Properties

Label 2166.4.a.j.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 $1$

Related objects

Downloads

Learn more

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 \(-0.513280\pi\)
−0.0417074 + 0.999130i \(0.513280\pi\)
\(14\) 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 \(-0.327440\pi\)
0.515948 + 0.856620i \(0.327440\pi\)
\(30\) −72.5410 −0.441471
\(31\) −60.5035 −0.350540 −0.175270 0.984520i \(-0.556080\pi\)
−0.175270 + 0.984520i \(0.556080\pi\)
\(32\) −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 \(-0.574859\pi\)
−0.233014 + 0.972473i \(0.574859\pi\)
\(38\) 0 0
\(39\) 11.7295 0.0481595
\(40\) 96.7214 0.382325
\(41\) −249.353 −0.949813 −0.474906 0.880036i \(-0.657518\pi\)
−0.474906 + 0.880036i \(0.657518\pi\)
\(42\) −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 \(-0.0679267\pi\)
0.977317 + 0.211782i \(0.0679267\pi\)
\(54\) 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 \(-0.216856\pi\)
0.776771 + 0.629783i \(0.216856\pi\)
\(60\) 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 \(-0.522576\pi\)
−0.0708641 + 0.997486i \(0.522576\pi\)
\(68\) −176.053 −0.313963
\(69\) 27.3344 0.0476909
\(70\) −16.2918 −0.0278177
\(71\) −44.4183 −0.0742463 −0.0371231 0.999311i \(-0.511819\pi\)
−0.0371231 + 0.999311i \(0.511819\pi\)
\(72\) −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 \(-0.687310\pi\)
−0.555073 + 0.831802i \(0.687310\pi\)
\(80\) −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 \(-0.295556\pi\)
0.599023 + 0.800732i \(0.295556\pi\)
\(90\) 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 \(-0.356479\pi\)
0.435761 + 0.900062i \(0.356479\pi\)
\(98\) 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 \(-0.291774\pi\)
0.608493 + 0.793559i \(0.291774\pi\)
\(104\) 31.2786 0.0294916
\(105\) −24.4377 −0.0227131
\(106\) −1508.37 −1.38213
\(107\) −783.565 −0.707945 −0.353972 0.935256i \(-0.615169\pi\)
−0.353972 + 0.935256i \(0.615169\pi\)
\(108\) −108.000 −0.0962250
\(109\) 2013.17 1.76905 0.884524 0.466494i \(-0.154483\pi\)
0.884524 + 0.466494i \(0.154483\pi\)
\(110\) 385.538 0.334178
\(111\) 314.656 0.269062
\(112\) −10.7802 −0.00909493
\(113\) 10.6506 0.00886655 0.00443327 0.999990i \(-0.498589\pi\)
0.00443327 + 0.999990i \(0.498589\pi\)
\(114\) 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 \(-0.394371\pi\)
0.325786 + 0.945444i \(0.394371\pi\)
\(128\) −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 \(-0.732362\pi\)
−0.666860 + 0.745183i \(0.732362\pi\)
\(152\) 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 \(-0.229527\pi\)
0.751092 + 0.660197i \(0.229527\pi\)
\(168\) −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 \(-0.318109\pi\)
0.540832 + 0.841130i \(0.318109\pi\)
\(174\) 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 \(-0.287587\pi\)
0.618880 + 0.785485i \(0.287587\pi\)
\(180\) −435.246 −0.180230
\(181\) −4403.67 −1.80841 −0.904204 0.427100i \(-0.859535\pi\)
−0.904204 + 0.427100i \(0.859535\pi\)
\(182\) −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 \(-0.302155\pi\)
0.582296 + 0.812977i \(0.302155\pi\)
\(194\) −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 \(-0.585637\pi\)
−0.265804 + 0.964027i \(0.585637\pi\)
\(212\) 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 \(-0.476968\pi\)
0.0722939 + 0.997383i \(0.476968\pi\)
\(224\) 21.5604 0.00643109
\(225\) 190.550 0.0564592
\(226\) −21.3011 −0.00626960
\(227\) −2786.59 −0.814768 −0.407384 0.913257i \(-0.633559\pi\)
−0.407384 + 0.913257i \(0.633559\pi\)
\(228\) 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 \(-0.393492\pi\)
0.328396 + 0.944540i \(0.393492\pi\)
\(242\) 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 \(-0.564989\pi\)
−0.202752 + 0.979230i \(0.564989\pi\)
\(258\) −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 \(-0.537040\pi\)
−0.116104 + 0.993237i \(0.537040\pi\)
\(270\) −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 \(-0.215300\pi\)
0.779840 + 0.625979i \(0.215300\pi\)
\(282\) 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 \(-0.381738\pi\)
0.363041 + 0.931773i \(0.381738\pi\)
\(294\) −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 \(-0.643436\pi\)
−0.435523 + 0.900178i \(0.643436\pi\)
\(308\) −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 \(-0.668624\pi\)
−0.505316 + 0.862935i \(0.668624\pi\)
\(318\) 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 \(-0.744484\pi\)
−0.694747 + 0.719254i \(0.744484\pi\)
\(332\) −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 \(-0.506777\pi\)
−0.0212894 + 0.999773i \(0.506777\pi\)
\(338\) 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 \(-0.672710\pi\)
−0.516350 + 0.856378i \(0.672710\pi\)
\(374\) 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 \(-0.831708\pi\)
−0.863461 + 0.504415i \(0.831708\pi\)
\(380\) 0 0
\(381\) −2797.62 −0.376185
\(382\) 4335.93 0.580748
\(383\) −10550.9 −1.40764 −0.703822 0.710376i \(-0.748525\pi\)
−0.703822 + 0.710376i \(0.748525\pi\)
\(384\) 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 \(-0.550398\pi\)
−0.157671 + 0.987492i \(0.550398\pi\)
\(402\) −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 \(-0.661679\pi\)
−0.486370 + 0.873753i \(0.661679\pi\)
\(410\) −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 \(-0.585627\pi\)
−0.265772 + 0.964036i \(0.585627\pi\)
\(422\) 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 \(-0.789329\pi\)
−0.788861 + 0.614571i \(0.789329\pi\)
\(432\) −432.000 −0.0481125
\(433\) 13929.0 1.54592 0.772962 0.634452i \(-0.218774\pi\)
0.772962 + 0.634452i \(0.218774\pi\)
\(434\) −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 \(-0.591617\pi\)
−0.283866 + 0.958864i \(0.591617\pi\)
\(440\) 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 \(-0.887472\pi\)
−0.938161 + 0.346199i \(0.887472\pi\)
\(450\) −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 \(-0.702070\pi\)
−0.593033 + 0.805178i \(0.702070\pi\)
\(488\) 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 \(-0.409709\pi\)
0.279869 + 0.960038i \(0.409709\pi\)
\(510\) 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 \(-0.469220\pi\)
0.0965464 + 0.995328i \(0.469220\pi\)
\(522\) −2900.72 −0.243220
\(523\) 672.621 0.0562364 0.0281182 0.999605i \(-0.491049\pi\)
0.0281182 + 0.999605i \(0.491049\pi\)
\(524\) 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 \(-0.577254\pi\)
−0.240326 + 0.970692i \(0.577254\pi\)
\(548\) −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 \(-0.538009\pi\)
−0.119126 + 0.992879i \(0.538009\pi\)
\(564\) −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 \(-0.224309\pi\)
0.761814 + 0.647796i \(0.224309\pi\)
\(570\) 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 \(-0.541068\pi\)
−0.128662 + 0.991688i \(0.541068\pi\)
\(600\) 508.133 0.0345741
\(601\) −12419.2 −0.842910 −0.421455 0.906849i \(-0.638480\pi\)
−0.421455 + 0.906849i \(0.638480\pi\)
\(602\) −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 \(-0.458010\pi\)
0.131534 + 0.991312i \(0.458010\pi\)
\(608\) 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 \(-0.422256\pi\)
0.241819 + 0.970321i \(0.422256\pi\)
\(642\) −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 \(-0.557344\pi\)
−0.179179 + 0.983816i \(0.557344\pi\)
\(660\) 2313.23 0.136428
\(661\) 5076.16 0.298698 0.149349 0.988785i \(-0.452282\pi\)
0.149349 + 0.988785i \(0.452282\pi\)
\(662\) 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 \(-0.645456\pi\)
−0.441225 + 0.897397i \(0.645456\pi\)
\(674\) 526.826 0.0301077
\(675\) −571.650 −0.0325967
\(676\) −8726.85 −0.496521
\(677\) 7518.29 0.426811 0.213406 0.976964i \(-0.431544\pi\)
0.213406 + 0.976964i \(0.431544\pi\)
\(678\) 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 \(-0.323851\pi\)
0.525574 + 0.850748i \(0.323851\pi\)
\(684\) 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 \(-0.617850\pi\)
−0.361835 + 0.932242i \(0.617850\pi\)
\(744\) −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 \(-0.375369\pi\)
0.381612 + 0.924323i \(0.375369\pi\)
\(752\) 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 \(-0.796246\pi\)
−0.802028 + 0.597286i \(0.796246\pi\)
\(774\) 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 \(-0.738741\pi\)
−0.681658 + 0.731671i \(0.738741\pi\)
\(788\) 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 \(-0.519198\pi\)
−0.0602752 + 0.998182i \(0.519198\pi\)
\(798\) 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 \(-0.279461\pi\)
0.638728 + 0.769432i \(0.279461\pi\)
\(812\) −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 \(-0.139205\pi\)
0.905887 + 0.423519i \(0.139205\pi\)
\(828\) −328.012 −0.0137672
\(829\) −33228.8 −1.39214 −0.696070 0.717974i \(-0.745070\pi\)
−0.696070 + 0.717974i \(0.745070\pi\)
\(830\) −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 \(-0.761626\pi\)
−0.732456 + 0.680814i \(0.761626\pi\)
\(840\) 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 \(-0.321407\pi\)
0.532088 + 0.846689i \(0.321407\pi\)
\(858\) −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 \(-0.364463\pi\)
0.413052 + 0.910707i \(0.364463\pi\)
\(864\) 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 \(-0.441069\pi\)
0.184082 + 0.982911i \(0.441069\pi\)
\(878\) 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 \(-0.539321\pi\)
−0.123215 + 0.992380i \(0.539321\pi\)
\(888\) −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 \(-0.913952\pi\)
−0.963683 + 0.267048i \(0.913952\pi\)
\(908\) −11146.4 −0.407384
\(909\) 8193.34 0.298962
\(910\) 63.6982 0.00232041
\(911\) −16500.2 −0.600084 −0.300042 0.953926i \(-0.597001\pi\)
−0.300042 + 0.953926i \(0.597001\pi\)
\(912\) 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 \(-0.262424\pi\)
0.678975 + 0.734161i \(0.262424\pi\)
\(942\) −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 \(-0.419646\pi\)
0.249768 + 0.968306i \(0.419646\pi\)
\(954\) −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 \(-0.335196\pi\)
0.494922 + 0.868937i \(0.335196\pi\)
\(972\) −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 \(-0.447016\pi\)
0.165685 + 0.986179i \(0.447016\pi\)
\(978\) 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 \(-0.616105\pi\)
−0.356719 + 0.934212i \(0.616105\pi\)
\(984\) −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 \(-0.512721\pi\)
−0.0399528 + 0.999202i \(0.512721\pi\)
\(992\) 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.j.1.1 2
19.18 odd 2 2166.4.a.p.1.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2166.4.a.j.1.1 2 1.1 even 1 trivial
2166.4.a.p.1.1 yes 2 19.18 odd 2