Properties

Label 4016.2.a.m.1.6
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 23
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(23\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 2008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.51727 q^{3} -0.472191 q^{5} -4.16870 q^{7} +3.33662 q^{9} +O(q^{10})\) \(q-2.51727 q^{3} -0.472191 q^{5} -4.16870 q^{7} +3.33662 q^{9} +0.304525 q^{11} +3.93359 q^{13} +1.18863 q^{15} +5.23074 q^{17} +3.05840 q^{19} +10.4937 q^{21} -7.82281 q^{23} -4.77704 q^{25} -0.847370 q^{27} -7.79678 q^{29} +9.12452 q^{31} -0.766569 q^{33} +1.96842 q^{35} -7.45897 q^{37} -9.90189 q^{39} -5.32993 q^{41} -10.2669 q^{43} -1.57552 q^{45} -8.20514 q^{47} +10.3781 q^{49} -13.1672 q^{51} -8.29482 q^{53} -0.143794 q^{55} -7.69881 q^{57} -3.03547 q^{59} -0.845264 q^{61} -13.9094 q^{63} -1.85741 q^{65} +5.94412 q^{67} +19.6921 q^{69} -6.20529 q^{71} +10.1038 q^{73} +12.0251 q^{75} -1.26947 q^{77} +9.74582 q^{79} -7.87682 q^{81} +4.98258 q^{83} -2.46991 q^{85} +19.6266 q^{87} +12.3965 q^{89} -16.3980 q^{91} -22.9688 q^{93} -1.44415 q^{95} +0.396603 q^{97} +1.01608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.51727 −1.45334 −0.726672 0.686985i \(-0.758934\pi\)
−0.726672 + 0.686985i \(0.758934\pi\)
\(4\) 0 0
\(5\) −0.472191 −0.211170 −0.105585 0.994410i \(-0.533672\pi\)
−0.105585 + 0.994410i \(0.533672\pi\)
\(6\) 0 0
\(7\) −4.16870 −1.57562 −0.787811 0.615918i \(-0.788785\pi\)
−0.787811 + 0.615918i \(0.788785\pi\)
\(8\) 0 0
\(9\) 3.33662 1.11221
\(10\) 0 0
\(11\) 0.304525 0.0918176 0.0459088 0.998946i \(-0.485382\pi\)
0.0459088 + 0.998946i \(0.485382\pi\)
\(12\) 0 0
\(13\) 3.93359 1.09098 0.545491 0.838117i \(-0.316343\pi\)
0.545491 + 0.838117i \(0.316343\pi\)
\(14\) 0 0
\(15\) 1.18863 0.306903
\(16\) 0 0
\(17\) 5.23074 1.26864 0.634320 0.773071i \(-0.281280\pi\)
0.634320 + 0.773071i \(0.281280\pi\)
\(18\) 0 0
\(19\) 3.05840 0.701646 0.350823 0.936442i \(-0.385902\pi\)
0.350823 + 0.936442i \(0.385902\pi\)
\(20\) 0 0
\(21\) 10.4937 2.28992
\(22\) 0 0
\(23\) −7.82281 −1.63117 −0.815585 0.578638i \(-0.803584\pi\)
−0.815585 + 0.578638i \(0.803584\pi\)
\(24\) 0 0
\(25\) −4.77704 −0.955407
\(26\) 0 0
\(27\) −0.847370 −0.163076
\(28\) 0 0
\(29\) −7.79678 −1.44782 −0.723912 0.689892i \(-0.757658\pi\)
−0.723912 + 0.689892i \(0.757658\pi\)
\(30\) 0 0
\(31\) 9.12452 1.63881 0.819406 0.573213i \(-0.194303\pi\)
0.819406 + 0.573213i \(0.194303\pi\)
\(32\) 0 0
\(33\) −0.766569 −0.133443
\(34\) 0 0
\(35\) 1.96842 0.332724
\(36\) 0 0
\(37\) −7.45897 −1.22625 −0.613123 0.789987i \(-0.710087\pi\)
−0.613123 + 0.789987i \(0.710087\pi\)
\(38\) 0 0
\(39\) −9.90189 −1.58557
\(40\) 0 0
\(41\) −5.32993 −0.832395 −0.416198 0.909274i \(-0.636638\pi\)
−0.416198 + 0.909274i \(0.636638\pi\)
\(42\) 0 0
\(43\) −10.2669 −1.56569 −0.782845 0.622216i \(-0.786232\pi\)
−0.782845 + 0.622216i \(0.786232\pi\)
\(44\) 0 0
\(45\) −1.57552 −0.234865
\(46\) 0 0
\(47\) −8.20514 −1.19684 −0.598421 0.801182i \(-0.704205\pi\)
−0.598421 + 0.801182i \(0.704205\pi\)
\(48\) 0 0
\(49\) 10.3781 1.48258
\(50\) 0 0
\(51\) −13.1672 −1.84377
\(52\) 0 0
\(53\) −8.29482 −1.13938 −0.569691 0.821859i \(-0.692937\pi\)
−0.569691 + 0.821859i \(0.692937\pi\)
\(54\) 0 0
\(55\) −0.143794 −0.0193891
\(56\) 0 0
\(57\) −7.69881 −1.01973
\(58\) 0 0
\(59\) −3.03547 −0.395184 −0.197592 0.980284i \(-0.563312\pi\)
−0.197592 + 0.980284i \(0.563312\pi\)
\(60\) 0 0
\(61\) −0.845264 −0.108225 −0.0541125 0.998535i \(-0.517233\pi\)
−0.0541125 + 0.998535i \(0.517233\pi\)
\(62\) 0 0
\(63\) −13.9094 −1.75242
\(64\) 0 0
\(65\) −1.85741 −0.230383
\(66\) 0 0
\(67\) 5.94412 0.726190 0.363095 0.931752i \(-0.381720\pi\)
0.363095 + 0.931752i \(0.381720\pi\)
\(68\) 0 0
\(69\) 19.6921 2.37065
\(70\) 0 0
\(71\) −6.20529 −0.736432 −0.368216 0.929740i \(-0.620031\pi\)
−0.368216 + 0.929740i \(0.620031\pi\)
\(72\) 0 0
\(73\) 10.1038 1.18256 0.591279 0.806467i \(-0.298623\pi\)
0.591279 + 0.806467i \(0.298623\pi\)
\(74\) 0 0
\(75\) 12.0251 1.38853
\(76\) 0 0
\(77\) −1.26947 −0.144670
\(78\) 0 0
\(79\) 9.74582 1.09649 0.548245 0.836318i \(-0.315296\pi\)
0.548245 + 0.836318i \(0.315296\pi\)
\(80\) 0 0
\(81\) −7.87682 −0.875202
\(82\) 0 0
\(83\) 4.98258 0.546909 0.273455 0.961885i \(-0.411834\pi\)
0.273455 + 0.961885i \(0.411834\pi\)
\(84\) 0 0
\(85\) −2.46991 −0.267899
\(86\) 0 0
\(87\) 19.6266 2.10419
\(88\) 0 0
\(89\) 12.3965 1.31403 0.657013 0.753879i \(-0.271820\pi\)
0.657013 + 0.753879i \(0.271820\pi\)
\(90\) 0 0
\(91\) −16.3980 −1.71897
\(92\) 0 0
\(93\) −22.9688 −2.38176
\(94\) 0 0
\(95\) −1.44415 −0.148167
\(96\) 0 0
\(97\) 0.396603 0.0402689 0.0201345 0.999797i \(-0.493591\pi\)
0.0201345 + 0.999797i \(0.493591\pi\)
\(98\) 0 0
\(99\) 1.01608 0.102120
\(100\) 0 0
\(101\) 18.5637 1.84716 0.923579 0.383408i \(-0.125250\pi\)
0.923579 + 0.383408i \(0.125250\pi\)
\(102\) 0 0
\(103\) 0.248464 0.0244819 0.0122409 0.999925i \(-0.496103\pi\)
0.0122409 + 0.999925i \(0.496103\pi\)
\(104\) 0 0
\(105\) −4.95504 −0.483563
\(106\) 0 0
\(107\) 10.0489 0.971464 0.485732 0.874108i \(-0.338553\pi\)
0.485732 + 0.874108i \(0.338553\pi\)
\(108\) 0 0
\(109\) 0.607413 0.0581796 0.0290898 0.999577i \(-0.490739\pi\)
0.0290898 + 0.999577i \(0.490739\pi\)
\(110\) 0 0
\(111\) 18.7762 1.78216
\(112\) 0 0
\(113\) 6.60924 0.621745 0.310872 0.950452i \(-0.399379\pi\)
0.310872 + 0.950452i \(0.399379\pi\)
\(114\) 0 0
\(115\) 3.69386 0.344454
\(116\) 0 0
\(117\) 13.1249 1.21340
\(118\) 0 0
\(119\) −21.8054 −1.99890
\(120\) 0 0
\(121\) −10.9073 −0.991570
\(122\) 0 0
\(123\) 13.4168 1.20976
\(124\) 0 0
\(125\) 4.61663 0.412924
\(126\) 0 0
\(127\) −9.82850 −0.872139 −0.436069 0.899913i \(-0.643630\pi\)
−0.436069 + 0.899913i \(0.643630\pi\)
\(128\) 0 0
\(129\) 25.8446 2.27549
\(130\) 0 0
\(131\) −13.6457 −1.19223 −0.596113 0.802900i \(-0.703289\pi\)
−0.596113 + 0.802900i \(0.703289\pi\)
\(132\) 0 0
\(133\) −12.7496 −1.10553
\(134\) 0 0
\(135\) 0.400120 0.0344369
\(136\) 0 0
\(137\) 11.4512 0.978341 0.489171 0.872188i \(-0.337300\pi\)
0.489171 + 0.872188i \(0.337300\pi\)
\(138\) 0 0
\(139\) 9.46034 0.802416 0.401208 0.915987i \(-0.368590\pi\)
0.401208 + 0.915987i \(0.368590\pi\)
\(140\) 0 0
\(141\) 20.6545 1.73942
\(142\) 0 0
\(143\) 1.19788 0.100171
\(144\) 0 0
\(145\) 3.68157 0.305737
\(146\) 0 0
\(147\) −26.1244 −2.15470
\(148\) 0 0
\(149\) 9.37862 0.768327 0.384163 0.923265i \(-0.374490\pi\)
0.384163 + 0.923265i \(0.374490\pi\)
\(150\) 0 0
\(151\) 11.0340 0.897938 0.448969 0.893547i \(-0.351791\pi\)
0.448969 + 0.893547i \(0.351791\pi\)
\(152\) 0 0
\(153\) 17.4530 1.41099
\(154\) 0 0
\(155\) −4.30852 −0.346068
\(156\) 0 0
\(157\) −20.0501 −1.60017 −0.800087 0.599884i \(-0.795213\pi\)
−0.800087 + 0.599884i \(0.795213\pi\)
\(158\) 0 0
\(159\) 20.8803 1.65591
\(160\) 0 0
\(161\) 32.6110 2.57010
\(162\) 0 0
\(163\) 11.5614 0.905561 0.452780 0.891622i \(-0.350432\pi\)
0.452780 + 0.891622i \(0.350432\pi\)
\(164\) 0 0
\(165\) 0.361967 0.0281791
\(166\) 0 0
\(167\) 16.8019 1.30017 0.650086 0.759861i \(-0.274733\pi\)
0.650086 + 0.759861i \(0.274733\pi\)
\(168\) 0 0
\(169\) 2.47315 0.190242
\(170\) 0 0
\(171\) 10.2047 0.780376
\(172\) 0 0
\(173\) −24.7209 −1.87950 −0.939749 0.341864i \(-0.888942\pi\)
−0.939749 + 0.341864i \(0.888942\pi\)
\(174\) 0 0
\(175\) 19.9140 1.50536
\(176\) 0 0
\(177\) 7.64108 0.574339
\(178\) 0 0
\(179\) 8.59975 0.642776 0.321388 0.946948i \(-0.395851\pi\)
0.321388 + 0.946948i \(0.395851\pi\)
\(180\) 0 0
\(181\) −22.4733 −1.67042 −0.835212 0.549928i \(-0.814655\pi\)
−0.835212 + 0.549928i \(0.814655\pi\)
\(182\) 0 0
\(183\) 2.12775 0.157288
\(184\) 0 0
\(185\) 3.52206 0.258947
\(186\) 0 0
\(187\) 1.59289 0.116483
\(188\) 0 0
\(189\) 3.53243 0.256947
\(190\) 0 0
\(191\) 9.86963 0.714141 0.357071 0.934077i \(-0.383776\pi\)
0.357071 + 0.934077i \(0.383776\pi\)
\(192\) 0 0
\(193\) 4.97722 0.358268 0.179134 0.983825i \(-0.442670\pi\)
0.179134 + 0.983825i \(0.442670\pi\)
\(194\) 0 0
\(195\) 4.67558 0.334826
\(196\) 0 0
\(197\) −5.49936 −0.391813 −0.195907 0.980623i \(-0.562765\pi\)
−0.195907 + 0.980623i \(0.562765\pi\)
\(198\) 0 0
\(199\) 1.22600 0.0869085 0.0434543 0.999055i \(-0.486164\pi\)
0.0434543 + 0.999055i \(0.486164\pi\)
\(200\) 0 0
\(201\) −14.9629 −1.05540
\(202\) 0 0
\(203\) 32.5024 2.28122
\(204\) 0 0
\(205\) 2.51674 0.175777
\(206\) 0 0
\(207\) −26.1018 −1.81420
\(208\) 0 0
\(209\) 0.931359 0.0644234
\(210\) 0 0
\(211\) −16.5606 −1.14008 −0.570041 0.821616i \(-0.693073\pi\)
−0.570041 + 0.821616i \(0.693073\pi\)
\(212\) 0 0
\(213\) 15.6204 1.07029
\(214\) 0 0
\(215\) 4.84795 0.330627
\(216\) 0 0
\(217\) −38.0374 −2.58215
\(218\) 0 0
\(219\) −25.4339 −1.71866
\(220\) 0 0
\(221\) 20.5756 1.38406
\(222\) 0 0
\(223\) 22.9580 1.53738 0.768692 0.639620i \(-0.220908\pi\)
0.768692 + 0.639620i \(0.220908\pi\)
\(224\) 0 0
\(225\) −15.9392 −1.06261
\(226\) 0 0
\(227\) −29.6756 −1.96964 −0.984821 0.173575i \(-0.944468\pi\)
−0.984821 + 0.173575i \(0.944468\pi\)
\(228\) 0 0
\(229\) 20.7268 1.36966 0.684832 0.728701i \(-0.259875\pi\)
0.684832 + 0.728701i \(0.259875\pi\)
\(230\) 0 0
\(231\) 3.19560 0.210255
\(232\) 0 0
\(233\) 0.322003 0.0210951 0.0105475 0.999944i \(-0.496643\pi\)
0.0105475 + 0.999944i \(0.496643\pi\)
\(234\) 0 0
\(235\) 3.87439 0.252738
\(236\) 0 0
\(237\) −24.5328 −1.59358
\(238\) 0 0
\(239\) −7.73473 −0.500318 −0.250159 0.968205i \(-0.580483\pi\)
−0.250159 + 0.968205i \(0.580483\pi\)
\(240\) 0 0
\(241\) 24.8205 1.59883 0.799414 0.600780i \(-0.205143\pi\)
0.799414 + 0.600780i \(0.205143\pi\)
\(242\) 0 0
\(243\) 22.3701 1.43505
\(244\) 0 0
\(245\) −4.90043 −0.313077
\(246\) 0 0
\(247\) 12.0305 0.765483
\(248\) 0 0
\(249\) −12.5425 −0.794847
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) −2.38224 −0.149770
\(254\) 0 0
\(255\) 6.21741 0.389349
\(256\) 0 0
\(257\) 29.0611 1.81278 0.906391 0.422440i \(-0.138826\pi\)
0.906391 + 0.422440i \(0.138826\pi\)
\(258\) 0 0
\(259\) 31.0942 1.93210
\(260\) 0 0
\(261\) −26.0149 −1.61028
\(262\) 0 0
\(263\) −4.26424 −0.262944 −0.131472 0.991320i \(-0.541970\pi\)
−0.131472 + 0.991320i \(0.541970\pi\)
\(264\) 0 0
\(265\) 3.91674 0.240603
\(266\) 0 0
\(267\) −31.2053 −1.90973
\(268\) 0 0
\(269\) −23.6535 −1.44218 −0.721089 0.692843i \(-0.756358\pi\)
−0.721089 + 0.692843i \(0.756358\pi\)
\(270\) 0 0
\(271\) 16.6254 1.00992 0.504961 0.863142i \(-0.331507\pi\)
0.504961 + 0.863142i \(0.331507\pi\)
\(272\) 0 0
\(273\) 41.2780 2.49826
\(274\) 0 0
\(275\) −1.45472 −0.0877232
\(276\) 0 0
\(277\) −8.78549 −0.527869 −0.263935 0.964541i \(-0.585020\pi\)
−0.263935 + 0.964541i \(0.585020\pi\)
\(278\) 0 0
\(279\) 30.4451 1.82270
\(280\) 0 0
\(281\) 11.4541 0.683293 0.341646 0.939829i \(-0.389015\pi\)
0.341646 + 0.939829i \(0.389015\pi\)
\(282\) 0 0
\(283\) −25.8433 −1.53623 −0.768114 0.640314i \(-0.778804\pi\)
−0.768114 + 0.640314i \(0.778804\pi\)
\(284\) 0 0
\(285\) 3.63531 0.215337
\(286\) 0 0
\(287\) 22.2189 1.31154
\(288\) 0 0
\(289\) 10.3606 0.609448
\(290\) 0 0
\(291\) −0.998355 −0.0585246
\(292\) 0 0
\(293\) −0.0646721 −0.00377819 −0.00188909 0.999998i \(-0.500601\pi\)
−0.00188909 + 0.999998i \(0.500601\pi\)
\(294\) 0 0
\(295\) 1.43332 0.0834512
\(296\) 0 0
\(297\) −0.258045 −0.0149733
\(298\) 0 0
\(299\) −30.7718 −1.77958
\(300\) 0 0
\(301\) 42.7997 2.46694
\(302\) 0 0
\(303\) −46.7298 −2.68456
\(304\) 0 0
\(305\) 0.399126 0.0228539
\(306\) 0 0
\(307\) −7.89727 −0.450721 −0.225361 0.974275i \(-0.572356\pi\)
−0.225361 + 0.974275i \(0.572356\pi\)
\(308\) 0 0
\(309\) −0.625450 −0.0355806
\(310\) 0 0
\(311\) 30.8494 1.74931 0.874656 0.484745i \(-0.161088\pi\)
0.874656 + 0.484745i \(0.161088\pi\)
\(312\) 0 0
\(313\) −14.9817 −0.846814 −0.423407 0.905940i \(-0.639166\pi\)
−0.423407 + 0.905940i \(0.639166\pi\)
\(314\) 0 0
\(315\) 6.56789 0.370059
\(316\) 0 0
\(317\) −6.55514 −0.368173 −0.184087 0.982910i \(-0.558933\pi\)
−0.184087 + 0.982910i \(0.558933\pi\)
\(318\) 0 0
\(319\) −2.37431 −0.132936
\(320\) 0 0
\(321\) −25.2958 −1.41187
\(322\) 0 0
\(323\) 15.9977 0.890136
\(324\) 0 0
\(325\) −18.7909 −1.04233
\(326\) 0 0
\(327\) −1.52902 −0.0845549
\(328\) 0 0
\(329\) 34.2048 1.88577
\(330\) 0 0
\(331\) 19.7693 1.08662 0.543310 0.839532i \(-0.317171\pi\)
0.543310 + 0.839532i \(0.317171\pi\)
\(332\) 0 0
\(333\) −24.8878 −1.36384
\(334\) 0 0
\(335\) −2.80676 −0.153350
\(336\) 0 0
\(337\) −21.3765 −1.16445 −0.582226 0.813027i \(-0.697818\pi\)
−0.582226 + 0.813027i \(0.697818\pi\)
\(338\) 0 0
\(339\) −16.6372 −0.903609
\(340\) 0 0
\(341\) 2.77864 0.150472
\(342\) 0 0
\(343\) −14.0822 −0.760367
\(344\) 0 0
\(345\) −9.29843 −0.500610
\(346\) 0 0
\(347\) 17.0719 0.916467 0.458234 0.888832i \(-0.348482\pi\)
0.458234 + 0.888832i \(0.348482\pi\)
\(348\) 0 0
\(349\) 21.5795 1.15512 0.577562 0.816347i \(-0.304004\pi\)
0.577562 + 0.816347i \(0.304004\pi\)
\(350\) 0 0
\(351\) −3.33321 −0.177913
\(352\) 0 0
\(353\) −7.78068 −0.414124 −0.207062 0.978328i \(-0.566390\pi\)
−0.207062 + 0.978328i \(0.566390\pi\)
\(354\) 0 0
\(355\) 2.93008 0.155513
\(356\) 0 0
\(357\) 54.8899 2.90508
\(358\) 0 0
\(359\) 13.3156 0.702773 0.351387 0.936230i \(-0.385710\pi\)
0.351387 + 0.936230i \(0.385710\pi\)
\(360\) 0 0
\(361\) −9.64617 −0.507693
\(362\) 0 0
\(363\) 27.4565 1.44109
\(364\) 0 0
\(365\) −4.77091 −0.249721
\(366\) 0 0
\(367\) 13.1444 0.686132 0.343066 0.939311i \(-0.388535\pi\)
0.343066 + 0.939311i \(0.388535\pi\)
\(368\) 0 0
\(369\) −17.7840 −0.925796
\(370\) 0 0
\(371\) 34.5786 1.79523
\(372\) 0 0
\(373\) 37.3600 1.93443 0.967215 0.253960i \(-0.0817333\pi\)
0.967215 + 0.253960i \(0.0817333\pi\)
\(374\) 0 0
\(375\) −11.6213 −0.600120
\(376\) 0 0
\(377\) −30.6693 −1.57955
\(378\) 0 0
\(379\) 2.82223 0.144968 0.0724841 0.997370i \(-0.476907\pi\)
0.0724841 + 0.997370i \(0.476907\pi\)
\(380\) 0 0
\(381\) 24.7410 1.26752
\(382\) 0 0
\(383\) 11.2386 0.574268 0.287134 0.957890i \(-0.407298\pi\)
0.287134 + 0.957890i \(0.407298\pi\)
\(384\) 0 0
\(385\) 0.599433 0.0305499
\(386\) 0 0
\(387\) −34.2568 −1.74137
\(388\) 0 0
\(389\) −23.0334 −1.16784 −0.583919 0.811812i \(-0.698482\pi\)
−0.583919 + 0.811812i \(0.698482\pi\)
\(390\) 0 0
\(391\) −40.9191 −2.06937
\(392\) 0 0
\(393\) 34.3497 1.73271
\(394\) 0 0
\(395\) −4.60189 −0.231546
\(396\) 0 0
\(397\) 39.2231 1.96855 0.984275 0.176642i \(-0.0565234\pi\)
0.984275 + 0.176642i \(0.0565234\pi\)
\(398\) 0 0
\(399\) 32.0940 1.60671
\(400\) 0 0
\(401\) −14.5312 −0.725654 −0.362827 0.931857i \(-0.618188\pi\)
−0.362827 + 0.931857i \(0.618188\pi\)
\(402\) 0 0
\(403\) 35.8921 1.78792
\(404\) 0 0
\(405\) 3.71936 0.184817
\(406\) 0 0
\(407\) −2.27144 −0.112591
\(408\) 0 0
\(409\) 28.0104 1.38503 0.692513 0.721405i \(-0.256503\pi\)
0.692513 + 0.721405i \(0.256503\pi\)
\(410\) 0 0
\(411\) −28.8257 −1.42187
\(412\) 0 0
\(413\) 12.6540 0.622661
\(414\) 0 0
\(415\) −2.35273 −0.115491
\(416\) 0 0
\(417\) −23.8142 −1.16619
\(418\) 0 0
\(419\) 4.01120 0.195960 0.0979799 0.995188i \(-0.468762\pi\)
0.0979799 + 0.995188i \(0.468762\pi\)
\(420\) 0 0
\(421\) −18.1701 −0.885555 −0.442777 0.896632i \(-0.646007\pi\)
−0.442777 + 0.896632i \(0.646007\pi\)
\(422\) 0 0
\(423\) −27.3775 −1.33114
\(424\) 0 0
\(425\) −24.9874 −1.21207
\(426\) 0 0
\(427\) 3.52365 0.170522
\(428\) 0 0
\(429\) −3.01537 −0.145583
\(430\) 0 0
\(431\) −30.3177 −1.46035 −0.730175 0.683260i \(-0.760562\pi\)
−0.730175 + 0.683260i \(0.760562\pi\)
\(432\) 0 0
\(433\) 35.4115 1.70177 0.850883 0.525355i \(-0.176067\pi\)
0.850883 + 0.525355i \(0.176067\pi\)
\(434\) 0 0
\(435\) −9.26748 −0.444342
\(436\) 0 0
\(437\) −23.9253 −1.14450
\(438\) 0 0
\(439\) 25.5194 1.21798 0.608988 0.793180i \(-0.291576\pi\)
0.608988 + 0.793180i \(0.291576\pi\)
\(440\) 0 0
\(441\) 34.6277 1.64894
\(442\) 0 0
\(443\) −32.1210 −1.52611 −0.763057 0.646331i \(-0.776302\pi\)
−0.763057 + 0.646331i \(0.776302\pi\)
\(444\) 0 0
\(445\) −5.85351 −0.277483
\(446\) 0 0
\(447\) −23.6085 −1.11664
\(448\) 0 0
\(449\) 5.85110 0.276130 0.138065 0.990423i \(-0.455912\pi\)
0.138065 + 0.990423i \(0.455912\pi\)
\(450\) 0 0
\(451\) −1.62309 −0.0764285
\(452\) 0 0
\(453\) −27.7756 −1.30501
\(454\) 0 0
\(455\) 7.74298 0.362996
\(456\) 0 0
\(457\) −18.4553 −0.863301 −0.431650 0.902041i \(-0.642069\pi\)
−0.431650 + 0.902041i \(0.642069\pi\)
\(458\) 0 0
\(459\) −4.43237 −0.206885
\(460\) 0 0
\(461\) 3.42093 0.159329 0.0796644 0.996822i \(-0.474615\pi\)
0.0796644 + 0.996822i \(0.474615\pi\)
\(462\) 0 0
\(463\) −0.00333581 −0.000155028 0 −7.75142e−5 1.00000i \(-0.500025\pi\)
−7.75142e−5 1.00000i \(0.500025\pi\)
\(464\) 0 0
\(465\) 10.8457 0.502956
\(466\) 0 0
\(467\) 15.7806 0.730238 0.365119 0.930961i \(-0.381028\pi\)
0.365119 + 0.930961i \(0.381028\pi\)
\(468\) 0 0
\(469\) −24.7793 −1.14420
\(470\) 0 0
\(471\) 50.4715 2.32560
\(472\) 0 0
\(473\) −3.12653 −0.143758
\(474\) 0 0
\(475\) −14.6101 −0.670357
\(476\) 0 0
\(477\) −27.6767 −1.26723
\(478\) 0 0
\(479\) −23.4049 −1.06940 −0.534700 0.845042i \(-0.679575\pi\)
−0.534700 + 0.845042i \(0.679575\pi\)
\(480\) 0 0
\(481\) −29.3405 −1.33781
\(482\) 0 0
\(483\) −82.0905 −3.73525
\(484\) 0 0
\(485\) −0.187272 −0.00850360
\(486\) 0 0
\(487\) 7.72620 0.350108 0.175054 0.984559i \(-0.443990\pi\)
0.175054 + 0.984559i \(0.443990\pi\)
\(488\) 0 0
\(489\) −29.1032 −1.31609
\(490\) 0 0
\(491\) 1.96908 0.0888635 0.0444318 0.999012i \(-0.485852\pi\)
0.0444318 + 0.999012i \(0.485852\pi\)
\(492\) 0 0
\(493\) −40.7829 −1.83677
\(494\) 0 0
\(495\) −0.479786 −0.0215648
\(496\) 0 0
\(497\) 25.8680 1.16034
\(498\) 0 0
\(499\) 23.8066 1.06573 0.532865 0.846200i \(-0.321115\pi\)
0.532865 + 0.846200i \(0.321115\pi\)
\(500\) 0 0
\(501\) −42.2949 −1.88960
\(502\) 0 0
\(503\) 35.6782 1.59081 0.795406 0.606076i \(-0.207257\pi\)
0.795406 + 0.606076i \(0.207257\pi\)
\(504\) 0 0
\(505\) −8.76562 −0.390065
\(506\) 0 0
\(507\) −6.22557 −0.276487
\(508\) 0 0
\(509\) 37.6993 1.67099 0.835496 0.549496i \(-0.185180\pi\)
0.835496 + 0.549496i \(0.185180\pi\)
\(510\) 0 0
\(511\) −42.1197 −1.86326
\(512\) 0 0
\(513\) −2.59160 −0.114422
\(514\) 0 0
\(515\) −0.117322 −0.00516984
\(516\) 0 0
\(517\) −2.49867 −0.109891
\(518\) 0 0
\(519\) 62.2292 2.73156
\(520\) 0 0
\(521\) −2.68569 −0.117662 −0.0588310 0.998268i \(-0.518737\pi\)
−0.0588310 + 0.998268i \(0.518737\pi\)
\(522\) 0 0
\(523\) −16.2403 −0.710138 −0.355069 0.934840i \(-0.615543\pi\)
−0.355069 + 0.934840i \(0.615543\pi\)
\(524\) 0 0
\(525\) −50.1289 −2.18781
\(526\) 0 0
\(527\) 47.7280 2.07906
\(528\) 0 0
\(529\) 38.1964 1.66071
\(530\) 0 0
\(531\) −10.1282 −0.439527
\(532\) 0 0
\(533\) −20.9658 −0.908128
\(534\) 0 0
\(535\) −4.74500 −0.205144
\(536\) 0 0
\(537\) −21.6479 −0.934174
\(538\) 0 0
\(539\) 3.16038 0.136127
\(540\) 0 0
\(541\) 32.7476 1.40793 0.703964 0.710236i \(-0.251412\pi\)
0.703964 + 0.710236i \(0.251412\pi\)
\(542\) 0 0
\(543\) 56.5711 2.42770
\(544\) 0 0
\(545\) −0.286815 −0.0122858
\(546\) 0 0
\(547\) 19.2228 0.821908 0.410954 0.911656i \(-0.365196\pi\)
0.410954 + 0.911656i \(0.365196\pi\)
\(548\) 0 0
\(549\) −2.82033 −0.120369
\(550\) 0 0
\(551\) −23.8457 −1.01586
\(552\) 0 0
\(553\) −40.6274 −1.72765
\(554\) 0 0
\(555\) −8.86595 −0.376339
\(556\) 0 0
\(557\) 18.9698 0.803778 0.401889 0.915689i \(-0.368354\pi\)
0.401889 + 0.915689i \(0.368354\pi\)
\(558\) 0 0
\(559\) −40.3859 −1.70814
\(560\) 0 0
\(561\) −4.00972 −0.169291
\(562\) 0 0
\(563\) 2.77977 0.117153 0.0585767 0.998283i \(-0.481344\pi\)
0.0585767 + 0.998283i \(0.481344\pi\)
\(564\) 0 0
\(565\) −3.12082 −0.131294
\(566\) 0 0
\(567\) 32.8361 1.37899
\(568\) 0 0
\(569\) 24.2475 1.01651 0.508254 0.861207i \(-0.330291\pi\)
0.508254 + 0.861207i \(0.330291\pi\)
\(570\) 0 0
\(571\) 24.1351 1.01002 0.505012 0.863112i \(-0.331488\pi\)
0.505012 + 0.863112i \(0.331488\pi\)
\(572\) 0 0
\(573\) −24.8445 −1.03789
\(574\) 0 0
\(575\) 37.3699 1.55843
\(576\) 0 0
\(577\) −8.81763 −0.367083 −0.183541 0.983012i \(-0.558756\pi\)
−0.183541 + 0.983012i \(0.558756\pi\)
\(578\) 0 0
\(579\) −12.5290 −0.520687
\(580\) 0 0
\(581\) −20.7709 −0.861722
\(582\) 0 0
\(583\) −2.52598 −0.104615
\(584\) 0 0
\(585\) −6.19747 −0.256234
\(586\) 0 0
\(587\) 15.0645 0.621780 0.310890 0.950446i \(-0.399373\pi\)
0.310890 + 0.950446i \(0.399373\pi\)
\(588\) 0 0
\(589\) 27.9065 1.14987
\(590\) 0 0
\(591\) 13.8434 0.569440
\(592\) 0 0
\(593\) 28.7573 1.18092 0.590461 0.807066i \(-0.298946\pi\)
0.590461 + 0.807066i \(0.298946\pi\)
\(594\) 0 0
\(595\) 10.2963 0.422107
\(596\) 0 0
\(597\) −3.08616 −0.126308
\(598\) 0 0
\(599\) 25.8141 1.05474 0.527368 0.849637i \(-0.323179\pi\)
0.527368 + 0.849637i \(0.323179\pi\)
\(600\) 0 0
\(601\) 2.64163 0.107754 0.0538771 0.998548i \(-0.482842\pi\)
0.0538771 + 0.998548i \(0.482842\pi\)
\(602\) 0 0
\(603\) 19.8333 0.807674
\(604\) 0 0
\(605\) 5.15031 0.209390
\(606\) 0 0
\(607\) 26.5488 1.07758 0.538792 0.842439i \(-0.318881\pi\)
0.538792 + 0.842439i \(0.318881\pi\)
\(608\) 0 0
\(609\) −81.8172 −3.31540
\(610\) 0 0
\(611\) −32.2757 −1.30573
\(612\) 0 0
\(613\) −36.7305 −1.48353 −0.741765 0.670659i \(-0.766011\pi\)
−0.741765 + 0.670659i \(0.766011\pi\)
\(614\) 0 0
\(615\) −6.33531 −0.255464
\(616\) 0 0
\(617\) 6.19526 0.249412 0.124706 0.992194i \(-0.460201\pi\)
0.124706 + 0.992194i \(0.460201\pi\)
\(618\) 0 0
\(619\) 0.382739 0.0153836 0.00769179 0.999970i \(-0.497552\pi\)
0.00769179 + 0.999970i \(0.497552\pi\)
\(620\) 0 0
\(621\) 6.62881 0.266005
\(622\) 0 0
\(623\) −51.6773 −2.07041
\(624\) 0 0
\(625\) 21.7052 0.868210
\(626\) 0 0
\(627\) −2.34448 −0.0936294
\(628\) 0 0
\(629\) −39.0159 −1.55567
\(630\) 0 0
\(631\) 27.6617 1.10120 0.550598 0.834771i \(-0.314400\pi\)
0.550598 + 0.834771i \(0.314400\pi\)
\(632\) 0 0
\(633\) 41.6875 1.65693
\(634\) 0 0
\(635\) 4.64093 0.184170
\(636\) 0 0
\(637\) 40.8231 1.61747
\(638\) 0 0
\(639\) −20.7047 −0.819066
\(640\) 0 0
\(641\) 32.6196 1.28840 0.644199 0.764858i \(-0.277191\pi\)
0.644199 + 0.764858i \(0.277191\pi\)
\(642\) 0 0
\(643\) 31.3759 1.23735 0.618673 0.785648i \(-0.287670\pi\)
0.618673 + 0.785648i \(0.287670\pi\)
\(644\) 0 0
\(645\) −12.2036 −0.480515
\(646\) 0 0
\(647\) −26.6413 −1.04738 −0.523688 0.851910i \(-0.675444\pi\)
−0.523688 + 0.851910i \(0.675444\pi\)
\(648\) 0 0
\(649\) −0.924375 −0.0362849
\(650\) 0 0
\(651\) 95.7502 3.75275
\(652\) 0 0
\(653\) 0.501126 0.0196106 0.00980529 0.999952i \(-0.496879\pi\)
0.00980529 + 0.999952i \(0.496879\pi\)
\(654\) 0 0
\(655\) 6.44336 0.251763
\(656\) 0 0
\(657\) 33.7125 1.31525
\(658\) 0 0
\(659\) −5.06507 −0.197307 −0.0986536 0.995122i \(-0.531454\pi\)
−0.0986536 + 0.995122i \(0.531454\pi\)
\(660\) 0 0
\(661\) −12.8951 −0.501561 −0.250780 0.968044i \(-0.580687\pi\)
−0.250780 + 0.968044i \(0.580687\pi\)
\(662\) 0 0
\(663\) −51.7942 −2.01152
\(664\) 0 0
\(665\) 6.02023 0.233455
\(666\) 0 0
\(667\) 60.9927 2.36165
\(668\) 0 0
\(669\) −57.7914 −2.23435
\(670\) 0 0
\(671\) −0.257404 −0.00993696
\(672\) 0 0
\(673\) −15.8230 −0.609933 −0.304966 0.952363i \(-0.598645\pi\)
−0.304966 + 0.952363i \(0.598645\pi\)
\(674\) 0 0
\(675\) 4.04792 0.155804
\(676\) 0 0
\(677\) −20.2826 −0.779523 −0.389761 0.920916i \(-0.627443\pi\)
−0.389761 + 0.920916i \(0.627443\pi\)
\(678\) 0 0
\(679\) −1.65332 −0.0634486
\(680\) 0 0
\(681\) 74.7014 2.86257
\(682\) 0 0
\(683\) 9.57134 0.366237 0.183119 0.983091i \(-0.441381\pi\)
0.183119 + 0.983091i \(0.441381\pi\)
\(684\) 0 0
\(685\) −5.40715 −0.206597
\(686\) 0 0
\(687\) −52.1748 −1.99059
\(688\) 0 0
\(689\) −32.6284 −1.24304
\(690\) 0 0
\(691\) −10.1320 −0.385441 −0.192721 0.981254i \(-0.561731\pi\)
−0.192721 + 0.981254i \(0.561731\pi\)
\(692\) 0 0
\(693\) −4.23575 −0.160903
\(694\) 0 0
\(695\) −4.46709 −0.169446
\(696\) 0 0
\(697\) −27.8795 −1.05601
\(698\) 0 0
\(699\) −0.810566 −0.0306584
\(700\) 0 0
\(701\) −5.86605 −0.221558 −0.110779 0.993845i \(-0.535335\pi\)
−0.110779 + 0.993845i \(0.535335\pi\)
\(702\) 0 0
\(703\) −22.8125 −0.860391
\(704\) 0 0
\(705\) −9.75287 −0.367314
\(706\) 0 0
\(707\) −77.3866 −2.91042
\(708\) 0 0
\(709\) −16.3570 −0.614301 −0.307151 0.951661i \(-0.599376\pi\)
−0.307151 + 0.951661i \(0.599376\pi\)
\(710\) 0 0
\(711\) 32.5181 1.21953
\(712\) 0 0
\(713\) −71.3794 −2.67318
\(714\) 0 0
\(715\) −0.565626 −0.0211532
\(716\) 0 0
\(717\) 19.4704 0.727134
\(718\) 0 0
\(719\) −8.70874 −0.324781 −0.162391 0.986727i \(-0.551920\pi\)
−0.162391 + 0.986727i \(0.551920\pi\)
\(720\) 0 0
\(721\) −1.03577 −0.0385742
\(722\) 0 0
\(723\) −62.4797 −2.32365
\(724\) 0 0
\(725\) 37.2455 1.38326
\(726\) 0 0
\(727\) −30.9035 −1.14615 −0.573074 0.819504i \(-0.694249\pi\)
−0.573074 + 0.819504i \(0.694249\pi\)
\(728\) 0 0
\(729\) −32.6811 −1.21041
\(730\) 0 0
\(731\) −53.7036 −1.98630
\(732\) 0 0
\(733\) 21.9242 0.809790 0.404895 0.914363i \(-0.367308\pi\)
0.404895 + 0.914363i \(0.367308\pi\)
\(734\) 0 0
\(735\) 12.3357 0.455009
\(736\) 0 0
\(737\) 1.81013 0.0666770
\(738\) 0 0
\(739\) −24.7830 −0.911656 −0.455828 0.890068i \(-0.650657\pi\)
−0.455828 + 0.890068i \(0.650657\pi\)
\(740\) 0 0
\(741\) −30.2840 −1.11251
\(742\) 0 0
\(743\) −11.7429 −0.430806 −0.215403 0.976525i \(-0.569107\pi\)
−0.215403 + 0.976525i \(0.569107\pi\)
\(744\) 0 0
\(745\) −4.42850 −0.162248
\(746\) 0 0
\(747\) 16.6250 0.608277
\(748\) 0 0
\(749\) −41.8909 −1.53066
\(750\) 0 0
\(751\) 18.5022 0.675153 0.337577 0.941298i \(-0.390393\pi\)
0.337577 + 0.941298i \(0.390393\pi\)
\(752\) 0 0
\(753\) −2.51727 −0.0917342
\(754\) 0 0
\(755\) −5.21018 −0.189618
\(756\) 0 0
\(757\) 35.1308 1.27685 0.638425 0.769684i \(-0.279586\pi\)
0.638425 + 0.769684i \(0.279586\pi\)
\(758\) 0 0
\(759\) 5.99673 0.217667
\(760\) 0 0
\(761\) −9.80837 −0.355553 −0.177777 0.984071i \(-0.556890\pi\)
−0.177777 + 0.984071i \(0.556890\pi\)
\(762\) 0 0
\(763\) −2.53212 −0.0916690
\(764\) 0 0
\(765\) −8.24115 −0.297959
\(766\) 0 0
\(767\) −11.9403 −0.431139
\(768\) 0 0
\(769\) 14.7856 0.533181 0.266590 0.963810i \(-0.414103\pi\)
0.266590 + 0.963810i \(0.414103\pi\)
\(770\) 0 0
\(771\) −73.1545 −2.63459
\(772\) 0 0
\(773\) 3.90318 0.140388 0.0701939 0.997533i \(-0.477638\pi\)
0.0701939 + 0.997533i \(0.477638\pi\)
\(774\) 0 0
\(775\) −43.5882 −1.56573
\(776\) 0 0
\(777\) −78.2724 −2.80801
\(778\) 0 0
\(779\) −16.3011 −0.584046
\(780\) 0 0
\(781\) −1.88966 −0.0676175
\(782\) 0 0
\(783\) 6.60675 0.236106
\(784\) 0 0
\(785\) 9.46749 0.337909
\(786\) 0 0
\(787\) 47.6348 1.69800 0.848999 0.528394i \(-0.177206\pi\)
0.848999 + 0.528394i \(0.177206\pi\)
\(788\) 0 0
\(789\) 10.7342 0.382148
\(790\) 0 0
\(791\) −27.5519 −0.979634
\(792\) 0 0
\(793\) −3.32492 −0.118071
\(794\) 0 0
\(795\) −9.85947 −0.349679
\(796\) 0 0
\(797\) −10.2414 −0.362769 −0.181384 0.983412i \(-0.558058\pi\)
−0.181384 + 0.983412i \(0.558058\pi\)
\(798\) 0 0
\(799\) −42.9189 −1.51836
\(800\) 0 0
\(801\) 41.3624 1.46147
\(802\) 0 0
\(803\) 3.07685 0.108580
\(804\) 0 0
\(805\) −15.3986 −0.542730
\(806\) 0 0
\(807\) 59.5420 2.09598
\(808\) 0 0
\(809\) 4.87595 0.171429 0.0857146 0.996320i \(-0.472683\pi\)
0.0857146 + 0.996320i \(0.472683\pi\)
\(810\) 0 0
\(811\) 23.0368 0.808932 0.404466 0.914553i \(-0.367457\pi\)
0.404466 + 0.914553i \(0.367457\pi\)
\(812\) 0 0
\(813\) −41.8506 −1.46776
\(814\) 0 0
\(815\) −5.45920 −0.191227
\(816\) 0 0
\(817\) −31.4004 −1.09856
\(818\) 0 0
\(819\) −54.7139 −1.91186
\(820\) 0 0
\(821\) −27.1590 −0.947857 −0.473928 0.880563i \(-0.657164\pi\)
−0.473928 + 0.880563i \(0.657164\pi\)
\(822\) 0 0
\(823\) −17.5575 −0.612017 −0.306009 0.952029i \(-0.598994\pi\)
−0.306009 + 0.952029i \(0.598994\pi\)
\(824\) 0 0
\(825\) 3.66193 0.127492
\(826\) 0 0
\(827\) −4.55165 −0.158276 −0.0791381 0.996864i \(-0.525217\pi\)
−0.0791381 + 0.996864i \(0.525217\pi\)
\(828\) 0 0
\(829\) 8.01539 0.278386 0.139193 0.990265i \(-0.455549\pi\)
0.139193 + 0.990265i \(0.455549\pi\)
\(830\) 0 0
\(831\) 22.1154 0.767175
\(832\) 0 0
\(833\) 54.2850 1.88086
\(834\) 0 0
\(835\) −7.93372 −0.274558
\(836\) 0 0
\(837\) −7.73184 −0.267252
\(838\) 0 0
\(839\) −25.0653 −0.865351 −0.432675 0.901550i \(-0.642430\pi\)
−0.432675 + 0.901550i \(0.642430\pi\)
\(840\) 0 0
\(841\) 31.7897 1.09620
\(842\) 0 0
\(843\) −28.8329 −0.993059
\(844\) 0 0
\(845\) −1.16780 −0.0401735
\(846\) 0 0
\(847\) 45.4691 1.56234
\(848\) 0 0
\(849\) 65.0545 2.23267
\(850\) 0 0
\(851\) 58.3501 2.00022
\(852\) 0 0
\(853\) 1.45894 0.0499531 0.0249765 0.999688i \(-0.492049\pi\)
0.0249765 + 0.999688i \(0.492049\pi\)
\(854\) 0 0
\(855\) −4.81858 −0.164792
\(856\) 0 0
\(857\) −31.1230 −1.06314 −0.531571 0.847014i \(-0.678398\pi\)
−0.531571 + 0.847014i \(0.678398\pi\)
\(858\) 0 0
\(859\) 7.21675 0.246232 0.123116 0.992392i \(-0.460711\pi\)
0.123116 + 0.992392i \(0.460711\pi\)
\(860\) 0 0
\(861\) −55.9308 −1.90612
\(862\) 0 0
\(863\) −43.9265 −1.49527 −0.747637 0.664107i \(-0.768812\pi\)
−0.747637 + 0.664107i \(0.768812\pi\)
\(864\) 0 0
\(865\) 11.6730 0.396894
\(866\) 0 0
\(867\) −26.0804 −0.885737
\(868\) 0 0
\(869\) 2.96784 0.100677
\(870\) 0 0
\(871\) 23.3817 0.792260
\(872\) 0 0
\(873\) 1.32332 0.0447874
\(874\) 0 0
\(875\) −19.2453 −0.650611
\(876\) 0 0
\(877\) −28.0980 −0.948802 −0.474401 0.880309i \(-0.657335\pi\)
−0.474401 + 0.880309i \(0.657335\pi\)
\(878\) 0 0
\(879\) 0.162797 0.00549100
\(880\) 0 0
\(881\) −35.2907 −1.18897 −0.594486 0.804106i \(-0.702645\pi\)
−0.594486 + 0.804106i \(0.702645\pi\)
\(882\) 0 0
\(883\) −12.2754 −0.413101 −0.206550 0.978436i \(-0.566224\pi\)
−0.206550 + 0.978436i \(0.566224\pi\)
\(884\) 0 0
\(885\) −3.60805 −0.121283
\(886\) 0 0
\(887\) −50.1769 −1.68478 −0.842388 0.538871i \(-0.818851\pi\)
−0.842388 + 0.538871i \(0.818851\pi\)
\(888\) 0 0
\(889\) 40.9721 1.37416
\(890\) 0 0
\(891\) −2.39868 −0.0803589
\(892\) 0 0
\(893\) −25.0946 −0.839760
\(894\) 0 0
\(895\) −4.06073 −0.135735
\(896\) 0 0
\(897\) 77.4607 2.58634
\(898\) 0 0
\(899\) −71.1418 −2.37271
\(900\) 0 0
\(901\) −43.3880 −1.44546
\(902\) 0 0
\(903\) −107.738 −3.58531
\(904\) 0 0
\(905\) 10.6117 0.352744
\(906\) 0 0
\(907\) 2.35584 0.0782244 0.0391122 0.999235i \(-0.487547\pi\)
0.0391122 + 0.999235i \(0.487547\pi\)
\(908\) 0 0
\(909\) 61.9401 2.05442
\(910\) 0 0
\(911\) −2.89328 −0.0958588 −0.0479294 0.998851i \(-0.515262\pi\)
−0.0479294 + 0.998851i \(0.515262\pi\)
\(912\) 0 0
\(913\) 1.51732 0.0502159
\(914\) 0 0
\(915\) −1.00471 −0.0332145
\(916\) 0 0
\(917\) 56.8847 1.87850
\(918\) 0 0
\(919\) −58.8755 −1.94212 −0.971062 0.238828i \(-0.923237\pi\)
−0.971062 + 0.238828i \(0.923237\pi\)
\(920\) 0 0
\(921\) 19.8795 0.655053
\(922\) 0 0
\(923\) −24.4091 −0.803435
\(924\) 0 0
\(925\) 35.6318 1.17157
\(926\) 0 0
\(927\) 0.829030 0.0272289
\(928\) 0 0
\(929\) 46.4055 1.52252 0.761258 0.648449i \(-0.224582\pi\)
0.761258 + 0.648449i \(0.224582\pi\)
\(930\) 0 0
\(931\) 31.7403 1.04025
\(932\) 0 0
\(933\) −77.6562 −2.54235
\(934\) 0 0
\(935\) −0.752147 −0.0245978
\(936\) 0 0
\(937\) 18.6150 0.608126 0.304063 0.952652i \(-0.401657\pi\)
0.304063 + 0.952652i \(0.401657\pi\)
\(938\) 0 0
\(939\) 37.7128 1.23071
\(940\) 0 0
\(941\) −14.0524 −0.458094 −0.229047 0.973415i \(-0.573561\pi\)
−0.229047 + 0.973415i \(0.573561\pi\)
\(942\) 0 0
\(943\) 41.6950 1.35778
\(944\) 0 0
\(945\) −1.66798 −0.0542595
\(946\) 0 0
\(947\) 14.6936 0.477479 0.238740 0.971084i \(-0.423266\pi\)
0.238740 + 0.971084i \(0.423266\pi\)
\(948\) 0 0
\(949\) 39.7442 1.29015
\(950\) 0 0
\(951\) 16.5010 0.535082
\(952\) 0 0
\(953\) −41.2058 −1.33479 −0.667394 0.744705i \(-0.732590\pi\)
−0.667394 + 0.744705i \(0.732590\pi\)
\(954\) 0 0
\(955\) −4.66035 −0.150805
\(956\) 0 0
\(957\) 5.97677 0.193201
\(958\) 0 0
\(959\) −47.7366 −1.54150
\(960\) 0 0
\(961\) 52.2569 1.68571
\(962\) 0 0
\(963\) 33.5294 1.08047
\(964\) 0 0
\(965\) −2.35020 −0.0756556
\(966\) 0 0
\(967\) 13.6081 0.437607 0.218804 0.975769i \(-0.429785\pi\)
0.218804 + 0.975769i \(0.429785\pi\)
\(968\) 0 0
\(969\) −40.2705 −1.29367
\(970\) 0 0
\(971\) 23.3940 0.750748 0.375374 0.926873i \(-0.377514\pi\)
0.375374 + 0.926873i \(0.377514\pi\)
\(972\) 0 0
\(973\) −39.4374 −1.26430
\(974\) 0 0
\(975\) 47.3017 1.51487
\(976\) 0 0
\(977\) −7.24136 −0.231672 −0.115836 0.993268i \(-0.536955\pi\)
−0.115836 + 0.993268i \(0.536955\pi\)
\(978\) 0 0
\(979\) 3.77504 0.120651
\(980\) 0 0
\(981\) 2.02671 0.0647078
\(982\) 0 0
\(983\) 4.90576 0.156469 0.0782347 0.996935i \(-0.475072\pi\)
0.0782347 + 0.996935i \(0.475072\pi\)
\(984\) 0 0
\(985\) 2.59675 0.0827393
\(986\) 0 0
\(987\) −86.1025 −2.74067
\(988\) 0 0
\(989\) 80.3162 2.55391
\(990\) 0 0
\(991\) −35.1041 −1.11512 −0.557559 0.830137i \(-0.688262\pi\)
−0.557559 + 0.830137i \(0.688262\pi\)
\(992\) 0 0
\(993\) −49.7646 −1.57923
\(994\) 0 0
\(995\) −0.578904 −0.0183525
\(996\) 0 0
\(997\) −44.9594 −1.42388 −0.711939 0.702241i \(-0.752183\pi\)
−0.711939 + 0.702241i \(0.752183\pi\)
\(998\) 0 0
\(999\) 6.32051 0.199972
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 4016.2.a.m.1.6 23
4.3 odd 2 2008.2.a.d.1.18 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.18 23 4.3 odd 2
4016.2.a.m.1.6 23 1.1 even 1 trivial