Properties

Label 177.4.a.a.1.1
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.4433380710\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 34 x^{5} + 25 x^{4} + 315 x^{3} - 146 x^{2} - 736 x + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.60512\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.60512 q^{2} +3.00000 q^{3} +23.4174 q^{4} +12.9748 q^{5} -16.8154 q^{6} -18.2988 q^{7} -86.4162 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-5.60512 q^{2} +3.00000 q^{3} +23.4174 q^{4} +12.9748 q^{5} -16.8154 q^{6} -18.2988 q^{7} -86.4162 q^{8} +9.00000 q^{9} -72.7251 q^{10} -71.8350 q^{11} +70.2521 q^{12} +31.4840 q^{13} +102.567 q^{14} +38.9243 q^{15} +297.034 q^{16} -94.8120 q^{17} -50.4461 q^{18} -53.7002 q^{19} +303.835 q^{20} -54.8965 q^{21} +402.644 q^{22} -70.2521 q^{23} -259.249 q^{24} +43.3445 q^{25} -176.472 q^{26} +27.0000 q^{27} -428.510 q^{28} +20.2046 q^{29} -218.175 q^{30} -5.95239 q^{31} -973.582 q^{32} -215.505 q^{33} +531.432 q^{34} -237.423 q^{35} +210.756 q^{36} +167.214 q^{37} +300.996 q^{38} +94.4520 q^{39} -1121.23 q^{40} +248.975 q^{41} +307.701 q^{42} -472.012 q^{43} -1682.19 q^{44} +116.773 q^{45} +393.771 q^{46} -140.560 q^{47} +891.102 q^{48} -8.15281 q^{49} -242.951 q^{50} -284.436 q^{51} +737.272 q^{52} -21.3540 q^{53} -151.338 q^{54} -932.042 q^{55} +1581.32 q^{56} -161.100 q^{57} -113.249 q^{58} -59.0000 q^{59} +911.504 q^{60} +375.516 q^{61} +33.3639 q^{62} -164.689 q^{63} +3080.77 q^{64} +408.497 q^{65} +1207.93 q^{66} -410.115 q^{67} -2220.25 q^{68} -210.756 q^{69} +1330.78 q^{70} +420.452 q^{71} -777.746 q^{72} -865.694 q^{73} -937.256 q^{74} +130.033 q^{75} -1257.52 q^{76} +1314.50 q^{77} -529.415 q^{78} -53.7139 q^{79} +3853.95 q^{80} +81.0000 q^{81} -1395.54 q^{82} +39.4923 q^{83} -1285.53 q^{84} -1230.16 q^{85} +2645.68 q^{86} +60.6137 q^{87} +6207.70 q^{88} -354.864 q^{89} -654.526 q^{90} -576.120 q^{91} -1645.12 q^{92} -17.8572 q^{93} +787.856 q^{94} -696.747 q^{95} -2920.75 q^{96} -1419.08 q^{97} +45.6975 q^{98} -646.515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} - 79q^{10} - 131q^{11} + 66q^{12} - 123q^{13} - 117q^{14} - 84q^{15} + 202q^{16} - 235q^{17} - 72q^{18} - 80q^{19} + 61q^{20} - 177q^{21} + 688q^{22} - 274q^{23} - 351q^{24} + 193q^{25} - 180q^{26} + 189q^{27} - 118q^{28} - 406q^{29} - 237q^{30} - 346q^{31} - 854q^{32} - 393q^{33} + 178q^{34} - 424q^{35} + 198q^{36} - 157q^{37} - 129q^{38} - 369q^{39} - 590q^{40} - 825q^{41} - 351q^{42} - 815q^{43} - 1690q^{44} - 252q^{45} + 1457q^{46} - 1196q^{47} + 606q^{48} + 914q^{49} + 713q^{50} - 705q^{51} + 1030q^{52} - 900q^{53} - 216q^{54} - 1044q^{55} + 2172q^{56} - 240q^{57} + 1242q^{58} - 413q^{59} + 183q^{60} + 420q^{61} + 646q^{62} - 531q^{63} + 3541q^{64} + 190q^{65} + 2064q^{66} + 1316q^{67} - 611q^{68} - 822q^{69} + 4658q^{70} - 173q^{71} - 1053q^{72} - 418q^{73} + 660q^{74} + 579q^{75} + 1540q^{76} - 753q^{77} - 540q^{78} + 2635q^{79} + 6155q^{80} + 567q^{81} - 125q^{82} + 457q^{83} - 354q^{84} + 1270q^{85} + 3482q^{86} - 1218q^{87} + 7685q^{88} + 592q^{89} - 711q^{90} + 3179q^{91} - 3500q^{92} - 1038q^{93} + 2064q^{94} - 2250q^{95} - 2562q^{96} - 1906q^{97} + 2994q^{98} - 1179q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.60512 −1.98171 −0.990855 0.134934i \(-0.956918\pi\)
−0.990855 + 0.134934i \(0.956918\pi\)
\(3\) 3.00000 0.577350
\(4\) 23.4174 2.92717
\(5\) 12.9748 1.16050 0.580249 0.814439i \(-0.302955\pi\)
0.580249 + 0.814439i \(0.302955\pi\)
\(6\) −16.8154 −1.14414
\(7\) −18.2988 −0.988044 −0.494022 0.869449i \(-0.664474\pi\)
−0.494022 + 0.869449i \(0.664474\pi\)
\(8\) −86.4162 −3.81909
\(9\) 9.00000 0.333333
\(10\) −72.7251 −2.29977
\(11\) −71.8350 −1.96901 −0.984503 0.175370i \(-0.943888\pi\)
−0.984503 + 0.175370i \(0.943888\pi\)
\(12\) 70.2521 1.69000
\(13\) 31.4840 0.671699 0.335850 0.941916i \(-0.390977\pi\)
0.335850 + 0.941916i \(0.390977\pi\)
\(14\) 102.567 1.95802
\(15\) 38.9243 0.670014
\(16\) 297.034 4.64116
\(17\) −94.8120 −1.35266 −0.676332 0.736597i \(-0.736431\pi\)
−0.676332 + 0.736597i \(0.736431\pi\)
\(18\) −50.4461 −0.660570
\(19\) −53.7002 −0.648403 −0.324202 0.945988i \(-0.605096\pi\)
−0.324202 + 0.945988i \(0.605096\pi\)
\(20\) 303.835 3.39698
\(21\) −54.8965 −0.570447
\(22\) 402.644 3.90200
\(23\) −70.2521 −0.636894 −0.318447 0.947941i \(-0.603161\pi\)
−0.318447 + 0.947941i \(0.603161\pi\)
\(24\) −259.249 −2.20495
\(25\) 43.3445 0.346756
\(26\) −176.472 −1.33111
\(27\) 27.0000 0.192450
\(28\) −428.510 −2.89217
\(29\) 20.2046 0.129376 0.0646879 0.997906i \(-0.479395\pi\)
0.0646879 + 0.997906i \(0.479395\pi\)
\(30\) −218.175 −1.32777
\(31\) −5.95239 −0.0344865 −0.0172433 0.999851i \(-0.505489\pi\)
−0.0172433 + 0.999851i \(0.505489\pi\)
\(32\) −973.582 −5.37833
\(33\) −215.505 −1.13681
\(34\) 531.432 2.68059
\(35\) −237.423 −1.14662
\(36\) 210.756 0.975724
\(37\) 167.214 0.742969 0.371484 0.928439i \(-0.378849\pi\)
0.371484 + 0.928439i \(0.378849\pi\)
\(38\) 300.996 1.28495
\(39\) 94.4520 0.387806
\(40\) −1121.23 −4.43205
\(41\) 248.975 0.948376 0.474188 0.880424i \(-0.342742\pi\)
0.474188 + 0.880424i \(0.342742\pi\)
\(42\) 307.701 1.13046
\(43\) −472.012 −1.67398 −0.836990 0.547218i \(-0.815687\pi\)
−0.836990 + 0.547218i \(0.815687\pi\)
\(44\) −1682.19 −5.76361
\(45\) 116.773 0.386833
\(46\) 393.771 1.26214
\(47\) −140.560 −0.436230 −0.218115 0.975923i \(-0.569991\pi\)
−0.218115 + 0.975923i \(0.569991\pi\)
\(48\) 891.102 2.67957
\(49\) −8.15281 −0.0237691
\(50\) −242.951 −0.687169
\(51\) −284.436 −0.780961
\(52\) 737.272 1.96618
\(53\) −21.3540 −0.0553434 −0.0276717 0.999617i \(-0.508809\pi\)
−0.0276717 + 0.999617i \(0.508809\pi\)
\(54\) −151.338 −0.381380
\(55\) −932.042 −2.28503
\(56\) 1581.32 3.77343
\(57\) −161.100 −0.374356
\(58\) −113.249 −0.256385
\(59\) −59.0000 −0.130189
\(60\) 911.504 1.96125
\(61\) 375.516 0.788196 0.394098 0.919068i \(-0.371057\pi\)
0.394098 + 0.919068i \(0.371057\pi\)
\(62\) 33.3639 0.0683422
\(63\) −164.689 −0.329348
\(64\) 3080.77 6.01713
\(65\) 408.497 0.779505
\(66\) 1207.93 2.25282
\(67\) −410.115 −0.747814 −0.373907 0.927466i \(-0.621982\pi\)
−0.373907 + 0.927466i \(0.621982\pi\)
\(68\) −2220.25 −3.95948
\(69\) −210.756 −0.367711
\(70\) 1330.78 2.27227
\(71\) 420.452 0.702796 0.351398 0.936226i \(-0.385706\pi\)
0.351398 + 0.936226i \(0.385706\pi\)
\(72\) −777.746 −1.27303
\(73\) −865.694 −1.38797 −0.693985 0.719990i \(-0.744147\pi\)
−0.693985 + 0.719990i \(0.744147\pi\)
\(74\) −937.256 −1.47235
\(75\) 130.033 0.200200
\(76\) −1257.52 −1.89799
\(77\) 1314.50 1.94546
\(78\) −529.415 −0.768518
\(79\) −53.7139 −0.0764973 −0.0382486 0.999268i \(-0.512178\pi\)
−0.0382486 + 0.999268i \(0.512178\pi\)
\(80\) 3853.95 5.38606
\(81\) 81.0000 0.111111
\(82\) −1395.54 −1.87940
\(83\) 39.4923 0.0522270 0.0261135 0.999659i \(-0.491687\pi\)
0.0261135 + 0.999659i \(0.491687\pi\)
\(84\) −1285.53 −1.66980
\(85\) −1230.16 −1.56976
\(86\) 2645.68 3.31734
\(87\) 60.6137 0.0746951
\(88\) 6207.70 7.51981
\(89\) −354.864 −0.422646 −0.211323 0.977416i \(-0.567777\pi\)
−0.211323 + 0.977416i \(0.567777\pi\)
\(90\) −654.526 −0.766590
\(91\) −576.120 −0.663668
\(92\) −1645.12 −1.86430
\(93\) −17.8572 −0.0199108
\(94\) 787.856 0.864480
\(95\) −696.747 −0.752471
\(96\) −2920.75 −3.10518
\(97\) −1419.08 −1.48542 −0.742709 0.669614i \(-0.766460\pi\)
−0.742709 + 0.669614i \(0.766460\pi\)
\(98\) 45.6975 0.0471035
\(99\) −646.515 −0.656335
\(100\) 1015.01 1.01501
\(101\) 1095.50 1.07927 0.539635 0.841899i \(-0.318562\pi\)
0.539635 + 0.841899i \(0.318562\pi\)
\(102\) 1594.30 1.54764
\(103\) −240.220 −0.229802 −0.114901 0.993377i \(-0.536655\pi\)
−0.114901 + 0.993377i \(0.536655\pi\)
\(104\) −2720.73 −2.56528
\(105\) −712.269 −0.662003
\(106\) 119.692 0.109675
\(107\) −313.972 −0.283671 −0.141835 0.989890i \(-0.545300\pi\)
−0.141835 + 0.989890i \(0.545300\pi\)
\(108\) 632.269 0.563334
\(109\) −624.891 −0.549117 −0.274558 0.961570i \(-0.588532\pi\)
−0.274558 + 0.961570i \(0.588532\pi\)
\(110\) 5224.20 4.52826
\(111\) 501.643 0.428953
\(112\) −5435.38 −4.58567
\(113\) 201.896 0.168078 0.0840388 0.996462i \(-0.473218\pi\)
0.0840388 + 0.996462i \(0.473218\pi\)
\(114\) 902.987 0.741864
\(115\) −911.504 −0.739114
\(116\) 473.138 0.378705
\(117\) 283.356 0.223900
\(118\) 330.702 0.257997
\(119\) 1734.95 1.33649
\(120\) −3363.69 −2.55884
\(121\) 3829.26 2.87698
\(122\) −2104.81 −1.56197
\(123\) 746.926 0.547545
\(124\) −139.389 −0.100948
\(125\) −1059.46 −0.758089
\(126\) 923.104 0.652672
\(127\) 2526.09 1.76499 0.882496 0.470321i \(-0.155862\pi\)
0.882496 + 0.470321i \(0.155862\pi\)
\(128\) −9479.44 −6.54588
\(129\) −1416.04 −0.966473
\(130\) −2289.68 −1.54475
\(131\) 1418.96 0.946373 0.473186 0.880962i \(-0.343104\pi\)
0.473186 + 0.880962i \(0.343104\pi\)
\(132\) −5046.56 −3.32762
\(133\) 982.650 0.640651
\(134\) 2298.74 1.48195
\(135\) 350.319 0.223338
\(136\) 8193.29 5.16595
\(137\) −1921.39 −1.19821 −0.599106 0.800670i \(-0.704477\pi\)
−0.599106 + 0.800670i \(0.704477\pi\)
\(138\) 1181.31 0.728696
\(139\) −331.294 −0.202158 −0.101079 0.994878i \(-0.532229\pi\)
−0.101079 + 0.994878i \(0.532229\pi\)
\(140\) −5559.82 −3.35636
\(141\) −421.680 −0.251857
\(142\) −2356.69 −1.39274
\(143\) −2261.65 −1.32258
\(144\) 2673.31 1.54705
\(145\) 262.150 0.150140
\(146\) 4852.32 2.75055
\(147\) −24.4584 −0.0137231
\(148\) 3915.72 2.17480
\(149\) −2319.61 −1.27537 −0.637683 0.770299i \(-0.720107\pi\)
−0.637683 + 0.770299i \(0.720107\pi\)
\(150\) −728.853 −0.396737
\(151\) 1007.48 0.542962 0.271481 0.962444i \(-0.412487\pi\)
0.271481 + 0.962444i \(0.412487\pi\)
\(152\) 4640.56 2.47631
\(153\) −853.308 −0.450888
\(154\) −7367.91 −3.85534
\(155\) −77.2309 −0.0400215
\(156\) 2211.82 1.13517
\(157\) 1583.56 0.804982 0.402491 0.915424i \(-0.368144\pi\)
0.402491 + 0.915424i \(0.368144\pi\)
\(158\) 301.073 0.151595
\(159\) −64.0621 −0.0319525
\(160\) −12632.0 −6.24155
\(161\) 1285.53 0.629279
\(162\) −454.015 −0.220190
\(163\) −801.561 −0.385172 −0.192586 0.981280i \(-0.561687\pi\)
−0.192586 + 0.981280i \(0.561687\pi\)
\(164\) 5830.34 2.77606
\(165\) −2796.12 −1.31926
\(166\) −221.359 −0.103499
\(167\) 848.880 0.393343 0.196672 0.980469i \(-0.436987\pi\)
0.196672 + 0.980469i \(0.436987\pi\)
\(168\) 4743.95 2.17859
\(169\) −1205.76 −0.548820
\(170\) 6895.21 3.11081
\(171\) −483.301 −0.216134
\(172\) −11053.3 −4.90002
\(173\) 3645.72 1.60219 0.801095 0.598537i \(-0.204251\pi\)
0.801095 + 0.598537i \(0.204251\pi\)
\(174\) −339.747 −0.148024
\(175\) −793.153 −0.342610
\(176\) −21337.4 −9.13846
\(177\) −177.000 −0.0751646
\(178\) 1989.05 0.837562
\(179\) −1134.73 −0.473818 −0.236909 0.971532i \(-0.576134\pi\)
−0.236909 + 0.971532i \(0.576134\pi\)
\(180\) 2734.51 1.13233
\(181\) −2351.48 −0.965656 −0.482828 0.875715i \(-0.660390\pi\)
−0.482828 + 0.875715i \(0.660390\pi\)
\(182\) 3229.22 1.31520
\(183\) 1126.55 0.455065
\(184\) 6070.91 2.43236
\(185\) 2169.56 0.862214
\(186\) 100.092 0.0394574
\(187\) 6810.81 2.66340
\(188\) −3291.55 −1.27692
\(189\) −494.068 −0.190149
\(190\) 3905.35 1.49118
\(191\) 2659.35 1.00745 0.503727 0.863863i \(-0.331962\pi\)
0.503727 + 0.863863i \(0.331962\pi\)
\(192\) 9242.32 3.47399
\(193\) 191.102 0.0712735 0.0356368 0.999365i \(-0.488654\pi\)
0.0356368 + 0.999365i \(0.488654\pi\)
\(194\) 7954.11 2.94367
\(195\) 1225.49 0.450048
\(196\) −190.917 −0.0695763
\(197\) 4448.69 1.60891 0.804456 0.594012i \(-0.202457\pi\)
0.804456 + 0.594012i \(0.202457\pi\)
\(198\) 3623.79 1.30067
\(199\) 2989.63 1.06497 0.532485 0.846439i \(-0.321258\pi\)
0.532485 + 0.846439i \(0.321258\pi\)
\(200\) −3745.66 −1.32429
\(201\) −1230.35 −0.431750
\(202\) −6140.41 −2.13880
\(203\) −369.720 −0.127829
\(204\) −6660.74 −2.28601
\(205\) 3230.39 1.10059
\(206\) 1346.46 0.455400
\(207\) −632.268 −0.212298
\(208\) 9351.82 3.11746
\(209\) 3857.55 1.27671
\(210\) 3992.35 1.31190
\(211\) −1312.96 −0.428379 −0.214189 0.976792i \(-0.568711\pi\)
−0.214189 + 0.976792i \(0.568711\pi\)
\(212\) −500.055 −0.162000
\(213\) 1261.36 0.405759
\(214\) 1759.85 0.562153
\(215\) −6124.24 −1.94265
\(216\) −2333.24 −0.734985
\(217\) 108.922 0.0340742
\(218\) 3502.59 1.08819
\(219\) −2597.08 −0.801345
\(220\) −21826.0 −6.68866
\(221\) −2985.06 −0.908583
\(222\) −2811.77 −0.850060
\(223\) −1272.27 −0.382052 −0.191026 0.981585i \(-0.561181\pi\)
−0.191026 + 0.981585i \(0.561181\pi\)
\(224\) 17815.4 5.31403
\(225\) 390.100 0.115585
\(226\) −1131.65 −0.333081
\(227\) −1528.48 −0.446910 −0.223455 0.974714i \(-0.571734\pi\)
−0.223455 + 0.974714i \(0.571734\pi\)
\(228\) −3772.55 −1.09580
\(229\) −210.914 −0.0608629 −0.0304314 0.999537i \(-0.509688\pi\)
−0.0304314 + 0.999537i \(0.509688\pi\)
\(230\) 5109.09 1.46471
\(231\) 3943.49 1.12321
\(232\) −1746.00 −0.494098
\(233\) −2452.82 −0.689655 −0.344827 0.938666i \(-0.612063\pi\)
−0.344827 + 0.938666i \(0.612063\pi\)
\(234\) −1588.24 −0.443704
\(235\) −1823.73 −0.506244
\(236\) −1381.62 −0.381085
\(237\) −161.142 −0.0441657
\(238\) −9724.59 −2.64854
\(239\) 1180.65 0.319540 0.159770 0.987154i \(-0.448925\pi\)
0.159770 + 0.987154i \(0.448925\pi\)
\(240\) 11561.8 3.10964
\(241\) −2161.44 −0.577719 −0.288860 0.957371i \(-0.593276\pi\)
−0.288860 + 0.957371i \(0.593276\pi\)
\(242\) −21463.5 −5.70134
\(243\) 243.000 0.0641500
\(244\) 8793.60 2.30718
\(245\) −105.781 −0.0275840
\(246\) −4186.61 −1.08507
\(247\) −1690.70 −0.435532
\(248\) 514.383 0.131707
\(249\) 118.477 0.0301533
\(250\) 5938.41 1.50231
\(251\) −2174.07 −0.546718 −0.273359 0.961912i \(-0.588135\pi\)
−0.273359 + 0.961912i \(0.588135\pi\)
\(252\) −3856.59 −0.964058
\(253\) 5046.55 1.25405
\(254\) −14159.0 −3.49770
\(255\) −3690.49 −0.906303
\(256\) 28487.2 6.95489
\(257\) 6563.41 1.59305 0.796526 0.604604i \(-0.206669\pi\)
0.796526 + 0.604604i \(0.206669\pi\)
\(258\) 7937.05 1.91527
\(259\) −3059.82 −0.734086
\(260\) 9565.93 2.28175
\(261\) 181.841 0.0431252
\(262\) −7953.42 −1.87544
\(263\) −1733.36 −0.406401 −0.203201 0.979137i \(-0.565134\pi\)
−0.203201 + 0.979137i \(0.565134\pi\)
\(264\) 18623.1 4.34157
\(265\) −277.063 −0.0642259
\(266\) −5507.87 −1.26958
\(267\) −1064.59 −0.244015
\(268\) −9603.81 −2.18898
\(269\) 1240.79 0.281235 0.140618 0.990064i \(-0.455091\pi\)
0.140618 + 0.990064i \(0.455091\pi\)
\(270\) −1963.58 −0.442591
\(271\) −1238.86 −0.277695 −0.138848 0.990314i \(-0.544340\pi\)
−0.138848 + 0.990314i \(0.544340\pi\)
\(272\) −28162.4 −6.27793
\(273\) −1728.36 −0.383169
\(274\) 10769.6 2.37451
\(275\) −3113.65 −0.682764
\(276\) −4935.35 −1.07635
\(277\) −5349.92 −1.16045 −0.580226 0.814455i \(-0.697036\pi\)
−0.580226 + 0.814455i \(0.697036\pi\)
\(278\) 1856.94 0.400619
\(279\) −53.5716 −0.0114955
\(280\) 20517.2 4.37906
\(281\) −1010.45 −0.214514 −0.107257 0.994231i \(-0.534207\pi\)
−0.107257 + 0.994231i \(0.534207\pi\)
\(282\) 2363.57 0.499108
\(283\) −1311.57 −0.275493 −0.137746 0.990468i \(-0.543986\pi\)
−0.137746 + 0.990468i \(0.543986\pi\)
\(284\) 9845.88 2.05720
\(285\) −2090.24 −0.434439
\(286\) 12676.8 2.62097
\(287\) −4555.96 −0.937037
\(288\) −8762.24 −1.79278
\(289\) 4076.31 0.829699
\(290\) −1469.38 −0.297534
\(291\) −4257.24 −0.857607
\(292\) −20272.3 −4.06282
\(293\) −6982.71 −1.39227 −0.696134 0.717912i \(-0.745098\pi\)
−0.696134 + 0.717912i \(0.745098\pi\)
\(294\) 137.092 0.0271952
\(295\) −765.511 −0.151084
\(296\) −14450.0 −2.83747
\(297\) −1939.54 −0.378935
\(298\) 13001.7 2.52741
\(299\) −2211.81 −0.427801
\(300\) 3045.04 0.586018
\(301\) 8637.26 1.65397
\(302\) −5647.03 −1.07599
\(303\) 3286.50 0.623117
\(304\) −15950.8 −3.00934
\(305\) 4872.23 0.914700
\(306\) 4782.89 0.893529
\(307\) 2577.38 0.479148 0.239574 0.970878i \(-0.422992\pi\)
0.239574 + 0.970878i \(0.422992\pi\)
\(308\) 30782.0 5.69470
\(309\) −720.659 −0.132676
\(310\) 432.888 0.0793110
\(311\) 6320.88 1.15249 0.576244 0.817277i \(-0.304518\pi\)
0.576244 + 0.817277i \(0.304518\pi\)
\(312\) −8162.18 −1.48107
\(313\) −2703.12 −0.488145 −0.244073 0.969757i \(-0.578483\pi\)
−0.244073 + 0.969757i \(0.578483\pi\)
\(314\) −8876.07 −1.59524
\(315\) −2136.81 −0.382208
\(316\) −1257.84 −0.223921
\(317\) −8918.51 −1.58017 −0.790084 0.612999i \(-0.789963\pi\)
−0.790084 + 0.612999i \(0.789963\pi\)
\(318\) 359.076 0.0633206
\(319\) −1451.40 −0.254741
\(320\) 39972.3 6.98287
\(321\) −941.915 −0.163777
\(322\) −7205.55 −1.24705
\(323\) 5091.42 0.877071
\(324\) 1896.81 0.325241
\(325\) 1364.66 0.232915
\(326\) 4492.84 0.763299
\(327\) −1874.67 −0.317033
\(328\) −21515.5 −3.62193
\(329\) 2572.08 0.431014
\(330\) 15672.6 2.61439
\(331\) −8555.58 −1.42072 −0.710358 0.703841i \(-0.751467\pi\)
−0.710358 + 0.703841i \(0.751467\pi\)
\(332\) 924.805 0.152877
\(333\) 1504.93 0.247656
\(334\) −4758.07 −0.779491
\(335\) −5321.15 −0.867836
\(336\) −16306.1 −2.64754
\(337\) 6636.10 1.07268 0.536338 0.844003i \(-0.319807\pi\)
0.536338 + 0.844003i \(0.319807\pi\)
\(338\) 6758.42 1.08760
\(339\) 605.688 0.0970397
\(340\) −28807.2 −4.59497
\(341\) 427.590 0.0679041
\(342\) 2708.96 0.428315
\(343\) 6425.69 1.01153
\(344\) 40789.5 6.39308
\(345\) −2734.51 −0.426728
\(346\) −20434.7 −3.17507
\(347\) 10375.1 1.60508 0.802539 0.596599i \(-0.203482\pi\)
0.802539 + 0.596599i \(0.203482\pi\)
\(348\) 1419.41 0.218645
\(349\) −1257.24 −0.192832 −0.0964160 0.995341i \(-0.530738\pi\)
−0.0964160 + 0.995341i \(0.530738\pi\)
\(350\) 4445.72 0.678953
\(351\) 850.068 0.129269
\(352\) 69937.3 10.5900
\(353\) 10418.3 1.57085 0.785426 0.618955i \(-0.212444\pi\)
0.785426 + 0.618955i \(0.212444\pi\)
\(354\) 992.106 0.148954
\(355\) 5455.27 0.815593
\(356\) −8309.98 −1.23716
\(357\) 5204.84 0.771623
\(358\) 6360.27 0.938969
\(359\) 3999.50 0.587983 0.293991 0.955808i \(-0.405016\pi\)
0.293991 + 0.955808i \(0.405016\pi\)
\(360\) −10091.1 −1.47735
\(361\) −3975.29 −0.579573
\(362\) 13180.3 1.91365
\(363\) 11487.8 1.66103
\(364\) −13491.2 −1.94267
\(365\) −11232.2 −1.61074
\(366\) −6314.44 −0.901806
\(367\) −171.633 −0.0244119 −0.0122060 0.999926i \(-0.503885\pi\)
−0.0122060 + 0.999926i \(0.503885\pi\)
\(368\) −20867.3 −2.95593
\(369\) 2240.78 0.316125
\(370\) −12160.7 −1.70866
\(371\) 390.754 0.0546817
\(372\) −418.168 −0.0582823
\(373\) −10286.9 −1.42798 −0.713990 0.700156i \(-0.753114\pi\)
−0.713990 + 0.700156i \(0.753114\pi\)
\(374\) −38175.4 −5.27809
\(375\) −3178.38 −0.437683
\(376\) 12146.7 1.66600
\(377\) 636.121 0.0869015
\(378\) 2769.31 0.376820
\(379\) −4410.20 −0.597722 −0.298861 0.954297i \(-0.596607\pi\)
−0.298861 + 0.954297i \(0.596607\pi\)
\(380\) −16316.0 −2.20261
\(381\) 7578.26 1.01902
\(382\) −14906.0 −1.99648
\(383\) −3877.45 −0.517307 −0.258654 0.965970i \(-0.583279\pi\)
−0.258654 + 0.965970i \(0.583279\pi\)
\(384\) −28438.3 −3.77926
\(385\) 17055.3 2.25771
\(386\) −1071.15 −0.141243
\(387\) −4248.11 −0.557993
\(388\) −33231.1 −4.34807
\(389\) −8465.37 −1.10337 −0.551686 0.834052i \(-0.686015\pi\)
−0.551686 + 0.834052i \(0.686015\pi\)
\(390\) −6869.03 −0.891864
\(391\) 6660.74 0.861503
\(392\) 704.534 0.0907764
\(393\) 4256.87 0.546389
\(394\) −24935.4 −3.18840
\(395\) −696.925 −0.0887749
\(396\) −15139.7 −1.92120
\(397\) 13428.9 1.69768 0.848839 0.528652i \(-0.177302\pi\)
0.848839 + 0.528652i \(0.177302\pi\)
\(398\) −16757.2 −2.11046
\(399\) 2947.95 0.369880
\(400\) 12874.8 1.60935
\(401\) 12373.5 1.54091 0.770455 0.637494i \(-0.220029\pi\)
0.770455 + 0.637494i \(0.220029\pi\)
\(402\) 6896.23 0.855604
\(403\) −187.405 −0.0231646
\(404\) 25653.7 3.15921
\(405\) 1050.96 0.128944
\(406\) 2072.33 0.253320
\(407\) −12011.8 −1.46291
\(408\) 24579.9 2.98256
\(409\) 11757.4 1.42143 0.710717 0.703478i \(-0.248371\pi\)
0.710717 + 0.703478i \(0.248371\pi\)
\(410\) −18106.7 −2.18105
\(411\) −5764.16 −0.691788
\(412\) −5625.31 −0.672668
\(413\) 1079.63 0.128632
\(414\) 3543.94 0.420713
\(415\) 512.403 0.0606093
\(416\) −30652.3 −3.61262
\(417\) −993.881 −0.116716
\(418\) −21622.0 −2.53007
\(419\) 3644.71 0.424954 0.212477 0.977166i \(-0.431847\pi\)
0.212477 + 0.977166i \(0.431847\pi\)
\(420\) −16679.5 −1.93780
\(421\) −5025.23 −0.581745 −0.290873 0.956762i \(-0.593946\pi\)
−0.290873 + 0.956762i \(0.593946\pi\)
\(422\) 7359.30 0.848922
\(423\) −1265.04 −0.145410
\(424\) 1845.33 0.211362
\(425\) −4109.57 −0.469044
\(426\) −7070.06 −0.804097
\(427\) −6871.51 −0.778772
\(428\) −7352.39 −0.830353
\(429\) −6784.95 −0.763591
\(430\) 34327.1 3.84977
\(431\) −5974.34 −0.667688 −0.333844 0.942628i \(-0.608346\pi\)
−0.333844 + 0.942628i \(0.608346\pi\)
\(432\) 8019.92 0.893191
\(433\) 9508.16 1.05527 0.527636 0.849471i \(-0.323079\pi\)
0.527636 + 0.849471i \(0.323079\pi\)
\(434\) −610.520 −0.0675251
\(435\) 786.449 0.0866835
\(436\) −14633.3 −1.60736
\(437\) 3772.55 0.412964
\(438\) 14556.9 1.58803
\(439\) 9345.33 1.01601 0.508005 0.861354i \(-0.330383\pi\)
0.508005 + 0.861354i \(0.330383\pi\)
\(440\) 80543.5 8.72673
\(441\) −73.3753 −0.00792304
\(442\) 16731.6 1.80055
\(443\) 10777.7 1.15590 0.577952 0.816071i \(-0.303852\pi\)
0.577952 + 0.816071i \(0.303852\pi\)
\(444\) 11747.1 1.25562
\(445\) −4604.28 −0.490480
\(446\) 7131.23 0.757116
\(447\) −6958.82 −0.736333
\(448\) −56374.5 −5.94519
\(449\) −10690.1 −1.12360 −0.561801 0.827272i \(-0.689891\pi\)
−0.561801 + 0.827272i \(0.689891\pi\)
\(450\) −2186.56 −0.229056
\(451\) −17885.1 −1.86736
\(452\) 4727.87 0.491992
\(453\) 3022.43 0.313479
\(454\) 8567.29 0.885645
\(455\) −7475.02 −0.770186
\(456\) 13921.7 1.42970
\(457\) 14441.5 1.47822 0.739108 0.673587i \(-0.235247\pi\)
0.739108 + 0.673587i \(0.235247\pi\)
\(458\) 1182.20 0.120613
\(459\) −2559.92 −0.260320
\(460\) −21345.0 −2.16351
\(461\) −7427.54 −0.750402 −0.375201 0.926944i \(-0.622426\pi\)
−0.375201 + 0.926944i \(0.622426\pi\)
\(462\) −22103.7 −2.22588
\(463\) −16270.9 −1.63320 −0.816602 0.577201i \(-0.804145\pi\)
−0.816602 + 0.577201i \(0.804145\pi\)
\(464\) 6001.45 0.600453
\(465\) −231.693 −0.0231064
\(466\) 13748.3 1.36670
\(467\) −15580.7 −1.54387 −0.771935 0.635702i \(-0.780711\pi\)
−0.771935 + 0.635702i \(0.780711\pi\)
\(468\) 6635.45 0.655393
\(469\) 7504.63 0.738873
\(470\) 10222.2 1.00323
\(471\) 4750.69 0.464757
\(472\) 5098.55 0.497203
\(473\) 33907.0 3.29608
\(474\) 903.218 0.0875236
\(475\) −2327.60 −0.224838
\(476\) 40627.9 3.91214
\(477\) −192.186 −0.0184478
\(478\) −6617.69 −0.633235
\(479\) −10461.9 −0.997951 −0.498976 0.866616i \(-0.666290\pi\)
−0.498976 + 0.866616i \(0.666290\pi\)
\(480\) −37896.0 −3.60356
\(481\) 5264.57 0.499051
\(482\) 12115.1 1.14487
\(483\) 3856.59 0.363315
\(484\) 89671.2 8.42142
\(485\) −18412.2 −1.72383
\(486\) −1362.04 −0.127127
\(487\) −905.076 −0.0842154 −0.0421077 0.999113i \(-0.513407\pi\)
−0.0421077 + 0.999113i \(0.513407\pi\)
\(488\) −32450.7 −3.01019
\(489\) −2404.68 −0.222379
\(490\) 592.914 0.0546635
\(491\) −10221.5 −0.939491 −0.469746 0.882802i \(-0.655654\pi\)
−0.469746 + 0.882802i \(0.655654\pi\)
\(492\) 17491.0 1.60276
\(493\) −1915.64 −0.175002
\(494\) 9476.55 0.863097
\(495\) −8388.37 −0.761676
\(496\) −1768.06 −0.160057
\(497\) −7693.78 −0.694393
\(498\) −664.077 −0.0597550
\(499\) 16843.7 1.51108 0.755538 0.655104i \(-0.227375\pi\)
0.755538 + 0.655104i \(0.227375\pi\)
\(500\) −24809.8 −2.21906
\(501\) 2546.64 0.227097
\(502\) 12185.9 1.08344
\(503\) −8181.54 −0.725243 −0.362621 0.931937i \(-0.618118\pi\)
−0.362621 + 0.931937i \(0.618118\pi\)
\(504\) 14231.8 1.25781
\(505\) 14213.9 1.25249
\(506\) −28286.5 −2.48516
\(507\) −3617.28 −0.316862
\(508\) 59154.3 5.16643
\(509\) 5119.71 0.445830 0.222915 0.974838i \(-0.428443\pi\)
0.222915 + 0.974838i \(0.428443\pi\)
\(510\) 20685.6 1.79603
\(511\) 15841.2 1.37137
\(512\) −83838.7 −7.23669
\(513\) −1449.90 −0.124785
\(514\) −36788.7 −3.15697
\(515\) −3116.79 −0.266684
\(516\) −33159.8 −2.82903
\(517\) 10097.1 0.858938
\(518\) 17150.7 1.45474
\(519\) 10937.2 0.925025
\(520\) −35300.8 −2.97700
\(521\) 8611.23 0.724117 0.362058 0.932155i \(-0.382074\pi\)
0.362058 + 0.932155i \(0.382074\pi\)
\(522\) −1019.24 −0.0854617
\(523\) 1314.45 0.109899 0.0549493 0.998489i \(-0.482500\pi\)
0.0549493 + 0.998489i \(0.482500\pi\)
\(524\) 33228.2 2.77019
\(525\) −2379.46 −0.197806
\(526\) 9715.69 0.805369
\(527\) 564.358 0.0466486
\(528\) −64012.3 −5.27610
\(529\) −7231.65 −0.594366
\(530\) 1552.97 0.127277
\(531\) −531.000 −0.0433963
\(532\) 23011.1 1.87529
\(533\) 7838.73 0.637023
\(534\) 5967.16 0.483566
\(535\) −4073.71 −0.329199
\(536\) 35440.6 2.85597
\(537\) −3404.18 −0.273559
\(538\) −6954.77 −0.557326
\(539\) 585.657 0.0468015
\(540\) 8203.54 0.653748
\(541\) 6075.96 0.482858 0.241429 0.970419i \(-0.422384\pi\)
0.241429 + 0.970419i \(0.422384\pi\)
\(542\) 6943.96 0.550311
\(543\) −7054.43 −0.557522
\(544\) 92307.3 7.27508
\(545\) −8107.82 −0.637249
\(546\) 9687.67 0.759330
\(547\) −25132.5 −1.96451 −0.982256 0.187547i \(-0.939946\pi\)
−0.982256 + 0.187547i \(0.939946\pi\)
\(548\) −44993.8 −3.50737
\(549\) 3379.65 0.262732
\(550\) 17452.4 1.35304
\(551\) −1084.99 −0.0838876
\(552\) 18212.7 1.40432
\(553\) 982.901 0.0755827
\(554\) 29986.9 2.29968
\(555\) 6508.69 0.497799
\(556\) −7758.03 −0.591751
\(557\) 7094.80 0.539706 0.269853 0.962901i \(-0.413025\pi\)
0.269853 + 0.962901i \(0.413025\pi\)
\(558\) 300.275 0.0227807
\(559\) −14860.8 −1.12441
\(560\) −70522.7 −5.32166
\(561\) 20432.4 1.53772
\(562\) 5663.69 0.425104
\(563\) 13314.5 0.996695 0.498348 0.866977i \(-0.333940\pi\)
0.498348 + 0.866977i \(0.333940\pi\)
\(564\) −9874.64 −0.737229
\(565\) 2619.55 0.195054
\(566\) 7351.48 0.545947
\(567\) −1482.21 −0.109783
\(568\) −36333.9 −2.68404
\(569\) −10321.3 −0.760445 −0.380223 0.924895i \(-0.624153\pi\)
−0.380223 + 0.924895i \(0.624153\pi\)
\(570\) 11716.0 0.860932
\(571\) −17232.9 −1.26301 −0.631503 0.775374i \(-0.717562\pi\)
−0.631503 + 0.775374i \(0.717562\pi\)
\(572\) −52961.9 −3.87141
\(573\) 7978.04 0.581653
\(574\) 25536.7 1.85693
\(575\) −3045.04 −0.220847
\(576\) 27727.0 2.00571
\(577\) −14043.3 −1.01322 −0.506612 0.862174i \(-0.669102\pi\)
−0.506612 + 0.862174i \(0.669102\pi\)
\(578\) −22848.2 −1.64422
\(579\) 573.305 0.0411498
\(580\) 6138.85 0.439486
\(581\) −722.662 −0.0516026
\(582\) 23862.3 1.69953
\(583\) 1533.97 0.108971
\(584\) 74809.9 5.30078
\(585\) 3676.48 0.259835
\(586\) 39138.9 2.75907
\(587\) −3955.35 −0.278117 −0.139058 0.990284i \(-0.544408\pi\)
−0.139058 + 0.990284i \(0.544408\pi\)
\(588\) −572.752 −0.0401699
\(589\) 319.645 0.0223612
\(590\) 4290.78 0.299404
\(591\) 13346.1 0.928906
\(592\) 49668.3 3.44824
\(593\) −26744.5 −1.85205 −0.926026 0.377461i \(-0.876797\pi\)
−0.926026 + 0.377461i \(0.876797\pi\)
\(594\) 10871.4 0.750939
\(595\) 22510.5 1.55100
\(596\) −54319.1 −3.73322
\(597\) 8968.89 0.614861
\(598\) 12397.5 0.847778
\(599\) −23788.0 −1.62262 −0.811310 0.584616i \(-0.801245\pi\)
−0.811310 + 0.584616i \(0.801245\pi\)
\(600\) −11237.0 −0.764580
\(601\) 1191.30 0.0808552 0.0404276 0.999182i \(-0.487128\pi\)
0.0404276 + 0.999182i \(0.487128\pi\)
\(602\) −48412.9 −3.27768
\(603\) −3691.04 −0.249271
\(604\) 23592.4 1.58934
\(605\) 49683.8 3.33873
\(606\) −18421.2 −1.23484
\(607\) −24740.6 −1.65435 −0.827176 0.561943i \(-0.810054\pi\)
−0.827176 + 0.561943i \(0.810054\pi\)
\(608\) 52281.5 3.48733
\(609\) −1109.16 −0.0738020
\(610\) −27309.5 −1.81267
\(611\) −4425.39 −0.293015
\(612\) −19982.2 −1.31983
\(613\) −1524.99 −0.100479 −0.0502395 0.998737i \(-0.515998\pi\)
−0.0502395 + 0.998737i \(0.515998\pi\)
\(614\) −14446.5 −0.949533
\(615\) 9691.18 0.635425
\(616\) −113594. −7.42990
\(617\) 8382.64 0.546957 0.273479 0.961878i \(-0.411826\pi\)
0.273479 + 0.961878i \(0.411826\pi\)
\(618\) 4039.38 0.262925
\(619\) −14268.7 −0.926505 −0.463252 0.886226i \(-0.653318\pi\)
−0.463252 + 0.886226i \(0.653318\pi\)
\(620\) −1808.54 −0.117150
\(621\) −1896.81 −0.122570
\(622\) −35429.3 −2.28390
\(623\) 6493.60 0.417593
\(624\) 28055.5 1.79987
\(625\) −19164.3 −1.22652
\(626\) 15151.3 0.967361
\(627\) 11572.6 0.737108
\(628\) 37082.9 2.35632
\(629\) −15853.9 −1.00499
\(630\) 11977.1 0.757424
\(631\) 24816.1 1.56563 0.782816 0.622253i \(-0.213782\pi\)
0.782816 + 0.622253i \(0.213782\pi\)
\(632\) 4641.75 0.292150
\(633\) −3938.88 −0.247324
\(634\) 49989.3 3.13143
\(635\) 32775.4 2.04827
\(636\) −1500.16 −0.0935305
\(637\) −256.683 −0.0159657
\(638\) 8135.24 0.504823
\(639\) 3784.07 0.234265
\(640\) −122993. −7.59648
\(641\) −21073.3 −1.29851 −0.649256 0.760570i \(-0.724920\pi\)
−0.649256 + 0.760570i \(0.724920\pi\)
\(642\) 5279.55 0.324559
\(643\) −26526.1 −1.62688 −0.813442 0.581645i \(-0.802409\pi\)
−0.813442 + 0.581645i \(0.802409\pi\)
\(644\) 30103.7 1.84201
\(645\) −18372.7 −1.12159
\(646\) −28538.0 −1.73810
\(647\) 30487.8 1.85255 0.926274 0.376851i \(-0.122993\pi\)
0.926274 + 0.376851i \(0.122993\pi\)
\(648\) −6999.71 −0.424344
\(649\) 4238.26 0.256343
\(650\) −7649.06 −0.461571
\(651\) 326.766 0.0196727
\(652\) −18770.4 −1.12747
\(653\) −18787.9 −1.12592 −0.562962 0.826483i \(-0.690338\pi\)
−0.562962 + 0.826483i \(0.690338\pi\)
\(654\) 10507.8 0.628267
\(655\) 18410.6 1.09826
\(656\) 73954.1 4.40156
\(657\) −7791.24 −0.462657
\(658\) −14416.8 −0.854144
\(659\) −8131.03 −0.480637 −0.240319 0.970694i \(-0.577252\pi\)
−0.240319 + 0.970694i \(0.577252\pi\)
\(660\) −65477.9 −3.86170
\(661\) 28408.2 1.67164 0.835819 0.549005i \(-0.184993\pi\)
0.835819 + 0.549005i \(0.184993\pi\)
\(662\) 47955.0 2.81545
\(663\) −8955.18 −0.524571
\(664\) −3412.77 −0.199460
\(665\) 12749.7 0.743474
\(666\) −8435.30 −0.490783
\(667\) −1419.41 −0.0823986
\(668\) 19878.5 1.15138
\(669\) −3816.81 −0.220578
\(670\) 29825.7 1.71980
\(671\) −26975.2 −1.55196
\(672\) 53446.3 3.06806
\(673\) −10582.7 −0.606143 −0.303072 0.952968i \(-0.598012\pi\)
−0.303072 + 0.952968i \(0.598012\pi\)
\(674\) −37196.2 −2.12573
\(675\) 1170.30 0.0667332
\(676\) −28235.7 −1.60649
\(677\) −3227.86 −0.183245 −0.0916223 0.995794i \(-0.529205\pi\)
−0.0916223 + 0.995794i \(0.529205\pi\)
\(678\) −3394.95 −0.192304
\(679\) 25967.5 1.46766
\(680\) 106306. 5.99507
\(681\) −4585.43 −0.258023
\(682\) −2396.69 −0.134566
\(683\) −27107.0 −1.51863 −0.759313 0.650726i \(-0.774465\pi\)
−0.759313 + 0.650726i \(0.774465\pi\)
\(684\) −11317.6 −0.632662
\(685\) −24929.5 −1.39052
\(686\) −36016.7 −2.00456
\(687\) −632.743 −0.0351392
\(688\) −140204. −7.76921
\(689\) −672.310 −0.0371741
\(690\) 15327.3 0.845651
\(691\) 17579.1 0.967785 0.483893 0.875127i \(-0.339223\pi\)
0.483893 + 0.875127i \(0.339223\pi\)
\(692\) 85373.1 4.68988
\(693\) 11830.5 0.648488
\(694\) −58153.4 −3.18080
\(695\) −4298.46 −0.234604
\(696\) −5238.01 −0.285267
\(697\) −23605.8 −1.28283
\(698\) 7046.96 0.382137
\(699\) −7358.46 −0.398172
\(700\) −18573.6 −1.00288
\(701\) −26746.3 −1.44107 −0.720537 0.693416i \(-0.756105\pi\)
−0.720537 + 0.693416i \(0.756105\pi\)
\(702\) −4764.73 −0.256173
\(703\) −8979.43 −0.481743
\(704\) −221307. −11.8478
\(705\) −5471.20 −0.292280
\(706\) −58395.9 −3.11297
\(707\) −20046.4 −1.06637
\(708\) −4144.87 −0.220020
\(709\) −6249.37 −0.331029 −0.165515 0.986207i \(-0.552929\pi\)
−0.165515 + 0.986207i \(0.552929\pi\)
\(710\) −30577.4 −1.61627
\(711\) −483.425 −0.0254991
\(712\) 30666.0 1.61412
\(713\) 418.168 0.0219643
\(714\) −29173.8 −1.52913
\(715\) −29344.4 −1.53485
\(716\) −26572.3 −1.38695
\(717\) 3541.95 0.184486
\(718\) −22417.7 −1.16521
\(719\) −22521.4 −1.16816 −0.584079 0.811697i \(-0.698544\pi\)
−0.584079 + 0.811697i \(0.698544\pi\)
\(720\) 34685.5 1.79535
\(721\) 4395.74 0.227054
\(722\) 22282.0 1.14855
\(723\) −6484.31 −0.333546
\(724\) −55065.4 −2.82664
\(725\) 875.757 0.0448618
\(726\) −64390.4 −3.29167
\(727\) 31439.8 1.60390 0.801950 0.597391i \(-0.203796\pi\)
0.801950 + 0.597391i \(0.203796\pi\)
\(728\) 49786.1 2.53461
\(729\) 729.000 0.0370370
\(730\) 62957.7 3.19201
\(731\) 44752.4 2.26433
\(732\) 26380.8 1.33205
\(733\) 9684.11 0.487982 0.243991 0.969778i \(-0.421543\pi\)
0.243991 + 0.969778i \(0.421543\pi\)
\(734\) 962.024 0.0483773
\(735\) −317.342 −0.0159256
\(736\) 68396.2 3.42543
\(737\) 29460.6 1.47245
\(738\) −12559.8 −0.626468
\(739\) 2170.31 0.108033 0.0540164 0.998540i \(-0.482798\pi\)
0.0540164 + 0.998540i \(0.482798\pi\)
\(740\) 50805.5 2.52385
\(741\) −5072.09 −0.251454
\(742\) −2190.22 −0.108363
\(743\) 16314.2 0.805532 0.402766 0.915303i \(-0.368049\pi\)
0.402766 + 0.915303i \(0.368049\pi\)
\(744\) 1543.15 0.0760411
\(745\) −30096.4 −1.48006
\(746\) 57659.4 2.82984
\(747\) 355.430 0.0174090
\(748\) 159491. 7.79623
\(749\) 5745.31 0.280279
\(750\) 17815.2 0.867360
\(751\) −20763.2 −1.00887 −0.504433 0.863451i \(-0.668299\pi\)
−0.504433 + 0.863451i \(0.668299\pi\)
\(752\) −41751.1 −2.02461
\(753\) −6522.21 −0.315648
\(754\) −3565.53 −0.172214
\(755\) 13071.8 0.630106
\(756\) −11569.8 −0.556599
\(757\) −4504.44 −0.216270 −0.108135 0.994136i \(-0.534488\pi\)
−0.108135 + 0.994136i \(0.534488\pi\)
\(758\) 24719.7 1.18451
\(759\) 15139.7 0.724025
\(760\) 60210.2 2.87375
\(761\) −24834.5 −1.18298 −0.591492 0.806311i \(-0.701461\pi\)
−0.591492 + 0.806311i \(0.701461\pi\)
\(762\) −42477.0 −2.01940
\(763\) 11434.8 0.542552
\(764\) 62274.9 2.94899
\(765\) −11071.5 −0.523254
\(766\) 21733.6 1.02515
\(767\) −1857.56 −0.0874478
\(768\) 85461.6 4.01541
\(769\) 8928.62 0.418692 0.209346 0.977842i \(-0.432866\pi\)
0.209346 + 0.977842i \(0.432866\pi\)
\(770\) −95596.8 −4.47412
\(771\) 19690.2 0.919749
\(772\) 4475.09 0.208630
\(773\) 25882.5 1.20431 0.602154 0.798380i \(-0.294309\pi\)
0.602154 + 0.798380i \(0.294309\pi\)
\(774\) 23811.1 1.10578
\(775\) −258.003 −0.0119584
\(776\) 122631. 5.67295
\(777\) −9179.47 −0.423825
\(778\) 47449.4 2.18656
\(779\) −13370.0 −0.614930
\(780\) 28697.8 1.31737
\(781\) −30203.2 −1.38381
\(782\) −37334.2 −1.70725
\(783\) 545.524 0.0248984
\(784\) −2421.66 −0.110316
\(785\) 20546.4 0.934180
\(786\) −23860.3 −1.08278
\(787\) −19011.5 −0.861101 −0.430550 0.902567i \(-0.641680\pi\)
−0.430550 + 0.902567i \(0.641680\pi\)
\(788\) 104177. 4.70956
\(789\) −5200.08 −0.234636
\(790\) 3906.35 0.175926
\(791\) −3694.46 −0.166068
\(792\) 55869.3 2.50660
\(793\) 11822.8 0.529430
\(794\) −75270.7 −3.36430
\(795\) −831.190 −0.0370809
\(796\) 70009.2 3.11735
\(797\) −37188.2 −1.65279 −0.826395 0.563090i \(-0.809612\pi\)
−0.826395 + 0.563090i \(0.809612\pi\)
\(798\) −16523.6 −0.732994
\(799\) 13326.8 0.590072
\(800\) −42199.4 −1.86497
\(801\) −3193.78 −0.140882
\(802\) −69355.2 −3.05364
\(803\) 62187.1 2.73292
\(804\) −28811.4 −1.26381
\(805\) 16679.5 0.730278
\(806\) 1050.43 0.0459054
\(807\) 3722.37 0.162371
\(808\) −94668.9 −4.12183
\(809\) −42199.6 −1.83394 −0.916971 0.398955i \(-0.869373\pi\)
−0.916971 + 0.398955i \(0.869373\pi\)
\(810\) −5890.73 −0.255530
\(811\) 17958.8 0.777580 0.388790 0.921326i \(-0.372893\pi\)
0.388790 + 0.921326i \(0.372893\pi\)
\(812\) −8657.87 −0.374177
\(813\) −3716.58 −0.160327
\(814\) 67327.7 2.89906
\(815\) −10400.1 −0.446992
\(816\) −84487.2 −3.62456
\(817\) 25347.1 1.08541
\(818\) −65901.7 −2.81687
\(819\) −5185.08 −0.221223
\(820\) 75647.3 3.22161
\(821\) 12021.1 0.511009 0.255505 0.966808i \(-0.417758\pi\)
0.255505 + 0.966808i \(0.417758\pi\)
\(822\) 32308.8 1.37092
\(823\) −28070.3 −1.18891 −0.594453 0.804130i \(-0.702632\pi\)
−0.594453 + 0.804130i \(0.702632\pi\)
\(824\) 20758.9 0.877633
\(825\) −9340.94 −0.394194
\(826\) −6051.46 −0.254912
\(827\) 14096.2 0.592714 0.296357 0.955077i \(-0.404228\pi\)
0.296357 + 0.955077i \(0.404228\pi\)
\(828\) −14806.1 −0.621433
\(829\) 4924.66 0.206322 0.103161 0.994665i \(-0.467104\pi\)
0.103161 + 0.994665i \(0.467104\pi\)
\(830\) −2872.08 −0.120110
\(831\) −16049.8 −0.669988
\(832\) 96995.0 4.04170
\(833\) 772.984 0.0321516
\(834\) 5570.82 0.231297
\(835\) 11014.0 0.456474
\(836\) 90333.6 3.73715
\(837\) −160.715 −0.00663693
\(838\) −20429.0 −0.842135
\(839\) −9277.77 −0.381769 −0.190884 0.981613i \(-0.561136\pi\)
−0.190884 + 0.981613i \(0.561136\pi\)
\(840\) 61551.6 2.52825
\(841\) −23980.8 −0.983262
\(842\) 28167.0 1.15285
\(843\) −3031.35 −0.123850
\(844\) −30746.1 −1.25394
\(845\) −15644.4 −0.636905
\(846\) 7090.70 0.288160
\(847\) −70071.0 −2.84258
\(848\) −6342.87 −0.256858
\(849\) −3934.70 −0.159056
\(850\) 23034.7 0.929508
\(851\) −11747.1 −0.473192
\(852\) 29537.7 1.18773
\(853\) 20411.8 0.819329 0.409664 0.912236i \(-0.365646\pi\)
0.409664 + 0.912236i \(0.365646\pi\)
\(854\) 38515.6 1.54330
\(855\) −6270.72 −0.250824
\(856\) 27132.2 1.08337
\(857\) −27431.5 −1.09340 −0.546698 0.837330i \(-0.684116\pi\)
−0.546698 + 0.837330i \(0.684116\pi\)
\(858\) 38030.5 1.51322
\(859\) −11503.0 −0.456900 −0.228450 0.973556i \(-0.573366\pi\)
−0.228450 + 0.973556i \(0.573366\pi\)
\(860\) −143414. −5.68647
\(861\) −13667.9 −0.540998
\(862\) 33486.9 1.32316
\(863\) 15844.5 0.624973 0.312486 0.949922i \(-0.398838\pi\)
0.312486 + 0.949922i \(0.398838\pi\)
\(864\) −26286.7 −1.03506
\(865\) 47302.3 1.85934
\(866\) −53294.3 −2.09124
\(867\) 12228.9 0.479027
\(868\) 2550.66 0.0997410
\(869\) 3858.54 0.150624
\(870\) −4408.14 −0.171782
\(871\) −12912.1 −0.502306
\(872\) 54000.7 2.09713
\(873\) −12771.7 −0.495140
\(874\) −21145.6 −0.818375
\(875\) 19386.9 0.749025
\(876\) −60816.8 −2.34567
\(877\) 15555.2 0.598931 0.299465 0.954107i \(-0.403192\pi\)
0.299465 + 0.954107i \(0.403192\pi\)
\(878\) −52381.7 −2.01344
\(879\) −20948.1 −0.803826
\(880\) −276848. −10.6052
\(881\) 43893.6 1.67856 0.839281 0.543697i \(-0.182976\pi\)
0.839281 + 0.543697i \(0.182976\pi\)
\(882\) 411.277 0.0157012
\(883\) −10548.9 −0.402035 −0.201018 0.979588i \(-0.564425\pi\)
−0.201018 + 0.979588i \(0.564425\pi\)
\(884\) −69902.2 −2.65958
\(885\) −2296.53 −0.0872284
\(886\) −60410.5 −2.29067
\(887\) −15354.2 −0.581221 −0.290610 0.956841i \(-0.593858\pi\)
−0.290610 + 0.956841i \(0.593858\pi\)
\(888\) −43350.0 −1.63821
\(889\) −46224.4 −1.74389
\(890\) 25807.5 0.971989
\(891\) −5818.63 −0.218778
\(892\) −29793.2 −1.11833
\(893\) 7548.10 0.282853
\(894\) 39005.0 1.45920
\(895\) −14722.8 −0.549865
\(896\) 173463. 6.46761
\(897\) −6635.44 −0.246991
\(898\) 59919.3 2.22665
\(899\) −120.266 −0.00446172
\(900\) 9135.12 0.338338
\(901\) 2024.62 0.0748610
\(902\) 100248. 3.70056
\(903\) 25911.8 0.954918
\(904\) −17447.1 −0.641904
\(905\) −30509.8 −1.12064
\(906\) −16941.1 −0.621225
\(907\) −1432.55 −0.0524443 −0.0262222 0.999656i \(-0.508348\pi\)
−0.0262222 + 0.999656i \(0.508348\pi\)
\(908\) −35792.9 −1.30818
\(909\) 9859.50 0.359757
\(910\) 41898.4 1.52628
\(911\) −11210.0 −0.407688 −0.203844 0.979003i \(-0.565343\pi\)
−0.203844 + 0.979003i \(0.565343\pi\)
\(912\) −47852.3 −1.73744
\(913\) −2836.93 −0.102835
\(914\) −80946.3 −2.92939
\(915\) 14616.7 0.528102
\(916\) −4939.06 −0.178156
\(917\) −25965.2 −0.935058
\(918\) 14348.7 0.515879
\(919\) −6525.78 −0.234239 −0.117119 0.993118i \(-0.537366\pi\)
−0.117119 + 0.993118i \(0.537366\pi\)
\(920\) 78768.7 2.82275
\(921\) 7732.13 0.276636
\(922\) 41632.3 1.48708
\(923\) 13237.5 0.472067
\(924\) 92346.1 3.28784
\(925\) 7247.81 0.257629
\(926\) 91200.4 3.23654
\(927\) −2161.98 −0.0766005
\(928\) −19670.8 −0.695826
\(929\) 24465.6 0.864039 0.432019 0.901864i \(-0.357801\pi\)
0.432019 + 0.901864i \(0.357801\pi\)
\(930\) 1298.67 0.0457902
\(931\) 437.807 0.0154120
\(932\) −57438.6 −2.01874
\(933\) 18962.6 0.665390
\(934\) 87331.5 3.05950
\(935\) 88368.7 3.09087
\(936\) −24486.5 −0.855093
\(937\) 13782.7 0.480535 0.240268 0.970707i \(-0.422765\pi\)
0.240268 + 0.970707i \(0.422765\pi\)
\(938\) −42064.3 −1.46423
\(939\) −8109.36 −0.281831
\(940\) −42707.0 −1.48186
\(941\) 20827.9 0.721542 0.360771 0.932654i \(-0.382514\pi\)
0.360771 + 0.932654i \(0.382514\pi\)
\(942\) −26628.2 −0.921012
\(943\) −17491.0 −0.604015
\(944\) −17525.0 −0.604227
\(945\) −6410.42 −0.220668
\(946\) −190053. −6.53186
\(947\) 42181.4 1.44743 0.723713 0.690102i \(-0.242434\pi\)
0.723713 + 0.690102i \(0.242434\pi\)
\(948\) −3773.51 −0.129281
\(949\) −27255.5 −0.932298
\(950\) 13046.5 0.445563
\(951\) −26755.5 −0.912310
\(952\) −149928. −5.10418
\(953\) 13696.3 0.465548 0.232774 0.972531i \(-0.425220\pi\)
0.232774 + 0.972531i \(0.425220\pi\)
\(954\) 1077.23 0.0365582
\(955\) 34504.4 1.16915
\(956\) 27647.7 0.935347
\(957\) −4354.19 −0.147075
\(958\) 58640.5 1.97765
\(959\) 35159.1 1.18389
\(960\) 119917. 4.03156
\(961\) −29755.6 −0.998811
\(962\) −29508.5 −0.988975
\(963\) −2825.74 −0.0945570
\(964\) −50615.1 −1.69108
\(965\) 2479.50 0.0827128
\(966\) −21616.7 −0.719984
\(967\) −44658.0 −1.48511 −0.742557 0.669782i \(-0.766387\pi\)
−0.742557 + 0.669782i \(0.766387\pi\)
\(968\) −330910. −10.9875
\(969\) 15274.3 0.506377
\(970\) 103203. 3.41612
\(971\) 21045.1 0.695539 0.347770 0.937580i \(-0.386939\pi\)
0.347770 + 0.937580i \(0.386939\pi\)
\(972\) 5690.42 0.187778
\(973\) 6062.29 0.199741
\(974\) 5073.06 0.166890
\(975\) 4093.97 0.134474
\(976\) 111541. 3.65814
\(977\) 7509.77 0.245915 0.122957 0.992412i \(-0.460762\pi\)
0.122957 + 0.992412i \(0.460762\pi\)
\(978\) 13478.5 0.440691
\(979\) 25491.6 0.832192
\(980\) −2477.11 −0.0807431
\(981\) −5624.02 −0.183039
\(982\) 57292.8 1.86180
\(983\) −13912.8 −0.451424 −0.225712 0.974194i \(-0.572471\pi\)
−0.225712 + 0.974194i \(0.572471\pi\)
\(984\) −64546.5 −2.09112
\(985\) 57720.6 1.86714
\(986\) 10737.4 0.346803
\(987\) 7716.25 0.248846
\(988\) −39591.6 −1.27488
\(989\) 33159.8 1.06615
\(990\) 47017.8 1.50942
\(991\) 16460.0 0.527619 0.263810 0.964575i \(-0.415021\pi\)
0.263810 + 0.964575i \(0.415021\pi\)
\(992\) 5795.15 0.185480
\(993\) −25666.7 −0.820251
\(994\) 43124.6 1.37609
\(995\) 38789.7 1.23590
\(996\) 2774.42 0.0882638
\(997\) 24297.4 0.771823 0.385912 0.922536i \(-0.373887\pi\)
0.385912 + 0.922536i \(0.373887\pi\)
\(998\) −94410.9 −2.99451
\(999\) 4514.78 0.142984
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 177.4.a.a.1.1 7
3.2 odd 2 531.4.a.d.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.a.1.1 7 1.1 even 1 trivial
531.4.a.d.1.7 7 3.2 odd 2