Properties

Label 1900.2.a.d.1.1
Level $1900$
Weight $2$
Character 1900.1
Self dual yes
Analytic conductor $15.172$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.1715763840\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
Defining polynomial: \( x^{2} - 3 \) 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 380)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 1900.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73205 q^{3} -2.00000 q^{7} +4.46410 q^{9} +O(q^{10})\) \(q-2.73205 q^{3} -2.00000 q^{7} +4.46410 q^{9} -3.46410 q^{11} +2.73205 q^{13} +3.46410 q^{17} +1.00000 q^{19} +5.46410 q^{21} +3.46410 q^{23} -4.00000 q^{27} +3.46410 q^{29} -1.46410 q^{31} +9.46410 q^{33} -6.73205 q^{37} -7.46410 q^{39} -6.00000 q^{41} +4.92820 q^{43} -12.9282 q^{47} -3.00000 q^{49} -9.46410 q^{51} +10.7321 q^{53} -2.73205 q^{57} +6.92820 q^{59} +12.3923 q^{61} -8.92820 q^{63} -6.73205 q^{67} -9.46410 q^{69} -2.53590 q^{71} +0.535898 q^{73} +6.92820 q^{77} +2.92820 q^{79} -2.46410 q^{81} -3.46410 q^{83} -9.46410 q^{87} -15.4641 q^{89} -5.46410 q^{91} +4.00000 q^{93} +16.5885 q^{97} -15.4641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} - 4 q^{7} + 2 q^{9} + 2 q^{13} + 2 q^{19} + 4 q^{21} - 8 q^{27} + 4 q^{31} + 12 q^{33} - 10 q^{37} - 8 q^{39} - 12 q^{41} - 4 q^{43} - 12 q^{47} - 6 q^{49} - 12 q^{51} + 18 q^{53} - 2 q^{57} + 4 q^{61} - 4 q^{63} - 10 q^{67} - 12 q^{69} - 12 q^{71} + 8 q^{73} - 8 q^{79} + 2 q^{81} - 12 q^{87} - 24 q^{89} - 4 q^{91} + 8 q^{93} + 2 q^{97} - 24 q^{99}+O(q^{100}) \) 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
\(3\) −2.73205 −1.57735 −0.788675 0.614810i \(-0.789233\pi\)
−0.788675 + 0.614810i \(0.789233\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) 4.46410 1.48803
\(10\) 0 0
\(11\) −3.46410 −1.04447 −0.522233 0.852803i \(-0.674901\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(12\) 0 0
\(13\) 2.73205 0.757735 0.378867 0.925451i \(-0.376314\pi\)
0.378867 + 0.925451i \(0.376314\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.46410 0.840168 0.420084 0.907485i \(-0.362001\pi\)
0.420084 + 0.907485i \(0.362001\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 5.46410 1.19236
\(22\) 0 0
\(23\) 3.46410 0.722315 0.361158 0.932505i \(-0.382382\pi\)
0.361158 + 0.932505i \(0.382382\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 3.46410 0.643268 0.321634 0.946864i \(-0.395768\pi\)
0.321634 + 0.946864i \(0.395768\pi\)
\(30\) 0 0
\(31\) −1.46410 −0.262960 −0.131480 0.991319i \(-0.541973\pi\)
−0.131480 + 0.991319i \(0.541973\pi\)
\(32\) 0 0
\(33\) 9.46410 1.64749
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.73205 −1.10674 −0.553371 0.832935i \(-0.686659\pi\)
−0.553371 + 0.832935i \(0.686659\pi\)
\(38\) 0 0
\(39\) −7.46410 −1.19521
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 4.92820 0.751544 0.375772 0.926712i \(-0.377378\pi\)
0.375772 + 0.926712i \(0.377378\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.9282 −1.88577 −0.942886 0.333115i \(-0.891900\pi\)
−0.942886 + 0.333115i \(0.891900\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −9.46410 −1.32524
\(52\) 0 0
\(53\) 10.7321 1.47416 0.737080 0.675805i \(-0.236204\pi\)
0.737080 + 0.675805i \(0.236204\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.73205 −0.361869
\(58\) 0 0
\(59\) 6.92820 0.901975 0.450988 0.892530i \(-0.351072\pi\)
0.450988 + 0.892530i \(0.351072\pi\)
\(60\) 0 0
\(61\) 12.3923 1.58667 0.793336 0.608784i \(-0.208342\pi\)
0.793336 + 0.608784i \(0.208342\pi\)
\(62\) 0 0
\(63\) −8.92820 −1.12485
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.73205 −0.822451 −0.411225 0.911534i \(-0.634899\pi\)
−0.411225 + 0.911534i \(0.634899\pi\)
\(68\) 0 0
\(69\) −9.46410 −1.13934
\(70\) 0 0
\(71\) −2.53590 −0.300956 −0.150478 0.988613i \(-0.548081\pi\)
−0.150478 + 0.988613i \(0.548081\pi\)
\(72\) 0 0
\(73\) 0.535898 0.0627222 0.0313611 0.999508i \(-0.490016\pi\)
0.0313611 + 0.999508i \(0.490016\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.92820 0.789542
\(78\) 0 0
\(79\) 2.92820 0.329449 0.164724 0.986340i \(-0.447327\pi\)
0.164724 + 0.986340i \(0.447327\pi\)
\(80\) 0 0
\(81\) −2.46410 −0.273789
\(82\) 0 0
\(83\) −3.46410 −0.380235 −0.190117 0.981761i \(-0.560887\pi\)
−0.190117 + 0.981761i \(0.560887\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −9.46410 −1.01466
\(88\) 0 0
\(89\) −15.4641 −1.63919 −0.819596 0.572942i \(-0.805802\pi\)
−0.819596 + 0.572942i \(0.805802\pi\)
\(90\) 0 0
\(91\) −5.46410 −0.572793
\(92\) 0 0
\(93\) 4.00000 0.414781
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 16.5885 1.68430 0.842151 0.539241i \(-0.181289\pi\)
0.842151 + 0.539241i \(0.181289\pi\)
\(98\) 0 0
\(99\) −15.4641 −1.55420
\(100\) 0 0
\(101\) −16.3923 −1.63110 −0.815548 0.578690i \(-0.803564\pi\)
−0.815548 + 0.578690i \(0.803564\pi\)
\(102\) 0 0
\(103\) −13.6603 −1.34598 −0.672992 0.739649i \(-0.734991\pi\)
−0.672992 + 0.739649i \(0.734991\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.66025 0.547197 0.273599 0.961844i \(-0.411786\pi\)
0.273599 + 0.961844i \(0.411786\pi\)
\(108\) 0 0
\(109\) −14.3923 −1.37853 −0.689266 0.724508i \(-0.742067\pi\)
−0.689266 + 0.724508i \(0.742067\pi\)
\(110\) 0 0
\(111\) 18.3923 1.74572
\(112\) 0 0
\(113\) −12.5885 −1.18422 −0.592111 0.805856i \(-0.701705\pi\)
−0.592111 + 0.805856i \(0.701705\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 12.1962 1.12753
\(118\) 0 0
\(119\) −6.92820 −0.635107
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 16.3923 1.47804
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −20.5885 −1.82693 −0.913465 0.406917i \(-0.866604\pi\)
−0.913465 + 0.406917i \(0.866604\pi\)
\(128\) 0 0
\(129\) −13.4641 −1.18545
\(130\) 0 0
\(131\) −18.9282 −1.65376 −0.826882 0.562375i \(-0.809888\pi\)
−0.826882 + 0.562375i \(0.809888\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −17.3205 −1.47979 −0.739895 0.672722i \(-0.765125\pi\)
−0.739895 + 0.672722i \(0.765125\pi\)
\(138\) 0 0
\(139\) 11.4641 0.972372 0.486186 0.873855i \(-0.338388\pi\)
0.486186 + 0.873855i \(0.338388\pi\)
\(140\) 0 0
\(141\) 35.3205 2.97452
\(142\) 0 0
\(143\) −9.46410 −0.791428
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 8.19615 0.676007
\(148\) 0 0
\(149\) −4.39230 −0.359832 −0.179916 0.983682i \(-0.557583\pi\)
−0.179916 + 0.983682i \(0.557583\pi\)
\(150\) 0 0
\(151\) −8.39230 −0.682956 −0.341478 0.939890i \(-0.610927\pi\)
−0.341478 + 0.939890i \(0.610927\pi\)
\(152\) 0 0
\(153\) 15.4641 1.25020
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −23.4641 −1.87264 −0.936320 0.351149i \(-0.885791\pi\)
−0.936320 + 0.351149i \(0.885791\pi\)
\(158\) 0 0
\(159\) −29.3205 −2.32527
\(160\) 0 0
\(161\) −6.92820 −0.546019
\(162\) 0 0
\(163\) −7.07180 −0.553906 −0.276953 0.960883i \(-0.589325\pi\)
−0.276953 + 0.960883i \(0.589325\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.7321 0.830471 0.415236 0.909714i \(-0.363699\pi\)
0.415236 + 0.909714i \(0.363699\pi\)
\(168\) 0 0
\(169\) −5.53590 −0.425838
\(170\) 0 0
\(171\) 4.46410 0.341378
\(172\) 0 0
\(173\) −3.80385 −0.289201 −0.144601 0.989490i \(-0.546190\pi\)
−0.144601 + 0.989490i \(0.546190\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −18.9282 −1.42273
\(178\) 0 0
\(179\) 20.7846 1.55351 0.776757 0.629800i \(-0.216863\pi\)
0.776757 + 0.629800i \(0.216863\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) −33.8564 −2.50274
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −12.0000 −0.877527
\(188\) 0 0
\(189\) 8.00000 0.581914
\(190\) 0 0
\(191\) 6.92820 0.501307 0.250654 0.968077i \(-0.419354\pi\)
0.250654 + 0.968077i \(0.419354\pi\)
\(192\) 0 0
\(193\) 7.80385 0.561733 0.280867 0.959747i \(-0.409378\pi\)
0.280867 + 0.959747i \(0.409378\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.928203 −0.0661317 −0.0330659 0.999453i \(-0.510527\pi\)
−0.0330659 + 0.999453i \(0.510527\pi\)
\(198\) 0 0
\(199\) 26.9282 1.90889 0.954445 0.298387i \(-0.0964487\pi\)
0.954445 + 0.298387i \(0.0964487\pi\)
\(200\) 0 0
\(201\) 18.3923 1.29729
\(202\) 0 0
\(203\) −6.92820 −0.486265
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 15.4641 1.07483
\(208\) 0 0
\(209\) −3.46410 −0.239617
\(210\) 0 0
\(211\) 19.3205 1.33008 0.665039 0.746808i \(-0.268415\pi\)
0.665039 + 0.746808i \(0.268415\pi\)
\(212\) 0 0
\(213\) 6.92820 0.474713
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 2.92820 0.198779
\(218\) 0 0
\(219\) −1.46410 −0.0989348
\(220\) 0 0
\(221\) 9.46410 0.636624
\(222\) 0 0
\(223\) 9.66025 0.646898 0.323449 0.946246i \(-0.395158\pi\)
0.323449 + 0.946246i \(0.395158\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.19615 −0.543998 −0.271999 0.962298i \(-0.587685\pi\)
−0.271999 + 0.962298i \(0.587685\pi\)
\(228\) 0 0
\(229\) 17.4641 1.15406 0.577030 0.816723i \(-0.304212\pi\)
0.577030 + 0.816723i \(0.304212\pi\)
\(230\) 0 0
\(231\) −18.9282 −1.24538
\(232\) 0 0
\(233\) 0.928203 0.0608086 0.0304043 0.999538i \(-0.490321\pi\)
0.0304043 + 0.999538i \(0.490321\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −8.00000 −0.519656
\(238\) 0 0
\(239\) −13.8564 −0.896296 −0.448148 0.893959i \(-0.647916\pi\)
−0.448148 + 0.893959i \(0.647916\pi\)
\(240\) 0 0
\(241\) −11.8564 −0.763738 −0.381869 0.924216i \(-0.624719\pi\)
−0.381869 + 0.924216i \(0.624719\pi\)
\(242\) 0 0
\(243\) 18.7321 1.20166
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.73205 0.173836
\(248\) 0 0
\(249\) 9.46410 0.599763
\(250\) 0 0
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.1244 0.943431 0.471716 0.881751i \(-0.343635\pi\)
0.471716 + 0.881751i \(0.343635\pi\)
\(258\) 0 0
\(259\) 13.4641 0.836619
\(260\) 0 0
\(261\) 15.4641 0.957204
\(262\) 0 0
\(263\) −8.53590 −0.526346 −0.263173 0.964749i \(-0.584769\pi\)
−0.263173 + 0.964749i \(0.584769\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 42.2487 2.58558
\(268\) 0 0
\(269\) 10.3923 0.633630 0.316815 0.948487i \(-0.397387\pi\)
0.316815 + 0.948487i \(0.397387\pi\)
\(270\) 0 0
\(271\) −2.39230 −0.145322 −0.0726611 0.997357i \(-0.523149\pi\)
−0.0726611 + 0.997357i \(0.523149\pi\)
\(272\) 0 0
\(273\) 14.9282 0.903496
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −18.3923 −1.10509 −0.552543 0.833484i \(-0.686343\pi\)
−0.552543 + 0.833484i \(0.686343\pi\)
\(278\) 0 0
\(279\) −6.53590 −0.391294
\(280\) 0 0
\(281\) 0.928203 0.0553720 0.0276860 0.999617i \(-0.491186\pi\)
0.0276860 + 0.999617i \(0.491186\pi\)
\(282\) 0 0
\(283\) −18.3923 −1.09331 −0.546655 0.837358i \(-0.684099\pi\)
−0.546655 + 0.837358i \(0.684099\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) 0 0
\(289\) −5.00000 −0.294118
\(290\) 0 0
\(291\) −45.3205 −2.65674
\(292\) 0 0
\(293\) 5.66025 0.330676 0.165338 0.986237i \(-0.447129\pi\)
0.165338 + 0.986237i \(0.447129\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 13.8564 0.804030
\(298\) 0 0
\(299\) 9.46410 0.547323
\(300\) 0 0
\(301\) −9.85641 −0.568114
\(302\) 0 0
\(303\) 44.7846 2.57281
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 7.80385 0.445389 0.222695 0.974888i \(-0.428515\pi\)
0.222695 + 0.974888i \(0.428515\pi\)
\(308\) 0 0
\(309\) 37.3205 2.12309
\(310\) 0 0
\(311\) −1.60770 −0.0911640 −0.0455820 0.998961i \(-0.514514\pi\)
−0.0455820 + 0.998961i \(0.514514\pi\)
\(312\) 0 0
\(313\) −10.7846 −0.609582 −0.304791 0.952419i \(-0.598587\pi\)
−0.304791 + 0.952419i \(0.598587\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.12436 −0.175481 −0.0877406 0.996143i \(-0.527965\pi\)
−0.0877406 + 0.996143i \(0.527965\pi\)
\(318\) 0 0
\(319\) −12.0000 −0.671871
\(320\) 0 0
\(321\) −15.4641 −0.863122
\(322\) 0 0
\(323\) 3.46410 0.192748
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 39.3205 2.17443
\(328\) 0 0
\(329\) 25.8564 1.42551
\(330\) 0 0
\(331\) −22.2487 −1.22290 −0.611450 0.791283i \(-0.709413\pi\)
−0.611450 + 0.791283i \(0.709413\pi\)
\(332\) 0 0
\(333\) −30.0526 −1.64687
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 17.2679 0.940645 0.470323 0.882495i \(-0.344138\pi\)
0.470323 + 0.882495i \(0.344138\pi\)
\(338\) 0 0
\(339\) 34.3923 1.86793
\(340\) 0 0
\(341\) 5.07180 0.274653
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −31.1769 −1.67366 −0.836832 0.547459i \(-0.815595\pi\)
−0.836832 + 0.547459i \(0.815595\pi\)
\(348\) 0 0
\(349\) 20.9282 1.12026 0.560131 0.828404i \(-0.310751\pi\)
0.560131 + 0.828404i \(0.310751\pi\)
\(350\) 0 0
\(351\) −10.9282 −0.583304
\(352\) 0 0
\(353\) −1.60770 −0.0855690 −0.0427845 0.999084i \(-0.513623\pi\)
−0.0427845 + 0.999084i \(0.513623\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 18.9282 1.00179
\(358\) 0 0
\(359\) −8.53590 −0.450507 −0.225254 0.974300i \(-0.572321\pi\)
−0.225254 + 0.974300i \(0.572321\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −2.73205 −0.143395
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3.85641 −0.201303 −0.100651 0.994922i \(-0.532093\pi\)
−0.100651 + 0.994922i \(0.532093\pi\)
\(368\) 0 0
\(369\) −26.7846 −1.39435
\(370\) 0 0
\(371\) −21.4641 −1.11436
\(372\) 0 0
\(373\) 16.5885 0.858918 0.429459 0.903086i \(-0.358704\pi\)
0.429459 + 0.903086i \(0.358704\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.46410 0.487426
\(378\) 0 0
\(379\) 14.9282 0.766810 0.383405 0.923580i \(-0.374751\pi\)
0.383405 + 0.923580i \(0.374751\pi\)
\(380\) 0 0
\(381\) 56.2487 2.88171
\(382\) 0 0
\(383\) −6.33975 −0.323946 −0.161973 0.986795i \(-0.551786\pi\)
−0.161973 + 0.986795i \(0.551786\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 22.0000 1.11832
\(388\) 0 0
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) 0 0
\(393\) 51.7128 2.60857
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 19.4641 0.976875 0.488438 0.872599i \(-0.337567\pi\)
0.488438 + 0.872599i \(0.337567\pi\)
\(398\) 0 0
\(399\) 5.46410 0.273547
\(400\) 0 0
\(401\) 38.7846 1.93681 0.968405 0.249381i \(-0.0802271\pi\)
0.968405 + 0.249381i \(0.0802271\pi\)
\(402\) 0 0
\(403\) −4.00000 −0.199254
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 23.3205 1.15595
\(408\) 0 0
\(409\) −14.3923 −0.711654 −0.355827 0.934552i \(-0.615801\pi\)
−0.355827 + 0.934552i \(0.615801\pi\)
\(410\) 0 0
\(411\) 47.3205 2.33415
\(412\) 0 0
\(413\) −13.8564 −0.681829
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −31.3205 −1.53377
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 0 0
\(423\) −57.7128 −2.80609
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −24.7846 −1.19941
\(428\) 0 0
\(429\) 25.8564 1.24836
\(430\) 0 0
\(431\) −33.4641 −1.61191 −0.805955 0.591977i \(-0.798347\pi\)
−0.805955 + 0.591977i \(0.798347\pi\)
\(432\) 0 0
\(433\) 22.3397 1.07358 0.536790 0.843716i \(-0.319637\pi\)
0.536790 + 0.843716i \(0.319637\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.46410 0.165710
\(438\) 0 0
\(439\) −31.7128 −1.51357 −0.756785 0.653664i \(-0.773231\pi\)
−0.756785 + 0.653664i \(0.773231\pi\)
\(440\) 0 0
\(441\) −13.3923 −0.637729
\(442\) 0 0
\(443\) −13.6077 −0.646521 −0.323261 0.946310i \(-0.604779\pi\)
−0.323261 + 0.946310i \(0.604779\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.0000 0.567581
\(448\) 0 0
\(449\) −3.46410 −0.163481 −0.0817405 0.996654i \(-0.526048\pi\)
−0.0817405 + 0.996654i \(0.526048\pi\)
\(450\) 0 0
\(451\) 20.7846 0.978709
\(452\) 0 0
\(453\) 22.9282 1.07726
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −34.7846 −1.62716 −0.813578 0.581456i \(-0.802483\pi\)
−0.813578 + 0.581456i \(0.802483\pi\)
\(458\) 0 0
\(459\) −13.8564 −0.646762
\(460\) 0 0
\(461\) −21.7128 −1.01127 −0.505633 0.862749i \(-0.668741\pi\)
−0.505633 + 0.862749i \(0.668741\pi\)
\(462\) 0 0
\(463\) −4.53590 −0.210801 −0.105401 0.994430i \(-0.533612\pi\)
−0.105401 + 0.994430i \(0.533612\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.3205 1.35679 0.678396 0.734697i \(-0.262676\pi\)
0.678396 + 0.734697i \(0.262676\pi\)
\(468\) 0 0
\(469\) 13.4641 0.621714
\(470\) 0 0
\(471\) 64.1051 2.95381
\(472\) 0 0
\(473\) −17.0718 −0.784962
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 47.9090 2.19360
\(478\) 0 0
\(479\) −22.3923 −1.02313 −0.511565 0.859244i \(-0.670934\pi\)
−0.511565 + 0.859244i \(0.670934\pi\)
\(480\) 0 0
\(481\) −18.3923 −0.838617
\(482\) 0 0
\(483\) 18.9282 0.861263
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 12.1962 0.552660 0.276330 0.961063i \(-0.410882\pi\)
0.276330 + 0.961063i \(0.410882\pi\)
\(488\) 0 0
\(489\) 19.3205 0.873704
\(490\) 0 0
\(491\) 18.9282 0.854218 0.427109 0.904200i \(-0.359532\pi\)
0.427109 + 0.904200i \(0.359532\pi\)
\(492\) 0 0
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.07180 0.227501
\(498\) 0 0
\(499\) 23.4641 1.05040 0.525199 0.850980i \(-0.323991\pi\)
0.525199 + 0.850980i \(0.323991\pi\)
\(500\) 0 0
\(501\) −29.3205 −1.30994
\(502\) 0 0
\(503\) −15.4641 −0.689510 −0.344755 0.938693i \(-0.612038\pi\)
−0.344755 + 0.938693i \(0.612038\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 15.1244 0.671696
\(508\) 0 0
\(509\) −5.32051 −0.235827 −0.117914 0.993024i \(-0.537621\pi\)
−0.117914 + 0.993024i \(0.537621\pi\)
\(510\) 0 0
\(511\) −1.07180 −0.0474135
\(512\) 0 0
\(513\) −4.00000 −0.176604
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 44.7846 1.96962
\(518\) 0 0
\(519\) 10.3923 0.456172
\(520\) 0 0
\(521\) −14.7846 −0.647726 −0.323863 0.946104i \(-0.604982\pi\)
−0.323863 + 0.946104i \(0.604982\pi\)
\(522\) 0 0
\(523\) 37.3731 1.63421 0.817105 0.576489i \(-0.195578\pi\)
0.817105 + 0.576489i \(0.195578\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.07180 −0.220931
\(528\) 0 0
\(529\) −11.0000 −0.478261
\(530\) 0 0
\(531\) 30.9282 1.34217
\(532\) 0 0
\(533\) −16.3923 −0.710030
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −56.7846 −2.45044
\(538\) 0 0
\(539\) 10.3923 0.447628
\(540\) 0 0
\(541\) −29.1769 −1.25441 −0.627207 0.778853i \(-0.715802\pi\)
−0.627207 + 0.778853i \(0.715802\pi\)
\(542\) 0 0
\(543\) −38.2487 −1.64141
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −6.73205 −0.287842 −0.143921 0.989589i \(-0.545971\pi\)
−0.143921 + 0.989589i \(0.545971\pi\)
\(548\) 0 0
\(549\) 55.3205 2.36102
\(550\) 0 0
\(551\) 3.46410 0.147576
\(552\) 0 0
\(553\) −5.85641 −0.249040
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.32051 −0.225437 −0.112719 0.993627i \(-0.535956\pi\)
−0.112719 + 0.993627i \(0.535956\pi\)
\(558\) 0 0
\(559\) 13.4641 0.569471
\(560\) 0 0
\(561\) 32.7846 1.38417
\(562\) 0 0
\(563\) −44.1962 −1.86265 −0.931323 0.364195i \(-0.881344\pi\)
−0.931323 + 0.364195i \(0.881344\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.92820 0.206965
\(568\) 0 0
\(569\) −29.3205 −1.22918 −0.614590 0.788847i \(-0.710678\pi\)
−0.614590 + 0.788847i \(0.710678\pi\)
\(570\) 0 0
\(571\) 18.3923 0.769694 0.384847 0.922980i \(-0.374254\pi\)
0.384847 + 0.922980i \(0.374254\pi\)
\(572\) 0 0
\(573\) −18.9282 −0.790737
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 6.78461 0.282447 0.141223 0.989978i \(-0.454896\pi\)
0.141223 + 0.989978i \(0.454896\pi\)
\(578\) 0 0
\(579\) −21.3205 −0.886050
\(580\) 0 0
\(581\) 6.92820 0.287430
\(582\) 0 0
\(583\) −37.1769 −1.53971
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −43.1769 −1.78210 −0.891051 0.453903i \(-0.850031\pi\)
−0.891051 + 0.453903i \(0.850031\pi\)
\(588\) 0 0
\(589\) −1.46410 −0.0603273
\(590\) 0 0
\(591\) 2.53590 0.104313
\(592\) 0 0
\(593\) −31.8564 −1.30819 −0.654093 0.756414i \(-0.726949\pi\)
−0.654093 + 0.756414i \(0.726949\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −73.5692 −3.01099
\(598\) 0 0
\(599\) −20.7846 −0.849236 −0.424618 0.905373i \(-0.639592\pi\)
−0.424618 + 0.905373i \(0.639592\pi\)
\(600\) 0 0
\(601\) 24.6410 1.00513 0.502564 0.864540i \(-0.332390\pi\)
0.502564 + 0.864540i \(0.332390\pi\)
\(602\) 0 0
\(603\) −30.0526 −1.22383
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 39.9090 1.61985 0.809927 0.586530i \(-0.199506\pi\)
0.809927 + 0.586530i \(0.199506\pi\)
\(608\) 0 0
\(609\) 18.9282 0.767010
\(610\) 0 0
\(611\) −35.3205 −1.42891
\(612\) 0 0
\(613\) −6.39230 −0.258183 −0.129091 0.991633i \(-0.541206\pi\)
−0.129091 + 0.991633i \(0.541206\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.60770 −0.0647234 −0.0323617 0.999476i \(-0.510303\pi\)
−0.0323617 + 0.999476i \(0.510303\pi\)
\(618\) 0 0
\(619\) −2.39230 −0.0961549 −0.0480774 0.998844i \(-0.515309\pi\)
−0.0480774 + 0.998844i \(0.515309\pi\)
\(620\) 0 0
\(621\) −13.8564 −0.556038
\(622\) 0 0
\(623\) 30.9282 1.23911
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 9.46410 0.377960
\(628\) 0 0
\(629\) −23.3205 −0.929850
\(630\) 0 0
\(631\) 11.4641 0.456379 0.228189 0.973617i \(-0.426719\pi\)
0.228189 + 0.973617i \(0.426719\pi\)
\(632\) 0 0
\(633\) −52.7846 −2.09800
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −8.19615 −0.324743
\(638\) 0 0
\(639\) −11.3205 −0.447832
\(640\) 0 0
\(641\) −24.9282 −0.984605 −0.492302 0.870424i \(-0.663845\pi\)
−0.492302 + 0.870424i \(0.663845\pi\)
\(642\) 0 0
\(643\) 14.3923 0.567577 0.283789 0.958887i \(-0.408409\pi\)
0.283789 + 0.958887i \(0.408409\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.4641 −0.607957 −0.303978 0.952679i \(-0.598315\pi\)
−0.303978 + 0.952679i \(0.598315\pi\)
\(648\) 0 0
\(649\) −24.0000 −0.942082
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) 0 0
\(653\) −27.4641 −1.07475 −0.537377 0.843342i \(-0.680585\pi\)
−0.537377 + 0.843342i \(0.680585\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.39230 0.0933327
\(658\) 0 0
\(659\) 8.78461 0.342200 0.171100 0.985254i \(-0.445268\pi\)
0.171100 + 0.985254i \(0.445268\pi\)
\(660\) 0 0
\(661\) 5.21539 0.202855 0.101428 0.994843i \(-0.467659\pi\)
0.101428 + 0.994843i \(0.467659\pi\)
\(662\) 0 0
\(663\) −25.8564 −1.00418
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 0 0
\(669\) −26.3923 −1.02039
\(670\) 0 0
\(671\) −42.9282 −1.65722
\(672\) 0 0
\(673\) 50.7321 1.95558 0.977788 0.209594i \(-0.0672143\pi\)
0.977788 + 0.209594i \(0.0672143\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.9808 −0.652624 −0.326312 0.945262i \(-0.605806\pi\)
−0.326312 + 0.945262i \(0.605806\pi\)
\(678\) 0 0
\(679\) −33.1769 −1.27321
\(680\) 0 0
\(681\) 22.3923 0.858075
\(682\) 0 0
\(683\) 17.6603 0.675751 0.337875 0.941191i \(-0.390292\pi\)
0.337875 + 0.941191i \(0.390292\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −47.7128 −1.82036
\(688\) 0 0
\(689\) 29.3205 1.11702
\(690\) 0 0
\(691\) 51.1769 1.94686 0.973431 0.228981i \(-0.0735395\pi\)
0.973431 + 0.228981i \(0.0735395\pi\)
\(692\) 0 0
\(693\) 30.9282 1.17487
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −20.7846 −0.787273
\(698\) 0 0
\(699\) −2.53590 −0.0959165
\(700\) 0 0
\(701\) −26.5359 −1.00225 −0.501124 0.865376i \(-0.667080\pi\)
−0.501124 + 0.865376i \(0.667080\pi\)
\(702\) 0 0
\(703\) −6.73205 −0.253904
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 32.7846 1.23299
\(708\) 0 0
\(709\) −30.7846 −1.15614 −0.578070 0.815987i \(-0.696194\pi\)
−0.578070 + 0.815987i \(0.696194\pi\)
\(710\) 0 0
\(711\) 13.0718 0.490231
\(712\) 0 0
\(713\) −5.07180 −0.189940
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 37.8564 1.41377
\(718\) 0 0
\(719\) 17.3205 0.645946 0.322973 0.946408i \(-0.395318\pi\)
0.322973 + 0.946408i \(0.395318\pi\)
\(720\) 0 0
\(721\) 27.3205 1.01747
\(722\) 0 0
\(723\) 32.3923 1.20468
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −0.143594 −0.00532559 −0.00266279 0.999996i \(-0.500848\pi\)
−0.00266279 + 0.999996i \(0.500848\pi\)
\(728\) 0 0
\(729\) −43.7846 −1.62165
\(730\) 0 0
\(731\) 17.0718 0.631423
\(732\) 0 0
\(733\) −10.7846 −0.398339 −0.199169 0.979965i \(-0.563824\pi\)
−0.199169 + 0.979965i \(0.563824\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 23.3205 0.859022
\(738\) 0 0
\(739\) −28.0000 −1.03000 −0.514998 0.857191i \(-0.672207\pi\)
−0.514998 + 0.857191i \(0.672207\pi\)
\(740\) 0 0
\(741\) −7.46410 −0.274201
\(742\) 0 0
\(743\) −20.8756 −0.765853 −0.382927 0.923779i \(-0.625084\pi\)
−0.382927 + 0.923779i \(0.625084\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −15.4641 −0.565802
\(748\) 0 0
\(749\) −11.3205 −0.413642
\(750\) 0 0
\(751\) −25.4641 −0.929198 −0.464599 0.885521i \(-0.653802\pi\)
−0.464599 + 0.885521i \(0.653802\pi\)
\(752\) 0 0
\(753\) 65.5692 2.38948
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) 32.7846 1.19001
\(760\) 0 0
\(761\) 19.6077 0.710778 0.355389 0.934718i \(-0.384348\pi\)
0.355389 + 0.934718i \(0.384348\pi\)
\(762\) 0 0
\(763\) 28.7846 1.04207
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 18.9282 0.683458
\(768\) 0 0
\(769\) −30.5359 −1.10115 −0.550576 0.834785i \(-0.685592\pi\)
−0.550576 + 0.834785i \(0.685592\pi\)
\(770\) 0 0
\(771\) −41.3205 −1.48812
\(772\) 0 0
\(773\) −22.0526 −0.793175 −0.396588 0.917997i \(-0.629806\pi\)
−0.396588 + 0.917997i \(0.629806\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −36.7846 −1.31964
\(778\) 0 0
\(779\) −6.00000 −0.214972
\(780\) 0 0
\(781\) 8.78461 0.314338
\(782\) 0 0
\(783\) −13.8564 −0.495188
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 12.1962 0.434746 0.217373 0.976089i \(-0.430251\pi\)
0.217373 + 0.976089i \(0.430251\pi\)
\(788\) 0 0
\(789\) 23.3205 0.830232
\(790\) 0 0
\(791\) 25.1769 0.895188
\(792\) 0 0
\(793\) 33.8564 1.20228
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.66025 0.200496 0.100248 0.994962i \(-0.468036\pi\)
0.100248 + 0.994962i \(0.468036\pi\)
\(798\) 0 0
\(799\) −44.7846 −1.58437
\(800\) 0 0
\(801\) −69.0333 −2.43917
\(802\) 0 0
\(803\) −1.85641 −0.0655112
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −28.3923 −0.999456
\(808\) 0 0
\(809\) 9.71281 0.341484 0.170742 0.985316i \(-0.445383\pi\)
0.170742 + 0.985316i \(0.445383\pi\)
\(810\) 0 0
\(811\) 15.6077 0.548060 0.274030 0.961721i \(-0.411643\pi\)
0.274030 + 0.961721i \(0.411643\pi\)
\(812\) 0 0
\(813\) 6.53590 0.229224
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 4.92820 0.172416
\(818\) 0 0
\(819\) −24.3923 −0.852336
\(820\) 0 0
\(821\) −16.1436 −0.563415 −0.281708 0.959500i \(-0.590901\pi\)
−0.281708 + 0.959500i \(0.590901\pi\)
\(822\) 0 0
\(823\) 39.5692 1.37930 0.689648 0.724145i \(-0.257765\pi\)
0.689648 + 0.724145i \(0.257765\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 29.6603 1.03139 0.515694 0.856773i \(-0.327534\pi\)
0.515694 + 0.856773i \(0.327534\pi\)
\(828\) 0 0
\(829\) 8.24871 0.286490 0.143245 0.989687i \(-0.454246\pi\)
0.143245 + 0.989687i \(0.454246\pi\)
\(830\) 0 0
\(831\) 50.2487 1.74311
\(832\) 0 0
\(833\) −10.3923 −0.360072
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 5.85641 0.202427
\(838\) 0 0
\(839\) 18.9282 0.653474 0.326737 0.945115i \(-0.394051\pi\)
0.326737 + 0.945115i \(0.394051\pi\)
\(840\) 0 0
\(841\) −17.0000 −0.586207
\(842\) 0 0
\(843\) −2.53590 −0.0873410
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) 0 0
\(849\) 50.2487 1.72453
\(850\) 0 0
\(851\) −23.3205 −0.799417
\(852\) 0 0
\(853\) 44.6410 1.52848 0.764240 0.644932i \(-0.223114\pi\)
0.764240 + 0.644932i \(0.223114\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.80385 −0.129937 −0.0649685 0.997887i \(-0.520695\pi\)
−0.0649685 + 0.997887i \(0.520695\pi\)
\(858\) 0 0
\(859\) 47.7128 1.62794 0.813970 0.580907i \(-0.197302\pi\)
0.813970 + 0.580907i \(0.197302\pi\)
\(860\) 0 0
\(861\) −32.7846 −1.11730
\(862\) 0 0
\(863\) 37.2679 1.26862 0.634308 0.773081i \(-0.281285\pi\)
0.634308 + 0.773081i \(0.281285\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 13.6603 0.463927
\(868\) 0 0
\(869\) −10.1436 −0.344098
\(870\) 0 0
\(871\) −18.3923 −0.623199
\(872\) 0 0
\(873\) 74.0526 2.50630
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.980762 −0.0331180 −0.0165590 0.999863i \(-0.505271\pi\)
−0.0165590 + 0.999863i \(0.505271\pi\)
\(878\) 0 0
\(879\) −15.4641 −0.521591
\(880\) 0 0
\(881\) −0.679492 −0.0228927 −0.0114463 0.999934i \(-0.503644\pi\)
−0.0114463 + 0.999934i \(0.503644\pi\)
\(882\) 0 0
\(883\) 22.0000 0.740359 0.370179 0.928960i \(-0.379296\pi\)
0.370179 + 0.928960i \(0.379296\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −23.4115 −0.786083 −0.393041 0.919521i \(-0.628577\pi\)
−0.393041 + 0.919521i \(0.628577\pi\)
\(888\) 0 0
\(889\) 41.1769 1.38103
\(890\) 0 0
\(891\) 8.53590 0.285963
\(892\) 0 0
\(893\) −12.9282 −0.432626
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −25.8564 −0.863320
\(898\) 0 0
\(899\) −5.07180 −0.169154
\(900\) 0 0
\(901\) 37.1769 1.23854
\(902\) 0 0
\(903\) 26.9282 0.896114
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −7.41154 −0.246096 −0.123048 0.992401i \(-0.539267\pi\)
−0.123048 + 0.992401i \(0.539267\pi\)
\(908\) 0 0
\(909\) −73.1769 −2.42713
\(910\) 0 0
\(911\) 14.5359 0.481596 0.240798 0.970575i \(-0.422591\pi\)
0.240798 + 0.970575i \(0.422591\pi\)
\(912\) 0 0
\(913\) 12.0000 0.397142
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 37.8564 1.25013
\(918\) 0 0
\(919\) 44.4974 1.46783 0.733917 0.679239i \(-0.237690\pi\)
0.733917 + 0.679239i \(0.237690\pi\)
\(920\) 0 0
\(921\) −21.3205 −0.702535
\(922\) 0 0
\(923\) −6.92820 −0.228045
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −60.9808 −2.00287
\(928\) 0 0
\(929\) −47.5692 −1.56070 −0.780348 0.625346i \(-0.784958\pi\)
−0.780348 + 0.625346i \(0.784958\pi\)
\(930\) 0 0
\(931\) −3.00000 −0.0983210
\(932\) 0 0
\(933\) 4.39230 0.143798
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −51.1769 −1.67188 −0.835938 0.548823i \(-0.815076\pi\)
−0.835938 + 0.548823i \(0.815076\pi\)
\(938\) 0 0
\(939\) 29.4641 0.961525
\(940\) 0 0
\(941\) 52.6410 1.71605 0.858024 0.513610i \(-0.171692\pi\)
0.858024 + 0.513610i \(0.171692\pi\)
\(942\) 0 0
\(943\) −20.7846 −0.676840
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −6.67949 −0.217054 −0.108527 0.994093i \(-0.534613\pi\)
−0.108527 + 0.994093i \(0.534613\pi\)
\(948\) 0 0
\(949\) 1.46410 0.0475267
\(950\) 0 0
\(951\) 8.53590 0.276795
\(952\) 0 0
\(953\) −60.5885 −1.96265 −0.981326 0.192350i \(-0.938389\pi\)
−0.981326 + 0.192350i \(0.938389\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 32.7846 1.05978
\(958\) 0 0
\(959\) 34.6410 1.11862
\(960\) 0 0
\(961\) −28.8564 −0.930852
\(962\) 0 0
\(963\) 25.2679 0.814248
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 45.3205 1.45741 0.728705 0.684828i \(-0.240123\pi\)
0.728705 + 0.684828i \(0.240123\pi\)
\(968\) 0 0
\(969\) −9.46410 −0.304031
\(970\) 0 0
\(971\) −14.5359 −0.466479 −0.233240 0.972419i \(-0.574933\pi\)
−0.233240 + 0.972419i \(0.574933\pi\)
\(972\) 0 0
\(973\) −22.9282 −0.735044
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −32.1962 −1.03005 −0.515023 0.857176i \(-0.672217\pi\)
−0.515023 + 0.857176i \(0.672217\pi\)
\(978\) 0 0
\(979\) 53.5692 1.71208
\(980\) 0 0
\(981\) −64.2487 −2.05130
\(982\) 0 0
\(983\) 2.44486 0.0779790 0.0389895 0.999240i \(-0.487586\pi\)
0.0389895 + 0.999240i \(0.487586\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −70.6410 −2.24853
\(988\) 0 0
\(989\) 17.0718 0.542852
\(990\) 0 0
\(991\) −8.39230 −0.266590 −0.133295 0.991076i \(-0.542556\pi\)
−0.133295 + 0.991076i \(0.542556\pi\)
\(992\) 0 0
\(993\) 60.7846 1.92894
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −30.3923 −0.962534 −0.481267 0.876574i \(-0.659823\pi\)
−0.481267 + 0.876574i \(0.659823\pi\)
\(998\) 0 0
\(999\) 26.9282 0.851971
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 1900.2.a.d.1.1 2
4.3 odd 2 7600.2.a.bf.1.2 2
5.2 odd 4 1900.2.c.e.1749.4 4
5.3 odd 4 1900.2.c.e.1749.1 4
5.4 even 2 380.2.a.d.1.2 2
15.14 odd 2 3420.2.a.h.1.2 2
20.19 odd 2 1520.2.a.l.1.1 2
40.19 odd 2 6080.2.a.bj.1.2 2
40.29 even 2 6080.2.a.z.1.1 2
95.94 odd 2 7220.2.a.h.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.a.d.1.2 2 5.4 even 2
1520.2.a.l.1.1 2 20.19 odd 2
1900.2.a.d.1.1 2 1.1 even 1 trivial
1900.2.c.e.1749.1 4 5.3 odd 4
1900.2.c.e.1749.4 4 5.2 odd 4
3420.2.a.h.1.2 2 15.14 odd 2
6080.2.a.z.1.1 2 40.29 even 2
6080.2.a.bj.1.2 2 40.19 odd 2
7220.2.a.h.1.1 2 95.94 odd 2
7600.2.a.bf.1.2 2 4.3 odd 2