Properties

Label 1997.4.a.a.1.70
Level $1997$
Weight $4$
Character 1997.1
Self dual yes
Analytic conductor $117.827$
Analytic rank $1$
Dimension $239$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1997 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1997.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(117.826814281\)
Analytic rank: \(1\)
Dimension: \(239\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.70
Character \(\chi\) \(=\) 1997.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.76015 q^{2} -4.70524 q^{3} -0.381583 q^{4} -6.86551 q^{5} +12.9872 q^{6} +2.49796 q^{7} +23.1344 q^{8} -4.86067 q^{9} +O(q^{10})\) \(q-2.76015 q^{2} -4.70524 q^{3} -0.381583 q^{4} -6.86551 q^{5} +12.9872 q^{6} +2.49796 q^{7} +23.1344 q^{8} -4.86067 q^{9} +18.9498 q^{10} -15.4408 q^{11} +1.79544 q^{12} +54.8883 q^{13} -6.89475 q^{14} +32.3039 q^{15} -60.8017 q^{16} -123.147 q^{17} +13.4162 q^{18} -0.288606 q^{19} +2.61976 q^{20} -11.7535 q^{21} +42.6189 q^{22} +33.4262 q^{23} -108.853 q^{24} -77.8647 q^{25} -151.500 q^{26} +149.912 q^{27} -0.953179 q^{28} +31.0383 q^{29} -89.1636 q^{30} +303.690 q^{31} -17.2535 q^{32} +72.6527 q^{33} +339.903 q^{34} -17.1498 q^{35} +1.85475 q^{36} -339.589 q^{37} +0.796596 q^{38} -258.263 q^{39} -158.830 q^{40} -224.364 q^{41} +32.4415 q^{42} -176.107 q^{43} +5.89194 q^{44} +33.3710 q^{45} -92.2611 q^{46} -79.8613 q^{47} +286.087 q^{48} -336.760 q^{49} +214.918 q^{50} +579.435 q^{51} -20.9444 q^{52} +528.358 q^{53} -413.780 q^{54} +106.009 q^{55} +57.7889 q^{56} +1.35796 q^{57} -85.6703 q^{58} -67.2288 q^{59} -12.3266 q^{60} -545.544 q^{61} -838.229 q^{62} -12.1418 q^{63} +534.036 q^{64} -376.836 q^{65} -200.532 q^{66} +422.032 q^{67} +46.9906 q^{68} -157.278 q^{69} +47.3360 q^{70} +948.793 q^{71} -112.449 q^{72} -910.016 q^{73} +937.315 q^{74} +366.373 q^{75} +0.110127 q^{76} -38.5705 q^{77} +712.844 q^{78} +906.898 q^{79} +417.435 q^{80} -574.136 q^{81} +619.278 q^{82} +845.986 q^{83} +4.48494 q^{84} +845.465 q^{85} +486.082 q^{86} -146.043 q^{87} -357.214 q^{88} +592.804 q^{89} -92.1089 q^{90} +137.109 q^{91} -12.7548 q^{92} -1428.94 q^{93} +220.429 q^{94} +1.98143 q^{95} +81.1819 q^{96} -707.759 q^{97} +929.508 q^{98} +75.0526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 239q - 16q^{2} - 106q^{3} + 872q^{4} - 85q^{5} - 111q^{6} - 352q^{7} - 210q^{8} + 1961q^{9} + O(q^{10}) \) \( 239q - 16q^{2} - 106q^{3} + 872q^{4} - 85q^{5} - 111q^{6} - 352q^{7} - 210q^{8} + 1961q^{9} - 273q^{10} - 294q^{11} - 864q^{12} - 797q^{13} - 220q^{14} - 580q^{15} + 2816q^{16} - 439q^{17} - 536q^{18} - 1704q^{19} - 933q^{20} - 596q^{21} - 1046q^{22} - 829q^{23} - 1237q^{24} + 4364q^{25} - 818q^{26} - 3670q^{27} - 3690q^{28} - 316q^{29} - 888q^{30} - 2595q^{31} - 1881q^{32} - 2066q^{33} - 2605q^{34} - 2450q^{35} + 5863q^{36} - 1912q^{37} - 1709q^{38} - 914q^{39} - 3582q^{40} - 1064q^{41} - 3228q^{42} - 5184q^{43} - 2656q^{44} - 3967q^{45} - 2521q^{46} - 4909q^{47} - 7461q^{48} + 7193q^{49} - 1906q^{50} - 3240q^{51} - 9614q^{52} - 2722q^{53} - 3754q^{54} - 6018q^{55} - 2347q^{56} - 2032q^{57} - 6709q^{58} - 6318q^{59} - 5821q^{60} - 2990q^{61} - 2117q^{62} - 8738q^{63} + 6866q^{64} - 1738q^{65} - 3080q^{66} - 14729q^{67} - 3897q^{68} - 2080q^{69} - 7445q^{70} - 3240q^{71} - 8263q^{72} - 8828q^{73} - 3103q^{74} - 12716q^{75} - 14843q^{76} - 3818q^{77} - 8029q^{78} - 4794q^{79} - 10336q^{80} + 11899q^{81} - 13447q^{82} - 11434q^{83} - 7957q^{84} - 8188q^{85} - 5196q^{86} - 11266q^{87} - 11861q^{88} - 4845q^{89} - 7759q^{90} - 12734q^{91} - 8644q^{92} - 10130q^{93} - 6909q^{94} - 3686q^{95} - 11958q^{96} - 16108q^{97} - 6845q^{98} - 12372q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76015 −0.975860 −0.487930 0.872883i \(-0.662248\pi\)
−0.487930 + 0.872883i \(0.662248\pi\)
\(3\) −4.70524 −0.905525 −0.452762 0.891631i \(-0.649561\pi\)
−0.452762 + 0.891631i \(0.649561\pi\)
\(4\) −0.381583 −0.0476978
\(5\) −6.86551 −0.614070 −0.307035 0.951698i \(-0.599337\pi\)
−0.307035 + 0.951698i \(0.599337\pi\)
\(6\) 12.9872 0.883665
\(7\) 2.49796 0.134877 0.0674387 0.997723i \(-0.478517\pi\)
0.0674387 + 0.997723i \(0.478517\pi\)
\(8\) 23.1344 1.02241
\(9\) −4.86067 −0.180025
\(10\) 18.9498 0.599246
\(11\) −15.4408 −0.423234 −0.211617 0.977353i \(-0.567873\pi\)
−0.211617 + 0.977353i \(0.567873\pi\)
\(12\) 1.79544 0.0431916
\(13\) 54.8883 1.17102 0.585510 0.810665i \(-0.300894\pi\)
0.585510 + 0.810665i \(0.300894\pi\)
\(14\) −6.89475 −0.131621
\(15\) 32.3039 0.556056
\(16\) −60.8017 −0.950027
\(17\) −123.147 −1.75691 −0.878454 0.477826i \(-0.841425\pi\)
−0.878454 + 0.477826i \(0.841425\pi\)
\(18\) 13.4162 0.175679
\(19\) −0.288606 −0.00348478 −0.00174239 0.999998i \(-0.500555\pi\)
−0.00174239 + 0.999998i \(0.500555\pi\)
\(20\) 2.61976 0.0292898
\(21\) −11.7535 −0.122135
\(22\) 42.6189 0.413017
\(23\) 33.4262 0.303036 0.151518 0.988454i \(-0.451584\pi\)
0.151518 + 0.988454i \(0.451584\pi\)
\(24\) −108.853 −0.925814
\(25\) −77.8647 −0.622918
\(26\) −151.500 −1.14275
\(27\) 149.912 1.06854
\(28\) −0.953179 −0.00643335
\(29\) 31.0383 0.198747 0.0993736 0.995050i \(-0.468316\pi\)
0.0993736 + 0.995050i \(0.468316\pi\)
\(30\) −89.1636 −0.542632
\(31\) 303.690 1.75949 0.879747 0.475442i \(-0.157712\pi\)
0.879747 + 0.475442i \(0.157712\pi\)
\(32\) −17.2535 −0.0953129
\(33\) 72.6527 0.383249
\(34\) 339.903 1.71450
\(35\) −17.1498 −0.0828241
\(36\) 1.85475 0.00858679
\(37\) −339.589 −1.50887 −0.754433 0.656377i \(-0.772088\pi\)
−0.754433 + 0.656377i \(0.772088\pi\)
\(38\) 0.796596 0.00340066
\(39\) −258.263 −1.06039
\(40\) −158.830 −0.627829
\(41\) −224.364 −0.854629 −0.427314 0.904103i \(-0.640540\pi\)
−0.427314 + 0.904103i \(0.640540\pi\)
\(42\) 32.4415 0.119186
\(43\) −176.107 −0.624560 −0.312280 0.949990i \(-0.601093\pi\)
−0.312280 + 0.949990i \(0.601093\pi\)
\(44\) 5.89194 0.0201873
\(45\) 33.3710 0.110548
\(46\) −92.2611 −0.295721
\(47\) −79.8613 −0.247851 −0.123925 0.992292i \(-0.539548\pi\)
−0.123925 + 0.992292i \(0.539548\pi\)
\(48\) 286.087 0.860273
\(49\) −336.760 −0.981808
\(50\) 214.918 0.607880
\(51\) 579.435 1.59092
\(52\) −20.9444 −0.0558551
\(53\) 528.358 1.36935 0.684676 0.728848i \(-0.259944\pi\)
0.684676 + 0.728848i \(0.259944\pi\)
\(54\) −413.780 −1.04275
\(55\) 106.009 0.259895
\(56\) 57.7889 0.137899
\(57\) 1.35796 0.00315555
\(58\) −85.6703 −0.193949
\(59\) −67.2288 −0.148347 −0.0741733 0.997245i \(-0.523632\pi\)
−0.0741733 + 0.997245i \(0.523632\pi\)
\(60\) −12.3266 −0.0265226
\(61\) −545.544 −1.14508 −0.572539 0.819877i \(-0.694042\pi\)
−0.572539 + 0.819877i \(0.694042\pi\)
\(62\) −838.229 −1.71702
\(63\) −12.1418 −0.0242813
\(64\) 534.036 1.04304
\(65\) −376.836 −0.719089
\(66\) −200.532 −0.373997
\(67\) 422.032 0.769544 0.384772 0.923012i \(-0.374280\pi\)
0.384772 + 0.923012i \(0.374280\pi\)
\(68\) 46.9906 0.0838007
\(69\) −157.278 −0.274407
\(70\) 47.3360 0.0808247
\(71\) 948.793 1.58593 0.792965 0.609268i \(-0.208536\pi\)
0.792965 + 0.609268i \(0.208536\pi\)
\(72\) −112.449 −0.184058
\(73\) −910.016 −1.45903 −0.729516 0.683963i \(-0.760255\pi\)
−0.729516 + 0.683963i \(0.760255\pi\)
\(74\) 937.315 1.47244
\(75\) 366.373 0.564068
\(76\) 0.110127 0.000166216 0
\(77\) −38.5705 −0.0570847
\(78\) 712.844 1.03479
\(79\) 906.898 1.29157 0.645785 0.763520i \(-0.276530\pi\)
0.645785 + 0.763520i \(0.276530\pi\)
\(80\) 417.435 0.583383
\(81\) −574.136 −0.787566
\(82\) 619.278 0.833998
\(83\) 845.986 1.11878 0.559392 0.828904i \(-0.311035\pi\)
0.559392 + 0.828904i \(0.311035\pi\)
\(84\) 4.48494 0.00582556
\(85\) 845.465 1.07887
\(86\) 486.082 0.609483
\(87\) −146.043 −0.179971
\(88\) −357.214 −0.432717
\(89\) 592.804 0.706035 0.353018 0.935617i \(-0.385156\pi\)
0.353018 + 0.935617i \(0.385156\pi\)
\(90\) −92.1089 −0.107879
\(91\) 137.109 0.157944
\(92\) −12.7548 −0.0144542
\(93\) −1428.94 −1.59327
\(94\) 220.429 0.241867
\(95\) 1.98143 0.00213990
\(96\) 81.1819 0.0863082
\(97\) −707.759 −0.740846 −0.370423 0.928863i \(-0.620787\pi\)
−0.370423 + 0.928863i \(0.620787\pi\)
\(98\) 929.508 0.958107
\(99\) 75.0526 0.0761926
\(100\) 29.7118 0.0297118
\(101\) 880.965 0.867914 0.433957 0.900934i \(-0.357117\pi\)
0.433957 + 0.900934i \(0.357117\pi\)
\(102\) −1599.33 −1.55252
\(103\) 1152.87 1.10287 0.551437 0.834216i \(-0.314080\pi\)
0.551437 + 0.834216i \(0.314080\pi\)
\(104\) 1269.81 1.19726
\(105\) 80.6940 0.0749993
\(106\) −1458.35 −1.33629
\(107\) 1262.33 1.14051 0.570253 0.821469i \(-0.306845\pi\)
0.570253 + 0.821469i \(0.306845\pi\)
\(108\) −57.2039 −0.0509671
\(109\) 826.942 0.726667 0.363333 0.931659i \(-0.381639\pi\)
0.363333 + 0.931659i \(0.381639\pi\)
\(110\) −292.600 −0.253621
\(111\) 1597.85 1.36632
\(112\) −151.880 −0.128137
\(113\) 2205.93 1.83643 0.918216 0.396079i \(-0.129629\pi\)
0.918216 + 0.396079i \(0.129629\pi\)
\(114\) −3.74818 −0.00307938
\(115\) −229.488 −0.186086
\(116\) −11.8437 −0.00947981
\(117\) −266.794 −0.210813
\(118\) 185.561 0.144765
\(119\) −307.616 −0.236967
\(120\) 747.332 0.568515
\(121\) −1092.58 −0.820873
\(122\) 1505.78 1.11744
\(123\) 1055.69 0.773888
\(124\) −115.883 −0.0839241
\(125\) 1392.77 0.996585
\(126\) 33.5131 0.0236951
\(127\) 1427.88 0.997665 0.498832 0.866698i \(-0.333762\pi\)
0.498832 + 0.866698i \(0.333762\pi\)
\(128\) −1335.99 −0.922547
\(129\) 828.627 0.565555
\(130\) 1040.12 0.701730
\(131\) 434.209 0.289595 0.144798 0.989461i \(-0.453747\pi\)
0.144798 + 0.989461i \(0.453747\pi\)
\(132\) −27.7230 −0.0182801
\(133\) −0.720928 −0.000470018 0
\(134\) −1164.87 −0.750967
\(135\) −1029.22 −0.656160
\(136\) −2848.92 −1.79627
\(137\) −2534.82 −1.58076 −0.790382 0.612615i \(-0.790118\pi\)
−0.790382 + 0.612615i \(0.790118\pi\)
\(138\) 434.111 0.267783
\(139\) −1345.54 −0.821061 −0.410530 0.911847i \(-0.634656\pi\)
−0.410530 + 0.911847i \(0.634656\pi\)
\(140\) 6.54406 0.00395053
\(141\) 375.767 0.224435
\(142\) −2618.81 −1.54764
\(143\) −847.519 −0.495616
\(144\) 295.537 0.171028
\(145\) −213.094 −0.122045
\(146\) 2511.78 1.42381
\(147\) 1584.54 0.889052
\(148\) 129.581 0.0719696
\(149\) −2063.95 −1.13480 −0.567400 0.823442i \(-0.692051\pi\)
−0.567400 + 0.823442i \(0.692051\pi\)
\(150\) −1011.24 −0.550451
\(151\) −2.16365 −0.00116606 −0.000583030 1.00000i \(-0.500186\pi\)
−0.000583030 1.00000i \(0.500186\pi\)
\(152\) −6.67673 −0.00356286
\(153\) 598.575 0.316287
\(154\) 106.460 0.0557066
\(155\) −2084.99 −1.08045
\(156\) 98.5486 0.0505782
\(157\) 427.976 0.217555 0.108778 0.994066i \(-0.465306\pi\)
0.108778 + 0.994066i \(0.465306\pi\)
\(158\) −2503.17 −1.26039
\(159\) −2486.06 −1.23998
\(160\) 118.454 0.0585288
\(161\) 83.4973 0.0408727
\(162\) 1584.70 0.768554
\(163\) 2351.77 1.13009 0.565045 0.825060i \(-0.308859\pi\)
0.565045 + 0.825060i \(0.308859\pi\)
\(164\) 85.6134 0.0407639
\(165\) −498.798 −0.235342
\(166\) −2335.05 −1.09178
\(167\) −2932.07 −1.35863 −0.679313 0.733849i \(-0.737722\pi\)
−0.679313 + 0.733849i \(0.737722\pi\)
\(168\) −271.911 −0.124871
\(169\) 815.723 0.371290
\(170\) −2333.61 −1.05282
\(171\) 1.40282 0.000627347 0
\(172\) 67.1994 0.0297901
\(173\) 3365.39 1.47899 0.739496 0.673161i \(-0.235064\pi\)
0.739496 + 0.673161i \(0.235064\pi\)
\(174\) 403.100 0.175626
\(175\) −194.503 −0.0840175
\(176\) 938.827 0.402084
\(177\) 316.328 0.134331
\(178\) −1636.23 −0.688991
\(179\) 3263.23 1.36260 0.681300 0.732004i \(-0.261415\pi\)
0.681300 + 0.732004i \(0.261415\pi\)
\(180\) −12.7338 −0.00527289
\(181\) 1702.44 0.699125 0.349562 0.936913i \(-0.386330\pi\)
0.349562 + 0.936913i \(0.386330\pi\)
\(182\) −378.441 −0.154131
\(183\) 2566.92 1.03690
\(184\) 773.294 0.309826
\(185\) 2331.45 0.926549
\(186\) 3944.07 1.55480
\(187\) 1901.48 0.743583
\(188\) 30.4737 0.0118219
\(189\) 374.475 0.144122
\(190\) −5.46904 −0.00208824
\(191\) 353.912 0.134074 0.0670372 0.997750i \(-0.478645\pi\)
0.0670372 + 0.997750i \(0.478645\pi\)
\(192\) −2512.77 −0.944498
\(193\) 502.679 0.187480 0.0937399 0.995597i \(-0.470118\pi\)
0.0937399 + 0.995597i \(0.470118\pi\)
\(194\) 1953.52 0.722961
\(195\) 1773.11 0.651153
\(196\) 128.502 0.0468301
\(197\) 4482.60 1.62118 0.810589 0.585616i \(-0.199147\pi\)
0.810589 + 0.585616i \(0.199147\pi\)
\(198\) −207.156 −0.0743533
\(199\) −1710.76 −0.609412 −0.304706 0.952447i \(-0.598558\pi\)
−0.304706 + 0.952447i \(0.598558\pi\)
\(200\) −1801.35 −0.636875
\(201\) −1985.77 −0.696841
\(202\) −2431.60 −0.846963
\(203\) 77.5326 0.0268065
\(204\) −221.102 −0.0758836
\(205\) 1540.37 0.524802
\(206\) −3182.10 −1.07625
\(207\) −162.474 −0.0545541
\(208\) −3337.30 −1.11250
\(209\) 4.45631 0.00147488
\(210\) −222.727 −0.0731888
\(211\) −2833.39 −0.924447 −0.462224 0.886763i \(-0.652948\pi\)
−0.462224 + 0.886763i \(0.652948\pi\)
\(212\) −201.612 −0.0653151
\(213\) −4464.30 −1.43610
\(214\) −3484.22 −1.11297
\(215\) 1209.07 0.383524
\(216\) 3468.13 1.09248
\(217\) 758.606 0.237316
\(218\) −2282.48 −0.709125
\(219\) 4281.85 1.32119
\(220\) −40.4512 −0.0123964
\(221\) −6759.31 −2.05738
\(222\) −4410.30 −1.33333
\(223\) 1655.34 0.497084 0.248542 0.968621i \(-0.420049\pi\)
0.248542 + 0.968621i \(0.420049\pi\)
\(224\) −43.0986 −0.0128556
\(225\) 378.475 0.112141
\(226\) −6088.71 −1.79210
\(227\) −3305.13 −0.966384 −0.483192 0.875514i \(-0.660523\pi\)
−0.483192 + 0.875514i \(0.660523\pi\)
\(228\) −0.518175 −0.000150513 0
\(229\) −1705.88 −0.492261 −0.246130 0.969237i \(-0.579159\pi\)
−0.246130 + 0.969237i \(0.579159\pi\)
\(230\) 633.420 0.181593
\(231\) 181.484 0.0516916
\(232\) 718.053 0.203200
\(233\) 4341.32 1.22064 0.610320 0.792155i \(-0.291041\pi\)
0.610320 + 0.792155i \(0.291041\pi\)
\(234\) 736.390 0.205724
\(235\) 548.289 0.152198
\(236\) 25.6533 0.00707581
\(237\) −4267.18 −1.16955
\(238\) 849.065 0.231247
\(239\) −4440.74 −1.20187 −0.600936 0.799297i \(-0.705205\pi\)
−0.600936 + 0.799297i \(0.705205\pi\)
\(240\) −1964.13 −0.528268
\(241\) −4698.94 −1.25596 −0.627978 0.778231i \(-0.716117\pi\)
−0.627978 + 0.778231i \(0.716117\pi\)
\(242\) 3015.69 0.801057
\(243\) −1346.18 −0.355381
\(244\) 208.170 0.0546177
\(245\) 2312.03 0.602899
\(246\) −2913.86 −0.755206
\(247\) −15.8411 −0.00408075
\(248\) 7025.69 1.79892
\(249\) −3980.57 −1.01309
\(250\) −3844.25 −0.972528
\(251\) 1012.06 0.254505 0.127253 0.991870i \(-0.459384\pi\)
0.127253 + 0.991870i \(0.459384\pi\)
\(252\) 4.63309 0.00115816
\(253\) −516.126 −0.128255
\(254\) −3941.15 −0.973581
\(255\) −3978.12 −0.976939
\(256\) −584.756 −0.142763
\(257\) 3706.37 0.899599 0.449799 0.893130i \(-0.351495\pi\)
0.449799 + 0.893130i \(0.351495\pi\)
\(258\) −2287.13 −0.551902
\(259\) −848.280 −0.203512
\(260\) 143.794 0.0342990
\(261\) −150.867 −0.0357794
\(262\) −1198.48 −0.282604
\(263\) −4699.05 −1.10173 −0.550866 0.834594i \(-0.685702\pi\)
−0.550866 + 0.834594i \(0.685702\pi\)
\(264\) 1680.78 0.391836
\(265\) −3627.45 −0.840878
\(266\) 1.98987 0.000458671 0
\(267\) −2789.29 −0.639332
\(268\) −161.040 −0.0367056
\(269\) −3287.91 −0.745231 −0.372615 0.927986i \(-0.621539\pi\)
−0.372615 + 0.927986i \(0.621539\pi\)
\(270\) 2840.81 0.640320
\(271\) −6931.62 −1.55375 −0.776874 0.629656i \(-0.783196\pi\)
−0.776874 + 0.629656i \(0.783196\pi\)
\(272\) 7487.53 1.66911
\(273\) −645.131 −0.143022
\(274\) 6996.49 1.54260
\(275\) 1202.29 0.263640
\(276\) 60.0146 0.0130886
\(277\) 1539.28 0.333887 0.166943 0.985966i \(-0.446610\pi\)
0.166943 + 0.985966i \(0.446610\pi\)
\(278\) 3713.90 0.801240
\(279\) −1476.14 −0.316753
\(280\) −396.750 −0.0846799
\(281\) −312.911 −0.0664295 −0.0332147 0.999448i \(-0.510575\pi\)
−0.0332147 + 0.999448i \(0.510575\pi\)
\(282\) −1037.17 −0.219017
\(283\) 5483.72 1.15185 0.575925 0.817503i \(-0.304642\pi\)
0.575925 + 0.817503i \(0.304642\pi\)
\(284\) −362.043 −0.0756454
\(285\) −9.32311 −0.00193773
\(286\) 2339.28 0.483652
\(287\) −560.453 −0.115270
\(288\) 83.8635 0.0171587
\(289\) 10252.1 2.08673
\(290\) 588.171 0.119099
\(291\) 3330.18 0.670854
\(292\) 347.246 0.0695927
\(293\) −6967.04 −1.38914 −0.694572 0.719424i \(-0.744406\pi\)
−0.694572 + 0.719424i \(0.744406\pi\)
\(294\) −4373.56 −0.867590
\(295\) 461.560 0.0910952
\(296\) −7856.18 −1.54267
\(297\) −2314.76 −0.452243
\(298\) 5696.80 1.10741
\(299\) 1834.70 0.354862
\(300\) −139.801 −0.0269048
\(301\) −439.909 −0.0842390
\(302\) 5.97199 0.00113791
\(303\) −4145.16 −0.785918
\(304\) 17.5478 0.00331063
\(305\) 3745.44 0.703158
\(306\) −1652.16 −0.308652
\(307\) 3302.11 0.613882 0.306941 0.951729i \(-0.400695\pi\)
0.306941 + 0.951729i \(0.400695\pi\)
\(308\) 14.7178 0.00272281
\(309\) −5424.55 −0.998680
\(310\) 5754.87 1.05437
\(311\) 6004.63 1.09483 0.547414 0.836862i \(-0.315612\pi\)
0.547414 + 0.836862i \(0.315612\pi\)
\(312\) −5974.76 −1.08415
\(313\) −6848.58 −1.23676 −0.618378 0.785881i \(-0.712210\pi\)
−0.618378 + 0.785881i \(0.712210\pi\)
\(314\) −1181.28 −0.212303
\(315\) 83.3595 0.0149104
\(316\) −346.056 −0.0616050
\(317\) −5421.07 −0.960498 −0.480249 0.877132i \(-0.659454\pi\)
−0.480249 + 0.877132i \(0.659454\pi\)
\(318\) 6861.88 1.21005
\(319\) −479.256 −0.0841166
\(320\) −3666.43 −0.640499
\(321\) −5939.58 −1.03276
\(322\) −230.465 −0.0398860
\(323\) 35.5409 0.00612244
\(324\) 219.080 0.0375652
\(325\) −4273.86 −0.729450
\(326\) −6491.22 −1.10281
\(327\) −3890.96 −0.658015
\(328\) −5190.53 −0.873778
\(329\) −199.491 −0.0334294
\(330\) 1376.76 0.229661
\(331\) 8371.05 1.39007 0.695037 0.718974i \(-0.255388\pi\)
0.695037 + 0.718974i \(0.255388\pi\)
\(332\) −322.813 −0.0533635
\(333\) 1650.63 0.271633
\(334\) 8092.95 1.32583
\(335\) −2897.47 −0.472554
\(336\) 714.635 0.116031
\(337\) −2467.18 −0.398801 −0.199400 0.979918i \(-0.563899\pi\)
−0.199400 + 0.979918i \(0.563899\pi\)
\(338\) −2251.52 −0.362327
\(339\) −10379.5 −1.66294
\(340\) −322.615 −0.0514595
\(341\) −4689.21 −0.744678
\(342\) −3.87199 −0.000612202 0
\(343\) −1698.02 −0.267301
\(344\) −4074.13 −0.638554
\(345\) 1079.80 0.168505
\(346\) −9288.97 −1.44329
\(347\) −6834.38 −1.05732 −0.528658 0.848835i \(-0.677305\pi\)
−0.528658 + 0.848835i \(0.677305\pi\)
\(348\) 55.7274 0.00858420
\(349\) 1956.01 0.300008 0.150004 0.988685i \(-0.452071\pi\)
0.150004 + 0.988685i \(0.452071\pi\)
\(350\) 536.858 0.0819893
\(351\) 8228.43 1.25128
\(352\) 266.407 0.0403397
\(353\) 1914.47 0.288660 0.144330 0.989530i \(-0.453897\pi\)
0.144330 + 0.989530i \(0.453897\pi\)
\(354\) −873.112 −0.131089
\(355\) −6513.95 −0.973872
\(356\) −226.204 −0.0336763
\(357\) 1447.41 0.214580
\(358\) −9007.01 −1.32971
\(359\) 2456.04 0.361072 0.180536 0.983568i \(-0.442217\pi\)
0.180536 + 0.983568i \(0.442217\pi\)
\(360\) 772.018 0.113025
\(361\) −6858.92 −0.999988
\(362\) −4699.00 −0.682248
\(363\) 5140.87 0.743321
\(364\) −52.3184 −0.00753359
\(365\) 6247.73 0.895948
\(366\) −7085.08 −1.01187
\(367\) 6636.29 0.943901 0.471951 0.881625i \(-0.343550\pi\)
0.471951 + 0.881625i \(0.343550\pi\)
\(368\) −2032.37 −0.287893
\(369\) 1090.56 0.153854
\(370\) −6435.15 −0.904182
\(371\) 1319.82 0.184694
\(372\) 545.257 0.0759953
\(373\) 4512.98 0.626470 0.313235 0.949676i \(-0.398587\pi\)
0.313235 + 0.949676i \(0.398587\pi\)
\(374\) −5248.37 −0.725633
\(375\) −6553.33 −0.902433
\(376\) −1847.54 −0.253404
\(377\) 1703.64 0.232737
\(378\) −1033.61 −0.140643
\(379\) −9951.42 −1.34873 −0.674367 0.738396i \(-0.735583\pi\)
−0.674367 + 0.738396i \(0.735583\pi\)
\(380\) −0.756079 −0.000102068 0
\(381\) −6718.50 −0.903410
\(382\) −976.851 −0.130838
\(383\) 5502.85 0.734158 0.367079 0.930190i \(-0.380358\pi\)
0.367079 + 0.930190i \(0.380358\pi\)
\(384\) 6286.16 0.835389
\(385\) 264.807 0.0350540
\(386\) −1387.47 −0.182954
\(387\) 855.998 0.112436
\(388\) 270.068 0.0353367
\(389\) −3833.91 −0.499710 −0.249855 0.968283i \(-0.580383\pi\)
−0.249855 + 0.968283i \(0.580383\pi\)
\(390\) −4894.04 −0.635434
\(391\) −4116.32 −0.532407
\(392\) −7790.75 −1.00381
\(393\) −2043.06 −0.262236
\(394\) −12372.6 −1.58204
\(395\) −6226.32 −0.793114
\(396\) −28.6388 −0.00363422
\(397\) −14440.3 −1.82554 −0.912771 0.408472i \(-0.866062\pi\)
−0.912771 + 0.408472i \(0.866062\pi\)
\(398\) 4721.96 0.594700
\(399\) 3.39214 0.000425613 0
\(400\) 4734.31 0.591789
\(401\) −4805.51 −0.598444 −0.299222 0.954184i \(-0.596727\pi\)
−0.299222 + 0.954184i \(0.596727\pi\)
\(402\) 5481.01 0.680020
\(403\) 16669.0 2.06040
\(404\) −336.161 −0.0413976
\(405\) 3941.74 0.483621
\(406\) −214.001 −0.0261594
\(407\) 5243.52 0.638603
\(408\) 13404.9 1.62657
\(409\) −6112.32 −0.738961 −0.369480 0.929239i \(-0.620464\pi\)
−0.369480 + 0.929239i \(0.620464\pi\)
\(410\) −4251.66 −0.512133
\(411\) 11927.0 1.43142
\(412\) −439.917 −0.0526047
\(413\) −167.935 −0.0200086
\(414\) 448.451 0.0532371
\(415\) −5808.13 −0.687011
\(416\) −947.014 −0.111613
\(417\) 6331.11 0.743491
\(418\) −12.3001 −0.00143927
\(419\) −14627.9 −1.70554 −0.852768 0.522290i \(-0.825078\pi\)
−0.852768 + 0.522290i \(0.825078\pi\)
\(420\) −30.7914 −0.00357730
\(421\) 16469.9 1.90664 0.953320 0.301963i \(-0.0976419\pi\)
0.953320 + 0.301963i \(0.0976419\pi\)
\(422\) 7820.57 0.902131
\(423\) 388.180 0.0446192
\(424\) 12223.3 1.40003
\(425\) 9588.78 1.09441
\(426\) 12322.1 1.40143
\(427\) −1362.75 −0.154445
\(428\) −481.684 −0.0543997
\(429\) 3987.78 0.448792
\(430\) −3337.20 −0.374265
\(431\) 1203.13 0.134461 0.0672305 0.997737i \(-0.478584\pi\)
0.0672305 + 0.997737i \(0.478584\pi\)
\(432\) −9114.93 −1.01514
\(433\) 4300.84 0.477333 0.238666 0.971102i \(-0.423290\pi\)
0.238666 + 0.971102i \(0.423290\pi\)
\(434\) −2093.87 −0.231587
\(435\) 1002.66 0.110515
\(436\) −315.547 −0.0346604
\(437\) −9.64699 −0.00105601
\(438\) −11818.5 −1.28930
\(439\) 1859.26 0.202136 0.101068 0.994880i \(-0.467774\pi\)
0.101068 + 0.994880i \(0.467774\pi\)
\(440\) 2452.45 0.265719
\(441\) 1636.88 0.176750
\(442\) 18656.7 2.00771
\(443\) −2786.13 −0.298810 −0.149405 0.988776i \(-0.547736\pi\)
−0.149405 + 0.988776i \(0.547736\pi\)
\(444\) −609.711 −0.0651703
\(445\) −4069.91 −0.433555
\(446\) −4568.98 −0.485084
\(447\) 9711.38 1.02759
\(448\) 1334.00 0.140682
\(449\) 2409.64 0.253270 0.126635 0.991949i \(-0.459582\pi\)
0.126635 + 0.991949i \(0.459582\pi\)
\(450\) −1044.65 −0.109434
\(451\) 3464.36 0.361708
\(452\) −841.746 −0.0875938
\(453\) 10.1805 0.00105590
\(454\) 9122.65 0.943055
\(455\) −941.323 −0.0969888
\(456\) 31.4157 0.00322626
\(457\) −5589.61 −0.572147 −0.286073 0.958208i \(-0.592350\pi\)
−0.286073 + 0.958208i \(0.592350\pi\)
\(458\) 4708.48 0.480377
\(459\) −18461.2 −1.87733
\(460\) 87.5685 0.00887587
\(461\) 13715.7 1.38569 0.692845 0.721087i \(-0.256357\pi\)
0.692845 + 0.721087i \(0.256357\pi\)
\(462\) −500.922 −0.0504437
\(463\) −9049.10 −0.908309 −0.454155 0.890923i \(-0.650059\pi\)
−0.454155 + 0.890923i \(0.650059\pi\)
\(464\) −1887.18 −0.188815
\(465\) 9810.38 0.978377
\(466\) −11982.7 −1.19117
\(467\) −18246.6 −1.80803 −0.904017 0.427497i \(-0.859395\pi\)
−0.904017 + 0.427497i \(0.859395\pi\)
\(468\) 101.804 0.0100553
\(469\) 1054.22 0.103794
\(470\) −1513.36 −0.148524
\(471\) −2013.73 −0.197002
\(472\) −1555.30 −0.151670
\(473\) 2719.23 0.264335
\(474\) 11778.0 1.14131
\(475\) 22.4722 0.00217073
\(476\) 117.381 0.0113028
\(477\) −2568.18 −0.246517
\(478\) 12257.1 1.17286
\(479\) 13703.0 1.30711 0.653554 0.756880i \(-0.273277\pi\)
0.653554 + 0.756880i \(0.273277\pi\)
\(480\) −557.355 −0.0529993
\(481\) −18639.4 −1.76691
\(482\) 12969.8 1.22564
\(483\) −392.875 −0.0370113
\(484\) 416.910 0.0391538
\(485\) 4859.13 0.454931
\(486\) 3715.66 0.346802
\(487\) −20567.6 −1.91377 −0.956884 0.290471i \(-0.906188\pi\)
−0.956884 + 0.290471i \(0.906188\pi\)
\(488\) −12620.8 −1.17073
\(489\) −11065.6 −1.02332
\(490\) −6381.55 −0.588345
\(491\) 14643.4 1.34592 0.672961 0.739678i \(-0.265022\pi\)
0.672961 + 0.739678i \(0.265022\pi\)
\(492\) −402.832 −0.0369128
\(493\) −3822.26 −0.349181
\(494\) 43.7238 0.00398224
\(495\) −515.275 −0.0467876
\(496\) −18464.9 −1.67157
\(497\) 2370.05 0.213906
\(498\) 10987.0 0.988630
\(499\) 8198.31 0.735484 0.367742 0.929928i \(-0.380131\pi\)
0.367742 + 0.929928i \(0.380131\pi\)
\(500\) −531.457 −0.0475350
\(501\) 13796.1 1.23027
\(502\) −2793.44 −0.248361
\(503\) 16387.4 1.45264 0.726318 0.687359i \(-0.241230\pi\)
0.726318 + 0.687359i \(0.241230\pi\)
\(504\) −280.893 −0.0248253
\(505\) −6048.28 −0.532960
\(506\) 1424.59 0.125159
\(507\) −3838.18 −0.336212
\(508\) −544.852 −0.0475864
\(509\) 8403.79 0.731810 0.365905 0.930652i \(-0.380759\pi\)
0.365905 + 0.930652i \(0.380759\pi\)
\(510\) 10980.2 0.953356
\(511\) −2273.19 −0.196790
\(512\) 12301.9 1.06186
\(513\) −43.2656 −0.00372363
\(514\) −10230.1 −0.877882
\(515\) −7915.07 −0.677242
\(516\) −316.190 −0.0269757
\(517\) 1233.12 0.104899
\(518\) 2341.38 0.198599
\(519\) −15835.0 −1.33926
\(520\) −8717.88 −0.735201
\(521\) 11215.8 0.943133 0.471567 0.881830i \(-0.343689\pi\)
0.471567 + 0.881830i \(0.343689\pi\)
\(522\) 416.415 0.0349157
\(523\) 11281.6 0.943228 0.471614 0.881805i \(-0.343672\pi\)
0.471614 + 0.881805i \(0.343672\pi\)
\(524\) −165.686 −0.0138131
\(525\) 915.185 0.0760799
\(526\) 12970.1 1.07514
\(527\) −37398.4 −3.09127
\(528\) −4417.41 −0.364097
\(529\) −11049.7 −0.908169
\(530\) 10012.3 0.820579
\(531\) 326.777 0.0267061
\(532\) 0.275093 2.24188e−5 0
\(533\) −12315.0 −1.00079
\(534\) 7698.85 0.623899
\(535\) −8666.55 −0.700351
\(536\) 9763.47 0.786787
\(537\) −15354.3 −1.23387
\(538\) 9075.10 0.727241
\(539\) 5199.84 0.415535
\(540\) 392.734 0.0312974
\(541\) −15586.5 −1.23866 −0.619331 0.785130i \(-0.712596\pi\)
−0.619331 + 0.785130i \(0.712596\pi\)
\(542\) 19132.3 1.51624
\(543\) −8010.41 −0.633075
\(544\) 2124.71 0.167456
\(545\) −5677.38 −0.446224
\(546\) 1780.66 0.139570
\(547\) 6735.76 0.526508 0.263254 0.964726i \(-0.415204\pi\)
0.263254 + 0.964726i \(0.415204\pi\)
\(548\) 967.244 0.0753990
\(549\) 2651.71 0.206142
\(550\) −3318.51 −0.257276
\(551\) −8.95785 −0.000692590 0
\(552\) −3638.54 −0.280555
\(553\) 2265.40 0.174203
\(554\) −4248.65 −0.325827
\(555\) −10970.0 −0.839013
\(556\) 513.436 0.0391628
\(557\) −8407.74 −0.639583 −0.319791 0.947488i \(-0.603613\pi\)
−0.319791 + 0.947488i \(0.603613\pi\)
\(558\) 4074.36 0.309106
\(559\) −9666.21 −0.731373
\(560\) 1042.74 0.0786852
\(561\) −8946.94 −0.673333
\(562\) 863.679 0.0648258
\(563\) −8223.62 −0.615603 −0.307801 0.951451i \(-0.599593\pi\)
−0.307801 + 0.951451i \(0.599593\pi\)
\(564\) −143.386 −0.0107050
\(565\) −15144.9 −1.12770
\(566\) −15135.9 −1.12404
\(567\) −1434.17 −0.106225
\(568\) 21949.8 1.62146
\(569\) −9408.91 −0.693219 −0.346610 0.938009i \(-0.612667\pi\)
−0.346610 + 0.938009i \(0.612667\pi\)
\(570\) 25.7332 0.00189095
\(571\) −6287.40 −0.460805 −0.230402 0.973095i \(-0.574004\pi\)
−0.230402 + 0.973095i \(0.574004\pi\)
\(572\) 323.398 0.0236398
\(573\) −1665.24 −0.121408
\(574\) 1546.93 0.112487
\(575\) −2602.72 −0.188767
\(576\) −2595.77 −0.187773
\(577\) −13940.6 −1.00582 −0.502908 0.864340i \(-0.667736\pi\)
−0.502908 + 0.864340i \(0.667736\pi\)
\(578\) −28297.3 −2.03635
\(579\) −2365.23 −0.169768
\(580\) 81.3129 0.00582127
\(581\) 2113.24 0.150898
\(582\) −9191.79 −0.654660
\(583\) −8158.27 −0.579556
\(584\) −21052.7 −1.49172
\(585\) 1831.68 0.129454
\(586\) 19230.1 1.35561
\(587\) 4803.36 0.337744 0.168872 0.985638i \(-0.445988\pi\)
0.168872 + 0.985638i \(0.445988\pi\)
\(588\) −604.632 −0.0424058
\(589\) −87.6468 −0.00613145
\(590\) −1273.97 −0.0888961
\(591\) −21091.7 −1.46802
\(592\) 20647.6 1.43346
\(593\) 4097.31 0.283737 0.141869 0.989885i \(-0.454689\pi\)
0.141869 + 0.989885i \(0.454689\pi\)
\(594\) 6389.09 0.441326
\(595\) 2111.94 0.145514
\(596\) 787.567 0.0541275
\(597\) 8049.57 0.551837
\(598\) −5064.06 −0.346295
\(599\) −7088.01 −0.483486 −0.241743 0.970340i \(-0.577719\pi\)
−0.241743 + 0.970340i \(0.577719\pi\)
\(600\) 8475.81 0.576706
\(601\) 21025.9 1.42706 0.713529 0.700625i \(-0.247095\pi\)
0.713529 + 0.700625i \(0.247095\pi\)
\(602\) 1214.21 0.0822054
\(603\) −2051.36 −0.138537
\(604\) 0.825610 5.56186e−5 0
\(605\) 7501.14 0.504074
\(606\) 11441.3 0.766946
\(607\) −10388.6 −0.694660 −0.347330 0.937743i \(-0.612912\pi\)
−0.347330 + 0.937743i \(0.612912\pi\)
\(608\) 4.97946 0.000332144 0
\(609\) −364.810 −0.0242739
\(610\) −10338.0 −0.686184
\(611\) −4383.45 −0.290238
\(612\) −228.406 −0.0150862
\(613\) −7598.74 −0.500669 −0.250335 0.968159i \(-0.580541\pi\)
−0.250335 + 0.968159i \(0.580541\pi\)
\(614\) −9114.33 −0.599062
\(615\) −7247.84 −0.475221
\(616\) −892.306 −0.0583637
\(617\) −7419.80 −0.484132 −0.242066 0.970260i \(-0.577825\pi\)
−0.242066 + 0.970260i \(0.577825\pi\)
\(618\) 14972.6 0.974571
\(619\) 12600.2 0.818163 0.409082 0.912498i \(-0.365849\pi\)
0.409082 + 0.912498i \(0.365849\pi\)
\(620\) 795.595 0.0515353
\(621\) 5010.99 0.323807
\(622\) −16573.7 −1.06840
\(623\) 1480.80 0.0952281
\(624\) 15702.8 1.00740
\(625\) 171.007 0.0109444
\(626\) 18903.1 1.20690
\(627\) −20.9680 −0.00133554
\(628\) −163.308 −0.0103769
\(629\) 41819.2 2.65094
\(630\) −230.085 −0.0145505
\(631\) −13569.1 −0.856067 −0.428033 0.903763i \(-0.640793\pi\)
−0.428033 + 0.903763i \(0.640793\pi\)
\(632\) 20980.5 1.32051
\(633\) 13331.8 0.837110
\(634\) 14963.0 0.937311
\(635\) −9803.10 −0.612636
\(636\) 948.635 0.0591444
\(637\) −18484.2 −1.14972
\(638\) 1322.82 0.0820860
\(639\) −4611.77 −0.285507
\(640\) 9172.26 0.566509
\(641\) 3038.65 0.187238 0.0936188 0.995608i \(-0.470157\pi\)
0.0936188 + 0.995608i \(0.470157\pi\)
\(642\) 16394.1 1.00783
\(643\) −19815.3 −1.21530 −0.607650 0.794205i \(-0.707888\pi\)
−0.607650 + 0.794205i \(0.707888\pi\)
\(644\) −31.8611 −0.00194954
\(645\) −5688.95 −0.347290
\(646\) −98.0981 −0.00597464
\(647\) −7858.37 −0.477503 −0.238751 0.971081i \(-0.576738\pi\)
−0.238751 + 0.971081i \(0.576738\pi\)
\(648\) −13282.3 −0.805213
\(649\) 1038.07 0.0627853
\(650\) 11796.5 0.711841
\(651\) −3569.43 −0.214895
\(652\) −897.393 −0.0539028
\(653\) −18560.8 −1.11232 −0.556158 0.831077i \(-0.687725\pi\)
−0.556158 + 0.831077i \(0.687725\pi\)
\(654\) 10739.6 0.642130
\(655\) −2981.07 −0.177832
\(656\) 13641.7 0.811921
\(657\) 4423.29 0.262662
\(658\) 550.624 0.0326224
\(659\) 14576.9 0.861662 0.430831 0.902433i \(-0.358221\pi\)
0.430831 + 0.902433i \(0.358221\pi\)
\(660\) 190.333 0.0112253
\(661\) −21960.2 −1.29221 −0.646106 0.763248i \(-0.723604\pi\)
−0.646106 + 0.763248i \(0.723604\pi\)
\(662\) −23105.3 −1.35652
\(663\) 31804.2 1.86301
\(664\) 19571.4 1.14385
\(665\) 4.94954 0.000288624 0
\(666\) −4555.98 −0.265076
\(667\) 1037.49 0.0602276
\(668\) 1118.83 0.0648035
\(669\) −7788.78 −0.450122
\(670\) 7997.44 0.461147
\(671\) 8423.63 0.484636
\(672\) 202.789 0.0116410
\(673\) −5475.58 −0.313623 −0.156811 0.987629i \(-0.550121\pi\)
−0.156811 + 0.987629i \(0.550121\pi\)
\(674\) 6809.78 0.389173
\(675\) −11672.9 −0.665614
\(676\) −311.266 −0.0177097
\(677\) −581.517 −0.0330126 −0.0165063 0.999864i \(-0.505254\pi\)
−0.0165063 + 0.999864i \(0.505254\pi\)
\(678\) 28648.9 1.62279
\(679\) −1767.96 −0.0999233
\(680\) 19559.3 1.10304
\(681\) 15551.4 0.875084
\(682\) 12942.9 0.726701
\(683\) −13721.9 −0.768749 −0.384374 0.923177i \(-0.625583\pi\)
−0.384374 + 0.923177i \(0.625583\pi\)
\(684\) −0.535291 −2.99231e−5 0
\(685\) 17402.9 0.970700
\(686\) 4686.78 0.260848
\(687\) 8026.58 0.445754
\(688\) 10707.6 0.593349
\(689\) 29000.7 1.60354
\(690\) −2980.40 −0.164437
\(691\) −13268.5 −0.730476 −0.365238 0.930914i \(-0.619012\pi\)
−0.365238 + 0.930914i \(0.619012\pi\)
\(692\) −1284.17 −0.0705447
\(693\) 187.479 0.0102767
\(694\) 18863.9 1.03179
\(695\) 9237.84 0.504189
\(696\) −3378.62 −0.184003
\(697\) 27629.7 1.50150
\(698\) −5398.87 −0.292766
\(699\) −20427.0 −1.10532
\(700\) 74.2190 0.00400745
\(701\) −8331.99 −0.448923 −0.224461 0.974483i \(-0.572062\pi\)
−0.224461 + 0.974483i \(0.572062\pi\)
\(702\) −22711.7 −1.22108
\(703\) 98.0074 0.00525806
\(704\) −8245.94 −0.441450
\(705\) −2579.83 −0.137819
\(706\) −5284.22 −0.281691
\(707\) 2200.62 0.117062
\(708\) −120.705 −0.00640732
\(709\) −16348.8 −0.865996 −0.432998 0.901395i \(-0.642544\pi\)
−0.432998 + 0.901395i \(0.642544\pi\)
\(710\) 17979.5 0.950362
\(711\) −4408.13 −0.232514
\(712\) 13714.2 0.721855
\(713\) 10151.2 0.533191
\(714\) −3995.06 −0.209400
\(715\) 5818.65 0.304343
\(716\) −1245.19 −0.0649931
\(717\) 20894.8 1.08832
\(718\) −6779.03 −0.352355
\(719\) −12172.3 −0.631365 −0.315682 0.948865i \(-0.602233\pi\)
−0.315682 + 0.948865i \(0.602233\pi\)
\(720\) −2029.01 −0.105023
\(721\) 2879.84 0.148753
\(722\) 18931.6 0.975848
\(723\) 22109.7 1.13730
\(724\) −649.623 −0.0333467
\(725\) −2416.79 −0.123803
\(726\) −14189.5 −0.725377
\(727\) 29252.9 1.49234 0.746168 0.665757i \(-0.231891\pi\)
0.746168 + 0.665757i \(0.231891\pi\)
\(728\) 3171.93 0.161483
\(729\) 21835.8 1.10937
\(730\) −17244.7 −0.874320
\(731\) 21687.0 1.09729
\(732\) −979.491 −0.0494577
\(733\) 37664.4 1.89791 0.948955 0.315412i \(-0.102143\pi\)
0.948955 + 0.315412i \(0.102143\pi\)
\(734\) −18317.2 −0.921115
\(735\) −10878.7 −0.545940
\(736\) −576.718 −0.0288833
\(737\) −6516.52 −0.325697
\(738\) −3010.11 −0.150140
\(739\) −3929.89 −0.195620 −0.0978102 0.995205i \(-0.531184\pi\)
−0.0978102 + 0.995205i \(0.531184\pi\)
\(740\) −889.641 −0.0441944
\(741\) 74.5362 0.00369522
\(742\) −3642.90 −0.180236
\(743\) 11460.5 0.565877 0.282938 0.959138i \(-0.408691\pi\)
0.282938 + 0.959138i \(0.408691\pi\)
\(744\) −33057.6 −1.62896
\(745\) 14170.1 0.696847
\(746\) −12456.5 −0.611347
\(747\) −4112.06 −0.201409
\(748\) −725.572 −0.0354673
\(749\) 3153.26 0.153828
\(750\) 18088.2 0.880648
\(751\) −15877.5 −0.771477 −0.385738 0.922608i \(-0.626053\pi\)
−0.385738 + 0.922608i \(0.626053\pi\)
\(752\) 4855.71 0.235465
\(753\) −4762.00 −0.230461
\(754\) −4702.30 −0.227119
\(755\) 14.8546 0.000716043 0
\(756\) −142.893 −0.00687431
\(757\) −20218.6 −0.970750 −0.485375 0.874306i \(-0.661317\pi\)
−0.485375 + 0.874306i \(0.661317\pi\)
\(758\) 27467.4 1.31617
\(759\) 2428.50 0.116138
\(760\) 45.8392 0.00218785
\(761\) 23499.8 1.11940 0.559702 0.828694i \(-0.310915\pi\)
0.559702 + 0.828694i \(0.310915\pi\)
\(762\) 18544.1 0.881602
\(763\) 2065.67 0.0980109
\(764\) −135.047 −0.00639505
\(765\) −4109.53 −0.194223
\(766\) −15188.7 −0.716436
\(767\) −3690.07 −0.173717
\(768\) 2751.42 0.129275
\(769\) 29600.4 1.38806 0.694029 0.719947i \(-0.255834\pi\)
0.694029 + 0.719947i \(0.255834\pi\)
\(770\) −730.905 −0.0342078
\(771\) −17439.4 −0.814609
\(772\) −191.813 −0.00894238
\(773\) −27577.5 −1.28317 −0.641587 0.767050i \(-0.721724\pi\)
−0.641587 + 0.767050i \(0.721724\pi\)
\(774\) −2362.68 −0.109722
\(775\) −23646.7 −1.09602
\(776\) −16373.6 −0.757445
\(777\) 3991.36 0.184285
\(778\) 10582.2 0.487647
\(779\) 64.7529 0.00297819
\(780\) −676.587 −0.0310586
\(781\) −14650.1 −0.671219
\(782\) 11361.6 0.519555
\(783\) 4653.02 0.212370
\(784\) 20475.6 0.932744
\(785\) −2938.27 −0.133594
\(786\) 5639.14 0.255905
\(787\) 11651.2 0.527726 0.263863 0.964560i \(-0.415003\pi\)
0.263863 + 0.964560i \(0.415003\pi\)
\(788\) −1710.48 −0.0773266
\(789\) 22110.2 0.997646
\(790\) 17185.6 0.773968
\(791\) 5510.34 0.247693
\(792\) 1736.30 0.0778998
\(793\) −29944.0 −1.34091
\(794\) 39857.5 1.78147
\(795\) 17068.0 0.761436
\(796\) 652.798 0.0290676
\(797\) 31387.4 1.39498 0.697490 0.716595i \(-0.254300\pi\)
0.697490 + 0.716595i \(0.254300\pi\)
\(798\) −9.36281 −0.000415338 0
\(799\) 9834.66 0.435451
\(800\) 1343.44 0.0593721
\(801\) −2881.43 −0.127104
\(802\) 13263.9 0.583997
\(803\) 14051.4 0.617512
\(804\) 757.734 0.0332378
\(805\) −573.252 −0.0250987
\(806\) −46009.0 −2.01067
\(807\) 15470.4 0.674825
\(808\) 20380.6 0.887361
\(809\) −10893.6 −0.473422 −0.236711 0.971580i \(-0.576069\pi\)
−0.236711 + 0.971580i \(0.576069\pi\)
\(810\) −10879.8 −0.471946
\(811\) 29519.7 1.27815 0.639073 0.769146i \(-0.279318\pi\)
0.639073 + 0.769146i \(0.279318\pi\)
\(812\) −29.5851 −0.00127861
\(813\) 32615.0 1.40696
\(814\) −14472.9 −0.623187
\(815\) −16146.1 −0.693954
\(816\) −35230.7 −1.51142
\(817\) 50.8256 0.00217645
\(818\) 16870.9 0.721122
\(819\) −666.441 −0.0284339
\(820\) −587.780 −0.0250319
\(821\) −12375.9 −0.526092 −0.263046 0.964783i \(-0.584727\pi\)
−0.263046 + 0.964783i \(0.584727\pi\)
\(822\) −32920.2 −1.39687
\(823\) 269.809 0.0114276 0.00571382 0.999984i \(-0.498181\pi\)
0.00571382 + 0.999984i \(0.498181\pi\)
\(824\) 26671.1 1.12759
\(825\) −5657.08 −0.238733
\(826\) 463.526 0.0195256
\(827\) 31788.0 1.33661 0.668306 0.743887i \(-0.267020\pi\)
0.668306 + 0.743887i \(0.267020\pi\)
\(828\) 61.9971 0.00260211
\(829\) 16429.8 0.688336 0.344168 0.938908i \(-0.388161\pi\)
0.344168 + 0.938908i \(0.388161\pi\)
\(830\) 16031.3 0.670427
\(831\) −7242.71 −0.302343
\(832\) 29312.3 1.22142
\(833\) 41470.9 1.72495
\(834\) −17474.8 −0.725543
\(835\) 20130.2 0.834291
\(836\) −1.70045 −7.03484e−5 0
\(837\) 45526.9 1.88009
\(838\) 40375.2 1.66436
\(839\) −2939.79 −0.120969 −0.0604843 0.998169i \(-0.519265\pi\)
−0.0604843 + 0.998169i \(0.519265\pi\)
\(840\) 1866.81 0.0766798
\(841\) −23425.6 −0.960500
\(842\) −45459.4 −1.86061
\(843\) 1472.32 0.0601535
\(844\) 1081.17 0.0440941
\(845\) −5600.36 −0.227998
\(846\) −1071.43 −0.0435421
\(847\) −2729.23 −0.110717
\(848\) −32125.1 −1.30092
\(849\) −25802.3 −1.04303
\(850\) −26466.4 −1.06799
\(851\) −11351.1 −0.457241
\(852\) 1703.50 0.0684988
\(853\) 16894.9 0.678160 0.339080 0.940758i \(-0.389884\pi\)
0.339080 + 0.940758i \(0.389884\pi\)
\(854\) 3761.39 0.150717
\(855\) −9.63108 −0.000385235 0
\(856\) 29203.3 1.16606
\(857\) −27783.0 −1.10741 −0.553705 0.832713i \(-0.686786\pi\)
−0.553705 + 0.832713i \(0.686786\pi\)
\(858\) −11006.9 −0.437958
\(859\) −5869.41 −0.233134 −0.116567 0.993183i \(-0.537189\pi\)
−0.116567 + 0.993183i \(0.537189\pi\)
\(860\) −461.358 −0.0182932
\(861\) 2637.07 0.104380
\(862\) −3320.81 −0.131215
\(863\) −10920.8 −0.430763 −0.215381 0.976530i \(-0.569099\pi\)
−0.215381 + 0.976530i \(0.569099\pi\)
\(864\) −2586.51 −0.101846
\(865\) −23105.1 −0.908205
\(866\) −11870.9 −0.465810
\(867\) −48238.6 −1.88958
\(868\) −289.471 −0.0113195
\(869\) −14003.2 −0.546636
\(870\) −2767.49 −0.107847
\(871\) 23164.6 0.901152
\(872\) 19130.8 0.742949
\(873\) 3440.18 0.133371
\(874\) 26.6271 0.00103052
\(875\) 3479.09 0.134417
\(876\) −1633.88 −0.0630179
\(877\) −21819.5 −0.840127 −0.420063 0.907495i \(-0.637992\pi\)
−0.420063 + 0.907495i \(0.637992\pi\)
\(878\) −5131.82 −0.197256
\(879\) 32781.6 1.25790
\(880\) −6445.53 −0.246908
\(881\) 9861.42 0.377117 0.188558 0.982062i \(-0.439619\pi\)
0.188558 + 0.982062i \(0.439619\pi\)
\(882\) −4518.03 −0.172483
\(883\) −18010.0 −0.686393 −0.343197 0.939264i \(-0.611510\pi\)
−0.343197 + 0.939264i \(0.611510\pi\)
\(884\) 2579.23 0.0981324
\(885\) −2171.75 −0.0824889
\(886\) 7690.12 0.291597
\(887\) −11959.5 −0.452719 −0.226360 0.974044i \(-0.572682\pi\)
−0.226360 + 0.974044i \(0.572682\pi\)
\(888\) 36965.3 1.39693
\(889\) 3566.78 0.134562
\(890\) 11233.5 0.423089
\(891\) 8865.11 0.333325
\(892\) −631.648 −0.0237098
\(893\) 23.0485 0.000863704 0
\(894\) −26804.9 −1.00278
\(895\) −22403.8 −0.836732
\(896\) −3337.26 −0.124431
\(897\) −8632.73 −0.321336
\(898\) −6650.97 −0.247156
\(899\) 9426.03 0.349695
\(900\) −144.419 −0.00534886
\(901\) −65065.6 −2.40582
\(902\) −9562.15 −0.352976
\(903\) 2069.88 0.0762805
\(904\) 51033.0 1.87758
\(905\) −11688.1 −0.429312
\(906\) −28.0997 −0.00103041
\(907\) 24963.8 0.913902 0.456951 0.889492i \(-0.348941\pi\)
0.456951 + 0.889492i \(0.348941\pi\)
\(908\) 1261.18 0.0460944
\(909\) −4282.08 −0.156246
\(910\) 2598.19 0.0946475
\(911\) 51520.2 1.87370 0.936851 0.349730i \(-0.113727\pi\)
0.936851 + 0.349730i \(0.113727\pi\)
\(912\) −82.5665 −0.00299786
\(913\) −13062.7 −0.473507
\(914\) 15428.2 0.558335
\(915\) −17623.2 −0.636727
\(916\) 650.934 0.0234798
\(917\) 1084.64 0.0390598
\(918\) 50955.6 1.83201
\(919\) 4232.26 0.151914 0.0759572 0.997111i \(-0.475799\pi\)
0.0759572 + 0.997111i \(0.475799\pi\)
\(920\) −5309.06 −0.190255
\(921\) −15537.3 −0.555885
\(922\) −37857.3 −1.35224
\(923\) 52077.6 1.85716
\(924\) −69.2511 −0.00246558
\(925\) 26442.0 0.939899
\(926\) 24976.8 0.886382
\(927\) −5603.74 −0.198545
\(928\) −535.519 −0.0189432
\(929\) −33324.8 −1.17691 −0.588456 0.808529i \(-0.700264\pi\)
−0.588456 + 0.808529i \(0.700264\pi\)
\(930\) −27078.1 −0.954759
\(931\) 97.1911 0.00342138
\(932\) −1656.57 −0.0582218
\(933\) −28253.3 −0.991393
\(934\) 50363.3 1.76439
\(935\) −13054.6 −0.456612
\(936\) −6172.12 −0.215536
\(937\) 8530.17 0.297405 0.148703 0.988882i \(-0.452490\pi\)
0.148703 + 0.988882i \(0.452490\pi\)
\(938\) −2909.81 −0.101288
\(939\) 32224.3 1.11991
\(940\) −209.218 −0.00725949
\(941\) 20764.3 0.719339 0.359669 0.933080i \(-0.382890\pi\)
0.359669 + 0.933080i \(0.382890\pi\)
\(942\) 5558.19 0.192246
\(943\) −7499.63 −0.258984
\(944\) 4087.63 0.140933
\(945\) −2570.97 −0.0885011
\(946\) −7505.49 −0.257954
\(947\) −11879.1 −0.407622 −0.203811 0.979010i \(-0.565333\pi\)
−0.203811 + 0.979010i \(0.565333\pi\)
\(948\) 1628.28 0.0557849
\(949\) −49949.2 −1.70856
\(950\) −62.0267 −0.00211833
\(951\) 25507.5 0.869755
\(952\) −7116.51 −0.242277
\(953\) −40654.8 −1.38189 −0.690943 0.722909i \(-0.742805\pi\)
−0.690943 + 0.722909i \(0.742805\pi\)
\(954\) 7088.55 0.240566
\(955\) −2429.79 −0.0823311
\(956\) 1694.51 0.0573267
\(957\) 2255.02 0.0761697
\(958\) −37822.2 −1.27555
\(959\) −6331.89 −0.213209
\(960\) 17251.5 0.579988
\(961\) 62436.6 2.09582
\(962\) 51447.6 1.72426
\(963\) −6135.78 −0.205319
\(964\) 1793.03 0.0599063
\(965\) −3451.15 −0.115126
\(966\) 1084.39 0.0361178
\(967\) −29182.9 −0.970486 −0.485243 0.874379i \(-0.661269\pi\)
−0.485243 + 0.874379i \(0.661269\pi\)
\(968\) −25276.2 −0.839266
\(969\) −167.229 −0.00554402
\(970\) −13411.9 −0.443949
\(971\) 21283.8 0.703430 0.351715 0.936107i \(-0.385599\pi\)
0.351715 + 0.936107i \(0.385599\pi\)
\(972\) 513.679 0.0169509
\(973\) −3361.12 −0.110742
\(974\) 56769.5 1.86757
\(975\) 20109.6 0.660535
\(976\) 33170.0 1.08786
\(977\) 40886.1 1.33886 0.669428 0.742877i \(-0.266539\pi\)
0.669428 + 0.742877i \(0.266539\pi\)
\(978\) 30542.8 0.998621
\(979\) −9153.37 −0.298818
\(980\) −882.231 −0.0287570
\(981\) −4019.49 −0.130818
\(982\) −40418.0 −1.31343
\(983\) 8436.41 0.273733 0.136867 0.990589i \(-0.456297\pi\)
0.136867 + 0.990589i \(0.456297\pi\)
\(984\) 24422.7 0.791227
\(985\) −30775.3 −0.995516
\(986\) 10550.0 0.340751
\(987\) 938.653 0.0302712
\(988\) 6.04469 0.000194643 0
\(989\) −5886.58 −0.189264
\(990\) 1422.23 0.0456582
\(991\) −4587.60 −0.147053 −0.0735267 0.997293i \(-0.523425\pi\)
−0.0735267 + 0.997293i \(0.523425\pi\)
\(992\) −5239.71 −0.167703
\(993\) −39387.8 −1.25875
\(994\) −6541.69 −0.208742
\(995\) 11745.3 0.374222
\(996\) 1518.92 0.0483220
\(997\) 1524.36 0.0484221 0.0242111 0.999707i \(-0.492293\pi\)
0.0242111 + 0.999707i \(0.492293\pi\)
\(998\) −22628.5 −0.717730
\(999\) −50908.5 −1.61229
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 1997.4.a.a.1.70 239
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1997.4.a.a.1.70 239 1.1 even 1 trivial