Properties

Label 29.18.a.b.1.7
Level $29$
Weight $18$
Character 29.1
Self dual yes
Analytic conductor $53.134$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.1344053299\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-275.201 q^{2} +7065.32 q^{3} -55336.6 q^{4} -620891. q^{5} -1.94438e6 q^{6} +2.72618e7 q^{7} +5.12998e7 q^{8} -7.92215e7 q^{9} +O(q^{10})\) \(q-275.201 q^{2} +7065.32 q^{3} -55336.6 q^{4} -620891. q^{5} -1.94438e6 q^{6} +2.72618e7 q^{7} +5.12998e7 q^{8} -7.92215e7 q^{9} +1.70870e8 q^{10} +6.43661e7 q^{11} -3.90970e8 q^{12} +5.86404e8 q^{13} -7.50246e9 q^{14} -4.38679e9 q^{15} -6.86466e9 q^{16} -3.10293e10 q^{17} +2.18018e10 q^{18} +5.29680e10 q^{19} +3.43580e10 q^{20} +1.92613e11 q^{21} -1.77136e10 q^{22} +1.60419e11 q^{23} +3.62449e11 q^{24} -3.77434e11 q^{25} -1.61379e11 q^{26} -1.47214e12 q^{27} -1.50857e12 q^{28} +5.00246e11 q^{29} +1.20725e12 q^{30} +7.27024e11 q^{31} -4.83480e12 q^{32} +4.54767e11 q^{33} +8.53929e12 q^{34} -1.69266e13 q^{35} +4.38384e12 q^{36} -9.77502e12 q^{37} -1.45768e13 q^{38} +4.14313e12 q^{39} -3.18515e13 q^{40} -6.44608e13 q^{41} -5.30073e13 q^{42} +1.42883e14 q^{43} -3.56180e12 q^{44} +4.91879e13 q^{45} -4.41474e13 q^{46} +1.73045e14 q^{47} -4.85010e13 q^{48} +5.10574e14 q^{49} +1.03870e14 q^{50} -2.19232e14 q^{51} -3.24496e13 q^{52} -8.85198e13 q^{53} +4.05134e14 q^{54} -3.99643e13 q^{55} +1.39852e15 q^{56} +3.74236e14 q^{57} -1.37668e14 q^{58} +4.51204e14 q^{59} +2.42750e14 q^{60} +1.64260e15 q^{61} -2.00078e14 q^{62} -2.15972e15 q^{63} +2.23031e15 q^{64} -3.64093e14 q^{65} -1.25152e14 q^{66} +7.01809e14 q^{67} +1.71706e15 q^{68} +1.13341e15 q^{69} +4.65821e15 q^{70} +4.44430e15 q^{71} -4.06404e15 q^{72} -8.65761e14 q^{73} +2.69009e15 q^{74} -2.66669e15 q^{75} -2.93107e15 q^{76} +1.75474e15 q^{77} -1.14019e15 q^{78} +1.17326e16 q^{79} +4.26220e15 q^{80} -1.70462e14 q^{81} +1.77397e16 q^{82} +1.52260e16 q^{83} -1.06585e16 q^{84} +1.92658e16 q^{85} -3.93214e16 q^{86} +3.53440e15 q^{87} +3.30197e15 q^{88} +5.11031e16 q^{89} -1.35365e16 q^{90} +1.59864e16 q^{91} -8.87702e15 q^{92} +5.13665e15 q^{93} -4.76222e16 q^{94} -3.28873e16 q^{95} -3.41594e16 q^{96} +7.79795e16 q^{97} -1.40510e17 q^{98} -5.09918e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} - 224469478q^{10} + 1203139534q^{11} - 5164251122q^{12} + 3854339312q^{13} + 25262272904q^{14} + 28324474306q^{15} + 196520815922q^{16} + 76444714794q^{17} + 75758949126q^{18} + 246497292428q^{19} - 46900976670q^{20} + 360937126704q^{21} - 275001533522q^{22} + 213498528140q^{23} - 451123453870q^{24} + 3898884886997q^{25} - 3609347694206q^{26} - 2718903745978q^{27} - 5946174617200q^{28} + 10505174672181q^{29} - 20237658929454q^{30} + 16670029895798q^{31} - 42141001912046q^{32} - 7157109761394q^{33} + 12785761151136q^{34} + 46677934312888q^{35} + 132137824374868q^{36} + 53445659988410q^{37} + 76581637956388q^{38} + 79233849032530q^{39} + 193617444734146q^{40} - 20814769309298q^{41} + 76690667258352q^{42} + 185498647364454q^{43} + 315429066899678q^{44} - 486270821438526q^{45} + 261474367677132q^{46} + 389503471719450q^{47} - 101509672247630q^{48} + 730079062141437q^{49} + 1482269666368354q^{50} + 718238208473988q^{51} + 1966802817157170q^{52} + 747441265526156q^{53} + 5692893333117030q^{54} + 1639109418219546q^{55} + 5657219329125240q^{56} + 4694352396864932q^{57} + 128063081718016q^{58} + 5280258638332960q^{59} + 15251367906033378q^{60} + 5813675353074254q^{61} + 6242066590947250q^{62} + 10947760075450368q^{63} + 24583792057508902q^{64} + 19190799243789974q^{65} + 41877805444482390q^{66} + 13420580230958268q^{67} + 24771837384165388q^{68} + 30973047049935252q^{69} + 8505088080182440q^{70} + 4824462822979508q^{71} + 1180071997284592q^{72} + 11228916281304662q^{73} - 89132715356772q^{74} + 59161419576630296q^{75} + 57466858643173460q^{76} + 58741564492720064q^{77} + 142050530910210210q^{78} + 71718598015696758q^{79} + 48350023652407550q^{80} + 75805931446703569q^{81} + 188661890754420812q^{82} + 50769377111735608q^{83} + 198832046985593048q^{84} + 53422044849490784q^{85} + 35014892323844118q^{86} + 11988905533023326q^{87} + 37459283979085258q^{88} - 70981414576978018q^{89} + 57211029866143724q^{90} + 112933943315157320q^{91} - 103019729095759724q^{92} - 350358290646906646q^{93} - 150286322409612578q^{94} - 102561321856584476q^{95} - 213770098354021866q^{96} - 130930167251505210q^{97} - 537387515497557296q^{98} - 95267700931431064q^{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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −275.201 −0.760142 −0.380071 0.924957i \(-0.624100\pi\)
−0.380071 + 0.924957i \(0.624100\pi\)
\(3\) 7065.32 0.621729 0.310864 0.950454i \(-0.399382\pi\)
0.310864 + 0.950454i \(0.399382\pi\)
\(4\) −55336.6 −0.422184
\(5\) −620891. −0.710837 −0.355419 0.934707i \(-0.615662\pi\)
−0.355419 + 0.934707i \(0.615662\pi\)
\(6\) −1.94438e6 −0.472602
\(7\) 2.72618e7 1.78740 0.893698 0.448668i \(-0.148102\pi\)
0.893698 + 0.448668i \(0.148102\pi\)
\(8\) 5.12998e7 1.08106
\(9\) −7.92215e7 −0.613454
\(10\) 1.70870e8 0.540337
\(11\) 6.43661e7 0.0905357 0.0452678 0.998975i \(-0.485586\pi\)
0.0452678 + 0.998975i \(0.485586\pi\)
\(12\) −3.90970e8 −0.262484
\(13\) 5.86404e8 0.199379 0.0996893 0.995019i \(-0.468215\pi\)
0.0996893 + 0.995019i \(0.468215\pi\)
\(14\) −7.50246e9 −1.35867
\(15\) −4.38679e9 −0.441948
\(16\) −6.86466e9 −0.399576
\(17\) −3.10293e10 −1.07884 −0.539419 0.842037i \(-0.681356\pi\)
−0.539419 + 0.842037i \(0.681356\pi\)
\(18\) 2.18018e10 0.466312
\(19\) 5.29680e10 0.715497 0.357749 0.933818i \(-0.383544\pi\)
0.357749 + 0.933818i \(0.383544\pi\)
\(20\) 3.43580e10 0.300104
\(21\) 1.92613e11 1.11128
\(22\) −1.77136e10 −0.0688199
\(23\) 1.60419e11 0.427138 0.213569 0.976928i \(-0.431491\pi\)
0.213569 + 0.976928i \(0.431491\pi\)
\(24\) 3.62449e11 0.672127
\(25\) −3.77434e11 −0.494711
\(26\) −1.61379e11 −0.151556
\(27\) −1.47214e12 −1.00313
\(28\) −1.50857e12 −0.754611
\(29\) 5.00246e11 0.185695
\(30\) 1.20725e12 0.335943
\(31\) 7.27024e11 0.153100 0.0765498 0.997066i \(-0.475610\pi\)
0.0765498 + 0.997066i \(0.475610\pi\)
\(32\) −4.83480e12 −0.777328
\(33\) 4.54767e11 0.0562886
\(34\) 8.53929e12 0.820070
\(35\) −1.69266e13 −1.27055
\(36\) 4.38384e12 0.258991
\(37\) −9.77502e12 −0.457513 −0.228756 0.973484i \(-0.573466\pi\)
−0.228756 + 0.973484i \(0.573466\pi\)
\(38\) −1.45768e13 −0.543879
\(39\) 4.14313e12 0.123959
\(40\) −3.18515e13 −0.768459
\(41\) −6.44608e13 −1.26076 −0.630380 0.776286i \(-0.717101\pi\)
−0.630380 + 0.776286i \(0.717101\pi\)
\(42\) −5.30073e13 −0.844727
\(43\) 1.42883e14 1.86422 0.932110 0.362175i \(-0.117966\pi\)
0.932110 + 0.362175i \(0.117966\pi\)
\(44\) −3.56180e12 −0.0382227
\(45\) 4.91879e13 0.436066
\(46\) −4.41474e13 −0.324686
\(47\) 1.73045e14 1.06005 0.530027 0.847981i \(-0.322182\pi\)
0.530027 + 0.847981i \(0.322182\pi\)
\(48\) −4.85010e13 −0.248428
\(49\) 5.10574e14 2.19479
\(50\) 1.03870e14 0.376050
\(51\) −2.19232e14 −0.670745
\(52\) −3.24496e13 −0.0841745
\(53\) −8.85198e13 −0.195297 −0.0976485 0.995221i \(-0.531132\pi\)
−0.0976485 + 0.995221i \(0.531132\pi\)
\(54\) 4.05134e14 0.762521
\(55\) −3.99643e13 −0.0643561
\(56\) 1.39852e15 1.93229
\(57\) 3.74236e14 0.444845
\(58\) −1.37668e14 −0.141155
\(59\) 4.51204e14 0.400065 0.200033 0.979789i \(-0.435895\pi\)
0.200033 + 0.979789i \(0.435895\pi\)
\(60\) 2.42750e14 0.186583
\(61\) 1.64260e15 1.09705 0.548526 0.836133i \(-0.315189\pi\)
0.548526 + 0.836133i \(0.315189\pi\)
\(62\) −2.00078e14 −0.116377
\(63\) −2.15972e15 −1.09648
\(64\) 2.23031e15 0.990455
\(65\) −3.64093e14 −0.141726
\(66\) −1.25152e14 −0.0427873
\(67\) 7.01809e14 0.211146 0.105573 0.994412i \(-0.466332\pi\)
0.105573 + 0.994412i \(0.466332\pi\)
\(68\) 1.71706e15 0.455469
\(69\) 1.13341e15 0.265564
\(70\) 4.65821e15 0.965797
\(71\) 4.44430e15 0.816784 0.408392 0.912807i \(-0.366090\pi\)
0.408392 + 0.912807i \(0.366090\pi\)
\(72\) −4.06404e15 −0.663181
\(73\) −8.65761e14 −0.125648 −0.0628238 0.998025i \(-0.520011\pi\)
−0.0628238 + 0.998025i \(0.520011\pi\)
\(74\) 2.69009e15 0.347775
\(75\) −2.66669e15 −0.307576
\(76\) −2.93107e15 −0.302072
\(77\) 1.75474e15 0.161823
\(78\) −1.14019e15 −0.0942267
\(79\) 1.17326e16 0.870090 0.435045 0.900409i \(-0.356732\pi\)
0.435045 + 0.900409i \(0.356732\pi\)
\(80\) 4.26220e15 0.284033
\(81\) −1.70462e14 −0.0102213
\(82\) 1.77397e16 0.958357
\(83\) 1.52260e16 0.742032 0.371016 0.928626i \(-0.379009\pi\)
0.371016 + 0.928626i \(0.379009\pi\)
\(84\) −1.06585e16 −0.469163
\(85\) 1.92658e16 0.766879
\(86\) −3.93214e16 −1.41707
\(87\) 3.53440e15 0.115452
\(88\) 3.30197e15 0.0978747
\(89\) 5.11031e16 1.37604 0.688022 0.725690i \(-0.258479\pi\)
0.688022 + 0.725690i \(0.258479\pi\)
\(90\) −1.35365e16 −0.331472
\(91\) 1.59864e16 0.356368
\(92\) −8.87702e15 −0.180331
\(93\) 5.13665e15 0.0951865
\(94\) −4.76222e16 −0.805792
\(95\) −3.28873e16 −0.508602
\(96\) −3.41594e16 −0.483287
\(97\) 7.79795e16 1.01023 0.505116 0.863052i \(-0.331450\pi\)
0.505116 + 0.863052i \(0.331450\pi\)
\(98\) −1.40510e17 −1.66835
\(99\) −5.09918e15 −0.0555394
\(100\) 2.08859e16 0.208859
\(101\) −1.75244e16 −0.161031 −0.0805157 0.996753i \(-0.525657\pi\)
−0.0805157 + 0.996753i \(0.525657\pi\)
\(102\) 6.03328e16 0.509861
\(103\) 1.53601e16 0.119475 0.0597375 0.998214i \(-0.480974\pi\)
0.0597375 + 0.998214i \(0.480974\pi\)
\(104\) 3.00824e16 0.215540
\(105\) −1.19592e17 −0.789936
\(106\) 2.43607e16 0.148453
\(107\) 8.04122e16 0.452439 0.226219 0.974076i \(-0.427363\pi\)
0.226219 + 0.974076i \(0.427363\pi\)
\(108\) 8.14632e16 0.423506
\(109\) 1.20639e17 0.579914 0.289957 0.957040i \(-0.406359\pi\)
0.289957 + 0.957040i \(0.406359\pi\)
\(110\) 1.09982e16 0.0489198
\(111\) −6.90636e16 −0.284449
\(112\) −1.87143e17 −0.714201
\(113\) −3.07891e17 −1.08951 −0.544753 0.838596i \(-0.683377\pi\)
−0.544753 + 0.838596i \(0.683377\pi\)
\(114\) −1.02990e17 −0.338145
\(115\) −9.96025e16 −0.303626
\(116\) −2.76819e16 −0.0783977
\(117\) −4.64558e16 −0.122309
\(118\) −1.24172e17 −0.304106
\(119\) −8.45915e17 −1.92831
\(120\) −2.25041e17 −0.477773
\(121\) −5.01304e17 −0.991803
\(122\) −4.52044e17 −0.833916
\(123\) −4.55436e17 −0.783851
\(124\) −4.02310e16 −0.0646363
\(125\) 7.08047e17 1.06250
\(126\) 5.94356e17 0.833484
\(127\) 7.36322e17 0.965464 0.482732 0.875768i \(-0.339645\pi\)
0.482732 + 0.875768i \(0.339645\pi\)
\(128\) 1.99254e16 0.0244412
\(129\) 1.00951e18 1.15904
\(130\) 1.00199e17 0.107732
\(131\) −1.55798e18 −1.56948 −0.784739 0.619827i \(-0.787203\pi\)
−0.784739 + 0.619827i \(0.787203\pi\)
\(132\) −2.51652e16 −0.0237642
\(133\) 1.44400e18 1.27888
\(134\) −1.93138e17 −0.160501
\(135\) 9.14038e17 0.713062
\(136\) −1.59180e18 −1.16629
\(137\) 2.05599e18 1.41546 0.707728 0.706485i \(-0.249720\pi\)
0.707728 + 0.706485i \(0.249720\pi\)
\(138\) −3.11915e17 −0.201866
\(139\) −3.10190e18 −1.88800 −0.943999 0.329948i \(-0.892969\pi\)
−0.943999 + 0.329948i \(0.892969\pi\)
\(140\) 9.36659e17 0.536406
\(141\) 1.22262e18 0.659066
\(142\) −1.22307e18 −0.620872
\(143\) 3.77446e16 0.0180509
\(144\) 5.43829e17 0.245121
\(145\) −3.10598e17 −0.131999
\(146\) 2.38258e17 0.0955099
\(147\) 3.60737e18 1.36456
\(148\) 5.40916e17 0.193155
\(149\) 1.10187e18 0.371577 0.185789 0.982590i \(-0.440516\pi\)
0.185789 + 0.982590i \(0.440516\pi\)
\(150\) 7.33876e17 0.233801
\(151\) 3.18251e18 0.958221 0.479111 0.877754i \(-0.340959\pi\)
0.479111 + 0.877754i \(0.340959\pi\)
\(152\) 2.71725e18 0.773497
\(153\) 2.45819e18 0.661817
\(154\) −4.82905e17 −0.123009
\(155\) −4.51402e17 −0.108829
\(156\) −2.29266e17 −0.0523337
\(157\) 7.15203e18 1.54626 0.773129 0.634248i \(-0.218690\pi\)
0.773129 + 0.634248i \(0.218690\pi\)
\(158\) −3.22882e18 −0.661392
\(159\) −6.25420e17 −0.121422
\(160\) 3.00188e18 0.552553
\(161\) 4.37330e18 0.763465
\(162\) 4.69113e16 0.00776963
\(163\) −3.36022e18 −0.528169 −0.264084 0.964500i \(-0.585070\pi\)
−0.264084 + 0.964500i \(0.585070\pi\)
\(164\) 3.56704e18 0.532274
\(165\) −2.82361e17 −0.0400120
\(166\) −4.19021e18 −0.564050
\(167\) −5.61683e18 −0.718457 −0.359229 0.933250i \(-0.616960\pi\)
−0.359229 + 0.933250i \(0.616960\pi\)
\(168\) 9.88101e18 1.20136
\(169\) −8.30655e18 −0.960248
\(170\) −5.30197e18 −0.582937
\(171\) −4.19620e18 −0.438924
\(172\) −7.90663e18 −0.787045
\(173\) 1.01326e19 0.960129 0.480065 0.877233i \(-0.340613\pi\)
0.480065 + 0.877233i \(0.340613\pi\)
\(174\) −9.72669e17 −0.0877600
\(175\) −1.02895e19 −0.884244
\(176\) −4.41852e17 −0.0361759
\(177\) 3.18790e18 0.248732
\(178\) −1.40636e19 −1.04599
\(179\) −9.96774e18 −0.706880 −0.353440 0.935457i \(-0.614988\pi\)
−0.353440 + 0.935457i \(0.614988\pi\)
\(180\) −2.72189e18 −0.184100
\(181\) 4.00045e18 0.258132 0.129066 0.991636i \(-0.458802\pi\)
0.129066 + 0.991636i \(0.458802\pi\)
\(182\) −4.39947e18 −0.270891
\(183\) 1.16055e19 0.682069
\(184\) 8.22944e18 0.461763
\(185\) 6.06922e18 0.325217
\(186\) −1.41361e18 −0.0723552
\(187\) −1.99724e18 −0.0976734
\(188\) −9.57574e18 −0.447539
\(189\) −4.01332e19 −1.79299
\(190\) 9.05062e18 0.386610
\(191\) 3.18928e18 0.130289 0.0651447 0.997876i \(-0.479249\pi\)
0.0651447 + 0.997876i \(0.479249\pi\)
\(192\) 1.57578e19 0.615794
\(193\) −1.21602e19 −0.454679 −0.227340 0.973816i \(-0.573003\pi\)
−0.227340 + 0.973816i \(0.573003\pi\)
\(194\) −2.14600e19 −0.767919
\(195\) −2.57243e18 −0.0881149
\(196\) −2.82534e19 −0.926605
\(197\) 2.52396e19 0.792721 0.396360 0.918095i \(-0.370273\pi\)
0.396360 + 0.918095i \(0.370273\pi\)
\(198\) 1.40330e18 0.0422178
\(199\) 4.17039e19 1.20206 0.601029 0.799228i \(-0.294758\pi\)
0.601029 + 0.799228i \(0.294758\pi\)
\(200\) −1.93623e19 −0.534813
\(201\) 4.95850e18 0.131276
\(202\) 4.82272e18 0.122407
\(203\) 1.36376e19 0.331911
\(204\) 1.21315e19 0.283178
\(205\) 4.00231e19 0.896196
\(206\) −4.22710e18 −0.0908179
\(207\) −1.27086e19 −0.262029
\(208\) −4.02546e18 −0.0796668
\(209\) 3.40935e18 0.0647780
\(210\) 3.29117e19 0.600463
\(211\) −6.21552e19 −1.08912 −0.544561 0.838721i \(-0.683304\pi\)
−0.544561 + 0.838721i \(0.683304\pi\)
\(212\) 4.89838e18 0.0824513
\(213\) 3.14004e19 0.507818
\(214\) −2.21295e19 −0.343918
\(215\) −8.87144e19 −1.32516
\(216\) −7.55205e19 −1.08445
\(217\) 1.98200e19 0.273650
\(218\) −3.32000e19 −0.440817
\(219\) −6.11688e18 −0.0781187
\(220\) 2.21149e18 0.0271701
\(221\) −1.81957e19 −0.215097
\(222\) 1.90064e19 0.216221
\(223\) 1.25750e20 1.37694 0.688472 0.725263i \(-0.258282\pi\)
0.688472 + 0.725263i \(0.258282\pi\)
\(224\) −1.31805e20 −1.38939
\(225\) 2.99009e19 0.303482
\(226\) 8.47318e19 0.828180
\(227\) −1.65848e20 −1.56131 −0.780657 0.624960i \(-0.785115\pi\)
−0.780657 + 0.624960i \(0.785115\pi\)
\(228\) −2.07089e19 −0.187807
\(229\) −8.34006e19 −0.728731 −0.364366 0.931256i \(-0.618714\pi\)
−0.364366 + 0.931256i \(0.618714\pi\)
\(230\) 2.74107e19 0.230799
\(231\) 1.23978e19 0.100610
\(232\) 2.56625e19 0.200748
\(233\) 1.93098e20 1.45631 0.728154 0.685414i \(-0.240379\pi\)
0.728154 + 0.685414i \(0.240379\pi\)
\(234\) 1.27847e19 0.0929725
\(235\) −1.07442e20 −0.753526
\(236\) −2.49681e19 −0.168901
\(237\) 8.28946e19 0.540960
\(238\) 2.32796e20 1.46579
\(239\) 2.27368e20 1.38149 0.690745 0.723098i \(-0.257283\pi\)
0.690745 + 0.723098i \(0.257283\pi\)
\(240\) 3.01138e19 0.176592
\(241\) 1.33894e20 0.757909 0.378955 0.925415i \(-0.376284\pi\)
0.378955 + 0.925415i \(0.376284\pi\)
\(242\) 1.37959e20 0.753911
\(243\) 1.88908e20 0.996775
\(244\) −9.08957e19 −0.463159
\(245\) −3.17011e20 −1.56014
\(246\) 1.25336e20 0.595838
\(247\) 3.10606e19 0.142655
\(248\) 3.72962e19 0.165510
\(249\) 1.07577e20 0.461343
\(250\) −1.94855e20 −0.807647
\(251\) 2.46785e19 0.0988762 0.0494381 0.998777i \(-0.484257\pi\)
0.0494381 + 0.998777i \(0.484257\pi\)
\(252\) 1.19511e20 0.462919
\(253\) 1.03255e19 0.0386712
\(254\) −2.02636e20 −0.733889
\(255\) 1.36119e20 0.476790
\(256\) −2.97814e20 −1.00903
\(257\) 3.37458e20 1.10608 0.553042 0.833153i \(-0.313467\pi\)
0.553042 + 0.833153i \(0.313467\pi\)
\(258\) −2.77818e20 −0.881034
\(259\) −2.66485e20 −0.817757
\(260\) 2.01476e19 0.0598344
\(261\) −3.96303e19 −0.113915
\(262\) 4.28756e20 1.19303
\(263\) 6.61383e20 1.78168 0.890839 0.454319i \(-0.150117\pi\)
0.890839 + 0.454319i \(0.150117\pi\)
\(264\) 2.33294e19 0.0608515
\(265\) 5.49611e19 0.138824
\(266\) −3.97391e20 −0.972128
\(267\) 3.61060e20 0.855526
\(268\) −3.88357e19 −0.0891426
\(269\) −5.57024e20 −1.23874 −0.619369 0.785100i \(-0.712612\pi\)
−0.619369 + 0.785100i \(0.712612\pi\)
\(270\) −2.51544e20 −0.542028
\(271\) 6.76253e20 1.41212 0.706058 0.708154i \(-0.250472\pi\)
0.706058 + 0.708154i \(0.250472\pi\)
\(272\) 2.13006e20 0.431078
\(273\) 1.12949e20 0.221564
\(274\) −5.65810e20 −1.07595
\(275\) −2.42940e19 −0.0447890
\(276\) −6.27189e19 −0.112117
\(277\) 5.65903e20 0.980989 0.490494 0.871444i \(-0.336816\pi\)
0.490494 + 0.871444i \(0.336816\pi\)
\(278\) 8.53644e20 1.43515
\(279\) −5.75959e19 −0.0939195
\(280\) −8.68330e20 −1.37354
\(281\) −1.15115e21 −1.76656 −0.883282 0.468842i \(-0.844671\pi\)
−0.883282 + 0.468842i \(0.844671\pi\)
\(282\) −3.36466e20 −0.500984
\(283\) −6.78475e20 −0.980278 −0.490139 0.871644i \(-0.663054\pi\)
−0.490139 + 0.871644i \(0.663054\pi\)
\(284\) −2.45932e20 −0.344834
\(285\) −2.32359e20 −0.316212
\(286\) −1.03873e19 −0.0137212
\(287\) −1.75732e21 −2.25348
\(288\) 3.83020e20 0.476854
\(289\) 1.35579e20 0.163893
\(290\) 8.54769e19 0.100338
\(291\) 5.50950e20 0.628090
\(292\) 4.79083e19 0.0530464
\(293\) −3.70959e20 −0.398980 −0.199490 0.979900i \(-0.563929\pi\)
−0.199490 + 0.979900i \(0.563929\pi\)
\(294\) −9.92751e20 −1.03726
\(295\) −2.80148e20 −0.284381
\(296\) −5.01457e20 −0.494600
\(297\) −9.47560e19 −0.0908191
\(298\) −3.03237e20 −0.282451
\(299\) 9.40702e19 0.0851622
\(300\) 1.47566e20 0.129854
\(301\) 3.89523e21 3.33210
\(302\) −8.75829e20 −0.728384
\(303\) −1.23815e20 −0.100118
\(304\) −3.63607e20 −0.285896
\(305\) −1.01987e21 −0.779826
\(306\) −6.76496e20 −0.503075
\(307\) 5.52511e20 0.399636 0.199818 0.979833i \(-0.435965\pi\)
0.199818 + 0.979833i \(0.435965\pi\)
\(308\) −9.71011e19 −0.0683192
\(309\) 1.08524e20 0.0742810
\(310\) 1.24226e20 0.0827254
\(311\) −9.29008e20 −0.601944 −0.300972 0.953633i \(-0.597311\pi\)
−0.300972 + 0.953633i \(0.597311\pi\)
\(312\) 2.12542e20 0.134008
\(313\) 3.11081e21 1.90874 0.954371 0.298625i \(-0.0965278\pi\)
0.954371 + 0.298625i \(0.0965278\pi\)
\(314\) −1.96824e21 −1.17538
\(315\) 1.34095e21 0.779422
\(316\) −6.49242e20 −0.367339
\(317\) −3.94921e20 −0.217524 −0.108762 0.994068i \(-0.534689\pi\)
−0.108762 + 0.994068i \(0.534689\pi\)
\(318\) 1.72116e20 0.0922977
\(319\) 3.21989e19 0.0168121
\(320\) −1.38478e21 −0.704052
\(321\) 5.68137e20 0.281294
\(322\) −1.20354e21 −0.580342
\(323\) −1.64356e21 −0.771906
\(324\) 9.43279e18 0.00431527
\(325\) −2.21329e20 −0.0986347
\(326\) 9.24734e20 0.401483
\(327\) 8.52355e20 0.360549
\(328\) −3.30682e21 −1.36296
\(329\) 4.71753e21 1.89474
\(330\) 7.77059e19 0.0304148
\(331\) 3.35691e21 1.28056 0.640282 0.768140i \(-0.278817\pi\)
0.640282 + 0.768140i \(0.278817\pi\)
\(332\) −8.42556e20 −0.313274
\(333\) 7.74392e20 0.280663
\(334\) 1.54575e21 0.546129
\(335\) −4.35747e20 −0.150091
\(336\) −1.32222e21 −0.444039
\(337\) 8.44884e20 0.276658 0.138329 0.990386i \(-0.455827\pi\)
0.138329 + 0.990386i \(0.455827\pi\)
\(338\) 2.28597e21 0.729925
\(339\) −2.17535e21 −0.677378
\(340\) −1.06610e21 −0.323764
\(341\) 4.67957e19 0.0138610
\(342\) 1.15480e21 0.333645
\(343\) 7.57725e21 2.13556
\(344\) 7.32984e21 2.01534
\(345\) −7.03723e20 −0.188773
\(346\) −2.78850e21 −0.729834
\(347\) 3.04981e21 0.778883 0.389441 0.921051i \(-0.372668\pi\)
0.389441 + 0.921051i \(0.372668\pi\)
\(348\) −1.95581e20 −0.0487421
\(349\) 6.01583e21 1.46312 0.731559 0.681778i \(-0.238793\pi\)
0.731559 + 0.681778i \(0.238793\pi\)
\(350\) 2.83169e21 0.672151
\(351\) −8.63269e20 −0.200003
\(352\) −3.11198e20 −0.0703759
\(353\) −2.35616e21 −0.520139 −0.260070 0.965590i \(-0.583745\pi\)
−0.260070 + 0.965590i \(0.583745\pi\)
\(354\) −8.77312e20 −0.189072
\(355\) −2.75942e21 −0.580601
\(356\) −2.82787e21 −0.580945
\(357\) −5.97666e21 −1.19889
\(358\) 2.74313e21 0.537329
\(359\) 3.40797e21 0.651918 0.325959 0.945384i \(-0.394313\pi\)
0.325959 + 0.945384i \(0.394313\pi\)
\(360\) 2.52333e21 0.471414
\(361\) −2.67478e21 −0.488063
\(362\) −1.10093e21 −0.196217
\(363\) −3.54187e21 −0.616633
\(364\) −8.84633e20 −0.150453
\(365\) 5.37543e20 0.0893149
\(366\) −3.19383e21 −0.518469
\(367\) −8.06166e21 −1.27868 −0.639342 0.768923i \(-0.720793\pi\)
−0.639342 + 0.768923i \(0.720793\pi\)
\(368\) −1.10122e21 −0.170674
\(369\) 5.10668e21 0.773418
\(370\) −1.67025e21 −0.247211
\(371\) −2.41321e21 −0.349073
\(372\) −2.84245e20 −0.0401862
\(373\) −6.29484e21 −0.869880 −0.434940 0.900459i \(-0.643230\pi\)
−0.434940 + 0.900459i \(0.643230\pi\)
\(374\) 5.49641e20 0.0742456
\(375\) 5.00258e21 0.660584
\(376\) 8.87719e21 1.14598
\(377\) 2.93346e20 0.0370237
\(378\) 1.10447e22 1.36293
\(379\) −8.95460e21 −1.08047 −0.540235 0.841514i \(-0.681665\pi\)
−0.540235 + 0.841514i \(0.681665\pi\)
\(380\) 1.81987e21 0.214724
\(381\) 5.20234e21 0.600256
\(382\) −8.77693e20 −0.0990385
\(383\) −1.43335e22 −1.58185 −0.790923 0.611916i \(-0.790399\pi\)
−0.790923 + 0.611916i \(0.790399\pi\)
\(384\) 1.40779e20 0.0151958
\(385\) −1.08950e21 −0.115030
\(386\) 3.34651e21 0.345621
\(387\) −1.13194e22 −1.14361
\(388\) −4.31512e21 −0.426504
\(389\) −1.73259e22 −1.67542 −0.837712 0.546113i \(-0.816107\pi\)
−0.837712 + 0.546113i \(0.816107\pi\)
\(390\) 7.07935e20 0.0669798
\(391\) −4.97769e21 −0.460813
\(392\) 2.61923e22 2.37270
\(393\) −1.10076e22 −0.975789
\(394\) −6.94597e21 −0.602580
\(395\) −7.28467e21 −0.618492
\(396\) 2.82171e20 0.0234479
\(397\) 1.60638e22 1.30656 0.653280 0.757116i \(-0.273392\pi\)
0.653280 + 0.757116i \(0.273392\pi\)
\(398\) −1.14769e22 −0.913734
\(399\) 1.02023e22 0.795115
\(400\) 2.59096e21 0.197674
\(401\) −6.15988e21 −0.460092 −0.230046 0.973180i \(-0.573888\pi\)
−0.230046 + 0.973180i \(0.573888\pi\)
\(402\) −1.36458e21 −0.0997881
\(403\) 4.26330e20 0.0305248
\(404\) 9.69738e20 0.0679849
\(405\) 1.05838e20 0.00726567
\(406\) −3.75308e21 −0.252300
\(407\) −6.29181e20 −0.0414212
\(408\) −1.12466e22 −0.725117
\(409\) 6.89638e21 0.435485 0.217743 0.976006i \(-0.430131\pi\)
0.217743 + 0.976006i \(0.430131\pi\)
\(410\) −1.10144e22 −0.681236
\(411\) 1.45262e22 0.880029
\(412\) −8.49974e20 −0.0504405
\(413\) 1.23006e22 0.715075
\(414\) 3.49742e21 0.199180
\(415\) −9.45370e21 −0.527464
\(416\) −2.83515e21 −0.154982
\(417\) −2.19159e22 −1.17382
\(418\) −9.38255e20 −0.0492405
\(419\) −5.13587e21 −0.264116 −0.132058 0.991242i \(-0.542158\pi\)
−0.132058 + 0.991242i \(0.542158\pi\)
\(420\) 6.61779e21 0.333499
\(421\) 2.49739e22 1.23336 0.616678 0.787216i \(-0.288478\pi\)
0.616678 + 0.787216i \(0.288478\pi\)
\(422\) 1.71052e22 0.827888
\(423\) −1.37089e22 −0.650294
\(424\) −4.54104e21 −0.211128
\(425\) 1.17115e22 0.533713
\(426\) −8.64141e21 −0.386014
\(427\) 4.47801e22 1.96087
\(428\) −4.44973e21 −0.191013
\(429\) 2.66677e20 0.0112227
\(430\) 2.44143e22 1.00731
\(431\) −2.73222e22 −1.10525 −0.552623 0.833432i \(-0.686373\pi\)
−0.552623 + 0.833432i \(0.686373\pi\)
\(432\) 1.01057e22 0.400827
\(433\) −3.23696e22 −1.25890 −0.629449 0.777041i \(-0.716720\pi\)
−0.629449 + 0.777041i \(0.716720\pi\)
\(434\) −5.45447e21 −0.208013
\(435\) −2.19448e21 −0.0820676
\(436\) −6.67577e21 −0.244831
\(437\) 8.49706e21 0.305616
\(438\) 1.68337e21 0.0593813
\(439\) 2.52322e22 0.872986 0.436493 0.899708i \(-0.356220\pi\)
0.436493 + 0.899708i \(0.356220\pi\)
\(440\) −2.05016e21 −0.0695729
\(441\) −4.04485e22 −1.34640
\(442\) 5.00748e21 0.163504
\(443\) −5.07854e22 −1.62670 −0.813350 0.581775i \(-0.802358\pi\)
−0.813350 + 0.581775i \(0.802358\pi\)
\(444\) 3.82174e21 0.120090
\(445\) −3.17295e22 −0.978143
\(446\) −3.46065e22 −1.04667
\(447\) 7.78509e21 0.231020
\(448\) 6.08021e22 1.77034
\(449\) −3.71727e22 −1.06201 −0.531007 0.847367i \(-0.678186\pi\)
−0.531007 + 0.847367i \(0.678186\pi\)
\(450\) −8.22875e21 −0.230689
\(451\) −4.14909e21 −0.114144
\(452\) 1.70376e22 0.459973
\(453\) 2.24854e22 0.595754
\(454\) 4.56415e22 1.18682
\(455\) −9.92582e21 −0.253320
\(456\) 1.91982e22 0.480905
\(457\) 4.84965e22 1.19240 0.596201 0.802835i \(-0.296676\pi\)
0.596201 + 0.802835i \(0.296676\pi\)
\(458\) 2.29519e22 0.553939
\(459\) 4.56795e22 1.08222
\(460\) 5.51166e21 0.128186
\(461\) 1.78431e22 0.407393 0.203697 0.979034i \(-0.434704\pi\)
0.203697 + 0.979034i \(0.434704\pi\)
\(462\) −3.41187e21 −0.0764779
\(463\) −4.48460e21 −0.0986928 −0.0493464 0.998782i \(-0.515714\pi\)
−0.0493464 + 0.998782i \(0.515714\pi\)
\(464\) −3.43402e21 −0.0741994
\(465\) −3.18930e21 −0.0676621
\(466\) −5.31408e22 −1.10700
\(467\) −1.51961e22 −0.310841 −0.155420 0.987848i \(-0.549673\pi\)
−0.155420 + 0.987848i \(0.549673\pi\)
\(468\) 2.57070e21 0.0516371
\(469\) 1.91326e22 0.377402
\(470\) 2.95682e22 0.572787
\(471\) 5.05313e22 0.961353
\(472\) 2.31467e22 0.432495
\(473\) 9.19680e21 0.168778
\(474\) −2.28126e22 −0.411206
\(475\) −1.99919e22 −0.353964
\(476\) 4.68100e22 0.814104
\(477\) 7.01267e21 0.119806
\(478\) −6.25720e22 −1.05013
\(479\) −1.74935e22 −0.288419 −0.144210 0.989547i \(-0.546064\pi\)
−0.144210 + 0.989547i \(0.546064\pi\)
\(480\) 2.12093e22 0.343538
\(481\) −5.73211e21 −0.0912182
\(482\) −3.68478e22 −0.576118
\(483\) 3.08987e22 0.474668
\(484\) 2.77404e22 0.418724
\(485\) −4.84167e22 −0.718110
\(486\) −5.19877e22 −0.757691
\(487\) 3.73949e22 0.535570 0.267785 0.963479i \(-0.413708\pi\)
0.267785 + 0.963479i \(0.413708\pi\)
\(488\) 8.42649e22 1.18598
\(489\) −2.37410e22 −0.328378
\(490\) 8.72416e22 1.18592
\(491\) −3.88156e22 −0.518577 −0.259289 0.965800i \(-0.583488\pi\)
−0.259289 + 0.965800i \(0.583488\pi\)
\(492\) 2.52022e22 0.330930
\(493\) −1.55223e22 −0.200335
\(494\) −8.54791e21 −0.108438
\(495\) 3.16603e21 0.0394795
\(496\) −4.99077e21 −0.0611749
\(497\) 1.21160e23 1.45992
\(498\) −2.96052e22 −0.350686
\(499\) 2.72246e22 0.317034 0.158517 0.987356i \(-0.449329\pi\)
0.158517 + 0.987356i \(0.449329\pi\)
\(500\) −3.91809e22 −0.448569
\(501\) −3.96846e22 −0.446685
\(502\) −6.79154e21 −0.0751600
\(503\) 9.46361e21 0.102974 0.0514872 0.998674i \(-0.483604\pi\)
0.0514872 + 0.998674i \(0.483604\pi\)
\(504\) −1.10793e23 −1.18537
\(505\) 1.08807e22 0.114467
\(506\) −2.84159e21 −0.0293956
\(507\) −5.86884e22 −0.597014
\(508\) −4.07455e22 −0.407604
\(509\) 1.55676e23 1.53152 0.765758 0.643128i \(-0.222364\pi\)
0.765758 + 0.643128i \(0.222364\pi\)
\(510\) −3.74601e22 −0.362428
\(511\) −2.36022e22 −0.224582
\(512\) 7.93470e22 0.742568
\(513\) −7.79764e22 −0.717737
\(514\) −9.28687e22 −0.840781
\(515\) −9.53693e21 −0.0849272
\(516\) −5.58628e22 −0.489328
\(517\) 1.11383e22 0.0959727
\(518\) 7.33368e22 0.621611
\(519\) 7.15901e22 0.596940
\(520\) −1.86779e22 −0.153214
\(521\) −3.31513e22 −0.267534 −0.133767 0.991013i \(-0.542707\pi\)
−0.133767 + 0.991013i \(0.542707\pi\)
\(522\) 1.09063e22 0.0865919
\(523\) −1.91253e23 −1.49397 −0.746987 0.664838i \(-0.768500\pi\)
−0.746987 + 0.664838i \(0.768500\pi\)
\(524\) 8.62131e22 0.662609
\(525\) −7.26988e22 −0.549760
\(526\) −1.82013e23 −1.35433
\(527\) −2.25591e22 −0.165170
\(528\) −3.12182e21 −0.0224916
\(529\) −1.15316e23 −0.817553
\(530\) −1.51253e22 −0.105526
\(531\) −3.57451e22 −0.245421
\(532\) −7.99061e22 −0.539922
\(533\) −3.78000e22 −0.251369
\(534\) −9.93639e22 −0.650321
\(535\) −4.99272e22 −0.321610
\(536\) 3.60027e22 0.228262
\(537\) −7.04252e22 −0.439488
\(538\) 1.53294e23 0.941617
\(539\) 3.28637e22 0.198706
\(540\) −5.05797e22 −0.301044
\(541\) −1.68705e22 −0.0988445 −0.0494222 0.998778i \(-0.515738\pi\)
−0.0494222 + 0.998778i \(0.515738\pi\)
\(542\) −1.86105e23 −1.07341
\(543\) 2.82645e22 0.160488
\(544\) 1.50021e23 0.838611
\(545\) −7.49038e22 −0.412225
\(546\) −3.10837e22 −0.168420
\(547\) −3.33920e23 −1.78135 −0.890677 0.454637i \(-0.849769\pi\)
−0.890677 + 0.454637i \(0.849769\pi\)
\(548\) −1.13771e23 −0.597583
\(549\) −1.30129e23 −0.672991
\(550\) 6.68572e21 0.0340460
\(551\) 2.64971e22 0.132865
\(552\) 5.81436e22 0.287091
\(553\) 3.19852e23 1.55520
\(554\) −1.55737e23 −0.745691
\(555\) 4.28810e22 0.202197
\(556\) 1.71648e23 0.797084
\(557\) 1.74292e23 0.797094 0.398547 0.917148i \(-0.369515\pi\)
0.398547 + 0.917148i \(0.369515\pi\)
\(558\) 1.58504e22 0.0713922
\(559\) 8.37869e22 0.371685
\(560\) 1.16195e23 0.507680
\(561\) −1.41111e22 −0.0607263
\(562\) 3.16798e23 1.34284
\(563\) 1.22487e23 0.511409 0.255704 0.966755i \(-0.417693\pi\)
0.255704 + 0.966755i \(0.417693\pi\)
\(564\) −6.76556e22 −0.278248
\(565\) 1.91167e23 0.774462
\(566\) 1.86717e23 0.745151
\(567\) −4.64711e21 −0.0182695
\(568\) 2.27992e23 0.882994
\(569\) −4.32759e23 −1.65117 −0.825584 0.564279i \(-0.809154\pi\)
−0.825584 + 0.564279i \(0.809154\pi\)
\(570\) 6.39455e22 0.240366
\(571\) 2.54448e23 0.942305 0.471153 0.882052i \(-0.343838\pi\)
0.471153 + 0.882052i \(0.343838\pi\)
\(572\) −2.08865e21 −0.00762079
\(573\) 2.25333e22 0.0810047
\(574\) 4.83615e23 1.71296
\(575\) −6.05475e22 −0.211310
\(576\) −1.76688e23 −0.607598
\(577\) 2.06031e23 0.698134 0.349067 0.937098i \(-0.386499\pi\)
0.349067 + 0.937098i \(0.386499\pi\)
\(578\) −3.73114e22 −0.124582
\(579\) −8.59159e22 −0.282687
\(580\) 1.71874e22 0.0557280
\(581\) 4.15089e23 1.32631
\(582\) −1.51622e23 −0.477437
\(583\) −5.69768e21 −0.0176813
\(584\) −4.44134e22 −0.135833
\(585\) 2.88440e22 0.0869421
\(586\) 1.02088e23 0.303281
\(587\) 1.82842e23 0.535368 0.267684 0.963507i \(-0.413742\pi\)
0.267684 + 0.963507i \(0.413742\pi\)
\(588\) −1.99619e23 −0.576097
\(589\) 3.85090e22 0.109542
\(590\) 7.70970e22 0.216170
\(591\) 1.78326e23 0.492857
\(592\) 6.71022e22 0.182811
\(593\) −1.91371e23 −0.513940 −0.256970 0.966419i \(-0.582724\pi\)
−0.256970 + 0.966419i \(0.582724\pi\)
\(594\) 2.60769e22 0.0690354
\(595\) 5.25221e23 1.37072
\(596\) −6.09740e22 −0.156874
\(597\) 2.94651e23 0.747353
\(598\) −2.58882e22 −0.0647353
\(599\) −7.84490e23 −1.93401 −0.967007 0.254750i \(-0.918007\pi\)
−0.967007 + 0.254750i \(0.918007\pi\)
\(600\) −1.36801e23 −0.332508
\(601\) −8.14238e23 −1.95127 −0.975637 0.219391i \(-0.929593\pi\)
−0.975637 + 0.219391i \(0.929593\pi\)
\(602\) −1.07197e24 −2.53287
\(603\) −5.55984e22 −0.129528
\(604\) −1.76109e23 −0.404546
\(605\) 3.11255e23 0.705011
\(606\) 3.40740e22 0.0761037
\(607\) 6.62130e23 1.45828 0.729138 0.684367i \(-0.239921\pi\)
0.729138 + 0.684367i \(0.239921\pi\)
\(608\) −2.56090e23 −0.556176
\(609\) 9.63540e22 0.206359
\(610\) 2.80670e23 0.592778
\(611\) 1.01474e23 0.211352
\(612\) −1.36028e23 −0.279409
\(613\) 7.28838e23 1.47644 0.738222 0.674557i \(-0.235665\pi\)
0.738222 + 0.674557i \(0.235665\pi\)
\(614\) −1.52052e23 −0.303780
\(615\) 2.82776e23 0.557190
\(616\) 9.00176e22 0.174941
\(617\) −1.98266e23 −0.380035 −0.190017 0.981781i \(-0.560854\pi\)
−0.190017 + 0.981781i \(0.560854\pi\)
\(618\) −2.98658e22 −0.0564641
\(619\) 1.01053e24 1.88442 0.942212 0.335017i \(-0.108742\pi\)
0.942212 + 0.335017i \(0.108742\pi\)
\(620\) 2.49791e22 0.0459459
\(621\) −2.36159e23 −0.428475
\(622\) 2.55664e23 0.457563
\(623\) 1.39316e24 2.45954
\(624\) −2.84412e22 −0.0495312
\(625\) −1.51661e23 −0.260551
\(626\) −8.56098e23 −1.45091
\(627\) 2.40881e22 0.0402744
\(628\) −3.95769e23 −0.652806
\(629\) 3.03312e23 0.493583
\(630\) −3.69030e23 −0.592471
\(631\) −7.58913e23 −1.20210 −0.601052 0.799210i \(-0.705252\pi\)
−0.601052 + 0.799210i \(0.705252\pi\)
\(632\) 6.01880e23 0.940621
\(633\) −4.39146e23 −0.677139
\(634\) 1.08683e23 0.165349
\(635\) −4.57175e23 −0.686287
\(636\) 3.46086e22 0.0512624
\(637\) 2.99403e23 0.437593
\(638\) −8.86117e21 −0.0127795
\(639\) −3.52084e23 −0.501059
\(640\) −1.23715e22 −0.0173737
\(641\) −8.99920e23 −1.24713 −0.623564 0.781772i \(-0.714316\pi\)
−0.623564 + 0.781772i \(0.714316\pi\)
\(642\) −1.56352e23 −0.213823
\(643\) −1.74644e23 −0.235700 −0.117850 0.993031i \(-0.537600\pi\)
−0.117850 + 0.993031i \(0.537600\pi\)
\(644\) −2.42003e23 −0.322323
\(645\) −6.26795e23 −0.823888
\(646\) 4.52309e23 0.586758
\(647\) −1.05814e24 −1.35474 −0.677372 0.735641i \(-0.736881\pi\)
−0.677372 + 0.735641i \(0.736881\pi\)
\(648\) −8.74467e21 −0.0110498
\(649\) 2.90423e22 0.0362202
\(650\) 6.09099e22 0.0749763
\(651\) 1.40034e23 0.170136
\(652\) 1.85943e23 0.222985
\(653\) −9.92357e23 −1.17464 −0.587321 0.809354i \(-0.699817\pi\)
−0.587321 + 0.809354i \(0.699817\pi\)
\(654\) −2.34569e23 −0.274069
\(655\) 9.67333e23 1.11564
\(656\) 4.42501e23 0.503770
\(657\) 6.85869e22 0.0770789
\(658\) −1.29827e24 −1.44027
\(659\) 7.39660e23 0.810039 0.405020 0.914308i \(-0.367265\pi\)
0.405020 + 0.914308i \(0.367265\pi\)
\(660\) 1.56249e22 0.0168925
\(661\) 1.28597e23 0.137252 0.0686258 0.997642i \(-0.478139\pi\)
0.0686258 + 0.997642i \(0.478139\pi\)
\(662\) −9.23824e23 −0.973411
\(663\) −1.28558e23 −0.133732
\(664\) 7.81092e23 0.802183
\(665\) −8.96568e23 −0.909074
\(666\) −2.13113e23 −0.213344
\(667\) 8.02489e22 0.0793176
\(668\) 3.10816e23 0.303321
\(669\) 8.88463e23 0.856086
\(670\) 1.19918e23 0.114090
\(671\) 1.05728e23 0.0993224
\(672\) −9.31247e23 −0.863825
\(673\) −1.05495e24 −0.966283 −0.483142 0.875542i \(-0.660504\pi\)
−0.483142 + 0.875542i \(0.660504\pi\)
\(674\) −2.32513e23 −0.210299
\(675\) 5.55636e23 0.496259
\(676\) 4.59656e23 0.405402
\(677\) 5.37510e23 0.468147 0.234074 0.972219i \(-0.424794\pi\)
0.234074 + 0.972219i \(0.424794\pi\)
\(678\) 5.98657e23 0.514903
\(679\) 2.12586e24 1.80568
\(680\) 9.88332e23 0.829043
\(681\) −1.17177e24 −0.970714
\(682\) −1.28782e22 −0.0105363
\(683\) −2.85014e23 −0.230298 −0.115149 0.993348i \(-0.536735\pi\)
−0.115149 + 0.993348i \(0.536735\pi\)
\(684\) 2.32204e23 0.185307
\(685\) −1.27655e24 −1.00616
\(686\) −2.08526e24 −1.62333
\(687\) −5.89251e23 −0.453073
\(688\) −9.80840e23 −0.744898
\(689\) −5.19083e22 −0.0389380
\(690\) 1.93665e23 0.143494
\(691\) 5.09992e23 0.373250 0.186625 0.982431i \(-0.440245\pi\)
0.186625 + 0.982431i \(0.440245\pi\)
\(692\) −5.60704e23 −0.405352
\(693\) −1.39013e23 −0.0992710
\(694\) −8.39310e23 −0.592061
\(695\) 1.92594e24 1.34206
\(696\) 1.81314e23 0.124811
\(697\) 2.00017e24 1.36016
\(698\) −1.65556e24 −1.11218
\(699\) 1.36430e24 0.905428
\(700\) 5.69387e23 0.373314
\(701\) −1.64225e24 −1.06374 −0.531869 0.846826i \(-0.678510\pi\)
−0.531869 + 0.846826i \(0.678510\pi\)
\(702\) 2.37572e23 0.152030
\(703\) −5.17764e23 −0.327349
\(704\) 1.43556e23 0.0896715
\(705\) −7.59113e23 −0.468489
\(706\) 6.48417e23 0.395379
\(707\) −4.77745e23 −0.287827
\(708\) −1.76407e23 −0.105011
\(709\) 1.30885e24 0.769831 0.384916 0.922952i \(-0.374231\pi\)
0.384916 + 0.922952i \(0.374231\pi\)
\(710\) 7.59396e23 0.441339
\(711\) −9.29475e23 −0.533760
\(712\) 2.62158e24 1.48759
\(713\) 1.16628e23 0.0653947
\(714\) 1.64478e24 0.911324
\(715\) −2.34352e22 −0.0128312
\(716\) 5.51580e23 0.298434
\(717\) 1.60643e24 0.858912
\(718\) −9.37876e23 −0.495550
\(719\) 8.51530e23 0.444636 0.222318 0.974974i \(-0.428638\pi\)
0.222318 + 0.974974i \(0.428638\pi\)
\(720\) −3.37658e23 −0.174241
\(721\) 4.18743e23 0.213549
\(722\) 7.36101e23 0.370997
\(723\) 9.46005e23 0.471214
\(724\) −2.21371e23 −0.108979
\(725\) −1.88810e23 −0.0918655
\(726\) 9.74725e23 0.468728
\(727\) −2.16935e24 −1.03107 −0.515533 0.856870i \(-0.672406\pi\)
−0.515533 + 0.856870i \(0.672406\pi\)
\(728\) 8.20099e23 0.385256
\(729\) 1.35671e24 0.629945
\(730\) −1.47932e23 −0.0678920
\(731\) −4.43355e24 −2.01119
\(732\) −6.42207e23 −0.287959
\(733\) 4.75782e23 0.210874 0.105437 0.994426i \(-0.466376\pi\)
0.105437 + 0.994426i \(0.466376\pi\)
\(734\) 2.21858e24 0.971981
\(735\) −2.23978e24 −0.969981
\(736\) −7.75593e23 −0.332026
\(737\) 4.51728e22 0.0191163
\(738\) −1.40536e24 −0.587908
\(739\) 4.65308e24 1.92426 0.962128 0.272598i \(-0.0878828\pi\)
0.962128 + 0.272598i \(0.0878828\pi\)
\(740\) −3.35850e23 −0.137302
\(741\) 2.19453e23 0.0886926
\(742\) 6.64116e23 0.265345
\(743\) −2.38022e24 −0.940181 −0.470091 0.882618i \(-0.655779\pi\)
−0.470091 + 0.882618i \(0.655779\pi\)
\(744\) 2.63509e23 0.102902
\(745\) −6.84144e23 −0.264131
\(746\) 1.73234e24 0.661232
\(747\) −1.20623e24 −0.455202
\(748\) 1.10520e23 0.0412362
\(749\) 2.19218e24 0.808687
\(750\) −1.37671e24 −0.502138
\(751\) 1.21739e24 0.439025 0.219512 0.975610i \(-0.429553\pi\)
0.219512 + 0.975610i \(0.429553\pi\)
\(752\) −1.18790e24 −0.423572
\(753\) 1.74361e23 0.0614742
\(754\) −8.07292e22 −0.0281432
\(755\) −1.97599e24 −0.681139
\(756\) 2.22083e24 0.756973
\(757\) −1.14951e24 −0.387434 −0.193717 0.981057i \(-0.562054\pi\)
−0.193717 + 0.981057i \(0.562054\pi\)
\(758\) 2.46431e24 0.821310
\(759\) 7.29532e22 0.0240430
\(760\) −1.68711e24 −0.549830
\(761\) −4.49008e24 −1.44705 −0.723527 0.690296i \(-0.757480\pi\)
−0.723527 + 0.690296i \(0.757480\pi\)
\(762\) −1.43169e24 −0.456280
\(763\) 3.28884e24 1.03654
\(764\) −1.76484e23 −0.0550062
\(765\) −1.52627e24 −0.470444
\(766\) 3.94460e24 1.20243
\(767\) 2.64588e23 0.0797644
\(768\) −2.10415e24 −0.627345
\(769\) 1.28099e24 0.377720 0.188860 0.982004i \(-0.439521\pi\)
0.188860 + 0.982004i \(0.439521\pi\)
\(770\) 2.99831e23 0.0874390
\(771\) 2.38425e24 0.687684
\(772\) 6.72906e23 0.191958
\(773\) 2.30942e24 0.651594 0.325797 0.945440i \(-0.394367\pi\)
0.325797 + 0.945440i \(0.394367\pi\)
\(774\) 3.11510e24 0.869308
\(775\) −2.74404e23 −0.0757400
\(776\) 4.00033e24 1.09212
\(777\) −1.88280e24 −0.508423
\(778\) 4.76810e24 1.27356
\(779\) −3.41436e24 −0.902071
\(780\) 1.42349e23 0.0372007
\(781\) 2.86063e23 0.0739481
\(782\) 1.36986e24 0.350283
\(783\) −7.36433e23 −0.186277
\(784\) −3.50492e24 −0.876984
\(785\) −4.44063e24 −1.09914
\(786\) 3.02930e24 0.741738
\(787\) 3.75479e24 0.909495 0.454747 0.890620i \(-0.349730\pi\)
0.454747 + 0.890620i \(0.349730\pi\)
\(788\) −1.39667e24 −0.334674
\(789\) 4.67288e24 1.10772
\(790\) 2.00475e24 0.470142
\(791\) −8.39365e24 −1.94738
\(792\) −2.61587e23 −0.0600415
\(793\) 9.63225e23 0.218729
\(794\) −4.42077e24 −0.993171
\(795\) 3.88318e23 0.0863111
\(796\) −2.30775e24 −0.507490
\(797\) −2.11929e24 −0.461099 −0.230550 0.973061i \(-0.574052\pi\)
−0.230550 + 0.973061i \(0.574052\pi\)
\(798\) −2.80769e24 −0.604400
\(799\) −5.36948e24 −1.14363
\(800\) 1.82482e24 0.384552
\(801\) −4.04847e24 −0.844139
\(802\) 1.69520e24 0.349735
\(803\) −5.57257e22 −0.0113756
\(804\) −2.74386e23 −0.0554225
\(805\) −2.71534e24 −0.542700
\(806\) −1.17326e23 −0.0232032
\(807\) −3.93555e24 −0.770159
\(808\) −8.98996e23 −0.174085
\(809\) 6.41483e24 1.22920 0.614601 0.788838i \(-0.289317\pi\)
0.614601 + 0.788838i \(0.289317\pi\)
\(810\) −2.91268e22 −0.00552294
\(811\) −7.63671e24 −1.43294 −0.716472 0.697616i \(-0.754244\pi\)
−0.716472 + 0.697616i \(0.754244\pi\)
\(812\) −7.54658e23 −0.140128
\(813\) 4.77794e24 0.877953
\(814\) 1.73151e23 0.0314860
\(815\) 2.08633e24 0.375442
\(816\) 1.50495e24 0.268014
\(817\) 7.56820e24 1.33384
\(818\) −1.89789e24 −0.331030
\(819\) −1.26647e24 −0.218615
\(820\) −2.21474e24 −0.378360
\(821\) 9.91280e24 1.67602 0.838010 0.545654i \(-0.183719\pi\)
0.838010 + 0.545654i \(0.183719\pi\)
\(822\) −3.99763e24 −0.668947
\(823\) −9.37680e24 −1.55295 −0.776473 0.630151i \(-0.782993\pi\)
−0.776473 + 0.630151i \(0.782993\pi\)
\(824\) 7.87968e23 0.129160
\(825\) −1.71645e23 −0.0278466
\(826\) −3.38514e24 −0.543559
\(827\) 6.91719e24 1.09934 0.549671 0.835381i \(-0.314753\pi\)
0.549671 + 0.835381i \(0.314753\pi\)
\(828\) 7.03251e23 0.110625
\(829\) −9.17167e24 −1.42802 −0.714011 0.700135i \(-0.753123\pi\)
−0.714011 + 0.700135i \(0.753123\pi\)
\(830\) 2.60166e24 0.400948
\(831\) 3.99828e24 0.609909
\(832\) 1.30786e24 0.197475
\(833\) −1.58428e25 −2.36782
\(834\) 6.03127e24 0.892272
\(835\) 3.48743e24 0.510706
\(836\) −1.88662e23 −0.0273483
\(837\) −1.07028e24 −0.153579
\(838\) 1.41339e24 0.200766
\(839\) 2.44624e24 0.343972 0.171986 0.985099i \(-0.444982\pi\)
0.171986 + 0.985099i \(0.444982\pi\)
\(840\) −6.13503e24 −0.853970
\(841\) 2.50246e23 0.0344828
\(842\) −6.87283e24 −0.937525
\(843\) −8.13326e24 −1.09832
\(844\) 3.43946e24 0.459811
\(845\) 5.15746e24 0.682580
\(846\) 3.77270e24 0.494316
\(847\) −1.36664e25 −1.77275
\(848\) 6.07658e23 0.0780360
\(849\) −4.79364e24 −0.609467
\(850\) −3.22302e24 −0.405698
\(851\) −1.56810e24 −0.195421
\(852\) −1.73759e24 −0.214393
\(853\) −1.00896e25 −1.23256 −0.616281 0.787526i \(-0.711361\pi\)
−0.616281 + 0.787526i \(0.711361\pi\)
\(854\) −1.23235e25 −1.49054
\(855\) 2.60538e24 0.312004
\(856\) 4.12513e24 0.489114
\(857\) 9.30465e24 1.09235 0.546177 0.837670i \(-0.316083\pi\)
0.546177 + 0.837670i \(0.316083\pi\)
\(858\) −7.33898e22 −0.00853087
\(859\) 2.35972e24 0.271593 0.135796 0.990737i \(-0.456641\pi\)
0.135796 + 0.990737i \(0.456641\pi\)
\(860\) 4.90915e24 0.559461
\(861\) −1.24160e25 −1.40105
\(862\) 7.51909e24 0.840143
\(863\) 1.26821e25 1.40313 0.701567 0.712603i \(-0.252484\pi\)
0.701567 + 0.712603i \(0.252484\pi\)
\(864\) 7.11751e24 0.779761
\(865\) −6.29125e24 −0.682495
\(866\) 8.90815e24 0.956942
\(867\) 9.57908e23 0.101897
\(868\) −1.09677e24 −0.115531
\(869\) 7.55183e23 0.0787742
\(870\) 6.03921e23 0.0623830
\(871\) 4.11544e23 0.0420980
\(872\) 6.18877e24 0.626923
\(873\) −6.17765e24 −0.619730
\(874\) −2.33840e24 −0.232312
\(875\) 1.93026e25 1.89910
\(876\) 3.38487e23 0.0329805
\(877\) −6.95139e24 −0.670772 −0.335386 0.942081i \(-0.608867\pi\)
−0.335386 + 0.942081i \(0.608867\pi\)
\(878\) −6.94393e24 −0.663593
\(879\) −2.62094e24 −0.248057
\(880\) 2.74342e23 0.0257151
\(881\) 1.17883e25 1.09435 0.547175 0.837018i \(-0.315703\pi\)
0.547175 + 0.837018i \(0.315703\pi\)
\(882\) 1.11314e25 1.02345
\(883\) −1.85904e24 −0.169286 −0.0846432 0.996411i \(-0.526975\pi\)
−0.0846432 + 0.996411i \(0.526975\pi\)
\(884\) 1.00689e24 0.0908107
\(885\) −1.97934e24 −0.176808
\(886\) 1.39762e25 1.23652
\(887\) 5.22940e24 0.458249 0.229124 0.973397i \(-0.426414\pi\)
0.229124 + 0.973397i \(0.426414\pi\)
\(888\) −3.54295e24 −0.307507
\(889\) 2.00734e25 1.72567
\(890\) 8.73197e24 0.743528
\(891\) −1.09720e22 −0.000925391 0
\(892\) −6.95857e24 −0.581325
\(893\) 9.16587e24 0.758466
\(894\) −2.14246e24 −0.175608
\(895\) 6.18888e24 0.502477
\(896\) 5.43203e23 0.0436862
\(897\) 6.64635e23 0.0529478
\(898\) 1.02300e25 0.807281
\(899\) 3.63691e23 0.0284299
\(900\) −1.65461e24 −0.128125
\(901\) 2.74671e24 0.210694
\(902\) 1.14183e24 0.0867655
\(903\) 2.75210e25 2.07166
\(904\) −1.57947e25 −1.17782
\(905\) −2.48385e24 −0.183490
\(906\) −6.18801e24 −0.452857
\(907\) 1.94030e25 1.40672 0.703358 0.710835i \(-0.251683\pi\)
0.703358 + 0.710835i \(0.251683\pi\)
\(908\) 9.17745e24 0.659163
\(909\) 1.38831e24 0.0987853
\(910\) 2.73159e24 0.192559
\(911\) 1.64184e25 1.14664 0.573318 0.819333i \(-0.305656\pi\)
0.573318 + 0.819333i \(0.305656\pi\)
\(912\) −2.56900e24 −0.177749
\(913\) 9.80041e23 0.0671804
\(914\) −1.33463e25 −0.906395
\(915\) −7.20573e24 −0.484840
\(916\) 4.61510e24 0.307659
\(917\) −4.24732e25 −2.80528
\(918\) −1.25710e25 −0.822637
\(919\) −1.78581e25 −1.15785 −0.578927 0.815380i \(-0.696528\pi\)
−0.578927 + 0.815380i \(0.696528\pi\)
\(920\) −5.10958e24 −0.328238
\(921\) 3.90367e24 0.248465
\(922\) −4.91045e24 −0.309676
\(923\) 2.60616e24 0.162849
\(924\) −6.86050e23 −0.0424760
\(925\) 3.68943e24 0.226336
\(926\) 1.23417e24 0.0750205
\(927\) −1.21685e24 −0.0732923
\(928\) −2.41859e24 −0.144346
\(929\) −5.31955e24 −0.314588 −0.157294 0.987552i \(-0.550277\pi\)
−0.157294 + 0.987552i \(0.550277\pi\)
\(930\) 8.77698e23 0.0514328
\(931\) 2.70441e25 1.57036
\(932\) −1.06854e25 −0.614830
\(933\) −6.56374e24 −0.374246
\(934\) 4.18197e24 0.236283
\(935\) 1.24007e24 0.0694299
\(936\) −2.38317e24 −0.132224
\(937\) −2.50045e25 −1.37478 −0.687388 0.726290i \(-0.741243\pi\)
−0.687388 + 0.726290i \(0.741243\pi\)
\(938\) −5.26530e24 −0.286879
\(939\) 2.19789e25 1.18672
\(940\) 5.94548e24 0.318127
\(941\) −1.25452e25 −0.665220 −0.332610 0.943065i \(-0.607929\pi\)
−0.332610 + 0.943065i \(0.607929\pi\)
\(942\) −1.39063e25 −0.730765
\(943\) −1.03407e25 −0.538519
\(944\) −3.09736e24 −0.159856
\(945\) 2.49183e25 1.27452
\(946\) −2.53097e24 −0.128296
\(947\) 2.41151e25 1.21148 0.605738 0.795664i \(-0.292878\pi\)
0.605738 + 0.795664i \(0.292878\pi\)
\(948\) −4.58710e24 −0.228385
\(949\) −5.07686e23 −0.0250514
\(950\) 5.50180e24 0.269063
\(951\) −2.79024e24 −0.135241
\(952\) −4.33952e25 −2.08463
\(953\) 1.36562e25 0.650190 0.325095 0.945681i \(-0.394604\pi\)
0.325095 + 0.945681i \(0.394604\pi\)
\(954\) −1.92989e24 −0.0910692
\(955\) −1.98020e24 −0.0926146
\(956\) −1.25818e25 −0.583244
\(957\) 2.27496e23 0.0104525
\(958\) 4.81422e24 0.219240
\(959\) 5.60500e25 2.52998
\(960\) −9.78388e24 −0.437729
\(961\) −2.20216e25 −0.976560
\(962\) 1.57748e24 0.0693388
\(963\) −6.37037e24 −0.277550
\(964\) −7.40925e24 −0.319977
\(965\) 7.55018e24 0.323203
\(966\) −8.50336e24 −0.360815
\(967\) 2.51961e25 1.05976 0.529881 0.848072i \(-0.322237\pi\)
0.529881 + 0.848072i \(0.322237\pi\)
\(968\) −2.57168e25 −1.07220
\(969\) −1.16123e25 −0.479916
\(970\) 1.33243e25 0.545865
\(971\) 1.28706e25 0.522678 0.261339 0.965247i \(-0.415836\pi\)
0.261339 + 0.965247i \(0.415836\pi\)
\(972\) −1.04535e25 −0.420823
\(973\) −8.45633e25 −3.37460
\(974\) −1.02911e25 −0.407109
\(975\) −1.56376e24 −0.0613240
\(976\) −1.12759e25 −0.438356
\(977\) −3.80187e25 −1.46519 −0.732594 0.680666i \(-0.761691\pi\)
−0.732594 + 0.680666i \(0.761691\pi\)
\(978\) 6.53354e24 0.249613
\(979\) 3.28931e24 0.124581
\(980\) 1.75423e25 0.658665
\(981\) −9.55723e24 −0.355750
\(982\) 1.06821e25 0.394192
\(983\) −1.73844e25 −0.635997 −0.317998 0.948091i \(-0.603011\pi\)
−0.317998 + 0.948091i \(0.603011\pi\)
\(984\) −2.33637e25 −0.847392
\(985\) −1.56711e25 −0.563495
\(986\) 4.27175e24 0.152283
\(987\) 3.33308e25 1.17801
\(988\) −1.71879e24 −0.0602266
\(989\) 2.29210e25 0.796280
\(990\) −8.71295e23 −0.0300100
\(991\) −9.50191e24 −0.324478 −0.162239 0.986752i \(-0.551871\pi\)
−0.162239 + 0.986752i \(0.551871\pi\)
\(992\) −3.51502e24 −0.119009
\(993\) 2.37176e25 0.796164
\(994\) −3.33432e25 −1.10974
\(995\) −2.58935e25 −0.854467
\(996\) −5.95292e24 −0.194772
\(997\) 1.19972e25 0.389198 0.194599 0.980883i \(-0.437659\pi\)
0.194599 + 0.980883i \(0.437659\pi\)
\(998\) −7.49222e24 −0.240991
\(999\) 1.43902e25 0.458945
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 29.18.a.b.1.7 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.18.a.b.1.7 21 1.1 even 1 trivial