LMFDB - Embedded newform 7.12.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,12,Mod(1,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	7.a (trivial)

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:	yes
Analytic conductor:	$5.37840226392$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 818x - 4704 $ x^3 - x^2 - 818*x - 4704
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$31.5985$ of defining polynomial
Character	$\chi$	$=$	7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+75.0789 q^{2} -240.378 q^{3} +3588.85 q^{4} +12842.0 q^{5} -18047.3 q^{6} -16807.0 q^{7} +115685. q^{8} -119365. q^{9} +O(q^{10})$	\(q+75.0789 q^{2} -240.378 q^{3} +3588.85 q^{4} +12842.0 q^{5} -18047.3 q^{6} -16807.0 q^{7} +115685. q^{8} -119365. q^{9} +964166. q^{10} -296700. q^{11} -862680. q^{12} -948262. q^{13} -1.26185e6 q^{14} -3.08694e6 q^{15} +1.33557e6 q^{16} +4.84445e6 q^{17} -8.96183e6 q^{18} +2.73546e6 q^{19} +4.60881e7 q^{20} +4.04003e6 q^{21} -2.22759e7 q^{22} -5.73212e7 q^{23} -2.78082e7 q^{24} +1.16090e8 q^{25} -7.11945e7 q^{26} +7.12750e7 q^{27} -6.03178e7 q^{28} +5.73542e7 q^{29} -2.31764e8 q^{30} +6.77483e7 q^{31} -1.36650e8 q^{32} +7.13202e7 q^{33} +3.63716e8 q^{34} -2.15836e8 q^{35} -4.28385e8 q^{36} +4.84599e8 q^{37} +2.05375e8 q^{38} +2.27941e8 q^{39} +1.48563e9 q^{40} -7.69966e8 q^{41} +3.03321e8 q^{42} +1.24757e8 q^{43} -1.06481e9 q^{44} -1.53290e9 q^{45} -4.30362e9 q^{46} +4.14735e8 q^{47} -3.21041e8 q^{48} +2.82475e8 q^{49} +8.71589e9 q^{50} -1.16450e9 q^{51} -3.40317e9 q^{52} +2.56254e9 q^{53} +5.35126e9 q^{54} -3.81023e9 q^{55} -1.94432e9 q^{56} -6.57544e8 q^{57} +4.30610e9 q^{58} +1.23711e9 q^{59} -1.10786e10 q^{60} +6.55308e9 q^{61} +5.08647e9 q^{62} +2.00618e9 q^{63} -1.29948e10 q^{64} -1.21776e10 q^{65} +5.35464e9 q^{66} -3.16334e9 q^{67} +1.73860e10 q^{68} +1.37788e10 q^{69} -1.62047e10 q^{70} -5.19886e9 q^{71} -1.38088e10 q^{72} -1.26822e10 q^{73} +3.63832e10 q^{74} -2.79054e10 q^{75} +9.81715e9 q^{76} +4.98664e9 q^{77} +1.71136e10 q^{78} -5.31261e9 q^{79} +1.71514e10 q^{80} +4.01229e9 q^{81} -5.78082e10 q^{82} +6.08801e10 q^{83} +1.44991e10 q^{84} +6.22126e10 q^{85} +9.36661e9 q^{86} -1.37867e10 q^{87} -3.43238e10 q^{88} +2.61042e10 q^{89} -1.15088e11 q^{90} +1.59374e10 q^{91} -2.05717e11 q^{92} -1.62852e10 q^{93} +3.11379e10 q^{94} +3.51289e10 q^{95} +3.28478e10 q^{96} -9.47577e10 q^{97} +2.12079e10 q^{98} +3.54158e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 77 q^{2} - 140 q^{3} + 5493 q^{4} + 5026 q^{5} + 64274 q^{6} - 50421 q^{7} + 125103 q^{8} + 658519 q^{9}+O(q^{10}) $ 3 * q + 77 * q^2 - 140 * q^3 + 5493 * q^4 + 5026 * q^5 + 64274 * q^6 - 50421 * q^7 + 125103 * q^8 + 658519 * q^9	\( 3 q + 77 q^{2} - 140 q^{3} + 5493 q^{4} + 5026 q^{5} + 64274 q^{6} - 50421 q^{7} + 125103 q^{8} + 658519 q^{9} + 610764 q^{10} - 1039052 q^{11} - 609154 q^{12} - 1881222 q^{13} - 1294139 q^{14} - 8220752 q^{15} - 9117711 q^{16} + 15797334 q^{17} + 38909 q^{18} + 12340356 q^{19} + 37982168 q^{20} + 2352980 q^{21} + 31890144 q^{22} + 7276752 q^{23} - 117296046 q^{24} + 68924781 q^{25} - 133487872 q^{26} + 205674616 q^{27} - 92320851 q^{28} - 126853406 q^{29} - 575391808 q^{30} + 162184512 q^{31} - 167636249 q^{32} + 786346624 q^{33} - 79664298 q^{34} - 84471982 q^{35} + 328076045 q^{36} + 567121338 q^{37} + 509512430 q^{38} - 660517760 q^{39} + 1827265440 q^{40} + 893682734 q^{41} - 1080253118 q^{42} + 460197828 q^{43} - 1666161688 q^{44} - 5048825558 q^{45} - 6171574224 q^{46} + 2723825664 q^{47} - 868401730 q^{48} + 847425747 q^{49} + 11374112959 q^{50} - 6836867112 q^{51} - 4409363868 q^{52} + 93426522 q^{53} + 23309429948 q^{54} - 4073739768 q^{55} - 2102606121 q^{56} + 3867165112 q^{57} - 2792521998 q^{58} + 5899174428 q^{59} - 16616994016 q^{60} + 2106807738 q^{61} + 22093555428 q^{62} - 11067728833 q^{63} - 9528592239 q^{64} - 4991087612 q^{65} - 21724126480 q^{66} - 27027285348 q^{67} + 26942000190 q^{68} - 9435687744 q^{69} - 10265110548 q^{70} + 16564049928 q^{71} - 19175918265 q^{72} + 6036803934 q^{73} + 29114537322 q^{74} + 6787422908 q^{75} + 19528279218 q^{76} + 17463346964 q^{77} - 25177551784 q^{78} - 54895016736 q^{79} + 58098552176 q^{80} + 117359146147 q^{81} - 88924869978 q^{82} + 123561203892 q^{83} + 10238051278 q^{84} + 45582888084 q^{85} + 59402678104 q^{86} - 117914423480 q^{87} - 97861591608 q^{88} - 91648411106 q^{89} - 285253455172 q^{90} + 31617698154 q^{91} - 147922642512 q^{92} + 220344467856 q^{93} + 132452618508 q^{94} - 19413413120 q^{95} - 214249905422 q^{96} - 71237114634 q^{97} + 21750594173 q^{98} - 177803449916 q^{99}+O(q^{100}) \) 3 * q + 77 * q^2 - 140 * q^3 + 5493 * q^4 + 5026 * q^5 + 64274 * q^6 - 50421 * q^7 + 125103 * q^8 + 658519 * q^9 + 610764 * q^10 - 1039052 * q^11 - 609154 * q^12 - 1881222 * q^13 - 1294139 * q^14 - 8220752 * q^15 - 9117711 * q^16 + 15797334 * q^17 + 38909 * q^18 + 12340356 * q^19 + 37982168 * q^20 + 2352980 * q^21 + 31890144 * q^22 + 7276752 * q^23 - 117296046 * q^24 + 68924781 * q^25 - 133487872 * q^26 + 205674616 * q^27 - 92320851 * q^28 - 126853406 * q^29 - 575391808 * q^30 + 162184512 * q^31 - 167636249 * q^32 + 786346624 * q^33 - 79664298 * q^34 - 84471982 * q^35 + 328076045 * q^36 + 567121338 * q^37 + 509512430 * q^38 - 660517760 * q^39 + 1827265440 * q^40 + 893682734 * q^41 - 1080253118 * q^42 + 460197828 * q^43 - 1666161688 * q^44 - 5048825558 * q^45 - 6171574224 * q^46 + 2723825664 * q^47 - 868401730 * q^48 + 847425747 * q^49 + 11374112959 * q^50 - 6836867112 * q^51 - 4409363868 * q^52 + 93426522 * q^53 + 23309429948 * q^54 - 4073739768 * q^55 - 2102606121 * q^56 + 3867165112 * q^57 - 2792521998 * q^58 + 5899174428 * q^59 - 16616994016 * q^60 + 2106807738 * q^61 + 22093555428 * q^62 - 11067728833 * q^63 - 9528592239 * q^64 - 4991087612 * q^65 - 21724126480 * q^66 - 27027285348 * q^67 + 26942000190 * q^68 - 9435687744 * q^69 - 10265110548 * q^70 + 16564049928 * q^71 - 19175918265 * q^72 + 6036803934 * q^73 + 29114537322 * q^74 + 6787422908 * q^75 + 19528279218 * q^76 + 17463346964 * q^77 - 25177551784 * q^78 - 54895016736 * q^79 + 58098552176 * q^80 + 117359146147 * q^81 - 88924869978 * q^82 + 123561203892 * q^83 + 10238051278 * q^84 + 45582888084 * q^85 + 59402678104 * q^86 - 117914423480 * q^87 - 97861591608 * q^88 - 91648411106 * q^89 - 285253455172 * q^90 + 31617698154 * q^91 - 147922642512 * q^92 + 220344467856 * q^93 + 132452618508 * q^94 - 19413413120 * q^95 - 214249905422 * q^96 - 71237114634 * q^97 + 21750594173 * q^98 - 177803449916 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	75.0789	1.65903	0.829513	−	0.558487i	$-0.188618\pi$
$2$	75.0789	1.65903	0.829513	+	0.558487i	$0.188618\pi$
$3$	−240.378	−0.571120	−0.285560	−	0.958361i	$-0.592180\pi$
$3$	−240.378	−0.571120	−0.285560	+	0.958361i	$0.592180\pi$
$4$	3588.85	1.75237
$5$	12842.0	1.83780	0.918901	−	0.394488i	$-0.129078\pi$
$5$	12842.0	1.83780	0.918901	+	0.394488i	$0.129078\pi$
$6$	−18047.3	−0.947504
$7$	−16807.0	−0.377964
$7$	−16807.0	−0.377964
$8$	115685.	1.24820
$9$	−119365.	−0.673822
$10$	964166.	3.04896
$11$	−296700.	−0.555467	−0.277733	−	0.960658i	$-0.589583\pi$
$11$	−296700.	−0.555467	−0.277733	+	0.960658i	$0.589583\pi$
$12$	−862680.	−1.00081
$13$	−948262.	−0.708337	−0.354168	−	0.935182i	$-0.615236\pi$
$13$	−948262.	−0.708337	−0.354168	+	0.935182i	$0.615236\pi$
$14$	−1.26185e6	−0.627053
$15$	−3.08694e6	−1.04961
$16$	1.33557e6	0.318424
$17$	4.84445e6	0.827514	0.413757	−	0.910387i	$-0.364216\pi$
$17$	4.84445e6	0.827514	0.413757	+	0.910387i	$0.364216\pi$
$18$	−8.96183e6	−1.11789
$19$	2.73546e6	0.253446	0.126723	−	0.991938i	$-0.459554\pi$
$19$	2.73546e6	0.253446	0.126723	+	0.991938i	$0.459554\pi$
$20$	4.60881e7	3.22050
$21$	4.04003e6	0.215863
$22$	−2.22759e7	−0.921534
$23$	−5.73212e7	−1.85700	−0.928501	−	0.371330i	$-0.878902\pi$
$23$	−5.73212e7	−1.85700	−0.928501	+	0.371330i	$0.878902\pi$
$24$	−2.78082e7	−0.712871
$25$	1.16090e8	2.37752
$26$	−7.11945e7	−1.17515
$27$	7.12750e7	0.955954
$28$	−6.03178e7	−0.662333
$29$	5.73542e7	0.519250	0.259625	−	0.965710i	$-0.416401\pi$
$29$	5.73542e7	0.519250	0.259625	+	0.965710i	$0.416401\pi$
$30$	−2.31764e8	−1.74132
$31$	6.77483e7	0.425020	0.212510	−	0.977159i	$-0.431836\pi$
$31$	6.77483e7	0.425020	0.212510	+	0.977159i	$0.431836\pi$
$32$	−1.36650e8	−0.719923
$33$	7.13202e7	0.317238
$34$	3.63716e8	1.37287
$35$	−2.15836e8	−0.694624
$36$	−4.28385e8	−1.18078
$37$	4.84599e8	1.14888	0.574438	−	0.818548i	$-0.305221\pi$
$37$	4.84599e8	1.14888	0.574438	+	0.818548i	$0.305221\pi$
$38$	2.05375e8	0.420474
$39$	2.27941e8	0.404546
$40$	1.48563e9	2.29394
$41$	−7.69966e8	−1.03791	−0.518956	−	0.854801i	$-0.673679\pi$
$41$	−7.69966e8	−1.03791	−0.518956	+	0.854801i	$0.673679\pi$
$42$	3.03321e8	0.358123
$43$	1.24757e8	0.129416	0.0647080	−	0.997904i	$-0.479388\pi$
$43$	1.24757e8	0.129416	0.0647080	+	0.997904i	$0.479388\pi$
$44$	−1.06481e9	−0.973382
$45$	−1.53290e9	−1.23835
$46$	−4.30362e9	−3.08081
$47$	4.14735e8	0.263774	0.131887	−	0.991265i	$-0.457896\pi$
$47$	4.14735e8	0.263774	0.131887	+	0.991265i	$0.457896\pi$
$48$	−3.21041e8	−0.181858
$49$	2.82475e8	0.142857
$50$	8.71589e9	3.94436
$51$	−1.16450e9	−0.472610
$52$	−3.40317e9	−1.24127
$53$	2.56254e9	0.841693	0.420846	−	0.907132i	$-0.361733\pi$
$53$	2.56254e9	0.841693	0.420846	+	0.907132i	$0.361733\pi$
$54$	5.35126e9	1.58595
$55$	−3.81023e9	−1.02084
$56$	−1.94432e9	−0.471774
$57$	−6.57544e8	−0.144748
$58$	4.30610e9	0.861449
$59$	1.23711e9	0.225279	0.112640	−	0.993636i	$-0.464069\pi$
$59$	1.23711e9	0.225279	0.112640	+	0.993636i	$0.464069\pi$
$60$	−1.10786e10	−1.83930
$61$	6.55308e9	0.993416	0.496708	−	0.867918i	$-0.334542\pi$
$61$	6.55308e9	0.993416	0.496708	+	0.867918i	$0.334542\pi$
$62$	5.08647e9	0.705119
$63$	2.00618e9	0.254681
$64$	−1.29948e10	−1.51280
$65$	−1.21776e10	−1.30178
$66$	5.35464e9	0.526307
$67$	−3.16334e9	−0.286243	−0.143121	−	0.989705i	$-0.545714\pi$
$67$	−3.16334e9	−0.286243	−0.143121	+	0.989705i	$0.545714\pi$
$68$	1.73860e10	1.45011
$69$	1.37788e10	1.06057
$70$	−1.62047e10	−1.15240
$71$	−5.19886e9	−0.341969	−0.170985	−	0.985274i	$-0.554695\pi$
$71$	−5.19886e9	−0.341969	−0.170985	+	0.985274i	$0.554695\pi$
$72$	−1.38088e10	−0.841062
$73$	−1.26822e10	−0.716010	−0.358005	−	0.933720i	$-0.616543\pi$
$73$	−1.26822e10	−0.716010	−0.358005	+	0.933720i	$0.616543\pi$
$74$	3.63832e10	1.90602
$75$	−2.79054e10	−1.35785
$76$	9.81715e9	0.444131
$77$	4.98664e9	0.209947
$78$	1.71136e10	0.671152
$79$	−5.31261e9	−0.194249	−0.0971245	−	0.995272i	$-0.530964\pi$
$79$	−5.31261e9	−0.194249	−0.0971245	+	0.995272i	$0.530964\pi$
$80$	1.71514e10	0.585200
$81$	4.01229e9	0.127857
$82$	−5.78082e10	−1.72192
$83$	6.08801e10	1.69647	0.848234	−	0.529621i	$-0.177666\pi$
$83$	6.08801e10	1.69647	0.848234	+	0.529621i	$0.177666\pi$
$84$	1.44991e10	0.378272
$85$	6.22126e10	1.52081
$86$	9.36661e9	0.214704
$87$	−1.37867e10	−0.296554
$88$	−3.43238e10	−0.693332
$89$	2.61042e10	0.495526	0.247763	−	0.968821i	$-0.420305\pi$
$89$	2.61042e10	0.495526	0.247763	+	0.968821i	$0.420305\pi$
$90$	−1.15088e11	−2.05446
$91$	1.59374e10	0.267726
$92$	−2.05717e11	−3.25415
$93$	−1.62852e10	−0.242737
$94$	3.11379e10	0.437608
$95$	3.51289e10	0.465784
$96$	3.28478e10	0.411163
$97$	−9.47577e10	−1.12039	−0.560196	−	0.828360i	$-0.689274\pi$
$97$	−9.47577e10	−1.12039	−0.560196	+	0.828360i	$0.689274\pi$
$98$	2.12079e10	0.237004
$99$	3.54158e10	0.374286
$100$	4.16628e11	4.16628
$101$	3.38404e10	0.320382	0.160191	−	0.987086i	$-0.448789\pi$
$101$	3.38404e10	0.320382	0.160191	+	0.987086i	$0.448789\pi$
$102$	−8.74293e10	−0.784072
$103$	−1.02725e11	−0.873111	−0.436556	−	0.899677i	$-0.643802\pi$
$103$	−1.02725e11	−0.873111	−0.436556	+	0.899677i	$0.643802\pi$
$104$	−1.09700e11	−0.884144
$105$	5.18822e10	0.396714
$106$	1.92393e11	1.39639
$107$	−1.53786e11	−1.06000	−0.530000	−	0.847998i	$-0.677808\pi$
$107$	−1.53786e11	−1.06000	−0.530000	+	0.847998i	$0.677808\pi$
$108$	2.55795e11	1.67518
$109$	2.02012e11	1.25757	0.628784	−	0.777580i	$-0.283553\pi$
$109$	2.02012e11	1.25757	0.628784	+	0.777580i	$0.283553\pi$
$110$	−2.86068e11	−1.69360
$111$	−1.16487e11	−0.656146
$112$	−2.24469e10	−0.120353
$113$	6.00511e10	0.306613	0.153306	−	0.988179i	$-0.451008\pi$
$113$	6.00511e10	0.306613	0.153306	+	0.988179i	$0.451008\pi$
$114$	−4.93677e10	−0.240141
$115$	−7.36121e11	−3.41280
$116$	2.05836e11	0.909917
$117$	1.13190e11	0.477293
$118$	9.28807e10	0.373744
$119$	−8.14206e10	−0.312771
$120$	−3.57114e11	−1.31012
$121$	−1.97281e11	−0.691457
$122$	4.91998e11	1.64810
$123$	1.85083e11	0.592772
$124$	2.43138e11	0.744791
$125$	8.63775e11	2.53160
$126$	1.50622e11	0.422522
$127$	−1.10088e11	−0.295678	−0.147839	−	0.989011i	$-0.547232\pi$
$127$	−1.10088e11	−0.295678	−0.147839	+	0.989011i	$0.547232\pi$
$128$	−6.95777e11	−1.78984
$129$	−2.99888e10	−0.0739121
$130$	−9.14282e11	−2.15969
$131$	−6.29292e11	−1.42515	−0.712574	−	0.701597i	$-0.752471\pi$
$131$	−6.29292e11	−1.42515	−0.712574	+	0.701597i	$0.752471\pi$
$132$	2.55957e11	0.555918
$133$	−4.59749e10	−0.0957936
$134$	−2.37500e11	−0.474884
$135$	9.15316e11	1.75685
$136$	5.60431e11	1.03290
$137$	3.68273e11	0.651939	0.325970	−	0.945380i	$-0.394309\pi$
$137$	3.68273e11	0.651939	0.325970	+	0.945380i	$0.394309\pi$
$138$	1.03449e12	1.75952
$139$	3.08141e11	0.503695	0.251847	−	0.967767i	$-0.418962\pi$
$139$	3.08141e11	0.503695	0.251847	+	0.967767i	$0.418962\pi$
$140$	−7.74603e11	−1.21724
$141$	−9.96931e10	−0.150647
$142$	−3.90325e11	−0.567336
$143$	2.81350e11	0.393458
$144$	−1.59421e11	−0.214561
$145$	7.36545e11	0.954279
$146$	−9.52166e11	−1.18788
$147$	−6.79008e10	−0.0815886
$148$	1.73915e12	2.01325
$149$	−1.49038e12	−1.66254	−0.831272	−	0.555866i	$-0.812387\pi$
$149$	−1.49038e12	−1.66254	−0.831272	+	0.555866i	$0.812387\pi$
$150$	−2.09511e12	−2.25271
$151$	−1.04571e12	−1.08402	−0.542012	−	0.840371i	$-0.682337\pi$
$151$	−1.04571e12	−1.08402	−0.542012	+	0.840371i	$0.682337\pi$
$152$	3.16452e11	0.316351
$153$	−5.78260e11	−0.557597
$154$	3.74392e11	0.348307
$155$	8.70026e11	0.781102
$156$	8.18046e11	0.708912
$157$	7.31838e11	0.612304	0.306152	−	0.951983i	$-0.400958\pi$
$157$	7.31838e11	0.612304	0.306152	+	0.951983i	$0.400958\pi$
$158$	−3.98865e11	−0.322264
$159$	−6.15978e11	−0.480708
$160$	−1.75487e12	−1.32308
$161$	9.63398e11	0.701881
$162$	3.01238e11	0.212118
$163$	−6.14012e11	−0.417970	−0.208985	−	0.977919i	$-0.567016\pi$
$163$	−6.14012e11	−0.417970	−0.208985	+	0.977919i	$0.567016\pi$
$164$	−2.76329e12	−1.81880
$165$	9.15896e11	0.583022
$166$	4.57081e12	2.81449
$167$	1.97427e12	1.17616	0.588079	−	0.808803i	$-0.299884\pi$
$167$	1.97427e12	1.17616	0.588079	+	0.808803i	$0.299884\pi$
$168$	4.67372e11	0.269440
$169$	−8.92960e11	−0.498259
$170$	4.67085e12	2.52306
$171$	−3.26519e11	−0.170777
$172$	4.47733e11	0.226784
$173$	−5.06956e11	−0.248723	−0.124362	−	0.992237i	$-0.539688\pi$
$173$	−5.06956e11	−0.248723	−0.124362	+	0.992237i	$0.539688\pi$
$174$	−1.03509e12	−0.491991
$175$	−1.95112e12	−0.898617
$176$	−3.96263e11	−0.176874
$177$	−2.97373e11	−0.128662
$178$	1.95988e12	0.822090
$179$	−3.01616e12	−1.22677	−0.613384	−	0.789785i	$-0.710192\pi$
$179$	−3.01616e12	−1.22677	−0.613384	+	0.789785i	$0.710192\pi$
$180$	−5.50133e12	−2.17005
$181$	−7.64786e11	−0.292623	−0.146311	−	0.989239i	$-0.546740\pi$
$181$	−7.64786e11	−0.292623	−0.146311	+	0.989239i	$0.546740\pi$
$182$	1.19657e12	0.444165
$183$	−1.57522e12	−0.567360
$184$	−6.63122e12	−2.31790
$185$	6.22324e12	2.11141
$186$	−1.22268e12	−0.402708
$187$	−1.43735e12	−0.459657
$188$	1.48842e12	0.462229
$189$	−1.19792e12	−0.361316
$190$	2.63744e12	0.772747
$191$	4.03652e12	1.14901	0.574505	−	0.818501i	$-0.305195\pi$
$191$	4.03652e12	1.14901	0.574505	+	0.818501i	$0.305195\pi$
$192$	3.12367e12	0.863988
$193$	3.45472e12	0.928642	0.464321	−	0.885667i	$-0.346298\pi$
$193$	3.45472e12	0.928642	0.464321	+	0.885667i	$0.346298\pi$
$194$	−7.11431e12	−1.85876
$195$	2.92723e12	0.743475
$196$	1.01376e12	0.250338
$197$	−7.78560e12	−1.86951	−0.934755	−	0.355294i	$-0.884381\pi$
$197$	−7.78560e12	−1.86951	−0.934755	+	0.355294i	$0.884381\pi$
$198$	2.65898e12	0.620949
$199$	−8.91325e11	−0.202462	−0.101231	−	0.994863i	$-0.532278\pi$
$199$	−8.91325e11	−0.202462	−0.101231	+	0.994863i	$0.532278\pi$
$200$	1.34299e13	2.96761
$201$	7.60397e11	0.163479
$202$	2.54070e12	0.531522
$203$	−9.63953e11	−0.196258
$204$	−4.17921e12	−0.828186
$205$	−9.88793e12	−1.90748
$206$	−7.71245e12	−1.44851
$207$	6.84217e12	1.25129
$208$	−1.26647e12	−0.225551
$209$	−8.11612e11	−0.140781
$210$	3.89526e12	0.658159
$211$	−2.18063e12	−0.358946	−0.179473	−	0.983763i	$-0.557439\pi$
$211$	−2.18063e12	−0.358946	−0.179473	+	0.983763i	$0.557439\pi$
$212$	9.19657e12	1.47496
$213$	1.24969e12	0.195305
$214$	−1.15461e13	−1.75857
$215$	1.60213e12	0.237841
$216$	8.24547e12	1.19322
$217$	−1.13865e12	−0.160642
$218$	1.51668e13	2.08634
$219$	3.04852e12	0.408928
$220$	−1.36744e13	−1.78888
$221$	−4.59381e12	−0.586158
$222$	−8.74572e12	−1.08856
$223$	3.25651e12	0.395435	0.197718	−	0.980259i	$-0.436647\pi$
$223$	3.25651e12	0.395435	0.197718	+	0.980259i	$0.436647\pi$
$224$	2.29668e12	0.272105
$225$	−1.38571e13	−1.60202
$226$	4.50858e12	0.508678
$227$	1.69284e13	1.86412	0.932062	−	0.362299i	$-0.118008\pi$
$227$	1.69284e13	1.86412	0.932062	+	0.362299i	$0.118008\pi$
$228$	−2.35983e12	−0.253652
$229$	1.36241e13	1.42960	0.714799	−	0.699330i	$-0.246518\pi$
$229$	1.36241e13	1.42960	0.714799	+	0.699330i	$0.246518\pi$
$230$	−5.52672e13	−5.66193
$231$	−1.19868e12	−0.119905
$232$	6.63504e12	0.648126
$233$	3.81941e12	0.364367	0.182184	−	0.983265i	$-0.441683\pi$
$233$	3.81941e12	0.364367	0.182184	+	0.983265i	$0.441683\pi$
$234$	8.49816e12	0.791841
$235$	5.32604e12	0.484765
$236$	4.43979e12	0.394772
$237$	1.27703e12	0.110940
$238$	−6.11298e12	−0.518895
$239$	1.32633e13	1.10018	0.550089	−	0.835106i	$-0.314594\pi$
$239$	1.32633e13	1.10018	0.550089	+	0.835106i	$0.314594\pi$
$240$	−4.12281e12	−0.334220
$241$	−3.11410e12	−0.246739	−0.123370	−	0.992361i	$-0.539370\pi$
$241$	−3.11410e12	−0.246739	−0.123370	+	0.992361i	$0.539370\pi$
$242$	−1.48116e13	−1.14714
$243$	−1.35906e13	−1.02898
$244$	2.35180e13	1.74083
$245$	3.62756e12	0.262543
$246$	1.38958e13	0.983425
$247$	−2.59393e12	−0.179525
$248$	7.83748e12	0.530508
$249$	−1.46342e13	−0.968888
$250$	6.48513e13	4.20000
$251$	1.63330e13	1.03481	0.517404	−	0.855741i	$-0.326898\pi$
$251$	1.63330e13	1.03481	0.517404	+	0.855741i	$0.326898\pi$
$252$	7.19986e12	0.446294
$253$	1.70072e13	1.03150
$254$	−8.26527e12	−0.490537
$255$	−1.49545e13	−0.868564
$256$	−2.56248e13	−1.45660
$257$	−3.00682e13	−1.67292	−0.836461	−	0.548026i	$-0.815379\pi$
$257$	−3.00682e13	−1.67292	−0.836461	+	0.548026i	$0.815379\pi$
$258$	−2.25153e12	−0.122622
$259$	−8.14466e12	−0.434234
$260$	−4.37036e13	−2.28120
$261$	−6.84612e12	−0.349882
$262$	−4.72466e13	−2.36436
$263$	5.29720e12	0.259591	0.129796	−	0.991541i	$-0.458568\pi$
$263$	5.29720e12	0.259591	0.129796	+	0.991541i	$0.458568\pi$
$264$	8.25069e12	0.395976
$265$	3.29082e13	1.54686
$266$	−3.45174e12	−0.158924
$267$	−6.27488e12	−0.283005
$268$	−1.13527e13	−0.501602
$269$	−3.03132e13	−1.31218	−0.656090	−	0.754682i	$-0.727791\pi$
$269$	−3.03132e13	−1.31218	−0.656090	+	0.754682i	$0.727791\pi$
$270$	6.87210e13	2.91467
$271$	−1.33113e13	−0.553208	−0.276604	−	0.960984i	$-0.589209\pi$
$271$	−1.33113e13	−0.553208	−0.276604	+	0.960984i	$0.589209\pi$
$272$	6.47008e12	0.263500
$273$	−3.83101e12	−0.152904
$274$	2.76496e13	1.08158
$275$	−3.44438e13	−1.32063
$276$	4.94499e13	1.85851
$277$	2.16437e12	0.0797429	0.0398714	−	0.999205i	$-0.487305\pi$
$277$	2.16437e12	0.0797429	0.0398714	+	0.999205i	$0.487305\pi$
$278$	2.31349e13	0.835643
$279$	−8.08681e12	−0.286387
$280$	−2.49690e13	−0.867027
$281$	−2.31969e13	−0.789850	−0.394925	−	0.918713i	$-0.629229\pi$
$281$	−2.31969e13	−0.789850	−0.394925	+	0.918713i	$0.629229\pi$
$282$	−7.48485e12	−0.249927
$283$	3.44158e13	1.12702	0.563511	−	0.826109i	$-0.309450\pi$
$283$	3.44158e13	1.12702	0.563511	+	0.826109i	$0.309450\pi$
$284$	−1.86579e13	−0.599255
$285$	−8.44420e12	−0.266019
$286$	2.11234e13	0.652756
$287$	1.29408e13	0.392294
$288$	1.63113e13	0.485100
$289$	−1.08032e13	−0.315221
$290$	5.52990e13	1.58317
$291$	2.27777e13	0.639879
$292$	−4.55145e13	−1.25471
$293$	3.91021e13	1.05786	0.528930	−	0.848666i	$-0.322594\pi$
$293$	3.91021e13	1.05786	0.528930	+	0.848666i	$0.322594\pi$
$294$	−5.09792e12	−0.135358
$295$	1.58870e13	0.414019
$296$	5.60610e13	1.43402
$297$	−2.11473e13	−0.531001
$298$	−1.11896e14	−2.75820
$299$	5.43555e13	1.31538
$300$	−1.00148e14	−2.37945
$301$	−2.09679e12	−0.0489146
$302$	−7.85110e13	−1.79842
$303$	−8.13449e12	−0.182977
$304$	3.65339e12	0.0807033
$305$	8.41548e13	1.82570
$306$	−4.34151e13	−0.925067
$307$	−7.37117e13	−1.54268	−0.771339	−	0.636424i	$-0.780413\pi$
$307$	−7.37117e13	−1.54268	−0.771339	+	0.636424i	$0.780413\pi$
$308$	1.78963e13	0.367904
$309$	2.46927e13	0.498652
$310$	6.53206e13	1.29587
$311$	−4.13489e13	−0.805901	−0.402951	−	0.915222i	$-0.632015\pi$
$311$	−4.13489e13	−0.805901	−0.402951	+	0.915222i	$0.632015\pi$
$312$	2.63694e13	0.504953
$313$	4.01237e13	0.754931	0.377465	−	0.926024i	$-0.376796\pi$
$313$	4.01237e13	0.754931	0.377465	+	0.926024i	$0.376796\pi$
$314$	5.49456e13	1.01583
$315$	2.57634e13	0.468053
$316$	−1.90661e13	−0.340396
$317$	9.84551e13	1.72748	0.863738	−	0.503940i	$-0.168117\pi$
$317$	9.84551e13	1.72748	0.863738	+	0.503940i	$0.168117\pi$
$318$	−4.62470e13	−0.797507
$319$	−1.70170e13	−0.288426
$320$	−1.66880e14	−2.78022
$321$	3.69667e13	0.605387
$322$	7.23309e13	1.16444
$323$	1.32518e13	0.209730
$324$	1.43995e13	0.224052
$325$	−1.10083e14	−1.68408
$326$	−4.60994e13	−0.693423
$327$	−4.85592e13	−0.718222
$328$	−8.90737e13	−1.29552
$329$	−6.97045e12	−0.0996973
$330$	6.87645e13	0.967248
$331$	−1.16367e14	−1.60982	−0.804910	−	0.593396i	$-0.797787\pi$
$331$	−1.16367e14	−1.60982	−0.804910	+	0.593396i	$0.797787\pi$
$332$	2.18489e14	2.97284
$333$	−5.78444e13	−0.774137
$334$	1.48226e14	1.95128
$335$	−4.06237e13	−0.526057
$336$	5.39573e12	0.0687360
$337$	7.04095e13	0.882403	0.441202	−	0.897408i	$-0.354552\pi$
$337$	7.04095e13	0.882403	0.441202	+	0.897408i	$0.354552\pi$
$338$	−6.70425e13	−0.826625
$339$	−1.44350e13	−0.175113
$340$	2.23271e14	2.66501
$341$	−2.01009e13	−0.236084
$342$	−2.45147e13	−0.283324
$343$	−4.74756e12	−0.0539949
$344$	1.44325e13	0.161537
$345$	1.76947e14	1.94912
$346$	−3.80617e13	−0.412638
$347$	7.89482e13	0.842423	0.421212	−	0.906962i	$-0.361605\pi$
$347$	7.89482e13	0.842423	0.421212	+	0.906962i	$0.361605\pi$
$348$	−4.94783e13	−0.519672
$349$	−7.77536e13	−0.803860	−0.401930	−	0.915670i	$-0.631661\pi$
$349$	−7.77536e13	−0.803860	−0.401930	+	0.915670i	$0.631661\pi$
$350$	−1.46488e14	−1.49083
$351$	−6.75874e13	−0.677137
$352$	4.05442e13	0.399894
$353$	1.32735e14	1.28892	0.644460	−	0.764638i	$-0.277082\pi$
$353$	1.32735e14	1.28892	0.644460	+	0.764638i	$0.277082\pi$
$354$	−2.23265e13	−0.213453
$355$	−6.67639e13	−0.628471
$356$	9.36842e13	0.868343
$357$	1.95717e13	0.178630
$358$	−2.26450e14	−2.03524
$359$	−1.00956e14	−0.893539	−0.446770	−	0.894649i	$-0.647426\pi$
$359$	−1.00956e14	−0.893539	−0.446770	+	0.894649i	$0.647426\pi$
$360$	−1.77333e14	−1.54571
$361$	−1.09008e14	−0.935765
$362$	−5.74193e13	−0.485468
$363$	4.74219e13	0.394905
$364$	5.71970e13	0.469155
$365$	−1.62865e14	−1.31588
$366$	−1.18265e14	−0.941265
$367$	2.42632e14	1.90233	0.951163	−	0.308689i	$-0.0998902\pi$
$367$	2.42632e14	1.90233	0.951163	+	0.308689i	$0.0998902\pi$
$368$	−7.65563e13	−0.591314
$369$	9.19073e13	0.699367
$370$	4.67234e14	3.50288
$371$	−4.30686e13	−0.318130
$372$	−5.84451e13	−0.425365
$373$	−1.17300e14	−0.841199	−0.420599	−	0.907246i	$-0.638180\pi$
$373$	−1.17300e14	−0.841199	−0.420599	+	0.907246i	$0.638180\pi$
$374$	−1.07915e14	−0.762582
$375$	−2.07632e14	−1.44585
$376$	4.79787e13	0.329242
$377$	−5.43868e13	−0.367804
$378$	−8.99385e13	−0.599433
$379$	1.91160e14	1.25569	0.627843	−	0.778340i	$-0.283938\pi$
$379$	1.91160e14	1.25569	0.627843	+	0.778340i	$0.283938\pi$
$380$	1.26072e14	0.816224
$381$	2.64627e13	0.168868
$382$	3.03058e14	1.90624
$383$	3.17604e14	1.96921	0.984605	−	0.174794i	$-0.0559260\pi$
$383$	3.17604e14	1.96921	0.984605	+	0.174794i	$0.0559260\pi$
$384$	1.67249e14	1.02222
$385$	6.40386e13	0.385841
$386$	2.59377e14	1.54064
$387$	−1.48917e13	−0.0872032
$388$	−3.40071e14	−1.96334
$389$	−6.10665e13	−0.347600	−0.173800	−	0.984781i	$-0.555605\pi$
$389$	−6.10665e13	−0.347600	−0.173800	+	0.984781i	$0.555605\pi$
$390$	2.19773e14	1.23344
$391$	−2.77690e14	−1.53669
$392$	3.26782e13	0.178314
$393$	1.51268e14	0.813932
$394$	−5.84534e14	−3.10156
$395$	−6.82247e13	−0.356991
$396$	1.27102e14	0.655886
$397$	−3.30117e14	−1.68004	−0.840022	−	0.542552i	$-0.817458\pi$
$397$	−3.30117e14	−1.68004	−0.840022	+	0.542552i	$0.817458\pi$
$398$	−6.69198e13	−0.335890
$399$	1.10513e13	0.0547097
$400$	1.55045e14	0.757058
$401$	1.82288e14	0.877936	0.438968	−	0.898503i	$-0.355344\pi$
$401$	1.82288e14	0.877936	0.438968	+	0.898503i	$0.355344\pi$
$402$	5.70898e13	0.271216
$403$	−6.42431e13	−0.301057
$404$	1.21448e14	0.561427
$405$	5.15259e13	0.234976
$406$	−7.23726e13	−0.325597
$407$	−1.43781e14	−0.638163
$408$	−1.34715e14	−0.589910
$409$	2.59396e13	0.112069	0.0560345	−	0.998429i	$-0.482154\pi$
$409$	2.59396e13	0.112069	0.0560345	+	0.998429i	$0.482154\pi$
$410$	−7.42375e14	−3.16455
$411$	−8.85248e13	−0.372336
$412$	−3.68663e14	−1.53001
$413$	−2.07921e13	−0.0851476
$414$	5.13703e14	2.07592
$415$	7.81824e14	3.11777
$416$	1.29580e14	0.509948
$417$	−7.40702e13	−0.287670
$418$	−6.09349e13	−0.233559
$419$	−1.93031e14	−0.730213	−0.365107	−	0.930966i	$-0.618967\pi$
$419$	−1.93031e14	−0.730213	−0.365107	+	0.930966i	$0.618967\pi$
$420$	1.86197e14	0.695188
$421$	−2.46783e13	−0.0909418	−0.0454709	−	0.998966i	$-0.514479\pi$
$421$	−2.46783e13	−0.0909418	−0.0454709	+	0.998966i	$0.514479\pi$
$422$	−1.63720e14	−0.595500
$423$	−4.95050e13	−0.177737
$424$	2.96448e14	1.05060
$425$	5.62390e14	1.96743
$426$	9.38254e13	0.324017
$427$	−1.10138e14	−0.375476
$428$	−5.51914e14	−1.85751
$429$	−6.76302e13	−0.224712
$430$	1.20286e14	0.394584
$431$	−2.40509e14	−0.778945	−0.389472	−	0.921038i	$-0.627343\pi$
$431$	−2.40509e14	−0.778945	−0.389472	+	0.921038i	$0.627343\pi$
$432$	9.51926e13	0.304398
$433$	−2.72119e14	−0.859163	−0.429581	−	0.903028i	$-0.641339\pi$
$433$	−2.72119e14	−0.859163	−0.429581	+	0.903028i	$0.641339\pi$
$434$	−8.54883e13	−0.266510
$435$	−1.77049e14	−0.545008
$436$	7.24990e14	2.20372
$437$	−1.56800e14	−0.470650
$438$	2.28880e14	0.678422
$439$	2.57515e13	0.0753785	0.0376893	−	0.999290i	$-0.488000\pi$
$439$	2.57515e13	0.0753785	0.0376893	+	0.999290i	$0.488000\pi$
$440$	−4.40788e14	−1.27421
$441$	−3.37178e13	−0.0962602
$442$	−3.44898e14	−0.972452
$443$	4.82782e14	1.34441	0.672203	−	0.740367i	$-0.265348\pi$
$443$	4.82782e14	1.34441	0.672203	+	0.740367i	$0.265348\pi$
$444$	−4.18054e14	−1.14981
$445$	3.35232e14	0.910678
$446$	2.44495e14	0.656037
$447$	3.58255e14	0.949513
$448$	2.18404e14	0.571783
$449$	1.71669e14	0.443953	0.221977	−	0.975052i	$-0.428749\pi$
$449$	1.71669e14	0.443953	0.221977	+	0.975052i	$0.428749\pi$
$450$	−1.04038e15	−2.65780
$451$	2.28449e14	0.576525
$452$	2.15514e14	0.537298
$453$	2.51366e14	0.619109
$454$	1.27097e15	3.09263
$455$	2.04669e14	0.492028
$456$	−7.60681e13	−0.180674
$457$	−6.43805e14	−1.51083	−0.755414	−	0.655247i	$-0.772564\pi$
$457$	−6.43805e14	−1.51083	−0.755414	+	0.655247i	$0.772564\pi$
$458$	1.02289e15	2.37174
$459$	3.45288e14	0.791065
$460$	−2.64183e15	−5.98048
$461$	−6.54825e14	−1.46477	−0.732387	−	0.680889i	$-0.761594\pi$
$461$	−6.54825e14	−1.46477	−0.732387	+	0.680889i	$0.761594\pi$
$462$	−8.99955e13	−0.198925
$463$	1.21047e14	0.264398	0.132199	−	0.991223i	$-0.457796\pi$
$463$	1.21047e14	0.264398	0.132199	+	0.991223i	$0.457796\pi$
$464$	7.66004e13	0.165342
$465$	−2.09135e14	−0.446103
$466$	2.86758e14	0.604495
$467$	−5.61529e14	−1.16985	−0.584924	−	0.811088i	$-0.698876\pi$
$467$	−5.61529e14	−1.16985	−0.584924	+	0.811088i	$0.698876\pi$
$468$	4.06221e14	0.836392
$469$	5.31662e13	0.108190
$470$	3.99873e14	0.804237
$471$	−1.75918e14	−0.349699
$472$	1.43115e14	0.281193
$473$	−3.70154e13	−0.0718863
$474$	9.58783e13	0.184052
$475$	3.17559e14	0.602572
$476$	−2.92206e14	−0.548089
$477$	−3.05879e14	−0.567151
$478$	9.95794e14	1.82522
$479$	−4.80818e14	−0.871235	−0.435618	−	0.900132i	$-0.643470\pi$
$479$	−4.80818e14	−0.871235	−0.435618	+	0.900132i	$0.643470\pi$
$480$	4.21832e14	0.755636
$481$	−4.59527e14	−0.813791
$482$	−2.33803e14	−0.409347
$483$	−2.31580e14	−0.400858
$484$	−7.08010e14	−1.21169
$485$	−1.21688e15	−2.05906
$486$	−1.02037e15	−1.70710
$487$	2.68675e14	0.444444	0.222222	−	0.974996i	$-0.428669\pi$
$487$	2.68675e14	0.444444	0.222222	+	0.974996i	$0.428669\pi$
$488$	7.58095e14	1.23998
$489$	1.47595e14	0.238711
$490$	2.72353e14	0.435566
$491$	3.73963e14	0.591399	0.295699	−	0.955281i	$-0.404447\pi$
$491$	3.73963e14	0.591399	0.295699	+	0.955281i	$0.404447\pi$
$492$	6.64234e14	1.03875
$493$	2.77850e14	0.429687
$494$	−1.94750e14	−0.297837
$495$	4.54810e14	0.687863
$496$	9.04824e13	0.135336
$497$	8.73772e13	0.129252
$498$	−1.09872e15	−1.60741
$499$	4.12165e14	0.596374	0.298187	−	0.954508i	$-0.403618\pi$
$499$	4.12165e14	0.596374	0.298187	+	0.954508i	$0.403618\pi$
$500$	3.09996e15	4.43630
$501$	−4.74571e14	−0.671728
$502$	1.22626e15	1.71677
$503$	6.67698e14	0.924605	0.462303	−	0.886722i	$-0.347023\pi$
$503$	6.67698e14	0.924605	0.462303	+	0.886722i	$0.347023\pi$
$504$	2.32085e14	0.317892
$505$	4.34580e14	0.588799
$506$	1.27688e15	1.71129
$507$	2.14648e14	0.284566
$508$	−3.95088e14	−0.518136
$509$	−9.75197e14	−1.26516	−0.632579	−	0.774496i	$-0.718003\pi$
$509$	−9.75197e14	−1.26516	−0.632579	+	0.774496i	$0.718003\pi$
$510$	−1.12277e15	−1.44097
$511$	2.13150e14	0.270626
$512$	−4.98933e14	−0.626696
$513$	1.94970e14	0.242283
$514$	−2.25749e15	−2.77542
$515$	−1.31919e15	−1.60461
$516$	−1.07625e14	−0.129521
$517$	−1.23052e14	−0.146518
$518$	−6.11492e14	−0.720406
$519$	1.21861e14	0.142051
$520$	−1.40877e15	−1.62488
$521$	−7.74860e13	−0.0884333	−0.0442166	−	0.999022i	$-0.514079\pi$
$521$	−7.74860e13	−0.0884333	−0.0442166	+	0.999022i	$0.514079\pi$
$522$	−5.13999e14	−0.580463
$523$	−6.80034e13	−0.0759926	−0.0379963	−	0.999278i	$-0.512098\pi$
$523$	−6.80034e13	−0.0759926	−0.0379963	+	0.999278i	$0.512098\pi$
$524$	−2.25843e15	−2.49738
$525$	4.69006e14	0.513218
$526$	3.97708e14	0.430668
$527$	3.28203e14	0.351710
$528$	9.52529e13	0.101016
$529$	2.33291e15	2.44846
$530$	2.47072e15	2.56629
$531$	−1.47668e14	−0.151798
$532$	−1.64997e14	−0.167866
$533$	7.30129e14	0.735191
$534$	−4.71112e14	−0.469512
$535$	−1.97492e15	−1.94807
$536$	−3.65952e14	−0.357287
$537$	7.25018e14	0.700632
$538$	−2.27588e15	−2.17694
$539$	−8.38105e13	−0.0793524
$540$	3.28493e15	3.07865
$541$	−6.11973e12	−0.00567737	−0.00283869	−	0.999996i	$-0.500904\pi$
$541$	−6.11973e12	−0.00567737	−0.00283869	+	0.999996i	$0.500904\pi$
$542$	−9.99397e14	−0.917787
$543$	1.83838e14	0.167123
$544$	−6.61996e14	−0.595747
$545$	2.59424e15	2.31116
$546$	−2.87628e14	−0.253671
$547$	9.48834e14	0.828438	0.414219	−	0.910177i	$-0.364055\pi$
$547$	9.48834e14	0.828438	0.414219	+	0.910177i	$0.364055\pi$
$548$	1.32168e15	1.14244
$549$	−7.82211e14	−0.669385
$550$	−2.58601e15	−2.19096
$551$	1.56890e14	0.131602
$552$	1.59400e15	1.32380
$553$	8.92890e13	0.0734192
$554$	1.62498e14	0.132296
$555$	−1.49593e15	−1.20587
$556$	1.10587e15	0.882658
$557$	−9.38168e13	−0.0741441	−0.0370721	−	0.999313i	$-0.511803\pi$
$557$	−9.38168e13	−0.0741441	−0.0370721	+	0.999313i	$0.511803\pi$
$558$	−6.07149e14	−0.475124
$559$	−1.18302e14	−0.0916701
$560$	−2.88263e14	−0.221185
$561$	3.45507e14	0.262519
$562$	−1.74160e15	−1.31038
$563$	2.23606e15	1.66604	0.833022	−	0.553240i	$-0.186609\pi$
$563$	2.23606e15	1.66604	0.833022	+	0.553240i	$0.186609\pi$
$564$	−3.57783e14	−0.263989
$565$	7.71179e14	0.563493
$566$	2.58390e15	1.86976
$567$	−6.74345e13	−0.0483254
$568$	−6.01431e14	−0.426845
$569$	−1.25117e15	−0.879427	−0.439714	−	0.898138i	$-0.644920\pi$
$569$	−1.25117e15	−0.879427	−0.439714	+	0.898138i	$0.644920\pi$
$570$	−6.33982e14	−0.441332
$571$	4.25534e14	0.293384	0.146692	−	0.989182i	$-0.453137\pi$
$571$	4.25534e14	0.293384	0.146692	+	0.989182i	$0.453137\pi$
$572$	1.00972e15	0.689482
$573$	−9.70290e14	−0.656223
$574$	9.71583e14	0.650825
$575$	−6.65440e15	−4.41505
$576$	1.55113e15	1.01935
$577$	4.60573e14	0.299800	0.149900	−	0.988701i	$-0.452105\pi$
$577$	4.60573e14	0.299800	0.149900	+	0.988701i	$0.452105\pi$
$578$	−8.11094e14	−0.522960
$579$	−8.30439e14	−0.530366
$580$	2.64335e15	1.67225
$581$	−1.02321e15	−0.641205
$582$	1.71012e15	1.06158
$583$	−7.60307e14	−0.467533
$584$	−1.46714e15	−0.893721
$585$	1.45359e15	0.877169
$586$	2.93574e15	1.75502
$587$	−2.74470e14	−0.162549	−0.0812747	−	0.996692i	$-0.525899\pi$
$587$	−2.74470e14	−0.162549	−0.0812747	+	0.996692i	$0.525899\pi$
$588$	−2.43686e14	−0.142973
$589$	1.85323e14	0.107720
$590$	1.19278e15	0.686868
$591$	1.87149e15	1.06771
$592$	6.47214e14	0.365830
$593$	−1.70765e15	−0.956306	−0.478153	−	0.878277i	$-0.658694\pi$
$593$	−1.70765e15	−0.956306	−0.478153	+	0.878277i	$0.658694\pi$
$594$	−1.58772e15	−0.880944
$595$	−1.04561e15	−0.574811
$596$	−5.34876e15	−2.91339
$597$	2.14255e14	0.115630
$598$	4.08096e15	2.18225
$599$	9.91528e14	0.525360	0.262680	−	0.964883i	$-0.415394\pi$
$599$	9.91528e14	0.525360	0.262680	+	0.964883i	$0.415394\pi$
$600$	−3.22824e15	−1.69486
$601$	4.40763e14	0.229296	0.114648	−	0.993406i	$-0.463426\pi$
$601$	4.40763e14	0.229296	0.114648	+	0.993406i	$0.463426\pi$
$602$	−1.57425e14	−0.0811506
$603$	3.77593e14	0.192876
$604$	−3.75290e15	−1.89961
$605$	−2.53348e15	−1.27076
$606$	−6.10729e14	−0.303563
$607$	3.55720e15	1.75215	0.876073	−	0.482179i	$-0.160155\pi$
$607$	3.55720e15	1.75215	0.876073	+	0.482179i	$0.160155\pi$
$608$	−3.73802e14	−0.182462
$609$	2.31713e14	0.112087
$610$	6.31826e15	3.02889
$611$	−3.93277e14	−0.186841
$612$	−2.07529e15	−0.977114
$613$	−2.59171e15	−1.20935	−0.604677	−	0.796471i	$-0.706698\pi$
$613$	−2.59171e15	−1.20935	−0.604677	+	0.796471i	$0.706698\pi$
$614$	−5.53420e15	−2.55934
$615$	2.37684e15	1.08940
$616$	5.76881e14	0.262055
$617$	3.54753e15	1.59720	0.798598	−	0.601865i	$-0.205575\pi$
$617$	3.54753e15	1.59720	0.798598	+	0.601865i	$0.205575\pi$
$618$	1.85390e15	0.827276
$619$	−1.39578e14	−0.0617332	−0.0308666	−	0.999524i	$-0.509827\pi$
$619$	−1.39578e14	−0.0617332	−0.0308666	+	0.999524i	$0.509827\pi$
$620$	3.12239e15	1.36878
$621$	−4.08557e15	−1.77521
$622$	−3.10443e15	−1.33701
$623$	−4.38734e14	−0.187291
$624$	3.04431e14	0.128817
$625$	5.42419e15	2.27507
$626$	3.01245e15	1.25245
$627$	1.95093e14	0.0804028
$628$	2.62645e15	1.07298
$629$	2.34762e15	0.950711
$630$	1.93429e15	0.776511
$631$	−3.43724e15	−1.36788	−0.683940	−	0.729538i	$-0.739735\pi$
$631$	−3.43724e15	−1.36788	−0.683940	+	0.729538i	$0.739735\pi$
$632$	−6.14590e14	−0.242461
$633$	5.24176e14	0.205001
$634$	7.39190e15	2.86593
$635$	−1.41375e15	−0.543397
$636$	−2.21065e15	−0.842377
$637$	−2.67860e14	−0.101191
$638$	−1.27762e15	−0.478507
$639$	6.20564e14	0.230426
$640$	−8.93519e15	−3.28938
$641$	2.62912e15	0.959604	0.479802	−	0.877377i	$-0.340709\pi$
$641$	2.62912e15	0.959604	0.479802	+	0.877377i	$0.340709\pi$
$642$	2.77542e15	1.00435
$643$	−5.30439e15	−1.90316	−0.951580	−	0.307402i	$-0.900541\pi$
$643$	−5.30439e15	−1.90316	−0.951580	+	0.307402i	$0.900541\pi$
$644$	3.45749e15	1.22995
$645$	−3.85117e14	−0.135836
$646$	9.94931e14	0.347948
$647$	4.10529e15	1.42354	0.711772	−	0.702411i	$-0.247893\pi$
$647$	4.10529e15	1.42354	0.711772	+	0.702411i	$0.247893\pi$
$648$	4.64163e14	0.159591
$649$	−3.67050e14	−0.125135
$650$	−8.26495e15	−2.79394
$651$	2.73705e14	0.0917461
$652$	−2.20360e15	−0.732437
$653$	1.02450e15	0.337668	0.168834	−	0.985644i	$-0.446000\pi$
$653$	1.02450e15	0.337668	0.168834	+	0.985644i	$0.446000\pi$
$654$	−3.64577e15	−1.19155
$655$	−8.08139e15	−2.61914
$656$	−1.02834e15	−0.330496
$657$	1.51382e15	0.482463
$658$	−5.23334e14	−0.165400
$659$	4.38308e15	1.37376	0.686879	−	0.726772i	$-0.258980\pi$
$659$	4.38308e15	1.37376	0.686879	+	0.726772i	$0.258980\pi$
$660$	3.28701e15	1.02167
$661$	4.50552e13	0.0138879	0.00694396	−	0.999976i	$-0.497790\pi$
$661$	4.50552e13	0.0138879	0.00694396	+	0.999976i	$0.497790\pi$
$662$	−8.73675e15	−2.67073
$663$	1.10425e15	0.334767
$664$	7.04293e15	2.11753
$665$	−5.90411e14	−0.176050
$666$	−4.34290e15	−1.28431
$667$	−3.28762e15	−0.964248
$668$	7.08535e15	2.06106
$669$	−7.82793e14	−0.225841
$670$	−3.04998e15	−0.872743
$671$	−1.94430e15	−0.551810
$672$	−5.52072e14	−0.155405
$673$	−4.46760e15	−1.24736	−0.623680	−	0.781680i	$-0.714363\pi$
$673$	−4.46760e15	−1.24736	−0.623680	+	0.781680i	$0.714363\pi$
$674$	5.28627e15	1.46393
$675$	8.27430e15	2.27280
$676$	−3.20470e15	−0.873133
$677$	3.64624e15	0.985390	0.492695	−	0.870202i	$-0.336012\pi$
$677$	3.64624e15	0.985390	0.492695	+	0.870202i	$0.336012\pi$
$678$	−1.08376e15	−0.290516
$679$	1.59259e15	0.423468
$680$	7.19708e15	1.89827
$681$	−4.06922e15	−1.06464
$682$	−1.50916e15	−0.391670
$683$	3.18228e15	0.819266	0.409633	−	0.912250i	$-0.365657\pi$
$683$	3.18228e15	0.819266	0.409633	+	0.912250i	$0.365657\pi$
$684$	−1.17183e15	−0.299265
$685$	4.72938e15	1.19814
$686$	−3.56442e14	−0.0895790
$687$	−3.27494e15	−0.816473
$688$	1.66621e14	0.0412091
$689$	−2.42996e15	−0.596202
$690$	1.32850e16	3.23364
$691$	1.57604e15	0.380572	0.190286	−	0.981729i	$-0.439058\pi$
$691$	1.57604e15	0.380572	0.190286	+	0.981729i	$0.439058\pi$
$692$	−1.81939e15	−0.435855
$693$	−5.95233e14	−0.141467
$694$	5.92735e15	1.39760
$695$	3.95715e15	0.925691
$696$	−1.59492e15	−0.370158
$697$	−3.73006e15	−0.858886
$698$	−5.83766e15	−1.33362
$699$	−9.18103e14	−0.208098
$700$	−7.00227e15	−1.57471
$701$	−6.70015e14	−0.149498	−0.0747490	−	0.997202i	$-0.523816\pi$
$701$	−6.70015e14	−0.149498	−0.0747490	+	0.997202i	$0.523816\pi$
$702$	−5.07439e15	−1.12339
$703$	1.32560e15	0.291178
$704$	3.85557e15	0.840308
$705$	−1.28026e15	−0.276859
$706$	9.96564e15	2.13835
$707$	−5.68756e14	−0.121093
$708$	−1.06723e15	−0.225462
$709$	−3.01814e15	−0.632682	−0.316341	−	0.948646i	$-0.602454\pi$
$709$	−3.01814e15	−0.632682	−0.316341	+	0.948646i	$0.602454\pi$
$710$	−5.01256e15	−1.04265
$711$	6.34142e14	0.130889
$712$	3.01988e15	0.618514
$713$	−3.88342e15	−0.789263
$714$	1.46942e15	0.296351
$715$	3.61310e15	0.723097
$716$	−1.08245e16	−2.14975
$717$	−3.18820e15	−0.628334
$718$	−7.57969e15	−1.48240
$719$	1.31186e15	0.254611	0.127306	−	0.991864i	$-0.459367\pi$
$719$	1.31186e15	0.254611	0.127306	+	0.991864i	$0.459367\pi$
$720$	−2.04728e15	−0.394320
$721$	1.72649e15	0.330005
$722$	−8.18417e15	−1.55246
$723$	7.48560e14	0.140918
$724$	−2.74470e15	−0.512782
$725$	6.65824e15	1.23453
$726$	3.56039e15	0.655157
$727$	6.88687e15	1.25772	0.628858	−	0.777520i	$-0.283523\pi$
$727$	6.88687e15	1.25772	0.628858	+	0.777520i	$0.283523\pi$
$728$	1.84373e15	0.334175
$729$	2.55612e15	0.459812
$730$	−1.22277e16	−2.18309
$731$	6.04378e14	0.107093
$732$	−5.65321e15	−0.994224
$733$	6.41619e14	0.111997	0.0559984	−	0.998431i	$-0.482166\pi$
$733$	6.41619e14	0.111997	0.0559984	+	0.998431i	$0.482166\pi$
$734$	1.82166e16	3.15601
$735$	−8.71984e14	−0.149944
$736$	7.83297e15	1.33690
$737$	9.38563e14	0.158998
$738$	6.90031e15	1.16027
$739$	4.67251e15	0.779840	0.389920	−	0.920849i	$-0.372503\pi$
$739$	4.67251e15	0.779840	0.389920	+	0.920849i	$0.372503\pi$
$740$	2.23343e16	3.69996
$741$	6.23524e14	0.102530
$742$	−3.23355e15	−0.527786
$743$	−7.76269e15	−1.25769	−0.628845	−	0.777531i	$-0.716472\pi$
$743$	−7.76269e15	−1.25769	−0.628845	+	0.777531i	$0.716472\pi$
$744$	−1.88396e15	−0.302984
$745$	−1.91395e16	−3.05543
$746$	−8.80675e15	−1.39557
$747$	−7.26698e15	−1.14312
$748$	−5.15843e15	−0.805487
$749$	2.58468e15	0.400642
$750$	−1.55888e16	−2.39870
$751$	8.98132e15	1.37189	0.685947	−	0.727652i	$-0.259388\pi$
$751$	8.98132e15	1.37189	0.685947	+	0.727652i	$0.259388\pi$
$752$	5.53906e14	0.0839920
$753$	−3.92609e15	−0.591000
$754$	−4.08331e15	−0.610196
$755$	−1.34291e16	−1.99222
$756$	−4.29915e15	−0.633159
$757$	7.26465e15	1.06215	0.531077	−	0.847324i	$-0.321787\pi$
$757$	7.26465e15	1.06215	0.531077	+	0.847324i	$0.321787\pi$
$758$	1.43521e16	2.08321
$759$	−4.08816e15	−0.589112
$760$	4.06389e15	0.581390
$761$	1.93961e15	0.275485	0.137743	−	0.990468i	$-0.456015\pi$
$761$	1.93961e15	0.275485	0.137743	+	0.990468i	$0.456015\pi$
$762$	1.98679e15	0.280156
$763$	−3.39521e15	−0.475316
$764$	1.44865e16	2.01349
$765$	−7.42603e15	−1.02475
$766$	2.38453e16	3.26697
$767$	−1.17310e15	−0.159574
$768$	6.15964e15	0.831895
$769$	−1.17348e16	−1.57356	−0.786778	−	0.617236i	$-0.788252\pi$
$769$	−1.17348e16	−1.57356	−0.786778	+	0.617236i	$0.788252\pi$
$770$	4.80795e15	0.640120
$771$	7.22774e15	0.955440
$772$	1.23985e16	1.62732
$773$	−1.21535e15	−0.158385	−0.0791927	−	0.996859i	$-0.525234\pi$
$773$	−1.21535e15	−0.158385	−0.0791927	+	0.996859i	$0.525234\pi$
$774$	−1.11805e15	−0.144672
$775$	7.86488e15	1.01049
$776$	−1.09621e16	−1.39847
$777$	1.95780e15	0.248000
$778$	−4.58481e15	−0.576678
$779$	−2.10621e15	−0.263055
$780$	1.05054e16	1.30284
$781$	1.54250e15	0.189952
$782$	−2.08487e16	−2.54942
$783$	4.08793e15	0.496379
$784$	3.77264e14	0.0454891
$785$	9.39829e15	1.12529
$786$	1.13570e16	1.35033
$787$	1.10958e16	1.31007	0.655037	−	0.755597i	$-0.272653\pi$
$787$	1.10958e16	1.31007	0.655037	+	0.755597i	$0.272653\pi$
$788$	−2.79413e16	−3.27607
$789$	−1.27333e15	−0.148258
$790$	−5.12224e15	−0.592258
$791$	−1.00928e15	−0.115889
$792$	4.09708e15	0.467182
$793$	−6.21403e15	−0.703673
$794$	−2.47849e16	−2.78724
$795$	−7.91041e15	−0.883446
$796$	−3.19883e15	−0.354788
$797$	2.89815e15	0.319228	0.159614	−	0.987180i	$-0.448975\pi$
$797$	2.89815e15	0.319228	0.159614	+	0.987180i	$0.448975\pi$
$798$	8.29723e14	0.0907648
$799$	2.00916e15	0.218277
$800$	−1.58637e16	−1.71163
$801$	−3.11595e15	−0.333896
$802$	1.36860e16	1.45652
$803$	3.76281e15	0.397720
$804$	2.72895e15	0.286475
$805$	1.23720e16	1.28992
$806$	−4.82331e15	−0.499462
$807$	7.28661e15	0.749413
$808$	3.91484e15	0.399900
$809$	1.72365e16	1.74876	0.874382	−	0.485239i	$-0.161267\pi$
$809$	1.72365e16	1.74876	0.874382	+	0.485239i	$0.161267\pi$
$810$	3.86851e15	0.389831
$811$	−1.70839e16	−1.70991	−0.854955	−	0.518703i	$-0.826415\pi$
$811$	−1.70839e16	−1.70991	−0.854955	+	0.518703i	$0.826415\pi$
$812$	−3.45948e15	−0.343916
$813$	3.19974e15	0.315949
$814$	−1.07949e16	−1.05873
$815$	−7.88516e15	−0.768146
$816$	−1.55526e15	−0.150490
$817$	3.41267e14	0.0328000
$818$	1.94752e15	0.185926
$819$	−1.90238e15	−0.180400
$820$	−3.54863e16	−3.34260
$821$	−6.91050e15	−0.646580	−0.323290	−	0.946300i	$-0.604789\pi$
$821$	−6.91050e15	−0.646580	−0.323290	+	0.946300i	$0.604789\pi$
$822$	−6.64635e15	−0.617715
$823$	−3.31021e15	−0.305602	−0.152801	−	0.988257i	$-0.548829\pi$
$823$	−3.31021e15	−0.305602	−0.152801	+	0.988257i	$0.548829\pi$
$824$	−1.18837e16	−1.08981
$825$	8.27954e15	0.754240
$826$	−1.56105e15	−0.141262
$827$	1.10601e16	0.994209	0.497105	−	0.867691i	$-0.334397\pi$
$827$	1.10601e16	0.994209	0.497105	+	0.867691i	$0.334397\pi$
$828$	2.45555e16	2.19272
$829$	−7.31880e15	−0.649217	−0.324608	−	0.945849i	$-0.605232\pi$
$829$	−7.31880e15	−0.649217	−0.324608	+	0.945849i	$0.605232\pi$
$830$	5.86985e16	5.17247
$831$	−5.20266e14	−0.0455428
$832$	1.23225e16	1.07157
$833$	1.36844e15	0.118216
$834$	−5.56111e15	−0.477253
$835$	2.53536e16	2.16155
$836$	−2.91275e15	−0.246700
$837$	4.82876e15	0.406299
$838$	−1.44926e16	−1.21144
$839$	2.25034e16	1.86878	0.934389	−	0.356254i	$-0.115946\pi$
$839$	2.25034e16	1.86878	0.934389	+	0.356254i	$0.115946\pi$
$840$	6.00201e15	0.495177
$841$	−8.91100e15	−0.730379
$842$	−1.85282e15	−0.150875
$843$	5.57602e15	0.451099
$844$	−7.82596e15	−0.629005
$845$	−1.14674e16	−0.915701
$846$	−3.71678e15	−0.294870
$847$	3.31570e15	0.261346
$848$	3.42244e15	0.268015
$849$	−8.27280e15	−0.643665
$850$	4.22237e16	3.26401
$851$	−2.77778e16	−2.13346
$852$	4.48495e15	0.342247
$853$	−3.38053e15	−0.256309	−0.128155	−	0.991754i	$-0.540905\pi$
$853$	−3.38053e15	−0.256309	−0.128155	+	0.991754i	$0.540905\pi$
$854$	−8.26901e15	−0.622925
$855$	−4.19317e15	−0.313855
$856$	−1.77908e16	−1.32309
$857$	7.53868e15	0.557058	0.278529	−	0.960428i	$-0.410153\pi$
$857$	7.53868e15	0.557058	0.278529	+	0.960428i	$0.410153\pi$
$858$	−5.07760e15	−0.372803
$859$	−6.00947e15	−0.438403	−0.219202	−	0.975680i	$-0.570345\pi$
$859$	−6.00947e15	−0.438403	−0.219202	+	0.975680i	$0.570345\pi$
$860$	5.74980e15	0.416785
$861$	−3.11069e15	−0.224047
$862$	−1.80572e16	−1.29229
$863$	−5.14484e15	−0.365858	−0.182929	−	0.983126i	$-0.558558\pi$
$863$	−5.14484e15	−0.365858	−0.182929	+	0.983126i	$0.558558\pi$
$864$	−9.73977e15	−0.688213
$865$	−6.51034e15	−0.457104
$866$	−2.04304e16	−1.42537
$867$	2.59685e15	0.180029
$868$	−4.08643e15	−0.281504
$869$	1.57625e15	0.107899
$870$	−1.32927e16	−0.904183
$871$	2.99967e15	0.202756
$872$	2.33698e16	1.56969
$873$	1.13108e16	0.754944
$874$	−1.17724e16	−0.780820
$875$	−1.45175e16	−0.956856
$876$	1.09407e16	0.716591
$877$	1.86741e16	1.21546	0.607731	−	0.794143i	$-0.292080\pi$
$877$	1.86741e16	1.21546	0.607731	+	0.794143i	$0.292080\pi$
$878$	1.93340e15	0.125055
$879$	−9.39928e15	−0.604165
$880$	−5.08882e15	−0.325059
$881$	1.46317e16	0.928809	0.464405	−	0.885623i	$-0.346268\pi$
$881$	1.46317e16	0.928809	0.464405	+	0.885623i	$0.346268\pi$
$882$	−2.53150e15	−0.159698
$883$	−8.15342e15	−0.511159	−0.255579	−	0.966788i	$-0.582266\pi$
$883$	−8.15342e15	−0.511159	−0.255579	+	0.966788i	$0.582266\pi$
$884$	−1.64865e16	−1.02716
$885$	−3.81888e15	−0.236455
$886$	3.62467e16	2.23040
$887$	−1.63433e16	−0.999449	−0.499724	−	0.866185i	$-0.666565\pi$
$887$	−1.63433e16	−0.999449	−0.499724	+	0.866185i	$0.666565\pi$
$888$	−1.34758e16	−0.819000
$889$	1.85025e15	0.111756
$890$	2.51688e16	1.51084
$891$	−1.19045e15	−0.0710203
$892$	1.16871e16	0.692948
$893$	1.13449e15	0.0668525
$894$	2.68974e16	1.57527
$895$	−3.87336e16	−2.25456
$896$	1.16939e16	0.676497
$897$	−1.30659e16	−0.751242
$898$	1.28887e16	0.736530
$899$	3.88565e15	0.220692
$900$	−4.97310e16	−2.80733
$901$	1.24141e16	0.696512
$902$	1.71517e16	0.956471
$903$	5.04021e14	0.0279361
$904$	6.94703e15	0.382713
$905$	−9.82141e15	−0.537782
$906$	1.88723e16	1.02712
$907$	8.57490e15	0.463862	0.231931	−	0.972732i	$-0.425496\pi$
$907$	8.57490e15	0.463862	0.231931	+	0.972732i	$0.425496\pi$
$908$	6.07536e16	3.26663
$909$	−4.03938e15	−0.215880
$910$	1.53663e16	0.816287
$911$	−2.70231e16	−1.42687	−0.713434	−	0.700722i	$-0.752861\pi$
$911$	−2.70231e16	−1.42687	−0.713434	+	0.700722i	$0.752861\pi$
$912$	−8.78194e14	−0.0460913
$913$	−1.80631e16	−0.942332
$914$	−4.83362e16	−2.50650
$915$	−2.02290e16	−1.04270
$916$	4.88950e16	2.50518
$917$	1.05765e16	0.538656
$918$	2.59239e16	1.31240
$919$	1.18618e16	0.596920	0.298460	−	0.954422i	$-0.403527\pi$
$919$	1.18618e16	0.596920	0.298460	+	0.954422i	$0.403527\pi$
$920$	−8.51584e16	−4.25985
$921$	1.77187e16	0.881055
$922$	−4.91636e16	−2.43010
$923$	4.92988e15	0.242229
$924$	−4.30188e15	−0.210117
$925$	5.62570e16	2.73147
$926$	9.08807e15	0.438643
$927$	1.22618e16	0.588321
$928$	−7.83748e15	−0.373820
$929$	3.20207e16	1.51825	0.759127	−	0.650943i	$-0.225626\pi$
$929$	3.20207e16	1.51825	0.759127	+	0.650943i	$0.225626\pi$
$930$	−1.57016e16	−0.740097
$931$	7.72700e14	0.0362066
$932$	1.37073e16	0.638505
$933$	9.93936e15	0.460267
$934$	−4.21590e16	−1.94081
$935$	−1.84585e16	−0.844758
$936$	1.30944e16	0.595755
$937$	−3.05829e16	−1.38328	−0.691640	−	0.722242i	$-0.743112\pi$
$937$	−3.05829e16	−1.38328	−0.691640	+	0.722242i	$0.743112\pi$
$938$	3.99166e15	0.179489
$939$	−9.64485e15	−0.431156
$940$	1.91143e16	0.849486
$941$	8.51390e15	0.376171	0.188086	−	0.982153i	$-0.439772\pi$
$941$	8.51390e15	0.376171	0.188086	+	0.982153i	$0.439772\pi$
$942$	−1.32077e16	−0.580160
$943$	4.41354e16	1.92740
$944$	1.65224e15	0.0717343
$945$	−1.53837e16	−0.664028
$946$	−2.77908e15	−0.119261
$947$	−2.20524e16	−0.940873	−0.470437	−	0.882434i	$-0.655904\pi$
$947$	−2.20524e16	−0.940873	−0.470437	+	0.882434i	$0.655904\pi$
$948$	4.58308e15	0.194407
$949$	1.20260e16	0.507176
$950$	2.38420e16	0.999683
$951$	−2.36664e16	−0.986597
$952$	−9.41917e15	−0.390400
$953$	−9.59401e15	−0.395357	−0.197678	−	0.980267i	$-0.563340\pi$
$953$	−9.59401e15	−0.395357	−0.197678	+	0.980267i	$0.563340\pi$
$954$	−2.29651e16	−0.940918
$955$	5.18371e16	2.11165
$956$	4.75999e16	1.92792
$957$	4.09052e15	0.164726
$958$	−3.60993e16	−1.44540
$959$	−6.18957e15	−0.246410
$960$	4.01142e16	1.58784
$961$	−2.08186e16	−0.819358
$962$	−3.45008e16	−1.35010
$963$	1.83567e16	0.714251
$964$	−1.11760e16	−0.432378
$965$	4.43657e16	1.70666
$966$	−1.73867e16	−0.665035
$967$	−3.89915e16	−1.48294	−0.741471	−	0.670984i	$-0.765872\pi$
$967$	−3.89915e16	−1.48294	−0.741471	+	0.670984i	$0.765872\pi$
$968$	−2.28225e16	−0.863074
$969$	−3.18544e15	−0.119781
$970$	−9.13622e16	−3.41603
$971$	1.62866e16	0.605515	0.302758	−	0.953068i	$-0.402093\pi$
$971$	1.62866e16	0.605515	0.302758	+	0.953068i	$0.402093\pi$
$972$	−4.87747e16	−1.80314
$973$	−5.17892e15	−0.190379
$974$	2.01718e16	0.737345
$975$	2.64616e16	0.961814
$976$	8.75207e15	0.316327
$977$	−2.56328e14	−0.00921245	−0.00460622	−	0.999989i	$-0.501466\pi$
$977$	−2.56328e14	−0.00921245	−0.00460622	+	0.999989i	$0.501466\pi$
$978$	1.10813e16	0.396028
$979$	−7.74514e15	−0.275248
$980$	1.30187e16	0.460072
$981$	−2.41132e16	−0.847376
$982$	2.80767e16	0.981146
$983$	5.37016e16	1.86614	0.933068	−	0.359700i	$-0.117121\pi$
$983$	5.37016e16	1.86614	0.933068	+	0.359700i	$0.117121\pi$
$984$	2.14114e16	0.739897
$985$	−9.99829e16	−3.43579
$986$	2.08607e16	0.712861
$987$	1.67554e15	0.0569391
$988$	−9.30923e15	−0.314594
$989$	−7.15121e15	−0.240326
$990$	3.41467e16	1.14118
$991$	−1.05930e16	−0.352056	−0.176028	−	0.984385i	$-0.556325\pi$
$991$	−1.05930e16	−0.352056	−0.176028	+	0.984385i	$0.556325\pi$
$992$	−9.25784e15	−0.305982
$993$	2.79722e16	0.919401
$994$	6.56019e15	0.214433
$995$	−1.14464e16	−0.372086
$996$	−5.25200e16	−1.69785
$997$	−5.16179e15	−0.165950	−0.0829749	−	0.996552i	$-0.526442\pi$
$997$	−5.16179e15	−0.165950	−0.0829749	+	0.996552i	$0.526442\pi$
$998$	3.09449e16	0.989399
$999$	3.45398e16	1.09827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.12.a.b.1.3	✓	3
3.2	odd	2		63.12.a.d.1.1		3
4.3	odd	2		112.12.a.h.1.2		3
5.2	odd	4		175.12.b.b.99.6		6
5.3	odd	4		175.12.b.b.99.1		6
5.4	even	2		175.12.a.b.1.1		3
7.2	even	3		49.12.c.g.18.1		6
7.3	odd	6		49.12.c.f.30.1		6
7.4	even	3		49.12.c.g.30.1		6
7.5	odd	6		49.12.c.f.18.1		6
7.6	odd	2		49.12.a.d.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.12.a.b.1.3	✓	3	1.1	even	1	trivial
49.12.a.d.1.3		3	7.6	odd	2
49.12.c.f.18.1		6	7.5	odd	6
49.12.c.f.30.1		6	7.3	odd	6
49.12.c.g.18.1		6	7.2	even	3
49.12.c.g.30.1		6	7.4	even	3
63.12.a.d.1.1		3	3.2	odd	2
112.12.a.h.1.2		3	4.3	odd	2
175.12.a.b.1.1		3	5.4	even	2
175.12.b.b.99.1		6	5.3	odd	4
175.12.b.b.99.6		6	5.2	odd	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)

\(f(q)\)	\(=\)	\(q+75.0789 q^{2} -240.378 q^{3} +3588.85 q^{4} +12842.0 q^{5} -18047.3 q^{6} -16807.0 q^{7} +115685. q^{8} -119365. q^{9} +O(q^{10})\)	\(q+75.0789 q^{2} -240.378 q^{3} +3588.85 q^{4} +12842.0 q^{5} -18047.3 q^{6} -16807.0 q^{7} +115685. q^{8} -119365. q^{9} +964166. q^{10} -296700. q^{11} -862680. q^{12} -948262. q^{13} -1.26185e6 q^{14} -3.08694e6 q^{15} +1.33557e6 q^{16} +4.84445e6 q^{17} -8.96183e6 q^{18} +2.73546e6 q^{19} +4.60881e7 q^{20} +4.04003e6 q^{21} -2.22759e7 q^{22} -5.73212e7 q^{23} -2.78082e7 q^{24} +1.16090e8 q^{25} -7.11945e7 q^{26} +7.12750e7 q^{27} -6.03178e7 q^{28} +5.73542e7 q^{29} -2.31764e8 q^{30} +6.77483e7 q^{31} -1.36650e8 q^{32} +7.13202e7 q^{33} +3.63716e8 q^{34} -2.15836e8 q^{35} -4.28385e8 q^{36} +4.84599e8 q^{37} +2.05375e8 q^{38} +2.27941e8 q^{39} +1.48563e9 q^{40} -7.69966e8 q^{41} +3.03321e8 q^{42} +1.24757e8 q^{43} -1.06481e9 q^{44} -1.53290e9 q^{45} -4.30362e9 q^{46} +4.14735e8 q^{47} -3.21041e8 q^{48} +2.82475e8 q^{49} +8.71589e9 q^{50} -1.16450e9 q^{51} -3.40317e9 q^{52} +2.56254e9 q^{53} +5.35126e9 q^{54} -3.81023e9 q^{55} -1.94432e9 q^{56} -6.57544e8 q^{57} +4.30610e9 q^{58} +1.23711e9 q^{59} -1.10786e10 q^{60} +6.55308e9 q^{61} +5.08647e9 q^{62} +2.00618e9 q^{63} -1.29948e10 q^{64} -1.21776e10 q^{65} +5.35464e9 q^{66} -3.16334e9 q^{67} +1.73860e10 q^{68} +1.37788e10 q^{69} -1.62047e10 q^{70} -5.19886e9 q^{71} -1.38088e10 q^{72} -1.26822e10 q^{73} +3.63832e10 q^{74} -2.79054e10 q^{75} +9.81715e9 q^{76} +4.98664e9 q^{77} +1.71136e10 q^{78} -5.31261e9 q^{79} +1.71514e10 q^{80} +4.01229e9 q^{81} -5.78082e10 q^{82} +6.08801e10 q^{83} +1.44991e10 q^{84} +6.22126e10 q^{85} +9.36661e9 q^{86} -1.37867e10 q^{87} -3.43238e10 q^{88} +2.61042e10 q^{89} -1.15088e11 q^{90} +1.59374e10 q^{91} -2.05717e11 q^{92} -1.62852e10 q^{93} +3.11379e10 q^{94} +3.51289e10 q^{95} +3.28478e10 q^{96} -9.47577e10 q^{97} +2.12079e10 q^{98} +3.54158e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 77 q^{2} - 140 q^{3} + 5493 q^{4} + 5026 q^{5} + 64274 q^{6} - 50421 q^{7} + 125103 q^{8} + 658519 q^{9}+O(q^{10}) \) 3 * q + 77 * q^2 - 140 * q^3 + 5493 * q^4 + 5026 * q^5 + 64274 * q^6 - 50421 * q^7 + 125103 * q^8 + 658519 * q^9	\( 3 q + 77 q^{2} - 140 q^{3} + 5493 q^{4} + 5026 q^{5} + 64274 q^{6} - 50421 q^{7} + 125103 q^{8} + 658519 q^{9} + 610764 q^{10} - 1039052 q^{11} - 609154 q^{12} - 1881222 q^{13} - 1294139 q^{14} - 8220752 q^{15} - 9117711 q^{16} + 15797334 q^{17} + 38909 q^{18} + 12340356 q^{19} + 37982168 q^{20} + 2352980 q^{21} + 31890144 q^{22} + 7276752 q^{23} - 117296046 q^{24} + 68924781 q^{25} - 133487872 q^{26} + 205674616 q^{27} - 92320851 q^{28} - 126853406 q^{29} - 575391808 q^{30} + 162184512 q^{31} - 167636249 q^{32} + 786346624 q^{33} - 79664298 q^{34} - 84471982 q^{35} + 328076045 q^{36} + 567121338 q^{37} + 509512430 q^{38} - 660517760 q^{39} + 1827265440 q^{40} + 893682734 q^{41} - 1080253118 q^{42} + 460197828 q^{43} - 1666161688 q^{44} - 5048825558 q^{45} - 6171574224 q^{46} + 2723825664 q^{47} - 868401730 q^{48} + 847425747 q^{49} + 11374112959 q^{50} - 6836867112 q^{51} - 4409363868 q^{52} + 93426522 q^{53} + 23309429948 q^{54} - 4073739768 q^{55} - 2102606121 q^{56} + 3867165112 q^{57} - 2792521998 q^{58} + 5899174428 q^{59} - 16616994016 q^{60} + 2106807738 q^{61} + 22093555428 q^{62} - 11067728833 q^{63} - 9528592239 q^{64} - 4991087612 q^{65} - 21724126480 q^{66} - 27027285348 q^{67} + 26942000190 q^{68} - 9435687744 q^{69} - 10265110548 q^{70} + 16564049928 q^{71} - 19175918265 q^{72} + 6036803934 q^{73} + 29114537322 q^{74} + 6787422908 q^{75} + 19528279218 q^{76} + 17463346964 q^{77} - 25177551784 q^{78} - 54895016736 q^{79} + 58098552176 q^{80} + 117359146147 q^{81} - 88924869978 q^{82} + 123561203892 q^{83} + 10238051278 q^{84} + 45582888084 q^{85} + 59402678104 q^{86} - 117914423480 q^{87} - 97861591608 q^{88} - 91648411106 q^{89} - 285253455172 q^{90} + 31617698154 q^{91} - 147922642512 q^{92} + 220344467856 q^{93} + 132452618508 q^{94} - 19413413120 q^{95} - 214249905422 q^{96} - 71237114634 q^{97} + 21750594173 q^{98} - 177803449916 q^{99}+O(q^{100}) \) 3 * q + 77 * q^2 - 140 * q^3 + 5493 * q^4 + 5026 * q^5 + 64274 * q^6 - 50421 * q^7 + 125103 * q^8 + 658519 * q^9 + 610764 * q^10 - 1039052 * q^11 - 609154 * q^12 - 1881222 * q^13 - 1294139 * q^14 - 8220752 * q^15 - 9117711 * q^16 + 15797334 * q^17 + 38909 * q^18 + 12340356 * q^19 + 37982168 * q^20 + 2352980 * q^21 + 31890144 * q^22 + 7276752 * q^23 - 117296046 * q^24 + 68924781 * q^25 - 133487872 * q^26 + 205674616 * q^27 - 92320851 * q^28 - 126853406 * q^29 - 575391808 * q^30 + 162184512 * q^31 - 167636249 * q^32 + 786346624 * q^33 - 79664298 * q^34 - 84471982 * q^35 + 328076045 * q^36 + 567121338 * q^37 + 509512430 * q^38 - 660517760 * q^39 + 1827265440 * q^40 + 893682734 * q^41 - 1080253118 * q^42 + 460197828 * q^43 - 1666161688 * q^44 - 5048825558 * q^45 - 6171574224 * q^46 + 2723825664 * q^47 - 868401730 * q^48 + 847425747 * q^49 + 11374112959 * q^50 - 6836867112 * q^51 - 4409363868 * q^52 + 93426522 * q^53 + 23309429948 * q^54 - 4073739768 * q^55 - 2102606121 * q^56 + 3867165112 * q^57 - 2792521998 * q^58 + 5899174428 * q^59 - 16616994016 * q^60 + 2106807738 * q^61 + 22093555428 * q^62 - 11067728833 * q^63 - 9528592239 * q^64 - 4991087612 * q^65 - 21724126480 * q^66 - 27027285348 * q^67 + 26942000190 * q^68 - 9435687744 * q^69 - 10265110548 * q^70 + 16564049928 * q^71 - 19175918265 * q^72 + 6036803934 * q^73 + 29114537322 * q^74 + 6787422908 * q^75 + 19528279218 * q^76 + 17463346964 * q^77 - 25177551784 * q^78 - 54895016736 * q^79 + 58098552176 * q^80 + 117359146147 * q^81 - 88924869978 * q^82 + 123561203892 * q^83 + 10238051278 * q^84 + 45582888084 * q^85 + 59402678104 * q^86 - 117914423480 * q^87 - 97861591608 * q^88 - 91648411106 * q^89 - 285253455172 * q^90 + 31617698154 * q^91 - 147922642512 * q^92 + 220344467856 * q^93 + 132452618508 * q^94 - 19413413120 * q^95 - 214249905422 * q^96 - 71237114634 * q^97 + 21750594173 * q^98 - 177803449916 * q^99

Introduction

L-functions

Modular forms

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