Properties

Label 1849.4.a.j.1.9
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 1.9
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.08033 q^{2} -6.02226 q^{3} +8.64912 q^{4} +2.18258 q^{5} +24.5728 q^{6} +8.90728 q^{7} -2.64861 q^{8} +9.26767 q^{9} +O(q^{10})\) \(q-4.08033 q^{2} -6.02226 q^{3} +8.64912 q^{4} +2.18258 q^{5} +24.5728 q^{6} +8.90728 q^{7} -2.64861 q^{8} +9.26767 q^{9} -8.90564 q^{10} +2.96222 q^{11} -52.0873 q^{12} +15.9248 q^{13} -36.3447 q^{14} -13.1441 q^{15} -58.3857 q^{16} -54.4270 q^{17} -37.8152 q^{18} +136.251 q^{19} +18.8774 q^{20} -53.6420 q^{21} -12.0868 q^{22} +153.274 q^{23} +15.9506 q^{24} -120.236 q^{25} -64.9786 q^{26} +106.789 q^{27} +77.0401 q^{28} +69.4344 q^{29} +53.6321 q^{30} -13.1165 q^{31} +259.422 q^{32} -17.8393 q^{33} +222.080 q^{34} +19.4408 q^{35} +80.1572 q^{36} -306.611 q^{37} -555.948 q^{38} -95.9035 q^{39} -5.78080 q^{40} -27.1862 q^{41} +218.877 q^{42} +25.6206 q^{44} +20.2274 q^{45} -625.409 q^{46} -621.994 q^{47} +351.614 q^{48} -263.660 q^{49} +490.604 q^{50} +327.774 q^{51} +137.736 q^{52} -97.9357 q^{53} -435.734 q^{54} +6.46527 q^{55} -23.5919 q^{56} -820.538 q^{57} -283.315 q^{58} -417.172 q^{59} -113.684 q^{60} -608.416 q^{61} +53.5198 q^{62} +82.5498 q^{63} -591.443 q^{64} +34.7572 q^{65} +72.7902 q^{66} +772.902 q^{67} -470.745 q^{68} -923.057 q^{69} -79.3251 q^{70} +858.225 q^{71} -24.5464 q^{72} +14.7922 q^{73} +1251.07 q^{74} +724.095 q^{75} +1178.45 q^{76} +26.3853 q^{77} +391.318 q^{78} +872.351 q^{79} -127.431 q^{80} -893.337 q^{81} +110.929 q^{82} -1057.72 q^{83} -463.956 q^{84} -118.791 q^{85} -418.152 q^{87} -7.84576 q^{88} -444.661 q^{89} -82.5346 q^{90} +141.847 q^{91} +1325.69 q^{92} +78.9912 q^{93} +2537.94 q^{94} +297.378 q^{95} -1562.31 q^{96} +150.389 q^{97} +1075.82 q^{98} +27.4529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.08033 −1.44262 −0.721308 0.692615i \(-0.756459\pi\)
−0.721308 + 0.692615i \(0.756459\pi\)
\(3\) −6.02226 −1.15899 −0.579493 0.814977i \(-0.696749\pi\)
−0.579493 + 0.814977i \(0.696749\pi\)
\(4\) 8.64912 1.08114
\(5\) 2.18258 0.195216 0.0976078 0.995225i \(-0.468881\pi\)
0.0976078 + 0.995225i \(0.468881\pi\)
\(6\) 24.5728 1.67197
\(7\) 8.90728 0.480948 0.240474 0.970656i \(-0.422697\pi\)
0.240474 + 0.970656i \(0.422697\pi\)
\(8\) −2.64861 −0.117053
\(9\) 9.26767 0.343247
\(10\) −8.90564 −0.281621
\(11\) 2.96222 0.0811948 0.0405974 0.999176i \(-0.487074\pi\)
0.0405974 + 0.999176i \(0.487074\pi\)
\(12\) −52.0873 −1.25302
\(13\) 15.9248 0.339750 0.169875 0.985466i \(-0.445664\pi\)
0.169875 + 0.985466i \(0.445664\pi\)
\(14\) −36.3447 −0.693823
\(15\) −13.1441 −0.226252
\(16\) −58.3857 −0.912277
\(17\) −54.4270 −0.776499 −0.388250 0.921554i \(-0.626920\pi\)
−0.388250 + 0.921554i \(0.626920\pi\)
\(18\) −37.8152 −0.495174
\(19\) 136.251 1.64516 0.822580 0.568649i \(-0.192534\pi\)
0.822580 + 0.568649i \(0.192534\pi\)
\(20\) 18.8774 0.211055
\(21\) −53.6420 −0.557412
\(22\) −12.0868 −0.117133
\(23\) 153.274 1.38956 0.694780 0.719223i \(-0.255502\pi\)
0.694780 + 0.719223i \(0.255502\pi\)
\(24\) 15.9506 0.135663
\(25\) −120.236 −0.961891
\(26\) −64.9786 −0.490129
\(27\) 106.789 0.761167
\(28\) 77.0401 0.519972
\(29\) 69.4344 0.444608 0.222304 0.974977i \(-0.428642\pi\)
0.222304 + 0.974977i \(0.428642\pi\)
\(30\) 53.6321 0.326395
\(31\) −13.1165 −0.0759935 −0.0379968 0.999278i \(-0.512098\pi\)
−0.0379968 + 0.999278i \(0.512098\pi\)
\(32\) 259.422 1.43312
\(33\) −17.8393 −0.0941036
\(34\) 222.080 1.12019
\(35\) 19.4408 0.0938886
\(36\) 80.1572 0.371098
\(37\) −306.611 −1.36234 −0.681168 0.732127i \(-0.738528\pi\)
−0.681168 + 0.732127i \(0.738528\pi\)
\(38\) −555.948 −2.37333
\(39\) −95.9035 −0.393765
\(40\) −5.78080 −0.0228506
\(41\) −27.1862 −0.103555 −0.0517776 0.998659i \(-0.516489\pi\)
−0.0517776 + 0.998659i \(0.516489\pi\)
\(42\) 218.877 0.804131
\(43\) 0 0
\(44\) 25.6206 0.0877829
\(45\) 20.2274 0.0670072
\(46\) −625.409 −2.00460
\(47\) −621.994 −1.93037 −0.965183 0.261576i \(-0.915758\pi\)
−0.965183 + 0.261576i \(0.915758\pi\)
\(48\) 351.614 1.05732
\(49\) −263.660 −0.768689
\(50\) 490.604 1.38764
\(51\) 327.774 0.899951
\(52\) 137.736 0.367317
\(53\) −97.9357 −0.253821 −0.126910 0.991914i \(-0.540506\pi\)
−0.126910 + 0.991914i \(0.540506\pi\)
\(54\) −435.734 −1.09807
\(55\) 6.46527 0.0158505
\(56\) −23.5919 −0.0562965
\(57\) −820.538 −1.90672
\(58\) −283.315 −0.641399
\(59\) −417.172 −0.920529 −0.460264 0.887782i \(-0.652245\pi\)
−0.460264 + 0.887782i \(0.652245\pi\)
\(60\) −113.684 −0.244610
\(61\) −608.416 −1.27704 −0.638522 0.769604i \(-0.720454\pi\)
−0.638522 + 0.769604i \(0.720454\pi\)
\(62\) 53.5198 0.109629
\(63\) 82.5498 0.165084
\(64\) −591.443 −1.15516
\(65\) 34.7572 0.0663245
\(66\) 72.7902 0.135755
\(67\) 772.902 1.40933 0.704664 0.709541i \(-0.251098\pi\)
0.704664 + 0.709541i \(0.251098\pi\)
\(68\) −470.745 −0.839504
\(69\) −923.057 −1.61048
\(70\) −79.3251 −0.135445
\(71\) 858.225 1.43454 0.717272 0.696793i \(-0.245391\pi\)
0.717272 + 0.696793i \(0.245391\pi\)
\(72\) −24.5464 −0.0401781
\(73\) 14.7922 0.0237164 0.0118582 0.999930i \(-0.496225\pi\)
0.0118582 + 0.999930i \(0.496225\pi\)
\(74\) 1251.07 1.96533
\(75\) 724.095 1.11482
\(76\) 1178.45 1.77865
\(77\) 26.3853 0.0390505
\(78\) 391.318 0.568052
\(79\) 872.351 1.24237 0.621185 0.783664i \(-0.286652\pi\)
0.621185 + 0.783664i \(0.286652\pi\)
\(80\) −127.431 −0.178091
\(81\) −893.337 −1.22543
\(82\) 110.929 0.149390
\(83\) −1057.72 −1.39880 −0.699399 0.714732i \(-0.746549\pi\)
−0.699399 + 0.714732i \(0.746549\pi\)
\(84\) −463.956 −0.602640
\(85\) −118.791 −0.151585
\(86\) 0 0
\(87\) −418.152 −0.515295
\(88\) −7.84576 −0.00950411
\(89\) −444.661 −0.529596 −0.264798 0.964304i \(-0.585305\pi\)
−0.264798 + 0.964304i \(0.585305\pi\)
\(90\) −82.5346 −0.0966656
\(91\) 141.847 0.163402
\(92\) 1325.69 1.50231
\(93\) 78.9912 0.0880754
\(94\) 2537.94 2.78478
\(95\) 297.378 0.321161
\(96\) −1562.31 −1.66096
\(97\) 150.389 0.157420 0.0787098 0.996898i \(-0.474920\pi\)
0.0787098 + 0.996898i \(0.474920\pi\)
\(98\) 1075.82 1.10892
\(99\) 27.4529 0.0278699
\(100\) −1039.94 −1.03994
\(101\) 400.658 0.394722 0.197361 0.980331i \(-0.436763\pi\)
0.197361 + 0.980331i \(0.436763\pi\)
\(102\) −1337.43 −1.29828
\(103\) 956.042 0.914579 0.457290 0.889318i \(-0.348820\pi\)
0.457290 + 0.889318i \(0.348820\pi\)
\(104\) −42.1786 −0.0397688
\(105\) −117.078 −0.108816
\(106\) 399.610 0.366166
\(107\) 589.174 0.532314 0.266157 0.963930i \(-0.414246\pi\)
0.266157 + 0.963930i \(0.414246\pi\)
\(108\) 923.629 0.822928
\(109\) 845.145 0.742662 0.371331 0.928500i \(-0.378901\pi\)
0.371331 + 0.928500i \(0.378901\pi\)
\(110\) −26.3805 −0.0228662
\(111\) 1846.49 1.57893
\(112\) −520.058 −0.438758
\(113\) −216.642 −0.180353 −0.0901767 0.995926i \(-0.528743\pi\)
−0.0901767 + 0.995926i \(0.528743\pi\)
\(114\) 3348.07 2.75066
\(115\) 334.533 0.271264
\(116\) 600.546 0.480684
\(117\) 147.586 0.116618
\(118\) 1702.20 1.32797
\(119\) −484.797 −0.373456
\(120\) 34.8135 0.0264835
\(121\) −1322.23 −0.993407
\(122\) 2482.54 1.84228
\(123\) 163.722 0.120019
\(124\) −113.446 −0.0821596
\(125\) −535.247 −0.382992
\(126\) −336.831 −0.238153
\(127\) 448.568 0.313417 0.156708 0.987645i \(-0.449912\pi\)
0.156708 + 0.987645i \(0.449912\pi\)
\(128\) 337.906 0.233336
\(129\) 0 0
\(130\) −141.821 −0.0956808
\(131\) 1293.46 0.862675 0.431338 0.902191i \(-0.358042\pi\)
0.431338 + 0.902191i \(0.358042\pi\)
\(132\) −154.294 −0.101739
\(133\) 1213.62 0.791237
\(134\) −3153.70 −2.03312
\(135\) 233.075 0.148592
\(136\) 144.156 0.0908917
\(137\) 2103.91 1.31204 0.656019 0.754744i \(-0.272239\pi\)
0.656019 + 0.754744i \(0.272239\pi\)
\(138\) 3766.38 2.32330
\(139\) −2683.27 −1.63735 −0.818676 0.574255i \(-0.805292\pi\)
−0.818676 + 0.574255i \(0.805292\pi\)
\(140\) 168.146 0.101507
\(141\) 3745.81 2.23727
\(142\) −3501.85 −2.06950
\(143\) 47.1728 0.0275859
\(144\) −541.100 −0.313136
\(145\) 151.546 0.0867945
\(146\) −60.3571 −0.0342136
\(147\) 1587.83 0.890899
\(148\) −2651.91 −1.47288
\(149\) −2733.30 −1.50283 −0.751413 0.659832i \(-0.770627\pi\)
−0.751413 + 0.659832i \(0.770627\pi\)
\(150\) −2954.55 −1.60825
\(151\) 2187.16 1.17873 0.589367 0.807865i \(-0.299377\pi\)
0.589367 + 0.807865i \(0.299377\pi\)
\(152\) −360.875 −0.192571
\(153\) −504.411 −0.266531
\(154\) −107.661 −0.0563348
\(155\) −28.6278 −0.0148351
\(156\) −829.480 −0.425715
\(157\) 2618.77 1.33122 0.665608 0.746302i \(-0.268172\pi\)
0.665608 + 0.746302i \(0.268172\pi\)
\(158\) −3559.48 −1.79226
\(159\) 589.795 0.294175
\(160\) 566.209 0.279767
\(161\) 1365.26 0.668306
\(162\) 3645.11 1.76782
\(163\) 556.769 0.267543 0.133772 0.991012i \(-0.457291\pi\)
0.133772 + 0.991012i \(0.457291\pi\)
\(164\) −235.136 −0.111958
\(165\) −38.9356 −0.0183705
\(166\) 4315.86 2.01793
\(167\) −84.4752 −0.0391430 −0.0195715 0.999808i \(-0.506230\pi\)
−0.0195715 + 0.999808i \(0.506230\pi\)
\(168\) 142.077 0.0652468
\(169\) −1943.40 −0.884570
\(170\) 484.707 0.218679
\(171\) 1262.73 0.564697
\(172\) 0 0
\(173\) −1870.04 −0.821829 −0.410914 0.911674i \(-0.634790\pi\)
−0.410914 + 0.911674i \(0.634790\pi\)
\(174\) 1706.20 0.743372
\(175\) −1070.98 −0.462620
\(176\) −172.951 −0.0740721
\(177\) 2512.32 1.06688
\(178\) 1814.37 0.764003
\(179\) −590.661 −0.246637 −0.123319 0.992367i \(-0.539354\pi\)
−0.123319 + 0.992367i \(0.539354\pi\)
\(180\) 174.949 0.0724441
\(181\) 1963.05 0.806147 0.403073 0.915168i \(-0.367942\pi\)
0.403073 + 0.915168i \(0.367942\pi\)
\(182\) −578.783 −0.235726
\(183\) 3664.04 1.48007
\(184\) −405.963 −0.162652
\(185\) −669.201 −0.265949
\(186\) −322.311 −0.127059
\(187\) −161.225 −0.0630477
\(188\) −5379.70 −2.08699
\(189\) 951.198 0.366082
\(190\) −1213.40 −0.463312
\(191\) −3347.99 −1.26833 −0.634167 0.773196i \(-0.718657\pi\)
−0.634167 + 0.773196i \(0.718657\pi\)
\(192\) 3561.82 1.33881
\(193\) 3819.93 1.42469 0.712344 0.701831i \(-0.247634\pi\)
0.712344 + 0.701831i \(0.247634\pi\)
\(194\) −613.637 −0.227096
\(195\) −209.317 −0.0768692
\(196\) −2280.43 −0.831060
\(197\) 3154.91 1.14100 0.570502 0.821296i \(-0.306749\pi\)
0.570502 + 0.821296i \(0.306749\pi\)
\(198\) −112.017 −0.0402055
\(199\) 5307.46 1.89063 0.945317 0.326154i \(-0.105753\pi\)
0.945317 + 0.326154i \(0.105753\pi\)
\(200\) 318.459 0.112592
\(201\) −4654.62 −1.63339
\(202\) −1634.82 −0.569432
\(203\) 618.472 0.213834
\(204\) 2834.95 0.972973
\(205\) −59.3359 −0.0202156
\(206\) −3900.97 −1.31939
\(207\) 1420.49 0.476962
\(208\) −929.782 −0.309946
\(209\) 403.604 0.133578
\(210\) 477.717 0.156979
\(211\) −2869.87 −0.936352 −0.468176 0.883635i \(-0.655089\pi\)
−0.468176 + 0.883635i \(0.655089\pi\)
\(212\) −847.058 −0.274416
\(213\) −5168.46 −1.66262
\(214\) −2404.02 −0.767924
\(215\) 0 0
\(216\) −282.842 −0.0890970
\(217\) −116.833 −0.0365489
\(218\) −3448.47 −1.07138
\(219\) −89.0825 −0.0274869
\(220\) 55.9189 0.0171366
\(221\) −866.740 −0.263816
\(222\) −7534.29 −2.27779
\(223\) −6510.38 −1.95501 −0.977506 0.210908i \(-0.932358\pi\)
−0.977506 + 0.210908i \(0.932358\pi\)
\(224\) 2310.75 0.689255
\(225\) −1114.31 −0.330166
\(226\) 883.970 0.260181
\(227\) 1210.57 0.353958 0.176979 0.984215i \(-0.443368\pi\)
0.176979 + 0.984215i \(0.443368\pi\)
\(228\) −7096.93 −2.06143
\(229\) −1712.57 −0.494192 −0.247096 0.968991i \(-0.579476\pi\)
−0.247096 + 0.968991i \(0.579476\pi\)
\(230\) −1365.00 −0.391329
\(231\) −158.899 −0.0452589
\(232\) −183.905 −0.0520428
\(233\) −4497.51 −1.26456 −0.632278 0.774741i \(-0.717880\pi\)
−0.632278 + 0.774741i \(0.717880\pi\)
\(234\) −602.200 −0.168235
\(235\) −1357.55 −0.376838
\(236\) −3608.17 −0.995220
\(237\) −5253.53 −1.43989
\(238\) 1978.13 0.538753
\(239\) 6253.68 1.69254 0.846270 0.532754i \(-0.178843\pi\)
0.846270 + 0.532754i \(0.178843\pi\)
\(240\) 767.425 0.206405
\(241\) 4314.12 1.15310 0.576550 0.817062i \(-0.304399\pi\)
0.576550 + 0.817062i \(0.304399\pi\)
\(242\) 5395.12 1.43310
\(243\) 2496.62 0.659087
\(244\) −5262.26 −1.38066
\(245\) −575.459 −0.150060
\(246\) −668.041 −0.173141
\(247\) 2169.77 0.558943
\(248\) 34.7406 0.00889528
\(249\) 6369.89 1.62119
\(250\) 2183.99 0.552510
\(251\) −6821.84 −1.71550 −0.857750 0.514067i \(-0.828138\pi\)
−0.857750 + 0.514067i \(0.828138\pi\)
\(252\) 713.983 0.178479
\(253\) 454.032 0.112825
\(254\) −1830.31 −0.452140
\(255\) 715.392 0.175685
\(256\) 3352.77 0.818548
\(257\) 2048.98 0.497322 0.248661 0.968591i \(-0.420009\pi\)
0.248661 + 0.968591i \(0.420009\pi\)
\(258\) 0 0
\(259\) −2731.07 −0.655213
\(260\) 300.619 0.0717061
\(261\) 643.495 0.152611
\(262\) −5277.76 −1.24451
\(263\) −2225.75 −0.521847 −0.260923 0.965360i \(-0.584027\pi\)
−0.260923 + 0.965360i \(0.584027\pi\)
\(264\) 47.2493 0.0110151
\(265\) −213.752 −0.0495498
\(266\) −4951.99 −1.14145
\(267\) 2677.87 0.613794
\(268\) 6684.92 1.52368
\(269\) −639.777 −0.145011 −0.0725054 0.997368i \(-0.523099\pi\)
−0.0725054 + 0.997368i \(0.523099\pi\)
\(270\) −951.023 −0.214361
\(271\) 2033.22 0.455754 0.227877 0.973690i \(-0.426822\pi\)
0.227877 + 0.973690i \(0.426822\pi\)
\(272\) 3177.76 0.708382
\(273\) −854.240 −0.189381
\(274\) −8584.66 −1.89277
\(275\) −356.166 −0.0781005
\(276\) −7983.63 −1.74115
\(277\) 855.321 0.185528 0.0927640 0.995688i \(-0.470430\pi\)
0.0927640 + 0.995688i \(0.470430\pi\)
\(278\) 10948.6 2.36207
\(279\) −121.560 −0.0260845
\(280\) −51.4912 −0.0109900
\(281\) 6456.77 1.37074 0.685372 0.728194i \(-0.259640\pi\)
0.685372 + 0.728194i \(0.259640\pi\)
\(282\) −15284.2 −3.22751
\(283\) 2550.24 0.535676 0.267838 0.963464i \(-0.413691\pi\)
0.267838 + 0.963464i \(0.413691\pi\)
\(284\) 7422.89 1.55094
\(285\) −1790.89 −0.372221
\(286\) −192.481 −0.0397959
\(287\) −242.155 −0.0498047
\(288\) 2404.24 0.491913
\(289\) −1950.70 −0.397049
\(290\) −618.358 −0.125211
\(291\) −905.683 −0.182447
\(292\) 127.939 0.0256407
\(293\) −5438.66 −1.08440 −0.542201 0.840249i \(-0.682409\pi\)
−0.542201 + 0.840249i \(0.682409\pi\)
\(294\) −6478.88 −1.28523
\(295\) −910.511 −0.179702
\(296\) 812.092 0.159466
\(297\) 316.332 0.0618028
\(298\) 11152.8 2.16800
\(299\) 2440.86 0.472103
\(300\) 6262.78 1.20527
\(301\) 0 0
\(302\) −8924.36 −1.70046
\(303\) −2412.87 −0.457477
\(304\) −7955.09 −1.50084
\(305\) −1327.91 −0.249299
\(306\) 2058.17 0.384502
\(307\) −5098.12 −0.947769 −0.473884 0.880587i \(-0.657149\pi\)
−0.473884 + 0.880587i \(0.657149\pi\)
\(308\) 228.210 0.0422190
\(309\) −5757.54 −1.05998
\(310\) 116.811 0.0214014
\(311\) 608.278 0.110908 0.0554539 0.998461i \(-0.482339\pi\)
0.0554539 + 0.998461i \(0.482339\pi\)
\(312\) 254.011 0.0460915
\(313\) −8591.81 −1.55156 −0.775779 0.631005i \(-0.782643\pi\)
−0.775779 + 0.631005i \(0.782643\pi\)
\(314\) −10685.5 −1.92043
\(315\) 180.171 0.0322270
\(316\) 7545.07 1.34317
\(317\) −3275.74 −0.580391 −0.290196 0.956967i \(-0.593720\pi\)
−0.290196 + 0.956967i \(0.593720\pi\)
\(318\) −2406.56 −0.424381
\(319\) 205.680 0.0360999
\(320\) −1290.87 −0.225506
\(321\) −3548.16 −0.616944
\(322\) −5570.70 −0.964108
\(323\) −7415.72 −1.27747
\(324\) −7726.58 −1.32486
\(325\) −1914.74 −0.326802
\(326\) −2271.80 −0.385962
\(327\) −5089.69 −0.860735
\(328\) 72.0055 0.0121215
\(329\) −5540.28 −0.928406
\(330\) 158.870 0.0265016
\(331\) 7793.65 1.29419 0.647096 0.762409i \(-0.275983\pi\)
0.647096 + 0.762409i \(0.275983\pi\)
\(332\) −9148.37 −1.51230
\(333\) −2841.57 −0.467618
\(334\) 344.687 0.0564684
\(335\) 1686.92 0.275123
\(336\) 3131.93 0.508514
\(337\) −1219.14 −0.197065 −0.0985324 0.995134i \(-0.531415\pi\)
−0.0985324 + 0.995134i \(0.531415\pi\)
\(338\) 7929.72 1.27609
\(339\) 1304.67 0.209027
\(340\) −1027.44 −0.163884
\(341\) −38.8540 −0.00617028
\(342\) −5152.34 −0.814640
\(343\) −5403.70 −0.850648
\(344\) 0 0
\(345\) −2014.64 −0.314391
\(346\) 7630.38 1.18558
\(347\) 8942.44 1.38344 0.691722 0.722164i \(-0.256852\pi\)
0.691722 + 0.722164i \(0.256852\pi\)
\(348\) −3616.65 −0.557105
\(349\) −11578.0 −1.77581 −0.887904 0.460030i \(-0.847839\pi\)
−0.887904 + 0.460030i \(0.847839\pi\)
\(350\) 4369.95 0.667382
\(351\) 1700.59 0.258607
\(352\) 768.465 0.116362
\(353\) −7587.38 −1.14401 −0.572005 0.820250i \(-0.693834\pi\)
−0.572005 + 0.820250i \(0.693834\pi\)
\(354\) −10251.1 −1.53910
\(355\) 1873.14 0.280045
\(356\) −3845.93 −0.572567
\(357\) 2919.57 0.432830
\(358\) 2410.09 0.355803
\(359\) 8406.81 1.23592 0.617959 0.786211i \(-0.287960\pi\)
0.617959 + 0.786211i \(0.287960\pi\)
\(360\) −53.5745 −0.00784340
\(361\) 11705.3 1.70655
\(362\) −8009.91 −1.16296
\(363\) 7962.79 1.15134
\(364\) 1226.85 0.176661
\(365\) 32.2851 0.00462981
\(366\) −14950.5 −2.13518
\(367\) −5733.44 −0.815486 −0.407743 0.913097i \(-0.633684\pi\)
−0.407743 + 0.913097i \(0.633684\pi\)
\(368\) −8949.02 −1.26766
\(369\) −251.952 −0.0355450
\(370\) 2730.56 0.383663
\(371\) −872.341 −0.122075
\(372\) 683.204 0.0952218
\(373\) 3701.87 0.513875 0.256938 0.966428i \(-0.417286\pi\)
0.256938 + 0.966428i \(0.417286\pi\)
\(374\) 657.850 0.0909536
\(375\) 3223.40 0.443882
\(376\) 1647.42 0.225955
\(377\) 1105.73 0.151056
\(378\) −3881.20 −0.528115
\(379\) −1981.11 −0.268504 −0.134252 0.990947i \(-0.542863\pi\)
−0.134252 + 0.990947i \(0.542863\pi\)
\(380\) 2572.05 0.347220
\(381\) −2701.39 −0.363246
\(382\) 13660.9 1.82972
\(383\) −4324.44 −0.576942 −0.288471 0.957489i \(-0.593147\pi\)
−0.288471 + 0.957489i \(0.593147\pi\)
\(384\) −2034.96 −0.270433
\(385\) 57.5880 0.00762327
\(386\) −15586.6 −2.05528
\(387\) 0 0
\(388\) 1300.73 0.170192
\(389\) −13257.2 −1.72793 −0.863967 0.503548i \(-0.832028\pi\)
−0.863967 + 0.503548i \(0.832028\pi\)
\(390\) 854.082 0.110893
\(391\) −8342.25 −1.07899
\(392\) 698.333 0.0899774
\(393\) −7789.58 −0.999828
\(394\) −12873.1 −1.64603
\(395\) 1903.97 0.242530
\(396\) 237.443 0.0301312
\(397\) 2355.52 0.297784 0.148892 0.988853i \(-0.452429\pi\)
0.148892 + 0.988853i \(0.452429\pi\)
\(398\) −21656.2 −2.72746
\(399\) −7308.76 −0.917032
\(400\) 7020.09 0.877511
\(401\) −3462.47 −0.431191 −0.215595 0.976483i \(-0.569169\pi\)
−0.215595 + 0.976483i \(0.569169\pi\)
\(402\) 18992.4 2.35636
\(403\) −208.878 −0.0258188
\(404\) 3465.33 0.426750
\(405\) −1949.78 −0.239223
\(406\) −2523.57 −0.308480
\(407\) −908.248 −0.110615
\(408\) −868.145 −0.105342
\(409\) 7101.00 0.858489 0.429244 0.903188i \(-0.358780\pi\)
0.429244 + 0.903188i \(0.358780\pi\)
\(410\) 242.110 0.0291633
\(411\) −12670.3 −1.52063
\(412\) 8268.92 0.988788
\(413\) −3715.87 −0.442727
\(414\) −5796.09 −0.688073
\(415\) −2308.56 −0.273067
\(416\) 4131.25 0.486902
\(417\) 16159.4 1.89767
\(418\) −1646.84 −0.192702
\(419\) −7575.88 −0.883308 −0.441654 0.897185i \(-0.645608\pi\)
−0.441654 + 0.897185i \(0.645608\pi\)
\(420\) −1012.62 −0.117645
\(421\) 2054.30 0.237816 0.118908 0.992905i \(-0.462061\pi\)
0.118908 + 0.992905i \(0.462061\pi\)
\(422\) 11710.0 1.35080
\(423\) −5764.44 −0.662592
\(424\) 259.394 0.0297105
\(425\) 6544.10 0.746907
\(426\) 21089.0 2.39851
\(427\) −5419.33 −0.614192
\(428\) 5095.83 0.575505
\(429\) −284.087 −0.0319717
\(430\) 0 0
\(431\) −17175.1 −1.91948 −0.959742 0.280884i \(-0.909372\pi\)
−0.959742 + 0.280884i \(0.909372\pi\)
\(432\) −6234.94 −0.694395
\(433\) 7628.21 0.846624 0.423312 0.905984i \(-0.360867\pi\)
0.423312 + 0.905984i \(0.360867\pi\)
\(434\) 476.716 0.0527261
\(435\) −912.650 −0.100594
\(436\) 7309.76 0.802922
\(437\) 20883.7 2.28605
\(438\) 363.486 0.0396531
\(439\) −6478.18 −0.704298 −0.352149 0.935944i \(-0.614549\pi\)
−0.352149 + 0.935944i \(0.614549\pi\)
\(440\) −17.1240 −0.00185535
\(441\) −2443.52 −0.263850
\(442\) 3536.59 0.380584
\(443\) 3350.48 0.359336 0.179668 0.983727i \(-0.442498\pi\)
0.179668 + 0.983727i \(0.442498\pi\)
\(444\) 15970.5 1.70704
\(445\) −970.508 −0.103385
\(446\) 26564.5 2.82033
\(447\) 16460.7 1.74175
\(448\) −5268.15 −0.555573
\(449\) −14358.1 −1.50913 −0.754567 0.656223i \(-0.772153\pi\)
−0.754567 + 0.656223i \(0.772153\pi\)
\(450\) 4546.76 0.476303
\(451\) −80.5313 −0.00840814
\(452\) −1873.76 −0.194987
\(453\) −13171.7 −1.36614
\(454\) −4939.53 −0.510625
\(455\) 309.592 0.0318987
\(456\) 2173.28 0.223187
\(457\) −3151.07 −0.322540 −0.161270 0.986910i \(-0.551559\pi\)
−0.161270 + 0.986910i \(0.551559\pi\)
\(458\) 6987.86 0.712929
\(459\) −5812.19 −0.591046
\(460\) 2893.41 0.293274
\(461\) 1289.67 0.130295 0.0651475 0.997876i \(-0.479248\pi\)
0.0651475 + 0.997876i \(0.479248\pi\)
\(462\) 648.363 0.0652912
\(463\) 9807.31 0.984416 0.492208 0.870478i \(-0.336190\pi\)
0.492208 + 0.870478i \(0.336190\pi\)
\(464\) −4053.98 −0.405606
\(465\) 172.404 0.0171937
\(466\) 18351.3 1.82427
\(467\) −2759.08 −0.273394 −0.136697 0.990613i \(-0.543649\pi\)
−0.136697 + 0.990613i \(0.543649\pi\)
\(468\) 1276.49 0.126081
\(469\) 6884.46 0.677814
\(470\) 5539.26 0.543632
\(471\) −15770.9 −1.54286
\(472\) 1104.93 0.107751
\(473\) 0 0
\(474\) 21436.1 2.07720
\(475\) −16382.3 −1.58246
\(476\) −4193.06 −0.403758
\(477\) −907.636 −0.0871233
\(478\) −25517.1 −2.44168
\(479\) 6246.31 0.595828 0.297914 0.954593i \(-0.403709\pi\)
0.297914 + 0.954593i \(0.403709\pi\)
\(480\) −3409.86 −0.324246
\(481\) −4882.72 −0.462854
\(482\) −17603.0 −1.66348
\(483\) −8221.93 −0.774557
\(484\) −11436.1 −1.07401
\(485\) 328.236 0.0307308
\(486\) −10187.0 −0.950809
\(487\) −7223.74 −0.672154 −0.336077 0.941835i \(-0.609100\pi\)
−0.336077 + 0.941835i \(0.609100\pi\)
\(488\) 1611.46 0.149482
\(489\) −3353.01 −0.310079
\(490\) 2348.06 0.216479
\(491\) 9289.33 0.853812 0.426906 0.904296i \(-0.359603\pi\)
0.426906 + 0.904296i \(0.359603\pi\)
\(492\) 1416.05 0.129757
\(493\) −3779.11 −0.345238
\(494\) −8853.37 −0.806340
\(495\) 59.9180 0.00544064
\(496\) 765.818 0.0693271
\(497\) 7644.46 0.689941
\(498\) −25991.3 −2.33875
\(499\) 3220.27 0.288896 0.144448 0.989512i \(-0.453859\pi\)
0.144448 + 0.989512i \(0.453859\pi\)
\(500\) −4629.42 −0.414068
\(501\) 508.732 0.0453662
\(502\) 27835.4 2.47481
\(503\) −164.938 −0.0146207 −0.00731035 0.999973i \(-0.502327\pi\)
−0.00731035 + 0.999973i \(0.502327\pi\)
\(504\) −218.642 −0.0193236
\(505\) 874.466 0.0770559
\(506\) −1852.60 −0.162763
\(507\) 11703.7 1.02520
\(508\) 3879.71 0.338847
\(509\) −11574.1 −1.00788 −0.503940 0.863738i \(-0.668117\pi\)
−0.503940 + 0.863738i \(0.668117\pi\)
\(510\) −2919.04 −0.253445
\(511\) 131.758 0.0114063
\(512\) −16383.7 −1.41419
\(513\) 14550.0 1.25224
\(514\) −8360.52 −0.717445
\(515\) 2086.64 0.178540
\(516\) 0 0
\(517\) −1842.48 −0.156736
\(518\) 11143.7 0.945221
\(519\) 11261.9 0.952487
\(520\) −92.0581 −0.00776349
\(521\) −16300.3 −1.37069 −0.685343 0.728220i \(-0.740348\pi\)
−0.685343 + 0.728220i \(0.740348\pi\)
\(522\) −2625.67 −0.220158
\(523\) 12912.3 1.07957 0.539785 0.841803i \(-0.318506\pi\)
0.539785 + 0.841803i \(0.318506\pi\)
\(524\) 11187.3 0.932672
\(525\) 6449.72 0.536169
\(526\) 9081.81 0.752824
\(527\) 713.893 0.0590089
\(528\) 1041.56 0.0858485
\(529\) 11326.0 0.930875
\(530\) 872.181 0.0714813
\(531\) −3866.22 −0.315969
\(532\) 10496.8 0.855437
\(533\) −432.935 −0.0351829
\(534\) −10926.6 −0.885468
\(535\) 1285.92 0.103916
\(536\) −2047.12 −0.164966
\(537\) 3557.12 0.285849
\(538\) 2610.50 0.209195
\(539\) −781.020 −0.0624135
\(540\) 2015.89 0.160648
\(541\) −2148.68 −0.170756 −0.0853780 0.996349i \(-0.527210\pi\)
−0.0853780 + 0.996349i \(0.527210\pi\)
\(542\) −8296.22 −0.657478
\(543\) −11822.0 −0.934312
\(544\) −14119.6 −1.11281
\(545\) 1844.59 0.144979
\(546\) 3485.58 0.273204
\(547\) −7515.40 −0.587450 −0.293725 0.955890i \(-0.594895\pi\)
−0.293725 + 0.955890i \(0.594895\pi\)
\(548\) 18197.0 1.41850
\(549\) −5638.60 −0.438341
\(550\) 1453.28 0.112669
\(551\) 9460.49 0.731452
\(552\) 2444.82 0.188512
\(553\) 7770.28 0.597515
\(554\) −3489.99 −0.267646
\(555\) 4030.11 0.308232
\(556\) −23207.9 −1.77021
\(557\) 13442.7 1.02259 0.511297 0.859404i \(-0.329165\pi\)
0.511297 + 0.859404i \(0.329165\pi\)
\(558\) 496.004 0.0376300
\(559\) 0 0
\(560\) −1135.07 −0.0856524
\(561\) 970.938 0.0730713
\(562\) −26345.8 −1.97746
\(563\) 14488.6 1.08458 0.542291 0.840191i \(-0.317557\pi\)
0.542291 + 0.840191i \(0.317557\pi\)
\(564\) 32398.0 2.41880
\(565\) −472.837 −0.0352078
\(566\) −10405.8 −0.772774
\(567\) −7957.21 −0.589368
\(568\) −2273.10 −0.167918
\(569\) −7940.71 −0.585047 −0.292524 0.956258i \(-0.594495\pi\)
−0.292524 + 0.956258i \(0.594495\pi\)
\(570\) 7307.41 0.536972
\(571\) −16716.9 −1.22518 −0.612592 0.790400i \(-0.709873\pi\)
−0.612592 + 0.790400i \(0.709873\pi\)
\(572\) 408.003 0.0298242
\(573\) 20162.5 1.46998
\(574\) 988.072 0.0718490
\(575\) −18429.1 −1.33660
\(576\) −5481.29 −0.396506
\(577\) 22899.6 1.65221 0.826104 0.563518i \(-0.190552\pi\)
0.826104 + 0.563518i \(0.190552\pi\)
\(578\) 7959.51 0.572789
\(579\) −23004.6 −1.65119
\(580\) 1310.74 0.0938370
\(581\) −9421.44 −0.672749
\(582\) 3695.49 0.263201
\(583\) −290.107 −0.0206089
\(584\) −39.1788 −0.00277608
\(585\) 322.118 0.0227657
\(586\) 22191.6 1.56438
\(587\) −21550.7 −1.51532 −0.757661 0.652648i \(-0.773658\pi\)
−0.757661 + 0.652648i \(0.773658\pi\)
\(588\) 13733.3 0.963186
\(589\) −1787.14 −0.125022
\(590\) 3715.19 0.259240
\(591\) −18999.7 −1.32241
\(592\) 17901.7 1.24283
\(593\) 26777.0 1.85430 0.927149 0.374694i \(-0.122252\pi\)
0.927149 + 0.374694i \(0.122252\pi\)
\(594\) −1290.74 −0.0891577
\(595\) −1058.11 −0.0729044
\(596\) −23640.7 −1.62476
\(597\) −31962.9 −2.19122
\(598\) −9959.53 −0.681063
\(599\) −8296.25 −0.565903 −0.282951 0.959134i \(-0.591313\pi\)
−0.282951 + 0.959134i \(0.591313\pi\)
\(600\) −1917.85 −0.130493
\(601\) −1874.08 −0.127197 −0.0635984 0.997976i \(-0.520258\pi\)
−0.0635984 + 0.997976i \(0.520258\pi\)
\(602\) 0 0
\(603\) 7163.00 0.483748
\(604\) 18917.0 1.27438
\(605\) −2885.86 −0.193929
\(606\) 9845.30 0.659963
\(607\) 2574.28 0.172136 0.0860681 0.996289i \(-0.472570\pi\)
0.0860681 + 0.996289i \(0.472570\pi\)
\(608\) 35346.4 2.35771
\(609\) −3724.60 −0.247830
\(610\) 5418.33 0.359642
\(611\) −9905.15 −0.655842
\(612\) −4362.71 −0.288157
\(613\) 8303.26 0.547089 0.273545 0.961859i \(-0.411804\pi\)
0.273545 + 0.961859i \(0.411804\pi\)
\(614\) 20802.0 1.36727
\(615\) 357.336 0.0234296
\(616\) −69.8844 −0.00457098
\(617\) −28299.9 −1.84653 −0.923267 0.384159i \(-0.874491\pi\)
−0.923267 + 0.384159i \(0.874491\pi\)
\(618\) 23492.7 1.52915
\(619\) −24822.2 −1.61178 −0.805888 0.592069i \(-0.798311\pi\)
−0.805888 + 0.592069i \(0.798311\pi\)
\(620\) −247.606 −0.0160388
\(621\) 16368.0 1.05769
\(622\) −2481.98 −0.159997
\(623\) −3960.73 −0.254708
\(624\) 5599.39 0.359223
\(625\) 13861.3 0.887125
\(626\) 35057.4 2.23830
\(627\) −2430.61 −0.154816
\(628\) 22650.1 1.43923
\(629\) 16687.9 1.05785
\(630\) −735.159 −0.0464911
\(631\) −15805.6 −0.997162 −0.498581 0.866843i \(-0.666145\pi\)
−0.498581 + 0.866843i \(0.666145\pi\)
\(632\) −2310.52 −0.145423
\(633\) 17283.1 1.08522
\(634\) 13366.1 0.837281
\(635\) 979.034 0.0611839
\(636\) 5101.20 0.318044
\(637\) −4198.74 −0.261162
\(638\) −839.243 −0.0520783
\(639\) 7953.75 0.492403
\(640\) 737.506 0.0455508
\(641\) −4409.29 −0.271695 −0.135847 0.990730i \(-0.543376\pi\)
−0.135847 + 0.990730i \(0.543376\pi\)
\(642\) 14477.7 0.890013
\(643\) −22435.9 −1.37603 −0.688014 0.725698i \(-0.741517\pi\)
−0.688014 + 0.725698i \(0.741517\pi\)
\(644\) 11808.3 0.722532
\(645\) 0 0
\(646\) 30258.6 1.84289
\(647\) −7104.96 −0.431723 −0.215862 0.976424i \(-0.569256\pi\)
−0.215862 + 0.976424i \(0.569256\pi\)
\(648\) 2366.10 0.143440
\(649\) −1235.76 −0.0747422
\(650\) 7812.79 0.471450
\(651\) 703.597 0.0423597
\(652\) 4815.56 0.289252
\(653\) −6201.10 −0.371620 −0.185810 0.982586i \(-0.559491\pi\)
−0.185810 + 0.982586i \(0.559491\pi\)
\(654\) 20767.6 1.24171
\(655\) 2823.08 0.168408
\(656\) 1587.28 0.0944710
\(657\) 137.089 0.00814058
\(658\) 22606.2 1.33933
\(659\) −24325.9 −1.43794 −0.718971 0.695041i \(-0.755386\pi\)
−0.718971 + 0.695041i \(0.755386\pi\)
\(660\) −336.758 −0.0198611
\(661\) 4195.11 0.246855 0.123427 0.992354i \(-0.460611\pi\)
0.123427 + 0.992354i \(0.460611\pi\)
\(662\) −31800.7 −1.86702
\(663\) 5219.74 0.305758
\(664\) 2801.50 0.163734
\(665\) 2648.83 0.154462
\(666\) 11594.5 0.674593
\(667\) 10642.5 0.617810
\(668\) −730.636 −0.0423191
\(669\) 39207.3 2.26583
\(670\) −6883.19 −0.396897
\(671\) −1802.26 −0.103689
\(672\) −13915.9 −0.798837
\(673\) 30476.3 1.74558 0.872789 0.488097i \(-0.162309\pi\)
0.872789 + 0.488097i \(0.162309\pi\)
\(674\) 4974.50 0.284289
\(675\) −12839.9 −0.732160
\(676\) −16808.7 −0.956343
\(677\) −13889.1 −0.788482 −0.394241 0.919007i \(-0.628992\pi\)
−0.394241 + 0.919007i \(0.628992\pi\)
\(678\) −5323.50 −0.301545
\(679\) 1339.56 0.0757106
\(680\) 314.631 0.0177435
\(681\) −7290.38 −0.410232
\(682\) 158.537 0.00890134
\(683\) −10181.3 −0.570388 −0.285194 0.958470i \(-0.592058\pi\)
−0.285194 + 0.958470i \(0.592058\pi\)
\(684\) 10921.5 0.610516
\(685\) 4591.95 0.256130
\(686\) 22048.9 1.22716
\(687\) 10313.6 0.572761
\(688\) 0 0
\(689\) −1559.61 −0.0862357
\(690\) 8220.42 0.453545
\(691\) −16877.9 −0.929182 −0.464591 0.885525i \(-0.653799\pi\)
−0.464591 + 0.885525i \(0.653799\pi\)
\(692\) −16174.2 −0.888511
\(693\) 244.531 0.0134040
\(694\) −36488.1 −1.99578
\(695\) −5856.44 −0.319637
\(696\) 1107.52 0.0603169
\(697\) 1479.66 0.0804105
\(698\) 47242.1 2.56181
\(699\) 27085.2 1.46560
\(700\) −9263.02 −0.500156
\(701\) −22820.0 −1.22953 −0.614765 0.788710i \(-0.710749\pi\)
−0.614765 + 0.788710i \(0.710749\pi\)
\(702\) −6938.98 −0.373070
\(703\) −41775.9 −2.24126
\(704\) −1751.98 −0.0937931
\(705\) 8175.53 0.436749
\(706\) 30959.1 1.65037
\(707\) 3568.77 0.189841
\(708\) 21729.4 1.15345
\(709\) 1810.88 0.0959226 0.0479613 0.998849i \(-0.484728\pi\)
0.0479613 + 0.998849i \(0.484728\pi\)
\(710\) −7643.05 −0.403998
\(711\) 8084.66 0.426440
\(712\) 1177.73 0.0619908
\(713\) −2010.43 −0.105597
\(714\) −11912.8 −0.624407
\(715\) 102.958 0.00538521
\(716\) −5108.69 −0.266649
\(717\) −37661.3 −1.96163
\(718\) −34302.6 −1.78295
\(719\) 16290.1 0.844951 0.422476 0.906374i \(-0.361161\pi\)
0.422476 + 0.906374i \(0.361161\pi\)
\(720\) −1180.99 −0.0611291
\(721\) 8515.74 0.439865
\(722\) −47761.3 −2.46190
\(723\) −25980.8 −1.33643
\(724\) 16978.7 0.871557
\(725\) −8348.54 −0.427665
\(726\) −32490.8 −1.66095
\(727\) −9094.37 −0.463950 −0.231975 0.972722i \(-0.574519\pi\)
−0.231975 + 0.972722i \(0.574519\pi\)
\(728\) −375.697 −0.0191267
\(729\) 9084.82 0.461557
\(730\) −131.734 −0.00667903
\(731\) 0 0
\(732\) 31690.7 1.60017
\(733\) −12269.4 −0.618256 −0.309128 0.951020i \(-0.600037\pi\)
−0.309128 + 0.951020i \(0.600037\pi\)
\(734\) 23394.4 1.17643
\(735\) 3465.57 0.173917
\(736\) 39762.7 1.99140
\(737\) 2289.51 0.114430
\(738\) 1028.05 0.0512778
\(739\) 1437.99 0.0715794 0.0357897 0.999359i \(-0.488605\pi\)
0.0357897 + 0.999359i \(0.488605\pi\)
\(740\) −5788.00 −0.287529
\(741\) −13066.9 −0.647807
\(742\) 3559.44 0.176107
\(743\) 28488.6 1.40666 0.703328 0.710865i \(-0.251696\pi\)
0.703328 + 0.710865i \(0.251696\pi\)
\(744\) −209.217 −0.0103095
\(745\) −5965.65 −0.293375
\(746\) −15104.9 −0.741325
\(747\) −9802.63 −0.480133
\(748\) −1394.45 −0.0681633
\(749\) 5247.94 0.256015
\(750\) −13152.5 −0.640351
\(751\) −16276.2 −0.790850 −0.395425 0.918498i \(-0.629403\pi\)
−0.395425 + 0.918498i \(0.629403\pi\)
\(752\) 36315.6 1.76103
\(753\) 41082.9 1.98824
\(754\) −4511.75 −0.217915
\(755\) 4773.65 0.230107
\(756\) 8227.02 0.395786
\(757\) 12549.2 0.602519 0.301259 0.953542i \(-0.402593\pi\)
0.301259 + 0.953542i \(0.402593\pi\)
\(758\) 8083.60 0.387348
\(759\) −2734.30 −0.130763
\(760\) −787.637 −0.0375929
\(761\) −20472.0 −0.975179 −0.487589 0.873073i \(-0.662124\pi\)
−0.487589 + 0.873073i \(0.662124\pi\)
\(762\) 11022.6 0.524024
\(763\) 7527.94 0.357182
\(764\) −28957.1 −1.37125
\(765\) −1100.92 −0.0520310
\(766\) 17645.2 0.832305
\(767\) −6643.39 −0.312750
\(768\) −20191.3 −0.948685
\(769\) 21892.6 1.02662 0.513309 0.858204i \(-0.328420\pi\)
0.513309 + 0.858204i \(0.328420\pi\)
\(770\) −234.978 −0.0109974
\(771\) −12339.5 −0.576389
\(772\) 33039.0 1.54029
\(773\) 33744.5 1.57012 0.785061 0.619419i \(-0.212632\pi\)
0.785061 + 0.619419i \(0.212632\pi\)
\(774\) 0 0
\(775\) 1577.08 0.0730975
\(776\) −398.322 −0.0184264
\(777\) 16447.2 0.759383
\(778\) 54093.8 2.49275
\(779\) −3704.13 −0.170365
\(780\) −1810.41 −0.0831063
\(781\) 2542.25 0.116477
\(782\) 34039.2 1.55657
\(783\) 7414.82 0.338421
\(784\) 15394.0 0.701257
\(785\) 5715.67 0.259874
\(786\) 31784.1 1.44237
\(787\) 40966.7 1.85553 0.927767 0.373159i \(-0.121725\pi\)
0.927767 + 0.373159i \(0.121725\pi\)
\(788\) 27287.2 1.23358
\(789\) 13404.1 0.604813
\(790\) −7768.85 −0.349877
\(791\) −1929.69 −0.0867406
\(792\) −72.7120 −0.00326226
\(793\) −9688.91 −0.433876
\(794\) −9611.30 −0.429587
\(795\) 1287.27 0.0574275
\(796\) 45904.9 2.04404
\(797\) −253.103 −0.0112489 −0.00562445 0.999984i \(-0.501790\pi\)
−0.00562445 + 0.999984i \(0.501790\pi\)
\(798\) 29822.2 1.32292
\(799\) 33853.3 1.49893
\(800\) −31192.0 −1.37850
\(801\) −4120.98 −0.181782
\(802\) 14128.0 0.622042
\(803\) 43.8177 0.00192565
\(804\) −40258.4 −1.76592
\(805\) 2979.78 0.130464
\(806\) 852.294 0.0372466
\(807\) 3852.91 0.168065
\(808\) −1061.19 −0.0462034
\(809\) −25849.5 −1.12339 −0.561694 0.827345i \(-0.689850\pi\)
−0.561694 + 0.827345i \(0.689850\pi\)
\(810\) 7955.74 0.345107
\(811\) 24298.3 1.05207 0.526036 0.850463i \(-0.323678\pi\)
0.526036 + 0.850463i \(0.323678\pi\)
\(812\) 5349.24 0.231184
\(813\) −12244.6 −0.528212
\(814\) 3705.95 0.159574
\(815\) 1215.19 0.0522286
\(816\) −19137.3 −0.821005
\(817\) 0 0
\(818\) −28974.4 −1.23847
\(819\) 1314.59 0.0560873
\(820\) −513.203 −0.0218559
\(821\) −16567.0 −0.704253 −0.352127 0.935952i \(-0.614541\pi\)
−0.352127 + 0.935952i \(0.614541\pi\)
\(822\) 51699.1 2.19369
\(823\) −19573.2 −0.829013 −0.414506 0.910046i \(-0.636046\pi\)
−0.414506 + 0.910046i \(0.636046\pi\)
\(824\) −2532.18 −0.107054
\(825\) 2144.93 0.0905174
\(826\) 15162.0 0.638684
\(827\) −34803.1 −1.46339 −0.731695 0.681632i \(-0.761270\pi\)
−0.731695 + 0.681632i \(0.761270\pi\)
\(828\) 12286.0 0.515663
\(829\) 8559.16 0.358591 0.179295 0.983795i \(-0.442618\pi\)
0.179295 + 0.983795i \(0.442618\pi\)
\(830\) 9419.70 0.393931
\(831\) −5150.97 −0.215024
\(832\) −9418.62 −0.392466
\(833\) 14350.2 0.596886
\(834\) −65935.6 −2.73760
\(835\) −184.374 −0.00764134
\(836\) 3490.82 0.144417
\(837\) −1400.70 −0.0578438
\(838\) 30912.1 1.27427
\(839\) −11133.3 −0.458124 −0.229062 0.973412i \(-0.573566\pi\)
−0.229062 + 0.973412i \(0.573566\pi\)
\(840\) 310.094 0.0127372
\(841\) −19567.9 −0.802323
\(842\) −8382.24 −0.343077
\(843\) −38884.4 −1.58867
\(844\) −24821.9 −1.01233
\(845\) −4241.62 −0.172682
\(846\) 23520.8 0.955866
\(847\) −11777.4 −0.477777
\(848\) 5718.05 0.231555
\(849\) −15358.2 −0.620841
\(850\) −26702.1 −1.07750
\(851\) −46995.5 −1.89305
\(852\) −44702.6 −1.79752
\(853\) 39508.0 1.58585 0.792923 0.609321i \(-0.208558\pi\)
0.792923 + 0.609321i \(0.208558\pi\)
\(854\) 22112.7 0.886043
\(855\) 2756.00 0.110238
\(856\) −1560.49 −0.0623090
\(857\) −25368.9 −1.01118 −0.505592 0.862773i \(-0.668726\pi\)
−0.505592 + 0.862773i \(0.668726\pi\)
\(858\) 1159.17 0.0461229
\(859\) −15928.9 −0.632696 −0.316348 0.948643i \(-0.602457\pi\)
−0.316348 + 0.948643i \(0.602457\pi\)
\(860\) 0 0
\(861\) 1458.32 0.0577229
\(862\) 70080.3 2.76908
\(863\) 18377.5 0.724885 0.362442 0.932006i \(-0.381943\pi\)
0.362442 + 0.932006i \(0.381943\pi\)
\(864\) 27703.4 1.09084
\(865\) −4081.50 −0.160434
\(866\) −31125.6 −1.22135
\(867\) 11747.6 0.460174
\(868\) −1010.50 −0.0395145
\(869\) 2584.10 0.100874
\(870\) 3723.91 0.145118
\(871\) 12308.3 0.478820
\(872\) −2238.46 −0.0869310
\(873\) 1393.76 0.0540338
\(874\) −85212.5 −3.29789
\(875\) −4767.60 −0.184199
\(876\) −770.485 −0.0297172
\(877\) 46868.1 1.80459 0.902293 0.431124i \(-0.141883\pi\)
0.902293 + 0.431124i \(0.141883\pi\)
\(878\) 26433.1 1.01603
\(879\) 32753.1 1.25681
\(880\) −377.480 −0.0144600
\(881\) −24976.8 −0.955153 −0.477577 0.878590i \(-0.658485\pi\)
−0.477577 + 0.878590i \(0.658485\pi\)
\(882\) 9970.36 0.380634
\(883\) 44574.5 1.69881 0.849406 0.527740i \(-0.176960\pi\)
0.849406 + 0.527740i \(0.176960\pi\)
\(884\) −7496.54 −0.285221
\(885\) 5483.34 0.208272
\(886\) −13671.1 −0.518384
\(887\) −18914.5 −0.715994 −0.357997 0.933723i \(-0.616540\pi\)
−0.357997 + 0.933723i \(0.616540\pi\)
\(888\) −4890.63 −0.184819
\(889\) 3995.52 0.150737
\(890\) 3960.00 0.149145
\(891\) −2646.26 −0.0994984
\(892\) −56309.1 −2.11364
\(893\) −84747.1 −3.17576
\(894\) −67165.1 −2.51268
\(895\) −1289.16 −0.0481474
\(896\) 3009.83 0.112222
\(897\) −14699.5 −0.547160
\(898\) 58585.8 2.17710
\(899\) −910.739 −0.0337874
\(900\) −9637.80 −0.356956
\(901\) 5330.35 0.197092
\(902\) 328.595 0.0121297
\(903\) 0 0
\(904\) 573.799 0.0211109
\(905\) 4284.51 0.157372
\(906\) 53744.8 1.97081
\(907\) −9458.37 −0.346262 −0.173131 0.984899i \(-0.555388\pi\)
−0.173131 + 0.984899i \(0.555388\pi\)
\(908\) 10470.4 0.382678
\(909\) 3713.16 0.135487
\(910\) −1263.24 −0.0460175
\(911\) 33612.0 1.22241 0.611206 0.791472i \(-0.290685\pi\)
0.611206 + 0.791472i \(0.290685\pi\)
\(912\) 47907.7 1.73945
\(913\) −3133.21 −0.113575
\(914\) 12857.4 0.465302
\(915\) 7997.05 0.288934
\(916\) −14812.2 −0.534290
\(917\) 11521.2 0.414902
\(918\) 23715.7 0.852651
\(919\) −28693.2 −1.02993 −0.514963 0.857212i \(-0.672195\pi\)
−0.514963 + 0.857212i \(0.672195\pi\)
\(920\) −886.046 −0.0317523
\(921\) 30702.2 1.09845
\(922\) −5262.29 −0.187965
\(923\) 13667.1 0.487386
\(924\) −1374.34 −0.0489312
\(925\) 36865.7 1.31042
\(926\) −40017.1 −1.42013
\(927\) 8860.28 0.313927
\(928\) 18012.8 0.637176
\(929\) −18092.0 −0.638946 −0.319473 0.947595i \(-0.603506\pi\)
−0.319473 + 0.947595i \(0.603506\pi\)
\(930\) −703.468 −0.0248039
\(931\) −35923.9 −1.26462
\(932\) −38899.5 −1.36716
\(933\) −3663.21 −0.128540
\(934\) 11258.0 0.394402
\(935\) −351.885 −0.0123079
\(936\) −390.898 −0.0136505
\(937\) 17209.8 0.600021 0.300010 0.953936i \(-0.403010\pi\)
0.300010 + 0.953936i \(0.403010\pi\)
\(938\) −28090.9 −0.977825
\(939\) 51742.1 1.79823
\(940\) −11741.6 −0.407414
\(941\) −48758.8 −1.68915 −0.844576 0.535436i \(-0.820147\pi\)
−0.844576 + 0.535436i \(0.820147\pi\)
\(942\) 64350.7 2.22575
\(943\) −4166.93 −0.143896
\(944\) 24356.9 0.839777
\(945\) 2076.06 0.0714649
\(946\) 0 0
\(947\) −32685.7 −1.12159 −0.560794 0.827956i \(-0.689504\pi\)
−0.560794 + 0.827956i \(0.689504\pi\)
\(948\) −45438.4 −1.55672
\(949\) 235.563 0.00805764
\(950\) 66845.2 2.28289
\(951\) 19727.4 0.672665
\(952\) 1284.04 0.0437142
\(953\) 14271.7 0.485105 0.242552 0.970138i \(-0.422015\pi\)
0.242552 + 0.970138i \(0.422015\pi\)
\(954\) 3703.46 0.125685
\(955\) −7307.24 −0.247599
\(956\) 54088.8 1.82987
\(957\) −1238.66 −0.0418392
\(958\) −25487.0 −0.859550
\(959\) 18740.1 0.631022
\(960\) 7773.95 0.261358
\(961\) −29619.0 −0.994225
\(962\) 19923.1 0.667720
\(963\) 5460.27 0.182715
\(964\) 37313.3 1.24666
\(965\) 8337.30 0.278121
\(966\) 33548.2 1.11739
\(967\) 18223.7 0.606034 0.303017 0.952985i \(-0.402006\pi\)
0.303017 + 0.952985i \(0.402006\pi\)
\(968\) 3502.06 0.116281
\(969\) 44659.4 1.48056
\(970\) −1339.31 −0.0443327
\(971\) 27591.5 0.911899 0.455949 0.890006i \(-0.349300\pi\)
0.455949 + 0.890006i \(0.349300\pi\)
\(972\) 21593.5 0.712565
\(973\) −23900.6 −0.787482
\(974\) 29475.3 0.969660
\(975\) 11531.1 0.378759
\(976\) 35522.8 1.16502
\(977\) −26884.2 −0.880348 −0.440174 0.897912i \(-0.645083\pi\)
−0.440174 + 0.897912i \(0.645083\pi\)
\(978\) 13681.4 0.447324
\(979\) −1317.18 −0.0430004
\(980\) −4977.21 −0.162236
\(981\) 7832.52 0.254917
\(982\) −37903.6 −1.23172
\(983\) −11678.2 −0.378918 −0.189459 0.981889i \(-0.560673\pi\)
−0.189459 + 0.981889i \(0.560673\pi\)
\(984\) −433.636 −0.0140486
\(985\) 6885.83 0.222742
\(986\) 15420.0 0.498046
\(987\) 33365.0 1.07601
\(988\) 18766.6 0.604296
\(989\) 0 0
\(990\) −244.485 −0.00784875
\(991\) 37149.5 1.19081 0.595406 0.803425i \(-0.296991\pi\)
0.595406 + 0.803425i \(0.296991\pi\)
\(992\) −3402.72 −0.108908
\(993\) −46935.4 −1.49995
\(994\) −31191.9 −0.995320
\(995\) 11583.9 0.369081
\(996\) 55093.9 1.75273
\(997\) 59233.9 1.88160 0.940800 0.338962i \(-0.110076\pi\)
0.940800 + 0.338962i \(0.110076\pi\)
\(998\) −13139.8 −0.416765
\(999\) −32742.6 −1.03697
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.j.1.9 yes 50
43.42 odd 2 1849.4.a.i.1.42 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.42 50 43.42 odd 2
1849.4.a.j.1.9 yes 50 1.1 even 1 trivial