Properties

Label 1859.4.a.a.1.2
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.684550701\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
Defining polynomial: \(x^{2} - 3\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 11)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.73205\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.732051 q^{2} +5.92820 q^{3} -7.46410 q^{4} +12.8564 q^{5} +4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} +O(q^{10})\) \(q+0.732051 q^{2} +5.92820 q^{3} -7.46410 q^{4} +12.8564 q^{5} +4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} +9.41154 q^{10} +11.0000 q^{11} -44.2487 q^{12} -12.3923 q^{14} +76.2154 q^{15} +51.4256 q^{16} -82.7846 q^{17} +5.96152 q^{18} +67.9230 q^{19} -95.9615 q^{20} -100.354 q^{21} +8.05256 q^{22} +13.3538 q^{23} -67.1103 q^{24} +40.2872 q^{25} -111.785 q^{27} +126.354 q^{28} +168.995 q^{29} +55.7935 q^{30} +65.4974 q^{31} +128.210 q^{32} +65.2102 q^{33} -60.6025 q^{34} -217.636 q^{35} -60.7846 q^{36} -40.8564 q^{37} +49.7231 q^{38} -145.541 q^{40} -274.928 q^{41} -73.4641 q^{42} -2.28719 q^{43} -82.1051 q^{44} +104.697 q^{45} +9.77568 q^{46} -71.8461 q^{47} +304.862 q^{48} -56.4359 q^{49} +29.4923 q^{50} -490.764 q^{51} -149.005 q^{53} -81.8320 q^{54} +141.420 q^{55} +191.636 q^{56} +402.662 q^{57} +123.713 q^{58} -545.631 q^{59} -568.879 q^{60} +101.303 q^{61} +47.9474 q^{62} -137.856 q^{63} -317.549 q^{64} +47.7372 q^{66} -411.641 q^{67} +617.913 q^{68} +79.1642 q^{69} -159.321 q^{70} +470.636 q^{71} -92.1896 q^{72} -610.600 q^{73} -29.9090 q^{74} +238.831 q^{75} -506.985 q^{76} -186.210 q^{77} -978.225 q^{79} +661.149 q^{80} -882.559 q^{81} -201.261 q^{82} -26.1539 q^{83} +749.051 q^{84} -1064.31 q^{85} -1.67434 q^{86} +1001.84 q^{87} -124.526 q^{88} +352.887 q^{89} +76.6438 q^{90} -99.6743 q^{92} +388.282 q^{93} -52.5950 q^{94} +873.246 q^{95} +760.056 q^{96} -847.585 q^{97} -41.3140 q^{98} +89.5795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 26q^{6} - 20q^{7} + 12q^{8} + 44q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 26q^{6} - 20q^{7} + 12q^{8} + 44q^{9} + 50q^{10} + 22q^{11} - 40q^{12} - 4q^{14} + 194q^{15} - 8q^{16} - 124q^{17} - 92q^{18} - 72q^{19} - 88q^{20} - 76q^{21} - 22q^{22} - 98q^{23} - 252q^{24} + 136q^{25} - 182q^{27} + 128q^{28} + 144q^{29} - 266q^{30} + 34q^{31} + 104q^{32} - 22q^{33} + 52q^{34} - 172q^{35} - 80q^{36} - 54q^{37} + 432q^{38} - 492q^{40} - 536q^{41} - 140q^{42} - 60q^{43} - 88q^{44} - 428q^{45} + 314q^{46} + 272q^{47} + 776q^{48} - 390q^{49} - 232q^{50} - 164q^{51} - 492q^{53} + 110q^{54} - 22q^{55} + 120q^{56} + 1512q^{57} + 192q^{58} - 634q^{59} - 632q^{60} + 840q^{61} + 134q^{62} - 248q^{63} + 224q^{64} + 286q^{66} - 754q^{67} + 640q^{68} + 962q^{69} - 284q^{70} + 678q^{71} + 744q^{72} + 400q^{73} + 6q^{74} - 520q^{75} - 432q^{76} - 220q^{77} + 316q^{79} + 1544q^{80} - 1294q^{81} + 512q^{82} - 468q^{83} + 736q^{84} - 452q^{85} + 156q^{86} + 1200q^{87} + 132q^{88} + 1842q^{89} + 1532q^{90} - 40q^{92} + 638q^{93} - 992q^{94} + 2952q^{95} + 952q^{96} - 2194q^{97} + 870q^{98} + 484q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.732051 0.258819 0.129410 0.991591i \(-0.458692\pi\)
0.129410 + 0.991591i \(0.458692\pi\)
\(3\) 5.92820 1.14088 0.570442 0.821338i \(-0.306772\pi\)
0.570442 + 0.821338i \(0.306772\pi\)
\(4\) −7.46410 −0.933013
\(5\) 12.8564 1.14991 0.574956 0.818184i \(-0.305019\pi\)
0.574956 + 0.818184i \(0.305019\pi\)
\(6\) 4.33975 0.295282
\(7\) −16.9282 −0.914037 −0.457019 0.889457i \(-0.651083\pi\)
−0.457019 + 0.889457i \(0.651083\pi\)
\(8\) −11.3205 −0.500301
\(9\) 8.14359 0.301615
\(10\) 9.41154 0.297619
\(11\) 11.0000 0.301511
\(12\) −44.2487 −1.06446
\(13\) 0 0
\(14\) −12.3923 −0.236570
\(15\) 76.2154 1.31192
\(16\) 51.4256 0.803525
\(17\) −82.7846 −1.18107 −0.590536 0.807011i \(-0.701084\pi\)
−0.590536 + 0.807011i \(0.701084\pi\)
\(18\) 5.96152 0.0780636
\(19\) 67.9230 0.820138 0.410069 0.912055i \(-0.365505\pi\)
0.410069 + 0.912055i \(0.365505\pi\)
\(20\) −95.9615 −1.07288
\(21\) −100.354 −1.04281
\(22\) 8.05256 0.0780369
\(23\) 13.3538 0.121064 0.0605319 0.998166i \(-0.480720\pi\)
0.0605319 + 0.998166i \(0.480720\pi\)
\(24\) −67.1103 −0.570784
\(25\) 40.2872 0.322297
\(26\) 0 0
\(27\) −111.785 −0.796776
\(28\) 126.354 0.852808
\(29\) 168.995 1.08212 0.541061 0.840983i \(-0.318023\pi\)
0.541061 + 0.840983i \(0.318023\pi\)
\(30\) 55.7935 0.339549
\(31\) 65.4974 0.379474 0.189737 0.981835i \(-0.439237\pi\)
0.189737 + 0.981835i \(0.439237\pi\)
\(32\) 128.210 0.708268
\(33\) 65.2102 0.343989
\(34\) −60.6025 −0.305684
\(35\) −217.636 −1.05106
\(36\) −60.7846 −0.281410
\(37\) −40.8564 −0.181534 −0.0907669 0.995872i \(-0.528932\pi\)
−0.0907669 + 0.995872i \(0.528932\pi\)
\(38\) 49.7231 0.212267
\(39\) 0 0
\(40\) −145.541 −0.575302
\(41\) −274.928 −1.04723 −0.523617 0.851954i \(-0.675418\pi\)
−0.523617 + 0.851954i \(0.675418\pi\)
\(42\) −73.4641 −0.269899
\(43\) −2.28719 −0.00811146 −0.00405573 0.999992i \(-0.501291\pi\)
−0.00405573 + 0.999992i \(0.501291\pi\)
\(44\) −82.1051 −0.281314
\(45\) 104.697 0.346830
\(46\) 9.77568 0.0313336
\(47\) −71.8461 −0.222975 −0.111488 0.993766i \(-0.535562\pi\)
−0.111488 + 0.993766i \(0.535562\pi\)
\(48\) 304.862 0.916729
\(49\) −56.4359 −0.164536
\(50\) 29.4923 0.0834167
\(51\) −490.764 −1.34746
\(52\) 0 0
\(53\) −149.005 −0.386178 −0.193089 0.981181i \(-0.561851\pi\)
−0.193089 + 0.981181i \(0.561851\pi\)
\(54\) −81.8320 −0.206221
\(55\) 141.420 0.346711
\(56\) 191.636 0.457293
\(57\) 402.662 0.935681
\(58\) 123.713 0.280074
\(59\) −545.631 −1.20398 −0.601992 0.798502i \(-0.705626\pi\)
−0.601992 + 0.798502i \(0.705626\pi\)
\(60\) −568.879 −1.22403
\(61\) 101.303 0.212631 0.106315 0.994332i \(-0.466095\pi\)
0.106315 + 0.994332i \(0.466095\pi\)
\(62\) 47.9474 0.0982150
\(63\) −137.856 −0.275687
\(64\) −317.549 −0.620212
\(65\) 0 0
\(66\) 47.7372 0.0890310
\(67\) −411.641 −0.750596 −0.375298 0.926904i \(-0.622460\pi\)
−0.375298 + 0.926904i \(0.622460\pi\)
\(68\) 617.913 1.10195
\(69\) 79.1642 0.138120
\(70\) −159.321 −0.272035
\(71\) 470.636 0.786679 0.393339 0.919393i \(-0.371320\pi\)
0.393339 + 0.919393i \(0.371320\pi\)
\(72\) −92.1896 −0.150898
\(73\) −610.600 −0.978977 −0.489488 0.872010i \(-0.662816\pi\)
−0.489488 + 0.872010i \(0.662816\pi\)
\(74\) −29.9090 −0.0469844
\(75\) 238.831 0.367704
\(76\) −506.985 −0.765199
\(77\) −186.210 −0.275593
\(78\) 0 0
\(79\) −978.225 −1.39315 −0.696576 0.717483i \(-0.745294\pi\)
−0.696576 + 0.717483i \(0.745294\pi\)
\(80\) 661.149 0.923983
\(81\) −882.559 −1.21064
\(82\) −201.261 −0.271044
\(83\) −26.1539 −0.0345875 −0.0172938 0.999850i \(-0.505505\pi\)
−0.0172938 + 0.999850i \(0.505505\pi\)
\(84\) 749.051 0.972955
\(85\) −1064.31 −1.35813
\(86\) −1.67434 −0.00209940
\(87\) 1001.84 1.23458
\(88\) −124.526 −0.150846
\(89\) 352.887 0.420292 0.210146 0.977670i \(-0.432606\pi\)
0.210146 + 0.977670i \(0.432606\pi\)
\(90\) 76.6438 0.0897663
\(91\) 0 0
\(92\) −99.6743 −0.112954
\(93\) 388.282 0.432935
\(94\) −52.5950 −0.0577102
\(95\) 873.246 0.943086
\(96\) 760.056 0.808051
\(97\) −847.585 −0.887208 −0.443604 0.896223i \(-0.646300\pi\)
−0.443604 + 0.896223i \(0.646300\pi\)
\(98\) −41.3140 −0.0425851
\(99\) 89.5795 0.0909402
\(100\) −300.708 −0.300708
\(101\) 1293.46 1.27430 0.637150 0.770740i \(-0.280113\pi\)
0.637150 + 0.770740i \(0.280113\pi\)
\(102\) −359.264 −0.348750
\(103\) −1725.24 −1.65042 −0.825209 0.564828i \(-0.808943\pi\)
−0.825209 + 0.564828i \(0.808943\pi\)
\(104\) 0 0
\(105\) −1290.19 −1.19914
\(106\) −109.079 −0.0999502
\(107\) −484.179 −0.437452 −0.218726 0.975786i \(-0.570190\pi\)
−0.218726 + 0.975786i \(0.570190\pi\)
\(108\) 834.372 0.743402
\(109\) 64.2563 0.0564645 0.0282323 0.999601i \(-0.491012\pi\)
0.0282323 + 0.999601i \(0.491012\pi\)
\(110\) 103.527 0.0897355
\(111\) −242.205 −0.207109
\(112\) −870.543 −0.734452
\(113\) −2005.08 −1.66922 −0.834612 0.550839i \(-0.814308\pi\)
−0.834612 + 0.550839i \(0.814308\pi\)
\(114\) 294.769 0.242172
\(115\) 171.682 0.139213
\(116\) −1261.39 −1.00963
\(117\) 0 0
\(118\) −399.429 −0.311614
\(119\) 1401.39 1.07954
\(120\) −862.797 −0.656352
\(121\) 121.000 0.0909091
\(122\) 74.1587 0.0550329
\(123\) −1629.83 −1.19477
\(124\) −488.879 −0.354054
\(125\) −1089.10 −0.779298
\(126\) −100.918 −0.0713530
\(127\) 109.605 0.0765816 0.0382908 0.999267i \(-0.487809\pi\)
0.0382908 + 0.999267i \(0.487809\pi\)
\(128\) −1258.14 −0.868791
\(129\) −13.5589 −0.00925423
\(130\) 0 0
\(131\) 1156.71 0.771469 0.385734 0.922610i \(-0.373948\pi\)
0.385734 + 0.922610i \(0.373948\pi\)
\(132\) −486.736 −0.320946
\(133\) −1149.82 −0.749636
\(134\) −301.342 −0.194269
\(135\) −1437.15 −0.916223
\(136\) 937.164 0.590891
\(137\) −198.323 −0.123678 −0.0618391 0.998086i \(-0.519697\pi\)
−0.0618391 + 0.998086i \(0.519697\pi\)
\(138\) 57.9522 0.0357480
\(139\) −2900.14 −1.76969 −0.884844 0.465888i \(-0.845735\pi\)
−0.884844 + 0.465888i \(0.845735\pi\)
\(140\) 1624.46 0.980654
\(141\) −425.918 −0.254389
\(142\) 344.529 0.203607
\(143\) 0 0
\(144\) 418.789 0.242355
\(145\) 2172.67 1.24435
\(146\) −446.990 −0.253378
\(147\) −334.564 −0.187717
\(148\) 304.956 0.169373
\(149\) −3488.34 −1.91796 −0.958980 0.283472i \(-0.908514\pi\)
−0.958980 + 0.283472i \(0.908514\pi\)
\(150\) 174.836 0.0951687
\(151\) 1163.32 0.626953 0.313477 0.949596i \(-0.398506\pi\)
0.313477 + 0.949596i \(0.398506\pi\)
\(152\) −768.923 −0.410315
\(153\) −674.164 −0.356228
\(154\) −136.315 −0.0713286
\(155\) 842.061 0.436361
\(156\) 0 0
\(157\) 342.057 0.173880 0.0869398 0.996214i \(-0.472291\pi\)
0.0869398 + 0.996214i \(0.472291\pi\)
\(158\) −716.111 −0.360574
\(159\) −883.333 −0.440584
\(160\) 1648.32 0.814446
\(161\) −226.056 −0.110657
\(162\) −646.078 −0.313338
\(163\) 1394.89 0.670285 0.335142 0.942167i \(-0.391216\pi\)
0.335142 + 0.942167i \(0.391216\pi\)
\(164\) 2052.09 0.977082
\(165\) 838.369 0.395557
\(166\) −19.1460 −0.00895191
\(167\) −478.703 −0.221815 −0.110908 0.993831i \(-0.535376\pi\)
−0.110908 + 0.993831i \(0.535376\pi\)
\(168\) 1136.06 0.521718
\(169\) 0 0
\(170\) −779.131 −0.351509
\(171\) 553.138 0.247365
\(172\) 17.0718 0.00756809
\(173\) 1808.58 0.794822 0.397411 0.917641i \(-0.369909\pi\)
0.397411 + 0.917641i \(0.369909\pi\)
\(174\) 733.395 0.319532
\(175\) −681.990 −0.294592
\(176\) 565.682 0.242272
\(177\) −3234.61 −1.37361
\(178\) 258.331 0.108780
\(179\) −4429.85 −1.84973 −0.924867 0.380292i \(-0.875824\pi\)
−0.924867 + 0.380292i \(0.875824\pi\)
\(180\) −781.472 −0.323597
\(181\) 3409.17 1.40001 0.700005 0.714138i \(-0.253181\pi\)
0.700005 + 0.714138i \(0.253181\pi\)
\(182\) 0 0
\(183\) 600.543 0.242587
\(184\) −151.172 −0.0605682
\(185\) −525.267 −0.208748
\(186\) 284.242 0.112052
\(187\) −910.631 −0.356106
\(188\) 536.267 0.208039
\(189\) 1892.31 0.728283
\(190\) 639.261 0.244089
\(191\) 2923.75 1.10762 0.553810 0.832643i \(-0.313173\pi\)
0.553810 + 0.832643i \(0.313173\pi\)
\(192\) −1882.49 −0.707590
\(193\) 2484.18 0.926505 0.463253 0.886226i \(-0.346682\pi\)
0.463253 + 0.886226i \(0.346682\pi\)
\(194\) −620.475 −0.229626
\(195\) 0 0
\(196\) 421.244 0.153514
\(197\) 5125.67 1.85375 0.926876 0.375369i \(-0.122484\pi\)
0.926876 + 0.375369i \(0.122484\pi\)
\(198\) 65.5768 0.0235371
\(199\) −7.69219 −0.00274013 −0.00137006 0.999999i \(-0.500436\pi\)
−0.00137006 + 0.999999i \(0.500436\pi\)
\(200\) −456.071 −0.161246
\(201\) −2440.29 −0.856343
\(202\) 946.879 0.329813
\(203\) −2860.78 −0.989100
\(204\) 3663.11 1.25720
\(205\) −3534.59 −1.20423
\(206\) −1262.96 −0.427160
\(207\) 108.748 0.0365146
\(208\) 0 0
\(209\) 747.154 0.247281
\(210\) −944.484 −0.310360
\(211\) 3107.34 1.01383 0.506915 0.861996i \(-0.330786\pi\)
0.506915 + 0.861996i \(0.330786\pi\)
\(212\) 1112.19 0.360309
\(213\) 2790.03 0.897509
\(214\) −354.444 −0.113221
\(215\) −29.4050 −0.00932746
\(216\) 1265.46 0.398628
\(217\) −1108.75 −0.346853
\(218\) 47.0388 0.0146141
\(219\) −3619.76 −1.11690
\(220\) −1055.58 −0.323486
\(221\) 0 0
\(222\) −177.306 −0.0536037
\(223\) 12.3185 0.00369913 0.00184957 0.999998i \(-0.499411\pi\)
0.00184957 + 0.999998i \(0.499411\pi\)
\(224\) −2170.37 −0.647383
\(225\) 328.082 0.0972096
\(226\) −1467.82 −0.432027
\(227\) −4615.90 −1.34964 −0.674820 0.737983i \(-0.735779\pi\)
−0.674820 + 0.737983i \(0.735779\pi\)
\(228\) −3005.51 −0.873003
\(229\) −5074.63 −1.46437 −0.732186 0.681105i \(-0.761500\pi\)
−0.732186 + 0.681105i \(0.761500\pi\)
\(230\) 125.680 0.0360309
\(231\) −1103.89 −0.314419
\(232\) −1913.11 −0.541386
\(233\) 211.683 0.0595184 0.0297592 0.999557i \(-0.490526\pi\)
0.0297592 + 0.999557i \(0.490526\pi\)
\(234\) 0 0
\(235\) −923.683 −0.256402
\(236\) 4072.64 1.12333
\(237\) −5799.12 −1.58942
\(238\) 1025.89 0.279406
\(239\) −4312.49 −1.16716 −0.583581 0.812055i \(-0.698349\pi\)
−0.583581 + 0.812055i \(0.698349\pi\)
\(240\) 3919.42 1.05416
\(241\) 996.584 0.266372 0.133186 0.991091i \(-0.457479\pi\)
0.133186 + 0.991091i \(0.457479\pi\)
\(242\) 88.5781 0.0235290
\(243\) −2213.80 −0.584426
\(244\) −756.133 −0.198387
\(245\) −725.563 −0.189202
\(246\) −1193.12 −0.309230
\(247\) 0 0
\(248\) −741.464 −0.189851
\(249\) −155.046 −0.0394603
\(250\) −797.278 −0.201697
\(251\) −276.892 −0.0696306 −0.0348153 0.999394i \(-0.511084\pi\)
−0.0348153 + 0.999394i \(0.511084\pi\)
\(252\) 1028.97 0.257219
\(253\) 146.892 0.0365021
\(254\) 80.2364 0.0198208
\(255\) −6309.46 −1.54947
\(256\) 1619.36 0.395352
\(257\) −3235.18 −0.785233 −0.392617 0.919702i \(-0.628430\pi\)
−0.392617 + 0.919702i \(0.628430\pi\)
\(258\) −9.92581 −0.00239517
\(259\) 691.626 0.165929
\(260\) 0 0
\(261\) 1376.23 0.326384
\(262\) 846.772 0.199671
\(263\) 207.944 0.0487544 0.0243772 0.999703i \(-0.492240\pi\)
0.0243772 + 0.999703i \(0.492240\pi\)
\(264\) −738.213 −0.172098
\(265\) −1915.67 −0.444071
\(266\) −841.723 −0.194020
\(267\) 2091.99 0.479504
\(268\) 3072.53 0.700316
\(269\) 5033.04 1.14078 0.570390 0.821374i \(-0.306792\pi\)
0.570390 + 0.821374i \(0.306792\pi\)
\(270\) −1052.07 −0.237136
\(271\) −1487.01 −0.333319 −0.166660 0.986015i \(-0.553298\pi\)
−0.166660 + 0.986015i \(0.553298\pi\)
\(272\) −4257.25 −0.949021
\(273\) 0 0
\(274\) −145.183 −0.0320102
\(275\) 443.159 0.0971764
\(276\) −590.890 −0.128867
\(277\) −235.836 −0.0511552 −0.0255776 0.999673i \(-0.508142\pi\)
−0.0255776 + 0.999673i \(0.508142\pi\)
\(278\) −2123.05 −0.458029
\(279\) 533.384 0.114455
\(280\) 2463.75 0.525847
\(281\) 4915.01 1.04343 0.521717 0.853118i \(-0.325292\pi\)
0.521717 + 0.853118i \(0.325292\pi\)
\(282\) −311.794 −0.0658406
\(283\) −5199.56 −1.09216 −0.546081 0.837733i \(-0.683881\pi\)
−0.546081 + 0.837733i \(0.683881\pi\)
\(284\) −3512.87 −0.733981
\(285\) 5176.78 1.07595
\(286\) 0 0
\(287\) 4654.04 0.957210
\(288\) 1044.09 0.213624
\(289\) 1940.29 0.394930
\(290\) 1590.50 0.322060
\(291\) −5024.65 −1.01220
\(292\) 4557.58 0.913398
\(293\) 8880.92 1.77075 0.885373 0.464881i \(-0.153903\pi\)
0.885373 + 0.464881i \(0.153903\pi\)
\(294\) −244.918 −0.0485846
\(295\) −7014.85 −1.38448
\(296\) 462.515 0.0908215
\(297\) −1229.63 −0.240237
\(298\) −2553.64 −0.496405
\(299\) 0 0
\(300\) −1782.66 −0.343072
\(301\) 38.7180 0.00741417
\(302\) 851.612 0.162267
\(303\) 7667.90 1.45383
\(304\) 3492.99 0.659001
\(305\) 1302.39 0.244507
\(306\) −493.522 −0.0921987
\(307\) 1497.93 0.278474 0.139237 0.990259i \(-0.455535\pi\)
0.139237 + 0.990259i \(0.455535\pi\)
\(308\) 1389.89 0.257131
\(309\) −10227.6 −1.88293
\(310\) 616.432 0.112939
\(311\) −7484.71 −1.36469 −0.682345 0.731030i \(-0.739040\pi\)
−0.682345 + 0.731030i \(0.739040\pi\)
\(312\) 0 0
\(313\) −658.363 −0.118891 −0.0594455 0.998232i \(-0.518933\pi\)
−0.0594455 + 0.998232i \(0.518933\pi\)
\(314\) 250.403 0.0450034
\(315\) −1772.34 −0.317016
\(316\) 7301.57 1.29983
\(317\) −233.708 −0.0414080 −0.0207040 0.999786i \(-0.506591\pi\)
−0.0207040 + 0.999786i \(0.506591\pi\)
\(318\) −646.645 −0.114032
\(319\) 1858.94 0.326272
\(320\) −4082.53 −0.713189
\(321\) −2870.31 −0.499082
\(322\) −165.485 −0.0286401
\(323\) −5622.98 −0.968641
\(324\) 6587.51 1.12955
\(325\) 0 0
\(326\) 1021.13 0.173482
\(327\) 380.924 0.0644194
\(328\) 3112.33 0.523931
\(329\) 1216.23 0.203808
\(330\) 613.729 0.102378
\(331\) −8532.95 −1.41696 −0.708480 0.705731i \(-0.750619\pi\)
−0.708480 + 0.705731i \(0.750619\pi\)
\(332\) 195.215 0.0322706
\(333\) −332.718 −0.0547533
\(334\) −350.435 −0.0574100
\(335\) −5292.22 −0.863120
\(336\) −5160.76 −0.837924
\(337\) 11691.2 1.88979 0.944895 0.327373i \(-0.106163\pi\)
0.944895 + 0.327373i \(0.106163\pi\)
\(338\) 0 0
\(339\) −11886.5 −1.90439
\(340\) 7944.14 1.26715
\(341\) 720.472 0.114416
\(342\) 404.925 0.0640229
\(343\) 6761.73 1.06443
\(344\) 25.8921 0.00405817
\(345\) 1017.77 0.158825
\(346\) 1323.98 0.205715
\(347\) 4598.79 0.711459 0.355729 0.934589i \(-0.384232\pi\)
0.355729 + 0.934589i \(0.384232\pi\)
\(348\) −7477.80 −1.15187
\(349\) −6720.27 −1.03074 −0.515369 0.856968i \(-0.672345\pi\)
−0.515369 + 0.856968i \(0.672345\pi\)
\(350\) −499.251 −0.0762460
\(351\) 0 0
\(352\) 1410.31 0.213551
\(353\) −5738.70 −0.865270 −0.432635 0.901569i \(-0.642416\pi\)
−0.432635 + 0.901569i \(0.642416\pi\)
\(354\) −2367.90 −0.355515
\(355\) 6050.69 0.904611
\(356\) −2633.99 −0.392138
\(357\) 8307.75 1.23163
\(358\) −3242.87 −0.478746
\(359\) 4115.27 0.605001 0.302501 0.953149i \(-0.402179\pi\)
0.302501 + 0.953149i \(0.402179\pi\)
\(360\) −1185.23 −0.173519
\(361\) −2245.46 −0.327374
\(362\) 2495.69 0.362349
\(363\) 717.313 0.103717
\(364\) 0 0
\(365\) −7850.12 −1.12574
\(366\) 439.628 0.0627861
\(367\) 9662.99 1.37440 0.687199 0.726469i \(-0.258840\pi\)
0.687199 + 0.726469i \(0.258840\pi\)
\(368\) 686.729 0.0972778
\(369\) −2238.90 −0.315861
\(370\) −384.522 −0.0540279
\(371\) 2522.39 0.352981
\(372\) −2898.18 −0.403934
\(373\) −141.780 −0.0196812 −0.00984062 0.999952i \(-0.503132\pi\)
−0.00984062 + 0.999952i \(0.503132\pi\)
\(374\) −666.628 −0.0921671
\(375\) −6456.42 −0.889088
\(376\) 813.334 0.111555
\(377\) 0 0
\(378\) 1385.27 0.188494
\(379\) 2819.73 0.382163 0.191082 0.981574i \(-0.438800\pi\)
0.191082 + 0.981574i \(0.438800\pi\)
\(380\) −6518.00 −0.879911
\(381\) 649.760 0.0873707
\(382\) 2140.34 0.286673
\(383\) 6337.84 0.845557 0.422778 0.906233i \(-0.361055\pi\)
0.422778 + 0.906233i \(0.361055\pi\)
\(384\) −7458.53 −0.991189
\(385\) −2393.99 −0.316907
\(386\) 1818.55 0.239797
\(387\) −18.6259 −0.00244653
\(388\) 6326.46 0.827776
\(389\) −8805.25 −1.14767 −0.573836 0.818970i \(-0.694545\pi\)
−0.573836 + 0.818970i \(0.694545\pi\)
\(390\) 0 0
\(391\) −1105.49 −0.142985
\(392\) 638.883 0.0823176
\(393\) 6857.23 0.880156
\(394\) 3752.25 0.479786
\(395\) −12576.5 −1.60200
\(396\) −668.631 −0.0848484
\(397\) −4315.26 −0.545534 −0.272767 0.962080i \(-0.587939\pi\)
−0.272767 + 0.962080i \(0.587939\pi\)
\(398\) −5.63108 −0.000709197 0
\(399\) −6816.34 −0.855247
\(400\) 2071.79 0.258974
\(401\) −361.681 −0.0450411 −0.0225206 0.999746i \(-0.507169\pi\)
−0.0225206 + 0.999746i \(0.507169\pi\)
\(402\) −1786.42 −0.221638
\(403\) 0 0
\(404\) −9654.53 −1.18894
\(405\) −11346.5 −1.39213
\(406\) −2094.24 −0.255998
\(407\) −449.420 −0.0547345
\(408\) 5555.70 0.674137
\(409\) −9220.50 −1.11473 −0.557365 0.830268i \(-0.688188\pi\)
−0.557365 + 0.830268i \(0.688188\pi\)
\(410\) −2587.50 −0.311677
\(411\) −1175.70 −0.141102
\(412\) 12877.4 1.53986
\(413\) 9236.55 1.10049
\(414\) 79.6092 0.00945067
\(415\) −336.245 −0.0397726
\(416\) 0 0
\(417\) −17192.6 −2.01901
\(418\) 546.954 0.0640010
\(419\) −14912.9 −1.73876 −0.869380 0.494144i \(-0.835481\pi\)
−0.869380 + 0.494144i \(0.835481\pi\)
\(420\) 9630.11 1.11881
\(421\) 13486.0 1.56121 0.780603 0.625027i \(-0.214912\pi\)
0.780603 + 0.625027i \(0.214912\pi\)
\(422\) 2274.73 0.262399
\(423\) −585.085 −0.0672525
\(424\) 1686.81 0.193205
\(425\) −3335.16 −0.380656
\(426\) 2042.44 0.232292
\(427\) −1714.87 −0.194352
\(428\) 3613.96 0.408148
\(429\) 0 0
\(430\) −21.5260 −0.00241413
\(431\) −406.334 −0.0454116 −0.0227058 0.999742i \(-0.507228\pi\)
−0.0227058 + 0.999742i \(0.507228\pi\)
\(432\) −5748.59 −0.640230
\(433\) −1766.69 −0.196078 −0.0980391 0.995183i \(-0.531257\pi\)
−0.0980391 + 0.995183i \(0.531257\pi\)
\(434\) −811.664 −0.0897722
\(435\) 12880.0 1.41965
\(436\) −479.615 −0.0526821
\(437\) 907.033 0.0992889
\(438\) −2649.85 −0.289075
\(439\) 7824.19 0.850634 0.425317 0.905044i \(-0.360163\pi\)
0.425317 + 0.905044i \(0.360163\pi\)
\(440\) −1600.95 −0.173460
\(441\) −459.591 −0.0496265
\(442\) 0 0
\(443\) 11667.9 1.25137 0.625686 0.780075i \(-0.284819\pi\)
0.625686 + 0.780075i \(0.284819\pi\)
\(444\) 1807.84 0.193235
\(445\) 4536.86 0.483299
\(446\) 9.01776 0.000957406 0
\(447\) −20679.6 −2.18817
\(448\) 5375.53 0.566897
\(449\) −16975.3 −1.78421 −0.892107 0.451825i \(-0.850773\pi\)
−0.892107 + 0.451825i \(0.850773\pi\)
\(450\) 240.173 0.0251597
\(451\) −3024.21 −0.315753
\(452\) 14966.1 1.55741
\(453\) 6896.42 0.715280
\(454\) −3379.07 −0.349312
\(455\) 0 0
\(456\) −4558.33 −0.468122
\(457\) 16192.9 1.65748 0.828741 0.559632i \(-0.189057\pi\)
0.828741 + 0.559632i \(0.189057\pi\)
\(458\) −3714.89 −0.379007
\(459\) 9254.05 0.941050
\(460\) −1281.45 −0.129887
\(461\) −8586.04 −0.867444 −0.433722 0.901047i \(-0.642800\pi\)
−0.433722 + 0.901047i \(0.642800\pi\)
\(462\) −808.105 −0.0813776
\(463\) 7917.20 0.794694 0.397347 0.917668i \(-0.369931\pi\)
0.397347 + 0.917668i \(0.369931\pi\)
\(464\) 8690.67 0.869513
\(465\) 4991.91 0.497837
\(466\) 154.962 0.0154045
\(467\) −15155.0 −1.50169 −0.750844 0.660480i \(-0.770353\pi\)
−0.750844 + 0.660480i \(0.770353\pi\)
\(468\) 0 0
\(469\) 6968.34 0.686073
\(470\) −676.183 −0.0663617
\(471\) 2027.78 0.198376
\(472\) 6176.82 0.602354
\(473\) −25.1591 −0.00244570
\(474\) −4245.25 −0.411373
\(475\) 2736.43 0.264328
\(476\) −10460.2 −1.00723
\(477\) −1213.44 −0.116477
\(478\) −3156.96 −0.302084
\(479\) −10001.1 −0.953993 −0.476996 0.878905i \(-0.658275\pi\)
−0.476996 + 0.878905i \(0.658275\pi\)
\(480\) 9771.59 0.929188
\(481\) 0 0
\(482\) 729.550 0.0689421
\(483\) −1340.11 −0.126246
\(484\) −903.156 −0.0848193
\(485\) −10896.9 −1.02021
\(486\) −1620.62 −0.151261
\(487\) −7044.54 −0.655480 −0.327740 0.944768i \(-0.606287\pi\)
−0.327740 + 0.944768i \(0.606287\pi\)
\(488\) −1146.80 −0.106379
\(489\) 8269.21 0.764717
\(490\) −531.149 −0.0489691
\(491\) −13326.4 −1.22487 −0.612437 0.790520i \(-0.709811\pi\)
−0.612437 + 0.790520i \(0.709811\pi\)
\(492\) 12165.2 1.11474
\(493\) −13990.2 −1.27806
\(494\) 0 0
\(495\) 1151.67 0.104573
\(496\) 3368.25 0.304917
\(497\) −7967.02 −0.719054
\(498\) −113.501 −0.0102131
\(499\) 20069.1 1.80044 0.900218 0.435440i \(-0.143407\pi\)
0.900218 + 0.435440i \(0.143407\pi\)
\(500\) 8129.17 0.727095
\(501\) −2837.85 −0.253065
\(502\) −202.699 −0.0180217
\(503\) 7782.35 0.689856 0.344928 0.938629i \(-0.387903\pi\)
0.344928 + 0.938629i \(0.387903\pi\)
\(504\) 1560.60 0.137926
\(505\) 16629.3 1.46533
\(506\) 107.532 0.00944744
\(507\) 0 0
\(508\) −818.102 −0.0714516
\(509\) 1475.93 0.128526 0.0642628 0.997933i \(-0.479530\pi\)
0.0642628 + 0.997933i \(0.479530\pi\)
\(510\) −4618.85 −0.401031
\(511\) 10336.4 0.894821
\(512\) 11250.6 0.971116
\(513\) −7592.75 −0.653466
\(514\) −2368.32 −0.203233
\(515\) −22180.4 −1.89784
\(516\) 101.205 0.00863431
\(517\) −790.307 −0.0672295
\(518\) 506.305 0.0429455
\(519\) 10721.7 0.906799
\(520\) 0 0
\(521\) 7609.43 0.639875 0.319938 0.947439i \(-0.396338\pi\)
0.319938 + 0.947439i \(0.396338\pi\)
\(522\) 1007.47 0.0844744
\(523\) 12452.9 1.04116 0.520581 0.853812i \(-0.325715\pi\)
0.520581 + 0.853812i \(0.325715\pi\)
\(524\) −8633.82 −0.719790
\(525\) −4042.97 −0.336095
\(526\) 152.226 0.0126186
\(527\) −5422.18 −0.448186
\(528\) 3353.48 0.276404
\(529\) −11988.7 −0.985344
\(530\) −1402.37 −0.114934
\(531\) −4443.39 −0.363139
\(532\) 8582.34 0.699420
\(533\) 0 0
\(534\) 1531.44 0.124105
\(535\) −6224.81 −0.503031
\(536\) 4659.99 0.375524
\(537\) −26261.0 −2.11033
\(538\) 3684.44 0.295255
\(539\) −620.795 −0.0496095
\(540\) 10727.0 0.854847
\(541\) −9312.17 −0.740039 −0.370020 0.929024i \(-0.620649\pi\)
−0.370020 + 0.929024i \(0.620649\pi\)
\(542\) −1088.57 −0.0862693
\(543\) 20210.3 1.59725
\(544\) −10613.8 −0.836515
\(545\) 826.105 0.0649292
\(546\) 0 0
\(547\) −11018.6 −0.861278 −0.430639 0.902524i \(-0.641712\pi\)
−0.430639 + 0.902524i \(0.641712\pi\)
\(548\) 1480.31 0.115393
\(549\) 824.968 0.0641325
\(550\) 324.415 0.0251511
\(551\) 11478.6 0.887490
\(552\) −896.179 −0.0691013
\(553\) 16559.6 1.27339
\(554\) −172.644 −0.0132399
\(555\) −3113.89 −0.238157
\(556\) 21646.9 1.65114
\(557\) 12018.4 0.914250 0.457125 0.889403i \(-0.348879\pi\)
0.457125 + 0.889403i \(0.348879\pi\)
\(558\) 390.464 0.0296231
\(559\) 0 0
\(560\) −11192.1 −0.844555
\(561\) −5398.40 −0.406276
\(562\) 3598.04 0.270061
\(563\) −8763.89 −0.656046 −0.328023 0.944670i \(-0.606382\pi\)
−0.328023 + 0.944670i \(0.606382\pi\)
\(564\) 3179.10 0.237348
\(565\) −25778.1 −1.91946
\(566\) −3806.34 −0.282672
\(567\) 14940.1 1.10657
\(568\) −5327.84 −0.393576
\(569\) −10273.2 −0.756895 −0.378447 0.925623i \(-0.623542\pi\)
−0.378447 + 0.925623i \(0.623542\pi\)
\(570\) 3789.67 0.278477
\(571\) 2602.62 0.190747 0.0953734 0.995442i \(-0.469596\pi\)
0.0953734 + 0.995442i \(0.469596\pi\)
\(572\) 0 0
\(573\) 17332.6 1.26366
\(574\) 3406.99 0.247744
\(575\) 537.988 0.0390185
\(576\) −2585.99 −0.187065
\(577\) 19727.0 1.42331 0.711653 0.702532i \(-0.247947\pi\)
0.711653 + 0.702532i \(0.247947\pi\)
\(578\) 1420.39 0.102215
\(579\) 14726.7 1.05703
\(580\) −16217.0 −1.16099
\(581\) 442.739 0.0316143
\(582\) −3678.30 −0.261977
\(583\) −1639.06 −0.116437
\(584\) 6912.30 0.489783
\(585\) 0 0
\(586\) 6501.28 0.458303
\(587\) 10116.2 0.711309 0.355654 0.934618i \(-0.384258\pi\)
0.355654 + 0.934618i \(0.384258\pi\)
\(588\) 2497.22 0.175142
\(589\) 4448.78 0.311221
\(590\) −5135.23 −0.358329
\(591\) 30386.0 2.11491
\(592\) −2101.07 −0.145867
\(593\) −3130.32 −0.216774 −0.108387 0.994109i \(-0.534569\pi\)
−0.108387 + 0.994109i \(0.534569\pi\)
\(594\) −900.152 −0.0621779
\(595\) 18016.9 1.24138
\(596\) 26037.3 1.78948
\(597\) −45.6009 −0.00312616
\(598\) 0 0
\(599\) 10080.1 0.687581 0.343790 0.939046i \(-0.388289\pi\)
0.343790 + 0.939046i \(0.388289\pi\)
\(600\) −2703.68 −0.183962
\(601\) 4777.02 0.324224 0.162112 0.986772i \(-0.448169\pi\)
0.162112 + 0.986772i \(0.448169\pi\)
\(602\) 28.3435 0.00191893
\(603\) −3352.24 −0.226391
\(604\) −8683.16 −0.584955
\(605\) 1555.63 0.104537
\(606\) 5613.29 0.376278
\(607\) −2571.35 −0.171941 −0.0859703 0.996298i \(-0.527399\pi\)
−0.0859703 + 0.996298i \(0.527399\pi\)
\(608\) 8708.43 0.580877
\(609\) −16959.3 −1.12845
\(610\) 953.414 0.0632830
\(611\) 0 0
\(612\) 5032.03 0.332366
\(613\) −12711.9 −0.837564 −0.418782 0.908087i \(-0.637543\pi\)
−0.418782 + 0.908087i \(0.637543\pi\)
\(614\) 1096.56 0.0720744
\(615\) −20953.8 −1.37388
\(616\) 2107.99 0.137879
\(617\) −16236.1 −1.05939 −0.529693 0.848189i \(-0.677693\pi\)
−0.529693 + 0.848189i \(0.677693\pi\)
\(618\) −7487.11 −0.487339
\(619\) −12657.3 −0.821874 −0.410937 0.911664i \(-0.634798\pi\)
−0.410937 + 0.911664i \(0.634798\pi\)
\(620\) −6285.23 −0.407131
\(621\) −1492.75 −0.0964607
\(622\) −5479.19 −0.353208
\(623\) −5973.75 −0.384162
\(624\) 0 0
\(625\) −19037.8 −1.21842
\(626\) −481.955 −0.0307713
\(627\) 4429.28 0.282119
\(628\) −2553.15 −0.162232
\(629\) 3382.28 0.214404
\(630\) −1297.44 −0.0820497
\(631\) 3949.97 0.249201 0.124600 0.992207i \(-0.460235\pi\)
0.124600 + 0.992207i \(0.460235\pi\)
\(632\) 11074.0 0.696994
\(633\) 18421.0 1.15666
\(634\) −171.086 −0.0107172
\(635\) 1409.13 0.0880621
\(636\) 6593.29 0.411070
\(637\) 0 0
\(638\) 1360.84 0.0844455
\(639\) 3832.67 0.237274
\(640\) −16175.2 −0.999033
\(641\) −7398.27 −0.455872 −0.227936 0.973676i \(-0.573198\pi\)
−0.227936 + 0.973676i \(0.573198\pi\)
\(642\) −2101.22 −0.129172
\(643\) 12491.7 0.766134 0.383067 0.923721i \(-0.374868\pi\)
0.383067 + 0.923721i \(0.374868\pi\)
\(644\) 1687.31 0.103244
\(645\) −174.319 −0.0106415
\(646\) −4116.31 −0.250703
\(647\) −10472.0 −0.636315 −0.318158 0.948038i \(-0.603064\pi\)
−0.318158 + 0.948038i \(0.603064\pi\)
\(648\) 9991.02 0.605685
\(649\) −6001.94 −0.363015
\(650\) 0 0
\(651\) −6572.92 −0.395719
\(652\) −10411.6 −0.625384
\(653\) 6337.94 0.379820 0.189910 0.981801i \(-0.439180\pi\)
0.189910 + 0.981801i \(0.439180\pi\)
\(654\) 278.856 0.0166730
\(655\) 14871.2 0.887121
\(656\) −14138.4 −0.841479
\(657\) −4972.48 −0.295274
\(658\) 890.339 0.0527493
\(659\) 15196.7 0.898302 0.449151 0.893456i \(-0.351726\pi\)
0.449151 + 0.893456i \(0.351726\pi\)
\(660\) −6257.67 −0.369060
\(661\) −2298.17 −0.135232 −0.0676161 0.997711i \(-0.521539\pi\)
−0.0676161 + 0.997711i \(0.521539\pi\)
\(662\) −6246.55 −0.366736
\(663\) 0 0
\(664\) 296.075 0.0173042
\(665\) −14782.5 −0.862016
\(666\) −243.566 −0.0141712
\(667\) 2256.73 0.131006
\(668\) 3573.09 0.206956
\(669\) 73.0265 0.00422028
\(670\) −3874.18 −0.223392
\(671\) 1114.33 0.0641106
\(672\) −12866.4 −0.738589
\(673\) 23199.6 1.32880 0.664398 0.747379i \(-0.268688\pi\)
0.664398 + 0.747379i \(0.268688\pi\)
\(674\) 8558.54 0.489114
\(675\) −4503.49 −0.256799
\(676\) 0 0
\(677\) −2145.38 −0.121793 −0.0608963 0.998144i \(-0.519396\pi\)
−0.0608963 + 0.998144i \(0.519396\pi\)
\(678\) −8701.55 −0.492892
\(679\) 14348.1 0.810941
\(680\) 12048.6 0.679472
\(681\) −27364.0 −1.53978
\(682\) 527.422 0.0296129
\(683\) 29544.6 1.65519 0.827593 0.561329i \(-0.189710\pi\)
0.827593 + 0.561329i \(0.189710\pi\)
\(684\) −4128.68 −0.230795
\(685\) −2549.72 −0.142219
\(686\) 4949.93 0.275495
\(687\) −30083.4 −1.67068
\(688\) −117.620 −0.00651776
\(689\) 0 0
\(690\) 745.057 0.0411070
\(691\) −27803.1 −1.53065 −0.765325 0.643644i \(-0.777422\pi\)
−0.765325 + 0.643644i \(0.777422\pi\)
\(692\) −13499.5 −0.741579
\(693\) −1516.42 −0.0831227
\(694\) 3366.55 0.184139
\(695\) −37285.4 −2.03498
\(696\) −11341.3 −0.617659
\(697\) 22759.8 1.23686
\(698\) −4919.58 −0.266775
\(699\) 1254.90 0.0679036
\(700\) 5090.44 0.274858
\(701\) −19697.8 −1.06130 −0.530652 0.847590i \(-0.678053\pi\)
−0.530652 + 0.847590i \(0.678053\pi\)
\(702\) 0 0
\(703\) −2775.09 −0.148883
\(704\) −3493.03 −0.187001
\(705\) −5475.78 −0.292524
\(706\) −4201.02 −0.223948
\(707\) −21896.0 −1.16476
\(708\) 24143.5 1.28159
\(709\) −19122.5 −1.01292 −0.506460 0.862263i \(-0.669046\pi\)
−0.506460 + 0.862263i \(0.669046\pi\)
\(710\) 4429.41 0.234131
\(711\) −7966.27 −0.420195
\(712\) −3994.86 −0.210272
\(713\) 874.641 0.0459405
\(714\) 6081.70 0.318770
\(715\) 0 0
\(716\) 33064.8 1.72582
\(717\) −25565.3 −1.33160
\(718\) 3012.59 0.156586
\(719\) 1837.44 0.0953060 0.0476530 0.998864i \(-0.484826\pi\)
0.0476530 + 0.998864i \(0.484826\pi\)
\(720\) 5384.13 0.278687
\(721\) 29205.2 1.50854
\(722\) −1643.79 −0.0847307
\(723\) 5907.95 0.303899
\(724\) −25446.4 −1.30623
\(725\) 6808.33 0.348765
\(726\) 525.109 0.0268438
\(727\) −7555.46 −0.385442 −0.192721 0.981254i \(-0.561731\pi\)
−0.192721 + 0.981254i \(0.561731\pi\)
\(728\) 0 0
\(729\) 10705.2 0.543881
\(730\) −5746.69 −0.291362
\(731\) 189.344 0.00958021
\(732\) −4482.51 −0.226337
\(733\) −11984.6 −0.603905 −0.301952 0.953323i \(-0.597638\pi\)
−0.301952 + 0.953323i \(0.597638\pi\)
\(734\) 7073.80 0.355720
\(735\) −4301.29 −0.215858
\(736\) 1712.10 0.0857456
\(737\) −4528.05 −0.226313
\(738\) −1638.99 −0.0817508
\(739\) 27142.5 1.35109 0.675543 0.737321i \(-0.263909\pi\)
0.675543 + 0.737321i \(0.263909\pi\)
\(740\) 3920.64 0.194764
\(741\) 0 0
\(742\) 1846.52 0.0913582
\(743\) 29222.6 1.44290 0.721450 0.692467i \(-0.243476\pi\)
0.721450 + 0.692467i \(0.243476\pi\)
\(744\) −4395.55 −0.216598
\(745\) −44847.6 −2.20549
\(746\) −103.790 −0.00509388
\(747\) −212.987 −0.0104321
\(748\) 6797.04 0.332252
\(749\) 8196.29 0.399847
\(750\) −4726.43 −0.230113
\(751\) −8859.39 −0.430471 −0.215236 0.976562i \(-0.569052\pi\)
−0.215236 + 0.976562i \(0.569052\pi\)
\(752\) −3694.73 −0.179166
\(753\) −1641.47 −0.0794404
\(754\) 0 0
\(755\) 14956.2 0.720941
\(756\) −14124.4 −0.679497
\(757\) 35734.4 1.71571 0.857853 0.513896i \(-0.171798\pi\)
0.857853 + 0.513896i \(0.171798\pi\)
\(758\) 2064.19 0.0989112
\(759\) 870.806 0.0416446
\(760\) −9885.59 −0.471826
\(761\) −34394.7 −1.63838 −0.819189 0.573524i \(-0.805576\pi\)
−0.819189 + 0.573524i \(0.805576\pi\)
\(762\) 475.658 0.0226132
\(763\) −1087.74 −0.0516107
\(764\) −21823.2 −1.03342
\(765\) −8667.33 −0.409631
\(766\) 4639.62 0.218846
\(767\) 0 0
\(768\) 9599.92 0.451051
\(769\) 11602.7 0.544091 0.272045 0.962284i \(-0.412300\pi\)
0.272045 + 0.962284i \(0.412300\pi\)
\(770\) −1752.53 −0.0820216
\(771\) −19178.8 −0.895859
\(772\) −18542.2 −0.864441
\(773\) 12680.6 0.590026 0.295013 0.955493i \(-0.404676\pi\)
0.295013 + 0.955493i \(0.404676\pi\)
\(774\) −13.6351 −0.000633210 0
\(775\) 2638.71 0.122303
\(776\) 9595.09 0.443871
\(777\) 4100.10 0.189305
\(778\) −6445.89 −0.297039
\(779\) −18674.0 −0.858876
\(780\) 0 0
\(781\) 5176.99 0.237193
\(782\) −809.276 −0.0370072
\(783\) −18891.0 −0.862210
\(784\) −2902.25 −0.132209
\(785\) 4397.62 0.199946
\(786\) 5019.84 0.227801
\(787\) 4417.61 0.200090 0.100045 0.994983i \(-0.468101\pi\)
0.100045 + 0.994983i \(0.468101\pi\)
\(788\) −38258.5 −1.72957
\(789\) 1232.74 0.0556231
\(790\) −9206.61 −0.414628
\(791\) 33942.4 1.52573
\(792\) −1014.09 −0.0454974
\(793\) 0 0
\(794\) −3158.99 −0.141194
\(795\) −11356.5 −0.506633
\(796\) 57.4153 0.00255657
\(797\) −27030.1 −1.20132 −0.600661 0.799504i \(-0.705096\pi\)
−0.600661 + 0.799504i \(0.705096\pi\)
\(798\) −4989.91 −0.221354
\(799\) 5947.75 0.263350
\(800\) 5165.23 0.228273
\(801\) 2873.77 0.126766
\(802\) −264.769 −0.0116575
\(803\) −6716.60 −0.295173
\(804\) 18214.6 0.798979
\(805\) −2906.27 −0.127246
\(806\) 0 0
\(807\) 29836.9 1.30150
\(808\) −14642.6 −0.637533
\(809\) 23647.0 1.02767 0.513835 0.857889i \(-0.328224\pi\)
0.513835 + 0.857889i \(0.328224\pi\)
\(810\) −8306.24 −0.360311
\(811\) −33486.1 −1.44988 −0.724941 0.688811i \(-0.758133\pi\)
−0.724941 + 0.688811i \(0.758133\pi\)
\(812\) 21353.1 0.922843
\(813\) −8815.30 −0.380278
\(814\) −328.999 −0.0141663
\(815\) 17933.3 0.770768
\(816\) −25237.8 −1.08272
\(817\) −155.353 −0.00665251
\(818\) −6749.88 −0.288513
\(819\) 0 0
\(820\) 26382.5 1.12356
\(821\) −2605.69 −0.110766 −0.0553832 0.998465i \(-0.517638\pi\)
−0.0553832 + 0.998465i \(0.517638\pi\)
\(822\) −860.673 −0.0365200
\(823\) 31976.2 1.35434 0.677169 0.735828i \(-0.263207\pi\)
0.677169 + 0.735828i \(0.263207\pi\)
\(824\) 19530.6 0.825705
\(825\) 2627.14 0.110867
\(826\) 6761.62 0.284827
\(827\) 37759.0 1.58768 0.793839 0.608128i \(-0.208079\pi\)
0.793839 + 0.608128i \(0.208079\pi\)
\(828\) −811.707 −0.0340686
\(829\) −1137.55 −0.0476584 −0.0238292 0.999716i \(-0.507586\pi\)
−0.0238292 + 0.999716i \(0.507586\pi\)
\(830\) −246.149 −0.0102939
\(831\) −1398.08 −0.0583621
\(832\) 0 0
\(833\) 4672.03 0.194329
\(834\) −12585.9 −0.522557
\(835\) −6154.40 −0.255068
\(836\) −5576.83 −0.230716
\(837\) −7321.60 −0.302356
\(838\) −10917.0 −0.450024
\(839\) 37372.2 1.53782 0.768911 0.639356i \(-0.220799\pi\)
0.768911 + 0.639356i \(0.220799\pi\)
\(840\) 14605.6 0.599930
\(841\) 4170.26 0.170989
\(842\) 9872.44 0.404070
\(843\) 29137.2 1.19044
\(844\) −23193.5 −0.945917
\(845\) 0 0
\(846\) −428.312 −0.0174062
\(847\) −2048.31 −0.0830943
\(848\) −7662.68 −0.310304
\(849\) −30824.0 −1.24603
\(850\) −2441.51 −0.0985211
\(851\) −545.589 −0.0219772
\(852\) −20825.0 −0.837387
\(853\) 22490.8 0.902780 0.451390 0.892327i \(-0.350928\pi\)
0.451390 + 0.892327i \(0.350928\pi\)
\(854\) −1255.37 −0.0503021
\(855\) 7111.36 0.284449
\(856\) 5481.16 0.218858
\(857\) 43409.5 1.73027 0.865135 0.501539i \(-0.167233\pi\)
0.865135 + 0.501539i \(0.167233\pi\)
\(858\) 0 0
\(859\) 29533.2 1.17306 0.586532 0.809926i \(-0.300493\pi\)
0.586532 + 0.809926i \(0.300493\pi\)
\(860\) 219.482 0.00870264
\(861\) 27590.1 1.09207
\(862\) −297.457 −0.0117534
\(863\) −14351.6 −0.566090 −0.283045 0.959107i \(-0.591345\pi\)
−0.283045 + 0.959107i \(0.591345\pi\)
\(864\) −14331.9 −0.564331
\(865\) 23251.9 0.913975
\(866\) −1293.31 −0.0507488
\(867\) 11502.4 0.450569
\(868\) 8275.85 0.323618
\(869\) −10760.5 −0.420051
\(870\) 9428.82 0.367433
\(871\) 0 0
\(872\) −727.413 −0.0282492
\(873\) −6902.39 −0.267595
\(874\) 663.994 0.0256979
\(875\) 18436.5 0.712307
\(876\) 27018.3 1.04208
\(877\) 43248.7 1.66523 0.832614 0.553854i \(-0.186844\pi\)
0.832614 + 0.553854i \(0.186844\pi\)
\(878\) 5727.71 0.220160
\(879\) 52647.9 2.02021
\(880\) 7272.64 0.278591
\(881\) 3816.13 0.145935 0.0729675 0.997334i \(-0.476753\pi\)
0.0729675 + 0.997334i \(0.476753\pi\)
\(882\) −336.444 −0.0128443
\(883\) 48787.6 1.85938 0.929690 0.368343i \(-0.120075\pi\)
0.929690 + 0.368343i \(0.120075\pi\)
\(884\) 0 0
\(885\) −41585.5 −1.57953
\(886\) 8541.49 0.323879
\(887\) 41495.1 1.57077 0.785384 0.619009i \(-0.212466\pi\)
0.785384 + 0.619009i \(0.212466\pi\)
\(888\) 2741.88 0.103617
\(889\) −1855.41 −0.0699984
\(890\) 3321.21 0.125087
\(891\) −9708.15 −0.365023
\(892\) −91.9464 −0.00345134
\(893\) −4880.01 −0.182870
\(894\) −15138.5 −0.566340
\(895\) −56951.9 −2.12703
\(896\) 21298.1 0.794107
\(897\) 0 0
\(898\) −12426.7 −0.461788
\(899\) 11068.7 0.410637
\(900\) −2448.84 −0.0906978
\(901\) 12335.3 0.456104
\(902\) −2213.88 −0.0817228
\(903\) 229.528 0.00845871
\(904\) 22698.5 0.835113
\(905\) 43829.7 1.60989
\(906\) 5048.53 0.185128
\(907\) 21615.3 0.791316 0.395658 0.918398i \(-0.370517\pi\)
0.395658 + 0.918398i \(0.370517\pi\)
\(908\) 34453.6 1.25923
\(909\) 10533.4 0.384347
\(910\) 0 0
\(911\) 3646.35 0.132611 0.0663057 0.997799i \(-0.478879\pi\)
0.0663057 + 0.997799i \(0.478879\pi\)
\(912\) 20707.1 0.751844
\(913\) −287.693 −0.0104285
\(914\) 11854.0 0.428988
\(915\) 7720.82 0.278954
\(916\) 37877.6 1.36628
\(917\) −19581.1 −0.705151
\(918\) 6774.43 0.243562
\(919\) 31280.0 1.12278 0.561388 0.827553i \(-0.310267\pi\)
0.561388 + 0.827553i \(0.310267\pi\)
\(920\) −1943.53 −0.0696482
\(921\) 8880.05 0.317707
\(922\) −6285.42 −0.224511
\(923\) 0 0
\(924\) 8239.56 0.293357
\(925\) −1645.99 −0.0585079
\(926\) 5795.79 0.205682
\(927\) −14049.7 −0.497790
\(928\) 21666.9 0.766433
\(929\) −6557.92 −0.231602 −0.115801 0.993272i \(-0.536944\pi\)
−0.115801 + 0.993272i \(0.536944\pi\)
\(930\) 3654.33 0.128850
\(931\) −3833.30 −0.134942
\(932\) −1580.02 −0.0555314
\(933\) −44370.9 −1.55695
\(934\) −11094.2 −0.388665
\(935\) −11707.4 −0.409491
\(936\) 0 0
\(937\) −24473.3 −0.853265 −0.426632 0.904425i \(-0.640300\pi\)
−0.426632 + 0.904425i \(0.640300\pi\)
\(938\) 5101.18 0.177569
\(939\) −3902.91 −0.135641
\(940\) 6894.46 0.239226
\(941\) −15420.8 −0.534224 −0.267112 0.963665i \(-0.586069\pi\)
−0.267112 + 0.963665i \(0.586069\pi\)
\(942\) 1484.44 0.0513436
\(943\) −3671.34 −0.126782
\(944\) −28059.4 −0.967432
\(945\) 24328.3 0.837461
\(946\) −18.4177 −0.000632993 0
\(947\) 33141.2 1.13722 0.568608 0.822609i \(-0.307482\pi\)
0.568608 + 0.822609i \(0.307482\pi\)
\(948\) 43285.2 1.48295
\(949\) 0 0
\(950\) 2003.20 0.0684132
\(951\) −1385.47 −0.0472417
\(952\) −15864.5 −0.540096
\(953\) −20735.4 −0.704813 −0.352406 0.935847i \(-0.614637\pi\)
−0.352406 + 0.935847i \(0.614637\pi\)
\(954\) −888.298 −0.0301464
\(955\) 37589.0 1.27367
\(956\) 32188.9 1.08898
\(957\) 11020.2 0.372239
\(958\) −7321.32 −0.246911
\(959\) 3357.26 0.113046
\(960\) −24202.1 −0.813666
\(961\) −25501.1 −0.856000
\(962\) 0 0
\(963\) −3942.96 −0.131942
\(964\) −7438.60 −0.248528
\(965\) 31937.7 1.06540
\(966\) −981.027 −0.0326750
\(967\) 8178.87 0.271990 0.135995 0.990710i \(-0.456577\pi\)
0.135995 + 0.990710i \(0.456577\pi\)
\(968\) −1369.78 −0.0454819
\(969\) −33334.2 −1.10511
\(970\) −7977.08 −0.264050
\(971\) −20576.1 −0.680039 −0.340020 0.940418i \(-0.610434\pi\)
−0.340020 + 0.940418i \(0.610434\pi\)
\(972\) 16524.1 0.545277
\(973\) 49094.1 1.61756
\(974\) −5156.96 −0.169651
\(975\) 0 0
\(976\) 5209.55 0.170854
\(977\) −14541.9 −0.476188 −0.238094 0.971242i \(-0.576523\pi\)
−0.238094 + 0.971242i \(0.576523\pi\)
\(978\) 6053.48 0.197923
\(979\) 3881.76 0.126723
\(980\) 5415.68 0.176528
\(981\) 523.277 0.0170305
\(982\) −9755.62 −0.317021
\(983\) 29285.7 0.950223 0.475111 0.879926i \(-0.342408\pi\)
0.475111 + 0.879926i \(0.342408\pi\)
\(984\) 18450.5 0.597745
\(985\) 65897.7 2.13165
\(986\) −10241.5 −0.330787
\(987\) 7210.03 0.232521
\(988\) 0 0
\(989\) −30.5427 −0.000982004 0
\(990\) 843.082 0.0270655
\(991\) −38085.9 −1.22083 −0.610413 0.792083i \(-0.708997\pi\)
−0.610413 + 0.792083i \(0.708997\pi\)
\(992\) 8397.44 0.268769
\(993\) −50585.1 −1.61658
\(994\) −5832.26 −0.186105
\(995\) −98.8940 −0.00315090
\(996\) 1157.28 0.0368170
\(997\) −26803.6 −0.851434 −0.425717 0.904856i \(-0.639978\pi\)
−0.425717 + 0.904856i \(0.639978\pi\)
\(998\) 14691.6 0.465987
\(999\) 4567.12 0.144642
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 1859.4.a.a.1.2 2
13.12 even 2 11.4.a.a.1.1 2
39.38 odd 2 99.4.a.c.1.2 2
52.51 odd 2 176.4.a.i.1.1 2
65.12 odd 4 275.4.b.c.199.2 4
65.38 odd 4 275.4.b.c.199.3 4
65.64 even 2 275.4.a.b.1.2 2
91.90 odd 2 539.4.a.e.1.1 2
104.51 odd 2 704.4.a.n.1.2 2
104.77 even 2 704.4.a.p.1.1 2
143.25 even 10 121.4.c.c.9.1 8
143.38 even 10 121.4.c.c.3.2 8
143.51 odd 10 121.4.c.f.27.2 8
143.64 even 10 121.4.c.c.81.2 8
143.90 odd 10 121.4.c.f.81.1 8
143.103 even 10 121.4.c.c.27.1 8
143.116 odd 10 121.4.c.f.3.1 8
143.129 odd 10 121.4.c.f.9.2 8
143.142 odd 2 121.4.a.c.1.2 2
156.155 even 2 1584.4.a.bc.1.2 2
195.194 odd 2 2475.4.a.q.1.1 2
429.428 even 2 1089.4.a.v.1.1 2
572.571 even 2 1936.4.a.w.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.4.a.a.1.1 2 13.12 even 2
99.4.a.c.1.2 2 39.38 odd 2
121.4.a.c.1.2 2 143.142 odd 2
121.4.c.c.3.2 8 143.38 even 10
121.4.c.c.9.1 8 143.25 even 10
121.4.c.c.27.1 8 143.103 even 10
121.4.c.c.81.2 8 143.64 even 10
121.4.c.f.3.1 8 143.116 odd 10
121.4.c.f.9.2 8 143.129 odd 10
121.4.c.f.27.2 8 143.51 odd 10
121.4.c.f.81.1 8 143.90 odd 10
176.4.a.i.1.1 2 52.51 odd 2
275.4.a.b.1.2 2 65.64 even 2
275.4.b.c.199.2 4 65.12 odd 4
275.4.b.c.199.3 4 65.38 odd 4
539.4.a.e.1.1 2 91.90 odd 2
704.4.a.n.1.2 2 104.51 odd 2
704.4.a.p.1.1 2 104.77 even 2
1089.4.a.v.1.1 2 429.428 even 2
1584.4.a.bc.1.2 2 156.155 even 2
1859.4.a.a.1.2 2 1.1 even 1 trivial
1936.4.a.w.1.1 2 572.571 even 2
2475.4.a.q.1.1 2 195.194 odd 2