Properties

Label 5225.2.a.bc.1.14
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $30$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.379302 q^{2} -2.60759 q^{3} -1.85613 q^{4} +0.989065 q^{6} -4.15654 q^{7} +1.46264 q^{8} +3.79954 q^{9} +O(q^{10})\) \(q-0.379302 q^{2} -2.60759 q^{3} -1.85613 q^{4} +0.989065 q^{6} -4.15654 q^{7} +1.46264 q^{8} +3.79954 q^{9} +1.00000 q^{11} +4.84003 q^{12} -0.808855 q^{13} +1.57658 q^{14} +3.15748 q^{16} -5.26829 q^{17} -1.44117 q^{18} +1.00000 q^{19} +10.8386 q^{21} -0.379302 q^{22} -2.49456 q^{23} -3.81396 q^{24} +0.306800 q^{26} -2.08489 q^{27} +7.71508 q^{28} -2.90329 q^{29} +2.50775 q^{31} -4.12291 q^{32} -2.60759 q^{33} +1.99827 q^{34} -7.05245 q^{36} +2.11138 q^{37} -0.379302 q^{38} +2.10917 q^{39} -11.9805 q^{41} -4.11109 q^{42} -1.42063 q^{43} -1.85613 q^{44} +0.946192 q^{46} -4.28038 q^{47} -8.23342 q^{48} +10.2768 q^{49} +13.7376 q^{51} +1.50134 q^{52} -7.81180 q^{53} +0.790801 q^{54} -6.07951 q^{56} -2.60759 q^{57} +1.10122 q^{58} -9.86819 q^{59} -1.27005 q^{61} -0.951193 q^{62} -15.7930 q^{63} -4.75113 q^{64} +0.989065 q^{66} +7.58859 q^{67} +9.77863 q^{68} +6.50480 q^{69} -8.49943 q^{71} +5.55735 q^{72} -6.86804 q^{73} -0.800850 q^{74} -1.85613 q^{76} -4.15654 q^{77} -0.800010 q^{78} +3.74373 q^{79} -5.96210 q^{81} +4.54421 q^{82} -15.8542 q^{83} -20.1178 q^{84} +0.538847 q^{86} +7.57060 q^{87} +1.46264 q^{88} -1.09693 q^{89} +3.36204 q^{91} +4.63023 q^{92} -6.53919 q^{93} +1.62356 q^{94} +10.7509 q^{96} -9.76079 q^{97} -3.89801 q^{98} +3.79954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 42 q^{4} + 12 q^{6} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 42 q^{4} + 12 q^{6} + 40 q^{9} + 30 q^{11} - 4 q^{14} + 66 q^{16} + 30 q^{19} + 14 q^{21} + 22 q^{24} + 30 q^{29} + 26 q^{31} + 12 q^{34} + 78 q^{36} + 64 q^{39} + 22 q^{41} + 42 q^{44} + 28 q^{46} + 60 q^{49} + 64 q^{51} + 62 q^{54} - 32 q^{56} - 14 q^{59} + 78 q^{61} + 90 q^{64} + 12 q^{66} - 28 q^{69} + 20 q^{71} + 42 q^{74} + 42 q^{76} + 102 q^{79} + 42 q^{81} + 98 q^{84} - 52 q^{86} - 8 q^{89} + 56 q^{91} + 40 q^{94} - 74 q^{96} + 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.379302 −0.268207 −0.134103 0.990967i \(-0.542815\pi\)
−0.134103 + 0.990967i \(0.542815\pi\)
\(3\) −2.60759 −1.50549 −0.752747 0.658309i \(-0.771272\pi\)
−0.752747 + 0.658309i \(0.771272\pi\)
\(4\) −1.85613 −0.928065
\(5\) 0 0
\(6\) 0.989065 0.403784
\(7\) −4.15654 −1.57102 −0.785512 0.618847i \(-0.787600\pi\)
−0.785512 + 0.618847i \(0.787600\pi\)
\(8\) 1.46264 0.517120
\(9\) 3.79954 1.26651
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 4.84003 1.39720
\(13\) −0.808855 −0.224336 −0.112168 0.993689i \(-0.535780\pi\)
−0.112168 + 0.993689i \(0.535780\pi\)
\(14\) 1.57658 0.421359
\(15\) 0 0
\(16\) 3.15748 0.789370
\(17\) −5.26829 −1.27775 −0.638874 0.769311i \(-0.720599\pi\)
−0.638874 + 0.769311i \(0.720599\pi\)
\(18\) −1.44117 −0.339688
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 10.8386 2.36517
\(22\) −0.379302 −0.0808674
\(23\) −2.49456 −0.520152 −0.260076 0.965588i \(-0.583748\pi\)
−0.260076 + 0.965588i \(0.583748\pi\)
\(24\) −3.81396 −0.778522
\(25\) 0 0
\(26\) 0.306800 0.0601685
\(27\) −2.08489 −0.401237
\(28\) 7.71508 1.45801
\(29\) −2.90329 −0.539127 −0.269564 0.962983i \(-0.586879\pi\)
−0.269564 + 0.962983i \(0.586879\pi\)
\(30\) 0 0
\(31\) 2.50775 0.450405 0.225202 0.974312i \(-0.427696\pi\)
0.225202 + 0.974312i \(0.427696\pi\)
\(32\) −4.12291 −0.728835
\(33\) −2.60759 −0.453924
\(34\) 1.99827 0.342701
\(35\) 0 0
\(36\) −7.05245 −1.17541
\(37\) 2.11138 0.347109 0.173554 0.984824i \(-0.444475\pi\)
0.173554 + 0.984824i \(0.444475\pi\)
\(38\) −0.379302 −0.0615309
\(39\) 2.10917 0.337737
\(40\) 0 0
\(41\) −11.9805 −1.87104 −0.935518 0.353280i \(-0.885066\pi\)
−0.935518 + 0.353280i \(0.885066\pi\)
\(42\) −4.11109 −0.634354
\(43\) −1.42063 −0.216644 −0.108322 0.994116i \(-0.534548\pi\)
−0.108322 + 0.994116i \(0.534548\pi\)
\(44\) −1.85613 −0.279822
\(45\) 0 0
\(46\) 0.946192 0.139508
\(47\) −4.28038 −0.624358 −0.312179 0.950023i \(-0.601059\pi\)
−0.312179 + 0.950023i \(0.601059\pi\)
\(48\) −8.23342 −1.18839
\(49\) 10.2768 1.46812
\(50\) 0 0
\(51\) 13.7376 1.92364
\(52\) 1.50134 0.208199
\(53\) −7.81180 −1.07303 −0.536517 0.843890i \(-0.680260\pi\)
−0.536517 + 0.843890i \(0.680260\pi\)
\(54\) 0.790801 0.107614
\(55\) 0 0
\(56\) −6.07951 −0.812408
\(57\) −2.60759 −0.345384
\(58\) 1.10122 0.144598
\(59\) −9.86819 −1.28473 −0.642365 0.766399i \(-0.722047\pi\)
−0.642365 + 0.766399i \(0.722047\pi\)
\(60\) 0 0
\(61\) −1.27005 −0.162613 −0.0813063 0.996689i \(-0.525909\pi\)
−0.0813063 + 0.996689i \(0.525909\pi\)
\(62\) −0.951193 −0.120802
\(63\) −15.7930 −1.98972
\(64\) −4.75113 −0.593892
\(65\) 0 0
\(66\) 0.989065 0.121745
\(67\) 7.58859 0.927094 0.463547 0.886072i \(-0.346577\pi\)
0.463547 + 0.886072i \(0.346577\pi\)
\(68\) 9.77863 1.18583
\(69\) 6.50480 0.783086
\(70\) 0 0
\(71\) −8.49943 −1.00870 −0.504348 0.863500i \(-0.668267\pi\)
−0.504348 + 0.863500i \(0.668267\pi\)
\(72\) 5.55735 0.654940
\(73\) −6.86804 −0.803844 −0.401922 0.915674i \(-0.631658\pi\)
−0.401922 + 0.915674i \(0.631658\pi\)
\(74\) −0.800850 −0.0930969
\(75\) 0 0
\(76\) −1.85613 −0.212913
\(77\) −4.15654 −0.473681
\(78\) −0.800010 −0.0905833
\(79\) 3.74373 0.421202 0.210601 0.977572i \(-0.432458\pi\)
0.210601 + 0.977572i \(0.432458\pi\)
\(80\) 0 0
\(81\) −5.96210 −0.662455
\(82\) 4.54421 0.501824
\(83\) −15.8542 −1.74022 −0.870110 0.492857i \(-0.835952\pi\)
−0.870110 + 0.492857i \(0.835952\pi\)
\(84\) −20.1178 −2.19503
\(85\) 0 0
\(86\) 0.538847 0.0581054
\(87\) 7.57060 0.811653
\(88\) 1.46264 0.155918
\(89\) −1.09693 −0.116274 −0.0581369 0.998309i \(-0.518516\pi\)
−0.0581369 + 0.998309i \(0.518516\pi\)
\(90\) 0 0
\(91\) 3.36204 0.352437
\(92\) 4.63023 0.482735
\(93\) −6.53919 −0.678082
\(94\) 1.62356 0.167457
\(95\) 0 0
\(96\) 10.7509 1.09726
\(97\) −9.76079 −0.991058 −0.495529 0.868591i \(-0.665026\pi\)
−0.495529 + 0.868591i \(0.665026\pi\)
\(98\) −3.89801 −0.393759
\(99\) 3.79954 0.381869
\(100\) 0 0
\(101\) −15.2672 −1.51915 −0.759573 0.650423i \(-0.774592\pi\)
−0.759573 + 0.650423i \(0.774592\pi\)
\(102\) −5.21068 −0.515934
\(103\) −9.87892 −0.973399 −0.486699 0.873570i \(-0.661799\pi\)
−0.486699 + 0.873570i \(0.661799\pi\)
\(104\) −1.18306 −0.116009
\(105\) 0 0
\(106\) 2.96303 0.287795
\(107\) 1.88410 0.182143 0.0910713 0.995844i \(-0.470971\pi\)
0.0910713 + 0.995844i \(0.470971\pi\)
\(108\) 3.86982 0.372374
\(109\) −2.50045 −0.239499 −0.119750 0.992804i \(-0.538209\pi\)
−0.119750 + 0.992804i \(0.538209\pi\)
\(110\) 0 0
\(111\) −5.50562 −0.522570
\(112\) −13.1242 −1.24012
\(113\) −0.200129 −0.0188266 −0.00941328 0.999956i \(-0.502996\pi\)
−0.00941328 + 0.999956i \(0.502996\pi\)
\(114\) 0.989065 0.0926344
\(115\) 0 0
\(116\) 5.38888 0.500345
\(117\) −3.07328 −0.284125
\(118\) 3.74302 0.344573
\(119\) 21.8978 2.00737
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0.481730 0.0436138
\(123\) 31.2402 2.81683
\(124\) −4.65471 −0.418005
\(125\) 0 0
\(126\) 5.99029 0.533658
\(127\) 9.37956 0.832301 0.416151 0.909296i \(-0.363379\pi\)
0.416151 + 0.909296i \(0.363379\pi\)
\(128\) 10.0479 0.888120
\(129\) 3.70442 0.326156
\(130\) 0 0
\(131\) 10.0207 0.875513 0.437756 0.899094i \(-0.355773\pi\)
0.437756 + 0.899094i \(0.355773\pi\)
\(132\) 4.84003 0.421271
\(133\) −4.15654 −0.360418
\(134\) −2.87836 −0.248653
\(135\) 0 0
\(136\) −7.70559 −0.660749
\(137\) −14.3772 −1.22833 −0.614165 0.789178i \(-0.710507\pi\)
−0.614165 + 0.789178i \(0.710507\pi\)
\(138\) −2.46728 −0.210029
\(139\) −11.9706 −1.01533 −0.507665 0.861555i \(-0.669491\pi\)
−0.507665 + 0.861555i \(0.669491\pi\)
\(140\) 0 0
\(141\) 11.1615 0.939968
\(142\) 3.22385 0.270539
\(143\) −0.808855 −0.0676399
\(144\) 11.9970 0.999749
\(145\) 0 0
\(146\) 2.60506 0.215596
\(147\) −26.7977 −2.21024
\(148\) −3.91900 −0.322139
\(149\) 19.0313 1.55911 0.779554 0.626335i \(-0.215446\pi\)
0.779554 + 0.626335i \(0.215446\pi\)
\(150\) 0 0
\(151\) −9.88955 −0.804800 −0.402400 0.915464i \(-0.631824\pi\)
−0.402400 + 0.915464i \(0.631824\pi\)
\(152\) 1.46264 0.118636
\(153\) −20.0171 −1.61829
\(154\) 1.57658 0.127045
\(155\) 0 0
\(156\) −3.91489 −0.313442
\(157\) −18.4940 −1.47598 −0.737991 0.674811i \(-0.764225\pi\)
−0.737991 + 0.674811i \(0.764225\pi\)
\(158\) −1.42000 −0.112969
\(159\) 20.3700 1.61545
\(160\) 0 0
\(161\) 10.3687 0.817171
\(162\) 2.26143 0.177675
\(163\) −20.3815 −1.59640 −0.798202 0.602390i \(-0.794215\pi\)
−0.798202 + 0.602390i \(0.794215\pi\)
\(164\) 22.2373 1.73644
\(165\) 0 0
\(166\) 6.01351 0.466739
\(167\) −6.53284 −0.505526 −0.252763 0.967528i \(-0.581339\pi\)
−0.252763 + 0.967528i \(0.581339\pi\)
\(168\) 15.8529 1.22308
\(169\) −12.3458 −0.949673
\(170\) 0 0
\(171\) 3.79954 0.290558
\(172\) 2.63687 0.201060
\(173\) −6.56825 −0.499375 −0.249687 0.968327i \(-0.580328\pi\)
−0.249687 + 0.968327i \(0.580328\pi\)
\(174\) −2.87154 −0.217691
\(175\) 0 0
\(176\) 3.15748 0.238004
\(177\) 25.7322 1.93415
\(178\) 0.416066 0.0311854
\(179\) 19.1738 1.43312 0.716560 0.697525i \(-0.245716\pi\)
0.716560 + 0.697525i \(0.245716\pi\)
\(180\) 0 0
\(181\) −7.26851 −0.540264 −0.270132 0.962823i \(-0.587067\pi\)
−0.270132 + 0.962823i \(0.587067\pi\)
\(182\) −1.27523 −0.0945261
\(183\) 3.31176 0.244813
\(184\) −3.64864 −0.268981
\(185\) 0 0
\(186\) 2.48032 0.181866
\(187\) −5.26829 −0.385255
\(188\) 7.94495 0.579445
\(189\) 8.66591 0.630352
\(190\) 0 0
\(191\) −17.1715 −1.24249 −0.621244 0.783617i \(-0.713372\pi\)
−0.621244 + 0.783617i \(0.713372\pi\)
\(192\) 12.3890 0.894101
\(193\) −1.24791 −0.0898268 −0.0449134 0.998991i \(-0.514301\pi\)
−0.0449134 + 0.998991i \(0.514301\pi\)
\(194\) 3.70228 0.265808
\(195\) 0 0
\(196\) −19.0751 −1.36251
\(197\) 15.8699 1.13068 0.565341 0.824857i \(-0.308745\pi\)
0.565341 + 0.824857i \(0.308745\pi\)
\(198\) −1.44117 −0.102420
\(199\) 16.5207 1.17112 0.585560 0.810629i \(-0.300875\pi\)
0.585560 + 0.810629i \(0.300875\pi\)
\(200\) 0 0
\(201\) −19.7880 −1.39573
\(202\) 5.79088 0.407445
\(203\) 12.0676 0.846982
\(204\) −25.4987 −1.78527
\(205\) 0 0
\(206\) 3.74709 0.261072
\(207\) −9.47820 −0.658780
\(208\) −2.55394 −0.177084
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) 16.4238 1.13066 0.565330 0.824865i \(-0.308749\pi\)
0.565330 + 0.824865i \(0.308749\pi\)
\(212\) 14.4997 0.995845
\(213\) 22.1631 1.51859
\(214\) −0.714642 −0.0488519
\(215\) 0 0
\(216\) −3.04943 −0.207488
\(217\) −10.4235 −0.707596
\(218\) 0.948424 0.0642353
\(219\) 17.9091 1.21018
\(220\) 0 0
\(221\) 4.26128 0.286645
\(222\) 2.08829 0.140157
\(223\) 21.2434 1.42256 0.711281 0.702908i \(-0.248116\pi\)
0.711281 + 0.702908i \(0.248116\pi\)
\(224\) 17.1370 1.14502
\(225\) 0 0
\(226\) 0.0759093 0.00504941
\(227\) 29.4936 1.95756 0.978780 0.204913i \(-0.0656912\pi\)
0.978780 + 0.204913i \(0.0656912\pi\)
\(228\) 4.84003 0.320539
\(229\) −25.8556 −1.70859 −0.854293 0.519792i \(-0.826009\pi\)
−0.854293 + 0.519792i \(0.826009\pi\)
\(230\) 0 0
\(231\) 10.8386 0.713125
\(232\) −4.24646 −0.278794
\(233\) 9.22686 0.604472 0.302236 0.953233i \(-0.402267\pi\)
0.302236 + 0.953233i \(0.402267\pi\)
\(234\) 1.16570 0.0762043
\(235\) 0 0
\(236\) 18.3167 1.19231
\(237\) −9.76212 −0.634118
\(238\) −8.30589 −0.538391
\(239\) −12.3546 −0.799151 −0.399575 0.916700i \(-0.630842\pi\)
−0.399575 + 0.916700i \(0.630842\pi\)
\(240\) 0 0
\(241\) 15.2993 0.985511 0.492756 0.870168i \(-0.335990\pi\)
0.492756 + 0.870168i \(0.335990\pi\)
\(242\) −0.379302 −0.0243824
\(243\) 21.8014 1.39856
\(244\) 2.35737 0.150915
\(245\) 0 0
\(246\) −11.8495 −0.755494
\(247\) −0.808855 −0.0514662
\(248\) 3.66792 0.232913
\(249\) 41.3412 2.61989
\(250\) 0 0
\(251\) −14.6172 −0.922631 −0.461316 0.887236i \(-0.652622\pi\)
−0.461316 + 0.887236i \(0.652622\pi\)
\(252\) 29.3138 1.84659
\(253\) −2.49456 −0.156832
\(254\) −3.55768 −0.223229
\(255\) 0 0
\(256\) 5.69107 0.355692
\(257\) −27.7037 −1.72811 −0.864055 0.503397i \(-0.832083\pi\)
−0.864055 + 0.503397i \(0.832083\pi\)
\(258\) −1.40509 −0.0874774
\(259\) −8.77603 −0.545316
\(260\) 0 0
\(261\) −11.0312 −0.682813
\(262\) −3.80087 −0.234818
\(263\) −21.3961 −1.31934 −0.659669 0.751556i \(-0.729303\pi\)
−0.659669 + 0.751556i \(0.729303\pi\)
\(264\) −3.81396 −0.234733
\(265\) 0 0
\(266\) 1.57658 0.0966664
\(267\) 2.86034 0.175050
\(268\) −14.0854 −0.860403
\(269\) −11.8616 −0.723214 −0.361607 0.932331i \(-0.617772\pi\)
−0.361607 + 0.932331i \(0.617772\pi\)
\(270\) 0 0
\(271\) 28.2159 1.71400 0.856998 0.515319i \(-0.172327\pi\)
0.856998 + 0.515319i \(0.172327\pi\)
\(272\) −16.6345 −1.00862
\(273\) −8.76683 −0.530593
\(274\) 5.45331 0.329446
\(275\) 0 0
\(276\) −12.0738 −0.726755
\(277\) 14.9525 0.898407 0.449203 0.893430i \(-0.351708\pi\)
0.449203 + 0.893430i \(0.351708\pi\)
\(278\) 4.54045 0.272318
\(279\) 9.52830 0.570444
\(280\) 0 0
\(281\) −18.8813 −1.12637 −0.563183 0.826332i \(-0.690423\pi\)
−0.563183 + 0.826332i \(0.690423\pi\)
\(282\) −4.23358 −0.252106
\(283\) 9.06589 0.538912 0.269456 0.963013i \(-0.413156\pi\)
0.269456 + 0.963013i \(0.413156\pi\)
\(284\) 15.7760 0.936136
\(285\) 0 0
\(286\) 0.306800 0.0181415
\(287\) 49.7973 2.93944
\(288\) −15.6652 −0.923080
\(289\) 10.7549 0.632639
\(290\) 0 0
\(291\) 25.4522 1.49203
\(292\) 12.7480 0.746019
\(293\) 23.4422 1.36951 0.684754 0.728774i \(-0.259909\pi\)
0.684754 + 0.728774i \(0.259909\pi\)
\(294\) 10.1644 0.592801
\(295\) 0 0
\(296\) 3.08818 0.179497
\(297\) −2.08489 −0.120977
\(298\) −7.21862 −0.418163
\(299\) 2.01774 0.116689
\(300\) 0 0
\(301\) 5.90490 0.340353
\(302\) 3.75112 0.215853
\(303\) 39.8107 2.28707
\(304\) 3.15748 0.181094
\(305\) 0 0
\(306\) 7.59252 0.434035
\(307\) −6.48182 −0.369937 −0.184969 0.982744i \(-0.559218\pi\)
−0.184969 + 0.982744i \(0.559218\pi\)
\(308\) 7.71508 0.439607
\(309\) 25.7602 1.46545
\(310\) 0 0
\(311\) −19.0114 −1.07804 −0.539018 0.842295i \(-0.681204\pi\)
−0.539018 + 0.842295i \(0.681204\pi\)
\(312\) 3.08494 0.174651
\(313\) 23.6268 1.33547 0.667733 0.744400i \(-0.267265\pi\)
0.667733 + 0.744400i \(0.267265\pi\)
\(314\) 7.01480 0.395868
\(315\) 0 0
\(316\) −6.94885 −0.390903
\(317\) −8.90271 −0.500026 −0.250013 0.968242i \(-0.580435\pi\)
−0.250013 + 0.968242i \(0.580435\pi\)
\(318\) −7.72638 −0.433274
\(319\) −2.90329 −0.162553
\(320\) 0 0
\(321\) −4.91296 −0.274215
\(322\) −3.93288 −0.219171
\(323\) −5.26829 −0.293135
\(324\) 11.0664 0.614801
\(325\) 0 0
\(326\) 7.73074 0.428166
\(327\) 6.52015 0.360565
\(328\) −17.5231 −0.967550
\(329\) 17.7916 0.980881
\(330\) 0 0
\(331\) 26.3865 1.45033 0.725167 0.688573i \(-0.241763\pi\)
0.725167 + 0.688573i \(0.241763\pi\)
\(332\) 29.4274 1.61504
\(333\) 8.02228 0.439618
\(334\) 2.47792 0.135586
\(335\) 0 0
\(336\) 34.2225 1.86699
\(337\) −16.0943 −0.876712 −0.438356 0.898801i \(-0.644439\pi\)
−0.438356 + 0.898801i \(0.644439\pi\)
\(338\) 4.68277 0.254709
\(339\) 0.521855 0.0283433
\(340\) 0 0
\(341\) 2.50775 0.135802
\(342\) −1.44117 −0.0779298
\(343\) −13.6202 −0.735420
\(344\) −2.07787 −0.112031
\(345\) 0 0
\(346\) 2.49135 0.133936
\(347\) 5.88918 0.316148 0.158074 0.987427i \(-0.449472\pi\)
0.158074 + 0.987427i \(0.449472\pi\)
\(348\) −14.0520 −0.753267
\(349\) 12.9912 0.695405 0.347702 0.937605i \(-0.386962\pi\)
0.347702 + 0.937605i \(0.386962\pi\)
\(350\) 0 0
\(351\) 1.68637 0.0900119
\(352\) −4.12291 −0.219752
\(353\) 4.89707 0.260645 0.130322 0.991472i \(-0.458399\pi\)
0.130322 + 0.991472i \(0.458399\pi\)
\(354\) −9.76028 −0.518753
\(355\) 0 0
\(356\) 2.03604 0.107910
\(357\) −57.1007 −3.02209
\(358\) −7.27267 −0.384373
\(359\) 7.98358 0.421357 0.210679 0.977555i \(-0.432433\pi\)
0.210679 + 0.977555i \(0.432433\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 2.75696 0.144903
\(363\) −2.60759 −0.136863
\(364\) −6.24038 −0.327085
\(365\) 0 0
\(366\) −1.25616 −0.0656604
\(367\) −29.4369 −1.53659 −0.768296 0.640095i \(-0.778895\pi\)
−0.768296 + 0.640095i \(0.778895\pi\)
\(368\) −7.87653 −0.410592
\(369\) −45.5203 −2.36969
\(370\) 0 0
\(371\) 32.4700 1.68576
\(372\) 12.1376 0.629304
\(373\) 30.5927 1.58403 0.792016 0.610500i \(-0.209032\pi\)
0.792016 + 0.610500i \(0.209032\pi\)
\(374\) 1.99827 0.103328
\(375\) 0 0
\(376\) −6.26064 −0.322868
\(377\) 2.34834 0.120946
\(378\) −3.28700 −0.169065
\(379\) −22.1797 −1.13930 −0.569648 0.821889i \(-0.692920\pi\)
−0.569648 + 0.821889i \(0.692920\pi\)
\(380\) 0 0
\(381\) −24.4581 −1.25303
\(382\) 6.51319 0.333244
\(383\) −13.7921 −0.704743 −0.352371 0.935860i \(-0.614625\pi\)
−0.352371 + 0.935860i \(0.614625\pi\)
\(384\) −26.2009 −1.33706
\(385\) 0 0
\(386\) 0.473336 0.0240922
\(387\) −5.39775 −0.274383
\(388\) 18.1173 0.919766
\(389\) 35.3099 1.79029 0.895143 0.445780i \(-0.147074\pi\)
0.895143 + 0.445780i \(0.147074\pi\)
\(390\) 0 0
\(391\) 13.1421 0.664623
\(392\) 15.0312 0.759192
\(393\) −26.1299 −1.31808
\(394\) −6.01947 −0.303257
\(395\) 0 0
\(396\) −7.05245 −0.354399
\(397\) −23.0739 −1.15805 −0.579024 0.815311i \(-0.696566\pi\)
−0.579024 + 0.815311i \(0.696566\pi\)
\(398\) −6.26632 −0.314102
\(399\) 10.8386 0.542607
\(400\) 0 0
\(401\) −34.5824 −1.72696 −0.863480 0.504382i \(-0.831720\pi\)
−0.863480 + 0.504382i \(0.831720\pi\)
\(402\) 7.50561 0.374346
\(403\) −2.02841 −0.101042
\(404\) 28.3379 1.40987
\(405\) 0 0
\(406\) −4.57727 −0.227166
\(407\) 2.11138 0.104657
\(408\) 20.0931 0.994755
\(409\) 15.3598 0.759492 0.379746 0.925091i \(-0.376011\pi\)
0.379746 + 0.925091i \(0.376011\pi\)
\(410\) 0 0
\(411\) 37.4900 1.84924
\(412\) 18.3366 0.903377
\(413\) 41.0175 2.01834
\(414\) 3.59510 0.176689
\(415\) 0 0
\(416\) 3.33484 0.163504
\(417\) 31.2143 1.52857
\(418\) −0.379302 −0.0185523
\(419\) 8.90005 0.434796 0.217398 0.976083i \(-0.430243\pi\)
0.217398 + 0.976083i \(0.430243\pi\)
\(420\) 0 0
\(421\) −8.72937 −0.425443 −0.212722 0.977113i \(-0.568233\pi\)
−0.212722 + 0.977113i \(0.568233\pi\)
\(422\) −6.22957 −0.303251
\(423\) −16.2635 −0.790759
\(424\) −11.4258 −0.554887
\(425\) 0 0
\(426\) −8.40648 −0.407296
\(427\) 5.27899 0.255468
\(428\) −3.49713 −0.169040
\(429\) 2.10917 0.101832
\(430\) 0 0
\(431\) −24.5037 −1.18030 −0.590150 0.807293i \(-0.700932\pi\)
−0.590150 + 0.807293i \(0.700932\pi\)
\(432\) −6.58299 −0.316724
\(433\) −34.3038 −1.64853 −0.824267 0.566201i \(-0.808413\pi\)
−0.824267 + 0.566201i \(0.808413\pi\)
\(434\) 3.95367 0.189782
\(435\) 0 0
\(436\) 4.64115 0.222271
\(437\) −2.49456 −0.119331
\(438\) −6.79294 −0.324579
\(439\) −1.73839 −0.0829686 −0.0414843 0.999139i \(-0.513209\pi\)
−0.0414843 + 0.999139i \(0.513209\pi\)
\(440\) 0 0
\(441\) 39.0472 1.85939
\(442\) −1.61631 −0.0768801
\(443\) −3.00190 −0.142624 −0.0713122 0.997454i \(-0.522719\pi\)
−0.0713122 + 0.997454i \(0.522719\pi\)
\(444\) 10.2191 0.484979
\(445\) 0 0
\(446\) −8.05765 −0.381541
\(447\) −49.6260 −2.34723
\(448\) 19.7483 0.933018
\(449\) −38.5044 −1.81713 −0.908567 0.417740i \(-0.862822\pi\)
−0.908567 + 0.417740i \(0.862822\pi\)
\(450\) 0 0
\(451\) −11.9805 −0.564138
\(452\) 0.371466 0.0174723
\(453\) 25.7879 1.21162
\(454\) −11.1870 −0.525031
\(455\) 0 0
\(456\) −3.81396 −0.178605
\(457\) −0.420486 −0.0196695 −0.00983476 0.999952i \(-0.503131\pi\)
−0.00983476 + 0.999952i \(0.503131\pi\)
\(458\) 9.80707 0.458254
\(459\) 10.9838 0.512679
\(460\) 0 0
\(461\) 21.4596 0.999471 0.499736 0.866178i \(-0.333430\pi\)
0.499736 + 0.866178i \(0.333430\pi\)
\(462\) −4.11109 −0.191265
\(463\) 0.392364 0.0182347 0.00911735 0.999958i \(-0.497098\pi\)
0.00911735 + 0.999958i \(0.497098\pi\)
\(464\) −9.16708 −0.425571
\(465\) 0 0
\(466\) −3.49976 −0.162123
\(467\) −2.01666 −0.0933201 −0.0466600 0.998911i \(-0.514858\pi\)
−0.0466600 + 0.998911i \(0.514858\pi\)
\(468\) 5.70441 0.263687
\(469\) −31.5423 −1.45649
\(470\) 0 0
\(471\) 48.2248 2.22208
\(472\) −14.4336 −0.664359
\(473\) −1.42063 −0.0653206
\(474\) 3.70279 0.170075
\(475\) 0 0
\(476\) −40.6452 −1.86297
\(477\) −29.6813 −1.35901
\(478\) 4.68611 0.214338
\(479\) −26.7805 −1.22363 −0.611817 0.790999i \(-0.709561\pi\)
−0.611817 + 0.790999i \(0.709561\pi\)
\(480\) 0 0
\(481\) −1.70780 −0.0778690
\(482\) −5.80303 −0.264321
\(483\) −27.0375 −1.23025
\(484\) −1.85613 −0.0843696
\(485\) 0 0
\(486\) −8.26930 −0.375103
\(487\) 28.2429 1.27981 0.639905 0.768454i \(-0.278974\pi\)
0.639905 + 0.768454i \(0.278974\pi\)
\(488\) −1.85762 −0.0840903
\(489\) 53.1467 2.40338
\(490\) 0 0
\(491\) 26.3559 1.18943 0.594713 0.803938i \(-0.297266\pi\)
0.594713 + 0.803938i \(0.297266\pi\)
\(492\) −57.9859 −2.61421
\(493\) 15.2954 0.688869
\(494\) 0.306800 0.0138036
\(495\) 0 0
\(496\) 7.91816 0.355536
\(497\) 35.3282 1.58469
\(498\) −15.6808 −0.702673
\(499\) 7.09609 0.317665 0.158832 0.987306i \(-0.449227\pi\)
0.158832 + 0.987306i \(0.449227\pi\)
\(500\) 0 0
\(501\) 17.0350 0.761067
\(502\) 5.54434 0.247456
\(503\) 22.7720 1.01535 0.507677 0.861548i \(-0.330504\pi\)
0.507677 + 0.861548i \(0.330504\pi\)
\(504\) −23.0994 −1.02893
\(505\) 0 0
\(506\) 0.946192 0.0420634
\(507\) 32.1927 1.42973
\(508\) −17.4097 −0.772430
\(509\) −26.6561 −1.18151 −0.590756 0.806850i \(-0.701171\pi\)
−0.590756 + 0.806850i \(0.701171\pi\)
\(510\) 0 0
\(511\) 28.5473 1.26286
\(512\) −22.2545 −0.983519
\(513\) −2.08489 −0.0920500
\(514\) 10.5081 0.463491
\(515\) 0 0
\(516\) −6.87589 −0.302694
\(517\) −4.28038 −0.188251
\(518\) 3.32876 0.146257
\(519\) 17.1273 0.751806
\(520\) 0 0
\(521\) −32.0959 −1.40615 −0.703073 0.711118i \(-0.748189\pi\)
−0.703073 + 0.711118i \(0.748189\pi\)
\(522\) 4.18414 0.183135
\(523\) 21.7074 0.949200 0.474600 0.880202i \(-0.342593\pi\)
0.474600 + 0.880202i \(0.342593\pi\)
\(524\) −18.5997 −0.812533
\(525\) 0 0
\(526\) 8.11556 0.353855
\(527\) −13.2115 −0.575504
\(528\) −8.23342 −0.358314
\(529\) −16.7772 −0.729442
\(530\) 0 0
\(531\) −37.4946 −1.62713
\(532\) 7.71508 0.334491
\(533\) 9.69047 0.419741
\(534\) −1.08493 −0.0469495
\(535\) 0 0
\(536\) 11.0994 0.479419
\(537\) −49.9976 −2.15756
\(538\) 4.49912 0.193971
\(539\) 10.2768 0.442653
\(540\) 0 0
\(541\) −22.6922 −0.975615 −0.487808 0.872951i \(-0.662203\pi\)
−0.487808 + 0.872951i \(0.662203\pi\)
\(542\) −10.7024 −0.459706
\(543\) 18.9533 0.813365
\(544\) 21.7207 0.931267
\(545\) 0 0
\(546\) 3.32527 0.142309
\(547\) 25.9252 1.10848 0.554240 0.832357i \(-0.313009\pi\)
0.554240 + 0.832357i \(0.313009\pi\)
\(548\) 26.6860 1.13997
\(549\) −4.82559 −0.205951
\(550\) 0 0
\(551\) −2.90329 −0.123684
\(552\) 9.51417 0.404950
\(553\) −15.5609 −0.661719
\(554\) −5.67150 −0.240959
\(555\) 0 0
\(556\) 22.2189 0.942292
\(557\) −15.4699 −0.655482 −0.327741 0.944768i \(-0.606287\pi\)
−0.327741 + 0.944768i \(0.606287\pi\)
\(558\) −3.61410 −0.152997
\(559\) 1.14908 0.0486011
\(560\) 0 0
\(561\) 13.7376 0.580000
\(562\) 7.16172 0.302099
\(563\) 30.6255 1.29071 0.645356 0.763882i \(-0.276709\pi\)
0.645356 + 0.763882i \(0.276709\pi\)
\(564\) −20.7172 −0.872351
\(565\) 0 0
\(566\) −3.43871 −0.144540
\(567\) 24.7817 1.04073
\(568\) −12.4316 −0.521617
\(569\) 19.1437 0.802546 0.401273 0.915959i \(-0.368568\pi\)
0.401273 + 0.915959i \(0.368568\pi\)
\(570\) 0 0
\(571\) −28.1015 −1.17601 −0.588005 0.808858i \(-0.700086\pi\)
−0.588005 + 0.808858i \(0.700086\pi\)
\(572\) 1.50134 0.0627742
\(573\) 44.7764 1.87056
\(574\) −18.8882 −0.788378
\(575\) 0 0
\(576\) −18.0521 −0.752172
\(577\) 40.6479 1.69219 0.846096 0.533030i \(-0.178947\pi\)
0.846096 + 0.533030i \(0.178947\pi\)
\(578\) −4.07934 −0.169678
\(579\) 3.25405 0.135234
\(580\) 0 0
\(581\) 65.8984 2.73393
\(582\) −9.65405 −0.400173
\(583\) −7.81180 −0.323532
\(584\) −10.0455 −0.415684
\(585\) 0 0
\(586\) −8.89167 −0.367312
\(587\) 21.8347 0.901215 0.450608 0.892722i \(-0.351207\pi\)
0.450608 + 0.892722i \(0.351207\pi\)
\(588\) 49.7401 2.05125
\(589\) 2.50775 0.103330
\(590\) 0 0
\(591\) −41.3822 −1.70224
\(592\) 6.66664 0.273997
\(593\) −12.4080 −0.509536 −0.254768 0.967002i \(-0.581999\pi\)
−0.254768 + 0.967002i \(0.581999\pi\)
\(594\) 0.790801 0.0324470
\(595\) 0 0
\(596\) −35.3246 −1.44695
\(597\) −43.0792 −1.76311
\(598\) −0.765332 −0.0312968
\(599\) 10.3034 0.420987 0.210493 0.977595i \(-0.432493\pi\)
0.210493 + 0.977595i \(0.432493\pi\)
\(600\) 0 0
\(601\) −5.81116 −0.237042 −0.118521 0.992952i \(-0.537815\pi\)
−0.118521 + 0.992952i \(0.537815\pi\)
\(602\) −2.23974 −0.0912850
\(603\) 28.8332 1.17418
\(604\) 18.3563 0.746907
\(605\) 0 0
\(606\) −15.1003 −0.613407
\(607\) 9.67871 0.392847 0.196423 0.980519i \(-0.437067\pi\)
0.196423 + 0.980519i \(0.437067\pi\)
\(608\) −4.12291 −0.167206
\(609\) −31.4675 −1.27513
\(610\) 0 0
\(611\) 3.46221 0.140066
\(612\) 37.1543 1.50188
\(613\) −39.9792 −1.61474 −0.807372 0.590043i \(-0.799111\pi\)
−0.807372 + 0.590043i \(0.799111\pi\)
\(614\) 2.45857 0.0992197
\(615\) 0 0
\(616\) −6.07951 −0.244950
\(617\) 15.4332 0.621317 0.310658 0.950522i \(-0.399451\pi\)
0.310658 + 0.950522i \(0.399451\pi\)
\(618\) −9.77089 −0.393043
\(619\) −47.7611 −1.91968 −0.959840 0.280549i \(-0.909484\pi\)
−0.959840 + 0.280549i \(0.909484\pi\)
\(620\) 0 0
\(621\) 5.20088 0.208704
\(622\) 7.21104 0.289136
\(623\) 4.55941 0.182669
\(624\) 6.65965 0.266599
\(625\) 0 0
\(626\) −8.96169 −0.358181
\(627\) −2.60759 −0.104137
\(628\) 34.3273 1.36981
\(629\) −11.1234 −0.443517
\(630\) 0 0
\(631\) −0.352780 −0.0140439 −0.00702197 0.999975i \(-0.502235\pi\)
−0.00702197 + 0.999975i \(0.502235\pi\)
\(632\) 5.47572 0.217812
\(633\) −42.8266 −1.70220
\(634\) 3.37681 0.134110
\(635\) 0 0
\(636\) −37.8094 −1.49924
\(637\) −8.31245 −0.329351
\(638\) 1.10122 0.0435978
\(639\) −32.2940 −1.27753
\(640\) 0 0
\(641\) −9.12385 −0.360370 −0.180185 0.983633i \(-0.557670\pi\)
−0.180185 + 0.983633i \(0.557670\pi\)
\(642\) 1.86350 0.0735463
\(643\) 7.36034 0.290263 0.145132 0.989412i \(-0.453639\pi\)
0.145132 + 0.989412i \(0.453639\pi\)
\(644\) −19.2457 −0.758388
\(645\) 0 0
\(646\) 1.99827 0.0786209
\(647\) 34.5602 1.35870 0.679352 0.733813i \(-0.262261\pi\)
0.679352 + 0.733813i \(0.262261\pi\)
\(648\) −8.72038 −0.342569
\(649\) −9.86819 −0.387360
\(650\) 0 0
\(651\) 27.1804 1.06528
\(652\) 37.8307 1.48157
\(653\) −17.1242 −0.670124 −0.335062 0.942196i \(-0.608757\pi\)
−0.335062 + 0.942196i \(0.608757\pi\)
\(654\) −2.47310 −0.0967060
\(655\) 0 0
\(656\) −37.8281 −1.47694
\(657\) −26.0954 −1.01808
\(658\) −6.74837 −0.263079
\(659\) −32.1685 −1.25311 −0.626553 0.779379i \(-0.715535\pi\)
−0.626553 + 0.779379i \(0.715535\pi\)
\(660\) 0 0
\(661\) −6.38995 −0.248540 −0.124270 0.992248i \(-0.539659\pi\)
−0.124270 + 0.992248i \(0.539659\pi\)
\(662\) −10.0084 −0.388989
\(663\) −11.1117 −0.431543
\(664\) −23.1889 −0.899903
\(665\) 0 0
\(666\) −3.04286 −0.117909
\(667\) 7.24243 0.280428
\(668\) 12.1258 0.469161
\(669\) −55.3941 −2.14166
\(670\) 0 0
\(671\) −1.27005 −0.0490296
\(672\) −44.6864 −1.72382
\(673\) −50.2048 −1.93525 −0.967626 0.252387i \(-0.918784\pi\)
−0.967626 + 0.252387i \(0.918784\pi\)
\(674\) 6.10459 0.235140
\(675\) 0 0
\(676\) 22.9153 0.881359
\(677\) 13.9577 0.536438 0.268219 0.963358i \(-0.413565\pi\)
0.268219 + 0.963358i \(0.413565\pi\)
\(678\) −0.197941 −0.00760186
\(679\) 40.5711 1.55698
\(680\) 0 0
\(681\) −76.9074 −2.94710
\(682\) −0.951193 −0.0364231
\(683\) 10.8435 0.414916 0.207458 0.978244i \(-0.433481\pi\)
0.207458 + 0.978244i \(0.433481\pi\)
\(684\) −7.05245 −0.269657
\(685\) 0 0
\(686\) 5.16615 0.197245
\(687\) 67.4209 2.57227
\(688\) −4.48561 −0.171012
\(689\) 6.31862 0.240720
\(690\) 0 0
\(691\) 33.2982 1.26672 0.633361 0.773857i \(-0.281675\pi\)
0.633361 + 0.773857i \(0.281675\pi\)
\(692\) 12.1915 0.463452
\(693\) −15.7930 −0.599925
\(694\) −2.23378 −0.0847930
\(695\) 0 0
\(696\) 11.0730 0.419722
\(697\) 63.1166 2.39071
\(698\) −4.92760 −0.186512
\(699\) −24.0599 −0.910029
\(700\) 0 0
\(701\) 12.9091 0.487568 0.243784 0.969830i \(-0.421611\pi\)
0.243784 + 0.969830i \(0.421611\pi\)
\(702\) −0.639644 −0.0241418
\(703\) 2.11138 0.0796322
\(704\) −4.75113 −0.179065
\(705\) 0 0
\(706\) −1.85747 −0.0699067
\(707\) 63.4588 2.38661
\(708\) −47.7624 −1.79502
\(709\) 5.26917 0.197888 0.0989438 0.995093i \(-0.468454\pi\)
0.0989438 + 0.995093i \(0.468454\pi\)
\(710\) 0 0
\(711\) 14.2245 0.533459
\(712\) −1.60440 −0.0601276
\(713\) −6.25573 −0.234279
\(714\) 21.6584 0.810545
\(715\) 0 0
\(716\) −35.5891 −1.33003
\(717\) 32.2157 1.20312
\(718\) −3.02818 −0.113011
\(719\) −2.43393 −0.0907703 −0.0453851 0.998970i \(-0.514452\pi\)
−0.0453851 + 0.998970i \(0.514452\pi\)
\(720\) 0 0
\(721\) 41.0621 1.52923
\(722\) −0.379302 −0.0141161
\(723\) −39.8942 −1.48368
\(724\) 13.4913 0.501400
\(725\) 0 0
\(726\) 0.989065 0.0367076
\(727\) −28.7825 −1.06748 −0.533742 0.845647i \(-0.679215\pi\)
−0.533742 + 0.845647i \(0.679215\pi\)
\(728\) 4.91744 0.182252
\(729\) −38.9629 −1.44307
\(730\) 0 0
\(731\) 7.48429 0.276816
\(732\) −6.14706 −0.227202
\(733\) −16.6212 −0.613918 −0.306959 0.951723i \(-0.599311\pi\)
−0.306959 + 0.951723i \(0.599311\pi\)
\(734\) 11.1655 0.412125
\(735\) 0 0
\(736\) 10.2849 0.379105
\(737\) 7.58859 0.279529
\(738\) 17.2659 0.635568
\(739\) 8.17863 0.300856 0.150428 0.988621i \(-0.451935\pi\)
0.150428 + 0.988621i \(0.451935\pi\)
\(740\) 0 0
\(741\) 2.10917 0.0774822
\(742\) −12.3159 −0.452133
\(743\) −33.8950 −1.24349 −0.621744 0.783221i \(-0.713575\pi\)
−0.621744 + 0.783221i \(0.713575\pi\)
\(744\) −9.56445 −0.350650
\(745\) 0 0
\(746\) −11.6039 −0.424848
\(747\) −60.2386 −2.20401
\(748\) 9.77863 0.357542
\(749\) −7.83133 −0.286150
\(750\) 0 0
\(751\) 46.2851 1.68897 0.844483 0.535582i \(-0.179908\pi\)
0.844483 + 0.535582i \(0.179908\pi\)
\(752\) −13.5152 −0.492849
\(753\) 38.1158 1.38902
\(754\) −0.890730 −0.0324385
\(755\) 0 0
\(756\) −16.0851 −0.585008
\(757\) 25.3179 0.920196 0.460098 0.887868i \(-0.347814\pi\)
0.460098 + 0.887868i \(0.347814\pi\)
\(758\) 8.41280 0.305567
\(759\) 6.50480 0.236109
\(760\) 0 0
\(761\) 26.4498 0.958805 0.479403 0.877595i \(-0.340853\pi\)
0.479403 + 0.877595i \(0.340853\pi\)
\(762\) 9.27699 0.336070
\(763\) 10.3932 0.376259
\(764\) 31.8726 1.15311
\(765\) 0 0
\(766\) 5.23136 0.189017
\(767\) 7.98194 0.288211
\(768\) −14.8400 −0.535492
\(769\) 5.11765 0.184547 0.0922735 0.995734i \(-0.470587\pi\)
0.0922735 + 0.995734i \(0.470587\pi\)
\(770\) 0 0
\(771\) 72.2400 2.60166
\(772\) 2.31629 0.0833651
\(773\) 8.91322 0.320586 0.160293 0.987069i \(-0.448756\pi\)
0.160293 + 0.987069i \(0.448756\pi\)
\(774\) 2.04737 0.0735913
\(775\) 0 0
\(776\) −14.2765 −0.512496
\(777\) 22.8843 0.820970
\(778\) −13.3931 −0.480167
\(779\) −11.9805 −0.429245
\(780\) 0 0
\(781\) −8.49943 −0.304133
\(782\) −4.98481 −0.178256
\(783\) 6.05303 0.216318
\(784\) 32.4488 1.15889
\(785\) 0 0
\(786\) 9.91112 0.353518
\(787\) 32.0672 1.14307 0.571535 0.820577i \(-0.306348\pi\)
0.571535 + 0.820577i \(0.306348\pi\)
\(788\) −29.4566 −1.04935
\(789\) 55.7922 1.98626
\(790\) 0 0
\(791\) 0.831844 0.0295770
\(792\) 5.55735 0.197472
\(793\) 1.02728 0.0364799
\(794\) 8.75198 0.310596
\(795\) 0 0
\(796\) −30.6645 −1.08687
\(797\) −25.9956 −0.920811 −0.460406 0.887709i \(-0.652296\pi\)
−0.460406 + 0.887709i \(0.652296\pi\)
\(798\) −4.11109 −0.145531
\(799\) 22.5503 0.797772
\(800\) 0 0
\(801\) −4.16782 −0.147263
\(802\) 13.1172 0.463183
\(803\) −6.86804 −0.242368
\(804\) 36.7290 1.29533
\(805\) 0 0
\(806\) 0.769378 0.0271002
\(807\) 30.9302 1.08879
\(808\) −22.3304 −0.785581
\(809\) 49.2061 1.72999 0.864997 0.501776i \(-0.167320\pi\)
0.864997 + 0.501776i \(0.167320\pi\)
\(810\) 0 0
\(811\) −44.5693 −1.56504 −0.782520 0.622626i \(-0.786066\pi\)
−0.782520 + 0.622626i \(0.786066\pi\)
\(812\) −22.3991 −0.786054
\(813\) −73.5757 −2.58041
\(814\) −0.800850 −0.0280698
\(815\) 0 0
\(816\) 43.3761 1.51847
\(817\) −1.42063 −0.0497015
\(818\) −5.82599 −0.203701
\(819\) 12.7742 0.446367
\(820\) 0 0
\(821\) −9.78163 −0.341381 −0.170691 0.985325i \(-0.554600\pi\)
−0.170691 + 0.985325i \(0.554600\pi\)
\(822\) −14.2200 −0.495980
\(823\) 21.5392 0.750809 0.375405 0.926861i \(-0.377504\pi\)
0.375405 + 0.926861i \(0.377504\pi\)
\(824\) −14.4493 −0.503364
\(825\) 0 0
\(826\) −15.5580 −0.541333
\(827\) 35.5256 1.23535 0.617673 0.786435i \(-0.288075\pi\)
0.617673 + 0.786435i \(0.288075\pi\)
\(828\) 17.5928 0.611391
\(829\) −2.59741 −0.0902119 −0.0451059 0.998982i \(-0.514363\pi\)
−0.0451059 + 0.998982i \(0.514363\pi\)
\(830\) 0 0
\(831\) −38.9900 −1.35255
\(832\) 3.84298 0.133231
\(833\) −54.1412 −1.87588
\(834\) −11.8397 −0.409974
\(835\) 0 0
\(836\) −1.85613 −0.0641956
\(837\) −5.22837 −0.180719
\(838\) −3.37580 −0.116615
\(839\) −1.00128 −0.0345680 −0.0172840 0.999851i \(-0.505502\pi\)
−0.0172840 + 0.999851i \(0.505502\pi\)
\(840\) 0 0
\(841\) −20.5709 −0.709342
\(842\) 3.31106 0.114107
\(843\) 49.2348 1.69574
\(844\) −30.4847 −1.04933
\(845\) 0 0
\(846\) 6.16877 0.212087
\(847\) −4.15654 −0.142820
\(848\) −24.6656 −0.847020
\(849\) −23.6402 −0.811329
\(850\) 0 0
\(851\) −5.26697 −0.180549
\(852\) −41.1375 −1.40935
\(853\) −3.93139 −0.134608 −0.0673042 0.997733i \(-0.521440\pi\)
−0.0673042 + 0.997733i \(0.521440\pi\)
\(854\) −2.00233 −0.0685183
\(855\) 0 0
\(856\) 2.75575 0.0941896
\(857\) −37.5655 −1.28321 −0.641606 0.767034i \(-0.721732\pi\)
−0.641606 + 0.767034i \(0.721732\pi\)
\(858\) −0.800010 −0.0273119
\(859\) 37.8019 1.28978 0.644892 0.764273i \(-0.276902\pi\)
0.644892 + 0.764273i \(0.276902\pi\)
\(860\) 0 0
\(861\) −129.851 −4.42531
\(862\) 9.29429 0.316565
\(863\) 23.3269 0.794057 0.397029 0.917806i \(-0.370041\pi\)
0.397029 + 0.917806i \(0.370041\pi\)
\(864\) 8.59580 0.292435
\(865\) 0 0
\(866\) 13.0115 0.442148
\(867\) −28.0443 −0.952435
\(868\) 19.3475 0.656696
\(869\) 3.74373 0.126997
\(870\) 0 0
\(871\) −6.13807 −0.207981
\(872\) −3.65724 −0.123850
\(873\) −37.0865 −1.25519
\(874\) 0.946192 0.0320054
\(875\) 0 0
\(876\) −33.2416 −1.12313
\(877\) −20.7999 −0.702361 −0.351181 0.936308i \(-0.614220\pi\)
−0.351181 + 0.936308i \(0.614220\pi\)
\(878\) 0.659372 0.0222527
\(879\) −61.1278 −2.06179
\(880\) 0 0
\(881\) 52.3897 1.76506 0.882528 0.470261i \(-0.155840\pi\)
0.882528 + 0.470261i \(0.155840\pi\)
\(882\) −14.8107 −0.498701
\(883\) 27.1774 0.914591 0.457295 0.889315i \(-0.348818\pi\)
0.457295 + 0.889315i \(0.348818\pi\)
\(884\) −7.90950 −0.266025
\(885\) 0 0
\(886\) 1.13862 0.0382528
\(887\) −35.2309 −1.18294 −0.591469 0.806328i \(-0.701452\pi\)
−0.591469 + 0.806328i \(0.701452\pi\)
\(888\) −8.05272 −0.270232
\(889\) −38.9865 −1.30757
\(890\) 0 0
\(891\) −5.96210 −0.199738
\(892\) −39.4305 −1.32023
\(893\) −4.28038 −0.143238
\(894\) 18.8232 0.629543
\(895\) 0 0
\(896\) −41.7646 −1.39526
\(897\) −5.26145 −0.175675
\(898\) 14.6048 0.487367
\(899\) −7.28071 −0.242825
\(900\) 0 0
\(901\) 41.1548 1.37107
\(902\) 4.54421 0.151306
\(903\) −15.3976 −0.512399
\(904\) −0.292716 −0.00973559
\(905\) 0 0
\(906\) −9.78140 −0.324965
\(907\) −4.04284 −0.134240 −0.0671201 0.997745i \(-0.521381\pi\)
−0.0671201 + 0.997745i \(0.521381\pi\)
\(908\) −54.7440 −1.81674
\(909\) −58.0085 −1.92402
\(910\) 0 0
\(911\) −25.4464 −0.843077 −0.421539 0.906810i \(-0.638510\pi\)
−0.421539 + 0.906810i \(0.638510\pi\)
\(912\) −8.23342 −0.272636
\(913\) −15.8542 −0.524696
\(914\) 0.159491 0.00527550
\(915\) 0 0
\(916\) 47.9913 1.58568
\(917\) −41.6514 −1.37545
\(918\) −4.16617 −0.137504
\(919\) −27.9210 −0.921028 −0.460514 0.887652i \(-0.652335\pi\)
−0.460514 + 0.887652i \(0.652335\pi\)
\(920\) 0 0
\(921\) 16.9020 0.556938
\(922\) −8.13965 −0.268065
\(923\) 6.87481 0.226287
\(924\) −20.1178 −0.661826
\(925\) 0 0
\(926\) −0.148824 −0.00489067
\(927\) −37.5354 −1.23282
\(928\) 11.9700 0.392935
\(929\) −29.7603 −0.976405 −0.488203 0.872730i \(-0.662347\pi\)
−0.488203 + 0.872730i \(0.662347\pi\)
\(930\) 0 0
\(931\) 10.2768 0.336809
\(932\) −17.1262 −0.560989
\(933\) 49.5739 1.62298
\(934\) 0.764924 0.0250291
\(935\) 0 0
\(936\) −4.49510 −0.146927
\(937\) 33.0699 1.08035 0.540173 0.841554i \(-0.318359\pi\)
0.540173 + 0.841554i \(0.318359\pi\)
\(938\) 11.9640 0.390640
\(939\) −61.6092 −2.01054
\(940\) 0 0
\(941\) 17.9201 0.584178 0.292089 0.956391i \(-0.405650\pi\)
0.292089 + 0.956391i \(0.405650\pi\)
\(942\) −18.2918 −0.595978
\(943\) 29.8860 0.973223
\(944\) −31.1586 −1.01413
\(945\) 0 0
\(946\) 0.538847 0.0175194
\(947\) −13.3998 −0.435434 −0.217717 0.976012i \(-0.569861\pi\)
−0.217717 + 0.976012i \(0.569861\pi\)
\(948\) 18.1198 0.588503
\(949\) 5.55526 0.180331
\(950\) 0 0
\(951\) 23.2147 0.752787
\(952\) 32.0286 1.03805
\(953\) 42.3132 1.37066 0.685330 0.728232i \(-0.259658\pi\)
0.685330 + 0.728232i \(0.259658\pi\)
\(954\) 11.2582 0.364496
\(955\) 0 0
\(956\) 22.9317 0.741664
\(957\) 7.57060 0.244723
\(958\) 10.1579 0.328187
\(959\) 59.7595 1.92973
\(960\) 0 0
\(961\) −24.7112 −0.797136
\(962\) 0.647772 0.0208850
\(963\) 7.15871 0.230686
\(964\) −28.3974 −0.914619
\(965\) 0 0
\(966\) 10.2554 0.329961
\(967\) −49.4182 −1.58918 −0.794591 0.607145i \(-0.792315\pi\)
−0.794591 + 0.607145i \(0.792315\pi\)
\(968\) 1.46264 0.0470109
\(969\) 13.7376 0.441314
\(970\) 0 0
\(971\) −46.5589 −1.49415 −0.747074 0.664741i \(-0.768542\pi\)
−0.747074 + 0.664741i \(0.768542\pi\)
\(972\) −40.4662 −1.29795
\(973\) 49.7561 1.59511
\(974\) −10.7126 −0.343254
\(975\) 0 0
\(976\) −4.01014 −0.128362
\(977\) 13.8329 0.442552 0.221276 0.975211i \(-0.428978\pi\)
0.221276 + 0.975211i \(0.428978\pi\)
\(978\) −20.1586 −0.644602
\(979\) −1.09693 −0.0350579
\(980\) 0 0
\(981\) −9.50056 −0.303329
\(982\) −9.99684 −0.319012
\(983\) −11.2618 −0.359195 −0.179598 0.983740i \(-0.557480\pi\)
−0.179598 + 0.983740i \(0.557480\pi\)
\(984\) 45.6931 1.45664
\(985\) 0 0
\(986\) −5.80156 −0.184759
\(987\) −46.3932 −1.47671
\(988\) 1.50134 0.0477640
\(989\) 3.54385 0.112688
\(990\) 0 0
\(991\) −8.44195 −0.268167 −0.134084 0.990970i \(-0.542809\pi\)
−0.134084 + 0.990970i \(0.542809\pi\)
\(992\) −10.3392 −0.328271
\(993\) −68.8053 −2.18347
\(994\) −13.4000 −0.425024
\(995\) 0 0
\(996\) −76.7347 −2.43143
\(997\) −16.9634 −0.537236 −0.268618 0.963247i \(-0.586567\pi\)
−0.268618 + 0.963247i \(0.586567\pi\)
\(998\) −2.69156 −0.0851999
\(999\) −4.40199 −0.139273
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 5225.2.a.bc.1.14 30
5.2 odd 4 1045.2.b.e.419.14 30
5.3 odd 4 1045.2.b.e.419.17 yes 30
5.4 even 2 inner 5225.2.a.bc.1.17 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.b.e.419.14 30 5.2 odd 4
1045.2.b.e.419.17 yes 30 5.3 odd 4
5225.2.a.bc.1.14 30 1.1 even 1 trivial
5225.2.a.bc.1.17 30 5.4 even 2 inner