Properties

Label 1849.4.a.g.1.7
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $30$
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: \(30\)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.60614 q^{2} +0.812227 q^{3} +5.00427 q^{4} -5.99647 q^{5} -2.92901 q^{6} +26.3629 q^{7} +10.8030 q^{8} -26.3403 q^{9} +O(q^{10})\) \(q-3.60614 q^{2} +0.812227 q^{3} +5.00427 q^{4} -5.99647 q^{5} -2.92901 q^{6} +26.3629 q^{7} +10.8030 q^{8} -26.3403 q^{9} +21.6241 q^{10} -27.0936 q^{11} +4.06461 q^{12} +83.2869 q^{13} -95.0685 q^{14} -4.87050 q^{15} -78.9914 q^{16} +19.3669 q^{17} +94.9869 q^{18} +1.45555 q^{19} -30.0080 q^{20} +21.4127 q^{21} +97.7034 q^{22} +56.8171 q^{23} +8.77451 q^{24} -89.0423 q^{25} -300.344 q^{26} -43.3244 q^{27} +131.927 q^{28} -187.383 q^{29} +17.5637 q^{30} +65.8760 q^{31} +198.430 q^{32} -22.0062 q^{33} -69.8398 q^{34} -158.085 q^{35} -131.814 q^{36} +164.226 q^{37} -5.24893 q^{38} +67.6479 q^{39} -64.7800 q^{40} -273.507 q^{41} -77.2172 q^{42} -135.584 q^{44} +157.949 q^{45} -204.891 q^{46} +111.518 q^{47} -64.1590 q^{48} +352.003 q^{49} +321.099 q^{50} +15.7303 q^{51} +416.790 q^{52} -637.668 q^{53} +156.234 q^{54} +162.466 q^{55} +284.799 q^{56} +1.18224 q^{57} +675.729 q^{58} +810.839 q^{59} -24.3733 q^{60} -789.470 q^{61} -237.558 q^{62} -694.407 q^{63} -83.6366 q^{64} -499.427 q^{65} +79.3573 q^{66} +125.028 q^{67} +96.9172 q^{68} +46.1484 q^{69} +570.075 q^{70} -731.846 q^{71} -284.555 q^{72} -432.763 q^{73} -592.222 q^{74} -72.3226 q^{75} +7.28398 q^{76} -714.266 q^{77} -243.948 q^{78} +119.998 q^{79} +473.670 q^{80} +675.998 q^{81} +986.305 q^{82} -45.8667 q^{83} +107.155 q^{84} -116.133 q^{85} -152.197 q^{87} -292.693 q^{88} -942.217 q^{89} -569.586 q^{90} +2195.68 q^{91} +284.328 q^{92} +53.5063 q^{93} -402.148 q^{94} -8.72818 q^{95} +161.170 q^{96} +355.167 q^{97} -1269.37 q^{98} +713.653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 6q^{2} - 2q^{3} + 114q^{4} - 27q^{5} + 8q^{6} - 48q^{7} - 90q^{8} + 216q^{9} + O(q^{10}) \) \( 30q - 6q^{2} - 2q^{3} + 114q^{4} - 27q^{5} + 8q^{6} - 48q^{7} - 90q^{8} + 216q^{9} - 27q^{10} + 80q^{11} + 36q^{12} - 13q^{13} + 36q^{14} + 16q^{15} + 318q^{16} + 66q^{17} - 80q^{18} - 254q^{19} - 312q^{20} - 548q^{21} - 305q^{22} - 105q^{23} + 123q^{24} + 523q^{25} - 549q^{26} + 10q^{27} - 578q^{28} - 793q^{29} - 1560q^{30} - 359q^{31} - 676q^{32} - 208q^{33} - 1007q^{34} - 514q^{35} + 776q^{36} - 510q^{37} - 2066q^{38} - 898q^{39} - 1248q^{40} - 270q^{41} + 915q^{42} + 3256q^{44} - 807q^{45} - 1960q^{46} + 1421q^{47} + 632q^{48} + 386q^{49} + 141q^{50} - 209q^{51} + 2825q^{52} - 21q^{53} + 2368q^{54} - 2258q^{55} + 2521q^{56} - 1723q^{57} - 347q^{58} + 1752q^{59} + 2711q^{60} - 1759q^{61} - 395q^{62} - 2204q^{63} + 222q^{64} - 1151q^{65} + 160q^{66} - 3001q^{67} + 1921q^{68} - 1660q^{69} - 1597q^{70} - 727q^{71} - 9100q^{72} - 4623q^{73} - 2649q^{74} - 1027q^{75} - 874q^{76} - 3556q^{77} - 4979q^{78} + 546q^{79} - 5809q^{80} - 410q^{81} + 4397q^{82} - 492q^{83} - 10611q^{84} + 1723q^{85} + 5937q^{87} - 3974q^{88} - 5218q^{89} + 10492q^{90} - 1104q^{91} + 1060q^{92} - 1997q^{93} + 2134q^{94} + 6346q^{95} - 11984q^{96} + 2590q^{97} - 6270q^{98} - 2693q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.60614 −1.27496 −0.637482 0.770465i \(-0.720024\pi\)
−0.637482 + 0.770465i \(0.720024\pi\)
\(3\) 0.812227 0.156313 0.0781566 0.996941i \(-0.475097\pi\)
0.0781566 + 0.996941i \(0.475097\pi\)
\(4\) 5.00427 0.625534
\(5\) −5.99647 −0.536341 −0.268170 0.963371i \(-0.586419\pi\)
−0.268170 + 0.963371i \(0.586419\pi\)
\(6\) −2.92901 −0.199294
\(7\) 26.3629 1.42346 0.711732 0.702451i \(-0.247911\pi\)
0.711732 + 0.702451i \(0.247911\pi\)
\(8\) 10.8030 0.477431
\(9\) −26.3403 −0.975566
\(10\) 21.6241 0.683815
\(11\) −27.0936 −0.742639 −0.371319 0.928505i \(-0.621095\pi\)
−0.371319 + 0.928505i \(0.621095\pi\)
\(12\) 4.06461 0.0977792
\(13\) 83.2869 1.77689 0.888447 0.458979i \(-0.151785\pi\)
0.888447 + 0.458979i \(0.151785\pi\)
\(14\) −95.0685 −1.81487
\(15\) −4.87050 −0.0838371
\(16\) −78.9914 −1.23424
\(17\) 19.3669 0.276304 0.138152 0.990411i \(-0.455884\pi\)
0.138152 + 0.990411i \(0.455884\pi\)
\(18\) 94.9869 1.24381
\(19\) 1.45555 0.0175751 0.00878754 0.999961i \(-0.497203\pi\)
0.00878754 + 0.999961i \(0.497203\pi\)
\(20\) −30.0080 −0.335499
\(21\) 21.4127 0.222506
\(22\) 97.7034 0.946838
\(23\) 56.8171 0.515095 0.257548 0.966266i \(-0.417086\pi\)
0.257548 + 0.966266i \(0.417086\pi\)
\(24\) 8.77451 0.0746287
\(25\) −89.0423 −0.712339
\(26\) −300.344 −2.26548
\(27\) −43.3244 −0.308807
\(28\) 131.927 0.890425
\(29\) −187.383 −1.19987 −0.599933 0.800050i \(-0.704806\pi\)
−0.599933 + 0.800050i \(0.704806\pi\)
\(30\) 17.5637 0.106889
\(31\) 65.8760 0.381667 0.190834 0.981622i \(-0.438881\pi\)
0.190834 + 0.981622i \(0.438881\pi\)
\(32\) 198.430 1.09618
\(33\) −22.0062 −0.116084
\(34\) −69.8398 −0.352277
\(35\) −158.085 −0.763462
\(36\) −131.814 −0.610250
\(37\) 164.226 0.729691 0.364845 0.931068i \(-0.381122\pi\)
0.364845 + 0.931068i \(0.381122\pi\)
\(38\) −5.24893 −0.0224076
\(39\) 67.6479 0.277752
\(40\) −64.7800 −0.256066
\(41\) −273.507 −1.04182 −0.520910 0.853612i \(-0.674407\pi\)
−0.520910 + 0.853612i \(0.674407\pi\)
\(42\) −77.2172 −0.283687
\(43\) 0 0
\(44\) −135.584 −0.464546
\(45\) 157.949 0.523236
\(46\) −204.891 −0.656728
\(47\) 111.518 0.346096 0.173048 0.984913i \(-0.444638\pi\)
0.173048 + 0.984913i \(0.444638\pi\)
\(48\) −64.1590 −0.192928
\(49\) 352.003 1.02625
\(50\) 321.099 0.908206
\(51\) 15.7303 0.0431899
\(52\) 416.790 1.11151
\(53\) −637.668 −1.65265 −0.826324 0.563194i \(-0.809572\pi\)
−0.826324 + 0.563194i \(0.809572\pi\)
\(54\) 156.234 0.393718
\(55\) 162.466 0.398308
\(56\) 284.799 0.679605
\(57\) 1.18224 0.00274722
\(58\) 675.729 1.52979
\(59\) 810.839 1.78919 0.894596 0.446876i \(-0.147464\pi\)
0.894596 + 0.446876i \(0.147464\pi\)
\(60\) −24.3733 −0.0524430
\(61\) −789.470 −1.65707 −0.828535 0.559938i \(-0.810825\pi\)
−0.828535 + 0.559938i \(0.810825\pi\)
\(62\) −237.558 −0.486612
\(63\) −694.407 −1.38868
\(64\) −83.6366 −0.163353
\(65\) −499.427 −0.953021
\(66\) 79.3573 0.148003
\(67\) 125.028 0.227979 0.113990 0.993482i \(-0.463637\pi\)
0.113990 + 0.993482i \(0.463637\pi\)
\(68\) 96.9172 0.172837
\(69\) 46.1484 0.0805162
\(70\) 570.075 0.973386
\(71\) −731.846 −1.22330 −0.611649 0.791130i \(-0.709493\pi\)
−0.611649 + 0.791130i \(0.709493\pi\)
\(72\) −284.555 −0.465765
\(73\) −432.763 −0.693850 −0.346925 0.937893i \(-0.612774\pi\)
−0.346925 + 0.937893i \(0.612774\pi\)
\(74\) −592.222 −0.930330
\(75\) −72.3226 −0.111348
\(76\) 7.28398 0.0109938
\(77\) −714.266 −1.05712
\(78\) −243.948 −0.354124
\(79\) 119.998 0.170896 0.0854482 0.996343i \(-0.472768\pi\)
0.0854482 + 0.996343i \(0.472768\pi\)
\(80\) 473.670 0.661974
\(81\) 675.998 0.927296
\(82\) 986.305 1.32828
\(83\) −45.8667 −0.0606570 −0.0303285 0.999540i \(-0.509655\pi\)
−0.0303285 + 0.999540i \(0.509655\pi\)
\(84\) 107.155 0.139185
\(85\) −116.133 −0.148193
\(86\) 0 0
\(87\) −152.197 −0.187555
\(88\) −292.693 −0.354559
\(89\) −942.217 −1.12219 −0.561094 0.827752i \(-0.689619\pi\)
−0.561094 + 0.827752i \(0.689619\pi\)
\(90\) −569.586 −0.667107
\(91\) 2195.68 2.52934
\(92\) 284.328 0.322210
\(93\) 53.5063 0.0596596
\(94\) −402.148 −0.441260
\(95\) −8.72818 −0.00942624
\(96\) 161.170 0.171348
\(97\) 355.167 0.371770 0.185885 0.982571i \(-0.440485\pi\)
0.185885 + 0.982571i \(0.440485\pi\)
\(98\) −1269.37 −1.30843
\(99\) 713.653 0.724493
\(100\) −445.592 −0.445592
\(101\) −217.765 −0.214539 −0.107270 0.994230i \(-0.534211\pi\)
−0.107270 + 0.994230i \(0.534211\pi\)
\(102\) −56.7258 −0.0550656
\(103\) 1538.74 1.47201 0.736005 0.676976i \(-0.236710\pi\)
0.736005 + 0.676976i \(0.236710\pi\)
\(104\) 899.750 0.848344
\(105\) −128.401 −0.119339
\(106\) 2299.52 2.10707
\(107\) 932.741 0.842724 0.421362 0.906893i \(-0.361552\pi\)
0.421362 + 0.906893i \(0.361552\pi\)
\(108\) −216.807 −0.193169
\(109\) 1859.77 1.63426 0.817129 0.576455i \(-0.195564\pi\)
0.817129 + 0.576455i \(0.195564\pi\)
\(110\) −585.876 −0.507828
\(111\) 133.389 0.114060
\(112\) −2082.44 −1.75690
\(113\) 1298.13 1.08069 0.540344 0.841444i \(-0.318294\pi\)
0.540344 + 0.841444i \(0.318294\pi\)
\(114\) −4.26332 −0.00350260
\(115\) −340.702 −0.276267
\(116\) −937.714 −0.750557
\(117\) −2193.80 −1.73348
\(118\) −2924.00 −2.28116
\(119\) 510.568 0.393308
\(120\) −52.6161 −0.0400264
\(121\) −596.937 −0.448488
\(122\) 2846.94 2.11270
\(123\) −222.150 −0.162850
\(124\) 329.661 0.238746
\(125\) 1283.50 0.918397
\(126\) 2504.13 1.77052
\(127\) −444.380 −0.310491 −0.155245 0.987876i \(-0.549617\pi\)
−0.155245 + 0.987876i \(0.549617\pi\)
\(128\) −1285.84 −0.887914
\(129\) 0 0
\(130\) 1801.01 1.21507
\(131\) −800.630 −0.533980 −0.266990 0.963699i \(-0.586029\pi\)
−0.266990 + 0.963699i \(0.586029\pi\)
\(132\) −110.125 −0.0726146
\(133\) 38.3726 0.0250175
\(134\) −450.869 −0.290665
\(135\) 259.794 0.165626
\(136\) 209.221 0.131916
\(137\) −1117.24 −0.696735 −0.348367 0.937358i \(-0.613264\pi\)
−0.348367 + 0.937358i \(0.613264\pi\)
\(138\) −166.418 −0.102655
\(139\) −2130.76 −1.30021 −0.650105 0.759845i \(-0.725275\pi\)
−0.650105 + 0.759845i \(0.725275\pi\)
\(140\) −791.098 −0.477571
\(141\) 90.5776 0.0540994
\(142\) 2639.14 1.55966
\(143\) −2256.54 −1.31959
\(144\) 2080.66 1.20408
\(145\) 1123.64 0.643537
\(146\) 1560.60 0.884634
\(147\) 285.907 0.160416
\(148\) 821.831 0.456446
\(149\) 307.578 0.169113 0.0845563 0.996419i \(-0.473053\pi\)
0.0845563 + 0.996419i \(0.473053\pi\)
\(150\) 260.806 0.141965
\(151\) −2633.15 −1.41909 −0.709545 0.704661i \(-0.751099\pi\)
−0.709545 + 0.704661i \(0.751099\pi\)
\(152\) 15.7244 0.00839089
\(153\) −510.130 −0.269553
\(154\) 2575.75 1.34779
\(155\) −395.024 −0.204704
\(156\) 338.528 0.173743
\(157\) 918.529 0.466921 0.233461 0.972366i \(-0.424995\pi\)
0.233461 + 0.972366i \(0.424995\pi\)
\(158\) −432.729 −0.217887
\(159\) −517.931 −0.258331
\(160\) −1189.88 −0.587928
\(161\) 1497.87 0.733219
\(162\) −2437.75 −1.18227
\(163\) 823.215 0.395578 0.197789 0.980245i \(-0.436624\pi\)
0.197789 + 0.980245i \(0.436624\pi\)
\(164\) −1368.70 −0.651694
\(165\) 131.959 0.0622607
\(166\) 165.402 0.0773355
\(167\) 1814.13 0.840607 0.420304 0.907384i \(-0.361924\pi\)
0.420304 + 0.907384i \(0.361924\pi\)
\(168\) 231.322 0.106231
\(169\) 4739.70 2.15735
\(170\) 418.793 0.188941
\(171\) −38.3397 −0.0171457
\(172\) 0 0
\(173\) −4328.67 −1.90233 −0.951163 0.308690i \(-0.900110\pi\)
−0.951163 + 0.308690i \(0.900110\pi\)
\(174\) 548.845 0.239126
\(175\) −2347.41 −1.01399
\(176\) 2140.16 0.916595
\(177\) 658.586 0.279674
\(178\) 3397.77 1.43075
\(179\) −2571.96 −1.07395 −0.536976 0.843598i \(-0.680433\pi\)
−0.536976 + 0.843598i \(0.680433\pi\)
\(180\) 790.419 0.327302
\(181\) 4230.81 1.73742 0.868712 0.495317i \(-0.164948\pi\)
0.868712 + 0.495317i \(0.164948\pi\)
\(182\) −7917.95 −3.22482
\(183\) −641.229 −0.259022
\(184\) 613.797 0.245922
\(185\) −984.776 −0.391363
\(186\) −192.951 −0.0760639
\(187\) −524.719 −0.205194
\(188\) 558.064 0.216495
\(189\) −1142.16 −0.439576
\(190\) 31.4751 0.0120181
\(191\) 1341.08 0.508048 0.254024 0.967198i \(-0.418246\pi\)
0.254024 + 0.967198i \(0.418246\pi\)
\(192\) −67.9319 −0.0255342
\(193\) −2927.70 −1.09192 −0.545959 0.837812i \(-0.683835\pi\)
−0.545959 + 0.837812i \(0.683835\pi\)
\(194\) −1280.78 −0.473994
\(195\) −405.648 −0.148970
\(196\) 1761.52 0.641953
\(197\) 429.316 0.155266 0.0776332 0.996982i \(-0.475264\pi\)
0.0776332 + 0.996982i \(0.475264\pi\)
\(198\) −2573.54 −0.923703
\(199\) 2549.43 0.908164 0.454082 0.890960i \(-0.349967\pi\)
0.454082 + 0.890960i \(0.349967\pi\)
\(200\) −961.926 −0.340092
\(201\) 101.551 0.0356361
\(202\) 785.293 0.273530
\(203\) −4939.96 −1.70796
\(204\) 78.7188 0.0270168
\(205\) 1640.08 0.558770
\(206\) −5548.93 −1.87676
\(207\) −1496.58 −0.502510
\(208\) −6578.95 −2.19312
\(209\) −39.4362 −0.0130519
\(210\) 463.031 0.152153
\(211\) 3496.49 1.14080 0.570398 0.821368i \(-0.306789\pi\)
0.570398 + 0.821368i \(0.306789\pi\)
\(212\) −3191.06 −1.03379
\(213\) −594.425 −0.191217
\(214\) −3363.60 −1.07444
\(215\) 0 0
\(216\) −468.035 −0.147434
\(217\) 1736.68 0.543289
\(218\) −6706.62 −2.08362
\(219\) −351.502 −0.108458
\(220\) 813.024 0.249155
\(221\) 1613.01 0.490962
\(222\) −481.019 −0.145423
\(223\) 5415.25 1.62615 0.813076 0.582158i \(-0.197792\pi\)
0.813076 + 0.582158i \(0.197792\pi\)
\(224\) 5231.20 1.56038
\(225\) 2345.40 0.694933
\(226\) −4681.24 −1.37784
\(227\) −3228.62 −0.944014 −0.472007 0.881595i \(-0.656470\pi\)
−0.472007 + 0.881595i \(0.656470\pi\)
\(228\) 5.91625 0.00171848
\(229\) −4595.18 −1.32602 −0.663010 0.748611i \(-0.730721\pi\)
−0.663010 + 0.748611i \(0.730721\pi\)
\(230\) 1228.62 0.352230
\(231\) −580.146 −0.165242
\(232\) −2024.30 −0.572853
\(233\) −248.763 −0.0699442 −0.0349721 0.999388i \(-0.511134\pi\)
−0.0349721 + 0.999388i \(0.511134\pi\)
\(234\) 7911.16 2.21012
\(235\) −668.712 −0.185625
\(236\) 4057.66 1.11920
\(237\) 97.4655 0.0267133
\(238\) −1841.18 −0.501454
\(239\) 4503.78 1.21893 0.609467 0.792811i \(-0.291383\pi\)
0.609467 + 0.792811i \(0.291383\pi\)
\(240\) 384.728 0.103475
\(241\) −508.539 −0.135925 −0.0679625 0.997688i \(-0.521650\pi\)
−0.0679625 + 0.997688i \(0.521650\pi\)
\(242\) 2152.64 0.571806
\(243\) 1718.82 0.453756
\(244\) −3950.72 −1.03655
\(245\) −2110.78 −0.550419
\(246\) 801.104 0.207628
\(247\) 121.228 0.0312291
\(248\) 711.660 0.182220
\(249\) −37.2542 −0.00948148
\(250\) −4628.48 −1.17092
\(251\) 4760.66 1.19717 0.598586 0.801059i \(-0.295730\pi\)
0.598586 + 0.801059i \(0.295730\pi\)
\(252\) −3475.00 −0.868669
\(253\) −1539.38 −0.382530
\(254\) 1602.50 0.395865
\(255\) −94.3264 −0.0231645
\(256\) 5306.00 1.29541
\(257\) 2086.48 0.506423 0.253212 0.967411i \(-0.418513\pi\)
0.253212 + 0.967411i \(0.418513\pi\)
\(258\) 0 0
\(259\) 4329.47 1.03869
\(260\) −2499.27 −0.596147
\(261\) 4935.72 1.17055
\(262\) 2887.19 0.680806
\(263\) −7112.50 −1.66759 −0.833793 0.552077i \(-0.813835\pi\)
−0.833793 + 0.552077i \(0.813835\pi\)
\(264\) −237.733 −0.0554222
\(265\) 3823.76 0.886383
\(266\) −138.377 −0.0318964
\(267\) −765.294 −0.175413
\(268\) 625.674 0.142609
\(269\) −5421.57 −1.22884 −0.614422 0.788977i \(-0.710611\pi\)
−0.614422 + 0.788977i \(0.710611\pi\)
\(270\) −936.854 −0.211167
\(271\) 6809.33 1.52634 0.763169 0.646199i \(-0.223643\pi\)
0.763169 + 0.646199i \(0.223643\pi\)
\(272\) −1529.82 −0.341025
\(273\) 1783.39 0.395370
\(274\) 4028.95 0.888312
\(275\) 2412.48 0.529010
\(276\) 230.939 0.0503656
\(277\) −6687.15 −1.45051 −0.725256 0.688480i \(-0.758278\pi\)
−0.725256 + 0.688480i \(0.758278\pi\)
\(278\) 7683.84 1.65772
\(279\) −1735.19 −0.372342
\(280\) −1707.79 −0.364500
\(281\) −6052.56 −1.28493 −0.642465 0.766315i \(-0.722088\pi\)
−0.642465 + 0.766315i \(0.722088\pi\)
\(282\) −326.636 −0.0689747
\(283\) −3810.80 −0.800453 −0.400227 0.916416i \(-0.631069\pi\)
−0.400227 + 0.916416i \(0.631069\pi\)
\(284\) −3662.35 −0.765214
\(285\) −7.08926 −0.00147344
\(286\) 8137.41 1.68243
\(287\) −7210.44 −1.48299
\(288\) −5226.71 −1.06940
\(289\) −4537.92 −0.923656
\(290\) −4051.99 −0.820487
\(291\) 288.476 0.0581126
\(292\) −2165.66 −0.434027
\(293\) −1344.32 −0.268041 −0.134020 0.990979i \(-0.542789\pi\)
−0.134020 + 0.990979i \(0.542789\pi\)
\(294\) −1031.02 −0.204525
\(295\) −4862.18 −0.959616
\(296\) 1774.14 0.348377
\(297\) 1173.81 0.229332
\(298\) −1109.17 −0.215613
\(299\) 4732.12 0.915270
\(300\) −361.922 −0.0696519
\(301\) 0 0
\(302\) 9495.51 1.80929
\(303\) −176.875 −0.0335353
\(304\) −114.976 −0.0216919
\(305\) 4734.03 0.888754
\(306\) 1839.60 0.343670
\(307\) −8180.21 −1.52075 −0.760374 0.649486i \(-0.774984\pi\)
−0.760374 + 0.649486i \(0.774984\pi\)
\(308\) −3574.38 −0.661264
\(309\) 1249.81 0.230095
\(310\) 1424.51 0.260990
\(311\) 198.784 0.0362445 0.0181222 0.999836i \(-0.494231\pi\)
0.0181222 + 0.999836i \(0.494231\pi\)
\(312\) 730.801 0.132607
\(313\) 326.674 0.0589926 0.0294963 0.999565i \(-0.490610\pi\)
0.0294963 + 0.999565i \(0.490610\pi\)
\(314\) −3312.35 −0.595308
\(315\) 4163.99 0.744807
\(316\) 600.502 0.106901
\(317\) −2068.44 −0.366484 −0.183242 0.983068i \(-0.558659\pi\)
−0.183242 + 0.983068i \(0.558659\pi\)
\(318\) 1867.73 0.329363
\(319\) 5076.87 0.891067
\(320\) 501.525 0.0876128
\(321\) 757.597 0.131729
\(322\) −5401.52 −0.934829
\(323\) 28.1895 0.00485606
\(324\) 3382.88 0.580055
\(325\) −7416.06 −1.26575
\(326\) −2968.63 −0.504348
\(327\) 1510.56 0.255456
\(328\) −2954.70 −0.497397
\(329\) 2939.93 0.492655
\(330\) −475.864 −0.0793802
\(331\) −3764.18 −0.625069 −0.312535 0.949906i \(-0.601178\pi\)
−0.312535 + 0.949906i \(0.601178\pi\)
\(332\) −229.530 −0.0379430
\(333\) −4325.76 −0.711862
\(334\) −6542.01 −1.07174
\(335\) −749.727 −0.122274
\(336\) −1691.42 −0.274626
\(337\) −5712.02 −0.923305 −0.461653 0.887061i \(-0.652743\pi\)
−0.461653 + 0.887061i \(0.652743\pi\)
\(338\) −17092.1 −2.75055
\(339\) 1054.38 0.168926
\(340\) −581.162 −0.0926997
\(341\) −1784.82 −0.283441
\(342\) 138.258 0.0218601
\(343\) 237.353 0.0373640
\(344\) 0 0
\(345\) −276.728 −0.0431841
\(346\) 15609.8 2.42540
\(347\) −12550.3 −1.94160 −0.970802 0.239881i \(-0.922892\pi\)
−0.970802 + 0.239881i \(0.922892\pi\)
\(348\) −761.637 −0.117322
\(349\) −5215.06 −0.799874 −0.399937 0.916543i \(-0.630968\pi\)
−0.399937 + 0.916543i \(0.630968\pi\)
\(350\) 8465.12 1.29280
\(351\) −3608.36 −0.548717
\(352\) −5376.19 −0.814068
\(353\) −2092.54 −0.315509 −0.157754 0.987478i \(-0.550425\pi\)
−0.157754 + 0.987478i \(0.550425\pi\)
\(354\) −2374.95 −0.356575
\(355\) 4388.49 0.656104
\(356\) −4715.11 −0.701967
\(357\) 414.697 0.0614792
\(358\) 9274.86 1.36925
\(359\) −10088.2 −1.48310 −0.741549 0.670898i \(-0.765909\pi\)
−0.741549 + 0.670898i \(0.765909\pi\)
\(360\) 1706.32 0.249809
\(361\) −6856.88 −0.999691
\(362\) −15256.9 −2.21515
\(363\) −484.848 −0.0701045
\(364\) 10987.8 1.58219
\(365\) 2595.05 0.372140
\(366\) 2312.36 0.330244
\(367\) −2565.33 −0.364876 −0.182438 0.983217i \(-0.558399\pi\)
−0.182438 + 0.983217i \(0.558399\pi\)
\(368\) −4488.07 −0.635752
\(369\) 7204.25 1.01636
\(370\) 3551.24 0.498974
\(371\) −16810.8 −2.35249
\(372\) 267.760 0.0373191
\(373\) 907.539 0.125980 0.0629900 0.998014i \(-0.479936\pi\)
0.0629900 + 0.998014i \(0.479936\pi\)
\(374\) 1892.21 0.261615
\(375\) 1042.49 0.143558
\(376\) 1204.73 0.165237
\(377\) −15606.5 −2.13203
\(378\) 4118.79 0.560443
\(379\) 9411.80 1.27560 0.637799 0.770203i \(-0.279845\pi\)
0.637799 + 0.770203i \(0.279845\pi\)
\(380\) −43.6782 −0.00589643
\(381\) −360.937 −0.0485338
\(382\) −4836.12 −0.647743
\(383\) −10469.6 −1.39680 −0.698398 0.715710i \(-0.746103\pi\)
−0.698398 + 0.715710i \(0.746103\pi\)
\(384\) −1044.39 −0.138793
\(385\) 4283.08 0.566976
\(386\) 10557.7 1.39216
\(387\) 0 0
\(388\) 1777.35 0.232555
\(389\) 6173.88 0.804700 0.402350 0.915486i \(-0.368194\pi\)
0.402350 + 0.915486i \(0.368194\pi\)
\(390\) 1462.83 0.189931
\(391\) 1100.37 0.142323
\(392\) 3802.70 0.489963
\(393\) −650.294 −0.0834681
\(394\) −1548.17 −0.197959
\(395\) −719.564 −0.0916587
\(396\) 3571.31 0.453195
\(397\) −3847.68 −0.486422 −0.243211 0.969973i \(-0.578201\pi\)
−0.243211 + 0.969973i \(0.578201\pi\)
\(398\) −9193.63 −1.15788
\(399\) 31.1673 0.00391056
\(400\) 7033.58 0.879198
\(401\) −2160.31 −0.269029 −0.134515 0.990912i \(-0.542948\pi\)
−0.134515 + 0.990912i \(0.542948\pi\)
\(402\) −366.208 −0.0454348
\(403\) 5486.61 0.678182
\(404\) −1089.76 −0.134202
\(405\) −4053.61 −0.497346
\(406\) 17814.2 2.17759
\(407\) −4449.47 −0.541897
\(408\) 169.935 0.0206202
\(409\) −4818.22 −0.582508 −0.291254 0.956646i \(-0.594073\pi\)
−0.291254 + 0.956646i \(0.594073\pi\)
\(410\) −5914.35 −0.712412
\(411\) −907.457 −0.108909
\(412\) 7700.30 0.920792
\(413\) 21376.1 2.54685
\(414\) 5396.88 0.640682
\(415\) 275.039 0.0325328
\(416\) 16526.6 1.94780
\(417\) −1730.66 −0.203240
\(418\) 142.212 0.0166408
\(419\) −924.481 −0.107790 −0.0538948 0.998547i \(-0.517164\pi\)
−0.0538948 + 0.998547i \(0.517164\pi\)
\(420\) −642.551 −0.0746507
\(421\) −14389.0 −1.66574 −0.832870 0.553468i \(-0.813304\pi\)
−0.832870 + 0.553468i \(0.813304\pi\)
\(422\) −12608.8 −1.45448
\(423\) −2937.40 −0.337640
\(424\) −6888.74 −0.789025
\(425\) −1724.47 −0.196822
\(426\) 2143.58 0.243795
\(427\) −20812.7 −2.35878
\(428\) 4667.69 0.527153
\(429\) −1832.82 −0.206269
\(430\) 0 0
\(431\) 2076.77 0.232098 0.116049 0.993243i \(-0.462977\pi\)
0.116049 + 0.993243i \(0.462977\pi\)
\(432\) 3422.26 0.381142
\(433\) 1585.85 0.176007 0.0880033 0.996120i \(-0.471951\pi\)
0.0880033 + 0.996120i \(0.471951\pi\)
\(434\) −6262.73 −0.692674
\(435\) 912.647 0.100593
\(436\) 9306.82 1.02228
\(437\) 82.7003 0.00905284
\(438\) 1267.57 0.138280
\(439\) −278.813 −0.0303121 −0.0151561 0.999885i \(-0.504825\pi\)
−0.0151561 + 0.999885i \(0.504825\pi\)
\(440\) 1755.12 0.190164
\(441\) −9271.87 −1.00117
\(442\) −5816.74 −0.625959
\(443\) 4961.81 0.532151 0.266075 0.963952i \(-0.414273\pi\)
0.266075 + 0.963952i \(0.414273\pi\)
\(444\) 667.513 0.0713486
\(445\) 5649.98 0.601875
\(446\) −19528.2 −2.07328
\(447\) 249.823 0.0264345
\(448\) −2204.91 −0.232527
\(449\) −12048.2 −1.26634 −0.633171 0.774012i \(-0.718247\pi\)
−0.633171 + 0.774012i \(0.718247\pi\)
\(450\) −8457.85 −0.886015
\(451\) 7410.29 0.773696
\(452\) 6496.19 0.676007
\(453\) −2138.71 −0.221822
\(454\) 11642.9 1.20358
\(455\) −13166.4 −1.35659
\(456\) 12.7718 0.00131161
\(457\) −12738.5 −1.30390 −0.651948 0.758263i \(-0.726048\pi\)
−0.651948 + 0.758263i \(0.726048\pi\)
\(458\) 16570.9 1.69063
\(459\) −839.060 −0.0853245
\(460\) −1704.97 −0.172814
\(461\) 4651.57 0.469947 0.234973 0.972002i \(-0.424500\pi\)
0.234973 + 0.972002i \(0.424500\pi\)
\(462\) 2092.09 0.210677
\(463\) −217.350 −0.0218166 −0.0109083 0.999941i \(-0.503472\pi\)
−0.0109083 + 0.999941i \(0.503472\pi\)
\(464\) 14801.6 1.48092
\(465\) −320.849 −0.0319979
\(466\) 897.075 0.0891764
\(467\) 1915.22 0.189777 0.0948887 0.995488i \(-0.469750\pi\)
0.0948887 + 0.995488i \(0.469750\pi\)
\(468\) −10978.4 −1.08435
\(469\) 3296.10 0.324520
\(470\) 2411.47 0.236666
\(471\) 746.054 0.0729859
\(472\) 8759.52 0.854215
\(473\) 0 0
\(474\) −351.474 −0.0340586
\(475\) −129.606 −0.0125194
\(476\) 2555.02 0.246028
\(477\) 16796.3 1.61227
\(478\) −16241.3 −1.55410
\(479\) −11167.6 −1.06526 −0.532630 0.846348i \(-0.678796\pi\)
−0.532630 + 0.846348i \(0.678796\pi\)
\(480\) −966.454 −0.0919008
\(481\) 13677.9 1.29658
\(482\) 1833.87 0.173299
\(483\) 1216.61 0.114612
\(484\) −2987.24 −0.280544
\(485\) −2129.75 −0.199396
\(486\) −6198.33 −0.578522
\(487\) 18058.4 1.68030 0.840150 0.542354i \(-0.182467\pi\)
0.840150 + 0.542354i \(0.182467\pi\)
\(488\) −8528.66 −0.791136
\(489\) 668.638 0.0618340
\(490\) 7611.77 0.701765
\(491\) 19234.3 1.76789 0.883945 0.467592i \(-0.154878\pi\)
0.883945 + 0.467592i \(0.154878\pi\)
\(492\) −1111.70 −0.101868
\(493\) −3629.02 −0.331527
\(494\) −437.167 −0.0398160
\(495\) −4279.40 −0.388575
\(496\) −5203.64 −0.471069
\(497\) −19293.6 −1.74132
\(498\) 134.344 0.0120886
\(499\) −9828.54 −0.881735 −0.440868 0.897572i \(-0.645329\pi\)
−0.440868 + 0.897572i \(0.645329\pi\)
\(500\) 6422.98 0.574489
\(501\) 1473.48 0.131398
\(502\) −17167.6 −1.52635
\(503\) 11481.5 1.01776 0.508880 0.860838i \(-0.330060\pi\)
0.508880 + 0.860838i \(0.330060\pi\)
\(504\) −7501.69 −0.663000
\(505\) 1305.82 0.115066
\(506\) 5551.23 0.487712
\(507\) 3849.72 0.337223
\(508\) −2223.80 −0.194223
\(509\) −3994.60 −0.347854 −0.173927 0.984759i \(-0.555646\pi\)
−0.173927 + 0.984759i \(0.555646\pi\)
\(510\) 340.155 0.0295339
\(511\) −11408.9 −0.987670
\(512\) −8847.52 −0.763689
\(513\) −63.0610 −0.00542731
\(514\) −7524.13 −0.645672
\(515\) −9227.04 −0.789499
\(516\) 0 0
\(517\) −3021.41 −0.257024
\(518\) −15612.7 −1.32429
\(519\) −3515.86 −0.297359
\(520\) −5395.33 −0.455001
\(521\) −6982.25 −0.587136 −0.293568 0.955938i \(-0.594843\pi\)
−0.293568 + 0.955938i \(0.594843\pi\)
\(522\) −17798.9 −1.49241
\(523\) −8757.64 −0.732208 −0.366104 0.930574i \(-0.619309\pi\)
−0.366104 + 0.930574i \(0.619309\pi\)
\(524\) −4006.57 −0.334023
\(525\) −1906.63 −0.158500
\(526\) 25648.7 2.12611
\(527\) 1275.81 0.105456
\(528\) 1738.30 0.143276
\(529\) −8938.81 −0.734677
\(530\) −13789.0 −1.13011
\(531\) −21357.7 −1.74547
\(532\) 192.027 0.0156493
\(533\) −22779.5 −1.85120
\(534\) 2759.76 0.223645
\(535\) −5593.16 −0.451987
\(536\) 1350.68 0.108844
\(537\) −2089.02 −0.167873
\(538\) 19551.0 1.56673
\(539\) −9537.04 −0.762132
\(540\) 1300.08 0.103605
\(541\) −3230.72 −0.256746 −0.128373 0.991726i \(-0.540976\pi\)
−0.128373 + 0.991726i \(0.540976\pi\)
\(542\) −24555.4 −1.94603
\(543\) 3436.38 0.271582
\(544\) 3842.98 0.302879
\(545\) −11152.1 −0.876519
\(546\) −6431.18 −0.504082
\(547\) −441.868 −0.0345391 −0.0172696 0.999851i \(-0.505497\pi\)
−0.0172696 + 0.999851i \(0.505497\pi\)
\(548\) −5591.00 −0.435831
\(549\) 20794.9 1.61658
\(550\) −8699.74 −0.674469
\(551\) −272.745 −0.0210877
\(552\) 498.542 0.0384409
\(553\) 3163.49 0.243265
\(554\) 24114.8 1.84935
\(555\) −799.861 −0.0611752
\(556\) −10662.9 −0.813325
\(557\) −12443.5 −0.946586 −0.473293 0.880905i \(-0.656935\pi\)
−0.473293 + 0.880905i \(0.656935\pi\)
\(558\) 6257.36 0.474722
\(559\) 0 0
\(560\) 12487.3 0.942296
\(561\) −426.191 −0.0320745
\(562\) 21826.4 1.63824
\(563\) 12004.7 0.898647 0.449324 0.893369i \(-0.351665\pi\)
0.449324 + 0.893369i \(0.351665\pi\)
\(564\) 453.275 0.0338410
\(565\) −7784.20 −0.579617
\(566\) 13742.3 1.02055
\(567\) 17821.3 1.31997
\(568\) −7906.14 −0.584040
\(569\) −17399.4 −1.28194 −0.640969 0.767567i \(-0.721467\pi\)
−0.640969 + 0.767567i \(0.721467\pi\)
\(570\) 25.5649 0.00187859
\(571\) 187.663 0.0137539 0.00687694 0.999976i \(-0.497811\pi\)
0.00687694 + 0.999976i \(0.497811\pi\)
\(572\) −11292.3 −0.825449
\(573\) 1089.26 0.0794145
\(574\) 26001.9 1.89076
\(575\) −5059.13 −0.366922
\(576\) 2203.01 0.159361
\(577\) −15258.1 −1.10087 −0.550437 0.834877i \(-0.685539\pi\)
−0.550437 + 0.834877i \(0.685539\pi\)
\(578\) 16364.4 1.17763
\(579\) −2377.96 −0.170681
\(580\) 5622.98 0.402554
\(581\) −1209.18 −0.0863430
\(582\) −1040.29 −0.0740915
\(583\) 17276.7 1.22732
\(584\) −4675.15 −0.331265
\(585\) 13155.1 0.929735
\(586\) 4847.81 0.341743
\(587\) −20653.7 −1.45225 −0.726124 0.687563i \(-0.758680\pi\)
−0.726124 + 0.687563i \(0.758680\pi\)
\(588\) 1430.75 0.100346
\(589\) 95.8860 0.00670783
\(590\) 17533.7 1.22348
\(591\) 348.702 0.0242702
\(592\) −12972.4 −0.900614
\(593\) 2747.81 0.190285 0.0951426 0.995464i \(-0.469669\pi\)
0.0951426 + 0.995464i \(0.469669\pi\)
\(594\) −4232.94 −0.292390
\(595\) −3061.61 −0.210947
\(596\) 1539.20 0.105786
\(597\) 2070.72 0.141958
\(598\) −17064.7 −1.16694
\(599\) 23896.4 1.63002 0.815008 0.579450i \(-0.196733\pi\)
0.815008 + 0.579450i \(0.196733\pi\)
\(600\) −781.302 −0.0531609
\(601\) −15868.2 −1.07700 −0.538501 0.842625i \(-0.681009\pi\)
−0.538501 + 0.842625i \(0.681009\pi\)
\(602\) 0 0
\(603\) −3293.27 −0.222409
\(604\) −13177.0 −0.887689
\(605\) 3579.52 0.240542
\(606\) 637.837 0.0427563
\(607\) −8394.74 −0.561338 −0.280669 0.959805i \(-0.590556\pi\)
−0.280669 + 0.959805i \(0.590556\pi\)
\(608\) 288.826 0.0192655
\(609\) −4012.37 −0.266977
\(610\) −17071.6 −1.13313
\(611\) 9287.95 0.614976
\(612\) −2552.83 −0.168614
\(613\) −1487.66 −0.0980197 −0.0490099 0.998798i \(-0.515607\pi\)
−0.0490099 + 0.998798i \(0.515607\pi\)
\(614\) 29499.0 1.93890
\(615\) 1332.11 0.0873432
\(616\) −7716.23 −0.504701
\(617\) 7581.38 0.494676 0.247338 0.968929i \(-0.420444\pi\)
0.247338 + 0.968929i \(0.420444\pi\)
\(618\) −4506.99 −0.293362
\(619\) −328.731 −0.0213454 −0.0106727 0.999943i \(-0.503397\pi\)
−0.0106727 + 0.999943i \(0.503397\pi\)
\(620\) −1976.81 −0.128049
\(621\) −2461.57 −0.159065
\(622\) −716.845 −0.0462104
\(623\) −24839.6 −1.59739
\(624\) −5343.60 −0.342813
\(625\) 3433.82 0.219765
\(626\) −1178.03 −0.0752135
\(627\) −32.0311 −0.00204019
\(628\) 4596.57 0.292075
\(629\) 3180.54 0.201616
\(630\) −15016.0 −0.949603
\(631\) 20258.2 1.27807 0.639037 0.769176i \(-0.279333\pi\)
0.639037 + 0.769176i \(0.279333\pi\)
\(632\) 1296.34 0.0815911
\(633\) 2839.94 0.178322
\(634\) 7459.10 0.467253
\(635\) 2664.71 0.166529
\(636\) −2591.87 −0.161595
\(637\) 29317.3 1.82354
\(638\) −18307.9 −1.13608
\(639\) 19277.0 1.19341
\(640\) 7710.48 0.476224
\(641\) 7317.96 0.450924 0.225462 0.974252i \(-0.427611\pi\)
0.225462 + 0.974252i \(0.427611\pi\)
\(642\) −2732.00 −0.167950
\(643\) 14629.6 0.897253 0.448627 0.893719i \(-0.351913\pi\)
0.448627 + 0.893719i \(0.351913\pi\)
\(644\) 7495.73 0.458654
\(645\) 0 0
\(646\) −101.656 −0.00619130
\(647\) 6446.09 0.391688 0.195844 0.980635i \(-0.437255\pi\)
0.195844 + 0.980635i \(0.437255\pi\)
\(648\) 7302.83 0.442719
\(649\) −21968.6 −1.32872
\(650\) 26743.4 1.61379
\(651\) 1410.58 0.0849233
\(652\) 4119.59 0.247447
\(653\) −15267.7 −0.914961 −0.457480 0.889220i \(-0.651248\pi\)
−0.457480 + 0.889220i \(0.651248\pi\)
\(654\) −5447.29 −0.325697
\(655\) 4800.96 0.286395
\(656\) 21604.7 1.28586
\(657\) 11399.1 0.676897
\(658\) −10601.8 −0.628118
\(659\) −13991.4 −0.827055 −0.413527 0.910492i \(-0.635703\pi\)
−0.413527 + 0.910492i \(0.635703\pi\)
\(660\) 660.360 0.0389462
\(661\) 17096.8 1.00603 0.503016 0.864277i \(-0.332224\pi\)
0.503016 + 0.864277i \(0.332224\pi\)
\(662\) 13574.2 0.796941
\(663\) 1310.13 0.0767439
\(664\) −495.499 −0.0289595
\(665\) −230.100 −0.0134179
\(666\) 15599.3 0.907598
\(667\) −10646.6 −0.618045
\(668\) 9078.39 0.525829
\(669\) 4398.41 0.254189
\(670\) 2703.62 0.155896
\(671\) 21389.6 1.23060
\(672\) 4248.92 0.243907
\(673\) −9239.00 −0.529179 −0.264589 0.964361i \(-0.585236\pi\)
−0.264589 + 0.964361i \(0.585236\pi\)
\(674\) 20598.4 1.17718
\(675\) 3857.71 0.219975
\(676\) 23718.8 1.34950
\(677\) 4341.97 0.246493 0.123246 0.992376i \(-0.460669\pi\)
0.123246 + 0.992376i \(0.460669\pi\)
\(678\) −3802.23 −0.215374
\(679\) 9363.23 0.529202
\(680\) −1254.59 −0.0707519
\(681\) −2622.37 −0.147562
\(682\) 6436.31 0.361377
\(683\) 935.126 0.0523889 0.0261944 0.999657i \(-0.491661\pi\)
0.0261944 + 0.999657i \(0.491661\pi\)
\(684\) −191.862 −0.0107252
\(685\) 6699.53 0.373687
\(686\) −855.928 −0.0476377
\(687\) −3732.33 −0.207274
\(688\) 0 0
\(689\) −53109.3 −2.93658
\(690\) 997.920 0.0550582
\(691\) −14883.7 −0.819398 −0.409699 0.912221i \(-0.634366\pi\)
−0.409699 + 0.912221i \(0.634366\pi\)
\(692\) −21661.8 −1.18997
\(693\) 18814.0 1.03129
\(694\) 45258.3 2.47548
\(695\) 12777.1 0.697355
\(696\) −1644.19 −0.0895444
\(697\) −5296.98 −0.287859
\(698\) 18806.3 1.01981
\(699\) −202.052 −0.0109332
\(700\) −11747.1 −0.634284
\(701\) −6934.09 −0.373605 −0.186802 0.982398i \(-0.559812\pi\)
−0.186802 + 0.982398i \(0.559812\pi\)
\(702\) 13012.2 0.699595
\(703\) 239.039 0.0128244
\(704\) 2266.02 0.121312
\(705\) −543.146 −0.0290157
\(706\) 7545.99 0.402262
\(707\) −5740.93 −0.305389
\(708\) 3295.74 0.174946
\(709\) 904.231 0.0478972 0.0239486 0.999713i \(-0.492376\pi\)
0.0239486 + 0.999713i \(0.492376\pi\)
\(710\) −15825.5 −0.836509
\(711\) −3160.78 −0.166721
\(712\) −10178.8 −0.535767
\(713\) 3742.89 0.196595
\(714\) −1495.46 −0.0783838
\(715\) 13531.3 0.707750
\(716\) −12870.8 −0.671793
\(717\) 3658.09 0.190535
\(718\) 36379.3 1.89090
\(719\) −23525.7 −1.22025 −0.610125 0.792306i \(-0.708881\pi\)
−0.610125 + 0.792306i \(0.708881\pi\)
\(720\) −12476.6 −0.645799
\(721\) 40565.8 2.09535
\(722\) 24726.9 1.27457
\(723\) −413.049 −0.0212469
\(724\) 21172.1 1.08682
\(725\) 16685.0 0.854710
\(726\) 1748.43 0.0893808
\(727\) 33029.9 1.68502 0.842512 0.538678i \(-0.181076\pi\)
0.842512 + 0.538678i \(0.181076\pi\)
\(728\) 23720.0 1.20759
\(729\) −16855.9 −0.856368
\(730\) −9358.12 −0.474465
\(731\) 0 0
\(732\) −3208.88 −0.162027
\(733\) 4063.29 0.204749 0.102375 0.994746i \(-0.467356\pi\)
0.102375 + 0.994746i \(0.467356\pi\)
\(734\) 9250.96 0.465203
\(735\) −1714.43 −0.0860377
\(736\) 11274.2 0.564639
\(737\) −3387.46 −0.169306
\(738\) −25979.6 −1.29583
\(739\) −9373.56 −0.466593 −0.233296 0.972406i \(-0.574951\pi\)
−0.233296 + 0.972406i \(0.574951\pi\)
\(740\) −4928.09 −0.244811
\(741\) 98.4650 0.00488151
\(742\) 60622.1 2.99934
\(743\) −21092.5 −1.04147 −0.520734 0.853719i \(-0.674341\pi\)
−0.520734 + 0.853719i \(0.674341\pi\)
\(744\) 578.030 0.0284833
\(745\) −1844.38 −0.0907020
\(746\) −3272.71 −0.160620
\(747\) 1208.14 0.0591749
\(748\) −2625.84 −0.128356
\(749\) 24589.8 1.19959
\(750\) −3759.38 −0.183031
\(751\) −15261.7 −0.741555 −0.370777 0.928722i \(-0.620909\pi\)
−0.370777 + 0.928722i \(0.620909\pi\)
\(752\) −8808.93 −0.427166
\(753\) 3866.73 0.187134
\(754\) 56279.4 2.71827
\(755\) 15789.6 0.761115
\(756\) −5715.67 −0.274969
\(757\) −6955.07 −0.333932 −0.166966 0.985963i \(-0.553397\pi\)
−0.166966 + 0.985963i \(0.553397\pi\)
\(758\) −33940.3 −1.62634
\(759\) −1250.33 −0.0597944
\(760\) −94.2908 −0.00450038
\(761\) 3295.92 0.157000 0.0785000 0.996914i \(-0.474987\pi\)
0.0785000 + 0.996914i \(0.474987\pi\)
\(762\) 1301.59 0.0618789
\(763\) 49029.1 2.32631
\(764\) 6711.13 0.317801
\(765\) 3058.98 0.144572
\(766\) 37755.0 1.78086
\(767\) 67532.3 3.17920
\(768\) 4309.68 0.202490
\(769\) −5722.67 −0.268355 −0.134177 0.990957i \(-0.542839\pi\)
−0.134177 + 0.990957i \(0.542839\pi\)
\(770\) −15445.4 −0.722875
\(771\) 1694.69 0.0791606
\(772\) −14651.0 −0.683032
\(773\) 17526.3 0.815494 0.407747 0.913095i \(-0.366315\pi\)
0.407747 + 0.913095i \(0.366315\pi\)
\(774\) 0 0
\(775\) −5865.75 −0.271876
\(776\) 3836.88 0.177495
\(777\) 3516.51 0.162361
\(778\) −22263.9 −1.02596
\(779\) −398.104 −0.0183101
\(780\) −2029.98 −0.0931856
\(781\) 19828.3 0.908468
\(782\) −3968.10 −0.181456
\(783\) 8118.25 0.370527
\(784\) −27805.2 −1.26664
\(785\) −5507.94 −0.250429
\(786\) 2345.05 0.106419
\(787\) 35884.3 1.62533 0.812667 0.582729i \(-0.198015\pi\)
0.812667 + 0.582729i \(0.198015\pi\)
\(788\) 2148.41 0.0971244
\(789\) −5776.96 −0.260666
\(790\) 2594.85 0.116862
\(791\) 34222.5 1.53832
\(792\) 7709.61 0.345895
\(793\) −65752.5 −2.94444
\(794\) 13875.3 0.620171
\(795\) 3105.76 0.138553
\(796\) 12758.1 0.568088
\(797\) 26874.0 1.19439 0.597194 0.802097i \(-0.296282\pi\)
0.597194 + 0.802097i \(0.296282\pi\)
\(798\) −112.394 −0.00498583
\(799\) 2159.75 0.0956276
\(800\) −17668.7 −0.780853
\(801\) 24818.3 1.09477
\(802\) 7790.38 0.343003
\(803\) 11725.1 0.515280
\(804\) 508.189 0.0222916
\(805\) −8981.91 −0.393255
\(806\) −19785.5 −0.864658
\(807\) −4403.55 −0.192085
\(808\) −2352.53 −0.102428
\(809\) 16365.2 0.711212 0.355606 0.934636i \(-0.384274\pi\)
0.355606 + 0.934636i \(0.384274\pi\)
\(810\) 14617.9 0.634099
\(811\) 9500.55 0.411356 0.205678 0.978620i \(-0.434060\pi\)
0.205678 + 0.978620i \(0.434060\pi\)
\(812\) −24720.9 −1.06839
\(813\) 5530.72 0.238587
\(814\) 16045.4 0.690899
\(815\) −4936.39 −0.212165
\(816\) −1242.56 −0.0533068
\(817\) 0 0
\(818\) 17375.2 0.742677
\(819\) −57835.0 −2.46754
\(820\) 8207.39 0.349530
\(821\) −10038.9 −0.426748 −0.213374 0.976971i \(-0.568445\pi\)
−0.213374 + 0.976971i \(0.568445\pi\)
\(822\) 3272.42 0.138855
\(823\) −23596.1 −0.999403 −0.499702 0.866198i \(-0.666557\pi\)
−0.499702 + 0.866198i \(0.666557\pi\)
\(824\) 16623.1 0.702783
\(825\) 1959.48 0.0826913
\(826\) −77085.3 −3.24714
\(827\) 29302.6 1.23211 0.616053 0.787705i \(-0.288731\pi\)
0.616053 + 0.787705i \(0.288731\pi\)
\(828\) −7489.29 −0.314337
\(829\) 16593.4 0.695190 0.347595 0.937645i \(-0.386998\pi\)
0.347595 + 0.937645i \(0.386998\pi\)
\(830\) −991.829 −0.0414782
\(831\) −5431.48 −0.226734
\(832\) −6965.83 −0.290261
\(833\) 6817.21 0.283556
\(834\) 6241.02 0.259123
\(835\) −10878.4 −0.450852
\(836\) −197.349 −0.00816443
\(837\) −2854.04 −0.117861
\(838\) 3333.81 0.137428
\(839\) 16106.7 0.662772 0.331386 0.943495i \(-0.392484\pi\)
0.331386 + 0.943495i \(0.392484\pi\)
\(840\) −1387.11 −0.0569762
\(841\) 10723.3 0.439677
\(842\) 51888.8 2.12376
\(843\) −4916.05 −0.200852
\(844\) 17497.4 0.713607
\(845\) −28421.5 −1.15708
\(846\) 10592.7 0.430478
\(847\) −15737.0 −0.638406
\(848\) 50370.3 2.03977
\(849\) −3095.23 −0.125121
\(850\) 6218.70 0.250941
\(851\) 9330.84 0.375860
\(852\) −2974.66 −0.119613
\(853\) 16973.0 0.681293 0.340647 0.940191i \(-0.389354\pi\)
0.340647 + 0.940191i \(0.389354\pi\)
\(854\) 75053.7 3.00736
\(855\) 229.903 0.00919592
\(856\) 10076.4 0.402342
\(857\) −10313.8 −0.411101 −0.205551 0.978647i \(-0.565898\pi\)
−0.205551 + 0.978647i \(0.565898\pi\)
\(858\) 6609.43 0.262986
\(859\) −22942.2 −0.911267 −0.455634 0.890167i \(-0.650587\pi\)
−0.455634 + 0.890167i \(0.650587\pi\)
\(860\) 0 0
\(861\) −5856.51 −0.231811
\(862\) −7489.11 −0.295917
\(863\) 19747.4 0.778920 0.389460 0.921043i \(-0.372662\pi\)
0.389460 + 0.921043i \(0.372662\pi\)
\(864\) −8596.88 −0.338509
\(865\) 25956.7 1.02029
\(866\) −5718.79 −0.224402
\(867\) −3685.82 −0.144380
\(868\) 8690.84 0.339846
\(869\) −3251.17 −0.126914
\(870\) −3291.14 −0.128253
\(871\) 10413.2 0.405095
\(872\) 20091.2 0.780245
\(873\) −9355.20 −0.362687
\(874\) −298.229 −0.0115421
\(875\) 33836.8 1.30730
\(876\) −1759.01 −0.0678441
\(877\) 9726.70 0.374512 0.187256 0.982311i \(-0.440041\pi\)
0.187256 + 0.982311i \(0.440041\pi\)
\(878\) 1005.44 0.0386469
\(879\) −1091.89 −0.0418983
\(880\) −12833.4 −0.491608
\(881\) 16960.9 0.648613 0.324306 0.945952i \(-0.394869\pi\)
0.324306 + 0.945952i \(0.394869\pi\)
\(882\) 33435.7 1.27646
\(883\) 23172.9 0.883159 0.441579 0.897222i \(-0.354418\pi\)
0.441579 + 0.897222i \(0.354418\pi\)
\(884\) 8071.93 0.307114
\(885\) −3949.19 −0.150001
\(886\) −17893.0 −0.678473
\(887\) 38740.7 1.46650 0.733250 0.679959i \(-0.238002\pi\)
0.733250 + 0.679959i \(0.238002\pi\)
\(888\) 1441.00 0.0544559
\(889\) −11715.2 −0.441972
\(890\) −20374.6 −0.767370
\(891\) −18315.2 −0.688646
\(892\) 27099.4 1.01721
\(893\) 162.320 0.00608267
\(894\) −900.898 −0.0337031
\(895\) 15422.7 0.576004
\(896\) −33898.4 −1.26391
\(897\) 3843.56 0.143069
\(898\) 43447.4 1.61454
\(899\) −12344.0 −0.457949
\(900\) 11737.0 0.434705
\(901\) −12349.6 −0.456633
\(902\) −26722.6 −0.986434
\(903\) 0 0
\(904\) 14023.7 0.515954
\(905\) −25370.0 −0.931852
\(906\) 7712.51 0.282816
\(907\) 11304.7 0.413855 0.206928 0.978356i \(-0.433654\pi\)
0.206928 + 0.978356i \(0.433654\pi\)
\(908\) −16156.9 −0.590513
\(909\) 5736.00 0.209297
\(910\) 47479.8 1.72960
\(911\) −15797.8 −0.574537 −0.287269 0.957850i \(-0.592747\pi\)
−0.287269 + 0.957850i \(0.592747\pi\)
\(912\) −93.3868 −0.00339073
\(913\) 1242.69 0.0450462
\(914\) 45936.8 1.66242
\(915\) 3845.11 0.138924
\(916\) −22995.6 −0.829470
\(917\) −21107.0 −0.760101
\(918\) 3025.77 0.108786
\(919\) 38867.9 1.39514 0.697570 0.716517i \(-0.254265\pi\)
0.697570 + 0.716517i \(0.254265\pi\)
\(920\) −3680.62 −0.131898
\(921\) −6644.19 −0.237713
\(922\) −16774.2 −0.599165
\(923\) −60953.1 −2.17367
\(924\) −2903.21 −0.103364
\(925\) −14623.0 −0.519787
\(926\) 783.795 0.0278154
\(927\) −40531.0 −1.43604
\(928\) −37182.4 −1.31527
\(929\) −13829.3 −0.488400 −0.244200 0.969725i \(-0.578525\pi\)
−0.244200 + 0.969725i \(0.578525\pi\)
\(930\) 1157.03 0.0407961
\(931\) 512.359 0.0180364
\(932\) −1244.88 −0.0437525
\(933\) 161.458 0.00566549
\(934\) −6906.58 −0.241959
\(935\) 3146.46 0.110054
\(936\) −23699.7 −0.827616
\(937\) −40293.0 −1.40482 −0.702410 0.711773i \(-0.747893\pi\)
−0.702410 + 0.711773i \(0.747893\pi\)
\(938\) −11886.2 −0.413751
\(939\) 265.333 0.00922132
\(940\) −3346.42 −0.116115
\(941\) −18141.7 −0.628482 −0.314241 0.949343i \(-0.601750\pi\)
−0.314241 + 0.949343i \(0.601750\pi\)
\(942\) −2690.38 −0.0930544
\(943\) −15539.9 −0.536636
\(944\) −64049.4 −2.20829
\(945\) 6848.92 0.235762
\(946\) 0 0
\(947\) −42305.7 −1.45169 −0.725845 0.687858i \(-0.758551\pi\)
−0.725845 + 0.687858i \(0.758551\pi\)
\(948\) 487.744 0.0167101
\(949\) −36043.5 −1.23290
\(950\) 467.377 0.0159618
\(951\) −1680.04 −0.0572862
\(952\) 5515.68 0.187777
\(953\) −34528.2 −1.17364 −0.586819 0.809718i \(-0.699620\pi\)
−0.586819 + 0.809718i \(0.699620\pi\)
\(954\) −60570.0 −2.05558
\(955\) −8041.75 −0.272487
\(956\) 22538.1 0.762485
\(957\) 4123.57 0.139285
\(958\) 40271.9 1.35817
\(959\) −29453.8 −0.991777
\(960\) 407.352 0.0136950
\(961\) −25451.4 −0.854330
\(962\) −49324.3 −1.65310
\(963\) −24568.7 −0.822133
\(964\) −2544.87 −0.0850257
\(965\) 17555.9 0.585641
\(966\) −4387.26 −0.146126
\(967\) −29151.9 −0.969454 −0.484727 0.874666i \(-0.661081\pi\)
−0.484727 + 0.874666i \(0.661081\pi\)
\(968\) −6448.72 −0.214122
\(969\) 22.8963 0.000759066 0
\(970\) 7680.18 0.254222
\(971\) 4560.27 0.150717 0.0753584 0.997157i \(-0.475990\pi\)
0.0753584 + 0.997157i \(0.475990\pi\)
\(972\) 8601.46 0.283840
\(973\) −56173.2 −1.85080
\(974\) −65121.3 −2.14232
\(975\) −6023.52 −0.197853
\(976\) 62361.3 2.04522
\(977\) 23774.7 0.778526 0.389263 0.921127i \(-0.372730\pi\)
0.389263 + 0.921127i \(0.372730\pi\)
\(978\) −2411.20 −0.0788362
\(979\) 25528.0 0.833381
\(980\) −10562.9 −0.344306
\(981\) −48987.0 −1.59433
\(982\) −69361.8 −2.25400
\(983\) 53606.1 1.73934 0.869669 0.493636i \(-0.164333\pi\)
0.869669 + 0.493636i \(0.164333\pi\)
\(984\) −2399.89 −0.0777496
\(985\) −2574.38 −0.0832757
\(986\) 13086.8 0.422685
\(987\) 2387.89 0.0770085
\(988\) 606.660 0.0195348
\(989\) 0 0
\(990\) 15432.1 0.495420
\(991\) 33076.1 1.06024 0.530119 0.847923i \(-0.322147\pi\)
0.530119 + 0.847923i \(0.322147\pi\)
\(992\) 13071.8 0.418377
\(993\) −3057.37 −0.0977065
\(994\) 69575.4 2.22012
\(995\) −15287.6 −0.487085
\(996\) −186.430 −0.00593099
\(997\) 31969.9 1.01554 0.507772 0.861491i \(-0.330469\pi\)
0.507772 + 0.861491i \(0.330469\pi\)
\(998\) 35443.1 1.12418
\(999\) −7114.99 −0.225334
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.g.1.7 30
43.8 odd 14 43.4.e.a.21.3 60
43.27 odd 14 43.4.e.a.41.3 yes 60
43.42 odd 2 1849.4.a.h.1.24 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.e.a.21.3 60 43.8 odd 14
43.4.e.a.41.3 yes 60 43.27 odd 14
1849.4.a.g.1.7 30 1.1 even 1 trivial
1849.4.a.h.1.24 30 43.42 odd 2