Properties

Label 35.4.a.a.1.1
Level $35$
Weight $4$
Character 35.1
Self dual yes
Analytic conductor $2.065$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 35.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.06506685020\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 35.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -8.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} +7.00000 q^{7} -15.0000 q^{8} +37.0000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -8.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} +7.00000 q^{7} -15.0000 q^{8} +37.0000 q^{9} -5.00000 q^{10} +12.0000 q^{11} +56.0000 q^{12} -78.0000 q^{13} +7.00000 q^{14} +40.0000 q^{15} +41.0000 q^{16} -94.0000 q^{17} +37.0000 q^{18} +40.0000 q^{19} +35.0000 q^{20} -56.0000 q^{21} +12.0000 q^{22} +32.0000 q^{23} +120.000 q^{24} +25.0000 q^{25} -78.0000 q^{26} -80.0000 q^{27} -49.0000 q^{28} -50.0000 q^{29} +40.0000 q^{30} -248.000 q^{31} +161.000 q^{32} -96.0000 q^{33} -94.0000 q^{34} -35.0000 q^{35} -259.000 q^{36} -434.000 q^{37} +40.0000 q^{38} +624.000 q^{39} +75.0000 q^{40} +402.000 q^{41} -56.0000 q^{42} -68.0000 q^{43} -84.0000 q^{44} -185.000 q^{45} +32.0000 q^{46} +536.000 q^{47} -328.000 q^{48} +49.0000 q^{49} +25.0000 q^{50} +752.000 q^{51} +546.000 q^{52} +22.0000 q^{53} -80.0000 q^{54} -60.0000 q^{55} -105.000 q^{56} -320.000 q^{57} -50.0000 q^{58} -560.000 q^{59} -280.000 q^{60} -278.000 q^{61} -248.000 q^{62} +259.000 q^{63} -167.000 q^{64} +390.000 q^{65} -96.0000 q^{66} -164.000 q^{67} +658.000 q^{68} -256.000 q^{69} -35.0000 q^{70} +672.000 q^{71} -555.000 q^{72} +82.0000 q^{73} -434.000 q^{74} -200.000 q^{75} -280.000 q^{76} +84.0000 q^{77} +624.000 q^{78} -1000.00 q^{79} -205.000 q^{80} -359.000 q^{81} +402.000 q^{82} -448.000 q^{83} +392.000 q^{84} +470.000 q^{85} -68.0000 q^{86} +400.000 q^{87} -180.000 q^{88} -870.000 q^{89} -185.000 q^{90} -546.000 q^{91} -224.000 q^{92} +1984.00 q^{93} +536.000 q^{94} -200.000 q^{95} -1288.00 q^{96} +1026.00 q^{97} +49.0000 q^{98} +444.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.353553 0.176777 0.984251i \(-0.443433\pi\)
0.176777 + 0.984251i \(0.443433\pi\)
\(3\) −8.00000 −1.53960 −0.769800 0.638285i \(-0.779644\pi\)
−0.769800 + 0.638285i \(0.779644\pi\)
\(4\) −7.00000 −0.875000
\(5\) −5.00000 −0.447214
\(6\) −8.00000 −0.544331
\(7\) 7.00000 0.377964
\(8\) −15.0000 −0.662913
\(9\) 37.0000 1.37037
\(10\) −5.00000 −0.158114
\(11\) 12.0000 0.328921 0.164461 0.986384i \(-0.447412\pi\)
0.164461 + 0.986384i \(0.447412\pi\)
\(12\) 56.0000 1.34715
\(13\) −78.0000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 7.00000 0.133631
\(15\) 40.0000 0.688530
\(16\) 41.0000 0.640625
\(17\) −94.0000 −1.34108 −0.670540 0.741874i \(-0.733937\pi\)
−0.670540 + 0.741874i \(0.733937\pi\)
\(18\) 37.0000 0.484499
\(19\) 40.0000 0.482980 0.241490 0.970403i \(-0.422364\pi\)
0.241490 + 0.970403i \(0.422364\pi\)
\(20\) 35.0000 0.391312
\(21\) −56.0000 −0.581914
\(22\) 12.0000 0.116291
\(23\) 32.0000 0.290107 0.145054 0.989424i \(-0.453665\pi\)
0.145054 + 0.989424i \(0.453665\pi\)
\(24\) 120.000 1.02062
\(25\) 25.0000 0.200000
\(26\) −78.0000 −0.588348
\(27\) −80.0000 −0.570222
\(28\) −49.0000 −0.330719
\(29\) −50.0000 −0.320164 −0.160082 0.987104i \(-0.551176\pi\)
−0.160082 + 0.987104i \(0.551176\pi\)
\(30\) 40.0000 0.243432
\(31\) −248.000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 161.000 0.889408
\(33\) −96.0000 −0.506408
\(34\) −94.0000 −0.474143
\(35\) −35.0000 −0.169031
\(36\) −259.000 −1.19907
\(37\) −434.000 −1.92836 −0.964178 0.265257i \(-0.914543\pi\)
−0.964178 + 0.265257i \(0.914543\pi\)
\(38\) 40.0000 0.170759
\(39\) 624.000 2.56205
\(40\) 75.0000 0.296464
\(41\) 402.000 1.53126 0.765632 0.643278i \(-0.222426\pi\)
0.765632 + 0.643278i \(0.222426\pi\)
\(42\) −56.0000 −0.205738
\(43\) −68.0000 −0.241161 −0.120580 0.992704i \(-0.538476\pi\)
−0.120580 + 0.992704i \(0.538476\pi\)
\(44\) −84.0000 −0.287806
\(45\) −185.000 −0.612848
\(46\) 32.0000 0.102568
\(47\) 536.000 1.66348 0.831741 0.555164i \(-0.187345\pi\)
0.831741 + 0.555164i \(0.187345\pi\)
\(48\) −328.000 −0.986307
\(49\) 49.0000 0.142857
\(50\) 25.0000 0.0707107
\(51\) 752.000 2.06473
\(52\) 546.000 1.45609
\(53\) 22.0000 0.0570176 0.0285088 0.999594i \(-0.490924\pi\)
0.0285088 + 0.999594i \(0.490924\pi\)
\(54\) −80.0000 −0.201604
\(55\) −60.0000 −0.147098
\(56\) −105.000 −0.250557
\(57\) −320.000 −0.743597
\(58\) −50.0000 −0.113195
\(59\) −560.000 −1.23569 −0.617846 0.786299i \(-0.711994\pi\)
−0.617846 + 0.786299i \(0.711994\pi\)
\(60\) −280.000 −0.602464
\(61\) −278.000 −0.583512 −0.291756 0.956493i \(-0.594240\pi\)
−0.291756 + 0.956493i \(0.594240\pi\)
\(62\) −248.000 −0.508001
\(63\) 259.000 0.517951
\(64\) −167.000 −0.326172
\(65\) 390.000 0.744208
\(66\) −96.0000 −0.179042
\(67\) −164.000 −0.299042 −0.149521 0.988759i \(-0.547773\pi\)
−0.149521 + 0.988759i \(0.547773\pi\)
\(68\) 658.000 1.17344
\(69\) −256.000 −0.446649
\(70\) −35.0000 −0.0597614
\(71\) 672.000 1.12326 0.561632 0.827387i \(-0.310174\pi\)
0.561632 + 0.827387i \(0.310174\pi\)
\(72\) −555.000 −0.908436
\(73\) 82.0000 0.131471 0.0657354 0.997837i \(-0.479061\pi\)
0.0657354 + 0.997837i \(0.479061\pi\)
\(74\) −434.000 −0.681777
\(75\) −200.000 −0.307920
\(76\) −280.000 −0.422608
\(77\) 84.0000 0.124321
\(78\) 624.000 0.905822
\(79\) −1000.00 −1.42416 −0.712081 0.702097i \(-0.752247\pi\)
−0.712081 + 0.702097i \(0.752247\pi\)
\(80\) −205.000 −0.286496
\(81\) −359.000 −0.492455
\(82\) 402.000 0.541384
\(83\) −448.000 −0.592463 −0.296231 0.955116i \(-0.595730\pi\)
−0.296231 + 0.955116i \(0.595730\pi\)
\(84\) 392.000 0.509175
\(85\) 470.000 0.599749
\(86\) −68.0000 −0.0852631
\(87\) 400.000 0.492925
\(88\) −180.000 −0.218046
\(89\) −870.000 −1.03618 −0.518089 0.855327i \(-0.673356\pi\)
−0.518089 + 0.855327i \(0.673356\pi\)
\(90\) −185.000 −0.216675
\(91\) −546.000 −0.628971
\(92\) −224.000 −0.253844
\(93\) 1984.00 2.21216
\(94\) 536.000 0.588130
\(95\) −200.000 −0.215995
\(96\) −1288.00 −1.36933
\(97\) 1026.00 1.07396 0.536982 0.843594i \(-0.319564\pi\)
0.536982 + 0.843594i \(0.319564\pi\)
\(98\) 49.0000 0.0505076
\(99\) 444.000 0.450744
\(100\) −175.000 −0.175000
\(101\) 482.000 0.474859 0.237430 0.971405i \(-0.423695\pi\)
0.237430 + 0.971405i \(0.423695\pi\)
\(102\) 752.000 0.729991
\(103\) 272.000 0.260203 0.130102 0.991501i \(-0.458470\pi\)
0.130102 + 0.991501i \(0.458470\pi\)
\(104\) 1170.00 1.10315
\(105\) 280.000 0.260240
\(106\) 22.0000 0.0201588
\(107\) −444.000 −0.401150 −0.200575 0.979678i \(-0.564281\pi\)
−0.200575 + 0.979678i \(0.564281\pi\)
\(108\) 560.000 0.498945
\(109\) −1170.00 −1.02813 −0.514063 0.857753i \(-0.671860\pi\)
−0.514063 + 0.857753i \(0.671860\pi\)
\(110\) −60.0000 −0.0520071
\(111\) 3472.00 2.96890
\(112\) 287.000 0.242133
\(113\) −798.000 −0.664332 −0.332166 0.943221i \(-0.607779\pi\)
−0.332166 + 0.943221i \(0.607779\pi\)
\(114\) −320.000 −0.262901
\(115\) −160.000 −0.129740
\(116\) 350.000 0.280144
\(117\) −2886.00 −2.28043
\(118\) −560.000 −0.436883
\(119\) −658.000 −0.506880
\(120\) −600.000 −0.456435
\(121\) −1187.00 −0.891811
\(122\) −278.000 −0.206303
\(123\) −3216.00 −2.35754
\(124\) 1736.00 1.25724
\(125\) −125.000 −0.0894427
\(126\) 259.000 0.183123
\(127\) 776.000 0.542196 0.271098 0.962552i \(-0.412613\pi\)
0.271098 + 0.962552i \(0.412613\pi\)
\(128\) −1455.00 −1.00473
\(129\) 544.000 0.371291
\(130\) 390.000 0.263117
\(131\) 1112.00 0.741648 0.370824 0.928703i \(-0.379075\pi\)
0.370824 + 0.928703i \(0.379075\pi\)
\(132\) 672.000 0.443107
\(133\) 280.000 0.182549
\(134\) −164.000 −0.105727
\(135\) 400.000 0.255011
\(136\) 1410.00 0.889018
\(137\) −694.000 −0.432791 −0.216396 0.976306i \(-0.569430\pi\)
−0.216396 + 0.976306i \(0.569430\pi\)
\(138\) −256.000 −0.157914
\(139\) 360.000 0.219675 0.109837 0.993950i \(-0.464967\pi\)
0.109837 + 0.993950i \(0.464967\pi\)
\(140\) 245.000 0.147902
\(141\) −4288.00 −2.56110
\(142\) 672.000 0.397134
\(143\) −936.000 −0.547358
\(144\) 1517.00 0.877894
\(145\) 250.000 0.143182
\(146\) 82.0000 0.0464820
\(147\) −392.000 −0.219943
\(148\) 3038.00 1.68731
\(149\) 2270.00 1.24809 0.624046 0.781388i \(-0.285488\pi\)
0.624046 + 0.781388i \(0.285488\pi\)
\(150\) −200.000 −0.108866
\(151\) 632.000 0.340606 0.170303 0.985392i \(-0.445525\pi\)
0.170303 + 0.985392i \(0.445525\pi\)
\(152\) −600.000 −0.320174
\(153\) −3478.00 −1.83778
\(154\) 84.0000 0.0439540
\(155\) 1240.00 0.642575
\(156\) −4368.00 −2.24179
\(157\) −734.000 −0.373118 −0.186559 0.982444i \(-0.559734\pi\)
−0.186559 + 0.982444i \(0.559734\pi\)
\(158\) −1000.00 −0.503517
\(159\) −176.000 −0.0877843
\(160\) −805.000 −0.397755
\(161\) 224.000 0.109650
\(162\) −359.000 −0.174109
\(163\) 2532.00 1.21670 0.608348 0.793670i \(-0.291832\pi\)
0.608348 + 0.793670i \(0.291832\pi\)
\(164\) −2814.00 −1.33986
\(165\) 480.000 0.226472
\(166\) −448.000 −0.209467
\(167\) 416.000 0.192761 0.0963804 0.995345i \(-0.469273\pi\)
0.0963804 + 0.995345i \(0.469273\pi\)
\(168\) 840.000 0.385758
\(169\) 3887.00 1.76923
\(170\) 470.000 0.212043
\(171\) 1480.00 0.661862
\(172\) 476.000 0.211015
\(173\) 3042.00 1.33687 0.668436 0.743769i \(-0.266964\pi\)
0.668436 + 0.743769i \(0.266964\pi\)
\(174\) 400.000 0.174275
\(175\) 175.000 0.0755929
\(176\) 492.000 0.210715
\(177\) 4480.00 1.90247
\(178\) −870.000 −0.366344
\(179\) −180.000 −0.0751611 −0.0375805 0.999294i \(-0.511965\pi\)
−0.0375805 + 0.999294i \(0.511965\pi\)
\(180\) 1295.00 0.536242
\(181\) −1958.00 −0.804072 −0.402036 0.915624i \(-0.631697\pi\)
−0.402036 + 0.915624i \(0.631697\pi\)
\(182\) −546.000 −0.222375
\(183\) 2224.00 0.898376
\(184\) −480.000 −0.192316
\(185\) 2170.00 0.862387
\(186\) 1984.00 0.782118
\(187\) −1128.00 −0.441110
\(188\) −3752.00 −1.45555
\(189\) −560.000 −0.215524
\(190\) −200.000 −0.0763659
\(191\) −2888.00 −1.09408 −0.547038 0.837108i \(-0.684245\pi\)
−0.547038 + 0.837108i \(0.684245\pi\)
\(192\) 1336.00 0.502174
\(193\) 1602.00 0.597484 0.298742 0.954334i \(-0.403433\pi\)
0.298742 + 0.954334i \(0.403433\pi\)
\(194\) 1026.00 0.379704
\(195\) −3120.00 −1.14578
\(196\) −343.000 −0.125000
\(197\) −4794.00 −1.73380 −0.866899 0.498483i \(-0.833891\pi\)
−0.866899 + 0.498483i \(0.833891\pi\)
\(198\) 444.000 0.159362
\(199\) 1280.00 0.455964 0.227982 0.973665i \(-0.426787\pi\)
0.227982 + 0.973665i \(0.426787\pi\)
\(200\) −375.000 −0.132583
\(201\) 1312.00 0.460405
\(202\) 482.000 0.167888
\(203\) −350.000 −0.121011
\(204\) −5264.00 −1.80664
\(205\) −2010.00 −0.684802
\(206\) 272.000 0.0919958
\(207\) 1184.00 0.397554
\(208\) −3198.00 −1.06606
\(209\) 480.000 0.158863
\(210\) 280.000 0.0920087
\(211\) −68.0000 −0.0221863 −0.0110932 0.999938i \(-0.503531\pi\)
−0.0110932 + 0.999938i \(0.503531\pi\)
\(212\) −154.000 −0.0498904
\(213\) −5376.00 −1.72938
\(214\) −444.000 −0.141828
\(215\) 340.000 0.107850
\(216\) 1200.00 0.378008
\(217\) −1736.00 −0.543075
\(218\) −1170.00 −0.363497
\(219\) −656.000 −0.202413
\(220\) 420.000 0.128711
\(221\) 7332.00 2.23169
\(222\) 3472.00 1.04966
\(223\) −1728.00 −0.518903 −0.259452 0.965756i \(-0.583542\pi\)
−0.259452 + 0.965756i \(0.583542\pi\)
\(224\) 1127.00 0.336165
\(225\) 925.000 0.274074
\(226\) −798.000 −0.234877
\(227\) −4864.00 −1.42218 −0.711090 0.703101i \(-0.751798\pi\)
−0.711090 + 0.703101i \(0.751798\pi\)
\(228\) 2240.00 0.650647
\(229\) −5510.00 −1.59000 −0.795002 0.606606i \(-0.792530\pi\)
−0.795002 + 0.606606i \(0.792530\pi\)
\(230\) −160.000 −0.0458699
\(231\) −672.000 −0.191404
\(232\) 750.000 0.212241
\(233\) 5322.00 1.49638 0.748188 0.663486i \(-0.230924\pi\)
0.748188 + 0.663486i \(0.230924\pi\)
\(234\) −2886.00 −0.806255
\(235\) −2680.00 −0.743932
\(236\) 3920.00 1.08123
\(237\) 8000.00 2.19264
\(238\) −658.000 −0.179209
\(239\) −1840.00 −0.497990 −0.248995 0.968505i \(-0.580100\pi\)
−0.248995 + 0.968505i \(0.580100\pi\)
\(240\) 1640.00 0.441090
\(241\) −438.000 −0.117071 −0.0585354 0.998285i \(-0.518643\pi\)
−0.0585354 + 0.998285i \(0.518643\pi\)
\(242\) −1187.00 −0.315303
\(243\) 5032.00 1.32841
\(244\) 1946.00 0.510573
\(245\) −245.000 −0.0638877
\(246\) −3216.00 −0.833515
\(247\) −3120.00 −0.803728
\(248\) 3720.00 0.952501
\(249\) 3584.00 0.912156
\(250\) −125.000 −0.0316228
\(251\) 5592.00 1.40623 0.703115 0.711076i \(-0.251792\pi\)
0.703115 + 0.711076i \(0.251792\pi\)
\(252\) −1813.00 −0.453207
\(253\) 384.000 0.0954224
\(254\) 776.000 0.191695
\(255\) −3760.00 −0.923374
\(256\) −119.000 −0.0290527
\(257\) −1974.00 −0.479123 −0.239562 0.970881i \(-0.577004\pi\)
−0.239562 + 0.970881i \(0.577004\pi\)
\(258\) 544.000 0.131271
\(259\) −3038.00 −0.728850
\(260\) −2730.00 −0.651182
\(261\) −1850.00 −0.438744
\(262\) 1112.00 0.262212
\(263\) −728.000 −0.170686 −0.0853430 0.996352i \(-0.527199\pi\)
−0.0853430 + 0.996352i \(0.527199\pi\)
\(264\) 1440.00 0.335704
\(265\) −110.000 −0.0254990
\(266\) 280.000 0.0645410
\(267\) 6960.00 1.59530
\(268\) 1148.00 0.261661
\(269\) 5810.00 1.31688 0.658442 0.752631i \(-0.271216\pi\)
0.658442 + 0.752631i \(0.271216\pi\)
\(270\) 400.000 0.0901601
\(271\) −6528.00 −1.46328 −0.731638 0.681693i \(-0.761244\pi\)
−0.731638 + 0.681693i \(0.761244\pi\)
\(272\) −3854.00 −0.859129
\(273\) 4368.00 0.968364
\(274\) −694.000 −0.153015
\(275\) 300.000 0.0657843
\(276\) 1792.00 0.390818
\(277\) 5126.00 1.11188 0.555941 0.831222i \(-0.312358\pi\)
0.555941 + 0.831222i \(0.312358\pi\)
\(278\) 360.000 0.0776668
\(279\) −9176.00 −1.96901
\(280\) 525.000 0.112053
\(281\) −2358.00 −0.500592 −0.250296 0.968169i \(-0.580528\pi\)
−0.250296 + 0.968169i \(0.580528\pi\)
\(282\) −4288.00 −0.905485
\(283\) 392.000 0.0823392 0.0411696 0.999152i \(-0.486892\pi\)
0.0411696 + 0.999152i \(0.486892\pi\)
\(284\) −4704.00 −0.982856
\(285\) 1600.00 0.332547
\(286\) −936.000 −0.193520
\(287\) 2814.00 0.578764
\(288\) 5957.00 1.21882
\(289\) 3923.00 0.798494
\(290\) 250.000 0.0506224
\(291\) −8208.00 −1.65348
\(292\) −574.000 −0.115037
\(293\) 1202.00 0.239664 0.119832 0.992794i \(-0.461764\pi\)
0.119832 + 0.992794i \(0.461764\pi\)
\(294\) −392.000 −0.0777616
\(295\) 2800.00 0.552618
\(296\) 6510.00 1.27833
\(297\) −960.000 −0.187558
\(298\) 2270.00 0.441267
\(299\) −2496.00 −0.482767
\(300\) 1400.00 0.269430
\(301\) −476.000 −0.0911501
\(302\) 632.000 0.120422
\(303\) −3856.00 −0.731094
\(304\) 1640.00 0.309409
\(305\) 1390.00 0.260955
\(306\) −3478.00 −0.649752
\(307\) −6384.00 −1.18682 −0.593411 0.804900i \(-0.702219\pi\)
−0.593411 + 0.804900i \(0.702219\pi\)
\(308\) −588.000 −0.108781
\(309\) −2176.00 −0.400609
\(310\) 1240.00 0.227185
\(311\) −4968.00 −0.905818 −0.452909 0.891557i \(-0.649614\pi\)
−0.452909 + 0.891557i \(0.649614\pi\)
\(312\) −9360.00 −1.69842
\(313\) −2758.00 −0.498056 −0.249028 0.968496i \(-0.580111\pi\)
−0.249028 + 0.968496i \(0.580111\pi\)
\(314\) −734.000 −0.131917
\(315\) −1295.00 −0.231635
\(316\) 7000.00 1.24614
\(317\) −6274.00 −1.11162 −0.555809 0.831310i \(-0.687591\pi\)
−0.555809 + 0.831310i \(0.687591\pi\)
\(318\) −176.000 −0.0310364
\(319\) −600.000 −0.105309
\(320\) 835.000 0.145868
\(321\) 3552.00 0.617612
\(322\) 224.000 0.0387672
\(323\) −3760.00 −0.647715
\(324\) 2513.00 0.430898
\(325\) −1950.00 −0.332820
\(326\) 2532.00 0.430167
\(327\) 9360.00 1.58290
\(328\) −6030.00 −1.01509
\(329\) 3752.00 0.628737
\(330\) 480.000 0.0800701
\(331\) 1932.00 0.320823 0.160411 0.987050i \(-0.448718\pi\)
0.160411 + 0.987050i \(0.448718\pi\)
\(332\) 3136.00 0.518405
\(333\) −16058.0 −2.64256
\(334\) 416.000 0.0681512
\(335\) 820.000 0.133735
\(336\) −2296.00 −0.372789
\(337\) 2386.00 0.385679 0.192839 0.981230i \(-0.438230\pi\)
0.192839 + 0.981230i \(0.438230\pi\)
\(338\) 3887.00 0.625518
\(339\) 6384.00 1.02281
\(340\) −3290.00 −0.524780
\(341\) −2976.00 −0.472608
\(342\) 1480.00 0.234004
\(343\) 343.000 0.0539949
\(344\) 1020.00 0.159868
\(345\) 1280.00 0.199747
\(346\) 3042.00 0.472656
\(347\) 6076.00 0.939991 0.469995 0.882669i \(-0.344256\pi\)
0.469995 + 0.882669i \(0.344256\pi\)
\(348\) −2800.00 −0.431310
\(349\) 2210.00 0.338964 0.169482 0.985533i \(-0.445790\pi\)
0.169482 + 0.985533i \(0.445790\pi\)
\(350\) 175.000 0.0267261
\(351\) 6240.00 0.948908
\(352\) 1932.00 0.292545
\(353\) −2598.00 −0.391721 −0.195861 0.980632i \(-0.562750\pi\)
−0.195861 + 0.980632i \(0.562750\pi\)
\(354\) 4480.00 0.672625
\(355\) −3360.00 −0.502339
\(356\) 6090.00 0.906655
\(357\) 5264.00 0.780393
\(358\) −180.000 −0.0265735
\(359\) −13320.0 −1.95822 −0.979112 0.203320i \(-0.934827\pi\)
−0.979112 + 0.203320i \(0.934827\pi\)
\(360\) 2775.00 0.406265
\(361\) −5259.00 −0.766730
\(362\) −1958.00 −0.284282
\(363\) 9496.00 1.37303
\(364\) 3822.00 0.550350
\(365\) −410.000 −0.0587956
\(366\) 2224.00 0.317624
\(367\) 10816.0 1.53839 0.769197 0.639012i \(-0.220656\pi\)
0.769197 + 0.639012i \(0.220656\pi\)
\(368\) 1312.00 0.185850
\(369\) 14874.0 2.09840
\(370\) 2170.00 0.304900
\(371\) 154.000 0.0215506
\(372\) −13888.0 −1.93564
\(373\) −11098.0 −1.54057 −0.770285 0.637700i \(-0.779886\pi\)
−0.770285 + 0.637700i \(0.779886\pi\)
\(374\) −1128.00 −0.155956
\(375\) 1000.00 0.137706
\(376\) −8040.00 −1.10274
\(377\) 3900.00 0.532786
\(378\) −560.000 −0.0761992
\(379\) 7100.00 0.962276 0.481138 0.876645i \(-0.340224\pi\)
0.481138 + 0.876645i \(0.340224\pi\)
\(380\) 1400.00 0.188996
\(381\) −6208.00 −0.834765
\(382\) −2888.00 −0.386814
\(383\) −728.000 −0.0971255 −0.0485627 0.998820i \(-0.515464\pi\)
−0.0485627 + 0.998820i \(0.515464\pi\)
\(384\) 11640.0 1.54688
\(385\) −420.000 −0.0555979
\(386\) 1602.00 0.211243
\(387\) −2516.00 −0.330479
\(388\) −7182.00 −0.939719
\(389\) −6810.00 −0.887611 −0.443806 0.896123i \(-0.646372\pi\)
−0.443806 + 0.896123i \(0.646372\pi\)
\(390\) −3120.00 −0.405096
\(391\) −3008.00 −0.389057
\(392\) −735.000 −0.0947018
\(393\) −8896.00 −1.14184
\(394\) −4794.00 −0.612990
\(395\) 5000.00 0.636905
\(396\) −3108.00 −0.394401
\(397\) −574.000 −0.0725648 −0.0362824 0.999342i \(-0.511552\pi\)
−0.0362824 + 0.999342i \(0.511552\pi\)
\(398\) 1280.00 0.161208
\(399\) −2240.00 −0.281053
\(400\) 1025.00 0.128125
\(401\) 6162.00 0.767371 0.383685 0.923464i \(-0.374655\pi\)
0.383685 + 0.923464i \(0.374655\pi\)
\(402\) 1312.00 0.162778
\(403\) 19344.0 2.39105
\(404\) −3374.00 −0.415502
\(405\) 1795.00 0.220233
\(406\) −350.000 −0.0427838
\(407\) −5208.00 −0.634278
\(408\) −11280.0 −1.36873
\(409\) 8210.00 0.992563 0.496282 0.868162i \(-0.334698\pi\)
0.496282 + 0.868162i \(0.334698\pi\)
\(410\) −2010.00 −0.242114
\(411\) 5552.00 0.666326
\(412\) −1904.00 −0.227678
\(413\) −3920.00 −0.467047
\(414\) 1184.00 0.140557
\(415\) 2240.00 0.264957
\(416\) −12558.0 −1.48006
\(417\) −2880.00 −0.338212
\(418\) 480.000 0.0561664
\(419\) 4800.00 0.559655 0.279827 0.960050i \(-0.409723\pi\)
0.279827 + 0.960050i \(0.409723\pi\)
\(420\) −1960.00 −0.227710
\(421\) −9938.00 −1.15047 −0.575236 0.817988i \(-0.695090\pi\)
−0.575236 + 0.817988i \(0.695090\pi\)
\(422\) −68.0000 −0.00784405
\(423\) 19832.0 2.27959
\(424\) −330.000 −0.0377977
\(425\) −2350.00 −0.268216
\(426\) −5376.00 −0.611427
\(427\) −1946.00 −0.220547
\(428\) 3108.00 0.351007
\(429\) 7488.00 0.842713
\(430\) 340.000 0.0381308
\(431\) −9248.00 −1.03355 −0.516776 0.856121i \(-0.672868\pi\)
−0.516776 + 0.856121i \(0.672868\pi\)
\(432\) −3280.00 −0.365299
\(433\) −1118.00 −0.124082 −0.0620412 0.998074i \(-0.519761\pi\)
−0.0620412 + 0.998074i \(0.519761\pi\)
\(434\) −1736.00 −0.192006
\(435\) −2000.00 −0.220443
\(436\) 8190.00 0.899610
\(437\) 1280.00 0.140116
\(438\) −656.000 −0.0715637
\(439\) −11960.0 −1.30027 −0.650136 0.759818i \(-0.725288\pi\)
−0.650136 + 0.759818i \(0.725288\pi\)
\(440\) 900.000 0.0975132
\(441\) 1813.00 0.195767
\(442\) 7332.00 0.789022
\(443\) 7332.00 0.786352 0.393176 0.919463i \(-0.371376\pi\)
0.393176 + 0.919463i \(0.371376\pi\)
\(444\) −24304.0 −2.59779
\(445\) 4350.00 0.463393
\(446\) −1728.00 −0.183460
\(447\) −18160.0 −1.92156
\(448\) −1169.00 −0.123281
\(449\) 1890.00 0.198652 0.0993259 0.995055i \(-0.468331\pi\)
0.0993259 + 0.995055i \(0.468331\pi\)
\(450\) 925.000 0.0968998
\(451\) 4824.00 0.503666
\(452\) 5586.00 0.581291
\(453\) −5056.00 −0.524396
\(454\) −4864.00 −0.502817
\(455\) 2730.00 0.281284
\(456\) 4800.00 0.492940
\(457\) −7014.00 −0.717945 −0.358973 0.933348i \(-0.616873\pi\)
−0.358973 + 0.933348i \(0.616873\pi\)
\(458\) −5510.00 −0.562152
\(459\) 7520.00 0.764714
\(460\) 1120.00 0.113522
\(461\) −8318.00 −0.840364 −0.420182 0.907440i \(-0.638034\pi\)
−0.420182 + 0.907440i \(0.638034\pi\)
\(462\) −672.000 −0.0676716
\(463\) 6432.00 0.645616 0.322808 0.946464i \(-0.395373\pi\)
0.322808 + 0.946464i \(0.395373\pi\)
\(464\) −2050.00 −0.205105
\(465\) −9920.00 −0.989310
\(466\) 5322.00 0.529049
\(467\) −10064.0 −0.997230 −0.498615 0.866824i \(-0.666158\pi\)
−0.498615 + 0.866824i \(0.666158\pi\)
\(468\) 20202.0 1.99538
\(469\) −1148.00 −0.113027
\(470\) −2680.00 −0.263020
\(471\) 5872.00 0.574453
\(472\) 8400.00 0.819155
\(473\) −816.000 −0.0793229
\(474\) 8000.00 0.775216
\(475\) 1000.00 0.0965961
\(476\) 4606.00 0.443520
\(477\) 814.000 0.0781352
\(478\) −1840.00 −0.176066
\(479\) 1400.00 0.133544 0.0667721 0.997768i \(-0.478730\pi\)
0.0667721 + 0.997768i \(0.478730\pi\)
\(480\) 6440.00 0.612384
\(481\) 33852.0 3.20898
\(482\) −438.000 −0.0413908
\(483\) −1792.00 −0.168817
\(484\) 8309.00 0.780334
\(485\) −5130.00 −0.480291
\(486\) 5032.00 0.469663
\(487\) 13376.0 1.24461 0.622304 0.782775i \(-0.286197\pi\)
0.622304 + 0.782775i \(0.286197\pi\)
\(488\) 4170.00 0.386818
\(489\) −20256.0 −1.87323
\(490\) −245.000 −0.0225877
\(491\) 7092.00 0.651848 0.325924 0.945396i \(-0.394325\pi\)
0.325924 + 0.945396i \(0.394325\pi\)
\(492\) 22512.0 2.06284
\(493\) 4700.00 0.429366
\(494\) −3120.00 −0.284161
\(495\) −2220.00 −0.201579
\(496\) −10168.0 −0.920477
\(497\) 4704.00 0.424554
\(498\) 3584.00 0.322496
\(499\) −820.000 −0.0735636 −0.0367818 0.999323i \(-0.511711\pi\)
−0.0367818 + 0.999323i \(0.511711\pi\)
\(500\) 875.000 0.0782624
\(501\) −3328.00 −0.296775
\(502\) 5592.00 0.497178
\(503\) −4568.00 −0.404925 −0.202462 0.979290i \(-0.564894\pi\)
−0.202462 + 0.979290i \(0.564894\pi\)
\(504\) −3885.00 −0.343356
\(505\) −2410.00 −0.212364
\(506\) 384.000 0.0337369
\(507\) −31096.0 −2.72391
\(508\) −5432.00 −0.474421
\(509\) 19810.0 1.72507 0.862537 0.505994i \(-0.168874\pi\)
0.862537 + 0.505994i \(0.168874\pi\)
\(510\) −3760.00 −0.326462
\(511\) 574.000 0.0496913
\(512\) 11521.0 0.994455
\(513\) −3200.00 −0.275406
\(514\) −1974.00 −0.169396
\(515\) −1360.00 −0.116367
\(516\) −3808.00 −0.324880
\(517\) 6432.00 0.547155
\(518\) −3038.00 −0.257687
\(519\) −24336.0 −2.05825
\(520\) −5850.00 −0.493345
\(521\) −1838.00 −0.154557 −0.0772785 0.997010i \(-0.524623\pi\)
−0.0772785 + 0.997010i \(0.524623\pi\)
\(522\) −1850.00 −0.155119
\(523\) 2072.00 0.173236 0.0866178 0.996242i \(-0.472394\pi\)
0.0866178 + 0.996242i \(0.472394\pi\)
\(524\) −7784.00 −0.648942
\(525\) −1400.00 −0.116383
\(526\) −728.000 −0.0603466
\(527\) 23312.0 1.92692
\(528\) −3936.00 −0.324417
\(529\) −11143.0 −0.915838
\(530\) −110.000 −0.00901527
\(531\) −20720.0 −1.69335
\(532\) −1960.00 −0.159731
\(533\) −31356.0 −2.54818
\(534\) 6960.00 0.564024
\(535\) 2220.00 0.179400
\(536\) 2460.00 0.198238
\(537\) 1440.00 0.115718
\(538\) 5810.00 0.465589
\(539\) 588.000 0.0469888
\(540\) −2800.00 −0.223135
\(541\) −3498.00 −0.277987 −0.138993 0.990293i \(-0.544387\pi\)
−0.138993 + 0.990293i \(0.544387\pi\)
\(542\) −6528.00 −0.517346
\(543\) 15664.0 1.23795
\(544\) −15134.0 −1.19277
\(545\) 5850.00 0.459792
\(546\) 4368.00 0.342368
\(547\) 5076.00 0.396772 0.198386 0.980124i \(-0.436430\pi\)
0.198386 + 0.980124i \(0.436430\pi\)
\(548\) 4858.00 0.378692
\(549\) −10286.0 −0.799628
\(550\) 300.000 0.0232583
\(551\) −2000.00 −0.154633
\(552\) 3840.00 0.296089
\(553\) −7000.00 −0.538283
\(554\) 5126.00 0.393110
\(555\) −17360.0 −1.32773
\(556\) −2520.00 −0.192215
\(557\) −8674.00 −0.659837 −0.329918 0.944009i \(-0.607021\pi\)
−0.329918 + 0.944009i \(0.607021\pi\)
\(558\) −9176.00 −0.696149
\(559\) 5304.00 0.401315
\(560\) −1435.00 −0.108285
\(561\) 9024.00 0.679133
\(562\) −2358.00 −0.176986
\(563\) 16072.0 1.20312 0.601558 0.798829i \(-0.294547\pi\)
0.601558 + 0.798829i \(0.294547\pi\)
\(564\) 30016.0 2.24096
\(565\) 3990.00 0.297098
\(566\) 392.000 0.0291113
\(567\) −2513.00 −0.186131
\(568\) −10080.0 −0.744626
\(569\) 2730.00 0.201138 0.100569 0.994930i \(-0.467934\pi\)
0.100569 + 0.994930i \(0.467934\pi\)
\(570\) 1600.00 0.117573
\(571\) 19932.0 1.46082 0.730410 0.683009i \(-0.239329\pi\)
0.730410 + 0.683009i \(0.239329\pi\)
\(572\) 6552.00 0.478939
\(573\) 23104.0 1.68444
\(574\) 2814.00 0.204624
\(575\) 800.000 0.0580214
\(576\) −6179.00 −0.446976
\(577\) −20054.0 −1.44690 −0.723448 0.690379i \(-0.757444\pi\)
−0.723448 + 0.690379i \(0.757444\pi\)
\(578\) 3923.00 0.282310
\(579\) −12816.0 −0.919887
\(580\) −1750.00 −0.125284
\(581\) −3136.00 −0.223930
\(582\) −8208.00 −0.584592
\(583\) 264.000 0.0187543
\(584\) −1230.00 −0.0871537
\(585\) 14430.0 1.01984
\(586\) 1202.00 0.0847341
\(587\) −2544.00 −0.178879 −0.0894396 0.995992i \(-0.528508\pi\)
−0.0894396 + 0.995992i \(0.528508\pi\)
\(588\) 2744.00 0.192450
\(589\) −9920.00 −0.693967
\(590\) 2800.00 0.195380
\(591\) 38352.0 2.66936
\(592\) −17794.0 −1.23535
\(593\) 14202.0 0.983484 0.491742 0.870741i \(-0.336360\pi\)
0.491742 + 0.870741i \(0.336360\pi\)
\(594\) −960.000 −0.0663119
\(595\) 3290.00 0.226684
\(596\) −15890.0 −1.09208
\(597\) −10240.0 −0.702002
\(598\) −2496.00 −0.170684
\(599\) −19600.0 −1.33695 −0.668476 0.743734i \(-0.733053\pi\)
−0.668476 + 0.743734i \(0.733053\pi\)
\(600\) 3000.00 0.204124
\(601\) −27078.0 −1.83783 −0.918914 0.394458i \(-0.870932\pi\)
−0.918914 + 0.394458i \(0.870932\pi\)
\(602\) −476.000 −0.0322264
\(603\) −6068.00 −0.409798
\(604\) −4424.00 −0.298030
\(605\) 5935.00 0.398830
\(606\) −3856.00 −0.258481
\(607\) −2704.00 −0.180811 −0.0904053 0.995905i \(-0.528816\pi\)
−0.0904053 + 0.995905i \(0.528816\pi\)
\(608\) 6440.00 0.429567
\(609\) 2800.00 0.186308
\(610\) 1390.00 0.0922614
\(611\) −41808.0 −2.76820
\(612\) 24346.0 1.60805
\(613\) 12702.0 0.836915 0.418458 0.908236i \(-0.362571\pi\)
0.418458 + 0.908236i \(0.362571\pi\)
\(614\) −6384.00 −0.419605
\(615\) 16080.0 1.05432
\(616\) −1260.00 −0.0824137
\(617\) 12666.0 0.826441 0.413220 0.910631i \(-0.364404\pi\)
0.413220 + 0.910631i \(0.364404\pi\)
\(618\) −2176.00 −0.141637
\(619\) 960.000 0.0623355 0.0311677 0.999514i \(-0.490077\pi\)
0.0311677 + 0.999514i \(0.490077\pi\)
\(620\) −8680.00 −0.562254
\(621\) −2560.00 −0.165426
\(622\) −4968.00 −0.320255
\(623\) −6090.00 −0.391638
\(624\) 25584.0 1.64131
\(625\) 625.000 0.0400000
\(626\) −2758.00 −0.176089
\(627\) −3840.00 −0.244585
\(628\) 5138.00 0.326479
\(629\) 40796.0 2.58608
\(630\) −1295.00 −0.0818953
\(631\) 23232.0 1.46569 0.732846 0.680395i \(-0.238192\pi\)
0.732846 + 0.680395i \(0.238192\pi\)
\(632\) 15000.0 0.944095
\(633\) 544.000 0.0341581
\(634\) −6274.00 −0.393016
\(635\) −3880.00 −0.242477
\(636\) 1232.00 0.0768113
\(637\) −3822.00 −0.237729
\(638\) −600.000 −0.0372323
\(639\) 24864.0 1.53929
\(640\) 7275.00 0.449328
\(641\) 12162.0 0.749407 0.374704 0.927145i \(-0.377744\pi\)
0.374704 + 0.927145i \(0.377744\pi\)
\(642\) 3552.00 0.218359
\(643\) −488.000 −0.0299298 −0.0149649 0.999888i \(-0.504764\pi\)
−0.0149649 + 0.999888i \(0.504764\pi\)
\(644\) −1568.00 −0.0959439
\(645\) −2720.00 −0.166046
\(646\) −3760.00 −0.229002
\(647\) −3984.00 −0.242082 −0.121041 0.992647i \(-0.538623\pi\)
−0.121041 + 0.992647i \(0.538623\pi\)
\(648\) 5385.00 0.326455
\(649\) −6720.00 −0.406445
\(650\) −1950.00 −0.117670
\(651\) 13888.0 0.836119
\(652\) −17724.0 −1.06461
\(653\) −30538.0 −1.83008 −0.915042 0.403360i \(-0.867842\pi\)
−0.915042 + 0.403360i \(0.867842\pi\)
\(654\) 9360.00 0.559641
\(655\) −5560.00 −0.331675
\(656\) 16482.0 0.980966
\(657\) 3034.00 0.180164
\(658\) 3752.00 0.222292
\(659\) 22740.0 1.34420 0.672098 0.740463i \(-0.265394\pi\)
0.672098 + 0.740463i \(0.265394\pi\)
\(660\) −3360.00 −0.198163
\(661\) −18718.0 −1.10143 −0.550715 0.834693i \(-0.685645\pi\)
−0.550715 + 0.834693i \(0.685645\pi\)
\(662\) 1932.00 0.113428
\(663\) −58656.0 −3.43591
\(664\) 6720.00 0.392751
\(665\) −1400.00 −0.0816386
\(666\) −16058.0 −0.934287
\(667\) −1600.00 −0.0928819
\(668\) −2912.00 −0.168666
\(669\) 13824.0 0.798904
\(670\) 820.000 0.0472826
\(671\) −3336.00 −0.191930
\(672\) −9016.00 −0.517559
\(673\) 10802.0 0.618702 0.309351 0.950948i \(-0.399888\pi\)
0.309351 + 0.950948i \(0.399888\pi\)
\(674\) 2386.00 0.136358
\(675\) −2000.00 −0.114044
\(676\) −27209.0 −1.54808
\(677\) 346.000 0.0196423 0.00982117 0.999952i \(-0.496874\pi\)
0.00982117 + 0.999952i \(0.496874\pi\)
\(678\) 6384.00 0.361617
\(679\) 7182.00 0.405920
\(680\) −7050.00 −0.397581
\(681\) 38912.0 2.18959
\(682\) −2976.00 −0.167092
\(683\) −11628.0 −0.651439 −0.325720 0.945466i \(-0.605607\pi\)
−0.325720 + 0.945466i \(0.605607\pi\)
\(684\) −10360.0 −0.579129
\(685\) 3470.00 0.193550
\(686\) 343.000 0.0190901
\(687\) 44080.0 2.44797
\(688\) −2788.00 −0.154493
\(689\) −1716.00 −0.0948830
\(690\) 1280.00 0.0706214
\(691\) 2472.00 0.136092 0.0680458 0.997682i \(-0.478324\pi\)
0.0680458 + 0.997682i \(0.478324\pi\)
\(692\) −21294.0 −1.16976
\(693\) 3108.00 0.170365
\(694\) 6076.00 0.332337
\(695\) −1800.00 −0.0982416
\(696\) −6000.00 −0.326766
\(697\) −37788.0 −2.05355
\(698\) 2210.00 0.119842
\(699\) −42576.0 −2.30382
\(700\) −1225.00 −0.0661438
\(701\) −2018.00 −0.108729 −0.0543643 0.998521i \(-0.517313\pi\)
−0.0543643 + 0.998521i \(0.517313\pi\)
\(702\) 6240.00 0.335489
\(703\) −17360.0 −0.931358
\(704\) −2004.00 −0.107285
\(705\) 21440.0 1.14536
\(706\) −2598.00 −0.138494
\(707\) 3374.00 0.179480
\(708\) −31360.0 −1.66466
\(709\) 790.000 0.0418464 0.0209232 0.999781i \(-0.493339\pi\)
0.0209232 + 0.999781i \(0.493339\pi\)
\(710\) −3360.00 −0.177604
\(711\) −37000.0 −1.95163
\(712\) 13050.0 0.686895
\(713\) −7936.00 −0.416838
\(714\) 5264.00 0.275911
\(715\) 4680.00 0.244786
\(716\) 1260.00 0.0657659
\(717\) 14720.0 0.766706
\(718\) −13320.0 −0.692337
\(719\) 18200.0 0.944013 0.472007 0.881595i \(-0.343530\pi\)
0.472007 + 0.881595i \(0.343530\pi\)
\(720\) −7585.00 −0.392606
\(721\) 1904.00 0.0983477
\(722\) −5259.00 −0.271080
\(723\) 3504.00 0.180242
\(724\) 13706.0 0.703563
\(725\) −1250.00 −0.0640329
\(726\) 9496.00 0.485440
\(727\) 29056.0 1.48229 0.741147 0.671343i \(-0.234282\pi\)
0.741147 + 0.671343i \(0.234282\pi\)
\(728\) 8190.00 0.416953
\(729\) −30563.0 −1.55276
\(730\) −410.000 −0.0207874
\(731\) 6392.00 0.323415
\(732\) −15568.0 −0.786079
\(733\) 7082.00 0.356862 0.178431 0.983952i \(-0.442898\pi\)
0.178431 + 0.983952i \(0.442898\pi\)
\(734\) 10816.0 0.543904
\(735\) 1960.00 0.0983615
\(736\) 5152.00 0.258023
\(737\) −1968.00 −0.0983612
\(738\) 14874.0 0.741896
\(739\) 11060.0 0.550539 0.275270 0.961367i \(-0.411233\pi\)
0.275270 + 0.961367i \(0.411233\pi\)
\(740\) −15190.0 −0.754589
\(741\) 24960.0 1.23742
\(742\) 154.000 0.00761930
\(743\) 33072.0 1.63297 0.816483 0.577369i \(-0.195921\pi\)
0.816483 + 0.577369i \(0.195921\pi\)
\(744\) −29760.0 −1.46647
\(745\) −11350.0 −0.558164
\(746\) −11098.0 −0.544674
\(747\) −16576.0 −0.811893
\(748\) 7896.00 0.385971
\(749\) −3108.00 −0.151621
\(750\) 1000.00 0.0486864
\(751\) 29072.0 1.41259 0.706293 0.707919i \(-0.250366\pi\)
0.706293 + 0.707919i \(0.250366\pi\)
\(752\) 21976.0 1.06567
\(753\) −44736.0 −2.16503
\(754\) 3900.00 0.188368
\(755\) −3160.00 −0.152323
\(756\) 3920.00 0.188583
\(757\) −13234.0 −0.635400 −0.317700 0.948191i \(-0.602911\pi\)
−0.317700 + 0.948191i \(0.602911\pi\)
\(758\) 7100.00 0.340216
\(759\) −3072.00 −0.146912
\(760\) 3000.00 0.143186
\(761\) −22398.0 −1.06692 −0.533460 0.845825i \(-0.679109\pi\)
−0.533460 + 0.845825i \(0.679109\pi\)
\(762\) −6208.00 −0.295134
\(763\) −8190.00 −0.388595
\(764\) 20216.0 0.957316
\(765\) 17390.0 0.821878
\(766\) −728.000 −0.0343390
\(767\) 43680.0 2.05631
\(768\) 952.000 0.0447296
\(769\) 6890.00 0.323095 0.161547 0.986865i \(-0.448352\pi\)
0.161547 + 0.986865i \(0.448352\pi\)
\(770\) −420.000 −0.0196568
\(771\) 15792.0 0.737659
\(772\) −11214.0 −0.522799
\(773\) 16722.0 0.778071 0.389035 0.921223i \(-0.372808\pi\)
0.389035 + 0.921223i \(0.372808\pi\)
\(774\) −2516.00 −0.116842
\(775\) −6200.00 −0.287368
\(776\) −15390.0 −0.711944
\(777\) 24304.0 1.12214
\(778\) −6810.00 −0.313818
\(779\) 16080.0 0.739571
\(780\) 21840.0 1.00256
\(781\) 8064.00 0.369466
\(782\) −3008.00 −0.137552
\(783\) 4000.00 0.182565
\(784\) 2009.00 0.0915179
\(785\) 3670.00 0.166864
\(786\) −8896.00 −0.403702
\(787\) −32624.0 −1.47766 −0.738831 0.673891i \(-0.764622\pi\)
−0.738831 + 0.673891i \(0.764622\pi\)
\(788\) 33558.0 1.51707
\(789\) 5824.00 0.262788
\(790\) 5000.00 0.225180
\(791\) −5586.00 −0.251094
\(792\) −6660.00 −0.298804
\(793\) 21684.0 0.971023
\(794\) −574.000 −0.0256555
\(795\) 880.000 0.0392583
\(796\) −8960.00 −0.398968
\(797\) 11346.0 0.504261 0.252130 0.967693i \(-0.418869\pi\)
0.252130 + 0.967693i \(0.418869\pi\)
\(798\) −2240.00 −0.0993673
\(799\) −50384.0 −2.23086
\(800\) 4025.00 0.177882
\(801\) −32190.0 −1.41995
\(802\) 6162.00 0.271306
\(803\) 984.000 0.0432436
\(804\) −9184.00 −0.402854
\(805\) −1120.00 −0.0490370
\(806\) 19344.0 0.845364
\(807\) −46480.0 −2.02748
\(808\) −7230.00 −0.314790
\(809\) −35190.0 −1.52931 −0.764657 0.644438i \(-0.777091\pi\)
−0.764657 + 0.644438i \(0.777091\pi\)
\(810\) 1795.00 0.0778640
\(811\) 30432.0 1.31765 0.658824 0.752297i \(-0.271054\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(812\) 2450.00 0.105884
\(813\) 52224.0 2.25286
\(814\) −5208.00 −0.224251
\(815\) −12660.0 −0.544123
\(816\) 30832.0 1.32272
\(817\) −2720.00 −0.116476
\(818\) 8210.00 0.350924
\(819\) −20202.0 −0.861923
\(820\) 14070.0 0.599202
\(821\) 12702.0 0.539955 0.269977 0.962867i \(-0.412984\pi\)
0.269977 + 0.962867i \(0.412984\pi\)
\(822\) 5552.00 0.235582
\(823\) 16952.0 0.717995 0.358997 0.933339i \(-0.383119\pi\)
0.358997 + 0.933339i \(0.383119\pi\)
\(824\) −4080.00 −0.172492
\(825\) −2400.00 −0.101282
\(826\) −3920.00 −0.165126
\(827\) −25404.0 −1.06818 −0.534089 0.845428i \(-0.679345\pi\)
−0.534089 + 0.845428i \(0.679345\pi\)
\(828\) −8288.00 −0.347860
\(829\) 26250.0 1.09976 0.549879 0.835244i \(-0.314674\pi\)
0.549879 + 0.835244i \(0.314674\pi\)
\(830\) 2240.00 0.0936765
\(831\) −41008.0 −1.71186
\(832\) 13026.0 0.542783
\(833\) −4606.00 −0.191583
\(834\) −2880.00 −0.119576
\(835\) −2080.00 −0.0862052
\(836\) −3360.00 −0.139005
\(837\) 19840.0 0.819320
\(838\) 4800.00 0.197868
\(839\) −15360.0 −0.632045 −0.316023 0.948752i \(-0.602348\pi\)
−0.316023 + 0.948752i \(0.602348\pi\)
\(840\) −4200.00 −0.172516
\(841\) −21889.0 −0.897495
\(842\) −9938.00 −0.406753
\(843\) 18864.0 0.770713
\(844\) 476.000 0.0194130
\(845\) −19435.0 −0.791224
\(846\) 19832.0 0.805955
\(847\) −8309.00 −0.337073
\(848\) 902.000 0.0365269
\(849\) −3136.00 −0.126769
\(850\) −2350.00 −0.0948286
\(851\) −13888.0 −0.559430
\(852\) 37632.0 1.51321
\(853\) 10362.0 0.415930 0.207965 0.978136i \(-0.433316\pi\)
0.207965 + 0.978136i \(0.433316\pi\)
\(854\) −1946.00 −0.0779751
\(855\) −7400.00 −0.295994
\(856\) 6660.00 0.265928
\(857\) 4506.00 0.179606 0.0898028 0.995960i \(-0.471376\pi\)
0.0898028 + 0.995960i \(0.471376\pi\)
\(858\) 7488.00 0.297944
\(859\) 24200.0 0.961226 0.480613 0.876933i \(-0.340414\pi\)
0.480613 + 0.876933i \(0.340414\pi\)
\(860\) −2380.00 −0.0943690
\(861\) −22512.0 −0.891065
\(862\) −9248.00 −0.365415
\(863\) −37008.0 −1.45975 −0.729877 0.683579i \(-0.760422\pi\)
−0.729877 + 0.683579i \(0.760422\pi\)
\(864\) −12880.0 −0.507160
\(865\) −15210.0 −0.597868
\(866\) −1118.00 −0.0438697
\(867\) −31384.0 −1.22936
\(868\) 12152.0 0.475191
\(869\) −12000.0 −0.468437
\(870\) −2000.00 −0.0779383
\(871\) 12792.0 0.497635
\(872\) 17550.0 0.681557
\(873\) 37962.0 1.47173
\(874\) 1280.00 0.0495385
\(875\) −875.000 −0.0338062
\(876\) 4592.00 0.177111
\(877\) 3446.00 0.132683 0.0663416 0.997797i \(-0.478867\pi\)
0.0663416 + 0.997797i \(0.478867\pi\)
\(878\) −11960.0 −0.459716
\(879\) −9616.00 −0.368987
\(880\) −2460.00 −0.0942348
\(881\) −16158.0 −0.617908 −0.308954 0.951077i \(-0.599979\pi\)
−0.308954 + 0.951077i \(0.599979\pi\)
\(882\) 1813.00 0.0692142
\(883\) −44708.0 −1.70390 −0.851950 0.523623i \(-0.824580\pi\)
−0.851950 + 0.523623i \(0.824580\pi\)
\(884\) −51324.0 −1.95273
\(885\) −22400.0 −0.850811
\(886\) 7332.00 0.278017
\(887\) −23504.0 −0.889726 −0.444863 0.895599i \(-0.646748\pi\)
−0.444863 + 0.895599i \(0.646748\pi\)
\(888\) −52080.0 −1.96812
\(889\) 5432.00 0.204931
\(890\) 4350.00 0.163834
\(891\) −4308.00 −0.161979
\(892\) 12096.0 0.454040
\(893\) 21440.0 0.803429
\(894\) −18160.0 −0.679375
\(895\) 900.000 0.0336131
\(896\) −10185.0 −0.379751
\(897\) 19968.0 0.743269
\(898\) 1890.00 0.0702340
\(899\) 12400.0 0.460026
\(900\) −6475.00 −0.239815
\(901\) −2068.00 −0.0764651
\(902\) 4824.00 0.178073
\(903\) 3808.00 0.140335
\(904\) 11970.0 0.440394
\(905\) 9790.00 0.359592
\(906\) −5056.00 −0.185402
\(907\) 42436.0 1.55354 0.776772 0.629782i \(-0.216856\pi\)
0.776772 + 0.629782i \(0.216856\pi\)
\(908\) 34048.0 1.24441
\(909\) 17834.0 0.650733
\(910\) 2730.00 0.0994490
\(911\) −7968.00 −0.289782 −0.144891 0.989448i \(-0.546283\pi\)
−0.144891 + 0.989448i \(0.546283\pi\)
\(912\) −13120.0 −0.476367
\(913\) −5376.00 −0.194874
\(914\) −7014.00 −0.253832
\(915\) −11120.0 −0.401766
\(916\) 38570.0 1.39125
\(917\) 7784.00 0.280317
\(918\) 7520.00 0.270367
\(919\) 14880.0 0.534109 0.267054 0.963681i \(-0.413950\pi\)
0.267054 + 0.963681i \(0.413950\pi\)
\(920\) 2400.00 0.0860061
\(921\) 51072.0 1.82723
\(922\) −8318.00 −0.297114
\(923\) −52416.0 −1.86922
\(924\) 4704.00 0.167479
\(925\) −10850.0 −0.385671
\(926\) 6432.00 0.228260
\(927\) 10064.0 0.356575
\(928\) −8050.00 −0.284757
\(929\) 27610.0 0.975086 0.487543 0.873099i \(-0.337893\pi\)
0.487543 + 0.873099i \(0.337893\pi\)
\(930\) −9920.00 −0.349774
\(931\) 1960.00 0.0689972
\(932\) −37254.0 −1.30933
\(933\) 39744.0 1.39460
\(934\) −10064.0 −0.352574
\(935\) 5640.00 0.197270
\(936\) 43290.0 1.51173
\(937\) −28094.0 −0.979499 −0.489750 0.871863i \(-0.662912\pi\)
−0.489750 + 0.871863i \(0.662912\pi\)
\(938\) −1148.00 −0.0399611
\(939\) 22064.0 0.766807
\(940\) 18760.0 0.650940
\(941\) −12198.0 −0.422575 −0.211288 0.977424i \(-0.567766\pi\)
−0.211288 + 0.977424i \(0.567766\pi\)
\(942\) 5872.00 0.203100
\(943\) 12864.0 0.444231
\(944\) −22960.0 −0.791615
\(945\) 2800.00 0.0963852
\(946\) −816.000 −0.0280449
\(947\) 31316.0 1.07459 0.537293 0.843396i \(-0.319447\pi\)
0.537293 + 0.843396i \(0.319447\pi\)
\(948\) −56000.0 −1.91856
\(949\) −6396.00 −0.218781
\(950\) 1000.00 0.0341519
\(951\) 50192.0 1.71145
\(952\) 9870.00 0.336017
\(953\) 27322.0 0.928695 0.464348 0.885653i \(-0.346289\pi\)
0.464348 + 0.885653i \(0.346289\pi\)
\(954\) 814.000 0.0276250
\(955\) 14440.0 0.489285
\(956\) 12880.0 0.435742
\(957\) 4800.00 0.162134
\(958\) 1400.00 0.0472150
\(959\) −4858.00 −0.163580
\(960\) −6680.00 −0.224579
\(961\) 31713.0 1.06452
\(962\) 33852.0 1.13454
\(963\) −16428.0 −0.549725
\(964\) 3066.00 0.102437
\(965\) −8010.00 −0.267203
\(966\) −1792.00 −0.0596860
\(967\) 5296.00 0.176120 0.0880599 0.996115i \(-0.471933\pi\)
0.0880599 + 0.996115i \(0.471933\pi\)
\(968\) 17805.0 0.591193
\(969\) 30080.0 0.997223
\(970\) −5130.00 −0.169809
\(971\) 512.000 0.0169216 0.00846079 0.999964i \(-0.497307\pi\)
0.00846079 + 0.999964i \(0.497307\pi\)
\(972\) −35224.0 −1.16236
\(973\) 2520.00 0.0830293
\(974\) 13376.0 0.440036
\(975\) 15600.0 0.512410
\(976\) −11398.0 −0.373813
\(977\) −20734.0 −0.678955 −0.339478 0.940614i \(-0.610250\pi\)
−0.339478 + 0.940614i \(0.610250\pi\)
\(978\) −20256.0 −0.662286
\(979\) −10440.0 −0.340821
\(980\) 1715.00 0.0559017
\(981\) −43290.0 −1.40891
\(982\) 7092.00 0.230463
\(983\) −61168.0 −1.98470 −0.992348 0.123472i \(-0.960597\pi\)
−0.992348 + 0.123472i \(0.960597\pi\)
\(984\) 48240.0 1.56284
\(985\) 23970.0 0.775378
\(986\) 4700.00 0.151804
\(987\) −30016.0 −0.968004
\(988\) 21840.0 0.703262
\(989\) −2176.00 −0.0699624
\(990\) −2220.00 −0.0712689
\(991\) −47928.0 −1.53631 −0.768155 0.640264i \(-0.778825\pi\)
−0.768155 + 0.640264i \(0.778825\pi\)
\(992\) −39928.0 −1.27794
\(993\) −15456.0 −0.493939
\(994\) 4704.00 0.150102
\(995\) −6400.00 −0.203913
\(996\) −25088.0 −0.798136
\(997\) −9454.00 −0.300312 −0.150156 0.988662i \(-0.547978\pi\)
−0.150156 + 0.988662i \(0.547978\pi\)
\(998\) −820.000 −0.0260087
\(999\) 34720.0 1.09959
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 35.4.a.a.1.1 1
3.2 odd 2 315.4.a.c.1.1 1
4.3 odd 2 560.4.a.p.1.1 1
5.2 odd 4 175.4.b.a.99.2 2
5.3 odd 4 175.4.b.a.99.1 2
5.4 even 2 175.4.a.a.1.1 1
7.2 even 3 245.4.e.e.116.1 2
7.3 odd 6 245.4.e.b.226.1 2
7.4 even 3 245.4.e.e.226.1 2
7.5 odd 6 245.4.e.b.116.1 2
7.6 odd 2 245.4.a.d.1.1 1
8.3 odd 2 2240.4.a.b.1.1 1
8.5 even 2 2240.4.a.bk.1.1 1
15.14 odd 2 1575.4.a.g.1.1 1
21.20 even 2 2205.4.a.i.1.1 1
35.34 odd 2 1225.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.4.a.a.1.1 1 1.1 even 1 trivial
175.4.a.a.1.1 1 5.4 even 2
175.4.b.a.99.1 2 5.3 odd 4
175.4.b.a.99.2 2 5.2 odd 4
245.4.a.d.1.1 1 7.6 odd 2
245.4.e.b.116.1 2 7.5 odd 6
245.4.e.b.226.1 2 7.3 odd 6
245.4.e.e.116.1 2 7.2 even 3
245.4.e.e.226.1 2 7.4 even 3
315.4.a.c.1.1 1 3.2 odd 2
560.4.a.p.1.1 1 4.3 odd 2
1225.4.a.e.1.1 1 35.34 odd 2
1575.4.a.g.1.1 1 15.14 odd 2
2205.4.a.i.1.1 1 21.20 even 2
2240.4.a.b.1.1 1 8.3 odd 2
2240.4.a.bk.1.1 1 8.5 even 2