Properties

Label 7448.2.a.bq.1.4
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4725794254\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 15x^{6} - x^{5} + 66x^{4} + 4x^{3} - 76x^{2} + 8x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 1064)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.436576\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.436576 q^{3} -0.299640 q^{5} -2.80940 q^{9} +O(q^{10})\) \(q-0.436576 q^{3} -0.299640 q^{5} -2.80940 q^{9} -5.18938 q^{11} -1.26174 q^{13} +0.130816 q^{15} +1.95892 q^{17} +1.00000 q^{19} -1.49106 q^{23} -4.91022 q^{25} +2.53625 q^{27} -0.530372 q^{29} +1.94838 q^{31} +2.26556 q^{33} +4.19347 q^{37} +0.550846 q^{39} -2.00000 q^{41} +5.51755 q^{43} +0.841808 q^{45} -8.54096 q^{47} -0.855216 q^{51} -11.7557 q^{53} +1.55494 q^{55} -0.436576 q^{57} -12.8152 q^{59} -5.93580 q^{61} +0.378068 q^{65} +5.50772 q^{67} +0.650963 q^{69} +2.28016 q^{71} -4.69240 q^{73} +2.14368 q^{75} +5.69468 q^{79} +7.32094 q^{81} +1.46325 q^{83} -0.586969 q^{85} +0.231548 q^{87} -3.85050 q^{89} -0.850616 q^{93} -0.299640 q^{95} -9.69800 q^{97} +14.5791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{5} + 6 q^{9} + 9 q^{11} + 8 q^{15} + 4 q^{17} + 8 q^{19} + 25 q^{23} + 15 q^{25} + 3 q^{27} + 6 q^{29} + 8 q^{33} + 13 q^{37} - 11 q^{39} - 16 q^{41} + 17 q^{43} + 17 q^{45} - 24 q^{47} + 5 q^{51} + 2 q^{53} + 5 q^{55} + 2 q^{59} - 13 q^{61} - 26 q^{65} + 2 q^{67} - 11 q^{69} + 10 q^{71} + 5 q^{73} - 20 q^{75} + 16 q^{79} - 12 q^{81} - 43 q^{83} + 24 q^{85} + 20 q^{87} + 8 q^{89} + 2 q^{93} - q^{95} - 12 q^{97} + 37 q^{99}+O(q^{100}) \) 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
\(3\) −0.436576 −0.252057 −0.126029 0.992027i \(-0.540223\pi\)
−0.126029 + 0.992027i \(0.540223\pi\)
\(4\) 0 0
\(5\) −0.299640 −0.134003 −0.0670015 0.997753i \(-0.521343\pi\)
−0.0670015 + 0.997753i \(0.521343\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.80940 −0.936467
\(10\) 0 0
\(11\) −5.18938 −1.56466 −0.782329 0.622866i \(-0.785968\pi\)
−0.782329 + 0.622866i \(0.785968\pi\)
\(12\) 0 0
\(13\) −1.26174 −0.349944 −0.174972 0.984573i \(-0.555984\pi\)
−0.174972 + 0.984573i \(0.555984\pi\)
\(14\) 0 0
\(15\) 0.130816 0.0337764
\(16\) 0 0
\(17\) 1.95892 0.475107 0.237553 0.971374i \(-0.423655\pi\)
0.237553 + 0.971374i \(0.423655\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.49106 −0.310908 −0.155454 0.987843i \(-0.549684\pi\)
−0.155454 + 0.987843i \(0.549684\pi\)
\(24\) 0 0
\(25\) −4.91022 −0.982043
\(26\) 0 0
\(27\) 2.53625 0.488101
\(28\) 0 0
\(29\) −0.530372 −0.0984876 −0.0492438 0.998787i \(-0.515681\pi\)
−0.0492438 + 0.998787i \(0.515681\pi\)
\(30\) 0 0
\(31\) 1.94838 0.349939 0.174970 0.984574i \(-0.444017\pi\)
0.174970 + 0.984574i \(0.444017\pi\)
\(32\) 0 0
\(33\) 2.26556 0.394383
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.19347 0.689402 0.344701 0.938713i \(-0.387980\pi\)
0.344701 + 0.938713i \(0.387980\pi\)
\(38\) 0 0
\(39\) 0.550846 0.0882060
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 5.51755 0.841418 0.420709 0.907196i \(-0.361781\pi\)
0.420709 + 0.907196i \(0.361781\pi\)
\(44\) 0 0
\(45\) 0.841808 0.125489
\(46\) 0 0
\(47\) −8.54096 −1.24583 −0.622913 0.782291i \(-0.714051\pi\)
−0.622913 + 0.782291i \(0.714051\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −0.855216 −0.119754
\(52\) 0 0
\(53\) −11.7557 −1.61477 −0.807383 0.590028i \(-0.799117\pi\)
−0.807383 + 0.590028i \(0.799117\pi\)
\(54\) 0 0
\(55\) 1.55494 0.209669
\(56\) 0 0
\(57\) −0.436576 −0.0578259
\(58\) 0 0
\(59\) −12.8152 −1.66840 −0.834198 0.551465i \(-0.814069\pi\)
−0.834198 + 0.551465i \(0.814069\pi\)
\(60\) 0 0
\(61\) −5.93580 −0.760002 −0.380001 0.924986i \(-0.624076\pi\)
−0.380001 + 0.924986i \(0.624076\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.378068 0.0468936
\(66\) 0 0
\(67\) 5.50772 0.672875 0.336438 0.941706i \(-0.390778\pi\)
0.336438 + 0.941706i \(0.390778\pi\)
\(68\) 0 0
\(69\) 0.650963 0.0783667
\(70\) 0 0
\(71\) 2.28016 0.270605 0.135303 0.990804i \(-0.456799\pi\)
0.135303 + 0.990804i \(0.456799\pi\)
\(72\) 0 0
\(73\) −4.69240 −0.549203 −0.274602 0.961558i \(-0.588546\pi\)
−0.274602 + 0.961558i \(0.588546\pi\)
\(74\) 0 0
\(75\) 2.14368 0.247531
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.69468 0.640702 0.320351 0.947299i \(-0.396199\pi\)
0.320351 + 0.947299i \(0.396199\pi\)
\(80\) 0 0
\(81\) 7.32094 0.813438
\(82\) 0 0
\(83\) 1.46325 0.160613 0.0803065 0.996770i \(-0.474410\pi\)
0.0803065 + 0.996770i \(0.474410\pi\)
\(84\) 0 0
\(85\) −0.586969 −0.0636657
\(86\) 0 0
\(87\) 0.231548 0.0248245
\(88\) 0 0
\(89\) −3.85050 −0.408152 −0.204076 0.978955i \(-0.565419\pi\)
−0.204076 + 0.978955i \(0.565419\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −0.850616 −0.0882048
\(94\) 0 0
\(95\) −0.299640 −0.0307424
\(96\) 0 0
\(97\) −9.69800 −0.984683 −0.492341 0.870402i \(-0.663859\pi\)
−0.492341 + 0.870402i \(0.663859\pi\)
\(98\) 0 0
\(99\) 14.5791 1.46525
\(100\) 0 0
\(101\) 16.3807 1.62994 0.814969 0.579505i \(-0.196754\pi\)
0.814969 + 0.579505i \(0.196754\pi\)
\(102\) 0 0
\(103\) 4.87782 0.480625 0.240313 0.970696i \(-0.422750\pi\)
0.240313 + 0.970696i \(0.422750\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.35554 0.711087 0.355543 0.934660i \(-0.384296\pi\)
0.355543 + 0.934660i \(0.384296\pi\)
\(108\) 0 0
\(109\) 4.38871 0.420362 0.210181 0.977663i \(-0.432595\pi\)
0.210181 + 0.977663i \(0.432595\pi\)
\(110\) 0 0
\(111\) −1.83077 −0.173769
\(112\) 0 0
\(113\) 6.60321 0.621178 0.310589 0.950544i \(-0.399474\pi\)
0.310589 + 0.950544i \(0.399474\pi\)
\(114\) 0 0
\(115\) 0.446782 0.0416626
\(116\) 0 0
\(117\) 3.54474 0.327711
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 15.9297 1.44815
\(122\) 0 0
\(123\) 0.873152 0.0787295
\(124\) 0 0
\(125\) 2.96949 0.265600
\(126\) 0 0
\(127\) −2.94961 −0.261736 −0.130868 0.991400i \(-0.541776\pi\)
−0.130868 + 0.991400i \(0.541776\pi\)
\(128\) 0 0
\(129\) −2.40883 −0.212086
\(130\) 0 0
\(131\) −12.9890 −1.13486 −0.567428 0.823423i \(-0.692062\pi\)
−0.567428 + 0.823423i \(0.692062\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.759960 −0.0654069
\(136\) 0 0
\(137\) 13.6324 1.16469 0.582347 0.812940i \(-0.302134\pi\)
0.582347 + 0.812940i \(0.302134\pi\)
\(138\) 0 0
\(139\) 20.6698 1.75319 0.876596 0.481226i \(-0.159809\pi\)
0.876596 + 0.481226i \(0.159809\pi\)
\(140\) 0 0
\(141\) 3.72878 0.314020
\(142\) 0 0
\(143\) 6.54766 0.547543
\(144\) 0 0
\(145\) 0.158920 0.0131976
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.67426 −0.546777 −0.273388 0.961904i \(-0.588144\pi\)
−0.273388 + 0.961904i \(0.588144\pi\)
\(150\) 0 0
\(151\) 15.6647 1.27478 0.637388 0.770543i \(-0.280015\pi\)
0.637388 + 0.770543i \(0.280015\pi\)
\(152\) 0 0
\(153\) −5.50338 −0.444922
\(154\) 0 0
\(155\) −0.583812 −0.0468929
\(156\) 0 0
\(157\) 5.95923 0.475598 0.237799 0.971314i \(-0.423574\pi\)
0.237799 + 0.971314i \(0.423574\pi\)
\(158\) 0 0
\(159\) 5.13225 0.407014
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 17.4627 1.36779 0.683893 0.729582i \(-0.260286\pi\)
0.683893 + 0.729582i \(0.260286\pi\)
\(164\) 0 0
\(165\) −0.678852 −0.0528485
\(166\) 0 0
\(167\) 1.72621 0.133578 0.0667892 0.997767i \(-0.478724\pi\)
0.0667892 + 0.997767i \(0.478724\pi\)
\(168\) 0 0
\(169\) −11.4080 −0.877539
\(170\) 0 0
\(171\) −2.80940 −0.214840
\(172\) 0 0
\(173\) −0.879143 −0.0668400 −0.0334200 0.999441i \(-0.510640\pi\)
−0.0334200 + 0.999441i \(0.510640\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.59481 0.420531
\(178\) 0 0
\(179\) 7.34176 0.548749 0.274374 0.961623i \(-0.411529\pi\)
0.274374 + 0.961623i \(0.411529\pi\)
\(180\) 0 0
\(181\) −18.2504 −1.35654 −0.678270 0.734813i \(-0.737270\pi\)
−0.678270 + 0.734813i \(0.737270\pi\)
\(182\) 0 0
\(183\) 2.59143 0.191564
\(184\) 0 0
\(185\) −1.25653 −0.0923818
\(186\) 0 0
\(187\) −10.1656 −0.743379
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.37207 −0.533425 −0.266712 0.963776i \(-0.585937\pi\)
−0.266712 + 0.963776i \(0.585937\pi\)
\(192\) 0 0
\(193\) 1.46286 0.105299 0.0526493 0.998613i \(-0.483233\pi\)
0.0526493 + 0.998613i \(0.483233\pi\)
\(194\) 0 0
\(195\) −0.165055 −0.0118199
\(196\) 0 0
\(197\) 2.41230 0.171870 0.0859348 0.996301i \(-0.472612\pi\)
0.0859348 + 0.996301i \(0.472612\pi\)
\(198\) 0 0
\(199\) 15.9571 1.13117 0.565586 0.824689i \(-0.308650\pi\)
0.565586 + 0.824689i \(0.308650\pi\)
\(200\) 0 0
\(201\) −2.40454 −0.169603
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.599279 0.0418555
\(206\) 0 0
\(207\) 4.18899 0.291155
\(208\) 0 0
\(209\) −5.18938 −0.358957
\(210\) 0 0
\(211\) 13.2835 0.914474 0.457237 0.889345i \(-0.348839\pi\)
0.457237 + 0.889345i \(0.348839\pi\)
\(212\) 0 0
\(213\) −0.995464 −0.0682081
\(214\) 0 0
\(215\) −1.65328 −0.112753
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 2.04859 0.138431
\(220\) 0 0
\(221\) −2.47165 −0.166261
\(222\) 0 0
\(223\) −28.1602 −1.88574 −0.942872 0.333154i \(-0.891887\pi\)
−0.942872 + 0.333154i \(0.891887\pi\)
\(224\) 0 0
\(225\) 13.7948 0.919651
\(226\) 0 0
\(227\) 18.0776 1.19985 0.599926 0.800055i \(-0.295197\pi\)
0.599926 + 0.800055i \(0.295197\pi\)
\(228\) 0 0
\(229\) 7.21993 0.477106 0.238553 0.971129i \(-0.423327\pi\)
0.238553 + 0.971129i \(0.423327\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.77207 −0.312629 −0.156314 0.987707i \(-0.549961\pi\)
−0.156314 + 0.987707i \(0.549961\pi\)
\(234\) 0 0
\(235\) 2.55921 0.166944
\(236\) 0 0
\(237\) −2.48616 −0.161494
\(238\) 0 0
\(239\) 3.62602 0.234548 0.117274 0.993100i \(-0.462584\pi\)
0.117274 + 0.993100i \(0.462584\pi\)
\(240\) 0 0
\(241\) 17.3348 1.11663 0.558317 0.829628i \(-0.311447\pi\)
0.558317 + 0.829628i \(0.311447\pi\)
\(242\) 0 0
\(243\) −10.8049 −0.693134
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.26174 −0.0802827
\(248\) 0 0
\(249\) −0.638822 −0.0404837
\(250\) 0 0
\(251\) 9.71280 0.613067 0.306533 0.951860i \(-0.400831\pi\)
0.306533 + 0.951860i \(0.400831\pi\)
\(252\) 0 0
\(253\) 7.73770 0.486465
\(254\) 0 0
\(255\) 0.256257 0.0160474
\(256\) 0 0
\(257\) −7.18296 −0.448061 −0.224030 0.974582i \(-0.571921\pi\)
−0.224030 + 0.974582i \(0.571921\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.49003 0.0922304
\(262\) 0 0
\(263\) 2.74049 0.168986 0.0844928 0.996424i \(-0.473073\pi\)
0.0844928 + 0.996424i \(0.473073\pi\)
\(264\) 0 0
\(265\) 3.52247 0.216383
\(266\) 0 0
\(267\) 1.68104 0.102878
\(268\) 0 0
\(269\) 20.4080 1.24430 0.622148 0.782900i \(-0.286260\pi\)
0.622148 + 0.782900i \(0.286260\pi\)
\(270\) 0 0
\(271\) −14.7090 −0.893511 −0.446755 0.894656i \(-0.647421\pi\)
−0.446755 + 0.894656i \(0.647421\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 25.4810 1.53656
\(276\) 0 0
\(277\) 20.1018 1.20780 0.603901 0.797060i \(-0.293612\pi\)
0.603901 + 0.797060i \(0.293612\pi\)
\(278\) 0 0
\(279\) −5.47378 −0.327707
\(280\) 0 0
\(281\) 15.1058 0.901136 0.450568 0.892742i \(-0.351222\pi\)
0.450568 + 0.892742i \(0.351222\pi\)
\(282\) 0 0
\(283\) −5.05412 −0.300436 −0.150218 0.988653i \(-0.547998\pi\)
−0.150218 + 0.988653i \(0.547998\pi\)
\(284\) 0 0
\(285\) 0.130816 0.00774884
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.1627 −0.774274
\(290\) 0 0
\(291\) 4.23392 0.248196
\(292\) 0 0
\(293\) −13.5367 −0.790823 −0.395411 0.918504i \(-0.629398\pi\)
−0.395411 + 0.918504i \(0.629398\pi\)
\(294\) 0 0
\(295\) 3.83994 0.223570
\(296\) 0 0
\(297\) −13.1615 −0.763711
\(298\) 0 0
\(299\) 1.88134 0.108801
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −7.15141 −0.410838
\(304\) 0 0
\(305\) 1.77860 0.101842
\(306\) 0 0
\(307\) 0.853123 0.0486903 0.0243452 0.999704i \(-0.492250\pi\)
0.0243452 + 0.999704i \(0.492250\pi\)
\(308\) 0 0
\(309\) −2.12954 −0.121145
\(310\) 0 0
\(311\) 17.3930 0.986264 0.493132 0.869954i \(-0.335852\pi\)
0.493132 + 0.869954i \(0.335852\pi\)
\(312\) 0 0
\(313\) 24.0556 1.35971 0.679853 0.733349i \(-0.262044\pi\)
0.679853 + 0.733349i \(0.262044\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.45556 0.418746 0.209373 0.977836i \(-0.432858\pi\)
0.209373 + 0.977836i \(0.432858\pi\)
\(318\) 0 0
\(319\) 2.75230 0.154099
\(320\) 0 0
\(321\) −3.21125 −0.179235
\(322\) 0 0
\(323\) 1.95892 0.108997
\(324\) 0 0
\(325\) 6.19542 0.343660
\(326\) 0 0
\(327\) −1.91600 −0.105955
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 33.9268 1.86479 0.932393 0.361445i \(-0.117717\pi\)
0.932393 + 0.361445i \(0.117717\pi\)
\(332\) 0 0
\(333\) −11.7811 −0.645602
\(334\) 0 0
\(335\) −1.65033 −0.0901672
\(336\) 0 0
\(337\) −16.1792 −0.881336 −0.440668 0.897670i \(-0.645258\pi\)
−0.440668 + 0.897670i \(0.645258\pi\)
\(338\) 0 0
\(339\) −2.88280 −0.156572
\(340\) 0 0
\(341\) −10.1109 −0.547535
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.195054 −0.0105014
\(346\) 0 0
\(347\) −28.5014 −1.53003 −0.765016 0.644011i \(-0.777269\pi\)
−0.765016 + 0.644011i \(0.777269\pi\)
\(348\) 0 0
\(349\) −24.1291 −1.29160 −0.645801 0.763506i \(-0.723476\pi\)
−0.645801 + 0.763506i \(0.723476\pi\)
\(350\) 0 0
\(351\) −3.20009 −0.170808
\(352\) 0 0
\(353\) 24.4536 1.30154 0.650768 0.759277i \(-0.274447\pi\)
0.650768 + 0.759277i \(0.274447\pi\)
\(354\) 0 0
\(355\) −0.683227 −0.0362619
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 29.7393 1.56958 0.784789 0.619763i \(-0.212771\pi\)
0.784789 + 0.619763i \(0.212771\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −6.95452 −0.365018
\(364\) 0 0
\(365\) 1.40603 0.0735949
\(366\) 0 0
\(367\) 24.3245 1.26973 0.634865 0.772623i \(-0.281056\pi\)
0.634865 + 0.772623i \(0.281056\pi\)
\(368\) 0 0
\(369\) 5.61880 0.292503
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −25.1701 −1.30326 −0.651628 0.758539i \(-0.725914\pi\)
−0.651628 + 0.758539i \(0.725914\pi\)
\(374\) 0 0
\(375\) −1.29641 −0.0669463
\(376\) 0 0
\(377\) 0.669192 0.0344652
\(378\) 0 0
\(379\) 5.07880 0.260880 0.130440 0.991456i \(-0.458361\pi\)
0.130440 + 0.991456i \(0.458361\pi\)
\(380\) 0 0
\(381\) 1.28773 0.0659724
\(382\) 0 0
\(383\) 4.15115 0.212114 0.106057 0.994360i \(-0.466177\pi\)
0.106057 + 0.994360i \(0.466177\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −15.5010 −0.787960
\(388\) 0 0
\(389\) −7.83901 −0.397454 −0.198727 0.980055i \(-0.563681\pi\)
−0.198727 + 0.980055i \(0.563681\pi\)
\(390\) 0 0
\(391\) −2.92087 −0.147715
\(392\) 0 0
\(393\) 5.67070 0.286049
\(394\) 0 0
\(395\) −1.70635 −0.0858560
\(396\) 0 0
\(397\) 3.07757 0.154459 0.0772295 0.997013i \(-0.475393\pi\)
0.0772295 + 0.997013i \(0.475393\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −37.4966 −1.87249 −0.936246 0.351344i \(-0.885725\pi\)
−0.936246 + 0.351344i \(0.885725\pi\)
\(402\) 0 0
\(403\) −2.45835 −0.122459
\(404\) 0 0
\(405\) −2.19364 −0.109003
\(406\) 0 0
\(407\) −21.7615 −1.07868
\(408\) 0 0
\(409\) −34.7551 −1.71853 −0.859265 0.511530i \(-0.829079\pi\)
−0.859265 + 0.511530i \(0.829079\pi\)
\(410\) 0 0
\(411\) −5.95158 −0.293570
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −0.438449 −0.0215226
\(416\) 0 0
\(417\) −9.02396 −0.441905
\(418\) 0 0
\(419\) 21.5451 1.05255 0.526274 0.850315i \(-0.323589\pi\)
0.526274 + 0.850315i \(0.323589\pi\)
\(420\) 0 0
\(421\) 2.66307 0.129790 0.0648951 0.997892i \(-0.479329\pi\)
0.0648951 + 0.997892i \(0.479329\pi\)
\(422\) 0 0
\(423\) 23.9950 1.16668
\(424\) 0 0
\(425\) −9.61870 −0.466575
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2.85855 −0.138012
\(430\) 0 0
\(431\) −24.7176 −1.19060 −0.595302 0.803502i \(-0.702967\pi\)
−0.595302 + 0.803502i \(0.702967\pi\)
\(432\) 0 0
\(433\) −7.26963 −0.349356 −0.174678 0.984626i \(-0.555888\pi\)
−0.174678 + 0.984626i \(0.555888\pi\)
\(434\) 0 0
\(435\) −0.0693809 −0.00332656
\(436\) 0 0
\(437\) −1.49106 −0.0713272
\(438\) 0 0
\(439\) −35.0201 −1.67142 −0.835710 0.549171i \(-0.814944\pi\)
−0.835710 + 0.549171i \(0.814944\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.11969 −0.290755 −0.145378 0.989376i \(-0.546440\pi\)
−0.145378 + 0.989376i \(0.546440\pi\)
\(444\) 0 0
\(445\) 1.15376 0.0546936
\(446\) 0 0
\(447\) 2.91382 0.137819
\(448\) 0 0
\(449\) 34.7695 1.64087 0.820436 0.571738i \(-0.193731\pi\)
0.820436 + 0.571738i \(0.193731\pi\)
\(450\) 0 0
\(451\) 10.3788 0.488717
\(452\) 0 0
\(453\) −6.83884 −0.321317
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −22.5727 −1.05591 −0.527953 0.849274i \(-0.677040\pi\)
−0.527953 + 0.849274i \(0.677040\pi\)
\(458\) 0 0
\(459\) 4.96829 0.231900
\(460\) 0 0
\(461\) 25.1756 1.17254 0.586272 0.810115i \(-0.300595\pi\)
0.586272 + 0.810115i \(0.300595\pi\)
\(462\) 0 0
\(463\) −7.74829 −0.360093 −0.180047 0.983658i \(-0.557625\pi\)
−0.180047 + 0.983658i \(0.557625\pi\)
\(464\) 0 0
\(465\) 0.254878 0.0118197
\(466\) 0 0
\(467\) 31.0781 1.43812 0.719060 0.694948i \(-0.244572\pi\)
0.719060 + 0.694948i \(0.244572\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2.60166 −0.119878
\(472\) 0 0
\(473\) −28.6327 −1.31653
\(474\) 0 0
\(475\) −4.91022 −0.225296
\(476\) 0 0
\(477\) 33.0264 1.51217
\(478\) 0 0
\(479\) −27.3206 −1.24831 −0.624154 0.781301i \(-0.714556\pi\)
−0.624154 + 0.781301i \(0.714556\pi\)
\(480\) 0 0
\(481\) −5.29107 −0.241252
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.90591 0.131950
\(486\) 0 0
\(487\) 25.0903 1.13695 0.568475 0.822701i \(-0.307534\pi\)
0.568475 + 0.822701i \(0.307534\pi\)
\(488\) 0 0
\(489\) −7.62381 −0.344761
\(490\) 0 0
\(491\) 29.4362 1.32844 0.664219 0.747538i \(-0.268764\pi\)
0.664219 + 0.747538i \(0.268764\pi\)
\(492\) 0 0
\(493\) −1.03895 −0.0467921
\(494\) 0 0
\(495\) −4.36846 −0.196348
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 42.2479 1.89127 0.945637 0.325225i \(-0.105440\pi\)
0.945637 + 0.325225i \(0.105440\pi\)
\(500\) 0 0
\(501\) −0.753624 −0.0336694
\(502\) 0 0
\(503\) −9.25390 −0.412611 −0.206305 0.978488i \(-0.566144\pi\)
−0.206305 + 0.978488i \(0.566144\pi\)
\(504\) 0 0
\(505\) −4.90830 −0.218416
\(506\) 0 0
\(507\) 4.98046 0.221190
\(508\) 0 0
\(509\) −23.8049 −1.05514 −0.527568 0.849513i \(-0.676896\pi\)
−0.527568 + 0.849513i \(0.676896\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 2.53625 0.111978
\(514\) 0 0
\(515\) −1.46159 −0.0644052
\(516\) 0 0
\(517\) 44.3223 1.94929
\(518\) 0 0
\(519\) 0.383813 0.0168475
\(520\) 0 0
\(521\) 32.0845 1.40565 0.702823 0.711364i \(-0.251922\pi\)
0.702823 + 0.711364i \(0.251922\pi\)
\(522\) 0 0
\(523\) 17.5524 0.767513 0.383756 0.923434i \(-0.374630\pi\)
0.383756 + 0.923434i \(0.374630\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.81671 0.166259
\(528\) 0 0
\(529\) −20.7767 −0.903336
\(530\) 0 0
\(531\) 36.0030 1.56240
\(532\) 0 0
\(533\) 2.52348 0.109304
\(534\) 0 0
\(535\) −2.20401 −0.0952877
\(536\) 0 0
\(537\) −3.20524 −0.138316
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 33.3770 1.43499 0.717495 0.696564i \(-0.245289\pi\)
0.717495 + 0.696564i \(0.245289\pi\)
\(542\) 0 0
\(543\) 7.96768 0.341926
\(544\) 0 0
\(545\) −1.31503 −0.0563297
\(546\) 0 0
\(547\) 39.4470 1.68663 0.843316 0.537418i \(-0.180600\pi\)
0.843316 + 0.537418i \(0.180600\pi\)
\(548\) 0 0
\(549\) 16.6761 0.711717
\(550\) 0 0
\(551\) −0.530372 −0.0225946
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.548571 0.0232855
\(556\) 0 0
\(557\) −35.4844 −1.50352 −0.751760 0.659437i \(-0.770795\pi\)
−0.751760 + 0.659437i \(0.770795\pi\)
\(558\) 0 0
\(559\) −6.96172 −0.294449
\(560\) 0 0
\(561\) 4.43804 0.187374
\(562\) 0 0
\(563\) −44.7109 −1.88434 −0.942170 0.335135i \(-0.891218\pi\)
−0.942170 + 0.335135i \(0.891218\pi\)
\(564\) 0 0
\(565\) −1.97858 −0.0832396
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.03775 −0.378882 −0.189441 0.981892i \(-0.560668\pi\)
−0.189441 + 0.981892i \(0.560668\pi\)
\(570\) 0 0
\(571\) 16.9643 0.709933 0.354966 0.934879i \(-0.384492\pi\)
0.354966 + 0.934879i \(0.384492\pi\)
\(572\) 0 0
\(573\) 3.21847 0.134454
\(574\) 0 0
\(575\) 7.32144 0.305325
\(576\) 0 0
\(577\) −17.6676 −0.735514 −0.367757 0.929922i \(-0.619874\pi\)
−0.367757 + 0.929922i \(0.619874\pi\)
\(578\) 0 0
\(579\) −0.638648 −0.0265413
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 61.0047 2.52656
\(584\) 0 0
\(585\) −1.06214 −0.0439143
\(586\) 0 0
\(587\) −15.6759 −0.647014 −0.323507 0.946226i \(-0.604862\pi\)
−0.323507 + 0.946226i \(0.604862\pi\)
\(588\) 0 0
\(589\) 1.94838 0.0802816
\(590\) 0 0
\(591\) −1.05315 −0.0433210
\(592\) 0 0
\(593\) −16.5892 −0.681237 −0.340619 0.940202i \(-0.610636\pi\)
−0.340619 + 0.940202i \(0.610636\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.96651 −0.285120
\(598\) 0 0
\(599\) 48.6293 1.98694 0.993469 0.114105i \(-0.0364001\pi\)
0.993469 + 0.114105i \(0.0364001\pi\)
\(600\) 0 0
\(601\) −23.2984 −0.950362 −0.475181 0.879888i \(-0.657617\pi\)
−0.475181 + 0.879888i \(0.657617\pi\)
\(602\) 0 0
\(603\) −15.4734 −0.630125
\(604\) 0 0
\(605\) −4.77316 −0.194057
\(606\) 0 0
\(607\) 29.0822 1.18041 0.590206 0.807253i \(-0.299047\pi\)
0.590206 + 0.807253i \(0.299047\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10.7765 0.435970
\(612\) 0 0
\(613\) −11.0534 −0.446443 −0.223221 0.974768i \(-0.571657\pi\)
−0.223221 + 0.974768i \(0.571657\pi\)
\(614\) 0 0
\(615\) −0.261631 −0.0105500
\(616\) 0 0
\(617\) −37.7605 −1.52018 −0.760090 0.649817i \(-0.774845\pi\)
−0.760090 + 0.649817i \(0.774845\pi\)
\(618\) 0 0
\(619\) 0.628953 0.0252798 0.0126399 0.999920i \(-0.495976\pi\)
0.0126399 + 0.999920i \(0.495976\pi\)
\(620\) 0 0
\(621\) −3.78170 −0.151755
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 23.6613 0.946452
\(626\) 0 0
\(627\) 2.26556 0.0904778
\(628\) 0 0
\(629\) 8.21464 0.327539
\(630\) 0 0
\(631\) 17.1786 0.683870 0.341935 0.939724i \(-0.388918\pi\)
0.341935 + 0.939724i \(0.388918\pi\)
\(632\) 0 0
\(633\) −5.79926 −0.230500
\(634\) 0 0
\(635\) 0.883821 0.0350734
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −6.40589 −0.253413
\(640\) 0 0
\(641\) 8.13789 0.321427 0.160714 0.987001i \(-0.448620\pi\)
0.160714 + 0.987001i \(0.448620\pi\)
\(642\) 0 0
\(643\) 9.21363 0.363350 0.181675 0.983359i \(-0.441848\pi\)
0.181675 + 0.983359i \(0.441848\pi\)
\(644\) 0 0
\(645\) 0.721781 0.0284201
\(646\) 0 0
\(647\) −19.3022 −0.758850 −0.379425 0.925223i \(-0.623878\pi\)
−0.379425 + 0.925223i \(0.623878\pi\)
\(648\) 0 0
\(649\) 66.5029 2.61047
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.74407 0.185650 0.0928248 0.995682i \(-0.470410\pi\)
0.0928248 + 0.995682i \(0.470410\pi\)
\(654\) 0 0
\(655\) 3.89203 0.152074
\(656\) 0 0
\(657\) 13.1828 0.514311
\(658\) 0 0
\(659\) 15.2932 0.595738 0.297869 0.954607i \(-0.403724\pi\)
0.297869 + 0.954607i \(0.403724\pi\)
\(660\) 0 0
\(661\) 3.90935 0.152056 0.0760280 0.997106i \(-0.475776\pi\)
0.0760280 + 0.997106i \(0.475776\pi\)
\(662\) 0 0
\(663\) 1.07906 0.0419073
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.790818 0.0306206
\(668\) 0 0
\(669\) 12.2941 0.475316
\(670\) 0 0
\(671\) 30.8031 1.18914
\(672\) 0 0
\(673\) −1.12569 −0.0433923 −0.0216962 0.999765i \(-0.506907\pi\)
−0.0216962 + 0.999765i \(0.506907\pi\)
\(674\) 0 0
\(675\) −12.4535 −0.479336
\(676\) 0 0
\(677\) −41.0287 −1.57686 −0.788430 0.615125i \(-0.789106\pi\)
−0.788430 + 0.615125i \(0.789106\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −7.89225 −0.302432
\(682\) 0 0
\(683\) −5.73893 −0.219594 −0.109797 0.993954i \(-0.535020\pi\)
−0.109797 + 0.993954i \(0.535020\pi\)
\(684\) 0 0
\(685\) −4.08481 −0.156073
\(686\) 0 0
\(687\) −3.15205 −0.120258
\(688\) 0 0
\(689\) 14.8326 0.565078
\(690\) 0 0
\(691\) 4.36871 0.166194 0.0830968 0.996541i \(-0.473519\pi\)
0.0830968 + 0.996541i \(0.473519\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6.19350 −0.234933
\(696\) 0 0
\(697\) −3.91783 −0.148398
\(698\) 0 0
\(699\) 2.08337 0.0788004
\(700\) 0 0
\(701\) 36.2974 1.37093 0.685466 0.728105i \(-0.259598\pi\)
0.685466 + 0.728105i \(0.259598\pi\)
\(702\) 0 0
\(703\) 4.19347 0.158160
\(704\) 0 0
\(705\) −1.11729 −0.0420796
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 9.88287 0.371159 0.185580 0.982629i \(-0.440584\pi\)
0.185580 + 0.982629i \(0.440584\pi\)
\(710\) 0 0
\(711\) −15.9987 −0.599996
\(712\) 0 0
\(713\) −2.90516 −0.108799
\(714\) 0 0
\(715\) −1.96194 −0.0733723
\(716\) 0 0
\(717\) −1.58304 −0.0591196
\(718\) 0 0
\(719\) −27.9542 −1.04251 −0.521257 0.853399i \(-0.674537\pi\)
−0.521257 + 0.853399i \(0.674537\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −7.56797 −0.281456
\(724\) 0 0
\(725\) 2.60424 0.0967191
\(726\) 0 0
\(727\) 32.8007 1.21651 0.608255 0.793742i \(-0.291870\pi\)
0.608255 + 0.793742i \(0.291870\pi\)
\(728\) 0 0
\(729\) −17.2457 −0.638728
\(730\) 0 0
\(731\) 10.8084 0.399763
\(732\) 0 0
\(733\) 24.1861 0.893335 0.446668 0.894700i \(-0.352611\pi\)
0.446668 + 0.894700i \(0.352611\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −28.5817 −1.05282
\(738\) 0 0
\(739\) 26.4600 0.973346 0.486673 0.873584i \(-0.338210\pi\)
0.486673 + 0.873584i \(0.338210\pi\)
\(740\) 0 0
\(741\) 0.550846 0.0202358
\(742\) 0 0
\(743\) 33.3257 1.22260 0.611301 0.791398i \(-0.290646\pi\)
0.611301 + 0.791398i \(0.290646\pi\)
\(744\) 0 0
\(745\) 1.99987 0.0732697
\(746\) 0 0
\(747\) −4.11087 −0.150409
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −4.64306 −0.169428 −0.0847138 0.996405i \(-0.526998\pi\)
−0.0847138 + 0.996405i \(0.526998\pi\)
\(752\) 0 0
\(753\) −4.24038 −0.154528
\(754\) 0 0
\(755\) −4.69377 −0.170824
\(756\) 0 0
\(757\) 45.0481 1.63730 0.818651 0.574291i \(-0.194722\pi\)
0.818651 + 0.574291i \(0.194722\pi\)
\(758\) 0 0
\(759\) −3.37809 −0.122617
\(760\) 0 0
\(761\) 15.0127 0.544211 0.272106 0.962267i \(-0.412280\pi\)
0.272106 + 0.962267i \(0.412280\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1.64903 0.0596208
\(766\) 0 0
\(767\) 16.1695 0.583845
\(768\) 0 0
\(769\) 4.05311 0.146159 0.0730794 0.997326i \(-0.476717\pi\)
0.0730794 + 0.997326i \(0.476717\pi\)
\(770\) 0 0
\(771\) 3.13591 0.112937
\(772\) 0 0
\(773\) 12.3940 0.445782 0.222891 0.974843i \(-0.428451\pi\)
0.222891 + 0.974843i \(0.428451\pi\)
\(774\) 0 0
\(775\) −9.56697 −0.343656
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.00000 −0.0716574
\(780\) 0 0
\(781\) −11.8326 −0.423405
\(782\) 0 0
\(783\) −1.34515 −0.0480719
\(784\) 0 0
\(785\) −1.78562 −0.0637316
\(786\) 0 0
\(787\) −21.4231 −0.763653 −0.381826 0.924234i \(-0.624705\pi\)
−0.381826 + 0.924234i \(0.624705\pi\)
\(788\) 0 0
\(789\) −1.19643 −0.0425941
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 7.48945 0.265958
\(794\) 0 0
\(795\) −1.53782 −0.0545410
\(796\) 0 0
\(797\) −37.1622 −1.31635 −0.658175 0.752865i \(-0.728672\pi\)
−0.658175 + 0.752865i \(0.728672\pi\)
\(798\) 0 0
\(799\) −16.7310 −0.591901
\(800\) 0 0
\(801\) 10.8176 0.382221
\(802\) 0 0
\(803\) 24.3506 0.859315
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −8.90963 −0.313634
\(808\) 0 0
\(809\) 2.08416 0.0732752 0.0366376 0.999329i \(-0.488335\pi\)
0.0366376 + 0.999329i \(0.488335\pi\)
\(810\) 0 0
\(811\) −11.2776 −0.396009 −0.198005 0.980201i \(-0.563446\pi\)
−0.198005 + 0.980201i \(0.563446\pi\)
\(812\) 0 0
\(813\) 6.42162 0.225216
\(814\) 0 0
\(815\) −5.23252 −0.183287
\(816\) 0 0
\(817\) 5.51755 0.193035
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −42.5746 −1.48586 −0.742931 0.669368i \(-0.766565\pi\)
−0.742931 + 0.669368i \(0.766565\pi\)
\(822\) 0 0
\(823\) 21.6684 0.755313 0.377657 0.925946i \(-0.376730\pi\)
0.377657 + 0.925946i \(0.376730\pi\)
\(824\) 0 0
\(825\) −11.1244 −0.387302
\(826\) 0 0
\(827\) −31.7162 −1.10288 −0.551440 0.834215i \(-0.685921\pi\)
−0.551440 + 0.834215i \(0.685921\pi\)
\(828\) 0 0
\(829\) 18.2900 0.635237 0.317618 0.948219i \(-0.397117\pi\)
0.317618 + 0.948219i \(0.397117\pi\)
\(830\) 0 0
\(831\) −8.77598 −0.304435
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −0.517242 −0.0178999
\(836\) 0 0
\(837\) 4.94157 0.170806
\(838\) 0 0
\(839\) −29.8422 −1.03027 −0.515134 0.857109i \(-0.672258\pi\)
−0.515134 + 0.857109i \(0.672258\pi\)
\(840\) 0 0
\(841\) −28.7187 −0.990300
\(842\) 0 0
\(843\) −6.59483 −0.227138
\(844\) 0 0
\(845\) 3.41829 0.117593
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 2.20651 0.0757272
\(850\) 0 0
\(851\) −6.25272 −0.214341
\(852\) 0 0
\(853\) −17.2641 −0.591111 −0.295555 0.955326i \(-0.595505\pi\)
−0.295555 + 0.955326i \(0.595505\pi\)
\(854\) 0 0
\(855\) 0.841808 0.0287892
\(856\) 0 0
\(857\) −10.7193 −0.366165 −0.183082 0.983098i \(-0.558607\pi\)
−0.183082 + 0.983098i \(0.558607\pi\)
\(858\) 0 0
\(859\) −30.1030 −1.02710 −0.513551 0.858059i \(-0.671670\pi\)
−0.513551 + 0.858059i \(0.671670\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 37.5256 1.27739 0.638693 0.769462i \(-0.279476\pi\)
0.638693 + 0.769462i \(0.279476\pi\)
\(864\) 0 0
\(865\) 0.263426 0.00895676
\(866\) 0 0
\(867\) 5.74650 0.195161
\(868\) 0 0
\(869\) −29.5519 −1.00248
\(870\) 0 0
\(871\) −6.94932 −0.235469
\(872\) 0 0
\(873\) 27.2456 0.922123
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 34.1851 1.15435 0.577175 0.816621i \(-0.304155\pi\)
0.577175 + 0.816621i \(0.304155\pi\)
\(878\) 0 0
\(879\) 5.90980 0.199333
\(880\) 0 0
\(881\) −49.6527 −1.67284 −0.836420 0.548089i \(-0.815356\pi\)
−0.836420 + 0.548089i \(0.815356\pi\)
\(882\) 0 0
\(883\) −19.4134 −0.653314 −0.326657 0.945143i \(-0.605922\pi\)
−0.326657 + 0.945143i \(0.605922\pi\)
\(884\) 0 0
\(885\) −1.67643 −0.0563524
\(886\) 0 0
\(887\) 40.2570 1.35170 0.675849 0.737040i \(-0.263777\pi\)
0.675849 + 0.737040i \(0.263777\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −37.9911 −1.27275
\(892\) 0 0
\(893\) −8.54096 −0.285812
\(894\) 0 0
\(895\) −2.19988 −0.0735340
\(896\) 0 0
\(897\) −0.821347 −0.0274240
\(898\) 0 0
\(899\) −1.03337 −0.0344647
\(900\) 0 0
\(901\) −23.0284 −0.767186
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.46854 0.181780
\(906\) 0 0
\(907\) 32.6248 1.08329 0.541645 0.840608i \(-0.317802\pi\)
0.541645 + 0.840608i \(0.317802\pi\)
\(908\) 0 0
\(909\) −46.0199 −1.52638
\(910\) 0 0
\(911\) 21.6499 0.717292 0.358646 0.933474i \(-0.383238\pi\)
0.358646 + 0.933474i \(0.383238\pi\)
\(912\) 0 0
\(913\) −7.59338 −0.251304
\(914\) 0 0
\(915\) −0.776495 −0.0256701
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 15.6504 0.516260 0.258130 0.966110i \(-0.416894\pi\)
0.258130 + 0.966110i \(0.416894\pi\)
\(920\) 0 0
\(921\) −0.372453 −0.0122728
\(922\) 0 0
\(923\) −2.87697 −0.0946967
\(924\) 0 0
\(925\) −20.5908 −0.677022
\(926\) 0 0
\(927\) −13.7037 −0.450090
\(928\) 0 0
\(929\) −37.5335 −1.23143 −0.615717 0.787968i \(-0.711133\pi\)
−0.615717 + 0.787968i \(0.711133\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −7.59335 −0.248595
\(934\) 0 0
\(935\) 3.04600 0.0996150
\(936\) 0 0
\(937\) 47.1876 1.54155 0.770776 0.637106i \(-0.219869\pi\)
0.770776 + 0.637106i \(0.219869\pi\)
\(938\) 0 0
\(939\) −10.5021 −0.342724
\(940\) 0 0
\(941\) 55.2500 1.80110 0.900550 0.434753i \(-0.143164\pi\)
0.900550 + 0.434753i \(0.143164\pi\)
\(942\) 0 0
\(943\) 2.98213 0.0971114
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −44.1150 −1.43354 −0.716772 0.697308i \(-0.754381\pi\)
−0.716772 + 0.697308i \(0.754381\pi\)
\(948\) 0 0
\(949\) 5.92059 0.192191
\(950\) 0 0
\(951\) −3.25492 −0.105548
\(952\) 0 0
\(953\) −27.9855 −0.906540 −0.453270 0.891373i \(-0.649743\pi\)
−0.453270 + 0.891373i \(0.649743\pi\)
\(954\) 0 0
\(955\) 2.20897 0.0714805
\(956\) 0 0
\(957\) −1.20159 −0.0388419
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −27.2038 −0.877542
\(962\) 0 0
\(963\) −20.6647 −0.665909
\(964\) 0 0
\(965\) −0.438330 −0.0141103
\(966\) 0 0
\(967\) −50.3705 −1.61981 −0.809904 0.586563i \(-0.800481\pi\)
−0.809904 + 0.586563i \(0.800481\pi\)
\(968\) 0 0
\(969\) −0.855216 −0.0274735
\(970\) 0 0
\(971\) −10.7342 −0.344478 −0.172239 0.985055i \(-0.555100\pi\)
−0.172239 + 0.985055i \(0.555100\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −2.70478 −0.0866221
\(976\) 0 0
\(977\) 45.7183 1.46266 0.731329 0.682025i \(-0.238900\pi\)
0.731329 + 0.682025i \(0.238900\pi\)
\(978\) 0 0
\(979\) 19.9817 0.638618
\(980\) 0 0
\(981\) −12.3296 −0.393655
\(982\) 0 0
\(983\) −32.4020 −1.03346 −0.516731 0.856148i \(-0.672851\pi\)
−0.516731 + 0.856148i \(0.672851\pi\)
\(984\) 0 0
\(985\) −0.722822 −0.0230310
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.22701 −0.261604
\(990\) 0 0
\(991\) −16.4348 −0.522068 −0.261034 0.965330i \(-0.584063\pi\)
−0.261034 + 0.965330i \(0.584063\pi\)
\(992\) 0 0
\(993\) −14.8116 −0.470033
\(994\) 0 0
\(995\) −4.78139 −0.151580
\(996\) 0 0
\(997\) 10.8413 0.343347 0.171673 0.985154i \(-0.445083\pi\)
0.171673 + 0.985154i \(0.445083\pi\)
\(998\) 0 0
\(999\) 10.6357 0.336497
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 7448.2.a.bq.1.4 8
7.2 even 3 1064.2.q.n.305.5 16
7.4 even 3 1064.2.q.n.457.5 yes 16
7.6 odd 2 7448.2.a.br.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.q.n.305.5 16 7.2 even 3
1064.2.q.n.457.5 yes 16 7.4 even 3
7448.2.a.bq.1.4 8 1.1 even 1 trivial
7448.2.a.br.1.5 8 7.6 odd 2