Properties

Label 1815.4.a.r.1.3
Level $1815$
Weight $4$
Character 1815.1
Self dual yes
Analytic conductor $107.088$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(107.088466660\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.47528.1
Defining polynomial: \(x^{3} - x^{2} - 26 x - 22\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-4.06484\) of defining polynomial
Character \(\chi\) \(=\) 1815.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.06484 q^{2} +3.00000 q^{3} +17.6526 q^{4} -5.00000 q^{5} +15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+5.06484 q^{2} +3.00000 q^{3} +17.6526 q^{4} -5.00000 q^{5} +15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} -25.3242 q^{10} +52.9577 q^{12} -22.6949 q^{13} -138.953 q^{14} -15.0000 q^{15} +106.392 q^{16} +41.1755 q^{17} +45.5835 q^{18} +142.128 q^{19} -88.2628 q^{20} -82.3044 q^{21} +176.166 q^{23} +146.666 q^{24} +25.0000 q^{25} -114.946 q^{26} +27.0000 q^{27} -484.295 q^{28} -76.2044 q^{29} -75.9725 q^{30} +197.373 q^{31} +147.751 q^{32} +208.547 q^{34} +137.174 q^{35} +158.873 q^{36} +367.297 q^{37} +719.856 q^{38} -68.0846 q^{39} -244.443 q^{40} +238.279 q^{41} -416.858 q^{42} -30.2905 q^{43} -45.0000 q^{45} +892.254 q^{46} +137.390 q^{47} +319.177 q^{48} +409.668 q^{49} +126.621 q^{50} +123.526 q^{51} -400.623 q^{52} +638.665 q^{53} +136.751 q^{54} -1341.25 q^{56} +426.385 q^{57} -385.963 q^{58} +103.146 q^{59} -264.788 q^{60} -605.596 q^{61} +999.662 q^{62} -246.913 q^{63} -102.804 q^{64} +113.474 q^{65} -704.925 q^{67} +726.852 q^{68} +528.499 q^{69} +694.764 q^{70} -782.162 q^{71} +439.998 q^{72} +243.132 q^{73} +1860.30 q^{74} +75.0000 q^{75} +2508.93 q^{76} -344.837 q^{78} +532.874 q^{79} -531.962 q^{80} +81.0000 q^{81} +1206.84 q^{82} -1204.91 q^{83} -1452.88 q^{84} -205.877 q^{85} -153.416 q^{86} -228.613 q^{87} +1058.49 q^{89} -227.918 q^{90} +622.629 q^{91} +3109.79 q^{92} +592.119 q^{93} +695.857 q^{94} -710.641 q^{95} +443.254 q^{96} -85.1964 q^{97} +2074.90 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} - 10 q^{10} + 90 q^{12} - 114 q^{13} - 68 q^{14} - 45 q^{15} + 178 q^{16} + 104 q^{17} + 18 q^{18} + 58 q^{19} - 150 q^{20} - 30 q^{21} + 120 q^{23} - 54 q^{24} + 75 q^{25} - 120 q^{26} + 81 q^{27} - 676 q^{28} + 220 q^{29} - 30 q^{30} + 248 q^{31} + 258 q^{32} - 80 q^{34} + 50 q^{35} + 270 q^{36} + 838 q^{37} + 600 q^{38} - 342 q^{39} + 90 q^{40} - 156 q^{41} - 204 q^{42} - 122 q^{43} - 135 q^{45} + 1256 q^{46} + 504 q^{47} + 534 q^{48} + 279 q^{49} + 50 q^{50} + 312 q^{51} - 520 q^{52} + 282 q^{53} + 54 q^{54} - 1644 q^{56} + 174 q^{57} - 1644 q^{58} + 548 q^{59} - 450 q^{60} - 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} + 570 q^{65} - 428 q^{67} + 1704 q^{68} + 360 q^{69} + 340 q^{70} - 912 q^{71} - 162 q^{72} - 618 q^{73} + 1612 q^{74} + 225 q^{75} + 2752 q^{76} - 360 q^{78} + 542 q^{79} - 890 q^{80} + 243 q^{81} + 3372 q^{82} - 2028 q^{84} - 520 q^{85} - 1548 q^{86} + 660 q^{87} + 790 q^{89} - 90 q^{90} - 772 q^{91} + 1912 q^{92} + 744 q^{93} + 424 q^{94} - 290 q^{95} + 774 q^{96} + 2074 q^{97} + 3978 q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.06484 1.79069 0.895345 0.445373i \(-0.146929\pi\)
0.895345 + 0.445373i \(0.146929\pi\)
\(3\) 3.00000 0.577350
\(4\) 17.6526 2.20657
\(5\) −5.00000 −0.447214
\(6\) 15.1945 1.03386
\(7\) −27.4348 −1.48134 −0.740670 0.671869i \(-0.765492\pi\)
−0.740670 + 0.671869i \(0.765492\pi\)
\(8\) 48.8887 2.16059
\(9\) 9.00000 0.333333
\(10\) −25.3242 −0.800821
\(11\) 0 0
\(12\) 52.9577 1.27396
\(13\) −22.6949 −0.484187 −0.242093 0.970253i \(-0.577834\pi\)
−0.242093 + 0.970253i \(0.577834\pi\)
\(14\) −138.953 −2.65262
\(15\) −15.0000 −0.258199
\(16\) 106.392 1.66238
\(17\) 41.1755 0.587442 0.293721 0.955891i \(-0.405106\pi\)
0.293721 + 0.955891i \(0.405106\pi\)
\(18\) 45.5835 0.596897
\(19\) 142.128 1.71613 0.858064 0.513542i \(-0.171667\pi\)
0.858064 + 0.513542i \(0.171667\pi\)
\(20\) −88.2628 −0.986808
\(21\) −82.3044 −0.855252
\(22\) 0 0
\(23\) 176.166 1.59710 0.798548 0.601931i \(-0.205602\pi\)
0.798548 + 0.601931i \(0.205602\pi\)
\(24\) 146.666 1.24742
\(25\) 25.0000 0.200000
\(26\) −114.946 −0.867028
\(27\) 27.0000 0.192450
\(28\) −484.295 −3.26868
\(29\) −76.2044 −0.487959 −0.243979 0.969780i \(-0.578453\pi\)
−0.243979 + 0.969780i \(0.578453\pi\)
\(30\) −75.9725 −0.462354
\(31\) 197.373 1.14352 0.571762 0.820420i \(-0.306260\pi\)
0.571762 + 0.820420i \(0.306260\pi\)
\(32\) 147.751 0.816218
\(33\) 0 0
\(34\) 208.547 1.05193
\(35\) 137.174 0.662475
\(36\) 158.873 0.735523
\(37\) 367.297 1.63198 0.815989 0.578067i \(-0.196193\pi\)
0.815989 + 0.578067i \(0.196193\pi\)
\(38\) 719.856 3.07305
\(39\) −68.0846 −0.279545
\(40\) −244.443 −0.966247
\(41\) 238.279 0.907633 0.453817 0.891095i \(-0.350062\pi\)
0.453817 + 0.891095i \(0.350062\pi\)
\(42\) −416.858 −1.53149
\(43\) −30.2905 −0.107425 −0.0537123 0.998556i \(-0.517105\pi\)
−0.0537123 + 0.998556i \(0.517105\pi\)
\(44\) 0 0
\(45\) −45.0000 −0.149071
\(46\) 892.254 2.85990
\(47\) 137.390 0.426391 0.213195 0.977010i \(-0.431613\pi\)
0.213195 + 0.977010i \(0.431613\pi\)
\(48\) 319.177 0.959777
\(49\) 409.668 1.19437
\(50\) 126.621 0.358138
\(51\) 123.526 0.339160
\(52\) −400.623 −1.06839
\(53\) 638.665 1.65523 0.827617 0.561293i \(-0.189696\pi\)
0.827617 + 0.561293i \(0.189696\pi\)
\(54\) 136.751 0.344618
\(55\) 0 0
\(56\) −1341.25 −3.20057
\(57\) 426.385 0.990807
\(58\) −385.963 −0.873783
\(59\) 103.146 0.227601 0.113800 0.993504i \(-0.463698\pi\)
0.113800 + 0.993504i \(0.463698\pi\)
\(60\) −264.788 −0.569734
\(61\) −605.596 −1.27113 −0.635563 0.772049i \(-0.719232\pi\)
−0.635563 + 0.772049i \(0.719232\pi\)
\(62\) 999.662 2.04770
\(63\) −246.913 −0.493780
\(64\) −102.804 −0.200789
\(65\) 113.474 0.216535
\(66\) 0 0
\(67\) −704.925 −1.28538 −0.642688 0.766128i \(-0.722181\pi\)
−0.642688 + 0.766128i \(0.722181\pi\)
\(68\) 726.852 1.29623
\(69\) 528.499 0.922084
\(70\) 694.764 1.18629
\(71\) −782.162 −1.30740 −0.653701 0.756753i \(-0.726785\pi\)
−0.653701 + 0.756753i \(0.726785\pi\)
\(72\) 439.998 0.720198
\(73\) 243.132 0.389814 0.194907 0.980822i \(-0.437560\pi\)
0.194907 + 0.980822i \(0.437560\pi\)
\(74\) 1860.30 2.92237
\(75\) 75.0000 0.115470
\(76\) 2508.93 3.78676
\(77\) 0 0
\(78\) −344.837 −0.500579
\(79\) 532.874 0.758899 0.379449 0.925212i \(-0.376113\pi\)
0.379449 + 0.925212i \(0.376113\pi\)
\(80\) −531.962 −0.743440
\(81\) 81.0000 0.111111
\(82\) 1206.84 1.62529
\(83\) −1204.91 −1.59344 −0.796722 0.604345i \(-0.793435\pi\)
−0.796722 + 0.604345i \(0.793435\pi\)
\(84\) −1452.88 −1.88717
\(85\) −205.877 −0.262712
\(86\) −153.416 −0.192364
\(87\) −228.613 −0.281723
\(88\) 0 0
\(89\) 1058.49 1.26067 0.630337 0.776322i \(-0.282917\pi\)
0.630337 + 0.776322i \(0.282917\pi\)
\(90\) −227.918 −0.266940
\(91\) 622.629 0.717245
\(92\) 3109.79 3.52411
\(93\) 592.119 0.660214
\(94\) 695.857 0.763533
\(95\) −710.641 −0.767476
\(96\) 443.254 0.471244
\(97\) −85.1964 −0.0891792 −0.0445896 0.999005i \(-0.514198\pi\)
−0.0445896 + 0.999005i \(0.514198\pi\)
\(98\) 2074.90 2.13874
\(99\) 0 0
\(100\) 441.314 0.441314
\(101\) 7.81823 0.00770241 0.00385120 0.999993i \(-0.498774\pi\)
0.00385120 + 0.999993i \(0.498774\pi\)
\(102\) 625.641 0.607330
\(103\) 12.4770 0.0119359 0.00596794 0.999982i \(-0.498100\pi\)
0.00596794 + 0.999982i \(0.498100\pi\)
\(104\) −1109.52 −1.04613
\(105\) 411.522 0.382480
\(106\) 3234.73 2.96401
\(107\) 1376.81 1.24393 0.621967 0.783043i \(-0.286334\pi\)
0.621967 + 0.783043i \(0.286334\pi\)
\(108\) 476.619 0.424655
\(109\) −610.189 −0.536197 −0.268099 0.963391i \(-0.586395\pi\)
−0.268099 + 0.963391i \(0.586395\pi\)
\(110\) 0 0
\(111\) 1101.89 0.942223
\(112\) −2918.86 −2.46255
\(113\) −36.7727 −0.0306132 −0.0153066 0.999883i \(-0.504872\pi\)
−0.0153066 + 0.999883i \(0.504872\pi\)
\(114\) 2159.57 1.77423
\(115\) −880.832 −0.714243
\(116\) −1345.20 −1.07672
\(117\) −204.254 −0.161396
\(118\) 522.416 0.407562
\(119\) −1129.64 −0.870201
\(120\) −733.330 −0.557863
\(121\) 0 0
\(122\) −3067.25 −2.27619
\(123\) 714.838 0.524022
\(124\) 3484.14 2.52326
\(125\) −125.000 −0.0894427
\(126\) −1250.57 −0.884207
\(127\) 54.5310 0.0381011 0.0190506 0.999819i \(-0.493936\pi\)
0.0190506 + 0.999819i \(0.493936\pi\)
\(128\) −1702.69 −1.17577
\(129\) −90.8715 −0.0620216
\(130\) 574.729 0.387747
\(131\) −2377.83 −1.58589 −0.792947 0.609290i \(-0.791454\pi\)
−0.792947 + 0.609290i \(0.791454\pi\)
\(132\) 0 0
\(133\) −3899.26 −2.54217
\(134\) −3570.33 −2.30171
\(135\) −135.000 −0.0860663
\(136\) 2013.01 1.26922
\(137\) −3078.41 −1.91976 −0.959878 0.280417i \(-0.909527\pi\)
−0.959878 + 0.280417i \(0.909527\pi\)
\(138\) 2676.76 1.65117
\(139\) 1197.18 0.730530 0.365265 0.930904i \(-0.380978\pi\)
0.365265 + 0.930904i \(0.380978\pi\)
\(140\) 2421.47 1.46180
\(141\) 412.169 0.246177
\(142\) −3961.52 −2.34115
\(143\) 0 0
\(144\) 957.532 0.554128
\(145\) 381.022 0.218222
\(146\) 1231.42 0.698035
\(147\) 1229.00 0.689569
\(148\) 6483.73 3.60108
\(149\) 749.456 0.412066 0.206033 0.978545i \(-0.433945\pi\)
0.206033 + 0.978545i \(0.433945\pi\)
\(150\) 379.863 0.206771
\(151\) 2645.72 1.42586 0.712931 0.701234i \(-0.247367\pi\)
0.712931 + 0.701234i \(0.247367\pi\)
\(152\) 6948.46 3.70786
\(153\) 370.579 0.195814
\(154\) 0 0
\(155\) −986.865 −0.511399
\(156\) −1201.87 −0.616836
\(157\) −3475.74 −1.76684 −0.883422 0.468578i \(-0.844767\pi\)
−0.883422 + 0.468578i \(0.844767\pi\)
\(158\) 2698.92 1.35895
\(159\) 1916.00 0.955650
\(160\) −738.757 −0.365024
\(161\) −4833.09 −2.36584
\(162\) 410.252 0.198966
\(163\) 3518.89 1.69092 0.845462 0.534035i \(-0.179325\pi\)
0.845462 + 0.534035i \(0.179325\pi\)
\(164\) 4206.24 2.00276
\(165\) 0 0
\(166\) −6102.67 −2.85337
\(167\) −250.304 −0.115983 −0.0579914 0.998317i \(-0.518470\pi\)
−0.0579914 + 0.998317i \(0.518470\pi\)
\(168\) −4023.75 −1.84785
\(169\) −1681.94 −0.765563
\(170\) −1042.73 −0.470436
\(171\) 1279.15 0.572043
\(172\) −534.705 −0.237040
\(173\) −941.985 −0.413976 −0.206988 0.978344i \(-0.566366\pi\)
−0.206988 + 0.978344i \(0.566366\pi\)
\(174\) −1157.89 −0.504479
\(175\) −685.870 −0.296268
\(176\) 0 0
\(177\) 309.437 0.131405
\(178\) 5361.09 2.25748
\(179\) 336.037 0.140316 0.0701582 0.997536i \(-0.477650\pi\)
0.0701582 + 0.997536i \(0.477650\pi\)
\(180\) −794.365 −0.328936
\(181\) 1107.45 0.454784 0.227392 0.973803i \(-0.426980\pi\)
0.227392 + 0.973803i \(0.426980\pi\)
\(182\) 3153.52 1.28436
\(183\) −1816.79 −0.733885
\(184\) 8612.53 3.45068
\(185\) −1836.48 −0.729843
\(186\) 2998.98 1.18224
\(187\) 0 0
\(188\) 2425.28 0.940861
\(189\) −740.740 −0.285084
\(190\) −3599.28 −1.37431
\(191\) −4243.01 −1.60740 −0.803700 0.595035i \(-0.797138\pi\)
−0.803700 + 0.595035i \(0.797138\pi\)
\(192\) −308.411 −0.115925
\(193\) 3324.23 1.23981 0.619905 0.784677i \(-0.287171\pi\)
0.619905 + 0.784677i \(0.287171\pi\)
\(194\) −431.506 −0.159692
\(195\) 340.423 0.125016
\(196\) 7231.69 2.63546
\(197\) −2677.14 −0.968213 −0.484107 0.875009i \(-0.660855\pi\)
−0.484107 + 0.875009i \(0.660855\pi\)
\(198\) 0 0
\(199\) 2779.90 0.990261 0.495131 0.868819i \(-0.335120\pi\)
0.495131 + 0.868819i \(0.335120\pi\)
\(200\) 1222.22 0.432119
\(201\) −2114.77 −0.742113
\(202\) 39.5981 0.0137926
\(203\) 2090.65 0.722833
\(204\) 2180.56 0.748380
\(205\) −1191.40 −0.405906
\(206\) 63.1940 0.0213735
\(207\) 1585.50 0.532365
\(208\) −2414.56 −0.804903
\(209\) 0 0
\(210\) 2084.29 0.684904
\(211\) −3056.15 −0.997129 −0.498564 0.866853i \(-0.666139\pi\)
−0.498564 + 0.866853i \(0.666139\pi\)
\(212\) 11274.1 3.65239
\(213\) −2346.49 −0.754829
\(214\) 6973.30 2.22750
\(215\) 151.453 0.0480417
\(216\) 1319.99 0.415806
\(217\) −5414.89 −1.69395
\(218\) −3090.51 −0.960163
\(219\) 729.395 0.225059
\(220\) 0 0
\(221\) −934.472 −0.284432
\(222\) 5580.89 1.68723
\(223\) 571.375 0.171579 0.0857895 0.996313i \(-0.472659\pi\)
0.0857895 + 0.996313i \(0.472659\pi\)
\(224\) −4053.53 −1.20910
\(225\) 225.000 0.0666667
\(226\) −186.248 −0.0548187
\(227\) 1094.40 0.319989 0.159995 0.987118i \(-0.448852\pi\)
0.159995 + 0.987118i \(0.448852\pi\)
\(228\) 7526.78 2.18629
\(229\) −645.240 −0.186195 −0.0930975 0.995657i \(-0.529677\pi\)
−0.0930975 + 0.995657i \(0.529677\pi\)
\(230\) −4461.27 −1.27899
\(231\) 0 0
\(232\) −3725.53 −1.05428
\(233\) 2337.39 0.657201 0.328600 0.944469i \(-0.393423\pi\)
0.328600 + 0.944469i \(0.393423\pi\)
\(234\) −1034.51 −0.289009
\(235\) −686.949 −0.190688
\(236\) 1820.79 0.502217
\(237\) 1598.62 0.438151
\(238\) −5721.44 −1.55826
\(239\) 3656.91 0.989733 0.494866 0.868969i \(-0.335217\pi\)
0.494866 + 0.868969i \(0.335217\pi\)
\(240\) −1595.89 −0.429225
\(241\) 389.034 0.103983 0.0519914 0.998648i \(-0.483443\pi\)
0.0519914 + 0.998648i \(0.483443\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) −10690.3 −2.80483
\(245\) −2048.34 −0.534138
\(246\) 3620.53 0.938361
\(247\) −3225.58 −0.830927
\(248\) 9649.30 2.47069
\(249\) −3614.73 −0.919976
\(250\) −633.104 −0.160164
\(251\) 2299.55 0.578271 0.289135 0.957288i \(-0.406632\pi\)
0.289135 + 0.957288i \(0.406632\pi\)
\(252\) −4358.65 −1.08956
\(253\) 0 0
\(254\) 276.191 0.0682273
\(255\) −617.632 −0.151677
\(256\) −7801.44 −1.90465
\(257\) 4921.61 1.19456 0.597279 0.802033i \(-0.296248\pi\)
0.597279 + 0.802033i \(0.296248\pi\)
\(258\) −460.249 −0.111062
\(259\) −10076.7 −2.41752
\(260\) 2003.11 0.477799
\(261\) −685.840 −0.162653
\(262\) −12043.3 −2.83985
\(263\) 2575.61 0.603875 0.301938 0.953328i \(-0.402367\pi\)
0.301938 + 0.953328i \(0.402367\pi\)
\(264\) 0 0
\(265\) −3193.33 −0.740243
\(266\) −19749.1 −4.55224
\(267\) 3175.48 0.727850
\(268\) −12443.7 −2.83627
\(269\) −4794.97 −1.08682 −0.543410 0.839468i \(-0.682867\pi\)
−0.543410 + 0.839468i \(0.682867\pi\)
\(270\) −683.753 −0.154118
\(271\) −2729.47 −0.611821 −0.305910 0.952060i \(-0.598961\pi\)
−0.305910 + 0.952060i \(0.598961\pi\)
\(272\) 4380.76 0.976553
\(273\) 1867.89 0.414102
\(274\) −15591.7 −3.43769
\(275\) 0 0
\(276\) 9329.36 2.03464
\(277\) 3761.45 0.815898 0.407949 0.913005i \(-0.366244\pi\)
0.407949 + 0.913005i \(0.366244\pi\)
\(278\) 6063.53 1.30815
\(279\) 1776.36 0.381174
\(280\) 6706.25 1.43134
\(281\) 6434.87 1.36609 0.683046 0.730375i \(-0.260655\pi\)
0.683046 + 0.730375i \(0.260655\pi\)
\(282\) 2087.57 0.440826
\(283\) −3335.65 −0.700649 −0.350325 0.936628i \(-0.613929\pi\)
−0.350325 + 0.936628i \(0.613929\pi\)
\(284\) −13807.2 −2.88487
\(285\) −2131.92 −0.443103
\(286\) 0 0
\(287\) −6537.14 −1.34451
\(288\) 1329.76 0.272073
\(289\) −3217.58 −0.654912
\(290\) 1929.81 0.390768
\(291\) −255.589 −0.0514876
\(292\) 4291.89 0.860151
\(293\) 2878.93 0.574023 0.287012 0.957927i \(-0.407338\pi\)
0.287012 + 0.957927i \(0.407338\pi\)
\(294\) 6224.71 1.23480
\(295\) −515.729 −0.101786
\(296\) 17956.6 3.52604
\(297\) 0 0
\(298\) 3795.87 0.737883
\(299\) −3998.07 −0.773293
\(300\) 1323.94 0.254793
\(301\) 831.014 0.159132
\(302\) 13400.1 2.55328
\(303\) 23.4547 0.00444699
\(304\) 15121.4 2.85286
\(305\) 3027.98 0.568465
\(306\) 1876.92 0.350642
\(307\) 8154.28 1.51593 0.757963 0.652297i \(-0.226195\pi\)
0.757963 + 0.652297i \(0.226195\pi\)
\(308\) 0 0
\(309\) 37.4310 0.00689119
\(310\) −4998.31 −0.915757
\(311\) 3818.24 0.696182 0.348091 0.937461i \(-0.386830\pi\)
0.348091 + 0.937461i \(0.386830\pi\)
\(312\) −3328.57 −0.603984
\(313\) 2527.23 0.456381 0.228191 0.973616i \(-0.426719\pi\)
0.228191 + 0.973616i \(0.426719\pi\)
\(314\) −17604.1 −3.16387
\(315\) 1234.57 0.220825
\(316\) 9406.59 1.67456
\(317\) −11084.7 −1.96398 −0.981989 0.188937i \(-0.939496\pi\)
−0.981989 + 0.188937i \(0.939496\pi\)
\(318\) 9704.20 1.71127
\(319\) 0 0
\(320\) 514.019 0.0897954
\(321\) 4130.42 0.718186
\(322\) −24478.8 −4.23649
\(323\) 5852.19 1.00813
\(324\) 1429.86 0.245174
\(325\) −567.372 −0.0968373
\(326\) 17822.6 3.02792
\(327\) −1830.57 −0.309574
\(328\) 11649.1 1.96103
\(329\) −3769.26 −0.631629
\(330\) 0 0
\(331\) −9417.70 −1.56388 −0.781939 0.623355i \(-0.785769\pi\)
−0.781939 + 0.623355i \(0.785769\pi\)
\(332\) −21269.7 −3.51605
\(333\) 3305.67 0.543993
\(334\) −1267.75 −0.207689
\(335\) 3524.62 0.574838
\(336\) −8756.57 −1.42176
\(337\) 11263.2 1.82061 0.910305 0.413938i \(-0.135847\pi\)
0.910305 + 0.413938i \(0.135847\pi\)
\(338\) −8518.76 −1.37089
\(339\) −110.318 −0.0176745
\(340\) −3634.26 −0.579693
\(341\) 0 0
\(342\) 6478.70 1.02435
\(343\) −1829.03 −0.287925
\(344\) −1480.86 −0.232101
\(345\) −2642.49 −0.412369
\(346\) −4771.00 −0.741302
\(347\) 4213.25 0.651814 0.325907 0.945402i \(-0.394330\pi\)
0.325907 + 0.945402i \(0.394330\pi\)
\(348\) −4035.61 −0.621642
\(349\) −4987.07 −0.764905 −0.382452 0.923975i \(-0.624920\pi\)
−0.382452 + 0.923975i \(0.624920\pi\)
\(350\) −3473.82 −0.530524
\(351\) −612.762 −0.0931817
\(352\) 0 0
\(353\) −7633.47 −1.15096 −0.575480 0.817816i \(-0.695185\pi\)
−0.575480 + 0.817816i \(0.695185\pi\)
\(354\) 1567.25 0.235306
\(355\) 3910.81 0.584688
\(356\) 18685.1 2.78177
\(357\) −3388.92 −0.502411
\(358\) 1701.97 0.251263
\(359\) 3114.76 0.457913 0.228957 0.973437i \(-0.426469\pi\)
0.228957 + 0.973437i \(0.426469\pi\)
\(360\) −2199.99 −0.322082
\(361\) 13341.4 1.94510
\(362\) 5609.04 0.814378
\(363\) 0 0
\(364\) 10991.0 1.58265
\(365\) −1215.66 −0.174330
\(366\) −9201.74 −1.31416
\(367\) 5931.48 0.843653 0.421827 0.906677i \(-0.361389\pi\)
0.421827 + 0.906677i \(0.361389\pi\)
\(368\) 18742.8 2.65499
\(369\) 2144.51 0.302544
\(370\) −9301.49 −1.30692
\(371\) −17521.7 −2.45196
\(372\) 10452.4 1.45681
\(373\) −13918.9 −1.93215 −0.966073 0.258267i \(-0.916848\pi\)
−0.966073 + 0.258267i \(0.916848\pi\)
\(374\) 0 0
\(375\) −375.000 −0.0516398
\(376\) 6716.80 0.921257
\(377\) 1729.45 0.236263
\(378\) −3751.72 −0.510497
\(379\) −12267.3 −1.66261 −0.831303 0.555820i \(-0.812404\pi\)
−0.831303 + 0.555820i \(0.812404\pi\)
\(380\) −12544.6 −1.69349
\(381\) 163.593 0.0219977
\(382\) −21490.1 −2.87835
\(383\) −6935.04 −0.925233 −0.462616 0.886559i \(-0.653089\pi\)
−0.462616 + 0.886559i \(0.653089\pi\)
\(384\) −5108.08 −0.678830
\(385\) 0 0
\(386\) 16836.7 2.22012
\(387\) −272.615 −0.0358082
\(388\) −1503.93 −0.196780
\(389\) 2775.18 0.361715 0.180858 0.983509i \(-0.442113\pi\)
0.180858 + 0.983509i \(0.442113\pi\)
\(390\) 1724.19 0.223866
\(391\) 7253.73 0.938202
\(392\) 20028.1 2.58054
\(393\) −7133.50 −0.915617
\(394\) −13559.3 −1.73377
\(395\) −2664.37 −0.339390
\(396\) 0 0
\(397\) 10539.5 1.33240 0.666198 0.745775i \(-0.267921\pi\)
0.666198 + 0.745775i \(0.267921\pi\)
\(398\) 14079.7 1.77325
\(399\) −11697.8 −1.46772
\(400\) 2659.81 0.332477
\(401\) −12295.3 −1.53117 −0.765585 0.643334i \(-0.777550\pi\)
−0.765585 + 0.643334i \(0.777550\pi\)
\(402\) −10711.0 −1.32889
\(403\) −4479.35 −0.553679
\(404\) 138.012 0.0169959
\(405\) −405.000 −0.0496904
\(406\) 10588.8 1.29437
\(407\) 0 0
\(408\) 6039.04 0.732787
\(409\) 11545.7 1.39584 0.697918 0.716178i \(-0.254110\pi\)
0.697918 + 0.716178i \(0.254110\pi\)
\(410\) −6034.22 −0.726852
\(411\) −9235.24 −1.10837
\(412\) 220.251 0.0263374
\(413\) −2829.78 −0.337154
\(414\) 8030.28 0.953301
\(415\) 6024.54 0.712610
\(416\) −3353.20 −0.395202
\(417\) 3591.55 0.421772
\(418\) 0 0
\(419\) 1851.51 0.215876 0.107938 0.994158i \(-0.465575\pi\)
0.107938 + 0.994158i \(0.465575\pi\)
\(420\) 7264.42 0.843970
\(421\) −1303.60 −0.150911 −0.0754557 0.997149i \(-0.524041\pi\)
−0.0754557 + 0.997149i \(0.524041\pi\)
\(422\) −15478.9 −1.78555
\(423\) 1236.51 0.142130
\(424\) 31223.5 3.57629
\(425\) 1029.39 0.117488
\(426\) −11884.6 −1.35166
\(427\) 16614.4 1.88297
\(428\) 24304.2 2.74483
\(429\) 0 0
\(430\) 767.082 0.0860279
\(431\) −8228.85 −0.919652 −0.459826 0.888009i \(-0.652088\pi\)
−0.459826 + 0.888009i \(0.652088\pi\)
\(432\) 2872.60 0.319926
\(433\) 5830.21 0.647072 0.323536 0.946216i \(-0.395128\pi\)
0.323536 + 0.946216i \(0.395128\pi\)
\(434\) −27425.5 −3.03333
\(435\) 1143.07 0.125990
\(436\) −10771.4 −1.18316
\(437\) 25038.2 2.74082
\(438\) 3694.26 0.403011
\(439\) −14261.0 −1.55044 −0.775218 0.631694i \(-0.782360\pi\)
−0.775218 + 0.631694i \(0.782360\pi\)
\(440\) 0 0
\(441\) 3687.01 0.398123
\(442\) −4732.95 −0.509329
\(443\) 12025.7 1.28975 0.644875 0.764288i \(-0.276910\pi\)
0.644875 + 0.764288i \(0.276910\pi\)
\(444\) 19451.2 2.07908
\(445\) −5292.46 −0.563790
\(446\) 2893.92 0.307245
\(447\) 2248.37 0.237907
\(448\) 2820.40 0.297436
\(449\) −7073.28 −0.743449 −0.371725 0.928343i \(-0.621233\pi\)
−0.371725 + 0.928343i \(0.621233\pi\)
\(450\) 1139.59 0.119379
\(451\) 0 0
\(452\) −649.133 −0.0675501
\(453\) 7937.15 0.823222
\(454\) 5542.93 0.573001
\(455\) −3113.15 −0.320762
\(456\) 20845.4 2.14073
\(457\) −2732.31 −0.279677 −0.139838 0.990174i \(-0.544658\pi\)
−0.139838 + 0.990174i \(0.544658\pi\)
\(458\) −3268.04 −0.333418
\(459\) 1111.74 0.113053
\(460\) −15548.9 −1.57603
\(461\) 332.708 0.0336134 0.0168067 0.999859i \(-0.494650\pi\)
0.0168067 + 0.999859i \(0.494650\pi\)
\(462\) 0 0
\(463\) 8248.39 0.827937 0.413969 0.910291i \(-0.364142\pi\)
0.413969 + 0.910291i \(0.364142\pi\)
\(464\) −8107.58 −0.811174
\(465\) −2960.59 −0.295256
\(466\) 11838.5 1.17684
\(467\) 7359.35 0.729229 0.364615 0.931158i \(-0.381201\pi\)
0.364615 + 0.931158i \(0.381201\pi\)
\(468\) −3605.60 −0.356131
\(469\) 19339.5 1.90408
\(470\) −3479.28 −0.341462
\(471\) −10427.2 −1.02009
\(472\) 5042.66 0.491752
\(473\) 0 0
\(474\) 8096.76 0.784592
\(475\) 3553.21 0.343226
\(476\) −19941.0 −1.92016
\(477\) 5747.99 0.551745
\(478\) 18521.7 1.77230
\(479\) 10327.6 0.985140 0.492570 0.870273i \(-0.336058\pi\)
0.492570 + 0.870273i \(0.336058\pi\)
\(480\) −2216.27 −0.210747
\(481\) −8335.75 −0.790182
\(482\) 1970.39 0.186201
\(483\) −14499.3 −1.36592
\(484\) 0 0
\(485\) 425.982 0.0398822
\(486\) 1230.76 0.114873
\(487\) 9622.57 0.895360 0.447680 0.894194i \(-0.352250\pi\)
0.447680 + 0.894194i \(0.352250\pi\)
\(488\) −29606.8 −2.74639
\(489\) 10556.7 0.976256
\(490\) −10374.5 −0.956475
\(491\) 8993.59 0.826629 0.413315 0.910588i \(-0.364371\pi\)
0.413315 + 0.910588i \(0.364371\pi\)
\(492\) 12618.7 1.15629
\(493\) −3137.75 −0.286648
\(494\) −16337.0 −1.48793
\(495\) 0 0
\(496\) 20999.0 1.90097
\(497\) 21458.5 1.93671
\(498\) −18308.0 −1.64739
\(499\) 2623.70 0.235377 0.117688 0.993051i \(-0.462452\pi\)
0.117688 + 0.993051i \(0.462452\pi\)
\(500\) −2206.57 −0.197362
\(501\) −750.912 −0.0669627
\(502\) 11646.8 1.03550
\(503\) −13234.5 −1.17316 −0.586579 0.809892i \(-0.699526\pi\)
−0.586579 + 0.809892i \(0.699526\pi\)
\(504\) −12071.3 −1.06686
\(505\) −39.0912 −0.00344462
\(506\) 0 0
\(507\) −5045.83 −0.441998
\(508\) 962.612 0.0840728
\(509\) −12810.3 −1.11553 −0.557765 0.829999i \(-0.688341\pi\)
−0.557765 + 0.829999i \(0.688341\pi\)
\(510\) −3128.20 −0.271606
\(511\) −6670.26 −0.577446
\(512\) −25891.5 −2.23487
\(513\) 3837.46 0.330269
\(514\) 24927.1 2.13908
\(515\) −62.3850 −0.00533789
\(516\) −1604.12 −0.136855
\(517\) 0 0
\(518\) −51036.9 −4.32902
\(519\) −2825.95 −0.239009
\(520\) 5547.61 0.467844
\(521\) 1151.47 0.0968268 0.0484134 0.998827i \(-0.484584\pi\)
0.0484134 + 0.998827i \(0.484584\pi\)
\(522\) −3473.67 −0.291261
\(523\) 17319.1 1.44801 0.724005 0.689794i \(-0.242299\pi\)
0.724005 + 0.689794i \(0.242299\pi\)
\(524\) −41974.8 −3.49939
\(525\) −2057.61 −0.171050
\(526\) 13045.1 1.08135
\(527\) 8126.92 0.671754
\(528\) 0 0
\(529\) 18867.6 1.55072
\(530\) −16173.7 −1.32555
\(531\) 928.312 0.0758669
\(532\) −68831.9 −5.60948
\(533\) −5407.72 −0.439464
\(534\) 16083.3 1.30335
\(535\) −6884.03 −0.556304
\(536\) −34462.8 −2.77718
\(537\) 1008.11 0.0810117
\(538\) −24285.7 −1.94616
\(539\) 0 0
\(540\) −2383.10 −0.189911
\(541\) 7190.73 0.571449 0.285724 0.958312i \(-0.407766\pi\)
0.285724 + 0.958312i \(0.407766\pi\)
\(542\) −13824.3 −1.09558
\(543\) 3322.34 0.262570
\(544\) 6083.73 0.479481
\(545\) 3050.94 0.239795
\(546\) 9460.55 0.741527
\(547\) −18670.5 −1.45940 −0.729701 0.683766i \(-0.760341\pi\)
−0.729701 + 0.683766i \(0.760341\pi\)
\(548\) −54341.9 −4.23608
\(549\) −5450.37 −0.423709
\(550\) 0 0
\(551\) −10830.8 −0.837400
\(552\) 25837.6 1.99225
\(553\) −14619.3 −1.12419
\(554\) 19051.1 1.46102
\(555\) −5509.45 −0.421375
\(556\) 21133.3 1.61197
\(557\) 5510.44 0.419183 0.209591 0.977789i \(-0.432787\pi\)
0.209591 + 0.977789i \(0.432787\pi\)
\(558\) 8996.95 0.682565
\(559\) 687.439 0.0520136
\(560\) 14594.3 1.10129
\(561\) 0 0
\(562\) 32591.5 2.44625
\(563\) −3576.57 −0.267734 −0.133867 0.990999i \(-0.542740\pi\)
−0.133867 + 0.990999i \(0.542740\pi\)
\(564\) 7275.84 0.543206
\(565\) 183.864 0.0136906
\(566\) −16894.5 −1.25465
\(567\) −2222.22 −0.164593
\(568\) −38238.8 −2.82476
\(569\) −12285.2 −0.905138 −0.452569 0.891729i \(-0.649492\pi\)
−0.452569 + 0.891729i \(0.649492\pi\)
\(570\) −10797.8 −0.793459
\(571\) −13889.5 −1.01797 −0.508983 0.860777i \(-0.669978\pi\)
−0.508983 + 0.860777i \(0.669978\pi\)
\(572\) 0 0
\(573\) −12729.0 −0.928032
\(574\) −33109.5 −2.40761
\(575\) 4404.16 0.319419
\(576\) −925.234 −0.0669296
\(577\) 11579.4 0.835457 0.417728 0.908572i \(-0.362826\pi\)
0.417728 + 0.908572i \(0.362826\pi\)
\(578\) −16296.5 −1.17274
\(579\) 9972.69 0.715805
\(580\) 6726.02 0.481522
\(581\) 33056.4 2.36043
\(582\) −1294.52 −0.0921984
\(583\) 0 0
\(584\) 11886.4 0.842229
\(585\) 1021.27 0.0721783
\(586\) 14581.3 1.02790
\(587\) 26468.0 1.86107 0.930537 0.366199i \(-0.119341\pi\)
0.930537 + 0.366199i \(0.119341\pi\)
\(588\) 21695.1 1.52158
\(589\) 28052.3 1.96243
\(590\) −2612.08 −0.182267
\(591\) −8031.41 −0.558998
\(592\) 39077.6 2.71297
\(593\) −1059.52 −0.0733716 −0.0366858 0.999327i \(-0.511680\pi\)
−0.0366858 + 0.999327i \(0.511680\pi\)
\(594\) 0 0
\(595\) 5648.20 0.389166
\(596\) 13229.8 0.909253
\(597\) 8339.70 0.571728
\(598\) −20249.6 −1.38473
\(599\) −17858.7 −1.21817 −0.609086 0.793104i \(-0.708464\pi\)
−0.609086 + 0.793104i \(0.708464\pi\)
\(600\) 3666.65 0.249484
\(601\) 9650.91 0.655023 0.327511 0.944847i \(-0.393790\pi\)
0.327511 + 0.944847i \(0.393790\pi\)
\(602\) 4208.95 0.284957
\(603\) −6344.32 −0.428459
\(604\) 46703.7 3.14627
\(605\) 0 0
\(606\) 118.794 0.00796318
\(607\) −22754.9 −1.52157 −0.760786 0.649002i \(-0.775187\pi\)
−0.760786 + 0.649002i \(0.775187\pi\)
\(608\) 20999.6 1.40074
\(609\) 6271.96 0.417328
\(610\) 15336.2 1.01794
\(611\) −3118.04 −0.206453
\(612\) 6541.67 0.432077
\(613\) −13074.5 −0.861459 −0.430729 0.902481i \(-0.641744\pi\)
−0.430729 + 0.902481i \(0.641744\pi\)
\(614\) 41300.1 2.71455
\(615\) −3574.19 −0.234350
\(616\) 0 0
\(617\) −13393.0 −0.873878 −0.436939 0.899491i \(-0.643937\pi\)
−0.436939 + 0.899491i \(0.643937\pi\)
\(618\) 189.582 0.0123400
\(619\) −15965.3 −1.03667 −0.518336 0.855177i \(-0.673448\pi\)
−0.518336 + 0.855177i \(0.673448\pi\)
\(620\) −17420.7 −1.12844
\(621\) 4756.49 0.307361
\(622\) 19338.8 1.24665
\(623\) −29039.5 −1.86749
\(624\) −7243.69 −0.464711
\(625\) 625.000 0.0400000
\(626\) 12800.0 0.817237
\(627\) 0 0
\(628\) −61355.8 −3.89867
\(629\) 15123.6 0.958693
\(630\) 6252.87 0.395429
\(631\) 17698.3 1.11657 0.558287 0.829648i \(-0.311459\pi\)
0.558287 + 0.829648i \(0.311459\pi\)
\(632\) 26051.5 1.63967
\(633\) −9168.45 −0.575693
\(634\) −56142.4 −3.51688
\(635\) −272.655 −0.0170393
\(636\) 33822.2 2.10871
\(637\) −9297.37 −0.578297
\(638\) 0 0
\(639\) −7039.46 −0.435801
\(640\) 8513.47 0.525820
\(641\) 18264.8 1.12546 0.562728 0.826642i \(-0.309752\pi\)
0.562728 + 0.826642i \(0.309752\pi\)
\(642\) 20919.9 1.28605
\(643\) −15730.5 −0.964778 −0.482389 0.875957i \(-0.660231\pi\)
−0.482389 + 0.875957i \(0.660231\pi\)
\(644\) −85316.4 −5.22040
\(645\) 454.358 0.0277369
\(646\) 29640.4 1.80524
\(647\) 21176.6 1.28676 0.643382 0.765545i \(-0.277531\pi\)
0.643382 + 0.765545i \(0.277531\pi\)
\(648\) 3959.98 0.240066
\(649\) 0 0
\(650\) −2873.65 −0.173406
\(651\) −16244.7 −0.978001
\(652\) 62117.4 3.73114
\(653\) −28293.6 −1.69558 −0.847791 0.530331i \(-0.822068\pi\)
−0.847791 + 0.530331i \(0.822068\pi\)
\(654\) −9271.52 −0.554350
\(655\) 11889.2 0.709234
\(656\) 25351.1 1.50883
\(657\) 2188.18 0.129938
\(658\) −19090.7 −1.13105
\(659\) 3894.19 0.230191 0.115096 0.993354i \(-0.463283\pi\)
0.115096 + 0.993354i \(0.463283\pi\)
\(660\) 0 0
\(661\) −6063.63 −0.356805 −0.178402 0.983958i \(-0.557093\pi\)
−0.178402 + 0.983958i \(0.557093\pi\)
\(662\) −47699.1 −2.80042
\(663\) −2803.42 −0.164217
\(664\) −58906.4 −3.44279
\(665\) 19496.3 1.13689
\(666\) 16742.7 0.974123
\(667\) −13424.7 −0.779317
\(668\) −4418.51 −0.255924
\(669\) 1714.13 0.0990612
\(670\) 17851.6 1.02936
\(671\) 0 0
\(672\) −12160.6 −0.698072
\(673\) −17297.1 −0.990719 −0.495360 0.868688i \(-0.664964\pi\)
−0.495360 + 0.868688i \(0.664964\pi\)
\(674\) 57046.3 3.26015
\(675\) 675.000 0.0384900
\(676\) −29690.6 −1.68927
\(677\) 4640.36 0.263432 0.131716 0.991287i \(-0.457951\pi\)
0.131716 + 0.991287i \(0.457951\pi\)
\(678\) −558.744 −0.0316496
\(679\) 2337.35 0.132105
\(680\) −10065.1 −0.567614
\(681\) 3283.19 0.184746
\(682\) 0 0
\(683\) −14694.9 −0.823256 −0.411628 0.911352i \(-0.635040\pi\)
−0.411628 + 0.911352i \(0.635040\pi\)
\(684\) 22580.3 1.26225
\(685\) 15392.1 0.858541
\(686\) −9263.73 −0.515584
\(687\) −1935.72 −0.107500
\(688\) −3222.68 −0.178581
\(689\) −14494.4 −0.801442
\(690\) −13383.8 −0.738424
\(691\) −9905.09 −0.545307 −0.272654 0.962112i \(-0.587901\pi\)
−0.272654 + 0.962112i \(0.587901\pi\)
\(692\) −16628.4 −0.913466
\(693\) 0 0
\(694\) 21339.4 1.16720
\(695\) −5985.91 −0.326703
\(696\) −11176.6 −0.608689
\(697\) 9811.25 0.533182
\(698\) −25258.7 −1.36971
\(699\) 7012.18 0.379435
\(700\) −12107.4 −0.653736
\(701\) 947.946 0.0510748 0.0255374 0.999674i \(-0.491870\pi\)
0.0255374 + 0.999674i \(0.491870\pi\)
\(702\) −3103.54 −0.166860
\(703\) 52203.2 2.80069
\(704\) 0 0
\(705\) −2060.85 −0.110094
\(706\) −38662.3 −2.06101
\(707\) −214.492 −0.0114099
\(708\) 5462.36 0.289955
\(709\) −3310.76 −0.175371 −0.0876855 0.996148i \(-0.527947\pi\)
−0.0876855 + 0.996148i \(0.527947\pi\)
\(710\) 19807.6 1.04699
\(711\) 4795.87 0.252966
\(712\) 51748.3 2.72380
\(713\) 34770.5 1.82632
\(714\) −17164.3 −0.899662
\(715\) 0 0
\(716\) 5931.92 0.309618
\(717\) 10970.7 0.571423
\(718\) 15775.8 0.819981
\(719\) 3061.15 0.158778 0.0793892 0.996844i \(-0.474703\pi\)
0.0793892 + 0.996844i \(0.474703\pi\)
\(720\) −4787.66 −0.247813
\(721\) −342.304 −0.0176811
\(722\) 67572.1 3.48307
\(723\) 1167.10 0.0600345
\(724\) 19549.3 1.00351
\(725\) −1905.11 −0.0975918
\(726\) 0 0
\(727\) −7405.09 −0.377771 −0.188886 0.981999i \(-0.560488\pi\)
−0.188886 + 0.981999i \(0.560488\pi\)
\(728\) 30439.5 1.54967
\(729\) 729.000 0.0370370
\(730\) −6157.11 −0.312171
\(731\) −1247.23 −0.0631057
\(732\) −32071.0 −1.61937
\(733\) −29791.4 −1.50119 −0.750593 0.660765i \(-0.770232\pi\)
−0.750593 + 0.660765i \(0.770232\pi\)
\(734\) 30042.0 1.51072
\(735\) −6145.02 −0.308384
\(736\) 26028.8 1.30358
\(737\) 0 0
\(738\) 10861.6 0.541763
\(739\) 7150.93 0.355955 0.177978 0.984035i \(-0.443045\pi\)
0.177978 + 0.984035i \(0.443045\pi\)
\(740\) −32418.6 −1.61045
\(741\) −9676.75 −0.479736
\(742\) −88744.3 −4.39071
\(743\) 1940.69 0.0958239 0.0479120 0.998852i \(-0.484743\pi\)
0.0479120 + 0.998852i \(0.484743\pi\)
\(744\) 28947.9 1.42645
\(745\) −3747.28 −0.184282
\(746\) −70496.7 −3.45988
\(747\) −10844.2 −0.531148
\(748\) 0 0
\(749\) −37772.4 −1.84269
\(750\) −1899.31 −0.0924708
\(751\) −29491.2 −1.43295 −0.716476 0.697611i \(-0.754246\pi\)
−0.716476 + 0.697611i \(0.754246\pi\)
\(752\) 14617.2 0.708824
\(753\) 6898.64 0.333865
\(754\) 8759.38 0.423074
\(755\) −13228.6 −0.637665
\(756\) −13076.0 −0.629058
\(757\) 3542.54 0.170087 0.0850436 0.996377i \(-0.472897\pi\)
0.0850436 + 0.996377i \(0.472897\pi\)
\(758\) −62131.7 −2.97721
\(759\) 0 0
\(760\) −34742.3 −1.65820
\(761\) −8552.86 −0.407412 −0.203706 0.979032i \(-0.565299\pi\)
−0.203706 + 0.979032i \(0.565299\pi\)
\(762\) 828.572 0.0393911
\(763\) 16740.4 0.794290
\(764\) −74900.0 −3.54684
\(765\) −1852.90 −0.0875707
\(766\) −35124.9 −1.65680
\(767\) −2340.88 −0.110201
\(768\) −23404.3 −1.09965
\(769\) 3128.73 0.146716 0.0733582 0.997306i \(-0.476628\pi\)
0.0733582 + 0.997306i \(0.476628\pi\)
\(770\) 0 0
\(771\) 14764.8 0.689679
\(772\) 58681.2 2.73573
\(773\) −5364.51 −0.249609 −0.124805 0.992181i \(-0.539830\pi\)
−0.124805 + 0.992181i \(0.539830\pi\)
\(774\) −1380.75 −0.0641214
\(775\) 4934.32 0.228705
\(776\) −4165.14 −0.192680
\(777\) −30230.1 −1.39575
\(778\) 14055.8 0.647719
\(779\) 33866.2 1.55762
\(780\) 6009.34 0.275858
\(781\) 0 0
\(782\) 36738.9 1.68003
\(783\) −2057.52 −0.0939077
\(784\) 43585.6 1.98550
\(785\) 17378.7 0.790157
\(786\) −36130.0 −1.63959
\(787\) −12160.9 −0.550813 −0.275406 0.961328i \(-0.588812\pi\)
−0.275406 + 0.961328i \(0.588812\pi\)
\(788\) −47258.3 −2.13643
\(789\) 7726.84 0.348648
\(790\) −13494.6 −0.607742
\(791\) 1008.85 0.0453485
\(792\) 0 0
\(793\) 13743.9 0.615462
\(794\) 53380.7 2.38591
\(795\) −9579.98 −0.427380
\(796\) 49072.4 2.18508
\(797\) −581.179 −0.0258299 −0.0129149 0.999917i \(-0.504111\pi\)
−0.0129149 + 0.999917i \(0.504111\pi\)
\(798\) −59247.3 −2.62824
\(799\) 5657.09 0.250480
\(800\) 3693.78 0.163244
\(801\) 9526.43 0.420225
\(802\) −62273.8 −2.74185
\(803\) 0 0
\(804\) −37331.2 −1.63752
\(805\) 24165.4 1.05804
\(806\) −22687.2 −0.991467
\(807\) −14384.9 −0.627475
\(808\) 382.223 0.0166418
\(809\) −4763.37 −0.207010 −0.103505 0.994629i \(-0.533006\pi\)
−0.103505 + 0.994629i \(0.533006\pi\)
\(810\) −2051.26 −0.0889801
\(811\) 18055.4 0.781762 0.390881 0.920441i \(-0.372170\pi\)
0.390881 + 0.920441i \(0.372170\pi\)
\(812\) 36905.4 1.59498
\(813\) −8188.40 −0.353235
\(814\) 0 0
\(815\) −17594.4 −0.756205
\(816\) 13142.3 0.563813
\(817\) −4305.14 −0.184354
\(818\) 58476.9 2.49951
\(819\) 5603.66 0.239082
\(820\) −21031.2 −0.895660
\(821\) −1128.04 −0.0479522 −0.0239761 0.999713i \(-0.507633\pi\)
−0.0239761 + 0.999713i \(0.507633\pi\)
\(822\) −46775.0 −1.98475
\(823\) −32124.2 −1.36061 −0.680304 0.732930i \(-0.738152\pi\)
−0.680304 + 0.732930i \(0.738152\pi\)
\(824\) 609.984 0.0257886
\(825\) 0 0
\(826\) −14332.4 −0.603738
\(827\) −11914.2 −0.500964 −0.250482 0.968121i \(-0.580589\pi\)
−0.250482 + 0.968121i \(0.580589\pi\)
\(828\) 27988.1 1.17470
\(829\) −37721.6 −1.58037 −0.790185 0.612868i \(-0.790016\pi\)
−0.790185 + 0.612868i \(0.790016\pi\)
\(830\) 30513.3 1.27606
\(831\) 11284.4 0.471059
\(832\) 2333.12 0.0972192
\(833\) 16868.3 0.701622
\(834\) 18190.6 0.755262
\(835\) 1251.52 0.0518690
\(836\) 0 0
\(837\) 5329.07 0.220071
\(838\) 9377.57 0.386567
\(839\) −16550.5 −0.681034 −0.340517 0.940238i \(-0.610602\pi\)
−0.340517 + 0.940238i \(0.610602\pi\)
\(840\) 20118.8 0.826384
\(841\) −18581.9 −0.761896
\(842\) −6602.53 −0.270236
\(843\) 19304.6 0.788714
\(844\) −53948.9 −2.20023
\(845\) 8409.71 0.342370
\(846\) 6262.71 0.254511
\(847\) 0 0
\(848\) 67949.2 2.75163
\(849\) −10006.9 −0.404520
\(850\) 5213.67 0.210385
\(851\) 64705.3 2.60643
\(852\) −41421.5 −1.66558
\(853\) −1045.52 −0.0419672 −0.0209836 0.999780i \(-0.506680\pi\)
−0.0209836 + 0.999780i \(0.506680\pi\)
\(854\) 84149.3 3.37181
\(855\) −6395.77 −0.255825
\(856\) 67310.2 2.68764
\(857\) 14016.5 0.558688 0.279344 0.960191i \(-0.409883\pi\)
0.279344 + 0.960191i \(0.409883\pi\)
\(858\) 0 0
\(859\) −20476.3 −0.813319 −0.406660 0.913580i \(-0.633306\pi\)
−0.406660 + 0.913580i \(0.633306\pi\)
\(860\) 2673.53 0.106008
\(861\) −19611.4 −0.776255
\(862\) −41677.8 −1.64681
\(863\) 24083.0 0.949936 0.474968 0.880003i \(-0.342460\pi\)
0.474968 + 0.880003i \(0.342460\pi\)
\(864\) 3989.29 0.157081
\(865\) 4709.92 0.185135
\(866\) 29529.1 1.15871
\(867\) −9652.75 −0.378114
\(868\) −95586.6 −3.73781
\(869\) 0 0
\(870\) 5789.44 0.225610
\(871\) 15998.2 0.622362
\(872\) −29831.3 −1.15850
\(873\) −766.768 −0.0297264
\(874\) 126814. 4.90796
\(875\) 3429.35 0.132495
\(876\) 12875.7 0.496608
\(877\) −30432.5 −1.17176 −0.585879 0.810399i \(-0.699250\pi\)
−0.585879 + 0.810399i \(0.699250\pi\)
\(878\) −72229.7 −2.77635
\(879\) 8636.79 0.331413
\(880\) 0 0
\(881\) 24559.2 0.939183 0.469592 0.882884i \(-0.344401\pi\)
0.469592 + 0.882884i \(0.344401\pi\)
\(882\) 18674.1 0.712914
\(883\) 6013.88 0.229200 0.114600 0.993412i \(-0.463441\pi\)
0.114600 + 0.993412i \(0.463441\pi\)
\(884\) −16495.8 −0.627618
\(885\) −1547.19 −0.0587662
\(886\) 60908.3 2.30954
\(887\) −13395.5 −0.507075 −0.253538 0.967325i \(-0.581594\pi\)
−0.253538 + 0.967325i \(0.581594\pi\)
\(888\) 53869.9 2.03576
\(889\) −1496.05 −0.0564407
\(890\) −26805.4 −1.00957
\(891\) 0 0
\(892\) 10086.2 0.378601
\(893\) 19527.0 0.731741
\(894\) 11387.6 0.426017
\(895\) −1680.19 −0.0627514
\(896\) 46713.1 1.74171
\(897\) −11994.2 −0.446461
\(898\) −35825.0 −1.33129
\(899\) −15040.7 −0.557992
\(900\) 3971.83 0.147105
\(901\) 26297.3 0.972354
\(902\) 0 0
\(903\) 2493.04 0.0918751
\(904\) −1797.77 −0.0661426
\(905\) −5537.24 −0.203386
\(906\) 40200.3 1.47414
\(907\) −32078.9 −1.17438 −0.587189 0.809450i \(-0.699766\pi\)
−0.587189 + 0.809450i \(0.699766\pi\)
\(908\) 19318.9 0.706079
\(909\) 70.3641 0.00256747
\(910\) −15767.6 −0.574385
\(911\) −15992.0 −0.581600 −0.290800 0.956784i \(-0.593921\pi\)
−0.290800 + 0.956784i \(0.593921\pi\)
\(912\) 45364.1 1.64710
\(913\) 0 0
\(914\) −13838.7 −0.500814
\(915\) 9083.94 0.328203
\(916\) −11390.1 −0.410852
\(917\) 65235.4 2.34925
\(918\) 5630.77 0.202443
\(919\) −33876.1 −1.21596 −0.607980 0.793952i \(-0.708020\pi\)
−0.607980 + 0.793952i \(0.708020\pi\)
\(920\) −43062.7 −1.54319
\(921\) 24462.8 0.875220
\(922\) 1685.11 0.0601912
\(923\) 17751.1 0.633026
\(924\) 0 0
\(925\) 9182.42 0.326396
\(926\) 41776.7 1.48258
\(927\) 112.293 0.00397863
\(928\) −11259.3 −0.398281
\(929\) 21163.4 0.747416 0.373708 0.927546i \(-0.378086\pi\)
0.373708 + 0.927546i \(0.378086\pi\)
\(930\) −14994.9 −0.528713
\(931\) 58225.4 2.04969
\(932\) 41261.0 1.45016
\(933\) 11454.7 0.401941
\(934\) 37273.9 1.30582
\(935\) 0 0
\(936\) −9985.70 −0.348710
\(937\) 49771.9 1.73530 0.867650 0.497175i \(-0.165629\pi\)
0.867650 + 0.497175i \(0.165629\pi\)
\(938\) 97951.2 3.40962
\(939\) 7581.68 0.263492
\(940\) −12126.4 −0.420766
\(941\) −32194.6 −1.11532 −0.557659 0.830070i \(-0.688300\pi\)
−0.557659 + 0.830070i \(0.688300\pi\)
\(942\) −52812.2 −1.82666
\(943\) 41976.8 1.44958
\(944\) 10973.9 0.378359
\(945\) 3703.70 0.127493
\(946\) 0 0
\(947\) −30091.9 −1.03258 −0.516291 0.856413i \(-0.672688\pi\)
−0.516291 + 0.856413i \(0.672688\pi\)
\(948\) 28219.8 0.966810
\(949\) −5517.84 −0.188742
\(950\) 17996.4 0.614611
\(951\) −33254.2 −1.13390
\(952\) −55226.6 −1.88015
\(953\) −5710.17 −0.194093 −0.0970465 0.995280i \(-0.530940\pi\)
−0.0970465 + 0.995280i \(0.530940\pi\)
\(954\) 29112.6 0.988004
\(955\) 21215.0 0.718851
\(956\) 64553.9 2.18392
\(957\) 0 0
\(958\) 52307.8 1.76408
\(959\) 84455.7 2.84381
\(960\) 1542.06 0.0518434
\(961\) 9165.07 0.307646
\(962\) −42219.2 −1.41497
\(963\) 12391.3 0.414645
\(964\) 6867.44 0.229445
\(965\) −16621.2 −0.554460
\(966\) −73436.4 −2.44594
\(967\) −29638.4 −0.985634 −0.492817 0.870133i \(-0.664033\pi\)
−0.492817 + 0.870133i \(0.664033\pi\)
\(968\) 0 0
\(969\) 17556.6 0.582042
\(970\) 2157.53 0.0714166
\(971\) 21416.3 0.707808 0.353904 0.935282i \(-0.384854\pi\)
0.353904 + 0.935282i \(0.384854\pi\)
\(972\) 4289.57 0.141552
\(973\) −32844.5 −1.08216
\(974\) 48736.7 1.60331
\(975\) −1702.12 −0.0559090
\(976\) −64430.9 −2.11310
\(977\) 1038.84 0.0340177 0.0170088 0.999855i \(-0.494586\pi\)
0.0170088 + 0.999855i \(0.494586\pi\)
\(978\) 53467.8 1.74817
\(979\) 0 0
\(980\) −36158.5 −1.17861
\(981\) −5491.70 −0.178732
\(982\) 45551.1 1.48024
\(983\) −44173.6 −1.43329 −0.716643 0.697440i \(-0.754322\pi\)
−0.716643 + 0.697440i \(0.754322\pi\)
\(984\) 34947.4 1.13220
\(985\) 13385.7 0.432998
\(986\) −15892.2 −0.513297
\(987\) −11307.8 −0.364671
\(988\) −56939.8 −1.83350
\(989\) −5336.17 −0.171567
\(990\) 0 0
\(991\) −23940.9 −0.767414 −0.383707 0.923455i \(-0.625353\pi\)
−0.383707 + 0.923455i \(0.625353\pi\)
\(992\) 29162.1 0.933365
\(993\) −28253.1 −0.902905
\(994\) 108684. 3.46804
\(995\) −13899.5 −0.442858
\(996\) −63809.2 −2.02999
\(997\) −13557.9 −0.430674 −0.215337 0.976540i \(-0.569085\pi\)
−0.215337 + 0.976540i \(0.569085\pi\)
\(998\) 13288.6 0.421487
\(999\) 9917.01 0.314074
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 1815.4.a.r.1.3 3
11.10 odd 2 165.4.a.e.1.1 3
33.32 even 2 495.4.a.k.1.3 3
55.32 even 4 825.4.c.k.199.1 6
55.43 even 4 825.4.c.k.199.6 6
55.54 odd 2 825.4.a.r.1.3 3
165.164 even 2 2475.4.a.t.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.4.a.e.1.1 3 11.10 odd 2
495.4.a.k.1.3 3 33.32 even 2
825.4.a.r.1.3 3 55.54 odd 2
825.4.c.k.199.1 6 55.32 even 4
825.4.c.k.199.6 6 55.43 even 4
1815.4.a.r.1.3 3 1.1 even 1 trivial
2475.4.a.t.1.1 3 165.164 even 2