Properties

Label 6025.2.a.p.1.9
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 1.9
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.84209 q^{2} -1.69681 q^{3} +1.39329 q^{4} +3.12567 q^{6} +1.54055 q^{7} +1.11761 q^{8} -0.120844 q^{9} +O(q^{10})\) \(q-1.84209 q^{2} -1.69681 q^{3} +1.39329 q^{4} +3.12567 q^{6} +1.54055 q^{7} +1.11761 q^{8} -0.120844 q^{9} +2.53578 q^{11} -2.36415 q^{12} +6.36889 q^{13} -2.83783 q^{14} -4.84532 q^{16} -3.54355 q^{17} +0.222605 q^{18} +0.713569 q^{19} -2.61402 q^{21} -4.67113 q^{22} +1.66453 q^{23} -1.89637 q^{24} -11.7321 q^{26} +5.29547 q^{27} +2.14644 q^{28} -8.23983 q^{29} +10.5697 q^{31} +6.69029 q^{32} -4.30273 q^{33} +6.52753 q^{34} -0.168370 q^{36} -0.496832 q^{37} -1.31446 q^{38} -10.8068 q^{39} -8.92984 q^{41} +4.81525 q^{42} +1.50676 q^{43} +3.53308 q^{44} -3.06622 q^{46} +6.94849 q^{47} +8.22158 q^{48} -4.62670 q^{49} +6.01272 q^{51} +8.87372 q^{52} -9.87593 q^{53} -9.75473 q^{54} +1.72174 q^{56} -1.21079 q^{57} +15.1785 q^{58} -10.1744 q^{59} -9.13781 q^{61} -19.4703 q^{62} -0.186166 q^{63} -2.63346 q^{64} +7.92601 q^{66} -1.85057 q^{67} -4.93720 q^{68} -2.82439 q^{69} -9.47485 q^{71} -0.135056 q^{72} -8.88186 q^{73} +0.915209 q^{74} +0.994210 q^{76} +3.90650 q^{77} +19.9071 q^{78} -6.12948 q^{79} -8.62287 q^{81} +16.4496 q^{82} -0.835537 q^{83} -3.64209 q^{84} -2.77558 q^{86} +13.9814 q^{87} +2.83402 q^{88} +2.27480 q^{89} +9.81161 q^{91} +2.31918 q^{92} -17.9348 q^{93} -12.7997 q^{94} -11.3521 q^{96} -7.56572 q^{97} +8.52280 q^{98} -0.306433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.84209 −1.30255 −0.651277 0.758840i \(-0.725766\pi\)
−0.651277 + 0.758840i \(0.725766\pi\)
\(3\) −1.69681 −0.979652 −0.489826 0.871820i \(-0.662940\pi\)
−0.489826 + 0.871820i \(0.662940\pi\)
\(4\) 1.39329 0.696645
\(5\) 0 0
\(6\) 3.12567 1.27605
\(7\) 1.54055 0.582274 0.291137 0.956681i \(-0.405967\pi\)
0.291137 + 0.956681i \(0.405967\pi\)
\(8\) 1.11761 0.395136
\(9\) −0.120844 −0.0402812
\(10\) 0 0
\(11\) 2.53578 0.764566 0.382283 0.924045i \(-0.375138\pi\)
0.382283 + 0.924045i \(0.375138\pi\)
\(12\) −2.36415 −0.682470
\(13\) 6.36889 1.76641 0.883207 0.468984i \(-0.155380\pi\)
0.883207 + 0.468984i \(0.155380\pi\)
\(14\) −2.83783 −0.758442
\(15\) 0 0
\(16\) −4.84532 −1.21133
\(17\) −3.54355 −0.859437 −0.429719 0.902963i \(-0.641387\pi\)
−0.429719 + 0.902963i \(0.641387\pi\)
\(18\) 0.222605 0.0524684
\(19\) 0.713569 0.163704 0.0818520 0.996644i \(-0.473917\pi\)
0.0818520 + 0.996644i \(0.473917\pi\)
\(20\) 0 0
\(21\) −2.61402 −0.570426
\(22\) −4.67113 −0.995889
\(23\) 1.66453 0.347079 0.173540 0.984827i \(-0.444480\pi\)
0.173540 + 0.984827i \(0.444480\pi\)
\(24\) −1.89637 −0.387095
\(25\) 0 0
\(26\) −11.7321 −2.30085
\(27\) 5.29547 1.01911
\(28\) 2.14644 0.405638
\(29\) −8.23983 −1.53010 −0.765049 0.643972i \(-0.777285\pi\)
−0.765049 + 0.643972i \(0.777285\pi\)
\(30\) 0 0
\(31\) 10.5697 1.89838 0.949188 0.314711i \(-0.101908\pi\)
0.949188 + 0.314711i \(0.101908\pi\)
\(32\) 6.69029 1.18269
\(33\) −4.30273 −0.749009
\(34\) 6.52753 1.11946
\(35\) 0 0
\(36\) −0.168370 −0.0280617
\(37\) −0.496832 −0.0816787 −0.0408393 0.999166i \(-0.513003\pi\)
−0.0408393 + 0.999166i \(0.513003\pi\)
\(38\) −1.31446 −0.213233
\(39\) −10.8068 −1.73047
\(40\) 0 0
\(41\) −8.92984 −1.39461 −0.697303 0.716776i \(-0.745617\pi\)
−0.697303 + 0.716776i \(0.745617\pi\)
\(42\) 4.81525 0.743010
\(43\) 1.50676 0.229778 0.114889 0.993378i \(-0.463349\pi\)
0.114889 + 0.993378i \(0.463349\pi\)
\(44\) 3.53308 0.532632
\(45\) 0 0
\(46\) −3.06622 −0.452089
\(47\) 6.94849 1.01354 0.506771 0.862081i \(-0.330839\pi\)
0.506771 + 0.862081i \(0.330839\pi\)
\(48\) 8.22158 1.18668
\(49\) −4.62670 −0.660958
\(50\) 0 0
\(51\) 6.01272 0.841950
\(52\) 8.87372 1.23056
\(53\) −9.87593 −1.35656 −0.678281 0.734802i \(-0.737275\pi\)
−0.678281 + 0.734802i \(0.737275\pi\)
\(54\) −9.75473 −1.32745
\(55\) 0 0
\(56\) 1.72174 0.230077
\(57\) −1.21079 −0.160373
\(58\) 15.1785 1.99303
\(59\) −10.1744 −1.32459 −0.662296 0.749242i \(-0.730418\pi\)
−0.662296 + 0.749242i \(0.730418\pi\)
\(60\) 0 0
\(61\) −9.13781 −1.16998 −0.584988 0.811042i \(-0.698901\pi\)
−0.584988 + 0.811042i \(0.698901\pi\)
\(62\) −19.4703 −2.47273
\(63\) −0.186166 −0.0234547
\(64\) −2.63346 −0.329183
\(65\) 0 0
\(66\) 7.92601 0.975625
\(67\) −1.85057 −0.226083 −0.113041 0.993590i \(-0.536059\pi\)
−0.113041 + 0.993590i \(0.536059\pi\)
\(68\) −4.93720 −0.598723
\(69\) −2.82439 −0.340017
\(70\) 0 0
\(71\) −9.47485 −1.12446 −0.562229 0.826981i \(-0.690056\pi\)
−0.562229 + 0.826981i \(0.690056\pi\)
\(72\) −0.135056 −0.0159165
\(73\) −8.88186 −1.03954 −0.519771 0.854305i \(-0.673983\pi\)
−0.519771 + 0.854305i \(0.673983\pi\)
\(74\) 0.915209 0.106391
\(75\) 0 0
\(76\) 0.994210 0.114044
\(77\) 3.90650 0.445187
\(78\) 19.9071 2.25403
\(79\) −6.12948 −0.689621 −0.344810 0.938672i \(-0.612057\pi\)
−0.344810 + 0.938672i \(0.612057\pi\)
\(80\) 0 0
\(81\) −8.62287 −0.958096
\(82\) 16.4496 1.81655
\(83\) −0.835537 −0.0917122 −0.0458561 0.998948i \(-0.514602\pi\)
−0.0458561 + 0.998948i \(0.514602\pi\)
\(84\) −3.64209 −0.397384
\(85\) 0 0
\(86\) −2.77558 −0.299299
\(87\) 13.9814 1.49896
\(88\) 2.83402 0.302107
\(89\) 2.27480 0.241129 0.120564 0.992706i \(-0.461530\pi\)
0.120564 + 0.992706i \(0.461530\pi\)
\(90\) 0 0
\(91\) 9.81161 1.02854
\(92\) 2.31918 0.241791
\(93\) −17.9348 −1.85975
\(94\) −12.7997 −1.32019
\(95\) 0 0
\(96\) −11.3521 −1.15862
\(97\) −7.56572 −0.768182 −0.384091 0.923295i \(-0.625485\pi\)
−0.384091 + 0.923295i \(0.625485\pi\)
\(98\) 8.52280 0.860933
\(99\) −0.306433 −0.0307976
\(100\) 0 0
\(101\) −16.9324 −1.68483 −0.842417 0.538826i \(-0.818868\pi\)
−0.842417 + 0.538826i \(0.818868\pi\)
\(102\) −11.0760 −1.09668
\(103\) 2.83252 0.279096 0.139548 0.990215i \(-0.455435\pi\)
0.139548 + 0.990215i \(0.455435\pi\)
\(104\) 7.11795 0.697973
\(105\) 0 0
\(106\) 18.1923 1.76700
\(107\) 4.86488 0.470306 0.235153 0.971958i \(-0.424441\pi\)
0.235153 + 0.971958i \(0.424441\pi\)
\(108\) 7.37813 0.709961
\(109\) 10.2870 0.985317 0.492658 0.870223i \(-0.336025\pi\)
0.492658 + 0.870223i \(0.336025\pi\)
\(110\) 0 0
\(111\) 0.843029 0.0800167
\(112\) −7.46447 −0.705326
\(113\) 12.6981 1.19454 0.597270 0.802041i \(-0.296252\pi\)
0.597270 + 0.802041i \(0.296252\pi\)
\(114\) 2.23038 0.208894
\(115\) 0 0
\(116\) −11.4805 −1.06594
\(117\) −0.769640 −0.0711532
\(118\) 18.7421 1.72535
\(119\) −5.45902 −0.500427
\(120\) 0 0
\(121\) −4.56982 −0.415438
\(122\) 16.8326 1.52396
\(123\) 15.1522 1.36623
\(124\) 14.7267 1.32249
\(125\) 0 0
\(126\) 0.342934 0.0305510
\(127\) 1.17595 0.104349 0.0521743 0.998638i \(-0.483385\pi\)
0.0521743 + 0.998638i \(0.483385\pi\)
\(128\) −8.52951 −0.753909
\(129\) −2.55668 −0.225103
\(130\) 0 0
\(131\) 18.7573 1.63884 0.819418 0.573196i \(-0.194297\pi\)
0.819418 + 0.573196i \(0.194297\pi\)
\(132\) −5.99496 −0.521794
\(133\) 1.09929 0.0953205
\(134\) 3.40891 0.294485
\(135\) 0 0
\(136\) −3.96031 −0.339594
\(137\) −5.04016 −0.430610 −0.215305 0.976547i \(-0.569075\pi\)
−0.215305 + 0.976547i \(0.569075\pi\)
\(138\) 5.20278 0.442890
\(139\) −0.226430 −0.0192056 −0.00960278 0.999954i \(-0.503057\pi\)
−0.00960278 + 0.999954i \(0.503057\pi\)
\(140\) 0 0
\(141\) −11.7902 −0.992918
\(142\) 17.4535 1.46467
\(143\) 16.1501 1.35054
\(144\) 0.585526 0.0487938
\(145\) 0 0
\(146\) 16.3612 1.35406
\(147\) 7.85063 0.647509
\(148\) −0.692232 −0.0569011
\(149\) −4.00539 −0.328134 −0.164067 0.986449i \(-0.552461\pi\)
−0.164067 + 0.986449i \(0.552461\pi\)
\(150\) 0 0
\(151\) −5.73080 −0.466366 −0.233183 0.972433i \(-0.574914\pi\)
−0.233183 + 0.972433i \(0.574914\pi\)
\(152\) 0.797494 0.0646853
\(153\) 0.428215 0.0346191
\(154\) −7.19612 −0.579880
\(155\) 0 0
\(156\) −15.0570 −1.20552
\(157\) 4.02238 0.321021 0.160510 0.987034i \(-0.448686\pi\)
0.160510 + 0.987034i \(0.448686\pi\)
\(158\) 11.2911 0.898268
\(159\) 16.7575 1.32896
\(160\) 0 0
\(161\) 2.56430 0.202095
\(162\) 15.8841 1.24797
\(163\) −2.51003 −0.196601 −0.0983004 0.995157i \(-0.531341\pi\)
−0.0983004 + 0.995157i \(0.531341\pi\)
\(164\) −12.4419 −0.971546
\(165\) 0 0
\(166\) 1.53913 0.119460
\(167\) −25.3075 −1.95835 −0.979177 0.203008i \(-0.934928\pi\)
−0.979177 + 0.203008i \(0.934928\pi\)
\(168\) −2.92146 −0.225395
\(169\) 27.5628 2.12022
\(170\) 0 0
\(171\) −0.0862302 −0.00659419
\(172\) 2.09935 0.160074
\(173\) 19.0394 1.44754 0.723769 0.690043i \(-0.242408\pi\)
0.723769 + 0.690043i \(0.242408\pi\)
\(174\) −25.7550 −1.95248
\(175\) 0 0
\(176\) −12.2867 −0.926143
\(177\) 17.2640 1.29764
\(178\) −4.19039 −0.314083
\(179\) 12.3757 0.925007 0.462503 0.886618i \(-0.346951\pi\)
0.462503 + 0.886618i \(0.346951\pi\)
\(180\) 0 0
\(181\) 5.62774 0.418307 0.209153 0.977883i \(-0.432929\pi\)
0.209153 + 0.977883i \(0.432929\pi\)
\(182\) −18.0738 −1.33972
\(183\) 15.5051 1.14617
\(184\) 1.86030 0.137143
\(185\) 0 0
\(186\) 33.0374 2.42242
\(187\) −8.98566 −0.657097
\(188\) 9.68127 0.706079
\(189\) 8.15794 0.593403
\(190\) 0 0
\(191\) −16.0108 −1.15850 −0.579251 0.815149i \(-0.696655\pi\)
−0.579251 + 0.815149i \(0.696655\pi\)
\(192\) 4.46848 0.322485
\(193\) −6.92078 −0.498169 −0.249084 0.968482i \(-0.580130\pi\)
−0.249084 + 0.968482i \(0.580130\pi\)
\(194\) 13.9367 1.00060
\(195\) 0 0
\(196\) −6.44634 −0.460453
\(197\) 4.08208 0.290836 0.145418 0.989370i \(-0.453547\pi\)
0.145418 + 0.989370i \(0.453547\pi\)
\(198\) 0.564476 0.0401156
\(199\) 7.24353 0.513481 0.256740 0.966480i \(-0.417352\pi\)
0.256740 + 0.966480i \(0.417352\pi\)
\(200\) 0 0
\(201\) 3.14006 0.221483
\(202\) 31.1909 2.19459
\(203\) −12.6939 −0.890935
\(204\) 8.37747 0.586540
\(205\) 0 0
\(206\) −5.21775 −0.363538
\(207\) −0.201148 −0.0139808
\(208\) −30.8593 −2.13971
\(209\) 1.80945 0.125163
\(210\) 0 0
\(211\) 0.0986890 0.00679403 0.00339701 0.999994i \(-0.498919\pi\)
0.00339701 + 0.999994i \(0.498919\pi\)
\(212\) −13.7600 −0.945043
\(213\) 16.0770 1.10158
\(214\) −8.96154 −0.612598
\(215\) 0 0
\(216\) 5.91828 0.402688
\(217\) 16.2832 1.10537
\(218\) −18.9496 −1.28343
\(219\) 15.0708 1.01839
\(220\) 0 0
\(221\) −22.5685 −1.51812
\(222\) −1.55293 −0.104226
\(223\) −15.5911 −1.04406 −0.522028 0.852928i \(-0.674824\pi\)
−0.522028 + 0.852928i \(0.674824\pi\)
\(224\) 10.3067 0.688647
\(225\) 0 0
\(226\) −23.3911 −1.55595
\(227\) −24.7410 −1.64212 −0.821059 0.570843i \(-0.806616\pi\)
−0.821059 + 0.570843i \(0.806616\pi\)
\(228\) −1.68698 −0.111723
\(229\) −21.0262 −1.38945 −0.694725 0.719275i \(-0.744474\pi\)
−0.694725 + 0.719275i \(0.744474\pi\)
\(230\) 0 0
\(231\) −6.62858 −0.436128
\(232\) −9.20893 −0.604596
\(233\) 8.57165 0.561548 0.280774 0.959774i \(-0.409409\pi\)
0.280774 + 0.959774i \(0.409409\pi\)
\(234\) 1.41774 0.0926809
\(235\) 0 0
\(236\) −14.1759 −0.922771
\(237\) 10.4006 0.675589
\(238\) 10.0560 0.651833
\(239\) 22.7072 1.46880 0.734402 0.678715i \(-0.237463\pi\)
0.734402 + 0.678715i \(0.237463\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 8.41801 0.541130
\(243\) −1.25507 −0.0805127
\(244\) −12.7316 −0.815059
\(245\) 0 0
\(246\) −27.9117 −1.77959
\(247\) 4.54465 0.289169
\(248\) 11.8128 0.750115
\(249\) 1.41775 0.0898460
\(250\) 0 0
\(251\) −12.9356 −0.816489 −0.408244 0.912873i \(-0.633859\pi\)
−0.408244 + 0.912873i \(0.633859\pi\)
\(252\) −0.259383 −0.0163396
\(253\) 4.22089 0.265365
\(254\) −2.16620 −0.135920
\(255\) 0 0
\(256\) 20.9790 1.31119
\(257\) 10.8510 0.676865 0.338432 0.940991i \(-0.390103\pi\)
0.338432 + 0.940991i \(0.390103\pi\)
\(258\) 4.70963 0.293209
\(259\) −0.765395 −0.0475593
\(260\) 0 0
\(261\) 0.995730 0.0616341
\(262\) −34.5527 −2.13467
\(263\) −14.1032 −0.869638 −0.434819 0.900518i \(-0.643188\pi\)
−0.434819 + 0.900518i \(0.643188\pi\)
\(264\) −4.80878 −0.295960
\(265\) 0 0
\(266\) −2.02499 −0.124160
\(267\) −3.85991 −0.236222
\(268\) −2.57838 −0.157500
\(269\) −7.55668 −0.460739 −0.230370 0.973103i \(-0.573993\pi\)
−0.230370 + 0.973103i \(0.573993\pi\)
\(270\) 0 0
\(271\) 20.9578 1.27309 0.636546 0.771238i \(-0.280362\pi\)
0.636546 + 0.771238i \(0.280362\pi\)
\(272\) 17.1696 1.04106
\(273\) −16.6484 −1.00761
\(274\) 9.28443 0.560893
\(275\) 0 0
\(276\) −3.93520 −0.236871
\(277\) 14.9632 0.899052 0.449526 0.893267i \(-0.351593\pi\)
0.449526 + 0.893267i \(0.351593\pi\)
\(278\) 0.417105 0.0250163
\(279\) −1.27728 −0.0764688
\(280\) 0 0
\(281\) 30.7490 1.83433 0.917165 0.398507i \(-0.130471\pi\)
0.917165 + 0.398507i \(0.130471\pi\)
\(282\) 21.7187 1.29333
\(283\) −4.06104 −0.241404 −0.120702 0.992689i \(-0.538515\pi\)
−0.120702 + 0.992689i \(0.538515\pi\)
\(284\) −13.2012 −0.783349
\(285\) 0 0
\(286\) −29.7499 −1.75915
\(287\) −13.7569 −0.812043
\(288\) −0.808478 −0.0476400
\(289\) −4.44326 −0.261368
\(290\) 0 0
\(291\) 12.8376 0.752551
\(292\) −12.3750 −0.724193
\(293\) 18.7249 1.09392 0.546961 0.837158i \(-0.315785\pi\)
0.546961 + 0.837158i \(0.315785\pi\)
\(294\) −14.4615 −0.843415
\(295\) 0 0
\(296\) −0.555266 −0.0322742
\(297\) 13.4282 0.779180
\(298\) 7.37828 0.427412
\(299\) 10.6012 0.613085
\(300\) 0 0
\(301\) 2.32124 0.133794
\(302\) 10.5566 0.607467
\(303\) 28.7310 1.65055
\(304\) −3.45747 −0.198300
\(305\) 0 0
\(306\) −0.788810 −0.0450933
\(307\) 2.41046 0.137572 0.0687860 0.997631i \(-0.478087\pi\)
0.0687860 + 0.997631i \(0.478087\pi\)
\(308\) 5.44289 0.310137
\(309\) −4.80624 −0.273418
\(310\) 0 0
\(311\) −16.0513 −0.910183 −0.455092 0.890445i \(-0.650394\pi\)
−0.455092 + 0.890445i \(0.650394\pi\)
\(312\) −12.0778 −0.683771
\(313\) −6.01435 −0.339951 −0.169976 0.985448i \(-0.554369\pi\)
−0.169976 + 0.985448i \(0.554369\pi\)
\(314\) −7.40958 −0.418147
\(315\) 0 0
\(316\) −8.54015 −0.480421
\(317\) −27.5411 −1.54686 −0.773430 0.633881i \(-0.781461\pi\)
−0.773430 + 0.633881i \(0.781461\pi\)
\(318\) −30.8689 −1.73104
\(319\) −20.8944 −1.16986
\(320\) 0 0
\(321\) −8.25476 −0.460736
\(322\) −4.72366 −0.263240
\(323\) −2.52857 −0.140693
\(324\) −12.0142 −0.667453
\(325\) 0 0
\(326\) 4.62370 0.256083
\(327\) −17.4551 −0.965268
\(328\) −9.98010 −0.551059
\(329\) 10.7045 0.590158
\(330\) 0 0
\(331\) 0.248029 0.0136329 0.00681645 0.999977i \(-0.497830\pi\)
0.00681645 + 0.999977i \(0.497830\pi\)
\(332\) −1.16415 −0.0638909
\(333\) 0.0600390 0.00329011
\(334\) 46.6187 2.55086
\(335\) 0 0
\(336\) 12.6658 0.690974
\(337\) 21.1908 1.15433 0.577167 0.816626i \(-0.304158\pi\)
0.577167 + 0.816626i \(0.304158\pi\)
\(338\) −50.7731 −2.76169
\(339\) −21.5463 −1.17023
\(340\) 0 0
\(341\) 26.8024 1.45143
\(342\) 0.158844 0.00858929
\(343\) −17.9115 −0.967132
\(344\) 1.68397 0.0907936
\(345\) 0 0
\(346\) −35.0722 −1.88549
\(347\) −17.9531 −0.963775 −0.481887 0.876233i \(-0.660049\pi\)
−0.481887 + 0.876233i \(0.660049\pi\)
\(348\) 19.4802 1.04425
\(349\) 7.68481 0.411358 0.205679 0.978619i \(-0.434060\pi\)
0.205679 + 0.978619i \(0.434060\pi\)
\(350\) 0 0
\(351\) 33.7263 1.80018
\(352\) 16.9651 0.904243
\(353\) −25.0052 −1.33089 −0.665446 0.746446i \(-0.731759\pi\)
−0.665446 + 0.746446i \(0.731759\pi\)
\(354\) −31.8018 −1.69025
\(355\) 0 0
\(356\) 3.16946 0.167981
\(357\) 9.26291 0.490245
\(358\) −22.7972 −1.20487
\(359\) 7.21328 0.380703 0.190351 0.981716i \(-0.439037\pi\)
0.190351 + 0.981716i \(0.439037\pi\)
\(360\) 0 0
\(361\) −18.4908 −0.973201
\(362\) −10.3668 −0.544867
\(363\) 7.75410 0.406985
\(364\) 13.6704 0.716525
\(365\) 0 0
\(366\) −28.5618 −1.49295
\(367\) −10.0531 −0.524767 −0.262383 0.964964i \(-0.584509\pi\)
−0.262383 + 0.964964i \(0.584509\pi\)
\(368\) −8.06520 −0.420428
\(369\) 1.07911 0.0561764
\(370\) 0 0
\(371\) −15.2144 −0.789891
\(372\) −24.9883 −1.29558
\(373\) −31.7029 −1.64151 −0.820756 0.571279i \(-0.806447\pi\)
−0.820756 + 0.571279i \(0.806447\pi\)
\(374\) 16.5524 0.855904
\(375\) 0 0
\(376\) 7.76571 0.400486
\(377\) −52.4786 −2.70278
\(378\) −15.0277 −0.772939
\(379\) −8.44277 −0.433676 −0.216838 0.976208i \(-0.569574\pi\)
−0.216838 + 0.976208i \(0.569574\pi\)
\(380\) 0 0
\(381\) −1.99536 −0.102225
\(382\) 29.4933 1.50901
\(383\) 9.65154 0.493171 0.246585 0.969121i \(-0.420691\pi\)
0.246585 + 0.969121i \(0.420691\pi\)
\(384\) 14.4729 0.738569
\(385\) 0 0
\(386\) 12.7487 0.648891
\(387\) −0.182082 −0.00925574
\(388\) −10.5412 −0.535151
\(389\) 23.9535 1.21449 0.607246 0.794514i \(-0.292274\pi\)
0.607246 + 0.794514i \(0.292274\pi\)
\(390\) 0 0
\(391\) −5.89836 −0.298293
\(392\) −5.17086 −0.261168
\(393\) −31.8276 −1.60549
\(394\) −7.51955 −0.378829
\(395\) 0 0
\(396\) −0.426950 −0.0214550
\(397\) 26.7766 1.34388 0.671940 0.740606i \(-0.265461\pi\)
0.671940 + 0.740606i \(0.265461\pi\)
\(398\) −13.3432 −0.668836
\(399\) −1.86528 −0.0933810
\(400\) 0 0
\(401\) −25.2168 −1.25927 −0.629635 0.776891i \(-0.716795\pi\)
−0.629635 + 0.776891i \(0.716795\pi\)
\(402\) −5.78426 −0.288493
\(403\) 67.3173 3.35331
\(404\) −23.5917 −1.17373
\(405\) 0 0
\(406\) 23.3832 1.16049
\(407\) −1.25986 −0.0624488
\(408\) 6.71989 0.332684
\(409\) −13.2389 −0.654619 −0.327310 0.944917i \(-0.606142\pi\)
−0.327310 + 0.944917i \(0.606142\pi\)
\(410\) 0 0
\(411\) 8.55219 0.421848
\(412\) 3.94652 0.194431
\(413\) −15.6742 −0.771275
\(414\) 0.370533 0.0182107
\(415\) 0 0
\(416\) 42.6097 2.08911
\(417\) 0.384209 0.0188148
\(418\) −3.33318 −0.163031
\(419\) −18.5429 −0.905880 −0.452940 0.891541i \(-0.649625\pi\)
−0.452940 + 0.891541i \(0.649625\pi\)
\(420\) 0 0
\(421\) −25.9339 −1.26394 −0.631972 0.774992i \(-0.717754\pi\)
−0.631972 + 0.774992i \(0.717754\pi\)
\(422\) −0.181794 −0.00884958
\(423\) −0.839680 −0.0408266
\(424\) −11.0375 −0.536026
\(425\) 0 0
\(426\) −29.6153 −1.43486
\(427\) −14.0773 −0.681246
\(428\) 6.77819 0.327636
\(429\) −27.4036 −1.32306
\(430\) 0 0
\(431\) 22.5328 1.08537 0.542683 0.839937i \(-0.317408\pi\)
0.542683 + 0.839937i \(0.317408\pi\)
\(432\) −25.6583 −1.23448
\(433\) 33.5776 1.61364 0.806818 0.590801i \(-0.201188\pi\)
0.806818 + 0.590801i \(0.201188\pi\)
\(434\) −29.9950 −1.43981
\(435\) 0 0
\(436\) 14.3328 0.686416
\(437\) 1.18776 0.0568182
\(438\) −27.7618 −1.32651
\(439\) −3.64200 −0.173823 −0.0869116 0.996216i \(-0.527700\pi\)
−0.0869116 + 0.996216i \(0.527700\pi\)
\(440\) 0 0
\(441\) 0.559107 0.0266242
\(442\) 41.5732 1.97743
\(443\) −27.0746 −1.28635 −0.643177 0.765718i \(-0.722384\pi\)
−0.643177 + 0.765718i \(0.722384\pi\)
\(444\) 1.17458 0.0557433
\(445\) 0 0
\(446\) 28.7202 1.35994
\(447\) 6.79637 0.321457
\(448\) −4.05698 −0.191674
\(449\) 40.1427 1.89445 0.947224 0.320571i \(-0.103875\pi\)
0.947224 + 0.320571i \(0.103875\pi\)
\(450\) 0 0
\(451\) −22.6441 −1.06627
\(452\) 17.6922 0.832170
\(453\) 9.72407 0.456877
\(454\) 45.5751 2.13895
\(455\) 0 0
\(456\) −1.35319 −0.0633691
\(457\) 22.3710 1.04647 0.523236 0.852188i \(-0.324725\pi\)
0.523236 + 0.852188i \(0.324725\pi\)
\(458\) 38.7321 1.80983
\(459\) −18.7648 −0.875864
\(460\) 0 0
\(461\) −31.3342 −1.45938 −0.729689 0.683780i \(-0.760335\pi\)
−0.729689 + 0.683780i \(0.760335\pi\)
\(462\) 12.2104 0.568080
\(463\) 9.21061 0.428053 0.214027 0.976828i \(-0.431342\pi\)
0.214027 + 0.976828i \(0.431342\pi\)
\(464\) 39.9246 1.85345
\(465\) 0 0
\(466\) −15.7897 −0.731446
\(467\) 1.38103 0.0639065 0.0319532 0.999489i \(-0.489827\pi\)
0.0319532 + 0.999489i \(0.489827\pi\)
\(468\) −1.07233 −0.0495686
\(469\) −2.85089 −0.131642
\(470\) 0 0
\(471\) −6.82520 −0.314489
\(472\) −11.3710 −0.523394
\(473\) 3.82081 0.175681
\(474\) −19.1587 −0.879990
\(475\) 0 0
\(476\) −7.60600 −0.348620
\(477\) 1.19344 0.0546440
\(478\) −41.8286 −1.91320
\(479\) 1.68759 0.0771080 0.0385540 0.999257i \(-0.487725\pi\)
0.0385540 + 0.999257i \(0.487725\pi\)
\(480\) 0 0
\(481\) −3.16427 −0.144278
\(482\) −1.84209 −0.0839048
\(483\) −4.35112 −0.197983
\(484\) −6.36709 −0.289413
\(485\) 0 0
\(486\) 2.31195 0.104872
\(487\) 32.1394 1.45638 0.728188 0.685377i \(-0.240363\pi\)
0.728188 + 0.685377i \(0.240363\pi\)
\(488\) −10.2125 −0.462299
\(489\) 4.25904 0.192600
\(490\) 0 0
\(491\) −36.6379 −1.65345 −0.826723 0.562608i \(-0.809798\pi\)
−0.826723 + 0.562608i \(0.809798\pi\)
\(492\) 21.1115 0.951778
\(493\) 29.1982 1.31502
\(494\) −8.37164 −0.376658
\(495\) 0 0
\(496\) −51.2136 −2.29956
\(497\) −14.5965 −0.654742
\(498\) −2.61161 −0.117029
\(499\) 38.2943 1.71429 0.857145 0.515076i \(-0.172236\pi\)
0.857145 + 0.515076i \(0.172236\pi\)
\(500\) 0 0
\(501\) 42.9420 1.91851
\(502\) 23.8285 1.06352
\(503\) 36.2174 1.61485 0.807427 0.589967i \(-0.200859\pi\)
0.807427 + 0.589967i \(0.200859\pi\)
\(504\) −0.208061 −0.00926777
\(505\) 0 0
\(506\) −7.77525 −0.345652
\(507\) −46.7688 −2.07707
\(508\) 1.63844 0.0726940
\(509\) 18.3681 0.814153 0.407076 0.913394i \(-0.366548\pi\)
0.407076 + 0.913394i \(0.366548\pi\)
\(510\) 0 0
\(511\) −13.6830 −0.605298
\(512\) −21.5862 −0.953985
\(513\) 3.77869 0.166833
\(514\) −19.9885 −0.881653
\(515\) 0 0
\(516\) −3.56220 −0.156817
\(517\) 17.6198 0.774920
\(518\) 1.40993 0.0619486
\(519\) −32.3062 −1.41808
\(520\) 0 0
\(521\) −37.0378 −1.62265 −0.811327 0.584593i \(-0.801254\pi\)
−0.811327 + 0.584593i \(0.801254\pi\)
\(522\) −1.83422 −0.0802817
\(523\) −20.9663 −0.916791 −0.458395 0.888748i \(-0.651576\pi\)
−0.458395 + 0.888748i \(0.651576\pi\)
\(524\) 26.1344 1.14169
\(525\) 0 0
\(526\) 25.9793 1.13275
\(527\) −37.4543 −1.63153
\(528\) 20.8481 0.907298
\(529\) −20.2293 −0.879536
\(530\) 0 0
\(531\) 1.22951 0.0533561
\(532\) 1.53163 0.0664046
\(533\) −56.8732 −2.46345
\(534\) 7.11029 0.307692
\(535\) 0 0
\(536\) −2.06822 −0.0893334
\(537\) −20.9993 −0.906185
\(538\) 13.9201 0.600137
\(539\) −11.7323 −0.505346
\(540\) 0 0
\(541\) 9.75202 0.419272 0.209636 0.977779i \(-0.432772\pi\)
0.209636 + 0.977779i \(0.432772\pi\)
\(542\) −38.6060 −1.65827
\(543\) −9.54920 −0.409795
\(544\) −23.7074 −1.01645
\(545\) 0 0
\(546\) 30.6678 1.31246
\(547\) −30.8874 −1.32065 −0.660326 0.750979i \(-0.729582\pi\)
−0.660326 + 0.750979i \(0.729582\pi\)
\(548\) −7.02241 −0.299983
\(549\) 1.10424 0.0471280
\(550\) 0 0
\(551\) −5.87969 −0.250483
\(552\) −3.15658 −0.134353
\(553\) −9.44278 −0.401548
\(554\) −27.5636 −1.17106
\(555\) 0 0
\(556\) −0.315483 −0.0133795
\(557\) −25.1804 −1.06693 −0.533463 0.845823i \(-0.679110\pi\)
−0.533463 + 0.845823i \(0.679110\pi\)
\(558\) 2.35286 0.0996047
\(559\) 9.59638 0.405884
\(560\) 0 0
\(561\) 15.2469 0.643726
\(562\) −56.6424 −2.38931
\(563\) −37.8072 −1.59338 −0.796692 0.604386i \(-0.793419\pi\)
−0.796692 + 0.604386i \(0.793419\pi\)
\(564\) −16.4272 −0.691712
\(565\) 0 0
\(566\) 7.48080 0.314441
\(567\) −13.2840 −0.557874
\(568\) −10.5892 −0.444313
\(569\) −9.89011 −0.414615 −0.207307 0.978276i \(-0.566470\pi\)
−0.207307 + 0.978276i \(0.566470\pi\)
\(570\) 0 0
\(571\) −20.8124 −0.870972 −0.435486 0.900196i \(-0.643423\pi\)
−0.435486 + 0.900196i \(0.643423\pi\)
\(572\) 22.5018 0.940848
\(573\) 27.1673 1.13493
\(574\) 25.3414 1.05773
\(575\) 0 0
\(576\) 0.318237 0.0132599
\(577\) −22.7214 −0.945906 −0.472953 0.881088i \(-0.656812\pi\)
−0.472953 + 0.881088i \(0.656812\pi\)
\(578\) 8.18487 0.340446
\(579\) 11.7432 0.488032
\(580\) 0 0
\(581\) −1.28719 −0.0534016
\(582\) −23.6479 −0.980238
\(583\) −25.0432 −1.03718
\(584\) −9.92647 −0.410760
\(585\) 0 0
\(586\) −34.4930 −1.42489
\(587\) −26.2568 −1.08373 −0.541866 0.840465i \(-0.682282\pi\)
−0.541866 + 0.840465i \(0.682282\pi\)
\(588\) 10.9382 0.451084
\(589\) 7.54222 0.310772
\(590\) 0 0
\(591\) −6.92650 −0.284918
\(592\) 2.40731 0.0989399
\(593\) 16.3255 0.670406 0.335203 0.942146i \(-0.391195\pi\)
0.335203 + 0.942146i \(0.391195\pi\)
\(594\) −24.7358 −1.01492
\(595\) 0 0
\(596\) −5.58067 −0.228593
\(597\) −12.2909 −0.503032
\(598\) −19.5284 −0.798576
\(599\) −45.7396 −1.86887 −0.934436 0.356132i \(-0.884095\pi\)
−0.934436 + 0.356132i \(0.884095\pi\)
\(600\) 0 0
\(601\) −17.3734 −0.708676 −0.354338 0.935117i \(-0.615294\pi\)
−0.354338 + 0.935117i \(0.615294\pi\)
\(602\) −4.27592 −0.174274
\(603\) 0.223629 0.00910688
\(604\) −7.98467 −0.324892
\(605\) 0 0
\(606\) −52.9250 −2.14993
\(607\) −4.48838 −0.182178 −0.0910890 0.995843i \(-0.529035\pi\)
−0.0910890 + 0.995843i \(0.529035\pi\)
\(608\) 4.77399 0.193611
\(609\) 21.5391 0.872807
\(610\) 0 0
\(611\) 44.2542 1.79033
\(612\) 0.596628 0.0241173
\(613\) 29.9448 1.20946 0.604730 0.796430i \(-0.293281\pi\)
0.604730 + 0.796430i \(0.293281\pi\)
\(614\) −4.44028 −0.179195
\(615\) 0 0
\(616\) 4.36595 0.175909
\(617\) 48.0028 1.93252 0.966261 0.257566i \(-0.0829205\pi\)
0.966261 + 0.257566i \(0.0829205\pi\)
\(618\) 8.85352 0.356141
\(619\) −6.70266 −0.269403 −0.134701 0.990886i \(-0.543008\pi\)
−0.134701 + 0.990886i \(0.543008\pi\)
\(620\) 0 0
\(621\) 8.81449 0.353713
\(622\) 29.5678 1.18556
\(623\) 3.50445 0.140403
\(624\) 52.3624 2.09617
\(625\) 0 0
\(626\) 11.0790 0.442805
\(627\) −3.07030 −0.122616
\(628\) 5.60434 0.223638
\(629\) 1.76055 0.0701977
\(630\) 0 0
\(631\) −7.36072 −0.293025 −0.146513 0.989209i \(-0.546805\pi\)
−0.146513 + 0.989209i \(0.546805\pi\)
\(632\) −6.85039 −0.272494
\(633\) −0.167456 −0.00665579
\(634\) 50.7331 2.01487
\(635\) 0 0
\(636\) 23.3481 0.925814
\(637\) −29.4670 −1.16752
\(638\) 38.4893 1.52381
\(639\) 1.14497 0.0452945
\(640\) 0 0
\(641\) −37.1888 −1.46887 −0.734434 0.678680i \(-0.762552\pi\)
−0.734434 + 0.678680i \(0.762552\pi\)
\(642\) 15.2060 0.600133
\(643\) −27.0935 −1.06846 −0.534232 0.845338i \(-0.679399\pi\)
−0.534232 + 0.845338i \(0.679399\pi\)
\(644\) 3.57281 0.140789
\(645\) 0 0
\(646\) 4.65785 0.183261
\(647\) −16.1175 −0.633646 −0.316823 0.948485i \(-0.602616\pi\)
−0.316823 + 0.948485i \(0.602616\pi\)
\(648\) −9.63702 −0.378578
\(649\) −25.8000 −1.01274
\(650\) 0 0
\(651\) −27.6294 −1.08288
\(652\) −3.49720 −0.136961
\(653\) 11.7529 0.459928 0.229964 0.973199i \(-0.426139\pi\)
0.229964 + 0.973199i \(0.426139\pi\)
\(654\) 32.1538 1.25731
\(655\) 0 0
\(656\) 43.2680 1.68933
\(657\) 1.07331 0.0418740
\(658\) −19.7186 −0.768713
\(659\) −12.7347 −0.496075 −0.248038 0.968750i \(-0.579786\pi\)
−0.248038 + 0.968750i \(0.579786\pi\)
\(660\) 0 0
\(661\) −2.32682 −0.0905028 −0.0452514 0.998976i \(-0.514409\pi\)
−0.0452514 + 0.998976i \(0.514409\pi\)
\(662\) −0.456891 −0.0177576
\(663\) 38.2944 1.48723
\(664\) −0.933807 −0.0362387
\(665\) 0 0
\(666\) −0.110597 −0.00428555
\(667\) −13.7155 −0.531065
\(668\) −35.2607 −1.36428
\(669\) 26.4551 1.02281
\(670\) 0 0
\(671\) −23.1715 −0.894525
\(672\) −17.4885 −0.674635
\(673\) −21.2017 −0.817267 −0.408633 0.912699i \(-0.633995\pi\)
−0.408633 + 0.912699i \(0.633995\pi\)
\(674\) −39.0353 −1.50358
\(675\) 0 0
\(676\) 38.4030 1.47704
\(677\) −51.8603 −1.99315 −0.996576 0.0826794i \(-0.973652\pi\)
−0.996576 + 0.0826794i \(0.973652\pi\)
\(678\) 39.6902 1.52429
\(679\) −11.6554 −0.447292
\(680\) 0 0
\(681\) 41.9807 1.60870
\(682\) −49.3725 −1.89057
\(683\) −22.4656 −0.859621 −0.429811 0.902919i \(-0.641420\pi\)
−0.429811 + 0.902919i \(0.641420\pi\)
\(684\) −0.120144 −0.00459381
\(685\) 0 0
\(686\) 32.9946 1.25974
\(687\) 35.6774 1.36118
\(688\) −7.30073 −0.278338
\(689\) −62.8987 −2.39625
\(690\) 0 0
\(691\) 51.2504 1.94966 0.974829 0.222953i \(-0.0715698\pi\)
0.974829 + 0.222953i \(0.0715698\pi\)
\(692\) 26.5274 1.00842
\(693\) −0.472075 −0.0179327
\(694\) 33.0713 1.25537
\(695\) 0 0
\(696\) 15.6258 0.592294
\(697\) 31.6433 1.19858
\(698\) −14.1561 −0.535816
\(699\) −14.5444 −0.550121
\(700\) 0 0
\(701\) 0.425393 0.0160669 0.00803344 0.999968i \(-0.497443\pi\)
0.00803344 + 0.999968i \(0.497443\pi\)
\(702\) −62.1268 −2.34483
\(703\) −0.354524 −0.0133711
\(704\) −6.67788 −0.251682
\(705\) 0 0
\(706\) 46.0618 1.73356
\(707\) −26.0852 −0.981035
\(708\) 24.0537 0.903995
\(709\) −15.9902 −0.600523 −0.300261 0.953857i \(-0.597074\pi\)
−0.300261 + 0.953857i \(0.597074\pi\)
\(710\) 0 0
\(711\) 0.740709 0.0277787
\(712\) 2.54235 0.0952785
\(713\) 17.5936 0.658886
\(714\) −17.0631 −0.638570
\(715\) 0 0
\(716\) 17.2430 0.644402
\(717\) −38.5297 −1.43892
\(718\) −13.2875 −0.495885
\(719\) −26.2235 −0.977973 −0.488986 0.872291i \(-0.662633\pi\)
−0.488986 + 0.872291i \(0.662633\pi\)
\(720\) 0 0
\(721\) 4.36364 0.162510
\(722\) 34.0617 1.26765
\(723\) −1.69681 −0.0631050
\(724\) 7.84108 0.291412
\(725\) 0 0
\(726\) −14.2837 −0.530120
\(727\) 25.2570 0.936730 0.468365 0.883535i \(-0.344843\pi\)
0.468365 + 0.883535i \(0.344843\pi\)
\(728\) 10.9656 0.406411
\(729\) 27.9982 1.03697
\(730\) 0 0
\(731\) −5.33927 −0.197480
\(732\) 21.6031 0.798474
\(733\) −8.92252 −0.329561 −0.164780 0.986330i \(-0.552692\pi\)
−0.164780 + 0.986330i \(0.552692\pi\)
\(734\) 18.5187 0.683537
\(735\) 0 0
\(736\) 11.1362 0.410486
\(737\) −4.69263 −0.172855
\(738\) −1.98782 −0.0731728
\(739\) −14.2439 −0.523970 −0.261985 0.965072i \(-0.584377\pi\)
−0.261985 + 0.965072i \(0.584377\pi\)
\(740\) 0 0
\(741\) −7.71139 −0.283285
\(742\) 28.0262 1.02887
\(743\) −14.9854 −0.549762 −0.274881 0.961478i \(-0.588638\pi\)
−0.274881 + 0.961478i \(0.588638\pi\)
\(744\) −20.0441 −0.734852
\(745\) 0 0
\(746\) 58.3995 2.13816
\(747\) 0.100969 0.00369427
\(748\) −12.5196 −0.457763
\(749\) 7.49459 0.273847
\(750\) 0 0
\(751\) −29.1216 −1.06266 −0.531330 0.847165i \(-0.678308\pi\)
−0.531330 + 0.847165i \(0.678308\pi\)
\(752\) −33.6677 −1.22773
\(753\) 21.9492 0.799875
\(754\) 96.6702 3.52052
\(755\) 0 0
\(756\) 11.3664 0.413392
\(757\) 29.9865 1.08988 0.544940 0.838475i \(-0.316553\pi\)
0.544940 + 0.838475i \(0.316553\pi\)
\(758\) 15.5523 0.564886
\(759\) −7.16204 −0.259966
\(760\) 0 0
\(761\) 2.01232 0.0729466 0.0364733 0.999335i \(-0.488388\pi\)
0.0364733 + 0.999335i \(0.488388\pi\)
\(762\) 3.67563 0.133154
\(763\) 15.8477 0.573724
\(764\) −22.3077 −0.807065
\(765\) 0 0
\(766\) −17.7790 −0.642381
\(767\) −64.7996 −2.33978
\(768\) −35.5974 −1.28451
\(769\) 46.1301 1.66350 0.831748 0.555154i \(-0.187341\pi\)
0.831748 + 0.555154i \(0.187341\pi\)
\(770\) 0 0
\(771\) −18.4120 −0.663092
\(772\) −9.64266 −0.347047
\(773\) 48.0505 1.72826 0.864128 0.503272i \(-0.167870\pi\)
0.864128 + 0.503272i \(0.167870\pi\)
\(774\) 0.335411 0.0120561
\(775\) 0 0
\(776\) −8.45554 −0.303536
\(777\) 1.29873 0.0465916
\(778\) −44.1245 −1.58194
\(779\) −6.37206 −0.228303
\(780\) 0 0
\(781\) −24.0261 −0.859723
\(782\) 10.8653 0.388542
\(783\) −43.6338 −1.55934
\(784\) 22.4179 0.800638
\(785\) 0 0
\(786\) 58.6292 2.09124
\(787\) 36.3244 1.29482 0.647412 0.762140i \(-0.275851\pi\)
0.647412 + 0.762140i \(0.275851\pi\)
\(788\) 5.68752 0.202610
\(789\) 23.9303 0.851943
\(790\) 0 0
\(791\) 19.5621 0.695548
\(792\) −0.342473 −0.0121692
\(793\) −58.1977 −2.06666
\(794\) −49.3249 −1.75048
\(795\) 0 0
\(796\) 10.0923 0.357714
\(797\) 36.6218 1.29721 0.648606 0.761124i \(-0.275352\pi\)
0.648606 + 0.761124i \(0.275352\pi\)
\(798\) 3.43602 0.121634
\(799\) −24.6223 −0.871075
\(800\) 0 0
\(801\) −0.274895 −0.00971295
\(802\) 46.4517 1.64027
\(803\) −22.5224 −0.794799
\(804\) 4.37501 0.154295
\(805\) 0 0
\(806\) −124.004 −4.36787
\(807\) 12.8222 0.451364
\(808\) −18.9238 −0.665738
\(809\) −34.5599 −1.21506 −0.607530 0.794297i \(-0.707840\pi\)
−0.607530 + 0.794297i \(0.707840\pi\)
\(810\) 0 0
\(811\) −17.3270 −0.608435 −0.304217 0.952603i \(-0.598395\pi\)
−0.304217 + 0.952603i \(0.598395\pi\)
\(812\) −17.6863 −0.620666
\(813\) −35.5613 −1.24719
\(814\) 2.32077 0.0813429
\(815\) 0 0
\(816\) −29.1336 −1.01988
\(817\) 1.07518 0.0376156
\(818\) 24.3871 0.852677
\(819\) −1.18567 −0.0414306
\(820\) 0 0
\(821\) 13.5004 0.471169 0.235584 0.971854i \(-0.424300\pi\)
0.235584 + 0.971854i \(0.424300\pi\)
\(822\) −15.7539 −0.549480
\(823\) 46.7783 1.63059 0.815295 0.579046i \(-0.196575\pi\)
0.815295 + 0.579046i \(0.196575\pi\)
\(824\) 3.16566 0.110281
\(825\) 0 0
\(826\) 28.8732 1.00463
\(827\) 44.0656 1.53231 0.766155 0.642656i \(-0.222167\pi\)
0.766155 + 0.642656i \(0.222167\pi\)
\(828\) −0.280258 −0.00973963
\(829\) −4.27440 −0.148456 −0.0742280 0.997241i \(-0.523649\pi\)
−0.0742280 + 0.997241i \(0.523649\pi\)
\(830\) 0 0
\(831\) −25.3897 −0.880759
\(832\) −16.7722 −0.581473
\(833\) 16.3950 0.568051
\(834\) −0.707746 −0.0245073
\(835\) 0 0
\(836\) 2.52110 0.0871940
\(837\) 55.9716 1.93466
\(838\) 34.1577 1.17996
\(839\) −31.6115 −1.09135 −0.545675 0.837997i \(-0.683727\pi\)
−0.545675 + 0.837997i \(0.683727\pi\)
\(840\) 0 0
\(841\) 38.8947 1.34120
\(842\) 47.7726 1.64635
\(843\) −52.1751 −1.79701
\(844\) 0.137502 0.00473303
\(845\) 0 0
\(846\) 1.54677 0.0531789
\(847\) −7.04004 −0.241899
\(848\) 47.8521 1.64325
\(849\) 6.89080 0.236492
\(850\) 0 0
\(851\) −0.826993 −0.0283490
\(852\) 22.3999 0.767409
\(853\) 5.03330 0.172337 0.0861684 0.996281i \(-0.472538\pi\)
0.0861684 + 0.996281i \(0.472538\pi\)
\(854\) 25.9316 0.887359
\(855\) 0 0
\(856\) 5.43705 0.185834
\(857\) 17.8339 0.609195 0.304598 0.952481i \(-0.401478\pi\)
0.304598 + 0.952481i \(0.401478\pi\)
\(858\) 50.4799 1.72336
\(859\) 29.9247 1.02102 0.510509 0.859873i \(-0.329457\pi\)
0.510509 + 0.859873i \(0.329457\pi\)
\(860\) 0 0
\(861\) 23.3428 0.795519
\(862\) −41.5074 −1.41375
\(863\) 21.1041 0.718392 0.359196 0.933262i \(-0.383051\pi\)
0.359196 + 0.933262i \(0.383051\pi\)
\(864\) 35.4282 1.20529
\(865\) 0 0
\(866\) −61.8529 −2.10185
\(867\) 7.53935 0.256050
\(868\) 22.6872 0.770053
\(869\) −15.5430 −0.527261
\(870\) 0 0
\(871\) −11.7861 −0.399356
\(872\) 11.4969 0.389334
\(873\) 0.914268 0.0309433
\(874\) −2.18796 −0.0740088
\(875\) 0 0
\(876\) 20.9980 0.709457
\(877\) −12.0202 −0.405892 −0.202946 0.979190i \(-0.565052\pi\)
−0.202946 + 0.979190i \(0.565052\pi\)
\(878\) 6.70889 0.226414
\(879\) −31.7726 −1.07166
\(880\) 0 0
\(881\) −15.0651 −0.507556 −0.253778 0.967263i \(-0.581673\pi\)
−0.253778 + 0.967263i \(0.581673\pi\)
\(882\) −1.02993 −0.0346794
\(883\) 3.17468 0.106836 0.0534182 0.998572i \(-0.482988\pi\)
0.0534182 + 0.998572i \(0.482988\pi\)
\(884\) −31.4445 −1.05759
\(885\) 0 0
\(886\) 49.8738 1.67554
\(887\) 33.6952 1.13137 0.565687 0.824620i \(-0.308611\pi\)
0.565687 + 0.824620i \(0.308611\pi\)
\(888\) 0.942179 0.0316175
\(889\) 1.81161 0.0607594
\(890\) 0 0
\(891\) −21.8657 −0.732528
\(892\) −21.7229 −0.727337
\(893\) 4.95823 0.165921
\(894\) −12.5195 −0.418715
\(895\) 0 0
\(896\) −13.1401 −0.438981
\(897\) −17.9883 −0.600610
\(898\) −73.9463 −2.46762
\(899\) −87.0925 −2.90470
\(900\) 0 0
\(901\) 34.9958 1.16588
\(902\) 41.7125 1.38887
\(903\) −3.93869 −0.131071
\(904\) 14.1916 0.472005
\(905\) 0 0
\(906\) −17.9126 −0.595106
\(907\) −15.5495 −0.516311 −0.258156 0.966103i \(-0.583115\pi\)
−0.258156 + 0.966103i \(0.583115\pi\)
\(908\) −34.4714 −1.14397
\(909\) 2.04617 0.0678671
\(910\) 0 0
\(911\) 47.4791 1.57305 0.786527 0.617556i \(-0.211877\pi\)
0.786527 + 0.617556i \(0.211877\pi\)
\(912\) 5.86667 0.194265
\(913\) −2.11874 −0.0701200
\(914\) −41.2094 −1.36309
\(915\) 0 0
\(916\) −29.2956 −0.967954
\(917\) 28.8966 0.954251
\(918\) 34.5664 1.14086
\(919\) −43.8093 −1.44514 −0.722568 0.691299i \(-0.757039\pi\)
−0.722568 + 0.691299i \(0.757039\pi\)
\(920\) 0 0
\(921\) −4.09008 −0.134773
\(922\) 57.7203 1.90092
\(923\) −60.3443 −1.98626
\(924\) −9.23554 −0.303827
\(925\) 0 0
\(926\) −16.9668 −0.557562
\(927\) −0.342292 −0.0112423
\(928\) −55.1268 −1.80963
\(929\) −23.2341 −0.762285 −0.381143 0.924516i \(-0.624469\pi\)
−0.381143 + 0.924516i \(0.624469\pi\)
\(930\) 0 0
\(931\) −3.30147 −0.108201
\(932\) 11.9428 0.391200
\(933\) 27.2359 0.891663
\(934\) −2.54398 −0.0832416
\(935\) 0 0
\(936\) −0.860159 −0.0281152
\(937\) −26.0794 −0.851975 −0.425988 0.904729i \(-0.640073\pi\)
−0.425988 + 0.904729i \(0.640073\pi\)
\(938\) 5.25160 0.171471
\(939\) 10.2052 0.333034
\(940\) 0 0
\(941\) −23.0611 −0.751771 −0.375885 0.926666i \(-0.622661\pi\)
−0.375885 + 0.926666i \(0.622661\pi\)
\(942\) 12.5726 0.409638
\(943\) −14.8640 −0.484039
\(944\) 49.2982 1.60452
\(945\) 0 0
\(946\) −7.03826 −0.228834
\(947\) 37.2266 1.20970 0.604851 0.796339i \(-0.293233\pi\)
0.604851 + 0.796339i \(0.293233\pi\)
\(948\) 14.4910 0.470646
\(949\) −56.5676 −1.83626
\(950\) 0 0
\(951\) 46.7319 1.51539
\(952\) −6.10107 −0.197737
\(953\) −23.0528 −0.746753 −0.373377 0.927680i \(-0.621800\pi\)
−0.373377 + 0.927680i \(0.621800\pi\)
\(954\) −2.19843 −0.0711767
\(955\) 0 0
\(956\) 31.6377 1.02324
\(957\) 35.4538 1.14606
\(958\) −3.10869 −0.100437
\(959\) −7.76463 −0.250733
\(960\) 0 0
\(961\) 80.7187 2.60383
\(962\) 5.82887 0.187930
\(963\) −0.587889 −0.0189445
\(964\) 1.39329 0.0448749
\(965\) 0 0
\(966\) 8.01515 0.257883
\(967\) 29.7340 0.956181 0.478090 0.878311i \(-0.341329\pi\)
0.478090 + 0.878311i \(0.341329\pi\)
\(968\) −5.10729 −0.164154
\(969\) 4.29049 0.137831
\(970\) 0 0
\(971\) −16.0126 −0.513868 −0.256934 0.966429i \(-0.582712\pi\)
−0.256934 + 0.966429i \(0.582712\pi\)
\(972\) −1.74868 −0.0560888
\(973\) −0.348827 −0.0111829
\(974\) −59.2037 −1.89701
\(975\) 0 0
\(976\) 44.2756 1.41723
\(977\) 16.8004 0.537493 0.268747 0.963211i \(-0.413391\pi\)
0.268747 + 0.963211i \(0.413391\pi\)
\(978\) −7.84553 −0.250872
\(979\) 5.76840 0.184359
\(980\) 0 0
\(981\) −1.24312 −0.0396897
\(982\) 67.4903 2.15370
\(983\) −19.1223 −0.609908 −0.304954 0.952367i \(-0.598641\pi\)
−0.304954 + 0.952367i \(0.598641\pi\)
\(984\) 16.9343 0.539846
\(985\) 0 0
\(986\) −53.7857 −1.71289
\(987\) −18.1635 −0.578150
\(988\) 6.33202 0.201448
\(989\) 2.50805 0.0797513
\(990\) 0 0
\(991\) −10.1892 −0.323670 −0.161835 0.986818i \(-0.551741\pi\)
−0.161835 + 0.986818i \(0.551741\pi\)
\(992\) 70.7144 2.24518
\(993\) −0.420857 −0.0133555
\(994\) 26.8880 0.852837
\(995\) 0 0
\(996\) 1.97533 0.0625908
\(997\) −16.0609 −0.508652 −0.254326 0.967118i \(-0.581854\pi\)
−0.254326 + 0.967118i \(0.581854\pi\)
\(998\) −70.5415 −2.23295
\(999\) −2.63096 −0.0832399
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.1.9 46
5.2 odd 4 1205.2.b.c.724.9 46
5.3 odd 4 1205.2.b.c.724.38 yes 46
5.4 even 2 inner 6025.2.a.p.1.38 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.9 46 5.2 odd 4
1205.2.b.c.724.38 yes 46 5.3 odd 4
6025.2.a.p.1.9 46 1.1 even 1 trivial
6025.2.a.p.1.38 46 5.4 even 2 inner