Properties

Label 507.4.a.p.1.2
Level $507$
Weight $4$
Character 507.1
Self dual yes
Analytic conductor $29.914$
Analytic rank $0$
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: \(0\)
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 1.2
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 \(-0.689580\pi\)
−0.560991 + 0.827822i \(0.689580\pi\)
\(3\) 3.00000 0.577350
\(4\) 2.07074 0.258842
\(5\) 6.74147 0.602975 0.301488 0.953470i \(-0.402517\pi\)
0.301488 + 0.953470i \(0.402517\pi\)
\(6\) −9.52033 −0.647776
\(7\) −14.1726 −0.765251 −0.382625 0.923904i \(-0.624980\pi\)
−0.382625 + 0.923904i \(0.624980\pi\)
\(8\) 18.8162 0.831565
\(9\) 9.00000 0.333333
\(10\) −21.3937 −0.676527
\(11\) 62.4956 1.71301 0.856507 0.516136i \(-0.172630\pi\)
0.856507 + 0.516136i \(0.172630\pi\)
\(12\) 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 \(-0.373380\pi\)
0.387382 + 0.921919i \(0.373380\pi\)
\(20\) 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 \(-0.535693\pi\)
−0.111897 + 0.993720i \(0.535693\pi\)
\(32\) 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 \(-0.109462\pi\)
0.941452 + 0.337147i \(0.109462\pi\)
\(38\) −203.625 −0.869270
\(39\) 0 0
\(40\) 126.849 0.501414
\(41\) −366.126 −1.39461 −0.697307 0.716772i \(-0.745619\pi\)
−0.697307 + 0.716772i \(0.745619\pi\)
\(42\) 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 \(-0.546156\pi\)
−0.144495 + 0.989506i \(0.546156\pi\)
\(48\) −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 \(-0.359684\pi\)
0.426677 + 0.904404i \(0.359684\pi\)
\(60\) 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 \(-0.210661\pi\)
0.788880 + 0.614547i \(0.210661\pi\)
\(68\) −121.381 −0.216464
\(69\) 32.7662 0.0571679
\(70\) 303.205 0.517713
\(71\) −607.506 −1.01546 −0.507730 0.861516i \(-0.669515\pi\)
−0.507730 + 0.861516i \(0.669515\pi\)
\(72\) 169.346 0.277188
\(73\) 980.958 1.57277 0.786387 0.617735i \(-0.211949\pi\)
0.786387 + 0.617735i \(0.211949\pi\)
\(74\) −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 \(-0.295106\pi\)
0.600155 + 0.799884i \(0.295106\pi\)
\(84\) −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 \(-0.711067\pi\)
−0.615552 + 0.788096i \(0.711067\pi\)
\(90\) −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 \(-0.315565\pi\)
0.547538 + 0.836781i \(0.315565\pi\)
\(98\) 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 \(-0.635533\pi\)
−0.413039 + 0.910713i \(0.635533\pi\)
\(110\) −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 \(-0.298890\pi\)
0.590604 + 0.806961i \(0.298890\pi\)
\(138\) −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 \(-0.158533\pi\)
0.878517 + 0.477711i \(0.158533\pi\)
\(150\) 757.366 0.412258
\(151\) 508.232 0.273903 0.136951 0.990578i \(-0.456270\pi\)
0.136951 + 0.990578i \(0.456270\pi\)
\(152\) 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 \(-0.502600\pi\)
−0.00816888 + 0.999967i \(0.502600\pi\)
\(164\) −758.149 −0.360985
\(165\) 1263.94 0.596348
\(166\) −2880.32 −1.34673
\(167\) −2210.67 −1.02435 −0.512176 0.858880i \(-0.671161\pi\)
−0.512176 + 0.858880i \(0.671161\pi\)
\(168\) −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 \(-0.515842\pi\)
−0.0497478 + 0.998762i \(0.515842\pi\)
\(194\) −3319.95 −1.22865
\(195\) 0 0
\(196\) −294.327 −0.107262
\(197\) −1231.03 −0.445216 −0.222608 0.974908i \(-0.571457\pi\)
−0.222608 + 0.974908i \(0.571457\pi\)
\(198\) −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 \(-0.164942\pi\)
0.868722 + 0.495300i \(0.164942\pi\)
\(224\) −1297.28 −0.386957
\(225\) −715.973 −0.212140
\(226\) −3048.09 −0.897149
\(227\) 2945.35 0.861189 0.430595 0.902545i \(-0.358304\pi\)
0.430595 + 0.902545i \(0.358304\pi\)
\(228\) 398.608 0.115783
\(229\) −3541.26 −1.02189 −0.510945 0.859613i \(-0.670704\pi\)
−0.510945 + 0.859613i \(0.670704\pi\)
\(230\) −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 \(-0.565755\pi\)
−0.205109 + 0.978739i \(0.565755\pi\)
\(240\) −1542.68 −0.414914
\(241\) 2392.47 0.639472 0.319736 0.947507i \(-0.396406\pi\)
0.319736 + 0.947507i \(0.396406\pi\)
\(242\) −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 \(-0.798364\pi\)
−0.805986 + 0.591935i \(0.798364\pi\)
\(272\) 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 \(-0.637679\pi\)
−0.419169 + 0.907908i \(0.637679\pi\)
\(282\) 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 \(-0.603455\pi\)
−0.319322 + 0.947646i \(0.603455\pi\)
\(294\) 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 \(-0.352930\pi\)
0.445771 + 0.895147i \(0.352930\pi\)
\(308\) −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 \(-0.483741\pi\)
0.0510569 + 0.998696i \(0.483741\pi\)
\(318\) −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 \(-0.458230\pi\)
0.130849 + 0.991402i \(0.458230\pi\)
\(332\) 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 \(-0.624546\pi\)
−0.381365 + 0.924425i \(0.624546\pi\)
\(350\) −3577.96 −0.546429
\(351\) 0 0
\(352\) 5720.49 0.866202
\(353\) 1575.34 0.237526 0.118763 0.992923i \(-0.462107\pi\)
0.118763 + 0.992923i \(0.462107\pi\)
\(354\) −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 \(-0.312237\pi\)
0.556258 + 0.831010i \(0.312237\pi\)
\(360\) 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 \(-0.498531\pi\)
0.00461363 + 0.999989i \(0.498531\pi\)
\(380\) 895.734 0.120922
\(381\) 6066.55 0.815745
\(382\) 7884.01 1.05597
\(383\) 1549.01 0.206659 0.103330 0.994647i \(-0.467050\pi\)
0.103330 + 0.994647i \(0.467050\pi\)
\(384\) −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 \(-0.374083\pi\)
0.385344 + 0.922773i \(0.374083\pi\)
\(398\) 10301.4 1.29740
\(399\) −2728.17 −0.342304
\(400\) 6068.11 0.758513
\(401\) 7592.37 0.945498 0.472749 0.881197i \(-0.343262\pi\)
0.472749 + 0.881197i \(0.343262\pi\)
\(402\) −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 \(-0.644057\pi\)
−0.437275 + 0.899328i \(0.644057\pi\)
\(410\) 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 \(-0.164206\pi\)
0.869865 + 0.493290i \(0.164206\pi\)
\(422\) −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 \(-0.630920\pi\)
−0.399800 + 0.916602i \(0.630920\pi\)
\(432\) −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 \(-0.400668\pi\)
0.307019 + 0.951703i \(0.400668\pi\)
\(450\) 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 \(-0.401429\pi\)
0.304743 + 0.952435i \(0.401429\pi\)
\(458\) 11238.0 1.14654
\(459\) −1582.66 −0.160942
\(460\) 152.470 0.0154542
\(461\) −1865.94 −0.188515 −0.0942576 0.995548i \(-0.530048\pi\)
−0.0942576 + 0.995548i \(0.530048\pi\)
\(462\) 8432.42 0.849160
\(463\) −6700.05 −0.672522 −0.336261 0.941769i \(-0.609162\pi\)
−0.336261 + 0.941769i \(0.609162\pi\)
\(464\) −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 \(-0.595028\pi\)
−0.294125 + 0.955767i \(0.595028\pi\)
\(480\) 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 \(-0.414282\pi\)
0.266047 + 0.963960i \(0.414282\pi\)
\(488\) −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 \(-0.614750\pi\)
−0.352741 + 0.935721i \(0.614750\pi\)
\(500\) −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 \(-0.277121\pi\)
0.644367 + 0.764717i \(0.277121\pi\)
\(510\) 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 \(-0.387840\pi\)
0.345116 + 0.938560i \(0.387840\pi\)
\(542\) 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 \(-0.386002\pi\)
0.350530 + 0.936552i \(0.386002\pi\)
\(558\) 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 \(-0.593690\pi\)
−0.290103 + 0.956995i \(0.593690\pi\)
\(578\) 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 \(-0.672113\pi\)
−0.514744 + 0.857344i \(0.672113\pi\)
\(588\) −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 \(-0.436361\pi\)
0.198600 + 0.980081i \(0.436361\pi\)
\(594\) −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 \(-0.317874\pi\)
0.541455 + 0.840730i \(0.317874\pi\)
\(614\) −15218.8 −1.00029
\(615\) −7404.68 −0.485505
\(616\) −16666.0 −1.09009
\(617\) 1290.89 0.0842289 0.0421145 0.999113i \(-0.486591\pi\)
0.0421145 + 0.999113i \(0.486591\pi\)
\(618\) −3690.36 −0.240207
\(619\) −26719.0 −1.73494 −0.867470 0.497490i \(-0.834255\pi\)
−0.867470 + 0.497490i \(0.834255\pi\)
\(620\) −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 \(-0.609563\pi\)
−0.337447 + 0.941345i \(0.609563\pi\)
\(632\) 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 \(-0.641250\pi\)
−0.429331 + 0.903147i \(0.641250\pi\)
\(644\) −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 \(-0.657162\pi\)
−0.473921 + 0.880568i \(0.657162\pi\)
\(662\) −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 \(-0.502309\pi\)
−0.00725369 + 0.999974i \(0.502309\pi\)
\(684\) 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 \(-0.505767\pi\)
−0.0181178 + 0.999836i \(0.505767\pi\)
\(692\) −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 \(-0.442208\pi\)
0.180562 + 0.983564i \(0.442208\pi\)
\(710\) 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 \(-0.640834\pi\)
−0.428149 + 0.903708i \(0.640834\pi\)
\(734\) −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 \(-0.613411\pi\)
−0.348800 + 0.937197i \(0.613411\pi\)
\(740\) 5915.75 0.293875
\(741\) 0 0
\(742\) 5932.73 0.293528
\(743\) −141.560 −0.00698971 −0.00349485 0.999994i \(-0.501112\pi\)
−0.00349485 + 0.999994i \(0.501112\pi\)
\(744\) −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 \(-0.503215\pi\)
−0.0101014 + 0.999949i \(0.503215\pi\)
\(762\) −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 \(-0.149023\pi\)
0.892396 + 0.451252i \(0.149023\pi\)
\(770\) 18949.0 0.886849
\(771\) −18582.8 −0.868019
\(772\) −552.413 −0.0257536
\(773\) −16683.3 −0.776268 −0.388134 0.921603i \(-0.626880\pi\)
−0.388134 + 0.921603i \(0.626880\pi\)
\(774\) 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 \(-0.846259\pi\)
−0.885609 + 0.464432i \(0.846259\pi\)
\(788\) −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 \(-0.445305\pi\)
0.170987 + 0.985273i \(0.445305\pi\)
\(812\) −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 \(-0.526685\pi\)
−0.0837353 + 0.996488i \(0.526685\pi\)
\(822\) −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 \(-0.415281\pi\)
0.263021 + 0.964790i \(0.415281\pi\)
\(828\) 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 \(-0.355966\pi\)
0.437213 + 0.899358i \(0.355966\pi\)
\(840\) −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 \(-0.254584\pi\)
0.696852 + 0.717215i \(0.254584\pi\)
\(854\) −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 \(-0.648644\pi\)
−0.450190 + 0.892933i \(0.648644\pi\)
\(864\) 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 \(-0.338678\pi\)
0.485388 + 0.874299i \(0.338678\pi\)
\(878\) −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 \(-0.773830\pi\)
−0.758014 + 0.652238i \(0.773830\pi\)
\(930\) 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 \(-0.776432\pi\)
−0.763319 + 0.646022i \(0.776432\pi\)
\(942\) 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 \(-0.775694\pi\)
−0.761820 + 0.647789i \(0.775694\pi\)
\(948\) 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 \(-0.455221\pi\)
0.140213 + 0.990121i \(0.455221\pi\)
\(968\) 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 \(-0.715799\pi\)
−0.627199 + 0.778859i \(0.715799\pi\)
\(978\) 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 \(-0.598715\pi\)
−0.305175 + 0.952296i \(0.598715\pi\)
\(984\) −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.p.1.2 yes 9
3.2 odd 2 1521.4.a.bf.1.8 9
13.5 odd 4 507.4.b.k.337.14 18
13.8 odd 4 507.4.b.k.337.5 18
13.12 even 2 507.4.a.o.1.8 9
39.38 odd 2 1521.4.a.bi.1.2 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.4.a.o.1.8 9 13.12 even 2
507.4.a.p.1.2 yes 9 1.1 even 1 trivial
507.4.b.k.337.5 18 13.8 odd 4
507.4.b.k.337.14 18 13.5 odd 4
1521.4.a.bf.1.8 9 3.2 odd 2
1521.4.a.bi.1.2 9 39.38 odd 2