Properties

Label 507.4.a.o.1.8
Level $507$
Weight $4$
Character 507.1
Self dual yes
Analytic conductor $29.914$
Analytic rank $1$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 507.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.9139683729\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 13^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(2.37150\) of defining polynomial
Character \(\chi\) \(=\) 507.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.17344 q^{2} +3.00000 q^{3} +2.07074 q^{4} -6.74147 q^{5} +9.52033 q^{6} +14.1726 q^{7} -18.8162 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+3.17344 q^{2} +3.00000 q^{3} +2.07074 q^{4} -6.74147 q^{5} +9.52033 q^{6} +14.1726 q^{7} -18.8162 q^{8} +9.00000 q^{9} -21.3937 q^{10} -62.4956 q^{11} +6.21221 q^{12} +44.9761 q^{14} -20.2244 q^{15} -76.2779 q^{16} -58.6172 q^{17} +28.5610 q^{18} -64.1652 q^{19} -13.9598 q^{20} +42.5179 q^{21} -198.326 q^{22} +10.9221 q^{23} -56.4485 q^{24} -79.5526 q^{25} +27.0000 q^{27} +29.3478 q^{28} +216.316 q^{29} -64.1810 q^{30} +38.6271 q^{31} -91.5342 q^{32} -187.487 q^{33} -186.018 q^{34} -95.5445 q^{35} +18.6366 q^{36} -423.770 q^{37} -203.625 q^{38} +126.849 q^{40} +366.126 q^{41} +134.928 q^{42} -128.297 q^{43} -129.412 q^{44} -60.6732 q^{45} +34.6605 q^{46} +93.1169 q^{47} -228.834 q^{48} -142.136 q^{49} -252.455 q^{50} -175.852 q^{51} +131.909 q^{53} +85.6829 q^{54} +421.313 q^{55} -266.675 q^{56} -192.496 q^{57} +686.467 q^{58} -386.729 q^{59} -41.8794 q^{60} -621.077 q^{61} +122.581 q^{62} +127.554 q^{63} +319.745 q^{64} -594.979 q^{66} -865.273 q^{67} -121.381 q^{68} +32.7662 q^{69} -303.205 q^{70} +607.506 q^{71} -169.346 q^{72} -980.958 q^{73} -1344.81 q^{74} -238.658 q^{75} -132.869 q^{76} -885.728 q^{77} +1331.91 q^{79} +514.226 q^{80} +81.0000 q^{81} +1161.88 q^{82} -907.633 q^{83} +88.0434 q^{84} +395.166 q^{85} -407.142 q^{86} +648.949 q^{87} +1175.93 q^{88} +1033.67 q^{89} -192.543 q^{90} +22.6167 q^{92} +115.881 q^{93} +295.501 q^{94} +432.568 q^{95} -274.603 q^{96} -1046.17 q^{97} -451.061 q^{98} -562.461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 6 q^{2} + 27 q^{3} + 44 q^{4} - 33 q^{5} - 18 q^{6} - 83 q^{7} - 87 q^{8} + 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - 6 q^{2} + 27 q^{3} + 44 q^{4} - 33 q^{5} - 18 q^{6} - 83 q^{7} - 87 q^{8} + 81 q^{9} - 54 q^{10} - 85 q^{11} + 132 q^{12} + 158 q^{14} - 99 q^{15} + 216 q^{16} + 178 q^{17} - 54 q^{18} - 352 q^{19} - 402 q^{20} - 249 q^{21} - 630 q^{22} + 150 q^{23} - 261 q^{24} - 20 q^{25} + 243 q^{27} - 940 q^{28} - 97 q^{29} - 162 q^{30} - 717 q^{31} - 707 q^{32} - 255 q^{33} - 632 q^{34} - 418 q^{35} + 396 q^{36} - 1108 q^{37} - 660 q^{38} - 1506 q^{40} - 334 q^{41} + 474 q^{42} + 242 q^{43} + 307 q^{44} - 297 q^{45} - 979 q^{46} + 184 q^{47} + 648 q^{48} - 38 q^{49} + 2031 q^{50} + 534 q^{51} - 151 q^{53} - 162 q^{54} + 2064 q^{55} + 2276 q^{56} - 1056 q^{57} - 1161 q^{58} - 537 q^{59} - 1206 q^{60} - 1340 q^{61} + 347 q^{62} - 747 q^{63} + 893 q^{64} - 1890 q^{66} - 2308 q^{67} + 2785 q^{68} + 450 q^{69} + 1420 q^{70} - 96 q^{71} - 783 q^{72} - 2505 q^{73} - 1191 q^{74} - 60 q^{75} - 2409 q^{76} - 2142 q^{77} - 1591 q^{79} + 2671 q^{80} + 729 q^{81} + 1517 q^{82} - 1539 q^{83} - 2820 q^{84} - 4296 q^{85} + 3763 q^{86} - 291 q^{87} - 3716 q^{88} + 592 q^{89} - 486 q^{90} + 515 q^{92} - 2151 q^{93} - 692 q^{94} + 4158 q^{95} - 2121 q^{96} - 1445 q^{97} - 1457 q^{98} - 765 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.17344 1.12198 0.560991 0.827822i \(-0.310420\pi\)
0.560991 + 0.827822i \(0.310420\pi\)
\(3\) 3.00000 0.577350
\(4\) 2.07074 0.258842
\(5\) −6.74147 −0.602975 −0.301488 0.953470i \(-0.597483\pi\)
−0.301488 + 0.953470i \(0.597483\pi\)
\(6\) 9.52033 0.647776
\(7\) 14.1726 0.765251 0.382625 0.923904i \(-0.375020\pi\)
0.382625 + 0.923904i \(0.375020\pi\)
\(8\) −18.8162 −0.831565
\(9\) 9.00000 0.333333
\(10\) −21.3937 −0.676527
\(11\) −62.4956 −1.71301 −0.856507 0.516136i \(-0.827370\pi\)
−0.856507 + 0.516136i \(0.827370\pi\)
\(12\) 6.21221 0.149442
\(13\) 0 0
\(14\) 44.9761 0.858597
\(15\) −20.2244 −0.348128
\(16\) −76.2779 −1.19184
\(17\) −58.6172 −0.836280 −0.418140 0.908383i \(-0.637318\pi\)
−0.418140 + 0.908383i \(0.637318\pi\)
\(18\) 28.5610 0.373994
\(19\) −64.1652 −0.774764 −0.387382 0.921919i \(-0.626620\pi\)
−0.387382 + 0.921919i \(0.626620\pi\)
\(20\) −13.9598 −0.156075
\(21\) 42.5179 0.441818
\(22\) −198.326 −1.92197
\(23\) 10.9221 0.0990177 0.0495088 0.998774i \(-0.484234\pi\)
0.0495088 + 0.998774i \(0.484234\pi\)
\(24\) −56.4485 −0.480105
\(25\) −79.5526 −0.636421
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 29.3478 0.198079
\(29\) 216.316 1.38514 0.692568 0.721353i \(-0.256479\pi\)
0.692568 + 0.721353i \(0.256479\pi\)
\(30\) −64.1810 −0.390593
\(31\) 38.6271 0.223795 0.111897 0.993720i \(-0.464307\pi\)
0.111897 + 0.993720i \(0.464307\pi\)
\(32\) −91.5342 −0.505660
\(33\) −187.487 −0.989009
\(34\) −186.018 −0.938290
\(35\) −95.5445 −0.461427
\(36\) 18.6366 0.0862807
\(37\) −423.770 −1.88290 −0.941452 0.337147i \(-0.890538\pi\)
−0.941452 + 0.337147i \(0.890538\pi\)
\(38\) −203.625 −0.869270
\(39\) 0 0
\(40\) 126.849 0.501414
\(41\) 366.126 1.39461 0.697307 0.716772i \(-0.254381\pi\)
0.697307 + 0.716772i \(0.254381\pi\)
\(42\) 134.928 0.495711
\(43\) −128.297 −0.455001 −0.227501 0.973778i \(-0.573055\pi\)
−0.227501 + 0.973778i \(0.573055\pi\)
\(44\) −129.412 −0.443400
\(45\) −60.6732 −0.200992
\(46\) 34.6605 0.111096
\(47\) 93.1169 0.288989 0.144495 0.989506i \(-0.453844\pi\)
0.144495 + 0.989506i \(0.453844\pi\)
\(48\) −228.834 −0.688111
\(49\) −142.136 −0.414391
\(50\) −252.455 −0.714052
\(51\) −175.852 −0.482826
\(52\) 0 0
\(53\) 131.909 0.341869 0.170934 0.985282i \(-0.445321\pi\)
0.170934 + 0.985282i \(0.445321\pi\)
\(54\) 85.6829 0.215925
\(55\) 421.313 1.03290
\(56\) −266.675 −0.636356
\(57\) −192.496 −0.447310
\(58\) 686.467 1.55410
\(59\) −386.729 −0.853353 −0.426677 0.904404i \(-0.640316\pi\)
−0.426677 + 0.904404i \(0.640316\pi\)
\(60\) −41.8794 −0.0901102
\(61\) −621.077 −1.30362 −0.651810 0.758382i \(-0.725990\pi\)
−0.651810 + 0.758382i \(0.725990\pi\)
\(62\) 122.581 0.251094
\(63\) 127.554 0.255084
\(64\) 319.745 0.624502
\(65\) 0 0
\(66\) −594.979 −1.10965
\(67\) −865.273 −1.57776 −0.788880 0.614547i \(-0.789339\pi\)
−0.788880 + 0.614547i \(0.789339\pi\)
\(68\) −121.381 −0.216464
\(69\) 32.7662 0.0571679
\(70\) −303.205 −0.517713
\(71\) 607.506 1.01546 0.507730 0.861516i \(-0.330485\pi\)
0.507730 + 0.861516i \(0.330485\pi\)
\(72\) −169.346 −0.277188
\(73\) −980.958 −1.57277 −0.786387 0.617735i \(-0.788051\pi\)
−0.786387 + 0.617735i \(0.788051\pi\)
\(74\) −1344.81 −2.11258
\(75\) −238.658 −0.367438
\(76\) −132.869 −0.200541
\(77\) −885.728 −1.31088
\(78\) 0 0
\(79\) 1331.91 1.89685 0.948425 0.317003i \(-0.102676\pi\)
0.948425 + 0.317003i \(0.102676\pi\)
\(80\) 514.226 0.718652
\(81\) 81.0000 0.111111
\(82\) 1161.88 1.56473
\(83\) −907.633 −1.20031 −0.600155 0.799884i \(-0.704894\pi\)
−0.600155 + 0.799884i \(0.704894\pi\)
\(84\) 88.0434 0.114361
\(85\) 395.166 0.504256
\(86\) −407.142 −0.510503
\(87\) 648.949 0.799708
\(88\) 1175.93 1.42448
\(89\) 1033.67 1.23110 0.615552 0.788096i \(-0.288933\pi\)
0.615552 + 0.788096i \(0.288933\pi\)
\(90\) −192.543 −0.225509
\(91\) 0 0
\(92\) 22.6167 0.0256299
\(93\) 115.881 0.129208
\(94\) 295.501 0.324240
\(95\) 432.568 0.467163
\(96\) −274.603 −0.291943
\(97\) −1046.17 −1.09508 −0.547538 0.836781i \(-0.684435\pi\)
−0.547538 + 0.836781i \(0.684435\pi\)
\(98\) −451.061 −0.464939
\(99\) −562.461 −0.571004
\(100\) −164.732 −0.164732
\(101\) 1416.64 1.39566 0.697828 0.716265i \(-0.254150\pi\)
0.697828 + 0.716265i \(0.254150\pi\)
\(102\) −558.055 −0.541722
\(103\) 387.629 0.370818 0.185409 0.982661i \(-0.440639\pi\)
0.185409 + 0.982661i \(0.440639\pi\)
\(104\) 0 0
\(105\) −286.633 −0.266405
\(106\) 418.605 0.383570
\(107\) 86.4526 0.0781092 0.0390546 0.999237i \(-0.487565\pi\)
0.0390546 + 0.999237i \(0.487565\pi\)
\(108\) 55.9099 0.0498142
\(109\) 940.072 0.826079 0.413039 0.910713i \(-0.364467\pi\)
0.413039 + 0.910713i \(0.364467\pi\)
\(110\) 1337.01 1.15890
\(111\) −1271.31 −1.08709
\(112\) −1081.06 −0.912059
\(113\) 960.499 0.799612 0.399806 0.916600i \(-0.369078\pi\)
0.399806 + 0.916600i \(0.369078\pi\)
\(114\) −610.874 −0.501873
\(115\) −73.6307 −0.0597052
\(116\) 447.934 0.358531
\(117\) 0 0
\(118\) −1227.26 −0.957447
\(119\) −830.760 −0.639964
\(120\) 380.546 0.289491
\(121\) 2574.71 1.93441
\(122\) −1970.95 −1.46264
\(123\) 1098.38 0.805181
\(124\) 79.9866 0.0579275
\(125\) 1378.99 0.986721
\(126\) 404.785 0.286199
\(127\) 2022.18 1.41291 0.706456 0.707757i \(-0.250293\pi\)
0.706456 + 0.707757i \(0.250293\pi\)
\(128\) 1746.97 1.20634
\(129\) −384.890 −0.262695
\(130\) 0 0
\(131\) 1857.90 1.23912 0.619561 0.784948i \(-0.287310\pi\)
0.619561 + 0.784948i \(0.287310\pi\)
\(132\) −388.236 −0.255997
\(133\) −909.390 −0.592888
\(134\) −2745.90 −1.77022
\(135\) −182.020 −0.116043
\(136\) 1102.95 0.695421
\(137\) −1894.12 −1.18121 −0.590604 0.806961i \(-0.701110\pi\)
−0.590604 + 0.806961i \(0.701110\pi\)
\(138\) 103.982 0.0641413
\(139\) −1226.08 −0.748165 −0.374082 0.927395i \(-0.622042\pi\)
−0.374082 + 0.927395i \(0.622042\pi\)
\(140\) −197.847 −0.119437
\(141\) 279.351 0.166848
\(142\) 1927.89 1.13933
\(143\) 0 0
\(144\) −686.501 −0.397281
\(145\) −1458.29 −0.835203
\(146\) −3113.01 −1.76462
\(147\) −426.409 −0.239249
\(148\) −877.517 −0.487375
\(149\) −3195.65 −1.75703 −0.878517 0.477711i \(-0.841467\pi\)
−0.878517 + 0.477711i \(0.841467\pi\)
\(150\) −757.366 −0.412258
\(151\) −508.232 −0.273903 −0.136951 0.990578i \(-0.543730\pi\)
−0.136951 + 0.990578i \(0.543730\pi\)
\(152\) 1207.34 0.644267
\(153\) −527.555 −0.278760
\(154\) −2810.81 −1.47079
\(155\) −260.404 −0.134943
\(156\) 0 0
\(157\) −1243.08 −0.631900 −0.315950 0.948776i \(-0.602323\pi\)
−0.315950 + 0.948776i \(0.602323\pi\)
\(158\) 4226.73 2.12823
\(159\) 395.726 0.197378
\(160\) 617.075 0.304901
\(161\) 154.794 0.0757734
\(162\) 257.049 0.124665
\(163\) 33.9996 0.0163378 0.00816888 0.999967i \(-0.497400\pi\)
0.00816888 + 0.999967i \(0.497400\pi\)
\(164\) 758.149 0.360985
\(165\) 1263.94 0.596348
\(166\) −2880.32 −1.34673
\(167\) 2210.67 1.02435 0.512176 0.858880i \(-0.328839\pi\)
0.512176 + 0.858880i \(0.328839\pi\)
\(168\) −800.025 −0.367400
\(169\) 0 0
\(170\) 1254.04 0.565766
\(171\) −577.487 −0.258255
\(172\) −265.668 −0.117773
\(173\) −661.307 −0.290626 −0.145313 0.989386i \(-0.546419\pi\)
−0.145313 + 0.989386i \(0.546419\pi\)
\(174\) 2059.40 0.897258
\(175\) −1127.47 −0.487021
\(176\) 4767.04 2.04164
\(177\) −1160.19 −0.492684
\(178\) 3280.28 1.38128
\(179\) −2325.05 −0.970850 −0.485425 0.874278i \(-0.661335\pi\)
−0.485425 + 0.874278i \(0.661335\pi\)
\(180\) −125.638 −0.0520251
\(181\) 2122.20 0.871503 0.435752 0.900067i \(-0.356483\pi\)
0.435752 + 0.900067i \(0.356483\pi\)
\(182\) 0 0
\(183\) −1863.23 −0.752645
\(184\) −205.511 −0.0823397
\(185\) 2856.84 1.13534
\(186\) 367.743 0.144969
\(187\) 3663.32 1.43256
\(188\) 192.820 0.0748025
\(189\) 382.661 0.147273
\(190\) 1372.73 0.524149
\(191\) −2484.37 −0.941166 −0.470583 0.882356i \(-0.655956\pi\)
−0.470583 + 0.882356i \(0.655956\pi\)
\(192\) 959.235 0.360556
\(193\) 266.771 0.0994955 0.0497478 0.998762i \(-0.484158\pi\)
0.0497478 + 0.998762i \(0.484158\pi\)
\(194\) −3319.95 −1.22865
\(195\) 0 0
\(196\) −294.327 −0.107262
\(197\) 1231.03 0.445216 0.222608 0.974908i \(-0.428543\pi\)
0.222608 + 0.974908i \(0.428543\pi\)
\(198\) −1784.94 −0.640656
\(199\) −3246.14 −1.15635 −0.578173 0.815914i \(-0.696234\pi\)
−0.578173 + 0.815914i \(0.696234\pi\)
\(200\) 1496.88 0.529225
\(201\) −2595.82 −0.910921
\(202\) 4495.63 1.56590
\(203\) 3065.77 1.05998
\(204\) −364.142 −0.124976
\(205\) −2468.23 −0.840919
\(206\) 1230.12 0.416051
\(207\) 98.2985 0.0330059
\(208\) 0 0
\(209\) 4010.05 1.32718
\(210\) −909.614 −0.298902
\(211\) 330.708 0.107900 0.0539500 0.998544i \(-0.482819\pi\)
0.0539500 + 0.998544i \(0.482819\pi\)
\(212\) 273.148 0.0884900
\(213\) 1822.52 0.586277
\(214\) 274.352 0.0876371
\(215\) 864.908 0.274355
\(216\) −508.037 −0.160035
\(217\) 547.449 0.171259
\(218\) 2983.26 0.926845
\(219\) −2942.87 −0.908041
\(220\) 872.427 0.267359
\(221\) 0 0
\(222\) −4034.43 −1.21970
\(223\) −5785.86 −1.73744 −0.868722 0.495300i \(-0.835058\pi\)
−0.868722 + 0.495300i \(0.835058\pi\)
\(224\) −1297.28 −0.386957
\(225\) −715.973 −0.212140
\(226\) 3048.09 0.897149
\(227\) −2945.35 −0.861189 −0.430595 0.902545i \(-0.641696\pi\)
−0.430595 + 0.902545i \(0.641696\pi\)
\(228\) −398.608 −0.115783
\(229\) 3541.26 1.02189 0.510945 0.859613i \(-0.329296\pi\)
0.510945 + 0.859613i \(0.329296\pi\)
\(230\) −233.663 −0.0669882
\(231\) −2657.18 −0.756840
\(232\) −4070.25 −1.15183
\(233\) 2340.76 0.658148 0.329074 0.944304i \(-0.393263\pi\)
0.329074 + 0.944304i \(0.393263\pi\)
\(234\) 0 0
\(235\) −627.745 −0.174253
\(236\) −800.814 −0.220884
\(237\) 3995.72 1.09515
\(238\) −2636.37 −0.718027
\(239\) 1515.70 0.410218 0.205109 0.978739i \(-0.434245\pi\)
0.205109 + 0.978739i \(0.434245\pi\)
\(240\) 1542.68 0.414914
\(241\) −2392.47 −0.639472 −0.319736 0.947507i \(-0.603594\pi\)
−0.319736 + 0.947507i \(0.603594\pi\)
\(242\) 8170.68 2.17038
\(243\) 243.000 0.0641500
\(244\) −1286.09 −0.337432
\(245\) 958.207 0.249868
\(246\) 3485.64 0.903398
\(247\) 0 0
\(248\) −726.815 −0.186100
\(249\) −2722.90 −0.692999
\(250\) 4376.13 1.10708
\(251\) −2198.78 −0.552931 −0.276465 0.961024i \(-0.589163\pi\)
−0.276465 + 0.961024i \(0.589163\pi\)
\(252\) 264.130 0.0660263
\(253\) −682.581 −0.169619
\(254\) 6417.29 1.58526
\(255\) 1185.50 0.291132
\(256\) 2985.94 0.728988
\(257\) −6194.26 −1.50345 −0.751727 0.659475i \(-0.770779\pi\)
−0.751727 + 0.659475i \(0.770779\pi\)
\(258\) −1221.43 −0.294739
\(259\) −6005.95 −1.44089
\(260\) 0 0
\(261\) 1946.85 0.461712
\(262\) 5895.92 1.39027
\(263\) −4181.74 −0.980445 −0.490222 0.871597i \(-0.663084\pi\)
−0.490222 + 0.871597i \(0.663084\pi\)
\(264\) 3527.79 0.822425
\(265\) −889.258 −0.206139
\(266\) −2885.90 −0.665210
\(267\) 3101.00 0.710778
\(268\) −1791.75 −0.408391
\(269\) 2767.69 0.627320 0.313660 0.949535i \(-0.398445\pi\)
0.313660 + 0.949535i \(0.398445\pi\)
\(270\) −577.629 −0.130198
\(271\) 7191.36 1.61197 0.805986 0.591935i \(-0.201636\pi\)
0.805986 + 0.591935i \(0.201636\pi\)
\(272\) 4471.20 0.996714
\(273\) 0 0
\(274\) −6010.88 −1.32529
\(275\) 4971.69 1.09020
\(276\) 67.8501 0.0147974
\(277\) 1317.27 0.285729 0.142864 0.989742i \(-0.454369\pi\)
0.142864 + 0.989742i \(0.454369\pi\)
\(278\) −3890.90 −0.839427
\(279\) 347.644 0.0745983
\(280\) 1797.78 0.383707
\(281\) 3948.92 0.838338 0.419169 0.907908i \(-0.362321\pi\)
0.419169 + 0.907908i \(0.362321\pi\)
\(282\) 886.503 0.187200
\(283\) −4981.52 −1.04636 −0.523181 0.852221i \(-0.675255\pi\)
−0.523181 + 0.852221i \(0.675255\pi\)
\(284\) 1257.99 0.262844
\(285\) 1297.70 0.269717
\(286\) 0 0
\(287\) 5188.97 1.06723
\(288\) −823.808 −0.168553
\(289\) −1477.03 −0.300636
\(290\) −4627.80 −0.937082
\(291\) −3138.50 −0.632242
\(292\) −2031.31 −0.407100
\(293\) 3203.02 0.638644 0.319322 0.947646i \(-0.396545\pi\)
0.319322 + 0.947646i \(0.396545\pi\)
\(294\) −1353.18 −0.268433
\(295\) 2607.12 0.514551
\(296\) 7973.74 1.56576
\(297\) −1687.38 −0.329670
\(298\) −10141.2 −1.97136
\(299\) 0 0
\(300\) −494.197 −0.0951083
\(301\) −1818.30 −0.348190
\(302\) −1612.84 −0.307314
\(303\) 4249.93 0.805782
\(304\) 4894.39 0.923396
\(305\) 4186.97 0.786051
\(306\) −1674.16 −0.312763
\(307\) −4795.67 −0.891542 −0.445771 0.895147i \(-0.647070\pi\)
−0.445771 + 0.895147i \(0.647070\pi\)
\(308\) −1834.11 −0.339312
\(309\) 1162.89 0.214092
\(310\) −826.376 −0.151403
\(311\) 630.213 0.114907 0.0574535 0.998348i \(-0.481702\pi\)
0.0574535 + 0.998348i \(0.481702\pi\)
\(312\) 0 0
\(313\) −9314.73 −1.68211 −0.841054 0.540952i \(-0.818064\pi\)
−0.841054 + 0.540952i \(0.818064\pi\)
\(314\) −3944.83 −0.708980
\(315\) −859.900 −0.153809
\(316\) 2758.02 0.490984
\(317\) −576.333 −0.102114 −0.0510569 0.998696i \(-0.516259\pi\)
−0.0510569 + 0.998696i \(0.516259\pi\)
\(318\) 1255.81 0.221455
\(319\) −13518.8 −2.37275
\(320\) −2155.55 −0.376559
\(321\) 259.358 0.0450964
\(322\) 491.231 0.0850163
\(323\) 3761.18 0.647919
\(324\) 167.730 0.0287602
\(325\) 0 0
\(326\) 107.896 0.0183307
\(327\) 2820.22 0.476937
\(328\) −6889.08 −1.15971
\(329\) 1319.71 0.221149
\(330\) 4011.03 0.669091
\(331\) −1575.95 −0.261699 −0.130849 0.991402i \(-0.541770\pi\)
−0.130849 + 0.991402i \(0.541770\pi\)
\(332\) −1879.47 −0.310691
\(333\) −3813.93 −0.627635
\(334\) 7015.44 1.14930
\(335\) 5833.22 0.951351
\(336\) −3243.18 −0.526577
\(337\) 9289.32 1.50155 0.750774 0.660559i \(-0.229681\pi\)
0.750774 + 0.660559i \(0.229681\pi\)
\(338\) 0 0
\(339\) 2881.50 0.461656
\(340\) 818.284 0.130523
\(341\) −2414.03 −0.383363
\(342\) −1832.62 −0.289757
\(343\) −6875.66 −1.08236
\(344\) 2414.05 0.378363
\(345\) −220.892 −0.0344708
\(346\) −2098.62 −0.326077
\(347\) −7701.82 −1.19151 −0.595757 0.803164i \(-0.703148\pi\)
−0.595757 + 0.803164i \(0.703148\pi\)
\(348\) 1343.80 0.206998
\(349\) 4972.89 0.762730 0.381365 0.924425i \(-0.375454\pi\)
0.381365 + 0.924425i \(0.375454\pi\)
\(350\) −3577.96 −0.546429
\(351\) 0 0
\(352\) 5720.49 0.866202
\(353\) −1575.34 −0.237526 −0.118763 0.992923i \(-0.537893\pi\)
−0.118763 + 0.992923i \(0.537893\pi\)
\(354\) −3681.79 −0.552782
\(355\) −4095.49 −0.612298
\(356\) 2140.45 0.318661
\(357\) −2492.28 −0.369483
\(358\) −7378.41 −1.08928
\(359\) −7567.42 −1.11252 −0.556258 0.831010i \(-0.687763\pi\)
−0.556258 + 0.831010i \(0.687763\pi\)
\(360\) 1141.64 0.167138
\(361\) −2741.83 −0.399741
\(362\) 6734.69 0.977810
\(363\) 7724.12 1.11683
\(364\) 0 0
\(365\) 6613.10 0.948344
\(366\) −5912.86 −0.844454
\(367\) 4368.25 0.621310 0.310655 0.950523i \(-0.399452\pi\)
0.310655 + 0.950523i \(0.399452\pi\)
\(368\) −833.112 −0.118014
\(369\) 3295.13 0.464872
\(370\) 9066.01 1.27384
\(371\) 1869.49 0.261615
\(372\) 239.960 0.0334445
\(373\) −801.944 −0.111322 −0.0556610 0.998450i \(-0.517727\pi\)
−0.0556610 + 0.998450i \(0.517727\pi\)
\(374\) 11625.3 1.60730
\(375\) 4136.96 0.569684
\(376\) −1752.10 −0.240313
\(377\) 0 0
\(378\) 1214.35 0.165237
\(379\) −68.0819 −0.00922727 −0.00461363 0.999989i \(-0.501469\pi\)
−0.00461363 + 0.999989i \(0.501469\pi\)
\(380\) 895.734 0.120922
\(381\) 6066.55 0.815745
\(382\) −7884.01 −1.05597
\(383\) −1549.01 −0.206659 −0.103330 0.994647i \(-0.532950\pi\)
−0.103330 + 0.994647i \(0.532950\pi\)
\(384\) 5240.90 0.696480
\(385\) 5971.11 0.790431
\(386\) 846.584 0.111632
\(387\) −1154.67 −0.151667
\(388\) −2166.34 −0.283451
\(389\) 7300.51 0.951544 0.475772 0.879569i \(-0.342169\pi\)
0.475772 + 0.879569i \(0.342169\pi\)
\(390\) 0 0
\(391\) −640.220 −0.0828065
\(392\) 2674.46 0.344594
\(393\) 5573.69 0.715408
\(394\) 3906.61 0.499524
\(395\) −8979.00 −1.14375
\(396\) −1164.71 −0.147800
\(397\) −6096.27 −0.770688 −0.385344 0.922773i \(-0.625917\pi\)
−0.385344 + 0.922773i \(0.625917\pi\)
\(398\) −10301.4 −1.29740
\(399\) −2728.17 −0.342304
\(400\) 6068.11 0.758513
\(401\) −7592.37 −0.945498 −0.472749 0.881197i \(-0.656738\pi\)
−0.472749 + 0.881197i \(0.656738\pi\)
\(402\) −8237.69 −1.02204
\(403\) 0 0
\(404\) 2933.49 0.361254
\(405\) −546.059 −0.0669973
\(406\) 9729.05 1.18927
\(407\) 26483.8 3.22544
\(408\) 3308.85 0.401502
\(409\) 7233.86 0.874551 0.437275 0.899328i \(-0.355943\pi\)
0.437275 + 0.899328i \(0.355943\pi\)
\(410\) −7832.77 −0.943495
\(411\) −5682.36 −0.681971
\(412\) 802.678 0.0959832
\(413\) −5480.97 −0.653029
\(414\) 311.945 0.0370320
\(415\) 6118.78 0.723757
\(416\) 0 0
\(417\) −3678.25 −0.431953
\(418\) 12725.6 1.48907
\(419\) −5312.55 −0.619416 −0.309708 0.950832i \(-0.600231\pi\)
−0.309708 + 0.950832i \(0.600231\pi\)
\(420\) −593.542 −0.0689569
\(421\) −15028.1 −1.73973 −0.869865 0.493290i \(-0.835794\pi\)
−0.869865 + 0.493290i \(0.835794\pi\)
\(422\) 1049.48 0.121062
\(423\) 838.052 0.0963297
\(424\) −2482.02 −0.284286
\(425\) 4663.15 0.532226
\(426\) 5783.66 0.657791
\(427\) −8802.31 −0.997596
\(428\) 179.020 0.0202179
\(429\) 0 0
\(430\) 2744.73 0.307821
\(431\) 7154.66 0.799600 0.399800 0.916602i \(-0.369080\pi\)
0.399800 + 0.916602i \(0.369080\pi\)
\(432\) −2059.50 −0.229370
\(433\) −9542.58 −1.05909 −0.529546 0.848281i \(-0.677638\pi\)
−0.529546 + 0.848281i \(0.677638\pi\)
\(434\) 1737.30 0.192150
\(435\) −4374.87 −0.482204
\(436\) 1946.64 0.213824
\(437\) −700.816 −0.0767153
\(438\) −9339.04 −1.01881
\(439\) 7070.70 0.768715 0.384358 0.923184i \(-0.374423\pi\)
0.384358 + 0.923184i \(0.374423\pi\)
\(440\) −7927.49 −0.858928
\(441\) −1279.23 −0.138130
\(442\) 0 0
\(443\) 2092.58 0.224428 0.112214 0.993684i \(-0.464206\pi\)
0.112214 + 0.993684i \(0.464206\pi\)
\(444\) −2632.55 −0.281386
\(445\) −6968.42 −0.742326
\(446\) −18361.1 −1.94938
\(447\) −9586.96 −1.01442
\(448\) 4531.63 0.477901
\(449\) −5842.05 −0.614038 −0.307019 0.951703i \(-0.599332\pi\)
−0.307019 + 0.951703i \(0.599332\pi\)
\(450\) −2272.10 −0.238017
\(451\) −22881.3 −2.38899
\(452\) 1988.94 0.206973
\(453\) −1524.69 −0.158138
\(454\) −9346.91 −0.966238
\(455\) 0 0
\(456\) 3622.03 0.371967
\(457\) −5954.40 −0.609486 −0.304743 0.952435i \(-0.598571\pi\)
−0.304743 + 0.952435i \(0.598571\pi\)
\(458\) 11238.0 1.14654
\(459\) −1582.66 −0.160942
\(460\) −152.470 −0.0154542
\(461\) 1865.94 0.188515 0.0942576 0.995548i \(-0.469952\pi\)
0.0942576 + 0.995548i \(0.469952\pi\)
\(462\) −8432.42 −0.849160
\(463\) 6700.05 0.672522 0.336261 0.941769i \(-0.390838\pi\)
0.336261 + 0.941769i \(0.390838\pi\)
\(464\) −16500.2 −1.65086
\(465\) −781.211 −0.0779093
\(466\) 7428.28 0.738430
\(467\) −16585.8 −1.64347 −0.821734 0.569871i \(-0.806993\pi\)
−0.821734 + 0.569871i \(0.806993\pi\)
\(468\) 0 0
\(469\) −12263.2 −1.20738
\(470\) −1992.11 −0.195509
\(471\) −3729.23 −0.364828
\(472\) 7276.77 0.709619
\(473\) 8017.98 0.779423
\(474\) 12680.2 1.22873
\(475\) 5104.51 0.493075
\(476\) −1720.29 −0.165649
\(477\) 1187.18 0.113956
\(478\) 4809.97 0.460257
\(479\) 6166.88 0.588250 0.294125 0.955767i \(-0.404972\pi\)
0.294125 + 0.955767i \(0.404972\pi\)
\(480\) 1851.23 0.176034
\(481\) 0 0
\(482\) −7592.38 −0.717476
\(483\) 464.383 0.0437478
\(484\) 5331.53 0.500708
\(485\) 7052.71 0.660303
\(486\) 771.146 0.0719751
\(487\) −5718.51 −0.532095 −0.266047 0.963960i \(-0.585718\pi\)
−0.266047 + 0.963960i \(0.585718\pi\)
\(488\) 11686.3 1.08405
\(489\) 101.999 0.00943261
\(490\) 3040.82 0.280347
\(491\) −21060.9 −1.93578 −0.967888 0.251383i \(-0.919115\pi\)
−0.967888 + 0.251383i \(0.919115\pi\)
\(492\) 2274.45 0.208415
\(493\) −12679.8 −1.15836
\(494\) 0 0
\(495\) 3791.81 0.344302
\(496\) −2946.40 −0.266728
\(497\) 8609.97 0.777082
\(498\) −8640.97 −0.777532
\(499\) 7863.87 0.705481 0.352741 0.935721i \(-0.385250\pi\)
0.352741 + 0.935721i \(0.385250\pi\)
\(500\) 2855.51 0.255405
\(501\) 6632.01 0.591410
\(502\) −6977.70 −0.620378
\(503\) −6504.06 −0.576544 −0.288272 0.957549i \(-0.593081\pi\)
−0.288272 + 0.957549i \(0.593081\pi\)
\(504\) −2400.07 −0.212119
\(505\) −9550.26 −0.841546
\(506\) −2166.13 −0.190309
\(507\) 0 0
\(508\) 4187.41 0.365721
\(509\) −14799.3 −1.28873 −0.644367 0.764717i \(-0.722879\pi\)
−0.644367 + 0.764717i \(0.722879\pi\)
\(510\) 3762.11 0.326645
\(511\) −13902.8 −1.20357
\(512\) −4500.03 −0.388428
\(513\) −1732.46 −0.149103
\(514\) −19657.1 −1.68685
\(515\) −2613.19 −0.223594
\(516\) −797.005 −0.0679965
\(517\) −5819.40 −0.495042
\(518\) −19059.5 −1.61666
\(519\) −1983.92 −0.167793
\(520\) 0 0
\(521\) −6633.65 −0.557822 −0.278911 0.960317i \(-0.589974\pi\)
−0.278911 + 0.960317i \(0.589974\pi\)
\(522\) 6178.20 0.518032
\(523\) 4527.41 0.378527 0.189264 0.981926i \(-0.439390\pi\)
0.189264 + 0.981926i \(0.439390\pi\)
\(524\) 3847.21 0.320737
\(525\) −3382.41 −0.281182
\(526\) −13270.5 −1.10004
\(527\) −2264.21 −0.187155
\(528\) 14301.1 1.17874
\(529\) −12047.7 −0.990195
\(530\) −2822.01 −0.231284
\(531\) −3480.56 −0.284451
\(532\) −1883.11 −0.153464
\(533\) 0 0
\(534\) 9840.83 0.797480
\(535\) −582.818 −0.0470980
\(536\) 16281.1 1.31201
\(537\) −6975.14 −0.560521
\(538\) 8783.11 0.703841
\(539\) 8882.89 0.709858
\(540\) −376.915 −0.0300367
\(541\) −8685.42 −0.690232 −0.345116 0.938560i \(-0.612160\pi\)
−0.345116 + 0.938560i \(0.612160\pi\)
\(542\) 22821.4 1.80860
\(543\) 6366.61 0.503162
\(544\) 5365.48 0.422873
\(545\) −6337.47 −0.498105
\(546\) 0 0
\(547\) 24656.6 1.92731 0.963657 0.267142i \(-0.0860793\pi\)
0.963657 + 0.267142i \(0.0860793\pi\)
\(548\) −3922.22 −0.305746
\(549\) −5589.70 −0.434540
\(550\) 15777.4 1.22318
\(551\) −13880.0 −1.07315
\(552\) −616.534 −0.0475388
\(553\) 18876.6 1.45157
\(554\) 4180.27 0.320582
\(555\) 8570.51 0.655492
\(556\) −2538.89 −0.193656
\(557\) −9215.90 −0.701059 −0.350530 0.936552i \(-0.613998\pi\)
−0.350530 + 0.936552i \(0.613998\pi\)
\(558\) 1103.23 0.0836979
\(559\) 0 0
\(560\) 7287.93 0.549949
\(561\) 10990.0 0.827088
\(562\) 12531.7 0.940600
\(563\) −19686.7 −1.47370 −0.736850 0.676056i \(-0.763688\pi\)
−0.736850 + 0.676056i \(0.763688\pi\)
\(564\) 578.461 0.0431873
\(565\) −6475.17 −0.482146
\(566\) −15808.6 −1.17400
\(567\) 1147.98 0.0850279
\(568\) −11430.9 −0.844422
\(569\) −3559.36 −0.262243 −0.131121 0.991366i \(-0.541858\pi\)
−0.131121 + 0.991366i \(0.541858\pi\)
\(570\) 4118.19 0.302617
\(571\) −710.968 −0.0521070 −0.0260535 0.999661i \(-0.508294\pi\)
−0.0260535 + 0.999661i \(0.508294\pi\)
\(572\) 0 0
\(573\) −7453.11 −0.543383
\(574\) 16466.9 1.19741
\(575\) −868.878 −0.0630169
\(576\) 2877.70 0.208167
\(577\) 8041.67 0.580206 0.290103 0.956995i \(-0.406310\pi\)
0.290103 + 0.956995i \(0.406310\pi\)
\(578\) −4687.26 −0.337308
\(579\) 800.314 0.0574438
\(580\) −3019.73 −0.216186
\(581\) −12863.6 −0.918538
\(582\) −9959.86 −0.709364
\(583\) −8243.72 −0.585626
\(584\) 18457.9 1.30786
\(585\) 0 0
\(586\) 10164.6 0.716546
\(587\) 14641.3 1.02949 0.514744 0.857344i \(-0.327887\pi\)
0.514744 + 0.857344i \(0.327887\pi\)
\(588\) −882.980 −0.0619277
\(589\) −2478.52 −0.173388
\(590\) 8273.56 0.577317
\(591\) 3693.10 0.257045
\(592\) 32324.3 2.24413
\(593\) −5735.76 −0.397200 −0.198600 0.980081i \(-0.563639\pi\)
−0.198600 + 0.980081i \(0.563639\pi\)
\(594\) −5354.81 −0.369883
\(595\) 5600.55 0.385882
\(596\) −6617.35 −0.454794
\(597\) −9738.43 −0.667617
\(598\) 0 0
\(599\) −16109.3 −1.09884 −0.549422 0.835545i \(-0.685152\pi\)
−0.549422 + 0.835545i \(0.685152\pi\)
\(600\) 4490.63 0.305548
\(601\) −21005.4 −1.42567 −0.712837 0.701330i \(-0.752590\pi\)
−0.712837 + 0.701330i \(0.752590\pi\)
\(602\) −5770.28 −0.390663
\(603\) −7787.46 −0.525920
\(604\) −1052.41 −0.0708975
\(605\) −17357.3 −1.16640
\(606\) 13486.9 0.904073
\(607\) 7478.16 0.500048 0.250024 0.968240i \(-0.419561\pi\)
0.250024 + 0.968240i \(0.419561\pi\)
\(608\) 5873.31 0.391767
\(609\) 9197.32 0.611977
\(610\) 13287.1 0.881934
\(611\) 0 0
\(612\) −1092.43 −0.0721548
\(613\) −16435.5 −1.08291 −0.541455 0.840730i \(-0.682126\pi\)
−0.541455 + 0.840730i \(0.682126\pi\)
\(614\) −15218.8 −1.00029
\(615\) −7404.68 −0.485505
\(616\) 16666.0 1.09009
\(617\) −1290.89 −0.0842289 −0.0421145 0.999113i \(-0.513409\pi\)
−0.0421145 + 0.999113i \(0.513409\pi\)
\(618\) 3690.36 0.240207
\(619\) 26719.0 1.73494 0.867470 0.497490i \(-0.165745\pi\)
0.867470 + 0.497490i \(0.165745\pi\)
\(620\) −539.227 −0.0349289
\(621\) 294.896 0.0190560
\(622\) 1999.94 0.128924
\(623\) 14649.8 0.942103
\(624\) 0 0
\(625\) 647.683 0.0414517
\(626\) −29559.8 −1.88729
\(627\) 12030.1 0.766248
\(628\) −2574.08 −0.163562
\(629\) 24840.2 1.57463
\(630\) −2728.84 −0.172571
\(631\) 10697.4 0.674893 0.337447 0.941345i \(-0.390437\pi\)
0.337447 + 0.941345i \(0.390437\pi\)
\(632\) −25061.4 −1.57735
\(633\) 992.125 0.0622961
\(634\) −1828.96 −0.114570
\(635\) −13632.5 −0.851951
\(636\) 819.444 0.0510897
\(637\) 0 0
\(638\) −42901.2 −2.66219
\(639\) 5467.56 0.338487
\(640\) −11777.1 −0.727393
\(641\) 23572.8 1.45253 0.726264 0.687416i \(-0.241255\pi\)
0.726264 + 0.687416i \(0.241255\pi\)
\(642\) 823.057 0.0505973
\(643\) 14000.3 0.858661 0.429331 0.903147i \(-0.358750\pi\)
0.429331 + 0.903147i \(0.358750\pi\)
\(644\) 320.538 0.0196133
\(645\) 2594.72 0.158399
\(646\) 11935.9 0.726953
\(647\) 614.196 0.0373207 0.0186604 0.999826i \(-0.494060\pi\)
0.0186604 + 0.999826i \(0.494060\pi\)
\(648\) −1524.11 −0.0923962
\(649\) 24168.9 1.46181
\(650\) 0 0
\(651\) 1642.35 0.0988765
\(652\) 70.4042 0.00422890
\(653\) −5333.42 −0.319622 −0.159811 0.987148i \(-0.551088\pi\)
−0.159811 + 0.987148i \(0.551088\pi\)
\(654\) 8949.79 0.535114
\(655\) −12524.9 −0.747161
\(656\) −27927.3 −1.66216
\(657\) −8828.62 −0.524258
\(658\) 4188.03 0.248125
\(659\) 21396.8 1.26480 0.632398 0.774644i \(-0.282071\pi\)
0.632398 + 0.774644i \(0.282071\pi\)
\(660\) 2617.28 0.154360
\(661\) 16107.9 0.947841 0.473921 0.880568i \(-0.342838\pi\)
0.473921 + 0.880568i \(0.342838\pi\)
\(662\) −5001.20 −0.293621
\(663\) 0 0
\(664\) 17078.2 0.998136
\(665\) 6130.63 0.357497
\(666\) −12103.3 −0.704194
\(667\) 2362.62 0.137153
\(668\) 4577.72 0.265145
\(669\) −17357.6 −1.00311
\(670\) 18511.4 1.06740
\(671\) 38814.6 2.23312
\(672\) −3891.85 −0.223410
\(673\) 20329.9 1.16443 0.582213 0.813036i \(-0.302187\pi\)
0.582213 + 0.813036i \(0.302187\pi\)
\(674\) 29479.1 1.68471
\(675\) −2147.92 −0.122479
\(676\) 0 0
\(677\) −24883.5 −1.41263 −0.706314 0.707899i \(-0.749643\pi\)
−0.706314 + 0.707899i \(0.749643\pi\)
\(678\) 9144.26 0.517969
\(679\) −14827.0 −0.838007
\(680\) −7435.51 −0.419322
\(681\) −8836.06 −0.497208
\(682\) −7660.78 −0.430127
\(683\) 258.953 0.0145074 0.00725369 0.999974i \(-0.497691\pi\)
0.00725369 + 0.999974i \(0.497691\pi\)
\(684\) −1195.82 −0.0668471
\(685\) 12769.1 0.712240
\(686\) −21819.5 −1.21439
\(687\) 10623.8 0.589989
\(688\) 9786.20 0.542290
\(689\) 0 0
\(690\) −700.989 −0.0386756
\(691\) 658.193 0.0362357 0.0181178 0.999836i \(-0.494233\pi\)
0.0181178 + 0.999836i \(0.494233\pi\)
\(692\) −1369.39 −0.0752262
\(693\) −7971.55 −0.436962
\(694\) −24441.3 −1.33686
\(695\) 8265.60 0.451125
\(696\) −12210.7 −0.665010
\(697\) −21461.2 −1.16629
\(698\) 15781.2 0.855768
\(699\) 7022.29 0.379982
\(700\) −2334.69 −0.126062
\(701\) −8222.16 −0.443005 −0.221503 0.975160i \(-0.571096\pi\)
−0.221503 + 0.975160i \(0.571096\pi\)
\(702\) 0 0
\(703\) 27191.3 1.45881
\(704\) −19982.7 −1.06978
\(705\) −1883.23 −0.100605
\(706\) −4999.25 −0.266500
\(707\) 20077.6 1.06803
\(708\) −2402.44 −0.127527
\(709\) −6817.51 −0.361124 −0.180562 0.983564i \(-0.557792\pi\)
−0.180562 + 0.983564i \(0.557792\pi\)
\(710\) −12996.8 −0.686987
\(711\) 11987.2 0.632283
\(712\) −19449.6 −1.02374
\(713\) 421.888 0.0221596
\(714\) −7909.11 −0.414553
\(715\) 0 0
\(716\) −4814.56 −0.251297
\(717\) 4547.09 0.236840
\(718\) −24014.8 −1.24822
\(719\) 23385.7 1.21299 0.606496 0.795087i \(-0.292575\pi\)
0.606496 + 0.795087i \(0.292575\pi\)
\(720\) 4628.03 0.239551
\(721\) 5493.73 0.283769
\(722\) −8701.03 −0.448502
\(723\) −7177.42 −0.369199
\(724\) 4394.52 0.225582
\(725\) −17208.5 −0.881529
\(726\) 24512.0 1.25307
\(727\) 20488.6 1.04523 0.522613 0.852570i \(-0.324957\pi\)
0.522613 + 0.852570i \(0.324957\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 20986.3 1.06402
\(731\) 7520.38 0.380508
\(732\) −3858.26 −0.194816
\(733\) 16993.4 0.856299 0.428149 0.903708i \(-0.359166\pi\)
0.428149 + 0.903708i \(0.359166\pi\)
\(734\) 13862.4 0.697099
\(735\) 2874.62 0.144261
\(736\) −999.742 −0.0500693
\(737\) 54075.8 2.70272
\(738\) 10456.9 0.521577
\(739\) 14014.3 0.697600 0.348800 0.937197i \(-0.386589\pi\)
0.348800 + 0.937197i \(0.386589\pi\)
\(740\) 5915.75 0.293875
\(741\) 0 0
\(742\) 5932.73 0.293528
\(743\) 141.560 0.00698971 0.00349485 0.999994i \(-0.498888\pi\)
0.00349485 + 0.999994i \(0.498888\pi\)
\(744\) −2180.45 −0.107445
\(745\) 21543.4 1.05945
\(746\) −2544.92 −0.124901
\(747\) −8168.70 −0.400103
\(748\) 7585.76 0.370806
\(749\) 1225.26 0.0597731
\(750\) 13128.4 0.639175
\(751\) 20734.3 1.00746 0.503732 0.863860i \(-0.331960\pi\)
0.503732 + 0.863860i \(0.331960\pi\)
\(752\) −7102.76 −0.344430
\(753\) −6596.34 −0.319235
\(754\) 0 0
\(755\) 3426.23 0.165157
\(756\) 792.391 0.0381203
\(757\) 17449.8 0.837812 0.418906 0.908030i \(-0.362414\pi\)
0.418906 + 0.908030i \(0.362414\pi\)
\(758\) −216.054 −0.0103528
\(759\) −2047.74 −0.0979293
\(760\) −8139.27 −0.388477
\(761\) 424.121 0.0202028 0.0101014 0.999949i \(-0.496785\pi\)
0.0101014 + 0.999949i \(0.496785\pi\)
\(762\) 19251.9 0.915251
\(763\) 13323.3 0.632157
\(764\) −5144.48 −0.243613
\(765\) 3556.49 0.168085
\(766\) −4915.68 −0.231868
\(767\) 0 0
\(768\) 8957.81 0.420882
\(769\) −38060.7 −1.78479 −0.892396 0.451252i \(-0.850977\pi\)
−0.892396 + 0.451252i \(0.850977\pi\)
\(770\) 18949.0 0.886849
\(771\) −18582.8 −0.868019
\(772\) 552.413 0.0257536
\(773\) 16683.3 0.776268 0.388134 0.921603i \(-0.373120\pi\)
0.388134 + 0.921603i \(0.373120\pi\)
\(774\) −3664.28 −0.170168
\(775\) −3072.89 −0.142428
\(776\) 19684.9 0.910627
\(777\) −18017.8 −0.831900
\(778\) 23167.7 1.06761
\(779\) −23492.5 −1.08050
\(780\) 0 0
\(781\) −37966.5 −1.73950
\(782\) −2031.70 −0.0929073
\(783\) 5840.54 0.266569
\(784\) 10841.9 0.493889
\(785\) 8380.17 0.381020
\(786\) 17687.8 0.802674
\(787\) 39105.2 1.77122 0.885609 0.464432i \(-0.153741\pi\)
0.885609 + 0.464432i \(0.153741\pi\)
\(788\) 2549.14 0.115240
\(789\) −12545.2 −0.566060
\(790\) −28494.3 −1.28327
\(791\) 13612.8 0.611903
\(792\) 10583.4 0.474827
\(793\) 0 0
\(794\) −19346.2 −0.864697
\(795\) −2667.78 −0.119014
\(796\) −6721.90 −0.299311
\(797\) −4346.93 −0.193195 −0.0965974 0.995324i \(-0.530796\pi\)
−0.0965974 + 0.995324i \(0.530796\pi\)
\(798\) −8657.69 −0.384059
\(799\) −5458.25 −0.241676
\(800\) 7281.78 0.321812
\(801\) 9302.99 0.410368
\(802\) −24093.9 −1.06083
\(803\) 61305.6 2.69418
\(804\) −5375.26 −0.235784
\(805\) −1043.54 −0.0456895
\(806\) 0 0
\(807\) 8303.07 0.362183
\(808\) −26655.8 −1.16058
\(809\) −23030.2 −1.00086 −0.500432 0.865776i \(-0.666826\pi\)
−0.500432 + 0.865776i \(0.666826\pi\)
\(810\) −1732.89 −0.0751697
\(811\) −7898.11 −0.341973 −0.170987 0.985273i \(-0.554695\pi\)
−0.170987 + 0.985273i \(0.554695\pi\)
\(812\) 6348.41 0.274366
\(813\) 21574.1 0.930672
\(814\) 84044.8 3.61888
\(815\) −229.207 −0.00985127
\(816\) 13413.6 0.575453
\(817\) 8232.18 0.352518
\(818\) 22956.2 0.981230
\(819\) 0 0
\(820\) −5111.04 −0.217665
\(821\) 3939.61 0.167471 0.0837353 0.996488i \(-0.473315\pi\)
0.0837353 + 0.996488i \(0.473315\pi\)
\(822\) −18032.6 −0.765159
\(823\) −17599.8 −0.745430 −0.372715 0.927946i \(-0.621573\pi\)
−0.372715 + 0.927946i \(0.621573\pi\)
\(824\) −7293.70 −0.308359
\(825\) 14915.1 0.629425
\(826\) −17393.6 −0.732687
\(827\) −12510.6 −0.526042 −0.263021 0.964790i \(-0.584719\pi\)
−0.263021 + 0.964790i \(0.584719\pi\)
\(828\) 203.550 0.00854331
\(829\) 28630.8 1.19950 0.599752 0.800186i \(-0.295266\pi\)
0.599752 + 0.800186i \(0.295266\pi\)
\(830\) 19417.6 0.812042
\(831\) 3951.80 0.164966
\(832\) 0 0
\(833\) 8331.62 0.346547
\(834\) −11672.7 −0.484643
\(835\) −14903.2 −0.617660
\(836\) 8303.75 0.343530
\(837\) 1042.93 0.0430693
\(838\) −16859.1 −0.694973
\(839\) −21250.3 −0.874426 −0.437213 0.899358i \(-0.644034\pi\)
−0.437213 + 0.899358i \(0.644034\pi\)
\(840\) 5393.34 0.221533
\(841\) 22403.7 0.918600
\(842\) −47690.9 −1.95194
\(843\) 11846.8 0.484015
\(844\) 684.810 0.0279291
\(845\) 0 0
\(846\) 2659.51 0.108080
\(847\) 36490.4 1.48031
\(848\) −10061.7 −0.407454
\(849\) −14944.6 −0.604118
\(850\) 14798.2 0.597147
\(851\) −4628.45 −0.186441
\(852\) 3773.96 0.151753
\(853\) −34721.1 −1.39370 −0.696852 0.717215i \(-0.745416\pi\)
−0.696852 + 0.717215i \(0.745416\pi\)
\(854\) −27933.6 −1.11928
\(855\) 3893.11 0.155721
\(856\) −1626.71 −0.0649529
\(857\) 4898.06 0.195233 0.0976163 0.995224i \(-0.468878\pi\)
0.0976163 + 0.995224i \(0.468878\pi\)
\(858\) 0 0
\(859\) −12564.2 −0.499051 −0.249526 0.968368i \(-0.580275\pi\)
−0.249526 + 0.968368i \(0.580275\pi\)
\(860\) 1791.00 0.0710145
\(861\) 15566.9 0.616166
\(862\) 22704.9 0.897137
\(863\) 22826.6 0.900380 0.450190 0.892933i \(-0.351356\pi\)
0.450190 + 0.892933i \(0.351356\pi\)
\(864\) −2471.42 −0.0973143
\(865\) 4458.18 0.175240
\(866\) −30282.8 −1.18828
\(867\) −4431.08 −0.173572
\(868\) 1133.62 0.0443291
\(869\) −83238.3 −3.24933
\(870\) −13883.4 −0.541024
\(871\) 0 0
\(872\) −17688.6 −0.686939
\(873\) −9415.51 −0.365025
\(874\) −2224.00 −0.0860731
\(875\) 19543.9 0.755089
\(876\) −6093.92 −0.235039
\(877\) −25212.7 −0.970776 −0.485388 0.874299i \(-0.661322\pi\)
−0.485388 + 0.874299i \(0.661322\pi\)
\(878\) 22438.5 0.862484
\(879\) 9609.07 0.368721
\(880\) −32136.9 −1.23106
\(881\) −18026.2 −0.689352 −0.344676 0.938722i \(-0.612011\pi\)
−0.344676 + 0.938722i \(0.612011\pi\)
\(882\) −4059.55 −0.154980
\(883\) −18833.1 −0.717764 −0.358882 0.933383i \(-0.616842\pi\)
−0.358882 + 0.933383i \(0.616842\pi\)
\(884\) 0 0
\(885\) 7821.37 0.297076
\(886\) 6640.68 0.251803
\(887\) 38451.4 1.45555 0.727775 0.685816i \(-0.240555\pi\)
0.727775 + 0.685816i \(0.240555\pi\)
\(888\) 23921.2 0.903991
\(889\) 28659.7 1.08123
\(890\) −22113.9 −0.832876
\(891\) −5062.15 −0.190335
\(892\) −11981.0 −0.449723
\(893\) −5974.86 −0.223898
\(894\) −30423.7 −1.13816
\(895\) 15674.2 0.585399
\(896\) 24759.1 0.923152
\(897\) 0 0
\(898\) −18539.4 −0.688940
\(899\) 8355.68 0.309986
\(900\) −1482.59 −0.0549108
\(901\) −7732.11 −0.285898
\(902\) −72612.3 −2.68041
\(903\) −5454.91 −0.201028
\(904\) −18072.9 −0.664929
\(905\) −14306.8 −0.525495
\(906\) −4838.53 −0.177428
\(907\) −5531.31 −0.202496 −0.101248 0.994861i \(-0.532284\pi\)
−0.101248 + 0.994861i \(0.532284\pi\)
\(908\) −6099.05 −0.222912
\(909\) 12749.8 0.465219
\(910\) 0 0
\(911\) 15695.2 0.570806 0.285403 0.958408i \(-0.407872\pi\)
0.285403 + 0.958408i \(0.407872\pi\)
\(912\) 14683.2 0.533123
\(913\) 56723.1 2.05615
\(914\) −18895.9 −0.683832
\(915\) 12560.9 0.453827
\(916\) 7333.01 0.264508
\(917\) 26331.3 0.948240
\(918\) −5022.49 −0.180574
\(919\) −51503.5 −1.84869 −0.924344 0.381561i \(-0.875386\pi\)
−0.924344 + 0.381561i \(0.875386\pi\)
\(920\) 1385.45 0.0496488
\(921\) −14387.0 −0.514732
\(922\) 5921.45 0.211510
\(923\) 0 0
\(924\) −5502.33 −0.195902
\(925\) 33712.0 1.19832
\(926\) 21262.2 0.754557
\(927\) 3488.66 0.123606
\(928\) −19800.3 −0.700407
\(929\) 42927.0 1.51603 0.758014 0.652238i \(-0.226170\pi\)
0.758014 + 0.652238i \(0.226170\pi\)
\(930\) −2479.13 −0.0874127
\(931\) 9120.20 0.321055
\(932\) 4847.10 0.170356
\(933\) 1890.64 0.0663416
\(934\) −52634.1 −1.84394
\(935\) −24696.2 −0.863797
\(936\) 0 0
\(937\) 44206.6 1.54127 0.770633 0.637280i \(-0.219940\pi\)
0.770633 + 0.637280i \(0.219940\pi\)
\(938\) −38916.6 −1.35466
\(939\) −27944.2 −0.971165
\(940\) −1299.89 −0.0451041
\(941\) 44067.7 1.52664 0.763319 0.646022i \(-0.223568\pi\)
0.763319 + 0.646022i \(0.223568\pi\)
\(942\) −11834.5 −0.409330
\(943\) 3998.85 0.138092
\(944\) 29498.9 1.01706
\(945\) −2579.70 −0.0888017
\(946\) 25444.6 0.874498
\(947\) 44402.5 1.52364 0.761820 0.647789i \(-0.224306\pi\)
0.761820 + 0.647789i \(0.224306\pi\)
\(948\) 8274.07 0.283470
\(949\) 0 0
\(950\) 16198.9 0.553221
\(951\) −1729.00 −0.0589554
\(952\) 15631.7 0.532172
\(953\) −10361.7 −0.352202 −0.176101 0.984372i \(-0.556349\pi\)
−0.176101 + 0.984372i \(0.556349\pi\)
\(954\) 3767.44 0.127857
\(955\) 16748.3 0.567500
\(956\) 3138.60 0.106182
\(957\) −40556.5 −1.36991
\(958\) 19570.2 0.660006
\(959\) −26844.7 −0.903920
\(960\) −6466.65 −0.217407
\(961\) −28298.9 −0.949916
\(962\) 0 0
\(963\) 778.073 0.0260364
\(964\) −4954.18 −0.165522
\(965\) −1798.43 −0.0599933
\(966\) 1473.69 0.0490842
\(967\) −8432.54 −0.280426 −0.140213 0.990121i \(-0.544779\pi\)
−0.140213 + 0.990121i \(0.544779\pi\)
\(968\) −48446.1 −1.60859
\(969\) 11283.5 0.374076
\(970\) 22381.4 0.740848
\(971\) −36917.1 −1.22011 −0.610055 0.792359i \(-0.708853\pi\)
−0.610055 + 0.792359i \(0.708853\pi\)
\(972\) 503.189 0.0166047
\(973\) −17376.8 −0.572534
\(974\) −18147.4 −0.597001
\(975\) 0 0
\(976\) 47374.5 1.55371
\(977\) 38306.9 1.25440 0.627199 0.778859i \(-0.284201\pi\)
0.627199 + 0.778859i \(0.284201\pi\)
\(978\) 323.687 0.0105832
\(979\) −64599.6 −2.10890
\(980\) 1984.19 0.0646763
\(981\) 8460.65 0.275360
\(982\) −66835.6 −2.17190
\(983\) 18810.9 0.610350 0.305175 0.952296i \(-0.401285\pi\)
0.305175 + 0.952296i \(0.401285\pi\)
\(984\) −20667.3 −0.669561
\(985\) −8298.97 −0.268454
\(986\) −40238.8 −1.29966
\(987\) 3959.14 0.127681
\(988\) 0 0
\(989\) −1401.26 −0.0450532
\(990\) 12033.1 0.386300
\(991\) −6492.09 −0.208101 −0.104051 0.994572i \(-0.533180\pi\)
−0.104051 + 0.994572i \(0.533180\pi\)
\(992\) −3535.71 −0.113164
\(993\) −4727.86 −0.151092
\(994\) 27323.2 0.871872
\(995\) 21883.8 0.697249
\(996\) −5638.41 −0.179377
\(997\) 48552.1 1.54229 0.771143 0.636662i \(-0.219685\pi\)
0.771143 + 0.636662i \(0.219685\pi\)
\(998\) 24955.5 0.791537
\(999\) −11441.8 −0.362365
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 507.4.a.o.1.8 9
3.2 odd 2 1521.4.a.bi.1.2 9
13.5 odd 4 507.4.b.k.337.5 18
13.8 odd 4 507.4.b.k.337.14 18
13.12 even 2 507.4.a.p.1.2 yes 9
39.38 odd 2 1521.4.a.bf.1.8 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.4.a.o.1.8 9 1.1 even 1 trivial
507.4.a.p.1.2 yes 9 13.12 even 2
507.4.b.k.337.5 18 13.5 odd 4
507.4.b.k.337.14 18 13.8 odd 4
1521.4.a.bf.1.8 9 39.38 odd 2
1521.4.a.bi.1.2 9 3.2 odd 2