Properties

Label 177.14.a.b.1.17
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+20.8810 q^{2} -729.000 q^{3} -7755.98 q^{4} +27865.9 q^{5} -15222.2 q^{6} +61118.3 q^{7} -333010. q^{8} +531441. q^{9} +O(q^{10})\) \(q+20.8810 q^{2} -729.000 q^{3} -7755.98 q^{4} +27865.9 q^{5} -15222.2 q^{6} +61118.3 q^{7} -333010. q^{8} +531441. q^{9} +581867. q^{10} -3.53045e6 q^{11} +5.65411e6 q^{12} +2.05403e7 q^{13} +1.27621e6 q^{14} -2.03142e7 q^{15} +5.65834e7 q^{16} -1.17268e8 q^{17} +1.10970e7 q^{18} +3.76293e6 q^{19} -2.16127e8 q^{20} -4.45552e7 q^{21} -7.37192e7 q^{22} -6.80717e8 q^{23} +2.42764e8 q^{24} -4.44197e8 q^{25} +4.28902e8 q^{26} -3.87420e8 q^{27} -4.74032e8 q^{28} +3.42738e9 q^{29} -4.24181e8 q^{30} -1.83633e9 q^{31} +3.90954e9 q^{32} +2.57370e9 q^{33} -2.44867e9 q^{34} +1.70311e9 q^{35} -4.12185e9 q^{36} +1.49290e10 q^{37} +7.85738e7 q^{38} -1.49739e10 q^{39} -9.27960e9 q^{40} +2.74461e10 q^{41} -9.30357e8 q^{42} -4.39208e10 q^{43} +2.73821e10 q^{44} +1.48091e10 q^{45} -1.42141e10 q^{46} +4.98609e10 q^{47} -4.12493e10 q^{48} -9.31536e10 q^{49} -9.27528e9 q^{50} +8.54883e10 q^{51} -1.59310e11 q^{52} +1.99807e11 q^{53} -8.08973e9 q^{54} -9.83789e10 q^{55} -2.03530e10 q^{56} -2.74318e9 q^{57} +7.15672e10 q^{58} -4.21805e10 q^{59} +1.57557e11 q^{60} +2.57022e11 q^{61} -3.83444e10 q^{62} +3.24807e10 q^{63} -3.81897e11 q^{64} +5.72374e11 q^{65} +5.37413e10 q^{66} +1.02262e11 q^{67} +9.09528e11 q^{68} +4.96243e11 q^{69} +3.55627e10 q^{70} -1.55726e12 q^{71} -1.76975e11 q^{72} +2.32473e12 q^{73} +3.11732e11 q^{74} +3.23820e11 q^{75} -2.91853e10 q^{76} -2.15775e11 q^{77} -3.12670e11 q^{78} -3.36486e11 q^{79} +1.57675e12 q^{80} +2.82430e11 q^{81} +5.73103e11 q^{82} +1.25533e12 q^{83} +3.45569e11 q^{84} -3.26777e12 q^{85} -9.17110e11 q^{86} -2.49856e12 q^{87} +1.17567e12 q^{88} +4.64185e12 q^{89} +3.09228e11 q^{90} +1.25539e12 q^{91} +5.27963e12 q^{92} +1.33868e12 q^{93} +1.04115e12 q^{94} +1.04857e11 q^{95} -2.85005e12 q^{96} +1.27449e12 q^{97} -1.94514e12 q^{98} -1.87622e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.8810 0.230705 0.115352 0.993325i \(-0.463200\pi\)
0.115352 + 0.993325i \(0.463200\pi\)
\(3\) −729.000 −0.577350
\(4\) −7755.98 −0.946775
\(5\) 27865.9 0.797567 0.398784 0.917045i \(-0.369432\pi\)
0.398784 + 0.917045i \(0.369432\pi\)
\(6\) −15222.2 −0.133197
\(7\) 61118.3 0.196351 0.0981756 0.995169i \(-0.468699\pi\)
0.0981756 + 0.995169i \(0.468699\pi\)
\(8\) −333010. −0.449130
\(9\) 531441. 0.333333
\(10\) 581867. 0.184002
\(11\) −3.53045e6 −0.600865 −0.300433 0.953803i \(-0.597131\pi\)
−0.300433 + 0.953803i \(0.597131\pi\)
\(12\) 5.65411e6 0.546621
\(13\) 2.05403e7 1.18025 0.590127 0.807311i \(-0.299078\pi\)
0.590127 + 0.807311i \(0.299078\pi\)
\(14\) 1.27621e6 0.0452991
\(15\) −2.03142e7 −0.460476
\(16\) 5.65834e7 0.843159
\(17\) −1.17268e8 −1.17831 −0.589157 0.808018i \(-0.700540\pi\)
−0.589157 + 0.808018i \(0.700540\pi\)
\(18\) 1.10970e7 0.0769015
\(19\) 3.76293e6 0.0183497 0.00917483 0.999958i \(-0.497080\pi\)
0.00917483 + 0.999958i \(0.497080\pi\)
\(20\) −2.16127e8 −0.755117
\(21\) −4.45552e7 −0.113363
\(22\) −7.37192e7 −0.138622
\(23\) −6.80717e8 −0.958818 −0.479409 0.877592i \(-0.659149\pi\)
−0.479409 + 0.877592i \(0.659149\pi\)
\(24\) 2.42764e8 0.259305
\(25\) −4.44197e8 −0.363886
\(26\) 4.28902e8 0.272290
\(27\) −3.87420e8 −0.192450
\(28\) −4.74032e8 −0.185901
\(29\) 3.42738e9 1.06998 0.534990 0.844859i \(-0.320315\pi\)
0.534990 + 0.844859i \(0.320315\pi\)
\(30\) −4.24181e8 −0.106234
\(31\) −1.83633e9 −0.371620 −0.185810 0.982586i \(-0.559491\pi\)
−0.185810 + 0.982586i \(0.559491\pi\)
\(32\) 3.90954e9 0.643651
\(33\) 2.57370e9 0.346910
\(34\) −2.44867e9 −0.271843
\(35\) 1.70311e9 0.156603
\(36\) −4.12185e9 −0.315592
\(37\) 1.49290e10 0.956573 0.478287 0.878204i \(-0.341258\pi\)
0.478287 + 0.878204i \(0.341258\pi\)
\(38\) 7.85738e7 0.00423335
\(39\) −1.49739e10 −0.681420
\(40\) −9.27960e9 −0.358211
\(41\) 2.74461e10 0.902373 0.451186 0.892430i \(-0.351001\pi\)
0.451186 + 0.892430i \(0.351001\pi\)
\(42\) −9.30357e8 −0.0261535
\(43\) −4.39208e10 −1.05956 −0.529780 0.848135i \(-0.677725\pi\)
−0.529780 + 0.848135i \(0.677725\pi\)
\(44\) 2.73821e10 0.568885
\(45\) 1.48091e10 0.265856
\(46\) −1.42141e10 −0.221204
\(47\) 4.98609e10 0.674721 0.337361 0.941375i \(-0.390466\pi\)
0.337361 + 0.941375i \(0.390466\pi\)
\(48\) −4.12493e10 −0.486798
\(49\) −9.31536e10 −0.961446
\(50\) −9.27528e9 −0.0839502
\(51\) 8.54883e10 0.680300
\(52\) −1.59310e11 −1.11744
\(53\) 1.99807e11 1.23828 0.619139 0.785282i \(-0.287482\pi\)
0.619139 + 0.785282i \(0.287482\pi\)
\(54\) −8.08973e9 −0.0443991
\(55\) −9.83789e10 −0.479231
\(56\) −2.03530e10 −0.0881873
\(57\) −2.74318e9 −0.0105942
\(58\) 7.15672e10 0.246849
\(59\) −4.21805e10 −0.130189
\(60\) 1.57557e11 0.435967
\(61\) 2.57022e11 0.638743 0.319372 0.947630i \(-0.396528\pi\)
0.319372 + 0.947630i \(0.396528\pi\)
\(62\) −3.83444e10 −0.0857345
\(63\) 3.24807e10 0.0654504
\(64\) −3.81897e11 −0.694666
\(65\) 5.72374e11 0.941332
\(66\) 5.37413e10 0.0800337
\(67\) 1.02262e11 0.138111 0.0690555 0.997613i \(-0.478001\pi\)
0.0690555 + 0.997613i \(0.478001\pi\)
\(68\) 9.09528e11 1.11560
\(69\) 4.96243e11 0.553574
\(70\) 3.55627e10 0.0361291
\(71\) −1.55726e12 −1.44272 −0.721361 0.692560i \(-0.756483\pi\)
−0.721361 + 0.692560i \(0.756483\pi\)
\(72\) −1.76975e11 −0.149710
\(73\) 2.32473e12 1.79793 0.898967 0.438017i \(-0.144319\pi\)
0.898967 + 0.438017i \(0.144319\pi\)
\(74\) 3.11732e11 0.220686
\(75\) 3.23820e11 0.210090
\(76\) −2.91853e10 −0.0173730
\(77\) −2.15775e11 −0.117981
\(78\) −3.12670e11 −0.157207
\(79\) −3.36486e11 −0.155737 −0.0778684 0.996964i \(-0.524811\pi\)
−0.0778684 + 0.996964i \(0.524811\pi\)
\(80\) 1.57675e12 0.672476
\(81\) 2.82430e11 0.111111
\(82\) 5.73103e11 0.208182
\(83\) 1.25533e12 0.421454 0.210727 0.977545i \(-0.432417\pi\)
0.210727 + 0.977545i \(0.432417\pi\)
\(84\) 3.45569e11 0.107330
\(85\) −3.26777e12 −0.939785
\(86\) −9.17110e11 −0.244445
\(87\) −2.49856e12 −0.617753
\(88\) 1.17567e12 0.269867
\(89\) 4.64185e12 0.990048 0.495024 0.868879i \(-0.335159\pi\)
0.495024 + 0.868879i \(0.335159\pi\)
\(90\) 3.09228e11 0.0613342
\(91\) 1.25539e12 0.231744
\(92\) 5.27963e12 0.907785
\(93\) 1.33868e12 0.214555
\(94\) 1.04115e12 0.155661
\(95\) 1.04857e11 0.0146351
\(96\) −2.85005e12 −0.371612
\(97\) 1.27449e12 0.155353 0.0776766 0.996979i \(-0.475250\pi\)
0.0776766 + 0.996979i \(0.475250\pi\)
\(98\) −1.94514e12 −0.221810
\(99\) −1.87622e12 −0.200288
\(100\) 3.44519e12 0.344519
\(101\) 1.32306e12 0.124020 0.0620098 0.998076i \(-0.480249\pi\)
0.0620098 + 0.998076i \(0.480249\pi\)
\(102\) 1.78508e12 0.156948
\(103\) 6.96661e12 0.574883 0.287442 0.957798i \(-0.407195\pi\)
0.287442 + 0.957798i \(0.407195\pi\)
\(104\) −6.84013e12 −0.530087
\(105\) −1.24157e12 −0.0904150
\(106\) 4.17217e12 0.285676
\(107\) −4.60780e12 −0.296824 −0.148412 0.988926i \(-0.547416\pi\)
−0.148412 + 0.988926i \(0.547416\pi\)
\(108\) 3.00483e12 0.182207
\(109\) 1.77365e11 0.0101297 0.00506484 0.999987i \(-0.498388\pi\)
0.00506484 + 0.999987i \(0.498388\pi\)
\(110\) −2.05425e12 −0.110561
\(111\) −1.08832e13 −0.552278
\(112\) 3.45828e12 0.165555
\(113\) 1.41676e12 0.0640155 0.0320077 0.999488i \(-0.489810\pi\)
0.0320077 + 0.999488i \(0.489810\pi\)
\(114\) −5.72803e10 −0.00244413
\(115\) −1.89688e13 −0.764722
\(116\) −2.65827e13 −1.01303
\(117\) 1.09160e13 0.393418
\(118\) −8.80772e11 −0.0300352
\(119\) −7.16721e12 −0.231364
\(120\) 6.76483e12 0.206814
\(121\) −2.20587e13 −0.638961
\(122\) 5.36687e12 0.147361
\(123\) −2.00082e13 −0.520985
\(124\) 1.42425e13 0.351841
\(125\) −4.63939e13 −1.08779
\(126\) 6.78230e11 0.0150997
\(127\) −7.29322e13 −1.54239 −0.771197 0.636597i \(-0.780342\pi\)
−0.771197 + 0.636597i \(0.780342\pi\)
\(128\) −4.00013e13 −0.803913
\(129\) 3.20183e13 0.611737
\(130\) 1.19517e13 0.217170
\(131\) −2.71938e13 −0.470118 −0.235059 0.971981i \(-0.575528\pi\)
−0.235059 + 0.971981i \(0.575528\pi\)
\(132\) −1.99615e13 −0.328446
\(133\) 2.29984e11 0.00360298
\(134\) 2.13533e12 0.0318629
\(135\) −1.07958e13 −0.153492
\(136\) 3.90514e13 0.529216
\(137\) −7.63322e12 −0.0986334 −0.0493167 0.998783i \(-0.515704\pi\)
−0.0493167 + 0.998783i \(0.515704\pi\)
\(138\) 1.03620e13 0.127712
\(139\) −3.56919e12 −0.0419733 −0.0209867 0.999780i \(-0.506681\pi\)
−0.0209867 + 0.999780i \(0.506681\pi\)
\(140\) −1.32093e13 −0.148268
\(141\) −3.63486e13 −0.389551
\(142\) −3.25172e13 −0.332842
\(143\) −7.25165e13 −0.709174
\(144\) 3.00708e13 0.281053
\(145\) 9.55069e13 0.853381
\(146\) 4.85426e13 0.414792
\(147\) 6.79090e13 0.555091
\(148\) −1.15789e14 −0.905660
\(149\) −3.99812e13 −0.299327 −0.149663 0.988737i \(-0.547819\pi\)
−0.149663 + 0.988737i \(0.547819\pi\)
\(150\) 6.76168e12 0.0484687
\(151\) −6.86589e13 −0.471353 −0.235677 0.971832i \(-0.575731\pi\)
−0.235677 + 0.971832i \(0.575731\pi\)
\(152\) −1.25309e12 −0.00824139
\(153\) −6.23210e13 −0.392771
\(154\) −4.50559e12 −0.0272187
\(155\) −5.11709e13 −0.296392
\(156\) 1.16137e14 0.645151
\(157\) 3.38824e14 1.80562 0.902811 0.430037i \(-0.141500\pi\)
0.902811 + 0.430037i \(0.141500\pi\)
\(158\) −7.02617e12 −0.0359292
\(159\) −1.45659e14 −0.714920
\(160\) 1.08943e14 0.513355
\(161\) −4.16043e13 −0.188265
\(162\) 5.89741e12 0.0256338
\(163\) −8.86561e13 −0.370245 −0.185122 0.982715i \(-0.559268\pi\)
−0.185122 + 0.982715i \(0.559268\pi\)
\(164\) −2.12872e14 −0.854344
\(165\) 7.17182e13 0.276684
\(166\) 2.62125e13 0.0972314
\(167\) −1.70881e14 −0.609590 −0.304795 0.952418i \(-0.598588\pi\)
−0.304795 + 0.952418i \(0.598588\pi\)
\(168\) 1.48373e13 0.0509149
\(169\) 1.19029e14 0.392999
\(170\) −6.82343e13 −0.216813
\(171\) 1.99978e12 0.00611655
\(172\) 3.40649e14 1.00316
\(173\) −3.02308e14 −0.857333 −0.428666 0.903463i \(-0.641016\pi\)
−0.428666 + 0.903463i \(0.641016\pi\)
\(174\) −5.21725e13 −0.142518
\(175\) −2.71486e13 −0.0714495
\(176\) −1.99765e14 −0.506625
\(177\) 3.07496e13 0.0751646
\(178\) 9.69265e13 0.228409
\(179\) −2.07521e14 −0.471539 −0.235769 0.971809i \(-0.575761\pi\)
−0.235769 + 0.971809i \(0.575761\pi\)
\(180\) −1.14859e14 −0.251706
\(181\) −6.71548e14 −1.41960 −0.709801 0.704402i \(-0.751215\pi\)
−0.709801 + 0.704402i \(0.751215\pi\)
\(182\) 2.62138e13 0.0534645
\(183\) −1.87369e14 −0.368778
\(184\) 2.26686e14 0.430634
\(185\) 4.16008e14 0.762932
\(186\) 2.79531e13 0.0494989
\(187\) 4.14008e14 0.708008
\(188\) −3.86721e14 −0.638810
\(189\) −2.36785e13 −0.0377878
\(190\) 2.18953e12 0.00337638
\(191\) 1.16600e15 1.73772 0.868861 0.495056i \(-0.164853\pi\)
0.868861 + 0.495056i \(0.164853\pi\)
\(192\) 2.78403e14 0.401065
\(193\) −1.23038e15 −1.71363 −0.856814 0.515625i \(-0.827560\pi\)
−0.856814 + 0.515625i \(0.827560\pi\)
\(194\) 2.66126e13 0.0358407
\(195\) −4.17260e14 −0.543478
\(196\) 7.22498e14 0.910274
\(197\) −1.51806e15 −1.85037 −0.925184 0.379520i \(-0.876089\pi\)
−0.925184 + 0.379520i \(0.876089\pi\)
\(198\) −3.91774e13 −0.0462075
\(199\) 3.24648e12 0.00370567 0.00185284 0.999998i \(-0.499410\pi\)
0.00185284 + 0.999998i \(0.499410\pi\)
\(200\) 1.47922e14 0.163432
\(201\) −7.45491e13 −0.0797385
\(202\) 2.76268e13 0.0286119
\(203\) 2.09476e14 0.210092
\(204\) −6.63046e14 −0.644091
\(205\) 7.64810e14 0.719703
\(206\) 1.45470e14 0.132628
\(207\) −3.61761e14 −0.319606
\(208\) 1.16224e15 0.995141
\(209\) −1.32848e13 −0.0110257
\(210\) −2.59252e13 −0.0208592
\(211\) 1.45830e15 1.13765 0.568827 0.822457i \(-0.307397\pi\)
0.568827 + 0.822457i \(0.307397\pi\)
\(212\) −1.54970e15 −1.17237
\(213\) 1.13524e15 0.832955
\(214\) −9.62155e13 −0.0684787
\(215\) −1.22389e15 −0.845070
\(216\) 1.29015e14 0.0864351
\(217\) −1.12233e14 −0.0729681
\(218\) 3.70356e12 0.00233696
\(219\) −1.69473e15 −1.03804
\(220\) 7.63025e14 0.453724
\(221\) −2.40872e15 −1.39071
\(222\) −2.27252e14 −0.127413
\(223\) −3.58918e15 −1.95440 −0.977199 0.212324i \(-0.931897\pi\)
−0.977199 + 0.212324i \(0.931897\pi\)
\(224\) 2.38944e14 0.126382
\(225\) −2.36065e14 −0.121295
\(226\) 2.95833e13 0.0147687
\(227\) −2.73313e14 −0.132584 −0.0662922 0.997800i \(-0.521117\pi\)
−0.0662922 + 0.997800i \(0.521117\pi\)
\(228\) 2.12760e13 0.0100303
\(229\) −3.13250e15 −1.43536 −0.717679 0.696374i \(-0.754795\pi\)
−0.717679 + 0.696374i \(0.754795\pi\)
\(230\) −3.96087e14 −0.176425
\(231\) 1.57300e14 0.0681162
\(232\) −1.14135e15 −0.480560
\(233\) 9.46506e14 0.387534 0.193767 0.981048i \(-0.437929\pi\)
0.193767 + 0.981048i \(0.437929\pi\)
\(234\) 2.27936e14 0.0907633
\(235\) 1.38942e15 0.538136
\(236\) 3.27152e14 0.123260
\(237\) 2.45299e14 0.0899147
\(238\) −1.49659e14 −0.0533766
\(239\) −2.20035e15 −0.763670 −0.381835 0.924231i \(-0.624708\pi\)
−0.381835 + 0.924231i \(0.624708\pi\)
\(240\) −1.14945e15 −0.388254
\(241\) −2.93638e15 −0.965388 −0.482694 0.875789i \(-0.660342\pi\)
−0.482694 + 0.875789i \(0.660342\pi\)
\(242\) −4.60607e14 −0.147411
\(243\) −2.05891e14 −0.0641500
\(244\) −1.99346e15 −0.604746
\(245\) −2.59580e15 −0.766818
\(246\) −4.17792e14 −0.120194
\(247\) 7.72918e13 0.0216573
\(248\) 6.11516e14 0.166906
\(249\) −9.15135e14 −0.243327
\(250\) −9.68750e14 −0.250958
\(251\) −1.95179e15 −0.492667 −0.246334 0.969185i \(-0.579226\pi\)
−0.246334 + 0.969185i \(0.579226\pi\)
\(252\) −2.51920e14 −0.0619668
\(253\) 2.40324e15 0.576120
\(254\) −1.52290e15 −0.355837
\(255\) 2.38220e15 0.542585
\(256\) 2.29323e15 0.509199
\(257\) 3.36927e15 0.729408 0.364704 0.931124i \(-0.381170\pi\)
0.364704 + 0.931124i \(0.381170\pi\)
\(258\) 6.68573e14 0.141131
\(259\) 9.12432e14 0.187824
\(260\) −4.43932e15 −0.891230
\(261\) 1.82145e15 0.356660
\(262\) −5.67834e14 −0.108458
\(263\) 3.60306e15 0.671366 0.335683 0.941975i \(-0.391033\pi\)
0.335683 + 0.941975i \(0.391033\pi\)
\(264\) −8.57066e14 −0.155808
\(265\) 5.56780e15 0.987610
\(266\) 4.80229e12 0.000831224 0
\(267\) −3.38391e15 −0.571605
\(268\) −7.93143e14 −0.130760
\(269\) 1.04709e16 1.68498 0.842488 0.538715i \(-0.181090\pi\)
0.842488 + 0.538715i \(0.181090\pi\)
\(270\) −2.25427e14 −0.0354113
\(271\) −9.34514e14 −0.143313 −0.0716565 0.997429i \(-0.522829\pi\)
−0.0716565 + 0.997429i \(0.522829\pi\)
\(272\) −6.63542e15 −0.993506
\(273\) −9.15178e14 −0.133798
\(274\) −1.59389e14 −0.0227552
\(275\) 1.56821e15 0.218647
\(276\) −3.84885e15 −0.524110
\(277\) −2.36833e15 −0.315009 −0.157504 0.987518i \(-0.550345\pi\)
−0.157504 + 0.987518i \(0.550345\pi\)
\(278\) −7.45283e13 −0.00968344
\(279\) −9.75901e14 −0.123873
\(280\) −5.67153e14 −0.0703353
\(281\) 3.80118e15 0.460604 0.230302 0.973119i \(-0.426029\pi\)
0.230302 + 0.973119i \(0.426029\pi\)
\(282\) −7.58996e14 −0.0898711
\(283\) −1.32742e16 −1.53602 −0.768009 0.640439i \(-0.778753\pi\)
−0.768009 + 0.640439i \(0.778753\pi\)
\(284\) 1.20781e16 1.36593
\(285\) −7.64410e13 −0.00844958
\(286\) −1.51422e15 −0.163610
\(287\) 1.67746e15 0.177182
\(288\) 2.07769e15 0.214550
\(289\) 3.84718e15 0.388425
\(290\) 1.99428e15 0.196879
\(291\) −9.29103e14 −0.0896932
\(292\) −1.80306e16 −1.70224
\(293\) −1.34267e16 −1.23973 −0.619867 0.784707i \(-0.712814\pi\)
−0.619867 + 0.784707i \(0.712814\pi\)
\(294\) 1.41801e15 0.128062
\(295\) −1.17540e15 −0.103834
\(296\) −4.97149e15 −0.429626
\(297\) 1.36777e15 0.115637
\(298\) −8.34848e14 −0.0690560
\(299\) −1.39822e16 −1.13165
\(300\) −2.51154e15 −0.198908
\(301\) −2.68436e15 −0.208046
\(302\) −1.43367e15 −0.108743
\(303\) −9.64510e14 −0.0716027
\(304\) 2.12920e14 0.0154717
\(305\) 7.16214e15 0.509441
\(306\) −1.30132e15 −0.0906142
\(307\) −1.64480e16 −1.12128 −0.560640 0.828060i \(-0.689445\pi\)
−0.560640 + 0.828060i \(0.689445\pi\)
\(308\) 1.67355e15 0.111701
\(309\) −5.07866e15 −0.331909
\(310\) −1.06850e15 −0.0683791
\(311\) −2.51091e15 −0.157358 −0.0786788 0.996900i \(-0.525070\pi\)
−0.0786788 + 0.996900i \(0.525070\pi\)
\(312\) 4.98645e15 0.306046
\(313\) −1.97719e16 −1.18853 −0.594264 0.804270i \(-0.702556\pi\)
−0.594264 + 0.804270i \(0.702556\pi\)
\(314\) 7.07499e15 0.416565
\(315\) 9.05104e14 0.0522011
\(316\) 2.60978e15 0.147448
\(317\) −3.53817e16 −1.95837 −0.979183 0.202979i \(-0.934938\pi\)
−0.979183 + 0.202979i \(0.934938\pi\)
\(318\) −3.04151e15 −0.164935
\(319\) −1.21002e16 −0.642914
\(320\) −1.06419e16 −0.554043
\(321\) 3.35909e15 0.171372
\(322\) −8.68739e14 −0.0434336
\(323\) −4.41271e14 −0.0216217
\(324\) −2.19052e15 −0.105197
\(325\) −9.12395e15 −0.429478
\(326\) −1.85123e15 −0.0854172
\(327\) −1.29299e14 −0.00584837
\(328\) −9.13983e15 −0.405283
\(329\) 3.04741e15 0.132482
\(330\) 1.49755e15 0.0638323
\(331\) 1.42799e16 0.596818 0.298409 0.954438i \(-0.403544\pi\)
0.298409 + 0.954438i \(0.403544\pi\)
\(332\) −9.73632e15 −0.399022
\(333\) 7.93386e15 0.318858
\(334\) −3.56817e15 −0.140635
\(335\) 2.84962e15 0.110153
\(336\) −2.52109e15 −0.0955834
\(337\) 4.09546e15 0.152303 0.0761514 0.997096i \(-0.475737\pi\)
0.0761514 + 0.997096i \(0.475737\pi\)
\(338\) 2.48545e15 0.0906666
\(339\) −1.03281e15 −0.0369594
\(340\) 2.53448e16 0.889765
\(341\) 6.48306e15 0.223294
\(342\) 4.17573e13 0.00141112
\(343\) −1.16151e16 −0.385132
\(344\) 1.46261e16 0.475880
\(345\) 1.38282e16 0.441512
\(346\) −6.31249e15 −0.197791
\(347\) −5.20554e16 −1.60075 −0.800377 0.599497i \(-0.795367\pi\)
−0.800377 + 0.599497i \(0.795367\pi\)
\(348\) 1.93788e16 0.584873
\(349\) 1.93726e16 0.573882 0.286941 0.957948i \(-0.407362\pi\)
0.286941 + 0.957948i \(0.407362\pi\)
\(350\) −5.66889e14 −0.0164837
\(351\) −7.95774e15 −0.227140
\(352\) −1.38024e16 −0.386747
\(353\) −3.79937e16 −1.04514 −0.522572 0.852595i \(-0.675027\pi\)
−0.522572 + 0.852595i \(0.675027\pi\)
\(354\) 6.42083e14 0.0173408
\(355\) −4.33944e16 −1.15067
\(356\) −3.60021e16 −0.937353
\(357\) 5.22490e15 0.133578
\(358\) −4.33325e15 −0.108786
\(359\) −2.18276e15 −0.0538136 −0.0269068 0.999638i \(-0.508566\pi\)
−0.0269068 + 0.999638i \(0.508566\pi\)
\(360\) −4.93156e15 −0.119404
\(361\) −4.20388e16 −0.999663
\(362\) −1.40226e16 −0.327509
\(363\) 1.60808e16 0.368904
\(364\) −9.73677e15 −0.219410
\(365\) 6.47805e16 1.43397
\(366\) −3.91245e15 −0.0850789
\(367\) 4.35444e16 0.930256 0.465128 0.885243i \(-0.346008\pi\)
0.465128 + 0.885243i \(0.346008\pi\)
\(368\) −3.85173e16 −0.808436
\(369\) 1.45860e16 0.300791
\(370\) 8.68667e15 0.176012
\(371\) 1.22119e16 0.243137
\(372\) −1.03828e16 −0.203136
\(373\) 5.44789e16 1.04742 0.523710 0.851896i \(-0.324547\pi\)
0.523710 + 0.851896i \(0.324547\pi\)
\(374\) 8.64490e15 0.163341
\(375\) 3.38211e16 0.628037
\(376\) −1.66042e16 −0.303038
\(377\) 7.03995e16 1.26285
\(378\) −4.94430e14 −0.00871782
\(379\) 5.34271e15 0.0925991 0.0462995 0.998928i \(-0.485257\pi\)
0.0462995 + 0.998928i \(0.485257\pi\)
\(380\) −8.13272e14 −0.0138561
\(381\) 5.31676e16 0.890501
\(382\) 2.43472e16 0.400900
\(383\) 9.80659e16 1.58754 0.793772 0.608215i \(-0.208114\pi\)
0.793772 + 0.608215i \(0.208114\pi\)
\(384\) 2.91609e16 0.464140
\(385\) −6.01275e15 −0.0940975
\(386\) −2.56916e16 −0.395342
\(387\) −2.33413e16 −0.353187
\(388\) −9.88492e15 −0.147085
\(389\) 9.92135e16 1.45177 0.725886 0.687815i \(-0.241430\pi\)
0.725886 + 0.687815i \(0.241430\pi\)
\(390\) −8.71281e15 −0.125383
\(391\) 7.98263e16 1.12979
\(392\) 3.10211e16 0.431814
\(393\) 1.98243e16 0.271422
\(394\) −3.16986e16 −0.426888
\(395\) −9.37648e15 −0.124211
\(396\) 1.45520e16 0.189628
\(397\) 1.17008e17 1.49995 0.749974 0.661467i \(-0.230066\pi\)
0.749974 + 0.661467i \(0.230066\pi\)
\(398\) 6.77897e13 0.000854916 0
\(399\) −1.67658e14 −0.00208018
\(400\) −2.51342e16 −0.306814
\(401\) −3.54991e16 −0.426362 −0.213181 0.977013i \(-0.568382\pi\)
−0.213181 + 0.977013i \(0.568382\pi\)
\(402\) −1.55666e15 −0.0183960
\(403\) −3.77188e16 −0.438606
\(404\) −1.02616e16 −0.117419
\(405\) 7.87014e15 0.0886186
\(406\) 4.37406e15 0.0484692
\(407\) −5.27059e16 −0.574772
\(408\) −2.84684e16 −0.305543
\(409\) 1.03752e17 1.09596 0.547981 0.836491i \(-0.315396\pi\)
0.547981 + 0.836491i \(0.315396\pi\)
\(410\) 1.59700e16 0.166039
\(411\) 5.56462e15 0.0569460
\(412\) −5.40329e16 −0.544285
\(413\) −2.57800e15 −0.0255628
\(414\) −7.55393e15 −0.0737345
\(415\) 3.49808e16 0.336138
\(416\) 8.03031e16 0.759671
\(417\) 2.60194e15 0.0242333
\(418\) −2.77401e14 −0.00254367
\(419\) −8.02079e16 −0.724146 −0.362073 0.932150i \(-0.617931\pi\)
−0.362073 + 0.932150i \(0.617931\pi\)
\(420\) 9.62959e15 0.0856027
\(421\) −9.31693e16 −0.815529 −0.407765 0.913087i \(-0.633692\pi\)
−0.407765 + 0.913087i \(0.633692\pi\)
\(422\) 3.04507e16 0.262462
\(423\) 2.64982e16 0.224907
\(424\) −6.65378e16 −0.556148
\(425\) 5.20901e16 0.428772
\(426\) 2.37050e16 0.192167
\(427\) 1.57087e16 0.125418
\(428\) 3.57381e16 0.281026
\(429\) 5.28645e16 0.409442
\(430\) −2.55561e16 −0.194962
\(431\) −9.15688e15 −0.0688090 −0.0344045 0.999408i \(-0.510953\pi\)
−0.0344045 + 0.999408i \(0.510953\pi\)
\(432\) −2.19216e16 −0.162266
\(433\) 2.30944e17 1.68397 0.841985 0.539500i \(-0.181387\pi\)
0.841985 + 0.539500i \(0.181387\pi\)
\(434\) −2.34354e15 −0.0168341
\(435\) −6.96246e16 −0.492700
\(436\) −1.37564e15 −0.00959053
\(437\) −2.56149e15 −0.0175940
\(438\) −3.53876e16 −0.239480
\(439\) 1.64700e16 0.109818 0.0549089 0.998491i \(-0.482513\pi\)
0.0549089 + 0.998491i \(0.482513\pi\)
\(440\) 3.27611e16 0.215237
\(441\) −4.95056e16 −0.320482
\(442\) −5.02965e16 −0.320843
\(443\) 6.01390e15 0.0378035 0.0189017 0.999821i \(-0.493983\pi\)
0.0189017 + 0.999821i \(0.493983\pi\)
\(444\) 8.44100e16 0.522883
\(445\) 1.29349e17 0.789630
\(446\) −7.49456e16 −0.450889
\(447\) 2.91463e16 0.172816
\(448\) −2.33409e16 −0.136399
\(449\) −3.81409e16 −0.219680 −0.109840 0.993949i \(-0.535034\pi\)
−0.109840 + 0.993949i \(0.535034\pi\)
\(450\) −4.92926e15 −0.0279834
\(451\) −9.68971e16 −0.542205
\(452\) −1.09883e16 −0.0606083
\(453\) 5.00523e16 0.272136
\(454\) −5.70705e15 −0.0305878
\(455\) 3.49825e16 0.184832
\(456\) 9.13505e14 0.00475817
\(457\) −7.74185e16 −0.397548 −0.198774 0.980045i \(-0.563696\pi\)
−0.198774 + 0.980045i \(0.563696\pi\)
\(458\) −6.54097e16 −0.331144
\(459\) 4.54320e16 0.226767
\(460\) 1.47122e17 0.724020
\(461\) −1.57961e17 −0.766466 −0.383233 0.923652i \(-0.625189\pi\)
−0.383233 + 0.923652i \(0.625189\pi\)
\(462\) 3.28458e15 0.0157147
\(463\) 2.66714e17 1.25826 0.629129 0.777301i \(-0.283412\pi\)
0.629129 + 0.777301i \(0.283412\pi\)
\(464\) 1.93933e17 0.902163
\(465\) 3.73036e16 0.171122
\(466\) 1.97640e16 0.0894059
\(467\) 2.59454e17 1.15745 0.578724 0.815524i \(-0.303551\pi\)
0.578724 + 0.815524i \(0.303551\pi\)
\(468\) −8.46641e16 −0.372478
\(469\) 6.25008e15 0.0271183
\(470\) 2.90124e16 0.124150
\(471\) −2.47003e17 −1.04248
\(472\) 1.40465e16 0.0584718
\(473\) 1.55060e17 0.636653
\(474\) 5.12208e15 0.0207437
\(475\) −1.67148e15 −0.00667719
\(476\) 5.55888e16 0.219049
\(477\) 1.06186e17 0.412759
\(478\) −4.59455e16 −0.176182
\(479\) −4.56981e17 −1.72869 −0.864345 0.502900i \(-0.832267\pi\)
−0.864345 + 0.502900i \(0.832267\pi\)
\(480\) −7.94191e16 −0.296386
\(481\) 3.06646e17 1.12900
\(482\) −6.13146e16 −0.222719
\(483\) 3.03295e16 0.108695
\(484\) 1.71087e17 0.604952
\(485\) 3.55148e16 0.123905
\(486\) −4.29921e15 −0.0147997
\(487\) −1.94911e17 −0.662062 −0.331031 0.943620i \(-0.607396\pi\)
−0.331031 + 0.943620i \(0.607396\pi\)
\(488\) −8.55908e16 −0.286879
\(489\) 6.46303e16 0.213761
\(490\) −5.42030e16 −0.176908
\(491\) −1.70429e17 −0.548926 −0.274463 0.961598i \(-0.588500\pi\)
−0.274463 + 0.961598i \(0.588500\pi\)
\(492\) 1.55183e17 0.493256
\(493\) −4.01922e17 −1.26077
\(494\) 1.61393e15 0.00499643
\(495\) −5.22826e16 −0.159744
\(496\) −1.03906e17 −0.313335
\(497\) −9.51771e16 −0.283280
\(498\) −1.91089e16 −0.0561366
\(499\) −1.61294e17 −0.467698 −0.233849 0.972273i \(-0.575132\pi\)
−0.233849 + 0.972273i \(0.575132\pi\)
\(500\) 3.59830e17 1.02989
\(501\) 1.24573e17 0.351947
\(502\) −4.07553e16 −0.113661
\(503\) 3.85274e17 1.06066 0.530332 0.847790i \(-0.322067\pi\)
0.530332 + 0.847790i \(0.322067\pi\)
\(504\) −1.08164e16 −0.0293958
\(505\) 3.68682e16 0.0989140
\(506\) 5.01820e16 0.132914
\(507\) −8.67725e16 −0.226898
\(508\) 5.65661e17 1.46030
\(509\) −3.52611e17 −0.898732 −0.449366 0.893348i \(-0.648350\pi\)
−0.449366 + 0.893348i \(0.648350\pi\)
\(510\) 4.97428e16 0.125177
\(511\) 1.42083e17 0.353027
\(512\) 3.75576e17 0.921388
\(513\) −1.45784e15 −0.00353139
\(514\) 7.03537e16 0.168278
\(515\) 1.94131e17 0.458508
\(516\) −2.48333e17 −0.579178
\(517\) −1.76031e17 −0.405417
\(518\) 1.90525e16 0.0433320
\(519\) 2.20382e17 0.494981
\(520\) −1.90606e17 −0.422780
\(521\) −6.82893e16 −0.149592 −0.0747959 0.997199i \(-0.523831\pi\)
−0.0747959 + 0.997199i \(0.523831\pi\)
\(522\) 3.80337e16 0.0822831
\(523\) 4.17689e17 0.892466 0.446233 0.894917i \(-0.352765\pi\)
0.446233 + 0.894917i \(0.352765\pi\)
\(524\) 2.10915e17 0.445096
\(525\) 1.97913e16 0.0412514
\(526\) 7.52356e16 0.154887
\(527\) 2.15343e17 0.437886
\(528\) 1.45629e17 0.292500
\(529\) −4.06601e16 −0.0806690
\(530\) 1.16261e17 0.227846
\(531\) −2.24165e16 −0.0433963
\(532\) −1.78375e15 −0.00341121
\(533\) 5.63752e17 1.06503
\(534\) −7.06594e16 −0.131872
\(535\) −1.28400e17 −0.236737
\(536\) −3.40543e16 −0.0620298
\(537\) 1.51283e17 0.272243
\(538\) 2.18643e17 0.388732
\(539\) 3.28874e17 0.577700
\(540\) 8.37321e16 0.145322
\(541\) −2.16614e17 −0.371454 −0.185727 0.982601i \(-0.559464\pi\)
−0.185727 + 0.982601i \(0.559464\pi\)
\(542\) −1.95136e16 −0.0330630
\(543\) 4.89559e17 0.819607
\(544\) −4.58463e17 −0.758423
\(545\) 4.94243e15 0.00807910
\(546\) −1.91098e16 −0.0308677
\(547\) −3.36177e17 −0.536600 −0.268300 0.963335i \(-0.586462\pi\)
−0.268300 + 0.963335i \(0.586462\pi\)
\(548\) 5.92031e16 0.0933837
\(549\) 1.36592e17 0.212914
\(550\) 3.27459e16 0.0504428
\(551\) 1.28970e16 0.0196338
\(552\) −1.65254e17 −0.248627
\(553\) −2.05655e16 −0.0305791
\(554\) −4.94530e16 −0.0726740
\(555\) −3.03270e17 −0.440479
\(556\) 2.76826e16 0.0397393
\(557\) −9.72448e17 −1.37977 −0.689886 0.723918i \(-0.742339\pi\)
−0.689886 + 0.723918i \(0.742339\pi\)
\(558\) −2.03778e16 −0.0285782
\(559\) −9.02147e17 −1.25055
\(560\) 9.63680e16 0.132042
\(561\) −3.01812e17 −0.408769
\(562\) 7.93724e16 0.106263
\(563\) 1.04329e18 1.38070 0.690352 0.723474i \(-0.257456\pi\)
0.690352 + 0.723474i \(0.257456\pi\)
\(564\) 2.81919e17 0.368817
\(565\) 3.94791e16 0.0510567
\(566\) −2.77179e17 −0.354367
\(567\) 1.72616e16 0.0218168
\(568\) 5.18584e17 0.647969
\(569\) −6.01984e17 −0.743627 −0.371813 0.928308i \(-0.621264\pi\)
−0.371813 + 0.928308i \(0.621264\pi\)
\(570\) −1.59616e15 −0.00194936
\(571\) 6.04687e17 0.730123 0.365061 0.930983i \(-0.381048\pi\)
0.365061 + 0.930983i \(0.381048\pi\)
\(572\) 5.62437e17 0.671428
\(573\) −8.50011e17 −1.00327
\(574\) 3.50270e16 0.0408767
\(575\) 3.02373e17 0.348901
\(576\) −2.02955e17 −0.231555
\(577\) −4.15422e17 −0.468648 −0.234324 0.972159i \(-0.575288\pi\)
−0.234324 + 0.972159i \(0.575288\pi\)
\(578\) 8.03330e16 0.0896114
\(579\) 8.96947e17 0.989364
\(580\) −7.40750e17 −0.807960
\(581\) 7.67236e16 0.0827530
\(582\) −1.94006e16 −0.0206926
\(583\) −7.05409e17 −0.744038
\(584\) −7.74157e17 −0.807506
\(585\) 3.04183e17 0.313777
\(586\) −2.80362e17 −0.286013
\(587\) −3.35130e17 −0.338116 −0.169058 0.985606i \(-0.554072\pi\)
−0.169058 + 0.985606i \(0.554072\pi\)
\(588\) −5.26701e17 −0.525547
\(589\) −6.90999e15 −0.00681911
\(590\) −2.45435e16 −0.0239551
\(591\) 1.10666e18 1.06831
\(592\) 8.44732e17 0.806543
\(593\) 1.79338e17 0.169363 0.0846814 0.996408i \(-0.473013\pi\)
0.0846814 + 0.996408i \(0.473013\pi\)
\(594\) 2.85603e16 0.0266779
\(595\) −1.99720e17 −0.184528
\(596\) 3.10094e17 0.283395
\(597\) −2.36668e15 −0.00213947
\(598\) −2.91961e17 −0.261076
\(599\) −5.06562e17 −0.448083 −0.224042 0.974580i \(-0.571925\pi\)
−0.224042 + 0.974580i \(0.571925\pi\)
\(600\) −1.07835e17 −0.0943577
\(601\) 2.32054e17 0.200865 0.100433 0.994944i \(-0.467977\pi\)
0.100433 + 0.994944i \(0.467977\pi\)
\(602\) −5.60522e16 −0.0479971
\(603\) 5.43463e16 0.0460370
\(604\) 5.32517e17 0.446266
\(605\) −6.14683e17 −0.509614
\(606\) −2.01399e16 −0.0165191
\(607\) −6.05840e17 −0.491622 −0.245811 0.969318i \(-0.579054\pi\)
−0.245811 + 0.969318i \(0.579054\pi\)
\(608\) 1.47113e16 0.0118108
\(609\) −1.52708e17 −0.121297
\(610\) 1.49553e17 0.117530
\(611\) 1.02416e18 0.796342
\(612\) 4.83360e17 0.371866
\(613\) −8.95906e17 −0.681976 −0.340988 0.940068i \(-0.610762\pi\)
−0.340988 + 0.940068i \(0.610762\pi\)
\(614\) −3.43451e17 −0.258684
\(615\) −5.57546e17 −0.415521
\(616\) 7.18551e16 0.0529887
\(617\) 1.60375e18 1.17026 0.585132 0.810938i \(-0.301043\pi\)
0.585132 + 0.810938i \(0.301043\pi\)
\(618\) −1.06047e17 −0.0765729
\(619\) −2.18879e18 −1.56392 −0.781961 0.623328i \(-0.785780\pi\)
−0.781961 + 0.623328i \(0.785780\pi\)
\(620\) 3.96881e17 0.280617
\(621\) 2.63724e17 0.184525
\(622\) −5.24302e16 −0.0363031
\(623\) 2.83702e17 0.194397
\(624\) −8.47274e17 −0.574545
\(625\) −7.50572e17 −0.503701
\(626\) −4.12856e17 −0.274199
\(627\) 9.68464e15 0.00636568
\(628\) −2.62792e18 −1.70952
\(629\) −1.75069e18 −1.12714
\(630\) 1.88995e16 0.0120430
\(631\) 3.75058e17 0.236541 0.118271 0.992981i \(-0.462265\pi\)
0.118271 + 0.992981i \(0.462265\pi\)
\(632\) 1.12053e17 0.0699461
\(633\) −1.06310e18 −0.656825
\(634\) −7.38806e17 −0.451804
\(635\) −2.03232e18 −1.23016
\(636\) 1.12973e18 0.676868
\(637\) −1.91340e18 −1.13475
\(638\) −2.52664e17 −0.148323
\(639\) −8.27593e17 −0.480907
\(640\) −1.11467e18 −0.641175
\(641\) −4.07307e17 −0.231924 −0.115962 0.993254i \(-0.536995\pi\)
−0.115962 + 0.993254i \(0.536995\pi\)
\(642\) 7.01411e16 0.0395362
\(643\) −1.69566e18 −0.946169 −0.473084 0.881017i \(-0.656859\pi\)
−0.473084 + 0.881017i \(0.656859\pi\)
\(644\) 3.22682e17 0.178245
\(645\) 8.92217e17 0.487901
\(646\) −9.21419e15 −0.00498822
\(647\) 6.79188e16 0.0364009 0.0182004 0.999834i \(-0.494206\pi\)
0.0182004 + 0.999834i \(0.494206\pi\)
\(648\) −9.40518e16 −0.0499033
\(649\) 1.48916e17 0.0782260
\(650\) −1.90517e17 −0.0990826
\(651\) 8.18180e16 0.0421282
\(652\) 6.87615e17 0.350539
\(653\) 4.22685e17 0.213345 0.106672 0.994294i \(-0.465980\pi\)
0.106672 + 0.994294i \(0.465980\pi\)
\(654\) −2.69989e15 −0.00134925
\(655\) −7.57779e17 −0.374950
\(656\) 1.55300e18 0.760844
\(657\) 1.23546e18 0.599311
\(658\) 6.36330e16 0.0305643
\(659\) −3.92987e18 −1.86906 −0.934529 0.355888i \(-0.884179\pi\)
−0.934529 + 0.355888i \(0.884179\pi\)
\(660\) −5.56245e17 −0.261958
\(661\) −1.79698e18 −0.837981 −0.418990 0.907991i \(-0.637616\pi\)
−0.418990 + 0.907991i \(0.637616\pi\)
\(662\) 2.98178e17 0.137689
\(663\) 1.75596e18 0.802927
\(664\) −4.18037e17 −0.189288
\(665\) 6.40870e15 0.00287362
\(666\) 1.65667e17 0.0735620
\(667\) −2.33308e18 −1.02592
\(668\) 1.32535e18 0.577145
\(669\) 2.61651e18 1.12837
\(670\) 5.95029e16 0.0254128
\(671\) −9.07402e17 −0.383799
\(672\) −1.74190e17 −0.0729665
\(673\) −1.61201e18 −0.668760 −0.334380 0.942438i \(-0.608527\pi\)
−0.334380 + 0.942438i \(0.608527\pi\)
\(674\) 8.55172e16 0.0351370
\(675\) 1.72091e17 0.0700299
\(676\) −9.23191e17 −0.372081
\(677\) 4.87247e17 0.194502 0.0972508 0.995260i \(-0.468995\pi\)
0.0972508 + 0.995260i \(0.468995\pi\)
\(678\) −2.15662e16 −0.00852670
\(679\) 7.78946e16 0.0305038
\(680\) 1.08820e18 0.422086
\(681\) 1.99245e17 0.0765477
\(682\) 1.35373e17 0.0515149
\(683\) −2.76053e18 −1.04054 −0.520268 0.854003i \(-0.674168\pi\)
−0.520268 + 0.854003i \(0.674168\pi\)
\(684\) −1.55102e16 −0.00579100
\(685\) −2.12706e17 −0.0786668
\(686\) −2.42534e17 −0.0888518
\(687\) 2.28359e18 0.828704
\(688\) −2.48519e18 −0.893377
\(689\) 4.10410e18 1.46148
\(690\) 2.88747e17 0.101859
\(691\) 2.87559e17 0.100489 0.0502447 0.998737i \(-0.484000\pi\)
0.0502447 + 0.998737i \(0.484000\pi\)
\(692\) 2.34469e18 0.811702
\(693\) −1.14672e17 −0.0393269
\(694\) −1.08697e18 −0.369301
\(695\) −9.94586e16 −0.0334766
\(696\) 8.32045e17 0.277451
\(697\) −3.21855e18 −1.06328
\(698\) 4.04519e17 0.132397
\(699\) −6.90003e17 −0.223743
\(700\) 2.10564e17 0.0676467
\(701\) −2.75660e17 −0.0877418 −0.0438709 0.999037i \(-0.513969\pi\)
−0.0438709 + 0.999037i \(0.513969\pi\)
\(702\) −1.66166e17 −0.0524022
\(703\) 5.61767e16 0.0175528
\(704\) 1.34827e18 0.417401
\(705\) −1.01289e18 −0.310693
\(706\) −7.93347e17 −0.241120
\(707\) 8.08630e16 0.0243514
\(708\) −2.38493e17 −0.0711640
\(709\) −2.00180e18 −0.591862 −0.295931 0.955209i \(-0.595630\pi\)
−0.295931 + 0.955209i \(0.595630\pi\)
\(710\) −9.06119e17 −0.265464
\(711\) −1.78823e17 −0.0519123
\(712\) −1.54578e18 −0.444660
\(713\) 1.25002e18 0.356316
\(714\) 1.09101e17 0.0308170
\(715\) −2.02073e18 −0.565614
\(716\) 1.60953e18 0.446441
\(717\) 1.60406e18 0.440905
\(718\) −4.55782e16 −0.0124151
\(719\) 2.24291e18 0.605444 0.302722 0.953079i \(-0.402105\pi\)
0.302722 + 0.953079i \(0.402105\pi\)
\(720\) 8.37948e17 0.224159
\(721\) 4.25787e17 0.112879
\(722\) −8.77813e17 −0.230627
\(723\) 2.14062e18 0.557367
\(724\) 5.20852e18 1.34404
\(725\) −1.52243e18 −0.389351
\(726\) 3.35782e17 0.0851079
\(727\) 7.17739e18 1.80299 0.901494 0.432792i \(-0.142472\pi\)
0.901494 + 0.432792i \(0.142472\pi\)
\(728\) −4.18057e17 −0.104083
\(729\) 1.50095e17 0.0370370
\(730\) 1.35268e18 0.330824
\(731\) 5.15050e18 1.24849
\(732\) 1.45323e18 0.349150
\(733\) −3.13330e18 −0.746150 −0.373075 0.927801i \(-0.621697\pi\)
−0.373075 + 0.927801i \(0.621697\pi\)
\(734\) 9.09250e17 0.214614
\(735\) 1.89234e18 0.442723
\(736\) −2.66129e18 −0.617144
\(737\) −3.61031e17 −0.0829862
\(738\) 3.04570e17 0.0693939
\(739\) −6.97251e18 −1.57471 −0.787354 0.616501i \(-0.788550\pi\)
−0.787354 + 0.616501i \(0.788550\pi\)
\(740\) −3.22655e18 −0.722325
\(741\) −5.63458e16 −0.0125038
\(742\) 2.54996e17 0.0560929
\(743\) −1.09913e18 −0.239674 −0.119837 0.992794i \(-0.538237\pi\)
−0.119837 + 0.992794i \(0.538237\pi\)
\(744\) −4.45795e17 −0.0963632
\(745\) −1.11411e18 −0.238733
\(746\) 1.13757e18 0.241645
\(747\) 6.67134e17 0.140485
\(748\) −3.21104e18 −0.670325
\(749\) −2.81621e17 −0.0582818
\(750\) 7.06219e17 0.144891
\(751\) 5.70536e17 0.116044 0.0580221 0.998315i \(-0.481521\pi\)
0.0580221 + 0.998315i \(0.481521\pi\)
\(752\) 2.82130e18 0.568897
\(753\) 1.42285e18 0.284442
\(754\) 1.47001e18 0.291345
\(755\) −1.91324e18 −0.375936
\(756\) 1.83650e17 0.0357766
\(757\) −7.79524e18 −1.50559 −0.752794 0.658256i \(-0.771295\pi\)
−0.752794 + 0.658256i \(0.771295\pi\)
\(758\) 1.11561e17 0.0213630
\(759\) −1.75196e18 −0.332623
\(760\) −3.49185e16 −0.00657306
\(761\) −6.74460e18 −1.25880 −0.629398 0.777083i \(-0.716699\pi\)
−0.629398 + 0.777083i \(0.716699\pi\)
\(762\) 1.11019e18 0.205443
\(763\) 1.08402e16 0.00198898
\(764\) −9.04345e18 −1.64523
\(765\) −1.73663e18 −0.313262
\(766\) 2.04771e18 0.366254
\(767\) −8.66402e17 −0.153656
\(768\) −1.67176e18 −0.293986
\(769\) 5.75544e17 0.100359 0.0501796 0.998740i \(-0.484021\pi\)
0.0501796 + 0.998740i \(0.484021\pi\)
\(770\) −1.25552e17 −0.0217087
\(771\) −2.45620e18 −0.421124
\(772\) 9.54281e18 1.62242
\(773\) 9.29101e18 1.56638 0.783188 0.621785i \(-0.213592\pi\)
0.783188 + 0.621785i \(0.213592\pi\)
\(774\) −4.87390e17 −0.0814818
\(775\) 8.15692e17 0.135228
\(776\) −4.24418e17 −0.0697738
\(777\) −6.65163e17 −0.108440
\(778\) 2.07168e18 0.334931
\(779\) 1.03278e17 0.0165582
\(780\) 3.23626e18 0.514552
\(781\) 5.49783e18 0.866881
\(782\) 1.66685e18 0.260647
\(783\) −1.32784e18 −0.205918
\(784\) −5.27095e18 −0.810652
\(785\) 9.44163e18 1.44011
\(786\) 4.13951e17 0.0626184
\(787\) 4.83303e18 0.725076 0.362538 0.931969i \(-0.381910\pi\)
0.362538 + 0.931969i \(0.381910\pi\)
\(788\) 1.17740e19 1.75188
\(789\) −2.62663e18 −0.387614
\(790\) −1.95790e17 −0.0286560
\(791\) 8.65896e16 0.0125695
\(792\) 6.24801e17 0.0899556
\(793\) 5.27931e18 0.753879
\(794\) 2.44324e18 0.346045
\(795\) −4.05893e18 −0.570197
\(796\) −2.51796e16 −0.00350844
\(797\) 6.31421e18 0.872649 0.436325 0.899789i \(-0.356280\pi\)
0.436325 + 0.899789i \(0.356280\pi\)
\(798\) −3.50087e15 −0.000479907 0
\(799\) −5.84709e18 −0.795034
\(800\) −1.73660e18 −0.234216
\(801\) 2.46687e18 0.330016
\(802\) −7.41257e17 −0.0983638
\(803\) −8.20733e18 −1.08032
\(804\) 5.78201e17 0.0754944
\(805\) −1.15934e18 −0.150154
\(806\) −7.87606e17 −0.101189
\(807\) −7.63328e18 −0.972821
\(808\) −4.40592e17 −0.0557009
\(809\) −4.14704e18 −0.520083 −0.260042 0.965597i \(-0.583736\pi\)
−0.260042 + 0.965597i \(0.583736\pi\)
\(810\) 1.64336e17 0.0204447
\(811\) −5.45234e18 −0.672895 −0.336447 0.941702i \(-0.609225\pi\)
−0.336447 + 0.941702i \(0.609225\pi\)
\(812\) −1.62469e18 −0.198910
\(813\) 6.81261e17 0.0827417
\(814\) −1.10055e18 −0.132603
\(815\) −2.47048e18 −0.295295
\(816\) 4.83722e18 0.573601
\(817\) −1.65271e17 −0.0194426
\(818\) 2.16645e18 0.252844
\(819\) 6.67165e17 0.0772481
\(820\) −5.93185e18 −0.681397
\(821\) 1.06447e19 1.21311 0.606557 0.795040i \(-0.292550\pi\)
0.606557 + 0.795040i \(0.292550\pi\)
\(822\) 1.16195e17 0.0131377
\(823\) 3.57380e17 0.0400895 0.0200448 0.999799i \(-0.493619\pi\)
0.0200448 + 0.999799i \(0.493619\pi\)
\(824\) −2.31995e18 −0.258197
\(825\) −1.14323e18 −0.126236
\(826\) −5.38312e16 −0.00589745
\(827\) 6.30493e18 0.685322 0.342661 0.939459i \(-0.388672\pi\)
0.342661 + 0.939459i \(0.388672\pi\)
\(828\) 2.80581e18 0.302595
\(829\) 5.39659e18 0.577451 0.288726 0.957412i \(-0.406768\pi\)
0.288726 + 0.957412i \(0.406768\pi\)
\(830\) 7.30435e17 0.0775486
\(831\) 1.72651e18 0.181871
\(832\) −7.84428e18 −0.819882
\(833\) 1.09239e19 1.13289
\(834\) 5.43311e16 0.00559074
\(835\) −4.76176e18 −0.486189
\(836\) 1.03037e17 0.0104388
\(837\) 7.11432e17 0.0715184
\(838\) −1.67482e18 −0.167064
\(839\) 9.98977e18 0.988787 0.494393 0.869238i \(-0.335390\pi\)
0.494393 + 0.869238i \(0.335390\pi\)
\(840\) 4.13455e17 0.0406081
\(841\) 1.48632e18 0.144856
\(842\) −1.94547e18 −0.188146
\(843\) −2.77106e18 −0.265930
\(844\) −1.13105e19 −1.07710
\(845\) 3.31686e18 0.313443
\(846\) 5.53308e17 0.0518871
\(847\) −1.34819e18 −0.125461
\(848\) 1.13058e19 1.04406
\(849\) 9.67689e18 0.886821
\(850\) 1.08769e18 0.0989198
\(851\) −1.01624e19 −0.917179
\(852\) −8.80493e18 −0.788622
\(853\) −1.07605e19 −0.956457 −0.478229 0.878235i \(-0.658721\pi\)
−0.478229 + 0.878235i \(0.658721\pi\)
\(854\) 3.28014e17 0.0289345
\(855\) 5.57255e16 0.00487836
\(856\) 1.53444e18 0.133313
\(857\) 1.67522e19 1.44443 0.722214 0.691670i \(-0.243125\pi\)
0.722214 + 0.691670i \(0.243125\pi\)
\(858\) 1.10386e18 0.0944600
\(859\) 7.92902e18 0.673385 0.336693 0.941615i \(-0.390692\pi\)
0.336693 + 0.941615i \(0.390692\pi\)
\(860\) 9.49248e18 0.800092
\(861\) −1.22287e18 −0.102296
\(862\) −1.91205e17 −0.0158746
\(863\) −2.18196e19 −1.79795 −0.898973 0.438003i \(-0.855686\pi\)
−0.898973 + 0.438003i \(0.855686\pi\)
\(864\) −1.51463e18 −0.123871
\(865\) −8.42406e18 −0.683781
\(866\) 4.82233e18 0.388500
\(867\) −2.80460e18 −0.224257
\(868\) 8.70479e17 0.0690844
\(869\) 1.18795e18 0.0935769
\(870\) −1.45383e18 −0.113668
\(871\) 2.10050e18 0.163006
\(872\) −5.90643e16 −0.00454954
\(873\) 6.77316e17 0.0517844
\(874\) −5.34866e16 −0.00405901
\(875\) −2.83551e18 −0.213589
\(876\) 1.31443e19 0.982788
\(877\) 9.66319e18 0.717171 0.358586 0.933497i \(-0.383259\pi\)
0.358586 + 0.933497i \(0.383259\pi\)
\(878\) 3.43909e17 0.0253355
\(879\) 9.78804e18 0.715761
\(880\) −5.56662e18 −0.404068
\(881\) 1.64352e19 1.18422 0.592109 0.805858i \(-0.298295\pi\)
0.592109 + 0.805858i \(0.298295\pi\)
\(882\) −1.03373e18 −0.0739367
\(883\) −1.84658e19 −1.31106 −0.655530 0.755169i \(-0.727555\pi\)
−0.655530 + 0.755169i \(0.727555\pi\)
\(884\) 1.86820e19 1.31669
\(885\) 8.56864e17 0.0599488
\(886\) 1.25576e17 0.00872144
\(887\) −7.06988e18 −0.487426 −0.243713 0.969847i \(-0.578365\pi\)
−0.243713 + 0.969847i \(0.578365\pi\)
\(888\) 3.62422e18 0.248045
\(889\) −4.45749e18 −0.302851
\(890\) 2.70094e18 0.182171
\(891\) −9.97102e17 −0.0667628
\(892\) 2.78376e19 1.85038
\(893\) 1.87623e17 0.0123809
\(894\) 6.08604e17 0.0398695
\(895\) −5.78275e18 −0.376084
\(896\) −2.44481e18 −0.157849
\(897\) 1.01930e19 0.653357
\(898\) −7.96420e17 −0.0506811
\(899\) −6.29380e18 −0.397626
\(900\) 1.83091e18 0.114840
\(901\) −2.34310e19 −1.45908
\(902\) −2.02331e18 −0.125089
\(903\) 1.95690e18 0.120115
\(904\) −4.71794e17 −0.0287513
\(905\) −1.87133e19 −1.13223
\(906\) 1.04514e18 0.0627830
\(907\) −1.27508e19 −0.760485 −0.380243 0.924887i \(-0.624160\pi\)
−0.380243 + 0.924887i \(0.624160\pi\)
\(908\) 2.11981e18 0.125528
\(909\) 7.03128e17 0.0413399
\(910\) 7.30469e17 0.0426415
\(911\) 4.48067e18 0.259701 0.129850 0.991534i \(-0.458550\pi\)
0.129850 + 0.991534i \(0.458550\pi\)
\(912\) −1.55218e17 −0.00893258
\(913\) −4.43187e18 −0.253237
\(914\) −1.61658e18 −0.0917161
\(915\) −5.22120e18 −0.294126
\(916\) 2.42956e19 1.35896
\(917\) −1.66204e18 −0.0923082
\(918\) 9.48665e17 0.0523161
\(919\) 2.04324e19 1.11884 0.559420 0.828885i \(-0.311024\pi\)
0.559420 + 0.828885i \(0.311024\pi\)
\(920\) 6.31679e18 0.343459
\(921\) 1.19906e19 0.647371
\(922\) −3.29838e18 −0.176827
\(923\) −3.19867e19 −1.70278
\(924\) −1.22001e18 −0.0644907
\(925\) −6.63140e18 −0.348084
\(926\) 5.56926e18 0.290286
\(927\) 3.70234e18 0.191628
\(928\) 1.33995e19 0.688693
\(929\) −2.01468e19 −1.02826 −0.514132 0.857711i \(-0.671886\pi\)
−0.514132 + 0.857711i \(0.671886\pi\)
\(930\) 7.78936e17 0.0394787
\(931\) −3.50531e17 −0.0176422
\(932\) −7.34108e18 −0.366908
\(933\) 1.83045e18 0.0908505
\(934\) 5.41767e18 0.267029
\(935\) 1.15367e19 0.564684
\(936\) −3.63512e18 −0.176696
\(937\) 1.03671e18 0.0500436 0.0250218 0.999687i \(-0.492034\pi\)
0.0250218 + 0.999687i \(0.492034\pi\)
\(938\) 1.30508e17 0.00625631
\(939\) 1.44137e19 0.686197
\(940\) −1.07763e19 −0.509494
\(941\) 1.67806e19 0.787908 0.393954 0.919130i \(-0.371107\pi\)
0.393954 + 0.919130i \(0.371107\pi\)
\(942\) −5.15767e18 −0.240504
\(943\) −1.86831e19 −0.865211
\(944\) −2.38672e18 −0.109770
\(945\) −6.59821e17 −0.0301383
\(946\) 3.23781e18 0.146879
\(947\) −1.59447e19 −0.718361 −0.359180 0.933268i \(-0.616944\pi\)
−0.359180 + 0.933268i \(0.616944\pi\)
\(948\) −1.90253e18 −0.0851290
\(949\) 4.77507e19 2.12202
\(950\) −3.49023e16 −0.00154046
\(951\) 2.57933e19 1.13066
\(952\) 2.38675e18 0.103912
\(953\) 2.88095e19 1.24575 0.622877 0.782320i \(-0.285964\pi\)
0.622877 + 0.782320i \(0.285964\pi\)
\(954\) 2.21726e18 0.0952254
\(955\) 3.24915e19 1.38595
\(956\) 1.70659e19 0.723024
\(957\) 8.82104e18 0.371186
\(958\) −9.54221e18 −0.398817
\(959\) −4.66529e17 −0.0193668
\(960\) 7.75793e18 0.319877
\(961\) −2.10454e19 −0.861898
\(962\) 6.40306e18 0.260465
\(963\) −2.44878e18 −0.0989414
\(964\) 2.27745e19 0.914006
\(965\) −3.42856e19 −1.36673
\(966\) 6.33310e17 0.0250764
\(967\) 2.32383e19 0.913972 0.456986 0.889474i \(-0.348929\pi\)
0.456986 + 0.889474i \(0.348929\pi\)
\(968\) 7.34575e18 0.286977
\(969\) 3.21687e17 0.0124833
\(970\) 7.41584e17 0.0285854
\(971\) 1.73052e19 0.662599 0.331299 0.943526i \(-0.392513\pi\)
0.331299 + 0.943526i \(0.392513\pi\)
\(972\) 1.59689e18 0.0607357
\(973\) −2.18143e17 −0.00824152
\(974\) −4.06994e18 −0.152741
\(975\) 6.65136e18 0.247959
\(976\) 1.45432e19 0.538562
\(977\) 2.76119e18 0.101574 0.0507868 0.998710i \(-0.483827\pi\)
0.0507868 + 0.998710i \(0.483827\pi\)
\(978\) 1.34954e18 0.0493157
\(979\) −1.63878e19 −0.594886
\(980\) 2.01330e19 0.726005
\(981\) 9.42590e16 0.00337656
\(982\) −3.55873e18 −0.126640
\(983\) 2.26212e19 0.799682 0.399841 0.916585i \(-0.369065\pi\)
0.399841 + 0.916585i \(0.369065\pi\)
\(984\) 6.66294e18 0.233990
\(985\) −4.23020e19 −1.47579
\(986\) −8.39253e18 −0.290866
\(987\) −2.22156e18 −0.0764887
\(988\) −5.99474e17 −0.0205046
\(989\) 2.98977e19 1.01592
\(990\) −1.09171e18 −0.0368536
\(991\) −4.68696e19 −1.57186 −0.785928 0.618318i \(-0.787814\pi\)
−0.785928 + 0.618318i \(0.787814\pi\)
\(992\) −7.17919e18 −0.239194
\(993\) −1.04100e19 −0.344573
\(994\) −1.98739e18 −0.0653540
\(995\) 9.04659e16 0.00295553
\(996\) 7.09778e18 0.230376
\(997\) −3.16586e19 −1.02087 −0.510437 0.859915i \(-0.670517\pi\)
−0.510437 + 0.859915i \(0.670517\pi\)
\(998\) −3.36799e18 −0.107900
\(999\) −5.78378e18 −0.184093
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 177.14.a.b.1.17 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.17 31 1.1 even 1 trivial