Properties

Label 8015.2.a.h.1.14
Level $8015$
Weight $2$
Character 8015.1
Self dual yes
Analytic conductor $64.000$
Analytic rank $1$
Dimension $38$
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] = [8015,2,Mod(1,8015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8015, 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("8015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.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: \(64.0000972201\)
Analytic rank: \(1\)
Dimension: \(38\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 8015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.08292 q^{2} -0.496145 q^{3} -0.827289 q^{4} +1.00000 q^{5} +0.537284 q^{6} +1.00000 q^{7} +3.06172 q^{8} -2.75384 q^{9} +O(q^{10})\) \(q-1.08292 q^{2} -0.496145 q^{3} -0.827289 q^{4} +1.00000 q^{5} +0.537284 q^{6} +1.00000 q^{7} +3.06172 q^{8} -2.75384 q^{9} -1.08292 q^{10} +0.0921526 q^{11} +0.410455 q^{12} +3.58582 q^{13} -1.08292 q^{14} -0.496145 q^{15} -1.66102 q^{16} +4.47425 q^{17} +2.98218 q^{18} +0.525247 q^{19} -0.827289 q^{20} -0.496145 q^{21} -0.0997937 q^{22} -6.03693 q^{23} -1.51906 q^{24} +1.00000 q^{25} -3.88315 q^{26} +2.85474 q^{27} -0.827289 q^{28} +6.16008 q^{29} +0.537284 q^{30} -6.08228 q^{31} -4.32470 q^{32} -0.0457210 q^{33} -4.84525 q^{34} +1.00000 q^{35} +2.27822 q^{36} -10.0087 q^{37} -0.568799 q^{38} -1.77909 q^{39} +3.06172 q^{40} +2.71787 q^{41} +0.537284 q^{42} +1.91268 q^{43} -0.0762367 q^{44} -2.75384 q^{45} +6.53750 q^{46} -8.05017 q^{47} +0.824105 q^{48} +1.00000 q^{49} -1.08292 q^{50} -2.21988 q^{51} -2.96651 q^{52} -6.29211 q^{53} -3.09145 q^{54} +0.0921526 q^{55} +3.06172 q^{56} -0.260599 q^{57} -6.67087 q^{58} -0.398133 q^{59} +0.410455 q^{60} -6.33993 q^{61} +6.58661 q^{62} -2.75384 q^{63} +8.00533 q^{64} +3.58582 q^{65} +0.0495121 q^{66} +9.17925 q^{67} -3.70150 q^{68} +2.99519 q^{69} -1.08292 q^{70} -5.90674 q^{71} -8.43149 q^{72} -2.48079 q^{73} +10.8386 q^{74} -0.496145 q^{75} -0.434531 q^{76} +0.0921526 q^{77} +1.92660 q^{78} -4.11562 q^{79} -1.66102 q^{80} +6.84516 q^{81} -2.94323 q^{82} +7.53603 q^{83} +0.410455 q^{84} +4.47425 q^{85} -2.07128 q^{86} -3.05630 q^{87} +0.282145 q^{88} -5.34892 q^{89} +2.98218 q^{90} +3.58582 q^{91} +4.99428 q^{92} +3.01769 q^{93} +8.71767 q^{94} +0.525247 q^{95} +2.14568 q^{96} -3.97960 q^{97} -1.08292 q^{98} -0.253773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.08292 −0.765739 −0.382869 0.923803i \(-0.625064\pi\)
−0.382869 + 0.923803i \(0.625064\pi\)
\(3\) −0.496145 −0.286450 −0.143225 0.989690i \(-0.545747\pi\)
−0.143225 + 0.989690i \(0.545747\pi\)
\(4\) −0.827289 −0.413644
\(5\) 1.00000 0.447214
\(6\) 0.537284 0.219345
\(7\) 1.00000 0.377964
\(8\) 3.06172 1.08248
\(9\) −2.75384 −0.917947
\(10\) −1.08292 −0.342449
\(11\) 0.0921526 0.0277850 0.0138925 0.999903i \(-0.495578\pi\)
0.0138925 + 0.999903i \(0.495578\pi\)
\(12\) 0.410455 0.118488
\(13\) 3.58582 0.994527 0.497264 0.867600i \(-0.334338\pi\)
0.497264 + 0.867600i \(0.334338\pi\)
\(14\) −1.08292 −0.289422
\(15\) −0.496145 −0.128104
\(16\) −1.66102 −0.415254
\(17\) 4.47425 1.08517 0.542583 0.840002i \(-0.317446\pi\)
0.542583 + 0.840002i \(0.317446\pi\)
\(18\) 2.98218 0.702907
\(19\) 0.525247 0.120500 0.0602499 0.998183i \(-0.480810\pi\)
0.0602499 + 0.998183i \(0.480810\pi\)
\(20\) −0.827289 −0.184987
\(21\) −0.496145 −0.108268
\(22\) −0.0997937 −0.0212761
\(23\) −6.03693 −1.25879 −0.629393 0.777087i \(-0.716697\pi\)
−0.629393 + 0.777087i \(0.716697\pi\)
\(24\) −1.51906 −0.310076
\(25\) 1.00000 0.200000
\(26\) −3.88315 −0.761548
\(27\) 2.85474 0.549395
\(28\) −0.827289 −0.156343
\(29\) 6.16008 1.14390 0.571950 0.820289i \(-0.306187\pi\)
0.571950 + 0.820289i \(0.306187\pi\)
\(30\) 0.537284 0.0980943
\(31\) −6.08228 −1.09241 −0.546205 0.837651i \(-0.683928\pi\)
−0.546205 + 0.837651i \(0.683928\pi\)
\(32\) −4.32470 −0.764506
\(33\) −0.0457210 −0.00795901
\(34\) −4.84525 −0.830953
\(35\) 1.00000 0.169031
\(36\) 2.27822 0.379703
\(37\) −10.0087 −1.64542 −0.822712 0.568459i \(-0.807540\pi\)
−0.822712 + 0.568459i \(0.807540\pi\)
\(38\) −0.568799 −0.0922714
\(39\) −1.77909 −0.284882
\(40\) 3.06172 0.484101
\(41\) 2.71787 0.424460 0.212230 0.977220i \(-0.431927\pi\)
0.212230 + 0.977220i \(0.431927\pi\)
\(42\) 0.537284 0.0829048
\(43\) 1.91268 0.291681 0.145841 0.989308i \(-0.453411\pi\)
0.145841 + 0.989308i \(0.453411\pi\)
\(44\) −0.0762367 −0.0114931
\(45\) −2.75384 −0.410518
\(46\) 6.53750 0.963902
\(47\) −8.05017 −1.17424 −0.587119 0.809501i \(-0.699738\pi\)
−0.587119 + 0.809501i \(0.699738\pi\)
\(48\) 0.824105 0.118949
\(49\) 1.00000 0.142857
\(50\) −1.08292 −0.153148
\(51\) −2.21988 −0.310845
\(52\) −2.96651 −0.411380
\(53\) −6.29211 −0.864287 −0.432144 0.901805i \(-0.642243\pi\)
−0.432144 + 0.901805i \(0.642243\pi\)
\(54\) −3.09145 −0.420693
\(55\) 0.0921526 0.0124258
\(56\) 3.06172 0.409140
\(57\) −0.260599 −0.0345171
\(58\) −6.67087 −0.875928
\(59\) −0.398133 −0.0518325 −0.0259163 0.999664i \(-0.508250\pi\)
−0.0259163 + 0.999664i \(0.508250\pi\)
\(60\) 0.410455 0.0529895
\(61\) −6.33993 −0.811744 −0.405872 0.913930i \(-0.633032\pi\)
−0.405872 + 0.913930i \(0.633032\pi\)
\(62\) 6.58661 0.836501
\(63\) −2.75384 −0.346951
\(64\) 8.00533 1.00067
\(65\) 3.58582 0.444766
\(66\) 0.0495121 0.00609452
\(67\) 9.17925 1.12142 0.560712 0.828011i \(-0.310528\pi\)
0.560712 + 0.828011i \(0.310528\pi\)
\(68\) −3.70150 −0.448873
\(69\) 2.99519 0.360579
\(70\) −1.08292 −0.129433
\(71\) −5.90674 −0.701001 −0.350501 0.936563i \(-0.613989\pi\)
−0.350501 + 0.936563i \(0.613989\pi\)
\(72\) −8.43149 −0.993661
\(73\) −2.48079 −0.290355 −0.145177 0.989406i \(-0.546375\pi\)
−0.145177 + 0.989406i \(0.546375\pi\)
\(74\) 10.8386 1.25996
\(75\) −0.496145 −0.0572899
\(76\) −0.434531 −0.0498441
\(77\) 0.0921526 0.0105018
\(78\) 1.92660 0.218145
\(79\) −4.11562 −0.463044 −0.231522 0.972830i \(-0.574371\pi\)
−0.231522 + 0.972830i \(0.574371\pi\)
\(80\) −1.66102 −0.185707
\(81\) 6.84516 0.760573
\(82\) −2.94323 −0.325025
\(83\) 7.53603 0.827187 0.413593 0.910462i \(-0.364273\pi\)
0.413593 + 0.910462i \(0.364273\pi\)
\(84\) 0.410455 0.0447843
\(85\) 4.47425 0.485301
\(86\) −2.07128 −0.223352
\(87\) −3.05630 −0.327669
\(88\) 0.282145 0.0300768
\(89\) −5.34892 −0.566985 −0.283492 0.958975i \(-0.591493\pi\)
−0.283492 + 0.958975i \(0.591493\pi\)
\(90\) 2.98218 0.314350
\(91\) 3.58582 0.375896
\(92\) 4.99428 0.520690
\(93\) 3.01769 0.312920
\(94\) 8.71767 0.899159
\(95\) 0.525247 0.0538892
\(96\) 2.14568 0.218992
\(97\) −3.97960 −0.404067 −0.202034 0.979379i \(-0.564755\pi\)
−0.202034 + 0.979379i \(0.564755\pi\)
\(98\) −1.08292 −0.109391
\(99\) −0.253773 −0.0255052
\(100\) −0.827289 −0.0827289
\(101\) −6.84384 −0.680987 −0.340494 0.940247i \(-0.610594\pi\)
−0.340494 + 0.940247i \(0.610594\pi\)
\(102\) 2.40395 0.238026
\(103\) 7.42107 0.731219 0.365610 0.930768i \(-0.380860\pi\)
0.365610 + 0.930768i \(0.380860\pi\)
\(104\) 10.9788 1.07656
\(105\) −0.496145 −0.0484188
\(106\) 6.81384 0.661818
\(107\) −7.58183 −0.732963 −0.366482 0.930425i \(-0.619438\pi\)
−0.366482 + 0.930425i \(0.619438\pi\)
\(108\) −2.36169 −0.227254
\(109\) 5.16970 0.495167 0.247584 0.968867i \(-0.420364\pi\)
0.247584 + 0.968867i \(0.420364\pi\)
\(110\) −0.0997937 −0.00951495
\(111\) 4.96578 0.471331
\(112\) −1.66102 −0.156951
\(113\) −18.3481 −1.72604 −0.863022 0.505166i \(-0.831431\pi\)
−0.863022 + 0.505166i \(0.831431\pi\)
\(114\) 0.282207 0.0264311
\(115\) −6.03693 −0.562946
\(116\) −5.09617 −0.473167
\(117\) −9.87477 −0.912923
\(118\) 0.431146 0.0396902
\(119\) 4.47425 0.410154
\(120\) −1.51906 −0.138670
\(121\) −10.9915 −0.999228
\(122\) 6.86562 0.621584
\(123\) −1.34846 −0.121586
\(124\) 5.03180 0.451869
\(125\) 1.00000 0.0894427
\(126\) 2.98218 0.265674
\(127\) 2.92115 0.259210 0.129605 0.991566i \(-0.458629\pi\)
0.129605 + 0.991566i \(0.458629\pi\)
\(128\) −0.0197165 −0.00174271
\(129\) −0.948968 −0.0835519
\(130\) −3.88315 −0.340575
\(131\) 13.6122 1.18931 0.594653 0.803982i \(-0.297289\pi\)
0.594653 + 0.803982i \(0.297289\pi\)
\(132\) 0.0378245 0.00329220
\(133\) 0.525247 0.0455447
\(134\) −9.94038 −0.858718
\(135\) 2.85474 0.245697
\(136\) 13.6989 1.17467
\(137\) 7.59167 0.648600 0.324300 0.945954i \(-0.394871\pi\)
0.324300 + 0.945954i \(0.394871\pi\)
\(138\) −3.24355 −0.276109
\(139\) 21.4764 1.82161 0.910803 0.412841i \(-0.135463\pi\)
0.910803 + 0.412841i \(0.135463\pi\)
\(140\) −0.827289 −0.0699186
\(141\) 3.99405 0.336360
\(142\) 6.39652 0.536784
\(143\) 0.330442 0.0276330
\(144\) 4.57417 0.381181
\(145\) 6.16008 0.511567
\(146\) 2.68649 0.222336
\(147\) −0.496145 −0.0409214
\(148\) 8.28010 0.680620
\(149\) 7.02415 0.575441 0.287720 0.957714i \(-0.407103\pi\)
0.287720 + 0.957714i \(0.407103\pi\)
\(150\) 0.537284 0.0438691
\(151\) −1.40307 −0.114180 −0.0570900 0.998369i \(-0.518182\pi\)
−0.0570900 + 0.998369i \(0.518182\pi\)
\(152\) 1.60816 0.130439
\(153\) −12.3214 −0.996124
\(154\) −0.0997937 −0.00804160
\(155\) −6.08228 −0.488541
\(156\) 1.47182 0.117840
\(157\) −14.2383 −1.13634 −0.568171 0.822910i \(-0.692349\pi\)
−0.568171 + 0.822910i \(0.692349\pi\)
\(158\) 4.45688 0.354571
\(159\) 3.12180 0.247575
\(160\) −4.32470 −0.341897
\(161\) −6.03693 −0.475777
\(162\) −7.41274 −0.582400
\(163\) 6.82867 0.534863 0.267431 0.963577i \(-0.413825\pi\)
0.267431 + 0.963577i \(0.413825\pi\)
\(164\) −2.24846 −0.175575
\(165\) −0.0457210 −0.00355938
\(166\) −8.16090 −0.633409
\(167\) −14.0012 −1.08344 −0.541722 0.840558i \(-0.682227\pi\)
−0.541722 + 0.840558i \(0.682227\pi\)
\(168\) −1.51906 −0.117198
\(169\) −0.141908 −0.0109160
\(170\) −4.84525 −0.371614
\(171\) −1.44645 −0.110612
\(172\) −1.58234 −0.120652
\(173\) −13.1344 −0.998588 −0.499294 0.866433i \(-0.666407\pi\)
−0.499294 + 0.866433i \(0.666407\pi\)
\(174\) 3.30972 0.250909
\(175\) 1.00000 0.0755929
\(176\) −0.153067 −0.0115379
\(177\) 0.197532 0.0148474
\(178\) 5.79244 0.434162
\(179\) −2.91378 −0.217786 −0.108893 0.994053i \(-0.534731\pi\)
−0.108893 + 0.994053i \(0.534731\pi\)
\(180\) 2.27822 0.169809
\(181\) −17.9103 −1.33126 −0.665630 0.746282i \(-0.731837\pi\)
−0.665630 + 0.746282i \(0.731837\pi\)
\(182\) −3.88315 −0.287838
\(183\) 3.14552 0.232524
\(184\) −18.4834 −1.36261
\(185\) −10.0087 −0.735856
\(186\) −3.26792 −0.239615
\(187\) 0.412314 0.0301514
\(188\) 6.65981 0.485717
\(189\) 2.85474 0.207652
\(190\) −0.568799 −0.0412650
\(191\) 20.3533 1.47271 0.736356 0.676594i \(-0.236545\pi\)
0.736356 + 0.676594i \(0.236545\pi\)
\(192\) −3.97180 −0.286640
\(193\) 12.9449 0.931794 0.465897 0.884839i \(-0.345732\pi\)
0.465897 + 0.884839i \(0.345732\pi\)
\(194\) 4.30958 0.309410
\(195\) −1.77909 −0.127403
\(196\) −0.827289 −0.0590920
\(197\) 8.99708 0.641015 0.320508 0.947246i \(-0.396146\pi\)
0.320508 + 0.947246i \(0.396146\pi\)
\(198\) 0.274816 0.0195303
\(199\) 16.0890 1.14052 0.570260 0.821465i \(-0.306843\pi\)
0.570260 + 0.821465i \(0.306843\pi\)
\(200\) 3.06172 0.216496
\(201\) −4.55424 −0.321231
\(202\) 7.41132 0.521458
\(203\) 6.16008 0.432353
\(204\) 1.83648 0.128579
\(205\) 2.71787 0.189824
\(206\) −8.03641 −0.559923
\(207\) 16.6247 1.15550
\(208\) −5.95610 −0.412981
\(209\) 0.0484028 0.00334809
\(210\) 0.537284 0.0370762
\(211\) −26.8260 −1.84678 −0.923390 0.383864i \(-0.874593\pi\)
−0.923390 + 0.383864i \(0.874593\pi\)
\(212\) 5.20539 0.357508
\(213\) 2.93060 0.200801
\(214\) 8.21050 0.561258
\(215\) 1.91268 0.130444
\(216\) 8.74042 0.594710
\(217\) −6.08228 −0.412892
\(218\) −5.59836 −0.379169
\(219\) 1.23083 0.0831720
\(220\) −0.0762367 −0.00513988
\(221\) 16.0439 1.07923
\(222\) −5.37753 −0.360916
\(223\) −19.5248 −1.30748 −0.653740 0.756719i \(-0.726801\pi\)
−0.653740 + 0.756719i \(0.726801\pi\)
\(224\) −4.32470 −0.288956
\(225\) −2.75384 −0.183589
\(226\) 19.8695 1.32170
\(227\) −12.1273 −0.804920 −0.402460 0.915438i \(-0.631845\pi\)
−0.402460 + 0.915438i \(0.631845\pi\)
\(228\) 0.215590 0.0142778
\(229\) −1.00000 −0.0660819
\(230\) 6.53750 0.431070
\(231\) −0.0457210 −0.00300822
\(232\) 18.8605 1.23825
\(233\) 7.40295 0.484983 0.242492 0.970154i \(-0.422035\pi\)
0.242492 + 0.970154i \(0.422035\pi\)
\(234\) 10.6936 0.699060
\(235\) −8.05017 −0.525135
\(236\) 0.329371 0.0214402
\(237\) 2.04195 0.132639
\(238\) −4.84525 −0.314071
\(239\) 21.7879 1.40934 0.704672 0.709534i \(-0.251094\pi\)
0.704672 + 0.709534i \(0.251094\pi\)
\(240\) 0.824105 0.0531958
\(241\) −4.08529 −0.263157 −0.131578 0.991306i \(-0.542005\pi\)
−0.131578 + 0.991306i \(0.542005\pi\)
\(242\) 11.9029 0.765148
\(243\) −11.9604 −0.767261
\(244\) 5.24495 0.335773
\(245\) 1.00000 0.0638877
\(246\) 1.46027 0.0931033
\(247\) 1.88344 0.119840
\(248\) −18.6223 −1.18251
\(249\) −3.73897 −0.236947
\(250\) −1.08292 −0.0684898
\(251\) −11.8988 −0.751045 −0.375522 0.926813i \(-0.622537\pi\)
−0.375522 + 0.926813i \(0.622537\pi\)
\(252\) 2.27822 0.143514
\(253\) −0.556318 −0.0349754
\(254\) −3.16337 −0.198487
\(255\) −2.21988 −0.139014
\(256\) −15.9893 −0.999331
\(257\) −10.4278 −0.650466 −0.325233 0.945634i \(-0.605443\pi\)
−0.325233 + 0.945634i \(0.605443\pi\)
\(258\) 1.02765 0.0639790
\(259\) −10.0087 −0.621912
\(260\) −2.96651 −0.183975
\(261\) −16.9639 −1.05004
\(262\) −14.7409 −0.910698
\(263\) 20.7297 1.27825 0.639123 0.769105i \(-0.279298\pi\)
0.639123 + 0.769105i \(0.279298\pi\)
\(264\) −0.139985 −0.00861549
\(265\) −6.29211 −0.386521
\(266\) −0.568799 −0.0348753
\(267\) 2.65384 0.162412
\(268\) −7.59389 −0.463871
\(269\) −17.8263 −1.08689 −0.543443 0.839446i \(-0.682880\pi\)
−0.543443 + 0.839446i \(0.682880\pi\)
\(270\) −3.09145 −0.188140
\(271\) 25.9613 1.57704 0.788518 0.615012i \(-0.210849\pi\)
0.788518 + 0.615012i \(0.210849\pi\)
\(272\) −7.43181 −0.450620
\(273\) −1.77909 −0.107675
\(274\) −8.22115 −0.496658
\(275\) 0.0921526 0.00555701
\(276\) −2.47789 −0.149151
\(277\) 4.33183 0.260275 0.130137 0.991496i \(-0.458458\pi\)
0.130137 + 0.991496i \(0.458458\pi\)
\(278\) −23.2572 −1.39487
\(279\) 16.7496 1.00277
\(280\) 3.06172 0.182973
\(281\) 0.643321 0.0383773 0.0191886 0.999816i \(-0.493892\pi\)
0.0191886 + 0.999816i \(0.493892\pi\)
\(282\) −4.32523 −0.257564
\(283\) −0.351072 −0.0208691 −0.0104345 0.999946i \(-0.503321\pi\)
−0.0104345 + 0.999946i \(0.503321\pi\)
\(284\) 4.88658 0.289965
\(285\) −0.260599 −0.0154365
\(286\) −0.357842 −0.0211596
\(287\) 2.71787 0.160431
\(288\) 11.9095 0.701776
\(289\) 3.01894 0.177585
\(290\) −6.67087 −0.391727
\(291\) 1.97446 0.115745
\(292\) 2.05233 0.120104
\(293\) −7.05482 −0.412147 −0.206073 0.978537i \(-0.566069\pi\)
−0.206073 + 0.978537i \(0.566069\pi\)
\(294\) 0.537284 0.0313351
\(295\) −0.398133 −0.0231802
\(296\) −30.6439 −1.78114
\(297\) 0.263072 0.0152650
\(298\) −7.60658 −0.440637
\(299\) −21.6473 −1.25190
\(300\) 0.410455 0.0236976
\(301\) 1.91268 0.110245
\(302\) 1.51941 0.0874321
\(303\) 3.39554 0.195068
\(304\) −0.872444 −0.0500381
\(305\) −6.33993 −0.363023
\(306\) 13.3430 0.762771
\(307\) −19.2504 −1.09868 −0.549340 0.835599i \(-0.685121\pi\)
−0.549340 + 0.835599i \(0.685121\pi\)
\(308\) −0.0762367 −0.00434399
\(309\) −3.68193 −0.209457
\(310\) 6.58661 0.374094
\(311\) 17.0756 0.968268 0.484134 0.874994i \(-0.339135\pi\)
0.484134 + 0.874994i \(0.339135\pi\)
\(312\) −5.44707 −0.308379
\(313\) −14.8552 −0.839664 −0.419832 0.907602i \(-0.637911\pi\)
−0.419832 + 0.907602i \(0.637911\pi\)
\(314\) 15.4189 0.870141
\(315\) −2.75384 −0.155161
\(316\) 3.40481 0.191535
\(317\) −34.4682 −1.93593 −0.967964 0.251091i \(-0.919211\pi\)
−0.967964 + 0.251091i \(0.919211\pi\)
\(318\) −3.38065 −0.189578
\(319\) 0.567668 0.0317833
\(320\) 8.00533 0.447511
\(321\) 3.76169 0.209957
\(322\) 6.53750 0.364321
\(323\) 2.35009 0.130762
\(324\) −5.66292 −0.314607
\(325\) 3.58582 0.198905
\(326\) −7.39489 −0.409565
\(327\) −2.56492 −0.141840
\(328\) 8.32136 0.459470
\(329\) −8.05017 −0.443820
\(330\) 0.0495121 0.00272555
\(331\) −34.5310 −1.89799 −0.948997 0.315284i \(-0.897900\pi\)
−0.948997 + 0.315284i \(0.897900\pi\)
\(332\) −6.23447 −0.342161
\(333\) 27.5624 1.51041
\(334\) 15.1621 0.829634
\(335\) 9.17925 0.501516
\(336\) 0.824105 0.0449586
\(337\) 5.60713 0.305440 0.152720 0.988269i \(-0.451197\pi\)
0.152720 + 0.988269i \(0.451197\pi\)
\(338\) 0.153675 0.00835882
\(339\) 9.10332 0.494425
\(340\) −3.70150 −0.200742
\(341\) −0.560498 −0.0303527
\(342\) 1.56638 0.0847002
\(343\) 1.00000 0.0539949
\(344\) 5.85610 0.315740
\(345\) 2.99519 0.161256
\(346\) 14.2234 0.764657
\(347\) 32.1558 1.72621 0.863106 0.505024i \(-0.168516\pi\)
0.863106 + 0.505024i \(0.168516\pi\)
\(348\) 2.52844 0.135539
\(349\) −5.42746 −0.290525 −0.145263 0.989393i \(-0.546403\pi\)
−0.145263 + 0.989393i \(0.546403\pi\)
\(350\) −1.08292 −0.0578844
\(351\) 10.2366 0.546388
\(352\) −0.398532 −0.0212418
\(353\) 11.6349 0.619262 0.309631 0.950857i \(-0.399794\pi\)
0.309631 + 0.950857i \(0.399794\pi\)
\(354\) −0.213911 −0.0113692
\(355\) −5.90674 −0.313497
\(356\) 4.42510 0.234530
\(357\) −2.21988 −0.117488
\(358\) 3.15539 0.166768
\(359\) 34.1213 1.80085 0.900426 0.435009i \(-0.143255\pi\)
0.900426 + 0.435009i \(0.143255\pi\)
\(360\) −8.43149 −0.444379
\(361\) −18.7241 −0.985480
\(362\) 19.3954 1.01940
\(363\) 5.45338 0.286228
\(364\) −2.96651 −0.155487
\(365\) −2.48079 −0.129851
\(366\) −3.40634 −0.178052
\(367\) 3.22270 0.168224 0.0841118 0.996456i \(-0.473195\pi\)
0.0841118 + 0.996456i \(0.473195\pi\)
\(368\) 10.0274 0.522716
\(369\) −7.48458 −0.389631
\(370\) 10.8386 0.563473
\(371\) −6.29211 −0.326670
\(372\) −2.49650 −0.129438
\(373\) 13.3019 0.688745 0.344373 0.938833i \(-0.388092\pi\)
0.344373 + 0.938833i \(0.388092\pi\)
\(374\) −0.446502 −0.0230881
\(375\) −0.496145 −0.0256208
\(376\) −24.6474 −1.27109
\(377\) 22.0889 1.13764
\(378\) −3.09145 −0.159007
\(379\) 10.4707 0.537842 0.268921 0.963162i \(-0.413333\pi\)
0.268921 + 0.963162i \(0.413333\pi\)
\(380\) −0.434531 −0.0222909
\(381\) −1.44931 −0.0742506
\(382\) −22.0409 −1.12771
\(383\) −6.11139 −0.312277 −0.156139 0.987735i \(-0.549905\pi\)
−0.156139 + 0.987735i \(0.549905\pi\)
\(384\) 0.00978226 0.000499199 0
\(385\) 0.0921526 0.00469653
\(386\) −14.0183 −0.713511
\(387\) −5.26722 −0.267748
\(388\) 3.29228 0.167140
\(389\) 14.3076 0.725422 0.362711 0.931902i \(-0.381851\pi\)
0.362711 + 0.931902i \(0.381851\pi\)
\(390\) 1.92660 0.0975574
\(391\) −27.0107 −1.36599
\(392\) 3.06172 0.154640
\(393\) −6.75364 −0.340676
\(394\) −9.74310 −0.490850
\(395\) −4.11562 −0.207080
\(396\) 0.209944 0.0105501
\(397\) 9.29598 0.466552 0.233276 0.972411i \(-0.425055\pi\)
0.233276 + 0.972411i \(0.425055\pi\)
\(398\) −17.4231 −0.873340
\(399\) −0.260599 −0.0130462
\(400\) −1.66102 −0.0830508
\(401\) −28.1185 −1.40417 −0.702084 0.712094i \(-0.747747\pi\)
−0.702084 + 0.712094i \(0.747747\pi\)
\(402\) 4.93187 0.245979
\(403\) −21.8100 −1.08643
\(404\) 5.66183 0.281686
\(405\) 6.84516 0.340138
\(406\) −6.67087 −0.331070
\(407\) −0.922329 −0.0457182
\(408\) −6.79665 −0.336484
\(409\) −3.62949 −0.179467 −0.0897333 0.995966i \(-0.528601\pi\)
−0.0897333 + 0.995966i \(0.528601\pi\)
\(410\) −2.94323 −0.145356
\(411\) −3.76657 −0.185791
\(412\) −6.13936 −0.302465
\(413\) −0.398133 −0.0195909
\(414\) −18.0032 −0.884810
\(415\) 7.53603 0.369929
\(416\) −15.5076 −0.760322
\(417\) −10.6554 −0.521798
\(418\) −0.0524163 −0.00256376
\(419\) −5.43796 −0.265662 −0.132831 0.991139i \(-0.542407\pi\)
−0.132831 + 0.991139i \(0.542407\pi\)
\(420\) 0.410455 0.0200282
\(421\) −10.6001 −0.516618 −0.258309 0.966062i \(-0.583165\pi\)
−0.258309 + 0.966062i \(0.583165\pi\)
\(422\) 29.0504 1.41415
\(423\) 22.1689 1.07789
\(424\) −19.2647 −0.935576
\(425\) 4.47425 0.217033
\(426\) −3.17360 −0.153761
\(427\) −6.33993 −0.306811
\(428\) 6.27236 0.303186
\(429\) −0.163947 −0.00791545
\(430\) −2.07128 −0.0998859
\(431\) −24.1090 −1.16129 −0.580644 0.814158i \(-0.697199\pi\)
−0.580644 + 0.814158i \(0.697199\pi\)
\(432\) −4.74177 −0.228139
\(433\) 5.07998 0.244128 0.122064 0.992522i \(-0.461049\pi\)
0.122064 + 0.992522i \(0.461049\pi\)
\(434\) 6.58661 0.316168
\(435\) −3.05630 −0.146538
\(436\) −4.27683 −0.204823
\(437\) −3.17088 −0.151684
\(438\) −1.33289 −0.0636880
\(439\) 23.4909 1.12116 0.560579 0.828101i \(-0.310579\pi\)
0.560579 + 0.828101i \(0.310579\pi\)
\(440\) 0.282145 0.0134508
\(441\) −2.75384 −0.131135
\(442\) −17.3742 −0.826406
\(443\) −10.5882 −0.503063 −0.251531 0.967849i \(-0.580934\pi\)
−0.251531 + 0.967849i \(0.580934\pi\)
\(444\) −4.10813 −0.194963
\(445\) −5.34892 −0.253563
\(446\) 21.1438 1.00119
\(447\) −3.48500 −0.164835
\(448\) 8.00533 0.378216
\(449\) −7.52686 −0.355214 −0.177607 0.984101i \(-0.556836\pi\)
−0.177607 + 0.984101i \(0.556836\pi\)
\(450\) 2.98218 0.140581
\(451\) 0.250459 0.0117936
\(452\) 15.1792 0.713968
\(453\) 0.696125 0.0327068
\(454\) 13.1329 0.616358
\(455\) 3.58582 0.168106
\(456\) −0.797880 −0.0373642
\(457\) 31.8197 1.48846 0.744232 0.667922i \(-0.232816\pi\)
0.744232 + 0.667922i \(0.232816\pi\)
\(458\) 1.08292 0.0506014
\(459\) 12.7728 0.596185
\(460\) 4.99428 0.232860
\(461\) −5.79119 −0.269723 −0.134861 0.990864i \(-0.543059\pi\)
−0.134861 + 0.990864i \(0.543059\pi\)
\(462\) 0.0495121 0.00230351
\(463\) 11.2474 0.522712 0.261356 0.965243i \(-0.415830\pi\)
0.261356 + 0.965243i \(0.415830\pi\)
\(464\) −10.2320 −0.475009
\(465\) 3.01769 0.139942
\(466\) −8.01678 −0.371370
\(467\) −7.91399 −0.366216 −0.183108 0.983093i \(-0.558616\pi\)
−0.183108 + 0.983093i \(0.558616\pi\)
\(468\) 8.16928 0.377625
\(469\) 9.17925 0.423858
\(470\) 8.71767 0.402116
\(471\) 7.06428 0.325505
\(472\) −1.21897 −0.0561078
\(473\) 0.176259 0.00810437
\(474\) −2.21126 −0.101567
\(475\) 0.525247 0.0241000
\(476\) −3.70150 −0.169658
\(477\) 17.3275 0.793370
\(478\) −23.5945 −1.07919
\(479\) −35.2829 −1.61212 −0.806059 0.591836i \(-0.798403\pi\)
−0.806059 + 0.591836i \(0.798403\pi\)
\(480\) 2.14568 0.0979364
\(481\) −35.8895 −1.63642
\(482\) 4.42404 0.201509
\(483\) 2.99519 0.136286
\(484\) 9.09315 0.413325
\(485\) −3.97960 −0.180704
\(486\) 12.9521 0.587521
\(487\) 27.4557 1.24414 0.622068 0.782963i \(-0.286293\pi\)
0.622068 + 0.782963i \(0.286293\pi\)
\(488\) −19.4111 −0.878699
\(489\) −3.38801 −0.153211
\(490\) −1.08292 −0.0489213
\(491\) −39.9202 −1.80158 −0.900788 0.434260i \(-0.857010\pi\)
−0.900788 + 0.434260i \(0.857010\pi\)
\(492\) 1.11556 0.0502935
\(493\) 27.5618 1.24132
\(494\) −2.03961 −0.0917664
\(495\) −0.253773 −0.0114063
\(496\) 10.1028 0.453628
\(497\) −5.90674 −0.264954
\(498\) 4.04899 0.181440
\(499\) −32.0474 −1.43464 −0.717318 0.696746i \(-0.754631\pi\)
−0.717318 + 0.696746i \(0.754631\pi\)
\(500\) −0.827289 −0.0369975
\(501\) 6.94661 0.310352
\(502\) 12.8854 0.575104
\(503\) 27.6593 1.23327 0.616634 0.787250i \(-0.288496\pi\)
0.616634 + 0.787250i \(0.288496\pi\)
\(504\) −8.43149 −0.375568
\(505\) −6.84384 −0.304547
\(506\) 0.602447 0.0267820
\(507\) 0.0704071 0.00312689
\(508\) −2.41663 −0.107221
\(509\) −20.6035 −0.913232 −0.456616 0.889664i \(-0.650939\pi\)
−0.456616 + 0.889664i \(0.650939\pi\)
\(510\) 2.40395 0.106449
\(511\) −2.48079 −0.109744
\(512\) 17.3545 0.766969
\(513\) 1.49944 0.0662020
\(514\) 11.2924 0.498087
\(515\) 7.42107 0.327011
\(516\) 0.785070 0.0345608
\(517\) −0.741844 −0.0326262
\(518\) 10.8386 0.476222
\(519\) 6.51655 0.286045
\(520\) 10.9788 0.481451
\(521\) −13.9391 −0.610684 −0.305342 0.952243i \(-0.598771\pi\)
−0.305342 + 0.952243i \(0.598771\pi\)
\(522\) 18.3705 0.804055
\(523\) 2.19327 0.0959049 0.0479525 0.998850i \(-0.484730\pi\)
0.0479525 + 0.998850i \(0.484730\pi\)
\(524\) −11.2612 −0.491950
\(525\) −0.496145 −0.0216535
\(526\) −22.4485 −0.978802
\(527\) −27.2137 −1.18545
\(528\) 0.0759434 0.00330501
\(529\) 13.4445 0.584544
\(530\) 6.81384 0.295974
\(531\) 1.09640 0.0475795
\(532\) −0.434531 −0.0188393
\(533\) 9.74578 0.422137
\(534\) −2.87389 −0.124366
\(535\) −7.58183 −0.327791
\(536\) 28.1043 1.21392
\(537\) 1.44566 0.0623848
\(538\) 19.3044 0.832271
\(539\) 0.0921526 0.00396929
\(540\) −2.36169 −0.101631
\(541\) −14.2180 −0.611281 −0.305640 0.952147i \(-0.598871\pi\)
−0.305640 + 0.952147i \(0.598871\pi\)
\(542\) −28.1139 −1.20760
\(543\) 8.88610 0.381339
\(544\) −19.3498 −0.829616
\(545\) 5.16970 0.221446
\(546\) 1.92660 0.0824511
\(547\) 25.9106 1.10786 0.553928 0.832565i \(-0.313128\pi\)
0.553928 + 0.832565i \(0.313128\pi\)
\(548\) −6.28050 −0.268290
\(549\) 17.4591 0.745138
\(550\) −0.0997937 −0.00425522
\(551\) 3.23556 0.137840
\(552\) 9.17045 0.390320
\(553\) −4.11562 −0.175014
\(554\) −4.69102 −0.199302
\(555\) 4.96578 0.210786
\(556\) −17.7672 −0.753497
\(557\) −38.5855 −1.63492 −0.817459 0.575987i \(-0.804618\pi\)
−0.817459 + 0.575987i \(0.804618\pi\)
\(558\) −18.1385 −0.767863
\(559\) 6.85853 0.290085
\(560\) −1.66102 −0.0701908
\(561\) −0.204567 −0.00863685
\(562\) −0.696663 −0.0293870
\(563\) −17.2874 −0.728575 −0.364288 0.931286i \(-0.618687\pi\)
−0.364288 + 0.931286i \(0.618687\pi\)
\(564\) −3.30423 −0.139133
\(565\) −18.3481 −0.771911
\(566\) 0.380182 0.0159802
\(567\) 6.84516 0.287469
\(568\) −18.0848 −0.758821
\(569\) 13.9836 0.586224 0.293112 0.956078i \(-0.405309\pi\)
0.293112 + 0.956078i \(0.405309\pi\)
\(570\) 0.282207 0.0118203
\(571\) −32.9814 −1.38023 −0.690114 0.723701i \(-0.742439\pi\)
−0.690114 + 0.723701i \(0.742439\pi\)
\(572\) −0.273371 −0.0114302
\(573\) −10.0982 −0.421858
\(574\) −2.94323 −0.122848
\(575\) −6.03693 −0.251757
\(576\) −22.0454 −0.918558
\(577\) 8.21231 0.341883 0.170941 0.985281i \(-0.445319\pi\)
0.170941 + 0.985281i \(0.445319\pi\)
\(578\) −3.26926 −0.135983
\(579\) −6.42255 −0.266912
\(580\) −5.09617 −0.211607
\(581\) 7.53603 0.312647
\(582\) −2.13818 −0.0886303
\(583\) −0.579834 −0.0240143
\(584\) −7.59549 −0.314304
\(585\) −9.87477 −0.408271
\(586\) 7.63979 0.315597
\(587\) −20.5589 −0.848558 −0.424279 0.905532i \(-0.639472\pi\)
−0.424279 + 0.905532i \(0.639472\pi\)
\(588\) 0.410455 0.0169269
\(589\) −3.19470 −0.131635
\(590\) 0.431146 0.0177500
\(591\) −4.46386 −0.183619
\(592\) 16.6247 0.683269
\(593\) −7.79482 −0.320095 −0.160048 0.987109i \(-0.551165\pi\)
−0.160048 + 0.987109i \(0.551165\pi\)
\(594\) −0.284885 −0.0116890
\(595\) 4.47425 0.183426
\(596\) −5.81100 −0.238028
\(597\) −7.98248 −0.326701
\(598\) 23.4423 0.958626
\(599\) −16.4055 −0.670311 −0.335156 0.942163i \(-0.608789\pi\)
−0.335156 + 0.942163i \(0.608789\pi\)
\(600\) −1.51906 −0.0620153
\(601\) −33.6730 −1.37355 −0.686776 0.726869i \(-0.740975\pi\)
−0.686776 + 0.726869i \(0.740975\pi\)
\(602\) −2.07128 −0.0844190
\(603\) −25.2782 −1.02941
\(604\) 1.16074 0.0472299
\(605\) −10.9915 −0.446868
\(606\) −3.67709 −0.149371
\(607\) −36.3829 −1.47674 −0.738368 0.674398i \(-0.764403\pi\)
−0.738368 + 0.674398i \(0.764403\pi\)
\(608\) −2.27153 −0.0921229
\(609\) −3.05630 −0.123847
\(610\) 6.86562 0.277981
\(611\) −28.8664 −1.16781
\(612\) 10.1933 0.412041
\(613\) 6.31778 0.255173 0.127586 0.991827i \(-0.459277\pi\)
0.127586 + 0.991827i \(0.459277\pi\)
\(614\) 20.8466 0.841302
\(615\) −1.34846 −0.0543750
\(616\) 0.282145 0.0113680
\(617\) −43.1501 −1.73716 −0.868578 0.495552i \(-0.834966\pi\)
−0.868578 + 0.495552i \(0.834966\pi\)
\(618\) 3.98722 0.160390
\(619\) −37.5255 −1.50828 −0.754140 0.656714i \(-0.771946\pi\)
−0.754140 + 0.656714i \(0.771946\pi\)
\(620\) 5.03180 0.202082
\(621\) −17.2339 −0.691571
\(622\) −18.4915 −0.741440
\(623\) −5.34892 −0.214300
\(624\) 2.95509 0.118298
\(625\) 1.00000 0.0400000
\(626\) 16.0869 0.642964
\(627\) −0.0240148 −0.000959060 0
\(628\) 11.7792 0.470042
\(629\) −44.7816 −1.78556
\(630\) 2.98218 0.118813
\(631\) −28.3186 −1.12735 −0.563673 0.825998i \(-0.690612\pi\)
−0.563673 + 0.825998i \(0.690612\pi\)
\(632\) −12.6009 −0.501237
\(633\) 13.3096 0.529009
\(634\) 37.3262 1.48241
\(635\) 2.92115 0.115922
\(636\) −2.58263 −0.102408
\(637\) 3.58582 0.142075
\(638\) −0.614737 −0.0243377
\(639\) 16.2662 0.643482
\(640\) −0.0197165 −0.000779365 0
\(641\) −9.73555 −0.384531 −0.192266 0.981343i \(-0.561584\pi\)
−0.192266 + 0.981343i \(0.561584\pi\)
\(642\) −4.07360 −0.160772
\(643\) 2.03037 0.0800699 0.0400350 0.999198i \(-0.487253\pi\)
0.0400350 + 0.999198i \(0.487253\pi\)
\(644\) 4.99428 0.196802
\(645\) −0.948968 −0.0373656
\(646\) −2.54495 −0.100130
\(647\) 12.0928 0.475419 0.237709 0.971336i \(-0.423603\pi\)
0.237709 + 0.971336i \(0.423603\pi\)
\(648\) 20.9580 0.823306
\(649\) −0.0366890 −0.00144017
\(650\) −3.88315 −0.152310
\(651\) 3.01769 0.118273
\(652\) −5.64928 −0.221243
\(653\) 26.9774 1.05571 0.527854 0.849335i \(-0.322997\pi\)
0.527854 + 0.849335i \(0.322997\pi\)
\(654\) 2.77760 0.108613
\(655\) 13.6122 0.531874
\(656\) −4.51443 −0.176259
\(657\) 6.83170 0.266530
\(658\) 8.71767 0.339850
\(659\) −11.4446 −0.445817 −0.222909 0.974839i \(-0.571555\pi\)
−0.222909 + 0.974839i \(0.571555\pi\)
\(660\) 0.0378245 0.00147232
\(661\) −9.38431 −0.365007 −0.182504 0.983205i \(-0.558420\pi\)
−0.182504 + 0.983205i \(0.558420\pi\)
\(662\) 37.3942 1.45337
\(663\) −7.96008 −0.309144
\(664\) 23.0732 0.895415
\(665\) 0.525247 0.0203682
\(666\) −29.8478 −1.15658
\(667\) −37.1880 −1.43992
\(668\) 11.5830 0.448160
\(669\) 9.68716 0.374527
\(670\) −9.94038 −0.384030
\(671\) −0.584240 −0.0225543
\(672\) 2.14568 0.0827713
\(673\) −0.676710 −0.0260853 −0.0130426 0.999915i \(-0.504152\pi\)
−0.0130426 + 0.999915i \(0.504152\pi\)
\(674\) −6.07207 −0.233887
\(675\) 2.85474 0.109879
\(676\) 0.117399 0.00451535
\(677\) −1.76667 −0.0678988 −0.0339494 0.999424i \(-0.510809\pi\)
−0.0339494 + 0.999424i \(0.510809\pi\)
\(678\) −9.85815 −0.378600
\(679\) −3.97960 −0.152723
\(680\) 13.6989 0.525330
\(681\) 6.01692 0.230569
\(682\) 0.606973 0.0232422
\(683\) 29.9167 1.14473 0.572365 0.819999i \(-0.306026\pi\)
0.572365 + 0.819999i \(0.306026\pi\)
\(684\) 1.19663 0.0457542
\(685\) 7.59167 0.290063
\(686\) −1.08292 −0.0413460
\(687\) 0.496145 0.0189291
\(688\) −3.17700 −0.121122
\(689\) −22.5624 −0.859557
\(690\) −3.24355 −0.123480
\(691\) 27.3310 1.03972 0.519861 0.854251i \(-0.325984\pi\)
0.519861 + 0.854251i \(0.325984\pi\)
\(692\) 10.8659 0.413060
\(693\) −0.253773 −0.00964005
\(694\) −34.8220 −1.32183
\(695\) 21.4764 0.814647
\(696\) −9.35753 −0.354696
\(697\) 12.1604 0.460609
\(698\) 5.87749 0.222466
\(699\) −3.67294 −0.138923
\(700\) −0.827289 −0.0312686
\(701\) 7.06259 0.266750 0.133375 0.991066i \(-0.457418\pi\)
0.133375 + 0.991066i \(0.457418\pi\)
\(702\) −11.0854 −0.418390
\(703\) −5.25705 −0.198273
\(704\) 0.737711 0.0278035
\(705\) 3.99405 0.150425
\(706\) −12.5996 −0.474193
\(707\) −6.84384 −0.257389
\(708\) −0.163416 −0.00614154
\(709\) 13.7222 0.515349 0.257674 0.966232i \(-0.417044\pi\)
0.257674 + 0.966232i \(0.417044\pi\)
\(710\) 6.39652 0.240057
\(711\) 11.3338 0.425050
\(712\) −16.3769 −0.613751
\(713\) 36.7183 1.37511
\(714\) 2.40395 0.0899654
\(715\) 0.330442 0.0123578
\(716\) 2.41054 0.0900861
\(717\) −10.8100 −0.403706
\(718\) −36.9505 −1.37898
\(719\) 13.0806 0.487823 0.243911 0.969798i \(-0.421569\pi\)
0.243911 + 0.969798i \(0.421569\pi\)
\(720\) 4.57417 0.170469
\(721\) 7.42107 0.276375
\(722\) 20.2767 0.754620
\(723\) 2.02690 0.0753812
\(724\) 14.8170 0.550668
\(725\) 6.16008 0.228780
\(726\) −5.90557 −0.219176
\(727\) −21.6440 −0.802730 −0.401365 0.915918i \(-0.631464\pi\)
−0.401365 + 0.915918i \(0.631464\pi\)
\(728\) 10.9788 0.406901
\(729\) −14.6014 −0.540791
\(730\) 2.68649 0.0994316
\(731\) 8.55782 0.316522
\(732\) −2.60226 −0.0961821
\(733\) −26.3017 −0.971476 −0.485738 0.874105i \(-0.661449\pi\)
−0.485738 + 0.874105i \(0.661449\pi\)
\(734\) −3.48992 −0.128815
\(735\) −0.496145 −0.0183006
\(736\) 26.1079 0.962350
\(737\) 0.845891 0.0311588
\(738\) 8.10518 0.298356
\(739\) −25.1474 −0.925062 −0.462531 0.886603i \(-0.653059\pi\)
−0.462531 + 0.886603i \(0.653059\pi\)
\(740\) 8.28010 0.304383
\(741\) −0.934459 −0.0343282
\(742\) 6.81384 0.250144
\(743\) −33.0359 −1.21197 −0.605985 0.795476i \(-0.707221\pi\)
−0.605985 + 0.795476i \(0.707221\pi\)
\(744\) 9.23934 0.338731
\(745\) 7.02415 0.257345
\(746\) −14.4048 −0.527399
\(747\) −20.7530 −0.759313
\(748\) −0.341102 −0.0124719
\(749\) −7.58183 −0.277034
\(750\) 0.537284 0.0196189
\(751\) −24.1765 −0.882215 −0.441107 0.897454i \(-0.645414\pi\)
−0.441107 + 0.897454i \(0.645414\pi\)
\(752\) 13.3715 0.487607
\(753\) 5.90352 0.215136
\(754\) −23.9205 −0.871134
\(755\) −1.40307 −0.0510629
\(756\) −2.36169 −0.0858940
\(757\) 25.0399 0.910091 0.455046 0.890468i \(-0.349623\pi\)
0.455046 + 0.890468i \(0.349623\pi\)
\(758\) −11.3389 −0.411846
\(759\) 0.276015 0.0100187
\(760\) 1.60816 0.0583341
\(761\) −34.1549 −1.23811 −0.619057 0.785346i \(-0.712485\pi\)
−0.619057 + 0.785346i \(0.712485\pi\)
\(762\) 1.56949 0.0568566
\(763\) 5.16970 0.187156
\(764\) −16.8380 −0.609179
\(765\) −12.3214 −0.445480
\(766\) 6.61813 0.239123
\(767\) −1.42763 −0.0515489
\(768\) 7.93301 0.286258
\(769\) −40.3438 −1.45483 −0.727417 0.686196i \(-0.759279\pi\)
−0.727417 + 0.686196i \(0.759279\pi\)
\(770\) −0.0997937 −0.00359631
\(771\) 5.17368 0.186326
\(772\) −10.7092 −0.385431
\(773\) 12.9638 0.466276 0.233138 0.972444i \(-0.425101\pi\)
0.233138 + 0.972444i \(0.425101\pi\)
\(774\) 5.70397 0.205025
\(775\) −6.08228 −0.218482
\(776\) −12.1844 −0.437395
\(777\) 4.96578 0.178146
\(778\) −15.4939 −0.555484
\(779\) 1.42755 0.0511473
\(780\) 1.47182 0.0526995
\(781\) −0.544321 −0.0194773
\(782\) 29.2504 1.04599
\(783\) 17.5854 0.628452
\(784\) −1.66102 −0.0593220
\(785\) −14.2383 −0.508188
\(786\) 7.31364 0.260869
\(787\) 6.33820 0.225932 0.112966 0.993599i \(-0.463965\pi\)
0.112966 + 0.993599i \(0.463965\pi\)
\(788\) −7.44318 −0.265152
\(789\) −10.2849 −0.366153
\(790\) 4.45688 0.158569
\(791\) −18.3481 −0.652383
\(792\) −0.776984 −0.0276089
\(793\) −22.7338 −0.807302
\(794\) −10.0668 −0.357257
\(795\) 3.12180 0.110719
\(796\) −13.3102 −0.471769
\(797\) −1.25700 −0.0445253 −0.0222626 0.999752i \(-0.507087\pi\)
−0.0222626 + 0.999752i \(0.507087\pi\)
\(798\) 0.282207 0.00999002
\(799\) −36.0185 −1.27424
\(800\) −4.32470 −0.152901
\(801\) 14.7301 0.520462
\(802\) 30.4500 1.07523
\(803\) −0.228611 −0.00806752
\(804\) 3.76767 0.132875
\(805\) −6.03693 −0.212774
\(806\) 23.6184 0.831923
\(807\) 8.84441 0.311338
\(808\) −20.9539 −0.737157
\(809\) −14.8380 −0.521677 −0.260838 0.965382i \(-0.583999\pi\)
−0.260838 + 0.965382i \(0.583999\pi\)
\(810\) −7.41274 −0.260457
\(811\) 32.0316 1.12478 0.562391 0.826871i \(-0.309882\pi\)
0.562391 + 0.826871i \(0.309882\pi\)
\(812\) −5.09617 −0.178840
\(813\) −12.8806 −0.451741
\(814\) 0.998807 0.0350082
\(815\) 6.82867 0.239198
\(816\) 3.68726 0.129080
\(817\) 1.00463 0.0351475
\(818\) 3.93044 0.137425
\(819\) −9.87477 −0.345052
\(820\) −2.24846 −0.0785197
\(821\) −3.11135 −0.108587 −0.0542935 0.998525i \(-0.517291\pi\)
−0.0542935 + 0.998525i \(0.517291\pi\)
\(822\) 4.07888 0.142267
\(823\) −4.42018 −0.154078 −0.0770389 0.997028i \(-0.524547\pi\)
−0.0770389 + 0.997028i \(0.524547\pi\)
\(824\) 22.7212 0.791532
\(825\) −0.0457210 −0.00159180
\(826\) 0.431146 0.0150015
\(827\) −18.7164 −0.650834 −0.325417 0.945571i \(-0.605505\pi\)
−0.325417 + 0.945571i \(0.605505\pi\)
\(828\) −13.7535 −0.477966
\(829\) −45.0927 −1.56613 −0.783067 0.621938i \(-0.786346\pi\)
−0.783067 + 0.621938i \(0.786346\pi\)
\(830\) −8.16090 −0.283269
\(831\) −2.14922 −0.0745556
\(832\) 28.7056 0.995189
\(833\) 4.47425 0.155024
\(834\) 11.5389 0.399561
\(835\) −14.0012 −0.484531
\(836\) −0.0400431 −0.00138492
\(837\) −17.3633 −0.600165
\(838\) 5.88887 0.203427
\(839\) 23.2397 0.802322 0.401161 0.916008i \(-0.368607\pi\)
0.401161 + 0.916008i \(0.368607\pi\)
\(840\) −1.51906 −0.0524125
\(841\) 8.94665 0.308505
\(842\) 11.4791 0.395595
\(843\) −0.319180 −0.0109932
\(844\) 22.1929 0.763910
\(845\) −0.141908 −0.00488179
\(846\) −24.0071 −0.825380
\(847\) −10.9915 −0.377673
\(848\) 10.4513 0.358899
\(849\) 0.174183 0.00597793
\(850\) −4.84525 −0.166191
\(851\) 60.4219 2.07124
\(852\) −2.42445 −0.0830604
\(853\) 19.3513 0.662577 0.331289 0.943529i \(-0.392517\pi\)
0.331289 + 0.943529i \(0.392517\pi\)
\(854\) 6.86562 0.234937
\(855\) −1.44645 −0.0494674
\(856\) −23.2135 −0.793419
\(857\) −50.6166 −1.72903 −0.864515 0.502606i \(-0.832375\pi\)
−0.864515 + 0.502606i \(0.832375\pi\)
\(858\) 0.177542 0.00606117
\(859\) −45.5330 −1.55356 −0.776782 0.629769i \(-0.783150\pi\)
−0.776782 + 0.629769i \(0.783150\pi\)
\(860\) −1.58234 −0.0539573
\(861\) −1.34846 −0.0459553
\(862\) 26.1080 0.889243
\(863\) −25.5847 −0.870912 −0.435456 0.900210i \(-0.643413\pi\)
−0.435456 + 0.900210i \(0.643413\pi\)
\(864\) −12.3459 −0.420016
\(865\) −13.1344 −0.446582
\(866\) −5.50120 −0.186938
\(867\) −1.49783 −0.0508690
\(868\) 5.03180 0.170790
\(869\) −0.379265 −0.0128657
\(870\) 3.30972 0.112210
\(871\) 32.9151 1.11529
\(872\) 15.8282 0.536010
\(873\) 10.9592 0.370912
\(874\) 3.43380 0.116150
\(875\) 1.00000 0.0338062
\(876\) −1.01825 −0.0344036
\(877\) −1.43205 −0.0483570 −0.0241785 0.999708i \(-0.507697\pi\)
−0.0241785 + 0.999708i \(0.507697\pi\)
\(878\) −25.4387 −0.858514
\(879\) 3.50021 0.118059
\(880\) −0.153067 −0.00515989
\(881\) −23.8094 −0.802157 −0.401079 0.916044i \(-0.631365\pi\)
−0.401079 + 0.916044i \(0.631365\pi\)
\(882\) 2.98218 0.100415
\(883\) −5.39787 −0.181653 −0.0908264 0.995867i \(-0.528951\pi\)
−0.0908264 + 0.995867i \(0.528951\pi\)
\(884\) −13.2729 −0.446416
\(885\) 0.197532 0.00663996
\(886\) 11.4662 0.385215
\(887\) 45.6190 1.53173 0.765867 0.642999i \(-0.222310\pi\)
0.765867 + 0.642999i \(0.222310\pi\)
\(888\) 15.2038 0.510207
\(889\) 2.92115 0.0979722
\(890\) 5.79244 0.194163
\(891\) 0.630799 0.0211325
\(892\) 16.1527 0.540832
\(893\) −4.22833 −0.141496
\(894\) 3.77397 0.126220
\(895\) −2.91378 −0.0973971
\(896\) −0.0197165 −0.000658683 0
\(897\) 10.7402 0.358605
\(898\) 8.15097 0.272001
\(899\) −37.4674 −1.24961
\(900\) 2.27822 0.0759407
\(901\) −28.1525 −0.937895
\(902\) −0.271226 −0.00903084
\(903\) −0.948968 −0.0315797
\(904\) −56.1768 −1.86841
\(905\) −17.9103 −0.595358
\(906\) −0.753846 −0.0250449
\(907\) 24.0144 0.797385 0.398693 0.917085i \(-0.369464\pi\)
0.398693 + 0.917085i \(0.369464\pi\)
\(908\) 10.0328 0.332951
\(909\) 18.8468 0.625110
\(910\) −3.88315 −0.128725
\(911\) 10.3576 0.343162 0.171581 0.985170i \(-0.445112\pi\)
0.171581 + 0.985170i \(0.445112\pi\)
\(912\) 0.432859 0.0143334
\(913\) 0.694465 0.0229834
\(914\) −34.4581 −1.13977
\(915\) 3.14552 0.103988
\(916\) 0.827289 0.0273344
\(917\) 13.6122 0.449516
\(918\) −13.8319 −0.456522
\(919\) −31.3961 −1.03566 −0.517830 0.855483i \(-0.673260\pi\)
−0.517830 + 0.855483i \(0.673260\pi\)
\(920\) −18.4834 −0.609379
\(921\) 9.55100 0.314716
\(922\) 6.27139 0.206537
\(923\) −21.1805 −0.697165
\(924\) 0.0378245 0.00124433
\(925\) −10.0087 −0.329085
\(926\) −12.1800 −0.400261
\(927\) −20.4364 −0.671220
\(928\) −26.6405 −0.874518
\(929\) 31.6122 1.03716 0.518581 0.855028i \(-0.326460\pi\)
0.518581 + 0.855028i \(0.326460\pi\)
\(930\) −3.26792 −0.107159
\(931\) 0.525247 0.0172143
\(932\) −6.12437 −0.200610
\(933\) −8.47197 −0.277360
\(934\) 8.57020 0.280426
\(935\) 0.412314 0.0134841
\(936\) −30.2338 −0.988223
\(937\) −8.18678 −0.267450 −0.133725 0.991018i \(-0.542694\pi\)
−0.133725 + 0.991018i \(0.542694\pi\)
\(938\) −9.94038 −0.324565
\(939\) 7.37032 0.240521
\(940\) 6.65981 0.217219
\(941\) 10.4548 0.340817 0.170408 0.985374i \(-0.445491\pi\)
0.170408 + 0.985374i \(0.445491\pi\)
\(942\) −7.65003 −0.249252
\(943\) −16.4076 −0.534304
\(944\) 0.661306 0.0215237
\(945\) 2.85474 0.0928647
\(946\) −0.190874 −0.00620583
\(947\) 28.5930 0.929149 0.464574 0.885534i \(-0.346207\pi\)
0.464574 + 0.885534i \(0.346207\pi\)
\(948\) −1.68928 −0.0548652
\(949\) −8.89567 −0.288766
\(950\) −0.568799 −0.0184543
\(951\) 17.1012 0.554545
\(952\) 13.6989 0.443984
\(953\) −50.0926 −1.62266 −0.811330 0.584589i \(-0.801256\pi\)
−0.811330 + 0.584589i \(0.801256\pi\)
\(954\) −18.7642 −0.607514
\(955\) 20.3533 0.658617
\(956\) −18.0249 −0.582967
\(957\) −0.281645 −0.00910431
\(958\) 38.2085 1.23446
\(959\) 7.59167 0.245148
\(960\) −3.97180 −0.128189
\(961\) 5.99416 0.193360
\(962\) 38.8653 1.25307
\(963\) 20.8791 0.672821
\(964\) 3.37972 0.108853
\(965\) 12.9449 0.416711
\(966\) −3.24355 −0.104359
\(967\) 35.1678 1.13092 0.565459 0.824776i \(-0.308699\pi\)
0.565459 + 0.824776i \(0.308699\pi\)
\(968\) −33.6529 −1.08165
\(969\) −1.16598 −0.0374568
\(970\) 4.30958 0.138372
\(971\) 44.8228 1.43843 0.719216 0.694787i \(-0.244501\pi\)
0.719216 + 0.694787i \(0.244501\pi\)
\(972\) 9.89471 0.317373
\(973\) 21.4764 0.688503
\(974\) −29.7323 −0.952683
\(975\) −1.77909 −0.0569764
\(976\) 10.5307 0.337080
\(977\) −2.07108 −0.0662598 −0.0331299 0.999451i \(-0.510548\pi\)
−0.0331299 + 0.999451i \(0.510548\pi\)
\(978\) 3.66894 0.117320
\(979\) −0.492917 −0.0157537
\(980\) −0.827289 −0.0264268
\(981\) −14.2365 −0.454537
\(982\) 43.2303 1.37954
\(983\) −20.8932 −0.666390 −0.333195 0.942858i \(-0.608127\pi\)
−0.333195 + 0.942858i \(0.608127\pi\)
\(984\) −4.12860 −0.131615
\(985\) 8.99708 0.286671
\(986\) −29.8471 −0.950527
\(987\) 3.99405 0.127132
\(988\) −1.55815 −0.0495713
\(989\) −11.5467 −0.367164
\(990\) 0.274816 0.00873422
\(991\) 32.1016 1.01974 0.509870 0.860251i \(-0.329693\pi\)
0.509870 + 0.860251i \(0.329693\pi\)
\(992\) 26.3040 0.835154
\(993\) 17.1324 0.543680
\(994\) 6.39652 0.202885
\(995\) 16.0890 0.510056
\(996\) 3.09320 0.0980119
\(997\) −3.83217 −0.121366 −0.0606829 0.998157i \(-0.519328\pi\)
−0.0606829 + 0.998157i \(0.519328\pi\)
\(998\) 34.7047 1.09856
\(999\) −28.5723 −0.903987
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 8015.2.a.h.1.14 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.h.1.14 38 1.1 even 1 trivial