Properties

Label 49.10.c.d.30.2
Level $49$
Weight $10$
Character 49.30
Analytic conductor $25.237$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [49,10,Mod(18,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.18");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\), degree \(2\), not 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: \(25.2367559720\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 427x^{4} - 3606x^{3} + 183492x^{2} - 858816x + 4064256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 30.2
Root \(-11.1179 + 19.2567i\) of defining polynomial
Character \(\chi\) \(=\) 49.30
Dual form 49.10.c.d.18.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.68036 + 11.5707i) q^{2} +(-81.7073 - 141.521i) q^{3} +(166.746 + 288.812i) q^{4} +(-961.094 + 1664.66i) q^{5} +2183.34 q^{6} -11296.4 q^{8} +(-3510.66 + 6080.64i) q^{9} +(-12840.9 - 22241.1i) q^{10} +(45099.9 + 78115.4i) q^{11} +(27248.6 - 47196.0i) q^{12} -3199.89 q^{13} +314114. q^{15} +(-9909.84 + 17164.3i) q^{16} +(-58247.1 - 100887. i) q^{17} +(-46904.9 - 81241.8i) q^{18} +(71224.7 - 123365. i) q^{19} -641033. q^{20} -1.20514e6 q^{22} +(-636955. + 1.10324e6i) q^{23} +(922996. + 1.59868e6i) q^{24} +(-870842. - 1.50834e6i) q^{25} +(21376.4 - 37025.0i) q^{26} -2.06910e6 q^{27} -1.42931e6 q^{29} +(-2.09839e6 + 3.63452e6i) q^{30} +(-4.83747e6 - 8.37875e6i) q^{31} +(-3.02427e6 - 5.23820e6i) q^{32} +(7.36999e6 - 1.27652e7i) q^{33} +1.55645e6 q^{34} -2.34155e6 q^{36} +(4.33872e6 - 7.51488e6i) q^{37} +(951614. + 1.64824e6i) q^{38} +(261454. + 452851. i) q^{39} +(1.08569e7 - 1.88047e7i) q^{40} +1.32544e7 q^{41} -2.97554e7 q^{43} +(-1.50404e7 + 2.60508e7i) q^{44} +(-6.74815e6 - 1.16881e7i) q^{45} +(-8.51018e6 - 1.47401e7i) q^{46} +(5.39846e6 - 9.35041e6i) q^{47} +3.23882e6 q^{48} +2.32702e7 q^{50} +(-9.51843e6 + 1.64864e7i) q^{51} +(-533567. - 924164. i) q^{52} +(-3.53700e7 - 6.12626e7i) q^{53} +(1.38224e7 - 2.39410e7i) q^{54} -1.73381e8 q^{55} -2.32783e7 q^{57} +(9.54828e6 - 1.65381e7i) q^{58} +(-3.20200e6 - 5.54603e6i) q^{59} +(5.23770e7 + 9.07197e7i) q^{60} +(-8.45948e7 + 1.46523e8i) q^{61} +1.29264e8 q^{62} +7.06653e7 q^{64} +(3.07539e6 - 5.32673e6i) q^{65} +(9.84684e7 + 1.70552e8i) q^{66} +(5.81380e7 + 1.00698e8i) q^{67} +(1.94249e7 - 3.36449e7i) q^{68} +2.08176e8 q^{69} +1.44496e8 q^{71} +(3.96577e7 - 6.86892e7i) q^{72} +(-8.00775e7 - 1.38698e8i) q^{73} +(5.79684e7 + 1.00404e8i) q^{74} +(-1.42308e8 + 2.46485e8i) q^{75} +4.75056e7 q^{76} -6.98643e6 q^{78} +(2.44661e8 - 4.23766e8i) q^{79} +(-1.90486e7 - 3.29931e7i) q^{80} +(2.38161e8 + 4.12507e8i) q^{81} +(-8.85441e7 + 1.53363e8i) q^{82} -8.31590e7 q^{83} +2.23924e8 q^{85} +(1.98777e8 - 3.44291e8i) q^{86} +(1.16785e8 + 2.02277e8i) q^{87} +(-5.09466e8 - 8.82421e8i) q^{88} +(-1.04042e6 + 1.80205e6i) q^{89} +1.80320e8 q^{90} -4.24838e8 q^{92} +(-7.90513e8 + 1.36921e9i) q^{93} +(7.21274e7 + 1.24928e8i) q^{94} +(1.36907e8 + 2.37131e8i) q^{95} +(-4.94210e8 + 8.55998e8i) q^{96} -3.15885e8 q^{97} -6.33322e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 21 q^{2} - 84 q^{3} - 1557 q^{4} - 1554 q^{5} + 9828 q^{6} + 28110 q^{8} + 26001 q^{9} + 97860 q^{10} + 3444 q^{11} + 106386 q^{12} - 39564 q^{13} + 400608 q^{15} - 482961 q^{16} - 1016694 q^{17}+ \cdots - 3801958344 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.68036 + 11.5707i −0.295233 + 0.511359i −0.975039 0.222033i \(-0.928731\pi\)
0.679806 + 0.733392i \(0.262064\pi\)
\(3\) −81.7073 141.521i −0.582392 1.00873i −0.995195 0.0979117i \(-0.968784\pi\)
0.412804 0.910820i \(-0.364550\pi\)
\(4\) 166.746 + 288.812i 0.325675 + 0.564085i
\(5\) −961.094 + 1664.66i −0.687703 + 1.19114i 0.284876 + 0.958564i \(0.408048\pi\)
−0.972579 + 0.232572i \(0.925286\pi\)
\(6\) 2183.34 0.687765
\(7\) 0 0
\(8\) −11296.4 −0.975066
\(9\) −3510.66 + 6080.64i −0.178360 + 0.308928i
\(10\) −12840.9 22241.1i −0.406065 0.703326i
\(11\) 45099.9 + 78115.4i 0.928772 + 1.60868i 0.785380 + 0.619014i \(0.212467\pi\)
0.143391 + 0.989666i \(0.454199\pi\)
\(12\) 27248.6 47196.0i 0.379341 0.657037i
\(13\) −3199.89 −0.0310734 −0.0155367 0.999879i \(-0.504946\pi\)
−0.0155367 + 0.999879i \(0.504946\pi\)
\(14\) 0 0
\(15\) 314114. 1.60205
\(16\) −9909.84 + 17164.3i −0.0378030 + 0.0654768i
\(17\) −58247.1 100887.i −0.169143 0.292965i 0.768976 0.639278i \(-0.220767\pi\)
−0.938119 + 0.346313i \(0.887433\pi\)
\(18\) −46904.9 81241.8i −0.105316 0.182412i
\(19\) 71224.7 123365.i 0.125383 0.217170i −0.796499 0.604639i \(-0.793317\pi\)
0.921883 + 0.387469i \(0.126651\pi\)
\(20\) −641033. −0.895870
\(21\) 0 0
\(22\) −1.20514e6 −1.09682
\(23\) −636955. + 1.10324e6i −0.474606 + 0.822043i −0.999577 0.0290778i \(-0.990743\pi\)
0.524971 + 0.851120i \(0.324076\pi\)
\(24\) 922996. + 1.59868e6i 0.567870 + 0.983580i
\(25\) −870842. 1.50834e6i −0.445871 0.772272i
\(26\) 21376.4 37025.0i 0.00917391 0.0158897i
\(27\) −2.06910e6 −0.749282
\(28\) 0 0
\(29\) −1.42931e6 −0.375262 −0.187631 0.982240i \(-0.560081\pi\)
−0.187631 + 0.982240i \(0.560081\pi\)
\(30\) −2.09839e6 + 3.63452e6i −0.472978 + 0.819222i
\(31\) −4.83747e6 8.37875e6i −0.940786 1.62949i −0.763977 0.645244i \(-0.776756\pi\)
−0.176809 0.984245i \(-0.556578\pi\)
\(32\) −3.02427e6 5.23820e6i −0.509854 0.883094i
\(33\) 7.36999e6 1.27652e7i 1.08182 1.87376i
\(34\) 1.55645e6 0.199747
\(35\) 0 0
\(36\) −2.34155e6 −0.232349
\(37\) 4.33872e6 7.51488e6i 0.380587 0.659196i −0.610559 0.791971i \(-0.709055\pi\)
0.991146 + 0.132775i \(0.0423886\pi\)
\(38\) 951614. + 1.64824e6i 0.0740346 + 0.128232i
\(39\) 261454. + 452851.i 0.0180969 + 0.0313448i
\(40\) 1.08569e7 1.88047e7i 0.670556 1.16144i
\(41\) 1.32544e7 0.732541 0.366271 0.930508i \(-0.380634\pi\)
0.366271 + 0.930508i \(0.380634\pi\)
\(42\) 0 0
\(43\) −2.97554e7 −1.32726 −0.663632 0.748060i \(-0.730986\pi\)
−0.663632 + 0.748060i \(0.730986\pi\)
\(44\) −1.50404e7 + 2.60508e7i −0.604955 + 1.04781i
\(45\) −6.74815e6 1.16881e7i −0.245317 0.424902i
\(46\) −8.51018e6 1.47401e7i −0.280239 0.485388i
\(47\) 5.39846e6 9.35041e6i 0.161373 0.279506i −0.773989 0.633200i \(-0.781741\pi\)
0.935361 + 0.353694i \(0.115075\pi\)
\(48\) 3.23882e6 0.0880647
\(49\) 0 0
\(50\) 2.32702e7 0.526544
\(51\) −9.51843e6 + 1.64864e7i −0.197015 + 0.341240i
\(52\) −533567. 924164.i −0.0101198 0.0175281i
\(53\) −3.53700e7 6.12626e7i −0.615734 1.06648i −0.990255 0.139264i \(-0.955526\pi\)
0.374521 0.927218i \(-0.377807\pi\)
\(54\) 1.38224e7 2.39410e7i 0.221213 0.383152i
\(55\) −1.73381e8 −2.55488
\(56\) 0 0
\(57\) −2.32783e7 −0.292089
\(58\) 9.54828e6 1.65381e7i 0.110790 0.191893i
\(59\) −3.20200e6 5.54603e6i −0.0344023 0.0595865i 0.848312 0.529497i \(-0.177619\pi\)
−0.882714 + 0.469911i \(0.844286\pi\)
\(60\) 5.23770e7 + 9.07197e7i 0.521747 + 0.903693i
\(61\) −8.45948e7 + 1.46523e8i −0.782275 + 1.35494i 0.148338 + 0.988937i \(0.452608\pi\)
−0.930613 + 0.366004i \(0.880726\pi\)
\(62\) 1.29264e8 1.11100
\(63\) 0 0
\(64\) 7.06653e7 0.526498
\(65\) 3.07539e6 5.32673e6i 0.0213693 0.0370127i
\(66\) 9.84684e7 + 1.70552e8i 0.638777 + 1.10639i
\(67\) 5.81380e7 + 1.00698e8i 0.352471 + 0.610498i 0.986682 0.162662i \(-0.0520081\pi\)
−0.634210 + 0.773160i \(0.718675\pi\)
\(68\) 1.94249e7 3.36449e7i 0.110171 0.190822i
\(69\) 2.08176e8 1.10563
\(70\) 0 0
\(71\) 1.44496e8 0.674826 0.337413 0.941357i \(-0.390448\pi\)
0.337413 + 0.941357i \(0.390448\pi\)
\(72\) 3.96577e7 6.86892e7i 0.173913 0.301226i
\(73\) −8.00775e7 1.38698e8i −0.330033 0.571634i 0.652485 0.757802i \(-0.273727\pi\)
−0.982518 + 0.186168i \(0.940393\pi\)
\(74\) 5.79684e7 + 1.00404e8i 0.224724 + 0.389233i
\(75\) −1.42308e8 + 2.46485e8i −0.519343 + 0.899529i
\(76\) 4.75056e7 0.163337
\(77\) 0 0
\(78\) −6.98643e6 −0.0213712
\(79\) 2.44661e8 4.23766e8i 0.706713 1.22406i −0.259357 0.965782i \(-0.583511\pi\)
0.966070 0.258281i \(-0.0831561\pi\)
\(80\) −1.90486e7 3.29931e7i −0.0519945 0.0900572i
\(81\) 2.38161e8 + 4.12507e8i 0.614735 + 1.06475i
\(82\) −8.85441e7 + 1.53363e8i −0.216270 + 0.374591i
\(83\) −8.31590e7 −0.192335 −0.0961674 0.995365i \(-0.530658\pi\)
−0.0961674 + 0.995365i \(0.530658\pi\)
\(84\) 0 0
\(85\) 2.23924e8 0.465281
\(86\) 1.98777e8 3.44291e8i 0.391852 0.678708i
\(87\) 1.16785e8 + 2.02277e8i 0.218549 + 0.378538i
\(88\) −5.09466e8 8.82421e8i −0.905614 1.56857i
\(89\) −1.04042e6 + 1.80205e6i −0.00175773 + 0.00304448i −0.866903 0.498477i \(-0.833893\pi\)
0.865145 + 0.501521i \(0.167226\pi\)
\(90\) 1.80320e8 0.289703
\(91\) 0 0
\(92\) −4.24838e8 −0.618270
\(93\) −7.90513e8 + 1.36921e9i −1.09581 + 1.89800i
\(94\) 7.21274e7 + 1.24928e8i 0.0952851 + 0.165039i
\(95\) 1.36907e8 + 2.37131e8i 0.172453 + 0.298697i
\(96\) −4.94210e8 + 8.55998e8i −0.593870 + 1.02861i
\(97\) −3.15885e8 −0.362290 −0.181145 0.983456i \(-0.557980\pi\)
−0.181145 + 0.983456i \(0.557980\pi\)
\(98\) 0 0
\(99\) −6.33322e8 −0.662623
\(100\) 2.90418e8 5.03019e8i 0.290418 0.503019i
\(101\) 2.87420e8 + 4.97827e8i 0.274835 + 0.476028i 0.970093 0.242732i \(-0.0780436\pi\)
−0.695259 + 0.718760i \(0.744710\pi\)
\(102\) −1.27173e8 2.20270e8i −0.116331 0.201491i
\(103\) 7.59350e8 1.31523e9i 0.664775 1.15142i −0.314571 0.949234i \(-0.601861\pi\)
0.979346 0.202190i \(-0.0648059\pi\)
\(104\) 3.61471e7 0.0302987
\(105\) 0 0
\(106\) 9.45137e8 0.727140
\(107\) 1.00932e8 1.74819e8i 0.0744390 0.128932i −0.826403 0.563079i \(-0.809617\pi\)
0.900842 + 0.434147i \(0.142950\pi\)
\(108\) −3.45014e8 5.97581e8i −0.244022 0.422659i
\(109\) 4.36976e8 + 7.56865e8i 0.296509 + 0.513569i 0.975335 0.220730i \(-0.0708441\pi\)
−0.678826 + 0.734300i \(0.737511\pi\)
\(110\) 1.15825e9 2.00615e9i 0.754284 1.30646i
\(111\) −1.41802e9 −0.886603
\(112\) 0 0
\(113\) 1.52955e9 0.882491 0.441245 0.897386i \(-0.354537\pi\)
0.441245 + 0.897386i \(0.354537\pi\)
\(114\) 1.55508e8 2.69347e8i 0.0862343 0.149362i
\(115\) −1.22435e9 2.12063e9i −0.652777 1.13064i
\(116\) −2.38330e8 4.12800e8i −0.122213 0.211680i
\(117\) 1.12337e7 1.94573e7i 0.00554226 0.00959947i
\(118\) 8.55621e7 0.0406268
\(119\) 0 0
\(120\) −3.54834e9 −1.56210
\(121\) −2.88904e9 + 5.00396e9i −1.22523 + 2.12217i
\(122\) −1.13025e9 1.95765e9i −0.461907 0.800046i
\(123\) −1.08298e9 1.87578e9i −0.426626 0.738938i
\(124\) 1.61325e9 2.79424e9i 0.612781 1.06137i
\(125\) −4.06429e8 −0.148898
\(126\) 0 0
\(127\) −8.71958e8 −0.297426 −0.148713 0.988880i \(-0.547513\pi\)
−0.148713 + 0.988880i \(0.547513\pi\)
\(128\) 1.07636e9 1.86431e9i 0.354415 0.613865i
\(129\) 2.43123e9 + 4.21101e9i 0.772987 + 1.33885i
\(130\) 4.10895e7 + 7.11690e7i 0.0126179 + 0.0218548i
\(131\) −1.12202e9 + 1.94339e9i −0.332874 + 0.576554i −0.983074 0.183209i \(-0.941352\pi\)
0.650200 + 0.759763i \(0.274685\pi\)
\(132\) 4.91565e9 1.40928
\(133\) 0 0
\(134\) −1.55353e9 −0.416245
\(135\) 1.98860e9 3.44436e9i 0.515283 0.892497i
\(136\) 6.57981e8 + 1.13966e9i 0.164926 + 0.285660i
\(137\) −2.08071e9 3.60389e9i −0.504624 0.874035i −0.999986 0.00534799i \(-0.998298\pi\)
0.495361 0.868687i \(-0.335036\pi\)
\(138\) −1.39069e9 + 2.40874e9i −0.326418 + 0.565372i
\(139\) −6.03383e9 −1.37097 −0.685483 0.728089i \(-0.740409\pi\)
−0.685483 + 0.728089i \(0.740409\pi\)
\(140\) 0 0
\(141\) −1.76438e9 −0.375928
\(142\) −9.65283e8 + 1.67192e9i −0.199231 + 0.345078i
\(143\) −1.44315e8 2.49960e8i −0.0288601 0.0499872i
\(144\) −6.95801e7 1.20516e8i −0.0134851 0.0233569i
\(145\) 1.37370e9 2.37931e9i 0.258069 0.446988i
\(146\) 2.13979e9 0.389747
\(147\) 0 0
\(148\) 2.89385e9 0.495790
\(149\) 2.18916e9 3.79173e9i 0.363864 0.630231i −0.624729 0.780841i \(-0.714791\pi\)
0.988593 + 0.150611i \(0.0481240\pi\)
\(150\) −1.90134e9 3.29322e9i −0.306655 0.531141i
\(151\) 1.34682e9 + 2.33277e9i 0.210821 + 0.365153i 0.951972 0.306186i \(-0.0990529\pi\)
−0.741151 + 0.671339i \(0.765720\pi\)
\(152\) −8.04581e8 + 1.39358e9i −0.122257 + 0.211755i
\(153\) 8.17943e8 0.120673
\(154\) 0 0
\(155\) 1.85971e10 2.58793
\(156\) −8.71925e7 + 1.51022e8i −0.0117874 + 0.0204164i
\(157\) 6.65221e8 + 1.15220e9i 0.0873810 + 0.151348i 0.906403 0.422413i \(-0.138817\pi\)
−0.819022 + 0.573762i \(0.805484\pi\)
\(158\) 3.26885e9 + 5.66181e9i 0.417290 + 0.722768i
\(159\) −5.77997e9 + 1.00112e10i −0.717197 + 1.24222i
\(160\) 1.16265e10 1.40251
\(161\) 0 0
\(162\) −6.36401e9 −0.725961
\(163\) 1.78047e9 3.08387e9i 0.197556 0.342177i −0.750179 0.661234i \(-0.770033\pi\)
0.947736 + 0.319057i \(0.103366\pi\)
\(164\) 2.21011e9 + 3.82802e9i 0.238570 + 0.413216i
\(165\) 1.41665e10 + 2.45371e10i 1.48794 + 2.57719i
\(166\) 5.55532e8 9.62210e8i 0.0567836 0.0983521i
\(167\) −1.04285e10 −1.03752 −0.518762 0.854919i \(-0.673607\pi\)
−0.518762 + 0.854919i \(0.673607\pi\)
\(168\) 0 0
\(169\) −1.05943e10 −0.999034
\(170\) −1.49589e9 + 2.59096e9i −0.137366 + 0.237926i
\(171\) 5.00092e8 + 8.66184e8i 0.0447267 + 0.0774690i
\(172\) −4.96157e9 8.59369e9i −0.432256 0.748690i
\(173\) −1.02358e10 + 1.77290e10i −0.868793 + 1.50479i −0.00556121 + 0.999985i \(0.501770\pi\)
−0.863231 + 0.504808i \(0.831563\pi\)
\(174\) −3.12066e9 −0.258092
\(175\) 0 0
\(176\) −1.78773e9 −0.140442
\(177\) −5.23254e8 + 9.06302e8i −0.0400712 + 0.0694054i
\(178\) −1.39007e7 2.40768e7i −0.00103788 0.00179766i
\(179\) −2.73353e9 4.73461e9i −0.199014 0.344703i 0.749195 0.662350i \(-0.230441\pi\)
−0.948209 + 0.317647i \(0.897107\pi\)
\(180\) 2.25045e9 3.89789e9i 0.159787 0.276760i
\(181\) −2.11628e9 −0.146561 −0.0732807 0.997311i \(-0.523347\pi\)
−0.0732807 + 0.997311i \(0.523347\pi\)
\(182\) 0 0
\(183\) 2.76481e10 1.82236
\(184\) 7.19528e9 1.24626e10i 0.462773 0.801546i
\(185\) 8.33984e9 + 1.44450e10i 0.523462 + 0.906662i
\(186\) −1.05618e10 1.82936e10i −0.647040 1.12071i
\(187\) 5.25389e9 9.10000e9i 0.314191 0.544194i
\(188\) 3.60068e9 0.210220
\(189\) 0 0
\(190\) −3.65836e9 −0.203655
\(191\) −8.62104e9 + 1.49321e10i −0.468715 + 0.811839i −0.999361 0.0357551i \(-0.988616\pi\)
0.530645 + 0.847594i \(0.321950\pi\)
\(192\) −5.77387e9 1.00006e10i −0.306628 0.531095i
\(193\) −1.01015e10 1.74963e10i −0.524055 0.907691i −0.999608 0.0280032i \(-0.991085\pi\)
0.475552 0.879687i \(-0.342248\pi\)
\(194\) 2.11023e9 3.65502e9i 0.106960 0.185260i
\(195\) −1.00513e9 −0.0497812
\(196\) 0 0
\(197\) −2.22592e10 −1.05296 −0.526481 0.850187i \(-0.676489\pi\)
−0.526481 + 0.850187i \(0.676489\pi\)
\(198\) 4.23082e9 7.32800e9i 0.195628 0.338838i
\(199\) −8.52940e9 1.47733e10i −0.385549 0.667790i 0.606296 0.795239i \(-0.292655\pi\)
−0.991845 + 0.127449i \(0.959321\pi\)
\(200\) 9.83736e9 + 1.70388e10i 0.434754 + 0.753016i
\(201\) 9.50060e9 1.64555e10i 0.410553 0.711098i
\(202\) −7.68029e9 −0.324561
\(203\) 0 0
\(204\) −6.34862e9 −0.256651
\(205\) −1.27387e10 + 2.20641e10i −0.503771 + 0.872557i
\(206\) 1.01455e10 + 1.75725e10i 0.392527 + 0.679877i
\(207\) −4.47227e9 7.74619e9i −0.169302 0.293239i
\(208\) 3.17104e7 5.49239e7i 0.00117467 0.00203459i
\(209\) 1.28489e10 0.465810
\(210\) 0 0
\(211\) −3.19873e10 −1.11098 −0.555490 0.831523i \(-0.687469\pi\)
−0.555490 + 0.831523i \(0.687469\pi\)
\(212\) 1.17956e10 2.04305e10i 0.401058 0.694653i
\(213\) −1.18063e10 2.04492e10i −0.393013 0.680719i
\(214\) 1.34852e9 + 2.33571e9i 0.0439537 + 0.0761300i
\(215\) 2.85977e10 4.95327e10i 0.912763 1.58095i
\(216\) 2.33734e10 0.730599
\(217\) 0 0
\(218\) −1.16766e10 −0.350157
\(219\) −1.30858e10 + 2.26653e10i −0.384417 + 0.665830i
\(220\) −2.89105e10 5.00745e10i −0.832059 1.44117i
\(221\) 1.86384e8 + 3.22827e8i 0.00525586 + 0.00910342i
\(222\) 9.47289e9 1.64075e10i 0.261754 0.453372i
\(223\) −2.30967e10 −0.625428 −0.312714 0.949847i \(-0.601238\pi\)
−0.312714 + 0.949847i \(0.601238\pi\)
\(224\) 0 0
\(225\) 1.22289e10 0.318102
\(226\) −1.02179e10 + 1.76980e10i −0.260540 + 0.451269i
\(227\) 1.15447e10 + 1.99960e10i 0.288580 + 0.499836i 0.973471 0.228810i \(-0.0734835\pi\)
−0.684891 + 0.728646i \(0.740150\pi\)
\(228\) −3.88156e9 6.72305e9i −0.0951260 0.164763i
\(229\) −2.12748e10 + 3.68490e10i −0.511218 + 0.885455i 0.488698 + 0.872453i \(0.337472\pi\)
−0.999915 + 0.0130017i \(0.995861\pi\)
\(230\) 3.27164e10 0.770885
\(231\) 0 0
\(232\) 1.61460e10 0.365905
\(233\) 6.33397e9 1.09708e10i 0.140791 0.243857i −0.787004 0.616948i \(-0.788369\pi\)
0.927795 + 0.373091i \(0.121702\pi\)
\(234\) 1.50090e8 + 2.59964e8i 0.00327252 + 0.00566816i
\(235\) 1.03769e10 + 1.79733e10i 0.221953 + 0.384434i
\(236\) 1.06784e9 1.84955e9i 0.0224079 0.0388117i
\(237\) −7.99624e10 −1.64633
\(238\) 0 0
\(239\) 6.37875e10 1.26458 0.632289 0.774733i \(-0.282116\pi\)
0.632289 + 0.774733i \(0.282116\pi\)
\(240\) −3.11282e9 + 5.39156e9i −0.0605624 + 0.104897i
\(241\) 1.45802e10 + 2.52537e10i 0.278412 + 0.482223i 0.970990 0.239119i \(-0.0768587\pi\)
−0.692579 + 0.721342i \(0.743525\pi\)
\(242\) −3.85996e10 6.68565e10i −0.723459 1.25307i
\(243\) 1.85559e10 3.21398e10i 0.341393 0.591309i
\(244\) −5.64232e10 −1.01907
\(245\) 0 0
\(246\) 2.89388e10 0.503816
\(247\) −2.27911e8 + 3.94753e8i −0.00389609 + 0.00674823i
\(248\) 5.46459e10 + 9.46494e10i 0.917328 + 1.58886i
\(249\) 6.79470e9 + 1.17688e10i 0.112014 + 0.194014i
\(250\) 2.71509e9 4.70268e9i 0.0439597 0.0761404i
\(251\) 6.28939e10 1.00018 0.500088 0.865974i \(-0.333301\pi\)
0.500088 + 0.865974i \(0.333301\pi\)
\(252\) 0 0
\(253\) −1.14907e11 −1.76320
\(254\) 5.82500e9 1.00892e10i 0.0878100 0.152091i
\(255\) −1.82962e10 3.16900e10i −0.270976 0.469344i
\(256\) 3.24712e10 + 5.62419e10i 0.472519 + 0.818427i
\(257\) −5.72402e10 + 9.91429e10i −0.818469 + 1.41763i 0.0883418 + 0.996090i \(0.471843\pi\)
−0.906810 + 0.421539i \(0.861490\pi\)
\(258\) −6.49660e10 −0.912845
\(259\) 0 0
\(260\) 2.05123e9 0.0278378
\(261\) 5.01780e9 8.69109e9i 0.0669316 0.115929i
\(262\) −1.49910e10 2.59651e10i −0.196551 0.340436i
\(263\) −7.03523e9 1.21854e10i −0.0906728 0.157050i 0.817122 0.576465i \(-0.195568\pi\)
−0.907794 + 0.419415i \(0.862235\pi\)
\(264\) −8.32541e10 + 1.44200e11i −1.05484 + 1.82704i
\(265\) 1.35975e11 1.69377
\(266\) 0 0
\(267\) 3.40038e8 0.00409475
\(268\) −1.93885e10 + 3.35819e10i −0.229582 + 0.397648i
\(269\) −4.19572e10 7.26719e10i −0.488563 0.846216i 0.511350 0.859372i \(-0.329146\pi\)
−0.999913 + 0.0131560i \(0.995812\pi\)
\(270\) 2.65692e10 + 4.60192e10i 0.304257 + 0.526989i
\(271\) −9.92007e9 + 1.71821e10i −0.111726 + 0.193514i −0.916466 0.400112i \(-0.868971\pi\)
0.804740 + 0.593627i \(0.202304\pi\)
\(272\) 2.30888e9 0.0255765
\(273\) 0 0
\(274\) 5.55995e10 0.595927
\(275\) 7.85499e10 1.36052e11i 0.828225 1.43453i
\(276\) 3.47123e10 + 6.01235e10i 0.360075 + 0.623668i
\(277\) 3.58956e10 + 6.21729e10i 0.366338 + 0.634516i 0.988990 0.147983i \(-0.0472781\pi\)
−0.622652 + 0.782499i \(0.713945\pi\)
\(278\) 4.03082e10 6.98158e10i 0.404754 0.701055i
\(279\) 6.79308e10 0.671194
\(280\) 0 0
\(281\) 1.02853e11 0.984101 0.492050 0.870567i \(-0.336248\pi\)
0.492050 + 0.870567i \(0.336248\pi\)
\(282\) 1.17867e10 2.04151e10i 0.110986 0.192234i
\(283\) 2.76441e10 + 4.78810e10i 0.256191 + 0.443736i 0.965218 0.261445i \(-0.0841990\pi\)
−0.709027 + 0.705181i \(0.750866\pi\)
\(284\) 2.40940e10 + 4.17320e10i 0.219774 + 0.380660i
\(285\) 2.23727e10 3.87506e10i 0.200870 0.347918i
\(286\) 3.85630e9 0.0340819
\(287\) 0 0
\(288\) 4.24688e10 0.363750
\(289\) 5.25085e10 9.09474e10i 0.442781 0.766920i
\(290\) 1.83536e10 + 3.17894e10i 0.152381 + 0.263931i
\(291\) 2.58101e10 + 4.47044e10i 0.210995 + 0.365453i
\(292\) 2.67051e10 4.62546e10i 0.214967 0.372334i
\(293\) 1.05721e11 0.838028 0.419014 0.907980i \(-0.362376\pi\)
0.419014 + 0.907980i \(0.362376\pi\)
\(294\) 0 0
\(295\) 1.23097e10 0.0946343
\(296\) −4.90118e10 + 8.48909e10i −0.371097 + 0.642760i
\(297\) −9.33164e10 1.61629e11i −0.695912 1.20535i
\(298\) 2.92487e10 + 5.06603e10i 0.214849 + 0.372130i
\(299\) 2.03818e9 3.53024e9i 0.0147477 0.0255437i
\(300\) −9.49171e10 −0.676548
\(301\) 0 0
\(302\) −3.59891e10 −0.248966
\(303\) 4.69687e10 8.13521e10i 0.320123 0.554469i
\(304\) 1.41165e9 + 2.44505e9i 0.00947974 + 0.0164194i
\(305\) −1.62607e11 2.81644e11i −1.07595 1.86359i
\(306\) −5.46416e9 + 9.46420e9i −0.0356268 + 0.0617074i
\(307\) −8.10064e10 −0.520471 −0.260236 0.965545i \(-0.583800\pi\)
−0.260236 + 0.965545i \(0.583800\pi\)
\(308\) 0 0
\(309\) −2.48178e11 −1.54864
\(310\) −1.24235e11 + 2.15182e11i −0.764041 + 1.32336i
\(311\) 1.59217e11 + 2.75772e11i 0.965091 + 1.67159i 0.709369 + 0.704837i \(0.248980\pi\)
0.255722 + 0.966750i \(0.417687\pi\)
\(312\) −2.95348e9 5.11558e9i −0.0176457 0.0305632i
\(313\) −6.44379e10 + 1.11610e11i −0.379483 + 0.657283i −0.990987 0.133958i \(-0.957231\pi\)
0.611504 + 0.791241i \(0.290565\pi\)
\(314\) −1.77757e10 −0.103191
\(315\) 0 0
\(316\) 1.63185e11 0.920635
\(317\) 3.72361e10 6.44948e10i 0.207108 0.358722i −0.743694 0.668520i \(-0.766928\pi\)
0.950802 + 0.309798i \(0.100261\pi\)
\(318\) −7.72245e10 1.33757e11i −0.423480 0.733490i
\(319\) −6.44616e10 1.11651e11i −0.348532 0.603676i
\(320\) −6.79160e10 + 1.17634e11i −0.362074 + 0.627131i
\(321\) −3.29874e10 −0.173411
\(322\) 0 0
\(323\) −1.65945e10 −0.0848309
\(324\) −7.94246e10 + 1.37567e11i −0.400408 + 0.693526i
\(325\) 2.78660e9 + 4.82652e9i 0.0138548 + 0.0239971i
\(326\) 2.37884e10 + 4.12027e10i 0.116650 + 0.202044i
\(327\) 7.14082e10 1.23683e11i 0.345369 0.598197i
\(328\) −1.49726e11 −0.714276
\(329\) 0 0
\(330\) −3.78550e11 −1.75715
\(331\) −1.41920e11 + 2.45813e11i −0.649857 + 1.12559i 0.333300 + 0.942821i \(0.391838\pi\)
−0.983157 + 0.182764i \(0.941495\pi\)
\(332\) −1.38664e10 2.40173e10i −0.0626386 0.108493i
\(333\) 3.04635e10 + 5.27644e10i 0.135763 + 0.235148i
\(334\) 6.96662e10 1.20665e11i 0.306311 0.530547i
\(335\) −2.23505e11 −0.969583
\(336\) 0 0
\(337\) −5.61414e9 −0.0237109 −0.0118555 0.999930i \(-0.503774\pi\)
−0.0118555 + 0.999930i \(0.503774\pi\)
\(338\) 7.07735e10 1.22583e11i 0.294948 0.510865i
\(339\) −1.24975e11 2.16463e11i −0.513955 0.890197i
\(340\) 3.73383e10 + 6.46719e10i 0.151530 + 0.262458i
\(341\) 4.36339e11 7.55762e11i 1.74755 3.02685i
\(342\) −1.33632e10 −0.0528192
\(343\) 0 0
\(344\) 3.36128e11 1.29417
\(345\) −2.00076e11 + 3.46542e11i −0.760343 + 1.31695i
\(346\) −1.36758e11 2.36872e11i −0.512993 0.888529i
\(347\) −1.69923e11 2.94315e11i −0.629171 1.08976i −0.987718 0.156245i \(-0.950061\pi\)
0.358547 0.933512i \(-0.383272\pi\)
\(348\) −3.89466e10 + 6.74576e10i −0.142352 + 0.246561i
\(349\) 3.46718e10 0.125101 0.0625506 0.998042i \(-0.480077\pi\)
0.0625506 + 0.998042i \(0.480077\pi\)
\(350\) 0 0
\(351\) 6.62089e9 0.0232828
\(352\) 2.72789e11 4.72485e11i 0.947077 1.64039i
\(353\) 1.73450e11 + 3.00424e11i 0.594550 + 1.02979i 0.993610 + 0.112866i \(0.0360031\pi\)
−0.399060 + 0.916925i \(0.630664\pi\)
\(354\) −6.99105e9 1.21088e10i −0.0236607 0.0409815i
\(355\) −1.38874e11 + 2.40537e11i −0.464080 + 0.803811i
\(356\) −6.93939e8 −0.00228979
\(357\) 0 0
\(358\) 7.30438e10 0.235023
\(359\) 1.25506e11 2.17382e11i 0.398785 0.690715i −0.594792 0.803880i \(-0.702765\pi\)
0.993576 + 0.113165i \(0.0360988\pi\)
\(360\) 7.62296e10 + 1.32034e11i 0.239201 + 0.414308i
\(361\) 1.51198e11 + 2.61882e11i 0.468558 + 0.811566i
\(362\) 1.41375e10 2.44869e10i 0.0432698 0.0749455i
\(363\) 9.44221e11 2.85426
\(364\) 0 0
\(365\) 3.07848e11 0.907859
\(366\) −1.84699e11 + 3.19908e11i −0.538022 + 0.931881i
\(367\) −2.39936e11 4.15581e11i −0.690394 1.19580i −0.971709 0.236183i \(-0.924104\pi\)
0.281314 0.959616i \(-0.409230\pi\)
\(368\) −1.26243e10 2.18658e10i −0.0358831 0.0621514i
\(369\) −4.65316e10 + 8.05951e10i −0.130656 + 0.226303i
\(370\) −2.22853e11 −0.618173
\(371\) 0 0
\(372\) −5.27258e11 −1.42751
\(373\) 9.23970e10 1.60036e11i 0.247154 0.428084i −0.715581 0.698530i \(-0.753838\pi\)
0.962735 + 0.270446i \(0.0871713\pi\)
\(374\) 7.01957e10 + 1.21583e11i 0.185519 + 0.321328i
\(375\) 3.32082e10 + 5.75183e10i 0.0867171 + 0.150198i
\(376\) −6.09831e10 + 1.05626e11i −0.157349 + 0.272536i
\(377\) 4.57361e9 0.0116607
\(378\) 0 0
\(379\) −7.08908e11 −1.76487 −0.882437 0.470431i \(-0.844098\pi\)
−0.882437 + 0.470431i \(0.844098\pi\)
\(380\) −4.56574e10 + 7.90809e10i −0.112327 + 0.194556i
\(381\) 7.12453e10 + 1.23401e11i 0.173218 + 0.300023i
\(382\) −1.15183e11 1.99503e11i −0.276761 0.479364i
\(383\) −6.18945e10 + 1.07204e11i −0.146980 + 0.254576i −0.930110 0.367282i \(-0.880289\pi\)
0.783130 + 0.621858i \(0.213622\pi\)
\(384\) −3.51785e11 −0.825633
\(385\) 0 0
\(386\) 2.69926e11 0.618874
\(387\) 1.04461e11 1.80932e11i 0.236731 0.410029i
\(388\) −5.26724e10 9.12313e10i −0.117989 0.204362i
\(389\) 1.48985e11 + 2.58050e11i 0.329891 + 0.571388i 0.982490 0.186315i \(-0.0596547\pi\)
−0.652599 + 0.757704i \(0.726321\pi\)
\(390\) 6.71462e9 1.16301e10i 0.0146971 0.0254561i
\(391\) 1.48403e11 0.321106
\(392\) 0 0
\(393\) 3.66708e11 0.775451
\(394\) 1.48700e11 2.57556e11i 0.310869 0.538441i
\(395\) 4.70285e11 + 8.14557e11i 0.972018 + 1.68358i
\(396\) −1.05604e11 1.82911e11i −0.215800 0.373776i
\(397\) −2.66713e11 + 4.61960e11i −0.538873 + 0.933356i 0.460092 + 0.887871i \(0.347817\pi\)
−0.998965 + 0.0454846i \(0.985517\pi\)
\(398\) 2.27918e11 0.455307
\(399\) 0 0
\(400\) 3.45196e10 0.0674212
\(401\) −2.07820e11 + 3.59954e11i −0.401363 + 0.695181i −0.993891 0.110369i \(-0.964797\pi\)
0.592528 + 0.805550i \(0.298130\pi\)
\(402\) 1.26935e11 + 2.19858e11i 0.242418 + 0.419879i
\(403\) 1.54794e10 + 2.68110e10i 0.0292335 + 0.0506338i
\(404\) −9.58521e10 + 1.66021e11i −0.179013 + 0.310060i
\(405\) −9.15581e11 −1.69102
\(406\) 0 0
\(407\) 7.82704e11 1.41391
\(408\) 1.07524e11 1.86237e11i 0.192103 0.332732i
\(409\) −5.39891e11 9.35118e11i −0.954006 1.65239i −0.736627 0.676299i \(-0.763583\pi\)
−0.217379 0.976087i \(-0.569751\pi\)
\(410\) −1.70198e11 2.94792e11i −0.297460 0.515215i
\(411\) −3.40018e11 + 5.88928e11i −0.587778 + 1.01806i
\(412\) 5.06473e11 0.866002
\(413\) 0 0
\(414\) 1.19505e11 0.199934
\(415\) 7.99237e10 1.38432e11i 0.132269 0.229097i
\(416\) 9.67733e9 + 1.67616e10i 0.0158429 + 0.0274408i
\(417\) 4.93008e11 + 8.53914e11i 0.798439 + 1.38294i
\(418\) −8.58355e10 + 1.48671e11i −0.137522 + 0.238196i
\(419\) −2.20998e11 −0.350289 −0.175144 0.984543i \(-0.556039\pi\)
−0.175144 + 0.984543i \(0.556039\pi\)
\(420\) 0 0
\(421\) 3.47478e11 0.539086 0.269543 0.962988i \(-0.413127\pi\)
0.269543 + 0.962988i \(0.413127\pi\)
\(422\) 2.13687e11 3.70116e11i 0.327998 0.568109i
\(423\) 3.79043e10 + 6.56522e10i 0.0575648 + 0.0997052i
\(424\) 3.99552e11 + 6.92045e11i 0.600381 + 1.03989i
\(425\) −1.01448e11 + 1.75713e11i −0.150832 + 0.261249i
\(426\) 3.15483e11 0.464122
\(427\) 0 0
\(428\) 6.73196e10 0.0969716
\(429\) −2.35831e10 + 4.08472e10i −0.0336158 + 0.0582243i
\(430\) 3.82086e11 + 6.61792e11i 0.538956 + 0.933499i
\(431\) −6.17869e10 1.07018e11i −0.0862479 0.149386i 0.819674 0.572830i \(-0.194154\pi\)
−0.905922 + 0.423444i \(0.860821\pi\)
\(432\) 2.05045e10 3.55148e10i 0.0283251 0.0490606i
\(433\) −7.27679e11 −0.994820 −0.497410 0.867516i \(-0.665716\pi\)
−0.497410 + 0.867516i \(0.665716\pi\)
\(434\) 0 0
\(435\) −4.48964e11 −0.601188
\(436\) −1.45728e11 + 2.52408e11i −0.193131 + 0.334513i
\(437\) 9.07340e10 + 1.57156e11i 0.119015 + 0.206141i
\(438\) −1.74836e11 3.02825e11i −0.226985 0.393150i
\(439\) 2.92983e11 5.07461e11i 0.376489 0.652097i −0.614060 0.789259i \(-0.710465\pi\)
0.990549 + 0.137162i \(0.0437981\pi\)
\(440\) 1.95858e12 2.49117
\(441\) 0 0
\(442\) −4.98045e9 −0.00620681
\(443\) 1.05773e11 1.83204e11i 0.130484 0.226006i −0.793379 0.608728i \(-0.791680\pi\)
0.923863 + 0.382722i \(0.125013\pi\)
\(444\) −2.36448e11 4.09541e11i −0.288744 0.500120i
\(445\) −1.99988e9 3.46389e9i −0.00241759 0.00418739i
\(446\) 1.54294e11 2.67245e11i 0.184647 0.319818i
\(447\) −7.15480e11 −0.847645
\(448\) 0 0
\(449\) −9.21048e11 −1.06948 −0.534741 0.845016i \(-0.679591\pi\)
−0.534741 + 0.845016i \(0.679591\pi\)
\(450\) −8.16936e10 + 1.41497e11i −0.0939143 + 0.162664i
\(451\) 5.97772e11 + 1.03537e12i 0.680363 + 1.17842i
\(452\) 2.55045e11 + 4.41751e11i 0.287405 + 0.497800i
\(453\) 2.20090e11 3.81208e11i 0.245561 0.425324i
\(454\) −3.08491e11 −0.340794
\(455\) 0 0
\(456\) 2.62961e11 0.284806
\(457\) −4.05592e11 + 7.02506e11i −0.434977 + 0.753403i −0.997294 0.0735191i \(-0.976577\pi\)
0.562316 + 0.826922i \(0.309910\pi\)
\(458\) −2.84247e11 4.92330e11i −0.301857 0.522831i
\(459\) 1.20519e11 + 2.08746e11i 0.126736 + 0.219513i
\(460\) 4.08309e11 7.07212e11i 0.425186 0.736444i
\(461\) −1.90069e11 −0.196001 −0.0980004 0.995186i \(-0.531245\pi\)
−0.0980004 + 0.995186i \(0.531245\pi\)
\(462\) 0 0
\(463\) 4.76945e11 0.482341 0.241170 0.970483i \(-0.422469\pi\)
0.241170 + 0.970483i \(0.422469\pi\)
\(464\) 1.41642e10 2.45331e10i 0.0141860 0.0245709i
\(465\) −1.51952e12 2.63188e12i −1.50719 2.61052i
\(466\) 8.46264e10 + 1.46577e11i 0.0831322 + 0.143989i
\(467\) −5.31958e11 + 9.21379e11i −0.517549 + 0.896422i 0.482243 + 0.876038i \(0.339822\pi\)
−0.999792 + 0.0203841i \(0.993511\pi\)
\(468\) 7.49268e9 0.00721990
\(469\) 0 0
\(470\) −2.77285e11 −0.262111
\(471\) 1.08707e11 1.88286e11i 0.101780 0.176288i
\(472\) 3.61710e10 + 6.26500e10i 0.0335445 + 0.0581008i
\(473\) −1.34196e12 2.32435e12i −1.23272 2.13514i
\(474\) 5.34178e11 9.25223e11i 0.486053 0.841868i
\(475\) −2.48102e11 −0.223619
\(476\) 0 0
\(477\) 4.96687e11 0.439289
\(478\) −4.26124e11 + 7.38068e11i −0.373345 + 0.646653i
\(479\) 4.21707e11 + 7.30419e11i 0.366017 + 0.633960i 0.988939 0.148324i \(-0.0473878\pi\)
−0.622922 + 0.782284i \(0.714054\pi\)
\(480\) −9.49966e11 1.64539e12i −0.816812 1.41476i
\(481\) −1.38834e10 + 2.40468e10i −0.0118261 + 0.0204835i
\(482\) −3.89605e11 −0.328785
\(483\) 0 0
\(484\) −1.92694e12 −1.59611
\(485\) 3.03595e11 5.25842e11i 0.249148 0.431537i
\(486\) 2.47920e11 + 4.29411e11i 0.201581 + 0.349148i
\(487\) −5.76008e11 9.97675e11i −0.464032 0.803728i 0.535125 0.844773i \(-0.320265\pi\)
−0.999157 + 0.0410453i \(0.986931\pi\)
\(488\) 9.55615e11 1.65517e12i 0.762770 1.32116i
\(489\) −5.81910e11 −0.460220
\(490\) 0 0
\(491\) −9.68703e11 −0.752184 −0.376092 0.926582i \(-0.622732\pi\)
−0.376092 + 0.926582i \(0.622732\pi\)
\(492\) 3.61164e11 6.25554e11i 0.277883 0.481307i
\(493\) 8.32530e10 + 1.44198e11i 0.0634729 + 0.109938i
\(494\) −3.04506e9 5.27419e9i −0.00230051 0.00398460i
\(495\) 6.08682e11 1.05427e12i 0.455688 0.789274i
\(496\) 1.91754e11 0.142258
\(497\) 0 0
\(498\) −1.81564e11 −0.132281
\(499\) −1.31410e12 + 2.27609e12i −0.948805 + 1.64338i −0.200857 + 0.979621i \(0.564373\pi\)
−0.747948 + 0.663758i \(0.768961\pi\)
\(500\) −6.77702e10 1.17381e11i −0.0484924 0.0839913i
\(501\) 8.52085e11 + 1.47585e12i 0.604245 + 1.04658i
\(502\) −4.20154e11 + 7.27728e11i −0.295285 + 0.511449i
\(503\) 3.95070e11 0.275181 0.137590 0.990489i \(-0.456064\pi\)
0.137590 + 0.990489i \(0.456064\pi\)
\(504\) 0 0
\(505\) −1.10495e12 −0.756019
\(506\) 7.67618e11 1.32955e12i 0.520556 0.901630i
\(507\) 8.65628e11 + 1.49931e12i 0.581829 + 1.00776i
\(508\) −1.45395e11 2.51832e11i −0.0968641 0.167774i
\(509\) −3.32078e11 + 5.75177e11i −0.219286 + 0.379814i −0.954590 0.297923i \(-0.903706\pi\)
0.735304 + 0.677737i \(0.237039\pi\)
\(510\) 4.88901e11 0.320004
\(511\) 0 0
\(512\) 2.34512e11 0.150817
\(513\) −1.47371e11 + 2.55255e11i −0.0939474 + 0.162722i
\(514\) −7.64770e11 1.32462e12i −0.483278 0.837062i
\(515\) 1.45961e12 + 2.52813e12i 0.914336 + 1.58368i
\(516\) −8.10793e11 + 1.40433e12i −0.503485 + 0.872061i
\(517\) 9.73882e11 0.599513
\(518\) 0 0
\(519\) 3.34537e12 2.02391
\(520\) −3.47408e10 + 6.01728e10i −0.0208365 + 0.0360898i
\(521\) −2.61383e11 4.52729e11i −0.155420 0.269196i 0.777792 0.628522i \(-0.216340\pi\)
−0.933212 + 0.359326i \(0.883007\pi\)
\(522\) 6.70415e10 + 1.16119e11i 0.0395209 + 0.0684522i
\(523\) 1.54568e12 2.67719e12i 0.903360 1.56467i 0.0802570 0.996774i \(-0.474426\pi\)
0.823103 0.567892i \(-0.192241\pi\)
\(524\) −7.48366e11 −0.433634
\(525\) 0 0
\(526\) 1.87991e11 0.107078
\(527\) −5.63538e11 + 9.76076e11i −0.318255 + 0.551234i
\(528\) 1.46071e11 + 2.53002e11i 0.0817920 + 0.141668i
\(529\) 8.91523e10 + 1.54416e11i 0.0494974 + 0.0857319i
\(530\) −9.08365e11 + 1.57334e12i −0.500057 + 0.866124i
\(531\) 4.49645e10 0.0245440
\(532\) 0 0
\(533\) −4.24125e10 −0.0227626
\(534\) −2.27158e9 + 3.93449e9i −0.00120891 + 0.00209389i
\(535\) 1.94010e11 + 3.36035e11i 0.102384 + 0.177334i
\(536\) −6.56749e11 1.13752e12i −0.343683 0.595276i
\(537\) −4.46698e11 + 7.73704e11i −0.231809 + 0.401504i
\(538\) 1.12116e12 0.576960
\(539\) 0 0
\(540\) 1.32636e12 0.671259
\(541\) 7.37449e11 1.27730e12i 0.370121 0.641069i −0.619462 0.785026i \(-0.712649\pi\)
0.989584 + 0.143957i \(0.0459827\pi\)
\(542\) −1.32539e11 2.29565e11i −0.0659702 0.114264i
\(543\) 1.72916e11 + 2.99499e11i 0.0853561 + 0.147841i
\(544\) −3.52311e11 + 6.10220e11i −0.172477 + 0.298739i
\(545\) −1.67990e12 −0.815642
\(546\) 0 0
\(547\) 2.12294e12 1.01390 0.506949 0.861976i \(-0.330773\pi\)
0.506949 + 0.861976i \(0.330773\pi\)
\(548\) 6.93897e11 1.20186e12i 0.328687 0.569302i
\(549\) −5.93967e11 1.02878e12i −0.279053 0.483334i
\(550\) 1.04948e12 + 1.81776e12i 0.489039 + 0.847040i
\(551\) −1.01802e11 + 1.76326e11i −0.0470515 + 0.0814957i
\(552\) −2.35163e12 −1.07806
\(553\) 0 0
\(554\) −9.59181e11 −0.432620
\(555\) 1.36285e12 2.36053e12i 0.609719 1.05606i
\(556\) −1.00611e12 1.74264e12i −0.446489 0.773341i
\(557\) 1.76428e12 + 3.05583e12i 0.776641 + 1.34518i 0.933868 + 0.357619i \(0.116411\pi\)
−0.157227 + 0.987563i \(0.550255\pi\)
\(558\) −4.53803e11 + 7.86009e11i −0.198159 + 0.343221i
\(559\) 9.52137e10 0.0412426
\(560\) 0 0
\(561\) −1.71712e12 −0.731928
\(562\) −6.87097e11 + 1.19009e12i −0.290539 + 0.503228i
\(563\) 1.67640e12 + 2.90361e12i 0.703218 + 1.21801i 0.967331 + 0.253517i \(0.0815875\pi\)
−0.264113 + 0.964492i \(0.585079\pi\)
\(564\) −2.94202e11 5.09572e11i −0.122430 0.212056i
\(565\) −1.47004e12 + 2.54618e12i −0.606892 + 1.05117i
\(566\) −7.38691e11 −0.302544
\(567\) 0 0
\(568\) −1.63228e12 −0.658000
\(569\) −1.49682e12 + 2.59257e12i −0.598637 + 1.03687i 0.394385 + 0.918945i \(0.370958\pi\)
−0.993022 + 0.117925i \(0.962376\pi\)
\(570\) 2.98915e11 + 5.17736e11i 0.118607 + 0.205434i
\(571\) −2.33634e12 4.04665e12i −0.919756 1.59306i −0.799785 0.600287i \(-0.795053\pi\)
−0.119971 0.992777i \(-0.538280\pi\)
\(572\) 4.81276e10 8.33595e10i 0.0187980 0.0325592i
\(573\) 2.81761e12 1.09190
\(574\) 0 0
\(575\) 2.21875e12 0.846453
\(576\) −2.48082e11 + 4.29690e11i −0.0939061 + 0.162650i
\(577\) 1.81399e12 + 3.14193e12i 0.681310 + 1.18006i 0.974581 + 0.224034i \(0.0719228\pi\)
−0.293271 + 0.956029i \(0.594744\pi\)
\(578\) 7.01551e11 + 1.21512e12i 0.261447 + 0.452840i
\(579\) −1.65073e12 + 2.85915e12i −0.610411 + 1.05726i
\(580\) 9.16232e11 0.336186
\(581\) 0 0
\(582\) −6.89683e11 −0.249170
\(583\) 3.19037e12 5.52588e12i 1.14375 1.98104i
\(584\) 9.04585e11 + 1.56679e12i 0.321804 + 0.557381i
\(585\) 2.15933e10 + 3.74007e10i 0.00762286 + 0.0132032i
\(586\) −7.06258e11 + 1.22327e12i −0.247414 + 0.428533i
\(587\) 3.97200e12 1.38082 0.690411 0.723417i \(-0.257430\pi\)
0.690411 + 0.723417i \(0.257430\pi\)
\(588\) 0 0
\(589\) −1.37819e12 −0.471835
\(590\) −8.22332e10 + 1.42432e11i −0.0279392 + 0.0483921i
\(591\) 1.81874e12 + 3.15015e12i 0.613236 + 1.06216i
\(592\) 8.59921e10 + 1.48943e11i 0.0287747 + 0.0498392i
\(593\) −1.33718e12 + 2.31606e12i −0.444061 + 0.769137i −0.997986 0.0634297i \(-0.979796\pi\)
0.553925 + 0.832567i \(0.313129\pi\)
\(594\) 2.49355e12 0.821825
\(595\) 0 0
\(596\) 1.46013e12 0.474005
\(597\) −1.39383e12 + 2.41418e12i −0.449081 + 0.777831i
\(598\) 2.72316e10 + 4.71665e10i 0.00870799 + 0.0150827i
\(599\) −2.42261e12 4.19608e12i −0.768887 1.33175i −0.938167 0.346184i \(-0.887477\pi\)
0.169279 0.985568i \(-0.445856\pi\)
\(600\) 1.60757e12 2.78439e12i 0.506394 0.877100i
\(601\) −4.64764e12 −1.45311 −0.726553 0.687110i \(-0.758879\pi\)
−0.726553 + 0.687110i \(0.758879\pi\)
\(602\) 0 0
\(603\) −8.16411e11 −0.251467
\(604\) −4.49153e11 + 7.77956e11i −0.137318 + 0.237842i
\(605\) −5.55327e12 9.61855e12i −1.68519 2.91884i
\(606\) 6.27536e11 + 1.08692e12i 0.189022 + 0.327395i
\(607\) 3.26224e12 5.65036e12i 0.975363 1.68938i 0.296633 0.954992i \(-0.404136\pi\)
0.678731 0.734387i \(-0.262530\pi\)
\(608\) −8.61613e11 −0.255709
\(609\) 0 0
\(610\) 4.34510e12 1.27062
\(611\) −1.72745e10 + 2.99203e10i −0.00501440 + 0.00868520i
\(612\) 1.36388e11 + 2.36232e11i 0.0393003 + 0.0680701i
\(613\) 4.77268e11 + 8.26652e11i 0.136518 + 0.236456i 0.926176 0.377091i \(-0.123075\pi\)
−0.789658 + 0.613547i \(0.789742\pi\)
\(614\) 5.41152e11 9.37303e11i 0.153660 0.266148i
\(615\) 4.16338e12 1.17357
\(616\) 0 0
\(617\) −4.50764e12 −1.25218 −0.626088 0.779752i \(-0.715345\pi\)
−0.626088 + 0.779752i \(0.715345\pi\)
\(618\) 1.65792e12 2.87160e12i 0.457209 0.791909i
\(619\) −1.82173e12 3.15533e12i −0.498742 0.863847i 0.501257 0.865298i \(-0.332871\pi\)
−0.999999 + 0.00145199i \(0.999538\pi\)
\(620\) 3.10098e12 + 5.37105e12i 0.842822 + 1.45981i
\(621\) 1.31793e12 2.28272e12i 0.355614 0.615942i
\(622\) −4.25452e12 −1.13971
\(623\) 0 0
\(624\) −1.03639e10 −0.00273647
\(625\) 2.09148e12 3.62255e12i 0.548269 0.949630i
\(626\) −8.60937e11 1.49119e12i −0.224072 0.388104i
\(627\) −1.04985e12 1.81840e12i −0.271284 0.469877i
\(628\) −2.21845e11 + 3.84247e11i −0.0569156 + 0.0985807i
\(629\) −1.01087e12 −0.257495
\(630\) 0 0
\(631\) 3.61498e12 0.907766 0.453883 0.891061i \(-0.350038\pi\)
0.453883 + 0.891061i \(0.350038\pi\)
\(632\) −2.76378e12 + 4.78701e12i −0.689092 + 1.19354i
\(633\) 2.61359e12 + 4.52687e12i 0.647025 + 1.12068i
\(634\) 4.97501e11 + 8.61698e11i 0.122290 + 0.211813i
\(635\) 8.38034e11 1.45152e12i 0.204541 0.354275i
\(636\) −3.85513e12 −0.934292
\(637\) 0 0
\(638\) 1.72251e12 0.411593
\(639\) −5.07275e11 + 8.78626e11i −0.120362 + 0.208473i
\(640\) 2.06896e12 + 3.58355e12i 0.487465 + 0.844313i
\(641\) 1.33152e12 + 2.30626e12i 0.311521 + 0.539570i 0.978692 0.205335i \(-0.0658283\pi\)
−0.667171 + 0.744905i \(0.732495\pi\)
\(642\) 2.20368e11 3.81688e11i 0.0511965 0.0886750i
\(643\) 4.09899e12 0.945644 0.472822 0.881158i \(-0.343235\pi\)
0.472822 + 0.881158i \(0.343235\pi\)
\(644\) 0 0
\(645\) −9.34656e12 −2.12634
\(646\) 1.10858e11 1.92011e11i 0.0250449 0.0433790i
\(647\) −3.05663e12 5.29423e12i −0.685761 1.18777i −0.973197 0.229973i \(-0.926136\pi\)
0.287436 0.957800i \(-0.407197\pi\)
\(648\) −2.69036e12 4.65983e12i −0.599408 1.03820i
\(649\) 2.88820e11 5.00251e11i 0.0639037 0.110685i
\(650\) −7.44619e10 −0.0163615
\(651\) 0 0
\(652\) 1.18754e12 0.257356
\(653\) −3.83135e12 + 6.63609e12i −0.824598 + 1.42825i 0.0776274 + 0.996982i \(0.475266\pi\)
−0.902226 + 0.431264i \(0.858068\pi\)
\(654\) 9.54066e11 + 1.65249e12i 0.203929 + 0.353215i
\(655\) −2.15673e12 3.73557e12i −0.457836 0.792996i
\(656\) −1.31349e11 + 2.27503e11i −0.0276923 + 0.0479644i
\(657\) 1.12450e12 0.235459
\(658\) 0 0
\(659\) −8.20110e9 −0.00169390 −0.000846950 1.00000i \(-0.500270\pi\)
−0.000846950 1.00000i \(0.500270\pi\)
\(660\) −4.72440e12 + 8.18291e12i −0.969168 + 1.67865i
\(661\) −1.60461e12 2.77927e12i −0.326936 0.566270i 0.654966 0.755658i \(-0.272683\pi\)
−0.981902 + 0.189388i \(0.939350\pi\)
\(662\) −1.89615e12 3.28424e12i −0.383719 0.664620i
\(663\) 3.04579e10 5.27546e10i 0.00612194 0.0106035i
\(664\) 9.39395e11 0.187539
\(665\) 0 0
\(666\) −8.14030e11 −0.160327
\(667\) 9.10404e11 1.57687e12i 0.178102 0.308481i
\(668\) −1.73891e12 3.01188e12i −0.337895 0.585252i
\(669\) 1.88717e12 + 3.26867e12i 0.364244 + 0.630889i
\(670\) 1.49309e12 2.58611e12i 0.286253 0.495805i
\(671\) −1.52609e13 −2.90622
\(672\) 0 0
\(673\) −4.91229e12 −0.923031 −0.461515 0.887132i \(-0.652694\pi\)
−0.461515 + 0.887132i \(0.652694\pi\)
\(674\) 3.75045e10 6.49596e10i 0.00700025 0.0121248i
\(675\) 1.80186e12 + 3.12092e12i 0.334083 + 0.578649i
\(676\) −1.76655e12 3.05975e12i −0.325360 0.563541i
\(677\) 1.55955e12 2.70122e12i 0.285332 0.494209i −0.687358 0.726319i \(-0.741230\pi\)
0.972690 + 0.232110i \(0.0745628\pi\)
\(678\) 3.33952e12 0.606946
\(679\) 0 0
\(680\) −2.52953e12 −0.453680
\(681\) 1.88657e12 3.26764e12i 0.336133 0.582200i
\(682\) 5.82981e12 + 1.00975e13i 1.03187 + 1.78725i
\(683\) −1.45903e12 2.52712e12i −0.256550 0.444357i 0.708766 0.705444i \(-0.249252\pi\)
−0.965315 + 0.261087i \(0.915919\pi\)
\(684\) −1.66776e11 + 2.88865e11i −0.0291327 + 0.0504594i
\(685\) 7.99902e12 1.38813
\(686\) 0 0
\(687\) 6.95322e12 1.19092
\(688\) 2.94871e11 5.10731e11i 0.0501746 0.0869049i
\(689\) 1.13180e11 + 1.96033e11i 0.0191330 + 0.0331393i
\(690\) −2.67316e12 4.63006e12i −0.448957 0.777616i
\(691\) −2.37348e12 + 4.11100e12i −0.396037 + 0.685955i −0.993233 0.116140i \(-0.962948\pi\)
0.597196 + 0.802095i \(0.296281\pi\)
\(692\) −6.82712e12 −1.13178
\(693\) 0 0
\(694\) 4.54058e12 0.743009
\(695\) 5.79908e12 1.00443e13i 0.942817 1.63301i
\(696\) −1.31924e12 2.28500e12i −0.213100 0.369100i
\(697\) −7.72030e11 1.33719e12i −0.123904 0.214609i
\(698\) −2.31620e11 + 4.01177e11i −0.0369340 + 0.0639716i
\(699\) −2.07013e12 −0.327981
\(700\) 0 0
\(701\) −2.24423e11 −0.0351023 −0.0175512 0.999846i \(-0.505587\pi\)
−0.0175512 + 0.999846i \(0.505587\pi\)
\(702\) −4.42300e10 + 7.66085e10i −0.00687384 + 0.0119058i
\(703\) −6.18048e11 1.07049e12i −0.0954385 0.165304i
\(704\) 3.18700e12 + 5.52005e12i 0.488996 + 0.846966i
\(705\) 1.69573e12 2.93709e12i 0.258527 0.447782i
\(706\) −4.63484e12 −0.702123
\(707\) 0 0
\(708\) −3.49001e11 −0.0522007
\(709\) −2.12731e12 + 3.68462e12i −0.316172 + 0.547626i −0.979686 0.200538i \(-0.935731\pi\)
0.663514 + 0.748164i \(0.269064\pi\)
\(710\) −1.85546e12 3.21374e12i −0.274024 0.474623i
\(711\) 1.71784e12 + 2.97539e12i 0.252099 + 0.436648i
\(712\) 1.17529e10 2.03567e10i 0.00171390 0.00296857i
\(713\) 1.23250e13 1.78601
\(714\) 0 0
\(715\) 5.54800e11 0.0793888
\(716\) 9.11606e11 1.57895e12i 0.129628 0.224522i
\(717\) −5.21191e12 9.02729e12i −0.736479 1.27562i
\(718\) 1.67685e12 + 2.90438e12i 0.235469 + 0.407844i
\(719\) 2.14465e12 3.71465e12i 0.299280 0.518368i −0.676692 0.736267i \(-0.736587\pi\)
0.975971 + 0.217899i \(0.0699203\pi\)
\(720\) 2.67492e11 0.0370950
\(721\) 0 0
\(722\) −4.04023e12 −0.553335
\(723\) 2.38262e12 4.12682e12i 0.324289 0.561685i
\(724\) −3.52880e11 6.11207e11i −0.0477314 0.0826732i
\(725\) 1.24470e12 + 2.15588e12i 0.167318 + 0.289804i
\(726\) −6.30774e12 + 1.09253e13i −0.842673 + 1.45955i
\(727\) 1.28935e13 1.71185 0.855926 0.517098i \(-0.172988\pi\)
0.855926 + 0.517098i \(0.172988\pi\)
\(728\) 0 0
\(729\) 3.31084e12 0.434174
\(730\) −2.05654e12 + 3.56203e12i −0.268030 + 0.464242i
\(731\) 1.73316e12 + 3.00193e12i 0.224497 + 0.388841i
\(732\) 4.61019e12 + 7.98508e12i 0.593497 + 1.02797i
\(733\) −1.35724e12 + 2.35080e12i −0.173655 + 0.300780i −0.939695 0.342013i \(-0.888891\pi\)
0.766040 + 0.642793i \(0.222225\pi\)
\(734\) 6.41143e12 0.815309
\(735\) 0 0
\(736\) 7.70531e12 0.967921
\(737\) −5.24405e12 + 9.08295e12i −0.654731 + 1.13403i
\(738\) −6.21696e11 1.07681e12i −0.0771480 0.133624i
\(739\) 4.81290e12 + 8.33618e12i 0.593617 + 1.02818i 0.993740 + 0.111714i \(0.0356340\pi\)
−0.400123 + 0.916461i \(0.631033\pi\)
\(740\) −2.78126e12 + 4.81729e12i −0.340957 + 0.590554i
\(741\) 7.44880e10 0.00907620
\(742\) 0 0
\(743\) −1.24362e13 −1.49706 −0.748529 0.663103i \(-0.769239\pi\)
−0.748529 + 0.663103i \(0.769239\pi\)
\(744\) 8.92993e12 1.54671e13i 1.06849 1.85068i
\(745\) 4.20797e12 + 7.28842e12i 0.500460 + 0.866823i
\(746\) 1.23449e12 + 2.13820e12i 0.145936 + 0.252769i
\(747\) 2.91943e11 5.05660e11i 0.0343048 0.0594177i
\(748\) 3.50425e12 0.409296
\(749\) 0 0
\(750\) −8.87371e11 −0.102407
\(751\) −2.13480e12 + 3.69758e12i −0.244893 + 0.424168i −0.962102 0.272691i \(-0.912086\pi\)
0.717208 + 0.696859i \(0.245420\pi\)
\(752\) 1.06996e11 + 1.85322e11i 0.0122008 + 0.0211323i
\(753\) −5.13889e12 8.90081e12i −0.582494 1.00891i
\(754\) −3.05534e10 + 5.29200e10i −0.00344262 + 0.00596278i
\(755\) −5.17770e12 −0.579930
\(756\) 0 0
\(757\) 9.76840e12 1.08116 0.540582 0.841291i \(-0.318204\pi\)
0.540582 + 0.841291i \(0.318204\pi\)
\(758\) 4.73576e12 8.20258e12i 0.521049 0.902484i
\(759\) 9.38871e12 + 1.62617e13i 1.02688 + 1.77860i
\(760\) −1.54656e12 2.67872e12i −0.168153 0.291250i
\(761\) −6.16679e12 + 1.06812e13i −0.666543 + 1.15449i 0.312321 + 0.949977i \(0.398893\pi\)
−0.978864 + 0.204510i \(0.934440\pi\)
\(762\) −1.90378e12 −0.204559
\(763\) 0 0
\(764\) −5.75008e12 −0.610595
\(765\) −7.86121e11 + 1.36160e12i −0.0829875 + 0.143739i
\(766\) −8.26955e11 1.43233e12i −0.0867865 0.150319i
\(767\) 1.02460e10 + 1.77467e10i 0.00106900 + 0.00185156i
\(768\) 5.30627e12 9.19074e12i 0.550382 0.953290i
\(769\) −1.68919e13 −1.74185 −0.870926 0.491415i \(-0.836480\pi\)
−0.870926 + 0.491415i \(0.836480\pi\)
\(770\) 0 0
\(771\) 1.87078e13 1.90668
\(772\) 3.36875e12 5.83485e12i 0.341343 0.591224i
\(773\) −7.35930e12 1.27467e13i −0.741359 1.28407i −0.951877 0.306481i \(-0.900848\pi\)
0.210518 0.977590i \(-0.432485\pi\)
\(774\) 1.39567e12 + 2.41738e12i 0.139781 + 0.242108i
\(775\) −8.42535e12 + 1.45931e13i −0.838939 + 1.45308i
\(776\) 3.56835e12 0.353257
\(777\) 0 0
\(778\) −3.98111e12 −0.389579
\(779\) 9.44040e11 1.63512e12i 0.0918484 0.159086i
\(780\) −1.67601e11 2.90293e11i −0.0162125 0.0280809i
\(781\) 6.51674e12 + 1.12873e13i 0.626760 + 1.08558i
\(782\) −9.91388e11 + 1.71713e12i −0.0948010 + 0.164200i
\(783\) 2.95738e12 0.281177
\(784\) 0 0
\(785\) −2.55736e12 −0.240369
\(786\) −2.44974e12 + 4.24308e12i −0.228939 + 0.396534i
\(787\) 9.12328e12 + 1.58020e13i 0.847744 + 1.46834i 0.883217 + 0.468965i \(0.155373\pi\)
−0.0354729 + 0.999371i \(0.511294\pi\)
\(788\) −3.71163e12 6.42873e12i −0.342923 0.593960i
\(789\) −1.14966e12 + 1.99127e12i −0.105614 + 0.182929i
\(790\) −1.25667e13 −1.14789
\(791\) 0 0
\(792\) 7.15424e12 0.646101
\(793\) 2.70694e11 4.68855e11i 0.0243080 0.0421027i
\(794\) −3.56348e12 6.17212e12i −0.318186 0.551115i
\(795\) −1.11102e13 1.92434e13i −0.986437 1.70856i
\(796\) 2.84448e12 4.92678e12i 0.251127 0.434965i
\(797\) −1.21558e13 −1.06714 −0.533568 0.845757i \(-0.679149\pi\)
−0.533568 + 0.845757i \(0.679149\pi\)
\(798\) 0 0
\(799\) −1.25778e12 −0.109180
\(800\) −5.26733e12 + 9.12328e12i −0.454659 + 0.787492i
\(801\) −7.30510e9 1.26528e10i −0.000627017 0.00108603i
\(802\) −2.77662e12 4.80925e12i −0.236991 0.410481i
\(803\) 7.22298e12 1.25106e13i 0.613051 1.06184i
\(804\) 6.33673e12 0.534827
\(805\) 0 0
\(806\) −4.13631e11 −0.0345227
\(807\) −6.85641e12 + 1.18757e13i −0.569070 + 0.985659i
\(808\) −3.24681e12 5.62364e12i −0.267982 0.464158i
\(809\) 1.30946e12 + 2.26806e12i 0.107479 + 0.186160i 0.914749 0.404024i \(-0.132389\pi\)
−0.807269 + 0.590184i \(0.799055\pi\)
\(810\) 6.11641e12 1.05939e13i 0.499246 0.864719i
\(811\) 1.16994e13 0.949662 0.474831 0.880077i \(-0.342509\pi\)
0.474831 + 0.880077i \(0.342509\pi\)
\(812\) 0 0
\(813\) 3.24217e12 0.260272
\(814\) −5.22875e12 + 9.05646e12i −0.417434 + 0.723017i
\(815\) 3.42240e12 + 5.92777e12i 0.271720 + 0.470633i
\(816\) −1.88652e11 3.26755e11i −0.0148955 0.0257998i
\(817\) −2.11932e12 + 3.67077e12i −0.166417 + 0.288242i
\(818\) 1.44267e13 1.12662
\(819\) 0 0
\(820\) −8.49649e12 −0.656262
\(821\) −2.58836e12 + 4.48318e12i −0.198830 + 0.344383i −0.948149 0.317826i \(-0.897047\pi\)
0.749320 + 0.662209i \(0.230381\pi\)
\(822\) −4.54288e12 7.86850e12i −0.347063 0.601131i
\(823\) 3.92009e12 + 6.78979e12i 0.297849 + 0.515890i 0.975644 0.219362i \(-0.0703974\pi\)
−0.677795 + 0.735251i \(0.737064\pi\)
\(824\) −8.57790e12 + 1.48574e13i −0.648200 + 1.12271i
\(825\) −2.56724e13 −1.92941
\(826\) 0 0
\(827\) −1.43263e13 −1.06502 −0.532512 0.846422i \(-0.678752\pi\)
−0.532512 + 0.846422i \(0.678752\pi\)
\(828\) 1.49146e12 2.58329e12i 0.110275 0.191001i
\(829\) −2.47773e12 4.29155e12i −0.182204 0.315587i 0.760427 0.649424i \(-0.224990\pi\)
−0.942631 + 0.333837i \(0.891657\pi\)
\(830\) 1.06784e12 + 1.84955e12i 0.0781005 + 0.135274i
\(831\) 5.86586e12 1.01600e13i 0.426704 0.739073i
\(832\) −2.26121e11 −0.0163601
\(833\) 0 0
\(834\) −1.31739e13 −0.942902
\(835\) 1.00228e13 1.73600e13i 0.713508 1.23583i
\(836\) 2.14250e12 + 3.71092e12i 0.151703 + 0.262757i
\(837\) 1.00092e13 + 1.73365e13i 0.704914 + 1.22095i
\(838\) 1.47635e12 2.55711e12i 0.103417 0.179123i
\(839\) 7.38235e12 0.514358 0.257179 0.966364i \(-0.417207\pi\)
0.257179 + 0.966364i \(0.417207\pi\)
\(840\) 0 0
\(841\) −1.24642e13 −0.859179
\(842\) −2.32128e12 + 4.02058e12i −0.159156 + 0.275666i
\(843\) −8.40386e12 1.45559e13i −0.573132 0.992694i
\(844\) −5.33373e12 9.23830e12i −0.361818 0.626687i
\(845\) 1.01821e13 1.76359e13i 0.687039 1.18999i
\(846\) −1.01286e12 −0.0679802
\(847\) 0 0
\(848\) 1.40204e12 0.0931065
\(849\) 4.51745e12 7.82446e12i 0.298407 0.516856i
\(850\) −1.35542e12 2.34766e12i −0.0890613 0.154259i
\(851\) 5.52714e12 + 9.57329e12i 0.361258 + 0.625717i
\(852\) 3.93731e12 6.81962e12i 0.255989 0.443386i
\(853\) 2.13356e13 1.37985 0.689927 0.723879i \(-0.257643\pi\)
0.689927 + 0.723879i \(0.257643\pi\)
\(854\) 0 0
\(855\) −1.92254e12 −0.123035
\(856\) −1.14016e12 + 1.97482e12i −0.0725829 + 0.125717i
\(857\) −8.25038e12 1.42901e13i −0.522468 0.904942i −0.999658 0.0261416i \(-0.991678\pi\)
0.477190 0.878800i \(-0.341655\pi\)
\(858\) −3.15088e11 5.45748e11i −0.0198490 0.0343795i
\(859\) 9.74083e12 1.68716e13i 0.610417 1.05727i −0.380753 0.924677i \(-0.624335\pi\)
0.991170 0.132597i \(-0.0423315\pi\)
\(860\) 1.90742e13 1.18906
\(861\) 0 0
\(862\) 1.65103e12 0.101853
\(863\) −8.05297e12 + 1.39482e13i −0.494205 + 0.855989i −0.999978 0.00667822i \(-0.997874\pi\)
0.505772 + 0.862667i \(0.331208\pi\)
\(864\) 6.25754e12 + 1.08384e13i 0.382025 + 0.661686i
\(865\) −1.96752e13 3.40785e13i −1.19494 2.06970i
\(866\) 4.86116e12 8.41978e12i 0.293704 0.508710i
\(867\) −1.71613e13 −1.03149
\(868\) 0 0
\(869\) 4.41368e13 2.62550
\(870\) 2.99924e12 5.19484e12i 0.177491 0.307423i
\(871\) −1.86035e11 3.22222e11i −0.0109525 0.0189703i
\(872\) −4.93624e12 8.54983e12i −0.289116 0.500764i
\(873\) 1.10896e12 1.92078e12i 0.0646180 0.111922i
\(874\) −2.42454e12 −0.140549
\(875\) 0 0
\(876\) −8.72801e12 −0.500780
\(877\) 9.24594e12 1.60144e13i 0.527780 0.914142i −0.471696 0.881761i \(-0.656358\pi\)
0.999476 0.0323804i \(-0.0103088\pi\)
\(878\) 3.91446e12 + 6.78005e12i 0.222304 + 0.385041i
\(879\) −8.63821e12 1.49618e13i −0.488061 0.845346i
\(880\) 1.71818e12 2.97598e12i 0.0965821 0.167285i
\(881\) −2.83078e13 −1.58312 −0.791562 0.611089i \(-0.790732\pi\)
−0.791562 + 0.611089i \(0.790732\pi\)
\(882\) 0 0
\(883\) −7.32328e12 −0.405399 −0.202700 0.979241i \(-0.564971\pi\)
−0.202700 + 0.979241i \(0.564971\pi\)
\(884\) −6.21574e10 + 1.07660e11i −0.00342340 + 0.00592951i
\(885\) −1.00579e12 1.74208e12i −0.0551142 0.0954606i
\(886\) 1.41321e12 + 2.44774e12i 0.0770466 + 0.133449i
\(887\) −7.56860e12 + 1.31092e13i −0.410544 + 0.711083i −0.994949 0.100379i \(-0.967994\pi\)
0.584406 + 0.811462i \(0.301328\pi\)
\(888\) 1.60185e13 0.864496
\(889\) 0 0
\(890\) 5.34396e10 0.00285501
\(891\) −2.14821e13 + 3.72081e13i −1.14190 + 1.97782i
\(892\) −3.85126e12 6.67059e12i −0.203686 0.352795i
\(893\) −7.69008e11 1.33196e12i −0.0404669 0.0700907i
\(894\) 4.77967e12 8.27863e12i 0.250253 0.433451i
\(895\) 1.05087e13 0.547451
\(896\) 0 0
\(897\) −6.66138e11 −0.0343556
\(898\) 6.15293e12 1.06572e13i 0.315747 0.546889i
\(899\) 6.91423e12 + 1.19758e13i 0.353041 + 0.611485i
\(900\) 2.03912e12 + 3.53186e12i 0.103598 + 0.179437i
\(901\) −4.12040e12 + 7.13674e12i −0.208294 + 0.360776i
\(902\) −1.59733e13 −0.803463
\(903\) 0 0
\(904\) −1.72783e13 −0.860487
\(905\) 2.03395e12 3.52290e12i 0.100791 0.174575i
\(906\) 2.94057e12 + 5.09321e12i 0.144995 + 0.251139i
\(907\) 1.12169e13 + 1.94282e13i 0.550349 + 0.953233i 0.998249 + 0.0591491i \(0.0188387\pi\)
−0.447900 + 0.894084i \(0.647828\pi\)
\(908\) −3.85006e12 + 6.66849e12i −0.187967 + 0.325568i
\(909\) −4.03614e12 −0.196078
\(910\) 0 0
\(911\) −6.34178e12 −0.305055 −0.152528 0.988299i \(-0.548741\pi\)
−0.152528 + 0.988299i \(0.548741\pi\)
\(912\) 2.30684e11 3.99557e11i 0.0110418 0.0191250i
\(913\) −3.75047e12 6.49600e12i −0.178635 0.309405i
\(914\) −5.41901e12 9.38600e12i −0.256839 0.444859i
\(915\) −2.65724e13 + 4.60247e13i −1.25324 + 2.17068i
\(916\) −1.41899e13 −0.665963
\(917\) 0 0
\(918\) −3.22045e12 −0.149667
\(919\) −4.52236e12 + 7.83295e12i −0.209144 + 0.362248i −0.951445 0.307819i \(-0.900401\pi\)
0.742301 + 0.670066i \(0.233734\pi\)
\(920\) 1.38307e13 + 2.39555e13i 0.636500 + 1.10245i
\(921\) 6.61882e12 + 1.14641e13i 0.303118 + 0.525016i
\(922\) 1.26973e12 2.19924e12i 0.0578659 0.100227i
\(923\) −4.62369e11 −0.0209692
\(924\) 0 0
\(925\) −1.51134e13 −0.678771
\(926\) −3.18617e12 + 5.51860e12i −0.142403 + 0.246649i
\(927\) 5.33164e12 + 9.23467e12i 0.237138 + 0.410736i
\(928\) 4.32261e12 + 7.48698e12i 0.191329 + 0.331391i
\(929\) −4.25320e12 + 7.36677e12i −0.187346 + 0.324494i −0.944365 0.328900i \(-0.893322\pi\)
0.757018 + 0.653394i \(0.226655\pi\)
\(930\) 4.06037e13 1.77988
\(931\) 0 0
\(932\) 4.22464e12 0.183408
\(933\) 2.60184e13 4.50652e13i 1.12412 1.94704i
\(934\) −7.10735e12 1.23103e13i −0.305595 0.529307i
\(935\) 1.00990e13 + 1.74919e13i 0.432140 + 0.748488i
\(936\) −1.26900e11 + 2.19797e11i −0.00540407 + 0.00936012i
\(937\) −3.00276e13 −1.27260 −0.636300 0.771442i \(-0.719536\pi\)
−0.636300 + 0.771442i \(0.719536\pi\)
\(938\) 0 0
\(939\) 2.10602e13 0.884030
\(940\) −3.46059e12 + 5.99392e12i −0.144569 + 0.250401i
\(941\) 1.57991e13 + 2.73649e13i 0.656870 + 1.13773i 0.981422 + 0.191864i \(0.0614532\pi\)
−0.324552 + 0.945868i \(0.605213\pi\)
\(942\) 1.45240e12 + 2.51563e12i 0.0600976 + 0.104092i
\(943\) −8.44245e12 + 1.46227e13i −0.347669 + 0.602180i
\(944\) 1.26925e11 0.00520205
\(945\) 0 0
\(946\) 3.58592e13 1.45576
\(947\) 4.42442e12 7.66332e12i 0.178765 0.309630i −0.762693 0.646761i \(-0.776123\pi\)
0.941458 + 0.337131i \(0.109457\pi\)
\(948\) −1.33334e13 2.30941e13i −0.536170 0.928673i
\(949\) 2.56239e11 + 4.43819e11i 0.0102553 + 0.0177626i
\(950\) 1.65741e12 2.87072e12i 0.0660198 0.114350i
\(951\) −1.21698e13 −0.482473
\(952\) 0 0
\(953\) −4.90260e12 −0.192534 −0.0962672 0.995356i \(-0.530690\pi\)
−0.0962672 + 0.995356i \(0.530690\pi\)
\(954\) −3.31805e12 + 5.74704e12i −0.129693 + 0.224634i
\(955\) −1.65713e13 2.87023e13i −0.644674 1.11661i
\(956\) 1.06363e13 + 1.84226e13i 0.411841 + 0.713329i
\(957\) −1.05340e13 + 1.82454e13i −0.405965 + 0.703151i
\(958\) −1.12686e13 −0.432241
\(959\) 0 0
\(960\) 2.21969e13 0.843476
\(961\) −3.35824e13 + 5.81665e13i −1.27016 + 2.19998i
\(962\) −1.85492e11 3.21282e11i −0.00698294 0.0120948i
\(963\) 7.08673e11 + 1.22746e12i 0.0265539 + 0.0459926i
\(964\) −4.86237e12 + 8.42188e12i −0.181343 + 0.314096i
\(965\) 3.88339e13 1.44158
\(966\) 0 0
\(967\) 1.55633e13 0.572378 0.286189 0.958173i \(-0.407612\pi\)
0.286189 + 0.958173i \(0.407612\pi\)
\(968\) 3.26356e13 5.65266e13i 1.19468 2.06925i
\(969\) 1.35590e12 + 2.34848e12i 0.0494048 + 0.0855716i
\(970\) 4.05625e12 + 7.02564e12i 0.147113 + 0.254808i
\(971\) 1.24598e13 2.15811e13i 0.449806 0.779087i −0.548567 0.836107i \(-0.684826\pi\)
0.998373 + 0.0570194i \(0.0181597\pi\)
\(972\) 1.23765e13 0.444732
\(973\) 0 0
\(974\) 1.53918e13 0.547991
\(975\) 4.55370e11 7.88724e11i 0.0161378 0.0279515i
\(976\) −1.67664e12 2.90403e12i −0.0591448 0.102442i
\(977\) −2.23949e12 3.87891e12i −0.0786364 0.136202i 0.824025 0.566553i \(-0.191723\pi\)
−0.902662 + 0.430351i \(0.858390\pi\)
\(978\) 3.88737e12 6.73312e12i 0.135872 0.235338i
\(979\) −1.87691e11 −0.00653012
\(980\) 0 0
\(981\) −6.13629e12 −0.211542
\(982\) 6.47129e12 1.12086e13i 0.222070 0.384636i
\(983\) 7.16166e12 + 1.24044e13i 0.244637 + 0.423724i 0.962030 0.272945i \(-0.0879978\pi\)
−0.717392 + 0.696669i \(0.754664\pi\)
\(984\) 1.22337e13 + 2.11895e13i 0.415988 + 0.720513i
\(985\) 2.13932e13 3.70542e13i 0.724125 1.25422i
\(986\) −2.22464e12 −0.0749572
\(987\) 0 0
\(988\) −1.52013e11 −0.00507543
\(989\) 1.89528e13 3.28273e13i 0.629928 1.09107i
\(990\) 8.13244e12 + 1.40858e13i 0.269068 + 0.466040i
\(991\) 1.14287e13 + 1.97951e13i 0.376415 + 0.651969i 0.990538 0.137241i \(-0.0438235\pi\)
−0.614123 + 0.789210i \(0.710490\pi\)
\(992\) −2.92597e13 + 5.06793e13i −0.959328 + 1.66160i
\(993\) 4.63836e13 1.51388
\(994\) 0 0
\(995\) 3.27902e13 1.06057
\(996\) −2.26597e12 + 3.92478e12i −0.0729604 + 0.126371i
\(997\) 1.33566e13 + 2.31343e13i 0.428121 + 0.741528i 0.996706 0.0810966i \(-0.0258422\pi\)
−0.568585 + 0.822625i \(0.692509\pi\)
\(998\) −1.75574e13 3.04103e13i −0.560237 0.970359i
\(999\) −8.97726e12 + 1.55491e13i −0.285167 + 0.493924i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 49.10.c.d.30.2 6
7.2 even 3 7.10.a.b.1.2 3
7.3 odd 6 49.10.c.e.18.2 6
7.4 even 3 inner 49.10.c.d.18.2 6
7.5 odd 6 49.10.a.c.1.2 3
7.6 odd 2 49.10.c.e.30.2 6
21.2 odd 6 63.10.a.e.1.2 3
28.23 odd 6 112.10.a.h.1.1 3
35.2 odd 12 175.10.b.d.99.4 6
35.9 even 6 175.10.a.d.1.2 3
35.23 odd 12 175.10.b.d.99.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.10.a.b.1.2 3 7.2 even 3
49.10.a.c.1.2 3 7.5 odd 6
49.10.c.d.18.2 6 7.4 even 3 inner
49.10.c.d.30.2 6 1.1 even 1 trivial
49.10.c.e.18.2 6 7.3 odd 6
49.10.c.e.30.2 6 7.6 odd 2
63.10.a.e.1.2 3 21.2 odd 6
112.10.a.h.1.1 3 28.23 odd 6
175.10.a.d.1.2 3 35.9 even 6
175.10.b.d.99.3 6 35.23 odd 12
175.10.b.d.99.4 6 35.2 odd 12