Properties

Label 6025.2.a.i.1.5
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $15$
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] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.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: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} - 699 x^{6} - 297 x^{5} + 394 x^{4} + 89 x^{3} - 57 x^{2} - 17 x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.09783\) of defining polynomial
Character \(\chi\) \(=\) 6025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.09783 q^{2} -1.80555 q^{3} -0.794772 q^{4} +1.98218 q^{6} +0.928281 q^{7} +3.06818 q^{8} +0.259998 q^{9} +O(q^{10})\) \(q-1.09783 q^{2} -1.80555 q^{3} -0.794772 q^{4} +1.98218 q^{6} +0.928281 q^{7} +3.06818 q^{8} +0.259998 q^{9} -0.401264 q^{11} +1.43500 q^{12} +6.69327 q^{13} -1.01909 q^{14} -1.77880 q^{16} +1.90485 q^{17} -0.285433 q^{18} -0.291750 q^{19} -1.67605 q^{21} +0.440520 q^{22} -2.38576 q^{23} -5.53974 q^{24} -7.34806 q^{26} +4.94720 q^{27} -0.737771 q^{28} -2.80478 q^{29} -3.86854 q^{31} -4.18355 q^{32} +0.724502 q^{33} -2.09120 q^{34} -0.206639 q^{36} -7.87504 q^{37} +0.320292 q^{38} -12.0850 q^{39} -1.82266 q^{41} +1.84002 q^{42} -5.42284 q^{43} +0.318914 q^{44} +2.61916 q^{46} -2.33696 q^{47} +3.21170 q^{48} -6.13829 q^{49} -3.43930 q^{51} -5.31962 q^{52} +6.48568 q^{53} -5.43118 q^{54} +2.84813 q^{56} +0.526768 q^{57} +3.07917 q^{58} -4.02672 q^{59} +9.23608 q^{61} +4.24700 q^{62} +0.241351 q^{63} +8.15041 q^{64} -0.795379 q^{66} -4.99709 q^{67} -1.51392 q^{68} +4.30760 q^{69} +8.92064 q^{71} +0.797720 q^{72} +11.9653 q^{73} +8.64545 q^{74} +0.231875 q^{76} -0.372486 q^{77} +13.2673 q^{78} +0.645240 q^{79} -9.71239 q^{81} +2.00097 q^{82} +8.84272 q^{83} +1.33208 q^{84} +5.95335 q^{86} +5.06416 q^{87} -1.23115 q^{88} -10.4841 q^{89} +6.21323 q^{91} +1.89613 q^{92} +6.98484 q^{93} +2.56558 q^{94} +7.55359 q^{96} +9.30216 q^{97} +6.73880 q^{98} -0.104328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09783 −0.776282 −0.388141 0.921600i \(-0.626883\pi\)
−0.388141 + 0.921600i \(0.626883\pi\)
\(3\) −1.80555 −1.04243 −0.521216 0.853425i \(-0.674522\pi\)
−0.521216 + 0.853425i \(0.674522\pi\)
\(4\) −0.794772 −0.397386
\(5\) 0 0
\(6\) 1.98218 0.809222
\(7\) 0.928281 0.350857 0.175429 0.984492i \(-0.443869\pi\)
0.175429 + 0.984492i \(0.443869\pi\)
\(8\) 3.06818 1.08477
\(9\) 0.259998 0.0866658
\(10\) 0 0
\(11\) −0.401264 −0.120986 −0.0604929 0.998169i \(-0.519267\pi\)
−0.0604929 + 0.998169i \(0.519267\pi\)
\(12\) 1.43500 0.414248
\(13\) 6.69327 1.85638 0.928189 0.372108i \(-0.121365\pi\)
0.928189 + 0.372108i \(0.121365\pi\)
\(14\) −1.01909 −0.272364
\(15\) 0 0
\(16\) −1.77880 −0.444699
\(17\) 1.90485 0.461994 0.230997 0.972954i \(-0.425801\pi\)
0.230997 + 0.972954i \(0.425801\pi\)
\(18\) −0.285433 −0.0672772
\(19\) −0.291750 −0.0669321 −0.0334660 0.999440i \(-0.510655\pi\)
−0.0334660 + 0.999440i \(0.510655\pi\)
\(20\) 0 0
\(21\) −1.67605 −0.365745
\(22\) 0.440520 0.0939191
\(23\) −2.38576 −0.497465 −0.248733 0.968572i \(-0.580014\pi\)
−0.248733 + 0.968572i \(0.580014\pi\)
\(24\) −5.53974 −1.13080
\(25\) 0 0
\(26\) −7.34806 −1.44107
\(27\) 4.94720 0.952089
\(28\) −0.737771 −0.139426
\(29\) −2.80478 −0.520835 −0.260417 0.965496i \(-0.583860\pi\)
−0.260417 + 0.965496i \(0.583860\pi\)
\(30\) 0 0
\(31\) −3.86854 −0.694811 −0.347406 0.937715i \(-0.612937\pi\)
−0.347406 + 0.937715i \(0.612937\pi\)
\(32\) −4.18355 −0.739554
\(33\) 0.724502 0.126120
\(34\) −2.09120 −0.358638
\(35\) 0 0
\(36\) −0.206639 −0.0344398
\(37\) −7.87504 −1.29465 −0.647325 0.762214i \(-0.724112\pi\)
−0.647325 + 0.762214i \(0.724112\pi\)
\(38\) 0.320292 0.0519582
\(39\) −12.0850 −1.93515
\(40\) 0 0
\(41\) −1.82266 −0.284652 −0.142326 0.989820i \(-0.545458\pi\)
−0.142326 + 0.989820i \(0.545458\pi\)
\(42\) 1.84002 0.283921
\(43\) −5.42284 −0.826975 −0.413488 0.910510i \(-0.635690\pi\)
−0.413488 + 0.910510i \(0.635690\pi\)
\(44\) 0.318914 0.0480780
\(45\) 0 0
\(46\) 2.61916 0.386174
\(47\) −2.33696 −0.340880 −0.170440 0.985368i \(-0.554519\pi\)
−0.170440 + 0.985368i \(0.554519\pi\)
\(48\) 3.21170 0.463569
\(49\) −6.13829 −0.876899
\(50\) 0 0
\(51\) −3.43930 −0.481598
\(52\) −5.31962 −0.737698
\(53\) 6.48568 0.890877 0.445439 0.895312i \(-0.353048\pi\)
0.445439 + 0.895312i \(0.353048\pi\)
\(54\) −5.43118 −0.739090
\(55\) 0 0
\(56\) 2.84813 0.380598
\(57\) 0.526768 0.0697722
\(58\) 3.07917 0.404315
\(59\) −4.02672 −0.524234 −0.262117 0.965036i \(-0.584421\pi\)
−0.262117 + 0.965036i \(0.584421\pi\)
\(60\) 0 0
\(61\) 9.23608 1.18256 0.591279 0.806467i \(-0.298623\pi\)
0.591279 + 0.806467i \(0.298623\pi\)
\(62\) 4.24700 0.539370
\(63\) 0.241351 0.0304073
\(64\) 8.15041 1.01880
\(65\) 0 0
\(66\) −0.795379 −0.0979044
\(67\) −4.99709 −0.610492 −0.305246 0.952274i \(-0.598739\pi\)
−0.305246 + 0.952274i \(0.598739\pi\)
\(68\) −1.51392 −0.183590
\(69\) 4.30760 0.518574
\(70\) 0 0
\(71\) 8.92064 1.05868 0.529342 0.848408i \(-0.322439\pi\)
0.529342 + 0.848408i \(0.322439\pi\)
\(72\) 0.797720 0.0940121
\(73\) 11.9653 1.40043 0.700217 0.713930i \(-0.253086\pi\)
0.700217 + 0.713930i \(0.253086\pi\)
\(74\) 8.64545 1.00501
\(75\) 0 0
\(76\) 0.231875 0.0265979
\(77\) −0.372486 −0.0424487
\(78\) 13.2673 1.50222
\(79\) 0.645240 0.0725952 0.0362976 0.999341i \(-0.488444\pi\)
0.0362976 + 0.999341i \(0.488444\pi\)
\(80\) 0 0
\(81\) −9.71239 −1.07915
\(82\) 2.00097 0.220970
\(83\) 8.84272 0.970614 0.485307 0.874344i \(-0.338708\pi\)
0.485307 + 0.874344i \(0.338708\pi\)
\(84\) 1.33208 0.145342
\(85\) 0 0
\(86\) 5.95335 0.641966
\(87\) 5.06416 0.542935
\(88\) −1.23115 −0.131241
\(89\) −10.4841 −1.11131 −0.555657 0.831411i \(-0.687533\pi\)
−0.555657 + 0.831411i \(0.687533\pi\)
\(90\) 0 0
\(91\) 6.21323 0.651324
\(92\) 1.89613 0.197686
\(93\) 6.98484 0.724294
\(94\) 2.56558 0.264619
\(95\) 0 0
\(96\) 7.55359 0.770935
\(97\) 9.30216 0.944492 0.472246 0.881467i \(-0.343443\pi\)
0.472246 + 0.881467i \(0.343443\pi\)
\(98\) 6.73880 0.680721
\(99\) −0.104328 −0.0104853
\(100\) 0 0
\(101\) −9.73764 −0.968932 −0.484466 0.874810i \(-0.660986\pi\)
−0.484466 + 0.874810i \(0.660986\pi\)
\(102\) 3.77576 0.373856
\(103\) −1.69308 −0.166824 −0.0834120 0.996515i \(-0.526582\pi\)
−0.0834120 + 0.996515i \(0.526582\pi\)
\(104\) 20.5362 2.01374
\(105\) 0 0
\(106\) −7.12017 −0.691572
\(107\) −14.9785 −1.44803 −0.724014 0.689785i \(-0.757705\pi\)
−0.724014 + 0.689785i \(0.757705\pi\)
\(108\) −3.93189 −0.378347
\(109\) 0.343011 0.0328545 0.0164272 0.999865i \(-0.494771\pi\)
0.0164272 + 0.999865i \(0.494771\pi\)
\(110\) 0 0
\(111\) 14.2188 1.34958
\(112\) −1.65122 −0.156026
\(113\) −5.70596 −0.536772 −0.268386 0.963311i \(-0.586490\pi\)
−0.268386 + 0.963311i \(0.586490\pi\)
\(114\) −0.578302 −0.0541629
\(115\) 0 0
\(116\) 2.22916 0.206972
\(117\) 1.74023 0.160885
\(118\) 4.42065 0.406954
\(119\) 1.76824 0.162094
\(120\) 0 0
\(121\) −10.8390 −0.985362
\(122\) −10.1396 −0.917999
\(123\) 3.29090 0.296731
\(124\) 3.07461 0.276108
\(125\) 0 0
\(126\) −0.264962 −0.0236047
\(127\) −0.639748 −0.0567684 −0.0283842 0.999597i \(-0.509036\pi\)
−0.0283842 + 0.999597i \(0.509036\pi\)
\(128\) −0.580660 −0.0513236
\(129\) 9.79119 0.862066
\(130\) 0 0
\(131\) −2.53486 −0.221472 −0.110736 0.993850i \(-0.535321\pi\)
−0.110736 + 0.993850i \(0.535321\pi\)
\(132\) −0.575813 −0.0501181
\(133\) −0.270826 −0.0234836
\(134\) 5.48595 0.473914
\(135\) 0 0
\(136\) 5.84443 0.501155
\(137\) 3.35377 0.286532 0.143266 0.989684i \(-0.454240\pi\)
0.143266 + 0.989684i \(0.454240\pi\)
\(138\) −4.72901 −0.402560
\(139\) −6.27168 −0.531957 −0.265978 0.963979i \(-0.585695\pi\)
−0.265978 + 0.963979i \(0.585695\pi\)
\(140\) 0 0
\(141\) 4.21948 0.355345
\(142\) −9.79334 −0.821838
\(143\) −2.68577 −0.224595
\(144\) −0.462482 −0.0385402
\(145\) 0 0
\(146\) −13.1359 −1.08713
\(147\) 11.0830 0.914108
\(148\) 6.25886 0.514475
\(149\) 8.33806 0.683080 0.341540 0.939867i \(-0.389051\pi\)
0.341540 + 0.939867i \(0.389051\pi\)
\(150\) 0 0
\(151\) 20.1838 1.64254 0.821269 0.570541i \(-0.193267\pi\)
0.821269 + 0.570541i \(0.193267\pi\)
\(152\) −0.895142 −0.0726056
\(153\) 0.495256 0.0400391
\(154\) 0.408926 0.0329522
\(155\) 0 0
\(156\) 9.60482 0.769001
\(157\) −4.99089 −0.398316 −0.199158 0.979967i \(-0.563821\pi\)
−0.199158 + 0.979967i \(0.563821\pi\)
\(158\) −0.708363 −0.0563544
\(159\) −11.7102 −0.928680
\(160\) 0 0
\(161\) −2.21466 −0.174539
\(162\) 10.6625 0.837729
\(163\) 12.7050 0.995133 0.497567 0.867426i \(-0.334227\pi\)
0.497567 + 0.867426i \(0.334227\pi\)
\(164\) 1.44860 0.113117
\(165\) 0 0
\(166\) −9.70779 −0.753471
\(167\) −15.1031 −1.16871 −0.584357 0.811497i \(-0.698653\pi\)
−0.584357 + 0.811497i \(0.698653\pi\)
\(168\) −5.14244 −0.396748
\(169\) 31.7998 2.44614
\(170\) 0 0
\(171\) −0.0758543 −0.00580072
\(172\) 4.30992 0.328628
\(173\) 1.07463 0.0817025 0.0408513 0.999165i \(-0.486993\pi\)
0.0408513 + 0.999165i \(0.486993\pi\)
\(174\) −5.55958 −0.421471
\(175\) 0 0
\(176\) 0.713767 0.0538022
\(177\) 7.27042 0.546479
\(178\) 11.5098 0.862694
\(179\) −12.6395 −0.944719 −0.472360 0.881406i \(-0.656598\pi\)
−0.472360 + 0.881406i \(0.656598\pi\)
\(180\) 0 0
\(181\) −8.01905 −0.596051 −0.298026 0.954558i \(-0.596328\pi\)
−0.298026 + 0.954558i \(0.596328\pi\)
\(182\) −6.82107 −0.505611
\(183\) −16.6762 −1.23274
\(184\) −7.31994 −0.539633
\(185\) 0 0
\(186\) −7.66816 −0.562257
\(187\) −0.764349 −0.0558947
\(188\) 1.85735 0.135461
\(189\) 4.59239 0.334047
\(190\) 0 0
\(191\) −2.52209 −0.182492 −0.0912460 0.995828i \(-0.529085\pi\)
−0.0912460 + 0.995828i \(0.529085\pi\)
\(192\) −14.7159 −1.06203
\(193\) 27.1349 1.95322 0.976608 0.215029i \(-0.0689845\pi\)
0.976608 + 0.215029i \(0.0689845\pi\)
\(194\) −10.2122 −0.733192
\(195\) 0 0
\(196\) 4.87854 0.348467
\(197\) 1.17329 0.0835934 0.0417967 0.999126i \(-0.486692\pi\)
0.0417967 + 0.999126i \(0.486692\pi\)
\(198\) 0.114534 0.00813958
\(199\) −26.8259 −1.90164 −0.950819 0.309747i \(-0.899756\pi\)
−0.950819 + 0.309747i \(0.899756\pi\)
\(200\) 0 0
\(201\) 9.02248 0.636397
\(202\) 10.6903 0.752164
\(203\) −2.60362 −0.182739
\(204\) 2.73345 0.191380
\(205\) 0 0
\(206\) 1.85871 0.129503
\(207\) −0.620292 −0.0431132
\(208\) −11.9060 −0.825529
\(209\) 0.117069 0.00809783
\(210\) 0 0
\(211\) 3.07752 0.211865 0.105933 0.994373i \(-0.466217\pi\)
0.105933 + 0.994373i \(0.466217\pi\)
\(212\) −5.15464 −0.354022
\(213\) −16.1066 −1.10361
\(214\) 16.4439 1.12408
\(215\) 0 0
\(216\) 15.1789 1.03279
\(217\) −3.59110 −0.243780
\(218\) −0.376567 −0.0255043
\(219\) −21.6039 −1.45986
\(220\) 0 0
\(221\) 12.7497 0.857636
\(222\) −15.6098 −1.04766
\(223\) 4.73624 0.317162 0.158581 0.987346i \(-0.449308\pi\)
0.158581 + 0.987346i \(0.449308\pi\)
\(224\) −3.88351 −0.259478
\(225\) 0 0
\(226\) 6.26417 0.416687
\(227\) 4.73421 0.314221 0.157110 0.987581i \(-0.449782\pi\)
0.157110 + 0.987581i \(0.449782\pi\)
\(228\) −0.418661 −0.0277265
\(229\) 8.01736 0.529802 0.264901 0.964276i \(-0.414661\pi\)
0.264901 + 0.964276i \(0.414661\pi\)
\(230\) 0 0
\(231\) 0.672541 0.0442500
\(232\) −8.60557 −0.564984
\(233\) −5.44207 −0.356522 −0.178261 0.983983i \(-0.557047\pi\)
−0.178261 + 0.983983i \(0.557047\pi\)
\(234\) −1.91048 −0.124892
\(235\) 0 0
\(236\) 3.20032 0.208323
\(237\) −1.16501 −0.0756756
\(238\) −1.94122 −0.125831
\(239\) 4.22052 0.273003 0.136501 0.990640i \(-0.456414\pi\)
0.136501 + 0.990640i \(0.456414\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) 11.8994 0.764919
\(243\) 2.69457 0.172857
\(244\) −7.34057 −0.469932
\(245\) 0 0
\(246\) −3.61285 −0.230347
\(247\) −1.95276 −0.124251
\(248\) −11.8694 −0.753707
\(249\) −15.9659 −1.01180
\(250\) 0 0
\(251\) −3.40591 −0.214979 −0.107490 0.994206i \(-0.534281\pi\)
−0.107490 + 0.994206i \(0.534281\pi\)
\(252\) −0.191819 −0.0120834
\(253\) 0.957321 0.0601862
\(254\) 0.702334 0.0440683
\(255\) 0 0
\(256\) −15.6634 −0.978960
\(257\) 13.2411 0.825955 0.412978 0.910741i \(-0.364489\pi\)
0.412978 + 0.910741i \(0.364489\pi\)
\(258\) −10.7490 −0.669207
\(259\) −7.31025 −0.454237
\(260\) 0 0
\(261\) −0.729236 −0.0451386
\(262\) 2.78285 0.171925
\(263\) −21.0871 −1.30029 −0.650144 0.759811i \(-0.725291\pi\)
−0.650144 + 0.759811i \(0.725291\pi\)
\(264\) 2.22290 0.136810
\(265\) 0 0
\(266\) 0.297321 0.0182299
\(267\) 18.9296 1.15847
\(268\) 3.97155 0.242601
\(269\) −13.9324 −0.849475 −0.424737 0.905317i \(-0.639634\pi\)
−0.424737 + 0.905317i \(0.639634\pi\)
\(270\) 0 0
\(271\) 10.6583 0.647444 0.323722 0.946152i \(-0.395066\pi\)
0.323722 + 0.946152i \(0.395066\pi\)
\(272\) −3.38834 −0.205448
\(273\) −11.2183 −0.678961
\(274\) −3.68187 −0.222430
\(275\) 0 0
\(276\) −3.42356 −0.206074
\(277\) −2.42918 −0.145955 −0.0729777 0.997334i \(-0.523250\pi\)
−0.0729777 + 0.997334i \(0.523250\pi\)
\(278\) 6.88523 0.412949
\(279\) −1.00581 −0.0602164
\(280\) 0 0
\(281\) 25.2305 1.50513 0.752564 0.658519i \(-0.228817\pi\)
0.752564 + 0.658519i \(0.228817\pi\)
\(282\) −4.63227 −0.275848
\(283\) −20.0356 −1.19099 −0.595495 0.803359i \(-0.703044\pi\)
−0.595495 + 0.803359i \(0.703044\pi\)
\(284\) −7.08987 −0.420706
\(285\) 0 0
\(286\) 2.94852 0.174349
\(287\) −1.69194 −0.0998723
\(288\) −1.08771 −0.0640941
\(289\) −13.3715 −0.786561
\(290\) 0 0
\(291\) −16.7955 −0.984569
\(292\) −9.50970 −0.556513
\(293\) 22.8324 1.33388 0.666942 0.745110i \(-0.267603\pi\)
0.666942 + 0.745110i \(0.267603\pi\)
\(294\) −12.1672 −0.709606
\(295\) 0 0
\(296\) −24.1621 −1.40439
\(297\) −1.98514 −0.115189
\(298\) −9.15376 −0.530263
\(299\) −15.9685 −0.923484
\(300\) 0 0
\(301\) −5.03392 −0.290150
\(302\) −22.1584 −1.27507
\(303\) 17.5818 1.01005
\(304\) 0.518964 0.0297646
\(305\) 0 0
\(306\) −0.543707 −0.0310817
\(307\) 2.39567 0.136728 0.0683639 0.997660i \(-0.478222\pi\)
0.0683639 + 0.997660i \(0.478222\pi\)
\(308\) 0.296041 0.0168685
\(309\) 3.05693 0.173903
\(310\) 0 0
\(311\) 6.15705 0.349134 0.174567 0.984645i \(-0.444147\pi\)
0.174567 + 0.984645i \(0.444147\pi\)
\(312\) −37.0790 −2.09918
\(313\) 1.65380 0.0934784 0.0467392 0.998907i \(-0.485117\pi\)
0.0467392 + 0.998907i \(0.485117\pi\)
\(314\) 5.47914 0.309206
\(315\) 0 0
\(316\) −0.512818 −0.0288483
\(317\) 7.44426 0.418111 0.209056 0.977904i \(-0.432961\pi\)
0.209056 + 0.977904i \(0.432961\pi\)
\(318\) 12.8558 0.720918
\(319\) 1.12546 0.0630136
\(320\) 0 0
\(321\) 27.0444 1.50947
\(322\) 2.43131 0.135492
\(323\) −0.555740 −0.0309222
\(324\) 7.71913 0.428841
\(325\) 0 0
\(326\) −13.9479 −0.772504
\(327\) −0.619322 −0.0342486
\(328\) −5.59226 −0.308781
\(329\) −2.16935 −0.119600
\(330\) 0 0
\(331\) −28.5075 −1.56691 −0.783456 0.621447i \(-0.786545\pi\)
−0.783456 + 0.621447i \(0.786545\pi\)
\(332\) −7.02794 −0.385708
\(333\) −2.04749 −0.112202
\(334\) 16.5806 0.907252
\(335\) 0 0
\(336\) 2.98136 0.162646
\(337\) −1.51329 −0.0824341 −0.0412170 0.999150i \(-0.513124\pi\)
−0.0412170 + 0.999150i \(0.513124\pi\)
\(338\) −34.9108 −1.89890
\(339\) 10.3024 0.559549
\(340\) 0 0
\(341\) 1.55231 0.0840623
\(342\) 0.0832751 0.00450300
\(343\) −12.1960 −0.658524
\(344\) −16.6383 −0.897075
\(345\) 0 0
\(346\) −1.17976 −0.0634242
\(347\) 18.5796 0.997407 0.498704 0.866773i \(-0.333810\pi\)
0.498704 + 0.866773i \(0.333810\pi\)
\(348\) −4.02485 −0.215755
\(349\) −14.6495 −0.784170 −0.392085 0.919929i \(-0.628246\pi\)
−0.392085 + 0.919929i \(0.628246\pi\)
\(350\) 0 0
\(351\) 33.1129 1.76744
\(352\) 1.67871 0.0894755
\(353\) −15.6676 −0.833901 −0.416951 0.908929i \(-0.636901\pi\)
−0.416951 + 0.908929i \(0.636901\pi\)
\(354\) −7.98168 −0.424222
\(355\) 0 0
\(356\) 8.33248 0.441621
\(357\) −3.19263 −0.168972
\(358\) 13.8760 0.733369
\(359\) −13.6489 −0.720362 −0.360181 0.932882i \(-0.617285\pi\)
−0.360181 + 0.932882i \(0.617285\pi\)
\(360\) 0 0
\(361\) −18.9149 −0.995520
\(362\) 8.80355 0.462704
\(363\) 19.5703 1.02717
\(364\) −4.93810 −0.258827
\(365\) 0 0
\(366\) 18.3076 0.956952
\(367\) 3.98812 0.208178 0.104089 0.994568i \(-0.466807\pi\)
0.104089 + 0.994568i \(0.466807\pi\)
\(368\) 4.24378 0.221222
\(369\) −0.473888 −0.0246696
\(370\) 0 0
\(371\) 6.02054 0.312571
\(372\) −5.55135 −0.287824
\(373\) 19.1389 0.990977 0.495488 0.868615i \(-0.334989\pi\)
0.495488 + 0.868615i \(0.334989\pi\)
\(374\) 0.839124 0.0433901
\(375\) 0 0
\(376\) −7.17021 −0.369775
\(377\) −18.7731 −0.966866
\(378\) −5.04166 −0.259315
\(379\) −15.3139 −0.786624 −0.393312 0.919405i \(-0.628671\pi\)
−0.393312 + 0.919405i \(0.628671\pi\)
\(380\) 0 0
\(381\) 1.15509 0.0591773
\(382\) 2.76882 0.141665
\(383\) −33.7339 −1.72372 −0.861860 0.507146i \(-0.830701\pi\)
−0.861860 + 0.507146i \(0.830701\pi\)
\(384\) 1.04841 0.0535014
\(385\) 0 0
\(386\) −29.7895 −1.51625
\(387\) −1.40992 −0.0716705
\(388\) −7.39310 −0.375328
\(389\) 13.4176 0.680297 0.340148 0.940372i \(-0.389523\pi\)
0.340148 + 0.940372i \(0.389523\pi\)
\(390\) 0 0
\(391\) −4.54452 −0.229826
\(392\) −18.8334 −0.951230
\(393\) 4.57681 0.230870
\(394\) −1.28807 −0.0648921
\(395\) 0 0
\(396\) 0.0829167 0.00416672
\(397\) −31.1766 −1.56471 −0.782354 0.622834i \(-0.785981\pi\)
−0.782354 + 0.622834i \(0.785981\pi\)
\(398\) 29.4503 1.47621
\(399\) 0.488989 0.0244801
\(400\) 0 0
\(401\) −5.98879 −0.299066 −0.149533 0.988757i \(-0.547777\pi\)
−0.149533 + 0.988757i \(0.547777\pi\)
\(402\) −9.90514 −0.494024
\(403\) −25.8932 −1.28983
\(404\) 7.73920 0.385040
\(405\) 0 0
\(406\) 2.85833 0.141857
\(407\) 3.15998 0.156634
\(408\) −10.5524 −0.522421
\(409\) 16.5919 0.820418 0.410209 0.911991i \(-0.365456\pi\)
0.410209 + 0.911991i \(0.365456\pi\)
\(410\) 0 0
\(411\) −6.05539 −0.298690
\(412\) 1.34561 0.0662935
\(413\) −3.73792 −0.183931
\(414\) 0.680974 0.0334681
\(415\) 0 0
\(416\) −28.0016 −1.37289
\(417\) 11.3238 0.554529
\(418\) −0.128522 −0.00628620
\(419\) −21.8938 −1.06958 −0.534791 0.844985i \(-0.679610\pi\)
−0.534791 + 0.844985i \(0.679610\pi\)
\(420\) 0 0
\(421\) 16.8937 0.823350 0.411675 0.911331i \(-0.364944\pi\)
0.411675 + 0.911331i \(0.364944\pi\)
\(422\) −3.37859 −0.164467
\(423\) −0.607603 −0.0295427
\(424\) 19.8993 0.966393
\(425\) 0 0
\(426\) 17.6823 0.856711
\(427\) 8.57367 0.414909
\(428\) 11.9045 0.575426
\(429\) 4.84928 0.234126
\(430\) 0 0
\(431\) 18.4132 0.886935 0.443467 0.896291i \(-0.353748\pi\)
0.443467 + 0.896291i \(0.353748\pi\)
\(432\) −8.80006 −0.423393
\(433\) −33.0770 −1.58958 −0.794790 0.606885i \(-0.792419\pi\)
−0.794790 + 0.606885i \(0.792419\pi\)
\(434\) 3.94241 0.189242
\(435\) 0 0
\(436\) −0.272615 −0.0130559
\(437\) 0.696046 0.0332964
\(438\) 23.7174 1.13326
\(439\) −8.31851 −0.397021 −0.198510 0.980099i \(-0.563610\pi\)
−0.198510 + 0.980099i \(0.563610\pi\)
\(440\) 0 0
\(441\) −1.59594 −0.0759972
\(442\) −13.9970 −0.665768
\(443\) 4.36551 0.207412 0.103706 0.994608i \(-0.466930\pi\)
0.103706 + 0.994608i \(0.466930\pi\)
\(444\) −11.3007 −0.536306
\(445\) 0 0
\(446\) −5.19958 −0.246207
\(447\) −15.0548 −0.712065
\(448\) 7.56587 0.357454
\(449\) −8.00996 −0.378013 −0.189007 0.981976i \(-0.560527\pi\)
−0.189007 + 0.981976i \(0.560527\pi\)
\(450\) 0 0
\(451\) 0.731370 0.0344389
\(452\) 4.53494 0.213306
\(453\) −36.4429 −1.71223
\(454\) −5.19735 −0.243924
\(455\) 0 0
\(456\) 1.61622 0.0756865
\(457\) −27.6916 −1.29536 −0.647680 0.761912i \(-0.724261\pi\)
−0.647680 + 0.761912i \(0.724261\pi\)
\(458\) −8.80169 −0.411276
\(459\) 9.42368 0.439860
\(460\) 0 0
\(461\) −2.49433 −0.116173 −0.0580864 0.998312i \(-0.518500\pi\)
−0.0580864 + 0.998312i \(0.518500\pi\)
\(462\) −0.738335 −0.0343505
\(463\) 32.6945 1.51944 0.759721 0.650249i \(-0.225335\pi\)
0.759721 + 0.650249i \(0.225335\pi\)
\(464\) 4.98913 0.231614
\(465\) 0 0
\(466\) 5.97446 0.276762
\(467\) −36.7488 −1.70053 −0.850266 0.526353i \(-0.823559\pi\)
−0.850266 + 0.526353i \(0.823559\pi\)
\(468\) −1.38309 −0.0639333
\(469\) −4.63871 −0.214196
\(470\) 0 0
\(471\) 9.01128 0.415218
\(472\) −12.3547 −0.568671
\(473\) 2.17599 0.100052
\(474\) 1.27898 0.0587456
\(475\) 0 0
\(476\) −1.40534 −0.0644138
\(477\) 1.68626 0.0772086
\(478\) −4.63341 −0.211927
\(479\) 4.00850 0.183153 0.0915764 0.995798i \(-0.470809\pi\)
0.0915764 + 0.995798i \(0.470809\pi\)
\(480\) 0 0
\(481\) −52.7098 −2.40336
\(482\) 1.09783 0.0500047
\(483\) 3.99866 0.181945
\(484\) 8.61452 0.391569
\(485\) 0 0
\(486\) −2.95818 −0.134186
\(487\) 32.2540 1.46157 0.730785 0.682608i \(-0.239154\pi\)
0.730785 + 0.682608i \(0.239154\pi\)
\(488\) 28.3380 1.28280
\(489\) −22.9395 −1.03736
\(490\) 0 0
\(491\) −22.2117 −1.00240 −0.501201 0.865331i \(-0.667108\pi\)
−0.501201 + 0.865331i \(0.667108\pi\)
\(492\) −2.61552 −0.117917
\(493\) −5.34269 −0.240622
\(494\) 2.14380 0.0964541
\(495\) 0 0
\(496\) 6.88135 0.308982
\(497\) 8.28086 0.371447
\(498\) 17.5279 0.785442
\(499\) 24.4248 1.09340 0.546701 0.837328i \(-0.315883\pi\)
0.546701 + 0.837328i \(0.315883\pi\)
\(500\) 0 0
\(501\) 27.2694 1.21831
\(502\) 3.73910 0.166884
\(503\) −38.7703 −1.72868 −0.864341 0.502907i \(-0.832264\pi\)
−0.864341 + 0.502907i \(0.832264\pi\)
\(504\) 0.740508 0.0329848
\(505\) 0 0
\(506\) −1.05097 −0.0467215
\(507\) −57.4161 −2.54994
\(508\) 0.508453 0.0225590
\(509\) −42.1763 −1.86943 −0.934715 0.355397i \(-0.884346\pi\)
−0.934715 + 0.355397i \(0.884346\pi\)
\(510\) 0 0
\(511\) 11.1072 0.491353
\(512\) 18.3570 0.811273
\(513\) −1.44335 −0.0637253
\(514\) −14.5364 −0.641174
\(515\) 0 0
\(516\) −7.78176 −0.342573
\(517\) 0.937738 0.0412417
\(518\) 8.02541 0.352616
\(519\) −1.94029 −0.0851694
\(520\) 0 0
\(521\) 3.76641 0.165009 0.0825047 0.996591i \(-0.473708\pi\)
0.0825047 + 0.996591i \(0.473708\pi\)
\(522\) 0.800576 0.0350403
\(523\) 25.8240 1.12920 0.564602 0.825363i \(-0.309030\pi\)
0.564602 + 0.825363i \(0.309030\pi\)
\(524\) 2.01464 0.0880098
\(525\) 0 0
\(526\) 23.1501 1.00939
\(527\) −7.36900 −0.320999
\(528\) −1.28874 −0.0560852
\(529\) −17.3082 −0.752528
\(530\) 0 0
\(531\) −1.04694 −0.0454332
\(532\) 0.215245 0.00933205
\(533\) −12.1996 −0.528422
\(534\) −20.7814 −0.899300
\(535\) 0 0
\(536\) −15.3320 −0.662241
\(537\) 22.8212 0.984806
\(538\) 15.2954 0.659432
\(539\) 2.46308 0.106092
\(540\) 0 0
\(541\) −28.4742 −1.22420 −0.612100 0.790780i \(-0.709675\pi\)
−0.612100 + 0.790780i \(0.709675\pi\)
\(542\) −11.7010 −0.502599
\(543\) 14.4788 0.621343
\(544\) −7.96904 −0.341670
\(545\) 0 0
\(546\) 12.3158 0.527066
\(547\) −25.6501 −1.09672 −0.548360 0.836242i \(-0.684748\pi\)
−0.548360 + 0.836242i \(0.684748\pi\)
\(548\) −2.66548 −0.113864
\(549\) 2.40136 0.102487
\(550\) 0 0
\(551\) 0.818295 0.0348605
\(552\) 13.2165 0.562531
\(553\) 0.598964 0.0254705
\(554\) 2.66683 0.113303
\(555\) 0 0
\(556\) 4.98455 0.211392
\(557\) 24.0410 1.01865 0.509325 0.860574i \(-0.329895\pi\)
0.509325 + 0.860574i \(0.329895\pi\)
\(558\) 1.10421 0.0467449
\(559\) −36.2965 −1.53518
\(560\) 0 0
\(561\) 1.38007 0.0582665
\(562\) −27.6988 −1.16840
\(563\) −44.9292 −1.89354 −0.946771 0.321909i \(-0.895675\pi\)
−0.946771 + 0.321909i \(0.895675\pi\)
\(564\) −3.35352 −0.141209
\(565\) 0 0
\(566\) 21.9956 0.924544
\(567\) −9.01583 −0.378629
\(568\) 27.3701 1.14843
\(569\) −2.81272 −0.117915 −0.0589577 0.998260i \(-0.518778\pi\)
−0.0589577 + 0.998260i \(0.518778\pi\)
\(570\) 0 0
\(571\) −11.4480 −0.479085 −0.239543 0.970886i \(-0.576997\pi\)
−0.239543 + 0.970886i \(0.576997\pi\)
\(572\) 2.13457 0.0892510
\(573\) 4.55375 0.190236
\(574\) 1.85746 0.0775291
\(575\) 0 0
\(576\) 2.11909 0.0882953
\(577\) 27.0956 1.12801 0.564003 0.825773i \(-0.309261\pi\)
0.564003 + 0.825773i \(0.309261\pi\)
\(578\) 14.6797 0.610594
\(579\) −48.9934 −2.03610
\(580\) 0 0
\(581\) 8.20853 0.340547
\(582\) 18.4386 0.764304
\(583\) −2.60247 −0.107783
\(584\) 36.7118 1.51914
\(585\) 0 0
\(586\) −25.0661 −1.03547
\(587\) 17.1328 0.707146 0.353573 0.935407i \(-0.384967\pi\)
0.353573 + 0.935407i \(0.384967\pi\)
\(588\) −8.80843 −0.363254
\(589\) 1.12865 0.0465052
\(590\) 0 0
\(591\) −2.11843 −0.0871405
\(592\) 14.0081 0.575729
\(593\) 2.35285 0.0966198 0.0483099 0.998832i \(-0.484616\pi\)
0.0483099 + 0.998832i \(0.484616\pi\)
\(594\) 2.17934 0.0894194
\(595\) 0 0
\(596\) −6.62685 −0.271446
\(597\) 48.4354 1.98233
\(598\) 17.5307 0.716884
\(599\) −15.3944 −0.628999 −0.314499 0.949258i \(-0.601837\pi\)
−0.314499 + 0.949258i \(0.601837\pi\)
\(600\) 0 0
\(601\) −37.6544 −1.53596 −0.767978 0.640477i \(-0.778737\pi\)
−0.767978 + 0.640477i \(0.778737\pi\)
\(602\) 5.52638 0.225238
\(603\) −1.29923 −0.0529088
\(604\) −16.0415 −0.652721
\(605\) 0 0
\(606\) −19.3018 −0.784081
\(607\) 2.72064 0.110427 0.0552137 0.998475i \(-0.482416\pi\)
0.0552137 + 0.998475i \(0.482416\pi\)
\(608\) 1.22055 0.0494999
\(609\) 4.70096 0.190493
\(610\) 0 0
\(611\) −15.6419 −0.632803
\(612\) −0.393616 −0.0159110
\(613\) −23.7816 −0.960528 −0.480264 0.877124i \(-0.659459\pi\)
−0.480264 + 0.877124i \(0.659459\pi\)
\(614\) −2.63003 −0.106139
\(615\) 0 0
\(616\) −1.14286 −0.0460469
\(617\) −15.5878 −0.627541 −0.313770 0.949499i \(-0.601592\pi\)
−0.313770 + 0.949499i \(0.601592\pi\)
\(618\) −3.35599 −0.134998
\(619\) 2.18172 0.0876906 0.0438453 0.999038i \(-0.486039\pi\)
0.0438453 + 0.999038i \(0.486039\pi\)
\(620\) 0 0
\(621\) −11.8028 −0.473631
\(622\) −6.75939 −0.271027
\(623\) −9.73221 −0.389913
\(624\) 21.4968 0.860559
\(625\) 0 0
\(626\) −1.81559 −0.0725656
\(627\) −0.211373 −0.00844144
\(628\) 3.96661 0.158285
\(629\) −15.0008 −0.598120
\(630\) 0 0
\(631\) −37.6467 −1.49869 −0.749345 0.662180i \(-0.769632\pi\)
−0.749345 + 0.662180i \(0.769632\pi\)
\(632\) 1.97971 0.0787488
\(633\) −5.55661 −0.220855
\(634\) −8.17253 −0.324573
\(635\) 0 0
\(636\) 9.30694 0.369044
\(637\) −41.0853 −1.62786
\(638\) −1.23556 −0.0489163
\(639\) 2.31934 0.0917518
\(640\) 0 0
\(641\) 0.393382 0.0155376 0.00776882 0.999970i \(-0.497527\pi\)
0.00776882 + 0.999970i \(0.497527\pi\)
\(642\) −29.6902 −1.17178
\(643\) 39.1158 1.54258 0.771288 0.636486i \(-0.219613\pi\)
0.771288 + 0.636486i \(0.219613\pi\)
\(644\) 1.76014 0.0693594
\(645\) 0 0
\(646\) 0.610108 0.0240044
\(647\) 38.5541 1.51572 0.757859 0.652419i \(-0.226246\pi\)
0.757859 + 0.652419i \(0.226246\pi\)
\(648\) −29.7994 −1.17063
\(649\) 1.61578 0.0634249
\(650\) 0 0
\(651\) 6.48389 0.254124
\(652\) −10.0976 −0.395452
\(653\) −14.8795 −0.582281 −0.291141 0.956680i \(-0.594035\pi\)
−0.291141 + 0.956680i \(0.594035\pi\)
\(654\) 0.679909 0.0265866
\(655\) 0 0
\(656\) 3.24214 0.126584
\(657\) 3.11095 0.121370
\(658\) 2.38158 0.0928436
\(659\) 15.0109 0.584743 0.292371 0.956305i \(-0.405556\pi\)
0.292371 + 0.956305i \(0.405556\pi\)
\(660\) 0 0
\(661\) −20.4143 −0.794024 −0.397012 0.917813i \(-0.629953\pi\)
−0.397012 + 0.917813i \(0.629953\pi\)
\(662\) 31.2963 1.21637
\(663\) −23.0201 −0.894028
\(664\) 27.1311 1.05289
\(665\) 0 0
\(666\) 2.24780 0.0871003
\(667\) 6.69153 0.259097
\(668\) 12.0035 0.464430
\(669\) −8.55150 −0.330620
\(670\) 0 0
\(671\) −3.70611 −0.143073
\(672\) 7.01186 0.270488
\(673\) 35.8056 1.38020 0.690102 0.723712i \(-0.257566\pi\)
0.690102 + 0.723712i \(0.257566\pi\)
\(674\) 1.66133 0.0639921
\(675\) 0 0
\(676\) −25.2736 −0.972062
\(677\) −34.1574 −1.31278 −0.656388 0.754424i \(-0.727917\pi\)
−0.656388 + 0.754424i \(0.727917\pi\)
\(678\) −11.3103 −0.434368
\(679\) 8.63502 0.331382
\(680\) 0 0
\(681\) −8.54784 −0.327554
\(682\) −1.70417 −0.0652561
\(683\) 12.9413 0.495185 0.247593 0.968864i \(-0.420361\pi\)
0.247593 + 0.968864i \(0.420361\pi\)
\(684\) 0.0602869 0.00230513
\(685\) 0 0
\(686\) 13.3892 0.511200
\(687\) −14.4757 −0.552283
\(688\) 9.64612 0.367755
\(689\) 43.4104 1.65381
\(690\) 0 0
\(691\) 0.406449 0.0154620 0.00773102 0.999970i \(-0.497539\pi\)
0.00773102 + 0.999970i \(0.497539\pi\)
\(692\) −0.854084 −0.0324674
\(693\) −0.0968455 −0.00367886
\(694\) −20.3973 −0.774270
\(695\) 0 0
\(696\) 15.5378 0.588957
\(697\) −3.47190 −0.131508
\(698\) 16.0826 0.608737
\(699\) 9.82591 0.371650
\(700\) 0 0
\(701\) 11.1730 0.422000 0.211000 0.977486i \(-0.432328\pi\)
0.211000 + 0.977486i \(0.432328\pi\)
\(702\) −36.3524 −1.37203
\(703\) 2.29755 0.0866536
\(704\) −3.27047 −0.123261
\(705\) 0 0
\(706\) 17.2003 0.647343
\(707\) −9.03927 −0.339957
\(708\) −5.77833 −0.217163
\(709\) 4.23412 0.159016 0.0795078 0.996834i \(-0.474665\pi\)
0.0795078 + 0.996834i \(0.474665\pi\)
\(710\) 0 0
\(711\) 0.167761 0.00629152
\(712\) −32.1672 −1.20552
\(713\) 9.22942 0.345644
\(714\) 3.50496 0.131170
\(715\) 0 0
\(716\) 10.0455 0.375418
\(717\) −7.62034 −0.284587
\(718\) 14.9842 0.559204
\(719\) −2.66311 −0.0993173 −0.0496586 0.998766i \(-0.515813\pi\)
−0.0496586 + 0.998766i \(0.515813\pi\)
\(720\) 0 0
\(721\) −1.57165 −0.0585314
\(722\) 20.7653 0.772805
\(723\) 1.80555 0.0671490
\(724\) 6.37331 0.236862
\(725\) 0 0
\(726\) −21.4848 −0.797377
\(727\) 7.67222 0.284547 0.142273 0.989827i \(-0.454559\pi\)
0.142273 + 0.989827i \(0.454559\pi\)
\(728\) 19.0633 0.706534
\(729\) 24.2720 0.898963
\(730\) 0 0
\(731\) −10.3297 −0.382058
\(732\) 13.2537 0.489872
\(733\) 44.4174 1.64059 0.820297 0.571938i \(-0.193808\pi\)
0.820297 + 0.571938i \(0.193808\pi\)
\(734\) −4.37827 −0.161605
\(735\) 0 0
\(736\) 9.98094 0.367902
\(737\) 2.00516 0.0738609
\(738\) 0.520248 0.0191506
\(739\) −38.5453 −1.41791 −0.708955 0.705253i \(-0.750833\pi\)
−0.708955 + 0.705253i \(0.750833\pi\)
\(740\) 0 0
\(741\) 3.52580 0.129524
\(742\) −6.60952 −0.242643
\(743\) −26.0745 −0.956579 −0.478289 0.878202i \(-0.658743\pi\)
−0.478289 + 0.878202i \(0.658743\pi\)
\(744\) 21.4307 0.785689
\(745\) 0 0
\(746\) −21.0113 −0.769278
\(747\) 2.29908 0.0841191
\(748\) 0.607483 0.0222118
\(749\) −13.9043 −0.508051
\(750\) 0 0
\(751\) −4.56686 −0.166647 −0.0833235 0.996523i \(-0.526553\pi\)
−0.0833235 + 0.996523i \(0.526553\pi\)
\(752\) 4.15697 0.151589
\(753\) 6.14953 0.224101
\(754\) 20.6097 0.750561
\(755\) 0 0
\(756\) −3.64990 −0.132746
\(757\) 30.9168 1.12369 0.561844 0.827243i \(-0.310092\pi\)
0.561844 + 0.827243i \(0.310092\pi\)
\(758\) 16.8121 0.610642
\(759\) −1.72849 −0.0627401
\(760\) 0 0
\(761\) 10.8579 0.393598 0.196799 0.980444i \(-0.436945\pi\)
0.196799 + 0.980444i \(0.436945\pi\)
\(762\) −1.26810 −0.0459383
\(763\) 0.318410 0.0115272
\(764\) 2.00449 0.0725197
\(765\) 0 0
\(766\) 37.0340 1.33809
\(767\) −26.9519 −0.973177
\(768\) 28.2809 1.02050
\(769\) 48.3748 1.74444 0.872220 0.489113i \(-0.162680\pi\)
0.872220 + 0.489113i \(0.162680\pi\)
\(770\) 0 0
\(771\) −23.9074 −0.861003
\(772\) −21.5661 −0.776180
\(773\) −46.1527 −1.66000 −0.829999 0.557765i \(-0.811659\pi\)
−0.829999 + 0.557765i \(0.811659\pi\)
\(774\) 1.54786 0.0556365
\(775\) 0 0
\(776\) 28.5407 1.02455
\(777\) 13.1990 0.473511
\(778\) −14.7302 −0.528102
\(779\) 0.531762 0.0190524
\(780\) 0 0
\(781\) −3.57954 −0.128086
\(782\) 4.98910 0.178410
\(783\) −13.8758 −0.495881
\(784\) 10.9188 0.389956
\(785\) 0 0
\(786\) −5.02456 −0.179220
\(787\) 1.78318 0.0635635 0.0317818 0.999495i \(-0.489882\pi\)
0.0317818 + 0.999495i \(0.489882\pi\)
\(788\) −0.932497 −0.0332188
\(789\) 38.0738 1.35546
\(790\) 0 0
\(791\) −5.29674 −0.188330
\(792\) −0.320097 −0.0113741
\(793\) 61.8195 2.19528
\(794\) 34.2266 1.21466
\(795\) 0 0
\(796\) 21.3205 0.755684
\(797\) 23.4124 0.829310 0.414655 0.909979i \(-0.363902\pi\)
0.414655 + 0.909979i \(0.363902\pi\)
\(798\) −0.536826 −0.0190034
\(799\) −4.45155 −0.157485
\(800\) 0 0
\(801\) −2.72585 −0.0963130
\(802\) 6.57467 0.232160
\(803\) −4.80126 −0.169433
\(804\) −7.17081 −0.252895
\(805\) 0 0
\(806\) 28.4263 1.00127
\(807\) 25.1556 0.885520
\(808\) −29.8768 −1.05106
\(809\) −2.49926 −0.0878692 −0.0439346 0.999034i \(-0.513989\pi\)
−0.0439346 + 0.999034i \(0.513989\pi\)
\(810\) 0 0
\(811\) −24.8265 −0.871778 −0.435889 0.900001i \(-0.643566\pi\)
−0.435889 + 0.900001i \(0.643566\pi\)
\(812\) 2.06929 0.0726177
\(813\) −19.2440 −0.674916
\(814\) −3.46911 −0.121592
\(815\) 0 0
\(816\) 6.11780 0.214166
\(817\) 1.58211 0.0553512
\(818\) −18.2151 −0.636876
\(819\) 1.61543 0.0564475
\(820\) 0 0
\(821\) 46.4914 1.62256 0.811280 0.584657i \(-0.198771\pi\)
0.811280 + 0.584657i \(0.198771\pi\)
\(822\) 6.64778 0.231868
\(823\) 18.3671 0.640237 0.320118 0.947378i \(-0.396277\pi\)
0.320118 + 0.947378i \(0.396277\pi\)
\(824\) −5.19467 −0.180965
\(825\) 0 0
\(826\) 4.10360 0.142783
\(827\) 17.3399 0.602968 0.301484 0.953471i \(-0.402518\pi\)
0.301484 + 0.953471i \(0.402518\pi\)
\(828\) 0.492990 0.0171326
\(829\) 23.9714 0.832560 0.416280 0.909236i \(-0.363334\pi\)
0.416280 + 0.909236i \(0.363334\pi\)
\(830\) 0 0
\(831\) 4.38600 0.152149
\(832\) 54.5529 1.89128
\(833\) −11.6925 −0.405122
\(834\) −12.4316 −0.430471
\(835\) 0 0
\(836\) −0.0930431 −0.00321796
\(837\) −19.1385 −0.661522
\(838\) 24.0356 0.830297
\(839\) −40.4460 −1.39635 −0.698175 0.715927i \(-0.746004\pi\)
−0.698175 + 0.715927i \(0.746004\pi\)
\(840\) 0 0
\(841\) −21.1332 −0.728731
\(842\) −18.5464 −0.639152
\(843\) −45.5549 −1.56899
\(844\) −2.44593 −0.0841923
\(845\) 0 0
\(846\) 0.667044 0.0229334
\(847\) −10.0616 −0.345722
\(848\) −11.5367 −0.396172
\(849\) 36.1751 1.24153
\(850\) 0 0
\(851\) 18.7880 0.644043
\(852\) 12.8011 0.438558
\(853\) 0.00791683 0.000271067 0 0.000135534 1.00000i \(-0.499957\pi\)
0.000135534 1.00000i \(0.499957\pi\)
\(854\) −9.41243 −0.322087
\(855\) 0 0
\(856\) −45.9568 −1.57077
\(857\) −46.1409 −1.57614 −0.788072 0.615583i \(-0.788921\pi\)
−0.788072 + 0.615583i \(0.788921\pi\)
\(858\) −5.32368 −0.181748
\(859\) 14.7880 0.504560 0.252280 0.967654i \(-0.418820\pi\)
0.252280 + 0.967654i \(0.418820\pi\)
\(860\) 0 0
\(861\) 3.05488 0.104110
\(862\) −20.2146 −0.688512
\(863\) −44.4021 −1.51147 −0.755733 0.654880i \(-0.772719\pi\)
−0.755733 + 0.654880i \(0.772719\pi\)
\(864\) −20.6969 −0.704122
\(865\) 0 0
\(866\) 36.3129 1.23396
\(867\) 24.1429 0.819937
\(868\) 2.85410 0.0968745
\(869\) −0.258912 −0.00878298
\(870\) 0 0
\(871\) −33.4469 −1.13330
\(872\) 1.05242 0.0356394
\(873\) 2.41854 0.0818552
\(874\) −0.764139 −0.0258474
\(875\) 0 0
\(876\) 17.1702 0.580127
\(877\) 25.0137 0.844654 0.422327 0.906444i \(-0.361213\pi\)
0.422327 + 0.906444i \(0.361213\pi\)
\(878\) 9.13230 0.308200
\(879\) −41.2250 −1.39048
\(880\) 0 0
\(881\) 26.6234 0.896966 0.448483 0.893791i \(-0.351964\pi\)
0.448483 + 0.893791i \(0.351964\pi\)
\(882\) 1.75207 0.0589953
\(883\) 27.5946 0.928632 0.464316 0.885670i \(-0.346300\pi\)
0.464316 + 0.885670i \(0.346300\pi\)
\(884\) −10.1331 −0.340812
\(885\) 0 0
\(886\) −4.79258 −0.161010
\(887\) 24.3390 0.817222 0.408611 0.912709i \(-0.366013\pi\)
0.408611 + 0.912709i \(0.366013\pi\)
\(888\) 43.6257 1.46398
\(889\) −0.593866 −0.0199176
\(890\) 0 0
\(891\) 3.89724 0.130562
\(892\) −3.76423 −0.126036
\(893\) 0.681807 0.0228158
\(894\) 16.5275 0.552764
\(895\) 0 0
\(896\) −0.539016 −0.0180072
\(897\) 28.8319 0.962670
\(898\) 8.79356 0.293445
\(899\) 10.8504 0.361882
\(900\) 0 0
\(901\) 12.3543 0.411580
\(902\) −0.802919 −0.0267343
\(903\) 9.08897 0.302462
\(904\) −17.5069 −0.582272
\(905\) 0 0
\(906\) 40.0080 1.32918
\(907\) 14.8454 0.492934 0.246467 0.969151i \(-0.420730\pi\)
0.246467 + 0.969151i \(0.420730\pi\)
\(908\) −3.76262 −0.124867
\(909\) −2.53176 −0.0839733
\(910\) 0 0
\(911\) −29.0619 −0.962863 −0.481432 0.876484i \(-0.659883\pi\)
−0.481432 + 0.876484i \(0.659883\pi\)
\(912\) −0.937013 −0.0310276
\(913\) −3.54827 −0.117431
\(914\) 30.4007 1.00557
\(915\) 0 0
\(916\) −6.37197 −0.210536
\(917\) −2.35306 −0.0777050
\(918\) −10.3456 −0.341455
\(919\) 21.9333 0.723513 0.361756 0.932273i \(-0.382177\pi\)
0.361756 + 0.932273i \(0.382177\pi\)
\(920\) 0 0
\(921\) −4.32549 −0.142530
\(922\) 2.73835 0.0901829
\(923\) 59.7082 1.96532
\(924\) −0.534516 −0.0175843
\(925\) 0 0
\(926\) −35.8930 −1.17952
\(927\) −0.440196 −0.0144579
\(928\) 11.7339 0.385185
\(929\) 42.5016 1.39443 0.697217 0.716860i \(-0.254421\pi\)
0.697217 + 0.716860i \(0.254421\pi\)
\(930\) 0 0
\(931\) 1.79085 0.0586927
\(932\) 4.32520 0.141677
\(933\) −11.1168 −0.363949
\(934\) 40.3439 1.32009
\(935\) 0 0
\(936\) 5.33935 0.174522
\(937\) 39.0038 1.27420 0.637099 0.770782i \(-0.280134\pi\)
0.637099 + 0.770782i \(0.280134\pi\)
\(938\) 5.09251 0.166276
\(939\) −2.98601 −0.0974449
\(940\) 0 0
\(941\) −16.4491 −0.536226 −0.268113 0.963387i \(-0.586400\pi\)
−0.268113 + 0.963387i \(0.586400\pi\)
\(942\) −9.89284 −0.322326
\(943\) 4.34844 0.141605
\(944\) 7.16271 0.233126
\(945\) 0 0
\(946\) −2.38887 −0.0776688
\(947\) −13.2820 −0.431606 −0.215803 0.976437i \(-0.569237\pi\)
−0.215803 + 0.976437i \(0.569237\pi\)
\(948\) 0.925917 0.0300724
\(949\) 80.0871 2.59974
\(950\) 0 0
\(951\) −13.4410 −0.435853
\(952\) 5.42527 0.175834
\(953\) −35.6158 −1.15371 −0.576855 0.816847i \(-0.695720\pi\)
−0.576855 + 0.816847i \(0.695720\pi\)
\(954\) −1.85123 −0.0599357
\(955\) 0 0
\(956\) −3.35435 −0.108487
\(957\) −2.03207 −0.0656874
\(958\) −4.40064 −0.142178
\(959\) 3.11324 0.100532
\(960\) 0 0
\(961\) −16.0344 −0.517237
\(962\) 57.8663 1.86569
\(963\) −3.89438 −0.125495
\(964\) 0.794772 0.0255979
\(965\) 0 0
\(966\) −4.38985 −0.141241
\(967\) −58.4495 −1.87961 −0.939805 0.341711i \(-0.888994\pi\)
−0.939805 + 0.341711i \(0.888994\pi\)
\(968\) −33.2560 −1.06889
\(969\) 1.00342 0.0322343
\(970\) 0 0
\(971\) −43.6770 −1.40166 −0.700831 0.713328i \(-0.747187\pi\)
−0.700831 + 0.713328i \(0.747187\pi\)
\(972\) −2.14157 −0.0686909
\(973\) −5.82188 −0.186641
\(974\) −35.4094 −1.13459
\(975\) 0 0
\(976\) −16.4291 −0.525882
\(977\) 6.96622 0.222869 0.111435 0.993772i \(-0.464455\pi\)
0.111435 + 0.993772i \(0.464455\pi\)
\(978\) 25.1836 0.805284
\(979\) 4.20691 0.134453
\(980\) 0 0
\(981\) 0.0891819 0.00284736
\(982\) 24.3847 0.778147
\(983\) −7.12795 −0.227346 −0.113673 0.993518i \(-0.536262\pi\)
−0.113673 + 0.993518i \(0.536262\pi\)
\(984\) 10.0971 0.321883
\(985\) 0 0
\(986\) 5.86536 0.186791
\(987\) 3.91687 0.124675
\(988\) 1.55200 0.0493757
\(989\) 12.9376 0.411391
\(990\) 0 0
\(991\) −13.1981 −0.419252 −0.209626 0.977782i \(-0.567225\pi\)
−0.209626 + 0.977782i \(0.567225\pi\)
\(992\) 16.1842 0.513850
\(993\) 51.4716 1.63340
\(994\) −9.09097 −0.288348
\(995\) 0 0
\(996\) 12.6893 0.402075
\(997\) −5.19129 −0.164410 −0.0822049 0.996615i \(-0.526196\pi\)
−0.0822049 + 0.996615i \(0.526196\pi\)
\(998\) −26.8142 −0.848789
\(999\) −38.9594 −1.23262
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6025.2.a.i.1.5 15
5.4 even 2 1205.2.a.c.1.11 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.a.c.1.11 15 5.4 even 2
6025.2.a.i.1.5 15 1.1 even 1 trivial