Properties

Label 177.10.a.d.1.14
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 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+14.9387 q^{2} +81.0000 q^{3} -288.835 q^{4} -659.121 q^{5} +1210.04 q^{6} -8231.50 q^{7} -11963.4 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+14.9387 q^{2} +81.0000 q^{3} -288.835 q^{4} -659.121 q^{5} +1210.04 q^{6} -8231.50 q^{7} -11963.4 q^{8} +6561.00 q^{9} -9846.43 q^{10} -86127.8 q^{11} -23395.6 q^{12} +43784.4 q^{13} -122968. q^{14} -53388.8 q^{15} -30835.3 q^{16} -393685. q^{17} +98013.0 q^{18} +166782. q^{19} +190377. q^{20} -666752. q^{21} -1.28664e6 q^{22} +1.77150e6 q^{23} -969039. q^{24} -1.51868e6 q^{25} +654084. q^{26} +531441. q^{27} +2.37754e6 q^{28} +3.21566e6 q^{29} -797561. q^{30} -2.76369e6 q^{31} +5.66464e6 q^{32} -6.97635e6 q^{33} -5.88115e6 q^{34} +5.42556e6 q^{35} -1.89504e6 q^{36} -427809. q^{37} +2.49151e6 q^{38} +3.54654e6 q^{39} +7.88536e6 q^{40} +1.68281e7 q^{41} -9.96042e6 q^{42} +206120. q^{43} +2.48767e7 q^{44} -4.32449e6 q^{45} +2.64639e7 q^{46} -1.61351e7 q^{47} -2.49766e6 q^{48} +2.74040e7 q^{49} -2.26872e7 q^{50} -3.18885e7 q^{51} -1.26465e7 q^{52} -8.10150e6 q^{53} +7.93905e6 q^{54} +5.67687e7 q^{55} +9.84771e7 q^{56} +1.35093e7 q^{57} +4.80379e7 q^{58} -1.21174e7 q^{59} +1.54205e7 q^{60} +3.93336e7 q^{61} -4.12860e7 q^{62} -5.40069e7 q^{63} +1.00410e8 q^{64} -2.88593e7 q^{65} -1.04218e8 q^{66} +3.07030e8 q^{67} +1.13710e8 q^{68} +1.43491e8 q^{69} +8.10509e7 q^{70} -2.50251e8 q^{71} -7.84922e7 q^{72} -1.16174e8 q^{73} -6.39091e6 q^{74} -1.23013e8 q^{75} -4.81724e7 q^{76} +7.08961e8 q^{77} +5.29808e7 q^{78} -3.26619e8 q^{79} +2.03242e7 q^{80} +4.30467e7 q^{81} +2.51390e8 q^{82} +4.90102e8 q^{83} +1.92581e8 q^{84} +2.59486e8 q^{85} +3.07917e6 q^{86} +2.60469e8 q^{87} +1.03039e9 q^{88} -6.22951e8 q^{89} -6.46024e7 q^{90} -3.60412e8 q^{91} -5.11670e8 q^{92} -2.23859e8 q^{93} -2.41038e8 q^{94} -1.09929e8 q^{95} +4.58836e8 q^{96} +6.21194e8 q^{97} +4.09381e8 q^{98} -5.65085e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 14.9387 0.660205 0.330102 0.943945i \(-0.392917\pi\)
0.330102 + 0.943945i \(0.392917\pi\)
\(3\) 81.0000 0.577350
\(4\) −288.835 −0.564130
\(5\) −659.121 −0.471629 −0.235814 0.971798i \(-0.575776\pi\)
−0.235814 + 0.971798i \(0.575776\pi\)
\(6\) 1210.04 0.381169
\(7\) −8231.50 −1.29580 −0.647900 0.761726i \(-0.724352\pi\)
−0.647900 + 0.761726i \(0.724352\pi\)
\(8\) −11963.4 −1.03265
\(9\) 6561.00 0.333333
\(10\) −9846.43 −0.311371
\(11\) −86127.8 −1.77368 −0.886842 0.462073i \(-0.847106\pi\)
−0.886842 + 0.462073i \(0.847106\pi\)
\(12\) −23395.6 −0.325701
\(13\) 43784.4 0.425182 0.212591 0.977141i \(-0.431810\pi\)
0.212591 + 0.977141i \(0.431810\pi\)
\(14\) −122968. −0.855493
\(15\) −53388.8 −0.272295
\(16\) −30835.3 −0.117627
\(17\) −393685. −1.14322 −0.571608 0.820527i \(-0.693680\pi\)
−0.571608 + 0.820527i \(0.693680\pi\)
\(18\) 98013.0 0.220068
\(19\) 166782. 0.293601 0.146800 0.989166i \(-0.453102\pi\)
0.146800 + 0.989166i \(0.453102\pi\)
\(20\) 190377. 0.266060
\(21\) −666752. −0.748130
\(22\) −1.28664e6 −1.17099
\(23\) 1.77150e6 1.31998 0.659988 0.751276i \(-0.270561\pi\)
0.659988 + 0.751276i \(0.270561\pi\)
\(24\) −969039. −0.596198
\(25\) −1.51868e6 −0.777566
\(26\) 654084. 0.280707
\(27\) 531441. 0.192450
\(28\) 2.37754e6 0.730999
\(29\) 3.21566e6 0.844266 0.422133 0.906534i \(-0.361281\pi\)
0.422133 + 0.906534i \(0.361281\pi\)
\(30\) −797561. −0.179770
\(31\) −2.76369e6 −0.537479 −0.268739 0.963213i \(-0.586607\pi\)
−0.268739 + 0.963213i \(0.586607\pi\)
\(32\) 5.66464e6 0.954988
\(33\) −6.97635e6 −1.02404
\(34\) −5.88115e6 −0.754757
\(35\) 5.42556e6 0.611136
\(36\) −1.89504e6 −0.188043
\(37\) −427809. −0.0375268 −0.0187634 0.999824i \(-0.505973\pi\)
−0.0187634 + 0.999824i \(0.505973\pi\)
\(38\) 2.49151e6 0.193837
\(39\) 3.54654e6 0.245479
\(40\) 7.88536e6 0.487025
\(41\) 1.68281e7 0.930053 0.465026 0.885297i \(-0.346045\pi\)
0.465026 + 0.885297i \(0.346045\pi\)
\(42\) −9.96042e6 −0.493919
\(43\) 206120. 0.00919416 0.00459708 0.999989i \(-0.498537\pi\)
0.00459708 + 0.999989i \(0.498537\pi\)
\(44\) 2.48767e7 1.00059
\(45\) −4.32449e6 −0.157210
\(46\) 2.64639e7 0.871454
\(47\) −1.61351e7 −0.482317 −0.241158 0.970486i \(-0.577527\pi\)
−0.241158 + 0.970486i \(0.577527\pi\)
\(48\) −2.49766e6 −0.0679122
\(49\) 2.74040e7 0.679097
\(50\) −2.26872e7 −0.513353
\(51\) −3.18885e7 −0.660036
\(52\) −1.26465e7 −0.239858
\(53\) −8.10150e6 −0.141034 −0.0705171 0.997511i \(-0.522465\pi\)
−0.0705171 + 0.997511i \(0.522465\pi\)
\(54\) 7.93905e6 0.127056
\(55\) 5.67687e7 0.836520
\(56\) 9.84771e7 1.33810
\(57\) 1.35093e7 0.169511
\(58\) 4.80379e7 0.557389
\(59\) −1.21174e7 −0.130189
\(60\) 1.54205e7 0.153610
\(61\) 3.93336e7 0.363731 0.181865 0.983323i \(-0.441787\pi\)
0.181865 + 0.983323i \(0.441787\pi\)
\(62\) −4.12860e7 −0.354846
\(63\) −5.40069e7 −0.431933
\(64\) 1.00410e8 0.748114
\(65\) −2.88593e7 −0.200528
\(66\) −1.04218e8 −0.676074
\(67\) 3.07030e8 1.86142 0.930710 0.365757i \(-0.119190\pi\)
0.930710 + 0.365757i \(0.119190\pi\)
\(68\) 1.13710e8 0.644923
\(69\) 1.43491e8 0.762088
\(70\) 8.10509e7 0.403475
\(71\) −2.50251e8 −1.16873 −0.584365 0.811491i \(-0.698656\pi\)
−0.584365 + 0.811491i \(0.698656\pi\)
\(72\) −7.84922e7 −0.344215
\(73\) −1.16174e8 −0.478801 −0.239400 0.970921i \(-0.576951\pi\)
−0.239400 + 0.970921i \(0.576951\pi\)
\(74\) −6.39091e6 −0.0247754
\(75\) −1.23013e8 −0.448928
\(76\) −4.81724e7 −0.165629
\(77\) 7.08961e8 2.29834
\(78\) 5.29808e7 0.162066
\(79\) −3.26619e8 −0.943451 −0.471725 0.881746i \(-0.656369\pi\)
−0.471725 + 0.881746i \(0.656369\pi\)
\(80\) 2.03242e7 0.0554764
\(81\) 4.30467e7 0.111111
\(82\) 2.51390e8 0.614025
\(83\) 4.90102e8 1.13354 0.566768 0.823878i \(-0.308194\pi\)
0.566768 + 0.823878i \(0.308194\pi\)
\(84\) 1.92581e8 0.422043
\(85\) 2.59486e8 0.539174
\(86\) 3.07917e6 0.00607003
\(87\) 2.60469e8 0.487437
\(88\) 1.03039e9 1.83159
\(89\) −6.22951e8 −1.05244 −0.526222 0.850347i \(-0.676392\pi\)
−0.526222 + 0.850347i \(0.676392\pi\)
\(90\) −6.46024e7 −0.103790
\(91\) −3.60412e8 −0.550951
\(92\) −5.11670e8 −0.744638
\(93\) −2.23859e8 −0.310314
\(94\) −2.41038e8 −0.318428
\(95\) −1.09929e8 −0.138471
\(96\) 4.58836e8 0.551362
\(97\) 6.21194e8 0.712450 0.356225 0.934400i \(-0.384064\pi\)
0.356225 + 0.934400i \(0.384064\pi\)
\(98\) 4.09381e8 0.448343
\(99\) −5.65085e8 −0.591228
\(100\) 4.38648e8 0.438648
\(101\) 6.76739e8 0.647105 0.323553 0.946210i \(-0.395123\pi\)
0.323553 + 0.946210i \(0.395123\pi\)
\(102\) −4.76373e8 −0.435759
\(103\) −1.66672e9 −1.45914 −0.729568 0.683908i \(-0.760279\pi\)
−0.729568 + 0.683908i \(0.760279\pi\)
\(104\) −5.23813e8 −0.439062
\(105\) 4.39470e8 0.352840
\(106\) −1.21026e8 −0.0931114
\(107\) −6.75823e8 −0.498432 −0.249216 0.968448i \(-0.580173\pi\)
−0.249216 + 0.968448i \(0.580173\pi\)
\(108\) −1.53499e8 −0.108567
\(109\) −2.20524e8 −0.149636 −0.0748181 0.997197i \(-0.523838\pi\)
−0.0748181 + 0.997197i \(0.523838\pi\)
\(110\) 8.48051e8 0.552275
\(111\) −3.46525e7 −0.0216661
\(112\) 2.53821e8 0.152422
\(113\) −3.21303e9 −1.85379 −0.926897 0.375315i \(-0.877535\pi\)
−0.926897 + 0.375315i \(0.877535\pi\)
\(114\) 2.01812e8 0.111912
\(115\) −1.16763e9 −0.622538
\(116\) −9.28795e8 −0.476276
\(117\) 2.87270e8 0.141727
\(118\) −1.81018e8 −0.0859513
\(119\) 3.24062e9 1.48138
\(120\) 6.38714e8 0.281184
\(121\) 5.06005e9 2.14596
\(122\) 5.87594e8 0.240137
\(123\) 1.36308e9 0.536966
\(124\) 7.98249e8 0.303208
\(125\) 2.28834e9 0.838351
\(126\) −8.06794e8 −0.285164
\(127\) −1.49943e9 −0.511458 −0.255729 0.966748i \(-0.582316\pi\)
−0.255729 + 0.966748i \(0.582316\pi\)
\(128\) −1.40030e9 −0.461079
\(129\) 1.66957e7 0.00530825
\(130\) −4.31120e8 −0.132389
\(131\) 5.72810e9 1.69938 0.849688 0.527285i \(-0.176790\pi\)
0.849688 + 0.527285i \(0.176790\pi\)
\(132\) 2.01501e9 0.577690
\(133\) −1.37286e9 −0.380448
\(134\) 4.58664e9 1.22892
\(135\) −3.50284e8 −0.0907650
\(136\) 4.70983e9 1.18054
\(137\) 6.47967e9 1.57149 0.785743 0.618553i \(-0.212281\pi\)
0.785743 + 0.618553i \(0.212281\pi\)
\(138\) 2.14358e9 0.503134
\(139\) 7.53691e9 1.71249 0.856243 0.516574i \(-0.172793\pi\)
0.856243 + 0.516574i \(0.172793\pi\)
\(140\) −1.56709e9 −0.344760
\(141\) −1.30695e9 −0.278466
\(142\) −3.73844e9 −0.771600
\(143\) −3.77106e9 −0.754138
\(144\) −2.02310e8 −0.0392091
\(145\) −2.11951e9 −0.398180
\(146\) −1.73549e9 −0.316107
\(147\) 2.21972e9 0.392077
\(148\) 1.23566e8 0.0211700
\(149\) −8.64441e8 −0.143680 −0.0718402 0.997416i \(-0.522887\pi\)
−0.0718402 + 0.997416i \(0.522887\pi\)
\(150\) −1.83766e9 −0.296384
\(151\) 6.27824e8 0.0982747 0.0491373 0.998792i \(-0.484353\pi\)
0.0491373 + 0.998792i \(0.484353\pi\)
\(152\) −1.99529e9 −0.303186
\(153\) −2.58297e9 −0.381072
\(154\) 1.05910e10 1.51737
\(155\) 1.82161e9 0.253490
\(156\) −1.02436e9 −0.138482
\(157\) 3.90127e9 0.512458 0.256229 0.966616i \(-0.417520\pi\)
0.256229 + 0.966616i \(0.417520\pi\)
\(158\) −4.87927e9 −0.622870
\(159\) −6.56222e8 −0.0814261
\(160\) −3.73369e9 −0.450400
\(161\) −1.45821e10 −1.71042
\(162\) 6.43063e8 0.0733561
\(163\) 2.75564e9 0.305758 0.152879 0.988245i \(-0.451146\pi\)
0.152879 + 0.988245i \(0.451146\pi\)
\(164\) −4.86053e9 −0.524671
\(165\) 4.59826e9 0.482965
\(166\) 7.32150e9 0.748365
\(167\) 2.26288e9 0.225132 0.112566 0.993644i \(-0.464093\pi\)
0.112566 + 0.993644i \(0.464093\pi\)
\(168\) 7.97665e9 0.772554
\(169\) −8.68742e9 −0.819220
\(170\) 3.87639e9 0.355965
\(171\) 1.09426e9 0.0978670
\(172\) −5.95346e7 −0.00518670
\(173\) −8.51022e9 −0.722326 −0.361163 0.932503i \(-0.617620\pi\)
−0.361163 + 0.932503i \(0.617620\pi\)
\(174\) 3.89107e9 0.321808
\(175\) 1.25011e10 1.00757
\(176\) 2.65578e9 0.208634
\(177\) −9.81506e8 −0.0751646
\(178\) −9.30609e9 −0.694828
\(179\) −5.31698e9 −0.387103 −0.193551 0.981090i \(-0.562001\pi\)
−0.193551 + 0.981090i \(0.562001\pi\)
\(180\) 1.24906e9 0.0886866
\(181\) 5.56101e9 0.385124 0.192562 0.981285i \(-0.438320\pi\)
0.192562 + 0.981285i \(0.438320\pi\)
\(182\) −5.38409e9 −0.363740
\(183\) 3.18602e9 0.210000
\(184\) −2.11932e10 −1.36307
\(185\) 2.81978e8 0.0176987
\(186\) −3.34416e9 −0.204870
\(187\) 3.39072e10 2.02771
\(188\) 4.66039e9 0.272089
\(189\) −4.37456e9 −0.249377
\(190\) −1.64221e9 −0.0914190
\(191\) 3.29917e10 1.79372 0.896860 0.442315i \(-0.145843\pi\)
0.896860 + 0.442315i \(0.145843\pi\)
\(192\) 8.13323e9 0.431924
\(193\) −2.35302e10 −1.22072 −0.610362 0.792122i \(-0.708976\pi\)
−0.610362 + 0.792122i \(0.708976\pi\)
\(194\) 9.27984e9 0.470362
\(195\) −2.33760e9 −0.115775
\(196\) −7.91523e9 −0.383099
\(197\) 2.75263e10 1.30212 0.651059 0.759027i \(-0.274325\pi\)
0.651059 + 0.759027i \(0.274325\pi\)
\(198\) −8.44164e9 −0.390331
\(199\) 2.17126e10 0.981459 0.490729 0.871312i \(-0.336730\pi\)
0.490729 + 0.871312i \(0.336730\pi\)
\(200\) 1.81687e10 0.802951
\(201\) 2.48694e10 1.07469
\(202\) 1.01096e10 0.427222
\(203\) −2.64697e10 −1.09400
\(204\) 9.21049e9 0.372346
\(205\) −1.10918e10 −0.438640
\(206\) −2.48987e10 −0.963328
\(207\) 1.16228e10 0.439992
\(208\) −1.35011e9 −0.0500130
\(209\) −1.43646e10 −0.520755
\(210\) 6.56512e9 0.232946
\(211\) 1.08182e10 0.375736 0.187868 0.982194i \(-0.439842\pi\)
0.187868 + 0.982194i \(0.439842\pi\)
\(212\) 2.33999e9 0.0795616
\(213\) −2.02704e10 −0.674766
\(214\) −1.00959e10 −0.329067
\(215\) −1.35858e8 −0.00433623
\(216\) −6.35787e9 −0.198733
\(217\) 2.27493e10 0.696465
\(218\) −3.29435e9 −0.0987905
\(219\) −9.41007e9 −0.276436
\(220\) −1.63968e10 −0.471906
\(221\) −1.72373e10 −0.486075
\(222\) −5.17664e8 −0.0143041
\(223\) 2.01070e10 0.544472 0.272236 0.962230i \(-0.412237\pi\)
0.272236 + 0.962230i \(0.412237\pi\)
\(224\) −4.66285e10 −1.23747
\(225\) −9.96409e9 −0.259189
\(226\) −4.79986e10 −1.22388
\(227\) −2.29052e8 −0.00572555 −0.00286278 0.999996i \(-0.500911\pi\)
−0.00286278 + 0.999996i \(0.500911\pi\)
\(228\) −3.90196e9 −0.0956260
\(229\) −3.35826e10 −0.806964 −0.403482 0.914988i \(-0.632200\pi\)
−0.403482 + 0.914988i \(0.632200\pi\)
\(230\) −1.74429e10 −0.411003
\(231\) 5.74259e10 1.32695
\(232\) −3.84704e10 −0.871828
\(233\) −1.09191e10 −0.242709 −0.121355 0.992609i \(-0.538724\pi\)
−0.121355 + 0.992609i \(0.538724\pi\)
\(234\) 4.29144e9 0.0935690
\(235\) 1.06350e10 0.227474
\(236\) 3.49991e9 0.0734435
\(237\) −2.64561e10 −0.544702
\(238\) 4.84107e10 0.978014
\(239\) 2.51977e10 0.499540 0.249770 0.968305i \(-0.419645\pi\)
0.249770 + 0.968305i \(0.419645\pi\)
\(240\) 1.64626e9 0.0320293
\(241\) 1.20750e10 0.230574 0.115287 0.993332i \(-0.463221\pi\)
0.115287 + 0.993332i \(0.463221\pi\)
\(242\) 7.55907e10 1.41677
\(243\) 3.48678e9 0.0641500
\(244\) −1.13609e10 −0.205191
\(245\) −1.80626e10 −0.320282
\(246\) 2.03626e10 0.354507
\(247\) 7.30245e9 0.124834
\(248\) 3.30632e10 0.555025
\(249\) 3.96983e10 0.654447
\(250\) 3.41849e10 0.553483
\(251\) 3.53064e10 0.561464 0.280732 0.959786i \(-0.409423\pi\)
0.280732 + 0.959786i \(0.409423\pi\)
\(252\) 1.55991e10 0.243666
\(253\) −1.52575e11 −2.34122
\(254\) −2.23996e10 −0.337667
\(255\) 2.10184e10 0.311292
\(256\) −7.23287e10 −1.05252
\(257\) −7.46059e10 −1.06678 −0.533389 0.845870i \(-0.679082\pi\)
−0.533389 + 0.845870i \(0.679082\pi\)
\(258\) 2.49413e8 0.00350453
\(259\) 3.52151e9 0.0486272
\(260\) 8.33555e9 0.113124
\(261\) 2.10980e10 0.281422
\(262\) 8.55705e10 1.12194
\(263\) −5.39550e10 −0.695394 −0.347697 0.937607i \(-0.613036\pi\)
−0.347697 + 0.937607i \(0.613036\pi\)
\(264\) 8.34612e10 1.05747
\(265\) 5.33987e9 0.0665157
\(266\) −2.05088e10 −0.251174
\(267\) −5.04590e10 −0.607629
\(268\) −8.86809e10 −1.05008
\(269\) −1.57685e11 −1.83614 −0.918069 0.396421i \(-0.870252\pi\)
−0.918069 + 0.396421i \(0.870252\pi\)
\(270\) −5.23280e9 −0.0599235
\(271\) −1.52312e11 −1.71543 −0.857715 0.514126i \(-0.828117\pi\)
−0.857715 + 0.514126i \(0.828117\pi\)
\(272\) 1.21394e10 0.134474
\(273\) −2.91933e10 −0.318091
\(274\) 9.67980e10 1.03750
\(275\) 1.30801e11 1.37916
\(276\) −4.14453e10 −0.429917
\(277\) −1.28972e11 −1.31624 −0.658122 0.752911i \(-0.728649\pi\)
−0.658122 + 0.752911i \(0.728649\pi\)
\(278\) 1.12592e11 1.13059
\(279\) −1.81326e10 −0.179160
\(280\) −6.49084e10 −0.631087
\(281\) −2.04040e11 −1.95225 −0.976127 0.217199i \(-0.930308\pi\)
−0.976127 + 0.217199i \(0.930308\pi\)
\(282\) −1.95241e10 −0.183844
\(283\) −5.36671e10 −0.497358 −0.248679 0.968586i \(-0.579996\pi\)
−0.248679 + 0.968586i \(0.579996\pi\)
\(284\) 7.22812e10 0.659315
\(285\) −8.90428e9 −0.0799461
\(286\) −5.63348e10 −0.497886
\(287\) −1.38520e11 −1.20516
\(288\) 3.71657e10 0.318329
\(289\) 3.63999e10 0.306944
\(290\) −3.16628e10 −0.262880
\(291\) 5.03167e10 0.411333
\(292\) 3.35550e10 0.270106
\(293\) 2.48437e11 1.96930 0.984650 0.174538i \(-0.0558432\pi\)
0.984650 + 0.174538i \(0.0558432\pi\)
\(294\) 3.31599e10 0.258851
\(295\) 7.98681e9 0.0614008
\(296\) 5.11806e9 0.0387519
\(297\) −4.57718e10 −0.341346
\(298\) −1.29136e10 −0.0948584
\(299\) 7.75641e10 0.561230
\(300\) 3.55305e10 0.253254
\(301\) −1.69668e9 −0.0119138
\(302\) 9.37889e9 0.0648814
\(303\) 5.48158e10 0.373606
\(304\) −5.14277e9 −0.0345355
\(305\) −2.59256e10 −0.171546
\(306\) −3.85862e10 −0.251586
\(307\) −1.85724e11 −1.19329 −0.596645 0.802506i \(-0.703500\pi\)
−0.596645 + 0.802506i \(0.703500\pi\)
\(308\) −2.04772e11 −1.29656
\(309\) −1.35005e11 −0.842433
\(310\) 2.72125e10 0.167356
\(311\) −2.85134e11 −1.72834 −0.864168 0.503204i \(-0.832154\pi\)
−0.864168 + 0.503204i \(0.832154\pi\)
\(312\) −4.24288e10 −0.253493
\(313\) 1.05330e11 0.620301 0.310150 0.950688i \(-0.399621\pi\)
0.310150 + 0.950688i \(0.399621\pi\)
\(314\) 5.82801e10 0.338327
\(315\) 3.55971e10 0.203712
\(316\) 9.43388e10 0.532229
\(317\) 2.12753e11 1.18334 0.591668 0.806181i \(-0.298469\pi\)
0.591668 + 0.806181i \(0.298469\pi\)
\(318\) −9.80312e9 −0.0537579
\(319\) −2.76958e11 −1.49746
\(320\) −6.61825e10 −0.352832
\(321\) −5.47416e10 −0.287770
\(322\) −2.17838e11 −1.12923
\(323\) −6.56595e10 −0.335650
\(324\) −1.24334e10 −0.0626811
\(325\) −6.64947e10 −0.330607
\(326\) 4.11657e10 0.201863
\(327\) −1.78624e10 −0.0863925
\(328\) −2.01322e11 −0.960415
\(329\) 1.32816e11 0.624986
\(330\) 6.86922e10 0.318856
\(331\) 2.45717e11 1.12515 0.562574 0.826747i \(-0.309811\pi\)
0.562574 + 0.826747i \(0.309811\pi\)
\(332\) −1.41558e11 −0.639461
\(333\) −2.80685e9 −0.0125089
\(334\) 3.38045e10 0.148633
\(335\) −2.02370e11 −0.877899
\(336\) 2.05595e10 0.0880006
\(337\) 2.46465e11 1.04093 0.520463 0.853884i \(-0.325759\pi\)
0.520463 + 0.853884i \(0.325759\pi\)
\(338\) −1.29779e11 −0.540853
\(339\) −2.60255e11 −1.07029
\(340\) −7.49485e10 −0.304164
\(341\) 2.38030e11 0.953318
\(342\) 1.63468e10 0.0646122
\(343\) 1.06595e11 0.415826
\(344\) −2.46591e9 −0.00949431
\(345\) −9.45783e10 −0.359423
\(346\) −1.27132e11 −0.476883
\(347\) −1.08361e10 −0.0401227 −0.0200614 0.999799i \(-0.506386\pi\)
−0.0200614 + 0.999799i \(0.506386\pi\)
\(348\) −7.52324e10 −0.274978
\(349\) 1.74996e11 0.631411 0.315706 0.948857i \(-0.397759\pi\)
0.315706 + 0.948857i \(0.397759\pi\)
\(350\) 1.86750e11 0.665202
\(351\) 2.32688e10 0.0818263
\(352\) −4.87883e11 −1.69385
\(353\) −1.94568e11 −0.666937 −0.333469 0.942761i \(-0.608219\pi\)
−0.333469 + 0.942761i \(0.608219\pi\)
\(354\) −1.46624e10 −0.0496240
\(355\) 1.64946e11 0.551206
\(356\) 1.79930e11 0.593715
\(357\) 2.62490e11 0.855275
\(358\) −7.94289e10 −0.255567
\(359\) −5.27532e10 −0.167619 −0.0838097 0.996482i \(-0.526709\pi\)
−0.0838097 + 0.996482i \(0.526709\pi\)
\(360\) 5.17359e10 0.162342
\(361\) −2.94872e11 −0.913798
\(362\) 8.30744e10 0.254260
\(363\) 4.09864e11 1.23897
\(364\) 1.04099e11 0.310808
\(365\) 7.65726e10 0.225816
\(366\) 4.75951e10 0.138643
\(367\) −8.20938e10 −0.236218 −0.118109 0.993001i \(-0.537683\pi\)
−0.118109 + 0.993001i \(0.537683\pi\)
\(368\) −5.46247e10 −0.155265
\(369\) 1.10409e11 0.310018
\(370\) 4.21239e9 0.0116848
\(371\) 6.66875e10 0.182752
\(372\) 6.46581e10 0.175057
\(373\) 1.57190e11 0.420469 0.210235 0.977651i \(-0.432577\pi\)
0.210235 + 0.977651i \(0.432577\pi\)
\(374\) 5.06530e11 1.33870
\(375\) 1.85356e11 0.484022
\(376\) 1.93032e11 0.498062
\(377\) 1.40796e11 0.358967
\(378\) −6.53503e10 −0.164640
\(379\) 6.72895e11 1.67522 0.837608 0.546272i \(-0.183953\pi\)
0.837608 + 0.546272i \(0.183953\pi\)
\(380\) 3.17514e10 0.0781155
\(381\) −1.21454e11 −0.295291
\(382\) 4.92854e11 1.18422
\(383\) 6.60882e11 1.56939 0.784693 0.619885i \(-0.212821\pi\)
0.784693 + 0.619885i \(0.212821\pi\)
\(384\) −1.13424e11 −0.266204
\(385\) −4.67291e11 −1.08396
\(386\) −3.51511e11 −0.805928
\(387\) 1.35235e9 0.00306472
\(388\) −1.79422e11 −0.401914
\(389\) 5.11385e11 1.13234 0.566168 0.824290i \(-0.308425\pi\)
0.566168 + 0.824290i \(0.308425\pi\)
\(390\) −3.49208e10 −0.0764351
\(391\) −6.97413e11 −1.50902
\(392\) −3.27846e11 −0.701267
\(393\) 4.63976e11 0.981136
\(394\) 4.11208e11 0.859664
\(395\) 2.15281e11 0.444959
\(396\) 1.63216e11 0.333529
\(397\) 4.60522e11 0.930450 0.465225 0.885192i \(-0.345973\pi\)
0.465225 + 0.885192i \(0.345973\pi\)
\(398\) 3.24358e11 0.647964
\(399\) −1.11202e11 −0.219652
\(400\) 4.68291e10 0.0914631
\(401\) 9.41887e11 1.81907 0.909535 0.415628i \(-0.136438\pi\)
0.909535 + 0.415628i \(0.136438\pi\)
\(402\) 3.71518e11 0.709516
\(403\) −1.21007e11 −0.228526
\(404\) −1.95466e11 −0.365051
\(405\) −2.83730e10 −0.0524032
\(406\) −3.95424e11 −0.722264
\(407\) 3.68462e10 0.0665607
\(408\) 3.81496e11 0.681584
\(409\) −5.60303e11 −0.990075 −0.495037 0.868872i \(-0.664846\pi\)
−0.495037 + 0.868872i \(0.664846\pi\)
\(410\) −1.65697e11 −0.289592
\(411\) 5.24853e11 0.907298
\(412\) 4.81407e11 0.823142
\(413\) 9.97441e10 0.168699
\(414\) 1.73630e11 0.290485
\(415\) −3.23037e11 −0.534608
\(416\) 2.48023e11 0.406043
\(417\) 6.10490e11 0.988704
\(418\) −2.14588e11 −0.343805
\(419\) 3.78397e11 0.599770 0.299885 0.953975i \(-0.403052\pi\)
0.299885 + 0.953975i \(0.403052\pi\)
\(420\) −1.26934e11 −0.199047
\(421\) −5.95120e11 −0.923284 −0.461642 0.887066i \(-0.652739\pi\)
−0.461642 + 0.887066i \(0.652739\pi\)
\(422\) 1.61610e11 0.248063
\(423\) −1.05863e11 −0.160772
\(424\) 9.69219e10 0.145638
\(425\) 5.97883e11 0.888927
\(426\) −3.02813e11 −0.445484
\(427\) −3.23775e11 −0.471322
\(428\) 1.95201e11 0.281180
\(429\) −3.05456e11 −0.435402
\(430\) −2.02955e9 −0.00286280
\(431\) 4.27432e11 0.596650 0.298325 0.954464i \(-0.403572\pi\)
0.298325 + 0.954464i \(0.403572\pi\)
\(432\) −1.63871e10 −0.0226374
\(433\) −3.45341e11 −0.472121 −0.236060 0.971738i \(-0.575856\pi\)
−0.236060 + 0.971738i \(0.575856\pi\)
\(434\) 3.39846e11 0.459809
\(435\) −1.71680e11 −0.229890
\(436\) 6.36949e10 0.0844142
\(437\) 2.95454e11 0.387546
\(438\) −1.40574e11 −0.182504
\(439\) −1.03278e12 −1.32714 −0.663569 0.748115i \(-0.730959\pi\)
−0.663569 + 0.748115i \(0.730959\pi\)
\(440\) −6.79149e11 −0.863829
\(441\) 1.79798e11 0.226366
\(442\) −2.57503e11 −0.320909
\(443\) 8.02607e11 0.990116 0.495058 0.868860i \(-0.335147\pi\)
0.495058 + 0.868860i \(0.335147\pi\)
\(444\) 1.00088e10 0.0122225
\(445\) 4.10600e11 0.496363
\(446\) 3.00373e11 0.359463
\(447\) −7.00197e10 −0.0829539
\(448\) −8.26527e11 −0.969407
\(449\) 1.00537e12 1.16739 0.583695 0.811973i \(-0.301606\pi\)
0.583695 + 0.811973i \(0.301606\pi\)
\(450\) −1.48851e11 −0.171118
\(451\) −1.44937e12 −1.64962
\(452\) 9.28034e11 1.04578
\(453\) 5.08538e10 0.0567389
\(454\) −3.42174e9 −0.00378004
\(455\) 2.37555e11 0.259844
\(456\) −1.61618e11 −0.175044
\(457\) 1.37752e11 0.147732 0.0738662 0.997268i \(-0.476466\pi\)
0.0738662 + 0.997268i \(0.476466\pi\)
\(458\) −5.01681e11 −0.532761
\(459\) −2.09220e11 −0.220012
\(460\) 3.37253e11 0.351193
\(461\) −1.33388e11 −0.137551 −0.0687754 0.997632i \(-0.521909\pi\)
−0.0687754 + 0.997632i \(0.521909\pi\)
\(462\) 8.57869e11 0.876056
\(463\) 9.07405e11 0.917671 0.458835 0.888521i \(-0.348267\pi\)
0.458835 + 0.888521i \(0.348267\pi\)
\(464\) −9.91560e10 −0.0993088
\(465\) 1.47550e11 0.146353
\(466\) −1.63118e11 −0.160238
\(467\) 6.91974e11 0.673230 0.336615 0.941642i \(-0.390718\pi\)
0.336615 + 0.941642i \(0.390718\pi\)
\(468\) −8.29734e10 −0.0799526
\(469\) −2.52732e12 −2.41203
\(470\) 1.58874e11 0.150180
\(471\) 3.16003e11 0.295868
\(472\) 1.44965e11 0.134439
\(473\) −1.77527e10 −0.0163075
\(474\) −3.95221e11 −0.359614
\(475\) −2.53289e11 −0.228294
\(476\) −9.36002e11 −0.835691
\(477\) −5.31540e10 −0.0470114
\(478\) 3.76421e11 0.329798
\(479\) −4.51704e11 −0.392053 −0.196026 0.980599i \(-0.562804\pi\)
−0.196026 + 0.980599i \(0.562804\pi\)
\(480\) −3.02429e11 −0.260038
\(481\) −1.87314e10 −0.0159557
\(482\) 1.80385e11 0.152226
\(483\) −1.18115e12 −0.987514
\(484\) −1.46152e12 −1.21060
\(485\) −4.09442e11 −0.336012
\(486\) 5.20881e10 0.0423521
\(487\) −5.57074e11 −0.448779 −0.224389 0.974500i \(-0.572039\pi\)
−0.224389 + 0.974500i \(0.572039\pi\)
\(488\) −4.70566e11 −0.375605
\(489\) 2.23207e11 0.176530
\(490\) −2.69832e11 −0.211451
\(491\) 1.62345e12 1.26059 0.630294 0.776356i \(-0.282934\pi\)
0.630294 + 0.776356i \(0.282934\pi\)
\(492\) −3.93703e11 −0.302919
\(493\) −1.26596e12 −0.965179
\(494\) 1.09089e11 0.0824159
\(495\) 3.72459e11 0.278840
\(496\) 8.52192e10 0.0632222
\(497\) 2.05994e12 1.51444
\(498\) 5.93041e11 0.432069
\(499\) 4.33241e11 0.312808 0.156404 0.987693i \(-0.450010\pi\)
0.156404 + 0.987693i \(0.450010\pi\)
\(500\) −6.60953e11 −0.472939
\(501\) 1.83293e11 0.129980
\(502\) 5.27433e11 0.370681
\(503\) 4.25950e11 0.296690 0.148345 0.988936i \(-0.452605\pi\)
0.148345 + 0.988936i \(0.452605\pi\)
\(504\) 6.46108e11 0.446034
\(505\) −4.46053e11 −0.305193
\(506\) −2.27928e12 −1.54568
\(507\) −7.03681e11 −0.472977
\(508\) 4.33088e11 0.288529
\(509\) 2.93128e11 0.193565 0.0967826 0.995306i \(-0.469145\pi\)
0.0967826 + 0.995306i \(0.469145\pi\)
\(510\) 3.13988e11 0.205516
\(511\) 9.56284e11 0.620430
\(512\) −3.63546e11 −0.233800
\(513\) 8.86347e10 0.0565035
\(514\) −1.11452e12 −0.704292
\(515\) 1.09857e12 0.688171
\(516\) −4.82230e9 −0.00299454
\(517\) 1.38968e12 0.855478
\(518\) 5.26068e10 0.0321039
\(519\) −6.89328e11 −0.417035
\(520\) 3.45256e11 0.207074
\(521\) 2.47094e12 1.46924 0.734619 0.678480i \(-0.237361\pi\)
0.734619 + 0.678480i \(0.237361\pi\)
\(522\) 3.15177e11 0.185796
\(523\) 8.42425e11 0.492350 0.246175 0.969225i \(-0.420826\pi\)
0.246175 + 0.969225i \(0.420826\pi\)
\(524\) −1.65447e12 −0.958669
\(525\) 1.01259e12 0.581721
\(526\) −8.06019e11 −0.459102
\(527\) 1.08802e12 0.614455
\(528\) 2.15118e11 0.120455
\(529\) 1.33706e12 0.742335
\(530\) 7.97709e10 0.0439140
\(531\) −7.95020e10 −0.0433963
\(532\) 3.96531e11 0.214622
\(533\) 7.36809e11 0.395441
\(534\) −7.53793e11 −0.401159
\(535\) 4.45449e11 0.235075
\(536\) −3.67314e12 −1.92219
\(537\) −4.30675e11 −0.223494
\(538\) −2.35561e12 −1.21223
\(539\) −2.36025e12 −1.20450
\(540\) 1.01174e11 0.0512033
\(541\) 2.49463e12 1.25204 0.626020 0.779807i \(-0.284683\pi\)
0.626020 + 0.779807i \(0.284683\pi\)
\(542\) −2.27535e12 −1.13253
\(543\) 4.50442e11 0.222351
\(544\) −2.23008e12 −1.09176
\(545\) 1.45352e11 0.0705727
\(546\) −4.36111e11 −0.210005
\(547\) −1.57770e12 −0.753496 −0.376748 0.926316i \(-0.622958\pi\)
−0.376748 + 0.926316i \(0.622958\pi\)
\(548\) −1.87155e12 −0.886522
\(549\) 2.58068e11 0.121244
\(550\) 1.95400e12 0.910526
\(551\) 5.36314e11 0.247877
\(552\) −1.71665e12 −0.786967
\(553\) 2.68856e12 1.22252
\(554\) −1.92668e12 −0.868990
\(555\) 2.28402e10 0.0102184
\(556\) −2.17692e12 −0.966064
\(557\) −1.90613e12 −0.839081 −0.419541 0.907737i \(-0.637809\pi\)
−0.419541 + 0.907737i \(0.637809\pi\)
\(558\) −2.70877e11 −0.118282
\(559\) 9.02485e9 0.00390919
\(560\) −1.67299e11 −0.0718864
\(561\) 2.74648e12 1.17070
\(562\) −3.04809e12 −1.28889
\(563\) 6.38448e11 0.267817 0.133908 0.990994i \(-0.457247\pi\)
0.133908 + 0.990994i \(0.457247\pi\)
\(564\) 3.77491e11 0.157091
\(565\) 2.11778e12 0.874303
\(566\) −8.01719e11 −0.328358
\(567\) −3.54339e11 −0.143978
\(568\) 2.99387e12 1.20688
\(569\) 1.23249e12 0.492923 0.246462 0.969153i \(-0.420732\pi\)
0.246462 + 0.969153i \(0.420732\pi\)
\(570\) −1.33019e11 −0.0527808
\(571\) −3.41184e12 −1.34316 −0.671578 0.740934i \(-0.734383\pi\)
−0.671578 + 0.740934i \(0.734383\pi\)
\(572\) 1.08921e12 0.425432
\(573\) 2.67233e12 1.03560
\(574\) −2.06932e12 −0.795653
\(575\) −2.69035e12 −1.02637
\(576\) 6.58791e11 0.249371
\(577\) 2.65784e12 0.998247 0.499124 0.866531i \(-0.333655\pi\)
0.499124 + 0.866531i \(0.333655\pi\)
\(578\) 5.43768e11 0.202646
\(579\) −1.90595e12 −0.704786
\(580\) 6.12188e11 0.224625
\(581\) −4.03428e12 −1.46883
\(582\) 7.51667e11 0.271564
\(583\) 6.97765e11 0.250150
\(584\) 1.38984e12 0.494432
\(585\) −1.89346e11 −0.0668427
\(586\) 3.71133e12 1.30014
\(587\) 4.49754e11 0.156352 0.0781761 0.996940i \(-0.475090\pi\)
0.0781761 + 0.996940i \(0.475090\pi\)
\(588\) −6.41133e11 −0.221182
\(589\) −4.60933e11 −0.157804
\(590\) 1.19313e11 0.0405371
\(591\) 2.22963e12 0.751778
\(592\) 1.31916e10 0.00441418
\(593\) −4.61485e12 −1.53254 −0.766270 0.642519i \(-0.777889\pi\)
−0.766270 + 0.642519i \(0.777889\pi\)
\(594\) −6.83773e11 −0.225358
\(595\) −2.13596e12 −0.698661
\(596\) 2.49680e11 0.0810544
\(597\) 1.75872e12 0.566645
\(598\) 1.15871e12 0.370526
\(599\) 3.35316e11 0.106422 0.0532112 0.998583i \(-0.483054\pi\)
0.0532112 + 0.998583i \(0.483054\pi\)
\(600\) 1.47166e12 0.463584
\(601\) −4.48338e12 −1.40175 −0.700874 0.713285i \(-0.747207\pi\)
−0.700874 + 0.713285i \(0.747207\pi\)
\(602\) −2.53462e10 −0.00786554
\(603\) 2.01443e12 0.620473
\(604\) −1.81337e11 −0.0554397
\(605\) −3.33519e12 −1.01209
\(606\) 8.18879e11 0.246657
\(607\) −5.01602e10 −0.0149972 −0.00749859 0.999972i \(-0.502387\pi\)
−0.00749859 + 0.999972i \(0.502387\pi\)
\(608\) 9.44760e11 0.280385
\(609\) −2.14405e12 −0.631621
\(610\) −3.87296e11 −0.113255
\(611\) −7.06468e11 −0.205072
\(612\) 7.46050e11 0.214974
\(613\) −3.93106e11 −0.112444 −0.0562222 0.998418i \(-0.517906\pi\)
−0.0562222 + 0.998418i \(0.517906\pi\)
\(614\) −2.77448e12 −0.787815
\(615\) −8.98432e11 −0.253249
\(616\) −8.48162e12 −2.37337
\(617\) −1.85080e12 −0.514135 −0.257068 0.966393i \(-0.582756\pi\)
−0.257068 + 0.966393i \(0.582756\pi\)
\(618\) −2.01680e12 −0.556178
\(619\) 1.79639e12 0.491803 0.245902 0.969295i \(-0.420916\pi\)
0.245902 + 0.969295i \(0.420916\pi\)
\(620\) −5.26143e11 −0.143002
\(621\) 9.41448e11 0.254029
\(622\) −4.25954e12 −1.14105
\(623\) 5.12782e12 1.36376
\(624\) −1.09359e11 −0.0288750
\(625\) 1.45788e12 0.382176
\(626\) 1.57349e12 0.409525
\(627\) −1.16353e12 −0.300658
\(628\) −1.12682e12 −0.289093
\(629\) 1.68422e11 0.0429013
\(630\) 5.31775e11 0.134492
\(631\) 5.34615e12 1.34248 0.671242 0.741238i \(-0.265761\pi\)
0.671242 + 0.741238i \(0.265761\pi\)
\(632\) 3.90749e12 0.974250
\(633\) 8.76272e11 0.216931
\(634\) 3.17825e12 0.781244
\(635\) 9.88308e11 0.241218
\(636\) 1.89540e11 0.0459349
\(637\) 1.19987e12 0.288740
\(638\) −4.13740e12 −0.988631
\(639\) −1.64190e12 −0.389576
\(640\) 9.22966e11 0.217458
\(641\) 7.05261e12 1.65002 0.825010 0.565119i \(-0.191170\pi\)
0.825010 + 0.565119i \(0.191170\pi\)
\(642\) −8.17770e11 −0.189987
\(643\) 6.00675e12 1.38577 0.692883 0.721050i \(-0.256340\pi\)
0.692883 + 0.721050i \(0.256340\pi\)
\(644\) 4.21182e12 0.964901
\(645\) −1.10045e10 −0.00250352
\(646\) −9.80869e11 −0.221597
\(647\) 2.10525e12 0.472318 0.236159 0.971714i \(-0.424111\pi\)
0.236159 + 0.971714i \(0.424111\pi\)
\(648\) −5.14987e11 −0.114738
\(649\) 1.04364e12 0.230914
\(650\) −9.93347e11 −0.218268
\(651\) 1.84269e12 0.402104
\(652\) −7.95924e11 −0.172487
\(653\) −1.86207e12 −0.400763 −0.200381 0.979718i \(-0.564218\pi\)
−0.200381 + 0.979718i \(0.564218\pi\)
\(654\) −2.66842e11 −0.0570367
\(655\) −3.77551e12 −0.801475
\(656\) −5.18899e11 −0.109400
\(657\) −7.62216e11 −0.159600
\(658\) 1.98411e12 0.412619
\(659\) −3.37856e12 −0.697826 −0.348913 0.937155i \(-0.613449\pi\)
−0.348913 + 0.937155i \(0.613449\pi\)
\(660\) −1.32814e12 −0.272455
\(661\) −5.46765e12 −1.11402 −0.557011 0.830505i \(-0.688052\pi\)
−0.557011 + 0.830505i \(0.688052\pi\)
\(662\) 3.67070e12 0.742828
\(663\) −1.39622e12 −0.280636
\(664\) −5.86331e12 −1.17054
\(665\) 9.04884e11 0.179430
\(666\) −4.19308e10 −0.00825846
\(667\) 5.69655e12 1.11441
\(668\) −6.53598e11 −0.127004
\(669\) 1.62867e12 0.314351
\(670\) −3.02315e12 −0.579593
\(671\) −3.38772e12 −0.645143
\(672\) −3.77691e12 −0.714455
\(673\) 3.35135e12 0.629727 0.314863 0.949137i \(-0.398041\pi\)
0.314863 + 0.949137i \(0.398041\pi\)
\(674\) 3.68187e12 0.687224
\(675\) −8.07091e11 −0.149643
\(676\) 2.50923e12 0.462147
\(677\) 7.13136e12 1.30474 0.652369 0.757901i \(-0.273775\pi\)
0.652369 + 0.757901i \(0.273775\pi\)
\(678\) −3.88788e12 −0.706610
\(679\) −5.11336e12 −0.923192
\(680\) −3.10435e12 −0.556776
\(681\) −1.85532e10 −0.00330565
\(682\) 3.55587e12 0.629385
\(683\) −1.19390e12 −0.209930 −0.104965 0.994476i \(-0.533473\pi\)
−0.104965 + 0.994476i \(0.533473\pi\)
\(684\) −3.16059e11 −0.0552097
\(685\) −4.27089e12 −0.741158
\(686\) 1.59239e12 0.274530
\(687\) −2.72019e12 −0.465901
\(688\) −6.35577e9 −0.00108149
\(689\) −3.54720e11 −0.0599652
\(690\) −1.41288e12 −0.237292
\(691\) 6.77087e12 1.12978 0.564889 0.825167i \(-0.308919\pi\)
0.564889 + 0.825167i \(0.308919\pi\)
\(692\) 2.45805e12 0.407486
\(693\) 4.65149e12 0.766113
\(694\) −1.61878e11 −0.0264892
\(695\) −4.96774e12 −0.807657
\(696\) −3.11610e12 −0.503350
\(697\) −6.62496e12 −1.06325
\(698\) 2.61421e12 0.416861
\(699\) −8.84449e11 −0.140128
\(700\) −3.61074e12 −0.568401
\(701\) 4.91860e12 0.769326 0.384663 0.923057i \(-0.374318\pi\)
0.384663 + 0.923057i \(0.374318\pi\)
\(702\) 3.47607e11 0.0540221
\(703\) −7.13507e10 −0.0110179
\(704\) −8.64811e12 −1.32692
\(705\) 8.61436e11 0.131332
\(706\) −2.90660e12 −0.440315
\(707\) −5.57058e12 −0.838519
\(708\) 2.83493e11 0.0424026
\(709\) 9.93757e11 0.147697 0.0738486 0.997269i \(-0.476472\pi\)
0.0738486 + 0.997269i \(0.476472\pi\)
\(710\) 2.46408e12 0.363909
\(711\) −2.14295e12 −0.314484
\(712\) 7.45264e12 1.08680
\(713\) −4.89587e12 −0.709459
\(714\) 3.92127e12 0.564656
\(715\) 2.48558e12 0.355673
\(716\) 1.53573e12 0.218376
\(717\) 2.04101e12 0.288409
\(718\) −7.88066e11 −0.110663
\(719\) −1.06186e13 −1.48179 −0.740896 0.671620i \(-0.765599\pi\)
−0.740896 + 0.671620i \(0.765599\pi\)
\(720\) 1.33347e11 0.0184921
\(721\) 1.37196e13 1.89075
\(722\) −4.40500e12 −0.603294
\(723\) 9.78077e11 0.133122
\(724\) −1.60621e12 −0.217260
\(725\) −4.88358e12 −0.656473
\(726\) 6.12285e12 0.817972
\(727\) 6.74440e12 0.895444 0.447722 0.894173i \(-0.352235\pi\)
0.447722 + 0.894173i \(0.352235\pi\)
\(728\) 4.31177e12 0.568937
\(729\) 2.82430e11 0.0370370
\(730\) 1.14390e12 0.149085
\(731\) −8.11463e10 −0.0105109
\(732\) −9.20234e11 −0.118467
\(733\) −5.61091e12 −0.717903 −0.358952 0.933356i \(-0.616866\pi\)
−0.358952 + 0.933356i \(0.616866\pi\)
\(734\) −1.22638e12 −0.155952
\(735\) −1.46307e12 −0.184915
\(736\) 1.00349e13 1.26056
\(737\) −2.64438e13 −3.30157
\(738\) 1.64937e12 0.204675
\(739\) −3.89121e12 −0.479938 −0.239969 0.970781i \(-0.577137\pi\)
−0.239969 + 0.970781i \(0.577137\pi\)
\(740\) −8.14449e10 −0.00998438
\(741\) 5.91498e11 0.0720728
\(742\) 9.96227e11 0.120654
\(743\) 8.15319e12 0.981472 0.490736 0.871308i \(-0.336728\pi\)
0.490736 + 0.871308i \(0.336728\pi\)
\(744\) 2.67812e12 0.320444
\(745\) 5.69772e11 0.0677638
\(746\) 2.34821e12 0.277596
\(747\) 3.21556e12 0.377845
\(748\) −9.79357e12 −1.14389
\(749\) 5.56303e12 0.645868
\(750\) 2.76898e12 0.319554
\(751\) 5.69916e12 0.653779 0.326890 0.945063i \(-0.393999\pi\)
0.326890 + 0.945063i \(0.393999\pi\)
\(752\) 4.97532e11 0.0567337
\(753\) 2.85982e12 0.324161
\(754\) 2.10331e12 0.236991
\(755\) −4.13812e11 −0.0463492
\(756\) 1.26352e12 0.140681
\(757\) 1.69661e13 1.87781 0.938903 0.344181i \(-0.111844\pi\)
0.938903 + 0.344181i \(0.111844\pi\)
\(758\) 1.00522e13 1.10599
\(759\) −1.23586e13 −1.35170
\(760\) 1.31513e12 0.142991
\(761\) 1.54543e13 1.67039 0.835197 0.549951i \(-0.185354\pi\)
0.835197 + 0.549951i \(0.185354\pi\)
\(762\) −1.81437e12 −0.194952
\(763\) 1.81524e12 0.193898
\(764\) −9.52914e12 −1.01189
\(765\) 1.70249e12 0.179725
\(766\) 9.87274e12 1.03612
\(767\) −5.30552e11 −0.0553540
\(768\) −5.85862e12 −0.607673
\(769\) 1.60580e12 0.165586 0.0827929 0.996567i \(-0.473616\pi\)
0.0827929 + 0.996567i \(0.473616\pi\)
\(770\) −6.98074e12 −0.715637
\(771\) −6.04308e12 −0.615904
\(772\) 6.79633e12 0.688647
\(773\) 2.75508e11 0.0277541 0.0138771 0.999904i \(-0.495583\pi\)
0.0138771 + 0.999904i \(0.495583\pi\)
\(774\) 2.02024e10 0.00202334
\(775\) 4.19717e12 0.417925
\(776\) −7.43161e12 −0.735708
\(777\) 2.85242e11 0.0280749
\(778\) 7.63945e12 0.747573
\(779\) 2.80662e12 0.273064
\(780\) 6.75180e11 0.0653121
\(781\) 2.15536e13 2.07296
\(782\) −1.04185e13 −0.996260
\(783\) 1.70894e12 0.162479
\(784\) −8.45011e11 −0.0798804
\(785\) −2.57141e12 −0.241690
\(786\) 6.93121e12 0.647750
\(787\) −1.60435e13 −1.49078 −0.745388 0.666630i \(-0.767736\pi\)
−0.745388 + 0.666630i \(0.767736\pi\)
\(788\) −7.95055e12 −0.734564
\(789\) −4.37035e12 −0.401486
\(790\) 3.21603e12 0.293764
\(791\) 2.64481e13 2.40215
\(792\) 6.76036e12 0.610529
\(793\) 1.72220e12 0.154652
\(794\) 6.87961e12 0.614287
\(795\) 4.32530e11 0.0384029
\(796\) −6.27134e12 −0.553670
\(797\) −1.39687e13 −1.22629 −0.613147 0.789969i \(-0.710097\pi\)
−0.613147 + 0.789969i \(0.710097\pi\)
\(798\) −1.66122e12 −0.145015
\(799\) 6.35216e12 0.551393
\(800\) −8.60281e12 −0.742566
\(801\) −4.08718e12 −0.350815
\(802\) 1.40706e13 1.20096
\(803\) 1.00058e13 0.849242
\(804\) −7.18316e12 −0.606266
\(805\) 9.61137e12 0.806685
\(806\) −1.80768e12 −0.150874
\(807\) −1.27725e13 −1.06009
\(808\) −8.09613e12 −0.668230
\(809\) 1.35440e13 1.11167 0.555837 0.831292i \(-0.312398\pi\)
0.555837 + 0.831292i \(0.312398\pi\)
\(810\) −4.23856e11 −0.0345968
\(811\) −1.41243e12 −0.114650 −0.0573248 0.998356i \(-0.518257\pi\)
−0.0573248 + 0.998356i \(0.518257\pi\)
\(812\) 7.64537e12 0.617158
\(813\) −1.23373e13 −0.990404
\(814\) 5.50435e11 0.0439437
\(815\) −1.81630e12 −0.144204
\(816\) 9.83291e11 0.0776384
\(817\) 3.43771e10 0.00269942
\(818\) −8.37021e12 −0.653652
\(819\) −2.36466e12 −0.183650
\(820\) 3.20368e12 0.247450
\(821\) 2.53017e13 1.94359 0.971796 0.235825i \(-0.0757792\pi\)
0.971796 + 0.235825i \(0.0757792\pi\)
\(822\) 7.84064e12 0.599002
\(823\) −1.45843e13 −1.10812 −0.554058 0.832478i \(-0.686922\pi\)
−0.554058 + 0.832478i \(0.686922\pi\)
\(824\) 1.99397e13 1.50677
\(825\) 1.05949e13 0.796257
\(826\) 1.49005e12 0.111376
\(827\) 1.46399e13 1.08834 0.544168 0.838976i \(-0.316845\pi\)
0.544168 + 0.838976i \(0.316845\pi\)
\(828\) −3.35707e12 −0.248213
\(829\) −1.65806e13 −1.21929 −0.609643 0.792676i \(-0.708687\pi\)
−0.609643 + 0.792676i \(0.708687\pi\)
\(830\) −4.82575e12 −0.352951
\(831\) −1.04467e13 −0.759934
\(832\) 4.39641e12 0.318085
\(833\) −1.07885e13 −0.776355
\(834\) 9.11994e12 0.652747
\(835\) −1.49151e12 −0.106179
\(836\) 4.14898e12 0.293774
\(837\) −1.46874e12 −0.103438
\(838\) 5.65277e12 0.395971
\(839\) 1.08528e13 0.756161 0.378081 0.925773i \(-0.376584\pi\)
0.378081 + 0.925773i \(0.376584\pi\)
\(840\) −5.25758e12 −0.364358
\(841\) −4.16666e12 −0.287214
\(842\) −8.89033e12 −0.609556
\(843\) −1.65272e13 −1.12713
\(844\) −3.12466e12 −0.211964
\(845\) 5.72606e12 0.386368
\(846\) −1.58145e12 −0.106143
\(847\) −4.16518e13 −2.78073
\(848\) 2.49812e11 0.0165895
\(849\) −4.34704e12 −0.287150
\(850\) 8.93161e12 0.586873
\(851\) −7.57863e11 −0.0495345
\(852\) 5.85478e12 0.380656
\(853\) −1.79309e12 −0.115966 −0.0579830 0.998318i \(-0.518467\pi\)
−0.0579830 + 0.998318i \(0.518467\pi\)
\(854\) −4.83678e12 −0.311169
\(855\) −7.21247e11 −0.0461569
\(856\) 8.08517e12 0.514703
\(857\) −3.89475e12 −0.246641 −0.123321 0.992367i \(-0.539354\pi\)
−0.123321 + 0.992367i \(0.539354\pi\)
\(858\) −4.56312e12 −0.287454
\(859\) 2.04353e13 1.28059 0.640296 0.768128i \(-0.278812\pi\)
0.640296 + 0.768128i \(0.278812\pi\)
\(860\) 3.92405e10 0.00244620
\(861\) −1.12202e13 −0.695801
\(862\) 6.38529e12 0.393911
\(863\) 1.13116e13 0.694184 0.347092 0.937831i \(-0.387169\pi\)
0.347092 + 0.937831i \(0.387169\pi\)
\(864\) 3.01042e12 0.183787
\(865\) 5.60927e12 0.340670
\(866\) −5.15896e12 −0.311696
\(867\) 2.94839e12 0.177214
\(868\) −6.57078e12 −0.392897
\(869\) 2.81310e13 1.67338
\(870\) −2.56469e12 −0.151774
\(871\) 1.34431e13 0.791442
\(872\) 2.63823e12 0.154521
\(873\) 4.07565e12 0.237483
\(874\) 4.41371e12 0.255860
\(875\) −1.88365e13 −1.08634
\(876\) 2.71795e12 0.155946
\(877\) −1.74232e13 −0.994554 −0.497277 0.867592i \(-0.665667\pi\)
−0.497277 + 0.867592i \(0.665667\pi\)
\(878\) −1.54284e13 −0.876182
\(879\) 2.01234e13 1.13698
\(880\) −1.75048e12 −0.0983977
\(881\) 2.59628e13 1.45198 0.725990 0.687705i \(-0.241382\pi\)
0.725990 + 0.687705i \(0.241382\pi\)
\(882\) 2.68595e12 0.149448
\(883\) −5.63113e12 −0.311725 −0.155863 0.987779i \(-0.549816\pi\)
−0.155863 + 0.987779i \(0.549816\pi\)
\(884\) 4.97872e12 0.274209
\(885\) 6.46932e11 0.0354498
\(886\) 1.19899e13 0.653679
\(887\) 1.90980e13 1.03593 0.517966 0.855401i \(-0.326690\pi\)
0.517966 + 0.855401i \(0.326690\pi\)
\(888\) 4.14563e11 0.0223734
\(889\) 1.23426e13 0.662747
\(890\) 6.13384e12 0.327701
\(891\) −3.70752e12 −0.197076
\(892\) −5.80760e12 −0.307153
\(893\) −2.69105e12 −0.141609
\(894\) −1.04601e12 −0.0547665
\(895\) 3.50453e12 0.182569
\(896\) 1.15265e13 0.597466
\(897\) 6.28269e12 0.324026
\(898\) 1.50189e13 0.770716
\(899\) −8.88709e12 −0.453775
\(900\) 2.87797e12 0.146216
\(901\) 3.18944e12 0.161233
\(902\) −2.16517e13 −1.08909
\(903\) −1.37431e11 −0.00687843
\(904\) 3.84389e13 1.91431
\(905\) −3.66538e12 −0.181635
\(906\) 7.59690e11 0.0374593
\(907\) 1.92812e13 0.946021 0.473010 0.881057i \(-0.343167\pi\)
0.473010 + 0.881057i \(0.343167\pi\)
\(908\) 6.61581e10 0.00322996
\(909\) 4.44008e12 0.215702
\(910\) 3.54877e12 0.171550
\(911\) −2.56601e13 −1.23431 −0.617156 0.786841i \(-0.711715\pi\)
−0.617156 + 0.786841i \(0.711715\pi\)
\(912\) −4.16564e11 −0.0199391
\(913\) −4.22114e13 −2.01053
\(914\) 2.05784e12 0.0975336
\(915\) −2.09998e12 −0.0990420
\(916\) 9.69981e12 0.455233
\(917\) −4.71509e13 −2.20205
\(918\) −3.12548e12 −0.145253
\(919\) −6.69649e12 −0.309690 −0.154845 0.987939i \(-0.549488\pi\)
−0.154845 + 0.987939i \(0.549488\pi\)
\(920\) 1.39689e13 0.642862
\(921\) −1.50437e13 −0.688946
\(922\) −1.99265e12 −0.0908117
\(923\) −1.09571e13 −0.496922
\(924\) −1.65866e13 −0.748571
\(925\) 6.49706e11 0.0291796
\(926\) 1.35555e13 0.605850
\(927\) −1.09354e13 −0.486379
\(928\) 1.82156e13 0.806264
\(929\) 6.76027e12 0.297778 0.148889 0.988854i \(-0.452430\pi\)
0.148889 + 0.988854i \(0.452430\pi\)
\(930\) 2.20421e12 0.0966228
\(931\) 4.57049e12 0.199384
\(932\) 3.15382e12 0.136919
\(933\) −2.30959e13 −0.997855
\(934\) 1.03372e13 0.444470
\(935\) −2.23490e13 −0.956324
\(936\) −3.43674e12 −0.146354
\(937\) −5.69718e12 −0.241453 −0.120726 0.992686i \(-0.538522\pi\)
−0.120726 + 0.992686i \(0.538522\pi\)
\(938\) −3.77549e13 −1.59243
\(939\) 8.53172e12 0.358131
\(940\) −3.07176e12 −0.128325
\(941\) −3.10428e13 −1.29065 −0.645324 0.763909i \(-0.723278\pi\)
−0.645324 + 0.763909i \(0.723278\pi\)
\(942\) 4.72069e12 0.195333
\(943\) 2.98110e13 1.22765
\(944\) 3.73643e11 0.0153138
\(945\) 2.88336e12 0.117613
\(946\) −2.65202e11 −0.0107663
\(947\) 1.01142e13 0.408653 0.204327 0.978903i \(-0.434500\pi\)
0.204327 + 0.978903i \(0.434500\pi\)
\(948\) 7.64144e12 0.307282
\(949\) −5.08660e12 −0.203577
\(950\) −3.78381e12 −0.150721
\(951\) 1.72330e13 0.683200
\(952\) −3.87689e13 −1.52974
\(953\) 3.44106e13 1.35137 0.675685 0.737190i \(-0.263848\pi\)
0.675685 + 0.737190i \(0.263848\pi\)
\(954\) −7.94052e11 −0.0310371
\(955\) −2.17455e13 −0.845970
\(956\) −7.27796e12 −0.281805
\(957\) −2.24336e13 −0.864560
\(958\) −6.74789e12 −0.258835
\(959\) −5.33374e13 −2.03633
\(960\) −5.36078e12 −0.203708
\(961\) −1.88017e13 −0.711116
\(962\) −2.79823e11 −0.0105340
\(963\) −4.43407e12 −0.166144
\(964\) −3.48768e12 −0.130074
\(965\) 1.55093e13 0.575729
\(966\) −1.76449e13 −0.651961
\(967\) 1.44722e13 0.532251 0.266125 0.963938i \(-0.414256\pi\)
0.266125 + 0.963938i \(0.414256\pi\)
\(968\) −6.05356e13 −2.21601
\(969\) −5.31842e12 −0.193787
\(970\) −6.11654e12 −0.221836
\(971\) −2.63133e12 −0.0949922 −0.0474961 0.998871i \(-0.515124\pi\)
−0.0474961 + 0.998871i \(0.515124\pi\)
\(972\) −1.00710e12 −0.0361890
\(973\) −6.20401e13 −2.21904
\(974\) −8.32197e12 −0.296286
\(975\) −5.38607e12 −0.190876
\(976\) −1.21286e12 −0.0427847
\(977\) −3.44811e13 −1.21075 −0.605376 0.795940i \(-0.706977\pi\)
−0.605376 + 0.795940i \(0.706977\pi\)
\(978\) 3.33442e12 0.116546
\(979\) 5.36534e13 1.86670
\(980\) 5.21709e12 0.180680
\(981\) −1.44686e12 −0.0498787
\(982\) 2.42523e13 0.832246
\(983\) 1.43917e13 0.491612 0.245806 0.969319i \(-0.420947\pi\)
0.245806 + 0.969319i \(0.420947\pi\)
\(984\) −1.63071e13 −0.554496
\(985\) −1.81432e13 −0.614116
\(986\) −1.89118e13 −0.637216
\(987\) 1.07581e13 0.360836
\(988\) −2.10920e12 −0.0704225
\(989\) 3.65142e11 0.0121361
\(990\) 5.56406e12 0.184092
\(991\) −4.60608e13 −1.51705 −0.758525 0.651644i \(-0.774080\pi\)
−0.758525 + 0.651644i \(0.774080\pi\)
\(992\) −1.56553e13 −0.513286
\(993\) 1.99031e13 0.649604
\(994\) 3.07729e13 0.999839
\(995\) −1.43112e13 −0.462884
\(996\) −1.14662e13 −0.369193
\(997\) −4.62562e13 −1.48266 −0.741330 0.671141i \(-0.765804\pi\)
−0.741330 + 0.671141i \(0.765804\pi\)
\(998\) 6.47207e12 0.206517
\(999\) −2.27355e11 −0.00722204
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.1.14 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.14 22 1.1 even 1 trivial