Properties

Label 177.10.a.c.1.1
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-43.0478 q^{2} -81.0000 q^{3} +1341.12 q^{4} +1406.99 q^{5} +3486.87 q^{6} +9392.26 q^{7} -35691.7 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-43.0478 q^{2} -81.0000 q^{3} +1341.12 q^{4} +1406.99 q^{5} +3486.87 q^{6} +9392.26 q^{7} -35691.7 q^{8} +6561.00 q^{9} -60567.9 q^{10} -91317.4 q^{11} -108630. q^{12} -95999.0 q^{13} -404316. q^{14} -113966. q^{15} +849797. q^{16} -211722. q^{17} -282437. q^{18} +541235. q^{19} +1.88694e6 q^{20} -760773. q^{21} +3.93101e6 q^{22} -1.61537e6 q^{23} +2.89102e6 q^{24} +26500.4 q^{25} +4.13255e6 q^{26} -531441. q^{27} +1.25961e7 q^{28} -791228. q^{29} +4.90600e6 q^{30} -7.46932e6 q^{31} -1.83078e7 q^{32} +7.39671e6 q^{33} +9.11416e6 q^{34} +1.32148e7 q^{35} +8.79906e6 q^{36} +8.37244e6 q^{37} -2.32990e7 q^{38} +7.77592e6 q^{39} -5.02179e7 q^{40} +1.08503e7 q^{41} +3.27496e7 q^{42} -4.24616e6 q^{43} -1.22467e8 q^{44} +9.23127e6 q^{45} +6.95381e7 q^{46} +6.51641e7 q^{47} -6.88335e7 q^{48} +4.78609e7 q^{49} -1.14078e6 q^{50} +1.71495e7 q^{51} -1.28746e8 q^{52} -3.72234e7 q^{53} +2.28774e7 q^{54} -1.28483e8 q^{55} -3.35225e8 q^{56} -4.38401e7 q^{57} +3.40607e7 q^{58} +1.21174e7 q^{59} -1.52842e8 q^{60} -1.44885e8 q^{61} +3.21538e8 q^{62} +6.16226e7 q^{63} +3.53015e8 q^{64} -1.35070e8 q^{65} -3.18412e8 q^{66} +7.39201e7 q^{67} -2.83943e8 q^{68} +1.30845e8 q^{69} -5.68870e8 q^{70} -3.81369e7 q^{71} -2.34173e8 q^{72} +3.89371e8 q^{73} -3.60415e8 q^{74} -2.14653e6 q^{75} +7.25859e8 q^{76} -8.57676e8 q^{77} -3.34737e8 q^{78} +6.34743e8 q^{79} +1.19566e9 q^{80} +4.30467e7 q^{81} -4.67081e8 q^{82} -6.48065e8 q^{83} -1.02028e9 q^{84} -2.97891e8 q^{85} +1.82788e8 q^{86} +6.40895e7 q^{87} +3.25927e9 q^{88} +9.28667e8 q^{89} -3.97386e8 q^{90} -9.01647e8 q^{91} -2.16640e9 q^{92} +6.05015e8 q^{93} -2.80517e9 q^{94} +7.61513e8 q^{95} +1.48293e9 q^{96} -2.03472e8 q^{97} -2.06031e9 q^{98} -5.99133e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −43.0478 −1.90246 −0.951232 0.308477i \(-0.900181\pi\)
−0.951232 + 0.308477i \(0.900181\pi\)
\(3\) −81.0000 −0.577350
\(4\) 1341.12 2.61937
\(5\) 1406.99 1.00676 0.503381 0.864065i \(-0.332089\pi\)
0.503381 + 0.864065i \(0.332089\pi\)
\(6\) 3486.87 1.09839
\(7\) 9392.26 1.47853 0.739263 0.673417i \(-0.235174\pi\)
0.739263 + 0.673417i \(0.235174\pi\)
\(8\) −35691.7 −3.08079
\(9\) 6561.00 0.333333
\(10\) −60567.9 −1.91533
\(11\) −91317.4 −1.88056 −0.940278 0.340407i \(-0.889435\pi\)
−0.940278 + 0.340407i \(0.889435\pi\)
\(12\) −108630. −1.51229
\(13\) −95999.0 −0.932227 −0.466114 0.884725i \(-0.654346\pi\)
−0.466114 + 0.884725i \(0.654346\pi\)
\(14\) −404316. −2.81284
\(15\) −113966. −0.581254
\(16\) 849797. 3.24172
\(17\) −211722. −0.614816 −0.307408 0.951578i \(-0.599462\pi\)
−0.307408 + 0.951578i \(0.599462\pi\)
\(18\) −282437. −0.634154
\(19\) 541235. 0.952785 0.476392 0.879233i \(-0.341944\pi\)
0.476392 + 0.879233i \(0.341944\pi\)
\(20\) 1.88694e6 2.63708
\(21\) −760773. −0.853627
\(22\) 3.93101e6 3.57769
\(23\) −1.61537e6 −1.20364 −0.601820 0.798632i \(-0.705557\pi\)
−0.601820 + 0.798632i \(0.705557\pi\)
\(24\) 2.89102e6 1.77869
\(25\) 26500.4 0.0135682
\(26\) 4.13255e6 1.77353
\(27\) −531441. −0.192450
\(28\) 1.25961e7 3.87280
\(29\) −791228. −0.207736 −0.103868 0.994591i \(-0.533122\pi\)
−0.103868 + 0.994591i \(0.533122\pi\)
\(30\) 4.90600e6 1.10581
\(31\) −7.46932e6 −1.45262 −0.726312 0.687365i \(-0.758767\pi\)
−0.726312 + 0.687365i \(0.758767\pi\)
\(32\) −1.83078e7 −3.08646
\(33\) 7.39671e6 1.08574
\(34\) 9.11416e6 1.16967
\(35\) 1.32148e7 1.48852
\(36\) 8.79906e6 0.873122
\(37\) 8.37244e6 0.734419 0.367210 0.930138i \(-0.380313\pi\)
0.367210 + 0.930138i \(0.380313\pi\)
\(38\) −2.32990e7 −1.81264
\(39\) 7.77592e6 0.538222
\(40\) −5.02179e7 −3.10162
\(41\) 1.08503e7 0.599672 0.299836 0.953991i \(-0.403068\pi\)
0.299836 + 0.953991i \(0.403068\pi\)
\(42\) 3.27496e7 1.62399
\(43\) −4.24616e6 −0.189404 −0.0947018 0.995506i \(-0.530190\pi\)
−0.0947018 + 0.995506i \(0.530190\pi\)
\(44\) −1.22467e8 −4.92587
\(45\) 9.23127e6 0.335587
\(46\) 6.95381e7 2.28988
\(47\) 6.51641e7 1.94790 0.973952 0.226753i \(-0.0728109\pi\)
0.973952 + 0.226753i \(0.0728109\pi\)
\(48\) −6.88335e7 −1.87161
\(49\) 4.78609e7 1.18604
\(50\) −1.14078e6 −0.0258130
\(51\) 1.71495e7 0.354964
\(52\) −1.28746e8 −2.44185
\(53\) −3.72234e7 −0.647999 −0.324000 0.946057i \(-0.605028\pi\)
−0.324000 + 0.946057i \(0.605028\pi\)
\(54\) 2.28774e7 0.366129
\(55\) −1.28483e8 −1.89327
\(56\) −3.35225e8 −4.55502
\(57\) −4.38401e7 −0.550091
\(58\) 3.40607e7 0.395209
\(59\) 1.21174e7 0.130189
\(60\) −1.52842e8 −1.52252
\(61\) −1.44885e8 −1.33980 −0.669899 0.742452i \(-0.733663\pi\)
−0.669899 + 0.742452i \(0.733663\pi\)
\(62\) 3.21538e8 2.76356
\(63\) 6.16226e7 0.492842
\(64\) 3.53015e8 2.63016
\(65\) −1.35070e8 −0.938530
\(66\) −3.18412e8 −2.06558
\(67\) 7.39201e7 0.448152 0.224076 0.974572i \(-0.428064\pi\)
0.224076 + 0.974572i \(0.428064\pi\)
\(68\) −2.83943e8 −1.61043
\(69\) 1.30845e8 0.694922
\(70\) −5.68870e8 −2.83186
\(71\) −3.81369e7 −0.178108 −0.0890540 0.996027i \(-0.528384\pi\)
−0.0890540 + 0.996027i \(0.528384\pi\)
\(72\) −2.34173e8 −1.02693
\(73\) 3.89371e8 1.60476 0.802381 0.596812i \(-0.203566\pi\)
0.802381 + 0.596812i \(0.203566\pi\)
\(74\) −3.60415e8 −1.39721
\(75\) −2.14653e6 −0.00783360
\(76\) 7.25859e8 2.49569
\(77\) −8.57676e8 −2.78045
\(78\) −3.34737e8 −1.02395
\(79\) 6.34743e8 1.83348 0.916740 0.399484i \(-0.130811\pi\)
0.916740 + 0.399484i \(0.130811\pi\)
\(80\) 1.19566e9 3.26364
\(81\) 4.30467e7 0.111111
\(82\) −4.67081e8 −1.14085
\(83\) −6.48065e8 −1.49888 −0.749440 0.662072i \(-0.769677\pi\)
−0.749440 + 0.662072i \(0.769677\pi\)
\(84\) −1.02028e9 −2.23596
\(85\) −2.97891e8 −0.618973
\(86\) 1.82788e8 0.360333
\(87\) 6.40895e7 0.119936
\(88\) 3.25927e9 5.79359
\(89\) 9.28667e8 1.56893 0.784467 0.620170i \(-0.212936\pi\)
0.784467 + 0.620170i \(0.212936\pi\)
\(90\) −3.97386e8 −0.638442
\(91\) −9.01647e8 −1.37832
\(92\) −2.16640e9 −3.15277
\(93\) 6.05015e8 0.838673
\(94\) −2.80517e9 −3.70582
\(95\) 7.61513e8 0.959227
\(96\) 1.48293e9 1.78197
\(97\) −2.03472e8 −0.233363 −0.116681 0.993169i \(-0.537226\pi\)
−0.116681 + 0.993169i \(0.537226\pi\)
\(98\) −2.06031e9 −2.25639
\(99\) −5.99133e8 −0.626852
\(100\) 3.55401e7 0.0355401
\(101\) 9.78160e8 0.935327 0.467664 0.883907i \(-0.345096\pi\)
0.467664 + 0.883907i \(0.345096\pi\)
\(102\) −7.38247e8 −0.675307
\(103\) 2.03791e9 1.78409 0.892046 0.451944i \(-0.149269\pi\)
0.892046 + 0.451944i \(0.149269\pi\)
\(104\) 3.42636e9 2.87199
\(105\) −1.07040e9 −0.859398
\(106\) 1.60239e9 1.23279
\(107\) 1.58504e9 1.16900 0.584498 0.811395i \(-0.301291\pi\)
0.584498 + 0.811395i \(0.301291\pi\)
\(108\) −7.12724e8 −0.504097
\(109\) −2.17290e8 −0.147442 −0.0737210 0.997279i \(-0.523487\pi\)
−0.0737210 + 0.997279i \(0.523487\pi\)
\(110\) 5.53090e9 3.60188
\(111\) −6.78167e8 −0.424017
\(112\) 7.98151e9 4.79296
\(113\) −4.49722e8 −0.259472 −0.129736 0.991549i \(-0.541413\pi\)
−0.129736 + 0.991549i \(0.541413\pi\)
\(114\) 1.88722e9 1.04653
\(115\) −2.27281e9 −1.21178
\(116\) −1.06113e9 −0.544136
\(117\) −6.29850e8 −0.310742
\(118\) −5.21626e8 −0.247680
\(119\) −1.98855e9 −0.909021
\(120\) 4.06765e9 1.79072
\(121\) 5.98091e9 2.53649
\(122\) 6.23699e9 2.54892
\(123\) −8.78873e8 −0.346221
\(124\) −1.00172e10 −3.80496
\(125\) −2.71074e9 −0.993101
\(126\) −2.65272e9 −0.937613
\(127\) −1.52670e9 −0.520760 −0.260380 0.965506i \(-0.583848\pi\)
−0.260380 + 0.965506i \(0.583848\pi\)
\(128\) −5.82293e9 −1.91733
\(129\) 3.43939e8 0.109352
\(130\) 5.81446e9 1.78552
\(131\) 4.32322e9 1.28259 0.641293 0.767296i \(-0.278398\pi\)
0.641293 + 0.767296i \(0.278398\pi\)
\(132\) 9.91984e9 2.84395
\(133\) 5.08342e9 1.40872
\(134\) −3.18210e9 −0.852594
\(135\) −7.47733e8 −0.193751
\(136\) 7.55670e9 1.89412
\(137\) −1.97115e9 −0.478055 −0.239027 0.971013i \(-0.576829\pi\)
−0.239027 + 0.971013i \(0.576829\pi\)
\(138\) −5.63259e9 −1.32206
\(139\) −5.60538e9 −1.27362 −0.636808 0.771022i \(-0.719746\pi\)
−0.636808 + 0.771022i \(0.719746\pi\)
\(140\) 1.77226e10 3.89899
\(141\) −5.27829e9 −1.12462
\(142\) 1.64171e9 0.338844
\(143\) 8.76638e9 1.75311
\(144\) 5.57552e9 1.08057
\(145\) −1.11325e9 −0.209140
\(146\) −1.67616e10 −3.05300
\(147\) −3.87673e9 −0.684759
\(148\) 1.12284e10 1.92371
\(149\) −8.07747e9 −1.34257 −0.671286 0.741199i \(-0.734258\pi\)
−0.671286 + 0.741199i \(0.734258\pi\)
\(150\) 9.24035e7 0.0149031
\(151\) −1.58290e9 −0.247775 −0.123887 0.992296i \(-0.539536\pi\)
−0.123887 + 0.992296i \(0.539536\pi\)
\(152\) −1.93176e10 −2.93533
\(153\) −1.38911e9 −0.204939
\(154\) 3.69211e10 5.28970
\(155\) −1.05093e10 −1.46245
\(156\) 1.04284e10 1.40980
\(157\) 9.59055e9 1.25978 0.629891 0.776684i \(-0.283100\pi\)
0.629891 + 0.776684i \(0.283100\pi\)
\(158\) −2.73243e10 −3.48813
\(159\) 3.01509e9 0.374123
\(160\) −2.57589e10 −3.10733
\(161\) −1.51720e10 −1.77961
\(162\) −1.85307e9 −0.211385
\(163\) −8.10312e8 −0.0899100 −0.0449550 0.998989i \(-0.514314\pi\)
−0.0449550 + 0.998989i \(0.514314\pi\)
\(164\) 1.45515e10 1.57076
\(165\) 1.04071e10 1.09308
\(166\) 2.78978e10 2.85156
\(167\) −6.45350e9 −0.642054 −0.321027 0.947070i \(-0.604028\pi\)
−0.321027 + 0.947070i \(0.604028\pi\)
\(168\) 2.71532e10 2.62984
\(169\) −1.38869e9 −0.130953
\(170\) 1.28236e10 1.17757
\(171\) 3.55104e9 0.317595
\(172\) −5.69459e9 −0.496117
\(173\) 7.09399e9 0.602120 0.301060 0.953605i \(-0.402660\pi\)
0.301060 + 0.953605i \(0.402660\pi\)
\(174\) −2.75891e9 −0.228174
\(175\) 2.48898e8 0.0200609
\(176\) −7.76012e10 −6.09623
\(177\) −9.81506e8 −0.0751646
\(178\) −3.99771e10 −2.98484
\(179\) −5.11714e8 −0.0372554 −0.0186277 0.999826i \(-0.505930\pi\)
−0.0186277 + 0.999826i \(0.505930\pi\)
\(180\) 1.23802e10 0.879026
\(181\) 1.04870e10 0.726270 0.363135 0.931736i \(-0.381706\pi\)
0.363135 + 0.931736i \(0.381706\pi\)
\(182\) 3.88140e10 2.62221
\(183\) 1.17357e10 0.773533
\(184\) 5.76552e10 3.70816
\(185\) 1.17799e10 0.739385
\(186\) −2.60446e10 −1.59554
\(187\) 1.93339e10 1.15620
\(188\) 8.73926e10 5.10228
\(189\) −4.99143e9 −0.284542
\(190\) −3.27815e10 −1.82489
\(191\) 2.74695e10 1.49348 0.746742 0.665113i \(-0.231617\pi\)
0.746742 + 0.665113i \(0.231617\pi\)
\(192\) −2.85942e10 −1.51853
\(193\) 2.61307e10 1.35564 0.677818 0.735229i \(-0.262926\pi\)
0.677818 + 0.735229i \(0.262926\pi\)
\(194\) 8.75902e9 0.443964
\(195\) 1.09407e10 0.541861
\(196\) 6.41870e10 3.10667
\(197\) 8.12867e9 0.384522 0.192261 0.981344i \(-0.438418\pi\)
0.192261 + 0.981344i \(0.438418\pi\)
\(198\) 2.57914e10 1.19256
\(199\) −1.27199e10 −0.574970 −0.287485 0.957785i \(-0.592819\pi\)
−0.287485 + 0.957785i \(0.592819\pi\)
\(200\) −9.45842e8 −0.0418007
\(201\) −5.98753e9 −0.258741
\(202\) −4.21077e10 −1.77943
\(203\) −7.43142e9 −0.307142
\(204\) 2.29994e10 0.929782
\(205\) 1.52663e10 0.603727
\(206\) −8.77276e10 −3.39417
\(207\) −1.05984e10 −0.401213
\(208\) −8.15797e10 −3.02202
\(209\) −4.94242e10 −1.79177
\(210\) 4.60784e10 1.63497
\(211\) 2.05227e10 0.712794 0.356397 0.934335i \(-0.384005\pi\)
0.356397 + 0.934335i \(0.384005\pi\)
\(212\) −4.99209e10 −1.69735
\(213\) 3.08909e9 0.102831
\(214\) −6.82325e10 −2.22397
\(215\) −5.97431e9 −0.190684
\(216\) 1.89680e10 0.592898
\(217\) −7.01537e10 −2.14774
\(218\) 9.35388e9 0.280503
\(219\) −3.15391e10 −0.926510
\(220\) −1.72310e11 −4.95917
\(221\) 2.03251e10 0.573149
\(222\) 2.91936e10 0.806677
\(223\) 5.32991e10 1.44327 0.721636 0.692272i \(-0.243390\pi\)
0.721636 + 0.692272i \(0.243390\pi\)
\(224\) −1.71951e11 −4.56341
\(225\) 1.73869e8 0.00452273
\(226\) 1.93596e10 0.493637
\(227\) 5.29374e9 0.132326 0.0661631 0.997809i \(-0.478924\pi\)
0.0661631 + 0.997809i \(0.478924\pi\)
\(228\) −5.87946e10 −1.44089
\(229\) −5.14989e10 −1.23748 −0.618741 0.785595i \(-0.712357\pi\)
−0.618741 + 0.785595i \(0.712357\pi\)
\(230\) 9.78396e10 2.30536
\(231\) 6.94718e10 1.60529
\(232\) 2.82402e10 0.639989
\(233\) −1.19187e10 −0.264927 −0.132463 0.991188i \(-0.542289\pi\)
−0.132463 + 0.991188i \(0.542289\pi\)
\(234\) 2.71137e10 0.591176
\(235\) 9.16853e10 1.96107
\(236\) 1.62508e10 0.341013
\(237\) −5.14142e10 −1.05856
\(238\) 8.56026e10 1.72938
\(239\) −1.75163e10 −0.347258 −0.173629 0.984811i \(-0.555549\pi\)
−0.173629 + 0.984811i \(0.555549\pi\)
\(240\) −9.68482e10 −1.88426
\(241\) −4.35459e10 −0.831516 −0.415758 0.909475i \(-0.636484\pi\)
−0.415758 + 0.909475i \(0.636484\pi\)
\(242\) −2.57465e11 −4.82558
\(243\) −3.48678e9 −0.0641500
\(244\) −1.94308e11 −3.50942
\(245\) 6.73398e10 1.19406
\(246\) 3.78336e10 0.658672
\(247\) −5.19581e10 −0.888212
\(248\) 2.66592e11 4.47522
\(249\) 5.24932e10 0.865379
\(250\) 1.16692e11 1.88934
\(251\) −3.57888e10 −0.569136 −0.284568 0.958656i \(-0.591850\pi\)
−0.284568 + 0.958656i \(0.591850\pi\)
\(252\) 8.26430e10 1.29093
\(253\) 1.47511e11 2.26351
\(254\) 6.57212e10 0.990727
\(255\) 2.41292e10 0.357364
\(256\) 6.99210e10 1.01748
\(257\) −3.73067e10 −0.533443 −0.266722 0.963774i \(-0.585940\pi\)
−0.266722 + 0.963774i \(0.585940\pi\)
\(258\) −1.48058e10 −0.208039
\(259\) 7.86361e10 1.08586
\(260\) −1.81144e11 −2.45836
\(261\) −5.19125e9 −0.0692452
\(262\) −1.86105e11 −2.44007
\(263\) 6.39270e10 0.823917 0.411958 0.911203i \(-0.364845\pi\)
0.411958 + 0.911203i \(0.364845\pi\)
\(264\) −2.64001e11 −3.34493
\(265\) −5.23730e10 −0.652380
\(266\) −2.18830e11 −2.68003
\(267\) −7.52220e10 −0.905825
\(268\) 9.91354e10 1.17388
\(269\) 2.59531e10 0.302206 0.151103 0.988518i \(-0.451717\pi\)
0.151103 + 0.988518i \(0.451717\pi\)
\(270\) 3.21883e10 0.368605
\(271\) 1.93051e10 0.217425 0.108713 0.994073i \(-0.465327\pi\)
0.108713 + 0.994073i \(0.465327\pi\)
\(272\) −1.79921e11 −1.99306
\(273\) 7.30334e10 0.795774
\(274\) 8.48538e10 0.909482
\(275\) −2.41994e9 −0.0255157
\(276\) 1.75478e11 1.82025
\(277\) 8.64529e10 0.882308 0.441154 0.897431i \(-0.354569\pi\)
0.441154 + 0.897431i \(0.354569\pi\)
\(278\) 2.41299e11 2.42301
\(279\) −4.90062e10 −0.484208
\(280\) −4.71659e11 −4.58582
\(281\) 1.52176e11 1.45602 0.728009 0.685568i \(-0.240446\pi\)
0.728009 + 0.685568i \(0.240446\pi\)
\(282\) 2.27219e11 2.13955
\(283\) −3.14215e10 −0.291197 −0.145599 0.989344i \(-0.546511\pi\)
−0.145599 + 0.989344i \(0.546511\pi\)
\(284\) −5.11461e10 −0.466530
\(285\) −6.16826e10 −0.553810
\(286\) −3.77374e11 −3.33522
\(287\) 1.01909e11 0.886630
\(288\) −1.20117e11 −1.02882
\(289\) −7.37618e10 −0.622001
\(290\) 4.79231e10 0.397881
\(291\) 1.64812e10 0.134732
\(292\) 5.22192e11 4.20346
\(293\) −3.53857e10 −0.280494 −0.140247 0.990117i \(-0.544790\pi\)
−0.140247 + 0.990117i \(0.544790\pi\)
\(294\) 1.66885e11 1.30273
\(295\) 1.70490e10 0.131069
\(296\) −2.98826e11 −2.26259
\(297\) 4.85298e10 0.361913
\(298\) 3.47718e11 2.55419
\(299\) 1.55074e11 1.12207
\(300\) −2.87875e9 −0.0205191
\(301\) −3.98810e10 −0.280038
\(302\) 6.81404e10 0.471382
\(303\) −7.92309e10 −0.540011
\(304\) 4.59940e11 3.08866
\(305\) −2.03852e11 −1.34886
\(306\) 5.97980e10 0.389889
\(307\) 2.21134e11 1.42080 0.710401 0.703797i \(-0.248514\pi\)
0.710401 + 0.703797i \(0.248514\pi\)
\(308\) −1.15024e12 −7.28302
\(309\) −1.65071e11 −1.03005
\(310\) 4.52401e11 2.78225
\(311\) −5.85330e10 −0.354796 −0.177398 0.984139i \(-0.556768\pi\)
−0.177398 + 0.984139i \(0.556768\pi\)
\(312\) −2.77535e11 −1.65815
\(313\) 2.93275e11 1.72713 0.863565 0.504238i \(-0.168227\pi\)
0.863565 + 0.504238i \(0.168227\pi\)
\(314\) −4.12852e11 −2.39669
\(315\) 8.67025e10 0.496174
\(316\) 8.51265e11 4.80256
\(317\) 1.45588e11 0.809766 0.404883 0.914368i \(-0.367312\pi\)
0.404883 + 0.914368i \(0.367312\pi\)
\(318\) −1.29793e11 −0.711754
\(319\) 7.22529e10 0.390658
\(320\) 4.96689e11 2.64795
\(321\) −1.28388e11 −0.674920
\(322\) 6.53120e11 3.38565
\(323\) −1.14591e11 −0.585788
\(324\) 5.77306e10 0.291041
\(325\) −2.54401e9 −0.0126486
\(326\) 3.48822e10 0.171051
\(327\) 1.76005e10 0.0851256
\(328\) −3.87265e11 −1.84746
\(329\) 6.12037e11 2.88003
\(330\) −4.48003e11 −2.07955
\(331\) −1.57130e11 −0.719503 −0.359752 0.933048i \(-0.617139\pi\)
−0.359752 + 0.933048i \(0.617139\pi\)
\(332\) −8.69130e11 −3.92612
\(333\) 5.49316e10 0.244806
\(334\) 2.77809e11 1.22148
\(335\) 1.04005e11 0.451182
\(336\) −6.46502e11 −2.76722
\(337\) −8.26938e10 −0.349252 −0.174626 0.984635i \(-0.555872\pi\)
−0.174626 + 0.984635i \(0.555872\pi\)
\(338\) 5.97799e10 0.249132
\(339\) 3.64275e10 0.149806
\(340\) −3.99506e11 −1.62132
\(341\) 6.82078e11 2.73174
\(342\) −1.52865e11 −0.604213
\(343\) 7.05101e10 0.275060
\(344\) 1.51552e11 0.583512
\(345\) 1.84098e11 0.699620
\(346\) −3.05381e11 −1.14551
\(347\) −8.62359e10 −0.319305 −0.159652 0.987173i \(-0.551037\pi\)
−0.159652 + 0.987173i \(0.551037\pi\)
\(348\) 8.59514e10 0.314157
\(349\) −1.91363e11 −0.690467 −0.345234 0.938517i \(-0.612200\pi\)
−0.345234 + 0.938517i \(0.612200\pi\)
\(350\) −1.07145e10 −0.0381652
\(351\) 5.10178e10 0.179407
\(352\) 1.67182e12 5.80427
\(353\) 1.10169e11 0.377637 0.188818 0.982012i \(-0.439534\pi\)
0.188818 + 0.982012i \(0.439534\pi\)
\(354\) 4.22517e10 0.142998
\(355\) −5.36584e10 −0.179312
\(356\) 1.24545e12 4.10962
\(357\) 1.61072e11 0.524824
\(358\) 2.20282e10 0.0708770
\(359\) 1.08108e11 0.343504 0.171752 0.985140i \(-0.445057\pi\)
0.171752 + 0.985140i \(0.445057\pi\)
\(360\) −3.29479e11 −1.03387
\(361\) −2.97521e10 −0.0922009
\(362\) −4.51443e11 −1.38170
\(363\) −4.84454e11 −1.46444
\(364\) −1.20921e12 −3.61033
\(365\) 5.47842e11 1.61561
\(366\) −5.05196e11 −1.47162
\(367\) 4.90550e11 1.41152 0.705758 0.708453i \(-0.250607\pi\)
0.705758 + 0.708453i \(0.250607\pi\)
\(368\) −1.37274e12 −3.90186
\(369\) 7.11887e10 0.199891
\(370\) −5.07101e11 −1.40665
\(371\) −3.49612e11 −0.958083
\(372\) 8.11395e11 2.19679
\(373\) 1.38340e11 0.370049 0.185025 0.982734i \(-0.440764\pi\)
0.185025 + 0.982734i \(0.440764\pi\)
\(374\) −8.32282e11 −2.19962
\(375\) 2.19570e11 0.573367
\(376\) −2.32581e12 −6.00108
\(377\) 7.59571e10 0.193657
\(378\) 2.14870e11 0.541331
\(379\) −5.56221e11 −1.38475 −0.692374 0.721538i \(-0.743435\pi\)
−0.692374 + 0.721538i \(0.743435\pi\)
\(380\) 1.02128e12 2.51257
\(381\) 1.23663e11 0.300661
\(382\) −1.18250e12 −2.84130
\(383\) 4.78507e11 1.13630 0.568151 0.822925i \(-0.307659\pi\)
0.568151 + 0.822925i \(0.307659\pi\)
\(384\) 4.71657e11 1.10697
\(385\) −1.20674e12 −2.79925
\(386\) −1.12487e12 −2.57905
\(387\) −2.78590e10 −0.0631345
\(388\) −2.72879e11 −0.611263
\(389\) 7.44731e11 1.64902 0.824511 0.565846i \(-0.191450\pi\)
0.824511 + 0.565846i \(0.191450\pi\)
\(390\) −4.70972e11 −1.03087
\(391\) 3.42009e11 0.740017
\(392\) −1.70823e12 −3.65393
\(393\) −3.50181e11 −0.740501
\(394\) −3.49922e11 −0.731539
\(395\) 8.93079e11 1.84588
\(396\) −8.03507e11 −1.64196
\(397\) 1.80985e11 0.365666 0.182833 0.983144i \(-0.441473\pi\)
0.182833 + 0.983144i \(0.441473\pi\)
\(398\) 5.47565e11 1.09386
\(399\) −4.11757e11 −0.813323
\(400\) 2.25199e10 0.0439843
\(401\) −1.61745e11 −0.312378 −0.156189 0.987727i \(-0.549921\pi\)
−0.156189 + 0.987727i \(0.549921\pi\)
\(402\) 2.57750e11 0.492245
\(403\) 7.17047e11 1.35418
\(404\) 1.31183e12 2.44997
\(405\) 6.05664e10 0.111862
\(406\) 3.19906e11 0.584327
\(407\) −7.64549e11 −1.38112
\(408\) −6.12093e11 −1.09357
\(409\) −6.20792e11 −1.09696 −0.548481 0.836163i \(-0.684794\pi\)
−0.548481 + 0.836163i \(0.684794\pi\)
\(410\) −6.57179e11 −1.14857
\(411\) 1.59663e11 0.276005
\(412\) 2.73307e12 4.67319
\(413\) 1.13809e11 0.192488
\(414\) 4.56240e11 0.763293
\(415\) −9.11821e11 −1.50901
\(416\) 1.75753e12 2.87728
\(417\) 4.54036e11 0.735322
\(418\) 2.12760e12 3.40877
\(419\) 2.41725e10 0.0383141 0.0191570 0.999816i \(-0.493902\pi\)
0.0191570 + 0.999816i \(0.493902\pi\)
\(420\) −1.43553e12 −2.25108
\(421\) 1.42904e11 0.221705 0.110853 0.993837i \(-0.464642\pi\)
0.110853 + 0.993837i \(0.464642\pi\)
\(422\) −8.83459e11 −1.35606
\(423\) 4.27541e11 0.649302
\(424\) 1.32856e12 1.99635
\(425\) −5.61071e9 −0.00834195
\(426\) −1.32979e11 −0.195632
\(427\) −1.36080e12 −1.98092
\(428\) 2.12572e12 3.06203
\(429\) −7.10077e11 −1.01216
\(430\) 2.57181e11 0.362770
\(431\) 3.06890e11 0.428386 0.214193 0.976791i \(-0.431288\pi\)
0.214193 + 0.976791i \(0.431288\pi\)
\(432\) −4.51617e11 −0.623869
\(433\) −8.43663e11 −1.15338 −0.576692 0.816962i \(-0.695657\pi\)
−0.576692 + 0.816962i \(0.695657\pi\)
\(434\) 3.01997e12 4.08600
\(435\) 9.01734e10 0.120747
\(436\) −2.91411e11 −0.386205
\(437\) −8.74294e11 −1.14681
\(438\) 1.35769e12 1.76265
\(439\) 1.15544e12 1.48476 0.742381 0.669978i \(-0.233697\pi\)
0.742381 + 0.669978i \(0.233697\pi\)
\(440\) 4.58576e12 5.83277
\(441\) 3.14015e11 0.395346
\(442\) −8.74951e11 −1.09039
\(443\) 2.56485e11 0.316407 0.158203 0.987407i \(-0.449430\pi\)
0.158203 + 0.987407i \(0.449430\pi\)
\(444\) −9.09501e11 −1.11066
\(445\) 1.30663e12 1.57954
\(446\) −2.29441e12 −2.74577
\(447\) 6.54275e11 0.775134
\(448\) 3.31560e12 3.88876
\(449\) 2.28813e11 0.265688 0.132844 0.991137i \(-0.457589\pi\)
0.132844 + 0.991137i \(0.457589\pi\)
\(450\) −7.48468e9 −0.00860433
\(451\) −9.90819e11 −1.12772
\(452\) −6.03129e11 −0.679653
\(453\) 1.28215e11 0.143053
\(454\) −2.27884e11 −0.251746
\(455\) −1.26861e12 −1.38764
\(456\) 1.56472e12 1.69471
\(457\) −1.63048e12 −1.74860 −0.874302 0.485383i \(-0.838680\pi\)
−0.874302 + 0.485383i \(0.838680\pi\)
\(458\) 2.21692e12 2.35426
\(459\) 1.12518e11 0.118321
\(460\) −3.04810e12 −3.17409
\(461\) 1.64115e12 1.69237 0.846185 0.532889i \(-0.178894\pi\)
0.846185 + 0.532889i \(0.178894\pi\)
\(462\) −2.99061e12 −3.05401
\(463\) 5.78729e11 0.585276 0.292638 0.956223i \(-0.405467\pi\)
0.292638 + 0.956223i \(0.405467\pi\)
\(464\) −6.72383e11 −0.673420
\(465\) 8.51250e11 0.844343
\(466\) 5.13073e11 0.504014
\(467\) 1.23952e11 0.120594 0.0602971 0.998180i \(-0.480795\pi\)
0.0602971 + 0.998180i \(0.480795\pi\)
\(468\) −8.44701e11 −0.813948
\(469\) 6.94276e11 0.662605
\(470\) −3.94685e12 −3.73087
\(471\) −7.76835e11 −0.727335
\(472\) −4.32489e11 −0.401084
\(473\) 3.87748e11 0.356184
\(474\) 2.21327e12 2.01387
\(475\) 1.43429e10 0.0129276
\(476\) −2.66687e12 −2.38106
\(477\) −2.44223e11 −0.216000
\(478\) 7.54038e11 0.660645
\(479\) −1.76694e12 −1.53360 −0.766799 0.641888i \(-0.778152\pi\)
−0.766799 + 0.641888i \(0.778152\pi\)
\(480\) 2.08647e12 1.79402
\(481\) −8.03746e11 −0.684646
\(482\) 1.87456e12 1.58193
\(483\) 1.22893e12 1.02746
\(484\) 8.02110e12 6.64400
\(485\) −2.86283e11 −0.234940
\(486\) 1.50099e11 0.122043
\(487\) −8.92659e11 −0.719126 −0.359563 0.933121i \(-0.617074\pi\)
−0.359563 + 0.933121i \(0.617074\pi\)
\(488\) 5.17119e12 4.12763
\(489\) 6.56353e10 0.0519096
\(490\) −2.89883e12 −2.27165
\(491\) 1.42507e12 1.10654 0.553272 0.833001i \(-0.313379\pi\)
0.553272 + 0.833001i \(0.313379\pi\)
\(492\) −1.17867e12 −0.906879
\(493\) 1.67520e11 0.127719
\(494\) 2.23668e12 1.68979
\(495\) −8.42975e11 −0.631090
\(496\) −6.34740e12 −4.70900
\(497\) −3.58192e11 −0.263337
\(498\) −2.25972e12 −1.64635
\(499\) 1.91332e12 1.38145 0.690724 0.723119i \(-0.257292\pi\)
0.690724 + 0.723119i \(0.257292\pi\)
\(500\) −3.63542e12 −2.60130
\(501\) 5.22734e11 0.370690
\(502\) 1.54063e12 1.08276
\(503\) −5.38097e11 −0.374804 −0.187402 0.982283i \(-0.560007\pi\)
−0.187402 + 0.982283i \(0.560007\pi\)
\(504\) −2.19941e12 −1.51834
\(505\) 1.37626e12 0.941651
\(506\) −6.35004e12 −4.30625
\(507\) 1.12484e11 0.0756055
\(508\) −2.04748e12 −1.36406
\(509\) 1.31123e11 0.0865861 0.0432931 0.999062i \(-0.486215\pi\)
0.0432931 + 0.999062i \(0.486215\pi\)
\(510\) −1.03871e12 −0.679873
\(511\) 3.65707e12 2.37268
\(512\) −2.86079e10 −0.0183980
\(513\) −2.87635e11 −0.183364
\(514\) 1.60597e12 1.01486
\(515\) 2.86732e12 1.79615
\(516\) 4.61262e11 0.286434
\(517\) −5.95061e12 −3.66314
\(518\) −3.38511e12 −2.06580
\(519\) −5.74613e11 −0.347634
\(520\) 4.82087e12 2.89141
\(521\) −2.11305e12 −1.25643 −0.628217 0.778038i \(-0.716215\pi\)
−0.628217 + 0.778038i \(0.716215\pi\)
\(522\) 2.23472e11 0.131736
\(523\) 1.87618e12 1.09652 0.548260 0.836308i \(-0.315291\pi\)
0.548260 + 0.836308i \(0.315291\pi\)
\(524\) 5.79794e12 3.35956
\(525\) −2.01608e10 −0.0115822
\(526\) −2.75192e12 −1.56747
\(527\) 1.58142e12 0.893097
\(528\) 6.28570e12 3.51966
\(529\) 8.08263e11 0.448748
\(530\) 2.25454e12 1.24113
\(531\) 7.95020e10 0.0433963
\(532\) 6.81746e12 3.68995
\(533\) −1.04162e12 −0.559031
\(534\) 3.23815e12 1.72330
\(535\) 2.23014e12 1.17690
\(536\) −2.63833e12 −1.38066
\(537\) 4.14489e10 0.0215094
\(538\) −1.11722e12 −0.574936
\(539\) −4.37053e12 −2.23041
\(540\) −1.00280e12 −0.507506
\(541\) −3.86621e12 −1.94043 −0.970215 0.242245i \(-0.922116\pi\)
−0.970215 + 0.242245i \(0.922116\pi\)
\(542\) −8.31041e11 −0.413643
\(543\) −8.49448e11 −0.419312
\(544\) 3.87616e12 1.89761
\(545\) −3.05726e11 −0.148439
\(546\) −3.14393e12 −1.51393
\(547\) 1.83738e12 0.877520 0.438760 0.898604i \(-0.355418\pi\)
0.438760 + 0.898604i \(0.355418\pi\)
\(548\) −2.64354e12 −1.25220
\(549\) −9.50591e11 −0.446599
\(550\) 1.04173e11 0.0485428
\(551\) −4.28241e11 −0.197927
\(552\) −4.67007e12 −2.14091
\(553\) 5.96167e12 2.71085
\(554\) −3.72161e12 −1.67856
\(555\) −9.54176e11 −0.426884
\(556\) −7.51747e12 −3.33607
\(557\) −3.55935e12 −1.56683 −0.783416 0.621498i \(-0.786524\pi\)
−0.783416 + 0.621498i \(0.786524\pi\)
\(558\) 2.10961e12 0.921188
\(559\) 4.07627e11 0.176567
\(560\) 1.12299e13 4.82537
\(561\) −1.56604e12 −0.667530
\(562\) −6.55083e12 −2.77002
\(563\) −8.83644e11 −0.370672 −0.185336 0.982675i \(-0.559337\pi\)
−0.185336 + 0.982675i \(0.559337\pi\)
\(564\) −7.07880e12 −2.94580
\(565\) −6.32755e11 −0.261227
\(566\) 1.35263e12 0.553993
\(567\) 4.04306e11 0.164281
\(568\) 1.36117e12 0.548713
\(569\) 2.04350e12 0.817277 0.408638 0.912696i \(-0.366004\pi\)
0.408638 + 0.912696i \(0.366004\pi\)
\(570\) 2.65530e12 1.05360
\(571\) −4.45400e12 −1.75343 −0.876713 0.481013i \(-0.840269\pi\)
−0.876713 + 0.481013i \(0.840269\pi\)
\(572\) 1.17567e13 4.59203
\(573\) −2.22503e12 −0.862264
\(574\) −4.38695e12 −1.68678
\(575\) −4.28079e10 −0.0163312
\(576\) 2.31613e12 0.876722
\(577\) −2.33300e12 −0.876240 −0.438120 0.898916i \(-0.644356\pi\)
−0.438120 + 0.898916i \(0.644356\pi\)
\(578\) 3.17528e12 1.18333
\(579\) −2.11659e12 −0.782677
\(580\) −1.49300e12 −0.547815
\(581\) −6.08679e12 −2.21613
\(582\) −7.09481e11 −0.256323
\(583\) 3.39914e12 1.21860
\(584\) −1.38973e13 −4.94393
\(585\) −8.86193e11 −0.312843
\(586\) 1.52328e12 0.533629
\(587\) 5.05430e12 1.75707 0.878537 0.477675i \(-0.158520\pi\)
0.878537 + 0.477675i \(0.158520\pi\)
\(588\) −5.19914e12 −1.79363
\(589\) −4.04266e12 −1.38404
\(590\) −7.33924e11 −0.249354
\(591\) −6.58422e11 −0.222004
\(592\) 7.11487e12 2.38078
\(593\) 1.63563e12 0.543174 0.271587 0.962414i \(-0.412452\pi\)
0.271587 + 0.962414i \(0.412452\pi\)
\(594\) −2.08910e12 −0.688527
\(595\) −2.79787e12 −0.915168
\(596\) −1.08328e13 −3.51669
\(597\) 1.03031e12 0.331959
\(598\) −6.67559e12 −2.13469
\(599\) −3.15815e12 −1.00233 −0.501166 0.865351i \(-0.667095\pi\)
−0.501166 + 0.865351i \(0.667095\pi\)
\(600\) 7.66132e10 0.0241337
\(601\) −2.98906e12 −0.934542 −0.467271 0.884114i \(-0.654763\pi\)
−0.467271 + 0.884114i \(0.654763\pi\)
\(602\) 1.71679e12 0.532762
\(603\) 4.84990e11 0.149384
\(604\) −2.12285e12 −0.649013
\(605\) 8.41510e12 2.55364
\(606\) 3.41072e12 1.02735
\(607\) 6.12469e12 1.83120 0.915599 0.402093i \(-0.131717\pi\)
0.915599 + 0.402093i \(0.131717\pi\)
\(608\) −9.90882e12 −2.94073
\(609\) 6.01945e11 0.177329
\(610\) 8.77539e12 2.56615
\(611\) −6.25569e12 −1.81589
\(612\) −1.86295e12 −0.536810
\(613\) 6.70042e12 1.91659 0.958296 0.285777i \(-0.0922518\pi\)
0.958296 + 0.285777i \(0.0922518\pi\)
\(614\) −9.51936e12 −2.70302
\(615\) −1.23657e12 −0.348562
\(616\) 3.06119e13 8.56597
\(617\) 1.04834e12 0.291218 0.145609 0.989342i \(-0.453486\pi\)
0.145609 + 0.989342i \(0.453486\pi\)
\(618\) 7.10593e12 1.95963
\(619\) −4.85801e12 −1.33000 −0.664998 0.746845i \(-0.731568\pi\)
−0.664998 + 0.746845i \(0.731568\pi\)
\(620\) −1.40941e13 −3.83068
\(621\) 8.58473e11 0.231641
\(622\) 2.51972e12 0.674987
\(623\) 8.72228e12 2.31971
\(624\) 6.60795e12 1.74476
\(625\) −3.86575e12 −1.01338
\(626\) −1.26248e13 −3.28580
\(627\) 4.00336e12 1.03448
\(628\) 1.28620e13 3.29983
\(629\) −1.77263e12 −0.451533
\(630\) −3.73235e12 −0.943953
\(631\) −1.79785e12 −0.451463 −0.225732 0.974190i \(-0.572477\pi\)
−0.225732 + 0.974190i \(0.572477\pi\)
\(632\) −2.26550e13 −5.64856
\(633\) −1.66234e12 −0.411532
\(634\) −6.26726e12 −1.54055
\(635\) −2.14806e12 −0.524281
\(636\) 4.04359e12 0.979964
\(637\) −4.59460e12 −1.10566
\(638\) −3.11033e12 −0.743213
\(639\) −2.50217e11 −0.0593693
\(640\) −8.19281e12 −1.93029
\(641\) 6.11084e12 1.42968 0.714841 0.699287i \(-0.246499\pi\)
0.714841 + 0.699287i \(0.246499\pi\)
\(642\) 5.52683e12 1.28401
\(643\) 4.26512e12 0.983969 0.491985 0.870604i \(-0.336272\pi\)
0.491985 + 0.870604i \(0.336272\pi\)
\(644\) −2.03474e13 −4.66146
\(645\) 4.83919e11 0.110092
\(646\) 4.93291e12 1.11444
\(647\) 2.63397e12 0.590937 0.295468 0.955353i \(-0.404524\pi\)
0.295468 + 0.955353i \(0.404524\pi\)
\(648\) −1.53641e12 −0.342310
\(649\) −1.10653e12 −0.244828
\(650\) 1.09514e11 0.0240636
\(651\) 5.68245e12 1.24000
\(652\) −1.08672e12 −0.235507
\(653\) 4.18813e11 0.0901386 0.0450693 0.998984i \(-0.485649\pi\)
0.0450693 + 0.998984i \(0.485649\pi\)
\(654\) −7.57664e11 −0.161948
\(655\) 6.08273e12 1.29126
\(656\) 9.22054e12 1.94397
\(657\) 2.55466e12 0.534921
\(658\) −2.63469e13 −5.47914
\(659\) 7.75877e12 1.60254 0.801270 0.598303i \(-0.204158\pi\)
0.801270 + 0.598303i \(0.204158\pi\)
\(660\) 1.39571e13 2.86318
\(661\) −5.87003e12 −1.19601 −0.598003 0.801494i \(-0.704039\pi\)
−0.598003 + 0.801494i \(0.704039\pi\)
\(662\) 6.76410e12 1.36883
\(663\) −1.64633e12 −0.330907
\(664\) 2.31305e13 4.61773
\(665\) 7.15233e12 1.41824
\(666\) −2.36468e12 −0.465735
\(667\) 1.27813e12 0.250039
\(668\) −8.65490e12 −1.68177
\(669\) −4.31723e12 −0.833274
\(670\) −4.47719e12 −0.858358
\(671\) 1.32305e13 2.51956
\(672\) 1.39281e13 2.63469
\(673\) −3.16408e12 −0.594537 −0.297269 0.954794i \(-0.596076\pi\)
−0.297269 + 0.954794i \(0.596076\pi\)
\(674\) 3.55979e12 0.664439
\(675\) −1.40834e10 −0.00261120
\(676\) −1.86239e12 −0.343013
\(677\) −2.79236e12 −0.510884 −0.255442 0.966824i \(-0.582221\pi\)
−0.255442 + 0.966824i \(0.582221\pi\)
\(678\) −1.56812e12 −0.285001
\(679\) −1.91106e12 −0.345033
\(680\) 1.06322e13 1.90692
\(681\) −4.28793e11 −0.0763986
\(682\) −2.93620e13 −5.19704
\(683\) −3.47599e12 −0.611203 −0.305601 0.952160i \(-0.598857\pi\)
−0.305601 + 0.952160i \(0.598857\pi\)
\(684\) 4.76236e12 0.831898
\(685\) −2.77339e12 −0.481287
\(686\) −3.03531e12 −0.523292
\(687\) 4.17141e12 0.714460
\(688\) −3.60837e12 −0.613993
\(689\) 3.57341e12 0.604082
\(690\) −7.92500e12 −1.33100
\(691\) 1.64952e12 0.275236 0.137618 0.990485i \(-0.456055\pi\)
0.137618 + 0.990485i \(0.456055\pi\)
\(692\) 9.51387e12 1.57717
\(693\) −5.62721e12 −0.926817
\(694\) 3.71227e12 0.607466
\(695\) −7.88672e12 −1.28223
\(696\) −2.28746e12 −0.369498
\(697\) −2.29724e12 −0.368688
\(698\) 8.23776e12 1.31359
\(699\) 9.65412e11 0.152956
\(700\) 3.33802e11 0.0525469
\(701\) −6.16418e12 −0.964149 −0.482075 0.876130i \(-0.660117\pi\)
−0.482075 + 0.876130i \(0.660117\pi\)
\(702\) −2.19621e12 −0.341316
\(703\) 4.53146e12 0.699744
\(704\) −3.22364e13 −4.94617
\(705\) −7.42651e12 −1.13223
\(706\) −4.74255e12 −0.718440
\(707\) 9.18713e12 1.38290
\(708\) −1.31631e12 −0.196884
\(709\) −2.98907e12 −0.444251 −0.222126 0.975018i \(-0.571300\pi\)
−0.222126 + 0.975018i \(0.571300\pi\)
\(710\) 2.30988e12 0.341135
\(711\) 4.16455e12 0.611160
\(712\) −3.31457e13 −4.83355
\(713\) 1.20657e13 1.74844
\(714\) −6.93381e12 −0.998458
\(715\) 1.23342e13 1.76496
\(716\) −6.86268e11 −0.0975855
\(717\) 1.41882e12 0.200489
\(718\) −4.65381e12 −0.653504
\(719\) −5.59992e12 −0.781451 −0.390725 0.920507i \(-0.627776\pi\)
−0.390725 + 0.920507i \(0.627776\pi\)
\(720\) 7.84471e12 1.08788
\(721\) 1.91406e13 2.63783
\(722\) 1.28076e12 0.175409
\(723\) 3.52722e12 0.480076
\(724\) 1.40643e13 1.90237
\(725\) −2.09678e10 −0.00281860
\(726\) 2.08547e13 2.78605
\(727\) −1.19722e13 −1.58953 −0.794766 0.606915i \(-0.792407\pi\)
−0.794766 + 0.606915i \(0.792407\pi\)
\(728\) 3.21813e13 4.24631
\(729\) 2.82430e11 0.0370370
\(730\) −2.35834e13 −3.07364
\(731\) 8.99004e11 0.116448
\(732\) 1.57389e13 2.02617
\(733\) 1.91201e12 0.244637 0.122319 0.992491i \(-0.460967\pi\)
0.122319 + 0.992491i \(0.460967\pi\)
\(734\) −2.11171e13 −2.68536
\(735\) −5.45453e12 −0.689388
\(736\) 2.95738e13 3.71499
\(737\) −6.75019e12 −0.842776
\(738\) −3.06452e12 −0.380285
\(739\) −2.40092e12 −0.296127 −0.148064 0.988978i \(-0.547304\pi\)
−0.148064 + 0.988978i \(0.547304\pi\)
\(740\) 1.57983e13 1.93672
\(741\) 4.20860e12 0.512809
\(742\) 1.50500e13 1.82272
\(743\) 1.35259e13 1.62823 0.814115 0.580704i \(-0.197223\pi\)
0.814115 + 0.580704i \(0.197223\pi\)
\(744\) −2.15940e13 −2.58377
\(745\) −1.13649e13 −1.35165
\(746\) −5.95525e12 −0.704005
\(747\) −4.25195e12 −0.499627
\(748\) 2.59290e13 3.02850
\(749\) 1.48871e13 1.72839
\(750\) −9.45203e12 −1.09081
\(751\) 7.22749e11 0.0829102 0.0414551 0.999140i \(-0.486801\pi\)
0.0414551 + 0.999140i \(0.486801\pi\)
\(752\) 5.53762e13 6.31456
\(753\) 2.89890e12 0.328591
\(754\) −3.26979e12 −0.368425
\(755\) −2.22713e12 −0.249450
\(756\) −6.69409e12 −0.745321
\(757\) 3.45878e12 0.382817 0.191408 0.981510i \(-0.438694\pi\)
0.191408 + 0.981510i \(0.438694\pi\)
\(758\) 2.39441e13 2.63443
\(759\) −1.19484e13 −1.30684
\(760\) −2.71797e13 −2.95517
\(761\) −5.90424e12 −0.638165 −0.319082 0.947727i \(-0.603375\pi\)
−0.319082 + 0.947727i \(0.603375\pi\)
\(762\) −5.32342e12 −0.571996
\(763\) −2.04085e12 −0.217997
\(764\) 3.68398e13 3.91199
\(765\) −1.95446e12 −0.206324
\(766\) −2.05987e13 −2.16177
\(767\) −1.16325e12 −0.121366
\(768\) −5.66360e12 −0.587445
\(769\) 5.87096e12 0.605397 0.302698 0.953086i \(-0.402112\pi\)
0.302698 + 0.953086i \(0.402112\pi\)
\(770\) 5.19477e13 5.32547
\(771\) 3.02184e12 0.307983
\(772\) 3.50443e13 3.55091
\(773\) −5.51376e12 −0.555444 −0.277722 0.960661i \(-0.589579\pi\)
−0.277722 + 0.960661i \(0.589579\pi\)
\(774\) 1.19927e12 0.120111
\(775\) −1.97940e11 −0.0197095
\(776\) 7.26224e12 0.718941
\(777\) −6.36952e12 −0.626920
\(778\) −3.20591e13 −3.13720
\(779\) 5.87256e12 0.571358
\(780\) 1.46727e13 1.41933
\(781\) 3.48257e12 0.334942
\(782\) −1.47227e13 −1.40786
\(783\) 4.20491e11 0.0399787
\(784\) 4.06720e13 3.84480
\(785\) 1.34938e13 1.26830
\(786\) 1.50745e13 1.40878
\(787\) 1.26668e13 1.17701 0.588506 0.808493i \(-0.299716\pi\)
0.588506 + 0.808493i \(0.299716\pi\)
\(788\) 1.09015e13 1.00720
\(789\) −5.17809e12 −0.475689
\(790\) −3.84451e13 −3.51171
\(791\) −4.22390e12 −0.383636
\(792\) 2.13841e13 1.93120
\(793\) 1.39088e13 1.24900
\(794\) −7.79100e12 −0.695666
\(795\) 4.24221e12 0.376652
\(796\) −1.70589e13 −1.50606
\(797\) 6.19605e12 0.543942 0.271971 0.962306i \(-0.412325\pi\)
0.271971 + 0.962306i \(0.412325\pi\)
\(798\) 1.77252e13 1.54732
\(799\) −1.37966e13 −1.19760
\(800\) −4.85163e11 −0.0418777
\(801\) 6.09298e12 0.522978
\(802\) 6.96277e12 0.594288
\(803\) −3.55563e13 −3.01785
\(804\) −8.02997e12 −0.677738
\(805\) −2.13468e13 −1.79164
\(806\) −3.08673e13 −2.57627
\(807\) −2.10220e12 −0.174479
\(808\) −3.49121e13 −2.88154
\(809\) 1.96912e13 1.61623 0.808115 0.589025i \(-0.200488\pi\)
0.808115 + 0.589025i \(0.200488\pi\)
\(810\) −2.60725e12 −0.212814
\(811\) 1.93716e13 1.57243 0.786214 0.617954i \(-0.212038\pi\)
0.786214 + 0.617954i \(0.212038\pi\)
\(812\) −9.96639e12 −0.804518
\(813\) −1.56371e12 −0.125530
\(814\) 3.29122e13 2.62752
\(815\) −1.14010e12 −0.0905179
\(816\) 1.45736e13 1.15069
\(817\) −2.29817e12 −0.180461
\(818\) 2.67237e13 2.08693
\(819\) −5.91571e12 −0.459440
\(820\) 2.04738e13 1.58138
\(821\) 2.11291e13 1.62307 0.811534 0.584306i \(-0.198633\pi\)
0.811534 + 0.584306i \(0.198633\pi\)
\(822\) −6.87316e12 −0.525089
\(823\) 5.74360e12 0.436400 0.218200 0.975904i \(-0.429982\pi\)
0.218200 + 0.975904i \(0.429982\pi\)
\(824\) −7.27363e13 −5.49641
\(825\) 1.96016e11 0.0147315
\(826\) −4.89925e12 −0.366201
\(827\) 1.75144e13 1.30203 0.651014 0.759065i \(-0.274344\pi\)
0.651014 + 0.759065i \(0.274344\pi\)
\(828\) −1.42137e13 −1.05092
\(829\) −1.10876e13 −0.815346 −0.407673 0.913128i \(-0.633660\pi\)
−0.407673 + 0.913128i \(0.633660\pi\)
\(830\) 3.92519e13 2.87084
\(831\) −7.00268e12 −0.509401
\(832\) −3.38891e13 −2.45191
\(833\) −1.01332e13 −0.729195
\(834\) −1.95453e13 −1.39892
\(835\) −9.08002e12 −0.646395
\(836\) −6.62836e13 −4.69329
\(837\) 3.96950e12 0.279558
\(838\) −1.04057e12 −0.0728911
\(839\) −1.87455e13 −1.30607 −0.653037 0.757326i \(-0.726505\pi\)
−0.653037 + 0.757326i \(0.726505\pi\)
\(840\) 3.82044e13 2.64762
\(841\) −1.38811e13 −0.956846
\(842\) −6.15173e12 −0.421786
\(843\) −1.23262e13 −0.840632
\(844\) 2.75234e13 1.86707
\(845\) −1.95387e12 −0.131838
\(846\) −1.84047e13 −1.23527
\(847\) 5.61743e13 3.75027
\(848\) −3.16323e13 −2.10063
\(849\) 2.54514e12 0.168123
\(850\) 2.41529e11 0.0158702
\(851\) −1.35246e13 −0.883976
\(852\) 4.14283e12 0.269351
\(853\) −2.19866e11 −0.0142196 −0.00710979 0.999975i \(-0.502263\pi\)
−0.00710979 + 0.999975i \(0.502263\pi\)
\(854\) 5.85794e13 3.76864
\(855\) 4.99629e12 0.319742
\(856\) −5.65727e13 −3.60143
\(857\) −6.57112e12 −0.416127 −0.208063 0.978115i \(-0.566716\pi\)
−0.208063 + 0.978115i \(0.566716\pi\)
\(858\) 3.05673e13 1.92559
\(859\) 7.59316e12 0.475832 0.237916 0.971286i \(-0.423536\pi\)
0.237916 + 0.971286i \(0.423536\pi\)
\(860\) −8.01224e12 −0.499472
\(861\) −8.25460e12 −0.511896
\(862\) −1.32110e13 −0.814988
\(863\) 3.32127e12 0.203824 0.101912 0.994793i \(-0.467504\pi\)
0.101912 + 0.994793i \(0.467504\pi\)
\(864\) 9.72951e12 0.593990
\(865\) 9.98119e12 0.606191
\(866\) 3.63179e13 2.19427
\(867\) 5.97470e12 0.359112
\(868\) −9.40843e13 −5.62572
\(869\) −5.79631e13 −3.44796
\(870\) −3.88177e12 −0.229717
\(871\) −7.09625e12 −0.417780
\(872\) 7.75545e12 0.454237
\(873\) −1.33498e12 −0.0777876
\(874\) 3.76365e13 2.18176
\(875\) −2.54600e13 −1.46833
\(876\) −4.22975e13 −2.42687
\(877\) −1.16297e13 −0.663850 −0.331925 0.943306i \(-0.607698\pi\)
−0.331925 + 0.943306i \(0.607698\pi\)
\(878\) −4.97391e13 −2.82470
\(879\) 2.86624e12 0.161943
\(880\) −1.09184e14 −6.13745
\(881\) −1.87746e13 −1.04998 −0.524989 0.851109i \(-0.675930\pi\)
−0.524989 + 0.851109i \(0.675930\pi\)
\(882\) −1.35177e13 −0.752131
\(883\) −2.23134e13 −1.23521 −0.617606 0.786487i \(-0.711897\pi\)
−0.617606 + 0.786487i \(0.711897\pi\)
\(884\) 2.72583e13 1.50129
\(885\) −1.38097e12 −0.0756728
\(886\) −1.10411e13 −0.601952
\(887\) −2.09890e13 −1.13850 −0.569252 0.822163i \(-0.692767\pi\)
−0.569252 + 0.822163i \(0.692767\pi\)
\(888\) 2.42049e13 1.30631
\(889\) −1.43392e13 −0.769957
\(890\) −5.62474e13 −3.00502
\(891\) −3.93091e12 −0.208951
\(892\) 7.14803e13 3.78046
\(893\) 3.52691e13 1.85593
\(894\) −2.81651e13 −1.47466
\(895\) −7.19978e11 −0.0375073
\(896\) −5.46905e13 −2.83482
\(897\) −1.25610e13 −0.647825
\(898\) −9.84991e12 −0.505462
\(899\) 5.90993e12 0.301762
\(900\) 2.33178e11 0.0118467
\(901\) 7.88100e12 0.398401
\(902\) 4.26526e13 2.14544
\(903\) 3.23036e12 0.161680
\(904\) 1.60513e13 0.799379
\(905\) 1.47551e13 0.731181
\(906\) −5.51937e12 −0.272153
\(907\) 1.25923e13 0.617837 0.308918 0.951089i \(-0.400033\pi\)
0.308918 + 0.951089i \(0.400033\pi\)
\(908\) 7.09951e12 0.346611
\(909\) 6.41771e12 0.311776
\(910\) 5.46109e13 2.63994
\(911\) 5.34987e12 0.257342 0.128671 0.991687i \(-0.458929\pi\)
0.128671 + 0.991687i \(0.458929\pi\)
\(912\) −3.72551e13 −1.78324
\(913\) 5.91796e13 2.81873
\(914\) 7.01884e13 3.32665
\(915\) 1.65120e13 0.778763
\(916\) −6.90661e13 −3.24142
\(917\) 4.06048e13 1.89633
\(918\) −4.84364e12 −0.225102
\(919\) 1.31005e13 0.605855 0.302928 0.953014i \(-0.402036\pi\)
0.302928 + 0.953014i \(0.402036\pi\)
\(920\) 8.11203e13 3.73323
\(921\) −1.79119e13 −0.820301
\(922\) −7.06482e13 −3.21967
\(923\) 3.66111e12 0.166037
\(924\) 9.31697e13 4.20485
\(925\) 2.21873e11 0.00996474
\(926\) −2.49130e13 −1.11347
\(927\) 1.33707e13 0.594697
\(928\) 1.44856e13 0.641168
\(929\) 3.45106e13 1.52014 0.760068 0.649844i \(-0.225166\pi\)
0.760068 + 0.649844i \(0.225166\pi\)
\(930\) −3.66445e13 −1.60633
\(931\) 2.59040e13 1.13004
\(932\) −1.59843e13 −0.693941
\(933\) 4.74117e12 0.204842
\(934\) −5.33585e12 −0.229426
\(935\) 2.72026e13 1.16401
\(936\) 2.24804e13 0.957331
\(937\) −7.78758e12 −0.330046 −0.165023 0.986290i \(-0.552770\pi\)
−0.165023 + 0.986290i \(0.552770\pi\)
\(938\) −2.98871e13 −1.26058
\(939\) −2.37552e13 −0.997159
\(940\) 1.22961e14 5.13678
\(941\) 1.47575e13 0.613565 0.306783 0.951780i \(-0.400748\pi\)
0.306783 + 0.951780i \(0.400748\pi\)
\(942\) 3.34410e13 1.38373
\(943\) −1.75272e13 −0.721789
\(944\) 1.02973e13 0.422036
\(945\) −7.02290e12 −0.286466
\(946\) −1.66917e13 −0.677627
\(947\) 3.13338e12 0.126601 0.0633007 0.997994i \(-0.479837\pi\)
0.0633007 + 0.997994i \(0.479837\pi\)
\(948\) −6.89524e13 −2.77276
\(949\) −3.73792e13 −1.49600
\(950\) −6.17432e11 −0.0245942
\(951\) −1.17926e13 −0.467519
\(952\) 7.09745e13 2.80050
\(953\) 4.43314e13 1.74098 0.870489 0.492188i \(-0.163803\pi\)
0.870489 + 0.492188i \(0.163803\pi\)
\(954\) 1.05133e13 0.410932
\(955\) 3.86494e13 1.50358
\(956\) −2.34914e13 −0.909595
\(957\) −5.85248e12 −0.225547
\(958\) 7.60628e13 2.91761
\(959\) −1.85136e13 −0.706816
\(960\) −4.02318e13 −1.52879
\(961\) 2.93510e13 1.11012
\(962\) 3.45995e13 1.30251
\(963\) 1.03994e13 0.389665
\(964\) −5.84001e13 −2.17804
\(965\) 3.67657e13 1.36480
\(966\) −5.29027e13 −1.95470
\(967\) 1.93571e13 0.711902 0.355951 0.934505i \(-0.384157\pi\)
0.355951 + 0.934505i \(0.384157\pi\)
\(968\) −2.13469e14 −7.81439
\(969\) 9.28190e12 0.338205
\(970\) 1.23239e13 0.446966
\(971\) −2.51710e13 −0.908686 −0.454343 0.890827i \(-0.650126\pi\)
−0.454343 + 0.890827i \(0.650126\pi\)
\(972\) −4.67618e12 −0.168032
\(973\) −5.26472e13 −1.88307
\(974\) 3.84270e13 1.36811
\(975\) 2.06065e11 0.00730269
\(976\) −1.23123e14 −4.34325
\(977\) 5.15806e13 1.81118 0.905589 0.424156i \(-0.139429\pi\)
0.905589 + 0.424156i \(0.139429\pi\)
\(978\) −2.82546e12 −0.0987561
\(979\) −8.48034e13 −2.95047
\(980\) 9.03105e13 3.12767
\(981\) −1.42564e12 −0.0491473
\(982\) −6.13461e13 −2.10516
\(983\) 1.68835e13 0.576730 0.288365 0.957521i \(-0.406888\pi\)
0.288365 + 0.957521i \(0.406888\pi\)
\(984\) 3.13684e13 1.06663
\(985\) 1.14370e13 0.387122
\(986\) −7.21139e12 −0.242981
\(987\) −4.95750e13 −1.66278
\(988\) −6.96818e13 −2.32655
\(989\) 6.85911e12 0.227974
\(990\) 3.62883e13 1.20063
\(991\) −5.05426e12 −0.166466 −0.0832331 0.996530i \(-0.526525\pi\)
−0.0832331 + 0.996530i \(0.526525\pi\)
\(992\) 1.36747e14 4.48347
\(993\) 1.27275e13 0.415406
\(994\) 1.54194e13 0.500989
\(995\) −1.78968e13 −0.578858
\(996\) 7.03995e13 2.26674
\(997\) −1.81696e13 −0.582394 −0.291197 0.956663i \(-0.594054\pi\)
−0.291197 + 0.956663i \(0.594054\pi\)
\(998\) −8.23641e13 −2.62815
\(999\) −4.44946e12 −0.141339
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 177.10.a.c.1.1 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.1 22 1.1 even 1 trivial