Properties

Label 1925.2.a.bb.1.1
Level $1925$
Weight $2$
Character 1925.1
Self dual yes
Analytic conductor $15.371$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1925,2,Mod(1,1925)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1925, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1925.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1925.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(15.3712023891\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 13x^{5} + 12x^{4} + 47x^{3} - 37x^{2} - 35x + 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.71503\) of defining polynomial
Character \(\chi\) \(=\) 1925.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.71503 q^{2} +0.525975 q^{3} +5.37138 q^{4} -1.42804 q^{6} -1.00000 q^{7} -9.15341 q^{8} -2.72335 q^{9} +O(q^{10})\) \(q-2.71503 q^{2} +0.525975 q^{3} +5.37138 q^{4} -1.42804 q^{6} -1.00000 q^{7} -9.15341 q^{8} -2.72335 q^{9} +1.00000 q^{11} +2.82522 q^{12} +5.27345 q^{13} +2.71503 q^{14} +14.1090 q^{16} -5.04671 q^{17} +7.39398 q^{18} +6.37138 q^{19} -0.525975 q^{21} -2.71503 q^{22} -7.72930 q^{23} -4.81447 q^{24} -14.3176 q^{26} -3.01034 q^{27} -5.37138 q^{28} +7.19109 q^{29} -7.15734 q^{31} -19.9995 q^{32} +0.525975 q^{33} +13.7020 q^{34} -14.6282 q^{36} -3.65636 q^{37} -17.2985 q^{38} +2.77370 q^{39} +4.14263 q^{41} +1.42804 q^{42} +10.2054 q^{43} +5.37138 q^{44} +20.9853 q^{46} +11.4487 q^{47} +7.42099 q^{48} +1.00000 q^{49} -2.65445 q^{51} +28.3257 q^{52} +0.365435 q^{53} +8.17316 q^{54} +9.15341 q^{56} +3.35119 q^{57} -19.5240 q^{58} -2.10828 q^{59} -11.3378 q^{61} +19.4324 q^{62} +2.72335 q^{63} +26.0813 q^{64} -1.42804 q^{66} +4.94537 q^{67} -27.1078 q^{68} -4.06542 q^{69} +1.72737 q^{71} +24.9279 q^{72} +11.9342 q^{73} +9.92711 q^{74} +34.2232 q^{76} -1.00000 q^{77} -7.53069 q^{78} -5.40955 q^{79} +6.58668 q^{81} -11.2474 q^{82} +2.04363 q^{83} -2.82522 q^{84} -27.7079 q^{86} +3.78234 q^{87} -9.15341 q^{88} -1.29607 q^{89} -5.27345 q^{91} -41.5170 q^{92} -3.76458 q^{93} -31.0836 q^{94} -10.5193 q^{96} +1.05710 q^{97} -2.71503 q^{98} -2.72335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - q^{2} + 13 q^{4} + 3 q^{6} - 7 q^{7} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - q^{2} + 13 q^{4} + 3 q^{6} - 7 q^{7} + 9 q^{9} + 7 q^{11} + 9 q^{12} + 3 q^{13} + q^{14} + 21 q^{16} + 2 q^{17} - 8 q^{18} + 20 q^{19} - q^{22} - 11 q^{23} + 18 q^{24} - 13 q^{26} + 12 q^{27} - 13 q^{28} + 4 q^{29} + 6 q^{31} - q^{32} - 7 q^{34} + 12 q^{36} - 19 q^{37} - 3 q^{38} - 10 q^{39} + 24 q^{41} - 3 q^{42} + 13 q^{44} + 33 q^{46} + q^{47} + 15 q^{48} + 7 q^{49} + 19 q^{51} + 29 q^{52} - 7 q^{53} + 9 q^{54} + 9 q^{57} - 37 q^{58} + 9 q^{59} + 18 q^{61} + 40 q^{62} - 9 q^{63} + 8 q^{64} + 3 q^{66} - 18 q^{68} - 15 q^{69} + 18 q^{71} + 64 q^{72} - 5 q^{73} - 24 q^{74} + 88 q^{76} - 7 q^{77} - 79 q^{78} + 25 q^{79} - q^{81} + 60 q^{82} + 17 q^{83} - 9 q^{84} - 41 q^{86} + 24 q^{87} - 16 q^{89} - 3 q^{91} - 28 q^{92} - 26 q^{93} - 31 q^{94} + 17 q^{96} + 4 q^{97} - q^{98} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71503 −1.91982 −0.959908 0.280316i \(-0.909561\pi\)
−0.959908 + 0.280316i \(0.909561\pi\)
\(3\) 0.525975 0.303672 0.151836 0.988406i \(-0.451481\pi\)
0.151836 + 0.988406i \(0.451481\pi\)
\(4\) 5.37138 2.68569
\(5\) 0 0
\(6\) −1.42804 −0.582994
\(7\) −1.00000 −0.377964
\(8\) −9.15341 −3.23622
\(9\) −2.72335 −0.907783
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 2.82522 0.815570
\(13\) 5.27345 1.46259 0.731296 0.682061i \(-0.238916\pi\)
0.731296 + 0.682061i \(0.238916\pi\)
\(14\) 2.71503 0.725622
\(15\) 0 0
\(16\) 14.1090 3.52725
\(17\) −5.04671 −1.22401 −0.612004 0.790855i \(-0.709636\pi\)
−0.612004 + 0.790855i \(0.709636\pi\)
\(18\) 7.39398 1.74278
\(19\) 6.37138 1.46170 0.730848 0.682540i \(-0.239125\pi\)
0.730848 + 0.682540i \(0.239125\pi\)
\(20\) 0 0
\(21\) −0.525975 −0.114777
\(22\) −2.71503 −0.578846
\(23\) −7.72930 −1.61167 −0.805835 0.592140i \(-0.798283\pi\)
−0.805835 + 0.592140i \(0.798283\pi\)
\(24\) −4.81447 −0.982749
\(25\) 0 0
\(26\) −14.3176 −2.80791
\(27\) −3.01034 −0.579340
\(28\) −5.37138 −1.01510
\(29\) 7.19109 1.33535 0.667676 0.744452i \(-0.267289\pi\)
0.667676 + 0.744452i \(0.267289\pi\)
\(30\) 0 0
\(31\) −7.15734 −1.28550 −0.642748 0.766078i \(-0.722206\pi\)
−0.642748 + 0.766078i \(0.722206\pi\)
\(32\) −19.9995 −3.53545
\(33\) 0.525975 0.0915606
\(34\) 13.7020 2.34987
\(35\) 0 0
\(36\) −14.6282 −2.43803
\(37\) −3.65636 −0.601101 −0.300551 0.953766i \(-0.597170\pi\)
−0.300551 + 0.953766i \(0.597170\pi\)
\(38\) −17.2985 −2.80619
\(39\) 2.77370 0.444148
\(40\) 0 0
\(41\) 4.14263 0.646970 0.323485 0.946233i \(-0.395145\pi\)
0.323485 + 0.946233i \(0.395145\pi\)
\(42\) 1.42804 0.220351
\(43\) 10.2054 1.55630 0.778151 0.628077i \(-0.216158\pi\)
0.778151 + 0.628077i \(0.216158\pi\)
\(44\) 5.37138 0.809767
\(45\) 0 0
\(46\) 20.9853 3.09411
\(47\) 11.4487 1.66997 0.834984 0.550275i \(-0.185477\pi\)
0.834984 + 0.550275i \(0.185477\pi\)
\(48\) 7.42099 1.07113
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −2.65445 −0.371697
\(52\) 28.3257 3.92807
\(53\) 0.365435 0.0501964 0.0250982 0.999685i \(-0.492010\pi\)
0.0250982 + 0.999685i \(0.492010\pi\)
\(54\) 8.17316 1.11223
\(55\) 0 0
\(56\) 9.15341 1.22318
\(57\) 3.35119 0.443876
\(58\) −19.5240 −2.56363
\(59\) −2.10828 −0.274474 −0.137237 0.990538i \(-0.543822\pi\)
−0.137237 + 0.990538i \(0.543822\pi\)
\(60\) 0 0
\(61\) −11.3378 −1.45165 −0.725826 0.687879i \(-0.758542\pi\)
−0.725826 + 0.687879i \(0.758542\pi\)
\(62\) 19.4324 2.46792
\(63\) 2.72335 0.343110
\(64\) 26.0813 3.26017
\(65\) 0 0
\(66\) −1.42804 −0.175779
\(67\) 4.94537 0.604173 0.302086 0.953281i \(-0.402317\pi\)
0.302086 + 0.953281i \(0.402317\pi\)
\(68\) −27.1078 −3.28731
\(69\) −4.06542 −0.489419
\(70\) 0 0
\(71\) 1.72737 0.205001 0.102500 0.994733i \(-0.467316\pi\)
0.102500 + 0.994733i \(0.467316\pi\)
\(72\) 24.9279 2.93779
\(73\) 11.9342 1.39679 0.698397 0.715710i \(-0.253897\pi\)
0.698397 + 0.715710i \(0.253897\pi\)
\(74\) 9.92711 1.15400
\(75\) 0 0
\(76\) 34.2232 3.92567
\(77\) −1.00000 −0.113961
\(78\) −7.53069 −0.852682
\(79\) −5.40955 −0.608622 −0.304311 0.952573i \(-0.598426\pi\)
−0.304311 + 0.952573i \(0.598426\pi\)
\(80\) 0 0
\(81\) 6.58668 0.731854
\(82\) −11.2474 −1.24206
\(83\) 2.04363 0.224318 0.112159 0.993690i \(-0.464223\pi\)
0.112159 + 0.993690i \(0.464223\pi\)
\(84\) −2.82522 −0.308256
\(85\) 0 0
\(86\) −27.7079 −2.98781
\(87\) 3.78234 0.405509
\(88\) −9.15341 −0.975757
\(89\) −1.29607 −0.137383 −0.0686916 0.997638i \(-0.521882\pi\)
−0.0686916 + 0.997638i \(0.521882\pi\)
\(90\) 0 0
\(91\) −5.27345 −0.552808
\(92\) −41.5170 −4.32845
\(93\) −3.76458 −0.390369
\(94\) −31.0836 −3.20603
\(95\) 0 0
\(96\) −10.5193 −1.07362
\(97\) 1.05710 0.107332 0.0536661 0.998559i \(-0.482909\pi\)
0.0536661 + 0.998559i \(0.482909\pi\)
\(98\) −2.71503 −0.274259
\(99\) −2.72335 −0.273707
\(100\) 0 0
\(101\) −6.85373 −0.681972 −0.340986 0.940068i \(-0.610761\pi\)
−0.340986 + 0.940068i \(0.610761\pi\)
\(102\) 7.20690 0.713589
\(103\) −0.393263 −0.0387494 −0.0193747 0.999812i \(-0.506168\pi\)
−0.0193747 + 0.999812i \(0.506168\pi\)
\(104\) −48.2700 −4.73327
\(105\) 0 0
\(106\) −0.992168 −0.0963678
\(107\) 9.74434 0.942021 0.471011 0.882128i \(-0.343889\pi\)
0.471011 + 0.882128i \(0.343889\pi\)
\(108\) −16.1697 −1.55593
\(109\) −0.103367 −0.00990075 −0.00495038 0.999988i \(-0.501576\pi\)
−0.00495038 + 0.999988i \(0.501576\pi\)
\(110\) 0 0
\(111\) −1.92315 −0.182538
\(112\) −14.1090 −1.33318
\(113\) 10.6373 1.00068 0.500338 0.865830i \(-0.333209\pi\)
0.500338 + 0.865830i \(0.333209\pi\)
\(114\) −9.09858 −0.852160
\(115\) 0 0
\(116\) 38.6261 3.58634
\(117\) −14.3614 −1.32772
\(118\) 5.72404 0.526940
\(119\) 5.04671 0.462631
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 30.7824 2.78690
\(123\) 2.17892 0.196467
\(124\) −38.4448 −3.45245
\(125\) 0 0
\(126\) −7.39398 −0.658708
\(127\) 17.3047 1.53554 0.767772 0.640723i \(-0.221365\pi\)
0.767772 + 0.640723i \(0.221365\pi\)
\(128\) −30.8125 −2.72347
\(129\) 5.36777 0.472606
\(130\) 0 0
\(131\) −4.21188 −0.367994 −0.183997 0.982927i \(-0.558904\pi\)
−0.183997 + 0.982927i \(0.558904\pi\)
\(132\) 2.82522 0.245903
\(133\) −6.37138 −0.552469
\(134\) −13.4268 −1.15990
\(135\) 0 0
\(136\) 46.1946 3.96116
\(137\) −10.0108 −0.855280 −0.427640 0.903949i \(-0.640655\pi\)
−0.427640 + 0.903949i \(0.640655\pi\)
\(138\) 11.0377 0.939595
\(139\) 16.5921 1.40732 0.703662 0.710535i \(-0.251547\pi\)
0.703662 + 0.710535i \(0.251547\pi\)
\(140\) 0 0
\(141\) 6.02174 0.507122
\(142\) −4.68985 −0.393564
\(143\) 5.27345 0.440988
\(144\) −38.4238 −3.20198
\(145\) 0 0
\(146\) −32.4018 −2.68159
\(147\) 0.525975 0.0433817
\(148\) −19.6397 −1.61437
\(149\) 16.3802 1.34192 0.670959 0.741495i \(-0.265883\pi\)
0.670959 + 0.741495i \(0.265883\pi\)
\(150\) 0 0
\(151\) −1.72876 −0.140685 −0.0703424 0.997523i \(-0.522409\pi\)
−0.0703424 + 0.997523i \(0.522409\pi\)
\(152\) −58.3199 −4.73037
\(153\) 13.7440 1.11113
\(154\) 2.71503 0.218783
\(155\) 0 0
\(156\) 14.8986 1.19284
\(157\) 11.2513 0.897954 0.448977 0.893543i \(-0.351789\pi\)
0.448977 + 0.893543i \(0.351789\pi\)
\(158\) 14.6871 1.16844
\(159\) 0.192210 0.0152432
\(160\) 0 0
\(161\) 7.72930 0.609154
\(162\) −17.8830 −1.40502
\(163\) −6.30843 −0.494114 −0.247057 0.969001i \(-0.579464\pi\)
−0.247057 + 0.969001i \(0.579464\pi\)
\(164\) 22.2517 1.73756
\(165\) 0 0
\(166\) −5.54852 −0.430648
\(167\) −11.8399 −0.916201 −0.458100 0.888900i \(-0.651470\pi\)
−0.458100 + 0.888900i \(0.651470\pi\)
\(168\) 4.81447 0.371444
\(169\) 14.8093 1.13917
\(170\) 0 0
\(171\) −17.3515 −1.32690
\(172\) 54.8169 4.17975
\(173\) −10.5394 −0.801295 −0.400647 0.916232i \(-0.631215\pi\)
−0.400647 + 0.916232i \(0.631215\pi\)
\(174\) −10.2692 −0.778502
\(175\) 0 0
\(176\) 14.1090 1.06351
\(177\) −1.10890 −0.0833502
\(178\) 3.51887 0.263750
\(179\) 11.0794 0.828110 0.414055 0.910252i \(-0.364112\pi\)
0.414055 + 0.910252i \(0.364112\pi\)
\(180\) 0 0
\(181\) 6.70122 0.498098 0.249049 0.968491i \(-0.419882\pi\)
0.249049 + 0.968491i \(0.419882\pi\)
\(182\) 14.3176 1.06129
\(183\) −5.96338 −0.440826
\(184\) 70.7494 5.21572
\(185\) 0 0
\(186\) 10.2210 0.749437
\(187\) −5.04671 −0.369052
\(188\) 61.4955 4.48502
\(189\) 3.01034 0.218970
\(190\) 0 0
\(191\) 21.1680 1.53167 0.765833 0.643040i \(-0.222327\pi\)
0.765833 + 0.643040i \(0.222327\pi\)
\(192\) 13.7181 0.990022
\(193\) −10.7288 −0.772275 −0.386138 0.922441i \(-0.626191\pi\)
−0.386138 + 0.922441i \(0.626191\pi\)
\(194\) −2.87006 −0.206058
\(195\) 0 0
\(196\) 5.37138 0.383670
\(197\) 16.1526 1.15082 0.575412 0.817864i \(-0.304842\pi\)
0.575412 + 0.817864i \(0.304842\pi\)
\(198\) 7.39398 0.525467
\(199\) −12.6432 −0.896254 −0.448127 0.893970i \(-0.647909\pi\)
−0.448127 + 0.893970i \(0.647909\pi\)
\(200\) 0 0
\(201\) 2.60114 0.183470
\(202\) 18.6081 1.30926
\(203\) −7.19109 −0.504716
\(204\) −14.2581 −0.998263
\(205\) 0 0
\(206\) 1.06772 0.0743917
\(207\) 21.0496 1.46305
\(208\) 74.4031 5.15893
\(209\) 6.37138 0.440718
\(210\) 0 0
\(211\) −8.48920 −0.584420 −0.292210 0.956354i \(-0.594391\pi\)
−0.292210 + 0.956354i \(0.594391\pi\)
\(212\) 1.96289 0.134812
\(213\) 0.908552 0.0622530
\(214\) −26.4562 −1.80851
\(215\) 0 0
\(216\) 27.5549 1.87487
\(217\) 7.15734 0.485872
\(218\) 0.280644 0.0190076
\(219\) 6.27711 0.424167
\(220\) 0 0
\(221\) −26.6136 −1.79022
\(222\) 5.22142 0.350439
\(223\) 7.53215 0.504390 0.252195 0.967676i \(-0.418848\pi\)
0.252195 + 0.967676i \(0.418848\pi\)
\(224\) 19.9995 1.33628
\(225\) 0 0
\(226\) −28.8807 −1.92111
\(227\) −17.6460 −1.17120 −0.585602 0.810599i \(-0.699142\pi\)
−0.585602 + 0.810599i \(0.699142\pi\)
\(228\) 18.0005 1.19211
\(229\) 13.2705 0.876939 0.438469 0.898746i \(-0.355521\pi\)
0.438469 + 0.898746i \(0.355521\pi\)
\(230\) 0 0
\(231\) −0.525975 −0.0346066
\(232\) −65.8230 −4.32149
\(233\) 10.3195 0.676051 0.338025 0.941137i \(-0.390241\pi\)
0.338025 + 0.941137i \(0.390241\pi\)
\(234\) 38.9917 2.54897
\(235\) 0 0
\(236\) −11.3244 −0.737154
\(237\) −2.84529 −0.184822
\(238\) −13.7020 −0.888167
\(239\) −2.77046 −0.179206 −0.0896032 0.995978i \(-0.528560\pi\)
−0.0896032 + 0.995978i \(0.528560\pi\)
\(240\) 0 0
\(241\) 18.9346 1.21968 0.609841 0.792524i \(-0.291233\pi\)
0.609841 + 0.792524i \(0.291233\pi\)
\(242\) −2.71503 −0.174529
\(243\) 12.4955 0.801584
\(244\) −60.8995 −3.89869
\(245\) 0 0
\(246\) −5.91583 −0.377180
\(247\) 33.5992 2.13786
\(248\) 65.5140 4.16015
\(249\) 1.07490 0.0681190
\(250\) 0 0
\(251\) 8.48777 0.535743 0.267872 0.963455i \(-0.413680\pi\)
0.267872 + 0.963455i \(0.413680\pi\)
\(252\) 14.6282 0.921487
\(253\) −7.72930 −0.485937
\(254\) −46.9828 −2.94796
\(255\) 0 0
\(256\) 31.4942 1.96839
\(257\) 1.10707 0.0690573 0.0345286 0.999404i \(-0.489007\pi\)
0.0345286 + 0.999404i \(0.489007\pi\)
\(258\) −14.5736 −0.907316
\(259\) 3.65636 0.227195
\(260\) 0 0
\(261\) −19.5839 −1.21221
\(262\) 11.4354 0.706481
\(263\) 26.3914 1.62737 0.813683 0.581309i \(-0.197459\pi\)
0.813683 + 0.581309i \(0.197459\pi\)
\(264\) −4.81447 −0.296310
\(265\) 0 0
\(266\) 17.2985 1.06064
\(267\) −0.681701 −0.0417194
\(268\) 26.5635 1.62262
\(269\) 6.04003 0.368267 0.184134 0.982901i \(-0.441052\pi\)
0.184134 + 0.982901i \(0.441052\pi\)
\(270\) 0 0
\(271\) 4.27547 0.259716 0.129858 0.991533i \(-0.458548\pi\)
0.129858 + 0.991533i \(0.458548\pi\)
\(272\) −71.2041 −4.31738
\(273\) −2.77370 −0.167872
\(274\) 27.1796 1.64198
\(275\) 0 0
\(276\) −21.8369 −1.31443
\(277\) 9.61128 0.577486 0.288743 0.957407i \(-0.406763\pi\)
0.288743 + 0.957407i \(0.406763\pi\)
\(278\) −45.0480 −2.70180
\(279\) 19.4919 1.16695
\(280\) 0 0
\(281\) −12.4966 −0.745483 −0.372741 0.927935i \(-0.621582\pi\)
−0.372741 + 0.927935i \(0.621582\pi\)
\(282\) −16.3492 −0.973581
\(283\) 12.6457 0.751711 0.375856 0.926678i \(-0.377349\pi\)
0.375856 + 0.926678i \(0.377349\pi\)
\(284\) 9.27835 0.550569
\(285\) 0 0
\(286\) −14.3176 −0.846615
\(287\) −4.14263 −0.244532
\(288\) 54.4658 3.20943
\(289\) 8.46931 0.498195
\(290\) 0 0
\(291\) 0.556009 0.0325938
\(292\) 64.1033 3.75136
\(293\) 20.3335 1.18790 0.593948 0.804503i \(-0.297568\pi\)
0.593948 + 0.804503i \(0.297568\pi\)
\(294\) −1.42804 −0.0832849
\(295\) 0 0
\(296\) 33.4681 1.94529
\(297\) −3.01034 −0.174678
\(298\) −44.4727 −2.57623
\(299\) −40.7601 −2.35722
\(300\) 0 0
\(301\) −10.2054 −0.588227
\(302\) 4.69365 0.270089
\(303\) −3.60489 −0.207096
\(304\) 89.8939 5.15577
\(305\) 0 0
\(306\) −37.3153 −2.13317
\(307\) −27.0342 −1.54292 −0.771462 0.636276i \(-0.780474\pi\)
−0.771462 + 0.636276i \(0.780474\pi\)
\(308\) −5.37138 −0.306063
\(309\) −0.206847 −0.0117671
\(310\) 0 0
\(311\) 29.0710 1.64847 0.824234 0.566250i \(-0.191606\pi\)
0.824234 + 0.566250i \(0.191606\pi\)
\(312\) −25.3888 −1.43736
\(313\) 18.0949 1.02279 0.511393 0.859347i \(-0.329130\pi\)
0.511393 + 0.859347i \(0.329130\pi\)
\(314\) −30.5477 −1.72391
\(315\) 0 0
\(316\) −29.0568 −1.63457
\(317\) 0.617596 0.0346876 0.0173438 0.999850i \(-0.494479\pi\)
0.0173438 + 0.999850i \(0.494479\pi\)
\(318\) −0.521856 −0.0292642
\(319\) 7.19109 0.402624
\(320\) 0 0
\(321\) 5.12528 0.286065
\(322\) −20.9853 −1.16946
\(323\) −32.1546 −1.78913
\(324\) 35.3796 1.96553
\(325\) 0 0
\(326\) 17.1276 0.948609
\(327\) −0.0543684 −0.00300658
\(328\) −37.9192 −2.09374
\(329\) −11.4487 −0.631188
\(330\) 0 0
\(331\) 22.1826 1.21927 0.609634 0.792683i \(-0.291317\pi\)
0.609634 + 0.792683i \(0.291317\pi\)
\(332\) 10.9771 0.602448
\(333\) 9.95754 0.545670
\(334\) 32.1457 1.75894
\(335\) 0 0
\(336\) −7.42099 −0.404848
\(337\) 2.50380 0.136391 0.0681953 0.997672i \(-0.478276\pi\)
0.0681953 + 0.997672i \(0.478276\pi\)
\(338\) −40.2076 −2.18700
\(339\) 5.59497 0.303877
\(340\) 0 0
\(341\) −7.15734 −0.387592
\(342\) 47.1099 2.54741
\(343\) −1.00000 −0.0539949
\(344\) −93.4138 −5.03654
\(345\) 0 0
\(346\) 28.6148 1.53834
\(347\) −20.9259 −1.12336 −0.561681 0.827354i \(-0.689845\pi\)
−0.561681 + 0.827354i \(0.689845\pi\)
\(348\) 20.3164 1.08907
\(349\) −16.2685 −0.870830 −0.435415 0.900230i \(-0.643398\pi\)
−0.435415 + 0.900230i \(0.643398\pi\)
\(350\) 0 0
\(351\) −15.8749 −0.847338
\(352\) −19.9995 −1.06598
\(353\) 19.2778 1.02605 0.513027 0.858372i \(-0.328524\pi\)
0.513027 + 0.858372i \(0.328524\pi\)
\(354\) 3.01070 0.160017
\(355\) 0 0
\(356\) −6.96169 −0.368969
\(357\) 2.65445 0.140488
\(358\) −30.0808 −1.58982
\(359\) −13.5857 −0.717026 −0.358513 0.933525i \(-0.616716\pi\)
−0.358513 + 0.933525i \(0.616716\pi\)
\(360\) 0 0
\(361\) 21.5945 1.13655
\(362\) −18.1940 −0.956256
\(363\) 0.525975 0.0276065
\(364\) −28.3257 −1.48467
\(365\) 0 0
\(366\) 16.1908 0.846304
\(367\) −6.40691 −0.334438 −0.167219 0.985920i \(-0.553479\pi\)
−0.167219 + 0.985920i \(0.553479\pi\)
\(368\) −109.053 −5.68477
\(369\) −11.2818 −0.587309
\(370\) 0 0
\(371\) −0.365435 −0.0189725
\(372\) −20.2210 −1.04841
\(373\) 14.7026 0.761274 0.380637 0.924725i \(-0.375705\pi\)
0.380637 + 0.924725i \(0.375705\pi\)
\(374\) 13.7020 0.708512
\(375\) 0 0
\(376\) −104.795 −5.40438
\(377\) 37.9218 1.95307
\(378\) −8.17316 −0.420382
\(379\) −3.65587 −0.187790 −0.0938948 0.995582i \(-0.529932\pi\)
−0.0938948 + 0.995582i \(0.529932\pi\)
\(380\) 0 0
\(381\) 9.10185 0.466302
\(382\) −57.4719 −2.94052
\(383\) 23.4296 1.19720 0.598598 0.801050i \(-0.295725\pi\)
0.598598 + 0.801050i \(0.295725\pi\)
\(384\) −16.2066 −0.827041
\(385\) 0 0
\(386\) 29.1290 1.48263
\(387\) −27.7928 −1.41279
\(388\) 5.67809 0.288261
\(389\) 0.508487 0.0257813 0.0128907 0.999917i \(-0.495897\pi\)
0.0128907 + 0.999917i \(0.495897\pi\)
\(390\) 0 0
\(391\) 39.0076 1.97270
\(392\) −9.15341 −0.462317
\(393\) −2.21535 −0.111749
\(394\) −43.8548 −2.20937
\(395\) 0 0
\(396\) −14.6282 −0.735093
\(397\) −12.0457 −0.604556 −0.302278 0.953220i \(-0.597747\pi\)
−0.302278 + 0.953220i \(0.597747\pi\)
\(398\) 34.3267 1.72064
\(399\) −3.35119 −0.167769
\(400\) 0 0
\(401\) −37.9084 −1.89305 −0.946527 0.322623i \(-0.895435\pi\)
−0.946527 + 0.322623i \(0.895435\pi\)
\(402\) −7.06217 −0.352229
\(403\) −37.7438 −1.88016
\(404\) −36.8140 −1.83157
\(405\) 0 0
\(406\) 19.5240 0.968961
\(407\) −3.65636 −0.181239
\(408\) 24.2972 1.20289
\(409\) 38.3939 1.89846 0.949228 0.314590i \(-0.101867\pi\)
0.949228 + 0.314590i \(0.101867\pi\)
\(410\) 0 0
\(411\) −5.26543 −0.259725
\(412\) −2.11237 −0.104069
\(413\) 2.10828 0.103742
\(414\) −57.1502 −2.80878
\(415\) 0 0
\(416\) −105.467 −5.17092
\(417\) 8.72704 0.427365
\(418\) −17.2985 −0.846097
\(419\) 18.8624 0.921491 0.460745 0.887532i \(-0.347582\pi\)
0.460745 + 0.887532i \(0.347582\pi\)
\(420\) 0 0
\(421\) −30.0677 −1.46541 −0.732706 0.680545i \(-0.761743\pi\)
−0.732706 + 0.680545i \(0.761743\pi\)
\(422\) 23.0484 1.12198
\(423\) −31.1789 −1.51597
\(424\) −3.34498 −0.162447
\(425\) 0 0
\(426\) −2.46675 −0.119514
\(427\) 11.3378 0.548673
\(428\) 52.3406 2.52998
\(429\) 2.77370 0.133916
\(430\) 0 0
\(431\) 22.4992 1.08375 0.541875 0.840459i \(-0.317715\pi\)
0.541875 + 0.840459i \(0.317715\pi\)
\(432\) −42.4729 −2.04348
\(433\) −16.0344 −0.770564 −0.385282 0.922799i \(-0.625896\pi\)
−0.385282 + 0.922799i \(0.625896\pi\)
\(434\) −19.4324 −0.932784
\(435\) 0 0
\(436\) −0.555223 −0.0265904
\(437\) −49.2463 −2.35577
\(438\) −17.0425 −0.814323
\(439\) 41.6376 1.98726 0.993628 0.112707i \(-0.0359523\pi\)
0.993628 + 0.112707i \(0.0359523\pi\)
\(440\) 0 0
\(441\) −2.72335 −0.129683
\(442\) 72.2566 3.43690
\(443\) 11.3656 0.539997 0.269998 0.962861i \(-0.412977\pi\)
0.269998 + 0.962861i \(0.412977\pi\)
\(444\) −10.3300 −0.490240
\(445\) 0 0
\(446\) −20.4500 −0.968336
\(447\) 8.61558 0.407503
\(448\) −26.0813 −1.23223
\(449\) −4.10578 −0.193764 −0.0968820 0.995296i \(-0.530887\pi\)
−0.0968820 + 0.995296i \(0.530887\pi\)
\(450\) 0 0
\(451\) 4.14263 0.195069
\(452\) 57.1372 2.68751
\(453\) −0.909288 −0.0427221
\(454\) 47.9093 2.24849
\(455\) 0 0
\(456\) −30.6748 −1.43648
\(457\) 15.3963 0.720207 0.360104 0.932912i \(-0.382741\pi\)
0.360104 + 0.932912i \(0.382741\pi\)
\(458\) −36.0298 −1.68356
\(459\) 15.1923 0.709117
\(460\) 0 0
\(461\) −19.5380 −0.909977 −0.454989 0.890497i \(-0.650357\pi\)
−0.454989 + 0.890497i \(0.650357\pi\)
\(462\) 1.42804 0.0664384
\(463\) 4.84367 0.225104 0.112552 0.993646i \(-0.464097\pi\)
0.112552 + 0.993646i \(0.464097\pi\)
\(464\) 101.459 4.71012
\(465\) 0 0
\(466\) −28.0177 −1.29789
\(467\) 22.0487 1.02029 0.510147 0.860087i \(-0.329591\pi\)
0.510147 + 0.860087i \(0.329591\pi\)
\(468\) −77.1408 −3.56584
\(469\) −4.94537 −0.228356
\(470\) 0 0
\(471\) 5.91792 0.272683
\(472\) 19.2979 0.888259
\(473\) 10.2054 0.469243
\(474\) 7.72505 0.354823
\(475\) 0 0
\(476\) 27.1078 1.24249
\(477\) −0.995208 −0.0455675
\(478\) 7.52189 0.344043
\(479\) −5.66221 −0.258713 −0.129356 0.991598i \(-0.541291\pi\)
−0.129356 + 0.991598i \(0.541291\pi\)
\(480\) 0 0
\(481\) −19.2816 −0.879165
\(482\) −51.4079 −2.34156
\(483\) 4.06542 0.184983
\(484\) 5.37138 0.244154
\(485\) 0 0
\(486\) −33.9255 −1.53889
\(487\) −41.5337 −1.88207 −0.941035 0.338310i \(-0.890145\pi\)
−0.941035 + 0.338310i \(0.890145\pi\)
\(488\) 103.779 4.69786
\(489\) −3.31808 −0.150049
\(490\) 0 0
\(491\) 8.02259 0.362054 0.181027 0.983478i \(-0.442058\pi\)
0.181027 + 0.983478i \(0.442058\pi\)
\(492\) 11.7038 0.527649
\(493\) −36.2914 −1.63448
\(494\) −91.2227 −4.10430
\(495\) 0 0
\(496\) −100.983 −4.53427
\(497\) −1.72737 −0.0774830
\(498\) −2.91838 −0.130776
\(499\) −11.6103 −0.519748 −0.259874 0.965643i \(-0.583681\pi\)
−0.259874 + 0.965643i \(0.583681\pi\)
\(500\) 0 0
\(501\) −6.22751 −0.278225
\(502\) −23.0445 −1.02853
\(503\) −0.173084 −0.00771742 −0.00385871 0.999993i \(-0.501228\pi\)
−0.00385871 + 0.999993i \(0.501228\pi\)
\(504\) −24.9279 −1.11038
\(505\) 0 0
\(506\) 20.9853 0.932909
\(507\) 7.78930 0.345935
\(508\) 92.9503 4.12400
\(509\) −31.9779 −1.41740 −0.708698 0.705512i \(-0.750717\pi\)
−0.708698 + 0.705512i \(0.750717\pi\)
\(510\) 0 0
\(511\) −11.9342 −0.527939
\(512\) −23.8827 −1.05548
\(513\) −19.1800 −0.846819
\(514\) −3.00573 −0.132577
\(515\) 0 0
\(516\) 28.8323 1.26927
\(517\) 11.4487 0.503514
\(518\) −9.92711 −0.436172
\(519\) −5.54346 −0.243331
\(520\) 0 0
\(521\) −13.2941 −0.582425 −0.291212 0.956658i \(-0.594059\pi\)
−0.291212 + 0.956658i \(0.594059\pi\)
\(522\) 53.1707 2.32722
\(523\) 24.9187 1.08962 0.544810 0.838559i \(-0.316602\pi\)
0.544810 + 0.838559i \(0.316602\pi\)
\(524\) −22.6236 −0.988319
\(525\) 0 0
\(526\) −71.6535 −3.12424
\(527\) 36.1210 1.57346
\(528\) 7.42099 0.322957
\(529\) 36.7421 1.59748
\(530\) 0 0
\(531\) 5.74158 0.249163
\(532\) −34.2232 −1.48376
\(533\) 21.8459 0.946253
\(534\) 1.85084 0.0800936
\(535\) 0 0
\(536\) −45.2670 −1.95523
\(537\) 5.82747 0.251474
\(538\) −16.3989 −0.707005
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −7.59578 −0.326568 −0.163284 0.986579i \(-0.552209\pi\)
−0.163284 + 0.986579i \(0.552209\pi\)
\(542\) −11.6080 −0.498607
\(543\) 3.52468 0.151258
\(544\) 100.932 4.32742
\(545\) 0 0
\(546\) 7.53069 0.322284
\(547\) −5.60892 −0.239820 −0.119910 0.992785i \(-0.538261\pi\)
−0.119910 + 0.992785i \(0.538261\pi\)
\(548\) −53.7718 −2.29702
\(549\) 30.8767 1.31778
\(550\) 0 0
\(551\) 45.8172 1.95188
\(552\) 37.2125 1.58387
\(553\) 5.40955 0.230038
\(554\) −26.0949 −1.10867
\(555\) 0 0
\(556\) 89.1226 3.77964
\(557\) −3.14063 −0.133073 −0.0665364 0.997784i \(-0.521195\pi\)
−0.0665364 + 0.997784i \(0.521195\pi\)
\(558\) −52.9212 −2.24033
\(559\) 53.8174 2.27623
\(560\) 0 0
\(561\) −2.65445 −0.112071
\(562\) 33.9286 1.43119
\(563\) −34.9166 −1.47156 −0.735779 0.677222i \(-0.763184\pi\)
−0.735779 + 0.677222i \(0.763184\pi\)
\(564\) 32.3451 1.36197
\(565\) 0 0
\(566\) −34.3336 −1.44315
\(567\) −6.58668 −0.276615
\(568\) −15.8113 −0.663427
\(569\) −16.9318 −0.709817 −0.354909 0.934901i \(-0.615488\pi\)
−0.354909 + 0.934901i \(0.615488\pi\)
\(570\) 0 0
\(571\) 2.06027 0.0862195 0.0431098 0.999070i \(-0.486273\pi\)
0.0431098 + 0.999070i \(0.486273\pi\)
\(572\) 28.3257 1.18436
\(573\) 11.1339 0.465124
\(574\) 11.2474 0.469456
\(575\) 0 0
\(576\) −71.0286 −2.95953
\(577\) −35.4282 −1.47489 −0.737447 0.675405i \(-0.763969\pi\)
−0.737447 + 0.675405i \(0.763969\pi\)
\(578\) −22.9944 −0.956442
\(579\) −5.64308 −0.234518
\(580\) 0 0
\(581\) −2.04363 −0.0847841
\(582\) −1.50958 −0.0625741
\(583\) 0.365435 0.0151348
\(584\) −109.239 −4.52033
\(585\) 0 0
\(586\) −55.2061 −2.28054
\(587\) −29.5569 −1.21995 −0.609973 0.792423i \(-0.708820\pi\)
−0.609973 + 0.792423i \(0.708820\pi\)
\(588\) 2.82522 0.116510
\(589\) −45.6022 −1.87900
\(590\) 0 0
\(591\) 8.49586 0.349473
\(592\) −51.5875 −2.12023
\(593\) −38.8831 −1.59674 −0.798369 0.602169i \(-0.794303\pi\)
−0.798369 + 0.602169i \(0.794303\pi\)
\(594\) 8.17316 0.335349
\(595\) 0 0
\(596\) 87.9843 3.60398
\(597\) −6.65002 −0.272167
\(598\) 110.665 4.52542
\(599\) −7.75954 −0.317046 −0.158523 0.987355i \(-0.550673\pi\)
−0.158523 + 0.987355i \(0.550673\pi\)
\(600\) 0 0
\(601\) −14.3951 −0.587187 −0.293594 0.955930i \(-0.594851\pi\)
−0.293594 + 0.955930i \(0.594851\pi\)
\(602\) 27.7079 1.12929
\(603\) −13.4680 −0.548458
\(604\) −9.28586 −0.377836
\(605\) 0 0
\(606\) 9.78739 0.397586
\(607\) 30.9908 1.25788 0.628939 0.777454i \(-0.283489\pi\)
0.628939 + 0.777454i \(0.283489\pi\)
\(608\) −127.425 −5.16776
\(609\) −3.78234 −0.153268
\(610\) 0 0
\(611\) 60.3742 2.44248
\(612\) 73.8241 2.98416
\(613\) −46.1777 −1.86510 −0.932551 0.361039i \(-0.882422\pi\)
−0.932551 + 0.361039i \(0.882422\pi\)
\(614\) 73.3987 2.96213
\(615\) 0 0
\(616\) 9.15341 0.368801
\(617\) −23.1545 −0.932167 −0.466083 0.884741i \(-0.654335\pi\)
−0.466083 + 0.884741i \(0.654335\pi\)
\(618\) 0.561595 0.0225907
\(619\) 7.98316 0.320870 0.160435 0.987046i \(-0.448710\pi\)
0.160435 + 0.987046i \(0.448710\pi\)
\(620\) 0 0
\(621\) 23.2678 0.933706
\(622\) −78.9287 −3.16475
\(623\) 1.29607 0.0519259
\(624\) 39.1342 1.56662
\(625\) 0 0
\(626\) −49.1283 −1.96356
\(627\) 3.35119 0.133834
\(628\) 60.4352 2.41163
\(629\) 18.4526 0.735752
\(630\) 0 0
\(631\) 3.41825 0.136078 0.0680392 0.997683i \(-0.478326\pi\)
0.0680392 + 0.997683i \(0.478326\pi\)
\(632\) 49.5159 1.96963
\(633\) −4.46511 −0.177472
\(634\) −1.67679 −0.0665939
\(635\) 0 0
\(636\) 1.03243 0.0409387
\(637\) 5.27345 0.208942
\(638\) −19.5240 −0.772963
\(639\) −4.70422 −0.186096
\(640\) 0 0
\(641\) −10.6627 −0.421151 −0.210575 0.977578i \(-0.567534\pi\)
−0.210575 + 0.977578i \(0.567534\pi\)
\(642\) −13.9153 −0.549193
\(643\) −7.99093 −0.315131 −0.157566 0.987508i \(-0.550365\pi\)
−0.157566 + 0.987508i \(0.550365\pi\)
\(644\) 41.5170 1.63600
\(645\) 0 0
\(646\) 87.3006 3.43479
\(647\) 1.37419 0.0540251 0.0270126 0.999635i \(-0.491401\pi\)
0.0270126 + 0.999635i \(0.491401\pi\)
\(648\) −60.2906 −2.36844
\(649\) −2.10828 −0.0827571
\(650\) 0 0
\(651\) 3.76458 0.147546
\(652\) −33.8850 −1.32704
\(653\) 7.97082 0.311922 0.155961 0.987763i \(-0.450153\pi\)
0.155961 + 0.987763i \(0.450153\pi\)
\(654\) 0.147612 0.00577208
\(655\) 0 0
\(656\) 58.4484 2.28203
\(657\) −32.5011 −1.26799
\(658\) 31.0836 1.21177
\(659\) 10.1116 0.393891 0.196946 0.980414i \(-0.436898\pi\)
0.196946 + 0.980414i \(0.436898\pi\)
\(660\) 0 0
\(661\) 13.4985 0.525033 0.262516 0.964928i \(-0.415448\pi\)
0.262516 + 0.964928i \(0.415448\pi\)
\(662\) −60.2265 −2.34077
\(663\) −13.9981 −0.543641
\(664\) −18.7062 −0.725941
\(665\) 0 0
\(666\) −27.0350 −1.04759
\(667\) −55.5821 −2.15215
\(668\) −63.5968 −2.46063
\(669\) 3.96172 0.153169
\(670\) 0 0
\(671\) −11.3378 −0.437689
\(672\) 10.5193 0.405790
\(673\) 22.8185 0.879588 0.439794 0.898099i \(-0.355051\pi\)
0.439794 + 0.898099i \(0.355051\pi\)
\(674\) −6.79789 −0.261845
\(675\) 0 0
\(676\) 79.5462 3.05947
\(677\) −32.1403 −1.23525 −0.617627 0.786471i \(-0.711906\pi\)
−0.617627 + 0.786471i \(0.711906\pi\)
\(678\) −15.1905 −0.583388
\(679\) −1.05710 −0.0405678
\(680\) 0 0
\(681\) −9.28134 −0.355662
\(682\) 19.4324 0.744104
\(683\) 16.6797 0.638233 0.319116 0.947716i \(-0.396614\pi\)
0.319116 + 0.947716i \(0.396614\pi\)
\(684\) −93.2016 −3.56365
\(685\) 0 0
\(686\) 2.71503 0.103660
\(687\) 6.97995 0.266302
\(688\) 143.987 5.48947
\(689\) 1.92710 0.0734168
\(690\) 0 0
\(691\) −8.41565 −0.320146 −0.160073 0.987105i \(-0.551173\pi\)
−0.160073 + 0.987105i \(0.551173\pi\)
\(692\) −56.6111 −2.15203
\(693\) 2.72335 0.103452
\(694\) 56.8144 2.15665
\(695\) 0 0
\(696\) −34.6213 −1.31232
\(697\) −20.9067 −0.791896
\(698\) 44.1693 1.67183
\(699\) 5.42778 0.205298
\(700\) 0 0
\(701\) 42.3923 1.60113 0.800567 0.599244i \(-0.204532\pi\)
0.800567 + 0.599244i \(0.204532\pi\)
\(702\) 43.1008 1.62673
\(703\) −23.2960 −0.878627
\(704\) 26.0813 0.982978
\(705\) 0 0
\(706\) −52.3398 −1.96984
\(707\) 6.85373 0.257761
\(708\) −5.95634 −0.223853
\(709\) −40.9740 −1.53881 −0.769405 0.638761i \(-0.779447\pi\)
−0.769405 + 0.638761i \(0.779447\pi\)
\(710\) 0 0
\(711\) 14.7321 0.552497
\(712\) 11.8635 0.444602
\(713\) 55.3212 2.07180
\(714\) −7.20690 −0.269711
\(715\) 0 0
\(716\) 59.5115 2.22405
\(717\) −1.45720 −0.0544199
\(718\) 36.8856 1.37656
\(719\) −43.0602 −1.60587 −0.802937 0.596063i \(-0.796731\pi\)
−0.802937 + 0.596063i \(0.796731\pi\)
\(720\) 0 0
\(721\) 0.393263 0.0146459
\(722\) −58.6298 −2.18198
\(723\) 9.95911 0.370383
\(724\) 35.9948 1.33774
\(725\) 0 0
\(726\) −1.42804 −0.0529995
\(727\) −32.1941 −1.19401 −0.597006 0.802237i \(-0.703643\pi\)
−0.597006 + 0.802237i \(0.703643\pi\)
\(728\) 48.2700 1.78901
\(729\) −13.1878 −0.488435
\(730\) 0 0
\(731\) −51.5035 −1.90493
\(732\) −32.0316 −1.18392
\(733\) −12.8367 −0.474134 −0.237067 0.971493i \(-0.576186\pi\)
−0.237067 + 0.971493i \(0.576186\pi\)
\(734\) 17.3949 0.642059
\(735\) 0 0
\(736\) 154.582 5.69799
\(737\) 4.94537 0.182165
\(738\) 30.6305 1.12752
\(739\) 21.8387 0.803351 0.401676 0.915782i \(-0.368428\pi\)
0.401676 + 0.915782i \(0.368428\pi\)
\(740\) 0 0
\(741\) 17.6723 0.649209
\(742\) 0.992168 0.0364236
\(743\) 28.0653 1.02962 0.514809 0.857305i \(-0.327863\pi\)
0.514809 + 0.857305i \(0.327863\pi\)
\(744\) 34.4588 1.26332
\(745\) 0 0
\(746\) −39.9181 −1.46151
\(747\) −5.56552 −0.203632
\(748\) −27.1078 −0.991161
\(749\) −9.74434 −0.356051
\(750\) 0 0
\(751\) −36.7954 −1.34268 −0.671342 0.741148i \(-0.734282\pi\)
−0.671342 + 0.741148i \(0.734282\pi\)
\(752\) 161.530 5.89039
\(753\) 4.46436 0.162690
\(754\) −102.959 −3.74954
\(755\) 0 0
\(756\) 16.1697 0.588086
\(757\) −35.2014 −1.27942 −0.639709 0.768617i \(-0.720945\pi\)
−0.639709 + 0.768617i \(0.720945\pi\)
\(758\) 9.92581 0.360522
\(759\) −4.06542 −0.147565
\(760\) 0 0
\(761\) 30.6132 1.10973 0.554865 0.831941i \(-0.312770\pi\)
0.554865 + 0.831941i \(0.312770\pi\)
\(762\) −24.7118 −0.895214
\(763\) 0.103367 0.00374213
\(764\) 113.702 4.11358
\(765\) 0 0
\(766\) −63.6120 −2.29840
\(767\) −11.1179 −0.401444
\(768\) 16.5652 0.597745
\(769\) −47.6690 −1.71899 −0.859493 0.511147i \(-0.829221\pi\)
−0.859493 + 0.511147i \(0.829221\pi\)
\(770\) 0 0
\(771\) 0.582293 0.0209708
\(772\) −57.6284 −2.07409
\(773\) 1.89344 0.0681024 0.0340512 0.999420i \(-0.489159\pi\)
0.0340512 + 0.999420i \(0.489159\pi\)
\(774\) 75.4582 2.71229
\(775\) 0 0
\(776\) −9.67607 −0.347351
\(777\) 1.92315 0.0689927
\(778\) −1.38056 −0.0494954
\(779\) 26.3943 0.945673
\(780\) 0 0
\(781\) 1.72737 0.0618100
\(782\) −105.907 −3.78721
\(783\) −21.6476 −0.773623
\(784\) 14.1090 0.503893
\(785\) 0 0
\(786\) 6.01473 0.214538
\(787\) 26.8097 0.955663 0.477831 0.878452i \(-0.341423\pi\)
0.477831 + 0.878452i \(0.341423\pi\)
\(788\) 86.7618 3.09076
\(789\) 13.8812 0.494185
\(790\) 0 0
\(791\) −10.6373 −0.378220
\(792\) 24.9279 0.885776
\(793\) −59.7891 −2.12317
\(794\) 32.7044 1.16064
\(795\) 0 0
\(796\) −67.9116 −2.40706
\(797\) −40.9793 −1.45156 −0.725781 0.687926i \(-0.758522\pi\)
−0.725781 + 0.687926i \(0.758522\pi\)
\(798\) 9.09858 0.322086
\(799\) −57.7784 −2.04405
\(800\) 0 0
\(801\) 3.52965 0.124714
\(802\) 102.922 3.63432
\(803\) 11.9342 0.421149
\(804\) 13.9717 0.492745
\(805\) 0 0
\(806\) 102.476 3.60955
\(807\) 3.17691 0.111832
\(808\) 62.7350 2.20701
\(809\) 40.8891 1.43758 0.718792 0.695225i \(-0.244695\pi\)
0.718792 + 0.695225i \(0.244695\pi\)
\(810\) 0 0
\(811\) 28.6998 1.00778 0.503892 0.863766i \(-0.331901\pi\)
0.503892 + 0.863766i \(0.331901\pi\)
\(812\) −38.6261 −1.35551
\(813\) 2.24879 0.0788685
\(814\) 9.92711 0.347945
\(815\) 0 0
\(816\) −37.4516 −1.31107
\(817\) 65.0223 2.27484
\(818\) −104.241 −3.64468
\(819\) 14.3614 0.501829
\(820\) 0 0
\(821\) −14.3816 −0.501922 −0.250961 0.967997i \(-0.580747\pi\)
−0.250961 + 0.967997i \(0.580747\pi\)
\(822\) 14.2958 0.498623
\(823\) −11.5388 −0.402217 −0.201109 0.979569i \(-0.564454\pi\)
−0.201109 + 0.979569i \(0.564454\pi\)
\(824\) 3.59970 0.125401
\(825\) 0 0
\(826\) −5.72404 −0.199165
\(827\) −3.11653 −0.108372 −0.0541861 0.998531i \(-0.517256\pi\)
−0.0541861 + 0.998531i \(0.517256\pi\)
\(828\) 113.065 3.92930
\(829\) −19.0261 −0.660804 −0.330402 0.943840i \(-0.607184\pi\)
−0.330402 + 0.943840i \(0.607184\pi\)
\(830\) 0 0
\(831\) 5.05530 0.175366
\(832\) 137.539 4.76829
\(833\) −5.04671 −0.174858
\(834\) −23.6942 −0.820462
\(835\) 0 0
\(836\) 34.2232 1.18363
\(837\) 21.5460 0.744740
\(838\) −51.2121 −1.76909
\(839\) 6.17238 0.213094 0.106547 0.994308i \(-0.466021\pi\)
0.106547 + 0.994308i \(0.466021\pi\)
\(840\) 0 0
\(841\) 22.7118 0.783164
\(842\) 81.6348 2.81332
\(843\) −6.57289 −0.226382
\(844\) −45.5987 −1.56957
\(845\) 0 0
\(846\) 84.6516 2.91038
\(847\) −1.00000 −0.0343604
\(848\) 5.15593 0.177055
\(849\) 6.65135 0.228274
\(850\) 0 0
\(851\) 28.2611 0.968777
\(852\) 4.88018 0.167192
\(853\) 37.9832 1.30052 0.650261 0.759711i \(-0.274660\pi\)
0.650261 + 0.759711i \(0.274660\pi\)
\(854\) −30.7824 −1.05335
\(855\) 0 0
\(856\) −89.1940 −3.04859
\(857\) 32.8604 1.12249 0.561245 0.827650i \(-0.310323\pi\)
0.561245 + 0.827650i \(0.310323\pi\)
\(858\) −7.53069 −0.257093
\(859\) 19.3742 0.661038 0.330519 0.943799i \(-0.392776\pi\)
0.330519 + 0.943799i \(0.392776\pi\)
\(860\) 0 0
\(861\) −2.17892 −0.0742574
\(862\) −61.0861 −2.08060
\(863\) −21.7480 −0.740309 −0.370154 0.928970i \(-0.620695\pi\)
−0.370154 + 0.928970i \(0.620695\pi\)
\(864\) 60.2054 2.04823
\(865\) 0 0
\(866\) 43.5338 1.47934
\(867\) 4.45465 0.151288
\(868\) 38.4448 1.30490
\(869\) −5.40955 −0.183507
\(870\) 0 0
\(871\) 26.0791 0.883658
\(872\) 0.946159 0.0320410
\(873\) −2.87885 −0.0974344
\(874\) 133.705 4.52265
\(875\) 0 0
\(876\) 33.7167 1.13918
\(877\) −23.8741 −0.806170 −0.403085 0.915163i \(-0.632062\pi\)
−0.403085 + 0.915163i \(0.632062\pi\)
\(878\) −113.047 −3.81517
\(879\) 10.6949 0.360731
\(880\) 0 0
\(881\) −28.2243 −0.950901 −0.475451 0.879742i \(-0.657715\pi\)
−0.475451 + 0.879742i \(0.657715\pi\)
\(882\) 7.39398 0.248968
\(883\) −1.43110 −0.0481603 −0.0240801 0.999710i \(-0.507666\pi\)
−0.0240801 + 0.999710i \(0.507666\pi\)
\(884\) −142.952 −4.80799
\(885\) 0 0
\(886\) −30.8580 −1.03669
\(887\) −11.8013 −0.396249 −0.198124 0.980177i \(-0.563485\pi\)
−0.198124 + 0.980177i \(0.563485\pi\)
\(888\) 17.6034 0.590732
\(889\) −17.3047 −0.580381
\(890\) 0 0
\(891\) 6.58668 0.220662
\(892\) 40.4581 1.35464
\(893\) 72.9442 2.44098
\(894\) −23.3915 −0.782330
\(895\) 0 0
\(896\) 30.8125 1.02937
\(897\) −21.4388 −0.715820
\(898\) 11.1473 0.371991
\(899\) −51.4691 −1.71659
\(900\) 0 0
\(901\) −1.84425 −0.0614408
\(902\) −11.2474 −0.374496
\(903\) −5.36777 −0.178628
\(904\) −97.3678 −3.23840
\(905\) 0 0
\(906\) 2.46874 0.0820185
\(907\) −6.23945 −0.207177 −0.103589 0.994620i \(-0.533033\pi\)
−0.103589 + 0.994620i \(0.533033\pi\)
\(908\) −94.7832 −3.14549
\(909\) 18.6651 0.619082
\(910\) 0 0
\(911\) 18.7801 0.622212 0.311106 0.950375i \(-0.399301\pi\)
0.311106 + 0.950375i \(0.399301\pi\)
\(912\) 47.2820 1.56566
\(913\) 2.04363 0.0676343
\(914\) −41.8013 −1.38267
\(915\) 0 0
\(916\) 71.2809 2.35519
\(917\) 4.21188 0.139089
\(918\) −41.2476 −1.36137
\(919\) −13.6006 −0.448641 −0.224321 0.974515i \(-0.572016\pi\)
−0.224321 + 0.974515i \(0.572016\pi\)
\(920\) 0 0
\(921\) −14.2193 −0.468543
\(922\) 53.0464 1.74699
\(923\) 9.10918 0.299832
\(924\) −2.82522 −0.0929428
\(925\) 0 0
\(926\) −13.1507 −0.432159
\(927\) 1.07099 0.0351760
\(928\) −143.819 −4.72107
\(929\) −9.66398 −0.317065 −0.158533 0.987354i \(-0.550676\pi\)
−0.158533 + 0.987354i \(0.550676\pi\)
\(930\) 0 0
\(931\) 6.37138 0.208814
\(932\) 55.4298 1.81566
\(933\) 15.2907 0.500593
\(934\) −59.8630 −1.95878
\(935\) 0 0
\(936\) 131.456 4.29678
\(937\) −24.4712 −0.799440 −0.399720 0.916637i \(-0.630893\pi\)
−0.399720 + 0.916637i \(0.630893\pi\)
\(938\) 13.4268 0.438401
\(939\) 9.51749 0.310592
\(940\) 0 0
\(941\) 56.5314 1.84287 0.921435 0.388532i \(-0.127018\pi\)
0.921435 + 0.388532i \(0.127018\pi\)
\(942\) −16.0673 −0.523502
\(943\) −32.0196 −1.04270
\(944\) −29.7457 −0.968140
\(945\) 0 0
\(946\) −27.7079 −0.900860
\(947\) 19.3925 0.630171 0.315085 0.949063i \(-0.397967\pi\)
0.315085 + 0.949063i \(0.397967\pi\)
\(948\) −15.2832 −0.496374
\(949\) 62.9345 2.04294
\(950\) 0 0
\(951\) 0.324840 0.0105337
\(952\) −46.1946 −1.49718
\(953\) 55.8965 1.81067 0.905333 0.424702i \(-0.139621\pi\)
0.905333 + 0.424702i \(0.139621\pi\)
\(954\) 2.70202 0.0874811
\(955\) 0 0
\(956\) −14.8812 −0.481293
\(957\) 3.78234 0.122266
\(958\) 15.3731 0.496681
\(959\) 10.0108 0.323265
\(960\) 0 0
\(961\) 20.2275 0.652500
\(962\) 52.3501 1.68784
\(963\) −26.5373 −0.855151
\(964\) 101.705 3.27569
\(965\) 0 0
\(966\) −11.0377 −0.355133
\(967\) 48.7740 1.56847 0.784233 0.620466i \(-0.213057\pi\)
0.784233 + 0.620466i \(0.213057\pi\)
\(968\) −9.15341 −0.294202
\(969\) −16.9125 −0.543308
\(970\) 0 0
\(971\) 24.6694 0.791677 0.395839 0.918320i \(-0.370454\pi\)
0.395839 + 0.918320i \(0.370454\pi\)
\(972\) 67.1179 2.15281
\(973\) −16.5921 −0.531918
\(974\) 112.765 3.61323
\(975\) 0 0
\(976\) −159.965 −5.12034
\(977\) −22.3101 −0.713762 −0.356881 0.934150i \(-0.616160\pi\)
−0.356881 + 0.934150i \(0.616160\pi\)
\(978\) 9.00868 0.288066
\(979\) −1.29607 −0.0414226
\(980\) 0 0
\(981\) 0.281504 0.00898774
\(982\) −21.7816 −0.695078
\(983\) 57.4546 1.83252 0.916259 0.400587i \(-0.131194\pi\)
0.916259 + 0.400587i \(0.131194\pi\)
\(984\) −19.9446 −0.635809
\(985\) 0 0
\(986\) 98.5321 3.13790
\(987\) −6.02174 −0.191674
\(988\) 180.474 5.74164
\(989\) −78.8803 −2.50825
\(990\) 0 0
\(991\) −34.4406 −1.09404 −0.547021 0.837119i \(-0.684238\pi\)
−0.547021 + 0.837119i \(0.684238\pi\)
\(992\) 143.144 4.54481
\(993\) 11.6675 0.370257
\(994\) 4.68985 0.148753
\(995\) 0 0
\(996\) 5.77370 0.182947
\(997\) −25.7609 −0.815856 −0.407928 0.913014i \(-0.633749\pi\)
−0.407928 + 0.913014i \(0.633749\pi\)
\(998\) 31.5223 0.997819
\(999\) 11.0069 0.348242
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 1925.2.a.bb.1.1 7
5.2 odd 4 1925.2.b.r.1849.1 14
5.3 odd 4 1925.2.b.r.1849.14 14
5.4 even 2 1925.2.a.bd.1.7 yes 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1925.2.a.bb.1.1 7 1.1 even 1 trivial
1925.2.a.bd.1.7 yes 7 5.4 even 2
1925.2.b.r.1849.1 14 5.2 odd 4
1925.2.b.r.1849.14 14 5.3 odd 4