Properties

Label 177.10.a.a.1.18
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
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: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+30.4984 q^{2} +81.0000 q^{3} +418.150 q^{4} +1050.93 q^{5} +2470.37 q^{6} -5890.68 q^{7} -2862.26 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+30.4984 q^{2} +81.0000 q^{3} +418.150 q^{4} +1050.93 q^{5} +2470.37 q^{6} -5890.68 q^{7} -2862.26 q^{8} +6561.00 q^{9} +32051.7 q^{10} +26388.8 q^{11} +33870.2 q^{12} -71180.0 q^{13} -179656. q^{14} +85125.4 q^{15} -301387. q^{16} -660629. q^{17} +200100. q^{18} -713962. q^{19} +439447. q^{20} -477145. q^{21} +804816. q^{22} +1.72289e6 q^{23} -231843. q^{24} -848670. q^{25} -2.17087e6 q^{26} +531441. q^{27} -2.46319e6 q^{28} -882627. q^{29} +2.59619e6 q^{30} +8.02994e6 q^{31} -7.72634e6 q^{32} +2.13749e6 q^{33} -2.01481e7 q^{34} -6.19069e6 q^{35} +2.74348e6 q^{36} -1.38423e7 q^{37} -2.17747e7 q^{38} -5.76558e6 q^{39} -3.00804e6 q^{40} -1.60785e7 q^{41} -1.45521e7 q^{42} -1.63480e7 q^{43} +1.10345e7 q^{44} +6.89516e6 q^{45} +5.25454e7 q^{46} +4.25996e7 q^{47} -2.44124e7 q^{48} -5.65355e6 q^{49} -2.58830e7 q^{50} -5.35109e7 q^{51} -2.97639e7 q^{52} +5.47396e6 q^{53} +1.62081e7 q^{54} +2.77328e7 q^{55} +1.68607e7 q^{56} -5.78309e7 q^{57} -2.69187e7 q^{58} +1.21174e7 q^{59} +3.55952e7 q^{60} -1.55390e8 q^{61} +2.44900e8 q^{62} -3.86487e7 q^{63} -8.13305e7 q^{64} -7.48053e7 q^{65} +6.51901e7 q^{66} +1.19205e8 q^{67} -2.76242e8 q^{68} +1.39554e8 q^{69} -1.88806e8 q^{70} +5.29891e7 q^{71} -1.87793e7 q^{72} -1.44959e8 q^{73} -4.22167e8 q^{74} -6.87422e7 q^{75} -2.98543e8 q^{76} -1.55448e8 q^{77} -1.75841e8 q^{78} +3.12409e8 q^{79} -3.16737e8 q^{80} +4.30467e7 q^{81} -4.90367e8 q^{82} +5.07060e7 q^{83} -1.99518e8 q^{84} -6.94275e8 q^{85} -4.98587e8 q^{86} -7.14928e7 q^{87} -7.55317e7 q^{88} +6.65499e8 q^{89} +2.10291e8 q^{90} +4.19298e8 q^{91} +7.20428e8 q^{92} +6.50425e8 q^{93} +1.29922e9 q^{94} -7.50324e8 q^{95} -6.25834e8 q^{96} -1.11643e9 q^{97} -1.72424e8 q^{98} +1.73137e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 30.4984 1.34785 0.673925 0.738800i \(-0.264607\pi\)
0.673925 + 0.738800i \(0.264607\pi\)
\(3\) 81.0000 0.577350
\(4\) 418.150 0.816700
\(5\) 1050.93 0.751985 0.375992 0.926623i \(-0.377302\pi\)
0.375992 + 0.926623i \(0.377302\pi\)
\(6\) 2470.37 0.778182
\(7\) −5890.68 −0.927308 −0.463654 0.886016i \(-0.653462\pi\)
−0.463654 + 0.886016i \(0.653462\pi\)
\(8\) −2862.26 −0.247061
\(9\) 6561.00 0.333333
\(10\) 32051.7 1.01356
\(11\) 26388.8 0.543442 0.271721 0.962376i \(-0.412407\pi\)
0.271721 + 0.962376i \(0.412407\pi\)
\(12\) 33870.2 0.471522
\(13\) −71180.0 −0.691215 −0.345607 0.938379i \(-0.612327\pi\)
−0.345607 + 0.938379i \(0.612327\pi\)
\(14\) −179656. −1.24987
\(15\) 85125.4 0.434159
\(16\) −301387. −1.14970
\(17\) −660629. −1.91839 −0.959196 0.282742i \(-0.908756\pi\)
−0.959196 + 0.282742i \(0.908756\pi\)
\(18\) 200100. 0.449283
\(19\) −713962. −1.25685 −0.628425 0.777870i \(-0.716300\pi\)
−0.628425 + 0.777870i \(0.716300\pi\)
\(20\) 439447. 0.614146
\(21\) −477145. −0.535381
\(22\) 804816. 0.732478
\(23\) 1.72289e6 1.28376 0.641878 0.766806i \(-0.278155\pi\)
0.641878 + 0.766806i \(0.278155\pi\)
\(24\) −231843. −0.142641
\(25\) −848670. −0.434519
\(26\) −2.17087e6 −0.931654
\(27\) 531441. 0.192450
\(28\) −2.46319e6 −0.757332
\(29\) −882627. −0.231732 −0.115866 0.993265i \(-0.536964\pi\)
−0.115866 + 0.993265i \(0.536964\pi\)
\(30\) 2.59619e6 0.585181
\(31\) 8.02994e6 1.56165 0.780827 0.624748i \(-0.214798\pi\)
0.780827 + 0.624748i \(0.214798\pi\)
\(32\) −7.72634e6 −1.30256
\(33\) 2.13749e6 0.313756
\(34\) −2.01481e7 −2.58570
\(35\) −6.19069e6 −0.697321
\(36\) 2.74348e6 0.272233
\(37\) −1.38423e7 −1.21423 −0.607113 0.794615i \(-0.707673\pi\)
−0.607113 + 0.794615i \(0.707673\pi\)
\(38\) −2.17747e7 −1.69405
\(39\) −5.76558e6 −0.399073
\(40\) −3.00804e6 −0.185786
\(41\) −1.60785e7 −0.888623 −0.444311 0.895872i \(-0.646552\pi\)
−0.444311 + 0.895872i \(0.646552\pi\)
\(42\) −1.45521e7 −0.721614
\(43\) −1.63480e7 −0.729216 −0.364608 0.931161i \(-0.618797\pi\)
−0.364608 + 0.931161i \(0.618797\pi\)
\(44\) 1.10345e7 0.443829
\(45\) 6.89516e6 0.250662
\(46\) 5.25454e7 1.73031
\(47\) 4.25996e7 1.27340 0.636701 0.771111i \(-0.280299\pi\)
0.636701 + 0.771111i \(0.280299\pi\)
\(48\) −2.44124e7 −0.663780
\(49\) −5.65355e6 −0.140100
\(50\) −2.58830e7 −0.585666
\(51\) −5.35109e7 −1.10758
\(52\) −2.97639e7 −0.564515
\(53\) 5.47396e6 0.0952928 0.0476464 0.998864i \(-0.484828\pi\)
0.0476464 + 0.998864i \(0.484828\pi\)
\(54\) 1.62081e7 0.259394
\(55\) 2.77328e7 0.408660
\(56\) 1.68607e7 0.229102
\(57\) −5.78309e7 −0.725643
\(58\) −2.69187e7 −0.312340
\(59\) 1.21174e7 0.130189
\(60\) 3.55952e7 0.354577
\(61\) −1.55390e8 −1.43694 −0.718471 0.695557i \(-0.755158\pi\)
−0.718471 + 0.695557i \(0.755158\pi\)
\(62\) 2.44900e8 2.10487
\(63\) −3.86487e7 −0.309103
\(64\) −8.13305e7 −0.605959
\(65\) −7.48053e7 −0.519783
\(66\) 6.51901e7 0.422896
\(67\) 1.19205e8 0.722702 0.361351 0.932430i \(-0.382316\pi\)
0.361351 + 0.932430i \(0.382316\pi\)
\(68\) −2.76242e8 −1.56675
\(69\) 1.39554e8 0.741177
\(70\) −1.88806e8 −0.939885
\(71\) 5.29891e7 0.247471 0.123736 0.992315i \(-0.460513\pi\)
0.123736 + 0.992315i \(0.460513\pi\)
\(72\) −1.87793e7 −0.0823537
\(73\) −1.44959e8 −0.597437 −0.298719 0.954341i \(-0.596559\pi\)
−0.298719 + 0.954341i \(0.596559\pi\)
\(74\) −4.22167e8 −1.63660
\(75\) −6.87422e7 −0.250870
\(76\) −2.98543e8 −1.02647
\(77\) −1.55448e8 −0.503938
\(78\) −1.75841e8 −0.537891
\(79\) 3.12409e8 0.902406 0.451203 0.892421i \(-0.350995\pi\)
0.451203 + 0.892421i \(0.350995\pi\)
\(80\) −3.16737e8 −0.864558
\(81\) 4.30467e7 0.111111
\(82\) −4.90367e8 −1.19773
\(83\) 5.07060e7 0.117276 0.0586379 0.998279i \(-0.481324\pi\)
0.0586379 + 0.998279i \(0.481324\pi\)
\(84\) −1.99518e8 −0.437246
\(85\) −6.94275e8 −1.44260
\(86\) −4.98587e8 −0.982874
\(87\) −7.14928e7 −0.133791
\(88\) −7.55317e7 −0.134263
\(89\) 6.65499e8 1.12433 0.562163 0.827026i \(-0.309969\pi\)
0.562163 + 0.827026i \(0.309969\pi\)
\(90\) 2.10291e8 0.337854
\(91\) 4.19298e8 0.640969
\(92\) 7.20428e8 1.04844
\(93\) 6.50425e8 0.901621
\(94\) 1.29922e9 1.71635
\(95\) −7.50324e8 −0.945132
\(96\) −6.25834e8 −0.752036
\(97\) −1.11643e9 −1.28044 −0.640221 0.768191i \(-0.721157\pi\)
−0.640221 + 0.768191i \(0.721157\pi\)
\(98\) −1.72424e8 −0.188834
\(99\) 1.73137e8 0.181147
\(100\) −3.54872e8 −0.354872
\(101\) −7.41591e8 −0.709118 −0.354559 0.935034i \(-0.615369\pi\)
−0.354559 + 0.935034i \(0.615369\pi\)
\(102\) −1.63200e9 −1.49286
\(103\) 1.65068e7 0.0144509 0.00722547 0.999974i \(-0.497700\pi\)
0.00722547 + 0.999974i \(0.497700\pi\)
\(104\) 2.03736e8 0.170772
\(105\) −5.01446e8 −0.402599
\(106\) 1.66947e8 0.128440
\(107\) 2.51369e9 1.85389 0.926945 0.375197i \(-0.122425\pi\)
0.926945 + 0.375197i \(0.122425\pi\)
\(108\) 2.22222e8 0.157174
\(109\) −1.57567e9 −1.06917 −0.534583 0.845116i \(-0.679531\pi\)
−0.534583 + 0.845116i \(0.679531\pi\)
\(110\) 8.45806e8 0.550812
\(111\) −1.12122e9 −0.701034
\(112\) 1.77537e9 1.06613
\(113\) −4.34260e8 −0.250551 −0.125276 0.992122i \(-0.539982\pi\)
−0.125276 + 0.992122i \(0.539982\pi\)
\(114\) −1.76375e9 −0.978058
\(115\) 1.81064e9 0.965366
\(116\) −3.69071e8 −0.189256
\(117\) −4.67012e8 −0.230405
\(118\) 3.69560e8 0.175475
\(119\) 3.89155e9 1.77894
\(120\) −2.43651e8 −0.107264
\(121\) −1.66158e9 −0.704671
\(122\) −4.73915e9 −1.93678
\(123\) −1.30236e9 −0.513046
\(124\) 3.35772e9 1.27540
\(125\) −2.94449e9 −1.07874
\(126\) −1.17872e9 −0.416624
\(127\) −2.00644e9 −0.684400 −0.342200 0.939627i \(-0.611172\pi\)
−0.342200 + 0.939627i \(0.611172\pi\)
\(128\) 1.47544e9 0.485821
\(129\) −1.32419e9 −0.421013
\(130\) −2.28144e9 −0.700590
\(131\) −5.58693e9 −1.65750 −0.828748 0.559621i \(-0.810947\pi\)
−0.828748 + 0.559621i \(0.810947\pi\)
\(132\) 8.93794e8 0.256245
\(133\) 4.20572e9 1.16549
\(134\) 3.63557e9 0.974094
\(135\) 5.58508e8 0.144720
\(136\) 1.89089e9 0.473960
\(137\) 1.77995e9 0.431683 0.215841 0.976428i \(-0.430751\pi\)
0.215841 + 0.976428i \(0.430751\pi\)
\(138\) 4.25618e9 0.998996
\(139\) −3.20102e9 −0.727313 −0.363656 0.931533i \(-0.618472\pi\)
−0.363656 + 0.931533i \(0.618472\pi\)
\(140\) −2.58864e9 −0.569502
\(141\) 3.45057e9 0.735199
\(142\) 1.61608e9 0.333554
\(143\) −1.87836e9 −0.375635
\(144\) −1.97740e9 −0.383234
\(145\) −9.27580e8 −0.174259
\(146\) −4.42101e9 −0.805256
\(147\) −4.57938e8 −0.0808870
\(148\) −5.78815e9 −0.991659
\(149\) 2.75929e8 0.0458626 0.0229313 0.999737i \(-0.492700\pi\)
0.0229313 + 0.999737i \(0.492700\pi\)
\(150\) −2.09653e9 −0.338135
\(151\) 2.26643e9 0.354770 0.177385 0.984142i \(-0.443236\pi\)
0.177385 + 0.984142i \(0.443236\pi\)
\(152\) 2.04354e9 0.310519
\(153\) −4.33439e9 −0.639464
\(154\) −4.74091e9 −0.679232
\(155\) 8.43891e9 1.17434
\(156\) −2.41088e9 −0.325923
\(157\) 5.86242e9 0.770067 0.385033 0.922903i \(-0.374190\pi\)
0.385033 + 0.922903i \(0.374190\pi\)
\(158\) 9.52798e9 1.21631
\(159\) 4.43391e8 0.0550173
\(160\) −8.11985e9 −0.979508
\(161\) −1.01490e10 −1.19044
\(162\) 1.31285e9 0.149761
\(163\) −4.17928e8 −0.0463722 −0.0231861 0.999731i \(-0.507381\pi\)
−0.0231861 + 0.999731i \(0.507381\pi\)
\(164\) −6.72322e9 −0.725738
\(165\) 2.24636e9 0.235940
\(166\) 1.54645e9 0.158070
\(167\) 9.44876e9 0.940049 0.470025 0.882653i \(-0.344245\pi\)
0.470025 + 0.882653i \(0.344245\pi\)
\(168\) 1.36571e9 0.132272
\(169\) −5.53790e9 −0.522222
\(170\) −2.11743e10 −1.94441
\(171\) −4.68430e9 −0.418950
\(172\) −6.83592e9 −0.595551
\(173\) 1.95277e10 1.65746 0.828732 0.559645i \(-0.189063\pi\)
0.828732 + 0.559645i \(0.189063\pi\)
\(174\) −2.18041e9 −0.180330
\(175\) 4.99924e9 0.402933
\(176\) −7.95325e9 −0.624795
\(177\) 9.81506e8 0.0751646
\(178\) 2.02966e10 1.51542
\(179\) 1.59226e10 1.15924 0.579621 0.814886i \(-0.303201\pi\)
0.579621 + 0.814886i \(0.303201\pi\)
\(180\) 2.88321e9 0.204715
\(181\) −1.76554e10 −1.22271 −0.611357 0.791355i \(-0.709376\pi\)
−0.611357 + 0.791355i \(0.709376\pi\)
\(182\) 1.27879e10 0.863930
\(183\) −1.25866e10 −0.829619
\(184\) −4.93137e9 −0.317166
\(185\) −1.45473e10 −0.913080
\(186\) 1.98369e10 1.21525
\(187\) −1.74332e10 −1.04253
\(188\) 1.78130e10 1.03999
\(189\) −3.13055e9 −0.178460
\(190\) −2.28837e10 −1.27390
\(191\) 1.53998e10 0.837271 0.418635 0.908154i \(-0.362509\pi\)
0.418635 + 0.908154i \(0.362509\pi\)
\(192\) −6.58777e9 −0.349851
\(193\) −2.04849e10 −1.06274 −0.531368 0.847141i \(-0.678322\pi\)
−0.531368 + 0.847141i \(0.678322\pi\)
\(194\) −3.40494e10 −1.72584
\(195\) −6.05923e9 −0.300097
\(196\) −2.36404e9 −0.114420
\(197\) 3.47341e10 1.64308 0.821539 0.570152i \(-0.193116\pi\)
0.821539 + 0.570152i \(0.193116\pi\)
\(198\) 5.28040e9 0.244159
\(199\) −3.86058e10 −1.74507 −0.872536 0.488549i \(-0.837526\pi\)
−0.872536 + 0.488549i \(0.837526\pi\)
\(200\) 2.42911e9 0.107353
\(201\) 9.65564e9 0.417252
\(202\) −2.26173e10 −0.955785
\(203\) 5.19927e9 0.214887
\(204\) −2.23756e10 −0.904564
\(205\) −1.68974e10 −0.668231
\(206\) 5.03431e8 0.0194777
\(207\) 1.13039e10 0.427919
\(208\) 2.14528e10 0.794690
\(209\) −1.88406e10 −0.683025
\(210\) −1.52933e10 −0.542643
\(211\) −4.41749e10 −1.53428 −0.767139 0.641480i \(-0.778321\pi\)
−0.767139 + 0.641480i \(0.778321\pi\)
\(212\) 2.28894e9 0.0778256
\(213\) 4.29212e9 0.142877
\(214\) 7.66633e10 2.49877
\(215\) −1.71806e10 −0.548359
\(216\) −1.52112e9 −0.0475469
\(217\) −4.73018e10 −1.44813
\(218\) −4.80552e10 −1.44107
\(219\) −1.17417e10 −0.344930
\(220\) 1.15965e10 0.333752
\(221\) 4.70236e10 1.32602
\(222\) −3.41955e10 −0.944889
\(223\) 6.94229e9 0.187988 0.0939942 0.995573i \(-0.470036\pi\)
0.0939942 + 0.995573i \(0.470036\pi\)
\(224\) 4.55134e10 1.20788
\(225\) −5.56812e9 −0.144840
\(226\) −1.32442e10 −0.337706
\(227\) −8.88310e9 −0.222049 −0.111024 0.993818i \(-0.535413\pi\)
−0.111024 + 0.993818i \(0.535413\pi\)
\(228\) −2.41820e10 −0.592632
\(229\) 3.07383e10 0.738619 0.369310 0.929306i \(-0.379594\pi\)
0.369310 + 0.929306i \(0.379594\pi\)
\(230\) 5.52216e10 1.30117
\(231\) −1.25913e10 −0.290948
\(232\) 2.52631e9 0.0572520
\(233\) 2.08242e10 0.462879 0.231440 0.972849i \(-0.425656\pi\)
0.231440 + 0.972849i \(0.425656\pi\)
\(234\) −1.42431e10 −0.310551
\(235\) 4.47692e10 0.957578
\(236\) 5.06688e9 0.106325
\(237\) 2.53052e10 0.521005
\(238\) 1.18686e11 2.39774
\(239\) 8.52149e10 1.68937 0.844686 0.535263i \(-0.179787\pi\)
0.844686 + 0.535263i \(0.179787\pi\)
\(240\) −2.56557e10 −0.499153
\(241\) −8.04735e9 −0.153665 −0.0768327 0.997044i \(-0.524481\pi\)
−0.0768327 + 0.997044i \(0.524481\pi\)
\(242\) −5.06754e10 −0.949791
\(243\) 3.48678e9 0.0641500
\(244\) −6.49765e10 −1.17355
\(245\) −5.94149e9 −0.105353
\(246\) −3.97197e10 −0.691510
\(247\) 5.08198e10 0.868754
\(248\) −2.29838e10 −0.385824
\(249\) 4.10719e9 0.0677092
\(250\) −8.98022e10 −1.45397
\(251\) 6.99285e10 1.11205 0.556023 0.831167i \(-0.312327\pi\)
0.556023 + 0.831167i \(0.312327\pi\)
\(252\) −1.61610e10 −0.252444
\(253\) 4.54651e10 0.697647
\(254\) −6.11932e10 −0.922468
\(255\) −5.62363e10 −0.832886
\(256\) 8.66397e10 1.26077
\(257\) 5.86319e10 0.838369 0.419184 0.907901i \(-0.362316\pi\)
0.419184 + 0.907901i \(0.362316\pi\)
\(258\) −4.03855e10 −0.567463
\(259\) 8.15403e10 1.12596
\(260\) −3.12798e10 −0.424507
\(261\) −5.79092e9 −0.0772441
\(262\) −1.70392e11 −2.23406
\(263\) −8.46098e10 −1.09048 −0.545242 0.838278i \(-0.683562\pi\)
−0.545242 + 0.838278i \(0.683562\pi\)
\(264\) −6.11807e9 −0.0775169
\(265\) 5.75275e9 0.0716587
\(266\) 1.28267e11 1.57090
\(267\) 5.39054e10 0.649130
\(268\) 4.98458e10 0.590231
\(269\) 1.49829e11 1.74466 0.872329 0.488919i \(-0.162609\pi\)
0.872329 + 0.488919i \(0.162609\pi\)
\(270\) 1.70336e10 0.195060
\(271\) −5.86333e10 −0.660362 −0.330181 0.943918i \(-0.607110\pi\)
−0.330181 + 0.943918i \(0.607110\pi\)
\(272\) 1.99105e11 2.20558
\(273\) 3.39632e10 0.370064
\(274\) 5.42855e10 0.581844
\(275\) −2.23954e10 −0.236136
\(276\) 5.83547e10 0.605319
\(277\) 1.55859e11 1.59064 0.795321 0.606189i \(-0.207303\pi\)
0.795321 + 0.606189i \(0.207303\pi\)
\(278\) −9.76258e10 −0.980309
\(279\) 5.26844e10 0.520551
\(280\) 1.77194e10 0.172281
\(281\) −9.66239e9 −0.0924499 −0.0462249 0.998931i \(-0.514719\pi\)
−0.0462249 + 0.998931i \(0.514719\pi\)
\(282\) 1.05237e11 0.990938
\(283\) −6.44213e10 −0.597023 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(284\) 2.21574e10 0.202110
\(285\) −6.07762e10 −0.545672
\(286\) −5.72868e10 −0.506299
\(287\) 9.47130e10 0.824027
\(288\) −5.06925e10 −0.434188
\(289\) 3.17843e11 2.68023
\(290\) −2.82897e10 −0.234875
\(291\) −9.04310e10 −0.739263
\(292\) −6.06146e10 −0.487927
\(293\) −6.96073e10 −0.551760 −0.275880 0.961192i \(-0.588969\pi\)
−0.275880 + 0.961192i \(0.588969\pi\)
\(294\) −1.39664e10 −0.109024
\(295\) 1.27345e10 0.0979001
\(296\) 3.96202e10 0.299988
\(297\) 1.40241e10 0.104585
\(298\) 8.41538e9 0.0618159
\(299\) −1.22635e11 −0.887352
\(300\) −2.87446e10 −0.204885
\(301\) 9.63007e10 0.676208
\(302\) 6.91225e10 0.478177
\(303\) −6.00689e10 −0.409409
\(304\) 2.15179e11 1.44500
\(305\) −1.63304e11 −1.08056
\(306\) −1.32192e11 −0.861902
\(307\) 1.21751e11 0.782255 0.391128 0.920336i \(-0.372085\pi\)
0.391128 + 0.920336i \(0.372085\pi\)
\(308\) −6.50006e10 −0.411566
\(309\) 1.33705e9 0.00834326
\(310\) 2.57373e11 1.58283
\(311\) −1.26038e11 −0.763979 −0.381989 0.924167i \(-0.624761\pi\)
−0.381989 + 0.924167i \(0.624761\pi\)
\(312\) 1.65026e10 0.0985954
\(313\) −5.96233e10 −0.351129 −0.175564 0.984468i \(-0.556175\pi\)
−0.175564 + 0.984468i \(0.556175\pi\)
\(314\) 1.78794e11 1.03793
\(315\) −4.06171e10 −0.232440
\(316\) 1.30634e11 0.736995
\(317\) 1.37551e11 0.765064 0.382532 0.923942i \(-0.375052\pi\)
0.382532 + 0.923942i \(0.375052\pi\)
\(318\) 1.35227e10 0.0741551
\(319\) −2.32915e10 −0.125933
\(320\) −8.54727e10 −0.455672
\(321\) 2.03609e11 1.07034
\(322\) −3.09528e11 −1.60453
\(323\) 4.71664e11 2.41113
\(324\) 1.80000e10 0.0907444
\(325\) 6.04083e10 0.300346
\(326\) −1.27461e10 −0.0625027
\(327\) −1.27629e11 −0.617283
\(328\) 4.60208e10 0.219544
\(329\) −2.50940e11 −1.18083
\(330\) 6.85103e10 0.318012
\(331\) −3.56768e11 −1.63365 −0.816827 0.576882i \(-0.804269\pi\)
−0.816827 + 0.576882i \(0.804269\pi\)
\(332\) 2.12027e10 0.0957791
\(333\) −9.08192e10 −0.404742
\(334\) 2.88172e11 1.26705
\(335\) 1.25277e11 0.543461
\(336\) 1.43805e11 0.615529
\(337\) −3.33498e10 −0.140851 −0.0704253 0.997517i \(-0.522436\pi\)
−0.0704253 + 0.997517i \(0.522436\pi\)
\(338\) −1.68897e11 −0.703877
\(339\) −3.51750e10 −0.144656
\(340\) −2.90311e11 −1.17817
\(341\) 2.11901e11 0.848667
\(342\) −1.42864e11 −0.564682
\(343\) 2.71013e11 1.05722
\(344\) 4.67922e10 0.180161
\(345\) 1.46662e11 0.557354
\(346\) 5.95564e11 2.23401
\(347\) −4.01239e11 −1.48567 −0.742833 0.669477i \(-0.766518\pi\)
−0.742833 + 0.669477i \(0.766518\pi\)
\(348\) −2.98947e10 −0.109267
\(349\) 4.22628e11 1.52491 0.762455 0.647042i \(-0.223994\pi\)
0.762455 + 0.647042i \(0.223994\pi\)
\(350\) 1.52469e11 0.543093
\(351\) −3.78280e10 −0.133024
\(352\) −2.03889e11 −0.707867
\(353\) −5.37777e11 −1.84338 −0.921692 0.387923i \(-0.873193\pi\)
−0.921692 + 0.387923i \(0.873193\pi\)
\(354\) 2.99343e10 0.101311
\(355\) 5.56879e10 0.186094
\(356\) 2.78279e11 0.918237
\(357\) 3.15216e11 1.02707
\(358\) 4.85612e11 1.56248
\(359\) −2.09495e11 −0.665654 −0.332827 0.942988i \(-0.608003\pi\)
−0.332827 + 0.942988i \(0.608003\pi\)
\(360\) −1.97357e10 −0.0619287
\(361\) 1.87053e11 0.579673
\(362\) −5.38462e11 −1.64803
\(363\) −1.34588e11 −0.406842
\(364\) 1.75330e11 0.523479
\(365\) −1.52342e11 −0.449264
\(366\) −3.83871e11 −1.11820
\(367\) −1.37201e11 −0.394783 −0.197392 0.980325i \(-0.563247\pi\)
−0.197392 + 0.980325i \(0.563247\pi\)
\(368\) −5.19258e11 −1.47594
\(369\) −1.05491e11 −0.296208
\(370\) −4.43668e11 −1.23069
\(371\) −3.22453e10 −0.0883657
\(372\) 2.71975e11 0.736354
\(373\) 3.50710e11 0.938119 0.469060 0.883166i \(-0.344593\pi\)
0.469060 + 0.883166i \(0.344593\pi\)
\(374\) −5.31684e11 −1.40518
\(375\) −2.38504e11 −0.622809
\(376\) −1.21931e11 −0.314608
\(377\) 6.28254e10 0.160177
\(378\) −9.54765e10 −0.240538
\(379\) −3.57636e11 −0.890358 −0.445179 0.895442i \(-0.646860\pi\)
−0.445179 + 0.895442i \(0.646860\pi\)
\(380\) −3.13748e11 −0.771890
\(381\) −1.62522e11 −0.395138
\(382\) 4.69670e11 1.12852
\(383\) 1.83871e10 0.0436635 0.0218318 0.999762i \(-0.493050\pi\)
0.0218318 + 0.999762i \(0.493050\pi\)
\(384\) 1.19511e11 0.280489
\(385\) −1.63365e11 −0.378953
\(386\) −6.24755e11 −1.43241
\(387\) −1.07259e11 −0.243072
\(388\) −4.66837e11 −1.04574
\(389\) −5.36462e11 −1.18786 −0.593931 0.804516i \(-0.702425\pi\)
−0.593931 + 0.804516i \(0.702425\pi\)
\(390\) −1.84797e11 −0.404486
\(391\) −1.13819e12 −2.46275
\(392\) 1.61819e10 0.0346133
\(393\) −4.52542e11 −0.956956
\(394\) 1.05933e12 2.21462
\(395\) 3.28321e11 0.678596
\(396\) 7.23973e10 0.147943
\(397\) 1.88055e11 0.379951 0.189976 0.981789i \(-0.439159\pi\)
0.189976 + 0.981789i \(0.439159\pi\)
\(398\) −1.17741e12 −2.35210
\(399\) 3.40663e11 0.672894
\(400\) 2.55778e11 0.499567
\(401\) 2.08200e11 0.402097 0.201048 0.979581i \(-0.435565\pi\)
0.201048 + 0.979581i \(0.435565\pi\)
\(402\) 2.94481e11 0.562394
\(403\) −5.71571e11 −1.07944
\(404\) −3.10097e11 −0.579137
\(405\) 4.52391e10 0.0835539
\(406\) 1.58569e11 0.289636
\(407\) −3.65281e11 −0.659861
\(408\) 1.53162e11 0.273641
\(409\) −9.77641e10 −0.172753 −0.0863763 0.996263i \(-0.527529\pi\)
−0.0863763 + 0.996263i \(0.527529\pi\)
\(410\) −5.15342e11 −0.900675
\(411\) 1.44176e11 0.249232
\(412\) 6.90234e9 0.0118021
\(413\) −7.13794e10 −0.120725
\(414\) 3.44750e11 0.576771
\(415\) 5.32885e10 0.0881896
\(416\) 5.49961e11 0.900351
\(417\) −2.59282e11 −0.419914
\(418\) −5.74608e11 −0.920615
\(419\) −6.06783e11 −0.961767 −0.480884 0.876784i \(-0.659684\pi\)
−0.480884 + 0.876784i \(0.659684\pi\)
\(420\) −2.09680e11 −0.328802
\(421\) 9.96114e11 1.54540 0.772698 0.634774i \(-0.218907\pi\)
0.772698 + 0.634774i \(0.218907\pi\)
\(422\) −1.34726e12 −2.06798
\(423\) 2.79496e11 0.424467
\(424\) −1.56679e10 −0.0235431
\(425\) 5.60656e11 0.833578
\(426\) 1.30903e11 0.192577
\(427\) 9.15353e11 1.33249
\(428\) 1.05110e12 1.51407
\(429\) −1.52147e11 −0.216873
\(430\) −5.23980e11 −0.739106
\(431\) 9.84981e11 1.37493 0.687465 0.726218i \(-0.258724\pi\)
0.687465 + 0.726218i \(0.258724\pi\)
\(432\) −1.60170e11 −0.221260
\(433\) −5.50407e11 −0.752468 −0.376234 0.926525i \(-0.622781\pi\)
−0.376234 + 0.926525i \(0.622781\pi\)
\(434\) −1.44263e12 −1.95187
\(435\) −7.51340e10 −0.100609
\(436\) −6.58865e11 −0.873187
\(437\) −1.23008e12 −1.61349
\(438\) −3.58102e11 −0.464915
\(439\) −4.59045e10 −0.0589882 −0.0294941 0.999565i \(-0.509390\pi\)
−0.0294941 + 0.999565i \(0.509390\pi\)
\(440\) −7.93786e10 −0.100964
\(441\) −3.70930e10 −0.0467001
\(442\) 1.43414e12 1.78728
\(443\) −6.41010e11 −0.790766 −0.395383 0.918516i \(-0.629388\pi\)
−0.395383 + 0.918516i \(0.629388\pi\)
\(444\) −4.68840e11 −0.572534
\(445\) 6.99393e11 0.845476
\(446\) 2.11729e11 0.253380
\(447\) 2.23502e10 0.0264788
\(448\) 4.79092e11 0.561911
\(449\) −1.04339e11 −0.121154 −0.0605771 0.998164i \(-0.519294\pi\)
−0.0605771 + 0.998164i \(0.519294\pi\)
\(450\) −1.69819e11 −0.195222
\(451\) −4.24292e11 −0.482914
\(452\) −1.81586e11 −0.204625
\(453\) 1.83581e11 0.204827
\(454\) −2.70920e11 −0.299288
\(455\) 4.40654e11 0.481999
\(456\) 1.65527e11 0.179278
\(457\) −9.29917e11 −0.997289 −0.498645 0.866807i \(-0.666169\pi\)
−0.498645 + 0.866807i \(0.666169\pi\)
\(458\) 9.37469e11 0.995548
\(459\) −3.51085e11 −0.369195
\(460\) 7.57120e11 0.788414
\(461\) −1.57666e12 −1.62586 −0.812931 0.582361i \(-0.802129\pi\)
−0.812931 + 0.582361i \(0.802129\pi\)
\(462\) −3.84014e11 −0.392155
\(463\) −1.49875e12 −1.51571 −0.757853 0.652426i \(-0.773751\pi\)
−0.757853 + 0.652426i \(0.773751\pi\)
\(464\) 2.66013e11 0.266423
\(465\) 6.83552e11 0.678005
\(466\) 6.35106e11 0.623892
\(467\) −1.06084e12 −1.03210 −0.516050 0.856558i \(-0.672598\pi\)
−0.516050 + 0.856558i \(0.672598\pi\)
\(468\) −1.95281e11 −0.188172
\(469\) −7.02201e11 −0.670168
\(470\) 1.36539e12 1.29067
\(471\) 4.74856e11 0.444598
\(472\) −3.46831e10 −0.0321646
\(473\) −4.31404e11 −0.396286
\(474\) 7.71766e11 0.702236
\(475\) 6.05918e11 0.546125
\(476\) 1.62725e12 1.45286
\(477\) 3.59146e10 0.0317643
\(478\) 2.59892e12 2.27702
\(479\) 1.62236e12 1.40811 0.704056 0.710144i \(-0.251370\pi\)
0.704056 + 0.710144i \(0.251370\pi\)
\(480\) −6.57708e11 −0.565519
\(481\) 9.85293e11 0.839291
\(482\) −2.45431e11 −0.207118
\(483\) −8.22069e11 −0.687300
\(484\) −6.94789e11 −0.575505
\(485\) −1.17329e12 −0.962872
\(486\) 1.06341e11 0.0864646
\(487\) 9.85769e11 0.794136 0.397068 0.917789i \(-0.370028\pi\)
0.397068 + 0.917789i \(0.370028\pi\)
\(488\) 4.44767e11 0.355013
\(489\) −3.38522e10 −0.0267730
\(490\) −1.81206e11 −0.142000
\(491\) 1.97389e12 1.53270 0.766348 0.642425i \(-0.222072\pi\)
0.766348 + 0.642425i \(0.222072\pi\)
\(492\) −5.44581e11 −0.419005
\(493\) 5.83089e11 0.444553
\(494\) 1.54992e12 1.17095
\(495\) 1.81955e11 0.136220
\(496\) −2.42012e12 −1.79543
\(497\) −3.12142e11 −0.229482
\(498\) 1.25263e11 0.0912618
\(499\) −9.09868e11 −0.656941 −0.328470 0.944514i \(-0.606533\pi\)
−0.328470 + 0.944514i \(0.606533\pi\)
\(500\) −1.23124e12 −0.881004
\(501\) 7.65349e11 0.542738
\(502\) 2.13271e12 1.49887
\(503\) 3.29409e11 0.229446 0.114723 0.993398i \(-0.463402\pi\)
0.114723 + 0.993398i \(0.463402\pi\)
\(504\) 1.10623e11 0.0763672
\(505\) −7.79361e11 −0.533246
\(506\) 1.38661e12 0.940323
\(507\) −4.48570e11 −0.301505
\(508\) −8.38995e11 −0.558949
\(509\) −1.73073e12 −1.14288 −0.571440 0.820644i \(-0.693615\pi\)
−0.571440 + 0.820644i \(0.693615\pi\)
\(510\) −1.71511e12 −1.12261
\(511\) 8.53906e11 0.554008
\(512\) 1.88694e12 1.21351
\(513\) −3.79428e11 −0.241881
\(514\) 1.78818e12 1.13000
\(515\) 1.73475e10 0.0108669
\(516\) −5.53709e11 −0.343841
\(517\) 1.12415e12 0.692019
\(518\) 2.48685e12 1.51763
\(519\) 1.58175e12 0.956938
\(520\) 2.14112e11 0.128418
\(521\) −7.85423e11 −0.467018 −0.233509 0.972355i \(-0.575021\pi\)
−0.233509 + 0.972355i \(0.575021\pi\)
\(522\) −1.76614e11 −0.104113
\(523\) 1.11757e12 0.653155 0.326577 0.945170i \(-0.394105\pi\)
0.326577 + 0.945170i \(0.394105\pi\)
\(524\) −2.33618e12 −1.35368
\(525\) 4.04938e11 0.232633
\(526\) −2.58046e12 −1.46981
\(527\) −5.30481e12 −2.99586
\(528\) −6.44214e11 −0.360726
\(529\) 1.16720e12 0.648032
\(530\) 1.75449e11 0.0965852
\(531\) 7.95020e10 0.0433963
\(532\) 1.75862e12 0.951853
\(533\) 1.14447e12 0.614229
\(534\) 1.64403e12 0.874930
\(535\) 2.64171e12 1.39410
\(536\) −3.41197e11 −0.178552
\(537\) 1.28973e12 0.669289
\(538\) 4.56954e12 2.35154
\(539\) −1.49191e11 −0.0761363
\(540\) 2.33540e11 0.118192
\(541\) 2.85930e12 1.43507 0.717534 0.696523i \(-0.245271\pi\)
0.717534 + 0.696523i \(0.245271\pi\)
\(542\) −1.78822e12 −0.890070
\(543\) −1.43009e12 −0.705934
\(544\) 5.10424e12 2.49883
\(545\) −1.65592e12 −0.803996
\(546\) 1.03582e12 0.498790
\(547\) −1.85565e12 −0.886244 −0.443122 0.896461i \(-0.646129\pi\)
−0.443122 + 0.896461i \(0.646129\pi\)
\(548\) 7.44286e11 0.352555
\(549\) −1.01951e12 −0.478981
\(550\) −6.83023e11 −0.318275
\(551\) 6.30162e11 0.291253
\(552\) −3.99441e11 −0.183116
\(553\) −1.84030e12 −0.836809
\(554\) 4.75344e12 2.14395
\(555\) −1.17833e12 −0.527167
\(556\) −1.33851e12 −0.593996
\(557\) 7.86874e10 0.0346383 0.0173192 0.999850i \(-0.494487\pi\)
0.0173192 + 0.999850i \(0.494487\pi\)
\(558\) 1.60679e12 0.701625
\(559\) 1.16365e12 0.504045
\(560\) 1.86580e12 0.801711
\(561\) −1.41209e12 −0.601907
\(562\) −2.94687e11 −0.124609
\(563\) −1.24500e12 −0.522253 −0.261127 0.965305i \(-0.584094\pi\)
−0.261127 + 0.965305i \(0.584094\pi\)
\(564\) 1.44286e12 0.600437
\(565\) −4.56377e11 −0.188411
\(566\) −1.96475e12 −0.804697
\(567\) −2.53574e11 −0.103034
\(568\) −1.51669e11 −0.0611405
\(569\) 4.98949e11 0.199550 0.0997748 0.995010i \(-0.468188\pi\)
0.0997748 + 0.995010i \(0.468188\pi\)
\(570\) −1.85358e12 −0.735485
\(571\) −4.33571e12 −1.70686 −0.853430 0.521207i \(-0.825482\pi\)
−0.853430 + 0.521207i \(0.825482\pi\)
\(572\) −7.85435e11 −0.306781
\(573\) 1.24739e12 0.483398
\(574\) 2.88859e12 1.11066
\(575\) −1.46217e12 −0.557817
\(576\) −5.33609e11 −0.201986
\(577\) −2.90292e12 −1.09029 −0.545146 0.838341i \(-0.683526\pi\)
−0.545146 + 0.838341i \(0.683526\pi\)
\(578\) 9.69368e12 3.61255
\(579\) −1.65927e12 −0.613571
\(580\) −3.87868e11 −0.142317
\(581\) −2.98693e11 −0.108751
\(582\) −2.75800e12 −0.996416
\(583\) 1.44451e11 0.0517861
\(584\) 4.14910e11 0.147603
\(585\) −4.90797e11 −0.173261
\(586\) −2.12291e12 −0.743690
\(587\) −5.13323e11 −0.178451 −0.0892256 0.996011i \(-0.528439\pi\)
−0.0892256 + 0.996011i \(0.528439\pi\)
\(588\) −1.91487e11 −0.0660604
\(589\) −5.73307e12 −1.96276
\(590\) 3.88382e11 0.131955
\(591\) 2.81346e12 0.948632
\(592\) 4.17189e12 1.39600
\(593\) −3.36316e12 −1.11687 −0.558434 0.829549i \(-0.688598\pi\)
−0.558434 + 0.829549i \(0.688598\pi\)
\(594\) 4.27712e11 0.140965
\(595\) 4.08975e12 1.33774
\(596\) 1.15380e11 0.0374560
\(597\) −3.12707e12 −1.00752
\(598\) −3.74018e12 −1.19602
\(599\) −2.69284e12 −0.854654 −0.427327 0.904097i \(-0.640545\pi\)
−0.427327 + 0.904097i \(0.640545\pi\)
\(600\) 1.96758e11 0.0619801
\(601\) −2.40549e12 −0.752087 −0.376044 0.926602i \(-0.622716\pi\)
−0.376044 + 0.926602i \(0.622716\pi\)
\(602\) 2.93701e12 0.911427
\(603\) 7.82107e11 0.240901
\(604\) 9.47710e11 0.289741
\(605\) −1.74620e12 −0.529902
\(606\) −1.83200e12 −0.551823
\(607\) −5.07434e12 −1.51716 −0.758578 0.651582i \(-0.774106\pi\)
−0.758578 + 0.651582i \(0.774106\pi\)
\(608\) 5.51631e12 1.63713
\(609\) 4.21141e11 0.124065
\(610\) −4.98051e12 −1.45643
\(611\) −3.03224e12 −0.880194
\(612\) −1.81242e12 −0.522250
\(613\) −6.48764e12 −1.85573 −0.927865 0.372917i \(-0.878358\pi\)
−0.927865 + 0.372917i \(0.878358\pi\)
\(614\) 3.71320e12 1.05436
\(615\) −1.36869e12 −0.385803
\(616\) 4.44933e11 0.124503
\(617\) −3.61489e12 −1.00418 −0.502090 0.864815i \(-0.667435\pi\)
−0.502090 + 0.864815i \(0.667435\pi\)
\(618\) 4.07779e10 0.0112455
\(619\) 4.35188e12 1.19143 0.595715 0.803196i \(-0.296869\pi\)
0.595715 + 0.803196i \(0.296869\pi\)
\(620\) 3.52873e12 0.959083
\(621\) 9.15615e11 0.247059
\(622\) −3.84397e12 −1.02973
\(623\) −3.92024e12 −1.04260
\(624\) 1.73767e12 0.458815
\(625\) −1.43690e12 −0.376674
\(626\) −1.81841e12 −0.473269
\(627\) −1.52609e12 −0.394345
\(628\) 2.45137e12 0.628913
\(629\) 9.14461e12 2.32936
\(630\) −1.23876e12 −0.313295
\(631\) 4.90105e12 1.23071 0.615356 0.788249i \(-0.289012\pi\)
0.615356 + 0.788249i \(0.289012\pi\)
\(632\) −8.94197e11 −0.222950
\(633\) −3.57816e12 −0.885816
\(634\) 4.19509e12 1.03119
\(635\) −2.10863e12 −0.514658
\(636\) 1.85404e11 0.0449326
\(637\) 4.02420e11 0.0968394
\(638\) −7.10353e11 −0.169739
\(639\) 3.47662e11 0.0824903
\(640\) 1.55058e12 0.365330
\(641\) 3.31638e12 0.775895 0.387947 0.921681i \(-0.373184\pi\)
0.387947 + 0.921681i \(0.373184\pi\)
\(642\) 6.20973e12 1.44266
\(643\) 3.46709e12 0.799864 0.399932 0.916545i \(-0.369034\pi\)
0.399932 + 0.916545i \(0.369034\pi\)
\(644\) −4.24381e12 −0.972230
\(645\) −1.39163e12 −0.316595
\(646\) 1.43850e13 3.24984
\(647\) −4.53182e11 −0.101672 −0.0508362 0.998707i \(-0.516189\pi\)
−0.0508362 + 0.998707i \(0.516189\pi\)
\(648\) −1.23211e11 −0.0274512
\(649\) 3.19763e11 0.0707501
\(650\) 1.84236e12 0.404821
\(651\) −3.83144e12 −0.836080
\(652\) −1.74757e11 −0.0378721
\(653\) −6.66887e12 −1.43530 −0.717651 0.696403i \(-0.754783\pi\)
−0.717651 + 0.696403i \(0.754783\pi\)
\(654\) −3.89247e12 −0.832005
\(655\) −5.87148e12 −1.24641
\(656\) 4.84585e12 1.02165
\(657\) −9.51076e11 −0.199146
\(658\) −7.65327e12 −1.59159
\(659\) −1.64690e12 −0.340160 −0.170080 0.985430i \(-0.554403\pi\)
−0.170080 + 0.985430i \(0.554403\pi\)
\(660\) 9.39315e11 0.192692
\(661\) 3.47144e12 0.707298 0.353649 0.935378i \(-0.384941\pi\)
0.353649 + 0.935378i \(0.384941\pi\)
\(662\) −1.08808e13 −2.20192
\(663\) 3.80891e12 0.765578
\(664\) −1.45134e11 −0.0289743
\(665\) 4.41992e12 0.876429
\(666\) −2.76984e12 −0.545532
\(667\) −1.52067e12 −0.297488
\(668\) 3.95100e12 0.767738
\(669\) 5.62326e11 0.108535
\(670\) 3.82073e12 0.732504
\(671\) −4.10056e12 −0.780894
\(672\) 3.68658e12 0.697368
\(673\) −9.62726e12 −1.80898 −0.904492 0.426490i \(-0.859750\pi\)
−0.904492 + 0.426490i \(0.859750\pi\)
\(674\) −1.01711e12 −0.189846
\(675\) −4.51018e11 −0.0836232
\(676\) −2.31568e12 −0.426499
\(677\) 5.03997e12 0.922101 0.461051 0.887374i \(-0.347473\pi\)
0.461051 + 0.887374i \(0.347473\pi\)
\(678\) −1.07278e12 −0.194974
\(679\) 6.57654e12 1.18736
\(680\) 1.98720e12 0.356411
\(681\) −7.19531e11 −0.128200
\(682\) 6.46262e12 1.14388
\(683\) −2.29099e11 −0.0402837 −0.0201419 0.999797i \(-0.506412\pi\)
−0.0201419 + 0.999797i \(0.506412\pi\)
\(684\) −1.95874e12 −0.342157
\(685\) 1.87060e12 0.324619
\(686\) 8.26546e12 1.42498
\(687\) 2.48980e12 0.426442
\(688\) 4.92708e12 0.838381
\(689\) −3.89636e11 −0.0658678
\(690\) 4.47295e12 0.751230
\(691\) 3.62693e12 0.605184 0.302592 0.953120i \(-0.402148\pi\)
0.302592 + 0.953120i \(0.402148\pi\)
\(692\) 8.16553e12 1.35365
\(693\) −1.01989e12 −0.167979
\(694\) −1.22371e13 −2.00245
\(695\) −3.36405e12 −0.546928
\(696\) 2.04631e11 0.0330545
\(697\) 1.06219e13 1.70473
\(698\) 1.28895e13 2.05535
\(699\) 1.68676e12 0.267243
\(700\) 2.09043e12 0.329075
\(701\) −5.66301e12 −0.885760 −0.442880 0.896581i \(-0.646043\pi\)
−0.442880 + 0.896581i \(0.646043\pi\)
\(702\) −1.15369e12 −0.179297
\(703\) 9.88285e12 1.52610
\(704\) −2.14622e12 −0.329304
\(705\) 3.62631e12 0.552858
\(706\) −1.64013e13 −2.48460
\(707\) 4.36847e12 0.657571
\(708\) 4.10417e11 0.0613869
\(709\) −5.22597e12 −0.776710 −0.388355 0.921510i \(-0.626957\pi\)
−0.388355 + 0.921510i \(0.626957\pi\)
\(710\) 1.69839e12 0.250827
\(711\) 2.04972e12 0.300802
\(712\) −1.90483e12 −0.277777
\(713\) 1.38347e13 2.00478
\(714\) 9.61356e12 1.38434
\(715\) −1.97402e12 −0.282472
\(716\) 6.65802e12 0.946753
\(717\) 6.90241e12 0.975359
\(718\) −6.38925e12 −0.897202
\(719\) 1.17100e13 1.63409 0.817047 0.576571i \(-0.195610\pi\)
0.817047 + 0.576571i \(0.195610\pi\)
\(720\) −2.07811e12 −0.288186
\(721\) −9.72364e10 −0.0134005
\(722\) 5.70482e12 0.781312
\(723\) −6.51835e11 −0.0887187
\(724\) −7.38262e12 −0.998590
\(725\) 7.49059e11 0.100692
\(726\) −4.10471e12 −0.548362
\(727\) −1.35866e13 −1.80388 −0.901938 0.431866i \(-0.857855\pi\)
−0.901938 + 0.431866i \(0.857855\pi\)
\(728\) −1.20014e12 −0.158358
\(729\) 2.82430e11 0.0370370
\(730\) −4.64618e12 −0.605540
\(731\) 1.08000e13 1.39892
\(732\) −5.26309e12 −0.677550
\(733\) −1.02246e13 −1.30822 −0.654110 0.756400i \(-0.726956\pi\)
−0.654110 + 0.756400i \(0.726956\pi\)
\(734\) −4.18439e12 −0.532108
\(735\) −4.81261e11 −0.0608258
\(736\) −1.33117e13 −1.67218
\(737\) 3.14569e12 0.392747
\(738\) −3.21730e12 −0.399243
\(739\) −1.29123e13 −1.59259 −0.796293 0.604912i \(-0.793208\pi\)
−0.796293 + 0.604912i \(0.793208\pi\)
\(740\) −6.08295e12 −0.745712
\(741\) 4.11640e12 0.501575
\(742\) −9.83429e11 −0.119104
\(743\) −5.53690e11 −0.0666526 −0.0333263 0.999445i \(-0.510610\pi\)
−0.0333263 + 0.999445i \(0.510610\pi\)
\(744\) −1.86169e12 −0.222755
\(745\) 2.89982e11 0.0344880
\(746\) 1.06961e13 1.26444
\(747\) 3.32682e11 0.0390919
\(748\) −7.28970e12 −0.851437
\(749\) −1.48073e13 −1.71913
\(750\) −7.27398e12 −0.839453
\(751\) 1.51274e13 1.73534 0.867668 0.497145i \(-0.165618\pi\)
0.867668 + 0.497145i \(0.165618\pi\)
\(752\) −1.28390e13 −1.46403
\(753\) 5.66421e12 0.642040
\(754\) 1.91607e12 0.215894
\(755\) 2.38187e12 0.266782
\(756\) −1.30904e12 −0.145749
\(757\) −2.24958e12 −0.248983 −0.124492 0.992221i \(-0.539730\pi\)
−0.124492 + 0.992221i \(0.539730\pi\)
\(758\) −1.09073e13 −1.20007
\(759\) 3.68267e12 0.402787
\(760\) 2.14762e12 0.233505
\(761\) 7.95249e12 0.859552 0.429776 0.902936i \(-0.358593\pi\)
0.429776 + 0.902936i \(0.358593\pi\)
\(762\) −4.95665e12 −0.532587
\(763\) 9.28173e12 0.991445
\(764\) 6.43945e12 0.683799
\(765\) −4.55514e12 −0.480867
\(766\) 5.60777e11 0.0588519
\(767\) −8.62514e11 −0.0899885
\(768\) 7.01782e12 0.727908
\(769\) −6.25524e12 −0.645023 −0.322512 0.946565i \(-0.604527\pi\)
−0.322512 + 0.946565i \(0.604527\pi\)
\(770\) −4.98237e12 −0.510772
\(771\) 4.74918e12 0.484032
\(772\) −8.56576e12 −0.867936
\(773\) −1.29802e13 −1.30760 −0.653799 0.756668i \(-0.726826\pi\)
−0.653799 + 0.756668i \(0.726826\pi\)
\(774\) −3.27123e12 −0.327625
\(775\) −6.81477e12 −0.678568
\(776\) 3.19552e12 0.316347
\(777\) 6.60477e12 0.650074
\(778\) −1.63612e13 −1.60106
\(779\) 1.14794e13 1.11687
\(780\) −2.53367e12 −0.245089
\(781\) 1.39832e12 0.134486
\(782\) −3.47130e13 −3.31942
\(783\) −4.69064e11 −0.0445969
\(784\) 1.70391e12 0.161074
\(785\) 6.16100e12 0.579079
\(786\) −1.38018e13 −1.28983
\(787\) −3.91811e12 −0.364074 −0.182037 0.983292i \(-0.558269\pi\)
−0.182037 + 0.983292i \(0.558269\pi\)
\(788\) 1.45241e13 1.34190
\(789\) −6.85339e12 −0.629592
\(790\) 1.00132e13 0.914646
\(791\) 2.55808e12 0.232338
\(792\) −4.95563e11 −0.0447544
\(793\) 1.10607e13 0.993236
\(794\) 5.73538e12 0.512118
\(795\) 4.65973e11 0.0413722
\(796\) −1.61430e13 −1.42520
\(797\) −1.59762e13 −1.40253 −0.701265 0.712901i \(-0.747381\pi\)
−0.701265 + 0.712901i \(0.747381\pi\)
\(798\) 1.03897e13 0.906961
\(799\) −2.81425e13 −2.44288
\(800\) 6.55711e12 0.565989
\(801\) 4.36634e12 0.374775
\(802\) 6.34975e12 0.541966
\(803\) −3.82530e12 −0.324672
\(804\) 4.03751e12 0.340770
\(805\) −1.06659e13 −0.895191
\(806\) −1.74320e13 −1.45492
\(807\) 1.21361e13 1.00728
\(808\) 2.12263e12 0.175195
\(809\) −2.07097e13 −1.69983 −0.849916 0.526918i \(-0.823348\pi\)
−0.849916 + 0.526918i \(0.823348\pi\)
\(810\) 1.37972e12 0.112618
\(811\) 1.63462e13 1.32685 0.663426 0.748242i \(-0.269102\pi\)
0.663426 + 0.748242i \(0.269102\pi\)
\(812\) 2.17408e12 0.175498
\(813\) −4.74930e12 −0.381260
\(814\) −1.11405e13 −0.889394
\(815\) −4.39213e11 −0.0348712
\(816\) 1.61275e13 1.27339
\(817\) 1.16718e13 0.916516
\(818\) −2.98165e12 −0.232845
\(819\) 2.75102e12 0.213656
\(820\) −7.06564e12 −0.545744
\(821\) −7.95905e12 −0.611388 −0.305694 0.952130i \(-0.598888\pi\)
−0.305694 + 0.952130i \(0.598888\pi\)
\(822\) 4.39713e12 0.335928
\(823\) −7.99086e12 −0.607148 −0.303574 0.952808i \(-0.598180\pi\)
−0.303574 + 0.952808i \(0.598180\pi\)
\(824\) −4.72469e10 −0.00357027
\(825\) −1.81403e12 −0.136333
\(826\) −2.17696e12 −0.162719
\(827\) −1.49770e13 −1.11339 −0.556697 0.830715i \(-0.687932\pi\)
−0.556697 + 0.830715i \(0.687932\pi\)
\(828\) 4.72673e12 0.349481
\(829\) 1.45469e13 1.06973 0.534865 0.844937i \(-0.320362\pi\)
0.534865 + 0.844937i \(0.320362\pi\)
\(830\) 1.62521e12 0.118866
\(831\) 1.26246e13 0.918357
\(832\) 5.78911e12 0.418848
\(833\) 3.73490e12 0.268767
\(834\) −7.90769e12 −0.565981
\(835\) 9.92999e12 0.706903
\(836\) −7.87820e12 −0.557826
\(837\) 4.26744e12 0.300540
\(838\) −1.85059e13 −1.29632
\(839\) −1.37194e13 −0.955886 −0.477943 0.878391i \(-0.658617\pi\)
−0.477943 + 0.878391i \(0.658617\pi\)
\(840\) 1.43527e12 0.0994665
\(841\) −1.37281e13 −0.946300
\(842\) 3.03799e13 2.08296
\(843\) −7.82654e11 −0.0533760
\(844\) −1.84717e13 −1.25305
\(845\) −5.81995e12 −0.392703
\(846\) 8.52417e12 0.572118
\(847\) 9.78782e12 0.653447
\(848\) −1.64978e12 −0.109558
\(849\) −5.21813e12 −0.344691
\(850\) 1.70991e13 1.12354
\(851\) −2.38487e13 −1.55877
\(852\) 1.79475e12 0.116688
\(853\) 1.65135e13 1.06799 0.533997 0.845486i \(-0.320689\pi\)
0.533997 + 0.845486i \(0.320689\pi\)
\(854\) 2.79168e13 1.79599
\(855\) −4.92288e12 −0.315044
\(856\) −7.19483e12 −0.458024
\(857\) −1.96681e12 −0.124551 −0.0622756 0.998059i \(-0.519836\pi\)
−0.0622756 + 0.998059i \(0.519836\pi\)
\(858\) −4.64023e12 −0.292312
\(859\) 2.16110e13 1.35427 0.677136 0.735858i \(-0.263221\pi\)
0.677136 + 0.735858i \(0.263221\pi\)
\(860\) −7.18408e12 −0.447845
\(861\) 7.67176e12 0.475752
\(862\) 3.00403e13 1.85320
\(863\) −7.52982e12 −0.462100 −0.231050 0.972942i \(-0.574216\pi\)
−0.231050 + 0.972942i \(0.574216\pi\)
\(864\) −4.10609e12 −0.250679
\(865\) 2.05223e13 1.24639
\(866\) −1.67865e13 −1.01421
\(867\) 2.57452e13 1.54743
\(868\) −1.97792e13 −1.18269
\(869\) 8.24411e12 0.490405
\(870\) −2.29146e12 −0.135605
\(871\) −8.48505e12 −0.499543
\(872\) 4.50997e12 0.264149
\(873\) −7.32491e12 −0.426814
\(874\) −3.75154e13 −2.17474
\(875\) 1.73450e13 1.00032
\(876\) −4.90979e12 −0.281705
\(877\) 1.51055e13 0.862259 0.431129 0.902290i \(-0.358115\pi\)
0.431129 + 0.902290i \(0.358115\pi\)
\(878\) −1.40001e12 −0.0795073
\(879\) −5.63819e12 −0.318559
\(880\) −8.35832e12 −0.469837
\(881\) −2.32110e13 −1.29808 −0.649042 0.760752i \(-0.724830\pi\)
−0.649042 + 0.760752i \(0.724830\pi\)
\(882\) −1.13127e12 −0.0629447
\(883\) 1.44144e13 0.797947 0.398974 0.916962i \(-0.369367\pi\)
0.398974 + 0.916962i \(0.369367\pi\)
\(884\) 1.96629e13 1.08296
\(885\) 1.03150e12 0.0565226
\(886\) −1.95498e13 −1.06583
\(887\) 8.64043e12 0.468683 0.234341 0.972154i \(-0.424707\pi\)
0.234341 + 0.972154i \(0.424707\pi\)
\(888\) 3.20924e12 0.173198
\(889\) 1.18193e13 0.634649
\(890\) 2.13303e13 1.13957
\(891\) 1.13595e12 0.0603824
\(892\) 2.90292e12 0.153530
\(893\) −3.04145e13 −1.60048
\(894\) 6.81645e11 0.0356894
\(895\) 1.67335e13 0.871733
\(896\) −8.69133e12 −0.450506
\(897\) −9.93347e12 −0.512313
\(898\) −3.18217e12 −0.163298
\(899\) −7.08744e12 −0.361885
\(900\) −2.32831e12 −0.118291
\(901\) −3.61625e12 −0.182809
\(902\) −1.29402e13 −0.650896
\(903\) 7.80036e12 0.390409
\(904\) 1.24297e12 0.0619015
\(905\) −1.85546e13 −0.919462
\(906\) 5.59893e12 0.276075
\(907\) −2.82043e12 −0.138383 −0.0691915 0.997603i \(-0.522042\pi\)
−0.0691915 + 0.997603i \(0.522042\pi\)
\(908\) −3.71447e12 −0.181347
\(909\) −4.86558e12 −0.236373
\(910\) 1.34392e13 0.649662
\(911\) 1.47354e13 0.708807 0.354404 0.935093i \(-0.384684\pi\)
0.354404 + 0.935093i \(0.384684\pi\)
\(912\) 1.74295e13 0.834273
\(913\) 1.33807e12 0.0637325
\(914\) −2.83609e13 −1.34420
\(915\) −1.32276e13 −0.623861
\(916\) 1.28532e13 0.603230
\(917\) 3.29108e13 1.53701
\(918\) −1.07075e13 −0.497619
\(919\) −9.13825e12 −0.422613 −0.211307 0.977420i \(-0.567772\pi\)
−0.211307 + 0.977420i \(0.567772\pi\)
\(920\) −5.18253e12 −0.238504
\(921\) 9.86180e12 0.451635
\(922\) −4.80855e13 −2.19142
\(923\) −3.77177e12 −0.171056
\(924\) −5.26505e12 −0.237618
\(925\) 1.17475e13 0.527604
\(926\) −4.57094e13 −2.04294
\(927\) 1.08301e11 0.00481698
\(928\) 6.81948e12 0.301846
\(929\) 2.70772e13 1.19271 0.596354 0.802722i \(-0.296616\pi\)
0.596354 + 0.802722i \(0.296616\pi\)
\(930\) 2.08472e13 0.913849
\(931\) 4.03642e12 0.176085
\(932\) 8.70767e12 0.378033
\(933\) −1.02091e13 −0.441083
\(934\) −3.23538e13 −1.39112
\(935\) −1.83211e13 −0.783970
\(936\) 1.33671e12 0.0569241
\(937\) −4.22187e9 −0.000178927 0 −8.94637e−5 1.00000i \(-0.500028\pi\)
−8.94637e−5 1.00000i \(0.500028\pi\)
\(938\) −2.14160e13 −0.903285
\(939\) −4.82949e12 −0.202724
\(940\) 1.87203e13 0.782054
\(941\) −1.65925e13 −0.689857 −0.344929 0.938629i \(-0.612097\pi\)
−0.344929 + 0.938629i \(0.612097\pi\)
\(942\) 1.44823e13 0.599252
\(943\) −2.77015e13 −1.14078
\(944\) −3.65202e12 −0.149678
\(945\) −3.28999e12 −0.134200
\(946\) −1.31571e13 −0.534135
\(947\) 1.81520e13 0.733415 0.366708 0.930336i \(-0.380485\pi\)
0.366708 + 0.930336i \(0.380485\pi\)
\(948\) 1.05814e13 0.425504
\(949\) 1.03182e13 0.412957
\(950\) 1.84795e13 0.736095
\(951\) 1.11417e13 0.441710
\(952\) −1.11386e13 −0.439507
\(953\) 4.04715e13 1.58939 0.794696 0.607008i \(-0.207630\pi\)
0.794696 + 0.607008i \(0.207630\pi\)
\(954\) 1.09534e12 0.0428135
\(955\) 1.61842e13 0.629615
\(956\) 3.56326e13 1.37971
\(957\) −1.88661e12 −0.0727074
\(958\) 4.94793e13 1.89793
\(959\) −1.04851e13 −0.400303
\(960\) −6.92329e12 −0.263083
\(961\) 3.80403e13 1.43876
\(962\) 3.00498e13 1.13124
\(963\) 1.64923e13 0.617963
\(964\) −3.36500e12 −0.125498
\(965\) −2.15282e13 −0.799161
\(966\) −2.50718e13 −0.926377
\(967\) −8.58992e12 −0.315915 −0.157957 0.987446i \(-0.550491\pi\)
−0.157957 + 0.987446i \(0.550491\pi\)
\(968\) 4.75587e12 0.174097
\(969\) 3.82047e13 1.39207
\(970\) −3.57835e13 −1.29781
\(971\) 1.58363e13 0.571697 0.285849 0.958275i \(-0.407725\pi\)
0.285849 + 0.958275i \(0.407725\pi\)
\(972\) 1.45800e12 0.0523913
\(973\) 1.88561e13 0.674443
\(974\) 3.00643e13 1.07038
\(975\) 4.89307e12 0.173405
\(976\) 4.68326e13 1.65205
\(977\) −2.81128e13 −0.987141 −0.493571 0.869706i \(-0.664309\pi\)
−0.493571 + 0.869706i \(0.664309\pi\)
\(978\) −1.03244e12 −0.0360860
\(979\) 1.75617e13 0.611005
\(980\) −2.48444e12 −0.0860420
\(981\) −1.03379e13 −0.356388
\(982\) 6.02004e13 2.06585
\(983\) −7.66030e11 −0.0261671 −0.0130835 0.999914i \(-0.504165\pi\)
−0.0130835 + 0.999914i \(0.504165\pi\)
\(984\) 3.72768e12 0.126754
\(985\) 3.65032e13 1.23557
\(986\) 1.77833e13 0.599191
\(987\) −2.03262e13 −0.681755
\(988\) 2.12503e13 0.709511
\(989\) −2.81658e13 −0.936136
\(990\) 5.54933e12 0.183604
\(991\) −3.40219e13 −1.12054 −0.560270 0.828310i \(-0.689303\pi\)
−0.560270 + 0.828310i \(0.689303\pi\)
\(992\) −6.20420e13 −2.03415
\(993\) −2.88982e13 −0.943191
\(994\) −9.51982e12 −0.309307
\(995\) −4.05720e13 −1.31227
\(996\) 1.71742e12 0.0552981
\(997\) −2.09508e13 −0.671540 −0.335770 0.941944i \(-0.608996\pi\)
−0.335770 + 0.941944i \(0.608996\pi\)
\(998\) −2.77495e13 −0.885457
\(999\) −7.35635e12 −0.233678
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.a.1.18 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.18 21 1.1 even 1 trivial