Properties

Label 6025.2.a.p.1.11
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 1.11
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.70963 q^{2} -1.38336 q^{3} +0.922819 q^{4} +2.36503 q^{6} -5.05937 q^{7} +1.84158 q^{8} -1.08631 q^{9} +O(q^{10})\) \(q-1.70963 q^{2} -1.38336 q^{3} +0.922819 q^{4} +2.36503 q^{6} -5.05937 q^{7} +1.84158 q^{8} -1.08631 q^{9} -5.25074 q^{11} -1.27659 q^{12} +2.84467 q^{13} +8.64964 q^{14} -4.99404 q^{16} +6.16813 q^{17} +1.85719 q^{18} +1.47178 q^{19} +6.99894 q^{21} +8.97680 q^{22} -2.54443 q^{23} -2.54756 q^{24} -4.86332 q^{26} +5.65285 q^{27} -4.66889 q^{28} -9.53193 q^{29} -7.94968 q^{31} +4.85479 q^{32} +7.26367 q^{33} -10.5452 q^{34} -1.00247 q^{36} -8.85694 q^{37} -2.51619 q^{38} -3.93520 q^{39} +1.60908 q^{41} -11.9656 q^{42} -0.0179130 q^{43} -4.84548 q^{44} +4.35003 q^{46} +5.95134 q^{47} +6.90856 q^{48} +18.5973 q^{49} -8.53275 q^{51} +2.62511 q^{52} +8.07317 q^{53} -9.66425 q^{54} -9.31723 q^{56} -2.03600 q^{57} +16.2960 q^{58} -3.28732 q^{59} +7.19911 q^{61} +13.5910 q^{62} +5.49606 q^{63} +1.68822 q^{64} -12.4182 q^{66} +2.92491 q^{67} +5.69207 q^{68} +3.51987 q^{69} -4.49618 q^{71} -2.00053 q^{72} -4.29619 q^{73} +15.1421 q^{74} +1.35819 q^{76} +26.5655 q^{77} +6.72772 q^{78} +2.34077 q^{79} -4.56099 q^{81} -2.75093 q^{82} +9.27436 q^{83} +6.45875 q^{84} +0.0306245 q^{86} +13.1861 q^{87} -9.66964 q^{88} +13.8608 q^{89} -14.3922 q^{91} -2.34805 q^{92} +10.9973 q^{93} -10.1746 q^{94} -6.71593 q^{96} -11.0653 q^{97} -31.7944 q^{98} +5.70395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70963 −1.20889 −0.604444 0.796648i \(-0.706605\pi\)
−0.604444 + 0.796648i \(0.706605\pi\)
\(3\) −1.38336 −0.798684 −0.399342 0.916802i \(-0.630761\pi\)
−0.399342 + 0.916802i \(0.630761\pi\)
\(4\) 0.922819 0.461409
\(5\) 0 0
\(6\) 2.36503 0.965519
\(7\) −5.05937 −1.91226 −0.956132 0.292936i \(-0.905368\pi\)
−0.956132 + 0.292936i \(0.905368\pi\)
\(8\) 1.84158 0.651096
\(9\) −1.08631 −0.362104
\(10\) 0 0
\(11\) −5.25074 −1.58316 −0.791579 0.611066i \(-0.790741\pi\)
−0.791579 + 0.611066i \(0.790741\pi\)
\(12\) −1.27659 −0.368520
\(13\) 2.84467 0.788969 0.394485 0.918903i \(-0.370923\pi\)
0.394485 + 0.918903i \(0.370923\pi\)
\(14\) 8.64964 2.31171
\(15\) 0 0
\(16\) −4.99404 −1.24851
\(17\) 6.16813 1.49599 0.747996 0.663704i \(-0.231016\pi\)
0.747996 + 0.663704i \(0.231016\pi\)
\(18\) 1.85719 0.437743
\(19\) 1.47178 0.337649 0.168825 0.985646i \(-0.446003\pi\)
0.168825 + 0.985646i \(0.446003\pi\)
\(20\) 0 0
\(21\) 6.99894 1.52729
\(22\) 8.97680 1.91386
\(23\) −2.54443 −0.530551 −0.265275 0.964173i \(-0.585463\pi\)
−0.265275 + 0.964173i \(0.585463\pi\)
\(24\) −2.54756 −0.520019
\(25\) 0 0
\(26\) −4.86332 −0.953775
\(27\) 5.65285 1.08789
\(28\) −4.66889 −0.882336
\(29\) −9.53193 −1.77003 −0.885017 0.465558i \(-0.845854\pi\)
−0.885017 + 0.465558i \(0.845854\pi\)
\(30\) 0 0
\(31\) −7.94968 −1.42780 −0.713902 0.700245i \(-0.753074\pi\)
−0.713902 + 0.700245i \(0.753074\pi\)
\(32\) 4.85479 0.858214
\(33\) 7.26367 1.26444
\(34\) −10.5452 −1.80849
\(35\) 0 0
\(36\) −1.00247 −0.167078
\(37\) −8.85694 −1.45607 −0.728036 0.685539i \(-0.759567\pi\)
−0.728036 + 0.685539i \(0.759567\pi\)
\(38\) −2.51619 −0.408180
\(39\) −3.93520 −0.630137
\(40\) 0 0
\(41\) 1.60908 0.251297 0.125648 0.992075i \(-0.459899\pi\)
0.125648 + 0.992075i \(0.459899\pi\)
\(42\) −11.9656 −1.84633
\(43\) −0.0179130 −0.00273171 −0.00136585 0.999999i \(-0.500435\pi\)
−0.00136585 + 0.999999i \(0.500435\pi\)
\(44\) −4.84548 −0.730484
\(45\) 0 0
\(46\) 4.35003 0.641376
\(47\) 5.95134 0.868092 0.434046 0.900891i \(-0.357085\pi\)
0.434046 + 0.900891i \(0.357085\pi\)
\(48\) 6.90856 0.997165
\(49\) 18.5973 2.65675
\(50\) 0 0
\(51\) −8.53275 −1.19482
\(52\) 2.62511 0.364038
\(53\) 8.07317 1.10894 0.554468 0.832205i \(-0.312922\pi\)
0.554468 + 0.832205i \(0.312922\pi\)
\(54\) −9.66425 −1.31514
\(55\) 0 0
\(56\) −9.31723 −1.24507
\(57\) −2.03600 −0.269675
\(58\) 16.2960 2.13977
\(59\) −3.28732 −0.427973 −0.213986 0.976837i \(-0.568645\pi\)
−0.213986 + 0.976837i \(0.568645\pi\)
\(60\) 0 0
\(61\) 7.19911 0.921751 0.460876 0.887465i \(-0.347535\pi\)
0.460876 + 0.887465i \(0.347535\pi\)
\(62\) 13.5910 1.72606
\(63\) 5.49606 0.692439
\(64\) 1.68822 0.211027
\(65\) 0 0
\(66\) −12.4182 −1.52857
\(67\) 2.92491 0.357335 0.178667 0.983910i \(-0.442821\pi\)
0.178667 + 0.983910i \(0.442821\pi\)
\(68\) 5.69207 0.690264
\(69\) 3.51987 0.423742
\(70\) 0 0
\(71\) −4.49618 −0.533599 −0.266799 0.963752i \(-0.585966\pi\)
−0.266799 + 0.963752i \(0.585966\pi\)
\(72\) −2.00053 −0.235765
\(73\) −4.29619 −0.502831 −0.251416 0.967879i \(-0.580896\pi\)
−0.251416 + 0.967879i \(0.580896\pi\)
\(74\) 15.1421 1.76023
\(75\) 0 0
\(76\) 1.35819 0.155795
\(77\) 26.5655 3.02742
\(78\) 6.72772 0.761765
\(79\) 2.34077 0.263357 0.131679 0.991292i \(-0.457963\pi\)
0.131679 + 0.991292i \(0.457963\pi\)
\(80\) 0 0
\(81\) −4.56099 −0.506776
\(82\) −2.75093 −0.303790
\(83\) 9.27436 1.01799 0.508997 0.860768i \(-0.330016\pi\)
0.508997 + 0.860768i \(0.330016\pi\)
\(84\) 6.45875 0.704708
\(85\) 0 0
\(86\) 0.0306245 0.00330232
\(87\) 13.1861 1.41370
\(88\) −9.66964 −1.03079
\(89\) 13.8608 1.46924 0.734619 0.678479i \(-0.237361\pi\)
0.734619 + 0.678479i \(0.237361\pi\)
\(90\) 0 0
\(91\) −14.3922 −1.50872
\(92\) −2.34805 −0.244801
\(93\) 10.9973 1.14036
\(94\) −10.1746 −1.04943
\(95\) 0 0
\(96\) −6.71593 −0.685441
\(97\) −11.0653 −1.12351 −0.561756 0.827303i \(-0.689874\pi\)
−0.561756 + 0.827303i \(0.689874\pi\)
\(98\) −31.7944 −3.21172
\(99\) 5.70395 0.573269
\(100\) 0 0
\(101\) 0.249085 0.0247849 0.0123924 0.999923i \(-0.496055\pi\)
0.0123924 + 0.999923i \(0.496055\pi\)
\(102\) 14.5878 1.44441
\(103\) 13.4549 1.32575 0.662875 0.748730i \(-0.269336\pi\)
0.662875 + 0.748730i \(0.269336\pi\)
\(104\) 5.23867 0.513694
\(105\) 0 0
\(106\) −13.8021 −1.34058
\(107\) 1.30787 0.126437 0.0632185 0.998000i \(-0.479864\pi\)
0.0632185 + 0.998000i \(0.479864\pi\)
\(108\) 5.21655 0.501963
\(109\) 19.2547 1.84426 0.922131 0.386878i \(-0.126446\pi\)
0.922131 + 0.386878i \(0.126446\pi\)
\(110\) 0 0
\(111\) 12.2523 1.16294
\(112\) 25.2667 2.38748
\(113\) 17.0383 1.60283 0.801415 0.598108i \(-0.204081\pi\)
0.801415 + 0.598108i \(0.204081\pi\)
\(114\) 3.48080 0.326007
\(115\) 0 0
\(116\) −8.79624 −0.816710
\(117\) −3.09020 −0.285689
\(118\) 5.62009 0.517371
\(119\) −31.2069 −2.86073
\(120\) 0 0
\(121\) 16.5703 1.50639
\(122\) −12.3078 −1.11429
\(123\) −2.22594 −0.200707
\(124\) −7.33611 −0.658802
\(125\) 0 0
\(126\) −9.39621 −0.837081
\(127\) −10.0749 −0.894007 −0.447004 0.894532i \(-0.647509\pi\)
−0.447004 + 0.894532i \(0.647509\pi\)
\(128\) −12.5958 −1.11332
\(129\) 0.0247801 0.00218177
\(130\) 0 0
\(131\) 5.37122 0.469285 0.234643 0.972082i \(-0.424608\pi\)
0.234643 + 0.972082i \(0.424608\pi\)
\(132\) 6.70305 0.583426
\(133\) −7.44628 −0.645675
\(134\) −5.00050 −0.431978
\(135\) 0 0
\(136\) 11.3591 0.974034
\(137\) −10.2584 −0.876436 −0.438218 0.898869i \(-0.644390\pi\)
−0.438218 + 0.898869i \(0.644390\pi\)
\(138\) −6.01766 −0.512257
\(139\) 14.6133 1.23949 0.619743 0.784805i \(-0.287237\pi\)
0.619743 + 0.784805i \(0.287237\pi\)
\(140\) 0 0
\(141\) −8.23285 −0.693331
\(142\) 7.68679 0.645061
\(143\) −14.9366 −1.24906
\(144\) 5.42509 0.452091
\(145\) 0 0
\(146\) 7.34488 0.607866
\(147\) −25.7267 −2.12191
\(148\) −8.17335 −0.671845
\(149\) −15.8135 −1.29549 −0.647747 0.761856i \(-0.724289\pi\)
−0.647747 + 0.761856i \(0.724289\pi\)
\(150\) 0 0
\(151\) −15.2888 −1.24419 −0.622093 0.782944i \(-0.713717\pi\)
−0.622093 + 0.782944i \(0.713717\pi\)
\(152\) 2.71039 0.219842
\(153\) −6.70052 −0.541705
\(154\) −45.4170 −3.65981
\(155\) 0 0
\(156\) −3.63148 −0.290751
\(157\) −0.857546 −0.0684396 −0.0342198 0.999414i \(-0.510895\pi\)
−0.0342198 + 0.999414i \(0.510895\pi\)
\(158\) −4.00184 −0.318369
\(159\) −11.1681 −0.885689
\(160\) 0 0
\(161\) 12.8732 1.01455
\(162\) 7.79758 0.612635
\(163\) −9.36765 −0.733731 −0.366866 0.930274i \(-0.619569\pi\)
−0.366866 + 0.930274i \(0.619569\pi\)
\(164\) 1.48489 0.115951
\(165\) 0 0
\(166\) −15.8557 −1.23064
\(167\) −2.74053 −0.212069 −0.106034 0.994362i \(-0.533815\pi\)
−0.106034 + 0.994362i \(0.533815\pi\)
\(168\) 12.8891 0.994415
\(169\) −4.90786 −0.377528
\(170\) 0 0
\(171\) −1.59881 −0.122264
\(172\) −0.0165304 −0.00126043
\(173\) −1.88911 −0.143627 −0.0718134 0.997418i \(-0.522879\pi\)
−0.0718134 + 0.997418i \(0.522879\pi\)
\(174\) −22.5433 −1.70900
\(175\) 0 0
\(176\) 26.2224 1.97659
\(177\) 4.54755 0.341815
\(178\) −23.6967 −1.77614
\(179\) −0.490228 −0.0366413 −0.0183207 0.999832i \(-0.505832\pi\)
−0.0183207 + 0.999832i \(0.505832\pi\)
\(180\) 0 0
\(181\) 0.282628 0.0210076 0.0105038 0.999945i \(-0.496656\pi\)
0.0105038 + 0.999945i \(0.496656\pi\)
\(182\) 24.6053 1.82387
\(183\) −9.95896 −0.736188
\(184\) −4.68577 −0.345439
\(185\) 0 0
\(186\) −18.8012 −1.37857
\(187\) −32.3873 −2.36839
\(188\) 5.49201 0.400546
\(189\) −28.5999 −2.08033
\(190\) 0 0
\(191\) 18.5700 1.34368 0.671840 0.740696i \(-0.265504\pi\)
0.671840 + 0.740696i \(0.265504\pi\)
\(192\) −2.33541 −0.168544
\(193\) 25.6312 1.84498 0.922488 0.386026i \(-0.126153\pi\)
0.922488 + 0.386026i \(0.126153\pi\)
\(194\) 18.9175 1.35820
\(195\) 0 0
\(196\) 17.1619 1.22585
\(197\) 12.1900 0.868499 0.434250 0.900793i \(-0.357014\pi\)
0.434250 + 0.900793i \(0.357014\pi\)
\(198\) −9.75162 −0.693017
\(199\) 6.70955 0.475628 0.237814 0.971311i \(-0.423569\pi\)
0.237814 + 0.971311i \(0.423569\pi\)
\(200\) 0 0
\(201\) −4.04621 −0.285398
\(202\) −0.425842 −0.0299621
\(203\) 48.2256 3.38477
\(204\) −7.87418 −0.551303
\(205\) 0 0
\(206\) −23.0028 −1.60268
\(207\) 2.76405 0.192115
\(208\) −14.2064 −0.985036
\(209\) −7.72794 −0.534552
\(210\) 0 0
\(211\) 7.92574 0.545630 0.272815 0.962066i \(-0.412045\pi\)
0.272815 + 0.962066i \(0.412045\pi\)
\(212\) 7.45007 0.511673
\(213\) 6.21984 0.426177
\(214\) −2.23597 −0.152848
\(215\) 0 0
\(216\) 10.4101 0.708321
\(217\) 40.2204 2.73034
\(218\) −32.9183 −2.22951
\(219\) 5.94318 0.401603
\(220\) 0 0
\(221\) 17.5463 1.18029
\(222\) −20.9469 −1.40587
\(223\) 18.7959 1.25867 0.629335 0.777134i \(-0.283327\pi\)
0.629335 + 0.777134i \(0.283327\pi\)
\(224\) −24.5622 −1.64113
\(225\) 0 0
\(226\) −29.1292 −1.93764
\(227\) −1.76519 −0.117160 −0.0585799 0.998283i \(-0.518657\pi\)
−0.0585799 + 0.998283i \(0.518657\pi\)
\(228\) −1.87886 −0.124431
\(229\) −21.1776 −1.39945 −0.699726 0.714411i \(-0.746695\pi\)
−0.699726 + 0.714411i \(0.746695\pi\)
\(230\) 0 0
\(231\) −36.7496 −2.41795
\(232\) −17.5538 −1.15246
\(233\) 6.09009 0.398975 0.199488 0.979900i \(-0.436072\pi\)
0.199488 + 0.979900i \(0.436072\pi\)
\(234\) 5.28308 0.345366
\(235\) 0 0
\(236\) −3.03360 −0.197471
\(237\) −3.23813 −0.210339
\(238\) 53.3521 3.45830
\(239\) −1.39490 −0.0902286 −0.0451143 0.998982i \(-0.514365\pi\)
−0.0451143 + 0.998982i \(0.514365\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −28.3290 −1.82106
\(243\) −10.6490 −0.683137
\(244\) 6.64347 0.425305
\(245\) 0 0
\(246\) 3.80553 0.242632
\(247\) 4.18672 0.266395
\(248\) −14.6399 −0.929637
\(249\) −12.8298 −0.813055
\(250\) 0 0
\(251\) 10.4868 0.661920 0.330960 0.943645i \(-0.392627\pi\)
0.330960 + 0.943645i \(0.392627\pi\)
\(252\) 5.07187 0.319498
\(253\) 13.3602 0.839946
\(254\) 17.2244 1.08075
\(255\) 0 0
\(256\) 18.1577 1.13485
\(257\) 14.8521 0.926448 0.463224 0.886241i \(-0.346692\pi\)
0.463224 + 0.886241i \(0.346692\pi\)
\(258\) −0.0423647 −0.00263751
\(259\) 44.8106 2.78439
\(260\) 0 0
\(261\) 10.3547 0.640937
\(262\) −9.18277 −0.567313
\(263\) −1.20965 −0.0745901 −0.0372951 0.999304i \(-0.511874\pi\)
−0.0372951 + 0.999304i \(0.511874\pi\)
\(264\) 13.3766 0.823273
\(265\) 0 0
\(266\) 12.7304 0.780548
\(267\) −19.1744 −1.17346
\(268\) 2.69916 0.164878
\(269\) 15.6437 0.953811 0.476905 0.878955i \(-0.341758\pi\)
0.476905 + 0.878955i \(0.341758\pi\)
\(270\) 0 0
\(271\) −25.9732 −1.57776 −0.788880 0.614547i \(-0.789339\pi\)
−0.788880 + 0.614547i \(0.789339\pi\)
\(272\) −30.8039 −1.86776
\(273\) 19.9097 1.20499
\(274\) 17.5380 1.05951
\(275\) 0 0
\(276\) 3.24820 0.195519
\(277\) −11.7554 −0.706312 −0.353156 0.935564i \(-0.614892\pi\)
−0.353156 + 0.935564i \(0.614892\pi\)
\(278\) −24.9833 −1.49840
\(279\) 8.63584 0.517014
\(280\) 0 0
\(281\) −6.68164 −0.398593 −0.199297 0.979939i \(-0.563866\pi\)
−0.199297 + 0.979939i \(0.563866\pi\)
\(282\) 14.0751 0.838159
\(283\) −7.36154 −0.437598 −0.218799 0.975770i \(-0.570214\pi\)
−0.218799 + 0.975770i \(0.570214\pi\)
\(284\) −4.14916 −0.246207
\(285\) 0 0
\(286\) 25.5360 1.50998
\(287\) −8.14096 −0.480546
\(288\) −5.27382 −0.310763
\(289\) 21.0458 1.23799
\(290\) 0 0
\(291\) 15.3073 0.897331
\(292\) −3.96461 −0.232011
\(293\) −12.0504 −0.703992 −0.351996 0.936001i \(-0.614497\pi\)
−0.351996 + 0.936001i \(0.614497\pi\)
\(294\) 43.9831 2.56515
\(295\) 0 0
\(296\) −16.3107 −0.948042
\(297\) −29.6816 −1.72230
\(298\) 27.0352 1.56611
\(299\) −7.23807 −0.418588
\(300\) 0 0
\(301\) 0.0906285 0.00522374
\(302\) 26.1381 1.50408
\(303\) −0.344574 −0.0197953
\(304\) −7.35013 −0.421559
\(305\) 0 0
\(306\) 11.4554 0.654860
\(307\) 25.7906 1.47195 0.735974 0.677010i \(-0.236725\pi\)
0.735974 + 0.677010i \(0.236725\pi\)
\(308\) 24.5151 1.39688
\(309\) −18.6130 −1.05886
\(310\) 0 0
\(311\) −19.1825 −1.08774 −0.543869 0.839170i \(-0.683041\pi\)
−0.543869 + 0.839170i \(0.683041\pi\)
\(312\) −7.24698 −0.410279
\(313\) −4.33448 −0.245000 −0.122500 0.992469i \(-0.539091\pi\)
−0.122500 + 0.992469i \(0.539091\pi\)
\(314\) 1.46608 0.0827358
\(315\) 0 0
\(316\) 2.16011 0.121516
\(317\) 7.30667 0.410383 0.205192 0.978722i \(-0.434218\pi\)
0.205192 + 0.978722i \(0.434218\pi\)
\(318\) 19.0933 1.07070
\(319\) 50.0497 2.80225
\(320\) 0 0
\(321\) −1.80926 −0.100983
\(322\) −22.0084 −1.22648
\(323\) 9.07813 0.505121
\(324\) −4.20896 −0.233831
\(325\) 0 0
\(326\) 16.0152 0.886998
\(327\) −26.6361 −1.47298
\(328\) 2.96325 0.163618
\(329\) −30.1101 −1.66002
\(330\) 0 0
\(331\) 1.02032 0.0560821 0.0280411 0.999607i \(-0.491073\pi\)
0.0280411 + 0.999607i \(0.491073\pi\)
\(332\) 8.55856 0.469712
\(333\) 9.62141 0.527250
\(334\) 4.68529 0.256367
\(335\) 0 0
\(336\) −34.9530 −1.90684
\(337\) 18.9655 1.03312 0.516559 0.856251i \(-0.327213\pi\)
0.516559 + 0.856251i \(0.327213\pi\)
\(338\) 8.39060 0.456389
\(339\) −23.5702 −1.28015
\(340\) 0 0
\(341\) 41.7417 2.26044
\(342\) 2.73337 0.147804
\(343\) −58.6750 −3.16815
\(344\) −0.0329881 −0.00177860
\(345\) 0 0
\(346\) 3.22968 0.173629
\(347\) −31.3900 −1.68510 −0.842550 0.538617i \(-0.818947\pi\)
−0.842550 + 0.538617i \(0.818947\pi\)
\(348\) 12.1684 0.652293
\(349\) −12.0895 −0.647139 −0.323569 0.946204i \(-0.604883\pi\)
−0.323569 + 0.946204i \(0.604883\pi\)
\(350\) 0 0
\(351\) 16.0805 0.858312
\(352\) −25.4913 −1.35869
\(353\) −4.93700 −0.262770 −0.131385 0.991331i \(-0.541942\pi\)
−0.131385 + 0.991331i \(0.541942\pi\)
\(354\) −7.77461 −0.413216
\(355\) 0 0
\(356\) 12.7910 0.677921
\(357\) 43.1704 2.28482
\(358\) 0.838106 0.0442953
\(359\) 0.458022 0.0241735 0.0120867 0.999927i \(-0.496153\pi\)
0.0120867 + 0.999927i \(0.496153\pi\)
\(360\) 0 0
\(361\) −16.8339 −0.885993
\(362\) −0.483189 −0.0253958
\(363\) −22.9227 −1.20313
\(364\) −13.2814 −0.696136
\(365\) 0 0
\(366\) 17.0261 0.889968
\(367\) −16.2642 −0.848987 −0.424493 0.905431i \(-0.639548\pi\)
−0.424493 + 0.905431i \(0.639548\pi\)
\(368\) 12.7070 0.662398
\(369\) −1.74797 −0.0909957
\(370\) 0 0
\(371\) −40.8452 −2.12058
\(372\) 10.1485 0.526175
\(373\) 19.6620 1.01806 0.509029 0.860749i \(-0.330005\pi\)
0.509029 + 0.860749i \(0.330005\pi\)
\(374\) 55.3701 2.86312
\(375\) 0 0
\(376\) 10.9598 0.565211
\(377\) −27.1152 −1.39650
\(378\) 48.8950 2.51489
\(379\) −38.4555 −1.97533 −0.987664 0.156587i \(-0.949951\pi\)
−0.987664 + 0.156587i \(0.949951\pi\)
\(380\) 0 0
\(381\) 13.9373 0.714029
\(382\) −31.7478 −1.62436
\(383\) −25.5844 −1.30730 −0.653652 0.756796i \(-0.726764\pi\)
−0.653652 + 0.756796i \(0.726764\pi\)
\(384\) 17.4245 0.889192
\(385\) 0 0
\(386\) −43.8198 −2.23037
\(387\) 0.0194591 0.000989162 0
\(388\) −10.2113 −0.518399
\(389\) 1.54506 0.0783376 0.0391688 0.999233i \(-0.487529\pi\)
0.0391688 + 0.999233i \(0.487529\pi\)
\(390\) 0 0
\(391\) −15.6944 −0.793699
\(392\) 34.2483 1.72980
\(393\) −7.43033 −0.374811
\(394\) −20.8403 −1.04992
\(395\) 0 0
\(396\) 5.26371 0.264511
\(397\) −15.9215 −0.799078 −0.399539 0.916716i \(-0.630830\pi\)
−0.399539 + 0.916716i \(0.630830\pi\)
\(398\) −11.4708 −0.574980
\(399\) 10.3009 0.515690
\(400\) 0 0
\(401\) −16.9817 −0.848024 −0.424012 0.905657i \(-0.639379\pi\)
−0.424012 + 0.905657i \(0.639379\pi\)
\(402\) 6.91750 0.345014
\(403\) −22.6142 −1.12649
\(404\) 0.229860 0.0114360
\(405\) 0 0
\(406\) −82.4477 −4.09181
\(407\) 46.5055 2.30519
\(408\) −15.7137 −0.777945
\(409\) −26.2104 −1.29602 −0.648010 0.761631i \(-0.724399\pi\)
−0.648010 + 0.761631i \(0.724399\pi\)
\(410\) 0 0
\(411\) 14.1911 0.699995
\(412\) 12.4164 0.611714
\(413\) 16.6318 0.818397
\(414\) −4.72549 −0.232245
\(415\) 0 0
\(416\) 13.8103 0.677104
\(417\) −20.2155 −0.989957
\(418\) 13.2119 0.646214
\(419\) −14.5100 −0.708862 −0.354431 0.935082i \(-0.615325\pi\)
−0.354431 + 0.935082i \(0.615325\pi\)
\(420\) 0 0
\(421\) 14.9113 0.726732 0.363366 0.931646i \(-0.381627\pi\)
0.363366 + 0.931646i \(0.381627\pi\)
\(422\) −13.5500 −0.659606
\(423\) −6.46502 −0.314340
\(424\) 14.8674 0.722023
\(425\) 0 0
\(426\) −10.6336 −0.515200
\(427\) −36.4230 −1.76263
\(428\) 1.20693 0.0583392
\(429\) 20.6627 0.997606
\(430\) 0 0
\(431\) −27.0648 −1.30367 −0.651833 0.758363i \(-0.726000\pi\)
−0.651833 + 0.758363i \(0.726000\pi\)
\(432\) −28.2306 −1.35824
\(433\) 32.9065 1.58139 0.790693 0.612212i \(-0.209720\pi\)
0.790693 + 0.612212i \(0.209720\pi\)
\(434\) −68.7618 −3.30067
\(435\) 0 0
\(436\) 17.7686 0.850960
\(437\) −3.74484 −0.179140
\(438\) −10.1606 −0.485493
\(439\) −18.6369 −0.889490 −0.444745 0.895657i \(-0.646706\pi\)
−0.444745 + 0.895657i \(0.646706\pi\)
\(440\) 0 0
\(441\) −20.2025 −0.962022
\(442\) −29.9976 −1.42684
\(443\) 0.950840 0.0451758 0.0225879 0.999745i \(-0.492809\pi\)
0.0225879 + 0.999745i \(0.492809\pi\)
\(444\) 11.3067 0.536592
\(445\) 0 0
\(446\) −32.1340 −1.52159
\(447\) 21.8758 1.03469
\(448\) −8.54132 −0.403539
\(449\) 12.1598 0.573858 0.286929 0.957952i \(-0.407366\pi\)
0.286929 + 0.957952i \(0.407366\pi\)
\(450\) 0 0
\(451\) −8.44889 −0.397843
\(452\) 15.7233 0.739561
\(453\) 21.1499 0.993710
\(454\) 3.01781 0.141633
\(455\) 0 0
\(456\) −3.74945 −0.175584
\(457\) 34.9685 1.63576 0.817880 0.575389i \(-0.195149\pi\)
0.817880 + 0.575389i \(0.195149\pi\)
\(458\) 36.2057 1.69178
\(459\) 34.8675 1.62747
\(460\) 0 0
\(461\) −10.2125 −0.475646 −0.237823 0.971309i \(-0.576434\pi\)
−0.237823 + 0.971309i \(0.576434\pi\)
\(462\) 62.8281 2.92303
\(463\) 17.4281 0.809951 0.404976 0.914328i \(-0.367280\pi\)
0.404976 + 0.914328i \(0.367280\pi\)
\(464\) 47.6029 2.20991
\(465\) 0 0
\(466\) −10.4118 −0.482316
\(467\) 18.9150 0.875281 0.437640 0.899150i \(-0.355814\pi\)
0.437640 + 0.899150i \(0.355814\pi\)
\(468\) −2.85169 −0.131820
\(469\) −14.7982 −0.683318
\(470\) 0 0
\(471\) 1.18630 0.0546616
\(472\) −6.05385 −0.278651
\(473\) 0.0940565 0.00432472
\(474\) 5.53599 0.254277
\(475\) 0 0
\(476\) −28.7983 −1.31997
\(477\) −8.76999 −0.401550
\(478\) 2.38476 0.109076
\(479\) −19.0476 −0.870306 −0.435153 0.900357i \(-0.643306\pi\)
−0.435153 + 0.900357i \(0.643306\pi\)
\(480\) 0 0
\(481\) −25.1951 −1.14880
\(482\) −1.70963 −0.0778713
\(483\) −17.8083 −0.810307
\(484\) 15.2914 0.695063
\(485\) 0 0
\(486\) 18.2059 0.825835
\(487\) −22.4723 −1.01832 −0.509159 0.860673i \(-0.670043\pi\)
−0.509159 + 0.860673i \(0.670043\pi\)
\(488\) 13.2577 0.600148
\(489\) 12.9588 0.586019
\(490\) 0 0
\(491\) −7.02401 −0.316989 −0.158495 0.987360i \(-0.550664\pi\)
−0.158495 + 0.987360i \(0.550664\pi\)
\(492\) −2.05414 −0.0926079
\(493\) −58.7942 −2.64796
\(494\) −7.15773 −0.322041
\(495\) 0 0
\(496\) 39.7010 1.78263
\(497\) 22.7479 1.02038
\(498\) 21.9341 0.982892
\(499\) 21.8733 0.979183 0.489592 0.871952i \(-0.337146\pi\)
0.489592 + 0.871952i \(0.337146\pi\)
\(500\) 0 0
\(501\) 3.79115 0.169376
\(502\) −17.9285 −0.800187
\(503\) 30.0983 1.34202 0.671009 0.741449i \(-0.265861\pi\)
0.671009 + 0.741449i \(0.265861\pi\)
\(504\) 10.1214 0.450844
\(505\) 0 0
\(506\) −22.8409 −1.01540
\(507\) 6.78934 0.301525
\(508\) −9.29735 −0.412503
\(509\) 7.77815 0.344761 0.172380 0.985030i \(-0.444854\pi\)
0.172380 + 0.985030i \(0.444854\pi\)
\(510\) 0 0
\(511\) 21.7360 0.961546
\(512\) −5.85120 −0.258589
\(513\) 8.31974 0.367326
\(514\) −25.3915 −1.11997
\(515\) 0 0
\(516\) 0.0228676 0.00100669
\(517\) −31.2490 −1.37433
\(518\) −76.6093 −3.36602
\(519\) 2.61333 0.114712
\(520\) 0 0
\(521\) −14.0318 −0.614746 −0.307373 0.951589i \(-0.599450\pi\)
−0.307373 + 0.951589i \(0.599450\pi\)
\(522\) −17.7026 −0.774821
\(523\) −2.80012 −0.122440 −0.0612202 0.998124i \(-0.519499\pi\)
−0.0612202 + 0.998124i \(0.519499\pi\)
\(524\) 4.95666 0.216533
\(525\) 0 0
\(526\) 2.06805 0.0901711
\(527\) −49.0347 −2.13598
\(528\) −36.2751 −1.57867
\(529\) −16.5259 −0.718516
\(530\) 0 0
\(531\) 3.57106 0.154971
\(532\) −6.87157 −0.297920
\(533\) 4.57731 0.198265
\(534\) 32.7811 1.41858
\(535\) 0 0
\(536\) 5.38645 0.232659
\(537\) 0.678162 0.0292648
\(538\) −26.7448 −1.15305
\(539\) −97.6495 −4.20606
\(540\) 0 0
\(541\) 31.2317 1.34276 0.671379 0.741114i \(-0.265702\pi\)
0.671379 + 0.741114i \(0.265702\pi\)
\(542\) 44.4045 1.90734
\(543\) −0.390977 −0.0167784
\(544\) 29.9450 1.28388
\(545\) 0 0
\(546\) −34.0381 −1.45669
\(547\) −42.9144 −1.83489 −0.917444 0.397865i \(-0.869751\pi\)
−0.917444 + 0.397865i \(0.869751\pi\)
\(548\) −9.46666 −0.404396
\(549\) −7.82048 −0.333770
\(550\) 0 0
\(551\) −14.0289 −0.597651
\(552\) 6.48211 0.275897
\(553\) −11.8428 −0.503609
\(554\) 20.0973 0.853852
\(555\) 0 0
\(556\) 13.4854 0.571910
\(557\) −39.2314 −1.66229 −0.831145 0.556056i \(-0.812314\pi\)
−0.831145 + 0.556056i \(0.812314\pi\)
\(558\) −14.7641 −0.625012
\(559\) −0.0509565 −0.00215523
\(560\) 0 0
\(561\) 44.8033 1.89160
\(562\) 11.4231 0.481855
\(563\) −9.68487 −0.408169 −0.204084 0.978953i \(-0.565422\pi\)
−0.204084 + 0.978953i \(0.565422\pi\)
\(564\) −7.59743 −0.319909
\(565\) 0 0
\(566\) 12.5855 0.529007
\(567\) 23.0757 0.969090
\(568\) −8.28006 −0.347424
\(569\) −12.8438 −0.538441 −0.269221 0.963079i \(-0.586766\pi\)
−0.269221 + 0.963079i \(0.586766\pi\)
\(570\) 0 0
\(571\) 8.76755 0.366910 0.183455 0.983028i \(-0.441272\pi\)
0.183455 + 0.983028i \(0.441272\pi\)
\(572\) −13.7838 −0.576329
\(573\) −25.6890 −1.07318
\(574\) 13.9180 0.580926
\(575\) 0 0
\(576\) −1.83393 −0.0764138
\(577\) 42.9318 1.78727 0.893637 0.448791i \(-0.148145\pi\)
0.893637 + 0.448791i \(0.148145\pi\)
\(578\) −35.9805 −1.49659
\(579\) −35.4572 −1.47355
\(580\) 0 0
\(581\) −46.9225 −1.94667
\(582\) −26.1698 −1.08477
\(583\) −42.3901 −1.75562
\(584\) −7.91177 −0.327391
\(585\) 0 0
\(586\) 20.6017 0.851047
\(587\) 39.1573 1.61619 0.808097 0.589049i \(-0.200497\pi\)
0.808097 + 0.589049i \(0.200497\pi\)
\(588\) −23.7411 −0.979067
\(589\) −11.7002 −0.482097
\(590\) 0 0
\(591\) −16.8631 −0.693656
\(592\) 44.2320 1.81792
\(593\) −21.3089 −0.875050 −0.437525 0.899206i \(-0.644145\pi\)
−0.437525 + 0.899206i \(0.644145\pi\)
\(594\) 50.7445 2.08207
\(595\) 0 0
\(596\) −14.5930 −0.597753
\(597\) −9.28173 −0.379876
\(598\) 12.3744 0.506026
\(599\) −7.76975 −0.317463 −0.158732 0.987322i \(-0.550740\pi\)
−0.158732 + 0.987322i \(0.550740\pi\)
\(600\) 0 0
\(601\) 16.9993 0.693415 0.346707 0.937973i \(-0.387300\pi\)
0.346707 + 0.937973i \(0.387300\pi\)
\(602\) −0.154941 −0.00631492
\(603\) −3.17737 −0.129392
\(604\) −14.1088 −0.574079
\(605\) 0 0
\(606\) 0.589093 0.0239303
\(607\) 20.7512 0.842267 0.421133 0.906999i \(-0.361632\pi\)
0.421133 + 0.906999i \(0.361632\pi\)
\(608\) 7.14518 0.289775
\(609\) −66.7134 −2.70336
\(610\) 0 0
\(611\) 16.9296 0.684898
\(612\) −6.18337 −0.249948
\(613\) 17.5567 0.709108 0.354554 0.935035i \(-0.384633\pi\)
0.354554 + 0.935035i \(0.384633\pi\)
\(614\) −44.0923 −1.77942
\(615\) 0 0
\(616\) 48.9224 1.97114
\(617\) −6.03640 −0.243016 −0.121508 0.992590i \(-0.538773\pi\)
−0.121508 + 0.992590i \(0.538773\pi\)
\(618\) 31.8212 1.28004
\(619\) −21.4216 −0.861008 −0.430504 0.902589i \(-0.641664\pi\)
−0.430504 + 0.902589i \(0.641664\pi\)
\(620\) 0 0
\(621\) −14.3833 −0.577181
\(622\) 32.7948 1.31495
\(623\) −70.1268 −2.80957
\(624\) 19.6526 0.786733
\(625\) 0 0
\(626\) 7.41034 0.296177
\(627\) 10.6905 0.426938
\(628\) −0.791359 −0.0315787
\(629\) −54.6308 −2.17827
\(630\) 0 0
\(631\) 17.0323 0.678044 0.339022 0.940778i \(-0.389904\pi\)
0.339022 + 0.940778i \(0.389904\pi\)
\(632\) 4.31071 0.171471
\(633\) −10.9642 −0.435786
\(634\) −12.4917 −0.496107
\(635\) 0 0
\(636\) −10.3061 −0.408665
\(637\) 52.9031 2.09610
\(638\) −85.5662 −3.38760
\(639\) 4.88426 0.193218
\(640\) 0 0
\(641\) −5.88960 −0.232625 −0.116313 0.993213i \(-0.537107\pi\)
−0.116313 + 0.993213i \(0.537107\pi\)
\(642\) 3.09316 0.122077
\(643\) 27.5753 1.08746 0.543731 0.839259i \(-0.317011\pi\)
0.543731 + 0.839259i \(0.317011\pi\)
\(644\) 11.8797 0.468124
\(645\) 0 0
\(646\) −15.5202 −0.610634
\(647\) −26.2229 −1.03093 −0.515465 0.856911i \(-0.672381\pi\)
−0.515465 + 0.856911i \(0.672381\pi\)
\(648\) −8.39940 −0.329960
\(649\) 17.2609 0.677549
\(650\) 0 0
\(651\) −55.6393 −2.18068
\(652\) −8.64464 −0.338550
\(653\) 5.20569 0.203714 0.101857 0.994799i \(-0.467522\pi\)
0.101857 + 0.994799i \(0.467522\pi\)
\(654\) 45.5378 1.78067
\(655\) 0 0
\(656\) −8.03584 −0.313747
\(657\) 4.66701 0.182077
\(658\) 51.4769 2.00678
\(659\) −7.97812 −0.310783 −0.155392 0.987853i \(-0.549664\pi\)
−0.155392 + 0.987853i \(0.549664\pi\)
\(660\) 0 0
\(661\) 17.0900 0.664724 0.332362 0.943152i \(-0.392154\pi\)
0.332362 + 0.943152i \(0.392154\pi\)
\(662\) −1.74437 −0.0677970
\(663\) −24.2728 −0.942679
\(664\) 17.0795 0.662811
\(665\) 0 0
\(666\) −16.4490 −0.637386
\(667\) 24.2533 0.939093
\(668\) −2.52902 −0.0978506
\(669\) −26.0016 −1.00528
\(670\) 0 0
\(671\) −37.8007 −1.45928
\(672\) 33.9784 1.31074
\(673\) 40.1751 1.54864 0.774319 0.632796i \(-0.218093\pi\)
0.774319 + 0.632796i \(0.218093\pi\)
\(674\) −32.4240 −1.24892
\(675\) 0 0
\(676\) −4.52907 −0.174195
\(677\) −9.73259 −0.374054 −0.187027 0.982355i \(-0.559885\pi\)
−0.187027 + 0.982355i \(0.559885\pi\)
\(678\) 40.2961 1.54756
\(679\) 55.9836 2.14845
\(680\) 0 0
\(681\) 2.44190 0.0935736
\(682\) −71.3627 −2.73262
\(683\) −9.78489 −0.374408 −0.187204 0.982321i \(-0.559943\pi\)
−0.187204 + 0.982321i \(0.559943\pi\)
\(684\) −1.47541 −0.0564139
\(685\) 0 0
\(686\) 100.312 3.82994
\(687\) 29.2962 1.11772
\(688\) 0.0894582 0.00341056
\(689\) 22.9655 0.874916
\(690\) 0 0
\(691\) 3.54792 0.134969 0.0674846 0.997720i \(-0.478503\pi\)
0.0674846 + 0.997720i \(0.478503\pi\)
\(692\) −1.74331 −0.0662707
\(693\) −28.8584 −1.09624
\(694\) 53.6651 2.03710
\(695\) 0 0
\(696\) 24.2832 0.920452
\(697\) 9.92505 0.375938
\(698\) 20.6686 0.782318
\(699\) −8.42479 −0.318655
\(700\) 0 0
\(701\) 21.2003 0.800724 0.400362 0.916357i \(-0.368884\pi\)
0.400362 + 0.916357i \(0.368884\pi\)
\(702\) −27.4916 −1.03760
\(703\) −13.0355 −0.491642
\(704\) −8.86439 −0.334089
\(705\) 0 0
\(706\) 8.44042 0.317659
\(707\) −1.26021 −0.0473952
\(708\) 4.19656 0.157717
\(709\) 35.8330 1.34574 0.672869 0.739762i \(-0.265062\pi\)
0.672869 + 0.739762i \(0.265062\pi\)
\(710\) 0 0
\(711\) −2.54281 −0.0953628
\(712\) 25.5257 0.956615
\(713\) 20.2274 0.757523
\(714\) −73.8052 −2.76209
\(715\) 0 0
\(716\) −0.452391 −0.0169067
\(717\) 1.92965 0.0720641
\(718\) −0.783046 −0.0292230
\(719\) −17.4449 −0.650586 −0.325293 0.945613i \(-0.605463\pi\)
−0.325293 + 0.945613i \(0.605463\pi\)
\(720\) 0 0
\(721\) −68.0734 −2.53518
\(722\) 28.7796 1.07107
\(723\) −1.38336 −0.0514477
\(724\) 0.260815 0.00969310
\(725\) 0 0
\(726\) 39.1892 1.45445
\(727\) 2.83872 0.105282 0.0526411 0.998613i \(-0.483236\pi\)
0.0526411 + 0.998613i \(0.483236\pi\)
\(728\) −26.5044 −0.982319
\(729\) 28.4144 1.05239
\(730\) 0 0
\(731\) −0.110490 −0.00408661
\(732\) −9.19032 −0.339684
\(733\) 19.1179 0.706135 0.353067 0.935598i \(-0.385139\pi\)
0.353067 + 0.935598i \(0.385139\pi\)
\(734\) 27.8058 1.02633
\(735\) 0 0
\(736\) −12.3527 −0.455326
\(737\) −15.3580 −0.565718
\(738\) 2.98837 0.110004
\(739\) −10.7460 −0.395299 −0.197650 0.980273i \(-0.563331\pi\)
−0.197650 + 0.980273i \(0.563331\pi\)
\(740\) 0 0
\(741\) −5.79175 −0.212765
\(742\) 69.8300 2.56354
\(743\) 21.9385 0.804846 0.402423 0.915454i \(-0.368168\pi\)
0.402423 + 0.915454i \(0.368168\pi\)
\(744\) 20.2523 0.742486
\(745\) 0 0
\(746\) −33.6146 −1.23072
\(747\) −10.0749 −0.368620
\(748\) −29.8876 −1.09280
\(749\) −6.61702 −0.241781
\(750\) 0 0
\(751\) −24.7399 −0.902773 −0.451386 0.892329i \(-0.649070\pi\)
−0.451386 + 0.892329i \(0.649070\pi\)
\(752\) −29.7212 −1.08382
\(753\) −14.5070 −0.528665
\(754\) 46.3568 1.68821
\(755\) 0 0
\(756\) −26.3925 −0.959885
\(757\) −15.0100 −0.545546 −0.272773 0.962078i \(-0.587941\pi\)
−0.272773 + 0.962078i \(0.587941\pi\)
\(758\) 65.7446 2.38795
\(759\) −18.4819 −0.670851
\(760\) 0 0
\(761\) −26.0521 −0.944389 −0.472194 0.881495i \(-0.656538\pi\)
−0.472194 + 0.881495i \(0.656538\pi\)
\(762\) −23.8275 −0.863181
\(763\) −97.4166 −3.52672
\(764\) 17.1368 0.619987
\(765\) 0 0
\(766\) 43.7398 1.58038
\(767\) −9.35134 −0.337657
\(768\) −25.1186 −0.906389
\(769\) −24.4144 −0.880407 −0.440203 0.897898i \(-0.645094\pi\)
−0.440203 + 0.897898i \(0.645094\pi\)
\(770\) 0 0
\(771\) −20.5458 −0.739939
\(772\) 23.6530 0.851289
\(773\) −41.9248 −1.50793 −0.753966 0.656914i \(-0.771862\pi\)
−0.753966 + 0.656914i \(0.771862\pi\)
\(774\) −0.0332678 −0.00119579
\(775\) 0 0
\(776\) −20.3776 −0.731514
\(777\) −61.9892 −2.22385
\(778\) −2.64147 −0.0947014
\(779\) 2.36822 0.0848502
\(780\) 0 0
\(781\) 23.6083 0.844771
\(782\) 26.8315 0.959494
\(783\) −53.8825 −1.92560
\(784\) −92.8756 −3.31699
\(785\) 0 0
\(786\) 12.7031 0.453104
\(787\) −42.1295 −1.50176 −0.750878 0.660441i \(-0.770369\pi\)
−0.750878 + 0.660441i \(0.770369\pi\)
\(788\) 11.2491 0.400734
\(789\) 1.67338 0.0595739
\(790\) 0 0
\(791\) −86.2033 −3.06504
\(792\) 10.5043 0.373253
\(793\) 20.4791 0.727233
\(794\) 27.2198 0.965995
\(795\) 0 0
\(796\) 6.19170 0.219459
\(797\) −32.8495 −1.16359 −0.581795 0.813335i \(-0.697649\pi\)
−0.581795 + 0.813335i \(0.697649\pi\)
\(798\) −17.6107 −0.623411
\(799\) 36.7086 1.29866
\(800\) 0 0
\(801\) −15.0571 −0.532018
\(802\) 29.0323 1.02517
\(803\) 22.5582 0.796062
\(804\) −3.73392 −0.131685
\(805\) 0 0
\(806\) 38.6618 1.36180
\(807\) −21.6408 −0.761793
\(808\) 0.458709 0.0161373
\(809\) 21.0371 0.739625 0.369812 0.929106i \(-0.379422\pi\)
0.369812 + 0.929106i \(0.379422\pi\)
\(810\) 0 0
\(811\) 38.1121 1.33830 0.669149 0.743128i \(-0.266659\pi\)
0.669149 + 0.743128i \(0.266659\pi\)
\(812\) 44.5035 1.56177
\(813\) 35.9303 1.26013
\(814\) −79.5070 −2.78672
\(815\) 0 0
\(816\) 42.6129 1.49175
\(817\) −0.0263640 −0.000922359 0
\(818\) 44.8100 1.56674
\(819\) 15.6345 0.546313
\(820\) 0 0
\(821\) −13.3082 −0.464459 −0.232230 0.972661i \(-0.574602\pi\)
−0.232230 + 0.972661i \(0.574602\pi\)
\(822\) −24.2614 −0.846215
\(823\) −9.58043 −0.333953 −0.166976 0.985961i \(-0.553400\pi\)
−0.166976 + 0.985961i \(0.553400\pi\)
\(824\) 24.7782 0.863190
\(825\) 0 0
\(826\) −28.4341 −0.989350
\(827\) −5.10249 −0.177431 −0.0887154 0.996057i \(-0.528276\pi\)
−0.0887154 + 0.996057i \(0.528276\pi\)
\(828\) 2.55072 0.0886435
\(829\) −38.5370 −1.33845 −0.669223 0.743061i \(-0.733373\pi\)
−0.669223 + 0.743061i \(0.733373\pi\)
\(830\) 0 0
\(831\) 16.2619 0.564120
\(832\) 4.80241 0.166494
\(833\) 114.710 3.97448
\(834\) 34.5609 1.19675
\(835\) 0 0
\(836\) −7.13148 −0.246647
\(837\) −44.9383 −1.55330
\(838\) 24.8067 0.856934
\(839\) 9.97929 0.344524 0.172262 0.985051i \(-0.444893\pi\)
0.172262 + 0.985051i \(0.444893\pi\)
\(840\) 0 0
\(841\) 61.8576 2.13302
\(842\) −25.4927 −0.878537
\(843\) 9.24312 0.318350
\(844\) 7.31402 0.251759
\(845\) 0 0
\(846\) 11.0528 0.380002
\(847\) −83.8354 −2.88062
\(848\) −40.3178 −1.38452
\(849\) 10.1837 0.349503
\(850\) 0 0
\(851\) 22.5359 0.772520
\(852\) 5.73979 0.196642
\(853\) 0.528777 0.0181050 0.00905250 0.999959i \(-0.497118\pi\)
0.00905250 + 0.999959i \(0.497118\pi\)
\(854\) 62.2697 2.13082
\(855\) 0 0
\(856\) 2.40855 0.0823225
\(857\) −13.2208 −0.451615 −0.225808 0.974172i \(-0.572502\pi\)
−0.225808 + 0.974172i \(0.572502\pi\)
\(858\) −35.3255 −1.20599
\(859\) 15.8466 0.540679 0.270339 0.962765i \(-0.412864\pi\)
0.270339 + 0.962765i \(0.412864\pi\)
\(860\) 0 0
\(861\) 11.2619 0.383804
\(862\) 46.2707 1.57599
\(863\) −42.9425 −1.46178 −0.730890 0.682495i \(-0.760895\pi\)
−0.730890 + 0.682495i \(0.760895\pi\)
\(864\) 27.4434 0.933642
\(865\) 0 0
\(866\) −56.2578 −1.91172
\(867\) −29.1140 −0.988763
\(868\) 37.1161 1.25980
\(869\) −12.2908 −0.416937
\(870\) 0 0
\(871\) 8.32040 0.281926
\(872\) 35.4589 1.20079
\(873\) 12.0204 0.406829
\(874\) 6.40228 0.216560
\(875\) 0 0
\(876\) 5.48448 0.185303
\(877\) −13.9351 −0.470554 −0.235277 0.971928i \(-0.575600\pi\)
−0.235277 + 0.971928i \(0.575600\pi\)
\(878\) 31.8621 1.07529
\(879\) 16.6701 0.562267
\(880\) 0 0
\(881\) 38.0645 1.28243 0.641213 0.767363i \(-0.278431\pi\)
0.641213 + 0.767363i \(0.278431\pi\)
\(882\) 34.5386 1.16298
\(883\) 50.9419 1.71433 0.857165 0.515042i \(-0.172224\pi\)
0.857165 + 0.515042i \(0.172224\pi\)
\(884\) 16.1920 0.544597
\(885\) 0 0
\(886\) −1.62558 −0.0546124
\(887\) −51.0399 −1.71375 −0.856875 0.515523i \(-0.827597\pi\)
−0.856875 + 0.515523i \(0.827597\pi\)
\(888\) 22.5636 0.757186
\(889\) 50.9729 1.70958
\(890\) 0 0
\(891\) 23.9486 0.802307
\(892\) 17.3452 0.580762
\(893\) 8.75906 0.293111
\(894\) −37.3994 −1.25082
\(895\) 0 0
\(896\) 63.7268 2.12896
\(897\) 10.0129 0.334320
\(898\) −20.7887 −0.693729
\(899\) 75.7758 2.52726
\(900\) 0 0
\(901\) 49.7964 1.65896
\(902\) 14.4444 0.480947
\(903\) −0.125372 −0.00417212
\(904\) 31.3774 1.04360
\(905\) 0 0
\(906\) −36.1585 −1.20128
\(907\) 20.9409 0.695333 0.347666 0.937618i \(-0.386974\pi\)
0.347666 + 0.937618i \(0.386974\pi\)
\(908\) −1.62895 −0.0540586
\(909\) −0.270584 −0.00897471
\(910\) 0 0
\(911\) −28.0321 −0.928744 −0.464372 0.885640i \(-0.653720\pi\)
−0.464372 + 0.885640i \(0.653720\pi\)
\(912\) 10.1679 0.336692
\(913\) −48.6973 −1.61165
\(914\) −59.7831 −1.97745
\(915\) 0 0
\(916\) −19.5430 −0.645720
\(917\) −27.1750 −0.897398
\(918\) −59.6103 −1.96743
\(919\) −21.5713 −0.711572 −0.355786 0.934567i \(-0.615787\pi\)
−0.355786 + 0.934567i \(0.615787\pi\)
\(920\) 0 0
\(921\) −35.6777 −1.17562
\(922\) 17.4596 0.575002
\(923\) −12.7901 −0.420993
\(924\) −33.9133 −1.11566
\(925\) 0 0
\(926\) −29.7955 −0.979140
\(927\) −14.6162 −0.480060
\(928\) −46.2755 −1.51907
\(929\) 12.2984 0.403499 0.201749 0.979437i \(-0.435337\pi\)
0.201749 + 0.979437i \(0.435337\pi\)
\(930\) 0 0
\(931\) 27.3711 0.897051
\(932\) 5.62005 0.184091
\(933\) 26.5363 0.868758
\(934\) −32.3375 −1.05812
\(935\) 0 0
\(936\) −5.69084 −0.186011
\(937\) 0.227516 0.00743264 0.00371632 0.999993i \(-0.498817\pi\)
0.00371632 + 0.999993i \(0.498817\pi\)
\(938\) 25.2994 0.826055
\(939\) 5.99615 0.195677
\(940\) 0 0
\(941\) 31.0857 1.01336 0.506682 0.862133i \(-0.330872\pi\)
0.506682 + 0.862133i \(0.330872\pi\)
\(942\) −2.02812 −0.0660797
\(943\) −4.09421 −0.133326
\(944\) 16.4170 0.534329
\(945\) 0 0
\(946\) −0.160801 −0.00522810
\(947\) 28.5537 0.927871 0.463935 0.885869i \(-0.346437\pi\)
0.463935 + 0.885869i \(0.346437\pi\)
\(948\) −2.98821 −0.0970525
\(949\) −12.2212 −0.396718
\(950\) 0 0
\(951\) −10.1078 −0.327767
\(952\) −57.4699 −1.86261
\(953\) −21.7444 −0.704372 −0.352186 0.935930i \(-0.614561\pi\)
−0.352186 + 0.935930i \(0.614561\pi\)
\(954\) 14.9934 0.485429
\(955\) 0 0
\(956\) −1.28724 −0.0416323
\(957\) −69.2368 −2.23811
\(958\) 32.5642 1.05210
\(959\) 51.9012 1.67598
\(960\) 0 0
\(961\) 32.1974 1.03863
\(962\) 43.0741 1.38877
\(963\) −1.42076 −0.0457834
\(964\) 0.922819 0.0297220
\(965\) 0 0
\(966\) 30.4456 0.979570
\(967\) 11.6791 0.375576 0.187788 0.982210i \(-0.439868\pi\)
0.187788 + 0.982210i \(0.439868\pi\)
\(968\) 30.5155 0.980805
\(969\) −12.5583 −0.403432
\(970\) 0 0
\(971\) −8.70745 −0.279435 −0.139718 0.990191i \(-0.544619\pi\)
−0.139718 + 0.990191i \(0.544619\pi\)
\(972\) −9.82714 −0.315206
\(973\) −73.9342 −2.37022
\(974\) 38.4192 1.23103
\(975\) 0 0
\(976\) −35.9527 −1.15082
\(977\) −44.5056 −1.42386 −0.711930 0.702250i \(-0.752179\pi\)
−0.711930 + 0.702250i \(0.752179\pi\)
\(978\) −22.1548 −0.708431
\(979\) −72.7794 −2.32604
\(980\) 0 0
\(981\) −20.9166 −0.667815
\(982\) 12.0084 0.383204
\(983\) −43.9573 −1.40202 −0.701010 0.713152i \(-0.747267\pi\)
−0.701010 + 0.713152i \(0.747267\pi\)
\(984\) −4.09925 −0.130679
\(985\) 0 0
\(986\) 100.516 3.20108
\(987\) 41.6531 1.32583
\(988\) 3.86359 0.122917
\(989\) 0.0455784 0.00144931
\(990\) 0 0
\(991\) 19.5023 0.619510 0.309755 0.950816i \(-0.399753\pi\)
0.309755 + 0.950816i \(0.399753\pi\)
\(992\) −38.5940 −1.22536
\(993\) −1.41148 −0.0447919
\(994\) −38.8903 −1.23353
\(995\) 0 0
\(996\) −11.8396 −0.375151
\(997\) 53.0288 1.67944 0.839719 0.543021i \(-0.182720\pi\)
0.839719 + 0.543021i \(0.182720\pi\)
\(998\) −37.3951 −1.18372
\(999\) −50.0669 −1.58405
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.1.11 46
5.2 odd 4 1205.2.b.c.724.11 46
5.3 odd 4 1205.2.b.c.724.36 yes 46
5.4 even 2 inner 6025.2.a.p.1.36 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.11 46 5.2 odd 4
1205.2.b.c.724.36 yes 46 5.3 odd 4
6025.2.a.p.1.11 46 1.1 even 1 trivial
6025.2.a.p.1.36 46 5.4 even 2 inner