Properties

Label 6160.2.a.bd.1.2
Level $6160$
Weight $2$
Character 6160.1
Self dual yes
Analytic conductor $49.188$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6160.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.1878476451\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.404.1
Defining polynomial: \( x^{3} - x^{2} - 5x - 1 \) 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 3080)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.210756\) of defining polynomial
Character \(\chi\) \(=\) 6160.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.21076 q^{3} -1.00000 q^{5} +1.00000 q^{7} -1.53407 q^{9} +O(q^{10})\) \(q-1.21076 q^{3} -1.00000 q^{5} +1.00000 q^{7} -1.53407 q^{9} +1.00000 q^{11} -1.21076 q^{13} +1.21076 q^{15} +4.27890 q^{17} -7.06814 q^{19} -1.21076 q^{21} +2.95558 q^{23} +1.00000 q^{25} +5.48965 q^{27} -2.00000 q^{29} +6.16634 q^{31} -1.21076 q^{33} -1.00000 q^{35} -4.95558 q^{37} +1.46593 q^{39} +0.166338 q^{41} -6.44523 q^{43} +1.53407 q^{45} +2.70041 q^{47} +1.00000 q^{49} -5.18070 q^{51} +4.11256 q^{53} -1.00000 q^{55} +8.55779 q^{57} +14.7241 q^{59} -14.3915 q^{61} -1.53407 q^{63} +1.21076 q^{65} +9.60221 q^{67} -3.57849 q^{69} -6.13628 q^{71} -12.2789 q^{73} -1.21076 q^{75} +1.00000 q^{77} +12.1126 q^{79} -2.04442 q^{81} +1.48965 q^{83} -4.27890 q^{85} +2.42151 q^{87} +2.42151 q^{89} -1.21076 q^{91} -7.46593 q^{93} +7.06814 q^{95} -7.71477 q^{97} -1.53407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} - 3 q^{5} + 3 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{3} - 3 q^{5} + 3 q^{7} + 3 q^{9} + 3 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} - 6 q^{19} - 2 q^{21} - 2 q^{23} + 3 q^{25} - 2 q^{27} - 6 q^{29} + 6 q^{31} - 2 q^{33} - 3 q^{35} - 4 q^{37} + 12 q^{39} - 12 q^{41} + 10 q^{43} - 3 q^{45} - 12 q^{47} + 3 q^{49} + 4 q^{51} + 8 q^{53} - 3 q^{55} - 8 q^{57} - 2 q^{59} - 22 q^{61} + 3 q^{63} + 2 q^{65} + 6 q^{67} - 14 q^{69} + 12 q^{71} - 20 q^{73} - 2 q^{75} + 3 q^{77} + 32 q^{79} - 17 q^{81} - 14 q^{83} + 4 q^{85} + 4 q^{87} + 4 q^{89} - 2 q^{91} - 30 q^{93} + 6 q^{95} + 4 q^{97} + 3 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.21076 −0.699030 −0.349515 0.936931i \(-0.613654\pi\)
−0.349515 + 0.936931i \(0.613654\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −1.53407 −0.511357
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.21076 −0.335803 −0.167902 0.985804i \(-0.553699\pi\)
−0.167902 + 0.985804i \(0.553699\pi\)
\(14\) 0 0
\(15\) 1.21076 0.312616
\(16\) 0 0
\(17\) 4.27890 1.03778 0.518892 0.854840i \(-0.326345\pi\)
0.518892 + 0.854840i \(0.326345\pi\)
\(18\) 0 0
\(19\) −7.06814 −1.62154 −0.810771 0.585363i \(-0.800952\pi\)
−0.810771 + 0.585363i \(0.800952\pi\)
\(20\) 0 0
\(21\) −1.21076 −0.264209
\(22\) 0 0
\(23\) 2.95558 0.616281 0.308141 0.951341i \(-0.400293\pi\)
0.308141 + 0.951341i \(0.400293\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.48965 1.05648
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 6.16634 1.10751 0.553753 0.832681i \(-0.313195\pi\)
0.553753 + 0.832681i \(0.313195\pi\)
\(32\) 0 0
\(33\) −1.21076 −0.210766
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −4.95558 −0.814693 −0.407346 0.913274i \(-0.633546\pi\)
−0.407346 + 0.913274i \(0.633546\pi\)
\(38\) 0 0
\(39\) 1.46593 0.234737
\(40\) 0 0
\(41\) 0.166338 0.0259776 0.0129888 0.999916i \(-0.495865\pi\)
0.0129888 + 0.999916i \(0.495865\pi\)
\(42\) 0 0
\(43\) −6.44523 −0.982889 −0.491444 0.870909i \(-0.663531\pi\)
−0.491444 + 0.870909i \(0.663531\pi\)
\(44\) 0 0
\(45\) 1.53407 0.228686
\(46\) 0 0
\(47\) 2.70041 0.393895 0.196947 0.980414i \(-0.436897\pi\)
0.196947 + 0.980414i \(0.436897\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −5.18070 −0.725443
\(52\) 0 0
\(53\) 4.11256 0.564903 0.282452 0.959282i \(-0.408852\pi\)
0.282452 + 0.959282i \(0.408852\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 8.55779 1.13351
\(58\) 0 0
\(59\) 14.7241 1.91692 0.958459 0.285229i \(-0.0920698\pi\)
0.958459 + 0.285229i \(0.0920698\pi\)
\(60\) 0 0
\(61\) −14.3915 −1.84264 −0.921318 0.388809i \(-0.872887\pi\)
−0.921318 + 0.388809i \(0.872887\pi\)
\(62\) 0 0
\(63\) −1.53407 −0.193275
\(64\) 0 0
\(65\) 1.21076 0.150176
\(66\) 0 0
\(67\) 9.60221 1.17310 0.586548 0.809914i \(-0.300486\pi\)
0.586548 + 0.809914i \(0.300486\pi\)
\(68\) 0 0
\(69\) −3.57849 −0.430799
\(70\) 0 0
\(71\) −6.13628 −0.728243 −0.364121 0.931352i \(-0.618631\pi\)
−0.364121 + 0.931352i \(0.618631\pi\)
\(72\) 0 0
\(73\) −12.2789 −1.43714 −0.718568 0.695457i \(-0.755202\pi\)
−0.718568 + 0.695457i \(0.755202\pi\)
\(74\) 0 0
\(75\) −1.21076 −0.139806
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 12.1126 1.36277 0.681385 0.731926i \(-0.261378\pi\)
0.681385 + 0.731926i \(0.261378\pi\)
\(80\) 0 0
\(81\) −2.04442 −0.227158
\(82\) 0 0
\(83\) 1.48965 0.163511 0.0817553 0.996652i \(-0.473947\pi\)
0.0817553 + 0.996652i \(0.473947\pi\)
\(84\) 0 0
\(85\) −4.27890 −0.464111
\(86\) 0 0
\(87\) 2.42151 0.259613
\(88\) 0 0
\(89\) 2.42151 0.256680 0.128340 0.991730i \(-0.459035\pi\)
0.128340 + 0.991730i \(0.459035\pi\)
\(90\) 0 0
\(91\) −1.21076 −0.126922
\(92\) 0 0
\(93\) −7.46593 −0.774181
\(94\) 0 0
\(95\) 7.06814 0.725176
\(96\) 0 0
\(97\) −7.71477 −0.783316 −0.391658 0.920111i \(-0.628098\pi\)
−0.391658 + 0.920111i \(0.628098\pi\)
\(98\) 0 0
\(99\) −1.53407 −0.154180
\(100\) 0 0
\(101\) −14.0775 −1.40076 −0.700382 0.713768i \(-0.746987\pi\)
−0.700382 + 0.713768i \(0.746987\pi\)
\(102\) 0 0
\(103\) 13.7685 1.35666 0.678328 0.734760i \(-0.262705\pi\)
0.678328 + 0.734760i \(0.262705\pi\)
\(104\) 0 0
\(105\) 1.21076 0.118158
\(106\) 0 0
\(107\) 5.91116 0.571454 0.285727 0.958311i \(-0.407765\pi\)
0.285727 + 0.958311i \(0.407765\pi\)
\(108\) 0 0
\(109\) 0.421512 0.0403735 0.0201868 0.999796i \(-0.493574\pi\)
0.0201868 + 0.999796i \(0.493574\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −13.7148 −1.29018 −0.645088 0.764108i \(-0.723179\pi\)
−0.645088 + 0.764108i \(0.723179\pi\)
\(114\) 0 0
\(115\) −2.95558 −0.275609
\(116\) 0 0
\(117\) 1.85738 0.171715
\(118\) 0 0
\(119\) 4.27890 0.392246
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −0.201395 −0.0181591
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −9.62593 −0.854163 −0.427082 0.904213i \(-0.640458\pi\)
−0.427082 + 0.904213i \(0.640458\pi\)
\(128\) 0 0
\(129\) 7.80361 0.687069
\(130\) 0 0
\(131\) −14.9793 −1.30875 −0.654374 0.756171i \(-0.727068\pi\)
−0.654374 + 0.756171i \(0.727068\pi\)
\(132\) 0 0
\(133\) −7.06814 −0.612886
\(134\) 0 0
\(135\) −5.48965 −0.472474
\(136\) 0 0
\(137\) 22.0237 1.88161 0.940807 0.338943i \(-0.110069\pi\)
0.940807 + 0.338943i \(0.110069\pi\)
\(138\) 0 0
\(139\) −3.26454 −0.276894 −0.138447 0.990370i \(-0.544211\pi\)
−0.138447 + 0.990370i \(0.544211\pi\)
\(140\) 0 0
\(141\) −3.26953 −0.275345
\(142\) 0 0
\(143\) −1.21076 −0.101248
\(144\) 0 0
\(145\) 2.00000 0.166091
\(146\) 0 0
\(147\) −1.21076 −0.0998615
\(148\) 0 0
\(149\) −1.66732 −0.136593 −0.0682963 0.997665i \(-0.521756\pi\)
−0.0682963 + 0.997665i \(0.521756\pi\)
\(150\) 0 0
\(151\) −11.8273 −0.962494 −0.481247 0.876585i \(-0.659816\pi\)
−0.481247 + 0.876585i \(0.659816\pi\)
\(152\) 0 0
\(153\) −6.56413 −0.530678
\(154\) 0 0
\(155\) −6.16634 −0.495292
\(156\) 0 0
\(157\) 10.1363 0.808963 0.404482 0.914546i \(-0.367452\pi\)
0.404482 + 0.914546i \(0.367452\pi\)
\(158\) 0 0
\(159\) −4.97930 −0.394885
\(160\) 0 0
\(161\) 2.95558 0.232932
\(162\) 0 0
\(163\) 2.39779 0.187809 0.0939047 0.995581i \(-0.470065\pi\)
0.0939047 + 0.995581i \(0.470065\pi\)
\(164\) 0 0
\(165\) 1.21076 0.0942572
\(166\) 0 0
\(167\) −13.8223 −1.06960 −0.534802 0.844977i \(-0.679614\pi\)
−0.534802 + 0.844977i \(0.679614\pi\)
\(168\) 0 0
\(169\) −11.5341 −0.887236
\(170\) 0 0
\(171\) 10.8430 0.829187
\(172\) 0 0
\(173\) −18.1901 −1.38296 −0.691482 0.722393i \(-0.743042\pi\)
−0.691482 + 0.722393i \(0.743042\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) −17.8273 −1.33998
\(178\) 0 0
\(179\) −15.5972 −1.16579 −0.582895 0.812547i \(-0.698080\pi\)
−0.582895 + 0.812547i \(0.698080\pi\)
\(180\) 0 0
\(181\) 19.2044 1.42745 0.713727 0.700424i \(-0.247006\pi\)
0.713727 + 0.700424i \(0.247006\pi\)
\(182\) 0 0
\(183\) 17.4245 1.28806
\(184\) 0 0
\(185\) 4.95558 0.364342
\(186\) 0 0
\(187\) 4.27890 0.312904
\(188\) 0 0
\(189\) 5.48965 0.399313
\(190\) 0 0
\(191\) 14.4215 1.04350 0.521752 0.853097i \(-0.325279\pi\)
0.521752 + 0.853097i \(0.325279\pi\)
\(192\) 0 0
\(193\) −4.62291 −0.332764 −0.166382 0.986061i \(-0.553208\pi\)
−0.166382 + 0.986061i \(0.553208\pi\)
\(194\) 0 0
\(195\) −1.46593 −0.104977
\(196\) 0 0
\(197\) 3.37709 0.240608 0.120304 0.992737i \(-0.461613\pi\)
0.120304 + 0.992737i \(0.461613\pi\)
\(198\) 0 0
\(199\) −21.7923 −1.54481 −0.772407 0.635128i \(-0.780947\pi\)
−0.772407 + 0.635128i \(0.780947\pi\)
\(200\) 0 0
\(201\) −11.6259 −0.820030
\(202\) 0 0
\(203\) −2.00000 −0.140372
\(204\) 0 0
\(205\) −0.166338 −0.0116175
\(206\) 0 0
\(207\) −4.53407 −0.315140
\(208\) 0 0
\(209\) −7.06814 −0.488913
\(210\) 0 0
\(211\) 25.4483 1.75193 0.875965 0.482374i \(-0.160225\pi\)
0.875965 + 0.482374i \(0.160225\pi\)
\(212\) 0 0
\(213\) 7.42954 0.509064
\(214\) 0 0
\(215\) 6.44523 0.439561
\(216\) 0 0
\(217\) 6.16634 0.418598
\(218\) 0 0
\(219\) 14.8667 1.00460
\(220\) 0 0
\(221\) −5.18070 −0.348492
\(222\) 0 0
\(223\) −14.0538 −0.941111 −0.470555 0.882370i \(-0.655946\pi\)
−0.470555 + 0.882370i \(0.655946\pi\)
\(224\) 0 0
\(225\) −1.53407 −0.102271
\(226\) 0 0
\(227\) −25.2933 −1.67877 −0.839386 0.543535i \(-0.817085\pi\)
−0.839386 + 0.543535i \(0.817085\pi\)
\(228\) 0 0
\(229\) 21.3120 1.40834 0.704168 0.710034i \(-0.251320\pi\)
0.704168 + 0.710034i \(0.251320\pi\)
\(230\) 0 0
\(231\) −1.21076 −0.0796619
\(232\) 0 0
\(233\) −12.7305 −0.834000 −0.417000 0.908906i \(-0.636919\pi\)
−0.417000 + 0.908906i \(0.636919\pi\)
\(234\) 0 0
\(235\) −2.70041 −0.176155
\(236\) 0 0
\(237\) −14.6654 −0.952617
\(238\) 0 0
\(239\) 20.7829 1.34433 0.672167 0.740399i \(-0.265364\pi\)
0.672167 + 0.740399i \(0.265364\pi\)
\(240\) 0 0
\(241\) −23.8811 −1.53832 −0.769159 0.639058i \(-0.779324\pi\)
−0.769159 + 0.639058i \(0.779324\pi\)
\(242\) 0 0
\(243\) −13.9937 −0.897694
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 8.55779 0.544519
\(248\) 0 0
\(249\) −1.80361 −0.114299
\(250\) 0 0
\(251\) −8.76552 −0.553275 −0.276637 0.960974i \(-0.589220\pi\)
−0.276637 + 0.960974i \(0.589220\pi\)
\(252\) 0 0
\(253\) 2.95558 0.185816
\(254\) 0 0
\(255\) 5.18070 0.324428
\(256\) 0 0
\(257\) 20.8905 1.30311 0.651556 0.758601i \(-0.274117\pi\)
0.651556 + 0.758601i \(0.274117\pi\)
\(258\) 0 0
\(259\) −4.95558 −0.307925
\(260\) 0 0
\(261\) 3.06814 0.189913
\(262\) 0 0
\(263\) 0.960582 0.0592320 0.0296160 0.999561i \(-0.490572\pi\)
0.0296160 + 0.999561i \(0.490572\pi\)
\(264\) 0 0
\(265\) −4.11256 −0.252632
\(266\) 0 0
\(267\) −2.93186 −0.179427
\(268\) 0 0
\(269\) −28.2726 −1.72381 −0.861904 0.507071i \(-0.830728\pi\)
−0.861904 + 0.507071i \(0.830728\pi\)
\(270\) 0 0
\(271\) 19.5371 1.18679 0.593397 0.804910i \(-0.297786\pi\)
0.593397 + 0.804910i \(0.297786\pi\)
\(272\) 0 0
\(273\) 1.46593 0.0887221
\(274\) 0 0
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) 3.04442 0.182921 0.0914607 0.995809i \(-0.470846\pi\)
0.0914607 + 0.995809i \(0.470846\pi\)
\(278\) 0 0
\(279\) −9.45960 −0.566331
\(280\) 0 0
\(281\) 14.0474 0.838000 0.419000 0.907986i \(-0.362381\pi\)
0.419000 + 0.907986i \(0.362381\pi\)
\(282\) 0 0
\(283\) −10.7542 −0.639270 −0.319635 0.947541i \(-0.603560\pi\)
−0.319635 + 0.947541i \(0.603560\pi\)
\(284\) 0 0
\(285\) −8.55779 −0.506920
\(286\) 0 0
\(287\) 0.166338 0.00981861
\(288\) 0 0
\(289\) 1.30895 0.0769973
\(290\) 0 0
\(291\) 9.34070 0.547562
\(292\) 0 0
\(293\) −21.6323 −1.26377 −0.631885 0.775062i \(-0.717719\pi\)
−0.631885 + 0.775062i \(0.717719\pi\)
\(294\) 0 0
\(295\) −14.7241 −0.857272
\(296\) 0 0
\(297\) 5.48965 0.318542
\(298\) 0 0
\(299\) −3.57849 −0.206949
\(300\) 0 0
\(301\) −6.44523 −0.371497
\(302\) 0 0
\(303\) 17.0444 0.979176
\(304\) 0 0
\(305\) 14.3915 0.824052
\(306\) 0 0
\(307\) −31.7335 −1.81113 −0.905563 0.424212i \(-0.860551\pi\)
−0.905563 + 0.424212i \(0.860551\pi\)
\(308\) 0 0
\(309\) −16.6704 −0.948343
\(310\) 0 0
\(311\) −30.6353 −1.73717 −0.868584 0.495542i \(-0.834970\pi\)
−0.868584 + 0.495542i \(0.834970\pi\)
\(312\) 0 0
\(313\) −17.5972 −0.994653 −0.497327 0.867563i \(-0.665685\pi\)
−0.497327 + 0.867563i \(0.665685\pi\)
\(314\) 0 0
\(315\) 1.53407 0.0864351
\(316\) 0 0
\(317\) −4.97930 −0.279666 −0.139833 0.990175i \(-0.544657\pi\)
−0.139833 + 0.990175i \(0.544657\pi\)
\(318\) 0 0
\(319\) −2.00000 −0.111979
\(320\) 0 0
\(321\) −7.15698 −0.399463
\(322\) 0 0
\(323\) −30.2438 −1.68281
\(324\) 0 0
\(325\) −1.21076 −0.0671607
\(326\) 0 0
\(327\) −0.510348 −0.0282223
\(328\) 0 0
\(329\) 2.70041 0.148878
\(330\) 0 0
\(331\) 6.19639 0.340585 0.170292 0.985394i \(-0.445529\pi\)
0.170292 + 0.985394i \(0.445529\pi\)
\(332\) 0 0
\(333\) 7.60221 0.416599
\(334\) 0 0
\(335\) −9.60221 −0.524625
\(336\) 0 0
\(337\) −25.5134 −1.38980 −0.694901 0.719105i \(-0.744552\pi\)
−0.694901 + 0.719105i \(0.744552\pi\)
\(338\) 0 0
\(339\) 16.6052 0.901873
\(340\) 0 0
\(341\) 6.16634 0.333926
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 3.57849 0.192659
\(346\) 0 0
\(347\) −11.4659 −0.615523 −0.307762 0.951463i \(-0.599580\pi\)
−0.307762 + 0.951463i \(0.599580\pi\)
\(348\) 0 0
\(349\) 0.812966 0.0435171 0.0217585 0.999763i \(-0.493073\pi\)
0.0217585 + 0.999763i \(0.493073\pi\)
\(350\) 0 0
\(351\) −6.64663 −0.354771
\(352\) 0 0
\(353\) −0.754187 −0.0401413 −0.0200707 0.999799i \(-0.506389\pi\)
−0.0200707 + 0.999799i \(0.506389\pi\)
\(354\) 0 0
\(355\) 6.13628 0.325680
\(356\) 0 0
\(357\) −5.18070 −0.274192
\(358\) 0 0
\(359\) −30.0712 −1.58710 −0.793548 0.608508i \(-0.791768\pi\)
−0.793548 + 0.608508i \(0.791768\pi\)
\(360\) 0 0
\(361\) 30.9586 1.62940
\(362\) 0 0
\(363\) −1.21076 −0.0635482
\(364\) 0 0
\(365\) 12.2789 0.642707
\(366\) 0 0
\(367\) −8.23145 −0.429678 −0.214839 0.976649i \(-0.568923\pi\)
−0.214839 + 0.976649i \(0.568923\pi\)
\(368\) 0 0
\(369\) −0.255174 −0.0132838
\(370\) 0 0
\(371\) 4.11256 0.213513
\(372\) 0 0
\(373\) −24.2201 −1.25407 −0.627035 0.778991i \(-0.715732\pi\)
−0.627035 + 0.778991i \(0.715732\pi\)
\(374\) 0 0
\(375\) 1.21076 0.0625232
\(376\) 0 0
\(377\) 2.42151 0.124714
\(378\) 0 0
\(379\) 0.843024 0.0433032 0.0216516 0.999766i \(-0.493108\pi\)
0.0216516 + 0.999766i \(0.493108\pi\)
\(380\) 0 0
\(381\) 11.6547 0.597086
\(382\) 0 0
\(383\) −31.2869 −1.59869 −0.799344 0.600874i \(-0.794819\pi\)
−0.799344 + 0.600874i \(0.794819\pi\)
\(384\) 0 0
\(385\) −1.00000 −0.0509647
\(386\) 0 0
\(387\) 9.88744 0.502607
\(388\) 0 0
\(389\) −25.0869 −1.27195 −0.635977 0.771708i \(-0.719403\pi\)
−0.635977 + 0.771708i \(0.719403\pi\)
\(390\) 0 0
\(391\) 12.6466 0.639568
\(392\) 0 0
\(393\) 18.1363 0.914854
\(394\) 0 0
\(395\) −12.1126 −0.609449
\(396\) 0 0
\(397\) −3.77488 −0.189456 −0.0947280 0.995503i \(-0.530198\pi\)
−0.0947280 + 0.995503i \(0.530198\pi\)
\(398\) 0 0
\(399\) 8.55779 0.428425
\(400\) 0 0
\(401\) −8.31395 −0.415179 −0.207589 0.978216i \(-0.566562\pi\)
−0.207589 + 0.978216i \(0.566562\pi\)
\(402\) 0 0
\(403\) −7.46593 −0.371904
\(404\) 0 0
\(405\) 2.04442 0.101588
\(406\) 0 0
\(407\) −4.95558 −0.245639
\(408\) 0 0
\(409\) 26.2138 1.29619 0.648094 0.761560i \(-0.275566\pi\)
0.648094 + 0.761560i \(0.275566\pi\)
\(410\) 0 0
\(411\) −26.6654 −1.31530
\(412\) 0 0
\(413\) 14.7241 0.724527
\(414\) 0 0
\(415\) −1.48965 −0.0731241
\(416\) 0 0
\(417\) 3.95256 0.193557
\(418\) 0 0
\(419\) 24.8417 1.21360 0.606798 0.794856i \(-0.292454\pi\)
0.606798 + 0.794856i \(0.292454\pi\)
\(420\) 0 0
\(421\) −14.1126 −0.687804 −0.343902 0.939006i \(-0.611749\pi\)
−0.343902 + 0.939006i \(0.611749\pi\)
\(422\) 0 0
\(423\) −4.14262 −0.201421
\(424\) 0 0
\(425\) 4.27890 0.207557
\(426\) 0 0
\(427\) −14.3915 −0.696451
\(428\) 0 0
\(429\) 1.46593 0.0707758
\(430\) 0 0
\(431\) 33.2281 1.60054 0.800272 0.599638i \(-0.204689\pi\)
0.800272 + 0.599638i \(0.204689\pi\)
\(432\) 0 0
\(433\) −27.4008 −1.31680 −0.658400 0.752669i \(-0.728766\pi\)
−0.658400 + 0.752669i \(0.728766\pi\)
\(434\) 0 0
\(435\) −2.42151 −0.116103
\(436\) 0 0
\(437\) −20.8905 −0.999327
\(438\) 0 0
\(439\) 38.9192 1.85751 0.928756 0.370692i \(-0.120879\pi\)
0.928756 + 0.370692i \(0.120879\pi\)
\(440\) 0 0
\(441\) −1.53407 −0.0730510
\(442\) 0 0
\(443\) −5.04442 −0.239668 −0.119834 0.992794i \(-0.538236\pi\)
−0.119834 + 0.992794i \(0.538236\pi\)
\(444\) 0 0
\(445\) −2.42151 −0.114791
\(446\) 0 0
\(447\) 2.01872 0.0954823
\(448\) 0 0
\(449\) 20.8667 0.984763 0.492381 0.870380i \(-0.336127\pi\)
0.492381 + 0.870380i \(0.336127\pi\)
\(450\) 0 0
\(451\) 0.166338 0.00783254
\(452\) 0 0
\(453\) 14.3200 0.672813
\(454\) 0 0
\(455\) 1.21076 0.0567611
\(456\) 0 0
\(457\) −3.77988 −0.176815 −0.0884077 0.996084i \(-0.528178\pi\)
−0.0884077 + 0.996084i \(0.528178\pi\)
\(458\) 0 0
\(459\) 23.4897 1.09640
\(460\) 0 0
\(461\) −17.7923 −0.828669 −0.414334 0.910125i \(-0.635986\pi\)
−0.414334 + 0.910125i \(0.635986\pi\)
\(462\) 0 0
\(463\) 22.0524 1.02486 0.512432 0.858728i \(-0.328745\pi\)
0.512432 + 0.858728i \(0.328745\pi\)
\(464\) 0 0
\(465\) 7.46593 0.346224
\(466\) 0 0
\(467\) −28.9255 −1.33851 −0.669257 0.743031i \(-0.733387\pi\)
−0.669257 + 0.743031i \(0.733387\pi\)
\(468\) 0 0
\(469\) 9.60221 0.443389
\(470\) 0 0
\(471\) −12.2726 −0.565490
\(472\) 0 0
\(473\) −6.44523 −0.296352
\(474\) 0 0
\(475\) −7.06814 −0.324309
\(476\) 0 0
\(477\) −6.30895 −0.288867
\(478\) 0 0
\(479\) 14.8430 0.678195 0.339098 0.940751i \(-0.389878\pi\)
0.339098 + 0.940751i \(0.389878\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) 0 0
\(483\) −3.57849 −0.162827
\(484\) 0 0
\(485\) 7.71477 0.350310
\(486\) 0 0
\(487\) −6.55279 −0.296935 −0.148468 0.988917i \(-0.547434\pi\)
−0.148468 + 0.988917i \(0.547434\pi\)
\(488\) 0 0
\(489\) −2.90314 −0.131284
\(490\) 0 0
\(491\) −1.58349 −0.0714618 −0.0357309 0.999361i \(-0.511376\pi\)
−0.0357309 + 0.999361i \(0.511376\pi\)
\(492\) 0 0
\(493\) −8.55779 −0.385424
\(494\) 0 0
\(495\) 1.53407 0.0689513
\(496\) 0 0
\(497\) −6.13628 −0.275250
\(498\) 0 0
\(499\) 8.61791 0.385790 0.192895 0.981219i \(-0.438212\pi\)
0.192895 + 0.981219i \(0.438212\pi\)
\(500\) 0 0
\(501\) 16.7355 0.747685
\(502\) 0 0
\(503\) −23.3534 −1.04128 −0.520638 0.853778i \(-0.674306\pi\)
−0.520638 + 0.853778i \(0.674306\pi\)
\(504\) 0 0
\(505\) 14.0775 0.626441
\(506\) 0 0
\(507\) 13.9649 0.620205
\(508\) 0 0
\(509\) 23.8510 1.05718 0.528590 0.848878i \(-0.322721\pi\)
0.528590 + 0.848878i \(0.322721\pi\)
\(510\) 0 0
\(511\) −12.2789 −0.543186
\(512\) 0 0
\(513\) −38.8016 −1.71313
\(514\) 0 0
\(515\) −13.7685 −0.606715
\(516\) 0 0
\(517\) 2.70041 0.118764
\(518\) 0 0
\(519\) 22.0237 0.966734
\(520\) 0 0
\(521\) −36.7128 −1.60842 −0.804208 0.594347i \(-0.797410\pi\)
−0.804208 + 0.594347i \(0.797410\pi\)
\(522\) 0 0
\(523\) 21.5972 0.944380 0.472190 0.881497i \(-0.343464\pi\)
0.472190 + 0.881497i \(0.343464\pi\)
\(524\) 0 0
\(525\) −1.21076 −0.0528417
\(526\) 0 0
\(527\) 26.3851 1.14935
\(528\) 0 0
\(529\) −14.2645 −0.620197
\(530\) 0 0
\(531\) −22.5878 −0.980229
\(532\) 0 0
\(533\) −0.201395 −0.00872336
\(534\) 0 0
\(535\) −5.91116 −0.255562
\(536\) 0 0
\(537\) 18.8844 0.814923
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −5.48965 −0.236019 −0.118009 0.993012i \(-0.537651\pi\)
−0.118009 + 0.993012i \(0.537651\pi\)
\(542\) 0 0
\(543\) −23.2519 −0.997833
\(544\) 0 0
\(545\) −0.421512 −0.0180556
\(546\) 0 0
\(547\) −27.7148 −1.18500 −0.592499 0.805571i \(-0.701859\pi\)
−0.592499 + 0.805571i \(0.701859\pi\)
\(548\) 0 0
\(549\) 22.0775 0.942245
\(550\) 0 0
\(551\) 14.1363 0.602226
\(552\) 0 0
\(553\) 12.1126 0.515078
\(554\) 0 0
\(555\) −6.00000 −0.254686
\(556\) 0 0
\(557\) −5.18070 −0.219513 −0.109757 0.993958i \(-0.535007\pi\)
−0.109757 + 0.993958i \(0.535007\pi\)
\(558\) 0 0
\(559\) 7.80361 0.330057
\(560\) 0 0
\(561\) −5.18070 −0.218729
\(562\) 0 0
\(563\) −8.96058 −0.377643 −0.188822 0.982011i \(-0.560467\pi\)
−0.188822 + 0.982011i \(0.560467\pi\)
\(564\) 0 0
\(565\) 13.7148 0.576985
\(566\) 0 0
\(567\) −2.04442 −0.0858575
\(568\) 0 0
\(569\) −19.4008 −0.813325 −0.406662 0.913579i \(-0.633307\pi\)
−0.406662 + 0.913579i \(0.633307\pi\)
\(570\) 0 0
\(571\) −35.5845 −1.48917 −0.744583 0.667529i \(-0.767352\pi\)
−0.744583 + 0.667529i \(0.767352\pi\)
\(572\) 0 0
\(573\) −17.4609 −0.729441
\(574\) 0 0
\(575\) 2.95558 0.123256
\(576\) 0 0
\(577\) 11.6673 0.485717 0.242859 0.970062i \(-0.421915\pi\)
0.242859 + 0.970062i \(0.421915\pi\)
\(578\) 0 0
\(579\) 5.59721 0.232612
\(580\) 0 0
\(581\) 1.48965 0.0618012
\(582\) 0 0
\(583\) 4.11256 0.170325
\(584\) 0 0
\(585\) −1.85738 −0.0767934
\(586\) 0 0
\(587\) −10.3865 −0.428695 −0.214347 0.976757i \(-0.568762\pi\)
−0.214347 + 0.976757i \(0.568762\pi\)
\(588\) 0 0
\(589\) −43.5845 −1.79587
\(590\) 0 0
\(591\) −4.08884 −0.168192
\(592\) 0 0
\(593\) −0.367732 −0.0151010 −0.00755048 0.999971i \(-0.502403\pi\)
−0.00755048 + 0.999971i \(0.502403\pi\)
\(594\) 0 0
\(595\) −4.27890 −0.175418
\(596\) 0 0
\(597\) 26.3851 1.07987
\(598\) 0 0
\(599\) −2.93186 −0.119793 −0.0598963 0.998205i \(-0.519077\pi\)
−0.0598963 + 0.998205i \(0.519077\pi\)
\(600\) 0 0
\(601\) −2.58785 −0.105561 −0.0527803 0.998606i \(-0.516808\pi\)
−0.0527803 + 0.998606i \(0.516808\pi\)
\(602\) 0 0
\(603\) −14.7305 −0.599871
\(604\) 0 0
\(605\) −1.00000 −0.0406558
\(606\) 0 0
\(607\) −6.27256 −0.254595 −0.127298 0.991865i \(-0.540630\pi\)
−0.127298 + 0.991865i \(0.540630\pi\)
\(608\) 0 0
\(609\) 2.42151 0.0981246
\(610\) 0 0
\(611\) −3.26953 −0.132271
\(612\) 0 0
\(613\) −5.84605 −0.236120 −0.118060 0.993006i \(-0.537667\pi\)
−0.118060 + 0.993006i \(0.537667\pi\)
\(614\) 0 0
\(615\) 0.201395 0.00812101
\(616\) 0 0
\(617\) 14.8667 0.598513 0.299256 0.954173i \(-0.403261\pi\)
0.299256 + 0.954173i \(0.403261\pi\)
\(618\) 0 0
\(619\) −16.6166 −0.667876 −0.333938 0.942595i \(-0.608378\pi\)
−0.333938 + 0.942595i \(0.608378\pi\)
\(620\) 0 0
\(621\) 16.2251 0.651092
\(622\) 0 0
\(623\) 2.42151 0.0970158
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 8.55779 0.341765
\(628\) 0 0
\(629\) −21.2044 −0.845476
\(630\) 0 0
\(631\) 47.2519 1.88107 0.940534 0.339701i \(-0.110326\pi\)
0.940534 + 0.339701i \(0.110326\pi\)
\(632\) 0 0
\(633\) −30.8116 −1.22465
\(634\) 0 0
\(635\) 9.62593 0.381993
\(636\) 0 0
\(637\) −1.21076 −0.0479719
\(638\) 0 0
\(639\) 9.41349 0.372392
\(640\) 0 0
\(641\) −14.7305 −0.581818 −0.290909 0.956751i \(-0.593958\pi\)
−0.290909 + 0.956751i \(0.593958\pi\)
\(642\) 0 0
\(643\) −11.5909 −0.457100 −0.228550 0.973532i \(-0.573398\pi\)
−0.228550 + 0.973532i \(0.573398\pi\)
\(644\) 0 0
\(645\) −7.80361 −0.307267
\(646\) 0 0
\(647\) −20.6116 −0.810325 −0.405162 0.914245i \(-0.632785\pi\)
−0.405162 + 0.914245i \(0.632785\pi\)
\(648\) 0 0
\(649\) 14.7241 0.577973
\(650\) 0 0
\(651\) −7.46593 −0.292613
\(652\) 0 0
\(653\) 8.24384 0.322606 0.161303 0.986905i \(-0.448430\pi\)
0.161303 + 0.986905i \(0.448430\pi\)
\(654\) 0 0
\(655\) 14.9793 0.585290
\(656\) 0 0
\(657\) 18.8367 0.734889
\(658\) 0 0
\(659\) −29.9536 −1.16683 −0.583413 0.812175i \(-0.698283\pi\)
−0.583413 + 0.812175i \(0.698283\pi\)
\(660\) 0 0
\(661\) 34.2913 1.33378 0.666888 0.745158i \(-0.267626\pi\)
0.666888 + 0.745158i \(0.267626\pi\)
\(662\) 0 0
\(663\) 6.27256 0.243606
\(664\) 0 0
\(665\) 7.06814 0.274091
\(666\) 0 0
\(667\) −5.91116 −0.228881
\(668\) 0 0
\(669\) 17.0157 0.657865
\(670\) 0 0
\(671\) −14.3915 −0.555576
\(672\) 0 0
\(673\) 26.8541 1.03515 0.517574 0.855638i \(-0.326835\pi\)
0.517574 + 0.855638i \(0.326835\pi\)
\(674\) 0 0
\(675\) 5.48965 0.211297
\(676\) 0 0
\(677\) 40.5227 1.55742 0.778708 0.627387i \(-0.215876\pi\)
0.778708 + 0.627387i \(0.215876\pi\)
\(678\) 0 0
\(679\) −7.71477 −0.296066
\(680\) 0 0
\(681\) 30.6240 1.17351
\(682\) 0 0
\(683\) −42.8855 −1.64097 −0.820483 0.571670i \(-0.806296\pi\)
−0.820483 + 0.571670i \(0.806296\pi\)
\(684\) 0 0
\(685\) −22.0237 −0.841483
\(686\) 0 0
\(687\) −25.8036 −0.984469
\(688\) 0 0
\(689\) −4.97930 −0.189696
\(690\) 0 0
\(691\) 1.63727 0.0622846 0.0311423 0.999515i \(-0.490085\pi\)
0.0311423 + 0.999515i \(0.490085\pi\)
\(692\) 0 0
\(693\) −1.53407 −0.0582745
\(694\) 0 0
\(695\) 3.26454 0.123831
\(696\) 0 0
\(697\) 0.711742 0.0269592
\(698\) 0 0
\(699\) 15.4135 0.582992
\(700\) 0 0
\(701\) 27.8036 1.05013 0.525064 0.851063i \(-0.324041\pi\)
0.525064 + 0.851063i \(0.324041\pi\)
\(702\) 0 0
\(703\) 35.0267 1.32106
\(704\) 0 0
\(705\) 3.26953 0.123138
\(706\) 0 0
\(707\) −14.0775 −0.529439
\(708\) 0 0
\(709\) −33.9172 −1.27379 −0.636894 0.770951i \(-0.719781\pi\)
−0.636894 + 0.770951i \(0.719781\pi\)
\(710\) 0 0
\(711\) −18.5815 −0.696861
\(712\) 0 0
\(713\) 18.2251 0.682536
\(714\) 0 0
\(715\) 1.21076 0.0452797
\(716\) 0 0
\(717\) −25.1630 −0.939731
\(718\) 0 0
\(719\) −28.6640 −1.06899 −0.534494 0.845172i \(-0.679498\pi\)
−0.534494 + 0.845172i \(0.679498\pi\)
\(720\) 0 0
\(721\) 13.7685 0.512768
\(722\) 0 0
\(723\) 28.9142 1.07533
\(724\) 0 0
\(725\) −2.00000 −0.0742781
\(726\) 0 0
\(727\) 20.0538 0.743754 0.371877 0.928282i \(-0.378714\pi\)
0.371877 + 0.928282i \(0.378714\pi\)
\(728\) 0 0
\(729\) 23.0762 0.854673
\(730\) 0 0
\(731\) −27.5785 −1.02003
\(732\) 0 0
\(733\) −19.8160 −0.731920 −0.365960 0.930631i \(-0.619259\pi\)
−0.365960 + 0.930631i \(0.619259\pi\)
\(734\) 0 0
\(735\) 1.21076 0.0446594
\(736\) 0 0
\(737\) 9.60221 0.353702
\(738\) 0 0
\(739\) −6.80163 −0.250202 −0.125101 0.992144i \(-0.539926\pi\)
−0.125101 + 0.992144i \(0.539926\pi\)
\(740\) 0 0
\(741\) −10.3614 −0.380635
\(742\) 0 0
\(743\) −8.79558 −0.322678 −0.161339 0.986899i \(-0.551581\pi\)
−0.161339 + 0.986899i \(0.551581\pi\)
\(744\) 0 0
\(745\) 1.66732 0.0610860
\(746\) 0 0
\(747\) −2.28523 −0.0836122
\(748\) 0 0
\(749\) 5.91116 0.215989
\(750\) 0 0
\(751\) 31.9873 1.16723 0.583617 0.812029i \(-0.301637\pi\)
0.583617 + 0.812029i \(0.301637\pi\)
\(752\) 0 0
\(753\) 10.6129 0.386756
\(754\) 0 0
\(755\) 11.8273 0.430441
\(756\) 0 0
\(757\) 11.5310 0.419103 0.209551 0.977798i \(-0.432800\pi\)
0.209551 + 0.977798i \(0.432800\pi\)
\(758\) 0 0
\(759\) −3.57849 −0.129891
\(760\) 0 0
\(761\) −18.7716 −0.680469 −0.340235 0.940341i \(-0.610506\pi\)
−0.340235 + 0.940341i \(0.610506\pi\)
\(762\) 0 0
\(763\) 0.421512 0.0152598
\(764\) 0 0
\(765\) 6.56413 0.237327
\(766\) 0 0
\(767\) −17.8273 −0.643707
\(768\) 0 0
\(769\) −15.2759 −0.550862 −0.275431 0.961321i \(-0.588821\pi\)
−0.275431 + 0.961321i \(0.588821\pi\)
\(770\) 0 0
\(771\) −25.2933 −0.910914
\(772\) 0 0
\(773\) −17.0080 −0.611736 −0.305868 0.952074i \(-0.598947\pi\)
−0.305868 + 0.952074i \(0.598947\pi\)
\(774\) 0 0
\(775\) 6.16634 0.221501
\(776\) 0 0
\(777\) 6.00000 0.215249
\(778\) 0 0
\(779\) −1.17570 −0.0421238
\(780\) 0 0
\(781\) −6.13628 −0.219573
\(782\) 0 0
\(783\) −10.9793 −0.392368
\(784\) 0 0
\(785\) −10.1363 −0.361779
\(786\) 0 0
\(787\) 39.5845 1.41104 0.705518 0.708692i \(-0.250714\pi\)
0.705518 + 0.708692i \(0.250714\pi\)
\(788\) 0 0
\(789\) −1.16303 −0.0414050
\(790\) 0 0
\(791\) −13.7148 −0.487641
\(792\) 0 0
\(793\) 17.4245 0.618764
\(794\) 0 0
\(795\) 4.97930 0.176598
\(796\) 0 0
\(797\) −26.1363 −0.925795 −0.462897 0.886412i \(-0.653190\pi\)
−0.462897 + 0.886412i \(0.653190\pi\)
\(798\) 0 0
\(799\) 11.5548 0.408778
\(800\) 0 0
\(801\) −3.71477 −0.131255
\(802\) 0 0
\(803\) −12.2789 −0.433313
\(804\) 0 0
\(805\) −2.95558 −0.104171
\(806\) 0 0
\(807\) 34.2312 1.20499
\(808\) 0 0
\(809\) 28.3614 0.997134 0.498567 0.866851i \(-0.333860\pi\)
0.498567 + 0.866851i \(0.333860\pi\)
\(810\) 0 0
\(811\) −0.421512 −0.0148013 −0.00740064 0.999973i \(-0.502356\pi\)
−0.00740064 + 0.999973i \(0.502356\pi\)
\(812\) 0 0
\(813\) −23.6547 −0.829605
\(814\) 0 0
\(815\) −2.39779 −0.0839909
\(816\) 0 0
\(817\) 45.5558 1.59380
\(818\) 0 0
\(819\) 1.85738 0.0649023
\(820\) 0 0
\(821\) −9.61988 −0.335736 −0.167868 0.985809i \(-0.553688\pi\)
−0.167868 + 0.985809i \(0.553688\pi\)
\(822\) 0 0
\(823\) 46.3150 1.61444 0.807220 0.590251i \(-0.200971\pi\)
0.807220 + 0.590251i \(0.200971\pi\)
\(824\) 0 0
\(825\) −1.21076 −0.0421531
\(826\) 0 0
\(827\) −15.1206 −0.525794 −0.262897 0.964824i \(-0.584678\pi\)
−0.262897 + 0.964824i \(0.584678\pi\)
\(828\) 0 0
\(829\) 17.4295 0.605353 0.302676 0.953093i \(-0.402120\pi\)
0.302676 + 0.953093i \(0.402120\pi\)
\(830\) 0 0
\(831\) −3.68605 −0.127868
\(832\) 0 0
\(833\) 4.27890 0.148255
\(834\) 0 0
\(835\) 13.8223 0.478341
\(836\) 0 0
\(837\) 33.8510 1.17006
\(838\) 0 0
\(839\) 20.3313 0.701916 0.350958 0.936391i \(-0.385856\pi\)
0.350958 + 0.936391i \(0.385856\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) −17.0080 −0.585788
\(844\) 0 0
\(845\) 11.5341 0.396784
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 13.0207 0.446869
\(850\) 0 0
\(851\) −14.6466 −0.502080
\(852\) 0 0
\(853\) 5.31831 0.182096 0.0910478 0.995847i \(-0.470978\pi\)
0.0910478 + 0.995847i \(0.470978\pi\)
\(854\) 0 0
\(855\) −10.8430 −0.370824
\(856\) 0 0
\(857\) 41.5495 1.41930 0.709652 0.704553i \(-0.248852\pi\)
0.709652 + 0.704553i \(0.248852\pi\)
\(858\) 0 0
\(859\) 37.8110 1.29009 0.645047 0.764143i \(-0.276838\pi\)
0.645047 + 0.764143i \(0.276838\pi\)
\(860\) 0 0
\(861\) −0.201395 −0.00686351
\(862\) 0 0
\(863\) 1.26953 0.0432155 0.0216077 0.999767i \(-0.493122\pi\)
0.0216077 + 0.999767i \(0.493122\pi\)
\(864\) 0 0
\(865\) 18.1901 0.618481
\(866\) 0 0
\(867\) −1.58482 −0.0538234
\(868\) 0 0
\(869\) 12.1126 0.410890
\(870\) 0 0
\(871\) −11.6259 −0.393930
\(872\) 0 0
\(873\) 11.8350 0.400554
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 56.4800 1.90719 0.953597 0.301085i \(-0.0973489\pi\)
0.953597 + 0.301085i \(0.0973489\pi\)
\(878\) 0 0
\(879\) 26.1914 0.883414
\(880\) 0 0
\(881\) 4.04744 0.136362 0.0681809 0.997673i \(-0.478280\pi\)
0.0681809 + 0.997673i \(0.478280\pi\)
\(882\) 0 0
\(883\) 16.9843 0.571567 0.285784 0.958294i \(-0.407746\pi\)
0.285784 + 0.958294i \(0.407746\pi\)
\(884\) 0 0
\(885\) 17.8273 0.599259
\(886\) 0 0
\(887\) −18.8717 −0.633651 −0.316826 0.948484i \(-0.602617\pi\)
−0.316826 + 0.948484i \(0.602617\pi\)
\(888\) 0 0
\(889\) −9.62593 −0.322843
\(890\) 0 0
\(891\) −2.04442 −0.0684906
\(892\) 0 0
\(893\) −19.0869 −0.638718
\(894\) 0 0
\(895\) 15.5972 0.521357
\(896\) 0 0
\(897\) 4.33268 0.144664
\(898\) 0 0
\(899\) −12.3327 −0.411318
\(900\) 0 0
\(901\) 17.5972 0.586248
\(902\) 0 0
\(903\) 7.80361 0.259688
\(904\) 0 0
\(905\) −19.2044 −0.638377
\(906\) 0 0
\(907\) 0.426511 0.0141621 0.00708104 0.999975i \(-0.497746\pi\)
0.00708104 + 0.999975i \(0.497746\pi\)
\(908\) 0 0
\(909\) 21.5959 0.716290
\(910\) 0 0
\(911\) 35.1944 1.16604 0.583022 0.812457i \(-0.301870\pi\)
0.583022 + 0.812457i \(0.301870\pi\)
\(912\) 0 0
\(913\) 1.48965 0.0493003
\(914\) 0 0
\(915\) −17.4245 −0.576037
\(916\) 0 0
\(917\) −14.9793 −0.494660
\(918\) 0 0
\(919\) 44.7829 1.47725 0.738626 0.674116i \(-0.235475\pi\)
0.738626 + 0.674116i \(0.235475\pi\)
\(920\) 0 0
\(921\) 38.4215 1.26603
\(922\) 0 0
\(923\) 7.42954 0.244546
\(924\) 0 0
\(925\) −4.95558 −0.162939
\(926\) 0 0
\(927\) −21.1219 −0.693735
\(928\) 0 0
\(929\) −43.6921 −1.43349 −0.716746 0.697335i \(-0.754369\pi\)
−0.716746 + 0.697335i \(0.754369\pi\)
\(930\) 0 0
\(931\) −7.06814 −0.231649
\(932\) 0 0
\(933\) 37.0919 1.21433
\(934\) 0 0
\(935\) −4.27890 −0.139935
\(936\) 0 0
\(937\) −38.5989 −1.26097 −0.630486 0.776201i \(-0.717144\pi\)
−0.630486 + 0.776201i \(0.717144\pi\)
\(938\) 0 0
\(939\) 21.3059 0.695293
\(940\) 0 0
\(941\) −8.25517 −0.269111 −0.134555 0.990906i \(-0.542961\pi\)
−0.134555 + 0.990906i \(0.542961\pi\)
\(942\) 0 0
\(943\) 0.491625 0.0160095
\(944\) 0 0
\(945\) −5.48965 −0.178578
\(946\) 0 0
\(947\) −35.8935 −1.16638 −0.583191 0.812335i \(-0.698196\pi\)
−0.583191 + 0.812335i \(0.698196\pi\)
\(948\) 0 0
\(949\) 14.8667 0.482595
\(950\) 0 0
\(951\) 6.02872 0.195495
\(952\) 0 0
\(953\) 50.9616 1.65081 0.825405 0.564542i \(-0.190947\pi\)
0.825405 + 0.564542i \(0.190947\pi\)
\(954\) 0 0
\(955\) −14.4215 −0.466669
\(956\) 0 0
\(957\) 2.42151 0.0782764
\(958\) 0 0
\(959\) 22.0237 0.711183
\(960\) 0 0
\(961\) 7.02372 0.226572
\(962\) 0 0
\(963\) −9.06814 −0.292217
\(964\) 0 0
\(965\) 4.62291 0.148817
\(966\) 0 0
\(967\) −6.62291 −0.212978 −0.106489 0.994314i \(-0.533961\pi\)
−0.106489 + 0.994314i \(0.533961\pi\)
\(968\) 0 0
\(969\) 36.6179 1.17634
\(970\) 0 0
\(971\) −26.2552 −0.842569 −0.421284 0.906929i \(-0.638421\pi\)
−0.421284 + 0.906929i \(0.638421\pi\)
\(972\) 0 0
\(973\) −3.26454 −0.104656
\(974\) 0 0
\(975\) 1.46593 0.0469473
\(976\) 0 0
\(977\) 57.3594 1.83509 0.917545 0.397631i \(-0.130168\pi\)
0.917545 + 0.397631i \(0.130168\pi\)
\(978\) 0 0
\(979\) 2.42151 0.0773919
\(980\) 0 0
\(981\) −0.646629 −0.0206453
\(982\) 0 0
\(983\) −14.3577 −0.457941 −0.228970 0.973433i \(-0.573536\pi\)
−0.228970 + 0.973433i \(0.573536\pi\)
\(984\) 0 0
\(985\) −3.37709 −0.107603
\(986\) 0 0
\(987\) −3.26953 −0.104070
\(988\) 0 0
\(989\) −19.0494 −0.605736
\(990\) 0 0
\(991\) 30.1964 0.959220 0.479610 0.877482i \(-0.340778\pi\)
0.479610 + 0.877482i \(0.340778\pi\)
\(992\) 0 0
\(993\) −7.50232 −0.238079
\(994\) 0 0
\(995\) 21.7923 0.690861
\(996\) 0 0
\(997\) 14.9730 0.474199 0.237099 0.971485i \(-0.423803\pi\)
0.237099 + 0.971485i \(0.423803\pi\)
\(998\) 0 0
\(999\) −27.2044 −0.860710
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 6160.2.a.bd.1.2 3
4.3 odd 2 3080.2.a.m.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3080.2.a.m.1.2 3 4.3 odd 2
6160.2.a.bd.1.2 3 1.1 even 1 trivial