Properties

Label 4235.2.a.q.1.1
Level $4235$
Weight $2$
Character 4235.1
Self dual yes
Analytic conductor $33.817$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4235.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.8166452560\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
Defining polynomial: \(x^{3} - x^{2} - 3 x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 385)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.311108\) of defining polynomial
Character \(\chi\) \(=\) 4235.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.21432 q^{2} -0.688892 q^{3} -0.525428 q^{4} -1.00000 q^{5} +0.836535 q^{6} +1.00000 q^{7} +3.06668 q^{8} -2.52543 q^{9} +O(q^{10})\) \(q-1.21432 q^{2} -0.688892 q^{3} -0.525428 q^{4} -1.00000 q^{5} +0.836535 q^{6} +1.00000 q^{7} +3.06668 q^{8} -2.52543 q^{9} +1.21432 q^{10} +0.361963 q^{12} +3.73975 q^{13} -1.21432 q^{14} +0.688892 q^{15} -2.67307 q^{16} -0.0666765 q^{17} +3.06668 q^{18} -6.42864 q^{19} +0.525428 q^{20} -0.688892 q^{21} -1.09679 q^{23} -2.11261 q^{24} +1.00000 q^{25} -4.54125 q^{26} +3.80642 q^{27} -0.525428 q^{28} +7.80642 q^{29} -0.836535 q^{30} -5.59210 q^{31} -2.88739 q^{32} +0.0809666 q^{34} -1.00000 q^{35} +1.32693 q^{36} +1.33185 q^{37} +7.80642 q^{38} -2.57628 q^{39} -3.06668 q^{40} -6.64296 q^{41} +0.836535 q^{42} +11.7605 q^{43} +2.52543 q^{45} +1.33185 q^{46} -2.26025 q^{47} +1.84146 q^{48} +1.00000 q^{49} -1.21432 q^{50} +0.0459330 q^{51} -1.96497 q^{52} -1.71900 q^{53} -4.62222 q^{54} +3.06668 q^{56} +4.42864 q^{57} -9.47949 q^{58} +2.54125 q^{59} -0.361963 q^{60} -14.4494 q^{61} +6.79060 q^{62} -2.52543 q^{63} +8.85236 q^{64} -3.73975 q^{65} +10.3827 q^{67} +0.0350337 q^{68} +0.755569 q^{69} +1.21432 q^{70} -12.5620 q^{71} -7.74467 q^{72} -1.17775 q^{73} -1.61729 q^{74} -0.688892 q^{75} +3.37778 q^{76} +3.12843 q^{78} +8.51606 q^{79} +2.67307 q^{80} +4.95407 q^{81} +8.06668 q^{82} +12.1017 q^{83} +0.361963 q^{84} +0.0666765 q^{85} -14.2810 q^{86} -5.37778 q^{87} +15.6128 q^{89} -3.06668 q^{90} +3.73975 q^{91} +0.576283 q^{92} +3.85236 q^{93} +2.74467 q^{94} +6.42864 q^{95} +1.98910 q^{96} -13.4193 q^{97} -1.21432 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9} + O(q^{10}) \) \( 3 q + 3 q^{2} - 2 q^{3} + 5 q^{4} - 3 q^{5} - 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9} - 3 q^{10} - 12 q^{12} - 2 q^{13} + 3 q^{14} + 2 q^{15} + 5 q^{16} + 9 q^{18} - 6 q^{19} - 5 q^{20} - 2 q^{21} - 10 q^{23} - 26 q^{24} + 3 q^{25} - 20 q^{26} - 2 q^{27} + 5 q^{28} + 10 q^{29} + 4 q^{30} - 10 q^{31} + 11 q^{32} - 6 q^{34} - 3 q^{35} + 17 q^{36} - 16 q^{37} + 10 q^{38} + 12 q^{39} - 9 q^{40} - 4 q^{42} + 2 q^{43} + q^{45} - 16 q^{46} - 20 q^{47} - 34 q^{48} + 3 q^{49} + 3 q^{50} + 20 q^{51} - 32 q^{52} - 12 q^{53} - 14 q^{54} + 9 q^{56} - 2 q^{58} + 14 q^{59} + 12 q^{60} - 10 q^{61} - 6 q^{62} - q^{63} + 33 q^{64} + 2 q^{65} - 2 q^{67} - 26 q^{68} + 2 q^{69} - 3 q^{70} - 24 q^{71} + 23 q^{72} - 4 q^{73} - 38 q^{74} - 2 q^{75} + 10 q^{76} + 42 q^{78} - 8 q^{79} - 5 q^{80} - 5 q^{81} + 24 q^{82} + 10 q^{83} - 12 q^{84} - 36 q^{86} - 16 q^{87} + 20 q^{89} - 9 q^{90} - 2 q^{91} - 18 q^{92} + 18 q^{93} - 38 q^{94} + 6 q^{95} - 40 q^{96} + 3 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21432 −0.858654 −0.429327 0.903149i \(-0.641249\pi\)
−0.429327 + 0.903149i \(0.641249\pi\)
\(3\) −0.688892 −0.397732 −0.198866 0.980027i \(-0.563726\pi\)
−0.198866 + 0.980027i \(0.563726\pi\)
\(4\) −0.525428 −0.262714
\(5\) −1.00000 −0.447214
\(6\) 0.836535 0.341514
\(7\) 1.00000 0.377964
\(8\) 3.06668 1.08423
\(9\) −2.52543 −0.841809
\(10\) 1.21432 0.384002
\(11\) 0 0
\(12\) 0.361963 0.104490
\(13\) 3.73975 1.03722 0.518610 0.855011i \(-0.326450\pi\)
0.518610 + 0.855011i \(0.326450\pi\)
\(14\) −1.21432 −0.324541
\(15\) 0.688892 0.177871
\(16\) −2.67307 −0.668268
\(17\) −0.0666765 −0.0161714 −0.00808572 0.999967i \(-0.502574\pi\)
−0.00808572 + 0.999967i \(0.502574\pi\)
\(18\) 3.06668 0.722823
\(19\) −6.42864 −1.47483 −0.737416 0.675439i \(-0.763954\pi\)
−0.737416 + 0.675439i \(0.763954\pi\)
\(20\) 0.525428 0.117489
\(21\) −0.688892 −0.150329
\(22\) 0 0
\(23\) −1.09679 −0.228696 −0.114348 0.993441i \(-0.536478\pi\)
−0.114348 + 0.993441i \(0.536478\pi\)
\(24\) −2.11261 −0.431235
\(25\) 1.00000 0.200000
\(26\) −4.54125 −0.890612
\(27\) 3.80642 0.732547
\(28\) −0.525428 −0.0992965
\(29\) 7.80642 1.44962 0.724808 0.688951i \(-0.241928\pi\)
0.724808 + 0.688951i \(0.241928\pi\)
\(30\) −0.836535 −0.152730
\(31\) −5.59210 −1.00437 −0.502186 0.864760i \(-0.667471\pi\)
−0.502186 + 0.864760i \(0.667471\pi\)
\(32\) −2.88739 −0.510423
\(33\) 0 0
\(34\) 0.0809666 0.0138857
\(35\) −1.00000 −0.169031
\(36\) 1.32693 0.221155
\(37\) 1.33185 0.218955 0.109478 0.993989i \(-0.465082\pi\)
0.109478 + 0.993989i \(0.465082\pi\)
\(38\) 7.80642 1.26637
\(39\) −2.57628 −0.412535
\(40\) −3.06668 −0.484884
\(41\) −6.64296 −1.03746 −0.518728 0.854939i \(-0.673594\pi\)
−0.518728 + 0.854939i \(0.673594\pi\)
\(42\) 0.836535 0.129080
\(43\) 11.7605 1.79346 0.896729 0.442580i \(-0.145937\pi\)
0.896729 + 0.442580i \(0.145937\pi\)
\(44\) 0 0
\(45\) 2.52543 0.376469
\(46\) 1.33185 0.196371
\(47\) −2.26025 −0.329692 −0.164846 0.986319i \(-0.552713\pi\)
−0.164846 + 0.986319i \(0.552713\pi\)
\(48\) 1.84146 0.265792
\(49\) 1.00000 0.142857
\(50\) −1.21432 −0.171731
\(51\) 0.0459330 0.00643190
\(52\) −1.96497 −0.272492
\(53\) −1.71900 −0.236123 −0.118062 0.993006i \(-0.537668\pi\)
−0.118062 + 0.993006i \(0.537668\pi\)
\(54\) −4.62222 −0.629004
\(55\) 0 0
\(56\) 3.06668 0.409802
\(57\) 4.42864 0.586588
\(58\) −9.47949 −1.24472
\(59\) 2.54125 0.330842 0.165421 0.986223i \(-0.447102\pi\)
0.165421 + 0.986223i \(0.447102\pi\)
\(60\) −0.361963 −0.0467292
\(61\) −14.4494 −1.85005 −0.925027 0.379901i \(-0.875958\pi\)
−0.925027 + 0.379901i \(0.875958\pi\)
\(62\) 6.79060 0.862407
\(63\) −2.52543 −0.318174
\(64\) 8.85236 1.10654
\(65\) −3.73975 −0.463859
\(66\) 0 0
\(67\) 10.3827 1.26845 0.634225 0.773149i \(-0.281319\pi\)
0.634225 + 0.773149i \(0.281319\pi\)
\(68\) 0.0350337 0.00424846
\(69\) 0.755569 0.0909598
\(70\) 1.21432 0.145139
\(71\) −12.5620 −1.49083 −0.745417 0.666598i \(-0.767750\pi\)
−0.745417 + 0.666598i \(0.767750\pi\)
\(72\) −7.74467 −0.912718
\(73\) −1.17775 −0.137846 −0.0689229 0.997622i \(-0.521956\pi\)
−0.0689229 + 0.997622i \(0.521956\pi\)
\(74\) −1.61729 −0.188007
\(75\) −0.688892 −0.0795464
\(76\) 3.37778 0.387458
\(77\) 0 0
\(78\) 3.12843 0.354225
\(79\) 8.51606 0.958132 0.479066 0.877779i \(-0.340976\pi\)
0.479066 + 0.877779i \(0.340976\pi\)
\(80\) 2.67307 0.298858
\(81\) 4.95407 0.550452
\(82\) 8.06668 0.890815
\(83\) 12.1017 1.32834 0.664168 0.747584i \(-0.268786\pi\)
0.664168 + 0.747584i \(0.268786\pi\)
\(84\) 0.361963 0.0394934
\(85\) 0.0666765 0.00723209
\(86\) −14.2810 −1.53996
\(87\) −5.37778 −0.576559
\(88\) 0 0
\(89\) 15.6128 1.65496 0.827479 0.561496i \(-0.189774\pi\)
0.827479 + 0.561496i \(0.189774\pi\)
\(90\) −3.06668 −0.323256
\(91\) 3.73975 0.392032
\(92\) 0.576283 0.0600816
\(93\) 3.85236 0.399471
\(94\) 2.74467 0.283091
\(95\) 6.42864 0.659564
\(96\) 1.98910 0.203012
\(97\) −13.4193 −1.36252 −0.681260 0.732041i \(-0.738568\pi\)
−0.681260 + 0.732041i \(0.738568\pi\)
\(98\) −1.21432 −0.122665
\(99\) 0 0
\(100\) −0.525428 −0.0525428
\(101\) 8.44938 0.840745 0.420373 0.907352i \(-0.361899\pi\)
0.420373 + 0.907352i \(0.361899\pi\)
\(102\) −0.0557773 −0.00552277
\(103\) −9.54617 −0.940612 −0.470306 0.882503i \(-0.655856\pi\)
−0.470306 + 0.882503i \(0.655856\pi\)
\(104\) 11.4686 1.12459
\(105\) 0.688892 0.0672290
\(106\) 2.08742 0.202748
\(107\) 8.56199 0.827719 0.413860 0.910341i \(-0.364180\pi\)
0.413860 + 0.910341i \(0.364180\pi\)
\(108\) −2.00000 −0.192450
\(109\) 6.99063 0.669581 0.334791 0.942293i \(-0.391334\pi\)
0.334791 + 0.942293i \(0.391334\pi\)
\(110\) 0 0
\(111\) −0.917502 −0.0870854
\(112\) −2.67307 −0.252581
\(113\) −1.57136 −0.147821 −0.0739106 0.997265i \(-0.523548\pi\)
−0.0739106 + 0.997265i \(0.523548\pi\)
\(114\) −5.37778 −0.503676
\(115\) 1.09679 0.102276
\(116\) −4.10171 −0.380834
\(117\) −9.44446 −0.873141
\(118\) −3.08589 −0.284079
\(119\) −0.0666765 −0.00611223
\(120\) 2.11261 0.192854
\(121\) 0 0
\(122\) 17.5462 1.58856
\(123\) 4.57628 0.412630
\(124\) 2.93825 0.263862
\(125\) −1.00000 −0.0894427
\(126\) 3.06668 0.273201
\(127\) 13.3778 1.18709 0.593543 0.804802i \(-0.297729\pi\)
0.593543 + 0.804802i \(0.297729\pi\)
\(128\) −4.97481 −0.439715
\(129\) −8.10171 −0.713316
\(130\) 4.54125 0.398294
\(131\) 2.75557 0.240755 0.120378 0.992728i \(-0.461589\pi\)
0.120378 + 0.992728i \(0.461589\pi\)
\(132\) 0 0
\(133\) −6.42864 −0.557434
\(134\) −12.6079 −1.08916
\(135\) −3.80642 −0.327605
\(136\) −0.204475 −0.0175336
\(137\) −17.8938 −1.52877 −0.764387 0.644758i \(-0.776958\pi\)
−0.764387 + 0.644758i \(0.776958\pi\)
\(138\) −0.917502 −0.0781030
\(139\) 3.86665 0.327965 0.163982 0.986463i \(-0.447566\pi\)
0.163982 + 0.986463i \(0.447566\pi\)
\(140\) 0.525428 0.0444067
\(141\) 1.55707 0.131129
\(142\) 15.2543 1.28011
\(143\) 0 0
\(144\) 6.75065 0.562554
\(145\) −7.80642 −0.648288
\(146\) 1.43017 0.118362
\(147\) −0.688892 −0.0568189
\(148\) −0.699791 −0.0575225
\(149\) −4.88892 −0.400516 −0.200258 0.979743i \(-0.564178\pi\)
−0.200258 + 0.979743i \(0.564178\pi\)
\(150\) 0.836535 0.0683028
\(151\) −22.1891 −1.80573 −0.902863 0.429929i \(-0.858539\pi\)
−0.902863 + 0.429929i \(0.858539\pi\)
\(152\) −19.7146 −1.59906
\(153\) 0.168387 0.0136133
\(154\) 0 0
\(155\) 5.59210 0.449169
\(156\) 1.35365 0.108379
\(157\) −4.81579 −0.384342 −0.192171 0.981361i \(-0.561553\pi\)
−0.192171 + 0.981361i \(0.561553\pi\)
\(158\) −10.3412 −0.822703
\(159\) 1.18421 0.0939138
\(160\) 2.88739 0.228268
\(161\) −1.09679 −0.0864390
\(162\) −6.01582 −0.472648
\(163\) 6.08742 0.476804 0.238402 0.971167i \(-0.423376\pi\)
0.238402 + 0.971167i \(0.423376\pi\)
\(164\) 3.49039 0.272554
\(165\) 0 0
\(166\) −14.6953 −1.14058
\(167\) 3.67307 0.284231 0.142115 0.989850i \(-0.454610\pi\)
0.142115 + 0.989850i \(0.454610\pi\)
\(168\) −2.11261 −0.162991
\(169\) 0.985710 0.0758238
\(170\) −0.0809666 −0.00620986
\(171\) 16.2351 1.24153
\(172\) −6.17929 −0.471166
\(173\) 0.628669 0.0477968 0.0238984 0.999714i \(-0.492392\pi\)
0.0238984 + 0.999714i \(0.492392\pi\)
\(174\) 6.53035 0.495065
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) −1.75065 −0.131587
\(178\) −18.9590 −1.42104
\(179\) −7.70471 −0.575877 −0.287939 0.957649i \(-0.592970\pi\)
−0.287939 + 0.957649i \(0.592970\pi\)
\(180\) −1.32693 −0.0989035
\(181\) 10.9175 0.811492 0.405746 0.913986i \(-0.367012\pi\)
0.405746 + 0.913986i \(0.367012\pi\)
\(182\) −4.54125 −0.336620
\(183\) 9.95407 0.735826
\(184\) −3.36349 −0.247960
\(185\) −1.33185 −0.0979197
\(186\) −4.67799 −0.343007
\(187\) 0 0
\(188\) 1.18760 0.0866146
\(189\) 3.80642 0.276877
\(190\) −7.80642 −0.566338
\(191\) −10.9175 −0.789963 −0.394981 0.918689i \(-0.629249\pi\)
−0.394981 + 0.918689i \(0.629249\pi\)
\(192\) −6.09832 −0.440108
\(193\) −11.7003 −0.842204 −0.421102 0.907013i \(-0.638357\pi\)
−0.421102 + 0.907013i \(0.638357\pi\)
\(194\) 16.2953 1.16993
\(195\) 2.57628 0.184491
\(196\) −0.525428 −0.0375305
\(197\) −10.8430 −0.772531 −0.386265 0.922388i \(-0.626235\pi\)
−0.386265 + 0.922388i \(0.626235\pi\)
\(198\) 0 0
\(199\) 2.08097 0.147516 0.0737579 0.997276i \(-0.476501\pi\)
0.0737579 + 0.997276i \(0.476501\pi\)
\(200\) 3.06668 0.216847
\(201\) −7.15257 −0.504503
\(202\) −10.2603 −0.721909
\(203\) 7.80642 0.547904
\(204\) −0.0241344 −0.00168975
\(205\) 6.64296 0.463964
\(206\) 11.5921 0.807660
\(207\) 2.76986 0.192518
\(208\) −9.99661 −0.693140
\(209\) 0 0
\(210\) −0.836535 −0.0577264
\(211\) −23.0923 −1.58974 −0.794871 0.606778i \(-0.792462\pi\)
−0.794871 + 0.606778i \(0.792462\pi\)
\(212\) 0.903212 0.0620328
\(213\) 8.65386 0.592953
\(214\) −10.3970 −0.710724
\(215\) −11.7605 −0.802059
\(216\) 11.6731 0.794252
\(217\) −5.59210 −0.379617
\(218\) −8.48886 −0.574938
\(219\) 0.811346 0.0548257
\(220\) 0 0
\(221\) −0.249353 −0.0167733
\(222\) 1.11414 0.0747762
\(223\) −21.5462 −1.44284 −0.721419 0.692499i \(-0.756510\pi\)
−0.721419 + 0.692499i \(0.756510\pi\)
\(224\) −2.88739 −0.192922
\(225\) −2.52543 −0.168362
\(226\) 1.90813 0.126927
\(227\) 27.2257 1.80703 0.903516 0.428553i \(-0.140977\pi\)
0.903516 + 0.428553i \(0.140977\pi\)
\(228\) −2.32693 −0.154105
\(229\) 25.0005 1.65208 0.826039 0.563613i \(-0.190589\pi\)
0.826039 + 0.563613i \(0.190589\pi\)
\(230\) −1.33185 −0.0878197
\(231\) 0 0
\(232\) 23.9398 1.57172
\(233\) 3.65878 0.239695 0.119847 0.992792i \(-0.461759\pi\)
0.119847 + 0.992792i \(0.461759\pi\)
\(234\) 11.4686 0.749726
\(235\) 2.26025 0.147443
\(236\) −1.33524 −0.0869169
\(237\) −5.86665 −0.381080
\(238\) 0.0809666 0.00524829
\(239\) −14.7052 −0.951200 −0.475600 0.879662i \(-0.657769\pi\)
−0.475600 + 0.879662i \(0.657769\pi\)
\(240\) −1.84146 −0.118866
\(241\) −13.6938 −0.882096 −0.441048 0.897483i \(-0.645393\pi\)
−0.441048 + 0.897483i \(0.645393\pi\)
\(242\) 0 0
\(243\) −14.8321 −0.951479
\(244\) 7.59210 0.486035
\(245\) −1.00000 −0.0638877
\(246\) −5.55707 −0.354306
\(247\) −24.0415 −1.52972
\(248\) −17.1492 −1.08897
\(249\) −8.33677 −0.528322
\(250\) 1.21432 0.0768003
\(251\) −11.0114 −0.695032 −0.347516 0.937674i \(-0.612975\pi\)
−0.347516 + 0.937674i \(0.612975\pi\)
\(252\) 1.32693 0.0835887
\(253\) 0 0
\(254\) −16.2449 −1.01930
\(255\) −0.0459330 −0.00287643
\(256\) −11.6637 −0.728981
\(257\) −15.9496 −0.994910 −0.497455 0.867490i \(-0.665732\pi\)
−0.497455 + 0.867490i \(0.665732\pi\)
\(258\) 9.83807 0.612491
\(259\) 1.33185 0.0827572
\(260\) 1.96497 0.121862
\(261\) −19.7146 −1.22030
\(262\) −3.34614 −0.206725
\(263\) 5.11108 0.315163 0.157581 0.987506i \(-0.449630\pi\)
0.157581 + 0.987506i \(0.449630\pi\)
\(264\) 0 0
\(265\) 1.71900 0.105598
\(266\) 7.80642 0.478643
\(267\) −10.7556 −0.658230
\(268\) −5.45536 −0.333239
\(269\) −18.2351 −1.11181 −0.555906 0.831245i \(-0.687628\pi\)
−0.555906 + 0.831245i \(0.687628\pi\)
\(270\) 4.62222 0.281299
\(271\) −6.23506 −0.378753 −0.189377 0.981905i \(-0.560647\pi\)
−0.189377 + 0.981905i \(0.560647\pi\)
\(272\) 0.178231 0.0108068
\(273\) −2.57628 −0.155924
\(274\) 21.7288 1.31269
\(275\) 0 0
\(276\) −0.396997 −0.0238964
\(277\) −6.32248 −0.379881 −0.189941 0.981796i \(-0.560830\pi\)
−0.189941 + 0.981796i \(0.560830\pi\)
\(278\) −4.69535 −0.281608
\(279\) 14.1225 0.845489
\(280\) −3.06668 −0.183269
\(281\) 25.2257 1.50484 0.752419 0.658684i \(-0.228887\pi\)
0.752419 + 0.658684i \(0.228887\pi\)
\(282\) −1.89078 −0.112594
\(283\) −13.4193 −0.797693 −0.398846 0.917018i \(-0.630589\pi\)
−0.398846 + 0.917018i \(0.630589\pi\)
\(284\) 6.60042 0.391663
\(285\) −4.42864 −0.262330
\(286\) 0 0
\(287\) −6.64296 −0.392121
\(288\) 7.29190 0.429679
\(289\) −16.9956 −0.999738
\(290\) 9.47949 0.556655
\(291\) 9.24443 0.541918
\(292\) 0.618825 0.0362140
\(293\) −17.6064 −1.02858 −0.514288 0.857617i \(-0.671944\pi\)
−0.514288 + 0.857617i \(0.671944\pi\)
\(294\) 0.836535 0.0487877
\(295\) −2.54125 −0.147957
\(296\) 4.08436 0.237398
\(297\) 0 0
\(298\) 5.93671 0.343905
\(299\) −4.10171 −0.237208
\(300\) 0.361963 0.0208979
\(301\) 11.7605 0.677863
\(302\) 26.9447 1.55049
\(303\) −5.82071 −0.334391
\(304\) 17.1842 0.985582
\(305\) 14.4494 0.827369
\(306\) −0.204475 −0.0116891
\(307\) −26.3368 −1.50312 −0.751560 0.659665i \(-0.770698\pi\)
−0.751560 + 0.659665i \(0.770698\pi\)
\(308\) 0 0
\(309\) 6.57628 0.374112
\(310\) −6.79060 −0.385680
\(311\) 5.96052 0.337990 0.168995 0.985617i \(-0.445948\pi\)
0.168995 + 0.985617i \(0.445948\pi\)
\(312\) −7.90063 −0.447285
\(313\) −5.52098 −0.312064 −0.156032 0.987752i \(-0.549870\pi\)
−0.156032 + 0.987752i \(0.549870\pi\)
\(314\) 5.84791 0.330017
\(315\) 2.52543 0.142292
\(316\) −4.47457 −0.251714
\(317\) −15.7146 −0.882618 −0.441309 0.897355i \(-0.645486\pi\)
−0.441309 + 0.897355i \(0.645486\pi\)
\(318\) −1.43801 −0.0806395
\(319\) 0 0
\(320\) −8.85236 −0.494862
\(321\) −5.89829 −0.329210
\(322\) 1.33185 0.0742212
\(323\) 0.428639 0.0238501
\(324\) −2.60300 −0.144611
\(325\) 3.73975 0.207444
\(326\) −7.39207 −0.409409
\(327\) −4.81579 −0.266314
\(328\) −20.3718 −1.12484
\(329\) −2.26025 −0.124612
\(330\) 0 0
\(331\) 18.2351 1.00229 0.501145 0.865363i \(-0.332912\pi\)
0.501145 + 0.865363i \(0.332912\pi\)
\(332\) −6.35857 −0.348972
\(333\) −3.36349 −0.184318
\(334\) −4.46028 −0.244056
\(335\) −10.3827 −0.567268
\(336\) 1.84146 0.100460
\(337\) −32.2908 −1.75899 −0.879497 0.475904i \(-0.842121\pi\)
−0.879497 + 0.475904i \(0.842121\pi\)
\(338\) −1.19697 −0.0651064
\(339\) 1.08250 0.0587932
\(340\) −0.0350337 −0.00189997
\(341\) 0 0
\(342\) −19.7146 −1.06604
\(343\) 1.00000 0.0539949
\(344\) 36.0656 1.94453
\(345\) −0.755569 −0.0406785
\(346\) −0.763405 −0.0410409
\(347\) −22.6909 −1.21811 −0.609056 0.793127i \(-0.708451\pi\)
−0.609056 + 0.793127i \(0.708451\pi\)
\(348\) 2.82564 0.151470
\(349\) −16.9097 −0.905154 −0.452577 0.891725i \(-0.649495\pi\)
−0.452577 + 0.891725i \(0.649495\pi\)
\(350\) −1.21432 −0.0649081
\(351\) 14.2351 0.759811
\(352\) 0 0
\(353\) 24.3970 1.29852 0.649261 0.760566i \(-0.275078\pi\)
0.649261 + 0.760566i \(0.275078\pi\)
\(354\) 2.12584 0.112987
\(355\) 12.5620 0.666721
\(356\) −8.20342 −0.434780
\(357\) 0.0459330 0.00243103
\(358\) 9.35599 0.494479
\(359\) 32.8113 1.73172 0.865858 0.500289i \(-0.166773\pi\)
0.865858 + 0.500289i \(0.166773\pi\)
\(360\) 7.74467 0.408180
\(361\) 22.3274 1.17513
\(362\) −13.2573 −0.696790
\(363\) 0 0
\(364\) −1.96497 −0.102992
\(365\) 1.17775 0.0616465
\(366\) −12.0874 −0.631820
\(367\) −6.94269 −0.362406 −0.181203 0.983446i \(-0.557999\pi\)
−0.181203 + 0.983446i \(0.557999\pi\)
\(368\) 2.93179 0.152830
\(369\) 16.7763 0.873340
\(370\) 1.61729 0.0840791
\(371\) −1.71900 −0.0892462
\(372\) −2.02413 −0.104946
\(373\) −36.9733 −1.91440 −0.957202 0.289421i \(-0.906537\pi\)
−0.957202 + 0.289421i \(0.906537\pi\)
\(374\) 0 0
\(375\) 0.688892 0.0355742
\(376\) −6.93146 −0.357463
\(377\) 29.1941 1.50357
\(378\) −4.62222 −0.237741
\(379\) −23.6414 −1.21438 −0.607189 0.794557i \(-0.707703\pi\)
−0.607189 + 0.794557i \(0.707703\pi\)
\(380\) −3.37778 −0.173277
\(381\) −9.21585 −0.472142
\(382\) 13.2573 0.678304
\(383\) 13.7210 0.701111 0.350555 0.936542i \(-0.385993\pi\)
0.350555 + 0.936542i \(0.385993\pi\)
\(384\) 3.42711 0.174889
\(385\) 0 0
\(386\) 14.2079 0.723161
\(387\) −29.7003 −1.50975
\(388\) 7.05086 0.357953
\(389\) −15.5526 −0.788549 −0.394275 0.918993i \(-0.629004\pi\)
−0.394275 + 0.918993i \(0.629004\pi\)
\(390\) −3.12843 −0.158414
\(391\) 0.0731300 0.00369835
\(392\) 3.06668 0.154891
\(393\) −1.89829 −0.0957561
\(394\) 13.1669 0.663337
\(395\) −8.51606 −0.428489
\(396\) 0 0
\(397\) −0.253799 −0.0127378 −0.00636891 0.999980i \(-0.502027\pi\)
−0.00636891 + 0.999980i \(0.502027\pi\)
\(398\) −2.52696 −0.126665
\(399\) 4.42864 0.221709
\(400\) −2.67307 −0.133654
\(401\) 20.3684 1.01715 0.508575 0.861018i \(-0.330172\pi\)
0.508575 + 0.861018i \(0.330172\pi\)
\(402\) 8.68550 0.433193
\(403\) −20.9131 −1.04175
\(404\) −4.43954 −0.220875
\(405\) −4.95407 −0.246170
\(406\) −9.47949 −0.470459
\(407\) 0 0
\(408\) 0.140862 0.00697368
\(409\) −12.1225 −0.599417 −0.299708 0.954031i \(-0.596889\pi\)
−0.299708 + 0.954031i \(0.596889\pi\)
\(410\) −8.06668 −0.398385
\(411\) 12.3269 0.608043
\(412\) 5.01582 0.247112
\(413\) 2.54125 0.125047
\(414\) −3.36349 −0.165307
\(415\) −12.1017 −0.594050
\(416\) −10.7981 −0.529421
\(417\) −2.66370 −0.130442
\(418\) 0 0
\(419\) −21.4400 −1.04741 −0.523707 0.851899i \(-0.675451\pi\)
−0.523707 + 0.851899i \(0.675451\pi\)
\(420\) −0.361963 −0.0176620
\(421\) 29.8622 1.45539 0.727697 0.685898i \(-0.240591\pi\)
0.727697 + 0.685898i \(0.240591\pi\)
\(422\) 28.0415 1.36504
\(423\) 5.70810 0.277538
\(424\) −5.27163 −0.256013
\(425\) −0.0666765 −0.00323429
\(426\) −10.5086 −0.509141
\(427\) −14.4494 −0.699255
\(428\) −4.49871 −0.217453
\(429\) 0 0
\(430\) 14.2810 0.688691
\(431\) 19.6588 0.946930 0.473465 0.880813i \(-0.343003\pi\)
0.473465 + 0.880813i \(0.343003\pi\)
\(432\) −10.1748 −0.489537
\(433\) −32.9719 −1.58453 −0.792264 0.610178i \(-0.791098\pi\)
−0.792264 + 0.610178i \(0.791098\pi\)
\(434\) 6.79060 0.325959
\(435\) 5.37778 0.257845
\(436\) −3.67307 −0.175908
\(437\) 7.05086 0.337288
\(438\) −0.985233 −0.0470763
\(439\) 0.815792 0.0389356 0.0194678 0.999810i \(-0.493803\pi\)
0.0194678 + 0.999810i \(0.493803\pi\)
\(440\) 0 0
\(441\) −2.52543 −0.120258
\(442\) 0.302795 0.0144025
\(443\) 24.9763 1.18666 0.593331 0.804959i \(-0.297813\pi\)
0.593331 + 0.804959i \(0.297813\pi\)
\(444\) 0.482081 0.0228785
\(445\) −15.6128 −0.740120
\(446\) 26.1639 1.23890
\(447\) 3.36794 0.159298
\(448\) 8.85236 0.418235
\(449\) 0.414349 0.0195544 0.00977718 0.999952i \(-0.496888\pi\)
0.00977718 + 0.999952i \(0.496888\pi\)
\(450\) 3.06668 0.144565
\(451\) 0 0
\(452\) 0.825636 0.0388347
\(453\) 15.2859 0.718195
\(454\) −33.0607 −1.55162
\(455\) −3.73975 −0.175322
\(456\) 13.5812 0.635998
\(457\) −9.33185 −0.436526 −0.218263 0.975890i \(-0.570039\pi\)
−0.218263 + 0.975890i \(0.570039\pi\)
\(458\) −30.3586 −1.41856
\(459\) −0.253799 −0.0118463
\(460\) −0.576283 −0.0268693
\(461\) −29.9891 −1.39673 −0.698366 0.715741i \(-0.746089\pi\)
−0.698366 + 0.715741i \(0.746089\pi\)
\(462\) 0 0
\(463\) −31.5353 −1.46557 −0.732784 0.680461i \(-0.761780\pi\)
−0.732784 + 0.680461i \(0.761780\pi\)
\(464\) −20.8671 −0.968732
\(465\) −3.85236 −0.178649
\(466\) −4.44293 −0.205815
\(467\) −5.67952 −0.262817 −0.131409 0.991328i \(-0.541950\pi\)
−0.131409 + 0.991328i \(0.541950\pi\)
\(468\) 4.96238 0.229386
\(469\) 10.3827 0.479429
\(470\) −2.74467 −0.126602
\(471\) 3.31756 0.152865
\(472\) 7.79319 0.358711
\(473\) 0 0
\(474\) 7.12399 0.327215
\(475\) −6.42864 −0.294966
\(476\) 0.0350337 0.00160577
\(477\) 4.34122 0.198771
\(478\) 17.8568 0.816751
\(479\) 39.4608 1.80301 0.901504 0.432771i \(-0.142464\pi\)
0.901504 + 0.432771i \(0.142464\pi\)
\(480\) −1.98910 −0.0907896
\(481\) 4.98079 0.227104
\(482\) 16.6287 0.757415
\(483\) 0.755569 0.0343796
\(484\) 0 0
\(485\) 13.4193 0.609338
\(486\) 18.0109 0.816991
\(487\) −3.19850 −0.144938 −0.0724689 0.997371i \(-0.523088\pi\)
−0.0724689 + 0.997371i \(0.523088\pi\)
\(488\) −44.3116 −2.00589
\(489\) −4.19358 −0.189640
\(490\) 1.21432 0.0548574
\(491\) −26.3511 −1.18921 −0.594603 0.804019i \(-0.702691\pi\)
−0.594603 + 0.804019i \(0.702691\pi\)
\(492\) −2.40451 −0.108403
\(493\) −0.520505 −0.0234424
\(494\) 29.1941 1.31350
\(495\) 0 0
\(496\) 14.9481 0.671189
\(497\) −12.5620 −0.563482
\(498\) 10.1235 0.453645
\(499\) 3.52987 0.158019 0.0790094 0.996874i \(-0.474824\pi\)
0.0790094 + 0.996874i \(0.474824\pi\)
\(500\) 0.525428 0.0234978
\(501\) −2.53035 −0.113048
\(502\) 13.3713 0.596792
\(503\) −22.7368 −1.01379 −0.506893 0.862009i \(-0.669206\pi\)
−0.506893 + 0.862009i \(0.669206\pi\)
\(504\) −7.74467 −0.344975
\(505\) −8.44938 −0.375993
\(506\) 0 0
\(507\) −0.679048 −0.0301576
\(508\) −7.02906 −0.311864
\(509\) −36.2351 −1.60609 −0.803045 0.595918i \(-0.796788\pi\)
−0.803045 + 0.595918i \(0.796788\pi\)
\(510\) 0.0557773 0.00246986
\(511\) −1.17775 −0.0521008
\(512\) 24.1131 1.06566
\(513\) −24.4701 −1.08038
\(514\) 19.3679 0.854283
\(515\) 9.54617 0.420655
\(516\) 4.25686 0.187398
\(517\) 0 0
\(518\) −1.61729 −0.0710598
\(519\) −0.433085 −0.0190103
\(520\) −11.4686 −0.502931
\(521\) −6.79706 −0.297784 −0.148892 0.988853i \(-0.547571\pi\)
−0.148892 + 0.988853i \(0.547571\pi\)
\(522\) 23.9398 1.04782
\(523\) −34.0701 −1.48978 −0.744890 0.667187i \(-0.767498\pi\)
−0.744890 + 0.667187i \(0.767498\pi\)
\(524\) −1.44785 −0.0632497
\(525\) −0.688892 −0.0300657
\(526\) −6.20648 −0.270616
\(527\) 0.372862 0.0162421
\(528\) 0 0
\(529\) −21.7971 −0.947698
\(530\) −2.08742 −0.0906717
\(531\) −6.41774 −0.278506
\(532\) 3.37778 0.146446
\(533\) −24.8430 −1.07607
\(534\) 13.0607 0.565192
\(535\) −8.56199 −0.370167
\(536\) 31.8404 1.37530
\(537\) 5.30772 0.229045
\(538\) 22.1432 0.954661
\(539\) 0 0
\(540\) 2.00000 0.0860663
\(541\) 27.1941 1.16916 0.584582 0.811335i \(-0.301259\pi\)
0.584582 + 0.811335i \(0.301259\pi\)
\(542\) 7.57136 0.325218
\(543\) −7.52098 −0.322756
\(544\) 0.192521 0.00825428
\(545\) −6.99063 −0.299446
\(546\) 3.12843 0.133884
\(547\) 40.2449 1.72075 0.860374 0.509663i \(-0.170230\pi\)
0.860374 + 0.509663i \(0.170230\pi\)
\(548\) 9.40192 0.401630
\(549\) 36.4909 1.55739
\(550\) 0 0
\(551\) −50.1847 −2.13794
\(552\) 2.31708 0.0986217
\(553\) 8.51606 0.362140
\(554\) 7.67752 0.326186
\(555\) 0.917502 0.0389458
\(556\) −2.03164 −0.0861608
\(557\) 7.09679 0.300701 0.150350 0.988633i \(-0.451960\pi\)
0.150350 + 0.988633i \(0.451960\pi\)
\(558\) −17.1492 −0.725982
\(559\) 43.9813 1.86021
\(560\) 2.67307 0.112958
\(561\) 0 0
\(562\) −30.6321 −1.29214
\(563\) 18.7971 0.792201 0.396101 0.918207i \(-0.370363\pi\)
0.396101 + 0.918207i \(0.370363\pi\)
\(564\) −0.818128 −0.0344494
\(565\) 1.57136 0.0661076
\(566\) 16.2953 0.684942
\(567\) 4.95407 0.208051
\(568\) −38.5236 −1.61641
\(569\) 0.0316429 0.00132654 0.000663269 1.00000i \(-0.499789\pi\)
0.000663269 1.00000i \(0.499789\pi\)
\(570\) 5.37778 0.225251
\(571\) −0.0503787 −0.00210828 −0.00105414 0.999999i \(-0.500336\pi\)
−0.00105414 + 0.999999i \(0.500336\pi\)
\(572\) 0 0
\(573\) 7.52098 0.314194
\(574\) 8.06668 0.336697
\(575\) −1.09679 −0.0457392
\(576\) −22.3560 −0.931499
\(577\) −13.6316 −0.567490 −0.283745 0.958900i \(-0.591577\pi\)
−0.283745 + 0.958900i \(0.591577\pi\)
\(578\) 20.6380 0.858429
\(579\) 8.06022 0.334971
\(580\) 4.10171 0.170314
\(581\) 12.1017 0.502064
\(582\) −11.2257 −0.465320
\(583\) 0 0
\(584\) −3.61179 −0.149457
\(585\) 9.44446 0.390480
\(586\) 21.3798 0.883191
\(587\) 1.63804 0.0676090 0.0338045 0.999428i \(-0.489238\pi\)
0.0338045 + 0.999428i \(0.489238\pi\)
\(588\) 0.361963 0.0149271
\(589\) 35.9496 1.48128
\(590\) 3.08589 0.127044
\(591\) 7.46965 0.307260
\(592\) −3.56013 −0.146321
\(593\) −8.46367 −0.347561 −0.173781 0.984784i \(-0.555598\pi\)
−0.173781 + 0.984784i \(0.555598\pi\)
\(594\) 0 0
\(595\) 0.0666765 0.00273347
\(596\) 2.56877 0.105221
\(597\) −1.43356 −0.0586718
\(598\) 4.98079 0.203680
\(599\) −26.9590 −1.10151 −0.550757 0.834665i \(-0.685661\pi\)
−0.550757 + 0.834665i \(0.685661\pi\)
\(600\) −2.11261 −0.0862469
\(601\) 16.4909 0.672677 0.336338 0.941741i \(-0.390811\pi\)
0.336338 + 0.941741i \(0.390811\pi\)
\(602\) −14.2810 −0.582050
\(603\) −26.2208 −1.06779
\(604\) 11.6588 0.474389
\(605\) 0 0
\(606\) 7.06821 0.287126
\(607\) −19.5526 −0.793617 −0.396808 0.917902i \(-0.629882\pi\)
−0.396808 + 0.917902i \(0.629882\pi\)
\(608\) 18.5620 0.752788
\(609\) −5.37778 −0.217919
\(610\) −17.5462 −0.710424
\(611\) −8.45277 −0.341963
\(612\) −0.0884751 −0.00357639
\(613\) 39.5955 1.59925 0.799623 0.600502i \(-0.205032\pi\)
0.799623 + 0.600502i \(0.205032\pi\)
\(614\) 31.9813 1.29066
\(615\) −4.57628 −0.184534
\(616\) 0 0
\(617\) 23.1669 0.932662 0.466331 0.884610i \(-0.345575\pi\)
0.466331 + 0.884610i \(0.345575\pi\)
\(618\) −7.98571 −0.321232
\(619\) 3.43017 0.137870 0.0689351 0.997621i \(-0.478040\pi\)
0.0689351 + 0.997621i \(0.478040\pi\)
\(620\) −2.93825 −0.118003
\(621\) −4.17484 −0.167531
\(622\) −7.23798 −0.290216
\(623\) 15.6128 0.625516
\(624\) 6.88659 0.275684
\(625\) 1.00000 0.0400000
\(626\) 6.70424 0.267955
\(627\) 0 0
\(628\) 2.53035 0.100972
\(629\) −0.0888033 −0.00354082
\(630\) −3.06668 −0.122179
\(631\) 10.9590 0.436270 0.218135 0.975919i \(-0.430003\pi\)
0.218135 + 0.975919i \(0.430003\pi\)
\(632\) 26.1160 1.03884
\(633\) 15.9081 0.632292
\(634\) 19.0825 0.757863
\(635\) −13.3778 −0.530881
\(636\) −0.622216 −0.0246725
\(637\) 3.73975 0.148174
\(638\) 0 0
\(639\) 31.7244 1.25500
\(640\) 4.97481 0.196647
\(641\) −14.9862 −0.591919 −0.295959 0.955201i \(-0.595639\pi\)
−0.295959 + 0.955201i \(0.595639\pi\)
\(642\) 7.16241 0.282678
\(643\) −14.4222 −0.568755 −0.284378 0.958712i \(-0.591787\pi\)
−0.284378 + 0.958712i \(0.591787\pi\)
\(644\) 0.576283 0.0227087
\(645\) 8.10171 0.319005
\(646\) −0.520505 −0.0204790
\(647\) −33.7309 −1.32610 −0.663048 0.748577i \(-0.730738\pi\)
−0.663048 + 0.748577i \(0.730738\pi\)
\(648\) 15.1925 0.596819
\(649\) 0 0
\(650\) −4.54125 −0.178122
\(651\) 3.85236 0.150986
\(652\) −3.19850 −0.125263
\(653\) 36.7971 1.43998 0.719990 0.693984i \(-0.244146\pi\)
0.719990 + 0.693984i \(0.244146\pi\)
\(654\) 5.84791 0.228671
\(655\) −2.75557 −0.107669
\(656\) 17.7571 0.693298
\(657\) 2.97433 0.116040
\(658\) 2.74467 0.106998
\(659\) −3.79213 −0.147721 −0.0738603 0.997269i \(-0.523532\pi\)
−0.0738603 + 0.997269i \(0.523532\pi\)
\(660\) 0 0
\(661\) −35.2543 −1.37123 −0.685616 0.727963i \(-0.740467\pi\)
−0.685616 + 0.727963i \(0.740467\pi\)
\(662\) −22.1432 −0.860620
\(663\) 0.171778 0.00667129
\(664\) 37.1120 1.44023
\(665\) 6.42864 0.249292
\(666\) 4.08436 0.158266
\(667\) −8.56199 −0.331522
\(668\) −1.92993 −0.0746713
\(669\) 14.8430 0.573863
\(670\) 12.6079 0.487087
\(671\) 0 0
\(672\) 1.98910 0.0767312
\(673\) 35.1383 1.35448 0.677240 0.735762i \(-0.263176\pi\)
0.677240 + 0.735762i \(0.263176\pi\)
\(674\) 39.2114 1.51037
\(675\) 3.80642 0.146509
\(676\) −0.517919 −0.0199200
\(677\) −23.1907 −0.891290 −0.445645 0.895210i \(-0.647026\pi\)
−0.445645 + 0.895210i \(0.647026\pi\)
\(678\) −1.31450 −0.0504830
\(679\) −13.4193 −0.514984
\(680\) 0.204475 0.00784127
\(681\) −18.7556 −0.718715
\(682\) 0 0
\(683\) −7.74758 −0.296453 −0.148227 0.988953i \(-0.547356\pi\)
−0.148227 + 0.988953i \(0.547356\pi\)
\(684\) −8.53035 −0.326166
\(685\) 17.8938 0.683689
\(686\) −1.21432 −0.0463629
\(687\) −17.2226 −0.657084
\(688\) −31.4366 −1.19851
\(689\) −6.42864 −0.244912
\(690\) 0.917502 0.0349287
\(691\) −14.7763 −0.562117 −0.281059 0.959691i \(-0.590686\pi\)
−0.281059 + 0.959691i \(0.590686\pi\)
\(692\) −0.330320 −0.0125569
\(693\) 0 0
\(694\) 27.5540 1.04594
\(695\) −3.86665 −0.146670
\(696\) −16.4919 −0.625125
\(697\) 0.442930 0.0167772
\(698\) 20.5337 0.777214
\(699\) −2.52051 −0.0953343
\(700\) −0.525428 −0.0198593
\(701\) 19.8765 0.750725 0.375362 0.926878i \(-0.377518\pi\)
0.375362 + 0.926878i \(0.377518\pi\)
\(702\) −17.2859 −0.652415
\(703\) −8.56199 −0.322922
\(704\) 0 0
\(705\) −1.55707 −0.0586427
\(706\) −29.6258 −1.11498
\(707\) 8.44938 0.317772
\(708\) 0.919838 0.0345696
\(709\) 0.368416 0.0138362 0.00691808 0.999976i \(-0.497798\pi\)
0.00691808 + 0.999976i \(0.497798\pi\)
\(710\) −15.2543 −0.572483
\(711\) −21.5067 −0.806564
\(712\) 47.8796 1.79436
\(713\) 6.13335 0.229696
\(714\) −0.0557773 −0.00208741
\(715\) 0 0
\(716\) 4.04827 0.151291
\(717\) 10.1303 0.378323
\(718\) −39.8435 −1.48694
\(719\) −5.86865 −0.218864 −0.109432 0.993994i \(-0.534903\pi\)
−0.109432 + 0.993994i \(0.534903\pi\)
\(720\) −6.75065 −0.251582
\(721\) −9.54617 −0.355518
\(722\) −27.1126 −1.00903
\(723\) 9.43356 0.350838
\(724\) −5.73636 −0.213190
\(725\) 7.80642 0.289923
\(726\) 0 0
\(727\) 1.19066 0.0441592 0.0220796 0.999756i \(-0.492971\pi\)
0.0220796 + 0.999756i \(0.492971\pi\)
\(728\) 11.4686 0.425054
\(729\) −4.64449 −0.172018
\(730\) −1.43017 −0.0529330
\(731\) −0.784149 −0.0290028
\(732\) −5.23014 −0.193312
\(733\) −19.6795 −0.726880 −0.363440 0.931618i \(-0.618398\pi\)
−0.363440 + 0.931618i \(0.618398\pi\)
\(734\) 8.43065 0.311181
\(735\) 0.688892 0.0254102
\(736\) 3.16686 0.116732
\(737\) 0 0
\(738\) −20.3718 −0.749897
\(739\) −27.1427 −0.998461 −0.499231 0.866469i \(-0.666384\pi\)
−0.499231 + 0.866469i \(0.666384\pi\)
\(740\) 0.699791 0.0257248
\(741\) 16.5620 0.608420
\(742\) 2.08742 0.0766316
\(743\) 31.0509 1.13915 0.569573 0.821941i \(-0.307109\pi\)
0.569573 + 0.821941i \(0.307109\pi\)
\(744\) 11.8139 0.433120
\(745\) 4.88892 0.179116
\(746\) 44.8974 1.64381
\(747\) −30.5620 −1.11820
\(748\) 0 0
\(749\) 8.56199 0.312848
\(750\) −0.836535 −0.0305460
\(751\) −35.8292 −1.30743 −0.653713 0.756743i \(-0.726789\pi\)
−0.653713 + 0.756743i \(0.726789\pi\)
\(752\) 6.04182 0.220322
\(753\) 7.58565 0.276436
\(754\) −35.4509 −1.29105
\(755\) 22.1891 0.807545
\(756\) −2.00000 −0.0727393
\(757\) −1.15563 −0.0420020 −0.0210010 0.999779i \(-0.506685\pi\)
−0.0210010 + 0.999779i \(0.506685\pi\)
\(758\) 28.7083 1.04273
\(759\) 0 0
\(760\) 19.7146 0.715122
\(761\) −36.5640 −1.32544 −0.662722 0.748866i \(-0.730599\pi\)
−0.662722 + 0.748866i \(0.730599\pi\)
\(762\) 11.1910 0.405407
\(763\) 6.99063 0.253078
\(764\) 5.73636 0.207534
\(765\) −0.168387 −0.00608804
\(766\) −16.6617 −0.602012
\(767\) 9.50363 0.343156
\(768\) 8.03503 0.289939
\(769\) 38.7545 1.39752 0.698762 0.715354i \(-0.253735\pi\)
0.698762 + 0.715354i \(0.253735\pi\)
\(770\) 0 0
\(771\) 10.9876 0.395708
\(772\) 6.14764 0.221259
\(773\) 55.3372 1.99034 0.995171 0.0981537i \(-0.0312937\pi\)
0.995171 + 0.0981537i \(0.0312937\pi\)
\(774\) 36.0656 1.29635
\(775\) −5.59210 −0.200874
\(776\) −41.1526 −1.47729
\(777\) −0.917502 −0.0329152
\(778\) 18.8859 0.677091
\(779\) 42.7052 1.53007
\(780\) −1.35365 −0.0484684
\(781\) 0 0
\(782\) −0.0888033 −0.00317560
\(783\) 29.7146 1.06191
\(784\) −2.67307 −0.0954668
\(785\) 4.81579 0.171883
\(786\) 2.30513 0.0822213
\(787\) 13.6731 0.487392 0.243696 0.969852i \(-0.421640\pi\)
0.243696 + 0.969852i \(0.421640\pi\)
\(788\) 5.69721 0.202955
\(789\) −3.52098 −0.125350
\(790\) 10.3412 0.367924
\(791\) −1.57136 −0.0558711
\(792\) 0 0
\(793\) −54.0370 −1.91891
\(794\) 0.308193 0.0109374
\(795\) −1.18421 −0.0419995
\(796\) −1.09340 −0.0387544
\(797\) 17.8765 0.633218 0.316609 0.948556i \(-0.397456\pi\)
0.316609 + 0.948556i \(0.397456\pi\)
\(798\) −5.37778 −0.190372
\(799\) 0.150706 0.00533159
\(800\) −2.88739 −0.102085
\(801\) −39.4291 −1.39316
\(802\) −24.7338 −0.873380
\(803\) 0 0
\(804\) 3.75815 0.132540
\(805\) 1.09679 0.0386567
\(806\) 25.3951 0.894506
\(807\) 12.5620 0.442203
\(808\) 25.9115 0.911564
\(809\) −14.6450 −0.514890 −0.257445 0.966293i \(-0.582881\pi\)
−0.257445 + 0.966293i \(0.582881\pi\)
\(810\) 6.01582 0.211374
\(811\) −30.2667 −1.06281 −0.531404 0.847119i \(-0.678335\pi\)
−0.531404 + 0.847119i \(0.678335\pi\)
\(812\) −4.10171 −0.143942
\(813\) 4.29529 0.150642
\(814\) 0 0
\(815\) −6.08742 −0.213233
\(816\) −0.122782 −0.00429823
\(817\) −75.6040 −2.64505
\(818\) 14.7205 0.514691
\(819\) −9.44446 −0.330016
\(820\) −3.49039 −0.121890
\(821\) −10.4286 −0.363962 −0.181981 0.983302i \(-0.558251\pi\)
−0.181981 + 0.983302i \(0.558251\pi\)
\(822\) −14.9688 −0.522098
\(823\) 4.28100 0.149226 0.0746131 0.997213i \(-0.476228\pi\)
0.0746131 + 0.997213i \(0.476228\pi\)
\(824\) −29.2750 −1.01984
\(825\) 0 0
\(826\) −3.08589 −0.107372
\(827\) 13.8336 0.481042 0.240521 0.970644i \(-0.422682\pi\)
0.240521 + 0.970644i \(0.422682\pi\)
\(828\) −1.45536 −0.0505773
\(829\) 10.8573 0.377089 0.188544 0.982065i \(-0.439623\pi\)
0.188544 + 0.982065i \(0.439623\pi\)
\(830\) 14.6953 0.510083
\(831\) 4.35551 0.151091
\(832\) 33.1056 1.14773
\(833\) −0.0666765 −0.00231021
\(834\) 3.23459 0.112005
\(835\) −3.67307 −0.127112
\(836\) 0 0
\(837\) −21.2859 −0.735749
\(838\) 26.0350 0.899365
\(839\) 52.4820 1.81188 0.905940 0.423407i \(-0.139166\pi\)
0.905940 + 0.423407i \(0.139166\pi\)
\(840\) 2.11261 0.0728920
\(841\) 31.9403 1.10139
\(842\) −36.2623 −1.24968
\(843\) −17.3778 −0.598523
\(844\) 12.1334 0.417647
\(845\) −0.985710 −0.0339095
\(846\) −6.93146 −0.238309
\(847\) 0 0
\(848\) 4.59502 0.157794
\(849\) 9.24443 0.317268
\(850\) 0.0809666 0.00277713
\(851\) −1.46076 −0.0500742
\(852\) −4.54698 −0.155777
\(853\) −9.89184 −0.338690 −0.169345 0.985557i \(-0.554165\pi\)
−0.169345 + 0.985557i \(0.554165\pi\)
\(854\) 17.5462 0.600418
\(855\) −16.2351 −0.555227
\(856\) 26.2569 0.897441
\(857\) 3.58766 0.122552 0.0612760 0.998121i \(-0.480483\pi\)
0.0612760 + 0.998121i \(0.480483\pi\)
\(858\) 0 0
\(859\) −17.2050 −0.587025 −0.293513 0.955955i \(-0.594824\pi\)
−0.293513 + 0.955955i \(0.594824\pi\)
\(860\) 6.17929 0.210712
\(861\) 4.57628 0.155959
\(862\) −23.8720 −0.813085
\(863\) 15.0781 0.513263 0.256631 0.966509i \(-0.417387\pi\)
0.256631 + 0.966509i \(0.417387\pi\)
\(864\) −10.9906 −0.373909
\(865\) −0.628669 −0.0213754
\(866\) 40.0384 1.36056
\(867\) 11.7081 0.397628
\(868\) 2.93825 0.0997306
\(869\) 0 0
\(870\) −6.53035 −0.221400
\(871\) 38.8287 1.31566
\(872\) 21.4380 0.725983
\(873\) 33.8894 1.14698
\(874\) −8.56199 −0.289614
\(875\) −1.00000 −0.0338062
\(876\) −0.426304 −0.0144035
\(877\) 31.4750 1.06284 0.531418 0.847109i \(-0.321659\pi\)
0.531418 + 0.847109i \(0.321659\pi\)
\(878\) −0.990632 −0.0334322
\(879\) 12.1289 0.409098
\(880\) 0 0
\(881\) −47.1209 −1.58754 −0.793772 0.608215i \(-0.791886\pi\)
−0.793772 + 0.608215i \(0.791886\pi\)
\(882\) 3.06668 0.103260
\(883\) 33.8118 1.13786 0.568929 0.822386i \(-0.307358\pi\)
0.568929 + 0.822386i \(0.307358\pi\)
\(884\) 0.131017 0.00440658
\(885\) 1.75065 0.0588473
\(886\) −30.3293 −1.01893
\(887\) 31.6258 1.06189 0.530944 0.847407i \(-0.321837\pi\)
0.530944 + 0.847407i \(0.321837\pi\)
\(888\) −2.81368 −0.0944210
\(889\) 13.3778 0.448676
\(890\) 18.9590 0.635507
\(891\) 0 0
\(892\) 11.3210 0.379054
\(893\) 14.5303 0.486240
\(894\) −4.08976 −0.136782
\(895\) 7.70471 0.257540
\(896\) −4.97481 −0.166197
\(897\) 2.82564 0.0943452
\(898\) −0.503153 −0.0167904
\(899\) −43.6543 −1.45595
\(900\) 1.32693 0.0442310
\(901\) 0.114617 0.00381845
\(902\) 0 0
\(903\) −8.10171 −0.269608
\(904\) −4.81885 −0.160273
\(905\) −10.9175 −0.362910
\(906\) −18.5620 −0.616681
\(907\) −46.8943 −1.55710 −0.778550 0.627582i \(-0.784045\pi\)
−0.778550 + 0.627582i \(0.784045\pi\)
\(908\) −14.3051 −0.474732
\(909\) −21.3383 −0.707747
\(910\) 4.54125 0.150541
\(911\) −28.5620 −0.946301 −0.473151 0.880982i \(-0.656883\pi\)
−0.473151 + 0.880982i \(0.656883\pi\)
\(912\) −11.8381 −0.391998
\(913\) 0 0
\(914\) 11.3319 0.374824
\(915\) −9.95407 −0.329071
\(916\) −13.1359 −0.434024
\(917\) 2.75557 0.0909969
\(918\) 0.308193 0.0101719
\(919\) −30.3555 −1.00134 −0.500668 0.865639i \(-0.666912\pi\)
−0.500668 + 0.865639i \(0.666912\pi\)
\(920\) 3.36349 0.110891
\(921\) 18.1432 0.597839
\(922\) 36.4164 1.19931
\(923\) −46.9787 −1.54632
\(924\) 0 0
\(925\) 1.33185 0.0437910
\(926\) 38.2939 1.25842
\(927\) 24.1082 0.791816
\(928\) −22.5402 −0.739918
\(929\) 2.71408 0.0890461 0.0445231 0.999008i \(-0.485823\pi\)
0.0445231 + 0.999008i \(0.485823\pi\)
\(930\) 4.67799 0.153397
\(931\) −6.42864 −0.210690
\(932\) −1.92242 −0.0629711
\(933\) −4.10616 −0.134430
\(934\) 6.89676 0.225669
\(935\) 0 0
\(936\) −28.9631 −0.946689
\(937\) −13.7081 −0.447824 −0.223912 0.974609i \(-0.571883\pi\)
−0.223912 + 0.974609i \(0.571883\pi\)
\(938\) −12.6079 −0.411663
\(939\) 3.80336 0.124118
\(940\) −1.18760 −0.0387352
\(941\) 21.1635 0.689909 0.344955 0.938619i \(-0.387894\pi\)
0.344955 + 0.938619i \(0.387894\pi\)
\(942\) −4.02858 −0.131258
\(943\) 7.28592 0.237262
\(944\) −6.79294 −0.221091
\(945\) −3.80642 −0.123823
\(946\) 0 0
\(947\) −14.8746 −0.483361 −0.241680 0.970356i \(-0.577699\pi\)
−0.241680 + 0.970356i \(0.577699\pi\)
\(948\) 3.08250 0.100115
\(949\) −4.40451 −0.142976
\(950\) 7.80642 0.253274
\(951\) 10.8256 0.351045
\(952\) −0.204475 −0.00662709
\(953\) −35.0968 −1.13690 −0.568448 0.822719i \(-0.692456\pi\)
−0.568448 + 0.822719i \(0.692456\pi\)
\(954\) −5.27163 −0.170675
\(955\) 10.9175 0.353282
\(956\) 7.72651 0.249893
\(957\) 0 0
\(958\) −47.9180 −1.54816
\(959\) −17.8938 −0.577822
\(960\) 6.09832 0.196822
\(961\) 0.271628 0.00876221
\(962\) −6.04827 −0.195004
\(963\) −21.6227 −0.696782
\(964\) 7.19511 0.231739
\(965\) 11.7003 0.376645
\(966\) −0.917502 −0.0295201
\(967\) 53.0879 1.70719 0.853596 0.520936i \(-0.174417\pi\)
0.853596 + 0.520936i \(0.174417\pi\)
\(968\) 0 0
\(969\) −0.295286 −0.00948597
\(970\) −16.2953 −0.523210
\(971\) 21.4400 0.688043 0.344021 0.938962i \(-0.388211\pi\)
0.344021 + 0.938962i \(0.388211\pi\)
\(972\) 7.79319 0.249967
\(973\) 3.86665 0.123959
\(974\) 3.88400 0.124451
\(975\) −2.57628 −0.0825071
\(976\) 38.6242 1.23633
\(977\) −54.0415 −1.72894 −0.864470 0.502684i \(-0.832346\pi\)
−0.864470 + 0.502684i \(0.832346\pi\)
\(978\) 5.09234 0.162835
\(979\) 0 0
\(980\) 0.525428 0.0167842
\(981\) −17.6543 −0.563660
\(982\) 31.9986 1.02112
\(983\) −38.3432 −1.22296 −0.611480 0.791260i \(-0.709425\pi\)
−0.611480 + 0.791260i \(0.709425\pi\)
\(984\) 14.0340 0.447387
\(985\) 10.8430 0.345486
\(986\) 0.632060 0.0201289
\(987\) 1.55707 0.0495621
\(988\) 12.6321 0.401879
\(989\) −12.8988 −0.410157
\(990\) 0 0
\(991\) 51.6543 1.64085 0.820427 0.571751i \(-0.193736\pi\)
0.820427 + 0.571751i \(0.193736\pi\)
\(992\) 16.1466 0.512655
\(993\) −12.5620 −0.398643
\(994\) 15.2543 0.483836
\(995\) −2.08097 −0.0659711
\(996\) 4.38037 0.138797
\(997\) −41.4445 −1.31256 −0.656280 0.754518i \(-0.727871\pi\)
−0.656280 + 0.754518i \(0.727871\pi\)
\(998\) −4.28639 −0.135683
\(999\) 5.06959 0.160395
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 4235.2.a.q.1.1 3
11.10 odd 2 385.2.a.f.1.3 3
33.32 even 2 3465.2.a.bh.1.1 3
44.43 even 2 6160.2.a.bn.1.2 3
55.32 even 4 1925.2.b.n.1849.4 6
55.43 even 4 1925.2.b.n.1849.3 6
55.54 odd 2 1925.2.a.v.1.1 3
77.76 even 2 2695.2.a.g.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
385.2.a.f.1.3 3 11.10 odd 2
1925.2.a.v.1.1 3 55.54 odd 2
1925.2.b.n.1849.3 6 55.43 even 4
1925.2.b.n.1849.4 6 55.32 even 4
2695.2.a.g.1.3 3 77.76 even 2
3465.2.a.bh.1.1 3 33.32 even 2
4235.2.a.q.1.1 3 1.1 even 1 trivial
6160.2.a.bn.1.2 3 44.43 even 2