Properties

Label 75.9.d.d.74.10
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 74.10
Root \(17.0371i\) of defining polynomial
Character \(\chi\) \(=\) 75.74
Dual form 75.9.d.d.74.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.03414 q^{2} +(-79.6728 + 14.6031i) q^{3} -246.794 q^{4} +(241.739 - 44.3080i) q^{6} -59.7348i q^{7} +1525.55 q^{8} +(6134.50 - 2326.94i) q^{9} +O(q^{10})\) \(q-3.03414 q^{2} +(-79.6728 + 14.6031i) q^{3} -246.794 q^{4} +(241.739 - 44.3080i) q^{6} -59.7348i q^{7} +1525.55 q^{8} +(6134.50 - 2326.94i) q^{9} +21885.6i q^{11} +(19662.8 - 3603.96i) q^{12} +38460.5i q^{13} +181.244i q^{14} +58550.5 q^{16} -36101.0 q^{17} +(-18612.9 + 7060.28i) q^{18} +136807. q^{19} +(872.314 + 4759.23i) q^{21} -66404.0i q^{22} -235710. q^{23} +(-121545. + 22277.8i) q^{24} -116695. i q^{26} +(-454772. + 274977. i) q^{27} +14742.2i q^{28} -896225. i q^{29} +68043.4 q^{31} -568191. q^{32} +(-319598. - 1.74369e6i) q^{33} +109535. q^{34} +(-1.51396e6 + 574275. i) q^{36} -66517.7i q^{37} -415091. q^{38} +(-561643. - 3.06425e6i) q^{39} +3.76632e6i q^{41} +(-2646.73 - 14440.2i) q^{42} +2.03993e6i q^{43} -5.40123e6i q^{44} +715178. q^{46} -5.93447e6 q^{47} +(-4.66488e6 + 855021. i) q^{48} +5.76123e6 q^{49} +(2.87626e6 - 527187. i) q^{51} -9.49181e6i q^{52} -1.31066e7 q^{53} +(1.37984e6 - 834319. i) q^{54} -91128.3i q^{56} +(-1.08998e7 + 1.99781e6i) q^{57} +2.71928e6i q^{58} -1.58410e7i q^{59} -3.51489e6 q^{61} -206453. q^{62} +(-138999. - 366443. i) q^{63} -1.32650e7 q^{64} +(969706. + 5.29059e6i) q^{66} +1.39297e7i q^{67} +8.90950e6 q^{68} +(1.87797e7 - 3.44210e6i) q^{69} +1.51547e7i q^{71} +(9.35847e6 - 3.54986e6i) q^{72} -3.93167e7i q^{73} +201824. i q^{74} -3.37631e7 q^{76} +1.30733e6 q^{77} +(1.70411e6 + 9.29738e6i) q^{78} -3.15613e7 q^{79} +(3.22174e7 - 2.85492e7i) q^{81} -1.14275e7i q^{82} +4.88680e7 q^{83} +(-215282. - 1.17455e6i) q^{84} -6.18943e6i q^{86} +(1.30877e7 + 7.14048e7i) q^{87} +3.33875e7i q^{88} +1.09263e8i q^{89} +2.29743e6 q^{91} +5.81718e7 q^{92} +(-5.42120e6 + 993646. i) q^{93} +1.80060e7 q^{94} +(4.52694e7 - 8.29737e6i) q^{96} -1.16098e8i q^{97} -1.74804e7 q^{98} +(5.09265e7 + 1.34257e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 3108 q^{4} + 4514 q^{6} + 22414 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.03414 −0.189634 −0.0948170 0.995495i \(-0.530227\pi\)
−0.0948170 + 0.995495i \(0.530227\pi\)
\(3\) −79.6728 + 14.6031i −0.983614 + 0.180286i
\(4\) −246.794 −0.964039
\(5\) 0 0
\(6\) 241.739 44.3080i 0.186527 0.0341882i
\(7\) 59.7348i 0.0248791i −0.999923 0.0124396i \(-0.996040\pi\)
0.999923 0.0124396i \(-0.00395974\pi\)
\(8\) 1525.55 0.372448
\(9\) 6134.50 2326.94i 0.934994 0.354663i
\(10\) 0 0
\(11\) 21885.6i 1.49482i 0.664366 + 0.747408i \(0.268702\pi\)
−0.664366 + 0.747408i \(0.731298\pi\)
\(12\) 19662.8 3603.96i 0.948243 0.173802i
\(13\) 38460.5i 1.34661i 0.739366 + 0.673304i \(0.235125\pi\)
−0.739366 + 0.673304i \(0.764875\pi\)
\(14\) 181.244i 0.00471792i
\(15\) 0 0
\(16\) 58550.5 0.893410
\(17\) −36101.0 −0.432238 −0.216119 0.976367i \(-0.569340\pi\)
−0.216119 + 0.976367i \(0.569340\pi\)
\(18\) −18612.9 + 7060.28i −0.177307 + 0.0672561i
\(19\) 136807. 1.04977 0.524884 0.851174i \(-0.324109\pi\)
0.524884 + 0.851174i \(0.324109\pi\)
\(20\) 0 0
\(21\) 872.314 + 4759.23i 0.00448534 + 0.0244715i
\(22\) 66404.0i 0.283468i
\(23\) −235710. −0.842300 −0.421150 0.906991i \(-0.638373\pi\)
−0.421150 + 0.906991i \(0.638373\pi\)
\(24\) −121545. + 22277.8i −0.366346 + 0.0671470i
\(25\) 0 0
\(26\) 116695.i 0.255363i
\(27\) −454772. + 274977.i −0.855733 + 0.517417i
\(28\) 14742.2i 0.0239844i
\(29\) 896225.i 1.26714i −0.773685 0.633571i \(-0.781588\pi\)
0.773685 0.633571i \(-0.218412\pi\)
\(30\) 0 0
\(31\) 68043.4 0.0736782 0.0368391 0.999321i \(-0.488271\pi\)
0.0368391 + 0.999321i \(0.488271\pi\)
\(32\) −568191. −0.541869
\(33\) −319598. 1.74369e6i −0.269493 1.47032i
\(34\) 109535. 0.0819670
\(35\) 0 0
\(36\) −1.51396e6 + 574275.i −0.901371 + 0.341909i
\(37\) 66517.7i 0.0354920i −0.999843 0.0177460i \(-0.994351\pi\)
0.999843 0.0177460i \(-0.00564902\pi\)
\(38\) −415091. −0.199071
\(39\) −561643. 3.06425e6i −0.242774 1.32454i
\(40\) 0 0
\(41\) 3.76632e6i 1.33285i 0.745572 + 0.666425i \(0.232176\pi\)
−0.745572 + 0.666425i \(0.767824\pi\)
\(42\) −2646.73 14440.2i −0.000850573 0.00464062i
\(43\) 2.03993e6i 0.596679i 0.954460 + 0.298339i \(0.0964327\pi\)
−0.954460 + 0.298339i \(0.903567\pi\)
\(44\) 5.40123e6i 1.44106i
\(45\) 0 0
\(46\) 715178. 0.159729
\(47\) −5.93447e6 −1.21616 −0.608080 0.793876i \(-0.708060\pi\)
−0.608080 + 0.793876i \(0.708060\pi\)
\(48\) −4.66488e6 + 855021.i −0.878771 + 0.161069i
\(49\) 5.76123e6 0.999381
\(50\) 0 0
\(51\) 2.87626e6 527187.i 0.425156 0.0779263i
\(52\) 9.49181e6i 1.29818i
\(53\) −1.31066e7 −1.66107 −0.830534 0.556969i \(-0.811964\pi\)
−0.830534 + 0.556969i \(0.811964\pi\)
\(54\) 1.37984e6 834319.i 0.162276 0.0981199i
\(55\) 0 0
\(56\) 91128.3i 0.00926619i
\(57\) −1.08998e7 + 1.99781e6i −1.03257 + 0.189258i
\(58\) 2.71928e6i 0.240293i
\(59\) 1.58410e7i 1.30730i −0.756799 0.653648i \(-0.773238\pi\)
0.756799 0.653648i \(-0.226762\pi\)
\(60\) 0 0
\(61\) −3.51489e6 −0.253859 −0.126929 0.991912i \(-0.540512\pi\)
−0.126929 + 0.991912i \(0.540512\pi\)
\(62\) −206453. −0.0139719
\(63\) −138999. 366443.i −0.00882370 0.0232618i
\(64\) −1.32650e7 −0.790653
\(65\) 0 0
\(66\) 969706. + 5.29059e6i 0.0511051 + 0.278823i
\(67\) 1.39297e7i 0.691263i 0.938370 + 0.345632i \(0.112335\pi\)
−0.938370 + 0.345632i \(0.887665\pi\)
\(68\) 8.90950e6 0.416695
\(69\) 1.87797e7 3.44210e6i 0.828498 0.151854i
\(70\) 0 0
\(71\) 1.51547e7i 0.596367i 0.954508 + 0.298184i \(0.0963808\pi\)
−0.954508 + 0.298184i \(0.903619\pi\)
\(72\) 9.35847e6 3.54986e6i 0.348237 0.132094i
\(73\) 3.93167e7i 1.38448i −0.721669 0.692238i \(-0.756625\pi\)
0.721669 0.692238i \(-0.243375\pi\)
\(74\) 201824.i 0.00673049i
\(75\) 0 0
\(76\) −3.37631e7 −1.01202
\(77\) 1.30733e6 0.0371897
\(78\) 1.70411e6 + 9.29738e6i 0.0460382 + 0.251178i
\(79\) −3.15613e7 −0.810301 −0.405151 0.914250i \(-0.632781\pi\)
−0.405151 + 0.914250i \(0.632781\pi\)
\(80\) 0 0
\(81\) 3.22174e7 2.85492e7i 0.748429 0.663215i
\(82\) 1.14275e7i 0.252754i
\(83\) 4.88680e7 1.02970 0.514852 0.857279i \(-0.327847\pi\)
0.514852 + 0.857279i \(0.327847\pi\)
\(84\) −215282. 1.17455e6i −0.00432405 0.0235914i
\(85\) 0 0
\(86\) 6.18943e6i 0.113151i
\(87\) 1.30877e7 + 7.14048e7i 0.228447 + 1.24638i
\(88\) 3.33875e7i 0.556741i
\(89\) 1.09263e8i 1.74145i 0.491766 + 0.870727i \(0.336352\pi\)
−0.491766 + 0.870727i \(0.663648\pi\)
\(90\) 0 0
\(91\) 2.29743e6 0.0335024
\(92\) 5.81718e7 0.812010
\(93\) −5.42120e6 + 993646.i −0.0724709 + 0.0132831i
\(94\) 1.80060e7 0.230625
\(95\) 0 0
\(96\) 4.52694e7 8.29737e6i 0.532990 0.0976912i
\(97\) 1.16098e8i 1.31140i −0.755020 0.655702i \(-0.772373\pi\)
0.755020 0.655702i \(-0.227627\pi\)
\(98\) −1.74804e7 −0.189517
\(99\) 5.09265e7 + 1.34257e8i 0.530155 + 1.39764i
\(100\) 0 0
\(101\) 1.46015e8i 1.40318i −0.712582 0.701589i \(-0.752474\pi\)
0.712582 0.701589i \(-0.247526\pi\)
\(102\) −8.72700e6 + 1.59956e6i −0.0806239 + 0.0147775i
\(103\) 1.60527e8i 1.42626i 0.701032 + 0.713130i \(0.252723\pi\)
−0.701032 + 0.713130i \(0.747277\pi\)
\(104\) 5.86733e7i 0.501542i
\(105\) 0 0
\(106\) 3.97673e7 0.314995
\(107\) 1.10586e8 0.843654 0.421827 0.906676i \(-0.361389\pi\)
0.421827 + 0.906676i \(0.361389\pi\)
\(108\) 1.12235e8 6.78626e7i 0.824960 0.498810i
\(109\) −1.53065e8 −1.08435 −0.542176 0.840265i \(-0.682400\pi\)
−0.542176 + 0.840265i \(0.682400\pi\)
\(110\) 0 0
\(111\) 971367. + 5.29965e6i 0.00639869 + 0.0349104i
\(112\) 3.49750e6i 0.0222273i
\(113\) 1.01707e8 0.623791 0.311895 0.950116i \(-0.399036\pi\)
0.311895 + 0.950116i \(0.399036\pi\)
\(114\) 3.30714e7 6.06163e6i 0.195810 0.0358897i
\(115\) 0 0
\(116\) 2.21183e8i 1.22157i
\(117\) 8.94953e7 + 2.35936e8i 0.477592 + 1.25907i
\(118\) 4.80638e7i 0.247908i
\(119\) 2.15648e6i 0.0107537i
\(120\) 0 0
\(121\) −2.64620e8 −1.23447
\(122\) 1.06647e7 0.0481402
\(123\) −5.50000e7 3.00073e8i −0.240294 1.31101i
\(124\) −1.67927e7 −0.0710287
\(125\) 0 0
\(126\) 421744. + 1.11184e6i 0.00167327 + 0.00441123i
\(127\) 4.85620e8i 1.86673i −0.358928 0.933365i \(-0.616858\pi\)
0.358928 0.933365i \(-0.383142\pi\)
\(128\) 1.85705e8 0.691804
\(129\) −2.97893e7 1.62527e8i −0.107573 0.586902i
\(130\) 0 0
\(131\) 2.26001e8i 0.767407i −0.923456 0.383704i \(-0.874648\pi\)
0.923456 0.383704i \(-0.125352\pi\)
\(132\) 7.88749e7 + 4.30331e8i 0.259802 + 1.41745i
\(133\) 8.17211e6i 0.0261173i
\(134\) 4.22648e7i 0.131087i
\(135\) 0 0
\(136\) −5.50738e7 −0.160986
\(137\) −5.46283e8 −1.55073 −0.775364 0.631515i \(-0.782434\pi\)
−0.775364 + 0.631515i \(0.782434\pi\)
\(138\) −5.69802e7 + 1.04438e7i −0.157111 + 0.0287967i
\(139\) −2.15686e8 −0.577779 −0.288890 0.957362i \(-0.593286\pi\)
−0.288890 + 0.957362i \(0.593286\pi\)
\(140\) 0 0
\(141\) 4.72816e8 8.66618e7i 1.19623 0.219256i
\(142\) 4.59815e7i 0.113091i
\(143\) −8.41730e8 −2.01293
\(144\) 3.59178e8 1.36244e8i 0.835333 0.316859i
\(145\) 0 0
\(146\) 1.19292e8i 0.262544i
\(147\) −4.59013e8 + 8.41320e7i −0.983005 + 0.180174i
\(148\) 1.64162e7i 0.0342157i
\(149\) 4.32442e8i 0.877371i −0.898641 0.438685i \(-0.855444\pi\)
0.898641 0.438685i \(-0.144556\pi\)
\(150\) 0 0
\(151\) −3.22279e8 −0.619904 −0.309952 0.950752i \(-0.600313\pi\)
−0.309952 + 0.950752i \(0.600313\pi\)
\(152\) 2.08705e8 0.390984
\(153\) −2.21461e8 + 8.40049e7i −0.404140 + 0.153299i
\(154\) −3.96663e6 −0.00705242
\(155\) 0 0
\(156\) 1.38610e8 + 7.56239e8i 0.234043 + 1.27691i
\(157\) 5.59602e8i 0.921045i −0.887648 0.460522i \(-0.847662\pi\)
0.887648 0.460522i \(-0.152338\pi\)
\(158\) 9.57615e7 0.153661
\(159\) 1.04424e9 1.91398e8i 1.63385 0.299466i
\(160\) 0 0
\(161\) 1.40801e7i 0.0209557i
\(162\) −9.77522e7 + 8.66225e7i −0.141927 + 0.125768i
\(163\) 4.67465e8i 0.662215i 0.943593 + 0.331107i \(0.107422\pi\)
−0.943593 + 0.331107i \(0.892578\pi\)
\(164\) 9.29504e8i 1.28492i
\(165\) 0 0
\(166\) −1.48273e8 −0.195267
\(167\) −4.54837e8 −0.584776 −0.292388 0.956300i \(-0.594450\pi\)
−0.292388 + 0.956300i \(0.594450\pi\)
\(168\) 1.33076e6 + 7.26044e6i 0.00167056 + 0.00911435i
\(169\) −6.63477e8 −0.813353
\(170\) 0 0
\(171\) 8.39240e8 3.18341e8i 0.981526 0.372313i
\(172\) 5.03442e8i 0.575222i
\(173\) −8.28969e8 −0.925452 −0.462726 0.886501i \(-0.653129\pi\)
−0.462726 + 0.886501i \(0.653129\pi\)
\(174\) −3.97099e7 2.16652e8i −0.0433214 0.236356i
\(175\) 0 0
\(176\) 1.28141e9i 1.33548i
\(177\) 2.31328e8 + 1.26209e9i 0.235686 + 1.28587i
\(178\) 3.31519e8i 0.330239i
\(179\) 1.84168e8i 0.179392i 0.995969 + 0.0896959i \(0.0285895\pi\)
−0.995969 + 0.0896959i \(0.971410\pi\)
\(180\) 0 0
\(181\) −1.14139e9 −1.06345 −0.531727 0.846916i \(-0.678457\pi\)
−0.531727 + 0.846916i \(0.678457\pi\)
\(182\) −6.97072e6 −0.00635319
\(183\) 2.80041e8 5.13283e7i 0.249699 0.0457670i
\(184\) −3.59587e8 −0.313713
\(185\) 0 0
\(186\) 1.64487e7 3.01486e6i 0.0137429 0.00251893i
\(187\) 7.90091e8i 0.646116i
\(188\) 1.46459e9 1.17243
\(189\) 1.64257e7 + 2.71657e7i 0.0128729 + 0.0212899i
\(190\) 0 0
\(191\) 1.62451e9i 1.22064i −0.792153 0.610322i \(-0.791040\pi\)
0.792153 0.610322i \(-0.208960\pi\)
\(192\) 1.05686e9 1.93710e8i 0.777698 0.142543i
\(193\) 1.50247e9i 1.08287i −0.840743 0.541434i \(-0.817882\pi\)
0.840743 0.541434i \(-0.182118\pi\)
\(194\) 3.52257e8i 0.248687i
\(195\) 0 0
\(196\) −1.42184e9 −0.963442
\(197\) −1.00297e9 −0.665924 −0.332962 0.942940i \(-0.608048\pi\)
−0.332962 + 0.942940i \(0.608048\pi\)
\(198\) −1.54518e8 4.07355e8i −0.100535 0.265041i
\(199\) −6.24974e8 −0.398520 −0.199260 0.979947i \(-0.563854\pi\)
−0.199260 + 0.979947i \(0.563854\pi\)
\(200\) 0 0
\(201\) −2.03418e8 1.10982e9i −0.124625 0.679936i
\(202\) 4.43031e8i 0.266090i
\(203\) −5.35358e7 −0.0315254
\(204\) −7.09845e8 + 1.30107e8i −0.409867 + 0.0751240i
\(205\) 0 0
\(206\) 4.87061e8i 0.270467i
\(207\) −1.44596e9 + 5.48484e8i −0.787545 + 0.298732i
\(208\) 2.25188e9i 1.20307i
\(209\) 2.99410e9i 1.56921i
\(210\) 0 0
\(211\) 3.84677e9 1.94073 0.970367 0.241636i \(-0.0776839\pi\)
0.970367 + 0.241636i \(0.0776839\pi\)
\(212\) 3.23463e9 1.60133
\(213\) −2.21306e8 1.20742e9i −0.107516 0.586596i
\(214\) −3.35533e8 −0.159985
\(215\) 0 0
\(216\) −6.93776e8 + 4.19490e8i −0.318716 + 0.192711i
\(217\) 4.06455e6i 0.00183305i
\(218\) 4.64422e8 0.205630
\(219\) 5.74147e8 + 3.13247e9i 0.249601 + 1.36179i
\(220\) 0 0
\(221\) 1.38846e9i 0.582055i
\(222\) −2.94727e6 1.60799e7i −0.00121341 0.00662020i
\(223\) 3.37297e9i 1.36393i 0.731383 + 0.681967i \(0.238875\pi\)
−0.731383 + 0.681967i \(0.761125\pi\)
\(224\) 3.39408e7i 0.0134812i
\(225\) 0 0
\(226\) −3.08595e8 −0.118292
\(227\) 2.59338e9 0.976705 0.488352 0.872646i \(-0.337598\pi\)
0.488352 + 0.872646i \(0.337598\pi\)
\(228\) 2.69000e9 4.93046e8i 0.995434 0.182452i
\(229\) 2.81270e9 1.02278 0.511389 0.859349i \(-0.329131\pi\)
0.511389 + 0.859349i \(0.329131\pi\)
\(230\) 0 0
\(231\) −1.04159e8 + 1.90911e7i −0.0365803 + 0.00670476i
\(232\) 1.36724e9i 0.471945i
\(233\) 3.25957e9 1.10595 0.552977 0.833196i \(-0.313492\pi\)
0.552977 + 0.833196i \(0.313492\pi\)
\(234\) −2.71542e8 7.15862e8i −0.0905676 0.238762i
\(235\) 0 0
\(236\) 3.90946e9i 1.26028i
\(237\) 2.51458e9 4.60894e8i 0.797024 0.146086i
\(238\) 6.54308e6i 0.00203927i
\(239\) 1.97409e9i 0.605028i 0.953145 + 0.302514i \(0.0978260\pi\)
−0.953145 + 0.302514i \(0.902174\pi\)
\(240\) 0 0
\(241\) 4.48773e8 0.133033 0.0665163 0.997785i \(-0.478812\pi\)
0.0665163 + 0.997785i \(0.478812\pi\)
\(242\) 8.02895e8 0.234098
\(243\) −2.14994e9 + 2.74507e9i −0.616597 + 0.787279i
\(244\) 8.67453e8 0.244730
\(245\) 0 0
\(246\) 1.66878e8 + 9.10464e8i 0.0455678 + 0.248612i
\(247\) 5.26165e9i 1.41362i
\(248\) 1.03803e8 0.0274413
\(249\) −3.89345e9 + 7.13626e8i −1.01283 + 0.185641i
\(250\) 0 0
\(251\) 2.31424e9i 0.583060i −0.956562 0.291530i \(-0.905836\pi\)
0.956562 0.291530i \(-0.0941644\pi\)
\(252\) 3.43042e7 + 9.04359e7i 0.00850639 + 0.0224253i
\(253\) 5.15865e9i 1.25908i
\(254\) 1.47344e9i 0.353995i
\(255\) 0 0
\(256\) 2.83238e9 0.659464
\(257\) −5.64145e9 −1.29318 −0.646589 0.762839i \(-0.723805\pi\)
−0.646589 + 0.762839i \(0.723805\pi\)
\(258\) 9.03850e7 + 4.93129e8i 0.0203994 + 0.111296i
\(259\) −3.97342e6 −0.000883010
\(260\) 0 0
\(261\) −2.08547e9 5.49789e9i −0.449408 1.18477i
\(262\) 6.85721e8i 0.145526i
\(263\) −3.58501e9 −0.749320 −0.374660 0.927162i \(-0.622240\pi\)
−0.374660 + 0.927162i \(0.622240\pi\)
\(264\) −4.87562e8 2.66008e9i −0.100372 0.547619i
\(265\) 0 0
\(266\) 2.47954e7i 0.00495272i
\(267\) −1.59558e9 8.70527e9i −0.313959 1.71292i
\(268\) 3.43777e9i 0.666405i
\(269\) 6.68399e9i 1.27652i −0.769822 0.638259i \(-0.779655\pi\)
0.769822 0.638259i \(-0.220345\pi\)
\(270\) 0 0
\(271\) −3.71996e9 −0.689702 −0.344851 0.938658i \(-0.612070\pi\)
−0.344851 + 0.938658i \(0.612070\pi\)
\(272\) −2.11373e9 −0.386166
\(273\) −1.83042e8 + 3.35496e7i −0.0329535 + 0.00604000i
\(274\) 1.65750e9 0.294071
\(275\) 0 0
\(276\) −4.63471e9 + 8.49490e8i −0.798704 + 0.146394i
\(277\) 3.64024e9i 0.618317i 0.951011 + 0.309158i \(0.100047\pi\)
−0.951011 + 0.309158i \(0.899953\pi\)
\(278\) 6.54421e8 0.109567
\(279\) 4.17412e8 1.58333e8i 0.0688887 0.0261309i
\(280\) 0 0
\(281\) 1.06642e9i 0.171041i 0.996336 + 0.0855207i \(0.0272554\pi\)
−0.996336 + 0.0855207i \(0.972745\pi\)
\(282\) −1.43459e9 + 2.62944e8i −0.226846 + 0.0415784i
\(283\) 4.50485e9i 0.702319i −0.936316 0.351160i \(-0.885787\pi\)
0.936316 0.351160i \(-0.114213\pi\)
\(284\) 3.74009e9i 0.574921i
\(285\) 0 0
\(286\) 2.55393e9 0.381720
\(287\) 2.24980e8 0.0331601
\(288\) −3.48557e9 + 1.32215e9i −0.506645 + 0.192181i
\(289\) −5.67248e9 −0.813170
\(290\) 0 0
\(291\) 1.69539e9 + 9.24982e9i 0.236427 + 1.28992i
\(292\) 9.70312e9i 1.33469i
\(293\) −7.62525e9 −1.03463 −0.517313 0.855796i \(-0.673068\pi\)
−0.517313 + 0.855796i \(0.673068\pi\)
\(294\) 1.39271e9 2.55268e8i 0.186411 0.0341671i
\(295\) 0 0
\(296\) 1.01476e8i 0.0132189i
\(297\) −6.01803e9 9.95295e9i −0.773443 1.27916i
\(298\) 1.31209e9i 0.166379i
\(299\) 9.06552e9i 1.13425i
\(300\) 0 0
\(301\) 1.21855e8 0.0148448
\(302\) 9.77840e8 0.117555
\(303\) 2.13228e9 + 1.16334e10i 0.252972 + 1.38019i
\(304\) 8.01010e9 0.937873
\(305\) 0 0
\(306\) 6.71945e8 2.54883e8i 0.0766387 0.0290707i
\(307\) 5.35640e9i 0.603003i −0.953466 0.301501i \(-0.902512\pi\)
0.953466 0.301501i \(-0.0974878\pi\)
\(308\) −3.22641e8 −0.0358523
\(309\) −2.34419e9 1.27896e10i −0.257134 1.40289i
\(310\) 0 0
\(311\) 8.46968e9i 0.905369i 0.891671 + 0.452685i \(0.149534\pi\)
−0.891671 + 0.452685i \(0.850466\pi\)
\(312\) −8.56814e8 4.67466e9i −0.0904207 0.493324i
\(313\) 3.96394e9i 0.413000i −0.978447 0.206500i \(-0.933793\pi\)
0.978447 0.206500i \(-0.0662073\pi\)
\(314\) 1.69791e9i 0.174661i
\(315\) 0 0
\(316\) 7.78914e9 0.781162
\(317\) −1.64274e9 −0.162679 −0.0813393 0.996686i \(-0.525920\pi\)
−0.0813393 + 0.996686i \(0.525920\pi\)
\(318\) −3.16837e9 + 5.80728e8i −0.309833 + 0.0567890i
\(319\) 1.96144e10 1.89414
\(320\) 0 0
\(321\) −8.81067e9 + 1.61490e9i −0.829830 + 0.152099i
\(322\) 4.27210e7i 0.00397391i
\(323\) −4.93885e9 −0.453750
\(324\) −7.95106e9 + 7.04578e9i −0.721514 + 0.639365i
\(325\) 0 0
\(326\) 1.41836e9i 0.125578i
\(327\) 1.21951e10 2.23523e9i 1.06658 0.195493i
\(328\) 5.74570e9i 0.496418i
\(329\) 3.54494e8i 0.0302570i
\(330\) 0 0
\(331\) 7.10076e9 0.591552 0.295776 0.955257i \(-0.404422\pi\)
0.295776 + 0.955257i \(0.404422\pi\)
\(332\) −1.20603e10 −0.992675
\(333\) −1.54783e8 4.08053e8i −0.0125877 0.0331848i
\(334\) 1.38004e9 0.110893
\(335\) 0 0
\(336\) 5.10745e7 + 2.78656e8i 0.00400725 + 0.0218630i
\(337\) 2.32757e10i 1.80461i 0.431099 + 0.902305i \(0.358126\pi\)
−0.431099 + 0.902305i \(0.641874\pi\)
\(338\) 2.01308e9 0.154239
\(339\) −8.10331e9 + 1.48525e9i −0.613569 + 0.112460i
\(340\) 0 0
\(341\) 1.48917e9i 0.110135i
\(342\) −2.54637e9 + 9.65893e8i −0.186131 + 0.0706032i
\(343\) 6.88505e8i 0.0497428i
\(344\) 3.11201e9i 0.222232i
\(345\) 0 0
\(346\) 2.51521e9 0.175497
\(347\) 1.85680e9 0.128070 0.0640351 0.997948i \(-0.479603\pi\)
0.0640351 + 0.997948i \(0.479603\pi\)
\(348\) −3.22996e9 1.76223e10i −0.220232 1.20156i
\(349\) −1.48512e10 −1.00106 −0.500529 0.865720i \(-0.666861\pi\)
−0.500529 + 0.865720i \(0.666861\pi\)
\(350\) 0 0
\(351\) −1.05757e10 1.74907e10i −0.696758 1.15234i
\(352\) 1.24352e10i 0.809994i
\(353\) 1.49807e10 0.964791 0.482396 0.875954i \(-0.339767\pi\)
0.482396 + 0.875954i \(0.339767\pi\)
\(354\) −7.01881e8 3.82937e9i −0.0446941 0.243845i
\(355\) 0 0
\(356\) 2.69654e10i 1.67883i
\(357\) −3.14914e7 1.71813e8i −0.00193874 0.0105775i
\(358\) 5.58793e8i 0.0340188i
\(359\) 2.40350e10i 1.44699i 0.690327 + 0.723497i \(0.257466\pi\)
−0.690327 + 0.723497i \(0.742534\pi\)
\(360\) 0 0
\(361\) 1.73251e9 0.102011
\(362\) 3.46313e9 0.201667
\(363\) 2.10830e10 3.86428e9i 1.21424 0.222557i
\(364\) −5.66991e8 −0.0322976
\(365\) 0 0
\(366\) −8.49683e8 + 1.55737e8i −0.0473514 + 0.00867898i
\(367\) 6.35979e9i 0.350573i 0.984517 + 0.175287i \(0.0560852\pi\)
−0.984517 + 0.175287i \(0.943915\pi\)
\(368\) −1.38009e10 −0.752519
\(369\) 8.76400e9 + 2.31045e10i 0.472712 + 1.24621i
\(370\) 0 0
\(371\) 7.82921e8i 0.0413259i
\(372\) 1.33792e9 2.45226e8i 0.0698648 0.0128054i
\(373\) 9.55992e9i 0.493877i −0.969031 0.246939i \(-0.920575\pi\)
0.969031 0.246939i \(-0.0794246\pi\)
\(374\) 2.39725e9i 0.122526i
\(375\) 0 0
\(376\) −9.05333e9 −0.452957
\(377\) 3.44693e10 1.70634
\(378\) −4.98378e7 8.24245e7i −0.00244114 0.00403728i
\(379\) −1.47270e9 −0.0713767 −0.0356883 0.999363i \(-0.511362\pi\)
−0.0356883 + 0.999363i \(0.511362\pi\)
\(380\) 0 0
\(381\) 7.09157e9 + 3.86907e10i 0.336544 + 1.83614i
\(382\) 4.92900e9i 0.231476i
\(383\) 3.53991e10 1.64512 0.822559 0.568680i \(-0.192546\pi\)
0.822559 + 0.568680i \(0.192546\pi\)
\(384\) −1.47956e10 + 2.71187e9i −0.680468 + 0.124722i
\(385\) 0 0
\(386\) 4.55870e9i 0.205349i
\(387\) 4.74679e9 + 1.25139e10i 0.211620 + 0.557891i
\(388\) 2.86522e10i 1.26424i
\(389\) 1.00866e10i 0.440502i −0.975443 0.220251i \(-0.929312\pi\)
0.975443 0.220251i \(-0.0706877\pi\)
\(390\) 0 0
\(391\) 8.50936e9 0.364074
\(392\) 8.78904e9 0.372218
\(393\) 3.30033e9 + 1.80062e10i 0.138352 + 0.754833i
\(394\) 3.04316e9 0.126282
\(395\) 0 0
\(396\) −1.25684e10 3.31338e10i −0.511090 1.34738i
\(397\) 1.16090e10i 0.467339i −0.972316 0.233670i \(-0.924927\pi\)
0.972316 0.233670i \(-0.0750734\pi\)
\(398\) 1.89626e9 0.0755729
\(399\) 1.19338e8 + 6.51095e8i 0.00470857 + 0.0256893i
\(400\) 0 0
\(401\) 1.62151e10i 0.627108i 0.949570 + 0.313554i \(0.101520\pi\)
−0.949570 + 0.313554i \(0.898480\pi\)
\(402\) 6.17198e8 + 3.36735e9i 0.0236331 + 0.128939i
\(403\) 2.61698e9i 0.0992157i
\(404\) 3.60357e10i 1.35272i
\(405\) 0 0
\(406\) 1.62435e8 0.00597828
\(407\) 1.45578e9 0.0530540
\(408\) 4.38788e9 8.04249e8i 0.158349 0.0290235i
\(409\) 8.05756e9 0.287945 0.143973 0.989582i \(-0.454012\pi\)
0.143973 + 0.989582i \(0.454012\pi\)
\(410\) 0 0
\(411\) 4.35239e10 7.97744e9i 1.52532 0.279574i
\(412\) 3.96171e10i 1.37497i
\(413\) −9.46257e8 −0.0325244
\(414\) 4.38726e9 1.66418e9i 0.149345 0.0566498i
\(415\) 0 0
\(416\) 2.18529e10i 0.729685i
\(417\) 1.71843e10 3.14969e9i 0.568312 0.104165i
\(418\) 9.08451e9i 0.297575i
\(419\) 1.33632e10i 0.433567i 0.976220 + 0.216783i \(0.0695565\pi\)
−0.976220 + 0.216783i \(0.930443\pi\)
\(420\) 0 0
\(421\) −4.39642e10 −1.39949 −0.699747 0.714391i \(-0.746704\pi\)
−0.699747 + 0.714391i \(0.746704\pi\)
\(422\) −1.16716e10 −0.368029
\(423\) −3.64050e10 + 1.38092e10i −1.13710 + 0.431327i
\(424\) −1.99948e10 −0.618662
\(425\) 0 0
\(426\) 6.71474e8 + 3.66347e9i 0.0203888 + 0.111238i
\(427\) 2.09961e8i 0.00631578i
\(428\) −2.72919e10 −0.813315
\(429\) 6.70630e10 1.22919e10i 1.97995 0.362902i
\(430\) 0 0
\(431\) 1.47674e10i 0.427950i 0.976839 + 0.213975i \(0.0686412\pi\)
−0.976839 + 0.213975i \(0.931359\pi\)
\(432\) −2.66271e10 + 1.61000e10i −0.764521 + 0.462266i
\(433\) 1.57125e8i 0.00446986i 0.999998 + 0.00223493i \(0.000711401\pi\)
−0.999998 + 0.00223493i \(0.999289\pi\)
\(434\) 1.23324e7i 0.000347608i
\(435\) 0 0
\(436\) 3.77756e10 1.04536
\(437\) −3.22467e10 −0.884219
\(438\) −1.74204e9 9.50436e9i −0.0473328 0.258242i
\(439\) −6.17824e10 −1.66344 −0.831719 0.555197i \(-0.812643\pi\)
−0.831719 + 0.555197i \(0.812643\pi\)
\(440\) 0 0
\(441\) 3.53423e10 1.34061e10i 0.934416 0.354443i
\(442\) 4.21279e9i 0.110377i
\(443\) 8.26926e9 0.214710 0.107355 0.994221i \(-0.465762\pi\)
0.107355 + 0.994221i \(0.465762\pi\)
\(444\) −2.39727e8 1.30792e9i −0.00616859 0.0336550i
\(445\) 0 0
\(446\) 1.02341e10i 0.258648i
\(447\) 6.31501e9 + 3.44539e10i 0.158177 + 0.862995i
\(448\) 7.92379e8i 0.0196708i
\(449\) 7.95461e10i 1.95719i −0.205788 0.978597i \(-0.565976\pi\)
0.205788 0.978597i \(-0.434024\pi\)
\(450\) 0 0
\(451\) −8.24281e10 −1.99236
\(452\) −2.51008e10 −0.601358
\(453\) 2.56769e10 4.70628e9i 0.609746 0.111760i
\(454\) −7.86870e9 −0.185216
\(455\) 0 0
\(456\) −1.66281e10 + 3.04775e9i −0.384578 + 0.0704888i
\(457\) 2.02591e10i 0.464467i −0.972660 0.232234i \(-0.925397\pi\)
0.972660 0.232234i \(-0.0746034\pi\)
\(458\) −8.53413e9 −0.193953
\(459\) 1.64177e10 9.92693e9i 0.369881 0.223648i
\(460\) 0 0
\(461\) 3.97783e10i 0.880729i 0.897819 + 0.440364i \(0.145151\pi\)
−0.897819 + 0.440364i \(0.854849\pi\)
\(462\) 3.16032e8 5.79251e7i 0.00693687 0.00127145i
\(463\) 3.84754e10i 0.837258i −0.908157 0.418629i \(-0.862511\pi\)
0.908157 0.418629i \(-0.137489\pi\)
\(464\) 5.24745e10i 1.13208i
\(465\) 0 0
\(466\) −9.89001e9 −0.209726
\(467\) 2.20915e10 0.464470 0.232235 0.972660i \(-0.425396\pi\)
0.232235 + 0.972660i \(0.425396\pi\)
\(468\) −2.20869e10 5.82275e10i −0.460417 1.21379i
\(469\) 8.32089e8 0.0171980
\(470\) 0 0
\(471\) 8.17194e9 + 4.45850e10i 0.166051 + 0.905953i
\(472\) 2.41662e10i 0.486900i
\(473\) −4.46450e10 −0.891925
\(474\) −7.62958e9 + 1.39842e9i −0.151143 + 0.0277028i
\(475\) 0 0
\(476\) 5.32207e8i 0.0103670i
\(477\) −8.04025e10 + 3.04984e10i −1.55309 + 0.589119i
\(478\) 5.98968e9i 0.114734i
\(479\) 2.39823e10i 0.455564i −0.973712 0.227782i \(-0.926853\pi\)
0.973712 0.227782i \(-0.0731473\pi\)
\(480\) 0 0
\(481\) 2.55830e9 0.0477938
\(482\) −1.36164e9 −0.0252275
\(483\) −2.05613e8 1.12180e9i −0.00377800 0.0206123i
\(484\) 6.53066e10 1.19008
\(485\) 0 0
\(486\) 6.52323e9 8.32894e9i 0.116928 0.149295i
\(487\) 4.42866e10i 0.787329i −0.919254 0.393664i \(-0.871207\pi\)
0.919254 0.393664i \(-0.128793\pi\)
\(488\) −5.36213e9 −0.0945492
\(489\) −6.82645e9 3.72442e10i −0.119388 0.651364i
\(490\) 0 0
\(491\) 3.70873e10i 0.638116i 0.947735 + 0.319058i \(0.103366\pi\)
−0.947735 + 0.319058i \(0.896634\pi\)
\(492\) 1.35737e10 + 7.40562e10i 0.231652 + 1.26387i
\(493\) 3.23546e10i 0.547707i
\(494\) 1.59646e10i 0.268071i
\(495\) 0 0
\(496\) 3.98398e9 0.0658249
\(497\) 9.05262e8 0.0148371
\(498\) 1.18133e10 2.16524e9i 0.192067 0.0352038i
\(499\) −4.56047e10 −0.735541 −0.367771 0.929917i \(-0.619879\pi\)
−0.367771 + 0.929917i \(0.619879\pi\)
\(500\) 0 0
\(501\) 3.62381e10 6.64204e9i 0.575194 0.105427i
\(502\) 7.02173e9i 0.110568i
\(503\) 3.73919e10 0.584125 0.292063 0.956399i \(-0.405658\pi\)
0.292063 + 0.956399i \(0.405658\pi\)
\(504\) −2.12050e8 5.59026e8i −0.00328637 0.00866383i
\(505\) 0 0
\(506\) 1.56521e10i 0.238765i
\(507\) 5.28610e10 9.68884e9i 0.800026 0.146636i
\(508\) 1.19848e11i 1.79960i
\(509\) 4.63948e9i 0.0691192i 0.999403 + 0.0345596i \(0.0110029\pi\)
−0.999403 + 0.0345596i \(0.988997\pi\)
\(510\) 0 0
\(511\) −2.34857e9 −0.0344445
\(512\) −5.61342e10 −0.816861
\(513\) −6.22158e10 + 3.76187e10i −0.898321 + 0.543168i
\(514\) 1.71170e10 0.245230
\(515\) 0 0
\(516\) 7.35182e9 + 4.01106e10i 0.103704 + 0.565796i
\(517\) 1.29879e11i 1.81793i
\(518\) 1.20559e7 0.000167449
\(519\) 6.60462e10 1.21055e10i 0.910288 0.166846i
\(520\) 0 0
\(521\) 5.90088e10i 0.800877i −0.916324 0.400439i \(-0.868858\pi\)
0.916324 0.400439i \(-0.131142\pi\)
\(522\) 6.32760e9 + 1.66814e10i 0.0852230 + 0.224673i
\(523\) 6.02622e9i 0.0805449i 0.999189 + 0.0402725i \(0.0128226\pi\)
−0.999189 + 0.0402725i \(0.987177\pi\)
\(524\) 5.57758e10i 0.739811i
\(525\) 0 0
\(526\) 1.08774e10 0.142096
\(527\) −2.45643e9 −0.0318465
\(528\) −1.87126e10 1.02094e11i −0.240768 1.31360i
\(529\) −2.27518e10 −0.290531
\(530\) 0 0
\(531\) −3.68610e10 9.71764e10i −0.463649 1.22231i
\(532\) 2.01683e9i 0.0251781i
\(533\) −1.44854e11 −1.79483
\(534\) 4.84121e9 + 2.64130e10i 0.0595373 + 0.324828i
\(535\) 0 0
\(536\) 2.12505e10i 0.257460i
\(537\) −2.68943e9 1.46732e10i −0.0323417 0.176452i
\(538\) 2.02802e10i 0.242071i
\(539\) 1.26088e11i 1.49389i
\(540\) 0 0
\(541\) 4.00361e10 0.467372 0.233686 0.972312i \(-0.424921\pi\)
0.233686 + 0.972312i \(0.424921\pi\)
\(542\) 1.12869e10 0.130791
\(543\) 9.09374e10 1.66678e10i 1.04603 0.191725i
\(544\) 2.05123e10 0.234217
\(545\) 0 0
\(546\) 5.55377e8 1.01794e8i 0.00624909 0.00114539i
\(547\) 7.70856e10i 0.861041i 0.902581 + 0.430521i \(0.141670\pi\)
−0.902581 + 0.430521i \(0.858330\pi\)
\(548\) 1.34819e11 1.49496
\(549\) −2.15621e10 + 8.17894e9i −0.237356 + 0.0900342i
\(550\) 0 0
\(551\) 1.22610e11i 1.33020i
\(552\) 2.86493e10 5.25109e9i 0.308573 0.0565579i
\(553\) 1.88531e9i 0.0201596i
\(554\) 1.10450e10i 0.117254i
\(555\) 0 0
\(556\) 5.32299e10 0.557002
\(557\) 1.00834e10 0.104758 0.0523789 0.998627i \(-0.483320\pi\)
0.0523789 + 0.998627i \(0.483320\pi\)
\(558\) −1.26649e9 + 4.80405e8i −0.0130636 + 0.00495531i
\(559\) −7.84565e10 −0.803492
\(560\) 0 0
\(561\) 1.15378e10 + 6.29487e10i 0.116485 + 0.635529i
\(562\) 3.23566e9i 0.0324352i
\(563\) 1.17038e11 1.16492 0.582458 0.812861i \(-0.302091\pi\)
0.582458 + 0.812861i \(0.302091\pi\)
\(564\) −1.16688e11 + 2.13876e10i −1.15321 + 0.211371i
\(565\) 0 0
\(566\) 1.36684e10i 0.133184i
\(567\) −1.70538e9 1.92450e9i −0.0165002 0.0186202i
\(568\) 2.31192e10i 0.222116i
\(569\) 2.10738e10i 0.201045i 0.994935 + 0.100522i \(0.0320514\pi\)
−0.994935 + 0.100522i \(0.967949\pi\)
\(570\) 0 0
\(571\) −1.66672e11 −1.56790 −0.783949 0.620826i \(-0.786798\pi\)
−0.783949 + 0.620826i \(0.786798\pi\)
\(572\) 2.07734e11 1.94054
\(573\) 2.37229e10 + 1.29429e11i 0.220065 + 1.20064i
\(574\) −6.82621e8 −0.00628829
\(575\) 0 0
\(576\) −8.13739e10 + 3.08668e10i −0.739256 + 0.280415i
\(577\) 9.88790e10i 0.892074i 0.895014 + 0.446037i \(0.147165\pi\)
−0.895014 + 0.446037i \(0.852835\pi\)
\(578\) 1.72111e10 0.154205
\(579\) 2.19407e10 + 1.19706e11i 0.195225 + 1.06512i
\(580\) 0 0
\(581\) 2.91912e9i 0.0256181i
\(582\) −5.14405e9 2.80653e10i −0.0448346 0.244612i
\(583\) 2.86846e11i 2.48299i
\(584\) 5.99795e10i 0.515646i
\(585\) 0 0
\(586\) 2.31361e10 0.196200
\(587\) 4.94023e10 0.416097 0.208049 0.978118i \(-0.433289\pi\)
0.208049 + 0.978118i \(0.433289\pi\)
\(588\) 1.13282e11 2.07633e10i 0.947656 0.173695i
\(589\) 9.30879e9 0.0773450
\(590\) 0 0
\(591\) 7.99097e10 1.46465e10i 0.655012 0.120056i
\(592\) 3.89465e9i 0.0317089i
\(593\) 5.39077e10 0.435945 0.217973 0.975955i \(-0.430056\pi\)
0.217973 + 0.975955i \(0.430056\pi\)
\(594\) 1.82596e10 + 3.01987e10i 0.146671 + 0.242573i
\(595\) 0 0
\(596\) 1.06724e11i 0.845820i
\(597\) 4.97934e10 9.12658e9i 0.391990 0.0718474i
\(598\) 2.75061e10i 0.215092i
\(599\) 1.84260e11i 1.43128i 0.698469 + 0.715640i \(0.253865\pi\)
−0.698469 + 0.715640i \(0.746135\pi\)
\(600\) 0 0
\(601\) −4.09269e9 −0.0313698 −0.0156849 0.999877i \(-0.504993\pi\)
−0.0156849 + 0.999877i \(0.504993\pi\)
\(602\) −3.69724e8 −0.00281509
\(603\) 3.24137e10 + 8.54519e10i 0.245165 + 0.646327i
\(604\) 7.95365e10 0.597611
\(605\) 0 0
\(606\) −6.46964e9 3.52975e10i −0.0479722 0.261730i
\(607\) 1.45907e11i 1.07478i 0.843333 + 0.537392i \(0.180590\pi\)
−0.843333 + 0.537392i \(0.819410\pi\)
\(608\) −7.77323e10 −0.568836
\(609\) 4.26535e9 7.81790e8i 0.0310088 0.00568357i
\(610\) 0 0
\(611\) 2.28243e11i 1.63769i
\(612\) 5.46553e10 2.07319e10i 0.389607 0.147786i
\(613\) 9.26923e10i 0.656450i −0.944600 0.328225i \(-0.893550\pi\)
0.944600 0.328225i \(-0.106450\pi\)
\(614\) 1.62521e10i 0.114350i
\(615\) 0 0
\(616\) 1.99440e9 0.0138512
\(617\) −2.27799e11 −1.57185 −0.785925 0.618322i \(-0.787813\pi\)
−0.785925 + 0.618322i \(0.787813\pi\)
\(618\) 7.11262e9 + 3.88055e10i 0.0487613 + 0.266036i
\(619\) −1.05797e11 −0.720627 −0.360313 0.932831i \(-0.617330\pi\)
−0.360313 + 0.932831i \(0.617330\pi\)
\(620\) 0 0
\(621\) 1.07194e11 6.48148e10i 0.720784 0.435820i
\(622\) 2.56982e10i 0.171689i
\(623\) 6.52679e9 0.0433259
\(624\) −3.28845e10 1.79414e11i −0.216897 1.18336i
\(625\) 0 0
\(626\) 1.20272e10i 0.0783187i
\(627\) −4.37231e10 2.38548e11i −0.282905 1.54350i
\(628\) 1.38106e11i 0.887923i
\(629\) 2.40135e9i 0.0153410i
\(630\) 0 0
\(631\) 2.99698e11 1.89045 0.945227 0.326414i \(-0.105840\pi\)
0.945227 + 0.326414i \(0.105840\pi\)
\(632\) −4.81483e10 −0.301795
\(633\) −3.06483e11 + 5.61748e10i −1.90893 + 0.349886i
\(634\) 4.98429e9 0.0308494
\(635\) 0 0
\(636\) −2.57712e11 + 4.72358e10i −1.57509 + 0.288697i
\(637\) 2.21580e11i 1.34577i
\(638\) −5.95129e10 −0.359194
\(639\) 3.52641e10 + 9.29665e10i 0.211509 + 0.557600i
\(640\) 0 0
\(641\) 7.79955e10i 0.461995i 0.972954 + 0.230998i \(0.0741989\pi\)
−0.972954 + 0.230998i \(0.925801\pi\)
\(642\) 2.67328e10 4.89983e9i 0.157364 0.0288430i
\(643\) 1.10441e11i 0.646081i 0.946385 + 0.323041i \(0.104705\pi\)
−0.946385 + 0.323041i \(0.895295\pi\)
\(644\) 3.47488e9i 0.0202021i
\(645\) 0 0
\(646\) 1.49852e10 0.0860463
\(647\) 1.12591e11 0.642521 0.321261 0.946991i \(-0.395893\pi\)
0.321261 + 0.946991i \(0.395893\pi\)
\(648\) 4.91492e10 4.35533e10i 0.278751 0.247014i
\(649\) 3.46689e11 1.95417
\(650\) 0 0
\(651\) 5.93552e7 + 3.23834e8i 0.000330472 + 0.00180301i
\(652\) 1.15368e11i 0.638401i
\(653\) −1.11018e11 −0.610578 −0.305289 0.952260i \(-0.598753\pi\)
−0.305289 + 0.952260i \(0.598753\pi\)
\(654\) −3.70018e10 + 6.78201e9i −0.202261 + 0.0370721i
\(655\) 0 0
\(656\) 2.20520e11i 1.19078i
\(657\) −9.14877e10 2.41188e11i −0.491022 1.29448i
\(658\) 1.07559e9i 0.00573775i
\(659\) 1.20450e11i 0.638653i −0.947645 0.319326i \(-0.896543\pi\)
0.947645 0.319326i \(-0.103457\pi\)
\(660\) 0 0
\(661\) −3.14150e10 −0.164563 −0.0822813 0.996609i \(-0.526221\pi\)
−0.0822813 + 0.996609i \(0.526221\pi\)
\(662\) −2.15447e10 −0.112178
\(663\) 2.02759e10 + 1.10622e11i 0.104936 + 0.572518i
\(664\) 7.45506e10 0.383512
\(665\) 0 0
\(666\) 4.69634e8 + 1.23809e9i 0.00238705 + 0.00629297i
\(667\) 2.11249e11i 1.06731i
\(668\) 1.12251e11 0.563747
\(669\) −4.92559e10 2.68734e11i −0.245897 1.34158i
\(670\) 0 0
\(671\) 7.69253e10i 0.379472i
\(672\) −4.95641e8 2.70415e9i −0.00243047 0.0132603i
\(673\) 3.66345e11i 1.78579i −0.450265 0.892895i \(-0.648671\pi\)
0.450265 0.892895i \(-0.351329\pi\)
\(674\) 7.06218e10i 0.342215i
\(675\) 0 0
\(676\) 1.63742e11 0.784104
\(677\) −2.51302e11 −1.19630 −0.598152 0.801382i \(-0.704098\pi\)
−0.598152 + 0.801382i \(0.704098\pi\)
\(678\) 2.45866e10 4.50645e9i 0.116354 0.0213263i
\(679\) −6.93506e9 −0.0326266
\(680\) 0 0
\(681\) −2.06622e11 + 3.78715e10i −0.960701 + 0.176086i
\(682\) 4.51835e9i 0.0208854i
\(683\) −2.45748e11 −1.12929 −0.564646 0.825333i \(-0.690987\pi\)
−0.564646 + 0.825333i \(0.690987\pi\)
\(684\) −2.07119e11 + 7.85647e10i −0.946230 + 0.358925i
\(685\) 0 0
\(686\) 2.08902e9i 0.00943293i
\(687\) −2.24095e11 + 4.10742e10i −1.00602 + 0.184392i
\(688\) 1.19439e11i 0.533079i
\(689\) 5.04087e11i 2.23681i
\(690\) 0 0
\(691\) −1.44391e11 −0.633326 −0.316663 0.948538i \(-0.602562\pi\)
−0.316663 + 0.948538i \(0.602562\pi\)
\(692\) 2.04584e11 0.892171
\(693\) 8.01981e9 3.04208e9i 0.0347721 0.0131898i
\(694\) −5.63381e9 −0.0242864
\(695\) 0 0
\(696\) 1.99659e10 + 1.08931e11i 0.0850848 + 0.464212i
\(697\) 1.35968e11i 0.576109i
\(698\) 4.50606e10 0.189835
\(699\) −2.59699e11 + 4.76000e10i −1.08783 + 0.199388i
\(700\) 0 0
\(701\) 2.23367e11i 0.925009i 0.886617 + 0.462505i \(0.153049\pi\)
−0.886617 + 0.462505i \(0.846951\pi\)
\(702\) 3.20883e10 + 5.30694e10i 0.132129 + 0.218522i
\(703\) 9.10007e9i 0.0372583i
\(704\) 2.90312e11i 1.18188i
\(705\) 0 0
\(706\) −4.54536e10 −0.182957
\(707\) −8.72218e9 −0.0349098
\(708\) −5.70903e10 3.11477e11i −0.227211 1.23963i
\(709\) 8.44074e9 0.0334038 0.0167019 0.999861i \(-0.494683\pi\)
0.0167019 + 0.999861i \(0.494683\pi\)
\(710\) 0 0
\(711\) −1.93613e11 + 7.34414e10i −0.757627 + 0.287384i
\(712\) 1.66686e11i 0.648602i
\(713\) −1.60385e10 −0.0620591
\(714\) 9.55494e7 + 5.21305e8i 0.000367650 + 0.00200585i
\(715\) 0 0
\(716\) 4.54516e10i 0.172941i
\(717\) −2.88279e10 1.57281e11i −0.109078 0.595115i
\(718\) 7.29257e10i 0.274399i
\(719\) 3.06358e11i 1.14634i 0.819436 + 0.573171i \(0.194287\pi\)
−0.819436 + 0.573171i \(0.805713\pi\)
\(720\) 0 0
\(721\) 9.58903e9 0.0354841
\(722\) −5.25668e9 −0.0193447
\(723\) −3.57550e10 + 6.55348e9i −0.130853 + 0.0239839i
\(724\) 2.81687e11 1.02521
\(725\) 0 0
\(726\) −6.39689e10 + 1.17248e10i −0.230262 + 0.0422044i
\(727\) 2.35218e10i 0.0842040i 0.999113 + 0.0421020i \(0.0134054\pi\)
−0.999113 + 0.0421020i \(0.986595\pi\)
\(728\) 3.50484e9 0.0124779
\(729\) 1.31205e11 2.50103e11i 0.464559 0.885542i
\(730\) 0 0
\(731\) 7.36433e10i 0.257907i
\(732\) −6.91123e10 + 1.26675e10i −0.240719 + 0.0441212i
\(733\) 6.21715e10i 0.215365i 0.994185 + 0.107683i \(0.0343430\pi\)
−0.994185 + 0.107683i \(0.965657\pi\)
\(734\) 1.92965e10i 0.0664806i
\(735\) 0 0
\(736\) 1.33928e11 0.456416
\(737\) −3.04860e11 −1.03331
\(738\) −2.65912e10 7.01022e10i −0.0896423 0.236323i
\(739\) 3.85080e10 0.129114 0.0645570 0.997914i \(-0.479437\pi\)
0.0645570 + 0.997914i \(0.479437\pi\)
\(740\) 0 0
\(741\) −7.68365e10 4.19210e11i −0.254856 1.39046i
\(742\) 2.37549e9i 0.00783679i
\(743\) 1.81380e10 0.0595160 0.0297580 0.999557i \(-0.490526\pi\)
0.0297580 + 0.999557i \(0.490526\pi\)
\(744\) −8.27031e9 + 1.51586e9i −0.0269917 + 0.00494727i
\(745\) 0 0
\(746\) 2.90062e10i 0.0936558i
\(747\) 2.99781e11 1.13713e11i 0.962767 0.365198i
\(748\) 1.94990e11i 0.622881i
\(749\) 6.60582e9i 0.0209894i
\(750\) 0 0
\(751\) 4.66054e11 1.46513 0.732566 0.680696i \(-0.238323\pi\)
0.732566 + 0.680696i \(0.238323\pi\)
\(752\) −3.47466e11 −1.08653
\(753\) 3.37951e10 + 1.84382e11i 0.105117 + 0.573506i
\(754\) −1.04585e11 −0.323581
\(755\) 0 0
\(756\) −4.05376e9 6.70433e9i −0.0124100 0.0205243i
\(757\) 1.01684e11i 0.309649i 0.987942 + 0.154825i \(0.0494812\pi\)
−0.987942 + 0.154825i \(0.950519\pi\)
\(758\) 4.46837e9 0.0135354
\(759\) 7.53324e10 + 4.11004e11i 0.226994 + 1.23845i
\(760\) 0 0
\(761\) 1.11642e9i 0.00332880i 0.999999 + 0.00166440i \(0.000529796\pi\)
−0.999999 + 0.00166440i \(0.999470\pi\)
\(762\) −2.15168e10 1.17393e11i −0.0638202 0.348195i
\(763\) 9.14331e9i 0.0269777i
\(764\) 4.00920e11i 1.17675i
\(765\) 0 0
\(766\) −1.07406e11 −0.311970
\(767\) 6.09251e11 1.76041
\(768\) −2.25663e11 + 4.13615e10i −0.648658 + 0.118892i
\(769\) −5.25128e11 −1.50162 −0.750810 0.660519i \(-0.770336\pi\)
−0.750810 + 0.660519i \(0.770336\pi\)
\(770\) 0 0
\(771\) 4.49470e11 8.23828e10i 1.27199 0.233141i
\(772\) 3.70800e11i 1.04393i
\(773\) −1.88899e11 −0.529067 −0.264534 0.964376i \(-0.585218\pi\)
−0.264534 + 0.964376i \(0.585218\pi\)
\(774\) −1.44024e10 3.79690e10i −0.0401303 0.105795i
\(775\) 0 0
\(776\) 1.77113e11i 0.488430i
\(777\) 3.16573e8 5.80244e7i 0.000868541 0.000159194i
\(778\) 3.06043e10i 0.0835342i
\(779\) 5.15257e11i 1.39918i
\(780\) 0 0
\(781\) −3.31670e11 −0.891459
\(782\) −2.58186e10 −0.0690408
\(783\) 2.46441e11 + 4.07578e11i 0.655641 + 1.08434i
\(784\) 3.37323e11 0.892857
\(785\) 0 0
\(786\) −1.00137e10 5.46333e10i −0.0262363 0.143142i
\(787\) 6.60029e11i 1.72054i −0.509842 0.860268i \(-0.670296\pi\)
0.509842 0.860268i \(-0.329704\pi\)
\(788\) 2.47528e11 0.641977
\(789\) 2.85627e11 5.23523e10i 0.737042 0.135091i
\(790\) 0 0
\(791\) 6.07547e9i 0.0155194i
\(792\) 7.76909e10 + 2.04816e11i 0.197455 + 0.520550i
\(793\) 1.35184e11i 0.341848i
\(794\) 3.52233e10i 0.0886234i
\(795\) 0 0
\(796\) 1.54240e11 0.384189
\(797\) 5.73881e11 1.42229 0.711146 0.703044i \(-0.248176\pi\)
0.711146 + 0.703044i \(0.248176\pi\)
\(798\) −3.62090e8 1.97551e9i −0.000892904 0.00487157i
\(799\) 2.14240e11 0.525671
\(800\) 0 0
\(801\) 2.54248e11 + 6.70272e11i 0.617629 + 1.62825i
\(802\) 4.91990e10i 0.118921i
\(803\) 8.60469e11 2.06954
\(804\) 5.02022e10 + 2.73897e11i 0.120143 + 0.655485i
\(805\) 0 0
\(806\) 7.94029e9i 0.0188147i
\(807\) 9.76071e10 + 5.32532e11i 0.230138 + 1.25560i
\(808\) 2.22753e11i 0.522611i
\(809\) 2.07320e11i 0.484002i −0.970276 0.242001i \(-0.922196\pi\)
0.970276 0.242001i \(-0.0778038\pi\)
\(810\) 0 0
\(811\) −6.06207e11 −1.40132 −0.700660 0.713495i \(-0.747111\pi\)
−0.700660 + 0.713495i \(0.747111\pi\)
\(812\) 1.32123e10 0.0303917
\(813\) 2.96380e11 5.43231e10i 0.678400 0.124343i
\(814\) −4.41704e9 −0.0100608
\(815\) 0 0
\(816\) 1.68407e11 3.08671e10i 0.379838 0.0696201i
\(817\) 2.79076e11i 0.626374i
\(818\) −2.44478e10 −0.0546042
\(819\) 1.40936e10 5.34598e9i 0.0313246 0.0118821i
\(820\) 0 0
\(821\) 1.56657e11i 0.344808i 0.985026 + 0.172404i \(0.0551535\pi\)
−0.985026 + 0.172404i \(0.944846\pi\)
\(822\) −1.32058e11 + 2.42047e10i −0.289252 + 0.0530167i
\(823\) 3.65723e11i 0.797173i 0.917131 + 0.398587i \(0.130499\pi\)
−0.917131 + 0.398587i \(0.869501\pi\)
\(824\) 2.44892e11i 0.531208i
\(825\) 0 0
\(826\) 2.87108e9 0.00616772
\(827\) 5.22532e11 1.11710 0.558549 0.829472i \(-0.311358\pi\)
0.558549 + 0.829472i \(0.311358\pi\)
\(828\) 3.56855e11 1.35362e11i 0.759224 0.287990i
\(829\) −7.56111e11 −1.60091 −0.800456 0.599391i \(-0.795409\pi\)
−0.800456 + 0.599391i \(0.795409\pi\)
\(830\) 0 0
\(831\) −5.31589e10 2.90028e11i −0.111474 0.608185i
\(832\) 5.10177e11i 1.06470i
\(833\) −2.07986e11 −0.431971
\(834\) −5.21395e10 + 9.55659e9i −0.107771 + 0.0197533i
\(835\) 0 0
\(836\) 7.38925e11i 1.51278i
\(837\) −3.09442e10 + 1.87103e10i −0.0630489 + 0.0381224i
\(838\) 4.05460e10i 0.0822189i
\(839\) 4.63197e11i 0.934799i 0.884046 + 0.467400i \(0.154809\pi\)
−0.884046 + 0.467400i \(0.845191\pi\)
\(840\) 0 0
\(841\) −3.02974e11 −0.605649
\(842\) 1.33394e11 0.265391
\(843\) −1.55730e10 8.49642e10i −0.0308363 0.168239i
\(844\) −9.49359e11 −1.87094
\(845\) 0 0
\(846\) 1.10458e11 4.18990e10i 0.215633 0.0817942i
\(847\) 1.58070e10i 0.0307126i
\(848\) −7.67399e11 −1.48401
\(849\) 6.57849e10 + 3.58914e11i 0.126618 + 0.690811i
\(850\) 0 0
\(851\) 1.56789e10i 0.0298949i
\(852\) 5.46170e10 + 2.97983e11i 0.103650 + 0.565501i
\(853\) 6.78685e11i 1.28195i −0.767561 0.640976i \(-0.778530\pi\)
0.767561 0.640976i \(-0.221470\pi\)
\(854\) 6.37051e8i 0.00119769i
\(855\) 0 0
\(856\) 1.68704e11 0.314217
\(857\) −1.02265e12 −1.89584 −0.947921 0.318506i \(-0.896819\pi\)
−0.947921 + 0.318506i \(0.896819\pi\)
\(858\) −2.03479e11 + 3.72953e10i −0.375465 + 0.0688185i
\(859\) 1.64678e11 0.302457 0.151228 0.988499i \(-0.451677\pi\)
0.151228 + 0.988499i \(0.451677\pi\)
\(860\) 0 0
\(861\) −1.79248e10 + 3.28541e9i −0.0326168 + 0.00597829i
\(862\) 4.48062e10i 0.0811539i
\(863\) 9.97986e11 1.79921 0.899604 0.436707i \(-0.143855\pi\)
0.899604 + 0.436707i \(0.143855\pi\)
\(864\) 2.58397e11 1.56239e11i 0.463695 0.280373i
\(865\) 0 0
\(866\) 4.76740e8i 0.000847637i
\(867\) 4.51942e11 8.28359e10i 0.799846 0.146603i
\(868\) 1.00311e9i 0.00176713i
\(869\) 6.90738e11i 1.21125i
\(870\) 0 0
\(871\) −5.35744e11 −0.930861
\(872\) −2.33508e11 −0.403865
\(873\) −2.70153e11 7.12201e11i −0.465106 1.22616i
\(874\) 9.78411e10 0.167678
\(875\) 0 0
\(876\) −1.41696e11 7.73075e11i −0.240625 1.31282i
\(877\) 2.30212e10i 0.0389160i 0.999811 + 0.0194580i \(0.00619407\pi\)
−0.999811 + 0.0194580i \(0.993806\pi\)
\(878\) 1.87457e11 0.315444
\(879\) 6.07525e11 1.11352e11i 1.01767 0.186528i
\(880\) 0 0
\(881\) 4.23415e10i 0.0702851i 0.999382 + 0.0351425i \(0.0111885\pi\)
−0.999382 + 0.0351425i \(0.988811\pi\)
\(882\) −1.07233e11 + 4.06759e10i −0.177197 + 0.0672145i
\(883\) 8.49512e11i 1.39742i 0.715406 + 0.698709i \(0.246242\pi\)
−0.715406 + 0.698709i \(0.753758\pi\)
\(884\) 3.42664e11i 0.561124i
\(885\) 0 0
\(886\) −2.50901e10 −0.0407162
\(887\) −2.62546e11 −0.424142 −0.212071 0.977254i \(-0.568021\pi\)
−0.212071 + 0.977254i \(0.568021\pi\)
\(888\) 1.48187e9 + 8.08488e9i 0.00238318 + 0.0130023i
\(889\) −2.90084e10 −0.0464426
\(890\) 0 0
\(891\) 6.24817e11 + 7.05097e11i 0.991384 + 1.11876i
\(892\) 8.32429e11i 1.31489i
\(893\) −8.11876e11 −1.27668
\(894\) −1.91606e10 1.04538e11i −0.0299958 0.163653i
\(895\) 0 0
\(896\) 1.10930e10i 0.0172115i
\(897\) 1.32385e11 + 7.22275e11i 0.204488 + 1.11566i
\(898\) 2.41354e11i 0.371150i
\(899\) 6.09822e10i 0.0933608i
\(900\) 0 0
\(901\) 4.73162e11 0.717977
\(902\) 2.50098e11 0.377820
\(903\) −9.70848e9 + 1.77946e9i −0.0146016 + 0.00267631i
\(904\) 1.55160e11 0.232330
\(905\) 0 0
\(906\) −7.79072e10 + 1.42795e10i −0.115629 + 0.0211934i
\(907\) 8.67841e11i 1.28236i −0.767389 0.641182i \(-0.778445\pi\)
0.767389 0.641182i \(-0.221555\pi\)
\(908\) −6.40032e11 −0.941582
\(909\) −3.39769e11 8.95730e11i −0.497655 1.31196i
\(910\) 0 0
\(911\) 7.78413e11i 1.13015i 0.825039 + 0.565075i \(0.191153\pi\)
−0.825039 + 0.565075i \(0.808847\pi\)
\(912\) −6.38187e11 + 1.16973e11i −0.922505 + 0.169085i
\(913\) 1.06951e12i 1.53922i
\(914\) 6.14690e10i 0.0880787i
\(915\) 0 0
\(916\) −6.94157e11 −0.985998
\(917\) −1.35001e10 −0.0190924
\(918\) −4.98136e10 + 3.01197e10i −0.0701419 + 0.0424112i
\(919\) 3.08965e11 0.433159 0.216579 0.976265i \(-0.430510\pi\)
0.216579 + 0.976265i \(0.430510\pi\)
\(920\) 0 0
\(921\) 7.82202e10 + 4.26759e11i 0.108713 + 0.593122i
\(922\) 1.20693e11i 0.167016i
\(923\) −5.82857e11 −0.803073
\(924\) 2.57057e10 4.71157e9i 0.0352648 0.00646365i
\(925\) 0 0
\(926\) 1.16740e11i 0.158772i
\(927\) 3.73537e11 + 9.84752e11i 0.505842 + 1.33355i
\(928\) 5.09227e11i 0.686625i
\(929\) 1.36481e12i 1.83235i −0.400781 0.916174i \(-0.631261\pi\)
0.400781 0.916174i \(-0.368739\pi\)
\(930\) 0 0
\(931\) 7.88175e11 1.04912
\(932\) −8.04443e11 −1.06618
\(933\) −1.23684e11 6.74803e11i −0.163225 0.890534i
\(934\) −6.70288e10 −0.0880793
\(935\) 0 0
\(936\) 1.36529e11 + 3.59931e11i 0.177878 + 0.468939i
\(937\) 9.26920e11i 1.20250i −0.799062 0.601249i \(-0.794670\pi\)
0.799062 0.601249i \(-0.205330\pi\)
\(938\) −2.52468e9 −0.00326133
\(939\) 5.78859e10 + 3.15818e11i 0.0744578 + 0.406232i
\(940\) 0 0
\(941\) 4.30760e11i 0.549385i 0.961532 + 0.274692i \(0.0885761\pi\)
−0.961532 + 0.274692i \(0.911424\pi\)
\(942\) −2.47948e10 1.35277e11i −0.0314889 0.171799i
\(943\) 8.87758e11i 1.12266i
\(944\) 9.27497e11i 1.16795i
\(945\) 0 0
\(946\) 1.35459e11 0.169139
\(947\) 5.20879e11 0.647645 0.323823 0.946118i \(-0.395032\pi\)
0.323823 + 0.946118i \(0.395032\pi\)
\(948\) −6.20582e11 + 1.13746e11i −0.768362 + 0.140832i
\(949\) 1.51214e12 1.86435
\(950\) 0 0
\(951\) 1.30881e11 2.39891e10i 0.160013 0.0293286i
\(952\) 3.28982e9i 0.00400520i
\(953\) 1.01657e12 1.23243 0.616217 0.787576i \(-0.288664\pi\)
0.616217 + 0.787576i \(0.288664\pi\)
\(954\) 2.43953e11 9.25363e10i 0.294518 0.111717i
\(955\) 0 0
\(956\) 4.87194e11i 0.583271i
\(957\) −1.56274e12 + 2.86432e11i −1.86311 + 0.341487i
\(958\) 7.27658e10i 0.0863903i
\(959\) 3.26321e10i 0.0385807i
\(960\) 0 0
\(961\) −8.48261e11 −0.994572
\(962\) −7.76226e9 −0.00906333
\(963\) 6.78388e11 2.57327e11i 0.788811 0.299213i
\(964\) −1.10754e11 −0.128249
\(965\) 0 0
\(966\) 6.23860e8 + 3.40370e9i 0.000716438 + 0.00390879i
\(967\) 1.25609e12i 1.43653i 0.695769 + 0.718266i \(0.255064\pi\)
−0.695769 + 0.718266i \(0.744936\pi\)
\(968\) −4.03691e11 −0.459777
\(969\) 3.93492e11 7.21227e10i 0.446315 0.0818045i
\(970\) 0 0
\(971\) 3.77457e11i 0.424610i 0.977203 + 0.212305i \(0.0680971\pi\)
−0.977203 + 0.212305i \(0.931903\pi\)
\(972\) 5.30592e11 6.77467e11i 0.594423 0.758968i
\(973\) 1.28839e10i 0.0143746i
\(974\) 1.34372e11i 0.149304i
\(975\) 0 0
\(976\) −2.05798e11 −0.226800
\(977\) 4.90276e11 0.538100 0.269050 0.963126i \(-0.413290\pi\)
0.269050 + 0.963126i \(0.413290\pi\)
\(978\) 2.07124e10 + 1.13004e11i 0.0226400 + 0.123521i
\(979\) −2.39128e12 −2.60315
\(980\) 0 0
\(981\) −9.38978e11 + 3.56174e11i −1.01386 + 0.384580i
\(982\) 1.12528e11i 0.121008i
\(983\) −8.66068e11 −0.927551 −0.463775 0.885953i \(-0.653506\pi\)
−0.463775 + 0.885953i \(0.653506\pi\)
\(984\) −8.39052e10 4.57776e11i −0.0894970 0.488284i
\(985\) 0 0
\(986\) 9.81685e10i 0.103864i
\(987\) −5.17672e9 2.82435e10i −0.00545490 0.0297612i
\(988\) 1.29854e12i 1.36279i
\(989\) 4.80831e11i 0.502582i
\(990\) 0 0
\(991\) 5.45022e10 0.0565093 0.0282546 0.999601i \(-0.491005\pi\)
0.0282546 + 0.999601i \(0.491005\pi\)
\(992\) −3.86616e10 −0.0399240
\(993\) −5.65737e11 + 1.03693e11i −0.581859 + 0.106648i
\(994\) −2.74669e9 −0.00281362
\(995\) 0 0
\(996\) 9.60880e11 1.76119e11i 0.976409 0.178965i
\(997\) 7.54906e10i 0.0764033i 0.999270 + 0.0382017i \(0.0121629\pi\)
−0.999270 + 0.0382017i \(0.987837\pi\)
\(998\) 1.38371e11 0.139484
\(999\) 1.82908e10 + 3.02504e10i 0.0183642 + 0.0303717i
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.74.10 20
3.2 odd 2 inner 75.9.d.d.74.12 20
5.2 odd 4 75.9.c.f.26.5 yes 10
5.3 odd 4 75.9.c.e.26.6 yes 10
5.4 even 2 inner 75.9.d.d.74.11 20
15.2 even 4 75.9.c.f.26.6 yes 10
15.8 even 4 75.9.c.e.26.5 10
15.14 odd 2 inner 75.9.d.d.74.9 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.9.c.e.26.5 10 15.8 even 4
75.9.c.e.26.6 yes 10 5.3 odd 4
75.9.c.f.26.5 yes 10 5.2 odd 4
75.9.c.f.26.6 yes 10 15.2 even 4
75.9.d.d.74.9 20 15.14 odd 2 inner
75.9.d.d.74.10 20 1.1 even 1 trivial
75.9.d.d.74.11 20 5.4 even 2 inner
75.9.d.d.74.12 20 3.2 odd 2 inner