Properties

Label 177.10.a.d.1.3
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 1.3
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-38.0945 q^{2} +81.0000 q^{3} +939.188 q^{4} -310.159 q^{5} -3085.65 q^{6} -4492.16 q^{7} -16273.5 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-38.0945 q^{2} +81.0000 q^{3} +939.188 q^{4} -310.159 q^{5} -3085.65 q^{6} -4492.16 q^{7} -16273.5 q^{8} +6561.00 q^{9} +11815.4 q^{10} -57757.0 q^{11} +76074.2 q^{12} -158171. q^{13} +171126. q^{14} -25122.9 q^{15} +139065. q^{16} -406420. q^{17} -249938. q^{18} -588628. q^{19} -291298. q^{20} -363865. q^{21} +2.20022e6 q^{22} -2.03523e6 q^{23} -1.31815e6 q^{24} -1.85693e6 q^{25} +6.02545e6 q^{26} +531441. q^{27} -4.21898e6 q^{28} +4.76982e6 q^{29} +957044. q^{30} +1.42127e6 q^{31} +3.03440e6 q^{32} -4.67832e6 q^{33} +1.54823e7 q^{34} +1.39329e6 q^{35} +6.16201e6 q^{36} -404459. q^{37} +2.24234e7 q^{38} -1.28119e7 q^{39} +5.04737e6 q^{40} -7.85636e6 q^{41} +1.38612e7 q^{42} +6.47482e6 q^{43} -5.42447e7 q^{44} -2.03496e6 q^{45} +7.75309e7 q^{46} +1.12002e7 q^{47} +1.12643e7 q^{48} -2.01741e7 q^{49} +7.07386e7 q^{50} -3.29200e7 q^{51} -1.48553e8 q^{52} +5.38315e7 q^{53} -2.02450e7 q^{54} +1.79139e7 q^{55} +7.31031e7 q^{56} -4.76788e7 q^{57} -1.81704e8 q^{58} -1.21174e7 q^{59} -2.35951e7 q^{60} -1.25526e8 q^{61} -5.41425e7 q^{62} -2.94731e7 q^{63} -1.86795e8 q^{64} +4.90583e7 q^{65} +1.78218e8 q^{66} -8.34881e7 q^{67} -3.81705e8 q^{68} -1.64853e8 q^{69} -5.30764e7 q^{70} -2.26370e8 q^{71} -1.06770e8 q^{72} +3.98191e7 q^{73} +1.54076e7 q^{74} -1.50411e8 q^{75} -5.52832e8 q^{76} +2.59454e8 q^{77} +4.88061e8 q^{78} -4.27187e8 q^{79} -4.31324e7 q^{80} +4.30467e7 q^{81} +2.99284e8 q^{82} +6.54358e8 q^{83} -3.41737e8 q^{84} +1.26055e8 q^{85} -2.46655e8 q^{86} +3.86356e8 q^{87} +9.39908e8 q^{88} -8.81746e8 q^{89} +7.75205e7 q^{90} +7.10531e8 q^{91} -1.91146e9 q^{92} +1.15123e8 q^{93} -4.26665e8 q^{94} +1.82568e8 q^{95} +2.45787e8 q^{96} -1.21147e8 q^{97} +7.68522e8 q^{98} -3.78944e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −38.0945 −1.68355 −0.841777 0.539826i \(-0.818490\pi\)
−0.841777 + 0.539826i \(0.818490\pi\)
\(3\) 81.0000 0.577350
\(4\) 939.188 1.83435
\(5\) −310.159 −0.221932 −0.110966 0.993824i \(-0.535394\pi\)
−0.110966 + 0.993824i \(0.535394\pi\)
\(6\) −3085.65 −0.972000
\(7\) −4492.16 −0.707154 −0.353577 0.935405i \(-0.615035\pi\)
−0.353577 + 0.935405i \(0.615035\pi\)
\(8\) −16273.5 −1.40467
\(9\) 6561.00 0.333333
\(10\) 11815.4 0.373634
\(11\) −57757.0 −1.18943 −0.594713 0.803938i \(-0.702735\pi\)
−0.594713 + 0.803938i \(0.702735\pi\)
\(12\) 76074.2 1.05906
\(13\) −158171. −1.53597 −0.767985 0.640468i \(-0.778740\pi\)
−0.767985 + 0.640468i \(0.778740\pi\)
\(14\) 171126. 1.19053
\(15\) −25122.9 −0.128132
\(16\) 139065. 0.530492
\(17\) −406420. −1.18020 −0.590099 0.807331i \(-0.700911\pi\)
−0.590099 + 0.807331i \(0.700911\pi\)
\(18\) −249938. −0.561184
\(19\) −588628. −1.03621 −0.518107 0.855316i \(-0.673363\pi\)
−0.518107 + 0.855316i \(0.673363\pi\)
\(20\) −291298. −0.407101
\(21\) −363865. −0.408275
\(22\) 2.20022e6 2.00246
\(23\) −2.03523e6 −1.51648 −0.758242 0.651973i \(-0.773941\pi\)
−0.758242 + 0.651973i \(0.773941\pi\)
\(24\) −1.31815e6 −0.810989
\(25\) −1.85693e6 −0.950746
\(26\) 6.02545e6 2.58589
\(27\) 531441. 0.192450
\(28\) −4.21898e6 −1.29717
\(29\) 4.76982e6 1.25231 0.626154 0.779699i \(-0.284628\pi\)
0.626154 + 0.779699i \(0.284628\pi\)
\(30\) 957044. 0.215718
\(31\) 1.42127e6 0.276407 0.138203 0.990404i \(-0.455867\pi\)
0.138203 + 0.990404i \(0.455867\pi\)
\(32\) 3.03440e6 0.511562
\(33\) −4.67832e6 −0.686716
\(34\) 1.54823e7 1.98693
\(35\) 1.39329e6 0.156940
\(36\) 6.16201e6 0.611450
\(37\) −404459. −0.0354786 −0.0177393 0.999843i \(-0.505647\pi\)
−0.0177393 + 0.999843i \(0.505647\pi\)
\(38\) 2.24234e7 1.74452
\(39\) −1.28119e7 −0.886792
\(40\) 5.04737e6 0.311742
\(41\) −7.85636e6 −0.434204 −0.217102 0.976149i \(-0.569660\pi\)
−0.217102 + 0.976149i \(0.569660\pi\)
\(42\) 1.38612e7 0.687353
\(43\) 6.47482e6 0.288815 0.144407 0.989518i \(-0.453872\pi\)
0.144407 + 0.989518i \(0.453872\pi\)
\(44\) −5.42447e7 −2.18183
\(45\) −2.03496e6 −0.0739773
\(46\) 7.75309e7 2.55308
\(47\) 1.12002e7 0.334800 0.167400 0.985889i \(-0.446463\pi\)
0.167400 + 0.985889i \(0.446463\pi\)
\(48\) 1.12643e7 0.306280
\(49\) −2.01741e7 −0.499933
\(50\) 7.07386e7 1.60063
\(51\) −3.29200e7 −0.681388
\(52\) −1.48553e8 −2.81751
\(53\) 5.38315e7 0.937120 0.468560 0.883432i \(-0.344773\pi\)
0.468560 + 0.883432i \(0.344773\pi\)
\(54\) −2.02450e7 −0.324000
\(55\) 1.79139e7 0.263972
\(56\) 7.31031e7 0.993321
\(57\) −4.76788e7 −0.598258
\(58\) −1.81704e8 −2.10833
\(59\) −1.21174e7 −0.130189
\(60\) −2.35951e7 −0.235040
\(61\) −1.25526e8 −1.16078 −0.580388 0.814340i \(-0.697099\pi\)
−0.580388 + 0.814340i \(0.697099\pi\)
\(62\) −5.41425e7 −0.465346
\(63\) −2.94731e7 −0.235718
\(64\) −1.86795e8 −1.39173
\(65\) 4.90583e7 0.340881
\(66\) 1.78218e8 1.15612
\(67\) −8.34881e7 −0.506160 −0.253080 0.967445i \(-0.581444\pi\)
−0.253080 + 0.967445i \(0.581444\pi\)
\(68\) −3.81705e8 −2.16490
\(69\) −1.64853e8 −0.875542
\(70\) −5.30764e7 −0.264217
\(71\) −2.26370e8 −1.05720 −0.528598 0.848872i \(-0.677282\pi\)
−0.528598 + 0.848872i \(0.677282\pi\)
\(72\) −1.06770e8 −0.468225
\(73\) 3.98191e7 0.164111 0.0820557 0.996628i \(-0.473851\pi\)
0.0820557 + 0.996628i \(0.473851\pi\)
\(74\) 1.54076e7 0.0597301
\(75\) −1.50411e8 −0.548914
\(76\) −5.52832e8 −1.90078
\(77\) 2.59454e8 0.841108
\(78\) 4.88061e8 1.49296
\(79\) −4.27187e8 −1.23395 −0.616973 0.786984i \(-0.711641\pi\)
−0.616973 + 0.786984i \(0.711641\pi\)
\(80\) −4.31324e7 −0.117733
\(81\) 4.30467e7 0.111111
\(82\) 2.99284e8 0.731006
\(83\) 6.54358e8 1.51343 0.756717 0.653742i \(-0.226802\pi\)
0.756717 + 0.653742i \(0.226802\pi\)
\(84\) −3.41737e8 −0.748920
\(85\) 1.26055e8 0.261924
\(86\) −2.46655e8 −0.486235
\(87\) 3.86356e8 0.723020
\(88\) 9.39908e8 1.67076
\(89\) −8.81746e8 −1.48966 −0.744832 0.667252i \(-0.767470\pi\)
−0.744832 + 0.667252i \(0.767470\pi\)
\(90\) 7.75205e7 0.124545
\(91\) 7.10531e8 1.08617
\(92\) −1.91146e9 −2.78176
\(93\) 1.15123e8 0.159584
\(94\) −4.26665e8 −0.563653
\(95\) 1.82568e8 0.229969
\(96\) 2.45787e8 0.295351
\(97\) −1.21147e8 −0.138944 −0.0694719 0.997584i \(-0.522131\pi\)
−0.0694719 + 0.997584i \(0.522131\pi\)
\(98\) 7.68522e8 0.841665
\(99\) −3.78944e8 −0.396476
\(100\) −1.74400e9 −1.74400
\(101\) 7.20450e8 0.688902 0.344451 0.938804i \(-0.388065\pi\)
0.344451 + 0.938804i \(0.388065\pi\)
\(102\) 1.25407e9 1.14715
\(103\) 8.16532e7 0.0714835 0.0357418 0.999361i \(-0.488621\pi\)
0.0357418 + 0.999361i \(0.488621\pi\)
\(104\) 2.57400e9 2.15754
\(105\) 1.12856e8 0.0906094
\(106\) −2.05068e9 −1.57769
\(107\) 2.38390e9 1.75817 0.879084 0.476666i \(-0.158155\pi\)
0.879084 + 0.476666i \(0.158155\pi\)
\(108\) 4.99123e8 0.353021
\(109\) 1.05053e9 0.712838 0.356419 0.934326i \(-0.383997\pi\)
0.356419 + 0.934326i \(0.383997\pi\)
\(110\) −6.82420e8 −0.444411
\(111\) −3.27612e7 −0.0204836
\(112\) −6.24704e8 −0.375140
\(113\) 1.25128e9 0.721943 0.360971 0.932577i \(-0.382445\pi\)
0.360971 + 0.932577i \(0.382445\pi\)
\(114\) 1.81630e9 1.00720
\(115\) 6.31245e8 0.336556
\(116\) 4.47976e9 2.29717
\(117\) −1.03776e9 −0.511990
\(118\) 4.61604e8 0.219180
\(119\) 1.82570e9 0.834581
\(120\) 4.08837e8 0.179984
\(121\) 9.77927e8 0.414737
\(122\) 4.78183e9 1.95423
\(123\) −6.36365e8 −0.250688
\(124\) 1.33484e9 0.507027
\(125\) 1.18172e9 0.432933
\(126\) 1.12276e9 0.396844
\(127\) −5.45028e9 −1.85910 −0.929549 0.368699i \(-0.879803\pi\)
−0.929549 + 0.368699i \(0.879803\pi\)
\(128\) 5.56226e9 1.83150
\(129\) 5.24460e8 0.166747
\(130\) −1.86885e9 −0.573891
\(131\) −4.37579e9 −1.29818 −0.649092 0.760710i \(-0.724851\pi\)
−0.649092 + 0.760710i \(0.724851\pi\)
\(132\) −4.39382e9 −1.25968
\(133\) 2.64421e9 0.732763
\(134\) 3.18044e9 0.852148
\(135\) −1.64831e8 −0.0427108
\(136\) 6.61387e9 1.65779
\(137\) −6.28431e9 −1.52410 −0.762052 0.647515i \(-0.775808\pi\)
−0.762052 + 0.647515i \(0.775808\pi\)
\(138\) 6.28000e9 1.47402
\(139\) 9.44036e8 0.214497 0.107249 0.994232i \(-0.465796\pi\)
0.107249 + 0.994232i \(0.465796\pi\)
\(140\) 1.30856e9 0.287883
\(141\) 9.07216e8 0.193297
\(142\) 8.62342e9 1.77985
\(143\) 9.13550e9 1.82692
\(144\) 9.12408e8 0.176831
\(145\) −1.47941e9 −0.277927
\(146\) −1.51689e9 −0.276290
\(147\) −1.63410e9 −0.288637
\(148\) −3.79863e8 −0.0650802
\(149\) 6.46830e9 1.07511 0.537553 0.843230i \(-0.319349\pi\)
0.537553 + 0.843230i \(0.319349\pi\)
\(150\) 5.72983e9 0.924125
\(151\) −9.85249e9 −1.54223 −0.771116 0.636695i \(-0.780301\pi\)
−0.771116 + 0.636695i \(0.780301\pi\)
\(152\) 9.57902e9 1.45554
\(153\) −2.66652e9 −0.393399
\(154\) −9.88375e9 −1.41605
\(155\) −4.40820e8 −0.0613435
\(156\) −1.20328e10 −1.62669
\(157\) −8.11415e9 −1.06585 −0.532923 0.846164i \(-0.678906\pi\)
−0.532923 + 0.846164i \(0.678906\pi\)
\(158\) 1.62735e10 2.07741
\(159\) 4.36035e9 0.541047
\(160\) −9.41149e8 −0.113532
\(161\) 9.14257e9 1.07239
\(162\) −1.63984e9 −0.187061
\(163\) 9.11000e9 1.01082 0.505410 0.862879i \(-0.331341\pi\)
0.505410 + 0.862879i \(0.331341\pi\)
\(164\) −7.37859e9 −0.796483
\(165\) 1.45102e9 0.152404
\(166\) −2.49274e10 −2.54795
\(167\) 1.33957e10 1.33272 0.666362 0.745629i \(-0.267851\pi\)
0.666362 + 0.745629i \(0.267851\pi\)
\(168\) 5.92135e9 0.573494
\(169\) 1.44137e10 1.35920
\(170\) −4.80200e9 −0.440962
\(171\) −3.86199e9 −0.345405
\(172\) 6.08107e9 0.529788
\(173\) 1.43423e9 0.121733 0.0608667 0.998146i \(-0.480614\pi\)
0.0608667 + 0.998146i \(0.480614\pi\)
\(174\) −1.47180e10 −1.21724
\(175\) 8.34161e9 0.672324
\(176\) −8.03200e9 −0.630982
\(177\) −9.81506e8 −0.0751646
\(178\) 3.35896e10 2.50793
\(179\) 5.05798e9 0.368246 0.184123 0.982903i \(-0.441055\pi\)
0.184123 + 0.982903i \(0.441055\pi\)
\(180\) −1.91121e9 −0.135700
\(181\) 7.33273e9 0.507823 0.253911 0.967228i \(-0.418283\pi\)
0.253911 + 0.967228i \(0.418283\pi\)
\(182\) −2.70673e10 −1.82862
\(183\) −1.01676e10 −0.670174
\(184\) 3.31202e10 2.13017
\(185\) 1.25447e8 0.00787384
\(186\) −4.38554e9 −0.268667
\(187\) 2.34736e10 1.40376
\(188\) 1.05191e10 0.614140
\(189\) −2.38732e9 −0.136092
\(190\) −6.95484e9 −0.387165
\(191\) 6.28320e9 0.341610 0.170805 0.985305i \(-0.445363\pi\)
0.170805 + 0.985305i \(0.445363\pi\)
\(192\) −1.51304e10 −0.803518
\(193\) 2.89695e10 1.50291 0.751454 0.659785i \(-0.229353\pi\)
0.751454 + 0.659785i \(0.229353\pi\)
\(194\) 4.61502e9 0.233919
\(195\) 3.97372e9 0.196808
\(196\) −1.89473e10 −0.917053
\(197\) −3.19275e10 −1.51031 −0.755156 0.655545i \(-0.772439\pi\)
−0.755156 + 0.655545i \(0.772439\pi\)
\(198\) 1.44357e10 0.667488
\(199\) −4.30163e10 −1.94444 −0.972220 0.234070i \(-0.924795\pi\)
−0.972220 + 0.234070i \(0.924795\pi\)
\(200\) 3.02187e10 1.33549
\(201\) −6.76254e9 −0.292232
\(202\) −2.74451e10 −1.15980
\(203\) −2.14268e10 −0.885574
\(204\) −3.09181e10 −1.24990
\(205\) 2.43672e9 0.0963638
\(206\) −3.11054e9 −0.120346
\(207\) −1.33531e10 −0.505495
\(208\) −2.19961e10 −0.814820
\(209\) 3.39974e10 1.23250
\(210\) −4.29919e9 −0.152546
\(211\) 4.42161e10 1.53571 0.767855 0.640623i \(-0.221324\pi\)
0.767855 + 0.640623i \(0.221324\pi\)
\(212\) 5.05579e10 1.71901
\(213\) −1.83359e10 −0.610372
\(214\) −9.08133e10 −2.95997
\(215\) −2.00823e9 −0.0640973
\(216\) −8.64840e9 −0.270330
\(217\) −6.38457e9 −0.195462
\(218\) −4.00195e10 −1.20010
\(219\) 3.22535e9 0.0947497
\(220\) 1.68245e10 0.484217
\(221\) 6.42840e10 1.81275
\(222\) 1.24802e9 0.0344852
\(223\) −3.54715e10 −0.960523 −0.480262 0.877125i \(-0.659458\pi\)
−0.480262 + 0.877125i \(0.659458\pi\)
\(224\) −1.36310e10 −0.361753
\(225\) −1.21833e10 −0.316915
\(226\) −4.76670e10 −1.21543
\(227\) 3.93316e10 0.983163 0.491581 0.870832i \(-0.336419\pi\)
0.491581 + 0.870832i \(0.336419\pi\)
\(228\) −4.47794e10 −1.09742
\(229\) −4.92726e9 −0.118398 −0.0591992 0.998246i \(-0.518855\pi\)
−0.0591992 + 0.998246i \(0.518855\pi\)
\(230\) −2.40469e10 −0.566610
\(231\) 2.10158e10 0.485614
\(232\) −7.76216e10 −1.75908
\(233\) −5.84819e10 −1.29993 −0.649964 0.759965i \(-0.725216\pi\)
−0.649964 + 0.759965i \(0.725216\pi\)
\(234\) 3.95330e10 0.861962
\(235\) −3.47384e9 −0.0743028
\(236\) −1.13805e10 −0.238812
\(237\) −3.46021e10 −0.712419
\(238\) −6.95492e10 −1.40506
\(239\) −2.25238e10 −0.446530 −0.223265 0.974758i \(-0.571672\pi\)
−0.223265 + 0.974758i \(0.571672\pi\)
\(240\) −3.49373e9 −0.0679733
\(241\) −3.91475e10 −0.747527 −0.373764 0.927524i \(-0.621933\pi\)
−0.373764 + 0.927524i \(0.621933\pi\)
\(242\) −3.72536e10 −0.698231
\(243\) 3.48678e9 0.0641500
\(244\) −1.17892e11 −2.12927
\(245\) 6.25719e9 0.110951
\(246\) 2.42420e10 0.422046
\(247\) 9.31040e10 1.59159
\(248\) −2.31290e10 −0.388262
\(249\) 5.30030e10 0.873782
\(250\) −4.50171e10 −0.728866
\(251\) 9.22468e10 1.46696 0.733482 0.679709i \(-0.237894\pi\)
0.733482 + 0.679709i \(0.237894\pi\)
\(252\) −2.76807e10 −0.432389
\(253\) 1.17549e11 1.80375
\(254\) 2.07625e11 3.12989
\(255\) 1.02105e10 0.151222
\(256\) −1.16252e11 −1.69169
\(257\) −1.22545e11 −1.75226 −0.876129 0.482076i \(-0.839883\pi\)
−0.876129 + 0.482076i \(0.839883\pi\)
\(258\) −1.99790e10 −0.280728
\(259\) 1.81689e9 0.0250888
\(260\) 4.60750e10 0.625295
\(261\) 3.12948e10 0.417436
\(262\) 1.66694e11 2.18556
\(263\) 3.47682e10 0.448106 0.224053 0.974577i \(-0.428071\pi\)
0.224053 + 0.974577i \(0.428071\pi\)
\(264\) 7.61325e10 0.964612
\(265\) −1.66964e10 −0.207977
\(266\) −1.00730e11 −1.23364
\(267\) −7.14214e10 −0.860058
\(268\) −7.84110e10 −0.928476
\(269\) 3.58870e10 0.417881 0.208940 0.977928i \(-0.432999\pi\)
0.208940 + 0.977928i \(0.432999\pi\)
\(270\) 6.27916e9 0.0719060
\(271\) 5.73561e10 0.645978 0.322989 0.946403i \(-0.395312\pi\)
0.322989 + 0.946403i \(0.395312\pi\)
\(272\) −5.65189e10 −0.626086
\(273\) 5.75530e10 0.627099
\(274\) 2.39397e11 2.56591
\(275\) 1.07251e11 1.13084
\(276\) −1.54828e11 −1.60605
\(277\) −1.63860e11 −1.67230 −0.836152 0.548498i \(-0.815200\pi\)
−0.836152 + 0.548498i \(0.815200\pi\)
\(278\) −3.59625e10 −0.361118
\(279\) 9.32495e9 0.0921356
\(280\) −2.26736e10 −0.220450
\(281\) −4.45125e10 −0.425896 −0.212948 0.977064i \(-0.568306\pi\)
−0.212948 + 0.977064i \(0.568306\pi\)
\(282\) −3.45599e10 −0.325425
\(283\) 8.38421e10 0.777004 0.388502 0.921448i \(-0.372993\pi\)
0.388502 + 0.921448i \(0.372993\pi\)
\(284\) −2.12603e11 −1.93927
\(285\) 1.47880e10 0.132773
\(286\) −3.48012e11 −3.07572
\(287\) 3.52920e10 0.307049
\(288\) 1.99087e10 0.170521
\(289\) 4.65893e10 0.392867
\(290\) 5.63571e10 0.467905
\(291\) −9.81288e9 −0.0802192
\(292\) 3.73976e10 0.301038
\(293\) 1.10535e10 0.0876186 0.0438093 0.999040i \(-0.486051\pi\)
0.0438093 + 0.999040i \(0.486051\pi\)
\(294\) 6.22503e10 0.485935
\(295\) 3.75831e9 0.0288931
\(296\) 6.58195e9 0.0498359
\(297\) −3.06945e10 −0.228905
\(298\) −2.46406e11 −1.81000
\(299\) 3.21915e11 2.32927
\(300\) −1.41264e11 −1.00690
\(301\) −2.90859e10 −0.204237
\(302\) 3.75325e11 2.59643
\(303\) 5.83564e10 0.397738
\(304\) −8.18577e10 −0.549703
\(305\) 3.89330e10 0.257613
\(306\) 1.01580e11 0.662309
\(307\) 1.66454e11 1.06948 0.534740 0.845017i \(-0.320409\pi\)
0.534740 + 0.845017i \(0.320409\pi\)
\(308\) 2.43676e11 1.54289
\(309\) 6.61391e9 0.0412710
\(310\) 1.67928e10 0.103275
\(311\) −1.85159e11 −1.12233 −0.561167 0.827702i \(-0.689648\pi\)
−0.561167 + 0.827702i \(0.689648\pi\)
\(312\) 2.08494e11 1.24565
\(313\) 1.58942e11 0.936030 0.468015 0.883720i \(-0.344969\pi\)
0.468015 + 0.883720i \(0.344969\pi\)
\(314\) 3.09104e11 1.79441
\(315\) 9.14134e9 0.0523134
\(316\) −4.01209e11 −2.26349
\(317\) 1.97998e11 1.10127 0.550635 0.834746i \(-0.314386\pi\)
0.550635 + 0.834746i \(0.314386\pi\)
\(318\) −1.66105e11 −0.910881
\(319\) −2.75491e11 −1.48953
\(320\) 5.79363e10 0.308870
\(321\) 1.93096e11 1.01508
\(322\) −3.48281e11 −1.80542
\(323\) 2.39230e11 1.22294
\(324\) 4.04289e10 0.203817
\(325\) 2.93712e11 1.46032
\(326\) −3.47040e11 −1.70177
\(327\) 8.50933e10 0.411557
\(328\) 1.27850e11 0.609915
\(329\) −5.03130e10 −0.236755
\(330\) −5.52760e10 −0.256581
\(331\) −1.52643e11 −0.698960 −0.349480 0.936944i \(-0.613642\pi\)
−0.349480 + 0.936944i \(0.613642\pi\)
\(332\) 6.14565e11 2.77617
\(333\) −2.65365e9 −0.0118262
\(334\) −5.10300e11 −2.24371
\(335\) 2.58946e10 0.112333
\(336\) −5.06010e10 −0.216587
\(337\) −2.98538e11 −1.26085 −0.630426 0.776249i \(-0.717120\pi\)
−0.630426 + 0.776249i \(0.717120\pi\)
\(338\) −5.49081e11 −2.28829
\(339\) 1.01354e11 0.416814
\(340\) 1.18389e11 0.480460
\(341\) −8.20883e10 −0.328766
\(342\) 1.47120e11 0.581507
\(343\) 2.71900e11 1.06068
\(344\) −1.05368e11 −0.405691
\(345\) 5.11308e10 0.194311
\(346\) −5.46360e10 −0.204945
\(347\) 3.17389e11 1.17519 0.587597 0.809154i \(-0.300074\pi\)
0.587597 + 0.809154i \(0.300074\pi\)
\(348\) 3.62860e11 1.32627
\(349\) 4.57145e10 0.164945 0.0824725 0.996593i \(-0.473718\pi\)
0.0824725 + 0.996593i \(0.473718\pi\)
\(350\) −3.17769e11 −1.13189
\(351\) −8.40587e10 −0.295597
\(352\) −1.75258e11 −0.608466
\(353\) −2.23119e11 −0.764803 −0.382401 0.923996i \(-0.624903\pi\)
−0.382401 + 0.923996i \(0.624903\pi\)
\(354\) 3.73899e10 0.126544
\(355\) 7.02106e10 0.234626
\(356\) −8.28125e11 −2.73257
\(357\) 1.47882e11 0.481846
\(358\) −1.92681e11 −0.619962
\(359\) −2.18766e10 −0.0695112 −0.0347556 0.999396i \(-0.511065\pi\)
−0.0347556 + 0.999396i \(0.511065\pi\)
\(360\) 3.31158e10 0.103914
\(361\) 2.37947e10 0.0737390
\(362\) −2.79336e11 −0.854946
\(363\) 7.92121e10 0.239448
\(364\) 6.67322e11 1.99241
\(365\) −1.23503e10 −0.0364216
\(366\) 3.87328e11 1.12827
\(367\) −3.93075e11 −1.13104 −0.565520 0.824734i \(-0.691325\pi\)
−0.565520 + 0.824734i \(0.691325\pi\)
\(368\) −2.83030e11 −0.804483
\(369\) −5.15456e10 −0.144735
\(370\) −4.77882e9 −0.0132560
\(371\) −2.41820e11 −0.662688
\(372\) 1.08122e11 0.292732
\(373\) −1.13683e11 −0.304094 −0.152047 0.988373i \(-0.548586\pi\)
−0.152047 + 0.988373i \(0.548586\pi\)
\(374\) −8.94214e11 −2.36330
\(375\) 9.57196e10 0.249954
\(376\) −1.82266e11 −0.470284
\(377\) −7.54449e11 −1.92351
\(378\) 9.09436e10 0.229118
\(379\) −6.69019e11 −1.66557 −0.832783 0.553599i \(-0.813254\pi\)
−0.832783 + 0.553599i \(0.813254\pi\)
\(380\) 1.71466e11 0.421844
\(381\) −4.41473e11 −1.07335
\(382\) −2.39355e11 −0.575118
\(383\) −1.08110e11 −0.256728 −0.128364 0.991727i \(-0.540973\pi\)
−0.128364 + 0.991727i \(0.540973\pi\)
\(384\) 4.50543e11 1.05741
\(385\) −8.04720e10 −0.186669
\(386\) −1.10358e12 −2.53023
\(387\) 4.24813e10 0.0962716
\(388\) −1.13780e11 −0.254872
\(389\) −7.24664e10 −0.160459 −0.0802294 0.996776i \(-0.525565\pi\)
−0.0802294 + 0.996776i \(0.525565\pi\)
\(390\) −1.51377e11 −0.331336
\(391\) 8.27157e11 1.78975
\(392\) 3.28303e11 0.702244
\(393\) −3.54439e11 −0.749507
\(394\) 1.21626e12 2.54269
\(395\) 1.32496e11 0.273852
\(396\) −3.55899e11 −0.727275
\(397\) 2.66907e11 0.539265 0.269632 0.962963i \(-0.413098\pi\)
0.269632 + 0.962963i \(0.413098\pi\)
\(398\) 1.63868e12 3.27357
\(399\) 2.14181e11 0.423061
\(400\) −2.58234e11 −0.504364
\(401\) 5.84873e11 1.12957 0.564783 0.825239i \(-0.308960\pi\)
0.564783 + 0.825239i \(0.308960\pi\)
\(402\) 2.57615e11 0.491988
\(403\) −2.24804e11 −0.424552
\(404\) 6.76638e11 1.26369
\(405\) −1.33513e10 −0.0246591
\(406\) 8.16242e11 1.49091
\(407\) 2.33603e10 0.0421992
\(408\) 5.35723e11 0.957127
\(409\) 6.63222e11 1.17194 0.585968 0.810334i \(-0.300714\pi\)
0.585968 + 0.810334i \(0.300714\pi\)
\(410\) −9.28256e10 −0.162234
\(411\) −5.09029e11 −0.879942
\(412\) 7.66877e10 0.131126
\(413\) 5.44331e10 0.0920636
\(414\) 5.08680e11 0.851027
\(415\) −2.02955e11 −0.335880
\(416\) −4.79955e11 −0.785744
\(417\) 7.64669e10 0.123840
\(418\) −1.29511e12 −2.07498
\(419\) −5.68468e11 −0.901038 −0.450519 0.892767i \(-0.648761\pi\)
−0.450519 + 0.892767i \(0.648761\pi\)
\(420\) 1.05993e11 0.166209
\(421\) −1.97121e11 −0.305819 −0.152910 0.988240i \(-0.548864\pi\)
−0.152910 + 0.988240i \(0.548864\pi\)
\(422\) −1.68439e12 −2.58545
\(423\) 7.34845e10 0.111600
\(424\) −8.76027e11 −1.31635
\(425\) 7.54692e11 1.12207
\(426\) 6.98497e11 1.02759
\(427\) 5.63881e11 0.820847
\(428\) 2.23893e12 3.22510
\(429\) 7.39976e11 1.05477
\(430\) 7.65023e10 0.107911
\(431\) −1.11083e12 −1.55060 −0.775301 0.631592i \(-0.782402\pi\)
−0.775301 + 0.631592i \(0.782402\pi\)
\(432\) 7.39050e10 0.102093
\(433\) 1.29398e12 1.76901 0.884506 0.466528i \(-0.154495\pi\)
0.884506 + 0.466528i \(0.154495\pi\)
\(434\) 2.43217e11 0.329071
\(435\) −1.19832e11 −0.160461
\(436\) 9.86649e11 1.30760
\(437\) 1.19799e12 1.57140
\(438\) −1.22868e11 −0.159516
\(439\) −4.93869e10 −0.0634631 −0.0317316 0.999496i \(-0.510102\pi\)
−0.0317316 + 0.999496i \(0.510102\pi\)
\(440\) −2.91521e11 −0.370794
\(441\) −1.32362e11 −0.166644
\(442\) −2.44886e12 −3.05186
\(443\) −1.04957e12 −1.29477 −0.647386 0.762162i \(-0.724138\pi\)
−0.647386 + 0.762162i \(0.724138\pi\)
\(444\) −3.07689e10 −0.0375741
\(445\) 2.73482e11 0.330604
\(446\) 1.35127e12 1.61709
\(447\) 5.23932e11 0.620713
\(448\) 8.39115e11 0.984170
\(449\) 5.61708e11 0.652232 0.326116 0.945330i \(-0.394260\pi\)
0.326116 + 0.945330i \(0.394260\pi\)
\(450\) 4.64116e11 0.533544
\(451\) 4.53760e11 0.516454
\(452\) 1.17519e12 1.32430
\(453\) −7.98051e11 −0.890408
\(454\) −1.49832e12 −1.65521
\(455\) −2.20378e11 −0.241055
\(456\) 7.75901e11 0.840358
\(457\) 2.07985e11 0.223054 0.111527 0.993761i \(-0.464426\pi\)
0.111527 + 0.993761i \(0.464426\pi\)
\(458\) 1.87701e11 0.199330
\(459\) −2.15988e11 −0.227129
\(460\) 5.92857e11 0.617362
\(461\) −9.15854e11 −0.944435 −0.472217 0.881482i \(-0.656546\pi\)
−0.472217 + 0.881482i \(0.656546\pi\)
\(462\) −8.00584e11 −0.817557
\(463\) 1.29254e12 1.30716 0.653580 0.756857i \(-0.273266\pi\)
0.653580 + 0.756857i \(0.273266\pi\)
\(464\) 6.63317e11 0.664340
\(465\) −3.57064e10 −0.0354167
\(466\) 2.22784e12 2.18850
\(467\) −1.89579e12 −1.84444 −0.922218 0.386669i \(-0.873626\pi\)
−0.922218 + 0.386669i \(0.873626\pi\)
\(468\) −9.74653e11 −0.939169
\(469\) 3.75042e11 0.357933
\(470\) 1.32334e11 0.125093
\(471\) −6.57246e11 −0.615367
\(472\) 1.97192e11 0.182873
\(473\) −3.73966e11 −0.343524
\(474\) 1.31815e12 1.19940
\(475\) 1.09304e12 0.985176
\(476\) 1.71468e12 1.53092
\(477\) 3.53189e11 0.312373
\(478\) 8.58031e11 0.751757
\(479\) −8.05471e11 −0.699101 −0.349551 0.936917i \(-0.613666\pi\)
−0.349551 + 0.936917i \(0.613666\pi\)
\(480\) −7.62330e10 −0.0655477
\(481\) 6.39738e10 0.0544941
\(482\) 1.49130e12 1.25850
\(483\) 7.40548e11 0.619143
\(484\) 9.18457e11 0.760772
\(485\) 3.75748e10 0.0308361
\(486\) −1.32827e11 −0.108000
\(487\) −8.81732e11 −0.710324 −0.355162 0.934805i \(-0.615574\pi\)
−0.355162 + 0.934805i \(0.615574\pi\)
\(488\) 2.04274e12 1.63051
\(489\) 7.37910e11 0.583597
\(490\) −2.38364e11 −0.186792
\(491\) 1.27407e12 0.989299 0.494649 0.869093i \(-0.335296\pi\)
0.494649 + 0.869093i \(0.335296\pi\)
\(492\) −5.97666e11 −0.459849
\(493\) −1.93855e12 −1.47797
\(494\) −3.54675e12 −2.67953
\(495\) 1.17533e11 0.0879906
\(496\) 1.97649e11 0.146632
\(497\) 1.01689e12 0.747600
\(498\) −2.01912e12 −1.47106
\(499\) −1.28674e12 −0.929050 −0.464525 0.885560i \(-0.653775\pi\)
−0.464525 + 0.885560i \(0.653775\pi\)
\(500\) 1.10986e12 0.794151
\(501\) 1.08505e12 0.769448
\(502\) −3.51409e12 −2.46971
\(503\) 2.49635e12 1.73880 0.869401 0.494107i \(-0.164505\pi\)
0.869401 + 0.494107i \(0.164505\pi\)
\(504\) 4.79629e11 0.331107
\(505\) −2.23454e11 −0.152889
\(506\) −4.47795e12 −3.03670
\(507\) 1.16751e12 0.784736
\(508\) −5.11884e12 −3.41024
\(509\) −7.37598e11 −0.487068 −0.243534 0.969892i \(-0.578307\pi\)
−0.243534 + 0.969892i \(0.578307\pi\)
\(510\) −3.88962e11 −0.254590
\(511\) −1.78874e11 −0.116052
\(512\) 1.58068e12 1.01655
\(513\) −3.12821e11 −0.199419
\(514\) 4.66830e12 2.95002
\(515\) −2.53255e10 −0.0158645
\(516\) 4.92567e11 0.305873
\(517\) −6.46890e11 −0.398220
\(518\) −6.92136e10 −0.0422384
\(519\) 1.16172e11 0.0702828
\(520\) −7.98350e11 −0.478826
\(521\) −9.55838e11 −0.568348 −0.284174 0.958773i \(-0.591719\pi\)
−0.284174 + 0.958773i \(0.591719\pi\)
\(522\) −1.19216e12 −0.702776
\(523\) −2.33681e12 −1.36573 −0.682867 0.730542i \(-0.739267\pi\)
−0.682867 + 0.730542i \(0.739267\pi\)
\(524\) −4.10969e12 −2.38132
\(525\) 6.75670e11 0.388166
\(526\) −1.32447e12 −0.754411
\(527\) −5.77632e11 −0.326215
\(528\) −6.50592e11 −0.364298
\(529\) 2.34100e12 1.29972
\(530\) 6.36039e11 0.350140
\(531\) −7.95020e10 −0.0433963
\(532\) 2.48341e12 1.34414
\(533\) 1.24265e12 0.666924
\(534\) 2.72076e12 1.44795
\(535\) −7.39388e11 −0.390194
\(536\) 1.35864e12 0.710990
\(537\) 4.09696e11 0.212607
\(538\) −1.36710e12 −0.703525
\(539\) 1.16520e12 0.594634
\(540\) −1.54808e11 −0.0783467
\(541\) −5.47294e10 −0.0274684 −0.0137342 0.999906i \(-0.504372\pi\)
−0.0137342 + 0.999906i \(0.504372\pi\)
\(542\) −2.18495e12 −1.08754
\(543\) 5.93951e11 0.293191
\(544\) −1.23324e12 −0.603745
\(545\) −3.25833e11 −0.158202
\(546\) −2.19245e12 −1.05575
\(547\) 4.41803e11 0.211002 0.105501 0.994419i \(-0.466355\pi\)
0.105501 + 0.994419i \(0.466355\pi\)
\(548\) −5.90214e12 −2.79574
\(549\) −8.23574e11 −0.386925
\(550\) −4.08565e12 −1.90383
\(551\) −2.80765e12 −1.29766
\(552\) 2.68274e12 1.22985
\(553\) 1.91899e12 0.872589
\(554\) 6.24217e12 2.81541
\(555\) 1.01612e10 0.00454596
\(556\) 8.86627e11 0.393463
\(557\) 3.93748e12 1.73329 0.866643 0.498929i \(-0.166273\pi\)
0.866643 + 0.498929i \(0.166273\pi\)
\(558\) −3.55229e11 −0.155115
\(559\) −1.02413e12 −0.443611
\(560\) 1.93758e11 0.0832555
\(561\) 1.90136e12 0.810461
\(562\) 1.69568e12 0.717018
\(563\) −2.31827e11 −0.0972472 −0.0486236 0.998817i \(-0.515483\pi\)
−0.0486236 + 0.998817i \(0.515483\pi\)
\(564\) 8.52046e11 0.354574
\(565\) −3.88097e11 −0.160222
\(566\) −3.19392e12 −1.30813
\(567\) −1.93373e11 −0.0785726
\(568\) 3.68382e12 1.48502
\(569\) 1.34218e12 0.536792 0.268396 0.963309i \(-0.413506\pi\)
0.268396 + 0.963309i \(0.413506\pi\)
\(570\) −5.63342e11 −0.223530
\(571\) 8.66924e11 0.341286 0.170643 0.985333i \(-0.445416\pi\)
0.170643 + 0.985333i \(0.445416\pi\)
\(572\) 8.57995e12 3.35122
\(573\) 5.08939e11 0.197229
\(574\) −1.34443e12 −0.516933
\(575\) 3.77927e12 1.44179
\(576\) −1.22556e12 −0.463911
\(577\) 3.24740e11 0.121968 0.0609839 0.998139i \(-0.480576\pi\)
0.0609839 + 0.998139i \(0.480576\pi\)
\(578\) −1.77479e12 −0.661413
\(579\) 2.34653e12 0.867704
\(580\) −1.38944e12 −0.509816
\(581\) −2.93948e12 −1.07023
\(582\) 3.73817e11 0.135053
\(583\) −3.10915e12 −1.11464
\(584\) −6.47995e11 −0.230523
\(585\) 3.21872e11 0.113627
\(586\) −4.21078e11 −0.147511
\(587\) −8.84855e11 −0.307610 −0.153805 0.988101i \(-0.549153\pi\)
−0.153805 + 0.988101i \(0.549153\pi\)
\(588\) −1.53473e12 −0.529461
\(589\) −8.36598e11 −0.286417
\(590\) −1.43171e11 −0.0486430
\(591\) −2.58613e12 −0.871979
\(592\) −5.62462e10 −0.0188211
\(593\) −1.35974e12 −0.451553 −0.225777 0.974179i \(-0.572492\pi\)
−0.225777 + 0.974179i \(0.572492\pi\)
\(594\) 1.16929e12 0.385374
\(595\) −5.66259e11 −0.185220
\(596\) 6.07494e12 1.97212
\(597\) −3.48432e12 −1.12262
\(598\) −1.22632e13 −3.92145
\(599\) 1.06411e11 0.0337728 0.0168864 0.999857i \(-0.494625\pi\)
0.0168864 + 0.999857i \(0.494625\pi\)
\(600\) 2.44771e12 0.771045
\(601\) −3.77150e12 −1.17918 −0.589589 0.807704i \(-0.700710\pi\)
−0.589589 + 0.807704i \(0.700710\pi\)
\(602\) 1.10801e12 0.343843
\(603\) −5.47766e11 −0.168720
\(604\) −9.25333e12 −2.82899
\(605\) −3.03313e11 −0.0920433
\(606\) −2.22306e12 −0.669613
\(607\) 4.83527e12 1.44568 0.722839 0.691017i \(-0.242837\pi\)
0.722839 + 0.691017i \(0.242837\pi\)
\(608\) −1.78613e12 −0.530088
\(609\) −1.73557e12 −0.511287
\(610\) −1.48313e12 −0.433706
\(611\) −1.77155e12 −0.514242
\(612\) −2.50436e12 −0.721632
\(613\) 9.11706e11 0.260785 0.130393 0.991462i \(-0.458376\pi\)
0.130393 + 0.991462i \(0.458376\pi\)
\(614\) −6.34099e12 −1.80053
\(615\) 1.97375e11 0.0556356
\(616\) −4.22222e12 −1.18148
\(617\) 3.14494e12 0.873633 0.436816 0.899551i \(-0.356106\pi\)
0.436816 + 0.899551i \(0.356106\pi\)
\(618\) −2.51953e11 −0.0694820
\(619\) −5.36136e12 −1.46780 −0.733900 0.679257i \(-0.762302\pi\)
−0.733900 + 0.679257i \(0.762302\pi\)
\(620\) −4.14013e11 −0.112526
\(621\) −1.08160e12 −0.291847
\(622\) 7.05352e12 1.88951
\(623\) 3.96094e12 1.05342
\(624\) −1.78169e12 −0.470437
\(625\) 3.26029e12 0.854665
\(626\) −6.05482e12 −1.57586
\(627\) 2.75379e12 0.711585
\(628\) −7.62071e12 −1.95514
\(629\) 1.64380e11 0.0418718
\(630\) −3.48235e11 −0.0880723
\(631\) 4.20961e11 0.105708 0.0528542 0.998602i \(-0.483168\pi\)
0.0528542 + 0.998602i \(0.483168\pi\)
\(632\) 6.95182e12 1.73329
\(633\) 3.58150e12 0.886643
\(634\) −7.54262e12 −1.85405
\(635\) 1.69046e12 0.412593
\(636\) 4.09519e12 0.992469
\(637\) 3.19097e12 0.767883
\(638\) 1.04947e13 2.50770
\(639\) −1.48521e12 −0.352399
\(640\) −1.72519e12 −0.406468
\(641\) −7.18622e12 −1.68128 −0.840639 0.541596i \(-0.817820\pi\)
−0.840639 + 0.541596i \(0.817820\pi\)
\(642\) −7.35588e12 −1.70894
\(643\) 8.02563e11 0.185153 0.0925763 0.995706i \(-0.470490\pi\)
0.0925763 + 0.995706i \(0.470490\pi\)
\(644\) 8.58658e12 1.96713
\(645\) −1.62666e11 −0.0370066
\(646\) −9.11334e12 −2.05888
\(647\) −3.90264e12 −0.875568 −0.437784 0.899080i \(-0.644236\pi\)
−0.437784 + 0.899080i \(0.644236\pi\)
\(648\) −7.00520e11 −0.156075
\(649\) 6.99863e11 0.154850
\(650\) −1.11888e13 −2.45852
\(651\) −5.17150e11 −0.112850
\(652\) 8.55600e12 1.85420
\(653\) 2.14699e12 0.462084 0.231042 0.972944i \(-0.425787\pi\)
0.231042 + 0.972944i \(0.425787\pi\)
\(654\) −3.24158e12 −0.692879
\(655\) 1.35719e12 0.288108
\(656\) −1.09255e12 −0.230342
\(657\) 2.61253e11 0.0547038
\(658\) 1.91665e12 0.398589
\(659\) −2.75092e11 −0.0568191 −0.0284096 0.999596i \(-0.509044\pi\)
−0.0284096 + 0.999596i \(0.509044\pi\)
\(660\) 1.36278e12 0.279563
\(661\) 3.39394e12 0.691509 0.345755 0.938325i \(-0.387623\pi\)
0.345755 + 0.938325i \(0.387623\pi\)
\(662\) 5.81487e12 1.17674
\(663\) 5.20700e12 1.04659
\(664\) −1.06487e13 −2.12588
\(665\) −8.20126e11 −0.162623
\(666\) 1.01090e11 0.0199100
\(667\) −9.70767e12 −1.89910
\(668\) 1.25810e13 2.44468
\(669\) −2.87319e12 −0.554558
\(670\) −9.86442e11 −0.189119
\(671\) 7.24999e12 1.38066
\(672\) −1.10411e12 −0.208858
\(673\) −1.26928e12 −0.238501 −0.119251 0.992864i \(-0.538049\pi\)
−0.119251 + 0.992864i \(0.538049\pi\)
\(674\) 1.13726e13 2.12271
\(675\) −9.86847e11 −0.182971
\(676\) 1.35371e13 2.49325
\(677\) −9.30849e12 −1.70306 −0.851530 0.524306i \(-0.824325\pi\)
−0.851530 + 0.524306i \(0.824325\pi\)
\(678\) −3.86102e12 −0.701728
\(679\) 5.44210e11 0.0982546
\(680\) −2.05135e12 −0.367917
\(681\) 3.18586e12 0.567629
\(682\) 3.12711e12 0.553495
\(683\) −7.85825e12 −1.38176 −0.690880 0.722969i \(-0.742777\pi\)
−0.690880 + 0.722969i \(0.742777\pi\)
\(684\) −3.62713e12 −0.633593
\(685\) 1.94914e12 0.338248
\(686\) −1.03579e13 −1.78572
\(687\) −3.99108e11 −0.0683573
\(688\) 9.00423e11 0.153214
\(689\) −8.51460e12 −1.43939
\(690\) −1.94780e12 −0.327133
\(691\) −1.07981e12 −0.180176 −0.0900880 0.995934i \(-0.528715\pi\)
−0.0900880 + 0.995934i \(0.528715\pi\)
\(692\) 1.34701e12 0.223302
\(693\) 1.70228e12 0.280369
\(694\) −1.20908e13 −1.97850
\(695\) −2.92802e11 −0.0476038
\(696\) −6.28735e12 −1.01561
\(697\) 3.19298e12 0.512447
\(698\) −1.74147e12 −0.277694
\(699\) −4.73703e12 −0.750514
\(700\) 7.83433e12 1.23328
\(701\) −6.14310e11 −0.0960853 −0.0480426 0.998845i \(-0.515298\pi\)
−0.0480426 + 0.998845i \(0.515298\pi\)
\(702\) 3.20217e12 0.497654
\(703\) 2.38076e11 0.0367634
\(704\) 1.07887e13 1.65537
\(705\) −2.81381e11 −0.0428987
\(706\) 8.49958e12 1.28759
\(707\) −3.23637e12 −0.487160
\(708\) −9.21819e11 −0.137878
\(709\) 8.40205e11 0.124875 0.0624377 0.998049i \(-0.480113\pi\)
0.0624377 + 0.998049i \(0.480113\pi\)
\(710\) −2.67464e12 −0.395005
\(711\) −2.80277e12 −0.411315
\(712\) 1.43491e13 2.09249
\(713\) −2.89261e12 −0.419166
\(714\) −5.63348e12 −0.811213
\(715\) −2.83346e12 −0.405453
\(716\) 4.75039e12 0.675493
\(717\) −1.82443e12 −0.257804
\(718\) 8.33377e11 0.117026
\(719\) 1.19567e13 1.66852 0.834259 0.551373i \(-0.185896\pi\)
0.834259 + 0.551373i \(0.185896\pi\)
\(720\) −2.82992e11 −0.0392444
\(721\) −3.66799e11 −0.0505498
\(722\) −9.06445e11 −0.124144
\(723\) −3.17094e12 −0.431585
\(724\) 6.88681e12 0.931525
\(725\) −8.85721e12 −1.19063
\(726\) −3.01754e12 −0.403124
\(727\) 1.29650e13 1.72135 0.860674 0.509157i \(-0.170043\pi\)
0.860674 + 0.509157i \(0.170043\pi\)
\(728\) −1.15628e13 −1.52571
\(729\) 2.82430e11 0.0370370
\(730\) 4.70477e11 0.0613176
\(731\) −2.63150e12 −0.340859
\(732\) −9.54926e12 −1.22933
\(733\) 4.24918e12 0.543673 0.271836 0.962344i \(-0.412369\pi\)
0.271836 + 0.962344i \(0.412369\pi\)
\(734\) 1.49740e13 1.90417
\(735\) 5.06833e11 0.0640577
\(736\) −6.17570e12 −0.775776
\(737\) 4.82203e12 0.602041
\(738\) 1.96360e12 0.243669
\(739\) 1.58146e13 1.95056 0.975279 0.220979i \(-0.0709252\pi\)
0.975279 + 0.220979i \(0.0709252\pi\)
\(740\) 1.17818e11 0.0144434
\(741\) 7.54142e12 0.918907
\(742\) 9.21199e12 1.11567
\(743\) −4.05714e11 −0.0488394 −0.0244197 0.999702i \(-0.507774\pi\)
−0.0244197 + 0.999702i \(0.507774\pi\)
\(744\) −1.87345e12 −0.224163
\(745\) −2.00620e12 −0.238601
\(746\) 4.33071e12 0.511958
\(747\) 4.29324e12 0.504478
\(748\) 2.20461e13 2.57499
\(749\) −1.07088e13 −1.24330
\(750\) −3.64639e12 −0.420811
\(751\) 6.14962e12 0.705453 0.352727 0.935726i \(-0.385255\pi\)
0.352727 + 0.935726i \(0.385255\pi\)
\(752\) 1.55756e12 0.177609
\(753\) 7.47199e12 0.846952
\(754\) 2.87403e13 3.23833
\(755\) 3.05584e12 0.342271
\(756\) −2.24214e12 −0.249640
\(757\) 8.16991e12 0.904245 0.452122 0.891956i \(-0.350667\pi\)
0.452122 + 0.891956i \(0.350667\pi\)
\(758\) 2.54859e13 2.80407
\(759\) 9.52145e12 1.04139
\(760\) −2.97102e12 −0.323031
\(761\) 1.02310e13 1.10583 0.552916 0.833237i \(-0.313515\pi\)
0.552916 + 0.833237i \(0.313515\pi\)
\(762\) 1.68177e13 1.80704
\(763\) −4.71917e12 −0.504086
\(764\) 5.90110e12 0.626632
\(765\) 8.27047e11 0.0873079
\(766\) 4.11841e12 0.432215
\(767\) 1.91662e12 0.199966
\(768\) −9.41640e12 −0.976696
\(769\) 1.60525e13 1.65529 0.827647 0.561249i \(-0.189679\pi\)
0.827647 + 0.561249i \(0.189679\pi\)
\(770\) 3.06554e12 0.314267
\(771\) −9.92618e12 −1.01167
\(772\) 2.72078e13 2.75686
\(773\) 1.14431e13 1.15276 0.576378 0.817183i \(-0.304465\pi\)
0.576378 + 0.817183i \(0.304465\pi\)
\(774\) −1.61830e12 −0.162078
\(775\) −2.63919e12 −0.262793
\(776\) 1.97148e12 0.195171
\(777\) 1.47168e11 0.0144850
\(778\) 2.76057e12 0.270141
\(779\) 4.62447e12 0.449928
\(780\) 3.73207e12 0.361014
\(781\) 1.30744e13 1.25746
\(782\) −3.15101e13 −3.01314
\(783\) 2.53488e12 0.241007
\(784\) −2.80552e12 −0.265211
\(785\) 2.51668e12 0.236545
\(786\) 1.35022e13 1.26183
\(787\) 7.94547e12 0.738301 0.369150 0.929370i \(-0.379649\pi\)
0.369150 + 0.929370i \(0.379649\pi\)
\(788\) −2.99859e13 −2.77044
\(789\) 2.81622e12 0.258714
\(790\) −5.04736e12 −0.461044
\(791\) −5.62096e12 −0.510525
\(792\) 6.16674e12 0.556919
\(793\) 1.98546e13 1.78292
\(794\) −1.01677e13 −0.907881
\(795\) −1.35240e12 −0.120076
\(796\) −4.04004e13 −3.56678
\(797\) 3.65709e12 0.321050 0.160525 0.987032i \(-0.448681\pi\)
0.160525 + 0.987032i \(0.448681\pi\)
\(798\) −8.15910e12 −0.712245
\(799\) −4.55198e12 −0.395130
\(800\) −5.63466e12 −0.486366
\(801\) −5.78514e12 −0.496555
\(802\) −2.22804e13 −1.90169
\(803\) −2.29983e12 −0.195198
\(804\) −6.35129e12 −0.536056
\(805\) −2.83565e12 −0.237997
\(806\) 8.56379e12 0.714757
\(807\) 2.90685e12 0.241264
\(808\) −1.17242e13 −0.967683
\(809\) −8.52827e12 −0.699991 −0.349995 0.936751i \(-0.613817\pi\)
−0.349995 + 0.936751i \(0.613817\pi\)
\(810\) 5.08612e11 0.0415149
\(811\) −9.42454e11 −0.0765009 −0.0382504 0.999268i \(-0.512178\pi\)
−0.0382504 + 0.999268i \(0.512178\pi\)
\(812\) −2.01238e13 −1.62445
\(813\) 4.64584e12 0.372956
\(814\) −8.89899e11 −0.0710446
\(815\) −2.82555e12 −0.224333
\(816\) −4.57803e12 −0.361471
\(817\) −3.81126e12 −0.299274
\(818\) −2.52651e13 −1.97302
\(819\) 4.66179e12 0.362056
\(820\) 2.28854e12 0.176765
\(821\) −1.99364e13 −1.53145 −0.765725 0.643168i \(-0.777620\pi\)
−0.765725 + 0.643168i \(0.777620\pi\)
\(822\) 1.93912e13 1.48143
\(823\) 6.25923e12 0.475578 0.237789 0.971317i \(-0.423577\pi\)
0.237789 + 0.971317i \(0.423577\pi\)
\(824\) −1.32878e12 −0.100411
\(825\) 8.68729e12 0.652893
\(826\) −2.07360e12 −0.154994
\(827\) 1.22495e13 0.910633 0.455317 0.890330i \(-0.349526\pi\)
0.455317 + 0.890330i \(0.349526\pi\)
\(828\) −1.25411e13 −0.927254
\(829\) −8.99661e12 −0.661582 −0.330791 0.943704i \(-0.607315\pi\)
−0.330791 + 0.943704i \(0.607315\pi\)
\(830\) 7.73147e12 0.565471
\(831\) −1.32727e13 −0.965505
\(832\) 2.95457e13 2.13766
\(833\) 8.19916e12 0.590020
\(834\) −2.91296e12 −0.208491
\(835\) −4.15479e12 −0.295774
\(836\) 3.19299e13 2.26084
\(837\) 7.55321e11 0.0531945
\(838\) 2.16555e13 1.51695
\(839\) −8.68437e12 −0.605076 −0.302538 0.953137i \(-0.597834\pi\)
−0.302538 + 0.953137i \(0.597834\pi\)
\(840\) −1.83656e12 −0.127277
\(841\) 8.24405e12 0.568275
\(842\) 7.50924e12 0.514863
\(843\) −3.60551e12 −0.245891
\(844\) 4.15272e13 2.81703
\(845\) −4.47053e12 −0.301650
\(846\) −2.79935e12 −0.187884
\(847\) −4.39300e12 −0.293283
\(848\) 7.48610e12 0.497135
\(849\) 6.79121e12 0.448603
\(850\) −2.87496e13 −1.88906
\(851\) 8.23166e11 0.0538027
\(852\) −1.72209e13 −1.11964
\(853\) −6.24777e12 −0.404068 −0.202034 0.979379i \(-0.564755\pi\)
−0.202034 + 0.979379i \(0.564755\pi\)
\(854\) −2.14807e13 −1.38194
\(855\) 1.19783e12 0.0766563
\(856\) −3.87943e13 −2.46965
\(857\) −1.55002e13 −0.981578 −0.490789 0.871278i \(-0.663291\pi\)
−0.490789 + 0.871278i \(0.663291\pi\)
\(858\) −2.81890e13 −1.77577
\(859\) −1.19277e13 −0.747459 −0.373730 0.927538i \(-0.621921\pi\)
−0.373730 + 0.927538i \(0.621921\pi\)
\(860\) −1.88610e12 −0.117577
\(861\) 2.85865e12 0.177275
\(862\) 4.23165e13 2.61052
\(863\) −1.61967e13 −0.993982 −0.496991 0.867756i \(-0.665562\pi\)
−0.496991 + 0.867756i \(0.665562\pi\)
\(864\) 1.61261e12 0.0984502
\(865\) −4.44838e11 −0.0270165
\(866\) −4.92933e13 −2.97823
\(867\) 3.77373e12 0.226822
\(868\) −5.99631e12 −0.358546
\(869\) 2.46731e13 1.46769
\(870\) 4.56493e12 0.270145
\(871\) 1.32054e13 0.777447
\(872\) −1.70959e13 −1.00131
\(873\) −7.94844e11 −0.0463146
\(874\) −4.56368e13 −2.64554
\(875\) −5.30849e12 −0.306150
\(876\) 3.02921e12 0.173804
\(877\) −1.35706e13 −0.774643 −0.387322 0.921945i \(-0.626600\pi\)
−0.387322 + 0.921945i \(0.626600\pi\)
\(878\) 1.88137e12 0.106844
\(879\) 8.95335e11 0.0505866
\(880\) 2.49120e12 0.140035
\(881\) −1.21126e13 −0.677401 −0.338700 0.940894i \(-0.609987\pi\)
−0.338700 + 0.940894i \(0.609987\pi\)
\(882\) 5.04227e12 0.280555
\(883\) −2.64760e13 −1.46564 −0.732822 0.680420i \(-0.761797\pi\)
−0.732822 + 0.680420i \(0.761797\pi\)
\(884\) 6.03747e13 3.32522
\(885\) 3.04423e11 0.0166814
\(886\) 3.99827e13 2.17982
\(887\) 2.95615e12 0.160350 0.0801752 0.996781i \(-0.474452\pi\)
0.0801752 + 0.996781i \(0.474452\pi\)
\(888\) 5.33138e11 0.0287728
\(889\) 2.44835e13 1.31467
\(890\) −1.04181e13 −0.556590
\(891\) −2.48625e12 −0.132159
\(892\) −3.33144e13 −1.76194
\(893\) −6.59274e12 −0.346924
\(894\) −1.99589e13 −1.04500
\(895\) −1.56878e12 −0.0817256
\(896\) −2.49865e13 −1.29515
\(897\) 2.60751e13 1.34481
\(898\) −2.13980e13 −1.09807
\(899\) 6.77920e12 0.346147
\(900\) −1.14424e13 −0.581334
\(901\) −2.18782e13 −1.10599
\(902\) −1.72857e13 −0.869478
\(903\) −2.35596e12 −0.117916
\(904\) −2.03627e13 −1.01409
\(905\) −2.27431e12 −0.112702
\(906\) 3.04013e13 1.49905
\(907\) −2.48130e13 −1.21744 −0.608718 0.793386i \(-0.708316\pi\)
−0.608718 + 0.793386i \(0.708316\pi\)
\(908\) 3.69398e13 1.80347
\(909\) 4.72687e12 0.229634
\(910\) 8.39517e12 0.405829
\(911\) −2.19699e13 −1.05681 −0.528404 0.848993i \(-0.677209\pi\)
−0.528404 + 0.848993i \(0.677209\pi\)
\(912\) −6.63047e12 −0.317371
\(913\) −3.77938e13 −1.80012
\(914\) −7.92309e12 −0.375523
\(915\) 3.15357e12 0.148733
\(916\) −4.62762e12 −0.217184
\(917\) 1.96568e13 0.918015
\(918\) 8.22795e12 0.382384
\(919\) 6.05423e12 0.279988 0.139994 0.990152i \(-0.455292\pi\)
0.139994 + 0.990152i \(0.455292\pi\)
\(920\) −1.02726e13 −0.472752
\(921\) 1.34828e13 0.617465
\(922\) 3.48890e13 1.59001
\(923\) 3.58052e13 1.62382
\(924\) 1.97377e13 0.890786
\(925\) 7.51050e11 0.0337311
\(926\) −4.92385e13 −2.20067
\(927\) 5.35727e11 0.0238278
\(928\) 1.44736e13 0.640633
\(929\) 2.20766e13 0.972437 0.486219 0.873837i \(-0.338376\pi\)
0.486219 + 0.873837i \(0.338376\pi\)
\(930\) 1.36022e12 0.0596259
\(931\) 1.18750e13 0.518038
\(932\) −5.49255e13 −2.38453
\(933\) −1.49979e13 −0.647980
\(934\) 7.22190e13 3.10521
\(935\) −7.28056e12 −0.311539
\(936\) 1.68880e13 0.719179
\(937\) −2.81671e13 −1.19375 −0.596875 0.802334i \(-0.703591\pi\)
−0.596875 + 0.802334i \(0.703591\pi\)
\(938\) −1.42870e13 −0.602600
\(939\) 1.28743e13 0.540417
\(940\) −3.26259e12 −0.136297
\(941\) −3.07024e12 −0.127650 −0.0638248 0.997961i \(-0.520330\pi\)
−0.0638248 + 0.997961i \(0.520330\pi\)
\(942\) 2.50374e13 1.03600
\(943\) 1.59895e13 0.658463
\(944\) −1.68511e12 −0.0690642
\(945\) 7.40449e11 0.0302031
\(946\) 1.42460e13 0.578341
\(947\) −1.07551e13 −0.434550 −0.217275 0.976110i \(-0.569717\pi\)
−0.217275 + 0.976110i \(0.569717\pi\)
\(948\) −3.24979e13 −1.30683
\(949\) −6.29824e12 −0.252070
\(950\) −4.16387e13 −1.65860
\(951\) 1.60378e13 0.635818
\(952\) −2.97105e13 −1.17231
\(953\) −3.95867e13 −1.55465 −0.777323 0.629102i \(-0.783423\pi\)
−0.777323 + 0.629102i \(0.783423\pi\)
\(954\) −1.34545e13 −0.525897
\(955\) −1.94879e12 −0.0758142
\(956\) −2.11540e13 −0.819093
\(957\) −2.23148e13 −0.859980
\(958\) 3.06840e13 1.17697
\(959\) 2.82301e13 1.07778
\(960\) 4.69284e12 0.178326
\(961\) −2.44196e13 −0.923599
\(962\) −2.43705e12 −0.0917436
\(963\) 1.56408e13 0.586056
\(964\) −3.67668e13 −1.37123
\(965\) −8.98515e12 −0.333543
\(966\) −2.82108e13 −1.04236
\(967\) 1.84320e13 0.677881 0.338941 0.940808i \(-0.389931\pi\)
0.338941 + 0.940808i \(0.389931\pi\)
\(968\) −1.59143e13 −0.582570
\(969\) 1.93776e13 0.706063
\(970\) −1.43139e12 −0.0519141
\(971\) −3.67568e13 −1.32694 −0.663470 0.748203i \(-0.730917\pi\)
−0.663470 + 0.748203i \(0.730917\pi\)
\(972\) 3.27474e12 0.117674
\(973\) −4.24076e12 −0.151683
\(974\) 3.35891e13 1.19587
\(975\) 2.37907e13 0.843115
\(976\) −1.74563e13 −0.615782
\(977\) 2.58039e13 0.906066 0.453033 0.891494i \(-0.350342\pi\)
0.453033 + 0.891494i \(0.350342\pi\)
\(978\) −2.81103e13 −0.982517
\(979\) 5.09270e13 1.77185
\(980\) 5.87668e12 0.203523
\(981\) 6.89256e12 0.237613
\(982\) −4.85351e13 −1.66554
\(983\) −3.96549e13 −1.35459 −0.677293 0.735713i \(-0.736847\pi\)
−0.677293 + 0.735713i \(0.736847\pi\)
\(984\) 1.03559e13 0.352135
\(985\) 9.90261e12 0.335186
\(986\) 7.38480e13 2.48824
\(987\) −4.07536e12 −0.136691
\(988\) 8.74421e13 2.91954
\(989\) −1.31777e13 −0.437983
\(990\) −4.47736e12 −0.148137
\(991\) 3.92245e13 1.29189 0.645946 0.763383i \(-0.276463\pi\)
0.645946 + 0.763383i \(0.276463\pi\)
\(992\) 4.31270e12 0.141399
\(993\) −1.23641e13 −0.403545
\(994\) −3.87378e13 −1.25862
\(995\) 1.33419e13 0.431533
\(996\) 4.97797e13 1.60282
\(997\) 4.61994e12 0.148084 0.0740420 0.997255i \(-0.476410\pi\)
0.0740420 + 0.997255i \(0.476410\pi\)
\(998\) 4.90178e13 1.56411
\(999\) −2.14946e11 −0.00682786
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.d.1.3 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.3 22 1.1 even 1 trivial