Properties

Label 4560.2.a.br.1.1
Level $4560$
Weight $2$
Character 4560.1
Self dual yes
Analytic conductor $36.412$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4560.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.4117833217\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.564.1
Defining polynomial: \(x^{3} - x^{2} - 5 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 1140)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.571993\) of defining polynomial
Character \(\chi\) \(=\) 4560.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} -4.67282 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} -4.67282 q^{7} +1.00000 q^{9} -5.81681 q^{11} -2.67282 q^{13} -1.00000 q^{15} -6.48963 q^{17} +1.00000 q^{19} +4.67282 q^{21} -8.20166 q^{23} +1.00000 q^{25} -1.00000 q^{27} -3.81681 q^{29} +6.20166 q^{31} +5.81681 q^{33} -4.67282 q^{35} -12.0185 q^{37} +2.67282 q^{39} +0.183190 q^{41} +6.96080 q^{43} +1.00000 q^{45} +4.20166 q^{47} +14.8353 q^{49} +6.48963 q^{51} +10.7776 q^{53} -5.81681 q^{55} -1.00000 q^{57} +7.05767 q^{59} +5.14399 q^{61} -4.67282 q^{63} -2.67282 q^{65} -10.6913 q^{67} +8.20166 q^{69} -11.0577 q^{71} -4.28797 q^{73} -1.00000 q^{75} +27.1809 q^{77} +6.28797 q^{79} +1.00000 q^{81} -1.14399 q^{83} -6.48963 q^{85} +3.81681 q^{87} -3.81681 q^{89} +12.4896 q^{91} -6.20166 q^{93} +1.00000 q^{95} -6.67282 q^{97} -5.81681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} + 3 q^{5} - 4 q^{7} + 3 q^{9} + O(q^{10}) \) \( 3 q - 3 q^{3} + 3 q^{5} - 4 q^{7} + 3 q^{9} - 6 q^{11} + 2 q^{13} - 3 q^{15} + 2 q^{17} + 3 q^{19} + 4 q^{21} - 6 q^{23} + 3 q^{25} - 3 q^{27} + 6 q^{33} - 4 q^{35} - 6 q^{37} - 2 q^{39} + 12 q^{41} + 8 q^{43} + 3 q^{45} - 6 q^{47} + 3 q^{49} - 2 q^{51} + 8 q^{53} - 6 q^{55} - 3 q^{57} + 4 q^{59} + 14 q^{61} - 4 q^{63} + 2 q^{65} + 8 q^{67} + 6 q^{69} - 16 q^{71} - 10 q^{73} - 3 q^{75} + 20 q^{77} + 16 q^{79} + 3 q^{81} - 2 q^{83} + 2 q^{85} + 16 q^{91} + 3 q^{95} - 10 q^{97} - 6 q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −4.67282 −1.76616 −0.883081 0.469221i \(-0.844535\pi\)
−0.883081 + 0.469221i \(0.844535\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.81681 −1.75383 −0.876917 0.480642i \(-0.840404\pi\)
−0.876917 + 0.480642i \(0.840404\pi\)
\(12\) 0 0
\(13\) −2.67282 −0.741308 −0.370654 0.928771i \(-0.620866\pi\)
−0.370654 + 0.928771i \(0.620866\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −6.48963 −1.57397 −0.786984 0.616974i \(-0.788358\pi\)
−0.786984 + 0.616974i \(0.788358\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 4.67282 1.01969
\(22\) 0 0
\(23\) −8.20166 −1.71016 −0.855082 0.518492i \(-0.826493\pi\)
−0.855082 + 0.518492i \(0.826493\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −3.81681 −0.708764 −0.354382 0.935101i \(-0.615309\pi\)
−0.354382 + 0.935101i \(0.615309\pi\)
\(30\) 0 0
\(31\) 6.20166 1.11385 0.556926 0.830562i \(-0.311981\pi\)
0.556926 + 0.830562i \(0.311981\pi\)
\(32\) 0 0
\(33\) 5.81681 1.01258
\(34\) 0 0
\(35\) −4.67282 −0.789851
\(36\) 0 0
\(37\) −12.0185 −1.97582 −0.987912 0.155014i \(-0.950458\pi\)
−0.987912 + 0.155014i \(0.950458\pi\)
\(38\) 0 0
\(39\) 2.67282 0.427994
\(40\) 0 0
\(41\) 0.183190 0.0286094 0.0143047 0.999898i \(-0.495447\pi\)
0.0143047 + 0.999898i \(0.495447\pi\)
\(42\) 0 0
\(43\) 6.96080 1.06151 0.530756 0.847525i \(-0.321908\pi\)
0.530756 + 0.847525i \(0.321908\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 4.20166 0.612875 0.306438 0.951891i \(-0.400863\pi\)
0.306438 + 0.951891i \(0.400863\pi\)
\(48\) 0 0
\(49\) 14.8353 2.11933
\(50\) 0 0
\(51\) 6.48963 0.908731
\(52\) 0 0
\(53\) 10.7776 1.48042 0.740209 0.672377i \(-0.234727\pi\)
0.740209 + 0.672377i \(0.234727\pi\)
\(54\) 0 0
\(55\) −5.81681 −0.784339
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 7.05767 0.918831 0.459415 0.888221i \(-0.348059\pi\)
0.459415 + 0.888221i \(0.348059\pi\)
\(60\) 0 0
\(61\) 5.14399 0.658620 0.329310 0.944222i \(-0.393184\pi\)
0.329310 + 0.944222i \(0.393184\pi\)
\(62\) 0 0
\(63\) −4.67282 −0.588720
\(64\) 0 0
\(65\) −2.67282 −0.331523
\(66\) 0 0
\(67\) −10.6913 −1.30615 −0.653075 0.757293i \(-0.726521\pi\)
−0.653075 + 0.757293i \(0.726521\pi\)
\(68\) 0 0
\(69\) 8.20166 0.987364
\(70\) 0 0
\(71\) −11.0577 −1.31230 −0.656152 0.754629i \(-0.727817\pi\)
−0.656152 + 0.754629i \(0.727817\pi\)
\(72\) 0 0
\(73\) −4.28797 −0.501869 −0.250935 0.968004i \(-0.580738\pi\)
−0.250935 + 0.968004i \(0.580738\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 27.1809 3.09755
\(78\) 0 0
\(79\) 6.28797 0.707452 0.353726 0.935349i \(-0.384914\pi\)
0.353726 + 0.935349i \(0.384914\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −1.14399 −0.125569 −0.0627844 0.998027i \(-0.519998\pi\)
−0.0627844 + 0.998027i \(0.519998\pi\)
\(84\) 0 0
\(85\) −6.48963 −0.703900
\(86\) 0 0
\(87\) 3.81681 0.409205
\(88\) 0 0
\(89\) −3.81681 −0.404581 −0.202291 0.979326i \(-0.564839\pi\)
−0.202291 + 0.979326i \(0.564839\pi\)
\(90\) 0 0
\(91\) 12.4896 1.30927
\(92\) 0 0
\(93\) −6.20166 −0.643082
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) −6.67282 −0.677523 −0.338761 0.940872i \(-0.610008\pi\)
−0.338761 + 0.940872i \(0.610008\pi\)
\(98\) 0 0
\(99\) −5.81681 −0.584611
\(100\) 0 0
\(101\) 0.654353 0.0651105 0.0325553 0.999470i \(-0.489636\pi\)
0.0325553 + 0.999470i \(0.489636\pi\)
\(102\) 0 0
\(103\) 1.71203 0.168691 0.0843455 0.996437i \(-0.473120\pi\)
0.0843455 + 0.996437i \(0.473120\pi\)
\(104\) 0 0
\(105\) 4.67282 0.456021
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −9.05767 −0.867568 −0.433784 0.901017i \(-0.642822\pi\)
−0.433784 + 0.901017i \(0.642822\pi\)
\(110\) 0 0
\(111\) 12.0185 1.14074
\(112\) 0 0
\(113\) 11.5473 1.08628 0.543140 0.839642i \(-0.317235\pi\)
0.543140 + 0.839642i \(0.317235\pi\)
\(114\) 0 0
\(115\) −8.20166 −0.764809
\(116\) 0 0
\(117\) −2.67282 −0.247103
\(118\) 0 0
\(119\) 30.3249 2.77988
\(120\) 0 0
\(121\) 22.8353 2.07593
\(122\) 0 0
\(123\) −0.183190 −0.0165177
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 0 0
\(129\) −6.96080 −0.612864
\(130\) 0 0
\(131\) −2.18319 −0.190746 −0.0953731 0.995442i \(-0.530404\pi\)
−0.0953731 + 0.995442i \(0.530404\pi\)
\(132\) 0 0
\(133\) −4.67282 −0.405185
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) 4.36638 0.370351 0.185176 0.982705i \(-0.440715\pi\)
0.185176 + 0.982705i \(0.440715\pi\)
\(140\) 0 0
\(141\) −4.20166 −0.353844
\(142\) 0 0
\(143\) 15.5473 1.30013
\(144\) 0 0
\(145\) −3.81681 −0.316969
\(146\) 0 0
\(147\) −14.8353 −1.22359
\(148\) 0 0
\(149\) 4.28797 0.351284 0.175642 0.984454i \(-0.443800\pi\)
0.175642 + 0.984454i \(0.443800\pi\)
\(150\) 0 0
\(151\) −16.8930 −1.37473 −0.687365 0.726313i \(-0.741233\pi\)
−0.687365 + 0.726313i \(0.741233\pi\)
\(152\) 0 0
\(153\) −6.48963 −0.524656
\(154\) 0 0
\(155\) 6.20166 0.498129
\(156\) 0 0
\(157\) 16.3249 1.30287 0.651435 0.758704i \(-0.274167\pi\)
0.651435 + 0.758704i \(0.274167\pi\)
\(158\) 0 0
\(159\) −10.7776 −0.854720
\(160\) 0 0
\(161\) 38.3249 3.02043
\(162\) 0 0
\(163\) 18.0185 1.41132 0.705658 0.708553i \(-0.250652\pi\)
0.705658 + 0.708553i \(0.250652\pi\)
\(164\) 0 0
\(165\) 5.81681 0.452838
\(166\) 0 0
\(167\) 7.14399 0.552818 0.276409 0.961040i \(-0.410856\pi\)
0.276409 + 0.961040i \(0.410856\pi\)
\(168\) 0 0
\(169\) −5.85601 −0.450463
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) 0 0
\(173\) −22.4112 −1.70389 −0.851947 0.523628i \(-0.824578\pi\)
−0.851947 + 0.523628i \(0.824578\pi\)
\(174\) 0 0
\(175\) −4.67282 −0.353232
\(176\) 0 0
\(177\) −7.05767 −0.530487
\(178\) 0 0
\(179\) −16.0369 −1.19866 −0.599329 0.800503i \(-0.704566\pi\)
−0.599329 + 0.800503i \(0.704566\pi\)
\(180\) 0 0
\(181\) −11.9216 −0.886125 −0.443063 0.896491i \(-0.646108\pi\)
−0.443063 + 0.896491i \(0.646108\pi\)
\(182\) 0 0
\(183\) −5.14399 −0.380254
\(184\) 0 0
\(185\) −12.0185 −0.883616
\(186\) 0 0
\(187\) 37.7490 2.76048
\(188\) 0 0
\(189\) 4.67282 0.339898
\(190\) 0 0
\(191\) −8.47116 −0.612952 −0.306476 0.951878i \(-0.599150\pi\)
−0.306476 + 0.951878i \(0.599150\pi\)
\(192\) 0 0
\(193\) −13.7305 −0.988343 −0.494171 0.869364i \(-0.664528\pi\)
−0.494171 + 0.869364i \(0.664528\pi\)
\(194\) 0 0
\(195\) 2.67282 0.191405
\(196\) 0 0
\(197\) −19.4689 −1.38710 −0.693551 0.720408i \(-0.743955\pi\)
−0.693551 + 0.720408i \(0.743955\pi\)
\(198\) 0 0
\(199\) 0.942326 0.0667997 0.0333998 0.999442i \(-0.489367\pi\)
0.0333998 + 0.999442i \(0.489367\pi\)
\(200\) 0 0
\(201\) 10.6913 0.754106
\(202\) 0 0
\(203\) 17.8353 1.25179
\(204\) 0 0
\(205\) 0.183190 0.0127945
\(206\) 0 0
\(207\) −8.20166 −0.570055
\(208\) 0 0
\(209\) −5.81681 −0.402357
\(210\) 0 0
\(211\) 5.71203 0.393232 0.196616 0.980481i \(-0.437005\pi\)
0.196616 + 0.980481i \(0.437005\pi\)
\(212\) 0 0
\(213\) 11.0577 0.757659
\(214\) 0 0
\(215\) 6.96080 0.474722
\(216\) 0 0
\(217\) −28.9793 −1.96724
\(218\) 0 0
\(219\) 4.28797 0.289754
\(220\) 0 0
\(221\) 17.3456 1.16679
\(222\) 0 0
\(223\) 1.71203 0.114646 0.0573229 0.998356i \(-0.481744\pi\)
0.0573229 + 0.998356i \(0.481744\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 0.452692 0.0300462 0.0150231 0.999887i \(-0.495218\pi\)
0.0150231 + 0.999887i \(0.495218\pi\)
\(228\) 0 0
\(229\) −14.1233 −0.933291 −0.466645 0.884444i \(-0.654538\pi\)
−0.466645 + 0.884444i \(0.654538\pi\)
\(230\) 0 0
\(231\) −27.1809 −1.78837
\(232\) 0 0
\(233\) −11.7120 −0.767280 −0.383640 0.923483i \(-0.625330\pi\)
−0.383640 + 0.923483i \(0.625330\pi\)
\(234\) 0 0
\(235\) 4.20166 0.274086
\(236\) 0 0
\(237\) −6.28797 −0.408448
\(238\) 0 0
\(239\) −25.4874 −1.64864 −0.824321 0.566123i \(-0.808443\pi\)
−0.824321 + 0.566123i \(0.808443\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 14.8353 0.947791
\(246\) 0 0
\(247\) −2.67282 −0.170068
\(248\) 0 0
\(249\) 1.14399 0.0724972
\(250\) 0 0
\(251\) −3.12552 −0.197281 −0.0986404 0.995123i \(-0.531449\pi\)
−0.0986404 + 0.995123i \(0.531449\pi\)
\(252\) 0 0
\(253\) 47.7075 2.99935
\(254\) 0 0
\(255\) 6.48963 0.406397
\(256\) 0 0
\(257\) −14.5680 −0.908729 −0.454365 0.890816i \(-0.650134\pi\)
−0.454365 + 0.890816i \(0.650134\pi\)
\(258\) 0 0
\(259\) 56.1602 3.48962
\(260\) 0 0
\(261\) −3.81681 −0.236255
\(262\) 0 0
\(263\) −5.54731 −0.342062 −0.171031 0.985266i \(-0.554710\pi\)
−0.171031 + 0.985266i \(0.554710\pi\)
\(264\) 0 0
\(265\) 10.7776 0.662063
\(266\) 0 0
\(267\) 3.81681 0.233585
\(268\) 0 0
\(269\) 29.1625 1.77807 0.889033 0.457843i \(-0.151378\pi\)
0.889033 + 0.457843i \(0.151378\pi\)
\(270\) 0 0
\(271\) −1.92159 −0.116728 −0.0583642 0.998295i \(-0.518588\pi\)
−0.0583642 + 0.998295i \(0.518588\pi\)
\(272\) 0 0
\(273\) −12.4896 −0.755907
\(274\) 0 0
\(275\) −5.81681 −0.350767
\(276\) 0 0
\(277\) −26.9793 −1.62103 −0.810514 0.585720i \(-0.800812\pi\)
−0.810514 + 0.585720i \(0.800812\pi\)
\(278\) 0 0
\(279\) 6.20166 0.371284
\(280\) 0 0
\(281\) 4.39276 0.262050 0.131025 0.991379i \(-0.458173\pi\)
0.131025 + 0.991379i \(0.458173\pi\)
\(282\) 0 0
\(283\) 24.8824 1.47910 0.739552 0.673099i \(-0.235037\pi\)
0.739552 + 0.673099i \(0.235037\pi\)
\(284\) 0 0
\(285\) −1.00000 −0.0592349
\(286\) 0 0
\(287\) −0.856013 −0.0505289
\(288\) 0 0
\(289\) 25.1153 1.47737
\(290\) 0 0
\(291\) 6.67282 0.391168
\(292\) 0 0
\(293\) 1.83528 0.107218 0.0536091 0.998562i \(-0.482927\pi\)
0.0536091 + 0.998562i \(0.482927\pi\)
\(294\) 0 0
\(295\) 7.05767 0.410914
\(296\) 0 0
\(297\) 5.81681 0.337526
\(298\) 0 0
\(299\) 21.9216 1.26776
\(300\) 0 0
\(301\) −32.5266 −1.87480
\(302\) 0 0
\(303\) −0.654353 −0.0375916
\(304\) 0 0
\(305\) 5.14399 0.294544
\(306\) 0 0
\(307\) 12.3664 0.705787 0.352893 0.935664i \(-0.385198\pi\)
0.352893 + 0.935664i \(0.385198\pi\)
\(308\) 0 0
\(309\) −1.71203 −0.0973938
\(310\) 0 0
\(311\) 6.79608 0.385370 0.192685 0.981261i \(-0.438280\pi\)
0.192685 + 0.981261i \(0.438280\pi\)
\(312\) 0 0
\(313\) 5.23030 0.295634 0.147817 0.989015i \(-0.452775\pi\)
0.147817 + 0.989015i \(0.452775\pi\)
\(314\) 0 0
\(315\) −4.67282 −0.263284
\(316\) 0 0
\(317\) 31.7569 1.78364 0.891822 0.452387i \(-0.149427\pi\)
0.891822 + 0.452387i \(0.149427\pi\)
\(318\) 0 0
\(319\) 22.2017 1.24305
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.48963 −0.361093
\(324\) 0 0
\(325\) −2.67282 −0.148262
\(326\) 0 0
\(327\) 9.05767 0.500891
\(328\) 0 0
\(329\) −19.6336 −1.08244
\(330\) 0 0
\(331\) −12.8930 −0.708661 −0.354330 0.935120i \(-0.615291\pi\)
−0.354330 + 0.935120i \(0.615291\pi\)
\(332\) 0 0
\(333\) −12.0185 −0.658608
\(334\) 0 0
\(335\) −10.6913 −0.584128
\(336\) 0 0
\(337\) −24.2280 −1.31979 −0.659893 0.751360i \(-0.729398\pi\)
−0.659893 + 0.751360i \(0.729398\pi\)
\(338\) 0 0
\(339\) −11.5473 −0.627164
\(340\) 0 0
\(341\) −36.0739 −1.95351
\(342\) 0 0
\(343\) −36.6129 −1.97691
\(344\) 0 0
\(345\) 8.20166 0.441563
\(346\) 0 0
\(347\) 6.45269 0.346399 0.173199 0.984887i \(-0.444590\pi\)
0.173199 + 0.984887i \(0.444590\pi\)
\(348\) 0 0
\(349\) 11.3087 0.605341 0.302671 0.953095i \(-0.402122\pi\)
0.302671 + 0.953095i \(0.402122\pi\)
\(350\) 0 0
\(351\) 2.67282 0.142665
\(352\) 0 0
\(353\) −32.6913 −1.73998 −0.869991 0.493068i \(-0.835876\pi\)
−0.869991 + 0.493068i \(0.835876\pi\)
\(354\) 0 0
\(355\) −11.0577 −0.586880
\(356\) 0 0
\(357\) −30.3249 −1.60496
\(358\) 0 0
\(359\) −5.04711 −0.266376 −0.133188 0.991091i \(-0.542521\pi\)
−0.133188 + 0.991091i \(0.542521\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −22.8353 −1.19854
\(364\) 0 0
\(365\) −4.28797 −0.224443
\(366\) 0 0
\(367\) 34.2280 1.78669 0.893345 0.449372i \(-0.148352\pi\)
0.893345 + 0.449372i \(0.148352\pi\)
\(368\) 0 0
\(369\) 0.183190 0.00953648
\(370\) 0 0
\(371\) −50.3619 −2.61466
\(372\) 0 0
\(373\) 26.3064 1.36210 0.681048 0.732239i \(-0.261524\pi\)
0.681048 + 0.732239i \(0.261524\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 10.2017 0.525412
\(378\) 0 0
\(379\) 38.6050 1.98300 0.991502 0.130089i \(-0.0415262\pi\)
0.991502 + 0.130089i \(0.0415262\pi\)
\(380\) 0 0
\(381\) −4.00000 −0.204926
\(382\) 0 0
\(383\) −8.40332 −0.429390 −0.214695 0.976681i \(-0.568876\pi\)
−0.214695 + 0.976681i \(0.568876\pi\)
\(384\) 0 0
\(385\) 27.1809 1.38527
\(386\) 0 0
\(387\) 6.96080 0.353837
\(388\) 0 0
\(389\) 12.2880 0.623025 0.311512 0.950242i \(-0.399164\pi\)
0.311512 + 0.950242i \(0.399164\pi\)
\(390\) 0 0
\(391\) 53.2258 2.69174
\(392\) 0 0
\(393\) 2.18319 0.110127
\(394\) 0 0
\(395\) 6.28797 0.316382
\(396\) 0 0
\(397\) 34.6498 1.73903 0.869513 0.493911i \(-0.164433\pi\)
0.869513 + 0.493911i \(0.164433\pi\)
\(398\) 0 0
\(399\) 4.67282 0.233934
\(400\) 0 0
\(401\) −5.73840 −0.286562 −0.143281 0.989682i \(-0.545765\pi\)
−0.143281 + 0.989682i \(0.545765\pi\)
\(402\) 0 0
\(403\) −16.5759 −0.825707
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 69.9092 3.46527
\(408\) 0 0
\(409\) 28.9009 1.42906 0.714528 0.699607i \(-0.246642\pi\)
0.714528 + 0.699607i \(0.246642\pi\)
\(410\) 0 0
\(411\) −2.00000 −0.0986527
\(412\) 0 0
\(413\) −32.9793 −1.62280
\(414\) 0 0
\(415\) −1.14399 −0.0561561
\(416\) 0 0
\(417\) −4.36638 −0.213823
\(418\) 0 0
\(419\) 4.87448 0.238134 0.119067 0.992886i \(-0.462010\pi\)
0.119067 + 0.992886i \(0.462010\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) 4.20166 0.204292
\(424\) 0 0
\(425\) −6.48963 −0.314793
\(426\) 0 0
\(427\) −24.0369 −1.16323
\(428\) 0 0
\(429\) −15.5473 −0.750631
\(430\) 0 0
\(431\) −10.6544 −0.513202 −0.256601 0.966517i \(-0.582603\pi\)
−0.256601 + 0.966517i \(0.582603\pi\)
\(432\) 0 0
\(433\) −6.88239 −0.330747 −0.165373 0.986231i \(-0.552883\pi\)
−0.165373 + 0.986231i \(0.552883\pi\)
\(434\) 0 0
\(435\) 3.81681 0.183002
\(436\) 0 0
\(437\) −8.20166 −0.392339
\(438\) 0 0
\(439\) −40.0739 −1.91262 −0.956311 0.292351i \(-0.905562\pi\)
−0.956311 + 0.292351i \(0.905562\pi\)
\(440\) 0 0
\(441\) 14.8353 0.706442
\(442\) 0 0
\(443\) 30.8930 1.46777 0.733884 0.679274i \(-0.237705\pi\)
0.733884 + 0.679274i \(0.237705\pi\)
\(444\) 0 0
\(445\) −3.81681 −0.180934
\(446\) 0 0
\(447\) −4.28797 −0.202814
\(448\) 0 0
\(449\) −12.7961 −0.603884 −0.301942 0.953326i \(-0.597635\pi\)
−0.301942 + 0.953326i \(0.597635\pi\)
\(450\) 0 0
\(451\) −1.06558 −0.0501762
\(452\) 0 0
\(453\) 16.8930 0.793700
\(454\) 0 0
\(455\) 12.4896 0.585523
\(456\) 0 0
\(457\) 28.3249 1.32498 0.662492 0.749069i \(-0.269499\pi\)
0.662492 + 0.749069i \(0.269499\pi\)
\(458\) 0 0
\(459\) 6.48963 0.302910
\(460\) 0 0
\(461\) 1.42405 0.0663248 0.0331624 0.999450i \(-0.489442\pi\)
0.0331624 + 0.999450i \(0.489442\pi\)
\(462\) 0 0
\(463\) −31.7305 −1.47464 −0.737321 0.675543i \(-0.763909\pi\)
−0.737321 + 0.675543i \(0.763909\pi\)
\(464\) 0 0
\(465\) −6.20166 −0.287595
\(466\) 0 0
\(467\) 14.4896 0.670500 0.335250 0.942129i \(-0.391179\pi\)
0.335250 + 0.942129i \(0.391179\pi\)
\(468\) 0 0
\(469\) 49.9585 2.30687
\(470\) 0 0
\(471\) −16.3249 −0.752212
\(472\) 0 0
\(473\) −40.4896 −1.86172
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 10.7776 0.493473
\(478\) 0 0
\(479\) 31.1994 1.42554 0.712768 0.701399i \(-0.247441\pi\)
0.712768 + 0.701399i \(0.247441\pi\)
\(480\) 0 0
\(481\) 32.1233 1.46469
\(482\) 0 0
\(483\) −38.3249 −1.74384
\(484\) 0 0
\(485\) −6.67282 −0.302997
\(486\) 0 0
\(487\) −38.3249 −1.73667 −0.868334 0.495980i \(-0.834809\pi\)
−0.868334 + 0.495980i \(0.834809\pi\)
\(488\) 0 0
\(489\) −18.0185 −0.814823
\(490\) 0 0
\(491\) −15.1625 −0.684272 −0.342136 0.939650i \(-0.611150\pi\)
−0.342136 + 0.939650i \(0.611150\pi\)
\(492\) 0 0
\(493\) 24.7697 1.11557
\(494\) 0 0
\(495\) −5.81681 −0.261446
\(496\) 0 0
\(497\) 51.6706 2.31774
\(498\) 0 0
\(499\) 26.9009 1.20425 0.602124 0.798403i \(-0.294321\pi\)
0.602124 + 0.798403i \(0.294321\pi\)
\(500\) 0 0
\(501\) −7.14399 −0.319170
\(502\) 0 0
\(503\) −34.8560 −1.55415 −0.777076 0.629406i \(-0.783298\pi\)
−0.777076 + 0.629406i \(0.783298\pi\)
\(504\) 0 0
\(505\) 0.654353 0.0291183
\(506\) 0 0
\(507\) 5.85601 0.260075
\(508\) 0 0
\(509\) −12.7591 −0.565539 −0.282769 0.959188i \(-0.591253\pi\)
−0.282769 + 0.959188i \(0.591253\pi\)
\(510\) 0 0
\(511\) 20.0369 0.886382
\(512\) 0 0
\(513\) −1.00000 −0.0441511
\(514\) 0 0
\(515\) 1.71203 0.0754409
\(516\) 0 0
\(517\) −24.4403 −1.07488
\(518\) 0 0
\(519\) 22.4112 0.983744
\(520\) 0 0
\(521\) 5.52884 0.242223 0.121111 0.992639i \(-0.461354\pi\)
0.121111 + 0.992639i \(0.461354\pi\)
\(522\) 0 0
\(523\) −11.0577 −0.483518 −0.241759 0.970336i \(-0.577724\pi\)
−0.241759 + 0.970336i \(0.577724\pi\)
\(524\) 0 0
\(525\) 4.67282 0.203939
\(526\) 0 0
\(527\) −40.2465 −1.75317
\(528\) 0 0
\(529\) 44.2672 1.92466
\(530\) 0 0
\(531\) 7.05767 0.306277
\(532\) 0 0
\(533\) −0.489634 −0.0212084
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 16.0369 0.692045
\(538\) 0 0
\(539\) −86.2940 −3.71695
\(540\) 0 0
\(541\) −23.9585 −1.03006 −0.515029 0.857173i \(-0.672219\pi\)
−0.515029 + 0.857173i \(0.672219\pi\)
\(542\) 0 0
\(543\) 11.9216 0.511605
\(544\) 0 0
\(545\) −9.05767 −0.387988
\(546\) 0 0
\(547\) −0.209567 −0.00896042 −0.00448021 0.999990i \(-0.501426\pi\)
−0.00448021 + 0.999990i \(0.501426\pi\)
\(548\) 0 0
\(549\) 5.14399 0.219540
\(550\) 0 0
\(551\) −3.81681 −0.162602
\(552\) 0 0
\(553\) −29.3826 −1.24947
\(554\) 0 0
\(555\) 12.0185 0.510156
\(556\) 0 0
\(557\) −14.9793 −0.634692 −0.317346 0.948310i \(-0.602792\pi\)
−0.317346 + 0.948310i \(0.602792\pi\)
\(558\) 0 0
\(559\) −18.6050 −0.786907
\(560\) 0 0
\(561\) −37.7490 −1.59376
\(562\) 0 0
\(563\) −16.6992 −0.703787 −0.351894 0.936040i \(-0.614462\pi\)
−0.351894 + 0.936040i \(0.614462\pi\)
\(564\) 0 0
\(565\) 11.5473 0.485799
\(566\) 0 0
\(567\) −4.67282 −0.196240
\(568\) 0 0
\(569\) 34.5450 1.44820 0.724102 0.689693i \(-0.242255\pi\)
0.724102 + 0.689693i \(0.242255\pi\)
\(570\) 0 0
\(571\) 5.92159 0.247811 0.123905 0.992294i \(-0.460458\pi\)
0.123905 + 0.992294i \(0.460458\pi\)
\(572\) 0 0
\(573\) 8.47116 0.353888
\(574\) 0 0
\(575\) −8.20166 −0.342033
\(576\) 0 0
\(577\) 24.6544 1.02637 0.513187 0.858277i \(-0.328465\pi\)
0.513187 + 0.858277i \(0.328465\pi\)
\(578\) 0 0
\(579\) 13.7305 0.570620
\(580\) 0 0
\(581\) 5.34565 0.221775
\(582\) 0 0
\(583\) −62.6913 −2.59641
\(584\) 0 0
\(585\) −2.67282 −0.110508
\(586\) 0 0
\(587\) −12.2017 −0.503616 −0.251808 0.967777i \(-0.581025\pi\)
−0.251808 + 0.967777i \(0.581025\pi\)
\(588\) 0 0
\(589\) 6.20166 0.255535
\(590\) 0 0
\(591\) 19.4689 0.800844
\(592\) 0 0
\(593\) −1.02073 −0.0419164 −0.0209582 0.999780i \(-0.506672\pi\)
−0.0209582 + 0.999780i \(0.506672\pi\)
\(594\) 0 0
\(595\) 30.3249 1.24320
\(596\) 0 0
\(597\) −0.942326 −0.0385668
\(598\) 0 0
\(599\) −7.42405 −0.303339 −0.151669 0.988431i \(-0.548465\pi\)
−0.151669 + 0.988431i \(0.548465\pi\)
\(600\) 0 0
\(601\) 19.3456 0.789125 0.394563 0.918869i \(-0.370896\pi\)
0.394563 + 0.918869i \(0.370896\pi\)
\(602\) 0 0
\(603\) −10.6913 −0.435383
\(604\) 0 0
\(605\) 22.8353 0.928386
\(606\) 0 0
\(607\) 16.0369 0.650919 0.325460 0.945556i \(-0.394481\pi\)
0.325460 + 0.945556i \(0.394481\pi\)
\(608\) 0 0
\(609\) −17.8353 −0.722722
\(610\) 0 0
\(611\) −11.2303 −0.454329
\(612\) 0 0
\(613\) −36.1523 −1.46018 −0.730089 0.683352i \(-0.760521\pi\)
−0.730089 + 0.683352i \(0.760521\pi\)
\(614\) 0 0
\(615\) −0.183190 −0.00738692
\(616\) 0 0
\(617\) −40.4482 −1.62838 −0.814191 0.580597i \(-0.802819\pi\)
−0.814191 + 0.580597i \(0.802819\pi\)
\(618\) 0 0
\(619\) 4.19376 0.168561 0.0842806 0.996442i \(-0.473141\pi\)
0.0842806 + 0.996442i \(0.473141\pi\)
\(620\) 0 0
\(621\) 8.20166 0.329121
\(622\) 0 0
\(623\) 17.8353 0.714555
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 5.81681 0.232301
\(628\) 0 0
\(629\) 77.9955 3.10988
\(630\) 0 0
\(631\) −5.30871 −0.211336 −0.105668 0.994401i \(-0.533698\pi\)
−0.105668 + 0.994401i \(0.533698\pi\)
\(632\) 0 0
\(633\) −5.71203 −0.227033
\(634\) 0 0
\(635\) 4.00000 0.158735
\(636\) 0 0
\(637\) −39.6521 −1.57107
\(638\) 0 0
\(639\) −11.0577 −0.437435
\(640\) 0 0
\(641\) −7.24086 −0.285997 −0.142998 0.989723i \(-0.545674\pi\)
−0.142998 + 0.989723i \(0.545674\pi\)
\(642\) 0 0
\(643\) −2.38485 −0.0940493 −0.0470247 0.998894i \(-0.514974\pi\)
−0.0470247 + 0.998894i \(0.514974\pi\)
\(644\) 0 0
\(645\) −6.96080 −0.274081
\(646\) 0 0
\(647\) −1.47342 −0.0579263 −0.0289631 0.999580i \(-0.509221\pi\)
−0.0289631 + 0.999580i \(0.509221\pi\)
\(648\) 0 0
\(649\) −41.0532 −1.61148
\(650\) 0 0
\(651\) 28.9793 1.13579
\(652\) 0 0
\(653\) −25.9137 −1.01408 −0.507040 0.861922i \(-0.669261\pi\)
−0.507040 + 0.861922i \(0.669261\pi\)
\(654\) 0 0
\(655\) −2.18319 −0.0853043
\(656\) 0 0
\(657\) −4.28797 −0.167290
\(658\) 0 0
\(659\) 24.9793 0.973054 0.486527 0.873666i \(-0.338264\pi\)
0.486527 + 0.873666i \(0.338264\pi\)
\(660\) 0 0
\(661\) 39.4195 1.53324 0.766621 0.642100i \(-0.221937\pi\)
0.766621 + 0.642100i \(0.221937\pi\)
\(662\) 0 0
\(663\) −17.3456 −0.673649
\(664\) 0 0
\(665\) −4.67282 −0.181204
\(666\) 0 0
\(667\) 31.3042 1.21210
\(668\) 0 0
\(669\) −1.71203 −0.0661908
\(670\) 0 0
\(671\) −29.9216 −1.15511
\(672\) 0 0
\(673\) 12.0185 0.463278 0.231639 0.972802i \(-0.425591\pi\)
0.231639 + 0.972802i \(0.425591\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 22.2017 0.853279 0.426640 0.904422i \(-0.359697\pi\)
0.426640 + 0.904422i \(0.359697\pi\)
\(678\) 0 0
\(679\) 31.1809 1.19661
\(680\) 0 0
\(681\) −0.452692 −0.0173472
\(682\) 0 0
\(683\) 32.0739 1.22727 0.613637 0.789589i \(-0.289706\pi\)
0.613637 + 0.789589i \(0.289706\pi\)
\(684\) 0 0
\(685\) 2.00000 0.0764161
\(686\) 0 0
\(687\) 14.1233 0.538836
\(688\) 0 0
\(689\) −28.8066 −1.09745
\(690\) 0 0
\(691\) −44.0369 −1.67524 −0.837622 0.546250i \(-0.816055\pi\)
−0.837622 + 0.546250i \(0.816055\pi\)
\(692\) 0 0
\(693\) 27.1809 1.03252
\(694\) 0 0
\(695\) 4.36638 0.165626
\(696\) 0 0
\(697\) −1.18883 −0.0450303
\(698\) 0 0
\(699\) 11.7120 0.442990
\(700\) 0 0
\(701\) −18.9793 −0.716837 −0.358419 0.933561i \(-0.616684\pi\)
−0.358419 + 0.933561i \(0.616684\pi\)
\(702\) 0 0
\(703\) −12.0185 −0.453285
\(704\) 0 0
\(705\) −4.20166 −0.158244
\(706\) 0 0
\(707\) −3.05767 −0.114996
\(708\) 0 0
\(709\) −2.12325 −0.0797405 −0.0398702 0.999205i \(-0.512694\pi\)
−0.0398702 + 0.999205i \(0.512694\pi\)
\(710\) 0 0
\(711\) 6.28797 0.235817
\(712\) 0 0
\(713\) −50.8639 −1.90487
\(714\) 0 0
\(715\) 15.5473 0.581436
\(716\) 0 0
\(717\) 25.4874 0.951843
\(718\) 0 0
\(719\) 11.5658 0.431331 0.215665 0.976467i \(-0.430808\pi\)
0.215665 + 0.976467i \(0.430808\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 0 0
\(723\) −14.0000 −0.520666
\(724\) 0 0
\(725\) −3.81681 −0.141753
\(726\) 0 0
\(727\) −32.3064 −1.19818 −0.599090 0.800682i \(-0.704471\pi\)
−0.599090 + 0.800682i \(0.704471\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −45.1730 −1.67078
\(732\) 0 0
\(733\) 18.4033 0.679742 0.339871 0.940472i \(-0.389617\pi\)
0.339871 + 0.940472i \(0.389617\pi\)
\(734\) 0 0
\(735\) −14.8353 −0.547208
\(736\) 0 0
\(737\) 62.1892 2.29077
\(738\) 0 0
\(739\) 28.0000 1.03000 0.514998 0.857191i \(-0.327793\pi\)
0.514998 + 0.857191i \(0.327793\pi\)
\(740\) 0 0
\(741\) 2.67282 0.0981886
\(742\) 0 0
\(743\) −33.5552 −1.23102 −0.615511 0.788129i \(-0.711050\pi\)
−0.615511 + 0.788129i \(0.711050\pi\)
\(744\) 0 0
\(745\) 4.28797 0.157099
\(746\) 0 0
\(747\) −1.14399 −0.0418563
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −9.06558 −0.330808 −0.165404 0.986226i \(-0.552893\pi\)
−0.165404 + 0.986226i \(0.552893\pi\)
\(752\) 0 0
\(753\) 3.12552 0.113900
\(754\) 0 0
\(755\) −16.8930 −0.614798
\(756\) 0 0
\(757\) 49.1316 1.78572 0.892858 0.450337i \(-0.148696\pi\)
0.892858 + 0.450337i \(0.148696\pi\)
\(758\) 0 0
\(759\) −47.7075 −1.73167
\(760\) 0 0
\(761\) −26.4033 −0.957120 −0.478560 0.878055i \(-0.658841\pi\)
−0.478560 + 0.878055i \(0.658841\pi\)
\(762\) 0 0
\(763\) 42.3249 1.53226
\(764\) 0 0
\(765\) −6.48963 −0.234633
\(766\) 0 0
\(767\) −18.8639 −0.681137
\(768\) 0 0
\(769\) 16.6913 0.601903 0.300952 0.953639i \(-0.402696\pi\)
0.300952 + 0.953639i \(0.402696\pi\)
\(770\) 0 0
\(771\) 14.5680 0.524655
\(772\) 0 0
\(773\) 37.8722 1.36217 0.681085 0.732205i \(-0.261509\pi\)
0.681085 + 0.732205i \(0.261509\pi\)
\(774\) 0 0
\(775\) 6.20166 0.222770
\(776\) 0 0
\(777\) −56.1602 −2.01474
\(778\) 0 0
\(779\) 0.183190 0.00656345
\(780\) 0 0
\(781\) 64.3204 2.30156
\(782\) 0 0
\(783\) 3.81681 0.136402
\(784\) 0 0
\(785\) 16.3249 0.582661
\(786\) 0 0
\(787\) 14.4817 0.516218 0.258109 0.966116i \(-0.416901\pi\)
0.258109 + 0.966116i \(0.416901\pi\)
\(788\) 0 0
\(789\) 5.54731 0.197489
\(790\) 0 0
\(791\) −53.9585 −1.91854
\(792\) 0 0
\(793\) −13.7490 −0.488240
\(794\) 0 0
\(795\) −10.7776 −0.382242
\(796\) 0 0
\(797\) −42.6419 −1.51045 −0.755227 0.655463i \(-0.772473\pi\)
−0.755227 + 0.655463i \(0.772473\pi\)
\(798\) 0 0
\(799\) −27.2672 −0.964646
\(800\) 0 0
\(801\) −3.81681 −0.134860
\(802\) 0 0
\(803\) 24.9423 0.880196
\(804\) 0 0
\(805\) 38.3249 1.35078
\(806\) 0 0
\(807\) −29.1625 −1.02657
\(808\) 0 0
\(809\) −41.6706 −1.46506 −0.732529 0.680735i \(-0.761660\pi\)
−0.732529 + 0.680735i \(0.761660\pi\)
\(810\) 0 0
\(811\) −53.9585 −1.89474 −0.947370 0.320140i \(-0.896270\pi\)
−0.947370 + 0.320140i \(0.896270\pi\)
\(812\) 0 0
\(813\) 1.92159 0.0673932
\(814\) 0 0
\(815\) 18.0185 0.631160
\(816\) 0 0
\(817\) 6.96080 0.243527
\(818\) 0 0
\(819\) 12.4896 0.436423
\(820\) 0 0
\(821\) 7.74897 0.270441 0.135220 0.990816i \(-0.456826\pi\)
0.135220 + 0.990816i \(0.456826\pi\)
\(822\) 0 0
\(823\) 38.0554 1.32653 0.663264 0.748385i \(-0.269171\pi\)
0.663264 + 0.748385i \(0.269171\pi\)
\(824\) 0 0
\(825\) 5.81681 0.202515
\(826\) 0 0
\(827\) 48.9299 1.70146 0.850730 0.525604i \(-0.176160\pi\)
0.850730 + 0.525604i \(0.176160\pi\)
\(828\) 0 0
\(829\) −18.0369 −0.626449 −0.313224 0.949679i \(-0.601409\pi\)
−0.313224 + 0.949679i \(0.601409\pi\)
\(830\) 0 0
\(831\) 26.9793 0.935900
\(832\) 0 0
\(833\) −96.2755 −3.33575
\(834\) 0 0
\(835\) 7.14399 0.247228
\(836\) 0 0
\(837\) −6.20166 −0.214361
\(838\) 0 0
\(839\) −27.0577 −0.934135 −0.467067 0.884222i \(-0.654689\pi\)
−0.467067 + 0.884222i \(0.654689\pi\)
\(840\) 0 0
\(841\) −14.4320 −0.497654
\(842\) 0 0
\(843\) −4.39276 −0.151295
\(844\) 0 0
\(845\) −5.85601 −0.201453
\(846\) 0 0
\(847\) −106.705 −3.66644
\(848\) 0 0
\(849\) −24.8824 −0.853961
\(850\) 0 0
\(851\) 98.5714 3.37898
\(852\) 0 0
\(853\) −41.6336 −1.42551 −0.712754 0.701414i \(-0.752552\pi\)
−0.712754 + 0.701414i \(0.752552\pi\)
\(854\) 0 0
\(855\) 1.00000 0.0341993
\(856\) 0 0
\(857\) 45.8722 1.56697 0.783483 0.621414i \(-0.213441\pi\)
0.783483 + 0.621414i \(0.213441\pi\)
\(858\) 0 0
\(859\) −30.5187 −1.04128 −0.520642 0.853775i \(-0.674307\pi\)
−0.520642 + 0.853775i \(0.674307\pi\)
\(860\) 0 0
\(861\) 0.856013 0.0291729
\(862\) 0 0
\(863\) −7.42405 −0.252718 −0.126359 0.991985i \(-0.540329\pi\)
−0.126359 + 0.991985i \(0.540329\pi\)
\(864\) 0 0
\(865\) −22.4112 −0.762005
\(866\) 0 0
\(867\) −25.1153 −0.852962
\(868\) 0 0
\(869\) −36.5759 −1.24075
\(870\) 0 0
\(871\) 28.5759 0.968259
\(872\) 0 0
\(873\) −6.67282 −0.225841
\(874\) 0 0
\(875\) −4.67282 −0.157970
\(876\) 0 0
\(877\) −24.0554 −0.812294 −0.406147 0.913808i \(-0.633128\pi\)
−0.406147 + 0.913808i \(0.633128\pi\)
\(878\) 0 0
\(879\) −1.83528 −0.0619025
\(880\) 0 0
\(881\) −0.481728 −0.0162298 −0.00811492 0.999967i \(-0.502583\pi\)
−0.00811492 + 0.999967i \(0.502583\pi\)
\(882\) 0 0
\(883\) −25.4056 −0.854966 −0.427483 0.904023i \(-0.640600\pi\)
−0.427483 + 0.904023i \(0.640600\pi\)
\(884\) 0 0
\(885\) −7.05767 −0.237241
\(886\) 0 0
\(887\) −28.2307 −0.947894 −0.473947 0.880553i \(-0.657171\pi\)
−0.473947 + 0.880553i \(0.657171\pi\)
\(888\) 0 0
\(889\) −18.6913 −0.626886
\(890\) 0 0
\(891\) −5.81681 −0.194870
\(892\) 0 0
\(893\) 4.20166 0.140603
\(894\) 0 0
\(895\) −16.0369 −0.536056
\(896\) 0 0
\(897\) −21.9216 −0.731941
\(898\) 0 0
\(899\) −23.6706 −0.789457
\(900\) 0 0
\(901\) −69.9427 −2.33013
\(902\) 0 0
\(903\) 32.5266 1.08242
\(904\) 0 0
\(905\) −11.9216 −0.396287
\(906\) 0 0
\(907\) 37.1888 1.23483 0.617417 0.786636i \(-0.288179\pi\)
0.617417 + 0.786636i \(0.288179\pi\)
\(908\) 0 0
\(909\) 0.654353 0.0217035
\(910\) 0 0
\(911\) −18.5187 −0.613551 −0.306775 0.951782i \(-0.599250\pi\)
−0.306775 + 0.951782i \(0.599250\pi\)
\(912\) 0 0
\(913\) 6.65435 0.220227
\(914\) 0 0
\(915\) −5.14399 −0.170055
\(916\) 0 0
\(917\) 10.2017 0.336889
\(918\) 0 0
\(919\) −12.3294 −0.406711 −0.203355 0.979105i \(-0.565185\pi\)
−0.203355 + 0.979105i \(0.565185\pi\)
\(920\) 0 0
\(921\) −12.3664 −0.407486
\(922\) 0 0
\(923\) 29.5552 0.972822
\(924\) 0 0
\(925\) −12.0185 −0.395165
\(926\) 0 0
\(927\) 1.71203 0.0562303
\(928\) 0 0
\(929\) −7.67508 −0.251811 −0.125906 0.992042i \(-0.540184\pi\)
−0.125906 + 0.992042i \(0.540184\pi\)
\(930\) 0 0
\(931\) 14.8353 0.486207
\(932\) 0 0
\(933\) −6.79608 −0.222494
\(934\) 0 0
\(935\) 37.7490 1.23452
\(936\) 0 0
\(937\) −9.05767 −0.295901 −0.147951 0.988995i \(-0.547268\pi\)
−0.147951 + 0.988995i \(0.547268\pi\)
\(938\) 0 0
\(939\) −5.23030 −0.170684
\(940\) 0 0
\(941\) −56.2201 −1.83272 −0.916362 0.400351i \(-0.868888\pi\)
−0.916362 + 0.400351i \(0.868888\pi\)
\(942\) 0 0
\(943\) −1.50246 −0.0489268
\(944\) 0 0
\(945\) 4.67282 0.152007
\(946\) 0 0
\(947\) 33.2179 1.07944 0.539718 0.841846i \(-0.318531\pi\)
0.539718 + 0.841846i \(0.318531\pi\)
\(948\) 0 0
\(949\) 11.4610 0.372040
\(950\) 0 0
\(951\) −31.7569 −1.02979
\(952\) 0 0
\(953\) 6.81455 0.220745 0.110372 0.993890i \(-0.464796\pi\)
0.110372 + 0.993890i \(0.464796\pi\)
\(954\) 0 0
\(955\) −8.47116 −0.274120
\(956\) 0 0
\(957\) −22.2017 −0.717678
\(958\) 0 0
\(959\) −9.34565 −0.301787
\(960\) 0 0
\(961\) 7.46060 0.240664
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −13.7305 −0.442000
\(966\) 0 0
\(967\) −45.2857 −1.45629 −0.728145 0.685423i \(-0.759617\pi\)
−0.728145 + 0.685423i \(0.759617\pi\)
\(968\) 0 0
\(969\) 6.48963 0.208477
\(970\) 0 0
\(971\) −15.0207 −0.482038 −0.241019 0.970520i \(-0.577482\pi\)
−0.241019 + 0.970520i \(0.577482\pi\)
\(972\) 0 0
\(973\) −20.4033 −0.654100
\(974\) 0 0
\(975\) 2.67282 0.0855989
\(976\) 0 0
\(977\) 6.77761 0.216835 0.108417 0.994105i \(-0.465422\pi\)
0.108417 + 0.994105i \(0.465422\pi\)
\(978\) 0 0
\(979\) 22.2017 0.709568
\(980\) 0 0
\(981\) −9.05767 −0.289189
\(982\) 0 0
\(983\) −33.1025 −1.05581 −0.527903 0.849305i \(-0.677022\pi\)
−0.527903 + 0.849305i \(0.677022\pi\)
\(984\) 0 0
\(985\) −19.4689 −0.620331
\(986\) 0 0
\(987\) 19.6336 0.624945
\(988\) 0 0
\(989\) −57.0901 −1.81536
\(990\) 0 0
\(991\) 47.2672 1.50149 0.750747 0.660590i \(-0.229694\pi\)
0.750747 + 0.660590i \(0.229694\pi\)
\(992\) 0 0
\(993\) 12.8930 0.409146
\(994\) 0 0
\(995\) 0.942326 0.0298737
\(996\) 0 0
\(997\) 4.09422 0.129665 0.0648326 0.997896i \(-0.479349\pi\)
0.0648326 + 0.997896i \(0.479349\pi\)
\(998\) 0 0
\(999\) 12.0185 0.380248
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 4560.2.a.br.1.1 3
4.3 odd 2 1140.2.a.g.1.3 3
12.11 even 2 3420.2.a.m.1.3 3
20.3 even 4 5700.2.f.q.3649.4 6
20.7 even 4 5700.2.f.q.3649.3 6
20.19 odd 2 5700.2.a.w.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1140.2.a.g.1.3 3 4.3 odd 2
3420.2.a.m.1.3 3 12.11 even 2
4560.2.a.br.1.1 3 1.1 even 1 trivial
5700.2.a.w.1.1 3 20.19 odd 2
5700.2.f.q.3649.3 6 20.7 even 4
5700.2.f.q.3649.4 6 20.3 even 4