Properties

Label 6025.2.a.f.1.7
Level 6025
Weight 2
Character 6025.1
Self dual yes
Analytic conductor 48.110
Analytic rank 1
Dimension 7
CM no
Inner twists 1

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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: \(7\)
Coefficient field: 7.7.31056073.1
Defining polynomial: \(x^{7} - 3 x^{6} - 3 x^{5} + 11 x^{4} + x^{3} - 9 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 241)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.60363\) of defining polynomial
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.60363 q^{2} -0.980039 q^{3} +4.77887 q^{4} -2.55166 q^{6} +1.30586 q^{7} +7.23513 q^{8} -2.03952 q^{9} +O(q^{10})\) \(q+2.60363 q^{2} -0.980039 q^{3} +4.77887 q^{4} -2.55166 q^{6} +1.30586 q^{7} +7.23513 q^{8} -2.03952 q^{9} -3.27094 q^{11} -4.68348 q^{12} -4.30649 q^{13} +3.39998 q^{14} +9.27984 q^{16} +1.02456 q^{17} -5.31016 q^{18} -7.01250 q^{19} -1.27980 q^{21} -8.51631 q^{22} -0.835873 q^{23} -7.09071 q^{24} -11.2125 q^{26} +4.93893 q^{27} +6.24054 q^{28} -1.11761 q^{29} -3.97344 q^{31} +9.69098 q^{32} +3.20565 q^{33} +2.66758 q^{34} -9.74661 q^{36} +11.3098 q^{37} -18.2579 q^{38} +4.22053 q^{39} +1.22869 q^{41} -3.33211 q^{42} -10.8406 q^{43} -15.6314 q^{44} -2.17630 q^{46} +0.151820 q^{47} -9.09461 q^{48} -5.29473 q^{49} -1.00411 q^{51} -20.5801 q^{52} -3.02053 q^{53} +12.8591 q^{54} +9.44808 q^{56} +6.87252 q^{57} -2.90984 q^{58} -4.15373 q^{59} +5.62714 q^{61} -10.3454 q^{62} -2.66334 q^{63} +6.67199 q^{64} +8.34632 q^{66} -12.9934 q^{67} +4.89626 q^{68} +0.819188 q^{69} -11.2862 q^{71} -14.7562 q^{72} -11.7148 q^{73} +29.4464 q^{74} -33.5118 q^{76} -4.27140 q^{77} +10.9887 q^{78} -1.66517 q^{79} +1.27823 q^{81} +3.19906 q^{82} +2.34322 q^{83} -6.11597 q^{84} -28.2250 q^{86} +1.09530 q^{87} -23.6657 q^{88} +18.1099 q^{89} -5.62368 q^{91} -3.99453 q^{92} +3.89413 q^{93} +0.395283 q^{94} -9.49754 q^{96} +7.17873 q^{97} -13.7855 q^{98} +6.67116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} + 3q^{3} + 2q^{4} - 5q^{6} + 7q^{7} + 6q^{8} - 2q^{9} + O(q^{10}) \) \( 7q + 4q^{2} + 3q^{3} + 2q^{4} - 5q^{6} + 7q^{7} + 6q^{8} - 2q^{9} - 18q^{11} - q^{12} + q^{13} - 6q^{14} + 4q^{16} + 2q^{17} - 8q^{18} - 6q^{19} - 2q^{21} - 10q^{22} + 22q^{23} - 3q^{24} + 8q^{26} - 3q^{27} - 9q^{28} - 16q^{29} - 18q^{31} + 6q^{32} - 4q^{33} + 11q^{34} - 7q^{36} - 8q^{37} - 16q^{38} - 9q^{39} - 15q^{41} - 19q^{42} - 14q^{43} - 4q^{44} + 11q^{46} + 10q^{47} - 31q^{48} + 6q^{49} + 13q^{51} - 27q^{52} - 15q^{53} + 16q^{54} + 13q^{56} - 14q^{57} - 17q^{58} - 18q^{59} + 4q^{61} - 13q^{62} + 16q^{63} + 2q^{64} + 16q^{66} - 18q^{67} + 15q^{68} + 26q^{69} - 50q^{71} - 30q^{72} + 10q^{74} - 20q^{76} - 17q^{77} + 32q^{78} - 15q^{79} - 9q^{81} - 45q^{82} + 24q^{83} + 6q^{84} - 23q^{86} - 12q^{87} - 8q^{88} - 13q^{89} - 12q^{91} + 10q^{92} - 14q^{93} - 32q^{94} - 15q^{96} - q^{97} - 9q^{98} - 20q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.60363 1.84104 0.920521 0.390694i \(-0.127765\pi\)
0.920521 + 0.390694i \(0.127765\pi\)
\(3\) −0.980039 −0.565826 −0.282913 0.959146i \(-0.591301\pi\)
−0.282913 + 0.959146i \(0.591301\pi\)
\(4\) 4.77887 2.38943
\(5\) 0 0
\(6\) −2.55166 −1.04171
\(7\) 1.30586 0.493569 0.246785 0.969070i \(-0.420626\pi\)
0.246785 + 0.969070i \(0.420626\pi\)
\(8\) 7.23513 2.55801
\(9\) −2.03952 −0.679841
\(10\) 0 0
\(11\) −3.27094 −0.986226 −0.493113 0.869965i \(-0.664141\pi\)
−0.493113 + 0.869965i \(0.664141\pi\)
\(12\) −4.68348 −1.35200
\(13\) −4.30649 −1.19441 −0.597203 0.802090i \(-0.703721\pi\)
−0.597203 + 0.802090i \(0.703721\pi\)
\(14\) 3.39998 0.908682
\(15\) 0 0
\(16\) 9.27984 2.31996
\(17\) 1.02456 0.248493 0.124247 0.992251i \(-0.460349\pi\)
0.124247 + 0.992251i \(0.460349\pi\)
\(18\) −5.31016 −1.25162
\(19\) −7.01250 −1.60878 −0.804388 0.594104i \(-0.797507\pi\)
−0.804388 + 0.594104i \(0.797507\pi\)
\(20\) 0 0
\(21\) −1.27980 −0.279274
\(22\) −8.51631 −1.81568
\(23\) −0.835873 −0.174292 −0.0871458 0.996196i \(-0.527775\pi\)
−0.0871458 + 0.996196i \(0.527775\pi\)
\(24\) −7.09071 −1.44739
\(25\) 0 0
\(26\) −11.2125 −2.19895
\(27\) 4.93893 0.950498
\(28\) 6.24054 1.17935
\(29\) −1.11761 −0.207535 −0.103767 0.994602i \(-0.533090\pi\)
−0.103767 + 0.994602i \(0.533090\pi\)
\(30\) 0 0
\(31\) −3.97344 −0.713652 −0.356826 0.934171i \(-0.616141\pi\)
−0.356826 + 0.934171i \(0.616141\pi\)
\(32\) 9.69098 1.71314
\(33\) 3.20565 0.558032
\(34\) 2.66758 0.457486
\(35\) 0 0
\(36\) −9.74661 −1.62444
\(37\) 11.3098 1.85932 0.929658 0.368423i \(-0.120102\pi\)
0.929658 + 0.368423i \(0.120102\pi\)
\(38\) −18.2579 −2.96182
\(39\) 4.22053 0.675825
\(40\) 0 0
\(41\) 1.22869 0.191890 0.0959448 0.995387i \(-0.469413\pi\)
0.0959448 + 0.995387i \(0.469413\pi\)
\(42\) −3.33211 −0.514156
\(43\) −10.8406 −1.65318 −0.826591 0.562804i \(-0.809723\pi\)
−0.826591 + 0.562804i \(0.809723\pi\)
\(44\) −15.6314 −2.35652
\(45\) 0 0
\(46\) −2.17630 −0.320878
\(47\) 0.151820 0.0221453 0.0110726 0.999939i \(-0.496475\pi\)
0.0110726 + 0.999939i \(0.496475\pi\)
\(48\) −9.09461 −1.31269
\(49\) −5.29473 −0.756389
\(50\) 0 0
\(51\) −1.00411 −0.140604
\(52\) −20.5801 −2.85395
\(53\) −3.02053 −0.414902 −0.207451 0.978245i \(-0.566517\pi\)
−0.207451 + 0.978245i \(0.566517\pi\)
\(54\) 12.8591 1.74991
\(55\) 0 0
\(56\) 9.44808 1.26255
\(57\) 6.87252 0.910287
\(58\) −2.90984 −0.382080
\(59\) −4.15373 −0.540769 −0.270385 0.962752i \(-0.587151\pi\)
−0.270385 + 0.962752i \(0.587151\pi\)
\(60\) 0 0
\(61\) 5.62714 0.720482 0.360241 0.932859i \(-0.382694\pi\)
0.360241 + 0.932859i \(0.382694\pi\)
\(62\) −10.3454 −1.31386
\(63\) −2.66334 −0.335549
\(64\) 6.67199 0.833999
\(65\) 0 0
\(66\) 8.34632 1.02736
\(67\) −12.9934 −1.58740 −0.793700 0.608309i \(-0.791848\pi\)
−0.793700 + 0.608309i \(0.791848\pi\)
\(68\) 4.89626 0.593758
\(69\) 0.819188 0.0986187
\(70\) 0 0
\(71\) −11.2862 −1.33942 −0.669711 0.742622i \(-0.733582\pi\)
−0.669711 + 0.742622i \(0.733582\pi\)
\(72\) −14.7562 −1.73904
\(73\) −11.7148 −1.37112 −0.685560 0.728017i \(-0.740442\pi\)
−0.685560 + 0.728017i \(0.740442\pi\)
\(74\) 29.4464 3.42308
\(75\) 0 0
\(76\) −33.5118 −3.84407
\(77\) −4.27140 −0.486771
\(78\) 10.9887 1.24422
\(79\) −1.66517 −0.187346 −0.0936732 0.995603i \(-0.529861\pi\)
−0.0936732 + 0.995603i \(0.529861\pi\)
\(80\) 0 0
\(81\) 1.27823 0.142025
\(82\) 3.19906 0.353277
\(83\) 2.34322 0.257201 0.128601 0.991696i \(-0.458951\pi\)
0.128601 + 0.991696i \(0.458951\pi\)
\(84\) −6.11597 −0.667308
\(85\) 0 0
\(86\) −28.2250 −3.04358
\(87\) 1.09530 0.117429
\(88\) −23.6657 −2.52277
\(89\) 18.1099 1.91965 0.959825 0.280598i \(-0.0905329\pi\)
0.959825 + 0.280598i \(0.0905329\pi\)
\(90\) 0 0
\(91\) −5.62368 −0.589522
\(92\) −3.99453 −0.416458
\(93\) 3.89413 0.403802
\(94\) 0.395283 0.0407703
\(95\) 0 0
\(96\) −9.49754 −0.969338
\(97\) 7.17873 0.728890 0.364445 0.931225i \(-0.381259\pi\)
0.364445 + 0.931225i \(0.381259\pi\)
\(98\) −13.7855 −1.39254
\(99\) 6.67116 0.670477
\(100\) 0 0
\(101\) −5.48113 −0.545393 −0.272696 0.962100i \(-0.587915\pi\)
−0.272696 + 0.962100i \(0.587915\pi\)
\(102\) −2.61433 −0.258858
\(103\) 15.7371 1.55062 0.775311 0.631580i \(-0.217593\pi\)
0.775311 + 0.631580i \(0.217593\pi\)
\(104\) −31.1580 −3.05530
\(105\) 0 0
\(106\) −7.86433 −0.763851
\(107\) 11.1816 1.08097 0.540483 0.841355i \(-0.318242\pi\)
0.540483 + 0.841355i \(0.318242\pi\)
\(108\) 23.6025 2.27115
\(109\) −0.296424 −0.0283922 −0.0141961 0.999899i \(-0.504519\pi\)
−0.0141961 + 0.999899i \(0.504519\pi\)
\(110\) 0 0
\(111\) −11.0840 −1.05205
\(112\) 12.1182 1.14506
\(113\) −10.5881 −0.996045 −0.498023 0.867164i \(-0.665940\pi\)
−0.498023 + 0.867164i \(0.665940\pi\)
\(114\) 17.8935 1.67588
\(115\) 0 0
\(116\) −5.34091 −0.495891
\(117\) 8.78319 0.812006
\(118\) −10.8147 −0.995578
\(119\) 1.33794 0.122649
\(120\) 0 0
\(121\) −0.300940 −0.0273582
\(122\) 14.6510 1.32644
\(123\) −1.20417 −0.108576
\(124\) −18.9886 −1.70522
\(125\) 0 0
\(126\) −6.93433 −0.617759
\(127\) −14.6989 −1.30432 −0.652160 0.758081i \(-0.726137\pi\)
−0.652160 + 0.758081i \(0.726137\pi\)
\(128\) −2.01059 −0.177713
\(129\) 10.6242 0.935413
\(130\) 0 0
\(131\) 9.63853 0.842122 0.421061 0.907032i \(-0.361658\pi\)
0.421061 + 0.907032i \(0.361658\pi\)
\(132\) 15.3194 1.33338
\(133\) −9.15735 −0.794043
\(134\) −33.8300 −2.92247
\(135\) 0 0
\(136\) 7.41286 0.635647
\(137\) −23.2376 −1.98532 −0.992661 0.120933i \(-0.961411\pi\)
−0.992661 + 0.120933i \(0.961411\pi\)
\(138\) 2.13286 0.181561
\(139\) −1.29376 −0.109736 −0.0548678 0.998494i \(-0.517474\pi\)
−0.0548678 + 0.998494i \(0.517474\pi\)
\(140\) 0 0
\(141\) −0.148790 −0.0125304
\(142\) −29.3850 −2.46593
\(143\) 14.0863 1.17795
\(144\) −18.9265 −1.57720
\(145\) 0 0
\(146\) −30.5011 −2.52429
\(147\) 5.18904 0.427985
\(148\) 54.0480 4.44271
\(149\) 17.5316 1.43625 0.718123 0.695916i \(-0.245002\pi\)
0.718123 + 0.695916i \(0.245002\pi\)
\(150\) 0 0
\(151\) 5.26990 0.428858 0.214429 0.976740i \(-0.431211\pi\)
0.214429 + 0.976740i \(0.431211\pi\)
\(152\) −50.7363 −4.11526
\(153\) −2.08962 −0.168936
\(154\) −11.1211 −0.896166
\(155\) 0 0
\(156\) 20.1693 1.61484
\(157\) 14.2165 1.13460 0.567299 0.823512i \(-0.307988\pi\)
0.567299 + 0.823512i \(0.307988\pi\)
\(158\) −4.33548 −0.344912
\(159\) 2.96024 0.234762
\(160\) 0 0
\(161\) −1.09153 −0.0860250
\(162\) 3.32802 0.261474
\(163\) 15.9688 1.25077 0.625386 0.780315i \(-0.284941\pi\)
0.625386 + 0.780315i \(0.284941\pi\)
\(164\) 5.87176 0.458508
\(165\) 0 0
\(166\) 6.10086 0.473518
\(167\) 21.5275 1.66585 0.832925 0.553386i \(-0.186665\pi\)
0.832925 + 0.553386i \(0.186665\pi\)
\(168\) −9.25949 −0.714385
\(169\) 5.54585 0.426604
\(170\) 0 0
\(171\) 14.3021 1.09371
\(172\) −51.8060 −3.95017
\(173\) 5.82531 0.442890 0.221445 0.975173i \(-0.428923\pi\)
0.221445 + 0.975173i \(0.428923\pi\)
\(174\) 2.85175 0.216191
\(175\) 0 0
\(176\) −30.3538 −2.28801
\(177\) 4.07081 0.305981
\(178\) 47.1515 3.53416
\(179\) −6.03932 −0.451400 −0.225700 0.974197i \(-0.572467\pi\)
−0.225700 + 0.974197i \(0.572467\pi\)
\(180\) 0 0
\(181\) −4.03706 −0.300073 −0.150036 0.988680i \(-0.547939\pi\)
−0.150036 + 0.988680i \(0.547939\pi\)
\(182\) −14.6420 −1.08533
\(183\) −5.51482 −0.407667
\(184\) −6.04765 −0.445839
\(185\) 0 0
\(186\) 10.1389 0.743417
\(187\) −3.35129 −0.245071
\(188\) 0.725529 0.0529146
\(189\) 6.44956 0.469136
\(190\) 0 0
\(191\) −16.4803 −1.19247 −0.596235 0.802810i \(-0.703337\pi\)
−0.596235 + 0.802810i \(0.703337\pi\)
\(192\) −6.53881 −0.471898
\(193\) 23.0631 1.66012 0.830060 0.557674i \(-0.188306\pi\)
0.830060 + 0.557674i \(0.188306\pi\)
\(194\) 18.6907 1.34192
\(195\) 0 0
\(196\) −25.3028 −1.80734
\(197\) 13.5540 0.965680 0.482840 0.875709i \(-0.339605\pi\)
0.482840 + 0.875709i \(0.339605\pi\)
\(198\) 17.3692 1.23438
\(199\) −25.6725 −1.81988 −0.909938 0.414745i \(-0.863871\pi\)
−0.909938 + 0.414745i \(0.863871\pi\)
\(200\) 0 0
\(201\) 12.7341 0.898192
\(202\) −14.2708 −1.00409
\(203\) −1.45944 −0.102433
\(204\) −4.79852 −0.335964
\(205\) 0 0
\(206\) 40.9735 2.85476
\(207\) 1.70478 0.118491
\(208\) −39.9635 −2.77097
\(209\) 22.9375 1.58662
\(210\) 0 0
\(211\) 5.18301 0.356813 0.178407 0.983957i \(-0.442906\pi\)
0.178407 + 0.983957i \(0.442906\pi\)
\(212\) −14.4347 −0.991380
\(213\) 11.0609 0.757879
\(214\) 29.1127 1.99010
\(215\) 0 0
\(216\) 35.7338 2.43138
\(217\) −5.18877 −0.352237
\(218\) −0.771777 −0.0522713
\(219\) 11.4810 0.775815
\(220\) 0 0
\(221\) −4.41227 −0.296802
\(222\) −28.8587 −1.93687
\(223\) 6.50914 0.435884 0.217942 0.975962i \(-0.430066\pi\)
0.217942 + 0.975962i \(0.430066\pi\)
\(224\) 12.6551 0.845553
\(225\) 0 0
\(226\) −27.5675 −1.83376
\(227\) −11.0460 −0.733150 −0.366575 0.930389i \(-0.619470\pi\)
−0.366575 + 0.930389i \(0.619470\pi\)
\(228\) 32.8429 2.17507
\(229\) 8.95679 0.591881 0.295941 0.955206i \(-0.404367\pi\)
0.295941 + 0.955206i \(0.404367\pi\)
\(230\) 0 0
\(231\) 4.18614 0.275428
\(232\) −8.08605 −0.530875
\(233\) 6.46647 0.423632 0.211816 0.977310i \(-0.432062\pi\)
0.211816 + 0.977310i \(0.432062\pi\)
\(234\) 22.8681 1.49494
\(235\) 0 0
\(236\) −19.8501 −1.29213
\(237\) 1.63193 0.106005
\(238\) 3.48349 0.225801
\(239\) −25.0588 −1.62092 −0.810460 0.585794i \(-0.800783\pi\)
−0.810460 + 0.585794i \(0.800783\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) −0.783536 −0.0503676
\(243\) −16.0695 −1.03086
\(244\) 26.8914 1.72154
\(245\) 0 0
\(246\) −3.13520 −0.199893
\(247\) 30.1992 1.92153
\(248\) −28.7484 −1.82552
\(249\) −2.29644 −0.145531
\(250\) 0 0
\(251\) −12.5611 −0.792847 −0.396424 0.918068i \(-0.629749\pi\)
−0.396424 + 0.918068i \(0.629749\pi\)
\(252\) −12.7277 −0.801772
\(253\) 2.73409 0.171891
\(254\) −38.2706 −2.40131
\(255\) 0 0
\(256\) −18.5788 −1.16117
\(257\) −16.0367 −1.00034 −0.500171 0.865927i \(-0.666730\pi\)
−0.500171 + 0.865927i \(0.666730\pi\)
\(258\) 27.6616 1.72213
\(259\) 14.7690 0.917702
\(260\) 0 0
\(261\) 2.27939 0.141091
\(262\) 25.0951 1.55038
\(263\) −3.33210 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(264\) 23.1933 1.42745
\(265\) 0 0
\(266\) −23.8423 −1.46187
\(267\) −17.7485 −1.08619
\(268\) −62.0939 −3.79299
\(269\) −7.44101 −0.453686 −0.226843 0.973931i \(-0.572840\pi\)
−0.226843 + 0.973931i \(0.572840\pi\)
\(270\) 0 0
\(271\) −20.6031 −1.25155 −0.625774 0.780005i \(-0.715217\pi\)
−0.625774 + 0.780005i \(0.715217\pi\)
\(272\) 9.50779 0.576495
\(273\) 5.51143 0.333567
\(274\) −60.5020 −3.65506
\(275\) 0 0
\(276\) 3.91479 0.235643
\(277\) −5.17667 −0.311036 −0.155518 0.987833i \(-0.549705\pi\)
−0.155518 + 0.987833i \(0.549705\pi\)
\(278\) −3.36848 −0.202028
\(279\) 8.10393 0.485170
\(280\) 0 0
\(281\) −14.1821 −0.846031 −0.423015 0.906123i \(-0.639028\pi\)
−0.423015 + 0.906123i \(0.639028\pi\)
\(282\) −0.387393 −0.0230689
\(283\) 7.05196 0.419196 0.209598 0.977788i \(-0.432785\pi\)
0.209598 + 0.977788i \(0.432785\pi\)
\(284\) −53.9351 −3.20046
\(285\) 0 0
\(286\) 36.6754 2.16866
\(287\) 1.60450 0.0947109
\(288\) −19.7650 −1.16466
\(289\) −15.9503 −0.938251
\(290\) 0 0
\(291\) −7.03544 −0.412425
\(292\) −55.9837 −3.27620
\(293\) 2.78966 0.162974 0.0814869 0.996674i \(-0.474033\pi\)
0.0814869 + 0.996674i \(0.474033\pi\)
\(294\) 13.5103 0.787937
\(295\) 0 0
\(296\) 81.8278 4.75614
\(297\) −16.1550 −0.937405
\(298\) 45.6458 2.64419
\(299\) 3.59968 0.208175
\(300\) 0 0
\(301\) −14.1564 −0.815960
\(302\) 13.7208 0.789546
\(303\) 5.37172 0.308597
\(304\) −65.0749 −3.73230
\(305\) 0 0
\(306\) −5.44060 −0.311018
\(307\) −19.8285 −1.13167 −0.565837 0.824517i \(-0.691447\pi\)
−0.565837 + 0.824517i \(0.691447\pi\)
\(308\) −20.4124 −1.16311
\(309\) −15.4230 −0.877382
\(310\) 0 0
\(311\) 33.5109 1.90023 0.950114 0.311902i \(-0.100966\pi\)
0.950114 + 0.311902i \(0.100966\pi\)
\(312\) 30.5361 1.72877
\(313\) −19.4152 −1.09741 −0.548705 0.836016i \(-0.684879\pi\)
−0.548705 + 0.836016i \(0.684879\pi\)
\(314\) 37.0144 2.08884
\(315\) 0 0
\(316\) −7.95763 −0.447652
\(317\) 11.7255 0.658569 0.329284 0.944231i \(-0.393193\pi\)
0.329284 + 0.944231i \(0.393193\pi\)
\(318\) 7.70735 0.432207
\(319\) 3.65564 0.204676
\(320\) 0 0
\(321\) −10.9584 −0.611638
\(322\) −2.84195 −0.158376
\(323\) −7.18475 −0.399770
\(324\) 6.10847 0.339359
\(325\) 0 0
\(326\) 41.5768 2.30272
\(327\) 0.290507 0.0160651
\(328\) 8.88976 0.490855
\(329\) 0.198256 0.0109302
\(330\) 0 0
\(331\) 4.93072 0.271017 0.135509 0.990776i \(-0.456733\pi\)
0.135509 + 0.990776i \(0.456733\pi\)
\(332\) 11.1979 0.614566
\(333\) −23.0666 −1.26404
\(334\) 56.0496 3.06690
\(335\) 0 0
\(336\) −11.8763 −0.647905
\(337\) −34.4425 −1.87620 −0.938100 0.346364i \(-0.887416\pi\)
−0.938100 + 0.346364i \(0.887416\pi\)
\(338\) 14.4393 0.785395
\(339\) 10.3768 0.563588
\(340\) 0 0
\(341\) 12.9969 0.703822
\(342\) 37.2374 2.01357
\(343\) −16.0552 −0.866900
\(344\) −78.4334 −4.22885
\(345\) 0 0
\(346\) 15.1669 0.815378
\(347\) 23.4553 1.25915 0.629574 0.776940i \(-0.283229\pi\)
0.629574 + 0.776940i \(0.283229\pi\)
\(348\) 5.23430 0.280588
\(349\) 15.8727 0.849648 0.424824 0.905276i \(-0.360336\pi\)
0.424824 + 0.905276i \(0.360336\pi\)
\(350\) 0 0
\(351\) −21.2694 −1.13528
\(352\) −31.6986 −1.68954
\(353\) 28.4598 1.51476 0.757382 0.652972i \(-0.226478\pi\)
0.757382 + 0.652972i \(0.226478\pi\)
\(354\) 10.5989 0.563324
\(355\) 0 0
\(356\) 86.5450 4.58688
\(357\) −1.31123 −0.0693978
\(358\) −15.7241 −0.831047
\(359\) −0.772338 −0.0407625 −0.0203812 0.999792i \(-0.506488\pi\)
−0.0203812 + 0.999792i \(0.506488\pi\)
\(360\) 0 0
\(361\) 30.1751 1.58816
\(362\) −10.5110 −0.552446
\(363\) 0.294933 0.0154800
\(364\) −26.8748 −1.40862
\(365\) 0 0
\(366\) −14.3585 −0.750532
\(367\) 23.3631 1.21954 0.609772 0.792577i \(-0.291261\pi\)
0.609772 + 0.792577i \(0.291261\pi\)
\(368\) −7.75677 −0.404350
\(369\) −2.50595 −0.130454
\(370\) 0 0
\(371\) −3.94439 −0.204783
\(372\) 18.6095 0.964859
\(373\) −27.7831 −1.43855 −0.719277 0.694724i \(-0.755527\pi\)
−0.719277 + 0.694724i \(0.755527\pi\)
\(374\) −8.72550 −0.451185
\(375\) 0 0
\(376\) 1.09844 0.0566477
\(377\) 4.81297 0.247881
\(378\) 16.7922 0.863700
\(379\) 7.33328 0.376685 0.188343 0.982103i \(-0.439688\pi\)
0.188343 + 0.982103i \(0.439688\pi\)
\(380\) 0 0
\(381\) 14.4055 0.738018
\(382\) −42.9084 −2.19539
\(383\) 33.4931 1.71142 0.855708 0.517459i \(-0.173122\pi\)
0.855708 + 0.517459i \(0.173122\pi\)
\(384\) 1.97046 0.100554
\(385\) 0 0
\(386\) 60.0477 3.05635
\(387\) 22.1097 1.12390
\(388\) 34.3062 1.74163
\(389\) 15.6882 0.795425 0.397713 0.917510i \(-0.369804\pi\)
0.397713 + 0.917510i \(0.369804\pi\)
\(390\) 0 0
\(391\) −0.856405 −0.0433103
\(392\) −38.3080 −1.93485
\(393\) −9.44613 −0.476494
\(394\) 35.2894 1.77786
\(395\) 0 0
\(396\) 31.8806 1.60206
\(397\) −8.34483 −0.418815 −0.209408 0.977828i \(-0.567154\pi\)
−0.209408 + 0.977828i \(0.567154\pi\)
\(398\) −66.8416 −3.35047
\(399\) 8.97456 0.449290
\(400\) 0 0
\(401\) −38.5766 −1.92642 −0.963211 0.268747i \(-0.913391\pi\)
−0.963211 + 0.268747i \(0.913391\pi\)
\(402\) 33.1548 1.65361
\(403\) 17.1116 0.852389
\(404\) −26.1936 −1.30318
\(405\) 0 0
\(406\) −3.79985 −0.188583
\(407\) −36.9936 −1.83371
\(408\) −7.26489 −0.359666
\(409\) −19.5415 −0.966266 −0.483133 0.875547i \(-0.660501\pi\)
−0.483133 + 0.875547i \(0.660501\pi\)
\(410\) 0 0
\(411\) 22.7737 1.12335
\(412\) 75.2055 3.70511
\(413\) −5.42419 −0.266907
\(414\) 4.43862 0.218146
\(415\) 0 0
\(416\) −41.7341 −2.04618
\(417\) 1.26794 0.0620912
\(418\) 59.7206 2.92103
\(419\) −29.7748 −1.45459 −0.727297 0.686323i \(-0.759224\pi\)
−0.727297 + 0.686323i \(0.759224\pi\)
\(420\) 0 0
\(421\) −4.78920 −0.233411 −0.116706 0.993167i \(-0.537233\pi\)
−0.116706 + 0.993167i \(0.537233\pi\)
\(422\) 13.4946 0.656908
\(423\) −0.309641 −0.0150553
\(424\) −21.8539 −1.06132
\(425\) 0 0
\(426\) 28.7984 1.39529
\(427\) 7.34827 0.355608
\(428\) 53.4354 2.58290
\(429\) −13.8051 −0.666517
\(430\) 0 0
\(431\) 5.35939 0.258153 0.129076 0.991635i \(-0.458799\pi\)
0.129076 + 0.991635i \(0.458799\pi\)
\(432\) 45.8325 2.20512
\(433\) −21.5028 −1.03336 −0.516680 0.856179i \(-0.672832\pi\)
−0.516680 + 0.856179i \(0.672832\pi\)
\(434\) −13.5096 −0.648482
\(435\) 0 0
\(436\) −1.41657 −0.0678414
\(437\) 5.86156 0.280396
\(438\) 29.8923 1.42831
\(439\) 4.22306 0.201556 0.100778 0.994909i \(-0.467867\pi\)
0.100778 + 0.994909i \(0.467867\pi\)
\(440\) 0 0
\(441\) 10.7987 0.514225
\(442\) −11.4879 −0.546424
\(443\) −8.34030 −0.396260 −0.198130 0.980176i \(-0.563487\pi\)
−0.198130 + 0.980176i \(0.563487\pi\)
\(444\) −52.9691 −2.51380
\(445\) 0 0
\(446\) 16.9474 0.802481
\(447\) −17.1817 −0.812665
\(448\) 8.71269 0.411636
\(449\) 15.7796 0.744684 0.372342 0.928096i \(-0.378555\pi\)
0.372342 + 0.928096i \(0.378555\pi\)
\(450\) 0 0
\(451\) −4.01898 −0.189247
\(452\) −50.5992 −2.37998
\(453\) −5.16470 −0.242659
\(454\) −28.7597 −1.34976
\(455\) 0 0
\(456\) 49.7236 2.32852
\(457\) 8.71419 0.407633 0.203816 0.979009i \(-0.434665\pi\)
0.203816 + 0.979009i \(0.434665\pi\)
\(458\) 23.3201 1.08968
\(459\) 5.06025 0.236192
\(460\) 0 0
\(461\) 24.9140 1.16036 0.580181 0.814487i \(-0.302982\pi\)
0.580181 + 0.814487i \(0.302982\pi\)
\(462\) 10.8991 0.507074
\(463\) 2.87272 0.133507 0.0667534 0.997770i \(-0.478736\pi\)
0.0667534 + 0.997770i \(0.478736\pi\)
\(464\) −10.3712 −0.481473
\(465\) 0 0
\(466\) 16.8363 0.779925
\(467\) −4.87474 −0.225576 −0.112788 0.993619i \(-0.535978\pi\)
−0.112788 + 0.993619i \(0.535978\pi\)
\(468\) 41.9737 1.94023
\(469\) −16.9676 −0.783492
\(470\) 0 0
\(471\) −13.9327 −0.641985
\(472\) −30.0528 −1.38329
\(473\) 35.4591 1.63041
\(474\) 4.24894 0.195160
\(475\) 0 0
\(476\) 6.39383 0.293061
\(477\) 6.16044 0.282067
\(478\) −65.2438 −2.98418
\(479\) 0.194055 0.00886661 0.00443331 0.999990i \(-0.498589\pi\)
0.00443331 + 0.999990i \(0.498589\pi\)
\(480\) 0 0
\(481\) −48.7055 −2.22078
\(482\) −2.60363 −0.118592
\(483\) 1.06975 0.0486752
\(484\) −1.43815 −0.0653707
\(485\) 0 0
\(486\) −41.8390 −1.89785
\(487\) 30.7592 1.39383 0.696915 0.717154i \(-0.254555\pi\)
0.696915 + 0.717154i \(0.254555\pi\)
\(488\) 40.7131 1.84300
\(489\) −15.6500 −0.707719
\(490\) 0 0
\(491\) −21.5528 −0.972663 −0.486332 0.873774i \(-0.661665\pi\)
−0.486332 + 0.873774i \(0.661665\pi\)
\(492\) −5.75456 −0.259436
\(493\) −1.14506 −0.0515710
\(494\) 78.6275 3.53762
\(495\) 0 0
\(496\) −36.8729 −1.65564
\(497\) −14.7382 −0.661097
\(498\) −5.97908 −0.267929
\(499\) 21.8992 0.980341 0.490170 0.871627i \(-0.336935\pi\)
0.490170 + 0.871627i \(0.336935\pi\)
\(500\) 0 0
\(501\) −21.0978 −0.942581
\(502\) −32.7043 −1.45966
\(503\) −4.44114 −0.198021 −0.0990104 0.995086i \(-0.531568\pi\)
−0.0990104 + 0.995086i \(0.531568\pi\)
\(504\) −19.2696 −0.858336
\(505\) 0 0
\(506\) 7.11855 0.316458
\(507\) −5.43515 −0.241383
\(508\) −70.2443 −3.11659
\(509\) 29.6966 1.31628 0.658140 0.752895i \(-0.271343\pi\)
0.658140 + 0.752895i \(0.271343\pi\)
\(510\) 0 0
\(511\) −15.2980 −0.676742
\(512\) −44.3511 −1.96006
\(513\) −34.6342 −1.52914
\(514\) −41.7536 −1.84167
\(515\) 0 0
\(516\) 50.7719 2.23511
\(517\) −0.496595 −0.0218402
\(518\) 38.4530 1.68953
\(519\) −5.70903 −0.250598
\(520\) 0 0
\(521\) −32.5336 −1.42532 −0.712661 0.701509i \(-0.752510\pi\)
−0.712661 + 0.701509i \(0.752510\pi\)
\(522\) 5.93468 0.259754
\(523\) 21.6812 0.948053 0.474027 0.880510i \(-0.342800\pi\)
0.474027 + 0.880510i \(0.342800\pi\)
\(524\) 46.0612 2.01219
\(525\) 0 0
\(526\) −8.67555 −0.378272
\(527\) −4.07105 −0.177338
\(528\) 29.7479 1.29461
\(529\) −22.3013 −0.969622
\(530\) 0 0
\(531\) 8.47162 0.367637
\(532\) −43.7618 −1.89731
\(533\) −5.29135 −0.229194
\(534\) −46.2103 −1.99972
\(535\) 0 0
\(536\) −94.0092 −4.06058
\(537\) 5.91877 0.255414
\(538\) −19.3736 −0.835255
\(539\) 17.3187 0.745971
\(540\) 0 0
\(541\) 6.08311 0.261533 0.130767 0.991413i \(-0.458256\pi\)
0.130767 + 0.991413i \(0.458256\pi\)
\(542\) −53.6427 −2.30415
\(543\) 3.95648 0.169789
\(544\) 9.92903 0.425703
\(545\) 0 0
\(546\) 14.3497 0.614110
\(547\) 12.1956 0.521447 0.260723 0.965414i \(-0.416039\pi\)
0.260723 + 0.965414i \(0.416039\pi\)
\(548\) −111.049 −4.74379
\(549\) −11.4767 −0.489813
\(550\) 0 0
\(551\) 7.83723 0.333877
\(552\) 5.92694 0.252267
\(553\) −2.17448 −0.0924684
\(554\) −13.4781 −0.572630
\(555\) 0 0
\(556\) −6.18273 −0.262206
\(557\) 37.5982 1.59309 0.796544 0.604581i \(-0.206659\pi\)
0.796544 + 0.604581i \(0.206659\pi\)
\(558\) 21.0996 0.893217
\(559\) 46.6851 1.97457
\(560\) 0 0
\(561\) 3.28439 0.138667
\(562\) −36.9248 −1.55758
\(563\) −20.6037 −0.868342 −0.434171 0.900830i \(-0.642959\pi\)
−0.434171 + 0.900830i \(0.642959\pi\)
\(564\) −0.711047 −0.0299405
\(565\) 0 0
\(566\) 18.3607 0.771756
\(567\) 1.66919 0.0700992
\(568\) −81.6569 −3.42625
\(569\) 20.5762 0.862601 0.431301 0.902208i \(-0.358055\pi\)
0.431301 + 0.902208i \(0.358055\pi\)
\(570\) 0 0
\(571\) 37.1320 1.55392 0.776962 0.629547i \(-0.216760\pi\)
0.776962 + 0.629547i \(0.216760\pi\)
\(572\) 67.3165 2.81464
\(573\) 16.1513 0.674730
\(574\) 4.17753 0.174367
\(575\) 0 0
\(576\) −13.6077 −0.566986
\(577\) 34.7064 1.44484 0.722422 0.691452i \(-0.243029\pi\)
0.722422 + 0.691452i \(0.243029\pi\)
\(578\) −41.5285 −1.72736
\(579\) −22.6028 −0.939339
\(580\) 0 0
\(581\) 3.05992 0.126947
\(582\) −18.3176 −0.759291
\(583\) 9.87998 0.409187
\(584\) −84.7585 −3.50733
\(585\) 0 0
\(586\) 7.26324 0.300042
\(587\) 1.14455 0.0472405 0.0236203 0.999721i \(-0.492481\pi\)
0.0236203 + 0.999721i \(0.492481\pi\)
\(588\) 24.7977 1.02264
\(589\) 27.8638 1.14811
\(590\) 0 0
\(591\) −13.2834 −0.546407
\(592\) 104.953 4.31354
\(593\) −3.60735 −0.148136 −0.0740680 0.997253i \(-0.523598\pi\)
−0.0740680 + 0.997253i \(0.523598\pi\)
\(594\) −42.0615 −1.72580
\(595\) 0 0
\(596\) 83.7813 3.43181
\(597\) 25.1601 1.02973
\(598\) 9.37222 0.383258
\(599\) −31.6723 −1.29410 −0.647048 0.762449i \(-0.723997\pi\)
−0.647048 + 0.762449i \(0.723997\pi\)
\(600\) 0 0
\(601\) 6.55665 0.267451 0.133726 0.991018i \(-0.457306\pi\)
0.133726 + 0.991018i \(0.457306\pi\)
\(602\) −36.8579 −1.50222
\(603\) 26.5004 1.07918
\(604\) 25.1841 1.02473
\(605\) 0 0
\(606\) 13.9859 0.568140
\(607\) 9.16648 0.372056 0.186028 0.982544i \(-0.440438\pi\)
0.186028 + 0.982544i \(0.440438\pi\)
\(608\) −67.9579 −2.75606
\(609\) 1.43031 0.0579592
\(610\) 0 0
\(611\) −0.653812 −0.0264504
\(612\) −9.98603 −0.403661
\(613\) −7.92345 −0.320025 −0.160012 0.987115i \(-0.551153\pi\)
−0.160012 + 0.987115i \(0.551153\pi\)
\(614\) −51.6260 −2.08346
\(615\) 0 0
\(616\) −30.9041 −1.24516
\(617\) −16.5959 −0.668126 −0.334063 0.942551i \(-0.608420\pi\)
−0.334063 + 0.942551i \(0.608420\pi\)
\(618\) −40.1556 −1.61530
\(619\) 4.49086 0.180503 0.0902514 0.995919i \(-0.471233\pi\)
0.0902514 + 0.995919i \(0.471233\pi\)
\(620\) 0 0
\(621\) −4.12832 −0.165664
\(622\) 87.2498 3.49840
\(623\) 23.6491 0.947481
\(624\) 39.1658 1.56789
\(625\) 0 0
\(626\) −50.5499 −2.02038
\(627\) −22.4796 −0.897749
\(628\) 67.9387 2.71105
\(629\) 11.5876 0.462028
\(630\) 0 0
\(631\) −5.96553 −0.237484 −0.118742 0.992925i \(-0.537886\pi\)
−0.118742 + 0.992925i \(0.537886\pi\)
\(632\) −12.0477 −0.479233
\(633\) −5.07955 −0.201894
\(634\) 30.5288 1.21245
\(635\) 0 0
\(636\) 14.1466 0.560949
\(637\) 22.8017 0.903435
\(638\) 9.51791 0.376818
\(639\) 23.0184 0.910594
\(640\) 0 0
\(641\) −1.73375 −0.0684789 −0.0342395 0.999414i \(-0.510901\pi\)
−0.0342395 + 0.999414i \(0.510901\pi\)
\(642\) −28.5316 −1.12605
\(643\) −38.3312 −1.51163 −0.755817 0.654783i \(-0.772760\pi\)
−0.755817 + 0.654783i \(0.772760\pi\)
\(644\) −5.21630 −0.205551
\(645\) 0 0
\(646\) −18.7064 −0.735994
\(647\) −29.2098 −1.14836 −0.574178 0.818730i \(-0.694678\pi\)
−0.574178 + 0.818730i \(0.694678\pi\)
\(648\) 9.24813 0.363301
\(649\) 13.5866 0.533321
\(650\) 0 0
\(651\) 5.08520 0.199305
\(652\) 76.3127 2.98864
\(653\) 42.7952 1.67471 0.837353 0.546662i \(-0.184102\pi\)
0.837353 + 0.546662i \(0.184102\pi\)
\(654\) 0.756371 0.0295765
\(655\) 0 0
\(656\) 11.4021 0.445177
\(657\) 23.8927 0.932143
\(658\) 0.516185 0.0201230
\(659\) −23.7004 −0.923238 −0.461619 0.887078i \(-0.652731\pi\)
−0.461619 + 0.887078i \(0.652731\pi\)
\(660\) 0 0
\(661\) 24.1228 0.938268 0.469134 0.883127i \(-0.344566\pi\)
0.469134 + 0.883127i \(0.344566\pi\)
\(662\) 12.8378 0.498954
\(663\) 4.32420 0.167938
\(664\) 16.9535 0.657923
\(665\) 0 0
\(666\) −60.0567 −2.32715
\(667\) 0.934180 0.0361716
\(668\) 102.877 3.98044
\(669\) −6.37921 −0.246634
\(670\) 0 0
\(671\) −18.4061 −0.710558
\(672\) −12.4025 −0.478436
\(673\) 3.67522 0.141669 0.0708346 0.997488i \(-0.477434\pi\)
0.0708346 + 0.997488i \(0.477434\pi\)
\(674\) −89.6753 −3.45416
\(675\) 0 0
\(676\) 26.5029 1.01934
\(677\) −45.7769 −1.75935 −0.879675 0.475575i \(-0.842240\pi\)
−0.879675 + 0.475575i \(0.842240\pi\)
\(678\) 27.0172 1.03759
\(679\) 9.37443 0.359758
\(680\) 0 0
\(681\) 10.8255 0.414835
\(682\) 33.8391 1.29577
\(683\) 1.52419 0.0583215 0.0291608 0.999575i \(-0.490717\pi\)
0.0291608 + 0.999575i \(0.490717\pi\)
\(684\) 68.3481 2.61335
\(685\) 0 0
\(686\) −41.8018 −1.59600
\(687\) −8.77800 −0.334902
\(688\) −100.599 −3.83532
\(689\) 13.0079 0.495561
\(690\) 0 0
\(691\) 20.3036 0.772386 0.386193 0.922418i \(-0.373790\pi\)
0.386193 + 0.922418i \(0.373790\pi\)
\(692\) 27.8384 1.05826
\(693\) 8.71162 0.330927
\(694\) 61.0689 2.31814
\(695\) 0 0
\(696\) 7.92465 0.300383
\(697\) 1.25888 0.0476833
\(698\) 41.3267 1.56424
\(699\) −6.33739 −0.239702
\(700\) 0 0
\(701\) −10.3863 −0.392285 −0.196143 0.980575i \(-0.562842\pi\)
−0.196143 + 0.980575i \(0.562842\pi\)
\(702\) −55.3777 −2.09010
\(703\) −79.3098 −2.99123
\(704\) −21.8237 −0.822511
\(705\) 0 0
\(706\) 74.0988 2.78874
\(707\) −7.15759 −0.269189
\(708\) 19.4539 0.731122
\(709\) 34.9053 1.31090 0.655448 0.755240i \(-0.272480\pi\)
0.655448 + 0.755240i \(0.272480\pi\)
\(710\) 0 0
\(711\) 3.39615 0.127366
\(712\) 131.028 4.91048
\(713\) 3.32129 0.124383
\(714\) −3.41396 −0.127764
\(715\) 0 0
\(716\) −28.8611 −1.07859
\(717\) 24.5586 0.917159
\(718\) −2.01088 −0.0750454
\(719\) 5.17696 0.193068 0.0965341 0.995330i \(-0.469224\pi\)
0.0965341 + 0.995330i \(0.469224\pi\)
\(720\) 0 0
\(721\) 20.5505 0.765339
\(722\) 78.5646 2.92387
\(723\) 0.980039 0.0364480
\(724\) −19.2926 −0.717003
\(725\) 0 0
\(726\) 0.767896 0.0284993
\(727\) 7.00384 0.259758 0.129879 0.991530i \(-0.458541\pi\)
0.129879 + 0.991530i \(0.458541\pi\)
\(728\) −40.6881 −1.50800
\(729\) 11.9141 0.441262
\(730\) 0 0
\(731\) −11.1069 −0.410804
\(732\) −26.3546 −0.974094
\(733\) 1.22518 0.0452530 0.0226265 0.999744i \(-0.492797\pi\)
0.0226265 + 0.999744i \(0.492797\pi\)
\(734\) 60.8288 2.24523
\(735\) 0 0
\(736\) −8.10042 −0.298586
\(737\) 42.5008 1.56554
\(738\) −6.52455 −0.240172
\(739\) −31.4569 −1.15716 −0.578580 0.815625i \(-0.696393\pi\)
−0.578580 + 0.815625i \(0.696393\pi\)
\(740\) 0 0
\(741\) −29.5964 −1.08725
\(742\) −10.2697 −0.377014
\(743\) −17.5176 −0.642659 −0.321330 0.946967i \(-0.604130\pi\)
−0.321330 + 0.946967i \(0.604130\pi\)
\(744\) 28.1745 1.03293
\(745\) 0 0
\(746\) −72.3368 −2.64844
\(747\) −4.77904 −0.174856
\(748\) −16.0154 −0.585580
\(749\) 14.6016 0.533532
\(750\) 0 0
\(751\) −35.2893 −1.28773 −0.643863 0.765141i \(-0.722669\pi\)
−0.643863 + 0.765141i \(0.722669\pi\)
\(752\) 1.40887 0.0513761
\(753\) 12.3103 0.448614
\(754\) 12.5312 0.456359
\(755\) 0 0
\(756\) 30.8216 1.12097
\(757\) 17.2974 0.628686 0.314343 0.949309i \(-0.398216\pi\)
0.314343 + 0.949309i \(0.398216\pi\)
\(758\) 19.0931 0.693493
\(759\) −2.67952 −0.0972603
\(760\) 0 0
\(761\) 9.53250 0.345553 0.172776 0.984961i \(-0.444726\pi\)
0.172776 + 0.984961i \(0.444726\pi\)
\(762\) 37.5066 1.35872
\(763\) −0.387088 −0.0140135
\(764\) −78.7570 −2.84933
\(765\) 0 0
\(766\) 87.2034 3.15079
\(767\) 17.8880 0.645897
\(768\) 18.2079 0.657023
\(769\) −37.0399 −1.33569 −0.667847 0.744299i \(-0.732784\pi\)
−0.667847 + 0.744299i \(0.732784\pi\)
\(770\) 0 0
\(771\) 15.7166 0.566019
\(772\) 110.216 3.96675
\(773\) 6.97450 0.250855 0.125428 0.992103i \(-0.459970\pi\)
0.125428 + 0.992103i \(0.459970\pi\)
\(774\) 57.5655 2.06915
\(775\) 0 0
\(776\) 51.9391 1.86450
\(777\) −14.4742 −0.519259
\(778\) 40.8463 1.46441
\(779\) −8.61621 −0.308708
\(780\) 0 0
\(781\) 36.9164 1.32097
\(782\) −2.22976 −0.0797360
\(783\) −5.51980 −0.197261
\(784\) −49.1342 −1.75479
\(785\) 0 0
\(786\) −24.5942 −0.877246
\(787\) −29.9359 −1.06710 −0.533550 0.845768i \(-0.679143\pi\)
−0.533550 + 0.845768i \(0.679143\pi\)
\(788\) 64.7726 2.30743
\(789\) 3.26559 0.116258
\(790\) 0 0
\(791\) −13.8266 −0.491617
\(792\) 48.2667 1.71508
\(793\) −24.2332 −0.860547
\(794\) −21.7268 −0.771056
\(795\) 0 0
\(796\) −122.685 −4.34847
\(797\) 10.7103 0.379380 0.189690 0.981844i \(-0.439252\pi\)
0.189690 + 0.981844i \(0.439252\pi\)
\(798\) 23.3664 0.827162
\(799\) 0.155550 0.00550295
\(800\) 0 0
\(801\) −36.9357 −1.30506
\(802\) −100.439 −3.54662
\(803\) 38.3186 1.35223
\(804\) 60.8544 2.14617
\(805\) 0 0
\(806\) 44.5522 1.56928
\(807\) 7.29248 0.256707
\(808\) −39.6567 −1.39512
\(809\) −30.4625 −1.07100 −0.535502 0.844534i \(-0.679878\pi\)
−0.535502 + 0.844534i \(0.679878\pi\)
\(810\) 0 0
\(811\) −6.38159 −0.224088 −0.112044 0.993703i \(-0.535740\pi\)
−0.112044 + 0.993703i \(0.535740\pi\)
\(812\) −6.97449 −0.244757
\(813\) 20.1918 0.708158
\(814\) −96.3176 −3.37593
\(815\) 0 0
\(816\) −9.31801 −0.326196
\(817\) 76.0199 2.65960
\(818\) −50.8788 −1.77894
\(819\) 11.4696 0.400781
\(820\) 0 0
\(821\) −31.3814 −1.09522 −0.547609 0.836734i \(-0.684462\pi\)
−0.547609 + 0.836734i \(0.684462\pi\)
\(822\) 59.2943 2.06813
\(823\) 8.61720 0.300377 0.150188 0.988657i \(-0.452012\pi\)
0.150188 + 0.988657i \(0.452012\pi\)
\(824\) 113.860 3.96650
\(825\) 0 0
\(826\) −14.1226 −0.491387
\(827\) 18.2047 0.633039 0.316520 0.948586i \(-0.397486\pi\)
0.316520 + 0.948586i \(0.397486\pi\)
\(828\) 8.14693 0.283125
\(829\) 38.0162 1.32036 0.660179 0.751108i \(-0.270480\pi\)
0.660179 + 0.751108i \(0.270480\pi\)
\(830\) 0 0
\(831\) 5.07334 0.175992
\(832\) −28.7328 −0.996132
\(833\) −5.42479 −0.187958
\(834\) 3.30124 0.114313
\(835\) 0 0
\(836\) 109.615 3.79112
\(837\) −19.6246 −0.678324
\(838\) −77.5224 −2.67797
\(839\) 45.6228 1.57507 0.787537 0.616267i \(-0.211356\pi\)
0.787537 + 0.616267i \(0.211356\pi\)
\(840\) 0 0
\(841\) −27.7509 −0.956929
\(842\) −12.4693 −0.429720
\(843\) 13.8990 0.478706
\(844\) 24.7689 0.852582
\(845\) 0 0
\(846\) −0.806189 −0.0277174
\(847\) −0.392987 −0.0135032
\(848\) −28.0300 −0.962556
\(849\) −6.91120 −0.237192
\(850\) 0 0
\(851\) −9.45354 −0.324063
\(852\) 52.8585 1.81090
\(853\) −17.2406 −0.590307 −0.295153 0.955450i \(-0.595371\pi\)
−0.295153 + 0.955450i \(0.595371\pi\)
\(854\) 19.1321 0.654689
\(855\) 0 0
\(856\) 80.9003 2.76512
\(857\) −9.87638 −0.337371 −0.168685 0.985670i \(-0.553952\pi\)
−0.168685 + 0.985670i \(0.553952\pi\)
\(858\) −35.9433 −1.22708
\(859\) 25.8904 0.883369 0.441685 0.897170i \(-0.354381\pi\)
0.441685 + 0.897170i \(0.354381\pi\)
\(860\) 0 0
\(861\) −1.57248 −0.0535899
\(862\) 13.9538 0.475270
\(863\) 14.8445 0.505311 0.252656 0.967556i \(-0.418696\pi\)
0.252656 + 0.967556i \(0.418696\pi\)
\(864\) 47.8630 1.62833
\(865\) 0 0
\(866\) −55.9853 −1.90246
\(867\) 15.6319 0.530887
\(868\) −24.7964 −0.841646
\(869\) 5.44668 0.184766
\(870\) 0 0
\(871\) 55.9561 1.89600
\(872\) −2.14467 −0.0726275
\(873\) −14.6412 −0.495529
\(874\) 15.2613 0.516221
\(875\) 0 0
\(876\) 54.8662 1.85376
\(877\) −42.0781 −1.42088 −0.710439 0.703759i \(-0.751503\pi\)
−0.710439 + 0.703759i \(0.751503\pi\)
\(878\) 10.9953 0.371072
\(879\) −2.73398 −0.0922148
\(880\) 0 0
\(881\) −19.0418 −0.641534 −0.320767 0.947158i \(-0.603941\pi\)
−0.320767 + 0.947158i \(0.603941\pi\)
\(882\) 28.1158 0.946709
\(883\) −6.51087 −0.219108 −0.109554 0.993981i \(-0.534942\pi\)
−0.109554 + 0.993981i \(0.534942\pi\)
\(884\) −21.0857 −0.709188
\(885\) 0 0
\(886\) −21.7150 −0.729531
\(887\) −5.59140 −0.187741 −0.0938704 0.995584i \(-0.529924\pi\)
−0.0938704 + 0.995584i \(0.529924\pi\)
\(888\) −80.1944 −2.69115
\(889\) −19.1948 −0.643773
\(890\) 0 0
\(891\) −4.18100 −0.140069
\(892\) 31.1063 1.04152
\(893\) −1.06464 −0.0356268
\(894\) −44.7346 −1.49615
\(895\) 0 0
\(896\) −2.62555 −0.0877135
\(897\) −3.52783 −0.117791
\(898\) 41.0841 1.37099
\(899\) 4.44076 0.148108
\(900\) 0 0
\(901\) −3.09473 −0.103100
\(902\) −10.4639 −0.348411
\(903\) 13.8738 0.461691
\(904\) −76.6063 −2.54789
\(905\) 0 0
\(906\) −13.4470 −0.446745
\(907\) −18.3915 −0.610681 −0.305340 0.952243i \(-0.598770\pi\)
−0.305340 + 0.952243i \(0.598770\pi\)
\(908\) −52.7874 −1.75181
\(909\) 11.1789 0.370780
\(910\) 0 0
\(911\) −38.2665 −1.26783 −0.633913 0.773404i \(-0.718552\pi\)
−0.633913 + 0.773404i \(0.718552\pi\)
\(912\) 63.7759 2.11183
\(913\) −7.66452 −0.253659
\(914\) 22.6885 0.750469
\(915\) 0 0
\(916\) 42.8033 1.41426
\(917\) 12.5866 0.415646
\(918\) 13.1750 0.434840
\(919\) −4.89962 −0.161624 −0.0808118 0.996729i \(-0.525751\pi\)
−0.0808118 + 0.996729i \(0.525751\pi\)
\(920\) 0 0
\(921\) 19.4327 0.640330
\(922\) 64.8669 2.13628
\(923\) 48.6038 1.59981
\(924\) 20.0050 0.658116
\(925\) 0 0
\(926\) 7.47949 0.245791
\(927\) −32.0962 −1.05418
\(928\) −10.8307 −0.355536
\(929\) 17.9381 0.588528 0.294264 0.955724i \(-0.404925\pi\)
0.294264 + 0.955724i \(0.404925\pi\)
\(930\) 0 0
\(931\) 37.1292 1.21686
\(932\) 30.9024 1.01224
\(933\) −32.8420 −1.07520
\(934\) −12.6920 −0.415295
\(935\) 0 0
\(936\) 63.5475 2.07712
\(937\) −29.8369 −0.974730 −0.487365 0.873198i \(-0.662042\pi\)
−0.487365 + 0.873198i \(0.662042\pi\)
\(938\) −44.1773 −1.44244
\(939\) 19.0276 0.620943
\(940\) 0 0
\(941\) 26.8047 0.873809 0.436904 0.899508i \(-0.356075\pi\)
0.436904 + 0.899508i \(0.356075\pi\)
\(942\) −36.2755 −1.18192
\(943\) −1.02703 −0.0334448
\(944\) −38.5459 −1.25456
\(945\) 0 0
\(946\) 92.3222 3.00165
\(947\) −2.94622 −0.0957393 −0.0478697 0.998854i \(-0.515243\pi\)
−0.0478697 + 0.998854i \(0.515243\pi\)
\(948\) 7.79879 0.253293
\(949\) 50.4499 1.63767
\(950\) 0 0
\(951\) −11.4914 −0.372635
\(952\) 9.68017 0.313736
\(953\) 4.62861 0.149935 0.0749676 0.997186i \(-0.476115\pi\)
0.0749676 + 0.997186i \(0.476115\pi\)
\(954\) 16.0395 0.519297
\(955\) 0 0
\(956\) −119.753 −3.87308
\(957\) −3.58267 −0.115811
\(958\) 0.505247 0.0163238
\(959\) −30.3451 −0.979894
\(960\) 0 0
\(961\) −15.2117 −0.490702
\(962\) −126.811 −4.08854
\(963\) −22.8051 −0.734885
\(964\) −4.77887 −0.153917
\(965\) 0 0
\(966\) 2.78522 0.0896130
\(967\) −20.1721 −0.648689 −0.324345 0.945939i \(-0.605144\pi\)
−0.324345 + 0.945939i \(0.605144\pi\)
\(968\) −2.17734 −0.0699825
\(969\) 7.04134 0.226200
\(970\) 0 0
\(971\) 30.0251 0.963550 0.481775 0.876295i \(-0.339992\pi\)
0.481775 + 0.876295i \(0.339992\pi\)
\(972\) −76.7940 −2.46317
\(973\) −1.68948 −0.0541621
\(974\) 80.0853 2.56610
\(975\) 0 0
\(976\) 52.2190 1.67149
\(977\) −57.7096 −1.84629 −0.923147 0.384448i \(-0.874392\pi\)
−0.923147 + 0.384448i \(0.874392\pi\)
\(978\) −40.7469 −1.30294
\(979\) −59.2366 −1.89321
\(980\) 0 0
\(981\) 0.604563 0.0193022
\(982\) −56.1154 −1.79071
\(983\) 3.33817 0.106471 0.0532356 0.998582i \(-0.483047\pi\)
0.0532356 + 0.998582i \(0.483047\pi\)
\(984\) −8.71231 −0.277738
\(985\) 0 0
\(986\) −2.98132 −0.0949444
\(987\) −0.194299 −0.00618460
\(988\) 144.318 4.59137
\(989\) 9.06139 0.288136
\(990\) 0 0
\(991\) 4.48757 0.142552 0.0712762 0.997457i \(-0.477293\pi\)
0.0712762 + 0.997457i \(0.477293\pi\)
\(992\) −38.5065 −1.22258
\(993\) −4.83230 −0.153349
\(994\) −38.3727 −1.21711
\(995\) 0 0
\(996\) −10.9744 −0.347737
\(997\) 47.4116 1.50154 0.750770 0.660564i \(-0.229683\pi\)
0.750770 + 0.660564i \(0.229683\pi\)
\(998\) 57.0172 1.80485
\(999\) 55.8582 1.76728
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.f.1.7 7
5.4 even 2 241.2.a.a.1.1 7
15.14 odd 2 2169.2.a.e.1.7 7
20.19 odd 2 3856.2.a.j.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.1 7 5.4 even 2
2169.2.a.e.1.7 7 15.14 odd 2
3856.2.a.j.1.2 7 20.19 odd 2
6025.2.a.f.1.7 7 1.1 even 1 trivial