Properties

Label 1859.2.a.h.1.3
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.756.1
Defining polynomial: \( x^{3} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.60168\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.60168 q^{3} -1.00000 q^{4} +3.76873 q^{5} +2.60168 q^{6} +0.167055 q^{7} -3.00000 q^{8} +3.76873 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.60168 q^{3} -1.00000 q^{4} +3.76873 q^{5} +2.60168 q^{6} +0.167055 q^{7} -3.00000 q^{8} +3.76873 q^{9} +3.76873 q^{10} +1.00000 q^{11} -2.60168 q^{12} +0.167055 q^{14} +9.80504 q^{15} -1.00000 q^{16} +4.37041 q^{17} +3.76873 q^{18} -3.37041 q^{19} -3.76873 q^{20} +0.434624 q^{21} +1.00000 q^{22} -5.20336 q^{23} -7.80504 q^{24} +9.20336 q^{25} +2.00000 q^{27} -0.167055 q^{28} +1.93579 q^{29} +9.80504 q^{30} +6.86925 q^{31} +5.00000 q^{32} +2.60168 q^{33} +4.37041 q^{34} +0.629587 q^{35} -3.76873 q^{36} +8.63798 q^{37} -3.37041 q^{38} -11.3062 q^{40} -1.26757 q^{41} +0.434624 q^{42} -7.20336 q^{43} -1.00000 q^{44} +14.2034 q^{45} -5.20336 q^{46} -10.1391 q^{47} -2.60168 q^{48} -6.97209 q^{49} +9.20336 q^{50} +11.3704 q^{51} +1.33411 q^{53} +2.00000 q^{54} +3.76873 q^{55} -0.501166 q^{56} -8.76873 q^{57} +1.93579 q^{58} +2.13915 q^{59} -9.80504 q^{60} -4.80504 q^{61} +6.86925 q^{62} +0.629587 q^{63} +7.00000 q^{64} +2.60168 q^{66} -4.13915 q^{67} -4.37041 q^{68} -13.5375 q^{69} +0.629587 q^{70} +6.00000 q^{71} -11.3062 q^{72} +14.2420 q^{73} +8.63798 q^{74} +23.9442 q^{75} +3.37041 q^{76} +0.167055 q^{77} -14.5738 q^{79} -3.76873 q^{80} -6.10284 q^{81} -1.26757 q^{82} -10.5738 q^{83} -0.434624 q^{84} +16.4709 q^{85} -7.20336 q^{86} +5.03630 q^{87} -3.00000 q^{88} +14.3062 q^{89} +14.2034 q^{90} +5.20336 q^{92} +17.8716 q^{93} -10.1391 q^{94} -12.7022 q^{95} +13.0084 q^{96} +3.56538 q^{97} -6.97209 q^{98} +3.76873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 9 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 6 q^{15} - 3 q^{16} - 3 q^{17} + 3 q^{18} + 6 q^{19} - 3 q^{20} - 6 q^{21} + 3 q^{22} + 12 q^{25} + 6 q^{27} - 3 q^{29} + 6 q^{30} + 6 q^{31} + 15 q^{32} - 3 q^{34} + 18 q^{35} - 3 q^{36} + 3 q^{37} + 6 q^{38} - 9 q^{40} + 3 q^{41} - 6 q^{42} - 6 q^{43} - 3 q^{44} + 27 q^{45} - 6 q^{47} + 3 q^{49} + 12 q^{50} + 18 q^{51} + 3 q^{53} + 6 q^{54} + 3 q^{55} - 18 q^{57} - 3 q^{58} - 18 q^{59} - 6 q^{60} + 9 q^{61} + 6 q^{62} + 18 q^{63} + 21 q^{64} + 12 q^{67} + 3 q^{68} - 24 q^{69} + 18 q^{70} + 18 q^{71} - 9 q^{72} + 9 q^{73} + 3 q^{74} + 24 q^{75} - 6 q^{76} - 12 q^{79} - 3 q^{80} - 9 q^{81} + 3 q^{82} + 6 q^{84} + 27 q^{85} - 6 q^{86} - 9 q^{88} + 18 q^{89} + 27 q^{90} + 36 q^{93} - 6 q^{94} - 24 q^{95} + 18 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 2.60168 1.50208 0.751040 0.660257i \(-0.229552\pi\)
0.751040 + 0.660257i \(0.229552\pi\)
\(4\) −1.00000 −0.500000
\(5\) 3.76873 1.68543 0.842715 0.538361i \(-0.180956\pi\)
0.842715 + 0.538361i \(0.180956\pi\)
\(6\) 2.60168 1.06213
\(7\) 0.167055 0.0631409 0.0315705 0.999502i \(-0.489949\pi\)
0.0315705 + 0.999502i \(0.489949\pi\)
\(8\) −3.00000 −1.06066
\(9\) 3.76873 1.25624
\(10\) 3.76873 1.19178
\(11\) 1.00000 0.301511
\(12\) −2.60168 −0.751040
\(13\) 0 0
\(14\) 0.167055 0.0446474
\(15\) 9.80504 2.53165
\(16\) −1.00000 −0.250000
\(17\) 4.37041 1.05998 0.529990 0.848004i \(-0.322195\pi\)
0.529990 + 0.848004i \(0.322195\pi\)
\(18\) 3.76873 0.888299
\(19\) −3.37041 −0.773226 −0.386613 0.922242i \(-0.626355\pi\)
−0.386613 + 0.922242i \(0.626355\pi\)
\(20\) −3.76873 −0.842715
\(21\) 0.434624 0.0948427
\(22\) 1.00000 0.213201
\(23\) −5.20336 −1.08498 −0.542488 0.840064i \(-0.682517\pi\)
−0.542488 + 0.840064i \(0.682517\pi\)
\(24\) −7.80504 −1.59320
\(25\) 9.20336 1.84067
\(26\) 0 0
\(27\) 2.00000 0.384900
\(28\) −0.167055 −0.0315705
\(29\) 1.93579 0.359467 0.179734 0.983715i \(-0.442476\pi\)
0.179734 + 0.983715i \(0.442476\pi\)
\(30\) 9.80504 1.79015
\(31\) 6.86925 1.23375 0.616877 0.787060i \(-0.288398\pi\)
0.616877 + 0.787060i \(0.288398\pi\)
\(32\) 5.00000 0.883883
\(33\) 2.60168 0.452894
\(34\) 4.37041 0.749520
\(35\) 0.629587 0.106420
\(36\) −3.76873 −0.628122
\(37\) 8.63798 1.42008 0.710038 0.704164i \(-0.248678\pi\)
0.710038 + 0.704164i \(0.248678\pi\)
\(38\) −3.37041 −0.546753
\(39\) 0 0
\(40\) −11.3062 −1.78767
\(41\) −1.26757 −0.197961 −0.0989805 0.995089i \(-0.531558\pi\)
−0.0989805 + 0.995089i \(0.531558\pi\)
\(42\) 0.434624 0.0670639
\(43\) −7.20336 −1.09850 −0.549251 0.835657i \(-0.685087\pi\)
−0.549251 + 0.835657i \(0.685087\pi\)
\(44\) −1.00000 −0.150756
\(45\) 14.2034 2.11731
\(46\) −5.20336 −0.767193
\(47\) −10.1391 −1.47895 −0.739473 0.673186i \(-0.764925\pi\)
−0.739473 + 0.673186i \(0.764925\pi\)
\(48\) −2.60168 −0.375520
\(49\) −6.97209 −0.996013
\(50\) 9.20336 1.30155
\(51\) 11.3704 1.59218
\(52\) 0 0
\(53\) 1.33411 0.183254 0.0916271 0.995793i \(-0.470793\pi\)
0.0916271 + 0.995793i \(0.470793\pi\)
\(54\) 2.00000 0.272166
\(55\) 3.76873 0.508176
\(56\) −0.501166 −0.0669711
\(57\) −8.76873 −1.16145
\(58\) 1.93579 0.254182
\(59\) 2.13915 0.278493 0.139247 0.990258i \(-0.455532\pi\)
0.139247 + 0.990258i \(0.455532\pi\)
\(60\) −9.80504 −1.26582
\(61\) −4.80504 −0.615222 −0.307611 0.951512i \(-0.599530\pi\)
−0.307611 + 0.951512i \(0.599530\pi\)
\(62\) 6.86925 0.872395
\(63\) 0.629587 0.0793205
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 2.60168 0.320245
\(67\) −4.13915 −0.505677 −0.252839 0.967508i \(-0.581364\pi\)
−0.252839 + 0.967508i \(0.581364\pi\)
\(68\) −4.37041 −0.529990
\(69\) −13.5375 −1.62972
\(70\) 0.629587 0.0752500
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −11.3062 −1.33245
\(73\) 14.2420 1.66690 0.833450 0.552596i \(-0.186363\pi\)
0.833450 + 0.552596i \(0.186363\pi\)
\(74\) 8.63798 1.00415
\(75\) 23.9442 2.76484
\(76\) 3.37041 0.386613
\(77\) 0.167055 0.0190377
\(78\) 0 0
\(79\) −14.5738 −1.63968 −0.819839 0.572595i \(-0.805937\pi\)
−0.819839 + 0.572595i \(0.805937\pi\)
\(80\) −3.76873 −0.421357
\(81\) −6.10284 −0.678094
\(82\) −1.26757 −0.139980
\(83\) −10.5738 −1.16062 −0.580311 0.814395i \(-0.697069\pi\)
−0.580311 + 0.814395i \(0.697069\pi\)
\(84\) −0.434624 −0.0474214
\(85\) 16.4709 1.78652
\(86\) −7.20336 −0.776758
\(87\) 5.03630 0.539948
\(88\) −3.00000 −0.319801
\(89\) 14.3062 1.51645 0.758227 0.651990i \(-0.226066\pi\)
0.758227 + 0.651990i \(0.226066\pi\)
\(90\) 14.2034 1.49717
\(91\) 0 0
\(92\) 5.20336 0.542488
\(93\) 17.8716 1.85320
\(94\) −10.1391 −1.04577
\(95\) −12.7022 −1.30322
\(96\) 13.0084 1.32766
\(97\) 3.56538 0.362009 0.181005 0.983482i \(-0.442065\pi\)
0.181005 + 0.983482i \(0.442065\pi\)
\(98\) −6.97209 −0.704288
\(99\) 3.76873 0.378772
\(100\) −9.20336 −0.920336
\(101\) −12.0363 −1.19766 −0.598828 0.800877i \(-0.704367\pi\)
−0.598828 + 0.800877i \(0.704367\pi\)
\(102\) 11.3704 1.12584
\(103\) −6.40672 −0.631273 −0.315636 0.948880i \(-0.602218\pi\)
−0.315636 + 0.948880i \(0.602218\pi\)
\(104\) 0 0
\(105\) 1.63798 0.159851
\(106\) 1.33411 0.129580
\(107\) −13.7045 −1.32487 −0.662433 0.749121i \(-0.730476\pi\)
−0.662433 + 0.749121i \(0.730476\pi\)
\(108\) −2.00000 −0.192450
\(109\) −8.84134 −0.846847 −0.423423 0.905932i \(-0.639172\pi\)
−0.423423 + 0.905932i \(0.639172\pi\)
\(110\) 3.76873 0.359335
\(111\) 22.4733 2.13307
\(112\) −0.167055 −0.0157852
\(113\) 4.56538 0.429474 0.214737 0.976672i \(-0.431110\pi\)
0.214737 + 0.976672i \(0.431110\pi\)
\(114\) −8.76873 −0.821267
\(115\) −19.6101 −1.82865
\(116\) −1.93579 −0.179734
\(117\) 0 0
\(118\) 2.13915 0.196925
\(119\) 0.730100 0.0669282
\(120\) −29.4151 −2.68522
\(121\) 1.00000 0.0909091
\(122\) −4.80504 −0.435028
\(123\) −3.29781 −0.297353
\(124\) −6.86925 −0.616877
\(125\) 15.8413 1.41689
\(126\) 0.629587 0.0560880
\(127\) −1.33178 −0.118176 −0.0590882 0.998253i \(-0.518819\pi\)
−0.0590882 + 0.998253i \(0.518819\pi\)
\(128\) −3.00000 −0.265165
\(129\) −18.7408 −1.65004
\(130\) 0 0
\(131\) 13.7045 1.19737 0.598685 0.800985i \(-0.295690\pi\)
0.598685 + 0.800985i \(0.295690\pi\)
\(132\) −2.60168 −0.226447
\(133\) −0.563045 −0.0488222
\(134\) −4.13915 −0.357568
\(135\) 7.53747 0.648722
\(136\) −13.1112 −1.12428
\(137\) −13.6403 −1.16537 −0.582685 0.812698i \(-0.697998\pi\)
−0.582685 + 0.812698i \(0.697998\pi\)
\(138\) −13.5375 −1.15239
\(139\) 0.869248 0.0737286 0.0368643 0.999320i \(-0.488263\pi\)
0.0368643 + 0.999320i \(0.488263\pi\)
\(140\) −0.629587 −0.0532098
\(141\) −26.3788 −2.22150
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) −3.76873 −0.314061
\(145\) 7.29548 0.605856
\(146\) 14.2420 1.17868
\(147\) −18.1391 −1.49609
\(148\) −8.63798 −0.710038
\(149\) 1.16706 0.0956089 0.0478044 0.998857i \(-0.484778\pi\)
0.0478044 + 0.998857i \(0.484778\pi\)
\(150\) 23.9442 1.95503
\(151\) −10.7408 −0.874076 −0.437038 0.899443i \(-0.643972\pi\)
−0.437038 + 0.899443i \(0.643972\pi\)
\(152\) 10.1112 0.820130
\(153\) 16.4709 1.33160
\(154\) 0.167055 0.0134617
\(155\) 25.8884 2.07940
\(156\) 0 0
\(157\) −4.59328 −0.366584 −0.183292 0.983059i \(-0.558675\pi\)
−0.183292 + 0.983059i \(0.558675\pi\)
\(158\) −14.5738 −1.15943
\(159\) 3.47093 0.275262
\(160\) 18.8437 1.48972
\(161\) −0.869248 −0.0685063
\(162\) −6.10284 −0.479485
\(163\) 11.3425 0.888414 0.444207 0.895924i \(-0.353486\pi\)
0.444207 + 0.895924i \(0.353486\pi\)
\(164\) 1.26757 0.0989805
\(165\) 9.80504 0.763321
\(166\) −10.5738 −0.820684
\(167\) 17.2760 1.33685 0.668427 0.743778i \(-0.266968\pi\)
0.668427 + 0.743778i \(0.266968\pi\)
\(168\) −1.30387 −0.100596
\(169\) 0 0
\(170\) 16.4709 1.26326
\(171\) −12.7022 −0.971361
\(172\) 7.20336 0.549251
\(173\) −12.8413 −0.976309 −0.488155 0.872757i \(-0.662330\pi\)
−0.488155 + 0.872757i \(0.662330\pi\)
\(174\) 5.03630 0.381801
\(175\) 1.53747 0.116222
\(176\) −1.00000 −0.0753778
\(177\) 5.56538 0.418319
\(178\) 14.3062 1.07230
\(179\) −4.93579 −0.368918 −0.184459 0.982840i \(-0.559053\pi\)
−0.184459 + 0.982840i \(0.559053\pi\)
\(180\) −14.2034 −1.05866
\(181\) 0.637982 0.0474208 0.0237104 0.999719i \(-0.492452\pi\)
0.0237104 + 0.999719i \(0.492452\pi\)
\(182\) 0 0
\(183\) −12.5012 −0.924113
\(184\) 15.6101 1.15079
\(185\) 32.5543 2.39344
\(186\) 17.8716 1.31041
\(187\) 4.37041 0.319596
\(188\) 10.1391 0.739473
\(189\) 0.334110 0.0243030
\(190\) −12.7022 −0.921514
\(191\) 26.1391 1.89136 0.945681 0.325096i \(-0.105396\pi\)
0.945681 + 0.325096i \(0.105396\pi\)
\(192\) 18.2118 1.31432
\(193\) −11.1391 −0.801813 −0.400907 0.916119i \(-0.631305\pi\)
−0.400907 + 0.916119i \(0.631305\pi\)
\(194\) 3.56538 0.255979
\(195\) 0 0
\(196\) 6.97209 0.498007
\(197\) 15.5375 1.10700 0.553499 0.832850i \(-0.313292\pi\)
0.553499 + 0.832850i \(0.313292\pi\)
\(198\) 3.76873 0.267832
\(199\) −11.6766 −0.827733 −0.413867 0.910337i \(-0.635822\pi\)
−0.413867 + 0.910337i \(0.635822\pi\)
\(200\) −27.6101 −1.95233
\(201\) −10.7687 −0.759568
\(202\) −12.0363 −0.846871
\(203\) 0.323384 0.0226971
\(204\) −11.3704 −0.796088
\(205\) −4.77713 −0.333649
\(206\) −6.40672 −0.446377
\(207\) −19.6101 −1.36299
\(208\) 0 0
\(209\) −3.37041 −0.233136
\(210\) 1.63798 0.113032
\(211\) −4.57377 −0.314871 −0.157436 0.987529i \(-0.550323\pi\)
−0.157436 + 0.987529i \(0.550323\pi\)
\(212\) −1.33411 −0.0916271
\(213\) 15.6101 1.06958
\(214\) −13.7045 −0.936822
\(215\) −27.1475 −1.85145
\(216\) −6.00000 −0.408248
\(217\) 1.14754 0.0779003
\(218\) −8.84134 −0.598811
\(219\) 37.0531 2.50382
\(220\) −3.76873 −0.254088
\(221\) 0 0
\(222\) 22.4733 1.50831
\(223\) −9.06421 −0.606984 −0.303492 0.952834i \(-0.598153\pi\)
−0.303492 + 0.952834i \(0.598153\pi\)
\(224\) 0.835276 0.0558092
\(225\) 34.6850 2.31233
\(226\) 4.56538 0.303684
\(227\) −13.2034 −0.876338 −0.438169 0.898893i \(-0.644373\pi\)
−0.438169 + 0.898893i \(0.644373\pi\)
\(228\) 8.76873 0.580724
\(229\) 2.02791 0.134008 0.0670039 0.997753i \(-0.478656\pi\)
0.0670039 + 0.997753i \(0.478656\pi\)
\(230\) −19.6101 −1.29305
\(231\) 0.434624 0.0285962
\(232\) −5.80737 −0.381272
\(233\) −12.7408 −0.834679 −0.417340 0.908751i \(-0.637037\pi\)
−0.417340 + 0.908751i \(0.637037\pi\)
\(234\) 0 0
\(235\) −38.2118 −2.49266
\(236\) −2.13915 −0.139247
\(237\) −37.9163 −2.46293
\(238\) 0.730100 0.0473254
\(239\) 4.07261 0.263435 0.131717 0.991287i \(-0.457951\pi\)
0.131717 + 0.991287i \(0.457951\pi\)
\(240\) −9.80504 −0.632912
\(241\) −18.9828 −1.22279 −0.611395 0.791325i \(-0.709392\pi\)
−0.611395 + 0.791325i \(0.709392\pi\)
\(242\) 1.00000 0.0642824
\(243\) −21.8776 −1.40345
\(244\) 4.80504 0.307611
\(245\) −26.2760 −1.67871
\(246\) −3.29781 −0.210261
\(247\) 0 0
\(248\) −20.6077 −1.30859
\(249\) −27.5096 −1.74335
\(250\) 15.8413 1.00189
\(251\) 10.3402 0.652666 0.326333 0.945255i \(-0.394187\pi\)
0.326333 + 0.945255i \(0.394187\pi\)
\(252\) −0.629587 −0.0396602
\(253\) −5.20336 −0.327132
\(254\) −1.33178 −0.0835633
\(255\) 42.8521 2.68350
\(256\) −17.0000 −1.06250
\(257\) 24.1755 1.50802 0.754012 0.656861i \(-0.228116\pi\)
0.754012 + 0.656861i \(0.228116\pi\)
\(258\) −18.7408 −1.16675
\(259\) 1.44302 0.0896649
\(260\) 0 0
\(261\) 7.29548 0.451579
\(262\) 13.7045 0.846668
\(263\) −10.7408 −0.662308 −0.331154 0.943577i \(-0.607438\pi\)
−0.331154 + 0.943577i \(0.607438\pi\)
\(264\) −7.80504 −0.480367
\(265\) 5.02791 0.308862
\(266\) −0.563045 −0.0345225
\(267\) 37.2201 2.27784
\(268\) 4.13915 0.252839
\(269\) 17.6659 1.07711 0.538554 0.842591i \(-0.318971\pi\)
0.538554 + 0.842591i \(0.318971\pi\)
\(270\) 7.53747 0.458716
\(271\) 8.74083 0.530967 0.265484 0.964115i \(-0.414468\pi\)
0.265484 + 0.964115i \(0.414468\pi\)
\(272\) −4.37041 −0.264995
\(273\) 0 0
\(274\) −13.6403 −0.824041
\(275\) 9.20336 0.554983
\(276\) 13.5375 0.814860
\(277\) 29.2118 1.75516 0.877582 0.479426i \(-0.159155\pi\)
0.877582 + 0.479426i \(0.159155\pi\)
\(278\) 0.869248 0.0521340
\(279\) 25.8884 1.54990
\(280\) −1.88876 −0.112875
\(281\) −10.8050 −0.644574 −0.322287 0.946642i \(-0.604452\pi\)
−0.322287 + 0.946642i \(0.604452\pi\)
\(282\) −26.3788 −1.57084
\(283\) 10.2397 0.608685 0.304342 0.952563i \(-0.401563\pi\)
0.304342 + 0.952563i \(0.401563\pi\)
\(284\) −6.00000 −0.356034
\(285\) −33.0470 −1.95754
\(286\) 0 0
\(287\) −0.211754 −0.0124994
\(288\) 18.8437 1.11037
\(289\) 2.10051 0.123560
\(290\) 7.29548 0.428405
\(291\) 9.27596 0.543767
\(292\) −14.2420 −0.833450
\(293\) 3.96370 0.231562 0.115781 0.993275i \(-0.463063\pi\)
0.115781 + 0.993275i \(0.463063\pi\)
\(294\) −18.1391 −1.05790
\(295\) 8.06188 0.469381
\(296\) −25.9139 −1.50622
\(297\) 2.00000 0.116052
\(298\) 1.16706 0.0676057
\(299\) 0 0
\(300\) −23.9442 −1.38242
\(301\) −1.20336 −0.0693604
\(302\) −10.7408 −0.618065
\(303\) −31.3146 −1.79898
\(304\) 3.37041 0.193306
\(305\) −18.1089 −1.03691
\(306\) 16.4709 0.941580
\(307\) 14.2397 0.812700 0.406350 0.913717i \(-0.366801\pi\)
0.406350 + 0.913717i \(0.366801\pi\)
\(308\) −0.167055 −0.00951885
\(309\) −16.6682 −0.948222
\(310\) 25.8884 1.47036
\(311\) 11.8776 0.673519 0.336760 0.941591i \(-0.390669\pi\)
0.336760 + 0.941591i \(0.390669\pi\)
\(312\) 0 0
\(313\) 7.89949 0.446505 0.223253 0.974761i \(-0.428332\pi\)
0.223253 + 0.974761i \(0.428332\pi\)
\(314\) −4.59328 −0.259214
\(315\) 2.37274 0.133689
\(316\) 14.5738 0.819839
\(317\) 27.3230 1.53461 0.767306 0.641281i \(-0.221597\pi\)
0.767306 + 0.641281i \(0.221597\pi\)
\(318\) 3.47093 0.194640
\(319\) 1.93579 0.108383
\(320\) 26.3811 1.47475
\(321\) −35.6548 −1.99006
\(322\) −0.869248 −0.0484413
\(323\) −14.7301 −0.819605
\(324\) 6.10284 0.339047
\(325\) 0 0
\(326\) 11.3425 0.628203
\(327\) −23.0023 −1.27203
\(328\) 3.80271 0.209969
\(329\) −1.69380 −0.0933821
\(330\) 9.80504 0.539750
\(331\) 4.74083 0.260579 0.130290 0.991476i \(-0.458409\pi\)
0.130290 + 0.991476i \(0.458409\pi\)
\(332\) 10.5738 0.580311
\(333\) 32.5543 1.78396
\(334\) 17.2760 0.945299
\(335\) −15.5993 −0.852283
\(336\) −0.434624 −0.0237107
\(337\) −32.4430 −1.76728 −0.883642 0.468163i \(-0.844916\pi\)
−0.883642 + 0.468163i \(0.844916\pi\)
\(338\) 0 0
\(339\) 11.8776 0.645105
\(340\) −16.4709 −0.893261
\(341\) 6.86925 0.371991
\(342\) −12.7022 −0.686856
\(343\) −2.33411 −0.126030
\(344\) 21.6101 1.16514
\(345\) −51.0191 −2.74678
\(346\) −12.8413 −0.690355
\(347\) −11.8329 −0.635226 −0.317613 0.948220i \(-0.602881\pi\)
−0.317613 + 0.948220i \(0.602881\pi\)
\(348\) −5.03630 −0.269974
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) 1.53747 0.0821812
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) −10.2034 −0.543070 −0.271535 0.962429i \(-0.587531\pi\)
−0.271535 + 0.962429i \(0.587531\pi\)
\(354\) 5.56538 0.295796
\(355\) 22.6124 1.20014
\(356\) −14.3062 −0.758227
\(357\) 1.89949 0.100531
\(358\) −4.93579 −0.260865
\(359\) −13.5375 −0.714480 −0.357240 0.934013i \(-0.616282\pi\)
−0.357240 + 0.934013i \(0.616282\pi\)
\(360\) −42.6101 −2.24575
\(361\) −7.64031 −0.402122
\(362\) 0.637982 0.0335316
\(363\) 2.60168 0.136553
\(364\) 0 0
\(365\) 53.6743 2.80944
\(366\) −12.5012 −0.653446
\(367\) −11.1475 −0.581897 −0.290949 0.956739i \(-0.593971\pi\)
−0.290949 + 0.956739i \(0.593971\pi\)
\(368\) 5.20336 0.271244
\(369\) −4.77713 −0.248687
\(370\) 32.5543 1.69242
\(371\) 0.222870 0.0115708
\(372\) −17.8716 −0.926598
\(373\) −27.3123 −1.41418 −0.707088 0.707126i \(-0.749991\pi\)
−0.707088 + 0.707126i \(0.749991\pi\)
\(374\) 4.37041 0.225989
\(375\) 41.2141 2.12829
\(376\) 30.4174 1.56866
\(377\) 0 0
\(378\) 0.334110 0.0171848
\(379\) 18.4067 0.945490 0.472745 0.881199i \(-0.343263\pi\)
0.472745 + 0.881199i \(0.343263\pi\)
\(380\) 12.7022 0.651609
\(381\) −3.46486 −0.177510
\(382\) 26.1391 1.33740
\(383\) −25.8716 −1.32198 −0.660988 0.750397i \(-0.729863\pi\)
−0.660988 + 0.750397i \(0.729863\pi\)
\(384\) −7.80504 −0.398299
\(385\) 0.629587 0.0320867
\(386\) −11.1391 −0.566968
\(387\) −27.1475 −1.37999
\(388\) −3.56538 −0.181005
\(389\) 20.7153 1.05030 0.525152 0.851008i \(-0.324008\pi\)
0.525152 + 0.851008i \(0.324008\pi\)
\(390\) 0 0
\(391\) −22.7408 −1.15005
\(392\) 20.9163 1.05643
\(393\) 35.6548 1.79855
\(394\) 15.5375 0.782766
\(395\) −54.9247 −2.76356
\(396\) −3.76873 −0.189386
\(397\) −21.5822 −1.08318 −0.541589 0.840643i \(-0.682177\pi\)
−0.541589 + 0.840643i \(0.682177\pi\)
\(398\) −11.6766 −0.585296
\(399\) −1.46486 −0.0733348
\(400\) −9.20336 −0.460168
\(401\) 0.203358 0.0101552 0.00507761 0.999987i \(-0.498384\pi\)
0.00507761 + 0.999987i \(0.498384\pi\)
\(402\) −10.7687 −0.537096
\(403\) 0 0
\(404\) 12.0363 0.598828
\(405\) −23.0000 −1.14288
\(406\) 0.323384 0.0160493
\(407\) 8.63798 0.428169
\(408\) −34.1112 −1.68876
\(409\) 0.0921180 0.00455494 0.00227747 0.999997i \(-0.499275\pi\)
0.00227747 + 0.999997i \(0.499275\pi\)
\(410\) −4.77713 −0.235926
\(411\) −35.4877 −1.75048
\(412\) 6.40672 0.315636
\(413\) 0.357356 0.0175843
\(414\) −19.6101 −0.963783
\(415\) −39.8497 −1.95615
\(416\) 0 0
\(417\) 2.26150 0.110746
\(418\) −3.37041 −0.164852
\(419\) 10.1284 0.494806 0.247403 0.968913i \(-0.420423\pi\)
0.247403 + 0.968913i \(0.420423\pi\)
\(420\) −1.63798 −0.0799253
\(421\) −6.58217 −0.320795 −0.160398 0.987052i \(-0.551278\pi\)
−0.160398 + 0.987052i \(0.551278\pi\)
\(422\) −4.57377 −0.222648
\(423\) −38.2118 −1.85792
\(424\) −4.00233 −0.194370
\(425\) 40.2225 1.95108
\(426\) 15.6101 0.756311
\(427\) −0.802706 −0.0388457
\(428\) 13.7045 0.662433
\(429\) 0 0
\(430\) −27.1475 −1.30917
\(431\) 17.4988 0.842889 0.421445 0.906854i \(-0.361523\pi\)
0.421445 + 0.906854i \(0.361523\pi\)
\(432\) −2.00000 −0.0962250
\(433\) −8.69380 −0.417797 −0.208899 0.977937i \(-0.566988\pi\)
−0.208899 + 0.977937i \(0.566988\pi\)
\(434\) 1.14754 0.0550838
\(435\) 18.9805 0.910045
\(436\) 8.84134 0.423423
\(437\) 17.5375 0.838931
\(438\) 37.0531 1.77047
\(439\) −24.5738 −1.17284 −0.586421 0.810006i \(-0.699464\pi\)
−0.586421 + 0.810006i \(0.699464\pi\)
\(440\) −11.3062 −0.539002
\(441\) −26.2760 −1.25124
\(442\) 0 0
\(443\) −17.2699 −0.820518 −0.410259 0.911969i \(-0.634562\pi\)
−0.410259 + 0.911969i \(0.634562\pi\)
\(444\) −22.4733 −1.06653
\(445\) 53.9163 2.55588
\(446\) −9.06421 −0.429203
\(447\) 3.03630 0.143612
\(448\) 1.16939 0.0552483
\(449\) 16.3230 0.770330 0.385165 0.922848i \(-0.374145\pi\)
0.385165 + 0.922848i \(0.374145\pi\)
\(450\) 34.6850 1.63507
\(451\) −1.26757 −0.0596875
\(452\) −4.56538 −0.214737
\(453\) −27.9442 −1.31293
\(454\) −13.2034 −0.619664
\(455\) 0 0
\(456\) 26.3062 1.23190
\(457\) 21.4174 1.00187 0.500933 0.865486i \(-0.332990\pi\)
0.500933 + 0.865486i \(0.332990\pi\)
\(458\) 2.02791 0.0947579
\(459\) 8.74083 0.407987
\(460\) 19.6101 0.914324
\(461\) −17.8074 −0.829372 −0.414686 0.909965i \(-0.636109\pi\)
−0.414686 + 0.909965i \(0.636109\pi\)
\(462\) 0.434624 0.0202205
\(463\) 4.80271 0.223201 0.111600 0.993753i \(-0.464402\pi\)
0.111600 + 0.993753i \(0.464402\pi\)
\(464\) −1.93579 −0.0898668
\(465\) 67.3532 3.12343
\(466\) −12.7408 −0.590207
\(467\) −2.80737 −0.129910 −0.0649548 0.997888i \(-0.520690\pi\)
−0.0649548 + 0.997888i \(0.520690\pi\)
\(468\) 0 0
\(469\) −0.691466 −0.0319289
\(470\) −38.2118 −1.76258
\(471\) −11.9502 −0.550638
\(472\) −6.41744 −0.295387
\(473\) −7.20336 −0.331211
\(474\) −37.9163 −1.74155
\(475\) −31.0191 −1.42325
\(476\) −0.730100 −0.0334641
\(477\) 5.02791 0.230212
\(478\) 4.07261 0.186277
\(479\) 11.8329 0.540661 0.270331 0.962768i \(-0.412867\pi\)
0.270331 + 0.962768i \(0.412867\pi\)
\(480\) 49.0252 2.23768
\(481\) 0 0
\(482\) −18.9828 −0.864644
\(483\) −2.26150 −0.102902
\(484\) −1.00000 −0.0454545
\(485\) 13.4370 0.610141
\(486\) −21.8776 −0.992390
\(487\) −16.4174 −0.743945 −0.371973 0.928244i \(-0.621318\pi\)
−0.371973 + 0.928244i \(0.621318\pi\)
\(488\) 14.4151 0.652541
\(489\) 29.5096 1.33447
\(490\) −26.2760 −1.18703
\(491\) 7.83294 0.353496 0.176748 0.984256i \(-0.443442\pi\)
0.176748 + 0.984256i \(0.443442\pi\)
\(492\) 3.29781 0.148677
\(493\) 8.46020 0.381028
\(494\) 0 0
\(495\) 14.2034 0.638393
\(496\) −6.86925 −0.308438
\(497\) 1.00233 0.0449607
\(498\) −27.5096 −1.23273
\(499\) 12.2722 0.549381 0.274690 0.961533i \(-0.411425\pi\)
0.274690 + 0.961533i \(0.411425\pi\)
\(500\) −15.8413 −0.708446
\(501\) 44.9465 2.00806
\(502\) 10.3402 0.461505
\(503\) 1.10891 0.0494438 0.0247219 0.999694i \(-0.492130\pi\)
0.0247219 + 0.999694i \(0.492130\pi\)
\(504\) −1.88876 −0.0841320
\(505\) −45.3616 −2.01857
\(506\) −5.20336 −0.231317
\(507\) 0 0
\(508\) 1.33178 0.0590882
\(509\) −23.8692 −1.05799 −0.528993 0.848626i \(-0.677430\pi\)
−0.528993 + 0.848626i \(0.677430\pi\)
\(510\) 42.8521 1.89752
\(511\) 2.37920 0.105250
\(512\) −11.0000 −0.486136
\(513\) −6.74083 −0.297615
\(514\) 24.1755 1.06633
\(515\) −24.1452 −1.06397
\(516\) 18.7408 0.825019
\(517\) −10.1391 −0.445919
\(518\) 1.44302 0.0634026
\(519\) −33.4090 −1.46649
\(520\) 0 0
\(521\) 18.3318 0.803130 0.401565 0.915831i \(-0.368466\pi\)
0.401565 + 0.915831i \(0.368466\pi\)
\(522\) 7.29548 0.319314
\(523\) −10.4407 −0.456539 −0.228270 0.973598i \(-0.573307\pi\)
−0.228270 + 0.973598i \(0.573307\pi\)
\(524\) −13.7045 −0.598685
\(525\) 4.00000 0.174574
\(526\) −10.7408 −0.468322
\(527\) 30.0215 1.30776
\(528\) −2.60168 −0.113224
\(529\) 4.07494 0.177171
\(530\) 5.02791 0.218398
\(531\) 8.06188 0.349856
\(532\) 0.563045 0.0244111
\(533\) 0 0
\(534\) 37.2201 1.61067
\(535\) −51.6487 −2.23297
\(536\) 12.4174 0.536352
\(537\) −12.8413 −0.554145
\(538\) 17.6659 0.761631
\(539\) −6.97209 −0.300309
\(540\) −7.53747 −0.324361
\(541\) −11.0554 −0.475310 −0.237655 0.971350i \(-0.576379\pi\)
−0.237655 + 0.971350i \(0.576379\pi\)
\(542\) 8.74083 0.375451
\(543\) 1.65983 0.0712299
\(544\) 21.8521 0.936900
\(545\) −33.3207 −1.42730
\(546\) 0 0
\(547\) 25.3532 1.08403 0.542013 0.840370i \(-0.317662\pi\)
0.542013 + 0.840370i \(0.317662\pi\)
\(548\) 13.6403 0.582685
\(549\) −18.1089 −0.772869
\(550\) 9.20336 0.392433
\(551\) −6.52441 −0.277949
\(552\) 40.6124 1.72858
\(553\) −2.43462 −0.103531
\(554\) 29.2118 1.24109
\(555\) 84.6957 3.59513
\(556\) −0.869248 −0.0368643
\(557\) 20.3425 0.861940 0.430970 0.902366i \(-0.358172\pi\)
0.430970 + 0.902366i \(0.358172\pi\)
\(558\) 25.8884 1.09594
\(559\) 0 0
\(560\) −0.629587 −0.0266049
\(561\) 11.3704 0.480059
\(562\) −10.8050 −0.455783
\(563\) −6.77480 −0.285524 −0.142762 0.989757i \(-0.545598\pi\)
−0.142762 + 0.989757i \(0.545598\pi\)
\(564\) 26.3788 1.11075
\(565\) 17.2057 0.723849
\(566\) 10.2397 0.430405
\(567\) −1.01951 −0.0428155
\(568\) −18.0000 −0.755263
\(569\) 16.8739 0.707391 0.353696 0.935361i \(-0.384925\pi\)
0.353696 + 0.935361i \(0.384925\pi\)
\(570\) −33.0470 −1.38419
\(571\) 44.9973 1.88308 0.941539 0.336905i \(-0.109380\pi\)
0.941539 + 0.336905i \(0.109380\pi\)
\(572\) 0 0
\(573\) 68.0057 2.84098
\(574\) −0.211754 −0.00883844
\(575\) −47.8884 −1.99708
\(576\) 26.3811 1.09921
\(577\) −19.5119 −0.812291 −0.406145 0.913808i \(-0.633127\pi\)
−0.406145 + 0.913808i \(0.633127\pi\)
\(578\) 2.10051 0.0873698
\(579\) −28.9805 −1.20439
\(580\) −7.29548 −0.302928
\(581\) −1.76640 −0.0732828
\(582\) 9.27596 0.384501
\(583\) 1.33411 0.0552532
\(584\) −42.7260 −1.76801
\(585\) 0 0
\(586\) 3.96370 0.163739
\(587\) 16.6789 0.688414 0.344207 0.938894i \(-0.388148\pi\)
0.344207 + 0.938894i \(0.388148\pi\)
\(588\) 18.1391 0.748046
\(589\) −23.1522 −0.953970
\(590\) 8.06188 0.331902
\(591\) 40.4235 1.66280
\(592\) −8.63798 −0.355019
\(593\) −29.4128 −1.20784 −0.603919 0.797046i \(-0.706395\pi\)
−0.603919 + 0.797046i \(0.706395\pi\)
\(594\) 2.00000 0.0820610
\(595\) 2.75155 0.112803
\(596\) −1.16706 −0.0478044
\(597\) −30.3788 −1.24332
\(598\) 0 0
\(599\) 6.12842 0.250400 0.125200 0.992131i \(-0.460043\pi\)
0.125200 + 0.992131i \(0.460043\pi\)
\(600\) −71.8326 −2.93255
\(601\) 25.0061 1.02002 0.510009 0.860169i \(-0.329642\pi\)
0.510009 + 0.860169i \(0.329642\pi\)
\(602\) −1.20336 −0.0490452
\(603\) −15.5993 −0.635255
\(604\) 10.7408 0.437038
\(605\) 3.76873 0.153221
\(606\) −31.3146 −1.27207
\(607\) 32.4407 1.31673 0.658363 0.752700i \(-0.271249\pi\)
0.658363 + 0.752700i \(0.271249\pi\)
\(608\) −16.8521 −0.683442
\(609\) 0.841340 0.0340928
\(610\) −18.1089 −0.733208
\(611\) 0 0
\(612\) −16.4709 −0.665798
\(613\) −16.5714 −0.669314 −0.334657 0.942340i \(-0.608620\pi\)
−0.334657 + 0.942340i \(0.608620\pi\)
\(614\) 14.2397 0.574666
\(615\) −12.4286 −0.501168
\(616\) −0.501166 −0.0201925
\(617\) −17.8692 −0.719389 −0.359694 0.933070i \(-0.617119\pi\)
−0.359694 + 0.933070i \(0.617119\pi\)
\(618\) −16.6682 −0.670494
\(619\) −27.4151 −1.10191 −0.550953 0.834536i \(-0.685736\pi\)
−0.550953 + 0.834536i \(0.685736\pi\)
\(620\) −25.8884 −1.03970
\(621\) −10.4067 −0.417607
\(622\) 11.8776 0.476250
\(623\) 2.38993 0.0957503
\(624\) 0 0
\(625\) 13.6850 0.547400
\(626\) 7.89949 0.315727
\(627\) −8.76873 −0.350190
\(628\) 4.59328 0.183292
\(629\) 37.7516 1.50525
\(630\) 2.37274 0.0945324
\(631\) 6.54586 0.260587 0.130293 0.991475i \(-0.458408\pi\)
0.130293 + 0.991475i \(0.458408\pi\)
\(632\) 43.7213 1.73914
\(633\) −11.8995 −0.472962
\(634\) 27.3230 1.08513
\(635\) −5.01912 −0.199178
\(636\) −3.47093 −0.137631
\(637\) 0 0
\(638\) 1.93579 0.0766386
\(639\) 22.6124 0.894533
\(640\) −11.3062 −0.446917
\(641\) 2.07494 0.0819551 0.0409775 0.999160i \(-0.486953\pi\)
0.0409775 + 0.999160i \(0.486953\pi\)
\(642\) −35.6548 −1.40718
\(643\) −12.2676 −0.483786 −0.241893 0.970303i \(-0.577768\pi\)
−0.241893 + 0.970303i \(0.577768\pi\)
\(644\) 0.869248 0.0342532
\(645\) −70.6292 −2.78102
\(646\) −14.7301 −0.579548
\(647\) 47.0871 1.85118 0.925592 0.378523i \(-0.123568\pi\)
0.925592 + 0.378523i \(0.123568\pi\)
\(648\) 18.3085 0.719227
\(649\) 2.13915 0.0839689
\(650\) 0 0
\(651\) 2.98554 0.117013
\(652\) −11.3425 −0.444207
\(653\) −21.1028 −0.825818 −0.412909 0.910772i \(-0.635487\pi\)
−0.412909 + 0.910772i \(0.635487\pi\)
\(654\) −23.0023 −0.899462
\(655\) 51.6487 2.01808
\(656\) 1.26757 0.0494902
\(657\) 53.6743 2.09403
\(658\) −1.69380 −0.0660311
\(659\) −18.3895 −0.716355 −0.358177 0.933654i \(-0.616602\pi\)
−0.358177 + 0.933654i \(0.616602\pi\)
\(660\) −9.80504 −0.381661
\(661\) 16.6938 0.649313 0.324657 0.945832i \(-0.394751\pi\)
0.324657 + 0.945832i \(0.394751\pi\)
\(662\) 4.74083 0.184257
\(663\) 0 0
\(664\) 31.7213 1.23103
\(665\) −2.12197 −0.0822864
\(666\) 32.5543 1.26145
\(667\) −10.0726 −0.390013
\(668\) −17.2760 −0.668427
\(669\) −23.5822 −0.911739
\(670\) −15.5993 −0.602655
\(671\) −4.80504 −0.185496
\(672\) 2.17312 0.0838299
\(673\) 29.6185 1.14171 0.570854 0.821052i \(-0.306612\pi\)
0.570854 + 0.821052i \(0.306612\pi\)
\(674\) −32.4430 −1.24966
\(675\) 18.4067 0.708475
\(676\) 0 0
\(677\) −22.6124 −0.869065 −0.434533 0.900656i \(-0.643086\pi\)
−0.434533 + 0.900656i \(0.643086\pi\)
\(678\) 11.8776 0.456158
\(679\) 0.595615 0.0228576
\(680\) −49.4128 −1.89489
\(681\) −34.3509 −1.31633
\(682\) 6.86925 0.263037
\(683\) 33.1429 1.26818 0.634089 0.773260i \(-0.281375\pi\)
0.634089 + 0.773260i \(0.281375\pi\)
\(684\) 12.7022 0.485680
\(685\) −51.4067 −1.96415
\(686\) −2.33411 −0.0891167
\(687\) 5.27596 0.201291
\(688\) 7.20336 0.274625
\(689\) 0 0
\(690\) −51.0191 −1.94226
\(691\) 16.2057 0.616493 0.308247 0.951306i \(-0.400258\pi\)
0.308247 + 0.951306i \(0.400258\pi\)
\(692\) 12.8413 0.488155
\(693\) 0.629587 0.0239160
\(694\) −11.8329 −0.449172
\(695\) 3.27596 0.124264
\(696\) −15.1089 −0.572702
\(697\) −5.53980 −0.209835
\(698\) 30.0000 1.13552
\(699\) −33.1475 −1.25376
\(700\) −1.53747 −0.0581109
\(701\) 16.7855 0.633981 0.316990 0.948429i \(-0.397328\pi\)
0.316990 + 0.948429i \(0.397328\pi\)
\(702\) 0 0
\(703\) −29.1136 −1.09804
\(704\) 7.00000 0.263822
\(705\) −99.4147 −3.74418
\(706\) −10.2034 −0.384008
\(707\) −2.01073 −0.0756212
\(708\) −5.56538 −0.209160
\(709\) 27.6292 1.03764 0.518818 0.854885i \(-0.326372\pi\)
0.518818 + 0.854885i \(0.326372\pi\)
\(710\) 22.6124 0.848628
\(711\) −54.9247 −2.05984
\(712\) −42.9186 −1.60844
\(713\) −35.7432 −1.33859
\(714\) 1.89949 0.0710865
\(715\) 0 0
\(716\) 4.93579 0.184459
\(717\) 10.5956 0.395700
\(718\) −13.5375 −0.505214
\(719\) 9.40905 0.350898 0.175449 0.984488i \(-0.443862\pi\)
0.175449 + 0.984488i \(0.443862\pi\)
\(720\) −14.2034 −0.529328
\(721\) −1.07028 −0.0398591
\(722\) −7.64031 −0.284343
\(723\) −49.3872 −1.83673
\(724\) −0.637982 −0.0237104
\(725\) 17.8158 0.661661
\(726\) 2.60168 0.0965574
\(727\) 20.6682 0.766542 0.383271 0.923636i \(-0.374798\pi\)
0.383271 + 0.923636i \(0.374798\pi\)
\(728\) 0 0
\(729\) −38.6101 −1.43000
\(730\) 53.6743 1.98657
\(731\) −31.4817 −1.16439
\(732\) 12.5012 0.462056
\(733\) 26.1368 0.965385 0.482693 0.875790i \(-0.339659\pi\)
0.482693 + 0.875790i \(0.339659\pi\)
\(734\) −11.1475 −0.411463
\(735\) −68.3616 −2.52156
\(736\) −26.0168 −0.958992
\(737\) −4.13915 −0.152467
\(738\) −4.77713 −0.175849
\(739\) −16.4793 −0.606202 −0.303101 0.952958i \(-0.598022\pi\)
−0.303101 + 0.952958i \(0.598022\pi\)
\(740\) −32.5543 −1.19672
\(741\) 0 0
\(742\) 0.222870 0.00818182
\(743\) 29.6440 1.08753 0.543767 0.839236i \(-0.316997\pi\)
0.543767 + 0.839236i \(0.316997\pi\)
\(744\) −53.6147 −1.96561
\(745\) 4.39832 0.161142
\(746\) −27.3123 −0.999973
\(747\) −39.8497 −1.45803
\(748\) −4.37041 −0.159798
\(749\) −2.28941 −0.0836533
\(750\) 41.2141 1.50493
\(751\) 25.3486 0.924982 0.462491 0.886624i \(-0.346956\pi\)
0.462491 + 0.886624i \(0.346956\pi\)
\(752\) 10.1391 0.369737
\(753\) 26.9018 0.980357
\(754\) 0 0
\(755\) −40.4793 −1.47319
\(756\) −0.334110 −0.0121515
\(757\) 31.7320 1.15332 0.576660 0.816984i \(-0.304356\pi\)
0.576660 + 0.816984i \(0.304356\pi\)
\(758\) 18.4067 0.668562
\(759\) −13.5375 −0.491379
\(760\) 38.1066 1.38227
\(761\) −43.8837 −1.59078 −0.795392 0.606096i \(-0.792735\pi\)
−0.795392 + 0.606096i \(0.792735\pi\)
\(762\) −3.46486 −0.125519
\(763\) −1.47699 −0.0534707
\(764\) −26.1391 −0.945681
\(765\) 62.0745 2.24431
\(766\) −25.8716 −0.934778
\(767\) 0 0
\(768\) −44.2285 −1.59596
\(769\) −15.6147 −0.563082 −0.281541 0.959549i \(-0.590846\pi\)
−0.281541 + 0.959549i \(0.590846\pi\)
\(770\) 0.629587 0.0226887
\(771\) 62.8968 2.26517
\(772\) 11.1391 0.400907
\(773\) −22.2504 −0.800291 −0.400145 0.916452i \(-0.631040\pi\)
−0.400145 + 0.916452i \(0.631040\pi\)
\(774\) −27.1475 −0.975798
\(775\) 63.2201 2.27093
\(776\) −10.6961 −0.383969
\(777\) 3.75427 0.134684
\(778\) 20.7153 0.742678
\(779\) 4.27223 0.153069
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) −22.7408 −0.813210
\(783\) 3.87158 0.138359
\(784\) 6.97209 0.249003
\(785\) −17.3109 −0.617851
\(786\) 35.6548 1.27176
\(787\) 53.9828 1.92428 0.962140 0.272556i \(-0.0878691\pi\)
0.962140 + 0.272556i \(0.0878691\pi\)
\(788\) −15.5375 −0.553499
\(789\) −27.9442 −0.994839
\(790\) −54.9247 −1.95413
\(791\) 0.762670 0.0271174
\(792\) −11.3062 −0.401748
\(793\) 0 0
\(794\) −21.5822 −0.765922
\(795\) 13.0810 0.463935
\(796\) 11.6766 0.413867
\(797\) −32.9912 −1.16861 −0.584304 0.811535i \(-0.698633\pi\)
−0.584304 + 0.811535i \(0.698633\pi\)
\(798\) −1.46486 −0.0518556
\(799\) −44.3123 −1.56766
\(800\) 46.0168 1.62694
\(801\) 53.9163 1.90504
\(802\) 0.203358 0.00718083
\(803\) 14.2420 0.502589
\(804\) 10.7687 0.379784
\(805\) −3.27596 −0.115463
\(806\) 0 0
\(807\) 45.9610 1.61790
\(808\) 36.1089 1.27031
\(809\) −32.7771 −1.15238 −0.576191 0.817315i \(-0.695462\pi\)
−0.576191 + 0.817315i \(0.695462\pi\)
\(810\) −23.0000 −0.808138
\(811\) 4.94185 0.173532 0.0867660 0.996229i \(-0.472347\pi\)
0.0867660 + 0.996229i \(0.472347\pi\)
\(812\) −0.323384 −0.0113485
\(813\) 22.7408 0.797556
\(814\) 8.63798 0.302761
\(815\) 42.7469 1.49736
\(816\) −11.3704 −0.398044
\(817\) 24.2783 0.849390
\(818\) 0.0921180 0.00322083
\(819\) 0 0
\(820\) 4.77713 0.166825
\(821\) −19.8158 −0.691575 −0.345787 0.938313i \(-0.612388\pi\)
−0.345787 + 0.938313i \(0.612388\pi\)
\(822\) −35.4877 −1.23778
\(823\) 28.1499 0.981243 0.490621 0.871373i \(-0.336770\pi\)
0.490621 + 0.871373i \(0.336770\pi\)
\(824\) 19.2201 0.669566
\(825\) 23.9442 0.833630
\(826\) 0.357356 0.0124340
\(827\) 33.0578 1.14953 0.574765 0.818318i \(-0.305093\pi\)
0.574765 + 0.818318i \(0.305093\pi\)
\(828\) 19.6101 0.681497
\(829\) −14.9721 −0.520002 −0.260001 0.965608i \(-0.583723\pi\)
−0.260001 + 0.965608i \(0.583723\pi\)
\(830\) −39.8497 −1.38320
\(831\) 75.9996 2.63640
\(832\) 0 0
\(833\) −30.4709 −1.05576
\(834\) 2.26150 0.0783095
\(835\) 65.1085 2.25317
\(836\) 3.37041 0.116568
\(837\) 13.7385 0.474872
\(838\) 10.1284 0.349880
\(839\) −13.0131 −0.449261 −0.224630 0.974444i \(-0.572117\pi\)
−0.224630 + 0.974444i \(0.572117\pi\)
\(840\) −4.91395 −0.169547
\(841\) −25.2527 −0.870783
\(842\) −6.58217 −0.226836
\(843\) −28.1112 −0.968203
\(844\) 4.57377 0.157436
\(845\) 0 0
\(846\) −38.2118 −1.31375
\(847\) 0.167055 0.00574008
\(848\) −1.33411 −0.0458135
\(849\) 26.6403 0.914293
\(850\) 40.2225 1.37962
\(851\) −44.9465 −1.54075
\(852\) −15.6101 −0.534792
\(853\) 25.3448 0.867791 0.433895 0.900963i \(-0.357139\pi\)
0.433895 + 0.900963i \(0.357139\pi\)
\(854\) −0.802706 −0.0274680
\(855\) −47.8712 −1.63716
\(856\) 41.1136 1.40523
\(857\) 49.5627 1.69303 0.846514 0.532366i \(-0.178697\pi\)
0.846514 + 0.532366i \(0.178697\pi\)
\(858\) 0 0
\(859\) −55.6208 −1.89776 −0.948879 0.315641i \(-0.897780\pi\)
−0.948879 + 0.315641i \(0.897780\pi\)
\(860\) 27.1475 0.925724
\(861\) −0.550916 −0.0187752
\(862\) 17.4988 0.596013
\(863\) 10.6124 0.361250 0.180625 0.983552i \(-0.442188\pi\)
0.180625 + 0.983552i \(0.442188\pi\)
\(864\) 10.0000 0.340207
\(865\) −48.3956 −1.64550
\(866\) −8.69380 −0.295427
\(867\) 5.46486 0.185596
\(868\) −1.14754 −0.0389502
\(869\) −14.5738 −0.494381
\(870\) 18.9805 0.643499
\(871\) 0 0
\(872\) 26.5240 0.898217
\(873\) 13.4370 0.454772
\(874\) 17.5375 0.593214
\(875\) 2.64638 0.0894639
\(876\) −37.0531 −1.25191
\(877\) 53.8474 1.81830 0.909149 0.416471i \(-0.136733\pi\)
0.909149 + 0.416471i \(0.136733\pi\)
\(878\) −24.5738 −0.829325
\(879\) 10.3123 0.347824
\(880\) −3.76873 −0.127044
\(881\) −1.20103 −0.0404636 −0.0202318 0.999795i \(-0.506440\pi\)
−0.0202318 + 0.999795i \(0.506440\pi\)
\(882\) −26.2760 −0.884758
\(883\) 58.4793 1.96799 0.983993 0.178207i \(-0.0570298\pi\)
0.983993 + 0.178207i \(0.0570298\pi\)
\(884\) 0 0
\(885\) 20.9744 0.705048
\(886\) −17.2699 −0.580194
\(887\) −27.3364 −0.917868 −0.458934 0.888470i \(-0.651769\pi\)
−0.458934 + 0.888470i \(0.651769\pi\)
\(888\) −67.4198 −2.26246
\(889\) −0.222481 −0.00746176
\(890\) 53.9163 1.80728
\(891\) −6.10284 −0.204453
\(892\) 9.06421 0.303492
\(893\) 34.1731 1.14356
\(894\) 3.03630 0.101549
\(895\) −18.6017 −0.621786
\(896\) −0.501166 −0.0167428
\(897\) 0 0
\(898\) 16.3230 0.544705
\(899\) 13.2974 0.443494
\(900\) −34.6850 −1.15617
\(901\) 5.83061 0.194246
\(902\) −1.26757 −0.0422054
\(903\) −3.13075 −0.104185
\(904\) −13.6961 −0.455526
\(905\) 2.40439 0.0799245
\(906\) −27.9442 −0.928383
\(907\) −17.6598 −0.586385 −0.293192 0.956053i \(-0.594718\pi\)
−0.293192 + 0.956053i \(0.594718\pi\)
\(908\) 13.2034 0.438169
\(909\) −45.3616 −1.50455
\(910\) 0 0
\(911\) −20.8074 −0.689379 −0.344689 0.938717i \(-0.612016\pi\)
−0.344689 + 0.938717i \(0.612016\pi\)
\(912\) 8.76873 0.290362
\(913\) −10.5738 −0.349941
\(914\) 21.4174 0.708426
\(915\) −47.1136 −1.55753
\(916\) −2.02791 −0.0670039
\(917\) 2.28941 0.0756030
\(918\) 8.74083 0.288490
\(919\) 57.3700 1.89246 0.946231 0.323491i \(-0.104857\pi\)
0.946231 + 0.323491i \(0.104857\pi\)
\(920\) 58.8302 1.93958
\(921\) 37.0470 1.22074
\(922\) −17.8074 −0.586454
\(923\) 0 0
\(924\) −0.434624 −0.0142981
\(925\) 79.4984 2.61389
\(926\) 4.80271 0.157827
\(927\) −24.1452 −0.793033
\(928\) 9.67895 0.317727
\(929\) 47.1452 1.54678 0.773392 0.633928i \(-0.218558\pi\)
0.773392 + 0.633928i \(0.218558\pi\)
\(930\) 67.3532 2.20860
\(931\) 23.4988 0.770143
\(932\) 12.7408 0.417340
\(933\) 30.9018 1.01168
\(934\) −2.80737 −0.0918599
\(935\) 16.4709 0.538657
\(936\) 0 0
\(937\) 24.2820 0.793259 0.396630 0.917979i \(-0.370180\pi\)
0.396630 + 0.917979i \(0.370180\pi\)
\(938\) −0.691466 −0.0225772
\(939\) 20.5519 0.670687
\(940\) 38.2118 1.24633
\(941\) 12.7408 0.415339 0.207670 0.978199i \(-0.433412\pi\)
0.207670 + 0.978199i \(0.433412\pi\)
\(942\) −11.9502 −0.389360
\(943\) 6.59561 0.214783
\(944\) −2.13915 −0.0696233
\(945\) 1.25917 0.0409609
\(946\) −7.20336 −0.234201
\(947\) −11.0749 −0.359887 −0.179944 0.983677i \(-0.557592\pi\)
−0.179944 + 0.983677i \(0.557592\pi\)
\(948\) 37.9163 1.23146
\(949\) 0 0
\(950\) −31.0191 −1.00639
\(951\) 71.0857 2.30511
\(952\) −2.19030 −0.0709880
\(953\) 50.3677 1.63157 0.815785 0.578356i \(-0.196305\pi\)
0.815785 + 0.578356i \(0.196305\pi\)
\(954\) 5.02791 0.162785
\(955\) 98.5115 3.18776
\(956\) −4.07261 −0.131717
\(957\) 5.03630 0.162801
\(958\) 11.8329 0.382305
\(959\) −2.27868 −0.0735826
\(960\) 68.6353 2.21519
\(961\) 16.1866 0.522147
\(962\) 0 0
\(963\) −51.6487 −1.66436
\(964\) 18.9828 0.611395
\(965\) −41.9805 −1.35140
\(966\) −2.26150 −0.0727627
\(967\) 47.7213 1.53461 0.767307 0.641280i \(-0.221596\pi\)
0.767307 + 0.641280i \(0.221596\pi\)
\(968\) −3.00000 −0.0964237
\(969\) −38.3230 −1.23111
\(970\) 13.4370 0.431435
\(971\) −30.7469 −0.986715 −0.493357 0.869827i \(-0.664231\pi\)
−0.493357 + 0.869827i \(0.664231\pi\)
\(972\) 21.8776 0.701726
\(973\) 0.145212 0.00465529
\(974\) −16.4174 −0.526049
\(975\) 0 0
\(976\) 4.80504 0.153805
\(977\) −22.6426 −0.724402 −0.362201 0.932100i \(-0.617975\pi\)
−0.362201 + 0.932100i \(0.617975\pi\)
\(978\) 29.5096 0.943612
\(979\) 14.3062 0.457228
\(980\) 26.2760 0.839355
\(981\) −33.3207 −1.06385
\(982\) 7.83294 0.249959
\(983\) 2.40672 0.0767623 0.0383812 0.999263i \(-0.487780\pi\)
0.0383812 + 0.999263i \(0.487780\pi\)
\(984\) 9.89342 0.315391
\(985\) 58.5566 1.86577
\(986\) 8.46020 0.269428
\(987\) −4.40672 −0.140267
\(988\) 0 0
\(989\) 37.4817 1.19185
\(990\) 14.2034 0.451412
\(991\) 13.2094 0.419611 0.209806 0.977743i \(-0.432717\pi\)
0.209806 + 0.977743i \(0.432717\pi\)
\(992\) 34.3462 1.09049
\(993\) 12.3341 0.391411
\(994\) 1.00233 0.0317920
\(995\) −44.0061 −1.39509
\(996\) 27.5096 0.871674
\(997\) 17.2565 0.546517 0.273259 0.961941i \(-0.411899\pi\)
0.273259 + 0.961941i \(0.411899\pi\)
\(998\) 12.2722 0.388471
\(999\) 17.2760 0.546587
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 1859.2.a.h.1.3 3
13.3 even 3 143.2.e.a.100.1 6
13.9 even 3 143.2.e.a.133.1 yes 6
13.12 even 2 1859.2.a.e.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.e.a.100.1 6 13.3 even 3
143.2.e.a.133.1 yes 6 13.9 even 3
1859.2.a.e.1.3 3 13.12 even 2
1859.2.a.h.1.3 3 1.1 even 1 trivial