Properties

Label 7595.2.a.bf.1.20
Level $7595$
Weight $2$
Character 7595.1
Self dual yes
Analytic conductor $60.646$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7595,2,Mod(1,7595)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7595, 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("7595.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7595.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: \(60.6463803352\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 1085)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 7595.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.26981 q^{2} -3.30996 q^{3} +3.15205 q^{4} +1.00000 q^{5} -7.51299 q^{6} +2.61493 q^{8} +7.95585 q^{9} +O(q^{10})\) \(q+2.26981 q^{2} -3.30996 q^{3} +3.15205 q^{4} +1.00000 q^{5} -7.51299 q^{6} +2.61493 q^{8} +7.95585 q^{9} +2.26981 q^{10} +4.85520 q^{11} -10.4332 q^{12} -6.52160 q^{13} -3.30996 q^{15} -0.368699 q^{16} +0.221263 q^{17} +18.0583 q^{18} +2.71231 q^{19} +3.15205 q^{20} +11.0204 q^{22} -6.33498 q^{23} -8.65531 q^{24} +1.00000 q^{25} -14.8028 q^{26} -16.4037 q^{27} -2.63217 q^{29} -7.51299 q^{30} -1.00000 q^{31} -6.06673 q^{32} -16.0705 q^{33} +0.502225 q^{34} +25.0772 q^{36} -0.742795 q^{37} +6.15643 q^{38} +21.5863 q^{39} +2.61493 q^{40} +9.28495 q^{41} -8.26124 q^{43} +15.3038 q^{44} +7.95585 q^{45} -14.3792 q^{46} +5.97344 q^{47} +1.22038 q^{48} +2.26981 q^{50} -0.732372 q^{51} -20.5564 q^{52} -4.45885 q^{53} -37.2333 q^{54} +4.85520 q^{55} -8.97765 q^{57} -5.97452 q^{58} -4.95499 q^{59} -10.4332 q^{60} -14.2834 q^{61} -2.26981 q^{62} -13.0329 q^{64} -6.52160 q^{65} -36.4771 q^{66} -6.21873 q^{67} +0.697431 q^{68} +20.9685 q^{69} -2.00532 q^{71} +20.8040 q^{72} +3.28275 q^{73} -1.68600 q^{74} -3.30996 q^{75} +8.54933 q^{76} +48.9967 q^{78} +4.84953 q^{79} -0.368699 q^{80} +30.4280 q^{81} +21.0751 q^{82} +5.94885 q^{83} +0.221263 q^{85} -18.7515 q^{86} +8.71237 q^{87} +12.6960 q^{88} +3.33533 q^{89} +18.0583 q^{90} -19.9681 q^{92} +3.30996 q^{93} +13.5586 q^{94} +2.71231 q^{95} +20.0807 q^{96} +7.08455 q^{97} +38.6273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.26981 1.60500 0.802500 0.596653i \(-0.203503\pi\)
0.802500 + 0.596653i \(0.203503\pi\)
\(3\) −3.30996 −1.91101 −0.955504 0.294979i \(-0.904687\pi\)
−0.955504 + 0.294979i \(0.904687\pi\)
\(4\) 3.15205 1.57602
\(5\) 1.00000 0.447214
\(6\) −7.51299 −3.06717
\(7\) 0 0
\(8\) 2.61493 0.924516
\(9\) 7.95585 2.65195
\(10\) 2.26981 0.717778
\(11\) 4.85520 1.46390 0.731949 0.681359i \(-0.238611\pi\)
0.731949 + 0.681359i \(0.238611\pi\)
\(12\) −10.4332 −3.01179
\(13\) −6.52160 −1.80877 −0.904383 0.426721i \(-0.859669\pi\)
−0.904383 + 0.426721i \(0.859669\pi\)
\(14\) 0 0
\(15\) −3.30996 −0.854629
\(16\) −0.368699 −0.0921748
\(17\) 0.221263 0.0536641 0.0268321 0.999640i \(-0.491458\pi\)
0.0268321 + 0.999640i \(0.491458\pi\)
\(18\) 18.0583 4.25638
\(19\) 2.71231 0.622247 0.311123 0.950370i \(-0.399295\pi\)
0.311123 + 0.950370i \(0.399295\pi\)
\(20\) 3.15205 0.704819
\(21\) 0 0
\(22\) 11.0204 2.34956
\(23\) −6.33498 −1.32093 −0.660467 0.750855i \(-0.729642\pi\)
−0.660467 + 0.750855i \(0.729642\pi\)
\(24\) −8.65531 −1.76676
\(25\) 1.00000 0.200000
\(26\) −14.8028 −2.90307
\(27\) −16.4037 −3.15689
\(28\) 0 0
\(29\) −2.63217 −0.488781 −0.244391 0.969677i \(-0.578588\pi\)
−0.244391 + 0.969677i \(0.578588\pi\)
\(30\) −7.51299 −1.37168
\(31\) −1.00000 −0.179605
\(32\) −6.06673 −1.07246
\(33\) −16.0705 −2.79752
\(34\) 0.502225 0.0861309
\(35\) 0 0
\(36\) 25.0772 4.17953
\(37\) −0.742795 −0.122115 −0.0610574 0.998134i \(-0.519447\pi\)
−0.0610574 + 0.998134i \(0.519447\pi\)
\(38\) 6.15643 0.998706
\(39\) 21.5863 3.45657
\(40\) 2.61493 0.413456
\(41\) 9.28495 1.45007 0.725033 0.688715i \(-0.241825\pi\)
0.725033 + 0.688715i \(0.241825\pi\)
\(42\) 0 0
\(43\) −8.26124 −1.25983 −0.629914 0.776665i \(-0.716910\pi\)
−0.629914 + 0.776665i \(0.716910\pi\)
\(44\) 15.3038 2.30714
\(45\) 7.95585 1.18599
\(46\) −14.3792 −2.12010
\(47\) 5.97344 0.871315 0.435658 0.900112i \(-0.356516\pi\)
0.435658 + 0.900112i \(0.356516\pi\)
\(48\) 1.22038 0.176147
\(49\) 0 0
\(50\) 2.26981 0.321000
\(51\) −0.732372 −0.102553
\(52\) −20.5564 −2.85066
\(53\) −4.45885 −0.612471 −0.306235 0.951956i \(-0.599069\pi\)
−0.306235 + 0.951956i \(0.599069\pi\)
\(54\) −37.2333 −5.06681
\(55\) 4.85520 0.654676
\(56\) 0 0
\(57\) −8.97765 −1.18912
\(58\) −5.97452 −0.784493
\(59\) −4.95499 −0.645085 −0.322543 0.946555i \(-0.604538\pi\)
−0.322543 + 0.946555i \(0.604538\pi\)
\(60\) −10.4332 −1.34691
\(61\) −14.2834 −1.82880 −0.914401 0.404809i \(-0.867338\pi\)
−0.914401 + 0.404809i \(0.867338\pi\)
\(62\) −2.26981 −0.288266
\(63\) 0 0
\(64\) −13.0329 −1.62912
\(65\) −6.52160 −0.808905
\(66\) −36.4771 −4.49002
\(67\) −6.21873 −0.759739 −0.379870 0.925040i \(-0.624031\pi\)
−0.379870 + 0.925040i \(0.624031\pi\)
\(68\) 0.697431 0.0845759
\(69\) 20.9685 2.52431
\(70\) 0 0
\(71\) −2.00532 −0.237988 −0.118994 0.992895i \(-0.537967\pi\)
−0.118994 + 0.992895i \(0.537967\pi\)
\(72\) 20.8040 2.45177
\(73\) 3.28275 0.384216 0.192108 0.981374i \(-0.438468\pi\)
0.192108 + 0.981374i \(0.438468\pi\)
\(74\) −1.68600 −0.195994
\(75\) −3.30996 −0.382202
\(76\) 8.54933 0.980675
\(77\) 0 0
\(78\) 48.9967 5.54779
\(79\) 4.84953 0.545615 0.272807 0.962069i \(-0.412048\pi\)
0.272807 + 0.962069i \(0.412048\pi\)
\(80\) −0.368699 −0.0412218
\(81\) 30.4280 3.38089
\(82\) 21.0751 2.32735
\(83\) 5.94885 0.652971 0.326486 0.945202i \(-0.394136\pi\)
0.326486 + 0.945202i \(0.394136\pi\)
\(84\) 0 0
\(85\) 0.221263 0.0239993
\(86\) −18.7515 −2.02202
\(87\) 8.71237 0.934064
\(88\) 12.6960 1.35340
\(89\) 3.33533 0.353545 0.176772 0.984252i \(-0.443434\pi\)
0.176772 + 0.984252i \(0.443434\pi\)
\(90\) 18.0583 1.90351
\(91\) 0 0
\(92\) −19.9681 −2.08182
\(93\) 3.30996 0.343227
\(94\) 13.5586 1.39846
\(95\) 2.71231 0.278277
\(96\) 20.0807 2.04947
\(97\) 7.08455 0.719327 0.359663 0.933082i \(-0.382892\pi\)
0.359663 + 0.933082i \(0.382892\pi\)
\(98\) 0 0
\(99\) 38.6273 3.88219
\(100\) 3.15205 0.315205
\(101\) −8.88272 −0.883863 −0.441932 0.897049i \(-0.645707\pi\)
−0.441932 + 0.897049i \(0.645707\pi\)
\(102\) −1.66235 −0.164597
\(103\) 1.05449 0.103902 0.0519509 0.998650i \(-0.483456\pi\)
0.0519509 + 0.998650i \(0.483456\pi\)
\(104\) −17.0535 −1.67223
\(105\) 0 0
\(106\) −10.1208 −0.983015
\(107\) 8.87370 0.857853 0.428927 0.903339i \(-0.358892\pi\)
0.428927 + 0.903339i \(0.358892\pi\)
\(108\) −51.7051 −4.97533
\(109\) 1.81005 0.173371 0.0866855 0.996236i \(-0.472372\pi\)
0.0866855 + 0.996236i \(0.472372\pi\)
\(110\) 11.0204 1.05075
\(111\) 2.45862 0.233362
\(112\) 0 0
\(113\) −12.2479 −1.15219 −0.576094 0.817383i \(-0.695424\pi\)
−0.576094 + 0.817383i \(0.695424\pi\)
\(114\) −20.3776 −1.90853
\(115\) −6.33498 −0.590740
\(116\) −8.29671 −0.770330
\(117\) −51.8849 −4.79676
\(118\) −11.2469 −1.03536
\(119\) 0 0
\(120\) −8.65531 −0.790118
\(121\) 12.5730 1.14300
\(122\) −32.4206 −2.93523
\(123\) −30.7328 −2.77109
\(124\) −3.15205 −0.283062
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 1.57855 0.140073 0.0700366 0.997544i \(-0.477688\pi\)
0.0700366 + 0.997544i \(0.477688\pi\)
\(128\) −17.4489 −1.54228
\(129\) 27.3444 2.40754
\(130\) −14.8028 −1.29829
\(131\) −10.5229 −0.919390 −0.459695 0.888077i \(-0.652041\pi\)
−0.459695 + 0.888077i \(0.652041\pi\)
\(132\) −50.6551 −4.40896
\(133\) 0 0
\(134\) −14.1154 −1.21938
\(135\) −16.4037 −1.41180
\(136\) 0.578586 0.0496134
\(137\) 8.93351 0.763242 0.381621 0.924319i \(-0.375366\pi\)
0.381621 + 0.924319i \(0.375366\pi\)
\(138\) 47.5946 4.05152
\(139\) 0.362168 0.0307187 0.0153594 0.999882i \(-0.495111\pi\)
0.0153594 + 0.999882i \(0.495111\pi\)
\(140\) 0 0
\(141\) −19.7718 −1.66509
\(142\) −4.55170 −0.381970
\(143\) −31.6637 −2.64785
\(144\) −2.93331 −0.244443
\(145\) −2.63217 −0.218590
\(146\) 7.45122 0.616667
\(147\) 0 0
\(148\) −2.34132 −0.192456
\(149\) −14.4149 −1.18092 −0.590458 0.807068i \(-0.701053\pi\)
−0.590458 + 0.807068i \(0.701053\pi\)
\(150\) −7.51299 −0.613433
\(151\) 13.5523 1.10287 0.551436 0.834217i \(-0.314080\pi\)
0.551436 + 0.834217i \(0.314080\pi\)
\(152\) 7.09249 0.575277
\(153\) 1.76033 0.142315
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 68.0409 5.44763
\(157\) −20.0346 −1.59894 −0.799469 0.600708i \(-0.794886\pi\)
−0.799469 + 0.600708i \(0.794886\pi\)
\(158\) 11.0075 0.875711
\(159\) 14.7586 1.17044
\(160\) −6.06673 −0.479617
\(161\) 0 0
\(162\) 69.0658 5.42633
\(163\) −1.17177 −0.0917803 −0.0458901 0.998946i \(-0.514612\pi\)
−0.0458901 + 0.998946i \(0.514612\pi\)
\(164\) 29.2666 2.28534
\(165\) −16.0705 −1.25109
\(166\) 13.5028 1.04802
\(167\) −16.1871 −1.25259 −0.626297 0.779584i \(-0.715430\pi\)
−0.626297 + 0.779584i \(0.715430\pi\)
\(168\) 0 0
\(169\) 29.5313 2.27164
\(170\) 0.502225 0.0385189
\(171\) 21.5787 1.65017
\(172\) −26.0398 −1.98552
\(173\) −7.19520 −0.547041 −0.273521 0.961866i \(-0.588188\pi\)
−0.273521 + 0.961866i \(0.588188\pi\)
\(174\) 19.7754 1.49917
\(175\) 0 0
\(176\) −1.79011 −0.134935
\(177\) 16.4008 1.23276
\(178\) 7.57058 0.567439
\(179\) 19.4195 1.45148 0.725740 0.687969i \(-0.241497\pi\)
0.725740 + 0.687969i \(0.241497\pi\)
\(180\) 25.0772 1.86914
\(181\) −18.1665 −1.35030 −0.675152 0.737679i \(-0.735922\pi\)
−0.675152 + 0.737679i \(0.735922\pi\)
\(182\) 0 0
\(183\) 47.2775 3.49486
\(184\) −16.5655 −1.22123
\(185\) −0.742795 −0.0546114
\(186\) 7.51299 0.550879
\(187\) 1.07428 0.0785589
\(188\) 18.8285 1.37321
\(189\) 0 0
\(190\) 6.15643 0.446635
\(191\) −26.7503 −1.93558 −0.967790 0.251757i \(-0.918991\pi\)
−0.967790 + 0.251757i \(0.918991\pi\)
\(192\) 43.1385 3.11326
\(193\) −12.5988 −0.906884 −0.453442 0.891286i \(-0.649804\pi\)
−0.453442 + 0.891286i \(0.649804\pi\)
\(194\) 16.0806 1.15452
\(195\) 21.5863 1.54582
\(196\) 0 0
\(197\) −17.5580 −1.25096 −0.625478 0.780242i \(-0.715096\pi\)
−0.625478 + 0.780242i \(0.715096\pi\)
\(198\) 87.6766 6.23091
\(199\) −20.2841 −1.43790 −0.718949 0.695063i \(-0.755377\pi\)
−0.718949 + 0.695063i \(0.755377\pi\)
\(200\) 2.61493 0.184903
\(201\) 20.5838 1.45187
\(202\) −20.1621 −1.41860
\(203\) 0 0
\(204\) −2.30847 −0.161625
\(205\) 9.28495 0.648489
\(206\) 2.39349 0.166762
\(207\) −50.4001 −3.50305
\(208\) 2.40451 0.166723
\(209\) 13.1688 0.910906
\(210\) 0 0
\(211\) −10.3326 −0.711327 −0.355664 0.934614i \(-0.615745\pi\)
−0.355664 + 0.934614i \(0.615745\pi\)
\(212\) −14.0545 −0.965268
\(213\) 6.63754 0.454797
\(214\) 20.1416 1.37685
\(215\) −8.26124 −0.563412
\(216\) −42.8944 −2.91860
\(217\) 0 0
\(218\) 4.10846 0.278260
\(219\) −10.8658 −0.734240
\(220\) 15.3038 1.03178
\(221\) −1.44299 −0.0970659
\(222\) 5.58061 0.374546
\(223\) 29.2750 1.96040 0.980199 0.198013i \(-0.0634489\pi\)
0.980199 + 0.198013i \(0.0634489\pi\)
\(224\) 0 0
\(225\) 7.95585 0.530390
\(226\) −27.8005 −1.84926
\(227\) 3.12495 0.207410 0.103705 0.994608i \(-0.466930\pi\)
0.103705 + 0.994608i \(0.466930\pi\)
\(228\) −28.2980 −1.87408
\(229\) −6.02790 −0.398335 −0.199167 0.979965i \(-0.563824\pi\)
−0.199167 + 0.979965i \(0.563824\pi\)
\(230\) −14.3792 −0.948137
\(231\) 0 0
\(232\) −6.88292 −0.451886
\(233\) −6.82987 −0.447440 −0.223720 0.974653i \(-0.571820\pi\)
−0.223720 + 0.974653i \(0.571820\pi\)
\(234\) −117.769 −7.69880
\(235\) 5.97344 0.389664
\(236\) −15.6184 −1.01667
\(237\) −16.0518 −1.04267
\(238\) 0 0
\(239\) −3.19383 −0.206591 −0.103296 0.994651i \(-0.532939\pi\)
−0.103296 + 0.994651i \(0.532939\pi\)
\(240\) 1.22038 0.0787752
\(241\) 12.5996 0.811614 0.405807 0.913959i \(-0.366991\pi\)
0.405807 + 0.913959i \(0.366991\pi\)
\(242\) 28.5383 1.83451
\(243\) −51.5045 −3.30402
\(244\) −45.0219 −2.88223
\(245\) 0 0
\(246\) −69.7577 −4.44759
\(247\) −17.6886 −1.12550
\(248\) −2.61493 −0.166048
\(249\) −19.6905 −1.24783
\(250\) 2.26981 0.143556
\(251\) 9.93678 0.627204 0.313602 0.949555i \(-0.398464\pi\)
0.313602 + 0.949555i \(0.398464\pi\)
\(252\) 0 0
\(253\) −30.7576 −1.93371
\(254\) 3.58300 0.224817
\(255\) −0.732372 −0.0458629
\(256\) −13.5397 −0.846234
\(257\) −6.22505 −0.388308 −0.194154 0.980971i \(-0.562196\pi\)
−0.194154 + 0.980971i \(0.562196\pi\)
\(258\) 62.0666 3.86410
\(259\) 0 0
\(260\) −20.5564 −1.27485
\(261\) −20.9411 −1.29622
\(262\) −23.8850 −1.47562
\(263\) −4.73589 −0.292028 −0.146014 0.989283i \(-0.546644\pi\)
−0.146014 + 0.989283i \(0.546644\pi\)
\(264\) −42.0233 −2.58635
\(265\) −4.45885 −0.273905
\(266\) 0 0
\(267\) −11.0398 −0.675627
\(268\) −19.6017 −1.19737
\(269\) 9.32217 0.568383 0.284191 0.958768i \(-0.408275\pi\)
0.284191 + 0.958768i \(0.408275\pi\)
\(270\) −37.2333 −2.26594
\(271\) −26.4572 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(272\) −0.0815794 −0.00494648
\(273\) 0 0
\(274\) 20.2774 1.22500
\(275\) 4.85520 0.292780
\(276\) 66.0938 3.97838
\(277\) 4.34480 0.261054 0.130527 0.991445i \(-0.458333\pi\)
0.130527 + 0.991445i \(0.458333\pi\)
\(278\) 0.822054 0.0493035
\(279\) −7.95585 −0.476304
\(280\) 0 0
\(281\) −29.7466 −1.77453 −0.887267 0.461256i \(-0.847399\pi\)
−0.887267 + 0.461256i \(0.847399\pi\)
\(282\) −44.8784 −2.67247
\(283\) 28.5915 1.69959 0.849794 0.527116i \(-0.176726\pi\)
0.849794 + 0.527116i \(0.176726\pi\)
\(284\) −6.32087 −0.375074
\(285\) −8.97765 −0.531790
\(286\) −71.8707 −4.24980
\(287\) 0 0
\(288\) −48.2660 −2.84410
\(289\) −16.9510 −0.997120
\(290\) −5.97452 −0.350836
\(291\) −23.4496 −1.37464
\(292\) 10.3474 0.605534
\(293\) 5.06369 0.295824 0.147912 0.989001i \(-0.452745\pi\)
0.147912 + 0.989001i \(0.452745\pi\)
\(294\) 0 0
\(295\) −4.95499 −0.288491
\(296\) −1.94235 −0.112897
\(297\) −79.6432 −4.62137
\(298\) −32.7192 −1.89537
\(299\) 41.3142 2.38926
\(300\) −10.4332 −0.602358
\(301\) 0 0
\(302\) 30.7612 1.77011
\(303\) 29.4015 1.68907
\(304\) −1.00003 −0.0573554
\(305\) −14.2834 −0.817865
\(306\) 3.99563 0.228415
\(307\) 13.7978 0.787482 0.393741 0.919221i \(-0.371181\pi\)
0.393741 + 0.919221i \(0.371181\pi\)
\(308\) 0 0
\(309\) −3.49032 −0.198557
\(310\) −2.26981 −0.128917
\(311\) −15.0651 −0.854261 −0.427130 0.904190i \(-0.640475\pi\)
−0.427130 + 0.904190i \(0.640475\pi\)
\(312\) 56.4465 3.19565
\(313\) −11.7420 −0.663696 −0.331848 0.943333i \(-0.607672\pi\)
−0.331848 + 0.943333i \(0.607672\pi\)
\(314\) −45.4748 −2.56629
\(315\) 0 0
\(316\) 15.2859 0.859901
\(317\) 12.7836 0.718001 0.359000 0.933337i \(-0.383118\pi\)
0.359000 + 0.933337i \(0.383118\pi\)
\(318\) 33.4993 1.87855
\(319\) −12.7797 −0.715526
\(320\) −13.0329 −0.728564
\(321\) −29.3716 −1.63936
\(322\) 0 0
\(323\) 0.600134 0.0333923
\(324\) 95.9105 5.32836
\(325\) −6.52160 −0.361753
\(326\) −2.65970 −0.147307
\(327\) −5.99118 −0.331313
\(328\) 24.2795 1.34061
\(329\) 0 0
\(330\) −36.4771 −2.00800
\(331\) −2.31971 −0.127503 −0.0637514 0.997966i \(-0.520306\pi\)
−0.0637514 + 0.997966i \(0.520306\pi\)
\(332\) 18.7510 1.02910
\(333\) −5.90956 −0.323842
\(334\) −36.7417 −2.01041
\(335\) −6.21873 −0.339766
\(336\) 0 0
\(337\) 17.4313 0.949543 0.474772 0.880109i \(-0.342531\pi\)
0.474772 + 0.880109i \(0.342531\pi\)
\(338\) 67.0305 3.64598
\(339\) 40.5402 2.20184
\(340\) 0.697431 0.0378235
\(341\) −4.85520 −0.262924
\(342\) 48.9797 2.64852
\(343\) 0 0
\(344\) −21.6025 −1.16473
\(345\) 20.9685 1.12891
\(346\) −16.3318 −0.878001
\(347\) −23.0300 −1.23631 −0.618157 0.786055i \(-0.712120\pi\)
−0.618157 + 0.786055i \(0.712120\pi\)
\(348\) 27.4618 1.47211
\(349\) −5.45256 −0.291869 −0.145934 0.989294i \(-0.546619\pi\)
−0.145934 + 0.989294i \(0.546619\pi\)
\(350\) 0 0
\(351\) 106.978 5.71008
\(352\) −29.4552 −1.56997
\(353\) −5.47366 −0.291334 −0.145667 0.989334i \(-0.546533\pi\)
−0.145667 + 0.989334i \(0.546533\pi\)
\(354\) 37.2268 1.97858
\(355\) −2.00532 −0.106431
\(356\) 10.5131 0.557195
\(357\) 0 0
\(358\) 44.0786 2.32963
\(359\) 10.9587 0.578377 0.289188 0.957272i \(-0.406615\pi\)
0.289188 + 0.957272i \(0.406615\pi\)
\(360\) 20.8040 1.09647
\(361\) −11.6434 −0.612809
\(362\) −41.2345 −2.16724
\(363\) −41.6162 −2.18428
\(364\) 0 0
\(365\) 3.28275 0.171827
\(366\) 107.311 5.60924
\(367\) −27.0586 −1.41245 −0.706223 0.707989i \(-0.749603\pi\)
−0.706223 + 0.707989i \(0.749603\pi\)
\(368\) 2.33570 0.121757
\(369\) 73.8696 3.84550
\(370\) −1.68600 −0.0876512
\(371\) 0 0
\(372\) 10.4332 0.540934
\(373\) −8.72757 −0.451896 −0.225948 0.974139i \(-0.572548\pi\)
−0.225948 + 0.974139i \(0.572548\pi\)
\(374\) 2.43841 0.126087
\(375\) −3.30996 −0.170926
\(376\) 15.6201 0.805545
\(377\) 17.1659 0.884091
\(378\) 0 0
\(379\) −16.2865 −0.836583 −0.418292 0.908313i \(-0.637371\pi\)
−0.418292 + 0.908313i \(0.637371\pi\)
\(380\) 8.54933 0.438571
\(381\) −5.22493 −0.267681
\(382\) −60.7181 −3.10661
\(383\) 17.7948 0.909273 0.454636 0.890677i \(-0.349769\pi\)
0.454636 + 0.890677i \(0.349769\pi\)
\(384\) 57.7551 2.94730
\(385\) 0 0
\(386\) −28.5970 −1.45555
\(387\) −65.7252 −3.34100
\(388\) 22.3308 1.13368
\(389\) −26.7480 −1.35618 −0.678089 0.734980i \(-0.737191\pi\)
−0.678089 + 0.734980i \(0.737191\pi\)
\(390\) 48.9967 2.48105
\(391\) −1.40170 −0.0708868
\(392\) 0 0
\(393\) 34.8304 1.75696
\(394\) −39.8534 −2.00778
\(395\) 4.84953 0.244006
\(396\) 121.755 6.11842
\(397\) −17.0250 −0.854460 −0.427230 0.904143i \(-0.640511\pi\)
−0.427230 + 0.904143i \(0.640511\pi\)
\(398\) −46.0410 −2.30783
\(399\) 0 0
\(400\) −0.368699 −0.0184350
\(401\) 7.88405 0.393711 0.196855 0.980433i \(-0.436927\pi\)
0.196855 + 0.980433i \(0.436927\pi\)
\(402\) 46.7213 2.33025
\(403\) 6.52160 0.324864
\(404\) −27.9987 −1.39299
\(405\) 30.4280 1.51198
\(406\) 0 0
\(407\) −3.60642 −0.178764
\(408\) −1.91510 −0.0948115
\(409\) −18.6570 −0.922529 −0.461264 0.887263i \(-0.652604\pi\)
−0.461264 + 0.887263i \(0.652604\pi\)
\(410\) 21.0751 1.04082
\(411\) −29.5696 −1.45856
\(412\) 3.32380 0.163752
\(413\) 0 0
\(414\) −114.399 −5.62239
\(415\) 5.94885 0.292018
\(416\) 39.5648 1.93982
\(417\) −1.19876 −0.0587037
\(418\) 29.8907 1.46200
\(419\) −12.1866 −0.595354 −0.297677 0.954667i \(-0.596212\pi\)
−0.297677 + 0.954667i \(0.596212\pi\)
\(420\) 0 0
\(421\) 39.8586 1.94259 0.971295 0.237878i \(-0.0764518\pi\)
0.971295 + 0.237878i \(0.0764518\pi\)
\(422\) −23.4531 −1.14168
\(423\) 47.5238 2.31068
\(424\) −11.6596 −0.566239
\(425\) 0.221263 0.0107328
\(426\) 15.0660 0.729948
\(427\) 0 0
\(428\) 27.9703 1.35200
\(429\) 104.806 5.06007
\(430\) −18.7515 −0.904276
\(431\) 13.5975 0.654969 0.327484 0.944857i \(-0.393799\pi\)
0.327484 + 0.944857i \(0.393799\pi\)
\(432\) 6.04802 0.290985
\(433\) −8.05133 −0.386922 −0.193461 0.981108i \(-0.561971\pi\)
−0.193461 + 0.981108i \(0.561971\pi\)
\(434\) 0 0
\(435\) 8.71237 0.417726
\(436\) 5.70535 0.273237
\(437\) −17.1824 −0.821947
\(438\) −24.6632 −1.17846
\(439\) −3.48742 −0.166445 −0.0832227 0.996531i \(-0.526521\pi\)
−0.0832227 + 0.996531i \(0.526521\pi\)
\(440\) 12.6960 0.605258
\(441\) 0 0
\(442\) −3.27531 −0.155791
\(443\) −25.2297 −1.19870 −0.599351 0.800487i \(-0.704574\pi\)
−0.599351 + 0.800487i \(0.704574\pi\)
\(444\) 7.74969 0.367784
\(445\) 3.33533 0.158110
\(446\) 66.4487 3.14644
\(447\) 47.7128 2.25674
\(448\) 0 0
\(449\) 13.3510 0.630074 0.315037 0.949079i \(-0.397983\pi\)
0.315037 + 0.949079i \(0.397983\pi\)
\(450\) 18.0583 0.851276
\(451\) 45.0803 2.12275
\(452\) −38.6061 −1.81588
\(453\) −44.8576 −2.10760
\(454\) 7.09305 0.332893
\(455\) 0 0
\(456\) −23.4759 −1.09936
\(457\) −13.7798 −0.644590 −0.322295 0.946639i \(-0.604454\pi\)
−0.322295 + 0.946639i \(0.604454\pi\)
\(458\) −13.6822 −0.639327
\(459\) −3.62953 −0.169412
\(460\) −19.9681 −0.931019
\(461\) −12.7671 −0.594625 −0.297313 0.954780i \(-0.596090\pi\)
−0.297313 + 0.954780i \(0.596090\pi\)
\(462\) 0 0
\(463\) 32.4272 1.50702 0.753510 0.657437i \(-0.228359\pi\)
0.753510 + 0.657437i \(0.228359\pi\)
\(464\) 0.970477 0.0450533
\(465\) 3.30996 0.153496
\(466\) −15.5025 −0.718141
\(467\) 12.7508 0.590037 0.295018 0.955492i \(-0.404674\pi\)
0.295018 + 0.955492i \(0.404674\pi\)
\(468\) −163.544 −7.55980
\(469\) 0 0
\(470\) 13.5586 0.625410
\(471\) 66.3139 3.05558
\(472\) −12.9569 −0.596392
\(473\) −40.1100 −1.84426
\(474\) −36.4345 −1.67349
\(475\) 2.71231 0.124449
\(476\) 0 0
\(477\) −35.4740 −1.62424
\(478\) −7.24938 −0.331579
\(479\) −4.12861 −0.188641 −0.0943205 0.995542i \(-0.530068\pi\)
−0.0943205 + 0.995542i \(0.530068\pi\)
\(480\) 20.0807 0.916552
\(481\) 4.84421 0.220877
\(482\) 28.5988 1.30264
\(483\) 0 0
\(484\) 39.6307 1.80139
\(485\) 7.08455 0.321693
\(486\) −116.906 −5.30294
\(487\) −13.9539 −0.632310 −0.316155 0.948708i \(-0.602392\pi\)
−0.316155 + 0.948708i \(0.602392\pi\)
\(488\) −37.3501 −1.69076
\(489\) 3.87852 0.175393
\(490\) 0 0
\(491\) 8.00929 0.361454 0.180727 0.983533i \(-0.442155\pi\)
0.180727 + 0.983533i \(0.442155\pi\)
\(492\) −96.8713 −4.36729
\(493\) −0.582401 −0.0262300
\(494\) −40.1498 −1.80643
\(495\) 38.6273 1.73617
\(496\) 0.368699 0.0165551
\(497\) 0 0
\(498\) −44.6937 −2.00277
\(499\) −8.50410 −0.380696 −0.190348 0.981717i \(-0.560962\pi\)
−0.190348 + 0.981717i \(0.560962\pi\)
\(500\) 3.15205 0.140964
\(501\) 53.5787 2.39372
\(502\) 22.5546 1.00666
\(503\) 33.2571 1.48286 0.741430 0.671030i \(-0.234148\pi\)
0.741430 + 0.671030i \(0.234148\pi\)
\(504\) 0 0
\(505\) −8.88272 −0.395276
\(506\) −69.8140 −3.10361
\(507\) −97.7475 −4.34112
\(508\) 4.97565 0.220759
\(509\) −33.9903 −1.50659 −0.753297 0.657680i \(-0.771538\pi\)
−0.753297 + 0.657680i \(0.771538\pi\)
\(510\) −1.66235 −0.0736099
\(511\) 0 0
\(512\) 4.16504 0.184070
\(513\) −44.4919 −1.96436
\(514\) −14.1297 −0.623234
\(515\) 1.05449 0.0464663
\(516\) 86.1908 3.79434
\(517\) 29.0022 1.27552
\(518\) 0 0
\(519\) 23.8159 1.04540
\(520\) −17.0535 −0.747846
\(521\) −36.5661 −1.60199 −0.800995 0.598671i \(-0.795696\pi\)
−0.800995 + 0.598671i \(0.795696\pi\)
\(522\) −47.5324 −2.08044
\(523\) −18.1021 −0.791551 −0.395776 0.918347i \(-0.629524\pi\)
−0.395776 + 0.918347i \(0.629524\pi\)
\(524\) −33.1687 −1.44898
\(525\) 0 0
\(526\) −10.7496 −0.468704
\(527\) −0.221263 −0.00963836
\(528\) 5.92519 0.257861
\(529\) 17.1319 0.744867
\(530\) −10.1208 −0.439618
\(531\) −39.4212 −1.71073
\(532\) 0 0
\(533\) −60.5527 −2.62283
\(534\) −25.0583 −1.08438
\(535\) 8.87370 0.383644
\(536\) −16.2615 −0.702391
\(537\) −64.2778 −2.77379
\(538\) 21.1596 0.912254
\(539\) 0 0
\(540\) −51.7051 −2.22504
\(541\) 3.88174 0.166889 0.0834446 0.996512i \(-0.473408\pi\)
0.0834446 + 0.996512i \(0.473408\pi\)
\(542\) −60.0528 −2.57949
\(543\) 60.1304 2.58044
\(544\) −1.34234 −0.0575525
\(545\) 1.81005 0.0775338
\(546\) 0 0
\(547\) 13.0385 0.557485 0.278742 0.960366i \(-0.410082\pi\)
0.278742 + 0.960366i \(0.410082\pi\)
\(548\) 28.1588 1.20289
\(549\) −113.637 −4.84989
\(550\) 11.0204 0.469911
\(551\) −7.13925 −0.304142
\(552\) 54.8312 2.33377
\(553\) 0 0
\(554\) 9.86187 0.418991
\(555\) 2.45862 0.104363
\(556\) 1.14157 0.0484134
\(557\) 19.8954 0.842995 0.421498 0.906830i \(-0.361505\pi\)
0.421498 + 0.906830i \(0.361505\pi\)
\(558\) −18.0583 −0.764468
\(559\) 53.8765 2.27873
\(560\) 0 0
\(561\) −3.55581 −0.150127
\(562\) −67.5192 −2.84813
\(563\) 10.6555 0.449076 0.224538 0.974465i \(-0.427913\pi\)
0.224538 + 0.974465i \(0.427913\pi\)
\(564\) −62.3218 −2.62422
\(565\) −12.2479 −0.515275
\(566\) 64.8973 2.72784
\(567\) 0 0
\(568\) −5.24377 −0.220024
\(569\) 20.1534 0.844874 0.422437 0.906392i \(-0.361175\pi\)
0.422437 + 0.906392i \(0.361175\pi\)
\(570\) −20.3776 −0.853522
\(571\) 9.74096 0.407646 0.203823 0.979008i \(-0.434663\pi\)
0.203823 + 0.979008i \(0.434663\pi\)
\(572\) −99.8054 −4.17308
\(573\) 88.5423 3.69891
\(574\) 0 0
\(575\) −6.33498 −0.264187
\(576\) −103.688 −4.32034
\(577\) 8.95924 0.372978 0.186489 0.982457i \(-0.440289\pi\)
0.186489 + 0.982457i \(0.440289\pi\)
\(578\) −38.4757 −1.60038
\(579\) 41.7017 1.73306
\(580\) −8.29671 −0.344502
\(581\) 0 0
\(582\) −53.2261 −2.20629
\(583\) −21.6486 −0.896595
\(584\) 8.58414 0.355214
\(585\) −51.8849 −2.14518
\(586\) 11.4936 0.474797
\(587\) −15.9725 −0.659255 −0.329627 0.944111i \(-0.606923\pi\)
−0.329627 + 0.944111i \(0.606923\pi\)
\(588\) 0 0
\(589\) −2.71231 −0.111759
\(590\) −11.2469 −0.463028
\(591\) 58.1163 2.39059
\(592\) 0.273868 0.0112559
\(593\) 29.2134 1.19965 0.599826 0.800131i \(-0.295237\pi\)
0.599826 + 0.800131i \(0.295237\pi\)
\(594\) −180.775 −7.41729
\(595\) 0 0
\(596\) −45.4365 −1.86115
\(597\) 67.1395 2.74784
\(598\) 93.7755 3.83476
\(599\) 15.9622 0.652199 0.326100 0.945335i \(-0.394266\pi\)
0.326100 + 0.945335i \(0.394266\pi\)
\(600\) −8.65531 −0.353352
\(601\) 10.6357 0.433839 0.216920 0.976189i \(-0.430399\pi\)
0.216920 + 0.976189i \(0.430399\pi\)
\(602\) 0 0
\(603\) −49.4753 −2.01479
\(604\) 42.7175 1.73815
\(605\) 12.5730 0.511165
\(606\) 66.7358 2.71096
\(607\) 46.1383 1.87269 0.936347 0.351076i \(-0.114184\pi\)
0.936347 + 0.351076i \(0.114184\pi\)
\(608\) −16.4549 −0.667333
\(609\) 0 0
\(610\) −32.4206 −1.31267
\(611\) −38.9564 −1.57601
\(612\) 5.54866 0.224291
\(613\) 30.6510 1.23798 0.618992 0.785398i \(-0.287542\pi\)
0.618992 + 0.785398i \(0.287542\pi\)
\(614\) 31.3184 1.26391
\(615\) −30.7328 −1.23927
\(616\) 0 0
\(617\) −20.2647 −0.815827 −0.407913 0.913021i \(-0.633743\pi\)
−0.407913 + 0.913021i \(0.633743\pi\)
\(618\) −7.92236 −0.318684
\(619\) 44.7318 1.79792 0.898962 0.438027i \(-0.144322\pi\)
0.898962 + 0.438027i \(0.144322\pi\)
\(620\) −3.15205 −0.126589
\(621\) 103.917 4.17004
\(622\) −34.1948 −1.37109
\(623\) 0 0
\(624\) −7.95883 −0.318608
\(625\) 1.00000 0.0400000
\(626\) −26.6521 −1.06523
\(627\) −43.5883 −1.74075
\(628\) −63.1501 −2.51996
\(629\) −0.164353 −0.00655318
\(630\) 0 0
\(631\) −14.0465 −0.559180 −0.279590 0.960119i \(-0.590199\pi\)
−0.279590 + 0.960119i \(0.590199\pi\)
\(632\) 12.6812 0.504430
\(633\) 34.2006 1.35935
\(634\) 29.0164 1.15239
\(635\) 1.57855 0.0626427
\(636\) 46.5199 1.84463
\(637\) 0 0
\(638\) −29.0075 −1.14842
\(639\) −15.9540 −0.631132
\(640\) −17.4489 −0.689727
\(641\) 11.6087 0.458515 0.229257 0.973366i \(-0.426370\pi\)
0.229257 + 0.973366i \(0.426370\pi\)
\(642\) −66.6681 −2.63118
\(643\) −0.937030 −0.0369529 −0.0184764 0.999829i \(-0.505882\pi\)
−0.0184764 + 0.999829i \(0.505882\pi\)
\(644\) 0 0
\(645\) 27.3444 1.07668
\(646\) 1.36219 0.0535947
\(647\) 31.4041 1.23462 0.617312 0.786718i \(-0.288222\pi\)
0.617312 + 0.786718i \(0.288222\pi\)
\(648\) 79.5670 3.12569
\(649\) −24.0575 −0.944339
\(650\) −14.8028 −0.580614
\(651\) 0 0
\(652\) −3.69348 −0.144648
\(653\) −20.8217 −0.814814 −0.407407 0.913247i \(-0.633567\pi\)
−0.407407 + 0.913247i \(0.633567\pi\)
\(654\) −13.5989 −0.531757
\(655\) −10.5229 −0.411164
\(656\) −3.42335 −0.133659
\(657\) 26.1170 1.01892
\(658\) 0 0
\(659\) −26.7895 −1.04357 −0.521786 0.853077i \(-0.674734\pi\)
−0.521786 + 0.853077i \(0.674734\pi\)
\(660\) −50.6551 −1.97175
\(661\) 45.5474 1.77159 0.885794 0.464078i \(-0.153614\pi\)
0.885794 + 0.464078i \(0.153614\pi\)
\(662\) −5.26530 −0.204642
\(663\) 4.77624 0.185494
\(664\) 15.5558 0.603682
\(665\) 0 0
\(666\) −13.4136 −0.519766
\(667\) 16.6747 0.645648
\(668\) −51.0225 −1.97412
\(669\) −96.8991 −3.74634
\(670\) −14.1154 −0.545324
\(671\) −69.3488 −2.67718
\(672\) 0 0
\(673\) 22.7733 0.877847 0.438923 0.898525i \(-0.355360\pi\)
0.438923 + 0.898525i \(0.355360\pi\)
\(674\) 39.5658 1.52402
\(675\) −16.4037 −0.631378
\(676\) 93.0840 3.58015
\(677\) 21.1995 0.814762 0.407381 0.913258i \(-0.366442\pi\)
0.407381 + 0.913258i \(0.366442\pi\)
\(678\) 92.0186 3.53395
\(679\) 0 0
\(680\) 0.578586 0.0221878
\(681\) −10.3435 −0.396362
\(682\) −11.0204 −0.421993
\(683\) 33.3840 1.27740 0.638701 0.769455i \(-0.279472\pi\)
0.638701 + 0.769455i \(0.279472\pi\)
\(684\) 68.0172 2.60070
\(685\) 8.93351 0.341332
\(686\) 0 0
\(687\) 19.9521 0.761221
\(688\) 3.04591 0.116124
\(689\) 29.0789 1.10782
\(690\) 47.5946 1.81190
\(691\) 12.0197 0.457251 0.228626 0.973514i \(-0.426577\pi\)
0.228626 + 0.973514i \(0.426577\pi\)
\(692\) −22.6796 −0.862149
\(693\) 0 0
\(694\) −52.2737 −1.98428
\(695\) 0.362168 0.0137378
\(696\) 22.7822 0.863558
\(697\) 2.05441 0.0778165
\(698\) −12.3763 −0.468449
\(699\) 22.6066 0.855061
\(700\) 0 0
\(701\) −7.66738 −0.289593 −0.144796 0.989461i \(-0.546253\pi\)
−0.144796 + 0.989461i \(0.546253\pi\)
\(702\) 242.821 9.16467
\(703\) −2.01469 −0.0759855
\(704\) −63.2776 −2.38486
\(705\) −19.7718 −0.744651
\(706\) −12.4242 −0.467590
\(707\) 0 0
\(708\) 51.6962 1.94286
\(709\) −26.8786 −1.00945 −0.504724 0.863281i \(-0.668406\pi\)
−0.504724 + 0.863281i \(0.668406\pi\)
\(710\) −4.55170 −0.170822
\(711\) 38.5821 1.44694
\(712\) 8.72166 0.326858
\(713\) 6.33498 0.237247
\(714\) 0 0
\(715\) −31.6637 −1.18416
\(716\) 61.2111 2.28757
\(717\) 10.5714 0.394798
\(718\) 24.8741 0.928295
\(719\) −12.3107 −0.459111 −0.229555 0.973296i \(-0.573727\pi\)
−0.229555 + 0.973296i \(0.573727\pi\)
\(720\) −2.93331 −0.109318
\(721\) 0 0
\(722\) −26.4283 −0.983558
\(723\) −41.7043 −1.55100
\(724\) −57.2616 −2.12811
\(725\) −2.63217 −0.0977562
\(726\) −94.4609 −3.50577
\(727\) 44.7359 1.65916 0.829582 0.558386i \(-0.188579\pi\)
0.829582 + 0.558386i \(0.188579\pi\)
\(728\) 0 0
\(729\) 79.1940 2.93311
\(730\) 7.45122 0.275782
\(731\) −1.82791 −0.0676075
\(732\) 149.021 5.50797
\(733\) −12.1879 −0.450170 −0.225085 0.974339i \(-0.572266\pi\)
−0.225085 + 0.974339i \(0.572266\pi\)
\(734\) −61.4179 −2.26698
\(735\) 0 0
\(736\) 38.4326 1.41664
\(737\) −30.1932 −1.11218
\(738\) 167.670 6.17203
\(739\) 24.7887 0.911869 0.455934 0.890013i \(-0.349305\pi\)
0.455934 + 0.890013i \(0.349305\pi\)
\(740\) −2.34132 −0.0860688
\(741\) 58.5486 2.15084
\(742\) 0 0
\(743\) −2.77641 −0.101857 −0.0509284 0.998702i \(-0.516218\pi\)
−0.0509284 + 0.998702i \(0.516218\pi\)
\(744\) 8.65531 0.317319
\(745\) −14.4149 −0.528122
\(746\) −19.8099 −0.725293
\(747\) 47.3282 1.73165
\(748\) 3.38617 0.123811
\(749\) 0 0
\(750\) −7.51299 −0.274336
\(751\) −32.9375 −1.20191 −0.600953 0.799284i \(-0.705212\pi\)
−0.600953 + 0.799284i \(0.705212\pi\)
\(752\) −2.20240 −0.0803133
\(753\) −32.8904 −1.19859
\(754\) 38.9635 1.41897
\(755\) 13.5523 0.493219
\(756\) 0 0
\(757\) 37.3710 1.35827 0.679137 0.734012i \(-0.262354\pi\)
0.679137 + 0.734012i \(0.262354\pi\)
\(758\) −36.9674 −1.34272
\(759\) 101.807 3.69534
\(760\) 7.09249 0.257272
\(761\) −33.3562 −1.20916 −0.604581 0.796543i \(-0.706660\pi\)
−0.604581 + 0.796543i \(0.706660\pi\)
\(762\) −11.8596 −0.429628
\(763\) 0 0
\(764\) −84.3180 −3.05052
\(765\) 1.76033 0.0636450
\(766\) 40.3909 1.45938
\(767\) 32.3145 1.16681
\(768\) 44.8161 1.61716
\(769\) 19.0794 0.688022 0.344011 0.938966i \(-0.388214\pi\)
0.344011 + 0.938966i \(0.388214\pi\)
\(770\) 0 0
\(771\) 20.6047 0.742059
\(772\) −39.7121 −1.42927
\(773\) 17.7851 0.639686 0.319843 0.947471i \(-0.396370\pi\)
0.319843 + 0.947471i \(0.396370\pi\)
\(774\) −149.184 −5.36230
\(775\) −1.00000 −0.0359211
\(776\) 18.5256 0.665029
\(777\) 0 0
\(778\) −60.7129 −2.17666
\(779\) 25.1837 0.902298
\(780\) 68.0409 2.43625
\(781\) −9.73624 −0.348390
\(782\) −3.18159 −0.113773
\(783\) 43.1772 1.54303
\(784\) 0 0
\(785\) −20.0346 −0.715067
\(786\) 79.0584 2.81992
\(787\) 52.5927 1.87473 0.937363 0.348353i \(-0.113259\pi\)
0.937363 + 0.348353i \(0.113259\pi\)
\(788\) −55.3436 −1.97154
\(789\) 15.6756 0.558067
\(790\) 11.0075 0.391630
\(791\) 0 0
\(792\) 101.008 3.58915
\(793\) 93.1507 3.30788
\(794\) −38.6435 −1.37141
\(795\) 14.7586 0.523435
\(796\) −63.9363 −2.26616
\(797\) −47.0498 −1.66659 −0.833295 0.552828i \(-0.813548\pi\)
−0.833295 + 0.552828i \(0.813548\pi\)
\(798\) 0 0
\(799\) 1.32170 0.0467584
\(800\) −6.06673 −0.214491
\(801\) 26.5354 0.937583
\(802\) 17.8953 0.631905
\(803\) 15.9384 0.562454
\(804\) 64.8810 2.28818
\(805\) 0 0
\(806\) 14.8028 0.521407
\(807\) −30.8560 −1.08618
\(808\) −23.2277 −0.817146
\(809\) 33.8768 1.19104 0.595522 0.803339i \(-0.296945\pi\)
0.595522 + 0.803339i \(0.296945\pi\)
\(810\) 69.0658 2.42673
\(811\) 20.0237 0.703127 0.351564 0.936164i \(-0.385650\pi\)
0.351564 + 0.936164i \(0.385650\pi\)
\(812\) 0 0
\(813\) 87.5722 3.07129
\(814\) −8.18589 −0.286915
\(815\) −1.17177 −0.0410454
\(816\) 0.270025 0.00945276
\(817\) −22.4070 −0.783923
\(818\) −42.3479 −1.48066
\(819\) 0 0
\(820\) 29.2666 1.02203
\(821\) −19.2432 −0.671594 −0.335797 0.941934i \(-0.609006\pi\)
−0.335797 + 0.941934i \(0.609006\pi\)
\(822\) −67.1174 −2.34099
\(823\) 25.7054 0.896035 0.448017 0.894025i \(-0.352130\pi\)
0.448017 + 0.894025i \(0.352130\pi\)
\(824\) 2.75741 0.0960589
\(825\) −16.0705 −0.559504
\(826\) 0 0
\(827\) 28.9408 1.00637 0.503186 0.864178i \(-0.332161\pi\)
0.503186 + 0.864178i \(0.332161\pi\)
\(828\) −158.864 −5.52089
\(829\) −44.9817 −1.56228 −0.781140 0.624356i \(-0.785361\pi\)
−0.781140 + 0.624356i \(0.785361\pi\)
\(830\) 13.5028 0.468688
\(831\) −14.3811 −0.498875
\(832\) 84.9957 2.94669
\(833\) 0 0
\(834\) −2.72097 −0.0942194
\(835\) −16.1871 −0.560177
\(836\) 41.5087 1.43561
\(837\) 16.4037 0.566994
\(838\) −27.6613 −0.955542
\(839\) 24.4461 0.843971 0.421986 0.906602i \(-0.361333\pi\)
0.421986 + 0.906602i \(0.361333\pi\)
\(840\) 0 0
\(841\) −22.0717 −0.761093
\(842\) 90.4716 3.11786
\(843\) 98.4601 3.39115
\(844\) −32.5689 −1.12107
\(845\) 29.5313 1.01591
\(846\) 107.870 3.70865
\(847\) 0 0
\(848\) 1.64397 0.0564543
\(849\) −94.6367 −3.24792
\(850\) 0.502225 0.0172262
\(851\) 4.70559 0.161305
\(852\) 20.9218 0.716770
\(853\) 1.57093 0.0537877 0.0268939 0.999638i \(-0.491438\pi\)
0.0268939 + 0.999638i \(0.491438\pi\)
\(854\) 0 0
\(855\) 21.5787 0.737977
\(856\) 23.2041 0.793100
\(857\) −0.0229703 −0.000784650 0 −0.000392325 1.00000i \(-0.500125\pi\)
−0.000392325 1.00000i \(0.500125\pi\)
\(858\) 237.889 8.12140
\(859\) −36.1735 −1.23422 −0.617111 0.786876i \(-0.711697\pi\)
−0.617111 + 0.786876i \(0.711697\pi\)
\(860\) −26.0398 −0.887950
\(861\) 0 0
\(862\) 30.8638 1.05122
\(863\) −14.1974 −0.483286 −0.241643 0.970365i \(-0.577686\pi\)
−0.241643 + 0.970365i \(0.577686\pi\)
\(864\) 99.5167 3.38563
\(865\) −7.19520 −0.244644
\(866\) −18.2750 −0.621010
\(867\) 56.1073 1.90550
\(868\) 0 0
\(869\) 23.5454 0.798725
\(870\) 19.7754 0.670450
\(871\) 40.5561 1.37419
\(872\) 4.73314 0.160284
\(873\) 56.3636 1.90762
\(874\) −39.0009 −1.31922
\(875\) 0 0
\(876\) −34.2494 −1.15718
\(877\) −2.21747 −0.0748787 −0.0374393 0.999299i \(-0.511920\pi\)
−0.0374393 + 0.999299i \(0.511920\pi\)
\(878\) −7.91578 −0.267145
\(879\) −16.7606 −0.565322
\(880\) −1.79011 −0.0603446
\(881\) −34.8836 −1.17526 −0.587629 0.809131i \(-0.699938\pi\)
−0.587629 + 0.809131i \(0.699938\pi\)
\(882\) 0 0
\(883\) −18.0834 −0.608556 −0.304278 0.952583i \(-0.598415\pi\)
−0.304278 + 0.952583i \(0.598415\pi\)
\(884\) −4.54837 −0.152978
\(885\) 16.4008 0.551308
\(886\) −57.2668 −1.92391
\(887\) −45.2723 −1.52009 −0.760047 0.649868i \(-0.774824\pi\)
−0.760047 + 0.649868i \(0.774824\pi\)
\(888\) 6.42912 0.215747
\(889\) 0 0
\(890\) 7.57058 0.253766
\(891\) 147.734 4.94928
\(892\) 92.2761 3.08963
\(893\) 16.2018 0.542173
\(894\) 108.299 3.62207
\(895\) 19.4195 0.649122
\(896\) 0 0
\(897\) −136.748 −4.56590
\(898\) 30.3043 1.01127
\(899\) 2.63217 0.0877877
\(900\) 25.0772 0.835907
\(901\) −0.986579 −0.0328677
\(902\) 102.324 3.40701
\(903\) 0 0
\(904\) −32.0275 −1.06522
\(905\) −18.1665 −0.603874
\(906\) −101.818 −3.38269
\(907\) 35.5609 1.18078 0.590390 0.807118i \(-0.298974\pi\)
0.590390 + 0.807118i \(0.298974\pi\)
\(908\) 9.84998 0.326883
\(909\) −70.6696 −2.34396
\(910\) 0 0
\(911\) −2.54849 −0.0844352 −0.0422176 0.999108i \(-0.513442\pi\)
−0.0422176 + 0.999108i \(0.513442\pi\)
\(912\) 3.31005 0.109607
\(913\) 28.8829 0.955884
\(914\) −31.2775 −1.03457
\(915\) 47.2775 1.56295
\(916\) −19.0002 −0.627785
\(917\) 0 0
\(918\) −8.23834 −0.271906
\(919\) −45.0193 −1.48505 −0.742525 0.669818i \(-0.766372\pi\)
−0.742525 + 0.669818i \(0.766372\pi\)
\(920\) −16.5655 −0.546148
\(921\) −45.6702 −1.50488
\(922\) −28.9790 −0.954373
\(923\) 13.0779 0.430465
\(924\) 0 0
\(925\) −0.742795 −0.0244229
\(926\) 73.6036 2.41877
\(927\) 8.38935 0.275542
\(928\) 15.9686 0.524197
\(929\) 25.9964 0.852913 0.426456 0.904508i \(-0.359762\pi\)
0.426456 + 0.904508i \(0.359762\pi\)
\(930\) 7.51299 0.246361
\(931\) 0 0
\(932\) −21.5281 −0.705176
\(933\) 49.8648 1.63250
\(934\) 28.9419 0.947009
\(935\) 1.07428 0.0351326
\(936\) −135.675 −4.43468
\(937\) −0.921896 −0.0301170 −0.0150585 0.999887i \(-0.504793\pi\)
−0.0150585 + 0.999887i \(0.504793\pi\)
\(938\) 0 0
\(939\) 38.8655 1.26833
\(940\) 18.8285 0.614119
\(941\) 18.4720 0.602170 0.301085 0.953597i \(-0.402651\pi\)
0.301085 + 0.953597i \(0.402651\pi\)
\(942\) 150.520 4.90421
\(943\) −58.8199 −1.91544
\(944\) 1.82690 0.0594606
\(945\) 0 0
\(946\) −91.0421 −2.96004
\(947\) 53.8622 1.75029 0.875143 0.483864i \(-0.160767\pi\)
0.875143 + 0.483864i \(0.160767\pi\)
\(948\) −50.5959 −1.64328
\(949\) −21.4088 −0.694958
\(950\) 6.15643 0.199741
\(951\) −42.3134 −1.37210
\(952\) 0 0
\(953\) −42.5163 −1.37724 −0.688620 0.725123i \(-0.741783\pi\)
−0.688620 + 0.725123i \(0.741783\pi\)
\(954\) −80.5192 −2.60691
\(955\) −26.7503 −0.865618
\(956\) −10.0671 −0.325593
\(957\) 42.3003 1.36738
\(958\) −9.37117 −0.302769
\(959\) 0 0
\(960\) 43.1385 1.39229
\(961\) 1.00000 0.0322581
\(962\) 10.9954 0.354508
\(963\) 70.5979 2.27498
\(964\) 39.7146 1.27912
\(965\) −12.5988 −0.405571
\(966\) 0 0
\(967\) 28.0210 0.901096 0.450548 0.892752i \(-0.351229\pi\)
0.450548 + 0.892752i \(0.351229\pi\)
\(968\) 32.8775 1.05672
\(969\) −1.98642 −0.0638130
\(970\) 16.0806 0.516317
\(971\) 49.7618 1.59693 0.798466 0.602040i \(-0.205645\pi\)
0.798466 + 0.602040i \(0.205645\pi\)
\(972\) −162.345 −5.20721
\(973\) 0 0
\(974\) −31.6727 −1.01486
\(975\) 21.5863 0.691313
\(976\) 5.26628 0.168569
\(977\) 44.8962 1.43636 0.718179 0.695859i \(-0.244976\pi\)
0.718179 + 0.695859i \(0.244976\pi\)
\(978\) 8.80351 0.281505
\(979\) 16.1937 0.517554
\(980\) 0 0
\(981\) 14.4005 0.459771
\(982\) 18.1796 0.580134
\(983\) −46.2226 −1.47427 −0.737136 0.675745i \(-0.763822\pi\)
−0.737136 + 0.675745i \(0.763822\pi\)
\(984\) −80.3641 −2.56191
\(985\) −17.5580 −0.559445
\(986\) −1.32194 −0.0420992
\(987\) 0 0
\(988\) −55.7553 −1.77381
\(989\) 52.3348 1.66415
\(990\) 87.6766 2.78655
\(991\) 49.0442 1.55794 0.778971 0.627060i \(-0.215742\pi\)
0.778971 + 0.627060i \(0.215742\pi\)
\(992\) 6.06673 0.192619
\(993\) 7.67815 0.243659
\(994\) 0 0
\(995\) −20.2841 −0.643048
\(996\) −62.0653 −1.96661
\(997\) −25.3966 −0.804319 −0.402160 0.915570i \(-0.631740\pi\)
−0.402160 + 0.915570i \(0.631740\pi\)
\(998\) −19.3027 −0.611016
\(999\) 12.1846 0.385503
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 7595.2.a.bf.1.20 21
7.3 odd 6 1085.2.j.d.156.2 42
7.5 odd 6 1085.2.j.d.466.2 yes 42
7.6 odd 2 7595.2.a.bg.1.20 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1085.2.j.d.156.2 42 7.3 odd 6
1085.2.j.d.466.2 yes 42 7.5 odd 6
7595.2.a.bf.1.20 21 1.1 even 1 trivial
7595.2.a.bg.1.20 21 7.6 odd 2