Properties

Label 1.28.a.a.1.2
Level $1$
Weight $28$
Character 1.1
Self dual yes
Analytic conductor $4.619$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 28 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.61855574838\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{18209}) \)
Defining polynomial: \(x^{2} - x - 4552\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{3}\cdot 3^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-66.9704\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+10433.6 q^{2} +2.15499e6 q^{3} -2.53577e7 q^{4} +4.86703e9 q^{5} +2.24843e10 q^{6} +2.14815e10 q^{7} -1.66495e12 q^{8} -2.98161e12 q^{9} +O(q^{10})\) \(q+10433.6 q^{2} +2.15499e6 q^{3} -2.53577e7 q^{4} +4.86703e9 q^{5} +2.24843e10 q^{6} +2.14815e10 q^{7} -1.66495e12 q^{8} -2.98161e12 q^{9} +5.07806e13 q^{10} -6.85469e13 q^{11} -5.46457e13 q^{12} -5.86777e14 q^{13} +2.24129e14 q^{14} +1.04884e16 q^{15} -1.39679e16 q^{16} -2.42814e16 q^{17} -3.11089e16 q^{18} +2.43094e17 q^{19} -1.23417e17 q^{20} +4.62924e16 q^{21} -7.15190e17 q^{22} +1.25668e17 q^{23} -3.58794e18 q^{24} +1.62374e19 q^{25} -6.12220e18 q^{26} -2.28584e19 q^{27} -5.44722e17 q^{28} -1.25483e19 q^{29} +1.09432e20 q^{30} -6.23745e19 q^{31} +7.77296e19 q^{32} -1.47718e20 q^{33} -2.53343e20 q^{34} +1.04551e20 q^{35} +7.56070e19 q^{36} +3.67692e20 q^{37} +2.53635e21 q^{38} -1.26450e21 q^{39} -8.10334e21 q^{40} +3.60988e21 q^{41} +4.82997e20 q^{42} +1.19560e22 q^{43} +1.73819e21 q^{44} -1.45116e22 q^{45} +1.31117e21 q^{46} +8.26632e21 q^{47} -3.01007e22 q^{48} -6.52509e22 q^{49} +1.69414e23 q^{50} -5.23263e22 q^{51} +1.48794e22 q^{52} +1.60547e23 q^{53} -2.38496e23 q^{54} -3.33619e23 q^{55} -3.57655e22 q^{56} +5.23866e23 q^{57} -1.30923e23 q^{58} +1.09336e24 q^{59} -2.65962e23 q^{60} -1.32576e24 q^{61} -6.50790e23 q^{62} -6.40495e22 q^{63} +2.68574e24 q^{64} -2.85586e24 q^{65} -1.54123e24 q^{66} +6.27072e24 q^{67} +6.15722e23 q^{68} +2.70814e23 q^{69} +1.09084e24 q^{70} -1.65578e25 q^{71} +4.96422e24 q^{72} -7.93292e24 q^{73} +3.83635e24 q^{74} +3.49914e25 q^{75} -6.16433e24 q^{76} -1.47249e24 q^{77} -1.31933e25 q^{78} +1.61913e25 q^{79} -6.79823e25 q^{80} -2.65232e25 q^{81} +3.76641e25 q^{82} +1.00338e26 q^{83} -1.17387e24 q^{84} -1.18178e26 q^{85} +1.24744e26 q^{86} -2.70414e25 q^{87} +1.14127e26 q^{88} -1.72766e26 q^{89} -1.51408e26 q^{90} -1.26049e25 q^{91} -3.18667e24 q^{92} -1.34416e26 q^{93} +8.62475e25 q^{94} +1.18315e27 q^{95} +1.67507e26 q^{96} -1.03077e27 q^{97} -6.80802e26 q^{98} +2.04380e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 8280q^{2} - 1286280q^{3} + 190623296q^{4} + 5443587900q^{5} + 86882873184q^{6} - 175391963600q^{7} - 3195032348160q^{8} + 1235136554154q^{9} + O(q^{10}) \) \( 2q - 8280q^{2} - 1286280q^{3} + 190623296q^{4} + 5443587900q^{5} + 86882873184q^{6} - 175391963600q^{7} - 3195032348160q^{8} + 1235136554154q^{9} + 39991096148400q^{10} + 138167337691944q^{11} - 797895007176960q^{12} - 753433801271060q^{13} + 3908340052811712q^{14} + 8504300488438800q^{15} - 14322995785166848q^{16} - 29753620331011740q^{17} - 110019470226337080q^{18} + 404565810372684760q^{19} + 1109219331427200q^{20} + 723787313583184704q^{21} - 4583556785578779360q^{22} + 2929078923121218960q^{23} + 1677495533792532480q^{24} + 9119218786673228750q^{25} - 3003459254146640016q^{26} - 11127665129740313040q^{27} - 43065656535315868160q^{28} - 15546679995448558260q^{29} + \)\(14\!\cdots\!00\)\(q^{30} + 28544554594467385024q^{31} + \)\(28\!\cdots\!20\)\(q^{32} - \)\(85\!\cdots\!60\)\(q^{33} - \)\(15\!\cdots\!68\)\(q^{34} - 8958395384765013600q^{35} + \)\(98\!\cdots\!92\)\(q^{36} + \)\(18\!\cdots\!80\)\(q^{37} - \)\(48\!\cdots\!40\)\(q^{38} - \)\(69\!\cdots\!72\)\(q^{39} - \)\(89\!\cdots\!00\)\(q^{40} + \)\(90\!\cdots\!64\)\(q^{41} - \)\(12\!\cdots\!40\)\(q^{42} + \)\(51\!\cdots\!00\)\(q^{43} + \)\(46\!\cdots\!12\)\(q^{44} - \)\(12\!\cdots\!00\)\(q^{45} - \)\(51\!\cdots\!16\)\(q^{46} - \)\(11\!\cdots\!60\)\(q^{47} - \)\(28\!\cdots\!40\)\(q^{48} - \)\(92\!\cdots\!14\)\(q^{49} + \)\(30\!\cdots\!00\)\(q^{50} - \)\(33\!\cdots\!56\)\(q^{51} - \)\(21\!\cdots\!00\)\(q^{52} + \)\(10\!\cdots\!20\)\(q^{53} - \)\(45\!\cdots\!40\)\(q^{54} - \)\(21\!\cdots\!00\)\(q^{55} + \)\(26\!\cdots\!40\)\(q^{56} - \)\(31\!\cdots\!80\)\(q^{57} - \)\(74\!\cdots\!60\)\(q^{58} + \)\(20\!\cdots\!80\)\(q^{59} - \)\(69\!\cdots\!00\)\(q^{60} + \)\(14\!\cdots\!44\)\(q^{61} - \)\(23\!\cdots\!60\)\(q^{62} - \)\(89\!\cdots\!20\)\(q^{63} - \)\(12\!\cdots\!24\)\(q^{64} - \)\(29\!\cdots\!00\)\(q^{65} + \)\(11\!\cdots\!48\)\(q^{66} + \)\(30\!\cdots\!60\)\(q^{67} - \)\(56\!\cdots\!80\)\(q^{68} - \)\(93\!\cdots\!72\)\(q^{69} + \)\(32\!\cdots\!00\)\(q^{70} - \)\(13\!\cdots\!16\)\(q^{71} - \)\(14\!\cdots\!20\)\(q^{72} + \)\(52\!\cdots\!60\)\(q^{73} - \)\(24\!\cdots\!28\)\(q^{74} + \)\(59\!\cdots\!00\)\(q^{75} + \)\(28\!\cdots\!80\)\(q^{76} - \)\(42\!\cdots\!00\)\(q^{77} - \)\(23\!\cdots\!00\)\(q^{78} + \)\(62\!\cdots\!40\)\(q^{79} - \)\(68\!\cdots\!00\)\(q^{80} - \)\(99\!\cdots\!78\)\(q^{81} - \)\(64\!\cdots\!60\)\(q^{82} + \)\(17\!\cdots\!80\)\(q^{83} + \)\(14\!\cdots\!92\)\(q^{84} - \)\(12\!\cdots\!00\)\(q^{85} + \)\(25\!\cdots\!84\)\(q^{86} - \)\(16\!\cdots\!20\)\(q^{87} - \)\(20\!\cdots\!20\)\(q^{88} - \)\(31\!\cdots\!80\)\(q^{89} - \)\(19\!\cdots\!00\)\(q^{90} + \)\(20\!\cdots\!04\)\(q^{91} + \)\(60\!\cdots\!60\)\(q^{92} - \)\(44\!\cdots\!60\)\(q^{93} + \)\(26\!\cdots\!92\)\(q^{94} + \)\(12\!\cdots\!00\)\(q^{95} - \)\(56\!\cdots\!56\)\(q^{96} - \)\(65\!\cdots\!60\)\(q^{97} - \)\(17\!\cdots\!40\)\(q^{98} + \)\(10\!\cdots\!88\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10433.6 0.900594 0.450297 0.892879i \(-0.351318\pi\)
0.450297 + 0.892879i \(0.351318\pi\)
\(3\) 2.15499e6 0.780384 0.390192 0.920733i \(-0.372409\pi\)
0.390192 + 0.920733i \(0.372409\pi\)
\(4\) −2.53577e7 −0.188930
\(5\) 4.86703e9 1.78307 0.891536 0.452950i \(-0.149629\pi\)
0.891536 + 0.452950i \(0.149629\pi\)
\(6\) 2.24843e10 0.702810
\(7\) 2.14815e10 0.0837994 0.0418997 0.999122i \(-0.486659\pi\)
0.0418997 + 0.999122i \(0.486659\pi\)
\(8\) −1.66495e12 −1.07074
\(9\) −2.98161e12 −0.391000
\(10\) 5.07806e13 1.60582
\(11\) −6.85469e13 −0.598668 −0.299334 0.954148i \(-0.596765\pi\)
−0.299334 + 0.954148i \(0.596765\pi\)
\(12\) −5.46457e13 −0.147438
\(13\) −5.86777e14 −0.537326 −0.268663 0.963234i \(-0.586582\pi\)
−0.268663 + 0.963234i \(0.586582\pi\)
\(14\) 2.24129e14 0.0754693
\(15\) 1.04884e16 1.39148
\(16\) −1.39679e16 −0.775376
\(17\) −2.42814e16 −0.594585 −0.297292 0.954786i \(-0.596084\pi\)
−0.297292 + 0.954786i \(0.596084\pi\)
\(18\) −3.11089e16 −0.352133
\(19\) 2.43094e17 1.32618 0.663088 0.748541i \(-0.269245\pi\)
0.663088 + 0.748541i \(0.269245\pi\)
\(20\) −1.23417e17 −0.336876
\(21\) 4.62924e16 0.0653957
\(22\) −7.15190e17 −0.539157
\(23\) 1.25668e17 0.0519877 0.0259938 0.999662i \(-0.491725\pi\)
0.0259938 + 0.999662i \(0.491725\pi\)
\(24\) −3.58794e18 −0.835591
\(25\) 1.62374e19 2.17934
\(26\) −6.12220e18 −0.483913
\(27\) −2.28584e19 −1.08551
\(28\) −5.44722e17 −0.0158322
\(29\) −1.25483e19 −0.227096 −0.113548 0.993532i \(-0.536222\pi\)
−0.113548 + 0.993532i \(0.536222\pi\)
\(30\) 1.09432e20 1.25316
\(31\) −6.23745e19 −0.458801 −0.229400 0.973332i \(-0.573677\pi\)
−0.229400 + 0.973332i \(0.573677\pi\)
\(32\) 7.77296e19 0.372445
\(33\) −1.47718e20 −0.467191
\(34\) −2.53343e20 −0.535480
\(35\) 1.04551e20 0.149420
\(36\) 7.56070e19 0.0738717
\(37\) 3.67692e20 0.248177 0.124088 0.992271i \(-0.460399\pi\)
0.124088 + 0.992271i \(0.460399\pi\)
\(38\) 2.53635e21 1.19435
\(39\) −1.26450e21 −0.419321
\(40\) −8.10334e21 −1.90921
\(41\) 3.60988e21 0.609412 0.304706 0.952446i \(-0.401442\pi\)
0.304706 + 0.952446i \(0.401442\pi\)
\(42\) 4.82997e20 0.0588950
\(43\) 1.19560e22 1.06111 0.530555 0.847651i \(-0.321984\pi\)
0.530555 + 0.847651i \(0.321984\pi\)
\(44\) 1.73819e21 0.113106
\(45\) −1.45116e22 −0.697182
\(46\) 1.31117e21 0.0468198
\(47\) 8.26632e21 0.220796 0.110398 0.993887i \(-0.464787\pi\)
0.110398 + 0.993887i \(0.464787\pi\)
\(48\) −3.01007e22 −0.605091
\(49\) −6.52509e22 −0.992978
\(50\) 1.69414e23 1.96270
\(51\) −5.23263e22 −0.464005
\(52\) 1.48794e22 0.101517
\(53\) 1.60547e23 0.846991 0.423496 0.905898i \(-0.360803\pi\)
0.423496 + 0.905898i \(0.360803\pi\)
\(54\) −2.38496e23 −0.977608
\(55\) −3.33619e23 −1.06747
\(56\) −3.57655e22 −0.0897277
\(57\) 5.23866e23 1.03493
\(58\) −1.30923e23 −0.204522
\(59\) 1.09336e24 1.35601 0.678004 0.735058i \(-0.262845\pi\)
0.678004 + 0.735058i \(0.262845\pi\)
\(60\) −2.65962e23 −0.262892
\(61\) −1.32576e24 −1.04837 −0.524183 0.851606i \(-0.675629\pi\)
−0.524183 + 0.851606i \(0.675629\pi\)
\(62\) −6.50790e23 −0.413193
\(63\) −6.40495e22 −0.0327656
\(64\) 2.68574e24 1.11080
\(65\) −2.85586e24 −0.958091
\(66\) −1.54123e24 −0.420750
\(67\) 6.27072e24 1.39736 0.698679 0.715435i \(-0.253771\pi\)
0.698679 + 0.715435i \(0.253771\pi\)
\(68\) 6.15722e23 0.112335
\(69\) 2.70814e23 0.0405704
\(70\) 1.09084e24 0.134567
\(71\) −1.65578e25 −1.68661 −0.843303 0.537438i \(-0.819392\pi\)
−0.843303 + 0.537438i \(0.819392\pi\)
\(72\) 4.96422e24 0.418661
\(73\) −7.93292e24 −0.555360 −0.277680 0.960674i \(-0.589565\pi\)
−0.277680 + 0.960674i \(0.589565\pi\)
\(74\) 3.83635e24 0.223506
\(75\) 3.49914e25 1.70073
\(76\) −6.16433e24 −0.250554
\(77\) −1.47249e24 −0.0501680
\(78\) −1.31933e25 −0.377638
\(79\) 1.61913e25 0.390227 0.195113 0.980781i \(-0.437493\pi\)
0.195113 + 0.980781i \(0.437493\pi\)
\(80\) −6.79823e25 −1.38255
\(81\) −2.65232e25 −0.456118
\(82\) 3.76641e25 0.548833
\(83\) 1.00338e26 1.24140 0.620698 0.784049i \(-0.286849\pi\)
0.620698 + 0.784049i \(0.286849\pi\)
\(84\) −1.17387e24 −0.0123552
\(85\) −1.18178e26 −1.06019
\(86\) 1.24744e26 0.955630
\(87\) −2.70414e25 −0.177223
\(88\) 1.14127e26 0.641020
\(89\) −1.72766e26 −0.833092 −0.416546 0.909115i \(-0.636759\pi\)
−0.416546 + 0.909115i \(0.636759\pi\)
\(90\) −1.51408e26 −0.627878
\(91\) −1.26049e25 −0.0450276
\(92\) −3.18667e24 −0.00982203
\(93\) −1.34416e26 −0.358041
\(94\) 8.62475e25 0.198848
\(95\) 1.18315e27 2.36467
\(96\) 1.67507e26 0.290650
\(97\) −1.03077e27 −1.55505 −0.777524 0.628853i \(-0.783525\pi\)
−0.777524 + 0.628853i \(0.783525\pi\)
\(98\) −6.80802e26 −0.894270
\(99\) 2.04380e26 0.234080
\(100\) −4.11743e26 −0.411743
\(101\) 4.65230e26 0.406751 0.203376 0.979101i \(-0.434809\pi\)
0.203376 + 0.979101i \(0.434809\pi\)
\(102\) −5.45951e26 −0.417880
\(103\) 7.02209e26 0.471155 0.235577 0.971856i \(-0.424302\pi\)
0.235577 + 0.971856i \(0.424302\pi\)
\(104\) 9.76953e26 0.575339
\(105\) 2.25306e26 0.116605
\(106\) 1.67509e27 0.762795
\(107\) −3.21175e27 −1.28843 −0.644215 0.764845i \(-0.722816\pi\)
−0.644215 + 0.764845i \(0.722816\pi\)
\(108\) 5.79639e26 0.205086
\(109\) 1.11613e27 0.348705 0.174353 0.984683i \(-0.444217\pi\)
0.174353 + 0.984683i \(0.444217\pi\)
\(110\) −3.48085e27 −0.961356
\(111\) 7.92373e26 0.193673
\(112\) −3.00052e26 −0.0649760
\(113\) −3.24502e27 −0.623244 −0.311622 0.950206i \(-0.600872\pi\)
−0.311622 + 0.950206i \(0.600872\pi\)
\(114\) 5.46581e27 0.932050
\(115\) 6.11632e26 0.0926978
\(116\) 3.18196e26 0.0429053
\(117\) 1.74954e27 0.210095
\(118\) 1.14077e28 1.22121
\(119\) −5.21601e26 −0.0498258
\(120\) −1.74626e28 −1.48992
\(121\) −8.41132e27 −0.641596
\(122\) −1.38325e28 −0.944152
\(123\) 7.77927e27 0.475576
\(124\) 1.58168e27 0.0866812
\(125\) 4.27656e28 2.10285
\(126\) −6.68266e26 −0.0295085
\(127\) −3.05563e28 −1.21269 −0.606346 0.795201i \(-0.707365\pi\)
−0.606346 + 0.795201i \(0.707365\pi\)
\(128\) 1.75893e28 0.627933
\(129\) 2.57650e28 0.828074
\(130\) −2.97969e28 −0.862852
\(131\) −3.92050e28 −1.02371 −0.511857 0.859071i \(-0.671042\pi\)
−0.511857 + 0.859071i \(0.671042\pi\)
\(132\) 3.74579e27 0.0882664
\(133\) 5.22203e27 0.111133
\(134\) 6.54262e28 1.25845
\(135\) −1.11253e29 −1.93555
\(136\) 4.04273e28 0.636648
\(137\) −1.05475e28 −0.150461 −0.0752305 0.997166i \(-0.523969\pi\)
−0.0752305 + 0.997166i \(0.523969\pi\)
\(138\) 2.82557e27 0.0365374
\(139\) 1.42615e29 1.67289 0.836443 0.548054i \(-0.184631\pi\)
0.836443 + 0.548054i \(0.184631\pi\)
\(140\) −2.65118e27 −0.0282300
\(141\) 1.78138e28 0.172306
\(142\) −1.72757e29 −1.51895
\(143\) 4.02217e28 0.321680
\(144\) 4.16469e28 0.303172
\(145\) −6.10727e28 −0.404929
\(146\) −8.27689e28 −0.500154
\(147\) −1.40615e29 −0.774904
\(148\) −9.32384e27 −0.0468880
\(149\) 1.04309e29 0.478968 0.239484 0.970900i \(-0.423022\pi\)
0.239484 + 0.970900i \(0.423022\pi\)
\(150\) 3.65086e29 1.53166
\(151\) 3.58958e29 1.37675 0.688374 0.725356i \(-0.258325\pi\)
0.688374 + 0.725356i \(0.258325\pi\)
\(152\) −4.04739e29 −1.42000
\(153\) 7.23978e28 0.232483
\(154\) −1.53634e28 −0.0451811
\(155\) −3.03578e29 −0.818074
\(156\) 3.20649e28 0.0792223
\(157\) −6.56383e29 −1.48769 −0.743844 0.668353i \(-0.767000\pi\)
−0.743844 + 0.668353i \(0.767000\pi\)
\(158\) 1.68934e29 0.351436
\(159\) 3.45978e29 0.660979
\(160\) 3.78312e29 0.664096
\(161\) 2.69955e27 0.00435654
\(162\) −2.76732e29 −0.410778
\(163\) 3.98777e29 0.544750 0.272375 0.962191i \(-0.412191\pi\)
0.272375 + 0.962191i \(0.412191\pi\)
\(164\) −9.15385e28 −0.115136
\(165\) −7.18947e29 −0.833036
\(166\) 1.04689e30 1.11799
\(167\) 6.97711e29 0.687074 0.343537 0.939139i \(-0.388375\pi\)
0.343537 + 0.939139i \(0.388375\pi\)
\(168\) −7.70744e28 −0.0700221
\(169\) −8.48226e29 −0.711280
\(170\) −1.23303e30 −0.954799
\(171\) −7.24813e29 −0.518536
\(172\) −3.03176e29 −0.200475
\(173\) 1.20460e30 0.736580 0.368290 0.929711i \(-0.379943\pi\)
0.368290 + 0.929711i \(0.379943\pi\)
\(174\) −2.82139e29 −0.159606
\(175\) 3.48803e29 0.182628
\(176\) 9.57457e29 0.464193
\(177\) 2.35619e30 1.05821
\(178\) −1.80257e30 −0.750278
\(179\) 3.25033e30 1.25433 0.627164 0.778887i \(-0.284215\pi\)
0.627164 + 0.778887i \(0.284215\pi\)
\(180\) 3.67981e29 0.131718
\(181\) −5.16248e30 −1.71474 −0.857369 0.514702i \(-0.827903\pi\)
−0.857369 + 0.514702i \(0.827903\pi\)
\(182\) −1.31514e29 −0.0405516
\(183\) −2.85700e30 −0.818128
\(184\) −2.09231e29 −0.0556655
\(185\) 1.78957e30 0.442517
\(186\) −1.40245e30 −0.322450
\(187\) 1.66442e30 0.355959
\(188\) −2.09615e29 −0.0417150
\(189\) −4.91033e29 −0.0909655
\(190\) 1.23445e31 2.12961
\(191\) −5.77134e30 −0.927526 −0.463763 0.885959i \(-0.653501\pi\)
−0.463763 + 0.885959i \(0.653501\pi\)
\(192\) 5.78775e30 0.866849
\(193\) −2.85746e30 −0.398985 −0.199492 0.979899i \(-0.563929\pi\)
−0.199492 + 0.979899i \(0.563929\pi\)
\(194\) −1.07547e31 −1.40047
\(195\) −6.15436e30 −0.747679
\(196\) 1.65462e30 0.187603
\(197\) 1.69381e31 1.79296 0.896482 0.443081i \(-0.146115\pi\)
0.896482 + 0.443081i \(0.146115\pi\)
\(198\) 2.13242e30 0.210811
\(199\) −8.37737e30 −0.773733 −0.386866 0.922136i \(-0.626443\pi\)
−0.386866 + 0.922136i \(0.626443\pi\)
\(200\) −2.70344e31 −2.33352
\(201\) 1.35134e31 1.09048
\(202\) 4.85402e30 0.366318
\(203\) −2.69555e29 −0.0190305
\(204\) 1.32688e30 0.0876644
\(205\) 1.75694e31 1.08663
\(206\) 7.32657e30 0.424319
\(207\) −3.74695e29 −0.0203272
\(208\) 8.19606e30 0.416630
\(209\) −1.66634e31 −0.793940
\(210\) 2.35076e30 0.105014
\(211\) −1.95424e31 −0.818776 −0.409388 0.912360i \(-0.634258\pi\)
−0.409388 + 0.912360i \(0.634258\pi\)
\(212\) −4.07112e30 −0.160022
\(213\) −3.56818e31 −1.31620
\(214\) −3.35101e31 −1.16035
\(215\) 5.81900e31 1.89204
\(216\) 3.80581e31 1.16231
\(217\) −1.33990e30 −0.0384472
\(218\) 1.16453e31 0.314042
\(219\) −1.70954e31 −0.433394
\(220\) 8.45984e30 0.201677
\(221\) 1.42478e31 0.319486
\(222\) 8.26730e30 0.174421
\(223\) −5.21969e30 −0.103640 −0.0518202 0.998656i \(-0.516502\pi\)
−0.0518202 + 0.998656i \(0.516502\pi\)
\(224\) 1.66975e30 0.0312106
\(225\) −4.84136e31 −0.852124
\(226\) −3.38572e31 −0.561290
\(227\) −1.42268e31 −0.222208 −0.111104 0.993809i \(-0.535439\pi\)
−0.111104 + 0.993809i \(0.535439\pi\)
\(228\) −1.32841e31 −0.195529
\(229\) 4.79201e31 0.664874 0.332437 0.943126i \(-0.392129\pi\)
0.332437 + 0.943126i \(0.392129\pi\)
\(230\) 6.38152e30 0.0834831
\(231\) −3.17320e30 −0.0391504
\(232\) 2.08922e31 0.243162
\(233\) −1.09089e31 −0.119805 −0.0599025 0.998204i \(-0.519079\pi\)
−0.0599025 + 0.998204i \(0.519079\pi\)
\(234\) 1.82540e31 0.189210
\(235\) 4.02324e31 0.393695
\(236\) −2.77252e31 −0.256190
\(237\) 3.48922e31 0.304527
\(238\) −5.44218e30 −0.0448729
\(239\) 1.93175e32 1.50515 0.752573 0.658509i \(-0.228813\pi\)
0.752573 + 0.658509i \(0.228813\pi\)
\(240\) −1.46501e32 −1.07892
\(241\) −1.37107e32 −0.954619 −0.477310 0.878735i \(-0.658388\pi\)
−0.477310 + 0.878735i \(0.658388\pi\)
\(242\) −8.77604e31 −0.577818
\(243\) 1.17152e32 0.729567
\(244\) 3.36183e31 0.198068
\(245\) −3.17578e32 −1.77055
\(246\) 8.11657e31 0.428301
\(247\) −1.42642e32 −0.712590
\(248\) 1.03850e32 0.491258
\(249\) 2.16227e32 0.968767
\(250\) 4.46199e32 1.89382
\(251\) 6.44860e31 0.259341 0.129670 0.991557i \(-0.458608\pi\)
0.129670 + 0.991557i \(0.458608\pi\)
\(252\) 1.62415e30 0.00619040
\(253\) −8.61418e30 −0.0311234
\(254\) −3.18812e32 −1.09214
\(255\) −2.54673e32 −0.827353
\(256\) −1.76955e32 −0.545284
\(257\) −1.37557e32 −0.402147 −0.201073 0.979576i \(-0.564443\pi\)
−0.201073 + 0.979576i \(0.564443\pi\)
\(258\) 2.68822e32 0.745758
\(259\) 7.89857e30 0.0207971
\(260\) 7.24182e31 0.181012
\(261\) 3.74140e31 0.0887948
\(262\) −4.09049e32 −0.921951
\(263\) −6.29327e31 −0.134733 −0.0673665 0.997728i \(-0.521460\pi\)
−0.0673665 + 0.997728i \(0.521460\pi\)
\(264\) 2.45942e32 0.500242
\(265\) 7.81388e32 1.51025
\(266\) 5.44846e31 0.100086
\(267\) −3.72309e32 −0.650132
\(268\) −1.59011e32 −0.264003
\(269\) 7.34021e32 1.15892 0.579459 0.815001i \(-0.303264\pi\)
0.579459 + 0.815001i \(0.303264\pi\)
\(270\) −1.16077e33 −1.74315
\(271\) 6.75590e32 0.965156 0.482578 0.875853i \(-0.339700\pi\)
0.482578 + 0.875853i \(0.339700\pi\)
\(272\) 3.39161e32 0.461027
\(273\) −2.71633e31 −0.0351388
\(274\) −1.10049e32 −0.135504
\(275\) −1.11302e33 −1.30470
\(276\) −6.86724e30 −0.00766496
\(277\) −1.48766e33 −1.58134 −0.790671 0.612241i \(-0.790268\pi\)
−0.790671 + 0.612241i \(0.790268\pi\)
\(278\) 1.48799e33 1.50659
\(279\) 1.85976e32 0.179391
\(280\) −1.74072e32 −0.159991
\(281\) 9.53617e32 0.835293 0.417646 0.908610i \(-0.362855\pi\)
0.417646 + 0.908610i \(0.362855\pi\)
\(282\) 1.85863e32 0.155178
\(283\) −1.55041e33 −1.23404 −0.617022 0.786946i \(-0.711661\pi\)
−0.617022 + 0.786946i \(0.711661\pi\)
\(284\) 4.19867e32 0.318650
\(285\) 2.54967e33 1.84535
\(286\) 4.19658e32 0.289703
\(287\) 7.75457e31 0.0510684
\(288\) −2.31760e32 −0.145626
\(289\) −1.07812e33 −0.646469
\(290\) −6.37208e32 −0.364677
\(291\) −2.22130e33 −1.21354
\(292\) 2.01161e32 0.104924
\(293\) −2.76230e33 −1.37581 −0.687903 0.725802i \(-0.741469\pi\)
−0.687903 + 0.725802i \(0.741469\pi\)
\(294\) −1.46712e33 −0.697874
\(295\) 5.32143e33 2.41786
\(296\) −6.12187e32 −0.265734
\(297\) 1.56687e33 0.649863
\(298\) 1.08832e33 0.431355
\(299\) −7.37394e31 −0.0279344
\(300\) −8.87303e32 −0.321318
\(301\) 2.56832e32 0.0889204
\(302\) 3.74522e33 1.23989
\(303\) 1.00257e33 0.317422
\(304\) −3.39552e33 −1.02828
\(305\) −6.45252e33 −1.86931
\(306\) 7.55370e32 0.209373
\(307\) 4.04426e33 1.07268 0.536341 0.844001i \(-0.319806\pi\)
0.536341 + 0.844001i \(0.319806\pi\)
\(308\) 3.73390e31 0.00947825
\(309\) 1.51325e33 0.367682
\(310\) −3.16741e33 −0.736753
\(311\) −2.20209e33 −0.490423 −0.245211 0.969470i \(-0.578857\pi\)
−0.245211 + 0.969470i \(0.578857\pi\)
\(312\) 2.10532e33 0.448985
\(313\) 1.52934e33 0.312361 0.156180 0.987729i \(-0.450082\pi\)
0.156180 + 0.987729i \(0.450082\pi\)
\(314\) −6.84844e33 −1.33980
\(315\) −3.11731e32 −0.0584234
\(316\) −4.10576e32 −0.0737255
\(317\) 5.64949e33 0.972096 0.486048 0.873932i \(-0.338438\pi\)
0.486048 + 0.873932i \(0.338438\pi\)
\(318\) 3.60980e33 0.595273
\(319\) 8.60143e32 0.135955
\(320\) 1.30716e34 1.98063
\(321\) −6.92129e33 −1.00547
\(322\) 2.81660e31 0.00392347
\(323\) −5.90268e33 −0.788525
\(324\) 6.72568e32 0.0861744
\(325\) −9.52773e33 −1.17102
\(326\) 4.16067e33 0.490598
\(327\) 2.40526e33 0.272124
\(328\) −6.01026e33 −0.652524
\(329\) 1.77573e32 0.0185026
\(330\) −7.50120e33 −0.750227
\(331\) −1.79482e33 −0.172323 −0.0861616 0.996281i \(-0.527460\pi\)
−0.0861616 + 0.996281i \(0.527460\pi\)
\(332\) −2.54434e33 −0.234537
\(333\) −1.09631e33 −0.0970372
\(334\) 7.27964e33 0.618775
\(335\) 3.05198e34 2.49159
\(336\) −6.46609e32 −0.0507062
\(337\) 3.56328e33 0.268439 0.134220 0.990952i \(-0.457147\pi\)
0.134220 + 0.990952i \(0.457147\pi\)
\(338\) −8.85005e33 −0.640575
\(339\) −6.99298e33 −0.486370
\(340\) 2.99674e33 0.200301
\(341\) 4.27557e33 0.274669
\(342\) −7.56241e33 −0.466990
\(343\) −2.81329e33 −0.167010
\(344\) −1.99060e34 −1.13618
\(345\) 1.31806e33 0.0723399
\(346\) 1.25683e34 0.663359
\(347\) −2.88728e34 −1.46569 −0.732843 0.680398i \(-0.761807\pi\)
−0.732843 + 0.680398i \(0.761807\pi\)
\(348\) 6.85708e32 0.0334826
\(349\) 1.78587e34 0.838893 0.419447 0.907780i \(-0.362224\pi\)
0.419447 + 0.907780i \(0.362224\pi\)
\(350\) 3.63927e33 0.164473
\(351\) 1.34128e34 0.583276
\(352\) −5.32812e33 −0.222971
\(353\) 2.71254e34 1.09249 0.546245 0.837626i \(-0.316057\pi\)
0.546245 + 0.837626i \(0.316057\pi\)
\(354\) 2.45835e34 0.953015
\(355\) −8.05870e34 −3.00734
\(356\) 4.38095e33 0.157396
\(357\) −1.12405e33 −0.0388833
\(358\) 3.39126e34 1.12964
\(359\) 2.08159e34 0.667760 0.333880 0.942616i \(-0.391642\pi\)
0.333880 + 0.942616i \(0.391642\pi\)
\(360\) 2.41610e34 0.746503
\(361\) 2.54943e34 0.758744
\(362\) −5.38633e34 −1.54428
\(363\) −1.81263e34 −0.500692
\(364\) 3.19631e32 0.00850707
\(365\) −3.86097e34 −0.990246
\(366\) −2.98088e34 −0.736801
\(367\) 1.50702e34 0.359028 0.179514 0.983755i \(-0.442547\pi\)
0.179514 + 0.983755i \(0.442547\pi\)
\(368\) −1.75533e33 −0.0403100
\(369\) −1.07633e34 −0.238280
\(370\) 1.86716e34 0.398528
\(371\) 3.44880e33 0.0709773
\(372\) 3.40850e33 0.0676446
\(373\) 3.06644e34 0.586901 0.293451 0.955974i \(-0.405196\pi\)
0.293451 + 0.955974i \(0.405196\pi\)
\(374\) 1.73658e34 0.320575
\(375\) 9.21594e34 1.64103
\(376\) −1.37630e34 −0.236416
\(377\) 7.36303e33 0.122025
\(378\) −5.12324e33 −0.0819230
\(379\) −2.54352e34 −0.392470 −0.196235 0.980557i \(-0.562872\pi\)
−0.196235 + 0.980557i \(0.562872\pi\)
\(380\) −3.00020e34 −0.446757
\(381\) −6.58485e34 −0.946365
\(382\) −6.02158e34 −0.835325
\(383\) 2.05837e34 0.275638 0.137819 0.990457i \(-0.455991\pi\)
0.137819 + 0.990457i \(0.455991\pi\)
\(384\) 3.79047e34 0.490029
\(385\) −7.16664e33 −0.0894532
\(386\) −2.98136e34 −0.359323
\(387\) −3.56480e34 −0.414894
\(388\) 2.61380e34 0.293795
\(389\) 6.64448e34 0.721342 0.360671 0.932693i \(-0.382548\pi\)
0.360671 + 0.932693i \(0.382548\pi\)
\(390\) −6.42121e34 −0.673356
\(391\) −3.05141e33 −0.0309111
\(392\) 1.08639e35 1.06322
\(393\) −8.44864e34 −0.798891
\(394\) 1.76726e35 1.61473
\(395\) 7.88037e34 0.695802
\(396\) −5.18262e33 −0.0442246
\(397\) −7.11637e34 −0.586931 −0.293465 0.955970i \(-0.594809\pi\)
−0.293465 + 0.955970i \(0.594809\pi\)
\(398\) −8.74061e34 −0.696819
\(399\) 1.12534e34 0.0867263
\(400\) −2.26802e35 −1.68981
\(401\) 7.78771e34 0.560997 0.280499 0.959854i \(-0.409500\pi\)
0.280499 + 0.959854i \(0.409500\pi\)
\(402\) 1.40993e35 0.982077
\(403\) 3.65999e34 0.246526
\(404\) −1.17972e34 −0.0768475
\(405\) −1.29089e35 −0.813292
\(406\) −2.81243e33 −0.0171388
\(407\) −2.52041e34 −0.148575
\(408\) 8.71204e34 0.496830
\(409\) −3.21718e35 −1.77505 −0.887526 0.460758i \(-0.847578\pi\)
−0.887526 + 0.460758i \(0.847578\pi\)
\(410\) 1.83312e35 0.978609
\(411\) −2.27299e34 −0.117417
\(412\) −1.78064e34 −0.0890153
\(413\) 2.34871e34 0.113633
\(414\) −3.90941e33 −0.0183066
\(415\) 4.88347e35 2.21350
\(416\) −4.56100e34 −0.200124
\(417\) 3.07335e35 1.30549
\(418\) −1.73859e35 −0.715018
\(419\) −4.31477e35 −1.71818 −0.859089 0.511827i \(-0.828969\pi\)
−0.859089 + 0.511827i \(0.828969\pi\)
\(420\) −5.71326e33 −0.0220302
\(421\) 5.01390e35 1.87227 0.936133 0.351647i \(-0.114378\pi\)
0.936133 + 0.351647i \(0.114378\pi\)
\(422\) −2.03898e35 −0.737385
\(423\) −2.46470e34 −0.0863313
\(424\) −2.67303e35 −0.906910
\(425\) −3.94267e35 −1.29580
\(426\) −3.72290e35 −1.18536
\(427\) −2.84793e34 −0.0878524
\(428\) 8.14427e34 0.243423
\(429\) 8.66775e34 0.251034
\(430\) 6.07131e35 1.70396
\(431\) 1.64027e35 0.446141 0.223070 0.974802i \(-0.428392\pi\)
0.223070 + 0.974802i \(0.428392\pi\)
\(432\) 3.19285e35 0.841682
\(433\) −1.75800e33 −0.00449193 −0.00224596 0.999997i \(-0.500715\pi\)
−0.00224596 + 0.999997i \(0.500715\pi\)
\(434\) −1.39799e34 −0.0346253
\(435\) −1.31611e35 −0.316000
\(436\) −2.83027e34 −0.0658809
\(437\) 3.05493e34 0.0689449
\(438\) −1.78366e35 −0.390312
\(439\) −3.72911e35 −0.791287 −0.395644 0.918404i \(-0.629478\pi\)
−0.395644 + 0.918404i \(0.629478\pi\)
\(440\) 5.55459e35 1.14298
\(441\) 1.94553e35 0.388255
\(442\) 1.48656e35 0.287727
\(443\) −5.23878e35 −0.983513 −0.491756 0.870733i \(-0.663645\pi\)
−0.491756 + 0.870733i \(0.663645\pi\)
\(444\) −2.00928e34 −0.0365907
\(445\) −8.40856e35 −1.48546
\(446\) −5.44602e34 −0.0933380
\(447\) 2.24784e35 0.373779
\(448\) 5.76938e34 0.0930841
\(449\) 6.50462e35 1.01835 0.509174 0.860664i \(-0.329951\pi\)
0.509174 + 0.860664i \(0.329951\pi\)
\(450\) −5.05128e35 −0.767418
\(451\) −2.47446e35 −0.364836
\(452\) 8.22863e34 0.117749
\(453\) 7.73550e35 1.07439
\(454\) −1.48437e35 −0.200119
\(455\) −6.13482e34 −0.0802875
\(456\) −8.72209e35 −1.10814
\(457\) 9.00061e35 1.11020 0.555102 0.831782i \(-0.312679\pi\)
0.555102 + 0.831782i \(0.312679\pi\)
\(458\) 4.99979e35 0.598781
\(459\) 5.55036e35 0.645431
\(460\) −1.55096e34 −0.0175134
\(461\) 3.94034e35 0.432087 0.216043 0.976384i \(-0.430685\pi\)
0.216043 + 0.976384i \(0.430685\pi\)
\(462\) −3.31079e34 −0.0352586
\(463\) −1.39468e36 −1.44255 −0.721276 0.692648i \(-0.756444\pi\)
−0.721276 + 0.692648i \(0.756444\pi\)
\(464\) 1.75273e35 0.176085
\(465\) −6.54209e35 −0.638412
\(466\) −1.13819e35 −0.107896
\(467\) 2.87062e35 0.264361 0.132180 0.991226i \(-0.457802\pi\)
0.132180 + 0.991226i \(0.457802\pi\)
\(468\) −4.43645e34 −0.0396932
\(469\) 1.34704e35 0.117098
\(470\) 4.19769e35 0.354559
\(471\) −1.41450e36 −1.16097
\(472\) −1.82039e36 −1.45194
\(473\) −8.19544e35 −0.635253
\(474\) 3.64051e35 0.274255
\(475\) 3.94722e36 2.89020
\(476\) 1.32266e34 0.00941360
\(477\) −4.78690e35 −0.331174
\(478\) 2.01551e36 1.35553
\(479\) 8.28285e35 0.541565 0.270782 0.962641i \(-0.412718\pi\)
0.270782 + 0.962641i \(0.412718\pi\)
\(480\) 8.15259e35 0.518250
\(481\) −2.15753e35 −0.133352
\(482\) −1.43052e36 −0.859725
\(483\) 5.81750e33 0.00339977
\(484\) 2.13292e35 0.121217
\(485\) −5.01679e36 −2.77276
\(486\) 1.22232e36 0.657044
\(487\) −1.69732e36 −0.887405 −0.443702 0.896174i \(-0.646335\pi\)
−0.443702 + 0.896174i \(0.646335\pi\)
\(488\) 2.20732e36 1.12253
\(489\) 8.59360e35 0.425114
\(490\) −3.31348e36 −1.59455
\(491\) 2.68983e36 1.25929 0.629645 0.776883i \(-0.283201\pi\)
0.629645 + 0.776883i \(0.283201\pi\)
\(492\) −1.97265e35 −0.0898505
\(493\) 3.04690e35 0.135028
\(494\) −1.48827e36 −0.641754
\(495\) 9.94724e35 0.417381
\(496\) 8.71242e35 0.355743
\(497\) −3.55685e35 −0.141337
\(498\) 2.25603e36 0.872466
\(499\) −4.36140e35 −0.164160 −0.0820802 0.996626i \(-0.526156\pi\)
−0.0820802 + 0.996626i \(0.526156\pi\)
\(500\) −1.08444e36 −0.397292
\(501\) 1.50356e36 0.536182
\(502\) 6.72821e35 0.233561
\(503\) −2.16228e36 −0.730708 −0.365354 0.930869i \(-0.619052\pi\)
−0.365354 + 0.930869i \(0.619052\pi\)
\(504\) 1.06639e35 0.0350835
\(505\) 2.26429e36 0.725267
\(506\) −8.98769e34 −0.0280295
\(507\) −1.82792e36 −0.555072
\(508\) 7.74839e35 0.229114
\(509\) 4.49619e36 1.29466 0.647328 0.762211i \(-0.275886\pi\)
0.647328 + 0.762211i \(0.275886\pi\)
\(510\) −2.65716e36 −0.745110
\(511\) −1.70411e35 −0.0465388
\(512\) −4.20707e36 −1.11901
\(513\) −5.55676e36 −1.43958
\(514\) −1.43521e36 −0.362171
\(515\) 3.41767e36 0.840103
\(516\) −6.53342e35 −0.156448
\(517\) −5.66630e35 −0.132184
\(518\) 8.24105e34 0.0187297
\(519\) 2.59590e36 0.574815
\(520\) 4.75486e36 1.02587
\(521\) 9.12580e35 0.191850 0.0959250 0.995389i \(-0.469419\pi\)
0.0959250 + 0.995389i \(0.469419\pi\)
\(522\) 3.90363e35 0.0799681
\(523\) 1.44280e35 0.0288027 0.0144013 0.999896i \(-0.495416\pi\)
0.0144013 + 0.999896i \(0.495416\pi\)
\(524\) 9.94150e35 0.193410
\(525\) 7.51667e35 0.142520
\(526\) −6.56615e35 −0.121340
\(527\) 1.51454e36 0.272796
\(528\) 2.06331e36 0.362249
\(529\) −5.82742e36 −0.997297
\(530\) 8.15269e36 1.36012
\(531\) −3.25998e36 −0.530199
\(532\) −1.32419e35 −0.0209963
\(533\) −2.11820e36 −0.327453
\(534\) −3.88452e36 −0.585505
\(535\) −1.56317e37 −2.29736
\(536\) −1.04404e37 −1.49621
\(537\) 7.00443e36 0.978858
\(538\) 7.65848e36 1.04371
\(539\) 4.47274e36 0.594464
\(540\) 2.82112e36 0.365683
\(541\) 6.50406e36 0.822284 0.411142 0.911571i \(-0.365130\pi\)
0.411142 + 0.911571i \(0.365130\pi\)
\(542\) 7.04883e36 0.869214
\(543\) −1.11251e37 −1.33815
\(544\) −1.88739e36 −0.221450
\(545\) 5.43226e36 0.621767
\(546\) −2.83411e35 −0.0316458
\(547\) 1.22652e37 1.33612 0.668058 0.744109i \(-0.267126\pi\)
0.668058 + 0.744109i \(0.267126\pi\)
\(548\) 2.67462e35 0.0284266
\(549\) 3.95291e36 0.409911
\(550\) −1.16128e37 −1.17501
\(551\) −3.05041e36 −0.301170
\(552\) −4.50891e35 −0.0434405
\(553\) 3.47814e35 0.0327008
\(554\) −1.55216e37 −1.42415
\(555\) 3.85650e36 0.345333
\(556\) −3.61640e36 −0.316058
\(557\) 1.32843e37 1.13317 0.566585 0.824003i \(-0.308264\pi\)
0.566585 + 0.824003i \(0.308264\pi\)
\(558\) 1.94040e36 0.161559
\(559\) −7.01549e36 −0.570162
\(560\) −1.46036e36 −0.115857
\(561\) 3.58680e36 0.277785
\(562\) 9.94966e36 0.752260
\(563\) −1.08601e37 −0.801624 −0.400812 0.916160i \(-0.631272\pi\)
−0.400812 + 0.916160i \(0.631272\pi\)
\(564\) −4.51719e35 −0.0325537
\(565\) −1.57936e37 −1.11129
\(566\) −1.61764e37 −1.11137
\(567\) −5.69757e35 −0.0382224
\(568\) 2.75678e37 1.80592
\(569\) −1.31614e37 −0.841948 −0.420974 0.907073i \(-0.638312\pi\)
−0.420974 + 0.907073i \(0.638312\pi\)
\(570\) 2.66023e37 1.66191
\(571\) 3.26297e37 1.99079 0.995395 0.0958616i \(-0.0305606\pi\)
0.995395 + 0.0958616i \(0.0305606\pi\)
\(572\) −1.01993e36 −0.0607750
\(573\) −1.24372e37 −0.723827
\(574\) 8.09080e35 0.0459919
\(575\) 2.04053e36 0.113299
\(576\) −8.00784e36 −0.434322
\(577\) −3.67195e36 −0.194547 −0.0972733 0.995258i \(-0.531012\pi\)
−0.0972733 + 0.995258i \(0.531012\pi\)
\(578\) −1.12487e37 −0.582206
\(579\) −6.15780e36 −0.311361
\(580\) 1.54867e36 0.0765033
\(581\) 2.15541e36 0.104028
\(582\) −2.31762e37 −1.09290
\(583\) −1.10050e37 −0.507067
\(584\) 1.32079e37 0.594648
\(585\) 8.51507e36 0.374614
\(586\) −2.88207e37 −1.23904
\(587\) −9.27744e36 −0.389775 −0.194888 0.980826i \(-0.562434\pi\)
−0.194888 + 0.980826i \(0.562434\pi\)
\(588\) 3.56568e36 0.146403
\(589\) −1.51629e37 −0.608451
\(590\) 5.55216e37 2.17751
\(591\) 3.65015e37 1.39920
\(592\) −5.13589e36 −0.192430
\(593\) −5.24575e36 −0.192119 −0.0960593 0.995376i \(-0.530624\pi\)
−0.0960593 + 0.995376i \(0.530624\pi\)
\(594\) 1.63481e37 0.585263
\(595\) −2.53865e36 −0.0888431
\(596\) −2.64504e36 −0.0904913
\(597\) −1.80531e37 −0.603809
\(598\) −7.69368e35 −0.0251575
\(599\) 4.76000e37 1.52176 0.760878 0.648894i \(-0.224768\pi\)
0.760878 + 0.648894i \(0.224768\pi\)
\(600\) −5.82588e37 −1.82104
\(601\) 1.70669e37 0.521613 0.260807 0.965391i \(-0.416012\pi\)
0.260807 + 0.965391i \(0.416012\pi\)
\(602\) 2.67968e36 0.0800812
\(603\) −1.86969e37 −0.546368
\(604\) −9.10235e36 −0.260109
\(605\) −4.09381e37 −1.14401
\(606\) 1.04604e37 0.285869
\(607\) 1.00572e37 0.268800 0.134400 0.990927i \(-0.457089\pi\)
0.134400 + 0.990927i \(0.457089\pi\)
\(608\) 1.88956e37 0.493928
\(609\) −5.80889e35 −0.0148511
\(610\) −6.73230e37 −1.68349
\(611\) −4.85049e36 −0.118640
\(612\) −1.83585e36 −0.0439230
\(613\) 5.68669e37 1.33089 0.665447 0.746445i \(-0.268241\pi\)
0.665447 + 0.746445i \(0.268241\pi\)
\(614\) 4.21962e37 0.966052
\(615\) 3.78619e37 0.847985
\(616\) 2.45161e36 0.0537171
\(617\) −4.13930e37 −0.887315 −0.443657 0.896196i \(-0.646319\pi\)
−0.443657 + 0.896196i \(0.646319\pi\)
\(618\) 1.57887e37 0.331132
\(619\) −3.55328e37 −0.729131 −0.364565 0.931178i \(-0.618782\pi\)
−0.364565 + 0.931178i \(0.618782\pi\)
\(620\) 7.69806e36 0.154559
\(621\) −2.87259e36 −0.0564334
\(622\) −2.29758e37 −0.441672
\(623\) −3.71127e36 −0.0698126
\(624\) 1.76624e37 0.325131
\(625\) 8.71634e37 1.57020
\(626\) 1.59566e37 0.281310
\(627\) −3.59094e37 −0.619578
\(628\) 1.66444e37 0.281069
\(629\) −8.92809e36 −0.147562
\(630\) −3.25247e36 −0.0526158
\(631\) −7.29607e37 −1.15529 −0.577647 0.816287i \(-0.696029\pi\)
−0.577647 + 0.816287i \(0.696029\pi\)
\(632\) −2.69577e37 −0.417833
\(633\) −4.21138e37 −0.638960
\(634\) 5.89445e37 0.875464
\(635\) −1.48718e38 −2.16232
\(636\) −8.77322e36 −0.124879
\(637\) 3.82878e37 0.533553
\(638\) 8.97439e36 0.122441
\(639\) 4.93688e37 0.659464
\(640\) 8.56075e37 1.11965
\(641\) 1.83496e37 0.234987 0.117494 0.993074i \(-0.462514\pi\)
0.117494 + 0.993074i \(0.462514\pi\)
\(642\) −7.22140e37 −0.905520
\(643\) 5.85846e37 0.719342 0.359671 0.933079i \(-0.382889\pi\)
0.359671 + 0.933079i \(0.382889\pi\)
\(644\) −6.84544e34 −0.000823080 0
\(645\) 1.25399e38 1.47651
\(646\) −6.15862e37 −0.710141
\(647\) 1.39594e38 1.57637 0.788187 0.615435i \(-0.211020\pi\)
0.788187 + 0.615435i \(0.211020\pi\)
\(648\) 4.41596e37 0.488386
\(649\) −7.49466e37 −0.811799
\(650\) −9.94085e37 −1.05461
\(651\) −2.88747e36 −0.0300036
\(652\) −1.01121e37 −0.102920
\(653\) −8.62301e37 −0.859668 −0.429834 0.902908i \(-0.641428\pi\)
−0.429834 + 0.902908i \(0.641428\pi\)
\(654\) 2.50955e37 0.245074
\(655\) −1.90812e38 −1.82536
\(656\) −5.04226e37 −0.472523
\(657\) 2.36529e37 0.217146
\(658\) 1.85272e36 0.0166633
\(659\) 1.30986e38 1.15418 0.577089 0.816681i \(-0.304189\pi\)
0.577089 + 0.816681i \(0.304189\pi\)
\(660\) 1.82309e37 0.157385
\(661\) 1.01882e38 0.861740 0.430870 0.902414i \(-0.358207\pi\)
0.430870 + 0.902414i \(0.358207\pi\)
\(662\) −1.87265e37 −0.155193
\(663\) 3.07039e37 0.249322
\(664\) −1.67057e38 −1.32922
\(665\) 2.54158e37 0.198158
\(666\) −1.14385e37 −0.0873911
\(667\) −1.57692e36 −0.0118062
\(668\) −1.76924e37 −0.129809
\(669\) −1.12484e37 −0.0808794
\(670\) 3.18431e38 2.24391
\(671\) 9.08768e37 0.627623
\(672\) 3.59829e36 0.0243563
\(673\) 2.29828e36 0.0152476 0.00762378 0.999971i \(-0.497573\pi\)
0.00762378 + 0.999971i \(0.497573\pi\)
\(674\) 3.71778e37 0.241755
\(675\) −3.71161e38 −2.36571
\(676\) 2.15091e37 0.134382
\(677\) 1.56923e37 0.0961033 0.0480516 0.998845i \(-0.484699\pi\)
0.0480516 + 0.998845i \(0.484699\pi\)
\(678\) −7.29619e37 −0.438022
\(679\) −2.21425e37 −0.130312
\(680\) 1.96761e38 1.13519
\(681\) −3.06587e37 −0.173408
\(682\) 4.46096e37 0.247366
\(683\) −1.85515e38 −1.00856 −0.504278 0.863542i \(-0.668241\pi\)
−0.504278 + 0.863542i \(0.668241\pi\)
\(684\) 1.83796e37 0.0979669
\(685\) −5.13352e37 −0.268283
\(686\) −2.93527e37 −0.150409
\(687\) 1.03267e38 0.518857
\(688\) −1.67000e38 −0.822759
\(689\) −9.42055e37 −0.455111
\(690\) 1.37521e37 0.0651489
\(691\) 1.36613e38 0.634655 0.317328 0.948316i \(-0.397215\pi\)
0.317328 + 0.948316i \(0.397215\pi\)
\(692\) −3.05459e37 −0.139162
\(693\) 4.39039e36 0.0196157
\(694\) −3.01247e38 −1.31999
\(695\) 6.94113e38 2.98288
\(696\) 4.50224e37 0.189760
\(697\) −8.76531e37 −0.362347
\(698\) 1.86331e38 0.755502
\(699\) −2.35085e37 −0.0934940
\(700\) −8.84486e36 −0.0345038
\(701\) −2.20458e38 −0.843594 −0.421797 0.906690i \(-0.638601\pi\)
−0.421797 + 0.906690i \(0.638601\pi\)
\(702\) 1.39944e38 0.525295
\(703\) 8.93839e37 0.329126
\(704\) −1.84099e38 −0.664999
\(705\) 8.67005e37 0.307233
\(706\) 2.83015e38 0.983889
\(707\) 9.99383e36 0.0340855
\(708\) −5.97476e37 −0.199927
\(709\) −5.82758e38 −1.91322 −0.956608 0.291376i \(-0.905887\pi\)
−0.956608 + 0.291376i \(0.905887\pi\)
\(710\) −8.40813e38 −2.70839
\(711\) −4.82763e37 −0.152579
\(712\) 2.87646e38 0.892027
\(713\) −7.83851e36 −0.0238520
\(714\) −1.17278e37 −0.0350181
\(715\) 1.95760e38 0.573579
\(716\) −8.24210e37 −0.236980
\(717\) 4.16290e38 1.17459
\(718\) 2.17185e38 0.601381
\(719\) 2.83019e38 0.769089 0.384544 0.923107i \(-0.374359\pi\)
0.384544 + 0.923107i \(0.374359\pi\)
\(720\) 2.02697e38 0.540578
\(721\) 1.50845e37 0.0394825
\(722\) 2.65997e38 0.683321
\(723\) −2.95465e38 −0.744970
\(724\) 1.30909e38 0.323965
\(725\) −2.03751e38 −0.494921
\(726\) −1.89123e38 −0.450920
\(727\) −2.87575e38 −0.673032 −0.336516 0.941678i \(-0.609249\pi\)
−0.336516 + 0.941678i \(0.609249\pi\)
\(728\) 2.09864e37 0.0482130
\(729\) 4.54717e38 1.02546
\(730\) −4.02839e38 −0.891810
\(731\) −2.90308e38 −0.630920
\(732\) 7.24472e37 0.154569
\(733\) 6.09181e38 1.27598 0.637989 0.770046i \(-0.279767\pi\)
0.637989 + 0.770046i \(0.279767\pi\)
\(734\) 1.57237e38 0.323339
\(735\) −6.84378e38 −1.38171
\(736\) 9.76816e36 0.0193625
\(737\) −4.29838e38 −0.836554
\(738\) −1.12300e38 −0.214594
\(739\) 5.52340e38 1.03635 0.518175 0.855275i \(-0.326612\pi\)
0.518175 + 0.855275i \(0.326612\pi\)
\(740\) −4.53794e37 −0.0836047
\(741\) −3.07393e38 −0.556094
\(742\) 3.59834e37 0.0639218
\(743\) −4.68741e38 −0.817680 −0.408840 0.912606i \(-0.634067\pi\)
−0.408840 + 0.912606i \(0.634067\pi\)
\(744\) 2.23796e38 0.383370
\(745\) 5.07674e38 0.854033
\(746\) 3.19940e38 0.528560
\(747\) −2.99169e38 −0.485387
\(748\) −4.22058e37 −0.0672513
\(749\) −6.89932e37 −0.107970
\(750\) 9.61555e38 1.47791
\(751\) −7.49018e38 −1.13071 −0.565357 0.824846i \(-0.691262\pi\)
−0.565357 + 0.824846i \(0.691262\pi\)
\(752\) −1.15463e38 −0.171200
\(753\) 1.38967e38 0.202385
\(754\) 7.68229e37 0.109895
\(755\) 1.74706e39 2.45484
\(756\) 1.24515e37 0.0171861
\(757\) −2.19892e38 −0.298137 −0.149068 0.988827i \(-0.547627\pi\)
−0.149068 + 0.988827i \(0.547627\pi\)
\(758\) −2.65381e38 −0.353456
\(759\) −1.85635e37 −0.0242882
\(760\) −1.96988e39 −2.53195
\(761\) 4.67111e38 0.589830 0.294915 0.955523i \(-0.404709\pi\)
0.294915 + 0.955523i \(0.404709\pi\)
\(762\) −6.87037e38 −0.852291
\(763\) 2.39762e37 0.0292213
\(764\) 1.46348e38 0.175237
\(765\) 3.52362e38 0.414534
\(766\) 2.14762e38 0.248238
\(767\) −6.41560e38 −0.728618
\(768\) −3.81336e38 −0.425531
\(769\) 9.38023e37 0.102851 0.0514254 0.998677i \(-0.483624\pi\)
0.0514254 + 0.998677i \(0.483624\pi\)
\(770\) −7.47739e37 −0.0805610
\(771\) −2.96433e38 −0.313829
\(772\) 7.24587e37 0.0753802
\(773\) 1.06611e39 1.08988 0.544942 0.838474i \(-0.316552\pi\)
0.544942 + 0.838474i \(0.316552\pi\)
\(774\) −3.71937e38 −0.373652
\(775\) −1.01280e39 −0.999885
\(776\) 1.71618e39 1.66506
\(777\) 1.70214e37 0.0162297
\(778\) 6.93258e38 0.649637
\(779\) 8.77542e38 0.808188
\(780\) 1.56061e38 0.141259
\(781\) 1.13498e39 1.00972
\(782\) −3.18372e37 −0.0278384
\(783\) 2.86834e38 0.246517
\(784\) 9.11420e38 0.769931
\(785\) −3.19463e39 −2.65266
\(786\) −8.81497e38 −0.719476
\(787\) −1.52283e39 −1.22177 −0.610887 0.791718i \(-0.709187\pi\)
−0.610887 + 0.791718i \(0.709187\pi\)
\(788\) −4.29513e38 −0.338744
\(789\) −1.35619e38 −0.105143
\(790\) 8.22206e38 0.626635
\(791\) −6.97078e37 −0.0522274
\(792\) −3.40282e38 −0.250639
\(793\) 7.77927e38 0.563314
\(794\) −7.42494e38 −0.528586
\(795\) 1.68388e39 1.17857
\(796\) 2.12431e38 0.146181
\(797\) −2.14824e39 −1.45343 −0.726717 0.686937i \(-0.758955\pi\)
−0.726717 + 0.686937i \(0.758955\pi\)
\(798\) 1.17414e38 0.0781052
\(799\) −2.00718e38 −0.131282
\(800\) 1.26213e39 0.811685
\(801\) 5.15121e38 0.325739
\(802\) 8.12538e38 0.505231
\(803\) 5.43777e38 0.332476
\(804\) −3.42668e38 −0.206024
\(805\) 1.31388e37 0.00776802
\(806\) 3.81869e38 0.222020
\(807\) 1.58181e39 0.904401
\(808\) −7.74583e38 −0.435526
\(809\) −1.44847e39 −0.800949 −0.400474 0.916308i \(-0.631155\pi\)
−0.400474 + 0.916308i \(0.631155\pi\)
\(810\) −1.34686e39 −0.732446
\(811\) −4.08234e38 −0.218337 −0.109169 0.994023i \(-0.534819\pi\)
−0.109169 + 0.994023i \(0.534819\pi\)
\(812\) 6.83531e36 0.00359544
\(813\) 1.45589e39 0.753193
\(814\) −2.62970e38 −0.133806
\(815\) 1.94086e39 0.971328
\(816\) 7.30889e38 0.359778
\(817\) 2.90643e39 1.40722
\(818\) −3.35668e39 −1.59860
\(819\) 3.75828e37 0.0176058
\(820\) −4.45520e38 −0.205296
\(821\) −2.94462e39 −1.33474 −0.667371 0.744726i \(-0.732580\pi\)
−0.667371 + 0.744726i \(0.732580\pi\)
\(822\) −2.37154e38 −0.105745
\(823\) −1.81936e39 −0.798032 −0.399016 0.916944i \(-0.630648\pi\)
−0.399016 + 0.916944i \(0.630648\pi\)
\(824\) −1.16914e39 −0.504486
\(825\) −2.39855e39 −1.01817
\(826\) 2.45055e38 0.102337
\(827\) 2.52233e39 1.03628 0.518141 0.855295i \(-0.326624\pi\)
0.518141 + 0.855295i \(0.326624\pi\)
\(828\) 9.50141e36 0.00384042
\(829\) 1.02531e39 0.407726 0.203863 0.978999i \(-0.434650\pi\)
0.203863 + 0.978999i \(0.434650\pi\)
\(830\) 5.09522e39 1.99346
\(831\) −3.20589e39 −1.23405
\(832\) −1.57593e39 −0.596861
\(833\) 1.58439e39 0.590409
\(834\) 3.20661e39 1.17572
\(835\) 3.39578e39 1.22510
\(836\) 4.22545e38 0.149999
\(837\) 1.42578e39 0.498035
\(838\) −4.50185e39 −1.54738
\(839\) −1.22528e39 −0.414429 −0.207214 0.978296i \(-0.566440\pi\)
−0.207214 + 0.978296i \(0.566440\pi\)
\(840\) −3.75123e38 −0.124854
\(841\) −2.89568e39 −0.948427
\(842\) 5.23130e39 1.68615
\(843\) 2.05504e39 0.651849
\(844\) 4.95552e38 0.154691
\(845\) −4.12834e39 −1.26826
\(846\) −2.57156e38 −0.0777495
\(847\) −1.80688e38 −0.0537654
\(848\) −2.24251e39 −0.656736
\(849\) −3.34112e39 −0.963028
\(850\) −4.11362e39 −1.16699
\(851\) 4.62073e37 0.0129021
\(852\) 9.04810e38 0.248670
\(853\) 2.17452e39 0.588235 0.294117 0.955769i \(-0.404974\pi\)
0.294117 + 0.955769i \(0.404974\pi\)
\(854\) −2.97142e38 −0.0791194
\(855\) −3.52769e39 −0.924586
\(856\) 5.34739e39 1.37958
\(857\) 4.29564e39 1.09091 0.545453 0.838142i \(-0.316358\pi\)
0.545453 + 0.838142i \(0.316358\pi\)
\(858\) 9.04358e38 0.226080
\(859\) −1.62483e39 −0.399853 −0.199927 0.979811i \(-0.564070\pi\)
−0.199927 + 0.979811i \(0.564070\pi\)
\(860\) −1.47557e39 −0.357462
\(861\) 1.67110e38 0.0398529
\(862\) 1.71139e39 0.401792
\(863\) 3.68820e39 0.852450 0.426225 0.904617i \(-0.359843\pi\)
0.426225 + 0.904617i \(0.359843\pi\)
\(864\) −1.77678e39 −0.404294
\(865\) 5.86281e39 1.31337
\(866\) −1.83423e37 −0.00404541
\(867\) −2.32335e39 −0.504494
\(868\) 3.39768e37 0.00726383
\(869\) −1.10987e39 −0.233616
\(870\) −1.37318e39 −0.284588
\(871\) −3.67952e39 −0.750838
\(872\) −1.85830e39 −0.373374
\(873\) 3.07336e39 0.608024
\(874\) 3.18739e38 0.0620913
\(875\) 9.18669e38 0.176218
\(876\) 4.33500e38 0.0818811
\(877\) −5.53156e39 −1.02885 −0.514426 0.857535i \(-0.671995\pi\)
−0.514426 + 0.857535i \(0.671995\pi\)
\(878\) −3.89080e39 −0.712629
\(879\) −5.95272e39 −1.07366
\(880\) 4.65997e39 0.827689
\(881\) 9.22430e39 1.61346 0.806731 0.590919i \(-0.201235\pi\)
0.806731 + 0.590919i \(0.201235\pi\)
\(882\) 2.02989e39 0.349660
\(883\) −7.47767e39 −1.26852 −0.634259 0.773120i \(-0.718695\pi\)
−0.634259 + 0.773120i \(0.718695\pi\)
\(884\) −3.61292e38 −0.0603605
\(885\) 1.14676e40 1.88686
\(886\) −5.46593e39 −0.885746
\(887\) −3.52542e39 −0.562655 −0.281328 0.959612i \(-0.590775\pi\)
−0.281328 + 0.959612i \(0.590775\pi\)
\(888\) −1.31926e39 −0.207374
\(889\) −6.56395e38 −0.101623
\(890\) −8.77315e39 −1.33780
\(891\) 1.81808e39 0.273064
\(892\) 1.32360e38 0.0195808
\(893\) 2.00950e39 0.292814
\(894\) 2.34531e39 0.336623
\(895\) 1.58194e40 2.23656
\(896\) 3.77844e38 0.0526204
\(897\) −1.58908e38 −0.0217995
\(898\) 6.78666e39 0.917118
\(899\) 7.82691e38 0.104192
\(900\) 1.22766e39 0.160992
\(901\) −3.89832e39 −0.503608
\(902\) −2.58175e39 −0.328569
\(903\) 5.53470e38 0.0693921
\(904\) 5.40278e39 0.667334
\(905\) −2.51259e40 −3.05750
\(906\) 8.07091e39 0.967591
\(907\) −1.16020e40 −1.37036 −0.685180 0.728374i \(-0.740276\pi\)
−0.685180 + 0.728374i \(0.740276\pi\)
\(908\) 3.60761e38 0.0419817
\(909\) −1.38713e39 −0.159040
\(910\) −6.40082e38 −0.0723064
\(911\) 1.03198e40 1.14861 0.574306 0.818640i \(-0.305272\pi\)
0.574306 + 0.818640i \(0.305272\pi\)
\(912\) −7.31732e39 −0.802457
\(913\) −6.87785e39 −0.743185
\(914\) 9.39087e39 0.999844
\(915\) −1.39051e40 −1.45878
\(916\) −1.21515e39 −0.125615
\(917\) −8.42181e38 −0.0857866
\(918\) 5.79102e39 0.581271
\(919\) 1.74754e40 1.72850 0.864248 0.503067i \(-0.167795\pi\)
0.864248 + 0.503067i \(0.167795\pi\)
\(920\) −1.01833e39 −0.0992555
\(921\) 8.71535e39 0.837104
\(922\) 4.11119e39 0.389135
\(923\) 9.71572e39 0.906258
\(924\) 8.04652e37 0.00739667
\(925\) 5.97035e39 0.540862
\(926\) −1.45515e40 −1.29915
\(927\) −2.09371e39 −0.184222
\(928\) −9.75371e38 −0.0845809
\(929\) 8.87284e39 0.758316 0.379158 0.925332i \(-0.376214\pi\)
0.379158 + 0.925332i \(0.376214\pi\)
\(930\) −6.82575e39 −0.574951
\(931\) −1.58621e40 −1.31686
\(932\) 2.76624e38 0.0226348
\(933\) −4.74549e39 −0.382718
\(934\) 2.99508e39 0.238082
\(935\) 8.10076e39 0.634701
\(936\) −2.91289e39 −0.224958
\(937\) −1.64530e39 −0.125245 −0.0626226 0.998037i \(-0.519946\pi\)
−0.0626226 + 0.998037i \(0.519946\pi\)
\(938\) 1.40545e39 0.105458
\(939\) 3.29572e39 0.243761
\(940\) −1.02020e39 −0.0743808
\(941\) −7.97642e38 −0.0573255 −0.0286628 0.999589i \(-0.509125\pi\)
−0.0286628 + 0.999589i \(0.509125\pi\)
\(942\) −1.47583e40 −1.04556
\(943\) 4.53648e38 0.0316819
\(944\) −1.52720e40 −1.05141
\(945\) −2.38987e39 −0.162198
\(946\) −8.55079e39 −0.572105
\(947\) 1.60271e40 1.05713 0.528566 0.848892i \(-0.322730\pi\)
0.528566 + 0.848892i \(0.322730\pi\)
\(948\) −8.84787e38 −0.0575342
\(949\) 4.65486e39 0.298410
\(950\) 4.11837e40 2.60289
\(951\) 1.21746e40 0.758608
\(952\) 8.68438e38 0.0533507
\(953\) −8.74550e39 −0.529701 −0.264850 0.964290i \(-0.585323\pi\)
−0.264850 + 0.964290i \(0.585323\pi\)
\(954\) −4.99446e39 −0.298253
\(955\) −2.80893e40 −1.65384
\(956\) −4.89847e39 −0.284367
\(957\) 1.85360e39 0.106098
\(958\) 8.64200e39 0.487730
\(959\) −2.26577e38 −0.0126085
\(960\) 2.81691e40 1.54565
\(961\) −1.45921e40 −0.789502
\(962\) −2.25108e39 −0.120096
\(963\) 9.57619e39 0.503776
\(964\) 3.47673e39 0.180356
\(965\) −1.39073e40 −0.711419
\(966\) 6.06974e37 0.00306182
\(967\) 1.60838e40 0.800075 0.400038 0.916499i \(-0.368997\pi\)
0.400038 + 0.916499i \(0.368997\pi\)
\(968\) 1.40044e40 0.686985
\(969\) −1.27202e40 −0.615352
\(970\) −5.23432e40 −2.49713
\(971\) 1.28013e40 0.602276 0.301138 0.953581i \(-0.402633\pi\)
0.301138 + 0.953581i \(0.402633\pi\)
\(972\) −2.97071e39 −0.137837
\(973\) 3.06359e39 0.140187
\(974\) −1.77091e40 −0.799192
\(975\) −2.05322e40 −0.913845
\(976\) 1.85181e40 0.812877
\(977\) −1.68476e40 −0.729392 −0.364696 0.931127i \(-0.618827\pi\)
−0.364696 + 0.931127i \(0.618827\pi\)
\(978\) 8.96622e39 0.382855
\(979\) 1.18426e40 0.498746
\(980\) 8.05306e39 0.334510
\(981\) −3.32788e39 −0.136344
\(982\) 2.80647e40 1.13411
\(983\) −3.82928e40 −1.52632 −0.763159 0.646211i \(-0.776353\pi\)
−0.763159 + 0.646211i \(0.776353\pi\)
\(984\) −1.29521e40 −0.509219
\(985\) 8.24383e40 3.19698
\(986\) 3.17901e39 0.121606
\(987\) 3.82668e38 0.0144391
\(988\) 3.61709e39 0.134630
\(989\) 1.50249e39 0.0551647
\(990\) 1.03785e40 0.375891
\(991\) 1.66034e40 0.593201 0.296600 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(992\) −4.84835e39 −0.170878
\(993\) −3.86783e39 −0.134478
\(994\) −3.71108e39 −0.127287
\(995\) −4.07729e40 −1.37962
\(996\) −5.48304e39 −0.183029
\(997\) −4.81089e39 −0.158431 −0.0792156 0.996858i \(-0.525242\pi\)
−0.0792156 + 0.996858i \(0.525242\pi\)
\(998\) −4.55051e39 −0.147842
\(999\) −8.40486e39 −0.269399
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 1.28.a.a.1.2 2
3.2 odd 2 9.28.a.d.1.1 2
4.3 odd 2 16.28.a.d.1.1 2
5.2 odd 4 25.28.b.a.24.3 4
5.3 odd 4 25.28.b.a.24.2 4
5.4 even 2 25.28.a.a.1.1 2
7.6 odd 2 49.28.a.b.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.28.a.a.1.2 2 1.1 even 1 trivial
9.28.a.d.1.1 2 3.2 odd 2
16.28.a.d.1.1 2 4.3 odd 2
25.28.a.a.1.1 2 5.4 even 2
25.28.b.a.24.2 4 5.3 odd 4
25.28.b.a.24.3 4 5.2 odd 4
49.28.a.b.1.2 2 7.6 odd 2