Properties

Label 2166.4.a.s.1.2
Level $2166$
Weight $4$
Character 2166.1
Self dual yes
Analytic conductor $127.798$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2166.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.798137072\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1524.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3}\cdot 3 \)
Twist minimal: no (minimal twist has level 114)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.27307\) of defining polynomial
Character \(\chi\) \(=\) 2166.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.21359 q^{5} +6.00000 q^{6} +31.4905 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.21359 q^{5} +6.00000 q^{6} +31.4905 q^{7} -8.00000 q^{8} +9.00000 q^{9} +10.4272 q^{10} -21.2113 q^{11} -12.0000 q^{12} +56.2769 q^{13} -62.9809 q^{14} +15.6408 q^{15} +16.0000 q^{16} +17.2792 q^{17} -18.0000 q^{18} -20.8543 q^{20} -94.4714 q^{21} +42.4225 q^{22} -206.316 q^{23} +24.0000 q^{24} -97.8185 q^{25} -112.554 q^{26} -27.0000 q^{27} +125.962 q^{28} +206.513 q^{29} -31.2815 q^{30} +129.624 q^{31} -32.0000 q^{32} +63.6338 q^{33} -34.5584 q^{34} -164.178 q^{35} +36.0000 q^{36} +440.212 q^{37} -168.831 q^{39} +41.7087 q^{40} +435.454 q^{41} +188.943 q^{42} +129.997 q^{43} -84.8451 q^{44} -46.9223 q^{45} +412.633 q^{46} +108.482 q^{47} -48.0000 q^{48} +648.649 q^{49} +195.637 q^{50} -51.8376 q^{51} +225.107 q^{52} -407.280 q^{53} +54.0000 q^{54} +110.587 q^{55} -251.924 q^{56} -413.027 q^{58} -116.245 q^{59} +62.5630 q^{60} -340.684 q^{61} -259.248 q^{62} +283.414 q^{63} +64.0000 q^{64} -293.404 q^{65} -127.268 q^{66} -210.745 q^{67} +69.1168 q^{68} +618.949 q^{69} +328.356 q^{70} +158.017 q^{71} -72.0000 q^{72} +573.547 q^{73} -880.424 q^{74} +293.456 q^{75} -667.952 q^{77} +337.661 q^{78} -885.297 q^{79} -83.4174 q^{80} +81.0000 q^{81} -870.907 q^{82} -573.632 q^{83} -377.886 q^{84} -90.0866 q^{85} -259.994 q^{86} -619.540 q^{87} +169.690 q^{88} +215.235 q^{89} +93.8446 q^{90} +1772.18 q^{91} -825.266 q^{92} -388.872 q^{93} -216.964 q^{94} +96.0000 q^{96} +528.974 q^{97} -1297.30 q^{98} -190.901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 6q^{2} - 9q^{3} + 12q^{4} + 2q^{5} + 18q^{6} - 17q^{7} - 24q^{8} + 27q^{9} + O(q^{10}) \) \( 3q - 6q^{2} - 9q^{3} + 12q^{4} + 2q^{5} + 18q^{6} - 17q^{7} - 24q^{8} + 27q^{9} - 4q^{10} - 52q^{11} - 36q^{12} + 75q^{13} + 34q^{14} - 6q^{15} + 48q^{16} - 48q^{17} - 54q^{18} + 8q^{20} + 51q^{21} + 104q^{22} - 238q^{23} + 72q^{24} + 229q^{25} - 150q^{26} - 81q^{27} - 68q^{28} - 8q^{29} + 12q^{30} + 107q^{31} - 96q^{32} + 156q^{33} + 96q^{34} - 294q^{35} + 108q^{36} + 305q^{37} - 225q^{39} - 16q^{40} + 16q^{41} - 102q^{42} - 331q^{43} - 208q^{44} + 18q^{45} + 476q^{46} - 766q^{47} - 144q^{48} + 1142q^{49} - 458q^{50} + 144q^{51} + 300q^{52} - 118q^{53} + 162q^{54} - 1400q^{55} + 136q^{56} + 16q^{58} + 936q^{59} - 24q^{60} - 399q^{61} - 214q^{62} - 153q^{63} + 192q^{64} + 370q^{65} - 312q^{66} + 61q^{67} - 192q^{68} + 714q^{69} + 588q^{70} + 974q^{71} - 216q^{72} + 91q^{73} - 610q^{74} - 687q^{75} - 36q^{77} + 450q^{78} - 321q^{79} + 32q^{80} + 243q^{81} - 32q^{82} - 2148q^{83} + 204q^{84} - 1680q^{85} + 662q^{86} + 24q^{87} + 416q^{88} + 1116q^{89} - 36q^{90} + 1367q^{91} - 952q^{92} - 321q^{93} + 1532q^{94} + 288q^{96} + 1382q^{97} - 2284q^{98} - 468q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) −5.21359 −0.466317 −0.233159 0.972439i \(-0.574906\pi\)
−0.233159 + 0.972439i \(0.574906\pi\)
\(6\) 6.00000 0.408248
\(7\) 31.4905 1.70033 0.850163 0.526520i \(-0.176504\pi\)
0.850163 + 0.526520i \(0.176504\pi\)
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) 10.4272 0.329736
\(11\) −21.2113 −0.581403 −0.290702 0.956814i \(-0.593889\pi\)
−0.290702 + 0.956814i \(0.593889\pi\)
\(12\) −12.0000 −0.288675
\(13\) 56.2769 1.20065 0.600323 0.799758i \(-0.295039\pi\)
0.600323 + 0.799758i \(0.295039\pi\)
\(14\) −62.9809 −1.20231
\(15\) 15.6408 0.269228
\(16\) 16.0000 0.250000
\(17\) 17.2792 0.246519 0.123259 0.992374i \(-0.460665\pi\)
0.123259 + 0.992374i \(0.460665\pi\)
\(18\) −18.0000 −0.235702
\(19\) 0 0
\(20\) −20.8543 −0.233159
\(21\) −94.4714 −0.981683
\(22\) 42.4225 0.411114
\(23\) −206.316 −1.87043 −0.935216 0.354077i \(-0.884795\pi\)
−0.935216 + 0.354077i \(0.884795\pi\)
\(24\) 24.0000 0.204124
\(25\) −97.8185 −0.782548
\(26\) −112.554 −0.848985
\(27\) −27.0000 −0.192450
\(28\) 125.962 0.850163
\(29\) 206.513 1.32236 0.661182 0.750226i \(-0.270055\pi\)
0.661182 + 0.750226i \(0.270055\pi\)
\(30\) −31.2815 −0.190373
\(31\) 129.624 0.751005 0.375503 0.926821i \(-0.377470\pi\)
0.375503 + 0.926821i \(0.377470\pi\)
\(32\) −32.0000 −0.176777
\(33\) 63.6338 0.335673
\(34\) −34.5584 −0.174315
\(35\) −164.178 −0.792891
\(36\) 36.0000 0.166667
\(37\) 440.212 1.95596 0.977979 0.208704i \(-0.0669245\pi\)
0.977979 + 0.208704i \(0.0669245\pi\)
\(38\) 0 0
\(39\) −168.831 −0.693193
\(40\) 41.7087 0.164868
\(41\) 435.454 1.65869 0.829347 0.558734i \(-0.188713\pi\)
0.829347 + 0.558734i \(0.188713\pi\)
\(42\) 188.943 0.694155
\(43\) 129.997 0.461031 0.230515 0.973069i \(-0.425959\pi\)
0.230515 + 0.973069i \(0.425959\pi\)
\(44\) −84.8451 −0.290702
\(45\) −46.9223 −0.155439
\(46\) 412.633 1.32260
\(47\) 108.482 0.336675 0.168338 0.985729i \(-0.446160\pi\)
0.168338 + 0.985729i \(0.446160\pi\)
\(48\) −48.0000 −0.144338
\(49\) 648.649 1.89111
\(50\) 195.637 0.553345
\(51\) −51.8376 −0.142328
\(52\) 225.107 0.600323
\(53\) −407.280 −1.05555 −0.527776 0.849384i \(-0.676974\pi\)
−0.527776 + 0.849384i \(0.676974\pi\)
\(54\) 54.0000 0.136083
\(55\) 110.587 0.271118
\(56\) −251.924 −0.601156
\(57\) 0 0
\(58\) −413.027 −0.935052
\(59\) −116.245 −0.256505 −0.128252 0.991742i \(-0.540937\pi\)
−0.128252 + 0.991742i \(0.540937\pi\)
\(60\) 62.5630 0.134614
\(61\) −340.684 −0.715085 −0.357542 0.933897i \(-0.616385\pi\)
−0.357542 + 0.933897i \(0.616385\pi\)
\(62\) −259.248 −0.531041
\(63\) 283.414 0.566775
\(64\) 64.0000 0.125000
\(65\) −293.404 −0.559882
\(66\) −127.268 −0.237357
\(67\) −210.745 −0.384278 −0.192139 0.981368i \(-0.561543\pi\)
−0.192139 + 0.981368i \(0.561543\pi\)
\(68\) 69.1168 0.123259
\(69\) 618.949 1.07989
\(70\) 328.356 0.560659
\(71\) 158.017 0.264130 0.132065 0.991241i \(-0.457839\pi\)
0.132065 + 0.991241i \(0.457839\pi\)
\(72\) −72.0000 −0.117851
\(73\) 573.547 0.919570 0.459785 0.888030i \(-0.347926\pi\)
0.459785 + 0.888030i \(0.347926\pi\)
\(74\) −880.424 −1.38307
\(75\) 293.456 0.451804
\(76\) 0 0
\(77\) −667.952 −0.988575
\(78\) 337.661 0.490162
\(79\) −885.297 −1.26081 −0.630403 0.776268i \(-0.717110\pi\)
−0.630403 + 0.776268i \(0.717110\pi\)
\(80\) −83.4174 −0.116579
\(81\) 81.0000 0.111111
\(82\) −870.907 −1.17287
\(83\) −573.632 −0.758606 −0.379303 0.925273i \(-0.623836\pi\)
−0.379303 + 0.925273i \(0.623836\pi\)
\(84\) −377.886 −0.490842
\(85\) −90.0866 −0.114956
\(86\) −259.994 −0.325998
\(87\) −619.540 −0.763467
\(88\) 169.690 0.205557
\(89\) 215.235 0.256347 0.128174 0.991752i \(-0.459089\pi\)
0.128174 + 0.991752i \(0.459089\pi\)
\(90\) 93.8446 0.109912
\(91\) 1772.18 2.04149
\(92\) −825.266 −0.935216
\(93\) −388.872 −0.433593
\(94\) −216.964 −0.238065
\(95\) 0 0
\(96\) 96.0000 0.102062
\(97\) 528.974 0.553703 0.276851 0.960913i \(-0.410709\pi\)
0.276851 + 0.960913i \(0.410709\pi\)
\(98\) −1297.30 −1.33721
\(99\) −190.901 −0.193801
\(100\) −391.274 −0.391274
\(101\) 1028.74 1.01350 0.506748 0.862094i \(-0.330848\pi\)
0.506748 + 0.862094i \(0.330848\pi\)
\(102\) 103.675 0.100641
\(103\) 108.300 0.103603 0.0518016 0.998657i \(-0.483504\pi\)
0.0518016 + 0.998657i \(0.483504\pi\)
\(104\) −450.215 −0.424492
\(105\) 492.535 0.457776
\(106\) 814.560 0.746388
\(107\) −1820.02 −1.64438 −0.822188 0.569215i \(-0.807247\pi\)
−0.822188 + 0.569215i \(0.807247\pi\)
\(108\) −108.000 −0.0962250
\(109\) −119.143 −0.104696 −0.0523480 0.998629i \(-0.516671\pi\)
−0.0523480 + 0.998629i \(0.516671\pi\)
\(110\) −221.174 −0.191710
\(111\) −1320.64 −1.12927
\(112\) 503.847 0.425081
\(113\) 1014.96 0.844949 0.422474 0.906375i \(-0.361162\pi\)
0.422474 + 0.906375i \(0.361162\pi\)
\(114\) 0 0
\(115\) 1075.65 0.872215
\(116\) 826.053 0.661182
\(117\) 506.492 0.400215
\(118\) 232.490 0.181376
\(119\) 544.130 0.419162
\(120\) −125.126 −0.0951866
\(121\) −881.082 −0.661970
\(122\) 681.369 0.505641
\(123\) −1306.36 −0.957647
\(124\) 518.496 0.375503
\(125\) 1161.68 0.831233
\(126\) −566.828 −0.400770
\(127\) 1028.20 0.718410 0.359205 0.933259i \(-0.383048\pi\)
0.359205 + 0.933259i \(0.383048\pi\)
\(128\) −128.000 −0.0883883
\(129\) −389.990 −0.266176
\(130\) 586.809 0.395896
\(131\) −1589.17 −1.05990 −0.529948 0.848030i \(-0.677788\pi\)
−0.529948 + 0.848030i \(0.677788\pi\)
\(132\) 254.535 0.167837
\(133\) 0 0
\(134\) 421.491 0.271726
\(135\) 140.767 0.0897428
\(136\) −138.234 −0.0871576
\(137\) −2325.07 −1.44995 −0.724977 0.688773i \(-0.758150\pi\)
−0.724977 + 0.688773i \(0.758150\pi\)
\(138\) −1237.90 −0.763601
\(139\) 635.056 0.387516 0.193758 0.981049i \(-0.437932\pi\)
0.193758 + 0.981049i \(0.437932\pi\)
\(140\) −656.713 −0.396446
\(141\) −325.446 −0.194380
\(142\) −316.034 −0.186768
\(143\) −1193.70 −0.698060
\(144\) 144.000 0.0833333
\(145\) −1076.67 −0.616641
\(146\) −1147.09 −0.650234
\(147\) −1945.95 −1.09183
\(148\) 1760.85 0.977979
\(149\) 1698.31 0.933767 0.466883 0.884319i \(-0.345377\pi\)
0.466883 + 0.884319i \(0.345377\pi\)
\(150\) −586.911 −0.319474
\(151\) −1632.38 −0.879745 −0.439873 0.898060i \(-0.644976\pi\)
−0.439873 + 0.898060i \(0.644976\pi\)
\(152\) 0 0
\(153\) 155.513 0.0821730
\(154\) 1335.90 0.699028
\(155\) −675.806 −0.350207
\(156\) −675.322 −0.346597
\(157\) 2962.57 1.50598 0.752990 0.658032i \(-0.228611\pi\)
0.752990 + 0.658032i \(0.228611\pi\)
\(158\) 1770.59 0.891525
\(159\) 1221.84 0.609423
\(160\) 166.835 0.0824340
\(161\) −6497.00 −3.18034
\(162\) −162.000 −0.0785674
\(163\) 626.972 0.301277 0.150639 0.988589i \(-0.451867\pi\)
0.150639 + 0.988589i \(0.451867\pi\)
\(164\) 1741.81 0.829347
\(165\) −331.760 −0.156530
\(166\) 1147.26 0.536415
\(167\) 1602.16 0.742387 0.371193 0.928556i \(-0.378949\pi\)
0.371193 + 0.928556i \(0.378949\pi\)
\(168\) 755.771 0.347077
\(169\) 970.087 0.441551
\(170\) 180.173 0.0812862
\(171\) 0 0
\(172\) 519.987 0.230515
\(173\) 2290.69 1.00669 0.503346 0.864085i \(-0.332102\pi\)
0.503346 + 0.864085i \(0.332102\pi\)
\(174\) 1239.08 0.539853
\(175\) −3080.35 −1.33059
\(176\) −339.380 −0.145351
\(177\) 348.734 0.148093
\(178\) −430.471 −0.181265
\(179\) −218.545 −0.0912558 −0.0456279 0.998959i \(-0.514529\pi\)
−0.0456279 + 0.998959i \(0.514529\pi\)
\(180\) −187.689 −0.0777196
\(181\) −3748.44 −1.53933 −0.769667 0.638446i \(-0.779578\pi\)
−0.769667 + 0.638446i \(0.779578\pi\)
\(182\) −3544.37 −1.44355
\(183\) 1022.05 0.412854
\(184\) 1650.53 0.661298
\(185\) −2295.08 −0.912097
\(186\) 777.744 0.306597
\(187\) −366.514 −0.143327
\(188\) 433.928 0.168338
\(189\) −850.242 −0.327228
\(190\) 0 0
\(191\) −141.733 −0.0536935 −0.0268467 0.999640i \(-0.508547\pi\)
−0.0268467 + 0.999640i \(0.508547\pi\)
\(192\) −192.000 −0.0721688
\(193\) −3909.89 −1.45824 −0.729120 0.684386i \(-0.760070\pi\)
−0.729120 + 0.684386i \(0.760070\pi\)
\(194\) −1057.95 −0.391527
\(195\) 880.213 0.323248
\(196\) 2594.60 0.945553
\(197\) 1203.16 0.435134 0.217567 0.976045i \(-0.430188\pi\)
0.217567 + 0.976045i \(0.430188\pi\)
\(198\) 381.803 0.137038
\(199\) 3703.46 1.31925 0.659626 0.751594i \(-0.270715\pi\)
0.659626 + 0.751594i \(0.270715\pi\)
\(200\) 782.548 0.276673
\(201\) 632.236 0.221863
\(202\) −2057.47 −0.716649
\(203\) 6503.20 2.24845
\(204\) −207.350 −0.0711639
\(205\) −2270.28 −0.773478
\(206\) −216.600 −0.0732586
\(207\) −1856.85 −0.623478
\(208\) 900.430 0.300161
\(209\) 0 0
\(210\) −985.069 −0.323696
\(211\) −25.6998 −0.00838506 −0.00419253 0.999991i \(-0.501335\pi\)
−0.00419253 + 0.999991i \(0.501335\pi\)
\(212\) −1629.12 −0.527776
\(213\) −474.052 −0.152495
\(214\) 3640.05 1.16275
\(215\) −677.749 −0.214987
\(216\) 216.000 0.0680414
\(217\) 4081.92 1.27695
\(218\) 238.287 0.0740312
\(219\) −1720.64 −0.530914
\(220\) 442.347 0.135559
\(221\) 972.419 0.295982
\(222\) 2641.27 0.798516
\(223\) −3105.19 −0.932461 −0.466230 0.884663i \(-0.654388\pi\)
−0.466230 + 0.884663i \(0.654388\pi\)
\(224\) −1007.69 −0.300578
\(225\) −880.367 −0.260849
\(226\) −2029.92 −0.597469
\(227\) 664.566 0.194312 0.0971560 0.995269i \(-0.469025\pi\)
0.0971560 + 0.995269i \(0.469025\pi\)
\(228\) 0 0
\(229\) −6031.99 −1.74063 −0.870317 0.492492i \(-0.836086\pi\)
−0.870317 + 0.492492i \(0.836086\pi\)
\(230\) −2151.30 −0.616749
\(231\) 2003.86 0.570754
\(232\) −1652.11 −0.467526
\(233\) −5758.16 −1.61901 −0.809506 0.587112i \(-0.800265\pi\)
−0.809506 + 0.587112i \(0.800265\pi\)
\(234\) −1012.98 −0.282995
\(235\) −565.581 −0.156998
\(236\) −464.979 −0.128252
\(237\) 2655.89 0.727927
\(238\) −1088.26 −0.296392
\(239\) −741.406 −0.200659 −0.100330 0.994954i \(-0.531990\pi\)
−0.100330 + 0.994954i \(0.531990\pi\)
\(240\) 250.252 0.0673071
\(241\) 5274.07 1.40968 0.704840 0.709367i \(-0.251019\pi\)
0.704840 + 0.709367i \(0.251019\pi\)
\(242\) 1762.16 0.468084
\(243\) −243.000 −0.0641500
\(244\) −1362.74 −0.357542
\(245\) −3381.79 −0.881855
\(246\) 2612.72 0.677159
\(247\) 0 0
\(248\) −1036.99 −0.265520
\(249\) 1720.90 0.437981
\(250\) −2323.37 −0.587771
\(251\) 2846.36 0.715778 0.357889 0.933764i \(-0.383497\pi\)
0.357889 + 0.933764i \(0.383497\pi\)
\(252\) 1133.66 0.283388
\(253\) 4376.23 1.08748
\(254\) −2056.40 −0.507993
\(255\) 270.260 0.0663699
\(256\) 256.000 0.0625000
\(257\) 6440.71 1.56327 0.781635 0.623736i \(-0.214386\pi\)
0.781635 + 0.623736i \(0.214386\pi\)
\(258\) 779.981 0.188215
\(259\) 13862.5 3.32576
\(260\) −1173.62 −0.279941
\(261\) 1858.62 0.440788
\(262\) 3178.34 0.749459
\(263\) 4140.40 0.970754 0.485377 0.874305i \(-0.338682\pi\)
0.485377 + 0.874305i \(0.338682\pi\)
\(264\) −509.070 −0.118678
\(265\) 2123.39 0.492222
\(266\) 0 0
\(267\) −645.706 −0.148002
\(268\) −842.982 −0.192139
\(269\) 3165.99 0.717599 0.358799 0.933415i \(-0.383186\pi\)
0.358799 + 0.933415i \(0.383186\pi\)
\(270\) −281.534 −0.0634578
\(271\) 6444.23 1.44450 0.722249 0.691633i \(-0.243109\pi\)
0.722249 + 0.691633i \(0.243109\pi\)
\(272\) 276.467 0.0616297
\(273\) −5316.55 −1.17865
\(274\) 4650.13 1.02527
\(275\) 2074.85 0.454976
\(276\) 2475.80 0.539947
\(277\) 399.738 0.0867073 0.0433537 0.999060i \(-0.486196\pi\)
0.0433537 + 0.999060i \(0.486196\pi\)
\(278\) −1270.11 −0.274015
\(279\) 1166.62 0.250335
\(280\) 1313.43 0.280329
\(281\) 630.367 0.133824 0.0669120 0.997759i \(-0.478685\pi\)
0.0669120 + 0.997759i \(0.478685\pi\)
\(282\) 650.892 0.137447
\(283\) 1996.63 0.419391 0.209695 0.977767i \(-0.432753\pi\)
0.209695 + 0.977767i \(0.432753\pi\)
\(284\) 632.069 0.132065
\(285\) 0 0
\(286\) 2387.41 0.493603
\(287\) 13712.6 2.82032
\(288\) −288.000 −0.0589256
\(289\) −4614.43 −0.939228
\(290\) 2153.35 0.436031
\(291\) −1586.92 −0.319680
\(292\) 2294.19 0.459785
\(293\) 9676.85 1.92945 0.964723 0.263268i \(-0.0848004\pi\)
0.964723 + 0.263268i \(0.0848004\pi\)
\(294\) 3891.89 0.772041
\(295\) 606.052 0.119613
\(296\) −3521.70 −0.691535
\(297\) 572.704 0.111891
\(298\) −3396.63 −0.660273
\(299\) −11610.8 −2.24573
\(300\) 1173.82 0.225902
\(301\) 4093.66 0.783902
\(302\) 3264.77 0.622074
\(303\) −3086.21 −0.585142
\(304\) 0 0
\(305\) 1776.19 0.333456
\(306\) −311.026 −0.0581051
\(307\) 6795.52 1.26332 0.631662 0.775244i \(-0.282373\pi\)
0.631662 + 0.775244i \(0.282373\pi\)
\(308\) −2671.81 −0.494287
\(309\) −324.901 −0.0598154
\(310\) 1351.61 0.247634
\(311\) −4418.47 −0.805622 −0.402811 0.915283i \(-0.631967\pi\)
−0.402811 + 0.915283i \(0.631967\pi\)
\(312\) 1350.64 0.245081
\(313\) −1391.56 −0.251296 −0.125648 0.992075i \(-0.540101\pi\)
−0.125648 + 0.992075i \(0.540101\pi\)
\(314\) −5925.14 −1.06489
\(315\) −1477.60 −0.264297
\(316\) −3541.19 −0.630403
\(317\) 5998.68 1.06284 0.531419 0.847109i \(-0.321659\pi\)
0.531419 + 0.847109i \(0.321659\pi\)
\(318\) −2443.68 −0.430927
\(319\) −4380.41 −0.768827
\(320\) −333.670 −0.0582897
\(321\) 5460.07 0.949381
\(322\) 12994.0 2.24884
\(323\) 0 0
\(324\) 324.000 0.0555556
\(325\) −5504.92 −0.939563
\(326\) −1253.94 −0.213035
\(327\) 357.430 0.0604462
\(328\) −3483.63 −0.586437
\(329\) 3416.15 0.572457
\(330\) 663.521 0.110684
\(331\) −6604.73 −1.09676 −0.548382 0.836228i \(-0.684756\pi\)
−0.548382 + 0.836228i \(0.684756\pi\)
\(332\) −2294.53 −0.379303
\(333\) 3961.91 0.651986
\(334\) −3204.31 −0.524947
\(335\) 1098.74 0.179196
\(336\) −1511.54 −0.245421
\(337\) −4792.90 −0.774735 −0.387367 0.921925i \(-0.626616\pi\)
−0.387367 + 0.921925i \(0.626616\pi\)
\(338\) −1940.17 −0.312223
\(339\) −3044.87 −0.487831
\(340\) −360.346 −0.0574780
\(341\) −2749.49 −0.436637
\(342\) 0 0
\(343\) 9625.03 1.51517
\(344\) −1039.97 −0.162999
\(345\) −3226.95 −0.503574
\(346\) −4581.37 −0.711839
\(347\) 4871.36 0.753627 0.376813 0.926289i \(-0.377020\pi\)
0.376813 + 0.926289i \(0.377020\pi\)
\(348\) −2478.16 −0.381734
\(349\) −2676.44 −0.410506 −0.205253 0.978709i \(-0.565802\pi\)
−0.205253 + 0.978709i \(0.565802\pi\)
\(350\) 6160.70 0.940867
\(351\) −1519.48 −0.231064
\(352\) 678.760 0.102779
\(353\) 3111.41 0.469132 0.234566 0.972100i \(-0.424633\pi\)
0.234566 + 0.972100i \(0.424633\pi\)
\(354\) −697.469 −0.104718
\(355\) −823.837 −0.123168
\(356\) 860.942 0.128174
\(357\) −1632.39 −0.242003
\(358\) 437.089 0.0645276
\(359\) −935.758 −0.137569 −0.0687847 0.997632i \(-0.521912\pi\)
−0.0687847 + 0.997632i \(0.521912\pi\)
\(360\) 375.378 0.0549560
\(361\) 0 0
\(362\) 7496.88 1.08847
\(363\) 2643.25 0.382189
\(364\) 7088.74 1.02074
\(365\) −2990.24 −0.428812
\(366\) −2044.11 −0.291932
\(367\) 11009.2 1.56588 0.782940 0.622097i \(-0.213719\pi\)
0.782940 + 0.622097i \(0.213719\pi\)
\(368\) −3301.06 −0.467608
\(369\) 3919.08 0.552898
\(370\) 4590.17 0.644950
\(371\) −12825.4 −1.79478
\(372\) −1555.49 −0.216797
\(373\) −6151.39 −0.853906 −0.426953 0.904274i \(-0.640413\pi\)
−0.426953 + 0.904274i \(0.640413\pi\)
\(374\) 733.027 0.101347
\(375\) −3485.05 −0.479913
\(376\) −867.857 −0.119033
\(377\) 11621.9 1.58769
\(378\) 1700.48 0.231385
\(379\) 13458.6 1.82407 0.912037 0.410109i \(-0.134509\pi\)
0.912037 + 0.410109i \(0.134509\pi\)
\(380\) 0 0
\(381\) −3084.60 −0.414774
\(382\) 283.466 0.0379670
\(383\) −11090.4 −1.47961 −0.739807 0.672819i \(-0.765083\pi\)
−0.739807 + 0.672819i \(0.765083\pi\)
\(384\) 384.000 0.0510310
\(385\) 3482.43 0.460990
\(386\) 7819.79 1.03113
\(387\) 1169.97 0.153677
\(388\) 2115.90 0.276851
\(389\) 1273.09 0.165933 0.0829667 0.996552i \(-0.473560\pi\)
0.0829667 + 0.996552i \(0.473560\pi\)
\(390\) −1760.43 −0.228571
\(391\) −3564.98 −0.461097
\(392\) −5189.19 −0.668607
\(393\) 4767.51 0.611931
\(394\) −2406.32 −0.307687
\(395\) 4615.57 0.587936
\(396\) −763.605 −0.0969006
\(397\) −12328.9 −1.55862 −0.779309 0.626640i \(-0.784430\pi\)
−0.779309 + 0.626640i \(0.784430\pi\)
\(398\) −7406.92 −0.932853
\(399\) 0 0
\(400\) −1565.10 −0.195637
\(401\) 9799.54 1.22036 0.610181 0.792262i \(-0.291097\pi\)
0.610181 + 0.792262i \(0.291097\pi\)
\(402\) −1264.47 −0.156881
\(403\) 7294.83 0.901691
\(404\) 4114.94 0.506748
\(405\) −422.301 −0.0518130
\(406\) −13006.4 −1.58989
\(407\) −9337.46 −1.13720
\(408\) 414.701 0.0503205
\(409\) 8084.65 0.977409 0.488705 0.872449i \(-0.337470\pi\)
0.488705 + 0.872449i \(0.337470\pi\)
\(410\) 4540.55 0.546931
\(411\) 6975.20 0.837132
\(412\) 433.201 0.0518016
\(413\) −3660.60 −0.436141
\(414\) 3713.70 0.440865
\(415\) 2990.68 0.353751
\(416\) −1800.86 −0.212246
\(417\) −1905.17 −0.223733
\(418\) 0 0
\(419\) −78.3882 −0.00913965 −0.00456983 0.999990i \(-0.501455\pi\)
−0.00456983 + 0.999990i \(0.501455\pi\)
\(420\) 1970.14 0.228888
\(421\) 7085.19 0.820216 0.410108 0.912037i \(-0.365491\pi\)
0.410108 + 0.912037i \(0.365491\pi\)
\(422\) 51.3996 0.00592914
\(423\) 976.339 0.112225
\(424\) 3258.24 0.373194
\(425\) −1690.23 −0.192913
\(426\) 948.103 0.107830
\(427\) −10728.3 −1.21588
\(428\) −7280.09 −0.822188
\(429\) 3581.11 0.403025
\(430\) 1355.50 0.152019
\(431\) −14901.4 −1.66537 −0.832686 0.553745i \(-0.813198\pi\)
−0.832686 + 0.553745i \(0.813198\pi\)
\(432\) −432.000 −0.0481125
\(433\) 4229.48 0.469413 0.234707 0.972066i \(-0.424587\pi\)
0.234707 + 0.972066i \(0.424587\pi\)
\(434\) −8163.84 −0.902942
\(435\) 3230.02 0.356018
\(436\) −476.573 −0.0523480
\(437\) 0 0
\(438\) 3441.28 0.375413
\(439\) 10521.5 1.14389 0.571943 0.820293i \(-0.306190\pi\)
0.571943 + 0.820293i \(0.306190\pi\)
\(440\) −884.694 −0.0958549
\(441\) 5837.84 0.630368
\(442\) −1944.84 −0.209291
\(443\) 13867.4 1.48727 0.743636 0.668585i \(-0.233100\pi\)
0.743636 + 0.668585i \(0.233100\pi\)
\(444\) −5282.55 −0.564636
\(445\) −1122.15 −0.119539
\(446\) 6210.38 0.659349
\(447\) −5094.94 −0.539111
\(448\) 2015.39 0.212541
\(449\) 9599.89 1.00901 0.504507 0.863408i \(-0.331674\pi\)
0.504507 + 0.863408i \(0.331674\pi\)
\(450\) 1760.73 0.184448
\(451\) −9236.52 −0.964370
\(452\) 4059.83 0.422474
\(453\) 4897.15 0.507921
\(454\) −1329.13 −0.137399
\(455\) −9239.44 −0.951981
\(456\) 0 0
\(457\) −6261.10 −0.640880 −0.320440 0.947269i \(-0.603831\pi\)
−0.320440 + 0.947269i \(0.603831\pi\)
\(458\) 12064.0 1.23081
\(459\) −466.538 −0.0474426
\(460\) 4302.59 0.436108
\(461\) −9825.55 −0.992671 −0.496336 0.868131i \(-0.665321\pi\)
−0.496336 + 0.868131i \(0.665321\pi\)
\(462\) −4007.71 −0.403584
\(463\) 9276.57 0.931142 0.465571 0.885011i \(-0.345849\pi\)
0.465571 + 0.885011i \(0.345849\pi\)
\(464\) 3304.21 0.330591
\(465\) 2027.42 0.202192
\(466\) 11516.3 1.14481
\(467\) 18209.4 1.80435 0.902174 0.431372i \(-0.141970\pi\)
0.902174 + 0.431372i \(0.141970\pi\)
\(468\) 2025.97 0.200108
\(469\) −6636.47 −0.653398
\(470\) 1131.16 0.111014
\(471\) −8887.71 −0.869478
\(472\) 929.958 0.0906881
\(473\) −2757.40 −0.268045
\(474\) −5311.78 −0.514722
\(475\) 0 0
\(476\) 2176.52 0.209581
\(477\) −3665.52 −0.351850
\(478\) 1482.81 0.141887
\(479\) 12741.7 1.21541 0.607706 0.794162i \(-0.292090\pi\)
0.607706 + 0.794162i \(0.292090\pi\)
\(480\) −500.504 −0.0475933
\(481\) 24773.8 2.34841
\(482\) −10548.1 −0.996794
\(483\) 19491.0 1.83617
\(484\) −3524.33 −0.330985
\(485\) −2757.85 −0.258201
\(486\) 486.000 0.0453609
\(487\) −5006.72 −0.465864 −0.232932 0.972493i \(-0.574832\pi\)
−0.232932 + 0.972493i \(0.574832\pi\)
\(488\) 2725.48 0.252821
\(489\) −1880.92 −0.173943
\(490\) 6763.58 0.623566
\(491\) 963.312 0.0885411 0.0442705 0.999020i \(-0.485904\pi\)
0.0442705 + 0.999020i \(0.485904\pi\)
\(492\) −5225.44 −0.478824
\(493\) 3568.38 0.325988
\(494\) 0 0
\(495\) 995.281 0.0903728
\(496\) 2073.98 0.187751
\(497\) 4976.04 0.449106
\(498\) −3441.79 −0.309700
\(499\) 4964.84 0.445405 0.222702 0.974886i \(-0.428512\pi\)
0.222702 + 0.974886i \(0.428512\pi\)
\(500\) 4646.73 0.415617
\(501\) −4806.47 −0.428617
\(502\) −5692.71 −0.506132
\(503\) −14768.5 −1.30913 −0.654567 0.756004i \(-0.727149\pi\)
−0.654567 + 0.756004i \(0.727149\pi\)
\(504\) −2267.31 −0.200385
\(505\) −5363.40 −0.472610
\(506\) −8752.46 −0.768962
\(507\) −2910.26 −0.254929
\(508\) 4112.80 0.359205
\(509\) 6015.92 0.523872 0.261936 0.965085i \(-0.415639\pi\)
0.261936 + 0.965085i \(0.415639\pi\)
\(510\) −540.520 −0.0469306
\(511\) 18061.3 1.56357
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −12881.4 −1.10540
\(515\) −564.632 −0.0483120
\(516\) −1559.96 −0.133088
\(517\) −2301.04 −0.195744
\(518\) −27725.0 −2.35167
\(519\) −6872.06 −0.581214
\(520\) 2347.23 0.197948
\(521\) 10009.4 0.841685 0.420842 0.907134i \(-0.361735\pi\)
0.420842 + 0.907134i \(0.361735\pi\)
\(522\) −3717.24 −0.311684
\(523\) 2488.09 0.208024 0.104012 0.994576i \(-0.466832\pi\)
0.104012 + 0.994576i \(0.466832\pi\)
\(524\) −6356.67 −0.529948
\(525\) 9241.05 0.768214
\(526\) −8280.81 −0.686427
\(527\) 2239.80 0.185137
\(528\) 1018.14 0.0839183
\(529\) 30399.5 2.49852
\(530\) −4246.78 −0.348053
\(531\) −1046.20 −0.0855016
\(532\) 0 0
\(533\) 24506.0 1.99150
\(534\) 1291.41 0.104653
\(535\) 9488.85 0.766802
\(536\) 1685.96 0.135863
\(537\) 655.634 0.0526866
\(538\) −6331.99 −0.507419
\(539\) −13758.7 −1.09949
\(540\) 563.067 0.0448714
\(541\) −9732.04 −0.773407 −0.386703 0.922204i \(-0.626386\pi\)
−0.386703 + 0.922204i \(0.626386\pi\)
\(542\) −12888.5 −1.02141
\(543\) 11245.3 0.888735
\(544\) −552.934 −0.0435788
\(545\) 621.164 0.0488216
\(546\) 10633.1 0.833434
\(547\) 12432.4 0.971791 0.485895 0.874017i \(-0.338494\pi\)
0.485895 + 0.874017i \(0.338494\pi\)
\(548\) −9300.26 −0.724977
\(549\) −3066.16 −0.238362
\(550\) −4149.71 −0.321717
\(551\) 0 0
\(552\) −4951.59 −0.381800
\(553\) −27878.4 −2.14378
\(554\) −799.476 −0.0613113
\(555\) 6885.25 0.526599
\(556\) 2540.22 0.193758
\(557\) −17905.5 −1.36208 −0.681041 0.732245i \(-0.738472\pi\)
−0.681041 + 0.732245i \(0.738472\pi\)
\(558\) −2333.23 −0.177014
\(559\) 7315.81 0.553535
\(560\) −2626.85 −0.198223
\(561\) 1099.54 0.0827498
\(562\) −1260.73 −0.0946278
\(563\) −1825.07 −0.136621 −0.0683106 0.997664i \(-0.521761\pi\)
−0.0683106 + 0.997664i \(0.521761\pi\)
\(564\) −1301.78 −0.0971898
\(565\) −5291.57 −0.394014
\(566\) −3993.27 −0.296554
\(567\) 2550.73 0.188925
\(568\) −1264.14 −0.0933839
\(569\) −4974.94 −0.366538 −0.183269 0.983063i \(-0.558668\pi\)
−0.183269 + 0.983063i \(0.558668\pi\)
\(570\) 0 0
\(571\) 14203.4 1.04097 0.520485 0.853871i \(-0.325751\pi\)
0.520485 + 0.853871i \(0.325751\pi\)
\(572\) −4774.81 −0.349030
\(573\) 425.200 0.0309999
\(574\) −27425.3 −1.99427
\(575\) 20181.6 1.46370
\(576\) 576.000 0.0416667
\(577\) 5279.89 0.380944 0.190472 0.981693i \(-0.438998\pi\)
0.190472 + 0.981693i \(0.438998\pi\)
\(578\) 9228.86 0.664135
\(579\) 11729.7 0.841915
\(580\) −4306.70 −0.308321
\(581\) −18063.9 −1.28988
\(582\) 3173.84 0.226048
\(583\) 8638.93 0.613701
\(584\) −4588.38 −0.325117
\(585\) −2640.64 −0.186627
\(586\) −19353.7 −1.36432
\(587\) 13228.6 0.930156 0.465078 0.885270i \(-0.346026\pi\)
0.465078 + 0.885270i \(0.346026\pi\)
\(588\) −7783.79 −0.545915
\(589\) 0 0
\(590\) −1212.10 −0.0845789
\(591\) −3609.47 −0.251225
\(592\) 7043.39 0.488989
\(593\) −696.480 −0.0482310 −0.0241155 0.999709i \(-0.507677\pi\)
−0.0241155 + 0.999709i \(0.507677\pi\)
\(594\) −1145.41 −0.0791190
\(595\) −2836.87 −0.195463
\(596\) 6793.25 0.466883
\(597\) −11110.4 −0.761671
\(598\) 23221.7 1.58797
\(599\) 22697.1 1.54821 0.774105 0.633058i \(-0.218200\pi\)
0.774105 + 0.633058i \(0.218200\pi\)
\(600\) −2347.64 −0.159737
\(601\) 15591.5 1.05822 0.529110 0.848553i \(-0.322526\pi\)
0.529110 + 0.848553i \(0.322526\pi\)
\(602\) −8187.32 −0.554302
\(603\) −1896.71 −0.128093
\(604\) −6529.54 −0.439873
\(605\) 4593.60 0.308688
\(606\) 6172.41 0.413758
\(607\) 13728.2 0.917975 0.458988 0.888443i \(-0.348212\pi\)
0.458988 + 0.888443i \(0.348212\pi\)
\(608\) 0 0
\(609\) −19509.6 −1.29814
\(610\) −3552.38 −0.235789
\(611\) 6105.03 0.404228
\(612\) 622.051 0.0410865
\(613\) 21971.3 1.44766 0.723829 0.689979i \(-0.242380\pi\)
0.723829 + 0.689979i \(0.242380\pi\)
\(614\) −13591.0 −0.893305
\(615\) 6810.83 0.446568
\(616\) 5343.62 0.349514
\(617\) −18518.7 −1.20832 −0.604160 0.796863i \(-0.706491\pi\)
−0.604160 + 0.796863i \(0.706491\pi\)
\(618\) 649.801 0.0422958
\(619\) −7363.53 −0.478134 −0.239067 0.971003i \(-0.576842\pi\)
−0.239067 + 0.971003i \(0.576842\pi\)
\(620\) −2703.22 −0.175103
\(621\) 5570.54 0.359965
\(622\) 8836.95 0.569661
\(623\) 6777.86 0.435874
\(624\) −2701.29 −0.173298
\(625\) 6170.78 0.394930
\(626\) 2783.12 0.177693
\(627\) 0 0
\(628\) 11850.3 0.752990
\(629\) 7606.51 0.482181
\(630\) 2955.21 0.186886
\(631\) −20379.0 −1.28570 −0.642848 0.765993i \(-0.722247\pi\)
−0.642848 + 0.765993i \(0.722247\pi\)
\(632\) 7082.38 0.445763
\(633\) 77.0995 0.00484112
\(634\) −11997.4 −0.751540
\(635\) −5360.61 −0.335007
\(636\) 4887.36 0.304711
\(637\) 36503.9 2.27055
\(638\) 8760.81 0.543643
\(639\) 1422.16 0.0880432
\(640\) 667.339 0.0412170
\(641\) 1986.25 0.122390 0.0611951 0.998126i \(-0.480509\pi\)
0.0611951 + 0.998126i \(0.480509\pi\)
\(642\) −10920.1 −0.671314
\(643\) −11156.6 −0.684254 −0.342127 0.939654i \(-0.611147\pi\)
−0.342127 + 0.939654i \(0.611147\pi\)
\(644\) −25988.0 −1.59017
\(645\) 2033.25 0.124123
\(646\) 0 0
\(647\) −18657.7 −1.13371 −0.566854 0.823818i \(-0.691840\pi\)
−0.566854 + 0.823818i \(0.691840\pi\)
\(648\) −648.000 −0.0392837
\(649\) 2465.70 0.149133
\(650\) 11009.8 0.664371
\(651\) −12245.8 −0.737249
\(652\) 2507.89 0.150639
\(653\) 7972.68 0.477787 0.238894 0.971046i \(-0.423215\pi\)
0.238894 + 0.971046i \(0.423215\pi\)
\(654\) −714.860 −0.0427420
\(655\) 8285.27 0.494248
\(656\) 6967.26 0.414673
\(657\) 5161.93 0.306523
\(658\) −6832.30 −0.404789
\(659\) 5327.61 0.314923 0.157461 0.987525i \(-0.449669\pi\)
0.157461 + 0.987525i \(0.449669\pi\)
\(660\) −1327.04 −0.0782652
\(661\) −6945.06 −0.408671 −0.204336 0.978901i \(-0.565503\pi\)
−0.204336 + 0.978901i \(0.565503\pi\)
\(662\) 13209.5 0.775530
\(663\) −2917.26 −0.170885
\(664\) 4589.06 0.268208
\(665\) 0 0
\(666\) −7923.82 −0.461024
\(667\) −42607.1 −2.47339
\(668\) 6408.63 0.371193
\(669\) 9315.57 0.538357
\(670\) −2197.48 −0.126710
\(671\) 7226.35 0.415753
\(672\) 3023.08 0.173539
\(673\) −8261.87 −0.473212 −0.236606 0.971606i \(-0.576035\pi\)
−0.236606 + 0.971606i \(0.576035\pi\)
\(674\) 9585.79 0.547820
\(675\) 2641.10 0.150601
\(676\) 3880.35 0.220775
\(677\) 12128.3 0.688523 0.344261 0.938874i \(-0.388129\pi\)
0.344261 + 0.938874i \(0.388129\pi\)
\(678\) 6089.75 0.344949
\(679\) 16657.6 0.941475
\(680\) 720.693 0.0406431
\(681\) −1993.70 −0.112186
\(682\) 5498.98 0.308749
\(683\) 3609.67 0.202226 0.101113 0.994875i \(-0.467760\pi\)
0.101113 + 0.994875i \(0.467760\pi\)
\(684\) 0 0
\(685\) 12121.9 0.676139
\(686\) −19250.1 −1.07139
\(687\) 18096.0 1.00496
\(688\) 2079.95 0.115258
\(689\) −22920.5 −1.26734
\(690\) 6453.89 0.356080
\(691\) −375.152 −0.0206534 −0.0103267 0.999947i \(-0.503287\pi\)
−0.0103267 + 0.999947i \(0.503287\pi\)
\(692\) 9162.75 0.503346
\(693\) −6011.57 −0.329525
\(694\) −9742.73 −0.532895
\(695\) −3310.92 −0.180705
\(696\) 4956.32 0.269926
\(697\) 7524.29 0.408899
\(698\) 5352.88 0.290271
\(699\) 17274.5 0.934737
\(700\) −12321.4 −0.665293
\(701\) 13800.4 0.743558 0.371779 0.928321i \(-0.378748\pi\)
0.371779 + 0.928321i \(0.378748\pi\)
\(702\) 3038.95 0.163387
\(703\) 0 0
\(704\) −1357.52 −0.0726754
\(705\) 1696.74 0.0906426
\(706\) −6222.82 −0.331727
\(707\) 32395.4 1.72327
\(708\) 1394.94 0.0740465
\(709\) −25345.2 −1.34254 −0.671270 0.741213i \(-0.734251\pi\)
−0.671270 + 0.741213i \(0.734251\pi\)
\(710\) 1647.67 0.0870931
\(711\) −7967.68 −0.420269
\(712\) −1721.88 −0.0906325
\(713\) −26743.6 −1.40470
\(714\) 3264.78 0.171122
\(715\) 6223.48 0.325517
\(716\) −874.179 −0.0456279
\(717\) 2224.22 0.115851
\(718\) 1871.52 0.0972763
\(719\) −19927.8 −1.03363 −0.516816 0.856097i \(-0.672883\pi\)
−0.516816 + 0.856097i \(0.672883\pi\)
\(720\) −750.756 −0.0388598
\(721\) 3410.42 0.176159
\(722\) 0 0
\(723\) −15822.2 −0.813879
\(724\) −14993.8 −0.769667
\(725\) −20200.8 −1.03481
\(726\) −5286.49 −0.270248
\(727\) 6658.48 0.339683 0.169841 0.985471i \(-0.445674\pi\)
0.169841 + 0.985471i \(0.445674\pi\)
\(728\) −14177.5 −0.721775
\(729\) 729.000 0.0370370
\(730\) 5980.48 0.303216
\(731\) 2246.24 0.113653
\(732\) 4088.21 0.206427
\(733\) 27502.1 1.38583 0.692914 0.721021i \(-0.256327\pi\)
0.692914 + 0.721021i \(0.256327\pi\)
\(734\) −22018.5 −1.10724
\(735\) 10145.4 0.509139
\(736\) 6602.13 0.330649
\(737\) 4470.18 0.223421
\(738\) −7838.17 −0.390958
\(739\) 12843.7 0.639327 0.319663 0.947531i \(-0.396430\pi\)
0.319663 + 0.947531i \(0.396430\pi\)
\(740\) −9180.34 −0.456049
\(741\) 0 0
\(742\) 25650.9 1.26910
\(743\) 4806.49 0.237326 0.118663 0.992935i \(-0.462139\pi\)
0.118663 + 0.992935i \(0.462139\pi\)
\(744\) 3110.98 0.153298
\(745\) −8854.31 −0.435432
\(746\) 12302.8 0.603803
\(747\) −5162.69 −0.252869
\(748\) −1466.05 −0.0716634
\(749\) −57313.4 −2.79598
\(750\) 6970.10 0.339350
\(751\) −4295.77 −0.208728 −0.104364 0.994539i \(-0.533281\pi\)
−0.104364 + 0.994539i \(0.533281\pi\)
\(752\) 1735.71 0.0841688
\(753\) −8539.07 −0.413255
\(754\) −23243.8 −1.12267
\(755\) 8510.58 0.410241
\(756\) −3400.97 −0.163614
\(757\) 20825.0 0.999866 0.499933 0.866064i \(-0.333358\pi\)
0.499933 + 0.866064i \(0.333358\pi\)
\(758\) −26917.3 −1.28981
\(759\) −13128.7 −0.627854
\(760\) 0 0
\(761\) −19534.2 −0.930507 −0.465253 0.885178i \(-0.654037\pi\)
−0.465253 + 0.885178i \(0.654037\pi\)
\(762\) 6169.21 0.293290
\(763\) −3751.88 −0.178017
\(764\) −566.933 −0.0268467
\(765\) −810.779 −0.0383187
\(766\) 22180.8 1.04625
\(767\) −6541.89 −0.307971
\(768\) −768.000 −0.0360844
\(769\) 568.457 0.0266568 0.0133284 0.999911i \(-0.495757\pi\)
0.0133284 + 0.999911i \(0.495757\pi\)
\(770\) −6964.86 −0.325969
\(771\) −19322.1 −0.902555
\(772\) −15639.6 −0.729120
\(773\) 96.9965 0.00451322 0.00225661 0.999997i \(-0.499282\pi\)
0.00225661 + 0.999997i \(0.499282\pi\)
\(774\) −2339.94 −0.108666
\(775\) −12679.6 −0.587698
\(776\) −4231.79 −0.195763
\(777\) −41587.5 −1.92013
\(778\) −2546.17 −0.117333
\(779\) 0 0
\(780\) 3520.85 0.161624
\(781\) −3351.75 −0.153566
\(782\) 7129.96 0.326045
\(783\) −5575.86 −0.254489
\(784\) 10378.4 0.472776
\(785\) −15445.6 −0.702265
\(786\) −9535.01 −0.432700
\(787\) 4906.36 0.222227 0.111114 0.993808i \(-0.464558\pi\)
0.111114 + 0.993808i \(0.464558\pi\)
\(788\) 4812.63 0.217567
\(789\) −12421.2 −0.560465
\(790\) −9231.15 −0.415734
\(791\) 31961.5 1.43669
\(792\) 1527.21 0.0685190
\(793\) −19172.7 −0.858564
\(794\) 24657.9 1.10211
\(795\) −6370.17 −0.284184
\(796\) 14813.8 0.659626
\(797\) −32043.3 −1.42413 −0.712066 0.702113i \(-0.752240\pi\)
−0.712066 + 0.702113i \(0.752240\pi\)
\(798\) 0 0
\(799\) 1874.48 0.0829968
\(800\) 3130.19 0.138336
\(801\) 1937.12 0.0854491
\(802\) −19599.1 −0.862927
\(803\) −12165.7 −0.534641
\(804\) 2528.95 0.110932
\(805\) 33872.7 1.48305
\(806\) −14589.7 −0.637592
\(807\) −9497.98 −0.414306
\(808\) −8229.89 −0.358325
\(809\) 18714.9 0.813326 0.406663 0.913578i \(-0.366692\pi\)
0.406663 + 0.913578i \(0.366692\pi\)
\(810\) 844.601 0.0366374
\(811\) −9129.34 −0.395283 −0.197641 0.980274i \(-0.563328\pi\)
−0.197641 + 0.980274i \(0.563328\pi\)
\(812\) 26012.8 1.12422
\(813\) −19332.7 −0.833981
\(814\) 18674.9 0.804122
\(815\) −3268.77 −0.140491
\(816\) −829.401 −0.0355819
\(817\) 0 0
\(818\) −16169.3 −0.691133
\(819\) 15949.7 0.680496
\(820\) −9081.10 −0.386739
\(821\) 22828.7 0.970436 0.485218 0.874393i \(-0.338740\pi\)
0.485218 + 0.874393i \(0.338740\pi\)
\(822\) −13950.4 −0.591942
\(823\) −37877.8 −1.60430 −0.802149 0.597124i \(-0.796310\pi\)
−0.802149 + 0.597124i \(0.796310\pi\)
\(824\) −866.401 −0.0366293
\(825\) −6224.56 −0.262681
\(826\) 7321.20 0.308399
\(827\) −4120.90 −0.173274 −0.0866370 0.996240i \(-0.527612\pi\)
−0.0866370 + 0.996240i \(0.527612\pi\)
\(828\) −7427.39 −0.311739
\(829\) −17959.7 −0.752431 −0.376216 0.926532i \(-0.622775\pi\)
−0.376216 + 0.926532i \(0.622775\pi\)
\(830\) −5981.36 −0.250140
\(831\) −1199.21 −0.0500605
\(832\) 3601.72 0.150081
\(833\) 11208.1 0.466193
\(834\) 3810.33 0.158203
\(835\) −8352.98 −0.346188
\(836\) 0 0
\(837\) −3499.85 −0.144531
\(838\) 156.776 0.00646271
\(839\) −48200.8 −1.98340 −0.991702 0.128559i \(-0.958965\pi\)
−0.991702 + 0.128559i \(0.958965\pi\)
\(840\) −3940.28 −0.161848
\(841\) 18258.7 0.748646
\(842\) −14170.4 −0.579980
\(843\) −1891.10 −0.0772633
\(844\) −102.799 −0.00419253
\(845\) −5057.63 −0.205903
\(846\) −1952.68 −0.0793551
\(847\) −27745.7 −1.12556
\(848\) −6516.48 −0.263888
\(849\) −5989.90 −0.242135
\(850\) 3380.45 0.136410
\(851\) −90823.0 −3.65849
\(852\) −1896.21 −0.0762476
\(853\) 36871.2 1.48001 0.740004 0.672603i \(-0.234824\pi\)
0.740004 + 0.672603i \(0.234824\pi\)
\(854\) 21456.6 0.859755
\(855\) 0 0
\(856\) 14560.2 0.581375
\(857\) 33670.9 1.34209 0.671047 0.741415i \(-0.265845\pi\)
0.671047 + 0.741415i \(0.265845\pi\)
\(858\) −7162.22 −0.284982
\(859\) 20846.5 0.828025 0.414013 0.910271i \(-0.364127\pi\)
0.414013 + 0.910271i \(0.364127\pi\)
\(860\) −2711.00 −0.107493
\(861\) −41137.9 −1.62831
\(862\) 29802.8 1.17760
\(863\) −47623.4 −1.87847 −0.939235 0.343275i \(-0.888464\pi\)
−0.939235 + 0.343275i \(0.888464\pi\)
\(864\) 864.000 0.0340207
\(865\) −11942.7 −0.469438
\(866\) −8458.97 −0.331925
\(867\) 13843.3 0.542264
\(868\) 16327.7 0.638476
\(869\) 18778.3 0.733037
\(870\) −6460.05 −0.251743
\(871\) −11860.1 −0.461382
\(872\) 953.147 0.0370156
\(873\) 4760.77 0.184568
\(874\) 0 0
\(875\) 36582.0 1.41337
\(876\) −6882.57 −0.265457
\(877\) −9397.35 −0.361831 −0.180916 0.983499i \(-0.557906\pi\)
−0.180916 + 0.983499i \(0.557906\pi\)
\(878\) −21043.1 −0.808850
\(879\) −29030.5 −1.11397
\(880\) 1769.39 0.0677796
\(881\) 49897.4 1.90816 0.954079 0.299555i \(-0.0968384\pi\)
0.954079 + 0.299555i \(0.0968384\pi\)
\(882\) −11675.7 −0.445738
\(883\) −3263.13 −0.124364 −0.0621818 0.998065i \(-0.519806\pi\)
−0.0621818 + 0.998065i \(0.519806\pi\)
\(884\) 3889.68 0.147991
\(885\) −1818.16 −0.0690584
\(886\) −27734.8 −1.05166
\(887\) 38617.6 1.46184 0.730921 0.682462i \(-0.239091\pi\)
0.730921 + 0.682462i \(0.239091\pi\)
\(888\) 10565.1 0.399258
\(889\) 32378.5 1.22153
\(890\) 2244.30 0.0845270
\(891\) −1718.11 −0.0646004
\(892\) −12420.8 −0.466230
\(893\) 0 0
\(894\) 10189.9 0.381209
\(895\) 1139.40 0.0425542
\(896\) −4030.78 −0.150289
\(897\) 34832.5 1.29657
\(898\) −19199.8 −0.713480
\(899\) 26769.1 0.993102
\(900\) −3521.47 −0.130425
\(901\) −7037.47 −0.260213
\(902\) 18473.0 0.681913
\(903\) −12281.0 −0.452586
\(904\) −8119.66 −0.298735
\(905\) 19542.8 0.717818
\(906\) −9794.31 −0.359155
\(907\) 580.444 0.0212496 0.0106248 0.999944i \(-0.496618\pi\)
0.0106248 + 0.999944i \(0.496618\pi\)
\(908\) 2658.27 0.0971560
\(909\) 9258.62 0.337832
\(910\) 18478.9 0.673153
\(911\) −16704.1 −0.607498 −0.303749 0.952752i \(-0.598238\pi\)
−0.303749 + 0.952752i \(0.598238\pi\)
\(912\) 0 0
\(913\) 12167.5 0.441056
\(914\) 12522.2 0.453170
\(915\) −5328.56 −0.192521
\(916\) −24128.0 −0.870317
\(917\) −50043.6 −1.80217
\(918\) 933.077 0.0335470
\(919\) 46725.6 1.67719 0.838594 0.544756i \(-0.183378\pi\)
0.838594 + 0.544756i \(0.183378\pi\)
\(920\) −8605.19 −0.308375
\(921\) −20386.6 −0.729381
\(922\) 19651.1 0.701925
\(923\) 8892.72 0.317126
\(924\) 8015.43 0.285377
\(925\) −43060.9 −1.53063
\(926\) −18553.1 −0.658417
\(927\) 974.702 0.0345344
\(928\) −6608.42 −0.233763
\(929\) −18196.1 −0.642621 −0.321310 0.946974i \(-0.604123\pi\)
−0.321310 + 0.946974i \(0.604123\pi\)
\(930\) −4054.84 −0.142971
\(931\) 0 0
\(932\) −23032.6 −0.809506
\(933\) 13255.4 0.465126
\(934\) −36418.8 −1.27587
\(935\) 1910.85 0.0668358
\(936\) −4051.93 −0.141497
\(937\) −28744.6 −1.00218 −0.501091 0.865395i \(-0.667068\pi\)
−0.501091 + 0.865395i \(0.667068\pi\)
\(938\) 13272.9 0.462022
\(939\) 4174.68 0.145086
\(940\) −2262.32 −0.0784988
\(941\) 11102.6 0.384628 0.192314 0.981333i \(-0.438401\pi\)
0.192314 + 0.981333i \(0.438401\pi\)
\(942\) 17775.4 0.614814
\(943\) −89841.3 −3.10248
\(944\) −1859.92 −0.0641262
\(945\) 4432.81 0.152592
\(946\) 5514.79 0.189536
\(947\) −34810.8 −1.19451 −0.597254 0.802052i \(-0.703741\pi\)
−0.597254 + 0.802052i \(0.703741\pi\)
\(948\) 10623.6 0.363964
\(949\) 32277.4 1.10408
\(950\) 0 0
\(951\) −17996.0 −0.613629
\(952\) −4353.04 −0.148196
\(953\) 33236.8 1.12974 0.564872 0.825178i \(-0.308925\pi\)
0.564872 + 0.825178i \(0.308925\pi\)
\(954\) 7331.04 0.248796
\(955\) 738.938 0.0250382
\(956\) −2965.62 −0.100330
\(957\) 13141.2 0.443882
\(958\) −25483.4 −0.859426
\(959\) −73217.4 −2.46539
\(960\) 1001.01 0.0336536
\(961\) −12988.6 −0.435991
\(962\) −49547.5 −1.66058
\(963\) −16380.2 −0.548126
\(964\) 21096.3 0.704840
\(965\) 20384.6 0.680003
\(966\) −38982.0 −1.29837
\(967\) −5203.54 −0.173045 −0.0865225 0.996250i \(-0.527575\pi\)
−0.0865225 + 0.996250i \(0.527575\pi\)
\(968\) 7048.66 0.234042
\(969\) 0 0
\(970\) 5515.70 0.182576
\(971\) −37036.4 −1.22405 −0.612026 0.790838i \(-0.709645\pi\)
−0.612026 + 0.790838i \(0.709645\pi\)
\(972\) −972.000 −0.0320750
\(973\) 19998.2 0.658903
\(974\) 10013.4 0.329416
\(975\) 16514.8 0.542457
\(976\) −5450.95 −0.178771
\(977\) 28630.1 0.937520 0.468760 0.883326i \(-0.344701\pi\)
0.468760 + 0.883326i \(0.344701\pi\)
\(978\) 3761.83 0.122996
\(979\) −4565.42 −0.149041
\(980\) −13527.2 −0.440928
\(981\) −1072.29 −0.0348987
\(982\) −1926.62 −0.0626080
\(983\) −25662.6 −0.832664 −0.416332 0.909213i \(-0.636685\pi\)
−0.416332 + 0.909213i \(0.636685\pi\)
\(984\) 10450.9 0.338579
\(985\) −6272.77 −0.202911
\(986\) −7136.77 −0.230508
\(987\) −10248.5 −0.330508
\(988\) 0 0
\(989\) −26820.5 −0.862327
\(990\) −1990.56 −0.0639032
\(991\) −23629.7 −0.757440 −0.378720 0.925511i \(-0.623636\pi\)
−0.378720 + 0.925511i \(0.623636\pi\)
\(992\) −4147.97 −0.132760
\(993\) 19814.2 0.633217
\(994\) −9952.07 −0.317566
\(995\) −19308.3 −0.615190
\(996\) 6883.58 0.218991
\(997\) 51303.6 1.62969 0.814845 0.579679i \(-0.196822\pi\)
0.814845 + 0.579679i \(0.196822\pi\)
\(998\) −9929.69 −0.314949
\(999\) −11885.7 −0.376424
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 2166.4.a.s.1.2 3
19.7 even 3 114.4.e.e.49.2 yes 6
19.11 even 3 114.4.e.e.7.2 6
19.18 odd 2 2166.4.a.w.1.2 3
57.11 odd 6 342.4.g.g.235.2 6
57.26 odd 6 342.4.g.g.163.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.4.e.e.7.2 6 19.11 even 3
114.4.e.e.49.2 yes 6 19.7 even 3
342.4.g.g.163.2 6 57.26 odd 6
342.4.g.g.235.2 6 57.11 odd 6
2166.4.a.s.1.2 3 1.1 even 1 trivial
2166.4.a.w.1.2 3 19.18 odd 2