Properties

Label 6039.2.a.i.1.6
Level $6039$
Weight $2$
Character 6039.1
Self dual yes
Analytic conductor $48.222$
Analytic rank $0$
Dimension $13$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6039.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2216577807\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Defining polynomial: \(x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} - 760 x^{4} - 742 x^{3} + 366 x^{2} + 236 x - 47\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2013)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.822526\) of defining polynomial
Character \(\chi\) \(=\) 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.822526 q^{2} -1.32345 q^{4} -2.11599 q^{5} +0.404149 q^{7} +2.73363 q^{8} +O(q^{10})\) \(q-0.822526 q^{2} -1.32345 q^{4} -2.11599 q^{5} +0.404149 q^{7} +2.73363 q^{8} +1.74046 q^{10} -1.00000 q^{11} +4.06066 q^{13} -0.332423 q^{14} +0.398423 q^{16} -0.0205369 q^{17} +3.97586 q^{19} +2.80041 q^{20} +0.822526 q^{22} +8.67841 q^{23} -0.522583 q^{25} -3.34000 q^{26} -0.534871 q^{28} +5.89217 q^{29} +5.40170 q^{31} -5.79496 q^{32} +0.0168922 q^{34} -0.855175 q^{35} +1.99527 q^{37} -3.27025 q^{38} -5.78433 q^{40} -6.26962 q^{41} +7.16134 q^{43} +1.32345 q^{44} -7.13822 q^{46} -8.53737 q^{47} -6.83666 q^{49} +0.429838 q^{50} -5.37409 q^{52} -5.18361 q^{53} +2.11599 q^{55} +1.10479 q^{56} -4.84647 q^{58} +0.638698 q^{59} -1.00000 q^{61} -4.44304 q^{62} +3.96966 q^{64} -8.59233 q^{65} +15.2035 q^{67} +0.0271796 q^{68} +0.703404 q^{70} -11.4793 q^{71} -15.0344 q^{73} -1.64116 q^{74} -5.26185 q^{76} -0.404149 q^{77} +10.9481 q^{79} -0.843060 q^{80} +5.15693 q^{82} -4.60944 q^{83} +0.0434559 q^{85} -5.89039 q^{86} -2.73363 q^{88} -12.7830 q^{89} +1.64111 q^{91} -11.4855 q^{92} +7.02221 q^{94} -8.41288 q^{95} -0.603085 q^{97} +5.62333 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13q - 2q^{2} + 16q^{4} - 3q^{5} + 11q^{7} - 9q^{8} + O(q^{10}) \) \( 13q - 2q^{2} + 16q^{4} - 3q^{5} + 11q^{7} - 9q^{8} + 6q^{10} - 13q^{11} + 13q^{13} - q^{14} + 18q^{16} - 17q^{17} + 14q^{19} + 7q^{20} + 2q^{22} - 7q^{23} + 18q^{25} + 10q^{26} + 19q^{28} + 6q^{29} + 27q^{31} - 5q^{32} + 6q^{34} - 14q^{35} + 10q^{37} - 2q^{38} + 8q^{40} - 3q^{41} + 29q^{43} - 16q^{44} - 24q^{46} - 8q^{47} + 8q^{49} + 27q^{50} + 37q^{52} + 24q^{53} + 3q^{55} - 24q^{56} - 5q^{58} - 13q^{59} - 13q^{61} - 39q^{62} + 47q^{64} + 11q^{65} + 44q^{67} + 8q^{68} - 12q^{70} - 3q^{71} + 48q^{73} + 22q^{74} + 47q^{76} - 11q^{77} - 17q^{79} + 26q^{80} + 56q^{82} - 50q^{83} + 8q^{85} - 18q^{86} + 9q^{88} + 15q^{89} + 47q^{91} - 14q^{92} + 45q^{94} + q^{95} + 27q^{97} - 47q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.822526 −0.581614 −0.290807 0.956782i \(-0.593924\pi\)
−0.290807 + 0.956782i \(0.593924\pi\)
\(3\) 0 0
\(4\) −1.32345 −0.661725
\(5\) −2.11599 −0.946300 −0.473150 0.880982i \(-0.656883\pi\)
−0.473150 + 0.880982i \(0.656883\pi\)
\(6\) 0 0
\(7\) 0.404149 0.152754 0.0763769 0.997079i \(-0.475665\pi\)
0.0763769 + 0.997079i \(0.475665\pi\)
\(8\) 2.73363 0.966482
\(9\) 0 0
\(10\) 1.74046 0.550381
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 4.06066 1.12623 0.563113 0.826380i \(-0.309604\pi\)
0.563113 + 0.826380i \(0.309604\pi\)
\(14\) −0.332423 −0.0888438
\(15\) 0 0
\(16\) 0.398423 0.0996058
\(17\) −0.0205369 −0.00498093 −0.00249047 0.999997i \(-0.500793\pi\)
−0.00249047 + 0.999997i \(0.500793\pi\)
\(18\) 0 0
\(19\) 3.97586 0.912124 0.456062 0.889948i \(-0.349259\pi\)
0.456062 + 0.889948i \(0.349259\pi\)
\(20\) 2.80041 0.626191
\(21\) 0 0
\(22\) 0.822526 0.175363
\(23\) 8.67841 1.80957 0.904787 0.425864i \(-0.140030\pi\)
0.904787 + 0.425864i \(0.140030\pi\)
\(24\) 0 0
\(25\) −0.522583 −0.104517
\(26\) −3.34000 −0.655028
\(27\) 0 0
\(28\) −0.534871 −0.101081
\(29\) 5.89217 1.09415 0.547075 0.837084i \(-0.315741\pi\)
0.547075 + 0.837084i \(0.315741\pi\)
\(30\) 0 0
\(31\) 5.40170 0.970174 0.485087 0.874466i \(-0.338788\pi\)
0.485087 + 0.874466i \(0.338788\pi\)
\(32\) −5.79496 −1.02441
\(33\) 0 0
\(34\) 0.0168922 0.00289698
\(35\) −0.855175 −0.144551
\(36\) 0 0
\(37\) 1.99527 0.328020 0.164010 0.986459i \(-0.447557\pi\)
0.164010 + 0.986459i \(0.447557\pi\)
\(38\) −3.27025 −0.530504
\(39\) 0 0
\(40\) −5.78433 −0.914582
\(41\) −6.26962 −0.979150 −0.489575 0.871961i \(-0.662848\pi\)
−0.489575 + 0.871961i \(0.662848\pi\)
\(42\) 0 0
\(43\) 7.16134 1.09209 0.546047 0.837754i \(-0.316132\pi\)
0.546047 + 0.837754i \(0.316132\pi\)
\(44\) 1.32345 0.199518
\(45\) 0 0
\(46\) −7.13822 −1.05247
\(47\) −8.53737 −1.24530 −0.622652 0.782499i \(-0.713945\pi\)
−0.622652 + 0.782499i \(0.713945\pi\)
\(48\) 0 0
\(49\) −6.83666 −0.976666
\(50\) 0.429838 0.0607883
\(51\) 0 0
\(52\) −5.37409 −0.745252
\(53\) −5.18361 −0.712024 −0.356012 0.934481i \(-0.615864\pi\)
−0.356012 + 0.934481i \(0.615864\pi\)
\(54\) 0 0
\(55\) 2.11599 0.285320
\(56\) 1.10479 0.147634
\(57\) 0 0
\(58\) −4.84647 −0.636372
\(59\) 0.638698 0.0831514 0.0415757 0.999135i \(-0.486762\pi\)
0.0415757 + 0.999135i \(0.486762\pi\)
\(60\) 0 0
\(61\) −1.00000 −0.128037
\(62\) −4.44304 −0.564267
\(63\) 0 0
\(64\) 3.96966 0.496208
\(65\) −8.59233 −1.06575
\(66\) 0 0
\(67\) 15.2035 1.85740 0.928700 0.370831i \(-0.120927\pi\)
0.928700 + 0.370831i \(0.120927\pi\)
\(68\) 0.0271796 0.00329601
\(69\) 0 0
\(70\) 0.703404 0.0840729
\(71\) −11.4793 −1.36234 −0.681168 0.732127i \(-0.738528\pi\)
−0.681168 + 0.732127i \(0.738528\pi\)
\(72\) 0 0
\(73\) −15.0344 −1.75965 −0.879823 0.475301i \(-0.842339\pi\)
−0.879823 + 0.475301i \(0.842339\pi\)
\(74\) −1.64116 −0.190781
\(75\) 0 0
\(76\) −5.26185 −0.603576
\(77\) −0.404149 −0.0460570
\(78\) 0 0
\(79\) 10.9481 1.23175 0.615877 0.787842i \(-0.288802\pi\)
0.615877 + 0.787842i \(0.288802\pi\)
\(80\) −0.843060 −0.0942570
\(81\) 0 0
\(82\) 5.15693 0.569487
\(83\) −4.60944 −0.505952 −0.252976 0.967473i \(-0.581409\pi\)
−0.252976 + 0.967473i \(0.581409\pi\)
\(84\) 0 0
\(85\) 0.0434559 0.00471346
\(86\) −5.89039 −0.635177
\(87\) 0 0
\(88\) −2.73363 −0.291405
\(89\) −12.7830 −1.35500 −0.677500 0.735523i \(-0.736937\pi\)
−0.677500 + 0.735523i \(0.736937\pi\)
\(90\) 0 0
\(91\) 1.64111 0.172035
\(92\) −11.4855 −1.19744
\(93\) 0 0
\(94\) 7.02221 0.724286
\(95\) −8.41288 −0.863143
\(96\) 0 0
\(97\) −0.603085 −0.0612340 −0.0306170 0.999531i \(-0.509747\pi\)
−0.0306170 + 0.999531i \(0.509747\pi\)
\(98\) 5.62333 0.568043
\(99\) 0 0
\(100\) 0.691613 0.0691613
\(101\) 14.6545 1.45818 0.729088 0.684420i \(-0.239944\pi\)
0.729088 + 0.684420i \(0.239944\pi\)
\(102\) 0 0
\(103\) 11.1666 1.10028 0.550138 0.835074i \(-0.314575\pi\)
0.550138 + 0.835074i \(0.314575\pi\)
\(104\) 11.1003 1.08848
\(105\) 0 0
\(106\) 4.26366 0.414123
\(107\) 8.54990 0.826550 0.413275 0.910606i \(-0.364385\pi\)
0.413275 + 0.910606i \(0.364385\pi\)
\(108\) 0 0
\(109\) 14.0443 1.34520 0.672598 0.740008i \(-0.265178\pi\)
0.672598 + 0.740008i \(0.265178\pi\)
\(110\) −1.74046 −0.165946
\(111\) 0 0
\(112\) 0.161022 0.0152152
\(113\) −9.57510 −0.900749 −0.450375 0.892840i \(-0.648710\pi\)
−0.450375 + 0.892840i \(0.648710\pi\)
\(114\) 0 0
\(115\) −18.3634 −1.71240
\(116\) −7.79800 −0.724026
\(117\) 0 0
\(118\) −0.525346 −0.0483620
\(119\) −0.00829997 −0.000760857 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0.822526 0.0744680
\(123\) 0 0
\(124\) −7.14889 −0.641989
\(125\) 11.6857 1.04520
\(126\) 0 0
\(127\) 6.13941 0.544785 0.272392 0.962186i \(-0.412185\pi\)
0.272392 + 0.962186i \(0.412185\pi\)
\(128\) 8.32478 0.735813
\(129\) 0 0
\(130\) 7.06741 0.619853
\(131\) −5.50042 −0.480574 −0.240287 0.970702i \(-0.577242\pi\)
−0.240287 + 0.970702i \(0.577242\pi\)
\(132\) 0 0
\(133\) 1.60684 0.139331
\(134\) −12.5053 −1.08029
\(135\) 0 0
\(136\) −0.0561402 −0.00481399
\(137\) 2.78969 0.238339 0.119170 0.992874i \(-0.461977\pi\)
0.119170 + 0.992874i \(0.461977\pi\)
\(138\) 0 0
\(139\) −11.0724 −0.939148 −0.469574 0.882893i \(-0.655592\pi\)
−0.469574 + 0.882893i \(0.655592\pi\)
\(140\) 1.13178 0.0956531
\(141\) 0 0
\(142\) 9.44198 0.792354
\(143\) −4.06066 −0.339570
\(144\) 0 0
\(145\) −12.4678 −1.03539
\(146\) 12.3662 1.02343
\(147\) 0 0
\(148\) −2.64064 −0.217059
\(149\) −0.473710 −0.0388079 −0.0194039 0.999812i \(-0.506177\pi\)
−0.0194039 + 0.999812i \(0.506177\pi\)
\(150\) 0 0
\(151\) 13.2622 1.07927 0.539633 0.841900i \(-0.318563\pi\)
0.539633 + 0.841900i \(0.318563\pi\)
\(152\) 10.8685 0.881552
\(153\) 0 0
\(154\) 0.332423 0.0267874
\(155\) −11.4300 −0.918076
\(156\) 0 0
\(157\) −12.7759 −1.01963 −0.509814 0.860285i \(-0.670286\pi\)
−0.509814 + 0.860285i \(0.670286\pi\)
\(158\) −9.00508 −0.716405
\(159\) 0 0
\(160\) 12.2621 0.969403
\(161\) 3.50737 0.276419
\(162\) 0 0
\(163\) 24.5359 1.92180 0.960900 0.276897i \(-0.0893060\pi\)
0.960900 + 0.276897i \(0.0893060\pi\)
\(164\) 8.29753 0.647928
\(165\) 0 0
\(166\) 3.79139 0.294269
\(167\) −3.95593 −0.306119 −0.153060 0.988217i \(-0.548913\pi\)
−0.153060 + 0.988217i \(0.548913\pi\)
\(168\) 0 0
\(169\) 3.48899 0.268384
\(170\) −0.0357436 −0.00274141
\(171\) 0 0
\(172\) −9.47768 −0.722666
\(173\) 21.5757 1.64037 0.820186 0.572097i \(-0.193870\pi\)
0.820186 + 0.572097i \(0.193870\pi\)
\(174\) 0 0
\(175\) −0.211201 −0.0159653
\(176\) −0.398423 −0.0300323
\(177\) 0 0
\(178\) 10.5144 0.788086
\(179\) 13.5654 1.01392 0.506962 0.861968i \(-0.330768\pi\)
0.506962 + 0.861968i \(0.330768\pi\)
\(180\) 0 0
\(181\) −20.9000 −1.55349 −0.776744 0.629817i \(-0.783130\pi\)
−0.776744 + 0.629817i \(0.783130\pi\)
\(182\) −1.34986 −0.100058
\(183\) 0 0
\(184\) 23.7235 1.74892
\(185\) −4.22197 −0.310405
\(186\) 0 0
\(187\) 0.0205369 0.00150181
\(188\) 11.2988 0.824049
\(189\) 0 0
\(190\) 6.91981 0.502016
\(191\) −2.45440 −0.177594 −0.0887971 0.996050i \(-0.528302\pi\)
−0.0887971 + 0.996050i \(0.528302\pi\)
\(192\) 0 0
\(193\) −8.31456 −0.598495 −0.299248 0.954176i \(-0.596736\pi\)
−0.299248 + 0.954176i \(0.596736\pi\)
\(194\) 0.496053 0.0356146
\(195\) 0 0
\(196\) 9.04799 0.646285
\(197\) −18.8004 −1.33947 −0.669736 0.742599i \(-0.733593\pi\)
−0.669736 + 0.742599i \(0.733593\pi\)
\(198\) 0 0
\(199\) −7.84162 −0.555877 −0.277939 0.960599i \(-0.589651\pi\)
−0.277939 + 0.960599i \(0.589651\pi\)
\(200\) −1.42855 −0.101013
\(201\) 0 0
\(202\) −12.0537 −0.848096
\(203\) 2.38131 0.167136
\(204\) 0 0
\(205\) 13.2665 0.926569
\(206\) −9.18480 −0.639935
\(207\) 0 0
\(208\) 1.61786 0.112179
\(209\) −3.97586 −0.275016
\(210\) 0 0
\(211\) −25.6632 −1.76673 −0.883364 0.468688i \(-0.844727\pi\)
−0.883364 + 0.468688i \(0.844727\pi\)
\(212\) 6.86025 0.471164
\(213\) 0 0
\(214\) −7.03252 −0.480733
\(215\) −15.1533 −1.03345
\(216\) 0 0
\(217\) 2.18309 0.148198
\(218\) −11.5518 −0.782385
\(219\) 0 0
\(220\) −2.80041 −0.188804
\(221\) −0.0833935 −0.00560966
\(222\) 0 0
\(223\) 1.31581 0.0881130 0.0440565 0.999029i \(-0.485972\pi\)
0.0440565 + 0.999029i \(0.485972\pi\)
\(224\) −2.34203 −0.156483
\(225\) 0 0
\(226\) 7.87577 0.523888
\(227\) −7.33476 −0.486825 −0.243413 0.969923i \(-0.578267\pi\)
−0.243413 + 0.969923i \(0.578267\pi\)
\(228\) 0 0
\(229\) −4.61757 −0.305137 −0.152569 0.988293i \(-0.548755\pi\)
−0.152569 + 0.988293i \(0.548755\pi\)
\(230\) 15.1044 0.995955
\(231\) 0 0
\(232\) 16.1070 1.05748
\(233\) −29.1255 −1.90807 −0.954036 0.299692i \(-0.903116\pi\)
−0.954036 + 0.299692i \(0.903116\pi\)
\(234\) 0 0
\(235\) 18.0650 1.17843
\(236\) −0.845285 −0.0550234
\(237\) 0 0
\(238\) 0.00682694 0.000442525 0
\(239\) 30.6121 1.98013 0.990064 0.140614i \(-0.0449077\pi\)
0.990064 + 0.140614i \(0.0449077\pi\)
\(240\) 0 0
\(241\) 22.3844 1.44191 0.720954 0.692983i \(-0.243704\pi\)
0.720954 + 0.692983i \(0.243704\pi\)
\(242\) −0.822526 −0.0528740
\(243\) 0 0
\(244\) 1.32345 0.0847253
\(245\) 14.4663 0.924219
\(246\) 0 0
\(247\) 16.1446 1.02726
\(248\) 14.7662 0.937656
\(249\) 0 0
\(250\) −9.61182 −0.607905
\(251\) −21.4637 −1.35478 −0.677390 0.735624i \(-0.736889\pi\)
−0.677390 + 0.735624i \(0.736889\pi\)
\(252\) 0 0
\(253\) −8.67841 −0.545607
\(254\) −5.04983 −0.316854
\(255\) 0 0
\(256\) −14.7867 −0.924167
\(257\) −4.42849 −0.276242 −0.138121 0.990415i \(-0.544106\pi\)
−0.138121 + 0.990415i \(0.544106\pi\)
\(258\) 0 0
\(259\) 0.806385 0.0501064
\(260\) 11.3715 0.705232
\(261\) 0 0
\(262\) 4.52424 0.279509
\(263\) 26.2060 1.61593 0.807966 0.589230i \(-0.200569\pi\)
0.807966 + 0.589230i \(0.200569\pi\)
\(264\) 0 0
\(265\) 10.9685 0.673788
\(266\) −1.32167 −0.0810366
\(267\) 0 0
\(268\) −20.1211 −1.22909
\(269\) 11.4188 0.696217 0.348109 0.937454i \(-0.386824\pi\)
0.348109 + 0.937454i \(0.386824\pi\)
\(270\) 0 0
\(271\) 2.05980 0.125124 0.0625620 0.998041i \(-0.480073\pi\)
0.0625620 + 0.998041i \(0.480073\pi\)
\(272\) −0.00818239 −0.000496130 0
\(273\) 0 0
\(274\) −2.29459 −0.138621
\(275\) 0.522583 0.0315129
\(276\) 0 0
\(277\) 27.0262 1.62385 0.811923 0.583765i \(-0.198421\pi\)
0.811923 + 0.583765i \(0.198421\pi\)
\(278\) 9.10733 0.546221
\(279\) 0 0
\(280\) −2.33773 −0.139706
\(281\) −4.85590 −0.289679 −0.144839 0.989455i \(-0.546267\pi\)
−0.144839 + 0.989455i \(0.546267\pi\)
\(282\) 0 0
\(283\) 15.0805 0.896442 0.448221 0.893923i \(-0.352058\pi\)
0.448221 + 0.893923i \(0.352058\pi\)
\(284\) 15.1922 0.901493
\(285\) 0 0
\(286\) 3.34000 0.197498
\(287\) −2.53386 −0.149569
\(288\) 0 0
\(289\) −16.9996 −0.999975
\(290\) 10.2551 0.602199
\(291\) 0 0
\(292\) 19.8973 1.16440
\(293\) 19.5057 1.13954 0.569769 0.821805i \(-0.307033\pi\)
0.569769 + 0.821805i \(0.307033\pi\)
\(294\) 0 0
\(295\) −1.35148 −0.0786861
\(296\) 5.45432 0.317026
\(297\) 0 0
\(298\) 0.389639 0.0225712
\(299\) 35.2401 2.03799
\(300\) 0 0
\(301\) 2.89425 0.166822
\(302\) −10.9085 −0.627716
\(303\) 0 0
\(304\) 1.58407 0.0908529
\(305\) 2.11599 0.121161
\(306\) 0 0
\(307\) 7.49773 0.427918 0.213959 0.976843i \(-0.431364\pi\)
0.213959 + 0.976843i \(0.431364\pi\)
\(308\) 0.534871 0.0304771
\(309\) 0 0
\(310\) 9.40143 0.533966
\(311\) −17.7437 −1.00616 −0.503078 0.864241i \(-0.667799\pi\)
−0.503078 + 0.864241i \(0.667799\pi\)
\(312\) 0 0
\(313\) 13.3708 0.755763 0.377882 0.925854i \(-0.376653\pi\)
0.377882 + 0.925854i \(0.376653\pi\)
\(314\) 10.5085 0.593030
\(315\) 0 0
\(316\) −14.4892 −0.815083
\(317\) 10.5527 0.592699 0.296350 0.955079i \(-0.404231\pi\)
0.296350 + 0.955079i \(0.404231\pi\)
\(318\) 0 0
\(319\) −5.89217 −0.329898
\(320\) −8.39977 −0.469561
\(321\) 0 0
\(322\) −2.88490 −0.160769
\(323\) −0.0816519 −0.00454323
\(324\) 0 0
\(325\) −2.12203 −0.117709
\(326\) −20.1814 −1.11775
\(327\) 0 0
\(328\) −17.1388 −0.946331
\(329\) −3.45037 −0.190225
\(330\) 0 0
\(331\) −5.63583 −0.309773 −0.154887 0.987932i \(-0.549501\pi\)
−0.154887 + 0.987932i \(0.549501\pi\)
\(332\) 6.10037 0.334801
\(333\) 0 0
\(334\) 3.25386 0.178043
\(335\) −32.1704 −1.75766
\(336\) 0 0
\(337\) 21.1177 1.15036 0.575178 0.818028i \(-0.304933\pi\)
0.575178 + 0.818028i \(0.304933\pi\)
\(338\) −2.86979 −0.156096
\(339\) 0 0
\(340\) −0.0575118 −0.00311901
\(341\) −5.40170 −0.292519
\(342\) 0 0
\(343\) −5.59207 −0.301943
\(344\) 19.5764 1.05549
\(345\) 0 0
\(346\) −17.7466 −0.954063
\(347\) 24.5687 1.31892 0.659458 0.751742i \(-0.270786\pi\)
0.659458 + 0.751742i \(0.270786\pi\)
\(348\) 0 0
\(349\) 3.91197 0.209403 0.104701 0.994504i \(-0.466611\pi\)
0.104701 + 0.994504i \(0.466611\pi\)
\(350\) 0.173719 0.00928565
\(351\) 0 0
\(352\) 5.79496 0.308873
\(353\) 28.5152 1.51771 0.758856 0.651259i \(-0.225759\pi\)
0.758856 + 0.651259i \(0.225759\pi\)
\(354\) 0 0
\(355\) 24.2900 1.28918
\(356\) 16.9177 0.896638
\(357\) 0 0
\(358\) −11.1579 −0.589712
\(359\) 27.2384 1.43759 0.718793 0.695224i \(-0.244695\pi\)
0.718793 + 0.695224i \(0.244695\pi\)
\(360\) 0 0
\(361\) −3.19255 −0.168029
\(362\) 17.1908 0.903530
\(363\) 0 0
\(364\) −2.17193 −0.113840
\(365\) 31.8127 1.66515
\(366\) 0 0
\(367\) −37.7100 −1.96845 −0.984224 0.176927i \(-0.943384\pi\)
−0.984224 + 0.176927i \(0.943384\pi\)
\(368\) 3.45768 0.180244
\(369\) 0 0
\(370\) 3.47268 0.180536
\(371\) −2.09495 −0.108764
\(372\) 0 0
\(373\) 4.83715 0.250458 0.125229 0.992128i \(-0.460033\pi\)
0.125229 + 0.992128i \(0.460033\pi\)
\(374\) −0.0168922 −0.000873472 0
\(375\) 0 0
\(376\) −23.3380 −1.20356
\(377\) 23.9261 1.23226
\(378\) 0 0
\(379\) −35.2816 −1.81229 −0.906146 0.422965i \(-0.860989\pi\)
−0.906146 + 0.422965i \(0.860989\pi\)
\(380\) 11.1340 0.571164
\(381\) 0 0
\(382\) 2.01881 0.103291
\(383\) −18.3228 −0.936253 −0.468127 0.883661i \(-0.655071\pi\)
−0.468127 + 0.883661i \(0.655071\pi\)
\(384\) 0 0
\(385\) 0.855175 0.0435838
\(386\) 6.83894 0.348093
\(387\) 0 0
\(388\) 0.798153 0.0405201
\(389\) 34.4388 1.74612 0.873059 0.487614i \(-0.162133\pi\)
0.873059 + 0.487614i \(0.162133\pi\)
\(390\) 0 0
\(391\) −0.178228 −0.00901337
\(392\) −18.6889 −0.943931
\(393\) 0 0
\(394\) 15.4638 0.779056
\(395\) −23.1660 −1.16561
\(396\) 0 0
\(397\) −6.67209 −0.334862 −0.167431 0.985884i \(-0.553547\pi\)
−0.167431 + 0.985884i \(0.553547\pi\)
\(398\) 6.44993 0.323306
\(399\) 0 0
\(400\) −0.208209 −0.0104105
\(401\) 19.4145 0.969515 0.484757 0.874649i \(-0.338908\pi\)
0.484757 + 0.874649i \(0.338908\pi\)
\(402\) 0 0
\(403\) 21.9345 1.09264
\(404\) −19.3945 −0.964912
\(405\) 0 0
\(406\) −1.95869 −0.0972083
\(407\) −1.99527 −0.0989018
\(408\) 0 0
\(409\) 0.767851 0.0379678 0.0189839 0.999820i \(-0.493957\pi\)
0.0189839 + 0.999820i \(0.493957\pi\)
\(410\) −10.9120 −0.538906
\(411\) 0 0
\(412\) −14.7784 −0.728080
\(413\) 0.258129 0.0127017
\(414\) 0 0
\(415\) 9.75354 0.478782
\(416\) −23.5314 −1.15372
\(417\) 0 0
\(418\) 3.27025 0.159953
\(419\) −17.3337 −0.846806 −0.423403 0.905941i \(-0.639165\pi\)
−0.423403 + 0.905941i \(0.639165\pi\)
\(420\) 0 0
\(421\) 12.0651 0.588016 0.294008 0.955803i \(-0.405011\pi\)
0.294008 + 0.955803i \(0.405011\pi\)
\(422\) 21.1087 1.02755
\(423\) 0 0
\(424\) −14.1700 −0.688158
\(425\) 0.0107322 0.000520590 0
\(426\) 0 0
\(427\) −0.404149 −0.0195581
\(428\) −11.3154 −0.546949
\(429\) 0 0
\(430\) 12.4640 0.601068
\(431\) 29.2010 1.40656 0.703282 0.710911i \(-0.251717\pi\)
0.703282 + 0.710911i \(0.251717\pi\)
\(432\) 0 0
\(433\) −35.8038 −1.72062 −0.860311 0.509769i \(-0.829731\pi\)
−0.860311 + 0.509769i \(0.829731\pi\)
\(434\) −1.79565 −0.0861939
\(435\) 0 0
\(436\) −18.5869 −0.890151
\(437\) 34.5041 1.65056
\(438\) 0 0
\(439\) 40.8584 1.95006 0.975032 0.222063i \(-0.0712791\pi\)
0.975032 + 0.222063i \(0.0712791\pi\)
\(440\) 5.78433 0.275757
\(441\) 0 0
\(442\) 0.0685934 0.00326265
\(443\) 27.9834 1.32953 0.664767 0.747051i \(-0.268531\pi\)
0.664767 + 0.747051i \(0.268531\pi\)
\(444\) 0 0
\(445\) 27.0488 1.28224
\(446\) −1.08229 −0.0512477
\(447\) 0 0
\(448\) 1.60433 0.0757977
\(449\) 25.0254 1.18102 0.590512 0.807029i \(-0.298926\pi\)
0.590512 + 0.807029i \(0.298926\pi\)
\(450\) 0 0
\(451\) 6.26962 0.295225
\(452\) 12.6722 0.596049
\(453\) 0 0
\(454\) 6.03303 0.283144
\(455\) −3.47258 −0.162797
\(456\) 0 0
\(457\) 3.70365 0.173249 0.0866247 0.996241i \(-0.472392\pi\)
0.0866247 + 0.996241i \(0.472392\pi\)
\(458\) 3.79807 0.177472
\(459\) 0 0
\(460\) 24.3031 1.13314
\(461\) 15.8022 0.735982 0.367991 0.929829i \(-0.380046\pi\)
0.367991 + 0.929829i \(0.380046\pi\)
\(462\) 0 0
\(463\) −25.2470 −1.17333 −0.586665 0.809830i \(-0.699559\pi\)
−0.586665 + 0.809830i \(0.699559\pi\)
\(464\) 2.34758 0.108984
\(465\) 0 0
\(466\) 23.9564 1.10976
\(467\) 17.2785 0.799552 0.399776 0.916613i \(-0.369088\pi\)
0.399776 + 0.916613i \(0.369088\pi\)
\(468\) 0 0
\(469\) 6.14447 0.283725
\(470\) −14.8589 −0.685391
\(471\) 0 0
\(472\) 1.74596 0.0803643
\(473\) −7.16134 −0.329279
\(474\) 0 0
\(475\) −2.07771 −0.0953321
\(476\) 0.0109846 0.000503478 0
\(477\) 0 0
\(478\) −25.1792 −1.15167
\(479\) −10.8839 −0.497297 −0.248648 0.968594i \(-0.579986\pi\)
−0.248648 + 0.968594i \(0.579986\pi\)
\(480\) 0 0
\(481\) 8.10212 0.369425
\(482\) −18.4118 −0.838634
\(483\) 0 0
\(484\) −1.32345 −0.0601569
\(485\) 1.27612 0.0579457
\(486\) 0 0
\(487\) 39.0162 1.76799 0.883997 0.467492i \(-0.154842\pi\)
0.883997 + 0.467492i \(0.154842\pi\)
\(488\) −2.73363 −0.123745
\(489\) 0 0
\(490\) −11.8989 −0.537539
\(491\) −30.0322 −1.35533 −0.677667 0.735369i \(-0.737009\pi\)
−0.677667 + 0.735369i \(0.737009\pi\)
\(492\) 0 0
\(493\) −0.121007 −0.00544989
\(494\) −13.2794 −0.597467
\(495\) 0 0
\(496\) 2.15216 0.0966350
\(497\) −4.63933 −0.208102
\(498\) 0 0
\(499\) 25.6100 1.14646 0.573232 0.819393i \(-0.305690\pi\)
0.573232 + 0.819393i \(0.305690\pi\)
\(500\) −15.4655 −0.691638
\(501\) 0 0
\(502\) 17.6545 0.787958
\(503\) 9.23707 0.411861 0.205930 0.978567i \(-0.433978\pi\)
0.205930 + 0.978567i \(0.433978\pi\)
\(504\) 0 0
\(505\) −31.0088 −1.37987
\(506\) 7.13822 0.317333
\(507\) 0 0
\(508\) −8.12521 −0.360498
\(509\) −32.4717 −1.43928 −0.719642 0.694345i \(-0.755694\pi\)
−0.719642 + 0.694345i \(0.755694\pi\)
\(510\) 0 0
\(511\) −6.07615 −0.268793
\(512\) −4.48713 −0.198305
\(513\) 0 0
\(514\) 3.64255 0.160666
\(515\) −23.6284 −1.04119
\(516\) 0 0
\(517\) 8.53737 0.375473
\(518\) −0.663273 −0.0291425
\(519\) 0 0
\(520\) −23.4882 −1.03003
\(521\) −12.2202 −0.535375 −0.267687 0.963506i \(-0.586259\pi\)
−0.267687 + 0.963506i \(0.586259\pi\)
\(522\) 0 0
\(523\) −24.8557 −1.08686 −0.543432 0.839453i \(-0.682876\pi\)
−0.543432 + 0.839453i \(0.682876\pi\)
\(524\) 7.27954 0.318008
\(525\) 0 0
\(526\) −21.5551 −0.939848
\(527\) −0.110934 −0.00483238
\(528\) 0 0
\(529\) 52.3148 2.27456
\(530\) −9.02186 −0.391884
\(531\) 0 0
\(532\) −2.12657 −0.0921986
\(533\) −25.4588 −1.10274
\(534\) 0 0
\(535\) −18.0915 −0.782164
\(536\) 41.5606 1.79515
\(537\) 0 0
\(538\) −9.39227 −0.404930
\(539\) 6.83666 0.294476
\(540\) 0 0
\(541\) 6.76305 0.290766 0.145383 0.989375i \(-0.453559\pi\)
0.145383 + 0.989375i \(0.453559\pi\)
\(542\) −1.69424 −0.0727739
\(543\) 0 0
\(544\) 0.119011 0.00510254
\(545\) −29.7175 −1.27296
\(546\) 0 0
\(547\) 22.0518 0.942865 0.471432 0.881902i \(-0.343737\pi\)
0.471432 + 0.881902i \(0.343737\pi\)
\(548\) −3.69202 −0.157715
\(549\) 0 0
\(550\) −0.429838 −0.0183284
\(551\) 23.4264 0.998000
\(552\) 0 0
\(553\) 4.42465 0.188155
\(554\) −22.2297 −0.944451
\(555\) 0 0
\(556\) 14.6538 0.621458
\(557\) −14.7373 −0.624438 −0.312219 0.950010i \(-0.601072\pi\)
−0.312219 + 0.950010i \(0.601072\pi\)
\(558\) 0 0
\(559\) 29.0798 1.22994
\(560\) −0.340722 −0.0143981
\(561\) 0 0
\(562\) 3.99411 0.168481
\(563\) 6.78450 0.285933 0.142966 0.989728i \(-0.454336\pi\)
0.142966 + 0.989728i \(0.454336\pi\)
\(564\) 0 0
\(565\) 20.2608 0.852379
\(566\) −12.4041 −0.521383
\(567\) 0 0
\(568\) −31.3800 −1.31667
\(569\) −10.9922 −0.460817 −0.230409 0.973094i \(-0.574006\pi\)
−0.230409 + 0.973094i \(0.574006\pi\)
\(570\) 0 0
\(571\) −41.9268 −1.75458 −0.877290 0.479961i \(-0.840651\pi\)
−0.877290 + 0.479961i \(0.840651\pi\)
\(572\) 5.37409 0.224702
\(573\) 0 0
\(574\) 2.08417 0.0869914
\(575\) −4.53519 −0.189130
\(576\) 0 0
\(577\) 22.2721 0.927200 0.463600 0.886045i \(-0.346558\pi\)
0.463600 + 0.886045i \(0.346558\pi\)
\(578\) 13.9826 0.581599
\(579\) 0 0
\(580\) 16.5005 0.685146
\(581\) −1.86290 −0.0772861
\(582\) 0 0
\(583\) 5.18361 0.214683
\(584\) −41.0985 −1.70067
\(585\) 0 0
\(586\) −16.0440 −0.662771
\(587\) 37.4028 1.54378 0.771888 0.635758i \(-0.219312\pi\)
0.771888 + 0.635758i \(0.219312\pi\)
\(588\) 0 0
\(589\) 21.4764 0.884920
\(590\) 1.11163 0.0457649
\(591\) 0 0
\(592\) 0.794962 0.0326727
\(593\) 39.4377 1.61951 0.809756 0.586767i \(-0.199600\pi\)
0.809756 + 0.586767i \(0.199600\pi\)
\(594\) 0 0
\(595\) 0.0175627 0.000719999 0
\(596\) 0.626932 0.0256801
\(597\) 0 0
\(598\) −28.9859 −1.18532
\(599\) −20.8174 −0.850578 −0.425289 0.905058i \(-0.639828\pi\)
−0.425289 + 0.905058i \(0.639828\pi\)
\(600\) 0 0
\(601\) 5.46084 0.222752 0.111376 0.993778i \(-0.464474\pi\)
0.111376 + 0.993778i \(0.464474\pi\)
\(602\) −2.38059 −0.0970258
\(603\) 0 0
\(604\) −17.5519 −0.714178
\(605\) −2.11599 −0.0860273
\(606\) 0 0
\(607\) 0.731366 0.0296852 0.0148426 0.999890i \(-0.495275\pi\)
0.0148426 + 0.999890i \(0.495275\pi\)
\(608\) −23.0400 −0.934394
\(609\) 0 0
\(610\) −1.74046 −0.0704691
\(611\) −34.6674 −1.40249
\(612\) 0 0
\(613\) 5.30018 0.214072 0.107036 0.994255i \(-0.465864\pi\)
0.107036 + 0.994255i \(0.465864\pi\)
\(614\) −6.16708 −0.248883
\(615\) 0 0
\(616\) −1.10479 −0.0445133
\(617\) 16.1004 0.648176 0.324088 0.946027i \(-0.394943\pi\)
0.324088 + 0.946027i \(0.394943\pi\)
\(618\) 0 0
\(619\) 16.9174 0.679968 0.339984 0.940431i \(-0.389578\pi\)
0.339984 + 0.940431i \(0.389578\pi\)
\(620\) 15.1270 0.607514
\(621\) 0 0
\(622\) 14.5947 0.585194
\(623\) −5.16625 −0.206981
\(624\) 0 0
\(625\) −22.1140 −0.884560
\(626\) −10.9978 −0.439562
\(627\) 0 0
\(628\) 16.9083 0.674714
\(629\) −0.0409767 −0.00163385
\(630\) 0 0
\(631\) −43.2520 −1.72184 −0.860918 0.508743i \(-0.830110\pi\)
−0.860918 + 0.508743i \(0.830110\pi\)
\(632\) 29.9279 1.19047
\(633\) 0 0
\(634\) −8.67988 −0.344722
\(635\) −12.9909 −0.515530
\(636\) 0 0
\(637\) −27.7614 −1.09995
\(638\) 4.84647 0.191873
\(639\) 0 0
\(640\) −17.6152 −0.696300
\(641\) −22.4987 −0.888644 −0.444322 0.895867i \(-0.646555\pi\)
−0.444322 + 0.895867i \(0.646555\pi\)
\(642\) 0 0
\(643\) 16.3425 0.644487 0.322243 0.946657i \(-0.395563\pi\)
0.322243 + 0.946657i \(0.395563\pi\)
\(644\) −4.64183 −0.182914
\(645\) 0 0
\(646\) 0.0671608 0.00264241
\(647\) 18.5358 0.728719 0.364360 0.931258i \(-0.381288\pi\)
0.364360 + 0.931258i \(0.381288\pi\)
\(648\) 0 0
\(649\) −0.638698 −0.0250711
\(650\) 1.74543 0.0684613
\(651\) 0 0
\(652\) −32.4720 −1.27170
\(653\) −38.4291 −1.50385 −0.751924 0.659249i \(-0.770874\pi\)
−0.751924 + 0.659249i \(0.770874\pi\)
\(654\) 0 0
\(655\) 11.6388 0.454767
\(656\) −2.49796 −0.0975291
\(657\) 0 0
\(658\) 2.83802 0.110637
\(659\) 13.0048 0.506594 0.253297 0.967389i \(-0.418485\pi\)
0.253297 + 0.967389i \(0.418485\pi\)
\(660\) 0 0
\(661\) 17.4699 0.679500 0.339750 0.940516i \(-0.389658\pi\)
0.339750 + 0.940516i \(0.389658\pi\)
\(662\) 4.63562 0.180168
\(663\) 0 0
\(664\) −12.6005 −0.488994
\(665\) −3.40006 −0.131848
\(666\) 0 0
\(667\) 51.1347 1.97994
\(668\) 5.23548 0.202567
\(669\) 0 0
\(670\) 26.4610 1.02228
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −21.0297 −0.810637 −0.405319 0.914175i \(-0.632839\pi\)
−0.405319 + 0.914175i \(0.632839\pi\)
\(674\) −17.3699 −0.669063
\(675\) 0 0
\(676\) −4.61751 −0.177596
\(677\) −38.9808 −1.49816 −0.749078 0.662482i \(-0.769503\pi\)
−0.749078 + 0.662482i \(0.769503\pi\)
\(678\) 0 0
\(679\) −0.243736 −0.00935373
\(680\) 0.118792 0.00455547
\(681\) 0 0
\(682\) 4.44304 0.170133
\(683\) 12.0413 0.460746 0.230373 0.973102i \(-0.426005\pi\)
0.230373 + 0.973102i \(0.426005\pi\)
\(684\) 0 0
\(685\) −5.90296 −0.225540
\(686\) 4.59962 0.175614
\(687\) 0 0
\(688\) 2.85325 0.108779
\(689\) −21.0489 −0.801899
\(690\) 0 0
\(691\) 20.6612 0.785988 0.392994 0.919541i \(-0.371439\pi\)
0.392994 + 0.919541i \(0.371439\pi\)
\(692\) −28.5544 −1.08548
\(693\) 0 0
\(694\) −20.2084 −0.767099
\(695\) 23.4291 0.888715
\(696\) 0 0
\(697\) 0.128759 0.00487708
\(698\) −3.21770 −0.121792
\(699\) 0 0
\(700\) 0.279514 0.0105647
\(701\) 11.9387 0.450920 0.225460 0.974252i \(-0.427612\pi\)
0.225460 + 0.974252i \(0.427612\pi\)
\(702\) 0 0
\(703\) 7.93291 0.299195
\(704\) −3.96966 −0.149612
\(705\) 0 0
\(706\) −23.4545 −0.882722
\(707\) 5.92260 0.222742
\(708\) 0 0
\(709\) −15.3955 −0.578189 −0.289095 0.957300i \(-0.593354\pi\)
−0.289095 + 0.957300i \(0.593354\pi\)
\(710\) −19.9792 −0.749804
\(711\) 0 0
\(712\) −34.9440 −1.30958
\(713\) 46.8782 1.75560
\(714\) 0 0
\(715\) 8.59233 0.321335
\(716\) −17.9531 −0.670939
\(717\) 0 0
\(718\) −22.4043 −0.836120
\(719\) −18.8466 −0.702859 −0.351430 0.936214i \(-0.614304\pi\)
−0.351430 + 0.936214i \(0.614304\pi\)
\(720\) 0 0
\(721\) 4.51296 0.168071
\(722\) 2.62596 0.0977280
\(723\) 0 0
\(724\) 27.6602 1.02798
\(725\) −3.07915 −0.114357
\(726\) 0 0
\(727\) −34.5785 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(728\) 4.48619 0.166269
\(729\) 0 0
\(730\) −26.1668 −0.968476
\(731\) −0.147072 −0.00543965
\(732\) 0 0
\(733\) −18.9209 −0.698859 −0.349430 0.936963i \(-0.613625\pi\)
−0.349430 + 0.936963i \(0.613625\pi\)
\(734\) 31.0175 1.14488
\(735\) 0 0
\(736\) −50.2911 −1.85375
\(737\) −15.2035 −0.560027
\(738\) 0 0
\(739\) 15.6521 0.575773 0.287886 0.957665i \(-0.407047\pi\)
0.287886 + 0.957665i \(0.407047\pi\)
\(740\) 5.58757 0.205403
\(741\) 0 0
\(742\) 1.72315 0.0632589
\(743\) −12.8846 −0.472691 −0.236346 0.971669i \(-0.575950\pi\)
−0.236346 + 0.971669i \(0.575950\pi\)
\(744\) 0 0
\(745\) 1.00237 0.0367239
\(746\) −3.97868 −0.145670
\(747\) 0 0
\(748\) −0.0271796 −0.000993785 0
\(749\) 3.45543 0.126259
\(750\) 0 0
\(751\) 4.34890 0.158693 0.0793467 0.996847i \(-0.474717\pi\)
0.0793467 + 0.996847i \(0.474717\pi\)
\(752\) −3.40149 −0.124039
\(753\) 0 0
\(754\) −19.6799 −0.716699
\(755\) −28.0628 −1.02131
\(756\) 0 0
\(757\) 39.4539 1.43398 0.716989 0.697085i \(-0.245520\pi\)
0.716989 + 0.697085i \(0.245520\pi\)
\(758\) 29.0200 1.05405
\(759\) 0 0
\(760\) −22.9977 −0.834213
\(761\) 38.6312 1.40038 0.700190 0.713957i \(-0.253099\pi\)
0.700190 + 0.713957i \(0.253099\pi\)
\(762\) 0 0
\(763\) 5.67597 0.205484
\(764\) 3.24828 0.117519
\(765\) 0 0
\(766\) 15.0710 0.544538
\(767\) 2.59354 0.0936472
\(768\) 0 0
\(769\) −29.2863 −1.05609 −0.528046 0.849216i \(-0.677075\pi\)
−0.528046 + 0.849216i \(0.677075\pi\)
\(770\) −0.703404 −0.0253489
\(771\) 0 0
\(772\) 11.0039 0.396039
\(773\) −1.46255 −0.0526041 −0.0263020 0.999654i \(-0.508373\pi\)
−0.0263020 + 0.999654i \(0.508373\pi\)
\(774\) 0 0
\(775\) −2.82284 −0.101399
\(776\) −1.64861 −0.0591816
\(777\) 0 0
\(778\) −28.3268 −1.01557
\(779\) −24.9271 −0.893107
\(780\) 0 0
\(781\) 11.4793 0.410760
\(782\) 0.146597 0.00524230
\(783\) 0 0
\(784\) −2.72389 −0.0972817
\(785\) 27.0337 0.964874
\(786\) 0 0
\(787\) 25.9663 0.925600 0.462800 0.886463i \(-0.346845\pi\)
0.462800 + 0.886463i \(0.346845\pi\)
\(788\) 24.8814 0.886363
\(789\) 0 0
\(790\) 19.0547 0.677934
\(791\) −3.86976 −0.137593
\(792\) 0 0
\(793\) −4.06066 −0.144198
\(794\) 5.48797 0.194761
\(795\) 0 0
\(796\) 10.3780 0.367838
\(797\) 31.4932 1.11555 0.557773 0.829993i \(-0.311656\pi\)
0.557773 + 0.829993i \(0.311656\pi\)
\(798\) 0 0
\(799\) 0.175331 0.00620278
\(800\) 3.02835 0.107068
\(801\) 0 0
\(802\) −15.9689 −0.563883
\(803\) 15.0344 0.530553
\(804\) 0 0
\(805\) −7.42156 −0.261576
\(806\) −18.0417 −0.635492
\(807\) 0 0
\(808\) 40.0599 1.40930
\(809\) −8.19184 −0.288010 −0.144005 0.989577i \(-0.545998\pi\)
−0.144005 + 0.989577i \(0.545998\pi\)
\(810\) 0 0
\(811\) 8.90734 0.312779 0.156389 0.987695i \(-0.450015\pi\)
0.156389 + 0.987695i \(0.450015\pi\)
\(812\) −3.15155 −0.110598
\(813\) 0 0
\(814\) 1.64116 0.0575227
\(815\) −51.9177 −1.81860
\(816\) 0 0
\(817\) 28.4725 0.996126
\(818\) −0.631577 −0.0220826
\(819\) 0 0
\(820\) −17.5575 −0.613135
\(821\) 25.1573 0.877995 0.438997 0.898488i \(-0.355334\pi\)
0.438997 + 0.898488i \(0.355334\pi\)
\(822\) 0 0
\(823\) 50.8751 1.77340 0.886698 0.462350i \(-0.152994\pi\)
0.886698 + 0.462350i \(0.152994\pi\)
\(824\) 30.5252 1.06340
\(825\) 0 0
\(826\) −0.212318 −0.00738748
\(827\) −43.4799 −1.51195 −0.755973 0.654603i \(-0.772836\pi\)
−0.755973 + 0.654603i \(0.772836\pi\)
\(828\) 0 0
\(829\) −34.9915 −1.21530 −0.607652 0.794203i \(-0.707889\pi\)
−0.607652 + 0.794203i \(0.707889\pi\)
\(830\) −8.02254 −0.278466
\(831\) 0 0
\(832\) 16.1195 0.558842
\(833\) 0.140404 0.00486471
\(834\) 0 0
\(835\) 8.37072 0.289681
\(836\) 5.26185 0.181985
\(837\) 0 0
\(838\) 14.2574 0.492514
\(839\) −31.5500 −1.08923 −0.544614 0.838687i \(-0.683324\pi\)
−0.544614 + 0.838687i \(0.683324\pi\)
\(840\) 0 0
\(841\) 5.71771 0.197162
\(842\) −9.92384 −0.341998
\(843\) 0 0
\(844\) 33.9640 1.16909
\(845\) −7.38267 −0.253972
\(846\) 0 0
\(847\) 0.404149 0.0138867
\(848\) −2.06527 −0.0709217
\(849\) 0 0
\(850\) −0.00882755 −0.000302782 0
\(851\) 17.3158 0.593577
\(852\) 0 0
\(853\) −4.60871 −0.157799 −0.0788997 0.996883i \(-0.525141\pi\)
−0.0788997 + 0.996883i \(0.525141\pi\)
\(854\) 0.332423 0.0113753
\(855\) 0 0
\(856\) 23.3722 0.798846
\(857\) −49.6081 −1.69458 −0.847290 0.531131i \(-0.821767\pi\)
−0.847290 + 0.531131i \(0.821767\pi\)
\(858\) 0 0
\(859\) −57.5877 −1.96487 −0.982433 0.186617i \(-0.940248\pi\)
−0.982433 + 0.186617i \(0.940248\pi\)
\(860\) 20.0547 0.683859
\(861\) 0 0
\(862\) −24.0186 −0.818077
\(863\) 40.8905 1.39193 0.695964 0.718076i \(-0.254977\pi\)
0.695964 + 0.718076i \(0.254977\pi\)
\(864\) 0 0
\(865\) −45.6540 −1.55228
\(866\) 29.4496 1.00074
\(867\) 0 0
\(868\) −2.88921 −0.0980663
\(869\) −10.9481 −0.371388
\(870\) 0 0
\(871\) 61.7362 2.09185
\(872\) 38.3918 1.30011
\(873\) 0 0
\(874\) −28.3806 −0.959987
\(875\) 4.72278 0.159659
\(876\) 0 0
\(877\) −7.81665 −0.263949 −0.131975 0.991253i \(-0.542132\pi\)
−0.131975 + 0.991253i \(0.542132\pi\)
\(878\) −33.6071 −1.13418
\(879\) 0 0
\(880\) 0.843060 0.0284196
\(881\) 16.7321 0.563719 0.281860 0.959456i \(-0.409049\pi\)
0.281860 + 0.959456i \(0.409049\pi\)
\(882\) 0 0
\(883\) −18.3230 −0.616617 −0.308308 0.951286i \(-0.599763\pi\)
−0.308308 + 0.951286i \(0.599763\pi\)
\(884\) 0.110367 0.00371205
\(885\) 0 0
\(886\) −23.0171 −0.773275
\(887\) −36.8957 −1.23884 −0.619419 0.785061i \(-0.712632\pi\)
−0.619419 + 0.785061i \(0.712632\pi\)
\(888\) 0 0
\(889\) 2.48124 0.0832180
\(890\) −22.2483 −0.745766
\(891\) 0 0
\(892\) −1.74141 −0.0583066
\(893\) −33.9434 −1.13587
\(894\) 0 0
\(895\) −28.7042 −0.959476
\(896\) 3.36445 0.112398
\(897\) 0 0
\(898\) −20.5841 −0.686900
\(899\) 31.8278 1.06152
\(900\) 0 0
\(901\) 0.106455 0.00354654
\(902\) −5.15693 −0.171707
\(903\) 0 0
\(904\) −26.1747 −0.870558
\(905\) 44.2243 1.47006
\(906\) 0 0
\(907\) −1.15826 −0.0384593 −0.0192297 0.999815i \(-0.506121\pi\)
−0.0192297 + 0.999815i \(0.506121\pi\)
\(908\) 9.70720 0.322145
\(909\) 0 0
\(910\) 2.85629 0.0946850
\(911\) 39.7016 1.31537 0.657686 0.753292i \(-0.271535\pi\)
0.657686 + 0.753292i \(0.271535\pi\)
\(912\) 0 0
\(913\) 4.60944 0.152550
\(914\) −3.04635 −0.100764
\(915\) 0 0
\(916\) 6.11112 0.201917
\(917\) −2.22299 −0.0734096
\(918\) 0 0
\(919\) 34.7872 1.14752 0.573762 0.819022i \(-0.305483\pi\)
0.573762 + 0.819022i \(0.305483\pi\)
\(920\) −50.1988 −1.65500
\(921\) 0 0
\(922\) −12.9977 −0.428057
\(923\) −46.6134 −1.53430
\(924\) 0 0
\(925\) −1.04269 −0.0342835
\(926\) 20.7663 0.682424
\(927\) 0 0
\(928\) −34.1449 −1.12086
\(929\) 16.5877 0.544226 0.272113 0.962265i \(-0.412278\pi\)
0.272113 + 0.962265i \(0.412278\pi\)
\(930\) 0 0
\(931\) −27.1816 −0.890841
\(932\) 38.5461 1.26262
\(933\) 0 0
\(934\) −14.2120 −0.465030
\(935\) −0.0434559 −0.00142116
\(936\) 0 0
\(937\) 29.0025 0.947470 0.473735 0.880667i \(-0.342905\pi\)
0.473735 + 0.880667i \(0.342905\pi\)
\(938\) −5.05399 −0.165018
\(939\) 0 0
\(940\) −23.9081 −0.779797
\(941\) −41.2410 −1.34442 −0.672210 0.740361i \(-0.734655\pi\)
−0.672210 + 0.740361i \(0.734655\pi\)
\(942\) 0 0
\(943\) −54.4103 −1.77184
\(944\) 0.254472 0.00828236
\(945\) 0 0
\(946\) 5.89039 0.191513
\(947\) 14.9009 0.484214 0.242107 0.970250i \(-0.422161\pi\)
0.242107 + 0.970250i \(0.422161\pi\)
\(948\) 0 0
\(949\) −61.0497 −1.98176
\(950\) 1.70897 0.0554465
\(951\) 0 0
\(952\) −0.0226890 −0.000735355 0
\(953\) 29.4563 0.954185 0.477092 0.878853i \(-0.341691\pi\)
0.477092 + 0.878853i \(0.341691\pi\)
\(954\) 0 0
\(955\) 5.19349 0.168057
\(956\) −40.5135 −1.31030
\(957\) 0 0
\(958\) 8.95227 0.289235
\(959\) 1.12745 0.0364073
\(960\) 0 0
\(961\) −1.82161 −0.0587617
\(962\) −6.66420 −0.214862
\(963\) 0 0
\(964\) −29.6247 −0.954147
\(965\) 17.5935 0.566356
\(966\) 0 0
\(967\) 39.2447 1.26202 0.631012 0.775773i \(-0.282640\pi\)
0.631012 + 0.775773i \(0.282640\pi\)
\(968\) 2.73363 0.0878620
\(969\) 0 0
\(970\) −1.04964 −0.0337020
\(971\) −19.0146 −0.610207 −0.305104 0.952319i \(-0.598691\pi\)
−0.305104 + 0.952319i \(0.598691\pi\)
\(972\) 0 0
\(973\) −4.47489 −0.143458
\(974\) −32.0919 −1.02829
\(975\) 0 0
\(976\) −0.398423 −0.0127532
\(977\) −15.7282 −0.503188 −0.251594 0.967833i \(-0.580955\pi\)
−0.251594 + 0.967833i \(0.580955\pi\)
\(978\) 0 0
\(979\) 12.7830 0.408548
\(980\) −19.1455 −0.611579
\(981\) 0 0
\(982\) 24.7023 0.788281
\(983\) 41.9230 1.33714 0.668568 0.743651i \(-0.266908\pi\)
0.668568 + 0.743651i \(0.266908\pi\)
\(984\) 0 0
\(985\) 39.7815 1.26754
\(986\) 0.0995315 0.00316973
\(987\) 0 0
\(988\) −21.3666 −0.679763
\(989\) 62.1491 1.97623
\(990\) 0 0
\(991\) 17.5601 0.557816 0.278908 0.960318i \(-0.410027\pi\)
0.278908 + 0.960318i \(0.410027\pi\)
\(992\) −31.3027 −0.993861
\(993\) 0 0
\(994\) 3.81597 0.121035
\(995\) 16.5928 0.526027
\(996\) 0 0
\(997\) −11.7778 −0.373008 −0.186504 0.982454i \(-0.559716\pi\)
−0.186504 + 0.982454i \(0.559716\pi\)
\(998\) −21.0649 −0.666799
\(999\) 0 0
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 6039.2.a.i.1.6 13
3.2 odd 2 2013.2.a.e.1.8 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.2.a.e.1.8 13 3.2 odd 2
6039.2.a.i.1.6 13 1.1 even 1 trivial