LMFDB - Embedded newform 16.12.e.a.5.21

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			5.21
Character	$\chi$	$=$	16.5
Dual form			16.12.e.a.13.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(45.2548 + 0.00312776i) q^{2} +(457.250 - 457.250i) q^{3} +(2048.00 + 0.283093i) q^{4} +(5575.43 + 5575.43i) q^{5} +(20694.2 - 20691.3i) q^{6} +55452.7i q^{7} +(92681.9 + 19.2170i) q^{8} -241008. i q^{9} +O(q^{10})$	\(q+(45.2548 + 0.00312776i) q^{2} +(457.250 - 457.250i) q^{3} +(2048.00 + 0.283093i) q^{4} +(5575.43 + 5575.43i) q^{5} +(20694.2 - 20691.3i) q^{6} +55452.7i q^{7} +(92681.9 + 19.2170i) q^{8} -241008. i q^{9} +(252298. + 252332. i) q^{10} +(-593916. - 593916. i) q^{11} +(936577. - 936318. i) q^{12} +(-320484. + 320484. i) q^{13} +(-173.443 + 2.50950e6i) q^{14} +5.09873e6 q^{15} +(4.19430e6 + 1159.55i) q^{16} -9.66759e6 q^{17} +(753.816 - 1.09068e7i) q^{18} +(6.35824e6 - 6.35824e6i) q^{19} +(1.14169e7 + 1.14201e7i) q^{20} +(2.53557e7 + 2.53557e7i) q^{21} +(-2.68757e7 - 2.68794e7i) q^{22} -1.96028e7i q^{23} +(4.23876e7 - 4.23700e7i) q^{24} +1.33426e7i q^{25} +(-1.45044e7 + 1.45024e7i) q^{26} +(-2.92004e7 - 2.92004e7i) q^{27} +(-15698.3 + 1.13567e8i) q^{28} +(-7.64662e7 + 7.64662e7i) q^{29} +(2.30742e8 + 15947.6i) q^{30} -1.66832e8 q^{31} +(1.89813e8 + 65593.9i) q^{32} -5.43136e8 q^{33} +(-4.37505e8 - 30237.9i) q^{34} +(-3.09173e8 + 3.09173e8i) q^{35} +(68227.6 - 4.93584e8i) q^{36} +(2.74973e7 + 2.74973e7i) q^{37} +(2.87761e8 - 2.87721e8i) q^{38} +2.93082e8i q^{39} +(5.16634e8 + 5.16848e8i) q^{40} -6.15454e8i q^{41} +(1.14739e9 + 1.14755e9i) q^{42} +(8.26623e8 + 8.26623e8i) q^{43} +(-1.21617e9 - 1.21651e9i) q^{44} +(1.34372e9 - 1.34372e9i) q^{45} +(61312.9 - 8.87121e8i) q^{46} +1.20677e9 q^{47} +(1.91838e9 - 1.91731e9i) q^{48} -1.09768e9 q^{49} +(-41732.6 + 6.03819e8i) q^{50} +(-4.42051e9 + 4.42051e9i) q^{51} +(-6.56441e8 + 6.56260e8i) q^{52} +(6.02601e8 + 6.02601e8i) q^{53} +(-1.32137e9 - 1.32155e9i) q^{54} -6.62267e9i q^{55} +(-1.06563e6 + 5.13946e9i) q^{56} -5.81461e9i q^{57} +(-3.46071e9 + 3.46023e9i) q^{58} +(3.88524e9 + 3.88524e9i) q^{59} +(1.04422e10 + 1.44341e6i) q^{60} +(-2.43319e9 + 2.43319e9i) q^{61} +(-7.54996e9 - 521811. i) q^{62} +1.33645e10 q^{63} +(8.58993e9 + 3.56213e6i) q^{64} -3.57367e9 q^{65} +(-2.45795e10 - 1.69880e6i) q^{66} +(8.86750e9 - 8.86750e9i) q^{67} +(-1.97992e10 - 2.73683e6i) q^{68} +(-8.96337e9 - 8.96337e9i) q^{69} +(-1.39925e10 + 1.39906e10i) q^{70} +2.93481e10i q^{71} +(4.63144e6 - 2.23371e10i) q^{72} +7.45154e9i q^{73} +(1.24430e9 + 1.24447e9i) q^{74} +(6.10092e9 + 6.10092e9i) q^{75} +(1.30235e10 - 1.30199e10i) q^{76} +(3.29342e10 - 3.29342e10i) q^{77} +(-916692. + 1.32634e10i) q^{78} -2.31480e10 q^{79} +(2.33786e10 + 2.33915e10i) q^{80} +1.59901e10 q^{81} +(1.92499e6 - 2.78523e10i) q^{82} +(4.40857e9 - 4.40857e9i) q^{83} +(5.19214e10 + 5.19358e10i) q^{84} +(-5.39010e10 - 5.39010e10i) q^{85} +(3.74061e10 + 3.74113e10i) q^{86} +6.99284e10i q^{87} +(-5.50338e10 - 5.50566e10i) q^{88} -4.82749e10i q^{89} +(6.08141e10 - 6.08057e10i) q^{90} +(-1.77717e10 - 1.77717e10i) q^{91} +(5.54941e6 - 4.01465e10i) q^{92} +(-7.62839e10 + 7.62839e10i) q^{93} +(5.46122e10 + 3.77449e6i) q^{94} +7.08998e10 q^{95} +(8.68217e10 - 8.67618e10i) q^{96} +9.19031e10 q^{97} +(-4.96752e10 - 3.43328e6i) q^{98} +(-1.43138e11 + 1.43138e11i) 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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	45.2548	+	0.00312776i	1.00000	+	6.91145e-5i
$2$	45.2548	+	0.00312776i	1.00000	+	6.91145e-5i
$3$	457.250	−	457.250i	1.08639	−	1.08639i	0.0904954	−	0.995897i	$-0.471155\pi$
$3$	457.250	−	457.250i	1.08639	−	1.08639i	0.995897	−	0.0904954i	$-0.0288451\pi$
$4$	2048.00	+	0.283093i	1.00000	+	0.000138229i
$5$	5575.43	+	5575.43i	0.797890	+	0.797890i	0.982763	−	0.184872i	$-0.0591872\pi$
$5$	5575.43	+	5575.43i	0.797890	+	0.797890i	−0.184872	+	0.982763i	$0.559187\pi$
$6$	20694.2	−	20691.3i	1.08647	−	1.08632i
$7$			55452.7i			1.24705i	0.781804	+	0.623525i	$0.214300\pi$
$7$			55452.7i			1.24705i	−0.781804	+	0.623525i	$0.785700\pi$
$8$	92681.9	+	19.2170i	1.00000	+	0.000207343i
$9$		−	241008.i		−	1.36050i
$10$	252298.	+	252332.i	0.797835	+	0.797945i
$11$	−593916.	−	593916.i	−1.11190	−	1.11190i	−0.992894	−	0.119004i	$-0.962030\pi$
$11$	−593916.	−	593916.i	−1.11190	−	1.11190i	−0.119004	−	0.992894i	$-0.537970\pi$
$12$	936577.	−	936318.i	1.08654	−	1.08624i
$13$	−320484.	+	320484.i	−0.239396	+	0.239396i	−0.816600	−	0.577204i	$-0.804144\pi$
$13$	−320484.	+	320484.i	−0.239396	+	0.239396i	0.577204	+	0.816600i	$0.304144\pi$
$14$	−173.443	+	2.50950e6i	−8.61891e−5	+	1.24705i
$15$	5.09873e6			1.73364
$16$	4.19430e6	+	1159.55i	1.00000	+	0.000276458i
$17$	−9.66759e6			−1.65139			−0.825694	−	0.564118i	$-0.809216\pi$
$17$	−9.66759e6			−1.65139			−0.825694	+	0.564118i	$0.809216\pi$
$18$	753.816	−	1.09068e7i	9.40300e−5	−	1.36050i
$19$	6.35824e6	−	6.35824e6i	0.589104	−	0.589104i	−0.348285	−	0.937389i	$-0.613236\pi$
$19$	6.35824e6	−	6.35824e6i	0.589104	−	0.589104i	0.937389	+	0.348285i	$0.113236\pi$
$20$	1.14169e7	+	1.14201e7i	0.797780	+	0.798000i
$21$	2.53557e7	+	2.53557e7i	1.35478	+	1.35478i
$22$	−2.68757e7	−	2.68794e7i	−1.11182	−	1.11197i
$23$		−	1.96028e7i		−	0.635060i	−0.948248	−	0.317530i	$-0.897147\pi$
$23$		−	1.96028e7i		−	0.635060i	0.948248	−	0.317530i	$-0.102853\pi$
$24$	4.23876e7	−	4.23700e7i	1.08662	−	1.08617i
$25$			1.33426e7i			0.273257i
$26$	−1.45044e7	+	1.45024e7i	−0.239413	+	0.239380i
$27$	−2.92004e7	−	2.92004e7i	−0.391641	−	0.391641i
$28$	−15698.3	+	1.13567e8i	−0.000172378	+	1.24705i
$29$	−7.64662e7	+	7.64662e7i	−0.692278	+	0.692278i	−0.962733	−	0.270454i	$-0.912826\pi$
$29$	−7.64662e7	+	7.64662e7i	−0.692278	+	0.692278i	0.270454	+	0.962733i	$0.412826\pi$
$30$	2.30742e8	+	15947.6i	1.73364	+	0.000119820i
$31$	−1.66832e8			−1.04662			−0.523311	−	0.852142i	$-0.675304\pi$
$31$	−1.66832e8			−1.04662			−0.523311	+	0.852142i	$0.675304\pi$
$32$	1.89813e8	+	65593.9i	1.00000	+	0.000345572i
$33$	−5.43136e8			−2.41591
$34$	−4.37505e8	−	30237.9i	−1.65139	−	0.000114135i
$35$	−3.09173e8	+	3.09173e8i	−0.995008	+	0.995008i
$36$	68227.6	−	4.93584e8i	0.000188060	−	1.36050i
$37$	2.74973e7	+	2.74973e7i	0.0651899	+	0.0651899i	0.738950	−	0.673760i	$-0.235322\pi$
$37$	2.74973e7	+	2.74973e7i	0.0651899	+	0.0651899i	−0.673760	+	0.738950i	$0.735322\pi$
$38$	2.87761e8	−	2.87721e8i	0.589145	−	0.589064i
$39$			2.93082e8i			0.520157i
$40$	5.16634e8	+	5.16848e8i	0.797725	+	0.798056i
$41$		−	6.15454e8i		−	0.829630i	−0.909906	−	0.414815i	$-0.863846\pi$
$41$		−	6.15454e8i		−	0.829630i	0.909906	−	0.414815i	$-0.136154\pi$
$42$	1.14739e9	+	1.14755e9i	1.35469	+	1.35488i
$43$	8.26623e8	+	8.26623e8i	0.857493	+	0.857493i	0.991042	−	0.133549i	$-0.0426373\pi$
$43$	8.26623e8	+	8.26623e8i	0.857493	+	0.857493i	−0.133549	+	0.991042i	$0.542637\pi$
$44$	−1.21617e9	−	1.21651e9i	−1.11174	−	1.11205i
$45$	1.34372e9	−	1.34372e9i	1.08553	−	1.08553i
$46$	61312.9	−	8.87121e8i	4.38918e−5	−	0.635060i
$47$	1.20677e9			0.767514			0.383757	−	0.923434i	$-0.374630\pi$
$47$	1.20677e9			0.767514			0.383757	+	0.923434i	$0.374630\pi$
$48$	1.91838e9	−	1.91731e9i	1.08669	−	1.08609i
$49$	−1.09768e9			−0.555132
$50$	−41732.6	+	6.03819e8i	−1.88860e−5	+	0.273257i
$51$	−4.42051e9	+	4.42051e9i	−1.79406	+	1.79406i
$52$	−6.56441e8	+	6.56260e8i	−0.239429	+	0.239363i
$53$	6.02601e8	+	6.02601e8i	0.197930	+	0.197930i	0.799112	−	0.601182i	$-0.205303\pi$
$53$	6.02601e8	+	6.02601e8i	0.197930	+	0.197930i	−0.601182	+	0.799112i	$0.705303\pi$
$54$	−1.32137e9	−	1.32155e9i	−0.391614	−	0.391668i
$55$		−	6.62267e9i		−	1.77435i
$56$	−1.06563e6	+	5.13946e9i	−0.000258567	+	1.24705i
$57$		−	5.81461e9i		−	1.28000i
$58$	−3.46071e9	+	3.46023e9i	−0.692326	+	0.692231i
$59$	3.88524e9	+	3.88524e9i	0.707508	+	0.707508i	0.966011	−	0.258502i	$-0.0832290\pi$
$59$	3.88524e9	+	3.88524e9i	0.707508	+	0.707508i	−0.258502	+	0.966011i	$0.583229\pi$
$60$	1.04422e10	+	1.44341e6i	1.73364	+	0.000239640i
$61$	−2.43319e9	+	2.43319e9i	−0.368861	+	0.368861i	−0.867062	−	0.498201i	$-0.833994\pi$
$61$	−2.43319e9	+	2.43319e9i	−0.368861	+	0.368861i	0.498201	+	0.867062i	$0.333994\pi$
$62$	−7.54996e9	−	521811.i	−1.04662	−	7.23368e-5i
$63$	1.33645e10			1.69661
$64$	8.58993e9	+	3.56213e6i	1.00000	+	0.000414687i
$65$	−3.57367e9			−0.382024
$66$	−2.45795e10	−	1.69880e6i	−2.41591	−	0.000166975i
$67$	8.86750e9	−	8.86750e9i	0.802398	−	0.802398i	−0.181072	−	0.983470i	$-0.557957\pi$
$67$	8.86750e9	−	8.86750e9i	0.802398	−	0.802398i	0.983470	+	0.181072i	$0.0579567\pi$
$68$	−1.97992e10	−	2.73683e6i	−1.65139	−	0.000228270i
$69$	−8.96337e9	−	8.96337e9i	−0.689924	−	0.689924i
$70$	−1.39925e10	+	1.39906e10i	−0.995077	+	0.994940i
$71$			2.93481e10i			1.93045i	0.261418	+	0.965226i	$0.415810\pi$
$71$			2.93481e10i			1.93045i	−0.261418	+	0.965226i	$0.584190\pi$
$72$	4.63144e6	−	2.23371e10i	0.000282090	−	1.36050i
$73$			7.45154e9i			0.420698i	0.977626	+	0.210349i	$0.0674600\pi$
$73$			7.45154e9i			0.420698i	−0.977626	+	0.210349i	$0.932540\pi$
$74$	1.24430e9	+	1.24447e9i	0.0651854	+	0.0651944i
$75$	6.10092e9	+	6.10092e9i	0.296865	+	0.296865i
$76$	1.30235e10	−	1.30199e10i	0.589186	−	0.589023i
$77$	3.29342e10	−	3.29342e10i	1.38659	−	1.38659i
$78$	−916692.	+	1.32634e10i	−3.59503e−5	+	0.520157i
$79$	−2.31480e10			−0.846378			−0.423189	−	0.906042i	$-0.639089\pi$
$79$	−2.31480e10			−0.846378			−0.423189	+	0.906042i	$0.639089\pi$
$80$	2.33786e10	+	2.33915e10i	0.797670	+	0.798111i
$81$	1.59901e10			0.509546
$82$	1.92499e6	−	2.78523e10i	5.73394e−5	−	0.829630i
$83$	4.40857e9	−	4.40857e9i	0.122848	−	0.122848i	−0.643010	−	0.765858i	$-0.722315\pi$
$83$	4.40857e9	−	4.40857e9i	0.122848	−	0.122848i	0.765858	+	0.643010i	$0.222315\pi$
$84$	5.19214e10	+	5.19358e10i	1.35460	+	1.35497i
$85$	−5.39010e10	−	5.39010e10i	−1.31763	−	1.31763i
$86$	3.74061e10	+	3.74113e10i	0.857434	+	0.857553i
$87$			6.99284e10i			1.50417i
$88$	−5.50338e10	−	5.50566e10i	−1.11167	−	1.11213i
$89$		−	4.82749e10i		−	0.916382i	−0.888854	−	0.458191i	$-0.848498\pi$
$89$		−	4.82749e10i		−	0.916382i	0.888854	−	0.458191i	$-0.151502\pi$
$90$	6.08141e10	−	6.08057e10i	1.08560	−	1.08545i
$91$	−1.77717e10	−	1.77717e10i	−0.298539	−	0.298539i
$92$	5.54941e6	−	4.01465e10i	8.77836e−5	−	0.635060i
$93$	−7.62839e10	+	7.62839e10i	−1.13704	+	1.13704i
$94$	5.46122e10	+	3.77449e6i	0.767514	+	5.30463e-5i
$95$	7.08998e10			0.940081
$96$	8.68217e10	−	8.67618e10i	1.08677	−	1.08602i
$97$	9.19031e10			1.08664			0.543320	−	0.839526i	$-0.317167\pi$
$97$	9.19031e10			1.08664			0.543320	+	0.839526i	$0.317167\pi$
$98$	−4.96752e10	−	3.43328e6i	−0.555132	−	3.83677e-5i
$99$	−1.43138e11	+	1.43138e11i	−1.51273	+	1.51273i
$100$	−3.77721e6	+	2.73257e10i	−3.77721e−5	+	0.273257i
$101$	−8.97475e10	−	8.97475e10i	−0.849679	−	0.849679i	0.140414	−	0.990093i	$-0.455157\pi$
$101$	−8.97475e10	−	8.97475e10i	−0.849679	−	0.849679i	−0.990093	+	0.140414i	$0.955157\pi$
$102$	−2.00063e11	+	2.00035e11i	−1.79418	+	1.79393i
$103$		−	1.00244e11i		−	0.852031i	−0.904716	−	0.426015i	$-0.859917\pi$
$103$		−	1.00244e11i		−	0.852031i	0.904716	−	0.426015i	$-0.140083\pi$
$104$	−2.97092e10	+	2.96969e10i	−0.239446	+	0.239347i
$105$			2.82738e11i			2.16194i
$106$	2.72687e10	+	2.72725e10i	0.197917	+	0.197944i
$107$	−2.34076e10	−	2.34076e10i	−0.161341	−	0.161341i	0.621819	−	0.783161i	$-0.286394\pi$
$107$	−2.34076e10	−	2.34076e10i	−0.161341	−	0.161341i	−0.783161	+	0.621819i	$0.786394\pi$
$108$	−5.97941e10	−	5.98106e10i	−0.391586	−	0.391695i
$109$	4.45007e10	−	4.45007e10i	0.277026	−	0.277026i	−0.554894	−	0.831921i	$-0.687241\pi$
$109$	4.45007e10	−	4.45007e10i	0.277026	−	0.277026i	0.831921	+	0.554894i	$0.187241\pi$
$110$	2.07141e7	−	2.99708e11i	0.000122633	−	1.77435i
$111$	2.51463e10			0.141644
$112$	−6.43001e7	+	2.32586e11i	−0.000344757	+	1.24705i
$113$	−2.35044e11			−1.20010			−0.600049	−	0.799963i	$-0.704852\pi$
$113$	−2.35044e11			−1.20010			−0.600049	+	0.799963i	$0.704852\pi$
$114$	1.81867e7	−	2.63139e11i	8.84663e−5	−	1.28000i
$115$	1.09294e11	−	1.09294e11i	0.506708	−	0.506708i
$116$	−1.56625e11	+	1.56581e11i	−0.692374	+	0.692183i
$117$	7.72391e10	+	7.72391e10i	0.325698	+	0.325698i
$118$	1.75814e11	+	1.75838e11i	0.707459	+	0.707557i
$119$		−	5.36094e11i		−	2.05936i
$120$	4.72560e11	+	9.79821e7i	1.73364	+	0.000359459i
$121$			4.20160e11i			1.47263i
$122$	−1.10121e11	+	1.10106e11i	−0.368887	+	0.368836i
$123$	−2.81416e11	−	2.81416e11i	−0.901304	−	0.901304i
$124$	−3.41672e11	−	4.72290e7i	−1.04662	−	0.000144674i
$125$	1.97847e11	−	1.97847e11i	0.579861	−	0.579861i
$126$	6.04810e11	+	4.18011e7i	1.69661	+	0.000117260i
$127$	6.24519e11			1.67736			0.838678	−	0.544628i	$-0.183329\pi$
$127$	6.24519e11			1.67736			0.838678	+	0.544628i	$0.183329\pi$
$128$	3.88736e11	+	1.88071e8i	1.00000	+	0.000483801i
$129$	7.55946e11			1.86315
$130$	−1.61726e11	−	1.11776e7i	−0.382024	−	2.64034e-5i
$131$	−4.84655e11	+	4.84655e11i	−1.09759	+	1.09759i	−0.102900	+	0.994692i	$0.532812\pi$
$131$	−4.84655e11	+	4.84655e11i	−1.09759	+	1.09759i	−0.994692	+	0.102900i	$0.967188\pi$
$132$	−1.11234e12	−	1.53758e8i	−2.41591	−	0.000333949i
$133$	3.52582e11	+	3.52582e11i	0.734642	+	0.734642i
$134$	4.01325e11	−	4.01270e11i	0.802453	−	0.802343i
$135$		−	3.25609e11i		−	0.624972i
$136$	−8.96011e11	−	1.85782e8i	−1.65139	−	0.000342404i
$137$		−	5.03802e11i		−	0.891860i	−0.895068	−	0.445930i	$-0.852873\pi$
$137$		−	5.03802e11i		−	0.891860i	0.895068	−	0.445930i	$-0.147127\pi$
$138$	−4.05608e11	−	4.05664e11i	−0.689876	−	0.689972i
$139$	2.16836e11	+	2.16836e11i	0.354446	+	0.354446i	0.861761	−	0.507315i	$-0.169362\pi$
$139$	2.16836e11	+	2.16836e11i	0.354446	+	0.354446i	−0.507315	+	0.861761i	$0.669362\pi$
$140$	−6.33273e11	+	6.33098e11i	−0.995146	+	0.994871i
$141$	5.51796e11	−	5.51796e11i	0.833822	−	0.833822i
$142$	−9.17939e7	+	1.32814e12i	−0.000133422	+	1.93045i
$143$	3.80681e11			0.532369
$144$	2.79460e8	−	1.01086e12i	0.000376120	−	1.36050i
$145$	−8.52664e11			−1.10472
$146$	−2.33067e7	+	3.37218e11i	−2.90763e−5	+	0.420698i
$147$	−5.01913e11	+	5.01913e11i	−0.603091	+	0.603091i
$148$	5.63066e10	+	5.63222e10i	0.0651809	+	0.0651989i
$149$	−4.15167e11	−	4.15167e11i	−0.463126	−	0.463126i	0.436553	−	0.899679i	$-0.356199\pi$
$149$	−4.15167e11	−	4.15167e11i	−0.463126	−	0.463126i	−0.899679	+	0.436553i	$0.856199\pi$
$150$	2.76077e11	+	2.76115e11i	0.296844	+	0.296885i
$151$		−	3.26377e11i		−	0.338334i	−0.985587	−	0.169167i	$-0.945892\pi$
$151$		−	3.26377e11i		−	0.338334i	0.985587	−	0.169167i	$-0.0541078\pi$
$152$	5.89416e11	−	5.89172e11i	0.589226	−	0.588982i
$153$			2.32997e12i			2.24671i
$154$	1.49054e12	−	1.49033e12i	1.38669	−	1.38650i
$155$	−9.30160e11	−	9.30160e11i	−0.835090	−	0.835090i
$156$	−8.29695e7	+	6.00233e11i	−7.19007e−5	+	0.520157i
$157$	−7.29021e11	+	7.29021e11i	−0.609947	+	0.609947i	−0.942932	−	0.332985i	$-0.891944\pi$
$157$	−7.29021e11	+	7.29021e11i	−0.609947	+	0.609947i	0.332985	+	0.942932i	$0.391944\pi$
$158$	−1.04756e12	−	7.24014e7i	−0.846378	−	5.84969e-5i
$159$	5.51078e11			0.430060
$160$	1.05792e12	+	1.05865e12i	0.797614	+	0.798166i
$161$	1.08703e12			0.791951
$162$	7.23629e11	+	5.00132e7i	0.509546	+	3.52170e-5i
$163$	−8.04342e11	+	8.04342e11i	−0.547531	+	0.547531i	−0.925726	−	0.378195i	$-0.876545\pi$
$163$	−8.04342e11	+	8.04342e11i	−0.547531	+	0.547531i	0.378195	+	0.925726i	$0.376545\pi$
$164$	1.74231e8	−	1.26045e12i	0.000114679	−	0.829630i
$165$	−3.02821e12	−	3.02821e12i	−1.92763	−	1.92763i
$166$	1.99523e11	−	1.99495e11i	0.122857	−	0.122840i
$167$			5.08675e11i			0.303040i	0.988454	+	0.151520i	$0.0484168\pi$
$167$			5.08675e11i			0.303040i	−0.988454	+	0.151520i	$0.951583\pi$
$168$	2.34953e12	+	2.35051e12i	1.35450	+	1.35507i
$169$			1.58674e12i			0.885379i
$170$	−2.43911e12	−	2.43945e12i	−1.31754	−	1.31772i
$171$	−1.53239e12	−	1.53239e12i	−0.801474	−	0.801474i
$172$	1.69269e12	+	1.69316e12i	0.857375	+	0.857612i
$173$	−8.77981e11	+	8.77981e11i	−0.430756	+	0.430756i	−0.888886	−	0.458129i	$-0.848520\pi$
$173$	−8.77981e11	+	8.77981e11i	−0.430756	+	0.430756i	0.458129	+	0.888886i	$0.348520\pi$
$174$	−2.18719e8	+	3.16460e12i	−0.000103960	+	1.50417i
$175$	−7.39886e11			−0.340766
$176$	−2.49037e12	−	2.49175e12i	−1.11159	−	1.11221i
$177$	3.55305e12			1.53726
$178$	1.50993e8	−	2.18467e12i	6.33352e−5	−	0.916382i
$179$	1.50802e12	−	1.50802e12i	0.613360	−	0.613360i	−0.330460	−	0.943820i	$-0.607204\pi$
$179$	1.50802e12	−	1.50802e12i	0.613360	−	0.613360i	0.943820	+	0.330460i	$0.107204\pi$
$180$	2.75232e12	−	2.75156e12i	1.08568	−	1.08538i
$181$	−4.49068e11	−	4.49068e11i	−0.171822	−	0.171822i	0.615957	−	0.787780i	$-0.288769\pi$
$181$	−4.49068e11	−	4.49068e11i	−0.171822	−	0.171822i	−0.787780	+	0.615957i	$0.788769\pi$
$182$	−8.04200e11	−	8.04311e11i	−0.298518	−	0.298560i
$183$			2.22516e12i			0.801456i
$184$	3.76706e8	−	1.81682e12i	0.000131675	−	0.635060i
$185$			3.06618e11i			0.104029i
$186$	−3.45246e12	+	3.45198e12i	−1.13712	+	1.13696i
$187$	5.74173e12	+	5.74173e12i	1.83618	+	1.83618i
$188$	2.47147e12	+	3.41628e8i	0.767514	+	0.000106093i
$189$	1.61924e12	−	1.61924e12i	0.488395	−	0.488395i
$190$	3.20856e12	+	2.21758e8i	0.940081	+	6.49732e-5i
$191$	4.96899e12			1.41444			0.707220	−	0.706993i	$-0.249949\pi$
$191$	4.96899e12			1.41444			0.707220	+	0.706993i	$0.249949\pi$
$192$	3.92937e12	−	3.92612e12i	1.08684	−	1.08594i
$193$	−2.71012e12			−0.728489			−0.364244	−	0.931303i	$-0.618673\pi$
$193$	−2.71012e12			−0.728489			−0.364244	+	0.931303i	$0.618673\pi$
$194$	4.15906e12	+	2.87451e8i	1.08664	+	7.51025e-5i
$195$	−1.63406e12	+	1.63406e12i	−0.415028	+	0.415028i
$196$	−2.24804e12	−	3.10745e8i	−0.555132	−	7.67353e-5i
$197$	−5.19796e12	−	5.19796e12i	−1.24816	−	1.24816i	−0.956533	−	0.291623i	$-0.905805\pi$
$197$	−5.19796e12	−	5.19796e12i	−1.24816	−	1.24816i	−0.291623	−	0.956533i	$-0.594195\pi$
$198$	−6.47815e12	+	6.47725e12i	−1.51284	+	1.51263i
$199$			1.24035e12i			0.281742i	0.990028	+	0.140871i	$0.0449903\pi$
$199$			1.24035e12i			0.281742i	−0.990028	+	0.140871i	$0.955010\pi$
$200$	−2.56405e8	+	1.23662e12i	−5.66581e−5	+	0.273257i
$201$		−	8.10933e12i		−	1.74344i
$202$	−4.06123e12	−	4.06179e12i	−0.849620	−	0.849738i
$203$	−4.24026e12	−	4.24026e12i	−0.863305	−	0.863305i
$204$	−9.05445e12	+	9.05194e12i	−1.79430	+	1.79381i
$205$	3.43142e12	−	3.43142e12i	0.661954	−	0.661954i
$206$	3.13541e8	−	4.53654e12i	5.88876e−5	−	0.852031i
$207$	−4.72443e12			−0.863997
$208$	−1.34458e12	+	1.34383e12i	−0.239463	+	0.239330i
$209$	−7.55252e12			−1.31005
$210$	−8.84338e8	+	1.27953e13i	−0.000149421	+	2.16194i
$211$	−2.59805e12	+	2.59805e12i	−0.427656	+	0.427656i	−0.887829	−	0.460173i	$-0.847787\pi$
$211$	−2.59805e12	+	2.59805e12i	−0.427656	+	0.427656i	0.460173	+	0.887829i	$0.347787\pi$
$212$	1.23396e12	+	1.23430e12i	0.197903	+	0.197958i
$213$	1.34194e13	+	1.34194e13i	2.09723	+	2.09723i
$214$	−1.05923e12	−	1.05938e12i	−0.161330	−	0.161353i
$215$			9.21755e12i			1.36837i
$216$	−2.70578e12	−	2.70691e12i	−0.391559	−	0.391722i
$217$		−	9.25129e12i		−	1.30519i
$218$	2.01401e12	−	2.01373e12i	0.277046	−	0.277007i
$219$	3.40722e12	+	3.40722e12i	0.457043	+	0.457043i
$220$	1.87483e9	−	1.35632e13i	0.000245266	−	1.77435i
$221$	3.09831e12	−	3.09831e12i	0.395336	−	0.395336i
$222$	1.13799e12	+	7.86515e7i	0.141644	+	9.78962e-6i
$223$	3.31901e12			0.403025			0.201512	−	0.979486i	$-0.435414\pi$
$223$	3.31901e12			0.403025			0.201512	+	0.979486i	$0.435414\pi$
$224$	−3.63736e9	+	1.05256e13i	−0.000430946	+	1.24705i
$225$	3.21568e12			0.371766
$226$	−1.06369e13	−	7.35161e8i	−1.20010	−	8.29442e-5i
$227$	2.66770e12	−	2.66770e12i	0.293762	−	0.293762i	−0.544803	−	0.838564i	$-0.683395\pi$
$227$	2.66770e12	−	2.66770e12i	0.293762	−	0.293762i	0.838564	+	0.544803i	$0.183395\pi$
$228$	1.64607e9	−	1.19083e13i	0.000176933	−	1.28000i
$229$	5.06633e12	+	5.06633e12i	0.531616	+	0.531616i	0.921053	−	0.389437i	$-0.127330\pi$
$229$	5.06633e12	+	5.06633e12i	0.531616	+	0.531616i	−0.389437	+	0.921053i	$0.627330\pi$
$230$	4.94642e12	−	4.94574e12i	0.506743	−	0.506673i
$231$		−	3.01184e13i		−	3.01277i
$232$	−7.08851e12	+	7.08557e12i	−0.692422	+	0.692135i
$233$			1.26560e13i			1.20737i	0.797224	+	0.603683i	$0.206301\pi$
$233$			1.26560e13i			1.20737i	−0.797224	+	0.603683i	$0.793699\pi$
$234$	3.49520e12	+	3.49568e12i	0.325675	+	0.325720i
$235$	6.72826e12	+	6.72826e12i	0.612392	+	0.612392i
$236$	7.95587e12	+	7.95807e12i	0.707410	+	0.707606i
$237$	−1.05844e13	+	1.05844e13i	−0.919498	+	0.919498i
$238$	1.67678e9	−	2.42609e13i	0.000142332	−	2.05936i
$239$	3.75926e12			0.311828			0.155914	−	0.987771i	$-0.450168\pi$
$239$	3.75926e12			0.311828			0.155914	+	0.987771i	$0.450168\pi$
$240$	2.13856e13	+	5.91222e9i	1.73364	+	0.000479279i
$241$	−5.53115e12			−0.438250			−0.219125	−	0.975697i	$-0.570320\pi$
$241$	−5.53115e12			−0.438250			−0.219125	+	0.975697i	$0.570320\pi$
$242$	−1.31416e9	+	1.90143e13i	−0.000101780	+	1.47263i
$243$	1.24842e13	−	1.24842e13i	0.945207	−	0.945207i
$244$	−4.98387e12	+	4.98249e12i	−0.368912	+	0.368810i
$245$	−6.12002e12	−	6.12002e12i	−0.442934	−	0.442934i
$246$	−1.27346e13	−	1.27363e13i	−0.901241	−	0.901366i
$247$			4.07543e12i			0.282059i
$248$	−1.54623e13	−	3.20601e9i	−1.04662	−	0.000217010i
$249$		−	4.03164e12i		−	0.266922i
$250$	8.95414e12	−	8.95290e12i	0.579901	−	0.579821i
$251$	−3.06972e12	−	3.06972e12i	−0.194488	−	0.194488i	0.603144	−	0.797632i	$-0.293914\pi$
$251$	−3.06972e12	−	3.06972e12i	−0.194488	−	0.194488i	−0.797632	+	0.603144i	$0.793914\pi$
$252$	2.73706e13	+	3.78341e9i	1.69661	+	0.000234520i
$253$	−1.16424e13	+	1.16424e13i	−0.706122	+	0.706122i
$254$	2.82625e13	+	1.95335e9i	1.67736	+	0.000115930i
$255$	−4.92924e13			−2.86292
$256$	1.75922e13	+	9.72699e9i	1.00000	+	0.000552916i
$257$	1.71375e12			0.0953489			0.0476745	−	0.998863i	$-0.484819\pi$
$257$	1.71375e12			0.0953489			0.0476745	+	0.998863i	$0.484819\pi$
$258$	3.42102e13	+	2.36442e9i	1.86315	+	0.000128770i
$259$	−1.52480e12	+	1.52480e12i	−0.0812950	+	0.0812950i
$260$	−7.31887e12	−	1.01168e9i	−0.382024	−	5.28068e-5i
$261$	1.84290e13	+	1.84290e13i	0.941842	+	0.941842i
$262$	−2.19345e13	+	2.19315e13i	−1.09767	+	1.09752i
$263$			1.01496e13i			0.497384i	0.968583	+	0.248692i	$0.0800007\pi$
$263$			1.01496e13i			0.497384i	−0.968583	+	0.248692i	$0.919999\pi$
$264$	−5.03388e13	−	1.04374e10i	−2.41591	−	0.000500924i
$265$			6.71951e12i			0.315853i
$266$	1.59549e13	+	1.59571e13i	0.734591	+	0.734693i
$267$	−2.20737e13	−	2.20737e13i	−0.995550	−	0.995550i
$268$	1.81632e13	−	1.81581e13i	0.802509	−	0.802287i
$269$	−1.30252e13	+	1.30252e13i	−0.563828	+	0.563828i	−0.930393	−	0.366564i	$-0.880534\pi$
$269$	−1.30252e13	+	1.30252e13i	−0.563828	+	0.563828i	0.366564	+	0.930393i	$0.380534\pi$
$270$	1.01843e9	−	1.47354e13i	4.31946e−5	−	0.624972i
$271$	−1.84540e13			−0.766934			−0.383467	−	0.923554i	$-0.625270\pi$
$271$	−1.84540e13			−0.766934			−0.383467	+	0.923554i	$0.625270\pi$
$272$	−4.05488e13	−	1.12100e10i	−1.65139	−	0.000456539i
$273$	−1.62522e13			−0.648661
$274$	1.57577e9	−	2.27995e13i	6.16404e−5	−	0.891860i
$275$	7.92441e12	−	7.92441e12i	0.303834	−	0.303834i
$276$	−1.83544e13	−	1.83595e13i	−0.689829	−	0.690019i
$277$	1.56562e13	+	1.56562e13i	0.576828	+	0.576828i	0.934028	−	0.357200i	$-0.116268\pi$
$277$	1.56562e13	+	1.56562e13i	0.576828	+	0.576828i	−0.357200	+	0.934028i	$0.616268\pi$
$278$	9.81220e12	+	9.81356e12i	0.354421	+	0.354470i
$279$			4.02078e13i			1.42393i
$280$	−2.86606e13	+	2.86488e13i	−0.995215	+	0.994802i
$281$		−	5.12053e13i		−	1.74353i	−0.489922	−	0.871766i	$-0.662975\pi$
$281$		−	5.12053e13i		−	1.74353i	0.489922	−	0.871766i	$-0.337025\pi$
$282$	2.49732e13	−	2.49697e13i	0.833879	−	0.833764i
$283$	3.68160e10	+	3.68160e10i	0.00120562	+	0.00120562i	0.707709	−	0.706504i	$-0.249729\pi$
$283$	3.68160e10	+	3.68160e10i	0.00120562	+	0.00120562i	−0.706504	+	0.707709i	$0.749729\pi$
$284$	−8.30823e9	+	6.01049e13i	−0.000266844	+	1.93045i
$285$	3.24189e13	−	3.24189e13i	1.02130	−	1.02130i
$286$	1.72276e13	+	1.19068e9i	0.532369	+	3.67944e-5i
$287$	3.41286e13			1.03459
$288$	1.58087e10	−	4.57463e13i	0.000470150	−	1.36050i
$289$	5.91905e13			1.72708
$290$	−3.85872e13	−	2.66693e9i	−1.10472	−	7.63524e-5i
$291$	4.20227e13	−	4.20227e13i	1.18052	−	1.18052i
$292$	−2.10948e9	+	1.52608e13i	−5.81526e−5	+	0.420698i
$293$	7.30934e12	+	7.30934e12i	0.197745	+	0.197745i	0.799033	−	0.601287i	$-0.205345\pi$
$293$	7.30934e12	+	7.30934e12i	0.197745	+	0.197745i	−0.601287	+	0.799033i	$0.705345\pi$
$294$	−2.27156e13	+	2.27124e13i	−0.603133	+	0.603050i
$295$			4.33237e13i			1.12903i
$296$	2.54797e12	+	2.54903e12i	0.0651764	+	0.0652034i
$297$			3.46851e13i			0.870929i
$298$	−1.87870e13	−	1.87896e13i	−0.463094	−	0.463158i
$299$	6.28237e12	+	6.28237e12i	0.152031	+	0.152031i
$300$	1.24930e13	+	1.24964e13i	0.296824	+	0.296906i
$301$	−4.58385e13	+	4.58385e13i	−1.06934	+	1.06934i
$302$	1.02083e9	−	1.47701e13i	2.33838e−5	−	0.338334i
$303$	−8.20741e13			−1.84617
$304$	2.66758e13	−	2.66610e13i	0.589267	−	0.588941i
$305$	−2.71322e13			−0.588621
$306$	−7.28758e9	+	1.05442e14i	−0.000155280	+	2.24671i
$307$	5.00023e13	−	5.00023e13i	1.04648	−	1.04648i	0.0476101	−	0.998866i	$-0.484840\pi$
$307$	5.00023e13	−	5.00023e13i	1.04648	−	1.04648i	0.998866	−	0.0476101i	$-0.0151605\pi$
$308$	6.74586e13	−	6.74400e13i	1.38678	−	1.38640i
$309$	−4.58367e13	−	4.58367e13i	−0.925639	−	0.925639i
$310$	−4.20913e13	−	4.20971e13i	−0.835032	−	0.835148i
$311$		−	8.72624e13i		−	1.70077i	−0.526163	−	0.850384i	$-0.676370\pi$
$311$		−	8.72624e13i		−	1.70077i	0.526163	−	0.850384i	$-0.323630\pi$
$312$	−5.63216e9	+	2.71634e13i	−0.000107851	+	0.520157i
$313$		−	5.00784e13i		−	0.942229i	−0.882072	−	0.471114i	$-0.843852\pi$
$313$		−	5.00784e13i		−	0.942229i	0.882072	−	0.471114i	$-0.156148\pi$
$314$	−3.29940e13	+	3.29895e13i	−0.609989	+	0.609905i
$315$	7.45130e13	+	7.45130e13i	1.35371	+	1.35371i
$316$	−4.74071e13	−	6.55303e9i	−0.846378	−	0.000116994i
$317$	5.46587e13	−	5.46587e13i	0.959033	−	0.959033i	−0.0401607	−	0.999193i	$-0.512787\pi$
$317$	5.46587e13	−	5.46587e13i	0.959033	−	0.959033i	0.999193	+	0.0401607i	$0.0127870\pi$
$318$	2.49390e13	+	1.72364e9i	0.430060	+	2.97234e-5i
$319$	9.08290e13			1.53949
$320$	4.78727e13	+	4.79124e13i	0.797559	+	0.798221i
$321$	−2.14062e13			−0.350560
$322$	4.91933e13	+	3.39997e9i	0.791951	+	5.47353e-5i
$323$	−6.14689e13	+	6.14689e13i	−0.972840	+	0.972840i
$324$	3.27477e13	+	4.52668e9i	0.509546	+	7.04340e-5i
$325$	−4.27610e12	−	4.27610e12i	−0.0654168	−	0.0654168i
$326$	−3.64029e13	+	3.63979e13i	−0.547569	+	0.547494i
$327$		−	4.06959e13i		−	0.601919i
$328$	1.18272e10	−	5.70415e13i	0.000172018	−	0.829630i
$329$			6.69187e13i			0.957128i
$330$	−1.37032e14	−	1.37051e14i	−1.92750	−	1.92777i
$331$	−1.49745e13	−	1.49745e13i	−0.207156	−	0.207156i	0.595901	−	0.803058i	$-0.296795\pi$
$331$	−1.49745e13	−	1.49745e13i	−0.207156	−	0.207156i	−0.803058	+	0.595901i	$0.796795\pi$
$332$	9.03000e12	−	9.02751e12i	0.122865	−	0.122831i
$333$	6.62706e12	−	6.62706e12i	0.0886906	−	0.0886906i
$334$	−1.59102e9	+	2.30200e13i	−2.09444e−5	+	0.303040i
$335$	9.88802e13			1.28045
$336$	1.06320e14	+	1.06379e14i	1.35441	+	1.35516i
$337$	−6.74796e12			−0.0845684			−0.0422842	−	0.999106i	$-0.513463\pi$
$337$	−6.74796e12			−0.0845684			−0.0422842	+	0.999106i	$0.513463\pi$
$338$	−4.96295e9	+	7.18077e13i	−6.11925e−5	+	0.885379i
$339$	−1.07474e14	+	1.07474e14i	−1.30378	+	1.30378i
$340$	−1.10374e14	−	1.10404e14i	−1.31744	−	1.31781i
$341$	9.90842e13	+	9.90842e13i	1.16374	+	1.16374i
$342$	−6.93431e13	−	6.93527e13i	−0.801419	−	0.801530i
$343$			4.87789e13i			0.554772i
$344$	7.65971e13	+	7.66288e13i	0.857315	+	0.857671i
$345$		−	9.99492e13i		−	1.10097i
$346$	−3.97356e13	+	3.97301e13i	−0.430786	+	0.430727i
$347$	−9.73980e13	−	9.73980e13i	−1.03929	−	1.03929i	−0.999196	−	0.0400971i	$-0.987233\pi$
$347$	−9.73980e13	−	9.73980e13i	−1.03929	−	1.03929i	−0.0400971	−	0.999196i	$-0.512767\pi$
$348$	−1.97962e10	+	1.43213e14i	−0.000207920	+	1.50417i
$349$	−8.34720e12	+	8.34720e12i	−0.0862980	+	0.0862980i	−0.748938	−	0.662640i	$-0.769436\pi$
$349$	−8.34720e12	+	8.34720e12i	−0.0862980	+	0.0862980i	0.662640	+	0.748938i	$0.269436\pi$
$350$	−3.34834e13	−	2.31419e9i	−0.340766	−	2.35518e-5i
$351$	1.87165e13			0.187515
$352$	−1.12694e14	−	1.12772e14i	−1.11151	−	1.11228i
$353$	−9.06184e13			−0.879945			−0.439973	−	0.898011i	$-0.645012\pi$
$353$	−9.06184e13			−0.879945			−0.439973	+	0.898011i	$0.645012\pi$
$354$	1.60793e14	+	1.11131e10i	1.53726	+	0.000106247i
$355$	−1.63628e14	+	1.63628e14i	−1.54029	+	1.54029i
$356$	1.36663e10	−	9.88670e13i	0.000126670	−	0.916382i
$357$	−2.45129e14	−	2.45129e14i	−2.23728	−	2.23728i
$358$	6.82499e13	−	6.82405e13i	0.613403	−	0.613318i
$359$			7.14917e13i			0.632756i	0.948633	+	0.316378i	$0.102467\pi$
$359$			7.14917e13i			0.632756i	−0.948633	+	0.316378i	$0.897533\pi$
$360$	1.24565e14	−	1.24513e14i	1.08575	−	1.08530i
$361$			3.56358e13i			0.305912i
$362$	−2.03211e13	−	2.03239e13i	−0.171811	−	0.171834i
$363$	1.92118e14	+	1.92118e14i	1.59986	+	1.59986i
$364$	−3.63914e13	−	3.64015e13i	−0.298498	−	0.298580i
$365$	−4.15455e13	+	4.15455e13i	−0.335671	+	0.335671i
$366$	−6.95976e9	+	1.00699e14i	−5.53922e−5	+	0.801456i
$367$	4.19051e12			0.0328552			0.0164276	−	0.999865i	$-0.494771\pi$
$367$	4.19051e12			0.0328552			0.0164276	+	0.999865i	$0.494771\pi$
$368$	2.27304e10	−	8.22200e13i	0.000175567	−	0.635060i
$369$	−1.48329e14			−1.12871
$370$	−9.59029e8	+	1.38760e13i	−7.18989e−6	+	0.104029i
$371$	−3.34159e13	+	3.34159e13i	−0.246829	+	0.246829i
$372$	−1.56251e14	+	1.56208e14i	−1.13720	+	1.13689i
$373$	1.12134e14	+	1.12134e14i	0.804153	+	0.804153i	0.983742	−	0.179589i	$-0.0574768\pi$
$373$	1.12134e14	+	1.12134e14i	0.804153	+	0.804153i	−0.179589	+	0.983742i	$0.557477\pi$
$374$	2.59823e14	+	2.59859e14i	1.83605	+	1.83630i
$375$		−	1.80931e14i		−	1.25991i
$376$	1.11846e14	+	2.31905e10i	0.767514	+	0.000159139i
$377$		−	4.90124e13i		−	0.331458i
$378$	7.32835e13	−	7.32734e13i	0.488429	−	0.488361i
$379$	−1.04153e14	−	1.04153e14i	−0.684154	−	0.684154i	0.276779	−	0.960934i	$-0.410733\pi$
$379$	−1.04153e14	−	1.04153e14i	−0.684154	−	0.684154i	−0.960934	+	0.276779i	$0.910733\pi$
$380$	1.45203e14	+	2.00712e10i	0.940081	+	0.000129946i
$381$	2.85561e14	−	2.85561e14i	1.82227	−	1.82227i
$382$	2.24871e14	+	1.55418e10i	1.41444	+	9.77583e-5i
$383$	−1.29233e14			−0.801274			−0.400637	−	0.916237i	$-0.631211\pi$
$383$	−1.29233e14			−0.801274			−0.400637	+	0.916237i	$0.631211\pi$
$384$	1.77835e14	−	1.77663e14i	1.08692	−	1.08587i
$385$	3.67245e14			2.21270
$386$	−1.22646e14	−	8.47660e9i	−0.728489	−	5.03491e-5i
$387$	1.99223e14	−	1.99223e14i	1.16662	−	1.16662i
$388$	1.88218e14	+	2.60171e10i	1.08664	+	0.000150205i
$389$	−2.24630e14	−	2.24630e14i	−1.27863	−	1.27863i	−0.941434	−	0.337198i	$-0.890521\pi$
$389$	−2.24630e14	−	2.24630e14i	−1.27863	−	1.27863i	−0.337198	−	0.941434i	$-0.609479\pi$
$390$	−7.39542e13	+	7.39440e13i	−0.415057	+	0.414999i
$391$			1.89512e14i			1.04873i
$392$	−1.01735e14	−	2.10940e10i	−0.555132	−	0.000115103i
$393$			4.43217e14i			2.38483i
$394$	−2.35217e14	−	2.35249e14i	−1.24807	−	1.24824i
$395$	−1.29060e14	−	1.29060e14i	−0.675316	−	0.675316i
$396$	−2.93188e14	+	2.93107e14i	−1.51294	+	1.51252i
$397$	−2.06448e14	+	2.06448e14i	−1.05066	+	1.05066i	−0.0520169	+	0.998646i	$0.516565\pi$
$397$	−2.06448e14	+	2.06448e14i	−1.05066	+	1.05066i	−0.998646	+	0.0520169i	$0.983435\pi$
$398$	−3.87952e9	+	5.61318e13i	−1.94725e−5	+	0.281742i
$399$	3.22436e14			1.59622
$400$	−1.54714e10	+	5.59631e13i	−7.55442e−5	+	0.273257i
$401$	1.77354e14			0.854177			0.427089	−	0.904210i	$-0.359539\pi$
$401$	1.77354e14			0.854177			0.427089	+	0.904210i	$0.359539\pi$
$402$	2.53641e10	−	3.66986e14i	0.000120497	−	1.74344i
$403$	5.34670e13	−	5.34670e13i	0.250558	−	0.250558i
$404$	−1.83777e14	−	1.83828e14i	−0.849561	−	0.849796i
$405$	8.91516e13	+	8.91516e13i	0.406562	+	0.406562i
$406$	−1.91879e14	−	1.91906e14i	−0.863246	−	0.863365i
$407$		−	3.26621e13i		−	0.144969i
$408$	−4.09786e14	+	4.09616e14i	−1.79443	+	1.79368i
$409$			3.56385e14i			1.53972i	0.638213	+	0.769860i	$0.279674\pi$
$409$			3.56385e14i			1.53972i	−0.638213	+	0.769860i	$0.720326\pi$
$410$	1.55299e14	−	1.55278e14i	0.661999	−	0.661908i
$411$	−2.30363e14	−	2.30363e14i	−0.968910	−	0.968910i
$412$	2.83785e10	−	2.05300e14i	0.000117775	−	0.852031i
$413$	−2.15447e14	+	2.15447e14i	−0.882298	+	0.882298i
$414$	−2.13803e14	−	1.47769e10i	−0.863997	−	5.97147e-5i
$415$	4.91593e13			0.196039
$416$	−6.08528e13	+	6.08108e13i	−0.239479	+	0.239314i
$417$	1.98296e14			0.770135
$418$	−3.41788e14	−	2.36225e10i	−1.31005	−	9.05433e-5i
$419$	2.71801e14	−	2.71801e14i	1.02819	−	1.02819i	0.0286012	−	0.999591i	$-0.490895\pi$
$419$	2.71801e14	−	2.71801e14i	1.02819	−	1.02819i	0.999591	−	0.0286012i	$-0.00910529\pi$
$420$	−8.00412e10	+	5.79048e14i	−0.000298842	+	2.16194i
$421$	5.71653e13	+	5.71653e13i	0.210660	+	0.210660i	0.804548	−	0.593888i	$-0.202408\pi$
$421$	5.71653e13	+	5.71653e13i	0.210660	+	0.210660i	−0.593888	+	0.804548i	$0.702408\pi$
$422$	−1.17583e14	+	1.17566e14i	−0.427686	+	0.427626i
$423$		−	2.90841e14i		−	1.04420i
$424$	5.58386e13	+	5.58618e13i	0.197889	+	0.197971i
$425$		−	1.28991e14i		−	0.451254i
$426$	6.07251e14	+	6.07335e14i	2.09708	+	2.09737i
$427$	−1.34927e14	−	1.34927e14i	−0.459988	−	0.459988i
$428$	−4.79321e13	−	4.79454e13i	−0.161319	−	0.161364i
$429$	1.74066e14	−	1.74066e14i	0.578361	−	0.578361i
$430$	−2.88303e10	+	4.17139e14i	−9.45742e−5	+	1.36837i
$431$	4.62177e13			0.149687			0.0748434	−	0.997195i	$-0.476154\pi$
$431$	4.62177e13			0.149687			0.0748434	+	0.997195i	$0.476154\pi$
$432$	−1.22441e14	−	1.22509e14i	−0.391532	−	0.391749i
$433$	−2.17070e14			−0.685356			−0.342678	−	0.939453i	$-0.611334\pi$
$433$	−2.17070e14			−0.685356			−0.342678	+	0.939453i	$0.611334\pi$
$434$	2.89358e10	−	4.18666e14i	9.02075e−5	−	1.30519i
$435$	−3.89880e14	+	3.89880e14i	−1.20016	+	1.20016i
$436$	9.11500e13	−	9.11248e13i	0.277065	−	0.276988i
$437$	−1.24639e14	−	1.24639e14i	−0.374117	−	0.374117i
$438$	1.54182e14	+	1.54204e14i	0.457011	+	0.457075i
$439$		−	2.67074e14i		−	0.781766i	−0.920440	−	0.390883i	$-0.872170\pi$
$439$		−	2.67074e14i		−	0.781766i	0.920440	−	0.390883i	$-0.127830\pi$
$440$	1.27268e11	−	6.13801e14i	0.000367899	−	1.77435i
$441$			2.64549e14i			0.755255i
$442$	1.40223e14	−	1.40204e14i	0.395364	−	0.395309i
$443$	2.39831e14	+	2.39831e14i	0.667858	+	0.667858i	0.957220	−	0.289362i	$-0.0934431\pi$
$443$	2.39831e14	+	2.39831e14i	0.667858	+	0.667858i	−0.289362	+	0.957220i	$0.593443\pi$
$444$	5.14995e13	+	7.11872e9i	0.141644	+	1.95792e-5i
$445$	2.69153e14	−	2.69153e14i	0.731172	−	0.731172i
$446$	1.50201e14	+	1.03811e10i	0.403025	+	2.78548e-5i
$447$	−3.79670e14			−1.00627
$448$	−1.97530e11	+	4.76335e14i	−0.000517135	+	1.24705i
$449$	5.87700e14			1.51985			0.759925	−	0.650011i	$-0.225236\pi$
$449$	5.87700e14			1.51985			0.759925	+	0.650011i	$0.225236\pi$
$450$	1.45525e14	+	1.00579e10i	0.371766	+	2.56944e-5i
$451$	−3.65528e14	+	3.65528e14i	−0.922464	+	0.922464i
$452$	−4.81369e14	−	6.65391e10i	−1.20010	−	0.000165888i
$453$	−1.49236e14	−	1.49236e14i	−0.367564	−	0.367564i
$454$	1.20735e14	−	1.20718e14i	0.293782	−	0.293742i
$455$		−	1.98170e14i		−	0.476403i
$456$	1.11739e11	−	5.38909e14i	0.000265399	−	1.28000i
$457$		−	4.52197e14i		−	1.06118i	−0.847629	−	0.530589i	$-0.821971\pi$
$457$		−	4.52197e14i		−	1.06118i	0.847629	−	0.530589i	$-0.178029\pi$
$458$	2.29260e14	+	2.29292e14i	0.531580	+	0.531653i
$459$	2.82297e14	+	2.82297e14i	0.646751	+	0.646751i
$460$	2.23865e14	−	2.23803e14i	0.506778	−	0.506638i
$461$	−5.12674e14	+	5.12674e14i	−1.14680	+	1.14680i	−0.159616	+	0.987179i	$0.551026\pi$
$461$	−5.12674e14	+	5.12674e14i	−1.14680	+	1.14680i	−0.987179	+	0.159616i	$0.948974\pi$
$462$	9.42031e10	−	1.36300e15i	0.000208226	−	3.01277i
$463$	2.55229e14			0.557486			0.278743	−	0.960366i	$-0.410082\pi$
$463$	2.55229e14			0.557486			0.278743	+	0.960366i	$0.410082\pi$
$464$	−3.20811e14	+	3.20634e14i	−0.692470	+	0.692087i
$465$	−8.50631e14			−1.81447
$466$	−3.95850e10	+	5.72745e14i	−8.34465e−5	+	1.20737i
$467$	1.22952e14	−	1.22952e14i	0.256148	−	0.256148i	−0.567337	−	0.823485i	$-0.692026\pi$
$467$	1.22952e14	−	1.22952e14i	0.256148	−	0.256148i	0.823485	+	0.567337i	$0.192026\pi$
$468$	1.58164e14	+	1.58208e14i	0.325653	+	0.325743i
$469$	4.91727e14	+	4.91727e14i	1.00063	+	1.00063i
$470$	3.04465e14	+	3.04507e14i	0.612350	+	0.612435i
$471$			6.66690e14i			1.32528i
$472$	3.60017e14	+	3.60166e14i	0.707362	+	0.707655i
$473$		−	9.81888e14i		−	1.90689i
$474$	−4.79029e14	+	4.78963e14i	−0.919562	+	0.919435i
$475$	8.48358e13	+	8.48358e13i	0.160977	+	0.160977i
$476$	1.51764e11	−	1.09792e15i	0.000284664	−	2.05936i
$477$	1.45232e14	−	1.45232e14i	0.269284	−	0.269284i
$478$	1.70125e14	+	1.17581e10i	0.311828	+	2.15518e-5i
$479$	2.71050e14			0.491139			0.245569	−	0.969379i	$-0.421025\pi$
$479$	2.71050e14			0.491139			0.245569	+	0.969379i	$0.421025\pi$
$480$	9.67802e14	+	3.34446e11i	1.73364	+	0.000599099i
$481$	−1.76249e13			−0.0312124
$482$	−2.50311e14	−	1.73001e10i	−0.438250	−	3.02894e-5i
$483$	4.97043e14	−	4.97043e14i	0.860369	−	0.860369i
$484$	−1.18944e11	+	8.60487e14i	−0.000203561	+	1.47263i
$485$	5.12399e14	+	5.12399e14i	0.867019	+	0.867019i
$486$	5.65011e14	−	5.64932e14i	0.945273	−	0.945142i
$487$			3.77246e14i			0.624045i	0.950075	+	0.312022i	$0.101006\pi$
$487$			3.77246e14i			0.624045i	−0.950075	+	0.312022i	$0.898994\pi$
$488$	−2.25560e14	+	2.25466e14i	−0.368938	+	0.368785i
$489$			7.35571e14i			1.18967i
$490$	−2.76941e14	−	2.76980e14i	−0.442904	−	0.442965i
$491$	−4.41994e14	−	4.41994e14i	−0.698985	−	0.698985i	0.265207	−	0.964192i	$-0.414560\pi$
$491$	−4.41994e14	−	4.41994e14i	−0.698985	−	0.698985i	−0.964192	+	0.265207i	$0.914560\pi$
$492$	−5.76261e14	−	5.76420e14i	−0.901179	−	0.901428i
$493$	7.39245e14	−	7.39245e14i	1.14322	−	1.14322i
$494$	−1.27470e10	+	1.84433e14i	−1.94943e−5	+	0.282059i
$495$	−1.59611e15			−2.41399
$496$	−6.99744e14	−	1.93450e11i	−1.04662	−	0.000289347i
$497$	−1.62743e15			−2.40737
$498$	1.26100e10	−	1.82451e14i	1.84482e−5	−	0.266922i
$499$	−5.44840e14	+	5.44840e14i	−0.788344	+	0.788344i	−0.981223	−	0.192878i	$-0.938218\pi$
$499$	−5.44840e14	+	5.44840e14i	−0.788344	+	0.788344i	0.192878	+	0.981223i	$0.438218\pi$
$500$	4.05246e14	−	4.05134e14i	0.579941	−	0.579781i
$501$	2.32592e14	+	2.32592e14i	0.329220	+	0.329220i
$502$	−1.38910e14	−	1.38929e14i	−0.194475	−	0.194502i
$503$		−	3.71015e14i		−	0.513768i	−0.966442	−	0.256884i	$-0.917304\pi$
$503$		−	3.71015e14i		−	0.513768i	0.966442	−	0.256884i	$-0.0826958\pi$
$504$	1.23865e15	+	2.56826e11i	1.69661	+	0.000351780i
$505$		−	1.00076e15i		−	1.35590i
$506$	−5.26911e14	+	5.26838e14i	−0.706171	+	0.706073i
$507$	7.25537e14	+	7.25537e14i	0.961869	+	0.961869i
$508$	1.27902e15	+	1.76797e11i	1.67736	+	0.000231859i
$509$	−7.69790e14	+	7.69790e14i	−0.998676	+	0.998676i	−0.999999	−	0.00132283i	$-0.999579\pi$
$509$	−7.69790e14	+	7.69790e14i	−0.998676	+	0.998676i	0.00132283	+	0.999999i	$0.499579\pi$
$510$	−2.23072e15	−	1.54175e11i	−2.86292	−	0.000197869i
$511$	−4.13208e14			−0.524631
$512$	7.96131e14	+	4.95218e11i	1.00000	+	0.000622030i
$513$	−3.71326e14			−0.461434
$514$	7.75556e13	+	5.36021e9i	0.0953489	+	6.58999e-6i
$515$	5.58905e14	−	5.58905e14i	0.679827	−	0.679827i
$516$	1.54818e15	+	2.14003e11i	1.86315	+	0.000257541i
$517$	−7.16720e14	−	7.16720e14i	−0.853398	−	0.853398i
$518$	−6.90093e13	+	6.89998e13i	−0.0813006	+	0.0812894i
$519$			8.02914e14i			0.935941i
$520$	−3.31214e14	−	6.86751e10i	−0.382024	−	7.92101e-5i
$521$		−	1.01193e14i		−	0.115489i	−0.998331	−	0.0577447i	$-0.981609\pi$
$521$		−	1.01193e14i		−	0.115489i	0.998331	−	0.0577447i	$-0.0183909\pi$
$522$	8.33942e14	+	8.34058e14i	0.941777	+	0.941907i
$523$	2.30526e14	+	2.30526e14i	0.257608	+	0.257608i	0.824081	−	0.566472i	$-0.191692\pi$
$523$	2.30526e14	+	2.30526e14i	0.257608	+	0.257608i	−0.566472	+	0.824081i	$0.691692\pi$
$524$	−9.92711e14	+	9.92437e14i	−1.09774	+	1.09744i
$525$	−3.38313e14	+	3.38313e14i	−0.370205	+	0.370205i
$526$	−3.17455e10	+	4.59318e14i	−3.43764e−5	+	0.497384i
$527$	1.61286e15			1.72838
$528$	−2.27808e15	−	6.29792e11i	−2.41591	−	0.000667899i
$529$	5.68541e14			0.596699
$530$	−2.10170e10	+	3.04090e14i	−2.18300e−5	+	0.315853i
$531$	9.36373e14	−	9.36373e14i	0.962562	−	0.962562i
$532$	7.21988e14	+	7.22187e14i	0.734541	+	0.734744i
$533$	1.97243e14	+	1.97243e14i	0.198610	+	0.198610i
$534$	−9.98873e14	−	9.99011e14i	−0.995481	−	0.995619i
$535$		−	2.61015e14i		−	0.257465i
$536$	8.22027e14	−	8.21686e14i	0.802564	−	0.802232i
$537$		−	1.37908e15i		−	1.33270i
$538$	−5.89494e14	+	5.89413e14i	−0.563867	+	0.563790i
$539$	6.51928e14	+	6.51928e14i	0.617250	+	0.617250i
$540$	9.21776e10	−	6.66847e14i	8.63892e−5	−	0.624972i
$541$	−3.94835e14	+	3.94835e14i	−0.366295	+	0.366295i	−0.866124	−	0.499829i	$-0.833396\pi$
$541$	−3.94835e14	+	3.94835e14i	−0.366295	+	0.366295i	0.499829	+	0.866124i	$0.333396\pi$
$542$	−8.35130e14	−	5.77196e10i	−0.766934	−	5.30063e-5i
$543$	−4.10672e14			−0.373333
$544$	−1.83503e15	−	6.34136e11i	−1.65139	−	0.000570674i
$545$	4.96221e14			0.442073
$546$	−7.35491e14	−	5.08331e10i	−0.648661	−	4.48319e-5i
$547$	2.85865e14	−	2.85865e14i	0.249592	−	0.249592i	−0.571211	−	0.820803i	$-0.693526\pi$
$547$	2.85865e14	−	2.85865e14i	0.249592	−	0.249592i	0.820803	+	0.571211i	$0.193526\pi$
$548$	1.42623e11	−	1.03179e15i	0.000123281	−	0.891860i
$549$	5.86419e14	+	5.86419e14i	0.501834	+	0.501834i
$550$	3.58643e14	−	3.58593e14i	0.303855	−	0.303813i
$551$			9.72382e14i			0.815648i
$552$	−8.30570e14	−	8.30914e14i	−0.689781	−	0.690067i
$553$		−	1.28362e15i		−	1.05547i
$554$	7.08468e14	+	7.08566e14i	0.576789	+	0.576868i
$555$	1.40201e14	+	1.40201e14i	0.113016	+	0.113016i
$556$	4.44019e14	+	4.44142e14i	0.354397	+	0.354495i
$557$	6.89000e13	−	6.89000e13i	0.0544522	−	0.0544522i	−0.679356	−	0.733809i	$-0.737741\pi$
$557$	6.89000e13	−	6.89000e13i	0.0544522	−	0.0544522i	0.733809	+	0.679356i	$0.237741\pi$
$558$	−1.25761e11	+	1.81960e15i	−9.84139e−5	+	1.42393i
$559$	−5.29838e14			−0.410562
$560$	−1.29712e15	+	1.29641e15i	−0.995283	+	0.994733i
$561$	5.25081e15			3.98961
$562$	1.60158e11	−	2.31729e15i	0.000120503	−	1.74353i
$563$	2.79657e14	−	2.79657e14i	0.208367	−	0.208367i	−0.595206	−	0.803573i	$-0.702930\pi$
$563$	2.79657e14	−	2.79657e14i	0.208367	−	0.208367i	0.803573	+	0.595206i	$0.202930\pi$
$564$	1.13023e15	−	1.12992e15i	0.833937	−	0.833707i
$565$	−1.31047e15	−	1.31047e15i	−0.957547	−	0.957547i
$566$	1.66599e12	+	1.66622e12i	0.00120554	+	0.00120570i
$567$			8.86694e14i			0.635429i
$568$	−5.63982e11	+	2.72004e15i	−0.000400266	+	1.93045i
$569$			1.64126e15i			1.15361i	0.816881	+	0.576807i	$0.195701\pi$
$569$			1.64126e15i			1.15361i	−0.816881	+	0.576807i	$0.804299\pi$
$570$	1.46721e15	−	1.46701e15i	1.02137	−	1.02123i
$571$	−1.29829e15	−	1.29829e15i	−0.895100	−	0.895100i	0.0998976	−	0.994998i	$-0.468148\pi$
$571$	−1.29829e15	−	1.29829e15i	−0.895100	−	0.895100i	−0.994998	+	0.0998976i	$0.968148\pi$
$572$	7.79634e14	+	1.07768e11i	0.532369	+	7.35887e-5i
$573$	2.27207e15	−	2.27207e15i	1.53664	−	1.53664i
$574$	1.54448e15	+	1.06746e11i	1.03459	+	7.15051e-5i
$575$	2.61553e14			0.173535
$576$	8.58502e11	−	2.07024e15i	0.000564180	−	1.36050i
$577$	−1.84725e15			−1.20242			−0.601212	−	0.799089i	$-0.705315\pi$
$577$	−1.84725e15			−1.20242			−0.601212	+	0.799089i	$0.705315\pi$
$578$	2.67865e15	+	1.85134e11i	1.72708	+	0.000119367i
$579$	−1.23920e15	+	1.23920e15i	−0.791424	+	0.791424i
$580$	−1.74626e15	−	2.41383e11i	−1.10472	−	0.000152705i
$581$	2.44467e14	+	2.44467e14i	0.153198	+	0.153198i
$582$	1.90186e15	−	1.90160e15i	1.18060	−	1.18044i
$583$		−	7.15788e14i		−	0.440157i
$584$	−1.43196e11	+	6.90623e14i	−8.72289e−5	+	0.420698i
$585$			8.61282e14i			0.519742i
$586$	3.30760e14	+	3.30806e14i	0.197732	+	0.197759i
$587$	7.54803e14	+	7.54803e14i	0.447017	+	0.447017i	0.894362	−	0.447345i	$-0.147630\pi$
$587$	7.54803e14	+	7.54803e14i	0.447017	+	0.447017i	−0.447345	+	0.894362i	$0.647630\pi$
$588$	−1.02806e15	+	1.02778e15i	−0.603175	+	0.603008i
$589$	−1.06076e15	+	1.06076e15i	−0.616570	+	0.616570i
$590$	−1.35506e11	+	1.96061e15i	−7.80321e−5	+	1.12903i
$591$	−4.75354e15			−2.71198
$592$	1.15300e14	+	1.15364e14i	0.0651719	+	0.0652079i
$593$	−2.83705e15			−1.58879			−0.794393	−	0.607404i	$-0.792211\pi$
$593$	−2.83705e15			−1.58879			−0.794393	+	0.607404i	$0.792211\pi$
$594$	−1.08487e11	+	1.56967e15i	−6.01938e−5	+	0.870929i
$595$	2.98896e15	−	2.98896e15i	1.64315	−	1.64315i
$596$	−8.50145e14	−	8.50380e14i	−0.463062	−	0.463190i
$597$	5.67150e14	+	5.67150e14i	0.306083	+	0.306083i
$598$	2.84288e14	+	2.84327e14i	0.152021	+	0.152042i
$599$			1.42147e15i			0.753167i	0.926383	+	0.376584i	$0.122901\pi$
$599$			1.42147e15i			0.753167i	−0.926383	+	0.376584i	$0.877099\pi$
$600$	5.65328e14	+	5.65562e14i	0.296803	+	0.296926i
$601$			1.37212e15i			0.713810i	0.934141	+	0.356905i	$0.116168\pi$
$601$			1.37212e15i			0.713810i	−0.934141	+	0.356905i	$0.883832\pi$
$602$	−2.07456e15	+	2.07427e15i	−1.06941	+	1.06926i
$603$	−2.13714e15	−	2.13714e15i	−1.09166	−	1.09166i
$604$	9.23949e10	−	6.68420e14i	4.67676e−5	−	0.338334i
$605$	−2.34257e15	+	2.34257e15i	−1.17500	+	1.17500i
$606$	−3.71425e15	−	2.56708e11i	−1.84617	−	0.000127597i
$607$	9.58569e14			0.472156			0.236078	−	0.971734i	$-0.424138\pi$
$607$	9.58569e14			0.472156			0.236078	+	0.971734i	$0.424138\pi$
$608$	1.20729e15	−	1.20646e15i	0.589308	−	0.588901i
$609$	−3.87772e15			−1.87578
$610$	−1.22786e15	−	8.48631e10i	−0.588621	−	4.06822e-5i
$611$	−3.86750e14	+	3.86750e14i	−0.183740	+	0.183740i
$612$	−6.59597e11	+	4.77177e15i	−0.000310560	+	2.24671i
$613$	1.16692e15	+	1.16692e15i	0.544512	+	0.544512i	0.924848	−	0.380336i	$-0.124192\pi$
$613$	1.16692e15	+	1.16692e15i	0.544512	+	0.544512i	−0.380336	+	0.924848i	$0.624192\pi$
$614$	2.26300e15	−	2.26269e15i	1.04655	−	1.04640i
$615$		−	3.13803e15i		−	1.43828i
$616$	3.05304e15	−	3.05177e15i	1.38688	−	1.38630i
$617$			1.66121e15i			0.747920i	0.927445	+	0.373960i	$0.122000\pi$
$617$			1.66121e15i			0.747920i	−0.927445	+	0.373960i	$0.878000\pi$
$618$	−2.07419e15	−	2.07448e15i	−0.925576	−	0.925703i
$619$	−1.32258e15	−	1.32258e15i	−0.584958	−	0.584958i	0.351304	−	0.936262i	$-0.385738\pi$
$619$	−1.32258e15	−	1.32258e15i	−0.584958	−	0.584958i	−0.936262	+	0.351304i	$0.885738\pi$
$620$	−1.90470e15	−	1.90523e15i	−0.834975	−	0.835205i
$621$	−5.72409e14	+	5.72409e14i	−0.248715	+	0.248715i
$622$	2.72936e11	−	3.94905e15i	0.000117548	−	1.70077i
$623$	2.67698e15			1.14277
$624$	−3.39843e11	+	1.22928e15i	−0.000143801	+	0.520157i
$625$	2.85766e15			1.19859
$626$	1.56633e11	−	2.26629e15i	6.51216e−5	−	0.942229i
$627$	−3.45339e15	+	3.45339e15i	−1.42323	+	1.42323i
$628$	−1.49324e15	+	1.49283e15i	−0.610031	+	0.609863i
$629$	−2.65832e14	−	2.65832e14i	−0.107654	−	0.107654i
$630$	3.37184e15	+	3.37231e15i	1.35361	+	1.35380i
$631$		−	3.87984e15i		−	1.54402i	−0.635612	−	0.772009i	$-0.719252\pi$
$631$		−	3.87984e15i		−	1.54402i	0.635612	−	0.772009i	$-0.280748\pi$
$632$	−2.14540e15	−	4.44834e11i	−0.846378	−	0.000175491i
$633$			2.37592e15i			0.929204i
$634$	2.47374e15	−	2.47340e15i	0.959099	−	0.958966i
$635$	3.48196e15	+	3.48196e15i	1.33835	+	1.33835i
$636$	1.12861e15	+	1.56006e11i	0.430060	+	5.94467e-5i
$637$	3.51788e14	−	3.51788e14i	0.132897	−	0.132897i
$638$	4.11045e15	+	2.84092e11i	1.53949	+	0.000106401i
$639$	7.07312e15			2.62637
$640$	2.16632e15	+	2.16842e15i	0.797504	+	0.798276i
$641$	−5.57445e14			−0.203462			−0.101731	−	0.994812i	$-0.532438\pi$
$641$	−5.57445e14			−0.203462			−0.101731	+	0.994812i	$0.532438\pi$
$642$	−9.68736e14	−	6.69536e10i	−0.350560	−	2.42288e-5i
$643$	−3.17954e15	+	3.17954e15i	−1.14079	+	1.14079i	−0.152480	+	0.988307i	$0.548726\pi$
$643$	−3.17954e15	+	3.17954e15i	−1.14079	+	1.14079i	−0.988307	+	0.152480i	$0.951274\pi$
$644$	2.22623e15	+	3.07730e11i	0.791951	+	0.000109471i
$645$	4.21472e15	+	4.21472e15i	1.48659	+	1.48659i
$646$	−2.78196e15	+	2.78157e15i	−0.972908	+	0.972773i
$647$		−	2.20708e15i		−	0.765324i	−0.923888	−	0.382662i	$-0.875007\pi$
$647$		−	2.20708e15i		−	0.765324i	0.923888	−	0.382662i	$-0.124993\pi$
$648$	1.48199e15	+	3.07281e11i	0.509546	+	0.000105651i
$649$		−	4.61501e15i		−	1.57335i
$650$	−1.93501e14	−	1.93528e14i	−0.0654123	−	0.0654214i
$651$	−4.23015e15	−	4.23015e15i	−1.41795	−	1.41795i
$652$	−1.64752e15	+	1.64707e15i	−0.547607	+	0.547456i
$653$	2.46010e15	−	2.46010e15i	0.810832	−	0.810832i	−0.173926	−	0.984759i	$-0.555645\pi$
$653$	2.46010e15	−	2.46010e15i	0.810832	−	0.810832i	0.984759	+	0.173926i	$0.0556455\pi$
$654$	1.27287e11	−	1.84169e15i	4.16013e−5	−	0.601919i
$655$	−5.40432e15			−1.75152
$656$	7.13649e11	−	2.58140e15i	0.000229358	−	0.829630i
$657$	1.79588e15			0.572358
$658$	−2.09306e11	+	3.02840e15i	−6.61514e−5	+	0.957128i
$659$	9.41322e13	−	9.41322e13i	0.0295032	−	0.0295032i	−0.692201	−	0.721704i	$-0.743359\pi$
$659$	9.41322e13	−	9.41322e13i	0.0295032	−	0.0295032i	0.721704	+	0.692201i	$0.243359\pi$
$660$	−6.20092e15	−	6.20264e15i	−1.92737	−	1.92790i
$661$	−1.97944e15	−	1.97944e15i	−0.610148	−	0.610148i	0.332837	−	0.942984i	$-0.391994\pi$
$661$	−1.97944e15	−	1.97944e15i	−0.610148	−	0.610148i	−0.942984	+	0.332837i	$0.891994\pi$
$662$	−6.77622e14	−	6.77716e14i	−0.207142	−	0.207171i
$663$		−	2.83340e15i		−	0.858981i
$664$	4.08679e14	−	4.08510e14i	0.122874	−	0.122823i
$665$			3.93159e15i			1.17233i
$666$	2.99927e14	−	2.99886e14i	0.0886967	−	0.0886845i
$667$	1.49895e15	+	1.49895e15i	0.439638	+	0.439638i
$668$	−1.44002e11	+	1.04177e15i	−4.18889e−5	+	0.303040i
$669$	1.51762e15	−	1.51762e15i	0.437843	−	0.437843i
$670$	4.47481e15	+	3.09274e11i	1.28045	+	8.84977e-5i
$671$	2.89022e15			0.820272
$672$	4.81118e15	+	4.81450e15i	1.35432	+	1.35525i
$673$	1.41200e15			0.394231			0.197116	−	0.980380i	$-0.436843\pi$
$673$	1.41200e15			0.394231			0.197116	+	0.980380i	$0.436843\pi$
$674$	−3.05378e14	−	2.11060e10i	−0.0845684	−	5.84490e-6i
$675$	3.89610e14	−	3.89610e14i	0.107019	−	0.107019i
$676$	−4.49195e11	+	3.24965e15i	−0.000122385	+	0.885379i
$677$	−4.85721e15	−	4.85721e15i	−1.31265	−	1.31265i	−0.919456	−	0.393194i	$-0.871370\pi$
$677$	−4.85721e15	−	4.85721e15i	−1.31265	−	1.31265i	−0.393194	−	0.919456i	$-0.628630\pi$
$678$	−4.86404e15	+	4.86337e15i	−1.30387	+	1.30369i
$679$			5.09628e15i			1.35509i
$680$	−4.99461e15	−	4.99668e15i	−1.31735	−	1.31790i
$681$		−	2.43961e15i		−	0.638281i
$682$	4.48373e15	+	4.48435e15i	1.16366	+	1.16382i
$683$	−8.68637e14	−	8.68637e14i	−0.223627	−	0.223627i	0.586397	−	0.810024i	$-0.300546\pi$
$683$	−8.68637e14	−	8.68637e14i	−0.223627	−	0.223627i	−0.810024	+	0.586397i	$0.800546\pi$
$684$	−3.13789e15	−	3.13876e15i	−0.801364	−	0.801585i
$685$	2.80891e15	−	2.80891e15i	0.711606	−	0.711606i
$686$	−1.52569e11	+	2.20748e15i	−3.83428e−5	+	0.554772i
$687$	4.63316e15			1.15509
$688$	3.46615e15	+	3.46806e15i	0.857256	+	0.857730i
$689$	−3.86248e14			−0.0947676
$690$	3.12618e11	−	4.52319e15i	7.60928e−5	−	1.10097i
$691$	−4.10027e15	+	4.10027e15i	−0.990110	+	0.990110i	−0.999952	−	0.00984162i	$-0.996867\pi$
$691$	−4.10027e15	+	4.10027e15i	−0.990110	+	0.990110i	0.00984162	+	0.999952i	$0.496867\pi$
$692$	−1.79835e15	+	1.79786e15i	−0.430816	+	0.430697i
$693$	−7.93741e15	−	7.93741e15i	−1.88645	−	1.88645i
$694$	−4.40743e15	−	4.40804e15i	−1.03922	−	1.03936i
$695$			2.41791e15i			0.565618i
$696$	−1.34381e12	+	6.48109e15i	−0.000311880	+	1.50417i
$697$			5.94996e15i			1.37004i
$698$	−3.77777e14	+	3.77725e14i	−0.0863040	+	0.0862921i
$699$	5.78696e15	+	5.78696e15i	1.31167	+	1.31167i
$700$	−1.51529e15	−	2.09456e11i	−0.340766	−	4.71036e-5i
$701$	4.09473e14	−	4.09473e14i	0.0913643	−	0.0913643i	−0.659947	−	0.751312i	$-0.729421\pi$
$701$	4.09473e14	−	4.09473e14i	0.0913643	−	0.0913643i	0.751312	+	0.659947i	$0.229421\pi$
$702$	8.47012e14	+	5.85407e10i	0.187515	+	1.29600e-5i
$703$	3.49669e14			0.0768073
$704$	−5.09958e15	−	5.10381e15i	−1.11144	−	1.11236i
$705$	6.15299e15			1.33060
$706$	−4.10092e15	−	2.83433e11i	−0.879945	−	6.08169e-5i
$707$	4.97674e15	−	4.97674e15i	1.05959	−	1.05959i
$708$	7.27664e15	+	1.00584e12i	1.53726	+	0.000212494i
$709$	−4.23628e13	−	4.23628e13i	−0.00888035	−	0.00888035i	0.702653	−	0.711533i	$-0.251999\pi$
$709$	−4.23628e13	−	4.23628e13i	−0.00888035	−	0.00888035i	−0.711533	+	0.702653i	$0.751999\pi$
$710$	−7.40548e15	+	7.40445e15i	−1.54039	+	1.54018i
$711$			5.57885e15i			1.15149i
$712$	9.27698e11	−	4.47421e15i	0.000190006	−	0.916382i
$713$			3.27037e15i			0.664668i
$714$	−1.10925e16	−	1.10940e16i	−2.23712	−	2.23743i
$715$	2.12246e15	+	2.12246e15i	0.424772	+	0.424772i
$716$	3.08885e15	−	3.08800e15i	0.613445	−	0.613275i
$717$	1.71892e15	−	1.71892e15i	0.338767	−	0.338767i
$718$	−2.23609e11	+	3.23534e15i	−4.37326e−5	+	0.632756i
$719$	3.44205e15			0.668049			0.334025	−	0.942564i	$-0.391593\pi$
$719$	3.44205e15			0.668049			0.334025	+	0.942564i	$0.391593\pi$
$720$	5.63754e15	−	5.63442e15i	1.08583	−	1.08523i
$721$	5.55882e15			1.06252
$722$	−1.11460e11	+	1.61269e15i	−2.11429e−5	+	0.305912i
$723$	−2.52912e15	+	2.52912e15i	−0.476111	+	0.476111i
$724$	−9.19564e14	−	9.19818e14i	−0.171799	−	0.171846i
$725$	−1.02026e15	−	1.02026e15i	−0.189170	−	0.189170i
$726$	8.69367e15	+	8.69487e15i	1.59975	+	1.59997i
$727$		−	8.86644e14i		−	0.161924i	−0.996717	−	0.0809618i	$-0.974201\pi$
$727$		−	8.86644e14i		−	0.161924i	0.996717	−	0.0809618i	$-0.0257992\pi$
$728$	−1.64677e15	−	1.64746e15i	−0.298477	−	0.298601i
$729$		−	8.58422e15i		−	1.54419i
$730$	−1.88027e15	+	1.88001e15i	−0.335694	+	0.335647i
$731$	−7.99145e15	−	7.99145e15i	−1.41605	−	1.41605i
$732$	−6.29926e11	+	4.55712e15i	−0.000110784	+	0.801456i
$733$	−7.89968e15	+	7.89968e15i	−1.37892	+	1.37892i	−0.532461	+	0.846455i	$0.678733\pi$
$733$	−7.89968e15	+	7.89968e15i	−1.37892	+	1.37892i	−0.846455	+	0.532461i	$0.821267\pi$
$734$	1.89641e14	+	1.31069e10i	0.0328552	+	2.27077e-6i
$735$	−5.59676e15			−0.962401
$736$	1.28582e12	−	3.72085e15i	0.000219459	−	0.635060i
$737$	−1.05331e16			−1.78437
$738$	−6.71262e15	−	4.63939e11i	−1.12871	−	7.80101e-5i
$739$	3.16961e15	−	3.16961e15i	0.529007	−	0.529007i	−0.391269	−	0.920276i	$-0.627964\pi$
$739$	3.16961e15	−	3.16961e15i	0.529007	−	0.529007i	0.920276	+	0.391269i	$0.127964\pi$
$740$	−8.68014e10	+	6.27954e14i	−1.43798e−5	+	0.104029i
$741$	1.86349e15	+	1.86349e15i	0.306427	+	0.306427i
$742$	−1.51233e15	+	1.51212e15i	−0.246846	+	0.246812i
$743$		−	1.94649e15i		−	0.315364i	−0.987490	−	0.157682i	$-0.949598\pi$
$743$		−	1.94649e15i		−	0.315364i	0.987490	−	0.157682i	$-0.0504022\pi$
$744$	−7.07161e15	+	7.06867e15i	−1.13728	+	1.13681i
$745$		−	4.62947e15i		−	0.739047i
$746$	5.07425e15	+	5.07495e15i	0.804097	+	0.804208i
$747$	−1.06250e15	−	1.06250e15i	−0.167134	−	0.167134i
$748$	1.17574e16	+	1.17607e16i	1.83592	+	1.83643i
$749$	1.29801e15	−	1.29801e15i	0.201201	−	0.201201i
$750$	5.65909e11	−	8.18799e15i	8.70782e−5	−	1.25991i
$751$	−8.22162e14			−0.125585			−0.0627925	−	0.998027i	$-0.520001\pi$
$751$	−8.22162e14			−0.125585			−0.0627925	+	0.998027i	$0.520001\pi$
$752$	5.06156e15	+	1.39931e12i	0.767514	+	0.000212185i
$753$	−2.80726e15			−0.422581
$754$	1.53299e11	−	2.21805e15i	2.29085e−5	−	0.331458i
$755$	1.81969e15	−	1.81969e15i	0.269954	−	0.269954i
$756$	3.31666e15	−	3.31575e15i	0.488463	−	0.488328i
$757$	1.22234e15	+	1.22234e15i	0.178716	+	0.178716i	0.790796	−	0.612080i	$-0.209667\pi$
$757$	1.22234e15	+	1.22234e15i	0.178716	+	0.178716i	−0.612080	+	0.790796i	$0.709667\pi$
$758$	−4.71308e15	−	4.71373e15i	−0.684107	−	0.684202i
$759$			1.06470e16i			1.53425i
$760$	6.57113e15	+	1.36248e12i	0.940081	+	0.000194920i
$761$			7.64079e15i			1.08523i	0.839981	+	0.542616i	$0.182566\pi$
$761$			7.64079e15i			1.08523i	−0.839981	+	0.542616i	$0.817434\pi$
$762$	1.29239e16	−	1.29221e16i	1.82239	−	1.82214i
$763$	2.46768e15	+	2.46768e15i	0.345466	+	0.345466i
$764$	1.01765e16	+	1.40669e12i	1.41444	+	0.000195517i
$765$	−1.29906e16	+	1.29906e16i	−1.79263	+	1.79263i
$766$	−5.84843e15	−	4.04211e11i	−0.801274	−	5.53796e-5i
$767$	−2.49031e15			−0.338750
$768$	8.04847e15	−	8.03958e15i	1.08699	−	1.08579i
$769$	4.51581e15			0.605537			0.302768	−	0.953064i	$-0.402089\pi$
$769$	4.51581e15			0.605537			0.302768	+	0.953064i	$0.402089\pi$
$770$	1.66196e16	+	1.14865e12i	2.21270	+	0.000152929i
$771$	7.83613e14	−	7.83613e14i	0.103586	−	0.103586i
$772$	−5.55032e15	−	7.67215e11i	−0.728489	−	0.000100698i
$773$	−1.07717e15	−	1.07717e15i	−0.140377	−	0.140377i	0.633426	−	0.773803i	$-0.281648\pi$
$773$	−1.07717e15	−	1.07717e15i	−0.140377	−	0.140377i	−0.773803	+	0.633426i	$0.781648\pi$
$774$	9.01641e15	−	9.01516e15i	1.16670	−	1.16654i
$775$		−	2.22598e15i		−	0.285997i
$776$	8.51775e15	+	1.76610e12i	1.08664	+	0.000225308i
$777$			1.39443e15i			0.176637i
$778$	−1.01649e16	−	1.01663e16i	−1.27854	−	1.27872i
$779$	−3.91321e15	−	3.91321e15i	−0.488739	−	0.488739i
$780$	−3.34702e15	+	3.34609e15i	−0.415085	+	0.414971i
$781$	1.74303e16	−	1.74303e16i	2.14647	−	2.14647i
$782$	−5.92748e11	+	8.57632e15i	−7.24824e−5	+	1.04873i
$783$	4.46569e15			0.542249
$784$	−4.60399e15	−	1.27281e12i	−0.555132	−	0.000153471i
$785$	−8.12921e15			−0.973342
$786$	−1.38628e12	+	2.00577e16i	−0.000164826	+	2.38483i
$787$	−4.70724e15	+	4.70724e15i	−0.555783	+	0.555783i	−0.928104	−	0.372321i	$-0.878562\pi$
$787$	−4.70724e15	+	4.70724e15i	−0.555783	+	0.555783i	0.372321	+	0.928104i	$0.378562\pi$
$788$	−1.06440e16	−	1.06469e16i	−1.24798	−	1.24833i
$789$	4.64090e15	+	4.64090e15i	0.540354	+	0.540354i
$790$	−5.84018e15	−	5.84099e15i	−0.675270	−	0.675363i
$791$		−	1.30338e16i		−	1.49658i
$792$	−1.32691e16	+	1.32636e16i	−1.51305	+	1.51242i
$793$		−	1.55960e15i		−	0.176608i
$794$	−9.34343e15	+	9.34214e15i	−1.05074	+	1.05059i
$795$	3.07250e15	+	3.07250e15i	0.343141	+	0.343141i
$796$	−3.51134e11	+	2.54024e15i	−3.89449e−5	+	0.281742i
$797$	7.24872e15	−	7.24872e15i	0.798436	−	0.798436i	−0.184412	−	0.982849i	$-0.559038\pi$
$797$	7.24872e15	−	7.24872e15i	0.798436	−	0.798436i	0.982849	+	0.184412i	$0.0590382\pi$
$798$	1.45918e16	+	1.00850e12i	1.59622	+	0.000110322i
$799$	−1.16666e16			−1.26746
$800$	−8.75197e11	+	2.53260e15i	−9.44302e−5	+	0.273257i
$801$	−1.16346e16			−1.24673
$802$	8.02614e15	+	5.54723e11i	0.854177	+	5.90360e-5i
$803$	4.42559e15	−	4.42559e15i	0.467773	−	0.467773i
$804$	2.29569e12	−	1.66079e16i	0.000240994	−	1.74344i
$805$	6.06064e15	+	6.06064e15i	0.631890	+	0.631890i
$806$	2.41981e15	−	2.41947e15i	0.250575	−	0.250540i
$807$			1.19115e16i			1.22508i
$808$	−8.31625e15	−	8.31969e15i	−0.849503	−	0.849855i
$809$		−	1.03410e16i		−	1.04917i	−0.851360	−	0.524583i	$-0.824221\pi$
$809$		−	1.03410e16i		−	1.04917i	0.851360	−	0.524583i	$-0.175779\pi$
$810$	4.03426e15	+	4.03482e15i	0.406533	+	0.406590i
$811$	1.11196e16	+	1.11196e16i	1.11295	+	1.11295i	0.992750	+	0.120200i	$0.0383536\pi$
$811$	1.11196e16	+	1.11196e16i	1.11295	+	1.11295i	0.120200	+	0.992750i	$0.461646\pi$
$812$	−8.68286e15	−	8.68526e15i	−0.863186	−	0.863425i
$813$	−8.43807e15	+	8.43807e15i	−0.833192	+	0.833192i
$814$	1.02159e11	−	1.47812e15i	1.00195e−5	−	0.144969i
$815$	−8.96910e15			−0.873740
$816$	−1.85461e16	+	1.85358e16i	−1.79455	+	1.79356i
$817$	1.05117e16			1.01031
$818$	−1.11469e12	+	1.61282e16i	−0.000106417	+	1.53972i
$819$	−4.28312e15	+	4.28312e15i	−0.406161	+	0.406161i
$820$	7.02852e15	−	7.02658e15i	0.662045	−	0.661862i
$821$	7.05917e15	+	7.05917e15i	0.660490	+	0.660490i	0.955496	−	0.295005i	$-0.0953215\pi$
$821$	7.05917e15	+	7.05917e15i	0.660490	+	0.660490i	−0.295005	+	0.955496i	$0.595321\pi$
$822$	−1.04243e16	−	1.04258e16i	−0.968843	−	0.968977i
$823$		−	1.30797e16i		−	1.20753i	−0.797163	−	0.603764i	$-0.793667\pi$
$823$		−	1.30797e16i		−	1.20753i	0.797163	−	0.603764i	$-0.206333\pi$
$824$	1.92639e12	−	9.29084e15i	0.000176663	−	0.852031i
$825$		−	7.24687e15i		−	0.660167i
$826$	−9.75069e15	+	9.74934e15i	−0.882359	+	0.882237i
$827$	8.30624e15	+	8.30624e15i	0.746662	+	0.746662i	0.973851	−	0.227189i	$-0.0729534\pi$
$827$	8.30624e15	+	8.30624e15i	0.746662	+	0.746662i	−0.227189	+	0.973851i	$0.572953\pi$
$828$	−9.67562e15	−	1.33745e12i	−0.863997	−	0.000119429i
$829$	−1.07494e16	+	1.07494e16i	−0.953531	+	0.953531i	−0.998967	−	0.0454367i	$-0.985532\pi$
$829$	−1.07494e16	+	1.07494e16i	−0.953531	+	0.953531i	0.0454367	+	0.998967i	$0.485532\pi$
$830$	2.22470e15	+	1.53759e11i	0.196039	+	1.35491e-5i
$831$	1.43176e16			1.25332
$832$	−2.75408e15	+	2.75179e15i	−0.239496	+	0.239297i
$833$	1.06119e16			0.916739
$834$	8.97387e15	+	6.20224e11i	0.770135	+	5.32274e-5i
$835$	−2.83608e15	+	2.83608e15i	−0.241793	+	0.241793i
$836$	−1.54676e16	−	2.13806e12i	−1.31005	−	0.000181087i
$837$	4.87156e15	+	4.87156e15i	0.409900	+	0.409900i
$838$	1.23012e16	−	1.22995e16i	1.02826	−	1.02812i
$839$		−	7.21546e15i		−	0.599202i	−0.954065	−	0.299601i	$-0.903146\pi$
$839$		−	7.21546e15i		−	0.599202i	0.954065	−	0.299601i	$-0.0968535\pi$
$840$	−5.43337e12	+	2.62047e16i	−0.000448264	+	2.16194i
$841$			5.06335e14i			0.0415011i
$842$	2.58683e15	+	2.58719e15i	0.210645	+	0.210674i
$843$	−2.34136e16	−	2.34136e16i	−1.89416	−	1.89416i
$844$	−5.32155e15	+	5.32008e15i	−0.427715	+	0.427597i
$845$	−8.84676e15	+	8.84676e15i	−0.706435	+	0.706435i
$846$	9.09683e11	−	1.31620e16i	7.21694e−5	−	1.04420i
$847$	−2.32990e16			−1.83645
$848$	2.52679e15	+	2.52819e15i	0.197876	+	0.197985i
$849$	3.36682e13			0.00261956
$850$	4.03454e11	−	5.83748e15i	3.11882e−5	−	0.451254i
$851$	5.39023e14	−	5.39023e14i	0.0413995	−	0.0413995i
$852$	2.74792e16	+	2.74868e16i	2.09694	+	2.09752i
$853$	2.11551e15	+	2.11551e15i	0.160397	+	0.160397i	0.782742	−	0.622346i	$-0.213820\pi$
$853$	2.11551e15	+	2.11551e15i	0.160397	+	0.160397i	−0.622346	+	0.782742i	$0.713820\pi$
$854$	−6.10569e15	−	6.10653e15i	−0.459956	−	0.460020i
$855$		−	1.70874e16i		−	1.27898i
$856$	−2.16901e15	−	2.16991e15i	−0.161308	−	0.161375i
$857$			5.60408e15i			0.414104i	0.978330	+	0.207052i	$0.0663870\pi$
$857$			5.60408e15i			0.414104i	−0.978330	+	0.207052i	$0.933613\pi$
$858$	7.87788e15	−	7.87679e15i	0.578401	−	0.578321i
$859$	−2.84823e14	−	2.84823e14i	−0.0207784	−	0.0207784i	0.696641	−	0.717420i	$-0.254677\pi$
$859$	−2.84823e14	−	2.84823e14i	−0.0207784	−	0.0207784i	−0.717420	+	0.696641i	$0.754677\pi$
$860$	−2.60942e12	+	1.88775e16i	−0.000189148	+	1.36837i
$861$	1.56053e16	−	1.56053e16i	1.12397	−	1.12397i
$862$	2.09158e15	+	1.44558e11i	0.149687	+	1.03455e-5i
$863$	2.14058e15			0.152220			0.0761102	−	0.997099i	$-0.475750\pi$
$863$	2.14058e15			0.152220			0.0761102	+	0.997099i	$0.475750\pi$
$864$	−5.54068e15	−	5.54451e15i	−0.391505	−	0.391776i
$865$	−9.79024e15			−0.687392
$866$	−9.82347e15	−	6.78944e11i	−0.685356	−	4.73680e-5i
$867$	2.70648e16	−	2.70648e16i	1.87629	−	1.87629i
$868$	2.61897e12	−	1.89466e16i	0.000180415	−	1.30519i
$869$	1.37479e16	+	1.37479e16i	0.941086	+	0.941086i
$870$	−1.76452e16	+	1.76428e16i	−1.20025	+	1.20008i
$871$			5.68378e15i			0.384182i
$872$	4.12526e15	−	4.12355e15i	0.277084	−	0.276969i
$873$		−	2.21494e16i		−	1.47837i
$874$	−5.64014e15	−	5.64092e15i	−0.374091	−	0.374142i
$875$	1.09711e16	+	1.09711e16i	0.723115	+	0.723115i
$876$	6.97701e15	+	6.97894e15i	0.456980	+	0.457106i
$877$	−6.91657e14	+	6.91657e14i	−0.0450187	+	0.0450187i	−0.729258	−	0.684239i	$-0.760134\pi$
$877$	−6.91657e14	+	6.91657e14i	−0.0450187	+	0.0450187i	0.684239	+	0.729258i	$0.260134\pi$
$878$	8.35344e11	−	1.20864e16i	5.40313e−5	−	0.781766i
$879$	6.68439e15			0.429658
$880$	7.67930e12	−	2.77775e16i	0.000490532	−	1.77434i
$881$	−1.27110e16			−0.806889			−0.403444	−	0.915004i	$-0.632187\pi$
$881$	−1.27110e16			−0.806889			−0.403444	+	0.915004i	$0.632187\pi$
$882$	−8.27446e11	+	1.19721e16i	−5.21991e−5	+	0.755255i
$883$	1.13706e16	−	1.13706e16i	0.712850	−	0.712850i	−0.254280	−	0.967131i	$-0.581839\pi$
$883$	1.13706e16	−	1.13706e16i	0.712850	−	0.712850i	0.967131	+	0.254280i	$0.0818386\pi$
$884$	6.34621e15	−	6.34445e15i	0.395391	−	0.395282i
$885$	1.98098e16	+	1.98098e16i	1.22657	+	1.22657i
$886$	1.08527e16	+	1.08542e16i	0.667812	+	0.667904i
$887$		−	4.64514e15i		−	0.284066i	−0.989862	−	0.142033i	$-0.954636\pi$
$887$		−	4.64514e15i		−	0.284066i	0.989862	−	0.142033i	$-0.0453639\pi$
$888$	2.33060e15	+	4.83235e11i	0.141644	+	2.93689e-5i
$889$			3.46313e16i			2.09175i
$890$	1.21813e16	−	1.21796e16i	0.731223	−	0.731122i
$891$	−9.49676e15	−	9.49676e15i	−0.566563	−	0.566563i
$892$	6.79733e15	+	9.39587e11i	0.403025	+	5.57096e-5i
$893$	7.67294e15	−	7.67294e15i	0.452146	−	0.452146i
$894$	−1.71819e16	−	1.18752e12i	−1.00627	−	6.95480e-5i
$895$	1.68157e16			0.978788
$896$	−1.04290e13	+	2.15565e16i	−0.000603324	+	1.24705i
$897$	5.74523e15			0.330331
$898$	2.65963e16	+	1.83819e12i	1.51985	+	0.000105044i
$899$	1.27570e16	−	1.27570e16i	0.724554	−	0.724554i
$900$	6.58572e15	+	9.10337e11i	0.371766	+	5.13888e-5i
$901$	−5.82570e15	−	5.82570e15i	−0.326860	−	0.326860i
$902$	−1.65430e16	+	1.65408e16i	−0.922528	+	0.922400i
$903$			4.19193e16i			2.32344i
$904$	−2.17843e16	−	4.51683e12i	−1.20010	−	0.000248832i
$905$		−	5.00749e15i		−	0.274191i
$906$	−6.75317e15	−	6.75411e15i	−0.367538	−	0.367589i
$907$	1.40963e16	+	1.40963e16i	0.762543	+	0.762543i	0.976781	−	0.214239i	$-0.0687270\pi$
$907$	1.40963e16	+	1.40963e16i	0.762543	+	0.762543i	−0.214239	+	0.976781i	$0.568727\pi$
$908$	5.46421e15	−	5.46270e15i	0.293802	−	0.293721i
$909$	−2.16299e16	+	2.16299e16i	−1.15599	+	1.15599i
$910$	6.19828e11	−	8.96813e15i	3.29263e−5	−	0.476403i
$911$	−2.45183e16			−1.29461			−0.647305	−	0.762231i	$-0.724104\pi$
$911$	−2.45183e16			−1.29461			−0.647305	+	0.762231i	$0.724104\pi$
$912$	6.74232e12	−	2.43882e16i	0.000353865	−	1.28000i
$913$	−5.23664e15			−0.273189
$914$	1.41436e12	−	2.04641e16i	7.33427e−5	−	1.06118i
$915$	−1.24062e16	+	1.24062e16i	−0.639474	+	0.639474i
$916$	1.03744e16	+	1.03773e16i	0.531543	+	0.531690i
$917$	−2.68755e16	−	2.68755e16i	−1.36875	−	1.36875i
$918$	1.27744e16	+	1.27762e16i	0.646706	+	0.646796i
$919$			1.71814e16i			0.864615i	0.901726	+	0.432307i	$0.142300\pi$
$919$			1.71814e16i			0.864615i	−0.901726	+	0.432307i	$0.857700\pi$
$920$	1.01317e16	−	1.01275e16i	0.506813	−	0.506603i
$921$		−	4.57271e16i		−	2.27377i
$922$	−2.32026e16	+	2.31994e16i	−1.14687	+	1.14672i
$923$	−9.40559e15	−	9.40559e15i	−0.462143	−	0.462143i
$924$	8.52629e12	−	6.16824e16i	0.000416451	−	3.01277i
$925$	−3.66887e14	+	3.66887e14i	−0.0178136	+	0.0178136i
$926$	1.15503e16	+	7.98295e11i	0.557486	+	3.85303e-5i
$927$	−2.41597e16			−1.15918
$928$	−1.45193e16	+	1.45092e16i	−0.692518	+	0.692039i
$929$	1.37942e16			0.654047			0.327024	−	0.945016i	$-0.393954\pi$
$929$	1.37942e16			0.654047			0.327024	+	0.945016i	$0.393954\pi$
$930$	−3.84952e16	−	2.66057e12i	−1.81447	−	0.000125406i
$931$	−6.97930e15	+	6.97930e15i	−0.327031	+	0.327031i
$932$	−3.58282e12	+	2.59195e16i	−0.000166893	+	1.20737i
$933$	−3.99007e16	−	3.99007e16i	−1.84770	−	1.84770i
$934$	5.56453e15	−	5.56377e15i	0.256166	−	0.256130i
$935$			6.40252e16i			2.93013i
$936$	7.15718e15	+	7.16015e15i	0.325630	+	0.325765i
$937$			3.53690e16i			1.59976i	0.600160	+	0.799880i	$0.295104\pi$
$937$			3.53690e16i			1.59976i	−0.600160	+	0.799880i	$0.704896\pi$
$938$	2.22515e16	+	2.22546e16i	1.00056	+	1.00070i
$939$	−2.28983e16	−	2.28983e16i	−1.02363	−	1.02363i
$940$	1.37776e16	+	1.37814e16i	0.612308	+	0.612477i
$941$	−2.22717e16	+	2.22717e16i	−0.984034	+	0.984034i	−0.999875	−	0.0158400i	$-0.994958\pi$
$941$	−2.22717e16	+	2.22717e16i	−0.984034	+	0.984034i	0.0158400	+	0.999875i	$0.494958\pi$
$942$	−2.08525e12	+	3.01709e16i	−9.15963e−5	+	1.32528i
$943$	−1.20646e16			−0.526865
$944$	1.62914e16	+	1.63004e16i	0.707313	+	0.707704i
$945$	1.80559e16			0.779371
$946$	3.07111e12	−	4.44352e16i	0.000131794	−	1.90689i
$947$	−2.09342e16	+	2.09342e16i	−0.893163	+	0.893163i	−0.994820	−	0.101656i	$-0.967586\pi$
$947$	−2.09342e16	+	2.09342e16i	−0.893163	+	0.893163i	0.101656	+	0.994820i	$0.467586\pi$
$948$	−2.16799e16	+	2.16739e16i	−0.919625	+	0.919371i
$949$	−2.38810e15	−	2.38810e15i	−0.100714	−	0.100714i
$950$	3.83896e15	+	3.83949e15i	0.160966	+	0.160988i
$951$		−	4.99854e16i		−	2.08377i
$952$	1.03021e13	−	4.96862e16i	0.000426995	−	2.05936i
$953$		−	2.34667e16i		−	0.967035i	−0.875335	−	0.483517i	$-0.839359\pi$
$953$		−	2.34667e16i		−	0.967035i	0.875335	−	0.483517i	$-0.160641\pi$
$954$	6.57288e15	−	6.57198e15i	0.269302	−	0.269265i
$955$	2.77043e16	+	2.77043e16i	1.12857	+	1.12857i
$956$	7.69897e15	+	1.06422e12i	0.311828	+	4.31036e-5i
$957$	4.15315e16	−	4.15315e16i	1.67249	−	1.67249i
$958$	1.22663e16	+	8.47780e11i	0.491139	+	3.39448e-5i
$959$	2.79372e16			1.11219
$960$	4.37977e16	+	1.81623e13i	1.73364	+	0.000718919i
$961$	2.42445e15			0.0954191
$962$	−7.97610e14	−	5.51264e10i	−0.0312124	−	2.15723e-6i
$963$	−5.64141e15	+	5.64141e15i	−0.219504	+	0.219504i
$964$	−1.13278e16	−	1.56583e12i	−0.438250	−	6.05788e-5i
$965$	−1.51101e16	−	1.51101e16i	−0.581254	−	0.581254i
$966$	2.24952e16	−	2.24921e16i	0.860429	−	0.860310i
$967$		−	3.94438e16i		−	1.50014i	−0.661357	−	0.750071i	$-0.730019\pi$
$967$		−	3.94438e16i		−	1.50014i	0.661357	−	0.750071i	$-0.269981\pi$
$968$	−8.07420e12	+	3.89412e16i	−0.000305341	+	1.47263i
$969$			5.62133e16i			2.11377i
$970$	2.31869e16	+	2.31901e16i	0.866959	+	0.867079i
$971$	1.82080e16	+	1.82080e16i	0.676948	+	0.676948i	0.959308	−	0.282360i	$-0.0911174\pi$
$971$	1.82080e16	+	1.82080e16i	0.676948	+	0.676948i	−0.282360	+	0.959308i	$0.591117\pi$
$972$	2.55712e16	−	2.55642e16i	0.945338	−	0.945077i
$973$	−1.20241e16	+	1.20241e16i	−0.442012	+	0.442012i
$974$	−1.17994e12	+	1.70722e16i	−4.31305e−5	+	0.624045i
$975$	−3.91049e15			−0.142137
$976$	−1.02084e16	+	1.02027e16i	−0.368963	+	0.368759i
$977$	−1.68239e16			−0.604652			−0.302326	−	0.953205i	$-0.597763\pi$
$977$	−1.68239e16			−0.604652			−0.302326	+	0.953205i	$0.597763\pi$
$978$	−2.30069e12	+	3.32881e16i	−8.22232e−5	+	1.18967i
$979$	−2.86712e16	+	2.86712e16i	−1.01892	+	1.01892i
$980$	−1.25321e16	−	1.25355e16i	−0.442873	−	0.442996i
$981$	−1.07250e16	−	1.07250e16i	−0.376893	−	0.376893i
$982$	−2.00010e16	−	2.00037e16i	−0.698937	−	0.699033i
$983$			1.79195e16i			0.622704i	0.950295	+	0.311352i	$0.100782\pi$
$983$			1.79195e16i			0.622704i	−0.950295	+	0.311352i	$0.899218\pi$
$984$	−2.60768e16	−	2.60876e16i	−0.901117	−	0.901491i
$985$		−	5.79617e16i		−	1.99178i
$986$	3.34567e16	−	3.34521e16i	1.14330	−	1.14314i
$987$	3.05986e16	+	3.05986e16i	1.03982	+	1.03982i
$988$	−1.15372e12	+	8.34647e15i	−3.89887e−5	+	0.282059i
$989$	1.62041e16	−	1.62041e16i	0.544560	−	0.544560i
$990$	−7.22319e16	−	4.99227e12i	−2.41399	−	0.000166842i
$991$	5.56476e16			1.84945			0.924723	−	0.380641i	$-0.124296\pi$
$991$	5.56476e16			1.84945			0.924723	+	0.380641i	$0.124296\pi$
$992$	−3.16668e16	−	1.09432e13i	−1.04662	−	0.000361684i
$993$	−1.36942e16			−0.450106
$994$	−7.36491e16	−	5.09022e12i	−2.40737	−	0.000166384i
$995$	−6.91548e15	+	6.91548e15i	−0.224800	+	0.224800i
$996$	1.14133e12	−	8.25679e15i	3.68964e−5	−	0.266922i
$997$	1.04105e16	+	1.04105e16i	0.334695	+	0.334695i	0.854366	−	0.519671i	$-0.173945\pi$
$997$	1.04105e16	+	1.04105e16i	0.334695	+	0.334695i	−0.519671	+	0.854366i	$0.673945\pi$
$998$	−2.46583e16	+	2.46549e16i	−0.788399	+	0.788290i
$999$		−	1.60586e15i		−	0.0510620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.12.e.a.5.21	✓	42
4.3	odd	2		64.12.e.a.49.2		42
8.3	odd	2		128.12.e.a.97.20		42
8.5	even	2		128.12.e.b.97.2		42
16.3	odd	4		64.12.e.a.17.2		42
16.5	even	4		128.12.e.b.33.2		42
16.11	odd	4		128.12.e.a.33.20		42
16.13	even	4	inner	16.12.e.a.13.21	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.21	✓	42	1.1	even	1	trivial
16.12.e.a.13.21	yes	42	16.13	even	4	inner
64.12.e.a.17.2		42	16.3	odd	4
64.12.e.a.49.2		42	4.3	odd	2
128.12.e.a.33.20		42	16.11	odd	4
128.12.e.a.97.20		42	8.3	odd	2
128.12.e.b.33.2		42	16.5	even	4
128.12.e.b.97.2		42	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(45.2548 + 0.00312776i) q^{2} +(457.250 - 457.250i) q^{3} +(2048.00 + 0.283093i) q^{4} +(5575.43 + 5575.43i) q^{5} +(20694.2 - 20691.3i) q^{6} +55452.7i q^{7} +(92681.9 + 19.2170i) q^{8} -241008. i q^{9} +O(q^{10})\)	\(q+(45.2548 + 0.00312776i) q^{2} +(457.250 - 457.250i) q^{3} +(2048.00 + 0.283093i) q^{4} +(5575.43 + 5575.43i) q^{5} +(20694.2 - 20691.3i) q^{6} +55452.7i q^{7} +(92681.9 + 19.2170i) q^{8} -241008. i q^{9} +(252298. + 252332. i) q^{10} +(-593916. - 593916. i) q^{11} +(936577. - 936318. i) q^{12} +(-320484. + 320484. i) q^{13} +(-173.443 + 2.50950e6i) q^{14} +5.09873e6 q^{15} +(4.19430e6 + 1159.55i) q^{16} -9.66759e6 q^{17} +(753.816 - 1.09068e7i) q^{18} +(6.35824e6 - 6.35824e6i) q^{19} +(1.14169e7 + 1.14201e7i) q^{20} +(2.53557e7 + 2.53557e7i) q^{21} +(-2.68757e7 - 2.68794e7i) q^{22} -1.96028e7i q^{23} +(4.23876e7 - 4.23700e7i) q^{24} +1.33426e7i q^{25} +(-1.45044e7 + 1.45024e7i) q^{26} +(-2.92004e7 - 2.92004e7i) q^{27} +(-15698.3 + 1.13567e8i) q^{28} +(-7.64662e7 + 7.64662e7i) q^{29} +(2.30742e8 + 15947.6i) q^{30} -1.66832e8 q^{31} +(1.89813e8 + 65593.9i) q^{32} -5.43136e8 q^{33} +(-4.37505e8 - 30237.9i) q^{34} +(-3.09173e8 + 3.09173e8i) q^{35} +(68227.6 - 4.93584e8i) q^{36} +(2.74973e7 + 2.74973e7i) q^{37} +(2.87761e8 - 2.87721e8i) q^{38} +2.93082e8i q^{39} +(5.16634e8 + 5.16848e8i) q^{40} -6.15454e8i q^{41} +(1.14739e9 + 1.14755e9i) q^{42} +(8.26623e8 + 8.26623e8i) q^{43} +(-1.21617e9 - 1.21651e9i) q^{44} +(1.34372e9 - 1.34372e9i) q^{45} +(61312.9 - 8.87121e8i) q^{46} +1.20677e9 q^{47} +(1.91838e9 - 1.91731e9i) q^{48} -1.09768e9 q^{49} +(-41732.6 + 6.03819e8i) q^{50} +(-4.42051e9 + 4.42051e9i) q^{51} +(-6.56441e8 + 6.56260e8i) q^{52} +(6.02601e8 + 6.02601e8i) q^{53} +(-1.32137e9 - 1.32155e9i) q^{54} -6.62267e9i q^{55} +(-1.06563e6 + 5.13946e9i) q^{56} -5.81461e9i q^{57} +(-3.46071e9 + 3.46023e9i) q^{58} +(3.88524e9 + 3.88524e9i) q^{59} +(1.04422e10 + 1.44341e6i) q^{60} +(-2.43319e9 + 2.43319e9i) q^{61} +(-7.54996e9 - 521811. i) q^{62} +1.33645e10 q^{63} +(8.58993e9 + 3.56213e6i) q^{64} -3.57367e9 q^{65} +(-2.45795e10 - 1.69880e6i) q^{66} +(8.86750e9 - 8.86750e9i) q^{67} +(-1.97992e10 - 2.73683e6i) q^{68} +(-8.96337e9 - 8.96337e9i) q^{69} +(-1.39925e10 + 1.39906e10i) q^{70} +2.93481e10i q^{71} +(4.63144e6 - 2.23371e10i) q^{72} +7.45154e9i q^{73} +(1.24430e9 + 1.24447e9i) q^{74} +(6.10092e9 + 6.10092e9i) q^{75} +(1.30235e10 - 1.30199e10i) q^{76} +(3.29342e10 - 3.29342e10i) q^{77} +(-916692. + 1.32634e10i) q^{78} -2.31480e10 q^{79} +(2.33786e10 + 2.33915e10i) q^{80} +1.59901e10 q^{81} +(1.92499e6 - 2.78523e10i) q^{82} +(4.40857e9 - 4.40857e9i) q^{83} +(5.19214e10 + 5.19358e10i) q^{84} +(-5.39010e10 - 5.39010e10i) q^{85} +(3.74061e10 + 3.74113e10i) q^{86} +6.99284e10i q^{87} +(-5.50338e10 - 5.50566e10i) q^{88} -4.82749e10i q^{89} +(6.08141e10 - 6.08057e10i) q^{90} +(-1.77717e10 - 1.77717e10i) q^{91} +(5.54941e6 - 4.01465e10i) q^{92} +(-7.62839e10 + 7.62839e10i) q^{93} +(5.46122e10 + 3.77449e6i) q^{94} +7.08998e10 q^{95} +(8.68217e10 - 8.67618e10i) q^{96} +9.19031e10 q^{97} +(-4.96752e10 - 3.43328e6i) q^{98} +(-1.43138e11 + 1.43138e11i) 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

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