Properties

Label 4025.2.a.p.1.1
Level 4025
Weight 2
Character 4025.1
Self dual yes
Analytic conductor 32.140
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1397868136\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.2147108.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 161)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.69017\)
Character \(\chi\) = 4025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69017 q^{2} +0.269842 q^{3} +5.23702 q^{4} -0.725921 q^{6} -1.00000 q^{7} -8.70812 q^{8} -2.92719 q^{9} +O(q^{10})\) \(q-2.69017 q^{2} +0.269842 q^{3} +5.23702 q^{4} -0.725921 q^{6} -1.00000 q^{7} -8.70812 q^{8} -2.92719 q^{9} -3.78810 q^{11} +1.41317 q^{12} -1.24125 q^{13} +2.69017 q^{14} +12.9523 q^{16} -5.98512 q^{17} +7.87463 q^{18} -3.38034 q^{19} -0.269842 q^{21} +10.1906 q^{22} +1.00000 q^{23} -2.34982 q^{24} +3.33918 q^{26} -1.59940 q^{27} -5.23702 q^{28} -7.02088 q^{29} +6.26984 q^{31} -17.4276 q^{32} -1.02219 q^{33} +16.1010 q^{34} -15.3297 q^{36} -4.84066 q^{37} +9.09369 q^{38} -0.334942 q^{39} -1.78094 q^{41} +0.725921 q^{42} -3.02219 q^{43} -19.8383 q^{44} -2.69017 q^{46} -3.90322 q^{47} +3.49508 q^{48} +1.00000 q^{49} -1.61504 q^{51} -6.50046 q^{52} +2.47403 q^{53} +4.30267 q^{54} +8.70812 q^{56} -0.912158 q^{57} +18.8873 q^{58} -2.89143 q^{59} -10.3518 q^{61} -16.8669 q^{62} +2.92719 q^{63} +20.9787 q^{64} +2.74986 q^{66} -11.4466 q^{67} -31.3442 q^{68} +0.269842 q^{69} +2.70157 q^{71} +25.4903 q^{72} +14.1893 q^{73} +13.0222 q^{74} -17.7029 q^{76} +3.78810 q^{77} +0.901051 q^{78} +3.31407 q^{79} +8.34997 q^{81} +4.79102 q^{82} -7.02219 q^{83} -1.41317 q^{84} +8.13020 q^{86} -1.89453 q^{87} +32.9872 q^{88} -1.59107 q^{89} +1.24125 q^{91} +5.23702 q^{92} +1.69187 q^{93} +10.5003 q^{94} -4.70271 q^{96} +11.6270 q^{97} -2.69017 q^{98} +11.0885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 2q^{2} + 12q^{4} - 3q^{6} - 5q^{7} - 3q^{8} + 11q^{9} + O(q^{10}) \) \( 5q - 2q^{2} + 12q^{4} - 3q^{6} - 5q^{7} - 3q^{8} + 11q^{9} - 4q^{11} - 3q^{12} + 6q^{13} + 2q^{14} + 10q^{16} + 12q^{17} + 19q^{18} + 6q^{19} - 14q^{22} + 5q^{23} - 36q^{24} + q^{26} - 12q^{28} - 4q^{29} + 30q^{31} - 8q^{32} + 22q^{33} + 6q^{34} - q^{36} - 4q^{37} + 40q^{38} + 16q^{39} + 6q^{41} + 3q^{42} + 12q^{43} - 26q^{44} - 2q^{46} - 10q^{47} - 25q^{48} + 5q^{49} - 4q^{51} + 21q^{52} - 16q^{53} + 33q^{54} + 3q^{56} - 6q^{57} - 13q^{58} + 22q^{59} - 18q^{61} - 15q^{62} - 11q^{63} + 25q^{64} + 4q^{66} + 2q^{67} - 12q^{68} + 4q^{71} + 41q^{72} + 2q^{73} + 38q^{74} + 10q^{76} + 4q^{77} - 41q^{78} + 30q^{79} - 3q^{81} + 7q^{82} - 8q^{83} + 3q^{84} + 8q^{86} + 12q^{87} - 4q^{88} - 20q^{89} - 6q^{91} + 12q^{92} + 26q^{93} - 25q^{94} - q^{96} + 12q^{97} - 2q^{98} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69017 −1.90224 −0.951119 0.308825i \(-0.900064\pi\)
−0.951119 + 0.308825i \(0.900064\pi\)
\(3\) 0.269842 0.155793 0.0778967 0.996961i \(-0.475180\pi\)
0.0778967 + 0.996961i \(0.475180\pi\)
\(4\) 5.23702 2.61851
\(5\) 0 0
\(6\) −0.725921 −0.296356
\(7\) −1.00000 −0.377964
\(8\) −8.70812 −3.07879
\(9\) −2.92719 −0.975728
\(10\) 0 0
\(11\) −3.78810 −1.14215 −0.571077 0.820896i \(-0.693474\pi\)
−0.571077 + 0.820896i \(0.693474\pi\)
\(12\) 1.41317 0.407946
\(13\) −1.24125 −0.344261 −0.172131 0.985074i \(-0.555065\pi\)
−0.172131 + 0.985074i \(0.555065\pi\)
\(14\) 2.69017 0.718978
\(15\) 0 0
\(16\) 12.9523 3.23807
\(17\) −5.98512 −1.45161 −0.725803 0.687903i \(-0.758532\pi\)
−0.725803 + 0.687903i \(0.758532\pi\)
\(18\) 7.87463 1.85607
\(19\) −3.38034 −0.775503 −0.387752 0.921764i \(-0.626748\pi\)
−0.387752 + 0.921764i \(0.626748\pi\)
\(20\) 0 0
\(21\) −0.269842 −0.0588844
\(22\) 10.1906 2.17265
\(23\) 1.00000 0.208514
\(24\) −2.34982 −0.479655
\(25\) 0 0
\(26\) 3.33918 0.654867
\(27\) −1.59940 −0.307805
\(28\) −5.23702 −0.989703
\(29\) −7.02088 −1.30374 −0.651872 0.758329i \(-0.726016\pi\)
−0.651872 + 0.758329i \(0.726016\pi\)
\(30\) 0 0
\(31\) 6.26984 1.12610 0.563048 0.826424i \(-0.309628\pi\)
0.563048 + 0.826424i \(0.309628\pi\)
\(32\) −17.4276 −3.08080
\(33\) −1.02219 −0.177940
\(34\) 16.1010 2.76130
\(35\) 0 0
\(36\) −15.3297 −2.55495
\(37\) −4.84066 −0.795799 −0.397899 0.917429i \(-0.630261\pi\)
−0.397899 + 0.917429i \(0.630261\pi\)
\(38\) 9.09369 1.47519
\(39\) −0.334942 −0.0536336
\(40\) 0 0
\(41\) −1.78094 −0.278135 −0.139068 0.990283i \(-0.544411\pi\)
−0.139068 + 0.990283i \(0.544411\pi\)
\(42\) 0.725921 0.112012
\(43\) −3.02219 −0.460879 −0.230440 0.973087i \(-0.574016\pi\)
−0.230440 + 0.973087i \(0.574016\pi\)
\(44\) −19.8383 −2.99074
\(45\) 0 0
\(46\) −2.69017 −0.396644
\(47\) −3.90322 −0.569343 −0.284671 0.958625i \(-0.591884\pi\)
−0.284671 + 0.958625i \(0.591884\pi\)
\(48\) 3.49508 0.504471
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.61504 −0.226151
\(52\) −6.50046 −0.901451
\(53\) 2.47403 0.339834 0.169917 0.985458i \(-0.445650\pi\)
0.169917 + 0.985458i \(0.445650\pi\)
\(54\) 4.30267 0.585519
\(55\) 0 0
\(56\) 8.70812 1.16367
\(57\) −0.912158 −0.120818
\(58\) 18.8873 2.48003
\(59\) −2.89143 −0.376433 −0.188216 0.982128i \(-0.560271\pi\)
−0.188216 + 0.982128i \(0.560271\pi\)
\(60\) 0 0
\(61\) −10.3518 −1.32541 −0.662703 0.748882i \(-0.730591\pi\)
−0.662703 + 0.748882i \(0.730591\pi\)
\(62\) −16.8669 −2.14210
\(63\) 2.92719 0.368791
\(64\) 20.9787 2.62234
\(65\) 0 0
\(66\) 2.74986 0.338484
\(67\) −11.4466 −1.39843 −0.699213 0.714913i \(-0.746466\pi\)
−0.699213 + 0.714913i \(0.746466\pi\)
\(68\) −31.3442 −3.80104
\(69\) 0.269842 0.0324852
\(70\) 0 0
\(71\) 2.70157 0.320617 0.160309 0.987067i \(-0.448751\pi\)
0.160309 + 0.987067i \(0.448751\pi\)
\(72\) 25.4903 3.00406
\(73\) 14.1893 1.66073 0.830367 0.557217i \(-0.188131\pi\)
0.830367 + 0.557217i \(0.188131\pi\)
\(74\) 13.0222 1.51380
\(75\) 0 0
\(76\) −17.7029 −2.03066
\(77\) 3.78810 0.431694
\(78\) 0.901051 0.102024
\(79\) 3.31407 0.372862 0.186431 0.982468i \(-0.440308\pi\)
0.186431 + 0.982468i \(0.440308\pi\)
\(80\) 0 0
\(81\) 8.34997 0.927774
\(82\) 4.79102 0.529080
\(83\) −7.02219 −0.770785 −0.385393 0.922753i \(-0.625934\pi\)
−0.385393 + 0.922753i \(0.625934\pi\)
\(84\) −1.41317 −0.154189
\(85\) 0 0
\(86\) 8.13020 0.876702
\(87\) −1.89453 −0.203115
\(88\) 32.9872 3.51645
\(89\) −1.59107 −0.168653 −0.0843265 0.996438i \(-0.526874\pi\)
−0.0843265 + 0.996438i \(0.526874\pi\)
\(90\) 0 0
\(91\) 1.24125 0.130119
\(92\) 5.23702 0.545997
\(93\) 1.69187 0.175438
\(94\) 10.5003 1.08302
\(95\) 0 0
\(96\) −4.70271 −0.479968
\(97\) 11.6270 1.18054 0.590270 0.807206i \(-0.299021\pi\)
0.590270 + 0.807206i \(0.299021\pi\)
\(98\) −2.69017 −0.271748
\(99\) 11.0885 1.11443
\(100\) 0 0
\(101\) −0.366626 −0.0364806 −0.0182403 0.999834i \(-0.505806\pi\)
−0.0182403 + 0.999834i \(0.505806\pi\)
\(102\) 4.34473 0.430192
\(103\) 0.474030 0.0467076 0.0233538 0.999727i \(-0.492566\pi\)
0.0233538 + 0.999727i \(0.492566\pi\)
\(104\) 10.8090 1.05991
\(105\) 0 0
\(106\) −6.65556 −0.646445
\(107\) 5.74697 0.555580 0.277790 0.960642i \(-0.410398\pi\)
0.277790 + 0.960642i \(0.410398\pi\)
\(108\) −8.37610 −0.805991
\(109\) 15.4877 1.48346 0.741728 0.670700i \(-0.234006\pi\)
0.741728 + 0.670700i \(0.234006\pi\)
\(110\) 0 0
\(111\) −1.30621 −0.123980
\(112\) −12.9523 −1.22388
\(113\) 4.48250 0.421678 0.210839 0.977521i \(-0.432380\pi\)
0.210839 + 0.977521i \(0.432380\pi\)
\(114\) 2.45386 0.229825
\(115\) 0 0
\(116\) −36.7684 −3.41386
\(117\) 3.63337 0.335906
\(118\) 7.77845 0.716064
\(119\) 5.98512 0.548655
\(120\) 0 0
\(121\) 3.34968 0.304516
\(122\) 27.8480 2.52124
\(123\) −0.480572 −0.0433317
\(124\) 32.8353 2.94869
\(125\) 0 0
\(126\) −7.87463 −0.701527
\(127\) 2.13061 0.189061 0.0945307 0.995522i \(-0.469865\pi\)
0.0945307 + 0.995522i \(0.469865\pi\)
\(128\) −21.5811 −1.90751
\(129\) −0.815514 −0.0718020
\(130\) 0 0
\(131\) −18.1242 −1.58352 −0.791760 0.610832i \(-0.790835\pi\)
−0.791760 + 0.610832i \(0.790835\pi\)
\(132\) −5.35321 −0.465937
\(133\) 3.38034 0.293113
\(134\) 30.7933 2.66014
\(135\) 0 0
\(136\) 52.1192 4.46918
\(137\) 15.3062 1.30770 0.653849 0.756625i \(-0.273153\pi\)
0.653849 + 0.756625i \(0.273153\pi\)
\(138\) −0.725921 −0.0617945
\(139\) 13.5273 1.14737 0.573687 0.819074i \(-0.305512\pi\)
0.573687 + 0.819074i \(0.305512\pi\)
\(140\) 0 0
\(141\) −1.05325 −0.0886998
\(142\) −7.26768 −0.609890
\(143\) 4.70198 0.393200
\(144\) −37.9138 −3.15948
\(145\) 0 0
\(146\) −38.1717 −3.15911
\(147\) 0.269842 0.0222562
\(148\) −25.3506 −2.08381
\(149\) 5.75773 0.471691 0.235846 0.971791i \(-0.424214\pi\)
0.235846 + 0.971791i \(0.424214\pi\)
\(150\) 0 0
\(151\) −9.57813 −0.779457 −0.389728 0.920930i \(-0.627431\pi\)
−0.389728 + 0.920930i \(0.627431\pi\)
\(152\) 29.4364 2.38761
\(153\) 17.5196 1.41637
\(154\) −10.1906 −0.821184
\(155\) 0 0
\(156\) −1.75410 −0.140440
\(157\) 5.03706 0.402001 0.201001 0.979591i \(-0.435581\pi\)
0.201001 + 0.979591i \(0.435581\pi\)
\(158\) −8.91540 −0.709271
\(159\) 0.667598 0.0529439
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) −22.4628 −1.76485
\(163\) 7.35713 0.576255 0.288127 0.957592i \(-0.406967\pi\)
0.288127 + 0.957592i \(0.406967\pi\)
\(164\) −9.32679 −0.728300
\(165\) 0 0
\(166\) 18.8909 1.46622
\(167\) −20.9904 −1.62428 −0.812142 0.583460i \(-0.801698\pi\)
−0.812142 + 0.583460i \(0.801698\pi\)
\(168\) 2.34982 0.181292
\(169\) −11.4593 −0.881484
\(170\) 0 0
\(171\) 9.89488 0.756681
\(172\) −15.8272 −1.20682
\(173\) 12.3369 0.937955 0.468978 0.883210i \(-0.344622\pi\)
0.468978 + 0.883210i \(0.344622\pi\)
\(174\) 5.09660 0.386372
\(175\) 0 0
\(176\) −49.0646 −3.69838
\(177\) −0.780231 −0.0586457
\(178\) 4.28025 0.320818
\(179\) −12.9082 −0.964807 −0.482404 0.875949i \(-0.660236\pi\)
−0.482404 + 0.875949i \(0.660236\pi\)
\(180\) 0 0
\(181\) −5.86925 −0.436258 −0.218129 0.975920i \(-0.569995\pi\)
−0.218129 + 0.975920i \(0.569995\pi\)
\(182\) −3.33918 −0.247516
\(183\) −2.79334 −0.206489
\(184\) −8.70812 −0.641971
\(185\) 0 0
\(186\) −4.55141 −0.333726
\(187\) 22.6722 1.65796
\(188\) −20.4412 −1.49083
\(189\) 1.59940 0.116340
\(190\) 0 0
\(191\) 11.9343 0.863539 0.431769 0.901984i \(-0.357889\pi\)
0.431769 + 0.901984i \(0.357889\pi\)
\(192\) 5.66094 0.408543
\(193\) −0.752900 −0.0541949 −0.0270975 0.999633i \(-0.508626\pi\)
−0.0270975 + 0.999633i \(0.508626\pi\)
\(194\) −31.2785 −2.24567
\(195\) 0 0
\(196\) 5.23702 0.374073
\(197\) −25.4074 −1.81020 −0.905100 0.425200i \(-0.860204\pi\)
−0.905100 + 0.425200i \(0.860204\pi\)
\(198\) −29.8298 −2.11991
\(199\) 15.1988 1.07741 0.538707 0.842493i \(-0.318913\pi\)
0.538707 + 0.842493i \(0.318913\pi\)
\(200\) 0 0
\(201\) −3.08878 −0.217866
\(202\) 0.986286 0.0693948
\(203\) 7.02088 0.492769
\(204\) −8.45798 −0.592177
\(205\) 0 0
\(206\) −1.27522 −0.0888489
\(207\) −2.92719 −0.203453
\(208\) −16.0771 −1.11474
\(209\) 12.8051 0.885744
\(210\) 0 0
\(211\) −24.2797 −1.67148 −0.835742 0.549123i \(-0.814962\pi\)
−0.835742 + 0.549123i \(0.814962\pi\)
\(212\) 12.9565 0.889858
\(213\) 0.728997 0.0499500
\(214\) −15.4603 −1.05685
\(215\) 0 0
\(216\) 13.9278 0.947667
\(217\) −6.26984 −0.425625
\(218\) −41.6647 −2.82189
\(219\) 3.82887 0.258731
\(220\) 0 0
\(221\) 7.42905 0.499732
\(222\) 3.51393 0.235840
\(223\) −17.7344 −1.18758 −0.593791 0.804619i \(-0.702369\pi\)
−0.593791 + 0.804619i \(0.702369\pi\)
\(224\) 17.4276 1.16443
\(225\) 0 0
\(226\) −12.0587 −0.802133
\(227\) 15.7087 1.04263 0.521313 0.853366i \(-0.325442\pi\)
0.521313 + 0.853366i \(0.325442\pi\)
\(228\) −4.77699 −0.316364
\(229\) −4.51633 −0.298448 −0.149224 0.988803i \(-0.547678\pi\)
−0.149224 + 0.988803i \(0.547678\pi\)
\(230\) 0 0
\(231\) 1.02219 0.0672550
\(232\) 61.1386 4.01395
\(233\) 16.2641 1.06549 0.532747 0.846275i \(-0.321160\pi\)
0.532747 + 0.846275i \(0.321160\pi\)
\(234\) −9.77439 −0.638972
\(235\) 0 0
\(236\) −15.1425 −0.985692
\(237\) 0.894275 0.0580894
\(238\) −16.1010 −1.04367
\(239\) 2.14756 0.138914 0.0694571 0.997585i \(-0.477873\pi\)
0.0694571 + 0.997585i \(0.477873\pi\)
\(240\) 0 0
\(241\) 12.4676 0.803111 0.401555 0.915835i \(-0.368470\pi\)
0.401555 + 0.915835i \(0.368470\pi\)
\(242\) −9.01121 −0.579262
\(243\) 7.05139 0.452347
\(244\) −54.2123 −3.47059
\(245\) 0 0
\(246\) 1.29282 0.0824271
\(247\) 4.19585 0.266976
\(248\) −54.5985 −3.46701
\(249\) −1.89488 −0.120083
\(250\) 0 0
\(251\) 4.91478 0.310218 0.155109 0.987897i \(-0.450427\pi\)
0.155109 + 0.987897i \(0.450427\pi\)
\(252\) 15.3297 0.965681
\(253\) −3.78810 −0.238156
\(254\) −5.73172 −0.359640
\(255\) 0 0
\(256\) 16.0993 1.00620
\(257\) −28.4782 −1.77642 −0.888212 0.459433i \(-0.848052\pi\)
−0.888212 + 0.459433i \(0.848052\pi\)
\(258\) 2.19387 0.136584
\(259\) 4.84066 0.300784
\(260\) 0 0
\(261\) 20.5514 1.27210
\(262\) 48.7572 3.01223
\(263\) −1.89322 −0.116741 −0.0583703 0.998295i \(-0.518590\pi\)
−0.0583703 + 0.998295i \(0.518590\pi\)
\(264\) 8.90134 0.547839
\(265\) 0 0
\(266\) −9.09369 −0.557570
\(267\) −0.429338 −0.0262750
\(268\) −59.9461 −3.66179
\(269\) −2.51156 −0.153133 −0.0765663 0.997064i \(-0.524396\pi\)
−0.0765663 + 0.997064i \(0.524396\pi\)
\(270\) 0 0
\(271\) 25.1098 1.52531 0.762656 0.646804i \(-0.223895\pi\)
0.762656 + 0.646804i \(0.223895\pi\)
\(272\) −77.5211 −4.70041
\(273\) 0.334942 0.0202716
\(274\) −41.1763 −2.48755
\(275\) 0 0
\(276\) 1.41317 0.0850627
\(277\) −9.48643 −0.569984 −0.284992 0.958530i \(-0.591991\pi\)
−0.284992 + 0.958530i \(0.591991\pi\)
\(278\) −36.3909 −2.18258
\(279\) −18.3530 −1.09876
\(280\) 0 0
\(281\) 8.71197 0.519713 0.259856 0.965647i \(-0.416325\pi\)
0.259856 + 0.965647i \(0.416325\pi\)
\(282\) 2.83343 0.168728
\(283\) −30.5543 −1.81627 −0.908133 0.418683i \(-0.862492\pi\)
−0.908133 + 0.418683i \(0.862492\pi\)
\(284\) 14.1482 0.839538
\(285\) 0 0
\(286\) −12.6491 −0.747959
\(287\) 1.78094 0.105125
\(288\) 51.0139 3.00602
\(289\) 18.8217 1.10716
\(290\) 0 0
\(291\) 3.13745 0.183920
\(292\) 74.3096 4.34864
\(293\) −12.7063 −0.742312 −0.371156 0.928570i \(-0.621039\pi\)
−0.371156 + 0.928570i \(0.621039\pi\)
\(294\) −0.725921 −0.0423366
\(295\) 0 0
\(296\) 42.1530 2.45009
\(297\) 6.05870 0.351561
\(298\) −15.4893 −0.897269
\(299\) −1.24125 −0.0717835
\(300\) 0 0
\(301\) 3.02219 0.174196
\(302\) 25.7668 1.48271
\(303\) −0.0989310 −0.00568344
\(304\) −43.7832 −2.51114
\(305\) 0 0
\(306\) −47.1306 −2.69428
\(307\) −22.1153 −1.26219 −0.631094 0.775706i \(-0.717394\pi\)
−0.631094 + 0.775706i \(0.717394\pi\)
\(308\) 19.8383 1.13039
\(309\) 0.127913 0.00727673
\(310\) 0 0
\(311\) 21.3945 1.21317 0.606586 0.795018i \(-0.292539\pi\)
0.606586 + 0.795018i \(0.292539\pi\)
\(312\) 2.91672 0.165127
\(313\) 29.9051 1.69034 0.845169 0.534498i \(-0.179499\pi\)
0.845169 + 0.534498i \(0.179499\pi\)
\(314\) −13.5506 −0.764702
\(315\) 0 0
\(316\) 17.3558 0.976341
\(317\) −7.06103 −0.396587 −0.198294 0.980143i \(-0.563540\pi\)
−0.198294 + 0.980143i \(0.563540\pi\)
\(318\) −1.79595 −0.100712
\(319\) 26.5958 1.48908
\(320\) 0 0
\(321\) 1.55077 0.0865557
\(322\) 2.69017 0.149917
\(323\) 20.2318 1.12573
\(324\) 43.7289 2.42938
\(325\) 0 0
\(326\) −19.7919 −1.09617
\(327\) 4.17925 0.231113
\(328\) 15.5086 0.856320
\(329\) 3.90322 0.215191
\(330\) 0 0
\(331\) 16.2063 0.890777 0.445388 0.895338i \(-0.353066\pi\)
0.445388 + 0.895338i \(0.353066\pi\)
\(332\) −36.7753 −2.01831
\(333\) 14.1695 0.776484
\(334\) 56.4677 3.08977
\(335\) 0 0
\(336\) −3.49508 −0.190672
\(337\) −5.21804 −0.284245 −0.142122 0.989849i \(-0.545393\pi\)
−0.142122 + 0.989849i \(0.545393\pi\)
\(338\) 30.8274 1.67679
\(339\) 1.20957 0.0656947
\(340\) 0 0
\(341\) −23.7508 −1.28618
\(342\) −26.6189 −1.43939
\(343\) −1.00000 −0.0539949
\(344\) 26.3176 1.41895
\(345\) 0 0
\(346\) −33.1883 −1.78421
\(347\) −4.19094 −0.224982 −0.112491 0.993653i \(-0.535883\pi\)
−0.112491 + 0.993653i \(0.535883\pi\)
\(348\) −9.92167 −0.531857
\(349\) −18.6611 −0.998903 −0.499452 0.866342i \(-0.666465\pi\)
−0.499452 + 0.866342i \(0.666465\pi\)
\(350\) 0 0
\(351\) 1.98526 0.105966
\(352\) 66.0176 3.51875
\(353\) 11.5781 0.616241 0.308121 0.951347i \(-0.400300\pi\)
0.308121 + 0.951347i \(0.400300\pi\)
\(354\) 2.09895 0.111558
\(355\) 0 0
\(356\) −8.33246 −0.441619
\(357\) 1.61504 0.0854769
\(358\) 34.7254 1.83529
\(359\) 29.4910 1.55647 0.778237 0.627970i \(-0.216114\pi\)
0.778237 + 0.627970i \(0.216114\pi\)
\(360\) 0 0
\(361\) −7.57330 −0.398595
\(362\) 15.7893 0.829866
\(363\) 0.903884 0.0474416
\(364\) 6.50046 0.340716
\(365\) 0 0
\(366\) 7.51455 0.392792
\(367\) 24.7858 1.29381 0.646903 0.762572i \(-0.276064\pi\)
0.646903 + 0.762572i \(0.276064\pi\)
\(368\) 12.9523 0.675185
\(369\) 5.21313 0.271385
\(370\) 0 0
\(371\) −2.47403 −0.128445
\(372\) 8.86033 0.459387
\(373\) −17.1524 −0.888117 −0.444058 0.895998i \(-0.646462\pi\)
−0.444058 + 0.895998i \(0.646462\pi\)
\(374\) −60.9922 −3.15383
\(375\) 0 0
\(376\) 33.9897 1.75288
\(377\) 8.71467 0.448829
\(378\) −4.30267 −0.221305
\(379\) 32.8211 1.68591 0.842953 0.537986i \(-0.180815\pi\)
0.842953 + 0.537986i \(0.180815\pi\)
\(380\) 0 0
\(381\) 0.574930 0.0294545
\(382\) −32.1054 −1.64266
\(383\) 8.42609 0.430553 0.215277 0.976553i \(-0.430935\pi\)
0.215277 + 0.976553i \(0.430935\pi\)
\(384\) −5.82348 −0.297178
\(385\) 0 0
\(386\) 2.02543 0.103092
\(387\) 8.84650 0.449693
\(388\) 60.8906 3.09125
\(389\) −25.3004 −1.28278 −0.641390 0.767215i \(-0.721642\pi\)
−0.641390 + 0.767215i \(0.721642\pi\)
\(390\) 0 0
\(391\) −5.98512 −0.302681
\(392\) −8.70812 −0.439827
\(393\) −4.89068 −0.246702
\(394\) 68.3501 3.44343
\(395\) 0 0
\(396\) 58.0704 2.91815
\(397\) −20.3650 −1.02209 −0.511045 0.859554i \(-0.670741\pi\)
−0.511045 + 0.859554i \(0.670741\pi\)
\(398\) −40.8874 −2.04950
\(399\) 0.912158 0.0456650
\(400\) 0 0
\(401\) 4.10277 0.204883 0.102441 0.994739i \(-0.467335\pi\)
0.102441 + 0.994739i \(0.467335\pi\)
\(402\) 8.30934 0.414432
\(403\) −7.78245 −0.387672
\(404\) −1.92002 −0.0955248
\(405\) 0 0
\(406\) −18.8873 −0.937363
\(407\) 18.3369 0.908925
\(408\) 14.0640 0.696269
\(409\) −26.8449 −1.32739 −0.663697 0.748002i \(-0.731013\pi\)
−0.663697 + 0.748002i \(0.731013\pi\)
\(410\) 0 0
\(411\) 4.13026 0.203731
\(412\) 2.48250 0.122304
\(413\) 2.89143 0.142278
\(414\) 7.87463 0.387017
\(415\) 0 0
\(416\) 21.6321 1.06060
\(417\) 3.65025 0.178753
\(418\) −34.4478 −1.68490
\(419\) 0.149494 0.00730327 0.00365163 0.999993i \(-0.498838\pi\)
0.00365163 + 0.999993i \(0.498838\pi\)
\(420\) 0 0
\(421\) −10.5269 −0.513049 −0.256524 0.966538i \(-0.582577\pi\)
−0.256524 + 0.966538i \(0.582577\pi\)
\(422\) 65.3165 3.17956
\(423\) 11.4254 0.555524
\(424\) −21.5442 −1.04628
\(425\) 0 0
\(426\) −1.96113 −0.0950168
\(427\) 10.3518 0.500956
\(428\) 30.0969 1.45479
\(429\) 1.26879 0.0612579
\(430\) 0 0
\(431\) −2.28665 −0.110144 −0.0550720 0.998482i \(-0.517539\pi\)
−0.0550720 + 0.998482i \(0.517539\pi\)
\(432\) −20.7160 −0.996697
\(433\) 20.4569 0.983094 0.491547 0.870851i \(-0.336432\pi\)
0.491547 + 0.870851i \(0.336432\pi\)
\(434\) 16.8669 0.809639
\(435\) 0 0
\(436\) 81.1096 3.88444
\(437\) −3.38034 −0.161704
\(438\) −10.3003 −0.492168
\(439\) 8.93821 0.426597 0.213299 0.976987i \(-0.431579\pi\)
0.213299 + 0.976987i \(0.431579\pi\)
\(440\) 0 0
\(441\) −2.92719 −0.139390
\(442\) −19.9854 −0.950609
\(443\) 6.71589 0.319082 0.159541 0.987191i \(-0.448999\pi\)
0.159541 + 0.987191i \(0.448999\pi\)
\(444\) −6.84066 −0.324643
\(445\) 0 0
\(446\) 47.7085 2.25906
\(447\) 1.55368 0.0734864
\(448\) −20.9787 −0.991151
\(449\) 39.7178 1.87440 0.937200 0.348792i \(-0.113408\pi\)
0.937200 + 0.348792i \(0.113408\pi\)
\(450\) 0 0
\(451\) 6.74636 0.317674
\(452\) 23.4749 1.10417
\(453\) −2.58458 −0.121434
\(454\) −42.2592 −1.98332
\(455\) 0 0
\(456\) 7.94318 0.371974
\(457\) 35.7388 1.67179 0.835895 0.548889i \(-0.184949\pi\)
0.835895 + 0.548889i \(0.184949\pi\)
\(458\) 12.1497 0.567719
\(459\) 9.57263 0.446812
\(460\) 0 0
\(461\) −18.3516 −0.854720 −0.427360 0.904082i \(-0.640556\pi\)
−0.427360 + 0.904082i \(0.640556\pi\)
\(462\) −2.74986 −0.127935
\(463\) −11.1821 −0.519678 −0.259839 0.965652i \(-0.583670\pi\)
−0.259839 + 0.965652i \(0.583670\pi\)
\(464\) −90.9365 −4.22162
\(465\) 0 0
\(466\) −43.7531 −2.02682
\(467\) −31.7231 −1.46797 −0.733984 0.679167i \(-0.762341\pi\)
−0.733984 + 0.679167i \(0.762341\pi\)
\(468\) 19.0280 0.879571
\(469\) 11.4466 0.528556
\(470\) 0 0
\(471\) 1.35921 0.0626292
\(472\) 25.1790 1.15896
\(473\) 11.4483 0.526395
\(474\) −2.40575 −0.110500
\(475\) 0 0
\(476\) 31.3442 1.43666
\(477\) −7.24194 −0.331586
\(478\) −5.77731 −0.264248
\(479\) −9.81725 −0.448562 −0.224281 0.974525i \(-0.572003\pi\)
−0.224281 + 0.974525i \(0.572003\pi\)
\(480\) 0 0
\(481\) 6.00847 0.273963
\(482\) −33.5400 −1.52771
\(483\) −0.269842 −0.0122782
\(484\) 17.5423 0.797378
\(485\) 0 0
\(486\) −18.9694 −0.860471
\(487\) 36.2778 1.64390 0.821952 0.569557i \(-0.192885\pi\)
0.821952 + 0.569557i \(0.192885\pi\)
\(488\) 90.1443 4.08064
\(489\) 1.98526 0.0897767
\(490\) 0 0
\(491\) −17.6053 −0.794514 −0.397257 0.917707i \(-0.630038\pi\)
−0.397257 + 0.917707i \(0.630038\pi\)
\(492\) −2.51676 −0.113464
\(493\) 42.0208 1.89252
\(494\) −11.2876 −0.507851
\(495\) 0 0
\(496\) 81.2089 3.64639
\(497\) −2.70157 −0.121182
\(498\) 5.09755 0.228427
\(499\) 12.1142 0.542308 0.271154 0.962536i \(-0.412595\pi\)
0.271154 + 0.962536i \(0.412595\pi\)
\(500\) 0 0
\(501\) −5.66408 −0.253053
\(502\) −13.2216 −0.590109
\(503\) −10.2723 −0.458020 −0.229010 0.973424i \(-0.573549\pi\)
−0.229010 + 0.973424i \(0.573549\pi\)
\(504\) −25.4903 −1.13543
\(505\) 0 0
\(506\) 10.1906 0.453029
\(507\) −3.09220 −0.137329
\(508\) 11.1581 0.495059
\(509\) −6.45082 −0.285928 −0.142964 0.989728i \(-0.545663\pi\)
−0.142964 + 0.989728i \(0.545663\pi\)
\(510\) 0 0
\(511\) −14.1893 −0.627698
\(512\) −0.147625 −0.00652419
\(513\) 5.40653 0.238704
\(514\) 76.6113 3.37918
\(515\) 0 0
\(516\) −4.27086 −0.188014
\(517\) 14.7858 0.650277
\(518\) −13.0222 −0.572162
\(519\) 3.32901 0.146127
\(520\) 0 0
\(521\) 34.4858 1.51085 0.755425 0.655235i \(-0.227430\pi\)
0.755425 + 0.655235i \(0.227430\pi\)
\(522\) −55.2868 −2.41984
\(523\) 25.7852 1.12751 0.563753 0.825943i \(-0.309357\pi\)
0.563753 + 0.825943i \(0.309357\pi\)
\(524\) −94.9168 −4.14646
\(525\) 0 0
\(526\) 5.09307 0.222068
\(527\) −37.5258 −1.63465
\(528\) −13.2397 −0.576183
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 8.46376 0.367296
\(532\) 17.7029 0.767518
\(533\) 2.21059 0.0957513
\(534\) 1.15499 0.0499814
\(535\) 0 0
\(536\) 99.6785 4.30546
\(537\) −3.48319 −0.150311
\(538\) 6.75653 0.291295
\(539\) −3.78810 −0.163165
\(540\) 0 0
\(541\) −21.1475 −0.909203 −0.454601 0.890695i \(-0.650218\pi\)
−0.454601 + 0.890695i \(0.650218\pi\)
\(542\) −67.5496 −2.90151
\(543\) −1.58377 −0.0679661
\(544\) 104.307 4.47211
\(545\) 0 0
\(546\) −0.901051 −0.0385614
\(547\) 3.97188 0.169825 0.0849126 0.996388i \(-0.472939\pi\)
0.0849126 + 0.996388i \(0.472939\pi\)
\(548\) 80.1589 3.42422
\(549\) 30.3015 1.29324
\(550\) 0 0
\(551\) 23.7329 1.01106
\(552\) −2.34982 −0.100015
\(553\) −3.31407 −0.140928
\(554\) 25.5201 1.08425
\(555\) 0 0
\(556\) 70.8429 3.00441
\(557\) 13.5585 0.574491 0.287246 0.957857i \(-0.407260\pi\)
0.287246 + 0.957857i \(0.407260\pi\)
\(558\) 49.3727 2.09011
\(559\) 3.75130 0.158663
\(560\) 0 0
\(561\) 6.11792 0.258299
\(562\) −23.4367 −0.988617
\(563\) 32.4740 1.36862 0.684309 0.729193i \(-0.260104\pi\)
0.684309 + 0.729193i \(0.260104\pi\)
\(564\) −5.51590 −0.232261
\(565\) 0 0
\(566\) 82.1963 3.45497
\(567\) −8.34997 −0.350666
\(568\) −23.5256 −0.987111
\(569\) −26.7707 −1.12228 −0.561142 0.827719i \(-0.689638\pi\)
−0.561142 + 0.827719i \(0.689638\pi\)
\(570\) 0 0
\(571\) 5.30884 0.222168 0.111084 0.993811i \(-0.464568\pi\)
0.111084 + 0.993811i \(0.464568\pi\)
\(572\) 24.6244 1.02960
\(573\) 3.22039 0.134534
\(574\) −4.79102 −0.199973
\(575\) 0 0
\(576\) −61.4086 −2.55869
\(577\) −43.9737 −1.83065 −0.915325 0.402717i \(-0.868066\pi\)
−0.915325 + 0.402717i \(0.868066\pi\)
\(578\) −50.6336 −2.10608
\(579\) −0.203164 −0.00844321
\(580\) 0 0
\(581\) 7.02219 0.291329
\(582\) −8.44026 −0.349860
\(583\) −9.37187 −0.388143
\(584\) −123.562 −5.11304
\(585\) 0 0
\(586\) 34.1822 1.41205
\(587\) 34.5314 1.42526 0.712631 0.701539i \(-0.247503\pi\)
0.712631 + 0.701539i \(0.247503\pi\)
\(588\) 1.41317 0.0582780
\(589\) −21.1942 −0.873292
\(590\) 0 0
\(591\) −6.85597 −0.282017
\(592\) −62.6976 −2.57686
\(593\) −2.06074 −0.0846245 −0.0423123 0.999104i \(-0.513472\pi\)
−0.0423123 + 0.999104i \(0.513472\pi\)
\(594\) −16.2989 −0.668753
\(595\) 0 0
\(596\) 30.1533 1.23513
\(597\) 4.10128 0.167854
\(598\) 3.33918 0.136549
\(599\) −28.2627 −1.15478 −0.577392 0.816467i \(-0.695930\pi\)
−0.577392 + 0.816467i \(0.695930\pi\)
\(600\) 0 0
\(601\) −25.0036 −1.01992 −0.509959 0.860199i \(-0.670340\pi\)
−0.509959 + 0.860199i \(0.670340\pi\)
\(602\) −8.13020 −0.331362
\(603\) 33.5064 1.36448
\(604\) −50.1608 −2.04101
\(605\) 0 0
\(606\) 0.266141 0.0108113
\(607\) 29.0255 1.17811 0.589054 0.808093i \(-0.299500\pi\)
0.589054 + 0.808093i \(0.299500\pi\)
\(608\) 58.9114 2.38917
\(609\) 1.89453 0.0767701
\(610\) 0 0
\(611\) 4.84487 0.196003
\(612\) 91.7502 3.70878
\(613\) 25.2180 1.01855 0.509274 0.860605i \(-0.329914\pi\)
0.509274 + 0.860605i \(0.329914\pi\)
\(614\) 59.4940 2.40098
\(615\) 0 0
\(616\) −32.9872 −1.32909
\(617\) −41.7462 −1.68064 −0.840319 0.542093i \(-0.817632\pi\)
−0.840319 + 0.542093i \(0.817632\pi\)
\(618\) −0.344109 −0.0138421
\(619\) −0.503782 −0.0202487 −0.0101243 0.999949i \(-0.503223\pi\)
−0.0101243 + 0.999949i \(0.503223\pi\)
\(620\) 0 0
\(621\) −1.59940 −0.0641819
\(622\) −57.5549 −2.30774
\(623\) 1.59107 0.0637449
\(624\) −4.33827 −0.173670
\(625\) 0 0
\(626\) −80.4499 −3.21543
\(627\) 3.45534 0.137993
\(628\) 26.3792 1.05264
\(629\) 28.9719 1.15519
\(630\) 0 0
\(631\) −17.6868 −0.704102 −0.352051 0.935981i \(-0.614516\pi\)
−0.352051 + 0.935981i \(0.614516\pi\)
\(632\) −28.8593 −1.14796
\(633\) −6.55168 −0.260406
\(634\) 18.9954 0.754403
\(635\) 0 0
\(636\) 3.49622 0.138634
\(637\) −1.24125 −0.0491802
\(638\) −71.5471 −2.83258
\(639\) −7.90799 −0.312835
\(640\) 0 0
\(641\) −37.4714 −1.48003 −0.740015 0.672590i \(-0.765182\pi\)
−0.740015 + 0.672590i \(0.765182\pi\)
\(642\) −4.17184 −0.164650
\(643\) −0.178907 −0.00705539 −0.00352770 0.999994i \(-0.501123\pi\)
−0.00352770 + 0.999994i \(0.501123\pi\)
\(644\) −5.23702 −0.206367
\(645\) 0 0
\(646\) −54.4269 −2.14140
\(647\) −2.94235 −0.115676 −0.0578379 0.998326i \(-0.518421\pi\)
−0.0578379 + 0.998326i \(0.518421\pi\)
\(648\) −72.7125 −2.85642
\(649\) 10.9530 0.429944
\(650\) 0 0
\(651\) −1.69187 −0.0663095
\(652\) 38.5294 1.50893
\(653\) −44.1719 −1.72858 −0.864290 0.502994i \(-0.832232\pi\)
−0.864290 + 0.502994i \(0.832232\pi\)
\(654\) −11.2429 −0.439631
\(655\) 0 0
\(656\) −23.0672 −0.900623
\(657\) −41.5347 −1.62042
\(658\) −10.5003 −0.409345
\(659\) 13.9282 0.542564 0.271282 0.962500i \(-0.412552\pi\)
0.271282 + 0.962500i \(0.412552\pi\)
\(660\) 0 0
\(661\) −2.15327 −0.0837525 −0.0418763 0.999123i \(-0.513334\pi\)
−0.0418763 + 0.999123i \(0.513334\pi\)
\(662\) −43.5976 −1.69447
\(663\) 2.00467 0.0778549
\(664\) 61.1501 2.37308
\(665\) 0 0
\(666\) −38.1184 −1.47706
\(667\) −7.02088 −0.271849
\(668\) −109.927 −4.25320
\(669\) −4.78548 −0.185017
\(670\) 0 0
\(671\) 39.2134 1.51382
\(672\) 4.70271 0.181411
\(673\) 2.96276 0.114206 0.0571030 0.998368i \(-0.481814\pi\)
0.0571030 + 0.998368i \(0.481814\pi\)
\(674\) 14.0374 0.540701
\(675\) 0 0
\(676\) −60.0125 −2.30817
\(677\) −9.59927 −0.368930 −0.184465 0.982839i \(-0.559055\pi\)
−0.184465 + 0.982839i \(0.559055\pi\)
\(678\) −3.25394 −0.124967
\(679\) −11.6270 −0.446202
\(680\) 0 0
\(681\) 4.23888 0.162434
\(682\) 63.8936 2.44661
\(683\) 24.1908 0.925636 0.462818 0.886453i \(-0.346838\pi\)
0.462818 + 0.886453i \(0.346838\pi\)
\(684\) 51.8196 1.98137
\(685\) 0 0
\(686\) 2.69017 0.102711
\(687\) −1.21870 −0.0464962
\(688\) −39.1443 −1.49236
\(689\) −3.07089 −0.116992
\(690\) 0 0
\(691\) 30.4784 1.15945 0.579726 0.814811i \(-0.303159\pi\)
0.579726 + 0.814811i \(0.303159\pi\)
\(692\) 64.6084 2.45604
\(693\) −11.0885 −0.421216
\(694\) 11.2743 0.427968
\(695\) 0 0
\(696\) 16.4978 0.625347
\(697\) 10.6591 0.403743
\(698\) 50.2014 1.90015
\(699\) 4.38873 0.165997
\(700\) 0 0
\(701\) 17.4101 0.657570 0.328785 0.944405i \(-0.393361\pi\)
0.328785 + 0.944405i \(0.393361\pi\)
\(702\) −5.34070 −0.201572
\(703\) 16.3631 0.617145
\(704\) −79.4694 −2.99512
\(705\) 0 0
\(706\) −31.1471 −1.17224
\(707\) 0.366626 0.0137884
\(708\) −4.08608 −0.153564
\(709\) 13.6465 0.512504 0.256252 0.966610i \(-0.417512\pi\)
0.256252 + 0.966610i \(0.417512\pi\)
\(710\) 0 0
\(711\) −9.70089 −0.363812
\(712\) 13.8552 0.519247
\(713\) 6.26984 0.234807
\(714\) −4.34473 −0.162597
\(715\) 0 0
\(716\) −67.6007 −2.52636
\(717\) 0.579503 0.0216419
\(718\) −79.3358 −2.96078
\(719\) −29.8264 −1.11234 −0.556169 0.831069i \(-0.687729\pi\)
−0.556169 + 0.831069i \(0.687729\pi\)
\(720\) 0 0
\(721\) −0.474030 −0.0176538
\(722\) 20.3735 0.758222
\(723\) 3.36429 0.125119
\(724\) −30.7373 −1.14234
\(725\) 0 0
\(726\) −2.43160 −0.0902452
\(727\) −6.92789 −0.256941 −0.128471 0.991713i \(-0.541007\pi\)
−0.128471 + 0.991713i \(0.541007\pi\)
\(728\) −10.8090 −0.400607
\(729\) −23.1471 −0.857302
\(730\) 0 0
\(731\) 18.0882 0.669015
\(732\) −14.6288 −0.540694
\(733\) 10.8092 0.399246 0.199623 0.979873i \(-0.436028\pi\)
0.199623 + 0.979873i \(0.436028\pi\)
\(734\) −66.6779 −2.46113
\(735\) 0 0
\(736\) −17.4276 −0.642391
\(737\) 43.3609 1.59722
\(738\) −14.0242 −0.516238
\(739\) 34.5455 1.27078 0.635388 0.772193i \(-0.280840\pi\)
0.635388 + 0.772193i \(0.280840\pi\)
\(740\) 0 0
\(741\) 1.13222 0.0415931
\(742\) 6.65556 0.244333
\(743\) −19.7750 −0.725475 −0.362737 0.931891i \(-0.618158\pi\)
−0.362737 + 0.931891i \(0.618158\pi\)
\(744\) −14.7330 −0.540137
\(745\) 0 0
\(746\) 46.1428 1.68941
\(747\) 20.5552 0.752077
\(748\) 118.735 4.34137
\(749\) −5.74697 −0.209990
\(750\) 0 0
\(751\) −31.0704 −1.13378 −0.566888 0.823795i \(-0.691853\pi\)
−0.566888 + 0.823795i \(0.691853\pi\)
\(752\) −50.5556 −1.84357
\(753\) 1.32622 0.0483300
\(754\) −23.4440 −0.853779
\(755\) 0 0
\(756\) 8.37610 0.304636
\(757\) −8.32104 −0.302433 −0.151217 0.988501i \(-0.548319\pi\)
−0.151217 + 0.988501i \(0.548319\pi\)
\(758\) −88.2944 −3.20700
\(759\) −1.02219 −0.0371031
\(760\) 0 0
\(761\) −3.82034 −0.138487 −0.0692436 0.997600i \(-0.522059\pi\)
−0.0692436 + 0.997600i \(0.522059\pi\)
\(762\) −1.54666 −0.0560295
\(763\) −15.4877 −0.560694
\(764\) 62.5004 2.26118
\(765\) 0 0
\(766\) −22.6676 −0.819014
\(767\) 3.58900 0.129591
\(768\) 4.34426 0.156760
\(769\) 8.05891 0.290612 0.145306 0.989387i \(-0.453583\pi\)
0.145306 + 0.989387i \(0.453583\pi\)
\(770\) 0 0
\(771\) −7.68463 −0.276755
\(772\) −3.94295 −0.141910
\(773\) 20.3254 0.731054 0.365527 0.930801i \(-0.380889\pi\)
0.365527 + 0.930801i \(0.380889\pi\)
\(774\) −23.7986 −0.855423
\(775\) 0 0
\(776\) −101.249 −3.63463
\(777\) 1.30621 0.0468601
\(778\) 68.0623 2.44015
\(779\) 6.02017 0.215695
\(780\) 0 0
\(781\) −10.2338 −0.366194
\(782\) 16.1010 0.575771
\(783\) 11.2292 0.401299
\(784\) 12.9523 0.462582
\(785\) 0 0
\(786\) 13.1567 0.469286
\(787\) 47.7951 1.70371 0.851856 0.523775i \(-0.175477\pi\)
0.851856 + 0.523775i \(0.175477\pi\)
\(788\) −133.059 −4.74002
\(789\) −0.510869 −0.0181874
\(790\) 0 0
\(791\) −4.48250 −0.159379
\(792\) −96.5597 −3.43110
\(793\) 12.8491 0.456286
\(794\) 54.7853 1.94426
\(795\) 0 0
\(796\) 79.5964 2.82122
\(797\) 7.57090 0.268175 0.134088 0.990969i \(-0.457190\pi\)
0.134088 + 0.990969i \(0.457190\pi\)
\(798\) −2.45386 −0.0868657
\(799\) 23.3612 0.826461
\(800\) 0 0
\(801\) 4.65736 0.164560
\(802\) −11.0372 −0.389735
\(803\) −53.7505 −1.89681
\(804\) −16.1760 −0.570483
\(805\) 0 0
\(806\) 20.9361 0.737444
\(807\) −0.677725 −0.0238571
\(808\) 3.19262 0.112316
\(809\) 8.55279 0.300700 0.150350 0.988633i \(-0.451960\pi\)
0.150350 + 0.988633i \(0.451960\pi\)
\(810\) 0 0
\(811\) −45.0023 −1.58024 −0.790122 0.612950i \(-0.789983\pi\)
−0.790122 + 0.612950i \(0.789983\pi\)
\(812\) 36.7684 1.29032
\(813\) 6.77568 0.237634
\(814\) −49.3293 −1.72899
\(815\) 0 0
\(816\) −20.9185 −0.732293
\(817\) 10.2160 0.357413
\(818\) 72.2173 2.52502
\(819\) −3.63337 −0.126960
\(820\) 0 0
\(821\) 41.4358 1.44612 0.723060 0.690785i \(-0.242735\pi\)
0.723060 + 0.690785i \(0.242735\pi\)
\(822\) −11.1111 −0.387544
\(823\) 19.1508 0.667553 0.333777 0.942652i \(-0.391677\pi\)
0.333777 + 0.942652i \(0.391677\pi\)
\(824\) −4.12791 −0.143803
\(825\) 0 0
\(826\) −7.77845 −0.270647
\(827\) 32.2820 1.12256 0.561278 0.827627i \(-0.310310\pi\)
0.561278 + 0.827627i \(0.310310\pi\)
\(828\) −15.3297 −0.532744
\(829\) 9.85700 0.342348 0.171174 0.985241i \(-0.445244\pi\)
0.171174 + 0.985241i \(0.445244\pi\)
\(830\) 0 0
\(831\) −2.55984 −0.0887998
\(832\) −26.0399 −0.902770
\(833\) −5.98512 −0.207372
\(834\) −9.81979 −0.340031
\(835\) 0 0
\(836\) 67.0603 2.31933
\(837\) −10.0280 −0.346619
\(838\) −0.402165 −0.0138925
\(839\) 11.7098 0.404267 0.202133 0.979358i \(-0.435213\pi\)
0.202133 + 0.979358i \(0.435213\pi\)
\(840\) 0 0
\(841\) 20.2927 0.699748
\(842\) 28.3191 0.975941
\(843\) 2.35086 0.0809678
\(844\) −127.153 −4.37679
\(845\) 0 0
\(846\) −30.7364 −1.05674
\(847\) −3.34968 −0.115096
\(848\) 32.0444 1.10041
\(849\) −8.24484 −0.282962
\(850\) 0 0
\(851\) −4.84066 −0.165936
\(852\) 3.81777 0.130795
\(853\) 29.2441 1.00130 0.500650 0.865650i \(-0.333094\pi\)
0.500650 + 0.865650i \(0.333094\pi\)
\(854\) −27.8480 −0.952938
\(855\) 0 0
\(856\) −50.0453 −1.71051
\(857\) −38.6873 −1.32153 −0.660766 0.750592i \(-0.729768\pi\)
−0.660766 + 0.750592i \(0.729768\pi\)
\(858\) −3.41327 −0.116527
\(859\) −49.3913 −1.68521 −0.842604 0.538534i \(-0.818979\pi\)
−0.842604 + 0.538534i \(0.818979\pi\)
\(860\) 0 0
\(861\) 0.480572 0.0163778
\(862\) 6.15148 0.209520
\(863\) 2.32156 0.0790267 0.0395134 0.999219i \(-0.487419\pi\)
0.0395134 + 0.999219i \(0.487419\pi\)
\(864\) 27.8738 0.948287
\(865\) 0 0
\(866\) −55.0325 −1.87008
\(867\) 5.07889 0.172488
\(868\) −32.8353 −1.11450
\(869\) −12.5540 −0.425865
\(870\) 0 0
\(871\) 14.2081 0.481424
\(872\) −134.869 −4.56725
\(873\) −34.0343 −1.15189
\(874\) 9.09369 0.307599
\(875\) 0 0
\(876\) 20.0519 0.677490
\(877\) −36.2775 −1.22500 −0.612502 0.790469i \(-0.709837\pi\)
−0.612502 + 0.790469i \(0.709837\pi\)
\(878\) −24.0453 −0.811490
\(879\) −3.42871 −0.115647
\(880\) 0 0
\(881\) 30.1252 1.01494 0.507472 0.861668i \(-0.330580\pi\)
0.507472 + 0.861668i \(0.330580\pi\)
\(882\) 7.87463 0.265152
\(883\) −1.94158 −0.0653394 −0.0326697 0.999466i \(-0.510401\pi\)
−0.0326697 + 0.999466i \(0.510401\pi\)
\(884\) 38.9060 1.30855
\(885\) 0 0
\(886\) −18.0669 −0.606969
\(887\) −52.3596 −1.75806 −0.879031 0.476765i \(-0.841809\pi\)
−0.879031 + 0.476765i \(0.841809\pi\)
\(888\) 11.3747 0.381709
\(889\) −2.13061 −0.0714585
\(890\) 0 0
\(891\) −31.6305 −1.05966
\(892\) −92.8752 −3.10969
\(893\) 13.1942 0.441527
\(894\) −4.17965 −0.139789
\(895\) 0 0
\(896\) 21.5811 0.720972
\(897\) −0.334942 −0.0111834
\(898\) −106.848 −3.56555
\(899\) −44.0198 −1.46814
\(900\) 0 0
\(901\) −14.8074 −0.493305
\(902\) −18.1489 −0.604291
\(903\) 0.815514 0.0271386
\(904\) −39.0342 −1.29826
\(905\) 0 0
\(906\) 6.95296 0.230997
\(907\) −9.62846 −0.319708 −0.159854 0.987141i \(-0.551102\pi\)
−0.159854 + 0.987141i \(0.551102\pi\)
\(908\) 82.2669 2.73012
\(909\) 1.07318 0.0355952
\(910\) 0 0
\(911\) −24.6036 −0.815154 −0.407577 0.913171i \(-0.633626\pi\)
−0.407577 + 0.913171i \(0.633626\pi\)
\(912\) −11.8145 −0.391219
\(913\) 26.6007 0.880356
\(914\) −96.1434 −3.18014
\(915\) 0 0
\(916\) −23.6521 −0.781488
\(917\) 18.1242 0.598514
\(918\) −25.7520 −0.849943
\(919\) 18.4685 0.609220 0.304610 0.952477i \(-0.401474\pi\)
0.304610 + 0.952477i \(0.401474\pi\)
\(920\) 0 0
\(921\) −5.96765 −0.196641
\(922\) 49.3690 1.62588
\(923\) −3.35333 −0.110376
\(924\) 5.35321 0.176108
\(925\) 0 0
\(926\) 30.0819 0.988551
\(927\) −1.38757 −0.0455739
\(928\) 122.357 4.01657
\(929\) 21.6032 0.708778 0.354389 0.935098i \(-0.384689\pi\)
0.354389 + 0.935098i \(0.384689\pi\)
\(930\) 0 0
\(931\) −3.38034 −0.110786
\(932\) 85.1751 2.79000
\(933\) 5.77314 0.189004
\(934\) 85.3404 2.79242
\(935\) 0 0
\(936\) −31.6399 −1.03418
\(937\) −4.95446 −0.161855 −0.0809276 0.996720i \(-0.525788\pi\)
−0.0809276 + 0.996720i \(0.525788\pi\)
\(938\) −30.7933 −1.00544
\(939\) 8.06967 0.263344
\(940\) 0 0
\(941\) −37.1398 −1.21072 −0.605361 0.795951i \(-0.706971\pi\)
−0.605361 + 0.795951i \(0.706971\pi\)
\(942\) −3.65651 −0.119136
\(943\) −1.78094 −0.0579953
\(944\) −37.4507 −1.21892
\(945\) 0 0
\(946\) −30.7980 −1.00133
\(947\) 11.0644 0.359543 0.179772 0.983708i \(-0.442464\pi\)
0.179772 + 0.983708i \(0.442464\pi\)
\(948\) 4.68333 0.152107
\(949\) −17.6125 −0.571726
\(950\) 0 0
\(951\) −1.90536 −0.0617857
\(952\) −52.1192 −1.68919
\(953\) −19.3888 −0.628065 −0.314033 0.949412i \(-0.601680\pi\)
−0.314033 + 0.949412i \(0.601680\pi\)
\(954\) 19.4821 0.630755
\(955\) 0 0
\(956\) 11.2468 0.363748
\(957\) 7.17665 0.231988
\(958\) 26.4101 0.853271
\(959\) −15.3062 −0.494263
\(960\) 0 0
\(961\) 8.31092 0.268094
\(962\) −16.1638 −0.521142
\(963\) −16.8224 −0.542095
\(964\) 65.2932 2.10295
\(965\) 0 0
\(966\) 0.725921 0.0233561
\(967\) 32.5154 1.04563 0.522813 0.852448i \(-0.324883\pi\)
0.522813 + 0.852448i \(0.324883\pi\)
\(968\) −29.1694 −0.937540
\(969\) 5.45938 0.175381
\(970\) 0 0
\(971\) 1.32316 0.0424622 0.0212311 0.999775i \(-0.493241\pi\)
0.0212311 + 0.999775i \(0.493241\pi\)
\(972\) 36.9282 1.18447
\(973\) −13.5273 −0.433667
\(974\) −97.5934 −3.12709
\(975\) 0 0
\(976\) −134.079 −4.29176
\(977\) 31.6195 1.01160 0.505799 0.862651i \(-0.331198\pi\)
0.505799 + 0.862651i \(0.331198\pi\)
\(978\) −5.34070 −0.170777
\(979\) 6.02713 0.192628
\(980\) 0 0
\(981\) −45.3355 −1.44745
\(982\) 47.3611 1.51135
\(983\) 12.1696 0.388149 0.194074 0.980987i \(-0.437830\pi\)
0.194074 + 0.980987i \(0.437830\pi\)
\(984\) 4.18488 0.133409
\(985\) 0 0
\(986\) −113.043 −3.60003
\(987\) 1.05325 0.0335254
\(988\) 21.9737 0.699078
\(989\) −3.02219 −0.0961000
\(990\) 0 0
\(991\) 2.18738 0.0694844 0.0347422 0.999396i \(-0.488939\pi\)
0.0347422 + 0.999396i \(0.488939\pi\)
\(992\) −109.269 −3.46928
\(993\) 4.37313 0.138777
\(994\) 7.26768 0.230517
\(995\) 0 0
\(996\) −9.92353 −0.314439
\(997\) 3.78052 0.119730 0.0598652 0.998206i \(-0.480933\pi\)
0.0598652 + 0.998206i \(0.480933\pi\)
\(998\) −32.5894 −1.03160
\(999\) 7.74216 0.244951
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 4025.2.a.p.1.1 5
5.4 even 2 161.2.a.d.1.5 5
15.14 odd 2 1449.2.a.r.1.1 5
20.19 odd 2 2576.2.a.bd.1.3 5
35.34 odd 2 1127.2.a.h.1.5 5
115.114 odd 2 3703.2.a.j.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.2.a.d.1.5 5 5.4 even 2
1127.2.a.h.1.5 5 35.34 odd 2
1449.2.a.r.1.1 5 15.14 odd 2
2576.2.a.bd.1.3 5 20.19 odd 2
3703.2.a.j.1.5 5 115.114 odd 2
4025.2.a.p.1.1 5 1.1 even 1 trivial