Properties

Label 983.4.a.b.1.6
Level $983$
Weight $4$
Character 983.1
Self dual yes
Analytic conductor $57.999$
Analytic rank $0$
Dimension $136$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [983,4,Mod(1,983)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(983, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("983.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 983.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(57.9988775356\)
Analytic rank: \(0\)
Dimension: \(136\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 983.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.25160 q^{2} +3.19215 q^{3} +19.5793 q^{4} -16.3542 q^{5} -16.7639 q^{6} -21.7601 q^{7} -60.8100 q^{8} -16.8102 q^{9} +O(q^{10})\) \(q-5.25160 q^{2} +3.19215 q^{3} +19.5793 q^{4} -16.3542 q^{5} -16.7639 q^{6} -21.7601 q^{7} -60.8100 q^{8} -16.8102 q^{9} +85.8857 q^{10} -6.52197 q^{11} +62.5001 q^{12} +3.49094 q^{13} +114.275 q^{14} -52.2050 q^{15} +162.715 q^{16} +11.0219 q^{17} +88.2804 q^{18} +84.4586 q^{19} -320.204 q^{20} -69.4615 q^{21} +34.2508 q^{22} -189.072 q^{23} -194.115 q^{24} +142.460 q^{25} -18.3330 q^{26} -139.849 q^{27} -426.048 q^{28} -188.736 q^{29} +274.160 q^{30} -221.190 q^{31} -368.035 q^{32} -20.8191 q^{33} -57.8827 q^{34} +355.869 q^{35} -329.132 q^{36} -94.6529 q^{37} -443.543 q^{38} +11.1436 q^{39} +994.498 q^{40} -464.280 q^{41} +364.784 q^{42} -414.429 q^{43} -127.696 q^{44} +274.917 q^{45} +992.932 q^{46} -449.696 q^{47} +519.411 q^{48} +130.501 q^{49} -748.142 q^{50} +35.1836 q^{51} +68.3502 q^{52} +412.692 q^{53} +734.429 q^{54} +106.662 q^{55} +1323.23 q^{56} +269.604 q^{57} +991.165 q^{58} +10.9547 q^{59} -1022.14 q^{60} -789.040 q^{61} +1161.60 q^{62} +365.791 q^{63} +631.054 q^{64} -57.0915 q^{65} +109.334 q^{66} +950.873 q^{67} +215.802 q^{68} -603.547 q^{69} -1868.88 q^{70} -416.952 q^{71} +1022.23 q^{72} +931.949 q^{73} +497.079 q^{74} +454.753 q^{75} +1653.64 q^{76} +141.919 q^{77} -58.5217 q^{78} -1200.42 q^{79} -2661.08 q^{80} +7.45706 q^{81} +2438.21 q^{82} -624.025 q^{83} -1360.01 q^{84} -180.255 q^{85} +2176.42 q^{86} -602.473 q^{87} +396.601 q^{88} -859.427 q^{89} -1443.75 q^{90} -75.9631 q^{91} -3701.90 q^{92} -706.071 q^{93} +2361.62 q^{94} -1381.25 q^{95} -1174.82 q^{96} +1054.60 q^{97} -685.341 q^{98} +109.635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.25160 −1.85672 −0.928361 0.371680i \(-0.878782\pi\)
−0.928361 + 0.371680i \(0.878782\pi\)
\(3\) 3.19215 0.614329 0.307165 0.951656i \(-0.400620\pi\)
0.307165 + 0.951656i \(0.400620\pi\)
\(4\) 19.5793 2.44741
\(5\) −16.3542 −1.46276 −0.731382 0.681968i \(-0.761124\pi\)
−0.731382 + 0.681968i \(0.761124\pi\)
\(6\) −16.7639 −1.14064
\(7\) −21.7601 −1.17493 −0.587467 0.809248i \(-0.699875\pi\)
−0.587467 + 0.809248i \(0.699875\pi\)
\(8\) −60.8100 −2.68745
\(9\) −16.8102 −0.622599
\(10\) 85.8857 2.71595
\(11\) −6.52197 −0.178768 −0.0893839 0.995997i \(-0.528490\pi\)
−0.0893839 + 0.995997i \(0.528490\pi\)
\(12\) 62.5001 1.50352
\(13\) 3.49094 0.0744778 0.0372389 0.999306i \(-0.488144\pi\)
0.0372389 + 0.999306i \(0.488144\pi\)
\(14\) 114.275 2.18153
\(15\) −52.2050 −0.898619
\(16\) 162.715 2.54242
\(17\) 11.0219 0.157248 0.0786238 0.996904i \(-0.474947\pi\)
0.0786238 + 0.996904i \(0.474947\pi\)
\(18\) 88.2804 1.15599
\(19\) 84.4586 1.01980 0.509898 0.860235i \(-0.329683\pi\)
0.509898 + 0.860235i \(0.329683\pi\)
\(20\) −320.204 −3.57999
\(21\) −69.4615 −0.721797
\(22\) 34.2508 0.331922
\(23\) −189.072 −1.71410 −0.857049 0.515234i \(-0.827705\pi\)
−0.857049 + 0.515234i \(0.827705\pi\)
\(24\) −194.115 −1.65098
\(25\) 142.460 1.13968
\(26\) −18.3330 −0.138285
\(27\) −139.849 −0.996811
\(28\) −426.048 −2.87555
\(29\) −188.736 −1.20853 −0.604265 0.796784i \(-0.706533\pi\)
−0.604265 + 0.796784i \(0.706533\pi\)
\(30\) 274.160 1.66849
\(31\) −221.190 −1.28151 −0.640756 0.767745i \(-0.721379\pi\)
−0.640756 + 0.767745i \(0.721379\pi\)
\(32\) −368.035 −2.03313
\(33\) −20.8191 −0.109822
\(34\) −57.8827 −0.291965
\(35\) 355.869 1.71865
\(36\) −329.132 −1.52376
\(37\) −94.6529 −0.420563 −0.210282 0.977641i \(-0.567438\pi\)
−0.210282 + 0.977641i \(0.567438\pi\)
\(38\) −443.543 −1.89348
\(39\) 11.1436 0.0457539
\(40\) 994.498 3.93110
\(41\) −464.280 −1.76850 −0.884248 0.467018i \(-0.845328\pi\)
−0.884248 + 0.467018i \(0.845328\pi\)
\(42\) 364.784 1.34018
\(43\) −414.429 −1.46976 −0.734882 0.678195i \(-0.762763\pi\)
−0.734882 + 0.678195i \(0.762763\pi\)
\(44\) −127.696 −0.437519
\(45\) 274.917 0.910716
\(46\) 992.932 3.18260
\(47\) −449.696 −1.39564 −0.697818 0.716276i \(-0.745845\pi\)
−0.697818 + 0.716276i \(0.745845\pi\)
\(48\) 519.411 1.56189
\(49\) 130.501 0.380471
\(50\) −748.142 −2.11607
\(51\) 35.1836 0.0966018
\(52\) 68.3502 0.182278
\(53\) 412.692 1.06958 0.534788 0.844986i \(-0.320391\pi\)
0.534788 + 0.844986i \(0.320391\pi\)
\(54\) 734.429 1.85080
\(55\) 106.662 0.261495
\(56\) 1323.23 3.15757
\(57\) 269.604 0.626491
\(58\) 991.165 2.24390
\(59\) 10.9547 0.0241726 0.0120863 0.999927i \(-0.496153\pi\)
0.0120863 + 0.999927i \(0.496153\pi\)
\(60\) −1022.14 −2.19929
\(61\) −789.040 −1.65617 −0.828084 0.560604i \(-0.810569\pi\)
−0.828084 + 0.560604i \(0.810569\pi\)
\(62\) 1161.60 2.37941
\(63\) 365.791 0.731513
\(64\) 631.054 1.23253
\(65\) −57.0915 −0.108943
\(66\) 109.334 0.203910
\(67\) 950.873 1.73385 0.866923 0.498442i \(-0.166094\pi\)
0.866923 + 0.498442i \(0.166094\pi\)
\(68\) 215.802 0.384850
\(69\) −603.547 −1.05302
\(70\) −1868.88 −3.19106
\(71\) −416.952 −0.696944 −0.348472 0.937319i \(-0.613299\pi\)
−0.348472 + 0.937319i \(0.613299\pi\)
\(72\) 1022.23 1.67320
\(73\) 931.949 1.49420 0.747099 0.664713i \(-0.231446\pi\)
0.747099 + 0.664713i \(0.231446\pi\)
\(74\) 497.079 0.780869
\(75\) 454.753 0.700138
\(76\) 1653.64 2.49586
\(77\) 141.919 0.210041
\(78\) −58.5217 −0.0849523
\(79\) −1200.42 −1.70959 −0.854796 0.518964i \(-0.826318\pi\)
−0.854796 + 0.518964i \(0.826318\pi\)
\(80\) −2661.08 −3.71897
\(81\) 7.45706 0.0102292
\(82\) 2438.21 3.28360
\(83\) −624.025 −0.825248 −0.412624 0.910901i \(-0.635388\pi\)
−0.412624 + 0.910901i \(0.635388\pi\)
\(84\) −1360.01 −1.76654
\(85\) −180.255 −0.230016
\(86\) 2176.42 2.72894
\(87\) −602.473 −0.742435
\(88\) 396.601 0.480429
\(89\) −859.427 −1.02358 −0.511792 0.859109i \(-0.671018\pi\)
−0.511792 + 0.859109i \(0.671018\pi\)
\(90\) −1443.75 −1.69095
\(91\) −75.9631 −0.0875065
\(92\) −3701.90 −4.19511
\(93\) −706.071 −0.787271
\(94\) 2361.62 2.59131
\(95\) −1381.25 −1.49172
\(96\) −1174.82 −1.24901
\(97\) 1054.60 1.10391 0.551953 0.833876i \(-0.313883\pi\)
0.551953 + 0.833876i \(0.313883\pi\)
\(98\) −685.341 −0.706428
\(99\) 109.635 0.111301
\(100\) 2789.27 2.78927
\(101\) −1997.46 −1.96787 −0.983934 0.178531i \(-0.942866\pi\)
−0.983934 + 0.178531i \(0.942866\pi\)
\(102\) −184.770 −0.179363
\(103\) −1517.46 −1.45164 −0.725822 0.687882i \(-0.758540\pi\)
−0.725822 + 0.687882i \(0.758540\pi\)
\(104\) −212.284 −0.200155
\(105\) 1135.99 1.05582
\(106\) −2167.29 −1.98591
\(107\) 1254.83 1.13373 0.566864 0.823812i \(-0.308157\pi\)
0.566864 + 0.823812i \(0.308157\pi\)
\(108\) −2738.14 −2.43961
\(109\) 1854.72 1.62982 0.814909 0.579589i \(-0.196787\pi\)
0.814909 + 0.579589i \(0.196787\pi\)
\(110\) −560.144 −0.485524
\(111\) −302.146 −0.258364
\(112\) −3540.70 −2.98718
\(113\) 1711.19 1.42456 0.712280 0.701896i \(-0.247663\pi\)
0.712280 + 0.701896i \(0.247663\pi\)
\(114\) −1415.86 −1.16322
\(115\) 3092.12 2.50732
\(116\) −3695.32 −2.95777
\(117\) −58.6833 −0.0463698
\(118\) −57.5299 −0.0448818
\(119\) −239.838 −0.184755
\(120\) 3174.59 2.41499
\(121\) −1288.46 −0.968042
\(122\) 4143.72 3.07504
\(123\) −1482.05 −1.08644
\(124\) −4330.75 −3.13639
\(125\) −285.541 −0.204316
\(126\) −1920.99 −1.35822
\(127\) −1496.34 −1.04550 −0.522752 0.852485i \(-0.675094\pi\)
−0.522752 + 0.852485i \(0.675094\pi\)
\(128\) −369.762 −0.255333
\(129\) −1322.92 −0.902920
\(130\) 299.822 0.202278
\(131\) 856.080 0.570962 0.285481 0.958384i \(-0.407847\pi\)
0.285481 + 0.958384i \(0.407847\pi\)
\(132\) −407.624 −0.268781
\(133\) −1837.83 −1.19819
\(134\) −4993.61 −3.21927
\(135\) 2287.11 1.45810
\(136\) −670.242 −0.422594
\(137\) 1396.58 0.870933 0.435467 0.900205i \(-0.356583\pi\)
0.435467 + 0.900205i \(0.356583\pi\)
\(138\) 3169.59 1.95517
\(139\) 1021.52 0.623338 0.311669 0.950191i \(-0.399112\pi\)
0.311669 + 0.950191i \(0.399112\pi\)
\(140\) 6967.67 4.20625
\(141\) −1435.50 −0.857380
\(142\) 2189.66 1.29403
\(143\) −22.7678 −0.0133142
\(144\) −2735.27 −1.58291
\(145\) 3086.62 1.76779
\(146\) −4894.23 −2.77431
\(147\) 416.580 0.233734
\(148\) −1853.24 −1.02929
\(149\) 1018.32 0.559895 0.279947 0.960015i \(-0.409683\pi\)
0.279947 + 0.960015i \(0.409683\pi\)
\(150\) −2388.18 −1.29996
\(151\) 2022.90 1.09021 0.545103 0.838369i \(-0.316491\pi\)
0.545103 + 0.838369i \(0.316491\pi\)
\(152\) −5135.92 −2.74065
\(153\) −185.280 −0.0979022
\(154\) −745.300 −0.389987
\(155\) 3617.38 1.87455
\(156\) 218.184 0.111979
\(157\) 1381.24 0.702133 0.351067 0.936351i \(-0.385819\pi\)
0.351067 + 0.936351i \(0.385819\pi\)
\(158\) 6304.12 3.17424
\(159\) 1317.37 0.657072
\(160\) 6018.92 2.97399
\(161\) 4114.23 2.01395
\(162\) −39.1615 −0.0189927
\(163\) −113.309 −0.0544483 −0.0272242 0.999629i \(-0.508667\pi\)
−0.0272242 + 0.999629i \(0.508667\pi\)
\(164\) −9090.28 −4.32824
\(165\) 340.480 0.160644
\(166\) 3277.13 1.53226
\(167\) −2529.48 −1.17208 −0.586039 0.810283i \(-0.699313\pi\)
−0.586039 + 0.810283i \(0.699313\pi\)
\(168\) 4223.95 1.93979
\(169\) −2184.81 −0.994453
\(170\) 946.625 0.427076
\(171\) −1419.76 −0.634924
\(172\) −8114.24 −3.59712
\(173\) 99.8907 0.0438991 0.0219496 0.999759i \(-0.493013\pi\)
0.0219496 + 0.999759i \(0.493013\pi\)
\(174\) 3163.95 1.37850
\(175\) −3099.94 −1.33905
\(176\) −1061.22 −0.454504
\(177\) 34.9691 0.0148500
\(178\) 4513.37 1.90051
\(179\) −3488.73 −1.45676 −0.728379 0.685175i \(-0.759726\pi\)
−0.728379 + 0.685175i \(0.759726\pi\)
\(180\) 5382.69 2.22890
\(181\) 988.302 0.405856 0.202928 0.979194i \(-0.434954\pi\)
0.202928 + 0.979194i \(0.434954\pi\)
\(182\) 398.928 0.162475
\(183\) −2518.73 −1.01743
\(184\) 11497.5 4.60655
\(185\) 1547.97 0.615185
\(186\) 3708.00 1.46174
\(187\) −71.8846 −0.0281108
\(188\) −8804.73 −3.41570
\(189\) 3043.12 1.17119
\(190\) 7253.79 2.76971
\(191\) 1005.98 0.381100 0.190550 0.981678i \(-0.438973\pi\)
0.190550 + 0.981678i \(0.438973\pi\)
\(192\) 2014.42 0.757178
\(193\) −1432.59 −0.534300 −0.267150 0.963655i \(-0.586082\pi\)
−0.267150 + 0.963655i \(0.586082\pi\)
\(194\) −5538.36 −2.04964
\(195\) −182.244 −0.0669272
\(196\) 2555.13 0.931169
\(197\) −2313.00 −0.836521 −0.418260 0.908327i \(-0.637360\pi\)
−0.418260 + 0.908327i \(0.637360\pi\)
\(198\) −575.762 −0.206655
\(199\) 1726.88 0.615151 0.307575 0.951524i \(-0.400482\pi\)
0.307575 + 0.951524i \(0.400482\pi\)
\(200\) −8662.97 −3.06282
\(201\) 3035.33 1.06515
\(202\) 10489.9 3.65378
\(203\) 4106.91 1.41994
\(204\) 688.871 0.236425
\(205\) 7592.92 2.58689
\(206\) 7969.07 2.69530
\(207\) 3178.34 1.06720
\(208\) 568.028 0.189354
\(209\) −550.836 −0.182307
\(210\) −5965.75 −1.96036
\(211\) 1869.97 0.610113 0.305057 0.952334i \(-0.401325\pi\)
0.305057 + 0.952334i \(0.401325\pi\)
\(212\) 8080.22 2.61770
\(213\) −1330.97 −0.428153
\(214\) −6589.86 −2.10502
\(215\) 6777.66 2.14992
\(216\) 8504.19 2.67887
\(217\) 4813.11 1.50569
\(218\) −9740.26 −3.02612
\(219\) 2974.92 0.917929
\(220\) 2088.36 0.639987
\(221\) 38.4768 0.0117114
\(222\) 1586.75 0.479711
\(223\) 882.245 0.264930 0.132465 0.991188i \(-0.457711\pi\)
0.132465 + 0.991188i \(0.457711\pi\)
\(224\) 8008.48 2.38879
\(225\) −2394.77 −0.709563
\(226\) −8986.49 −2.64501
\(227\) 4527.35 1.32375 0.661875 0.749615i \(-0.269761\pi\)
0.661875 + 0.749615i \(0.269761\pi\)
\(228\) 5278.67 1.53328
\(229\) 4795.91 1.38394 0.691971 0.721925i \(-0.256743\pi\)
0.691971 + 0.721925i \(0.256743\pi\)
\(230\) −16238.6 −4.65540
\(231\) 453.025 0.129034
\(232\) 11477.0 3.24786
\(233\) 162.353 0.0456486 0.0228243 0.999739i \(-0.492734\pi\)
0.0228243 + 0.999739i \(0.492734\pi\)
\(234\) 308.181 0.0860959
\(235\) 7354.41 2.04148
\(236\) 214.486 0.0591604
\(237\) −3831.92 −1.05025
\(238\) 1259.53 0.343039
\(239\) −1227.19 −0.332136 −0.166068 0.986114i \(-0.553107\pi\)
−0.166068 + 0.986114i \(0.553107\pi\)
\(240\) −8494.55 −2.28467
\(241\) −2659.74 −0.710908 −0.355454 0.934694i \(-0.615674\pi\)
−0.355454 + 0.934694i \(0.615674\pi\)
\(242\) 6766.50 1.79738
\(243\) 3799.72 1.00309
\(244\) −15448.9 −4.05333
\(245\) −2134.25 −0.556539
\(246\) 7783.14 2.01721
\(247\) 294.840 0.0759522
\(248\) 13450.5 3.44399
\(249\) −1991.98 −0.506974
\(250\) 1499.55 0.379359
\(251\) −4177.22 −1.05045 −0.525226 0.850963i \(-0.676019\pi\)
−0.525226 + 0.850963i \(0.676019\pi\)
\(252\) 7161.94 1.79032
\(253\) 1233.12 0.306426
\(254\) 7858.19 1.94121
\(255\) −575.400 −0.141306
\(256\) −3106.59 −0.758445
\(257\) −5934.53 −1.44041 −0.720205 0.693761i \(-0.755952\pi\)
−0.720205 + 0.693761i \(0.755952\pi\)
\(258\) 6947.45 1.67647
\(259\) 2059.66 0.494134
\(260\) −1117.81 −0.266630
\(261\) 3172.68 0.752430
\(262\) −4495.79 −1.06012
\(263\) −4269.77 −1.00108 −0.500542 0.865712i \(-0.666866\pi\)
−0.500542 + 0.865712i \(0.666866\pi\)
\(264\) 1266.01 0.295142
\(265\) −6749.24 −1.56454
\(266\) 9651.53 2.22471
\(267\) −2743.42 −0.628818
\(268\) 18617.4 4.24344
\(269\) −814.860 −0.184695 −0.0923473 0.995727i \(-0.529437\pi\)
−0.0923473 + 0.995727i \(0.529437\pi\)
\(270\) −12011.0 −2.70728
\(271\) −4508.81 −1.01067 −0.505333 0.862924i \(-0.668630\pi\)
−0.505333 + 0.862924i \(0.668630\pi\)
\(272\) 1793.43 0.399790
\(273\) −242.486 −0.0537578
\(274\) −7334.28 −1.61708
\(275\) −929.118 −0.203738
\(276\) −11817.0 −2.57718
\(277\) 3450.20 0.748385 0.374192 0.927351i \(-0.377920\pi\)
0.374192 + 0.927351i \(0.377920\pi\)
\(278\) −5364.60 −1.15737
\(279\) 3718.24 0.797869
\(280\) −21640.4 −4.61878
\(281\) 1003.25 0.212986 0.106493 0.994313i \(-0.466038\pi\)
0.106493 + 0.994313i \(0.466038\pi\)
\(282\) 7538.65 1.59192
\(283\) −1577.49 −0.331351 −0.165676 0.986180i \(-0.552980\pi\)
−0.165676 + 0.986180i \(0.552980\pi\)
\(284\) −8163.63 −1.70571
\(285\) −4409.16 −0.916408
\(286\) 119.567 0.0247208
\(287\) 10102.8 2.07787
\(288\) 6186.74 1.26582
\(289\) −4791.52 −0.975273
\(290\) −16209.7 −3.28230
\(291\) 3366.45 0.678161
\(292\) 18246.9 3.65692
\(293\) −3496.56 −0.697171 −0.348586 0.937277i \(-0.613338\pi\)
−0.348586 + 0.937277i \(0.613338\pi\)
\(294\) −2187.71 −0.433979
\(295\) −179.156 −0.0353588
\(296\) 5755.84 1.13024
\(297\) 912.088 0.178198
\(298\) −5347.83 −1.03957
\(299\) −660.039 −0.127662
\(300\) 8903.75 1.71353
\(301\) 9018.02 1.72688
\(302\) −10623.5 −2.02421
\(303\) −6376.19 −1.20892
\(304\) 13742.7 2.59276
\(305\) 12904.1 2.42258
\(306\) 973.019 0.181777
\(307\) −3774.37 −0.701677 −0.350838 0.936436i \(-0.614103\pi\)
−0.350838 + 0.936436i \(0.614103\pi\)
\(308\) 2778.67 0.514056
\(309\) −4843.95 −0.891788
\(310\) −18997.1 −3.48052
\(311\) 1945.44 0.354714 0.177357 0.984147i \(-0.443245\pi\)
0.177357 + 0.984147i \(0.443245\pi\)
\(312\) −677.641 −0.122961
\(313\) −7045.82 −1.27237 −0.636187 0.771535i \(-0.719489\pi\)
−0.636187 + 0.771535i \(0.719489\pi\)
\(314\) −7253.72 −1.30367
\(315\) −5982.22 −1.07003
\(316\) −23503.4 −4.18408
\(317\) −4684.02 −0.829908 −0.414954 0.909842i \(-0.636202\pi\)
−0.414954 + 0.909842i \(0.636202\pi\)
\(318\) −6918.32 −1.22000
\(319\) 1230.93 0.216046
\(320\) −10320.4 −1.80290
\(321\) 4005.60 0.696482
\(322\) −21606.3 −3.73935
\(323\) 930.896 0.160360
\(324\) 146.004 0.0250350
\(325\) 497.318 0.0848807
\(326\) 595.056 0.101095
\(327\) 5920.55 1.00125
\(328\) 28232.8 4.75274
\(329\) 9785.42 1.63978
\(330\) −1788.06 −0.298272
\(331\) 4675.61 0.776420 0.388210 0.921571i \(-0.373094\pi\)
0.388210 + 0.921571i \(0.373094\pi\)
\(332\) −12218.0 −2.01973
\(333\) 1591.13 0.261842
\(334\) 13283.8 2.17622
\(335\) −15550.8 −2.53621
\(336\) −11302.4 −1.83511
\(337\) 4748.09 0.767493 0.383746 0.923439i \(-0.374634\pi\)
0.383746 + 0.923439i \(0.374634\pi\)
\(338\) 11473.8 1.84642
\(339\) 5462.37 0.875149
\(340\) −3529.26 −0.562944
\(341\) 1442.59 0.229093
\(342\) 7456.04 1.17888
\(343\) 4623.99 0.727906
\(344\) 25201.4 3.94991
\(345\) 9870.52 1.54032
\(346\) −524.586 −0.0815084
\(347\) −3303.33 −0.511043 −0.255522 0.966803i \(-0.582247\pi\)
−0.255522 + 0.966803i \(0.582247\pi\)
\(348\) −11796.0 −1.81705
\(349\) 8912.11 1.36692 0.683459 0.729989i \(-0.260475\pi\)
0.683459 + 0.729989i \(0.260475\pi\)
\(350\) 16279.6 2.48624
\(351\) −488.203 −0.0742403
\(352\) 2400.31 0.363458
\(353\) −8512.10 −1.28344 −0.641719 0.766940i \(-0.721778\pi\)
−0.641719 + 0.766940i \(0.721778\pi\)
\(354\) −183.644 −0.0275722
\(355\) 6818.91 1.01946
\(356\) −16827.0 −2.50514
\(357\) −765.598 −0.113501
\(358\) 18321.4 2.70479
\(359\) −1173.62 −0.172538 −0.0862692 0.996272i \(-0.527495\pi\)
−0.0862692 + 0.996272i \(0.527495\pi\)
\(360\) −16717.7 −2.44750
\(361\) 274.254 0.0399846
\(362\) −5190.17 −0.753561
\(363\) −4112.97 −0.594697
\(364\) −1487.31 −0.214165
\(365\) −15241.3 −2.18566
\(366\) 13227.4 1.88909
\(367\) 8023.73 1.14124 0.570621 0.821214i \(-0.306703\pi\)
0.570621 + 0.821214i \(0.306703\pi\)
\(368\) −30764.9 −4.35797
\(369\) 7804.63 1.10106
\(370\) −8129.34 −1.14223
\(371\) −8980.21 −1.25668
\(372\) −13824.4 −1.92678
\(373\) −3193.38 −0.443289 −0.221644 0.975128i \(-0.571142\pi\)
−0.221644 + 0.975128i \(0.571142\pi\)
\(374\) 377.509 0.0521939
\(375\) −911.489 −0.125518
\(376\) 27346.0 3.75069
\(377\) −658.865 −0.0900086
\(378\) −15981.2 −2.17457
\(379\) 27.7049 0.00375490 0.00187745 0.999998i \(-0.499402\pi\)
0.00187745 + 0.999998i \(0.499402\pi\)
\(380\) −27044.0 −3.65086
\(381\) −4776.55 −0.642283
\(382\) −5283.00 −0.707596
\(383\) −7807.42 −1.04162 −0.520810 0.853673i \(-0.674370\pi\)
−0.520810 + 0.853673i \(0.674370\pi\)
\(384\) −1180.34 −0.156859
\(385\) −2320.96 −0.307240
\(386\) 7523.38 0.992047
\(387\) 6966.63 0.915074
\(388\) 20648.4 2.70171
\(389\) 3570.87 0.465425 0.232712 0.972546i \(-0.425240\pi\)
0.232712 + 0.972546i \(0.425240\pi\)
\(390\) 957.075 0.124265
\(391\) −2083.94 −0.269538
\(392\) −7935.79 −1.02249
\(393\) 2732.74 0.350759
\(394\) 12147.0 1.55319
\(395\) 19631.9 2.50073
\(396\) 2146.59 0.272399
\(397\) 13864.1 1.75269 0.876344 0.481686i \(-0.159976\pi\)
0.876344 + 0.481686i \(0.159976\pi\)
\(398\) −9068.86 −1.14216
\(399\) −5866.62 −0.736086
\(400\) 23180.4 2.89755
\(401\) −1546.00 −0.192527 −0.0962635 0.995356i \(-0.530689\pi\)
−0.0962635 + 0.995356i \(0.530689\pi\)
\(402\) −15940.3 −1.97769
\(403\) −772.160 −0.0954442
\(404\) −39108.9 −4.81619
\(405\) −121.954 −0.0149629
\(406\) −21567.8 −2.63644
\(407\) 617.323 0.0751832
\(408\) −2139.51 −0.259612
\(409\) −12761.0 −1.54276 −0.771381 0.636374i \(-0.780434\pi\)
−0.771381 + 0.636374i \(0.780434\pi\)
\(410\) −39875.0 −4.80314
\(411\) 4458.09 0.535040
\(412\) −29710.7 −3.55278
\(413\) −238.376 −0.0284012
\(414\) −16691.4 −1.98149
\(415\) 10205.4 1.20714
\(416\) −1284.79 −0.151423
\(417\) 3260.84 0.382935
\(418\) 2892.77 0.338493
\(419\) −4933.37 −0.575205 −0.287603 0.957750i \(-0.592858\pi\)
−0.287603 + 0.957750i \(0.592858\pi\)
\(420\) 22241.8 2.58403
\(421\) −373.053 −0.0431864 −0.0215932 0.999767i \(-0.506874\pi\)
−0.0215932 + 0.999767i \(0.506874\pi\)
\(422\) −9820.33 −1.13281
\(423\) 7559.47 0.868921
\(424\) −25095.8 −2.87443
\(425\) 1570.18 0.179212
\(426\) 6989.73 0.794962
\(427\) 17169.6 1.94589
\(428\) 24568.7 2.77470
\(429\) −72.6781 −0.00817933
\(430\) −35593.6 −3.99180
\(431\) 16001.3 1.78829 0.894147 0.447773i \(-0.147783\pi\)
0.894147 + 0.447773i \(0.147783\pi\)
\(432\) −22755.5 −2.53432
\(433\) −12904.4 −1.43220 −0.716101 0.697996i \(-0.754075\pi\)
−0.716101 + 0.697996i \(0.754075\pi\)
\(434\) −25276.5 −2.79565
\(435\) 9852.96 1.08601
\(436\) 36314.2 3.98884
\(437\) −15968.8 −1.74803
\(438\) −15623.1 −1.70434
\(439\) −14810.7 −1.61020 −0.805100 0.593140i \(-0.797888\pi\)
−0.805100 + 0.593140i \(0.797888\pi\)
\(440\) −6486.08 −0.702754
\(441\) −2193.75 −0.236881
\(442\) −202.065 −0.0217449
\(443\) 2959.44 0.317398 0.158699 0.987327i \(-0.449270\pi\)
0.158699 + 0.987327i \(0.449270\pi\)
\(444\) −5915.82 −0.632325
\(445\) 14055.2 1.49726
\(446\) −4633.20 −0.491902
\(447\) 3250.64 0.343960
\(448\) −13731.8 −1.44814
\(449\) 5227.49 0.549445 0.274722 0.961524i \(-0.411414\pi\)
0.274722 + 0.961524i \(0.411414\pi\)
\(450\) 12576.4 1.31746
\(451\) 3028.02 0.316150
\(452\) 33503.9 3.48649
\(453\) 6457.39 0.669746
\(454\) −23775.9 −2.45783
\(455\) 1242.32 0.128001
\(456\) −16394.6 −1.68366
\(457\) −3459.45 −0.354105 −0.177053 0.984201i \(-0.556656\pi\)
−0.177053 + 0.984201i \(0.556656\pi\)
\(458\) −25186.2 −2.56959
\(459\) −1541.40 −0.156746
\(460\) 60541.7 6.13646
\(461\) 177.559 0.0179387 0.00896937 0.999960i \(-0.497145\pi\)
0.00896937 + 0.999960i \(0.497145\pi\)
\(462\) −2379.11 −0.239580
\(463\) −5711.92 −0.573338 −0.286669 0.958030i \(-0.592548\pi\)
−0.286669 + 0.958030i \(0.592548\pi\)
\(464\) −30710.2 −3.07259
\(465\) 11547.2 1.15159
\(466\) −852.614 −0.0847567
\(467\) 287.505 0.0284886 0.0142443 0.999899i \(-0.495466\pi\)
0.0142443 + 0.999899i \(0.495466\pi\)
\(468\) −1148.98 −0.113486
\(469\) −20691.1 −2.03715
\(470\) −38622.4 −3.79047
\(471\) 4409.12 0.431341
\(472\) −666.157 −0.0649626
\(473\) 2702.89 0.262747
\(474\) 20123.7 1.95003
\(475\) 12032.0 1.16224
\(476\) −4695.86 −0.452173
\(477\) −6937.42 −0.665918
\(478\) 6444.74 0.616685
\(479\) −4273.72 −0.407664 −0.203832 0.979006i \(-0.565340\pi\)
−0.203832 + 0.979006i \(0.565340\pi\)
\(480\) 19213.3 1.82701
\(481\) −330.427 −0.0313226
\(482\) 13967.9 1.31996
\(483\) 13133.2 1.23723
\(484\) −25227.2 −2.36920
\(485\) −17247.2 −1.61475
\(486\) −19954.6 −1.86247
\(487\) 8386.70 0.780365 0.390183 0.920738i \(-0.372412\pi\)
0.390183 + 0.920738i \(0.372412\pi\)
\(488\) 47981.5 4.45086
\(489\) −361.700 −0.0334492
\(490\) 11208.2 1.03334
\(491\) −1244.80 −0.114413 −0.0572066 0.998362i \(-0.518219\pi\)
−0.0572066 + 0.998362i \(0.518219\pi\)
\(492\) −29017.5 −2.65897
\(493\) −2080.23 −0.190038
\(494\) −1548.38 −0.141022
\(495\) −1793.00 −0.162807
\(496\) −35990.9 −3.25815
\(497\) 9072.90 0.818864
\(498\) 10461.1 0.941310
\(499\) −14306.3 −1.28345 −0.641724 0.766936i \(-0.721780\pi\)
−0.641724 + 0.766936i \(0.721780\pi\)
\(500\) −5590.70 −0.500047
\(501\) −8074.48 −0.720042
\(502\) 21937.1 1.95040
\(503\) 18603.4 1.64907 0.824536 0.565810i \(-0.191436\pi\)
0.824536 + 0.565810i \(0.191436\pi\)
\(504\) −22243.7 −1.96590
\(505\) 32666.9 2.87853
\(506\) −6475.87 −0.568947
\(507\) −6974.25 −0.610922
\(508\) −29297.4 −2.55878
\(509\) −457.414 −0.0398321 −0.0199160 0.999802i \(-0.506340\pi\)
−0.0199160 + 0.999802i \(0.506340\pi\)
\(510\) 3021.77 0.262365
\(511\) −20279.3 −1.75558
\(512\) 19272.7 1.66355
\(513\) −11811.4 −1.01654
\(514\) 31165.8 2.67444
\(515\) 24816.8 2.12341
\(516\) −25901.9 −2.20982
\(517\) 2932.90 0.249495
\(518\) −10816.5 −0.917470
\(519\) 318.866 0.0269685
\(520\) 3471.73 0.292780
\(521\) 12189.4 1.02500 0.512502 0.858686i \(-0.328719\pi\)
0.512502 + 0.858686i \(0.328719\pi\)
\(522\) −16661.7 −1.39705
\(523\) 8493.84 0.710152 0.355076 0.934837i \(-0.384455\pi\)
0.355076 + 0.934837i \(0.384455\pi\)
\(524\) 16761.5 1.39738
\(525\) −9895.46 −0.822616
\(526\) 22423.1 1.85873
\(527\) −2437.94 −0.201515
\(528\) −3387.58 −0.279215
\(529\) 23581.3 1.93814
\(530\) 35444.3 2.90491
\(531\) −184.151 −0.0150499
\(532\) −35983.4 −2.93248
\(533\) −1620.77 −0.131714
\(534\) 14407.3 1.16754
\(535\) −20521.7 −1.65838
\(536\) −57822.6 −4.65962
\(537\) −11136.5 −0.894929
\(538\) 4279.32 0.342927
\(539\) −851.126 −0.0680159
\(540\) 44780.1 3.56857
\(541\) 10630.9 0.844840 0.422420 0.906400i \(-0.361181\pi\)
0.422420 + 0.906400i \(0.361181\pi\)
\(542\) 23678.5 1.87653
\(543\) 3154.81 0.249329
\(544\) −4056.46 −0.319704
\(545\) −30332.5 −2.38404
\(546\) 1273.44 0.0998133
\(547\) −2563.87 −0.200408 −0.100204 0.994967i \(-0.531949\pi\)
−0.100204 + 0.994967i \(0.531949\pi\)
\(548\) 27344.1 2.13154
\(549\) 13263.9 1.03113
\(550\) 4879.36 0.378285
\(551\) −15940.4 −1.23245
\(552\) 36701.7 2.82994
\(553\) 26121.2 2.00866
\(554\) −18119.1 −1.38954
\(555\) 4941.36 0.377926
\(556\) 20000.6 1.52557
\(557\) 8133.45 0.618717 0.309359 0.950945i \(-0.399886\pi\)
0.309359 + 0.950945i \(0.399886\pi\)
\(558\) −19526.7 −1.48142
\(559\) −1446.75 −0.109465
\(560\) 57905.2 4.36954
\(561\) −229.466 −0.0172693
\(562\) −5268.69 −0.395456
\(563\) 23461.2 1.75625 0.878126 0.478430i \(-0.158794\pi\)
0.878126 + 0.478430i \(0.158794\pi\)
\(564\) −28106.0 −2.09836
\(565\) −27985.1 −2.08379
\(566\) 8284.38 0.615227
\(567\) −162.266 −0.0120186
\(568\) 25354.8 1.87300
\(569\) −19192.0 −1.41401 −0.707005 0.707208i \(-0.749954\pi\)
−0.707005 + 0.707208i \(0.749954\pi\)
\(570\) 23155.2 1.70152
\(571\) −11353.4 −0.832094 −0.416047 0.909343i \(-0.636585\pi\)
−0.416047 + 0.909343i \(0.636585\pi\)
\(572\) −445.777 −0.0325855
\(573\) 3211.23 0.234121
\(574\) −53055.7 −3.85802
\(575\) −26935.2 −1.95352
\(576\) −10608.1 −0.767371
\(577\) −18870.2 −1.36148 −0.680742 0.732523i \(-0.738343\pi\)
−0.680742 + 0.732523i \(0.738343\pi\)
\(578\) 25163.1 1.81081
\(579\) −4573.04 −0.328237
\(580\) 60434.0 4.32652
\(581\) 13578.8 0.969613
\(582\) −17679.3 −1.25916
\(583\) −2691.56 −0.191206
\(584\) −56671.8 −4.01558
\(585\) 959.718 0.0678281
\(586\) 18362.5 1.29445
\(587\) 16464.9 1.15771 0.578857 0.815429i \(-0.303499\pi\)
0.578857 + 0.815429i \(0.303499\pi\)
\(588\) 8156.35 0.572045
\(589\) −18681.4 −1.30688
\(590\) 940.855 0.0656515
\(591\) −7383.45 −0.513899
\(592\) −15401.5 −1.06925
\(593\) 6169.75 0.427253 0.213627 0.976915i \(-0.431472\pi\)
0.213627 + 0.976915i \(0.431472\pi\)
\(594\) −4789.92 −0.330864
\(595\) 3922.36 0.270254
\(596\) 19938.1 1.37030
\(597\) 5512.45 0.377905
\(598\) 3466.26 0.237033
\(599\) −4488.46 −0.306166 −0.153083 0.988213i \(-0.548920\pi\)
−0.153083 + 0.988213i \(0.548920\pi\)
\(600\) −27653.5 −1.88158
\(601\) 1010.49 0.0685835 0.0342917 0.999412i \(-0.489082\pi\)
0.0342917 + 0.999412i \(0.489082\pi\)
\(602\) −47359.0 −3.20633
\(603\) −15984.4 −1.07949
\(604\) 39607.0 2.66819
\(605\) 21071.8 1.41602
\(606\) 33485.2 2.24463
\(607\) −4640.78 −0.310318 −0.155159 0.987889i \(-0.549589\pi\)
−0.155159 + 0.987889i \(0.549589\pi\)
\(608\) −31083.8 −2.07338
\(609\) 13109.9 0.872313
\(610\) −67767.3 −4.49806
\(611\) −1569.86 −0.103944
\(612\) −3627.66 −0.239607
\(613\) 8923.45 0.587953 0.293976 0.955813i \(-0.405021\pi\)
0.293976 + 0.955813i \(0.405021\pi\)
\(614\) 19821.5 1.30282
\(615\) 24237.7 1.58920
\(616\) −8630.06 −0.564473
\(617\) −13366.0 −0.872118 −0.436059 0.899918i \(-0.643626\pi\)
−0.436059 + 0.899918i \(0.643626\pi\)
\(618\) 25438.5 1.65580
\(619\) 5687.05 0.369276 0.184638 0.982807i \(-0.440889\pi\)
0.184638 + 0.982807i \(0.440889\pi\)
\(620\) 70825.9 4.58780
\(621\) 26441.5 1.70863
\(622\) −10216.7 −0.658604
\(623\) 18701.2 1.20264
\(624\) 1813.23 0.116326
\(625\) −13137.7 −0.840812
\(626\) 37001.8 2.36244
\(627\) −1758.35 −0.111996
\(628\) 27043.7 1.71841
\(629\) −1043.26 −0.0661325
\(630\) 31416.2 1.98675
\(631\) −25995.8 −1.64006 −0.820029 0.572322i \(-0.806043\pi\)
−0.820029 + 0.572322i \(0.806043\pi\)
\(632\) 72997.5 4.59444
\(633\) 5969.22 0.374811
\(634\) 24598.6 1.54091
\(635\) 24471.5 1.52932
\(636\) 25793.3 1.60813
\(637\) 455.572 0.0283366
\(638\) −6464.35 −0.401138
\(639\) 7009.03 0.433917
\(640\) 6047.16 0.373492
\(641\) −18961.1 −1.16836 −0.584181 0.811624i \(-0.698584\pi\)
−0.584181 + 0.811624i \(0.698584\pi\)
\(642\) −21035.8 −1.29317
\(643\) 5249.29 0.321947 0.160974 0.986959i \(-0.448537\pi\)
0.160974 + 0.986959i \(0.448537\pi\)
\(644\) 80553.8 4.92898
\(645\) 21635.3 1.32076
\(646\) −4888.69 −0.297745
\(647\) −7734.97 −0.470005 −0.235002 0.971995i \(-0.575510\pi\)
−0.235002 + 0.971995i \(0.575510\pi\)
\(648\) −453.464 −0.0274903
\(649\) −71.4464 −0.00432129
\(650\) −2611.72 −0.157600
\(651\) 15364.2 0.924991
\(652\) −2218.52 −0.133258
\(653\) 12141.7 0.727627 0.363813 0.931472i \(-0.381475\pi\)
0.363813 + 0.931472i \(0.381475\pi\)
\(654\) −31092.4 −1.85903
\(655\) −14000.5 −0.835183
\(656\) −75545.3 −4.49627
\(657\) −15666.2 −0.930286
\(658\) −51389.1 −3.04461
\(659\) 3176.91 0.187792 0.0938960 0.995582i \(-0.470068\pi\)
0.0938960 + 0.995582i \(0.470068\pi\)
\(660\) 6666.36 0.393163
\(661\) −27717.3 −1.63098 −0.815490 0.578771i \(-0.803532\pi\)
−0.815490 + 0.578771i \(0.803532\pi\)
\(662\) −24554.5 −1.44159
\(663\) 122.824 0.00719469
\(664\) 37946.9 2.21781
\(665\) 30056.2 1.75267
\(666\) −8355.99 −0.486168
\(667\) 35684.7 2.07154
\(668\) −49525.5 −2.86856
\(669\) 2816.26 0.162755
\(670\) 81666.4 4.70903
\(671\) 5146.09 0.296070
\(672\) 25564.3 1.46751
\(673\) 15612.4 0.894225 0.447113 0.894478i \(-0.352452\pi\)
0.447113 + 0.894478i \(0.352452\pi\)
\(674\) −24935.1 −1.42502
\(675\) −19922.8 −1.13604
\(676\) −42777.2 −2.43384
\(677\) −5554.98 −0.315355 −0.157677 0.987491i \(-0.550401\pi\)
−0.157677 + 0.987491i \(0.550401\pi\)
\(678\) −28686.2 −1.62491
\(679\) −22948.3 −1.29702
\(680\) 10961.3 0.618156
\(681\) 14452.0 0.813218
\(682\) −7575.92 −0.425362
\(683\) −4086.19 −0.228922 −0.114461 0.993428i \(-0.536514\pi\)
−0.114461 + 0.993428i \(0.536514\pi\)
\(684\) −27798.0 −1.55392
\(685\) −22839.9 −1.27397
\(686\) −24283.3 −1.35152
\(687\) 15309.3 0.850196
\(688\) −67433.9 −3.73677
\(689\) 1440.68 0.0796597
\(690\) −51836.1 −2.85995
\(691\) −23164.0 −1.27525 −0.637627 0.770345i \(-0.720084\pi\)
−0.637627 + 0.770345i \(0.720084\pi\)
\(692\) 1955.79 0.107439
\(693\) −2385.68 −0.130771
\(694\) 17347.8 0.948865
\(695\) −16706.1 −0.911796
\(696\) 36636.4 1.99525
\(697\) −5117.25 −0.278091
\(698\) −46802.9 −2.53799
\(699\) 518.256 0.0280433
\(700\) −60694.7 −3.27720
\(701\) 9795.28 0.527764 0.263882 0.964555i \(-0.414997\pi\)
0.263882 + 0.964555i \(0.414997\pi\)
\(702\) 2563.85 0.137844
\(703\) −7994.25 −0.428889
\(704\) −4115.71 −0.220336
\(705\) 23476.4 1.25414
\(706\) 44702.2 2.38299
\(707\) 43464.9 2.31212
\(708\) 684.672 0.0363440
\(709\) −24622.5 −1.30426 −0.652128 0.758109i \(-0.726123\pi\)
−0.652128 + 0.758109i \(0.726123\pi\)
\(710\) −35810.2 −1.89286
\(711\) 20179.3 1.06439
\(712\) 52261.7 2.75083
\(713\) 41820.9 2.19664
\(714\) 4020.62 0.210739
\(715\) 372.349 0.0194756
\(716\) −68306.9 −3.56529
\(717\) −3917.39 −0.204041
\(718\) 6163.39 0.320356
\(719\) −11684.0 −0.606033 −0.303017 0.952985i \(-0.597994\pi\)
−0.303017 + 0.952985i \(0.597994\pi\)
\(720\) 44733.2 2.31543
\(721\) 33020.0 1.70559
\(722\) −1440.27 −0.0742402
\(723\) −8490.29 −0.436732
\(724\) 19350.3 0.993297
\(725\) −26887.3 −1.37733
\(726\) 21599.7 1.10419
\(727\) −17381.1 −0.886699 −0.443350 0.896349i \(-0.646210\pi\)
−0.443350 + 0.896349i \(0.646210\pi\)
\(728\) 4619.31 0.235169
\(729\) 11927.9 0.606001
\(730\) 80041.1 4.05816
\(731\) −4567.81 −0.231117
\(732\) −49315.1 −2.49008
\(733\) −7832.92 −0.394701 −0.197350 0.980333i \(-0.563234\pi\)
−0.197350 + 0.980333i \(0.563234\pi\)
\(734\) −42137.5 −2.11897
\(735\) −6812.83 −0.341898
\(736\) 69585.3 3.48498
\(737\) −6201.56 −0.309956
\(738\) −40986.8 −2.04437
\(739\) −25124.2 −1.25062 −0.625309 0.780377i \(-0.715027\pi\)
−0.625309 + 0.780377i \(0.715027\pi\)
\(740\) 30308.2 1.50561
\(741\) 941.172 0.0466597
\(742\) 47160.5 2.33331
\(743\) 38845.7 1.91805 0.959026 0.283319i \(-0.0914357\pi\)
0.959026 + 0.283319i \(0.0914357\pi\)
\(744\) 42936.2 2.11575
\(745\) −16653.9 −0.818994
\(746\) 16770.3 0.823064
\(747\) 10490.0 0.513799
\(748\) −1407.45 −0.0687988
\(749\) −27305.2 −1.33206
\(750\) 4786.78 0.233051
\(751\) −5345.96 −0.259756 −0.129878 0.991530i \(-0.541459\pi\)
−0.129878 + 0.991530i \(0.541459\pi\)
\(752\) −73172.3 −3.54830
\(753\) −13334.3 −0.645324
\(754\) 3460.09 0.167121
\(755\) −33082.9 −1.59471
\(756\) 59582.2 2.86638
\(757\) −22152.0 −1.06358 −0.531788 0.846877i \(-0.678480\pi\)
−0.531788 + 0.846877i \(0.678480\pi\)
\(758\) −145.495 −0.00697180
\(759\) 3936.31 0.188246
\(760\) 83993.9 4.00892
\(761\) 20608.5 0.981678 0.490839 0.871250i \(-0.336690\pi\)
0.490839 + 0.871250i \(0.336690\pi\)
\(762\) 25084.5 1.19254
\(763\) −40358.9 −1.91493
\(764\) 19696.4 0.932709
\(765\) 3030.11 0.143208
\(766\) 41001.4 1.93400
\(767\) 38.2423 0.00180032
\(768\) −9916.71 −0.465935
\(769\) −6404.10 −0.300309 −0.150155 0.988663i \(-0.547977\pi\)
−0.150155 + 0.988663i \(0.547977\pi\)
\(770\) 12188.8 0.570459
\(771\) −18943.9 −0.884887
\(772\) −28049.1 −1.30765
\(773\) −13210.2 −0.614666 −0.307333 0.951602i \(-0.599437\pi\)
−0.307333 + 0.951602i \(0.599437\pi\)
\(774\) −36586.0 −1.69904
\(775\) −31510.7 −1.46051
\(776\) −64130.4 −2.96669
\(777\) 6574.73 0.303561
\(778\) −18752.8 −0.864164
\(779\) −39212.4 −1.80351
\(780\) −3568.22 −0.163799
\(781\) 2719.34 0.124591
\(782\) 10944.0 0.500457
\(783\) 26394.4 1.20467
\(784\) 21234.6 0.967318
\(785\) −22589.1 −1.02706
\(786\) −14351.2 −0.651262
\(787\) −19340.7 −0.876012 −0.438006 0.898972i \(-0.644315\pi\)
−0.438006 + 0.898972i \(0.644315\pi\)
\(788\) −45287.0 −2.04731
\(789\) −13629.7 −0.614995
\(790\) −103099. −4.64316
\(791\) −37235.6 −1.67376
\(792\) −6666.93 −0.299115
\(793\) −2754.49 −0.123348
\(794\) −72808.5 −3.25425
\(795\) −21544.6 −0.961142
\(796\) 33811.1 1.50553
\(797\) 23294.1 1.03528 0.517641 0.855598i \(-0.326810\pi\)
0.517641 + 0.855598i \(0.326810\pi\)
\(798\) 30809.1 1.36671
\(799\) −4956.51 −0.219460
\(800\) −52430.3 −2.31711
\(801\) 14447.1 0.637283
\(802\) 8118.95 0.357469
\(803\) −6078.14 −0.267115
\(804\) 59429.7 2.60687
\(805\) −67284.9 −2.94594
\(806\) 4055.08 0.177213
\(807\) −2601.15 −0.113463
\(808\) 121466. 5.28854
\(809\) −42696.9 −1.85555 −0.927777 0.373135i \(-0.878283\pi\)
−0.927777 + 0.373135i \(0.878283\pi\)
\(810\) 640.455 0.0277818
\(811\) 16497.6 0.714313 0.357156 0.934045i \(-0.383746\pi\)
0.357156 + 0.934045i \(0.383746\pi\)
\(812\) 80410.4 3.47519
\(813\) −14392.8 −0.620882
\(814\) −3241.94 −0.139594
\(815\) 1853.08 0.0796450
\(816\) 5724.91 0.245603
\(817\) −35002.1 −1.49886
\(818\) 67015.5 2.86448
\(819\) 1276.95 0.0544815
\(820\) 148664. 6.33120
\(821\) −26383.0 −1.12152 −0.560762 0.827977i \(-0.689492\pi\)
−0.560762 + 0.827977i \(0.689492\pi\)
\(822\) −23412.1 −0.993420
\(823\) −22798.2 −0.965609 −0.482805 0.875728i \(-0.660382\pi\)
−0.482805 + 0.875728i \(0.660382\pi\)
\(824\) 92276.4 3.90122
\(825\) −2965.88 −0.125162
\(826\) 1251.86 0.0527332
\(827\) 13799.9 0.580254 0.290127 0.956988i \(-0.406303\pi\)
0.290127 + 0.956988i \(0.406303\pi\)
\(828\) 62229.7 2.61187
\(829\) −25392.7 −1.06384 −0.531920 0.846795i \(-0.678529\pi\)
−0.531920 + 0.846795i \(0.678529\pi\)
\(830\) −53594.8 −2.24133
\(831\) 11013.6 0.459755
\(832\) 2202.97 0.0917960
\(833\) 1438.38 0.0598280
\(834\) −17124.6 −0.711003
\(835\) 41367.6 1.71447
\(836\) −10785.0 −0.446180
\(837\) 30933.1 1.27742
\(838\) 25908.1 1.06800
\(839\) 36314.1 1.49428 0.747140 0.664666i \(-0.231426\pi\)
0.747140 + 0.664666i \(0.231426\pi\)
\(840\) −69079.3 −2.83745
\(841\) 11232.2 0.460544
\(842\) 1959.12 0.0801851
\(843\) 3202.54 0.130844
\(844\) 36612.7 1.49320
\(845\) 35730.9 1.45465
\(846\) −39699.3 −1.61335
\(847\) 28037.1 1.13739
\(848\) 67151.2 2.71932
\(849\) −5035.60 −0.203559
\(850\) −8245.96 −0.332746
\(851\) 17896.2 0.720887
\(852\) −26059.5 −1.04787
\(853\) 24198.9 0.971343 0.485671 0.874141i \(-0.338575\pi\)
0.485671 + 0.874141i \(0.338575\pi\)
\(854\) −90167.8 −3.61297
\(855\) 23219.1 0.928745
\(856\) −76306.1 −3.04683
\(857\) −5309.45 −0.211630 −0.105815 0.994386i \(-0.533745\pi\)
−0.105815 + 0.994386i \(0.533745\pi\)
\(858\) 381.677 0.0151867
\(859\) 23054.1 0.915710 0.457855 0.889027i \(-0.348618\pi\)
0.457855 + 0.889027i \(0.348618\pi\)
\(860\) 132702. 5.26174
\(861\) 32249.5 1.27649
\(862\) −84032.4 −3.32036
\(863\) −18397.8 −0.725688 −0.362844 0.931850i \(-0.618194\pi\)
−0.362844 + 0.931850i \(0.618194\pi\)
\(864\) 51469.3 2.02664
\(865\) −1633.63 −0.0642140
\(866\) 67768.5 2.65920
\(867\) −15295.2 −0.599139
\(868\) 94237.4 3.68505
\(869\) 7829.10 0.305620
\(870\) −51743.8 −2.01641
\(871\) 3319.44 0.129133
\(872\) −112786. −4.38005
\(873\) −17728.1 −0.687290
\(874\) 83861.6 3.24561
\(875\) 6213.39 0.240058
\(876\) 58246.9 2.24655
\(877\) 2044.74 0.0787296 0.0393648 0.999225i \(-0.487467\pi\)
0.0393648 + 0.999225i \(0.487467\pi\)
\(878\) 77780.0 2.98969
\(879\) −11161.5 −0.428293
\(880\) 17355.4 0.664832
\(881\) 13291.6 0.508293 0.254147 0.967166i \(-0.418205\pi\)
0.254147 + 0.967166i \(0.418205\pi\)
\(882\) 11520.7 0.439821
\(883\) 39342.5 1.49941 0.749707 0.661770i \(-0.230195\pi\)
0.749707 + 0.661770i \(0.230195\pi\)
\(884\) 753.350 0.0286628
\(885\) −571.892 −0.0217220
\(886\) −15541.8 −0.589320
\(887\) −36087.9 −1.36608 −0.683040 0.730381i \(-0.739342\pi\)
−0.683040 + 0.730381i \(0.739342\pi\)
\(888\) 18373.5 0.694341
\(889\) 32560.5 1.22840
\(890\) −73812.5 −2.78000
\(891\) −48.6347 −0.00182865
\(892\) 17273.8 0.648395
\(893\) −37980.7 −1.42326
\(894\) −17071.1 −0.638638
\(895\) 57055.3 2.13089
\(896\) 8046.05 0.300000
\(897\) −2106.94 −0.0784267
\(898\) −27452.7 −1.02017
\(899\) 41746.4 1.54875
\(900\) −46888.1 −1.73659
\(901\) 4548.65 0.168188
\(902\) −15901.9 −0.587003
\(903\) 28786.9 1.06087
\(904\) −104057. −3.82843
\(905\) −16162.9 −0.593671
\(906\) −33911.7 −1.24353
\(907\) −8155.39 −0.298561 −0.149281 0.988795i \(-0.547696\pi\)
−0.149281 + 0.988795i \(0.547696\pi\)
\(908\) 88642.5 3.23976
\(909\) 33577.7 1.22519
\(910\) −6524.14 −0.237663
\(911\) 18432.4 0.670354 0.335177 0.942155i \(-0.391204\pi\)
0.335177 + 0.942155i \(0.391204\pi\)
\(912\) 43868.7 1.59281
\(913\) 4069.87 0.147528
\(914\) 18167.6 0.657475
\(915\) 41191.9 1.48826
\(916\) 93900.6 3.38708
\(917\) −18628.4 −0.670843
\(918\) 8094.82 0.291034
\(919\) −27174.8 −0.975425 −0.487712 0.873004i \(-0.662169\pi\)
−0.487712 + 0.873004i \(0.662169\pi\)
\(920\) −188032. −6.73829
\(921\) −12048.4 −0.431061
\(922\) −932.470 −0.0333072
\(923\) −1455.55 −0.0519069
\(924\) 8869.93 0.315800
\(925\) −13484.2 −0.479307
\(926\) 29996.7 1.06453
\(927\) 25508.7 0.903793
\(928\) 69461.5 2.45709
\(929\) −45169.7 −1.59523 −0.797616 0.603166i \(-0.793906\pi\)
−0.797616 + 0.603166i \(0.793906\pi\)
\(930\) −60641.4 −2.13818
\(931\) 11022.0 0.388002
\(932\) 3178.77 0.111721
\(933\) 6210.14 0.217911
\(934\) −1509.86 −0.0528953
\(935\) 1175.61 0.0411195
\(936\) 3568.53 0.124616
\(937\) −33372.6 −1.16354 −0.581769 0.813354i \(-0.697639\pi\)
−0.581769 + 0.813354i \(0.697639\pi\)
\(938\) 108661. 3.78243
\(939\) −22491.3 −0.781657
\(940\) 143994. 4.99636
\(941\) 38628.6 1.33821 0.669105 0.743168i \(-0.266678\pi\)
0.669105 + 0.743168i \(0.266678\pi\)
\(942\) −23155.0 −0.800880
\(943\) 87782.4 3.03138
\(944\) 1782.50 0.0614571
\(945\) −49767.8 −1.71317
\(946\) −14194.5 −0.487847
\(947\) −20614.4 −0.707367 −0.353684 0.935365i \(-0.615071\pi\)
−0.353684 + 0.935365i \(0.615071\pi\)
\(948\) −75026.4 −2.57040
\(949\) 3253.38 0.111285
\(950\) −63187.0 −2.15796
\(951\) −14952.1 −0.509837
\(952\) 14584.5 0.496520
\(953\) −38022.3 −1.29241 −0.646203 0.763166i \(-0.723644\pi\)
−0.646203 + 0.763166i \(0.723644\pi\)
\(954\) 36432.6 1.23642
\(955\) −16452.0 −0.557459
\(956\) −24027.6 −0.812876
\(957\) 3929.31 0.132724
\(958\) 22443.9 0.756919
\(959\) −30389.7 −1.02329
\(960\) −32944.2 −1.10757
\(961\) 19134.0 0.642273
\(962\) 1735.27 0.0581574
\(963\) −21093.9 −0.705858
\(964\) −52075.9 −1.73989
\(965\) 23428.8 0.781555
\(966\) −68970.5 −2.29719
\(967\) −11846.4 −0.393956 −0.196978 0.980408i \(-0.563113\pi\)
−0.196978 + 0.980408i \(0.563113\pi\)
\(968\) 78351.4 2.60156
\(969\) 2971.56 0.0985141
\(970\) 90575.4 2.99815
\(971\) 6248.67 0.206518 0.103259 0.994654i \(-0.467073\pi\)
0.103259 + 0.994654i \(0.467073\pi\)
\(972\) 74395.9 2.45499
\(973\) −22228.3 −0.732381
\(974\) −44043.6 −1.44892
\(975\) 1587.51 0.0521447
\(976\) −128389. −4.21068
\(977\) −38809.5 −1.27086 −0.635428 0.772160i \(-0.719176\pi\)
−0.635428 + 0.772160i \(0.719176\pi\)
\(978\) 1899.51 0.0621059
\(979\) 5605.15 0.182984
\(980\) −41787.1 −1.36208
\(981\) −31178.2 −1.01472
\(982\) 6537.17 0.212433
\(983\) −983.000 −0.0318950
\(984\) 90123.4 2.91975
\(985\) 37827.3 1.22363
\(986\) 10924.5 0.352848
\(987\) 31236.5 1.00736
\(988\) 5772.76 0.185887
\(989\) 78357.1 2.51932
\(990\) 9416.12 0.302287
\(991\) −47518.7 −1.52319 −0.761595 0.648053i \(-0.775583\pi\)
−0.761595 + 0.648053i \(0.775583\pi\)
\(992\) 81405.7 2.60548
\(993\) 14925.3 0.476977
\(994\) −47647.3 −1.52040
\(995\) −28241.7 −0.899820
\(996\) −39001.6 −1.24078
\(997\) −45562.4 −1.44732 −0.723659 0.690158i \(-0.757541\pi\)
−0.723659 + 0.690158i \(0.757541\pi\)
\(998\) 75131.2 2.38300
\(999\) 13237.1 0.419222
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 983.4.a.b.1.6 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.4.a.b.1.6 136 1.1 even 1 trivial