Properties

Label 1849.4.a.i.1.44
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.44
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.20684 q^{2} +4.82832 q^{3} +9.69750 q^{4} -7.01067 q^{5} +20.3120 q^{6} +27.8882 q^{7} +7.14112 q^{8} -3.68734 q^{9} +O(q^{10})\) \(q+4.20684 q^{2} +4.82832 q^{3} +9.69750 q^{4} -7.01067 q^{5} +20.3120 q^{6} +27.8882 q^{7} +7.14112 q^{8} -3.68734 q^{9} -29.4928 q^{10} -14.8584 q^{11} +46.8226 q^{12} -60.1508 q^{13} +117.321 q^{14} -33.8498 q^{15} -47.5385 q^{16} -53.5705 q^{17} -15.5121 q^{18} -77.3824 q^{19} -67.9860 q^{20} +134.653 q^{21} -62.5069 q^{22} +61.7129 q^{23} +34.4796 q^{24} -75.8505 q^{25} -253.045 q^{26} -148.168 q^{27} +270.446 q^{28} +53.9349 q^{29} -142.401 q^{30} -191.801 q^{31} -257.116 q^{32} -71.7411 q^{33} -225.363 q^{34} -195.515 q^{35} -35.7580 q^{36} -366.299 q^{37} -325.536 q^{38} -290.427 q^{39} -50.0641 q^{40} +5.32390 q^{41} +566.465 q^{42} -144.089 q^{44} +25.8508 q^{45} +259.616 q^{46} +559.264 q^{47} -229.531 q^{48} +434.753 q^{49} -319.091 q^{50} -258.655 q^{51} -583.312 q^{52} +97.6988 q^{53} -623.320 q^{54} +104.167 q^{55} +199.153 q^{56} -373.627 q^{57} +226.896 q^{58} +873.184 q^{59} -328.258 q^{60} +723.179 q^{61} -806.878 q^{62} -102.833 q^{63} -701.337 q^{64} +421.697 q^{65} -301.803 q^{66} -982.993 q^{67} -519.500 q^{68} +297.970 q^{69} -822.501 q^{70} +417.795 q^{71} -26.3318 q^{72} +219.278 q^{73} -1540.96 q^{74} -366.230 q^{75} -750.416 q^{76} -414.374 q^{77} -1221.78 q^{78} -801.309 q^{79} +333.277 q^{80} -615.845 q^{81} +22.3968 q^{82} -792.865 q^{83} +1305.80 q^{84} +375.565 q^{85} +260.415 q^{87} -106.106 q^{88} -1205.01 q^{89} +108.750 q^{90} -1677.50 q^{91} +598.461 q^{92} -926.078 q^{93} +2352.73 q^{94} +542.503 q^{95} -1241.44 q^{96} +577.561 q^{97} +1828.94 q^{98} +54.7880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.20684 1.48734 0.743671 0.668545i \(-0.233083\pi\)
0.743671 + 0.668545i \(0.233083\pi\)
\(3\) 4.82832 0.929210 0.464605 0.885518i \(-0.346196\pi\)
0.464605 + 0.885518i \(0.346196\pi\)
\(4\) 9.69750 1.21219
\(5\) −7.01067 −0.627054 −0.313527 0.949579i \(-0.601511\pi\)
−0.313527 + 0.949579i \(0.601511\pi\)
\(6\) 20.3120 1.38205
\(7\) 27.8882 1.50582 0.752911 0.658122i \(-0.228649\pi\)
0.752911 + 0.658122i \(0.228649\pi\)
\(8\) 7.14112 0.315596
\(9\) −3.68734 −0.136568
\(10\) −29.4928 −0.932644
\(11\) −14.8584 −0.407270 −0.203635 0.979047i \(-0.565276\pi\)
−0.203635 + 0.979047i \(0.565276\pi\)
\(12\) 46.8226 1.12638
\(13\) −60.1508 −1.28329 −0.641647 0.767000i \(-0.721749\pi\)
−0.641647 + 0.767000i \(0.721749\pi\)
\(14\) 117.321 2.23967
\(15\) −33.8498 −0.582665
\(16\) −47.5385 −0.742789
\(17\) −53.5705 −0.764280 −0.382140 0.924104i \(-0.624813\pi\)
−0.382140 + 0.924104i \(0.624813\pi\)
\(18\) −15.5121 −0.203124
\(19\) −77.3824 −0.934355 −0.467178 0.884163i \(-0.654729\pi\)
−0.467178 + 0.884163i \(0.654729\pi\)
\(20\) −67.9860 −0.760107
\(21\) 134.653 1.39923
\(22\) −62.5069 −0.605751
\(23\) 61.7129 0.559480 0.279740 0.960076i \(-0.409752\pi\)
0.279740 + 0.960076i \(0.409752\pi\)
\(24\) 34.4796 0.293255
\(25\) −75.8505 −0.606804
\(26\) −253.045 −1.90870
\(27\) −148.168 −1.05611
\(28\) 270.446 1.82534
\(29\) 53.9349 0.345361 0.172680 0.984978i \(-0.444757\pi\)
0.172680 + 0.984978i \(0.444757\pi\)
\(30\) −142.401 −0.866622
\(31\) −191.801 −1.11124 −0.555622 0.831435i \(-0.687520\pi\)
−0.555622 + 0.831435i \(0.687520\pi\)
\(32\) −257.116 −1.42038
\(33\) −71.7411 −0.378440
\(34\) −225.363 −1.13675
\(35\) −195.515 −0.944231
\(36\) −35.7580 −0.165546
\(37\) −366.299 −1.62755 −0.813774 0.581182i \(-0.802590\pi\)
−0.813774 + 0.581182i \(0.802590\pi\)
\(38\) −325.536 −1.38971
\(39\) −290.427 −1.19245
\(40\) −50.0641 −0.197896
\(41\) 5.32390 0.0202793 0.0101397 0.999949i \(-0.496772\pi\)
0.0101397 + 0.999949i \(0.496772\pi\)
\(42\) 566.465 2.08113
\(43\) 0 0
\(44\) −144.089 −0.493688
\(45\) 25.8508 0.0856356
\(46\) 259.616 0.832138
\(47\) 559.264 1.73568 0.867841 0.496843i \(-0.165507\pi\)
0.867841 + 0.496843i \(0.165507\pi\)
\(48\) −229.531 −0.690207
\(49\) 434.753 1.26750
\(50\) −319.091 −0.902525
\(51\) −258.655 −0.710177
\(52\) −583.312 −1.55559
\(53\) 97.6988 0.253207 0.126603 0.991953i \(-0.459592\pi\)
0.126603 + 0.991953i \(0.459592\pi\)
\(54\) −623.320 −1.57080
\(55\) 104.167 0.255380
\(56\) 199.153 0.475231
\(57\) −373.627 −0.868212
\(58\) 226.896 0.513670
\(59\) 873.184 1.92676 0.963380 0.268139i \(-0.0864086\pi\)
0.963380 + 0.268139i \(0.0864086\pi\)
\(60\) −328.258 −0.706299
\(61\) 723.179 1.51793 0.758964 0.651133i \(-0.225706\pi\)
0.758964 + 0.651133i \(0.225706\pi\)
\(62\) −806.878 −1.65280
\(63\) −102.833 −0.205648
\(64\) −701.337 −1.36980
\(65\) 421.697 0.804694
\(66\) −301.803 −0.562870
\(67\) −982.993 −1.79241 −0.896207 0.443637i \(-0.853688\pi\)
−0.896207 + 0.443637i \(0.853688\pi\)
\(68\) −519.500 −0.926451
\(69\) 297.970 0.519874
\(70\) −822.501 −1.40440
\(71\) 417.795 0.698354 0.349177 0.937057i \(-0.386461\pi\)
0.349177 + 0.937057i \(0.386461\pi\)
\(72\) −26.3318 −0.0431004
\(73\) 219.278 0.351569 0.175784 0.984429i \(-0.443754\pi\)
0.175784 + 0.984429i \(0.443754\pi\)
\(74\) −1540.96 −2.42072
\(75\) −366.230 −0.563848
\(76\) −750.416 −1.13261
\(77\) −414.374 −0.613277
\(78\) −1221.78 −1.77358
\(79\) −801.309 −1.14119 −0.570597 0.821230i \(-0.693288\pi\)
−0.570597 + 0.821230i \(0.693288\pi\)
\(80\) 333.277 0.465768
\(81\) −615.845 −0.844781
\(82\) 22.3968 0.0301623
\(83\) −792.865 −1.04853 −0.524266 0.851554i \(-0.675660\pi\)
−0.524266 + 0.851554i \(0.675660\pi\)
\(84\) 1305.80 1.69612
\(85\) 375.565 0.479244
\(86\) 0 0
\(87\) 260.415 0.320913
\(88\) −106.106 −0.128533
\(89\) −1205.01 −1.43518 −0.717589 0.696467i \(-0.754754\pi\)
−0.717589 + 0.696467i \(0.754754\pi\)
\(90\) 108.750 0.127370
\(91\) −1677.50 −1.93241
\(92\) 598.461 0.678194
\(93\) −926.078 −1.03258
\(94\) 2352.73 2.58155
\(95\) 542.503 0.585891
\(96\) −1241.44 −1.31983
\(97\) 577.561 0.604561 0.302281 0.953219i \(-0.402252\pi\)
0.302281 + 0.953219i \(0.402252\pi\)
\(98\) 1828.94 1.88521
\(99\) 54.7880 0.0556202
\(100\) −735.560 −0.735560
\(101\) 1590.84 1.56727 0.783635 0.621221i \(-0.213363\pi\)
0.783635 + 0.621221i \(0.213363\pi\)
\(102\) −1088.12 −1.05628
\(103\) 1356.26 1.29744 0.648718 0.761029i \(-0.275305\pi\)
0.648718 + 0.761029i \(0.275305\pi\)
\(104\) −429.544 −0.405002
\(105\) −944.010 −0.877390
\(106\) 411.003 0.376605
\(107\) 615.442 0.556047 0.278023 0.960574i \(-0.410321\pi\)
0.278023 + 0.960574i \(0.410321\pi\)
\(108\) −1436.86 −1.28020
\(109\) 1400.49 1.23067 0.615333 0.788267i \(-0.289022\pi\)
0.615333 + 0.788267i \(0.289022\pi\)
\(110\) 438.215 0.379838
\(111\) −1768.61 −1.51233
\(112\) −1325.76 −1.11851
\(113\) −1104.14 −0.919193 −0.459597 0.888128i \(-0.652006\pi\)
−0.459597 + 0.888128i \(0.652006\pi\)
\(114\) −1571.79 −1.29133
\(115\) −432.649 −0.350824
\(116\) 523.034 0.418642
\(117\) 221.797 0.175257
\(118\) 3673.35 2.86575
\(119\) −1493.99 −1.15087
\(120\) −241.725 −0.183887
\(121\) −1110.23 −0.834131
\(122\) 3042.30 2.25768
\(123\) 25.7055 0.0188438
\(124\) −1859.99 −1.34704
\(125\) 1408.10 1.00755
\(126\) −432.604 −0.305868
\(127\) 561.803 0.392535 0.196268 0.980550i \(-0.437118\pi\)
0.196268 + 0.980550i \(0.437118\pi\)
\(128\) −893.486 −0.616983
\(129\) 0 0
\(130\) 1774.01 1.19686
\(131\) −255.265 −0.170249 −0.0851245 0.996370i \(-0.527129\pi\)
−0.0851245 + 0.996370i \(0.527129\pi\)
\(132\) −695.709 −0.458740
\(133\) −2158.06 −1.40697
\(134\) −4135.29 −2.66593
\(135\) 1038.76 0.662238
\(136\) −382.553 −0.241204
\(137\) −1067.47 −0.665692 −0.332846 0.942981i \(-0.608009\pi\)
−0.332846 + 0.942981i \(0.608009\pi\)
\(138\) 1253.51 0.773231
\(139\) −476.139 −0.290544 −0.145272 0.989392i \(-0.546406\pi\)
−0.145272 + 0.989392i \(0.546406\pi\)
\(140\) −1896.01 −1.14459
\(141\) 2700.30 1.61281
\(142\) 1757.60 1.03869
\(143\) 893.744 0.522648
\(144\) 175.291 0.101441
\(145\) −378.120 −0.216560
\(146\) 922.466 0.522903
\(147\) 2099.13 1.17778
\(148\) −3552.19 −1.97289
\(149\) −517.779 −0.284685 −0.142343 0.989817i \(-0.545463\pi\)
−0.142343 + 0.989817i \(0.545463\pi\)
\(150\) −1540.67 −0.838636
\(151\) 1364.45 0.735347 0.367674 0.929955i \(-0.380154\pi\)
0.367674 + 0.929955i \(0.380154\pi\)
\(152\) −552.597 −0.294879
\(153\) 197.533 0.104376
\(154\) −1743.21 −0.912153
\(155\) 1344.66 0.696809
\(156\) −2816.42 −1.44547
\(157\) −2848.68 −1.44808 −0.724042 0.689756i \(-0.757718\pi\)
−0.724042 + 0.689756i \(0.757718\pi\)
\(158\) −3370.98 −1.69735
\(159\) 471.721 0.235282
\(160\) 1802.55 0.890653
\(161\) 1721.06 0.842477
\(162\) −2590.76 −1.25648
\(163\) −2047.22 −0.983745 −0.491873 0.870667i \(-0.663687\pi\)
−0.491873 + 0.870667i \(0.663687\pi\)
\(164\) 51.6285 0.0245824
\(165\) 502.953 0.237302
\(166\) −3335.45 −1.55953
\(167\) −900.176 −0.417112 −0.208556 0.978010i \(-0.566876\pi\)
−0.208556 + 0.978010i \(0.566876\pi\)
\(168\) 961.575 0.441590
\(169\) 1421.12 0.646845
\(170\) 1579.94 0.712801
\(171\) 285.336 0.127603
\(172\) 0 0
\(173\) 1843.61 0.810215 0.405108 0.914269i \(-0.367234\pi\)
0.405108 + 0.914269i \(0.367234\pi\)
\(174\) 1095.52 0.477307
\(175\) −2115.33 −0.913739
\(176\) 706.345 0.302516
\(177\) 4216.01 1.79037
\(178\) −5069.29 −2.13460
\(179\) −4436.88 −1.85267 −0.926335 0.376701i \(-0.877058\pi\)
−0.926335 + 0.376701i \(0.877058\pi\)
\(180\) 250.688 0.103806
\(181\) −3254.36 −1.33643 −0.668217 0.743966i \(-0.732942\pi\)
−0.668217 + 0.743966i \(0.732942\pi\)
\(182\) −7056.97 −2.87416
\(183\) 3491.74 1.41047
\(184\) 440.699 0.176569
\(185\) 2568.00 1.02056
\(186\) −3895.86 −1.53580
\(187\) 795.972 0.311269
\(188\) 5423.46 2.10397
\(189\) −4132.15 −1.59032
\(190\) 2282.22 0.871420
\(191\) 2246.48 0.851043 0.425522 0.904948i \(-0.360091\pi\)
0.425522 + 0.904948i \(0.360091\pi\)
\(192\) −3386.28 −1.27283
\(193\) −1020.49 −0.380605 −0.190302 0.981726i \(-0.560947\pi\)
−0.190302 + 0.981726i \(0.560947\pi\)
\(194\) 2429.71 0.899190
\(195\) 2036.09 0.747730
\(196\) 4216.02 1.53645
\(197\) 2025.70 0.732614 0.366307 0.930494i \(-0.380622\pi\)
0.366307 + 0.930494i \(0.380622\pi\)
\(198\) 230.484 0.0827263
\(199\) −2340.03 −0.833569 −0.416784 0.909005i \(-0.636843\pi\)
−0.416784 + 0.909005i \(0.636843\pi\)
\(200\) −541.657 −0.191505
\(201\) −4746.20 −1.66553
\(202\) 6692.40 2.33107
\(203\) 1504.15 0.520052
\(204\) −2508.31 −0.860868
\(205\) −37.3241 −0.0127162
\(206\) 5705.56 1.92973
\(207\) −227.557 −0.0764072
\(208\) 2859.48 0.953216
\(209\) 1149.78 0.380535
\(210\) −3971.30 −1.30498
\(211\) 3911.57 1.27622 0.638112 0.769943i \(-0.279716\pi\)
0.638112 + 0.769943i \(0.279716\pi\)
\(212\) 947.435 0.306934
\(213\) 2017.25 0.648918
\(214\) 2589.07 0.827032
\(215\) 0 0
\(216\) −1058.09 −0.333304
\(217\) −5349.00 −1.67333
\(218\) 5891.64 1.83042
\(219\) 1058.74 0.326681
\(220\) 1010.16 0.309569
\(221\) 3222.31 0.980796
\(222\) −7440.26 −2.24936
\(223\) 1.96080 0.000588811 0 0.000294406 1.00000i \(-0.499906\pi\)
0.000294406 1.00000i \(0.499906\pi\)
\(224\) −7170.50 −2.13884
\(225\) 279.687 0.0828701
\(226\) −4644.94 −1.36715
\(227\) 49.4069 0.0144461 0.00722303 0.999974i \(-0.497701\pi\)
0.00722303 + 0.999974i \(0.497701\pi\)
\(228\) −3623.25 −1.05244
\(229\) 1697.91 0.489960 0.244980 0.969528i \(-0.421219\pi\)
0.244980 + 0.969528i \(0.421219\pi\)
\(230\) −1820.09 −0.521795
\(231\) −2000.73 −0.569863
\(232\) 385.156 0.108995
\(233\) 3795.60 1.06720 0.533601 0.845736i \(-0.320838\pi\)
0.533601 + 0.845736i \(0.320838\pi\)
\(234\) 933.063 0.260668
\(235\) −3920.82 −1.08837
\(236\) 8467.70 2.33560
\(237\) −3868.97 −1.06041
\(238\) −6284.96 −1.71174
\(239\) −2950.09 −0.798433 −0.399216 0.916857i \(-0.630718\pi\)
−0.399216 + 0.916857i \(0.630718\pi\)
\(240\) 1609.17 0.432797
\(241\) −4078.25 −1.09005 −0.545027 0.838418i \(-0.683481\pi\)
−0.545027 + 0.838418i \(0.683481\pi\)
\(242\) −4670.55 −1.24064
\(243\) 1027.05 0.271132
\(244\) 7013.03 1.84001
\(245\) −3047.91 −0.794791
\(246\) 108.139 0.0280271
\(247\) 4654.61 1.19905
\(248\) −1369.68 −0.350704
\(249\) −3828.20 −0.974307
\(250\) 5923.64 1.49858
\(251\) −3528.89 −0.887417 −0.443708 0.896171i \(-0.646337\pi\)
−0.443708 + 0.896171i \(0.646337\pi\)
\(252\) −997.228 −0.249284
\(253\) −916.955 −0.227860
\(254\) 2363.42 0.583835
\(255\) 1813.35 0.445319
\(256\) 1851.94 0.452134
\(257\) −6455.09 −1.56676 −0.783380 0.621543i \(-0.786506\pi\)
−0.783380 + 0.621543i \(0.786506\pi\)
\(258\) 0 0
\(259\) −10215.4 −2.45080
\(260\) 4089.41 0.975441
\(261\) −198.877 −0.0471654
\(262\) −1073.86 −0.253219
\(263\) −3618.65 −0.848424 −0.424212 0.905563i \(-0.639449\pi\)
−0.424212 + 0.905563i \(0.639449\pi\)
\(264\) −512.312 −0.119434
\(265\) −684.935 −0.158774
\(266\) −9078.61 −2.09265
\(267\) −5818.17 −1.33358
\(268\) −9532.58 −2.17274
\(269\) 1258.66 0.285286 0.142643 0.989774i \(-0.454440\pi\)
0.142643 + 0.989774i \(0.454440\pi\)
\(270\) 4369.89 0.984975
\(271\) −4808.76 −1.07790 −0.538951 0.842337i \(-0.681179\pi\)
−0.538951 + 0.842337i \(0.681179\pi\)
\(272\) 2546.66 0.567698
\(273\) −8099.50 −1.79562
\(274\) −4490.66 −0.990112
\(275\) 1127.02 0.247133
\(276\) 2889.56 0.630185
\(277\) 6487.98 1.40731 0.703655 0.710542i \(-0.251550\pi\)
0.703655 + 0.710542i \(0.251550\pi\)
\(278\) −2003.04 −0.432138
\(279\) 707.237 0.151761
\(280\) −1396.20 −0.297996
\(281\) −1896.75 −0.402672 −0.201336 0.979522i \(-0.564528\pi\)
−0.201336 + 0.979522i \(0.564528\pi\)
\(282\) 11359.7 2.39880
\(283\) 448.018 0.0941057 0.0470528 0.998892i \(-0.485017\pi\)
0.0470528 + 0.998892i \(0.485017\pi\)
\(284\) 4051.57 0.846536
\(285\) 2619.38 0.544416
\(286\) 3759.84 0.777357
\(287\) 148.474 0.0305371
\(288\) 948.074 0.193978
\(289\) −2043.20 −0.415876
\(290\) −1590.69 −0.322099
\(291\) 2788.65 0.561765
\(292\) 2126.44 0.426167
\(293\) −2086.41 −0.416005 −0.208002 0.978128i \(-0.566696\pi\)
−0.208002 + 0.978128i \(0.566696\pi\)
\(294\) 8830.69 1.75176
\(295\) −6121.61 −1.20818
\(296\) −2615.79 −0.513647
\(297\) 2201.54 0.430123
\(298\) −2178.21 −0.423425
\(299\) −3712.08 −0.717977
\(300\) −3551.52 −0.683490
\(301\) 0 0
\(302\) 5740.03 1.09371
\(303\) 7681.08 1.45632
\(304\) 3678.64 0.694028
\(305\) −5069.97 −0.951822
\(306\) 830.989 0.155243
\(307\) 393.588 0.0731702 0.0365851 0.999331i \(-0.488352\pi\)
0.0365851 + 0.999331i \(0.488352\pi\)
\(308\) −4018.40 −0.743407
\(309\) 6548.44 1.20559
\(310\) 5656.75 1.03639
\(311\) 2153.14 0.392583 0.196292 0.980546i \(-0.437110\pi\)
0.196292 + 0.980546i \(0.437110\pi\)
\(312\) −2073.98 −0.376332
\(313\) −6023.57 −1.08777 −0.543886 0.839159i \(-0.683047\pi\)
−0.543886 + 0.839159i \(0.683047\pi\)
\(314\) −11983.9 −2.15380
\(315\) 720.932 0.128952
\(316\) −7770.69 −1.38334
\(317\) −6359.98 −1.12685 −0.563426 0.826166i \(-0.690517\pi\)
−0.563426 + 0.826166i \(0.690517\pi\)
\(318\) 1984.46 0.349946
\(319\) −801.387 −0.140655
\(320\) 4916.84 0.858937
\(321\) 2971.55 0.516684
\(322\) 7240.24 1.25305
\(323\) 4145.42 0.714109
\(324\) −5972.16 −1.02403
\(325\) 4562.47 0.778708
\(326\) −8612.32 −1.46317
\(327\) 6762.01 1.14355
\(328\) 38.0186 0.00640008
\(329\) 15596.9 2.61363
\(330\) 2115.84 0.352950
\(331\) 6984.33 1.15980 0.579900 0.814688i \(-0.303092\pi\)
0.579900 + 0.814688i \(0.303092\pi\)
\(332\) −7688.81 −1.27102
\(333\) 1350.67 0.222271
\(334\) −3786.90 −0.620389
\(335\) 6891.44 1.12394
\(336\) −6401.21 −1.03933
\(337\) 428.803 0.0693128 0.0346564 0.999399i \(-0.488966\pi\)
0.0346564 + 0.999399i \(0.488966\pi\)
\(338\) 5978.41 0.962079
\(339\) −5331.14 −0.854124
\(340\) 3642.05 0.580934
\(341\) 2849.86 0.452577
\(342\) 1200.36 0.189790
\(343\) 2558.83 0.402810
\(344\) 0 0
\(345\) −2088.97 −0.325989
\(346\) 7755.78 1.20507
\(347\) 871.352 0.134803 0.0674015 0.997726i \(-0.478529\pi\)
0.0674015 + 0.997726i \(0.478529\pi\)
\(348\) 2525.38 0.389007
\(349\) 2954.05 0.453085 0.226543 0.974001i \(-0.427258\pi\)
0.226543 + 0.974001i \(0.427258\pi\)
\(350\) −8898.87 −1.35904
\(351\) 8912.44 1.35530
\(352\) 3820.33 0.578478
\(353\) −1760.46 −0.265438 −0.132719 0.991154i \(-0.542371\pi\)
−0.132719 + 0.991154i \(0.542371\pi\)
\(354\) 17736.1 2.66289
\(355\) −2929.02 −0.437905
\(356\) −11685.6 −1.73971
\(357\) −7213.44 −1.06940
\(358\) −18665.2 −2.75555
\(359\) 9960.60 1.46435 0.732173 0.681119i \(-0.238506\pi\)
0.732173 + 0.681119i \(0.238506\pi\)
\(360\) 184.603 0.0270263
\(361\) −870.958 −0.126980
\(362\) −13690.6 −1.98774
\(363\) −5360.53 −0.775083
\(364\) −16267.5 −2.34245
\(365\) −1537.28 −0.220452
\(366\) 14689.2 2.09786
\(367\) 1291.52 0.183697 0.0918485 0.995773i \(-0.470722\pi\)
0.0918485 + 0.995773i \(0.470722\pi\)
\(368\) −2933.74 −0.415575
\(369\) −19.6310 −0.00276951
\(370\) 10803.2 1.51792
\(371\) 2724.65 0.381285
\(372\) −8980.64 −1.25168
\(373\) −7010.88 −0.973216 −0.486608 0.873620i \(-0.661766\pi\)
−0.486608 + 0.873620i \(0.661766\pi\)
\(374\) 3348.53 0.462963
\(375\) 6798.74 0.936228
\(376\) 3993.77 0.547774
\(377\) −3244.23 −0.443200
\(378\) −17383.3 −2.36534
\(379\) 2688.90 0.364431 0.182216 0.983259i \(-0.441673\pi\)
0.182216 + 0.983259i \(0.441673\pi\)
\(380\) 5260.92 0.710210
\(381\) 2712.57 0.364748
\(382\) 9450.56 1.26579
\(383\) −5518.96 −0.736307 −0.368153 0.929765i \(-0.620010\pi\)
−0.368153 + 0.929765i \(0.620010\pi\)
\(384\) −4314.04 −0.573307
\(385\) 2905.04 0.384558
\(386\) −4293.05 −0.566089
\(387\) 0 0
\(388\) 5600.90 0.732842
\(389\) 6817.59 0.888601 0.444300 0.895878i \(-0.353452\pi\)
0.444300 + 0.895878i \(0.353452\pi\)
\(390\) 8565.50 1.11213
\(391\) −3305.99 −0.427599
\(392\) 3104.62 0.400018
\(393\) −1232.50 −0.158197
\(394\) 8521.78 1.08965
\(395\) 5617.71 0.715589
\(396\) 531.307 0.0674222
\(397\) 5351.01 0.676472 0.338236 0.941061i \(-0.390170\pi\)
0.338236 + 0.941061i \(0.390170\pi\)
\(398\) −9844.12 −1.23980
\(399\) −10419.8 −1.30737
\(400\) 3605.82 0.450727
\(401\) −6590.42 −0.820723 −0.410362 0.911923i \(-0.634597\pi\)
−0.410362 + 0.911923i \(0.634597\pi\)
\(402\) −19966.5 −2.47721
\(403\) 11537.0 1.42605
\(404\) 15427.2 1.89983
\(405\) 4317.49 0.529723
\(406\) 6327.72 0.773496
\(407\) 5442.62 0.662852
\(408\) −1847.09 −0.224129
\(409\) 4132.15 0.499564 0.249782 0.968302i \(-0.419641\pi\)
0.249782 + 0.968302i \(0.419641\pi\)
\(410\) −157.017 −0.0189134
\(411\) −5154.07 −0.618568
\(412\) 13152.3 1.57274
\(413\) 24351.6 2.90136
\(414\) −957.295 −0.113644
\(415\) 5558.51 0.657486
\(416\) 15465.7 1.82276
\(417\) −2298.95 −0.269976
\(418\) 4836.94 0.565986
\(419\) 5101.36 0.594792 0.297396 0.954754i \(-0.403882\pi\)
0.297396 + 0.954754i \(0.403882\pi\)
\(420\) −9154.54 −1.06356
\(421\) −3542.08 −0.410048 −0.205024 0.978757i \(-0.565727\pi\)
−0.205024 + 0.978757i \(0.565727\pi\)
\(422\) 16455.3 1.89818
\(423\) −2062.20 −0.237039
\(424\) 697.679 0.0799111
\(425\) 4063.35 0.463768
\(426\) 8486.23 0.965163
\(427\) 20168.2 2.28573
\(428\) 5968.25 0.674033
\(429\) 4315.28 0.485650
\(430\) 0 0
\(431\) −8499.53 −0.949903 −0.474951 0.880012i \(-0.657534\pi\)
−0.474951 + 0.880012i \(0.657534\pi\)
\(432\) 7043.69 0.784467
\(433\) −7919.12 −0.878911 −0.439456 0.898264i \(-0.644829\pi\)
−0.439456 + 0.898264i \(0.644829\pi\)
\(434\) −22502.4 −2.48882
\(435\) −1825.68 −0.201230
\(436\) 13581.3 1.49180
\(437\) −4775.50 −0.522753
\(438\) 4453.96 0.485887
\(439\) 13630.2 1.48186 0.740929 0.671583i \(-0.234385\pi\)
0.740929 + 0.671583i \(0.234385\pi\)
\(440\) 743.872 0.0805970
\(441\) −1603.08 −0.173101
\(442\) 13555.7 1.45878
\(443\) −15066.5 −1.61587 −0.807936 0.589270i \(-0.799416\pi\)
−0.807936 + 0.589270i \(0.799416\pi\)
\(444\) −17151.1 −1.83323
\(445\) 8447.94 0.899934
\(446\) 8.24877 0.000875764 0
\(447\) −2500.00 −0.264533
\(448\) −19559.0 −2.06267
\(449\) −4920.86 −0.517215 −0.258608 0.965982i \(-0.583264\pi\)
−0.258608 + 0.965982i \(0.583264\pi\)
\(450\) 1176.60 0.123256
\(451\) −79.1046 −0.00825918
\(452\) −10707.4 −1.11423
\(453\) 6588.00 0.683292
\(454\) 207.847 0.0214862
\(455\) 11760.4 1.21173
\(456\) −2668.12 −0.274004
\(457\) 8415.53 0.861404 0.430702 0.902494i \(-0.358266\pi\)
0.430702 + 0.902494i \(0.358266\pi\)
\(458\) 7142.82 0.728738
\(459\) 7937.45 0.807164
\(460\) −4195.62 −0.425264
\(461\) −17706.4 −1.78887 −0.894437 0.447194i \(-0.852423\pi\)
−0.894437 + 0.447194i \(0.852423\pi\)
\(462\) −8416.76 −0.847582
\(463\) 9891.44 0.992860 0.496430 0.868077i \(-0.334644\pi\)
0.496430 + 0.868077i \(0.334644\pi\)
\(464\) −2563.98 −0.256530
\(465\) 6492.43 0.647482
\(466\) 15967.5 1.58730
\(467\) 5637.96 0.558659 0.279330 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(468\) 2150.87 0.212445
\(469\) −27413.9 −2.69906
\(470\) −16494.2 −1.61877
\(471\) −13754.3 −1.34557
\(472\) 6235.51 0.608078
\(473\) 0 0
\(474\) −16276.1 −1.57719
\(475\) 5869.49 0.566970
\(476\) −14487.9 −1.39507
\(477\) −360.249 −0.0345800
\(478\) −12410.6 −1.18754
\(479\) −16670.3 −1.59015 −0.795077 0.606508i \(-0.792570\pi\)
−0.795077 + 0.606508i \(0.792570\pi\)
\(480\) 8703.30 0.827603
\(481\) 22033.2 2.08862
\(482\) −17156.5 −1.62128
\(483\) 8309.84 0.782838
\(484\) −10766.4 −1.01112
\(485\) −4049.09 −0.379092
\(486\) 4320.62 0.403266
\(487\) 16410.3 1.52694 0.763470 0.645843i \(-0.223494\pi\)
0.763470 + 0.645843i \(0.223494\pi\)
\(488\) 5164.31 0.479052
\(489\) −9884.62 −0.914106
\(490\) −12822.1 −1.18213
\(491\) 3171.88 0.291538 0.145769 0.989319i \(-0.453434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(492\) 249.279 0.0228422
\(493\) −2889.32 −0.263952
\(494\) 19581.2 1.78340
\(495\) −384.101 −0.0348769
\(496\) 9117.94 0.825419
\(497\) 11651.6 1.05160
\(498\) −16104.6 −1.44913
\(499\) 10898.7 0.977737 0.488869 0.872357i \(-0.337410\pi\)
0.488869 + 0.872357i \(0.337410\pi\)
\(500\) 13655.0 1.22134
\(501\) −4346.34 −0.387585
\(502\) −14845.5 −1.31989
\(503\) 932.683 0.0826765 0.0413383 0.999145i \(-0.486838\pi\)
0.0413383 + 0.999145i \(0.486838\pi\)
\(504\) −734.346 −0.0649015
\(505\) −11152.8 −0.982763
\(506\) −3857.48 −0.338905
\(507\) 6861.61 0.601055
\(508\) 5448.09 0.475827
\(509\) −18569.3 −1.61703 −0.808517 0.588473i \(-0.799729\pi\)
−0.808517 + 0.588473i \(0.799729\pi\)
\(510\) 7628.47 0.662342
\(511\) 6115.26 0.529400
\(512\) 14938.7 1.28946
\(513\) 11465.6 0.986783
\(514\) −27155.5 −2.33031
\(515\) −9508.27 −0.813562
\(516\) 0 0
\(517\) −8309.76 −0.706892
\(518\) −42974.7 −3.64517
\(519\) 8901.54 0.752860
\(520\) 3011.39 0.253958
\(521\) −21616.7 −1.81774 −0.908872 0.417075i \(-0.863055\pi\)
−0.908872 + 0.417075i \(0.863055\pi\)
\(522\) −836.642 −0.0701510
\(523\) 7553.08 0.631498 0.315749 0.948843i \(-0.397744\pi\)
0.315749 + 0.948843i \(0.397744\pi\)
\(524\) −2475.43 −0.206374
\(525\) −10213.5 −0.849055
\(526\) −15223.1 −1.26190
\(527\) 10274.9 0.849301
\(528\) 3410.46 0.281101
\(529\) −8358.52 −0.686983
\(530\) −2881.41 −0.236152
\(531\) −3219.73 −0.263134
\(532\) −20927.8 −1.70552
\(533\) −320.237 −0.0260244
\(534\) −24476.1 −1.98349
\(535\) −4314.66 −0.348671
\(536\) −7019.67 −0.565678
\(537\) −21422.7 −1.72152
\(538\) 5294.98 0.424317
\(539\) −6459.73 −0.516216
\(540\) 10073.4 0.802757
\(541\) 17662.3 1.40363 0.701814 0.712360i \(-0.252374\pi\)
0.701814 + 0.712360i \(0.252374\pi\)
\(542\) −20229.7 −1.60321
\(543\) −15713.1 −1.24183
\(544\) 13773.8 1.08557
\(545\) −9818.38 −0.771694
\(546\) −34073.3 −2.67070
\(547\) 19855.5 1.55203 0.776016 0.630714i \(-0.217238\pi\)
0.776016 + 0.630714i \(0.217238\pi\)
\(548\) −10351.8 −0.806944
\(549\) −2666.61 −0.207301
\(550\) 4741.18 0.367572
\(551\) −4173.62 −0.322690
\(552\) 2127.84 0.164070
\(553\) −22347.1 −1.71843
\(554\) 27293.9 2.09315
\(555\) 12399.1 0.948314
\(556\) −4617.36 −0.352194
\(557\) 4237.59 0.322356 0.161178 0.986925i \(-0.448471\pi\)
0.161178 + 0.986925i \(0.448471\pi\)
\(558\) 2975.23 0.225720
\(559\) 0 0
\(560\) 9294.49 0.701364
\(561\) 3843.21 0.289234
\(562\) −7979.33 −0.598911
\(563\) 12500.8 0.935781 0.467890 0.883787i \(-0.345014\pi\)
0.467890 + 0.883787i \(0.345014\pi\)
\(564\) 26186.2 1.95503
\(565\) 7740.77 0.576383
\(566\) 1884.74 0.139967
\(567\) −17174.8 −1.27209
\(568\) 2983.52 0.220398
\(569\) 102.851 0.00757777 0.00378889 0.999993i \(-0.498794\pi\)
0.00378889 + 0.999993i \(0.498794\pi\)
\(570\) 11019.3 0.809733
\(571\) 16482.6 1.20801 0.604006 0.796979i \(-0.293570\pi\)
0.604006 + 0.796979i \(0.293570\pi\)
\(572\) 8667.09 0.633547
\(573\) 10846.7 0.790798
\(574\) 624.606 0.0454191
\(575\) −4680.95 −0.339494
\(576\) 2586.07 0.187071
\(577\) 12994.4 0.937547 0.468774 0.883318i \(-0.344696\pi\)
0.468774 + 0.883318i \(0.344696\pi\)
\(578\) −8595.42 −0.618550
\(579\) −4927.26 −0.353662
\(580\) −3666.82 −0.262511
\(581\) −22111.6 −1.57890
\(582\) 11731.4 0.835536
\(583\) −1451.65 −0.103124
\(584\) 1565.89 0.110954
\(585\) −1554.94 −0.109896
\(586\) −8777.20 −0.618742
\(587\) 3247.27 0.228329 0.114165 0.993462i \(-0.463581\pi\)
0.114165 + 0.993462i \(0.463581\pi\)
\(588\) 20356.3 1.42768
\(589\) 14842.1 1.03830
\(590\) −25752.6 −1.79698
\(591\) 9780.71 0.680752
\(592\) 17413.3 1.20892
\(593\) 6784.90 0.469852 0.234926 0.972013i \(-0.424515\pi\)
0.234926 + 0.972013i \(0.424515\pi\)
\(594\) 9261.54 0.639740
\(595\) 10473.8 0.721657
\(596\) −5021.16 −0.345092
\(597\) −11298.4 −0.774560
\(598\) −15616.1 −1.06788
\(599\) −14622.2 −0.997408 −0.498704 0.866772i \(-0.666190\pi\)
−0.498704 + 0.866772i \(0.666190\pi\)
\(600\) −2615.29 −0.177948
\(601\) −18858.5 −1.27995 −0.639977 0.768394i \(-0.721056\pi\)
−0.639977 + 0.768394i \(0.721056\pi\)
\(602\) 0 0
\(603\) 3624.63 0.244787
\(604\) 13231.8 0.891379
\(605\) 7783.45 0.523045
\(606\) 32313.1 2.16605
\(607\) 22932.4 1.53344 0.766718 0.641984i \(-0.221888\pi\)
0.766718 + 0.641984i \(0.221888\pi\)
\(608\) 19896.2 1.32714
\(609\) 7262.51 0.483238
\(610\) −21328.6 −1.41569
\(611\) −33640.2 −2.22739
\(612\) 1915.58 0.126524
\(613\) −15582.9 −1.02673 −0.513367 0.858169i \(-0.671602\pi\)
−0.513367 + 0.858169i \(0.671602\pi\)
\(614\) 1655.76 0.108829
\(615\) −180.213 −0.0118161
\(616\) −2959.10 −0.193548
\(617\) 9064.42 0.591442 0.295721 0.955274i \(-0.404440\pi\)
0.295721 + 0.955274i \(0.404440\pi\)
\(618\) 27548.2 1.79313
\(619\) −8539.07 −0.554466 −0.277233 0.960803i \(-0.589417\pi\)
−0.277233 + 0.960803i \(0.589417\pi\)
\(620\) 13039.8 0.844663
\(621\) −9143.90 −0.590873
\(622\) 9057.92 0.583906
\(623\) −33605.6 −2.16112
\(624\) 13806.5 0.885738
\(625\) −390.398 −0.0249855
\(626\) −25340.2 −1.61789
\(627\) 5551.50 0.353597
\(628\) −27625.0 −1.75535
\(629\) 19622.8 1.24390
\(630\) 3032.84 0.191796
\(631\) −15078.5 −0.951294 −0.475647 0.879636i \(-0.657786\pi\)
−0.475647 + 0.879636i \(0.657786\pi\)
\(632\) −5722.24 −0.360156
\(633\) 18886.3 1.18588
\(634\) −26755.4 −1.67602
\(635\) −3938.62 −0.246141
\(636\) 4574.52 0.285207
\(637\) −26150.7 −1.62658
\(638\) −3371.31 −0.209203
\(639\) −1540.55 −0.0953730
\(640\) 6263.94 0.386881
\(641\) −22253.5 −1.37123 −0.685616 0.727963i \(-0.740467\pi\)
−0.685616 + 0.727963i \(0.740467\pi\)
\(642\) 12500.8 0.768487
\(643\) 6114.37 0.375003 0.187502 0.982264i \(-0.439961\pi\)
0.187502 + 0.982264i \(0.439961\pi\)
\(644\) 16690.0 1.02124
\(645\) 0 0
\(646\) 17439.1 1.06212
\(647\) −4947.98 −0.300657 −0.150329 0.988636i \(-0.548033\pi\)
−0.150329 + 0.988636i \(0.548033\pi\)
\(648\) −4397.82 −0.266609
\(649\) −12974.1 −0.784713
\(650\) 19193.6 1.15821
\(651\) −25826.7 −1.55488
\(652\) −19852.9 −1.19248
\(653\) −21153.5 −1.26769 −0.633845 0.773460i \(-0.718524\pi\)
−0.633845 + 0.773460i \(0.718524\pi\)
\(654\) 28446.7 1.70085
\(655\) 1789.58 0.106755
\(656\) −253.090 −0.0150633
\(657\) −808.552 −0.0480131
\(658\) 65613.6 3.88736
\(659\) 15358.2 0.907843 0.453922 0.891042i \(-0.350025\pi\)
0.453922 + 0.891042i \(0.350025\pi\)
\(660\) 4877.39 0.287655
\(661\) −11989.6 −0.705511 −0.352755 0.935716i \(-0.614755\pi\)
−0.352755 + 0.935716i \(0.614755\pi\)
\(662\) 29382.0 1.72502
\(663\) 15558.3 0.911366
\(664\) −5661.94 −0.330913
\(665\) 15129.4 0.882248
\(666\) 5682.06 0.330594
\(667\) 3328.48 0.193222
\(668\) −8729.46 −0.505618
\(669\) 9.46737 0.000547129 0
\(670\) 28991.2 1.67168
\(671\) −10745.3 −0.618207
\(672\) −34621.5 −1.98743
\(673\) −19868.3 −1.13799 −0.568994 0.822342i \(-0.692667\pi\)
−0.568994 + 0.822342i \(0.692667\pi\)
\(674\) 1803.91 0.103092
\(675\) 11238.6 0.640852
\(676\) 13781.3 0.784097
\(677\) −11011.1 −0.625098 −0.312549 0.949902i \(-0.601183\pi\)
−0.312549 + 0.949902i \(0.601183\pi\)
\(678\) −22427.3 −1.27037
\(679\) 16107.2 0.910362
\(680\) 2681.96 0.151248
\(681\) 238.552 0.0134234
\(682\) 11988.9 0.673136
\(683\) −21704.9 −1.21598 −0.607989 0.793945i \(-0.708024\pi\)
−0.607989 + 0.793945i \(0.708024\pi\)
\(684\) 2767.04 0.154679
\(685\) 7483.66 0.417425
\(686\) 10764.6 0.599116
\(687\) 8198.03 0.455276
\(688\) 0 0
\(689\) −5876.66 −0.324939
\(690\) −8787.95 −0.484857
\(691\) −4124.20 −0.227051 −0.113525 0.993535i \(-0.536214\pi\)
−0.113525 + 0.993535i \(0.536214\pi\)
\(692\) 17878.4 0.982133
\(693\) 1527.94 0.0837542
\(694\) 3665.64 0.200498
\(695\) 3338.06 0.182187
\(696\) 1859.66 0.101279
\(697\) −285.204 −0.0154991
\(698\) 12427.2 0.673893
\(699\) 18326.4 0.991655
\(700\) −20513.5 −1.10762
\(701\) 27363.8 1.47435 0.737173 0.675704i \(-0.236160\pi\)
0.737173 + 0.675704i \(0.236160\pi\)
\(702\) 37493.2 2.01580
\(703\) 28345.1 1.52071
\(704\) 10420.7 0.557878
\(705\) −18930.9 −1.01132
\(706\) −7405.96 −0.394797
\(707\) 44365.7 2.36003
\(708\) 40884.8 2.17026
\(709\) 17078.7 0.904658 0.452329 0.891851i \(-0.350593\pi\)
0.452329 + 0.891851i \(0.350593\pi\)
\(710\) −12321.9 −0.651315
\(711\) 2954.70 0.155851
\(712\) −8605.13 −0.452936
\(713\) −11836.6 −0.621718
\(714\) −30345.8 −1.59056
\(715\) −6265.75 −0.327728
\(716\) −43026.6 −2.24578
\(717\) −14244.0 −0.741912
\(718\) 41902.6 2.17798
\(719\) −14080.8 −0.730356 −0.365178 0.930938i \(-0.618992\pi\)
−0.365178 + 0.930938i \(0.618992\pi\)
\(720\) −1228.91 −0.0636092
\(721\) 37823.6 1.95371
\(722\) −3663.98 −0.188863
\(723\) −19691.1 −1.01289
\(724\) −31559.2 −1.62001
\(725\) −4090.99 −0.209566
\(726\) −22550.9 −1.15281
\(727\) 29786.3 1.51955 0.759775 0.650186i \(-0.225309\pi\)
0.759775 + 0.650186i \(0.225309\pi\)
\(728\) −11979.2 −0.609862
\(729\) 21586.7 1.09672
\(730\) −6467.11 −0.327888
\(731\) 0 0
\(732\) 33861.1 1.70976
\(733\) −15924.8 −0.802452 −0.401226 0.915979i \(-0.631416\pi\)
−0.401226 + 0.915979i \(0.631416\pi\)
\(734\) 5433.22 0.273220
\(735\) −14716.3 −0.738528
\(736\) −15867.4 −0.794672
\(737\) 14605.7 0.729997
\(738\) −82.5846 −0.00411922
\(739\) 37584.1 1.87084 0.935421 0.353536i \(-0.115021\pi\)
0.935421 + 0.353536i \(0.115021\pi\)
\(740\) 24903.2 1.23711
\(741\) 22474.0 1.11417
\(742\) 11462.2 0.567101
\(743\) 17948.3 0.886219 0.443110 0.896467i \(-0.353875\pi\)
0.443110 + 0.896467i \(0.353875\pi\)
\(744\) −6613.23 −0.325878
\(745\) 3629.98 0.178513
\(746\) −29493.7 −1.44751
\(747\) 2923.56 0.143196
\(748\) 7718.94 0.377316
\(749\) 17163.6 0.837308
\(750\) 28601.2 1.39249
\(751\) 2386.72 0.115969 0.0579844 0.998317i \(-0.481533\pi\)
0.0579844 + 0.998317i \(0.481533\pi\)
\(752\) −26586.5 −1.28924
\(753\) −17038.6 −0.824597
\(754\) −13648.0 −0.659190
\(755\) −9565.72 −0.461102
\(756\) −40071.5 −1.92776
\(757\) −20527.4 −0.985574 −0.492787 0.870150i \(-0.664022\pi\)
−0.492787 + 0.870150i \(0.664022\pi\)
\(758\) 11311.8 0.542034
\(759\) −4427.35 −0.211729
\(760\) 3874.08 0.184905
\(761\) −21708.9 −1.03410 −0.517048 0.855957i \(-0.672969\pi\)
−0.517048 + 0.855957i \(0.672969\pi\)
\(762\) 11411.3 0.542505
\(763\) 39057.2 1.85316
\(764\) 21785.2 1.03162
\(765\) −1384.84 −0.0654496
\(766\) −23217.4 −1.09514
\(767\) −52522.7 −2.47260
\(768\) 8941.76 0.420128
\(769\) −3194.65 −0.149807 −0.0749037 0.997191i \(-0.523865\pi\)
−0.0749037 + 0.997191i \(0.523865\pi\)
\(770\) 12221.0 0.571969
\(771\) −31167.2 −1.45585
\(772\) −9896.23 −0.461364
\(773\) 9743.41 0.453359 0.226679 0.973969i \(-0.427213\pi\)
0.226679 + 0.973969i \(0.427213\pi\)
\(774\) 0 0
\(775\) 14548.2 0.674306
\(776\) 4124.43 0.190797
\(777\) −49323.4 −2.27731
\(778\) 28680.5 1.32165
\(779\) −411.976 −0.0189481
\(780\) 19745.0 0.906390
\(781\) −6207.76 −0.284419
\(782\) −13907.8 −0.635986
\(783\) −7991.45 −0.364739
\(784\) −20667.5 −0.941486
\(785\) 19971.1 0.908026
\(786\) −5184.93 −0.235293
\(787\) −10035.8 −0.454561 −0.227280 0.973829i \(-0.572983\pi\)
−0.227280 + 0.973829i \(0.572983\pi\)
\(788\) 19644.2 0.888066
\(789\) −17472.0 −0.788364
\(790\) 23632.8 1.06433
\(791\) −30792.5 −1.38414
\(792\) 391.248 0.0175535
\(793\) −43499.8 −1.94795
\(794\) 22510.8 1.00615
\(795\) −3307.08 −0.147535
\(796\) −22692.4 −1.01044
\(797\) 23138.7 1.02837 0.514187 0.857678i \(-0.328094\pi\)
0.514187 + 0.857678i \(0.328094\pi\)
\(798\) −43834.4 −1.94451
\(799\) −29960.1 −1.32655
\(800\) 19502.3 0.861890
\(801\) 4443.29 0.196000
\(802\) −27724.9 −1.22070
\(803\) −3258.11 −0.143183
\(804\) −46026.3 −2.01893
\(805\) −12065.8 −0.528278
\(806\) 48534.3 2.12103
\(807\) 6077.21 0.265090
\(808\) 11360.4 0.494624
\(809\) −2919.61 −0.126883 −0.0634413 0.997986i \(-0.520208\pi\)
−0.0634413 + 0.997986i \(0.520208\pi\)
\(810\) 18163.0 0.787879
\(811\) −16208.2 −0.701784 −0.350892 0.936416i \(-0.614122\pi\)
−0.350892 + 0.936416i \(0.614122\pi\)
\(812\) 14586.5 0.630401
\(813\) −23218.2 −1.00160
\(814\) 22896.2 0.985888
\(815\) 14352.4 0.616861
\(816\) 12296.1 0.527511
\(817\) 0 0
\(818\) 17383.3 0.743022
\(819\) 6185.51 0.263906
\(820\) −361.951 −0.0154145
\(821\) −17404.8 −0.739867 −0.369934 0.929058i \(-0.620620\pi\)
−0.369934 + 0.929058i \(0.620620\pi\)
\(822\) −21682.3 −0.920022
\(823\) 9581.39 0.405816 0.202908 0.979198i \(-0.434961\pi\)
0.202908 + 0.979198i \(0.434961\pi\)
\(824\) 9685.20 0.409466
\(825\) 5441.59 0.229639
\(826\) 102443. 4.31532
\(827\) −36359.4 −1.52883 −0.764414 0.644726i \(-0.776972\pi\)
−0.764414 + 0.644726i \(0.776972\pi\)
\(828\) −2206.73 −0.0926198
\(829\) 21898.1 0.917435 0.458717 0.888582i \(-0.348309\pi\)
0.458717 + 0.888582i \(0.348309\pi\)
\(830\) 23383.8 0.977907
\(831\) 31326.0 1.30769
\(832\) 42186.0 1.75785
\(833\) −23289.9 −0.968726
\(834\) −9671.32 −0.401547
\(835\) 6310.84 0.261552
\(836\) 11150.0 0.461280
\(837\) 28418.9 1.17360
\(838\) 21460.6 0.884659
\(839\) −5384.09 −0.221549 −0.110774 0.993846i \(-0.535333\pi\)
−0.110774 + 0.993846i \(0.535333\pi\)
\(840\) −6741.29 −0.276901
\(841\) −21480.0 −0.880726
\(842\) −14900.9 −0.609882
\(843\) −9158.12 −0.374167
\(844\) 37932.4 1.54702
\(845\) −9962.99 −0.405606
\(846\) −8675.34 −0.352558
\(847\) −30962.3 −1.25605
\(848\) −4644.45 −0.188079
\(849\) 2163.17 0.0874440
\(850\) 17093.9 0.689782
\(851\) −22605.4 −0.910579
\(852\) 19562.3 0.786610
\(853\) 3558.83 0.142851 0.0714255 0.997446i \(-0.477245\pi\)
0.0714255 + 0.997446i \(0.477245\pi\)
\(854\) 84844.3 3.39966
\(855\) −2000.39 −0.0800141
\(856\) 4394.94 0.175486
\(857\) −38994.7 −1.55430 −0.777149 0.629317i \(-0.783335\pi\)
−0.777149 + 0.629317i \(0.783335\pi\)
\(858\) 18153.7 0.722328
\(859\) −10894.1 −0.432715 −0.216358 0.976314i \(-0.569418\pi\)
−0.216358 + 0.976314i \(0.569418\pi\)
\(860\) 0 0
\(861\) 716.880 0.0283754
\(862\) −35756.2 −1.41283
\(863\) 48209.7 1.90160 0.950798 0.309811i \(-0.100266\pi\)
0.950798 + 0.309811i \(0.100266\pi\)
\(864\) 38096.4 1.50008
\(865\) −12925.0 −0.508048
\(866\) −33314.5 −1.30724
\(867\) −9865.22 −0.386436
\(868\) −51871.9 −2.02840
\(869\) 11906.2 0.464774
\(870\) −7680.36 −0.299297
\(871\) 59127.8 2.30019
\(872\) 10001.1 0.388393
\(873\) −2129.67 −0.0825639
\(874\) −20089.7 −0.777512
\(875\) 39269.3 1.51719
\(876\) 10267.2 0.395999
\(877\) 14792.4 0.569558 0.284779 0.958593i \(-0.408080\pi\)
0.284779 + 0.958593i \(0.408080\pi\)
\(878\) 57340.2 2.20403
\(879\) −10073.9 −0.386556
\(880\) −4951.96 −0.189694
\(881\) 9682.56 0.370277 0.185138 0.982712i \(-0.440727\pi\)
0.185138 + 0.982712i \(0.440727\pi\)
\(882\) −6743.92 −0.257460
\(883\) −19920.4 −0.759201 −0.379601 0.925150i \(-0.623939\pi\)
−0.379601 + 0.925150i \(0.623939\pi\)
\(884\) 31248.3 1.18891
\(885\) −29557.1 −1.12266
\(886\) −63382.4 −2.40336
\(887\) 41838.2 1.58375 0.791876 0.610682i \(-0.209105\pi\)
0.791876 + 0.610682i \(0.209105\pi\)
\(888\) −12629.9 −0.477286
\(889\) 15667.7 0.591089
\(890\) 35539.1 1.33851
\(891\) 9150.47 0.344054
\(892\) 19.0149 0.000713750 0
\(893\) −43277.2 −1.62174
\(894\) −10517.1 −0.393451
\(895\) 31105.5 1.16172
\(896\) −24917.7 −0.929066
\(897\) −17923.1 −0.667152
\(898\) −20701.3 −0.769276
\(899\) −10344.8 −0.383780
\(900\) 2712.26 0.100454
\(901\) −5233.78 −0.193521
\(902\) −332.780 −0.0122842
\(903\) 0 0
\(904\) −7884.80 −0.290094
\(905\) 22815.2 0.838016
\(906\) 27714.7 1.01629
\(907\) −35318.6 −1.29298 −0.646492 0.762921i \(-0.723765\pi\)
−0.646492 + 0.762921i \(0.723765\pi\)
\(908\) 479.124 0.0175113
\(909\) −5865.97 −0.214040
\(910\) 49474.1 1.80225
\(911\) 1355.47 0.0492959 0.0246480 0.999696i \(-0.492154\pi\)
0.0246480 + 0.999696i \(0.492154\pi\)
\(912\) 17761.7 0.644898
\(913\) 11780.7 0.427036
\(914\) 35402.8 1.28120
\(915\) −24479.4 −0.884443
\(916\) 16465.5 0.593924
\(917\) −7118.89 −0.256365
\(918\) 33391.6 1.20053
\(919\) 10499.0 0.376854 0.188427 0.982087i \(-0.439661\pi\)
0.188427 + 0.982087i \(0.439661\pi\)
\(920\) −3089.60 −0.110719
\(921\) 1900.37 0.0679905
\(922\) −74488.2 −2.66067
\(923\) −25130.7 −0.896194
\(924\) −19402.1 −0.690781
\(925\) 27784.0 0.987602
\(926\) 41611.7 1.47672
\(927\) −5000.99 −0.177189
\(928\) −13867.5 −0.490543
\(929\) 31511.5 1.11287 0.556436 0.830890i \(-0.312168\pi\)
0.556436 + 0.830890i \(0.312168\pi\)
\(930\) 27312.6 0.963028
\(931\) −33642.2 −1.18430
\(932\) 36807.9 1.29365
\(933\) 10396.1 0.364793
\(934\) 23718.0 0.830918
\(935\) −5580.30 −0.195182
\(936\) 1583.88 0.0553105
\(937\) −5299.66 −0.184773 −0.0923864 0.995723i \(-0.529450\pi\)
−0.0923864 + 0.995723i \(0.529450\pi\)
\(938\) −115326. −4.01442
\(939\) −29083.7 −1.01077
\(940\) −38022.1 −1.31930
\(941\) 34588.6 1.19825 0.599126 0.800655i \(-0.295515\pi\)
0.599126 + 0.800655i \(0.295515\pi\)
\(942\) −57862.2 −2.00133
\(943\) 328.553 0.0113459
\(944\) −41509.8 −1.43118
\(945\) 28969.1 0.997213
\(946\) 0 0
\(947\) −17342.1 −0.595083 −0.297541 0.954709i \(-0.596167\pi\)
−0.297541 + 0.954709i \(0.596167\pi\)
\(948\) −37519.4 −1.28541
\(949\) −13189.7 −0.451166
\(950\) 24692.0 0.843279
\(951\) −30708.0 −1.04708
\(952\) −10668.7 −0.363210
\(953\) −53043.0 −1.80297 −0.901485 0.432810i \(-0.857522\pi\)
−0.901485 + 0.432810i \(0.857522\pi\)
\(954\) −1515.51 −0.0514324
\(955\) −15749.3 −0.533650
\(956\) −28608.5 −0.967850
\(957\) −3869.35 −0.130698
\(958\) −70129.1 −2.36510
\(959\) −29769.7 −1.00241
\(960\) 23740.1 0.798133
\(961\) 6996.75 0.234861
\(962\) 92690.1 3.10650
\(963\) −2269.35 −0.0759384
\(964\) −39548.8 −1.32135
\(965\) 7154.34 0.238659
\(966\) 34958.2 1.16435
\(967\) 4560.36 0.151656 0.0758280 0.997121i \(-0.475840\pi\)
0.0758280 + 0.997121i \(0.475840\pi\)
\(968\) −7928.27 −0.263248
\(969\) 20015.4 0.663557
\(970\) −17033.9 −0.563840
\(971\) −27229.5 −0.899934 −0.449967 0.893045i \(-0.648564\pi\)
−0.449967 + 0.893045i \(0.648564\pi\)
\(972\) 9959.78 0.328663
\(973\) −13278.7 −0.437508
\(974\) 69035.3 2.27108
\(975\) 22029.0 0.723583
\(976\) −34378.8 −1.12750
\(977\) 31182.6 1.02110 0.510552 0.859847i \(-0.329441\pi\)
0.510552 + 0.859847i \(0.329441\pi\)
\(978\) −41583.0 −1.35959
\(979\) 17904.5 0.584506
\(980\) −29557.1 −0.963436
\(981\) −5164.09 −0.168070
\(982\) 13343.6 0.433617
\(983\) −28454.7 −0.923259 −0.461630 0.887073i \(-0.652735\pi\)
−0.461630 + 0.887073i \(0.652735\pi\)
\(984\) 183.566 0.00594702
\(985\) −14201.5 −0.459388
\(986\) −12154.9 −0.392588
\(987\) 75306.7 2.42861
\(988\) 45138.1 1.45348
\(989\) 0 0
\(990\) −1615.85 −0.0518739
\(991\) −40487.4 −1.29781 −0.648903 0.760871i \(-0.724772\pi\)
−0.648903 + 0.760871i \(0.724772\pi\)
\(992\) 49315.1 1.57838
\(993\) 33722.6 1.07770
\(994\) 49016.2 1.56409
\(995\) 16405.2 0.522692
\(996\) −37124.0 −1.18104
\(997\) −3912.73 −0.124290 −0.0621451 0.998067i \(-0.519794\pi\)
−0.0621451 + 0.998067i \(0.519794\pi\)
\(998\) 45848.9 1.45423
\(999\) 54273.9 1.71887
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 1849.4.a.i.1.44 50
43.42 odd 2 1849.4.a.j.1.7 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.44 50 1.1 even 1 trivial
1849.4.a.j.1.7 yes 50 43.42 odd 2