Properties

Label 6025.2.a.p.1.17
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.779313 q^{2} -2.96208 q^{3} -1.39267 q^{4} +2.30839 q^{6} -0.937135 q^{7} +2.64395 q^{8} +5.77395 q^{9} +O(q^{10})\) \(q-0.779313 q^{2} -2.96208 q^{3} -1.39267 q^{4} +2.30839 q^{6} -0.937135 q^{7} +2.64395 q^{8} +5.77395 q^{9} +1.14921 q^{11} +4.12521 q^{12} +5.29590 q^{13} +0.730321 q^{14} +0.724873 q^{16} +4.50874 q^{17} -4.49971 q^{18} -5.43811 q^{19} +2.77587 q^{21} -0.895592 q^{22} -1.97941 q^{23} -7.83161 q^{24} -4.12716 q^{26} -8.21666 q^{27} +1.30512 q^{28} -7.61477 q^{29} -9.12642 q^{31} -5.85281 q^{32} -3.40405 q^{33} -3.51372 q^{34} -8.04121 q^{36} +5.51656 q^{37} +4.23799 q^{38} -15.6869 q^{39} +6.55338 q^{41} -2.16327 q^{42} +0.588990 q^{43} -1.60047 q^{44} +1.54258 q^{46} -2.18888 q^{47} -2.14714 q^{48} -6.12178 q^{49} -13.3553 q^{51} -7.37544 q^{52} -1.78455 q^{53} +6.40335 q^{54} -2.47774 q^{56} +16.1081 q^{57} +5.93429 q^{58} +12.8940 q^{59} -11.6611 q^{61} +7.11234 q^{62} -5.41096 q^{63} +3.11143 q^{64} +2.65282 q^{66} +13.0749 q^{67} -6.27919 q^{68} +5.86318 q^{69} -3.64218 q^{71} +15.2660 q^{72} +7.30821 q^{73} -4.29913 q^{74} +7.57350 q^{76} -1.07696 q^{77} +12.2250 q^{78} +11.5369 q^{79} +7.01661 q^{81} -5.10713 q^{82} -14.6009 q^{83} -3.86588 q^{84} -0.459007 q^{86} +22.5556 q^{87} +3.03845 q^{88} -3.52126 q^{89} -4.96297 q^{91} +2.75667 q^{92} +27.0332 q^{93} +1.70582 q^{94} +17.3365 q^{96} -6.10294 q^{97} +4.77078 q^{98} +6.63546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.779313 −0.551058 −0.275529 0.961293i \(-0.588853\pi\)
−0.275529 + 0.961293i \(0.588853\pi\)
\(3\) −2.96208 −1.71016 −0.855080 0.518496i \(-0.826492\pi\)
−0.855080 + 0.518496i \(0.826492\pi\)
\(4\) −1.39267 −0.696335
\(5\) 0 0
\(6\) 2.30839 0.942397
\(7\) −0.937135 −0.354204 −0.177102 0.984193i \(-0.556672\pi\)
−0.177102 + 0.984193i \(0.556672\pi\)
\(8\) 2.64395 0.934779
\(9\) 5.77395 1.92465
\(10\) 0 0
\(11\) 1.14921 0.346499 0.173249 0.984878i \(-0.444573\pi\)
0.173249 + 0.984878i \(0.444573\pi\)
\(12\) 4.12521 1.19085
\(13\) 5.29590 1.46882 0.734409 0.678707i \(-0.237459\pi\)
0.734409 + 0.678707i \(0.237459\pi\)
\(14\) 0.730321 0.195187
\(15\) 0 0
\(16\) 0.724873 0.181218
\(17\) 4.50874 1.09353 0.546765 0.837286i \(-0.315859\pi\)
0.546765 + 0.837286i \(0.315859\pi\)
\(18\) −4.49971 −1.06059
\(19\) −5.43811 −1.24759 −0.623794 0.781589i \(-0.714410\pi\)
−0.623794 + 0.781589i \(0.714410\pi\)
\(20\) 0 0
\(21\) 2.77587 0.605745
\(22\) −0.895592 −0.190941
\(23\) −1.97941 −0.412736 −0.206368 0.978474i \(-0.566164\pi\)
−0.206368 + 0.978474i \(0.566164\pi\)
\(24\) −7.83161 −1.59862
\(25\) 0 0
\(26\) −4.12716 −0.809403
\(27\) −8.21666 −1.58130
\(28\) 1.30512 0.246644
\(29\) −7.61477 −1.41403 −0.707014 0.707200i \(-0.749958\pi\)
−0.707014 + 0.707200i \(0.749958\pi\)
\(30\) 0 0
\(31\) −9.12642 −1.63915 −0.819577 0.572969i \(-0.805792\pi\)
−0.819577 + 0.572969i \(0.805792\pi\)
\(32\) −5.85281 −1.03464
\(33\) −3.40405 −0.592569
\(34\) −3.51372 −0.602598
\(35\) 0 0
\(36\) −8.04121 −1.34020
\(37\) 5.51656 0.906917 0.453458 0.891277i \(-0.350190\pi\)
0.453458 + 0.891277i \(0.350190\pi\)
\(38\) 4.23799 0.687493
\(39\) −15.6869 −2.51191
\(40\) 0 0
\(41\) 6.55338 1.02347 0.511733 0.859145i \(-0.329004\pi\)
0.511733 + 0.859145i \(0.329004\pi\)
\(42\) −2.16327 −0.333800
\(43\) 0.588990 0.0898201 0.0449100 0.998991i \(-0.485700\pi\)
0.0449100 + 0.998991i \(0.485700\pi\)
\(44\) −1.60047 −0.241279
\(45\) 0 0
\(46\) 1.54258 0.227441
\(47\) −2.18888 −0.319281 −0.159640 0.987175i \(-0.551033\pi\)
−0.159640 + 0.987175i \(0.551033\pi\)
\(48\) −2.14714 −0.309912
\(49\) −6.12178 −0.874540
\(50\) 0 0
\(51\) −13.3553 −1.87011
\(52\) −7.37544 −1.02279
\(53\) −1.78455 −0.245127 −0.122564 0.992461i \(-0.539112\pi\)
−0.122564 + 0.992461i \(0.539112\pi\)
\(54\) 6.40335 0.871386
\(55\) 0 0
\(56\) −2.47774 −0.331102
\(57\) 16.1081 2.13358
\(58\) 5.93429 0.779211
\(59\) 12.8940 1.67866 0.839331 0.543621i \(-0.182947\pi\)
0.839331 + 0.543621i \(0.182947\pi\)
\(60\) 0 0
\(61\) −11.6611 −1.49305 −0.746527 0.665356i \(-0.768280\pi\)
−0.746527 + 0.665356i \(0.768280\pi\)
\(62\) 7.11234 0.903269
\(63\) −5.41096 −0.681717
\(64\) 3.11143 0.388928
\(65\) 0 0
\(66\) 2.65282 0.326540
\(67\) 13.0749 1.59735 0.798675 0.601762i \(-0.205535\pi\)
0.798675 + 0.601762i \(0.205535\pi\)
\(68\) −6.27919 −0.761463
\(69\) 5.86318 0.705844
\(70\) 0 0
\(71\) −3.64218 −0.432248 −0.216124 0.976366i \(-0.569342\pi\)
−0.216124 + 0.976366i \(0.569342\pi\)
\(72\) 15.2660 1.79912
\(73\) 7.30821 0.855362 0.427681 0.903930i \(-0.359331\pi\)
0.427681 + 0.903930i \(0.359331\pi\)
\(74\) −4.29913 −0.499763
\(75\) 0 0
\(76\) 7.57350 0.868740
\(77\) −1.07696 −0.122731
\(78\) 12.2250 1.38421
\(79\) 11.5369 1.29800 0.649001 0.760788i \(-0.275187\pi\)
0.649001 + 0.760788i \(0.275187\pi\)
\(80\) 0 0
\(81\) 7.01661 0.779624
\(82\) −5.10713 −0.563988
\(83\) −14.6009 −1.60266 −0.801330 0.598223i \(-0.795874\pi\)
−0.801330 + 0.598223i \(0.795874\pi\)
\(84\) −3.86588 −0.421802
\(85\) 0 0
\(86\) −0.459007 −0.0494960
\(87\) 22.5556 2.41821
\(88\) 3.03845 0.323900
\(89\) −3.52126 −0.373253 −0.186626 0.982431i \(-0.559755\pi\)
−0.186626 + 0.982431i \(0.559755\pi\)
\(90\) 0 0
\(91\) −4.96297 −0.520261
\(92\) 2.75667 0.287402
\(93\) 27.0332 2.80322
\(94\) 1.70582 0.175942
\(95\) 0 0
\(96\) 17.3365 1.76940
\(97\) −6.10294 −0.619660 −0.309830 0.950792i \(-0.600272\pi\)
−0.309830 + 0.950792i \(0.600272\pi\)
\(98\) 4.77078 0.481922
\(99\) 6.63546 0.666889
\(100\) 0 0
\(101\) 14.0435 1.39738 0.698690 0.715425i \(-0.253767\pi\)
0.698690 + 0.715425i \(0.253767\pi\)
\(102\) 10.4079 1.03054
\(103\) −3.35765 −0.330840 −0.165420 0.986223i \(-0.552898\pi\)
−0.165420 + 0.986223i \(0.552898\pi\)
\(104\) 14.0021 1.37302
\(105\) 0 0
\(106\) 1.39073 0.135079
\(107\) −11.9005 −1.15046 −0.575231 0.817991i \(-0.695088\pi\)
−0.575231 + 0.817991i \(0.695088\pi\)
\(108\) 11.4431 1.10111
\(109\) 3.16523 0.303174 0.151587 0.988444i \(-0.451562\pi\)
0.151587 + 0.988444i \(0.451562\pi\)
\(110\) 0 0
\(111\) −16.3405 −1.55097
\(112\) −0.679304 −0.0641882
\(113\) 20.3262 1.91213 0.956064 0.293159i \(-0.0947065\pi\)
0.956064 + 0.293159i \(0.0947065\pi\)
\(114\) −12.5533 −1.17572
\(115\) 0 0
\(116\) 10.6049 0.984638
\(117\) 30.5782 2.82696
\(118\) −10.0485 −0.925039
\(119\) −4.22529 −0.387332
\(120\) 0 0
\(121\) −9.67932 −0.879939
\(122\) 9.08766 0.822758
\(123\) −19.4117 −1.75029
\(124\) 12.7101 1.14140
\(125\) 0 0
\(126\) 4.21684 0.375666
\(127\) 2.92926 0.259930 0.129965 0.991519i \(-0.458514\pi\)
0.129965 + 0.991519i \(0.458514\pi\)
\(128\) 9.28084 0.820319
\(129\) −1.74464 −0.153607
\(130\) 0 0
\(131\) 1.87187 0.163546 0.0817732 0.996651i \(-0.473942\pi\)
0.0817732 + 0.996651i \(0.473942\pi\)
\(132\) 4.74072 0.412626
\(133\) 5.09624 0.441900
\(134\) −10.1894 −0.880232
\(135\) 0 0
\(136\) 11.9209 1.02221
\(137\) −5.93050 −0.506677 −0.253339 0.967378i \(-0.581529\pi\)
−0.253339 + 0.967378i \(0.581529\pi\)
\(138\) −4.56925 −0.388961
\(139\) −18.4127 −1.56174 −0.780871 0.624692i \(-0.785225\pi\)
−0.780871 + 0.624692i \(0.785225\pi\)
\(140\) 0 0
\(141\) 6.48365 0.546021
\(142\) 2.83840 0.238193
\(143\) 6.08608 0.508944
\(144\) 4.18538 0.348782
\(145\) 0 0
\(146\) −5.69539 −0.471354
\(147\) 18.1332 1.49560
\(148\) −7.68275 −0.631518
\(149\) 18.9945 1.55609 0.778044 0.628210i \(-0.216212\pi\)
0.778044 + 0.628210i \(0.216212\pi\)
\(150\) 0 0
\(151\) −6.67177 −0.542941 −0.271471 0.962447i \(-0.587510\pi\)
−0.271471 + 0.962447i \(0.587510\pi\)
\(152\) −14.3781 −1.16622
\(153\) 26.0332 2.10466
\(154\) 0.839290 0.0676319
\(155\) 0 0
\(156\) 21.8467 1.74913
\(157\) 18.4397 1.47165 0.735825 0.677172i \(-0.236794\pi\)
0.735825 + 0.677172i \(0.236794\pi\)
\(158\) −8.99085 −0.715274
\(159\) 5.28599 0.419207
\(160\) 0 0
\(161\) 1.85497 0.146192
\(162\) −5.46814 −0.429618
\(163\) −21.4962 −1.68371 −0.841857 0.539701i \(-0.818537\pi\)
−0.841857 + 0.539701i \(0.818537\pi\)
\(164\) −9.12669 −0.712675
\(165\) 0 0
\(166\) 11.3787 0.883158
\(167\) 1.19381 0.0923801 0.0461900 0.998933i \(-0.485292\pi\)
0.0461900 + 0.998933i \(0.485292\pi\)
\(168\) 7.33928 0.566237
\(169\) 15.0465 1.15743
\(170\) 0 0
\(171\) −31.3994 −2.40117
\(172\) −0.820269 −0.0625449
\(173\) 11.4268 0.868765 0.434383 0.900728i \(-0.356967\pi\)
0.434383 + 0.900728i \(0.356967\pi\)
\(174\) −17.5779 −1.33258
\(175\) 0 0
\(176\) 0.833029 0.0627919
\(177\) −38.1932 −2.87078
\(178\) 2.74417 0.205684
\(179\) −7.02801 −0.525298 −0.262649 0.964891i \(-0.584596\pi\)
−0.262649 + 0.964891i \(0.584596\pi\)
\(180\) 0 0
\(181\) −21.4027 −1.59085 −0.795423 0.606054i \(-0.792752\pi\)
−0.795423 + 0.606054i \(0.792752\pi\)
\(182\) 3.86771 0.286694
\(183\) 34.5412 2.55336
\(184\) −5.23347 −0.385816
\(185\) 0 0
\(186\) −21.0674 −1.54473
\(187\) 5.18147 0.378907
\(188\) 3.04839 0.222327
\(189\) 7.70012 0.560101
\(190\) 0 0
\(191\) −9.75588 −0.705911 −0.352955 0.935640i \(-0.614823\pi\)
−0.352955 + 0.935640i \(0.614823\pi\)
\(192\) −9.21631 −0.665130
\(193\) −24.2856 −1.74812 −0.874058 0.485822i \(-0.838520\pi\)
−0.874058 + 0.485822i \(0.838520\pi\)
\(194\) 4.75610 0.341468
\(195\) 0 0
\(196\) 8.52562 0.608973
\(197\) −8.38894 −0.597687 −0.298844 0.954302i \(-0.596601\pi\)
−0.298844 + 0.954302i \(0.596601\pi\)
\(198\) −5.17110 −0.367494
\(199\) 21.0515 1.49230 0.746152 0.665776i \(-0.231899\pi\)
0.746152 + 0.665776i \(0.231899\pi\)
\(200\) 0 0
\(201\) −38.7289 −2.73173
\(202\) −10.9443 −0.770037
\(203\) 7.13607 0.500854
\(204\) 18.5995 1.30222
\(205\) 0 0
\(206\) 2.61666 0.182312
\(207\) −11.4290 −0.794371
\(208\) 3.83886 0.266177
\(209\) −6.24951 −0.432288
\(210\) 0 0
\(211\) −4.81534 −0.331502 −0.165751 0.986168i \(-0.553005\pi\)
−0.165751 + 0.986168i \(0.553005\pi\)
\(212\) 2.48529 0.170691
\(213\) 10.7885 0.739213
\(214\) 9.27419 0.633971
\(215\) 0 0
\(216\) −21.7245 −1.47816
\(217\) 8.55269 0.580594
\(218\) −2.46671 −0.167066
\(219\) −21.6475 −1.46281
\(220\) 0 0
\(221\) 23.8778 1.60620
\(222\) 12.7344 0.854676
\(223\) 7.37973 0.494183 0.247092 0.968992i \(-0.420525\pi\)
0.247092 + 0.968992i \(0.420525\pi\)
\(224\) 5.48487 0.366473
\(225\) 0 0
\(226\) −15.8405 −1.05369
\(227\) −4.02000 −0.266817 −0.133408 0.991061i \(-0.542592\pi\)
−0.133408 + 0.991061i \(0.542592\pi\)
\(228\) −22.4333 −1.48568
\(229\) 1.91123 0.126298 0.0631488 0.998004i \(-0.479886\pi\)
0.0631488 + 0.998004i \(0.479886\pi\)
\(230\) 0 0
\(231\) 3.19005 0.209890
\(232\) −20.1331 −1.32180
\(233\) −16.8374 −1.10306 −0.551529 0.834156i \(-0.685955\pi\)
−0.551529 + 0.834156i \(0.685955\pi\)
\(234\) −23.8300 −1.55782
\(235\) 0 0
\(236\) −17.9572 −1.16891
\(237\) −34.1732 −2.21979
\(238\) 3.29283 0.213442
\(239\) 6.38331 0.412902 0.206451 0.978457i \(-0.433809\pi\)
0.206451 + 0.978457i \(0.433809\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 7.54323 0.484897
\(243\) 3.86618 0.248016
\(244\) 16.2401 1.03967
\(245\) 0 0
\(246\) 15.1278 0.964511
\(247\) −28.7997 −1.83248
\(248\) −24.1298 −1.53225
\(249\) 43.2492 2.74081
\(250\) 0 0
\(251\) 26.0168 1.64217 0.821084 0.570808i \(-0.193370\pi\)
0.821084 + 0.570808i \(0.193370\pi\)
\(252\) 7.53569 0.474704
\(253\) −2.27475 −0.143012
\(254\) −2.28281 −0.143236
\(255\) 0 0
\(256\) −13.4555 −0.840971
\(257\) −1.32748 −0.0828062 −0.0414031 0.999143i \(-0.513183\pi\)
−0.0414031 + 0.999143i \(0.513183\pi\)
\(258\) 1.35962 0.0846462
\(259\) −5.16976 −0.321233
\(260\) 0 0
\(261\) −43.9673 −2.72151
\(262\) −1.45878 −0.0901235
\(263\) 5.83143 0.359581 0.179791 0.983705i \(-0.442458\pi\)
0.179791 + 0.983705i \(0.442458\pi\)
\(264\) −9.00014 −0.553921
\(265\) 0 0
\(266\) −3.97157 −0.243512
\(267\) 10.4303 0.638322
\(268\) −18.2090 −1.11229
\(269\) −24.4579 −1.49123 −0.745613 0.666379i \(-0.767843\pi\)
−0.745613 + 0.666379i \(0.767843\pi\)
\(270\) 0 0
\(271\) 11.9379 0.725175 0.362587 0.931950i \(-0.381893\pi\)
0.362587 + 0.931950i \(0.381893\pi\)
\(272\) 3.26826 0.198168
\(273\) 14.7007 0.889729
\(274\) 4.62172 0.279208
\(275\) 0 0
\(276\) −8.16548 −0.491504
\(277\) 6.25065 0.375565 0.187783 0.982211i \(-0.439870\pi\)
0.187783 + 0.982211i \(0.439870\pi\)
\(278\) 14.3492 0.860611
\(279\) −52.6955 −3.15480
\(280\) 0 0
\(281\) −8.11210 −0.483927 −0.241964 0.970285i \(-0.577791\pi\)
−0.241964 + 0.970285i \(0.577791\pi\)
\(282\) −5.05279 −0.300889
\(283\) 11.6663 0.693489 0.346744 0.937960i \(-0.387287\pi\)
0.346744 + 0.937960i \(0.387287\pi\)
\(284\) 5.07236 0.300989
\(285\) 0 0
\(286\) −4.74296 −0.280457
\(287\) −6.14139 −0.362515
\(288\) −33.7938 −1.99132
\(289\) 3.32872 0.195807
\(290\) 0 0
\(291\) 18.0774 1.05972
\(292\) −10.1779 −0.595618
\(293\) −3.40169 −0.198729 −0.0993643 0.995051i \(-0.531681\pi\)
−0.0993643 + 0.995051i \(0.531681\pi\)
\(294\) −14.1315 −0.824164
\(295\) 0 0
\(296\) 14.5855 0.847766
\(297\) −9.44264 −0.547918
\(298\) −14.8026 −0.857494
\(299\) −10.4828 −0.606233
\(300\) 0 0
\(301\) −0.551963 −0.0318146
\(302\) 5.19940 0.299192
\(303\) −41.5980 −2.38974
\(304\) −3.94194 −0.226086
\(305\) 0 0
\(306\) −20.2880 −1.15979
\(307\) −7.98381 −0.455660 −0.227830 0.973701i \(-0.573163\pi\)
−0.227830 + 0.973701i \(0.573163\pi\)
\(308\) 1.49985 0.0854620
\(309\) 9.94566 0.565789
\(310\) 0 0
\(311\) −2.45484 −0.139201 −0.0696006 0.997575i \(-0.522172\pi\)
−0.0696006 + 0.997575i \(0.522172\pi\)
\(312\) −41.4754 −2.34808
\(313\) 25.7238 1.45400 0.726999 0.686639i \(-0.240915\pi\)
0.726999 + 0.686639i \(0.240915\pi\)
\(314\) −14.3703 −0.810964
\(315\) 0 0
\(316\) −16.0671 −0.903844
\(317\) 22.4950 1.26344 0.631722 0.775195i \(-0.282348\pi\)
0.631722 + 0.775195i \(0.282348\pi\)
\(318\) −4.11945 −0.231007
\(319\) −8.75095 −0.489959
\(320\) 0 0
\(321\) 35.2502 1.96747
\(322\) −1.44561 −0.0805604
\(323\) −24.5190 −1.36427
\(324\) −9.77183 −0.542880
\(325\) 0 0
\(326\) 16.7523 0.927823
\(327\) −9.37568 −0.518476
\(328\) 17.3268 0.956714
\(329\) 2.05127 0.113090
\(330\) 0 0
\(331\) −3.76999 −0.207217 −0.103609 0.994618i \(-0.533039\pi\)
−0.103609 + 0.994618i \(0.533039\pi\)
\(332\) 20.3343 1.11599
\(333\) 31.8523 1.74550
\(334\) −0.930355 −0.0509067
\(335\) 0 0
\(336\) 2.01216 0.109772
\(337\) 3.78082 0.205954 0.102977 0.994684i \(-0.467163\pi\)
0.102977 + 0.994684i \(0.467163\pi\)
\(338\) −11.7260 −0.637809
\(339\) −60.2079 −3.27004
\(340\) 0 0
\(341\) −10.4881 −0.567965
\(342\) 24.4699 1.32318
\(343\) 12.2969 0.663969
\(344\) 1.55726 0.0839619
\(345\) 0 0
\(346\) −8.90507 −0.478740
\(347\) 9.49456 0.509695 0.254847 0.966981i \(-0.417975\pi\)
0.254847 + 0.966981i \(0.417975\pi\)
\(348\) −31.4125 −1.68389
\(349\) 26.4076 1.41356 0.706782 0.707431i \(-0.250146\pi\)
0.706782 + 0.707431i \(0.250146\pi\)
\(350\) 0 0
\(351\) −43.5146 −2.32264
\(352\) −6.72609 −0.358502
\(353\) 25.8877 1.37786 0.688932 0.724826i \(-0.258080\pi\)
0.688932 + 0.724826i \(0.258080\pi\)
\(354\) 29.7645 1.58197
\(355\) 0 0
\(356\) 4.90396 0.259909
\(357\) 12.5157 0.662400
\(358\) 5.47702 0.289470
\(359\) 0.849860 0.0448539 0.0224269 0.999748i \(-0.492861\pi\)
0.0224269 + 0.999748i \(0.492861\pi\)
\(360\) 0 0
\(361\) 10.5730 0.556476
\(362\) 16.6794 0.876649
\(363\) 28.6710 1.50484
\(364\) 6.91178 0.362276
\(365\) 0 0
\(366\) −26.9184 −1.40705
\(367\) −18.0444 −0.941910 −0.470955 0.882157i \(-0.656091\pi\)
−0.470955 + 0.882157i \(0.656091\pi\)
\(368\) −1.43482 −0.0747952
\(369\) 37.8388 1.96981
\(370\) 0 0
\(371\) 1.67237 0.0868249
\(372\) −37.6484 −1.95198
\(373\) 34.8689 1.80544 0.902721 0.430227i \(-0.141567\pi\)
0.902721 + 0.430227i \(0.141567\pi\)
\(374\) −4.03799 −0.208799
\(375\) 0 0
\(376\) −5.78730 −0.298457
\(377\) −40.3271 −2.07695
\(378\) −6.00080 −0.308648
\(379\) 11.1638 0.573448 0.286724 0.958013i \(-0.407434\pi\)
0.286724 + 0.958013i \(0.407434\pi\)
\(380\) 0 0
\(381\) −8.67671 −0.444522
\(382\) 7.60289 0.388997
\(383\) −9.21579 −0.470905 −0.235452 0.971886i \(-0.575657\pi\)
−0.235452 + 0.971886i \(0.575657\pi\)
\(384\) −27.4906 −1.40288
\(385\) 0 0
\(386\) 18.9261 0.963313
\(387\) 3.40079 0.172872
\(388\) 8.49939 0.431491
\(389\) −10.9251 −0.553927 −0.276964 0.960880i \(-0.589328\pi\)
−0.276964 + 0.960880i \(0.589328\pi\)
\(390\) 0 0
\(391\) −8.92464 −0.451338
\(392\) −16.1857 −0.817501
\(393\) −5.54465 −0.279691
\(394\) 6.53762 0.329360
\(395\) 0 0
\(396\) −9.24101 −0.464378
\(397\) −1.95623 −0.0981802 −0.0490901 0.998794i \(-0.515632\pi\)
−0.0490901 + 0.998794i \(0.515632\pi\)
\(398\) −16.4057 −0.822346
\(399\) −15.0955 −0.755720
\(400\) 0 0
\(401\) −29.8774 −1.49201 −0.746003 0.665942i \(-0.768030\pi\)
−0.746003 + 0.665942i \(0.768030\pi\)
\(402\) 30.1819 1.50534
\(403\) −48.3326 −2.40762
\(404\) −19.5580 −0.973045
\(405\) 0 0
\(406\) −5.56123 −0.275999
\(407\) 6.33967 0.314246
\(408\) −35.3107 −1.74814
\(409\) 7.05462 0.348829 0.174414 0.984672i \(-0.444197\pi\)
0.174414 + 0.984672i \(0.444197\pi\)
\(410\) 0 0
\(411\) 17.5667 0.866499
\(412\) 4.67611 0.230375
\(413\) −12.0835 −0.594588
\(414\) 8.90678 0.437744
\(415\) 0 0
\(416\) −30.9959 −1.51970
\(417\) 54.5399 2.67083
\(418\) 4.87033 0.238216
\(419\) 12.1170 0.591956 0.295978 0.955195i \(-0.404355\pi\)
0.295978 + 0.955195i \(0.404355\pi\)
\(420\) 0 0
\(421\) −21.7833 −1.06165 −0.530827 0.847480i \(-0.678119\pi\)
−0.530827 + 0.847480i \(0.678119\pi\)
\(422\) 3.75266 0.182676
\(423\) −12.6385 −0.614503
\(424\) −4.71827 −0.229140
\(425\) 0 0
\(426\) −8.40759 −0.407349
\(427\) 10.9280 0.528845
\(428\) 16.5734 0.801107
\(429\) −18.0275 −0.870375
\(430\) 0 0
\(431\) −21.9318 −1.05642 −0.528208 0.849115i \(-0.677136\pi\)
−0.528208 + 0.849115i \(0.677136\pi\)
\(432\) −5.95604 −0.286560
\(433\) −10.5761 −0.508255 −0.254127 0.967171i \(-0.581788\pi\)
−0.254127 + 0.967171i \(0.581788\pi\)
\(434\) −6.66522 −0.319941
\(435\) 0 0
\(436\) −4.40812 −0.211111
\(437\) 10.7643 0.514924
\(438\) 16.8702 0.806090
\(439\) −22.5700 −1.07721 −0.538605 0.842558i \(-0.681048\pi\)
−0.538605 + 0.842558i \(0.681048\pi\)
\(440\) 0 0
\(441\) −35.3468 −1.68318
\(442\) −18.6083 −0.885107
\(443\) −1.91167 −0.0908261 −0.0454130 0.998968i \(-0.514460\pi\)
−0.0454130 + 0.998968i \(0.514460\pi\)
\(444\) 22.7570 1.08000
\(445\) 0 0
\(446\) −5.75112 −0.272324
\(447\) −56.2632 −2.66116
\(448\) −2.91583 −0.137760
\(449\) 4.65770 0.219810 0.109905 0.993942i \(-0.464945\pi\)
0.109905 + 0.993942i \(0.464945\pi\)
\(450\) 0 0
\(451\) 7.53118 0.354630
\(452\) −28.3077 −1.33148
\(453\) 19.7624 0.928517
\(454\) 3.13284 0.147031
\(455\) 0 0
\(456\) 42.5892 1.99442
\(457\) 23.5731 1.10270 0.551352 0.834272i \(-0.314112\pi\)
0.551352 + 0.834272i \(0.314112\pi\)
\(458\) −1.48945 −0.0695973
\(459\) −37.0468 −1.72920
\(460\) 0 0
\(461\) 9.11685 0.424614 0.212307 0.977203i \(-0.431902\pi\)
0.212307 + 0.977203i \(0.431902\pi\)
\(462\) −2.48605 −0.115661
\(463\) 25.7210 1.19535 0.597677 0.801737i \(-0.296090\pi\)
0.597677 + 0.801737i \(0.296090\pi\)
\(464\) −5.51975 −0.256248
\(465\) 0 0
\(466\) 13.1216 0.607848
\(467\) −7.86830 −0.364101 −0.182051 0.983289i \(-0.558274\pi\)
−0.182051 + 0.983289i \(0.558274\pi\)
\(468\) −42.5854 −1.96851
\(469\) −12.2529 −0.565787
\(470\) 0 0
\(471\) −54.6200 −2.51676
\(472\) 34.0912 1.56918
\(473\) 0.676871 0.0311226
\(474\) 26.6317 1.22323
\(475\) 0 0
\(476\) 5.88444 0.269713
\(477\) −10.3039 −0.471783
\(478\) −4.97460 −0.227533
\(479\) −10.1460 −0.463583 −0.231791 0.972766i \(-0.574459\pi\)
−0.231791 + 0.972766i \(0.574459\pi\)
\(480\) 0 0
\(481\) 29.2151 1.33210
\(482\) −0.779313 −0.0354967
\(483\) −5.49459 −0.250012
\(484\) 13.4801 0.612732
\(485\) 0 0
\(486\) −3.01297 −0.136671
\(487\) −28.2534 −1.28028 −0.640142 0.768257i \(-0.721124\pi\)
−0.640142 + 0.768257i \(0.721124\pi\)
\(488\) −30.8315 −1.39567
\(489\) 63.6736 2.87942
\(490\) 0 0
\(491\) 19.8733 0.896871 0.448435 0.893815i \(-0.351981\pi\)
0.448435 + 0.893815i \(0.351981\pi\)
\(492\) 27.0340 1.21879
\(493\) −34.3330 −1.54628
\(494\) 22.4440 1.00980
\(495\) 0 0
\(496\) −6.61550 −0.297045
\(497\) 3.41322 0.153104
\(498\) −33.7047 −1.51034
\(499\) 7.72762 0.345936 0.172968 0.984927i \(-0.444664\pi\)
0.172968 + 0.984927i \(0.444664\pi\)
\(500\) 0 0
\(501\) −3.53618 −0.157985
\(502\) −20.2753 −0.904929
\(503\) −1.22534 −0.0546350 −0.0273175 0.999627i \(-0.508697\pi\)
−0.0273175 + 0.999627i \(0.508697\pi\)
\(504\) −14.3063 −0.637255
\(505\) 0 0
\(506\) 1.77274 0.0788081
\(507\) −44.5691 −1.97938
\(508\) −4.07949 −0.180998
\(509\) −28.3605 −1.25706 −0.628529 0.777786i \(-0.716343\pi\)
−0.628529 + 0.777786i \(0.716343\pi\)
\(510\) 0 0
\(511\) −6.84878 −0.302972
\(512\) −8.07561 −0.356895
\(513\) 44.6831 1.97281
\(514\) 1.03453 0.0456310
\(515\) 0 0
\(516\) 2.42971 0.106962
\(517\) −2.51547 −0.110630
\(518\) 4.02886 0.177018
\(519\) −33.8472 −1.48573
\(520\) 0 0
\(521\) 21.5029 0.942058 0.471029 0.882118i \(-0.343883\pi\)
0.471029 + 0.882118i \(0.343883\pi\)
\(522\) 34.2643 1.49971
\(523\) −36.3389 −1.58899 −0.794495 0.607270i \(-0.792265\pi\)
−0.794495 + 0.607270i \(0.792265\pi\)
\(524\) −2.60690 −0.113883
\(525\) 0 0
\(526\) −4.54451 −0.198150
\(527\) −41.1487 −1.79246
\(528\) −2.46750 −0.107384
\(529\) −19.0819 −0.829649
\(530\) 0 0
\(531\) 74.4495 3.23083
\(532\) −7.09739 −0.307711
\(533\) 34.7060 1.50328
\(534\) −8.12845 −0.351752
\(535\) 0 0
\(536\) 34.5694 1.49317
\(537\) 20.8176 0.898344
\(538\) 19.0604 0.821752
\(539\) −7.03519 −0.303027
\(540\) 0 0
\(541\) −46.1952 −1.98609 −0.993044 0.117743i \(-0.962434\pi\)
−0.993044 + 0.117743i \(0.962434\pi\)
\(542\) −9.30335 −0.399613
\(543\) 63.3965 2.72060
\(544\) −26.3888 −1.13141
\(545\) 0 0
\(546\) −11.4565 −0.490292
\(547\) 1.66839 0.0713350 0.0356675 0.999364i \(-0.488644\pi\)
0.0356675 + 0.999364i \(0.488644\pi\)
\(548\) 8.25924 0.352817
\(549\) −67.3307 −2.87360
\(550\) 0 0
\(551\) 41.4100 1.76412
\(552\) 15.5020 0.659808
\(553\) −10.8116 −0.459757
\(554\) −4.87121 −0.206958
\(555\) 0 0
\(556\) 25.6428 1.08750
\(557\) −25.9993 −1.10163 −0.550813 0.834629i \(-0.685682\pi\)
−0.550813 + 0.834629i \(0.685682\pi\)
\(558\) 41.0663 1.73847
\(559\) 3.11923 0.131929
\(560\) 0 0
\(561\) −15.3480 −0.647991
\(562\) 6.32187 0.266672
\(563\) −33.6739 −1.41919 −0.709593 0.704612i \(-0.751121\pi\)
−0.709593 + 0.704612i \(0.751121\pi\)
\(564\) −9.02958 −0.380214
\(565\) 0 0
\(566\) −9.09169 −0.382152
\(567\) −6.57551 −0.276145
\(568\) −9.62977 −0.404056
\(569\) −16.6823 −0.699357 −0.349679 0.936870i \(-0.613709\pi\)
−0.349679 + 0.936870i \(0.613709\pi\)
\(570\) 0 0
\(571\) 23.2126 0.971417 0.485709 0.874121i \(-0.338562\pi\)
0.485709 + 0.874121i \(0.338562\pi\)
\(572\) −8.47591 −0.354395
\(573\) 28.8977 1.20722
\(574\) 4.78607 0.199767
\(575\) 0 0
\(576\) 17.9652 0.748550
\(577\) −25.4340 −1.05883 −0.529415 0.848363i \(-0.677588\pi\)
−0.529415 + 0.848363i \(0.677588\pi\)
\(578\) −2.59411 −0.107901
\(579\) 71.9360 2.98956
\(580\) 0 0
\(581\) 13.6830 0.567668
\(582\) −14.0880 −0.583966
\(583\) −2.05082 −0.0849362
\(584\) 19.3226 0.799574
\(585\) 0 0
\(586\) 2.65098 0.109511
\(587\) 37.2153 1.53604 0.768019 0.640427i \(-0.221243\pi\)
0.768019 + 0.640427i \(0.221243\pi\)
\(588\) −25.2536 −1.04144
\(589\) 49.6305 2.04499
\(590\) 0 0
\(591\) 24.8488 1.02214
\(592\) 3.99881 0.164350
\(593\) −35.8943 −1.47400 −0.737001 0.675891i \(-0.763759\pi\)
−0.737001 + 0.675891i \(0.763759\pi\)
\(594\) 7.35878 0.301934
\(595\) 0 0
\(596\) −26.4530 −1.08356
\(597\) −62.3564 −2.55208
\(598\) 8.16935 0.334070
\(599\) 1.76583 0.0721498 0.0360749 0.999349i \(-0.488515\pi\)
0.0360749 + 0.999349i \(0.488515\pi\)
\(600\) 0 0
\(601\) −13.7556 −0.561104 −0.280552 0.959839i \(-0.590518\pi\)
−0.280552 + 0.959839i \(0.590518\pi\)
\(602\) 0.430152 0.0175317
\(603\) 75.4936 3.07434
\(604\) 9.29158 0.378069
\(605\) 0 0
\(606\) 32.4179 1.31689
\(607\) −2.85876 −0.116034 −0.0580168 0.998316i \(-0.518478\pi\)
−0.0580168 + 0.998316i \(0.518478\pi\)
\(608\) 31.8282 1.29081
\(609\) −21.1376 −0.856540
\(610\) 0 0
\(611\) −11.5921 −0.468965
\(612\) −36.2557 −1.46555
\(613\) 18.3343 0.740517 0.370258 0.928929i \(-0.379269\pi\)
0.370258 + 0.928929i \(0.379269\pi\)
\(614\) 6.22189 0.251095
\(615\) 0 0
\(616\) −2.84744 −0.114726
\(617\) 1.66136 0.0668839 0.0334419 0.999441i \(-0.489353\pi\)
0.0334419 + 0.999441i \(0.489353\pi\)
\(618\) −7.75078 −0.311782
\(619\) 11.9123 0.478795 0.239397 0.970922i \(-0.423050\pi\)
0.239397 + 0.970922i \(0.423050\pi\)
\(620\) 0 0
\(621\) 16.2641 0.652658
\(622\) 1.91309 0.0767079
\(623\) 3.29989 0.132207
\(624\) −11.3710 −0.455205
\(625\) 0 0
\(626\) −20.0469 −0.801237
\(627\) 18.5116 0.739282
\(628\) −25.6805 −1.02476
\(629\) 24.8727 0.991740
\(630\) 0 0
\(631\) −17.1342 −0.682100 −0.341050 0.940045i \(-0.610783\pi\)
−0.341050 + 0.940045i \(0.610783\pi\)
\(632\) 30.5030 1.21334
\(633\) 14.2634 0.566921
\(634\) −17.5306 −0.696231
\(635\) 0 0
\(636\) −7.36165 −0.291908
\(637\) −32.4203 −1.28454
\(638\) 6.81973 0.269996
\(639\) −21.0298 −0.831925
\(640\) 0 0
\(641\) 24.2019 0.955920 0.477960 0.878382i \(-0.341376\pi\)
0.477960 + 0.878382i \(0.341376\pi\)
\(642\) −27.4710 −1.08419
\(643\) −11.2516 −0.443719 −0.221859 0.975079i \(-0.571213\pi\)
−0.221859 + 0.975079i \(0.571213\pi\)
\(644\) −2.58337 −0.101799
\(645\) 0 0
\(646\) 19.1080 0.751794
\(647\) 9.80682 0.385546 0.192773 0.981243i \(-0.438252\pi\)
0.192773 + 0.981243i \(0.438252\pi\)
\(648\) 18.5516 0.728776
\(649\) 14.8179 0.581654
\(650\) 0 0
\(651\) −25.3338 −0.992909
\(652\) 29.9371 1.17243
\(653\) −25.9551 −1.01570 −0.507851 0.861445i \(-0.669560\pi\)
−0.507851 + 0.861445i \(0.669560\pi\)
\(654\) 7.30659 0.285710
\(655\) 0 0
\(656\) 4.75037 0.185471
\(657\) 42.1972 1.64627
\(658\) −1.59859 −0.0623193
\(659\) 6.74808 0.262868 0.131434 0.991325i \(-0.458042\pi\)
0.131434 + 0.991325i \(0.458042\pi\)
\(660\) 0 0
\(661\) −4.87087 −0.189455 −0.0947274 0.995503i \(-0.530198\pi\)
−0.0947274 + 0.995503i \(0.530198\pi\)
\(662\) 2.93800 0.114189
\(663\) −70.7281 −2.74685
\(664\) −38.6042 −1.49813
\(665\) 0 0
\(666\) −24.8229 −0.961869
\(667\) 15.0728 0.583620
\(668\) −1.66259 −0.0643275
\(669\) −21.8594 −0.845133
\(670\) 0 0
\(671\) −13.4010 −0.517341
\(672\) −16.2467 −0.626728
\(673\) −35.9981 −1.38762 −0.693812 0.720156i \(-0.744070\pi\)
−0.693812 + 0.720156i \(0.744070\pi\)
\(674\) −2.94644 −0.113493
\(675\) 0 0
\(676\) −20.9549 −0.805957
\(677\) −15.8918 −0.610770 −0.305385 0.952229i \(-0.598785\pi\)
−0.305385 + 0.952229i \(0.598785\pi\)
\(678\) 46.9208 1.80198
\(679\) 5.71928 0.219486
\(680\) 0 0
\(681\) 11.9076 0.456299
\(682\) 8.17355 0.312982
\(683\) −5.17541 −0.198032 −0.0990159 0.995086i \(-0.531569\pi\)
−0.0990159 + 0.995086i \(0.531569\pi\)
\(684\) 43.7290 1.67202
\(685\) 0 0
\(686\) −9.58312 −0.365885
\(687\) −5.66123 −0.215989
\(688\) 0.426943 0.0162770
\(689\) −9.45081 −0.360047
\(690\) 0 0
\(691\) −3.53280 −0.134394 −0.0671971 0.997740i \(-0.521406\pi\)
−0.0671971 + 0.997740i \(0.521406\pi\)
\(692\) −15.9138 −0.604952
\(693\) −6.21832 −0.236214
\(694\) −7.39924 −0.280871
\(695\) 0 0
\(696\) 59.6360 2.26050
\(697\) 29.5474 1.11919
\(698\) −20.5798 −0.778956
\(699\) 49.8739 1.88641
\(700\) 0 0
\(701\) −14.0788 −0.531750 −0.265875 0.964007i \(-0.585661\pi\)
−0.265875 + 0.964007i \(0.585661\pi\)
\(702\) 33.9115 1.27991
\(703\) −29.9997 −1.13146
\(704\) 3.57567 0.134763
\(705\) 0 0
\(706\) −20.1746 −0.759283
\(707\) −13.1606 −0.494957
\(708\) 53.1906 1.99903
\(709\) −24.5746 −0.922919 −0.461459 0.887161i \(-0.652674\pi\)
−0.461459 + 0.887161i \(0.652674\pi\)
\(710\) 0 0
\(711\) 66.6134 2.49820
\(712\) −9.31005 −0.348909
\(713\) 18.0649 0.676537
\(714\) −9.75363 −0.365021
\(715\) 0 0
\(716\) 9.78771 0.365784
\(717\) −18.9079 −0.706129
\(718\) −0.662307 −0.0247171
\(719\) −15.7056 −0.585719 −0.292860 0.956155i \(-0.594607\pi\)
−0.292860 + 0.956155i \(0.594607\pi\)
\(720\) 0 0
\(721\) 3.14657 0.117185
\(722\) −8.23971 −0.306650
\(723\) −2.96208 −0.110161
\(724\) 29.8069 1.10776
\(725\) 0 0
\(726\) −22.3437 −0.829252
\(727\) −16.8688 −0.625629 −0.312815 0.949814i \(-0.601272\pi\)
−0.312815 + 0.949814i \(0.601272\pi\)
\(728\) −13.1219 −0.486328
\(729\) −32.5018 −1.20377
\(730\) 0 0
\(731\) 2.65560 0.0982209
\(732\) −48.1045 −1.77800
\(733\) −34.8667 −1.28783 −0.643915 0.765097i \(-0.722691\pi\)
−0.643915 + 0.765097i \(0.722691\pi\)
\(734\) 14.0622 0.519047
\(735\) 0 0
\(736\) 11.5851 0.427033
\(737\) 15.0257 0.553480
\(738\) −29.4883 −1.08548
\(739\) 33.6344 1.23726 0.618630 0.785682i \(-0.287688\pi\)
0.618630 + 0.785682i \(0.287688\pi\)
\(740\) 0 0
\(741\) 85.3071 3.13383
\(742\) −1.30330 −0.0478455
\(743\) −10.2069 −0.374456 −0.187228 0.982316i \(-0.559950\pi\)
−0.187228 + 0.982316i \(0.559950\pi\)
\(744\) 71.4746 2.62039
\(745\) 0 0
\(746\) −27.1738 −0.994902
\(747\) −84.3050 −3.08456
\(748\) −7.21608 −0.263846
\(749\) 11.1523 0.407498
\(750\) 0 0
\(751\) −41.5940 −1.51779 −0.758893 0.651215i \(-0.774260\pi\)
−0.758893 + 0.651215i \(0.774260\pi\)
\(752\) −1.58666 −0.0578595
\(753\) −77.0640 −2.80837
\(754\) 31.4274 1.14452
\(755\) 0 0
\(756\) −10.7237 −0.390018
\(757\) −4.35282 −0.158206 −0.0791030 0.996866i \(-0.525206\pi\)
−0.0791030 + 0.996866i \(0.525206\pi\)
\(758\) −8.70013 −0.316003
\(759\) 6.73801 0.244574
\(760\) 0 0
\(761\) 42.6619 1.54649 0.773247 0.634105i \(-0.218631\pi\)
0.773247 + 0.634105i \(0.218631\pi\)
\(762\) 6.76188 0.244957
\(763\) −2.96625 −0.107385
\(764\) 13.5867 0.491550
\(765\) 0 0
\(766\) 7.18199 0.259496
\(767\) 68.2855 2.46565
\(768\) 39.8564 1.43820
\(769\) −51.2508 −1.84815 −0.924076 0.382209i \(-0.875163\pi\)
−0.924076 + 0.382209i \(0.875163\pi\)
\(770\) 0 0
\(771\) 3.93212 0.141612
\(772\) 33.8218 1.21727
\(773\) −6.70584 −0.241192 −0.120596 0.992702i \(-0.538481\pi\)
−0.120596 + 0.992702i \(0.538481\pi\)
\(774\) −2.65028 −0.0952625
\(775\) 0 0
\(776\) −16.1359 −0.579245
\(777\) 15.3133 0.549360
\(778\) 8.51411 0.305246
\(779\) −35.6380 −1.27686
\(780\) 0 0
\(781\) −4.18562 −0.149773
\(782\) 6.95509 0.248714
\(783\) 62.5680 2.23600
\(784\) −4.43751 −0.158483
\(785\) 0 0
\(786\) 4.32102 0.154126
\(787\) 5.74043 0.204624 0.102312 0.994752i \(-0.467376\pi\)
0.102312 + 0.994752i \(0.467376\pi\)
\(788\) 11.6830 0.416191
\(789\) −17.2732 −0.614942
\(790\) 0 0
\(791\) −19.0484 −0.677282
\(792\) 17.5438 0.623393
\(793\) −61.7561 −2.19302
\(794\) 1.52451 0.0541030
\(795\) 0 0
\(796\) −29.3179 −1.03914
\(797\) −52.4171 −1.85671 −0.928355 0.371696i \(-0.878776\pi\)
−0.928355 + 0.371696i \(0.878776\pi\)
\(798\) 11.7641 0.416445
\(799\) −9.86908 −0.349143
\(800\) 0 0
\(801\) −20.3316 −0.718381
\(802\) 23.2839 0.822182
\(803\) 8.39865 0.296382
\(804\) 53.9366 1.90220
\(805\) 0 0
\(806\) 37.6663 1.32674
\(807\) 72.4465 2.55024
\(808\) 37.1303 1.30624
\(809\) 2.77810 0.0976727 0.0488363 0.998807i \(-0.484449\pi\)
0.0488363 + 0.998807i \(0.484449\pi\)
\(810\) 0 0
\(811\) 25.2489 0.886608 0.443304 0.896371i \(-0.353806\pi\)
0.443304 + 0.896371i \(0.353806\pi\)
\(812\) −9.93819 −0.348762
\(813\) −35.3610 −1.24017
\(814\) −4.94059 −0.173167
\(815\) 0 0
\(816\) −9.68087 −0.338898
\(817\) −3.20299 −0.112058
\(818\) −5.49776 −0.192225
\(819\) −28.6559 −1.00132
\(820\) 0 0
\(821\) −2.09135 −0.0729886 −0.0364943 0.999334i \(-0.511619\pi\)
−0.0364943 + 0.999334i \(0.511619\pi\)
\(822\) −13.6899 −0.477491
\(823\) −50.3771 −1.75604 −0.878018 0.478627i \(-0.841135\pi\)
−0.878018 + 0.478627i \(0.841135\pi\)
\(824\) −8.87748 −0.309262
\(825\) 0 0
\(826\) 9.41679 0.327652
\(827\) 26.9111 0.935792 0.467896 0.883784i \(-0.345012\pi\)
0.467896 + 0.883784i \(0.345012\pi\)
\(828\) 15.9168 0.553149
\(829\) 13.5623 0.471038 0.235519 0.971870i \(-0.424321\pi\)
0.235519 + 0.971870i \(0.424321\pi\)
\(830\) 0 0
\(831\) −18.5150 −0.642277
\(832\) 16.4778 0.571265
\(833\) −27.6015 −0.956335
\(834\) −42.5037 −1.47178
\(835\) 0 0
\(836\) 8.70351 0.301017
\(837\) 74.9888 2.59199
\(838\) −9.44296 −0.326202
\(839\) −33.3649 −1.15189 −0.575943 0.817490i \(-0.695365\pi\)
−0.575943 + 0.817490i \(0.695365\pi\)
\(840\) 0 0
\(841\) 28.9848 0.999475
\(842\) 16.9760 0.585033
\(843\) 24.0287 0.827594
\(844\) 6.70618 0.230836
\(845\) 0 0
\(846\) 9.84933 0.338627
\(847\) 9.07083 0.311677
\(848\) −1.29357 −0.0444215
\(849\) −34.5565 −1.18598
\(850\) 0 0
\(851\) −10.9195 −0.374317
\(852\) −15.0248 −0.514740
\(853\) 27.7557 0.950337 0.475169 0.879895i \(-0.342387\pi\)
0.475169 + 0.879895i \(0.342387\pi\)
\(854\) −8.51636 −0.291424
\(855\) 0 0
\(856\) −31.4643 −1.07543
\(857\) −12.2408 −0.418138 −0.209069 0.977901i \(-0.567043\pi\)
−0.209069 + 0.977901i \(0.567043\pi\)
\(858\) 14.0491 0.479627
\(859\) −24.3399 −0.830468 −0.415234 0.909715i \(-0.636300\pi\)
−0.415234 + 0.909715i \(0.636300\pi\)
\(860\) 0 0
\(861\) 18.1913 0.619959
\(862\) 17.0917 0.582147
\(863\) −40.2096 −1.36875 −0.684375 0.729130i \(-0.739925\pi\)
−0.684375 + 0.729130i \(0.739925\pi\)
\(864\) 48.0906 1.63607
\(865\) 0 0
\(866\) 8.24209 0.280078
\(867\) −9.85994 −0.334861
\(868\) −11.9111 −0.404288
\(869\) 13.2583 0.449756
\(870\) 0 0
\(871\) 69.2432 2.34622
\(872\) 8.36872 0.283401
\(873\) −35.2381 −1.19263
\(874\) −8.38872 −0.283753
\(875\) 0 0
\(876\) 30.1479 1.01860
\(877\) 12.1400 0.409938 0.204969 0.978768i \(-0.434291\pi\)
0.204969 + 0.978768i \(0.434291\pi\)
\(878\) 17.5891 0.593605
\(879\) 10.0761 0.339858
\(880\) 0 0
\(881\) −56.7812 −1.91301 −0.956504 0.291720i \(-0.905772\pi\)
−0.956504 + 0.291720i \(0.905772\pi\)
\(882\) 27.5462 0.927530
\(883\) −35.8130 −1.20520 −0.602602 0.798042i \(-0.705869\pi\)
−0.602602 + 0.798042i \(0.705869\pi\)
\(884\) −33.2539 −1.11845
\(885\) 0 0
\(886\) 1.48979 0.0500504
\(887\) −36.9095 −1.23930 −0.619650 0.784878i \(-0.712726\pi\)
−0.619650 + 0.784878i \(0.712726\pi\)
\(888\) −43.2036 −1.44982
\(889\) −2.74511 −0.0920680
\(890\) 0 0
\(891\) 8.06354 0.270139
\(892\) −10.2775 −0.344117
\(893\) 11.9034 0.398331
\(894\) 43.8467 1.46645
\(895\) 0 0
\(896\) −8.69740 −0.290560
\(897\) 31.0508 1.03676
\(898\) −3.62981 −0.121128
\(899\) 69.4957 2.31781
\(900\) 0 0
\(901\) −8.04608 −0.268054
\(902\) −5.86915 −0.195421
\(903\) 1.63496 0.0544081
\(904\) 53.7415 1.78742
\(905\) 0 0
\(906\) −15.4011 −0.511666
\(907\) 33.1417 1.10045 0.550226 0.835016i \(-0.314542\pi\)
0.550226 + 0.835016i \(0.314542\pi\)
\(908\) 5.59854 0.185794
\(909\) 81.0864 2.68946
\(910\) 0 0
\(911\) 26.7817 0.887317 0.443659 0.896196i \(-0.353680\pi\)
0.443659 + 0.896196i \(0.353680\pi\)
\(912\) 11.6764 0.386643
\(913\) −16.7795 −0.555320
\(914\) −18.3709 −0.607654
\(915\) 0 0
\(916\) −2.66172 −0.0879456
\(917\) −1.75420 −0.0579287
\(918\) 28.8710 0.952887
\(919\) 6.81208 0.224710 0.112355 0.993668i \(-0.464161\pi\)
0.112355 + 0.993668i \(0.464161\pi\)
\(920\) 0 0
\(921\) 23.6487 0.779252
\(922\) −7.10488 −0.233987
\(923\) −19.2886 −0.634893
\(924\) −4.44269 −0.146154
\(925\) 0 0
\(926\) −20.0447 −0.658709
\(927\) −19.3869 −0.636750
\(928\) 44.5678 1.46301
\(929\) −43.7006 −1.43377 −0.716885 0.697192i \(-0.754433\pi\)
−0.716885 + 0.697192i \(0.754433\pi\)
\(930\) 0 0
\(931\) 33.2909 1.09107
\(932\) 23.4490 0.768098
\(933\) 7.27144 0.238056
\(934\) 6.13187 0.200641
\(935\) 0 0
\(936\) 80.8474 2.64258
\(937\) 38.9852 1.27359 0.636795 0.771033i \(-0.280260\pi\)
0.636795 + 0.771033i \(0.280260\pi\)
\(938\) 9.54886 0.311781
\(939\) −76.1962 −2.48657
\(940\) 0 0
\(941\) −25.3412 −0.826100 −0.413050 0.910708i \(-0.635537\pi\)
−0.413050 + 0.910708i \(0.635537\pi\)
\(942\) 42.5661 1.38688
\(943\) −12.9718 −0.422420
\(944\) 9.34655 0.304204
\(945\) 0 0
\(946\) −0.527494 −0.0171503
\(947\) 9.82285 0.319200 0.159600 0.987182i \(-0.448980\pi\)
0.159600 + 0.987182i \(0.448980\pi\)
\(948\) 47.5921 1.54572
\(949\) 38.7035 1.25637
\(950\) 0 0
\(951\) −66.6320 −2.16069
\(952\) −11.1715 −0.362070
\(953\) 36.3432 1.17727 0.588636 0.808398i \(-0.299665\pi\)
0.588636 + 0.808398i \(0.299665\pi\)
\(954\) 8.02997 0.259980
\(955\) 0 0
\(956\) −8.88985 −0.287518
\(957\) 25.9211 0.837909
\(958\) 7.90691 0.255461
\(959\) 5.55768 0.179467
\(960\) 0 0
\(961\) 52.2916 1.68683
\(962\) −22.7677 −0.734061
\(963\) −68.7127 −2.21423
\(964\) −1.39267 −0.0448549
\(965\) 0 0
\(966\) 4.28201 0.137771
\(967\) 9.81331 0.315575 0.157787 0.987473i \(-0.449564\pi\)
0.157787 + 0.987473i \(0.449564\pi\)
\(968\) −25.5917 −0.822548
\(969\) 72.6274 2.33313
\(970\) 0 0
\(971\) −0.237615 −0.00762543 −0.00381272 0.999993i \(-0.501214\pi\)
−0.00381272 + 0.999993i \(0.501214\pi\)
\(972\) −5.38432 −0.172702
\(973\) 17.2552 0.553175
\(974\) 22.0183 0.705510
\(975\) 0 0
\(976\) −8.45283 −0.270569
\(977\) 9.69323 0.310114 0.155057 0.987906i \(-0.450444\pi\)
0.155057 + 0.987906i \(0.450444\pi\)
\(978\) −49.6217 −1.58673
\(979\) −4.04666 −0.129332
\(980\) 0 0
\(981\) 18.2759 0.583504
\(982\) −15.4876 −0.494228
\(983\) 60.7321 1.93705 0.968526 0.248913i \(-0.0800733\pi\)
0.968526 + 0.248913i \(0.0800733\pi\)
\(984\) −51.3235 −1.63613
\(985\) 0 0
\(986\) 26.7562 0.852090
\(987\) −6.07605 −0.193403
\(988\) 40.1085 1.27602
\(989\) −1.16585 −0.0370719
\(990\) 0 0
\(991\) −9.84269 −0.312663 −0.156332 0.987705i \(-0.549967\pi\)
−0.156332 + 0.987705i \(0.549967\pi\)
\(992\) 53.4152 1.69594
\(993\) 11.1670 0.354375
\(994\) −2.65997 −0.0843690
\(995\) 0 0
\(996\) −60.2319 −1.90852
\(997\) 45.6202 1.44481 0.722404 0.691471i \(-0.243037\pi\)
0.722404 + 0.691471i \(0.243037\pi\)
\(998\) −6.02223 −0.190630
\(999\) −45.3277 −1.43411
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 6025.2.a.p.1.17 46
5.2 odd 4 1205.2.b.c.724.17 46
5.3 odd 4 1205.2.b.c.724.30 yes 46
5.4 even 2 inner 6025.2.a.p.1.30 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.17 46 5.2 odd 4
1205.2.b.c.724.30 yes 46 5.3 odd 4
6025.2.a.p.1.17 46 1.1 even 1 trivial
6025.2.a.p.1.30 46 5.4 even 2 inner