Properties

Label 6025.2.a.p.1.15
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 1.15
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.09514 q^{2} -0.223927 q^{3} -0.800662 q^{4} +0.245232 q^{6} -2.26365 q^{7} +3.06713 q^{8} -2.94986 q^{9} +O(q^{10})\) \(q-1.09514 q^{2} -0.223927 q^{3} -0.800662 q^{4} +0.245232 q^{6} -2.26365 q^{7} +3.06713 q^{8} -2.94986 q^{9} -3.16701 q^{11} +0.179290 q^{12} +0.0649874 q^{13} +2.47902 q^{14} -1.75761 q^{16} -4.44087 q^{17} +3.23051 q^{18} +7.82407 q^{19} +0.506893 q^{21} +3.46833 q^{22} +2.53175 q^{23} -0.686812 q^{24} -0.0711705 q^{26} +1.33233 q^{27} +1.81242 q^{28} -6.53411 q^{29} +8.27459 q^{31} -4.20941 q^{32} +0.709178 q^{33} +4.86338 q^{34} +2.36184 q^{36} +2.73984 q^{37} -8.56847 q^{38} -0.0145524 q^{39} -7.52088 q^{41} -0.555120 q^{42} +10.7428 q^{43} +2.53570 q^{44} -2.77262 q^{46} -8.53037 q^{47} +0.393577 q^{48} -1.87588 q^{49} +0.994430 q^{51} -0.0520330 q^{52} -0.0654906 q^{53} -1.45909 q^{54} -6.94290 q^{56} -1.75202 q^{57} +7.15578 q^{58} +11.9066 q^{59} +7.88792 q^{61} -9.06186 q^{62} +6.67745 q^{63} +8.12514 q^{64} -0.776651 q^{66} +13.3617 q^{67} +3.55564 q^{68} -0.566926 q^{69} -8.56086 q^{71} -9.04758 q^{72} +16.6336 q^{73} -3.00052 q^{74} -6.26444 q^{76} +7.16900 q^{77} +0.0159370 q^{78} -0.725508 q^{79} +8.55123 q^{81} +8.23644 q^{82} +6.57206 q^{83} -0.405850 q^{84} -11.7649 q^{86} +1.46316 q^{87} -9.71361 q^{88} -10.8164 q^{89} -0.147109 q^{91} -2.02707 q^{92} -1.85290 q^{93} +9.34197 q^{94} +0.942600 q^{96} +9.64642 q^{97} +2.05436 q^{98} +9.34222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09514 −0.774383 −0.387191 0.921999i \(-0.626555\pi\)
−0.387191 + 0.921999i \(0.626555\pi\)
\(3\) −0.223927 −0.129284 −0.0646421 0.997909i \(-0.520591\pi\)
−0.0646421 + 0.997909i \(0.520591\pi\)
\(4\) −0.800662 −0.400331
\(5\) 0 0
\(6\) 0.245232 0.100116
\(7\) −2.26365 −0.855580 −0.427790 0.903878i \(-0.640708\pi\)
−0.427790 + 0.903878i \(0.640708\pi\)
\(8\) 3.06713 1.08439
\(9\) −2.94986 −0.983286
\(10\) 0 0
\(11\) −3.16701 −0.954889 −0.477444 0.878662i \(-0.658437\pi\)
−0.477444 + 0.878662i \(0.658437\pi\)
\(12\) 0.179290 0.0517565
\(13\) 0.0649874 0.0180243 0.00901213 0.999959i \(-0.497131\pi\)
0.00901213 + 0.999959i \(0.497131\pi\)
\(14\) 2.47902 0.662546
\(15\) 0 0
\(16\) −1.75761 −0.439404
\(17\) −4.44087 −1.07707 −0.538534 0.842604i \(-0.681022\pi\)
−0.538534 + 0.842604i \(0.681022\pi\)
\(18\) 3.23051 0.761439
\(19\) 7.82407 1.79496 0.897482 0.441050i \(-0.145394\pi\)
0.897482 + 0.441050i \(0.145394\pi\)
\(20\) 0 0
\(21\) 0.506893 0.110613
\(22\) 3.46833 0.739450
\(23\) 2.53175 0.527906 0.263953 0.964536i \(-0.414974\pi\)
0.263953 + 0.964536i \(0.414974\pi\)
\(24\) −0.686812 −0.140195
\(25\) 0 0
\(26\) −0.0711705 −0.0139577
\(27\) 1.33233 0.256408
\(28\) 1.81242 0.342515
\(29\) −6.53411 −1.21335 −0.606677 0.794949i \(-0.707498\pi\)
−0.606677 + 0.794949i \(0.707498\pi\)
\(30\) 0 0
\(31\) 8.27459 1.48616 0.743080 0.669202i \(-0.233364\pi\)
0.743080 + 0.669202i \(0.233364\pi\)
\(32\) −4.20941 −0.744126
\(33\) 0.709178 0.123452
\(34\) 4.86338 0.834063
\(35\) 0 0
\(36\) 2.36184 0.393640
\(37\) 2.73984 0.450428 0.225214 0.974309i \(-0.427692\pi\)
0.225214 + 0.974309i \(0.427692\pi\)
\(38\) −8.56847 −1.38999
\(39\) −0.0145524 −0.00233025
\(40\) 0 0
\(41\) −7.52088 −1.17456 −0.587282 0.809382i \(-0.699802\pi\)
−0.587282 + 0.809382i \(0.699802\pi\)
\(42\) −0.555120 −0.0856568
\(43\) 10.7428 1.63827 0.819134 0.573603i \(-0.194455\pi\)
0.819134 + 0.573603i \(0.194455\pi\)
\(44\) 2.53570 0.382272
\(45\) 0 0
\(46\) −2.77262 −0.408801
\(47\) −8.53037 −1.24428 −0.622141 0.782905i \(-0.713737\pi\)
−0.622141 + 0.782905i \(0.713737\pi\)
\(48\) 0.393577 0.0568080
\(49\) −1.87588 −0.267983
\(50\) 0 0
\(51\) 0.994430 0.139248
\(52\) −0.0520330 −0.00721567
\(53\) −0.0654906 −0.00899583 −0.00449791 0.999990i \(-0.501432\pi\)
−0.00449791 + 0.999990i \(0.501432\pi\)
\(54\) −1.45909 −0.198558
\(55\) 0 0
\(56\) −6.94290 −0.927784
\(57\) −1.75202 −0.232061
\(58\) 7.15578 0.939600
\(59\) 11.9066 1.55011 0.775055 0.631894i \(-0.217722\pi\)
0.775055 + 0.631894i \(0.217722\pi\)
\(60\) 0 0
\(61\) 7.88792 1.00995 0.504973 0.863135i \(-0.331503\pi\)
0.504973 + 0.863135i \(0.331503\pi\)
\(62\) −9.06186 −1.15086
\(63\) 6.67745 0.841279
\(64\) 8.12514 1.01564
\(65\) 0 0
\(66\) −0.776651 −0.0955992
\(67\) 13.3617 1.63240 0.816199 0.577771i \(-0.196077\pi\)
0.816199 + 0.577771i \(0.196077\pi\)
\(68\) 3.55564 0.431184
\(69\) −0.566926 −0.0682499
\(70\) 0 0
\(71\) −8.56086 −1.01599 −0.507994 0.861361i \(-0.669613\pi\)
−0.507994 + 0.861361i \(0.669613\pi\)
\(72\) −9.04758 −1.06627
\(73\) 16.6336 1.94682 0.973410 0.229068i \(-0.0735680\pi\)
0.973410 + 0.229068i \(0.0735680\pi\)
\(74\) −3.00052 −0.348803
\(75\) 0 0
\(76\) −6.26444 −0.718580
\(77\) 7.16900 0.816984
\(78\) 0.0159370 0.00180451
\(79\) −0.725508 −0.0816260 −0.0408130 0.999167i \(-0.512995\pi\)
−0.0408130 + 0.999167i \(0.512995\pi\)
\(80\) 0 0
\(81\) 8.55123 0.950136
\(82\) 8.23644 0.909562
\(83\) 6.57206 0.721378 0.360689 0.932686i \(-0.382542\pi\)
0.360689 + 0.932686i \(0.382542\pi\)
\(84\) −0.405850 −0.0442818
\(85\) 0 0
\(86\) −11.7649 −1.26865
\(87\) 1.46316 0.156868
\(88\) −9.71361 −1.03547
\(89\) −10.8164 −1.14654 −0.573269 0.819367i \(-0.694325\pi\)
−0.573269 + 0.819367i \(0.694325\pi\)
\(90\) 0 0
\(91\) −0.147109 −0.0154212
\(92\) −2.02707 −0.211337
\(93\) −1.85290 −0.192137
\(94\) 9.34197 0.963551
\(95\) 0 0
\(96\) 0.942600 0.0962038
\(97\) 9.64642 0.979445 0.489723 0.871878i \(-0.337098\pi\)
0.489723 + 0.871878i \(0.337098\pi\)
\(98\) 2.05436 0.207521
\(99\) 9.34222 0.938928
\(100\) 0 0
\(101\) −16.4798 −1.63980 −0.819902 0.572504i \(-0.805972\pi\)
−0.819902 + 0.572504i \(0.805972\pi\)
\(102\) −1.08904 −0.107831
\(103\) −10.7964 −1.06380 −0.531898 0.846808i \(-0.678521\pi\)
−0.531898 + 0.846808i \(0.678521\pi\)
\(104\) 0.199324 0.0195454
\(105\) 0 0
\(106\) 0.0717216 0.00696622
\(107\) −1.67365 −0.161798 −0.0808988 0.996722i \(-0.525779\pi\)
−0.0808988 + 0.996722i \(0.525779\pi\)
\(108\) −1.06675 −0.102648
\(109\) −16.9594 −1.62442 −0.812208 0.583368i \(-0.801735\pi\)
−0.812208 + 0.583368i \(0.801735\pi\)
\(110\) 0 0
\(111\) −0.613525 −0.0582332
\(112\) 3.97863 0.375945
\(113\) 8.64948 0.813675 0.406837 0.913501i \(-0.366632\pi\)
0.406837 + 0.913501i \(0.366632\pi\)
\(114\) 1.91871 0.179704
\(115\) 0 0
\(116\) 5.23162 0.485743
\(117\) −0.191703 −0.0177230
\(118\) −13.0394 −1.20038
\(119\) 10.0526 0.921518
\(120\) 0 0
\(121\) −0.970060 −0.0881872
\(122\) −8.63840 −0.782084
\(123\) 1.68413 0.151853
\(124\) −6.62515 −0.594956
\(125\) 0 0
\(126\) −7.31276 −0.651472
\(127\) −6.06109 −0.537835 −0.268918 0.963163i \(-0.586666\pi\)
−0.268918 + 0.963163i \(0.586666\pi\)
\(128\) −0.479360 −0.0423699
\(129\) −2.40561 −0.211802
\(130\) 0 0
\(131\) −6.54103 −0.571493 −0.285746 0.958305i \(-0.592241\pi\)
−0.285746 + 0.958305i \(0.592241\pi\)
\(132\) −0.567812 −0.0494217
\(133\) −17.7110 −1.53574
\(134\) −14.6330 −1.26410
\(135\) 0 0
\(136\) −13.6207 −1.16797
\(137\) 8.14464 0.695844 0.347922 0.937524i \(-0.386887\pi\)
0.347922 + 0.937524i \(0.386887\pi\)
\(138\) 0.620865 0.0528515
\(139\) −6.38850 −0.541865 −0.270933 0.962598i \(-0.587332\pi\)
−0.270933 + 0.962598i \(0.587332\pi\)
\(140\) 0 0
\(141\) 1.91018 0.160866
\(142\) 9.37537 0.786763
\(143\) −0.205816 −0.0172112
\(144\) 5.18471 0.432059
\(145\) 0 0
\(146\) −18.2162 −1.50758
\(147\) 0.420060 0.0346460
\(148\) −2.19369 −0.180320
\(149\) 9.29157 0.761195 0.380598 0.924741i \(-0.375718\pi\)
0.380598 + 0.924741i \(0.375718\pi\)
\(150\) 0 0
\(151\) −4.44437 −0.361677 −0.180839 0.983513i \(-0.557881\pi\)
−0.180839 + 0.983513i \(0.557881\pi\)
\(152\) 23.9974 1.94645
\(153\) 13.0999 1.05907
\(154\) −7.85108 −0.632658
\(155\) 0 0
\(156\) 0.0116516 0.000932873 0
\(157\) 0.260484 0.0207889 0.0103944 0.999946i \(-0.496691\pi\)
0.0103944 + 0.999946i \(0.496691\pi\)
\(158\) 0.794534 0.0632098
\(159\) 0.0146651 0.00116302
\(160\) 0 0
\(161\) −5.73099 −0.451666
\(162\) −9.36481 −0.735769
\(163\) −5.42016 −0.424539 −0.212270 0.977211i \(-0.568086\pi\)
−0.212270 + 0.977211i \(0.568086\pi\)
\(164\) 6.02169 0.470215
\(165\) 0 0
\(166\) −7.19735 −0.558623
\(167\) 22.0325 1.70492 0.852462 0.522789i \(-0.175109\pi\)
0.852462 + 0.522789i \(0.175109\pi\)
\(168\) 1.55470 0.119948
\(169\) −12.9958 −0.999675
\(170\) 0 0
\(171\) −23.0799 −1.76496
\(172\) −8.60139 −0.655849
\(173\) −18.0964 −1.37584 −0.687922 0.725785i \(-0.741477\pi\)
−0.687922 + 0.725785i \(0.741477\pi\)
\(174\) −1.60237 −0.121476
\(175\) 0 0
\(176\) 5.56638 0.419582
\(177\) −2.66621 −0.200405
\(178\) 11.8455 0.887859
\(179\) −17.4131 −1.30151 −0.650757 0.759286i \(-0.725548\pi\)
−0.650757 + 0.759286i \(0.725548\pi\)
\(180\) 0 0
\(181\) 6.69828 0.497879 0.248940 0.968519i \(-0.419918\pi\)
0.248940 + 0.968519i \(0.419918\pi\)
\(182\) 0.161105 0.0119419
\(183\) −1.76632 −0.130570
\(184\) 7.76518 0.572457
\(185\) 0 0
\(186\) 2.02919 0.148788
\(187\) 14.0643 1.02848
\(188\) 6.82995 0.498125
\(189\) −3.01594 −0.219377
\(190\) 0 0
\(191\) 18.2205 1.31839 0.659196 0.751971i \(-0.270897\pi\)
0.659196 + 0.751971i \(0.270897\pi\)
\(192\) −1.81944 −0.131307
\(193\) 5.88201 0.423396 0.211698 0.977335i \(-0.432101\pi\)
0.211698 + 0.977335i \(0.432101\pi\)
\(194\) −10.5642 −0.758466
\(195\) 0 0
\(196\) 1.50195 0.107282
\(197\) −18.3999 −1.31094 −0.655468 0.755223i \(-0.727528\pi\)
−0.655468 + 0.755223i \(0.727528\pi\)
\(198\) −10.2311 −0.727090
\(199\) 11.8695 0.841404 0.420702 0.907199i \(-0.361784\pi\)
0.420702 + 0.907199i \(0.361784\pi\)
\(200\) 0 0
\(201\) −2.99206 −0.211043
\(202\) 18.0478 1.26984
\(203\) 14.7909 1.03812
\(204\) −0.796203 −0.0557453
\(205\) 0 0
\(206\) 11.8235 0.823786
\(207\) −7.46829 −0.519082
\(208\) −0.114223 −0.00791992
\(209\) −24.7789 −1.71399
\(210\) 0 0
\(211\) 17.3377 1.19358 0.596788 0.802399i \(-0.296443\pi\)
0.596788 + 0.802399i \(0.296443\pi\)
\(212\) 0.0524359 0.00360131
\(213\) 1.91701 0.131351
\(214\) 1.83288 0.125293
\(215\) 0 0
\(216\) 4.08643 0.278046
\(217\) −18.7308 −1.27153
\(218\) 18.5730 1.25792
\(219\) −3.72472 −0.251693
\(220\) 0 0
\(221\) −0.288600 −0.0194134
\(222\) 0.671897 0.0450948
\(223\) 0.685671 0.0459159 0.0229580 0.999736i \(-0.492692\pi\)
0.0229580 + 0.999736i \(0.492692\pi\)
\(224\) 9.52864 0.636659
\(225\) 0 0
\(226\) −9.47242 −0.630096
\(227\) 23.7034 1.57325 0.786626 0.617429i \(-0.211826\pi\)
0.786626 + 0.617429i \(0.211826\pi\)
\(228\) 1.40278 0.0929011
\(229\) −18.1670 −1.20051 −0.600254 0.799810i \(-0.704934\pi\)
−0.600254 + 0.799810i \(0.704934\pi\)
\(230\) 0 0
\(231\) −1.60533 −0.105623
\(232\) −20.0409 −1.31575
\(233\) 1.69882 0.111293 0.0556466 0.998451i \(-0.482278\pi\)
0.0556466 + 0.998451i \(0.482278\pi\)
\(234\) 0.209943 0.0137244
\(235\) 0 0
\(236\) −9.53318 −0.620557
\(237\) 0.162461 0.0105530
\(238\) −11.0090 −0.713608
\(239\) 4.67855 0.302631 0.151315 0.988486i \(-0.451649\pi\)
0.151315 + 0.988486i \(0.451649\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 1.06235 0.0682907
\(243\) −5.91185 −0.379245
\(244\) −6.31556 −0.404313
\(245\) 0 0
\(246\) −1.84436 −0.117592
\(247\) 0.508466 0.0323529
\(248\) 25.3792 1.61158
\(249\) −1.47166 −0.0932628
\(250\) 0 0
\(251\) −6.44769 −0.406974 −0.203487 0.979078i \(-0.565228\pi\)
−0.203487 + 0.979078i \(0.565228\pi\)
\(252\) −5.34638 −0.336790
\(253\) −8.01806 −0.504091
\(254\) 6.63776 0.416490
\(255\) 0 0
\(256\) −15.7253 −0.982831
\(257\) 15.0125 0.936452 0.468226 0.883609i \(-0.344893\pi\)
0.468226 + 0.883609i \(0.344893\pi\)
\(258\) 2.63449 0.164016
\(259\) −6.20205 −0.385377
\(260\) 0 0
\(261\) 19.2747 1.19307
\(262\) 7.16336 0.442554
\(263\) −11.1566 −0.687945 −0.343973 0.938980i \(-0.611773\pi\)
−0.343973 + 0.938980i \(0.611773\pi\)
\(264\) 2.17514 0.133871
\(265\) 0 0
\(266\) 19.3960 1.18925
\(267\) 2.42209 0.148229
\(268\) −10.6983 −0.653500
\(269\) −13.5075 −0.823569 −0.411785 0.911281i \(-0.635094\pi\)
−0.411785 + 0.911281i \(0.635094\pi\)
\(270\) 0 0
\(271\) 13.0987 0.795687 0.397844 0.917453i \(-0.369759\pi\)
0.397844 + 0.917453i \(0.369759\pi\)
\(272\) 7.80533 0.473268
\(273\) 0.0329416 0.00199372
\(274\) −8.91954 −0.538849
\(275\) 0 0
\(276\) 0.453917 0.0273226
\(277\) −14.4487 −0.868135 −0.434068 0.900880i \(-0.642922\pi\)
−0.434068 + 0.900880i \(0.642922\pi\)
\(278\) 6.99631 0.419611
\(279\) −24.4089 −1.46132
\(280\) 0 0
\(281\) 1.77667 0.105988 0.0529938 0.998595i \(-0.483124\pi\)
0.0529938 + 0.998595i \(0.483124\pi\)
\(282\) −2.09192 −0.124572
\(283\) −18.4509 −1.09679 −0.548397 0.836218i \(-0.684762\pi\)
−0.548397 + 0.836218i \(0.684762\pi\)
\(284\) 6.85436 0.406732
\(285\) 0 0
\(286\) 0.225397 0.0133280
\(287\) 17.0247 1.00493
\(288\) 12.4172 0.731688
\(289\) 2.72130 0.160077
\(290\) 0 0
\(291\) −2.16009 −0.126627
\(292\) −13.3179 −0.779373
\(293\) 8.65394 0.505569 0.252784 0.967523i \(-0.418654\pi\)
0.252784 + 0.967523i \(0.418654\pi\)
\(294\) −0.460026 −0.0268293
\(295\) 0 0
\(296\) 8.40345 0.488440
\(297\) −4.21951 −0.244841
\(298\) −10.1756 −0.589456
\(299\) 0.164532 0.00951511
\(300\) 0 0
\(301\) −24.3180 −1.40167
\(302\) 4.86722 0.280077
\(303\) 3.69028 0.212001
\(304\) −13.7517 −0.788714
\(305\) 0 0
\(306\) −14.3463 −0.820123
\(307\) 6.61143 0.377334 0.188667 0.982041i \(-0.439583\pi\)
0.188667 + 0.982041i \(0.439583\pi\)
\(308\) −5.73995 −0.327064
\(309\) 2.41759 0.137532
\(310\) 0 0
\(311\) −19.4206 −1.10124 −0.550622 0.834755i \(-0.685609\pi\)
−0.550622 + 0.834755i \(0.685609\pi\)
\(312\) −0.0446341 −0.00252691
\(313\) −19.4518 −1.09948 −0.549740 0.835336i \(-0.685273\pi\)
−0.549740 + 0.835336i \(0.685273\pi\)
\(314\) −0.285267 −0.0160986
\(315\) 0 0
\(316\) 0.580887 0.0326774
\(317\) −0.792618 −0.0445179 −0.0222589 0.999752i \(-0.507086\pi\)
−0.0222589 + 0.999752i \(0.507086\pi\)
\(318\) −0.0160604 −0.000900622 0
\(319\) 20.6936 1.15862
\(320\) 0 0
\(321\) 0.374775 0.0209179
\(322\) 6.27626 0.349762
\(323\) −34.7457 −1.93330
\(324\) −6.84664 −0.380369
\(325\) 0 0
\(326\) 5.93584 0.328756
\(327\) 3.79767 0.210011
\(328\) −23.0675 −1.27369
\(329\) 19.3098 1.06458
\(330\) 0 0
\(331\) 14.6988 0.807917 0.403958 0.914777i \(-0.367634\pi\)
0.403958 + 0.914777i \(0.367634\pi\)
\(332\) −5.26201 −0.288790
\(333\) −8.08215 −0.442899
\(334\) −24.1287 −1.32026
\(335\) 0 0
\(336\) −0.890922 −0.0486038
\(337\) 17.3385 0.944487 0.472244 0.881468i \(-0.343444\pi\)
0.472244 + 0.881468i \(0.343444\pi\)
\(338\) 14.2322 0.774131
\(339\) −1.93685 −0.105195
\(340\) 0 0
\(341\) −26.2057 −1.41912
\(342\) 25.2758 1.36676
\(343\) 20.0919 1.08486
\(344\) 32.9496 1.77652
\(345\) 0 0
\(346\) 19.8181 1.06543
\(347\) −13.9745 −0.750188 −0.375094 0.926987i \(-0.622390\pi\)
−0.375094 + 0.926987i \(0.622390\pi\)
\(348\) −1.17150 −0.0627990
\(349\) 18.2257 0.975600 0.487800 0.872955i \(-0.337800\pi\)
0.487800 + 0.872955i \(0.337800\pi\)
\(350\) 0 0
\(351\) 0.0865848 0.00462156
\(352\) 13.3312 0.710557
\(353\) 25.1550 1.33886 0.669432 0.742873i \(-0.266537\pi\)
0.669432 + 0.742873i \(0.266537\pi\)
\(354\) 2.91988 0.155190
\(355\) 0 0
\(356\) 8.66030 0.458995
\(357\) −2.25104 −0.119138
\(358\) 19.0698 1.00787
\(359\) −6.05193 −0.319409 −0.159704 0.987165i \(-0.551054\pi\)
−0.159704 + 0.987165i \(0.551054\pi\)
\(360\) 0 0
\(361\) 42.2161 2.22190
\(362\) −7.33558 −0.385549
\(363\) 0.217222 0.0114012
\(364\) 0.117784 0.00617359
\(365\) 0 0
\(366\) 1.93437 0.101111
\(367\) −31.3055 −1.63413 −0.817067 0.576543i \(-0.804401\pi\)
−0.817067 + 0.576543i \(0.804401\pi\)
\(368\) −4.44984 −0.231964
\(369\) 22.1855 1.15493
\(370\) 0 0
\(371\) 0.148248 0.00769665
\(372\) 1.48355 0.0769185
\(373\) −17.5060 −0.906424 −0.453212 0.891403i \(-0.649722\pi\)
−0.453212 + 0.891403i \(0.649722\pi\)
\(374\) −15.4024 −0.796438
\(375\) 0 0
\(376\) −26.1637 −1.34929
\(377\) −0.424635 −0.0218698
\(378\) 3.30288 0.169882
\(379\) 0.569958 0.0292768 0.0146384 0.999893i \(-0.495340\pi\)
0.0146384 + 0.999893i \(0.495340\pi\)
\(380\) 0 0
\(381\) 1.35724 0.0695336
\(382\) −19.9541 −1.02094
\(383\) −24.0263 −1.22769 −0.613843 0.789428i \(-0.710377\pi\)
−0.613843 + 0.789428i \(0.710377\pi\)
\(384\) 0.107342 0.00547776
\(385\) 0 0
\(386\) −6.44164 −0.327871
\(387\) −31.6898 −1.61088
\(388\) −7.72353 −0.392103
\(389\) −13.5820 −0.688633 −0.344317 0.938854i \(-0.611889\pi\)
−0.344317 + 0.938854i \(0.611889\pi\)
\(390\) 0 0
\(391\) −11.2432 −0.568591
\(392\) −5.75356 −0.290599
\(393\) 1.46471 0.0738850
\(394\) 20.1505 1.01517
\(395\) 0 0
\(396\) −7.47997 −0.375882
\(397\) −9.52930 −0.478262 −0.239131 0.970987i \(-0.576863\pi\)
−0.239131 + 0.970987i \(0.576863\pi\)
\(398\) −12.9988 −0.651569
\(399\) 3.96596 0.198546
\(400\) 0 0
\(401\) 9.98608 0.498681 0.249341 0.968416i \(-0.419786\pi\)
0.249341 + 0.968416i \(0.419786\pi\)
\(402\) 3.27673 0.163428
\(403\) 0.537744 0.0267869
\(404\) 13.1948 0.656465
\(405\) 0 0
\(406\) −16.1982 −0.803903
\(407\) −8.67711 −0.430108
\(408\) 3.05004 0.150999
\(409\) −1.85693 −0.0918193 −0.0459097 0.998946i \(-0.514619\pi\)
−0.0459097 + 0.998946i \(0.514619\pi\)
\(410\) 0 0
\(411\) −1.82380 −0.0899616
\(412\) 8.64424 0.425871
\(413\) −26.9524 −1.32624
\(414\) 8.17884 0.401968
\(415\) 0 0
\(416\) −0.273559 −0.0134123
\(417\) 1.43056 0.0700546
\(418\) 27.1364 1.32729
\(419\) −9.53574 −0.465851 −0.232926 0.972495i \(-0.574830\pi\)
−0.232926 + 0.972495i \(0.574830\pi\)
\(420\) 0 0
\(421\) −21.1822 −1.03235 −0.516177 0.856482i \(-0.672645\pi\)
−0.516177 + 0.856482i \(0.672645\pi\)
\(422\) −18.9872 −0.924284
\(423\) 25.1634 1.22348
\(424\) −0.200868 −0.00975501
\(425\) 0 0
\(426\) −2.09940 −0.101716
\(427\) −17.8555 −0.864089
\(428\) 1.34003 0.0647726
\(429\) 0.0460876 0.00222513
\(430\) 0 0
\(431\) −35.7158 −1.72037 −0.860186 0.509981i \(-0.829652\pi\)
−0.860186 + 0.509981i \(0.829652\pi\)
\(432\) −2.34173 −0.112666
\(433\) −11.8322 −0.568618 −0.284309 0.958733i \(-0.591764\pi\)
−0.284309 + 0.958733i \(0.591764\pi\)
\(434\) 20.5129 0.984650
\(435\) 0 0
\(436\) 13.5788 0.650305
\(437\) 19.8086 0.947572
\(438\) 4.07910 0.194907
\(439\) 2.11764 0.101069 0.0505347 0.998722i \(-0.483907\pi\)
0.0505347 + 0.998722i \(0.483907\pi\)
\(440\) 0 0
\(441\) 5.53358 0.263504
\(442\) 0.316059 0.0150334
\(443\) −26.8075 −1.27366 −0.636832 0.771002i \(-0.719756\pi\)
−0.636832 + 0.771002i \(0.719756\pi\)
\(444\) 0.491226 0.0233126
\(445\) 0 0
\(446\) −0.750907 −0.0355565
\(447\) −2.08063 −0.0984106
\(448\) −18.3925 −0.868963
\(449\) −35.6307 −1.68152 −0.840759 0.541409i \(-0.817891\pi\)
−0.840759 + 0.541409i \(0.817891\pi\)
\(450\) 0 0
\(451\) 23.8187 1.12158
\(452\) −6.92532 −0.325739
\(453\) 0.995213 0.0467592
\(454\) −25.9587 −1.21830
\(455\) 0 0
\(456\) −5.37366 −0.251645
\(457\) 4.37323 0.204571 0.102286 0.994755i \(-0.467384\pi\)
0.102286 + 0.994755i \(0.467384\pi\)
\(458\) 19.8954 0.929652
\(459\) −5.91671 −0.276169
\(460\) 0 0
\(461\) 2.32865 0.108456 0.0542281 0.998529i \(-0.482730\pi\)
0.0542281 + 0.998529i \(0.482730\pi\)
\(462\) 1.75807 0.0817927
\(463\) 24.3683 1.13249 0.566246 0.824236i \(-0.308395\pi\)
0.566246 + 0.824236i \(0.308395\pi\)
\(464\) 11.4844 0.533152
\(465\) 0 0
\(466\) −1.86045 −0.0861835
\(467\) −42.0547 −1.94606 −0.973030 0.230678i \(-0.925906\pi\)
−0.973030 + 0.230678i \(0.925906\pi\)
\(468\) 0.153490 0.00709507
\(469\) −30.2463 −1.39665
\(470\) 0 0
\(471\) −0.0583294 −0.00268768
\(472\) 36.5191 1.68093
\(473\) −34.0226 −1.56436
\(474\) −0.177918 −0.00817203
\(475\) 0 0
\(476\) −8.04872 −0.368913
\(477\) 0.193188 0.00884547
\(478\) −5.12369 −0.234352
\(479\) −30.3166 −1.38520 −0.692600 0.721322i \(-0.743535\pi\)
−0.692600 + 0.721322i \(0.743535\pi\)
\(480\) 0 0
\(481\) 0.178055 0.00811862
\(482\) −1.09514 −0.0498824
\(483\) 1.28332 0.0583932
\(484\) 0.776690 0.0353041
\(485\) 0 0
\(486\) 6.47432 0.293681
\(487\) −16.4118 −0.743692 −0.371846 0.928295i \(-0.621275\pi\)
−0.371846 + 0.928295i \(0.621275\pi\)
\(488\) 24.1932 1.09518
\(489\) 1.21372 0.0548863
\(490\) 0 0
\(491\) −0.561056 −0.0253201 −0.0126600 0.999920i \(-0.504030\pi\)
−0.0126600 + 0.999920i \(0.504030\pi\)
\(492\) −1.34842 −0.0607914
\(493\) 29.0171 1.30686
\(494\) −0.556843 −0.0250535
\(495\) 0 0
\(496\) −14.5435 −0.653024
\(497\) 19.3788 0.869258
\(498\) 1.61168 0.0722211
\(499\) −39.1100 −1.75080 −0.875401 0.483397i \(-0.839403\pi\)
−0.875401 + 0.483397i \(0.839403\pi\)
\(500\) 0 0
\(501\) −4.93366 −0.220420
\(502\) 7.06114 0.315154
\(503\) 36.7064 1.63666 0.818329 0.574750i \(-0.194901\pi\)
0.818329 + 0.574750i \(0.194901\pi\)
\(504\) 20.4806 0.912277
\(505\) 0 0
\(506\) 8.78092 0.390360
\(507\) 2.91010 0.129242
\(508\) 4.85289 0.215312
\(509\) −20.8479 −0.924065 −0.462033 0.886863i \(-0.652880\pi\)
−0.462033 + 0.886863i \(0.652880\pi\)
\(510\) 0 0
\(511\) −37.6528 −1.66566
\(512\) 18.1802 0.803458
\(513\) 10.4243 0.460243
\(514\) −16.4408 −0.725172
\(515\) 0 0
\(516\) 1.92608 0.0847910
\(517\) 27.0158 1.18815
\(518\) 6.79213 0.298429
\(519\) 4.05227 0.177875
\(520\) 0 0
\(521\) −23.2776 −1.01981 −0.509904 0.860231i \(-0.670319\pi\)
−0.509904 + 0.860231i \(0.670319\pi\)
\(522\) −21.1085 −0.923895
\(523\) −16.3641 −0.715552 −0.357776 0.933807i \(-0.616465\pi\)
−0.357776 + 0.933807i \(0.616465\pi\)
\(524\) 5.23716 0.228786
\(525\) 0 0
\(526\) 12.2181 0.532733
\(527\) −36.7464 −1.60070
\(528\) −1.24646 −0.0542453
\(529\) −16.5903 −0.721316
\(530\) 0 0
\(531\) −35.1228 −1.52420
\(532\) 14.1805 0.614803
\(533\) −0.488762 −0.0211706
\(534\) −2.65253 −0.114786
\(535\) 0 0
\(536\) 40.9822 1.77016
\(537\) 3.89926 0.168265
\(538\) 14.7927 0.637758
\(539\) 5.94093 0.255894
\(540\) 0 0
\(541\) −23.0819 −0.992369 −0.496184 0.868217i \(-0.665266\pi\)
−0.496184 + 0.868217i \(0.665266\pi\)
\(542\) −14.3449 −0.616166
\(543\) −1.49993 −0.0643680
\(544\) 18.6934 0.801475
\(545\) 0 0
\(546\) −0.0360758 −0.00154390
\(547\) −17.3551 −0.742049 −0.371024 0.928623i \(-0.620993\pi\)
−0.371024 + 0.928623i \(0.620993\pi\)
\(548\) −6.52111 −0.278568
\(549\) −23.2682 −0.993064
\(550\) 0 0
\(551\) −51.1233 −2.17793
\(552\) −1.73883 −0.0740097
\(553\) 1.64230 0.0698376
\(554\) 15.8233 0.672269
\(555\) 0 0
\(556\) 5.11503 0.216926
\(557\) 6.28655 0.266370 0.133185 0.991091i \(-0.457480\pi\)
0.133185 + 0.991091i \(0.457480\pi\)
\(558\) 26.7312 1.13162
\(559\) 0.698149 0.0295285
\(560\) 0 0
\(561\) −3.14937 −0.132966
\(562\) −1.94571 −0.0820749
\(563\) −6.26725 −0.264133 −0.132067 0.991241i \(-0.542161\pi\)
−0.132067 + 0.991241i \(0.542161\pi\)
\(564\) −1.52941 −0.0643997
\(565\) 0 0
\(566\) 20.2064 0.849338
\(567\) −19.3570 −0.812917
\(568\) −26.2572 −1.10173
\(569\) 21.6171 0.906234 0.453117 0.891451i \(-0.350312\pi\)
0.453117 + 0.891451i \(0.350312\pi\)
\(570\) 0 0
\(571\) −36.4039 −1.52345 −0.761727 0.647898i \(-0.775648\pi\)
−0.761727 + 0.647898i \(0.775648\pi\)
\(572\) 0.164789 0.00689017
\(573\) −4.08007 −0.170447
\(574\) −18.6444 −0.778203
\(575\) 0 0
\(576\) −23.9680 −0.998666
\(577\) −31.3479 −1.30503 −0.652514 0.757776i \(-0.726286\pi\)
−0.652514 + 0.757776i \(0.726286\pi\)
\(578\) −2.98022 −0.123961
\(579\) −1.31714 −0.0547385
\(580\) 0 0
\(581\) −14.8769 −0.617196
\(582\) 2.36561 0.0980577
\(583\) 0.207409 0.00859002
\(584\) 51.0175 2.11112
\(585\) 0 0
\(586\) −9.47730 −0.391504
\(587\) 44.4381 1.83416 0.917079 0.398705i \(-0.130540\pi\)
0.917079 + 0.398705i \(0.130540\pi\)
\(588\) −0.336326 −0.0138699
\(589\) 64.7410 2.66761
\(590\) 0 0
\(591\) 4.12022 0.169483
\(592\) −4.81559 −0.197920
\(593\) 6.62491 0.272052 0.136026 0.990705i \(-0.456567\pi\)
0.136026 + 0.990705i \(0.456567\pi\)
\(594\) 4.62096 0.189600
\(595\) 0 0
\(596\) −7.43941 −0.304730
\(597\) −2.65789 −0.108780
\(598\) −0.180186 −0.00736834
\(599\) 24.8397 1.01492 0.507460 0.861675i \(-0.330584\pi\)
0.507460 + 0.861675i \(0.330584\pi\)
\(600\) 0 0
\(601\) −6.70931 −0.273679 −0.136839 0.990593i \(-0.543694\pi\)
−0.136839 + 0.990593i \(0.543694\pi\)
\(602\) 26.6317 1.08543
\(603\) −39.4152 −1.60511
\(604\) 3.55844 0.144791
\(605\) 0 0
\(606\) −4.04138 −0.164170
\(607\) 18.3020 0.742857 0.371428 0.928462i \(-0.378868\pi\)
0.371428 + 0.928462i \(0.378868\pi\)
\(608\) −32.9347 −1.33568
\(609\) −3.31209 −0.134213
\(610\) 0 0
\(611\) −0.554366 −0.0224273
\(612\) −10.4886 −0.423977
\(613\) 26.7397 1.08000 0.540002 0.841664i \(-0.318423\pi\)
0.540002 + 0.841664i \(0.318423\pi\)
\(614\) −7.24045 −0.292201
\(615\) 0 0
\(616\) 21.9882 0.885931
\(617\) 44.9237 1.80856 0.904280 0.426939i \(-0.140408\pi\)
0.904280 + 0.426939i \(0.140408\pi\)
\(618\) −2.64761 −0.106503
\(619\) 34.7225 1.39562 0.697808 0.716285i \(-0.254159\pi\)
0.697808 + 0.716285i \(0.254159\pi\)
\(620\) 0 0
\(621\) 3.37313 0.135359
\(622\) 21.2684 0.852784
\(623\) 24.4846 0.980954
\(624\) 0.0255776 0.00102392
\(625\) 0 0
\(626\) 21.3025 0.851418
\(627\) 5.54866 0.221592
\(628\) −0.208560 −0.00832244
\(629\) −12.1673 −0.485142
\(630\) 0 0
\(631\) −30.3033 −1.20635 −0.603177 0.797607i \(-0.706099\pi\)
−0.603177 + 0.797607i \(0.706099\pi\)
\(632\) −2.22522 −0.0885146
\(633\) −3.88237 −0.154311
\(634\) 0.868030 0.0344739
\(635\) 0 0
\(636\) −0.0117418 −0.000465593 0
\(637\) −0.121909 −0.00483019
\(638\) −22.6624 −0.897214
\(639\) 25.2533 0.999006
\(640\) 0 0
\(641\) 44.8929 1.77316 0.886582 0.462571i \(-0.153073\pi\)
0.886582 + 0.462571i \(0.153073\pi\)
\(642\) −0.410432 −0.0161984
\(643\) 0.746188 0.0294268 0.0147134 0.999892i \(-0.495316\pi\)
0.0147134 + 0.999892i \(0.495316\pi\)
\(644\) 4.58859 0.180816
\(645\) 0 0
\(646\) 38.0515 1.49711
\(647\) −25.5099 −1.00290 −0.501448 0.865188i \(-0.667199\pi\)
−0.501448 + 0.865188i \(0.667199\pi\)
\(648\) 26.2277 1.03032
\(649\) −37.7084 −1.48018
\(650\) 0 0
\(651\) 4.19433 0.164389
\(652\) 4.33972 0.169956
\(653\) 28.7035 1.12325 0.561627 0.827391i \(-0.310176\pi\)
0.561627 + 0.827391i \(0.310176\pi\)
\(654\) −4.15899 −0.162629
\(655\) 0 0
\(656\) 13.2188 0.516108
\(657\) −49.0669 −1.91428
\(658\) −21.1470 −0.824395
\(659\) 15.5090 0.604146 0.302073 0.953285i \(-0.402321\pi\)
0.302073 + 0.953285i \(0.402321\pi\)
\(660\) 0 0
\(661\) −28.9524 −1.12612 −0.563058 0.826417i \(-0.690375\pi\)
−0.563058 + 0.826417i \(0.690375\pi\)
\(662\) −16.0972 −0.625637
\(663\) 0.0646254 0.00250984
\(664\) 20.1573 0.782257
\(665\) 0 0
\(666\) 8.85111 0.342973
\(667\) −16.5427 −0.640536
\(668\) −17.6406 −0.682534
\(669\) −0.153540 −0.00593620
\(670\) 0 0
\(671\) −24.9811 −0.964385
\(672\) −2.13372 −0.0823100
\(673\) −35.4119 −1.36503 −0.682513 0.730873i \(-0.739113\pi\)
−0.682513 + 0.730873i \(0.739113\pi\)
\(674\) −18.9881 −0.731395
\(675\) 0 0
\(676\) 10.4052 0.400201
\(677\) −17.5836 −0.675791 −0.337896 0.941184i \(-0.609715\pi\)
−0.337896 + 0.941184i \(0.609715\pi\)
\(678\) 2.12113 0.0814615
\(679\) −21.8361 −0.837994
\(680\) 0 0
\(681\) −5.30784 −0.203397
\(682\) 28.6990 1.09894
\(683\) 29.9328 1.14535 0.572674 0.819783i \(-0.305906\pi\)
0.572674 + 0.819783i \(0.305906\pi\)
\(684\) 18.4792 0.706570
\(685\) 0 0
\(686\) −22.0035 −0.840098
\(687\) 4.06807 0.155207
\(688\) −18.8818 −0.719861
\(689\) −0.00425606 −0.000162143 0
\(690\) 0 0
\(691\) 13.2291 0.503260 0.251630 0.967823i \(-0.419033\pi\)
0.251630 + 0.967823i \(0.419033\pi\)
\(692\) 14.4891 0.550793
\(693\) −21.1475 −0.803328
\(694\) 15.3040 0.580933
\(695\) 0 0
\(696\) 4.48770 0.170106
\(697\) 33.3992 1.26509
\(698\) −19.9598 −0.755488
\(699\) −0.380411 −0.0143884
\(700\) 0 0
\(701\) 15.9444 0.602214 0.301107 0.953590i \(-0.402644\pi\)
0.301107 + 0.953590i \(0.402644\pi\)
\(702\) −0.0948228 −0.00357885
\(703\) 21.4367 0.808502
\(704\) −25.7324 −0.969825
\(705\) 0 0
\(706\) −27.5483 −1.03679
\(707\) 37.3046 1.40298
\(708\) 2.13474 0.0802283
\(709\) 37.1049 1.39351 0.696753 0.717312i \(-0.254628\pi\)
0.696753 + 0.717312i \(0.254628\pi\)
\(710\) 0 0
\(711\) 2.14014 0.0802617
\(712\) −33.1753 −1.24330
\(713\) 20.9492 0.784552
\(714\) 2.46521 0.0922583
\(715\) 0 0
\(716\) 13.9420 0.521037
\(717\) −1.04765 −0.0391254
\(718\) 6.62773 0.247345
\(719\) 5.70240 0.212664 0.106332 0.994331i \(-0.466089\pi\)
0.106332 + 0.994331i \(0.466089\pi\)
\(720\) 0 0
\(721\) 24.4392 0.910163
\(722\) −46.2326 −1.72060
\(723\) −0.223927 −0.00832793
\(724\) −5.36306 −0.199317
\(725\) 0 0
\(726\) −0.237890 −0.00882891
\(727\) 5.81600 0.215703 0.107852 0.994167i \(-0.465603\pi\)
0.107852 + 0.994167i \(0.465603\pi\)
\(728\) −0.451201 −0.0167226
\(729\) −24.3299 −0.901106
\(730\) 0 0
\(731\) −47.7075 −1.76453
\(732\) 1.41422 0.0522712
\(733\) −43.9492 −1.62330 −0.811651 0.584143i \(-0.801431\pi\)
−0.811651 + 0.584143i \(0.801431\pi\)
\(734\) 34.2840 1.26545
\(735\) 0 0
\(736\) −10.6572 −0.392828
\(737\) −42.3168 −1.55876
\(738\) −24.2963 −0.894359
\(739\) −22.5626 −0.829979 −0.414989 0.909826i \(-0.636215\pi\)
−0.414989 + 0.909826i \(0.636215\pi\)
\(740\) 0 0
\(741\) −0.113859 −0.00418272
\(742\) −0.162353 −0.00596015
\(743\) −7.18672 −0.263655 −0.131828 0.991273i \(-0.542085\pi\)
−0.131828 + 0.991273i \(0.542085\pi\)
\(744\) −5.68309 −0.208352
\(745\) 0 0
\(746\) 19.1715 0.701919
\(747\) −19.3866 −0.709320
\(748\) −11.2607 −0.411733
\(749\) 3.78855 0.138431
\(750\) 0 0
\(751\) 30.0828 1.09774 0.548868 0.835909i \(-0.315059\pi\)
0.548868 + 0.835909i \(0.315059\pi\)
\(752\) 14.9931 0.546742
\(753\) 1.44381 0.0526154
\(754\) 0.465036 0.0169356
\(755\) 0 0
\(756\) 2.41475 0.0878235
\(757\) 6.52000 0.236973 0.118487 0.992956i \(-0.462196\pi\)
0.118487 + 0.992956i \(0.462196\pi\)
\(758\) −0.624185 −0.0226714
\(759\) 1.79546 0.0651711
\(760\) 0 0
\(761\) 14.1010 0.511162 0.255581 0.966788i \(-0.417733\pi\)
0.255581 + 0.966788i \(0.417733\pi\)
\(762\) −1.48637 −0.0538456
\(763\) 38.3902 1.38982
\(764\) −14.5885 −0.527793
\(765\) 0 0
\(766\) 26.3122 0.950699
\(767\) 0.773780 0.0279396
\(768\) 3.52132 0.127065
\(769\) 18.1800 0.655589 0.327795 0.944749i \(-0.393695\pi\)
0.327795 + 0.944749i \(0.393695\pi\)
\(770\) 0 0
\(771\) −3.36169 −0.121068
\(772\) −4.70950 −0.169499
\(773\) −43.7032 −1.57190 −0.785948 0.618293i \(-0.787825\pi\)
−0.785948 + 0.618293i \(0.787825\pi\)
\(774\) 34.7049 1.24744
\(775\) 0 0
\(776\) 29.5868 1.06210
\(777\) 1.38881 0.0498232
\(778\) 14.8742 0.533266
\(779\) −58.8439 −2.10830
\(780\) 0 0
\(781\) 27.1123 0.970155
\(782\) 12.3129 0.440307
\(783\) −8.70561 −0.311113
\(784\) 3.29708 0.117753
\(785\) 0 0
\(786\) −1.60407 −0.0572153
\(787\) −20.3278 −0.724608 −0.362304 0.932060i \(-0.618010\pi\)
−0.362304 + 0.932060i \(0.618010\pi\)
\(788\) 14.7321 0.524808
\(789\) 2.49826 0.0889405
\(790\) 0 0
\(791\) −19.5794 −0.696164
\(792\) 28.6538 1.01817
\(793\) 0.512615 0.0182035
\(794\) 10.4359 0.370358
\(795\) 0 0
\(796\) −9.50343 −0.336840
\(797\) 8.91772 0.315882 0.157941 0.987449i \(-0.449514\pi\)
0.157941 + 0.987449i \(0.449514\pi\)
\(798\) −4.34329 −0.153751
\(799\) 37.8822 1.34018
\(800\) 0 0
\(801\) 31.9069 1.12737
\(802\) −10.9362 −0.386170
\(803\) −52.6789 −1.85900
\(804\) 2.39563 0.0844872
\(805\) 0 0
\(806\) −0.588906 −0.0207433
\(807\) 3.02470 0.106475
\(808\) −50.5457 −1.77819
\(809\) −23.4279 −0.823680 −0.411840 0.911256i \(-0.635114\pi\)
−0.411840 + 0.911256i \(0.635114\pi\)
\(810\) 0 0
\(811\) 17.8208 0.625774 0.312887 0.949790i \(-0.398704\pi\)
0.312887 + 0.949790i \(0.398704\pi\)
\(812\) −11.8426 −0.415592
\(813\) −2.93314 −0.102870
\(814\) 9.50267 0.333069
\(815\) 0 0
\(816\) −1.74782 −0.0611861
\(817\) 84.0527 2.94063
\(818\) 2.03360 0.0711033
\(819\) 0.433950 0.0151634
\(820\) 0 0
\(821\) 33.2196 1.15937 0.579686 0.814840i \(-0.303175\pi\)
0.579686 + 0.814840i \(0.303175\pi\)
\(822\) 1.99733 0.0696647
\(823\) −13.2155 −0.460663 −0.230331 0.973112i \(-0.573981\pi\)
−0.230331 + 0.973112i \(0.573981\pi\)
\(824\) −33.1138 −1.15357
\(825\) 0 0
\(826\) 29.5168 1.02702
\(827\) −47.8885 −1.66525 −0.832623 0.553840i \(-0.813162\pi\)
−0.832623 + 0.553840i \(0.813162\pi\)
\(828\) 5.97958 0.207805
\(829\) 50.0186 1.73722 0.868609 0.495498i \(-0.165015\pi\)
0.868609 + 0.495498i \(0.165015\pi\)
\(830\) 0 0
\(831\) 3.23544 0.112236
\(832\) 0.528031 0.0183062
\(833\) 8.33054 0.288636
\(834\) −1.56666 −0.0542491
\(835\) 0 0
\(836\) 19.8395 0.686164
\(837\) 11.0245 0.381063
\(838\) 10.4430 0.360747
\(839\) −23.0264 −0.794958 −0.397479 0.917611i \(-0.630115\pi\)
−0.397479 + 0.917611i \(0.630115\pi\)
\(840\) 0 0
\(841\) 13.6946 0.472227
\(842\) 23.1975 0.799438
\(843\) −0.397845 −0.0137025
\(844\) −13.8816 −0.477826
\(845\) 0 0
\(846\) −27.5575 −0.947446
\(847\) 2.19588 0.0754512
\(848\) 0.115107 0.00395280
\(849\) 4.13166 0.141798
\(850\) 0 0
\(851\) 6.93659 0.237783
\(852\) −1.53488 −0.0525840
\(853\) 39.2071 1.34243 0.671213 0.741265i \(-0.265774\pi\)
0.671213 + 0.741265i \(0.265774\pi\)
\(854\) 19.5543 0.669135
\(855\) 0 0
\(856\) −5.13328 −0.175452
\(857\) 36.7331 1.25478 0.627389 0.778706i \(-0.284124\pi\)
0.627389 + 0.778706i \(0.284124\pi\)
\(858\) −0.0504725 −0.00172310
\(859\) −47.6475 −1.62571 −0.812856 0.582465i \(-0.802088\pi\)
−0.812856 + 0.582465i \(0.802088\pi\)
\(860\) 0 0
\(861\) −3.81228 −0.129922
\(862\) 39.1139 1.33223
\(863\) 35.6174 1.21243 0.606215 0.795301i \(-0.292687\pi\)
0.606215 + 0.795301i \(0.292687\pi\)
\(864\) −5.60834 −0.190800
\(865\) 0 0
\(866\) 12.9579 0.440328
\(867\) −0.609373 −0.0206954
\(868\) 14.9970 0.509033
\(869\) 2.29769 0.0779438
\(870\) 0 0
\(871\) 0.868345 0.0294228
\(872\) −52.0166 −1.76150
\(873\) −28.4556 −0.963075
\(874\) −21.6932 −0.733784
\(875\) 0 0
\(876\) 2.98224 0.100761
\(877\) −39.1576 −1.32226 −0.661129 0.750272i \(-0.729922\pi\)
−0.661129 + 0.750272i \(0.729922\pi\)
\(878\) −2.31912 −0.0782664
\(879\) −1.93785 −0.0653621
\(880\) 0 0
\(881\) −30.9027 −1.04114 −0.520569 0.853820i \(-0.674280\pi\)
−0.520569 + 0.853820i \(0.674280\pi\)
\(882\) −6.06006 −0.204053
\(883\) 9.36408 0.315126 0.157563 0.987509i \(-0.449636\pi\)
0.157563 + 0.987509i \(0.449636\pi\)
\(884\) 0.231071 0.00777177
\(885\) 0 0
\(886\) 29.3581 0.986304
\(887\) −48.6485 −1.63346 −0.816728 0.577023i \(-0.804214\pi\)
−0.816728 + 0.577023i \(0.804214\pi\)
\(888\) −1.88176 −0.0631477
\(889\) 13.7202 0.460161
\(890\) 0 0
\(891\) −27.0818 −0.907274
\(892\) −0.548991 −0.0183816
\(893\) −66.7422 −2.23344
\(894\) 2.27859 0.0762074
\(895\) 0 0
\(896\) 1.08510 0.0362508
\(897\) −0.0368431 −0.00123015
\(898\) 39.0207 1.30214
\(899\) −54.0671 −1.80324
\(900\) 0 0
\(901\) 0.290835 0.00968913
\(902\) −26.0849 −0.868531
\(903\) 5.44546 0.181214
\(904\) 26.5290 0.882343
\(905\) 0 0
\(906\) −1.08990 −0.0362095
\(907\) −42.3130 −1.40498 −0.702489 0.711694i \(-0.747928\pi\)
−0.702489 + 0.711694i \(0.747928\pi\)
\(908\) −18.9785 −0.629822
\(909\) 48.6131 1.61240
\(910\) 0 0
\(911\) 2.03059 0.0672763 0.0336382 0.999434i \(-0.489291\pi\)
0.0336382 + 0.999434i \(0.489291\pi\)
\(912\) 3.07938 0.101968
\(913\) −20.8138 −0.688836
\(914\) −4.78931 −0.158416
\(915\) 0 0
\(916\) 14.5456 0.480601
\(917\) 14.8066 0.488958
\(918\) 6.47965 0.213860
\(919\) −24.5581 −0.810097 −0.405048 0.914295i \(-0.632745\pi\)
−0.405048 + 0.914295i \(0.632745\pi\)
\(920\) 0 0
\(921\) −1.48048 −0.0487833
\(922\) −2.55021 −0.0839866
\(923\) −0.556348 −0.0183124
\(924\) 1.28533 0.0422842
\(925\) 0 0
\(926\) −26.6868 −0.876983
\(927\) 31.8477 1.04602
\(928\) 27.5048 0.902888
\(929\) 6.26058 0.205403 0.102702 0.994712i \(-0.467251\pi\)
0.102702 + 0.994712i \(0.467251\pi\)
\(930\) 0 0
\(931\) −14.6770 −0.481020
\(932\) −1.36018 −0.0445541
\(933\) 4.34881 0.142374
\(934\) 46.0559 1.50700
\(935\) 0 0
\(936\) −0.587979 −0.0192187
\(937\) −21.1381 −0.690552 −0.345276 0.938501i \(-0.612215\pi\)
−0.345276 + 0.938501i \(0.612215\pi\)
\(938\) 33.1241 1.08154
\(939\) 4.35577 0.142145
\(940\) 0 0
\(941\) −3.32725 −0.108465 −0.0542327 0.998528i \(-0.517271\pi\)
−0.0542327 + 0.998528i \(0.517271\pi\)
\(942\) 0.0638790 0.00208129
\(943\) −19.0410 −0.620059
\(944\) −20.9272 −0.681124
\(945\) 0 0
\(946\) 37.2597 1.21142
\(947\) −3.04446 −0.0989318 −0.0494659 0.998776i \(-0.515752\pi\)
−0.0494659 + 0.998776i \(0.515752\pi\)
\(948\) −0.130076 −0.00422468
\(949\) 1.08098 0.0350900
\(950\) 0 0
\(951\) 0.177489 0.00575546
\(952\) 30.8325 0.999287
\(953\) 9.75807 0.316095 0.158047 0.987432i \(-0.449480\pi\)
0.158047 + 0.987432i \(0.449480\pi\)
\(954\) −0.211568 −0.00684978
\(955\) 0 0
\(956\) −3.74594 −0.121152
\(957\) −4.63385 −0.149791
\(958\) 33.2010 1.07267
\(959\) −18.4366 −0.595350
\(960\) 0 0
\(961\) 37.4688 1.20867
\(962\) −0.194996 −0.00628692
\(963\) 4.93702 0.159093
\(964\) −0.800662 −0.0257876
\(965\) 0 0
\(966\) −1.40542 −0.0452187
\(967\) −8.16066 −0.262429 −0.131215 0.991354i \(-0.541888\pi\)
−0.131215 + 0.991354i \(0.541888\pi\)
\(968\) −2.97529 −0.0956296
\(969\) 7.78049 0.249945
\(970\) 0 0
\(971\) 16.0914 0.516398 0.258199 0.966092i \(-0.416871\pi\)
0.258199 + 0.966092i \(0.416871\pi\)
\(972\) 4.73340 0.151824
\(973\) 14.4613 0.463609
\(974\) 17.9733 0.575902
\(975\) 0 0
\(976\) −13.8639 −0.443774
\(977\) 23.1058 0.739220 0.369610 0.929187i \(-0.379491\pi\)
0.369610 + 0.929187i \(0.379491\pi\)
\(978\) −1.32920 −0.0425030
\(979\) 34.2557 1.09482
\(980\) 0 0
\(981\) 50.0278 1.59727
\(982\) 0.614436 0.0196074
\(983\) 44.1346 1.40768 0.703838 0.710361i \(-0.251468\pi\)
0.703838 + 0.710361i \(0.251468\pi\)
\(984\) 5.16543 0.164668
\(985\) 0 0
\(986\) −31.7779 −1.01201
\(987\) −4.32398 −0.137634
\(988\) −0.407110 −0.0129519
\(989\) 27.1981 0.864851
\(990\) 0 0
\(991\) −5.42300 −0.172267 −0.0861337 0.996284i \(-0.527451\pi\)
−0.0861337 + 0.996284i \(0.527451\pi\)
\(992\) −34.8312 −1.10589
\(993\) −3.29145 −0.104451
\(994\) −21.2226 −0.673139
\(995\) 0 0
\(996\) 1.17830 0.0373360
\(997\) −56.5705 −1.79161 −0.895803 0.444451i \(-0.853399\pi\)
−0.895803 + 0.444451i \(0.853399\pi\)
\(998\) 42.8310 1.35579
\(999\) 3.65039 0.115493
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.1.15 46
5.2 odd 4 1205.2.b.c.724.15 46
5.3 odd 4 1205.2.b.c.724.32 yes 46
5.4 even 2 inner 6025.2.a.p.1.32 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.15 46 5.2 odd 4
1205.2.b.c.724.32 yes 46 5.3 odd 4
6025.2.a.p.1.15 46 1.1 even 1 trivial
6025.2.a.p.1.32 46 5.4 even 2 inner