Properties

Label 4235.2.a.bb.1.3
Level $4235$
Weight $2$
Character 4235.1
Self dual yes
Analytic conductor $33.817$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4235.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.8166452560\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.580017.1
Defining polynomial: \(x^{5} - 7 x^{3} - 4 x^{2} + 6 x + 3\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.470042\) of defining polynomial
Character \(\chi\) \(=\) 4235.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.470042 q^{2} -0.577925 q^{3} -1.77906 q^{4} -1.00000 q^{5} -0.271649 q^{6} +1.00000 q^{7} -1.77632 q^{8} -2.66600 q^{9} +O(q^{10})\) \(q+0.470042 q^{2} -0.577925 q^{3} -1.77906 q^{4} -1.00000 q^{5} -0.271649 q^{6} +1.00000 q^{7} -1.77632 q^{8} -2.66600 q^{9} -0.470042 q^{10} +1.02816 q^{12} -1.19839 q^{13} +0.470042 q^{14} +0.577925 q^{15} +2.72318 q^{16} +1.08534 q^{17} -1.25313 q^{18} +6.29189 q^{19} +1.77906 q^{20} -0.577925 q^{21} -6.35986 q^{23} +1.02658 q^{24} +1.00000 q^{25} -0.563295 q^{26} +3.27452 q^{27} -1.77906 q^{28} +6.79931 q^{29} +0.271649 q^{30} +9.46531 q^{31} +4.83264 q^{32} +0.510154 q^{34} -1.00000 q^{35} +4.74298 q^{36} -8.49980 q^{37} +2.95746 q^{38} +0.692581 q^{39} +1.77632 q^{40} +9.51571 q^{41} -0.271649 q^{42} -5.07339 q^{43} +2.66600 q^{45} -2.98940 q^{46} +3.89889 q^{47} -1.57379 q^{48} +1.00000 q^{49} +0.470042 q^{50} -0.627242 q^{51} +2.13201 q^{52} -12.2191 q^{53} +1.53916 q^{54} -1.77632 q^{56} -3.63624 q^{57} +3.19596 q^{58} -4.91466 q^{59} -1.02816 q^{60} -10.6033 q^{61} +4.44909 q^{62} -2.66600 q^{63} -3.17481 q^{64} +1.19839 q^{65} -5.09350 q^{67} -1.93088 q^{68} +3.67552 q^{69} -0.470042 q^{70} -7.24680 q^{71} +4.73567 q^{72} +10.2495 q^{73} -3.99527 q^{74} -0.577925 q^{75} -11.1937 q^{76} +0.325542 q^{78} -0.0718642 q^{79} -2.72318 q^{80} +6.10558 q^{81} +4.47278 q^{82} -9.16537 q^{83} +1.02816 q^{84} -1.08534 q^{85} -2.38471 q^{86} -3.92949 q^{87} -3.20656 q^{89} +1.25313 q^{90} -1.19839 q^{91} +11.3146 q^{92} -5.47024 q^{93} +1.83264 q^{94} -6.29189 q^{95} -2.79290 q^{96} -9.05358 q^{97} +0.470042 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 2q^{3} + 4q^{4} - 5q^{5} + 5q^{6} + 5q^{7} - 12q^{8} + 11q^{9} + O(q^{10}) \) \( 5q - 2q^{3} + 4q^{4} - 5q^{5} + 5q^{6} + 5q^{7} - 12q^{8} + 11q^{9} - 23q^{12} - 10q^{13} + 2q^{15} + 10q^{16} - 2q^{17} - 5q^{18} + 3q^{19} - 4q^{20} - 2q^{21} + 3q^{23} + 28q^{24} + 5q^{25} + 13q^{26} - 11q^{27} + 4q^{28} - q^{29} - 5q^{30} - 12q^{31} - 29q^{32} - 20q^{34} - 5q^{35} + 45q^{36} + 9q^{38} + 2q^{39} + 12q^{40} + 11q^{41} + 5q^{42} - 10q^{43} - 11q^{45} - 14q^{46} + 16q^{47} - 46q^{48} + 5q^{49} - 6q^{51} - 30q^{52} + 4q^{53} + 34q^{54} - 12q^{56} - 34q^{57} - 6q^{58} - 32q^{59} + 23q^{60} - 40q^{61} - q^{62} + 11q^{63} + 38q^{64} + 10q^{65} + 7q^{67} + 19q^{68} - 24q^{69} + 10q^{71} - 72q^{72} - 11q^{73} + 37q^{74} - 2q^{75} - 3q^{76} - 87q^{78} - 13q^{79} - 10q^{80} + q^{81} + 4q^{82} - 26q^{83} - 23q^{84} + 2q^{85} - 17q^{86} - 14q^{87} + 5q^{89} + 5q^{90} - 10q^{91} + 32q^{92} + 3q^{93} - 44q^{94} - 3q^{95} + 84q^{96} - 5q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.470042 0.332370 0.166185 0.986095i \(-0.446855\pi\)
0.166185 + 0.986095i \(0.446855\pi\)
\(3\) −0.577925 −0.333665 −0.166832 0.985985i \(-0.553354\pi\)
−0.166832 + 0.985985i \(0.553354\pi\)
\(4\) −1.77906 −0.889530
\(5\) −1.00000 −0.447214
\(6\) −0.271649 −0.110900
\(7\) 1.00000 0.377964
\(8\) −1.77632 −0.628023
\(9\) −2.66600 −0.888668
\(10\) −0.470042 −0.148640
\(11\) 0 0
\(12\) 1.02816 0.296805
\(13\) −1.19839 −0.332374 −0.166187 0.986094i \(-0.553146\pi\)
−0.166187 + 0.986094i \(0.553146\pi\)
\(14\) 0.470042 0.125624
\(15\) 0.577925 0.149220
\(16\) 2.72318 0.680794
\(17\) 1.08534 0.263233 0.131616 0.991301i \(-0.457983\pi\)
0.131616 + 0.991301i \(0.457983\pi\)
\(18\) −1.25313 −0.295367
\(19\) 6.29189 1.44346 0.721730 0.692175i \(-0.243347\pi\)
0.721730 + 0.692175i \(0.243347\pi\)
\(20\) 1.77906 0.397810
\(21\) −0.577925 −0.126114
\(22\) 0 0
\(23\) −6.35986 −1.32612 −0.663061 0.748565i \(-0.730743\pi\)
−0.663061 + 0.748565i \(0.730743\pi\)
\(24\) 1.02658 0.209549
\(25\) 1.00000 0.200000
\(26\) −0.563295 −0.110471
\(27\) 3.27452 0.630182
\(28\) −1.77906 −0.336211
\(29\) 6.79931 1.26260 0.631300 0.775539i \(-0.282522\pi\)
0.631300 + 0.775539i \(0.282522\pi\)
\(30\) 0.271649 0.0495961
\(31\) 9.46531 1.70002 0.850010 0.526767i \(-0.176596\pi\)
0.850010 + 0.526767i \(0.176596\pi\)
\(32\) 4.83264 0.854299
\(33\) 0 0
\(34\) 0.510154 0.0874906
\(35\) −1.00000 −0.169031
\(36\) 4.74298 0.790497
\(37\) −8.49980 −1.39736 −0.698680 0.715435i \(-0.746229\pi\)
−0.698680 + 0.715435i \(0.746229\pi\)
\(38\) 2.95746 0.479763
\(39\) 0.692581 0.110902
\(40\) 1.77632 0.280861
\(41\) 9.51571 1.48610 0.743052 0.669234i \(-0.233377\pi\)
0.743052 + 0.669234i \(0.233377\pi\)
\(42\) −0.271649 −0.0419163
\(43\) −5.07339 −0.773684 −0.386842 0.922146i \(-0.626434\pi\)
−0.386842 + 0.922146i \(0.626434\pi\)
\(44\) 0 0
\(45\) 2.66600 0.397424
\(46\) −2.98940 −0.440763
\(47\) 3.89889 0.568712 0.284356 0.958719i \(-0.408220\pi\)
0.284356 + 0.958719i \(0.408220\pi\)
\(48\) −1.57379 −0.227157
\(49\) 1.00000 0.142857
\(50\) 0.470042 0.0664740
\(51\) −0.627242 −0.0878315
\(52\) 2.13201 0.295657
\(53\) −12.2191 −1.67842 −0.839210 0.543808i \(-0.816982\pi\)
−0.839210 + 0.543808i \(0.816982\pi\)
\(54\) 1.53916 0.209454
\(55\) 0 0
\(56\) −1.77632 −0.237370
\(57\) −3.63624 −0.481632
\(58\) 3.19596 0.419650
\(59\) −4.91466 −0.639835 −0.319917 0.947445i \(-0.603655\pi\)
−0.319917 + 0.947445i \(0.603655\pi\)
\(60\) −1.02816 −0.132735
\(61\) −10.6033 −1.35762 −0.678810 0.734314i \(-0.737504\pi\)
−0.678810 + 0.734314i \(0.737504\pi\)
\(62\) 4.44909 0.565036
\(63\) −2.66600 −0.335885
\(64\) −3.17481 −0.396851
\(65\) 1.19839 0.148642
\(66\) 0 0
\(67\) −5.09350 −0.622270 −0.311135 0.950366i \(-0.600709\pi\)
−0.311135 + 0.950366i \(0.600709\pi\)
\(68\) −1.93088 −0.234153
\(69\) 3.67552 0.442481
\(70\) −0.470042 −0.0561808
\(71\) −7.24680 −0.860037 −0.430019 0.902820i \(-0.641493\pi\)
−0.430019 + 0.902820i \(0.641493\pi\)
\(72\) 4.73567 0.558104
\(73\) 10.2495 1.19962 0.599809 0.800143i \(-0.295243\pi\)
0.599809 + 0.800143i \(0.295243\pi\)
\(74\) −3.99527 −0.464440
\(75\) −0.577925 −0.0667330
\(76\) −11.1937 −1.28400
\(77\) 0 0
\(78\) 0.325542 0.0368604
\(79\) −0.0718642 −0.00808536 −0.00404268 0.999992i \(-0.501287\pi\)
−0.00404268 + 0.999992i \(0.501287\pi\)
\(80\) −2.72318 −0.304460
\(81\) 6.10558 0.678398
\(82\) 4.47278 0.493936
\(83\) −9.16537 −1.00603 −0.503015 0.864278i \(-0.667776\pi\)
−0.503015 + 0.864278i \(0.667776\pi\)
\(84\) 1.02816 0.112182
\(85\) −1.08534 −0.117721
\(86\) −2.38471 −0.257149
\(87\) −3.92949 −0.421285
\(88\) 0 0
\(89\) −3.20656 −0.339895 −0.169947 0.985453i \(-0.554360\pi\)
−0.169947 + 0.985453i \(0.554360\pi\)
\(90\) 1.25313 0.132092
\(91\) −1.19839 −0.125626
\(92\) 11.3146 1.17963
\(93\) −5.47024 −0.567237
\(94\) 1.83264 0.189023
\(95\) −6.29189 −0.645535
\(96\) −2.79290 −0.285050
\(97\) −9.05358 −0.919252 −0.459626 0.888113i \(-0.652017\pi\)
−0.459626 + 0.888113i \(0.652017\pi\)
\(98\) 0.470042 0.0474814
\(99\) 0 0
\(100\) −1.77906 −0.177906
\(101\) −2.41665 −0.240466 −0.120233 0.992746i \(-0.538364\pi\)
−0.120233 + 0.992746i \(0.538364\pi\)
\(102\) −0.294830 −0.0291926
\(103\) −13.1214 −1.29289 −0.646443 0.762963i \(-0.723744\pi\)
−0.646443 + 0.762963i \(0.723744\pi\)
\(104\) 2.12873 0.208739
\(105\) 0.577925 0.0563997
\(106\) −5.74348 −0.557856
\(107\) 13.6316 1.31782 0.658910 0.752222i \(-0.271018\pi\)
0.658910 + 0.752222i \(0.271018\pi\)
\(108\) −5.82557 −0.560566
\(109\) 7.14569 0.684433 0.342217 0.939621i \(-0.388822\pi\)
0.342217 + 0.939621i \(0.388822\pi\)
\(110\) 0 0
\(111\) 4.91225 0.466250
\(112\) 2.72318 0.257316
\(113\) 10.9216 1.02742 0.513710 0.857964i \(-0.328271\pi\)
0.513710 + 0.857964i \(0.328271\pi\)
\(114\) −1.70919 −0.160080
\(115\) 6.35986 0.593060
\(116\) −12.0964 −1.12312
\(117\) 3.19492 0.295370
\(118\) −2.31010 −0.212662
\(119\) 1.08534 0.0994926
\(120\) −1.02658 −0.0937133
\(121\) 0 0
\(122\) −4.98402 −0.451232
\(123\) −5.49936 −0.495861
\(124\) −16.8394 −1.51222
\(125\) −1.00000 −0.0894427
\(126\) −1.25313 −0.111638
\(127\) −11.2229 −0.995872 −0.497936 0.867214i \(-0.665909\pi\)
−0.497936 + 0.867214i \(0.665909\pi\)
\(128\) −11.1576 −0.986200
\(129\) 2.93204 0.258151
\(130\) 0.563295 0.0494043
\(131\) 17.3578 1.51656 0.758279 0.651930i \(-0.226040\pi\)
0.758279 + 0.651930i \(0.226040\pi\)
\(132\) 0 0
\(133\) 6.29189 0.545576
\(134\) −2.39416 −0.206824
\(135\) −3.27452 −0.281826
\(136\) −1.92790 −0.165316
\(137\) 18.8358 1.60925 0.804627 0.593780i \(-0.202365\pi\)
0.804627 + 0.593780i \(0.202365\pi\)
\(138\) 1.72765 0.147067
\(139\) −20.0886 −1.70390 −0.851948 0.523626i \(-0.824579\pi\)
−0.851948 + 0.523626i \(0.824579\pi\)
\(140\) 1.77906 0.150358
\(141\) −2.25327 −0.189759
\(142\) −3.40630 −0.285851
\(143\) 0 0
\(144\) −7.26000 −0.605000
\(145\) −6.79931 −0.564652
\(146\) 4.81772 0.398717
\(147\) −0.577925 −0.0476664
\(148\) 15.1217 1.24299
\(149\) −11.3747 −0.931850 −0.465925 0.884824i \(-0.654278\pi\)
−0.465925 + 0.884824i \(0.654278\pi\)
\(150\) −0.271649 −0.0221800
\(151\) −12.8036 −1.04195 −0.520973 0.853573i \(-0.674431\pi\)
−0.520973 + 0.853573i \(0.674431\pi\)
\(152\) −11.1764 −0.906526
\(153\) −2.89351 −0.233926
\(154\) 0 0
\(155\) −9.46531 −0.760272
\(156\) −1.23214 −0.0986504
\(157\) 8.23103 0.656908 0.328454 0.944520i \(-0.393472\pi\)
0.328454 + 0.944520i \(0.393472\pi\)
\(158\) −0.0337792 −0.00268733
\(159\) 7.06171 0.560030
\(160\) −4.83264 −0.382054
\(161\) −6.35986 −0.501227
\(162\) 2.86988 0.225479
\(163\) 6.30685 0.493991 0.246995 0.969017i \(-0.420557\pi\)
0.246995 + 0.969017i \(0.420557\pi\)
\(164\) −16.9290 −1.32193
\(165\) 0 0
\(166\) −4.30811 −0.334374
\(167\) −9.35034 −0.723551 −0.361776 0.932265i \(-0.617829\pi\)
−0.361776 + 0.932265i \(0.617829\pi\)
\(168\) 1.02658 0.0792022
\(169\) −11.5639 −0.889527
\(170\) −0.510154 −0.0391270
\(171\) −16.7742 −1.28276
\(172\) 9.02586 0.688216
\(173\) −6.98410 −0.530991 −0.265495 0.964112i \(-0.585536\pi\)
−0.265495 + 0.964112i \(0.585536\pi\)
\(174\) −1.84702 −0.140023
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 2.84031 0.213490
\(178\) −1.50722 −0.112971
\(179\) 13.0020 0.971812 0.485906 0.874011i \(-0.338490\pi\)
0.485906 + 0.874011i \(0.338490\pi\)
\(180\) −4.74298 −0.353521
\(181\) −18.2396 −1.35574 −0.677871 0.735181i \(-0.737097\pi\)
−0.677871 + 0.735181i \(0.737097\pi\)
\(182\) −0.563295 −0.0417542
\(183\) 6.12793 0.452990
\(184\) 11.2971 0.832836
\(185\) 8.49980 0.624918
\(186\) −2.57124 −0.188533
\(187\) 0 0
\(188\) −6.93636 −0.505886
\(189\) 3.27452 0.238186
\(190\) −2.95746 −0.214556
\(191\) −14.8793 −1.07663 −0.538315 0.842743i \(-0.680939\pi\)
−0.538315 + 0.842743i \(0.680939\pi\)
\(192\) 1.83480 0.132415
\(193\) 4.87672 0.351034 0.175517 0.984476i \(-0.443840\pi\)
0.175517 + 0.984476i \(0.443840\pi\)
\(194\) −4.25557 −0.305532
\(195\) −0.692581 −0.0495968
\(196\) −1.77906 −0.127076
\(197\) −21.3123 −1.51844 −0.759220 0.650834i \(-0.774420\pi\)
−0.759220 + 0.650834i \(0.774420\pi\)
\(198\) 0 0
\(199\) 1.08916 0.0772085 0.0386042 0.999255i \(-0.487709\pi\)
0.0386042 + 0.999255i \(0.487709\pi\)
\(200\) −1.77632 −0.125605
\(201\) 2.94366 0.207630
\(202\) −1.13593 −0.0799237
\(203\) 6.79931 0.477218
\(204\) 1.11590 0.0781288
\(205\) −9.51571 −0.664606
\(206\) −6.16759 −0.429716
\(207\) 16.9554 1.17848
\(208\) −3.26344 −0.226279
\(209\) 0 0
\(210\) 0.271649 0.0187456
\(211\) −22.9845 −1.58232 −0.791158 0.611612i \(-0.790521\pi\)
−0.791158 + 0.611612i \(0.790521\pi\)
\(212\) 21.7385 1.49301
\(213\) 4.18811 0.286964
\(214\) 6.40745 0.438004
\(215\) 5.07339 0.346002
\(216\) −5.81659 −0.395769
\(217\) 9.46531 0.642547
\(218\) 3.35878 0.227485
\(219\) −5.92346 −0.400271
\(220\) 0 0
\(221\) −1.30066 −0.0874918
\(222\) 2.30896 0.154967
\(223\) −23.3688 −1.56489 −0.782447 0.622717i \(-0.786029\pi\)
−0.782447 + 0.622717i \(0.786029\pi\)
\(224\) 4.83264 0.322895
\(225\) −2.66600 −0.177734
\(226\) 5.13363 0.341484
\(227\) −9.26282 −0.614795 −0.307398 0.951581i \(-0.599458\pi\)
−0.307398 + 0.951581i \(0.599458\pi\)
\(228\) 6.46909 0.428426
\(229\) 22.3739 1.47851 0.739255 0.673426i \(-0.235178\pi\)
0.739255 + 0.673426i \(0.235178\pi\)
\(230\) 2.98940 0.197115
\(231\) 0 0
\(232\) −12.0777 −0.792942
\(233\) −0.300984 −0.0197181 −0.00985907 0.999951i \(-0.503138\pi\)
−0.00985907 + 0.999951i \(0.503138\pi\)
\(234\) 1.50175 0.0981723
\(235\) −3.89889 −0.254336
\(236\) 8.74348 0.569152
\(237\) 0.0415321 0.00269780
\(238\) 0.510154 0.0330684
\(239\) 17.8086 1.15194 0.575972 0.817469i \(-0.304624\pi\)
0.575972 + 0.817469i \(0.304624\pi\)
\(240\) 1.57379 0.101588
\(241\) −14.8175 −0.954480 −0.477240 0.878773i \(-0.658363\pi\)
−0.477240 + 0.878773i \(0.658363\pi\)
\(242\) 0 0
\(243\) −13.3521 −0.856540
\(244\) 18.8640 1.20764
\(245\) −1.00000 −0.0638877
\(246\) −2.58493 −0.164809
\(247\) −7.54016 −0.479769
\(248\) −16.8134 −1.06765
\(249\) 5.29689 0.335677
\(250\) −0.470042 −0.0297281
\(251\) 4.92595 0.310923 0.155462 0.987842i \(-0.450313\pi\)
0.155462 + 0.987842i \(0.450313\pi\)
\(252\) 4.74298 0.298780
\(253\) 0 0
\(254\) −5.27524 −0.330998
\(255\) 0.627242 0.0392794
\(256\) 1.10508 0.0690674
\(257\) 10.6277 0.662940 0.331470 0.943466i \(-0.392455\pi\)
0.331470 + 0.943466i \(0.392455\pi\)
\(258\) 1.37818 0.0858018
\(259\) −8.49980 −0.528152
\(260\) −2.13201 −0.132222
\(261\) −18.1270 −1.12203
\(262\) 8.15890 0.504059
\(263\) −6.62908 −0.408766 −0.204383 0.978891i \(-0.565519\pi\)
−0.204383 + 0.978891i \(0.565519\pi\)
\(264\) 0 0
\(265\) 12.2191 0.750612
\(266\) 2.95746 0.181333
\(267\) 1.85315 0.113411
\(268\) 9.06165 0.553528
\(269\) 14.6214 0.891480 0.445740 0.895163i \(-0.352941\pi\)
0.445740 + 0.895163i \(0.352941\pi\)
\(270\) −1.53916 −0.0936705
\(271\) 5.00420 0.303984 0.151992 0.988382i \(-0.451431\pi\)
0.151992 + 0.988382i \(0.451431\pi\)
\(272\) 2.95556 0.179207
\(273\) 0.692581 0.0419169
\(274\) 8.85364 0.534868
\(275\) 0 0
\(276\) −6.53897 −0.393600
\(277\) −3.50429 −0.210552 −0.105276 0.994443i \(-0.533573\pi\)
−0.105276 + 0.994443i \(0.533573\pi\)
\(278\) −9.44251 −0.566324
\(279\) −25.2345 −1.51075
\(280\) 1.77632 0.106155
\(281\) 9.42495 0.562245 0.281123 0.959672i \(-0.409293\pi\)
0.281123 + 0.959672i \(0.409293\pi\)
\(282\) −1.05913 −0.0630703
\(283\) −15.9110 −0.945812 −0.472906 0.881113i \(-0.656795\pi\)
−0.472906 + 0.881113i \(0.656795\pi\)
\(284\) 12.8925 0.765029
\(285\) 3.63624 0.215392
\(286\) 0 0
\(287\) 9.51571 0.561695
\(288\) −12.8838 −0.759188
\(289\) −15.8220 −0.930709
\(290\) −3.19596 −0.187673
\(291\) 5.23229 0.306722
\(292\) −18.2346 −1.06710
\(293\) −15.3574 −0.897187 −0.448593 0.893736i \(-0.648075\pi\)
−0.448593 + 0.893736i \(0.648075\pi\)
\(294\) −0.271649 −0.0158429
\(295\) 4.91466 0.286143
\(296\) 15.0984 0.877574
\(297\) 0 0
\(298\) −5.34658 −0.309719
\(299\) 7.62161 0.440769
\(300\) 1.02816 0.0593610
\(301\) −5.07339 −0.292425
\(302\) −6.01825 −0.346312
\(303\) 1.39664 0.0802350
\(304\) 17.1339 0.982699
\(305\) 10.6033 0.607146
\(306\) −1.36007 −0.0777501
\(307\) 16.0662 0.916944 0.458472 0.888709i \(-0.348397\pi\)
0.458472 + 0.888709i \(0.348397\pi\)
\(308\) 0 0
\(309\) 7.58315 0.431391
\(310\) −4.44909 −0.252692
\(311\) 3.67098 0.208162 0.104081 0.994569i \(-0.466810\pi\)
0.104081 + 0.994569i \(0.466810\pi\)
\(312\) −1.23024 −0.0696489
\(313\) −4.45248 −0.251669 −0.125834 0.992051i \(-0.540161\pi\)
−0.125834 + 0.992051i \(0.540161\pi\)
\(314\) 3.86893 0.218336
\(315\) 2.66600 0.150212
\(316\) 0.127851 0.00719217
\(317\) −22.3020 −1.25261 −0.626304 0.779579i \(-0.715433\pi\)
−0.626304 + 0.779579i \(0.715433\pi\)
\(318\) 3.31930 0.186137
\(319\) 0 0
\(320\) 3.17481 0.177477
\(321\) −7.87806 −0.439710
\(322\) −2.98940 −0.166593
\(323\) 6.82882 0.379966
\(324\) −10.8622 −0.603455
\(325\) −1.19839 −0.0664749
\(326\) 2.96449 0.164188
\(327\) −4.12967 −0.228371
\(328\) −16.9029 −0.933308
\(329\) 3.89889 0.214953
\(330\) 0 0
\(331\) −8.43313 −0.463527 −0.231763 0.972772i \(-0.574450\pi\)
−0.231763 + 0.972772i \(0.574450\pi\)
\(332\) 16.3057 0.894894
\(333\) 22.6605 1.24179
\(334\) −4.39506 −0.240487
\(335\) 5.09350 0.278288
\(336\) −1.57379 −0.0858573
\(337\) −30.2983 −1.65045 −0.825226 0.564803i \(-0.808952\pi\)
−0.825226 + 0.564803i \(0.808952\pi\)
\(338\) −5.43550 −0.295652
\(339\) −6.31188 −0.342814
\(340\) 1.93088 0.104717
\(341\) 0 0
\(342\) −7.88459 −0.426350
\(343\) 1.00000 0.0539949
\(344\) 9.01195 0.485892
\(345\) −3.67552 −0.197883
\(346\) −3.28282 −0.176485
\(347\) −1.68714 −0.0905706 −0.0452853 0.998974i \(-0.514420\pi\)
−0.0452853 + 0.998974i \(0.514420\pi\)
\(348\) 6.99079 0.374746
\(349\) 26.2092 1.40295 0.701474 0.712695i \(-0.252526\pi\)
0.701474 + 0.712695i \(0.252526\pi\)
\(350\) 0.470042 0.0251248
\(351\) −3.92417 −0.209456
\(352\) 0 0
\(353\) 17.6788 0.940948 0.470474 0.882414i \(-0.344083\pi\)
0.470474 + 0.882414i \(0.344083\pi\)
\(354\) 1.33506 0.0709578
\(355\) 7.24680 0.384620
\(356\) 5.70466 0.302346
\(357\) −0.627242 −0.0331972
\(358\) 6.11147 0.323001
\(359\) −7.06393 −0.372820 −0.186410 0.982472i \(-0.559685\pi\)
−0.186410 + 0.982472i \(0.559685\pi\)
\(360\) −4.73567 −0.249592
\(361\) 20.5879 1.08358
\(362\) −8.57340 −0.450608
\(363\) 0 0
\(364\) 2.13201 0.111748
\(365\) −10.2495 −0.536486
\(366\) 2.88039 0.150560
\(367\) 9.09662 0.474840 0.237420 0.971407i \(-0.423698\pi\)
0.237420 + 0.971407i \(0.423698\pi\)
\(368\) −17.3190 −0.902816
\(369\) −25.3689 −1.32065
\(370\) 3.99527 0.207704
\(371\) −12.2191 −0.634383
\(372\) 9.73188 0.504574
\(373\) −33.9587 −1.75832 −0.879158 0.476531i \(-0.841894\pi\)
−0.879158 + 0.476531i \(0.841894\pi\)
\(374\) 0 0
\(375\) 0.577925 0.0298439
\(376\) −6.92567 −0.357164
\(377\) −8.14824 −0.419656
\(378\) 1.53916 0.0791661
\(379\) 20.7225 1.06445 0.532223 0.846604i \(-0.321357\pi\)
0.532223 + 0.846604i \(0.321357\pi\)
\(380\) 11.1937 0.574223
\(381\) 6.48599 0.332288
\(382\) −6.99392 −0.357840
\(383\) −17.5943 −0.899028 −0.449514 0.893273i \(-0.648403\pi\)
−0.449514 + 0.893273i \(0.648403\pi\)
\(384\) 6.44824 0.329060
\(385\) 0 0
\(386\) 2.29227 0.116673
\(387\) 13.5257 0.687548
\(388\) 16.1069 0.817702
\(389\) −23.3951 −1.18618 −0.593089 0.805137i \(-0.702092\pi\)
−0.593089 + 0.805137i \(0.702092\pi\)
\(390\) −0.325542 −0.0164845
\(391\) −6.90258 −0.349079
\(392\) −1.77632 −0.0897176
\(393\) −10.0315 −0.506022
\(394\) −10.0177 −0.504684
\(395\) 0.0718642 0.00361588
\(396\) 0 0
\(397\) 6.31381 0.316881 0.158441 0.987369i \(-0.449353\pi\)
0.158441 + 0.987369i \(0.449353\pi\)
\(398\) 0.511951 0.0256618
\(399\) −3.63624 −0.182040
\(400\) 2.72318 0.136159
\(401\) −29.4882 −1.47257 −0.736284 0.676672i \(-0.763421\pi\)
−0.736284 + 0.676672i \(0.763421\pi\)
\(402\) 1.38364 0.0690099
\(403\) −11.3432 −0.565043
\(404\) 4.29937 0.213902
\(405\) −6.10558 −0.303389
\(406\) 3.19596 0.158613
\(407\) 0 0
\(408\) 1.11418 0.0551602
\(409\) −22.1755 −1.09651 −0.548253 0.836313i \(-0.684707\pi\)
−0.548253 + 0.836313i \(0.684707\pi\)
\(410\) −4.47278 −0.220895
\(411\) −10.8857 −0.536952
\(412\) 23.3437 1.15006
\(413\) −4.91466 −0.241835
\(414\) 7.96976 0.391692
\(415\) 9.16537 0.449910
\(416\) −5.79141 −0.283947
\(417\) 11.6097 0.568530
\(418\) 0 0
\(419\) −23.8536 −1.16532 −0.582662 0.812715i \(-0.697989\pi\)
−0.582662 + 0.812715i \(0.697989\pi\)
\(420\) −1.02816 −0.0501692
\(421\) 15.7409 0.767162 0.383581 0.923507i \(-0.374691\pi\)
0.383581 + 0.923507i \(0.374691\pi\)
\(422\) −10.8037 −0.525914
\(423\) −10.3945 −0.505396
\(424\) 21.7050 1.05409
\(425\) 1.08534 0.0526465
\(426\) 1.96859 0.0953783
\(427\) −10.6033 −0.513132
\(428\) −24.2515 −1.17224
\(429\) 0 0
\(430\) 2.38471 0.115001
\(431\) 1.50575 0.0725294 0.0362647 0.999342i \(-0.488454\pi\)
0.0362647 + 0.999342i \(0.488454\pi\)
\(432\) 8.91710 0.429024
\(433\) 6.62788 0.318516 0.159258 0.987237i \(-0.449090\pi\)
0.159258 + 0.987237i \(0.449090\pi\)
\(434\) 4.44909 0.213563
\(435\) 3.92949 0.188404
\(436\) −12.7126 −0.608824
\(437\) −40.0156 −1.91420
\(438\) −2.78428 −0.133038
\(439\) 5.96524 0.284705 0.142353 0.989816i \(-0.454533\pi\)
0.142353 + 0.989816i \(0.454533\pi\)
\(440\) 0 0
\(441\) −2.66600 −0.126953
\(442\) −0.611365 −0.0290797
\(443\) 26.5172 1.25987 0.629936 0.776647i \(-0.283081\pi\)
0.629936 + 0.776647i \(0.283081\pi\)
\(444\) −8.73918 −0.414743
\(445\) 3.20656 0.152005
\(446\) −10.9843 −0.520124
\(447\) 6.57371 0.310926
\(448\) −3.17481 −0.149995
\(449\) 37.4390 1.76686 0.883429 0.468565i \(-0.155229\pi\)
0.883429 + 0.468565i \(0.155229\pi\)
\(450\) −1.25313 −0.0590733
\(451\) 0 0
\(452\) −19.4302 −0.913922
\(453\) 7.39954 0.347661
\(454\) −4.35392 −0.204339
\(455\) 1.19839 0.0561815
\(456\) 6.45912 0.302476
\(457\) −1.42603 −0.0667069 −0.0333535 0.999444i \(-0.510619\pi\)
−0.0333535 + 0.999444i \(0.510619\pi\)
\(458\) 10.5167 0.491412
\(459\) 3.55396 0.165885
\(460\) −11.3146 −0.527545
\(461\) −0.554469 −0.0258242 −0.0129121 0.999917i \(-0.504110\pi\)
−0.0129121 + 0.999917i \(0.504110\pi\)
\(462\) 0 0
\(463\) 16.2994 0.757495 0.378748 0.925500i \(-0.376355\pi\)
0.378748 + 0.925500i \(0.376355\pi\)
\(464\) 18.5157 0.859570
\(465\) 5.47024 0.253676
\(466\) −0.141475 −0.00655372
\(467\) −22.7720 −1.05376 −0.526880 0.849939i \(-0.676638\pi\)
−0.526880 + 0.849939i \(0.676638\pi\)
\(468\) −5.68396 −0.262741
\(469\) −5.09350 −0.235196
\(470\) −1.83264 −0.0845335
\(471\) −4.75691 −0.219187
\(472\) 8.73001 0.401831
\(473\) 0 0
\(474\) 0.0195218 0.000896668 0
\(475\) 6.29189 0.288692
\(476\) −1.93088 −0.0885017
\(477\) 32.5761 1.49156
\(478\) 8.37081 0.382872
\(479\) 14.7738 0.675033 0.337516 0.941320i \(-0.390413\pi\)
0.337516 + 0.941320i \(0.390413\pi\)
\(480\) 2.79290 0.127478
\(481\) 10.1861 0.464447
\(482\) −6.96486 −0.317240
\(483\) 3.67552 0.167242
\(484\) 0 0
\(485\) 9.05358 0.411102
\(486\) −6.27607 −0.284688
\(487\) −6.18415 −0.280231 −0.140115 0.990135i \(-0.544747\pi\)
−0.140115 + 0.990135i \(0.544747\pi\)
\(488\) 18.8349 0.852616
\(489\) −3.64488 −0.164827
\(490\) −0.470042 −0.0212343
\(491\) 36.2148 1.63435 0.817175 0.576389i \(-0.195539\pi\)
0.817175 + 0.576389i \(0.195539\pi\)
\(492\) 9.78370 0.441083
\(493\) 7.37953 0.332357
\(494\) −3.54420 −0.159461
\(495\) 0 0
\(496\) 25.7757 1.15736
\(497\) −7.24680 −0.325063
\(498\) 2.48976 0.111569
\(499\) −17.9874 −0.805227 −0.402614 0.915370i \(-0.631898\pi\)
−0.402614 + 0.915370i \(0.631898\pi\)
\(500\) 1.77906 0.0795620
\(501\) 5.40379 0.241424
\(502\) 2.31541 0.103342
\(503\) −20.1263 −0.897389 −0.448694 0.893685i \(-0.648111\pi\)
−0.448694 + 0.893685i \(0.648111\pi\)
\(504\) 4.73567 0.210943
\(505\) 2.41665 0.107540
\(506\) 0 0
\(507\) 6.68304 0.296804
\(508\) 19.9662 0.885858
\(509\) −22.3565 −0.990936 −0.495468 0.868626i \(-0.665003\pi\)
−0.495468 + 0.868626i \(0.665003\pi\)
\(510\) 0.294830 0.0130553
\(511\) 10.2495 0.453413
\(512\) 22.8346 1.00916
\(513\) 20.6030 0.909643
\(514\) 4.99549 0.220341
\(515\) 13.1214 0.578196
\(516\) −5.21627 −0.229633
\(517\) 0 0
\(518\) −3.99527 −0.175542
\(519\) 4.03628 0.177173
\(520\) −2.12873 −0.0933509
\(521\) −4.65362 −0.203879 −0.101939 0.994791i \(-0.532505\pi\)
−0.101939 + 0.994791i \(0.532505\pi\)
\(522\) −8.52044 −0.372930
\(523\) −28.6197 −1.25145 −0.625726 0.780043i \(-0.715197\pi\)
−0.625726 + 0.780043i \(0.715197\pi\)
\(524\) −30.8806 −1.34902
\(525\) −0.577925 −0.0252227
\(526\) −3.11595 −0.135862
\(527\) 10.2730 0.447501
\(528\) 0 0
\(529\) 17.4478 0.758600
\(530\) 5.74348 0.249481
\(531\) 13.1025 0.568600
\(532\) −11.1937 −0.485307
\(533\) −11.4036 −0.493943
\(534\) 0.871058 0.0376944
\(535\) −13.6316 −0.589347
\(536\) 9.04768 0.390800
\(537\) −7.51416 −0.324260
\(538\) 6.87265 0.296301
\(539\) 0 0
\(540\) 5.82557 0.250693
\(541\) 1.53468 0.0659810 0.0329905 0.999456i \(-0.489497\pi\)
0.0329905 + 0.999456i \(0.489497\pi\)
\(542\) 2.35219 0.101035
\(543\) 10.5411 0.452363
\(544\) 5.24504 0.224879
\(545\) −7.14569 −0.306088
\(546\) 0.325542 0.0139319
\(547\) 32.9352 1.40821 0.704104 0.710097i \(-0.251349\pi\)
0.704104 + 0.710097i \(0.251349\pi\)
\(548\) −33.5101 −1.43148
\(549\) 28.2686 1.20647
\(550\) 0 0
\(551\) 42.7805 1.82251
\(552\) −6.52889 −0.277888
\(553\) −0.0718642 −0.00305598
\(554\) −1.64716 −0.0699813
\(555\) −4.91225 −0.208513
\(556\) 35.7389 1.51567
\(557\) 25.5992 1.08467 0.542337 0.840161i \(-0.317539\pi\)
0.542337 + 0.840161i \(0.317539\pi\)
\(558\) −11.8613 −0.502129
\(559\) 6.07991 0.257153
\(560\) −2.72318 −0.115075
\(561\) 0 0
\(562\) 4.43012 0.186874
\(563\) −14.5421 −0.612876 −0.306438 0.951891i \(-0.599137\pi\)
−0.306438 + 0.951891i \(0.599137\pi\)
\(564\) 4.00870 0.168797
\(565\) −10.9216 −0.459476
\(566\) −7.47885 −0.314359
\(567\) 6.10558 0.256410
\(568\) 12.8726 0.540123
\(569\) −4.43273 −0.185830 −0.0929148 0.995674i \(-0.529618\pi\)
−0.0929148 + 0.995674i \(0.529618\pi\)
\(570\) 1.70919 0.0715900
\(571\) 25.7504 1.07762 0.538811 0.842427i \(-0.318874\pi\)
0.538811 + 0.842427i \(0.318874\pi\)
\(572\) 0 0
\(573\) 8.59914 0.359234
\(574\) 4.47278 0.186690
\(575\) −6.35986 −0.265224
\(576\) 8.46404 0.352668
\(577\) 42.5310 1.77059 0.885294 0.465031i \(-0.153957\pi\)
0.885294 + 0.465031i \(0.153957\pi\)
\(578\) −7.43703 −0.309340
\(579\) −2.81838 −0.117128
\(580\) 12.0964 0.502275
\(581\) −9.16537 −0.380243
\(582\) 2.45940 0.101945
\(583\) 0 0
\(584\) −18.2064 −0.753388
\(585\) −3.19492 −0.132094
\(586\) −7.21861 −0.298198
\(587\) 2.68746 0.110923 0.0554617 0.998461i \(-0.482337\pi\)
0.0554617 + 0.998461i \(0.482337\pi\)
\(588\) 1.02816 0.0424007
\(589\) 59.5547 2.45391
\(590\) 2.31010 0.0951053
\(591\) 12.3169 0.506651
\(592\) −23.1465 −0.951314
\(593\) 27.0766 1.11190 0.555952 0.831214i \(-0.312354\pi\)
0.555952 + 0.831214i \(0.312354\pi\)
\(594\) 0 0
\(595\) −1.08534 −0.0444944
\(596\) 20.2362 0.828909
\(597\) −0.629452 −0.0257618
\(598\) 3.58248 0.146498
\(599\) −16.1515 −0.659933 −0.329966 0.943993i \(-0.607037\pi\)
−0.329966 + 0.943993i \(0.607037\pi\)
\(600\) 1.02658 0.0419099
\(601\) 12.3469 0.503640 0.251820 0.967774i \(-0.418971\pi\)
0.251820 + 0.967774i \(0.418971\pi\)
\(602\) −2.38471 −0.0971934
\(603\) 13.5793 0.552991
\(604\) 22.7785 0.926842
\(605\) 0 0
\(606\) 0.656481 0.0266677
\(607\) 13.0242 0.528635 0.264318 0.964436i \(-0.414853\pi\)
0.264318 + 0.964436i \(0.414853\pi\)
\(608\) 30.4065 1.23315
\(609\) −3.92949 −0.159231
\(610\) 4.98402 0.201797
\(611\) −4.67241 −0.189025
\(612\) 5.14773 0.208085
\(613\) −21.3235 −0.861249 −0.430624 0.902531i \(-0.641707\pi\)
−0.430624 + 0.902531i \(0.641707\pi\)
\(614\) 7.55177 0.304765
\(615\) 5.49936 0.221756
\(616\) 0 0
\(617\) −38.5851 −1.55338 −0.776688 0.629886i \(-0.783102\pi\)
−0.776688 + 0.629886i \(0.783102\pi\)
\(618\) 3.56440 0.143381
\(619\) −43.6172 −1.75312 −0.876561 0.481290i \(-0.840168\pi\)
−0.876561 + 0.481290i \(0.840168\pi\)
\(620\) 16.8394 0.676285
\(621\) −20.8255 −0.835699
\(622\) 1.72552 0.0691870
\(623\) −3.20656 −0.128468
\(624\) 1.88602 0.0755012
\(625\) 1.00000 0.0400000
\(626\) −2.09285 −0.0836472
\(627\) 0 0
\(628\) −14.6435 −0.584339
\(629\) −9.22514 −0.367831
\(630\) 1.25313 0.0499261
\(631\) 4.87238 0.193966 0.0969831 0.995286i \(-0.469081\pi\)
0.0969831 + 0.995286i \(0.469081\pi\)
\(632\) 0.127654 0.00507779
\(633\) 13.2833 0.527963
\(634\) −10.4829 −0.416329
\(635\) 11.2229 0.445367
\(636\) −12.5632 −0.498163
\(637\) −1.19839 −0.0474821
\(638\) 0 0
\(639\) 19.3200 0.764287
\(640\) 11.1576 0.441042
\(641\) 34.8401 1.37610 0.688052 0.725662i \(-0.258466\pi\)
0.688052 + 0.725662i \(0.258466\pi\)
\(642\) −3.70302 −0.146147
\(643\) −32.0891 −1.26547 −0.632735 0.774368i \(-0.718068\pi\)
−0.632735 + 0.774368i \(0.718068\pi\)
\(644\) 11.3146 0.445857
\(645\) −2.93204 −0.115449
\(646\) 3.20983 0.126289
\(647\) 19.5279 0.767719 0.383860 0.923392i \(-0.374595\pi\)
0.383860 + 0.923392i \(0.374595\pi\)
\(648\) −10.8455 −0.426050
\(649\) 0 0
\(650\) −0.563295 −0.0220943
\(651\) −5.47024 −0.214395
\(652\) −11.2203 −0.439419
\(653\) 1.40985 0.0551716 0.0275858 0.999619i \(-0.491218\pi\)
0.0275858 + 0.999619i \(0.491218\pi\)
\(654\) −1.94112 −0.0759038
\(655\) −17.3578 −0.678226
\(656\) 25.9130 1.01173
\(657\) −27.3253 −1.06606
\(658\) 1.83264 0.0714439
\(659\) −18.6595 −0.726871 −0.363435 0.931619i \(-0.618396\pi\)
−0.363435 + 0.931619i \(0.618396\pi\)
\(660\) 0 0
\(661\) −2.08885 −0.0812468 −0.0406234 0.999175i \(-0.512934\pi\)
−0.0406234 + 0.999175i \(0.512934\pi\)
\(662\) −3.96393 −0.154062
\(663\) 0.751683 0.0291930
\(664\) 16.2806 0.631810
\(665\) −6.29189 −0.243989
\(666\) 10.6514 0.412733
\(667\) −43.2426 −1.67436
\(668\) 16.6348 0.643621
\(669\) 13.5054 0.522150
\(670\) 2.39416 0.0924945
\(671\) 0 0
\(672\) −2.79290 −0.107739
\(673\) −31.9112 −1.23009 −0.615043 0.788493i \(-0.710861\pi\)
−0.615043 + 0.788493i \(0.710861\pi\)
\(674\) −14.2415 −0.548561
\(675\) 3.27452 0.126036
\(676\) 20.5728 0.791261
\(677\) −4.07020 −0.156431 −0.0782153 0.996936i \(-0.524922\pi\)
−0.0782153 + 0.996936i \(0.524922\pi\)
\(678\) −2.96685 −0.113941
\(679\) −9.05358 −0.347445
\(680\) 1.92790 0.0739317
\(681\) 5.35321 0.205136
\(682\) 0 0
\(683\) 38.8897 1.48807 0.744036 0.668139i \(-0.232909\pi\)
0.744036 + 0.668139i \(0.232909\pi\)
\(684\) 29.8423 1.14105
\(685\) −18.8358 −0.719681
\(686\) 0.470042 0.0179463
\(687\) −12.9304 −0.493327
\(688\) −13.8157 −0.526720
\(689\) 14.6433 0.557864
\(690\) −1.72765 −0.0657705
\(691\) −47.2979 −1.79930 −0.899649 0.436613i \(-0.856178\pi\)
−0.899649 + 0.436613i \(0.856178\pi\)
\(692\) 12.4251 0.472332
\(693\) 0 0
\(694\) −0.793029 −0.0301030
\(695\) 20.0886 0.762005
\(696\) 6.98002 0.264577
\(697\) 10.3277 0.391191
\(698\) 12.3194 0.466298
\(699\) 0.173946 0.00657925
\(700\) −1.77906 −0.0672422
\(701\) −13.4974 −0.509791 −0.254896 0.966969i \(-0.582041\pi\)
−0.254896 + 0.966969i \(0.582041\pi\)
\(702\) −1.84452 −0.0696171
\(703\) −53.4799 −2.01703
\(704\) 0 0
\(705\) 2.25327 0.0848629
\(706\) 8.30979 0.312743
\(707\) −2.41665 −0.0908876
\(708\) −5.05307 −0.189906
\(709\) 16.3431 0.613776 0.306888 0.951746i \(-0.400712\pi\)
0.306888 + 0.951746i \(0.400712\pi\)
\(710\) 3.40630 0.127836
\(711\) 0.191590 0.00718520
\(712\) 5.69587 0.213462
\(713\) −60.1980 −2.25443
\(714\) −0.294830 −0.0110338
\(715\) 0 0
\(716\) −23.1313 −0.864456
\(717\) −10.2920 −0.384364
\(718\) −3.32035 −0.123914
\(719\) 5.59133 0.208521 0.104261 0.994550i \(-0.466752\pi\)
0.104261 + 0.994550i \(0.466752\pi\)
\(720\) 7.26000 0.270564
\(721\) −13.1214 −0.488665
\(722\) 9.67720 0.360148
\(723\) 8.56341 0.318476
\(724\) 32.4494 1.20597
\(725\) 6.79931 0.252520
\(726\) 0 0
\(727\) 15.1035 0.560159 0.280080 0.959977i \(-0.409639\pi\)
0.280080 + 0.959977i \(0.409639\pi\)
\(728\) 2.12873 0.0788959
\(729\) −10.6002 −0.392601
\(730\) −4.81772 −0.178312
\(731\) −5.50633 −0.203659
\(732\) −10.9020 −0.402948
\(733\) −13.0144 −0.480696 −0.240348 0.970687i \(-0.577262\pi\)
−0.240348 + 0.970687i \(0.577262\pi\)
\(734\) 4.27580 0.157823
\(735\) 0.577925 0.0213171
\(736\) −30.7349 −1.13290
\(737\) 0 0
\(738\) −11.9245 −0.438945
\(739\) 25.1956 0.926836 0.463418 0.886140i \(-0.346623\pi\)
0.463418 + 0.886140i \(0.346623\pi\)
\(740\) −15.1217 −0.555883
\(741\) 4.35765 0.160082
\(742\) −5.74348 −0.210850
\(743\) 38.2296 1.40251 0.701254 0.712911i \(-0.252624\pi\)
0.701254 + 0.712911i \(0.252624\pi\)
\(744\) 9.71688 0.356238
\(745\) 11.3747 0.416736
\(746\) −15.9620 −0.584412
\(747\) 24.4349 0.894026
\(748\) 0 0
\(749\) 13.6316 0.498089
\(750\) 0.271649 0.00991922
\(751\) −24.3760 −0.889494 −0.444747 0.895656i \(-0.646706\pi\)
−0.444747 + 0.895656i \(0.646706\pi\)
\(752\) 10.6174 0.387176
\(753\) −2.84683 −0.103744
\(754\) −3.83002 −0.139481
\(755\) 12.8036 0.465972
\(756\) −5.82557 −0.211874
\(757\) 28.9119 1.05082 0.525410 0.850849i \(-0.323912\pi\)
0.525410 + 0.850849i \(0.323912\pi\)
\(758\) 9.74047 0.353790
\(759\) 0 0
\(760\) 11.1764 0.405411
\(761\) 17.6334 0.639212 0.319606 0.947551i \(-0.396449\pi\)
0.319606 + 0.947551i \(0.396449\pi\)
\(762\) 3.04869 0.110442
\(763\) 7.14569 0.258691
\(764\) 26.4712 0.957696
\(765\) 2.89351 0.104615
\(766\) −8.27008 −0.298810
\(767\) 5.88970 0.212665
\(768\) −0.638652 −0.0230454
\(769\) −30.2925 −1.09237 −0.546187 0.837663i \(-0.683921\pi\)
−0.546187 + 0.837663i \(0.683921\pi\)
\(770\) 0 0
\(771\) −6.14203 −0.221200
\(772\) −8.67599 −0.312256
\(773\) −30.0549 −1.08100 −0.540500 0.841344i \(-0.681765\pi\)
−0.540500 + 0.841344i \(0.681765\pi\)
\(774\) 6.35763 0.228520
\(775\) 9.46531 0.340004
\(776\) 16.0820 0.577312
\(777\) 4.91225 0.176226
\(778\) −10.9967 −0.394250
\(779\) 59.8718 2.14513
\(780\) 1.23214 0.0441178
\(781\) 0 0
\(782\) −3.24451 −0.116023
\(783\) 22.2645 0.795668
\(784\) 2.72318 0.0972563
\(785\) −8.23103 −0.293778
\(786\) −4.71523 −0.168187
\(787\) 38.2530 1.36357 0.681787 0.731551i \(-0.261203\pi\)
0.681787 + 0.731551i \(0.261203\pi\)
\(788\) 37.9159 1.35070
\(789\) 3.83111 0.136391
\(790\) 0.0337792 0.00120181
\(791\) 10.9216 0.388329
\(792\) 0 0
\(793\) 12.7070 0.451238
\(794\) 2.96776 0.105322
\(795\) −7.06171 −0.250453
\(796\) −1.93768 −0.0686793
\(797\) −12.7361 −0.451135 −0.225568 0.974228i \(-0.572424\pi\)
−0.225568 + 0.974228i \(0.572424\pi\)
\(798\) −1.70919 −0.0605046
\(799\) 4.23161 0.149704
\(800\) 4.83264 0.170860
\(801\) 8.54870 0.302053
\(802\) −13.8607 −0.489438
\(803\) 0 0
\(804\) −5.23695 −0.184693
\(805\) 6.35986 0.224156
\(806\) −5.33177 −0.187803
\(807\) −8.45004 −0.297455
\(808\) 4.29274 0.151018
\(809\) 13.6911 0.481354 0.240677 0.970605i \(-0.422631\pi\)
0.240677 + 0.970605i \(0.422631\pi\)
\(810\) −2.86988 −0.100837
\(811\) −42.2475 −1.48351 −0.741756 0.670670i \(-0.766007\pi\)
−0.741756 + 0.670670i \(0.766007\pi\)
\(812\) −12.0964 −0.424500
\(813\) −2.89205 −0.101429
\(814\) 0 0
\(815\) −6.30685 −0.220919
\(816\) −1.70809 −0.0597952
\(817\) −31.9212 −1.11678
\(818\) −10.4234 −0.364446
\(819\) 3.19492 0.111640
\(820\) 16.9290 0.591187
\(821\) −31.6222 −1.10362 −0.551810 0.833970i \(-0.686063\pi\)
−0.551810 + 0.833970i \(0.686063\pi\)
\(822\) −5.11674 −0.178467
\(823\) 32.4818 1.13224 0.566122 0.824322i \(-0.308443\pi\)
0.566122 + 0.824322i \(0.308443\pi\)
\(824\) 23.3077 0.811962
\(825\) 0 0
\(826\) −2.31010 −0.0803786
\(827\) −51.6677 −1.79666 −0.898330 0.439321i \(-0.855219\pi\)
−0.898330 + 0.439321i \(0.855219\pi\)
\(828\) −30.1647 −1.04830
\(829\) 3.81406 0.132468 0.0662339 0.997804i \(-0.478902\pi\)
0.0662339 + 0.997804i \(0.478902\pi\)
\(830\) 4.30811 0.149537
\(831\) 2.02522 0.0702539
\(832\) 3.80467 0.131903
\(833\) 1.08534 0.0376047
\(834\) 5.45706 0.188962
\(835\) 9.35034 0.323582
\(836\) 0 0
\(837\) 30.9944 1.07132
\(838\) −11.2122 −0.387319
\(839\) −34.9994 −1.20831 −0.604157 0.796865i \(-0.706490\pi\)
−0.604157 + 0.796865i \(0.706490\pi\)
\(840\) −1.02658 −0.0354203
\(841\) 17.2306 0.594157
\(842\) 7.39887 0.254982
\(843\) −5.44691 −0.187602
\(844\) 40.8907 1.40752
\(845\) 11.5639 0.397809
\(846\) −4.88583 −0.167978
\(847\) 0 0
\(848\) −33.2747 −1.14266
\(849\) 9.19537 0.315584
\(850\) 0.510154 0.0174981
\(851\) 54.0576 1.85307
\(852\) −7.45089 −0.255263
\(853\) 51.6573 1.76871 0.884357 0.466812i \(-0.154597\pi\)
0.884357 + 0.466812i \(0.154597\pi\)
\(854\) −4.98402 −0.170550
\(855\) 16.7742 0.573666
\(856\) −24.2141 −0.827622
\(857\) 11.4832 0.392258 0.196129 0.980578i \(-0.437163\pi\)
0.196129 + 0.980578i \(0.437163\pi\)
\(858\) 0 0
\(859\) 11.5148 0.392880 0.196440 0.980516i \(-0.437062\pi\)
0.196440 + 0.980516i \(0.437062\pi\)
\(860\) −9.02586 −0.307779
\(861\) −5.49936 −0.187418
\(862\) 0.707766 0.0241066
\(863\) −27.5849 −0.938999 −0.469500 0.882933i \(-0.655566\pi\)
−0.469500 + 0.882933i \(0.655566\pi\)
\(864\) 15.8246 0.538364
\(865\) 6.98410 0.237466
\(866\) 3.11538 0.105865
\(867\) 9.14395 0.310545
\(868\) −16.8394 −0.571565
\(869\) 0 0
\(870\) 1.84702 0.0626200
\(871\) 6.10402 0.206827
\(872\) −12.6930 −0.429840
\(873\) 24.1369 0.816910
\(874\) −18.8090 −0.636224
\(875\) −1.00000 −0.0338062
\(876\) 10.5382 0.356053
\(877\) −50.2969 −1.69841 −0.849203 0.528067i \(-0.822917\pi\)
−0.849203 + 0.528067i \(0.822917\pi\)
\(878\) 2.80392 0.0946276
\(879\) 8.87540 0.299360
\(880\) 0 0
\(881\) −29.4455 −0.992044 −0.496022 0.868310i \(-0.665207\pi\)
−0.496022 + 0.868310i \(0.665207\pi\)
\(882\) −1.25313 −0.0421952
\(883\) 27.3839 0.921542 0.460771 0.887519i \(-0.347573\pi\)
0.460771 + 0.887519i \(0.347573\pi\)
\(884\) 2.31395 0.0778266
\(885\) −2.84031 −0.0954758
\(886\) 12.4642 0.418744
\(887\) −43.0693 −1.44612 −0.723062 0.690783i \(-0.757266\pi\)
−0.723062 + 0.690783i \(0.757266\pi\)
\(888\) −8.72571 −0.292816
\(889\) −11.2229 −0.376404
\(890\) 1.50722 0.0505221
\(891\) 0 0
\(892\) 41.5746 1.39202
\(893\) 24.5314 0.820912
\(894\) 3.08992 0.103342
\(895\) −13.0020 −0.434608
\(896\) −11.1576 −0.372749
\(897\) −4.40472 −0.147069
\(898\) 17.5979 0.587251
\(899\) 64.3575 2.14644
\(900\) 4.74298 0.158099
\(901\) −13.2618 −0.441815
\(902\) 0 0
\(903\) 2.93204 0.0975720
\(904\) −19.4003 −0.645244
\(905\) 18.2396 0.606306
\(906\) 3.47810 0.115552
\(907\) −30.1364 −1.00066 −0.500332 0.865834i \(-0.666789\pi\)
−0.500332 + 0.865834i \(0.666789\pi\)
\(908\) 16.4791 0.546879
\(909\) 6.44280 0.213694
\(910\) 0.563295 0.0186731
\(911\) 39.4333 1.30648 0.653242 0.757149i \(-0.273409\pi\)
0.653242 + 0.757149i \(0.273409\pi\)
\(912\) −9.90213 −0.327892
\(913\) 0 0
\(914\) −0.670295 −0.0221714
\(915\) −6.12793 −0.202583
\(916\) −39.8045 −1.31518
\(917\) 17.3578 0.573205
\(918\) 1.67051 0.0551350
\(919\) 16.9203 0.558149 0.279075 0.960269i \(-0.409972\pi\)
0.279075 + 0.960269i \(0.409972\pi\)
\(920\) −11.2971 −0.372455
\(921\) −9.28503 −0.305952
\(922\) −0.260624 −0.00858319
\(923\) 8.68452 0.285854
\(924\) 0 0
\(925\) −8.49980 −0.279472
\(926\) 7.66139 0.251769
\(927\) 34.9816 1.14895
\(928\) 32.8586 1.07864
\(929\) −41.8149 −1.37190 −0.685951 0.727648i \(-0.740613\pi\)
−0.685951 + 0.727648i \(0.740613\pi\)
\(930\) 2.57124 0.0843143
\(931\) 6.29189 0.206209
\(932\) 0.535469 0.0175399
\(933\) −2.12155 −0.0694565
\(934\) −10.7038 −0.350239
\(935\) 0 0
\(936\) −5.67519 −0.185500
\(937\) 10.7732 0.351947 0.175973 0.984395i \(-0.443693\pi\)
0.175973 + 0.984395i \(0.443693\pi\)
\(938\) −2.39416 −0.0781721
\(939\) 2.57320 0.0839731
\(940\) 6.93636 0.226239
\(941\) 10.4374 0.340249 0.170125 0.985423i \(-0.445583\pi\)
0.170125 + 0.985423i \(0.445583\pi\)
\(942\) −2.23595 −0.0728512
\(943\) −60.5186 −1.97076
\(944\) −13.3835 −0.435596
\(945\) −3.27452 −0.106520
\(946\) 0 0
\(947\) 25.7372 0.836348 0.418174 0.908367i \(-0.362670\pi\)
0.418174 + 0.908367i \(0.362670\pi\)
\(948\) −0.0738881 −0.00239978
\(949\) −12.2830 −0.398723
\(950\) 2.95746 0.0959525
\(951\) 12.8889 0.417951
\(952\) −1.92790 −0.0624837
\(953\) 22.0261 0.713496 0.356748 0.934201i \(-0.383885\pi\)
0.356748 + 0.934201i \(0.383885\pi\)
\(954\) 15.3121 0.495749
\(955\) 14.8793 0.481484
\(956\) −31.6826 −1.02469
\(957\) 0 0
\(958\) 6.94431 0.224361
\(959\) 18.8358 0.608241
\(960\) −1.83480 −0.0592179
\(961\) 58.5921 1.89007
\(962\) 4.78790 0.154368
\(963\) −36.3420 −1.17110
\(964\) 26.3612 0.849039
\(965\) −4.87672 −0.156987
\(966\) 1.72765 0.0555862
\(967\) −39.0647 −1.25624 −0.628118 0.778118i \(-0.716174\pi\)
−0.628118 + 0.778118i \(0.716174\pi\)
\(968\) 0 0
\(969\) −3.94654 −0.126781
\(970\) 4.25557 0.136638
\(971\) 27.4441 0.880723 0.440362 0.897820i \(-0.354850\pi\)
0.440362 + 0.897820i \(0.354850\pi\)
\(972\) 23.7543 0.761918
\(973\) −20.0886 −0.644012
\(974\) −2.90681 −0.0931403
\(975\) 0.692581 0.0221803
\(976\) −28.8748 −0.924259
\(977\) 13.7037 0.438420 0.219210 0.975678i \(-0.429652\pi\)
0.219210 + 0.975678i \(0.429652\pi\)
\(978\) −1.71325 −0.0547837
\(979\) 0 0
\(980\) 1.77906 0.0568300
\(981\) −19.0504 −0.608234
\(982\) 17.0225 0.543209
\(983\) 26.5600 0.847133 0.423566 0.905865i \(-0.360778\pi\)
0.423566 + 0.905865i \(0.360778\pi\)
\(984\) 9.76862 0.311412
\(985\) 21.3123 0.679067
\(986\) 3.46869 0.110466
\(987\) −2.25327 −0.0717222
\(988\) 13.4144 0.426769
\(989\) 32.2660 1.02600
\(990\) 0 0
\(991\) −55.9346 −1.77682 −0.888410 0.459051i \(-0.848190\pi\)
−0.888410 + 0.459051i \(0.848190\pi\)
\(992\) 45.7425 1.45232
\(993\) 4.87371 0.154663
\(994\) −3.40630 −0.108041
\(995\) −1.08916 −0.0345287
\(996\) −9.42349 −0.298595
\(997\) −1.89634 −0.0600578 −0.0300289 0.999549i \(-0.509560\pi\)
−0.0300289 + 0.999549i \(0.509560\pi\)
\(998\) −8.45484 −0.267633
\(999\) −27.8328 −0.880591
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 4235.2.a.bb.1.3 yes 5
11.10 odd 2 4235.2.a.ba.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4235.2.a.ba.1.3 5 11.10 odd 2
4235.2.a.bb.1.3 yes 5 1.1 even 1 trivial