Properties

Label 950.2.a.m.1.2
Level $950$
Weight $2$
Character 950.1
Self dual yes
Analytic conductor $7.586$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.91223\) of defining polynomial
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.25561 q^{3} +1.00000 q^{4} +2.25561 q^{6} +4.22547 q^{7} +1.00000 q^{8} +2.08777 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.25561 q^{3} +1.00000 q^{4} +2.25561 q^{6} +4.22547 q^{7} +1.00000 q^{8} +2.08777 q^{9} -5.13770 q^{11} +2.25561 q^{12} +3.16784 q^{13} +4.22547 q^{14} +1.00000 q^{16} -6.48108 q^{17} +2.08777 q^{18} -1.00000 q^{19} +9.53101 q^{21} -5.13770 q^{22} +7.56885 q^{23} +2.25561 q^{24} +3.16784 q^{26} -2.05763 q^{27} +4.22547 q^{28} +0.832162 q^{29} -4.51122 q^{31} +1.00000 q^{32} -11.5886 q^{33} -6.48108 q^{34} +2.08777 q^{36} +0.137699 q^{37} -1.00000 q^{38} +7.14540 q^{39} -11.6489 q^{41} +9.53101 q^{42} -2.51122 q^{43} -5.13770 q^{44} +7.56885 q^{46} -5.96216 q^{47} +2.25561 q^{48} +10.8546 q^{49} -14.6188 q^{51} +3.16784 q^{52} +0.225470 q^{53} -2.05763 q^{54} +4.22547 q^{56} -2.25561 q^{57} +0.832162 q^{58} +5.39331 q^{59} +14.4509 q^{61} -4.51122 q^{62} +8.82181 q^{63} +1.00000 q^{64} -11.5886 q^{66} -4.11021 q^{67} -6.48108 q^{68} +17.0724 q^{69} +3.82446 q^{71} +2.08777 q^{72} +4.70655 q^{73} +0.137699 q^{74} -1.00000 q^{76} -21.7092 q^{77} +7.14540 q^{78} +10.6265 q^{79} -10.9045 q^{81} -11.6489 q^{82} -12.0999 q^{83} +9.53101 q^{84} -2.51122 q^{86} +1.87703 q^{87} -5.13770 q^{88} -10.0000 q^{89} +13.3856 q^{91} +7.56885 q^{92} -10.1755 q^{93} -5.96216 q^{94} +2.25561 q^{96} +3.93972 q^{97} +10.8546 q^{98} -10.7263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + 13q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + 13q^{9} + 2q^{11} + 2q^{12} - 2q^{13} + 2q^{14} + 3q^{16} - 4q^{17} + 13q^{18} - 3q^{19} - 11q^{21} + 2q^{22} + 14q^{23} + 2q^{24} - 2q^{26} - 7q^{27} + 2q^{28} + 14q^{29} - 4q^{31} + 3q^{32} + 4q^{33} - 4q^{34} + 13q^{36} - 17q^{37} - 3q^{38} + 29q^{39} - 8q^{41} - 11q^{42} + 2q^{43} + 2q^{44} + 14q^{46} + 13q^{47} + 2q^{48} + 25q^{49} - 11q^{51} - 2q^{52} - 10q^{53} - 7q^{54} + 2q^{56} - 2q^{57} + 14q^{58} - 6q^{59} + 22q^{61} - 4q^{62} + 2q^{63} + 3q^{64} + 4q^{66} - 4q^{68} + 8q^{69} - 2q^{71} + 13q^{72} - 12q^{73} - 17q^{74} - 3q^{76} - 50q^{77} + 29q^{78} + 24q^{79} - q^{81} - 8q^{82} + 12q^{83} - 11q^{84} + 2q^{86} - 21q^{87} + 2q^{88} - 30q^{89} - 7q^{91} + 14q^{92} - 44q^{93} + 13q^{94} + 2q^{96} + 25q^{98} + 24q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.25561 1.30228 0.651138 0.758959i \(-0.274292\pi\)
0.651138 + 0.758959i \(0.274292\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 2.25561 0.920848
\(7\) 4.22547 1.59708 0.798539 0.601943i \(-0.205607\pi\)
0.798539 + 0.601943i \(0.205607\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.08777 0.695924
\(10\) 0 0
\(11\) −5.13770 −1.54907 −0.774537 0.632528i \(-0.782017\pi\)
−0.774537 + 0.632528i \(0.782017\pi\)
\(12\) 2.25561 0.651138
\(13\) 3.16784 0.878600 0.439300 0.898340i \(-0.355226\pi\)
0.439300 + 0.898340i \(0.355226\pi\)
\(14\) 4.22547 1.12930
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.48108 −1.57189 −0.785946 0.618295i \(-0.787824\pi\)
−0.785946 + 0.618295i \(0.787824\pi\)
\(18\) 2.08777 0.492092
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 9.53101 2.07984
\(22\) −5.13770 −1.09536
\(23\) 7.56885 1.57821 0.789107 0.614256i \(-0.210544\pi\)
0.789107 + 0.614256i \(0.210544\pi\)
\(24\) 2.25561 0.460424
\(25\) 0 0
\(26\) 3.16784 0.621264
\(27\) −2.05763 −0.395991
\(28\) 4.22547 0.798539
\(29\) 0.832162 0.154529 0.0772643 0.997011i \(-0.475381\pi\)
0.0772643 + 0.997011i \(0.475381\pi\)
\(30\) 0 0
\(31\) −4.51122 −0.810239 −0.405119 0.914264i \(-0.632770\pi\)
−0.405119 + 0.914264i \(0.632770\pi\)
\(32\) 1.00000 0.176777
\(33\) −11.5886 −2.01732
\(34\) −6.48108 −1.11150
\(35\) 0 0
\(36\) 2.08777 0.347962
\(37\) 0.137699 0.0226376 0.0113188 0.999936i \(-0.496397\pi\)
0.0113188 + 0.999936i \(0.496397\pi\)
\(38\) −1.00000 −0.162221
\(39\) 7.14540 1.14418
\(40\) 0 0
\(41\) −11.6489 −1.81926 −0.909628 0.415425i \(-0.863633\pi\)
−0.909628 + 0.415425i \(0.863633\pi\)
\(42\) 9.53101 1.47067
\(43\) −2.51122 −0.382957 −0.191479 0.981497i \(-0.561328\pi\)
−0.191479 + 0.981497i \(0.561328\pi\)
\(44\) −5.13770 −0.774537
\(45\) 0 0
\(46\) 7.56885 1.11597
\(47\) −5.96216 −0.869670 −0.434835 0.900510i \(-0.643193\pi\)
−0.434835 + 0.900510i \(0.643193\pi\)
\(48\) 2.25561 0.325569
\(49\) 10.8546 1.55066
\(50\) 0 0
\(51\) −14.6188 −2.04704
\(52\) 3.16784 0.439300
\(53\) 0.225470 0.0309707 0.0154853 0.999880i \(-0.495071\pi\)
0.0154853 + 0.999880i \(0.495071\pi\)
\(54\) −2.05763 −0.280008
\(55\) 0 0
\(56\) 4.22547 0.564652
\(57\) −2.25561 −0.298763
\(58\) 0.832162 0.109268
\(59\) 5.39331 0.702149 0.351074 0.936348i \(-0.385816\pi\)
0.351074 + 0.936348i \(0.385816\pi\)
\(60\) 0 0
\(61\) 14.4509 1.85025 0.925127 0.379659i \(-0.123959\pi\)
0.925127 + 0.379659i \(0.123959\pi\)
\(62\) −4.51122 −0.572925
\(63\) 8.82181 1.11144
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −11.5886 −1.42646
\(67\) −4.11021 −0.502142 −0.251071 0.967969i \(-0.580783\pi\)
−0.251071 + 0.967969i \(0.580783\pi\)
\(68\) −6.48108 −0.785946
\(69\) 17.0724 2.05527
\(70\) 0 0
\(71\) 3.82446 0.453880 0.226940 0.973909i \(-0.427128\pi\)
0.226940 + 0.973909i \(0.427128\pi\)
\(72\) 2.08777 0.246046
\(73\) 4.70655 0.550860 0.275430 0.961321i \(-0.411180\pi\)
0.275430 + 0.961321i \(0.411180\pi\)
\(74\) 0.137699 0.0160072
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) −21.7092 −2.47399
\(78\) 7.14540 0.809058
\(79\) 10.6265 1.19557 0.597786 0.801655i \(-0.296047\pi\)
0.597786 + 0.801655i \(0.296047\pi\)
\(80\) 0 0
\(81\) −10.9045 −1.21161
\(82\) −11.6489 −1.28641
\(83\) −12.0999 −1.32813 −0.664066 0.747674i \(-0.731171\pi\)
−0.664066 + 0.747674i \(0.731171\pi\)
\(84\) 9.53101 1.03992
\(85\) 0 0
\(86\) −2.51122 −0.270792
\(87\) 1.87703 0.201239
\(88\) −5.13770 −0.547681
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 13.3856 1.40319
\(92\) 7.56885 0.789107
\(93\) −10.1755 −1.05515
\(94\) −5.96216 −0.614950
\(95\) 0 0
\(96\) 2.25561 0.230212
\(97\) 3.93972 0.400018 0.200009 0.979794i \(-0.435903\pi\)
0.200009 + 0.979794i \(0.435903\pi\)
\(98\) 10.8546 1.09648
\(99\) −10.7263 −1.07804
\(100\) 0 0
\(101\) 3.19798 0.318211 0.159105 0.987262i \(-0.449139\pi\)
0.159105 + 0.987262i \(0.449139\pi\)
\(102\) −14.6188 −1.44747
\(103\) −10.6868 −1.05300 −0.526499 0.850176i \(-0.676496\pi\)
−0.526499 + 0.850176i \(0.676496\pi\)
\(104\) 3.16784 0.310632
\(105\) 0 0
\(106\) 0.225470 0.0218996
\(107\) 10.8168 1.04570 0.522848 0.852426i \(-0.324870\pi\)
0.522848 + 0.852426i \(0.324870\pi\)
\(108\) −2.05763 −0.197996
\(109\) 9.24791 0.885789 0.442894 0.896574i \(-0.353952\pi\)
0.442894 + 0.896574i \(0.353952\pi\)
\(110\) 0 0
\(111\) 0.310596 0.0294804
\(112\) 4.22547 0.399269
\(113\) 17.6489 1.66027 0.830135 0.557562i \(-0.188263\pi\)
0.830135 + 0.557562i \(0.188263\pi\)
\(114\) −2.25561 −0.211257
\(115\) 0 0
\(116\) 0.832162 0.0772643
\(117\) 6.61372 0.611439
\(118\) 5.39331 0.496494
\(119\) −27.3856 −2.51043
\(120\) 0 0
\(121\) 15.3960 1.39963
\(122\) 14.4509 1.30833
\(123\) −26.2754 −2.36917
\(124\) −4.51122 −0.405119
\(125\) 0 0
\(126\) 8.82181 0.785910
\(127\) −12.7866 −1.13463 −0.567314 0.823501i \(-0.692018\pi\)
−0.567314 + 0.823501i \(0.692018\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.66432 −0.498716
\(130\) 0 0
\(131\) −2.11526 −0.184811 −0.0924057 0.995721i \(-0.529456\pi\)
−0.0924057 + 0.995721i \(0.529456\pi\)
\(132\) −11.5886 −1.00866
\(133\) −4.22547 −0.366395
\(134\) −4.11021 −0.355068
\(135\) 0 0
\(136\) −6.48108 −0.555748
\(137\) −5.36317 −0.458206 −0.229103 0.973402i \(-0.573579\pi\)
−0.229103 + 0.973402i \(0.573579\pi\)
\(138\) 17.0724 1.45330
\(139\) −10.1601 −0.861771 −0.430886 0.902407i \(-0.641799\pi\)
−0.430886 + 0.902407i \(0.641799\pi\)
\(140\) 0 0
\(141\) −13.4483 −1.13255
\(142\) 3.82446 0.320941
\(143\) −16.2754 −1.36102
\(144\) 2.08777 0.173981
\(145\) 0 0
\(146\) 4.70655 0.389517
\(147\) 24.4837 2.01938
\(148\) 0.137699 0.0113188
\(149\) −5.93972 −0.486601 −0.243301 0.969951i \(-0.578230\pi\)
−0.243301 + 0.969951i \(0.578230\pi\)
\(150\) 0 0
\(151\) −15.2978 −1.24492 −0.622460 0.782652i \(-0.713867\pi\)
−0.622460 + 0.782652i \(0.713867\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −13.5310 −1.09392
\(154\) −21.7092 −1.74938
\(155\) 0 0
\(156\) 7.14540 0.572090
\(157\) −12.7866 −1.02048 −0.510242 0.860031i \(-0.670444\pi\)
−0.510242 + 0.860031i \(0.670444\pi\)
\(158\) 10.6265 0.845397
\(159\) 0.508572 0.0403324
\(160\) 0 0
\(161\) 31.9819 2.52053
\(162\) −10.9045 −0.856740
\(163\) −11.4734 −0.898664 −0.449332 0.893365i \(-0.648338\pi\)
−0.449332 + 0.893365i \(0.648338\pi\)
\(164\) −11.6489 −0.909628
\(165\) 0 0
\(166\) −12.0999 −0.939131
\(167\) 19.4131 1.50223 0.751115 0.660171i \(-0.229516\pi\)
0.751115 + 0.660171i \(0.229516\pi\)
\(168\) 9.53101 0.735333
\(169\) −2.96480 −0.228062
\(170\) 0 0
\(171\) −2.08777 −0.159656
\(172\) −2.51122 −0.191479
\(173\) 9.78662 0.744063 0.372031 0.928220i \(-0.378661\pi\)
0.372031 + 0.928220i \(0.378661\pi\)
\(174\) 1.87703 0.142297
\(175\) 0 0
\(176\) −5.13770 −0.387269
\(177\) 12.1652 0.914392
\(178\) −10.0000 −0.749532
\(179\) −6.82446 −0.510084 −0.255042 0.966930i \(-0.582089\pi\)
−0.255042 + 0.966930i \(0.582089\pi\)
\(180\) 0 0
\(181\) −0.137699 −0.0102351 −0.00511755 0.999987i \(-0.501629\pi\)
−0.00511755 + 0.999987i \(0.501629\pi\)
\(182\) 13.3856 0.992207
\(183\) 32.5957 2.40954
\(184\) 7.56885 0.557983
\(185\) 0 0
\(186\) −10.1755 −0.746107
\(187\) 33.2978 2.43498
\(188\) −5.96216 −0.434835
\(189\) −8.69446 −0.632429
\(190\) 0 0
\(191\) 19.3779 1.40214 0.701068 0.713095i \(-0.252707\pi\)
0.701068 + 0.713095i \(0.252707\pi\)
\(192\) 2.25561 0.162785
\(193\) −5.42851 −0.390752 −0.195376 0.980728i \(-0.562593\pi\)
−0.195376 + 0.980728i \(0.562593\pi\)
\(194\) 3.93972 0.282856
\(195\) 0 0
\(196\) 10.8546 0.775328
\(197\) −15.6489 −1.11494 −0.557470 0.830197i \(-0.688228\pi\)
−0.557470 + 0.830197i \(0.688228\pi\)
\(198\) −10.7263 −0.762288
\(199\) 18.0499 1.27953 0.639763 0.768572i \(-0.279033\pi\)
0.639763 + 0.768572i \(0.279033\pi\)
\(200\) 0 0
\(201\) −9.27102 −0.653927
\(202\) 3.19798 0.225009
\(203\) 3.51628 0.246794
\(204\) −14.6188 −1.02352
\(205\) 0 0
\(206\) −10.6868 −0.744582
\(207\) 15.8020 1.09832
\(208\) 3.16784 0.219650
\(209\) 5.13770 0.355382
\(210\) 0 0
\(211\) −7.50857 −0.516911 −0.258456 0.966023i \(-0.583214\pi\)
−0.258456 + 0.966023i \(0.583214\pi\)
\(212\) 0.225470 0.0154853
\(213\) 8.62648 0.591077
\(214\) 10.8168 0.739418
\(215\) 0 0
\(216\) −2.05763 −0.140004
\(217\) −19.0620 −1.29401
\(218\) 9.24791 0.626347
\(219\) 10.6161 0.717372
\(220\) 0 0
\(221\) −20.5310 −1.38106
\(222\) 0.310596 0.0208458
\(223\) 27.8091 1.86223 0.931116 0.364723i \(-0.118836\pi\)
0.931116 + 0.364723i \(0.118836\pi\)
\(224\) 4.22547 0.282326
\(225\) 0 0
\(226\) 17.6489 1.17399
\(227\) 8.91223 0.591525 0.295763 0.955261i \(-0.404426\pi\)
0.295763 + 0.955261i \(0.404426\pi\)
\(228\) −2.25561 −0.149381
\(229\) −13.6489 −0.901946 −0.450973 0.892538i \(-0.648923\pi\)
−0.450973 + 0.892538i \(0.648923\pi\)
\(230\) 0 0
\(231\) −48.9674 −3.22182
\(232\) 0.832162 0.0546341
\(233\) 23.2754 1.52482 0.762411 0.647093i \(-0.224015\pi\)
0.762411 + 0.647093i \(0.224015\pi\)
\(234\) 6.61372 0.432352
\(235\) 0 0
\(236\) 5.39331 0.351074
\(237\) 23.9692 1.55697
\(238\) −27.3856 −1.77515
\(239\) 3.72898 0.241208 0.120604 0.992701i \(-0.461517\pi\)
0.120604 + 0.992701i \(0.461517\pi\)
\(240\) 0 0
\(241\) −1.48878 −0.0959009 −0.0479505 0.998850i \(-0.515269\pi\)
−0.0479505 + 0.998850i \(0.515269\pi\)
\(242\) 15.3960 0.989689
\(243\) −18.4234 −1.18186
\(244\) 14.4509 0.925127
\(245\) 0 0
\(246\) −26.2754 −1.67526
\(247\) −3.16784 −0.201565
\(248\) −4.51122 −0.286463
\(249\) −27.2925 −1.72959
\(250\) 0 0
\(251\) −8.78662 −0.554606 −0.277303 0.960782i \(-0.589441\pi\)
−0.277303 + 0.960782i \(0.589441\pi\)
\(252\) 8.82181 0.555722
\(253\) −38.8865 −2.44477
\(254\) −12.7866 −0.802304
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 2.74175 0.171025 0.0855127 0.996337i \(-0.472747\pi\)
0.0855127 + 0.996337i \(0.472747\pi\)
\(258\) −5.66432 −0.352645
\(259\) 0.581844 0.0361540
\(260\) 0 0
\(261\) 1.73736 0.107540
\(262\) −2.11526 −0.130681
\(263\) 2.74704 0.169390 0.0846948 0.996407i \(-0.473008\pi\)
0.0846948 + 0.996407i \(0.473008\pi\)
\(264\) −11.5886 −0.713231
\(265\) 0 0
\(266\) −4.22547 −0.259080
\(267\) −22.5561 −1.38041
\(268\) −4.11021 −0.251071
\(269\) −9.74175 −0.593965 −0.296982 0.954883i \(-0.595980\pi\)
−0.296982 + 0.954883i \(0.595980\pi\)
\(270\) 0 0
\(271\) 26.3555 1.60098 0.800490 0.599346i \(-0.204573\pi\)
0.800490 + 0.599346i \(0.204573\pi\)
\(272\) −6.48108 −0.392973
\(273\) 30.1927 1.82734
\(274\) −5.36317 −0.324001
\(275\) 0 0
\(276\) 17.0724 1.02764
\(277\) −0.962158 −0.0578104 −0.0289052 0.999582i \(-0.509202\pi\)
−0.0289052 + 0.999582i \(0.509202\pi\)
\(278\) −10.1601 −0.609364
\(279\) −9.41839 −0.563864
\(280\) 0 0
\(281\) −14.6714 −0.875219 −0.437610 0.899165i \(-0.644175\pi\)
−0.437610 + 0.899165i \(0.644175\pi\)
\(282\) −13.4483 −0.800834
\(283\) −26.1601 −1.55506 −0.777529 0.628847i \(-0.783527\pi\)
−0.777529 + 0.628847i \(0.783527\pi\)
\(284\) 3.82446 0.226940
\(285\) 0 0
\(286\) −16.2754 −0.962384
\(287\) −49.2221 −2.90549
\(288\) 2.08777 0.123023
\(289\) 25.0044 1.47085
\(290\) 0 0
\(291\) 8.88647 0.520934
\(292\) 4.70655 0.275430
\(293\) −22.4657 −1.31246 −0.656229 0.754562i \(-0.727850\pi\)
−0.656229 + 0.754562i \(0.727850\pi\)
\(294\) 24.4837 1.42792
\(295\) 0 0
\(296\) 0.137699 0.00800360
\(297\) 10.5715 0.613420
\(298\) −5.93972 −0.344079
\(299\) 23.9769 1.38662
\(300\) 0 0
\(301\) −10.6111 −0.611612
\(302\) −15.2978 −0.880291
\(303\) 7.21338 0.414398
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) −13.5310 −0.773516
\(307\) 17.2204 0.982821 0.491410 0.870928i \(-0.336482\pi\)
0.491410 + 0.870928i \(0.336482\pi\)
\(308\) −21.7092 −1.23700
\(309\) −24.1051 −1.37129
\(310\) 0 0
\(311\) −7.87439 −0.446516 −0.223258 0.974759i \(-0.571669\pi\)
−0.223258 + 0.974759i \(0.571669\pi\)
\(312\) 7.14540 0.404529
\(313\) −25.1678 −1.42257 −0.711285 0.702904i \(-0.751887\pi\)
−0.711285 + 0.702904i \(0.751887\pi\)
\(314\) −12.7866 −0.721590
\(315\) 0 0
\(316\) 10.6265 0.597786
\(317\) −23.9045 −1.34261 −0.671306 0.741180i \(-0.734266\pi\)
−0.671306 + 0.741180i \(0.734266\pi\)
\(318\) 0.508572 0.0285193
\(319\) −4.27540 −0.239376
\(320\) 0 0
\(321\) 24.3984 1.36178
\(322\) 31.9819 1.78228
\(323\) 6.48108 0.360617
\(324\) −10.9045 −0.605807
\(325\) 0 0
\(326\) −11.4734 −0.635451
\(327\) 20.8597 1.15354
\(328\) −11.6489 −0.643204
\(329\) −25.1929 −1.38893
\(330\) 0 0
\(331\) 30.7565 1.69053 0.845264 0.534348i \(-0.179443\pi\)
0.845264 + 0.534348i \(0.179443\pi\)
\(332\) −12.0999 −0.664066
\(333\) 0.287484 0.0157540
\(334\) 19.4131 1.06224
\(335\) 0 0
\(336\) 9.53101 0.519959
\(337\) 13.4734 0.733942 0.366971 0.930232i \(-0.380395\pi\)
0.366971 + 0.930232i \(0.380395\pi\)
\(338\) −2.96480 −0.161264
\(339\) 39.8091 2.16213
\(340\) 0 0
\(341\) 23.1773 1.25512
\(342\) −2.08777 −0.112894
\(343\) 16.2875 0.879441
\(344\) −2.51122 −0.135396
\(345\) 0 0
\(346\) 9.78662 0.526132
\(347\) 28.9468 1.55394 0.776971 0.629536i \(-0.216755\pi\)
0.776971 + 0.629536i \(0.216755\pi\)
\(348\) 1.87703 0.100619
\(349\) 27.9243 1.49475 0.747377 0.664400i \(-0.231313\pi\)
0.747377 + 0.664400i \(0.231313\pi\)
\(350\) 0 0
\(351\) −6.51825 −0.347918
\(352\) −5.13770 −0.273840
\(353\) 28.3099 1.50678 0.753392 0.657571i \(-0.228416\pi\)
0.753392 + 0.657571i \(0.228416\pi\)
\(354\) 12.1652 0.646573
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) −61.7712 −3.26928
\(358\) −6.82446 −0.360684
\(359\) 2.60163 0.137309 0.0686545 0.997640i \(-0.478129\pi\)
0.0686545 + 0.997640i \(0.478129\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −0.137699 −0.00723731
\(363\) 34.7272 1.82271
\(364\) 13.3856 0.701596
\(365\) 0 0
\(366\) 32.5957 1.70380
\(367\) 11.6489 0.608069 0.304034 0.952661i \(-0.401666\pi\)
0.304034 + 0.952661i \(0.401666\pi\)
\(368\) 7.56885 0.394554
\(369\) −24.3203 −1.26606
\(370\) 0 0
\(371\) 0.952717 0.0494626
\(372\) −10.1755 −0.527577
\(373\) −12.8064 −0.663091 −0.331545 0.943439i \(-0.607570\pi\)
−0.331545 + 0.943439i \(0.607570\pi\)
\(374\) 33.2978 1.72179
\(375\) 0 0
\(376\) −5.96216 −0.307475
\(377\) 2.63615 0.135769
\(378\) −8.69446 −0.447195
\(379\) −20.9122 −1.07419 −0.537095 0.843522i \(-0.680478\pi\)
−0.537095 + 0.843522i \(0.680478\pi\)
\(380\) 0 0
\(381\) −28.8416 −1.47760
\(382\) 19.3779 0.991460
\(383\) 10.3511 0.528916 0.264458 0.964397i \(-0.414807\pi\)
0.264458 + 0.964397i \(0.414807\pi\)
\(384\) 2.25561 0.115106
\(385\) 0 0
\(386\) −5.42851 −0.276304
\(387\) −5.24285 −0.266509
\(388\) 3.93972 0.200009
\(389\) 6.56620 0.332920 0.166460 0.986048i \(-0.446766\pi\)
0.166460 + 0.986048i \(0.446766\pi\)
\(390\) 0 0
\(391\) −49.0543 −2.48078
\(392\) 10.8546 0.548240
\(393\) −4.77121 −0.240676
\(394\) −15.6489 −0.788381
\(395\) 0 0
\(396\) −10.7263 −0.539019
\(397\) 23.5284 1.18085 0.590427 0.807091i \(-0.298959\pi\)
0.590427 + 0.807091i \(0.298959\pi\)
\(398\) 18.0499 0.904761
\(399\) −9.53101 −0.477147
\(400\) 0 0
\(401\) 6.22041 0.310633 0.155316 0.987865i \(-0.450360\pi\)
0.155316 + 0.987865i \(0.450360\pi\)
\(402\) −9.27102 −0.462396
\(403\) −14.2908 −0.711876
\(404\) 3.19798 0.159105
\(405\) 0 0
\(406\) 3.51628 0.174510
\(407\) −0.707457 −0.0350674
\(408\) −14.6188 −0.723737
\(409\) −34.4905 −1.70545 −0.852723 0.522363i \(-0.825051\pi\)
−0.852723 + 0.522363i \(0.825051\pi\)
\(410\) 0 0
\(411\) −12.0972 −0.596711
\(412\) −10.6868 −0.526499
\(413\) 22.7893 1.12139
\(414\) 15.8020 0.776627
\(415\) 0 0
\(416\) 3.16784 0.155316
\(417\) −22.9173 −1.12226
\(418\) 5.13770 0.251293
\(419\) −10.6265 −0.519138 −0.259569 0.965725i \(-0.583580\pi\)
−0.259569 + 0.965725i \(0.583580\pi\)
\(420\) 0 0
\(421\) −1.98021 −0.0965095 −0.0482548 0.998835i \(-0.515366\pi\)
−0.0482548 + 0.998835i \(0.515366\pi\)
\(422\) −7.50857 −0.365512
\(423\) −12.4476 −0.605224
\(424\) 0.225470 0.0109498
\(425\) 0 0
\(426\) 8.62648 0.417954
\(427\) 61.0620 2.95500
\(428\) 10.8168 0.522848
\(429\) −36.7109 −1.77242
\(430\) 0 0
\(431\) 15.0774 0.726254 0.363127 0.931740i \(-0.381709\pi\)
0.363127 + 0.931740i \(0.381709\pi\)
\(432\) −2.05763 −0.0989979
\(433\) 13.5337 0.650386 0.325193 0.945648i \(-0.394571\pi\)
0.325193 + 0.945648i \(0.394571\pi\)
\(434\) −19.0620 −0.915006
\(435\) 0 0
\(436\) 9.24791 0.442894
\(437\) −7.56885 −0.362067
\(438\) 10.6161 0.507258
\(439\) 39.1773 1.86983 0.934915 0.354872i \(-0.115476\pi\)
0.934915 + 0.354872i \(0.115476\pi\)
\(440\) 0 0
\(441\) 22.6619 1.07914
\(442\) −20.5310 −0.976560
\(443\) 19.3132 0.917600 0.458800 0.888540i \(-0.348279\pi\)
0.458800 + 0.888540i \(0.348279\pi\)
\(444\) 0.310596 0.0147402
\(445\) 0 0
\(446\) 27.8091 1.31680
\(447\) −13.3977 −0.633689
\(448\) 4.22547 0.199635
\(449\) 41.4131 1.95440 0.977202 0.212310i \(-0.0680985\pi\)
0.977202 + 0.212310i \(0.0680985\pi\)
\(450\) 0 0
\(451\) 59.8486 2.81816
\(452\) 17.6489 0.830135
\(453\) −34.5059 −1.62123
\(454\) 8.91223 0.418272
\(455\) 0 0
\(456\) −2.25561 −0.105629
\(457\) −37.8392 −1.77004 −0.885021 0.465551i \(-0.845856\pi\)
−0.885021 + 0.465551i \(0.845856\pi\)
\(458\) −13.6489 −0.637772
\(459\) 13.3357 0.622456
\(460\) 0 0
\(461\) 1.58864 0.0739903 0.0369952 0.999315i \(-0.488221\pi\)
0.0369952 + 0.999315i \(0.488221\pi\)
\(462\) −48.9674 −2.27817
\(463\) 40.3581 1.87560 0.937800 0.347175i \(-0.112859\pi\)
0.937800 + 0.347175i \(0.112859\pi\)
\(464\) 0.832162 0.0386322
\(465\) 0 0
\(466\) 23.2754 1.07821
\(467\) −39.5130 −1.82844 −0.914221 0.405217i \(-0.867196\pi\)
−0.914221 + 0.405217i \(0.867196\pi\)
\(468\) 6.61372 0.305719
\(469\) −17.3676 −0.801959
\(470\) 0 0
\(471\) −28.8416 −1.32895
\(472\) 5.39331 0.248247
\(473\) 12.9019 0.593229
\(474\) 23.9692 1.10094
\(475\) 0 0
\(476\) −27.3856 −1.25522
\(477\) 0.470730 0.0215532
\(478\) 3.72898 0.170560
\(479\) 7.61107 0.347759 0.173879 0.984767i \(-0.444370\pi\)
0.173879 + 0.984767i \(0.444370\pi\)
\(480\) 0 0
\(481\) 0.436209 0.0198894
\(482\) −1.48878 −0.0678122
\(483\) 72.1388 3.28243
\(484\) 15.3960 0.699816
\(485\) 0 0
\(486\) −18.4234 −0.835705
\(487\) −20.3907 −0.923989 −0.461995 0.886883i \(-0.652866\pi\)
−0.461995 + 0.886883i \(0.652866\pi\)
\(488\) 14.4509 0.654163
\(489\) −25.8794 −1.17031
\(490\) 0 0
\(491\) 25.0224 1.12925 0.564623 0.825349i \(-0.309021\pi\)
0.564623 + 0.825349i \(0.309021\pi\)
\(492\) −26.2754 −1.18459
\(493\) −5.39331 −0.242902
\(494\) −3.16784 −0.142528
\(495\) 0 0
\(496\) −4.51122 −0.202560
\(497\) 16.1601 0.724881
\(498\) −27.2925 −1.22301
\(499\) 22.6111 1.01221 0.506105 0.862472i \(-0.331085\pi\)
0.506105 + 0.862472i \(0.331085\pi\)
\(500\) 0 0
\(501\) 43.7884 1.95632
\(502\) −8.78662 −0.392166
\(503\) 11.5035 0.512916 0.256458 0.966555i \(-0.417444\pi\)
0.256458 + 0.966555i \(0.417444\pi\)
\(504\) 8.82181 0.392955
\(505\) 0 0
\(506\) −38.8865 −1.72871
\(507\) −6.68744 −0.296999
\(508\) −12.7866 −0.567314
\(509\) 9.11526 0.404027 0.202013 0.979383i \(-0.435252\pi\)
0.202013 + 0.979383i \(0.435252\pi\)
\(510\) 0 0
\(511\) 19.8874 0.879766
\(512\) 1.00000 0.0441942
\(513\) 2.05763 0.0908467
\(514\) 2.74175 0.120933
\(515\) 0 0
\(516\) −5.66432 −0.249358
\(517\) 30.6318 1.34718
\(518\) 0.581844 0.0255648
\(519\) 22.0748 0.968975
\(520\) 0 0
\(521\) 15.4888 0.678576 0.339288 0.940683i \(-0.389814\pi\)
0.339288 + 0.940683i \(0.389814\pi\)
\(522\) 1.73736 0.0760423
\(523\) 4.34073 0.189807 0.0949035 0.995486i \(-0.469746\pi\)
0.0949035 + 0.995486i \(0.469746\pi\)
\(524\) −2.11526 −0.0924057
\(525\) 0 0
\(526\) 2.74704 0.119776
\(527\) 29.2376 1.27361
\(528\) −11.5886 −0.504331
\(529\) 34.2875 1.49076
\(530\) 0 0
\(531\) 11.2600 0.488642
\(532\) −4.22547 −0.183197
\(533\) −36.9019 −1.59840
\(534\) −22.5561 −0.976097
\(535\) 0 0
\(536\) −4.11021 −0.177534
\(537\) −15.3933 −0.664270
\(538\) −9.74175 −0.419996
\(539\) −55.7677 −2.40208
\(540\) 0 0
\(541\) 19.5491 0.840480 0.420240 0.907413i \(-0.361946\pi\)
0.420240 + 0.907413i \(0.361946\pi\)
\(542\) 26.3555 1.13206
\(543\) −0.310596 −0.0133289
\(544\) −6.48108 −0.277874
\(545\) 0 0
\(546\) 30.1927 1.29213
\(547\) −41.8038 −1.78740 −0.893700 0.448665i \(-0.851900\pi\)
−0.893700 + 0.448665i \(0.851900\pi\)
\(548\) −5.36317 −0.229103
\(549\) 30.1703 1.28763
\(550\) 0 0
\(551\) −0.832162 −0.0354513
\(552\) 17.0724 0.726648
\(553\) 44.9019 1.90942
\(554\) −0.962158 −0.0408782
\(555\) 0 0
\(556\) −10.1601 −0.430886
\(557\) −9.76418 −0.413722 −0.206861 0.978370i \(-0.566325\pi\)
−0.206861 + 0.978370i \(0.566325\pi\)
\(558\) −9.41839 −0.398712
\(559\) −7.95513 −0.336466
\(560\) 0 0
\(561\) 75.1069 3.17102
\(562\) −14.6714 −0.618874
\(563\) 11.4509 0.482600 0.241300 0.970451i \(-0.422426\pi\)
0.241300 + 0.970451i \(0.422426\pi\)
\(564\) −13.4483 −0.566275
\(565\) 0 0
\(566\) −26.1601 −1.09959
\(567\) −46.0767 −1.93504
\(568\) 3.82446 0.160471
\(569\) −13.4338 −0.563174 −0.281587 0.959536i \(-0.590861\pi\)
−0.281587 + 0.959536i \(0.590861\pi\)
\(570\) 0 0
\(571\) 37.6335 1.57491 0.787457 0.616370i \(-0.211397\pi\)
0.787457 + 0.616370i \(0.211397\pi\)
\(572\) −16.2754 −0.680509
\(573\) 43.7090 1.82597
\(574\) −49.2221 −2.05449
\(575\) 0 0
\(576\) 2.08777 0.0869905
\(577\) 1.56885 0.0653121 0.0326560 0.999467i \(-0.489603\pi\)
0.0326560 + 0.999467i \(0.489603\pi\)
\(578\) 25.0044 1.04005
\(579\) −12.2446 −0.508868
\(580\) 0 0
\(581\) −51.1276 −2.12113
\(582\) 8.88647 0.368356
\(583\) −1.15840 −0.0479759
\(584\) 4.70655 0.194758
\(585\) 0 0
\(586\) −22.4657 −0.928048
\(587\) 25.8693 1.06774 0.533871 0.845566i \(-0.320737\pi\)
0.533871 + 0.845566i \(0.320737\pi\)
\(588\) 24.4837 1.00969
\(589\) 4.51122 0.185881
\(590\) 0 0
\(591\) −35.2978 −1.45196
\(592\) 0.137699 0.00565940
\(593\) −28.9243 −1.18778 −0.593890 0.804547i \(-0.702408\pi\)
−0.593890 + 0.804547i \(0.702408\pi\)
\(594\) 10.5715 0.433754
\(595\) 0 0
\(596\) −5.93972 −0.243301
\(597\) 40.7136 1.66630
\(598\) 23.9769 0.980488
\(599\) 41.3581 1.68985 0.844923 0.534887i \(-0.179646\pi\)
0.844923 + 0.534887i \(0.179646\pi\)
\(600\) 0 0
\(601\) 2.68147 0.109379 0.0546897 0.998503i \(-0.482583\pi\)
0.0546897 + 0.998503i \(0.482583\pi\)
\(602\) −10.6111 −0.432475
\(603\) −8.58117 −0.349452
\(604\) −15.2978 −0.622460
\(605\) 0 0
\(606\) 7.21338 0.293024
\(607\) 3.31324 0.134480 0.0672401 0.997737i \(-0.478581\pi\)
0.0672401 + 0.997737i \(0.478581\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 7.93134 0.321394
\(610\) 0 0
\(611\) −18.8871 −0.764092
\(612\) −13.5310 −0.546959
\(613\) −10.0603 −0.406331 −0.203165 0.979144i \(-0.565123\pi\)
−0.203165 + 0.979144i \(0.565123\pi\)
\(614\) 17.2204 0.694959
\(615\) 0 0
\(616\) −21.7092 −0.874688
\(617\) −27.6265 −1.11220 −0.556100 0.831115i \(-0.687703\pi\)
−0.556100 + 0.831115i \(0.687703\pi\)
\(618\) −24.1051 −0.969651
\(619\) 16.6714 0.670078 0.335039 0.942204i \(-0.391250\pi\)
0.335039 + 0.942204i \(0.391250\pi\)
\(620\) 0 0
\(621\) −15.5739 −0.624959
\(622\) −7.87439 −0.315734
\(623\) −42.2547 −1.69290
\(624\) 7.14540 0.286045
\(625\) 0 0
\(626\) −25.1678 −1.00591
\(627\) 11.5886 0.462806
\(628\) −12.7866 −0.510242
\(629\) −0.892439 −0.0355839
\(630\) 0 0
\(631\) −0.709194 −0.0282326 −0.0141163 0.999900i \(-0.504494\pi\)
−0.0141163 + 0.999900i \(0.504494\pi\)
\(632\) 10.6265 0.422699
\(633\) −16.9364 −0.673162
\(634\) −23.9045 −0.949370
\(635\) 0 0
\(636\) 0.508572 0.0201662
\(637\) 34.3856 1.36241
\(638\) −4.27540 −0.169265
\(639\) 7.98459 0.315866
\(640\) 0 0
\(641\) −2.43553 −0.0961978 −0.0480989 0.998843i \(-0.515316\pi\)
−0.0480989 + 0.998843i \(0.515316\pi\)
\(642\) 24.3984 0.962927
\(643\) 7.70390 0.303812 0.151906 0.988395i \(-0.451459\pi\)
0.151906 + 0.988395i \(0.451459\pi\)
\(644\) 31.9819 1.26027
\(645\) 0 0
\(646\) 6.48108 0.254995
\(647\) −10.0499 −0.395103 −0.197552 0.980292i \(-0.563299\pi\)
−0.197552 + 0.980292i \(0.563299\pi\)
\(648\) −10.9045 −0.428370
\(649\) −27.7092 −1.08768
\(650\) 0 0
\(651\) −42.9964 −1.68516
\(652\) −11.4734 −0.449332
\(653\) −7.09283 −0.277564 −0.138782 0.990323i \(-0.544319\pi\)
−0.138782 + 0.990323i \(0.544319\pi\)
\(654\) 20.8597 0.815677
\(655\) 0 0
\(656\) −11.6489 −0.454814
\(657\) 9.82620 0.383356
\(658\) −25.1929 −0.982122
\(659\) −1.16346 −0.0453218 −0.0226609 0.999743i \(-0.507214\pi\)
−0.0226609 + 0.999743i \(0.507214\pi\)
\(660\) 0 0
\(661\) 1.79432 0.0697909 0.0348955 0.999391i \(-0.488890\pi\)
0.0348955 + 0.999391i \(0.488890\pi\)
\(662\) 30.7565 1.19538
\(663\) −46.3099 −1.79853
\(664\) −12.0999 −0.469566
\(665\) 0 0
\(666\) 0.287484 0.0111398
\(667\) 6.29851 0.243879
\(668\) 19.4131 0.751115
\(669\) 62.7263 2.42514
\(670\) 0 0
\(671\) −74.2446 −2.86618
\(672\) 9.53101 0.367667
\(673\) −25.2824 −0.974566 −0.487283 0.873244i \(-0.662012\pi\)
−0.487283 + 0.873244i \(0.662012\pi\)
\(674\) 13.4734 0.518975
\(675\) 0 0
\(676\) −2.96480 −0.114031
\(677\) −4.89682 −0.188200 −0.0941001 0.995563i \(-0.529997\pi\)
−0.0941001 + 0.995563i \(0.529997\pi\)
\(678\) 39.8091 1.52886
\(679\) 16.6472 0.638860
\(680\) 0 0
\(681\) 20.1025 0.770330
\(682\) 23.1773 0.887504
\(683\) 10.1980 0.390215 0.195107 0.980782i \(-0.437494\pi\)
0.195107 + 0.980782i \(0.437494\pi\)
\(684\) −2.08777 −0.0798279
\(685\) 0 0
\(686\) 16.2875 0.621859
\(687\) −30.7866 −1.17458
\(688\) −2.51122 −0.0957393
\(689\) 0.714253 0.0272109
\(690\) 0 0
\(691\) −39.9846 −1.52109 −0.760543 0.649288i \(-0.775067\pi\)
−0.760543 + 0.649288i \(0.775067\pi\)
\(692\) 9.78662 0.372031
\(693\) −45.3238 −1.72171
\(694\) 28.9468 1.09880
\(695\) 0 0
\(696\) 1.87703 0.0711487
\(697\) 75.4975 2.85967
\(698\) 27.9243 1.05695
\(699\) 52.5002 1.98574
\(700\) 0 0
\(701\) 4.91729 0.185723 0.0928617 0.995679i \(-0.470399\pi\)
0.0928617 + 0.995679i \(0.470399\pi\)
\(702\) −6.51825 −0.246015
\(703\) −0.137699 −0.00519342
\(704\) −5.13770 −0.193634
\(705\) 0 0
\(706\) 28.3099 1.06546
\(707\) 13.5130 0.508207
\(708\) 12.1652 0.457196
\(709\) −36.8865 −1.38530 −0.692650 0.721274i \(-0.743557\pi\)
−0.692650 + 0.721274i \(0.743557\pi\)
\(710\) 0 0
\(711\) 22.1857 0.832027
\(712\) −10.0000 −0.374766
\(713\) −34.1447 −1.27873
\(714\) −61.7712 −2.31173
\(715\) 0 0
\(716\) −6.82446 −0.255042
\(717\) 8.41113 0.314119
\(718\) 2.60163 0.0970921
\(719\) −23.8891 −0.890914 −0.445457 0.895303i \(-0.646959\pi\)
−0.445457 + 0.895303i \(0.646959\pi\)
\(720\) 0 0
\(721\) −45.1566 −1.68172
\(722\) 1.00000 0.0372161
\(723\) −3.35811 −0.124889
\(724\) −0.137699 −0.00511755
\(725\) 0 0
\(726\) 34.7272 1.28885
\(727\) 19.6894 0.730240 0.365120 0.930961i \(-0.381028\pi\)
0.365120 + 0.930961i \(0.381028\pi\)
\(728\) 13.3856 0.496104
\(729\) −8.84251 −0.327500
\(730\) 0 0
\(731\) 16.2754 0.601967
\(732\) 32.5957 1.20477
\(733\) 1.76418 0.0651615 0.0325808 0.999469i \(-0.489627\pi\)
0.0325808 + 0.999469i \(0.489627\pi\)
\(734\) 11.6489 0.429969
\(735\) 0 0
\(736\) 7.56885 0.278991
\(737\) 21.1170 0.777855
\(738\) −24.3203 −0.895241
\(739\) 28.1755 1.03645 0.518227 0.855243i \(-0.326592\pi\)
0.518227 + 0.855243i \(0.326592\pi\)
\(740\) 0 0
\(741\) −7.14540 −0.262493
\(742\) 0.952717 0.0349753
\(743\) −5.42851 −0.199153 −0.0995763 0.995030i \(-0.531749\pi\)
−0.0995763 + 0.995030i \(0.531749\pi\)
\(744\) −10.1755 −0.373053
\(745\) 0 0
\(746\) −12.8064 −0.468876
\(747\) −25.2617 −0.924278
\(748\) 33.2978 1.21749
\(749\) 45.7059 1.67006
\(750\) 0 0
\(751\) 25.8640 0.943792 0.471896 0.881654i \(-0.343570\pi\)
0.471896 + 0.881654i \(0.343570\pi\)
\(752\) −5.96216 −0.217418
\(753\) −19.8192 −0.722251
\(754\) 2.63615 0.0960031
\(755\) 0 0
\(756\) −8.69446 −0.316215
\(757\) −3.76947 −0.137004 −0.0685019 0.997651i \(-0.521822\pi\)
−0.0685019 + 0.997651i \(0.521822\pi\)
\(758\) −20.9122 −0.759566
\(759\) −87.7127 −3.18377
\(760\) 0 0
\(761\) 18.3605 0.665568 0.332784 0.943003i \(-0.392012\pi\)
0.332784 + 0.943003i \(0.392012\pi\)
\(762\) −28.8416 −1.04482
\(763\) 39.0767 1.41467
\(764\) 19.3779 0.701068
\(765\) 0 0
\(766\) 10.3511 0.374000
\(767\) 17.0851 0.616908
\(768\) 2.25561 0.0813923
\(769\) −38.1300 −1.37500 −0.687501 0.726183i \(-0.741292\pi\)
−0.687501 + 0.726183i \(0.741292\pi\)
\(770\) 0 0
\(771\) 6.18431 0.222722
\(772\) −5.42851 −0.195376
\(773\) −29.1575 −1.04872 −0.524361 0.851496i \(-0.675696\pi\)
−0.524361 + 0.851496i \(0.675696\pi\)
\(774\) −5.24285 −0.188450
\(775\) 0 0
\(776\) 3.93972 0.141428
\(777\) 1.31241 0.0470825
\(778\) 6.56620 0.235410
\(779\) 11.6489 0.417366
\(780\) 0 0
\(781\) −19.6489 −0.703094
\(782\) −49.0543 −1.75418
\(783\) −1.71228 −0.0611920
\(784\) 10.8546 0.387664
\(785\) 0 0
\(786\) −4.77121 −0.170183
\(787\) −47.0165 −1.67596 −0.837978 0.545704i \(-0.816262\pi\)
−0.837978 + 0.545704i \(0.816262\pi\)
\(788\) −15.6489 −0.557470
\(789\) 6.19624 0.220592
\(790\) 0 0
\(791\) 74.5750 2.65158
\(792\) −10.7263 −0.381144
\(793\) 45.7782 1.62563
\(794\) 23.5284 0.834990
\(795\) 0 0
\(796\) 18.0499 0.639763
\(797\) −42.6359 −1.51024 −0.755121 0.655586i \(-0.772422\pi\)
−0.755121 + 0.655586i \(0.772422\pi\)
\(798\) −9.53101 −0.337394
\(799\) 38.6412 1.36703
\(800\) 0 0
\(801\) −20.8777 −0.737678
\(802\) 6.22041 0.219650
\(803\) −24.1808 −0.853323
\(804\) −9.27102 −0.326964
\(805\) 0 0
\(806\) −14.2908 −0.503372
\(807\) −21.9736 −0.773506
\(808\) 3.19798 0.112504
\(809\) 49.4630 1.73903 0.869514 0.493909i \(-0.164432\pi\)
0.869514 + 0.493909i \(0.164432\pi\)
\(810\) 0 0
\(811\) −16.7816 −0.589280 −0.294640 0.955608i \(-0.595200\pi\)
−0.294640 + 0.955608i \(0.595200\pi\)
\(812\) 3.51628 0.123397
\(813\) 59.4476 2.08492
\(814\) −0.707457 −0.0247964
\(815\) 0 0
\(816\) −14.6188 −0.511760
\(817\) 2.51122 0.0878564
\(818\) −34.4905 −1.20593
\(819\) 27.9461 0.976515
\(820\) 0 0
\(821\) 11.5337 0.402527 0.201264 0.979537i \(-0.435495\pi\)
0.201264 + 0.979537i \(0.435495\pi\)
\(822\) −12.0972 −0.421939
\(823\) 32.6309 1.13744 0.568720 0.822531i \(-0.307439\pi\)
0.568720 + 0.822531i \(0.307439\pi\)
\(824\) −10.6868 −0.372291
\(825\) 0 0
\(826\) 22.7893 0.792940
\(827\) 6.64650 0.231122 0.115561 0.993300i \(-0.463133\pi\)
0.115561 + 0.993300i \(0.463133\pi\)
\(828\) 15.8020 0.549158
\(829\) −30.9217 −1.07395 −0.536977 0.843597i \(-0.680434\pi\)
−0.536977 + 0.843597i \(0.680434\pi\)
\(830\) 0 0
\(831\) −2.17025 −0.0752852
\(832\) 3.16784 0.109825
\(833\) −70.3495 −2.43747
\(834\) −22.9173 −0.793561
\(835\) 0 0
\(836\) 5.13770 0.177691
\(837\) 9.28243 0.320848
\(838\) −10.6265 −0.367086
\(839\) −48.7109 −1.68169 −0.840844 0.541277i \(-0.817941\pi\)
−0.840844 + 0.541277i \(0.817941\pi\)
\(840\) 0 0
\(841\) −28.3075 −0.976121
\(842\) −1.98021 −0.0682426
\(843\) −33.0928 −1.13978
\(844\) −7.50857 −0.258456
\(845\) 0 0
\(846\) −12.4476 −0.427958
\(847\) 65.0551 2.23532
\(848\) 0.225470 0.00774267
\(849\) −59.0070 −2.02512
\(850\) 0 0
\(851\) 1.04222 0.0357270
\(852\) 8.62648 0.295538
\(853\) 46.1447 1.57997 0.789983 0.613129i \(-0.210089\pi\)
0.789983 + 0.613129i \(0.210089\pi\)
\(854\) 61.0620 2.08950
\(855\) 0 0
\(856\) 10.8168 0.369709
\(857\) −8.40607 −0.287146 −0.143573 0.989640i \(-0.545859\pi\)
−0.143573 + 0.989640i \(0.545859\pi\)
\(858\) −36.7109 −1.25329
\(859\) −8.49581 −0.289873 −0.144937 0.989441i \(-0.546298\pi\)
−0.144937 + 0.989441i \(0.546298\pi\)
\(860\) 0 0
\(861\) −111.026 −3.78375
\(862\) 15.0774 0.513539
\(863\) 3.37352 0.114836 0.0574179 0.998350i \(-0.481713\pi\)
0.0574179 + 0.998350i \(0.481713\pi\)
\(864\) −2.05763 −0.0700021
\(865\) 0 0
\(866\) 13.5337 0.459892
\(867\) 56.4001 1.91545
\(868\) −19.0620 −0.647007
\(869\) −54.5957 −1.85203
\(870\) 0 0
\(871\) −13.0205 −0.441182
\(872\) 9.24791 0.313174
\(873\) 8.22524 0.278382
\(874\) −7.56885 −0.256020
\(875\) 0 0
\(876\) 10.6161 0.358686
\(877\) −13.2780 −0.448368 −0.224184 0.974547i \(-0.571972\pi\)
−0.224184 + 0.974547i \(0.571972\pi\)
\(878\) 39.1773 1.32217
\(879\) −50.6738 −1.70918
\(880\) 0 0
\(881\) −26.6489 −0.897825 −0.448912 0.893576i \(-0.648188\pi\)
−0.448912 + 0.893576i \(0.648188\pi\)
\(882\) 22.6619 0.763066
\(883\) −47.7884 −1.60821 −0.804103 0.594490i \(-0.797354\pi\)
−0.804103 + 0.594490i \(0.797354\pi\)
\(884\) −20.5310 −0.690532
\(885\) 0 0
\(886\) 19.3132 0.648841
\(887\) −36.3304 −1.21985 −0.609927 0.792457i \(-0.708801\pi\)
−0.609927 + 0.792457i \(0.708801\pi\)
\(888\) 0.310596 0.0104229
\(889\) −54.0295 −1.81209
\(890\) 0 0
\(891\) 56.0242 1.87688
\(892\) 27.8091 0.931116
\(893\) 5.96216 0.199516
\(894\) −13.3977 −0.448086
\(895\) 0 0
\(896\) 4.22547 0.141163
\(897\) 54.0825 1.80576
\(898\) 41.4131 1.38197
\(899\) −3.75406 −0.125205
\(900\) 0 0
\(901\) −1.46129 −0.0486826
\(902\) 59.8486 1.99274
\(903\) −23.9344 −0.796488
\(904\) 17.6489 0.586994
\(905\) 0 0
\(906\) −34.5059 −1.14638
\(907\) −39.3873 −1.30784 −0.653918 0.756566i \(-0.726876\pi\)
−0.653918 + 0.756566i \(0.726876\pi\)
\(908\) 8.91223 0.295763
\(909\) 6.67664 0.221450
\(910\) 0 0
\(911\) −20.5561 −0.681054 −0.340527 0.940235i \(-0.610605\pi\)
−0.340527 + 0.940235i \(0.610605\pi\)
\(912\) −2.25561 −0.0746907
\(913\) 62.1654 2.05738
\(914\) −37.8392 −1.25161
\(915\) 0 0
\(916\) −13.6489 −0.450973
\(917\) −8.93799 −0.295158
\(918\) 13.3357 0.440143
\(919\) 12.4054 0.409216 0.204608 0.978844i \(-0.434408\pi\)
0.204608 + 0.978844i \(0.434408\pi\)
\(920\) 0 0
\(921\) 38.8425 1.27990
\(922\) 1.58864 0.0523190
\(923\) 12.1153 0.398779
\(924\) −48.9674 −1.61091
\(925\) 0 0
\(926\) 40.3581 1.32625
\(927\) −22.3115 −0.732806
\(928\) 0.832162 0.0273171
\(929\) −31.3330 −1.02800 −0.514002 0.857789i \(-0.671838\pi\)
−0.514002 + 0.857789i \(0.671838\pi\)
\(930\) 0 0
\(931\) −10.8546 −0.355745
\(932\) 23.2754 0.762411
\(933\) −17.7615 −0.581487
\(934\) −39.5130 −1.29290
\(935\) 0 0
\(936\) 6.61372 0.216176
\(937\) 7.27299 0.237598 0.118799 0.992918i \(-0.462096\pi\)
0.118799 + 0.992918i \(0.462096\pi\)
\(938\) −17.3676 −0.567071
\(939\) −56.7688 −1.85258
\(940\) 0 0
\(941\) 6.72128 0.219107 0.109554 0.993981i \(-0.465058\pi\)
0.109554 + 0.993981i \(0.465058\pi\)
\(942\) −28.8416 −0.939710
\(943\) −88.1689 −2.87117
\(944\) 5.39331 0.175537
\(945\) 0 0
\(946\) 12.9019 0.419476
\(947\) 10.0757 0.327416 0.163708 0.986509i \(-0.447655\pi\)
0.163708 + 0.986509i \(0.447655\pi\)
\(948\) 23.9692 0.778483
\(949\) 14.9096 0.483986
\(950\) 0 0
\(951\) −53.9193 −1.74845
\(952\) −27.3856 −0.887573
\(953\) −8.14473 −0.263834 −0.131917 0.991261i \(-0.542113\pi\)
−0.131917 + 0.991261i \(0.542113\pi\)
\(954\) 0.470730 0.0152404
\(955\) 0 0
\(956\) 3.72898 0.120604
\(957\) −9.64363 −0.311734
\(958\) 7.61107 0.245903
\(959\) −22.6619 −0.731791
\(960\) 0 0
\(961\) −10.6489 −0.343513
\(962\) 0.436209 0.0140639
\(963\) 22.5829 0.727724
\(964\) −1.48878 −0.0479505
\(965\) 0 0
\(966\) 72.1388 2.32103
\(967\) 47.1773 1.51712 0.758560 0.651604i \(-0.225903\pi\)
0.758560 + 0.651604i \(0.225903\pi\)
\(968\) 15.3960 0.494845
\(969\) 14.6188 0.469623
\(970\) 0 0
\(971\) 0.230528 0.00739801 0.00369901 0.999993i \(-0.498823\pi\)
0.00369901 + 0.999993i \(0.498823\pi\)
\(972\) −18.4234 −0.590932
\(973\) −42.9313 −1.37632
\(974\) −20.3907 −0.653359
\(975\) 0 0
\(976\) 14.4509 0.462563
\(977\) −5.80905 −0.185848 −0.0929240 0.995673i \(-0.529621\pi\)
−0.0929240 + 0.995673i \(0.529621\pi\)
\(978\) −25.8794 −0.827533
\(979\) 51.3770 1.64202
\(980\) 0 0
\(981\) 19.3075 0.616441
\(982\) 25.0224 0.798498
\(983\) −22.3511 −0.712889 −0.356444 0.934317i \(-0.616011\pi\)
−0.356444 + 0.934317i \(0.616011\pi\)
\(984\) −26.2754 −0.837629
\(985\) 0 0
\(986\) −5.39331 −0.171758
\(987\) −56.8254 −1.80877
\(988\) −3.16784 −0.100782
\(989\) −19.0070 −0.604388
\(990\) 0 0
\(991\) −34.9415 −1.10995 −0.554976 0.831866i \(-0.687273\pi\)
−0.554976 + 0.831866i \(0.687273\pi\)
\(992\) −4.51122 −0.143231
\(993\) 69.3746 2.20154
\(994\) 16.1601 0.512568
\(995\) 0 0
\(996\) −27.2925 −0.864797
\(997\) −9.35282 −0.296207 −0.148103 0.988972i \(-0.547317\pi\)
−0.148103 + 0.988972i \(0.547317\pi\)
\(998\) 22.6111 0.715741
\(999\) −0.283334 −0.00896430
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 950.2.a.m.1.2 yes 3
3.2 odd 2 8550.2.a.cj.1.3 3
4.3 odd 2 7600.2.a.bm.1.2 3
5.2 odd 4 950.2.b.g.799.5 6
5.3 odd 4 950.2.b.g.799.2 6
5.4 even 2 950.2.a.k.1.2 3
15.14 odd 2 8550.2.a.co.1.1 3
20.19 odd 2 7600.2.a.cb.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.k.1.2 3 5.4 even 2
950.2.a.m.1.2 yes 3 1.1 even 1 trivial
950.2.b.g.799.2 6 5.3 odd 4
950.2.b.g.799.5 6 5.2 odd 4
7600.2.a.bm.1.2 3 4.3 odd 2
7600.2.a.cb.1.2 3 20.19 odd 2
8550.2.a.cj.1.3 3 3.2 odd 2
8550.2.a.co.1.1 3 15.14 odd 2