Properties

Label 6003.2.a.m.1.5
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 2001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.17662\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.17662 q^{2} -0.615555 q^{4} -2.85352 q^{5} +3.62966 q^{7} +3.07753 q^{8} +O(q^{10})\) \(q-1.17662 q^{2} -0.615555 q^{4} -2.85352 q^{5} +3.62966 q^{7} +3.07753 q^{8} +3.35752 q^{10} -1.39936 q^{11} +2.03682 q^{13} -4.27074 q^{14} -2.38998 q^{16} +0.256641 q^{17} +1.59337 q^{19} +1.75650 q^{20} +1.64652 q^{22} -1.00000 q^{23} +3.14260 q^{25} -2.39658 q^{26} -2.23426 q^{28} +1.00000 q^{29} +3.05203 q^{31} -3.34294 q^{32} -0.301970 q^{34} -10.3573 q^{35} -5.80359 q^{37} -1.87479 q^{38} -8.78179 q^{40} -10.7828 q^{41} -10.8584 q^{43} +0.861383 q^{44} +1.17662 q^{46} -10.2706 q^{47} +6.17441 q^{49} -3.69765 q^{50} -1.25378 q^{52} +9.74574 q^{53} +3.99311 q^{55} +11.1704 q^{56} -1.17662 q^{58} +4.00720 q^{59} +7.96095 q^{61} -3.59109 q^{62} +8.71335 q^{64} -5.81213 q^{65} +1.95063 q^{67} -0.157977 q^{68} +12.1867 q^{70} +12.4876 q^{71} -8.14520 q^{73} +6.82864 q^{74} -0.980806 q^{76} -5.07920 q^{77} +16.3016 q^{79} +6.81987 q^{80} +12.6873 q^{82} -6.27397 q^{83} -0.732331 q^{85} +12.7762 q^{86} -4.30657 q^{88} -3.67645 q^{89} +7.39297 q^{91} +0.615555 q^{92} +12.0846 q^{94} -4.54671 q^{95} +8.10595 q^{97} -7.26496 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17662 −0.831999 −0.415999 0.909365i \(-0.636568\pi\)
−0.415999 + 0.909365i \(0.636568\pi\)
\(3\) 0 0
\(4\) −0.615555 −0.307778
\(5\) −2.85352 −1.27613 −0.638067 0.769981i \(-0.720266\pi\)
−0.638067 + 0.769981i \(0.720266\pi\)
\(6\) 0 0
\(7\) 3.62966 1.37188 0.685941 0.727657i \(-0.259391\pi\)
0.685941 + 0.727657i \(0.259391\pi\)
\(8\) 3.07753 1.08807
\(9\) 0 0
\(10\) 3.35752 1.06174
\(11\) −1.39936 −0.421923 −0.210961 0.977494i \(-0.567659\pi\)
−0.210961 + 0.977494i \(0.567659\pi\)
\(12\) 0 0
\(13\) 2.03682 0.564913 0.282457 0.959280i \(-0.408851\pi\)
0.282457 + 0.959280i \(0.408851\pi\)
\(14\) −4.27074 −1.14140
\(15\) 0 0
\(16\) −2.38998 −0.597495
\(17\) 0.256641 0.0622445 0.0311223 0.999516i \(-0.490092\pi\)
0.0311223 + 0.999516i \(0.490092\pi\)
\(18\) 0 0
\(19\) 1.59337 0.365543 0.182772 0.983155i \(-0.441493\pi\)
0.182772 + 0.983155i \(0.441493\pi\)
\(20\) 1.75650 0.392766
\(21\) 0 0
\(22\) 1.64652 0.351039
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 3.14260 0.628519
\(26\) −2.39658 −0.470007
\(27\) 0 0
\(28\) −2.23426 −0.422235
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 3.05203 0.548160 0.274080 0.961707i \(-0.411627\pi\)
0.274080 + 0.961707i \(0.411627\pi\)
\(32\) −3.34294 −0.590954
\(33\) 0 0
\(34\) −0.301970 −0.0517874
\(35\) −10.3573 −1.75071
\(36\) 0 0
\(37\) −5.80359 −0.954104 −0.477052 0.878875i \(-0.658295\pi\)
−0.477052 + 0.878875i \(0.658295\pi\)
\(38\) −1.87479 −0.304132
\(39\) 0 0
\(40\) −8.78179 −1.38852
\(41\) −10.7828 −1.68399 −0.841993 0.539489i \(-0.818617\pi\)
−0.841993 + 0.539489i \(0.818617\pi\)
\(42\) 0 0
\(43\) −10.8584 −1.65589 −0.827944 0.560811i \(-0.810489\pi\)
−0.827944 + 0.560811i \(0.810489\pi\)
\(44\) 0.861383 0.129858
\(45\) 0 0
\(46\) 1.17662 0.173484
\(47\) −10.2706 −1.49812 −0.749060 0.662502i \(-0.769494\pi\)
−0.749060 + 0.662502i \(0.769494\pi\)
\(48\) 0 0
\(49\) 6.17441 0.882059
\(50\) −3.69765 −0.522927
\(51\) 0 0
\(52\) −1.25378 −0.173868
\(53\) 9.74574 1.33868 0.669340 0.742956i \(-0.266577\pi\)
0.669340 + 0.742956i \(0.266577\pi\)
\(54\) 0 0
\(55\) 3.99311 0.538430
\(56\) 11.1704 1.49270
\(57\) 0 0
\(58\) −1.17662 −0.154498
\(59\) 4.00720 0.521693 0.260846 0.965380i \(-0.415998\pi\)
0.260846 + 0.965380i \(0.415998\pi\)
\(60\) 0 0
\(61\) 7.96095 1.01930 0.509648 0.860383i \(-0.329776\pi\)
0.509648 + 0.860383i \(0.329776\pi\)
\(62\) −3.59109 −0.456068
\(63\) 0 0
\(64\) 8.71335 1.08917
\(65\) −5.81213 −0.720905
\(66\) 0 0
\(67\) 1.95063 0.238307 0.119154 0.992876i \(-0.461982\pi\)
0.119154 + 0.992876i \(0.461982\pi\)
\(68\) −0.157977 −0.0191575
\(69\) 0 0
\(70\) 12.1867 1.45658
\(71\) 12.4876 1.48200 0.741000 0.671505i \(-0.234352\pi\)
0.741000 + 0.671505i \(0.234352\pi\)
\(72\) 0 0
\(73\) −8.14520 −0.953323 −0.476662 0.879087i \(-0.658153\pi\)
−0.476662 + 0.879087i \(0.658153\pi\)
\(74\) 6.82864 0.793813
\(75\) 0 0
\(76\) −0.980806 −0.112506
\(77\) −5.07920 −0.578828
\(78\) 0 0
\(79\) 16.3016 1.83407 0.917037 0.398803i \(-0.130574\pi\)
0.917037 + 0.398803i \(0.130574\pi\)
\(80\) 6.81987 0.762484
\(81\) 0 0
\(82\) 12.6873 1.40107
\(83\) −6.27397 −0.688658 −0.344329 0.938849i \(-0.611894\pi\)
−0.344329 + 0.938849i \(0.611894\pi\)
\(84\) 0 0
\(85\) −0.732331 −0.0794324
\(86\) 12.7762 1.37770
\(87\) 0 0
\(88\) −4.30657 −0.459081
\(89\) −3.67645 −0.389702 −0.194851 0.980833i \(-0.562422\pi\)
−0.194851 + 0.980833i \(0.562422\pi\)
\(90\) 0 0
\(91\) 7.39297 0.774994
\(92\) 0.615555 0.0641761
\(93\) 0 0
\(94\) 12.0846 1.24643
\(95\) −4.54671 −0.466483
\(96\) 0 0
\(97\) 8.10595 0.823034 0.411517 0.911402i \(-0.364999\pi\)
0.411517 + 0.911402i \(0.364999\pi\)
\(98\) −7.26496 −0.733872
\(99\) 0 0
\(100\) −1.93444 −0.193444
\(101\) −10.7377 −1.06844 −0.534219 0.845346i \(-0.679394\pi\)
−0.534219 + 0.845346i \(0.679394\pi\)
\(102\) 0 0
\(103\) 8.05373 0.793557 0.396779 0.917914i \(-0.370128\pi\)
0.396779 + 0.917914i \(0.370128\pi\)
\(104\) 6.26838 0.614665
\(105\) 0 0
\(106\) −11.4671 −1.11378
\(107\) 5.29768 0.512146 0.256073 0.966657i \(-0.417571\pi\)
0.256073 + 0.966657i \(0.417571\pi\)
\(108\) 0 0
\(109\) 13.0862 1.25343 0.626715 0.779248i \(-0.284399\pi\)
0.626715 + 0.779248i \(0.284399\pi\)
\(110\) −4.69838 −0.447973
\(111\) 0 0
\(112\) −8.67481 −0.819693
\(113\) −15.5519 −1.46300 −0.731498 0.681843i \(-0.761179\pi\)
−0.731498 + 0.681843i \(0.761179\pi\)
\(114\) 0 0
\(115\) 2.85352 0.266092
\(116\) −0.615555 −0.0571529
\(117\) 0 0
\(118\) −4.71496 −0.434048
\(119\) 0.931518 0.0853921
\(120\) 0 0
\(121\) −9.04179 −0.821981
\(122\) −9.36705 −0.848053
\(123\) 0 0
\(124\) −1.87869 −0.168711
\(125\) 5.30015 0.474059
\(126\) 0 0
\(127\) −3.62028 −0.321248 −0.160624 0.987016i \(-0.551351\pi\)
−0.160624 + 0.987016i \(0.551351\pi\)
\(128\) −3.56645 −0.315233
\(129\) 0 0
\(130\) 6.83869 0.599793
\(131\) −18.8807 −1.64962 −0.824809 0.565412i \(-0.808717\pi\)
−0.824809 + 0.565412i \(0.808717\pi\)
\(132\) 0 0
\(133\) 5.78337 0.501482
\(134\) −2.29516 −0.198271
\(135\) 0 0
\(136\) 0.789819 0.0677264
\(137\) 2.83524 0.242231 0.121116 0.992638i \(-0.461353\pi\)
0.121116 + 0.992638i \(0.461353\pi\)
\(138\) 0 0
\(139\) −9.09684 −0.771584 −0.385792 0.922586i \(-0.626072\pi\)
−0.385792 + 0.922586i \(0.626072\pi\)
\(140\) 6.37550 0.538828
\(141\) 0 0
\(142\) −14.6932 −1.23302
\(143\) −2.85025 −0.238350
\(144\) 0 0
\(145\) −2.85352 −0.236972
\(146\) 9.58383 0.793164
\(147\) 0 0
\(148\) 3.57243 0.293652
\(149\) 10.6033 0.868654 0.434327 0.900755i \(-0.356986\pi\)
0.434327 + 0.900755i \(0.356986\pi\)
\(150\) 0 0
\(151\) 4.73059 0.384970 0.192485 0.981300i \(-0.438345\pi\)
0.192485 + 0.981300i \(0.438345\pi\)
\(152\) 4.90363 0.397737
\(153\) 0 0
\(154\) 5.97630 0.481584
\(155\) −8.70903 −0.699526
\(156\) 0 0
\(157\) −0.758791 −0.0605581 −0.0302791 0.999541i \(-0.509640\pi\)
−0.0302791 + 0.999541i \(0.509640\pi\)
\(158\) −19.1809 −1.52595
\(159\) 0 0
\(160\) 9.53917 0.754137
\(161\) −3.62966 −0.286057
\(162\) 0 0
\(163\) −20.4320 −1.60035 −0.800177 0.599763i \(-0.795261\pi\)
−0.800177 + 0.599763i \(0.795261\pi\)
\(164\) 6.63739 0.518293
\(165\) 0 0
\(166\) 7.38211 0.572963
\(167\) −9.96742 −0.771302 −0.385651 0.922645i \(-0.626023\pi\)
−0.385651 + 0.922645i \(0.626023\pi\)
\(168\) 0 0
\(169\) −8.85135 −0.680873
\(170\) 0.861678 0.0660877
\(171\) 0 0
\(172\) 6.68394 0.509645
\(173\) 25.3581 1.92794 0.963972 0.266004i \(-0.0857033\pi\)
0.963972 + 0.266004i \(0.0857033\pi\)
\(174\) 0 0
\(175\) 11.4065 0.862254
\(176\) 3.34444 0.252097
\(177\) 0 0
\(178\) 4.32580 0.324232
\(179\) −4.55470 −0.340434 −0.170217 0.985407i \(-0.554447\pi\)
−0.170217 + 0.985407i \(0.554447\pi\)
\(180\) 0 0
\(181\) −23.1724 −1.72239 −0.861195 0.508275i \(-0.830283\pi\)
−0.861195 + 0.508275i \(0.830283\pi\)
\(182\) −8.69875 −0.644794
\(183\) 0 0
\(184\) −3.07753 −0.226878
\(185\) 16.5607 1.21756
\(186\) 0 0
\(187\) −0.359133 −0.0262624
\(188\) 6.32212 0.461088
\(189\) 0 0
\(190\) 5.34977 0.388113
\(191\) −4.19705 −0.303688 −0.151844 0.988404i \(-0.548521\pi\)
−0.151844 + 0.988404i \(0.548521\pi\)
\(192\) 0 0
\(193\) −1.76911 −0.127344 −0.0636718 0.997971i \(-0.520281\pi\)
−0.0636718 + 0.997971i \(0.520281\pi\)
\(194\) −9.53766 −0.684764
\(195\) 0 0
\(196\) −3.80069 −0.271478
\(197\) 9.09621 0.648078 0.324039 0.946044i \(-0.394959\pi\)
0.324039 + 0.946044i \(0.394959\pi\)
\(198\) 0 0
\(199\) −5.30465 −0.376037 −0.188018 0.982166i \(-0.560206\pi\)
−0.188018 + 0.982166i \(0.560206\pi\)
\(200\) 9.67142 0.683873
\(201\) 0 0
\(202\) 12.6342 0.888939
\(203\) 3.62966 0.254752
\(204\) 0 0
\(205\) 30.7689 2.14899
\(206\) −9.47621 −0.660239
\(207\) 0 0
\(208\) −4.86797 −0.337533
\(209\) −2.22969 −0.154231
\(210\) 0 0
\(211\) 6.16689 0.424546 0.212273 0.977210i \(-0.431913\pi\)
0.212273 + 0.977210i \(0.431913\pi\)
\(212\) −5.99904 −0.412016
\(213\) 0 0
\(214\) −6.23337 −0.426105
\(215\) 30.9846 2.11314
\(216\) 0 0
\(217\) 11.0778 0.752010
\(218\) −15.3975 −1.04285
\(219\) 0 0
\(220\) −2.45798 −0.165717
\(221\) 0.522732 0.0351628
\(222\) 0 0
\(223\) −2.50370 −0.167660 −0.0838300 0.996480i \(-0.526715\pi\)
−0.0838300 + 0.996480i \(0.526715\pi\)
\(224\) −12.1337 −0.810719
\(225\) 0 0
\(226\) 18.2987 1.21721
\(227\) −6.26477 −0.415808 −0.207904 0.978149i \(-0.566664\pi\)
−0.207904 + 0.978149i \(0.566664\pi\)
\(228\) 0 0
\(229\) −21.4865 −1.41987 −0.709935 0.704267i \(-0.751276\pi\)
−0.709935 + 0.704267i \(0.751276\pi\)
\(230\) −3.35752 −0.221389
\(231\) 0 0
\(232\) 3.07753 0.202049
\(233\) 17.3695 1.13791 0.568955 0.822368i \(-0.307348\pi\)
0.568955 + 0.822368i \(0.307348\pi\)
\(234\) 0 0
\(235\) 29.3074 1.91180
\(236\) −2.46665 −0.160565
\(237\) 0 0
\(238\) −1.09605 −0.0710462
\(239\) 2.89711 0.187399 0.0936993 0.995601i \(-0.470131\pi\)
0.0936993 + 0.995601i \(0.470131\pi\)
\(240\) 0 0
\(241\) −3.98534 −0.256718 −0.128359 0.991728i \(-0.540971\pi\)
−0.128359 + 0.991728i \(0.540971\pi\)
\(242\) 10.6388 0.683887
\(243\) 0 0
\(244\) −4.90041 −0.313717
\(245\) −17.6188 −1.12563
\(246\) 0 0
\(247\) 3.24541 0.206500
\(248\) 9.39269 0.596436
\(249\) 0 0
\(250\) −6.23628 −0.394417
\(251\) 16.9698 1.07113 0.535564 0.844495i \(-0.320099\pi\)
0.535564 + 0.844495i \(0.320099\pi\)
\(252\) 0 0
\(253\) 1.39936 0.0879770
\(254\) 4.25971 0.267278
\(255\) 0 0
\(256\) −13.2303 −0.826895
\(257\) −7.22916 −0.450943 −0.225471 0.974250i \(-0.572392\pi\)
−0.225471 + 0.974250i \(0.572392\pi\)
\(258\) 0 0
\(259\) −21.0650 −1.30892
\(260\) 3.57769 0.221879
\(261\) 0 0
\(262\) 22.2155 1.37248
\(263\) 11.9092 0.734355 0.367177 0.930151i \(-0.380324\pi\)
0.367177 + 0.930151i \(0.380324\pi\)
\(264\) 0 0
\(265\) −27.8097 −1.70834
\(266\) −6.80486 −0.417233
\(267\) 0 0
\(268\) −1.20072 −0.0733456
\(269\) −17.5257 −1.06856 −0.534280 0.845307i \(-0.679417\pi\)
−0.534280 + 0.845307i \(0.679417\pi\)
\(270\) 0 0
\(271\) 27.8599 1.69237 0.846185 0.532889i \(-0.178894\pi\)
0.846185 + 0.532889i \(0.178894\pi\)
\(272\) −0.613367 −0.0371908
\(273\) 0 0
\(274\) −3.33601 −0.201536
\(275\) −4.39762 −0.265187
\(276\) 0 0
\(277\) 7.82340 0.470062 0.235031 0.971988i \(-0.424481\pi\)
0.235031 + 0.971988i \(0.424481\pi\)
\(278\) 10.7036 0.641957
\(279\) 0 0
\(280\) −31.8749 −1.90489
\(281\) 23.0361 1.37422 0.687111 0.726553i \(-0.258879\pi\)
0.687111 + 0.726553i \(0.258879\pi\)
\(282\) 0 0
\(283\) 10.5239 0.625581 0.312791 0.949822i \(-0.398736\pi\)
0.312791 + 0.949822i \(0.398736\pi\)
\(284\) −7.68678 −0.456127
\(285\) 0 0
\(286\) 3.35367 0.198307
\(287\) −39.1377 −2.31023
\(288\) 0 0
\(289\) −16.9341 −0.996126
\(290\) 3.35752 0.197161
\(291\) 0 0
\(292\) 5.01382 0.293412
\(293\) −19.5780 −1.14376 −0.571878 0.820339i \(-0.693785\pi\)
−0.571878 + 0.820339i \(0.693785\pi\)
\(294\) 0 0
\(295\) −11.4346 −0.665750
\(296\) −17.8607 −1.03813
\(297\) 0 0
\(298\) −12.4761 −0.722720
\(299\) −2.03682 −0.117793
\(300\) 0 0
\(301\) −39.4122 −2.27168
\(302\) −5.56613 −0.320295
\(303\) 0 0
\(304\) −3.80812 −0.218410
\(305\) −22.7168 −1.30076
\(306\) 0 0
\(307\) −16.3395 −0.932543 −0.466272 0.884642i \(-0.654403\pi\)
−0.466272 + 0.884642i \(0.654403\pi\)
\(308\) 3.12653 0.178150
\(309\) 0 0
\(310\) 10.2472 0.582005
\(311\) 14.4849 0.821361 0.410681 0.911779i \(-0.365291\pi\)
0.410681 + 0.911779i \(0.365291\pi\)
\(312\) 0 0
\(313\) −15.8990 −0.898663 −0.449331 0.893365i \(-0.648338\pi\)
−0.449331 + 0.893365i \(0.648338\pi\)
\(314\) 0.892812 0.0503843
\(315\) 0 0
\(316\) −10.0345 −0.564487
\(317\) 7.37522 0.414234 0.207117 0.978316i \(-0.433592\pi\)
0.207117 + 0.978316i \(0.433592\pi\)
\(318\) 0 0
\(319\) −1.39936 −0.0783491
\(320\) −24.8637 −1.38993
\(321\) 0 0
\(322\) 4.27074 0.237999
\(323\) 0.408923 0.0227531
\(324\) 0 0
\(325\) 6.40092 0.355059
\(326\) 24.0407 1.33149
\(327\) 0 0
\(328\) −33.1842 −1.83229
\(329\) −37.2787 −2.05524
\(330\) 0 0
\(331\) −2.22314 −0.122195 −0.0610974 0.998132i \(-0.519460\pi\)
−0.0610974 + 0.998132i \(0.519460\pi\)
\(332\) 3.86198 0.211954
\(333\) 0 0
\(334\) 11.7279 0.641722
\(335\) −5.56616 −0.304112
\(336\) 0 0
\(337\) −21.8928 −1.19258 −0.596288 0.802771i \(-0.703358\pi\)
−0.596288 + 0.802771i \(0.703358\pi\)
\(338\) 10.4147 0.566485
\(339\) 0 0
\(340\) 0.450790 0.0244475
\(341\) −4.27088 −0.231281
\(342\) 0 0
\(343\) −2.99661 −0.161802
\(344\) −33.4170 −1.80172
\(345\) 0 0
\(346\) −29.8370 −1.60405
\(347\) −32.5836 −1.74918 −0.874590 0.484863i \(-0.838869\pi\)
−0.874590 + 0.484863i \(0.838869\pi\)
\(348\) 0 0
\(349\) −23.5157 −1.25877 −0.629384 0.777094i \(-0.716693\pi\)
−0.629384 + 0.777094i \(0.716693\pi\)
\(350\) −13.4212 −0.717394
\(351\) 0 0
\(352\) 4.67798 0.249337
\(353\) 27.3657 1.45653 0.728263 0.685297i \(-0.240328\pi\)
0.728263 + 0.685297i \(0.240328\pi\)
\(354\) 0 0
\(355\) −35.6335 −1.89123
\(356\) 2.26306 0.119942
\(357\) 0 0
\(358\) 5.35917 0.283241
\(359\) −0.782857 −0.0413176 −0.0206588 0.999787i \(-0.506576\pi\)
−0.0206588 + 0.999787i \(0.506576\pi\)
\(360\) 0 0
\(361\) −16.4612 −0.866378
\(362\) 27.2652 1.43303
\(363\) 0 0
\(364\) −4.55079 −0.238526
\(365\) 23.2425 1.21657
\(366\) 0 0
\(367\) 0.508753 0.0265567 0.0132784 0.999912i \(-0.495773\pi\)
0.0132784 + 0.999912i \(0.495773\pi\)
\(368\) 2.38998 0.124586
\(369\) 0 0
\(370\) −19.4857 −1.01301
\(371\) 35.3737 1.83651
\(372\) 0 0
\(373\) −5.51685 −0.285651 −0.142826 0.989748i \(-0.545619\pi\)
−0.142826 + 0.989748i \(0.545619\pi\)
\(374\) 0.422564 0.0218503
\(375\) 0 0
\(376\) −31.6080 −1.63006
\(377\) 2.03682 0.104902
\(378\) 0 0
\(379\) −27.9568 −1.43605 −0.718023 0.696019i \(-0.754953\pi\)
−0.718023 + 0.696019i \(0.754953\pi\)
\(380\) 2.79875 0.143573
\(381\) 0 0
\(382\) 4.93835 0.252668
\(383\) −5.58188 −0.285221 −0.142610 0.989779i \(-0.545550\pi\)
−0.142610 + 0.989779i \(0.545550\pi\)
\(384\) 0 0
\(385\) 14.4936 0.738662
\(386\) 2.08158 0.105950
\(387\) 0 0
\(388\) −4.98966 −0.253312
\(389\) 3.74821 0.190042 0.0950210 0.995475i \(-0.469708\pi\)
0.0950210 + 0.995475i \(0.469708\pi\)
\(390\) 0 0
\(391\) −0.256641 −0.0129789
\(392\) 19.0019 0.959741
\(393\) 0 0
\(394\) −10.7028 −0.539201
\(395\) −46.5170 −2.34052
\(396\) 0 0
\(397\) 30.3805 1.52475 0.762377 0.647133i \(-0.224032\pi\)
0.762377 + 0.647133i \(0.224032\pi\)
\(398\) 6.24158 0.312862
\(399\) 0 0
\(400\) −7.51074 −0.375537
\(401\) −3.30262 −0.164925 −0.0824626 0.996594i \(-0.526278\pi\)
−0.0824626 + 0.996594i \(0.526278\pi\)
\(402\) 0 0
\(403\) 6.21644 0.309663
\(404\) 6.60963 0.328841
\(405\) 0 0
\(406\) −4.27074 −0.211953
\(407\) 8.12130 0.402558
\(408\) 0 0
\(409\) −6.51701 −0.322246 −0.161123 0.986934i \(-0.551512\pi\)
−0.161123 + 0.986934i \(0.551512\pi\)
\(410\) −36.2034 −1.78796
\(411\) 0 0
\(412\) −4.95751 −0.244239
\(413\) 14.5447 0.715700
\(414\) 0 0
\(415\) 17.9029 0.878820
\(416\) −6.80899 −0.333838
\(417\) 0 0
\(418\) 2.62351 0.128320
\(419\) −38.1773 −1.86508 −0.932541 0.361063i \(-0.882414\pi\)
−0.932541 + 0.361063i \(0.882414\pi\)
\(420\) 0 0
\(421\) −35.6872 −1.73929 −0.869644 0.493679i \(-0.835652\pi\)
−0.869644 + 0.493679i \(0.835652\pi\)
\(422\) −7.25612 −0.353222
\(423\) 0 0
\(424\) 29.9928 1.45658
\(425\) 0.806518 0.0391219
\(426\) 0 0
\(427\) 28.8955 1.39835
\(428\) −3.26101 −0.157627
\(429\) 0 0
\(430\) −36.4573 −1.75813
\(431\) −9.57775 −0.461344 −0.230672 0.973032i \(-0.574092\pi\)
−0.230672 + 0.973032i \(0.574092\pi\)
\(432\) 0 0
\(433\) 11.4518 0.550336 0.275168 0.961396i \(-0.411266\pi\)
0.275168 + 0.961396i \(0.411266\pi\)
\(434\) −13.0344 −0.625672
\(435\) 0 0
\(436\) −8.05528 −0.385778
\(437\) −1.59337 −0.0762211
\(438\) 0 0
\(439\) 18.4092 0.878624 0.439312 0.898335i \(-0.355222\pi\)
0.439312 + 0.898335i \(0.355222\pi\)
\(440\) 12.2889 0.585850
\(441\) 0 0
\(442\) −0.615059 −0.0292554
\(443\) −12.4019 −0.589232 −0.294616 0.955616i \(-0.595192\pi\)
−0.294616 + 0.955616i \(0.595192\pi\)
\(444\) 0 0
\(445\) 10.4908 0.497313
\(446\) 2.94591 0.139493
\(447\) 0 0
\(448\) 31.6265 1.49421
\(449\) 23.9157 1.12865 0.564327 0.825551i \(-0.309136\pi\)
0.564327 + 0.825551i \(0.309136\pi\)
\(450\) 0 0
\(451\) 15.0890 0.710512
\(452\) 9.57304 0.450278
\(453\) 0 0
\(454\) 7.37128 0.345952
\(455\) −21.0960 −0.988997
\(456\) 0 0
\(457\) 3.61853 0.169268 0.0846339 0.996412i \(-0.473028\pi\)
0.0846339 + 0.996412i \(0.473028\pi\)
\(458\) 25.2816 1.18133
\(459\) 0 0
\(460\) −1.75650 −0.0818973
\(461\) −7.97110 −0.371251 −0.185626 0.982621i \(-0.559431\pi\)
−0.185626 + 0.982621i \(0.559431\pi\)
\(462\) 0 0
\(463\) −26.8314 −1.24696 −0.623480 0.781840i \(-0.714282\pi\)
−0.623480 + 0.781840i \(0.714282\pi\)
\(464\) −2.38998 −0.110952
\(465\) 0 0
\(466\) −20.4373 −0.946740
\(467\) 12.0191 0.556175 0.278088 0.960556i \(-0.410299\pi\)
0.278088 + 0.960556i \(0.410299\pi\)
\(468\) 0 0
\(469\) 7.08011 0.326929
\(470\) −34.4838 −1.59062
\(471\) 0 0
\(472\) 12.3323 0.567638
\(473\) 15.1948 0.698657
\(474\) 0 0
\(475\) 5.00731 0.229751
\(476\) −0.573401 −0.0262818
\(477\) 0 0
\(478\) −3.40881 −0.155915
\(479\) −26.7408 −1.22182 −0.610909 0.791701i \(-0.709196\pi\)
−0.610909 + 0.791701i \(0.709196\pi\)
\(480\) 0 0
\(481\) −11.8209 −0.538986
\(482\) 4.68925 0.213589
\(483\) 0 0
\(484\) 5.56572 0.252987
\(485\) −23.1305 −1.05030
\(486\) 0 0
\(487\) −27.3823 −1.24081 −0.620405 0.784281i \(-0.713032\pi\)
−0.620405 + 0.784281i \(0.713032\pi\)
\(488\) 24.5000 1.10906
\(489\) 0 0
\(490\) 20.7307 0.936519
\(491\) 30.2527 1.36529 0.682644 0.730751i \(-0.260830\pi\)
0.682644 + 0.730751i \(0.260830\pi\)
\(492\) 0 0
\(493\) 0.256641 0.0115585
\(494\) −3.81863 −0.171808
\(495\) 0 0
\(496\) −7.29428 −0.327523
\(497\) 45.3255 2.03313
\(498\) 0 0
\(499\) −8.43684 −0.377685 −0.188842 0.982007i \(-0.560474\pi\)
−0.188842 + 0.982007i \(0.560474\pi\)
\(500\) −3.26253 −0.145905
\(501\) 0 0
\(502\) −19.9671 −0.891177
\(503\) −10.9875 −0.489907 −0.244953 0.969535i \(-0.578773\pi\)
−0.244953 + 0.969535i \(0.578773\pi\)
\(504\) 0 0
\(505\) 30.6402 1.36347
\(506\) −1.64652 −0.0731968
\(507\) 0 0
\(508\) 2.22849 0.0988730
\(509\) −13.4171 −0.594704 −0.297352 0.954768i \(-0.596103\pi\)
−0.297352 + 0.954768i \(0.596103\pi\)
\(510\) 0 0
\(511\) −29.5643 −1.30785
\(512\) 22.7000 1.00321
\(513\) 0 0
\(514\) 8.50601 0.375184
\(515\) −22.9815 −1.01269
\(516\) 0 0
\(517\) 14.3723 0.632091
\(518\) 24.7856 1.08902
\(519\) 0 0
\(520\) −17.8870 −0.784395
\(521\) −23.7404 −1.04008 −0.520042 0.854141i \(-0.674084\pi\)
−0.520042 + 0.854141i \(0.674084\pi\)
\(522\) 0 0
\(523\) −22.9883 −1.00521 −0.502604 0.864517i \(-0.667625\pi\)
−0.502604 + 0.864517i \(0.667625\pi\)
\(524\) 11.6221 0.507716
\(525\) 0 0
\(526\) −14.0127 −0.610982
\(527\) 0.783274 0.0341200
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 32.7215 1.42133
\(531\) 0 0
\(532\) −3.55999 −0.154345
\(533\) −21.9626 −0.951306
\(534\) 0 0
\(535\) −15.1170 −0.653567
\(536\) 6.00311 0.259295
\(537\) 0 0
\(538\) 20.6212 0.889042
\(539\) −8.64022 −0.372161
\(540\) 0 0
\(541\) −11.3013 −0.485881 −0.242940 0.970041i \(-0.578112\pi\)
−0.242940 + 0.970041i \(0.578112\pi\)
\(542\) −32.7807 −1.40805
\(543\) 0 0
\(544\) −0.857935 −0.0367837
\(545\) −37.3418 −1.59955
\(546\) 0 0
\(547\) −18.2391 −0.779847 −0.389924 0.920847i \(-0.627499\pi\)
−0.389924 + 0.920847i \(0.627499\pi\)
\(548\) −1.74525 −0.0745533
\(549\) 0 0
\(550\) 5.17435 0.220635
\(551\) 1.59337 0.0678797
\(552\) 0 0
\(553\) 59.1692 2.51613
\(554\) −9.20520 −0.391091
\(555\) 0 0
\(556\) 5.59961 0.237476
\(557\) 30.9415 1.31103 0.655516 0.755181i \(-0.272451\pi\)
0.655516 + 0.755181i \(0.272451\pi\)
\(558\) 0 0
\(559\) −22.1166 −0.935433
\(560\) 24.7538 1.04604
\(561\) 0 0
\(562\) −27.1049 −1.14335
\(563\) −41.8692 −1.76458 −0.882289 0.470709i \(-0.843998\pi\)
−0.882289 + 0.470709i \(0.843998\pi\)
\(564\) 0 0
\(565\) 44.3776 1.86698
\(566\) −12.3827 −0.520483
\(567\) 0 0
\(568\) 38.4308 1.61252
\(569\) −5.74370 −0.240788 −0.120394 0.992726i \(-0.538416\pi\)
−0.120394 + 0.992726i \(0.538416\pi\)
\(570\) 0 0
\(571\) 6.60570 0.276440 0.138220 0.990402i \(-0.455862\pi\)
0.138220 + 0.990402i \(0.455862\pi\)
\(572\) 1.75449 0.0733588
\(573\) 0 0
\(574\) 46.0504 1.92211
\(575\) −3.14260 −0.131055
\(576\) 0 0
\(577\) 42.1911 1.75644 0.878220 0.478258i \(-0.158731\pi\)
0.878220 + 0.478258i \(0.158731\pi\)
\(578\) 19.9251 0.828775
\(579\) 0 0
\(580\) 1.75650 0.0729348
\(581\) −22.7724 −0.944757
\(582\) 0 0
\(583\) −13.6378 −0.564820
\(584\) −25.0671 −1.03728
\(585\) 0 0
\(586\) 23.0359 0.951604
\(587\) −33.6266 −1.38792 −0.693959 0.720014i \(-0.744135\pi\)
−0.693959 + 0.720014i \(0.744135\pi\)
\(588\) 0 0
\(589\) 4.86300 0.200376
\(590\) 13.4543 0.553903
\(591\) 0 0
\(592\) 13.8705 0.570072
\(593\) −38.6906 −1.58883 −0.794417 0.607372i \(-0.792224\pi\)
−0.794417 + 0.607372i \(0.792224\pi\)
\(594\) 0 0
\(595\) −2.65811 −0.108972
\(596\) −6.52691 −0.267352
\(597\) 0 0
\(598\) 2.39658 0.0980033
\(599\) −32.5145 −1.32851 −0.664254 0.747507i \(-0.731251\pi\)
−0.664254 + 0.747507i \(0.731251\pi\)
\(600\) 0 0
\(601\) −11.4682 −0.467800 −0.233900 0.972261i \(-0.575149\pi\)
−0.233900 + 0.972261i \(0.575149\pi\)
\(602\) 46.3734 1.89004
\(603\) 0 0
\(604\) −2.91194 −0.118485
\(605\) 25.8010 1.04896
\(606\) 0 0
\(607\) −40.4823 −1.64313 −0.821564 0.570117i \(-0.806898\pi\)
−0.821564 + 0.570117i \(0.806898\pi\)
\(608\) −5.32653 −0.216019
\(609\) 0 0
\(610\) 26.7291 1.08223
\(611\) −20.9194 −0.846308
\(612\) 0 0
\(613\) −26.2959 −1.06208 −0.531041 0.847346i \(-0.678199\pi\)
−0.531041 + 0.847346i \(0.678199\pi\)
\(614\) 19.2254 0.775875
\(615\) 0 0
\(616\) −15.6314 −0.629805
\(617\) 2.31724 0.0932886 0.0466443 0.998912i \(-0.485147\pi\)
0.0466443 + 0.998912i \(0.485147\pi\)
\(618\) 0 0
\(619\) 17.3929 0.699079 0.349540 0.936922i \(-0.386338\pi\)
0.349540 + 0.936922i \(0.386338\pi\)
\(620\) 5.36089 0.215298
\(621\) 0 0
\(622\) −17.0432 −0.683372
\(623\) −13.3442 −0.534626
\(624\) 0 0
\(625\) −30.8371 −1.23348
\(626\) 18.7071 0.747687
\(627\) 0 0
\(628\) 0.467078 0.0186384
\(629\) −1.48944 −0.0593877
\(630\) 0 0
\(631\) −2.58190 −0.102784 −0.0513920 0.998679i \(-0.516366\pi\)
−0.0513920 + 0.998679i \(0.516366\pi\)
\(632\) 50.1686 1.99560
\(633\) 0 0
\(634\) −8.67787 −0.344642
\(635\) 10.3306 0.409956
\(636\) 0 0
\(637\) 12.5762 0.498287
\(638\) 1.64652 0.0651864
\(639\) 0 0
\(640\) 10.1770 0.402279
\(641\) 41.7793 1.65018 0.825092 0.564998i \(-0.191123\pi\)
0.825092 + 0.564998i \(0.191123\pi\)
\(642\) 0 0
\(643\) −14.2474 −0.561864 −0.280932 0.959728i \(-0.590644\pi\)
−0.280932 + 0.959728i \(0.590644\pi\)
\(644\) 2.23426 0.0880420
\(645\) 0 0
\(646\) −0.481149 −0.0189305
\(647\) 39.6911 1.56042 0.780209 0.625519i \(-0.215113\pi\)
0.780209 + 0.625519i \(0.215113\pi\)
\(648\) 0 0
\(649\) −5.60751 −0.220114
\(650\) −7.53147 −0.295409
\(651\) 0 0
\(652\) 12.5770 0.492554
\(653\) 11.1782 0.437438 0.218719 0.975788i \(-0.429812\pi\)
0.218719 + 0.975788i \(0.429812\pi\)
\(654\) 0 0
\(655\) 53.8766 2.10513
\(656\) 25.7706 1.00617
\(657\) 0 0
\(658\) 43.8631 1.70996
\(659\) −40.4792 −1.57684 −0.788422 0.615134i \(-0.789102\pi\)
−0.788422 + 0.615134i \(0.789102\pi\)
\(660\) 0 0
\(661\) 11.3921 0.443101 0.221551 0.975149i \(-0.428888\pi\)
0.221551 + 0.975149i \(0.428888\pi\)
\(662\) 2.61580 0.101666
\(663\) 0 0
\(664\) −19.3083 −0.749308
\(665\) −16.5030 −0.639959
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 6.13550 0.237390
\(669\) 0 0
\(670\) 6.54928 0.253021
\(671\) −11.1402 −0.430064
\(672\) 0 0
\(673\) 36.8502 1.42047 0.710235 0.703964i \(-0.248589\pi\)
0.710235 + 0.703964i \(0.248589\pi\)
\(674\) 25.7596 0.992222
\(675\) 0 0
\(676\) 5.44849 0.209557
\(677\) 18.5311 0.712209 0.356104 0.934446i \(-0.384105\pi\)
0.356104 + 0.934446i \(0.384105\pi\)
\(678\) 0 0
\(679\) 29.4218 1.12911
\(680\) −2.25377 −0.0864280
\(681\) 0 0
\(682\) 5.02522 0.192426
\(683\) −20.8679 −0.798489 −0.399244 0.916845i \(-0.630727\pi\)
−0.399244 + 0.916845i \(0.630727\pi\)
\(684\) 0 0
\(685\) −8.09043 −0.309119
\(686\) 3.52588 0.134619
\(687\) 0 0
\(688\) 25.9513 0.989385
\(689\) 19.8504 0.756238
\(690\) 0 0
\(691\) 12.5961 0.479178 0.239589 0.970874i \(-0.422987\pi\)
0.239589 + 0.970874i \(0.422987\pi\)
\(692\) −15.6093 −0.593378
\(693\) 0 0
\(694\) 38.3387 1.45532
\(695\) 25.9580 0.984645
\(696\) 0 0
\(697\) −2.76730 −0.104819
\(698\) 27.6692 1.04729
\(699\) 0 0
\(700\) −7.02136 −0.265383
\(701\) −37.2561 −1.40714 −0.703572 0.710624i \(-0.748413\pi\)
−0.703572 + 0.710624i \(0.748413\pi\)
\(702\) 0 0
\(703\) −9.24724 −0.348766
\(704\) −12.1931 −0.459545
\(705\) 0 0
\(706\) −32.1991 −1.21183
\(707\) −38.9740 −1.46577
\(708\) 0 0
\(709\) −4.74456 −0.178186 −0.0890928 0.996023i \(-0.528397\pi\)
−0.0890928 + 0.996023i \(0.528397\pi\)
\(710\) 41.9273 1.57350
\(711\) 0 0
\(712\) −11.3144 −0.424023
\(713\) −3.05203 −0.114299
\(714\) 0 0
\(715\) 8.13325 0.304166
\(716\) 2.80367 0.104778
\(717\) 0 0
\(718\) 0.921128 0.0343762
\(719\) 22.5184 0.839793 0.419897 0.907572i \(-0.362066\pi\)
0.419897 + 0.907572i \(0.362066\pi\)
\(720\) 0 0
\(721\) 29.2323 1.08867
\(722\) 19.3686 0.720826
\(723\) 0 0
\(724\) 14.2639 0.530113
\(725\) 3.14260 0.116713
\(726\) 0 0
\(727\) −16.0168 −0.594031 −0.297016 0.954873i \(-0.595991\pi\)
−0.297016 + 0.954873i \(0.595991\pi\)
\(728\) 22.7521 0.843248
\(729\) 0 0
\(730\) −27.3477 −1.01218
\(731\) −2.78670 −0.103070
\(732\) 0 0
\(733\) −48.9162 −1.80676 −0.903380 0.428840i \(-0.858922\pi\)
−0.903380 + 0.428840i \(0.858922\pi\)
\(734\) −0.598612 −0.0220952
\(735\) 0 0
\(736\) 3.34294 0.123223
\(737\) −2.72963 −0.100547
\(738\) 0 0
\(739\) 20.3156 0.747322 0.373661 0.927565i \(-0.378102\pi\)
0.373661 + 0.927565i \(0.378102\pi\)
\(740\) −10.1940 −0.374739
\(741\) 0 0
\(742\) −41.6215 −1.52797
\(743\) 10.8760 0.399003 0.199502 0.979898i \(-0.436068\pi\)
0.199502 + 0.979898i \(0.436068\pi\)
\(744\) 0 0
\(745\) −30.2567 −1.10852
\(746\) 6.49125 0.237662
\(747\) 0 0
\(748\) 0.221066 0.00808298
\(749\) 19.2287 0.702603
\(750\) 0 0
\(751\) 15.1517 0.552895 0.276447 0.961029i \(-0.410843\pi\)
0.276447 + 0.961029i \(0.410843\pi\)
\(752\) 24.5465 0.895119
\(753\) 0 0
\(754\) −2.39658 −0.0872782
\(755\) −13.4989 −0.491274
\(756\) 0 0
\(757\) 4.21203 0.153089 0.0765444 0.997066i \(-0.475611\pi\)
0.0765444 + 0.997066i \(0.475611\pi\)
\(758\) 32.8947 1.19479
\(759\) 0 0
\(760\) −13.9926 −0.507566
\(761\) 54.5237 1.97648 0.988242 0.152901i \(-0.0488614\pi\)
0.988242 + 0.152901i \(0.0488614\pi\)
\(762\) 0 0
\(763\) 47.4984 1.71956
\(764\) 2.58352 0.0934684
\(765\) 0 0
\(766\) 6.56778 0.237304
\(767\) 8.16195 0.294711
\(768\) 0 0
\(769\) 31.5349 1.13718 0.568590 0.822621i \(-0.307489\pi\)
0.568590 + 0.822621i \(0.307489\pi\)
\(770\) −17.0535 −0.614566
\(771\) 0 0
\(772\) 1.08899 0.0391935
\(773\) 10.3929 0.373806 0.186903 0.982378i \(-0.440155\pi\)
0.186903 + 0.982378i \(0.440155\pi\)
\(774\) 0 0
\(775\) 9.59128 0.344529
\(776\) 24.9463 0.895519
\(777\) 0 0
\(778\) −4.41024 −0.158115
\(779\) −17.1809 −0.615570
\(780\) 0 0
\(781\) −17.4746 −0.625290
\(782\) 0.301970 0.0107984
\(783\) 0 0
\(784\) −14.7567 −0.527026
\(785\) 2.16523 0.0772803
\(786\) 0 0
\(787\) −1.22731 −0.0437487 −0.0218744 0.999761i \(-0.506963\pi\)
−0.0218744 + 0.999761i \(0.506963\pi\)
\(788\) −5.59922 −0.199464
\(789\) 0 0
\(790\) 54.7330 1.94731
\(791\) −56.4479 −2.00706
\(792\) 0 0
\(793\) 16.2151 0.575814
\(794\) −35.7464 −1.26859
\(795\) 0 0
\(796\) 3.26530 0.115736
\(797\) −48.7301 −1.72611 −0.863054 0.505112i \(-0.831451\pi\)
−0.863054 + 0.505112i \(0.831451\pi\)
\(798\) 0 0
\(799\) −2.63585 −0.0932498
\(800\) −10.5055 −0.371426
\(801\) 0 0
\(802\) 3.88595 0.137218
\(803\) 11.3981 0.402229
\(804\) 0 0
\(805\) 10.3573 0.365047
\(806\) −7.31441 −0.257639
\(807\) 0 0
\(808\) −33.0454 −1.16253
\(809\) −40.2800 −1.41617 −0.708084 0.706128i \(-0.750440\pi\)
−0.708084 + 0.706128i \(0.750440\pi\)
\(810\) 0 0
\(811\) −29.8631 −1.04863 −0.524317 0.851523i \(-0.675679\pi\)
−0.524317 + 0.851523i \(0.675679\pi\)
\(812\) −2.23426 −0.0784070
\(813\) 0 0
\(814\) −9.55572 −0.334928
\(815\) 58.3031 2.04227
\(816\) 0 0
\(817\) −17.3014 −0.605299
\(818\) 7.66808 0.268108
\(819\) 0 0
\(820\) −18.9399 −0.661412
\(821\) 16.0595 0.560480 0.280240 0.959930i \(-0.409586\pi\)
0.280240 + 0.959930i \(0.409586\pi\)
\(822\) 0 0
\(823\) 13.8721 0.483552 0.241776 0.970332i \(-0.422270\pi\)
0.241776 + 0.970332i \(0.422270\pi\)
\(824\) 24.7855 0.863445
\(825\) 0 0
\(826\) −17.1137 −0.595462
\(827\) −41.4361 −1.44087 −0.720436 0.693521i \(-0.756058\pi\)
−0.720436 + 0.693521i \(0.756058\pi\)
\(828\) 0 0
\(829\) −17.5188 −0.608455 −0.304227 0.952599i \(-0.598398\pi\)
−0.304227 + 0.952599i \(0.598398\pi\)
\(830\) −21.0650 −0.731178
\(831\) 0 0
\(832\) 17.7476 0.615286
\(833\) 1.58461 0.0549033
\(834\) 0 0
\(835\) 28.4423 0.984285
\(836\) 1.37250 0.0474689
\(837\) 0 0
\(838\) 44.9203 1.55175
\(839\) −2.33207 −0.0805121 −0.0402561 0.999189i \(-0.512817\pi\)
−0.0402561 + 0.999189i \(0.512817\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 41.9904 1.44709
\(843\) 0 0
\(844\) −3.79606 −0.130666
\(845\) 25.2575 0.868885
\(846\) 0 0
\(847\) −32.8186 −1.12766
\(848\) −23.2921 −0.799855
\(849\) 0 0
\(850\) −0.948969 −0.0325494
\(851\) 5.80359 0.198944
\(852\) 0 0
\(853\) −34.2974 −1.17432 −0.587160 0.809471i \(-0.699754\pi\)
−0.587160 + 0.809471i \(0.699754\pi\)
\(854\) −33.9992 −1.16343
\(855\) 0 0
\(856\) 16.3037 0.557250
\(857\) −4.44845 −0.151956 −0.0759780 0.997109i \(-0.524208\pi\)
−0.0759780 + 0.997109i \(0.524208\pi\)
\(858\) 0 0
\(859\) 22.6653 0.773329 0.386664 0.922220i \(-0.373627\pi\)
0.386664 + 0.922220i \(0.373627\pi\)
\(860\) −19.0728 −0.650376
\(861\) 0 0
\(862\) 11.2694 0.383838
\(863\) 16.6196 0.565739 0.282870 0.959158i \(-0.408714\pi\)
0.282870 + 0.959158i \(0.408714\pi\)
\(864\) 0 0
\(865\) −72.3601 −2.46032
\(866\) −13.4744 −0.457879
\(867\) 0 0
\(868\) −6.81900 −0.231452
\(869\) −22.8118 −0.773838
\(870\) 0 0
\(871\) 3.97309 0.134623
\(872\) 40.2731 1.36382
\(873\) 0 0
\(874\) 1.87479 0.0634158
\(875\) 19.2377 0.650353
\(876\) 0 0
\(877\) 37.0821 1.25217 0.626087 0.779753i \(-0.284656\pi\)
0.626087 + 0.779753i \(0.284656\pi\)
\(878\) −21.6607 −0.731014
\(879\) 0 0
\(880\) −9.54345 −0.321709
\(881\) 25.6008 0.862511 0.431256 0.902230i \(-0.358071\pi\)
0.431256 + 0.902230i \(0.358071\pi\)
\(882\) 0 0
\(883\) 14.6206 0.492022 0.246011 0.969267i \(-0.420880\pi\)
0.246011 + 0.969267i \(0.420880\pi\)
\(884\) −0.321771 −0.0108223
\(885\) 0 0
\(886\) 14.5924 0.490240
\(887\) 40.2276 1.35071 0.675356 0.737492i \(-0.263990\pi\)
0.675356 + 0.737492i \(0.263990\pi\)
\(888\) 0 0
\(889\) −13.1404 −0.440714
\(890\) −12.3438 −0.413764
\(891\) 0 0
\(892\) 1.54116 0.0516020
\(893\) −16.3648 −0.547628
\(894\) 0 0
\(895\) 12.9969 0.434440
\(896\) −12.9450 −0.432462
\(897\) 0 0
\(898\) −28.1398 −0.939039
\(899\) 3.05203 0.101791
\(900\) 0 0
\(901\) 2.50115 0.0833255
\(902\) −17.7540 −0.591145
\(903\) 0 0
\(904\) −47.8613 −1.59184
\(905\) 66.1229 2.19800
\(906\) 0 0
\(907\) −48.0277 −1.59474 −0.797368 0.603494i \(-0.793775\pi\)
−0.797368 + 0.603494i \(0.793775\pi\)
\(908\) 3.85632 0.127976
\(909\) 0 0
\(910\) 24.8221 0.822844
\(911\) −33.9316 −1.12420 −0.562102 0.827068i \(-0.690007\pi\)
−0.562102 + 0.827068i \(0.690007\pi\)
\(912\) 0 0
\(913\) 8.77955 0.290561
\(914\) −4.25765 −0.140831
\(915\) 0 0
\(916\) 13.2262 0.437005
\(917\) −68.5306 −2.26308
\(918\) 0 0
\(919\) −0.863726 −0.0284917 −0.0142458 0.999899i \(-0.504535\pi\)
−0.0142458 + 0.999899i \(0.504535\pi\)
\(920\) 8.78179 0.289527
\(921\) 0 0
\(922\) 9.37899 0.308881
\(923\) 25.4350 0.837202
\(924\) 0 0
\(925\) −18.2383 −0.599672
\(926\) 31.5704 1.03747
\(927\) 0 0
\(928\) −3.34294 −0.109737
\(929\) −4.15824 −0.136427 −0.0682137 0.997671i \(-0.521730\pi\)
−0.0682137 + 0.997671i \(0.521730\pi\)
\(930\) 0 0
\(931\) 9.83810 0.322431
\(932\) −10.6919 −0.350224
\(933\) 0 0
\(934\) −14.1419 −0.462737
\(935\) 1.02479 0.0335143
\(936\) 0 0
\(937\) 33.0339 1.07917 0.539584 0.841931i \(-0.318581\pi\)
0.539584 + 0.841931i \(0.318581\pi\)
\(938\) −8.33063 −0.272005
\(939\) 0 0
\(940\) −18.0403 −0.588410
\(941\) 40.0659 1.30611 0.653056 0.757309i \(-0.273487\pi\)
0.653056 + 0.757309i \(0.273487\pi\)
\(942\) 0 0
\(943\) 10.7828 0.351135
\(944\) −9.57712 −0.311709
\(945\) 0 0
\(946\) −17.8785 −0.581282
\(947\) −5.68021 −0.184582 −0.0922911 0.995732i \(-0.529419\pi\)
−0.0922911 + 0.995732i \(0.529419\pi\)
\(948\) 0 0
\(949\) −16.5903 −0.538545
\(950\) −5.89172 −0.191153
\(951\) 0 0
\(952\) 2.86677 0.0929126
\(953\) −31.6297 −1.02459 −0.512293 0.858811i \(-0.671204\pi\)
−0.512293 + 0.858811i \(0.671204\pi\)
\(954\) 0 0
\(955\) 11.9764 0.387547
\(956\) −1.78333 −0.0576771
\(957\) 0 0
\(958\) 31.4639 1.01655
\(959\) 10.2910 0.332312
\(960\) 0 0
\(961\) −21.6851 −0.699521
\(962\) 13.9087 0.448436
\(963\) 0 0
\(964\) 2.45320 0.0790122
\(965\) 5.04821 0.162508
\(966\) 0 0
\(967\) 18.3461 0.589972 0.294986 0.955502i \(-0.404685\pi\)
0.294986 + 0.955502i \(0.404685\pi\)
\(968\) −27.8264 −0.894373
\(969\) 0 0
\(970\) 27.2159 0.873851
\(971\) 16.7230 0.536668 0.268334 0.963326i \(-0.413527\pi\)
0.268334 + 0.963326i \(0.413527\pi\)
\(972\) 0 0
\(973\) −33.0184 −1.05852
\(974\) 32.2187 1.03235
\(975\) 0 0
\(976\) −19.0265 −0.609024
\(977\) −23.7818 −0.760849 −0.380424 0.924812i \(-0.624222\pi\)
−0.380424 + 0.924812i \(0.624222\pi\)
\(978\) 0 0
\(979\) 5.14467 0.164424
\(980\) 10.8454 0.346442
\(981\) 0 0
\(982\) −35.5961 −1.13592
\(983\) −12.9711 −0.413714 −0.206857 0.978371i \(-0.566324\pi\)
−0.206857 + 0.978371i \(0.566324\pi\)
\(984\) 0 0
\(985\) −25.9563 −0.827035
\(986\) −0.301970 −0.00961668
\(987\) 0 0
\(988\) −1.99773 −0.0635562
\(989\) 10.8584 0.345276
\(990\) 0 0
\(991\) −42.1423 −1.33870 −0.669348 0.742949i \(-0.733426\pi\)
−0.669348 + 0.742949i \(0.733426\pi\)
\(992\) −10.2027 −0.323937
\(993\) 0 0
\(994\) −53.3311 −1.69156
\(995\) 15.1369 0.479873
\(996\) 0 0
\(997\) −53.5460 −1.69582 −0.847909 0.530142i \(-0.822139\pi\)
−0.847909 + 0.530142i \(0.822139\pi\)
\(998\) 9.92699 0.314233
\(999\) 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 6003.2.a.m.1.5 11
3.2 odd 2 2001.2.a.l.1.7 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.7 11 3.2 odd 2
6003.2.a.m.1.5 11 1.1 even 1 trivial