Properties

Label 1805.2.a.s.1.9
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $1$
Dimension $9$
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] = [1805,2,Mod(1,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, 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("1805.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.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: \(14.4129975648\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(3.22274\) of defining polynomial
Character \(\chi\) \(=\) 1805.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.22274 q^{2} -1.03700 q^{3} +2.94057 q^{4} +1.00000 q^{5} -2.30498 q^{6} -2.02508 q^{7} +2.09064 q^{8} -1.92463 q^{9} +O(q^{10})\) \(q+2.22274 q^{2} -1.03700 q^{3} +2.94057 q^{4} +1.00000 q^{5} -2.30498 q^{6} -2.02508 q^{7} +2.09064 q^{8} -1.92463 q^{9} +2.22274 q^{10} +0.0848155 q^{11} -3.04938 q^{12} -5.72097 q^{13} -4.50122 q^{14} -1.03700 q^{15} -1.23419 q^{16} -2.53072 q^{17} -4.27795 q^{18} +2.94057 q^{20} +2.10001 q^{21} +0.188523 q^{22} -0.309088 q^{23} -2.16800 q^{24} +1.00000 q^{25} -12.7162 q^{26} +5.10685 q^{27} -5.95489 q^{28} -2.62414 q^{29} -2.30498 q^{30} -8.07278 q^{31} -6.92456 q^{32} -0.0879538 q^{33} -5.62513 q^{34} -2.02508 q^{35} -5.65951 q^{36} +5.01303 q^{37} +5.93265 q^{39} +2.09064 q^{40} +5.88035 q^{41} +4.66777 q^{42} +0.650519 q^{43} +0.249406 q^{44} -1.92463 q^{45} -0.687021 q^{46} +6.90277 q^{47} +1.27985 q^{48} -2.89906 q^{49} +2.22274 q^{50} +2.62436 q^{51} -16.8229 q^{52} -14.5544 q^{53} +11.3512 q^{54} +0.0848155 q^{55} -4.23372 q^{56} -5.83278 q^{58} -7.47335 q^{59} -3.04938 q^{60} +13.3170 q^{61} -17.9437 q^{62} +3.89752 q^{63} -12.9231 q^{64} -5.72097 q^{65} -0.195498 q^{66} -8.88244 q^{67} -7.44175 q^{68} +0.320524 q^{69} -4.50122 q^{70} +14.3366 q^{71} -4.02371 q^{72} +10.8548 q^{73} +11.1426 q^{74} -1.03700 q^{75} -0.171758 q^{77} +13.1867 q^{78} -0.115898 q^{79} -1.23419 q^{80} +0.478079 q^{81} +13.0705 q^{82} -2.97552 q^{83} +6.17523 q^{84} -2.53072 q^{85} +1.44593 q^{86} +2.72124 q^{87} +0.177319 q^{88} +11.1259 q^{89} -4.27795 q^{90} +11.5854 q^{91} -0.908894 q^{92} +8.37148 q^{93} +15.3431 q^{94} +7.18078 q^{96} +0.225903 q^{97} -6.44385 q^{98} -0.163238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.22274 1.57171 0.785857 0.618408i \(-0.212222\pi\)
0.785857 + 0.618408i \(0.212222\pi\)
\(3\) −1.03700 −0.598713 −0.299356 0.954141i \(-0.596772\pi\)
−0.299356 + 0.954141i \(0.596772\pi\)
\(4\) 2.94057 1.47029
\(5\) 1.00000 0.447214
\(6\) −2.30498 −0.941006
\(7\) −2.02508 −0.765408 −0.382704 0.923871i \(-0.625007\pi\)
−0.382704 + 0.923871i \(0.625007\pi\)
\(8\) 2.09064 0.739154
\(9\) −1.92463 −0.641543
\(10\) 2.22274 0.702892
\(11\) 0.0848155 0.0255728 0.0127864 0.999918i \(-0.495930\pi\)
0.0127864 + 0.999918i \(0.495930\pi\)
\(12\) −3.04938 −0.880279
\(13\) −5.72097 −1.58671 −0.793356 0.608758i \(-0.791668\pi\)
−0.793356 + 0.608758i \(0.791668\pi\)
\(14\) −4.50122 −1.20300
\(15\) −1.03700 −0.267753
\(16\) −1.23419 −0.308546
\(17\) −2.53072 −0.613789 −0.306895 0.951743i \(-0.599290\pi\)
−0.306895 + 0.951743i \(0.599290\pi\)
\(18\) −4.27795 −1.00832
\(19\) 0 0
\(20\) 2.94057 0.657532
\(21\) 2.10001 0.458260
\(22\) 0.188523 0.0401932
\(23\) −0.309088 −0.0644492 −0.0322246 0.999481i \(-0.510259\pi\)
−0.0322246 + 0.999481i \(0.510259\pi\)
\(24\) −2.16800 −0.442541
\(25\) 1.00000 0.200000
\(26\) −12.7162 −2.49386
\(27\) 5.10685 0.982813
\(28\) −5.95489 −1.12537
\(29\) −2.62414 −0.487291 −0.243646 0.969864i \(-0.578343\pi\)
−0.243646 + 0.969864i \(0.578343\pi\)
\(30\) −2.30498 −0.420831
\(31\) −8.07278 −1.44991 −0.724957 0.688795i \(-0.758140\pi\)
−0.724957 + 0.688795i \(0.758140\pi\)
\(32\) −6.92456 −1.22410
\(33\) −0.0879538 −0.0153108
\(34\) −5.62513 −0.964701
\(35\) −2.02508 −0.342301
\(36\) −5.65951 −0.943251
\(37\) 5.01303 0.824136 0.412068 0.911153i \(-0.364807\pi\)
0.412068 + 0.911153i \(0.364807\pi\)
\(38\) 0 0
\(39\) 5.93265 0.949985
\(40\) 2.09064 0.330560
\(41\) 5.88035 0.918357 0.459179 0.888344i \(-0.348144\pi\)
0.459179 + 0.888344i \(0.348144\pi\)
\(42\) 4.66777 0.720253
\(43\) 0.650519 0.0992032 0.0496016 0.998769i \(-0.484205\pi\)
0.0496016 + 0.998769i \(0.484205\pi\)
\(44\) 0.249406 0.0375994
\(45\) −1.92463 −0.286907
\(46\) −0.687021 −0.101296
\(47\) 6.90277 1.00687 0.503437 0.864032i \(-0.332069\pi\)
0.503437 + 0.864032i \(0.332069\pi\)
\(48\) 1.27985 0.184731
\(49\) −2.89906 −0.414151
\(50\) 2.22274 0.314343
\(51\) 2.62436 0.367484
\(52\) −16.8229 −2.33292
\(53\) −14.5544 −1.99920 −0.999601 0.0282415i \(-0.991009\pi\)
−0.999601 + 0.0282415i \(0.991009\pi\)
\(54\) 11.3512 1.54470
\(55\) 0.0848155 0.0114365
\(56\) −4.23372 −0.565754
\(57\) 0 0
\(58\) −5.83278 −0.765882
\(59\) −7.47335 −0.972947 −0.486474 0.873695i \(-0.661717\pi\)
−0.486474 + 0.873695i \(0.661717\pi\)
\(60\) −3.04938 −0.393673
\(61\) 13.3170 1.70507 0.852534 0.522672i \(-0.175065\pi\)
0.852534 + 0.522672i \(0.175065\pi\)
\(62\) −17.9437 −2.27885
\(63\) 3.89752 0.491042
\(64\) −12.9231 −1.61539
\(65\) −5.72097 −0.709599
\(66\) −0.195498 −0.0240642
\(67\) −8.88244 −1.08516 −0.542582 0.840003i \(-0.682553\pi\)
−0.542582 + 0.840003i \(0.682553\pi\)
\(68\) −7.44175 −0.902445
\(69\) 0.320524 0.0385866
\(70\) −4.50122 −0.537999
\(71\) 14.3366 1.70144 0.850719 0.525620i \(-0.176167\pi\)
0.850719 + 0.525620i \(0.176167\pi\)
\(72\) −4.02371 −0.474199
\(73\) 10.8548 1.27046 0.635229 0.772324i \(-0.280906\pi\)
0.635229 + 0.772324i \(0.280906\pi\)
\(74\) 11.1426 1.29531
\(75\) −1.03700 −0.119743
\(76\) 0 0
\(77\) −0.171758 −0.0195737
\(78\) 13.1867 1.49310
\(79\) −0.115898 −0.0130395 −0.00651976 0.999979i \(-0.502075\pi\)
−0.00651976 + 0.999979i \(0.502075\pi\)
\(80\) −1.23419 −0.137986
\(81\) 0.478079 0.0531198
\(82\) 13.0705 1.44339
\(83\) −2.97552 −0.326606 −0.163303 0.986576i \(-0.552215\pi\)
−0.163303 + 0.986576i \(0.552215\pi\)
\(84\) 6.17523 0.673772
\(85\) −2.53072 −0.274495
\(86\) 1.44593 0.155919
\(87\) 2.72124 0.291747
\(88\) 0.177319 0.0189023
\(89\) 11.1259 1.17934 0.589670 0.807644i \(-0.299258\pi\)
0.589670 + 0.807644i \(0.299258\pi\)
\(90\) −4.27795 −0.450935
\(91\) 11.5854 1.21448
\(92\) −0.908894 −0.0947587
\(93\) 8.37148 0.868082
\(94\) 15.3431 1.58252
\(95\) 0 0
\(96\) 7.18078 0.732885
\(97\) 0.225903 0.0229370 0.0114685 0.999934i \(-0.496349\pi\)
0.0114685 + 0.999934i \(0.496349\pi\)
\(98\) −6.44385 −0.650927
\(99\) −0.163238 −0.0164061
\(100\) 2.94057 0.294057
\(101\) −12.6014 −1.25388 −0.626942 0.779066i \(-0.715694\pi\)
−0.626942 + 0.779066i \(0.715694\pi\)
\(102\) 5.83326 0.577579
\(103\) −17.7230 −1.74630 −0.873152 0.487448i \(-0.837928\pi\)
−0.873152 + 0.487448i \(0.837928\pi\)
\(104\) −11.9605 −1.17282
\(105\) 2.10001 0.204940
\(106\) −32.3507 −3.14217
\(107\) −5.09612 −0.492661 −0.246330 0.969186i \(-0.579225\pi\)
−0.246330 + 0.969186i \(0.579225\pi\)
\(108\) 15.0170 1.44502
\(109\) 6.13513 0.587639 0.293819 0.955861i \(-0.405074\pi\)
0.293819 + 0.955861i \(0.405074\pi\)
\(110\) 0.188523 0.0179749
\(111\) −5.19851 −0.493421
\(112\) 2.49932 0.236164
\(113\) −11.4316 −1.07539 −0.537697 0.843138i \(-0.680706\pi\)
−0.537697 + 0.843138i \(0.680706\pi\)
\(114\) 0 0
\(115\) −0.309088 −0.0288226
\(116\) −7.71648 −0.716457
\(117\) 11.0107 1.01794
\(118\) −16.6113 −1.52919
\(119\) 5.12490 0.469799
\(120\) −2.16800 −0.197910
\(121\) −10.9928 −0.999346
\(122\) 29.6002 2.67988
\(123\) −6.09794 −0.549832
\(124\) −23.7386 −2.13179
\(125\) 1.00000 0.0894427
\(126\) 8.66318 0.771777
\(127\) 1.43978 0.127760 0.0638799 0.997958i \(-0.479653\pi\)
0.0638799 + 0.997958i \(0.479653\pi\)
\(128\) −14.8756 −1.31483
\(129\) −0.674589 −0.0593942
\(130\) −12.7162 −1.11529
\(131\) −1.00345 −0.0876720 −0.0438360 0.999039i \(-0.513958\pi\)
−0.0438360 + 0.999039i \(0.513958\pi\)
\(132\) −0.258634 −0.0225112
\(133\) 0 0
\(134\) −19.7434 −1.70557
\(135\) 5.10685 0.439527
\(136\) −5.29083 −0.453685
\(137\) −10.4468 −0.892530 −0.446265 0.894901i \(-0.647246\pi\)
−0.446265 + 0.894901i \(0.647246\pi\)
\(138\) 0.712442 0.0606471
\(139\) 10.6846 0.906256 0.453128 0.891445i \(-0.350308\pi\)
0.453128 + 0.891445i \(0.350308\pi\)
\(140\) −5.95489 −0.503280
\(141\) −7.15819 −0.602828
\(142\) 31.8665 2.67417
\(143\) −0.485227 −0.0405767
\(144\) 2.37535 0.197946
\(145\) −2.62414 −0.217923
\(146\) 24.1274 1.99680
\(147\) 3.00632 0.247957
\(148\) 14.7412 1.21172
\(149\) −5.04462 −0.413271 −0.206636 0.978418i \(-0.566251\pi\)
−0.206636 + 0.978418i \(0.566251\pi\)
\(150\) −2.30498 −0.188201
\(151\) −20.8114 −1.69360 −0.846802 0.531909i \(-0.821475\pi\)
−0.846802 + 0.531909i \(0.821475\pi\)
\(152\) 0 0
\(153\) 4.87069 0.393772
\(154\) −0.381774 −0.0307642
\(155\) −8.07278 −0.648421
\(156\) 17.4454 1.39675
\(157\) 23.6158 1.88475 0.942374 0.334561i \(-0.108588\pi\)
0.942374 + 0.334561i \(0.108588\pi\)
\(158\) −0.257611 −0.0204944
\(159\) 15.0929 1.19695
\(160\) −6.92456 −0.547435
\(161\) 0.625927 0.0493299
\(162\) 1.06264 0.0834892
\(163\) −0.213533 −0.0167252 −0.00836258 0.999965i \(-0.502662\pi\)
−0.00836258 + 0.999965i \(0.502662\pi\)
\(164\) 17.2916 1.35025
\(165\) −0.0879538 −0.00684719
\(166\) −6.61382 −0.513332
\(167\) −19.7249 −1.52636 −0.763178 0.646188i \(-0.776362\pi\)
−0.763178 + 0.646188i \(0.776362\pi\)
\(168\) 4.39037 0.338724
\(169\) 19.7295 1.51765
\(170\) −5.62513 −0.431428
\(171\) 0 0
\(172\) 1.91290 0.145857
\(173\) −12.5749 −0.956051 −0.478026 0.878346i \(-0.658647\pi\)
−0.478026 + 0.878346i \(0.658647\pi\)
\(174\) 6.04861 0.458544
\(175\) −2.02508 −0.153082
\(176\) −0.104678 −0.00789041
\(177\) 7.74987 0.582516
\(178\) 24.7299 1.85358
\(179\) 10.8183 0.808596 0.404298 0.914627i \(-0.367516\pi\)
0.404298 + 0.914627i \(0.367516\pi\)
\(180\) −5.65951 −0.421835
\(181\) 5.41191 0.402264 0.201132 0.979564i \(-0.435538\pi\)
0.201132 + 0.979564i \(0.435538\pi\)
\(182\) 25.7514 1.90882
\(183\) −13.8098 −1.02085
\(184\) −0.646192 −0.0476379
\(185\) 5.01303 0.368565
\(186\) 18.6076 1.36438
\(187\) −0.214644 −0.0156963
\(188\) 20.2981 1.48039
\(189\) −10.3418 −0.752253
\(190\) 0 0
\(191\) 4.87144 0.352485 0.176243 0.984347i \(-0.443606\pi\)
0.176243 + 0.984347i \(0.443606\pi\)
\(192\) 13.4013 0.967155
\(193\) 1.38414 0.0996323 0.0498162 0.998758i \(-0.484136\pi\)
0.0498162 + 0.998758i \(0.484136\pi\)
\(194\) 0.502123 0.0360503
\(195\) 5.93265 0.424846
\(196\) −8.52488 −0.608920
\(197\) 6.40750 0.456515 0.228258 0.973601i \(-0.426697\pi\)
0.228258 + 0.973601i \(0.426697\pi\)
\(198\) −0.362836 −0.0257857
\(199\) 15.6405 1.10873 0.554363 0.832275i \(-0.312962\pi\)
0.554363 + 0.832275i \(0.312962\pi\)
\(200\) 2.09064 0.147831
\(201\) 9.21111 0.649701
\(202\) −28.0096 −1.97075
\(203\) 5.31410 0.372976
\(204\) 7.71711 0.540306
\(205\) 5.88035 0.410702
\(206\) −39.3937 −2.74469
\(207\) 0.594879 0.0413469
\(208\) 7.06074 0.489574
\(209\) 0 0
\(210\) 4.66777 0.322107
\(211\) −7.68384 −0.528978 −0.264489 0.964389i \(-0.585203\pi\)
−0.264489 + 0.964389i \(0.585203\pi\)
\(212\) −42.7983 −2.93940
\(213\) −14.8670 −1.01867
\(214\) −11.3274 −0.774322
\(215\) 0.650519 0.0443650
\(216\) 10.6766 0.726450
\(217\) 16.3480 1.10977
\(218\) 13.6368 0.923600
\(219\) −11.2564 −0.760640
\(220\) 0.249406 0.0168149
\(221\) 14.4782 0.973906
\(222\) −11.5549 −0.775517
\(223\) −2.47996 −0.166070 −0.0830351 0.996547i \(-0.526461\pi\)
−0.0830351 + 0.996547i \(0.526461\pi\)
\(224\) 14.0228 0.936936
\(225\) −1.92463 −0.128309
\(226\) −25.4095 −1.69021
\(227\) 0.453554 0.0301034 0.0150517 0.999887i \(-0.495209\pi\)
0.0150517 + 0.999887i \(0.495209\pi\)
\(228\) 0 0
\(229\) 0.993282 0.0656379 0.0328190 0.999461i \(-0.489552\pi\)
0.0328190 + 0.999461i \(0.489552\pi\)
\(230\) −0.687021 −0.0453008
\(231\) 0.178113 0.0117190
\(232\) −5.48615 −0.360183
\(233\) −4.26321 −0.279292 −0.139646 0.990201i \(-0.544597\pi\)
−0.139646 + 0.990201i \(0.544597\pi\)
\(234\) 24.4740 1.59992
\(235\) 6.90277 0.450287
\(236\) −21.9759 −1.43051
\(237\) 0.120186 0.00780693
\(238\) 11.3913 0.738390
\(239\) 24.4583 1.58207 0.791037 0.611768i \(-0.209541\pi\)
0.791037 + 0.611768i \(0.209541\pi\)
\(240\) 1.27985 0.0826141
\(241\) −4.39485 −0.283097 −0.141548 0.989931i \(-0.545208\pi\)
−0.141548 + 0.989931i \(0.545208\pi\)
\(242\) −24.4341 −1.57069
\(243\) −15.8163 −1.01462
\(244\) 39.1596 2.50694
\(245\) −2.89906 −0.185214
\(246\) −13.5541 −0.864179
\(247\) 0 0
\(248\) −16.8773 −1.07171
\(249\) 3.08562 0.195543
\(250\) 2.22274 0.140578
\(251\) −0.387468 −0.0244568 −0.0122284 0.999925i \(-0.503893\pi\)
−0.0122284 + 0.999925i \(0.503893\pi\)
\(252\) 11.4609 0.721972
\(253\) −0.0262154 −0.00164815
\(254\) 3.20025 0.200802
\(255\) 2.62436 0.164344
\(256\) −7.21836 −0.451148
\(257\) 2.85296 0.177963 0.0889814 0.996033i \(-0.471639\pi\)
0.0889814 + 0.996033i \(0.471639\pi\)
\(258\) −1.49944 −0.0933508
\(259\) −10.1518 −0.630800
\(260\) −16.8229 −1.04331
\(261\) 5.05050 0.312618
\(262\) −2.23041 −0.137795
\(263\) −10.8075 −0.666417 −0.333209 0.942853i \(-0.608131\pi\)
−0.333209 + 0.942853i \(0.608131\pi\)
\(264\) −0.183880 −0.0113170
\(265\) −14.5544 −0.894070
\(266\) 0 0
\(267\) −11.5375 −0.706086
\(268\) −26.1195 −1.59550
\(269\) −2.77764 −0.169356 −0.0846780 0.996408i \(-0.526986\pi\)
−0.0846780 + 0.996408i \(0.526986\pi\)
\(270\) 11.3512 0.690811
\(271\) 14.8624 0.902828 0.451414 0.892315i \(-0.350920\pi\)
0.451414 + 0.892315i \(0.350920\pi\)
\(272\) 3.12338 0.189382
\(273\) −12.0141 −0.727126
\(274\) −23.2205 −1.40280
\(275\) 0.0848155 0.00511457
\(276\) 0.942524 0.0567333
\(277\) 18.0876 1.08678 0.543389 0.839481i \(-0.317141\pi\)
0.543389 + 0.839481i \(0.317141\pi\)
\(278\) 23.7491 1.42438
\(279\) 15.5371 0.930181
\(280\) −4.23372 −0.253013
\(281\) 3.88426 0.231716 0.115858 0.993266i \(-0.463038\pi\)
0.115858 + 0.993266i \(0.463038\pi\)
\(282\) −15.9108 −0.947473
\(283\) −22.2860 −1.32477 −0.662383 0.749165i \(-0.730455\pi\)
−0.662383 + 0.749165i \(0.730455\pi\)
\(284\) 42.1577 2.50160
\(285\) 0 0
\(286\) −1.07853 −0.0637750
\(287\) −11.9082 −0.702918
\(288\) 13.3272 0.785313
\(289\) −10.5955 −0.623263
\(290\) −5.83278 −0.342513
\(291\) −0.234262 −0.0137327
\(292\) 31.9193 1.86794
\(293\) 24.4514 1.42846 0.714232 0.699909i \(-0.246776\pi\)
0.714232 + 0.699909i \(0.246776\pi\)
\(294\) 6.68228 0.389718
\(295\) −7.47335 −0.435115
\(296\) 10.4804 0.609164
\(297\) 0.433140 0.0251333
\(298\) −11.2129 −0.649544
\(299\) 1.76828 0.102262
\(300\) −3.04938 −0.176056
\(301\) −1.31735 −0.0759309
\(302\) −46.2582 −2.66186
\(303\) 13.0676 0.750717
\(304\) 0 0
\(305\) 13.3170 0.762529
\(306\) 10.8263 0.618897
\(307\) −6.42519 −0.366705 −0.183353 0.983047i \(-0.558695\pi\)
−0.183353 + 0.983047i \(0.558695\pi\)
\(308\) −0.505067 −0.0287789
\(309\) 18.3788 1.04553
\(310\) −17.9437 −1.01913
\(311\) −17.5640 −0.995963 −0.497982 0.867188i \(-0.665925\pi\)
−0.497982 + 0.867188i \(0.665925\pi\)
\(312\) 12.4031 0.702185
\(313\) −3.64359 −0.205948 −0.102974 0.994684i \(-0.532836\pi\)
−0.102974 + 0.994684i \(0.532836\pi\)
\(314\) 52.4918 2.96228
\(315\) 3.89752 0.219601
\(316\) −0.340806 −0.0191718
\(317\) −4.49901 −0.252689 −0.126345 0.991986i \(-0.540325\pi\)
−0.126345 + 0.991986i \(0.540325\pi\)
\(318\) 33.5477 1.88126
\(319\) −0.222568 −0.0124614
\(320\) −12.9231 −0.722424
\(321\) 5.28469 0.294962
\(322\) 1.39127 0.0775325
\(323\) 0 0
\(324\) 1.40582 0.0781013
\(325\) −5.72097 −0.317342
\(326\) −0.474627 −0.0262872
\(327\) −6.36214 −0.351827
\(328\) 12.2937 0.678807
\(329\) −13.9787 −0.770669
\(330\) −0.195498 −0.0107618
\(331\) −34.1003 −1.87432 −0.937161 0.348898i \(-0.886556\pi\)
−0.937161 + 0.348898i \(0.886556\pi\)
\(332\) −8.74974 −0.480204
\(333\) −9.64821 −0.528719
\(334\) −43.8433 −2.39900
\(335\) −8.88244 −0.485300
\(336\) −2.59180 −0.141394
\(337\) 0.968932 0.0527811 0.0263905 0.999652i \(-0.491599\pi\)
0.0263905 + 0.999652i \(0.491599\pi\)
\(338\) 43.8535 2.38532
\(339\) 11.8546 0.643852
\(340\) −7.44175 −0.403586
\(341\) −0.684697 −0.0370784
\(342\) 0 0
\(343\) 20.0464 1.08240
\(344\) 1.36000 0.0733264
\(345\) 0.320524 0.0172564
\(346\) −27.9507 −1.50264
\(347\) −23.5064 −1.26189 −0.630945 0.775827i \(-0.717333\pi\)
−0.630945 + 0.775827i \(0.717333\pi\)
\(348\) 8.00200 0.428952
\(349\) 19.4375 1.04047 0.520234 0.854024i \(-0.325845\pi\)
0.520234 + 0.854024i \(0.325845\pi\)
\(350\) −4.50122 −0.240600
\(351\) −29.2161 −1.55944
\(352\) −0.587310 −0.0313037
\(353\) −11.9646 −0.636814 −0.318407 0.947954i \(-0.603148\pi\)
−0.318407 + 0.947954i \(0.603148\pi\)
\(354\) 17.2259 0.915549
\(355\) 14.3366 0.760906
\(356\) 32.7164 1.73397
\(357\) −5.31453 −0.281275
\(358\) 24.0462 1.27088
\(359\) 17.1901 0.907256 0.453628 0.891191i \(-0.350129\pi\)
0.453628 + 0.891191i \(0.350129\pi\)
\(360\) −4.02371 −0.212068
\(361\) 0 0
\(362\) 12.0293 0.632244
\(363\) 11.3996 0.598321
\(364\) 34.0677 1.78563
\(365\) 10.8548 0.568166
\(366\) −30.6955 −1.60448
\(367\) −17.6232 −0.919924 −0.459962 0.887938i \(-0.652137\pi\)
−0.459962 + 0.887938i \(0.652137\pi\)
\(368\) 0.381471 0.0198856
\(369\) −11.3175 −0.589165
\(370\) 11.1426 0.579279
\(371\) 29.4738 1.53021
\(372\) 24.6169 1.27633
\(373\) 2.65476 0.137458 0.0687292 0.997635i \(-0.478106\pi\)
0.0687292 + 0.997635i \(0.478106\pi\)
\(374\) −0.477098 −0.0246701
\(375\) −1.03700 −0.0535505
\(376\) 14.4312 0.744234
\(377\) 15.0126 0.773190
\(378\) −22.9871 −1.18233
\(379\) 18.9795 0.974909 0.487455 0.873148i \(-0.337925\pi\)
0.487455 + 0.873148i \(0.337925\pi\)
\(380\) 0 0
\(381\) −1.49305 −0.0764914
\(382\) 10.8279 0.554006
\(383\) 11.9285 0.609519 0.304759 0.952429i \(-0.401424\pi\)
0.304759 + 0.952429i \(0.401424\pi\)
\(384\) 15.4260 0.787206
\(385\) −0.171758 −0.00875360
\(386\) 3.07657 0.156594
\(387\) −1.25201 −0.0636431
\(388\) 0.664283 0.0337239
\(389\) −9.76564 −0.495138 −0.247569 0.968870i \(-0.579632\pi\)
−0.247569 + 0.968870i \(0.579632\pi\)
\(390\) 13.1867 0.667737
\(391\) 0.782213 0.0395582
\(392\) −6.06089 −0.306121
\(393\) 1.04058 0.0524903
\(394\) 14.2422 0.717512
\(395\) −0.115898 −0.00583145
\(396\) −0.480014 −0.0241216
\(397\) 28.8426 1.44757 0.723784 0.690026i \(-0.242401\pi\)
0.723784 + 0.690026i \(0.242401\pi\)
\(398\) 34.7648 1.74260
\(399\) 0 0
\(400\) −1.23419 −0.0617093
\(401\) −6.27130 −0.313174 −0.156587 0.987664i \(-0.550049\pi\)
−0.156587 + 0.987664i \(0.550049\pi\)
\(402\) 20.4739 1.02114
\(403\) 46.1841 2.30059
\(404\) −37.0552 −1.84357
\(405\) 0.478079 0.0237559
\(406\) 11.8118 0.586212
\(407\) 0.425182 0.0210755
\(408\) 5.48660 0.271627
\(409\) −11.2239 −0.554988 −0.277494 0.960727i \(-0.589504\pi\)
−0.277494 + 0.960727i \(0.589504\pi\)
\(410\) 13.0705 0.645506
\(411\) 10.8333 0.534369
\(412\) −52.1159 −2.56756
\(413\) 15.1341 0.744701
\(414\) 1.32226 0.0649855
\(415\) −2.97552 −0.146063
\(416\) 39.6152 1.94229
\(417\) −11.0800 −0.542588
\(418\) 0 0
\(419\) −26.0754 −1.27387 −0.636934 0.770918i \(-0.719798\pi\)
−0.636934 + 0.770918i \(0.719798\pi\)
\(420\) 6.17523 0.301320
\(421\) 25.2605 1.23112 0.615562 0.788089i \(-0.288929\pi\)
0.615562 + 0.788089i \(0.288929\pi\)
\(422\) −17.0792 −0.831401
\(423\) −13.2853 −0.645952
\(424\) −30.4281 −1.47772
\(425\) −2.53072 −0.122758
\(426\) −33.0456 −1.60106
\(427\) −26.9680 −1.30507
\(428\) −14.9855 −0.724352
\(429\) 0.503181 0.0242938
\(430\) 1.44593 0.0697291
\(431\) −38.1890 −1.83950 −0.919749 0.392508i \(-0.871608\pi\)
−0.919749 + 0.392508i \(0.871608\pi\)
\(432\) −6.30280 −0.303243
\(433\) −2.62102 −0.125958 −0.0629792 0.998015i \(-0.520060\pi\)
−0.0629792 + 0.998015i \(0.520060\pi\)
\(434\) 36.3374 1.74425
\(435\) 2.72124 0.130473
\(436\) 18.0408 0.863997
\(437\) 0 0
\(438\) −25.0201 −1.19551
\(439\) −6.71666 −0.320569 −0.160284 0.987071i \(-0.551241\pi\)
−0.160284 + 0.987071i \(0.551241\pi\)
\(440\) 0.177319 0.00845335
\(441\) 5.57960 0.265695
\(442\) 32.1812 1.53070
\(443\) −26.0060 −1.23558 −0.617791 0.786342i \(-0.711972\pi\)
−0.617791 + 0.786342i \(0.711972\pi\)
\(444\) −15.2866 −0.725470
\(445\) 11.1259 0.527417
\(446\) −5.51230 −0.261015
\(447\) 5.23127 0.247431
\(448\) 26.1703 1.23643
\(449\) 27.5720 1.30120 0.650602 0.759419i \(-0.274517\pi\)
0.650602 + 0.759419i \(0.274517\pi\)
\(450\) −4.27795 −0.201664
\(451\) 0.498745 0.0234850
\(452\) −33.6154 −1.58114
\(453\) 21.5814 1.01398
\(454\) 1.00813 0.0473139
\(455\) 11.5854 0.543133
\(456\) 0 0
\(457\) 2.22524 0.104092 0.0520462 0.998645i \(-0.483426\pi\)
0.0520462 + 0.998645i \(0.483426\pi\)
\(458\) 2.20781 0.103164
\(459\) −12.9240 −0.603240
\(460\) −0.908894 −0.0423774
\(461\) 20.4553 0.952698 0.476349 0.879256i \(-0.341960\pi\)
0.476349 + 0.879256i \(0.341960\pi\)
\(462\) 0.395900 0.0184189
\(463\) −32.4300 −1.50715 −0.753575 0.657362i \(-0.771672\pi\)
−0.753575 + 0.657362i \(0.771672\pi\)
\(464\) 3.23868 0.150352
\(465\) 8.37148 0.388218
\(466\) −9.47601 −0.438968
\(467\) −6.92098 −0.320265 −0.160132 0.987096i \(-0.551192\pi\)
−0.160132 + 0.987096i \(0.551192\pi\)
\(468\) 32.3779 1.49667
\(469\) 17.9876 0.830592
\(470\) 15.3431 0.707723
\(471\) −24.4896 −1.12842
\(472\) −15.6241 −0.719158
\(473\) 0.0551741 0.00253691
\(474\) 0.267143 0.0122703
\(475\) 0 0
\(476\) 15.0701 0.690739
\(477\) 28.0118 1.28257
\(478\) 54.3644 2.48657
\(479\) −20.0438 −0.915825 −0.457913 0.888997i \(-0.651403\pi\)
−0.457913 + 0.888997i \(0.651403\pi\)
\(480\) 7.18078 0.327756
\(481\) −28.6794 −1.30767
\(482\) −9.76860 −0.444947
\(483\) −0.649087 −0.0295345
\(484\) −32.3251 −1.46932
\(485\) 0.225903 0.0102577
\(486\) −35.1555 −1.59469
\(487\) −7.12927 −0.323058 −0.161529 0.986868i \(-0.551643\pi\)
−0.161529 + 0.986868i \(0.551643\pi\)
\(488\) 27.8411 1.26031
\(489\) 0.221434 0.0100136
\(490\) −6.44385 −0.291103
\(491\) 16.5051 0.744865 0.372433 0.928059i \(-0.378524\pi\)
0.372433 + 0.928059i \(0.378524\pi\)
\(492\) −17.9314 −0.808410
\(493\) 6.64096 0.299094
\(494\) 0 0
\(495\) −0.163238 −0.00733702
\(496\) 9.96330 0.447366
\(497\) −29.0327 −1.30229
\(498\) 6.85854 0.307338
\(499\) −30.3605 −1.35912 −0.679562 0.733618i \(-0.737830\pi\)
−0.679562 + 0.733618i \(0.737830\pi\)
\(500\) 2.94057 0.131506
\(501\) 20.4547 0.913850
\(502\) −0.861241 −0.0384390
\(503\) −5.76940 −0.257245 −0.128622 0.991694i \(-0.541056\pi\)
−0.128622 + 0.991694i \(0.541056\pi\)
\(504\) 8.14833 0.362956
\(505\) −12.6014 −0.560754
\(506\) −0.0582700 −0.00259042
\(507\) −20.4595 −0.908639
\(508\) 4.23377 0.187843
\(509\) 38.8654 1.72268 0.861340 0.508029i \(-0.169626\pi\)
0.861340 + 0.508029i \(0.169626\pi\)
\(510\) 5.83326 0.258301
\(511\) −21.9818 −0.972418
\(512\) 13.7067 0.605755
\(513\) 0 0
\(514\) 6.34139 0.279707
\(515\) −17.7230 −0.780971
\(516\) −1.98368 −0.0873265
\(517\) 0.585462 0.0257486
\(518\) −22.5647 −0.991438
\(519\) 13.0402 0.572400
\(520\) −11.9605 −0.524503
\(521\) 36.5105 1.59956 0.799778 0.600296i \(-0.204951\pi\)
0.799778 + 0.600296i \(0.204951\pi\)
\(522\) 11.2259 0.491346
\(523\) −27.8101 −1.21605 −0.608025 0.793918i \(-0.708038\pi\)
−0.608025 + 0.793918i \(0.708038\pi\)
\(524\) −2.95072 −0.128903
\(525\) 2.10001 0.0916519
\(526\) −24.0222 −1.04742
\(527\) 20.4299 0.889941
\(528\) 0.108551 0.00472409
\(529\) −22.9045 −0.995846
\(530\) −32.3507 −1.40522
\(531\) 14.3834 0.624187
\(532\) 0 0
\(533\) −33.6413 −1.45717
\(534\) −25.6449 −1.10977
\(535\) −5.09612 −0.220325
\(536\) −18.5700 −0.802103
\(537\) −11.2186 −0.484117
\(538\) −6.17398 −0.266179
\(539\) −0.245885 −0.0105910
\(540\) 15.0170 0.646231
\(541\) −24.2484 −1.04252 −0.521261 0.853398i \(-0.674538\pi\)
−0.521261 + 0.853398i \(0.674538\pi\)
\(542\) 33.0353 1.41899
\(543\) −5.61216 −0.240841
\(544\) 17.5241 0.751340
\(545\) 6.13513 0.262800
\(546\) −26.7042 −1.14283
\(547\) 0.591692 0.0252989 0.0126495 0.999920i \(-0.495973\pi\)
0.0126495 + 0.999920i \(0.495973\pi\)
\(548\) −30.7195 −1.31227
\(549\) −25.6303 −1.09387
\(550\) 0.188523 0.00803864
\(551\) 0 0
\(552\) 0.670102 0.0285214
\(553\) 0.234702 0.00998056
\(554\) 40.2040 1.70810
\(555\) −5.19851 −0.220665
\(556\) 31.4188 1.33246
\(557\) −24.7130 −1.04712 −0.523561 0.851988i \(-0.675397\pi\)
−0.523561 + 0.851988i \(0.675397\pi\)
\(558\) 34.5349 1.46198
\(559\) −3.72160 −0.157407
\(560\) 2.49932 0.105616
\(561\) 0.222586 0.00939760
\(562\) 8.63370 0.364191
\(563\) −11.9955 −0.505550 −0.252775 0.967525i \(-0.581343\pi\)
−0.252775 + 0.967525i \(0.581343\pi\)
\(564\) −21.0492 −0.886329
\(565\) −11.4316 −0.480931
\(566\) −49.5360 −2.08215
\(567\) −0.968147 −0.0406583
\(568\) 29.9727 1.25763
\(569\) −33.9446 −1.42303 −0.711517 0.702669i \(-0.751991\pi\)
−0.711517 + 0.702669i \(0.751991\pi\)
\(570\) 0 0
\(571\) −3.81177 −0.159518 −0.0797588 0.996814i \(-0.525415\pi\)
−0.0797588 + 0.996814i \(0.525415\pi\)
\(572\) −1.42684 −0.0596594
\(573\) −5.05169 −0.211038
\(574\) −26.4688 −1.10479
\(575\) −0.309088 −0.0128898
\(576\) 24.8722 1.03634
\(577\) 1.65440 0.0688734 0.0344367 0.999407i \(-0.489036\pi\)
0.0344367 + 0.999407i \(0.489036\pi\)
\(578\) −23.5510 −0.979591
\(579\) −1.43535 −0.0596512
\(580\) −7.71648 −0.320409
\(581\) 6.02567 0.249987
\(582\) −0.520702 −0.0215838
\(583\) −1.23444 −0.0511253
\(584\) 22.6935 0.939064
\(585\) 11.0107 0.455238
\(586\) 54.3490 2.24514
\(587\) −29.4152 −1.21409 −0.607047 0.794666i \(-0.707646\pi\)
−0.607047 + 0.794666i \(0.707646\pi\)
\(588\) 8.84031 0.364568
\(589\) 0 0
\(590\) −16.6113 −0.683877
\(591\) −6.64458 −0.273322
\(592\) −6.18700 −0.254284
\(593\) 46.8254 1.92289 0.961445 0.274998i \(-0.0886770\pi\)
0.961445 + 0.274998i \(0.0886770\pi\)
\(594\) 0.962757 0.0395024
\(595\) 5.12490 0.210101
\(596\) −14.8340 −0.607626
\(597\) −16.2192 −0.663808
\(598\) 3.93043 0.160727
\(599\) −12.1717 −0.497321 −0.248660 0.968591i \(-0.579990\pi\)
−0.248660 + 0.968591i \(0.579990\pi\)
\(600\) −2.16800 −0.0885082
\(601\) −10.0391 −0.409504 −0.204752 0.978814i \(-0.565639\pi\)
−0.204752 + 0.978814i \(0.565639\pi\)
\(602\) −2.92813 −0.119342
\(603\) 17.0954 0.696179
\(604\) −61.1972 −2.49008
\(605\) −10.9928 −0.446921
\(606\) 29.0460 1.17991
\(607\) −20.5318 −0.833358 −0.416679 0.909054i \(-0.636806\pi\)
−0.416679 + 0.909054i \(0.636806\pi\)
\(608\) 0 0
\(609\) −5.51072 −0.223306
\(610\) 29.6002 1.19848
\(611\) −39.4906 −1.59762
\(612\) 14.3226 0.578957
\(613\) −36.4730 −1.47313 −0.736565 0.676367i \(-0.763553\pi\)
−0.736565 + 0.676367i \(0.763553\pi\)
\(614\) −14.2815 −0.576356
\(615\) −6.09794 −0.245893
\(616\) −0.359085 −0.0144679
\(617\) 21.4068 0.861805 0.430903 0.902398i \(-0.358195\pi\)
0.430903 + 0.902398i \(0.358195\pi\)
\(618\) 40.8513 1.64328
\(619\) −15.3752 −0.617981 −0.308991 0.951065i \(-0.599991\pi\)
−0.308991 + 0.951065i \(0.599991\pi\)
\(620\) −23.7386 −0.953364
\(621\) −1.57846 −0.0633415
\(622\) −39.0402 −1.56537
\(623\) −22.5308 −0.902676
\(624\) −7.32200 −0.293114
\(625\) 1.00000 0.0400000
\(626\) −8.09876 −0.323691
\(627\) 0 0
\(628\) 69.4440 2.77112
\(629\) −12.6866 −0.505846
\(630\) 8.66318 0.345149
\(631\) −29.7129 −1.18285 −0.591426 0.806359i \(-0.701435\pi\)
−0.591426 + 0.806359i \(0.701435\pi\)
\(632\) −0.242301 −0.00963822
\(633\) 7.96816 0.316706
\(634\) −10.0001 −0.397156
\(635\) 1.43978 0.0571359
\(636\) 44.3819 1.75986
\(637\) 16.5854 0.657138
\(638\) −0.494711 −0.0195858
\(639\) −27.5926 −1.09155
\(640\) −14.8756 −0.588010
\(641\) −19.1099 −0.754795 −0.377398 0.926051i \(-0.623181\pi\)
−0.377398 + 0.926051i \(0.623181\pi\)
\(642\) 11.7465 0.463597
\(643\) 16.2284 0.639984 0.319992 0.947420i \(-0.396320\pi\)
0.319992 + 0.947420i \(0.396320\pi\)
\(644\) 1.84058 0.0725291
\(645\) −0.674589 −0.0265619
\(646\) 0 0
\(647\) 26.6353 1.04714 0.523571 0.851982i \(-0.324600\pi\)
0.523571 + 0.851982i \(0.324600\pi\)
\(648\) 0.999492 0.0392637
\(649\) −0.633856 −0.0248810
\(650\) −12.7162 −0.498771
\(651\) −16.9529 −0.664437
\(652\) −0.627908 −0.0245908
\(653\) −40.8476 −1.59849 −0.799245 0.601005i \(-0.794767\pi\)
−0.799245 + 0.601005i \(0.794767\pi\)
\(654\) −14.1414 −0.552972
\(655\) −1.00345 −0.0392081
\(656\) −7.25745 −0.283356
\(657\) −20.8914 −0.815053
\(658\) −31.0709 −1.21127
\(659\) 18.3460 0.714658 0.357329 0.933979i \(-0.383688\pi\)
0.357329 + 0.933979i \(0.383688\pi\)
\(660\) −0.258634 −0.0100673
\(661\) 24.3103 0.945560 0.472780 0.881181i \(-0.343251\pi\)
0.472780 + 0.881181i \(0.343251\pi\)
\(662\) −75.7961 −2.94590
\(663\) −15.0139 −0.583090
\(664\) −6.22076 −0.241412
\(665\) 0 0
\(666\) −21.4455 −0.830995
\(667\) 0.811090 0.0314055
\(668\) −58.0024 −2.24418
\(669\) 2.57172 0.0994283
\(670\) −19.7434 −0.762752
\(671\) 1.12949 0.0436034
\(672\) −14.5416 −0.560956
\(673\) 31.5695 1.21691 0.608457 0.793587i \(-0.291789\pi\)
0.608457 + 0.793587i \(0.291789\pi\)
\(674\) 2.15368 0.0829568
\(675\) 5.10685 0.196563
\(676\) 58.0160 2.23138
\(677\) 12.4254 0.477545 0.238773 0.971076i \(-0.423255\pi\)
0.238773 + 0.971076i \(0.423255\pi\)
\(678\) 26.3496 1.01195
\(679\) −0.457471 −0.0175561
\(680\) −5.29083 −0.202894
\(681\) −0.470336 −0.0180233
\(682\) −1.52190 −0.0582766
\(683\) −9.71494 −0.371732 −0.185866 0.982575i \(-0.559509\pi\)
−0.185866 + 0.982575i \(0.559509\pi\)
\(684\) 0 0
\(685\) −10.4468 −0.399152
\(686\) 44.5579 1.70123
\(687\) −1.03003 −0.0392983
\(688\) −0.802861 −0.0306088
\(689\) 83.2653 3.17216
\(690\) 0.712442 0.0271222
\(691\) 38.5888 1.46799 0.733994 0.679156i \(-0.237654\pi\)
0.733994 + 0.679156i \(0.237654\pi\)
\(692\) −36.9774 −1.40567
\(693\) 0.330570 0.0125573
\(694\) −52.2486 −1.98333
\(695\) 10.6846 0.405290
\(696\) 5.68914 0.215646
\(697\) −14.8815 −0.563678
\(698\) 43.2046 1.63532
\(699\) 4.42096 0.167216
\(700\) −5.95489 −0.225074
\(701\) −18.2907 −0.690832 −0.345416 0.938450i \(-0.612262\pi\)
−0.345416 + 0.938450i \(0.612262\pi\)
\(702\) −64.9398 −2.45099
\(703\) 0 0
\(704\) −1.09608 −0.0413101
\(705\) −7.15819 −0.269593
\(706\) −26.5943 −1.00089
\(707\) 25.5188 0.959733
\(708\) 22.7890 0.856465
\(709\) −10.9453 −0.411060 −0.205530 0.978651i \(-0.565892\pi\)
−0.205530 + 0.978651i \(0.565892\pi\)
\(710\) 31.8665 1.19593
\(711\) 0.223060 0.00836541
\(712\) 23.2602 0.871714
\(713\) 2.49519 0.0934458
\(714\) −11.8128 −0.442084
\(715\) −0.485227 −0.0181465
\(716\) 31.8119 1.18887
\(717\) −25.3633 −0.947209
\(718\) 38.2090 1.42595
\(719\) −7.98877 −0.297931 −0.148965 0.988842i \(-0.547594\pi\)
−0.148965 + 0.988842i \(0.547594\pi\)
\(720\) 2.37535 0.0885240
\(721\) 35.8906 1.33663
\(722\) 0 0
\(723\) 4.55746 0.169494
\(724\) 15.9141 0.591443
\(725\) −2.62414 −0.0974582
\(726\) 25.3382 0.940390
\(727\) −13.5437 −0.502309 −0.251154 0.967947i \(-0.580810\pi\)
−0.251154 + 0.967947i \(0.580810\pi\)
\(728\) 24.2210 0.897689
\(729\) 14.9673 0.554344
\(730\) 24.1274 0.892995
\(731\) −1.64628 −0.0608898
\(732\) −40.6085 −1.50094
\(733\) 12.2354 0.451925 0.225962 0.974136i \(-0.427447\pi\)
0.225962 + 0.974136i \(0.427447\pi\)
\(734\) −39.1718 −1.44586
\(735\) 3.00632 0.110890
\(736\) 2.14030 0.0788923
\(737\) −0.753369 −0.0277507
\(738\) −25.1558 −0.926000
\(739\) −5.42922 −0.199717 −0.0998586 0.995002i \(-0.531839\pi\)
−0.0998586 + 0.995002i \(0.531839\pi\)
\(740\) 14.7412 0.541896
\(741\) 0 0
\(742\) 65.5126 2.40505
\(743\) 3.77234 0.138394 0.0691968 0.997603i \(-0.477956\pi\)
0.0691968 + 0.997603i \(0.477956\pi\)
\(744\) 17.5018 0.641646
\(745\) −5.04462 −0.184820
\(746\) 5.90084 0.216045
\(747\) 5.72678 0.209532
\(748\) −0.631176 −0.0230781
\(749\) 10.3201 0.377086
\(750\) −2.30498 −0.0841661
\(751\) 6.28316 0.229276 0.114638 0.993407i \(-0.463429\pi\)
0.114638 + 0.993407i \(0.463429\pi\)
\(752\) −8.51931 −0.310667
\(753\) 0.401805 0.0146426
\(754\) 33.3692 1.21523
\(755\) −20.8114 −0.757403
\(756\) −30.4107 −1.10603
\(757\) −50.8221 −1.84716 −0.923580 0.383406i \(-0.874751\pi\)
−0.923580 + 0.383406i \(0.874751\pi\)
\(758\) 42.1864 1.53228
\(759\) 0.0271854 0.000986768 0
\(760\) 0 0
\(761\) −10.2538 −0.371701 −0.185850 0.982578i \(-0.559504\pi\)
−0.185850 + 0.982578i \(0.559504\pi\)
\(762\) −3.31867 −0.120223
\(763\) −12.4241 −0.449783
\(764\) 14.3248 0.518254
\(765\) 4.87069 0.176100
\(766\) 26.5140 0.957989
\(767\) 42.7548 1.54379
\(768\) 7.48545 0.270108
\(769\) −1.50423 −0.0542440 −0.0271220 0.999632i \(-0.508634\pi\)
−0.0271220 + 0.999632i \(0.508634\pi\)
\(770\) −0.381774 −0.0137582
\(771\) −2.95852 −0.106549
\(772\) 4.07015 0.146488
\(773\) −37.3223 −1.34239 −0.671195 0.741281i \(-0.734219\pi\)
−0.671195 + 0.741281i \(0.734219\pi\)
\(774\) −2.78288 −0.100029
\(775\) −8.07278 −0.289983
\(776\) 0.472282 0.0169539
\(777\) 10.5274 0.377668
\(778\) −21.7065 −0.778215
\(779\) 0 0
\(780\) 17.4454 0.624645
\(781\) 1.21596 0.0435106
\(782\) 1.73866 0.0621742
\(783\) −13.4011 −0.478916
\(784\) 3.57797 0.127785
\(785\) 23.6158 0.842885
\(786\) 2.31294 0.0824998
\(787\) −32.9294 −1.17381 −0.586903 0.809657i \(-0.699653\pi\)
−0.586903 + 0.809657i \(0.699653\pi\)
\(788\) 18.8417 0.671208
\(789\) 11.2074 0.398993
\(790\) −0.257611 −0.00916538
\(791\) 23.1499 0.823115
\(792\) −0.341273 −0.0121266
\(793\) −76.1862 −2.70545
\(794\) 64.1096 2.27516
\(795\) 15.0929 0.535292
\(796\) 45.9920 1.63014
\(797\) 18.1078 0.641410 0.320705 0.947179i \(-0.396080\pi\)
0.320705 + 0.947179i \(0.396080\pi\)
\(798\) 0 0
\(799\) −17.4690 −0.618008
\(800\) −6.92456 −0.244820
\(801\) −21.4132 −0.756597
\(802\) −13.9395 −0.492220
\(803\) 0.920655 0.0324892
\(804\) 27.0859 0.955246
\(805\) 0.625927 0.0220610
\(806\) 102.655 3.61588
\(807\) 2.88042 0.101396
\(808\) −26.3450 −0.926814
\(809\) −7.85536 −0.276180 −0.138090 0.990420i \(-0.544096\pi\)
−0.138090 + 0.990420i \(0.544096\pi\)
\(810\) 1.06264 0.0373375
\(811\) 19.5323 0.685873 0.342936 0.939359i \(-0.388578\pi\)
0.342936 + 0.939359i \(0.388578\pi\)
\(812\) 15.6265 0.548382
\(813\) −15.4124 −0.540535
\(814\) 0.945069 0.0331247
\(815\) −0.213533 −0.00747972
\(816\) −3.23895 −0.113386
\(817\) 0 0
\(818\) −24.9479 −0.872282
\(819\) −22.2976 −0.779142
\(820\) 17.2916 0.603849
\(821\) −18.2498 −0.636922 −0.318461 0.947936i \(-0.603166\pi\)
−0.318461 + 0.947936i \(0.603166\pi\)
\(822\) 24.0797 0.839876
\(823\) 16.5637 0.577373 0.288687 0.957424i \(-0.406781\pi\)
0.288687 + 0.957424i \(0.406781\pi\)
\(824\) −37.0526 −1.29079
\(825\) −0.0879538 −0.00306216
\(826\) 33.6392 1.17046
\(827\) −16.7592 −0.582774 −0.291387 0.956605i \(-0.594117\pi\)
−0.291387 + 0.956605i \(0.594117\pi\)
\(828\) 1.74928 0.0607918
\(829\) 9.99830 0.347255 0.173628 0.984811i \(-0.444451\pi\)
0.173628 + 0.984811i \(0.444451\pi\)
\(830\) −6.61382 −0.229569
\(831\) −18.7569 −0.650668
\(832\) 73.9328 2.56316
\(833\) 7.33669 0.254201
\(834\) −24.6278 −0.852793
\(835\) −19.7249 −0.682607
\(836\) 0 0
\(837\) −41.2264 −1.42499
\(838\) −57.9589 −2.00216
\(839\) −45.5490 −1.57253 −0.786263 0.617892i \(-0.787987\pi\)
−0.786263 + 0.617892i \(0.787987\pi\)
\(840\) 4.39037 0.151482
\(841\) −22.1139 −0.762547
\(842\) 56.1476 1.93497
\(843\) −4.02798 −0.138731
\(844\) −22.5949 −0.777748
\(845\) 19.7295 0.678715
\(846\) −29.5297 −1.01525
\(847\) 22.2613 0.764907
\(848\) 17.9628 0.616847
\(849\) 23.1106 0.793155
\(850\) −5.62513 −0.192940
\(851\) −1.54946 −0.0531149
\(852\) −43.7176 −1.49774
\(853\) 25.5008 0.873129 0.436565 0.899673i \(-0.356195\pi\)
0.436565 + 0.899673i \(0.356195\pi\)
\(854\) −59.9428 −2.05120
\(855\) 0 0
\(856\) −10.6542 −0.364152
\(857\) 7.24518 0.247491 0.123745 0.992314i \(-0.460509\pi\)
0.123745 + 0.992314i \(0.460509\pi\)
\(858\) 1.11844 0.0381829
\(859\) −30.1074 −1.02725 −0.513625 0.858015i \(-0.671698\pi\)
−0.513625 + 0.858015i \(0.671698\pi\)
\(860\) 1.91290 0.0652292
\(861\) 12.3488 0.420846
\(862\) −84.8841 −2.89116
\(863\) −7.47961 −0.254609 −0.127305 0.991864i \(-0.540633\pi\)
−0.127305 + 0.991864i \(0.540633\pi\)
\(864\) −35.3627 −1.20306
\(865\) −12.5749 −0.427559
\(866\) −5.82585 −0.197971
\(867\) 10.9875 0.373156
\(868\) 48.0725 1.63169
\(869\) −0.00982994 −0.000333458 0
\(870\) 6.04861 0.205067
\(871\) 50.8162 1.72184
\(872\) 12.8264 0.434356
\(873\) −0.434779 −0.0147150
\(874\) 0 0
\(875\) −2.02508 −0.0684602
\(876\) −33.1004 −1.11836
\(877\) 24.6798 0.833377 0.416689 0.909049i \(-0.363191\pi\)
0.416689 + 0.909049i \(0.363191\pi\)
\(878\) −14.9294 −0.503843
\(879\) −25.3561 −0.855240
\(880\) −0.104678 −0.00352870
\(881\) 7.30247 0.246026 0.123013 0.992405i \(-0.460744\pi\)
0.123013 + 0.992405i \(0.460744\pi\)
\(882\) 12.4020 0.417597
\(883\) −43.8146 −1.47448 −0.737239 0.675632i \(-0.763871\pi\)
−0.737239 + 0.675632i \(0.763871\pi\)
\(884\) 42.5741 1.43192
\(885\) 7.74987 0.260509
\(886\) −57.8046 −1.94198
\(887\) 49.3920 1.65842 0.829211 0.558936i \(-0.188790\pi\)
0.829211 + 0.558936i \(0.188790\pi\)
\(888\) −10.8682 −0.364714
\(889\) −2.91567 −0.0977883
\(890\) 24.7299 0.828948
\(891\) 0.0405485 0.00135843
\(892\) −7.29249 −0.244170
\(893\) 0 0
\(894\) 11.6278 0.388890
\(895\) 10.8183 0.361615
\(896\) 30.1243 1.00638
\(897\) −1.83371 −0.0612258
\(898\) 61.2854 2.04512
\(899\) 21.1841 0.706530
\(900\) −5.65951 −0.188650
\(901\) 36.8331 1.22709
\(902\) 1.10858 0.0369117
\(903\) 1.36610 0.0454608
\(904\) −23.8994 −0.794882
\(905\) 5.41191 0.179898
\(906\) 47.9698 1.59369
\(907\) 10.6373 0.353206 0.176603 0.984282i \(-0.443489\pi\)
0.176603 + 0.984282i \(0.443489\pi\)
\(908\) 1.33371 0.0442606
\(909\) 24.2530 0.804420
\(910\) 25.7514 0.853649
\(911\) 40.5583 1.34376 0.671878 0.740662i \(-0.265488\pi\)
0.671878 + 0.740662i \(0.265488\pi\)
\(912\) 0 0
\(913\) −0.252371 −0.00835225
\(914\) 4.94613 0.163603
\(915\) −13.8098 −0.456536
\(916\) 2.92082 0.0965065
\(917\) 2.03207 0.0671048
\(918\) −28.7267 −0.948121
\(919\) 38.3456 1.26491 0.632453 0.774599i \(-0.282048\pi\)
0.632453 + 0.774599i \(0.282048\pi\)
\(920\) −0.646192 −0.0213043
\(921\) 6.66294 0.219551
\(922\) 45.4668 1.49737
\(923\) −82.0191 −2.69969
\(924\) 0.523755 0.0172303
\(925\) 5.01303 0.164827
\(926\) −72.0835 −2.36881
\(927\) 34.1103 1.12033
\(928\) 18.1710 0.596493
\(929\) 43.6424 1.43186 0.715931 0.698171i \(-0.246003\pi\)
0.715931 + 0.698171i \(0.246003\pi\)
\(930\) 18.6076 0.610168
\(931\) 0 0
\(932\) −12.5363 −0.410639
\(933\) 18.2139 0.596296
\(934\) −15.3835 −0.503365
\(935\) −0.214644 −0.00701961
\(936\) 23.0195 0.752417
\(937\) −35.9137 −1.17325 −0.586624 0.809859i \(-0.699543\pi\)
−0.586624 + 0.809859i \(0.699543\pi\)
\(938\) 39.9819 1.30545
\(939\) 3.77841 0.123304
\(940\) 20.2981 0.662051
\(941\) −30.9209 −1.00799 −0.503997 0.863706i \(-0.668138\pi\)
−0.503997 + 0.863706i \(0.668138\pi\)
\(942\) −54.4341 −1.77356
\(943\) −1.81754 −0.0591874
\(944\) 9.22350 0.300199
\(945\) −10.3418 −0.336418
\(946\) 0.122638 0.00398729
\(947\) 11.1663 0.362856 0.181428 0.983404i \(-0.441928\pi\)
0.181428 + 0.983404i \(0.441928\pi\)
\(948\) 0.353416 0.0114784
\(949\) −62.1000 −2.01585
\(950\) 0 0
\(951\) 4.66548 0.151288
\(952\) 10.7143 0.347254
\(953\) 7.40383 0.239834 0.119917 0.992784i \(-0.461737\pi\)
0.119917 + 0.992784i \(0.461737\pi\)
\(954\) 62.2630 2.01584
\(955\) 4.87144 0.157636
\(956\) 71.9213 2.32610
\(957\) 0.230803 0.00746081
\(958\) −44.5522 −1.43942
\(959\) 21.1556 0.683149
\(960\) 13.4013 0.432525
\(961\) 34.1697 1.10225
\(962\) −63.7468 −2.05528
\(963\) 9.80814 0.316063
\(964\) −12.9234 −0.416233
\(965\) 1.38414 0.0445569
\(966\) −1.44275 −0.0464197
\(967\) −17.5783 −0.565279 −0.282640 0.959226i \(-0.591210\pi\)
−0.282640 + 0.959226i \(0.591210\pi\)
\(968\) −22.9820 −0.738671
\(969\) 0 0
\(970\) 0.502123 0.0161222
\(971\) 5.31430 0.170544 0.0852721 0.996358i \(-0.472824\pi\)
0.0852721 + 0.996358i \(0.472824\pi\)
\(972\) −46.5090 −1.49178
\(973\) −21.6372 −0.693656
\(974\) −15.8465 −0.507755
\(975\) 5.93265 0.189997
\(976\) −16.4357 −0.526093
\(977\) −13.6507 −0.436723 −0.218362 0.975868i \(-0.570071\pi\)
−0.218362 + 0.975868i \(0.570071\pi\)
\(978\) 0.492189 0.0157385
\(979\) 0.943646 0.0301591
\(980\) −8.52488 −0.272317
\(981\) −11.8078 −0.376995
\(982\) 36.6866 1.17072
\(983\) −28.7597 −0.917291 −0.458646 0.888619i \(-0.651665\pi\)
−0.458646 + 0.888619i \(0.651665\pi\)
\(984\) −12.7486 −0.406411
\(985\) 6.40750 0.204160
\(986\) 14.7611 0.470090
\(987\) 14.4959 0.461409
\(988\) 0 0
\(989\) −0.201067 −0.00639357
\(990\) −0.362836 −0.0115317
\(991\) 56.4946 1.79461 0.897306 0.441410i \(-0.145521\pi\)
0.897306 + 0.441410i \(0.145521\pi\)
\(992\) 55.9004 1.77484
\(993\) 35.3621 1.12218
\(994\) −64.5321 −2.04683
\(995\) 15.6405 0.495837
\(996\) 9.07349 0.287505
\(997\) −14.1163 −0.447066 −0.223533 0.974696i \(-0.571759\pi\)
−0.223533 + 0.974696i \(0.571759\pi\)
\(998\) −67.4835 −2.13615
\(999\) 25.6007 0.809972
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 1805.2.a.s.1.9 9
5.4 even 2 9025.2.a.cf.1.1 9
19.3 odd 18 95.2.k.a.66.1 yes 18
19.13 odd 18 95.2.k.a.36.1 18
19.18 odd 2 1805.2.a.v.1.1 9
57.32 even 18 855.2.bs.c.226.3 18
57.41 even 18 855.2.bs.c.541.3 18
95.3 even 36 475.2.u.b.199.1 36
95.13 even 36 475.2.u.b.74.6 36
95.22 even 36 475.2.u.b.199.6 36
95.32 even 36 475.2.u.b.74.1 36
95.79 odd 18 475.2.l.c.351.3 18
95.89 odd 18 475.2.l.c.226.3 18
95.94 odd 2 9025.2.a.cc.1.9 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.a.36.1 18 19.13 odd 18
95.2.k.a.66.1 yes 18 19.3 odd 18
475.2.l.c.226.3 18 95.89 odd 18
475.2.l.c.351.3 18 95.79 odd 18
475.2.u.b.74.1 36 95.32 even 36
475.2.u.b.74.6 36 95.13 even 36
475.2.u.b.199.1 36 95.3 even 36
475.2.u.b.199.6 36 95.22 even 36
855.2.bs.c.226.3 18 57.32 even 18
855.2.bs.c.541.3 18 57.41 even 18
1805.2.a.s.1.9 9 1.1 even 1 trivial
1805.2.a.v.1.1 9 19.18 odd 2
9025.2.a.cc.1.9 9 95.94 odd 2
9025.2.a.cf.1.1 9 5.4 even 2