Properties

Label 15.11.c.a.11.10
Level $15$
Weight $11$
Character 15.11
Analytic conductor $9.530$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,11,Mod(11,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.11");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 15.c (of order \(2\), degree \(1\), 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: \(9.53035879011\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} + 11554 x^{12} + 52224391 x^{10} + 115670558124 x^{8} + 127683454012911 x^{6} + \cdots + 62\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{20}\cdot 5^{21} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.10
Root \(29.7613i\) of defining polynomial
Character \(\chi\) \(=\) 15.11
Dual form 15.11.c.a.11.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+27.5253i q^{2} +(-80.1400 - 229.405i) q^{3} +266.360 q^{4} +1397.54i q^{5} +(6314.43 - 2205.87i) q^{6} -24115.7 q^{7} +35517.5i q^{8} +(-46204.2 + 36769.0i) q^{9} +O(q^{10})\) \(q+27.5253i q^{2} +(-80.1400 - 229.405i) q^{3} +266.360 q^{4} +1397.54i q^{5} +(6314.43 - 2205.87i) q^{6} -24115.7 q^{7} +35517.5i q^{8} +(-46204.2 + 36769.0i) q^{9} -38467.7 q^{10} -218929. i q^{11} +(-21346.1 - 61104.3i) q^{12} -435784. q^{13} -663792. i q^{14} +(320603. - 111999. i) q^{15} -704876. q^{16} +1.40198e6i q^{17} +(-1.01208e6 - 1.27178e6i) q^{18} -3.96480e6 q^{19} +372249. i q^{20} +(1.93264e6 + 5.53227e6i) q^{21} +6.02608e6 q^{22} -1.21648e6i q^{23} +(8.14789e6 - 2.84637e6i) q^{24} -1.95312e6 q^{25} -1.19951e7i q^{26} +(1.21378e7 + 7.65279e6i) q^{27} -6.42347e6 q^{28} -1.00025e6i q^{29} +(3.08280e6 + 8.82468e6i) q^{30} +5.09524e7 q^{31} +1.69680e7i q^{32} +(-5.02234e7 + 1.75450e7i) q^{33} -3.85900e7 q^{34} -3.37028e7i q^{35} +(-1.23069e7 + 9.79379e6i) q^{36} +9.23155e6 q^{37} -1.09132e8i q^{38} +(3.49238e7 + 9.99710e7i) q^{39} -4.96372e7 q^{40} -4.72120e7i q^{41} +(-1.52277e8 + 5.31963e7i) q^{42} -7.55356e7 q^{43} -5.83140e7i q^{44} +(-5.13862e7 - 6.45723e7i) q^{45} +3.34839e7 q^{46} -1.53639e8i q^{47} +(5.64887e7 + 1.61702e8i) q^{48} +2.99094e8 q^{49} -5.37603e7i q^{50} +(3.21622e8 - 1.12355e8i) q^{51} -1.16076e8 q^{52} +3.89040e8i q^{53} +(-2.10645e8 + 3.34096e8i) q^{54} +3.05963e8 q^{55} -8.56531e8i q^{56} +(3.17739e8 + 9.09545e8i) q^{57} +2.75322e7 q^{58} +1.11064e8i q^{59} +(8.53958e7 - 2.98321e7i) q^{60} -6.20166e7 q^{61} +1.40248e9i q^{62} +(1.11425e9 - 8.86712e8i) q^{63} -1.18884e9 q^{64} -6.09027e8i q^{65} +(-4.82930e8 - 1.38241e9i) q^{66} -8.74334e8 q^{67} +3.73432e8i q^{68} +(-2.79066e8 + 9.74887e7i) q^{69} +9.27678e8 q^{70} -1.83375e9i q^{71} +(-1.30594e9 - 1.64106e9i) q^{72} +7.05499e7 q^{73} +2.54101e8i q^{74} +(1.56523e8 + 4.48056e8i) q^{75} -1.05606e9 q^{76} +5.27964e9i q^{77} +(-2.75173e9 + 9.61285e8i) q^{78} -6.40192e8 q^{79} -9.85094e8i q^{80} +(7.82866e8 - 3.39776e9i) q^{81} +1.29952e9 q^{82} +3.98887e9i q^{83} +(5.14777e8 + 1.47358e9i) q^{84} -1.95933e9 q^{85} -2.07914e9i q^{86} +(-2.29463e8 + 8.01602e7i) q^{87} +7.77582e9 q^{88} +3.01940e9i q^{89} +(1.77737e9 - 1.41442e9i) q^{90} +1.05093e10 q^{91} -3.24022e8i q^{92} +(-4.08333e9 - 1.16887e10i) q^{93} +4.22896e9 q^{94} -5.54098e9i q^{95} +(3.89255e9 - 1.35982e9i) q^{96} -1.02491e10 q^{97} +8.23264e9i q^{98} +(8.04981e9 + 1.01154e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 27.5253i 0.860164i 0.902790 + 0.430082i \(0.141515\pi\)
−0.902790 + 0.430082i \(0.858485\pi\)
\(3\) −80.1400 229.405i −0.329794 0.944053i
\(4\) 266.360 0.260117
\(5\) 1397.54i 0.447214i
\(6\) 6314.43 2205.87i 0.812041 0.283677i
\(7\) −24115.7 −1.43486 −0.717432 0.696629i \(-0.754682\pi\)
−0.717432 + 0.696629i \(0.754682\pi\)
\(8\) 35517.5i 1.08391i
\(9\) −46204.2 + 36769.0i −0.782472 + 0.622686i
\(10\) −38467.7 −0.384677
\(11\) 218929.i 1.35938i −0.733500 0.679689i \(-0.762115\pi\)
0.733500 0.679689i \(-0.237885\pi\)
\(12\) −21346.1 61104.3i −0.0857851 0.245564i
\(13\) −435784. −1.17369 −0.586847 0.809698i \(-0.699631\pi\)
−0.586847 + 0.809698i \(0.699631\pi\)
\(14\) 663792.i 1.23422i
\(15\) 320603. 111999.i 0.422193 0.147488i
\(16\) −704876. −0.672222
\(17\) 1.40198e6i 0.987412i 0.869629 + 0.493706i \(0.164358\pi\)
−0.869629 + 0.493706i \(0.835642\pi\)
\(18\) −1.01208e6 1.27178e6i −0.535613 0.673054i
\(19\) −3.96480e6 −1.60123 −0.800615 0.599180i \(-0.795494\pi\)
−0.800615 + 0.599180i \(0.795494\pi\)
\(20\) 372249.i 0.116328i
\(21\) 1.93264e6 + 5.53227e6i 0.473210 + 1.35459i
\(22\) 6.02608e6 1.16929
\(23\) 1.21648e6i 0.189002i −0.995525 0.0945009i \(-0.969874\pi\)
0.995525 0.0945009i \(-0.0301255\pi\)
\(24\) 8.14789e6 2.84637e6i 1.02327 0.357467i
\(25\) −1.95312e6 −0.200000
\(26\) 1.19951e7i 1.00957i
\(27\) 1.21378e7 + 7.65279e6i 0.845903 + 0.533336i
\(28\) −6.42347e6 −0.373233
\(29\) 1.00025e6i 0.0487663i −0.999703 0.0243831i \(-0.992238\pi\)
0.999703 0.0243831i \(-0.00776216\pi\)
\(30\) 3.08280e6 + 8.82468e6i 0.126864 + 0.363156i
\(31\) 5.09524e7 1.77974 0.889870 0.456215i \(-0.150795\pi\)
0.889870 + 0.456215i \(0.150795\pi\)
\(32\) 1.69680e7i 0.505687i
\(33\) −5.02234e7 + 1.75450e7i −1.28333 + 0.448315i
\(34\) −3.85900e7 −0.849336
\(35\) 3.37028e7i 0.641690i
\(36\) −1.23069e7 + 9.79379e6i −0.203534 + 0.161971i
\(37\) 9.23155e6 0.133127 0.0665635 0.997782i \(-0.478797\pi\)
0.0665635 + 0.997782i \(0.478797\pi\)
\(38\) 1.09132e8i 1.37732i
\(39\) 3.49238e7 + 9.99710e7i 0.387077 + 1.10803i
\(40\) −4.96372e7 −0.484738
\(41\) 4.72120e7i 0.407505i −0.979022 0.203753i \(-0.934686\pi\)
0.979022 0.203753i \(-0.0653138\pi\)
\(42\) −1.52277e8 + 5.31963e7i −1.16517 + 0.407038i
\(43\) −7.55356e7 −0.513818 −0.256909 0.966436i \(-0.582704\pi\)
−0.256909 + 0.966436i \(0.582704\pi\)
\(44\) 5.83140e7i 0.353598i
\(45\) −5.13862e7 6.45723e7i −0.278474 0.349932i
\(46\) 3.34839e7 0.162573
\(47\) 1.53639e8i 0.669905i −0.942235 0.334953i \(-0.891280\pi\)
0.942235 0.334953i \(-0.108720\pi\)
\(48\) 5.64887e7 + 1.61702e8i 0.221695 + 0.634613i
\(49\) 2.99094e8 1.05883
\(50\) 5.37603e7i 0.172033i
\(51\) 3.21622e8 1.12355e8i 0.932169 0.325643i
\(52\) −1.16076e8 −0.305298
\(53\) 3.89040e8i 0.930283i 0.885236 + 0.465141i \(0.153997\pi\)
−0.885236 + 0.465141i \(0.846003\pi\)
\(54\) −2.10645e8 + 3.34096e8i −0.458757 + 0.727616i
\(55\) 3.05963e8 0.607933
\(56\) 8.56531e8i 1.55526i
\(57\) 3.17739e8 + 9.09545e8i 0.528076 + 1.51165i
\(58\) 2.75322e7 0.0419470
\(59\) 1.11064e8i 0.155350i 0.996979 + 0.0776751i \(0.0247497\pi\)
−0.996979 + 0.0776751i \(0.975250\pi\)
\(60\) 8.53958e7 2.98321e7i 0.109820 0.0383643i
\(61\) −6.20166e7 −0.0734275 −0.0367138 0.999326i \(-0.511689\pi\)
−0.0367138 + 0.999326i \(0.511689\pi\)
\(62\) 1.40248e9i 1.53087i
\(63\) 1.11425e9 8.86712e8i 1.12274 0.893470i
\(64\) −1.18884e9 −1.10720
\(65\) 6.09027e8i 0.524892i
\(66\) −4.82930e8 1.38241e9i −0.385625 1.10387i
\(67\) −8.74334e8 −0.647595 −0.323798 0.946126i \(-0.604960\pi\)
−0.323798 + 0.946126i \(0.604960\pi\)
\(68\) 3.73432e8i 0.256843i
\(69\) −2.79066e8 + 9.74887e7i −0.178428 + 0.0623317i
\(70\) 9.27678e8 0.551959
\(71\) 1.83375e9i 1.01636i −0.861251 0.508180i \(-0.830319\pi\)
0.861251 0.508180i \(-0.169681\pi\)
\(72\) −1.30594e9 1.64106e9i −0.674935 0.848127i
\(73\) 7.05499e7 0.0340316 0.0170158 0.999855i \(-0.494583\pi\)
0.0170158 + 0.999855i \(0.494583\pi\)
\(74\) 2.54101e8i 0.114511i
\(75\) 1.56523e8 + 4.48056e8i 0.0659588 + 0.188811i
\(76\) −1.05606e9 −0.416507
\(77\) 5.27964e9i 1.95052i
\(78\) −2.75173e9 + 9.61285e8i −0.953087 + 0.332950i
\(79\) −6.40192e8 −0.208053 −0.104027 0.994575i \(-0.533173\pi\)
−0.104027 + 0.994575i \(0.533173\pi\)
\(80\) 9.85094e8i 0.300627i
\(81\) 7.82866e8 3.39776e9i 0.224524 0.974469i
\(82\) 1.29952e9 0.350521
\(83\) 3.98887e9i 1.01265i 0.862343 + 0.506325i \(0.168996\pi\)
−0.862343 + 0.506325i \(0.831004\pi\)
\(84\) 5.14777e8 + 1.47358e9i 0.123090 + 0.352351i
\(85\) −1.95933e9 −0.441584
\(86\) 2.07914e9i 0.441968i
\(87\) −2.29463e8 + 8.01602e7i −0.0460379 + 0.0160828i
\(88\) 7.77582e9 1.47344
\(89\) 3.01940e9i 0.540718i 0.962760 + 0.270359i \(0.0871424\pi\)
−0.962760 + 0.270359i \(0.912858\pi\)
\(90\) 1.77737e9 1.41442e9i 0.300999 0.239533i
\(91\) 1.05093e10 1.68409
\(92\) 3.24022e8i 0.0491626i
\(93\) −4.08333e9 1.16887e10i −0.586948 1.68017i
\(94\) 4.22896e9 0.576229
\(95\) 5.54098e9i 0.716091i
\(96\) 3.89255e9 1.35982e9i 0.477395 0.166773i
\(97\) −1.02491e10 −1.19351 −0.596754 0.802424i \(-0.703543\pi\)
−0.596754 + 0.802424i \(0.703543\pi\)
\(98\) 8.23264e9i 0.910770i
\(99\) 8.04981e9 + 1.01154e10i 0.846466 + 1.06368i
\(100\) −5.20234e8 −0.0520234
\(101\) 1.14343e10i 1.08793i 0.839106 + 0.543967i \(0.183079\pi\)
−0.839106 + 0.543967i \(0.816921\pi\)
\(102\) 3.09260e9 + 8.85272e9i 0.280106 + 0.801818i
\(103\) −1.84678e10 −1.59305 −0.796525 0.604606i \(-0.793331\pi\)
−0.796525 + 0.604606i \(0.793331\pi\)
\(104\) 1.54780e10i 1.27218i
\(105\) −7.73158e9 + 2.70094e9i −0.605790 + 0.211626i
\(106\) −1.07084e10 −0.800196
\(107\) 1.27274e10i 0.907449i −0.891142 0.453724i \(-0.850095\pi\)
0.891142 0.453724i \(-0.149905\pi\)
\(108\) 3.23302e9 + 2.03840e9i 0.220034 + 0.138730i
\(109\) −7.89967e9 −0.513425 −0.256712 0.966488i \(-0.582639\pi\)
−0.256712 + 0.966488i \(0.582639\pi\)
\(110\) 8.42171e9i 0.522922i
\(111\) −7.39816e8 2.11776e9i −0.0439045 0.125679i
\(112\) 1.69986e10 0.964546
\(113\) 1.24747e10i 0.677074i −0.940953 0.338537i \(-0.890068\pi\)
0.940953 0.338537i \(-0.109932\pi\)
\(114\) −2.50355e10 + 8.74585e9i −1.30026 + 0.454232i
\(115\) 1.70008e9 0.0845242
\(116\) 2.66427e8i 0.0126849i
\(117\) 2.01351e10 1.60234e10i 0.918382 0.730843i
\(118\) −3.05706e9 −0.133627
\(119\) 3.38099e10i 1.41680i
\(120\) 3.97793e9 + 1.13870e10i 0.159864 + 0.457619i
\(121\) −2.19926e10 −0.847910
\(122\) 1.70702e9i 0.0631597i
\(123\) −1.08307e10 + 3.78357e9i −0.384706 + 0.134393i
\(124\) 1.35717e10 0.462941
\(125\) 2.72958e9i 0.0894427i
\(126\) 2.44070e10 + 3.06700e10i 0.768531 + 0.965741i
\(127\) −1.29905e10 −0.393194 −0.196597 0.980484i \(-0.562989\pi\)
−0.196597 + 0.980484i \(0.562989\pi\)
\(128\) 1.53479e10i 0.446683i
\(129\) 6.05342e9 + 1.73282e10i 0.169454 + 0.485072i
\(130\) 1.67636e10 0.451493
\(131\) 4.93423e10i 1.27898i 0.768801 + 0.639488i \(0.220854\pi\)
−0.768801 + 0.639488i \(0.779146\pi\)
\(132\) −1.33775e10 + 4.67328e9i −0.333815 + 0.116614i
\(133\) 9.56142e10 2.29755
\(134\) 2.40663e10i 0.557038i
\(135\) −1.06951e10 + 1.69631e10i −0.238515 + 0.378299i
\(136\) −4.97949e10 −1.07026
\(137\) 2.13856e10i 0.443117i −0.975147 0.221559i \(-0.928886\pi\)
0.975147 0.221559i \(-0.0711144\pi\)
\(138\) −2.68340e9 7.68138e9i −0.0536155 0.153477i
\(139\) 3.80392e10 0.733090 0.366545 0.930400i \(-0.380541\pi\)
0.366545 + 0.930400i \(0.380541\pi\)
\(140\) 8.97707e9i 0.166915i
\(141\) −3.52456e10 + 1.23127e10i −0.632426 + 0.220931i
\(142\) 5.04743e10 0.874236
\(143\) 9.54059e10i 1.59549i
\(144\) 3.25682e10 2.59176e10i 0.525994 0.418583i
\(145\) 1.39789e9 0.0218089
\(146\) 1.94190e9i 0.0292727i
\(147\) −2.39694e10 6.86136e10i −0.349197 0.999594i
\(148\) 2.45892e9 0.0346286
\(149\) 3.55299e10i 0.483797i 0.970302 + 0.241898i \(0.0777701\pi\)
−0.970302 + 0.241898i \(0.922230\pi\)
\(150\) −1.23329e10 + 4.30835e9i −0.162408 + 0.0567354i
\(151\) −6.10213e9 −0.0777315 −0.0388657 0.999244i \(-0.512374\pi\)
−0.0388657 + 0.999244i \(0.512374\pi\)
\(152\) 1.40820e11i 1.73559i
\(153\) −5.15495e10 6.47775e10i −0.614848 0.772622i
\(154\) −1.45324e11 −1.67777
\(155\) 7.12082e10i 0.795924i
\(156\) 9.30229e9 + 2.66283e10i 0.100686 + 0.288217i
\(157\) −1.48553e11 −1.55734 −0.778668 0.627436i \(-0.784104\pi\)
−0.778668 + 0.627436i \(0.784104\pi\)
\(158\) 1.76214e10i 0.178960i
\(159\) 8.92477e10 3.11777e10i 0.878236 0.306802i
\(160\) −2.37135e10 −0.226150
\(161\) 2.93363e10i 0.271192i
\(162\) 9.35243e10 + 2.15486e10i 0.838203 + 0.193127i
\(163\) 1.30154e11 1.13115 0.565573 0.824698i \(-0.308655\pi\)
0.565573 + 0.824698i \(0.308655\pi\)
\(164\) 1.25754e10i 0.105999i
\(165\) −2.45199e10 7.01894e10i −0.200493 0.573920i
\(166\) −1.09795e11 −0.871045
\(167\) 1.61088e11i 1.24017i 0.784536 + 0.620083i \(0.212901\pi\)
−0.784536 + 0.620083i \(0.787099\pi\)
\(168\) −1.96492e11 + 6.86424e10i −1.46825 + 0.512916i
\(169\) 5.20495e10 0.377558
\(170\) 5.39311e10i 0.379835i
\(171\) 1.83190e11 1.45782e11i 1.25292 0.997063i
\(172\) −2.01197e10 −0.133653
\(173\) 1.51842e11i 0.979854i −0.871763 0.489927i \(-0.837023\pi\)
0.871763 0.489927i \(-0.162977\pi\)
\(174\) −2.20643e9 6.31602e9i −0.0138339 0.0396002i
\(175\) 4.71011e10 0.286973
\(176\) 1.54318e11i 0.913804i
\(177\) 2.54785e10 8.90064e9i 0.146659 0.0512336i
\(178\) −8.31098e10 −0.465106
\(179\) 2.98641e11i 1.62512i 0.582880 + 0.812558i \(0.301926\pi\)
−0.582880 + 0.812558i \(0.698074\pi\)
\(180\) −1.36872e10 1.71995e10i −0.0724358 0.0910233i
\(181\) 5.00350e10 0.257561 0.128781 0.991673i \(-0.458894\pi\)
0.128781 + 0.991673i \(0.458894\pi\)
\(182\) 2.89270e11i 1.44859i
\(183\) 4.97001e9 + 1.42269e10i 0.0242160 + 0.0693194i
\(184\) 4.32063e10 0.204861
\(185\) 1.29015e10i 0.0595362i
\(186\) 3.21735e11 1.12395e11i 1.44522 0.504871i
\(187\) 3.06935e11 1.34227
\(188\) 4.09234e10i 0.174254i
\(189\) −2.92712e11 1.84553e11i −1.21376 0.765265i
\(190\) 1.52517e11 0.615956
\(191\) 4.67558e11i 1.83937i −0.392660 0.919684i \(-0.628445\pi\)
0.392660 0.919684i \(-0.371555\pi\)
\(192\) 9.52738e10 + 2.72726e11i 0.365147 + 1.04525i
\(193\) 4.65772e10 0.173935 0.0869675 0.996211i \(-0.472282\pi\)
0.0869675 + 0.996211i \(0.472282\pi\)
\(194\) 2.82108e11i 1.02661i
\(195\) −1.39714e11 + 4.88074e10i −0.495526 + 0.173106i
\(196\) 7.96667e10 0.275421
\(197\) 1.04345e11i 0.351675i −0.984419 0.175837i \(-0.943737\pi\)
0.984419 0.175837i \(-0.0562633\pi\)
\(198\) −2.78430e11 + 2.21573e11i −0.914935 + 0.728100i
\(199\) −5.99954e10 −0.192244 −0.0961219 0.995370i \(-0.530644\pi\)
−0.0961219 + 0.995370i \(0.530644\pi\)
\(200\) 6.93701e10i 0.216782i
\(201\) 7.00691e10 + 2.00577e11i 0.213573 + 0.611364i
\(202\) −3.14732e11 −0.935803
\(203\) 2.41218e10i 0.0699729i
\(204\) 8.56672e10 2.99269e10i 0.242473 0.0847053i
\(205\) 6.59808e10 0.182242
\(206\) 5.08331e11i 1.37028i
\(207\) 4.47288e10 + 5.62065e10i 0.117689 + 0.147889i
\(208\) 3.07174e11 0.788983
\(209\) 8.68011e11i 2.17668i
\(210\) −7.43441e10 2.12814e11i −0.182033 0.521079i
\(211\) −7.49985e11 −1.79325 −0.896624 0.442792i \(-0.853988\pi\)
−0.896624 + 0.442792i \(0.853988\pi\)
\(212\) 1.03625e11i 0.241983i
\(213\) −4.20670e11 + 1.46956e11i −0.959497 + 0.335189i
\(214\) 3.50326e11 0.780555
\(215\) 1.05564e11i 0.229787i
\(216\) −2.71808e11 + 4.31104e11i −0.578087 + 0.916881i
\(217\) −1.22876e12 −2.55368
\(218\) 2.17441e11i 0.441630i
\(219\) −5.65387e9 1.61845e10i −0.0112234 0.0321276i
\(220\) 8.14963e10 0.158134
\(221\) 6.10962e11i 1.15892i
\(222\) 5.82920e10 2.03636e10i 0.108104 0.0377651i
\(223\) 1.06490e12 1.93101 0.965503 0.260394i \(-0.0838523\pi\)
0.965503 + 0.260394i \(0.0838523\pi\)
\(224\) 4.09197e11i 0.725591i
\(225\) 9.02425e10 7.18145e10i 0.156494 0.124537i
\(226\) 3.43368e11 0.582395
\(227\) 3.01663e10i 0.0500487i 0.999687 + 0.0250244i \(0.00796633\pi\)
−0.999687 + 0.0250244i \(0.992034\pi\)
\(228\) 8.46330e10 + 2.42266e11i 0.137362 + 0.393205i
\(229\) −8.11842e11 −1.28912 −0.644561 0.764553i \(-0.722960\pi\)
−0.644561 + 0.764553i \(0.722960\pi\)
\(230\) 4.67952e10i 0.0727047i
\(231\) 1.21118e12 4.23110e11i 1.84140 0.643271i
\(232\) 3.55265e10 0.0528581
\(233\) 5.24222e11i 0.763371i −0.924292 0.381685i \(-0.875344\pi\)
0.924292 0.381685i \(-0.124656\pi\)
\(234\) 4.41047e11 + 5.54223e11i 0.628645 + 0.789960i
\(235\) 2.14718e11 0.299591
\(236\) 2.95829e10i 0.0404093i
\(237\) 5.13049e10 + 1.46863e11i 0.0686147 + 0.196413i
\(238\) 9.30626e11 1.21868
\(239\) 1.66440e11i 0.213437i 0.994289 + 0.106718i \(0.0340343\pi\)
−0.994289 + 0.106718i \(0.965966\pi\)
\(240\) −2.25985e11 + 7.89454e10i −0.283808 + 0.0991449i
\(241\) −1.21763e12 −1.49772 −0.748862 0.662726i \(-0.769399\pi\)
−0.748862 + 0.662726i \(0.769399\pi\)
\(242\) 6.05352e11i 0.729342i
\(243\) −8.42202e11 + 9.27034e10i −0.993997 + 0.109412i
\(244\) −1.65187e10 −0.0190998
\(245\) 4.17997e11i 0.473524i
\(246\) −1.04144e11 2.98117e11i −0.115600 0.330911i
\(247\) 1.72780e12 1.87935
\(248\) 1.80970e12i 1.92907i
\(249\) 9.15065e11 3.19668e11i 0.955995 0.333966i
\(250\) 7.51323e10 0.0769354
\(251\) 1.64602e12i 1.65222i 0.563512 + 0.826108i \(0.309450\pi\)
−0.563512 + 0.826108i \(0.690550\pi\)
\(252\) 2.96791e11 2.36185e11i 0.292044 0.232407i
\(253\) −2.66323e11 −0.256925
\(254\) 3.57567e11i 0.338212i
\(255\) 1.57021e11 + 4.49480e11i 0.145632 + 0.416879i
\(256\) −7.94919e11 −0.722974
\(257\) 1.27887e11i 0.114067i 0.998372 + 0.0570336i \(0.0181642\pi\)
−0.998372 + 0.0570336i \(0.981836\pi\)
\(258\) −4.76964e11 + 1.66622e11i −0.417241 + 0.145759i
\(259\) −2.22626e11 −0.191019
\(260\) 1.62220e11i 0.136533i
\(261\) 3.67783e10 + 4.62158e10i 0.0303661 + 0.0381582i
\(262\) −1.35816e12 −1.10013
\(263\) 2.48857e12i 1.97775i −0.148741 0.988876i \(-0.547522\pi\)
0.148741 0.988876i \(-0.452478\pi\)
\(264\) −6.23154e11 1.78381e12i −0.485932 1.39101i
\(265\) −5.43700e11 −0.416035
\(266\) 2.63180e12i 1.97627i
\(267\) 6.92666e11 2.41975e11i 0.510467 0.178326i
\(268\) −2.32888e11 −0.168451
\(269\) 1.03039e12i 0.731547i −0.930704 0.365773i \(-0.880804\pi\)
0.930704 0.365773i \(-0.119196\pi\)
\(270\) −4.66913e11 2.94385e11i −0.325400 0.205162i
\(271\) 1.62656e12 1.11282 0.556409 0.830909i \(-0.312179\pi\)
0.556409 + 0.830909i \(0.312179\pi\)
\(272\) 9.88224e11i 0.663760i
\(273\) −8.42212e11 2.41088e12i −0.555403 1.58987i
\(274\) 5.88644e11 0.381154
\(275\) 4.27596e11i 0.271876i
\(276\) −7.43322e10 + 2.59671e10i −0.0464121 + 0.0162135i
\(277\) 1.37251e12 0.841624 0.420812 0.907148i \(-0.361745\pi\)
0.420812 + 0.907148i \(0.361745\pi\)
\(278\) 1.04704e12i 0.630578i
\(279\) −2.35421e12 + 1.87347e12i −1.39260 + 1.10822i
\(280\) 1.19704e12 0.695533
\(281\) 6.12902e11i 0.349832i −0.984583 0.174916i \(-0.944035\pi\)
0.984583 0.174916i \(-0.0559654\pi\)
\(282\) −3.38909e11 9.70145e11i −0.190037 0.543990i
\(283\) −9.61960e11 −0.529938 −0.264969 0.964257i \(-0.585362\pi\)
−0.264969 + 0.964257i \(0.585362\pi\)
\(284\) 4.88437e11i 0.264373i
\(285\) −1.27113e12 + 4.44054e11i −0.676028 + 0.236163i
\(286\) −2.62607e12 −1.37239
\(287\) 1.13855e12i 0.584714i
\(288\) −6.23897e11 7.83994e11i −0.314884 0.395685i
\(289\) 5.04362e10 0.0250180
\(290\) 3.84774e10i 0.0187593i
\(291\) 8.21359e11 + 2.35118e12i 0.393612 + 1.12673i
\(292\) 1.87917e10 0.00885220
\(293\) 3.28624e12i 1.52181i 0.648862 + 0.760906i \(0.275245\pi\)
−0.648862 + 0.760906i \(0.724755\pi\)
\(294\) 1.88861e12 6.59764e11i 0.859815 0.300367i
\(295\) −1.55216e11 −0.0694748
\(296\) 3.27882e11i 0.144297i
\(297\) 1.67542e12 2.65732e12i 0.725006 1.14990i
\(298\) −9.77971e11 −0.416145
\(299\) 5.30123e11i 0.221830i
\(300\) 4.16916e10 + 1.19344e11i 0.0171570 + 0.0491129i
\(301\) 1.82160e12 0.737259
\(302\) 1.67963e11i 0.0668618i
\(303\) 2.62309e12 9.16345e11i 1.02707 0.358795i
\(304\) 2.79469e12 1.07638
\(305\) 8.66708e10i 0.0328378i
\(306\) 1.78302e12 1.41891e12i 0.664582 0.528870i
\(307\) −4.36270e11 −0.159979 −0.0799896 0.996796i \(-0.525489\pi\)
−0.0799896 + 0.996796i \(0.525489\pi\)
\(308\) 1.40629e12i 0.507364i
\(309\) 1.48001e12 + 4.23661e12i 0.525379 + 1.50392i
\(310\) −1.96002e12 −0.684625
\(311\) 1.17043e11i 0.0402295i −0.999798 0.0201148i \(-0.993597\pi\)
0.999798 0.0201148i \(-0.00640316\pi\)
\(312\) −3.55072e12 + 1.24040e12i −1.20100 + 0.419556i
\(313\) 2.82819e12 0.941428 0.470714 0.882286i \(-0.343996\pi\)
0.470714 + 0.882286i \(0.343996\pi\)
\(314\) 4.08895e12i 1.33957i
\(315\) 1.23922e12 + 1.55721e12i 0.399572 + 0.502104i
\(316\) −1.70521e11 −0.0541182
\(317\) 4.21635e12i 1.31717i −0.752508 0.658583i \(-0.771156\pi\)
0.752508 0.658583i \(-0.228844\pi\)
\(318\) 8.58173e11 + 2.45657e12i 0.263900 + 0.755428i
\(319\) −2.18984e11 −0.0662918
\(320\) 1.66146e12i 0.495153i
\(321\) −2.91974e12 + 1.01998e12i −0.856680 + 0.299271i
\(322\) −8.07490e11 −0.233269
\(323\) 5.55859e12i 1.58107i
\(324\) 2.08524e11 9.05028e11i 0.0584025 0.253476i
\(325\) 8.51141e11 0.234739
\(326\) 3.58251e12i 0.972971i
\(327\) 6.33080e11 + 1.81222e12i 0.169324 + 0.484700i
\(328\) 1.67685e12 0.441698
\(329\) 3.70513e12i 0.961222i
\(330\) 1.93198e12 6.74916e11i 0.493666 0.172457i
\(331\) −3.65692e12 −0.920398 −0.460199 0.887816i \(-0.652222\pi\)
−0.460199 + 0.887816i \(0.652222\pi\)
\(332\) 1.06247e12i 0.263408i
\(333\) −4.26536e11 + 3.39435e11i −0.104168 + 0.0828963i
\(334\) −4.43398e12 −1.06675
\(335\) 1.22192e12i 0.289613i
\(336\) −1.36227e12 3.89956e12i −0.318102 0.910583i
\(337\) −3.50041e12 −0.805322 −0.402661 0.915349i \(-0.631915\pi\)
−0.402661 + 0.915349i \(0.631915\pi\)
\(338\) 1.43268e12i 0.324762i
\(339\) −2.86175e12 + 9.99718e11i −0.639194 + 0.223295i
\(340\) −5.21888e11 −0.114864
\(341\) 1.11550e13i 2.41934i
\(342\) 4.01268e12 + 5.04236e12i 0.857638 + 1.07771i
\(343\) −4.00774e11 −0.0844167
\(344\) 2.68284e12i 0.556932i
\(345\) −1.36245e11 3.90007e11i −0.0278756 0.0797953i
\(346\) 4.17949e12 0.842836
\(347\) 6.85033e12i 1.36165i 0.732448 + 0.680823i \(0.238378\pi\)
−0.732448 + 0.680823i \(0.761622\pi\)
\(348\) −6.11197e10 + 2.13515e10i −0.0119753 + 0.00418342i
\(349\) −5.11040e12 −0.987024 −0.493512 0.869739i \(-0.664287\pi\)
−0.493512 + 0.869739i \(0.664287\pi\)
\(350\) 1.29647e12i 0.246844i
\(351\) −5.28946e12 3.33497e12i −0.992832 0.625974i
\(352\) 3.71480e12 0.687420
\(353\) 2.89458e12i 0.528095i 0.964510 + 0.264047i \(0.0850575\pi\)
−0.964510 + 0.264047i \(0.914942\pi\)
\(354\) 2.44992e11 + 7.01304e11i 0.0440693 + 0.126151i
\(355\) 2.56274e12 0.454530
\(356\) 8.04248e11i 0.140650i
\(357\) −7.75615e12 + 2.70952e12i −1.33753 + 0.467253i
\(358\) −8.22017e12 −1.39787
\(359\) 5.87330e12i 0.984940i −0.870329 0.492470i \(-0.836094\pi\)
0.870329 0.492470i \(-0.163906\pi\)
\(360\) 2.29345e12 1.82511e12i 0.379294 0.301840i
\(361\) 9.58859e12 1.56394
\(362\) 1.37723e12i 0.221545i
\(363\) 1.76249e12 + 5.04521e12i 0.279636 + 0.800472i
\(364\) 2.79925e12 0.438061
\(365\) 9.85964e10i 0.0152194i
\(366\) −3.91599e11 + 1.36801e11i −0.0596261 + 0.0208297i
\(367\) −1.26759e12 −0.190392 −0.0951960 0.995459i \(-0.530348\pi\)
−0.0951960 + 0.995459i \(0.530348\pi\)
\(368\) 8.57467e11i 0.127051i
\(369\) 1.73594e12 + 2.18139e12i 0.253748 + 0.318861i
\(370\) −3.55117e11 −0.0512109
\(371\) 9.38199e12i 1.33483i
\(372\) −1.08764e12 3.11341e12i −0.152675 0.437041i
\(373\) 6.12110e10 0.00847785 0.00423892 0.999991i \(-0.498651\pi\)
0.00423892 + 0.999991i \(0.498651\pi\)
\(374\) 8.44847e12i 1.15457i
\(375\) −6.26178e11 + 2.18748e11i −0.0844387 + 0.0294977i
\(376\) 5.45689e12 0.726116
\(377\) 4.35894e11i 0.0572367i
\(378\) 5.07986e12 8.05697e12i 0.658253 1.04403i
\(379\) 8.02388e12 1.02610 0.513049 0.858360i \(-0.328516\pi\)
0.513049 + 0.858360i \(0.328516\pi\)
\(380\) 1.47590e12i 0.186268i
\(381\) 1.04106e12 + 2.98008e12i 0.129673 + 0.371196i
\(382\) 1.28696e13 1.58216
\(383\) 3.43547e12i 0.416862i −0.978037 0.208431i \(-0.933164\pi\)
0.978037 0.208431i \(-0.0668357\pi\)
\(384\) −3.52089e12 + 1.22998e12i −0.421693 + 0.147314i
\(385\) −7.37852e12 −0.872300
\(386\) 1.28205e12i 0.149613i
\(387\) 3.49006e12 2.77737e12i 0.402048 0.319948i
\(388\) −2.72994e12 −0.310452
\(389\) 1.43402e13i 1.60993i 0.593322 + 0.804965i \(0.297816\pi\)
−0.593322 + 0.804965i \(0.702184\pi\)
\(390\) −1.34344e12 3.84566e12i −0.148900 0.426234i
\(391\) 1.70549e12 0.186623
\(392\) 1.06231e13i 1.14768i
\(393\) 1.13194e13 3.95429e12i 1.20742 0.421799i
\(394\) 2.87213e12 0.302498
\(395\) 8.94695e11i 0.0930442i
\(396\) 2.14415e12 + 2.69435e12i 0.220180 + 0.276680i
\(397\) −7.76634e12 −0.787524 −0.393762 0.919212i \(-0.628827\pi\)
−0.393762 + 0.919212i \(0.628827\pi\)
\(398\) 1.65139e12i 0.165361i
\(399\) −7.66252e12 2.19344e13i −0.757717 2.16900i
\(400\) 1.37671e12 0.134444
\(401\) 1.13589e13i 1.09551i 0.836640 + 0.547754i \(0.184517\pi\)
−0.836640 + 0.547754i \(0.815483\pi\)
\(402\) −5.52092e12 + 1.92867e12i −0.525873 + 0.183708i
\(403\) −2.22043e13 −2.08887
\(404\) 3.04564e12i 0.282991i
\(405\) 4.74852e12 + 1.09409e12i 0.435796 + 0.100410i
\(406\) −6.63960e11 −0.0601882
\(407\) 2.02106e12i 0.180970i
\(408\) 3.99057e12 + 1.14232e13i 0.352967 + 1.01039i
\(409\) 9.79320e12 0.855673 0.427837 0.903856i \(-0.359276\pi\)
0.427837 + 0.903856i \(0.359276\pi\)
\(410\) 1.81614e12i 0.156758i
\(411\) −4.90596e12 + 1.71384e12i −0.418326 + 0.146138i
\(412\) −4.91909e12 −0.414380
\(413\) 2.67838e12i 0.222906i
\(414\) −1.54710e12 + 1.23117e12i −0.127208 + 0.101232i
\(415\) −5.57461e12 −0.452871
\(416\) 7.39440e12i 0.593521i
\(417\) −3.04846e12 8.72637e12i −0.241769 0.692076i
\(418\) −2.38922e13 −1.87230
\(419\) 1.97848e13i 1.53201i 0.642833 + 0.766006i \(0.277759\pi\)
−0.642833 + 0.766006i \(0.722241\pi\)
\(420\) −2.05938e12 + 7.19423e11i −0.157576 + 0.0550475i
\(421\) 9.74675e12 0.736970 0.368485 0.929634i \(-0.379877\pi\)
0.368485 + 0.929634i \(0.379877\pi\)
\(422\) 2.06435e13i 1.54249i
\(423\) 5.64917e12 + 7.09878e12i 0.417141 + 0.524182i
\(424\) −1.38177e13 −1.00834
\(425\) 2.73825e12i 0.197482i
\(426\) −4.04501e12 1.15791e13i −0.288318 0.825325i
\(427\) 1.49558e12 0.105358
\(428\) 3.39008e12i 0.236043i
\(429\) 2.18866e13 7.64583e12i 1.50623 0.526185i
\(430\) 2.90568e12 0.197654
\(431\) 1.81943e12i 0.122334i 0.998128 + 0.0611671i \(0.0194823\pi\)
−0.998128 + 0.0611671i \(0.980518\pi\)
\(432\) −8.55563e12 5.39427e12i −0.568635 0.358520i
\(433\) 1.88176e13 1.23631 0.618153 0.786058i \(-0.287881\pi\)
0.618153 + 0.786058i \(0.287881\pi\)
\(434\) 3.38218e13i 2.19659i
\(435\) −1.12027e11 3.20684e11i −0.00719246 0.0205888i
\(436\) −2.10416e12 −0.133551
\(437\) 4.82310e12i 0.302635i
\(438\) 4.45482e11 1.55624e11i 0.0276350 0.00965398i
\(439\) −1.31625e13 −0.807266 −0.403633 0.914921i \(-0.632253\pi\)
−0.403633 + 0.914921i \(0.632253\pi\)
\(440\) 1.08670e13i 0.658943i
\(441\) −1.38194e13 + 1.09974e13i −0.828506 + 0.659320i
\(442\) 1.68169e13 0.996861
\(443\) 1.22492e12i 0.0717943i 0.999355 + 0.0358972i \(0.0114289\pi\)
−0.999355 + 0.0358972i \(0.988571\pi\)
\(444\) −1.97057e11 5.64087e11i −0.0114203 0.0326912i
\(445\) −4.21974e12 −0.241817
\(446\) 2.93116e13i 1.66098i
\(447\) 8.15074e12 2.84737e12i 0.456730 0.159553i
\(448\) 2.86698e13 1.58867
\(449\) 2.63416e12i 0.144348i −0.997392 0.0721741i \(-0.977006\pi\)
0.997392 0.0721741i \(-0.0229937\pi\)
\(450\) 1.97671e12 + 2.48395e12i 0.107123 + 0.134611i
\(451\) −1.03361e13 −0.553954
\(452\) 3.32275e12i 0.176119i
\(453\) 4.89025e11 + 1.39986e12i 0.0256354 + 0.0733826i
\(454\) −8.30336e11 −0.0430501
\(455\) 1.46871e13i 0.753148i
\(456\) −3.23048e13 + 1.12853e13i −1.63848 + 0.572386i
\(457\) 2.23624e13 1.12186 0.560928 0.827864i \(-0.310444\pi\)
0.560928 + 0.827864i \(0.310444\pi\)
\(458\) 2.23462e13i 1.10886i
\(459\) −1.07291e13 + 1.70170e13i −0.526623 + 0.835255i
\(460\) 4.52834e11 0.0219862
\(461\) 9.31576e12i 0.447418i 0.974656 + 0.223709i \(0.0718165\pi\)
−0.974656 + 0.223709i \(0.928183\pi\)
\(462\) 1.16462e13 + 3.33379e13i 0.553319 + 1.58390i
\(463\) −7.64194e12 −0.359169 −0.179584 0.983743i \(-0.557475\pi\)
−0.179584 + 0.983743i \(0.557475\pi\)
\(464\) 7.05053e11i 0.0327817i
\(465\) 1.63355e13 5.70662e12i 0.751394 0.262491i
\(466\) 1.44293e13 0.656624
\(467\) 2.60999e13i 1.17504i −0.809209 0.587521i \(-0.800104\pi\)
0.809209 0.587521i \(-0.199896\pi\)
\(468\) 5.36317e12 4.26798e12i 0.238887 0.190105i
\(469\) 2.10852e13 0.929210
\(470\) 5.91016e12i 0.257697i
\(471\) 1.19050e13 + 3.40787e13i 0.513600 + 1.47021i
\(472\) −3.94470e12 −0.168385
\(473\) 1.65370e13i 0.698474i
\(474\) −4.04244e12 + 1.41218e12i −0.168948 + 0.0590200i
\(475\) 7.74375e12 0.320246
\(476\) 9.00560e12i 0.368534i
\(477\) −1.43046e13 1.79753e13i −0.579274 0.727920i
\(478\) −4.58131e12 −0.183591
\(479\) 4.08677e13i 1.62070i −0.585946 0.810350i \(-0.699277\pi\)
0.585946 0.810350i \(-0.300723\pi\)
\(480\) 1.90040e12 + 5.44000e12i 0.0745829 + 0.213498i
\(481\) −4.02296e12 −0.156250
\(482\) 3.35157e13i 1.28829i
\(483\) 6.72990e12 2.35101e12i 0.256019 0.0894374i
\(484\) −5.85795e12 −0.220556
\(485\) 1.43235e13i 0.533753i
\(486\) −2.55169e12 2.31818e13i −0.0941122 0.855000i
\(487\) 5.24504e12 0.191471 0.0957357 0.995407i \(-0.469480\pi\)
0.0957357 + 0.995407i \(0.469480\pi\)
\(488\) 2.20267e12i 0.0795887i
\(489\) −1.04305e13 2.98579e13i −0.373045 1.06786i
\(490\) −1.15055e13 −0.407309
\(491\) 3.09503e13i 1.08457i −0.840194 0.542285i \(-0.817559\pi\)
0.840194 0.542285i \(-0.182441\pi\)
\(492\) −2.88486e12 + 1.00779e12i −0.100069 + 0.0349579i
\(493\) 1.40234e12 0.0481524
\(494\) 4.75581e13i 1.61655i
\(495\) −1.41368e13 + 1.12500e13i −0.475690 + 0.378551i
\(496\) −3.59151e13 −1.19638
\(497\) 4.42221e13i 1.45834i
\(498\) 8.79894e12 + 2.51874e13i 0.287266 + 0.822313i
\(499\) 2.83274e12 0.0915595 0.0457798 0.998952i \(-0.485423\pi\)
0.0457798 + 0.998952i \(0.485423\pi\)
\(500\) 7.27050e11i 0.0232656i
\(501\) 3.69543e13 1.29096e13i 1.17078 0.409000i
\(502\) −4.53071e13 −1.42118
\(503\) 1.23847e13i 0.384634i 0.981333 + 0.192317i \(0.0616001\pi\)
−0.981333 + 0.192317i \(0.938400\pi\)
\(504\) 3.14938e13 + 3.95753e13i 0.968439 + 1.21695i
\(505\) −1.59799e13 −0.486539
\(506\) 7.33061e12i 0.220998i
\(507\) −4.17125e12 1.19404e13i −0.124516 0.356434i
\(508\) −3.46015e12 −0.102277
\(509\) 1.15213e13i 0.337220i −0.985683 0.168610i \(-0.946072\pi\)
0.985683 0.168610i \(-0.0539279\pi\)
\(510\) −1.23721e13 + 4.32204e12i −0.358584 + 0.125267i
\(511\) −1.70136e12 −0.0488306
\(512\) 3.75966e13i 1.06856i
\(513\) −4.81239e13 3.03418e13i −1.35449 0.853994i
\(514\) −3.52012e12 −0.0981165
\(515\) 2.58096e13i 0.712434i
\(516\) 1.61239e12 + 4.61555e12i 0.0440780 + 0.126175i
\(517\) −3.36362e13 −0.910655
\(518\) 6.12783e12i 0.164308i
\(519\) −3.48333e13 + 1.21686e13i −0.925034 + 0.323150i
\(520\) 2.16311e13 0.568935
\(521\) 5.60633e13i 1.46046i 0.683200 + 0.730231i \(0.260588\pi\)
−0.683200 + 0.730231i \(0.739412\pi\)
\(522\) −1.27210e12 + 1.01233e12i −0.0328223 + 0.0261198i
\(523\) −5.51546e13 −1.40953 −0.704763 0.709442i \(-0.748947\pi\)
−0.704763 + 0.709442i \(0.748947\pi\)
\(524\) 1.31428e13i 0.332684i
\(525\) −3.77468e12 1.08052e13i −0.0946419 0.270917i
\(526\) 6.84987e13 1.70119
\(527\) 7.14345e13i 1.75734i
\(528\) 3.54013e13 1.23670e13i 0.862679 0.301367i
\(529\) 3.99467e13 0.964278
\(530\) 1.49655e13i 0.357859i
\(531\) −4.08370e12 5.13160e12i −0.0967345 0.121557i
\(532\) 2.54678e13 0.597631
\(533\) 2.05743e13i 0.478286i
\(534\) 6.66042e12 + 1.90658e13i 0.153389 + 0.439085i
\(535\) 1.77871e13 0.405823
\(536\) 3.10542e13i 0.701933i
\(537\) 6.85097e13 2.39331e13i 1.53420 0.535954i
\(538\) 2.83619e13 0.629251
\(539\) 6.54804e13i 1.43935i
\(540\) −2.84875e12 + 4.51829e12i −0.0620419 + 0.0984022i
\(541\) −4.10912e13 −0.886671 −0.443336 0.896356i \(-0.646205\pi\)
−0.443336 + 0.896356i \(0.646205\pi\)
\(542\) 4.47715e13i 0.957206i
\(543\) −4.00980e12 1.14783e13i −0.0849423 0.243152i
\(544\) −2.37889e13 −0.499321
\(545\) 1.10401e13i 0.229610i
\(546\) 6.63600e13 2.31821e13i 1.36755 0.477738i
\(547\) −8.84674e11 −0.0180654 −0.00903268 0.999959i \(-0.502875\pi\)
−0.00903268 + 0.999959i \(0.502875\pi\)
\(548\) 5.69627e12i 0.115262i
\(549\) 2.86543e12 2.28029e12i 0.0574549 0.0457223i
\(550\) −1.17697e13 −0.233858
\(551\) 3.96580e12i 0.0780860i
\(552\) −3.46255e12 9.91174e12i −0.0675618 0.193399i
\(553\) 1.54387e13 0.298528
\(554\) 3.77788e13i 0.723935i
\(555\) 2.95966e12 1.03392e12i 0.0562053 0.0196347i
\(556\) 1.01321e13 0.190689
\(557\) 4.89810e13i 0.913591i 0.889572 + 0.456795i \(0.151003\pi\)
−0.889572 + 0.456795i \(0.848997\pi\)
\(558\) −5.15677e13 6.48004e13i −0.953251 1.19786i
\(559\) 3.29172e13 0.603065
\(560\) 2.37563e13i 0.431358i
\(561\) −2.45978e13 7.04124e13i −0.442672 1.26717i
\(562\) 1.68703e13 0.300913
\(563\) 8.08485e13i 1.42932i 0.699471 + 0.714661i \(0.253419\pi\)
−0.699471 + 0.714661i \(0.746581\pi\)
\(564\) −9.38803e12 + 3.27960e12i −0.164505 + 0.0574679i
\(565\) 1.74339e13 0.302797
\(566\) 2.64782e13i 0.455834i
\(567\) −1.88794e13 + 8.19396e13i −0.322161 + 1.39823i
\(568\) 6.51300e13 1.10164
\(569\) 4.70230e13i 0.788405i 0.919024 + 0.394203i \(0.128979\pi\)
−0.919024 + 0.394203i \(0.871021\pi\)
\(570\) −1.22227e13 3.49881e13i −0.203139 0.581495i
\(571\) 3.94741e13 0.650327 0.325164 0.945658i \(-0.394581\pi\)
0.325164 + 0.945658i \(0.394581\pi\)
\(572\) 2.54123e13i 0.415016i
\(573\) −1.07260e14 + 3.74701e13i −1.73646 + 0.606613i
\(574\) −3.13390e13 −0.502950
\(575\) 2.37594e12i 0.0378004i
\(576\) 5.49295e13 4.37125e13i 0.866349 0.689435i
\(577\) 2.72198e12 0.0425605 0.0212802 0.999774i \(-0.493226\pi\)
0.0212802 + 0.999774i \(0.493226\pi\)
\(578\) 1.38827e12i 0.0215196i
\(579\) −3.73270e12 1.06850e13i −0.0573628 0.164204i
\(580\) 3.72343e11 0.00567288
\(581\) 9.61945e13i 1.45301i
\(582\) −6.47169e13 + 2.26081e13i −0.969177 + 0.338571i
\(583\) 8.51723e13 1.26461
\(584\) 2.50575e12i 0.0368871i
\(585\) 2.23933e13 + 2.81396e13i 0.326843 + 0.410713i
\(586\) −9.04546e13 −1.30901
\(587\) 1.01511e14i 1.45654i −0.685293 0.728268i \(-0.740326\pi\)
0.685293 0.728268i \(-0.259674\pi\)
\(588\) −6.38449e12 1.82759e13i −0.0908321 0.260012i
\(589\) −2.02016e14 −2.84977
\(590\) 4.27237e12i 0.0597597i
\(591\) −2.39373e13 + 8.36222e12i −0.331999 + 0.115980i
\(592\) −6.50709e12 −0.0894908
\(593\) 3.33265e13i 0.454481i 0.973839 + 0.227241i \(0.0729704\pi\)
−0.973839 + 0.227241i \(0.927030\pi\)
\(594\) 7.31433e13 + 4.61164e13i 0.989105 + 0.623624i
\(595\) 4.72507e13 0.633613
\(596\) 9.46375e12i 0.125844i
\(597\) 4.80803e12 + 1.37632e13i 0.0634009 + 0.181488i
\(598\) −1.45918e13 −0.190810
\(599\) 8.32579e13i 1.07967i −0.841771 0.539835i \(-0.818487\pi\)
0.841771 0.539835i \(-0.181513\pi\)
\(600\) −1.59138e13 + 5.55932e12i −0.204653 + 0.0714933i
\(601\) −2.42358e13 −0.309091 −0.154545 0.987986i \(-0.549391\pi\)
−0.154545 + 0.987986i \(0.549391\pi\)
\(602\) 5.01400e13i 0.634164i
\(603\) 4.03979e13 3.21484e13i 0.506725 0.403249i
\(604\) −1.62536e12 −0.0202193
\(605\) 3.07356e13i 0.379197i
\(606\) 2.52226e13 + 7.22011e13i 0.308622 + 0.883447i
\(607\) −7.69672e13 −0.934033 −0.467016 0.884249i \(-0.654671\pi\)
−0.467016 + 0.884249i \(0.654671\pi\)
\(608\) 6.72749e13i 0.809720i
\(609\) 5.53366e12 1.93312e12i 0.0660581 0.0230767i
\(610\) 2.38564e12 0.0282459
\(611\) 6.69536e13i 0.786264i
\(612\) −1.37307e13 1.72541e13i −0.159932 0.200972i
\(613\) 1.31289e14 1.51679 0.758396 0.651794i \(-0.225983\pi\)
0.758396 + 0.651794i \(0.225983\pi\)
\(614\) 1.20084e13i 0.137608i
\(615\) −5.28770e12 1.51363e13i −0.0601023 0.172046i
\(616\) −1.87520e14 −2.11419
\(617\) 4.12100e13i 0.460869i −0.973088 0.230434i \(-0.925985\pi\)
0.973088 0.230434i \(-0.0740147\pi\)
\(618\) −1.16614e14 + 4.07377e13i −1.29362 + 0.451912i
\(619\) 1.33201e14 1.46574 0.732868 0.680371i \(-0.238181\pi\)
0.732868 + 0.680371i \(0.238181\pi\)
\(620\) 1.89670e13i 0.207033i
\(621\) 9.30947e12 1.47654e13i 0.100802 0.159877i
\(622\) 3.22165e12 0.0346040
\(623\) 7.28151e13i 0.775857i
\(624\) −2.46169e13 7.04672e13i −0.260202 0.744841i
\(625\) 3.81470e12 0.0400000
\(626\) 7.78467e13i 0.809783i
\(627\) 1.99126e14 6.95624e13i 2.05490 0.717855i
\(628\) −3.95685e13 −0.405090
\(629\) 1.29425e13i 0.131451i
\(630\) −4.28626e13 + 3.41098e13i −0.431892 + 0.343697i
\(631\) −3.77275e13 −0.377148 −0.188574 0.982059i \(-0.560386\pi\)
−0.188574 + 0.982059i \(0.560386\pi\)
\(632\) 2.27380e13i 0.225511i
\(633\) 6.01038e13 + 1.72050e14i 0.591403 + 1.69292i
\(634\) 1.16056e14 1.13298
\(635\) 1.81548e13i 0.175842i
\(636\) 2.37720e13 8.30448e12i 0.228444 0.0798045i
\(637\) −1.30340e14 −1.24275
\(638\) 6.02760e12i 0.0570219i
\(639\) 6.74250e13 + 8.47267e13i 0.632873 + 0.795272i
\(640\) 2.14494e13 0.199763
\(641\) 9.57378e13i 0.884695i −0.896844 0.442347i \(-0.854146\pi\)
0.896844 0.442347i \(-0.145854\pi\)
\(642\) −2.80751e13 8.03665e13i −0.257423 0.736885i
\(643\) 1.53187e14 1.39370 0.696849 0.717218i \(-0.254585\pi\)
0.696849 + 0.717218i \(0.254585\pi\)
\(644\) 7.81403e12i 0.0705416i
\(645\) −2.42170e13 + 8.45992e12i −0.216931 + 0.0757823i
\(646\) 1.53002e14 1.35998
\(647\) 1.03278e14i 0.910935i −0.890252 0.455468i \(-0.849472\pi\)
0.890252 0.455468i \(-0.150528\pi\)
\(648\) 1.20680e14 + 2.78054e13i 1.05623 + 0.243363i
\(649\) 2.43151e13 0.211180
\(650\) 2.34279e13i 0.201914i
\(651\) 9.84725e13 + 2.81883e14i 0.842190 + 2.41081i
\(652\) 3.46677e13 0.294230
\(653\) 4.61490e13i 0.388684i −0.980934 0.194342i \(-0.937743\pi\)
0.980934 0.194342i \(-0.0622572\pi\)
\(654\) −4.98819e13 + 1.74257e13i −0.416922 + 0.145647i
\(655\) −6.89579e13 −0.571976
\(656\) 3.32786e13i 0.273934i
\(657\) −3.25970e12 + 2.59405e12i −0.0266287 + 0.0211910i
\(658\) −1.01985e14 −0.826809
\(659\) 1.66936e14i 1.34315i 0.740939 + 0.671573i \(0.234381\pi\)
−0.740939 + 0.671573i \(0.765619\pi\)
\(660\) −6.53111e12 1.86956e13i −0.0521516 0.149287i
\(661\) −9.89499e9 −7.84166e−5 −3.92083e−5 1.00000i \(-0.500012\pi\)
−3.92083e−5 1.00000i \(0.500012\pi\)
\(662\) 1.00658e14i 0.791693i
\(663\) −1.40158e14 + 4.89625e13i −1.09408 + 0.382205i
\(664\) −1.41675e14 −1.09762
\(665\) 1.33625e14i 1.02749i
\(666\) −9.34303e12 1.17405e13i −0.0713045 0.0896017i
\(667\) −1.21679e12 −0.00921691
\(668\) 4.29073e13i 0.322589i
\(669\) −8.53409e13 2.44293e14i −0.636834 1.82297i
\(670\) 3.36336e13 0.249115
\(671\) 1.35772e13i 0.0998158i
\(672\) −9.38717e13 + 3.27930e13i −0.684997 + 0.239296i
\(673\) −1.95710e14 −1.41755 −0.708773 0.705436i \(-0.750751\pi\)
−0.708773 + 0.705436i \(0.750751\pi\)
\(674\) 9.63497e13i 0.692709i
\(675\) −2.37066e13 1.49469e13i −0.169181 0.106667i
\(676\) 1.38639e13 0.0982092
\(677\) 8.39435e13i 0.590261i 0.955457 + 0.295130i \(0.0953631\pi\)
−0.955457 + 0.295130i \(0.904637\pi\)
\(678\) −2.75175e13 7.87703e13i −0.192070 0.549812i
\(679\) 2.47164e14 1.71252
\(680\) 6.95905e13i 0.478636i
\(681\) 6.92030e12 2.41753e12i 0.0472486 0.0165058i
\(682\) 3.07044e14 2.08103
\(683\) 1.05484e14i 0.709717i −0.934920 0.354858i \(-0.884529\pi\)
0.934920 0.354858i \(-0.115471\pi\)
\(684\) 4.87946e13 3.88304e13i 0.325905 0.259353i
\(685\) 2.98873e13 0.198168
\(686\) 1.10314e13i 0.0726122i
\(687\) 6.50610e13 + 1.86240e14i 0.425145 + 1.21700i
\(688\) 5.32432e13 0.345400
\(689\) 1.69538e14i 1.09187i
\(690\) 1.07351e13 3.75017e12i 0.0686371 0.0239776i
\(691\) −2.96033e14 −1.87910 −0.939551 0.342409i \(-0.888757\pi\)
−0.939551 + 0.342409i \(0.888757\pi\)
\(692\) 4.04447e13i 0.254877i
\(693\) −1.94127e14 2.43941e14i −1.21456 1.52623i
\(694\) −1.88557e14 −1.17124
\(695\) 5.31614e13i 0.327848i
\(696\) −2.84709e12 8.14994e12i −0.0174323 0.0499009i
\(697\) 6.61905e13 0.402375
\(698\) 1.40665e14i 0.849003i
\(699\) −1.20259e14 + 4.20111e13i −0.720662 + 0.251755i
\(700\) 1.25458e13 0.0746465
\(701\) 3.27773e14i 1.93635i 0.250276 + 0.968175i \(0.419479\pi\)
−0.250276 + 0.968175i \(0.580521\pi\)
\(702\) 9.17958e13 1.45594e14i 0.538440 0.853998i
\(703\) −3.66013e13 −0.213167
\(704\) 2.60272e14i 1.50510i
\(705\) −1.72075e13 4.92573e13i −0.0988033 0.282829i
\(706\) −7.96740e13 −0.454248
\(707\) 2.75747e14i 1.56104i
\(708\) 6.78647e12 2.37078e12i 0.0381485 0.0133267i
\(709\) −4.95628e13 −0.276646 −0.138323 0.990387i \(-0.544171\pi\)
−0.138323 + 0.990387i \(0.544171\pi\)
\(710\) 7.05400e13i 0.390970i
\(711\) 2.95795e13 2.35392e13i 0.162796 0.129552i
\(712\) −1.07242e14 −0.586089
\(713\) 6.19826e13i 0.336374i
\(714\) −7.45803e13 2.13490e14i −0.401914 1.15050i
\(715\) −1.33334e14 −0.713527
\(716\) 7.95460e13i 0.422721i
\(717\) 3.81822e13 1.33385e13i 0.201495 0.0703902i
\(718\) 1.61664e14 0.847211
\(719\) 5.69586e13i 0.296425i −0.988956 0.148213i \(-0.952648\pi\)
0.988956 0.148213i \(-0.0473520\pi\)
\(720\) 3.62209e13 + 4.55154e13i 0.187196 + 0.235232i
\(721\) 4.45365e14 2.28581
\(722\) 2.63928e14i 1.34524i
\(723\) 9.75812e13 + 2.79331e14i 0.493940 + 1.41393i
\(724\) 1.33273e13 0.0669962
\(725\) 1.95362e12i 0.00975325i
\(726\) −1.38871e14 + 4.85129e13i −0.688537 + 0.240533i
\(727\) −2.81767e14 −1.38745 −0.693726 0.720239i \(-0.744032\pi\)
−0.693726 + 0.720239i \(0.744032\pi\)
\(728\) 3.73263e14i 1.82540i
\(729\) 8.87607e13 + 1.85776e14i 0.431105 + 0.902302i
\(730\) −2.71389e12 −0.0130912
\(731\) 1.05900e14i 0.507350i
\(732\) 1.32381e12 + 3.78948e12i 0.00629899 + 0.0180312i
\(733\) −1.04493e14 −0.493819 −0.246909 0.969039i \(-0.579415\pi\)
−0.246909 + 0.969039i \(0.579415\pi\)
\(734\) 3.48908e13i 0.163768i
\(735\) 9.58904e13 3.34982e13i 0.447032 0.156166i
\(736\) 2.06413e13 0.0955757
\(737\) 1.91417e14i 0.880327i
\(738\) −6.00434e13 + 4.77822e13i −0.274273 + 0.218265i
\(739\) −2.65253e13 −0.120348 −0.0601740 0.998188i \(-0.519166\pi\)
−0.0601740 + 0.998188i \(0.519166\pi\)
\(740\) 3.43644e12i 0.0154864i
\(741\) −1.38466e14 3.96365e14i −0.619800 1.77421i
\(742\) 2.58242e14 1.14817
\(743\) 1.68581e14i 0.744499i −0.928133 0.372249i \(-0.878587\pi\)
0.928133 0.372249i \(-0.121413\pi\)
\(744\) 4.15155e14 1.45030e14i 1.82115 0.636197i
\(745\) −4.96546e13 −0.216361
\(746\) 1.68485e12i 0.00729234i
\(747\) −1.46667e14 1.84302e14i −0.630563 0.792369i
\(748\) 8.17553e13 0.349147
\(749\) 3.06932e14i 1.30206i
\(750\) −6.02110e12 1.72357e13i −0.0253729 0.0726311i
\(751\) 1.56240e14 0.654021 0.327011 0.945021i \(-0.393959\pi\)
0.327011 + 0.945021i \(0.393959\pi\)
\(752\) 1.08297e14i 0.450325i
\(753\) 3.77605e14 1.31912e14i 1.55978 0.544891i
\(754\) −1.19981e13 −0.0492329
\(755\) 8.52799e12i 0.0347626i
\(756\) −7.79667e13 4.91575e13i −0.315719 0.199059i
\(757\) −1.61527e14 −0.649779 −0.324890 0.945752i \(-0.605327\pi\)
−0.324890 + 0.945752i \(0.605327\pi\)
\(758\) 2.20859e14i 0.882612i
\(759\) 2.13431e13 + 6.10958e13i 0.0847323 + 0.242551i
\(760\) 1.96802e14 0.776177
\(761\) 3.55804e14i 1.39408i −0.717033 0.697039i \(-0.754500\pi\)
0.717033 0.697039i \(-0.245500\pi\)
\(762\) −8.20276e13 + 2.86554e13i −0.319290 + 0.111540i
\(763\) 1.90507e14 0.736694
\(764\) 1.24539e14i 0.478451i
\(765\) 9.05293e13 7.20427e13i 0.345527 0.274968i
\(766\) 9.45622e13 0.358570
\(767\) 4.83998e13i 0.182334i
\(768\) 6.37048e13 + 1.82358e14i 0.238433 + 0.682526i
\(769\) 1.37014e13 0.0509489 0.0254744 0.999675i \(-0.491890\pi\)
0.0254744 + 0.999675i \(0.491890\pi\)
\(770\) 2.03096e14i 0.750321i
\(771\) 2.93379e13 1.02489e13i 0.107685 0.0376187i
\(772\) 1.24063e13 0.0452435
\(773\) 6.08347e13i 0.220421i −0.993908 0.110211i \(-0.964847\pi\)
0.993908 0.110211i \(-0.0351526\pi\)
\(774\) 7.64478e13 + 9.60648e13i 0.275208 + 0.345828i
\(775\) −9.95165e13 −0.355948
\(776\) 3.64021e14i 1.29365i
\(777\) 1.78412e13 + 5.10714e13i 0.0629969 + 0.180332i
\(778\) −3.94718e14 −1.38481
\(779\) 1.87186e14i 0.652509i
\(780\) −3.72142e13 + 1.30003e13i −0.128895 + 0.0450279i
\(781\) −4.01461e14 −1.38162
\(782\) 4.69439e13i 0.160526i
\(783\) 7.65472e12 1.21408e13i 0.0260088 0.0412515i
\(784\) −2.10824e14 −0.711770
\(785\) 2.07609e14i 0.696462i
\(786\) 1.08843e14 + 3.11568e14i 0.362817 + 1.03858i
\(787\) −8.80368e13 −0.291602 −0.145801 0.989314i \(-0.546576\pi\)
−0.145801 + 0.989314i \(0.546576\pi\)
\(788\) 2.77934e13i 0.0914766i
\(789\) −5.70891e14 + 1.99434e14i −1.86710 + 0.652251i
\(790\) 2.46267e13 0.0800333
\(791\) 3.00836e14i 0.971509i
\(792\) −3.59275e14 + 2.85909e14i −1.15293 + 0.917492i
\(793\) 2.70259e13 0.0861814
\(794\) 2.13770e14i 0.677400i
\(795\) 4.35721e13 + 1.24727e14i 0.137206 + 0.392759i
\(796\) −1.59804e13 −0.0500059
\(797\) 2.80333e14i 0.871731i 0.900012 + 0.435865i \(0.143558\pi\)
−0.900012 + 0.435865i \(0.856442\pi\)
\(798\) 6.03749e14 2.10913e14i 1.86570 0.651761i
\(799\) 2.15400e14 0.661472
\(800\) 3.31407e13i 0.101137i
\(801\) −1.11020e14 1.39509e14i −0.336698 0.423097i
\(802\) −3.12657e14 −0.942317
\(803\) 1.54454e13i 0.0462618i
\(804\) 1.86636e13 + 5.34256e13i 0.0555540 + 0.159026i
\(805\) −4.09988e13 −0.121281
\(806\) 6.11178e14i 1.79677i
\(807\) −2.36378e14 + 8.25758e13i −0.690619 + 0.241260i
\(808\) −4.06118e14 −1.17922
\(809\) 3.04518e14i 0.878759i 0.898302 + 0.439379i \(0.144802\pi\)
−0.898302 + 0.439379i \(0.855198\pi\)
\(810\) −3.01151e13 + 1.30704e14i −0.0863691 + 0.374856i
\(811\) 4.61813e14 1.31632 0.658161 0.752877i \(-0.271335\pi\)
0.658161 + 0.752877i \(0.271335\pi\)
\(812\) 6.42509e12i 0.0182012i
\(813\) −1.30353e14 3.73141e14i −0.367001 1.05056i
\(814\) 5.56301e13 0.155664
\(815\) 1.81895e14i 0.505864i
\(816\) −2.26703e14 + 7.91963e13i −0.626624 + 0.218904i
\(817\) 2.99484e14 0.822741
\(818\) 2.69560e14i 0.736020i
\(819\) −4.85572e14 + 3.86415e14i −1.31775 + 1.04866i
\(820\) 1.75746e13 0.0474043
\(821\) 2.35728e14i 0.631968i −0.948764 0.315984i \(-0.897665\pi\)
0.948764 0.315984i \(-0.102335\pi\)
\(822\) −4.71740e13 1.35038e14i −0.125702 0.359829i
\(823\) −6.77056e13 −0.179319 −0.0896593 0.995972i \(-0.528578\pi\)
−0.0896593 + 0.995972i \(0.528578\pi\)
\(824\) 6.55931e14i 1.72672i
\(825\) 9.80926e13 3.42676e13i 0.256665 0.0896630i
\(826\) 7.37232e13 0.191736
\(827\) 5.95756e14i 1.54007i −0.638001 0.770036i \(-0.720238\pi\)
0.638001 0.770036i \(-0.279762\pi\)
\(828\) 1.19140e13 + 1.49712e13i 0.0306129 + 0.0384684i
\(829\) 5.82336e14 1.48731 0.743654 0.668565i \(-0.233091\pi\)
0.743654 + 0.668565i \(0.233091\pi\)
\(830\) 1.53443e14i 0.389543i
\(831\) −1.09993e14 3.14861e14i −0.277563 0.794537i
\(832\) 5.18079e14 1.29951
\(833\) 4.19325e14i 1.04550i
\(834\) 2.40196e14 8.39097e13i 0.595299 0.207961i
\(835\) −2.25127e14 −0.554619
\(836\) 2.31203e14i 0.566191i
\(837\) 6.18450e14 + 3.89928e14i 1.50549 + 0.949200i
\(838\) −5.44583e14 −1.31778
\(839\) 5.35480e14i 1.28805i −0.765003 0.644026i \(-0.777263\pi\)
0.765003 0.644026i \(-0.222737\pi\)
\(840\) −9.59306e13 2.74606e14i −0.229383 0.656620i
\(841\) 4.19707e14 0.997622
\(842\) 2.68282e14i 0.633915i
\(843\) −1.40603e14 + 4.91180e13i −0.330260 + 0.115373i
\(844\) −1.99766e14 −0.466455
\(845\) 7.27414e13i 0.168849i
\(846\) −1.95396e14 + 1.55495e14i −0.450882 + 0.358810i
\(847\) 5.30368e14 1.21663
\(848\) 2.74225e14i 0.625356i
\(849\) 7.70915e13 + 2.20678e14i 0.174770 + 0.500289i
\(850\) 7.53710e13 0.169867
\(851\) 1.12300e13i 0.0251612i
\(852\) −1.12050e14 + 3.91433e13i −0.249582 + 0.0871885i
\(853\) −1.47772e14 −0.327225 −0.163612 0.986525i \(-0.552315\pi\)
−0.163612 + 0.986525i \(0.552315\pi\)
\(854\) 4.11661e13i 0.0906256i
\(855\) 2.03736e14 + 2.56016e14i 0.445900 + 0.560321i
\(856\) 4.52047e14 0.983591
\(857\) 8.21818e14i 1.77775i 0.458146 + 0.888877i \(0.348514\pi\)
−0.458146 + 0.888877i \(0.651486\pi\)
\(858\) 2.10453e14 + 6.02434e14i 0.452605 + 1.29561i
\(859\) −6.19313e14 −1.32417 −0.662086 0.749428i \(-0.730328\pi\)
−0.662086 + 0.749428i \(0.730328\pi\)
\(860\) 2.81181e13i 0.0597714i
\(861\) 2.61190e14 9.12436e13i 0.552001 0.192835i
\(862\) −5.00801e13 −0.105228
\(863\) 6.20768e14i 1.29681i −0.761297 0.648403i \(-0.775437\pi\)
0.761297 0.648403i \(-0.224563\pi\)
\(864\) −1.29853e14 + 2.05954e14i −0.269701 + 0.427762i
\(865\) 2.12206e14 0.438204
\(866\) 5.17960e14i 1.06343i
\(867\) −4.04196e12 1.15703e13i −0.00825080 0.0236183i
\(868\) −3.27291e14 −0.664257
\(869\) 1.40157e14i 0.282823i
\(870\) 8.82691e12 3.08358e12i 0.0177097 0.00618670i
\(871\) 3.81021e14 0.760078
\(872\) 2.80577e14i 0.556505i
\(873\) 4.73549e14 3.76848e14i 0.933886 0.743181i
\(874\) −1.32757e14 −0.260316
\(875\) 6.58257e13i 0.128338i
\(876\) −1.50596e12 4.31090e12i −0.00291940 0.00835694i
\(877\) −4.15719e14 −0.801313 −0.400656 0.916228i \(-0.631218\pi\)
−0.400656 + 0.916228i \(0.631218\pi\)
\(878\) 3.62302e14i 0.694381i
\(879\) 7.53879e14 2.63359e14i 1.43667 0.501885i
\(880\) −2.15666e14 −0.408665
\(881\) 9.63563e14i 1.81552i 0.419491 + 0.907759i \(0.362208\pi\)
−0.419491 + 0.907759i \(0.637792\pi\)
\(882\) −3.02706e14 3.80382e14i −0.567124 0.712652i
\(883\) −1.56289e14 −0.291156 −0.145578 0.989347i \(-0.546504\pi\)
−0.145578 + 0.989347i \(0.546504\pi\)
\(884\) 1.62736e14i 0.301455i
\(885\) 1.24390e13 + 3.56074e13i 0.0229124 + 0.0655878i
\(886\) −3.37163e13 −0.0617549
\(887\) 4.22682e14i 0.769831i −0.922952 0.384916i \(-0.874231\pi\)
0.922952 0.384916i \(-0.125769\pi\)
\(888\) 7.52176e13 2.62764e13i 0.136224 0.0475884i
\(889\) 3.13276e14 0.564180
\(890\) 1.16150e14i 0.208002i
\(891\) −7.43870e14 1.71392e14i −1.32467 0.305213i
\(892\) 2.83646e14 0.502288
\(893\) 6.09150e14i 1.07267i
\(894\) 7.83746e13 + 2.24351e14i 0.137242 + 0.392863i
\(895\) −4.17364e14 −0.726774
\(896\) 3.70127e14i 0.640930i
\(897\) 1.21613e14 4.24841e13i 0.209419 0.0731583i
\(898\) 7.25061e13 0.124163
\(899\) 5.09653e13i 0.0867912i
\(900\) 2.40370e13 1.91285e13i 0.0407069 0.0323943i
\(901\) −5.45428e14 −0.918572
\(902\) 2.84504e14i 0.476491i
\(903\) −1.45983e14 4.17883e14i −0.243144 0.696011i
\(904\) 4.43068e14 0.733886
\(905\) 6.99260e13i 0.115185i
\(906\) −3.85315e13 + 1.34605e13i −0.0631211 + 0.0220506i
\(907\) −4.69868e14 −0.765490 −0.382745 0.923854i \(-0.625021\pi\)
−0.382745 + 0.923854i \(0.625021\pi\)
\(908\) 8.03510e12i 0.0130185i
\(909\) −4.20428e14 5.28313e14i −0.677442 0.851278i
\(910\) −4.04267e14 −0.647831
\(911\) 4.83462e14i 0.770496i 0.922813 + 0.385248i \(0.125884\pi\)
−0.922813 + 0.385248i \(0.874116\pi\)
\(912\) −2.23967e14 6.41116e14i −0.354984 1.01616i
\(913\) 8.73280e14 1.37657
\(914\) 6.15531e14i 0.964981i
\(915\) −1.98827e13 + 6.94580e12i −0.0310006 + 0.0108297i
\(916\) −2.16242e14 −0.335323
\(917\) 1.18993e15i 1.83516i
\(918\) −4.68397e14 2.95321e14i −0.718457 0.452982i
\(919\) −6.42475e14 −0.980118 −0.490059 0.871689i \(-0.663025\pi\)
−0.490059 + 0.871689i \(0.663025\pi\)
\(920\) 6.03827e13i 0.0916164i
\(921\) 3.49627e13 + 1.00082e14i 0.0527602 + 0.151029i
\(922\) −2.56419e14 −0.384853
\(923\) 7.99118e14i 1.19289i
\(924\) 3.22609e14 1.12700e14i 0.478979 0.167326i
\(925\) −1.80304e13 −0.0266254
\(926\) 2.10346e14i 0.308944i
\(927\) 8.53290e14 6.79043e14i 1.24652 0.991970i
\(928\) 1.69723e13 0.0246605
\(929\) 1.29783e14i 0.187559i −0.995593 0.0937796i \(-0.970105\pi\)
0.995593 0.0937796i \(-0.0298949\pi\)
\(930\) 1.57076e14 + 4.49639e14i 0.225785 + 0.646322i
\(931\) −1.18585e15 −1.69543
\(932\) 1.39632e14i 0.198566i
\(933\) −2.68503e13 + 9.37985e12i −0.0379788 + 0.0132675i
\(934\) 7.18405e14 1.01073
\(935\) 4.28955e14i 0.600280i
\(936\) 5.69109e14 + 7.15147e14i 0.792167 + 0.995442i
\(937\) −4.95593e14 −0.686163 −0.343081 0.939306i \(-0.611471\pi\)
−0.343081 + 0.939306i \(0.611471\pi\)
\(938\) 5.80376e14i 0.799274i
\(939\) −2.26651e14 6.48801e14i −0.310477 0.888758i
\(940\) 5.71922e13 0.0779287
\(941\) 1.14019e15i 1.54536i −0.634794 0.772682i \(-0.718915\pi\)
0.634794 0.772682i \(-0.281085\pi\)
\(942\) −9.38026e14 + 3.27689e14i −1.26462 + 0.441781i
\(943\) −5.74325e13 −0.0770192
\(944\) 7.82861e13i 0.104430i
\(945\) 2.57920e14 4.09077e14i 0.342237 0.542808i
\(946\) −4.55184e14 −0.600802
\(947\) 5.62820e14i 0.738958i 0.929239 + 0.369479i \(0.120464\pi\)
−0.929239 + 0.369479i \(0.879536\pi\)
\(948\) 1.36656e13 + 3.91184e13i 0.0178479 + 0.0510905i
\(949\) −3.07445e13 −0.0399426
\(950\) 2.13149e14i 0.275464i
\(951\) −9.67251e14 + 3.37898e14i −1.24347 + 0.434394i
\(952\) 1.20084e15 1.53568
\(953\) 3.36550e14i 0.428140i −0.976818 0.214070i \(-0.931328\pi\)
0.976818 0.214070i \(-0.0686720\pi\)
\(954\) 4.94774e14 3.93738e14i 0.626131 0.498271i
\(955\) 6.53432e14 0.822590
\(956\) 4.43330e13i 0.0555185i
\(957\) 1.75494e13 + 5.02361e13i 0.0218627 + 0.0625830i
\(958\) 1.12489e15 1.39407
\(959\) 5.15730e14i 0.635813i
\(960\) −3.81146e14 + 1.33149e14i −0.467450 + 0.163299i
\(961\) 1.77652e15 2.16747
\(962\) 1.10733e14i 0.134401i
\(963\) 4.67975e14 + 5.88061e14i 0.565056 + 0.710053i
\(964\) −3.24329e14 −0.389584
\(965\) 6.50936e13i 0.0777861i
\(966\) 6.47122e13 + 1.85242e14i 0.0769309 + 0.220219i
\(967\) 1.61188e14 0.190634 0.0953172 0.995447i \(-0.469613\pi\)
0.0953172 + 0.995447i \(0.469613\pi\)
\(968\) 7.81122e14i 0.919056i
\(969\) −1.27517e15 + 4.45465e14i −1.49262 + 0.521429i
\(970\) 3.94258e14 0.459115
\(971\) 1.34616e15i 1.55955i 0.626060 + 0.779775i \(0.284666\pi\)
−0.626060 + 0.779775i \(0.715334\pi\)
\(972\) −2.24329e14 + 2.46925e13i −0.258556 + 0.0284599i
\(973\) −9.17343e14 −1.05188
\(974\) 1.44371e14i 0.164697i
\(975\) −6.82104e13 1.95256e14i −0.0774155 0.221606i
\(976\) 4.37140e13 0.0493596
\(977\) 1.10154e15i 1.23745i 0.785609 + 0.618724i \(0.212350\pi\)
−0.785609 + 0.618724i \(0.787650\pi\)
\(978\) 8.21846e14 2.87103e14i 0.918536 0.320880i
\(979\) 6.61035e14 0.735041
\(980\) 1.11338e14i 0.123172i
\(981\) 3.64998e14 2.90463e14i 0.401740 0.319702i
\(982\) 8.51916e14 0.932909
\(983\) 9.85641e14i 1.07387i −0.843624 0.536934i \(-0.819582\pi\)
0.843624 0.536934i \(-0.180418\pi\)
\(984\) −1.34383e14 3.84678e14i −0.145669 0.416986i
\(985\) 1.45827e14 0.157274
\(986\) 3.85997e13i 0.0414190i
\(987\) 8.49975e14 2.96929e14i 0.907445 0.317006i
\(988\) 4.60217e14 0.488852
\(989\) 9.18876e13i 0.0971126i
\(990\) −3.09658e14 3.89118e14i −0.325616 0.409172i
\(991\) −1.20714e15 −1.26296 −0.631481 0.775392i \(-0.717552\pi\)
−0.631481 + 0.775392i \(0.717552\pi\)
\(992\) 8.64562e14i 0.899991i
\(993\) 2.93066e14 + 8.38915e14i 0.303542 + 0.868904i
\(994\) −1.21723e15 −1.25441
\(995\) 8.38461e13i 0.0859740i
\(996\) 2.43737e14 8.51467e13i 0.248671 0.0868703i
\(997\) −1.43111e15 −1.45277 −0.726387 0.687286i \(-0.758802\pi\)
−0.726387 + 0.687286i \(0.758802\pi\)
\(998\) 7.79718e13i 0.0787563i
\(999\) 1.12051e14 + 7.06471e13i 0.112613 + 0.0710014i
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 15.11.c.a.11.10 yes 14
3.2 odd 2 inner 15.11.c.a.11.5 14
4.3 odd 2 240.11.l.b.161.10 14
5.2 odd 4 75.11.d.d.74.10 28
5.3 odd 4 75.11.d.d.74.19 28
5.4 even 2 75.11.c.g.26.5 14
12.11 even 2 240.11.l.b.161.9 14
15.2 even 4 75.11.d.d.74.20 28
15.8 even 4 75.11.d.d.74.9 28
15.14 odd 2 75.11.c.g.26.10 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.11.c.a.11.5 14 3.2 odd 2 inner
15.11.c.a.11.10 yes 14 1.1 even 1 trivial
75.11.c.g.26.5 14 5.4 even 2
75.11.c.g.26.10 14 15.14 odd 2
75.11.d.d.74.9 28 15.8 even 4
75.11.d.d.74.10 28 5.2 odd 4
75.11.d.d.74.19 28 5.3 odd 4
75.11.d.d.74.20 28 15.2 even 4
240.11.l.b.161.9 14 12.11 even 2
240.11.l.b.161.10 14 4.3 odd 2