Properties

Label 75.9.c.e.26.9
Level $75$
Weight $9$
Character 75.26
Analytic conductor $30.553$
Analytic rank $0$
Dimension $10$
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] = [75,9,Mod(26,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.26");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.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: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 1634x^{8} + 776307x^{6} + 148116566x^{4} + 10575941812x^{2} + 105274575720 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{8}\cdot 3^{11}\cdot 5^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 26.9
Root \(-13.5890i\) of defining polynomial
Character \(\chi\) \(=\) 75.26
Dual form 75.9.c.e.26.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+24.1370i q^{2} +(39.5746 + 70.6742i) q^{3} -326.594 q^{4} +(-1705.86 + 955.212i) q^{6} -1042.22 q^{7} -1703.92i q^{8} +(-3428.70 + 5593.81i) q^{9} +O(q^{10})\) \(q+24.1370i q^{2} +(39.5746 + 70.6742i) q^{3} -326.594 q^{4} +(-1705.86 + 955.212i) q^{6} -1042.22 q^{7} -1703.92i q^{8} +(-3428.70 + 5593.81i) q^{9} +19553.4i q^{11} +(-12924.8 - 23081.8i) q^{12} -29037.8 q^{13} -25156.0i q^{14} -42480.5 q^{16} -122230. i q^{17} +(-135018. - 82758.4i) q^{18} +189552. q^{19} +(-41245.5 - 73658.1i) q^{21} -471959. q^{22} -112212. i q^{23} +(120424. - 67432.2i) q^{24} -700886. i q^{26} +(-531028. - 20947.3i) q^{27} +340383. q^{28} +108842. i q^{29} -1.19254e6 q^{31} -1.46155e6i q^{32} +(-1.38192e6 + 773817. i) q^{33} +2.95026e6 q^{34} +(1.11979e6 - 1.82691e6i) q^{36} +2.84100e6 q^{37} +4.57521e6i q^{38} +(-1.14916e6 - 2.05223e6i) q^{39} +3.90516e6i q^{41} +(1.77788e6 - 995541. i) q^{42} +864712. q^{43} -6.38601e6i q^{44} +2.70846e6 q^{46} -1.48368e6i q^{47} +(-1.68115e6 - 3.00227e6i) q^{48} -4.67858e6 q^{49} +(8.63850e6 - 4.83720e6i) q^{51} +9.48358e6 q^{52} +3.65103e6i q^{53} +(505604. - 1.28174e7i) q^{54} +1.77586e6i q^{56} +(7.50144e6 + 1.33964e7i) q^{57} -2.62712e6 q^{58} -1.46586e7i q^{59} +1.60123e7 q^{61} -2.87844e7i q^{62} +(3.57345e6 - 5.82998e6i) q^{63} +2.44025e7 q^{64} +(-1.86776e7 - 3.33554e7i) q^{66} -2.14382e7 q^{67} +3.99195e7i q^{68} +(7.93050e6 - 4.44075e6i) q^{69} +4.10459e7i q^{71} +(9.53144e6 + 5.84224e6i) q^{72} -4.70244e7 q^{73} +6.85731e7i q^{74} -6.19065e7 q^{76} -2.03789e7i q^{77} +(4.95346e7 - 2.77373e7i) q^{78} -2.43754e7 q^{79} +(-1.95348e7 - 3.83590e7i) q^{81} -9.42589e7 q^{82} -6.88381e6i q^{83} +(1.34705e7 + 2.40563e7i) q^{84} +2.08715e7i q^{86} +(-7.69233e6 + 4.30738e6i) q^{87} +3.33174e7 q^{88} +3.39808e7i q^{89} +3.02638e7 q^{91} +3.66478e7i q^{92} +(-4.71945e7 - 8.42822e7i) q^{93} +3.58116e7 q^{94} +(1.03294e8 - 5.78405e7i) q^{96} -1.50338e7 q^{97} -1.12927e8i q^{98} +(-1.09378e8 - 6.70425e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 25 q^{3} - 1554 q^{4} + 2257 q^{6} + 1960 q^{7} - 11207 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 25 q^{3} - 1554 q^{4} + 2257 q^{6} + 1960 q^{7} - 11207 q^{9} - 5915 q^{12} - 16920 q^{13} + 44634 q^{16} - 224875 q^{18} - 143934 q^{19} + 673428 q^{21} + 818990 q^{22} - 1016859 q^{24} - 260830 q^{27} + 3810100 q^{28} - 3014060 q^{31} - 4677515 q^{33} + 4977146 q^{34} + 4500527 q^{36} + 3016760 q^{37} - 7513282 q^{39} - 4001760 q^{42} + 11747340 q^{43} - 13938636 q^{46} - 14748755 q^{48} + 8953546 q^{49} + 6209287 q^{51} - 38918320 q^{52} - 8886272 q^{54} + 14759525 q^{57} - 48407900 q^{58} + 1520220 q^{61} + 74748240 q^{63} - 4536998 q^{64} + 10465295 q^{66} - 16269290 q^{67} + 11394978 q^{69} + 172231185 q^{72} - 52090170 q^{73} - 29529046 q^{76} + 198205810 q^{78} + 8549896 q^{79} + 22612945 q^{81} - 295714190 q^{82} - 136883292 q^{84} + 318901610 q^{87} - 310673250 q^{88} - 107224264 q^{91} + 79679130 q^{93} + 356118596 q^{94} + 525424001 q^{96} - 402167800 q^{97} - 382421335 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 24.1370i 1.50856i 0.656552 + 0.754281i \(0.272014\pi\)
−0.656552 + 0.754281i \(0.727986\pi\)
\(3\) 39.5746 + 70.6742i 0.488576 + 0.872521i
\(4\) −326.594 −1.27576
\(5\) 0 0
\(6\) −1705.86 + 955.212i −1.31625 + 0.737047i
\(7\) −1042.22 −0.434077 −0.217039 0.976163i \(-0.569640\pi\)
−0.217039 + 0.976163i \(0.569640\pi\)
\(8\) 1703.92i 0.415997i
\(9\) −3428.70 + 5593.81i −0.522587 + 0.852586i
\(10\) 0 0
\(11\) 19553.4i 1.33552i 0.744376 + 0.667761i \(0.232747\pi\)
−0.744376 + 0.667761i \(0.767253\pi\)
\(12\) −12924.8 23081.8i −0.623304 1.11313i
\(13\) −29037.8 −1.01670 −0.508348 0.861152i \(-0.669743\pi\)
−0.508348 + 0.861152i \(0.669743\pi\)
\(14\) 25156.0i 0.654832i
\(15\) 0 0
\(16\) −42480.5 −0.648200
\(17\) 122230.i 1.46346i −0.681594 0.731731i \(-0.738713\pi\)
0.681594 0.731731i \(-0.261287\pi\)
\(18\) −135018. 82758.4i −1.28618 0.788355i
\(19\) 189552. 1.45450 0.727250 0.686373i \(-0.240798\pi\)
0.727250 + 0.686373i \(0.240798\pi\)
\(20\) 0 0
\(21\) −41245.5 73658.1i −0.212080 0.378742i
\(22\) −471959. −2.01472
\(23\) 112212.i 0.400985i −0.979695 0.200493i \(-0.935746\pi\)
0.979695 0.200493i \(-0.0642543\pi\)
\(24\) 120424. 67432.2i 0.362966 0.203246i
\(25\) 0 0
\(26\) 700886.i 1.53375i
\(27\) −531028. 20947.3i −0.999223 0.0394160i
\(28\) 340383. 0.553777
\(29\) 108842.i 0.153888i 0.997035 + 0.0769440i \(0.0245163\pi\)
−0.997035 + 0.0769440i \(0.975484\pi\)
\(30\) 0 0
\(31\) −1.19254e6 −1.29130 −0.645651 0.763633i \(-0.723414\pi\)
−0.645651 + 0.763633i \(0.723414\pi\)
\(32\) 1.46155e6i 1.39385i
\(33\) −1.38192e6 + 773817.i −1.16527 + 0.652503i
\(34\) 2.95026e6 2.20772
\(35\) 0 0
\(36\) 1.11979e6 1.82691e6i 0.666695 1.08769i
\(37\) 2.84100e6 1.51588 0.757939 0.652326i \(-0.226207\pi\)
0.757939 + 0.652326i \(0.226207\pi\)
\(38\) 4.57521e6i 2.19420i
\(39\) −1.14916e6 2.05223e6i −0.496733 0.887088i
\(40\) 0 0
\(41\) 3.90516e6i 1.38199i 0.722861 + 0.690993i \(0.242827\pi\)
−0.722861 + 0.690993i \(0.757173\pi\)
\(42\) 1.77788e6 995541.i 0.571355 0.319935i
\(43\) 864712. 0.252928 0.126464 0.991971i \(-0.459637\pi\)
0.126464 + 0.991971i \(0.459637\pi\)
\(44\) 6.38601e6i 1.70380i
\(45\) 0 0
\(46\) 2.70846e6 0.604911
\(47\) 1.48368e6i 0.304053i −0.988376 0.152026i \(-0.951420\pi\)
0.988376 0.152026i \(-0.0485799\pi\)
\(48\) −1.68115e6 3.00227e6i −0.316695 0.565569i
\(49\) −4.67858e6 −0.811577
\(50\) 0 0
\(51\) 8.63850e6 4.83720e6i 1.27690 0.715012i
\(52\) 9.48358e6 1.29706
\(53\) 3.65103e6i 0.462713i 0.972869 + 0.231357i \(0.0743164\pi\)
−0.972869 + 0.231357i \(0.925684\pi\)
\(54\) 505604. 1.28174e7i 0.0594615 1.50739i
\(55\) 0 0
\(56\) 1.77586e6i 0.180575i
\(57\) 7.50144e6 + 1.33964e7i 0.710633 + 1.26908i
\(58\) −2.62712e6 −0.232149
\(59\) 1.46586e7i 1.20972i −0.796332 0.604859i \(-0.793229\pi\)
0.796332 0.604859i \(-0.206771\pi\)
\(60\) 0 0
\(61\) 1.60123e7 1.15647 0.578234 0.815871i \(-0.303742\pi\)
0.578234 + 0.815871i \(0.303742\pi\)
\(62\) 2.87844e7i 1.94801i
\(63\) 3.57345e6 5.82998e6i 0.226843 0.370088i
\(64\) 2.44025e7 1.45450
\(65\) 0 0
\(66\) −1.86776e7 3.33554e7i −0.984341 1.75788i
\(67\) −2.14382e7 −1.06387 −0.531937 0.846784i \(-0.678536\pi\)
−0.531937 + 0.846784i \(0.678536\pi\)
\(68\) 3.99195e7i 1.86702i
\(69\) 7.93050e6 4.44075e6i 0.349868 0.195912i
\(70\) 0 0
\(71\) 4.10459e7i 1.61524i 0.589706 + 0.807618i \(0.299244\pi\)
−0.589706 + 0.807618i \(0.700756\pi\)
\(72\) 9.53144e6 + 5.84224e6i 0.354673 + 0.217395i
\(73\) −4.70244e7 −1.65589 −0.827946 0.560808i \(-0.810491\pi\)
−0.827946 + 0.560808i \(0.810491\pi\)
\(74\) 6.85731e7i 2.28679i
\(75\) 0 0
\(76\) −6.19065e7 −1.85559
\(77\) 2.03789e7i 0.579719i
\(78\) 4.95346e7 2.77373e7i 1.33823 0.749352i
\(79\) −2.43754e7 −0.625811 −0.312905 0.949784i \(-0.601302\pi\)
−0.312905 + 0.949784i \(0.601302\pi\)
\(80\) 0 0
\(81\) −1.95348e7 3.83590e7i −0.453805 0.891101i
\(82\) −9.42589e7 −2.08481
\(83\) 6.88381e6i 0.145050i −0.997367 0.0725248i \(-0.976894\pi\)
0.997367 0.0725248i \(-0.0231056\pi\)
\(84\) 1.34705e7 + 2.40563e7i 0.270562 + 0.483183i
\(85\) 0 0
\(86\) 2.08715e7i 0.381558i
\(87\) −7.69233e6 + 4.30738e6i −0.134271 + 0.0751859i
\(88\) 3.33174e7 0.555573
\(89\) 3.39808e7i 0.541593i 0.962637 + 0.270796i \(0.0872870\pi\)
−0.962637 + 0.270796i \(0.912713\pi\)
\(90\) 0 0
\(91\) 3.02638e7 0.441324
\(92\) 3.66478e7i 0.511560i
\(93\) −4.71945e7 8.42822e7i −0.630899 1.12669i
\(94\) 3.58116e7 0.458682
\(95\) 0 0
\(96\) 1.03294e8 5.78405e7i 1.21616 0.681000i
\(97\) −1.50338e7 −0.169817 −0.0849086 0.996389i \(-0.527060\pi\)
−0.0849086 + 0.996389i \(0.527060\pi\)
\(98\) 1.12927e8i 1.22431i
\(99\) −1.09378e8 6.70425e7i −1.13865 0.697927i
\(100\) 0 0
\(101\) 1.51577e8i 1.45663i 0.685244 + 0.728314i \(0.259696\pi\)
−0.685244 + 0.728314i \(0.740304\pi\)
\(102\) 1.16755e8 + 2.08507e8i 1.07864 + 1.92628i
\(103\) −4.88143e7 −0.433709 −0.216854 0.976204i \(-0.569580\pi\)
−0.216854 + 0.976204i \(0.569580\pi\)
\(104\) 4.94783e7i 0.422942i
\(105\) 0 0
\(106\) −8.81248e7 −0.698031
\(107\) 1.32340e6i 0.0100962i −0.999987 0.00504808i \(-0.998393\pi\)
0.999987 0.00504808i \(-0.00160686\pi\)
\(108\) 1.73431e8 + 6.84125e6i 1.27477 + 0.0502853i
\(109\) −1.70973e8 −1.21122 −0.605608 0.795763i \(-0.707070\pi\)
−0.605608 + 0.795763i \(0.707070\pi\)
\(110\) 0 0
\(111\) 1.12432e8 + 2.00785e8i 0.740621 + 1.32264i
\(112\) 4.42740e7 0.281369
\(113\) 3.37372e7i 0.206916i 0.994634 + 0.103458i \(0.0329908\pi\)
−0.994634 + 0.103458i \(0.967009\pi\)
\(114\) −3.23349e8 + 1.81062e8i −1.91449 + 1.07203i
\(115\) 0 0
\(116\) 3.55471e7i 0.196324i
\(117\) 9.95619e7 1.62432e8i 0.531312 0.866820i
\(118\) 3.53814e8 1.82493
\(119\) 1.27390e8i 0.635256i
\(120\) 0 0
\(121\) −1.67975e8 −0.783617
\(122\) 3.86488e8i 1.74460i
\(123\) −2.75995e8 + 1.54545e8i −1.20581 + 0.675205i
\(124\) 3.89478e8 1.64739
\(125\) 0 0
\(126\) 1.40718e8 + 8.62524e7i 0.558301 + 0.342207i
\(127\) −9.39184e7 −0.361024 −0.180512 0.983573i \(-0.557775\pi\)
−0.180512 + 0.983573i \(0.557775\pi\)
\(128\) 2.14845e8i 0.800361i
\(129\) 3.42206e7 + 6.11128e7i 0.123575 + 0.220685i
\(130\) 0 0
\(131\) 2.71847e8i 0.923079i −0.887120 0.461540i \(-0.847297\pi\)
0.887120 0.461540i \(-0.152703\pi\)
\(132\) 4.51326e8 2.52724e8i 1.48660 0.832436i
\(133\) −1.97555e8 −0.631365
\(134\) 5.17455e8i 1.60492i
\(135\) 0 0
\(136\) −2.08270e8 −0.608796
\(137\) 2.18688e8i 0.620788i −0.950608 0.310394i \(-0.899539\pi\)
0.950608 0.310394i \(-0.100461\pi\)
\(138\) 1.07186e8 + 1.91418e8i 0.295545 + 0.527798i
\(139\) 4.92467e8 1.31922 0.659611 0.751608i \(-0.270721\pi\)
0.659611 + 0.751608i \(0.270721\pi\)
\(140\) 0 0
\(141\) 1.04858e8 5.87161e7i 0.265293 0.148553i
\(142\) −9.90724e8 −2.43668
\(143\) 5.67787e8i 1.35782i
\(144\) 1.45653e8 2.37628e8i 0.338741 0.552646i
\(145\) 0 0
\(146\) 1.13503e9i 2.49801i
\(147\) −1.85153e8 3.30655e8i −0.396517 0.708118i
\(148\) −9.27853e8 −1.93389
\(149\) 2.38202e6i 0.00483283i −0.999997 0.00241641i \(-0.999231\pi\)
0.999997 0.00241641i \(-0.000769169\pi\)
\(150\) 0 0
\(151\) −2.94102e8 −0.565705 −0.282852 0.959163i \(-0.591281\pi\)
−0.282852 + 0.959163i \(0.591281\pi\)
\(152\) 3.22982e8i 0.605067i
\(153\) 6.83731e8 + 4.19089e8i 1.24773 + 0.764787i
\(154\) 4.91885e8 0.874542
\(155\) 0 0
\(156\) 3.75309e8 + 6.70245e8i 0.633710 + 1.13171i
\(157\) −5.15599e8 −0.848621 −0.424310 0.905517i \(-0.639483\pi\)
−0.424310 + 0.905517i \(0.639483\pi\)
\(158\) 5.88348e8i 0.944074i
\(159\) −2.58034e8 + 1.44488e8i −0.403727 + 0.226070i
\(160\) 0 0
\(161\) 1.16950e8i 0.174059i
\(162\) 9.25870e8 4.71511e8i 1.34428 0.684592i
\(163\) −7.26841e8 −1.02965 −0.514824 0.857296i \(-0.672143\pi\)
−0.514824 + 0.857296i \(0.672143\pi\)
\(164\) 1.27540e9i 1.76308i
\(165\) 0 0
\(166\) 1.66154e8 0.218816
\(167\) 3.33903e8i 0.429294i −0.976692 0.214647i \(-0.931140\pi\)
0.976692 0.214647i \(-0.0688601\pi\)
\(168\) −1.25508e8 + 7.02791e7i −0.157555 + 0.0882245i
\(169\) 2.74650e7 0.0336692
\(170\) 0 0
\(171\) −6.49915e8 + 1.06032e9i −0.760103 + 1.24009i
\(172\) −2.82410e8 −0.322675
\(173\) 1.32165e9i 1.47547i 0.675088 + 0.737737i \(0.264106\pi\)
−0.675088 + 0.737737i \(0.735894\pi\)
\(174\) −1.03967e8 1.85670e8i −0.113423 0.202555i
\(175\) 0 0
\(176\) 8.30636e8i 0.865685i
\(177\) 1.03599e9 5.80109e8i 1.05551 0.591039i
\(178\) −8.20193e8 −0.817026
\(179\) 1.09788e8i 0.106940i 0.998569 + 0.0534701i \(0.0170282\pi\)
−0.998569 + 0.0534701i \(0.982972\pi\)
\(180\) 0 0
\(181\) −3.65073e8 −0.340146 −0.170073 0.985431i \(-0.554400\pi\)
−0.170073 + 0.985431i \(0.554400\pi\)
\(182\) 7.30477e8i 0.665765i
\(183\) 6.33680e8 + 1.13166e9i 0.565023 + 1.00904i
\(184\) −1.91201e8 −0.166809
\(185\) 0 0
\(186\) 2.03432e9 1.13913e9i 1.69968 0.951750i
\(187\) 2.39000e9 1.95448
\(188\) 4.84561e8i 0.387898i
\(189\) 5.53448e8 + 2.18317e7i 0.433740 + 0.0171096i
\(190\) 0 0
\(191\) 2.14467e9i 1.61148i 0.592267 + 0.805742i \(0.298233\pi\)
−0.592267 + 0.805742i \(0.701767\pi\)
\(192\) 9.65721e8 + 1.72463e9i 0.710635 + 1.26909i
\(193\) 2.36470e9 1.70431 0.852153 0.523293i \(-0.175297\pi\)
0.852153 + 0.523293i \(0.175297\pi\)
\(194\) 3.62870e8i 0.256180i
\(195\) 0 0
\(196\) 1.52800e9 1.03538
\(197\) 2.37290e9i 1.57548i 0.616006 + 0.787742i \(0.288750\pi\)
−0.616006 + 0.787742i \(0.711250\pi\)
\(198\) 1.61820e9 2.64005e9i 1.05287 1.71772i
\(199\) −8.35564e8 −0.532804 −0.266402 0.963862i \(-0.585835\pi\)
−0.266402 + 0.963862i \(0.585835\pi\)
\(200\) 0 0
\(201\) −8.48411e8 1.51513e9i −0.519783 0.928252i
\(202\) −3.65862e9 −2.19741
\(203\) 1.13437e8i 0.0667993i
\(204\) −2.82128e9 + 1.57980e9i −1.62902 + 0.912182i
\(205\) 0 0
\(206\) 1.17823e9i 0.654276i
\(207\) 6.27694e8 + 3.84741e8i 0.341874 + 0.209550i
\(208\) 1.23354e9 0.659022
\(209\) 3.70638e9i 1.94251i
\(210\) 0 0
\(211\) −2.31595e9 −1.16842 −0.584211 0.811602i \(-0.698596\pi\)
−0.584211 + 0.811602i \(0.698596\pi\)
\(212\) 1.19240e9i 0.590310i
\(213\) −2.90089e9 + 1.62438e9i −1.40933 + 0.789165i
\(214\) 3.19429e7 0.0152307
\(215\) 0 0
\(216\) −3.56926e7 + 9.04831e8i −0.0163969 + 0.415674i
\(217\) 1.24289e9 0.560525
\(218\) 4.12678e9i 1.82720i
\(219\) −1.86097e9 3.32341e9i −0.809029 1.44480i
\(220\) 0 0
\(221\) 3.54929e9i 1.48789i
\(222\) −4.84635e9 + 2.71376e9i −1.99528 + 1.11727i
\(223\) 4.75871e8 0.192429 0.0962144 0.995361i \(-0.469327\pi\)
0.0962144 + 0.995361i \(0.469327\pi\)
\(224\) 1.52326e9i 0.605037i
\(225\) 0 0
\(226\) −8.14313e8 −0.312146
\(227\) 3.01408e9i 1.13515i −0.823323 0.567573i \(-0.807882\pi\)
0.823323 0.567573i \(-0.192118\pi\)
\(228\) −2.44993e9 4.37519e9i −0.906595 1.61904i
\(229\) 3.75337e9 1.36483 0.682416 0.730964i \(-0.260929\pi\)
0.682416 + 0.730964i \(0.260929\pi\)
\(230\) 0 0
\(231\) 1.44026e9 8.06488e8i 0.505818 0.283237i
\(232\) 1.85459e8 0.0640169
\(233\) 3.63111e9i 1.23201i 0.787741 + 0.616007i \(0.211251\pi\)
−0.787741 + 0.616007i \(0.788749\pi\)
\(234\) 3.92062e9 + 2.40312e9i 1.30765 + 0.801517i
\(235\) 0 0
\(236\) 4.78741e9i 1.54331i
\(237\) −9.64647e8 1.72271e9i −0.305756 0.546033i
\(238\) −3.07482e9 −0.958322
\(239\) 4.69757e9i 1.43973i 0.694112 + 0.719867i \(0.255797\pi\)
−0.694112 + 0.719867i \(0.744203\pi\)
\(240\) 0 0
\(241\) −3.46782e9 −1.02799 −0.513994 0.857794i \(-0.671835\pi\)
−0.513994 + 0.857794i \(0.671835\pi\)
\(242\) 4.05441e9i 1.18213i
\(243\) 1.93791e9 2.89865e9i 0.555787 0.831325i
\(244\) −5.22951e9 −1.47537
\(245\) 0 0
\(246\) −3.73026e9 6.66167e9i −1.01859 1.81904i
\(247\) −5.50417e9 −1.47878
\(248\) 2.03200e9i 0.537178i
\(249\) 4.86508e8 2.72424e8i 0.126559 0.0708677i
\(250\) 0 0
\(251\) 1.53777e9i 0.387432i 0.981058 + 0.193716i \(0.0620541\pi\)
−0.981058 + 0.193716i \(0.937946\pi\)
\(252\) −1.16707e9 + 1.90404e9i −0.289397 + 0.472143i
\(253\) 2.19412e9 0.535524
\(254\) 2.26691e9i 0.544626i
\(255\) 0 0
\(256\) 1.06133e9 0.247110
\(257\) 2.70241e9i 0.619467i 0.950823 + 0.309734i \(0.100240\pi\)
−0.950823 + 0.309734i \(0.899760\pi\)
\(258\) −1.47508e9 + 8.25983e8i −0.332917 + 0.186420i
\(259\) −2.96095e9 −0.658008
\(260\) 0 0
\(261\) −6.08842e8 3.73186e8i −0.131203 0.0804199i
\(262\) 6.56156e9 1.39252
\(263\) 3.23085e9i 0.675296i −0.941273 0.337648i \(-0.890369\pi\)
0.941273 0.337648i \(-0.109631\pi\)
\(264\) 1.31853e9 + 2.35469e9i 0.271439 + 0.484749i
\(265\) 0 0
\(266\) 4.76837e9i 0.952453i
\(267\) −2.40156e9 + 1.34478e9i −0.472552 + 0.264609i
\(268\) 7.00160e9 1.35724
\(269\) 8.82614e8i 0.168563i −0.996442 0.0842814i \(-0.973141\pi\)
0.996442 0.0842814i \(-0.0268595\pi\)
\(270\) 0 0
\(271\) 8.69735e9 1.61254 0.806269 0.591549i \(-0.201483\pi\)
0.806269 + 0.591549i \(0.201483\pi\)
\(272\) 5.19238e9i 0.948616i
\(273\) 1.19768e9 + 2.13887e9i 0.215620 + 0.385065i
\(274\) 5.27847e9 0.936496
\(275\) 0 0
\(276\) −2.59005e9 + 1.45032e9i −0.446347 + 0.249936i
\(277\) 8.57729e9 1.45690 0.728452 0.685097i \(-0.240240\pi\)
0.728452 + 0.685097i \(0.240240\pi\)
\(278\) 1.18867e10i 1.99013i
\(279\) 4.08887e9 6.67087e9i 0.674818 1.10095i
\(280\) 0 0
\(281\) 2.84302e9i 0.455990i −0.973662 0.227995i \(-0.926783\pi\)
0.973662 0.227995i \(-0.0732169\pi\)
\(282\) 1.41723e9 + 2.53096e9i 0.224101 + 0.400210i
\(283\) −9.94012e9 −1.54969 −0.774847 0.632149i \(-0.782173\pi\)
−0.774847 + 0.632149i \(0.782173\pi\)
\(284\) 1.34053e10i 2.06065i
\(285\) 0 0
\(286\) 1.37047e10 2.04835
\(287\) 4.07004e9i 0.599889i
\(288\) 8.17567e9 + 5.01123e9i 1.18837 + 0.728407i
\(289\) −7.96436e9 −1.14172
\(290\) 0 0
\(291\) −5.94957e8 1.06250e9i −0.0829686 0.148169i
\(292\) 1.53579e10 2.11252
\(293\) 4.76323e9i 0.646295i −0.946349 0.323147i \(-0.895259\pi\)
0.946349 0.323147i \(-0.104741\pi\)
\(294\) 7.98101e9 4.46904e9i 1.06824 0.598170i
\(295\) 0 0
\(296\) 4.84085e9i 0.630601i
\(297\) 4.09590e8 1.03834e10i 0.0526409 1.33448i
\(298\) 5.74949e7 0.00729062
\(299\) 3.25840e9i 0.407680i
\(300\) 0 0
\(301\) −9.01219e8 −0.109790
\(302\) 7.09873e9i 0.853400i
\(303\) −1.07126e10 + 5.99861e9i −1.27094 + 0.711673i
\(304\) −8.05225e9 −0.942807
\(305\) 0 0
\(306\) −1.01155e10 + 1.65032e10i −1.15373 + 1.88227i
\(307\) 3.26248e9 0.367277 0.183639 0.982994i \(-0.441212\pi\)
0.183639 + 0.982994i \(0.441212\pi\)
\(308\) 6.65563e9i 0.739581i
\(309\) −1.93181e9 3.44991e9i −0.211900 0.378420i
\(310\) 0 0
\(311\) 1.13691e10i 1.21530i 0.794204 + 0.607651i \(0.207888\pi\)
−0.794204 + 0.607651i \(0.792112\pi\)
\(312\) −3.49684e9 + 1.95808e9i −0.369026 + 0.206639i
\(313\) −2.83465e9 −0.295340 −0.147670 0.989037i \(-0.547177\pi\)
−0.147670 + 0.989037i \(0.547177\pi\)
\(314\) 1.24450e10i 1.28020i
\(315\) 0 0
\(316\) 7.96085e9 0.798383
\(317\) 4.84402e9i 0.479699i 0.970810 + 0.239850i \(0.0770981\pi\)
−0.970810 + 0.239850i \(0.922902\pi\)
\(318\) −3.48751e9 6.22816e9i −0.341041 0.609047i
\(319\) −2.12823e9 −0.205521
\(320\) 0 0
\(321\) 9.35303e7 5.23731e7i 0.00880911 0.00493274i
\(322\) −2.82281e9 −0.262578
\(323\) 2.31689e10i 2.12860i
\(324\) 6.37995e9 + 1.25278e10i 0.578945 + 1.13683i
\(325\) 0 0
\(326\) 1.75437e10i 1.55329i
\(327\) −6.76620e9 1.20834e10i −0.591771 1.05681i
\(328\) 6.65410e9 0.574902
\(329\) 1.54632e9i 0.131982i
\(330\) 0 0
\(331\) −5.47410e9 −0.456037 −0.228019 0.973657i \(-0.573225\pi\)
−0.228019 + 0.973657i \(0.573225\pi\)
\(332\) 2.24821e9i 0.185048i
\(333\) −9.74092e9 + 1.58920e10i −0.792179 + 1.29242i
\(334\) 8.05942e9 0.647616
\(335\) 0 0
\(336\) 1.75213e9 + 3.12903e9i 0.137470 + 0.245501i
\(337\) −2.30004e10 −1.78327 −0.891633 0.452759i \(-0.850440\pi\)
−0.891633 + 0.452759i \(0.850440\pi\)
\(338\) 6.62922e8i 0.0507920i
\(339\) −2.38435e9 + 1.33514e9i −0.180539 + 0.101094i
\(340\) 0 0
\(341\) 2.33183e10i 1.72456i
\(342\) −2.55929e10 1.56870e10i −1.87074 1.14666i
\(343\) 1.08843e10 0.786364
\(344\) 1.47340e9i 0.105217i
\(345\) 0 0
\(346\) −3.19006e10 −2.22584
\(347\) 2.27792e10i 1.57116i 0.618758 + 0.785582i \(0.287636\pi\)
−0.618758 + 0.785582i \(0.712364\pi\)
\(348\) 2.51227e9 1.40677e9i 0.171297 0.0959190i
\(349\) 2.25621e10 1.52082 0.760410 0.649444i \(-0.224998\pi\)
0.760410 + 0.649444i \(0.224998\pi\)
\(350\) 0 0
\(351\) 1.54199e10 + 6.08264e8i 1.01591 + 0.0400741i
\(352\) 2.85783e10 1.86151
\(353\) 8.56846e9i 0.551828i −0.961182 0.275914i \(-0.911019\pi\)
0.961182 0.275914i \(-0.0889806\pi\)
\(354\) 1.40021e10 + 2.50056e10i 0.891619 + 1.59229i
\(355\) 0 0
\(356\) 1.10979e10i 0.690941i
\(357\) −9.00321e9 + 5.04142e9i −0.554274 + 0.310370i
\(358\) −2.64994e9 −0.161326
\(359\) 3.45337e9i 0.207905i −0.994582 0.103953i \(-0.966851\pi\)
0.994582 0.103953i \(-0.0331490\pi\)
\(360\) 0 0
\(361\) 1.89463e10 1.11557
\(362\) 8.81177e9i 0.513132i
\(363\) −6.64756e9 1.18715e10i −0.382856 0.683722i
\(364\) −9.88397e9 −0.563023
\(365\) 0 0
\(366\) −2.73148e10 + 1.52951e10i −1.52220 + 0.852371i
\(367\) 7.52594e9 0.414855 0.207428 0.978250i \(-0.433491\pi\)
0.207428 + 0.978250i \(0.433491\pi\)
\(368\) 4.76682e9i 0.259919i
\(369\) −2.18448e10 1.33896e10i −1.17826 0.722209i
\(370\) 0 0
\(371\) 3.80518e9i 0.200853i
\(372\) 1.54134e10 + 2.75260e10i 0.804874 + 1.43738i
\(373\) 1.60977e10 0.831625 0.415812 0.909450i \(-0.363497\pi\)
0.415812 + 0.909450i \(0.363497\pi\)
\(374\) 5.76875e10i 2.94846i
\(375\) 0 0
\(376\) −2.52808e9 −0.126485
\(377\) 3.16054e9i 0.156457i
\(378\) −5.26951e8 + 1.33586e10i −0.0258109 + 0.654323i
\(379\) −7.26804e9 −0.352257 −0.176129 0.984367i \(-0.556358\pi\)
−0.176129 + 0.984367i \(0.556358\pi\)
\(380\) 0 0
\(381\) −3.71679e9 6.63761e9i −0.176387 0.315001i
\(382\) −5.17657e10 −2.43102
\(383\) 3.84730e9i 0.178797i −0.995996 0.0893987i \(-0.971505\pi\)
0.995996 0.0893987i \(-0.0284945\pi\)
\(384\) −1.51840e10 + 8.50242e9i −0.698332 + 0.391037i
\(385\) 0 0
\(386\) 5.70768e10i 2.57105i
\(387\) −2.96483e9 + 4.83704e9i −0.132177 + 0.215643i
\(388\) 4.90995e9 0.216646
\(389\) 1.64582e10i 0.718761i 0.933191 + 0.359380i \(0.117012\pi\)
−0.933191 + 0.359380i \(0.882988\pi\)
\(390\) 0 0
\(391\) −1.37157e10 −0.586826
\(392\) 7.97194e9i 0.337614i
\(393\) 1.92126e10 1.07582e10i 0.805407 0.450994i
\(394\) −5.72746e10 −2.37671
\(395\) 0 0
\(396\) 3.57222e10 + 2.18957e10i 1.45264 + 0.890385i
\(397\) 3.57344e10 1.43855 0.719273 0.694727i \(-0.244475\pi\)
0.719273 + 0.694727i \(0.244475\pi\)
\(398\) 2.01680e10i 0.803767i
\(399\) −7.81815e9 1.39620e10i −0.308470 0.550880i
\(400\) 0 0
\(401\) 7.65267e9i 0.295962i 0.988990 + 0.147981i \(0.0472774\pi\)
−0.988990 + 0.147981i \(0.952723\pi\)
\(402\) 3.65707e10 2.04781e10i 1.40033 0.784124i
\(403\) 3.46289e10 1.31286
\(404\) 4.95042e10i 1.85830i
\(405\) 0 0
\(406\) 2.73803e9 0.100771
\(407\) 5.55511e10i 2.02449i
\(408\) −8.24222e9 1.47193e10i −0.297443 0.531187i
\(409\) 1.89488e10 0.677154 0.338577 0.940939i \(-0.390054\pi\)
0.338577 + 0.940939i \(0.390054\pi\)
\(410\) 0 0
\(411\) 1.54556e10 8.65450e9i 0.541650 0.303302i
\(412\) 1.59425e10 0.553307
\(413\) 1.52775e10i 0.525111i
\(414\) −9.28649e9 + 1.51506e10i −0.316119 + 0.515738i
\(415\) 0 0
\(416\) 4.24404e10i 1.41712i
\(417\) 1.94892e10 + 3.48047e10i 0.644540 + 1.15105i
\(418\) −8.94607e10 −2.93040
\(419\) 8.62832e9i 0.279943i −0.990156 0.139972i \(-0.955299\pi\)
0.990156 0.139972i \(-0.0447012\pi\)
\(420\) 0 0
\(421\) 3.38470e10 1.07744 0.538718 0.842486i \(-0.318909\pi\)
0.538718 + 0.842486i \(0.318909\pi\)
\(422\) 5.59001e10i 1.76264i
\(423\) 8.29944e9 + 5.08709e9i 0.259231 + 0.158894i
\(424\) 6.22108e9 0.192487
\(425\) 0 0
\(426\) −3.92075e10 7.00186e10i −1.19050 2.12606i
\(427\) −1.66883e10 −0.501997
\(428\) 4.32214e8i 0.0128802i
\(429\) 4.01279e10 2.24700e10i 1.18473 0.663397i
\(430\) 0 0
\(431\) 2.98116e10i 0.863924i −0.901892 0.431962i \(-0.857821\pi\)
0.901892 0.431962i \(-0.142179\pi\)
\(432\) 2.25583e10 + 8.89850e8i 0.647697 + 0.0255495i
\(433\) −2.54166e9 −0.0723047 −0.0361524 0.999346i \(-0.511510\pi\)
−0.0361524 + 0.999346i \(0.511510\pi\)
\(434\) 2.99997e10i 0.845586i
\(435\) 0 0
\(436\) 5.58388e10 1.54522
\(437\) 2.12700e10i 0.583233i
\(438\) 8.02172e10 4.49183e10i 2.17957 1.22047i
\(439\) 1.11261e10 0.299559 0.149780 0.988719i \(-0.452144\pi\)
0.149780 + 0.988719i \(0.452144\pi\)
\(440\) 0 0
\(441\) 1.60414e10 2.61711e10i 0.424120 0.691939i
\(442\) −8.56691e10 −2.24458
\(443\) 3.00907e10i 0.781299i 0.920539 + 0.390650i \(0.127750\pi\)
−0.920539 + 0.390650i \(0.872250\pi\)
\(444\) −3.67194e10 6.55753e10i −0.944853 1.68736i
\(445\) 0 0
\(446\) 1.14861e10i 0.290291i
\(447\) 1.68348e8 9.42678e7i 0.00421674 0.00236120i
\(448\) −2.54328e10 −0.631367
\(449\) 2.46457e10i 0.606396i −0.952928 0.303198i \(-0.901946\pi\)
0.952928 0.303198i \(-0.0980543\pi\)
\(450\) 0 0
\(451\) −7.63591e10 −1.84567
\(452\) 1.10184e10i 0.263975i
\(453\) −1.16390e10 2.07854e10i −0.276390 0.493589i
\(454\) 7.27509e10 1.71244
\(455\) 0 0
\(456\) 2.28265e10 1.27819e10i 0.527934 0.295621i
\(457\) −1.18416e10 −0.271486 −0.135743 0.990744i \(-0.543342\pi\)
−0.135743 + 0.990744i \(0.543342\pi\)
\(458\) 9.05950e10i 2.05893i
\(459\) −2.56038e9 + 6.49074e10i −0.0576838 + 1.46232i
\(460\) 0 0
\(461\) 2.03656e10i 0.450913i 0.974253 + 0.225456i \(0.0723873\pi\)
−0.974253 + 0.225456i \(0.927613\pi\)
\(462\) 1.94662e10 + 3.47636e10i 0.427280 + 0.763057i
\(463\) 3.88105e10 0.844550 0.422275 0.906468i \(-0.361232\pi\)
0.422275 + 0.906468i \(0.361232\pi\)
\(464\) 4.62366e9i 0.0997502i
\(465\) 0 0
\(466\) −8.76440e10 −1.85857
\(467\) 6.67567e10i 1.40355i −0.712400 0.701774i \(-0.752392\pi\)
0.712400 0.701774i \(-0.247608\pi\)
\(468\) −3.25163e10 + 5.30494e10i −0.677825 + 1.10585i
\(469\) 2.23434e10 0.461803
\(470\) 0 0
\(471\) −2.04047e10 3.64396e10i −0.414616 0.740440i
\(472\) −2.49771e10 −0.503239
\(473\) 1.69080e10i 0.337791i
\(474\) 4.15810e10 2.32837e10i 0.823725 0.461252i
\(475\) 0 0
\(476\) 4.16049e10i 0.810432i
\(477\) −2.04232e10 1.25183e10i −0.394503 0.241808i
\(478\) −1.13385e11 −2.17193
\(479\) 1.01360e11i 1.92542i 0.270529 + 0.962712i \(0.412801\pi\)
−0.270529 + 0.962712i \(0.587199\pi\)
\(480\) 0 0
\(481\) −8.24964e10 −1.54119
\(482\) 8.37027e10i 1.55078i
\(483\) −8.26533e9 + 4.62824e9i −0.151870 + 0.0850408i
\(484\) 5.48597e10 0.999705
\(485\) 0 0
\(486\) 6.99647e10 + 4.67753e10i 1.25410 + 0.838439i
\(487\) −1.08507e10 −0.192905 −0.0964526 0.995338i \(-0.530750\pi\)
−0.0964526 + 0.995338i \(0.530750\pi\)
\(488\) 2.72837e10i 0.481088i
\(489\) −2.87645e10 5.13689e10i −0.503061 0.898390i
\(490\) 0 0
\(491\) 1.02973e10i 0.177173i −0.996068 0.0885864i \(-0.971765\pi\)
0.996068 0.0885864i \(-0.0282349\pi\)
\(492\) 9.01381e10 5.04736e10i 1.53833 0.861398i
\(493\) 1.33037e10 0.225209
\(494\) 1.32854e11i 2.23083i
\(495\) 0 0
\(496\) 5.06598e10 0.837022
\(497\) 4.27788e10i 0.701138i
\(498\) 6.57550e9 + 1.17428e10i 0.106908 + 0.190922i
\(499\) 6.76597e10 1.09126 0.545630 0.838026i \(-0.316290\pi\)
0.545630 + 0.838026i \(0.316290\pi\)
\(500\) 0 0
\(501\) 2.35984e10 1.32141e10i 0.374568 0.209743i
\(502\) −3.71171e10 −0.584465
\(503\) 2.55230e10i 0.398712i 0.979927 + 0.199356i \(0.0638850\pi\)
−0.979927 + 0.199356i \(0.936115\pi\)
\(504\) −9.93385e9 6.08890e9i −0.153956 0.0943662i
\(505\) 0 0
\(506\) 5.29595e10i 0.807871i
\(507\) 1.08692e9 + 1.94107e9i 0.0164500 + 0.0293771i
\(508\) 3.06732e10 0.460579
\(509\) 1.02891e11i 1.53287i −0.642320 0.766437i \(-0.722028\pi\)
0.642320 0.766437i \(-0.277972\pi\)
\(510\) 0 0
\(511\) 4.90098e10 0.718785
\(512\) 8.06177e10i 1.17314i
\(513\) −1.00657e11 3.97059e9i −1.45337 0.0573305i
\(514\) −6.52280e10 −0.934504
\(515\) 0 0
\(516\) −1.11763e10 1.99591e10i −0.157651 0.281541i
\(517\) 2.90110e10 0.406069
\(518\) 7.14683e10i 0.992646i
\(519\) −9.34065e10 + 5.23038e10i −1.28738 + 0.720881i
\(520\) 0 0
\(521\) 5.25006e10i 0.712547i −0.934382 0.356273i \(-0.884047\pi\)
0.934382 0.356273i \(-0.115953\pi\)
\(522\) 9.00759e9 1.46956e10i 0.121318 0.197927i
\(523\) 8.56285e10 1.14449 0.572245 0.820083i \(-0.306073\pi\)
0.572245 + 0.820083i \(0.306073\pi\)
\(524\) 8.87835e10i 1.17763i
\(525\) 0 0
\(526\) 7.79830e10 1.01872
\(527\) 1.45764e11i 1.88977i
\(528\) 5.87046e10 3.28721e10i 0.755329 0.422953i
\(529\) 6.57194e10 0.839211
\(530\) 0 0
\(531\) 8.19975e10 + 5.02599e10i 1.03139 + 0.632184i
\(532\) 6.45201e10 0.805469
\(533\) 1.13398e11i 1.40506i
\(534\) −3.24588e10 5.79665e10i −0.399179 0.712873i
\(535\) 0 0
\(536\) 3.65291e10i 0.442568i
\(537\) −7.75915e9 + 4.34480e9i −0.0933076 + 0.0522484i
\(538\) 2.13036e10 0.254287
\(539\) 9.14820e10i 1.08388i
\(540\) 0 0
\(541\) −2.14250e10 −0.250111 −0.125055 0.992150i \(-0.539911\pi\)
−0.125055 + 0.992150i \(0.539911\pi\)
\(542\) 2.09928e11i 2.43261i
\(543\) −1.44476e10 2.58013e10i −0.166187 0.296785i
\(544\) −1.78645e11 −2.03984
\(545\) 0 0
\(546\) −5.16259e10 + 2.89084e10i −0.580894 + 0.325277i
\(547\) 9.14990e8 0.0102204 0.00511019 0.999987i \(-0.498373\pi\)
0.00511019 + 0.999987i \(0.498373\pi\)
\(548\) 7.14222e10i 0.791974i
\(549\) −5.49012e10 + 8.95697e10i −0.604356 + 0.985989i
\(550\) 0 0
\(551\) 2.06312e10i 0.223830i
\(552\) −7.56671e9 1.35130e10i −0.0814987 0.145544i
\(553\) 2.54045e10 0.271650
\(554\) 2.07030e11i 2.19783i
\(555\) 0 0
\(556\) −1.60837e11 −1.68301
\(557\) 1.81764e11i 1.88837i −0.329416 0.944185i \(-0.606852\pi\)
0.329416 0.944185i \(-0.393148\pi\)
\(558\) 1.61015e11 + 9.86930e10i 1.66084 + 1.01800i
\(559\) −2.51093e10 −0.257151
\(560\) 0 0
\(561\) 9.45835e10 + 1.68912e11i 0.954913 + 1.70533i
\(562\) 6.86220e10 0.687889
\(563\) 4.19023e10i 0.417066i −0.978015 0.208533i \(-0.933131\pi\)
0.978015 0.208533i \(-0.0668689\pi\)
\(564\) −3.42460e10 + 1.91763e10i −0.338449 + 0.189517i
\(565\) 0 0
\(566\) 2.39924e11i 2.33781i
\(567\) 2.03596e10 + 3.99785e10i 0.196986 + 0.386807i
\(568\) 6.99391e10 0.671934
\(569\) 9.98358e10i 0.952439i −0.879326 0.476220i \(-0.842007\pi\)
0.879326 0.476220i \(-0.157993\pi\)
\(570\) 0 0
\(571\) 7.00315e10 0.658793 0.329397 0.944192i \(-0.393155\pi\)
0.329397 + 0.944192i \(0.393155\pi\)
\(572\) 1.85436e11i 1.73225i
\(573\) −1.51573e11 + 8.48743e10i −1.40605 + 0.787332i
\(574\) 9.82385e10 0.904970
\(575\) 0 0
\(576\) −8.36688e10 + 1.36503e11i −0.760105 + 1.24009i
\(577\) −5.16977e10 −0.466410 −0.233205 0.972428i \(-0.574921\pi\)
−0.233205 + 0.972428i \(0.574921\pi\)
\(578\) 1.92236e11i 1.72235i
\(579\) 9.35823e10 + 1.67124e11i 0.832683 + 1.48704i
\(580\) 0 0
\(581\) 7.17444e9i 0.0629627i
\(582\) 2.56456e10 1.43605e10i 0.223522 0.125163i
\(583\) −7.13899e10 −0.617963
\(584\) 8.01260e10i 0.688846i
\(585\) 0 0
\(586\) 1.14970e11 0.974976
\(587\) 7.90362e10i 0.665693i −0.942981 0.332846i \(-0.891991\pi\)
0.942981 0.332846i \(-0.108009\pi\)
\(588\) 6.04699e10 + 1.07990e11i 0.505859 + 0.903387i
\(589\) −2.26049e11 −1.87820
\(590\) 0 0
\(591\) −1.67703e11 + 9.39065e10i −1.37464 + 0.769743i
\(592\) −1.20687e11 −0.982592
\(593\) 2.38940e11i 1.93228i 0.258015 + 0.966141i \(0.416932\pi\)
−0.258015 + 0.966141i \(0.583068\pi\)
\(594\) 2.50624e11 + 9.88626e9i 2.01315 + 0.0794120i
\(595\) 0 0
\(596\) 7.77955e8i 0.00616551i
\(597\) −3.30671e10 5.90528e10i −0.260315 0.464883i
\(598\) −7.86478e10 −0.615010
\(599\) 1.75042e11i 1.35968i 0.733363 + 0.679838i \(0.237950\pi\)
−0.733363 + 0.679838i \(0.762050\pi\)
\(600\) 0 0
\(601\) −7.78052e10 −0.596363 −0.298181 0.954509i \(-0.596380\pi\)
−0.298181 + 0.954509i \(0.596380\pi\)
\(602\) 2.17527e10i 0.165626i
\(603\) 7.35052e10 1.19922e11i 0.555967 0.907043i
\(604\) 9.60518e10 0.721702
\(605\) 0 0
\(606\) −1.44788e11 2.58570e11i −1.07360 1.91729i
\(607\) 1.00711e11 0.741864 0.370932 0.928660i \(-0.379038\pi\)
0.370932 + 0.928660i \(0.379038\pi\)
\(608\) 2.77040e11i 2.02735i
\(609\) 8.01710e9 4.48924e9i 0.0582838 0.0326365i
\(610\) 0 0
\(611\) 4.30829e10i 0.309129i
\(612\) −2.23302e11 1.36872e11i −1.59180 0.975682i
\(613\) −1.66738e11 −1.18084 −0.590422 0.807094i \(-0.701039\pi\)
−0.590422 + 0.807094i \(0.701039\pi\)
\(614\) 7.87464e10i 0.554060i
\(615\) 0 0
\(616\) −3.47241e10 −0.241162
\(617\) 5.98004e10i 0.412632i 0.978485 + 0.206316i \(0.0661475\pi\)
−0.978485 + 0.206316i \(0.933852\pi\)
\(618\) 8.32705e10 4.66280e10i 0.570870 0.319664i
\(619\) −1.30260e11 −0.887254 −0.443627 0.896211i \(-0.646309\pi\)
−0.443627 + 0.896211i \(0.646309\pi\)
\(620\) 0 0
\(621\) −2.35054e9 + 5.95878e10i −0.0158052 + 0.400674i
\(622\) −2.74416e11 −1.83336
\(623\) 3.54154e10i 0.235093i
\(624\) 4.88169e10 + 8.71795e10i 0.321982 + 0.575011i
\(625\) 0 0
\(626\) 6.84200e10i 0.445539i
\(627\) −2.61945e11 + 1.46678e11i −1.69489 + 0.949065i
\(628\) 1.68392e11 1.08263
\(629\) 3.47255e11i 2.21843i
\(630\) 0 0
\(631\) −2.11689e11 −1.33530 −0.667652 0.744473i \(-0.732701\pi\)
−0.667652 + 0.744473i \(0.732701\pi\)
\(632\) 4.15338e10i 0.260335i
\(633\) −9.16529e10 1.63678e11i −0.570863 1.01947i
\(634\) −1.16920e11 −0.723656
\(635\) 0 0
\(636\) 8.42723e10 4.71890e10i 0.515058 0.288411i
\(637\) 1.35856e11 0.825126
\(638\) 5.13690e10i 0.310040i
\(639\) −2.29603e11 1.40734e11i −1.37713 0.844102i
\(640\) 0 0
\(641\) 9.94582e9i 0.0589126i 0.999566 + 0.0294563i \(0.00937759\pi\)
−0.999566 + 0.0294563i \(0.990622\pi\)
\(642\) 1.26413e9 + 2.25754e9i 0.00744134 + 0.0132891i
\(643\) −4.35787e10 −0.254935 −0.127468 0.991843i \(-0.540685\pi\)
−0.127468 + 0.991843i \(0.540685\pi\)
\(644\) 3.81950e10i 0.222057i
\(645\) 0 0
\(646\) 5.59227e11 3.21113
\(647\) 1.00404e11i 0.572973i −0.958084 0.286487i \(-0.907513\pi\)
0.958084 0.286487i \(-0.0924874\pi\)
\(648\) −6.53608e10 + 3.32858e10i −0.370695 + 0.188781i
\(649\) 2.86625e11 1.61560
\(650\) 0 0
\(651\) 4.91871e10 + 8.78405e10i 0.273859 + 0.489070i
\(652\) 2.37382e11 1.31358
\(653\) 9.51805e10i 0.523474i 0.965139 + 0.261737i \(0.0842954\pi\)
−0.965139 + 0.261737i \(0.915705\pi\)
\(654\) 2.91657e11 1.63316e11i 1.59427 0.892723i
\(655\) 0 0
\(656\) 1.65893e11i 0.895804i
\(657\) 1.61232e11 2.63046e11i 0.865348 1.41179i
\(658\) −3.73235e10 −0.199104
\(659\) 2.93955e11i 1.55862i 0.626641 + 0.779308i \(0.284429\pi\)
−0.626641 + 0.779308i \(0.715571\pi\)
\(660\) 0 0
\(661\) 2.39956e11 1.25697 0.628485 0.777822i \(-0.283675\pi\)
0.628485 + 0.777822i \(0.283675\pi\)
\(662\) 1.32128e11i 0.687960i
\(663\) −2.50843e11 + 1.40462e11i −1.29822 + 0.726949i
\(664\) −1.17295e10 −0.0603402
\(665\) 0 0
\(666\) −3.83585e11 2.35116e11i −1.94969 1.19505i
\(667\) 1.22134e10 0.0617068
\(668\) 1.09051e11i 0.547675i
\(669\) 1.88324e10 + 3.36318e10i 0.0940160 + 0.167898i
\(670\) 0 0
\(671\) 3.13094e11i 1.54449i
\(672\) −1.07655e11 + 6.02825e10i −0.527908 + 0.295607i
\(673\) 1.21923e11 0.594326 0.297163 0.954827i \(-0.403960\pi\)
0.297163 + 0.954827i \(0.403960\pi\)
\(674\) 5.55161e11i 2.69017i
\(675\) 0 0
\(676\) −8.96990e9 −0.0429537
\(677\) 3.04202e10i 0.144813i 0.997375 + 0.0724066i \(0.0230679\pi\)
−0.997375 + 0.0724066i \(0.976932\pi\)
\(678\) −3.22262e10 5.75510e10i −0.152507 0.272354i
\(679\) 1.56685e10 0.0737138
\(680\) 0 0
\(681\) 2.13018e11 1.19281e11i 0.990440 0.554605i
\(682\) 5.62832e11 2.60161
\(683\) 2.91193e11i 1.33813i 0.743204 + 0.669065i \(0.233305\pi\)
−0.743204 + 0.669065i \(0.766695\pi\)
\(684\) 2.12258e11 3.46293e11i 0.969707 1.58205i
\(685\) 0 0
\(686\) 2.62714e11i 1.18628i
\(687\) 1.48538e11 + 2.65267e11i 0.666824 + 1.19085i
\(688\) −3.67333e10 −0.163948
\(689\) 1.06018e11i 0.470438i
\(690\) 0 0
\(691\) −3.48484e11 −1.52852 −0.764260 0.644908i \(-0.776896\pi\)
−0.764260 + 0.644908i \(0.776896\pi\)
\(692\) 4.31642e11i 1.88235i
\(693\) 1.13996e11 + 6.98731e10i 0.494261 + 0.302954i
\(694\) −5.49822e11 −2.37020
\(695\) 0 0
\(696\) 7.33945e9 + 1.31071e10i 0.0312771 + 0.0558562i
\(697\) 4.77327e11 2.02248
\(698\) 5.44581e11i 2.29425i
\(699\) −2.56626e11 + 1.43700e11i −1.07496 + 0.601932i
\(700\) 0 0
\(701\) 1.23548e11i 0.511640i 0.966724 + 0.255820i \(0.0823455\pi\)
−0.966724 + 0.255820i \(0.917655\pi\)
\(702\) −1.46816e10 + 3.72190e11i −0.0604542 + 1.53256i
\(703\) 5.38516e11 2.20484
\(704\) 4.77151e11i 1.94252i
\(705\) 0 0
\(706\) 2.06817e11 0.832467
\(707\) 1.57977e11i 0.632289i
\(708\) −3.38346e11 + 1.89460e11i −1.34657 + 0.754023i
\(709\) 3.17753e11 1.25749 0.628744 0.777612i \(-0.283569\pi\)
0.628744 + 0.777612i \(0.283569\pi\)
\(710\) 0 0
\(711\) 8.35758e10 1.36351e11i 0.327041 0.533557i
\(712\) 5.79006e10 0.225301
\(713\) 1.33818e11i 0.517793i
\(714\) −1.21685e11 2.17310e11i −0.468213 0.836156i
\(715\) 0 0
\(716\) 3.58560e10i 0.136430i
\(717\) −3.31997e11 + 1.85905e11i −1.25620 + 0.703419i
\(718\) 8.33539e10 0.313638
\(719\) 2.47720e11i 0.926926i −0.886116 0.463463i \(-0.846607\pi\)
0.886116 0.463463i \(-0.153393\pi\)
\(720\) 0 0
\(721\) 5.08752e10 0.188263
\(722\) 4.57307e11i 1.68290i
\(723\) −1.37238e11 2.45085e11i −0.502250 0.896942i
\(724\) 1.19231e11 0.433944
\(725\) 0 0
\(726\) 2.86543e11 1.60452e11i 1.03144 0.577562i
\(727\) −2.06831e11 −0.740420 −0.370210 0.928948i \(-0.620714\pi\)
−0.370210 + 0.928948i \(0.620714\pi\)
\(728\) 5.15672e10i 0.183590i
\(729\) 2.81552e11 + 2.22472e10i 0.996893 + 0.0787707i
\(730\) 0 0
\(731\) 1.05693e11i 0.370151i
\(732\) −2.06956e11 3.69592e11i −0.720832 1.28730i
\(733\) 2.72921e11 0.945412 0.472706 0.881220i \(-0.343277\pi\)
0.472706 + 0.881220i \(0.343277\pi\)
\(734\) 1.81654e11i 0.625835i
\(735\) 0 0
\(736\) −1.64004e11 −0.558912
\(737\) 4.19190e11i 1.42083i
\(738\) 3.23185e11 5.27267e11i 1.08950 1.77748i
\(739\) 1.03105e10 0.0345702 0.0172851 0.999851i \(-0.494498\pi\)
0.0172851 + 0.999851i \(0.494498\pi\)
\(740\) 0 0
\(741\) −2.17826e11 3.89003e11i −0.722497 1.29027i
\(742\) 9.18454e10 0.303000
\(743\) 3.12920e11i 1.02678i −0.858154 0.513392i \(-0.828389\pi\)
0.858154 0.513392i \(-0.171611\pi\)
\(744\) −1.43610e11 + 8.04159e10i −0.468699 + 0.262452i
\(745\) 0 0
\(746\) 3.88549e11i 1.25456i
\(747\) 3.85067e10 + 2.36025e10i 0.123667 + 0.0758010i
\(748\) −7.80561e11 −2.49345
\(749\) 1.37927e9i 0.00438251i
\(750\) 0 0
\(751\) 2.76676e11 0.869783 0.434892 0.900483i \(-0.356787\pi\)
0.434892 + 0.900483i \(0.356787\pi\)
\(752\) 6.30275e10i 0.197087i
\(753\) −1.08681e11 + 6.08566e10i −0.338043 + 0.189290i
\(754\) 7.62858e10 0.236025
\(755\) 0 0
\(756\) −1.80753e11 7.13009e9i −0.553347 0.0218277i
\(757\) −1.25846e11 −0.383226 −0.191613 0.981471i \(-0.561372\pi\)
−0.191613 + 0.981471i \(0.561372\pi\)
\(758\) 1.75428e11i 0.531402i
\(759\) 8.68317e10 + 1.55068e11i 0.261644 + 0.467256i
\(760\) 0 0
\(761\) 4.11284e11i 1.22632i −0.789960 0.613159i \(-0.789899\pi\)
0.789960 0.613159i \(-0.210101\pi\)
\(762\) 1.60212e11 8.97120e10i 0.475198 0.266091i
\(763\) 1.78192e11 0.525762
\(764\) 7.00435e11i 2.05586i
\(765\) 0 0
\(766\) 9.28622e10 0.269727
\(767\) 4.25654e11i 1.22991i
\(768\) 4.20018e10 + 7.50087e10i 0.120732 + 0.215609i
\(769\) 4.51287e10 0.129047 0.0645235 0.997916i \(-0.479447\pi\)
0.0645235 + 0.997916i \(0.479447\pi\)
\(770\) 0 0
\(771\) −1.90991e11 + 1.06947e11i −0.540498 + 0.302657i
\(772\) −7.72298e11 −2.17428
\(773\) 3.86868e11i 1.08354i 0.840527 + 0.541770i \(0.182245\pi\)
−0.840527 + 0.541770i \(0.817755\pi\)
\(774\) −1.16751e11 7.15621e10i −0.325311 0.199397i
\(775\) 0 0
\(776\) 2.56164e10i 0.0706435i
\(777\) −1.17178e11 2.09263e11i −0.321487 0.574126i
\(778\) −3.97252e11 −1.08430
\(779\) 7.40231e11i 2.01010i
\(780\) 0 0
\(781\) −8.02585e11 −2.15718
\(782\) 3.31055e11i 0.885264i
\(783\) 2.27994e9 5.77982e10i 0.00606565 0.153768i
\(784\) 1.98748e11 0.526064
\(785\) 0 0
\(786\) 2.59671e11 + 4.63733e11i 0.680353 + 1.21501i
\(787\) −4.31897e11 −1.12585 −0.562926 0.826508i \(-0.690324\pi\)
−0.562926 + 0.826508i \(0.690324\pi\)
\(788\) 7.74973e11i 2.00993i
\(789\) 2.28338e11 1.27860e11i 0.589210 0.329933i
\(790\) 0 0
\(791\) 3.51615e10i 0.0898177i
\(792\) −1.14235e11 + 1.86372e11i −0.290335 + 0.473673i
\(793\) −4.64962e11 −1.17578
\(794\) 8.62519e11i 2.17014i
\(795\) 0 0
\(796\) 2.72890e11 0.679728
\(797\) 1.89233e11i 0.468991i −0.972117 0.234495i \(-0.924656\pi\)
0.972117 0.234495i \(-0.0753438\pi\)
\(798\) 3.37001e11 1.88707e11i 0.831036 0.465346i
\(799\) −1.81350e11 −0.444970
\(800\) 0 0
\(801\) −1.90082e11 1.16510e11i −0.461754 0.283030i
\(802\) −1.84712e11 −0.446477
\(803\) 9.19486e11i 2.21148i
\(804\) 2.77086e11 + 4.94833e11i 0.663117 + 1.18423i
\(805\) 0 0
\(806\) 8.35837e11i 1.98053i
\(807\) 6.23781e10 3.49291e10i 0.147075 0.0823557i
\(808\) 2.58276e11 0.605953
\(809\) 8.16650e10i 0.190652i 0.995446 + 0.0953261i \(0.0303894\pi\)
−0.995446 + 0.0953261i \(0.969611\pi\)
\(810\) 0 0
\(811\) −2.05160e11 −0.474252 −0.237126 0.971479i \(-0.576205\pi\)
−0.237126 + 0.971479i \(0.576205\pi\)
\(812\) 3.70479e10i 0.0852197i
\(813\) 3.44195e11 + 6.14679e11i 0.787847 + 1.40697i
\(814\) −1.34084e12 −3.05406
\(815\) 0 0
\(816\) −3.66967e11 + 2.05486e11i −0.827688 + 0.463471i
\(817\) 1.63908e11 0.367884
\(818\) 4.57366e11i 1.02153i
\(819\) −1.03765e11 + 1.69290e11i −0.230631 + 0.376267i
\(820\) 0 0
\(821\) 1.41950e10i 0.0312437i −0.999878 0.0156218i \(-0.995027\pi\)
0.999878 0.0156218i \(-0.00497278\pi\)
\(822\) 2.08894e11 + 3.73052e11i 0.457549 + 0.817113i
\(823\) 2.98009e11 0.649576 0.324788 0.945787i \(-0.394707\pi\)
0.324788 + 0.945787i \(0.394707\pi\)
\(824\) 8.31759e10i 0.180422i
\(825\) 0 0
\(826\) −3.68752e11 −0.792163
\(827\) 3.12011e11i 0.667034i 0.942744 + 0.333517i \(0.108235\pi\)
−0.942744 + 0.333517i \(0.891765\pi\)
\(828\) −2.05001e11 1.25654e11i −0.436149 0.267335i
\(829\) 2.42950e11 0.514397 0.257198 0.966359i \(-0.417201\pi\)
0.257198 + 0.966359i \(0.417201\pi\)
\(830\) 0 0
\(831\) 3.39443e11 + 6.06193e11i 0.711808 + 1.27118i
\(832\) −7.08596e11 −1.47879
\(833\) 5.71862e11i 1.18771i
\(834\) −8.40081e11 + 4.70410e11i −1.73643 + 0.972327i
\(835\) 0 0
\(836\) 1.21048e12i 2.47818i
\(837\) 6.33274e11 + 2.49806e10i 1.29030 + 0.0508980i
\(838\) 2.08262e11 0.422312
\(839\) 1.16205e11i 0.234519i 0.993101 + 0.117259i \(0.0374109\pi\)
−0.993101 + 0.117259i \(0.962589\pi\)
\(840\) 0 0
\(841\) 4.88400e11 0.976318
\(842\) 8.16963e11i 1.62538i
\(843\) 2.00928e11 1.12512e11i 0.397861 0.222786i
\(844\) 7.56376e11 1.49062
\(845\) 0 0
\(846\) −1.22787e11 + 2.00323e11i −0.239702 + 0.391066i
\(847\) 1.75067e11 0.340150
\(848\) 1.55097e11i 0.299931i
\(849\) −3.93377e11 7.02510e11i −0.757143 1.35214i
\(850\) 0 0
\(851\) 3.18794e11i 0.607844i
\(852\) 9.47412e11 5.30511e11i 1.79796 1.00678i
\(853\) 2.30678e11 0.435723 0.217861 0.975980i \(-0.430092\pi\)
0.217861 + 0.975980i \(0.430092\pi\)
\(854\) 4.02806e11i 0.757293i
\(855\) 0 0
\(856\) −2.25497e9 −0.00419997
\(857\) 6.99039e11i 1.29592i 0.761674 + 0.647960i \(0.224378\pi\)
−0.761674 + 0.647960i \(0.775622\pi\)
\(858\) 5.42357e11 + 9.68567e11i 1.00078 + 1.78723i
\(859\) 9.39004e10 0.172463 0.0862313 0.996275i \(-0.472518\pi\)
0.0862313 + 0.996275i \(0.472518\pi\)
\(860\) 0 0
\(861\) 2.87647e11 1.61070e11i 0.523416 0.293091i
\(862\) 7.19561e11 1.30328
\(863\) 7.27490e11i 1.31155i −0.754958 0.655773i \(-0.772343\pi\)
0.754958 0.655773i \(-0.227657\pi\)
\(864\) −3.06156e10 + 7.76126e11i −0.0549399 + 1.39276i
\(865\) 0 0
\(866\) 6.13481e10i 0.109076i
\(867\) −3.15187e11 5.62875e11i −0.557817 0.996175i
\(868\) −4.05921e11 −0.715094
\(869\) 4.76621e11i 0.835783i
\(870\) 0 0
\(871\) 6.22520e11 1.08164
\(872\) 2.91325e11i 0.503863i
\(873\) 5.15463e10 8.40963e10i 0.0887443 0.144784i
\(874\) 5.13394e11 0.879842
\(875\) 0 0
\(876\) 6.07783e11 + 1.08541e12i 1.03212 + 1.84322i
\(877\) 1.49532e11 0.252775 0.126388 0.991981i \(-0.459662\pi\)
0.126388 + 0.991981i \(0.459662\pi\)
\(878\) 2.68549e11i 0.451904i
\(879\) 3.36637e11 1.88503e11i 0.563906 0.315764i
\(880\) 0 0
\(881\) 9.01607e11i 1.49663i −0.663345 0.748314i \(-0.730864\pi\)
0.663345 0.748314i \(-0.269136\pi\)
\(882\) 6.31691e11 + 3.87192e11i 1.04383 + 0.639811i
\(883\) −7.05614e11 −1.16071 −0.580356 0.814363i \(-0.697086\pi\)
−0.580356 + 0.814363i \(0.697086\pi\)
\(884\) 1.15918e12i 1.89819i
\(885\) 0 0
\(886\) −7.26299e11 −1.17864
\(887\) 1.05583e12i 1.70568i 0.522170 + 0.852842i \(0.325123\pi\)
−0.522170 + 0.852842i \(0.674877\pi\)
\(888\) 3.42123e11 1.91575e11i 0.550213 0.308096i
\(889\) 9.78836e10 0.156712
\(890\) 0 0
\(891\) 7.50047e11 3.81971e11i 1.19008 0.606066i
\(892\) −1.55417e11 −0.245492
\(893\) 2.81234e11i 0.442245i
\(894\) 2.27534e9 + 4.06341e9i 0.00356202 + 0.00636122i
\(895\) 0 0
\(896\) 2.23916e11i 0.347419i
\(897\) −2.30285e11 + 1.28950e11i −0.355709 + 0.199182i
\(898\) 5.94873e11 0.914785
\(899\) 1.29799e11i 0.198716i
\(900\) 0 0
\(901\) 4.46265e11 0.677163
\(902\) 1.84308e12i 2.78431i
\(903\) −3.56654e10 6.36930e10i −0.0536410 0.0957945i
\(904\) 5.74856e10 0.0860766
\(905\) 0 0
\(906\) 5.01697e11 2.80930e11i 0.744610 0.416951i
\(907\) −3.67842e11 −0.543541 −0.271771 0.962362i \(-0.587609\pi\)
−0.271771 + 0.962362i \(0.587609\pi\)
\(908\) 9.84382e11i 1.44817i
\(909\) −8.47895e11 5.19712e11i −1.24190 0.761215i
\(910\) 0 0
\(911\) 9.64432e11i 1.40023i 0.714032 + 0.700113i \(0.246867\pi\)
−0.714032 + 0.700113i \(0.753133\pi\)
\(912\) −3.18665e11 5.69086e11i −0.460633 0.822619i
\(913\) 1.34602e11 0.193717
\(914\) 2.85821e11i 0.409553i
\(915\) 0 0
\(916\) −1.22583e12 −1.74120
\(917\) 2.83324e11i 0.400688i
\(918\) −1.56667e12 6.17999e10i −2.20601 0.0870196i
\(919\) −1.03446e12 −1.45028 −0.725138 0.688603i \(-0.758224\pi\)
−0.725138 + 0.688603i \(0.758224\pi\)
\(920\) 0 0
\(921\) 1.29111e11 + 2.30573e11i 0.179443 + 0.320457i
\(922\) −4.91563e11 −0.680229
\(923\) 1.19188e12i 1.64220i
\(924\) −4.70381e11 + 2.63394e11i −0.645301 + 0.361342i
\(925\) 0 0
\(926\) 9.36768e11i 1.27405i
\(927\) 1.67369e11 2.73058e11i 0.226651 0.369774i
\(928\) 1.59079e11 0.214496
\(929\) 1.47659e11i 0.198242i −0.995075 0.0991212i \(-0.968397\pi\)
0.995075 0.0991212i \(-0.0316031\pi\)
\(930\) 0 0
\(931\) −8.86833e11 −1.18044
\(932\) 1.18590e12i 1.57175i
\(933\) −8.03502e11 + 4.49928e11i −1.06038 + 0.593767i
\(934\) 1.61131e12 2.11734
\(935\) 0 0
\(936\) −2.76772e11 1.69646e11i −0.360595 0.221024i
\(937\) −3.27745e11 −0.425185 −0.212593 0.977141i \(-0.568191\pi\)
−0.212593 + 0.977141i \(0.568191\pi\)
\(938\) 5.39301e11i 0.696659i
\(939\) −1.12180e11 2.00337e11i −0.144296 0.257691i
\(940\) 0 0
\(941\) 3.29986e11i 0.420860i −0.977609 0.210430i \(-0.932514\pi\)
0.977609 0.210430i \(-0.0674864\pi\)
\(942\) 8.79542e11 4.92507e11i 1.11700 0.625473i
\(943\) 4.38207e11 0.554156
\(944\) 6.22704e11i 0.784140i
\(945\) 0 0
\(946\) −4.08109e11 −0.509579
\(947\) 2.28185e8i 0.000283718i 1.00000 0.000141859i \(4.51551e-5\pi\)
−1.00000 0.000141859i \(0.999955\pi\)
\(948\) 3.15048e11 + 5.62627e11i 0.390070 + 0.696606i
\(949\) 1.36549e12 1.68354
\(950\) 0 0
\(951\) −3.42347e11 + 1.91700e11i −0.418548 + 0.234369i
\(952\) 2.17063e11 0.264264
\(953\) 1.61330e11i 0.195588i −0.995207 0.0977942i \(-0.968821\pi\)
0.995207 0.0977942i \(-0.0311787\pi\)
\(954\) 3.02153e11 4.92954e11i 0.364782 0.595131i
\(955\) 0 0
\(956\) 1.53420e12i 1.83675i
\(957\) −8.42238e10 1.50411e11i −0.100412 0.179321i
\(958\) −2.44653e12 −2.90462
\(959\) 2.27921e11i 0.269470i
\(960\) 0 0
\(961\) 5.69271e11 0.667460
\(962\) 1.99122e12i 2.32497i
\(963\) 7.40286e9 + 4.53754e9i 0.00860784 + 0.00527612i
\(964\) 1.13257e12 1.31146
\(965\) 0 0
\(966\) −1.11712e11 1.99500e11i −0.128289 0.229105i
\(967\) −1.49948e12 −1.71489 −0.857444 0.514577i \(-0.827949\pi\)
−0.857444 + 0.514577i \(0.827949\pi\)
\(968\) 2.86217e11i 0.325982i
\(969\) 1.63744e12 9.16900e11i 1.85725 1.03998i
\(970\) 0 0
\(971\) 3.35149e11i 0.377017i −0.982072 0.188509i \(-0.939635\pi\)
0.982072 0.188509i \(-0.0603654\pi\)
\(972\) −6.32909e11 + 9.46682e11i −0.709049 + 1.06057i
\(973\) −5.13258e11 −0.572644
\(974\) 2.61904e11i 0.291009i
\(975\) 0 0
\(976\) −6.80209e11 −0.749623
\(977\) 8.22116e11i 0.902308i −0.892446 0.451154i \(-0.851012\pi\)
0.892446 0.451154i \(-0.148988\pi\)
\(978\) 1.23989e12 6.94287e11i 1.35528 0.758898i
\(979\) −6.64438e11 −0.723309
\(980\) 0 0
\(981\) 5.86215e11 9.56392e11i 0.632967 1.03267i
\(982\) 2.48545e11 0.267276
\(983\) 1.23984e12i 1.32786i 0.747795 + 0.663930i \(0.231113\pi\)
−0.747795 + 0.663930i \(0.768887\pi\)
\(984\) 2.63334e11 + 4.70274e11i 0.280883 + 0.501615i
\(985\) 0 0
\(986\) 3.21112e11i 0.339742i
\(987\) −1.09285e11 + 6.11951e10i −0.115158 + 0.0644834i
\(988\) 1.79763e12 1.88657
\(989\) 9.70311e10i 0.101420i
\(990\) 0 0
\(991\) 1.44437e12 1.49756 0.748782 0.662817i \(-0.230639\pi\)
0.748782 + 0.662817i \(0.230639\pi\)
\(992\) 1.74297e12i 1.79988i
\(993\) −2.16635e11 3.86878e11i −0.222809 0.397902i
\(994\) 1.03255e12 1.05771
\(995\) 0 0
\(996\) −1.58890e11 + 8.89721e10i −0.161458 + 0.0904100i
\(997\) 4.69939e11 0.475621 0.237810 0.971312i \(-0.423570\pi\)
0.237810 + 0.971312i \(0.423570\pi\)
\(998\) 1.63310e12i 1.64623i
\(999\) −1.50865e12 5.95112e10i −1.51470 0.0597498i
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 75.9.c.e.26.9 yes 10
3.2 odd 2 inner 75.9.c.e.26.2 10
5.2 odd 4 75.9.d.d.74.3 20
5.3 odd 4 75.9.d.d.74.18 20
5.4 even 2 75.9.c.f.26.2 yes 10
15.2 even 4 75.9.d.d.74.17 20
15.8 even 4 75.9.d.d.74.4 20
15.14 odd 2 75.9.c.f.26.9 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.9.c.e.26.2 10 3.2 odd 2 inner
75.9.c.e.26.9 yes 10 1.1 even 1 trivial
75.9.c.f.26.2 yes 10 5.4 even 2
75.9.c.f.26.9 yes 10 15.14 odd 2
75.9.d.d.74.3 20 5.2 odd 4
75.9.d.d.74.4 20 15.8 even 4
75.9.d.d.74.17 20 15.2 even 4
75.9.d.d.74.18 20 5.3 odd 4