Properties

Label 75.9.d.d.74.3
Level $75$
Weight $9$
Character 75.74
Analytic conductor $30.553$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,9,Mod(74,75)]
 
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, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.74");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 3278 x^{18} + 4245491 x^{16} + 2854629536 x^{14} + 1117319469691 x^{12} + 266849787342054 x^{10} + \cdots + 89\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{22}\cdot 5^{26} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 74.3
Root \(-12.5890i\) of defining polynomial
Character \(\chi\) \(=\) 75.74
Dual form 75.9.d.d.74.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-24.1370 q^{2} +(70.6742 - 39.5746i) q^{3} +326.594 q^{4} +(-1705.86 + 955.212i) q^{6} -1042.22i q^{7} -1703.92 q^{8} +(3428.70 - 5593.81i) q^{9} +O(q^{10})\) \(q-24.1370 q^{2} +(70.6742 - 39.5746i) q^{3} +326.594 q^{4} +(-1705.86 + 955.212i) q^{6} -1042.22i q^{7} -1703.92 q^{8} +(3428.70 - 5593.81i) q^{9} +19553.4i q^{11} +(23081.8 - 12924.8i) q^{12} +29037.8i q^{13} +25156.0i q^{14} -42480.5 q^{16} +122230. q^{17} +(-82758.4 + 135018. i) q^{18} -189552. q^{19} +(-41245.5 - 73658.1i) q^{21} -471959. i q^{22} -112212. q^{23} +(-120424. + 67432.2i) q^{24} -700886. i q^{26} +(20947.3 - 531028. i) q^{27} -340383. i q^{28} -108842. i q^{29} -1.19254e6 q^{31} +1.46155e6 q^{32} +(773817. + 1.38192e6i) q^{33} -2.95026e6 q^{34} +(1.11979e6 - 1.82691e6i) q^{36} +2.84100e6i q^{37} +4.57521e6 q^{38} +(1.14916e6 + 2.05223e6i) q^{39} +3.90516e6i q^{41} +(995541. + 1.77788e6i) q^{42} -864712. i q^{43} +6.38601e6i q^{44} +2.70846e6 q^{46} +1.48368e6 q^{47} +(-3.00227e6 + 1.68115e6i) q^{48} +4.67858e6 q^{49} +(8.63850e6 - 4.83720e6i) q^{51} +9.48358e6i q^{52} +3.65103e6 q^{53} +(-505604. + 1.28174e7i) q^{54} +1.77586e6i q^{56} +(-1.33964e7 + 7.50144e6i) q^{57} +2.62712e6i q^{58} +1.46586e7i q^{59} +1.60123e7 q^{61} +2.87844e7 q^{62} +(-5.82998e6 - 3.57345e6i) q^{63} -2.44025e7 q^{64} +(-1.86776e7 - 3.33554e7i) q^{66} -2.14382e7i q^{67} +3.99195e7 q^{68} +(-7.93050e6 + 4.44075e6i) q^{69} +4.10459e7i q^{71} +(-5.84224e6 + 9.53144e6i) q^{72} +4.70244e7i q^{73} -6.85731e7i q^{74} -6.19065e7 q^{76} +2.03789e7 q^{77} +(-2.77373e7 - 4.95346e7i) q^{78} +2.43754e7 q^{79} +(-1.95348e7 - 3.83590e7i) q^{81} -9.42589e7i q^{82} -6.88381e6 q^{83} +(-1.34705e7 - 2.40563e7i) q^{84} +2.08715e7i q^{86} +(-4.30738e6 - 7.69233e6i) q^{87} -3.33174e7i q^{88} -3.39808e7i q^{89} +3.02638e7 q^{91} -3.66478e7 q^{92} +(-8.42822e7 + 4.71945e7i) q^{93} -3.58116e7 q^{94} +(1.03294e8 - 5.78405e7i) q^{96} -1.50338e7i q^{97} -1.12927e8 q^{98} +(1.09378e8 + 6.70425e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9} + 89268 q^{16} + 287868 q^{19} + 1346856 q^{21} + 2033718 q^{24} - 6028120 q^{31} - 9954292 q^{34} + 9001054 q^{36} + 15026564 q^{39} - 27877272 q^{46} - 17907092 q^{49} + 12418574 q^{51} + 17772544 q^{54} + 3040440 q^{61} + 9073996 q^{64} + 20930590 q^{66} - 22789956 q^{69} - 59058092 q^{76} - 17099792 q^{79} + 45225890 q^{81} + 273766584 q^{84} - 214448528 q^{91} - 712237192 q^{94} + 1050848002 q^{96} + 764842670 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −24.1370 −1.50856 −0.754281 0.656552i \(-0.772014\pi\)
−0.754281 + 0.656552i \(0.772014\pi\)
\(3\) 70.6742 39.5746i 0.872521 0.488576i
\(4\) 326.594 1.27576
\(5\) 0 0
\(6\) −1705.86 + 955.212i −1.31625 + 0.737047i
\(7\) 1042.22i 0.434077i −0.976163 0.217039i \(-0.930360\pi\)
0.976163 0.217039i \(-0.0696398\pi\)
\(8\) −1703.92 −0.415997
\(9\) 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 \(0.767253\pi\)
\(12\) 23081.8 12924.8i 1.11313 0.623304i
\(13\) 29037.8i 1.01670i 0.861152 + 0.508348i \(0.169743\pi\)
−0.861152 + 0.508348i \(0.830257\pi\)
\(14\) 25156.0i 0.654832i
\(15\) 0 0
\(16\) −42480.5 −0.648200
\(17\) 122230. 1.46346 0.731731 0.681594i \(-0.238713\pi\)
0.731731 + 0.681594i \(0.238713\pi\)
\(18\) −82758.4 + 135018.i −0.788355 + 1.28618i
\(19\) −189552. −1.45450 −0.727250 0.686373i \(-0.759202\pi\)
−0.727250 + 0.686373i \(0.759202\pi\)
\(20\) 0 0
\(21\) −41245.5 73658.1i −0.212080 0.378742i
\(22\) 471959.i 2.01472i
\(23\) −112212. −0.400985 −0.200493 0.979695i \(-0.564254\pi\)
−0.200493 + 0.979695i \(0.564254\pi\)
\(24\) −120424. + 67432.2i −0.362966 + 0.203246i
\(25\) 0 0
\(26\) 700886.i 1.53375i
\(27\) 20947.3 531028.i 0.0394160 0.999223i
\(28\) 340383.i 0.553777i
\(29\) 108842.i 0.153888i −0.997035 0.0769440i \(-0.975484\pi\)
0.997035 0.0769440i \(-0.0245163\pi\)
\(30\) 0 0
\(31\) −1.19254e6 −1.29130 −0.645651 0.763633i \(-0.723414\pi\)
−0.645651 + 0.763633i \(0.723414\pi\)
\(32\) 1.46155e6 1.39385
\(33\) 773817. + 1.38192e6i 0.652503 + 1.16527i
\(34\) −2.95026e6 −2.20772
\(35\) 0 0
\(36\) 1.11979e6 1.82691e6i 0.666695 1.08769i
\(37\) 2.84100e6i 1.51588i 0.652326 + 0.757939i \(0.273793\pi\)
−0.652326 + 0.757939i \(0.726207\pi\)
\(38\) 4.57521e6 2.19420
\(39\) 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 \(0.757173\pi\)
\(42\) 995541. + 1.77788e6i 0.319935 + 0.571355i
\(43\) 864712.i 0.252928i −0.991971 0.126464i \(-0.959637\pi\)
0.991971 0.126464i \(-0.0403629\pi\)
\(44\) 6.38601e6i 1.70380i
\(45\) 0 0
\(46\) 2.70846e6 0.604911
\(47\) 1.48368e6 0.304053 0.152026 0.988376i \(-0.451420\pi\)
0.152026 + 0.988376i \(0.451420\pi\)
\(48\) −3.00227e6 + 1.68115e6i −0.565569 + 0.316695i
\(49\) 4.67858e6 0.811577
\(50\) 0 0
\(51\) 8.63850e6 4.83720e6i 1.27690 0.715012i
\(52\) 9.48358e6i 1.29706i
\(53\) 3.65103e6 0.462713 0.231357 0.972869i \(-0.425684\pi\)
0.231357 + 0.972869i \(0.425684\pi\)
\(54\) −505604. + 1.28174e7i −0.0594615 + 1.50739i
\(55\) 0 0
\(56\) 1.77586e6i 0.180575i
\(57\) −1.33964e7 + 7.50144e6i −1.26908 + 0.710633i
\(58\) 2.62712e6i 0.232149i
\(59\) 1.46586e7i 1.20972i 0.796332 + 0.604859i \(0.206771\pi\)
−0.796332 + 0.604859i \(0.793229\pi\)
\(60\) 0 0
\(61\) 1.60123e7 1.15647 0.578234 0.815871i \(-0.303742\pi\)
0.578234 + 0.815871i \(0.303742\pi\)
\(62\) 2.87844e7 1.94801
\(63\) −5.82998e6 3.57345e6i −0.370088 0.226843i
\(64\) −2.44025e7 −1.45450
\(65\) 0 0
\(66\) −1.86776e7 3.33554e7i −0.984341 1.75788i
\(67\) 2.14382e7i 1.06387i −0.846784 0.531937i \(-0.821464\pi\)
0.846784 0.531937i \(-0.178536\pi\)
\(68\) 3.99195e7 1.86702
\(69\) −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 \(0.700756\pi\)
\(72\) −5.84224e6 + 9.53144e6i −0.217395 + 0.354673i
\(73\) 4.70244e7i 1.65589i 0.560808 + 0.827946i \(0.310491\pi\)
−0.560808 + 0.827946i \(0.689509\pi\)
\(74\) 6.85731e7i 2.28679i
\(75\) 0 0
\(76\) −6.19065e7 −1.85559
\(77\) 2.03789e7 0.579719
\(78\) −2.77373e7 4.95346e7i −0.749352 1.33823i
\(79\) 2.43754e7 0.625811 0.312905 0.949784i \(-0.398698\pi\)
0.312905 + 0.949784i \(0.398698\pi\)
\(80\) 0 0
\(81\) −1.95348e7 3.83590e7i −0.453805 0.891101i
\(82\) 9.42589e7i 2.08481i
\(83\) −6.88381e6 −0.145050 −0.0725248 0.997367i \(-0.523106\pi\)
−0.0725248 + 0.997367i \(0.523106\pi\)
\(84\) −1.34705e7 2.40563e7i −0.270562 0.483183i
\(85\) 0 0
\(86\) 2.08715e7i 0.381558i
\(87\) −4.30738e6 7.69233e6i −0.0751859 0.134271i
\(88\) 3.33174e7i 0.555573i
\(89\) 3.39808e7i 0.541593i −0.962637 0.270796i \(-0.912713\pi\)
0.962637 0.270796i \(-0.0872870\pi\)
\(90\) 0 0
\(91\) 3.02638e7 0.441324
\(92\) −3.66478e7 −0.511560
\(93\) −8.42822e7 + 4.71945e7i −1.12669 + 0.630899i
\(94\) −3.58116e7 −0.458682
\(95\) 0 0
\(96\) 1.03294e8 5.78405e7i 1.21616 0.681000i
\(97\) 1.50338e7i 0.169817i −0.996389 0.0849086i \(-0.972940\pi\)
0.996389 0.0849086i \(-0.0270598\pi\)
\(98\) −1.12927e8 −1.22431
\(99\) 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 \(0.740304\pi\)
\(102\) −2.08507e8 + 1.16755e8i −1.92628 + 1.07864i
\(103\) 4.88143e7i 0.433709i 0.976204 + 0.216854i \(0.0695797\pi\)
−0.976204 + 0.216854i \(0.930420\pi\)
\(104\) 4.94783e7i 0.422942i
\(105\) 0 0
\(106\) −8.81248e7 −0.698031
\(107\) 1.32340e6 0.0100962 0.00504808 0.999987i \(-0.498393\pi\)
0.00504808 + 0.999987i \(0.498393\pi\)
\(108\) 6.84125e6 1.73431e8i 0.0502853 1.27477i
\(109\) 1.70973e8 1.21122 0.605608 0.795763i \(-0.292930\pi\)
0.605608 + 0.795763i \(0.292930\pi\)
\(110\) 0 0
\(111\) 1.12432e8 + 2.00785e8i 0.740621 + 1.32264i
\(112\) 4.42740e7i 0.281369i
\(113\) 3.37372e7 0.206916 0.103458 0.994634i \(-0.467009\pi\)
0.103458 + 0.994634i \(0.467009\pi\)
\(114\) 3.23349e8 1.81062e8i 1.91449 1.07203i
\(115\) 0 0
\(116\) 3.55471e7i 0.196324i
\(117\) 1.62432e8 + 9.95619e7i 0.866820 + 0.531312i
\(118\) 3.53814e8i 1.82493i
\(119\) 1.27390e8i 0.635256i
\(120\) 0 0
\(121\) −1.67975e8 −0.783617
\(122\) −3.86488e8 −1.74460
\(123\) 1.54545e8 + 2.75995e8i 0.675205 + 1.20581i
\(124\) −3.89478e8 −1.64739
\(125\) 0 0
\(126\) 1.40718e8 + 8.62524e7i 0.558301 + 0.342207i
\(127\) 9.39184e7i 0.361024i −0.983573 0.180512i \(-0.942225\pi\)
0.983573 0.180512i \(-0.0577754\pi\)
\(128\) 2.14845e8 0.800361
\(129\) −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 \(-0.152703\pi\)
\(132\) 2.52724e8 + 4.51326e8i 0.832436 + 1.48660i
\(133\) 1.97555e8i 0.631365i
\(134\) 5.17455e8i 1.60492i
\(135\) 0 0
\(136\) −2.08270e8 −0.608796
\(137\) 2.18688e8 0.620788 0.310394 0.950608i \(-0.399539\pi\)
0.310394 + 0.950608i \(0.399539\pi\)
\(138\) 1.91418e8 1.07186e8i 0.527798 0.295545i
\(139\) −4.92467e8 −1.31922 −0.659611 0.751608i \(-0.729279\pi\)
−0.659611 + 0.751608i \(0.729279\pi\)
\(140\) 0 0
\(141\) 1.04858e8 5.87161e7i 0.265293 0.148553i
\(142\) 9.90724e8i 2.43668i
\(143\) −5.67787e8 −1.35782
\(144\) −1.45653e8 + 2.37628e8i −0.338741 + 0.552646i
\(145\) 0 0
\(146\) 1.13503e9i 2.49801i
\(147\) 3.30655e8 1.85153e8i 0.708118 0.396517i
\(148\) 9.27853e8i 1.93389i
\(149\) 2.38202e6i 0.00483283i 0.999997 + 0.00241641i \(0.000769169\pi\)
−0.999997 + 0.00241641i \(0.999231\pi\)
\(150\) 0 0
\(151\) −2.94102e8 −0.565705 −0.282852 0.959163i \(-0.591281\pi\)
−0.282852 + 0.959163i \(0.591281\pi\)
\(152\) 3.22982e8 0.605067
\(153\) 4.19089e8 6.83731e8i 0.764787 1.24773i
\(154\) −4.91885e8 −0.874542
\(155\) 0 0
\(156\) 3.75309e8 + 6.70245e8i 0.633710 + 1.13171i
\(157\) 5.15599e8i 0.848621i −0.905517 0.424310i \(-0.860517\pi\)
0.905517 0.424310i \(-0.139483\pi\)
\(158\) −5.88348e8 −0.944074
\(159\) 2.58034e8 1.44488e8i 0.403727 0.226070i
\(160\) 0 0
\(161\) 1.16950e8i 0.174059i
\(162\) 4.71511e8 + 9.25870e8i 0.684592 + 1.34428i
\(163\) 7.26841e8i 1.02965i 0.857296 + 0.514824i \(0.172143\pi\)
−0.857296 + 0.514824i \(0.827857\pi\)
\(164\) 1.27540e9i 1.76308i
\(165\) 0 0
\(166\) 1.66154e8 0.218816
\(167\) 3.33903e8 0.429294 0.214647 0.976692i \(-0.431140\pi\)
0.214647 + 0.976692i \(0.431140\pi\)
\(168\) 7.02791e7 + 1.25508e8i 0.0882245 + 0.157555i
\(169\) −2.74650e7 −0.0336692
\(170\) 0 0
\(171\) −6.49915e8 + 1.06032e9i −0.760103 + 1.24009i
\(172\) 2.82410e8i 0.322675i
\(173\) 1.32165e9 1.47547 0.737737 0.675088i \(-0.235894\pi\)
0.737737 + 0.675088i \(0.235894\pi\)
\(174\) 1.03967e8 + 1.85670e8i 0.113423 + 0.202555i
\(175\) 0 0
\(176\) 8.30636e8i 0.865685i
\(177\) 5.80109e8 + 1.03599e9i 0.591039 + 1.05551i
\(178\) 8.20193e8i 0.817026i
\(179\) 1.09788e8i 0.106940i −0.998569 0.0534701i \(-0.982972\pi\)
0.998569 0.0534701i \(-0.0170282\pi\)
\(180\) 0 0
\(181\) −3.65073e8 −0.340146 −0.170073 0.985431i \(-0.554400\pi\)
−0.170073 + 0.985431i \(0.554400\pi\)
\(182\) −7.30477e8 −0.665765
\(183\) 1.13166e9 6.33680e8i 1.00904 0.565023i
\(184\) 1.91201e8 0.166809
\(185\) 0 0
\(186\) 2.03432e9 1.13913e9i 1.69968 0.951750i
\(187\) 2.39000e9i 1.95448i
\(188\) 4.84561e8 0.387898
\(189\) −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 \(0.701767\pi\)
\(192\) −1.72463e9 + 9.65721e8i −1.26909 + 0.710635i
\(193\) 2.36470e9i 1.70431i −0.523293 0.852153i \(-0.675297\pi\)
0.523293 0.852153i \(-0.324703\pi\)
\(194\) 3.62870e8i 0.256180i
\(195\) 0 0
\(196\) 1.52800e9 1.03538
\(197\) −2.37290e9 −1.57548 −0.787742 0.616006i \(-0.788750\pi\)
−0.787742 + 0.616006i \(0.788750\pi\)
\(198\) −2.64005e9 1.61820e9i −1.71772 1.05287i
\(199\) 8.35564e8 0.532804 0.266402 0.963862i \(-0.414165\pi\)
0.266402 + 0.963862i \(0.414165\pi\)
\(200\) 0 0
\(201\) −8.48411e8 1.51513e9i −0.519783 0.928252i
\(202\) 3.65862e9i 2.19741i
\(203\) −1.13437e8 −0.0667993
\(204\) 2.82128e9 1.57980e9i 1.62902 0.912182i
\(205\) 0 0
\(206\) 1.17823e9i 0.654276i
\(207\) −3.84741e8 + 6.27694e8i −0.209550 + 0.341874i
\(208\) 1.23354e9i 0.659022i
\(209\) 3.70638e9i 1.94251i
\(210\) 0 0
\(211\) −2.31595e9 −1.16842 −0.584211 0.811602i \(-0.698596\pi\)
−0.584211 + 0.811602i \(0.698596\pi\)
\(212\) 1.19240e9 0.590310
\(213\) 1.62438e9 + 2.90089e9i 0.789165 + 1.40933i
\(214\) −3.19429e7 −0.0152307
\(215\) 0 0
\(216\) −3.56926e7 + 9.04831e8i −0.0163969 + 0.415674i
\(217\) 1.24289e9i 0.560525i
\(218\) −4.12678e9 −1.82720
\(219\) 1.86097e9 + 3.32341e9i 0.809029 + 1.44480i
\(220\) 0 0
\(221\) 3.54929e9i 1.48789i
\(222\) −2.71376e9 4.84635e9i −1.11727 1.99528i
\(223\) 4.75871e8i 0.192429i −0.995361 0.0962144i \(-0.969327\pi\)
0.995361 0.0962144i \(-0.0306734\pi\)
\(224\) 1.52326e9i 0.605037i
\(225\) 0 0
\(226\) −8.14313e8 −0.312146
\(227\) 3.01408e9 1.13515 0.567573 0.823323i \(-0.307882\pi\)
0.567573 + 0.823323i \(0.307882\pi\)
\(228\) −4.37519e9 + 2.44993e9i −1.61904 + 0.906595i
\(229\) −3.75337e9 −1.36483 −0.682416 0.730964i \(-0.739071\pi\)
−0.682416 + 0.730964i \(0.739071\pi\)
\(230\) 0 0
\(231\) 1.44026e9 8.06488e8i 0.505818 0.283237i
\(232\) 1.85459e8i 0.0640169i
\(233\) 3.63111e9 1.23201 0.616007 0.787741i \(-0.288749\pi\)
0.616007 + 0.787741i \(0.288749\pi\)
\(234\) −3.92062e9 2.40312e9i −1.30765 0.801517i
\(235\) 0 0
\(236\) 4.78741e9i 1.54331i
\(237\) 1.72271e9 9.64647e8i 0.546033 0.305756i
\(238\) 3.07482e9i 0.958322i
\(239\) 4.69757e9i 1.43973i −0.694112 0.719867i \(-0.744203\pi\)
0.694112 0.719867i \(-0.255797\pi\)
\(240\) 0 0
\(241\) −3.46782e9 −1.02799 −0.513994 0.857794i \(-0.671835\pi\)
−0.513994 + 0.857794i \(0.671835\pi\)
\(242\) 4.05441e9 1.18213
\(243\) −2.89865e9 1.93791e9i −0.831325 0.555787i
\(244\) 5.22951e9 1.47537
\(245\) 0 0
\(246\) −3.73026e9 6.66167e9i −1.01859 1.81904i
\(247\) 5.50417e9i 1.47878i
\(248\) 2.03200e9 0.537178
\(249\) −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 \(0.937946\pi\)
\(252\) −1.90404e9 1.16707e9i −0.472143 0.289397i
\(253\) 2.19412e9i 0.535524i
\(254\) 2.26691e9i 0.544626i
\(255\) 0 0
\(256\) 1.06133e9 0.247110
\(257\) −2.70241e9 −0.619467 −0.309734 0.950823i \(-0.600240\pi\)
−0.309734 + 0.950823i \(0.600240\pi\)
\(258\) 8.25983e8 + 1.47508e9i 0.186420 + 0.332917i
\(259\) 2.96095e9 0.658008
\(260\) 0 0
\(261\) −6.08842e8 3.73186e8i −0.131203 0.0804199i
\(262\) 6.56156e9i 1.39252i
\(263\) −3.23085e9 −0.675296 −0.337648 0.941273i \(-0.609631\pi\)
−0.337648 + 0.941273i \(0.609631\pi\)
\(264\) −1.31853e9 2.35469e9i −0.271439 0.484749i
\(265\) 0 0
\(266\) 4.76837e9i 0.952453i
\(267\) −1.34478e9 2.40156e9i −0.264609 0.472552i
\(268\) 7.00160e9i 1.35724i
\(269\) 8.82614e8i 0.168563i 0.996442 + 0.0842814i \(0.0268595\pi\)
−0.996442 + 0.0842814i \(0.973141\pi\)
\(270\) 0 0
\(271\) 8.69735e9 1.61254 0.806269 0.591549i \(-0.201483\pi\)
0.806269 + 0.591549i \(0.201483\pi\)
\(272\) −5.19238e9 −0.948616
\(273\) 2.13887e9 1.19768e9i 0.385065 0.215620i
\(274\) −5.27847e9 −0.936496
\(275\) 0 0
\(276\) −2.59005e9 + 1.45032e9i −0.446347 + 0.249936i
\(277\) 8.57729e9i 1.45690i 0.685097 + 0.728452i \(0.259760\pi\)
−0.685097 + 0.728452i \(0.740240\pi\)
\(278\) 1.18867e10 1.99013
\(279\) −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 \(-0.0732169\pi\)
\(282\) −2.53096e9 + 1.41723e9i −0.400210 + 0.224101i
\(283\) 9.94012e9i 1.54969i 0.632149 + 0.774847i \(0.282173\pi\)
−0.632149 + 0.774847i \(0.717827\pi\)
\(284\) 1.34053e10i 2.06065i
\(285\) 0 0
\(286\) 1.37047e10 2.04835
\(287\) 4.07004e9 0.599889
\(288\) 5.01123e9 8.17567e9i 0.728407 1.18837i
\(289\) 7.96436e9 1.14172
\(290\) 0 0
\(291\) −5.94957e8 1.06250e9i −0.0829686 0.148169i
\(292\) 1.53579e10i 2.11252i
\(293\) −4.76323e9 −0.646295 −0.323147 0.946349i \(-0.604741\pi\)
−0.323147 + 0.946349i \(0.604741\pi\)
\(294\) −7.98101e9 + 4.46904e9i −1.06824 + 0.598170i
\(295\) 0 0
\(296\) 4.84085e9i 0.630601i
\(297\) 1.03834e10 + 4.09590e8i 1.33448 + 0.0526409i
\(298\) 5.74949e7i 0.00729062i
\(299\) 3.25840e9i 0.407680i
\(300\) 0 0
\(301\) −9.01219e8 −0.109790
\(302\) 7.09873e9 0.853400
\(303\) 5.99861e9 + 1.07126e10i 0.711673 + 1.27094i
\(304\) 8.05225e9 0.942807
\(305\) 0 0
\(306\) −1.01155e10 + 1.65032e10i −1.15373 + 1.88227i
\(307\) 3.26248e9i 0.367277i 0.982994 + 0.183639i \(0.0587876\pi\)
−0.982994 + 0.183639i \(0.941212\pi\)
\(308\) 6.65563e9 0.739581
\(309\) 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 \(0.792112\pi\)
\(312\) −1.95808e9 3.49684e9i −0.206639 0.369026i
\(313\) 2.83465e9i 0.295340i 0.989037 + 0.147670i \(0.0471774\pi\)
−0.989037 + 0.147670i \(0.952823\pi\)
\(314\) 1.24450e10i 1.28020i
\(315\) 0 0
\(316\) 7.96085e9 0.798383
\(317\) −4.84402e9 −0.479699 −0.239850 0.970810i \(-0.577098\pi\)
−0.239850 + 0.970810i \(0.577098\pi\)
\(318\) −6.22816e9 + 3.48751e9i −0.609047 + 0.341041i
\(319\) 2.12823e9 0.205521
\(320\) 0 0
\(321\) 9.35303e7 5.23731e7i 0.00880911 0.00493274i
\(322\) 2.82281e9i 0.262578i
\(323\) −2.31689e10 −2.12860
\(324\) −6.37995e9 1.25278e10i −0.578945 1.13683i
\(325\) 0 0
\(326\) 1.75437e10i 1.55329i
\(327\) 1.20834e10 6.76620e9i 1.05681 0.591771i
\(328\) 6.65410e9i 0.574902i
\(329\) 1.54632e9i 0.131982i
\(330\) 0 0
\(331\) −5.47410e9 −0.456037 −0.228019 0.973657i \(-0.573225\pi\)
−0.228019 + 0.973657i \(0.573225\pi\)
\(332\) −2.24821e9 −0.185048
\(333\) 1.58920e10 + 9.74092e9i 1.29242 + 0.792179i
\(334\) −8.05942e9 −0.647616
\(335\) 0 0
\(336\) 1.75213e9 + 3.12903e9i 0.137470 + 0.245501i
\(337\) 2.30004e10i 1.78327i −0.452759 0.891633i \(-0.649560\pi\)
0.452759 0.891633i \(-0.350440\pi\)
\(338\) 6.62922e8 0.0507920
\(339\) 2.38435e9 1.33514e9i 0.180539 0.101094i
\(340\) 0 0
\(341\) 2.33183e10i 1.72456i
\(342\) 1.56870e10 2.55929e10i 1.14666 1.87074i
\(343\) 1.08843e10i 0.786364i
\(344\) 1.47340e9i 0.105217i
\(345\) 0 0
\(346\) −3.19006e10 −2.22584
\(347\) −2.27792e10 −1.57116 −0.785582 0.618758i \(-0.787636\pi\)
−0.785582 + 0.618758i \(0.787636\pi\)
\(348\) −1.40677e9 2.51227e9i −0.0959190 0.171297i
\(349\) −2.25621e10 −1.52082 −0.760410 0.649444i \(-0.775002\pi\)
−0.760410 + 0.649444i \(0.775002\pi\)
\(350\) 0 0
\(351\) 1.54199e10 + 6.08264e8i 1.01591 + 0.0400741i
\(352\) 2.85783e10i 1.86151i
\(353\) −8.56846e9 −0.551828 −0.275914 0.961182i \(-0.588981\pi\)
−0.275914 + 0.961182i \(0.588981\pi\)
\(354\) −1.40021e10 2.50056e10i −0.891619 1.59229i
\(355\) 0 0
\(356\) 1.10979e10i 0.690941i
\(357\) −5.04142e9 9.00321e9i −0.310370 0.554274i
\(358\) 2.64994e9i 0.161326i
\(359\) 3.45337e9i 0.207905i 0.994582 + 0.103953i \(0.0331490\pi\)
−0.994582 + 0.103953i \(0.966851\pi\)
\(360\) 0 0
\(361\) 1.89463e10 1.11557
\(362\) 8.81177e9 0.513132
\(363\) −1.18715e10 + 6.64756e9i −0.683722 + 0.382856i
\(364\) 9.88397e9 0.563023
\(365\) 0 0
\(366\) −2.73148e10 + 1.52951e10i −1.52220 + 0.852371i
\(367\) 7.52594e9i 0.414855i 0.978250 + 0.207428i \(0.0665092\pi\)
−0.978250 + 0.207428i \(0.933491\pi\)
\(368\) 4.76682e9 0.259919
\(369\) 2.18448e10 + 1.33896e10i 1.17826 + 0.722209i
\(370\) 0 0
\(371\) 3.80518e9i 0.200853i
\(372\) −2.75260e10 + 1.54134e10i −1.43738 + 0.804874i
\(373\) 1.60977e10i 0.831625i −0.909450 0.415812i \(-0.863497\pi\)
0.909450 0.415812i \(-0.136503\pi\)
\(374\) 5.76875e10i 2.94846i
\(375\) 0 0
\(376\) −2.52808e9 −0.126485
\(377\) 3.16054e9 0.156457
\(378\) 1.33586e10 + 5.26951e8i 0.654323 + 0.0258109i
\(379\) 7.26804e9 0.352257 0.176129 0.984367i \(-0.443642\pi\)
0.176129 + 0.984367i \(0.443642\pi\)
\(380\) 0 0
\(381\) −3.71679e9 6.63761e9i −0.176387 0.315001i
\(382\) 5.17657e10i 2.43102i
\(383\) −3.84730e9 −0.178797 −0.0893987 0.995996i \(-0.528495\pi\)
−0.0893987 + 0.995996i \(0.528495\pi\)
\(384\) 1.51840e10 8.50242e9i 0.698332 0.391037i
\(385\) 0 0
\(386\) 5.70768e10i 2.57105i
\(387\) −4.83704e9 2.96483e9i −0.215643 0.132177i
\(388\) 4.90995e9i 0.216646i
\(389\) 1.64582e10i 0.718761i −0.933191 0.359380i \(-0.882988\pi\)
0.933191 0.359380i \(-0.117012\pi\)
\(390\) 0 0
\(391\) −1.37157e10 −0.586826
\(392\) −7.97194e9 −0.337614
\(393\) −1.07582e10 1.92126e10i −0.450994 0.805407i
\(394\) 5.72746e10 2.37671
\(395\) 0 0
\(396\) 3.57222e10 + 2.18957e10i 1.45264 + 0.890385i
\(397\) 3.57344e10i 1.43855i 0.694727 + 0.719273i \(0.255525\pi\)
−0.694727 + 0.719273i \(0.744475\pi\)
\(398\) −2.01680e10 −0.803767
\(399\) 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 \(0.952723\pi\)
\(402\) 2.04781e10 + 3.65707e10i 0.784124 + 1.40033i
\(403\) 3.46289e10i 1.31286i
\(404\) 4.95042e10i 1.85830i
\(405\) 0 0
\(406\) 2.73803e9 0.100771
\(407\) −5.55511e10 −2.02449
\(408\) −1.47193e10 + 8.24222e9i −0.531187 + 0.297443i
\(409\) −1.89488e10 −0.677154 −0.338577 0.940939i \(-0.609946\pi\)
−0.338577 + 0.940939i \(0.609946\pi\)
\(410\) 0 0
\(411\) 1.54556e10 8.65450e9i 0.541650 0.303302i
\(412\) 1.59425e10i 0.553307i
\(413\) 1.52775e10 0.525111
\(414\) 9.28649e9 1.51506e10i 0.316119 0.515738i
\(415\) 0 0
\(416\) 4.24404e10i 1.41712i
\(417\) −3.48047e10 + 1.94892e10i −1.15105 + 0.644540i
\(418\) 8.94607e10i 2.93040i
\(419\) 8.62832e9i 0.279943i 0.990156 + 0.139972i \(0.0447012\pi\)
−0.990156 + 0.139972i \(0.955299\pi\)
\(420\) 0 0
\(421\) 3.38470e10 1.07744 0.538718 0.842486i \(-0.318909\pi\)
0.538718 + 0.842486i \(0.318909\pi\)
\(422\) 5.59001e10 1.76264
\(423\) 5.08709e9 8.29944e9i 0.158894 0.259231i
\(424\) −6.22108e9 −0.192487
\(425\) 0 0
\(426\) −3.92075e10 7.00186e10i −1.19050 2.12606i
\(427\) 1.66883e10i 0.501997i
\(428\) 4.32214e8 0.0128802
\(429\) −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 \(-0.142179\pi\)
\(432\) −8.89850e8 + 2.25583e10i −0.0255495 + 0.647697i
\(433\) 2.54166e9i 0.0723047i 0.999346 + 0.0361524i \(0.0115102\pi\)
−0.999346 + 0.0361524i \(0.988490\pi\)
\(434\) 2.99997e10i 0.845586i
\(435\) 0 0
\(436\) 5.58388e10 1.54522
\(437\) 2.12700e10 0.583233
\(438\) −4.49183e10 8.02172e10i −1.22047 2.17957i
\(439\) −1.11261e10 −0.299559 −0.149780 0.988719i \(-0.547856\pi\)
−0.149780 + 0.988719i \(0.547856\pi\)
\(440\) 0 0
\(441\) 1.60414e10 2.61711e10i 0.424120 0.691939i
\(442\) 8.56691e10i 2.24458i
\(443\) 3.00907e10 0.781299 0.390650 0.920539i \(-0.372250\pi\)
0.390650 + 0.920539i \(0.372250\pi\)
\(444\) 3.67194e10 + 6.55753e10i 0.944853 + 1.68736i
\(445\) 0 0
\(446\) 1.14861e10i 0.290291i
\(447\) 9.42678e7 + 1.68348e8i 0.00236120 + 0.00421674i
\(448\) 2.54328e10i 0.631367i
\(449\) 2.46457e10i 0.606396i 0.952928 + 0.303198i \(0.0980543\pi\)
−0.952928 + 0.303198i \(0.901946\pi\)
\(450\) 0 0
\(451\) −7.63591e10 −1.84567
\(452\) 1.10184e10 0.263975
\(453\) −2.07854e10 + 1.16390e10i −0.493589 + 0.276390i
\(454\) −7.27509e10 −1.71244
\(455\) 0 0
\(456\) 2.28265e10 1.27819e10i 0.527934 0.295621i
\(457\) 1.18416e10i 0.271486i −0.990744 0.135743i \(-0.956658\pi\)
0.990744 0.135743i \(-0.0433421\pi\)
\(458\) 9.05950e10 2.05893
\(459\) 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 \(0.927613\pi\)
\(462\) −3.47636e10 + 1.94662e10i −0.763057 + 0.427280i
\(463\) 3.88105e10i 0.844550i −0.906468 0.422275i \(-0.861232\pi\)
0.906468 0.422275i \(-0.138768\pi\)
\(464\) 4.62366e9i 0.0997502i
\(465\) 0 0
\(466\) −8.76440e10 −1.85857
\(467\) 6.67567e10 1.40355 0.701774 0.712400i \(-0.252392\pi\)
0.701774 + 0.712400i \(0.252392\pi\)
\(468\) 5.30494e10 + 3.25163e10i 1.10585 + 0.677825i
\(469\) −2.23434e10 −0.461803
\(470\) 0 0
\(471\) −2.04047e10 3.64396e10i −0.414616 0.740440i
\(472\) 2.49771e10i 0.503239i
\(473\) 1.69080e10 0.337791
\(474\) −4.15810e10 + 2.32837e10i −0.823725 + 0.461252i
\(475\) 0 0
\(476\) 4.16049e10i 0.810432i
\(477\) 1.25183e10 2.04232e10i 0.241808 0.394503i
\(478\) 1.13385e11i 2.17193i
\(479\) 1.01360e11i 1.92542i −0.270529 0.962712i \(-0.587199\pi\)
0.270529 0.962712i \(-0.412801\pi\)
\(480\) 0 0
\(481\) −8.24964e10 −1.54119
\(482\) 8.37027e10 1.55078
\(483\) 4.62824e9 + 8.26533e9i 0.0850408 + 0.151870i
\(484\) −5.48597e10 −0.999705
\(485\) 0 0
\(486\) 6.99647e10 + 4.67753e10i 1.25410 + 0.838439i
\(487\) 1.08507e10i 0.192905i −0.995338 0.0964526i \(-0.969250\pi\)
0.995338 0.0964526i \(-0.0307496\pi\)
\(488\) −2.72837e10 −0.481088
\(489\) 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 \(-0.0282349\pi\)
\(492\) 5.04736e10 + 9.01381e10i 0.861398 + 1.53833i
\(493\) 1.33037e10i 0.225209i
\(494\) 1.32854e11i 2.23083i
\(495\) 0 0
\(496\) 5.06598e10 0.837022
\(497\) 4.27788e10 0.701138
\(498\) 1.17428e10 6.57550e9i 0.190922 0.106908i
\(499\) −6.76597e10 −1.09126 −0.545630 0.838026i \(-0.683710\pi\)
−0.545630 + 0.838026i \(0.683710\pi\)
\(500\) 0 0
\(501\) 2.35984e10 1.32141e10i 0.374568 0.209743i
\(502\) 3.71171e10i 0.584465i
\(503\) 2.55230e10 0.398712 0.199356 0.979927i \(-0.436115\pi\)
0.199356 + 0.979927i \(0.436115\pi\)
\(504\) 9.93385e9 + 6.08890e9i 0.153956 + 0.0943662i
\(505\) 0 0
\(506\) 5.29595e10i 0.807871i
\(507\) −1.94107e9 + 1.08692e9i −0.0293771 + 0.0164500i
\(508\) 3.06732e10i 0.460579i
\(509\) 1.02891e11i 1.53287i 0.642320 + 0.766437i \(0.277972\pi\)
−0.642320 + 0.766437i \(0.722028\pi\)
\(510\) 0 0
\(511\) 4.90098e10 0.718785
\(512\) −8.06177e10 −1.17314
\(513\) −3.97059e9 + 1.00657e11i −0.0573305 + 1.45337i
\(514\) 6.52280e10 0.934504
\(515\) 0 0
\(516\) −1.11763e10 1.99591e10i −0.157651 0.281541i
\(517\) 2.90110e10i 0.406069i
\(518\) −7.14683e10 −0.992646
\(519\) 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 \(-0.115953\pi\)
\(522\) 1.46956e10 + 9.00759e9i 0.197927 + 0.121318i
\(523\) 8.56285e10i 1.14449i −0.820083 0.572245i \(-0.806073\pi\)
0.820083 0.572245i \(-0.193927\pi\)
\(524\) 8.87835e10i 1.17763i
\(525\) 0 0
\(526\) 7.79830e10 1.01872
\(527\) −1.45764e11 −1.88977
\(528\) −3.28721e10 5.87046e10i −0.422953 0.755329i
\(529\) −6.57194e10 −0.839211
\(530\) 0 0
\(531\) 8.19975e10 + 5.02599e10i 1.03139 + 0.632184i
\(532\) 6.45201e10i 0.805469i
\(533\) −1.13398e11 −1.40506
\(534\) 3.24588e10 + 5.79665e10i 0.399179 + 0.712873i
\(535\) 0 0
\(536\) 3.65291e10i 0.442568i
\(537\) −4.34480e9 7.75915e9i −0.0522484 0.0933076i
\(538\) 2.13036e10i 0.254287i
\(539\) 9.14820e10i 1.08388i
\(540\) 0 0
\(541\) −2.14250e10 −0.250111 −0.125055 0.992150i \(-0.539911\pi\)
−0.125055 + 0.992150i \(0.539911\pi\)
\(542\) −2.09928e11 −2.43261
\(543\) −2.58013e10 + 1.44476e10i −0.296785 + 0.166187i
\(544\) 1.78645e11 2.03984
\(545\) 0 0
\(546\) −5.16259e10 + 2.89084e10i −0.580894 + 0.325277i
\(547\) 9.14990e8i 0.0102204i 0.999987 + 0.00511019i \(0.00162663\pi\)
−0.999987 + 0.00511019i \(0.998373\pi\)
\(548\) 7.14222e10 0.791974
\(549\) 5.49012e10 8.95697e10i 0.604356 0.985989i
\(550\) 0 0
\(551\) 2.06312e10i 0.223830i
\(552\) 1.35130e10 7.56671e9i 0.145544 0.0814987i
\(553\) 2.54045e10i 0.271650i
\(554\) 2.07030e11i 2.19783i
\(555\) 0 0
\(556\) −1.60837e11 −1.68301
\(557\) 1.81764e11 1.88837 0.944185 0.329416i \(-0.106852\pi\)
0.944185 + 0.329416i \(0.106852\pi\)
\(558\) 9.86930e10 1.61015e11i 1.01800 1.66084i
\(559\) 2.51093e10 0.257151
\(560\) 0 0
\(561\) 9.45835e10 + 1.68912e11i 0.954913 + 1.70533i
\(562\) 6.86220e10i 0.687889i
\(563\) −4.19023e10 −0.417066 −0.208533 0.978015i \(-0.566869\pi\)
−0.208533 + 0.978015i \(0.566869\pi\)
\(564\) 3.42460e10 1.91763e10i 0.338449 0.189517i
\(565\) 0 0
\(566\) 2.39924e11i 2.33781i
\(567\) −3.99785e10 + 2.03596e10i −0.386807 + 0.196986i
\(568\) 6.99391e10i 0.671934i
\(569\) 9.98358e10i 0.952439i 0.879326 + 0.476220i \(0.157993\pi\)
−0.879326 + 0.476220i \(0.842007\pi\)
\(570\) 0 0
\(571\) 7.00315e10 0.658793 0.329397 0.944192i \(-0.393155\pi\)
0.329397 + 0.944192i \(0.393155\pi\)
\(572\) −1.85436e11 −1.73225
\(573\) 8.48743e10 + 1.51573e11i 0.787332 + 1.40605i
\(574\) −9.82385e10 −0.904970
\(575\) 0 0
\(576\) −8.36688e10 + 1.36503e11i −0.760105 + 1.24009i
\(577\) 5.16977e10i 0.466410i −0.972428 0.233205i \(-0.925079\pi\)
0.972428 0.233205i \(-0.0749213\pi\)
\(578\) −1.92236e11 −1.72235
\(579\) −9.35823e10 1.67124e11i −0.832683 1.48704i
\(580\) 0 0
\(581\) 7.17444e9i 0.0629627i
\(582\) 1.43605e10 + 2.56456e10i 0.125163 + 0.223522i
\(583\) 7.13899e10i 0.617963i
\(584\) 8.01260e10i 0.688846i
\(585\) 0 0
\(586\) 1.14970e11 0.974976
\(587\) 7.90362e10 0.665693 0.332846 0.942981i \(-0.391991\pi\)
0.332846 + 0.942981i \(0.391991\pi\)
\(588\) 1.07990e11 6.04699e10i 0.903387 0.505859i
\(589\) 2.26049e11 1.87820
\(590\) 0 0
\(591\) −1.67703e11 + 9.39065e10i −1.37464 + 0.769743i
\(592\) 1.20687e11i 0.982592i
\(593\) 2.38940e11 1.93228 0.966141 0.258015i \(-0.0830683\pi\)
0.966141 + 0.258015i \(0.0830683\pi\)
\(594\) −2.50624e11 9.88626e9i −2.01315 0.0794120i
\(595\) 0 0
\(596\) 7.77955e8i 0.00616551i
\(597\) 5.90528e10 3.30671e10i 0.464883 0.260315i
\(598\) 7.86478e10i 0.615010i
\(599\) 1.75042e11i 1.35968i −0.733363 0.679838i \(-0.762050\pi\)
0.733363 0.679838i \(-0.237950\pi\)
\(600\) 0 0
\(601\) −7.78052e10 −0.596363 −0.298181 0.954509i \(-0.596380\pi\)
−0.298181 + 0.954509i \(0.596380\pi\)
\(602\) 2.17527e10 0.165626
\(603\) −1.19922e11 7.35052e10i −0.907043 0.555967i
\(604\) −9.60518e10 −0.721702
\(605\) 0 0
\(606\) −1.44788e11 2.58570e11i −1.07360 1.91729i
\(607\) 1.00711e11i 0.741864i 0.928660 + 0.370932i \(0.120962\pi\)
−0.928660 + 0.370932i \(0.879038\pi\)
\(608\) −2.77040e11 −2.02735
\(609\) −8.01710e9 + 4.48924e9i −0.0582838 + 0.0326365i
\(610\) 0 0
\(611\) 4.30829e10i 0.309129i
\(612\) 1.36872e11 2.23302e11i 0.975682 1.59180i
\(613\) 1.66738e11i 1.18084i 0.807094 + 0.590422i \(0.201039\pi\)
−0.807094 + 0.590422i \(0.798961\pi\)
\(614\) 7.87464e10i 0.554060i
\(615\) 0 0
\(616\) −3.47241e10 −0.241162
\(617\) −5.98004e10 −0.412632 −0.206316 0.978485i \(-0.566148\pi\)
−0.206316 + 0.978485i \(0.566148\pi\)
\(618\) −4.66280e10 8.32705e10i −0.319664 0.570870i
\(619\) 1.30260e11 0.887254 0.443627 0.896211i \(-0.353691\pi\)
0.443627 + 0.896211i \(0.353691\pi\)
\(620\) 0 0
\(621\) −2.35054e9 + 5.95878e10i −0.0158052 + 0.400674i
\(622\) 2.74416e11i 1.83336i
\(623\) −3.54154e10 −0.235093
\(624\) −4.88169e10 8.71795e10i −0.321982 0.575011i
\(625\) 0 0
\(626\) 6.84200e10i 0.445539i
\(627\) −1.46678e11 2.61945e11i −0.949065 1.69489i
\(628\) 1.68392e11i 1.08263i
\(629\) 3.47255e11i 2.21843i
\(630\) 0 0
\(631\) −2.11689e11 −1.33530 −0.667652 0.744473i \(-0.732701\pi\)
−0.667652 + 0.744473i \(0.732701\pi\)
\(632\) −4.15338e10 −0.260335
\(633\) −1.63678e11 + 9.16529e10i −1.01947 + 0.570863i
\(634\) 1.16920e11 0.723656
\(635\) 0 0
\(636\) 8.42723e10 4.71890e10i 0.515058 0.288411i
\(637\) 1.35856e11i 0.825126i
\(638\) −5.13690e10 −0.310040
\(639\) 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 \(0.990622\pi\)
\(642\) −2.25754e9 + 1.26413e9i −0.0132891 + 0.00744134i
\(643\) 4.35787e10i 0.254935i 0.991843 + 0.127468i \(0.0406849\pi\)
−0.991843 + 0.127468i \(0.959315\pi\)
\(644\) 3.81950e10i 0.222057i
\(645\) 0 0
\(646\) 5.59227e11 3.21113
\(647\) 1.00404e11 0.572973 0.286487 0.958084i \(-0.407513\pi\)
0.286487 + 0.958084i \(0.407513\pi\)
\(648\) 3.32858e10 + 6.53608e10i 0.188781 + 0.370695i
\(649\) −2.86625e11 −1.61560
\(650\) 0 0
\(651\) 4.91871e10 + 8.78405e10i 0.273859 + 0.489070i
\(652\) 2.37382e11i 1.31358i
\(653\) 9.51805e10 0.523474 0.261737 0.965139i \(-0.415705\pi\)
0.261737 + 0.965139i \(0.415705\pi\)
\(654\) −2.91657e11 + 1.63316e11i −1.59427 + 0.892723i
\(655\) 0 0
\(656\) 1.65893e11i 0.895804i
\(657\) 2.63046e11 + 1.61232e11i 1.41179 + 0.865348i
\(658\) 3.73235e10i 0.199104i
\(659\) 2.93955e11i 1.55862i −0.626641 0.779308i \(-0.715571\pi\)
0.626641 0.779308i \(-0.284429\pi\)
\(660\) 0 0
\(661\) 2.39956e11 1.25697 0.628485 0.777822i \(-0.283675\pi\)
0.628485 + 0.777822i \(0.283675\pi\)
\(662\) 1.32128e11 0.687960
\(663\) 1.40462e11 + 2.50843e11i 0.726949 + 1.29822i
\(664\) 1.17295e10 0.0603402
\(665\) 0 0
\(666\) −3.83585e11 2.35116e11i −1.94969 1.19505i
\(667\) 1.22134e10i 0.0617068i
\(668\) 1.09051e11 0.547675
\(669\) −1.88324e10 3.36318e10i −0.0940160 0.167898i
\(670\) 0 0
\(671\) 3.13094e11i 1.54449i
\(672\) −6.02825e10 1.07655e11i −0.295607 0.527908i
\(673\) 1.21923e11i 0.594326i −0.954827 0.297163i \(-0.903960\pi\)
0.954827 0.297163i \(-0.0960404\pi\)
\(674\) 5.55161e11i 2.69017i
\(675\) 0 0
\(676\) −8.96990e9 −0.0429537
\(677\) −3.04202e10 −0.144813 −0.0724066 0.997375i \(-0.523068\pi\)
−0.0724066 + 0.997375i \(0.523068\pi\)
\(678\) −5.75510e10 + 3.22262e10i −0.272354 + 0.152507i
\(679\) −1.56685e10 −0.0737138
\(680\) 0 0
\(681\) 2.13018e11 1.19281e11i 0.990440 0.554605i
\(682\) 5.62832e11i 2.60161i
\(683\) 2.91193e11 1.33813 0.669065 0.743204i \(-0.266695\pi\)
0.669065 + 0.743204i \(0.266695\pi\)
\(684\) −2.12258e11 + 3.46293e11i −0.969707 + 1.58205i
\(685\) 0 0
\(686\) 2.62714e11i 1.18628i
\(687\) −2.65267e11 + 1.48538e11i −1.19085 + 0.666824i
\(688\) 3.67333e10i 0.163948i
\(689\) 1.06018e11i 0.470438i
\(690\) 0 0
\(691\) −3.48484e11 −1.52852 −0.764260 0.644908i \(-0.776896\pi\)
−0.764260 + 0.644908i \(0.776896\pi\)
\(692\) 4.31642e11 1.88235
\(693\) 6.98731e10 1.13996e11i 0.302954 0.494261i
\(694\) 5.49822e11 2.37020
\(695\) 0 0
\(696\) 7.33945e9 + 1.31071e10i 0.0312771 + 0.0558562i
\(697\) 4.77327e11i 2.02248i
\(698\) 5.44581e11 2.29425
\(699\) 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 \(0.917655\pi\)
\(702\) −3.72190e11 1.46816e10i −1.53256 0.0604542i
\(703\) 5.38516e11i 2.20484i
\(704\) 4.77151e11i 1.94252i
\(705\) 0 0
\(706\) 2.06817e11 0.832467
\(707\) 1.57977e11 0.632289
\(708\) 1.89460e11 + 3.38346e11i 0.754023 + 1.34657i
\(709\) −3.17753e11 −1.25749 −0.628744 0.777612i \(-0.716431\pi\)
−0.628744 + 0.777612i \(0.716431\pi\)
\(710\) 0 0
\(711\) 8.35758e10 1.36351e11i 0.327041 0.533557i
\(712\) 5.79006e10i 0.225301i
\(713\) 1.33818e11 0.517793
\(714\) 1.21685e11 + 2.17310e11i 0.468213 + 0.836156i
\(715\) 0 0
\(716\) 3.58560e10i 0.136430i
\(717\) −1.85905e11 3.31997e11i −0.703419 1.25620i
\(718\) 8.33539e10i 0.313638i
\(719\) 2.47720e11i 0.926926i 0.886116 + 0.463463i \(0.153393\pi\)
−0.886116 + 0.463463i \(0.846607\pi\)
\(720\) 0 0
\(721\) 5.08752e10 0.188263
\(722\) −4.57307e11 −1.68290
\(723\) −2.45085e11 + 1.37238e11i −0.896942 + 0.502250i
\(724\) −1.19231e11 −0.433944
\(725\) 0 0
\(726\) 2.86543e11 1.60452e11i 1.03144 0.577562i
\(727\) 2.06831e11i 0.740420i −0.928948 0.370210i \(-0.879286\pi\)
0.928948 0.370210i \(-0.120714\pi\)
\(728\) −5.15672e10 −0.183590
\(729\) −2.81552e11 2.22472e10i −0.996893 0.0787707i
\(730\) 0 0
\(731\) 1.05693e11i 0.370151i
\(732\) 3.69592e11 2.06956e11i 1.28730 0.720832i
\(733\) 2.72921e11i 0.945412i −0.881220 0.472706i \(-0.843277\pi\)
0.881220 0.472706i \(-0.156723\pi\)
\(734\) 1.81654e11i 0.625835i
\(735\) 0 0
\(736\) −1.64004e11 −0.558912
\(737\) 4.19190e11 1.42083
\(738\) −5.27267e11 3.23185e11i −1.77748 1.08950i
\(739\) −1.03105e10 −0.0345702 −0.0172851 0.999851i \(-0.505502\pi\)
−0.0172851 + 0.999851i \(0.505502\pi\)
\(740\) 0 0
\(741\) −2.17826e11 3.89003e11i −0.722497 1.29027i
\(742\) 9.18454e10i 0.303000i
\(743\) −3.12920e11 −1.02678 −0.513392 0.858154i \(-0.671611\pi\)
−0.513392 + 0.858154i \(0.671611\pi\)
\(744\) 1.43610e11 8.04159e10i 0.468699 0.262452i
\(745\) 0 0
\(746\) 3.88549e11i 1.25456i
\(747\) −2.36025e10 + 3.85067e10i −0.0758010 + 0.123667i
\(748\) 7.80561e11i 2.49345i
\(749\) 1.37927e9i 0.00438251i
\(750\) 0 0
\(751\) 2.76676e11 0.869783 0.434892 0.900483i \(-0.356787\pi\)
0.434892 + 0.900483i \(0.356787\pi\)
\(752\) −6.30275e10 −0.197087
\(753\) 6.08566e10 + 1.08681e11i 0.189290 + 0.338043i
\(754\) −7.62858e10 −0.236025
\(755\) 0 0
\(756\) −1.80753e11 7.13009e9i −0.553347 0.0218277i
\(757\) 1.25846e11i 0.383226i −0.981471 0.191613i \(-0.938628\pi\)
0.981471 0.191613i \(-0.0613718\pi\)
\(758\) −1.75428e11 −0.531402
\(759\) −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 \(-0.210101\pi\)
\(762\) 8.97120e10 + 1.60212e11i 0.266091 + 0.475198i
\(763\) 1.78192e11i 0.525762i
\(764\) 7.00435e11i 2.05586i
\(765\) 0 0
\(766\) 9.28622e10 0.269727
\(767\) −4.25654e11 −1.22991
\(768\) 7.50087e10 4.20018e10i 0.215609 0.120732i
\(769\) −4.51287e10 −0.129047 −0.0645235 0.997916i \(-0.520553\pi\)
−0.0645235 + 0.997916i \(0.520553\pi\)
\(770\) 0 0
\(771\) −1.90991e11 + 1.06947e11i −0.540498 + 0.302657i
\(772\) 7.72298e11i 2.17428i
\(773\) 3.86868e11 1.08354 0.541770 0.840527i \(-0.317755\pi\)
0.541770 + 0.840527i \(0.317755\pi\)
\(774\) 1.16751e11 + 7.15621e10i 0.325311 + 0.199397i
\(775\) 0 0
\(776\) 2.56164e10i 0.0706435i
\(777\) 2.09263e11 1.17178e11i 0.574126 0.321487i
\(778\) 3.97252e11i 1.08430i
\(779\) 7.40231e11i 2.01010i
\(780\) 0 0
\(781\) −8.02585e11 −2.15718
\(782\) 3.31055e11 0.885264
\(783\) −5.77982e10 2.27994e9i −0.153768 0.00606565i
\(784\) −1.98748e11 −0.526064
\(785\) 0 0
\(786\) 2.59671e11 + 4.63733e11i 0.680353 + 1.21501i
\(787\) 4.31897e11i 1.12585i −0.826508 0.562926i \(-0.809676\pi\)
0.826508 0.562926i \(-0.190324\pi\)
\(788\) −7.74973e11 −2.00993
\(789\) −2.28338e11 + 1.27860e11i −0.589210 + 0.329933i
\(790\) 0 0
\(791\) 3.51615e10i 0.0898177i
\(792\) −1.86372e11 1.14235e11i −0.473673 0.290335i
\(793\) 4.64962e11i 1.17578i
\(794\) 8.62519e11i 2.17014i
\(795\) 0 0
\(796\) 2.72890e11 0.679728
\(797\) 1.89233e11 0.468991 0.234495 0.972117i \(-0.424656\pi\)
0.234495 + 0.972117i \(0.424656\pi\)
\(798\) −1.88707e11 3.37001e11i −0.465346 0.831036i
\(799\) 1.81350e11 0.444970
\(800\) 0 0
\(801\) −1.90082e11 1.16510e11i −0.461754 0.283030i
\(802\) 1.84712e11i 0.446477i
\(803\) −9.19486e11 −2.21148
\(804\) −2.77086e11 4.94833e11i −0.663117 1.18423i
\(805\) 0 0
\(806\) 8.35837e11i 1.98053i
\(807\) 3.49291e10 + 6.23781e10i 0.0823557 + 0.147075i
\(808\) 2.58276e11i 0.605953i
\(809\) 8.16650e10i 0.190652i −0.995446 0.0953261i \(-0.969611\pi\)
0.995446 0.0953261i \(-0.0303894\pi\)
\(810\) 0 0
\(811\) −2.05160e11 −0.474252 −0.237126 0.971479i \(-0.576205\pi\)
−0.237126 + 0.971479i \(0.576205\pi\)
\(812\) −3.70479e10 −0.0852197
\(813\) 6.14679e11 3.44195e11i 1.40697 0.787847i
\(814\) 1.34084e12 3.05406
\(815\) 0 0
\(816\) −3.66967e11 + 2.05486e11i −0.827688 + 0.463471i
\(817\) 1.63908e11i 0.367884i
\(818\) 4.57366e11 1.02153
\(819\) 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 \(-0.00497278\pi\)
\(822\) −3.73052e11 + 2.08894e11i −0.817113 + 0.457549i
\(823\) 2.98009e11i 0.649576i −0.945787 0.324788i \(-0.894707\pi\)
0.945787 0.324788i \(-0.105293\pi\)
\(824\) 8.31759e10i 0.180422i
\(825\) 0 0
\(826\) −3.68752e11 −0.792163
\(827\) −3.12011e11 −0.667034 −0.333517 0.942744i \(-0.608235\pi\)
−0.333517 + 0.942744i \(0.608235\pi\)
\(828\) −1.25654e11 + 2.05001e11i −0.267335 + 0.436149i
\(829\) −2.42950e11 −0.514397 −0.257198 0.966359i \(-0.582799\pi\)
−0.257198 + 0.966359i \(0.582799\pi\)
\(830\) 0 0
\(831\) 3.39443e11 + 6.06193e11i 0.711808 + 1.27118i
\(832\) 7.08596e11i 1.47879i
\(833\) 5.71862e11 1.18771
\(834\) 8.40081e11 4.70410e11i 1.73643 0.972327i
\(835\) 0 0
\(836\) 1.21048e12i 2.47818i
\(837\) −2.49806e10 + 6.33274e11i −0.0508980 + 1.29030i
\(838\) 2.08262e11i 0.422312i
\(839\) 1.16205e11i 0.234519i −0.993101 0.117259i \(-0.962589\pi\)
0.993101 0.117259i \(-0.0374109\pi\)
\(840\) 0 0
\(841\) 4.88400e11 0.976318
\(842\) −8.16963e11 −1.62538
\(843\) −1.12512e11 2.00928e11i −0.222786 0.397861i
\(844\) −7.56376e11 −1.49062
\(845\) 0 0
\(846\) −1.22787e11 + 2.00323e11i −0.239702 + 0.391066i
\(847\) 1.75067e11i 0.340150i
\(848\) −1.55097e11 −0.299931
\(849\) 3.93377e11 + 7.02510e11i 0.757143 + 1.35214i
\(850\) 0 0
\(851\) 3.18794e11i 0.607844i
\(852\) 5.30511e11 + 9.47412e11i 1.00678 + 1.79796i
\(853\) 2.30678e11i 0.435723i −0.975980 0.217861i \(-0.930092\pi\)
0.975980 0.217861i \(-0.0699080\pi\)
\(854\) 4.02806e11i 0.757293i
\(855\) 0 0
\(856\) −2.25497e9 −0.00419997
\(857\) −6.99039e11 −1.29592 −0.647960 0.761674i \(-0.724378\pi\)
−0.647960 + 0.761674i \(0.724378\pi\)
\(858\) 9.68567e11 5.42357e11i 1.78723 1.00078i
\(859\) −9.39004e10 −0.172463 −0.0862313 0.996275i \(-0.527482\pi\)
−0.0862313 + 0.996275i \(0.527482\pi\)
\(860\) 0 0
\(861\) 2.87647e11 1.61070e11i 0.523416 0.293091i
\(862\) 7.19561e11i 1.30328i
\(863\) −7.27490e11 −1.31155 −0.655773 0.754958i \(-0.727657\pi\)
−0.655773 + 0.754958i \(0.727657\pi\)
\(864\) 3.06156e10 7.76126e11i 0.0549399 1.39276i
\(865\) 0 0
\(866\) 6.13481e10i 0.109076i
\(867\) 5.62875e11 3.15187e11i 0.996175 0.557817i
\(868\) 4.05921e11i 0.715094i
\(869\) 4.76621e11i 0.835783i
\(870\) 0 0
\(871\) 6.22520e11 1.08164
\(872\) −2.91325e11 −0.503863
\(873\) −8.40963e10 5.15463e10i −0.144784 0.0887443i
\(874\) −5.13394e11 −0.879842
\(875\) 0 0
\(876\) 6.07783e11 + 1.08541e12i 1.03212 + 1.84322i
\(877\) 1.49532e11i 0.252775i 0.991981 + 0.126388i \(0.0403383\pi\)
−0.991981 + 0.126388i \(0.959662\pi\)
\(878\) 2.68549e11 0.451904
\(879\) −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 \(-0.269136\pi\)
\(882\) −3.87192e11 + 6.31691e11i −0.639811 + 1.04383i
\(883\) 7.05614e11i 1.16071i 0.814363 + 0.580356i \(0.197086\pi\)
−0.814363 + 0.580356i \(0.802914\pi\)
\(884\) 1.15918e12i 1.89819i
\(885\) 0 0
\(886\) −7.26299e11 −1.17864
\(887\) −1.05583e12 −1.70568 −0.852842 0.522170i \(-0.825123\pi\)
−0.852842 + 0.522170i \(0.825123\pi\)
\(888\) −1.91575e11 3.42123e11i −0.308096 0.550213i
\(889\) −9.78836e10 −0.156712
\(890\) 0 0
\(891\) 7.50047e11 3.81971e11i 1.19008 0.606066i
\(892\) 1.55417e11i 0.245492i
\(893\) −2.81234e11 −0.442245
\(894\) −2.27534e9 4.06341e9i −0.00356202 0.00636122i
\(895\) 0 0
\(896\) 2.23916e11i 0.347419i
\(897\) −1.28950e11 2.30285e11i −0.199182 0.355709i
\(898\) 5.94873e11i 0.914785i
\(899\) 1.29799e11i 0.198716i
\(900\) 0 0
\(901\) 4.46265e11 0.677163
\(902\) 1.84308e12 2.78431
\(903\) −6.36930e10 + 3.56654e10i −0.0957945 + 0.0536410i
\(904\) −5.74856e10 −0.0860766
\(905\) 0 0
\(906\) 5.01697e11 2.80930e11i 0.744610 0.416951i
\(907\) 3.67842e11i 0.543541i −0.962362 0.271771i \(-0.912391\pi\)
0.962362 0.271771i \(-0.0876092\pi\)
\(908\) 9.84382e11 1.44817
\(909\) 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 \(0.753133\pi\)
\(912\) 5.69086e11 3.18665e11i 0.822619 0.460633i
\(913\) 1.34602e11i 0.193717i
\(914\) 2.85821e11i 0.409553i
\(915\) 0 0
\(916\) −1.22583e12 −1.74120
\(917\) −2.83324e11 −0.400688
\(918\) −6.17999e10 + 1.56667e12i −0.0870196 + 2.20601i
\(919\) 1.03446e12 1.45028 0.725138 0.688603i \(-0.241776\pi\)
0.725138 + 0.688603i \(0.241776\pi\)
\(920\) 0 0
\(921\) 1.29111e11 + 2.30573e11i 0.179443 + 0.320457i
\(922\) 4.91563e11i 0.680229i
\(923\) −1.19188e12 −1.64220
\(924\) 4.70381e11 2.63394e11i 0.645301 0.361342i
\(925\) 0 0
\(926\) 9.36768e11i 1.27405i
\(927\) 2.73058e11 + 1.67369e11i 0.369774 + 0.226651i
\(928\) 1.59079e11i 0.214496i
\(929\) 1.47659e11i 0.198242i 0.995075 + 0.0991212i \(0.0316031\pi\)
−0.995075 + 0.0991212i \(0.968397\pi\)
\(930\) 0 0
\(931\) −8.86833e11 −1.18044
\(932\) 1.18590e12 1.57175
\(933\) 4.49928e11 + 8.03502e11i 0.593767 + 1.06038i
\(934\) −1.61131e12 −2.11734
\(935\) 0 0
\(936\) −2.76772e11 1.69646e11i −0.360595 0.221024i
\(937\) 3.27745e11i 0.425185i −0.977141 0.212593i \(-0.931809\pi\)
0.977141 0.212593i \(-0.0681908\pi\)
\(938\) 5.39301e11 0.696659
\(939\) 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 \(-0.0674864\pi\)
\(942\) 4.92507e11 + 8.79542e11i 0.625473 + 1.11700i
\(943\) 4.38207e11i 0.554156i
\(944\) 6.22704e11i 0.784140i
\(945\) 0 0
\(946\) −4.08109e11 −0.509579
\(947\) −2.28185e8 −0.000283718 −0.000141859 1.00000i \(-0.500045\pi\)
−0.000141859 1.00000i \(0.500045\pi\)
\(948\) 5.62627e11 3.15048e11i 0.696606 0.390070i
\(949\) −1.36549e12 −1.68354
\(950\) 0 0
\(951\) −3.42347e11 + 1.91700e11i −0.418548 + 0.234369i
\(952\) 2.17063e11i 0.264264i
\(953\) −1.61330e11 −0.195588 −0.0977942 0.995207i \(-0.531179\pi\)
−0.0977942 + 0.995207i \(0.531179\pi\)
\(954\) −3.02153e11 + 4.92954e11i −0.364782 + 0.595131i
\(955\) 0 0
\(956\) 1.53420e12i 1.83675i
\(957\) 1.50411e11 8.42238e10i 0.179321 0.100412i
\(958\) 2.44653e12i 2.90462i
\(959\) 2.27921e11i 0.269470i
\(960\) 0 0
\(961\) 5.69271e11 0.667460
\(962\) 1.99122e12 2.32497
\(963\) 4.53754e9 7.40286e9i 0.00527612 0.00860784i
\(964\) −1.13257e12 −1.31146
\(965\) 0 0
\(966\) −1.11712e11 1.99500e11i −0.128289 0.229105i
\(967\) 1.49948e12i 1.71489i −0.514577 0.857444i \(-0.672051\pi\)
0.514577 0.857444i \(-0.327949\pi\)
\(968\) 2.86217e11 0.325982
\(969\) −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 \(-0.0603654\pi\)
\(972\) −9.46682e11 6.32909e11i −1.06057 0.709049i
\(973\) 5.13258e11i 0.572644i
\(974\) 2.61904e11i 0.291009i
\(975\) 0 0
\(976\) −6.80209e11 −0.749623
\(977\) 8.22116e11 0.902308 0.451154 0.892446i \(-0.351012\pi\)
0.451154 + 0.892446i \(0.351012\pi\)
\(978\) −6.94287e11 1.23989e12i −0.758898 1.35528i
\(979\) 6.64438e11 0.723309
\(980\) 0 0
\(981\) 5.86215e11 9.56392e11i 0.632967 1.03267i
\(982\) 2.48545e11i 0.267276i
\(983\) 1.23984e12 1.32786 0.663930 0.747795i \(-0.268887\pi\)
0.663930 + 0.747795i \(0.268887\pi\)
\(984\) −2.63334e11 4.70274e11i −0.280883 0.501615i
\(985\) 0 0
\(986\) 3.21112e11i 0.339742i
\(987\) −6.11951e10 1.09285e11i −0.0644834 0.115158i
\(988\) 1.79763e12i 1.88657i
\(989\) 9.70311e10i 0.101420i
\(990\) 0 0
\(991\) 1.44437e12 1.49756 0.748782 0.662817i \(-0.230639\pi\)
0.748782 + 0.662817i \(0.230639\pi\)
\(992\) −1.74297e12 −1.79988
\(993\) −3.86878e11 + 2.16635e11i −0.397902 + 0.222809i
\(994\) −1.03255e12 −1.05771
\(995\) 0 0
\(996\) −1.58890e11 + 8.89721e10i −0.161458 + 0.0904100i
\(997\) 4.69939e11i 0.475621i 0.971312 + 0.237810i \(0.0764297\pi\)
−0.971312 + 0.237810i \(0.923570\pi\)
\(998\) 1.63310e12 1.64623
\(999\) 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.d.d.74.3 20
3.2 odd 2 inner 75.9.d.d.74.17 20
5.2 odd 4 75.9.c.f.26.2 yes 10
5.3 odd 4 75.9.c.e.26.9 yes 10
5.4 even 2 inner 75.9.d.d.74.18 20
15.2 even 4 75.9.c.f.26.9 yes 10
15.8 even 4 75.9.c.e.26.2 10
15.14 odd 2 inner 75.9.d.d.74.4 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.9.c.e.26.2 10 15.8 even 4
75.9.c.e.26.9 yes 10 5.3 odd 4
75.9.c.f.26.2 yes 10 5.2 odd 4
75.9.c.f.26.9 yes 10 15.2 even 4
75.9.d.d.74.3 20 1.1 even 1 trivial
75.9.d.d.74.4 20 15.14 odd 2 inner
75.9.d.d.74.17 20 3.2 odd 2 inner
75.9.d.d.74.18 20 5.4 even 2 inner