Properties

Label 3549.2.a.bh.1.10
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $15$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Defining polynomial: \(x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + 4553 x^{7} - 6393 x^{6} - 6785 x^{5} + 7806 x^{4} + 4632 x^{3} - 3811 x^{2} - 1041 x + 281\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(1.09372\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.09372 q^{2} +1.00000 q^{3} -0.803784 q^{4} +3.36980 q^{5} +1.09372 q^{6} -1.00000 q^{7} -3.06655 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.09372 q^{2} +1.00000 q^{3} -0.803784 q^{4} +3.36980 q^{5} +1.09372 q^{6} -1.00000 q^{7} -3.06655 q^{8} +1.00000 q^{9} +3.68561 q^{10} +0.408118 q^{11} -0.803784 q^{12} -1.09372 q^{14} +3.36980 q^{15} -1.74636 q^{16} +0.412077 q^{17} +1.09372 q^{18} -1.06384 q^{19} -2.70859 q^{20} -1.00000 q^{21} +0.446365 q^{22} +8.83682 q^{23} -3.06655 q^{24} +6.35555 q^{25} +1.00000 q^{27} +0.803784 q^{28} -3.54528 q^{29} +3.68561 q^{30} +1.89809 q^{31} +4.22306 q^{32} +0.408118 q^{33} +0.450696 q^{34} -3.36980 q^{35} -0.803784 q^{36} +4.79988 q^{37} -1.16354 q^{38} -10.3336 q^{40} +10.0404 q^{41} -1.09372 q^{42} -2.32877 q^{43} -0.328038 q^{44} +3.36980 q^{45} +9.66498 q^{46} +8.84728 q^{47} -1.74636 q^{48} +1.00000 q^{49} +6.95117 q^{50} +0.412077 q^{51} -4.18910 q^{53} +1.09372 q^{54} +1.37527 q^{55} +3.06655 q^{56} -1.06384 q^{57} -3.87753 q^{58} -11.4506 q^{59} -2.70859 q^{60} +11.6354 q^{61} +2.07598 q^{62} -1.00000 q^{63} +8.11156 q^{64} +0.446365 q^{66} +2.39553 q^{67} -0.331221 q^{68} +8.83682 q^{69} -3.68561 q^{70} +14.6773 q^{71} -3.06655 q^{72} -14.5666 q^{73} +5.24970 q^{74} +6.35555 q^{75} +0.855097 q^{76} -0.408118 q^{77} +4.27789 q^{79} -5.88489 q^{80} +1.00000 q^{81} +10.9814 q^{82} -4.60644 q^{83} +0.803784 q^{84} +1.38862 q^{85} -2.54702 q^{86} -3.54528 q^{87} -1.25151 q^{88} +14.3179 q^{89} +3.68561 q^{90} -7.10290 q^{92} +1.89809 q^{93} +9.67642 q^{94} -3.58493 q^{95} +4.22306 q^{96} -12.3236 q^{97} +1.09372 q^{98} +0.408118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09372 0.773374 0.386687 0.922211i \(-0.373619\pi\)
0.386687 + 0.922211i \(0.373619\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.803784 −0.401892
\(5\) 3.36980 1.50702 0.753510 0.657436i \(-0.228359\pi\)
0.753510 + 0.657436i \(0.228359\pi\)
\(6\) 1.09372 0.446508
\(7\) −1.00000 −0.377964
\(8\) −3.06655 −1.08419
\(9\) 1.00000 0.333333
\(10\) 3.68561 1.16549
\(11\) 0.408118 0.123052 0.0615260 0.998105i \(-0.480403\pi\)
0.0615260 + 0.998105i \(0.480403\pi\)
\(12\) −0.803784 −0.232032
\(13\) 0 0
\(14\) −1.09372 −0.292308
\(15\) 3.36980 0.870079
\(16\) −1.74636 −0.436591
\(17\) 0.412077 0.0999434 0.0499717 0.998751i \(-0.484087\pi\)
0.0499717 + 0.998751i \(0.484087\pi\)
\(18\) 1.09372 0.257791
\(19\) −1.06384 −0.244062 −0.122031 0.992526i \(-0.538941\pi\)
−0.122031 + 0.992526i \(0.538941\pi\)
\(20\) −2.70859 −0.605659
\(21\) −1.00000 −0.218218
\(22\) 0.446365 0.0951653
\(23\) 8.83682 1.84260 0.921302 0.388847i \(-0.127126\pi\)
0.921302 + 0.388847i \(0.127126\pi\)
\(24\) −3.06655 −0.625956
\(25\) 6.35555 1.27111
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0.803784 0.151901
\(29\) −3.54528 −0.658341 −0.329171 0.944270i \(-0.606769\pi\)
−0.329171 + 0.944270i \(0.606769\pi\)
\(30\) 3.68561 0.672896
\(31\) 1.89809 0.340908 0.170454 0.985366i \(-0.445477\pi\)
0.170454 + 0.985366i \(0.445477\pi\)
\(32\) 4.22306 0.746539
\(33\) 0.408118 0.0710441
\(34\) 0.450696 0.0772937
\(35\) −3.36980 −0.569600
\(36\) −0.803784 −0.133964
\(37\) 4.79988 0.789095 0.394547 0.918876i \(-0.370901\pi\)
0.394547 + 0.918876i \(0.370901\pi\)
\(38\) −1.16354 −0.188751
\(39\) 0 0
\(40\) −10.3336 −1.63389
\(41\) 10.0404 1.56805 0.784025 0.620729i \(-0.213163\pi\)
0.784025 + 0.620729i \(0.213163\pi\)
\(42\) −1.09372 −0.168764
\(43\) −2.32877 −0.355135 −0.177567 0.984109i \(-0.556823\pi\)
−0.177567 + 0.984109i \(0.556823\pi\)
\(44\) −0.328038 −0.0494536
\(45\) 3.36980 0.502340
\(46\) 9.66498 1.42502
\(47\) 8.84728 1.29051 0.645254 0.763968i \(-0.276751\pi\)
0.645254 + 0.763968i \(0.276751\pi\)
\(48\) −1.74636 −0.252066
\(49\) 1.00000 0.142857
\(50\) 6.95117 0.983044
\(51\) 0.412077 0.0577024
\(52\) 0 0
\(53\) −4.18910 −0.575418 −0.287709 0.957718i \(-0.592894\pi\)
−0.287709 + 0.957718i \(0.592894\pi\)
\(54\) 1.09372 0.148836
\(55\) 1.37527 0.185442
\(56\) 3.06655 0.409784
\(57\) −1.06384 −0.140909
\(58\) −3.87753 −0.509144
\(59\) −11.4506 −1.49074 −0.745369 0.666652i \(-0.767727\pi\)
−0.745369 + 0.666652i \(0.767727\pi\)
\(60\) −2.70859 −0.349678
\(61\) 11.6354 1.48976 0.744880 0.667199i \(-0.232507\pi\)
0.744880 + 0.667199i \(0.232507\pi\)
\(62\) 2.07598 0.263649
\(63\) −1.00000 −0.125988
\(64\) 8.11156 1.01395
\(65\) 0 0
\(66\) 0.446365 0.0549437
\(67\) 2.39553 0.292661 0.146330 0.989236i \(-0.453254\pi\)
0.146330 + 0.989236i \(0.453254\pi\)
\(68\) −0.331221 −0.0401665
\(69\) 8.83682 1.06383
\(70\) −3.68561 −0.440514
\(71\) 14.6773 1.74188 0.870939 0.491391i \(-0.163511\pi\)
0.870939 + 0.491391i \(0.163511\pi\)
\(72\) −3.06655 −0.361396
\(73\) −14.5666 −1.70489 −0.852447 0.522814i \(-0.824882\pi\)
−0.852447 + 0.522814i \(0.824882\pi\)
\(74\) 5.24970 0.610266
\(75\) 6.35555 0.733876
\(76\) 0.855097 0.0980864
\(77\) −0.408118 −0.0465093
\(78\) 0 0
\(79\) 4.27789 0.481300 0.240650 0.970612i \(-0.422639\pi\)
0.240650 + 0.970612i \(0.422639\pi\)
\(80\) −5.88489 −0.657951
\(81\) 1.00000 0.111111
\(82\) 10.9814 1.21269
\(83\) −4.60644 −0.505623 −0.252811 0.967516i \(-0.581355\pi\)
−0.252811 + 0.967516i \(0.581355\pi\)
\(84\) 0.803784 0.0877000
\(85\) 1.38862 0.150617
\(86\) −2.54702 −0.274652
\(87\) −3.54528 −0.380093
\(88\) −1.25151 −0.133411
\(89\) 14.3179 1.51769 0.758846 0.651271i \(-0.225764\pi\)
0.758846 + 0.651271i \(0.225764\pi\)
\(90\) 3.68561 0.388497
\(91\) 0 0
\(92\) −7.10290 −0.740528
\(93\) 1.89809 0.196823
\(94\) 9.67642 0.998046
\(95\) −3.58493 −0.367806
\(96\) 4.22306 0.431015
\(97\) −12.3236 −1.25127 −0.625633 0.780117i \(-0.715159\pi\)
−0.625633 + 0.780117i \(0.715159\pi\)
\(98\) 1.09372 0.110482
\(99\) 0.408118 0.0410174
\(100\) −5.10849 −0.510849
\(101\) −1.21016 −0.120416 −0.0602079 0.998186i \(-0.519176\pi\)
−0.0602079 + 0.998186i \(0.519176\pi\)
\(102\) 0.450696 0.0446255
\(103\) 13.5513 1.33525 0.667626 0.744497i \(-0.267311\pi\)
0.667626 + 0.744497i \(0.267311\pi\)
\(104\) 0 0
\(105\) −3.36980 −0.328859
\(106\) −4.58169 −0.445013
\(107\) 8.58829 0.830261 0.415131 0.909762i \(-0.363736\pi\)
0.415131 + 0.909762i \(0.363736\pi\)
\(108\) −0.803784 −0.0773442
\(109\) −19.6808 −1.88508 −0.942540 0.334093i \(-0.891570\pi\)
−0.942540 + 0.334093i \(0.891570\pi\)
\(110\) 1.50416 0.143416
\(111\) 4.79988 0.455584
\(112\) 1.74636 0.165016
\(113\) 1.36619 0.128520 0.0642602 0.997933i \(-0.479531\pi\)
0.0642602 + 0.997933i \(0.479531\pi\)
\(114\) −1.16354 −0.108975
\(115\) 29.7783 2.77684
\(116\) 2.84964 0.264582
\(117\) 0 0
\(118\) −12.5237 −1.15290
\(119\) −0.412077 −0.0377751
\(120\) −10.3336 −0.943328
\(121\) −10.8334 −0.984858
\(122\) 12.7258 1.15214
\(123\) 10.0404 0.905314
\(124\) −1.52566 −0.137008
\(125\) 4.56793 0.408568
\(126\) −1.09372 −0.0974360
\(127\) −16.5831 −1.47151 −0.735756 0.677247i \(-0.763173\pi\)
−0.735756 + 0.677247i \(0.763173\pi\)
\(128\) 0.425621 0.0376199
\(129\) −2.32877 −0.205037
\(130\) 0 0
\(131\) 9.76818 0.853449 0.426725 0.904382i \(-0.359667\pi\)
0.426725 + 0.904382i \(0.359667\pi\)
\(132\) −0.328038 −0.0285521
\(133\) 1.06384 0.0922466
\(134\) 2.62003 0.226336
\(135\) 3.36980 0.290026
\(136\) −1.26365 −0.108357
\(137\) −14.4867 −1.23768 −0.618839 0.785518i \(-0.712397\pi\)
−0.618839 + 0.785518i \(0.712397\pi\)
\(138\) 9.66498 0.822738
\(139\) −7.75313 −0.657612 −0.328806 0.944398i \(-0.606646\pi\)
−0.328806 + 0.944398i \(0.606646\pi\)
\(140\) 2.70859 0.228918
\(141\) 8.84728 0.745075
\(142\) 16.0528 1.34712
\(143\) 0 0
\(144\) −1.74636 −0.145530
\(145\) −11.9469 −0.992133
\(146\) −15.9318 −1.31852
\(147\) 1.00000 0.0824786
\(148\) −3.85806 −0.317131
\(149\) 2.67814 0.219402 0.109701 0.993965i \(-0.465011\pi\)
0.109701 + 0.993965i \(0.465011\pi\)
\(150\) 6.95117 0.567561
\(151\) −7.62102 −0.620190 −0.310095 0.950706i \(-0.600361\pi\)
−0.310095 + 0.950706i \(0.600361\pi\)
\(152\) 3.26231 0.264608
\(153\) 0.412077 0.0333145
\(154\) −0.446365 −0.0359691
\(155\) 6.39620 0.513755
\(156\) 0 0
\(157\) 18.1947 1.45209 0.726047 0.687645i \(-0.241355\pi\)
0.726047 + 0.687645i \(0.241355\pi\)
\(158\) 4.67880 0.372225
\(159\) −4.18910 −0.332218
\(160\) 14.2309 1.12505
\(161\) −8.83682 −0.696439
\(162\) 1.09372 0.0859305
\(163\) −19.5824 −1.53381 −0.766905 0.641760i \(-0.778204\pi\)
−0.766905 + 0.641760i \(0.778204\pi\)
\(164\) −8.07033 −0.630187
\(165\) 1.37527 0.107065
\(166\) −5.03814 −0.391036
\(167\) 6.00027 0.464315 0.232158 0.972678i \(-0.425422\pi\)
0.232158 + 0.972678i \(0.425422\pi\)
\(168\) 3.06655 0.236589
\(169\) 0 0
\(170\) 1.51875 0.116483
\(171\) −1.06384 −0.0813539
\(172\) 1.87183 0.142726
\(173\) −1.17561 −0.0893797 −0.0446899 0.999001i \(-0.514230\pi\)
−0.0446899 + 0.999001i \(0.514230\pi\)
\(174\) −3.87753 −0.293955
\(175\) −6.35555 −0.480434
\(176\) −0.712721 −0.0537234
\(177\) −11.4506 −0.860678
\(178\) 15.6597 1.17374
\(179\) 0.249567 0.0186535 0.00932677 0.999957i \(-0.497031\pi\)
0.00932677 + 0.999957i \(0.497031\pi\)
\(180\) −2.70859 −0.201886
\(181\) 0.442464 0.0328881 0.0164440 0.999865i \(-0.494765\pi\)
0.0164440 + 0.999865i \(0.494765\pi\)
\(182\) 0 0
\(183\) 11.6354 0.860113
\(184\) −27.0985 −1.99773
\(185\) 16.1746 1.18918
\(186\) 2.07598 0.152218
\(187\) 0.168176 0.0122982
\(188\) −7.11130 −0.518645
\(189\) −1.00000 −0.0727393
\(190\) −3.92089 −0.284452
\(191\) 15.8545 1.14719 0.573597 0.819138i \(-0.305548\pi\)
0.573597 + 0.819138i \(0.305548\pi\)
\(192\) 8.11156 0.585401
\(193\) 4.24322 0.305434 0.152717 0.988270i \(-0.451198\pi\)
0.152717 + 0.988270i \(0.451198\pi\)
\(194\) −13.4785 −0.967698
\(195\) 0 0
\(196\) −0.803784 −0.0574131
\(197\) 9.13404 0.650773 0.325387 0.945581i \(-0.394506\pi\)
0.325387 + 0.945581i \(0.394506\pi\)
\(198\) 0.446365 0.0317218
\(199\) 9.66460 0.685105 0.342553 0.939499i \(-0.388708\pi\)
0.342553 + 0.939499i \(0.388708\pi\)
\(200\) −19.4896 −1.37812
\(201\) 2.39553 0.168968
\(202\) −1.32358 −0.0931265
\(203\) 3.54528 0.248830
\(204\) −0.331221 −0.0231901
\(205\) 33.8342 2.36308
\(206\) 14.8213 1.03265
\(207\) 8.83682 0.614202
\(208\) 0 0
\(209\) −0.434172 −0.0300323
\(210\) −3.68561 −0.254331
\(211\) −24.0587 −1.65627 −0.828135 0.560528i \(-0.810598\pi\)
−0.828135 + 0.560528i \(0.810598\pi\)
\(212\) 3.36714 0.231256
\(213\) 14.6773 1.00567
\(214\) 9.39315 0.642103
\(215\) −7.84750 −0.535195
\(216\) −3.06655 −0.208652
\(217\) −1.89809 −0.128851
\(218\) −21.5252 −1.45787
\(219\) −14.5666 −0.984321
\(220\) −1.10542 −0.0745276
\(221\) 0 0
\(222\) 5.24970 0.352337
\(223\) −18.1487 −1.21532 −0.607662 0.794196i \(-0.707892\pi\)
−0.607662 + 0.794196i \(0.707892\pi\)
\(224\) −4.22306 −0.282165
\(225\) 6.35555 0.423703
\(226\) 1.49423 0.0993944
\(227\) −16.2228 −1.07674 −0.538372 0.842707i \(-0.680961\pi\)
−0.538372 + 0.842707i \(0.680961\pi\)
\(228\) 0.855097 0.0566302
\(229\) 0.980804 0.0648134 0.0324067 0.999475i \(-0.489683\pi\)
0.0324067 + 0.999475i \(0.489683\pi\)
\(230\) 32.5690 2.14754
\(231\) −0.408118 −0.0268522
\(232\) 10.8717 0.713765
\(233\) −19.4629 −1.27506 −0.637528 0.770427i \(-0.720043\pi\)
−0.637528 + 0.770427i \(0.720043\pi\)
\(234\) 0 0
\(235\) 29.8136 1.94482
\(236\) 9.20379 0.599116
\(237\) 4.27789 0.277879
\(238\) −0.450696 −0.0292143
\(239\) 18.7859 1.21516 0.607580 0.794259i \(-0.292141\pi\)
0.607580 + 0.794259i \(0.292141\pi\)
\(240\) −5.88489 −0.379868
\(241\) −9.08287 −0.585079 −0.292540 0.956253i \(-0.594500\pi\)
−0.292540 + 0.956253i \(0.594500\pi\)
\(242\) −11.8487 −0.761664
\(243\) 1.00000 0.0641500
\(244\) −9.35235 −0.598723
\(245\) 3.36980 0.215289
\(246\) 10.9814 0.700147
\(247\) 0 0
\(248\) −5.82059 −0.369608
\(249\) −4.60644 −0.291921
\(250\) 4.99602 0.315976
\(251\) 11.7323 0.740535 0.370267 0.928925i \(-0.379266\pi\)
0.370267 + 0.928925i \(0.379266\pi\)
\(252\) 0.803784 0.0506336
\(253\) 3.60646 0.226736
\(254\) −18.1372 −1.13803
\(255\) 1.38862 0.0869586
\(256\) −15.7576 −0.984851
\(257\) 20.0321 1.24957 0.624784 0.780797i \(-0.285187\pi\)
0.624784 + 0.780797i \(0.285187\pi\)
\(258\) −2.54702 −0.158570
\(259\) −4.79988 −0.298250
\(260\) 0 0
\(261\) −3.54528 −0.219447
\(262\) 10.6836 0.660036
\(263\) −5.06336 −0.312220 −0.156110 0.987740i \(-0.549895\pi\)
−0.156110 + 0.987740i \(0.549895\pi\)
\(264\) −1.25151 −0.0770252
\(265\) −14.1164 −0.867166
\(266\) 1.16354 0.0713412
\(267\) 14.3179 0.876239
\(268\) −1.92549 −0.117618
\(269\) 4.89625 0.298530 0.149265 0.988797i \(-0.452309\pi\)
0.149265 + 0.988797i \(0.452309\pi\)
\(270\) 3.68561 0.224299
\(271\) −27.2537 −1.65554 −0.827772 0.561064i \(-0.810392\pi\)
−0.827772 + 0.561064i \(0.810392\pi\)
\(272\) −0.719637 −0.0436344
\(273\) 0 0
\(274\) −15.8443 −0.957189
\(275\) 2.59381 0.156413
\(276\) −7.10290 −0.427544
\(277\) −2.91367 −0.175066 −0.0875328 0.996162i \(-0.527898\pi\)
−0.0875328 + 0.996162i \(0.527898\pi\)
\(278\) −8.47972 −0.508580
\(279\) 1.89809 0.113636
\(280\) 10.3336 0.617553
\(281\) −25.2705 −1.50751 −0.753757 0.657153i \(-0.771760\pi\)
−0.753757 + 0.657153i \(0.771760\pi\)
\(282\) 9.67642 0.576222
\(283\) 18.5059 1.10006 0.550031 0.835144i \(-0.314616\pi\)
0.550031 + 0.835144i \(0.314616\pi\)
\(284\) −11.7974 −0.700047
\(285\) −3.58493 −0.212353
\(286\) 0 0
\(287\) −10.0404 −0.592667
\(288\) 4.22306 0.248846
\(289\) −16.8302 −0.990011
\(290\) −13.0665 −0.767291
\(291\) −12.3236 −0.722419
\(292\) 11.7084 0.685183
\(293\) 5.10573 0.298280 0.149140 0.988816i \(-0.452350\pi\)
0.149140 + 0.988816i \(0.452350\pi\)
\(294\) 1.09372 0.0637868
\(295\) −38.5861 −2.24657
\(296\) −14.7190 −0.855527
\(297\) 0.408118 0.0236814
\(298\) 2.92912 0.169680
\(299\) 0 0
\(300\) −5.10849 −0.294939
\(301\) 2.32877 0.134228
\(302\) −8.33524 −0.479639
\(303\) −1.21016 −0.0695221
\(304\) 1.85785 0.106555
\(305\) 39.2090 2.24510
\(306\) 0.450696 0.0257646
\(307\) −0.145600 −0.00830986 −0.00415493 0.999991i \(-0.501323\pi\)
−0.00415493 + 0.999991i \(0.501323\pi\)
\(308\) 0.328038 0.0186917
\(309\) 13.5513 0.770908
\(310\) 6.99563 0.397325
\(311\) −27.0891 −1.53608 −0.768041 0.640400i \(-0.778769\pi\)
−0.768041 + 0.640400i \(0.778769\pi\)
\(312\) 0 0
\(313\) 29.6140 1.67388 0.836941 0.547293i \(-0.184342\pi\)
0.836941 + 0.547293i \(0.184342\pi\)
\(314\) 19.8998 1.12301
\(315\) −3.36980 −0.189867
\(316\) −3.43850 −0.193431
\(317\) −23.9730 −1.34646 −0.673229 0.739434i \(-0.735093\pi\)
−0.673229 + 0.739434i \(0.735093\pi\)
\(318\) −4.58169 −0.256929
\(319\) −1.44689 −0.0810102
\(320\) 27.3343 1.52804
\(321\) 8.58829 0.479352
\(322\) −9.66498 −0.538608
\(323\) −0.438384 −0.0243924
\(324\) −0.803784 −0.0446547
\(325\) 0 0
\(326\) −21.4176 −1.18621
\(327\) −19.6808 −1.08835
\(328\) −30.7894 −1.70006
\(329\) −8.84728 −0.487766
\(330\) 1.50416 0.0828013
\(331\) 5.54793 0.304942 0.152471 0.988308i \(-0.451277\pi\)
0.152471 + 0.988308i \(0.451277\pi\)
\(332\) 3.70258 0.203206
\(333\) 4.79988 0.263032
\(334\) 6.56260 0.359089
\(335\) 8.07247 0.441046
\(336\) 1.74636 0.0952719
\(337\) 5.52923 0.301196 0.150598 0.988595i \(-0.451880\pi\)
0.150598 + 0.988595i \(0.451880\pi\)
\(338\) 0 0
\(339\) 1.36619 0.0742013
\(340\) −1.11615 −0.0605317
\(341\) 0.774646 0.0419494
\(342\) −1.16354 −0.0629170
\(343\) −1.00000 −0.0539949
\(344\) 7.14129 0.385032
\(345\) 29.7783 1.60321
\(346\) −1.28578 −0.0691240
\(347\) 29.0528 1.55964 0.779818 0.626007i \(-0.215312\pi\)
0.779818 + 0.626007i \(0.215312\pi\)
\(348\) 2.84964 0.152757
\(349\) −15.4431 −0.826652 −0.413326 0.910583i \(-0.635633\pi\)
−0.413326 + 0.910583i \(0.635633\pi\)
\(350\) −6.95117 −0.371556
\(351\) 0 0
\(352\) 1.72351 0.0918632
\(353\) −18.6976 −0.995175 −0.497587 0.867414i \(-0.665781\pi\)
−0.497587 + 0.867414i \(0.665781\pi\)
\(354\) −12.5237 −0.665626
\(355\) 49.4596 2.62505
\(356\) −11.5085 −0.609948
\(357\) −0.412077 −0.0218094
\(358\) 0.272956 0.0144262
\(359\) 10.9693 0.578939 0.289470 0.957187i \(-0.406521\pi\)
0.289470 + 0.957187i \(0.406521\pi\)
\(360\) −10.3336 −0.544631
\(361\) −17.8682 −0.940434
\(362\) 0.483930 0.0254348
\(363\) −10.8334 −0.568608
\(364\) 0 0
\(365\) −49.0866 −2.56931
\(366\) 12.7258 0.665190
\(367\) 11.8585 0.619011 0.309505 0.950898i \(-0.399837\pi\)
0.309505 + 0.950898i \(0.399837\pi\)
\(368\) −15.4323 −0.804464
\(369\) 10.0404 0.522683
\(370\) 17.6905 0.919683
\(371\) 4.18910 0.217487
\(372\) −1.52566 −0.0791017
\(373\) 8.62231 0.446446 0.223223 0.974767i \(-0.428342\pi\)
0.223223 + 0.974767i \(0.428342\pi\)
\(374\) 0.183937 0.00951115
\(375\) 4.56793 0.235887
\(376\) −27.1306 −1.39915
\(377\) 0 0
\(378\) −1.09372 −0.0562547
\(379\) 30.5029 1.56683 0.783413 0.621501i \(-0.213477\pi\)
0.783413 + 0.621501i \(0.213477\pi\)
\(380\) 2.88151 0.147818
\(381\) −16.5831 −0.849578
\(382\) 17.3404 0.887211
\(383\) 25.7592 1.31623 0.658117 0.752915i \(-0.271353\pi\)
0.658117 + 0.752915i \(0.271353\pi\)
\(384\) 0.425621 0.0217199
\(385\) −1.37527 −0.0700905
\(386\) 4.64088 0.236215
\(387\) −2.32877 −0.118378
\(388\) 9.90547 0.502874
\(389\) 16.5425 0.838737 0.419368 0.907816i \(-0.362252\pi\)
0.419368 + 0.907816i \(0.362252\pi\)
\(390\) 0 0
\(391\) 3.64145 0.184156
\(392\) −3.06655 −0.154884
\(393\) 9.76818 0.492739
\(394\) 9.99005 0.503291
\(395\) 14.4156 0.725329
\(396\) −0.328038 −0.0164845
\(397\) 8.82355 0.442841 0.221421 0.975178i \(-0.428931\pi\)
0.221421 + 0.975178i \(0.428931\pi\)
\(398\) 10.5703 0.529843
\(399\) 1.06384 0.0532586
\(400\) −11.0991 −0.554955
\(401\) −10.8101 −0.539832 −0.269916 0.962884i \(-0.586996\pi\)
−0.269916 + 0.962884i \(0.586996\pi\)
\(402\) 2.62003 0.130675
\(403\) 0 0
\(404\) 0.972710 0.0483941
\(405\) 3.36980 0.167447
\(406\) 3.87753 0.192438
\(407\) 1.95891 0.0970998
\(408\) −1.26365 −0.0625602
\(409\) −19.5162 −0.965015 −0.482507 0.875892i \(-0.660274\pi\)
−0.482507 + 0.875892i \(0.660274\pi\)
\(410\) 37.0050 1.82755
\(411\) −14.4867 −0.714574
\(412\) −10.8923 −0.536627
\(413\) 11.4506 0.563446
\(414\) 9.66498 0.475008
\(415\) −15.5228 −0.761983
\(416\) 0 0
\(417\) −7.75313 −0.379672
\(418\) −0.474861 −0.0232262
\(419\) 2.14931 0.105001 0.0525004 0.998621i \(-0.483281\pi\)
0.0525004 + 0.998621i \(0.483281\pi\)
\(420\) 2.70859 0.132166
\(421\) 17.1850 0.837547 0.418774 0.908091i \(-0.362460\pi\)
0.418774 + 0.908091i \(0.362460\pi\)
\(422\) −26.3134 −1.28092
\(423\) 8.84728 0.430169
\(424\) 12.8461 0.623861
\(425\) 2.61898 0.127039
\(426\) 16.0528 0.777762
\(427\) −11.6354 −0.563076
\(428\) −6.90313 −0.333675
\(429\) 0 0
\(430\) −8.58294 −0.413906
\(431\) −12.4147 −0.597997 −0.298998 0.954254i \(-0.596653\pi\)
−0.298998 + 0.954254i \(0.596653\pi\)
\(432\) −1.74636 −0.0840219
\(433\) −1.89315 −0.0909791 −0.0454896 0.998965i \(-0.514485\pi\)
−0.0454896 + 0.998965i \(0.514485\pi\)
\(434\) −2.07598 −0.0996501
\(435\) −11.9469 −0.572808
\(436\) 15.8191 0.757599
\(437\) −9.40096 −0.449709
\(438\) −15.9318 −0.761249
\(439\) −4.57342 −0.218277 −0.109139 0.994027i \(-0.534809\pi\)
−0.109139 + 0.994027i \(0.534809\pi\)
\(440\) −4.21734 −0.201054
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 28.3955 1.34911 0.674556 0.738224i \(-0.264335\pi\)
0.674556 + 0.738224i \(0.264335\pi\)
\(444\) −3.85806 −0.183096
\(445\) 48.2484 2.28719
\(446\) −19.8495 −0.939901
\(447\) 2.67814 0.126672
\(448\) −8.11156 −0.383235
\(449\) −35.6530 −1.68257 −0.841284 0.540594i \(-0.818200\pi\)
−0.841284 + 0.540594i \(0.818200\pi\)
\(450\) 6.95117 0.327681
\(451\) 4.09767 0.192952
\(452\) −1.09812 −0.0516513
\(453\) −7.62102 −0.358067
\(454\) −17.7431 −0.832727
\(455\) 0 0
\(456\) 3.26231 0.152772
\(457\) −31.4697 −1.47209 −0.736045 0.676933i \(-0.763309\pi\)
−0.736045 + 0.676933i \(0.763309\pi\)
\(458\) 1.07272 0.0501250
\(459\) 0.412077 0.0192341
\(460\) −23.9353 −1.11599
\(461\) −21.2279 −0.988680 −0.494340 0.869269i \(-0.664590\pi\)
−0.494340 + 0.869269i \(0.664590\pi\)
\(462\) −0.446365 −0.0207668
\(463\) 8.12061 0.377397 0.188698 0.982035i \(-0.439573\pi\)
0.188698 + 0.982035i \(0.439573\pi\)
\(464\) 6.19134 0.287426
\(465\) 6.39620 0.296617
\(466\) −21.2869 −0.986095
\(467\) −26.8288 −1.24149 −0.620743 0.784014i \(-0.713169\pi\)
−0.620743 + 0.784014i \(0.713169\pi\)
\(468\) 0 0
\(469\) −2.39553 −0.110615
\(470\) 32.6076 1.50408
\(471\) 18.1947 0.838367
\(472\) 35.1137 1.61624
\(473\) −0.950413 −0.0437000
\(474\) 4.67880 0.214904
\(475\) −6.76129 −0.310229
\(476\) 0.331221 0.0151815
\(477\) −4.18910 −0.191806
\(478\) 20.5465 0.939773
\(479\) 9.75257 0.445606 0.222803 0.974863i \(-0.428479\pi\)
0.222803 + 0.974863i \(0.428479\pi\)
\(480\) 14.2309 0.649548
\(481\) 0 0
\(482\) −9.93409 −0.452485
\(483\) −8.83682 −0.402089
\(484\) 8.70775 0.395807
\(485\) −41.5279 −1.88568
\(486\) 1.09372 0.0496120
\(487\) −21.8869 −0.991791 −0.495895 0.868382i \(-0.665160\pi\)
−0.495895 + 0.868382i \(0.665160\pi\)
\(488\) −35.6805 −1.61518
\(489\) −19.5824 −0.885546
\(490\) 3.68561 0.166499
\(491\) 33.1640 1.49667 0.748336 0.663320i \(-0.230853\pi\)
0.748336 + 0.663320i \(0.230853\pi\)
\(492\) −8.07033 −0.363838
\(493\) −1.46093 −0.0657969
\(494\) 0 0
\(495\) 1.37527 0.0618140
\(496\) −3.31476 −0.148837
\(497\) −14.6773 −0.658368
\(498\) −5.03814 −0.225764
\(499\) 40.6778 1.82099 0.910494 0.413522i \(-0.135702\pi\)
0.910494 + 0.413522i \(0.135702\pi\)
\(500\) −3.67163 −0.164200
\(501\) 6.00027 0.268072
\(502\) 12.8318 0.572710
\(503\) −35.7797 −1.59534 −0.797669 0.603096i \(-0.793934\pi\)
−0.797669 + 0.603096i \(0.793934\pi\)
\(504\) 3.06655 0.136595
\(505\) −4.07801 −0.181469
\(506\) 3.94445 0.175352
\(507\) 0 0
\(508\) 13.3292 0.591389
\(509\) −39.4278 −1.74761 −0.873803 0.486279i \(-0.838354\pi\)
−0.873803 + 0.486279i \(0.838354\pi\)
\(510\) 1.51875 0.0672516
\(511\) 14.5666 0.644389
\(512\) −18.0856 −0.799278
\(513\) −1.06384 −0.0469697
\(514\) 21.9095 0.966385
\(515\) 45.6652 2.01225
\(516\) 1.87183 0.0824027
\(517\) 3.61073 0.158800
\(518\) −5.24970 −0.230659
\(519\) −1.17561 −0.0516034
\(520\) 0 0
\(521\) −37.1536 −1.62773 −0.813865 0.581055i \(-0.802640\pi\)
−0.813865 + 0.581055i \(0.802640\pi\)
\(522\) −3.87753 −0.169715
\(523\) −18.8684 −0.825057 −0.412529 0.910945i \(-0.635354\pi\)
−0.412529 + 0.910945i \(0.635354\pi\)
\(524\) −7.85150 −0.342995
\(525\) −6.35555 −0.277379
\(526\) −5.53788 −0.241463
\(527\) 0.782162 0.0340715
\(528\) −0.712721 −0.0310172
\(529\) 55.0894 2.39519
\(530\) −15.4394 −0.670644
\(531\) −11.4506 −0.496913
\(532\) −0.855097 −0.0370732
\(533\) 0 0
\(534\) 15.6597 0.677661
\(535\) 28.9408 1.25122
\(536\) −7.34601 −0.317299
\(537\) 0.249567 0.0107696
\(538\) 5.35511 0.230875
\(539\) 0.408118 0.0175789
\(540\) −2.70859 −0.116559
\(541\) 34.2960 1.47450 0.737250 0.675620i \(-0.236124\pi\)
0.737250 + 0.675620i \(0.236124\pi\)
\(542\) −29.8078 −1.28036
\(543\) 0.442464 0.0189879
\(544\) 1.74023 0.0746117
\(545\) −66.3204 −2.84085
\(546\) 0 0
\(547\) 30.2529 1.29352 0.646761 0.762693i \(-0.276123\pi\)
0.646761 + 0.762693i \(0.276123\pi\)
\(548\) 11.6441 0.497413
\(549\) 11.6354 0.496587
\(550\) 2.83689 0.120966
\(551\) 3.77160 0.160676
\(552\) −27.0985 −1.15339
\(553\) −4.27789 −0.181914
\(554\) −3.18673 −0.135391
\(555\) 16.1746 0.686575
\(556\) 6.23184 0.264289
\(557\) 23.7963 1.00828 0.504141 0.863622i \(-0.331809\pi\)
0.504141 + 0.863622i \(0.331809\pi\)
\(558\) 2.07598 0.0878831
\(559\) 0 0
\(560\) 5.88489 0.248682
\(561\) 0.168176 0.00710040
\(562\) −27.6388 −1.16587
\(563\) −20.0697 −0.845839 −0.422919 0.906167i \(-0.638995\pi\)
−0.422919 + 0.906167i \(0.638995\pi\)
\(564\) −7.11130 −0.299440
\(565\) 4.60379 0.193683
\(566\) 20.2402 0.850760
\(567\) −1.00000 −0.0419961
\(568\) −45.0087 −1.88852
\(569\) −35.6422 −1.49420 −0.747100 0.664712i \(-0.768554\pi\)
−0.747100 + 0.664712i \(0.768554\pi\)
\(570\) −3.92089 −0.164228
\(571\) 27.9511 1.16972 0.584859 0.811135i \(-0.301150\pi\)
0.584859 + 0.811135i \(0.301150\pi\)
\(572\) 0 0
\(573\) 15.8545 0.662333
\(574\) −10.9814 −0.458354
\(575\) 56.1629 2.34215
\(576\) 8.11156 0.337982
\(577\) 16.1295 0.671481 0.335741 0.941954i \(-0.391013\pi\)
0.335741 + 0.941954i \(0.391013\pi\)
\(578\) −18.4075 −0.765649
\(579\) 4.24322 0.176342
\(580\) 9.60270 0.398730
\(581\) 4.60644 0.191107
\(582\) −13.4785 −0.558701
\(583\) −1.70965 −0.0708063
\(584\) 44.6692 1.84842
\(585\) 0 0
\(586\) 5.58422 0.230682
\(587\) −25.2546 −1.04237 −0.521184 0.853445i \(-0.674509\pi\)
−0.521184 + 0.853445i \(0.674509\pi\)
\(588\) −0.803784 −0.0331475
\(589\) −2.01927 −0.0832025
\(590\) −42.2023 −1.73744
\(591\) 9.13404 0.375724
\(592\) −8.38233 −0.344512
\(593\) −3.67915 −0.151085 −0.0755424 0.997143i \(-0.524069\pi\)
−0.0755424 + 0.997143i \(0.524069\pi\)
\(594\) 0.446365 0.0183146
\(595\) −1.38862 −0.0569278
\(596\) −2.15264 −0.0881758
\(597\) 9.66460 0.395546
\(598\) 0 0
\(599\) −24.1745 −0.987744 −0.493872 0.869535i \(-0.664419\pi\)
−0.493872 + 0.869535i \(0.664419\pi\)
\(600\) −19.4896 −0.795659
\(601\) −9.85564 −0.402020 −0.201010 0.979589i \(-0.564422\pi\)
−0.201010 + 0.979589i \(0.564422\pi\)
\(602\) 2.54702 0.103809
\(603\) 2.39553 0.0975537
\(604\) 6.12566 0.249249
\(605\) −36.5065 −1.48420
\(606\) −1.32358 −0.0537666
\(607\) 4.87139 0.197724 0.0988619 0.995101i \(-0.468480\pi\)
0.0988619 + 0.995101i \(0.468480\pi\)
\(608\) −4.49266 −0.182202
\(609\) 3.54528 0.143662
\(610\) 42.8835 1.73630
\(611\) 0 0
\(612\) −0.331221 −0.0133888
\(613\) −19.7564 −0.797954 −0.398977 0.916961i \(-0.630635\pi\)
−0.398977 + 0.916961i \(0.630635\pi\)
\(614\) −0.159246 −0.00642663
\(615\) 33.8342 1.36433
\(616\) 1.25151 0.0504248
\(617\) −4.52746 −0.182269 −0.0911343 0.995839i \(-0.529049\pi\)
−0.0911343 + 0.995839i \(0.529049\pi\)
\(618\) 14.8213 0.596200
\(619\) −40.5342 −1.62921 −0.814604 0.580017i \(-0.803046\pi\)
−0.814604 + 0.580017i \(0.803046\pi\)
\(620\) −5.14116 −0.206474
\(621\) 8.83682 0.354609
\(622\) −29.6278 −1.18797
\(623\) −14.3179 −0.573633
\(624\) 0 0
\(625\) −16.3847 −0.655389
\(626\) 32.3893 1.29454
\(627\) −0.434172 −0.0173391
\(628\) −14.6246 −0.583585
\(629\) 1.97792 0.0788648
\(630\) −3.68561 −0.146838
\(631\) 9.09532 0.362079 0.181039 0.983476i \(-0.442054\pi\)
0.181039 + 0.983476i \(0.442054\pi\)
\(632\) −13.1183 −0.521819
\(633\) −24.0587 −0.956248
\(634\) −26.2197 −1.04132
\(635\) −55.8817 −2.21760
\(636\) 3.36714 0.133516
\(637\) 0 0
\(638\) −1.58249 −0.0626512
\(639\) 14.6773 0.580626
\(640\) 1.43426 0.0566940
\(641\) −27.6571 −1.09239 −0.546194 0.837658i \(-0.683924\pi\)
−0.546194 + 0.837658i \(0.683924\pi\)
\(642\) 9.39315 0.370718
\(643\) −27.7846 −1.09572 −0.547859 0.836571i \(-0.684557\pi\)
−0.547859 + 0.836571i \(0.684557\pi\)
\(644\) 7.10290 0.279893
\(645\) −7.84750 −0.308995
\(646\) −0.479468 −0.0188644
\(647\) −42.0045 −1.65137 −0.825685 0.564132i \(-0.809211\pi\)
−0.825685 + 0.564132i \(0.809211\pi\)
\(648\) −3.06655 −0.120465
\(649\) −4.67318 −0.183438
\(650\) 0 0
\(651\) −1.89809 −0.0743922
\(652\) 15.7400 0.616426
\(653\) −6.17528 −0.241657 −0.120829 0.992673i \(-0.538555\pi\)
−0.120829 + 0.992673i \(0.538555\pi\)
\(654\) −21.5252 −0.841703
\(655\) 32.9168 1.28617
\(656\) −17.5342 −0.684596
\(657\) −14.5666 −0.568298
\(658\) −9.67642 −0.377226
\(659\) −16.3984 −0.638790 −0.319395 0.947622i \(-0.603480\pi\)
−0.319395 + 0.947622i \(0.603480\pi\)
\(660\) −1.10542 −0.0430286
\(661\) −5.90374 −0.229629 −0.114814 0.993387i \(-0.536627\pi\)
−0.114814 + 0.993387i \(0.536627\pi\)
\(662\) 6.06786 0.235834
\(663\) 0 0
\(664\) 14.1259 0.548190
\(665\) 3.58493 0.139018
\(666\) 5.24970 0.203422
\(667\) −31.3290 −1.21306
\(668\) −4.82292 −0.186605
\(669\) −18.1487 −0.701668
\(670\) 8.82899 0.341094
\(671\) 4.74861 0.183318
\(672\) −4.22306 −0.162908
\(673\) −1.67667 −0.0646308 −0.0323154 0.999478i \(-0.510288\pi\)
−0.0323154 + 0.999478i \(0.510288\pi\)
\(674\) 6.04741 0.232937
\(675\) 6.35555 0.244625
\(676\) 0 0
\(677\) 33.3324 1.28107 0.640535 0.767929i \(-0.278713\pi\)
0.640535 + 0.767929i \(0.278713\pi\)
\(678\) 1.49423 0.0573854
\(679\) 12.3236 0.472934
\(680\) −4.25826 −0.163297
\(681\) −16.2228 −0.621659
\(682\) 0.847243 0.0324426
\(683\) −24.7425 −0.946746 −0.473373 0.880862i \(-0.656964\pi\)
−0.473373 + 0.880862i \(0.656964\pi\)
\(684\) 0.855097 0.0326955
\(685\) −48.8171 −1.86521
\(686\) −1.09372 −0.0417583
\(687\) 0.980804 0.0374200
\(688\) 4.06688 0.155048
\(689\) 0 0
\(690\) 32.5690 1.23988
\(691\) 48.1772 1.83275 0.916374 0.400323i \(-0.131102\pi\)
0.916374 + 0.400323i \(0.131102\pi\)
\(692\) 0.944934 0.0359210
\(693\) −0.408118 −0.0155031
\(694\) 31.7755 1.20618
\(695\) −26.1265 −0.991034
\(696\) 10.8717 0.412092
\(697\) 4.13743 0.156716
\(698\) −16.8904 −0.639311
\(699\) −19.4629 −0.736154
\(700\) 5.10849 0.193083
\(701\) 41.5798 1.57045 0.785224 0.619212i \(-0.212548\pi\)
0.785224 + 0.619212i \(0.212548\pi\)
\(702\) 0 0
\(703\) −5.10630 −0.192588
\(704\) 3.31047 0.124768
\(705\) 29.8136 1.12284
\(706\) −20.4499 −0.769642
\(707\) 1.21016 0.0455129
\(708\) 9.20379 0.345900
\(709\) −35.6206 −1.33776 −0.668879 0.743371i \(-0.733226\pi\)
−0.668879 + 0.743371i \(0.733226\pi\)
\(710\) 54.0948 2.03014
\(711\) 4.27789 0.160433
\(712\) −43.9064 −1.64546
\(713\) 16.7731 0.628158
\(714\) −0.450696 −0.0168669
\(715\) 0 0
\(716\) −0.200598 −0.00749671
\(717\) 18.7859 0.701573
\(718\) 11.9973 0.447737
\(719\) 8.40093 0.313302 0.156651 0.987654i \(-0.449930\pi\)
0.156651 + 0.987654i \(0.449930\pi\)
\(720\) −5.88489 −0.219317
\(721\) −13.5513 −0.504678
\(722\) −19.5428 −0.727308
\(723\) −9.08287 −0.337796
\(724\) −0.355645 −0.0132175
\(725\) −22.5322 −0.836824
\(726\) −11.8487 −0.439747
\(727\) −16.4191 −0.608950 −0.304475 0.952520i \(-0.598481\pi\)
−0.304475 + 0.952520i \(0.598481\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −53.6868 −1.98704
\(731\) −0.959635 −0.0354934
\(732\) −9.35235 −0.345673
\(733\) −50.9943 −1.88352 −0.941759 0.336288i \(-0.890829\pi\)
−0.941759 + 0.336288i \(0.890829\pi\)
\(734\) 12.9699 0.478727
\(735\) 3.36980 0.124297
\(736\) 37.3185 1.37558
\(737\) 0.977659 0.0360125
\(738\) 10.9814 0.404230
\(739\) −13.3896 −0.492545 −0.246272 0.969201i \(-0.579206\pi\)
−0.246272 + 0.969201i \(0.579206\pi\)
\(740\) −13.0009 −0.477923
\(741\) 0 0
\(742\) 4.58169 0.168199
\(743\) 35.2833 1.29442 0.647209 0.762313i \(-0.275936\pi\)
0.647209 + 0.762313i \(0.275936\pi\)
\(744\) −5.82059 −0.213393
\(745\) 9.02479 0.330643
\(746\) 9.43037 0.345270
\(747\) −4.60644 −0.168541
\(748\) −0.135177 −0.00494257
\(749\) −8.58829 −0.313809
\(750\) 4.99602 0.182429
\(751\) −17.2150 −0.628183 −0.314091 0.949393i \(-0.601700\pi\)
−0.314091 + 0.949393i \(0.601700\pi\)
\(752\) −15.4506 −0.563424
\(753\) 11.7323 0.427548
\(754\) 0 0
\(755\) −25.6813 −0.934639
\(756\) 0.803784 0.0292333
\(757\) 25.2096 0.916260 0.458130 0.888885i \(-0.348519\pi\)
0.458130 + 0.888885i \(0.348519\pi\)
\(758\) 33.3615 1.21174
\(759\) 3.60646 0.130906
\(760\) 10.9933 0.398770
\(761\) −5.13105 −0.186000 −0.0930001 0.995666i \(-0.529646\pi\)
−0.0930001 + 0.995666i \(0.529646\pi\)
\(762\) −18.1372 −0.657042
\(763\) 19.6808 0.712493
\(764\) −12.7436 −0.461048
\(765\) 1.38862 0.0502056
\(766\) 28.1733 1.01794
\(767\) 0 0
\(768\) −15.7576 −0.568604
\(769\) −20.5305 −0.740349 −0.370174 0.928962i \(-0.620702\pi\)
−0.370174 + 0.928962i \(0.620702\pi\)
\(770\) −1.50416 −0.0542062
\(771\) 20.0321 0.721439
\(772\) −3.41063 −0.122751
\(773\) −10.8128 −0.388911 −0.194455 0.980911i \(-0.562294\pi\)
−0.194455 + 0.980911i \(0.562294\pi\)
\(774\) −2.54702 −0.0915507
\(775\) 12.0634 0.433331
\(776\) 37.7907 1.35661
\(777\) −4.79988 −0.172195
\(778\) 18.0928 0.648658
\(779\) −10.6814 −0.382701
\(780\) 0 0
\(781\) 5.99007 0.214342
\(782\) 3.98272 0.142422
\(783\) −3.54528 −0.126698
\(784\) −1.74636 −0.0623701
\(785\) 61.3125 2.18834
\(786\) 10.6836 0.381072
\(787\) 30.3280 1.08108 0.540538 0.841320i \(-0.318221\pi\)
0.540538 + 0.841320i \(0.318221\pi\)
\(788\) −7.34180 −0.261541
\(789\) −5.06336 −0.180260
\(790\) 15.7666 0.560951
\(791\) −1.36619 −0.0485762
\(792\) −1.25151 −0.0444705
\(793\) 0 0
\(794\) 9.65047 0.342482
\(795\) −14.1164 −0.500659
\(796\) −7.76825 −0.275338
\(797\) −18.9162 −0.670046 −0.335023 0.942210i \(-0.608744\pi\)
−0.335023 + 0.942210i \(0.608744\pi\)
\(798\) 1.16354 0.0411888
\(799\) 3.64576 0.128978
\(800\) 26.8399 0.948934
\(801\) 14.3179 0.505897
\(802\) −11.8232 −0.417492
\(803\) −5.94489 −0.209791
\(804\) −1.92549 −0.0679068
\(805\) −29.7783 −1.04955
\(806\) 0 0
\(807\) 4.89625 0.172356
\(808\) 3.71102 0.130553
\(809\) 33.8433 1.18987 0.594934 0.803774i \(-0.297178\pi\)
0.594934 + 0.803774i \(0.297178\pi\)
\(810\) 3.68561 0.129499
\(811\) 29.5769 1.03859 0.519293 0.854596i \(-0.326195\pi\)
0.519293 + 0.854596i \(0.326195\pi\)
\(812\) −2.84964 −0.100003
\(813\) −27.2537 −0.955829
\(814\) 2.14250 0.0750945
\(815\) −65.9887 −2.31148
\(816\) −0.719637 −0.0251923
\(817\) 2.47744 0.0866747
\(818\) −21.3452 −0.746318
\(819\) 0 0
\(820\) −27.1954 −0.949704
\(821\) 12.1069 0.422533 0.211266 0.977429i \(-0.432241\pi\)
0.211266 + 0.977429i \(0.432241\pi\)
\(822\) −15.8443 −0.552633
\(823\) −55.2074 −1.92441 −0.962204 0.272330i \(-0.912206\pi\)
−0.962204 + 0.272330i \(0.912206\pi\)
\(824\) −41.5557 −1.44766
\(825\) 2.59381 0.0903049
\(826\) 12.5237 0.435755
\(827\) −30.5277 −1.06155 −0.530777 0.847512i \(-0.678100\pi\)
−0.530777 + 0.847512i \(0.678100\pi\)
\(828\) −7.10290 −0.246843
\(829\) −2.22089 −0.0771346 −0.0385673 0.999256i \(-0.512279\pi\)
−0.0385673 + 0.999256i \(0.512279\pi\)
\(830\) −16.9775 −0.589299
\(831\) −2.91367 −0.101074
\(832\) 0 0
\(833\) 0.412077 0.0142776
\(834\) −8.47972 −0.293629
\(835\) 20.2197 0.699732
\(836\) 0.348980 0.0120697
\(837\) 1.89809 0.0656077
\(838\) 2.35074 0.0812050
\(839\) −10.0791 −0.347970 −0.173985 0.984748i \(-0.555664\pi\)
−0.173985 + 0.984748i \(0.555664\pi\)
\(840\) 10.3336 0.356545
\(841\) −16.4310 −0.566587
\(842\) 18.7955 0.647737
\(843\) −25.2705 −0.870363
\(844\) 19.3380 0.665642
\(845\) 0 0
\(846\) 9.67642 0.332682
\(847\) 10.8334 0.372241
\(848\) 7.31570 0.251222
\(849\) 18.5059 0.635121
\(850\) 2.86442 0.0982488
\(851\) 42.4157 1.45399
\(852\) −11.7974 −0.404172
\(853\) 13.2747 0.454516 0.227258 0.973835i \(-0.427024\pi\)
0.227258 + 0.973835i \(0.427024\pi\)
\(854\) −12.7258 −0.435469
\(855\) −3.58493 −0.122602
\(856\) −26.3364 −0.900159
\(857\) 24.4586 0.835490 0.417745 0.908564i \(-0.362821\pi\)
0.417745 + 0.908564i \(0.362821\pi\)
\(858\) 0 0
\(859\) 2.20774 0.0753272 0.0376636 0.999290i \(-0.488008\pi\)
0.0376636 + 0.999290i \(0.488008\pi\)
\(860\) 6.30769 0.215091
\(861\) −10.0404 −0.342177
\(862\) −13.5782 −0.462476
\(863\) 9.06990 0.308743 0.154371 0.988013i \(-0.450665\pi\)
0.154371 + 0.988013i \(0.450665\pi\)
\(864\) 4.22306 0.143672
\(865\) −3.96156 −0.134697
\(866\) −2.07057 −0.0703609
\(867\) −16.8302 −0.571583
\(868\) 1.52566 0.0517842
\(869\) 1.74588 0.0592250
\(870\) −13.0665 −0.442995
\(871\) 0 0
\(872\) 60.3521 2.04378
\(873\) −12.3236 −0.417089
\(874\) −10.2820 −0.347793
\(875\) −4.56793 −0.154424
\(876\) 11.7084 0.395591
\(877\) −5.06468 −0.171022 −0.0855110 0.996337i \(-0.527252\pi\)
−0.0855110 + 0.996337i \(0.527252\pi\)
\(878\) −5.00202 −0.168810
\(879\) 5.10573 0.172212
\(880\) −2.40173 −0.0809622
\(881\) −10.4132 −0.350828 −0.175414 0.984495i \(-0.556126\pi\)
−0.175414 + 0.984495i \(0.556126\pi\)
\(882\) 1.09372 0.0368274
\(883\) 39.6733 1.33511 0.667556 0.744560i \(-0.267340\pi\)
0.667556 + 0.744560i \(0.267340\pi\)
\(884\) 0 0
\(885\) −38.5861 −1.29706
\(886\) 31.0567 1.04337
\(887\) −19.9363 −0.669394 −0.334697 0.942326i \(-0.608634\pi\)
−0.334697 + 0.942326i \(0.608634\pi\)
\(888\) −14.7190 −0.493939
\(889\) 16.5831 0.556179
\(890\) 52.7700 1.76886
\(891\) 0.408118 0.0136725
\(892\) 14.5876 0.488429
\(893\) −9.41209 −0.314964
\(894\) 2.92912 0.0979646
\(895\) 0.840992 0.0281113
\(896\) −0.425621 −0.0142190
\(897\) 0 0
\(898\) −38.9942 −1.30125
\(899\) −6.72927 −0.224434
\(900\) −5.10849 −0.170283
\(901\) −1.72623 −0.0575092
\(902\) 4.48169 0.149224
\(903\) 2.32877 0.0774967
\(904\) −4.18949 −0.139340
\(905\) 1.49101 0.0495630
\(906\) −8.33524 −0.276920
\(907\) 25.9765 0.862535 0.431268 0.902224i \(-0.358066\pi\)
0.431268 + 0.902224i \(0.358066\pi\)
\(908\) 13.0396 0.432735
\(909\) −1.21016 −0.0401386
\(910\) 0 0
\(911\) 26.4073 0.874911 0.437456 0.899240i \(-0.355880\pi\)
0.437456 + 0.899240i \(0.355880\pi\)
\(912\) 1.85785 0.0615196
\(913\) −1.87997 −0.0622179
\(914\) −34.4189 −1.13848
\(915\) 39.2090 1.29621
\(916\) −0.788355 −0.0260480
\(917\) −9.76818 −0.322574
\(918\) 0.450696 0.0148752
\(919\) −24.8301 −0.819068 −0.409534 0.912295i \(-0.634309\pi\)
−0.409534 + 0.912295i \(0.634309\pi\)
\(920\) −91.3166 −3.01062
\(921\) −0.145600 −0.00479770
\(922\) −23.2173 −0.764620
\(923\) 0 0
\(924\) 0.328038 0.0107917
\(925\) 30.5059 1.00303
\(926\) 8.88164 0.291869
\(927\) 13.5513 0.445084
\(928\) −14.9719 −0.491477
\(929\) −18.6678 −0.612472 −0.306236 0.951956i \(-0.599070\pi\)
−0.306236 + 0.951956i \(0.599070\pi\)
\(930\) 6.99563 0.229396
\(931\) −1.06384 −0.0348659
\(932\) 15.6439 0.512435
\(933\) −27.0891 −0.886858
\(934\) −29.3431 −0.960134
\(935\) 0.566719 0.0185337
\(936\) 0 0
\(937\) 2.93693 0.0959453 0.0479727 0.998849i \(-0.484724\pi\)
0.0479727 + 0.998849i \(0.484724\pi\)
\(938\) −2.62003 −0.0855472
\(939\) 29.6140 0.966416
\(940\) −23.9637 −0.781609
\(941\) −50.7259 −1.65362 −0.826808 0.562484i \(-0.809846\pi\)
−0.826808 + 0.562484i \(0.809846\pi\)
\(942\) 19.8998 0.648372
\(943\) 88.7254 2.88930
\(944\) 19.9969 0.650842
\(945\) −3.36980 −0.109620
\(946\) −1.03948 −0.0337965
\(947\) −25.8256 −0.839220 −0.419610 0.907704i \(-0.637833\pi\)
−0.419610 + 0.907704i \(0.637833\pi\)
\(948\) −3.43850 −0.111677
\(949\) 0 0
\(950\) −7.39493 −0.239923
\(951\) −23.9730 −0.777378
\(952\) 1.26365 0.0409553
\(953\) −42.6541 −1.38170 −0.690851 0.722998i \(-0.742764\pi\)
−0.690851 + 0.722998i \(0.742764\pi\)
\(954\) −4.58169 −0.148338
\(955\) 53.4266 1.72884
\(956\) −15.0998 −0.488363
\(957\) −1.44689 −0.0467713
\(958\) 10.6666 0.344621
\(959\) 14.4867 0.467798
\(960\) 27.3343 0.882212
\(961\) −27.3972 −0.883782
\(962\) 0 0
\(963\) 8.58829 0.276754
\(964\) 7.30067 0.235139
\(965\) 14.2988 0.460295
\(966\) −9.66498 −0.310966
\(967\) 37.4458 1.20418 0.602088 0.798430i \(-0.294336\pi\)
0.602088 + 0.798430i \(0.294336\pi\)
\(968\) 33.2212 1.06777
\(969\) −0.438384 −0.0140829
\(970\) −45.4197 −1.45834
\(971\) 22.1197 0.709855 0.354928 0.934894i \(-0.384505\pi\)
0.354928 + 0.934894i \(0.384505\pi\)
\(972\) −0.803784 −0.0257814
\(973\) 7.75313 0.248554
\(974\) −23.9381 −0.767026
\(975\) 0 0
\(976\) −20.3196 −0.650415
\(977\) 39.8028 1.27340 0.636702 0.771110i \(-0.280298\pi\)
0.636702 + 0.771110i \(0.280298\pi\)
\(978\) −21.4176 −0.684859
\(979\) 5.84337 0.186755
\(980\) −2.70859 −0.0865228
\(981\) −19.6808 −0.628360
\(982\) 36.2720 1.15749
\(983\) 21.8790 0.697832 0.348916 0.937154i \(-0.386550\pi\)
0.348916 + 0.937154i \(0.386550\pi\)
\(984\) −30.7894 −0.981530
\(985\) 30.7799 0.980729
\(986\) −1.59784 −0.0508856
\(987\) −8.84728 −0.281612
\(988\) 0 0
\(989\) −20.5790 −0.654373
\(990\) 1.50416 0.0478054
\(991\) 35.6459 1.13233 0.566164 0.824293i \(-0.308427\pi\)
0.566164 + 0.824293i \(0.308427\pi\)
\(992\) 8.01577 0.254501
\(993\) 5.54793 0.176058
\(994\) −16.0528 −0.509165
\(995\) 32.5678 1.03247
\(996\) 3.70258 0.117321
\(997\) 46.5398 1.47393 0.736965 0.675931i \(-0.236258\pi\)
0.736965 + 0.675931i \(0.236258\pi\)
\(998\) 44.4900 1.40831
\(999\) 4.79988 0.151861
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 3549.2.a.bh.1.10 yes 15
13.12 even 2 3549.2.a.bg.1.6 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.6 15 13.12 even 2
3549.2.a.bh.1.10 yes 15 1.1 even 1 trivial