060732 q^{69} - 27206453120 q^{70} - 20773133628 q^{72} + 14141420908 q^{74} + 28890034486 q^{75} - 11786004940 q^{76} - 22711870540 q^{77} + 37031200508 q^{78} + 48011833792 q^{79} - 8952586328 q^{80} - 90656394430 q^{81} - 81555388352 q^{82} + 55713221118 q^{83} + 61178517160 q^{84} - 84575506252 q^{85} + 10047297860 q^{86} - 162855622152 q^{88} + 160133627736 q^{90} - 147369662716 q^{91} - 169766721928 q^{92} - 69689773328 q^{93} + 160320530128 q^{94} + 375702304500 q^{95} + 230764310192 q^{96} - 4 q^{97} - 108887063494 q^{98} - 286271331106 q^{99}+O(q^{100}) \) 42 * q - 2 * q^2 - 2 * q^3 + 3080 * q^4 - 2 * q^5 + 30352 * q^6 + 74836 * q^8 - 988948 * q^10 - 540846 * q^11 + 2300260 * q^12 - 2 * q^13 - 1829956 * q^14 - 6075004 * q^15 - 3721448 * q^16 - 4 * q^17 - 32219106 * q^18 - 11291290 * q^19 + 68655164 * q^20 + 354292 * q^21 - 85011388 * q^22 - 66180944 * q^24 + 305685384 * q^26 - 66463304 * q^27 - 322075880 * q^28 + 77673206 * q^29 + 290643636 * q^30 + 343549808 * q^31 + 404698568 * q^32 - 4 * q^33 - 882461836 * q^34 - 434731684 * q^35 + 1854387628 * q^36 - 522762058 * q^37 - 1276252832 * q^38 - 483241016 * q^40 + 2372079160 * q^42 + 3824193658 * q^43 - 2657283740 * q^44 + 97301954 * q^45 - 1032658964 * q^46 - 4586900144 * q^47 - 1058870552 * q^48 - 8474257474 * q^49 + 6515930886 * q^50 + 7074245796 * q^51 - 13915491564 * q^52 - 2100608058 * q^53 + 4385621536 * q^54 + 12910845976 * q^56 - 21491153128 * q^58 + 955824746 * q^59 + 25615752768 * q^60 + 2150827022 * q^61 - 15814519760 * q^62 + 27758037828 * q^63 + 9674332160 * q^64 - 1884965292 * q^65 + 10932459412 * q^66 - 3186519018 * q^67 + 13817664656 * q^68 - 16193060732 * q^69 - 27206453120 * q^70 - 20773133628 * q^72 + 14141420908 * q^74 + 28890034486 * q^75 - 11786004940 * q^76 - 22711870540 * q^77 + 37031200508 * q^78 + 48011833792 * q^79 - 8952586328 * q^80 - 90656394430 * q^81 - 81555388352 * q^82 + 55713221118 * q^83 + 61178517160 * q^84 - 84575506252 * q^85 + 10047297860 * q^86 - 162855622152 * q^88 + 160133627736 * q^90 - 147369662716 * q^91 - 169766721928 * q^92 - 69689773328 * q^93 + 160320530128 * q^94 + 375702304500 * q^95 + 230764310192 * q^96 - 4 * q^97 - 108887063494 * q^98 - 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−33.6365	+	30.2752i	−0.743269	+	0.668993i
$2$	−33.6365	+	30.2752i	−0.743269	+	0.668993i
$3$	−4.32776	−	4.32776i	−0.0102824	−	0.0102824i	0.701947	−	0.712229i	$-0.252314\pi$
$3$	−4.32776	−	4.32776i	−0.0102824	−	0.0102824i	−0.712229	+	0.701947i	$0.752314\pi$
$4$	214.830	−	2036.70i	0.104898	−	0.994483i
$5$	2233.99	−	2233.99i	0.319703	−	0.319703i	−0.528950	−	0.848653i	$-0.677414\pi$
$5$	2233.99	−	2233.99i	0.319703	−	0.319703i	0.848653	+	0.528950i	$0.177414\pi$
$6$	276.594	+	14.5472i	0.0145215	+	0.000763741i
$7$			71414.8i			1.60601i	0.595970	+	0.803007i	$0.296768\pi$
$7$			71414.8i			1.60601i	−0.595970	+	0.803007i	$0.703232\pi$
$8$	54435.3	+	75011.5i	0.587335	+	0.809344i
$9$		−	177110.i		−	0.999789i
$10$	−7509.26	+	142778.i	−0.0237464	+	0.451505i
$11$	−236433.	+	236433.i	−0.442638	+	0.442638i	−0.892898	−	0.450259i	$-0.851331\pi$
$11$	−236433.	+	236433.i	−0.442638	+	0.442638i	0.450259	+	0.892898i	$0.351331\pi$
$12$	−9744.08	+	7884.62i	−0.0113043	+	0.00914711i
$13$	−282.811	−	282.811i	−0.000211256	−	0.000211256i	0.707001	−	0.707212i	$-0.250048\pi$
$13$	−282.811	−	282.811i	−0.000211256	−	0.000211256i	−0.707212	+	0.707001i	$0.750048\pi$
$14$	−2.16209e6	−	2.40215e6i	−1.07441	−	1.19370i
$15$	−19336.4			−0.00657466
$16$	−4.10200e6	−	875089.i	−0.977993	−	0.208638i
$17$	−8.99999e6			−1.53735			−0.768675	−	0.639639i	$-0.779084\pi$
$17$	−8.99999e6			−1.53735			−0.768675	+	0.639639i	$0.779084\pi$
$18$	5.36202e6	+	5.95735e6i	0.668851	+	0.743112i
$19$	−1.07066e7	−	1.07066e7i	−0.991986	−	0.991986i	0.00798250	−	0.999968i	$-0.497459\pi$
$19$	−1.07066e7	−	1.07066e7i	−0.991986	−	0.991986i	−0.999968	+	0.00798250i	$0.997459\pi$
$20$	−4.07005e6	−	5.02991e6i	−0.284403	−	0.351475i
$21$	309066.	−	309066.i	0.0165137	−	0.0165137i
$22$	794737.	−	1.51108e7i	0.0328775	−	0.625121i
$23$			3.55394e7i			1.15135i	0.817679	+	0.575675i	$0.195260\pi$
$23$			3.55394e7i			1.15135i	−0.817679	+	0.575675i	$0.804740\pi$
$24$	89049.0	−	560215.i	0.00228280	−	0.0143613i
$25$			3.88467e7i			0.795580i
$26$	18074.9	+	950.630i	0.000298348	+	1.56913e-5i
$27$	−1.53314e6	+	1.53314e6i	−0.0205627	+	0.0205627i
$28$	1.45451e8	+	1.53421e7i	1.59715	+	0.168467i
$29$	−4.42357e7	−	4.42357e7i	−0.400482	−	0.400482i	0.477921	−	0.878403i	$-0.341391\pi$
$29$	−4.42357e7	−	4.42357e7i	−0.400482	−	0.400482i	−0.878403	+	0.477921i	$0.841391\pi$
$30$	650408.	−	585412.i	0.00488674	−	0.00439840i
$31$	−1.07402e8			−0.673785			−0.336892	−	0.941543i	$-0.609376\pi$
$31$	−1.07402e8			−0.673785			−0.336892	+	0.941543i	$0.609376\pi$
$32$	1.64470e8	−	9.47537e7i	0.866489	−	0.499196i
$33$	2.04645e6			0.00910280
$34$	3.02728e8	−	2.72476e8i	1.14267	−	1.02848i
$35$	1.59540e8	+	1.59540e8i	0.513448	+	0.513448i
$36$	−3.60719e8	−	3.80485e7i	−0.994273	−	0.104875i
$37$	−4.45048e8	+	4.45048e8i	−1.05511	+	1.05511i	−0.0567195	+	0.998390i	$0.518064\pi$
$37$	−4.45048e8	+	4.45048e8i	−1.05511	+	1.05511i	−0.998390	+	0.0567195i	$0.981936\pi$
$38$	6.84274e8	+	3.59886e7i	1.40094	+	0.0736810i
$39$			2447.88i			4.34444e-6i
$40$	2.89183e8	+	4.59672e7i	0.446523	+	0.0709770i
$41$		−	1.29648e8i		−	0.174765i	−0.996175	−	0.0873824i	$-0.972150\pi$
$41$		−	1.29648e8i		−	0.174765i	0.996175	−	0.0873824i	$-0.0278502\pi$
$42$	−1.03888e6	+	1.97529e7i	−0.00122658	+	0.0233217i
$43$	−5.58350e8	+	5.58350e8i	−0.579202	+	0.579202i	−0.934683	−	0.355481i	$-0.884317\pi$
$43$	−5.58350e8	+	5.58350e8i	−0.579202	+	0.579202i	0.355481	+	0.934683i	$0.384317\pi$
$44$	4.30751e8	+	5.32337e8i	0.393765	+	0.486628i
$45$	−3.95662e8	−	3.95662e8i	−0.319636	−	0.319636i
$46$	−1.07596e9	−	1.19542e9i	−0.770244	−	0.855762i
$47$	4.62220e8			0.293975			0.146988	−	0.989138i	$-0.453042\pi$
$47$	4.62220e8			0.293975			0.146988	+	0.989138i	$0.453042\pi$
$48$	1.39653e7	+	2.15396e7i	0.00791085	+	0.0122015i
$49$	−3.12275e9			−1.57928
$50$	−1.17609e9	−	1.30667e9i	−0.532237	−	0.591330i
$51$	3.89498e7	+	3.89498e7i	0.0158077	+	0.0158077i
$52$	−636758.	+	515245.i	−0.000232250	+	0.000187930i
$53$	1.27823e9	−	1.27823e9i	0.419847	−	0.419847i	−0.465304	−	0.885151i	$-0.654055\pi$
$53$	1.27823e9	−	1.27823e9i	0.419847	−	0.419847i	0.885151	+	0.465304i	$0.154055\pi$
$54$	5.15342e6	−	9.79853e7i	0.00152732	−	0.0290399i
$55$			1.05638e9i			0.283026i
$56$	−5.35694e9	+	3.88749e9i	−1.29982	+	0.943267i
$57$			9.26709e7i			0.0204001i
$58$	2.82717e9	+	1.48692e8i	0.565586	+	0.0297463i
$59$	5.52124e9	−	5.52124e9i	1.00543	−	1.00543i	0.00544223	−	0.999985i	$-0.498268\pi$
$59$	5.52124e9	−	5.52124e9i	1.00543	−	1.00543i	0.999985	−	0.00544223i	$-0.00173232\pi$
$60$	−4.15403e6	+	3.93824e7i	−0.000689665	+	0.00653838i
$61$	−1.52419e9	−	1.52419e9i	−0.231060	−	0.231060i	0.582075	−	0.813135i	$-0.302241\pi$
$61$	−1.52419e9	−	1.52419e9i	−0.231060	−	0.231060i	−0.813135	+	0.582075i	$0.802241\pi$
$62$	3.61261e9	−	3.25160e9i	0.500803	−	0.450757i
$63$	1.26482e10			1.60567
$64$	−2.66353e9	+	8.16655e9i	−0.310076	+	0.950712i
$65$	−1.26360e6			−0.000135078
$66$	−6.88355e7	+	6.19567e7i	−0.00676583	+	0.00608971i
$67$	1.43834e10	+	1.43834e10i	1.30152	+	1.30152i	0.927368	+	0.374150i	$0.122065\pi$
$67$	1.43834e10	+	1.43834e10i	1.30152	+	1.30152i	0.374150	+	0.927368i	$0.377935\pi$
$68$	−1.93347e9	+	1.83303e10i	−0.161264	+	1.52887i
$69$	1.53806e8	−	1.53806e8i	0.0118387	−	0.0118387i
$70$	−1.01965e10	−	5.36272e8i	−0.725122	−	0.0381370i
$71$		−	7.48815e9i		−	0.492553i	−0.969200	−	0.246277i	$-0.920793\pi$
$71$		−	7.48815e9i		−	0.492553i	0.969200	−	0.246277i	$-0.0792072\pi$
$72$	1.32853e10	−	9.64101e9i	0.809173	−	0.587211i
$73$		−	1.59325e10i		−	0.899517i	−0.893150	−	0.449759i	$-0.851510\pi$
$73$		−	1.59325e10i		−	0.899517i	0.893150	−	0.449759i	$-0.148490\pi$
$74$	1.49597e9	−	2.84438e10i	0.0783696	−	1.49009i
$75$	1.68119e8	−	1.68119e8i	0.00818050	−	0.00818050i
$76$	−2.41062e10	+	1.95060e10i	−1.09057	+	0.882456i
$77$	−1.68848e10	−	1.68848e10i	−0.710883	−	0.710883i
$78$	−74109.8	−	82338.0i	−2.90640e−6	−	3.22909e-6i
$79$	6.06745e9			0.221849			0.110924	−	0.993829i	$-0.464619\pi$
$79$	6.06745e9			0.221849			0.110924	+	0.993829i	$0.464619\pi$
$80$	−1.11188e10	+	7.20890e9i	−0.379370	+	0.245965i
$81$	−3.13612e10			−0.999366
$82$	3.92511e9	+	4.36090e9i	0.116916	+	0.129897i
$83$	8.65455e9	+	8.65455e9i	0.241165	+	0.241165i	0.817332	−	0.576167i	$-0.195452\pi$
$83$	8.65455e9	+	8.65455e9i	0.241165	+	0.241165i	−0.576167	+	0.817332i	$0.695452\pi$
$84$	−5.63079e8	−	6.95872e8i	−0.0146904	−	0.0181549i
$85$	−2.01059e10	+	2.01059e10i	−0.491496	+	0.491496i
$86$	1.87682e9	−	3.56851e10i	0.0430210	−	0.817985i
$87$			3.82883e8i			0.00823587i
$88$	−3.06056e10	−	4.86491e9i	−0.618224	−	0.0982698i
$89$			5.51864e10i			1.04758i	0.851848	+	0.523790i	$0.175482\pi$
$89$			5.51864e10i			1.04758i	−0.851848	+	0.523790i	$0.824518\pi$
$90$	2.52874e10	+	1.32996e9i	0.451409	+	0.0237413i
$91$	2.01969e7	−	2.01969e7i	0.000339279	−	0.000339279i
$92$	7.23832e10	+	7.63493e9i	1.14500	+	0.120774i
$93$	4.64808e8	+	4.64808e8i	0.00692815	+	0.00692815i
$94$	−1.55475e10	+	1.39938e10i	−0.218503	+	0.196667i
$95$	−4.78368e10			−0.634282
$96$	−1.12186e9	−	3.01717e8i	−0.0140426	−	0.00377666i
$97$	−1.47835e11			−1.74797			−0.873985	−	0.485953i	$-0.838473\pi$
$97$	−1.47835e11			−1.74797			−0.873985	+	0.485953i	$0.838473\pi$
$98$	1.05038e11	−	9.45417e10i	1.17383	−	1.05653i
$99$	4.18746e10	+	4.18746e10i	0.442545	+	0.442545i
$100$	7.91191e10	+	8.34543e9i	0.791191	+	0.0834543i
$101$	1.14815e11	−	1.14815e11i	1.08700	−	1.08700i	0.0911655	−	0.995836i	$-0.470941\pi$
$101$	1.14815e11	−	1.14815e11i	1.08700	−	1.08700i	0.995836	−	0.0911655i	$-0.0290592\pi$
$102$	−2.48935e9	−	1.30924e8i	−0.0223246	−	0.00117414i
$103$			6.84942e9i			0.0582169i	0.999576	+	0.0291084i	$0.00926681\pi$
$103$			6.84942e9i			0.0582169i	−0.999576	+	0.0291084i	$0.990733\pi$
$104$	5.81919e6	−	3.66090e7i	4.69007e−5	−	0.000295056i
$105$		−	1.38090e9i		−	0.0105590i
$106$	−4.29659e9	+	8.16937e10i	−0.0311847	+	0.592934i
$107$	−1.10999e11	+	1.10999e11i	−0.765080	+	0.765080i	−0.977236	−	0.212156i	$-0.931952\pi$
$107$	−1.10999e11	+	1.10999e11i	−0.765080	+	0.765080i	0.212156	+	0.977236i	$0.431952\pi$
$108$	2.79318e9	+	3.45191e9i	0.0182923	+	0.0226062i
$109$	1.01764e11	+	1.01764e11i	0.633501	+	0.633501i	0.948944	−	0.315444i	$-0.102153\pi$
$109$	1.01764e11	+	1.01764e11i	0.633501	+	0.633501i	−0.315444	+	0.948944i	$0.602153\pi$
$110$	−3.19821e10	−	3.55330e10i	−0.189342	−	0.210364i
$111$	3.85212e9			0.0216982
$112$	6.24943e10	−	2.92944e11i	0.335075	−	1.57067i
$113$	9.78538e10			0.499627			0.249814	−	0.968294i	$-0.419631\pi$
$113$	9.78538e10			0.499627			0.249814	+	0.968294i	$0.419631\pi$
$114$	−2.80562e9	−	3.11712e9i	−0.0136475	−	0.0151627i
$115$	7.93948e10	+	7.93948e10i	0.368090	+	0.368090i
$116$	−9.95980e10	+	8.05917e10i	−0.440283	+	0.356263i
$117$	−5.00885e7	+	5.00885e7i	−0.000211211	+	0.000211211i
$118$	−1.85589e10	+	3.52872e11i	−0.0746794	+	1.41993i
$119$		−	6.42733e11i		−	2.46901i
$120$	−1.05258e9	−	1.45045e9i	−0.00386153	−	0.00532116i
$121$			1.73510e11i			0.608143i
$122$	9.74135e10	+	5.12335e9i	0.326317	+	0.0171623i
$123$	−5.61084e8	+	5.61084e8i	−0.00179701	+	0.00179701i
$124$	−2.30731e10	+	2.18745e11i	−0.0706783	+	0.670067i
$125$	1.95865e11	+	1.95865e11i	0.574053	+	0.574053i
$126$	−4.25443e11	+	3.82928e11i	−1.19345	+	1.07418i
$127$	−6.75185e11			−1.81344			−0.906718	−	0.421738i	$-0.861420\pi$
$127$	−6.75185e11			−1.81344			−0.906718	+	0.421738i	$0.861420\pi$
$128$	−1.57652e11	−	3.55333e11i	−0.405550	−	0.914073i
$129$	4.83281e9			0.0119112
$130$	4.25030e7	−	3.82556e7i	0.000100399	−	9.03663e-5i
$131$	1.39014e11	+	1.39014e11i	0.314823	+	0.314823i	0.846775	−	0.531952i	$-0.178541\pi$
$131$	1.39014e11	+	1.39014e11i	0.314823	+	0.314823i	−0.531952	+	0.846775i	$0.678541\pi$
$132$	4.39640e8	−	4.16801e9i	0.000954861	−	0.00905258i
$133$	7.64607e11	−	7.64607e11i	1.59314	−	1.59314i
$134$	−9.19267e11	−	4.83478e10i	−1.83808	−	0.0966719i
$135$			6.85004e9i			0.0131479i
$136$	−4.89917e11	−	6.75103e11i	−0.902940	−	1.24425i
$137$		−	7.40756e9i		−	0.0131133i	−0.999979	−	0.00655665i	$-0.997913\pi$
$137$		−	7.40756e9i		−	0.0131133i	0.999979	−	0.00655665i	$-0.00208706\pi$
$138$	−5.16997e8	+	9.83000e9i	−0.000879333	+	0.0167193i
$139$	−5.44962e10	+	5.44962e10i	−0.0890810	+	0.0890810i	−0.750243	−	0.661162i	$-0.770064\pi$
$139$	−5.44962e10	+	5.44962e10i	−0.0890810	+	0.0890810i	0.661162	+	0.750243i	$0.270064\pi$
$140$	3.59210e11	−	2.90662e11i	0.564474	−	0.456755i
$141$	−2.00038e9	−	2.00038e9i	−0.00302278	−	0.00302278i
$142$	2.26705e11	+	2.51875e11i	0.329515	+	0.366100i
$143$	1.33732e8			0.000187020
$144$	−1.54987e11	+	7.26503e11i	−0.208593	+	0.977786i
$145$	−1.97644e11			−0.256071
$146$	4.82360e11	+	5.35915e11i	0.601771	+	0.668583i
$147$	1.35145e10	+	1.35145e10i	0.0162388	+	0.0162388i
$148$	8.10821e11	+	1.00204e12i	0.938610	+	1.15997i
$149$	6.09273e11	−	6.09273e11i	0.679653	−	0.679653i	−0.280268	−	0.959922i	$-0.590423\pi$
$149$	6.09273e11	−	6.09273e11i	0.679653	−	0.679653i	0.959922	+	0.280268i	$0.0904235\pi$
$150$	−5.65108e8	+	1.07448e10i	−0.000607617	+	0.0115530i
$151$		−	6.86276e11i		−	0.711419i	−0.934597	−	0.355709i	$-0.884239\pi$
$151$		−	6.86276e11i		−	0.711419i	0.934597	−	0.355709i	$-0.115761\pi$
$152$	2.20301e11	−	1.38593e12i	0.220230	−	1.38549i
$153$			1.59398e12i			1.53703i
$154$	1.07914e12	+	5.67560e10i	1.00395	+	0.0528017i
$155$	−2.39934e11	+	2.39934e11i	−0.215411	+	0.215411i
$156$	4.98559e6	+	525878.i	4.32048e−6	+	4.55721e-7i
$157$	1.50923e12	+	1.50923e12i	1.26272	+	1.26272i	0.949769	+	0.312952i	$0.101318\pi$
$157$	1.50923e12	+	1.50923e12i	1.26272	+	1.26272i	0.312952	+	0.949769i	$0.398682\pi$
$158$	−2.04088e11	+	1.83693e11i	−0.164893	+	0.148415i
$159$	−1.10637e10			−0.00863411
$160$	1.55747e11	−	5.79105e11i	0.117425	−	0.436614i
$161$	−2.53804e12			−1.84908
$162$	1.05488e12	−	9.49464e11i	0.742797	−	0.668568i
$163$	1.16350e12	+	1.16350e12i	0.792017	+	0.792017i	0.981822	−	0.189805i	$-0.0607854\pi$
$163$	1.16350e12	+	1.16350e12i	0.792017	+	0.792017i	−0.189805	+	0.981822i	$0.560785\pi$
$164$	−2.64054e11	−	2.78522e10i	−0.173801	−	0.0183324i
$165$	4.57176e9	−	4.57176e9i	0.00291019	−	0.00291019i
$166$	−5.53127e11	−	2.90910e10i	−0.340589	−	0.0179129i
$167$		−	1.66142e12i		−	0.989777i	−0.868956	−	0.494889i	$-0.835209\pi$
$167$		−	1.66142e12i		−	0.989777i	0.868956	−	0.494889i	$-0.164791\pi$
$168$	4.00076e10	+	6.35942e9i	0.0230644	+	0.00366620i
$169$		−	1.79216e12i		−	1.00000i
$170$	6.75832e10	−	1.28500e12i	0.0365065	−	0.694121i
$171$	−1.89623e12	+	1.89623e12i	−0.991776	+	0.991776i
$172$	1.01724e12	+	1.25714e12i	0.515250	+	0.636764i
$173$	−2.50410e12	−	2.50410e12i	−1.22856	−	1.22856i	−0.964507	−	0.264058i	$-0.914939\pi$
$173$	−2.50410e12	−	2.50410e12i	−1.22856	−	1.22856i	−0.264058	−	0.964507i	$-0.585061\pi$
$174$	−1.15918e10	−	1.28788e10i	−0.00550974	−	0.00612147i
$175$	−2.77423e12			−1.27771
$176$	1.17675e12	−	7.62949e11i	0.525248	−	0.340546i
$177$	−4.77892e10			−0.0206765
$178$	−1.67078e12	−	1.85628e12i	−0.700823	−	0.778633i
$179$	2.08597e12	+	2.08597e12i	0.848431	+	0.848431i	0.989937	−	0.141506i	$-0.0451946\pi$
$179$	2.08597e12	+	2.08597e12i	0.848431	+	0.848431i	−0.141506	+	0.989937i	$0.545195\pi$
$180$	−8.90845e11	+	7.20845e11i	−0.351401	+	0.284343i
$181$	−1.90878e12	+	1.90878e12i	−0.730339	+	0.730339i	−0.970687	−	0.240348i	$-0.922739\pi$
$181$	−1.90878e12	+	1.90878e12i	−0.730339	+	0.730339i	0.240348	+	0.970687i	$0.422739\pi$
$182$	−6.78891e7	+	1.29082e9i	−2.52004e−5	+	0.000479151i
$183$			1.31927e10i			0.00475172i
$184$	−2.66587e12	+	1.93460e12i	−0.931838	+	0.676228i
$185$			1.98847e12i			0.674644i
$186$	−2.97066e10	−	1.56239e9i	−0.00978436	−	0.000514597i
$187$	2.12790e12	−	2.12790e12i	0.680490	−	0.680490i
$188$	9.92988e10	−	9.41405e11i	0.0308373	−	0.292353i
$189$	−1.09489e11	−	1.09489e11i	−0.0330240	−	0.0330240i
$190$	1.60906e12	−	1.44827e12i	0.471442	−	0.424330i
$191$	4.39175e12			1.25013			0.625064	−	0.780574i	$-0.285073\pi$
$191$	4.39175e12			1.25013			0.625064	+	0.780574i	$0.285073\pi$
$192$	4.68700e10	−	2.38158e10i	0.0129640	−	0.00658730i
$193$	−5.30994e12			−1.42733			−0.713665	−	0.700487i	$-0.752966\pi$
$193$	−5.30994e12			−1.42733			−0.713665	+	0.700487i	$0.752966\pi$
$194$	4.97267e12	−	4.47574e12i	1.29921	−	1.16938i
$195$	5.46854e6	+	5.46854e6i	1.38893e−6	+	1.38893e-6i
$196$	−6.70860e11	+	6.36011e12i	−0.165662	+	1.57057i
$197$	3.61540e12	−	3.61540e12i	0.868146	−	0.868146i	−0.124121	−	0.992267i	$-0.539611\pi$
$197$	3.61540e12	−	3.61540e12i	0.868146	−	0.868146i	0.992267	+	0.124121i	$0.0396112\pi$
$198$	−2.67628e12	−	1.40756e11i	−0.624989	−	0.0328706i
$199$			2.20956e12i			0.501897i	0.968000	+	0.250948i	$0.0807424\pi$
$199$			2.20956e12i			0.501897i	−0.968000	+	0.250948i	$0.919258\pi$
$200$	−2.91395e12	+	2.11463e12i	−0.643898	+	0.467272i
$201$		−	1.24496e11i		−	0.0267656i
$202$	−3.85934e11	+	7.33800e12i	−0.0807384	+	1.53513i
$203$	3.15908e12	−	3.15908e12i	0.643180	−	0.643180i
$204$	8.76967e10	−	7.09615e10i	0.0173787	−	0.0140623i
$205$	−2.89632e11	−	2.89632e11i	−0.0558729	−	0.0558729i
$206$	−2.07367e11	−	2.30391e11i	−0.0389467	−	0.0432708i
$207$	6.29437e12			1.15111
$208$	9.12606e8	+	1.40758e9i	0.000162531	+	0.000250682i
$209$	5.06278e12			0.878182
$210$	4.18071e10	+	4.64488e10i	0.00706388	+	0.00784817i
$211$	−1.33456e11	−	1.33456e11i	−0.0219676	−	0.0219676i	0.696038	−	0.718005i	$-0.254945\pi$
$211$	−1.33456e11	−	1.33456e11i	−0.0219676	−	0.0219676i	−0.718005	+	0.696038i	$0.754945\pi$
$212$	−2.32877e12	−	2.87797e12i	−0.373490	−	0.461572i
$213$	−3.24069e10	+	3.24069e10i	−0.00506465	+	0.00506465i
$214$	3.73106e11	−	7.09411e12i	0.0568273	−	1.08049i
$215$			2.49470e12i			0.370346i
$216$	−1.98460e11	−	3.15462e10i	−0.0287195	−	0.00456511i
$217$		−	7.67006e12i		−	1.08211i
$218$	−6.50389e12	−	3.42064e11i	−0.894669	−	0.0470541i
$219$	−6.89522e10	+	6.89522e10i	−0.00924923	+	0.00924923i
$220$	2.15153e12	+	2.26942e11i	0.281464	+	0.0296887i
$221$	2.54530e9	+	2.54530e9i	0.000324774	+	0.000324774i
$222$	−1.29572e11	+	1.16624e11i	−0.0161276	+	0.0145159i
$223$	1.71920e12			0.208761			0.104380	−	0.994537i	$-0.466714\pi$
$223$	1.71920e12			0.208761			0.104380	+	0.994537i	$0.466714\pi$
$224$	6.76682e12	+	1.17456e13i	0.801716	+	1.39159i
$225$	6.88012e12			0.795412
$226$	−3.29146e12	+	2.96254e12i	−0.371358	+	0.334247i
$227$	−4.83327e12	−	4.83327e12i	−0.532230	−	0.532230i	0.389006	−	0.921235i	$-0.372819\pi$
$227$	−4.83327e12	−	4.83327e12i	−0.532230	−	0.532230i	−0.921235	+	0.389006i	$0.872819\pi$
$228$	1.88743e11	+	1.99085e10i	0.0202875	+	0.00213992i
$229$	−7.49588e12	+	7.49588e12i	−0.786552	+	0.786552i	−0.980927	−	0.194375i	$-0.937732\pi$
$229$	−7.49588e12	+	7.49588e12i	−0.786552	+	0.786552i	0.194375	+	0.980927i	$0.437732\pi$
$230$	−5.07426e12	−	2.66875e11i	−0.519839	−	0.0273403i
$231$			1.46147e11i			0.0146192i
$232$	9.10203e11	−	5.72617e12i	0.0889108	−	0.559345i
$233$			3.54948e12i			0.338616i	0.985563	+	0.169308i	$0.0541532\pi$
$233$			3.54948e12i			0.338616i	−0.985563	+	0.169308i	$0.945847\pi$
$234$	1.68366e8	−	3.20124e9i	1.56879e−5	−	0.000298285i
$235$	1.03260e12	−	1.03260e12i	0.0939848	−	0.0939848i
$236$	−1.00590e13	−	1.24312e13i	−0.894414	−	1.10535i
$237$	−2.62585e10	−	2.62585e10i	−0.00228115	−	0.00228115i
$238$	1.94588e13	+	2.16193e13i	1.65175	+	1.83514i
$239$	−1.56707e13			−1.29987			−0.649936	−	0.759989i	$-0.725204\pi$
$239$	−1.56707e13			−1.29987			−0.649936	+	0.759989i	$0.725204\pi$
$240$	7.93178e10	+	1.69211e10i	0.00642997	+	0.00137172i
$241$	3.00251e12			0.237898			0.118949	−	0.992900i	$-0.462047\pi$
$241$	3.00251e12			0.237898			0.118949	+	0.992900i	$0.462047\pi$
$242$	−5.25305e12	−	5.83628e12i	−0.406843	−	0.452014i
$243$	4.07314e11	+	4.07314e11i	0.0308386	+	0.0308386i
$244$	−3.43176e12	+	2.77688e12i	−0.254023	+	0.205548i
$245$	−6.97620e12	+	6.97620e12i	−0.504900	+	0.504900i
$246$	1.88601e9	−	3.58598e10i	0.000133475	−	0.00253785i
$247$			6.05587e9i			0.000419125i
$248$	−5.84643e12	−	8.05635e12i	−0.395737	−	0.545324i
$249$		−	7.49096e10i		−	0.00495954i
$250$	−1.25181e13	−	6.58372e11i	−0.810712	−	0.0426385i
$251$	−1.12730e13	+	1.12730e13i	−0.714223	+	0.714223i	−0.967416	−	0.253193i	$-0.918519\pi$
$251$	−1.12730e13	+	1.12730e13i	−0.714223	+	0.714223i	0.253193	+	0.967416i	$0.418519\pi$
$252$	2.71722e12	−	2.57607e13i	0.168431	−	1.59682i
$253$	−8.40270e12	−	8.40270e12i	−0.509631	−	0.509631i
$254$	2.27109e13	−	2.04413e13i	1.34787	−	1.21317i
$255$	1.74027e11			0.0101076
$256$	1.60606e13	+	7.17923e12i	0.912941	+	0.408092i
$257$	2.38344e13			1.32609			0.663044	−	0.748580i	$-0.269264\pi$
$257$	2.38344e13			1.32609			0.663044	+	0.748580i	$0.269264\pi$
$258$	−1.62559e11	+	1.46314e11i	−0.00885324	+	0.00796852i
$259$	−3.17830e13	−	3.17830e13i	−1.69452	−	1.69452i
$260$	−2.71459e8	+	2.57357e9i	−1.41694e−5	+	0.000134333i
$261$	−7.83456e12	+	7.83456e12i	−0.400398	+	0.400398i
$262$	−8.88462e12	−	4.67276e11i	−0.444613	−	0.0233839i
$263$			3.02043e13i			1.48017i	0.672513	+	0.740085i	$0.265215\pi$
$263$			3.02043e13i			1.48017i	−0.672513	+	0.740085i	$0.734785\pi$
$264$	1.11399e11	+	1.53508e11i	0.00534639	+	0.00736730i
$265$		−	5.71111e12i		−	0.268453i
$266$	−2.57012e12	+	4.88673e13i	−0.118333	+	2.24993i
$267$	2.38833e11	−	2.38833e11i	0.0107717	−	0.0107717i
$268$	3.23847e13	−	2.62047e13i	1.43086	−	1.15781i
$269$	2.50045e13	+	2.50045e13i	1.08238	+	1.08238i	0.996287	+	0.0860954i	$0.0274390\pi$
$269$	2.50045e13	+	2.50045e13i	1.08238	+	1.08238i	0.0860954	+	0.996287i	$0.472561\pi$
$270$	−2.07386e11	−	2.30411e11i	−0.00879587	−	0.00977244i
$271$	5.39216e12			0.224095			0.112047	−	0.993703i	$-0.464259\pi$
$271$	5.39216e12			0.224095			0.112047	+	0.993703i	$0.464259\pi$
$272$	3.69180e13	+	7.87580e12i	1.50352	+	0.320749i
$273$	−1.74815e8			−6.97723e−6
$274$	2.24265e11	+	2.49164e11i	0.00877270	+	0.00974671i
$275$	−9.18465e12	−	9.18465e12i	−0.352154	−	0.352154i
$276$	−2.80215e11	−	3.46299e11i	−0.0105315	−	0.0130152i
$277$	9.61770e12	−	9.61770e12i	0.354350	−	0.354350i	−0.507375	−	0.861725i	$-0.669384\pi$
$277$	9.61770e12	−	9.61770e12i	0.354350	−	0.354350i	0.861725	+	0.507375i	$0.169384\pi$
$278$	1.83181e11	−	3.48294e12i	0.00661660	−	0.125806i
$279$			1.90218e13i			0.673642i
$280$	−3.28274e12	+	2.06520e13i	−0.113990	+	0.717121i
$281$			3.40138e12i			0.115817i	0.998322	+	0.0579083i	$0.0184431\pi$
$281$			3.40138e12i			0.115817i	−0.998322	+	0.0579083i	$0.981557\pi$
$282$	1.27848e11	+	6.72399e9i	0.00426896	+	0.000224521i
$283$	1.89776e13	−	1.89776e13i	0.621465	−	0.621465i	−0.324441	−	0.945906i	$-0.605176\pi$
$283$	1.89776e13	−	1.89776e13i	0.621465	−	0.621465i	0.945906	+	0.324441i	$0.105176\pi$
$284$	−1.52511e13	−	1.60868e12i	−0.489836	−	0.0516676i
$285$	2.07026e11	+	2.07026e11i	0.00652197	+	0.00652197i
$286$	−4.49828e9	+	4.04876e9i	−0.000139006	+	0.000125115i
$287$	9.25877e12			0.280675
$288$	−1.67818e13	−	2.91293e13i	−0.499091	−	0.866306i
$289$	4.67279e13			1.36345
$290$	6.64807e12	−	5.98371e12i	0.190330	−	0.171310i
$291$	6.39796e11	+	6.39796e11i	0.0179734	+	0.0179734i
$292$	−3.24498e13	−	3.42279e12i	−0.894555	−	0.0943571i
$293$	−2.15247e13	+	2.15247e13i	−0.582325	+	0.582325i	−0.935542	−	0.353217i	$-0.885088\pi$
$293$	−2.15247e13	+	2.15247e13i	−0.582325	+	0.582325i	0.353217	+	0.935542i	$0.385088\pi$
$294$	−8.63735e11	−	4.54271e10i	−0.0229335	−	0.00120616i
$295$		−	2.46688e13i		−	0.642877i
$296$	−5.76101e13	−	9.15742e12i	−1.47365	−	0.234244i
$297$		−	7.24969e11i		−	0.0182037i
$298$	−2.04798e12	+	3.89396e13i	−0.0504821	+	0.959848i
$299$	1.00509e10	−	1.00509e10i	0.000243229	−	0.000243229i
$300$	−3.06291e11	−	3.78525e11i	−0.00727725	−	0.00899348i
$301$	−3.98745e13	−	3.98745e13i	−0.930207	−	0.930207i
$302$	2.07771e13	+	2.30839e13i	0.475934	+	0.528775i
$303$	−9.93781e11			−0.0223540
$304$	3.45491e13	+	5.32875e13i	0.763190	+	1.17712i
$305$	−6.81006e12			−0.147741
$306$	−4.82581e13	−	5.36161e13i	−1.02826	−	1.14242i
$307$	−1.79843e13	−	1.79843e13i	−0.376386	−	0.376386i	0.493411	−	0.869796i	$-0.335750\pi$
$307$	−1.79843e13	−	1.79843e13i	−0.376386	−	0.376386i	−0.869796	+	0.493411i	$0.835750\pi$
$308$	−3.80168e13	+	3.07620e13i	−0.781531	+	0.632391i
$309$	2.96426e10	−	2.96426e10i	0.000598612	−	0.000598612i
$310$	8.06505e11	−	1.53346e13i	0.0159999	−	0.304217i
$311$			8.79750e12i			0.171466i	0.996318	+	0.0857328i	$0.0273231\pi$
$311$			8.79750e12i			0.171466i	−0.996318	+	0.0857328i	$0.972677\pi$
$312$	−1.83619e8	+	1.33251e8i	−3.51615e−6	+	2.55164e-6i
$313$		−	5.86822e13i		−	1.10411i	−0.833808	−	0.552055i	$-0.813844\pi$
$313$		−	5.86822e13i		−	1.10411i	0.833808	−	0.552055i	$-0.186156\pi$
$314$	−9.64574e13	−	5.07307e12i	−1.78329	−	0.0937902i
$315$	2.82561e13	−	2.82561e13i	0.513339	−	0.513339i
$316$	1.30347e12	−	1.23576e13i	0.0232714	−	0.220625i
$317$	−3.22343e13	−	3.22343e13i	−0.565578	−	0.565578i	0.365308	−	0.930887i	$-0.380964\pi$
$317$	−3.22343e13	−	3.22343e13i	−0.565578	−	0.565578i	−0.930887	+	0.365308i	$0.880964\pi$
$318$	3.72145e11	−	3.34956e11i	0.00641746	−	0.00577615i
$319$	2.09176e13			0.354538
$320$	1.22937e13	+	2.41943e13i	0.204813	+	0.403078i
$321$	9.60751e11			0.0157338
$322$	8.53708e13	−	7.68396e13i	1.37437	−	1.23702i
$323$	9.63590e13	+	9.63590e13i	1.52503	+	1.52503i
$324$	−6.73732e12	+	6.38733e13i	−0.104831	+	0.993852i
$325$	1.09863e10	−	1.09863e10i	0.000168071	−	0.000168071i
$326$	−7.43612e13	−	3.91094e12i	−1.11854	−	0.0588281i
$327$		−	8.80817e11i		−	0.0130279i
$328$	9.72508e12	−	7.05742e12i	0.141445	−	0.102645i
$329$			3.30094e13i			0.472128i
$330$	−1.53673e10	+	2.92189e11i	−0.000216158	+	0.00410996i
$331$	−3.78052e13	+	3.78052e13i	−0.522994	+	0.522994i	−0.918475	−	0.395480i	$-0.870578\pi$
$331$	−3.78052e13	+	3.78052e13i	−0.522994	+	0.522994i	0.395480	+	0.918475i	$0.370578\pi$
$332$	1.94860e13	−	1.57675e13i	0.265132	−	0.214537i
$333$	7.88223e13	+	7.88223e13i	1.05489	+	1.05489i
$334$	5.02996e13	+	5.58842e13i	0.662154	+	0.735671i
$335$	6.42649e13			0.832199
$336$	−1.53825e12	+	9.97329e11i	−0.0195957	+	0.0127049i
$337$	−1.14761e14			−1.43823			−0.719115	−	0.694891i	$-0.755453\pi$
$337$	−1.14761e14			−1.43823			−0.719115	+	0.694891i	$0.755453\pi$
$338$	5.42579e13	+	6.02820e13i	0.668993	+	0.743269i
$339$	−4.23488e11	−	4.23488e11i	−0.00513739	−	0.00513739i
$340$	3.66304e13	+	4.52691e13i	0.437228	+	0.540341i
$341$	2.53933e13	−	2.53933e13i	0.298243	−	0.298243i
$342$	6.37393e12	−	1.21192e14i	0.0736654	−	1.40065i
$343$		−	8.18001e13i		−	0.930329i
$344$	−7.22767e13	−	1.14887e13i	−0.808960	−	0.128588i
$345$		−	6.87203e11i		−	0.00756973i
$346$	1.60041e14	+	8.41718e12i	1.73505	+	0.0912532i
$347$	1.50582e13	−	1.50582e13i	0.160679	−	0.160679i	−0.622188	−	0.782868i	$-0.713756\pi$
$347$	1.50582e13	−	1.50582e13i	0.160679	−	0.160679i	0.782868	+	0.622188i	$0.213756\pi$
$348$	7.79817e11	+	8.22547e10i	0.00819044	+	0.000863922i
$349$	−3.37156e13	−	3.37156e13i	−0.348570	−	0.348570i	0.511006	−	0.859577i	$-0.329273\pi$
$349$	−3.37156e13	−	3.37156e13i	−0.348570	−	0.348570i	−0.859577	+	0.511006i	$0.829273\pi$
$350$	9.33153e13	−	8.39902e13i	0.949683	−	0.854780i
$351$	8.67176e8			8.68797e−6
$352$	−1.64834e13	+	6.12892e13i	−0.162578	+	0.604505i
$353$	−1.59363e14			−1.54748			−0.773741	−	0.633502i	$-0.781617\pi$
$353$	−1.59363e14			−1.54748			−0.773741	+	0.633502i	$0.781617\pi$
$354$	1.60746e12	−	1.44683e12i	0.0153682	−	0.0138324i
$355$	−1.67285e13	−	1.67285e13i	−0.157471	−	0.157471i
$356$	1.12398e14	+	1.18557e13i	1.04180	+	0.109888i
$357$	−2.78159e12	+	2.78159e12i	−0.0253874	+	0.0253874i
$358$	−1.33318e14	−	7.01170e12i	−1.19821	−	0.0630183i
$359$			9.53928e13i			0.844299i	0.906526	+	0.422150i	$0.138724\pi$
$359$			9.53928e13i			0.844299i	−0.906526	+	0.422150i	$0.861276\pi$
$360$	8.14123e12	−	5.12172e13i	0.0709620	−	0.446428i
$361$			1.12771e14i			0.968071i
$362$	6.41611e12	−	1.21994e14i	0.0542468	−	1.03143i
$363$	7.50910e11	−	7.50910e11i	0.00625319	−	0.00625319i
$364$	−3.67962e10	−	4.54740e10i	−0.000301818	−	0.000372997i
$365$	−3.55932e13	−	3.55932e13i	−0.287579	−	0.287579i
$366$	−3.99410e11	−	4.43755e11i	−0.00317887	−	0.00353181i
$367$	−4.96140e13			−0.388992			−0.194496	−	0.980903i	$-0.562307\pi$
$367$	−4.96140e13			−0.388992			−0.194496	+	0.980903i	$0.562307\pi$
$368$	3.11002e13	−	1.45783e14i	0.240215	−	1.12601i
$369$	−2.29619e13			−0.174728
$370$	−6.02012e13	−	6.68852e13i	−0.451332	−	0.501442i
$371$	9.12845e13	+	9.12845e13i	0.674280	+	0.674280i
$372$	1.04653e12	−	8.46820e11i	0.00761667	−	0.00616318i
$373$	5.68027e13	−	5.68027e13i	0.407353	−	0.407353i	−0.473462	−	0.880814i	$-0.656996\pi$
$373$	5.68027e13	−	5.68027e13i	0.407353	−	0.407353i	0.880814	+	0.473462i	$0.156996\pi$
$374$	−7.15263e12	+	1.35997e14i	−0.0505443	+	0.961030i
$375$		−	1.69531e12i		−	0.0118053i
$376$	2.51611e13	+	3.46719e13i	0.172662	+	0.237927i
$377$			2.50207e10i			0.000169208i
$378$	6.99760e12	+	3.68031e11i	0.0466385	+	0.00245290i
$379$	−1.11074e14	+	1.11074e14i	−0.729621	+	0.729621i	−0.970544	−	0.240923i	$-0.922550\pi$
$379$	−1.11074e14	+	1.11074e14i	−0.729621	+	0.729621i	0.240923	+	0.970544i	$0.422550\pi$
$380$	−1.02768e13	+	9.74293e13i	−0.0665346	+	0.630783i
$381$	2.92204e12	+	2.92204e12i	0.0186465	+	0.0186465i
$382$	−1.47723e14	+	1.32961e14i	−0.929181	+	0.836326i
$383$	−2.62650e14			−1.62849			−0.814244	−	0.580523i	$-0.802848\pi$
$383$	−2.62650e14			−1.62849			−0.814244	+	0.580523i	$0.802848\pi$
$384$	−8.55517e11	+	2.22008e12i	−0.00522886	+	0.0135689i
$385$	−7.54413e13			−0.454543
$386$	1.78608e14	−	1.60759e14i	1.06089	−	0.954873i
$387$	9.88892e13	+	9.88892e13i	0.579080	+	0.579080i
$388$	−3.17595e13	+	3.01097e14i	−0.183358	+	1.73833i
$389$	8.87826e13	−	8.87826e13i	0.505365	−	0.505365i	−0.407735	−	0.913100i	$-0.633681\pi$
$389$	8.87826e13	−	8.87826e13i	0.505365	−	0.505365i	0.913100	+	0.407735i	$0.133681\pi$
$390$	−3.49504e8	−	1.83817e7i	−1.96154e−6	−	1.03165e-7i
$391$		−	3.19854e14i		−	1.77003i
$392$	−1.69988e14	−	2.34242e14i	−0.927565	−	1.27818i
$393$		−	1.20324e12i		−	0.00647430i
$394$	−1.21527e13	+	2.31067e14i	−0.0644826	+	1.22605i
$395$	1.35547e13	−	1.35547e13i	0.0709258	−	0.0709258i
$396$	9.42820e13	−	7.62901e13i	0.486525	−	0.393681i
$397$	−2.85419e13	−	2.85419e13i	−0.145256	−	0.145256i	0.630739	−	0.775995i	$-0.282752\pi$
$397$	−2.85419e13	−	2.85419e13i	−0.145256	−	0.145256i	−0.775995	+	0.630739i	$0.782752\pi$
$398$	−6.68948e13	−	7.43219e13i	−0.335765	−	0.373044i
$399$	−6.61807e12			−0.0327628
$400$	3.39943e13	−	1.59349e14i	0.165988	−	0.778071i
$401$	2.56296e14			1.23438			0.617189	−	0.786815i	$-0.288271\pi$
$401$	2.56296e14			1.23438			0.617189	+	0.786815i	$0.288271\pi$
$402$	3.76913e12	+	4.18760e12i	0.0179060	+	0.0198940i
$403$	3.03743e10	+	3.03743e10i	0.000142341	+	0.000142341i
$404$	−2.09178e14	−	2.58509e14i	−0.966981	−	1.19503i
$405$	−7.00606e13	+	7.00606e13i	−0.319500	+	0.319500i
$406$	−1.06188e13	+	2.01902e14i	−0.0477730	+	0.908339i
$407$		−	2.10448e14i		−	0.934064i
$408$	−8.01440e11	+	5.04193e12i	−0.00350946	+	0.0220783i
$409$			1.52405e14i			0.658447i	0.944252	+	0.329224i	$0.106787\pi$
$409$			1.52405e14i			0.658447i	−0.944252	+	0.329224i	$0.893213\pi$
$410$	1.85109e13	+	9.73558e11i	0.0789071	+	0.00415003i
$411$	−3.20581e10	+	3.20581e10i	−0.000134837	+	0.000134837i
$412$	1.39502e13	+	1.47146e12i	0.0578957	+	0.00610681i
$413$	3.94298e14	+	3.94298e14i	1.61473	+	1.61473i
$414$	−2.11721e14	+	1.90563e14i	−0.855581	+	0.770081i
$415$	3.86684e13			0.154203
$416$	−7.33115e10	−	1.97167e10i	−0.000288509	−	7.75926e-5i
$417$	4.71693e11			0.00183194
$418$	−1.70294e14	+	1.53276e14i	−0.652725	+	0.587497i
$419$	−1.00355e14	−	1.00355e14i	−0.379631	−	0.379631i	0.491338	−	0.870969i	$-0.336508\pi$
$419$	−1.00355e14	−	1.00355e14i	−0.379631	−	0.379631i	−0.870969	+	0.491338i	$0.836508\pi$
$420$	−2.81249e12	−	2.96660e11i	−0.0105007	−	0.00110761i
$421$	2.77863e14	−	2.77863e14i	1.02395	−	1.02395i	0.0242456	−	0.999706i	$-0.492282\pi$
$421$	2.77863e14	−	2.77863e14i	1.02395	−	1.02395i	0.999706	−	0.0242456i	$-0.00771836\pi$
$422$	8.52937e12	+	4.48592e11i	0.0310241	+	0.00163167i
$423$		−	8.18636e13i		−	0.293913i
$424$	1.65463e14	+	2.63011e13i	0.586392	+	0.0932099i
$425$		−	3.49620e14i		−	1.22309i
$426$	1.08931e11	−	2.07118e12i	0.000376183	−	0.00715261i
$427$	1.08850e14	−	1.08850e14i	0.371086	−	0.371086i
$428$	2.02225e14	+	2.49917e14i	0.680604	+	0.841114i
$429$	−5.78760e8	−	5.78760e8i	−1.92302e−6	−	1.92302e-6i
$430$	−7.55275e13	−	8.39131e13i	−0.247759	−	0.275266i
$431$	7.56776e13			0.245099			0.122550	−	0.992462i	$-0.460893\pi$
$431$	7.56776e13			0.245099			0.122550	+	0.992462i	$0.460893\pi$
$432$	7.63056e12	−	4.94730e12i	0.0244003	−	0.0158200i
$433$	−2.91093e13			−0.0919070			−0.0459535	−	0.998944i	$-0.514633\pi$
$433$	−2.91093e13			−0.0919070			−0.0459535	+	0.998944i	$0.514633\pi$
$434$	2.32212e14	+	2.57994e14i	0.723922	+	0.804297i
$435$	8.55357e11	+	8.55357e11i	0.00263303	+	0.00263303i
$436$	2.29124e14	−	1.85400e14i	0.696458	−	0.563553i
$437$	3.80505e14	−	3.80505e14i	1.14212	−	1.14212i
$438$	2.31773e11	−	4.40685e12i	0.000686998	−	0.0130623i
$439$			3.40756e14i			0.997445i	0.866762	+	0.498723i	$0.166197\pi$
$439$			3.40756e14i			0.997445i	−0.866762	+	0.498723i	$0.833803\pi$
$440$	−7.92408e13	+	5.75044e13i	−0.229065	+	0.166231i
$441$			5.53069e14i			1.57894i
$442$	−1.62674e11	−	8.55566e9i	−0.000458666	−	2.41230e-5i
$443$	−2.82666e14	+	2.82666e14i	−0.787141	+	0.787141i	−0.981025	−	0.193884i	$-0.937892\pi$
$443$	−2.82666e14	+	2.82666e14i	−0.787141	+	0.787141i	0.193884	+	0.981025i	$0.437892\pi$
$444$	8.27552e11	−	7.84562e12i	0.00227609	−	0.0215785i
$445$	1.23286e14	+	1.23286e14i	0.334914	+	0.334914i
$446$	−5.78278e13	+	5.20490e13i	−0.155165	+	0.139660i
$447$	−5.27357e12			−0.0139770
$448$	−5.83213e14	−	1.90215e14i	−1.52686	−	0.497985i
$449$	−6.78315e13			−0.175419			−0.0877094	−	0.996146i	$-0.527955\pi$
$449$	−6.78315e13			−0.175419			−0.0877094	+	0.996146i	$0.527955\pi$
$450$	−2.31423e14	+	2.08297e14i	−0.591205	+	0.532125i
$451$	3.06531e13	+	3.06531e13i	0.0773576	+	0.0773576i
$452$	2.10219e13	−	1.99299e14i	0.0524097	−	0.496871i
$453$	−2.97004e12	+	2.97004e12i	−0.00731512	+	0.00731512i
$454$	3.08903e14	+	1.62464e13i	0.751648	+	0.0395320i
$455$		−	9.02395e10i		−	0.000216937i
$456$	−6.95138e12	+	5.04457e12i	−0.0165107	+	0.0119817i
$457$		−	1.33927e14i		−	0.314289i	−0.987576	−	0.157144i	$-0.949771\pi$
$457$		−	1.33927e14i		−	0.314289i	0.987576	−	0.157144i	$-0.0502288\pi$
$458$	2.51963e13	−	4.79074e14i	0.0584221	−	1.11082i
$459$	1.37982e13	−	1.37982e13i	0.0316121	−	0.0316121i
$460$	1.78760e14	−	1.44647e14i	0.404671	−	0.327448i
$461$	−4.21772e14	−	4.21772e14i	−0.943457	−	0.943457i	0.0550276	−	0.998485i	$-0.482475\pi$
$461$	−4.21772e14	−	4.21772e14i	−0.943457	−	0.943457i	−0.998485	+	0.0550276i	$0.982475\pi$
$462$	−4.42462e12	−	4.91588e12i	−0.00978015	−	0.0108660i
$463$	−5.89482e14			−1.28758			−0.643792	−	0.765201i	$-0.722640\pi$
$463$	−5.89482e14			−1.28758			−0.643792	+	0.765201i	$0.722640\pi$
$464$	1.42745e14	+	2.20165e14i	0.308113	+	0.475225i
$465$	2.07676e12			0.00442990
$466$	−1.07461e14	−	1.19392e14i	−0.226532	−	0.251683i
$467$	−3.66542e14	−	3.66542e14i	−0.763627	−	0.763627i	0.213349	−	0.976976i	$-0.431563\pi$
$467$	−3.66542e14	−	3.66542e14i	−0.763627	−	0.763627i	−0.976976	+	0.213349i	$0.931563\pi$
$468$	9.12549e10	+	1.12776e11i	0.000187890	+	0.000232201i
$469$	−1.02719e15	+	1.02719e15i	−2.09026	+	2.09026i
$470$	−3.47093e12	+	6.59950e13i	−0.00698084	+	0.132731i
$471$		−	1.30632e13i		−	0.0259677i
$472$	7.14707e14	+	1.13606e14i	1.40426	+	0.223214i
$473$		−	2.64025e14i		−	0.512754i
$474$	1.67822e12	+	8.82641e10i	0.00322158	+	0.000169435i
$475$	4.15914e14	−	4.15914e14i	0.789204	−	0.789204i
$476$	−1.30905e15	−	1.38078e14i	−2.45538	−	0.258993i
$477$	−2.26386e14	−	2.26386e14i	−0.419758	−	0.419758i
$478$	5.27109e14	−	4.74434e14i	0.966155	−	0.869605i
$479$	3.11241e14			0.563964			0.281982	−	0.959420i	$-0.409008\pi$
$479$	3.11241e14			0.563964			0.281982	+	0.959420i	$0.409008\pi$
$480$	−3.18026e12	+	1.83219e12i	−0.00569687	+	0.00328204i
$481$	2.51729e11			0.000445795
$482$	−1.00994e14	+	9.09015e13i	−0.176822	+	0.159152i
$483$	1.09840e13	+	1.09840e13i	0.0190131	+	0.0190131i
$484$	3.53388e14	+	3.72752e13i	0.604788	+	0.0637927i
$485$	−3.30263e14	+	3.30263e14i	−0.558832	+	0.558832i
$486$	−2.60321e13	−	1.36913e12i	−0.0435522	−	0.00229058i
$487$		−	1.03101e13i		−	0.0170551i	−0.999964	−	0.00852757i	$-0.997286\pi$
$487$		−	1.03101e13i		−	0.0170551i	0.999964	−	0.00852757i	$-0.00271444\pi$
$488$	3.13621e13	−	1.97302e14i	0.0512975	−	0.322717i
$489$		−	1.00707e13i		−	0.0162877i
$490$	2.34495e13	−	4.45861e14i	0.0375021	−	0.713051i
$491$	−4.62895e14	+	4.62895e14i	−0.732039	+	0.732039i	−0.971023	−	0.238984i	$-0.923186\pi$
$491$	−4.62895e14	+	4.62895e14i	−0.732039	+	0.732039i	0.238984	+	0.971023i	$0.423186\pi$
$492$	1.02222e12	+	1.26330e12i	0.00159859	+	0.00197560i
$493$	3.98121e14	+	3.98121e14i	0.615682	+	0.615682i
$494$	−1.83342e11	−	2.03698e11i	−0.000280391	−	0.000311523i
$495$	1.87095e14			0.282966
$496$	4.40561e14	+	9.39859e13i	0.658957	+	0.140577i
$497$	5.34765e14			0.791047
$498$	2.26790e12	+	2.51970e12i	0.00331789	+	0.00368627i
$499$	3.82763e14	+	3.82763e14i	0.553831	+	0.553831i	0.927544	−	0.373713i	$-0.121916\pi$
$499$	3.82763e14	+	3.82763e14i	0.553831	+	0.553831i	−0.373713	+	0.927544i	$0.621916\pi$
$500$	4.40996e14	−	3.56841e14i	0.631102	−	0.510669i
$501$	−7.19020e12	+	7.19020e12i	−0.0101773	+	0.0101773i
$502$	3.78926e13	−	7.20476e14i	0.0530498	−	1.00867i
$503$			1.37272e15i			1.90090i	0.310877	+	0.950450i	$0.399377\pi$
$503$			1.37272e15i			1.90090i	−0.310877	+	0.950450i	$0.600623\pi$
$504$	6.88511e14	+	9.48764e14i	0.943068	+	1.29954i
$505$		−	5.12991e14i		−	0.695036i
$506$	5.37031e14	+	2.82445e13i	0.719733	+	0.0378535i
$507$	−7.75604e12	+	7.75604e12i	−0.0102824	+	0.0102824i
$508$	−1.45050e14	+	1.37515e15i	−0.190225	+	1.80343i
$509$	−1.01553e15	−	1.01553e15i	−1.31748	−	1.31748i	−0.915764	−	0.401716i	$-0.868414\pi$
$509$	−1.01553e15	−	1.01553e15i	−1.31748	−	1.31748i	−0.401716	−	0.915764i	$-0.631586\pi$
$510$	−5.85367e12	+	5.26870e12i	−0.00751263	+	0.00676188i
$511$	1.13782e15			1.44464
$512$	−7.57576e14	+	2.44753e14i	−0.951571	+	0.307428i
$513$	3.28293e13			0.0407958
$514$	−8.01707e14	+	7.21591e14i	−0.985640	+	0.887144i
$515$	1.53016e13	+	1.53016e13i	0.0186121	+	0.0186121i
$516$	1.03823e12	−	9.84299e12i	0.00124946	−	0.0118455i
$517$	−1.09284e14	+	1.09284e14i	−0.130125	+	0.130125i
$518$	2.03131e15	+	1.06834e14i	2.39311	+	0.125863i
$519$			2.16743e13i			0.0252653i
$520$	−6.87843e10	−	9.47843e10i	−7.93361e−5	−	0.000109325i
$521$		−	1.84458e14i		−	0.210518i	−0.994445	−	0.105259i	$-0.966433\pi$
$521$		−	1.84458e14i		−	0.210518i	0.994445	−	0.105259i	$-0.0335672\pi$
$522$	2.63348e13	−	5.00720e14i	0.0297400	−	0.565466i
$523$	1.02732e15	−	1.02732e15i	1.14801	−	1.14801i	0.161066	−	0.986944i	$-0.448507\pi$
$523$	1.02732e15	−	1.02732e15i	1.14801	−	1.14801i	0.986944	−	0.161066i	$-0.0514931\pi$
$524$	3.12994e14	−	2.53266e14i	0.346110	−	0.280062i
$525$	1.20062e13	+	1.20062e13i	0.0131380	+	0.0131380i
$526$	−9.14439e14	−	1.01597e15i	−0.990223	−	1.10016i
$527$	9.66613e14			1.03584
$528$	−8.39455e12	−	1.79083e12i	−0.00890248	−	0.00189919i
$529$	−3.10240e14			−0.325605
$530$	1.72905e14	+	1.92102e14i	0.179593	+	0.199533i
$531$	−9.77865e14	−	9.77865e14i	−1.00521	−	1.00521i
$532$	−1.39302e15	−	1.72154e15i	−1.41724	−	1.75147i
$533$	−3.66658e10	+	3.66658e10i	−3.69200e−5	+	3.69200e-5i
$534$	−8.02805e11	+	1.52642e13i	−0.000800079	+	0.0152124i
$535$			4.95941e14i			0.489197i
$536$	−2.95956e14	+	1.86189e15i	−0.288949	+	1.81780i
$537$		−	1.80552e13i		−	0.0174479i
$538$	−1.59808e15	−	8.40491e13i	−1.52861	−	0.0803953i
$539$	7.38322e14	−	7.38322e14i	0.699049	−	0.699049i
$540$	1.39515e13	+	1.47159e12i	0.0130754	+	0.00137918i
$541$	3.99095e14	+	3.99095e14i	0.370247	+	0.370247i	0.867567	−	0.497320i	$-0.165683\pi$
$541$	3.99095e14	+	3.99095e14i	0.370247	+	0.370247i	−0.497320	+	0.867567i	$0.665683\pi$
$542$	−1.81373e14	+	1.63248e14i	−0.166563	+	0.149918i
$543$	1.65215e13			0.0150193
$544$	−1.48023e15	+	8.52783e14i	−1.33210	+	0.767440i
$545$	4.54679e14			0.405064
$546$	5.88016e9	−	5.29254e9i	5.18596e−6	−	4.66772e-6i
$547$	−5.81181e14	−	5.81181e14i	−0.507436	−	0.507436i	0.406303	−	0.913739i	$-0.366818\pi$
$547$	−5.81181e14	−	5.81181e14i	−0.507436	−	0.507436i	−0.913739	+	0.406303i	$0.866818\pi$
$548$	−1.50870e13	−	1.59137e12i	−0.0130410	−	0.00137555i
$549$	−2.69949e14	+	2.69949e14i	−0.231011	+	0.231011i
$550$	5.87006e14	+	3.08729e13i	0.497334	+	0.0261567i
$551$			9.47224e14i			0.794546i
$552$	1.99097e13	+	3.16475e12i	0.0165348	+	0.00262830i
$553$			4.33306e14i			0.356292i
$554$	−3.23286e13	+	6.14683e14i	−0.0263198	+	0.500435i
$555$	8.60562e12	−	8.60562e12i	0.00693698	−	0.00693698i
$556$	9.92851e13	+	1.22700e14i	0.0792452	+	0.0979339i
$557$	−5.50142e14	−	5.50142e14i	−0.434781	−	0.434781i	0.455470	−	0.890251i	$-0.349471\pi$
$557$	−5.50142e14	−	5.50142e14i	−0.434781	−	0.434781i	−0.890251	+	0.455470i	$0.849471\pi$
$558$	−5.75889e14	−	6.39828e14i	−0.450662	−	0.500697i
$559$	3.15815e11			0.000244719
$560$	−5.14822e14	−	7.94046e14i	−0.395024	−	0.609273i
$561$	−1.84181e13			−0.0139942
$562$	−1.02977e14	−	1.14411e14i	−0.0774804	−	0.0860829i
$563$	1.01942e15	+	1.01942e15i	0.759549	+	0.759549i	0.976240	−	0.216691i	$-0.0695264\pi$
$563$	1.01942e15	+	1.01942e15i	0.759549	+	0.759549i	−0.216691	+	0.976240i	$0.569526\pi$
$564$	−4.50391e12	+	3.64443e12i	−0.00332319	+	0.00268902i
$565$	2.18605e14	−	2.18605e14i	0.159732	−	0.159732i
$566$	−6.37906e13	+	1.21289e15i	−0.0461601	+	0.877671i
$567$		−	2.23965e15i		−	1.60499i
$568$	5.61697e14	−	4.07620e14i	0.398645	−	0.289294i
$569$		−	1.97572e15i		−	1.38870i	−0.719639	−	0.694349i	$-0.755693\pi$
$569$		−	1.97572e15i		−	1.38870i	0.719639	−	0.694349i	$-0.244307\pi$
$570$	−1.32314e13	−	6.95889e11i	−0.00921072	−	0.000484427i
$571$	−1.21475e15	+	1.21475e15i	−0.837506	+	0.837506i	−0.988530	−	0.151024i	$-0.951743\pi$
$571$	−1.21475e15	+	1.21475e15i	−0.837506	+	0.837506i	0.151024	+	0.988530i	$0.451743\pi$
$572$	2.87296e10	−	2.72372e11i	1.96179e−5	−	0.000185988i
$573$	−1.90064e13	−	1.90064e13i	−0.0128544	−	0.0128544i
$574$	−3.11433e14	+	2.80311e14i	−0.208617	+	0.187769i
$575$	−1.38059e15			−0.915990
$576$	1.44637e15	+	4.71736e14i	0.950511	+	0.310010i
$577$	2.06710e15			1.34553			0.672767	−	0.739855i	$-0.265106\pi$
$577$	2.06710e15			1.34553			0.672767	+	0.739855i	$0.265106\pi$
$578$	−1.57176e15	+	1.41470e15i	−1.01341	+	0.912137i
$579$	2.29801e13	+	2.29801e13i	0.0146764	+	0.0146764i
$580$	−4.24600e13	+	4.02543e14i	−0.0268612	+	0.254658i
$581$	−6.18063e14	+	6.18063e14i	−0.387315	+	0.387315i
$582$	−4.08904e13	−	2.15058e12i	−0.0253831	−	0.00133500i
$583$			6.04432e14i			0.371681i
$584$	1.19513e15	−	8.67293e14i	0.728019	−	0.528318i
$585$			2.23795e11i			0.000135050i
$586$	7.23523e13	−	1.37568e15i	0.0432529	−	0.822395i
$587$	−1.55286e15	+	1.55286e15i	−0.919649	+	0.919649i	−0.997004	−	0.0773550i	$-0.975353\pi$
$587$	−1.55286e15	+	1.55286e15i	−0.919649	+	0.919649i	0.0773550	+	0.997004i	$0.475353\pi$
$588$	3.04283e13	−	2.46217e13i	0.0178527	−	0.0144458i
$589$	1.14990e15	+	1.14990e15i	0.668385	+	0.668385i
$590$	7.46853e14	+	8.29774e14i	0.430080	+	0.477830i
$591$	−3.12932e13			−0.0178533
$592$	2.21504e15	−	1.43613e15i	1.25203	−	0.811754i
$593$	7.38350e13			0.0413487			0.0206743	−	0.999786i	$-0.493419\pi$
$593$	7.38350e13			0.0413487			0.0206743	+	0.999786i	$0.493419\pi$
$594$	2.19486e13	+	2.43854e13i	0.0121781	+	0.0135302i
$595$	−1.43586e15	−	1.43586e15i	−0.789349	−	0.789349i
$596$	−1.11002e15	−	1.37180e15i	−0.604610	−	0.747197i
$597$	9.56245e12	−	9.56245e12i	0.00516072	−	0.00516072i
$598$	−3.37848e10	+	6.42372e11i	−1.80661e−5	+	0.000343503i
$599$			7.76586e12i			0.00411474i	0.999998	+	0.00205737i	$0.000654881\pi$
$599$			7.76586e12i			0.00411474i	−0.999998	+	0.00205737i	$0.999345\pi$
$600$	2.17625e13	+	3.45926e12i	0.0114255	+	0.00181615i
$601$			2.17882e15i			1.13348i	0.823898	+	0.566738i	$0.191795\pi$
$601$			2.17882e15i			1.13348i	−0.823898	+	0.566738i	$0.808205\pi$
$602$	2.54844e15	+	1.34032e14i	1.31370	+	0.0690923i
$603$	2.54744e15	−	2.54744e15i	1.30124	−	1.30124i
$604$	−1.39774e15	−	1.47433e14i	−0.707494	−	0.0746261i
$605$	3.87621e14	+	3.87621e14i	0.194425	+	0.194425i
$606$	3.34273e13	−	3.00869e13i	0.0166151	−	0.0149547i
$607$	2.72034e14			0.133994			0.0669971	−	0.997753i	$-0.478658\pi$
$607$	2.72034e14			0.133994			0.0669971	+	0.997753i	$0.478658\pi$
$608$	−2.77540e15	−	7.46427e14i	−1.35474	−	0.364349i
$609$	−2.73435e13			−0.0132269
$610$	2.29067e14	−	2.06176e14i	0.109812	−	0.0988379i
$611$	−1.30721e11	−	1.30721e11i	−6.21039e−5	−	6.21039e-5i
$612$	3.24647e15	+	3.42436e14i	1.52855	+	0.161230i
$613$	−8.56076e14	+	8.56076e14i	−0.399466	+	0.399466i	−0.878045	−	0.478579i	$-0.841152\pi$
$613$	−8.56076e14	+	8.56076e14i	−0.399466	+	0.399466i	0.478579	+	0.878045i	$0.341152\pi$
$614$	1.14941e15	+	6.04518e13i	0.531555	+	0.0279565i
$615$			2.50692e12i			0.00114902i
$616$	3.47426e14	−	2.18569e15i	0.157823	−	0.992875i
$617$			1.51170e15i			0.680607i	0.940316	+	0.340304i	$0.110530\pi$
$617$			1.51170e15i			0.680607i	−0.940316	+	0.340304i	$0.889470\pi$
$618$	−9.96395e10	+	1.89451e12i	−4.44626e−5	+	0.000845396i
$619$	−1.60958e15	+	1.60958e15i	−0.711892	+	0.711892i	−0.966931	−	0.255038i	$-0.917912\pi$
$619$	−1.60958e15	+	1.60958e15i	−0.711892	+	0.711892i	0.255038	+	0.966931i	$0.417912\pi$
$620$	4.37129e14	+	5.40220e14i	0.191627	+	0.236819i
$621$	−5.44868e13	−	5.44868e13i	−0.0236749	−	0.0236749i
$622$	−2.66346e14	−	2.95917e14i	−0.114709	−	0.127445i
$623$	−3.94113e15			−1.68243
$624$	2.14211e9	−	1.00412e10i	9.06414e−7	−	4.24884e-6i
$625$	−1.02169e15			−0.428527
$626$	1.77661e15	+	1.97386e15i	0.738641	+	0.820651i
$627$	−2.19105e13	−	2.19105e13i	−0.00902985	−	0.00902985i
$628$	3.39808e15	−	2.74962e15i	1.38821	−	1.12330i
$629$	4.00543e15	−	4.00543e15i	1.62207	−	1.62207i
$630$	−9.49789e13	+	1.80589e15i	−0.0381289	+	0.724969i
$631$		−	7.27946e14i		−	0.289693i	−0.989454	−	0.144846i	$-0.953731\pi$
$631$		−	7.27946e14i		−	0.289693i	0.989454	−	0.144846i	$-0.0462688\pi$
$632$	3.30284e14	+	4.55129e14i	0.130300	+	0.179552i
$633$			1.15513e12i			0.000451762i
$634$	2.06015e15	+	1.08351e14i	0.798744	+	0.0420090i
$635$	−1.50836e15	+	1.50836e15i	−0.579761	+	0.579761i
$636$	−2.37682e12	+	2.25335e13i	−0.000905696	+	0.00858647i
$637$	8.83148e11	+	8.83148e11i	0.000333631	+	0.000333631i
$638$	−7.03594e14	+	6.33283e14i	−0.263517	+	0.237183i
$639$	−1.32622e15			−0.492449
$640$	−1.14601e15	−	4.41619e14i	−0.421888	−	0.162576i
$641$	−1.21415e15			−0.443153			−0.221576	−	0.975143i	$-0.571120\pi$
$641$	−1.21415e15			−0.443153			−0.221576	+	0.975143i	$0.571120\pi$
$642$	−3.23163e13	+	2.90869e13i	−0.0116944	+	0.0105258i
$643$	2.15423e15	+	2.15423e15i	0.772916	+	0.772916i	0.978615	−	0.205699i	$-0.0659469\pi$
$643$	2.15423e15	+	2.15423e15i	0.772916	+	0.772916i	−0.205699	+	0.978615i	$0.565947\pi$
$644$	−5.45247e14	+	5.16923e15i	−0.193964	+	1.83888i
$645$	1.07965e13	−	1.07965e13i	0.00380806	−	0.00380806i
$646$	−6.15846e15	−	3.23897e14i	−2.15374	−	0.113274i
$647$			3.90532e14i			0.135420i	0.997705	+	0.0677101i	$0.0215693\pi$
$647$			3.90532e14i			0.135420i	−0.997705	+	0.0677101i	$0.978431\pi$
$648$	−1.70715e15	−	2.35245e15i	−0.586962	−	0.808831i
$649$			2.61081e15i			0.890081i
$650$	−3.69288e10	+	7.02151e11i	−1.24837e−5	+	0.000237360i
$651$	−3.31942e13	+	3.31942e13i	−0.0111267	+	0.0111267i
$652$	2.61966e15	−	2.11975e15i	0.870728	−	0.704567i
$653$	1.73093e15	+	1.73093e15i	0.570501	+	0.570501i	0.932268	−	0.361767i	$-0.117826\pi$
$653$	1.73093e15	+	1.73093e15i	0.570501	+	0.570501i	−0.361767	+	0.932268i	$0.617826\pi$
$654$	2.66669e13	+	2.96276e13i	0.00871555	+	0.00968321i
$655$	6.21113e14			0.201300
$656$	−1.13453e14	+	5.31815e14i	−0.0364625	+	0.170919i
$657$	−2.82181e15			−0.899327
$658$	−9.99364e14	−	1.11032e15i	−0.315850	−	0.350918i
$659$	−1.30838e15	−	1.30838e15i	−0.410074	−	0.410074i	0.471690	−	0.881764i	$-0.343644\pi$
$659$	−1.30838e15	−	1.30838e15i	−0.410074	−	0.410074i	−0.881764	+	0.471690i	$0.843644\pi$
$660$	−8.32916e12	−	1.02935e13i	−0.00258887	−	0.00319941i
$661$	5.59792e14	−	5.59792e14i	0.172551	−	0.172551i	−0.615548	−	0.788099i	$-0.711065\pi$
$661$	5.59792e14	−	5.59792e14i	0.172551	−	0.172551i	0.788099	+	0.615548i	$0.211065\pi$
$662$	1.27077e14	−	2.41619e15i	0.0388461	−	0.738605i
$663$		−	2.20309e10i		−	6.67893e-6i
$664$	−1.78078e14	+	1.12030e15i	−0.0535409	+	0.336831i
$665$		−	3.41626e15i		−	1.01867i
$666$	−5.03766e15	−	2.64950e14i	−1.48978	−	0.0783530i
$667$	1.57211e15	−	1.57211e15i	0.461095	−	0.461095i
$668$	−3.38381e15	−	3.56922e14i	−0.984317	−	0.103825i
$669$	−7.44027e12	−	7.44027e12i	−0.00214657	−	0.00214657i
$670$	−2.16165e15	+	1.94563e15i	−0.618548	+	0.556735i
$671$	7.20739e14			0.204552
$672$	2.15471e13	−	8.01174e13i	0.00606537	−	0.0225526i
$673$	−1.85001e15			−0.516525			−0.258262	−	0.966075i	$-0.583150\pi$
$673$	−1.85001e15			−0.516525			−0.258262	+	0.966075i	$0.583150\pi$
$674$	3.86015e15	−	3.47440e15i	1.06899	−	0.962166i
$675$	−5.95573e13	−	5.95573e13i	−0.0163593	−	0.0163593i
$676$	−3.65010e15	−	3.85010e14i	−0.994483	−	0.104897i
$677$	2.70150e15	−	2.70150e15i	0.730073	−	0.730073i	−0.240561	−	0.970634i	$-0.577331\pi$
$677$	2.70150e15	−	2.70150e15i	0.730073	−	0.730073i	0.970634	+	0.240561i	$0.0773313\pi$
$678$	2.70658e13	+	1.42349e12i	0.00725534	+	0.000381586i
$679$		−	1.05576e16i		−	2.80726i
$680$	−2.60265e15	−	4.13704e14i	−0.686462	−	0.109117i
$681$			4.18345e13i			0.0109452i
$682$	−8.53560e13	+	1.62293e15i	−0.0221524	+	0.421197i
$683$	−1.32278e15	+	1.32278e15i	−0.340545	+	0.340545i	−0.856572	−	0.516027i	$-0.827410\pi$
$683$	−1.32278e15	+	1.32278e15i	−0.340545	+	0.340545i	0.516027	+	0.856572i	$0.327410\pi$
$684$	3.45470e15	+	4.26943e15i	0.882269	+	1.09034i
$685$	−1.65484e13	−	1.65484e13i	−0.00419236	−	0.00419236i
$686$	2.47651e15	+	2.75147e15i	0.622383	+	0.691484i
$687$	6.48807e13			0.0161753
$688$	2.77896e15	−	1.80175e15i	0.687299	−	0.445612i
$689$	−7.22995e11			−0.000177390
$690$	2.08052e13	+	2.31151e13i	0.00506409	+	0.00562634i
$691$	5.16356e15	+	5.16356e15i	1.24687	+	1.24687i	0.957096	+	0.289772i	$0.0935794\pi$
$691$	5.16356e15	+	5.16356e15i	1.24687	+	1.24687i	0.289772	+	0.957096i	$0.406421\pi$
$692$	−5.63806e15	+	4.56215e15i	−1.35066	+	1.09291i
$693$	−2.99047e15	+	2.99047e15i	−0.710733	+	0.710733i
$694$	−5.06159e13	+	9.62392e14i	−0.0119347	+	0.226921i
$695$			2.43488e14i			0.0569590i
$696$	−2.87206e13	+	2.08423e13i	−0.00666565	+	0.00483722i
$697$			1.16683e15i			0.268675i
$698$	2.15482e15	+	1.13330e14i	0.492273	+	0.0258905i
$699$	1.53613e13	−	1.53613e13i	0.00348180	−	0.00348180i
$700$	−5.95988e14	+	5.65027e15i	−0.134029	+	1.27066i
$701$	−1.42137e15	−	1.42137e15i	−0.317146	−	0.317146i	0.530524	−	0.847670i	$-0.321995\pi$
$701$	−1.42137e15	−	1.42137e15i	−0.317146	−	0.317146i	−0.847670	+	0.530524i	$0.821995\pi$
$702$	−2.91688e10	+	2.62539e10i	−6.45750e−6	+	5.81219e-6i
$703$	9.52988e15			2.09331
$704$	−1.30110e15	−	2.56059e15i	−0.283570	−	0.558073i
$705$	−8.93767e12			−0.00193279
$706$	5.36040e15	−	4.82473e15i	1.15020	−	1.03525i
$707$	8.19947e15	+	8.19947e15i	1.74574	+	1.74574i
$708$	−1.02666e13	+	9.73323e13i	−0.00216891	+	0.0205624i
$709$	3.04676e15	−	3.04676e15i	0.638682	−	0.638682i	−0.311549	−	0.950230i	$-0.600848\pi$
$709$	3.04676e15	−	3.04676e15i	0.638682	−	0.638682i	0.950230	+	0.311549i	$0.100848\pi$
$710$	1.06914e15	+	5.62304e13i	0.222390	+	0.0116963i
$711$		−	1.07460e15i		−	0.221802i
$712$	−4.13962e15	+	3.00409e15i	−0.847852	+	0.615280i
$713$		−	3.81699e15i		−	0.775761i
$714$	9.34993e12	−	1.77776e14i	0.00188568	−	0.0358537i
$715$	2.98756e11	−	2.98756e11i	5.97907e−5	−	5.97907e-5i
$716$	4.69663e15	−	3.80037e15i	0.932748	−	0.754752i
$717$	6.78192e13	+	6.78192e13i	0.0133659	+	0.0133659i
$718$	−2.88803e15	−	3.20868e15i	−0.564830	−	0.627541i
$719$	−6.32346e15			−1.22729			−0.613643	−	0.789583i	$-0.710297\pi$
$719$	−6.32346e15			−1.22729			−0.613643	+	0.789583i	$0.710297\pi$
$720$	1.27676e15	+	1.96924e15i	0.245913	+	0.379289i
$721$	−4.89150e14			−0.0934971
$722$	−3.41415e15	−	3.79322e15i	−0.647632	−	0.719537i
$723$	−1.29942e13	−	1.29942e13i	−0.00244617	−	0.00244617i
$724$	3.47756e15	+	4.29769e15i	0.649699	+	0.802921i
$725$	1.71841e15	−	1.71841e15i	0.318616	−	0.318616i
$726$	−2.52408e12	+	4.79919e13i	−0.000464464	+	0.00883114i
$727$			5.66978e15i			1.03544i	0.855549	+	0.517722i	$0.173220\pi$
$727$			5.66978e15i			1.03544i	−0.855549	+	0.517722i	$0.826780\pi$
$728$	2.61443e12	+	4.15576e11i	0.000473864	+	7.53231e-5i
$729$			5.55201e15i			0.998731i
$730$	2.27482e15	+	1.19642e14i	0.406136	+	0.0213603i
$731$	5.02515e15	−	5.02515e15i	0.890437	−	0.890437i
$732$	2.68695e13	+	2.83418e12i	0.00472551	+	0.000498444i
$733$	3.73094e14	+	3.73094e14i	0.0651248	+	0.0651248i	0.738919	−	0.673794i	$-0.235337\pi$
$733$	3.73094e14	+	3.73094e14i	0.0651248	+	0.0651248i	−0.673794	+	0.738919i	$0.735337\pi$
$734$	1.66884e15	−	1.50207e15i	0.289126	−	0.260233i
$735$	6.03826e13			0.0103832
$736$	3.36749e15	+	5.84518e15i	0.574749	+	0.997631i
$737$	−6.80143e15			−1.15220
$738$	7.72357e14	−	6.95174e14i	0.129870	−	0.116892i
$739$	−6.78605e15	−	6.78605e15i	−1.13259	−	1.13259i	−0.989745	−	0.142845i	$-0.954375\pi$
$739$	−6.78605e15	−	6.78605e15i	−1.13259	−	1.13259i	−0.142845	−	0.989745i	$-0.545625\pi$
$740$	4.04992e15	+	4.27183e14i	0.670922	+	0.0707684i
$741$	2.62084e10	−	2.62084e10i	4.30963e−6	−	4.30963e-6i
$742$	−5.83414e15	−	3.06840e14i	−0.952260	−	0.0500830i
$743$			5.57329e15i			0.902970i	0.892279	+	0.451485i	$0.149106\pi$
$743$			5.57329e15i			0.902970i	−0.892279	+	0.451485i	$0.850894\pi$
$744$	−9.56400e12	+	6.01679e13i	−0.00153811	+	0.00967640i
$745$		−	2.72222e15i		−	0.434575i
$746$	−1.90934e14	+	3.63036e15i	−0.0302566	+	0.575289i
$747$	1.53280e15	−	1.53280e15i	0.241114	−	0.241114i
$748$	−3.87676e15	−	4.79103e15i	−0.605354	−	0.748118i
$749$	−7.92695e15	−	7.92695e15i	−1.22873	−	1.22873i
$750$	5.13258e13	+	5.70244e13i	0.00789767	+	0.00877453i
$751$	2.77591e14			0.0424020			0.0212010	−	0.999775i	$-0.493251\pi$
$751$	2.77591e14			0.0424020			0.0212010	+	0.999775i	$0.493251\pi$
$752$	−1.89603e15	−	4.04484e14i	−0.287506	−	0.0613343i
$753$	9.75736e13			0.0146879
$754$	−7.57505e11	−	8.41608e11i	−0.000113199	−	0.000125767i
$755$	−1.53314e15	−	1.53314e15i	−0.227443	−	0.227443i
$756$	−2.46517e14	+	1.99474e14i	−0.0363059	+	0.0293776i
$757$	−9.24724e15	+	9.24724e15i	−1.35203	+	1.35203i	−0.468632	+	0.883393i	$0.655253\pi$
$757$	−9.24724e15	+	9.24724e15i	−1.35203	+	1.35203i	−0.883393	+	0.468632i	$0.844747\pi$
$758$	3.73360e14	−	7.09893e15i	0.0541935	−	1.03042i
$759$			7.27297e13i			0.0104805i
$760$	−2.60401e15	−	3.58831e15i	−0.372536	−	0.513352i
$761$			4.32114e15i			0.613738i	0.951752	+	0.306869i	$0.0992813\pi$
$761$			4.32114e15i			0.613738i	−0.951752	+	0.306869i	$0.900719\pi$
$762$	−1.86752e14	−	9.82201e12i	−0.0263338	−	0.00138499i
$763$	−7.26743e15	+	7.26743e15i	−1.01741	+	1.01741i
$764$	9.43481e14	−	8.94469e15i	0.131135	−	1.24323i
$765$	3.56095e15	+	3.56095e15i	0.491392	+	0.491392i
$766$	8.83464e15	−	7.95178e15i	1.21040	−	1.08945i
$767$	−3.12294e12			−0.000424804
$768$	−3.84365e13	−	1.00576e14i	−0.00519107	−	0.0135834i
$769$	−8.23143e15			−1.10377			−0.551887	−	0.833919i	$-0.686092\pi$
$769$	−8.23143e15			−1.10377			−0.551887	+	0.833919i	$0.686092\pi$
$770$	2.53758e15	−	2.28400e15i	0.337848	−	0.304086i
$771$	−1.03150e14	−	1.03150e14i	−0.0136354	−	0.0136354i
$772$	−1.14073e15	+	1.08148e16i	−0.149723	+	1.41946i
$773$	2.26542e15	−	2.26542e15i	0.295230	−	0.295230i	−0.543912	−	0.839142i	$-0.683057\pi$
$773$	2.26542e15	−	2.26542e15i	0.295230	−	0.295230i	0.839142	+	0.543912i	$0.183057\pi$
$774$	−6.32017e15	−	3.32402e14i	−0.817812	−	0.0430119i
$775$		−	4.17219e15i		−	0.536049i
$776$	−8.04747e15	−	1.10894e16i	−1.02664	−	1.41471i
$777$			2.75099e14i			0.0348476i
$778$	−2.98430e14	+	5.67425e15i	−0.0375366	+	0.713708i
$779$	−1.38808e15	+	1.38808e15i	−0.173364	+	0.173364i
$780$	1.23126e10	−	9.96298e9i	1.52697e−6	−	1.23557e-6i
$781$	1.77045e15	+	1.77045e15i	0.218023	+	0.218023i
$782$	9.68364e15	+	1.07588e16i	1.18414	+	1.31561i
$783$	1.35639e14			0.0164700
$784$	1.28095e16	+	2.73268e15i	1.54452	+	0.329497i
$785$	6.74322e15			0.807392
$786$	3.64282e13	+	4.04728e13i	0.00433126	+	0.00481215i
$787$	−7.53897e15	−	7.53897e15i	−0.890125	−	0.890125i	0.104410	−	0.994534i	$-0.466705\pi$
$787$	−7.53897e15	−	7.53897e15i	−0.890125	−	0.890125i	−0.994534	+	0.104410i	$0.966705\pi$
$788$	−6.58680e15	−	8.14020e15i	−0.772290	−	0.954423i
$789$	1.30717e14	−	1.30717e14i	0.0152198	−	0.0152198i
$790$	−4.55621e13	+	8.66300e14i	−0.00526810	+	0.100166i
$791$			6.98821e15i			0.802408i
$792$	−8.61622e14	+	5.42054e15i	−0.0982490	+	0.618093i
$793$			8.62116e11i			9.76254e-5i
$794$	1.82416e15	+	9.59394e13i	0.205140	+	0.0107891i
$795$	−2.47163e13	+	2.47163e13i	−0.00276035	+	0.00276035i
$796$	4.50022e15	+	4.74680e14i	0.499128	+	0.0526477i
$797$	9.70983e14	+	9.70983e14i	0.106953	+	0.106953i	0.758558	−	0.651606i	$-0.225904\pi$
$797$	9.70983e14	+	9.70983e14i	0.106953	+	0.106953i	−0.651606	+	0.758558i	$0.725904\pi$
$798$	2.22609e14	−	2.00363e14i	0.0243516	−	0.0219181i
$799$	−4.15998e15			−0.451943
$800$	3.68087e15	+	6.38913e15i	0.397151	+	0.689361i
$801$	9.77404e15			1.04736
$802$	−8.62091e15	+	7.75941e15i	−0.917475	+	0.825790i
$803$	3.76699e15	+	3.76699e15i	0.398161	+	0.398161i
$804$	−2.53561e14	−	2.67454e13i	−0.0266179	−	0.00280764i
$805$	−5.66997e15	+	5.66997e15i	−0.591157	+	0.591157i
$806$	−1.94127e12	−	1.02099e11i	−0.000201022	−	1.05725e-5i
$807$		−	2.16427e14i		−	0.0222591i
$808$	1.48624e16	+	2.36245e15i	1.51819	+	0.241324i
$809$		−	1.29235e16i		−	1.31118i	−0.755116	−	0.655591i	$-0.772419\pi$
$809$		−	1.29235e16i		−	1.31118i	0.755116	−	0.655591i	$-0.227581\pi$
$810$	2.35499e14	−	4.47769e15i	0.0237313	−	0.451218i
$811$	1.66331e15	−	1.66331e15i	0.166478	−	0.166478i	−0.618951	−	0.785430i	$-0.712442\pi$
$811$	1.66331e15	−	1.66331e15i	0.166478	−	0.166478i	0.785430	+	0.618951i	$0.212442\pi$
$812$	−5.75544e15	−	7.11277e15i	−0.572164	−	0.707100i
$813$	−2.33360e13	−	2.33360e13i	−0.00230424	−	0.00230424i
$814$	6.37136e15	+	7.07875e15i	0.624882	+	0.694261i
$815$	5.19851e15			0.506421
$816$	−1.25687e14	−	1.93857e14i	−0.0121618	−	0.0187579i
$817$	1.19560e16			1.14912
$818$	−4.61408e15	−	5.12637e15i	−0.440496	−	0.489403i
$819$	−3.57706e12	−	3.57706e12i	−0.000339207	−	0.000339207i
$820$	−6.52116e14	+	5.27673e14i	−0.0614255	+	0.0497037i
$821$	−1.85833e15	+	1.85833e15i	−0.173874	+	0.173874i	−0.788679	−	0.614805i	$-0.789235\pi$
$821$	−1.85833e15	+	1.85833e15i	−0.173874	+	0.173874i	0.614805	+	0.788679i	$0.289235\pi$
$822$	1.07759e11	−	2.04889e12i	1.00152e−5	−	0.000190425i
$823$			3.78648e15i			0.349572i	0.984606	+	0.174786i	$0.0559233\pi$
$823$			3.78648e15i			0.349572i	−0.984606	+	0.174786i	$0.944077\pi$
$824$	−5.13785e14	+	3.72850e14i	−0.0471175	+	0.0341928i
$825$			7.94979e13i			0.00724200i
$826$	−2.52003e16	−	1.32538e15i	−2.28042	−	0.119936i
$827$	9.50050e14	−	9.50050e14i	0.0854017	−	0.0854017i	−0.663115	−	0.748517i	$-0.730766\pi$
$827$	9.50050e14	−	9.50050e14i	0.0854017	−	0.0854017i	0.748517	+	0.663115i	$0.230766\pi$
$828$	1.35222e15	−	1.28197e16i	0.120748	−	1.14476i
$829$	4.90252e15	+	4.90252e15i	0.434880	+	0.434880i	0.890285	−	0.455405i	$-0.150505\pi$
$829$	4.90252e15	+	4.90252e15i	0.434880	+	0.434880i	−0.455405	+	0.890285i	$0.650505\pi$
$830$	−1.30067e15	+	1.17069e15i	−0.114614	+	0.103160i
$831$	−8.32462e13			−0.00728717
$832$	3.06287e12	−	1.55632e12i	0.000266348	−	0.000135338i
$833$	2.81047e16			2.42790
$834$	−1.58661e13	+	1.42806e13i	−0.00136162	+	0.00122555i
$835$	−3.71159e15	−	3.71159e15i	−0.316435	−	0.316435i
$836$	1.08764e15	−	1.03114e16i	0.0921191	−	0.873337i
$837$	1.64661e14	−	1.64661e14i	0.0138548	−	0.0138548i
$838$	6.41385e15	+	3.37329e14i	0.536138	+	0.0281975i
$839$		−	8.68913e15i		−	0.721582i	−0.932647	−	0.360791i	$-0.882507\pi$
$839$		−	8.68913e15i		−	0.721582i	0.932647	−	0.360791i	$-0.117493\pi$
$840$	1.03584e14	−	7.51699e13i	0.00854585	−	0.00620166i
$841$		−	8.28692e15i		−	0.679228i
$842$	−9.33998e14	+	1.77587e16i	−0.0760553	+	1.44609i
$843$	1.47204e13	−	1.47204e13i	0.00119088	−	0.00119088i
$844$	−3.00480e14	+	2.43139e14i	−0.0241508	+	0.0195421i
$845$	−4.00367e15	−	4.00367e15i	−0.319703	−	0.319703i
$846$	2.47843e15	+	2.75361e15i	0.196626	+	0.218457i
$847$	−1.23912e16			−0.976685
$848$	−6.36186e15	+	4.12473e15i	−0.498203	+	0.323012i
$849$	−1.64261e14			−0.0127804
$850$	1.05848e16	+	1.17600e16i	0.818235	+	0.909081i
$851$	−1.58167e16	−	1.58167e16i	−1.21480	−	1.21480i
$852$	5.90412e13	+	7.29651e13i	0.00450544	+	0.00556798i
$853$	6.96978e15	−	6.96978e15i	0.528444	−	0.528444i	−0.391664	−	0.920108i	$-0.628100\pi$
$853$	6.96978e15	−	6.96978e15i	0.528444	−	0.528444i	0.920108	+	0.391664i	$0.128100\pi$
$854$	−3.65883e14	+	6.95677e15i	−0.0275628	+	0.524070i
$855$			8.47235e15i			0.634148i
$856$	−1.43684e16	−	2.28393e15i	−1.06857	−	0.169855i
$857$			1.21335e16i			0.896583i	0.893887	+	0.448291i	$0.147967\pi$
$857$			1.21335e16i			0.896583i	−0.893887	+	0.448291i	$0.852033\pi$
$858$	3.69895e10	+	1.94542e9i	2.71580e−6	+	1.42834e-7i
$859$	1.79130e16	−	1.79130e16i	1.30679	−	1.30679i	0.383073	−	0.923718i	$-0.374866\pi$
$859$	1.79130e16	−	1.79130e16i	1.30679	−	1.30679i	0.923718	−	0.383073i	$-0.125134\pi$
$860$	5.08096e15	+	5.35937e14i	0.368302	+	0.0388483i
$861$	−4.00697e13	−	4.00697e13i	−0.00288602	−	0.00288602i
$862$	−2.54553e15	+	2.29115e15i	−0.182175	+	0.163970i
$863$	1.72118e16			1.22396			0.611981	−	0.790872i	$-0.290373\pi$
$863$	1.72118e16			1.22396			0.611981	+	0.790872i	$0.290373\pi$
$864$	−1.06885e14	+	3.97426e14i	−0.00755253	+	0.0280822i
$865$	−1.11883e16			−0.785552
$866$	9.79136e14	−	8.81289e14i	0.0683116	−	0.0614851i
$867$	−2.02227e14	−	2.02227e14i	−0.0140196	−	0.0140196i
$868$	−1.56216e16	−	1.64776e15i	−1.07614	−	0.113510i
$869$	−1.43455e15	+	1.43455e15i	−0.0981988	+	0.0981988i
$870$	−5.46673e13	−	2.87516e12i	−0.00371853	−	0.000195572i
$871$		−	8.13557e12i		−	0.000549906i
$872$	−2.09391e15	+	1.31730e16i	−0.140643	+	0.884797i
$873$			2.61831e16i			1.74760i
$874$	−1.27901e15	+	2.43187e16i	−0.0848325	+	1.61297i
$875$	−1.39877e16	+	1.39877e16i	−0.921936	+	0.921936i
$876$	1.25622e14	+	1.55248e14i	0.00822798	+	0.0101684i
$877$	1.33062e16	+	1.33062e16i	0.866077	+	0.866077i	0.992035	−	0.125959i	$-0.0402007\pi$
$877$	1.33062e16	+	1.33062e16i	0.866077	+	0.866077i	−0.125959	+	0.992035i	$0.540201\pi$
$878$	−1.03165e16	−	1.14619e16i	−0.667284	−	0.741370i
$879$	1.86307e14			0.0119754
$880$	9.24428e14	−	4.33328e15i	0.0590498	−	0.276797i
$881$	4.45823e15			0.283006			0.141503	−	0.989938i	$-0.454807\pi$
$881$	4.45823e15			0.283006			0.141503	+	0.989938i	$0.454807\pi$
$882$	−1.67442e16	−	1.86033e16i	−1.05630	−	1.17358i
$883$	−1.83650e16	−	1.83650e16i	−1.15135	−	1.15135i	−0.986282	−	0.165067i	$-0.947216\pi$
$883$	−1.83650e16	−	1.83650e16i	−1.15135	−	1.15135i	−0.165067	−	0.986282i	$-0.552784\pi$
$884$	5.73082e12	−	4.63720e12i	0.000357050	−	0.000288914i
$885$	−1.06761e14	+	1.06761e14i	−0.00661034	+	0.00661034i
$886$	9.50140e14	−	1.80656e16i	0.0584659	−	1.11165i
$887$			2.92053e16i			1.78600i	0.450055	+	0.893001i	$0.351405\pi$
$887$			2.92053e16i			1.78600i	−0.450055	+	0.893001i	$0.648595\pi$
$888$	2.09691e14	+	2.88954e14i	0.0127441	+	0.0175613i
$889$		−	4.82182e16i		−	2.91240i
$890$	−7.87942e15	−	4.14409e14i	−0.472987	−	0.0248762i
$891$	7.41482e15	−	7.41482e15i	0.442357	−	0.442357i
$892$	3.69335e14	−	3.50149e15i	0.0218985	−	0.207609i
$893$	−4.94879e15	−	4.94879e15i	−0.291619	−	0.291619i
$894$	1.77385e14	−	1.59658e14i	0.0103887	−	0.00935050i
$895$	9.32009e15			0.542492
$896$	2.53760e16	−	1.12587e16i	1.46801	−	0.651318i
$897$	−8.69961e10			−5.00197e−6
$898$	2.28161e15	−	2.05361e15i	0.130383	−	0.117354i
$899$	4.75098e15	+	4.75098e15i	0.269839	+	0.269839i
$900$	1.47806e15	−	1.40127e16i	0.0834367	−	0.791023i
$901$	−1.15040e16	+	1.15040e16i	−0.645452	+	0.645452i
$902$	−1.95909e15	−	1.03036e14i	−0.109249	−	0.00574583i
$903$			3.45134e14i			0.0191296i
$904$	5.32670e15	+	7.34016e15i	0.293449	+	0.404370i
$905$			8.52842e15i			0.466983i
$906$	9.98336e12	−	1.89820e14i	0.000543340	−	0.0103309i
$907$	−1.16249e16	+	1.16249e16i	−0.628852	+	0.628852i	−0.947779	−	0.318928i	$-0.896677\pi$
$907$	−1.16249e16	+	1.16249e16i	−0.628852	+	0.628852i	0.318928	+	0.947779i	$0.396677\pi$
$908$	−1.08823e16	+	8.80560e15i	−0.585123	+	0.473464i
$909$	−2.03348e16	−	2.03348e16i	−1.08677	−	1.08677i
$910$	2.73202e12	+	3.03534e12i	0.000145129	+	0.000161243i
$911$	−1.60745e16			−0.848763			−0.424381	−	0.905484i	$-0.639508\pi$
$911$	−1.60745e16			−0.848763			−0.424381	+	0.905484i	$0.639508\pi$
$912$	8.10953e13	−	3.80136e14i	0.00425622	−	0.0199511i
$913$	−4.09245e15			−0.213498
$914$	4.05466e15	+	4.50483e15i	0.210257	+	0.233601i
$915$	2.94723e13	+	2.94723e13i	0.00151914	+	0.00151914i
$916$	1.36565e16	+	1.68772e16i	0.699705	+	0.864720i
$917$	−9.92766e15	+	9.92766e15i	−0.505610	+	0.505610i
$918$	−4.63808e13	+	8.81867e14i	−0.00234803	+	0.0446445i
$919$		−	9.90101e15i		−	0.498246i	−0.968472	−	0.249123i	$-0.919858\pi$
$919$		−	9.90101e15i		−	0.498246i	0.968472	−	0.249123i	$-0.0801424\pi$
$920$	−1.63365e15	+	1.02774e16i	−0.0817194	+	0.514104i
$921$			1.55664e14i			0.00774033i
$922$	2.69561e16	+	1.41773e15i	1.33241	+	0.0700765i
$923$	−2.11773e12	+	2.11773e12i	−0.000104055	+	0.000104055i
$924$	2.97658e14	+	3.13968e13i	0.0145386	+	0.00153352i
$925$	−1.72886e16	−	1.72886e16i	−0.839424	−	0.839424i
$926$	1.98281e16	−	1.78467e16i	0.957021	−	0.861384i
$927$	1.21310e15			0.0582046
$928$	−1.14670e16	−	3.08396e15i	−0.546933	−	0.147094i
$929$	−8.35454e15			−0.396129			−0.198064	−	0.980189i	$-0.563466\pi$
$929$	−8.35454e15			−0.396129			−0.198064	+	0.980189i	$0.563466\pi$
$930$	−6.98548e13	+	6.28741e13i	−0.00329261	+	0.00296357i
$931$	3.34339e16	+	3.34339e16i	1.56662	+	1.56662i
$932$	7.22923e15	+	7.62535e14i	0.336748	+	0.0355200i
$933$	3.80735e13	−	3.80735e13i	0.00176308	−	0.00176308i
$934$	2.34263e16	+	1.23208e15i	1.07844	+	0.0567193i
$935$		−	9.50742e15i		−	0.435110i
$936$	−6.48381e12	−	1.03063e12i	−0.000294994	−	4.68907e-5i
$937$			1.76291e15i			0.0797375i	0.999205	+	0.0398687i	$0.0126940\pi$
$937$			1.76291e15i			0.0797375i	−0.999205	+	0.0398687i	$0.987306\pi$
$938$	3.45275e15	−	6.56493e16i	0.155256	−	2.95199i
$939$	−2.53962e14	+	2.53962e14i	−0.0113529	+	0.0113529i
$940$	−1.88126e15	−	2.32493e15i	−0.0836076	−	0.103325i
$941$	2.59086e16	+	2.59086e16i	1.14472	+	1.14472i	0.987575	+	0.157148i	$0.0502299\pi$
$941$	2.59086e16	+	2.59086e16i	1.14472	+	1.14472i	0.157148	+	0.987575i	$0.449770\pi$
$942$	3.95489e14	+	4.39399e14i	0.0173722	+	0.0193010i
$943$	4.60761e15			0.201215
$944$	−2.74797e16	+	1.78166e16i	−1.19307	+	0.773531i
$945$	−4.89194e14			−0.0211157
$946$	7.99341e15	+	8.88089e15i	0.343029	+	0.381114i
$947$	6.71626e15	+	6.71626e15i	0.286551	+	0.286551i	0.835715	−	0.549164i	$-0.185054\pi$
$947$	6.71626e15	+	6.71626e15i	0.286551	+	0.286551i	−0.549164	+	0.835715i	$0.685054\pi$
$948$	−5.91218e13	+	4.78395e13i	−0.00250785	+	0.00202928i
$949$	−4.50590e12	+	4.50590e12i	−0.000190028	+	0.000190028i
$950$	−1.39804e15	+	2.65818e16i	−0.0586191	+	1.11456i
$951$			2.79005e14i			0.0116310i
$952$	4.82124e16	−	3.49874e16i	1.99828	−	1.45013i
$953$			2.82628e16i			1.16467i	0.812948	+	0.582337i	$0.197862\pi$
$953$			2.82628e16i			1.16467i	−0.812948	+	0.582337i	$0.802138\pi$
$954$	1.44687e16	+	7.60966e14i	0.592809	+	0.0311781i
$955$	9.81115e15	−	9.81115e15i	0.399670	−	0.399670i
$956$	−3.36654e15	+	3.19166e16i	−0.136353	+	1.29270i
$957$	−9.05262e13	−	9.05262e13i	−0.00364551	−	0.00364551i
$958$	−1.04691e16	+	9.42287e15i	−0.419177	+	0.377288i
$959$	5.29009e14			0.0210601
$960$	5.15030e13	−	1.57912e14i	0.00203864	−	0.00625060i
$961$	−1.38734e16			−0.546014
$962$	−8.46729e12	+	7.62114e12i	−0.000331346	+	0.000298234i
$963$	1.96589e16	+	1.96589e16i	0.764918	+	0.764918i
$964$	6.45030e14	−	6.11522e15i	0.0249549	−	0.236586i
$965$	−1.18624e16	+	1.18624e16i	−0.456322	+	0.456322i
$966$	−7.02007e14	−	3.69213e13i	−0.0268514	−	0.00141222i
$967$		−	2.49897e16i		−	0.950419i	−0.879873	−	0.475210i	$-0.842372\pi$
$967$		−	2.49897e16i		−	0.950419i	0.879873	−	0.475210i	$-0.157628\pi$
$968$	−1.30153e16	+	9.44508e15i	−0.492197	+	0.357183i
$969$		−	8.34037e14i		−	0.0313621i
$970$	1.11013e15	−	2.11077e16i	0.0415079	−	0.789216i
$971$	3.04085e15	−	3.04085e15i	0.113055	−	0.113055i	−0.648316	−	0.761371i	$-0.724527\pi$
$971$	3.04085e15	−	3.04085e15i	0.113055	−	0.113055i	0.761371	+	0.648316i	$0.224527\pi$
$972$	9.17080e14	−	7.42074e14i	0.0339034	−	0.0274336i
$973$	−3.89184e15	−	3.89184e15i	−0.143065	−	0.143065i
$974$	3.12141e14	+	3.46797e14i	0.0114098	+	0.0126766i
$975$	−9.50919e10			−3.45635e−6
$976$	4.91842e15	+	7.58603e15i	0.177767	+	0.274183i
$977$	−4.17048e16			−1.49888			−0.749439	−	0.662074i	$-0.769676\pi$
$977$	−4.17048e16			−1.49888			−0.749439	+	0.662074i	$0.769676\pi$
$978$	3.04892e14	+	3.38743e14i	0.0108964	+	0.0121062i
$979$	−1.30479e16	−	1.30479e16i	−0.463699	−	0.463699i
$980$	1.27097e16	+	1.57071e16i	0.449152	+	0.555078i
$981$	1.80233e16	−	1.80233e16i	0.633367	−	0.633367i
$982$	1.55596e15	−	2.95844e16i	0.0543731	−	1.03383i
$983$			1.27193e16i			0.441997i	0.975274	+	0.220998i	$0.0709315\pi$
$983$			1.27193e16i			0.441997i	−0.975274	+	0.220998i	$0.929068\pi$
$984$	−7.26306e13	−	1.15450e13i	−0.00250984	−	0.000398952i
$985$		−	1.61536e16i		−	0.555098i
$986$	−2.54445e16	−	1.33823e15i	−0.869504	−	0.0457306i
$987$	1.42857e14	−	1.42857e14i	0.00485463	−	0.00485463i
$988$	1.23340e13	+	1.30098e12i	0.000416813	+	4.39652e-5i
$989$	−1.98434e16	−	1.98434e16i	−0.666864	−	0.666864i
$990$	−6.29323e15	+	5.66434e15i	−0.210320	+	0.189302i
$991$	3.48521e16			1.15831			0.579153	−	0.815219i	$-0.303383\pi$
$991$	3.48521e16			1.15831			0.579153	+	0.815219i	$0.303383\pi$
$992$	−1.76644e16	+	1.01767e16i	−0.583827	+	0.336351i
$993$	3.27223e14			0.0107553
$994$	−1.79876e16	+	1.61901e16i	−0.587961	+	0.529205i
$995$	4.93615e15	+	4.93615e15i	0.160458	+	0.160458i
$996$	−1.52568e14	−	1.60928e13i	−0.00493217	−	0.000520243i
$997$	2.81313e16	−	2.81313e16i	0.904411	−	0.904411i	−0.0914030	−	0.995814i	$-0.529135\pi$
$997$	2.81313e16	−	2.81313e16i	0.904411	−	0.904411i	0.995814	+	0.0914030i	$0.0291351\pi$
$998$	−2.44630e16	−	1.28661e15i	−0.782155	−	0.0411365i
$999$		−	1.36464e15i		−	0.0433918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.12.e.a.13.5	yes	42
4.3	odd	2		64.12.e.a.17.11		42
8.3	odd	2		128.12.e.a.33.11		42
8.5	even	2		128.12.e.b.33.11		42
16.3	odd	4		128.12.e.a.97.11		42
16.5	even	4	inner	16.12.e.a.5.5	✓	42
16.11	odd	4		64.12.e.a.49.11		42
16.13	even	4		128.12.e.b.97.11		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.5	✓	42	16.5	even	4	inner
16.12.e.a.13.5	yes	42	1.1	even	1	trivial
64.12.e.a.17.11		42	4.3	odd	2
64.12.e.a.49.11		42	16.11	odd	4
128.12.e.a.33.11		42	8.3	odd	2
128.12.e.a.97.11		42	16.3	odd	4
128.12.e.b.33.11		42	8.5	even	2
128.12.e.b.97.11		42	16.13	even	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-33.6365 + 30.2752i) q^{2} +(-4.32776 - 4.32776i) q^{3} +(214.830 - 2036.70i) q^{4} +(2233.99 - 2233.99i) q^{5} +(276.594 + 14.5472i) q^{6} +71414.8i q^{7} +(54435.3 + 75011.5i) q^{8} -177110. i q^{9} +O(q^{10})\)	\(q+(-33.6365 + 30.2752i) q^{2} +(-4.32776 - 4.32776i) q^{3} +(214.830 - 2036.70i) q^{4} +(2233.99 - 2233.99i) q^{5} +(276.594 + 14.5472i) q^{6} +71414.8i q^{7} +(54435.3 + 75011.5i) q^{8} -177110. i q^{9} +(-7509.26 + 142778. i) q^{10} +(-236433. + 236433. i) q^{11} +(-9744.08 + 7884.62i) q^{12} +(-282.811 - 282.811i) q^{13} +(-2.16209e6 - 2.40215e6i) q^{14} -19336.4 q^{15} +(-4.10200e6 - 875089. i) q^{16} -8.99999e6 q^{17} +(5.36202e6 + 5.95735e6i) q^{18} +(-1.07066e7 - 1.07066e7i) q^{19} +(-4.07005e6 - 5.02991e6i) q^{20} +(309066. - 309066. i) q^{21} +(794737. - 1.51108e7i) q^{22} +3.55394e7i q^{23} +(89049.0 - 560215. i) q^{24} +3.88467e7i q^{25} +(18074.9 + 950.630i) q^{26} +(-1.53314e6 + 1.53314e6i) q^{27} +(1.45451e8 + 1.53421e7i) q^{28} +(-4.42357e7 - 4.42357e7i) q^{29} +(650408. - 585412. i) q^{30} -1.07402e8 q^{31} +(1.64470e8 - 9.47537e7i) q^{32} +2.04645e6 q^{33} +(3.02728e8 - 2.72476e8i) q^{34} +(1.59540e8 + 1.59540e8i) q^{35} +(-3.60719e8 - 3.80485e7i) q^{36} +(-4.45048e8 + 4.45048e8i) q^{37} +(6.84274e8 + 3.59886e7i) q^{38} +2447.88i q^{39} +(2.89183e8 + 4.59672e7i) q^{40} -1.29648e8i q^{41} +(-1.03888e6 + 1.97529e7i) q^{42} +(-5.58350e8 + 5.58350e8i) q^{43} +(4.30751e8 + 5.32337e8i) q^{44} +(-3.95662e8 - 3.95662e8i) q^{45} +(-1.07596e9 - 1.19542e9i) q^{46} +4.62220e8 q^{47} +(1.39653e7 + 2.15396e7i) q^{48} -3.12275e9 q^{49} +(-1.17609e9 - 1.30667e9i) q^{50} +(3.89498e7 + 3.89498e7i) q^{51} +(-636758. + 515245. i) q^{52} +(1.27823e9 - 1.27823e9i) q^{53} +(5.15342e6 - 9.79853e7i) q^{54} +1.05638e9i q^{55} +(-5.35694e9 + 3.88749e9i) q^{56} +9.26709e7i q^{57} +(2.82717e9 + 1.48692e8i) q^{58} +(5.52124e9 - 5.52124e9i) q^{59} +(-4.15403e6 + 3.93824e7i) q^{60} +(-1.52419e9 - 1.52419e9i) q^{61} +(3.61261e9 - 3.25160e9i) q^{62} +1.26482e10 q^{63} +(-2.66353e9 + 8.16655e9i) q^{64} -1.26360e6 q^{65} +(-6.88355e7 + 6.19567e7i) q^{66} +(1.43834e10 + 1.43834e10i) q^{67} +(-1.93347e9 + 1.83303e10i) q^{68} +(1.53806e8 - 1.53806e8i) q^{69} +(-1.01965e10 - 5.36272e8i) q^{70} -7.48815e9i q^{71} +(1.32853e10 - 9.64101e9i) q^{72} -1.59325e10i q^{73} +(1.49597e9 - 2.84438e10i) q^{74} +(1.68119e8 - 1.68119e8i) q^{75} +(-2.41062e10 + 1.95060e10i) q^{76} +(-1.68848e10 - 1.68848e10i) q^{77} +(-74109.8 - 82338.0i) q^{78} +6.06745e9 q^{79} +(-1.11188e10 + 7.20890e9i) q^{80} -3.13612e10 q^{81} +(3.92511e9 + 4.36090e9i) q^{82} +(8.65455e9 + 8.65455e9i) q^{83} +(-5.63079e8 - 6.95872e8i) q^{84} +(-2.01059e10 + 2.01059e10i) q^{85} +(1.87682e9 - 3.56851e10i) q^{86} +3.82883e8i q^{87} +(-3.06056e10 - 4.86491e9i) q^{88} +5.51864e10i q^{89} +(2.52874e10 + 1.32996e9i) q^{90} +(2.01969e7 - 2.01969e7i) q^{91} +(7.23832e10 + 7.63493e9i) q^{92} +(4.64808e8 + 4.64808e8i) q^{93} +(-1.55475e10 + 1.39938e10i) q^{94} -4.78368e10 q^{95} +(-1.12186e9 - 3.01717e8i) q^{96} -1.47835e11 q^{97} +(1.05038e11 - 9.45417e10i) q^{98} +(4.18746e10 + 4.18746e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8}+O(q^{10}) \) 42 * q - 2 * q^2 - 2 * q^3 + 3080 * q^4 - 2 * q^5 + 30352 * q^6 + 74836 * q^8	\( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8} - 988948 q^{10} - 540846 q^{11} + 2300260 q^{12} - 2 q^{13} - 1829956 q^{14} - 6075004 q^{15} - 3721448 q^{16} - 4 q^{17} - 32219106 q^{18} - 11291290 q^{19} + 68655164 q^{20} + 354292 q^{21} - 85011388 q^{22} - 66180944 q^{24} + 305685384 q^{26} - 66463304 q^{27} - 322075880 q^{28} + 77673206 q^{29} + 290643636 q^{30} + 343549808 q^{31} + 404698568 q^{32} - 4 q^{33} - 882461836 q^{34} - 434731684 q^{35} + 1854387628 q^{36} - 522762058 q^{37} - 1276252832 q^{38} - 483241016 q^{40} + 2372079160 q^{42} + 3824193658 q^{43} - 2657283740 q^{44} + 97301954 q^{45} - 1032658964 q^{46} - 4586900144 q^{47} - 1058870552 q^{48} - 8474257474 q^{49} + 6515930886 q^{50} + 7074245796 q^{51} - 13915491564 q^{52} - 2100608058 q^{53} + 4385621536 q^{54} + 12910845976 q^{56} - 21491153128 q^{58} + 955824746 q^{59} + 25615752768 q^{60} + 2150827022 q^{61} - 15814519760 q^{62} + 27758037828 q^{63} + 9674332160 q^{64} - 1884965292 q^{65} + 10932459412 q^{66} - 3186519018 q^{67} + 13817664656 q^{68} - 16193060732 q^{69} - 27206453120 q^{70} - 20773133628 q^{72} + 14141420908 q^{74} + 28890034486 q^{75} - 11786004940 q^{76} - 22711870540 q^{77} + 37031200508 q^{78} + 48011833792 q^{79} - 8952586328 q^{80} - 90656394430 q^{81} - 81555388352 q^{82} + 55713221118 q^{83} + 61178517160 q^{84} - 84575506252 q^{85} + 10047297860 q^{86} - 162855622152 q^{88} + 160133627736 q^{90} - 147369662716 q^{91} - 169766721928 q^{92} - 69689773328 q^{93} + 160320530128 q^{94} + 375702304500 q^{95} + 230764310192 q^{96} - 4 q^{97} - 108887063494 q^{98} - 286271331106 q^{99}+O(q^{100}) \) 42 * q - 2 * q^2 - 2 * q^3 + 3080 * q^4 - 2 * q^5 + 30352 * q^6 + 74836 * q^8 - 988948 * q^10 - 540846 * q^11 + 2300260 * q^12 - 2 * q^13 - 1829956 * q^14 - 6075004 * q^15 - 3721448 * q^16 - 4 * q^17 - 32219106 * q^18 - 11291290 * q^19 + 68655164 * q^20 + 354292 * q^21 - 85011388 * q^22 - 66180944 * q^24 + 305685384 * q^26 - 66463304 * q^27 - 322075880 * q^28 + 77673206 * q^29 + 290643636 * q^30 + 343549808 * q^31 + 404698568 * q^32 - 4 * q^33 - 882461836 * q^34 - 434731684 * q^35 + 1854387628 * q^36 - 522762058 * q^37 - 1276252832 * q^38 - 483241016 * q^40 + 2372079160 * q^42 + 3824193658 * q^43 - 2657283740 * q^44 + 97301954 * q^45 - 1032658964 * q^46 - 4586900144 * q^47 - 1058870552 * q^48 - 8474257474 * q^49 + 6515930886 * q^50 + 7074245796 * q^51 - 13915491564 * q^52 - 2100608058 * q^53 + 4385621536 * q^54 + 12910845976 * q^56 - 21491153128 * q^58 + 955824746 * q^59 + 25615752768 * q^60 + 2150827022 * q^61 - 15814519760 * q^62 + 27758037828 * q^63 + 9674332160 * q^64 - 1884965292 * q^65 + 10932459412 * q^66 - 3186519018 * q^67 + 13817664656 * q^68 - 16193060732 * q^69 - 27206453120 * q^70 - 20773133628 * q^72 + 14141420908 * q^74 + 28890034486 * q^75 - 11786004940 * q^76 - 22711870540 * q^77 + 37031200508 * q^78 + 48011833792 * q^79 - 8952586328 * q^80 - 90656394430 * q^81 - 81555388352 * q^82 + 55713221118 * q^83 + 61178517160 * q^84 - 84575506252 * q^85 + 10047297860 * q^86 - 162855622152 * q^88 + 160133627736 * q^90 - 147369662716 * q^91 - 169766721928 * q^92 - 69689773328 * q^93 + 160320530128 * q^94 + 375702304500 * q^95 + 230764310192 * q^96 - 4 * q^97 - 108887063494 * q^98 - 286271331106 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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