Properties

Label 507.4.a.o.1.7
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 1.7
Root \(5.06791\) of defining polynomial
Character \(\chi\) \(=\) 507.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.82093 q^{2} +3.00000 q^{3} -0.0423641 q^{4} +3.41089 q^{5} +8.46278 q^{6} -13.3442 q^{7} -22.6869 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.82093 q^{2} +3.00000 q^{3} -0.0423641 q^{4} +3.41089 q^{5} +8.46278 q^{6} -13.3442 q^{7} -22.6869 q^{8} +9.00000 q^{9} +9.62187 q^{10} -35.4529 q^{11} -0.127092 q^{12} -37.6430 q^{14} +10.2327 q^{15} -63.6593 q^{16} +69.6526 q^{17} +25.3884 q^{18} -12.4014 q^{19} -0.144499 q^{20} -40.0325 q^{21} -100.010 q^{22} -126.251 q^{23} -68.0608 q^{24} -113.366 q^{25} +27.0000 q^{27} +0.565314 q^{28} -179.060 q^{29} +28.8656 q^{30} -255.935 q^{31} +1.91716 q^{32} -106.359 q^{33} +196.485 q^{34} -45.5155 q^{35} -0.381277 q^{36} -207.235 q^{37} -34.9833 q^{38} -77.3825 q^{40} +117.701 q^{41} -112.929 q^{42} +553.224 q^{43} +1.50193 q^{44} +30.6980 q^{45} -356.146 q^{46} -62.9185 q^{47} -190.978 q^{48} -164.933 q^{49} -319.797 q^{50} +208.958 q^{51} -147.031 q^{53} +76.1651 q^{54} -120.926 q^{55} +302.738 q^{56} -37.2041 q^{57} -505.115 q^{58} -274.087 q^{59} -0.433498 q^{60} +603.039 q^{61} -721.974 q^{62} -120.098 q^{63} +514.683 q^{64} -300.031 q^{66} +741.019 q^{67} -2.95077 q^{68} -378.754 q^{69} -128.396 q^{70} -572.574 q^{71} -204.182 q^{72} -26.7155 q^{73} -584.595 q^{74} -340.098 q^{75} +0.525372 q^{76} +473.090 q^{77} -207.798 q^{79} -217.135 q^{80} +81.0000 q^{81} +332.026 q^{82} +1031.37 q^{83} +1.69594 q^{84} +237.577 q^{85} +1560.60 q^{86} -537.179 q^{87} +804.318 q^{88} -1229.66 q^{89} +86.5968 q^{90} +5.34852 q^{92} -767.805 q^{93} -177.488 q^{94} -42.2996 q^{95} +5.75148 q^{96} -1795.12 q^{97} -465.264 q^{98} -319.076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 6 q^{2} + 27 q^{3} + 44 q^{4} - 33 q^{5} - 18 q^{6} - 83 q^{7} - 87 q^{8} + 81 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.82093 0.997349 0.498674 0.866789i \(-0.333820\pi\)
0.498674 + 0.866789i \(0.333820\pi\)
\(3\) 3.00000 0.577350
\(4\) −0.0423641 −0.00529552
\(5\) 3.41089 0.305079 0.152539 0.988297i \(-0.451255\pi\)
0.152539 + 0.988297i \(0.451255\pi\)
\(6\) 8.46278 0.575820
\(7\) −13.3442 −0.720518 −0.360259 0.932852i \(-0.617312\pi\)
−0.360259 + 0.932852i \(0.617312\pi\)
\(8\) −22.6869 −1.00263
\(9\) 9.00000 0.333333
\(10\) 9.62187 0.304270
\(11\) −35.4529 −0.971769 −0.485885 0.874023i \(-0.661502\pi\)
−0.485885 + 0.874023i \(0.661502\pi\)
\(12\) −0.127092 −0.00305737
\(13\) 0 0
\(14\) −37.6430 −0.718607
\(15\) 10.2327 0.176137
\(16\) −63.6593 −0.994676
\(17\) 69.6526 0.993720 0.496860 0.867831i \(-0.334486\pi\)
0.496860 + 0.867831i \(0.334486\pi\)
\(18\) 25.3884 0.332450
\(19\) −12.4014 −0.149740 −0.0748701 0.997193i \(-0.523854\pi\)
−0.0748701 + 0.997193i \(0.523854\pi\)
\(20\) −0.144499 −0.00161555
\(21\) −40.0325 −0.415991
\(22\) −100.010 −0.969193
\(23\) −126.251 −1.14457 −0.572287 0.820053i \(-0.693944\pi\)
−0.572287 + 0.820053i \(0.693944\pi\)
\(24\) −68.0608 −0.578869
\(25\) −113.366 −0.906927
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0.565314 0.00381551
\(29\) −179.060 −1.14657 −0.573286 0.819356i \(-0.694331\pi\)
−0.573286 + 0.819356i \(0.694331\pi\)
\(30\) 28.8656 0.175670
\(31\) −255.935 −1.48281 −0.741407 0.671055i \(-0.765841\pi\)
−0.741407 + 0.671055i \(0.765841\pi\)
\(32\) 1.91716 0.0105909
\(33\) −106.359 −0.561051
\(34\) 196.485 0.991085
\(35\) −45.5155 −0.219815
\(36\) −0.381277 −0.00176517
\(37\) −207.235 −0.920790 −0.460395 0.887714i \(-0.652292\pi\)
−0.460395 + 0.887714i \(0.652292\pi\)
\(38\) −34.9833 −0.149343
\(39\) 0 0
\(40\) −77.3825 −0.305881
\(41\) 117.701 0.448337 0.224169 0.974550i \(-0.428033\pi\)
0.224169 + 0.974550i \(0.428033\pi\)
\(42\) −112.929 −0.414888
\(43\) 553.224 1.96200 0.980998 0.194016i \(-0.0621515\pi\)
0.980998 + 0.194016i \(0.0621515\pi\)
\(44\) 1.50193 0.00514602
\(45\) 30.6980 0.101693
\(46\) −356.146 −1.14154
\(47\) −62.9185 −0.195268 −0.0976341 0.995222i \(-0.531127\pi\)
−0.0976341 + 0.995222i \(0.531127\pi\)
\(48\) −190.978 −0.574277
\(49\) −164.933 −0.480854
\(50\) −319.797 −0.904522
\(51\) 208.958 0.573724
\(52\) 0 0
\(53\) −147.031 −0.381061 −0.190531 0.981681i \(-0.561021\pi\)
−0.190531 + 0.981681i \(0.561021\pi\)
\(54\) 76.1651 0.191940
\(55\) −120.926 −0.296466
\(56\) 302.738 0.722413
\(57\) −37.2041 −0.0864526
\(58\) −505.115 −1.14353
\(59\) −274.087 −0.604798 −0.302399 0.953181i \(-0.597787\pi\)
−0.302399 + 0.953181i \(0.597787\pi\)
\(60\) −0.433498 −0.000932738 0
\(61\) 603.039 1.26576 0.632879 0.774251i \(-0.281873\pi\)
0.632879 + 0.774251i \(0.281873\pi\)
\(62\) −721.974 −1.47888
\(63\) −120.098 −0.240173
\(64\) 514.683 1.00524
\(65\) 0 0
\(66\) −300.031 −0.559564
\(67\) 741.019 1.35119 0.675596 0.737272i \(-0.263887\pi\)
0.675596 + 0.737272i \(0.263887\pi\)
\(68\) −2.95077 −0.00526226
\(69\) −378.754 −0.660820
\(70\) −128.396 −0.219232
\(71\) −572.574 −0.957071 −0.478536 0.878068i \(-0.658832\pi\)
−0.478536 + 0.878068i \(0.658832\pi\)
\(72\) −204.182 −0.334210
\(73\) −26.7155 −0.0428330 −0.0214165 0.999771i \(-0.506818\pi\)
−0.0214165 + 0.999771i \(0.506818\pi\)
\(74\) −584.595 −0.918349
\(75\) −340.098 −0.523614
\(76\) 0.525372 0.000792952 0
\(77\) 473.090 0.700177
\(78\) 0 0
\(79\) −207.798 −0.295938 −0.147969 0.988992i \(-0.547274\pi\)
−0.147969 + 0.988992i \(0.547274\pi\)
\(80\) −217.135 −0.303455
\(81\) 81.0000 0.111111
\(82\) 332.026 0.447149
\(83\) 1031.37 1.36395 0.681976 0.731374i \(-0.261121\pi\)
0.681976 + 0.731374i \(0.261121\pi\)
\(84\) 1.69594 0.00220289
\(85\) 237.577 0.303163
\(86\) 1560.60 1.95679
\(87\) −537.179 −0.661973
\(88\) 804.318 0.974325
\(89\) −1229.66 −1.46453 −0.732266 0.681019i \(-0.761537\pi\)
−0.732266 + 0.681019i \(0.761537\pi\)
\(90\) 86.5968 0.101423
\(91\) 0 0
\(92\) 5.34852 0.00606111
\(93\) −767.805 −0.856103
\(94\) −177.488 −0.194750
\(95\) −42.2996 −0.0456826
\(96\) 5.75148 0.00611467
\(97\) −1795.12 −1.87903 −0.939517 0.342502i \(-0.888726\pi\)
−0.939517 + 0.342502i \(0.888726\pi\)
\(98\) −465.264 −0.479579
\(99\) −319.076 −0.323923
\(100\) 4.80265 0.00480265
\(101\) −769.697 −0.758295 −0.379147 0.925336i \(-0.623783\pi\)
−0.379147 + 0.925336i \(0.623783\pi\)
\(102\) 589.455 0.572203
\(103\) 1543.66 1.47671 0.738357 0.674410i \(-0.235602\pi\)
0.738357 + 0.674410i \(0.235602\pi\)
\(104\) 0 0
\(105\) −136.546 −0.126910
\(106\) −414.764 −0.380051
\(107\) 2027.64 1.83196 0.915978 0.401228i \(-0.131417\pi\)
0.915978 + 0.401228i \(0.131417\pi\)
\(108\) −1.14383 −0.00101912
\(109\) −1644.97 −1.44550 −0.722751 0.691108i \(-0.757123\pi\)
−0.722751 + 0.691108i \(0.757123\pi\)
\(110\) −341.123 −0.295680
\(111\) −621.705 −0.531618
\(112\) 849.481 0.716682
\(113\) −654.514 −0.544880 −0.272440 0.962173i \(-0.587831\pi\)
−0.272440 + 0.962173i \(0.587831\pi\)
\(114\) −104.950 −0.0862234
\(115\) −430.629 −0.349186
\(116\) 7.58571 0.00607169
\(117\) 0 0
\(118\) −773.179 −0.603194
\(119\) −929.456 −0.715993
\(120\) −232.148 −0.176601
\(121\) −74.0896 −0.0556646
\(122\) 1701.13 1.26240
\(123\) 353.103 0.258848
\(124\) 10.8425 0.00785227
\(125\) −813.039 −0.581763
\(126\) −338.787 −0.239536
\(127\) 1325.54 0.926161 0.463080 0.886316i \(-0.346744\pi\)
0.463080 + 0.886316i \(0.346744\pi\)
\(128\) 1436.55 0.991983
\(129\) 1659.67 1.13276
\(130\) 0 0
\(131\) 930.114 0.620339 0.310170 0.950681i \(-0.399614\pi\)
0.310170 + 0.950681i \(0.399614\pi\)
\(132\) 4.50580 0.00297106
\(133\) 165.486 0.107891
\(134\) 2090.36 1.34761
\(135\) 92.0939 0.0587125
\(136\) −1580.20 −0.996333
\(137\) 2751.03 1.71559 0.857797 0.513989i \(-0.171833\pi\)
0.857797 + 0.513989i \(0.171833\pi\)
\(138\) −1068.44 −0.659068
\(139\) 2436.65 1.48686 0.743432 0.668812i \(-0.233197\pi\)
0.743432 + 0.668812i \(0.233197\pi\)
\(140\) 1.92822 0.00116403
\(141\) −188.755 −0.112738
\(142\) −1615.19 −0.954534
\(143\) 0 0
\(144\) −572.934 −0.331559
\(145\) −610.753 −0.349795
\(146\) −75.3624 −0.0427194
\(147\) −494.799 −0.277621
\(148\) 8.77933 0.00487606
\(149\) 1517.58 0.834397 0.417198 0.908815i \(-0.363012\pi\)
0.417198 + 0.908815i \(0.363012\pi\)
\(150\) −959.391 −0.522226
\(151\) −583.642 −0.314544 −0.157272 0.987555i \(-0.550270\pi\)
−0.157272 + 0.987555i \(0.550270\pi\)
\(152\) 281.349 0.150134
\(153\) 626.873 0.331240
\(154\) 1334.55 0.698321
\(155\) −872.965 −0.452376
\(156\) 0 0
\(157\) 26.0932 0.0132641 0.00663206 0.999978i \(-0.497889\pi\)
0.00663206 + 0.999978i \(0.497889\pi\)
\(158\) −586.184 −0.295154
\(159\) −441.093 −0.220006
\(160\) 6.53922 0.00323107
\(161\) 1684.72 0.824686
\(162\) 228.495 0.110817
\(163\) −17.0905 −0.00821246 −0.00410623 0.999992i \(-0.501307\pi\)
−0.00410623 + 0.999992i \(0.501307\pi\)
\(164\) −4.98631 −0.00237418
\(165\) −362.778 −0.171165
\(166\) 2909.43 1.36034
\(167\) −3919.48 −1.81616 −0.908079 0.418799i \(-0.862451\pi\)
−0.908079 + 0.418799i \(0.862451\pi\)
\(168\) 908.215 0.417085
\(169\) 0 0
\(170\) 670.188 0.302359
\(171\) −111.612 −0.0499134
\(172\) −23.4368 −0.0103898
\(173\) −1976.35 −0.868551 −0.434276 0.900780i \(-0.642996\pi\)
−0.434276 + 0.900780i \(0.642996\pi\)
\(174\) −1515.34 −0.660218
\(175\) 1512.77 0.653457
\(176\) 2256.91 0.966596
\(177\) −822.260 −0.349180
\(178\) −3468.77 −1.46065
\(179\) −2784.34 −1.16263 −0.581316 0.813678i \(-0.697462\pi\)
−0.581316 + 0.813678i \(0.697462\pi\)
\(180\) −1.30049 −0.000538517 0
\(181\) −1886.53 −0.774723 −0.387361 0.921928i \(-0.626613\pi\)
−0.387361 + 0.921928i \(0.626613\pi\)
\(182\) 0 0
\(183\) 1809.12 0.730786
\(184\) 2864.25 1.14758
\(185\) −706.855 −0.280914
\(186\) −2165.92 −0.853834
\(187\) −2469.39 −0.965666
\(188\) 2.66549 0.00103405
\(189\) −360.293 −0.138664
\(190\) −119.324 −0.0455615
\(191\) 2447.94 0.927364 0.463682 0.886002i \(-0.346528\pi\)
0.463682 + 0.886002i \(0.346528\pi\)
\(192\) 1544.05 0.580375
\(193\) 1925.66 0.718196 0.359098 0.933300i \(-0.383084\pi\)
0.359098 + 0.933300i \(0.383084\pi\)
\(194\) −5063.89 −1.87405
\(195\) 0 0
\(196\) 6.98724 0.00254637
\(197\) 1819.95 0.658203 0.329102 0.944294i \(-0.393254\pi\)
0.329102 + 0.944294i \(0.393254\pi\)
\(198\) −900.092 −0.323064
\(199\) −1273.97 −0.453816 −0.226908 0.973916i \(-0.572862\pi\)
−0.226908 + 0.973916i \(0.572862\pi\)
\(200\) 2571.92 0.909312
\(201\) 2223.06 0.780111
\(202\) −2171.26 −0.756284
\(203\) 2389.40 0.826125
\(204\) −8.85231 −0.00303817
\(205\) 401.465 0.136778
\(206\) 4354.56 1.47280
\(207\) −1136.26 −0.381525
\(208\) 0 0
\(209\) 439.664 0.145513
\(210\) −385.188 −0.126574
\(211\) −1319.44 −0.430492 −0.215246 0.976560i \(-0.569055\pi\)
−0.215246 + 0.976560i \(0.569055\pi\)
\(212\) 6.22884 0.00201792
\(213\) −1717.72 −0.552565
\(214\) 5719.83 1.82710
\(215\) 1886.98 0.598564
\(216\) −612.547 −0.192956
\(217\) 3415.24 1.06839
\(218\) −4640.35 −1.44167
\(219\) −80.1464 −0.0247296
\(220\) 5.12292 0.00156994
\(221\) 0 0
\(222\) −1753.79 −0.530209
\(223\) −1203.45 −0.361384 −0.180692 0.983540i \(-0.557834\pi\)
−0.180692 + 0.983540i \(0.557834\pi\)
\(224\) −25.5829 −0.00763095
\(225\) −1020.29 −0.302309
\(226\) −1846.34 −0.543436
\(227\) 4361.23 1.27518 0.637589 0.770377i \(-0.279932\pi\)
0.637589 + 0.770377i \(0.279932\pi\)
\(228\) 1.57612 0.000457811 0
\(229\) −5384.29 −1.55373 −0.776864 0.629669i \(-0.783191\pi\)
−0.776864 + 0.629669i \(0.783191\pi\)
\(230\) −1214.77 −0.348260
\(231\) 1419.27 0.404247
\(232\) 4062.32 1.14959
\(233\) −4913.60 −1.38155 −0.690774 0.723070i \(-0.742730\pi\)
−0.690774 + 0.723070i \(0.742730\pi\)
\(234\) 0 0
\(235\) −214.608 −0.0595722
\(236\) 11.6114 0.00320272
\(237\) −623.394 −0.170860
\(238\) −2621.93 −0.714094
\(239\) −963.718 −0.260827 −0.130414 0.991460i \(-0.541631\pi\)
−0.130414 + 0.991460i \(0.541631\pi\)
\(240\) −651.404 −0.175200
\(241\) −1544.48 −0.412817 −0.206409 0.978466i \(-0.566178\pi\)
−0.206409 + 0.978466i \(0.566178\pi\)
\(242\) −209.001 −0.0555170
\(243\) 243.000 0.0641500
\(244\) −25.5472 −0.00670284
\(245\) −562.568 −0.146698
\(246\) 996.079 0.258161
\(247\) 0 0
\(248\) 5806.38 1.48671
\(249\) 3094.12 0.787478
\(250\) −2293.52 −0.580221
\(251\) 3768.17 0.947588 0.473794 0.880636i \(-0.342884\pi\)
0.473794 + 0.880636i \(0.342884\pi\)
\(252\) 5.08783 0.00127184
\(253\) 4475.98 1.11226
\(254\) 3739.25 0.923705
\(255\) 712.731 0.175031
\(256\) −65.0695 −0.0158861
\(257\) 1282.68 0.311327 0.155664 0.987810i \(-0.450248\pi\)
0.155664 + 0.987810i \(0.450248\pi\)
\(258\) 4681.81 1.12976
\(259\) 2765.38 0.663445
\(260\) 0 0
\(261\) −1611.54 −0.382190
\(262\) 2623.78 0.618694
\(263\) 5029.74 1.17927 0.589633 0.807671i \(-0.299272\pi\)
0.589633 + 0.807671i \(0.299272\pi\)
\(264\) 2412.95 0.562527
\(265\) −501.506 −0.116254
\(266\) 466.824 0.107604
\(267\) −3688.97 −0.845548
\(268\) −31.3926 −0.00715526
\(269\) 5628.46 1.27574 0.637868 0.770146i \(-0.279816\pi\)
0.637868 + 0.770146i \(0.279816\pi\)
\(270\) 259.790 0.0585568
\(271\) −3368.39 −0.755037 −0.377518 0.926002i \(-0.623222\pi\)
−0.377518 + 0.926002i \(0.623222\pi\)
\(272\) −4434.03 −0.988429
\(273\) 0 0
\(274\) 7760.45 1.71104
\(275\) 4019.15 0.881324
\(276\) 16.0456 0.00349938
\(277\) −6507.75 −1.41160 −0.705799 0.708412i \(-0.749412\pi\)
−0.705799 + 0.708412i \(0.749412\pi\)
\(278\) 6873.62 1.48292
\(279\) −2303.41 −0.494272
\(280\) 1032.61 0.220393
\(281\) 3625.51 0.769680 0.384840 0.922983i \(-0.374257\pi\)
0.384840 + 0.922983i \(0.374257\pi\)
\(282\) −532.465 −0.112439
\(283\) −4635.41 −0.973662 −0.486831 0.873496i \(-0.661847\pi\)
−0.486831 + 0.873496i \(0.661847\pi\)
\(284\) 24.2566 0.00506819
\(285\) −126.899 −0.0263749
\(286\) 0 0
\(287\) −1570.62 −0.323035
\(288\) 17.2545 0.00353031
\(289\) −61.5178 −0.0125214
\(290\) −1722.89 −0.348867
\(291\) −5385.35 −1.08486
\(292\) 1.13178 0.000226823 0
\(293\) 2907.07 0.579634 0.289817 0.957082i \(-0.406406\pi\)
0.289817 + 0.957082i \(0.406406\pi\)
\(294\) −1395.79 −0.276885
\(295\) −934.879 −0.184511
\(296\) 4701.53 0.923212
\(297\) −957.229 −0.187017
\(298\) 4280.99 0.832185
\(299\) 0 0
\(300\) 14.4079 0.00277281
\(301\) −7382.32 −1.41365
\(302\) −1646.41 −0.313710
\(303\) −2309.09 −0.437802
\(304\) 789.461 0.148943
\(305\) 2056.90 0.386156
\(306\) 1768.36 0.330362
\(307\) −933.950 −0.173627 −0.0868133 0.996225i \(-0.527668\pi\)
−0.0868133 + 0.996225i \(0.527668\pi\)
\(308\) −20.0421 −0.00370780
\(309\) 4630.98 0.852581
\(310\) −2462.57 −0.451176
\(311\) −3633.55 −0.662508 −0.331254 0.943542i \(-0.607472\pi\)
−0.331254 + 0.943542i \(0.607472\pi\)
\(312\) 0 0
\(313\) −7507.26 −1.35570 −0.677852 0.735198i \(-0.737089\pi\)
−0.677852 + 0.735198i \(0.737089\pi\)
\(314\) 73.6071 0.0132289
\(315\) −409.639 −0.0732716
\(316\) 8.80319 0.00156715
\(317\) −1214.60 −0.215202 −0.107601 0.994194i \(-0.534317\pi\)
−0.107601 + 0.994194i \(0.534317\pi\)
\(318\) −1244.29 −0.219423
\(319\) 6348.19 1.11420
\(320\) 1755.52 0.306677
\(321\) 6082.92 1.05768
\(322\) 4752.47 0.822500
\(323\) −863.786 −0.148800
\(324\) −3.43149 −0.000588391 0
\(325\) 0 0
\(326\) −48.2111 −0.00819069
\(327\) −4934.92 −0.834561
\(328\) −2670.28 −0.449517
\(329\) 839.595 0.140694
\(330\) −1023.37 −0.170711
\(331\) −2443.20 −0.405712 −0.202856 0.979209i \(-0.565022\pi\)
−0.202856 + 0.979209i \(0.565022\pi\)
\(332\) −43.6933 −0.00722283
\(333\) −1865.12 −0.306930
\(334\) −11056.6 −1.81134
\(335\) 2527.53 0.412220
\(336\) 2548.44 0.413777
\(337\) 1890.96 0.305660 0.152830 0.988253i \(-0.451161\pi\)
0.152830 + 0.988253i \(0.451161\pi\)
\(338\) 0 0
\(339\) −1963.54 −0.314587
\(340\) −10.0647 −0.00160540
\(341\) 9073.64 1.44095
\(342\) −314.850 −0.0497811
\(343\) 6777.95 1.06698
\(344\) −12551.0 −1.96716
\(345\) −1291.89 −0.201602
\(346\) −5575.15 −0.866248
\(347\) −2791.57 −0.431872 −0.215936 0.976408i \(-0.569280\pi\)
−0.215936 + 0.976408i \(0.569280\pi\)
\(348\) 22.7571 0.00350549
\(349\) 6917.33 1.06096 0.530482 0.847696i \(-0.322011\pi\)
0.530482 + 0.847696i \(0.322011\pi\)
\(350\) 4267.43 0.651724
\(351\) 0 0
\(352\) −67.9690 −0.0102919
\(353\) −7638.37 −1.15170 −0.575849 0.817556i \(-0.695328\pi\)
−0.575849 + 0.817556i \(0.695328\pi\)
\(354\) −2319.54 −0.348254
\(355\) −1952.99 −0.291982
\(356\) 52.0933 0.00775545
\(357\) −2788.37 −0.413379
\(358\) −7854.42 −1.15955
\(359\) 5490.97 0.807249 0.403625 0.914925i \(-0.367750\pi\)
0.403625 + 0.914925i \(0.367750\pi\)
\(360\) −696.443 −0.101960
\(361\) −6705.21 −0.977578
\(362\) −5321.77 −0.772669
\(363\) −222.269 −0.0321380
\(364\) 0 0
\(365\) −91.1234 −0.0130674
\(366\) 5103.39 0.728848
\(367\) 6737.43 0.958287 0.479143 0.877737i \(-0.340947\pi\)
0.479143 + 0.877737i \(0.340947\pi\)
\(368\) 8037.07 1.13848
\(369\) 1059.31 0.149446
\(370\) −1993.99 −0.280169
\(371\) 1962.01 0.274561
\(372\) 32.5274 0.00453351
\(373\) −3930.42 −0.545602 −0.272801 0.962070i \(-0.587950\pi\)
−0.272801 + 0.962070i \(0.587950\pi\)
\(374\) −6965.97 −0.963106
\(375\) −2439.12 −0.335881
\(376\) 1427.43 0.195782
\(377\) 0 0
\(378\) −1016.36 −0.138296
\(379\) −11897.7 −1.61252 −0.806258 0.591563i \(-0.798511\pi\)
−0.806258 + 0.591563i \(0.798511\pi\)
\(380\) 1.79199 0.000241913 0
\(381\) 3976.61 0.534719
\(382\) 6905.46 0.924906
\(383\) −4748.31 −0.633492 −0.316746 0.948510i \(-0.602590\pi\)
−0.316746 + 0.948510i \(0.602590\pi\)
\(384\) 4309.64 0.572722
\(385\) 1613.66 0.213609
\(386\) 5432.14 0.716292
\(387\) 4979.02 0.653999
\(388\) 76.0485 0.00995046
\(389\) 11299.5 1.47277 0.736386 0.676561i \(-0.236531\pi\)
0.736386 + 0.676561i \(0.236531\pi\)
\(390\) 0 0
\(391\) −8793.73 −1.13739
\(392\) 3741.82 0.482119
\(393\) 2790.34 0.358153
\(394\) 5133.95 0.656458
\(395\) −708.776 −0.0902845
\(396\) 13.5174 0.00171534
\(397\) −13853.0 −1.75129 −0.875646 0.482953i \(-0.839564\pi\)
−0.875646 + 0.482953i \(0.839564\pi\)
\(398\) −3593.78 −0.452613
\(399\) 496.457 0.0622906
\(400\) 7216.79 0.902099
\(401\) −5434.64 −0.676790 −0.338395 0.941004i \(-0.609884\pi\)
−0.338395 + 0.941004i \(0.609884\pi\)
\(402\) 6271.08 0.778042
\(403\) 0 0
\(404\) 32.6076 0.00401556
\(405\) 276.282 0.0338977
\(406\) 6740.34 0.823935
\(407\) 7347.09 0.894795
\(408\) −4740.61 −0.575233
\(409\) 3472.43 0.419806 0.209903 0.977722i \(-0.432685\pi\)
0.209903 + 0.977722i \(0.432685\pi\)
\(410\) 1132.50 0.136416
\(411\) 8253.09 0.990498
\(412\) −65.3959 −0.00781996
\(413\) 3657.46 0.435767
\(414\) −3205.31 −0.380513
\(415\) 3517.90 0.416113
\(416\) 0 0
\(417\) 7309.95 0.858441
\(418\) 1240.26 0.145127
\(419\) −4261.65 −0.496886 −0.248443 0.968647i \(-0.579919\pi\)
−0.248443 + 0.968647i \(0.579919\pi\)
\(420\) 5.78467 0.000672055 0
\(421\) −6235.06 −0.721801 −0.360900 0.932604i \(-0.617531\pi\)
−0.360900 + 0.932604i \(0.617531\pi\)
\(422\) −3722.04 −0.429351
\(423\) −566.266 −0.0650894
\(424\) 3335.68 0.382064
\(425\) −7896.22 −0.901231
\(426\) −4845.57 −0.551100
\(427\) −8047.06 −0.912001
\(428\) −85.8992 −0.00970115
\(429\) 0 0
\(430\) 5323.05 0.596977
\(431\) −2520.58 −0.281698 −0.140849 0.990031i \(-0.544983\pi\)
−0.140849 + 0.990031i \(0.544983\pi\)
\(432\) −1718.80 −0.191426
\(433\) −1283.89 −0.142494 −0.0712468 0.997459i \(-0.522698\pi\)
−0.0712468 + 0.997459i \(0.522698\pi\)
\(434\) 9634.15 1.06556
\(435\) −1832.26 −0.201954
\(436\) 69.6878 0.00765468
\(437\) 1565.69 0.171389
\(438\) −226.087 −0.0246641
\(439\) −16942.0 −1.84190 −0.920951 0.389677i \(-0.872586\pi\)
−0.920951 + 0.389677i \(0.872586\pi\)
\(440\) 2743.44 0.297246
\(441\) −1484.40 −0.160285
\(442\) 0 0
\(443\) −2163.00 −0.231980 −0.115990 0.993250i \(-0.537004\pi\)
−0.115990 + 0.993250i \(0.537004\pi\)
\(444\) 26.3380 0.00281519
\(445\) −4194.22 −0.446798
\(446\) −3394.83 −0.360426
\(447\) 4552.75 0.481739
\(448\) −6868.01 −0.724293
\(449\) 1673.35 0.175880 0.0879400 0.996126i \(-0.471972\pi\)
0.0879400 + 0.996126i \(0.471972\pi\)
\(450\) −2878.17 −0.301507
\(451\) −4172.85 −0.435680
\(452\) 27.7279 0.00288542
\(453\) −1750.92 −0.181602
\(454\) 12302.7 1.27180
\(455\) 0 0
\(456\) 844.046 0.0866800
\(457\) 4652.38 0.476212 0.238106 0.971239i \(-0.423473\pi\)
0.238106 + 0.971239i \(0.423473\pi\)
\(458\) −15188.7 −1.54961
\(459\) 1880.62 0.191241
\(460\) 18.2432 0.00184912
\(461\) −3460.07 −0.349570 −0.174785 0.984607i \(-0.555923\pi\)
−0.174785 + 0.984607i \(0.555923\pi\)
\(462\) 4003.66 0.403176
\(463\) 2105.64 0.211355 0.105677 0.994400i \(-0.466299\pi\)
0.105677 + 0.994400i \(0.466299\pi\)
\(464\) 11398.8 1.14047
\(465\) −2618.89 −0.261179
\(466\) −13860.9 −1.37789
\(467\) −1415.88 −0.140298 −0.0701489 0.997537i \(-0.522347\pi\)
−0.0701489 + 0.997537i \(0.522347\pi\)
\(468\) 0 0
\(469\) −9888.28 −0.973557
\(470\) −605.393 −0.0594143
\(471\) 78.2797 0.00765804
\(472\) 6218.19 0.606388
\(473\) −19613.4 −1.90661
\(474\) −1758.55 −0.170407
\(475\) 1405.89 0.135803
\(476\) 39.3756 0.00379155
\(477\) −1323.28 −0.127020
\(478\) −2718.58 −0.260136
\(479\) 985.594 0.0940145 0.0470073 0.998895i \(-0.485032\pi\)
0.0470073 + 0.998895i \(0.485032\pi\)
\(480\) 19.6177 0.00186546
\(481\) 0 0
\(482\) −4356.88 −0.411723
\(483\) 5054.16 0.476133
\(484\) 3.13874 0.000294773 0
\(485\) −6122.93 −0.573254
\(486\) 685.486 0.0639800
\(487\) −14724.7 −1.37011 −0.685053 0.728494i \(-0.740221\pi\)
−0.685053 + 0.728494i \(0.740221\pi\)
\(488\) −13681.1 −1.26909
\(489\) −51.2715 −0.00474147
\(490\) −1586.96 −0.146310
\(491\) −16301.2 −1.49830 −0.749149 0.662401i \(-0.769537\pi\)
−0.749149 + 0.662401i \(0.769537\pi\)
\(492\) −14.9589 −0.00137073
\(493\) −12472.0 −1.13937
\(494\) 0 0
\(495\) −1088.33 −0.0988221
\(496\) 16292.6 1.47492
\(497\) 7640.53 0.689587
\(498\) 8728.30 0.785391
\(499\) −3230.42 −0.289806 −0.144903 0.989446i \(-0.546287\pi\)
−0.144903 + 0.989446i \(0.546287\pi\)
\(500\) 34.4437 0.00308074
\(501\) −11758.4 −1.04856
\(502\) 10629.7 0.945076
\(503\) −3577.57 −0.317129 −0.158565 0.987349i \(-0.550687\pi\)
−0.158565 + 0.987349i \(0.550687\pi\)
\(504\) 2724.65 0.240804
\(505\) −2625.35 −0.231340
\(506\) 12626.4 1.10931
\(507\) 0 0
\(508\) −56.1552 −0.00490450
\(509\) 13864.7 1.20735 0.603674 0.797231i \(-0.293703\pi\)
0.603674 + 0.797231i \(0.293703\pi\)
\(510\) 2010.56 0.174567
\(511\) 356.496 0.0308619
\(512\) −11675.9 −1.00783
\(513\) −334.836 −0.0288175
\(514\) 3618.34 0.310502
\(515\) 5265.25 0.450514
\(516\) −70.3105 −0.00599854
\(517\) 2230.64 0.189756
\(518\) 7800.94 0.661686
\(519\) −5929.06 −0.501458
\(520\) 0 0
\(521\) −9554.66 −0.803449 −0.401725 0.915760i \(-0.631589\pi\)
−0.401725 + 0.915760i \(0.631589\pi\)
\(522\) −4546.03 −0.381177
\(523\) −19809.1 −1.65620 −0.828098 0.560583i \(-0.810577\pi\)
−0.828098 + 0.560583i \(0.810577\pi\)
\(524\) −39.4035 −0.00328502
\(525\) 4538.32 0.377274
\(526\) 14188.5 1.17614
\(527\) −17826.5 −1.47350
\(528\) 6770.73 0.558064
\(529\) 3772.38 0.310050
\(530\) −1414.71 −0.115946
\(531\) −2466.78 −0.201599
\(532\) −7.01066 −0.000571336 0
\(533\) 0 0
\(534\) −10406.3 −0.843306
\(535\) 6916.05 0.558891
\(536\) −16811.4 −1.35475
\(537\) −8353.02 −0.671246
\(538\) 15877.5 1.27235
\(539\) 5847.36 0.467279
\(540\) −3.90148 −0.000310913 0
\(541\) 1011.14 0.0803551 0.0401775 0.999193i \(-0.487208\pi\)
0.0401775 + 0.999193i \(0.487208\pi\)
\(542\) −9501.98 −0.753035
\(543\) −5659.59 −0.447286
\(544\) 133.535 0.0105244
\(545\) −5610.81 −0.440992
\(546\) 0 0
\(547\) 15745.2 1.23074 0.615372 0.788237i \(-0.289006\pi\)
0.615372 + 0.788237i \(0.289006\pi\)
\(548\) −116.545 −0.00908495
\(549\) 5427.35 0.421919
\(550\) 11337.7 0.878987
\(551\) 2220.58 0.171688
\(552\) 8592.76 0.662558
\(553\) 2772.89 0.213229
\(554\) −18357.9 −1.40785
\(555\) −2120.57 −0.162186
\(556\) −103.227 −0.00787371
\(557\) −8510.94 −0.647433 −0.323716 0.946154i \(-0.604932\pi\)
−0.323716 + 0.946154i \(0.604932\pi\)
\(558\) −6497.76 −0.492961
\(559\) 0 0
\(560\) 2897.48 0.218645
\(561\) −7408.16 −0.557528
\(562\) 10227.3 0.767639
\(563\) 16764.1 1.25493 0.627463 0.778646i \(-0.284093\pi\)
0.627463 + 0.778646i \(0.284093\pi\)
\(564\) 7.99646 0.000597006 0
\(565\) −2232.47 −0.166232
\(566\) −13076.1 −0.971080
\(567\) −1080.88 −0.0800575
\(568\) 12990.0 0.959589
\(569\) 20755.4 1.52919 0.764597 0.644508i \(-0.222938\pi\)
0.764597 + 0.644508i \(0.222938\pi\)
\(570\) −357.972 −0.0263049
\(571\) −23408.6 −1.71562 −0.857810 0.513968i \(-0.828175\pi\)
−0.857810 + 0.513968i \(0.828175\pi\)
\(572\) 0 0
\(573\) 7343.81 0.535414
\(574\) −4430.62 −0.322179
\(575\) 14312.6 1.03805
\(576\) 4632.14 0.335080
\(577\) −10387.2 −0.749436 −0.374718 0.927139i \(-0.622261\pi\)
−0.374718 + 0.927139i \(0.622261\pi\)
\(578\) −173.537 −0.0124882
\(579\) 5776.97 0.414650
\(580\) 25.8740 0.00185234
\(581\) −13762.8 −0.982752
\(582\) −15191.7 −1.08198
\(583\) 5212.68 0.370304
\(584\) 606.092 0.0429457
\(585\) 0 0
\(586\) 8200.63 0.578097
\(587\) 2898.42 0.203800 0.101900 0.994795i \(-0.467508\pi\)
0.101900 + 0.994795i \(0.467508\pi\)
\(588\) 20.9617 0.00147015
\(589\) 3173.94 0.222037
\(590\) −2637.23 −0.184022
\(591\) 5459.85 0.380014
\(592\) 13192.4 0.915888
\(593\) −8805.33 −0.609766 −0.304883 0.952390i \(-0.598617\pi\)
−0.304883 + 0.952390i \(0.598617\pi\)
\(594\) −2700.27 −0.186521
\(595\) −3170.27 −0.218434
\(596\) −64.2910 −0.00441856
\(597\) −3821.91 −0.262011
\(598\) 0 0
\(599\) −20236.8 −1.38039 −0.690194 0.723624i \(-0.742475\pi\)
−0.690194 + 0.723624i \(0.742475\pi\)
\(600\) 7715.77 0.524992
\(601\) −9884.92 −0.670906 −0.335453 0.942057i \(-0.608889\pi\)
−0.335453 + 0.942057i \(0.608889\pi\)
\(602\) −20825.0 −1.40991
\(603\) 6669.17 0.450397
\(604\) 24.7255 0.00166567
\(605\) −252.711 −0.0169821
\(606\) −6513.78 −0.436641
\(607\) 22919.3 1.53256 0.766281 0.642505i \(-0.222105\pi\)
0.766281 + 0.642505i \(0.222105\pi\)
\(608\) −23.7754 −0.00158589
\(609\) 7168.21 0.476963
\(610\) 5802.36 0.385132
\(611\) 0 0
\(612\) −26.5569 −0.00175409
\(613\) −916.052 −0.0603572 −0.0301786 0.999545i \(-0.509608\pi\)
−0.0301786 + 0.999545i \(0.509608\pi\)
\(614\) −2634.61 −0.173166
\(615\) 1204.40 0.0789690
\(616\) −10733.0 −0.702019
\(617\) 30179.4 1.96917 0.984584 0.174915i \(-0.0559650\pi\)
0.984584 + 0.174915i \(0.0559650\pi\)
\(618\) 13063.7 0.850320
\(619\) −5571.12 −0.361748 −0.180874 0.983506i \(-0.557893\pi\)
−0.180874 + 0.983506i \(0.557893\pi\)
\(620\) 36.9824 0.00239556
\(621\) −3408.78 −0.220273
\(622\) −10250.0 −0.660751
\(623\) 16408.8 1.05522
\(624\) 0 0
\(625\) 11397.5 0.729443
\(626\) −21177.5 −1.35211
\(627\) 1318.99 0.0840120
\(628\) −1.10542 −7.02403e−5 0
\(629\) −14434.5 −0.915007
\(630\) −1155.56 −0.0730773
\(631\) 11360.1 0.716703 0.358352 0.933587i \(-0.383339\pi\)
0.358352 + 0.933587i \(0.383339\pi\)
\(632\) 4714.30 0.296717
\(633\) −3958.32 −0.248545
\(634\) −3426.31 −0.214631
\(635\) 4521.26 0.282552
\(636\) 18.6865 0.00116504
\(637\) 0 0
\(638\) 17907.8 1.11125
\(639\) −5153.17 −0.319024
\(640\) 4899.89 0.302633
\(641\) −24709.8 −1.52259 −0.761293 0.648408i \(-0.775435\pi\)
−0.761293 + 0.648408i \(0.775435\pi\)
\(642\) 17159.5 1.05488
\(643\) −15226.6 −0.933869 −0.466934 0.884292i \(-0.654642\pi\)
−0.466934 + 0.884292i \(0.654642\pi\)
\(644\) −71.3717 −0.00436714
\(645\) 5660.95 0.345581
\(646\) −2436.68 −0.148405
\(647\) 16706.6 1.01515 0.507576 0.861607i \(-0.330542\pi\)
0.507576 + 0.861607i \(0.330542\pi\)
\(648\) −1837.64 −0.111403
\(649\) 9717.18 0.587724
\(650\) 0 0
\(651\) 10245.7 0.616838
\(652\) 0.724024 4.34892e−5 0
\(653\) −28205.8 −1.69032 −0.845158 0.534516i \(-0.820494\pi\)
−0.845158 + 0.534516i \(0.820494\pi\)
\(654\) −13921.0 −0.832349
\(655\) 3172.51 0.189252
\(656\) −7492.77 −0.445951
\(657\) −240.439 −0.0142777
\(658\) 2368.44 0.140321
\(659\) −11424.2 −0.675299 −0.337649 0.941272i \(-0.609632\pi\)
−0.337649 + 0.941272i \(0.609632\pi\)
\(660\) 15.3688 0.000906407 0
\(661\) 26518.2 1.56042 0.780211 0.625516i \(-0.215112\pi\)
0.780211 + 0.625516i \(0.215112\pi\)
\(662\) −6892.10 −0.404636
\(663\) 0 0
\(664\) −23398.7 −1.36754
\(665\) 564.453 0.0329151
\(666\) −5261.36 −0.306116
\(667\) 22606.5 1.31234
\(668\) 166.045 0.00961749
\(669\) −3610.34 −0.208645
\(670\) 7129.98 0.411127
\(671\) −21379.5 −1.23002
\(672\) −76.7488 −0.00440573
\(673\) 22816.8 1.30687 0.653434 0.756984i \(-0.273328\pi\)
0.653434 + 0.756984i \(0.273328\pi\)
\(674\) 5334.27 0.304849
\(675\) −3060.88 −0.174538
\(676\) 0 0
\(677\) 17737.6 1.00696 0.503478 0.864008i \(-0.332053\pi\)
0.503478 + 0.864008i \(0.332053\pi\)
\(678\) −5539.01 −0.313753
\(679\) 23954.3 1.35388
\(680\) −5389.89 −0.303960
\(681\) 13083.7 0.736224
\(682\) 25596.1 1.43713
\(683\) 18878.4 1.05763 0.528816 0.848737i \(-0.322636\pi\)
0.528816 + 0.848737i \(0.322636\pi\)
\(684\) 4.72835 0.000264317 0
\(685\) 9383.45 0.523391
\(686\) 19120.1 1.06415
\(687\) −16152.9 −0.897045
\(688\) −35217.8 −1.95155
\(689\) 0 0
\(690\) −3644.32 −0.201068
\(691\) −11692.8 −0.643726 −0.321863 0.946786i \(-0.604309\pi\)
−0.321863 + 0.946786i \(0.604309\pi\)
\(692\) 83.7265 0.00459943
\(693\) 4257.81 0.233392
\(694\) −7874.82 −0.430726
\(695\) 8311.14 0.453611
\(696\) 12186.9 0.663714
\(697\) 8198.19 0.445522
\(698\) 19513.3 1.05815
\(699\) −14740.8 −0.797638
\(700\) −64.0873 −0.00346039
\(701\) 20658.1 1.11304 0.556522 0.830833i \(-0.312135\pi\)
0.556522 + 0.830833i \(0.312135\pi\)
\(702\) 0 0
\(703\) 2569.99 0.137879
\(704\) −18247.0 −0.976861
\(705\) −643.823 −0.0343940
\(706\) −21547.3 −1.14864
\(707\) 10271.0 0.546365
\(708\) 34.8343 0.00184909
\(709\) 20695.8 1.09626 0.548128 0.836394i \(-0.315341\pi\)
0.548128 + 0.836394i \(0.315341\pi\)
\(710\) −5509.23 −0.291208
\(711\) −1870.18 −0.0986461
\(712\) 27897.1 1.46838
\(713\) 32312.1 1.69719
\(714\) −7865.79 −0.412283
\(715\) 0 0
\(716\) 117.956 0.00615674
\(717\) −2891.16 −0.150589
\(718\) 15489.6 0.805109
\(719\) −26299.2 −1.36411 −0.682053 0.731302i \(-0.738913\pi\)
−0.682053 + 0.731302i \(0.738913\pi\)
\(720\) −1954.21 −0.101152
\(721\) −20598.9 −1.06400
\(722\) −18914.9 −0.974986
\(723\) −4633.45 −0.238340
\(724\) 79.9213 0.00410256
\(725\) 20299.3 1.03986
\(726\) −627.004 −0.0320528
\(727\) −16915.6 −0.862952 −0.431476 0.902125i \(-0.642007\pi\)
−0.431476 + 0.902125i \(0.642007\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −257.053 −0.0130328
\(731\) 38533.5 1.94967
\(732\) −76.6417 −0.00386989
\(733\) 13203.1 0.665302 0.332651 0.943050i \(-0.392057\pi\)
0.332651 + 0.943050i \(0.392057\pi\)
\(734\) 19005.8 0.955746
\(735\) −1687.70 −0.0846964
\(736\) −242.044 −0.0121221
\(737\) −26271.3 −1.31305
\(738\) 2988.24 0.149050
\(739\) 16813.9 0.836954 0.418477 0.908227i \(-0.362564\pi\)
0.418477 + 0.908227i \(0.362564\pi\)
\(740\) 29.9453 0.00148758
\(741\) 0 0
\(742\) 5534.68 0.273834
\(743\) 32682.1 1.61371 0.806857 0.590747i \(-0.201167\pi\)
0.806857 + 0.590747i \(0.201167\pi\)
\(744\) 17419.1 0.858355
\(745\) 5176.30 0.254557
\(746\) −11087.4 −0.544156
\(747\) 9282.37 0.454651
\(748\) 104.613 0.00511370
\(749\) −27057.2 −1.31996
\(750\) −6880.57 −0.334991
\(751\) 2157.76 0.104844 0.0524219 0.998625i \(-0.483306\pi\)
0.0524219 + 0.998625i \(0.483306\pi\)
\(752\) 4005.35 0.194229
\(753\) 11304.5 0.547090
\(754\) 0 0
\(755\) −1990.74 −0.0959606
\(756\) 15.2635 0.000734296 0
\(757\) 13769.6 0.661117 0.330558 0.943786i \(-0.392763\pi\)
0.330558 + 0.943786i \(0.392763\pi\)
\(758\) −33562.6 −1.60824
\(759\) 13427.9 0.642165
\(760\) 959.648 0.0458028
\(761\) −16905.2 −0.805272 −0.402636 0.915360i \(-0.631906\pi\)
−0.402636 + 0.915360i \(0.631906\pi\)
\(762\) 11217.7 0.533302
\(763\) 21950.8 1.04151
\(764\) −103.705 −0.00491087
\(765\) 2138.19 0.101054
\(766\) −13394.7 −0.631813
\(767\) 0 0
\(768\) −195.208 −0.00917185
\(769\) 1153.35 0.0540845 0.0270422 0.999634i \(-0.491391\pi\)
0.0270422 + 0.999634i \(0.491391\pi\)
\(770\) 4552.01 0.213043
\(771\) 3848.03 0.179745
\(772\) −81.5787 −0.00380322
\(773\) −20713.9 −0.963811 −0.481905 0.876223i \(-0.660055\pi\)
−0.481905 + 0.876223i \(0.660055\pi\)
\(774\) 14045.4 0.652265
\(775\) 29014.3 1.34480
\(776\) 40725.7 1.88398
\(777\) 8296.14 0.383040
\(778\) 31875.1 1.46887
\(779\) −1459.65 −0.0671341
\(780\) 0 0
\(781\) 20299.4 0.930053
\(782\) −24806.5 −1.13437
\(783\) −4834.61 −0.220658
\(784\) 10499.5 0.478294
\(785\) 89.0010 0.00404660
\(786\) 7871.35 0.357203
\(787\) 10870.2 0.492353 0.246177 0.969225i \(-0.420826\pi\)
0.246177 + 0.969225i \(0.420826\pi\)
\(788\) −77.1006 −0.00348553
\(789\) 15089.2 0.680850
\(790\) −1999.41 −0.0900451
\(791\) 8733.95 0.392596
\(792\) 7238.86 0.324775
\(793\) 0 0
\(794\) −39078.4 −1.74665
\(795\) −1504.52 −0.0671192
\(796\) 53.9706 0.00240319
\(797\) 12026.6 0.534511 0.267255 0.963626i \(-0.413883\pi\)
0.267255 + 0.963626i \(0.413883\pi\)
\(798\) 1400.47 0.0621255
\(799\) −4382.43 −0.194042
\(800\) −217.341 −0.00960519
\(801\) −11066.9 −0.488177
\(802\) −15330.7 −0.674996
\(803\) 947.142 0.0416238
\(804\) −94.1778 −0.00413109
\(805\) 5746.39 0.251594
\(806\) 0 0
\(807\) 16885.4 0.736547
\(808\) 17462.1 0.760289
\(809\) −32384.0 −1.40737 −0.703685 0.710512i \(-0.748463\pi\)
−0.703685 + 0.710512i \(0.748463\pi\)
\(810\) 779.371 0.0338078
\(811\) 42506.8 1.84046 0.920231 0.391375i \(-0.128000\pi\)
0.920231 + 0.391375i \(0.128000\pi\)
\(812\) −101.225 −0.00437476
\(813\) −10105.2 −0.435921
\(814\) 20725.6 0.892423
\(815\) −58.2937 −0.00250545
\(816\) −13302.1 −0.570670
\(817\) −6860.72 −0.293790
\(818\) 9795.47 0.418693
\(819\) 0 0
\(820\) −17.0077 −0.000724312 0
\(821\) −20052.6 −0.852427 −0.426213 0.904623i \(-0.640153\pi\)
−0.426213 + 0.904623i \(0.640153\pi\)
\(822\) 23281.4 0.987872
\(823\) −31625.5 −1.33948 −0.669742 0.742594i \(-0.733595\pi\)
−0.669742 + 0.742594i \(0.733595\pi\)
\(824\) −35020.9 −1.48060
\(825\) 12057.5 0.508832
\(826\) 10317.4 0.434612
\(827\) 5440.97 0.228780 0.114390 0.993436i \(-0.463509\pi\)
0.114390 + 0.993436i \(0.463509\pi\)
\(828\) 48.1367 0.00202037
\(829\) −24845.8 −1.04093 −0.520465 0.853883i \(-0.674241\pi\)
−0.520465 + 0.853883i \(0.674241\pi\)
\(830\) 9923.75 0.415010
\(831\) −19523.2 −0.814986
\(832\) 0 0
\(833\) −11488.0 −0.477834
\(834\) 20620.9 0.856165
\(835\) −13368.9 −0.554071
\(836\) −18.6260 −0.000770566 0
\(837\) −6910.24 −0.285368
\(838\) −12021.8 −0.495568
\(839\) 45887.8 1.88823 0.944113 0.329621i \(-0.106921\pi\)
0.944113 + 0.329621i \(0.106921\pi\)
\(840\) 3097.82 0.127244
\(841\) 7673.40 0.314625
\(842\) −17588.7 −0.719887
\(843\) 10876.5 0.444375
\(844\) 55.8969 0.00227968
\(845\) 0 0
\(846\) −1597.40 −0.0649168
\(847\) 988.665 0.0401073
\(848\) 9359.88 0.379033
\(849\) −13906.2 −0.562144
\(850\) −22274.7 −0.898842
\(851\) 26163.7 1.05391
\(852\) 72.7698 0.00292612
\(853\) −33655.3 −1.35092 −0.675460 0.737397i \(-0.736055\pi\)
−0.675460 + 0.737397i \(0.736055\pi\)
\(854\) −22700.2 −0.909583
\(855\) −380.696 −0.0152275
\(856\) −46000.9 −1.83677
\(857\) 41365.6 1.64880 0.824399 0.566009i \(-0.191513\pi\)
0.824399 + 0.566009i \(0.191513\pi\)
\(858\) 0 0
\(859\) 14866.0 0.590480 0.295240 0.955423i \(-0.404600\pi\)
0.295240 + 0.955423i \(0.404600\pi\)
\(860\) −79.9404 −0.00316970
\(861\) −4711.87 −0.186504
\(862\) −7110.37 −0.280952
\(863\) 15469.1 0.610167 0.305083 0.952326i \(-0.401316\pi\)
0.305083 + 0.952326i \(0.401316\pi\)
\(864\) 51.7634 0.00203822
\(865\) −6741.12 −0.264977
\(866\) −3621.76 −0.142116
\(867\) −184.553 −0.00722925
\(868\) −144.684 −0.00565770
\(869\) 7367.05 0.287584
\(870\) −5168.67 −0.201419
\(871\) 0 0
\(872\) 37319.4 1.44930
\(873\) −16156.0 −0.626345
\(874\) 4416.69 0.170934
\(875\) 10849.3 0.419171
\(876\) 3.39533 0.000130956 0
\(877\) 38100.7 1.46701 0.733505 0.679684i \(-0.237883\pi\)
0.733505 + 0.679684i \(0.237883\pi\)
\(878\) −47792.0 −1.83702
\(879\) 8721.21 0.334652
\(880\) 7698.06 0.294888
\(881\) 3879.84 0.148371 0.0741857 0.997244i \(-0.476364\pi\)
0.0741857 + 0.997244i \(0.476364\pi\)
\(882\) −4187.38 −0.159860
\(883\) 13046.5 0.497225 0.248613 0.968603i \(-0.420025\pi\)
0.248613 + 0.968603i \(0.420025\pi\)
\(884\) 0 0
\(885\) −2804.64 −0.106528
\(886\) −6101.66 −0.231365
\(887\) −32833.2 −1.24288 −0.621438 0.783463i \(-0.713451\pi\)
−0.621438 + 0.783463i \(0.713451\pi\)
\(888\) 14104.6 0.533017
\(889\) −17688.2 −0.667315
\(890\) −11831.6 −0.445613
\(891\) −2871.69 −0.107974
\(892\) 50.9829 0.00191372
\(893\) 780.274 0.0292395
\(894\) 12843.0 0.480462
\(895\) −9497.06 −0.354695
\(896\) −19169.5 −0.714741
\(897\) 0 0
\(898\) 4720.39 0.175414
\(899\) 45827.6 1.70015
\(900\) 43.2238 0.00160088
\(901\) −10241.1 −0.378668
\(902\) −11771.3 −0.434525
\(903\) −22147.0 −0.816173
\(904\) 14848.9 0.546314
\(905\) −6434.74 −0.236352
\(906\) −4939.23 −0.181120
\(907\) 21346.3 0.781468 0.390734 0.920504i \(-0.372221\pi\)
0.390734 + 0.920504i \(0.372221\pi\)
\(908\) −184.760 −0.00675272
\(909\) −6927.28 −0.252765
\(910\) 0 0
\(911\) 7792.71 0.283407 0.141704 0.989909i \(-0.454742\pi\)
0.141704 + 0.989909i \(0.454742\pi\)
\(912\) 2368.38 0.0859923
\(913\) −36565.2 −1.32545
\(914\) 13124.0 0.474950
\(915\) 6170.69 0.222947
\(916\) 228.101 0.00822779
\(917\) −12411.6 −0.446965
\(918\) 5305.09 0.190734
\(919\) −31352.0 −1.12536 −0.562681 0.826674i \(-0.690230\pi\)
−0.562681 + 0.826674i \(0.690230\pi\)
\(920\) 9769.64 0.350104
\(921\) −2801.85 −0.100243
\(922\) −9760.61 −0.348643
\(923\) 0 0
\(924\) −60.1262 −0.00214070
\(925\) 23493.4 0.835089
\(926\) 5939.85 0.210794
\(927\) 13893.0 0.492238
\(928\) −343.286 −0.0121432
\(929\) −12675.3 −0.447646 −0.223823 0.974630i \(-0.571854\pi\)
−0.223823 + 0.974630i \(0.571854\pi\)
\(930\) −7387.71 −0.260487
\(931\) 2045.39 0.0720032
\(932\) 208.161 0.00731601
\(933\) −10900.7 −0.382499
\(934\) −3994.09 −0.139926
\(935\) −8422.80 −0.294604
\(936\) 0 0
\(937\) −12308.5 −0.429138 −0.214569 0.976709i \(-0.568835\pi\)
−0.214569 + 0.976709i \(0.568835\pi\)
\(938\) −27894.1 −0.970976
\(939\) −22521.8 −0.782717
\(940\) 9.09167 0.000315466 0
\(941\) −20465.2 −0.708978 −0.354489 0.935060i \(-0.615345\pi\)
−0.354489 + 0.935060i \(0.615345\pi\)
\(942\) 220.821 0.00763774
\(943\) −14859.9 −0.513155
\(944\) 17448.2 0.601578
\(945\) −1228.92 −0.0423034
\(946\) −55328.0 −1.90155
\(947\) −11170.8 −0.383318 −0.191659 0.981462i \(-0.561387\pi\)
−0.191659 + 0.981462i \(0.561387\pi\)
\(948\) 26.4096 0.000904792 0
\(949\) 0 0
\(950\) 3965.91 0.135443
\(951\) −3643.81 −0.124247
\(952\) 21086.5 0.717876
\(953\) 14109.4 0.479587 0.239794 0.970824i \(-0.422920\pi\)
0.239794 + 0.970824i \(0.422920\pi\)
\(954\) −3732.87 −0.126684
\(955\) 8349.64 0.282919
\(956\) 40.8271 0.00138122
\(957\) 19044.6 0.643285
\(958\) 2780.29 0.0937653
\(959\) −36710.2 −1.23612
\(960\) 5266.57 0.177060
\(961\) 35711.6 1.19874
\(962\) 0 0
\(963\) 18248.8 0.610652
\(964\) 65.4307 0.00218608
\(965\) 6568.19 0.219106
\(966\) 14257.4 0.474870
\(967\) 40785.8 1.35634 0.678171 0.734904i \(-0.262773\pi\)
0.678171 + 0.734904i \(0.262773\pi\)
\(968\) 1680.87 0.0558110
\(969\) −2591.36 −0.0859096
\(970\) −17272.4 −0.571734
\(971\) 4230.29 0.139811 0.0699055 0.997554i \(-0.477730\pi\)
0.0699055 + 0.997554i \(0.477730\pi\)
\(972\) −10.2945 −0.000339708 0
\(973\) −32515.1 −1.07131
\(974\) −41537.4 −1.36647
\(975\) 0 0
\(976\) −38389.0 −1.25902
\(977\) 59925.0 1.96230 0.981151 0.193242i \(-0.0619004\pi\)
0.981151 + 0.193242i \(0.0619004\pi\)
\(978\) −144.633 −0.00472890
\(979\) 43594.9 1.42319
\(980\) 23.8327 0.000776844 0
\(981\) −14804.8 −0.481834
\(982\) −45984.6 −1.49433
\(983\) 23333.3 0.757087 0.378543 0.925584i \(-0.376425\pi\)
0.378543 + 0.925584i \(0.376425\pi\)
\(984\) −8010.83 −0.259528
\(985\) 6207.64 0.200804
\(986\) −35182.5 −1.13635
\(987\) 2518.79 0.0812298
\(988\) 0 0
\(989\) −69845.2 −2.24565
\(990\) −3070.11 −0.0985601
\(991\) −32523.5 −1.04253 −0.521263 0.853396i \(-0.674539\pi\)
−0.521263 + 0.853396i \(0.674539\pi\)
\(992\) −490.668 −0.0157044
\(993\) −7329.61 −0.234238
\(994\) 21553.4 0.687759
\(995\) −4345.37 −0.138450
\(996\) −131.080 −0.00417010
\(997\) −7114.35 −0.225992 −0.112996 0.993595i \(-0.536045\pi\)
−0.112996 + 0.993595i \(0.536045\pi\)
\(998\) −9112.77 −0.289038
\(999\) −5595.35 −0.177206
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.1.7 9
3.2 odd 2 1521.4.a.bi.1.3 9
13.5 odd 4 507.4.b.k.337.6 18
13.8 odd 4 507.4.b.k.337.13 18
13.12 even 2 507.4.a.p.1.3 yes 9
39.38 odd 2 1521.4.a.bf.1.7 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.4.a.o.1.7 9 1.1 even 1 trivial
507.4.a.p.1.3 yes 9 13.12 even 2
507.4.b.k.337.6 18 13.5 odd 4
507.4.b.k.337.13 18 13.8 odd 4
1521.4.a.bf.1.7 9 39.38 odd 2
1521.4.a.bi.1.3 9 3.2 odd 2