Properties

Label 6025.2.a.p.1.19
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 1.19
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.636788 q^{2} +2.24729 q^{3} -1.59450 q^{4} -1.43105 q^{6} +1.14493 q^{7} +2.28894 q^{8} +2.05030 q^{9} +O(q^{10})\) \(q-0.636788 q^{2} +2.24729 q^{3} -1.59450 q^{4} -1.43105 q^{6} +1.14493 q^{7} +2.28894 q^{8} +2.05030 q^{9} -0.440443 q^{11} -3.58330 q^{12} +0.0742578 q^{13} -0.729079 q^{14} +1.73143 q^{16} -3.83474 q^{17} -1.30561 q^{18} -4.81267 q^{19} +2.57299 q^{21} +0.280469 q^{22} +6.24519 q^{23} +5.14390 q^{24} -0.0472865 q^{26} -2.13425 q^{27} -1.82559 q^{28} +2.54550 q^{29} -0.429517 q^{31} -5.68043 q^{32} -0.989801 q^{33} +2.44192 q^{34} -3.26920 q^{36} -10.9158 q^{37} +3.06465 q^{38} +0.166878 q^{39} -4.91543 q^{41} -1.63845 q^{42} -1.72125 q^{43} +0.702286 q^{44} -3.97686 q^{46} +0.485128 q^{47} +3.89103 q^{48} -5.68913 q^{49} -8.61777 q^{51} -0.118404 q^{52} -2.29994 q^{53} +1.35907 q^{54} +2.62068 q^{56} -10.8155 q^{57} -1.62094 q^{58} -1.98580 q^{59} +8.96972 q^{61} +0.273511 q^{62} +2.34745 q^{63} +0.154367 q^{64} +0.630294 q^{66} +1.53915 q^{67} +6.11450 q^{68} +14.0347 q^{69} +14.1657 q^{71} +4.69300 q^{72} -15.2643 q^{73} +6.95108 q^{74} +7.67381 q^{76} -0.504277 q^{77} -0.106266 q^{78} +1.84814 q^{79} -10.9472 q^{81} +3.13009 q^{82} -1.08755 q^{83} -4.10263 q^{84} +1.09608 q^{86} +5.72046 q^{87} -1.00815 q^{88} +1.27098 q^{89} +0.0850201 q^{91} -9.95795 q^{92} -0.965247 q^{93} -0.308924 q^{94} -12.7656 q^{96} -14.7657 q^{97} +3.62277 q^{98} -0.903038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.636788 −0.450277 −0.225139 0.974327i \(-0.572284\pi\)
−0.225139 + 0.974327i \(0.572284\pi\)
\(3\) 2.24729 1.29747 0.648736 0.761014i \(-0.275298\pi\)
0.648736 + 0.761014i \(0.275298\pi\)
\(4\) −1.59450 −0.797250
\(5\) 0 0
\(6\) −1.43105 −0.584222
\(7\) 1.14493 0.432743 0.216372 0.976311i \(-0.430578\pi\)
0.216372 + 0.976311i \(0.430578\pi\)
\(8\) 2.28894 0.809261
\(9\) 2.05030 0.683433
\(10\) 0 0
\(11\) −0.440443 −0.132798 −0.0663992 0.997793i \(-0.521151\pi\)
−0.0663992 + 0.997793i \(0.521151\pi\)
\(12\) −3.58330 −1.03441
\(13\) 0.0742578 0.0205954 0.0102977 0.999947i \(-0.496722\pi\)
0.0102977 + 0.999947i \(0.496722\pi\)
\(14\) −0.729079 −0.194855
\(15\) 0 0
\(16\) 1.73143 0.432858
\(17\) −3.83474 −0.930062 −0.465031 0.885294i \(-0.653957\pi\)
−0.465031 + 0.885294i \(0.653957\pi\)
\(18\) −1.30561 −0.307734
\(19\) −4.81267 −1.10410 −0.552051 0.833810i \(-0.686155\pi\)
−0.552051 + 0.833810i \(0.686155\pi\)
\(20\) 0 0
\(21\) 2.57299 0.561472
\(22\) 0.280469 0.0597961
\(23\) 6.24519 1.30221 0.651106 0.758987i \(-0.274305\pi\)
0.651106 + 0.758987i \(0.274305\pi\)
\(24\) 5.14390 1.04999
\(25\) 0 0
\(26\) −0.0472865 −0.00927364
\(27\) −2.13425 −0.410737
\(28\) −1.82559 −0.345005
\(29\) 2.54550 0.472687 0.236343 0.971670i \(-0.424051\pi\)
0.236343 + 0.971670i \(0.424051\pi\)
\(30\) 0 0
\(31\) −0.429517 −0.0771435 −0.0385717 0.999256i \(-0.512281\pi\)
−0.0385717 + 0.999256i \(0.512281\pi\)
\(32\) −5.68043 −1.00417
\(33\) −0.989801 −0.172302
\(34\) 2.44192 0.418786
\(35\) 0 0
\(36\) −3.26920 −0.544867
\(37\) −10.9158 −1.79455 −0.897276 0.441470i \(-0.854457\pi\)
−0.897276 + 0.441470i \(0.854457\pi\)
\(38\) 3.06465 0.497153
\(39\) 0.166878 0.0267219
\(40\) 0 0
\(41\) −4.91543 −0.767662 −0.383831 0.923403i \(-0.625395\pi\)
−0.383831 + 0.923403i \(0.625395\pi\)
\(42\) −1.63845 −0.252818
\(43\) −1.72125 −0.262489 −0.131244 0.991350i \(-0.541897\pi\)
−0.131244 + 0.991350i \(0.541897\pi\)
\(44\) 0.702286 0.105874
\(45\) 0 0
\(46\) −3.97686 −0.586356
\(47\) 0.485128 0.0707631 0.0353816 0.999374i \(-0.488735\pi\)
0.0353816 + 0.999374i \(0.488735\pi\)
\(48\) 3.89103 0.561621
\(49\) −5.68913 −0.812733
\(50\) 0 0
\(51\) −8.61777 −1.20673
\(52\) −0.118404 −0.0164197
\(53\) −2.29994 −0.315921 −0.157960 0.987445i \(-0.550492\pi\)
−0.157960 + 0.987445i \(0.550492\pi\)
\(54\) 1.35907 0.184946
\(55\) 0 0
\(56\) 2.62068 0.350203
\(57\) −10.8155 −1.43254
\(58\) −1.62094 −0.212840
\(59\) −1.98580 −0.258530 −0.129265 0.991610i \(-0.541262\pi\)
−0.129265 + 0.991610i \(0.541262\pi\)
\(60\) 0 0
\(61\) 8.96972 1.14846 0.574228 0.818696i \(-0.305302\pi\)
0.574228 + 0.818696i \(0.305302\pi\)
\(62\) 0.273511 0.0347360
\(63\) 2.34745 0.295751
\(64\) 0.154367 0.0192959
\(65\) 0 0
\(66\) 0.630294 0.0775838
\(67\) 1.53915 0.188038 0.0940188 0.995570i \(-0.470029\pi\)
0.0940188 + 0.995570i \(0.470029\pi\)
\(68\) 6.11450 0.741492
\(69\) 14.0347 1.68958
\(70\) 0 0
\(71\) 14.1657 1.68116 0.840579 0.541688i \(-0.182215\pi\)
0.840579 + 0.541688i \(0.182215\pi\)
\(72\) 4.69300 0.553075
\(73\) −15.2643 −1.78656 −0.893278 0.449504i \(-0.851601\pi\)
−0.893278 + 0.449504i \(0.851601\pi\)
\(74\) 6.95108 0.808046
\(75\) 0 0
\(76\) 7.67381 0.880246
\(77\) −0.504277 −0.0574677
\(78\) −0.106266 −0.0120323
\(79\) 1.84814 0.207932 0.103966 0.994581i \(-0.466847\pi\)
0.103966 + 0.994581i \(0.466847\pi\)
\(80\) 0 0
\(81\) −10.9472 −1.21635
\(82\) 3.13009 0.345661
\(83\) −1.08755 −0.119375 −0.0596873 0.998217i \(-0.519010\pi\)
−0.0596873 + 0.998217i \(0.519010\pi\)
\(84\) −4.10263 −0.447634
\(85\) 0 0
\(86\) 1.09608 0.118193
\(87\) 5.72046 0.613298
\(88\) −1.00815 −0.107469
\(89\) 1.27098 0.134723 0.0673617 0.997729i \(-0.478542\pi\)
0.0673617 + 0.997729i \(0.478542\pi\)
\(90\) 0 0
\(91\) 0.0850201 0.00891252
\(92\) −9.95795 −1.03819
\(93\) −0.965247 −0.100091
\(94\) −0.308924 −0.0318630
\(95\) 0 0
\(96\) −12.7656 −1.30288
\(97\) −14.7657 −1.49923 −0.749614 0.661876i \(-0.769761\pi\)
−0.749614 + 0.661876i \(0.769761\pi\)
\(98\) 3.62277 0.365955
\(99\) −0.903038 −0.0907588
\(100\) 0 0
\(101\) −5.30890 −0.528255 −0.264127 0.964488i \(-0.585084\pi\)
−0.264127 + 0.964488i \(0.585084\pi\)
\(102\) 5.48770 0.543363
\(103\) −3.19134 −0.314452 −0.157226 0.987563i \(-0.550255\pi\)
−0.157226 + 0.987563i \(0.550255\pi\)
\(104\) 0.169971 0.0166671
\(105\) 0 0
\(106\) 1.46457 0.142252
\(107\) 9.30857 0.899893 0.449947 0.893055i \(-0.351443\pi\)
0.449947 + 0.893055i \(0.351443\pi\)
\(108\) 3.40307 0.327460
\(109\) 3.00453 0.287782 0.143891 0.989594i \(-0.454039\pi\)
0.143891 + 0.989594i \(0.454039\pi\)
\(110\) 0 0
\(111\) −24.5310 −2.32838
\(112\) 1.98237 0.187317
\(113\) −5.77781 −0.543530 −0.271765 0.962364i \(-0.587607\pi\)
−0.271765 + 0.962364i \(0.587607\pi\)
\(114\) 6.88716 0.645041
\(115\) 0 0
\(116\) −4.05879 −0.376850
\(117\) 0.152251 0.0140756
\(118\) 1.26454 0.116410
\(119\) −4.39052 −0.402478
\(120\) 0 0
\(121\) −10.8060 −0.982365
\(122\) −5.71182 −0.517124
\(123\) −11.0464 −0.996019
\(124\) 0.684865 0.0615027
\(125\) 0 0
\(126\) −1.49483 −0.133170
\(127\) 19.2286 1.70627 0.853133 0.521694i \(-0.174700\pi\)
0.853133 + 0.521694i \(0.174700\pi\)
\(128\) 11.2626 0.995479
\(129\) −3.86815 −0.340572
\(130\) 0 0
\(131\) −15.0685 −1.31654 −0.658271 0.752781i \(-0.728712\pi\)
−0.658271 + 0.752781i \(0.728712\pi\)
\(132\) 1.57824 0.137368
\(133\) −5.51018 −0.477793
\(134\) −0.980116 −0.0846691
\(135\) 0 0
\(136\) −8.77749 −0.752663
\(137\) −10.3778 −0.886638 −0.443319 0.896364i \(-0.646199\pi\)
−0.443319 + 0.896364i \(0.646199\pi\)
\(138\) −8.93715 −0.760781
\(139\) −2.30756 −0.195725 −0.0978623 0.995200i \(-0.531200\pi\)
−0.0978623 + 0.995200i \(0.531200\pi\)
\(140\) 0 0
\(141\) 1.09022 0.0918132
\(142\) −9.02055 −0.756988
\(143\) −0.0327063 −0.00273504
\(144\) 3.54995 0.295829
\(145\) 0 0
\(146\) 9.72016 0.804446
\(147\) −12.7851 −1.05450
\(148\) 17.4053 1.43071
\(149\) −11.1945 −0.917092 −0.458546 0.888671i \(-0.651630\pi\)
−0.458546 + 0.888671i \(0.651630\pi\)
\(150\) 0 0
\(151\) −6.66973 −0.542775 −0.271387 0.962470i \(-0.587482\pi\)
−0.271387 + 0.962470i \(0.587482\pi\)
\(152\) −11.0159 −0.893507
\(153\) −7.86237 −0.635635
\(154\) 0.321118 0.0258764
\(155\) 0 0
\(156\) −0.266088 −0.0213041
\(157\) 22.8522 1.82380 0.911901 0.410410i \(-0.134614\pi\)
0.911901 + 0.410410i \(0.134614\pi\)
\(158\) −1.17687 −0.0936269
\(159\) −5.16862 −0.409898
\(160\) 0 0
\(161\) 7.15031 0.563523
\(162\) 6.97103 0.547696
\(163\) −6.90573 −0.540898 −0.270449 0.962734i \(-0.587172\pi\)
−0.270449 + 0.962734i \(0.587172\pi\)
\(164\) 7.83766 0.612018
\(165\) 0 0
\(166\) 0.692542 0.0537517
\(167\) −2.49550 −0.193108 −0.0965538 0.995328i \(-0.530782\pi\)
−0.0965538 + 0.995328i \(0.530782\pi\)
\(168\) 5.88941 0.454378
\(169\) −12.9945 −0.999576
\(170\) 0 0
\(171\) −9.86741 −0.754580
\(172\) 2.74454 0.209269
\(173\) 0.427640 0.0325129 0.0162565 0.999868i \(-0.494825\pi\)
0.0162565 + 0.999868i \(0.494825\pi\)
\(174\) −3.64272 −0.276154
\(175\) 0 0
\(176\) −0.762597 −0.0574829
\(177\) −4.46267 −0.335435
\(178\) −0.809344 −0.0606629
\(179\) 6.01228 0.449379 0.224689 0.974430i \(-0.427863\pi\)
0.224689 + 0.974430i \(0.427863\pi\)
\(180\) 0 0
\(181\) 15.2285 1.13193 0.565963 0.824431i \(-0.308505\pi\)
0.565963 + 0.824431i \(0.308505\pi\)
\(182\) −0.0541398 −0.00401311
\(183\) 20.1575 1.49009
\(184\) 14.2948 1.05383
\(185\) 0 0
\(186\) 0.614658 0.0450689
\(187\) 1.68898 0.123511
\(188\) −0.773536 −0.0564159
\(189\) −2.44357 −0.177744
\(190\) 0 0
\(191\) −0.578755 −0.0418772 −0.0209386 0.999781i \(-0.506665\pi\)
−0.0209386 + 0.999781i \(0.506665\pi\)
\(192\) 0.346907 0.0250359
\(193\) 2.26365 0.162941 0.0814706 0.996676i \(-0.474038\pi\)
0.0814706 + 0.996676i \(0.474038\pi\)
\(194\) 9.40261 0.675068
\(195\) 0 0
\(196\) 9.07132 0.647952
\(197\) −12.3730 −0.881542 −0.440771 0.897620i \(-0.645295\pi\)
−0.440771 + 0.897620i \(0.645295\pi\)
\(198\) 0.575044 0.0408666
\(199\) 11.8775 0.841976 0.420988 0.907066i \(-0.361684\pi\)
0.420988 + 0.907066i \(0.361684\pi\)
\(200\) 0 0
\(201\) 3.45892 0.243974
\(202\) 3.38064 0.237861
\(203\) 2.91442 0.204552
\(204\) 13.7410 0.962065
\(205\) 0 0
\(206\) 2.03221 0.141590
\(207\) 12.8045 0.889974
\(208\) 0.128572 0.00891489
\(209\) 2.11971 0.146623
\(210\) 0 0
\(211\) −11.3488 −0.781281 −0.390641 0.920543i \(-0.627746\pi\)
−0.390641 + 0.920543i \(0.627746\pi\)
\(212\) 3.66725 0.251868
\(213\) 31.8344 2.18126
\(214\) −5.92759 −0.405202
\(215\) 0 0
\(216\) −4.88517 −0.332394
\(217\) −0.491767 −0.0333833
\(218\) −1.91325 −0.129582
\(219\) −34.3034 −2.31801
\(220\) 0 0
\(221\) −0.284760 −0.0191550
\(222\) 15.6211 1.04842
\(223\) 3.01780 0.202087 0.101043 0.994882i \(-0.467782\pi\)
0.101043 + 0.994882i \(0.467782\pi\)
\(224\) −6.50370 −0.434547
\(225\) 0 0
\(226\) 3.67924 0.244739
\(227\) −14.3773 −0.954257 −0.477129 0.878833i \(-0.658322\pi\)
−0.477129 + 0.878833i \(0.658322\pi\)
\(228\) 17.2452 1.14209
\(229\) −26.5382 −1.75369 −0.876847 0.480769i \(-0.840358\pi\)
−0.876847 + 0.480769i \(0.840358\pi\)
\(230\) 0 0
\(231\) −1.13325 −0.0745627
\(232\) 5.82648 0.382527
\(233\) −15.2500 −0.999061 −0.499530 0.866296i \(-0.666494\pi\)
−0.499530 + 0.866296i \(0.666494\pi\)
\(234\) −0.0969514 −0.00633791
\(235\) 0 0
\(236\) 3.16636 0.206113
\(237\) 4.15329 0.269785
\(238\) 2.79583 0.181227
\(239\) −9.98370 −0.645792 −0.322896 0.946434i \(-0.604656\pi\)
−0.322896 + 0.946434i \(0.604656\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 6.88114 0.442337
\(243\) −18.1987 −1.16745
\(244\) −14.3022 −0.915606
\(245\) 0 0
\(246\) 7.03421 0.448485
\(247\) −0.357378 −0.0227394
\(248\) −0.983137 −0.0624292
\(249\) −2.44405 −0.154885
\(250\) 0 0
\(251\) −19.2151 −1.21285 −0.606424 0.795141i \(-0.707397\pi\)
−0.606424 + 0.795141i \(0.707397\pi\)
\(252\) −3.74301 −0.235788
\(253\) −2.75065 −0.172932
\(254\) −12.2446 −0.768293
\(255\) 0 0
\(256\) −7.48060 −0.467538
\(257\) 29.6396 1.84887 0.924435 0.381339i \(-0.124537\pi\)
0.924435 + 0.381339i \(0.124537\pi\)
\(258\) 2.46320 0.153352
\(259\) −12.4979 −0.776580
\(260\) 0 0
\(261\) 5.21903 0.323050
\(262\) 9.59545 0.592809
\(263\) 24.3550 1.50180 0.750898 0.660418i \(-0.229621\pi\)
0.750898 + 0.660418i \(0.229621\pi\)
\(264\) −2.26559 −0.139438
\(265\) 0 0
\(266\) 3.50882 0.215139
\(267\) 2.85625 0.174800
\(268\) −2.45418 −0.149913
\(269\) −15.0768 −0.919248 −0.459624 0.888114i \(-0.652016\pi\)
−0.459624 + 0.888114i \(0.652016\pi\)
\(270\) 0 0
\(271\) 23.5456 1.43029 0.715146 0.698975i \(-0.246360\pi\)
0.715146 + 0.698975i \(0.246360\pi\)
\(272\) −6.63960 −0.402585
\(273\) 0.191064 0.0115637
\(274\) 6.60848 0.399233
\(275\) 0 0
\(276\) −22.3784 −1.34702
\(277\) −4.70682 −0.282806 −0.141403 0.989952i \(-0.545161\pi\)
−0.141403 + 0.989952i \(0.545161\pi\)
\(278\) 1.46943 0.0881304
\(279\) −0.880637 −0.0527224
\(280\) 0 0
\(281\) 2.94319 0.175576 0.0877879 0.996139i \(-0.472020\pi\)
0.0877879 + 0.996139i \(0.472020\pi\)
\(282\) −0.694240 −0.0413414
\(283\) −12.3920 −0.736628 −0.368314 0.929702i \(-0.620065\pi\)
−0.368314 + 0.929702i \(0.620065\pi\)
\(284\) −22.5872 −1.34030
\(285\) 0 0
\(286\) 0.0208270 0.00123153
\(287\) −5.62783 −0.332201
\(288\) −11.6466 −0.686281
\(289\) −2.29474 −0.134985
\(290\) 0 0
\(291\) −33.1827 −1.94521
\(292\) 24.3390 1.42433
\(293\) 11.0669 0.646532 0.323266 0.946308i \(-0.395219\pi\)
0.323266 + 0.946308i \(0.395219\pi\)
\(294\) 8.14141 0.474817
\(295\) 0 0
\(296\) −24.9856 −1.45226
\(297\) 0.940016 0.0545453
\(298\) 7.12855 0.412946
\(299\) 0.463754 0.0268196
\(300\) 0 0
\(301\) −1.97072 −0.113590
\(302\) 4.24720 0.244399
\(303\) −11.9306 −0.685396
\(304\) −8.33282 −0.477920
\(305\) 0 0
\(306\) 5.00666 0.286212
\(307\) 19.5529 1.11595 0.557973 0.829859i \(-0.311579\pi\)
0.557973 + 0.829859i \(0.311579\pi\)
\(308\) 0.804069 0.0458161
\(309\) −7.17184 −0.407992
\(310\) 0 0
\(311\) 6.79509 0.385314 0.192657 0.981266i \(-0.438289\pi\)
0.192657 + 0.981266i \(0.438289\pi\)
\(312\) 0.381974 0.0216250
\(313\) −4.82490 −0.272719 −0.136360 0.990659i \(-0.543540\pi\)
−0.136360 + 0.990659i \(0.543540\pi\)
\(314\) −14.5520 −0.821217
\(315\) 0 0
\(316\) −2.94686 −0.165774
\(317\) −4.07296 −0.228760 −0.114380 0.993437i \(-0.536488\pi\)
−0.114380 + 0.993437i \(0.536488\pi\)
\(318\) 3.29132 0.184568
\(319\) −1.12115 −0.0627721
\(320\) 0 0
\(321\) 20.9190 1.16759
\(322\) −4.55324 −0.253742
\(323\) 18.4554 1.02688
\(324\) 17.4553 0.969737
\(325\) 0 0
\(326\) 4.39749 0.243554
\(327\) 6.75204 0.373389
\(328\) −11.2511 −0.621239
\(329\) 0.555438 0.0306223
\(330\) 0 0
\(331\) −29.2742 −1.60906 −0.804528 0.593915i \(-0.797582\pi\)
−0.804528 + 0.593915i \(0.797582\pi\)
\(332\) 1.73411 0.0951714
\(333\) −22.3807 −1.22645
\(334\) 1.58911 0.0869520
\(335\) 0 0
\(336\) 4.45496 0.243038
\(337\) 3.70484 0.201816 0.100908 0.994896i \(-0.467825\pi\)
0.100908 + 0.994896i \(0.467825\pi\)
\(338\) 8.27474 0.450086
\(339\) −12.9844 −0.705215
\(340\) 0 0
\(341\) 0.189178 0.0102445
\(342\) 6.28345 0.339770
\(343\) −14.5282 −0.784448
\(344\) −3.93984 −0.212422
\(345\) 0 0
\(346\) −0.272317 −0.0146398
\(347\) 20.8963 1.12177 0.560886 0.827893i \(-0.310460\pi\)
0.560886 + 0.827893i \(0.310460\pi\)
\(348\) −9.12128 −0.488952
\(349\) −28.4273 −1.52168 −0.760840 0.648939i \(-0.775213\pi\)
−0.760840 + 0.648939i \(0.775213\pi\)
\(350\) 0 0
\(351\) −0.158485 −0.00845930
\(352\) 2.50190 0.133352
\(353\) −11.3118 −0.602067 −0.301033 0.953614i \(-0.597332\pi\)
−0.301033 + 0.953614i \(0.597332\pi\)
\(354\) 2.84178 0.151039
\(355\) 0 0
\(356\) −2.02657 −0.107408
\(357\) −9.86676 −0.522204
\(358\) −3.82855 −0.202345
\(359\) 10.1228 0.534263 0.267132 0.963660i \(-0.413924\pi\)
0.267132 + 0.963660i \(0.413924\pi\)
\(360\) 0 0
\(361\) 4.16181 0.219043
\(362\) −9.69733 −0.509680
\(363\) −24.2842 −1.27459
\(364\) −0.135565 −0.00710551
\(365\) 0 0
\(366\) −12.8361 −0.670953
\(367\) −3.11637 −0.162673 −0.0813366 0.996687i \(-0.525919\pi\)
−0.0813366 + 0.996687i \(0.525919\pi\)
\(368\) 10.8131 0.563673
\(369\) −10.0781 −0.524645
\(370\) 0 0
\(371\) −2.63327 −0.136713
\(372\) 1.53909 0.0797980
\(373\) −6.89555 −0.357038 −0.178519 0.983936i \(-0.557131\pi\)
−0.178519 + 0.983936i \(0.557131\pi\)
\(374\) −1.07553 −0.0556141
\(375\) 0 0
\(376\) 1.11043 0.0572659
\(377\) 0.189023 0.00973517
\(378\) 1.55604 0.0800341
\(379\) 26.3335 1.35266 0.676330 0.736599i \(-0.263569\pi\)
0.676330 + 0.736599i \(0.263569\pi\)
\(380\) 0 0
\(381\) 43.2123 2.21383
\(382\) 0.368545 0.0188564
\(383\) −38.3736 −1.96080 −0.980400 0.197019i \(-0.936874\pi\)
−0.980400 + 0.197019i \(0.936874\pi\)
\(384\) 25.3102 1.29161
\(385\) 0 0
\(386\) −1.44147 −0.0733688
\(387\) −3.52908 −0.179393
\(388\) 23.5439 1.19526
\(389\) 7.49361 0.379941 0.189970 0.981790i \(-0.439161\pi\)
0.189970 + 0.981790i \(0.439161\pi\)
\(390\) 0 0
\(391\) −23.9487 −1.21114
\(392\) −13.0221 −0.657713
\(393\) −33.8633 −1.70818
\(394\) 7.87901 0.396939
\(395\) 0 0
\(396\) 1.43990 0.0723575
\(397\) −5.36992 −0.269509 −0.134754 0.990879i \(-0.543025\pi\)
−0.134754 + 0.990879i \(0.543025\pi\)
\(398\) −7.56347 −0.379123
\(399\) −12.3830 −0.619923
\(400\) 0 0
\(401\) −24.6951 −1.23321 −0.616606 0.787272i \(-0.711493\pi\)
−0.616606 + 0.787272i \(0.711493\pi\)
\(402\) −2.20260 −0.109856
\(403\) −0.0318950 −0.00158880
\(404\) 8.46504 0.421151
\(405\) 0 0
\(406\) −1.85587 −0.0921052
\(407\) 4.80780 0.238314
\(408\) −19.7255 −0.976559
\(409\) −23.7785 −1.17577 −0.587885 0.808945i \(-0.700039\pi\)
−0.587885 + 0.808945i \(0.700039\pi\)
\(410\) 0 0
\(411\) −23.3220 −1.15039
\(412\) 5.08859 0.250697
\(413\) −2.27361 −0.111877
\(414\) −8.15375 −0.400735
\(415\) 0 0
\(416\) −0.421816 −0.0206812
\(417\) −5.18575 −0.253947
\(418\) −1.34980 −0.0660211
\(419\) −31.0372 −1.51627 −0.758133 0.652100i \(-0.773888\pi\)
−0.758133 + 0.652100i \(0.773888\pi\)
\(420\) 0 0
\(421\) −2.89741 −0.141211 −0.0706055 0.997504i \(-0.522493\pi\)
−0.0706055 + 0.997504i \(0.522493\pi\)
\(422\) 7.22676 0.351793
\(423\) 0.994656 0.0483618
\(424\) −5.26441 −0.255663
\(425\) 0 0
\(426\) −20.2718 −0.982170
\(427\) 10.2697 0.496987
\(428\) −14.8425 −0.717440
\(429\) −0.0735004 −0.00354863
\(430\) 0 0
\(431\) −30.6994 −1.47874 −0.739370 0.673299i \(-0.764877\pi\)
−0.739370 + 0.673299i \(0.764877\pi\)
\(432\) −3.69532 −0.177791
\(433\) 26.8147 1.28863 0.644316 0.764759i \(-0.277142\pi\)
0.644316 + 0.764759i \(0.277142\pi\)
\(434\) 0.313152 0.0150318
\(435\) 0 0
\(436\) −4.79073 −0.229434
\(437\) −30.0560 −1.43777
\(438\) 21.8440 1.04375
\(439\) −16.8791 −0.805594 −0.402797 0.915289i \(-0.631962\pi\)
−0.402797 + 0.915289i \(0.631962\pi\)
\(440\) 0 0
\(441\) −11.6644 −0.555448
\(442\) 0.181332 0.00862506
\(443\) 16.8323 0.799729 0.399864 0.916574i \(-0.369057\pi\)
0.399864 + 0.916574i \(0.369057\pi\)
\(444\) 39.1147 1.85630
\(445\) 0 0
\(446\) −1.92170 −0.0909951
\(447\) −25.1573 −1.18990
\(448\) 0.176740 0.00835017
\(449\) 14.1492 0.667741 0.333870 0.942619i \(-0.391645\pi\)
0.333870 + 0.942619i \(0.391645\pi\)
\(450\) 0 0
\(451\) 2.16497 0.101944
\(452\) 9.21272 0.433330
\(453\) −14.9888 −0.704235
\(454\) 9.15532 0.429680
\(455\) 0 0
\(456\) −24.7559 −1.15930
\(457\) −4.43915 −0.207655 −0.103827 0.994595i \(-0.533109\pi\)
−0.103827 + 0.994595i \(0.533109\pi\)
\(458\) 16.8992 0.789649
\(459\) 8.18432 0.382011
\(460\) 0 0
\(461\) 0.00973326 0.000453323 0 0.000226661 1.00000i \(-0.499928\pi\)
0.000226661 1.00000i \(0.499928\pi\)
\(462\) 0.721643 0.0335739
\(463\) 21.6957 1.00829 0.504143 0.863620i \(-0.331809\pi\)
0.504143 + 0.863620i \(0.331809\pi\)
\(464\) 4.40735 0.204606
\(465\) 0 0
\(466\) 9.71103 0.449855
\(467\) 24.0487 1.11284 0.556422 0.830900i \(-0.312174\pi\)
0.556422 + 0.830900i \(0.312174\pi\)
\(468\) −0.242764 −0.0112217
\(469\) 1.76223 0.0813721
\(470\) 0 0
\(471\) 51.3554 2.36633
\(472\) −4.54538 −0.209218
\(473\) 0.758114 0.0348581
\(474\) −2.64477 −0.121478
\(475\) 0 0
\(476\) 7.00068 0.320876
\(477\) −4.71556 −0.215911
\(478\) 6.35751 0.290786
\(479\) 19.0129 0.868720 0.434360 0.900739i \(-0.356975\pi\)
0.434360 + 0.900739i \(0.356975\pi\)
\(480\) 0 0
\(481\) −0.810585 −0.0369595
\(482\) −0.636788 −0.0290049
\(483\) 16.0688 0.731156
\(484\) 17.2302 0.783190
\(485\) 0 0
\(486\) 11.5887 0.525674
\(487\) −23.1741 −1.05012 −0.525058 0.851066i \(-0.675956\pi\)
−0.525058 + 0.851066i \(0.675956\pi\)
\(488\) 20.5311 0.929401
\(489\) −15.5191 −0.701800
\(490\) 0 0
\(491\) 17.8038 0.803473 0.401736 0.915755i \(-0.368407\pi\)
0.401736 + 0.915755i \(0.368407\pi\)
\(492\) 17.6135 0.794076
\(493\) −9.76133 −0.439628
\(494\) 0.227574 0.0102391
\(495\) 0 0
\(496\) −0.743679 −0.0333922
\(497\) 16.2188 0.727510
\(498\) 1.55634 0.0697413
\(499\) −13.6724 −0.612060 −0.306030 0.952022i \(-0.599001\pi\)
−0.306030 + 0.952022i \(0.599001\pi\)
\(500\) 0 0
\(501\) −5.60810 −0.250552
\(502\) 12.2360 0.546118
\(503\) −13.1075 −0.584433 −0.292216 0.956352i \(-0.594393\pi\)
−0.292216 + 0.956352i \(0.594393\pi\)
\(504\) 5.37317 0.239340
\(505\) 0 0
\(506\) 1.75158 0.0778672
\(507\) −29.2023 −1.29692
\(508\) −30.6601 −1.36032
\(509\) −14.6586 −0.649731 −0.324865 0.945760i \(-0.605319\pi\)
−0.324865 + 0.945760i \(0.605319\pi\)
\(510\) 0 0
\(511\) −17.4766 −0.773121
\(512\) −17.7616 −0.784957
\(513\) 10.2715 0.453496
\(514\) −18.8742 −0.832505
\(515\) 0 0
\(516\) 6.16777 0.271521
\(517\) −0.213671 −0.00939723
\(518\) 7.95851 0.349677
\(519\) 0.961031 0.0421846
\(520\) 0 0
\(521\) 5.24664 0.229859 0.114930 0.993374i \(-0.463336\pi\)
0.114930 + 0.993374i \(0.463336\pi\)
\(522\) −3.32342 −0.145462
\(523\) 26.4312 1.15575 0.577877 0.816124i \(-0.303881\pi\)
0.577877 + 0.816124i \(0.303881\pi\)
\(524\) 24.0267 1.04961
\(525\) 0 0
\(526\) −15.5090 −0.676225
\(527\) 1.64709 0.0717482
\(528\) −1.71377 −0.0745824
\(529\) 16.0023 0.695754
\(530\) 0 0
\(531\) −4.07149 −0.176687
\(532\) 8.78598 0.380921
\(533\) −0.365009 −0.0158103
\(534\) −1.81883 −0.0787083
\(535\) 0 0
\(536\) 3.52303 0.152172
\(537\) 13.5113 0.583056
\(538\) 9.60072 0.413916
\(539\) 2.50574 0.107930
\(540\) 0 0
\(541\) 40.6899 1.74940 0.874698 0.484668i \(-0.161060\pi\)
0.874698 + 0.484668i \(0.161060\pi\)
\(542\) −14.9936 −0.644028
\(543\) 34.2228 1.46864
\(544\) 21.7830 0.933938
\(545\) 0 0
\(546\) −0.121668 −0.00520689
\(547\) 16.6696 0.712740 0.356370 0.934345i \(-0.384014\pi\)
0.356370 + 0.934345i \(0.384014\pi\)
\(548\) 16.5475 0.706872
\(549\) 18.3906 0.784892
\(550\) 0 0
\(551\) −12.2506 −0.521895
\(552\) 32.1246 1.36731
\(553\) 2.11599 0.0899811
\(554\) 2.99725 0.127341
\(555\) 0 0
\(556\) 3.67940 0.156042
\(557\) −10.8329 −0.459006 −0.229503 0.973308i \(-0.573710\pi\)
−0.229503 + 0.973308i \(0.573710\pi\)
\(558\) 0.560780 0.0237397
\(559\) −0.127817 −0.00540606
\(560\) 0 0
\(561\) 3.79563 0.160252
\(562\) −1.87419 −0.0790578
\(563\) −28.6816 −1.20879 −0.604393 0.796686i \(-0.706584\pi\)
−0.604393 + 0.796686i \(0.706584\pi\)
\(564\) −1.73836 −0.0731981
\(565\) 0 0
\(566\) 7.89108 0.331687
\(567\) −12.5338 −0.526369
\(568\) 32.4244 1.36050
\(569\) 12.8372 0.538161 0.269081 0.963118i \(-0.413280\pi\)
0.269081 + 0.963118i \(0.413280\pi\)
\(570\) 0 0
\(571\) 2.68924 0.112541 0.0562707 0.998416i \(-0.482079\pi\)
0.0562707 + 0.998416i \(0.482079\pi\)
\(572\) 0.0521502 0.00218051
\(573\) −1.30063 −0.0543345
\(574\) 3.58374 0.149582
\(575\) 0 0
\(576\) 0.316498 0.0131874
\(577\) 3.19429 0.132980 0.0664900 0.997787i \(-0.478820\pi\)
0.0664900 + 0.997787i \(0.478820\pi\)
\(578\) 1.46126 0.0607806
\(579\) 5.08708 0.211412
\(580\) 0 0
\(581\) −1.24518 −0.0516586
\(582\) 21.1304 0.875882
\(583\) 1.01299 0.0419538
\(584\) −34.9391 −1.44579
\(585\) 0 0
\(586\) −7.04724 −0.291119
\(587\) 9.55051 0.394192 0.197096 0.980384i \(-0.436849\pi\)
0.197096 + 0.980384i \(0.436849\pi\)
\(588\) 20.3859 0.840699
\(589\) 2.06712 0.0851743
\(590\) 0 0
\(591\) −27.8058 −1.14378
\(592\) −18.9000 −0.776786
\(593\) −21.1508 −0.868559 −0.434280 0.900778i \(-0.642997\pi\)
−0.434280 + 0.900778i \(0.642997\pi\)
\(594\) −0.598591 −0.0245605
\(595\) 0 0
\(596\) 17.8497 0.731152
\(597\) 26.6922 1.09244
\(598\) −0.295313 −0.0120762
\(599\) 2.77929 0.113559 0.0567793 0.998387i \(-0.481917\pi\)
0.0567793 + 0.998387i \(0.481917\pi\)
\(600\) 0 0
\(601\) −18.5051 −0.754837 −0.377418 0.926043i \(-0.623188\pi\)
−0.377418 + 0.926043i \(0.623188\pi\)
\(602\) 1.25493 0.0511472
\(603\) 3.15572 0.128511
\(604\) 10.6349 0.432727
\(605\) 0 0
\(606\) 7.59728 0.308618
\(607\) −14.5288 −0.589706 −0.294853 0.955543i \(-0.595271\pi\)
−0.294853 + 0.955543i \(0.595271\pi\)
\(608\) 27.3380 1.10870
\(609\) 6.54954 0.265401
\(610\) 0 0
\(611\) 0.0360245 0.00145739
\(612\) 12.5365 0.506760
\(613\) −14.9699 −0.604627 −0.302314 0.953209i \(-0.597759\pi\)
−0.302314 + 0.953209i \(0.597759\pi\)
\(614\) −12.4511 −0.502485
\(615\) 0 0
\(616\) −1.15426 −0.0465063
\(617\) −0.478194 −0.0192514 −0.00962568 0.999954i \(-0.503064\pi\)
−0.00962568 + 0.999954i \(0.503064\pi\)
\(618\) 4.56695 0.183710
\(619\) 29.2455 1.17548 0.587738 0.809052i \(-0.300019\pi\)
0.587738 + 0.809052i \(0.300019\pi\)
\(620\) 0 0
\(621\) −13.3288 −0.534867
\(622\) −4.32704 −0.173498
\(623\) 1.45518 0.0583006
\(624\) 0.288939 0.0115668
\(625\) 0 0
\(626\) 3.07244 0.122799
\(627\) 4.76359 0.190239
\(628\) −36.4378 −1.45403
\(629\) 41.8594 1.66904
\(630\) 0 0
\(631\) 25.1784 1.00234 0.501168 0.865350i \(-0.332904\pi\)
0.501168 + 0.865350i \(0.332904\pi\)
\(632\) 4.23027 0.168271
\(633\) −25.5039 −1.01369
\(634\) 2.59362 0.103006
\(635\) 0 0
\(636\) 8.24137 0.326792
\(637\) −0.422462 −0.0167386
\(638\) 0.713932 0.0282648
\(639\) 29.0439 1.14896
\(640\) 0 0
\(641\) −47.7764 −1.88705 −0.943527 0.331297i \(-0.892514\pi\)
−0.943527 + 0.331297i \(0.892514\pi\)
\(642\) −13.3210 −0.525738
\(643\) −1.76572 −0.0696332 −0.0348166 0.999394i \(-0.511085\pi\)
−0.0348166 + 0.999394i \(0.511085\pi\)
\(644\) −11.4012 −0.449269
\(645\) 0 0
\(646\) −11.7522 −0.462383
\(647\) 17.7016 0.695921 0.347961 0.937509i \(-0.386874\pi\)
0.347961 + 0.937509i \(0.386874\pi\)
\(648\) −25.0574 −0.984347
\(649\) 0.874632 0.0343323
\(650\) 0 0
\(651\) −1.10514 −0.0433139
\(652\) 11.0112 0.431231
\(653\) −36.0403 −1.41037 −0.705183 0.709025i \(-0.749135\pi\)
−0.705183 + 0.709025i \(0.749135\pi\)
\(654\) −4.29962 −0.168129
\(655\) 0 0
\(656\) −8.51074 −0.332289
\(657\) −31.2965 −1.22099
\(658\) −0.353696 −0.0137885
\(659\) −31.7767 −1.23784 −0.618922 0.785452i \(-0.712431\pi\)
−0.618922 + 0.785452i \(0.712431\pi\)
\(660\) 0 0
\(661\) 34.0434 1.32413 0.662067 0.749445i \(-0.269679\pi\)
0.662067 + 0.749445i \(0.269679\pi\)
\(662\) 18.6415 0.724521
\(663\) −0.639936 −0.0248531
\(664\) −2.48934 −0.0966052
\(665\) 0 0
\(666\) 14.2518 0.552245
\(667\) 15.8971 0.615538
\(668\) 3.97907 0.153955
\(669\) 6.78186 0.262202
\(670\) 0 0
\(671\) −3.95065 −0.152513
\(672\) −14.6157 −0.563812
\(673\) 36.3663 1.40182 0.700909 0.713251i \(-0.252778\pi\)
0.700909 + 0.713251i \(0.252778\pi\)
\(674\) −2.35920 −0.0908731
\(675\) 0 0
\(676\) 20.7197 0.796912
\(677\) 27.7344 1.06592 0.532959 0.846141i \(-0.321080\pi\)
0.532959 + 0.846141i \(0.321080\pi\)
\(678\) 8.26831 0.317543
\(679\) −16.9057 −0.648781
\(680\) 0 0
\(681\) −32.3100 −1.23812
\(682\) −0.120466 −0.00461288
\(683\) −31.2794 −1.19687 −0.598437 0.801170i \(-0.704211\pi\)
−0.598437 + 0.801170i \(0.704211\pi\)
\(684\) 15.7336 0.601589
\(685\) 0 0
\(686\) 9.25138 0.353219
\(687\) −59.6390 −2.27537
\(688\) −2.98024 −0.113620
\(689\) −0.170788 −0.00650652
\(690\) 0 0
\(691\) 48.1424 1.83142 0.915712 0.401836i \(-0.131628\pi\)
0.915712 + 0.401836i \(0.131628\pi\)
\(692\) −0.681873 −0.0259209
\(693\) −1.03392 −0.0392753
\(694\) −13.3065 −0.505109
\(695\) 0 0
\(696\) 13.0938 0.496318
\(697\) 18.8494 0.713973
\(698\) 18.1022 0.685179
\(699\) −34.2711 −1.29625
\(700\) 0 0
\(701\) 23.3483 0.881852 0.440926 0.897543i \(-0.354650\pi\)
0.440926 + 0.897543i \(0.354650\pi\)
\(702\) 0.100921 0.00380903
\(703\) 52.5343 1.98137
\(704\) −0.0679898 −0.00256246
\(705\) 0 0
\(706\) 7.20323 0.271097
\(707\) −6.07832 −0.228599
\(708\) 7.11573 0.267425
\(709\) −39.2625 −1.47453 −0.737267 0.675601i \(-0.763884\pi\)
−0.737267 + 0.675601i \(0.763884\pi\)
\(710\) 0 0
\(711\) 3.78923 0.142107
\(712\) 2.90919 0.109026
\(713\) −2.68241 −0.100457
\(714\) 6.28304 0.235137
\(715\) 0 0
\(716\) −9.58658 −0.358267
\(717\) −22.4362 −0.837897
\(718\) −6.44611 −0.240567
\(719\) 2.50667 0.0934830 0.0467415 0.998907i \(-0.485116\pi\)
0.0467415 + 0.998907i \(0.485116\pi\)
\(720\) 0 0
\(721\) −3.65386 −0.136077
\(722\) −2.65019 −0.0986299
\(723\) 2.24729 0.0835775
\(724\) −24.2818 −0.902428
\(725\) 0 0
\(726\) 15.4639 0.573919
\(727\) 17.3890 0.644922 0.322461 0.946583i \(-0.395490\pi\)
0.322461 + 0.946583i \(0.395490\pi\)
\(728\) 0.194606 0.00721256
\(729\) −8.05612 −0.298375
\(730\) 0 0
\(731\) 6.60057 0.244131
\(732\) −32.1412 −1.18797
\(733\) −12.6365 −0.466739 −0.233370 0.972388i \(-0.574975\pi\)
−0.233370 + 0.972388i \(0.574975\pi\)
\(734\) 1.98447 0.0732481
\(735\) 0 0
\(736\) −35.4753 −1.30764
\(737\) −0.677909 −0.0249711
\(738\) 6.41762 0.236236
\(739\) 49.2503 1.81170 0.905850 0.423598i \(-0.139233\pi\)
0.905850 + 0.423598i \(0.139233\pi\)
\(740\) 0 0
\(741\) −0.803131 −0.0295038
\(742\) 1.67684 0.0615586
\(743\) 42.2847 1.55127 0.775637 0.631179i \(-0.217429\pi\)
0.775637 + 0.631179i \(0.217429\pi\)
\(744\) −2.20939 −0.0810002
\(745\) 0 0
\(746\) 4.39101 0.160766
\(747\) −2.22981 −0.0815845
\(748\) −2.69309 −0.0984690
\(749\) 10.6577 0.389423
\(750\) 0 0
\(751\) −44.6401 −1.62894 −0.814471 0.580204i \(-0.802973\pi\)
−0.814471 + 0.580204i \(0.802973\pi\)
\(752\) 0.839966 0.0306304
\(753\) −43.1819 −1.57364
\(754\) −0.120368 −0.00438353
\(755\) 0 0
\(756\) 3.89628 0.141706
\(757\) −28.3936 −1.03198 −0.515992 0.856593i \(-0.672577\pi\)
−0.515992 + 0.856593i \(0.672577\pi\)
\(758\) −16.7689 −0.609072
\(759\) −6.18149 −0.224374
\(760\) 0 0
\(761\) 27.7195 1.00483 0.502415 0.864627i \(-0.332445\pi\)
0.502415 + 0.864627i \(0.332445\pi\)
\(762\) −27.5171 −0.996838
\(763\) 3.43998 0.124536
\(764\) 0.922825 0.0333866
\(765\) 0 0
\(766\) 24.4359 0.882904
\(767\) −0.147461 −0.00532452
\(768\) −16.8111 −0.606617
\(769\) 35.1939 1.26912 0.634562 0.772872i \(-0.281181\pi\)
0.634562 + 0.772872i \(0.281181\pi\)
\(770\) 0 0
\(771\) 66.6088 2.39886
\(772\) −3.60939 −0.129905
\(773\) −0.165321 −0.00594618 −0.00297309 0.999996i \(-0.500946\pi\)
−0.00297309 + 0.999996i \(0.500946\pi\)
\(774\) 2.24728 0.0807768
\(775\) 0 0
\(776\) −33.7977 −1.21327
\(777\) −28.0863 −1.00759
\(778\) −4.77184 −0.171079
\(779\) 23.6564 0.847577
\(780\) 0 0
\(781\) −6.23918 −0.223255
\(782\) 15.2502 0.545348
\(783\) −5.43273 −0.194150
\(784\) −9.85035 −0.351798
\(785\) 0 0
\(786\) 21.5637 0.769153
\(787\) 22.9720 0.818863 0.409431 0.912341i \(-0.365727\pi\)
0.409431 + 0.912341i \(0.365727\pi\)
\(788\) 19.7288 0.702810
\(789\) 54.7328 1.94854
\(790\) 0 0
\(791\) −6.61519 −0.235209
\(792\) −2.06700 −0.0734476
\(793\) 0.666072 0.0236529
\(794\) 3.41950 0.121354
\(795\) 0 0
\(796\) −18.9387 −0.671265
\(797\) 32.6066 1.15499 0.577493 0.816395i \(-0.304031\pi\)
0.577493 + 0.816395i \(0.304031\pi\)
\(798\) 7.88532 0.279137
\(799\) −1.86034 −0.0658141
\(800\) 0 0
\(801\) 2.60588 0.0920743
\(802\) 15.7255 0.555288
\(803\) 6.72307 0.237252
\(804\) −5.51525 −0.194508
\(805\) 0 0
\(806\) 0.0203103 0.000715401 0
\(807\) −33.8818 −1.19270
\(808\) −12.1517 −0.427496
\(809\) 19.3356 0.679802 0.339901 0.940461i \(-0.389606\pi\)
0.339901 + 0.940461i \(0.389606\pi\)
\(810\) 0 0
\(811\) −45.2010 −1.58722 −0.793612 0.608425i \(-0.791802\pi\)
−0.793612 + 0.608425i \(0.791802\pi\)
\(812\) −4.64704 −0.163079
\(813\) 52.9137 1.85576
\(814\) −3.06155 −0.107307
\(815\) 0 0
\(816\) −14.9211 −0.522342
\(817\) 8.28383 0.289815
\(818\) 15.1419 0.529423
\(819\) 0.174316 0.00609111
\(820\) 0 0
\(821\) 29.4554 1.02800 0.514001 0.857790i \(-0.328163\pi\)
0.514001 + 0.857790i \(0.328163\pi\)
\(822\) 14.8512 0.517994
\(823\) −49.6297 −1.72998 −0.864991 0.501787i \(-0.832676\pi\)
−0.864991 + 0.501787i \(0.832676\pi\)
\(824\) −7.30476 −0.254473
\(825\) 0 0
\(826\) 1.44781 0.0503757
\(827\) 8.61123 0.299442 0.149721 0.988728i \(-0.452162\pi\)
0.149721 + 0.988728i \(0.452162\pi\)
\(828\) −20.4168 −0.709532
\(829\) −9.81975 −0.341054 −0.170527 0.985353i \(-0.554547\pi\)
−0.170527 + 0.985353i \(0.554547\pi\)
\(830\) 0 0
\(831\) −10.5776 −0.366932
\(832\) 0.0114630 0.000397406 0
\(833\) 21.8164 0.755892
\(834\) 3.30222 0.114347
\(835\) 0 0
\(836\) −3.37987 −0.116895
\(837\) 0.916698 0.0316857
\(838\) 19.7641 0.682740
\(839\) −5.45749 −0.188414 −0.0942068 0.995553i \(-0.530031\pi\)
−0.0942068 + 0.995553i \(0.530031\pi\)
\(840\) 0 0
\(841\) −22.5204 −0.776567
\(842\) 1.84504 0.0635841
\(843\) 6.61419 0.227805
\(844\) 18.0956 0.622876
\(845\) 0 0
\(846\) −0.633386 −0.0217762
\(847\) −12.3721 −0.425112
\(848\) −3.98219 −0.136749
\(849\) −27.8484 −0.955753
\(850\) 0 0
\(851\) −68.1714 −2.33689
\(852\) −50.7599 −1.73901
\(853\) 1.89562 0.0649050 0.0324525 0.999473i \(-0.489668\pi\)
0.0324525 + 0.999473i \(0.489668\pi\)
\(854\) −6.53964 −0.223782
\(855\) 0 0
\(856\) 21.3067 0.728249
\(857\) −40.1087 −1.37009 −0.685044 0.728502i \(-0.740217\pi\)
−0.685044 + 0.728502i \(0.740217\pi\)
\(858\) 0.0468042 0.00159787
\(859\) 56.6142 1.93165 0.965825 0.259195i \(-0.0834573\pi\)
0.965825 + 0.259195i \(0.0834573\pi\)
\(860\) 0 0
\(861\) −12.6474 −0.431021
\(862\) 19.5491 0.665843
\(863\) 15.4130 0.524664 0.262332 0.964978i \(-0.415508\pi\)
0.262332 + 0.964978i \(0.415508\pi\)
\(864\) 12.1235 0.412449
\(865\) 0 0
\(866\) −17.0753 −0.580242
\(867\) −5.15694 −0.175139
\(868\) 0.784123 0.0266149
\(869\) −0.813998 −0.0276130
\(870\) 0 0
\(871\) 0.114294 0.00387271
\(872\) 6.87718 0.232891
\(873\) −30.2740 −1.02462
\(874\) 19.1393 0.647398
\(875\) 0 0
\(876\) 54.6967 1.84803
\(877\) 2.57230 0.0868603 0.0434301 0.999056i \(-0.486171\pi\)
0.0434301 + 0.999056i \(0.486171\pi\)
\(878\) 10.7484 0.362741
\(879\) 24.8704 0.838857
\(880\) 0 0
\(881\) −50.0812 −1.68728 −0.843639 0.536910i \(-0.819591\pi\)
−0.843639 + 0.536910i \(0.819591\pi\)
\(882\) 7.42776 0.250106
\(883\) 29.8568 1.00476 0.502381 0.864646i \(-0.332457\pi\)
0.502381 + 0.864646i \(0.332457\pi\)
\(884\) 0.454049 0.0152713
\(885\) 0 0
\(886\) −10.7186 −0.360100
\(887\) 24.9301 0.837072 0.418536 0.908200i \(-0.362543\pi\)
0.418536 + 0.908200i \(0.362543\pi\)
\(888\) −56.1499 −1.88427
\(889\) 22.0155 0.738375
\(890\) 0 0
\(891\) 4.82160 0.161530
\(892\) −4.81188 −0.161114
\(893\) −2.33476 −0.0781298
\(894\) 16.0199 0.535786
\(895\) 0 0
\(896\) 12.8949 0.430787
\(897\) 1.04219 0.0347976
\(898\) −9.01003 −0.300669
\(899\) −1.09333 −0.0364647
\(900\) 0 0
\(901\) 8.81968 0.293826
\(902\) −1.37863 −0.0459032
\(903\) −4.42877 −0.147380
\(904\) −13.2250 −0.439858
\(905\) 0 0
\(906\) 9.54469 0.317101
\(907\) −27.8785 −0.925689 −0.462844 0.886440i \(-0.653171\pi\)
−0.462844 + 0.886440i \(0.653171\pi\)
\(908\) 22.9247 0.760782
\(909\) −10.8848 −0.361027
\(910\) 0 0
\(911\) −12.1116 −0.401275 −0.200638 0.979666i \(-0.564301\pi\)
−0.200638 + 0.979666i \(0.564301\pi\)
\(912\) −18.7262 −0.620087
\(913\) 0.479005 0.0158528
\(914\) 2.82680 0.0935022
\(915\) 0 0
\(916\) 42.3152 1.39813
\(917\) −17.2524 −0.569725
\(918\) −5.21168 −0.172011
\(919\) −15.4282 −0.508928 −0.254464 0.967082i \(-0.581899\pi\)
−0.254464 + 0.967082i \(0.581899\pi\)
\(920\) 0 0
\(921\) 43.9411 1.44791
\(922\) −0.00619803 −0.000204121 0
\(923\) 1.05191 0.0346241
\(924\) 1.80697 0.0594451
\(925\) 0 0
\(926\) −13.8156 −0.454008
\(927\) −6.54319 −0.214906
\(928\) −14.4595 −0.474657
\(929\) −17.1882 −0.563925 −0.281963 0.959425i \(-0.590985\pi\)
−0.281963 + 0.959425i \(0.590985\pi\)
\(930\) 0 0
\(931\) 27.3799 0.897341
\(932\) 24.3161 0.796501
\(933\) 15.2705 0.499935
\(934\) −15.3140 −0.501088
\(935\) 0 0
\(936\) 0.348492 0.0113908
\(937\) 55.7620 1.82167 0.910833 0.412775i \(-0.135440\pi\)
0.910833 + 0.412775i \(0.135440\pi\)
\(938\) −1.12217 −0.0366400
\(939\) −10.8429 −0.353846
\(940\) 0 0
\(941\) 16.8053 0.547836 0.273918 0.961753i \(-0.411680\pi\)
0.273918 + 0.961753i \(0.411680\pi\)
\(942\) −32.7025 −1.06551
\(943\) −30.6978 −0.999658
\(944\) −3.43828 −0.111907
\(945\) 0 0
\(946\) −0.482758 −0.0156958
\(947\) −13.5446 −0.440139 −0.220069 0.975484i \(-0.570628\pi\)
−0.220069 + 0.975484i \(0.570628\pi\)
\(948\) −6.62243 −0.215087
\(949\) −1.13350 −0.0367949
\(950\) 0 0
\(951\) −9.15312 −0.296810
\(952\) −10.0496 −0.325710
\(953\) −25.8635 −0.837802 −0.418901 0.908032i \(-0.637584\pi\)
−0.418901 + 0.908032i \(0.637584\pi\)
\(954\) 3.00281 0.0972197
\(955\) 0 0
\(956\) 15.9190 0.514858
\(957\) −2.51953 −0.0814450
\(958\) −12.1072 −0.391165
\(959\) −11.8819 −0.383687
\(960\) 0 0
\(961\) −30.8155 −0.994049
\(962\) 0.516171 0.0166420
\(963\) 19.0853 0.615016
\(964\) −1.59450 −0.0513554
\(965\) 0 0
\(966\) −10.2324 −0.329223
\(967\) −2.77504 −0.0892392 −0.0446196 0.999004i \(-0.514208\pi\)
−0.0446196 + 0.999004i \(0.514208\pi\)
\(968\) −24.7343 −0.794990
\(969\) 41.4745 1.33235
\(970\) 0 0
\(971\) 50.6358 1.62498 0.812490 0.582975i \(-0.198111\pi\)
0.812490 + 0.582975i \(0.198111\pi\)
\(972\) 29.0178 0.930746
\(973\) −2.64200 −0.0846986
\(974\) 14.7570 0.472844
\(975\) 0 0
\(976\) 15.5305 0.497118
\(977\) −45.4183 −1.45306 −0.726529 0.687135i \(-0.758868\pi\)
−0.726529 + 0.687135i \(0.758868\pi\)
\(978\) 9.88241 0.316005
\(979\) −0.559792 −0.0178910
\(980\) 0 0
\(981\) 6.16018 0.196680
\(982\) −11.3372 −0.361786
\(983\) 22.6856 0.723559 0.361780 0.932264i \(-0.382169\pi\)
0.361780 + 0.932264i \(0.382169\pi\)
\(984\) −25.2845 −0.806040
\(985\) 0 0
\(986\) 6.21590 0.197955
\(987\) 1.24823 0.0397315
\(988\) 0.569840 0.0181290
\(989\) −10.7496 −0.341816
\(990\) 0 0
\(991\) −42.6339 −1.35431 −0.677155 0.735841i \(-0.736787\pi\)
−0.677155 + 0.735841i \(0.736787\pi\)
\(992\) 2.43984 0.0774650
\(993\) −65.7875 −2.08770
\(994\) −10.3279 −0.327582
\(995\) 0 0
\(996\) 3.89703 0.123482
\(997\) 48.2019 1.52657 0.763285 0.646062i \(-0.223585\pi\)
0.763285 + 0.646062i \(0.223585\pi\)
\(998\) 8.70642 0.275597
\(999\) 23.2971 0.737089
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.1.19 46
5.2 odd 4 1205.2.b.c.724.19 46
5.3 odd 4 1205.2.b.c.724.28 yes 46
5.4 even 2 inner 6025.2.a.p.1.28 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.19 46 5.2 odd 4
1205.2.b.c.724.28 yes 46 5.3 odd 4
6025.2.a.p.1.19 46 1.1 even 1 trivial
6025.2.a.p.1.28 46 5.4 even 2 inner