Properties

Label 6025.2.a.p.1.5
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.36215 q^{2} +2.05253 q^{3} +3.57974 q^{4} -4.84838 q^{6} +3.07728 q^{7} -3.73158 q^{8} +1.21289 q^{9} +O(q^{10})\) \(q-2.36215 q^{2} +2.05253 q^{3} +3.57974 q^{4} -4.84838 q^{6} +3.07728 q^{7} -3.73158 q^{8} +1.21289 q^{9} +0.942447 q^{11} +7.34753 q^{12} -1.99403 q^{13} -7.26899 q^{14} +1.65507 q^{16} -3.11539 q^{17} -2.86502 q^{18} -6.33222 q^{19} +6.31621 q^{21} -2.22620 q^{22} -7.91084 q^{23} -7.65919 q^{24} +4.71020 q^{26} -3.66811 q^{27} +11.0159 q^{28} -1.63432 q^{29} +6.96040 q^{31} +3.55366 q^{32} +1.93440 q^{33} +7.35900 q^{34} +4.34182 q^{36} +0.864280 q^{37} +14.9576 q^{38} -4.09282 q^{39} +1.70732 q^{41} -14.9198 q^{42} +10.2266 q^{43} +3.37372 q^{44} +18.6866 q^{46} +6.49786 q^{47} +3.39707 q^{48} +2.46965 q^{49} -6.39443 q^{51} -7.13813 q^{52} -2.20905 q^{53} +8.66461 q^{54} -11.4831 q^{56} -12.9971 q^{57} +3.86050 q^{58} -7.69694 q^{59} -3.70322 q^{61} -16.4415 q^{62} +3.73239 q^{63} -11.7044 q^{64} -4.56935 q^{66} +7.96470 q^{67} -11.1523 q^{68} -16.2373 q^{69} -7.02031 q^{71} -4.52599 q^{72} +6.13583 q^{73} -2.04156 q^{74} -22.6677 q^{76} +2.90017 q^{77} +9.66784 q^{78} -14.0583 q^{79} -11.1676 q^{81} -4.03294 q^{82} -3.98789 q^{83} +22.6104 q^{84} -24.1566 q^{86} -3.35449 q^{87} -3.51682 q^{88} -11.7782 q^{89} -6.13620 q^{91} -28.3188 q^{92} +14.2864 q^{93} -15.3489 q^{94} +7.29399 q^{96} +17.6694 q^{97} -5.83367 q^{98} +1.14308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36215 −1.67029 −0.835145 0.550029i \(-0.814617\pi\)
−0.835145 + 0.550029i \(0.814617\pi\)
\(3\) 2.05253 1.18503 0.592515 0.805559i \(-0.298135\pi\)
0.592515 + 0.805559i \(0.298135\pi\)
\(4\) 3.57974 1.78987
\(5\) 0 0
\(6\) −4.84838 −1.97934
\(7\) 3.07728 1.16310 0.581551 0.813510i \(-0.302446\pi\)
0.581551 + 0.813510i \(0.302446\pi\)
\(8\) −3.73158 −1.31931
\(9\) 1.21289 0.404296
\(10\) 0 0
\(11\) 0.942447 0.284159 0.142079 0.989855i \(-0.454621\pi\)
0.142079 + 0.989855i \(0.454621\pi\)
\(12\) 7.34753 2.12105
\(13\) −1.99403 −0.553046 −0.276523 0.961007i \(-0.589182\pi\)
−0.276523 + 0.961007i \(0.589182\pi\)
\(14\) −7.26899 −1.94272
\(15\) 0 0
\(16\) 1.65507 0.413766
\(17\) −3.11539 −0.755592 −0.377796 0.925889i \(-0.623318\pi\)
−0.377796 + 0.925889i \(0.623318\pi\)
\(18\) −2.86502 −0.675291
\(19\) −6.33222 −1.45271 −0.726355 0.687320i \(-0.758787\pi\)
−0.726355 + 0.687320i \(0.758787\pi\)
\(20\) 0 0
\(21\) 6.31621 1.37831
\(22\) −2.22620 −0.474627
\(23\) −7.91084 −1.64952 −0.824762 0.565479i \(-0.808691\pi\)
−0.824762 + 0.565479i \(0.808691\pi\)
\(24\) −7.65919 −1.56343
\(25\) 0 0
\(26\) 4.71020 0.923747
\(27\) −3.66811 −0.705927
\(28\) 11.0159 2.08180
\(29\) −1.63432 −0.303485 −0.151742 0.988420i \(-0.548488\pi\)
−0.151742 + 0.988420i \(0.548488\pi\)
\(30\) 0 0
\(31\) 6.96040 1.25012 0.625062 0.780575i \(-0.285074\pi\)
0.625062 + 0.780575i \(0.285074\pi\)
\(32\) 3.55366 0.628203
\(33\) 1.93440 0.336736
\(34\) 7.35900 1.26206
\(35\) 0 0
\(36\) 4.34182 0.723637
\(37\) 0.864280 0.142087 0.0710434 0.997473i \(-0.477367\pi\)
0.0710434 + 0.997473i \(0.477367\pi\)
\(38\) 14.9576 2.42645
\(39\) −4.09282 −0.655375
\(40\) 0 0
\(41\) 1.70732 0.266639 0.133319 0.991073i \(-0.457436\pi\)
0.133319 + 0.991073i \(0.457436\pi\)
\(42\) −14.9198 −2.30218
\(43\) 10.2266 1.55953 0.779767 0.626069i \(-0.215337\pi\)
0.779767 + 0.626069i \(0.215337\pi\)
\(44\) 3.37372 0.508607
\(45\) 0 0
\(46\) 18.6866 2.75519
\(47\) 6.49786 0.947811 0.473905 0.880576i \(-0.342844\pi\)
0.473905 + 0.880576i \(0.342844\pi\)
\(48\) 3.39707 0.490326
\(49\) 2.46965 0.352807
\(50\) 0 0
\(51\) −6.39443 −0.895399
\(52\) −7.13813 −0.989880
\(53\) −2.20905 −0.303436 −0.151718 0.988424i \(-0.548481\pi\)
−0.151718 + 0.988424i \(0.548481\pi\)
\(54\) 8.66461 1.17910
\(55\) 0 0
\(56\) −11.4831 −1.53450
\(57\) −12.9971 −1.72150
\(58\) 3.86050 0.506908
\(59\) −7.69694 −1.00206 −0.501028 0.865431i \(-0.667045\pi\)
−0.501028 + 0.865431i \(0.667045\pi\)
\(60\) 0 0
\(61\) −3.70322 −0.474149 −0.237075 0.971491i \(-0.576189\pi\)
−0.237075 + 0.971491i \(0.576189\pi\)
\(62\) −16.4415 −2.08807
\(63\) 3.73239 0.470237
\(64\) −11.7044 −1.46305
\(65\) 0 0
\(66\) −4.56935 −0.562448
\(67\) 7.96470 0.973043 0.486521 0.873669i \(-0.338266\pi\)
0.486521 + 0.873669i \(0.338266\pi\)
\(68\) −11.1523 −1.35241
\(69\) −16.2373 −1.95474
\(70\) 0 0
\(71\) −7.02031 −0.833157 −0.416579 0.909100i \(-0.636771\pi\)
−0.416579 + 0.909100i \(0.636771\pi\)
\(72\) −4.52599 −0.533393
\(73\) 6.13583 0.718144 0.359072 0.933310i \(-0.383093\pi\)
0.359072 + 0.933310i \(0.383093\pi\)
\(74\) −2.04156 −0.237326
\(75\) 0 0
\(76\) −22.6677 −2.60016
\(77\) 2.90017 0.330505
\(78\) 9.66784 1.09467
\(79\) −14.0583 −1.58168 −0.790842 0.612021i \(-0.790357\pi\)
−0.790842 + 0.612021i \(0.790357\pi\)
\(80\) 0 0
\(81\) −11.1676 −1.24084
\(82\) −4.03294 −0.445364
\(83\) −3.98789 −0.437728 −0.218864 0.975755i \(-0.570235\pi\)
−0.218864 + 0.975755i \(0.570235\pi\)
\(84\) 22.6104 2.46700
\(85\) 0 0
\(86\) −24.1566 −2.60488
\(87\) −3.35449 −0.359639
\(88\) −3.51682 −0.374894
\(89\) −11.7782 −1.24849 −0.624245 0.781229i \(-0.714593\pi\)
−0.624245 + 0.781229i \(0.714593\pi\)
\(90\) 0 0
\(91\) −6.13620 −0.643249
\(92\) −28.3188 −2.95244
\(93\) 14.2864 1.48144
\(94\) −15.3489 −1.58312
\(95\) 0 0
\(96\) 7.29399 0.744440
\(97\) 17.6694 1.79405 0.897026 0.441978i \(-0.145723\pi\)
0.897026 + 0.441978i \(0.145723\pi\)
\(98\) −5.83367 −0.589290
\(99\) 1.14308 0.114884
\(100\) 0 0
\(101\) 9.05634 0.901140 0.450570 0.892741i \(-0.351221\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(102\) 15.1046 1.49558
\(103\) −2.20110 −0.216881 −0.108440 0.994103i \(-0.534586\pi\)
−0.108440 + 0.994103i \(0.534586\pi\)
\(104\) 7.44090 0.729641
\(105\) 0 0
\(106\) 5.21809 0.506826
\(107\) 7.08595 0.685024 0.342512 0.939513i \(-0.388722\pi\)
0.342512 + 0.939513i \(0.388722\pi\)
\(108\) −13.1309 −1.26352
\(109\) −7.57661 −0.725708 −0.362854 0.931846i \(-0.618198\pi\)
−0.362854 + 0.931846i \(0.618198\pi\)
\(110\) 0 0
\(111\) 1.77396 0.168377
\(112\) 5.09310 0.481253
\(113\) −17.7967 −1.67418 −0.837088 0.547069i \(-0.815744\pi\)
−0.837088 + 0.547069i \(0.815744\pi\)
\(114\) 30.7010 2.87541
\(115\) 0 0
\(116\) −5.85043 −0.543199
\(117\) −2.41854 −0.223594
\(118\) 18.1813 1.67373
\(119\) −9.58691 −0.878831
\(120\) 0 0
\(121\) −10.1118 −0.919254
\(122\) 8.74756 0.791967
\(123\) 3.50433 0.315975
\(124\) 24.9164 2.23756
\(125\) 0 0
\(126\) −8.81646 −0.785433
\(127\) −19.4716 −1.72782 −0.863912 0.503642i \(-0.831993\pi\)
−0.863912 + 0.503642i \(0.831993\pi\)
\(128\) 20.5402 1.81551
\(129\) 20.9903 1.84810
\(130\) 0 0
\(131\) −8.30848 −0.725915 −0.362958 0.931806i \(-0.618233\pi\)
−0.362958 + 0.931806i \(0.618233\pi\)
\(132\) 6.92466 0.602714
\(133\) −19.4860 −1.68965
\(134\) −18.8138 −1.62526
\(135\) 0 0
\(136\) 11.6253 0.996863
\(137\) 4.26661 0.364521 0.182261 0.983250i \(-0.441659\pi\)
0.182261 + 0.983250i \(0.441659\pi\)
\(138\) 38.3548 3.26498
\(139\) −4.25699 −0.361073 −0.180537 0.983568i \(-0.557783\pi\)
−0.180537 + 0.983568i \(0.557783\pi\)
\(140\) 0 0
\(141\) 13.3371 1.12318
\(142\) 16.5830 1.39162
\(143\) −1.87927 −0.157153
\(144\) 2.00741 0.167284
\(145\) 0 0
\(146\) −14.4937 −1.19951
\(147\) 5.06903 0.418086
\(148\) 3.09390 0.254317
\(149\) 6.80166 0.557214 0.278607 0.960405i \(-0.410127\pi\)
0.278607 + 0.960405i \(0.410127\pi\)
\(150\) 0 0
\(151\) −4.11661 −0.335005 −0.167503 0.985872i \(-0.553570\pi\)
−0.167503 + 0.985872i \(0.553570\pi\)
\(152\) 23.6292 1.91658
\(153\) −3.77861 −0.305483
\(154\) −6.85064 −0.552040
\(155\) 0 0
\(156\) −14.6512 −1.17304
\(157\) −19.2876 −1.53931 −0.769657 0.638457i \(-0.779573\pi\)
−0.769657 + 0.638457i \(0.779573\pi\)
\(158\) 33.2078 2.64187
\(159\) −4.53414 −0.359580
\(160\) 0 0
\(161\) −24.3439 −1.91857
\(162\) 26.3794 2.07256
\(163\) 1.77142 0.138749 0.0693743 0.997591i \(-0.477900\pi\)
0.0693743 + 0.997591i \(0.477900\pi\)
\(164\) 6.11176 0.477249
\(165\) 0 0
\(166\) 9.41999 0.731133
\(167\) −0.0398907 −0.00308683 −0.00154342 0.999999i \(-0.500491\pi\)
−0.00154342 + 0.999999i \(0.500491\pi\)
\(168\) −23.5695 −1.81842
\(169\) −9.02383 −0.694141
\(170\) 0 0
\(171\) −7.68027 −0.587325
\(172\) 36.6084 2.79137
\(173\) −16.1574 −1.22842 −0.614210 0.789142i \(-0.710525\pi\)
−0.614210 + 0.789142i \(0.710525\pi\)
\(174\) 7.92379 0.600701
\(175\) 0 0
\(176\) 1.55981 0.117575
\(177\) −15.7982 −1.18747
\(178\) 27.8219 2.08534
\(179\) 0.727604 0.0543837 0.0271918 0.999630i \(-0.491344\pi\)
0.0271918 + 0.999630i \(0.491344\pi\)
\(180\) 0 0
\(181\) 13.7237 1.02008 0.510039 0.860151i \(-0.329631\pi\)
0.510039 + 0.860151i \(0.329631\pi\)
\(182\) 14.4946 1.07441
\(183\) −7.60098 −0.561881
\(184\) 29.5200 2.17624
\(185\) 0 0
\(186\) −33.7467 −2.47443
\(187\) −2.93609 −0.214708
\(188\) 23.2607 1.69646
\(189\) −11.2878 −0.821066
\(190\) 0 0
\(191\) −12.2809 −0.888612 −0.444306 0.895875i \(-0.646550\pi\)
−0.444306 + 0.895875i \(0.646550\pi\)
\(192\) −24.0236 −1.73376
\(193\) 9.92702 0.714563 0.357281 0.933997i \(-0.383704\pi\)
0.357281 + 0.933997i \(0.383704\pi\)
\(194\) −41.7376 −2.99659
\(195\) 0 0
\(196\) 8.84070 0.631478
\(197\) −12.1160 −0.863229 −0.431614 0.902058i \(-0.642056\pi\)
−0.431614 + 0.902058i \(0.642056\pi\)
\(198\) −2.70013 −0.191890
\(199\) 13.7540 0.974995 0.487498 0.873124i \(-0.337910\pi\)
0.487498 + 0.873124i \(0.337910\pi\)
\(200\) 0 0
\(201\) 16.3478 1.15308
\(202\) −21.3924 −1.50517
\(203\) −5.02925 −0.352984
\(204\) −22.8904 −1.60265
\(205\) 0 0
\(206\) 5.19932 0.362254
\(207\) −9.59496 −0.666896
\(208\) −3.30026 −0.228832
\(209\) −5.96778 −0.412800
\(210\) 0 0
\(211\) −18.0235 −1.24079 −0.620396 0.784289i \(-0.713028\pi\)
−0.620396 + 0.784289i \(0.713028\pi\)
\(212\) −7.90781 −0.543111
\(213\) −14.4094 −0.987316
\(214\) −16.7381 −1.14419
\(215\) 0 0
\(216\) 13.6878 0.931339
\(217\) 21.4191 1.45402
\(218\) 17.8971 1.21214
\(219\) 12.5940 0.851022
\(220\) 0 0
\(221\) 6.21219 0.417877
\(222\) −4.19036 −0.281239
\(223\) 27.9985 1.87492 0.937458 0.348098i \(-0.113172\pi\)
0.937458 + 0.348098i \(0.113172\pi\)
\(224\) 10.9356 0.730665
\(225\) 0 0
\(226\) 42.0385 2.79636
\(227\) −12.7878 −0.848755 −0.424378 0.905485i \(-0.639507\pi\)
−0.424378 + 0.905485i \(0.639507\pi\)
\(228\) −46.5262 −3.08127
\(229\) −15.9201 −1.05203 −0.526015 0.850475i \(-0.676314\pi\)
−0.526015 + 0.850475i \(0.676314\pi\)
\(230\) 0 0
\(231\) 5.95270 0.391659
\(232\) 6.09859 0.400392
\(233\) 20.1234 1.31833 0.659165 0.751999i \(-0.270910\pi\)
0.659165 + 0.751999i \(0.270910\pi\)
\(234\) 5.71295 0.373467
\(235\) 0 0
\(236\) −27.5531 −1.79355
\(237\) −28.8551 −1.87434
\(238\) 22.6457 1.46790
\(239\) 4.68343 0.302946 0.151473 0.988461i \(-0.451598\pi\)
0.151473 + 0.988461i \(0.451598\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 23.8855 1.53542
\(243\) −11.9175 −0.764506
\(244\) −13.2566 −0.848665
\(245\) 0 0
\(246\) −8.27774 −0.527770
\(247\) 12.6267 0.803415
\(248\) −25.9733 −1.64931
\(249\) −8.18528 −0.518721
\(250\) 0 0
\(251\) −23.0713 −1.45625 −0.728123 0.685447i \(-0.759607\pi\)
−0.728123 + 0.685447i \(0.759607\pi\)
\(252\) 13.3610 0.841664
\(253\) −7.45555 −0.468727
\(254\) 45.9948 2.88597
\(255\) 0 0
\(256\) −25.1102 −1.56939
\(257\) −11.6020 −0.723715 −0.361857 0.932233i \(-0.617857\pi\)
−0.361857 + 0.932233i \(0.617857\pi\)
\(258\) −49.5822 −3.08686
\(259\) 2.65963 0.165261
\(260\) 0 0
\(261\) −1.98224 −0.122698
\(262\) 19.6259 1.21249
\(263\) −15.3744 −0.948024 −0.474012 0.880518i \(-0.657195\pi\)
−0.474012 + 0.880518i \(0.657195\pi\)
\(264\) −7.21838 −0.444261
\(265\) 0 0
\(266\) 46.0288 2.82221
\(267\) −24.1752 −1.47950
\(268\) 28.5116 1.74162
\(269\) 9.03287 0.550744 0.275372 0.961338i \(-0.411199\pi\)
0.275372 + 0.961338i \(0.411199\pi\)
\(270\) 0 0
\(271\) −25.0727 −1.52306 −0.761528 0.648132i \(-0.775550\pi\)
−0.761528 + 0.648132i \(0.775550\pi\)
\(272\) −5.15617 −0.312639
\(273\) −12.5947 −0.762269
\(274\) −10.0784 −0.608856
\(275\) 0 0
\(276\) −58.1252 −3.49873
\(277\) 10.5495 0.633855 0.316928 0.948450i \(-0.397349\pi\)
0.316928 + 0.948450i \(0.397349\pi\)
\(278\) 10.0556 0.603097
\(279\) 8.44218 0.505420
\(280\) 0 0
\(281\) 16.2094 0.966971 0.483485 0.875352i \(-0.339371\pi\)
0.483485 + 0.875352i \(0.339371\pi\)
\(282\) −31.5041 −1.87604
\(283\) 8.03684 0.477741 0.238870 0.971051i \(-0.423223\pi\)
0.238870 + 0.971051i \(0.423223\pi\)
\(284\) −25.1309 −1.49124
\(285\) 0 0
\(286\) 4.43912 0.262491
\(287\) 5.25390 0.310128
\(288\) 4.31018 0.253980
\(289\) −7.29437 −0.429081
\(290\) 0 0
\(291\) 36.2669 2.12600
\(292\) 21.9647 1.28539
\(293\) −26.1918 −1.53014 −0.765072 0.643945i \(-0.777297\pi\)
−0.765072 + 0.643945i \(0.777297\pi\)
\(294\) −11.9738 −0.698326
\(295\) 0 0
\(296\) −3.22513 −0.187457
\(297\) −3.45700 −0.200595
\(298\) −16.0665 −0.930709
\(299\) 15.7745 0.912262
\(300\) 0 0
\(301\) 31.4700 1.81390
\(302\) 9.72405 0.559556
\(303\) 18.5884 1.06788
\(304\) −10.4802 −0.601083
\(305\) 0 0
\(306\) 8.92564 0.510245
\(307\) −4.41238 −0.251828 −0.125914 0.992041i \(-0.540186\pi\)
−0.125914 + 0.992041i \(0.540186\pi\)
\(308\) 10.3819 0.591562
\(309\) −4.51783 −0.257010
\(310\) 0 0
\(311\) −13.2563 −0.751693 −0.375847 0.926682i \(-0.622648\pi\)
−0.375847 + 0.926682i \(0.622648\pi\)
\(312\) 15.2727 0.864646
\(313\) −22.1456 −1.25174 −0.625871 0.779927i \(-0.715256\pi\)
−0.625871 + 0.779927i \(0.715256\pi\)
\(314\) 45.5601 2.57110
\(315\) 0 0
\(316\) −50.3251 −2.83101
\(317\) −3.01320 −0.169238 −0.0846190 0.996413i \(-0.526967\pi\)
−0.0846190 + 0.996413i \(0.526967\pi\)
\(318\) 10.7103 0.600604
\(319\) −1.54026 −0.0862378
\(320\) 0 0
\(321\) 14.5441 0.811774
\(322\) 57.5038 3.20456
\(323\) 19.7273 1.09766
\(324\) −39.9770 −2.22094
\(325\) 0 0
\(326\) −4.18436 −0.231750
\(327\) −15.5512 −0.859985
\(328\) −6.37101 −0.351780
\(329\) 19.9957 1.10240
\(330\) 0 0
\(331\) 9.41939 0.517736 0.258868 0.965913i \(-0.416650\pi\)
0.258868 + 0.965913i \(0.416650\pi\)
\(332\) −14.2756 −0.783477
\(333\) 1.04827 0.0574451
\(334\) 0.0942276 0.00515591
\(335\) 0 0
\(336\) 10.4537 0.570299
\(337\) 17.0177 0.927011 0.463505 0.886094i \(-0.346591\pi\)
0.463505 + 0.886094i \(0.346591\pi\)
\(338\) 21.3156 1.15942
\(339\) −36.5284 −1.98395
\(340\) 0 0
\(341\) 6.55981 0.355234
\(342\) 18.1419 0.981003
\(343\) −13.9412 −0.752752
\(344\) −38.1612 −2.05752
\(345\) 0 0
\(346\) 38.1661 2.05182
\(347\) −23.6966 −1.27210 −0.636049 0.771649i \(-0.719432\pi\)
−0.636049 + 0.771649i \(0.719432\pi\)
\(348\) −12.0082 −0.643707
\(349\) 4.05897 0.217272 0.108636 0.994082i \(-0.465352\pi\)
0.108636 + 0.994082i \(0.465352\pi\)
\(350\) 0 0
\(351\) 7.31433 0.390410
\(352\) 3.34913 0.178509
\(353\) −15.8788 −0.845144 −0.422572 0.906329i \(-0.638873\pi\)
−0.422572 + 0.906329i \(0.638873\pi\)
\(354\) 37.3177 1.98342
\(355\) 0 0
\(356\) −42.1630 −2.23463
\(357\) −19.6774 −1.04144
\(358\) −1.71871 −0.0908366
\(359\) −4.02791 −0.212585 −0.106293 0.994335i \(-0.533898\pi\)
−0.106293 + 0.994335i \(0.533898\pi\)
\(360\) 0 0
\(361\) 21.0970 1.11037
\(362\) −32.4175 −1.70383
\(363\) −20.7548 −1.08934
\(364\) −21.9660 −1.15133
\(365\) 0 0
\(366\) 17.9546 0.938504
\(367\) 38.1519 1.99151 0.995757 0.0920267i \(-0.0293345\pi\)
0.995757 + 0.0920267i \(0.0293345\pi\)
\(368\) −13.0930 −0.682518
\(369\) 2.07079 0.107801
\(370\) 0 0
\(371\) −6.79785 −0.352927
\(372\) 51.1418 2.65158
\(373\) 20.3518 1.05377 0.526887 0.849935i \(-0.323359\pi\)
0.526887 + 0.849935i \(0.323359\pi\)
\(374\) 6.93547 0.358625
\(375\) 0 0
\(376\) −24.2473 −1.25046
\(377\) 3.25888 0.167841
\(378\) 26.6634 1.37142
\(379\) −30.2111 −1.55184 −0.775919 0.630833i \(-0.782713\pi\)
−0.775919 + 0.630833i \(0.782713\pi\)
\(380\) 0 0
\(381\) −39.9661 −2.04752
\(382\) 29.0092 1.48424
\(383\) −23.4619 −1.19885 −0.599425 0.800431i \(-0.704604\pi\)
−0.599425 + 0.800431i \(0.704604\pi\)
\(384\) 42.1594 2.15144
\(385\) 0 0
\(386\) −23.4491 −1.19353
\(387\) 12.4037 0.630513
\(388\) 63.2517 3.21112
\(389\) 0.990019 0.0501959 0.0250980 0.999685i \(-0.492010\pi\)
0.0250980 + 0.999685i \(0.492010\pi\)
\(390\) 0 0
\(391\) 24.6453 1.24637
\(392\) −9.21569 −0.465463
\(393\) −17.0534 −0.860231
\(394\) 28.6198 1.44184
\(395\) 0 0
\(396\) 4.09194 0.205628
\(397\) 4.90685 0.246268 0.123134 0.992390i \(-0.460706\pi\)
0.123134 + 0.992390i \(0.460706\pi\)
\(398\) −32.4890 −1.62853
\(399\) −39.9956 −2.00229
\(400\) 0 0
\(401\) −30.6157 −1.52888 −0.764439 0.644696i \(-0.776984\pi\)
−0.764439 + 0.644696i \(0.776984\pi\)
\(402\) −38.6159 −1.92599
\(403\) −13.8793 −0.691376
\(404\) 32.4194 1.61292
\(405\) 0 0
\(406\) 11.8798 0.589586
\(407\) 0.814538 0.0403752
\(408\) 23.8613 1.18131
\(409\) −4.00516 −0.198043 −0.0990213 0.995085i \(-0.531571\pi\)
−0.0990213 + 0.995085i \(0.531571\pi\)
\(410\) 0 0
\(411\) 8.75735 0.431968
\(412\) −7.87937 −0.388189
\(413\) −23.6856 −1.16549
\(414\) 22.6647 1.11391
\(415\) 0 0
\(416\) −7.08611 −0.347425
\(417\) −8.73761 −0.427883
\(418\) 14.0968 0.689496
\(419\) 31.4086 1.53441 0.767206 0.641401i \(-0.221646\pi\)
0.767206 + 0.641401i \(0.221646\pi\)
\(420\) 0 0
\(421\) 39.1136 1.90628 0.953141 0.302526i \(-0.0978298\pi\)
0.953141 + 0.302526i \(0.0978298\pi\)
\(422\) 42.5743 2.07248
\(423\) 7.88117 0.383196
\(424\) 8.24323 0.400327
\(425\) 0 0
\(426\) 34.0372 1.64911
\(427\) −11.3958 −0.551484
\(428\) 25.3659 1.22610
\(429\) −3.85727 −0.186231
\(430\) 0 0
\(431\) 7.68918 0.370375 0.185188 0.982703i \(-0.440711\pi\)
0.185188 + 0.982703i \(0.440711\pi\)
\(432\) −6.07096 −0.292089
\(433\) 4.67921 0.224869 0.112434 0.993659i \(-0.464135\pi\)
0.112434 + 0.993659i \(0.464135\pi\)
\(434\) −50.5951 −2.42864
\(435\) 0 0
\(436\) −27.1223 −1.29892
\(437\) 50.0932 2.39628
\(438\) −29.7488 −1.42145
\(439\) 14.7770 0.705270 0.352635 0.935761i \(-0.385286\pi\)
0.352635 + 0.935761i \(0.385286\pi\)
\(440\) 0 0
\(441\) 2.99540 0.142638
\(442\) −14.6741 −0.697976
\(443\) −3.71495 −0.176503 −0.0882513 0.996098i \(-0.528128\pi\)
−0.0882513 + 0.996098i \(0.528128\pi\)
\(444\) 6.35033 0.301373
\(445\) 0 0
\(446\) −66.1365 −3.13165
\(447\) 13.9606 0.660315
\(448\) −36.0177 −1.70168
\(449\) −23.6261 −1.11498 −0.557492 0.830183i \(-0.688236\pi\)
−0.557492 + 0.830183i \(0.688236\pi\)
\(450\) 0 0
\(451\) 1.60906 0.0757676
\(452\) −63.7077 −2.99656
\(453\) −8.44948 −0.396991
\(454\) 30.2066 1.41767
\(455\) 0 0
\(456\) 48.4997 2.27120
\(457\) 16.0363 0.750146 0.375073 0.926995i \(-0.377618\pi\)
0.375073 + 0.926995i \(0.377618\pi\)
\(458\) 37.6056 1.75720
\(459\) 11.4276 0.533393
\(460\) 0 0
\(461\) 23.0734 1.07464 0.537319 0.843379i \(-0.319437\pi\)
0.537319 + 0.843379i \(0.319437\pi\)
\(462\) −14.0612 −0.654184
\(463\) 34.0986 1.58470 0.792349 0.610068i \(-0.208858\pi\)
0.792349 + 0.610068i \(0.208858\pi\)
\(464\) −2.70490 −0.125572
\(465\) 0 0
\(466\) −47.5345 −2.20199
\(467\) 15.2453 0.705467 0.352734 0.935724i \(-0.385252\pi\)
0.352734 + 0.935724i \(0.385252\pi\)
\(468\) −8.65774 −0.400204
\(469\) 24.5096 1.13175
\(470\) 0 0
\(471\) −39.5883 −1.82413
\(472\) 28.7218 1.32203
\(473\) 9.63798 0.443155
\(474\) 68.1601 3.13070
\(475\) 0 0
\(476\) −34.3187 −1.57299
\(477\) −2.67932 −0.122678
\(478\) −11.0630 −0.506008
\(479\) 41.7622 1.90816 0.954082 0.299546i \(-0.0968351\pi\)
0.954082 + 0.299546i \(0.0968351\pi\)
\(480\) 0 0
\(481\) −1.72340 −0.0785805
\(482\) −2.36215 −0.107593
\(483\) −49.9666 −2.27356
\(484\) −36.1976 −1.64535
\(485\) 0 0
\(486\) 28.1508 1.27695
\(487\) 33.0645 1.49830 0.749148 0.662402i \(-0.230463\pi\)
0.749148 + 0.662402i \(0.230463\pi\)
\(488\) 13.8189 0.625551
\(489\) 3.63590 0.164421
\(490\) 0 0
\(491\) −12.6839 −0.572415 −0.286208 0.958168i \(-0.592395\pi\)
−0.286208 + 0.958168i \(0.592395\pi\)
\(492\) 12.5446 0.565554
\(493\) 5.09153 0.229311
\(494\) −29.8260 −1.34194
\(495\) 0 0
\(496\) 11.5199 0.517260
\(497\) −21.6035 −0.969047
\(498\) 19.3348 0.866415
\(499\) −15.4405 −0.691213 −0.345606 0.938380i \(-0.612327\pi\)
−0.345606 + 0.938380i \(0.612327\pi\)
\(500\) 0 0
\(501\) −0.0818768 −0.00365799
\(502\) 54.4977 2.43235
\(503\) 26.3951 1.17690 0.588450 0.808534i \(-0.299738\pi\)
0.588450 + 0.808534i \(0.299738\pi\)
\(504\) −13.9277 −0.620390
\(505\) 0 0
\(506\) 17.6111 0.782910
\(507\) −18.5217 −0.822577
\(508\) −69.7033 −3.09258
\(509\) 13.4761 0.597318 0.298659 0.954360i \(-0.403461\pi\)
0.298659 + 0.954360i \(0.403461\pi\)
\(510\) 0 0
\(511\) 18.8817 0.835275
\(512\) 18.2336 0.805817
\(513\) 23.2272 1.02551
\(514\) 27.4057 1.20881
\(515\) 0 0
\(516\) 75.1399 3.30785
\(517\) 6.12389 0.269328
\(518\) −6.28244 −0.276035
\(519\) −33.1635 −1.45572
\(520\) 0 0
\(521\) −23.7045 −1.03851 −0.519256 0.854619i \(-0.673791\pi\)
−0.519256 + 0.854619i \(0.673791\pi\)
\(522\) 4.68235 0.204941
\(523\) −3.98543 −0.174271 −0.0871354 0.996196i \(-0.527771\pi\)
−0.0871354 + 0.996196i \(0.527771\pi\)
\(524\) −29.7422 −1.29929
\(525\) 0 0
\(526\) 36.3165 1.58348
\(527\) −21.6843 −0.944584
\(528\) 3.20156 0.139330
\(529\) 39.5814 1.72093
\(530\) 0 0
\(531\) −9.33553 −0.405127
\(532\) −69.7548 −3.02426
\(533\) −3.40445 −0.147463
\(534\) 57.1053 2.47119
\(535\) 0 0
\(536\) −29.7209 −1.28375
\(537\) 1.49343 0.0644463
\(538\) −21.3370 −0.919902
\(539\) 2.32751 0.100253
\(540\) 0 0
\(541\) 14.3140 0.615405 0.307703 0.951483i \(-0.400440\pi\)
0.307703 + 0.951483i \(0.400440\pi\)
\(542\) 59.2253 2.54394
\(543\) 28.1684 1.20882
\(544\) −11.0710 −0.474666
\(545\) 0 0
\(546\) 29.7506 1.27321
\(547\) 25.1893 1.07702 0.538508 0.842621i \(-0.318988\pi\)
0.538508 + 0.842621i \(0.318988\pi\)
\(548\) 15.2734 0.652446
\(549\) −4.49159 −0.191696
\(550\) 0 0
\(551\) 10.3488 0.440876
\(552\) 60.5907 2.57891
\(553\) −43.2613 −1.83966
\(554\) −24.9194 −1.05872
\(555\) 0 0
\(556\) −15.2389 −0.646275
\(557\) −16.4450 −0.696798 −0.348399 0.937346i \(-0.613275\pi\)
−0.348399 + 0.937346i \(0.613275\pi\)
\(558\) −19.9417 −0.844199
\(559\) −20.3921 −0.862494
\(560\) 0 0
\(561\) −6.02641 −0.254435
\(562\) −38.2890 −1.61512
\(563\) 14.8796 0.627100 0.313550 0.949572i \(-0.398482\pi\)
0.313550 + 0.949572i \(0.398482\pi\)
\(564\) 47.7433 2.01035
\(565\) 0 0
\(566\) −18.9842 −0.797966
\(567\) −34.3657 −1.44322
\(568\) 26.1969 1.09920
\(569\) −37.4832 −1.57138 −0.785689 0.618622i \(-0.787691\pi\)
−0.785689 + 0.618622i \(0.787691\pi\)
\(570\) 0 0
\(571\) 1.58161 0.0661885 0.0330943 0.999452i \(-0.489464\pi\)
0.0330943 + 0.999452i \(0.489464\pi\)
\(572\) −6.72731 −0.281283
\(573\) −25.2069 −1.05303
\(574\) −12.4105 −0.518004
\(575\) 0 0
\(576\) −14.1961 −0.591504
\(577\) −37.7122 −1.56998 −0.784990 0.619508i \(-0.787332\pi\)
−0.784990 + 0.619508i \(0.787332\pi\)
\(578\) 17.2304 0.716689
\(579\) 20.3755 0.846778
\(580\) 0 0
\(581\) −12.2719 −0.509123
\(582\) −85.6678 −3.55105
\(583\) −2.08191 −0.0862238
\(584\) −22.8963 −0.947457
\(585\) 0 0
\(586\) 61.8690 2.55578
\(587\) −27.6567 −1.14151 −0.570756 0.821120i \(-0.693350\pi\)
−0.570756 + 0.821120i \(0.693350\pi\)
\(588\) 18.1458 0.748321
\(589\) −44.0748 −1.81607
\(590\) 0 0
\(591\) −24.8685 −1.02295
\(592\) 1.43044 0.0587907
\(593\) 18.1987 0.747329 0.373665 0.927564i \(-0.378101\pi\)
0.373665 + 0.927564i \(0.378101\pi\)
\(594\) 8.16593 0.335052
\(595\) 0 0
\(596\) 24.3482 0.997341
\(597\) 28.2305 1.15540
\(598\) −37.2617 −1.52374
\(599\) −7.12390 −0.291075 −0.145537 0.989353i \(-0.546491\pi\)
−0.145537 + 0.989353i \(0.546491\pi\)
\(600\) 0 0
\(601\) 11.3425 0.462672 0.231336 0.972874i \(-0.425690\pi\)
0.231336 + 0.972874i \(0.425690\pi\)
\(602\) −74.3367 −3.02974
\(603\) 9.66028 0.393397
\(604\) −14.7364 −0.599616
\(605\) 0 0
\(606\) −43.9086 −1.78367
\(607\) −9.88248 −0.401117 −0.200559 0.979682i \(-0.564276\pi\)
−0.200559 + 0.979682i \(0.564276\pi\)
\(608\) −22.5025 −0.912598
\(609\) −10.3227 −0.418297
\(610\) 0 0
\(611\) −12.9570 −0.524182
\(612\) −13.5265 −0.546775
\(613\) 6.32265 0.255369 0.127685 0.991815i \(-0.459245\pi\)
0.127685 + 0.991815i \(0.459245\pi\)
\(614\) 10.4227 0.420626
\(615\) 0 0
\(616\) −10.8222 −0.436040
\(617\) −28.4003 −1.14335 −0.571676 0.820480i \(-0.693707\pi\)
−0.571676 + 0.820480i \(0.693707\pi\)
\(618\) 10.6718 0.429282
\(619\) 14.3962 0.578633 0.289316 0.957234i \(-0.406572\pi\)
0.289316 + 0.957234i \(0.406572\pi\)
\(620\) 0 0
\(621\) 29.0178 1.16444
\(622\) 31.3132 1.25555
\(623\) −36.2449 −1.45212
\(624\) −6.77388 −0.271172
\(625\) 0 0
\(626\) 52.3111 2.09077
\(627\) −12.2491 −0.489180
\(628\) −69.0445 −2.75517
\(629\) −2.69257 −0.107360
\(630\) 0 0
\(631\) −16.4378 −0.654379 −0.327190 0.944959i \(-0.606102\pi\)
−0.327190 + 0.944959i \(0.606102\pi\)
\(632\) 52.4597 2.08674
\(633\) −36.9939 −1.47038
\(634\) 7.11761 0.282677
\(635\) 0 0
\(636\) −16.2310 −0.643602
\(637\) −4.92456 −0.195118
\(638\) 3.63831 0.144042
\(639\) −8.51484 −0.336842
\(640\) 0 0
\(641\) 9.38495 0.370683 0.185342 0.982674i \(-0.440661\pi\)
0.185342 + 0.982674i \(0.440661\pi\)
\(642\) −34.3554 −1.35590
\(643\) −2.90484 −0.114556 −0.0572778 0.998358i \(-0.518242\pi\)
−0.0572778 + 0.998358i \(0.518242\pi\)
\(644\) −87.1448 −3.43399
\(645\) 0 0
\(646\) −46.5988 −1.83341
\(647\) −16.2707 −0.639667 −0.319833 0.947474i \(-0.603627\pi\)
−0.319833 + 0.947474i \(0.603627\pi\)
\(648\) 41.6727 1.63706
\(649\) −7.25396 −0.284743
\(650\) 0 0
\(651\) 43.9634 1.72306
\(652\) 6.34124 0.248342
\(653\) −11.7812 −0.461035 −0.230517 0.973068i \(-0.574042\pi\)
−0.230517 + 0.973068i \(0.574042\pi\)
\(654\) 36.7343 1.43643
\(655\) 0 0
\(656\) 2.82573 0.110326
\(657\) 7.44207 0.290343
\(658\) −47.2329 −1.84133
\(659\) 47.0426 1.83252 0.916260 0.400583i \(-0.131193\pi\)
0.916260 + 0.400583i \(0.131193\pi\)
\(660\) 0 0
\(661\) −37.3779 −1.45383 −0.726916 0.686726i \(-0.759047\pi\)
−0.726916 + 0.686726i \(0.759047\pi\)
\(662\) −22.2500 −0.864770
\(663\) 12.7507 0.495197
\(664\) 14.8812 0.577501
\(665\) 0 0
\(666\) −2.47618 −0.0959500
\(667\) 12.9288 0.500606
\(668\) −0.142798 −0.00552503
\(669\) 57.4678 2.22183
\(670\) 0 0
\(671\) −3.49009 −0.134733
\(672\) 22.4456 0.865860
\(673\) 37.3014 1.43786 0.718931 0.695081i \(-0.244632\pi\)
0.718931 + 0.695081i \(0.244632\pi\)
\(674\) −40.1982 −1.54838
\(675\) 0 0
\(676\) −32.3030 −1.24242
\(677\) −21.0921 −0.810636 −0.405318 0.914176i \(-0.632839\pi\)
−0.405318 + 0.914176i \(0.632839\pi\)
\(678\) 86.2854 3.31377
\(679\) 54.3735 2.08667
\(680\) 0 0
\(681\) −26.2473 −1.00580
\(682\) −15.4952 −0.593343
\(683\) 30.1078 1.15204 0.576022 0.817434i \(-0.304604\pi\)
0.576022 + 0.817434i \(0.304604\pi\)
\(684\) −27.4934 −1.05124
\(685\) 0 0
\(686\) 32.9311 1.25731
\(687\) −32.6765 −1.24669
\(688\) 16.9256 0.645283
\(689\) 4.40491 0.167814
\(690\) 0 0
\(691\) −22.9001 −0.871162 −0.435581 0.900149i \(-0.643457\pi\)
−0.435581 + 0.900149i \(0.643457\pi\)
\(692\) −57.8391 −2.19871
\(693\) 3.51758 0.133622
\(694\) 55.9748 2.12477
\(695\) 0 0
\(696\) 12.5175 0.474476
\(697\) −5.31896 −0.201470
\(698\) −9.58790 −0.362907
\(699\) 41.3040 1.56226
\(700\) 0 0
\(701\) −12.7502 −0.481567 −0.240784 0.970579i \(-0.577404\pi\)
−0.240784 + 0.970579i \(0.577404\pi\)
\(702\) −17.2775 −0.652098
\(703\) −5.47281 −0.206411
\(704\) −11.0308 −0.415738
\(705\) 0 0
\(706\) 37.5081 1.41164
\(707\) 27.8689 1.04812
\(708\) −56.5536 −2.12541
\(709\) −30.5429 −1.14706 −0.573531 0.819184i \(-0.694427\pi\)
−0.573531 + 0.819184i \(0.694427\pi\)
\(710\) 0 0
\(711\) −17.0511 −0.639468
\(712\) 43.9514 1.64715
\(713\) −55.0626 −2.06211
\(714\) 46.4810 1.73951
\(715\) 0 0
\(716\) 2.60463 0.0973398
\(717\) 9.61289 0.359000
\(718\) 9.51453 0.355079
\(719\) −4.70422 −0.175438 −0.0877190 0.996145i \(-0.527958\pi\)
−0.0877190 + 0.996145i \(0.527958\pi\)
\(720\) 0 0
\(721\) −6.77340 −0.252255
\(722\) −49.8342 −1.85464
\(723\) 2.05253 0.0763345
\(724\) 49.1275 1.82581
\(725\) 0 0
\(726\) 49.0259 1.81952
\(727\) −34.0042 −1.26114 −0.630572 0.776130i \(-0.717180\pi\)
−0.630572 + 0.776130i \(0.717180\pi\)
\(728\) 22.8977 0.848646
\(729\) 9.04171 0.334878
\(730\) 0 0
\(731\) −31.8597 −1.17837
\(732\) −27.2096 −1.00569
\(733\) −16.4990 −0.609406 −0.304703 0.952447i \(-0.598557\pi\)
−0.304703 + 0.952447i \(0.598557\pi\)
\(734\) −90.1204 −3.32641
\(735\) 0 0
\(736\) −28.1124 −1.03624
\(737\) 7.50631 0.276498
\(738\) −4.89150 −0.180059
\(739\) 41.0735 1.51091 0.755456 0.655199i \(-0.227415\pi\)
0.755456 + 0.655199i \(0.227415\pi\)
\(740\) 0 0
\(741\) 25.9166 0.952071
\(742\) 16.0575 0.589490
\(743\) −6.32830 −0.232163 −0.116081 0.993240i \(-0.537033\pi\)
−0.116081 + 0.993240i \(0.537033\pi\)
\(744\) −53.3110 −1.95448
\(745\) 0 0
\(746\) −48.0739 −1.76011
\(747\) −4.83687 −0.176972
\(748\) −10.5104 −0.384299
\(749\) 21.8054 0.796753
\(750\) 0 0
\(751\) 53.2850 1.94440 0.972199 0.234157i \(-0.0752331\pi\)
0.972199 + 0.234157i \(0.0752331\pi\)
\(752\) 10.7544 0.392172
\(753\) −47.3545 −1.72569
\(754\) −7.69796 −0.280343
\(755\) 0 0
\(756\) −40.4074 −1.46960
\(757\) −38.5378 −1.40068 −0.700340 0.713810i \(-0.746968\pi\)
−0.700340 + 0.713810i \(0.746968\pi\)
\(758\) 71.3630 2.59202
\(759\) −15.3028 −0.555455
\(760\) 0 0
\(761\) −16.2682 −0.589723 −0.294861 0.955540i \(-0.595273\pi\)
−0.294861 + 0.955540i \(0.595273\pi\)
\(762\) 94.4057 3.41996
\(763\) −23.3153 −0.844072
\(764\) −43.9623 −1.59050
\(765\) 0 0
\(766\) 55.4206 2.00243
\(767\) 15.3480 0.554183
\(768\) −51.5394 −1.85977
\(769\) −35.5516 −1.28202 −0.641012 0.767531i \(-0.721485\pi\)
−0.641012 + 0.767531i \(0.721485\pi\)
\(770\) 0 0
\(771\) −23.8135 −0.857623
\(772\) 35.5362 1.27898
\(773\) 0.807556 0.0290458 0.0145229 0.999895i \(-0.495377\pi\)
0.0145229 + 0.999895i \(0.495377\pi\)
\(774\) −29.2993 −1.05314
\(775\) 0 0
\(776\) −65.9347 −2.36692
\(777\) 5.45898 0.195840
\(778\) −2.33857 −0.0838418
\(779\) −10.8111 −0.387349
\(780\) 0 0
\(781\) −6.61627 −0.236749
\(782\) −58.2159 −2.08180
\(783\) 5.99484 0.214238
\(784\) 4.08743 0.145980
\(785\) 0 0
\(786\) 40.2827 1.43684
\(787\) 13.8726 0.494504 0.247252 0.968951i \(-0.420472\pi\)
0.247252 + 0.968951i \(0.420472\pi\)
\(788\) −43.3721 −1.54507
\(789\) −31.5564 −1.12344
\(790\) 0 0
\(791\) −54.7655 −1.94724
\(792\) −4.26551 −0.151568
\(793\) 7.38435 0.262226
\(794\) −11.5907 −0.411338
\(795\) 0 0
\(796\) 49.2358 1.74512
\(797\) 3.24320 0.114880 0.0574400 0.998349i \(-0.481706\pi\)
0.0574400 + 0.998349i \(0.481706\pi\)
\(798\) 94.4756 3.34440
\(799\) −20.2433 −0.716158
\(800\) 0 0
\(801\) −14.2857 −0.504759
\(802\) 72.3189 2.55367
\(803\) 5.78269 0.204067
\(804\) 58.5209 2.06387
\(805\) 0 0
\(806\) 32.7849 1.15480
\(807\) 18.5403 0.652648
\(808\) −33.7945 −1.18889
\(809\) 54.4503 1.91437 0.957184 0.289479i \(-0.0934819\pi\)
0.957184 + 0.289479i \(0.0934819\pi\)
\(810\) 0 0
\(811\) −20.6483 −0.725059 −0.362530 0.931972i \(-0.618087\pi\)
−0.362530 + 0.931972i \(0.618087\pi\)
\(812\) −18.0034 −0.631796
\(813\) −51.4624 −1.80487
\(814\) −1.92406 −0.0674383
\(815\) 0 0
\(816\) −10.5832 −0.370486
\(817\) −64.7567 −2.26555
\(818\) 9.46079 0.330789
\(819\) −7.44252 −0.260063
\(820\) 0 0
\(821\) 20.0000 0.698006 0.349003 0.937122i \(-0.386520\pi\)
0.349003 + 0.937122i \(0.386520\pi\)
\(822\) −20.6862 −0.721513
\(823\) 25.3107 0.882277 0.441138 0.897439i \(-0.354575\pi\)
0.441138 + 0.897439i \(0.354575\pi\)
\(824\) 8.21359 0.286134
\(825\) 0 0
\(826\) 55.9490 1.94671
\(827\) 28.9282 1.00593 0.502966 0.864306i \(-0.332242\pi\)
0.502966 + 0.864306i \(0.332242\pi\)
\(828\) −34.3475 −1.19366
\(829\) 10.9469 0.380201 0.190100 0.981765i \(-0.439119\pi\)
0.190100 + 0.981765i \(0.439119\pi\)
\(830\) 0 0
\(831\) 21.6531 0.751137
\(832\) 23.3390 0.809133
\(833\) −7.69390 −0.266578
\(834\) 20.6395 0.714689
\(835\) 0 0
\(836\) −21.3631 −0.738859
\(837\) −25.5315 −0.882497
\(838\) −74.1918 −2.56291
\(839\) 16.6348 0.574298 0.287149 0.957886i \(-0.407293\pi\)
0.287149 + 0.957886i \(0.407293\pi\)
\(840\) 0 0
\(841\) −26.3290 −0.907897
\(842\) −92.3922 −3.18405
\(843\) 33.2703 1.14589
\(844\) −64.5196 −2.22086
\(845\) 0 0
\(846\) −18.6165 −0.640048
\(847\) −31.1168 −1.06919
\(848\) −3.65611 −0.125552
\(849\) 16.4959 0.566137
\(850\) 0 0
\(851\) −6.83719 −0.234376
\(852\) −51.5820 −1.76717
\(853\) −1.31481 −0.0450182 −0.0225091 0.999747i \(-0.507165\pi\)
−0.0225091 + 0.999747i \(0.507165\pi\)
\(854\) 26.9187 0.921138
\(855\) 0 0
\(856\) −26.4418 −0.903762
\(857\) −51.6669 −1.76491 −0.882454 0.470399i \(-0.844110\pi\)
−0.882454 + 0.470399i \(0.844110\pi\)
\(858\) 9.11143 0.311059
\(859\) −39.7084 −1.35483 −0.677417 0.735599i \(-0.736901\pi\)
−0.677417 + 0.735599i \(0.736901\pi\)
\(860\) 0 0
\(861\) 10.7838 0.367511
\(862\) −18.1630 −0.618634
\(863\) 28.5307 0.971196 0.485598 0.874182i \(-0.338602\pi\)
0.485598 + 0.874182i \(0.338602\pi\)
\(864\) −13.0352 −0.443466
\(865\) 0 0
\(866\) −11.0530 −0.375596
\(867\) −14.9719 −0.508473
\(868\) 76.6748 2.60251
\(869\) −13.2492 −0.449449
\(870\) 0 0
\(871\) −15.8819 −0.538137
\(872\) 28.2727 0.957436
\(873\) 21.4309 0.725327
\(874\) −118.327 −4.00249
\(875\) 0 0
\(876\) 45.0832 1.52322
\(877\) 4.60926 0.155644 0.0778219 0.996967i \(-0.475203\pi\)
0.0778219 + 0.996967i \(0.475203\pi\)
\(878\) −34.9055 −1.17801
\(879\) −53.7596 −1.81327
\(880\) 0 0
\(881\) −14.5627 −0.490630 −0.245315 0.969443i \(-0.578891\pi\)
−0.245315 + 0.969443i \(0.578891\pi\)
\(882\) −7.07559 −0.238247
\(883\) −4.65262 −0.156573 −0.0782866 0.996931i \(-0.524945\pi\)
−0.0782866 + 0.996931i \(0.524945\pi\)
\(884\) 22.2380 0.747946
\(885\) 0 0
\(886\) 8.77526 0.294810
\(887\) 8.77283 0.294563 0.147281 0.989095i \(-0.452948\pi\)
0.147281 + 0.989095i \(0.452948\pi\)
\(888\) −6.61969 −0.222142
\(889\) −59.9195 −2.00964
\(890\) 0 0
\(891\) −10.5248 −0.352595
\(892\) 100.227 3.35586
\(893\) −41.1459 −1.37689
\(894\) −32.9771 −1.10292
\(895\) 0 0
\(896\) 63.2079 2.11163
\(897\) 32.3776 1.08106
\(898\) 55.8083 1.86235
\(899\) −11.3755 −0.379394
\(900\) 0 0
\(901\) 6.88203 0.229274
\(902\) −3.80083 −0.126554
\(903\) 64.5931 2.14952
\(904\) 66.4100 2.20876
\(905\) 0 0
\(906\) 19.9589 0.663091
\(907\) −17.5415 −0.582457 −0.291229 0.956653i \(-0.594064\pi\)
−0.291229 + 0.956653i \(0.594064\pi\)
\(908\) −45.7770 −1.51916
\(909\) 10.9843 0.364327
\(910\) 0 0
\(911\) −26.2299 −0.869034 −0.434517 0.900664i \(-0.643081\pi\)
−0.434517 + 0.900664i \(0.643081\pi\)
\(912\) −21.5110 −0.712301
\(913\) −3.75838 −0.124384
\(914\) −37.8801 −1.25296
\(915\) 0 0
\(916\) −56.9898 −1.88300
\(917\) −25.5675 −0.844314
\(918\) −26.9936 −0.890921
\(919\) −26.0740 −0.860101 −0.430051 0.902805i \(-0.641504\pi\)
−0.430051 + 0.902805i \(0.641504\pi\)
\(920\) 0 0
\(921\) −9.05655 −0.298424
\(922\) −54.5029 −1.79496
\(923\) 13.9987 0.460774
\(924\) 21.3091 0.701019
\(925\) 0 0
\(926\) −80.5460 −2.64691
\(927\) −2.66969 −0.0876840
\(928\) −5.80780 −0.190650
\(929\) 22.2068 0.728582 0.364291 0.931285i \(-0.381311\pi\)
0.364291 + 0.931285i \(0.381311\pi\)
\(930\) 0 0
\(931\) −15.6383 −0.512526
\(932\) 72.0367 2.35964
\(933\) −27.2089 −0.890779
\(934\) −36.0116 −1.17834
\(935\) 0 0
\(936\) 9.02498 0.294991
\(937\) −39.4539 −1.28890 −0.644452 0.764645i \(-0.722914\pi\)
−0.644452 + 0.764645i \(0.722914\pi\)
\(938\) −57.8953 −1.89035
\(939\) −45.4545 −1.48335
\(940\) 0 0
\(941\) 7.12527 0.232277 0.116139 0.993233i \(-0.462948\pi\)
0.116139 + 0.993233i \(0.462948\pi\)
\(942\) 93.5135 3.04683
\(943\) −13.5063 −0.439827
\(944\) −12.7389 −0.414617
\(945\) 0 0
\(946\) −22.7663 −0.740198
\(947\) 47.2038 1.53392 0.766959 0.641696i \(-0.221769\pi\)
0.766959 + 0.641696i \(0.221769\pi\)
\(948\) −103.294 −3.35483
\(949\) −12.2350 −0.397166
\(950\) 0 0
\(951\) −6.18468 −0.200552
\(952\) 35.7744 1.15945
\(953\) −6.73058 −0.218025 −0.109013 0.994040i \(-0.534769\pi\)
−0.109013 + 0.994040i \(0.534769\pi\)
\(954\) 6.32896 0.204908
\(955\) 0 0
\(956\) 16.7655 0.542234
\(957\) −3.16143 −0.102194
\(958\) −98.6485 −3.18719
\(959\) 13.1296 0.423975
\(960\) 0 0
\(961\) 17.4472 0.562812
\(962\) 4.07094 0.131252
\(963\) 8.59446 0.276952
\(964\) 3.57974 0.115296
\(965\) 0 0
\(966\) 118.028 3.79750
\(967\) 51.9356 1.67014 0.835069 0.550146i \(-0.185428\pi\)
0.835069 + 0.550146i \(0.185428\pi\)
\(968\) 37.7330 1.21278
\(969\) 40.4909 1.30076
\(970\) 0 0
\(971\) 21.5150 0.690451 0.345225 0.938520i \(-0.387803\pi\)
0.345225 + 0.938520i \(0.387803\pi\)
\(972\) −42.6615 −1.36837
\(973\) −13.1000 −0.419965
\(974\) −78.1033 −2.50259
\(975\) 0 0
\(976\) −6.12908 −0.196187
\(977\) 1.00409 0.0321238 0.0160619 0.999871i \(-0.494887\pi\)
0.0160619 + 0.999871i \(0.494887\pi\)
\(978\) −8.58854 −0.274631
\(979\) −11.1004 −0.354769
\(980\) 0 0
\(981\) −9.18958 −0.293401
\(982\) 29.9612 0.956100
\(983\) 29.7602 0.949203 0.474601 0.880201i \(-0.342592\pi\)
0.474601 + 0.880201i \(0.342592\pi\)
\(984\) −13.0767 −0.416870
\(985\) 0 0
\(986\) −12.0269 −0.383016
\(987\) 41.0419 1.30638
\(988\) 45.2002 1.43801
\(989\) −80.9007 −2.57249
\(990\) 0 0
\(991\) −17.2504 −0.547976 −0.273988 0.961733i \(-0.588343\pi\)
−0.273988 + 0.961733i \(0.588343\pi\)
\(992\) 24.7349 0.785333
\(993\) 19.3336 0.613533
\(994\) 51.0305 1.61859
\(995\) 0 0
\(996\) −29.3012 −0.928444
\(997\) 36.3908 1.15251 0.576254 0.817271i \(-0.304514\pi\)
0.576254 + 0.817271i \(0.304514\pi\)
\(998\) 36.4728 1.15453
\(999\) −3.17027 −0.100303
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 6025.2.a.p.1.5 46
5.2 odd 4 1205.2.b.c.724.5 46
5.3 odd 4 1205.2.b.c.724.42 yes 46
5.4 even 2 inner 6025.2.a.p.1.42 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.5 46 5.2 odd 4
1205.2.b.c.724.42 yes 46 5.3 odd 4
6025.2.a.p.1.5 46 1.1 even 1 trivial
6025.2.a.p.1.42 46 5.4 even 2 inner