Properties

Label 2166.4.a.p.1.1
Level $2166$
Weight $4$
Character 2166.1
Self dual yes
Analytic conductor $127.798$
Analytic rank $1$
Dimension $2$
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: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 2166.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -12.0902 q^{5} +6.00000 q^{6} -0.673762 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -12.0902 q^{5} +6.00000 q^{6} -0.673762 q^{7} +8.00000 q^{8} +9.00000 q^{9} -24.1803 q^{10} +15.9443 q^{11} +12.0000 q^{12} +3.90983 q^{13} -1.34752 q^{14} -36.2705 q^{15} +16.0000 q^{16} -44.0132 q^{17} +18.0000 q^{18} -48.3607 q^{20} -2.02129 q^{21} +31.8885 q^{22} -9.11146 q^{23} +24.0000 q^{24} +21.1722 q^{25} +7.81966 q^{26} +27.0000 q^{27} -2.69505 q^{28} -161.151 q^{29} -72.5410 q^{30} +60.5035 q^{31} +32.0000 q^{32} +47.8328 q^{33} -88.0263 q^{34} +8.14590 q^{35} +36.0000 q^{36} +104.885 q^{37} +11.7295 q^{39} -96.7214 q^{40} +249.353 q^{41} -4.04257 q^{42} -6.90481 q^{43} +63.7771 q^{44} -108.812 q^{45} -18.2229 q^{46} +145.257 q^{47} +48.0000 q^{48} -342.546 q^{49} +42.3444 q^{50} -132.039 q^{51} +15.6393 q^{52} -754.187 q^{53} +54.0000 q^{54} -192.769 q^{55} -5.39010 q^{56} -322.302 q^{58} -704.046 q^{59} -145.082 q^{60} -32.5085 q^{61} +121.007 q^{62} -6.06386 q^{63} +64.0000 q^{64} -47.2705 q^{65} +95.6656 q^{66} +77.7264 q^{67} -176.053 q^{68} -27.3344 q^{69} +16.2918 q^{70} +44.4183 q^{71} +72.0000 q^{72} +280.735 q^{73} +209.771 q^{74} +63.5166 q^{75} -10.7426 q^{77} +23.4590 q^{78} +779.508 q^{79} -193.443 q^{80} +81.0000 q^{81} +498.705 q^{82} -274.023 q^{83} -8.08514 q^{84} +532.127 q^{85} -13.8096 q^{86} -483.453 q^{87} +127.554 q^{88} -1005.91 q^{89} -217.623 q^{90} -2.63430 q^{91} -36.4458 q^{92} +181.510 q^{93} +290.515 q^{94} +96.0000 q^{96} -832.600 q^{97} -685.092 q^{98} +143.498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} + 16 q^{8} + 18 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} + 16 q^{8} + 18 q^{9} - 26 q^{10} + 14 q^{11} + 24 q^{12} + 19 q^{13} - 34 q^{14} - 39 q^{15} + 32 q^{16} - 12 q^{17} + 36 q^{18} - 52 q^{20} - 51 q^{21} + 28 q^{22} - 54 q^{23} + 48 q^{24} - 103 q^{25} + 38 q^{26} + 54 q^{27} - 68 q^{28} - 130 q^{29} - 78 q^{30} - 239 q^{31} + 64 q^{32} + 42 q^{33} - 24 q^{34} + 23 q^{35} + 72 q^{36} - 148 q^{37} + 57 q^{39} - 104 q^{40} + 331 q^{41} - 102 q^{42} - 224 q^{43} + 56 q^{44} - 117 q^{45} - 108 q^{46} + 333 q^{47} + 96 q^{48} - 419 q^{49} - 206 q^{50} - 36 q^{51} + 76 q^{52} - 766 q^{53} + 108 q^{54} - 191 q^{55} - 136 q^{56} - 260 q^{58} - 460 q^{59} - 156 q^{60} + 494 q^{61} - 478 q^{62} - 153 q^{63} + 128 q^{64} - 61 q^{65} + 84 q^{66} - 133 q^{67} - 48 q^{68} - 162 q^{69} + 46 q^{70} - 459 q^{71} + 144 q^{72} + 396 q^{73} - 296 q^{74} - 309 q^{75} + 21 q^{77} + 114 q^{78} + 1000 q^{79} - 208 q^{80} + 162 q^{81} + 662 q^{82} - 74 q^{83} - 204 q^{84} + 503 q^{85} - 448 q^{86} - 390 q^{87} + 112 q^{88} - 1180 q^{89} - 234 q^{90} - 249 q^{91} - 216 q^{92} - 717 q^{93} + 666 q^{94} + 192 q^{96} - 1938 q^{97} - 838 q^{98} + 126 q^{99} + O(q^{100}) \)

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
\(5\) −12.0902 −1.08138 −0.540689 0.841223i \(-0.681836\pi\)
−0.540689 + 0.841223i \(0.681836\pi\)
\(6\) 6.00000 0.408248
\(7\) −0.673762 −0.0363797 −0.0181899 0.999835i \(-0.505790\pi\)
−0.0181899 + 0.999835i \(0.505790\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −24.1803 −0.764649
\(11\) 15.9443 0.437034 0.218517 0.975833i \(-0.429878\pi\)
0.218517 + 0.975833i \(0.429878\pi\)
\(12\) 12.0000 0.288675
\(13\) 3.90983 0.0834147 0.0417074 0.999130i \(-0.486720\pi\)
0.0417074 + 0.999130i \(0.486720\pi\)
\(14\) −1.34752 −0.0257244
\(15\) −36.2705 −0.624334
\(16\) 16.0000 0.250000
\(17\) −44.0132 −0.627927 −0.313963 0.949435i \(-0.601657\pi\)
−0.313963 + 0.949435i \(0.601657\pi\)
\(18\) 18.0000 0.235702
\(19\) 0 0
\(20\) −48.3607 −0.540689
\(21\) −2.02129 −0.0210038
\(22\) 31.8885 0.309030
\(23\) −9.11146 −0.0826030 −0.0413015 0.999147i \(-0.513150\pi\)
−0.0413015 + 0.999147i \(0.513150\pi\)
\(24\) 24.0000 0.204124
\(25\) 21.1722 0.169378
\(26\) 7.81966 0.0589831
\(27\) 27.0000 0.192450
\(28\) −2.69505 −0.0181899
\(29\) −161.151 −1.03190 −0.515948 0.856620i \(-0.672560\pi\)
−0.515948 + 0.856620i \(0.672560\pi\)
\(30\) −72.5410 −0.441471
\(31\) 60.5035 0.350540 0.175270 0.984520i \(-0.443920\pi\)
0.175270 + 0.984520i \(0.443920\pi\)
\(32\) 32.0000 0.176777
\(33\) 47.8328 0.252322
\(34\) −88.0263 −0.444011
\(35\) 8.14590 0.0393402
\(36\) 36.0000 0.166667
\(37\) 104.885 0.466029 0.233014 0.972473i \(-0.425141\pi\)
0.233014 + 0.972473i \(0.425141\pi\)
\(38\) 0 0
\(39\) 11.7295 0.0481595
\(40\) −96.7214 −0.382325
\(41\) 249.353 0.949813 0.474906 0.880036i \(-0.342482\pi\)
0.474906 + 0.880036i \(0.342482\pi\)
\(42\) −4.04257 −0.0148520
\(43\) −6.90481 −0.0244877 −0.0122439 0.999925i \(-0.503897\pi\)
−0.0122439 + 0.999925i \(0.503897\pi\)
\(44\) 63.7771 0.218517
\(45\) −108.812 −0.360459
\(46\) −18.2229 −0.0584092
\(47\) 145.257 0.450808 0.225404 0.974265i \(-0.427630\pi\)
0.225404 + 0.974265i \(0.427630\pi\)
\(48\) 48.0000 0.144338
\(49\) −342.546 −0.998677
\(50\) 42.3444 0.119768
\(51\) −132.039 −0.362534
\(52\) 15.6393 0.0417074
\(53\) −754.187 −1.95463 −0.977317 0.211782i \(-0.932073\pi\)
−0.977317 + 0.211782i \(0.932073\pi\)
\(54\) 54.0000 0.136083
\(55\) −192.769 −0.472599
\(56\) −5.39010 −0.0128622
\(57\) 0 0
\(58\) −322.302 −0.729660
\(59\) −704.046 −1.55354 −0.776771 0.629783i \(-0.783144\pi\)
−0.776771 + 0.629783i \(0.783144\pi\)
\(60\) −145.082 −0.312167
\(61\) −32.5085 −0.0682342 −0.0341171 0.999418i \(-0.510862\pi\)
−0.0341171 + 0.999418i \(0.510862\pi\)
\(62\) 121.007 0.247869
\(63\) −6.06386 −0.0121266
\(64\) 64.0000 0.125000
\(65\) −47.2705 −0.0902028
\(66\) 95.6656 0.178419
\(67\) 77.7264 0.141728 0.0708641 0.997486i \(-0.477424\pi\)
0.0708641 + 0.997486i \(0.477424\pi\)
\(68\) −176.053 −0.313963
\(69\) −27.3344 −0.0476909
\(70\) 16.2918 0.0278177
\(71\) 44.4183 0.0742463 0.0371231 0.999311i \(-0.488181\pi\)
0.0371231 + 0.999311i \(0.488181\pi\)
\(72\) 72.0000 0.117851
\(73\) 280.735 0.450103 0.225051 0.974347i \(-0.427745\pi\)
0.225051 + 0.974347i \(0.427745\pi\)
\(74\) 209.771 0.329532
\(75\) 63.5166 0.0977902
\(76\) 0 0
\(77\) −10.7426 −0.0158992
\(78\) 23.4590 0.0340539
\(79\) 779.508 1.11015 0.555073 0.831802i \(-0.312690\pi\)
0.555073 + 0.831802i \(0.312690\pi\)
\(80\) −193.443 −0.270344
\(81\) 81.0000 0.111111
\(82\) 498.705 0.671619
\(83\) −274.023 −0.362385 −0.181192 0.983448i \(-0.557996\pi\)
−0.181192 + 0.983448i \(0.557996\pi\)
\(84\) −8.08514 −0.0105019
\(85\) 532.127 0.679026
\(86\) −13.8096 −0.0173154
\(87\) −483.453 −0.595765
\(88\) 127.554 0.154515
\(89\) −1005.91 −1.19805 −0.599023 0.800732i \(-0.704444\pi\)
−0.599023 + 0.800732i \(0.704444\pi\)
\(90\) −217.623 −0.254883
\(91\) −2.63430 −0.00303461
\(92\) −36.4458 −0.0413015
\(93\) 181.510 0.202384
\(94\) 290.515 0.318769
\(95\) 0 0
\(96\) 96.0000 0.102062
\(97\) −832.600 −0.871523 −0.435761 0.900062i \(-0.643521\pi\)
−0.435761 + 0.900062i \(0.643521\pi\)
\(98\) −685.092 −0.706171
\(99\) 143.498 0.145678
\(100\) 84.6888 0.0846888
\(101\) 910.371 0.896885 0.448442 0.893812i \(-0.351979\pi\)
0.448442 + 0.893812i \(0.351979\pi\)
\(102\) −264.079 −0.256350
\(103\) −1272.16 −1.21699 −0.608493 0.793559i \(-0.708226\pi\)
−0.608493 + 0.793559i \(0.708226\pi\)
\(104\) 31.2786 0.0294916
\(105\) 24.4377 0.0227131
\(106\) −1508.37 −1.38213
\(107\) 783.565 0.707945 0.353972 0.935256i \(-0.384831\pi\)
0.353972 + 0.935256i \(0.384831\pi\)
\(108\) 108.000 0.0962250
\(109\) −2013.17 −1.76905 −0.884524 0.466494i \(-0.845517\pi\)
−0.884524 + 0.466494i \(0.845517\pi\)
\(110\) −385.538 −0.334178
\(111\) 314.656 0.269062
\(112\) −10.7802 −0.00909493
\(113\) −10.6506 −0.00886655 −0.00443327 0.999990i \(-0.501411\pi\)
−0.00443327 + 0.999990i \(0.501411\pi\)
\(114\) 0 0
\(115\) 110.159 0.0893251
\(116\) −644.604 −0.515948
\(117\) 35.1885 0.0278049
\(118\) −1408.09 −1.09852
\(119\) 29.6544 0.0228438
\(120\) −290.164 −0.220735
\(121\) −1076.78 −0.809001
\(122\) −65.0170 −0.0482489
\(123\) 748.058 0.548375
\(124\) 242.014 0.175270
\(125\) 1255.30 0.898216
\(126\) −12.1277 −0.00857479
\(127\) −932.541 −0.651572 −0.325786 0.945444i \(-0.605629\pi\)
−0.325786 + 0.945444i \(0.605629\pi\)
\(128\) 128.000 0.0883883
\(129\) −20.7144 −0.0141380
\(130\) −94.5410 −0.0637830
\(131\) 208.795 0.139256 0.0696278 0.997573i \(-0.477819\pi\)
0.0696278 + 0.997573i \(0.477819\pi\)
\(132\) 191.331 0.126161
\(133\) 0 0
\(134\) 155.453 0.100217
\(135\) −326.435 −0.208111
\(136\) −352.105 −0.222006
\(137\) −368.275 −0.229663 −0.114832 0.993385i \(-0.536633\pi\)
−0.114832 + 0.993385i \(0.536633\pi\)
\(138\) −54.6687 −0.0337226
\(139\) −1722.46 −1.05106 −0.525528 0.850776i \(-0.676132\pi\)
−0.525528 + 0.850776i \(0.676132\pi\)
\(140\) 32.5836 0.0196701
\(141\) 435.772 0.260274
\(142\) 88.8367 0.0525000
\(143\) 62.3394 0.0364551
\(144\) 144.000 0.0833333
\(145\) 1948.34 1.11587
\(146\) 561.469 0.318271
\(147\) −1027.64 −0.576586
\(148\) 419.542 0.233014
\(149\) −2688.05 −1.47795 −0.738973 0.673736i \(-0.764689\pi\)
−0.738973 + 0.673736i \(0.764689\pi\)
\(150\) 127.033 0.0691481
\(151\) 2474.74 1.33372 0.666860 0.745183i \(-0.267638\pi\)
0.666860 + 0.745183i \(0.267638\pi\)
\(152\) 0 0
\(153\) −396.118 −0.209309
\(154\) −21.4853 −0.0112424
\(155\) −731.497 −0.379066
\(156\) 46.9180 0.0240798
\(157\) −1209.81 −0.614991 −0.307495 0.951550i \(-0.599491\pi\)
−0.307495 + 0.951550i \(0.599491\pi\)
\(158\) 1559.02 0.784992
\(159\) −2262.56 −1.12851
\(160\) −386.885 −0.191162
\(161\) 6.13895 0.00300508
\(162\) 162.000 0.0785674
\(163\) 2745.03 1.31906 0.659531 0.751678i \(-0.270755\pi\)
0.659531 + 0.751678i \(0.270755\pi\)
\(164\) 997.410 0.474906
\(165\) −578.307 −0.272855
\(166\) −548.046 −0.256245
\(167\) −3241.89 −1.50218 −0.751092 0.660197i \(-0.770473\pi\)
−0.751092 + 0.660197i \(0.770473\pi\)
\(168\) −16.1703 −0.00742598
\(169\) −2181.71 −0.993042
\(170\) 1064.25 0.480144
\(171\) 0 0
\(172\) −27.6192 −0.0122439
\(173\) −2461.28 −1.08166 −0.540832 0.841130i \(-0.681891\pi\)
−0.540832 + 0.841130i \(0.681891\pi\)
\(174\) −966.906 −0.421270
\(175\) −14.2650 −0.00616191
\(176\) 255.108 0.109259
\(177\) −2112.14 −0.896938
\(178\) −2011.82 −0.847147
\(179\) −2964.26 −1.23776 −0.618880 0.785485i \(-0.712413\pi\)
−0.618880 + 0.785485i \(0.712413\pi\)
\(180\) −435.246 −0.180230
\(181\) 4403.67 1.80841 0.904204 0.427100i \(-0.140465\pi\)
0.904204 + 0.427100i \(0.140465\pi\)
\(182\) −5.26859 −0.00214579
\(183\) −97.5255 −0.0393950
\(184\) −72.8916 −0.0292046
\(185\) −1268.08 −0.503953
\(186\) 363.021 0.143107
\(187\) −701.758 −0.274426
\(188\) 581.029 0.225404
\(189\) −18.1916 −0.00700128
\(190\) 0 0
\(191\) −2167.97 −0.821302 −0.410651 0.911793i \(-0.634698\pi\)
−0.410651 + 0.911793i \(0.634698\pi\)
\(192\) 192.000 0.0721688
\(193\) −3122.55 −1.16459 −0.582296 0.812977i \(-0.697845\pi\)
−0.582296 + 0.812977i \(0.697845\pi\)
\(194\) −1665.20 −0.616260
\(195\) −141.812 −0.0520786
\(196\) −1370.18 −0.499338
\(197\) 202.429 0.0732106 0.0366053 0.999330i \(-0.488346\pi\)
0.0366053 + 0.999330i \(0.488346\pi\)
\(198\) 286.997 0.103010
\(199\) −1649.25 −0.587497 −0.293749 0.955883i \(-0.594903\pi\)
−0.293749 + 0.955883i \(0.594903\pi\)
\(200\) 169.378 0.0598841
\(201\) 233.179 0.0818268
\(202\) 1820.74 0.634193
\(203\) 108.577 0.0375401
\(204\) −528.158 −0.181267
\(205\) −3014.71 −1.02711
\(206\) −2544.32 −0.860540
\(207\) −82.0031 −0.0275343
\(208\) 62.5573 0.0208537
\(209\) 0 0
\(210\) 48.8754 0.0160606
\(211\) 1629.35 0.531608 0.265804 0.964027i \(-0.414363\pi\)
0.265804 + 0.964027i \(0.414363\pi\)
\(212\) −3016.75 −0.977317
\(213\) 133.255 0.0428661
\(214\) 1567.13 0.500593
\(215\) 83.4803 0.0264805
\(216\) 216.000 0.0680414
\(217\) −40.7649 −0.0127526
\(218\) −4026.33 −1.25091
\(219\) 842.204 0.259867
\(220\) −771.076 −0.236300
\(221\) −172.084 −0.0523784
\(222\) 629.313 0.190255
\(223\) −481.492 −0.144588 −0.0722939 0.997383i \(-0.523032\pi\)
−0.0722939 + 0.997383i \(0.523032\pi\)
\(224\) −21.5604 −0.00643109
\(225\) 190.550 0.0564592
\(226\) −21.3011 −0.00626960
\(227\) 2786.59 0.814768 0.407384 0.913257i \(-0.366441\pi\)
0.407384 + 0.913257i \(0.366441\pi\)
\(228\) 0 0
\(229\) 1437.72 0.414878 0.207439 0.978248i \(-0.433487\pi\)
0.207439 + 0.978248i \(0.433487\pi\)
\(230\) 220.318 0.0631624
\(231\) −32.2279 −0.00917941
\(232\) −1289.21 −0.364830
\(233\) −2782.74 −0.782419 −0.391209 0.920302i \(-0.627943\pi\)
−0.391209 + 0.920302i \(0.627943\pi\)
\(234\) 70.3769 0.0196610
\(235\) −1756.19 −0.487493
\(236\) −2816.19 −0.776771
\(237\) 2338.53 0.640943
\(238\) 59.3088 0.0161530
\(239\) 4530.56 1.22618 0.613091 0.790013i \(-0.289926\pi\)
0.613091 + 0.790013i \(0.289926\pi\)
\(240\) −580.328 −0.156083
\(241\) −2457.27 −0.656792 −0.328396 0.944540i \(-0.606508\pi\)
−0.328396 + 0.944540i \(0.606508\pi\)
\(242\) −2153.56 −0.572050
\(243\) 243.000 0.0641500
\(244\) −130.034 −0.0341171
\(245\) 4141.44 1.07995
\(246\) 1496.12 0.387759
\(247\) 0 0
\(248\) 484.028 0.123935
\(249\) −822.070 −0.209223
\(250\) 2510.59 0.635135
\(251\) −3211.61 −0.807631 −0.403815 0.914841i \(-0.632316\pi\)
−0.403815 + 0.914841i \(0.632316\pi\)
\(252\) −24.2554 −0.00606329
\(253\) −145.276 −0.0361004
\(254\) −1865.08 −0.460731
\(255\) 1596.38 0.392036
\(256\) 256.000 0.0625000
\(257\) 1670.69 0.405504 0.202752 0.979230i \(-0.435011\pi\)
0.202752 + 0.979230i \(0.435011\pi\)
\(258\) −41.4288 −0.00999708
\(259\) −70.6678 −0.0169540
\(260\) −189.082 −0.0451014
\(261\) −1450.36 −0.343965
\(262\) 417.590 0.0984686
\(263\) −7731.93 −1.81282 −0.906409 0.422402i \(-0.861187\pi\)
−0.906409 + 0.422402i \(0.861187\pi\)
\(264\) 382.663 0.0892093
\(265\) 9118.25 2.11370
\(266\) 0 0
\(267\) −3017.73 −0.691692
\(268\) 310.906 0.0708641
\(269\) 1024.48 0.232207 0.116104 0.993237i \(-0.462960\pi\)
0.116104 + 0.993237i \(0.462960\pi\)
\(270\) −652.869 −0.147157
\(271\) 1067.86 0.239366 0.119683 0.992812i \(-0.461812\pi\)
0.119683 + 0.992812i \(0.461812\pi\)
\(272\) −704.210 −0.156982
\(273\) −7.90289 −0.00175203
\(274\) −736.550 −0.162396
\(275\) 337.575 0.0740239
\(276\) −109.337 −0.0238454
\(277\) 311.065 0.0674733 0.0337367 0.999431i \(-0.489259\pi\)
0.0337367 + 0.999431i \(0.489259\pi\)
\(278\) −3444.91 −0.743209
\(279\) 544.531 0.116847
\(280\) 65.1672 0.0139089
\(281\) −7346.75 −1.55968 −0.779840 0.625979i \(-0.784700\pi\)
−0.779840 + 0.625979i \(0.784700\pi\)
\(282\) 871.544 0.184041
\(283\) 4046.95 0.850056 0.425028 0.905180i \(-0.360264\pi\)
0.425028 + 0.905180i \(0.360264\pi\)
\(284\) 177.673 0.0371231
\(285\) 0 0
\(286\) 124.679 0.0257777
\(287\) −168.004 −0.0345539
\(288\) 288.000 0.0589256
\(289\) −2975.84 −0.605708
\(290\) 3896.68 0.789039
\(291\) −2497.80 −0.503174
\(292\) 1122.94 0.225051
\(293\) −3641.56 −0.726083 −0.363041 0.931773i \(-0.618262\pi\)
−0.363041 + 0.931773i \(0.618262\pi\)
\(294\) −2055.28 −0.407708
\(295\) 8512.04 1.67997
\(296\) 839.084 0.164766
\(297\) 430.495 0.0841073
\(298\) −5376.10 −1.04506
\(299\) −35.6242 −0.00689031
\(300\) 254.067 0.0488951
\(301\) 4.65220 0.000890858 0
\(302\) 4949.49 0.943082
\(303\) 2731.11 0.517817
\(304\) 0 0
\(305\) 393.033 0.0737869
\(306\) −792.237 −0.148004
\(307\) 4685.42 0.871045 0.435523 0.900178i \(-0.356564\pi\)
0.435523 + 0.900178i \(0.356564\pi\)
\(308\) −42.9706 −0.00794960
\(309\) −3816.48 −0.702628
\(310\) −1462.99 −0.268040
\(311\) −2413.55 −0.440065 −0.220032 0.975493i \(-0.570616\pi\)
−0.220032 + 0.975493i \(0.570616\pi\)
\(312\) 93.8359 0.0170270
\(313\) −5062.23 −0.914167 −0.457084 0.889424i \(-0.651106\pi\)
−0.457084 + 0.889424i \(0.651106\pi\)
\(314\) −2419.63 −0.434864
\(315\) 73.3131 0.0131134
\(316\) 3118.03 0.555073
\(317\) 5704.03 1.01063 0.505316 0.862935i \(-0.331376\pi\)
0.505316 + 0.862935i \(0.331376\pi\)
\(318\) −4525.12 −0.797976
\(319\) −2569.43 −0.450974
\(320\) −773.771 −0.135172
\(321\) 2350.69 0.408732
\(322\) 12.2779 0.00212491
\(323\) 0 0
\(324\) 324.000 0.0555556
\(325\) 82.7797 0.0141286
\(326\) 5490.05 0.932717
\(327\) −6039.50 −1.02136
\(328\) 1994.82 0.335810
\(329\) −97.8689 −0.0164003
\(330\) −1156.61 −0.192938
\(331\) 8367.55 1.38949 0.694747 0.719254i \(-0.255516\pi\)
0.694747 + 0.719254i \(0.255516\pi\)
\(332\) −1096.09 −0.181192
\(333\) 943.969 0.155343
\(334\) −6483.78 −1.06221
\(335\) −939.725 −0.153262
\(336\) −32.3406 −0.00525096
\(337\) 263.413 0.0425787 0.0212894 0.999773i \(-0.493223\pi\)
0.0212894 + 0.999773i \(0.493223\pi\)
\(338\) −4363.43 −0.702187
\(339\) −31.9517 −0.00511910
\(340\) 2128.51 0.339513
\(341\) 964.684 0.153198
\(342\) 0 0
\(343\) 461.895 0.0727113
\(344\) −55.2384 −0.00865772
\(345\) 330.477 0.0515719
\(346\) −4922.57 −0.764853
\(347\) 4021.50 0.622148 0.311074 0.950386i \(-0.399311\pi\)
0.311074 + 0.950386i \(0.399311\pi\)
\(348\) −1933.81 −0.297883
\(349\) 453.400 0.0695414 0.0347707 0.999395i \(-0.488930\pi\)
0.0347707 + 0.999395i \(0.488930\pi\)
\(350\) −28.5301 −0.00435713
\(351\) 105.565 0.0160532
\(352\) 510.217 0.0772575
\(353\) −4547.61 −0.685680 −0.342840 0.939394i \(-0.611389\pi\)
−0.342840 + 0.939394i \(0.611389\pi\)
\(354\) −4224.28 −0.634231
\(355\) −537.025 −0.0802883
\(356\) −4023.63 −0.599023
\(357\) 88.9632 0.0131889
\(358\) −5928.52 −0.875229
\(359\) 8396.86 1.23445 0.617227 0.786785i \(-0.288256\pi\)
0.617227 + 0.786785i \(0.288256\pi\)
\(360\) −870.492 −0.127442
\(361\) 0 0
\(362\) 8807.33 1.27874
\(363\) −3230.34 −0.467077
\(364\) −10.5372 −0.00151730
\(365\) −3394.13 −0.486731
\(366\) −195.051 −0.0278565
\(367\) −5422.59 −0.771273 −0.385636 0.922651i \(-0.626018\pi\)
−0.385636 + 0.922651i \(0.626018\pi\)
\(368\) −145.783 −0.0206508
\(369\) 2244.17 0.316604
\(370\) −2536.17 −0.356349
\(371\) 508.143 0.0711091
\(372\) 726.042 0.101192
\(373\) 7439.39 1.03270 0.516350 0.856378i \(-0.327290\pi\)
0.516350 + 0.856378i \(0.327290\pi\)
\(374\) −1403.52 −0.194048
\(375\) 3765.89 0.518586
\(376\) 1162.06 0.159385
\(377\) −630.073 −0.0860753
\(378\) −36.3832 −0.00495065
\(379\) 12741.8 1.72692 0.863461 0.504415i \(-0.168292\pi\)
0.863461 + 0.504415i \(0.168292\pi\)
\(380\) 0 0
\(381\) −2797.62 −0.376185
\(382\) −4335.93 −0.580748
\(383\) 10550.9 1.40764 0.703822 0.710376i \(-0.251475\pi\)
0.703822 + 0.710376i \(0.251475\pi\)
\(384\) 384.000 0.0510310
\(385\) 129.880 0.0171930
\(386\) −6245.10 −0.823490
\(387\) −62.1432 −0.00816258
\(388\) −3330.40 −0.435761
\(389\) 6581.54 0.857834 0.428917 0.903344i \(-0.358895\pi\)
0.428917 + 0.903344i \(0.358895\pi\)
\(390\) −283.623 −0.0368252
\(391\) 401.024 0.0518687
\(392\) −2740.37 −0.353085
\(393\) 626.384 0.0803993
\(394\) 404.859 0.0517677
\(395\) −9424.39 −1.20049
\(396\) 573.994 0.0728391
\(397\) 2148.76 0.271646 0.135823 0.990733i \(-0.456632\pi\)
0.135823 + 0.990733i \(0.456632\pi\)
\(398\) −3298.49 −0.415423
\(399\) 0 0
\(400\) 338.755 0.0423444
\(401\) 2532.20 0.315342 0.157671 0.987492i \(-0.449602\pi\)
0.157671 + 0.987492i \(0.449602\pi\)
\(402\) 466.358 0.0578603
\(403\) 236.558 0.0292402
\(404\) 3641.49 0.448442
\(405\) −979.304 −0.120153
\(406\) 217.155 0.0265449
\(407\) 1672.32 0.203671
\(408\) −1056.32 −0.128175
\(409\) 8046.03 0.972740 0.486370 0.873753i \(-0.338321\pi\)
0.486370 + 0.873753i \(0.338321\pi\)
\(410\) −6029.43 −0.726274
\(411\) −1104.83 −0.132596
\(412\) −5088.64 −0.608493
\(413\) 474.360 0.0565175
\(414\) −164.006 −0.0194697
\(415\) 3312.99 0.391875
\(416\) 125.115 0.0147458
\(417\) −5167.37 −0.606828
\(418\) 0 0
\(419\) −10432.9 −1.21642 −0.608210 0.793776i \(-0.708112\pi\)
−0.608210 + 0.793776i \(0.708112\pi\)
\(420\) 97.7508 0.0113565
\(421\) 4591.58 0.531544 0.265772 0.964036i \(-0.414373\pi\)
0.265772 + 0.964036i \(0.414373\pi\)
\(422\) 3258.71 0.375904
\(423\) 1307.32 0.150269
\(424\) −6033.50 −0.691067
\(425\) −931.856 −0.106357
\(426\) 266.510 0.0303109
\(427\) 21.9030 0.00248234
\(428\) 3134.26 0.353972
\(429\) 187.018 0.0210474
\(430\) 166.961 0.0187245
\(431\) 14117.1 1.57772 0.788861 0.614571i \(-0.210671\pi\)
0.788861 + 0.614571i \(0.210671\pi\)
\(432\) 432.000 0.0481125
\(433\) −13929.0 −1.54592 −0.772962 0.634452i \(-0.781226\pi\)
−0.772962 + 0.634452i \(0.781226\pi\)
\(434\) −81.5299 −0.00901742
\(435\) 5845.03 0.644247
\(436\) −8052.66 −0.884524
\(437\) 0 0
\(438\) 1684.41 0.183754
\(439\) 5222.03 0.567731 0.283866 0.958864i \(-0.408383\pi\)
0.283866 + 0.958864i \(0.408383\pi\)
\(440\) −1542.15 −0.167089
\(441\) −3082.91 −0.332892
\(442\) −344.168 −0.0370371
\(443\) −10163.4 −1.09002 −0.545010 0.838430i \(-0.683474\pi\)
−0.545010 + 0.838430i \(0.683474\pi\)
\(444\) 1258.63 0.134531
\(445\) 12161.6 1.29554
\(446\) −962.984 −0.102239
\(447\) −8064.16 −0.853292
\(448\) −43.1208 −0.00454747
\(449\) 17851.6 1.87632 0.938161 0.346199i \(-0.112528\pi\)
0.938161 + 0.346199i \(0.112528\pi\)
\(450\) 381.100 0.0399227
\(451\) 3975.74 0.415101
\(452\) −42.6022 −0.00443327
\(453\) 7424.23 0.770024
\(454\) 5573.18 0.576128
\(455\) 31.8491 0.00328156
\(456\) 0 0
\(457\) −5037.95 −0.515679 −0.257839 0.966188i \(-0.583011\pi\)
−0.257839 + 0.966188i \(0.583011\pi\)
\(458\) 2875.44 0.293363
\(459\) −1188.36 −0.120845
\(460\) 440.636 0.0446625
\(461\) −11181.4 −1.12965 −0.564825 0.825211i \(-0.691056\pi\)
−0.564825 + 0.825211i \(0.691056\pi\)
\(462\) −64.4559 −0.00649082
\(463\) 18455.1 1.85244 0.926222 0.376978i \(-0.123037\pi\)
0.926222 + 0.376978i \(0.123037\pi\)
\(464\) −2578.41 −0.257974
\(465\) −2194.49 −0.218854
\(466\) −5565.48 −0.553253
\(467\) 6412.78 0.635435 0.317718 0.948185i \(-0.397084\pi\)
0.317718 + 0.948185i \(0.397084\pi\)
\(468\) 140.754 0.0139025
\(469\) −52.3691 −0.00515603
\(470\) −3512.37 −0.344710
\(471\) −3629.44 −0.355065
\(472\) −5632.37 −0.549260
\(473\) −110.092 −0.0107020
\(474\) 4677.05 0.453215
\(475\) 0 0
\(476\) 118.618 0.0114219
\(477\) −6787.69 −0.651545
\(478\) 9061.11 0.867041
\(479\) −8519.67 −0.812680 −0.406340 0.913722i \(-0.633195\pi\)
−0.406340 + 0.913722i \(0.633195\pi\)
\(480\) −1160.66 −0.110368
\(481\) 410.084 0.0388737
\(482\) −4914.55 −0.464422
\(483\) 18.4169 0.00173498
\(484\) −4307.12 −0.404500
\(485\) 10066.3 0.942445
\(486\) 486.000 0.0453609
\(487\) 12746.8 1.18607 0.593033 0.805178i \(-0.297930\pi\)
0.593033 + 0.805178i \(0.297930\pi\)
\(488\) −260.068 −0.0241244
\(489\) 8235.08 0.761560
\(490\) 8282.88 0.763637
\(491\) −5187.09 −0.476762 −0.238381 0.971172i \(-0.576617\pi\)
−0.238381 + 0.971172i \(0.576617\pi\)
\(492\) 2992.23 0.274187
\(493\) 7092.76 0.647955
\(494\) 0 0
\(495\) −1734.92 −0.157533
\(496\) 968.056 0.0876350
\(497\) −29.9274 −0.00270106
\(498\) −1644.14 −0.147943
\(499\) −10704.5 −0.960315 −0.480158 0.877182i \(-0.659421\pi\)
−0.480158 + 0.877182i \(0.659421\pi\)
\(500\) 5021.18 0.449108
\(501\) −9725.67 −0.867287
\(502\) −6423.23 −0.571081
\(503\) 13720.9 1.21627 0.608137 0.793832i \(-0.291917\pi\)
0.608137 + 0.793832i \(0.291917\pi\)
\(504\) −48.5109 −0.00428739
\(505\) −11006.5 −0.969871
\(506\) −290.551 −0.0255268
\(507\) −6545.14 −0.573333
\(508\) −3730.16 −0.325786
\(509\) −6427.78 −0.559737 −0.279869 0.960038i \(-0.590291\pi\)
−0.279869 + 0.960038i \(0.590291\pi\)
\(510\) 3192.76 0.277211
\(511\) −189.148 −0.0163746
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 3341.37 0.286735
\(515\) 15380.6 1.31602
\(516\) −82.8577 −0.00706900
\(517\) 2316.02 0.197018
\(518\) −141.336 −0.0119883
\(519\) −7383.85 −0.624500
\(520\) −378.164 −0.0318915
\(521\) −2296.27 −0.193093 −0.0965464 0.995328i \(-0.530780\pi\)
−0.0965464 + 0.995328i \(0.530780\pi\)
\(522\) −2900.72 −0.243220
\(523\) −672.621 −0.0562364 −0.0281182 0.999605i \(-0.508951\pi\)
−0.0281182 + 0.999605i \(0.508951\pi\)
\(524\) 835.179 0.0696278
\(525\) −42.7951 −0.00355758
\(526\) −15463.9 −1.28186
\(527\) −2662.95 −0.220114
\(528\) 765.325 0.0630805
\(529\) −12084.0 −0.993177
\(530\) 18236.5 1.49461
\(531\) −6336.42 −0.517848
\(532\) 0 0
\(533\) 974.926 0.0792284
\(534\) −6035.45 −0.489100
\(535\) −9473.43 −0.765556
\(536\) 621.811 0.0501085
\(537\) −8892.78 −0.714622
\(538\) 2048.96 0.164195
\(539\) −5461.65 −0.436456
\(540\) −1305.74 −0.104056
\(541\) −18524.3 −1.47213 −0.736065 0.676911i \(-0.763318\pi\)
−0.736065 + 0.676911i \(0.763318\pi\)
\(542\) 2135.73 0.169257
\(543\) 13211.0 1.04409
\(544\) −1408.42 −0.111003
\(545\) 24339.5 1.91301
\(546\) −15.8058 −0.00123887
\(547\) 6149.10 0.480652 0.240326 0.970692i \(-0.422746\pi\)
0.240326 + 0.970692i \(0.422746\pi\)
\(548\) −1473.10 −0.114832
\(549\) −292.576 −0.0227447
\(550\) 675.151 0.0523428
\(551\) 0 0
\(552\) −218.675 −0.0168613
\(553\) −525.203 −0.0403868
\(554\) 622.131 0.0477109
\(555\) −3804.25 −0.290957
\(556\) −6889.82 −0.525528
\(557\) −1151.85 −0.0876218 −0.0438109 0.999040i \(-0.513950\pi\)
−0.0438109 + 0.999040i \(0.513950\pi\)
\(558\) 1089.06 0.0826231
\(559\) −26.9966 −0.00204264
\(560\) 130.334 0.00983506
\(561\) −2105.27 −0.158440
\(562\) −14693.5 −1.10286
\(563\) 3182.72 0.238252 0.119126 0.992879i \(-0.461991\pi\)
0.119126 + 0.992879i \(0.461991\pi\)
\(564\) 1743.09 0.130137
\(565\) 128.767 0.00958809
\(566\) 8093.89 0.601081
\(567\) −54.5747 −0.00404219
\(568\) 355.347 0.0262500
\(569\) −20679.8 −1.52363 −0.761814 0.647796i \(-0.775691\pi\)
−0.761814 + 0.647796i \(0.775691\pi\)
\(570\) 0 0
\(571\) −2820.58 −0.206721 −0.103360 0.994644i \(-0.532960\pi\)
−0.103360 + 0.994644i \(0.532960\pi\)
\(572\) 249.358 0.0182276
\(573\) −6503.90 −0.474179
\(574\) −336.009 −0.0244333
\(575\) −192.910 −0.0139911
\(576\) 576.000 0.0416667
\(577\) 11208.6 0.808700 0.404350 0.914604i \(-0.367498\pi\)
0.404350 + 0.914604i \(0.367498\pi\)
\(578\) −5951.68 −0.428300
\(579\) −9367.65 −0.672377
\(580\) 7793.37 0.557934
\(581\) 184.626 0.0131835
\(582\) −4995.60 −0.355798
\(583\) −12025.0 −0.854242
\(584\) 2245.88 0.159135
\(585\) −425.435 −0.0300676
\(586\) −7283.12 −0.513418
\(587\) −209.871 −0.0147569 −0.00737846 0.999973i \(-0.502349\pi\)
−0.00737846 + 0.999973i \(0.502349\pi\)
\(588\) −4110.55 −0.288293
\(589\) 0 0
\(590\) 17024.1 1.18792
\(591\) 607.288 0.0422682
\(592\) 1678.17 0.116507
\(593\) 9737.59 0.674325 0.337163 0.941446i \(-0.390533\pi\)
0.337163 + 0.941446i \(0.390533\pi\)
\(594\) 860.991 0.0594729
\(595\) −358.527 −0.0247028
\(596\) −10752.2 −0.738973
\(597\) −4947.74 −0.339192
\(598\) −71.2485 −0.00487219
\(599\) 3772.44 0.257325 0.128662 0.991688i \(-0.458932\pi\)
0.128662 + 0.991688i \(0.458932\pi\)
\(600\) 508.133 0.0345741
\(601\) 12419.2 0.842910 0.421455 0.906849i \(-0.361520\pi\)
0.421455 + 0.906849i \(0.361520\pi\)
\(602\) 9.30439 0.000629931 0
\(603\) 699.537 0.0472427
\(604\) 9898.97 0.666860
\(605\) 13018.5 0.874836
\(606\) 5462.23 0.366152
\(607\) −3934.15 −0.263068 −0.131534 0.991312i \(-0.541990\pi\)
−0.131534 + 0.991312i \(0.541990\pi\)
\(608\) 0 0
\(609\) 325.732 0.0216738
\(610\) 786.067 0.0521753
\(611\) 567.932 0.0376040
\(612\) −1584.47 −0.104654
\(613\) −22886.6 −1.50796 −0.753980 0.656897i \(-0.771868\pi\)
−0.753980 + 0.656897i \(0.771868\pi\)
\(614\) 9370.84 0.615922
\(615\) −9044.14 −0.593000
\(616\) −85.9412 −0.00562121
\(617\) 5961.78 0.388999 0.194500 0.980903i \(-0.437692\pi\)
0.194500 + 0.980903i \(0.437692\pi\)
\(618\) −7632.96 −0.496833
\(619\) 15162.2 0.984526 0.492263 0.870447i \(-0.336170\pi\)
0.492263 + 0.870447i \(0.336170\pi\)
\(620\) −2925.99 −0.189533
\(621\) −246.009 −0.0158970
\(622\) −4827.11 −0.311173
\(623\) 677.743 0.0435846
\(624\) 187.672 0.0120399
\(625\) −17823.3 −1.14069
\(626\) −10124.5 −0.646414
\(627\) 0 0
\(628\) −4839.25 −0.307495
\(629\) −4616.34 −0.292632
\(630\) 146.626 0.00927258
\(631\) 19490.7 1.22966 0.614829 0.788661i \(-0.289225\pi\)
0.614829 + 0.788661i \(0.289225\pi\)
\(632\) 6236.07 0.392496
\(633\) 4888.06 0.306924
\(634\) 11408.1 0.714624
\(635\) 11274.6 0.704595
\(636\) −9050.25 −0.564254
\(637\) −1339.30 −0.0833044
\(638\) −5138.87 −0.318887
\(639\) 399.765 0.0247488
\(640\) −1547.54 −0.0955812
\(641\) −7848.89 −0.483639 −0.241819 0.970321i \(-0.577744\pi\)
−0.241819 + 0.970321i \(0.577744\pi\)
\(642\) 4701.39 0.289017
\(643\) −15640.8 −0.959272 −0.479636 0.877468i \(-0.659231\pi\)
−0.479636 + 0.877468i \(0.659231\pi\)
\(644\) 24.5558 0.00150254
\(645\) 250.441 0.0152885
\(646\) 0 0
\(647\) 5621.52 0.341584 0.170792 0.985307i \(-0.445367\pi\)
0.170792 + 0.985307i \(0.445367\pi\)
\(648\) 648.000 0.0392837
\(649\) −11225.5 −0.678952
\(650\) 165.559 0.00999043
\(651\) −122.295 −0.00736269
\(652\) 10980.1 0.659531
\(653\) −21586.7 −1.29365 −0.646824 0.762640i \(-0.723903\pi\)
−0.646824 + 0.762640i \(0.723903\pi\)
\(654\) −12079.0 −0.722211
\(655\) −2524.36 −0.150588
\(656\) 3989.64 0.237453
\(657\) 2526.61 0.150034
\(658\) −195.738 −0.0115967
\(659\) 6062.41 0.358358 0.179179 0.983816i \(-0.442656\pi\)
0.179179 + 0.983816i \(0.442656\pi\)
\(660\) −2313.23 −0.136428
\(661\) −5076.16 −0.298698 −0.149349 0.988785i \(-0.547718\pi\)
−0.149349 + 0.988785i \(0.547718\pi\)
\(662\) 16735.1 0.982520
\(663\) −516.252 −0.0302407
\(664\) −2192.19 −0.128122
\(665\) 0 0
\(666\) 1887.94 0.109844
\(667\) 1468.32 0.0852377
\(668\) −12967.6 −0.751092
\(669\) −1444.48 −0.0834778
\(670\) −1879.45 −0.108372
\(671\) −518.324 −0.0298207
\(672\) −64.6812 −0.00371299
\(673\) 15406.8 0.882450 0.441225 0.897397i \(-0.354544\pi\)
0.441225 + 0.897397i \(0.354544\pi\)
\(674\) 526.826 0.0301077
\(675\) 571.650 0.0325967
\(676\) −8726.85 −0.496521
\(677\) −7518.29 −0.426811 −0.213406 0.976964i \(-0.568456\pi\)
−0.213406 + 0.976964i \(0.568456\pi\)
\(678\) −63.9033 −0.00361975
\(679\) 560.974 0.0317058
\(680\) 4257.01 0.240072
\(681\) 8359.77 0.470407
\(682\) 1929.37 0.108327
\(683\) −18762.7 −1.05115 −0.525574 0.850748i \(-0.676149\pi\)
−0.525574 + 0.850748i \(0.676149\pi\)
\(684\) 0 0
\(685\) 4452.51 0.248353
\(686\) 923.790 0.0514147
\(687\) 4313.16 0.239530
\(688\) −110.477 −0.00612194
\(689\) −2948.74 −0.163045
\(690\) 660.954 0.0364668
\(691\) 30372.1 1.67208 0.836042 0.548666i \(-0.184864\pi\)
0.836042 + 0.548666i \(0.184864\pi\)
\(692\) −9845.14 −0.540832
\(693\) −96.6838 −0.00529973
\(694\) 8042.99 0.439925
\(695\) 20824.8 1.13659
\(696\) −3867.62 −0.210635
\(697\) −10974.8 −0.596413
\(698\) 906.800 0.0491732
\(699\) −8348.23 −0.451730
\(700\) −57.0601 −0.00308096
\(701\) −23215.5 −1.25084 −0.625420 0.780288i \(-0.715072\pi\)
−0.625420 + 0.780288i \(0.715072\pi\)
\(702\) 211.131 0.0113513
\(703\) 0 0
\(704\) 1020.43 0.0546293
\(705\) −5268.56 −0.281454
\(706\) −9095.22 −0.484849
\(707\) −613.374 −0.0326284
\(708\) −8448.56 −0.448469
\(709\) −2093.79 −0.110908 −0.0554540 0.998461i \(-0.517661\pi\)
−0.0554540 + 0.998461i \(0.517661\pi\)
\(710\) −1074.05 −0.0567724
\(711\) 7015.58 0.370049
\(712\) −8047.27 −0.423573
\(713\) −551.275 −0.0289557
\(714\) 177.926 0.00932595
\(715\) −753.694 −0.0394218
\(716\) −11857.0 −0.618880
\(717\) 13591.7 0.707936
\(718\) 16793.7 0.872891
\(719\) 10026.4 0.520059 0.260030 0.965601i \(-0.416268\pi\)
0.260030 + 0.965601i \(0.416268\pi\)
\(720\) −1740.98 −0.0901148
\(721\) 857.133 0.0442737
\(722\) 0 0
\(723\) −7371.82 −0.379199
\(724\) 17614.7 0.904204
\(725\) −3411.92 −0.174780
\(726\) −6460.68 −0.330273
\(727\) 31486.5 1.60628 0.803142 0.595787i \(-0.203160\pi\)
0.803142 + 0.595787i \(0.203160\pi\)
\(728\) −21.0744 −0.00107290
\(729\) 729.000 0.0370370
\(730\) −6788.26 −0.344171
\(731\) 303.902 0.0153765
\(732\) −390.102 −0.0196975
\(733\) −14789.2 −0.745227 −0.372614 0.927987i \(-0.621538\pi\)
−0.372614 + 0.927987i \(0.621538\pi\)
\(734\) −10845.2 −0.545372
\(735\) 12424.3 0.623507
\(736\) −291.567 −0.0146023
\(737\) 1239.29 0.0619401
\(738\) 4488.35 0.223873
\(739\) −34580.3 −1.72132 −0.860660 0.509179i \(-0.829949\pi\)
−0.860660 + 0.509179i \(0.829949\pi\)
\(740\) −5072.33 −0.251976
\(741\) 0 0
\(742\) 1016.29 0.0502817
\(743\) 14656.3 0.723670 0.361835 0.932242i \(-0.382150\pi\)
0.361835 + 0.932242i \(0.382150\pi\)
\(744\) 1452.08 0.0715537
\(745\) 32499.0 1.59822
\(746\) 14878.8 0.730229
\(747\) −2466.21 −0.120795
\(748\) −2807.03 −0.137213
\(749\) −527.936 −0.0257548
\(750\) 7531.77 0.366695
\(751\) −15707.7 −0.763224 −0.381612 0.924323i \(-0.624631\pi\)
−0.381612 + 0.924323i \(0.624631\pi\)
\(752\) 2324.12 0.112702
\(753\) −9634.84 −0.466286
\(754\) −1260.15 −0.0608644
\(755\) −29920.1 −1.44226
\(756\) −72.7663 −0.00350064
\(757\) −3495.32 −0.167820 −0.0839099 0.996473i \(-0.526741\pi\)
−0.0839099 + 0.996473i \(0.526741\pi\)
\(758\) 25483.7 1.22112
\(759\) −435.827 −0.0208426
\(760\) 0 0
\(761\) −9634.36 −0.458929 −0.229465 0.973317i \(-0.573698\pi\)
−0.229465 + 0.973317i \(0.573698\pi\)
\(762\) −5595.25 −0.266003
\(763\) 1356.39 0.0643575
\(764\) −8671.87 −0.410651
\(765\) 4789.14 0.226342
\(766\) 21101.9 0.995354
\(767\) −2752.70 −0.129588
\(768\) 768.000 0.0360844
\(769\) 3390.81 0.159006 0.0795031 0.996835i \(-0.474667\pi\)
0.0795031 + 0.996835i \(0.474667\pi\)
\(770\) 259.761 0.0121573
\(771\) 5012.06 0.234118
\(772\) −12490.2 −0.582296
\(773\) 34473.8 1.60406 0.802028 0.597286i \(-0.203754\pi\)
0.802028 + 0.597286i \(0.203754\pi\)
\(774\) −124.286 −0.00577182
\(775\) 1280.99 0.0593737
\(776\) −6660.80 −0.308130
\(777\) −212.003 −0.00978840
\(778\) 13163.1 0.606580
\(779\) 0 0
\(780\) −567.246 −0.0260393
\(781\) 708.218 0.0324482
\(782\) 802.048 0.0366767
\(783\) −4351.07 −0.198588
\(784\) −5480.74 −0.249669
\(785\) 14626.8 0.665037
\(786\) 1252.77 0.0568509
\(787\) 30099.5 1.36332 0.681658 0.731671i \(-0.261259\pi\)
0.681658 + 0.731671i \(0.261259\pi\)
\(788\) 809.717 0.0366053
\(789\) −23195.8 −1.04663
\(790\) −18848.8 −0.848873
\(791\) 7.17594 0.000322563 0
\(792\) 1147.99 0.0515050
\(793\) −127.103 −0.00569174
\(794\) 4297.53 0.192083
\(795\) 27354.8 1.22034
\(796\) −6596.98 −0.293749
\(797\) 2712.41 0.120550 0.0602752 0.998182i \(-0.480802\pi\)
0.0602752 + 0.998182i \(0.480802\pi\)
\(798\) 0 0
\(799\) −6393.23 −0.283074
\(800\) 677.511 0.0299420
\(801\) −9053.18 −0.399349
\(802\) 5064.40 0.222980
\(803\) 4476.11 0.196710
\(804\) 932.717 0.0409134
\(805\) −74.2210 −0.00324962
\(806\) 473.117 0.0206760
\(807\) 3073.45 0.134065
\(808\) 7282.97 0.317097
\(809\) 25242.2 1.09699 0.548497 0.836153i \(-0.315200\pi\)
0.548497 + 0.836153i \(0.315200\pi\)
\(810\) −1958.61 −0.0849611
\(811\) −29503.8 −1.27746 −0.638728 0.769432i \(-0.720539\pi\)
−0.638728 + 0.769432i \(0.720539\pi\)
\(812\) 434.310 0.0187700
\(813\) 3203.59 0.138198
\(814\) 3344.64 0.144017
\(815\) −33187.8 −1.42640
\(816\) −2112.63 −0.0906334
\(817\) 0 0
\(818\) 16092.1 0.687831
\(819\) −23.7087 −0.00101154
\(820\) −12058.9 −0.513553
\(821\) 401.572 0.0170706 0.00853530 0.999964i \(-0.497283\pi\)
0.00853530 + 0.999964i \(0.497283\pi\)
\(822\) −2209.65 −0.0937596
\(823\) 21122.7 0.894642 0.447321 0.894374i \(-0.352378\pi\)
0.447321 + 0.894374i \(0.352378\pi\)
\(824\) −10177.3 −0.430270
\(825\) 1012.73 0.0427377
\(826\) 948.720 0.0399639
\(827\) −43088.6 −1.81177 −0.905887 0.423519i \(-0.860795\pi\)
−0.905887 + 0.423519i \(0.860795\pi\)
\(828\) −328.012 −0.0137672
\(829\) 33228.8 1.39214 0.696070 0.717974i \(-0.254930\pi\)
0.696070 + 0.717974i \(0.254930\pi\)
\(830\) 6625.97 0.277097
\(831\) 933.196 0.0389557
\(832\) 250.229 0.0104268
\(833\) 15076.5 0.627096
\(834\) −10334.7 −0.429092
\(835\) 39195.0 1.62443
\(836\) 0 0
\(837\) 1633.59 0.0674615
\(838\) −20865.8 −0.860139
\(839\) 35600.4 1.46491 0.732456 0.680814i \(-0.238374\pi\)
0.732456 + 0.680814i \(0.238374\pi\)
\(840\) 195.502 0.00803029
\(841\) 1580.62 0.0648087
\(842\) 9183.16 0.375858
\(843\) −22040.2 −0.900482
\(844\) 6517.41 0.265804
\(845\) 26377.3 1.07385
\(846\) 2614.63 0.106256
\(847\) 725.494 0.0294312
\(848\) −12067.0 −0.488658
\(849\) 12140.8 0.490780
\(850\) −1863.71 −0.0752056
\(851\) −955.659 −0.0384954
\(852\) 533.020 0.0214331
\(853\) −8614.63 −0.345791 −0.172895 0.984940i \(-0.555312\pi\)
−0.172895 + 0.984940i \(0.555312\pi\)
\(854\) 43.8060 0.00175528
\(855\) 0 0
\(856\) 6268.52 0.250296
\(857\) −26698.4 −1.06418 −0.532088 0.846689i \(-0.678593\pi\)
−0.532088 + 0.846689i \(0.678593\pi\)
\(858\) 374.036 0.0148827
\(859\) 45356.8 1.80158 0.900788 0.434260i \(-0.142990\pi\)
0.900788 + 0.434260i \(0.142990\pi\)
\(860\) 333.921 0.0132402
\(861\) −504.013 −0.0199497
\(862\) 28234.3 1.11562
\(863\) −20943.6 −0.826104 −0.413052 0.910707i \(-0.635537\pi\)
−0.413052 + 0.910707i \(0.635537\pi\)
\(864\) 864.000 0.0340207
\(865\) 29757.4 1.16969
\(866\) −27858.0 −1.09313
\(867\) −8927.53 −0.349706
\(868\) −163.060 −0.00637628
\(869\) 12428.7 0.485172
\(870\) 11690.1 0.455552
\(871\) 303.897 0.0118222
\(872\) −16105.3 −0.625453
\(873\) −7493.40 −0.290508
\(874\) 0 0
\(875\) −845.771 −0.0326769
\(876\) 3368.81 0.129933
\(877\) −9561.82 −0.368164 −0.184082 0.982911i \(-0.558931\pi\)
−0.184082 + 0.982911i \(0.558931\pi\)
\(878\) 10444.1 0.401447
\(879\) −10924.7 −0.419204
\(880\) −3084.30 −0.118150
\(881\) 41424.3 1.58413 0.792065 0.610436i \(-0.209006\pi\)
0.792065 + 0.610436i \(0.209006\pi\)
\(882\) −6165.83 −0.235390
\(883\) 37078.3 1.41312 0.706559 0.707654i \(-0.250246\pi\)
0.706559 + 0.707654i \(0.250246\pi\)
\(884\) −688.336 −0.0261892
\(885\) 25536.1 0.969929
\(886\) −20326.8 −0.770760
\(887\) 6509.98 0.246430 0.123215 0.992380i \(-0.460679\pi\)
0.123215 + 0.992380i \(0.460679\pi\)
\(888\) 2517.25 0.0951277
\(889\) 628.311 0.0237040
\(890\) 24323.2 0.916085
\(891\) 1291.49 0.0485594
\(892\) −1925.97 −0.0722939
\(893\) 0 0
\(894\) −16128.3 −0.603369
\(895\) 35838.4 1.33849
\(896\) −86.2415 −0.00321554
\(897\) −106.873 −0.00397812
\(898\) 35703.2 1.32676
\(899\) −9750.19 −0.361721
\(900\) 762.200 0.0282296
\(901\) 33194.2 1.22737
\(902\) 7951.49 0.293521
\(903\) 13.9566 0.000514337 0
\(904\) −85.2045 −0.00313480
\(905\) −53241.1 −1.95557
\(906\) 14848.5 0.544489
\(907\) 52647.2 1.92737 0.963683 0.267048i \(-0.0860482\pi\)
0.963683 + 0.267048i \(0.0860482\pi\)
\(908\) 11146.4 0.407384
\(909\) 8193.34 0.298962
\(910\) 63.6982 0.00232041
\(911\) 16500.2 0.600084 0.300042 0.953926i \(-0.402999\pi\)
0.300042 + 0.953926i \(0.402999\pi\)
\(912\) 0 0
\(913\) −4369.10 −0.158375
\(914\) −10075.9 −0.364640
\(915\) 1179.10 0.0426009
\(916\) 5750.88 0.207439
\(917\) −140.678 −0.00506608
\(918\) −2376.71 −0.0854500
\(919\) 8761.75 0.314498 0.157249 0.987559i \(-0.449738\pi\)
0.157249 + 0.987559i \(0.449738\pi\)
\(920\) 881.272 0.0315812
\(921\) 14056.3 0.502898
\(922\) −22362.8 −0.798783
\(923\) 173.668 0.00619323
\(924\) −128.912 −0.00458970
\(925\) 2220.66 0.0789348
\(926\) 36910.2 1.30988
\(927\) −11449.4 −0.405662
\(928\) −5156.83 −0.182415
\(929\) −27264.8 −0.962893 −0.481446 0.876476i \(-0.659888\pi\)
−0.481446 + 0.876476i \(0.659888\pi\)
\(930\) −4388.98 −0.154753
\(931\) 0 0
\(932\) −11131.0 −0.391209
\(933\) −7240.66 −0.254071
\(934\) 12825.6 0.449321
\(935\) 8484.37 0.296758
\(936\) 281.508 0.00983052
\(937\) 23381.2 0.815186 0.407593 0.913164i \(-0.366368\pi\)
0.407593 + 0.913164i \(0.366368\pi\)
\(938\) −104.738 −0.00364587
\(939\) −15186.7 −0.527795
\(940\) −7024.74 −0.243747
\(941\) −39198.4 −1.35795 −0.678975 0.734161i \(-0.737576\pi\)
−0.678975 + 0.734161i \(0.737576\pi\)
\(942\) −7258.88 −0.251069
\(943\) −2271.96 −0.0784574
\(944\) −11264.7 −0.388386
\(945\) 219.939 0.00757103
\(946\) −220.184 −0.00756745
\(947\) 18505.7 0.635010 0.317505 0.948257i \(-0.397155\pi\)
0.317505 + 0.948257i \(0.397155\pi\)
\(948\) 9354.10 0.320472
\(949\) 1097.62 0.0375452
\(950\) 0 0
\(951\) 17112.1 0.583488
\(952\) 237.235 0.00807651
\(953\) −14696.2 −0.499535 −0.249768 0.968306i \(-0.580354\pi\)
−0.249768 + 0.968306i \(0.580354\pi\)
\(954\) −13575.4 −0.460712
\(955\) 26211.1 0.888137
\(956\) 18122.2 0.613091
\(957\) −7708.30 −0.260370
\(958\) −17039.3 −0.574651
\(959\) 248.130 0.00835509
\(960\) −2321.31 −0.0780417
\(961\) −26130.3 −0.877122
\(962\) 820.168 0.0274878
\(963\) 7052.08 0.235982
\(964\) −9829.09 −0.328396
\(965\) 37752.2 1.25936
\(966\) 36.8337 0.00122682
\(967\) −53986.4 −1.79533 −0.897666 0.440676i \(-0.854739\pi\)
−0.897666 + 0.440676i \(0.854739\pi\)
\(968\) −8614.24 −0.286025
\(969\) 0 0
\(970\) 20132.5 0.666409
\(971\) −29949.9 −0.989845 −0.494922 0.868937i \(-0.664804\pi\)
−0.494922 + 0.868937i \(0.664804\pi\)
\(972\) 972.000 0.0320750
\(973\) 1160.53 0.0382371
\(974\) 25493.7 0.838675
\(975\) 248.339 0.00815715
\(976\) −520.136 −0.0170586
\(977\) −10119.4 −0.331371 −0.165685 0.986179i \(-0.552984\pi\)
−0.165685 + 0.986179i \(0.552984\pi\)
\(978\) 16470.2 0.538505
\(979\) −16038.5 −0.523587
\(980\) 16565.8 0.539973
\(981\) −18118.5 −0.589683
\(982\) −10374.2 −0.337122
\(983\) 21988.0 0.713438 0.356719 0.934212i \(-0.383895\pi\)
0.356719 + 0.934212i \(0.383895\pi\)
\(984\) 5984.46 0.193880
\(985\) −2447.40 −0.0791683
\(986\) 14185.5 0.458173
\(987\) −293.607 −0.00946870
\(988\) 0 0
\(989\) 62.9128 0.00202276
\(990\) −3469.84 −0.111393
\(991\) 2492.80 0.0799056 0.0399528 0.999202i \(-0.487279\pi\)
0.0399528 + 0.999202i \(0.487279\pi\)
\(992\) 1936.11 0.0619673
\(993\) 25102.7 0.802224
\(994\) −59.8548 −0.00190994
\(995\) 19939.7 0.635306
\(996\) −3288.28 −0.104612
\(997\) 45403.2 1.44226 0.721130 0.692799i \(-0.243623\pi\)
0.721130 + 0.692799i \(0.243623\pi\)
\(998\) −21408.9 −0.679045
\(999\) 2831.91 0.0896873
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.p.1.1 yes 2
19.18 odd 2 2166.4.a.j.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2166.4.a.j.1.1 2 19.18 odd 2
2166.4.a.p.1.1 yes 2 1.1 even 1 trivial