Properties

Label 8013.2.a.c.1.8
Level $8013$
Weight $2$
Character 8013.1
Self dual yes
Analytic conductor $63.984$
Analytic rank $1$
Dimension $116$
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] = [8013,2,Mod(1,8013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8013, 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("8013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8013.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: \(63.9841271397\)
Analytic rank: \(1\)
Dimension: \(116\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.59210 q^{2} -1.00000 q^{3} +4.71896 q^{4} -1.33515 q^{5} +2.59210 q^{6} -1.92470 q^{7} -7.04781 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.59210 q^{2} -1.00000 q^{3} +4.71896 q^{4} -1.33515 q^{5} +2.59210 q^{6} -1.92470 q^{7} -7.04781 q^{8} +1.00000 q^{9} +3.46084 q^{10} -5.66323 q^{11} -4.71896 q^{12} +2.66191 q^{13} +4.98901 q^{14} +1.33515 q^{15} +8.83069 q^{16} -1.18763 q^{17} -2.59210 q^{18} -0.599888 q^{19} -6.30053 q^{20} +1.92470 q^{21} +14.6796 q^{22} -8.78251 q^{23} +7.04781 q^{24} -3.21737 q^{25} -6.89992 q^{26} -1.00000 q^{27} -9.08259 q^{28} +8.46066 q^{29} -3.46084 q^{30} +1.10076 q^{31} -8.79437 q^{32} +5.66323 q^{33} +3.07845 q^{34} +2.56977 q^{35} +4.71896 q^{36} +6.12882 q^{37} +1.55497 q^{38} -2.66191 q^{39} +9.40990 q^{40} -2.71046 q^{41} -4.98901 q^{42} +2.41047 q^{43} -26.7246 q^{44} -1.33515 q^{45} +22.7651 q^{46} -6.31667 q^{47} -8.83069 q^{48} -3.29553 q^{49} +8.33973 q^{50} +1.18763 q^{51} +12.5615 q^{52} +8.09769 q^{53} +2.59210 q^{54} +7.56128 q^{55} +13.5649 q^{56} +0.599888 q^{57} -21.9308 q^{58} +2.25320 q^{59} +6.30053 q^{60} +13.1292 q^{61} -2.85328 q^{62} -1.92470 q^{63} +5.13447 q^{64} -3.55405 q^{65} -14.6796 q^{66} +3.21350 q^{67} -5.60438 q^{68} +8.78251 q^{69} -6.66108 q^{70} -13.7699 q^{71} -7.04781 q^{72} -7.59790 q^{73} -15.8865 q^{74} +3.21737 q^{75} -2.83085 q^{76} +10.9000 q^{77} +6.89992 q^{78} +8.17323 q^{79} -11.7903 q^{80} +1.00000 q^{81} +7.02578 q^{82} +3.52602 q^{83} +9.08259 q^{84} +1.58566 q^{85} -6.24816 q^{86} -8.46066 q^{87} +39.9134 q^{88} +14.2282 q^{89} +3.46084 q^{90} -5.12338 q^{91} -41.4443 q^{92} -1.10076 q^{93} +16.3734 q^{94} +0.800942 q^{95} +8.79437 q^{96} -13.8523 q^{97} +8.54233 q^{98} -5.66323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59210 −1.83289 −0.916444 0.400162i \(-0.868954\pi\)
−0.916444 + 0.400162i \(0.868954\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.71896 2.35948
\(5\) −1.33515 −0.597098 −0.298549 0.954394i \(-0.596503\pi\)
−0.298549 + 0.954394i \(0.596503\pi\)
\(6\) 2.59210 1.05822
\(7\) −1.92470 −0.727468 −0.363734 0.931503i \(-0.618498\pi\)
−0.363734 + 0.931503i \(0.618498\pi\)
\(8\) −7.04781 −2.49178
\(9\) 1.00000 0.333333
\(10\) 3.46084 1.09441
\(11\) −5.66323 −1.70753 −0.853765 0.520659i \(-0.825686\pi\)
−0.853765 + 0.520659i \(0.825686\pi\)
\(12\) −4.71896 −1.36225
\(13\) 2.66191 0.738281 0.369140 0.929374i \(-0.379652\pi\)
0.369140 + 0.929374i \(0.379652\pi\)
\(14\) 4.98901 1.33337
\(15\) 1.33515 0.344735
\(16\) 8.83069 2.20767
\(17\) −1.18763 −0.288042 −0.144021 0.989575i \(-0.546003\pi\)
−0.144021 + 0.989575i \(0.546003\pi\)
\(18\) −2.59210 −0.610963
\(19\) −0.599888 −0.137624 −0.0688119 0.997630i \(-0.521921\pi\)
−0.0688119 + 0.997630i \(0.521921\pi\)
\(20\) −6.30053 −1.40884
\(21\) 1.92470 0.420004
\(22\) 14.6796 3.12971
\(23\) −8.78251 −1.83128 −0.915640 0.401999i \(-0.868315\pi\)
−0.915640 + 0.401999i \(0.868315\pi\)
\(24\) 7.04781 1.43863
\(25\) −3.21737 −0.643474
\(26\) −6.89992 −1.35319
\(27\) −1.00000 −0.192450
\(28\) −9.08259 −1.71645
\(29\) 8.46066 1.57110 0.785552 0.618795i \(-0.212379\pi\)
0.785552 + 0.618795i \(0.212379\pi\)
\(30\) −3.46084 −0.631861
\(31\) 1.10076 0.197702 0.0988512 0.995102i \(-0.468483\pi\)
0.0988512 + 0.995102i \(0.468483\pi\)
\(32\) −8.79437 −1.55464
\(33\) 5.66323 0.985843
\(34\) 3.07845 0.527949
\(35\) 2.56977 0.434370
\(36\) 4.71896 0.786494
\(37\) 6.12882 1.00757 0.503786 0.863829i \(-0.331940\pi\)
0.503786 + 0.863829i \(0.331940\pi\)
\(38\) 1.55497 0.252249
\(39\) −2.66191 −0.426247
\(40\) 9.40990 1.48784
\(41\) −2.71046 −0.423303 −0.211652 0.977345i \(-0.567884\pi\)
−0.211652 + 0.977345i \(0.567884\pi\)
\(42\) −4.98901 −0.769821
\(43\) 2.41047 0.367593 0.183796 0.982964i \(-0.441161\pi\)
0.183796 + 0.982964i \(0.441161\pi\)
\(44\) −26.7246 −4.02888
\(45\) −1.33515 −0.199033
\(46\) 22.7651 3.35653
\(47\) −6.31667 −0.921382 −0.460691 0.887561i \(-0.652398\pi\)
−0.460691 + 0.887561i \(0.652398\pi\)
\(48\) −8.83069 −1.27460
\(49\) −3.29553 −0.470790
\(50\) 8.33973 1.17942
\(51\) 1.18763 0.166301
\(52\) 12.5615 1.74196
\(53\) 8.09769 1.11230 0.556152 0.831081i \(-0.312277\pi\)
0.556152 + 0.831081i \(0.312277\pi\)
\(54\) 2.59210 0.352740
\(55\) 7.56128 1.01956
\(56\) 13.5649 1.81269
\(57\) 0.599888 0.0794572
\(58\) −21.9308 −2.87966
\(59\) 2.25320 0.293342 0.146671 0.989185i \(-0.453144\pi\)
0.146671 + 0.989185i \(0.453144\pi\)
\(60\) 6.30053 0.813395
\(61\) 13.1292 1.68103 0.840513 0.541791i \(-0.182254\pi\)
0.840513 + 0.541791i \(0.182254\pi\)
\(62\) −2.85328 −0.362366
\(63\) −1.92470 −0.242489
\(64\) 5.13447 0.641808
\(65\) −3.55405 −0.440826
\(66\) −14.6796 −1.80694
\(67\) 3.21350 0.392592 0.196296 0.980545i \(-0.437109\pi\)
0.196296 + 0.980545i \(0.437109\pi\)
\(68\) −5.60438 −0.679630
\(69\) 8.78251 1.05729
\(70\) −6.66108 −0.796152
\(71\) −13.7699 −1.63419 −0.817095 0.576503i \(-0.804417\pi\)
−0.817095 + 0.576503i \(0.804417\pi\)
\(72\) −7.04781 −0.830593
\(73\) −7.59790 −0.889267 −0.444634 0.895713i \(-0.646666\pi\)
−0.444634 + 0.895713i \(0.646666\pi\)
\(74\) −15.8865 −1.84677
\(75\) 3.21737 0.371510
\(76\) −2.83085 −0.324721
\(77\) 10.9000 1.24217
\(78\) 6.89992 0.781263
\(79\) 8.17323 0.919560 0.459780 0.888033i \(-0.347928\pi\)
0.459780 + 0.888033i \(0.347928\pi\)
\(80\) −11.7903 −1.31820
\(81\) 1.00000 0.111111
\(82\) 7.02578 0.775868
\(83\) 3.52602 0.387031 0.193516 0.981097i \(-0.438011\pi\)
0.193516 + 0.981097i \(0.438011\pi\)
\(84\) 9.08259 0.990992
\(85\) 1.58566 0.171990
\(86\) −6.24816 −0.673757
\(87\) −8.46066 −0.907078
\(88\) 39.9134 4.25479
\(89\) 14.2282 1.50818 0.754092 0.656769i \(-0.228077\pi\)
0.754092 + 0.656769i \(0.228077\pi\)
\(90\) 3.46084 0.364805
\(91\) −5.12338 −0.537076
\(92\) −41.4443 −4.32087
\(93\) −1.10076 −0.114144
\(94\) 16.3734 1.68879
\(95\) 0.800942 0.0821749
\(96\) 8.79437 0.897571
\(97\) −13.8523 −1.40649 −0.703243 0.710949i \(-0.748266\pi\)
−0.703243 + 0.710949i \(0.748266\pi\)
\(98\) 8.54233 0.862906
\(99\) −5.66323 −0.569176
\(100\) −15.1826 −1.51826
\(101\) 1.19183 0.118591 0.0592955 0.998240i \(-0.481115\pi\)
0.0592955 + 0.998240i \(0.481115\pi\)
\(102\) −3.07845 −0.304812
\(103\) 6.40546 0.631149 0.315574 0.948901i \(-0.397803\pi\)
0.315574 + 0.948901i \(0.397803\pi\)
\(104\) −18.7606 −1.83963
\(105\) −2.56977 −0.250784
\(106\) −20.9900 −2.03873
\(107\) 10.8032 1.04438 0.522190 0.852829i \(-0.325115\pi\)
0.522190 + 0.852829i \(0.325115\pi\)
\(108\) −4.71896 −0.454082
\(109\) 5.64865 0.541043 0.270521 0.962714i \(-0.412804\pi\)
0.270521 + 0.962714i \(0.412804\pi\)
\(110\) −19.5996 −1.86875
\(111\) −6.12882 −0.581721
\(112\) −16.9964 −1.60601
\(113\) 7.87519 0.740835 0.370418 0.928865i \(-0.379215\pi\)
0.370418 + 0.928865i \(0.379215\pi\)
\(114\) −1.55497 −0.145636
\(115\) 11.7260 1.09345
\(116\) 39.9255 3.70699
\(117\) 2.66191 0.246094
\(118\) −5.84052 −0.537663
\(119\) 2.28583 0.209542
\(120\) −9.40990 −0.859003
\(121\) 21.0722 1.91566
\(122\) −34.0322 −3.08113
\(123\) 2.71046 0.244394
\(124\) 5.19445 0.466475
\(125\) 10.9714 0.981315
\(126\) 4.98901 0.444456
\(127\) −17.9013 −1.58849 −0.794243 0.607600i \(-0.792132\pi\)
−0.794243 + 0.607600i \(0.792132\pi\)
\(128\) 4.27970 0.378276
\(129\) −2.41047 −0.212230
\(130\) 9.21245 0.807985
\(131\) 12.3361 1.07781 0.538906 0.842366i \(-0.318838\pi\)
0.538906 + 0.842366i \(0.318838\pi\)
\(132\) 26.7246 2.32608
\(133\) 1.15461 0.100117
\(134\) −8.32971 −0.719577
\(135\) 1.33515 0.114912
\(136\) 8.37019 0.717738
\(137\) 13.7818 1.17746 0.588728 0.808331i \(-0.299629\pi\)
0.588728 + 0.808331i \(0.299629\pi\)
\(138\) −22.7651 −1.93789
\(139\) 9.89703 0.839455 0.419728 0.907650i \(-0.362126\pi\)
0.419728 + 0.907650i \(0.362126\pi\)
\(140\) 12.1266 1.02489
\(141\) 6.31667 0.531960
\(142\) 35.6930 2.99529
\(143\) −15.0750 −1.26064
\(144\) 8.83069 0.735891
\(145\) −11.2963 −0.938104
\(146\) 19.6945 1.62993
\(147\) 3.29553 0.271811
\(148\) 28.9217 2.37735
\(149\) 4.06228 0.332795 0.166397 0.986059i \(-0.446787\pi\)
0.166397 + 0.986059i \(0.446787\pi\)
\(150\) −8.33973 −0.680936
\(151\) 2.18587 0.177884 0.0889419 0.996037i \(-0.471651\pi\)
0.0889419 + 0.996037i \(0.471651\pi\)
\(152\) 4.22790 0.342928
\(153\) −1.18763 −0.0960141
\(154\) −28.2539 −2.27677
\(155\) −1.46968 −0.118048
\(156\) −12.5615 −1.00572
\(157\) −7.10494 −0.567036 −0.283518 0.958967i \(-0.591502\pi\)
−0.283518 + 0.958967i \(0.591502\pi\)
\(158\) −21.1858 −1.68545
\(159\) −8.09769 −0.642189
\(160\) 11.7418 0.928272
\(161\) 16.9037 1.33220
\(162\) −2.59210 −0.203654
\(163\) 7.99813 0.626462 0.313231 0.949677i \(-0.398589\pi\)
0.313231 + 0.949677i \(0.398589\pi\)
\(164\) −12.7906 −0.998776
\(165\) −7.56128 −0.588645
\(166\) −9.13979 −0.709385
\(167\) −19.6208 −1.51831 −0.759153 0.650912i \(-0.774387\pi\)
−0.759153 + 0.650912i \(0.774387\pi\)
\(168\) −13.5649 −1.04656
\(169\) −5.91424 −0.454942
\(170\) −4.11020 −0.315238
\(171\) −0.599888 −0.0458746
\(172\) 11.3749 0.867328
\(173\) −12.9471 −0.984348 −0.492174 0.870497i \(-0.663798\pi\)
−0.492174 + 0.870497i \(0.663798\pi\)
\(174\) 21.9308 1.66257
\(175\) 6.19247 0.468107
\(176\) −50.0103 −3.76967
\(177\) −2.25320 −0.169361
\(178\) −36.8808 −2.76433
\(179\) −20.1566 −1.50658 −0.753288 0.657690i \(-0.771534\pi\)
−0.753288 + 0.657690i \(0.771534\pi\)
\(180\) −6.30053 −0.469614
\(181\) 3.86727 0.287452 0.143726 0.989618i \(-0.454092\pi\)
0.143726 + 0.989618i \(0.454092\pi\)
\(182\) 13.2803 0.984400
\(183\) −13.1292 −0.970541
\(184\) 61.8975 4.56314
\(185\) −8.18290 −0.601619
\(186\) 2.85328 0.209212
\(187\) 6.72582 0.491841
\(188\) −29.8082 −2.17398
\(189\) 1.92470 0.140001
\(190\) −2.07612 −0.150618
\(191\) −21.3873 −1.54753 −0.773767 0.633471i \(-0.781630\pi\)
−0.773767 + 0.633471i \(0.781630\pi\)
\(192\) −5.13447 −0.370548
\(193\) −13.5814 −0.977607 −0.488804 0.872394i \(-0.662567\pi\)
−0.488804 + 0.872394i \(0.662567\pi\)
\(194\) 35.9065 2.57793
\(195\) 3.55405 0.254511
\(196\) −15.5515 −1.11082
\(197\) −6.68640 −0.476386 −0.238193 0.971218i \(-0.576555\pi\)
−0.238193 + 0.971218i \(0.576555\pi\)
\(198\) 14.6796 1.04324
\(199\) 7.38514 0.523519 0.261759 0.965133i \(-0.415697\pi\)
0.261759 + 0.965133i \(0.415697\pi\)
\(200\) 22.6754 1.60339
\(201\) −3.21350 −0.226663
\(202\) −3.08933 −0.217364
\(203\) −16.2842 −1.14293
\(204\) 5.60438 0.392385
\(205\) 3.61888 0.252754
\(206\) −16.6036 −1.15683
\(207\) −8.78251 −0.610427
\(208\) 23.5065 1.62988
\(209\) 3.39731 0.234997
\(210\) 6.66108 0.459658
\(211\) −1.13038 −0.0778183 −0.0389091 0.999243i \(-0.512388\pi\)
−0.0389091 + 0.999243i \(0.512388\pi\)
\(212\) 38.2127 2.62446
\(213\) 13.7699 0.943500
\(214\) −28.0028 −1.91423
\(215\) −3.21834 −0.219489
\(216\) 7.04781 0.479543
\(217\) −2.11863 −0.143822
\(218\) −14.6419 −0.991672
\(219\) 7.59790 0.513419
\(220\) 35.6814 2.40564
\(221\) −3.16136 −0.212656
\(222\) 15.8865 1.06623
\(223\) 13.2540 0.887552 0.443776 0.896138i \(-0.353639\pi\)
0.443776 + 0.896138i \(0.353639\pi\)
\(224\) 16.9265 1.13095
\(225\) −3.21737 −0.214491
\(226\) −20.4132 −1.35787
\(227\) −10.7444 −0.713129 −0.356565 0.934271i \(-0.616052\pi\)
−0.356565 + 0.934271i \(0.616052\pi\)
\(228\) 2.83085 0.187478
\(229\) 17.4234 1.15137 0.575687 0.817670i \(-0.304735\pi\)
0.575687 + 0.817670i \(0.304735\pi\)
\(230\) −30.3949 −2.00418
\(231\) −10.9000 −0.717169
\(232\) −59.6292 −3.91485
\(233\) −2.61855 −0.171547 −0.0857736 0.996315i \(-0.527336\pi\)
−0.0857736 + 0.996315i \(0.527336\pi\)
\(234\) −6.89992 −0.451062
\(235\) 8.43372 0.550155
\(236\) 10.6328 0.692135
\(237\) −8.17323 −0.530908
\(238\) −5.92509 −0.384066
\(239\) 9.90679 0.640817 0.320408 0.947280i \(-0.396180\pi\)
0.320408 + 0.947280i \(0.396180\pi\)
\(240\) 11.7903 0.761061
\(241\) 15.2624 0.983137 0.491568 0.870839i \(-0.336424\pi\)
0.491568 + 0.870839i \(0.336424\pi\)
\(242\) −54.6212 −3.51119
\(243\) −1.00000 −0.0641500
\(244\) 61.9564 3.96635
\(245\) 4.40003 0.281108
\(246\) −7.02578 −0.447947
\(247\) −1.59685 −0.101605
\(248\) −7.75795 −0.492631
\(249\) −3.52602 −0.223453
\(250\) −28.4390 −1.79864
\(251\) −5.81591 −0.367097 −0.183549 0.983011i \(-0.558758\pi\)
−0.183549 + 0.983011i \(0.558758\pi\)
\(252\) −9.08259 −0.572149
\(253\) 49.7374 3.12696
\(254\) 46.4020 2.91152
\(255\) −1.58566 −0.0992982
\(256\) −21.3623 −1.33515
\(257\) 1.02291 0.0638072 0.0319036 0.999491i \(-0.489843\pi\)
0.0319036 + 0.999491i \(0.489843\pi\)
\(258\) 6.24816 0.388994
\(259\) −11.7961 −0.732976
\(260\) −16.7714 −1.04012
\(261\) 8.46066 0.523702
\(262\) −31.9764 −1.97551
\(263\) 18.3259 1.13002 0.565012 0.825083i \(-0.308872\pi\)
0.565012 + 0.825083i \(0.308872\pi\)
\(264\) −39.9134 −2.45650
\(265\) −10.8116 −0.664154
\(266\) −2.99285 −0.183503
\(267\) −14.2282 −0.870751
\(268\) 15.1644 0.926314
\(269\) −1.16220 −0.0708607 −0.0354303 0.999372i \(-0.511280\pi\)
−0.0354303 + 0.999372i \(0.511280\pi\)
\(270\) −3.46084 −0.210620
\(271\) −7.72761 −0.469419 −0.234710 0.972066i \(-0.575414\pi\)
−0.234710 + 0.972066i \(0.575414\pi\)
\(272\) −10.4876 −0.635903
\(273\) 5.12338 0.310081
\(274\) −35.7237 −2.15814
\(275\) 18.2207 1.09875
\(276\) 41.4443 2.49466
\(277\) −7.53433 −0.452694 −0.226347 0.974047i \(-0.572678\pi\)
−0.226347 + 0.974047i \(0.572678\pi\)
\(278\) −25.6541 −1.53863
\(279\) 1.10076 0.0659008
\(280\) −18.1112 −1.08235
\(281\) 22.6337 1.35021 0.675105 0.737721i \(-0.264098\pi\)
0.675105 + 0.737721i \(0.264098\pi\)
\(282\) −16.3734 −0.975023
\(283\) 13.0683 0.776827 0.388414 0.921485i \(-0.373023\pi\)
0.388414 + 0.921485i \(0.373023\pi\)
\(284\) −64.9798 −3.85584
\(285\) −0.800942 −0.0474437
\(286\) 39.0759 2.31061
\(287\) 5.21683 0.307940
\(288\) −8.79437 −0.518213
\(289\) −15.5895 −0.917032
\(290\) 29.2810 1.71944
\(291\) 13.8523 0.812035
\(292\) −35.8542 −2.09821
\(293\) 9.23361 0.539433 0.269717 0.962940i \(-0.413070\pi\)
0.269717 + 0.962940i \(0.413070\pi\)
\(294\) −8.54233 −0.498199
\(295\) −3.00837 −0.175154
\(296\) −43.1948 −2.51064
\(297\) 5.66323 0.328614
\(298\) −10.5298 −0.609976
\(299\) −23.3782 −1.35200
\(300\) 15.1826 0.876570
\(301\) −4.63942 −0.267412
\(302\) −5.66599 −0.326041
\(303\) −1.19183 −0.0684686
\(304\) −5.29743 −0.303828
\(305\) −17.5295 −1.00374
\(306\) 3.07845 0.175983
\(307\) −24.6556 −1.40717 −0.703584 0.710612i \(-0.748418\pi\)
−0.703584 + 0.710612i \(0.748418\pi\)
\(308\) 51.4368 2.93089
\(309\) −6.40546 −0.364394
\(310\) 3.80956 0.216368
\(311\) 4.54260 0.257587 0.128794 0.991671i \(-0.458890\pi\)
0.128794 + 0.991671i \(0.458890\pi\)
\(312\) 18.7606 1.06211
\(313\) 8.84780 0.500107 0.250054 0.968232i \(-0.419552\pi\)
0.250054 + 0.968232i \(0.419552\pi\)
\(314\) 18.4167 1.03931
\(315\) 2.56977 0.144790
\(316\) 38.5692 2.16968
\(317\) −13.6484 −0.766571 −0.383285 0.923630i \(-0.625207\pi\)
−0.383285 + 0.923630i \(0.625207\pi\)
\(318\) 20.9900 1.17706
\(319\) −47.9147 −2.68271
\(320\) −6.85529 −0.383222
\(321\) −10.8032 −0.602973
\(322\) −43.8160 −2.44177
\(323\) 0.712445 0.0396415
\(324\) 4.71896 0.262165
\(325\) −8.56434 −0.475064
\(326\) −20.7319 −1.14823
\(327\) −5.64865 −0.312371
\(328\) 19.1028 1.05478
\(329\) 12.1577 0.670276
\(330\) 19.5996 1.07892
\(331\) 22.1910 1.21973 0.609865 0.792505i \(-0.291224\pi\)
0.609865 + 0.792505i \(0.291224\pi\)
\(332\) 16.6392 0.913193
\(333\) 6.12882 0.335857
\(334\) 50.8591 2.78289
\(335\) −4.29052 −0.234416
\(336\) 16.9964 0.927231
\(337\) 4.77632 0.260183 0.130091 0.991502i \(-0.458473\pi\)
0.130091 + 0.991502i \(0.458473\pi\)
\(338\) 15.3303 0.833857
\(339\) −7.87519 −0.427721
\(340\) 7.48269 0.405806
\(341\) −6.23386 −0.337583
\(342\) 1.55497 0.0840831
\(343\) 19.8158 1.06995
\(344\) −16.9885 −0.915960
\(345\) −11.7260 −0.631306
\(346\) 33.5601 1.80420
\(347\) 22.3770 1.20126 0.600631 0.799527i \(-0.294916\pi\)
0.600631 + 0.799527i \(0.294916\pi\)
\(348\) −39.9255 −2.14023
\(349\) 31.5679 1.68979 0.844896 0.534931i \(-0.179662\pi\)
0.844896 + 0.534931i \(0.179662\pi\)
\(350\) −16.0515 −0.857988
\(351\) −2.66191 −0.142082
\(352\) 49.8046 2.65459
\(353\) −1.42915 −0.0760660 −0.0380330 0.999276i \(-0.512109\pi\)
−0.0380330 + 0.999276i \(0.512109\pi\)
\(354\) 5.84052 0.310420
\(355\) 18.3849 0.975772
\(356\) 67.1423 3.55853
\(357\) −2.28583 −0.120979
\(358\) 52.2479 2.76139
\(359\) −2.79564 −0.147548 −0.0737742 0.997275i \(-0.523504\pi\)
−0.0737742 + 0.997275i \(0.523504\pi\)
\(360\) 9.40990 0.495946
\(361\) −18.6401 −0.981060
\(362\) −10.0243 −0.526868
\(363\) −21.0722 −1.10600
\(364\) −24.1770 −1.26722
\(365\) 10.1444 0.530980
\(366\) 34.0322 1.77889
\(367\) −1.72620 −0.0901067 −0.0450533 0.998985i \(-0.514346\pi\)
−0.0450533 + 0.998985i \(0.514346\pi\)
\(368\) −77.5556 −4.04287
\(369\) −2.71046 −0.141101
\(370\) 21.2109 1.10270
\(371\) −15.5856 −0.809165
\(372\) −5.19445 −0.269320
\(373\) 24.1013 1.24792 0.623960 0.781456i \(-0.285523\pi\)
0.623960 + 0.781456i \(0.285523\pi\)
\(374\) −17.4340 −0.901489
\(375\) −10.9714 −0.566563
\(376\) 44.5188 2.29588
\(377\) 22.5215 1.15992
\(378\) −4.98901 −0.256607
\(379\) −1.42692 −0.0732961 −0.0366481 0.999328i \(-0.511668\pi\)
−0.0366481 + 0.999328i \(0.511668\pi\)
\(380\) 3.77962 0.193890
\(381\) 17.9013 0.917113
\(382\) 55.4380 2.83646
\(383\) 7.31360 0.373707 0.186854 0.982388i \(-0.440171\pi\)
0.186854 + 0.982388i \(0.440171\pi\)
\(384\) −4.27970 −0.218398
\(385\) −14.5532 −0.741699
\(386\) 35.2042 1.79185
\(387\) 2.41047 0.122531
\(388\) −65.3684 −3.31858
\(389\) 30.3479 1.53870 0.769351 0.638827i \(-0.220580\pi\)
0.769351 + 0.638827i \(0.220580\pi\)
\(390\) −9.21245 −0.466490
\(391\) 10.4304 0.527486
\(392\) 23.2263 1.17310
\(393\) −12.3361 −0.622275
\(394\) 17.3318 0.873163
\(395\) −10.9125 −0.549068
\(396\) −26.7246 −1.34296
\(397\) −16.0005 −0.803042 −0.401521 0.915850i \(-0.631518\pi\)
−0.401521 + 0.915850i \(0.631518\pi\)
\(398\) −19.1430 −0.959552
\(399\) −1.15461 −0.0578026
\(400\) −28.4116 −1.42058
\(401\) 13.3250 0.665417 0.332708 0.943030i \(-0.392038\pi\)
0.332708 + 0.943030i \(0.392038\pi\)
\(402\) 8.32971 0.415448
\(403\) 2.93012 0.145960
\(404\) 5.62418 0.279813
\(405\) −1.33515 −0.0663442
\(406\) 42.2103 2.09486
\(407\) −34.7089 −1.72046
\(408\) −8.37019 −0.414386
\(409\) −14.3936 −0.711719 −0.355859 0.934540i \(-0.615812\pi\)
−0.355859 + 0.934540i \(0.615812\pi\)
\(410\) −9.38048 −0.463269
\(411\) −13.7818 −0.679804
\(412\) 30.2271 1.48918
\(413\) −4.33674 −0.213397
\(414\) 22.7651 1.11884
\(415\) −4.70778 −0.231096
\(416\) −23.4098 −1.14776
\(417\) −9.89703 −0.484660
\(418\) −8.80615 −0.430723
\(419\) 33.7268 1.64766 0.823832 0.566834i \(-0.191832\pi\)
0.823832 + 0.566834i \(0.191832\pi\)
\(420\) −12.1266 −0.591719
\(421\) −33.8811 −1.65126 −0.825631 0.564211i \(-0.809181\pi\)
−0.825631 + 0.564211i \(0.809181\pi\)
\(422\) 2.93004 0.142632
\(423\) −6.31667 −0.307127
\(424\) −57.0710 −2.77161
\(425\) 3.82104 0.185348
\(426\) −35.6930 −1.72933
\(427\) −25.2698 −1.22289
\(428\) 50.9797 2.46420
\(429\) 15.0750 0.727829
\(430\) 8.34225 0.402299
\(431\) −31.2746 −1.50644 −0.753221 0.657767i \(-0.771501\pi\)
−0.753221 + 0.657767i \(0.771501\pi\)
\(432\) −8.83069 −0.424867
\(433\) 11.3752 0.546658 0.273329 0.961921i \(-0.411875\pi\)
0.273329 + 0.961921i \(0.411875\pi\)
\(434\) 5.49170 0.263610
\(435\) 11.2963 0.541614
\(436\) 26.6558 1.27658
\(437\) 5.26853 0.252028
\(438\) −19.6945 −0.941039
\(439\) 3.73198 0.178118 0.0890590 0.996026i \(-0.471614\pi\)
0.0890590 + 0.996026i \(0.471614\pi\)
\(440\) −53.2905 −2.54052
\(441\) −3.29553 −0.156930
\(442\) 8.19455 0.389775
\(443\) 20.1972 0.959600 0.479800 0.877378i \(-0.340709\pi\)
0.479800 + 0.877378i \(0.340709\pi\)
\(444\) −28.9217 −1.37256
\(445\) −18.9968 −0.900534
\(446\) −34.3556 −1.62678
\(447\) −4.06228 −0.192139
\(448\) −9.88231 −0.466895
\(449\) −11.8388 −0.558707 −0.279353 0.960188i \(-0.590120\pi\)
−0.279353 + 0.960188i \(0.590120\pi\)
\(450\) 8.33973 0.393139
\(451\) 15.3500 0.722803
\(452\) 37.1627 1.74799
\(453\) −2.18587 −0.102701
\(454\) 27.8504 1.30709
\(455\) 6.84049 0.320687
\(456\) −4.22790 −0.197990
\(457\) 11.3715 0.531935 0.265967 0.963982i \(-0.414309\pi\)
0.265967 + 0.963982i \(0.414309\pi\)
\(458\) −45.1632 −2.11034
\(459\) 1.18763 0.0554338
\(460\) 55.3345 2.57998
\(461\) −3.09897 −0.144333 −0.0721666 0.997393i \(-0.522991\pi\)
−0.0721666 + 0.997393i \(0.522991\pi\)
\(462\) 28.2539 1.31449
\(463\) −18.2777 −0.849439 −0.424719 0.905325i \(-0.639627\pi\)
−0.424719 + 0.905325i \(0.639627\pi\)
\(464\) 74.7134 3.46848
\(465\) 1.46968 0.0681549
\(466\) 6.78754 0.314427
\(467\) −32.9822 −1.52623 −0.763116 0.646261i \(-0.776332\pi\)
−0.763116 + 0.646261i \(0.776332\pi\)
\(468\) 12.5615 0.580653
\(469\) −6.18503 −0.285598
\(470\) −21.8610 −1.00837
\(471\) 7.10494 0.327378
\(472\) −15.8802 −0.730944
\(473\) −13.6510 −0.627675
\(474\) 21.1858 0.973096
\(475\) 1.93006 0.0885573
\(476\) 10.7867 0.494410
\(477\) 8.09769 0.370768
\(478\) −25.6793 −1.17455
\(479\) 18.9496 0.865831 0.432916 0.901434i \(-0.357485\pi\)
0.432916 + 0.901434i \(0.357485\pi\)
\(480\) −11.7418 −0.535938
\(481\) 16.3143 0.743870
\(482\) −39.5616 −1.80198
\(483\) −16.9037 −0.769145
\(484\) 99.4391 4.51996
\(485\) 18.4949 0.839810
\(486\) 2.59210 0.117580
\(487\) 6.49942 0.294517 0.147259 0.989098i \(-0.452955\pi\)
0.147259 + 0.989098i \(0.452955\pi\)
\(488\) −92.5324 −4.18875
\(489\) −7.99813 −0.361688
\(490\) −11.4053 −0.515239
\(491\) 24.4999 1.10567 0.552833 0.833292i \(-0.313547\pi\)
0.552833 + 0.833292i \(0.313547\pi\)
\(492\) 12.7906 0.576644
\(493\) −10.0481 −0.452545
\(494\) 4.13918 0.186231
\(495\) 7.56128 0.339854
\(496\) 9.72047 0.436462
\(497\) 26.5030 1.18882
\(498\) 9.13979 0.409564
\(499\) −5.46734 −0.244752 −0.122376 0.992484i \(-0.539051\pi\)
−0.122376 + 0.992484i \(0.539051\pi\)
\(500\) 51.7738 2.31540
\(501\) 19.6208 0.876595
\(502\) 15.0754 0.672848
\(503\) 4.71432 0.210201 0.105101 0.994462i \(-0.466484\pi\)
0.105101 + 0.994462i \(0.466484\pi\)
\(504\) 13.5649 0.604230
\(505\) −1.59127 −0.0708105
\(506\) −128.924 −5.73138
\(507\) 5.91424 0.262661
\(508\) −84.4757 −3.74800
\(509\) 31.6871 1.40451 0.702253 0.711927i \(-0.252178\pi\)
0.702253 + 0.711927i \(0.252178\pi\)
\(510\) 4.11020 0.182003
\(511\) 14.6237 0.646914
\(512\) 46.8138 2.06890
\(513\) 0.599888 0.0264857
\(514\) −2.65147 −0.116951
\(515\) −8.55226 −0.376858
\(516\) −11.3749 −0.500752
\(517\) 35.7728 1.57329
\(518\) 30.5767 1.34346
\(519\) 12.9471 0.568313
\(520\) 25.0483 1.09844
\(521\) −13.8384 −0.606271 −0.303135 0.952948i \(-0.598033\pi\)
−0.303135 + 0.952948i \(0.598033\pi\)
\(522\) −21.9308 −0.959887
\(523\) −0.360105 −0.0157463 −0.00787314 0.999969i \(-0.502506\pi\)
−0.00787314 + 0.999969i \(0.502506\pi\)
\(524\) 58.2137 2.54308
\(525\) −6.19247 −0.270262
\(526\) −47.5025 −2.07121
\(527\) −1.30729 −0.0569466
\(528\) 50.0103 2.17642
\(529\) 54.1325 2.35359
\(530\) 28.0248 1.21732
\(531\) 2.25320 0.0977807
\(532\) 5.44854 0.236224
\(533\) −7.21500 −0.312517
\(534\) 36.8808 1.59599
\(535\) −14.4239 −0.623598
\(536\) −22.6482 −0.978252
\(537\) 20.1566 0.869823
\(538\) 3.01254 0.129880
\(539\) 18.6634 0.803888
\(540\) 6.30053 0.271132
\(541\) −16.7493 −0.720110 −0.360055 0.932931i \(-0.617242\pi\)
−0.360055 + 0.932931i \(0.617242\pi\)
\(542\) 20.0307 0.860393
\(543\) −3.86727 −0.165961
\(544\) 10.4444 0.447802
\(545\) −7.54181 −0.323056
\(546\) −13.2803 −0.568344
\(547\) 3.90367 0.166909 0.0834544 0.996512i \(-0.473405\pi\)
0.0834544 + 0.996512i \(0.473405\pi\)
\(548\) 65.0356 2.77818
\(549\) 13.1292 0.560342
\(550\) −47.2298 −2.01389
\(551\) −5.07545 −0.216221
\(552\) −61.8975 −2.63453
\(553\) −15.7310 −0.668951
\(554\) 19.5297 0.829738
\(555\) 8.18290 0.347345
\(556\) 46.7037 1.98068
\(557\) −43.4383 −1.84054 −0.920269 0.391285i \(-0.872031\pi\)
−0.920269 + 0.391285i \(0.872031\pi\)
\(558\) −2.85328 −0.120789
\(559\) 6.41644 0.271387
\(560\) 22.6928 0.958946
\(561\) −6.72582 −0.283964
\(562\) −58.6686 −2.47479
\(563\) −15.0390 −0.633819 −0.316910 0.948456i \(-0.602645\pi\)
−0.316910 + 0.948456i \(0.602645\pi\)
\(564\) 29.8082 1.25515
\(565\) −10.5146 −0.442351
\(566\) −33.8742 −1.42384
\(567\) −1.92470 −0.0808298
\(568\) 97.0479 4.07204
\(569\) 18.3737 0.770267 0.385133 0.922861i \(-0.374155\pi\)
0.385133 + 0.922861i \(0.374155\pi\)
\(570\) 2.07612 0.0869591
\(571\) 4.40212 0.184223 0.0921116 0.995749i \(-0.470638\pi\)
0.0921116 + 0.995749i \(0.470638\pi\)
\(572\) −71.1384 −2.97445
\(573\) 21.3873 0.893469
\(574\) −13.5225 −0.564419
\(575\) 28.2566 1.17838
\(576\) 5.13447 0.213936
\(577\) −20.6063 −0.857850 −0.428925 0.903340i \(-0.641108\pi\)
−0.428925 + 0.903340i \(0.641108\pi\)
\(578\) 40.4096 1.68082
\(579\) 13.5814 0.564422
\(580\) −53.3067 −2.21344
\(581\) −6.78654 −0.281553
\(582\) −35.9065 −1.48837
\(583\) −45.8591 −1.89929
\(584\) 53.5486 2.21586
\(585\) −3.55405 −0.146942
\(586\) −23.9344 −0.988721
\(587\) 14.4066 0.594626 0.297313 0.954780i \(-0.403910\pi\)
0.297313 + 0.954780i \(0.403910\pi\)
\(588\) 15.5515 0.641332
\(589\) −0.660333 −0.0272086
\(590\) 7.79798 0.321038
\(591\) 6.68640 0.275042
\(592\) 54.1217 2.22439
\(593\) −28.8539 −1.18489 −0.592445 0.805611i \(-0.701837\pi\)
−0.592445 + 0.805611i \(0.701837\pi\)
\(594\) −14.6796 −0.602313
\(595\) −3.05193 −0.125117
\(596\) 19.1697 0.785223
\(597\) −7.38514 −0.302254
\(598\) 60.5986 2.47806
\(599\) −27.2122 −1.11186 −0.555930 0.831229i \(-0.687638\pi\)
−0.555930 + 0.831229i \(0.687638\pi\)
\(600\) −22.6754 −0.925720
\(601\) −1.60457 −0.0654518 −0.0327259 0.999464i \(-0.510419\pi\)
−0.0327259 + 0.999464i \(0.510419\pi\)
\(602\) 12.0258 0.490136
\(603\) 3.21350 0.130864
\(604\) 10.3151 0.419714
\(605\) −28.1346 −1.14384
\(606\) 3.08933 0.125495
\(607\) −24.9430 −1.01241 −0.506203 0.862414i \(-0.668951\pi\)
−0.506203 + 0.862414i \(0.668951\pi\)
\(608\) 5.27564 0.213955
\(609\) 16.2842 0.659870
\(610\) 45.4382 1.83974
\(611\) −16.8144 −0.680238
\(612\) −5.60438 −0.226543
\(613\) −3.55458 −0.143568 −0.0717841 0.997420i \(-0.522869\pi\)
−0.0717841 + 0.997420i \(0.522869\pi\)
\(614\) 63.9096 2.57918
\(615\) −3.61888 −0.145927
\(616\) −76.8214 −3.09522
\(617\) 9.32917 0.375578 0.187789 0.982209i \(-0.439868\pi\)
0.187789 + 0.982209i \(0.439868\pi\)
\(618\) 16.6036 0.667894
\(619\) −19.5010 −0.783810 −0.391905 0.920006i \(-0.628184\pi\)
−0.391905 + 0.920006i \(0.628184\pi\)
\(620\) −6.93538 −0.278531
\(621\) 8.78251 0.352430
\(622\) −11.7749 −0.472129
\(623\) −27.3850 −1.09716
\(624\) −23.5065 −0.941013
\(625\) 1.43831 0.0575323
\(626\) −22.9343 −0.916641
\(627\) −3.39731 −0.135675
\(628\) −33.5279 −1.33791
\(629\) −7.27876 −0.290223
\(630\) −6.66108 −0.265384
\(631\) 7.31759 0.291309 0.145654 0.989336i \(-0.453471\pi\)
0.145654 + 0.989336i \(0.453471\pi\)
\(632\) −57.6034 −2.29134
\(633\) 1.13038 0.0449284
\(634\) 35.3780 1.40504
\(635\) 23.9010 0.948482
\(636\) −38.2127 −1.51523
\(637\) −8.77240 −0.347575
\(638\) 124.199 4.91710
\(639\) −13.7699 −0.544730
\(640\) −5.71405 −0.225868
\(641\) −2.18932 −0.0864730 −0.0432365 0.999065i \(-0.513767\pi\)
−0.0432365 + 0.999065i \(0.513767\pi\)
\(642\) 28.0028 1.10518
\(643\) −43.2781 −1.70672 −0.853360 0.521322i \(-0.825439\pi\)
−0.853360 + 0.521322i \(0.825439\pi\)
\(644\) 79.7679 3.14330
\(645\) 3.21834 0.126722
\(646\) −1.84673 −0.0726584
\(647\) −49.1548 −1.93248 −0.966238 0.257651i \(-0.917052\pi\)
−0.966238 + 0.257651i \(0.917052\pi\)
\(648\) −7.04781 −0.276864
\(649\) −12.7604 −0.500890
\(650\) 22.1996 0.870740
\(651\) 2.11863 0.0830358
\(652\) 37.7429 1.47812
\(653\) −30.1831 −1.18116 −0.590579 0.806980i \(-0.701101\pi\)
−0.590579 + 0.806980i \(0.701101\pi\)
\(654\) 14.6419 0.572542
\(655\) −16.4706 −0.643560
\(656\) −23.9353 −0.934515
\(657\) −7.59790 −0.296422
\(658\) −31.5139 −1.22854
\(659\) 35.8803 1.39770 0.698850 0.715269i \(-0.253696\pi\)
0.698850 + 0.715269i \(0.253696\pi\)
\(660\) −35.6814 −1.38890
\(661\) −20.3966 −0.793336 −0.396668 0.917962i \(-0.629834\pi\)
−0.396668 + 0.917962i \(0.629834\pi\)
\(662\) −57.5213 −2.23563
\(663\) 3.16136 0.122777
\(664\) −24.8508 −0.964396
\(665\) −1.54157 −0.0597797
\(666\) −15.8865 −0.615589
\(667\) −74.3058 −2.87713
\(668\) −92.5900 −3.58242
\(669\) −13.2540 −0.512429
\(670\) 11.1214 0.429658
\(671\) −74.3539 −2.87040
\(672\) −16.9265 −0.652955
\(673\) 6.20553 0.239205 0.119603 0.992822i \(-0.461838\pi\)
0.119603 + 0.992822i \(0.461838\pi\)
\(674\) −12.3807 −0.476886
\(675\) 3.21737 0.123837
\(676\) −27.9091 −1.07343
\(677\) −20.9317 −0.804471 −0.402235 0.915536i \(-0.631767\pi\)
−0.402235 + 0.915536i \(0.631767\pi\)
\(678\) 20.4132 0.783966
\(679\) 26.6615 1.02317
\(680\) −11.1755 −0.428560
\(681\) 10.7444 0.411725
\(682\) 16.1588 0.618751
\(683\) −23.4911 −0.898863 −0.449431 0.893315i \(-0.648373\pi\)
−0.449431 + 0.893315i \(0.648373\pi\)
\(684\) −2.83085 −0.108240
\(685\) −18.4007 −0.703056
\(686\) −51.3645 −1.96110
\(687\) −17.4234 −0.664746
\(688\) 21.2861 0.811524
\(689\) 21.5553 0.821192
\(690\) 30.3949 1.15711
\(691\) 47.6607 1.81310 0.906550 0.422099i \(-0.138707\pi\)
0.906550 + 0.422099i \(0.138707\pi\)
\(692\) −61.0968 −2.32255
\(693\) 10.9000 0.414058
\(694\) −58.0034 −2.20178
\(695\) −13.2140 −0.501237
\(696\) 59.6292 2.26024
\(697\) 3.21902 0.121929
\(698\) −81.8271 −3.09720
\(699\) 2.61855 0.0990428
\(700\) 29.2220 1.10449
\(701\) 19.5223 0.737348 0.368674 0.929559i \(-0.379812\pi\)
0.368674 + 0.929559i \(0.379812\pi\)
\(702\) 6.89992 0.260421
\(703\) −3.67661 −0.138666
\(704\) −29.0777 −1.09591
\(705\) −8.43372 −0.317632
\(706\) 3.70449 0.139420
\(707\) −2.29391 −0.0862712
\(708\) −10.6328 −0.399605
\(709\) −22.8553 −0.858350 −0.429175 0.903221i \(-0.641196\pi\)
−0.429175 + 0.903221i \(0.641196\pi\)
\(710\) −47.6556 −1.78848
\(711\) 8.17323 0.306520
\(712\) −100.278 −3.75806
\(713\) −9.66744 −0.362048
\(714\) 5.92509 0.221741
\(715\) 20.1274 0.752723
\(716\) −95.1184 −3.55474
\(717\) −9.90679 −0.369976
\(718\) 7.24658 0.270440
\(719\) 6.89158 0.257013 0.128506 0.991709i \(-0.458982\pi\)
0.128506 + 0.991709i \(0.458982\pi\)
\(720\) −11.7903 −0.439399
\(721\) −12.3286 −0.459141
\(722\) 48.3170 1.79817
\(723\) −15.2624 −0.567614
\(724\) 18.2495 0.678238
\(725\) −27.2211 −1.01096
\(726\) 54.6212 2.02718
\(727\) −32.8801 −1.21945 −0.609727 0.792611i \(-0.708721\pi\)
−0.609727 + 0.792611i \(0.708721\pi\)
\(728\) 36.1086 1.33827
\(729\) 1.00000 0.0370370
\(730\) −26.2951 −0.973227
\(731\) −2.86274 −0.105882
\(732\) −61.9564 −2.28997
\(733\) 18.1015 0.668595 0.334297 0.942468i \(-0.391501\pi\)
0.334297 + 0.942468i \(0.391501\pi\)
\(734\) 4.47446 0.165156
\(735\) −4.40003 −0.162298
\(736\) 77.2366 2.84698
\(737\) −18.1988 −0.670362
\(738\) 7.02578 0.258623
\(739\) 40.1371 1.47647 0.738234 0.674545i \(-0.235660\pi\)
0.738234 + 0.674545i \(0.235660\pi\)
\(740\) −38.6148 −1.41951
\(741\) 1.59685 0.0586617
\(742\) 40.3994 1.48311
\(743\) −0.331346 −0.0121559 −0.00607795 0.999982i \(-0.501935\pi\)
−0.00607795 + 0.999982i \(0.501935\pi\)
\(744\) 7.75795 0.284420
\(745\) −5.42376 −0.198711
\(746\) −62.4730 −2.28730
\(747\) 3.52602 0.129010
\(748\) 31.7389 1.16049
\(749\) −20.7928 −0.759754
\(750\) 28.4390 1.03845
\(751\) 41.8168 1.52592 0.762958 0.646448i \(-0.223746\pi\)
0.762958 + 0.646448i \(0.223746\pi\)
\(752\) −55.7806 −2.03411
\(753\) 5.81591 0.211944
\(754\) −58.3779 −2.12600
\(755\) −2.91847 −0.106214
\(756\) 9.08259 0.330331
\(757\) −13.5037 −0.490799 −0.245399 0.969422i \(-0.578919\pi\)
−0.245399 + 0.969422i \(0.578919\pi\)
\(758\) 3.69872 0.134344
\(759\) −49.7374 −1.80535
\(760\) −5.64489 −0.204762
\(761\) −19.7797 −0.717015 −0.358508 0.933527i \(-0.616714\pi\)
−0.358508 + 0.933527i \(0.616714\pi\)
\(762\) −46.4020 −1.68097
\(763\) −10.8720 −0.393592
\(764\) −100.926 −3.65138
\(765\) 1.58566 0.0573298
\(766\) −18.9575 −0.684964
\(767\) 5.99782 0.216569
\(768\) 21.3623 0.770847
\(769\) −40.6590 −1.46620 −0.733100 0.680121i \(-0.761927\pi\)
−0.733100 + 0.680121i \(0.761927\pi\)
\(770\) 37.7233 1.35945
\(771\) −1.02291 −0.0368391
\(772\) −64.0899 −2.30665
\(773\) −39.5324 −1.42188 −0.710941 0.703252i \(-0.751731\pi\)
−0.710941 + 0.703252i \(0.751731\pi\)
\(774\) −6.24816 −0.224586
\(775\) −3.54155 −0.127216
\(776\) 97.6283 3.50465
\(777\) 11.7961 0.423184
\(778\) −78.6648 −2.82027
\(779\) 1.62598 0.0582566
\(780\) 16.7714 0.600514
\(781\) 77.9823 2.79043
\(782\) −27.0365 −0.966823
\(783\) −8.46066 −0.302359
\(784\) −29.1018 −1.03935
\(785\) 9.48617 0.338576
\(786\) 31.9764 1.14056
\(787\) −0.223829 −0.00797863 −0.00398932 0.999992i \(-0.501270\pi\)
−0.00398932 + 0.999992i \(0.501270\pi\)
\(788\) −31.5529 −1.12402
\(789\) −18.3259 −0.652420
\(790\) 28.2863 1.00638
\(791\) −15.1574 −0.538934
\(792\) 39.9134 1.41826
\(793\) 34.9488 1.24107
\(794\) 41.4748 1.47189
\(795\) 10.8116 0.383450
\(796\) 34.8502 1.23523
\(797\) −6.98307 −0.247353 −0.123677 0.992323i \(-0.539469\pi\)
−0.123677 + 0.992323i \(0.539469\pi\)
\(798\) 2.99285 0.105946
\(799\) 7.50186 0.265397
\(800\) 28.2947 1.00037
\(801\) 14.2282 0.502728
\(802\) −34.5396 −1.21963
\(803\) 43.0287 1.51845
\(804\) −15.1644 −0.534807
\(805\) −22.5690 −0.795453
\(806\) −7.59516 −0.267528
\(807\) 1.16220 0.0409114
\(808\) −8.39976 −0.295503
\(809\) −16.7969 −0.590546 −0.295273 0.955413i \(-0.595411\pi\)
−0.295273 + 0.955413i \(0.595411\pi\)
\(810\) 3.46084 0.121602
\(811\) −26.3047 −0.923681 −0.461841 0.886963i \(-0.652811\pi\)
−0.461841 + 0.886963i \(0.652811\pi\)
\(812\) −76.8447 −2.69672
\(813\) 7.72761 0.271019
\(814\) 89.9689 3.15341
\(815\) −10.6787 −0.374059
\(816\) 10.4876 0.367139
\(817\) −1.44601 −0.0505895
\(818\) 37.3096 1.30450
\(819\) −5.12338 −0.179025
\(820\) 17.0774 0.596367
\(821\) −6.57305 −0.229401 −0.114701 0.993400i \(-0.536591\pi\)
−0.114701 + 0.993400i \(0.536591\pi\)
\(822\) 35.7237 1.24601
\(823\) −28.5342 −0.994638 −0.497319 0.867568i \(-0.665682\pi\)
−0.497319 + 0.867568i \(0.665682\pi\)
\(824\) −45.1445 −1.57268
\(825\) −18.2207 −0.634364
\(826\) 11.2412 0.391133
\(827\) −5.47525 −0.190393 −0.0951965 0.995458i \(-0.530348\pi\)
−0.0951965 + 0.995458i \(0.530348\pi\)
\(828\) −41.4443 −1.44029
\(829\) 6.60113 0.229267 0.114633 0.993408i \(-0.463431\pi\)
0.114633 + 0.993408i \(0.463431\pi\)
\(830\) 12.2030 0.423573
\(831\) 7.53433 0.261363
\(832\) 13.6675 0.473835
\(833\) 3.91387 0.135607
\(834\) 25.6541 0.888328
\(835\) 26.1968 0.906578
\(836\) 16.0318 0.554471
\(837\) −1.10076 −0.0380478
\(838\) −87.4232 −3.01999
\(839\) −30.9677 −1.06912 −0.534562 0.845129i \(-0.679524\pi\)
−0.534562 + 0.845129i \(0.679524\pi\)
\(840\) 18.1112 0.624897
\(841\) 42.5827 1.46837
\(842\) 87.8230 3.02658
\(843\) −22.6337 −0.779544
\(844\) −5.33420 −0.183611
\(845\) 7.89641 0.271645
\(846\) 16.3734 0.562930
\(847\) −40.5577 −1.39358
\(848\) 71.5082 2.45560
\(849\) −13.0683 −0.448502
\(850\) −9.90450 −0.339722
\(851\) −53.8264 −1.84514
\(852\) 64.9798 2.22617
\(853\) 28.3716 0.971425 0.485713 0.874119i \(-0.338560\pi\)
0.485713 + 0.874119i \(0.338560\pi\)
\(854\) 65.5019 2.24143
\(855\) 0.800942 0.0273916
\(856\) −76.1386 −2.60237
\(857\) 16.2830 0.556217 0.278108 0.960550i \(-0.410293\pi\)
0.278108 + 0.960550i \(0.410293\pi\)
\(858\) −39.0759 −1.33403
\(859\) 10.8126 0.368922 0.184461 0.982840i \(-0.440946\pi\)
0.184461 + 0.982840i \(0.440946\pi\)
\(860\) −15.1872 −0.517880
\(861\) −5.21683 −0.177789
\(862\) 81.0667 2.76114
\(863\) 5.45175 0.185580 0.0927899 0.995686i \(-0.470422\pi\)
0.0927899 + 0.995686i \(0.470422\pi\)
\(864\) 8.79437 0.299190
\(865\) 17.2863 0.587752
\(866\) −29.4856 −1.00196
\(867\) 15.5895 0.529448
\(868\) −9.99775 −0.339346
\(869\) −46.2869 −1.57018
\(870\) −29.2810 −0.992719
\(871\) 8.55405 0.289843
\(872\) −39.8107 −1.34816
\(873\) −13.8523 −0.468829
\(874\) −13.6565 −0.461939
\(875\) −21.1167 −0.713876
\(876\) 35.8542 1.21140
\(877\) 12.5455 0.423633 0.211816 0.977310i \(-0.432062\pi\)
0.211816 + 0.977310i \(0.432062\pi\)
\(878\) −9.67366 −0.326470
\(879\) −9.23361 −0.311442
\(880\) 66.7713 2.25086
\(881\) −52.6564 −1.77404 −0.887019 0.461732i \(-0.847228\pi\)
−0.887019 + 0.461732i \(0.847228\pi\)
\(882\) 8.54233 0.287635
\(883\) −26.0560 −0.876856 −0.438428 0.898766i \(-0.644464\pi\)
−0.438428 + 0.898766i \(0.644464\pi\)
\(884\) −14.9183 −0.501758
\(885\) 3.00837 0.101125
\(886\) −52.3532 −1.75884
\(887\) 25.6479 0.861172 0.430586 0.902550i \(-0.358307\pi\)
0.430586 + 0.902550i \(0.358307\pi\)
\(888\) 43.1948 1.44952
\(889\) 34.4547 1.15557
\(890\) 49.2415 1.65058
\(891\) −5.66323 −0.189725
\(892\) 62.5451 2.09416
\(893\) 3.78930 0.126804
\(894\) 10.5298 0.352170
\(895\) 26.9122 0.899574
\(896\) −8.23714 −0.275184
\(897\) 23.3782 0.780577
\(898\) 30.6873 1.02405
\(899\) 9.31316 0.310611
\(900\) −15.1826 −0.506088
\(901\) −9.61705 −0.320390
\(902\) −39.7886 −1.32482
\(903\) 4.63942 0.154390
\(904\) −55.5029 −1.84600
\(905\) −5.16340 −0.171637
\(906\) 5.66599 0.188240
\(907\) −35.9104 −1.19238 −0.596192 0.802842i \(-0.703320\pi\)
−0.596192 + 0.802842i \(0.703320\pi\)
\(908\) −50.7023 −1.68261
\(909\) 1.19183 0.0395303
\(910\) −17.7312 −0.587784
\(911\) −3.39735 −0.112559 −0.0562796 0.998415i \(-0.517924\pi\)
−0.0562796 + 0.998415i \(0.517924\pi\)
\(912\) 5.29743 0.175415
\(913\) −19.9687 −0.660867
\(914\) −29.4759 −0.974977
\(915\) 17.5295 0.579508
\(916\) 82.2206 2.71664
\(917\) −23.7433 −0.784074
\(918\) −3.07845 −0.101604
\(919\) 23.3113 0.768969 0.384484 0.923131i \(-0.374379\pi\)
0.384484 + 0.923131i \(0.374379\pi\)
\(920\) −82.6426 −2.72465
\(921\) 24.6556 0.812429
\(922\) 8.03282 0.264547
\(923\) −36.6543 −1.20649
\(924\) −51.4368 −1.69215
\(925\) −19.7187 −0.648346
\(926\) 47.3777 1.55693
\(927\) 6.40546 0.210383
\(928\) −74.4061 −2.44250
\(929\) −9.14513 −0.300042 −0.150021 0.988683i \(-0.547934\pi\)
−0.150021 + 0.988683i \(0.547934\pi\)
\(930\) −3.80956 −0.124920
\(931\) 1.97695 0.0647919
\(932\) −12.3569 −0.404762
\(933\) −4.54260 −0.148718
\(934\) 85.4929 2.79741
\(935\) −8.97999 −0.293677
\(936\) −18.7606 −0.613211
\(937\) −36.3446 −1.18733 −0.593663 0.804714i \(-0.702319\pi\)
−0.593663 + 0.804714i \(0.702319\pi\)
\(938\) 16.0322 0.523470
\(939\) −8.84780 −0.288737
\(940\) 39.7984 1.29808
\(941\) −53.1095 −1.73132 −0.865660 0.500633i \(-0.833101\pi\)
−0.865660 + 0.500633i \(0.833101\pi\)
\(942\) −18.4167 −0.600048
\(943\) 23.8047 0.775186
\(944\) 19.8973 0.647603
\(945\) −2.56977 −0.0835945
\(946\) 35.3848 1.15046
\(947\) 10.0793 0.327533 0.163766 0.986499i \(-0.447636\pi\)
0.163766 + 0.986499i \(0.447636\pi\)
\(948\) −38.5692 −1.25267
\(949\) −20.2249 −0.656529
\(950\) −5.00291 −0.162316
\(951\) 13.6484 0.442580
\(952\) −16.1101 −0.522131
\(953\) 34.6734 1.12318 0.561590 0.827415i \(-0.310190\pi\)
0.561590 + 0.827415i \(0.310190\pi\)
\(954\) −20.9900 −0.679576
\(955\) 28.5553 0.924029
\(956\) 46.7498 1.51200
\(957\) 47.9147 1.54886
\(958\) −49.1193 −1.58697
\(959\) −26.5258 −0.856561
\(960\) 6.85529 0.221254
\(961\) −29.7883 −0.960914
\(962\) −42.2884 −1.36343
\(963\) 10.8032 0.348127
\(964\) 72.0227 2.31969
\(965\) 18.1332 0.583728
\(966\) 43.8160 1.40976
\(967\) −52.4429 −1.68645 −0.843225 0.537560i \(-0.819346\pi\)
−0.843225 + 0.537560i \(0.819346\pi\)
\(968\) −148.513 −4.77339
\(969\) −0.712445 −0.0228870
\(970\) −47.9406 −1.53928
\(971\) 59.5008 1.90947 0.954736 0.297454i \(-0.0961376\pi\)
0.954736 + 0.297454i \(0.0961376\pi\)
\(972\) −4.71896 −0.151361
\(973\) −19.0488 −0.610677
\(974\) −16.8471 −0.539817
\(975\) 8.56434 0.274278
\(976\) 115.940 3.71116
\(977\) 44.8184 1.43387 0.716934 0.697141i \(-0.245545\pi\)
0.716934 + 0.697141i \(0.245545\pi\)
\(978\) 20.7319 0.662934
\(979\) −80.5775 −2.57527
\(980\) 20.7636 0.663269
\(981\) 5.64865 0.180348
\(982\) −63.5061 −2.02656
\(983\) −33.0377 −1.05374 −0.526869 0.849946i \(-0.676634\pi\)
−0.526869 + 0.849946i \(0.676634\pi\)
\(984\) −19.1028 −0.608976
\(985\) 8.92736 0.284449
\(986\) 26.0457 0.829464
\(987\) −12.1577 −0.386984
\(988\) −7.53547 −0.239735
\(989\) −21.1699 −0.673165
\(990\) −19.5996 −0.622915
\(991\) 5.63576 0.179026 0.0895128 0.995986i \(-0.471469\pi\)
0.0895128 + 0.995986i \(0.471469\pi\)
\(992\) −9.68049 −0.307356
\(993\) −22.1910 −0.704211
\(994\) −68.6983 −2.17898
\(995\) −9.86029 −0.312592
\(996\) −16.6392 −0.527232
\(997\) 29.1755 0.923997 0.461998 0.886881i \(-0.347133\pi\)
0.461998 + 0.886881i \(0.347133\pi\)
\(998\) 14.1719 0.448603
\(999\) −6.12882 −0.193907
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 8013.2.a.c.1.8 116
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8013.2.a.c.1.8 116 1.1 even 1 trivial