Properties

Label 1849.4.a.i.1.19
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 1.19
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.06784 q^{2} -3.28982 q^{3} -3.72402 q^{4} +0.905592 q^{5} +6.80284 q^{6} +0.553732 q^{7} +24.2434 q^{8} -16.1771 q^{9} +O(q^{10})\) \(q-2.06784 q^{2} -3.28982 q^{3} -3.72402 q^{4} +0.905592 q^{5} +6.80284 q^{6} +0.553732 q^{7} +24.2434 q^{8} -16.1771 q^{9} -1.87262 q^{10} +36.0498 q^{11} +12.2514 q^{12} +72.5269 q^{13} -1.14503 q^{14} -2.97924 q^{15} -20.3395 q^{16} -42.3970 q^{17} +33.4516 q^{18} -54.5057 q^{19} -3.37245 q^{20} -1.82168 q^{21} -74.5453 q^{22} -113.780 q^{23} -79.7566 q^{24} -124.180 q^{25} -149.974 q^{26} +142.045 q^{27} -2.06211 q^{28} -18.9616 q^{29} +6.16060 q^{30} +45.5688 q^{31} -151.889 q^{32} -118.597 q^{33} +87.6703 q^{34} +0.501455 q^{35} +60.2437 q^{36} +56.1166 q^{37} +112.709 q^{38} -238.601 q^{39} +21.9547 q^{40} -51.8970 q^{41} +3.76695 q^{42} -134.250 q^{44} -14.6498 q^{45} +235.280 q^{46} +133.140 q^{47} +66.9133 q^{48} -342.693 q^{49} +256.785 q^{50} +139.479 q^{51} -270.092 q^{52} -368.545 q^{53} -293.727 q^{54} +32.6464 q^{55} +13.4244 q^{56} +179.314 q^{57} +39.2097 q^{58} +489.535 q^{59} +11.0947 q^{60} +592.623 q^{61} -94.2291 q^{62} -8.95775 q^{63} +476.798 q^{64} +65.6798 q^{65} +245.241 q^{66} +1060.37 q^{67} +157.887 q^{68} +374.318 q^{69} -1.03693 q^{70} -489.493 q^{71} -392.188 q^{72} +511.754 q^{73} -116.040 q^{74} +408.530 q^{75} +202.980 q^{76} +19.9619 q^{77} +493.389 q^{78} +197.197 q^{79} -18.4193 q^{80} -30.5219 q^{81} +107.315 q^{82} +391.934 q^{83} +6.78397 q^{84} -38.3944 q^{85} +62.3804 q^{87} +873.971 q^{88} +836.377 q^{89} +30.2935 q^{90} +40.1604 q^{91} +423.721 q^{92} -149.913 q^{93} -275.313 q^{94} -49.3599 q^{95} +499.687 q^{96} -1193.25 q^{97} +708.636 q^{98} -583.179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.06784 −0.731093 −0.365547 0.930793i \(-0.619118\pi\)
−0.365547 + 0.930793i \(0.619118\pi\)
\(3\) −3.28982 −0.633127 −0.316563 0.948571i \(-0.602529\pi\)
−0.316563 + 0.948571i \(0.602529\pi\)
\(4\) −3.72402 −0.465503
\(5\) 0.905592 0.0809986 0.0404993 0.999180i \(-0.487105\pi\)
0.0404993 + 0.999180i \(0.487105\pi\)
\(6\) 6.80284 0.462875
\(7\) 0.553732 0.0298987 0.0149493 0.999888i \(-0.495241\pi\)
0.0149493 + 0.999888i \(0.495241\pi\)
\(8\) 24.2434 1.07142
\(9\) −16.1771 −0.599151
\(10\) −1.87262 −0.0592175
\(11\) 36.0498 0.988128 0.494064 0.869425i \(-0.335511\pi\)
0.494064 + 0.869425i \(0.335511\pi\)
\(12\) 12.2514 0.294722
\(13\) 72.5269 1.54733 0.773667 0.633593i \(-0.218420\pi\)
0.773667 + 0.633593i \(0.218420\pi\)
\(14\) −1.14503 −0.0218587
\(15\) −2.97924 −0.0512824
\(16\) −20.3395 −0.317804
\(17\) −42.3970 −0.604869 −0.302435 0.953170i \(-0.597799\pi\)
−0.302435 + 0.953170i \(0.597799\pi\)
\(18\) 33.4516 0.438035
\(19\) −54.5057 −0.658130 −0.329065 0.944307i \(-0.606733\pi\)
−0.329065 + 0.944307i \(0.606733\pi\)
\(20\) −3.37245 −0.0377051
\(21\) −1.82168 −0.0189297
\(22\) −74.5453 −0.722414
\(23\) −113.780 −1.03152 −0.515758 0.856734i \(-0.672490\pi\)
−0.515758 + 0.856734i \(0.672490\pi\)
\(24\) −79.7566 −0.678344
\(25\) −124.180 −0.993439
\(26\) −149.974 −1.13125
\(27\) 142.045 1.01246
\(28\) −2.06211 −0.0139179
\(29\) −18.9616 −0.121417 −0.0607084 0.998156i \(-0.519336\pi\)
−0.0607084 + 0.998156i \(0.519336\pi\)
\(30\) 6.16060 0.0374922
\(31\) 45.5688 0.264013 0.132006 0.991249i \(-0.457858\pi\)
0.132006 + 0.991249i \(0.457858\pi\)
\(32\) −151.889 −0.839074
\(33\) −118.597 −0.625611
\(34\) 87.6703 0.442216
\(35\) 0.501455 0.00242175
\(36\) 60.2437 0.278906
\(37\) 56.1166 0.249338 0.124669 0.992198i \(-0.460213\pi\)
0.124669 + 0.992198i \(0.460213\pi\)
\(38\) 112.709 0.481154
\(39\) −238.601 −0.979658
\(40\) 21.9547 0.0867835
\(41\) −51.8970 −0.197682 −0.0988409 0.995103i \(-0.531513\pi\)
−0.0988409 + 0.995103i \(0.531513\pi\)
\(42\) 3.76695 0.0138393
\(43\) 0 0
\(44\) −134.250 −0.459977
\(45\) −14.6498 −0.0485304
\(46\) 235.280 0.754134
\(47\) 133.140 0.413202 0.206601 0.978425i \(-0.433760\pi\)
0.206601 + 0.978425i \(0.433760\pi\)
\(48\) 66.9133 0.201210
\(49\) −342.693 −0.999106
\(50\) 256.785 0.726297
\(51\) 139.479 0.382959
\(52\) −270.092 −0.720288
\(53\) −368.545 −0.955162 −0.477581 0.878588i \(-0.658486\pi\)
−0.477581 + 0.878588i \(0.658486\pi\)
\(54\) −293.727 −0.740206
\(55\) 32.6464 0.0800371
\(56\) 13.4244 0.0320340
\(57\) 179.314 0.416679
\(58\) 39.2097 0.0887670
\(59\) 489.535 1.08020 0.540102 0.841599i \(-0.318386\pi\)
0.540102 + 0.841599i \(0.318386\pi\)
\(60\) 11.0947 0.0238721
\(61\) 592.623 1.24389 0.621947 0.783059i \(-0.286342\pi\)
0.621947 + 0.783059i \(0.286342\pi\)
\(62\) −94.2291 −0.193018
\(63\) −8.95775 −0.0179138
\(64\) 476.798 0.931246
\(65\) 65.6798 0.125332
\(66\) 245.241 0.457380
\(67\) 1060.37 1.93350 0.966751 0.255719i \(-0.0823121\pi\)
0.966751 + 0.255719i \(0.0823121\pi\)
\(68\) 157.887 0.281568
\(69\) 374.318 0.653080
\(70\) −1.03693 −0.00177053
\(71\) −489.493 −0.818199 −0.409099 0.912490i \(-0.634157\pi\)
−0.409099 + 0.912490i \(0.634157\pi\)
\(72\) −392.188 −0.641941
\(73\) 511.754 0.820497 0.410248 0.911974i \(-0.365442\pi\)
0.410248 + 0.911974i \(0.365442\pi\)
\(74\) −116.040 −0.182289
\(75\) 408.530 0.628973
\(76\) 202.980 0.306361
\(77\) 19.9619 0.0295438
\(78\) 493.389 0.716222
\(79\) 197.197 0.280840 0.140420 0.990092i \(-0.455155\pi\)
0.140420 + 0.990092i \(0.455155\pi\)
\(80\) −18.4193 −0.0257417
\(81\) −30.5219 −0.0418681
\(82\) 107.315 0.144524
\(83\) 391.934 0.518318 0.259159 0.965835i \(-0.416555\pi\)
0.259159 + 0.965835i \(0.416555\pi\)
\(84\) 6.78397 0.00881181
\(85\) −38.3944 −0.0489936
\(86\) 0 0
\(87\) 62.3804 0.0768722
\(88\) 873.971 1.05870
\(89\) 836.377 0.996133 0.498066 0.867139i \(-0.334044\pi\)
0.498066 + 0.867139i \(0.334044\pi\)
\(90\) 30.2935 0.0354802
\(91\) 40.1604 0.0462633
\(92\) 423.721 0.480174
\(93\) −149.913 −0.167154
\(94\) −275.313 −0.302089
\(95\) −49.3599 −0.0533076
\(96\) 499.687 0.531240
\(97\) −1193.25 −1.24903 −0.624514 0.781013i \(-0.714703\pi\)
−0.624514 + 0.781013i \(0.714703\pi\)
\(98\) 708.636 0.730440
\(99\) −583.179 −0.592038
\(100\) 462.449 0.462449
\(101\) −1774.91 −1.74862 −0.874309 0.485370i \(-0.838685\pi\)
−0.874309 + 0.485370i \(0.838685\pi\)
\(102\) −288.420 −0.279979
\(103\) −1820.25 −1.74131 −0.870655 0.491894i \(-0.836305\pi\)
−0.870655 + 0.491894i \(0.836305\pi\)
\(104\) 1758.30 1.65784
\(105\) −1.64970 −0.00153328
\(106\) 762.094 0.698313
\(107\) −656.760 −0.593378 −0.296689 0.954974i \(-0.595882\pi\)
−0.296689 + 0.954974i \(0.595882\pi\)
\(108\) −528.978 −0.471305
\(109\) 518.425 0.455560 0.227780 0.973713i \(-0.426853\pi\)
0.227780 + 0.973713i \(0.426853\pi\)
\(110\) −67.5076 −0.0585145
\(111\) −184.614 −0.157863
\(112\) −11.2626 −0.00950194
\(113\) 1702.26 1.41713 0.708564 0.705647i \(-0.249343\pi\)
0.708564 + 0.705647i \(0.249343\pi\)
\(114\) −370.793 −0.304631
\(115\) −103.039 −0.0835514
\(116\) 70.6136 0.0565199
\(117\) −1173.27 −0.927086
\(118\) −1012.28 −0.789730
\(119\) −23.4765 −0.0180848
\(120\) −72.2270 −0.0549449
\(121\) −31.4145 −0.0236022
\(122\) −1225.45 −0.909402
\(123\) 170.732 0.125158
\(124\) −169.699 −0.122899
\(125\) −225.655 −0.161466
\(126\) 18.5232 0.0130967
\(127\) −1281.78 −0.895587 −0.447793 0.894137i \(-0.647790\pi\)
−0.447793 + 0.894137i \(0.647790\pi\)
\(128\) 229.166 0.158247
\(129\) 0 0
\(130\) −135.816 −0.0916293
\(131\) 2387.94 1.59263 0.796316 0.604880i \(-0.206779\pi\)
0.796316 + 0.604880i \(0.206779\pi\)
\(132\) 441.659 0.291223
\(133\) −30.1815 −0.0196772
\(134\) −2192.68 −1.41357
\(135\) 128.635 0.0820083
\(136\) −1027.85 −0.648069
\(137\) 3079.35 1.92034 0.960169 0.279418i \(-0.0901416\pi\)
0.960169 + 0.279418i \(0.0901416\pi\)
\(138\) −774.030 −0.477463
\(139\) −59.2952 −0.0361824 −0.0180912 0.999836i \(-0.505759\pi\)
−0.0180912 + 0.999836i \(0.505759\pi\)
\(140\) −1.86743 −0.00112733
\(141\) −438.007 −0.261609
\(142\) 1012.19 0.598180
\(143\) 2614.58 1.52896
\(144\) 329.033 0.190413
\(145\) −17.1715 −0.00983460
\(146\) −1058.23 −0.599859
\(147\) 1127.40 0.632561
\(148\) −208.979 −0.116068
\(149\) −2972.79 −1.63450 −0.817251 0.576283i \(-0.804503\pi\)
−0.817251 + 0.576283i \(0.804503\pi\)
\(150\) −844.776 −0.459838
\(151\) 181.367 0.0977443 0.0488722 0.998805i \(-0.484437\pi\)
0.0488722 + 0.998805i \(0.484437\pi\)
\(152\) −1321.41 −0.705133
\(153\) 685.859 0.362408
\(154\) −41.2781 −0.0215992
\(155\) 41.2667 0.0213847
\(156\) 888.554 0.456034
\(157\) −1001.66 −0.509180 −0.254590 0.967049i \(-0.581940\pi\)
−0.254590 + 0.967049i \(0.581940\pi\)
\(158\) −407.773 −0.205321
\(159\) 1212.45 0.604739
\(160\) −137.549 −0.0679639
\(161\) −63.0038 −0.0308410
\(162\) 63.1144 0.0306095
\(163\) 2683.64 1.28956 0.644781 0.764367i \(-0.276948\pi\)
0.644781 + 0.764367i \(0.276948\pi\)
\(164\) 193.266 0.0920214
\(165\) −107.401 −0.0506736
\(166\) −810.459 −0.378939
\(167\) −1580.13 −0.732178 −0.366089 0.930580i \(-0.619304\pi\)
−0.366089 + 0.930580i \(0.619304\pi\)
\(168\) −44.1638 −0.0202816
\(169\) 3063.15 1.39424
\(170\) 79.3936 0.0358189
\(171\) 881.742 0.394319
\(172\) 0 0
\(173\) −1218.41 −0.535456 −0.267728 0.963495i \(-0.586273\pi\)
−0.267728 + 0.963495i \(0.586273\pi\)
\(174\) −128.993 −0.0562008
\(175\) −68.7623 −0.0297025
\(176\) −733.234 −0.314032
\(177\) −1610.48 −0.683906
\(178\) −1729.50 −0.728266
\(179\) 3175.63 1.32602 0.663011 0.748610i \(-0.269278\pi\)
0.663011 + 0.748610i \(0.269278\pi\)
\(180\) 54.5563 0.0225910
\(181\) −2654.51 −1.09010 −0.545050 0.838403i \(-0.683490\pi\)
−0.545050 + 0.838403i \(0.683490\pi\)
\(182\) −83.0455 −0.0338228
\(183\) −1949.62 −0.787543
\(184\) −2758.43 −1.10519
\(185\) 50.8187 0.0201960
\(186\) 309.997 0.122205
\(187\) −1528.40 −0.597689
\(188\) −495.817 −0.192346
\(189\) 78.6547 0.0302714
\(190\) 102.069 0.0389728
\(191\) 757.828 0.287092 0.143546 0.989644i \(-0.454150\pi\)
0.143546 + 0.989644i \(0.454150\pi\)
\(192\) −1568.58 −0.589597
\(193\) 2143.88 0.799584 0.399792 0.916606i \(-0.369082\pi\)
0.399792 + 0.916606i \(0.369082\pi\)
\(194\) 2467.45 0.913156
\(195\) −216.075 −0.0793510
\(196\) 1276.20 0.465087
\(197\) −2151.99 −0.778289 −0.389144 0.921177i \(-0.627229\pi\)
−0.389144 + 0.921177i \(0.627229\pi\)
\(198\) 1205.92 0.432835
\(199\) 3651.57 1.30077 0.650384 0.759605i \(-0.274608\pi\)
0.650384 + 0.759605i \(0.274608\pi\)
\(200\) −3010.55 −1.06439
\(201\) −3488.43 −1.22415
\(202\) 3670.24 1.27840
\(203\) −10.4997 −0.00363020
\(204\) −519.421 −0.178268
\(205\) −46.9975 −0.0160120
\(206\) 3764.00 1.27306
\(207\) 1840.63 0.618033
\(208\) −1475.16 −0.491750
\(209\) −1964.92 −0.650316
\(210\) 3.41132 0.00112097
\(211\) −5708.59 −1.86254 −0.931270 0.364331i \(-0.881298\pi\)
−0.931270 + 0.364331i \(0.881298\pi\)
\(212\) 1372.47 0.444631
\(213\) 1610.34 0.518024
\(214\) 1358.08 0.433814
\(215\) 0 0
\(216\) 3443.66 1.08477
\(217\) 25.2329 0.00789364
\(218\) −1072.02 −0.333057
\(219\) −1683.58 −0.519478
\(220\) −121.576 −0.0372575
\(221\) −3074.92 −0.935935
\(222\) 381.752 0.115412
\(223\) −3393.14 −1.01893 −0.509465 0.860491i \(-0.670157\pi\)
−0.509465 + 0.860491i \(0.670157\pi\)
\(224\) −84.1056 −0.0250872
\(225\) 2008.87 0.595220
\(226\) −3520.01 −1.03605
\(227\) −5880.28 −1.71933 −0.859664 0.510859i \(-0.829327\pi\)
−0.859664 + 0.510859i \(0.829327\pi\)
\(228\) −667.769 −0.193965
\(229\) 3582.01 1.03365 0.516826 0.856091i \(-0.327114\pi\)
0.516826 + 0.856091i \(0.327114\pi\)
\(230\) 213.068 0.0610839
\(231\) −65.6711 −0.0187049
\(232\) −459.695 −0.130088
\(233\) 1730.14 0.486459 0.243230 0.969969i \(-0.421793\pi\)
0.243230 + 0.969969i \(0.421793\pi\)
\(234\) 2426.14 0.677786
\(235\) 120.571 0.0334688
\(236\) −1823.04 −0.502838
\(237\) −648.743 −0.177808
\(238\) 48.5458 0.0132217
\(239\) −4199.88 −1.13668 −0.568342 0.822792i \(-0.692415\pi\)
−0.568342 + 0.822792i \(0.692415\pi\)
\(240\) 60.5962 0.0162978
\(241\) 6623.20 1.77028 0.885141 0.465322i \(-0.154062\pi\)
0.885141 + 0.465322i \(0.154062\pi\)
\(242\) 64.9602 0.0172554
\(243\) −3734.80 −0.985957
\(244\) −2206.94 −0.579036
\(245\) −310.340 −0.0809262
\(246\) −353.047 −0.0915019
\(247\) −3953.13 −1.01835
\(248\) 1104.74 0.282868
\(249\) −1289.39 −0.328161
\(250\) 466.620 0.118047
\(251\) −2718.52 −0.683631 −0.341816 0.939767i \(-0.611042\pi\)
−0.341816 + 0.939767i \(0.611042\pi\)
\(252\) 33.3589 0.00833893
\(253\) −4101.76 −1.01927
\(254\) 2650.52 0.654757
\(255\) 126.311 0.0310192
\(256\) −4288.26 −1.04694
\(257\) 1570.63 0.381219 0.190609 0.981666i \(-0.438954\pi\)
0.190609 + 0.981666i \(0.438954\pi\)
\(258\) 0 0
\(259\) 31.0735 0.00745488
\(260\) −244.593 −0.0583424
\(261\) 306.744 0.0727469
\(262\) −4937.88 −1.16436
\(263\) −5434.10 −1.27407 −0.637036 0.770834i \(-0.719840\pi\)
−0.637036 + 0.770834i \(0.719840\pi\)
\(264\) −2875.21 −0.670291
\(265\) −333.752 −0.0773668
\(266\) 62.4107 0.0143859
\(267\) −2751.53 −0.630678
\(268\) −3948.84 −0.900051
\(269\) 1749.35 0.396505 0.198252 0.980151i \(-0.436473\pi\)
0.198252 + 0.980151i \(0.436473\pi\)
\(270\) −265.997 −0.0599557
\(271\) 4745.81 1.06379 0.531895 0.846810i \(-0.321480\pi\)
0.531895 + 0.846810i \(0.321480\pi\)
\(272\) 862.333 0.192230
\(273\) −132.121 −0.0292905
\(274\) −6367.61 −1.40395
\(275\) −4476.66 −0.981646
\(276\) −1393.97 −0.304011
\(277\) −5996.54 −1.30071 −0.650356 0.759630i \(-0.725380\pi\)
−0.650356 + 0.759630i \(0.725380\pi\)
\(278\) 122.613 0.0264527
\(279\) −737.169 −0.158183
\(280\) 12.1570 0.00259471
\(281\) 2534.71 0.538107 0.269054 0.963125i \(-0.413289\pi\)
0.269054 + 0.963125i \(0.413289\pi\)
\(282\) 905.731 0.191261
\(283\) 6608.32 1.38807 0.694035 0.719942i \(-0.255831\pi\)
0.694035 + 0.719942i \(0.255831\pi\)
\(284\) 1822.88 0.380874
\(285\) 162.385 0.0337505
\(286\) −5406.54 −1.11782
\(287\) −28.7370 −0.00591043
\(288\) 2457.11 0.502732
\(289\) −3115.50 −0.634133
\(290\) 35.5080 0.00719001
\(291\) 3925.57 0.790794
\(292\) −1905.78 −0.381943
\(293\) 6937.69 1.38329 0.691646 0.722237i \(-0.256886\pi\)
0.691646 + 0.722237i \(0.256886\pi\)
\(294\) −2331.29 −0.462461
\(295\) 443.319 0.0874951
\(296\) 1360.46 0.267146
\(297\) 5120.69 1.00045
\(298\) 6147.27 1.19497
\(299\) −8252.14 −1.59610
\(300\) −1521.37 −0.292789
\(301\) 0 0
\(302\) −375.038 −0.0714602
\(303\) 5839.15 1.10710
\(304\) 1108.62 0.209156
\(305\) 536.674 0.100754
\(306\) −1418.25 −0.264954
\(307\) −1685.77 −0.313394 −0.156697 0.987647i \(-0.550085\pi\)
−0.156697 + 0.987647i \(0.550085\pi\)
\(308\) −74.3385 −0.0137527
\(309\) 5988.32 1.10247
\(310\) −85.3332 −0.0156342
\(311\) 5016.27 0.914620 0.457310 0.889307i \(-0.348813\pi\)
0.457310 + 0.889307i \(0.348813\pi\)
\(312\) −5784.50 −1.04962
\(313\) −5995.54 −1.08271 −0.541354 0.840794i \(-0.682088\pi\)
−0.541354 + 0.840794i \(0.682088\pi\)
\(314\) 2071.28 0.372258
\(315\) −8.11207 −0.00145099
\(316\) −734.366 −0.130732
\(317\) −7839.42 −1.38898 −0.694488 0.719504i \(-0.744369\pi\)
−0.694488 + 0.719504i \(0.744369\pi\)
\(318\) −2507.16 −0.442120
\(319\) −683.563 −0.119975
\(320\) 431.785 0.0754297
\(321\) 2160.62 0.375683
\(322\) 130.282 0.0225476
\(323\) 2310.88 0.398082
\(324\) 113.664 0.0194897
\(325\) −9006.38 −1.53718
\(326\) −5549.34 −0.942790
\(327\) −1705.52 −0.288427
\(328\) −1258.16 −0.211800
\(329\) 73.7239 0.0123542
\(330\) 222.088 0.0370471
\(331\) −8960.38 −1.48794 −0.743968 0.668215i \(-0.767059\pi\)
−0.743968 + 0.668215i \(0.767059\pi\)
\(332\) −1459.57 −0.241278
\(333\) −907.801 −0.149391
\(334\) 3267.45 0.535291
\(335\) 960.262 0.156611
\(336\) 37.0520 0.00601593
\(337\) −11341.3 −1.83324 −0.916618 0.399765i \(-0.869092\pi\)
−0.916618 + 0.399765i \(0.869092\pi\)
\(338\) −6334.12 −1.01932
\(339\) −5600.14 −0.897221
\(340\) 142.982 0.0228067
\(341\) 1642.74 0.260878
\(342\) −1823.30 −0.288284
\(343\) −379.690 −0.0597707
\(344\) 0 0
\(345\) 338.979 0.0528986
\(346\) 2519.48 0.391468
\(347\) −4636.21 −0.717247 −0.358623 0.933482i \(-0.616754\pi\)
−0.358623 + 0.933482i \(0.616754\pi\)
\(348\) −232.306 −0.0357842
\(349\) −5902.79 −0.905355 −0.452678 0.891674i \(-0.649531\pi\)
−0.452678 + 0.891674i \(0.649531\pi\)
\(350\) 142.190 0.0217153
\(351\) 10302.1 1.56662
\(352\) −5475.55 −0.829113
\(353\) 9876.87 1.48921 0.744607 0.667503i \(-0.232637\pi\)
0.744607 + 0.667503i \(0.232637\pi\)
\(354\) 3330.23 0.499999
\(355\) −443.281 −0.0662730
\(356\) −3114.69 −0.463702
\(357\) 77.2337 0.0114500
\(358\) −6566.71 −0.969445
\(359\) −7475.25 −1.09897 −0.549483 0.835505i \(-0.685175\pi\)
−0.549483 + 0.835505i \(0.685175\pi\)
\(360\) −355.162 −0.0519964
\(361\) −3888.13 −0.566866
\(362\) 5489.11 0.796965
\(363\) 103.348 0.0149432
\(364\) −149.558 −0.0215357
\(365\) 463.440 0.0664591
\(366\) 4031.52 0.575767
\(367\) 4041.24 0.574799 0.287400 0.957811i \(-0.407209\pi\)
0.287400 + 0.957811i \(0.407209\pi\)
\(368\) 2314.24 0.327820
\(369\) 839.541 0.118441
\(370\) −105.085 −0.0147652
\(371\) −204.075 −0.0285581
\(372\) 558.280 0.0778104
\(373\) −5634.47 −0.782149 −0.391075 0.920359i \(-0.627897\pi\)
−0.391075 + 0.920359i \(0.627897\pi\)
\(374\) 3160.50 0.436966
\(375\) 742.366 0.102228
\(376\) 3227.77 0.442712
\(377\) −1375.23 −0.187872
\(378\) −162.646 −0.0221312
\(379\) 2008.13 0.272165 0.136082 0.990698i \(-0.456549\pi\)
0.136082 + 0.990698i \(0.456549\pi\)
\(380\) 183.817 0.0248148
\(381\) 4216.83 0.567020
\(382\) −1567.07 −0.209891
\(383\) −205.436 −0.0274080 −0.0137040 0.999906i \(-0.504362\pi\)
−0.0137040 + 0.999906i \(0.504362\pi\)
\(384\) −753.915 −0.100190
\(385\) 18.0773 0.00239300
\(386\) −4433.20 −0.584570
\(387\) 0 0
\(388\) 4443.68 0.581426
\(389\) −3601.09 −0.469363 −0.234682 0.972072i \(-0.575405\pi\)
−0.234682 + 0.972072i \(0.575405\pi\)
\(390\) 446.809 0.0580130
\(391\) 4823.95 0.623932
\(392\) −8308.07 −1.07046
\(393\) −7855.89 −1.00834
\(394\) 4449.98 0.569002
\(395\) 178.580 0.0227477
\(396\) 2171.77 0.275595
\(397\) −12924.6 −1.63392 −0.816962 0.576691i \(-0.804344\pi\)
−0.816962 + 0.576691i \(0.804344\pi\)
\(398\) −7550.87 −0.950983
\(399\) 99.2918 0.0124582
\(400\) 2525.75 0.315719
\(401\) 4108.28 0.511615 0.255807 0.966728i \(-0.417659\pi\)
0.255807 + 0.966728i \(0.417659\pi\)
\(402\) 7213.52 0.894969
\(403\) 3304.96 0.408516
\(404\) 6609.81 0.813986
\(405\) −27.6404 −0.00339126
\(406\) 21.7116 0.00265402
\(407\) 2022.99 0.246378
\(408\) 3381.44 0.410310
\(409\) 3060.09 0.369956 0.184978 0.982743i \(-0.440779\pi\)
0.184978 + 0.982743i \(0.440779\pi\)
\(410\) 97.1836 0.0117062
\(411\) −10130.5 −1.21582
\(412\) 6778.67 0.810585
\(413\) 271.071 0.0322967
\(414\) −3806.14 −0.451840
\(415\) 354.933 0.0419830
\(416\) −11016.0 −1.29833
\(417\) 195.071 0.0229081
\(418\) 4063.14 0.475442
\(419\) −4245.76 −0.495033 −0.247516 0.968884i \(-0.579614\pi\)
−0.247516 + 0.968884i \(0.579614\pi\)
\(420\) 6.14351 0.000713745 0
\(421\) 15790.0 1.82792 0.913962 0.405800i \(-0.133007\pi\)
0.913962 + 0.405800i \(0.133007\pi\)
\(422\) 11804.5 1.36169
\(423\) −2153.82 −0.247570
\(424\) −8934.81 −1.02338
\(425\) 5264.85 0.600901
\(426\) −3329.94 −0.378723
\(427\) 328.154 0.0371908
\(428\) 2445.79 0.276219
\(429\) −8601.50 −0.968028
\(430\) 0 0
\(431\) 9935.16 1.11035 0.555174 0.831734i \(-0.312652\pi\)
0.555174 + 0.831734i \(0.312652\pi\)
\(432\) −2889.12 −0.321766
\(433\) −5897.25 −0.654512 −0.327256 0.944936i \(-0.606124\pi\)
−0.327256 + 0.944936i \(0.606124\pi\)
\(434\) −52.1776 −0.00577098
\(435\) 56.4912 0.00622655
\(436\) −1930.62 −0.212065
\(437\) 6201.68 0.678871
\(438\) 3481.38 0.379787
\(439\) 5213.48 0.566801 0.283401 0.959002i \(-0.408537\pi\)
0.283401 + 0.959002i \(0.408537\pi\)
\(440\) 791.461 0.0857532
\(441\) 5543.77 0.598615
\(442\) 6358.46 0.684256
\(443\) −86.4536 −0.00927208 −0.00463604 0.999989i \(-0.501476\pi\)
−0.00463604 + 0.999989i \(0.501476\pi\)
\(444\) 687.505 0.0734855
\(445\) 757.417 0.0806854
\(446\) 7016.49 0.744933
\(447\) 9779.96 1.03485
\(448\) 264.018 0.0278430
\(449\) −4606.22 −0.484145 −0.242072 0.970258i \(-0.577827\pi\)
−0.242072 + 0.970258i \(0.577827\pi\)
\(450\) −4154.02 −0.435161
\(451\) −1870.88 −0.195335
\(452\) −6339.26 −0.659677
\(453\) −596.664 −0.0618846
\(454\) 12159.5 1.25699
\(455\) 36.3690 0.00374726
\(456\) 4347.19 0.446438
\(457\) 1481.01 0.151595 0.0757973 0.997123i \(-0.475850\pi\)
0.0757973 + 0.997123i \(0.475850\pi\)
\(458\) −7407.05 −0.755695
\(459\) −6022.28 −0.612409
\(460\) 383.718 0.0388934
\(461\) −10609.9 −1.07192 −0.535958 0.844244i \(-0.680050\pi\)
−0.535958 + 0.844244i \(0.680050\pi\)
\(462\) 135.798 0.0136751
\(463\) −9170.50 −0.920495 −0.460247 0.887791i \(-0.652239\pi\)
−0.460247 + 0.887791i \(0.652239\pi\)
\(464\) 385.670 0.0385868
\(465\) −135.760 −0.0135392
\(466\) −3577.65 −0.355647
\(467\) −3075.80 −0.304777 −0.152389 0.988321i \(-0.548697\pi\)
−0.152389 + 0.988321i \(0.548697\pi\)
\(468\) 4369.29 0.431561
\(469\) 587.160 0.0578092
\(470\) −249.321 −0.0244688
\(471\) 3295.29 0.322375
\(472\) 11868.0 1.15735
\(473\) 0 0
\(474\) 1341.50 0.129994
\(475\) 6768.51 0.653812
\(476\) 87.4272 0.00841853
\(477\) 5961.98 0.572286
\(478\) 8684.69 0.831022
\(479\) −8567.68 −0.817259 −0.408630 0.912700i \(-0.633993\pi\)
−0.408630 + 0.912700i \(0.633993\pi\)
\(480\) 452.513 0.0430298
\(481\) 4069.96 0.385809
\(482\) −13695.8 −1.29424
\(483\) 207.271 0.0195263
\(484\) 116.988 0.0109869
\(485\) −1080.59 −0.101170
\(486\) 7722.98 0.720827
\(487\) −7868.75 −0.732171 −0.366085 0.930581i \(-0.619302\pi\)
−0.366085 + 0.930581i \(0.619302\pi\)
\(488\) 14367.2 1.33273
\(489\) −8828.69 −0.816457
\(490\) 641.736 0.0591646
\(491\) −16285.2 −1.49683 −0.748414 0.663232i \(-0.769184\pi\)
−0.748414 + 0.663232i \(0.769184\pi\)
\(492\) −635.810 −0.0582612
\(493\) 803.916 0.0734413
\(494\) 8174.45 0.744506
\(495\) −528.123 −0.0479542
\(496\) −926.845 −0.0839044
\(497\) −271.048 −0.0244631
\(498\) 2666.27 0.239916
\(499\) −16520.2 −1.48206 −0.741030 0.671472i \(-0.765662\pi\)
−0.741030 + 0.671472i \(0.765662\pi\)
\(500\) 840.346 0.0751628
\(501\) 5198.33 0.463562
\(502\) 5621.47 0.499798
\(503\) −1294.17 −0.114720 −0.0573600 0.998354i \(-0.518268\pi\)
−0.0573600 + 0.998354i \(0.518268\pi\)
\(504\) −217.167 −0.0191932
\(505\) −1607.35 −0.141636
\(506\) 8481.80 0.745182
\(507\) −10077.2 −0.882732
\(508\) 4773.37 0.416898
\(509\) −5448.73 −0.474480 −0.237240 0.971451i \(-0.576243\pi\)
−0.237240 + 0.971451i \(0.576243\pi\)
\(510\) −261.191 −0.0226779
\(511\) 283.374 0.0245318
\(512\) 7034.13 0.607163
\(513\) −7742.25 −0.666333
\(514\) −3247.82 −0.278706
\(515\) −1648.41 −0.141044
\(516\) 0 0
\(517\) 4799.67 0.408296
\(518\) −64.2552 −0.00545021
\(519\) 4008.35 0.339012
\(520\) 1592.30 0.134283
\(521\) 16148.0 1.35788 0.678942 0.734192i \(-0.262439\pi\)
0.678942 + 0.734192i \(0.262439\pi\)
\(522\) −634.298 −0.0531848
\(523\) −4443.77 −0.371534 −0.185767 0.982594i \(-0.559477\pi\)
−0.185767 + 0.982594i \(0.559477\pi\)
\(524\) −8892.72 −0.741375
\(525\) 226.216 0.0188055
\(526\) 11236.9 0.931465
\(527\) −1931.98 −0.159693
\(528\) 2412.21 0.198822
\(529\) 778.997 0.0640254
\(530\) 690.147 0.0565624
\(531\) −7919.24 −0.647205
\(532\) 112.397 0.00915980
\(533\) −3763.93 −0.305880
\(534\) 5689.74 0.461085
\(535\) −594.757 −0.0480628
\(536\) 25707.0 2.07159
\(537\) −10447.3 −0.839540
\(538\) −3617.38 −0.289882
\(539\) −12354.0 −0.987245
\(540\) −479.039 −0.0381751
\(541\) −12789.1 −1.01635 −0.508176 0.861253i \(-0.669680\pi\)
−0.508176 + 0.861253i \(0.669680\pi\)
\(542\) −9813.59 −0.777730
\(543\) 8732.87 0.690172
\(544\) 6439.62 0.507530
\(545\) 469.481 0.0368998
\(546\) 273.205 0.0214141
\(547\) −6699.60 −0.523682 −0.261841 0.965111i \(-0.584330\pi\)
−0.261841 + 0.965111i \(0.584330\pi\)
\(548\) −11467.6 −0.893923
\(549\) −9586.89 −0.745280
\(550\) 9257.03 0.717674
\(551\) 1033.52 0.0799080
\(552\) 9074.75 0.699723
\(553\) 109.194 0.00839676
\(554\) 12399.9 0.950942
\(555\) −167.185 −0.0127867
\(556\) 220.817 0.0168430
\(557\) −1895.56 −0.144197 −0.0720983 0.997398i \(-0.522970\pi\)
−0.0720983 + 0.997398i \(0.522970\pi\)
\(558\) 1524.35 0.115647
\(559\) 0 0
\(560\) −10.1993 −0.000769644 0
\(561\) 5028.17 0.378413
\(562\) −5241.38 −0.393406
\(563\) −3891.98 −0.291345 −0.145673 0.989333i \(-0.546535\pi\)
−0.145673 + 0.989333i \(0.546535\pi\)
\(564\) 1631.15 0.121780
\(565\) 1541.56 0.114785
\(566\) −13665.0 −1.01481
\(567\) −16.9009 −0.00125180
\(568\) −11867.0 −0.876634
\(569\) −15271.0 −1.12512 −0.562559 0.826757i \(-0.690183\pi\)
−0.562559 + 0.826757i \(0.690183\pi\)
\(570\) −335.788 −0.0246747
\(571\) 14055.6 1.03014 0.515070 0.857148i \(-0.327766\pi\)
0.515070 + 0.857148i \(0.327766\pi\)
\(572\) −9736.74 −0.711737
\(573\) −2493.12 −0.181765
\(574\) 59.4237 0.00432107
\(575\) 14129.2 1.02475
\(576\) −7713.19 −0.557957
\(577\) 7860.86 0.567161 0.283581 0.958948i \(-0.408478\pi\)
0.283581 + 0.958948i \(0.408478\pi\)
\(578\) 6442.36 0.463610
\(579\) −7052.98 −0.506238
\(580\) 63.9471 0.00457803
\(581\) 217.026 0.0154970
\(582\) −8117.46 −0.578144
\(583\) −13286.0 −0.943823
\(584\) 12406.7 0.879096
\(585\) −1062.51 −0.0750927
\(586\) −14346.1 −1.01131
\(587\) 10247.7 0.720562 0.360281 0.932844i \(-0.382681\pi\)
0.360281 + 0.932844i \(0.382681\pi\)
\(588\) −4198.46 −0.294459
\(589\) −2483.76 −0.173755
\(590\) −916.715 −0.0639671
\(591\) 7079.66 0.492755
\(592\) −1141.38 −0.0792407
\(593\) −16157.0 −1.11887 −0.559435 0.828874i \(-0.688982\pi\)
−0.559435 + 0.828874i \(0.688982\pi\)
\(594\) −10588.8 −0.731419
\(595\) −21.2602 −0.00146484
\(596\) 11070.7 0.760865
\(597\) −12013.0 −0.823551
\(598\) 17064.1 1.16690
\(599\) −14102.1 −0.961933 −0.480967 0.876739i \(-0.659714\pi\)
−0.480967 + 0.876739i \(0.659714\pi\)
\(600\) 9904.17 0.673894
\(601\) −12470.6 −0.846397 −0.423198 0.906037i \(-0.639093\pi\)
−0.423198 + 0.906037i \(0.639093\pi\)
\(602\) 0 0
\(603\) −17153.7 −1.15846
\(604\) −675.413 −0.0455003
\(605\) −28.4487 −0.00191174
\(606\) −12074.4 −0.809391
\(607\) −18569.3 −1.24169 −0.620844 0.783934i \(-0.713210\pi\)
−0.620844 + 0.783934i \(0.713210\pi\)
\(608\) 8278.80 0.552220
\(609\) 34.5420 0.00229838
\(610\) −1109.76 −0.0736604
\(611\) 9656.24 0.639361
\(612\) −2554.15 −0.168702
\(613\) 25890.1 1.70586 0.852928 0.522028i \(-0.174824\pi\)
0.852928 + 0.522028i \(0.174824\pi\)
\(614\) 3485.91 0.229120
\(615\) 154.614 0.0101376
\(616\) 483.945 0.0316537
\(617\) −24758.2 −1.61544 −0.807720 0.589566i \(-0.799299\pi\)
−0.807720 + 0.589566i \(0.799299\pi\)
\(618\) −12382.9 −0.806009
\(619\) −5979.48 −0.388264 −0.194132 0.980975i \(-0.562189\pi\)
−0.194132 + 0.980975i \(0.562189\pi\)
\(620\) −153.678 −0.00995462
\(621\) −16161.9 −1.04437
\(622\) −10372.9 −0.668672
\(623\) 463.128 0.0297831
\(624\) 4853.01 0.311340
\(625\) 15318.1 0.980361
\(626\) 12397.8 0.791561
\(627\) 6464.23 0.411733
\(628\) 3730.21 0.237025
\(629\) −2379.17 −0.150817
\(630\) 16.7745 0.00106081
\(631\) 20733.7 1.30808 0.654038 0.756462i \(-0.273074\pi\)
0.654038 + 0.756462i \(0.273074\pi\)
\(632\) 4780.74 0.300898
\(633\) 18780.3 1.17922
\(634\) 16210.7 1.01547
\(635\) −1160.77 −0.0725413
\(636\) −4515.19 −0.281508
\(637\) −24854.5 −1.54595
\(638\) 1413.50 0.0877132
\(639\) 7918.56 0.490224
\(640\) 207.531 0.0128178
\(641\) −8796.35 −0.542020 −0.271010 0.962577i \(-0.587358\pi\)
−0.271010 + 0.962577i \(0.587358\pi\)
\(642\) −4467.83 −0.274659
\(643\) 12217.2 0.749299 0.374650 0.927166i \(-0.377763\pi\)
0.374650 + 0.927166i \(0.377763\pi\)
\(644\) 234.628 0.0143566
\(645\) 0 0
\(646\) −4778.53 −0.291035
\(647\) −11313.8 −0.687469 −0.343734 0.939067i \(-0.611692\pi\)
−0.343734 + 0.939067i \(0.611692\pi\)
\(648\) −739.955 −0.0448583
\(649\) 17647.6 1.06738
\(650\) 18623.8 1.12382
\(651\) −83.0117 −0.00499767
\(652\) −9993.92 −0.600295
\(653\) −6663.14 −0.399309 −0.199655 0.979866i \(-0.563982\pi\)
−0.199655 + 0.979866i \(0.563982\pi\)
\(654\) 3526.76 0.210867
\(655\) 2162.50 0.129001
\(656\) 1055.56 0.0628241
\(657\) −8278.67 −0.491601
\(658\) −152.449 −0.00903206
\(659\) 8919.91 0.527269 0.263634 0.964623i \(-0.415079\pi\)
0.263634 + 0.964623i \(0.415079\pi\)
\(660\) 399.963 0.0235887
\(661\) 20327.5 1.19614 0.598070 0.801444i \(-0.295934\pi\)
0.598070 + 0.801444i \(0.295934\pi\)
\(662\) 18528.7 1.08782
\(663\) 10115.9 0.592565
\(664\) 9501.84 0.555336
\(665\) −27.3321 −0.00159383
\(666\) 1877.19 0.109219
\(667\) 2157.46 0.125243
\(668\) 5884.42 0.340831
\(669\) 11162.8 0.645112
\(670\) −1985.67 −0.114497
\(671\) 21363.9 1.22913
\(672\) 276.692 0.0158834
\(673\) 28022.2 1.60502 0.802509 0.596640i \(-0.203498\pi\)
0.802509 + 0.596640i \(0.203498\pi\)
\(674\) 23452.1 1.34027
\(675\) −17639.1 −1.00582
\(676\) −11407.2 −0.649024
\(677\) 17930.8 1.01793 0.508963 0.860788i \(-0.330029\pi\)
0.508963 + 0.860788i \(0.330029\pi\)
\(678\) 11580.2 0.655952
\(679\) −660.738 −0.0373443
\(680\) −930.812 −0.0524927
\(681\) 19345.1 1.08855
\(682\) −3396.94 −0.190726
\(683\) 18761.7 1.05110 0.525548 0.850764i \(-0.323860\pi\)
0.525548 + 0.850764i \(0.323860\pi\)
\(684\) −3283.63 −0.183556
\(685\) 2788.63 0.155545
\(686\) 785.140 0.0436979
\(687\) −11784.2 −0.654432
\(688\) 0 0
\(689\) −26729.5 −1.47796
\(690\) −700.956 −0.0386738
\(691\) 28630.0 1.57617 0.788087 0.615564i \(-0.211072\pi\)
0.788087 + 0.615564i \(0.211072\pi\)
\(692\) 4537.38 0.249256
\(693\) −322.925 −0.0177012
\(694\) 9586.95 0.524374
\(695\) −53.6973 −0.00293073
\(696\) 1512.32 0.0823624
\(697\) 2200.28 0.119572
\(698\) 12206.0 0.661899
\(699\) −5691.84 −0.307990
\(700\) 256.072 0.0138266
\(701\) −15943.9 −0.859046 −0.429523 0.903056i \(-0.641318\pi\)
−0.429523 + 0.903056i \(0.641318\pi\)
\(702\) −21303.1 −1.14535
\(703\) −3058.67 −0.164097
\(704\) 17188.5 0.920191
\(705\) −396.656 −0.0211900
\(706\) −20423.8 −1.08875
\(707\) −982.825 −0.0522814
\(708\) 5997.48 0.318360
\(709\) −1364.07 −0.0722552 −0.0361276 0.999347i \(-0.511502\pi\)
−0.0361276 + 0.999347i \(0.511502\pi\)
\(710\) 916.636 0.0484517
\(711\) −3190.07 −0.168266
\(712\) 20276.7 1.06728
\(713\) −5184.84 −0.272333
\(714\) −159.707 −0.00837100
\(715\) 2367.74 0.123844
\(716\) −11826.1 −0.617267
\(717\) 13816.9 0.719665
\(718\) 15457.6 0.803446
\(719\) 36789.0 1.90820 0.954101 0.299484i \(-0.0968145\pi\)
0.954101 + 0.299484i \(0.0968145\pi\)
\(720\) 297.970 0.0154232
\(721\) −1007.93 −0.0520629
\(722\) 8040.05 0.414432
\(723\) −21789.2 −1.12081
\(724\) 9885.46 0.507445
\(725\) 2354.65 0.120620
\(726\) −213.708 −0.0109248
\(727\) −6053.05 −0.308797 −0.154398 0.988009i \(-0.549344\pi\)
−0.154398 + 0.988009i \(0.549344\pi\)
\(728\) 973.627 0.0495673
\(729\) 13110.9 0.666104
\(730\) −958.322 −0.0485878
\(731\) 0 0
\(732\) 7260.44 0.366603
\(733\) −970.290 −0.0488929 −0.0244464 0.999701i \(-0.507782\pi\)
−0.0244464 + 0.999701i \(0.507782\pi\)
\(734\) −8356.66 −0.420232
\(735\) 1020.97 0.0512366
\(736\) 17282.0 0.865519
\(737\) 38226.0 1.91055
\(738\) −1736.04 −0.0865915
\(739\) 1221.27 0.0607920 0.0303960 0.999538i \(-0.490323\pi\)
0.0303960 + 0.999538i \(0.490323\pi\)
\(740\) −189.250 −0.00940131
\(741\) 13005.1 0.644742
\(742\) 421.996 0.0208786
\(743\) 366.531 0.0180979 0.00904893 0.999959i \(-0.497120\pi\)
0.00904893 + 0.999959i \(0.497120\pi\)
\(744\) −3634.41 −0.179091
\(745\) −2692.14 −0.132392
\(746\) 11651.2 0.571824
\(747\) −6340.35 −0.310550
\(748\) 5691.80 0.278226
\(749\) −363.669 −0.0177412
\(750\) −1535.10 −0.0747385
\(751\) −37377.3 −1.81613 −0.908067 0.418825i \(-0.862442\pi\)
−0.908067 + 0.418825i \(0.862442\pi\)
\(752\) −2708.00 −0.131317
\(753\) 8943.45 0.432825
\(754\) 2843.76 0.137352
\(755\) 164.244 0.00791716
\(756\) −292.912 −0.0140914
\(757\) −21396.5 −1.02730 −0.513651 0.857999i \(-0.671707\pi\)
−0.513651 + 0.857999i \(0.671707\pi\)
\(758\) −4152.49 −0.198978
\(759\) 13494.1 0.645327
\(760\) −1196.65 −0.0571148
\(761\) −4078.78 −0.194291 −0.0971456 0.995270i \(-0.530971\pi\)
−0.0971456 + 0.995270i \(0.530971\pi\)
\(762\) −8719.74 −0.414544
\(763\) 287.068 0.0136207
\(764\) −2822.17 −0.133642
\(765\) 621.108 0.0293545
\(766\) 424.809 0.0200378
\(767\) 35504.5 1.67144
\(768\) 14107.6 0.662845
\(769\) −6968.46 −0.326774 −0.163387 0.986562i \(-0.552242\pi\)
−0.163387 + 0.986562i \(0.552242\pi\)
\(770\) −37.3811 −0.00174951
\(771\) −5167.10 −0.241360
\(772\) −7983.85 −0.372208
\(773\) 25350.9 1.17957 0.589785 0.807561i \(-0.299213\pi\)
0.589785 + 0.807561i \(0.299213\pi\)
\(774\) 0 0
\(775\) −5658.73 −0.262281
\(776\) −28928.4 −1.33823
\(777\) −102.226 −0.00471989
\(778\) 7446.48 0.343148
\(779\) 2828.68 0.130100
\(780\) 804.668 0.0369381
\(781\) −17646.1 −0.808485
\(782\) −9975.17 −0.456153
\(783\) −2693.40 −0.122930
\(784\) 6970.21 0.317520
\(785\) −907.096 −0.0412429
\(786\) 16244.7 0.737189
\(787\) −28392.5 −1.28600 −0.643000 0.765866i \(-0.722311\pi\)
−0.643000 + 0.765866i \(0.722311\pi\)
\(788\) 8014.06 0.362296
\(789\) 17877.2 0.806649
\(790\) −369.276 −0.0166307
\(791\) 942.597 0.0423703
\(792\) −14138.3 −0.634320
\(793\) 42981.1 1.92472
\(794\) 26726.1 1.19455
\(795\) 1097.98 0.0489830
\(796\) −13598.5 −0.605511
\(797\) −29905.5 −1.32912 −0.664559 0.747236i \(-0.731381\pi\)
−0.664559 + 0.747236i \(0.731381\pi\)
\(798\) −205.320 −0.00910808
\(799\) −5644.74 −0.249933
\(800\) 18861.5 0.833569
\(801\) −13530.1 −0.596833
\(802\) −8495.28 −0.374038
\(803\) 18448.6 0.810756
\(804\) 12991.0 0.569846
\(805\) −57.0558 −0.00249808
\(806\) −6834.14 −0.298663
\(807\) −5755.05 −0.251038
\(808\) −43030.0 −1.87350
\(809\) −28881.4 −1.25515 −0.627575 0.778556i \(-0.715952\pi\)
−0.627575 + 0.778556i \(0.715952\pi\)
\(810\) 57.1559 0.00247933
\(811\) 18301.8 0.792431 0.396216 0.918157i \(-0.370323\pi\)
0.396216 + 0.918157i \(0.370323\pi\)
\(812\) 39.1010 0.00168987
\(813\) −15612.9 −0.673514
\(814\) −4183.23 −0.180125
\(815\) 2430.28 0.104453
\(816\) −2836.92 −0.121706
\(817\) 0 0
\(818\) −6327.80 −0.270472
\(819\) −649.678 −0.0277187
\(820\) 175.020 0.00745361
\(821\) −12725.8 −0.540966 −0.270483 0.962725i \(-0.587183\pi\)
−0.270483 + 0.962725i \(0.587183\pi\)
\(822\) 20948.3 0.888876
\(823\) 33139.0 1.40359 0.701795 0.712379i \(-0.252382\pi\)
0.701795 + 0.712379i \(0.252382\pi\)
\(824\) −44129.2 −1.86567
\(825\) 14727.4 0.621506
\(826\) −560.533 −0.0236119
\(827\) −25709.7 −1.08103 −0.540516 0.841334i \(-0.681771\pi\)
−0.540516 + 0.841334i \(0.681771\pi\)
\(828\) −6854.56 −0.287696
\(829\) 19624.3 0.822173 0.411086 0.911596i \(-0.365149\pi\)
0.411086 + 0.911596i \(0.365149\pi\)
\(830\) −733.945 −0.0306935
\(831\) 19727.6 0.823516
\(832\) 34580.7 1.44095
\(833\) 14529.2 0.604329
\(834\) −403.376 −0.0167479
\(835\) −1430.95 −0.0593055
\(836\) 7317.39 0.302724
\(837\) 6472.81 0.267304
\(838\) 8779.56 0.361915
\(839\) −42930.4 −1.76653 −0.883266 0.468872i \(-0.844661\pi\)
−0.883266 + 0.468872i \(0.844661\pi\)
\(840\) −39.9944 −0.00164278
\(841\) −24029.5 −0.985258
\(842\) −32651.2 −1.33638
\(843\) −8338.74 −0.340690
\(844\) 21258.9 0.867017
\(845\) 2773.96 0.112932
\(846\) 4453.75 0.180997
\(847\) −17.3952 −0.000705674 0
\(848\) 7496.02 0.303555
\(849\) −21740.2 −0.878824
\(850\) −10886.9 −0.439315
\(851\) −6384.97 −0.257196
\(852\) −5996.96 −0.241141
\(853\) 29843.9 1.19793 0.598965 0.800775i \(-0.295579\pi\)
0.598965 + 0.800775i \(0.295579\pi\)
\(854\) −678.571 −0.0271899
\(855\) 798.499 0.0319393
\(856\) −15922.1 −0.635756
\(857\) −1444.80 −0.0575887 −0.0287943 0.999585i \(-0.509167\pi\)
−0.0287943 + 0.999585i \(0.509167\pi\)
\(858\) 17786.6 0.707719
\(859\) 43783.6 1.73909 0.869545 0.493854i \(-0.164412\pi\)
0.869545 + 0.493854i \(0.164412\pi\)
\(860\) 0 0
\(861\) 94.5397 0.00374205
\(862\) −20544.4 −0.811767
\(863\) −16285.3 −0.642362 −0.321181 0.947018i \(-0.604080\pi\)
−0.321181 + 0.947018i \(0.604080\pi\)
\(864\) −21575.0 −0.849533
\(865\) −1103.38 −0.0433712
\(866\) 12194.6 0.478510
\(867\) 10249.4 0.401487
\(868\) −93.9678 −0.00367451
\(869\) 7108.91 0.277506
\(870\) −116.815 −0.00455219
\(871\) 76905.3 2.99177
\(872\) 12568.4 0.488096
\(873\) 19303.2 0.748356
\(874\) −12824.1 −0.496318
\(875\) −124.953 −0.00482762
\(876\) 6269.69 0.241819
\(877\) 22308.4 0.858951 0.429476 0.903078i \(-0.358698\pi\)
0.429476 + 0.903078i \(0.358698\pi\)
\(878\) −10780.7 −0.414385
\(879\) −22823.8 −0.875799
\(880\) −664.011 −0.0254361
\(881\) −2607.01 −0.0996962 −0.0498481 0.998757i \(-0.515874\pi\)
−0.0498481 + 0.998757i \(0.515874\pi\)
\(882\) −11463.7 −0.437643
\(883\) 15569.0 0.593363 0.296682 0.954976i \(-0.404120\pi\)
0.296682 + 0.954976i \(0.404120\pi\)
\(884\) 11451.1 0.435680
\(885\) −1458.44 −0.0553955
\(886\) 178.772 0.00677876
\(887\) −10165.1 −0.384793 −0.192396 0.981317i \(-0.561626\pi\)
−0.192396 + 0.981317i \(0.561626\pi\)
\(888\) −4475.67 −0.169137
\(889\) −709.762 −0.0267769
\(890\) −1566.22 −0.0589885
\(891\) −1100.31 −0.0413711
\(892\) 12636.1 0.474315
\(893\) −7256.89 −0.271940
\(894\) −20223.4 −0.756569
\(895\) 2875.83 0.107406
\(896\) 126.896 0.00473137
\(897\) 27148.1 1.01053
\(898\) 9524.94 0.353955
\(899\) −864.059 −0.0320556
\(900\) −7481.06 −0.277076
\(901\) 15625.2 0.577748
\(902\) 3868.68 0.142808
\(903\) 0 0
\(904\) 41268.7 1.51834
\(905\) −2403.90 −0.0882967
\(906\) 1233.81 0.0452434
\(907\) 2372.67 0.0868613 0.0434307 0.999056i \(-0.486171\pi\)
0.0434307 + 0.999056i \(0.486171\pi\)
\(908\) 21898.3 0.800352
\(909\) 28712.9 1.04768
\(910\) −75.2054 −0.00273960
\(911\) 37280.3 1.35582 0.677909 0.735146i \(-0.262886\pi\)
0.677909 + 0.735146i \(0.262886\pi\)
\(912\) −3647.15 −0.132423
\(913\) 14129.1 0.512165
\(914\) −3062.50 −0.110830
\(915\) −1765.56 −0.0637899
\(916\) −13339.5 −0.481168
\(917\) 1322.28 0.0476176
\(918\) 12453.1 0.447728
\(919\) −23845.4 −0.855915 −0.427957 0.903799i \(-0.640767\pi\)
−0.427957 + 0.903799i \(0.640767\pi\)
\(920\) −2498.01 −0.0895186
\(921\) 5545.88 0.198418
\(922\) 21939.7 0.783671
\(923\) −35501.4 −1.26603
\(924\) 244.561 0.00870720
\(925\) −6968.55 −0.247702
\(926\) 18963.2 0.672967
\(927\) 29446.4 1.04331
\(928\) 2880.06 0.101878
\(929\) −51353.9 −1.81364 −0.906818 0.421523i \(-0.861496\pi\)
−0.906818 + 0.421523i \(0.861496\pi\)
\(930\) 280.731 0.00989842
\(931\) 18678.7 0.657541
\(932\) −6443.06 −0.226448
\(933\) −16502.6 −0.579070
\(934\) 6360.27 0.222821
\(935\) −1384.11 −0.0484120
\(936\) −28444.2 −0.993298
\(937\) 3092.80 0.107831 0.0539154 0.998546i \(-0.482830\pi\)
0.0539154 + 0.998546i \(0.482830\pi\)
\(938\) −1214.15 −0.0422639
\(939\) 19724.3 0.685492
\(940\) −449.008 −0.0155798
\(941\) −37935.7 −1.31421 −0.657103 0.753801i \(-0.728218\pi\)
−0.657103 + 0.753801i \(0.728218\pi\)
\(942\) −6814.14 −0.235686
\(943\) 5904.87 0.203912
\(944\) −9956.90 −0.343294
\(945\) 71.2291 0.00245194
\(946\) 0 0
\(947\) −54489.0 −1.86975 −0.934876 0.354974i \(-0.884490\pi\)
−0.934876 + 0.354974i \(0.884490\pi\)
\(948\) 2415.93 0.0827699
\(949\) 37115.9 1.26958
\(950\) −13996.2 −0.477997
\(951\) 25790.3 0.879398
\(952\) −569.152 −0.0193764
\(953\) 9955.68 0.338401 0.169200 0.985582i \(-0.445881\pi\)
0.169200 + 0.985582i \(0.445881\pi\)
\(954\) −12328.4 −0.418394
\(955\) 686.283 0.0232540
\(956\) 15640.4 0.529130
\(957\) 2248.80 0.0759596
\(958\) 17716.6 0.597493
\(959\) 1705.13 0.0574156
\(960\) −1420.49 −0.0477565
\(961\) −27714.5 −0.930297
\(962\) −8416.04 −0.282063
\(963\) 10624.5 0.355523
\(964\) −24665.0 −0.824071
\(965\) 1941.48 0.0647652
\(966\) −428.605 −0.0142755
\(967\) −33247.1 −1.10564 −0.552820 0.833301i \(-0.686448\pi\)
−0.552820 + 0.833301i \(0.686448\pi\)
\(968\) −761.595 −0.0252878
\(969\) −7602.37 −0.252037
\(970\) 2234.50 0.0739644
\(971\) −41308.7 −1.36525 −0.682626 0.730768i \(-0.739162\pi\)
−0.682626 + 0.730768i \(0.739162\pi\)
\(972\) 13908.5 0.458966
\(973\) −32.8336 −0.00108181
\(974\) 16271.3 0.535285
\(975\) 29629.4 0.973231
\(976\) −12053.6 −0.395315
\(977\) 45094.5 1.47666 0.738332 0.674437i \(-0.235614\pi\)
0.738332 + 0.674437i \(0.235614\pi\)
\(978\) 18256.4 0.596906
\(979\) 30151.2 0.984307
\(980\) 1155.71 0.0376714
\(981\) −8386.59 −0.272949
\(982\) 33675.3 1.09432
\(983\) −50236.2 −1.62999 −0.814997 0.579465i \(-0.803262\pi\)
−0.814997 + 0.579465i \(0.803262\pi\)
\(984\) 4139.13 0.134096
\(985\) −1948.82 −0.0630403
\(986\) −1662.37 −0.0536924
\(987\) −242.538 −0.00782177
\(988\) 14721.5 0.474043
\(989\) 0 0
\(990\) 1092.08 0.0350590
\(991\) −27459.8 −0.880210 −0.440105 0.897946i \(-0.645059\pi\)
−0.440105 + 0.897946i \(0.645059\pi\)
\(992\) −6921.38 −0.221526
\(993\) 29478.1 0.942052
\(994\) 560.484 0.0178848
\(995\) 3306.83 0.105360
\(996\) 4801.73 0.152760
\(997\) −47249.9 −1.50092 −0.750461 0.660915i \(-0.770168\pi\)
−0.750461 + 0.660915i \(0.770168\pi\)
\(998\) 34161.3 1.08352
\(999\) 7971.07 0.252446
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.1.19 50
43.42 odd 2 1849.4.a.j.1.32 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.19 50 1.1 even 1 trivial
1849.4.a.j.1.32 yes 50 43.42 odd 2