Properties

Label 8027.2.a.e.1.15
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $0$
Dimension $169$
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] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, 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("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.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: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(169\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.47225 q^{2} -1.54593 q^{3} +4.11203 q^{4} +3.04029 q^{5} +3.82192 q^{6} -2.57940 q^{7} -5.22147 q^{8} -0.610108 q^{9} +O(q^{10})\) \(q-2.47225 q^{2} -1.54593 q^{3} +4.11203 q^{4} +3.04029 q^{5} +3.82192 q^{6} -2.57940 q^{7} -5.22147 q^{8} -0.610108 q^{9} -7.51637 q^{10} +0.679395 q^{11} -6.35690 q^{12} -3.89012 q^{13} +6.37694 q^{14} -4.70007 q^{15} +4.68474 q^{16} +0.0690897 q^{17} +1.50834 q^{18} -6.13331 q^{19} +12.5018 q^{20} +3.98757 q^{21} -1.67964 q^{22} -1.00000 q^{23} +8.07202 q^{24} +4.24337 q^{25} +9.61735 q^{26} +5.58097 q^{27} -10.6066 q^{28} +4.44649 q^{29} +11.6198 q^{30} -10.6549 q^{31} -1.13890 q^{32} -1.05030 q^{33} -0.170807 q^{34} -7.84214 q^{35} -2.50878 q^{36} -2.59587 q^{37} +15.1631 q^{38} +6.01384 q^{39} -15.8748 q^{40} +3.98215 q^{41} -9.85829 q^{42} +4.63146 q^{43} +2.79370 q^{44} -1.85491 q^{45} +2.47225 q^{46} +1.84738 q^{47} -7.24226 q^{48} -0.346673 q^{49} -10.4907 q^{50} -0.106808 q^{51} -15.9963 q^{52} -0.186508 q^{53} -13.7976 q^{54} +2.06556 q^{55} +13.4683 q^{56} +9.48166 q^{57} -10.9928 q^{58} -1.79713 q^{59} -19.3268 q^{60} -13.9350 q^{61} +26.3416 q^{62} +1.57371 q^{63} -6.55382 q^{64} -11.8271 q^{65} +2.59660 q^{66} +0.579508 q^{67} +0.284099 q^{68} +1.54593 q^{69} +19.3878 q^{70} -11.4021 q^{71} +3.18566 q^{72} -0.353462 q^{73} +6.41764 q^{74} -6.55994 q^{75} -25.2204 q^{76} -1.75244 q^{77} -14.8677 q^{78} -8.28701 q^{79} +14.2430 q^{80} -6.79745 q^{81} -9.84488 q^{82} +1.38251 q^{83} +16.3970 q^{84} +0.210053 q^{85} -11.4501 q^{86} -6.87395 q^{87} -3.54745 q^{88} +4.90655 q^{89} +4.58579 q^{90} +10.0342 q^{91} -4.11203 q^{92} +16.4717 q^{93} -4.56719 q^{94} -18.6471 q^{95} +1.76066 q^{96} -8.39976 q^{97} +0.857062 q^{98} -0.414504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47225 −1.74815 −0.874073 0.485794i \(-0.838530\pi\)
−0.874073 + 0.485794i \(0.838530\pi\)
\(3\) −1.54593 −0.892542 −0.446271 0.894898i \(-0.647248\pi\)
−0.446271 + 0.894898i \(0.647248\pi\)
\(4\) 4.11203 2.05602
\(5\) 3.04029 1.35966 0.679830 0.733370i \(-0.262054\pi\)
0.679830 + 0.733370i \(0.262054\pi\)
\(6\) 3.82192 1.56029
\(7\) −2.57940 −0.974923 −0.487462 0.873144i \(-0.662077\pi\)
−0.487462 + 0.873144i \(0.662077\pi\)
\(8\) −5.22147 −1.84607
\(9\) −0.610108 −0.203369
\(10\) −7.51637 −2.37688
\(11\) 0.679395 0.204845 0.102423 0.994741i \(-0.467341\pi\)
0.102423 + 0.994741i \(0.467341\pi\)
\(12\) −6.35690 −1.83508
\(13\) −3.89012 −1.07892 −0.539462 0.842010i \(-0.681372\pi\)
−0.539462 + 0.842010i \(0.681372\pi\)
\(14\) 6.37694 1.70431
\(15\) −4.70007 −1.21355
\(16\) 4.68474 1.17118
\(17\) 0.0690897 0.0167567 0.00837836 0.999965i \(-0.497333\pi\)
0.00837836 + 0.999965i \(0.497333\pi\)
\(18\) 1.50834 0.355519
\(19\) −6.13331 −1.40708 −0.703539 0.710657i \(-0.748398\pi\)
−0.703539 + 0.710657i \(0.748398\pi\)
\(20\) 12.5018 2.79548
\(21\) 3.98757 0.870160
\(22\) −1.67964 −0.358100
\(23\) −1.00000 −0.208514
\(24\) 8.07202 1.64769
\(25\) 4.24337 0.848674
\(26\) 9.61735 1.88612
\(27\) 5.58097 1.07406
\(28\) −10.6066 −2.00446
\(29\) 4.44649 0.825692 0.412846 0.910801i \(-0.364535\pi\)
0.412846 + 0.910801i \(0.364535\pi\)
\(30\) 11.6198 2.12147
\(31\) −10.6549 −1.91368 −0.956839 0.290620i \(-0.906139\pi\)
−0.956839 + 0.290620i \(0.906139\pi\)
\(32\) −1.13890 −0.201332
\(33\) −1.05030 −0.182833
\(34\) −0.170807 −0.0292932
\(35\) −7.84214 −1.32556
\(36\) −2.50878 −0.418130
\(37\) −2.59587 −0.426758 −0.213379 0.976970i \(-0.568447\pi\)
−0.213379 + 0.976970i \(0.568447\pi\)
\(38\) 15.1631 2.45978
\(39\) 6.01384 0.962985
\(40\) −15.8748 −2.51003
\(41\) 3.98215 0.621908 0.310954 0.950425i \(-0.399352\pi\)
0.310954 + 0.950425i \(0.399352\pi\)
\(42\) −9.85829 −1.52117
\(43\) 4.63146 0.706290 0.353145 0.935569i \(-0.385112\pi\)
0.353145 + 0.935569i \(0.385112\pi\)
\(44\) 2.79370 0.421165
\(45\) −1.85491 −0.276513
\(46\) 2.47225 0.364514
\(47\) 1.84738 0.269468 0.134734 0.990882i \(-0.456982\pi\)
0.134734 + 0.990882i \(0.456982\pi\)
\(48\) −7.24226 −1.04533
\(49\) −0.346673 −0.0495247
\(50\) −10.4907 −1.48361
\(51\) −0.106808 −0.0149561
\(52\) −15.9963 −2.21829
\(53\) −0.186508 −0.0256188 −0.0128094 0.999918i \(-0.504077\pi\)
−0.0128094 + 0.999918i \(0.504077\pi\)
\(54\) −13.7976 −1.87761
\(55\) 2.06556 0.278520
\(56\) 13.4683 1.79978
\(57\) 9.48166 1.25588
\(58\) −10.9928 −1.44343
\(59\) −1.79713 −0.233966 −0.116983 0.993134i \(-0.537322\pi\)
−0.116983 + 0.993134i \(0.537322\pi\)
\(60\) −19.3268 −2.49508
\(61\) −13.9350 −1.78419 −0.892094 0.451849i \(-0.850765\pi\)
−0.892094 + 0.451849i \(0.850765\pi\)
\(62\) 26.3416 3.34539
\(63\) 1.57371 0.198269
\(64\) −6.55382 −0.819227
\(65\) −11.8271 −1.46697
\(66\) 2.59660 0.319619
\(67\) 0.579508 0.0707982 0.0353991 0.999373i \(-0.488730\pi\)
0.0353991 + 0.999373i \(0.488730\pi\)
\(68\) 0.284099 0.0344521
\(69\) 1.54593 0.186108
\(70\) 19.3878 2.31728
\(71\) −11.4021 −1.35318 −0.676591 0.736359i \(-0.736543\pi\)
−0.676591 + 0.736359i \(0.736543\pi\)
\(72\) 3.18566 0.375434
\(73\) −0.353462 −0.0413696 −0.0206848 0.999786i \(-0.506585\pi\)
−0.0206848 + 0.999786i \(0.506585\pi\)
\(74\) 6.41764 0.746035
\(75\) −6.55994 −0.757477
\(76\) −25.2204 −2.89297
\(77\) −1.75244 −0.199709
\(78\) −14.8677 −1.68344
\(79\) −8.28701 −0.932361 −0.466181 0.884690i \(-0.654370\pi\)
−0.466181 + 0.884690i \(0.654370\pi\)
\(80\) 14.2430 1.59241
\(81\) −6.79745 −0.755272
\(82\) −9.84488 −1.08719
\(83\) 1.38251 0.151750 0.0758749 0.997117i \(-0.475825\pi\)
0.0758749 + 0.997117i \(0.475825\pi\)
\(84\) 16.3970 1.78906
\(85\) 0.210053 0.0227834
\(86\) −11.4501 −1.23470
\(87\) −6.87395 −0.736964
\(88\) −3.54745 −0.378159
\(89\) 4.90655 0.520093 0.260046 0.965596i \(-0.416262\pi\)
0.260046 + 0.965596i \(0.416262\pi\)
\(90\) 4.58579 0.483385
\(91\) 10.0342 1.05187
\(92\) −4.11203 −0.428709
\(93\) 16.4717 1.70804
\(94\) −4.56719 −0.471070
\(95\) −18.6471 −1.91315
\(96\) 1.76066 0.179697
\(97\) −8.39976 −0.852867 −0.426433 0.904519i \(-0.640230\pi\)
−0.426433 + 0.904519i \(0.640230\pi\)
\(98\) 0.857062 0.0865764
\(99\) −0.414504 −0.0416593
\(100\) 17.4489 1.74489
\(101\) 12.8871 1.28232 0.641159 0.767408i \(-0.278454\pi\)
0.641159 + 0.767408i \(0.278454\pi\)
\(102\) 0.264056 0.0261454
\(103\) −7.15738 −0.705237 −0.352619 0.935767i \(-0.614709\pi\)
−0.352619 + 0.935767i \(0.614709\pi\)
\(104\) 20.3121 1.99177
\(105\) 12.1234 1.18312
\(106\) 0.461094 0.0447854
\(107\) −3.21772 −0.311069 −0.155534 0.987830i \(-0.549710\pi\)
−0.155534 + 0.987830i \(0.549710\pi\)
\(108\) 22.9491 2.20828
\(109\) −5.47802 −0.524700 −0.262350 0.964973i \(-0.584497\pi\)
−0.262350 + 0.964973i \(0.584497\pi\)
\(110\) −5.10659 −0.486894
\(111\) 4.01302 0.380899
\(112\) −12.0838 −1.14181
\(113\) 15.2001 1.42991 0.714953 0.699173i \(-0.246448\pi\)
0.714953 + 0.699173i \(0.246448\pi\)
\(114\) −23.4410 −2.19545
\(115\) −3.04029 −0.283509
\(116\) 18.2841 1.69764
\(117\) 2.37339 0.219420
\(118\) 4.44296 0.409008
\(119\) −0.178210 −0.0163365
\(120\) 24.5413 2.24030
\(121\) −10.5384 −0.958038
\(122\) 34.4507 3.11902
\(123\) −6.15612 −0.555079
\(124\) −43.8133 −3.93455
\(125\) −2.30037 −0.205752
\(126\) −3.89062 −0.346604
\(127\) −3.33793 −0.296194 −0.148097 0.988973i \(-0.547315\pi\)
−0.148097 + 0.988973i \(0.547315\pi\)
\(128\) 18.4805 1.63346
\(129\) −7.15990 −0.630394
\(130\) 29.2395 2.56448
\(131\) −17.7441 −1.55031 −0.775154 0.631772i \(-0.782328\pi\)
−0.775154 + 0.631772i \(0.782328\pi\)
\(132\) −4.31885 −0.375908
\(133\) 15.8203 1.37179
\(134\) −1.43269 −0.123766
\(135\) 16.9678 1.46035
\(136\) −0.360750 −0.0309341
\(137\) 11.2773 0.963489 0.481744 0.876312i \(-0.340003\pi\)
0.481744 + 0.876312i \(0.340003\pi\)
\(138\) −3.82192 −0.325344
\(139\) 3.12741 0.265264 0.132632 0.991165i \(-0.457657\pi\)
0.132632 + 0.991165i \(0.457657\pi\)
\(140\) −32.2471 −2.72538
\(141\) −2.85592 −0.240512
\(142\) 28.1889 2.36556
\(143\) −2.64293 −0.221013
\(144\) −2.85819 −0.238183
\(145\) 13.5186 1.12266
\(146\) 0.873848 0.0723202
\(147\) 0.535931 0.0442028
\(148\) −10.6743 −0.877421
\(149\) −10.0497 −0.823300 −0.411650 0.911342i \(-0.635047\pi\)
−0.411650 + 0.911342i \(0.635047\pi\)
\(150\) 16.2178 1.32418
\(151\) 13.3876 1.08947 0.544733 0.838609i \(-0.316631\pi\)
0.544733 + 0.838609i \(0.316631\pi\)
\(152\) 32.0249 2.59756
\(153\) −0.0421522 −0.00340780
\(154\) 4.33246 0.349120
\(155\) −32.3940 −2.60195
\(156\) 24.7291 1.97991
\(157\) 15.1877 1.21211 0.606055 0.795423i \(-0.292751\pi\)
0.606055 + 0.795423i \(0.292751\pi\)
\(158\) 20.4876 1.62990
\(159\) 0.288328 0.0228659
\(160\) −3.46260 −0.273742
\(161\) 2.57940 0.203286
\(162\) 16.8050 1.32033
\(163\) −0.574585 −0.0450049 −0.0225025 0.999747i \(-0.507163\pi\)
−0.0225025 + 0.999747i \(0.507163\pi\)
\(164\) 16.3747 1.27865
\(165\) −3.19321 −0.248591
\(166\) −3.41790 −0.265281
\(167\) −5.09417 −0.394199 −0.197099 0.980383i \(-0.563152\pi\)
−0.197099 + 0.980383i \(0.563152\pi\)
\(168\) −20.8210 −1.60638
\(169\) 2.13301 0.164078
\(170\) −0.519304 −0.0398288
\(171\) 3.74198 0.286156
\(172\) 19.0447 1.45214
\(173\) 1.41115 0.107288 0.0536440 0.998560i \(-0.482916\pi\)
0.0536440 + 0.998560i \(0.482916\pi\)
\(174\) 16.9941 1.28832
\(175\) −10.9454 −0.827392
\(176\) 3.18279 0.239912
\(177\) 2.77823 0.208825
\(178\) −12.1302 −0.909198
\(179\) 24.8613 1.85822 0.929110 0.369804i \(-0.120575\pi\)
0.929110 + 0.369804i \(0.120575\pi\)
\(180\) −7.62743 −0.568515
\(181\) 1.80062 0.133839 0.0669197 0.997758i \(-0.478683\pi\)
0.0669197 + 0.997758i \(0.478683\pi\)
\(182\) −24.8070 −1.83882
\(183\) 21.5424 1.59246
\(184\) 5.22147 0.384932
\(185\) −7.89219 −0.580245
\(186\) −40.7222 −2.98590
\(187\) 0.0469392 0.00343254
\(188\) 7.59649 0.554031
\(189\) −14.3956 −1.04712
\(190\) 46.1002 3.34446
\(191\) 6.39159 0.462479 0.231240 0.972897i \(-0.425722\pi\)
0.231240 + 0.972897i \(0.425722\pi\)
\(192\) 10.1317 0.731194
\(193\) 1.27887 0.0920553 0.0460276 0.998940i \(-0.485344\pi\)
0.0460276 + 0.998940i \(0.485344\pi\)
\(194\) 20.7663 1.49094
\(195\) 18.2838 1.30933
\(196\) −1.42553 −0.101824
\(197\) −1.50570 −0.107277 −0.0536385 0.998560i \(-0.517082\pi\)
−0.0536385 + 0.998560i \(0.517082\pi\)
\(198\) 1.02476 0.0728265
\(199\) 12.5661 0.890784 0.445392 0.895336i \(-0.353064\pi\)
0.445392 + 0.895336i \(0.353064\pi\)
\(200\) −22.1566 −1.56671
\(201\) −0.895878 −0.0631904
\(202\) −31.8603 −2.24168
\(203\) −11.4693 −0.804986
\(204\) −0.439197 −0.0307499
\(205\) 12.1069 0.845583
\(206\) 17.6948 1.23286
\(207\) 0.610108 0.0424054
\(208\) −18.2242 −1.26362
\(209\) −4.16694 −0.288234
\(210\) −29.9721 −2.06827
\(211\) 0.479113 0.0329835 0.0164917 0.999864i \(-0.494750\pi\)
0.0164917 + 0.999864i \(0.494750\pi\)
\(212\) −0.766926 −0.0526727
\(213\) 17.6268 1.20777
\(214\) 7.95502 0.543794
\(215\) 14.0810 0.960314
\(216\) −29.1409 −1.98278
\(217\) 27.4833 1.86569
\(218\) 13.5431 0.917252
\(219\) 0.546427 0.0369241
\(220\) 8.49365 0.572642
\(221\) −0.268767 −0.0180792
\(222\) −9.92120 −0.665867
\(223\) 23.1372 1.54938 0.774691 0.632340i \(-0.217905\pi\)
0.774691 + 0.632340i \(0.217905\pi\)
\(224\) 2.93769 0.196283
\(225\) −2.58891 −0.172594
\(226\) −37.5785 −2.49968
\(227\) 1.69490 0.112495 0.0562473 0.998417i \(-0.482086\pi\)
0.0562473 + 0.998417i \(0.482086\pi\)
\(228\) 38.9889 2.58210
\(229\) −13.8097 −0.912572 −0.456286 0.889833i \(-0.650821\pi\)
−0.456286 + 0.889833i \(0.650821\pi\)
\(230\) 7.51637 0.495615
\(231\) 2.70914 0.178248
\(232\) −23.2172 −1.52428
\(233\) 24.3195 1.59322 0.796611 0.604493i \(-0.206624\pi\)
0.796611 + 0.604493i \(0.206624\pi\)
\(234\) −5.86762 −0.383578
\(235\) 5.61658 0.366385
\(236\) −7.38986 −0.481039
\(237\) 12.8111 0.832171
\(238\) 0.440581 0.0285586
\(239\) −19.7790 −1.27940 −0.639698 0.768626i \(-0.720941\pi\)
−0.639698 + 0.768626i \(0.720941\pi\)
\(240\) −22.0186 −1.42129
\(241\) 4.76696 0.307067 0.153533 0.988143i \(-0.450935\pi\)
0.153533 + 0.988143i \(0.450935\pi\)
\(242\) 26.0536 1.67479
\(243\) −6.23454 −0.399946
\(244\) −57.3010 −3.66832
\(245\) −1.05399 −0.0673367
\(246\) 15.2195 0.970359
\(247\) 23.8593 1.51813
\(248\) 55.6343 3.53278
\(249\) −2.13725 −0.135443
\(250\) 5.68710 0.359684
\(251\) −11.4296 −0.721430 −0.360715 0.932676i \(-0.617467\pi\)
−0.360715 + 0.932676i \(0.617467\pi\)
\(252\) 6.47116 0.407645
\(253\) −0.679395 −0.0427132
\(254\) 8.25221 0.517790
\(255\) −0.324727 −0.0203352
\(256\) −32.5808 −2.03630
\(257\) 2.45900 0.153388 0.0766940 0.997055i \(-0.475564\pi\)
0.0766940 + 0.997055i \(0.475564\pi\)
\(258\) 17.7011 1.10202
\(259\) 6.69579 0.416056
\(260\) −48.6334 −3.01611
\(261\) −2.71284 −0.167920
\(262\) 43.8679 2.71017
\(263\) −16.4584 −1.01487 −0.507435 0.861690i \(-0.669406\pi\)
−0.507435 + 0.861690i \(0.669406\pi\)
\(264\) 5.48409 0.337523
\(265\) −0.567038 −0.0348329
\(266\) −39.1117 −2.39810
\(267\) −7.58516 −0.464205
\(268\) 2.38296 0.145562
\(269\) 6.84890 0.417585 0.208792 0.977960i \(-0.433047\pi\)
0.208792 + 0.977960i \(0.433047\pi\)
\(270\) −41.9486 −2.55291
\(271\) −23.1940 −1.40894 −0.704468 0.709736i \(-0.748814\pi\)
−0.704468 + 0.709736i \(0.748814\pi\)
\(272\) 0.323667 0.0196252
\(273\) −15.5121 −0.938837
\(274\) −27.8804 −1.68432
\(275\) 2.88293 0.173847
\(276\) 6.35690 0.382641
\(277\) 0.652386 0.0391981 0.0195990 0.999808i \(-0.493761\pi\)
0.0195990 + 0.999808i \(0.493761\pi\)
\(278\) −7.73175 −0.463719
\(279\) 6.50064 0.389183
\(280\) 40.9475 2.44708
\(281\) 5.89657 0.351760 0.175880 0.984412i \(-0.443723\pi\)
0.175880 + 0.984412i \(0.443723\pi\)
\(282\) 7.06055 0.420449
\(283\) −22.5163 −1.33846 −0.669228 0.743057i \(-0.733375\pi\)
−0.669228 + 0.743057i \(0.733375\pi\)
\(284\) −46.8858 −2.78216
\(285\) 28.8270 1.70756
\(286\) 6.53398 0.386363
\(287\) −10.2716 −0.606312
\(288\) 0.694854 0.0409447
\(289\) −16.9952 −0.999719
\(290\) −33.4214 −1.96257
\(291\) 12.9854 0.761219
\(292\) −1.45345 −0.0850566
\(293\) −1.41555 −0.0826972 −0.0413486 0.999145i \(-0.513165\pi\)
−0.0413486 + 0.999145i \(0.513165\pi\)
\(294\) −1.32496 −0.0772730
\(295\) −5.46380 −0.318115
\(296\) 13.5542 0.787825
\(297\) 3.79168 0.220016
\(298\) 24.8453 1.43925
\(299\) 3.89012 0.224971
\(300\) −26.9747 −1.55738
\(301\) −11.9464 −0.688579
\(302\) −33.0975 −1.90455
\(303\) −19.9226 −1.14452
\(304\) −28.7329 −1.64795
\(305\) −42.3663 −2.42589
\(306\) 0.104211 0.00595734
\(307\) −11.1987 −0.639143 −0.319571 0.947562i \(-0.603539\pi\)
−0.319571 + 0.947562i \(0.603539\pi\)
\(308\) −7.20607 −0.410604
\(309\) 11.0648 0.629454
\(310\) 80.0862 4.54859
\(311\) −17.3211 −0.982190 −0.491095 0.871106i \(-0.663403\pi\)
−0.491095 + 0.871106i \(0.663403\pi\)
\(312\) −31.4011 −1.77774
\(313\) −8.69105 −0.491247 −0.245624 0.969365i \(-0.578993\pi\)
−0.245624 + 0.969365i \(0.578993\pi\)
\(314\) −37.5478 −2.11895
\(315\) 4.78455 0.269579
\(316\) −34.0764 −1.91695
\(317\) 22.6414 1.27167 0.635835 0.771825i \(-0.280656\pi\)
0.635835 + 0.771825i \(0.280656\pi\)
\(318\) −0.712818 −0.0399729
\(319\) 3.02092 0.169139
\(320\) −19.9255 −1.11387
\(321\) 4.97436 0.277642
\(322\) −6.37694 −0.355373
\(323\) −0.423749 −0.0235780
\(324\) −27.9513 −1.55285
\(325\) −16.5072 −0.915655
\(326\) 1.42052 0.0786752
\(327\) 8.46863 0.468316
\(328\) −20.7927 −1.14808
\(329\) −4.76514 −0.262711
\(330\) 7.89441 0.434573
\(331\) 32.6386 1.79398 0.896990 0.442051i \(-0.145749\pi\)
0.896990 + 0.442051i \(0.145749\pi\)
\(332\) 5.68491 0.312000
\(333\) 1.58376 0.0867894
\(334\) 12.5941 0.689117
\(335\) 1.76187 0.0962615
\(336\) 18.6807 1.01912
\(337\) 2.59253 0.141224 0.0706121 0.997504i \(-0.477505\pi\)
0.0706121 + 0.997504i \(0.477505\pi\)
\(338\) −5.27335 −0.286832
\(339\) −23.4983 −1.27625
\(340\) 0.863744 0.0468431
\(341\) −7.23889 −0.392008
\(342\) −9.25112 −0.500243
\(343\) 18.9500 1.02321
\(344\) −24.1830 −1.30386
\(345\) 4.70007 0.253043
\(346\) −3.48872 −0.187555
\(347\) −31.8239 −1.70840 −0.854198 0.519947i \(-0.825952\pi\)
−0.854198 + 0.519947i \(0.825952\pi\)
\(348\) −28.2659 −1.51521
\(349\) 1.00000 0.0535288
\(350\) 27.0597 1.44640
\(351\) −21.7106 −1.15883
\(352\) −0.773766 −0.0412419
\(353\) 23.1930 1.23444 0.617219 0.786792i \(-0.288259\pi\)
0.617219 + 0.786792i \(0.288259\pi\)
\(354\) −6.86849 −0.365056
\(355\) −34.6657 −1.83987
\(356\) 20.1759 1.06932
\(357\) 0.275500 0.0145810
\(358\) −61.4634 −3.24844
\(359\) 7.50850 0.396284 0.198142 0.980173i \(-0.436509\pi\)
0.198142 + 0.980173i \(0.436509\pi\)
\(360\) 9.68534 0.510462
\(361\) 18.6175 0.979869
\(362\) −4.45160 −0.233971
\(363\) 16.2916 0.855089
\(364\) 41.2609 2.16266
\(365\) −1.07463 −0.0562486
\(366\) −53.2583 −2.78386
\(367\) 6.90912 0.360653 0.180327 0.983607i \(-0.442285\pi\)
0.180327 + 0.983607i \(0.442285\pi\)
\(368\) −4.68474 −0.244209
\(369\) −2.42954 −0.126477
\(370\) 19.5115 1.01435
\(371\) 0.481079 0.0249764
\(372\) 67.7322 3.51175
\(373\) 10.4648 0.541846 0.270923 0.962601i \(-0.412671\pi\)
0.270923 + 0.962601i \(0.412671\pi\)
\(374\) −0.116046 −0.00600058
\(375\) 3.55621 0.183642
\(376\) −9.64605 −0.497457
\(377\) −17.2974 −0.890859
\(378\) 35.5895 1.83052
\(379\) −16.5540 −0.850323 −0.425161 0.905118i \(-0.639783\pi\)
−0.425161 + 0.905118i \(0.639783\pi\)
\(380\) −76.6773 −3.93346
\(381\) 5.16020 0.264365
\(382\) −15.8016 −0.808481
\(383\) 24.6934 1.26177 0.630887 0.775874i \(-0.282691\pi\)
0.630887 + 0.775874i \(0.282691\pi\)
\(384\) −28.5695 −1.45793
\(385\) −5.32792 −0.271536
\(386\) −3.16170 −0.160926
\(387\) −2.82569 −0.143638
\(388\) −34.5401 −1.75351
\(389\) 14.9837 0.759706 0.379853 0.925047i \(-0.375975\pi\)
0.379853 + 0.925047i \(0.375975\pi\)
\(390\) −45.2022 −2.28890
\(391\) −0.0690897 −0.00349402
\(392\) 1.81014 0.0914260
\(393\) 27.4311 1.38371
\(394\) 3.72248 0.187536
\(395\) −25.1949 −1.26769
\(396\) −1.70445 −0.0856521
\(397\) −3.60294 −0.180827 −0.0904133 0.995904i \(-0.528819\pi\)
−0.0904133 + 0.995904i \(0.528819\pi\)
\(398\) −31.0665 −1.55722
\(399\) −24.4570 −1.22438
\(400\) 19.8791 0.993954
\(401\) −0.636892 −0.0318049 −0.0159024 0.999874i \(-0.505062\pi\)
−0.0159024 + 0.999874i \(0.505062\pi\)
\(402\) 2.21484 0.110466
\(403\) 41.4488 2.06471
\(404\) 52.9923 2.63647
\(405\) −20.6662 −1.02691
\(406\) 28.3550 1.40723
\(407\) −1.76362 −0.0874194
\(408\) 0.557694 0.0276099
\(409\) 13.4174 0.663449 0.331724 0.943376i \(-0.392370\pi\)
0.331724 + 0.943376i \(0.392370\pi\)
\(410\) −29.9313 −1.47820
\(411\) −17.4340 −0.859954
\(412\) −29.4314 −1.44998
\(413\) 4.63553 0.228099
\(414\) −1.50834 −0.0741309
\(415\) 4.20322 0.206328
\(416\) 4.43047 0.217222
\(417\) −4.83475 −0.236759
\(418\) 10.3017 0.503874
\(419\) 21.7682 1.06345 0.531723 0.846918i \(-0.321545\pi\)
0.531723 + 0.846918i \(0.321545\pi\)
\(420\) 49.8517 2.43252
\(421\) −3.99597 −0.194752 −0.0973759 0.995248i \(-0.531045\pi\)
−0.0973759 + 0.995248i \(0.531045\pi\)
\(422\) −1.18449 −0.0576600
\(423\) −1.12710 −0.0548015
\(424\) 0.973846 0.0472941
\(425\) 0.293173 0.0142210
\(426\) −43.5780 −2.11136
\(427\) 35.9439 1.73945
\(428\) −13.2314 −0.639562
\(429\) 4.08578 0.197263
\(430\) −34.8117 −1.67877
\(431\) 4.74019 0.228327 0.114163 0.993462i \(-0.463581\pi\)
0.114163 + 0.993462i \(0.463581\pi\)
\(432\) 26.1454 1.25792
\(433\) −31.4135 −1.50964 −0.754818 0.655934i \(-0.772275\pi\)
−0.754818 + 0.655934i \(0.772275\pi\)
\(434\) −67.9457 −3.26150
\(435\) −20.8988 −1.00202
\(436\) −22.5258 −1.07879
\(437\) 6.13331 0.293396
\(438\) −1.35091 −0.0645488
\(439\) −22.3705 −1.06768 −0.533842 0.845584i \(-0.679252\pi\)
−0.533842 + 0.845584i \(0.679252\pi\)
\(440\) −10.7853 −0.514167
\(441\) 0.211508 0.0100718
\(442\) 0.664460 0.0316051
\(443\) −29.2151 −1.38805 −0.694026 0.719950i \(-0.744165\pi\)
−0.694026 + 0.719950i \(0.744165\pi\)
\(444\) 16.5017 0.783135
\(445\) 14.9173 0.707149
\(446\) −57.2010 −2.70855
\(447\) 15.5360 0.734830
\(448\) 16.9049 0.798683
\(449\) 0.269793 0.0127323 0.00636617 0.999980i \(-0.497974\pi\)
0.00636617 + 0.999980i \(0.497974\pi\)
\(450\) 6.40045 0.301720
\(451\) 2.70546 0.127395
\(452\) 62.5033 2.93991
\(453\) −20.6962 −0.972395
\(454\) −4.19023 −0.196657
\(455\) 30.5068 1.43018
\(456\) −49.5082 −2.31843
\(457\) −16.7244 −0.782336 −0.391168 0.920319i \(-0.627929\pi\)
−0.391168 + 0.920319i \(0.627929\pi\)
\(458\) 34.1411 1.59531
\(459\) 0.385587 0.0179977
\(460\) −12.5018 −0.582898
\(461\) 9.73918 0.453599 0.226800 0.973941i \(-0.427174\pi\)
0.226800 + 0.973941i \(0.427174\pi\)
\(462\) −6.69767 −0.311604
\(463\) 4.90615 0.228008 0.114004 0.993480i \(-0.463632\pi\)
0.114004 + 0.993480i \(0.463632\pi\)
\(464\) 20.8306 0.967037
\(465\) 50.0788 2.32235
\(466\) −60.1238 −2.78518
\(467\) −2.11896 −0.0980537 −0.0490268 0.998797i \(-0.515612\pi\)
−0.0490268 + 0.998797i \(0.515612\pi\)
\(468\) 9.75946 0.451131
\(469\) −1.49479 −0.0690228
\(470\) −13.8856 −0.640495
\(471\) −23.4791 −1.08186
\(472\) 9.38367 0.431918
\(473\) 3.14659 0.144680
\(474\) −31.6723 −1.45476
\(475\) −26.0259 −1.19415
\(476\) −0.732806 −0.0335881
\(477\) 0.113790 0.00521008
\(478\) 48.8987 2.23657
\(479\) −4.18487 −0.191211 −0.0956057 0.995419i \(-0.530479\pi\)
−0.0956057 + 0.995419i \(0.530479\pi\)
\(480\) 5.35293 0.244327
\(481\) 10.0982 0.460439
\(482\) −11.7851 −0.536798
\(483\) −3.98757 −0.181441
\(484\) −43.3343 −1.96974
\(485\) −25.5377 −1.15961
\(486\) 15.4133 0.699164
\(487\) 17.8966 0.810973 0.405487 0.914101i \(-0.367102\pi\)
0.405487 + 0.914101i \(0.367102\pi\)
\(488\) 72.7610 3.29374
\(489\) 0.888266 0.0401688
\(490\) 2.60572 0.117714
\(491\) −2.31772 −0.104597 −0.0522987 0.998631i \(-0.516655\pi\)
−0.0522987 + 0.998631i \(0.516655\pi\)
\(492\) −25.3142 −1.14125
\(493\) 0.307207 0.0138359
\(494\) −58.9862 −2.65391
\(495\) −1.26021 −0.0566424
\(496\) −49.9154 −2.24127
\(497\) 29.4107 1.31925
\(498\) 5.28383 0.236774
\(499\) −6.34103 −0.283864 −0.141932 0.989876i \(-0.545331\pi\)
−0.141932 + 0.989876i \(0.545331\pi\)
\(500\) −9.45920 −0.423028
\(501\) 7.87522 0.351839
\(502\) 28.2568 1.26116
\(503\) 15.7946 0.704247 0.352123 0.935954i \(-0.385460\pi\)
0.352123 + 0.935954i \(0.385460\pi\)
\(504\) −8.21711 −0.366019
\(505\) 39.1807 1.74352
\(506\) 1.67964 0.0746690
\(507\) −3.29748 −0.146446
\(508\) −13.7257 −0.608979
\(509\) 35.4472 1.57117 0.785584 0.618755i \(-0.212362\pi\)
0.785584 + 0.618755i \(0.212362\pi\)
\(510\) 0.802806 0.0355488
\(511\) 0.911722 0.0403322
\(512\) 43.5870 1.92629
\(513\) −34.2298 −1.51128
\(514\) −6.07926 −0.268145
\(515\) −21.7605 −0.958883
\(516\) −29.4417 −1.29610
\(517\) 1.25510 0.0551993
\(518\) −16.5537 −0.727327
\(519\) −2.18154 −0.0957589
\(520\) 61.7548 2.70813
\(521\) 24.9491 1.09304 0.546520 0.837446i \(-0.315952\pi\)
0.546520 + 0.837446i \(0.315952\pi\)
\(522\) 6.70681 0.293549
\(523\) −20.8717 −0.912657 −0.456329 0.889811i \(-0.650836\pi\)
−0.456329 + 0.889811i \(0.650836\pi\)
\(524\) −72.9642 −3.18746
\(525\) 16.9208 0.738482
\(526\) 40.6894 1.77414
\(527\) −0.736144 −0.0320670
\(528\) −4.92036 −0.214131
\(529\) 1.00000 0.0434783
\(530\) 1.40186 0.0608930
\(531\) 1.09644 0.0475816
\(532\) 65.0535 2.82043
\(533\) −15.4910 −0.670991
\(534\) 18.7524 0.811497
\(535\) −9.78281 −0.422948
\(536\) −3.02589 −0.130698
\(537\) −38.4337 −1.65854
\(538\) −16.9322 −0.729999
\(539\) −0.235528 −0.0101449
\(540\) 69.7720 3.00251
\(541\) 27.8464 1.19721 0.598604 0.801045i \(-0.295722\pi\)
0.598604 + 0.801045i \(0.295722\pi\)
\(542\) 57.3414 2.46303
\(543\) −2.78363 −0.119457
\(544\) −0.0786865 −0.00337366
\(545\) −16.6548 −0.713413
\(546\) 38.3499 1.64122
\(547\) −30.9979 −1.32537 −0.662687 0.748896i \(-0.730584\pi\)
−0.662687 + 0.748896i \(0.730584\pi\)
\(548\) 46.3728 1.98095
\(549\) 8.50183 0.362849
\(550\) −7.12732 −0.303910
\(551\) −27.2717 −1.16181
\(552\) −8.07202 −0.343568
\(553\) 21.3755 0.908980
\(554\) −1.61286 −0.0685240
\(555\) 12.2008 0.517893
\(556\) 12.8600 0.545386
\(557\) 30.9356 1.31078 0.655392 0.755289i \(-0.272504\pi\)
0.655392 + 0.755289i \(0.272504\pi\)
\(558\) −16.0712 −0.680349
\(559\) −18.0169 −0.762034
\(560\) −36.7384 −1.55248
\(561\) −0.0725647 −0.00306368
\(562\) −14.5778 −0.614928
\(563\) 22.5371 0.949826 0.474913 0.880033i \(-0.342480\pi\)
0.474913 + 0.880033i \(0.342480\pi\)
\(564\) −11.7436 −0.494496
\(565\) 46.2128 1.94419
\(566\) 55.6660 2.33982
\(567\) 17.5334 0.736332
\(568\) 59.5358 2.49807
\(569\) −25.1604 −1.05478 −0.527390 0.849624i \(-0.676829\pi\)
−0.527390 + 0.849624i \(0.676829\pi\)
\(570\) −71.2676 −2.98507
\(571\) −13.3839 −0.560099 −0.280049 0.959986i \(-0.590351\pi\)
−0.280049 + 0.959986i \(0.590351\pi\)
\(572\) −10.8678 −0.454406
\(573\) −9.88094 −0.412782
\(574\) 25.3939 1.05992
\(575\) −4.24337 −0.176961
\(576\) 3.99853 0.166606
\(577\) −11.4045 −0.474776 −0.237388 0.971415i \(-0.576291\pi\)
−0.237388 + 0.971415i \(0.576291\pi\)
\(578\) 42.0165 1.74766
\(579\) −1.97704 −0.0821632
\(580\) 55.5890 2.30821
\(581\) −3.56604 −0.147944
\(582\) −32.1032 −1.33072
\(583\) −0.126713 −0.00524790
\(584\) 1.84559 0.0763712
\(585\) 7.21580 0.298337
\(586\) 3.49959 0.144567
\(587\) −22.0438 −0.909847 −0.454923 0.890531i \(-0.650333\pi\)
−0.454923 + 0.890531i \(0.650333\pi\)
\(588\) 2.20376 0.0908817
\(589\) 65.3498 2.69269
\(590\) 13.5079 0.556111
\(591\) 2.32771 0.0957492
\(592\) −12.1609 −0.499812
\(593\) 12.0502 0.494843 0.247421 0.968908i \(-0.420417\pi\)
0.247421 + 0.968908i \(0.420417\pi\)
\(594\) −9.37400 −0.384620
\(595\) −0.541811 −0.0222121
\(596\) −41.3245 −1.69272
\(597\) −19.4262 −0.795062
\(598\) −9.61735 −0.393283
\(599\) −33.3908 −1.36431 −0.682156 0.731207i \(-0.738957\pi\)
−0.682156 + 0.731207i \(0.738957\pi\)
\(600\) 34.2526 1.39836
\(601\) 36.2767 1.47976 0.739878 0.672741i \(-0.234883\pi\)
0.739878 + 0.672741i \(0.234883\pi\)
\(602\) 29.5345 1.20374
\(603\) −0.353562 −0.0143982
\(604\) 55.0502 2.23996
\(605\) −32.0399 −1.30261
\(606\) 49.2537 2.00079
\(607\) 15.6845 0.636613 0.318307 0.947988i \(-0.396886\pi\)
0.318307 + 0.947988i \(0.396886\pi\)
\(608\) 6.98525 0.283289
\(609\) 17.7307 0.718484
\(610\) 104.740 4.24081
\(611\) −7.18653 −0.290736
\(612\) −0.173331 −0.00700649
\(613\) −11.7294 −0.473747 −0.236874 0.971540i \(-0.576123\pi\)
−0.236874 + 0.971540i \(0.576123\pi\)
\(614\) 27.6860 1.11731
\(615\) −18.7164 −0.754718
\(616\) 9.15030 0.368676
\(617\) 15.6739 0.631007 0.315504 0.948924i \(-0.397827\pi\)
0.315504 + 0.948924i \(0.397827\pi\)
\(618\) −27.3549 −1.10038
\(619\) 17.5260 0.704429 0.352214 0.935919i \(-0.385429\pi\)
0.352214 + 0.935919i \(0.385429\pi\)
\(620\) −133.205 −5.34965
\(621\) −5.58097 −0.223956
\(622\) 42.8222 1.71701
\(623\) −12.6560 −0.507051
\(624\) 28.1733 1.12783
\(625\) −28.2107 −1.12843
\(626\) 21.4865 0.858772
\(627\) 6.44179 0.257260
\(628\) 62.4523 2.49212
\(629\) −0.179348 −0.00715106
\(630\) −11.8286 −0.471263
\(631\) 23.5801 0.938708 0.469354 0.883010i \(-0.344487\pi\)
0.469354 + 0.883010i \(0.344487\pi\)
\(632\) 43.2704 1.72120
\(633\) −0.740674 −0.0294391
\(634\) −55.9753 −2.22306
\(635\) −10.1483 −0.402723
\(636\) 1.18561 0.0470126
\(637\) 1.34860 0.0534334
\(638\) −7.46848 −0.295680
\(639\) 6.95652 0.275196
\(640\) 56.1861 2.22095
\(641\) −13.5642 −0.535755 −0.267878 0.963453i \(-0.586322\pi\)
−0.267878 + 0.963453i \(0.586322\pi\)
\(642\) −12.2979 −0.485359
\(643\) 43.0671 1.69840 0.849201 0.528070i \(-0.177084\pi\)
0.849201 + 0.528070i \(0.177084\pi\)
\(644\) 10.6066 0.417958
\(645\) −21.7682 −0.857121
\(646\) 1.04761 0.0412178
\(647\) −9.91026 −0.389613 −0.194806 0.980842i \(-0.562408\pi\)
−0.194806 + 0.980842i \(0.562408\pi\)
\(648\) 35.4927 1.39428
\(649\) −1.22096 −0.0479270
\(650\) 40.8100 1.60070
\(651\) −42.4872 −1.66520
\(652\) −2.36271 −0.0925309
\(653\) 38.9583 1.52456 0.762278 0.647249i \(-0.224081\pi\)
0.762278 + 0.647249i \(0.224081\pi\)
\(654\) −20.9366 −0.818685
\(655\) −53.9472 −2.10789
\(656\) 18.6553 0.728368
\(657\) 0.215650 0.00841331
\(658\) 11.7806 0.459257
\(659\) 2.59903 0.101244 0.0506219 0.998718i \(-0.483880\pi\)
0.0506219 + 0.998718i \(0.483880\pi\)
\(660\) −13.1306 −0.511107
\(661\) 13.5362 0.526496 0.263248 0.964728i \(-0.415206\pi\)
0.263248 + 0.964728i \(0.415206\pi\)
\(662\) −80.6908 −3.13614
\(663\) 0.415495 0.0161365
\(664\) −7.21872 −0.280141
\(665\) 48.0983 1.86517
\(666\) −3.91545 −0.151721
\(667\) −4.44649 −0.172169
\(668\) −20.9474 −0.810479
\(669\) −35.7684 −1.38289
\(670\) −4.35580 −0.168279
\(671\) −9.46735 −0.365483
\(672\) −4.54146 −0.175191
\(673\) 34.7451 1.33932 0.669662 0.742666i \(-0.266439\pi\)
0.669662 + 0.742666i \(0.266439\pi\)
\(674\) −6.40939 −0.246881
\(675\) 23.6821 0.911525
\(676\) 8.77101 0.337347
\(677\) −12.9411 −0.497367 −0.248683 0.968585i \(-0.579998\pi\)
−0.248683 + 0.968585i \(0.579998\pi\)
\(678\) 58.0936 2.23107
\(679\) 21.6664 0.831479
\(680\) −1.09679 −0.0420598
\(681\) −2.62020 −0.100406
\(682\) 17.8964 0.685287
\(683\) −37.6943 −1.44233 −0.721166 0.692763i \(-0.756393\pi\)
−0.721166 + 0.692763i \(0.756393\pi\)
\(684\) 15.3871 0.588342
\(685\) 34.2864 1.31002
\(686\) −46.8493 −1.78871
\(687\) 21.3488 0.814508
\(688\) 21.6971 0.827196
\(689\) 0.725537 0.0276408
\(690\) −11.6198 −0.442357
\(691\) −12.6084 −0.479648 −0.239824 0.970816i \(-0.577090\pi\)
−0.239824 + 0.970816i \(0.577090\pi\)
\(692\) 5.80270 0.220586
\(693\) 1.06917 0.0406146
\(694\) 78.6767 2.98653
\(695\) 9.50824 0.360668
\(696\) 35.8921 1.36049
\(697\) 0.275126 0.0104211
\(698\) −2.47225 −0.0935761
\(699\) −37.5961 −1.42202
\(700\) −45.0077 −1.70113
\(701\) −7.00099 −0.264424 −0.132212 0.991221i \(-0.542208\pi\)
−0.132212 + 0.991221i \(0.542208\pi\)
\(702\) 53.6741 2.02580
\(703\) 15.9213 0.600482
\(704\) −4.45263 −0.167815
\(705\) −8.68282 −0.327014
\(706\) −57.3389 −2.15798
\(707\) −33.2411 −1.25016
\(708\) 11.4242 0.429347
\(709\) −16.7033 −0.627305 −0.313653 0.949538i \(-0.601553\pi\)
−0.313653 + 0.949538i \(0.601553\pi\)
\(710\) 85.7025 3.21636
\(711\) 5.05597 0.189614
\(712\) −25.6194 −0.960127
\(713\) 10.6549 0.399029
\(714\) −0.681106 −0.0254898
\(715\) −8.03527 −0.300502
\(716\) 102.230 3.82053
\(717\) 30.5769 1.14191
\(718\) −18.5629 −0.692762
\(719\) −26.8149 −1.00003 −0.500014 0.866017i \(-0.666672\pi\)
−0.500014 + 0.866017i \(0.666672\pi\)
\(720\) −8.68974 −0.323848
\(721\) 18.4618 0.687552
\(722\) −46.0272 −1.71295
\(723\) −7.36937 −0.274070
\(724\) 7.40422 0.275176
\(725\) 18.8681 0.700743
\(726\) −40.2770 −1.49482
\(727\) 26.6700 0.989136 0.494568 0.869139i \(-0.335326\pi\)
0.494568 + 0.869139i \(0.335326\pi\)
\(728\) −52.3932 −1.94182
\(729\) 30.0305 1.11224
\(730\) 2.65675 0.0983308
\(731\) 0.319986 0.0118351
\(732\) 88.5832 3.27413
\(733\) −39.1691 −1.44674 −0.723371 0.690460i \(-0.757408\pi\)
−0.723371 + 0.690460i \(0.757408\pi\)
\(734\) −17.0811 −0.630474
\(735\) 1.62939 0.0601008
\(736\) 1.13890 0.0419805
\(737\) 0.393715 0.0145027
\(738\) 6.00644 0.221100
\(739\) 13.2423 0.487127 0.243564 0.969885i \(-0.421684\pi\)
0.243564 + 0.969885i \(0.421684\pi\)
\(740\) −32.4529 −1.19299
\(741\) −36.8848 −1.35500
\(742\) −1.18935 −0.0436624
\(743\) 0.846604 0.0310589 0.0155294 0.999879i \(-0.495057\pi\)
0.0155294 + 0.999879i \(0.495057\pi\)
\(744\) −86.0066 −3.15315
\(745\) −30.5539 −1.11941
\(746\) −25.8716 −0.947226
\(747\) −0.843478 −0.0308612
\(748\) 0.193016 0.00705735
\(749\) 8.29980 0.303268
\(750\) −8.79184 −0.321033
\(751\) 49.8816 1.82021 0.910103 0.414382i \(-0.136002\pi\)
0.910103 + 0.414382i \(0.136002\pi\)
\(752\) 8.65449 0.315597
\(753\) 17.6693 0.643906
\(754\) 42.7634 1.55735
\(755\) 40.7022 1.48130
\(756\) −59.1950 −2.15290
\(757\) 22.4527 0.816056 0.408028 0.912969i \(-0.366217\pi\)
0.408028 + 0.912969i \(0.366217\pi\)
\(758\) 40.9257 1.48649
\(759\) 1.05030 0.0381233
\(760\) 97.3651 3.53180
\(761\) 30.5909 1.10892 0.554459 0.832211i \(-0.312925\pi\)
0.554459 + 0.832211i \(0.312925\pi\)
\(762\) −12.7573 −0.462149
\(763\) 14.1300 0.511542
\(764\) 26.2824 0.950864
\(765\) −0.128155 −0.00463345
\(766\) −61.0484 −2.20577
\(767\) 6.99105 0.252432
\(768\) 50.3676 1.81748
\(769\) −14.8896 −0.536931 −0.268466 0.963289i \(-0.586517\pi\)
−0.268466 + 0.963289i \(0.586517\pi\)
\(770\) 13.1719 0.474684
\(771\) −3.80143 −0.136905
\(772\) 5.25876 0.189267
\(773\) 29.1942 1.05004 0.525021 0.851089i \(-0.324058\pi\)
0.525021 + 0.851089i \(0.324058\pi\)
\(774\) 6.98581 0.251100
\(775\) −45.2127 −1.62409
\(776\) 43.8591 1.57445
\(777\) −10.3512 −0.371347
\(778\) −37.0436 −1.32808
\(779\) −24.4238 −0.875073
\(780\) 75.1837 2.69201
\(781\) −7.74654 −0.277193
\(782\) 0.170807 0.00610805
\(783\) 24.8157 0.886840
\(784\) −1.62407 −0.0580025
\(785\) 46.1750 1.64806
\(786\) −67.8165 −2.41894
\(787\) 40.8189 1.45504 0.727518 0.686089i \(-0.240674\pi\)
0.727518 + 0.686089i \(0.240674\pi\)
\(788\) −6.19150 −0.220563
\(789\) 25.4435 0.905814
\(790\) 62.2882 2.21611
\(791\) −39.2072 −1.39405
\(792\) 2.16432 0.0769059
\(793\) 54.2086 1.92500
\(794\) 8.90738 0.316111
\(795\) 0.876600 0.0310898
\(796\) 51.6720 1.83147
\(797\) −2.65134 −0.0939151 −0.0469576 0.998897i \(-0.514953\pi\)
−0.0469576 + 0.998897i \(0.514953\pi\)
\(798\) 60.4639 2.14040
\(799\) 0.127635 0.00451540
\(800\) −4.83279 −0.170865
\(801\) −2.99352 −0.105771
\(802\) 1.57456 0.0555996
\(803\) −0.240141 −0.00847438
\(804\) −3.68388 −0.129920
\(805\) 7.84214 0.276399
\(806\) −102.472 −3.60942
\(807\) −10.5879 −0.372712
\(808\) −67.2899 −2.36725
\(809\) −38.1588 −1.34159 −0.670796 0.741642i \(-0.734047\pi\)
−0.670796 + 0.741642i \(0.734047\pi\)
\(810\) 51.0921 1.79519
\(811\) 0.414288 0.0145476 0.00727381 0.999974i \(-0.497685\pi\)
0.00727381 + 0.999974i \(0.497685\pi\)
\(812\) −47.1621 −1.65506
\(813\) 35.8563 1.25753
\(814\) 4.36011 0.152822
\(815\) −1.74690 −0.0611914
\(816\) −0.500366 −0.0175163
\(817\) −28.4062 −0.993806
\(818\) −33.1713 −1.15981
\(819\) −6.12193 −0.213918
\(820\) 49.7840 1.73853
\(821\) 18.0568 0.630187 0.315093 0.949061i \(-0.397964\pi\)
0.315093 + 0.949061i \(0.397964\pi\)
\(822\) 43.1011 1.50333
\(823\) 21.3426 0.743957 0.371979 0.928241i \(-0.378679\pi\)
0.371979 + 0.928241i \(0.378679\pi\)
\(824\) 37.3721 1.30192
\(825\) −4.45680 −0.155166
\(826\) −11.4602 −0.398751
\(827\) 15.2881 0.531621 0.265810 0.964025i \(-0.414361\pi\)
0.265810 + 0.964025i \(0.414361\pi\)
\(828\) 2.50878 0.0871862
\(829\) 4.06554 0.141202 0.0706010 0.997505i \(-0.477508\pi\)
0.0706010 + 0.997505i \(0.477508\pi\)
\(830\) −10.3914 −0.360692
\(831\) −1.00854 −0.0349859
\(832\) 25.4951 0.883884
\(833\) −0.0239515 −0.000829871 0
\(834\) 11.9527 0.413889
\(835\) −15.4878 −0.535976
\(836\) −17.1346 −0.592613
\(837\) −59.4647 −2.05540
\(838\) −53.8165 −1.85906
\(839\) −10.0183 −0.345869 −0.172934 0.984933i \(-0.555325\pi\)
−0.172934 + 0.984933i \(0.555325\pi\)
\(840\) −63.3019 −2.18412
\(841\) −9.22876 −0.318233
\(842\) 9.87905 0.340454
\(843\) −9.11568 −0.313961
\(844\) 1.97013 0.0678146
\(845\) 6.48498 0.223090
\(846\) 2.78648 0.0958011
\(847\) 27.1829 0.934014
\(848\) −0.873740 −0.0300044
\(849\) 34.8086 1.19463
\(850\) −0.724798 −0.0248604
\(851\) 2.59587 0.0889852
\(852\) 72.4821 2.48320
\(853\) 49.8617 1.70723 0.853616 0.520903i \(-0.174405\pi\)
0.853616 + 0.520903i \(0.174405\pi\)
\(854\) −88.8624 −3.04081
\(855\) 11.3767 0.389075
\(856\) 16.8012 0.574255
\(857\) −30.0651 −1.02700 −0.513502 0.858089i \(-0.671652\pi\)
−0.513502 + 0.858089i \(0.671652\pi\)
\(858\) −10.1011 −0.344845
\(859\) −36.5435 −1.24685 −0.623423 0.781884i \(-0.714259\pi\)
−0.623423 + 0.781884i \(0.714259\pi\)
\(860\) 57.9014 1.97442
\(861\) 15.8791 0.541159
\(862\) −11.7189 −0.399149
\(863\) 5.47399 0.186337 0.0931685 0.995650i \(-0.470300\pi\)
0.0931685 + 0.995650i \(0.470300\pi\)
\(864\) −6.35618 −0.216242
\(865\) 4.29031 0.145875
\(866\) 77.6621 2.63907
\(867\) 26.2734 0.892291
\(868\) 113.012 3.83588
\(869\) −5.63015 −0.190990
\(870\) 51.6671 1.75168
\(871\) −2.25436 −0.0763859
\(872\) 28.6034 0.968632
\(873\) 5.12476 0.173447
\(874\) −15.1631 −0.512899
\(875\) 5.93359 0.200592
\(876\) 2.24693 0.0759166
\(877\) 29.2603 0.988051 0.494026 0.869447i \(-0.335525\pi\)
0.494026 + 0.869447i \(0.335525\pi\)
\(878\) 55.3054 1.86647
\(879\) 2.18833 0.0738107
\(880\) 9.67660 0.326198
\(881\) 59.0302 1.98878 0.994389 0.105784i \(-0.0337352\pi\)
0.994389 + 0.105784i \(0.0337352\pi\)
\(882\) −0.522900 −0.0176070
\(883\) −7.71437 −0.259609 −0.129805 0.991540i \(-0.541435\pi\)
−0.129805 + 0.991540i \(0.541435\pi\)
\(884\) −1.10518 −0.0371712
\(885\) 8.44664 0.283931
\(886\) 72.2271 2.42652
\(887\) 48.6186 1.63245 0.816226 0.577733i \(-0.196062\pi\)
0.816226 + 0.577733i \(0.196062\pi\)
\(888\) −20.9539 −0.703166
\(889\) 8.60988 0.288766
\(890\) −36.8794 −1.23620
\(891\) −4.61815 −0.154714
\(892\) 95.1409 3.18555
\(893\) −11.3306 −0.379163
\(894\) −38.4090 −1.28459
\(895\) 75.5856 2.52655
\(896\) −47.6687 −1.59250
\(897\) −6.01384 −0.200796
\(898\) −0.666997 −0.0222580
\(899\) −47.3769 −1.58011
\(900\) −10.6457 −0.354856
\(901\) −0.0128858 −0.000429287 0
\(902\) −6.68857 −0.222705
\(903\) 18.4683 0.614585
\(904\) −79.3670 −2.63971
\(905\) 5.47442 0.181976
\(906\) 51.1663 1.69989
\(907\) −5.51377 −0.183082 −0.0915408 0.995801i \(-0.529179\pi\)
−0.0915408 + 0.995801i \(0.529179\pi\)
\(908\) 6.96949 0.231291
\(909\) −7.86254 −0.260784
\(910\) −75.4206 −2.50017
\(911\) 28.2552 0.936137 0.468068 0.883692i \(-0.344950\pi\)
0.468068 + 0.883692i \(0.344950\pi\)
\(912\) 44.4191 1.47086
\(913\) 0.939268 0.0310852
\(914\) 41.3470 1.36764
\(915\) 65.4953 2.16521
\(916\) −56.7860 −1.87626
\(917\) 45.7692 1.51143
\(918\) −0.953269 −0.0314626
\(919\) 41.0091 1.35276 0.676382 0.736551i \(-0.263547\pi\)
0.676382 + 0.736551i \(0.263547\pi\)
\(920\) 15.8748 0.523377
\(921\) 17.3124 0.570461
\(922\) −24.0777 −0.792957
\(923\) 44.3556 1.45998
\(924\) 11.1401 0.366481
\(925\) −11.0152 −0.362178
\(926\) −12.1292 −0.398592
\(927\) 4.36677 0.143424
\(928\) −5.06412 −0.166238
\(929\) −52.2165 −1.71317 −0.856584 0.516008i \(-0.827418\pi\)
−0.856584 + 0.516008i \(0.827418\pi\)
\(930\) −123.807 −4.05981
\(931\) 2.12625 0.0696851
\(932\) 100.002 3.27569
\(933\) 26.7772 0.876646
\(934\) 5.23860 0.171412
\(935\) 0.142709 0.00466708
\(936\) −12.3926 −0.405065
\(937\) −39.0391 −1.27535 −0.637676 0.770304i \(-0.720104\pi\)
−0.637676 + 0.770304i \(0.720104\pi\)
\(938\) 3.69549 0.120662
\(939\) 13.4357 0.438459
\(940\) 23.0955 0.753293
\(941\) −18.3020 −0.596627 −0.298314 0.954468i \(-0.596424\pi\)
−0.298314 + 0.954468i \(0.596424\pi\)
\(942\) 58.0462 1.89125
\(943\) −3.98215 −0.129677
\(944\) −8.41908 −0.274018
\(945\) −43.7667 −1.42373
\(946\) −7.77916 −0.252922
\(947\) 33.0394 1.07364 0.536819 0.843698i \(-0.319626\pi\)
0.536819 + 0.843698i \(0.319626\pi\)
\(948\) 52.6797 1.71096
\(949\) 1.37501 0.0446347
\(950\) 64.3426 2.08755
\(951\) −35.0020 −1.13502
\(952\) 0.930521 0.0301583
\(953\) −29.5717 −0.957920 −0.478960 0.877837i \(-0.658986\pi\)
−0.478960 + 0.877837i \(0.658986\pi\)
\(954\) −0.281317 −0.00910798
\(955\) 19.4323 0.628814
\(956\) −81.3318 −2.63046
\(957\) −4.67013 −0.150964
\(958\) 10.3460 0.334266
\(959\) −29.0888 −0.939328
\(960\) 30.8034 0.994175
\(961\) 82.5270 2.66216
\(962\) −24.9654 −0.804915
\(963\) 1.96316 0.0632618
\(964\) 19.6019 0.631334
\(965\) 3.88815 0.125164
\(966\) 9.85829 0.317185
\(967\) −17.5092 −0.563057 −0.281529 0.959553i \(-0.590841\pi\)
−0.281529 + 0.959553i \(0.590841\pi\)
\(968\) 55.0261 1.76861
\(969\) 0.655085 0.0210444
\(970\) 63.1357 2.02716
\(971\) 60.1243 1.92948 0.964741 0.263201i \(-0.0847783\pi\)
0.964741 + 0.263201i \(0.0847783\pi\)
\(972\) −25.6366 −0.822295
\(973\) −8.06686 −0.258612
\(974\) −44.2449 −1.41770
\(975\) 25.5190 0.817261
\(976\) −65.2816 −2.08961
\(977\) 31.5216 1.00846 0.504232 0.863568i \(-0.331776\pi\)
0.504232 + 0.863568i \(0.331776\pi\)
\(978\) −2.19602 −0.0702209
\(979\) 3.33349 0.106539
\(980\) −4.33402 −0.138445
\(981\) 3.34218 0.106708
\(982\) 5.72999 0.182851
\(983\) 5.40376 0.172353 0.0861765 0.996280i \(-0.472535\pi\)
0.0861765 + 0.996280i \(0.472535\pi\)
\(984\) 32.1440 1.02471
\(985\) −4.57778 −0.145860
\(986\) −0.759492 −0.0241872
\(987\) 7.36657 0.234480
\(988\) 98.1102 3.12130
\(989\) −4.63146 −0.147272
\(990\) 3.11557 0.0990192
\(991\) 52.9995 1.68358 0.841792 0.539802i \(-0.181501\pi\)
0.841792 + 0.539802i \(0.181501\pi\)
\(992\) 12.1349 0.385284
\(993\) −50.4569 −1.60120
\(994\) −72.7106 −2.30624
\(995\) 38.2045 1.21116
\(996\) −8.78846 −0.278473
\(997\) −12.3012 −0.389584 −0.194792 0.980845i \(-0.562403\pi\)
−0.194792 + 0.980845i \(0.562403\pi\)
\(998\) 15.6766 0.496235
\(999\) −14.4874 −0.458362
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 8027.2.a.e.1.15 169
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.e.1.15 169 1.1 even 1 trivial