Properties

Label 8003.2.a.a.1.5
Level $8003$
Weight $2$
Character 8003.1
Self dual yes
Analytic conductor $63.904$
Analytic rank $1$
Dimension $147$
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] = [8003,2,Mod(1,8003)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8003, 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("8003.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.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: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(147\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 8003.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.69176 q^{2} -2.97285 q^{3} +5.24555 q^{4} +2.64194 q^{5} +8.00219 q^{6} -3.02993 q^{7} -8.73623 q^{8} +5.83784 q^{9} +O(q^{10})\) \(q-2.69176 q^{2} -2.97285 q^{3} +5.24555 q^{4} +2.64194 q^{5} +8.00219 q^{6} -3.02993 q^{7} -8.73623 q^{8} +5.83784 q^{9} -7.11145 q^{10} +2.61803 q^{11} -15.5942 q^{12} -2.42112 q^{13} +8.15583 q^{14} -7.85409 q^{15} +13.0247 q^{16} +1.72491 q^{17} -15.7140 q^{18} +4.82635 q^{19} +13.8584 q^{20} +9.00753 q^{21} -7.04710 q^{22} +1.24633 q^{23} +25.9715 q^{24} +1.97984 q^{25} +6.51708 q^{26} -8.43648 q^{27} -15.8937 q^{28} -2.50530 q^{29} +21.1413 q^{30} -1.61887 q^{31} -17.5868 q^{32} -7.78302 q^{33} -4.64304 q^{34} -8.00489 q^{35} +30.6227 q^{36} -2.98440 q^{37} -12.9914 q^{38} +7.19764 q^{39} -23.0806 q^{40} -11.3971 q^{41} -24.2461 q^{42} +6.95620 q^{43} +13.7330 q^{44} +15.4232 q^{45} -3.35482 q^{46} +0.438274 q^{47} -38.7205 q^{48} +2.18048 q^{49} -5.32924 q^{50} -5.12790 q^{51} -12.7001 q^{52} +1.00000 q^{53} +22.7089 q^{54} +6.91668 q^{55} +26.4702 q^{56} -14.3480 q^{57} +6.74366 q^{58} +9.55262 q^{59} -41.1990 q^{60} +11.1952 q^{61} +4.35761 q^{62} -17.6883 q^{63} +21.2901 q^{64} -6.39646 q^{65} +20.9500 q^{66} +3.56140 q^{67} +9.04811 q^{68} -3.70516 q^{69} +21.5472 q^{70} -6.18168 q^{71} -51.0007 q^{72} +8.98494 q^{73} +8.03327 q^{74} -5.88576 q^{75} +25.3169 q^{76} -7.93246 q^{77} -19.3743 q^{78} +4.34119 q^{79} +34.4104 q^{80} +7.56686 q^{81} +30.6783 q^{82} +0.593632 q^{83} +47.2495 q^{84} +4.55711 q^{85} -18.7244 q^{86} +7.44789 q^{87} -22.8717 q^{88} -11.4237 q^{89} -41.5155 q^{90} +7.33584 q^{91} +6.53770 q^{92} +4.81267 q^{93} -1.17973 q^{94} +12.7509 q^{95} +52.2831 q^{96} -13.0544 q^{97} -5.86932 q^{98} +15.2837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69176 −1.90336 −0.951679 0.307093i \(-0.900644\pi\)
−0.951679 + 0.307093i \(0.900644\pi\)
\(3\) −2.97285 −1.71638 −0.858188 0.513335i \(-0.828410\pi\)
−0.858188 + 0.513335i \(0.828410\pi\)
\(4\) 5.24555 2.62277
\(5\) 2.64194 1.18151 0.590755 0.806851i \(-0.298830\pi\)
0.590755 + 0.806851i \(0.298830\pi\)
\(6\) 8.00219 3.26688
\(7\) −3.02993 −1.14521 −0.572603 0.819833i \(-0.694066\pi\)
−0.572603 + 0.819833i \(0.694066\pi\)
\(8\) −8.73623 −3.08872
\(9\) 5.83784 1.94595
\(10\) −7.11145 −2.24884
\(11\) 2.61803 0.789367 0.394683 0.918817i \(-0.370854\pi\)
0.394683 + 0.918817i \(0.370854\pi\)
\(12\) −15.5942 −4.50167
\(13\) −2.42112 −0.671499 −0.335750 0.941951i \(-0.608990\pi\)
−0.335750 + 0.941951i \(0.608990\pi\)
\(14\) 8.15583 2.17974
\(15\) −7.85409 −2.02792
\(16\) 13.0247 3.25617
\(17\) 1.72491 0.418352 0.209176 0.977878i \(-0.432922\pi\)
0.209176 + 0.977878i \(0.432922\pi\)
\(18\) −15.7140 −3.70384
\(19\) 4.82635 1.10724 0.553621 0.832769i \(-0.313246\pi\)
0.553621 + 0.832769i \(0.313246\pi\)
\(20\) 13.8584 3.09884
\(21\) 9.00753 1.96560
\(22\) −7.04710 −1.50245
\(23\) 1.24633 0.259878 0.129939 0.991522i \(-0.458522\pi\)
0.129939 + 0.991522i \(0.458522\pi\)
\(24\) 25.9715 5.30141
\(25\) 1.97984 0.395967
\(26\) 6.51708 1.27810
\(27\) −8.43648 −1.62360
\(28\) −15.8937 −3.00362
\(29\) −2.50530 −0.465223 −0.232611 0.972570i \(-0.574727\pi\)
−0.232611 + 0.972570i \(0.574727\pi\)
\(30\) 21.1413 3.85985
\(31\) −1.61887 −0.290758 −0.145379 0.989376i \(-0.546440\pi\)
−0.145379 + 0.989376i \(0.546440\pi\)
\(32\) −17.5868 −3.10894
\(33\) −7.78302 −1.35485
\(34\) −4.64304 −0.796275
\(35\) −8.00489 −1.35307
\(36\) 30.6227 5.10378
\(37\) −2.98440 −0.490632 −0.245316 0.969443i \(-0.578892\pi\)
−0.245316 + 0.969443i \(0.578892\pi\)
\(38\) −12.9914 −2.10748
\(39\) 7.19764 1.15255
\(40\) −23.0806 −3.64936
\(41\) −11.3971 −1.77994 −0.889968 0.456024i \(-0.849273\pi\)
−0.889968 + 0.456024i \(0.849273\pi\)
\(42\) −24.2461 −3.74125
\(43\) 6.95620 1.06081 0.530405 0.847744i \(-0.322040\pi\)
0.530405 + 0.847744i \(0.322040\pi\)
\(44\) 13.7330 2.07033
\(45\) 15.4232 2.29916
\(46\) −3.35482 −0.494642
\(47\) 0.438274 0.0639288 0.0319644 0.999489i \(-0.489824\pi\)
0.0319644 + 0.999489i \(0.489824\pi\)
\(48\) −38.7205 −5.58882
\(49\) 2.18048 0.311497
\(50\) −5.32924 −0.753668
\(51\) −5.12790 −0.718050
\(52\) −12.7001 −1.76119
\(53\) 1.00000 0.137361
\(54\) 22.7089 3.09029
\(55\) 6.91668 0.932645
\(56\) 26.4702 3.53722
\(57\) −14.3480 −1.90044
\(58\) 6.74366 0.885486
\(59\) 9.55262 1.24364 0.621822 0.783158i \(-0.286393\pi\)
0.621822 + 0.783158i \(0.286393\pi\)
\(60\) −41.1990 −5.31877
\(61\) 11.1952 1.43340 0.716698 0.697384i \(-0.245653\pi\)
0.716698 + 0.697384i \(0.245653\pi\)
\(62\) 4.35761 0.553417
\(63\) −17.6883 −2.22851
\(64\) 21.2901 2.66126
\(65\) −6.39646 −0.793383
\(66\) 20.9500 2.57877
\(67\) 3.56140 0.435095 0.217547 0.976050i \(-0.430194\pi\)
0.217547 + 0.976050i \(0.430194\pi\)
\(68\) 9.04811 1.09724
\(69\) −3.70516 −0.446049
\(70\) 21.5472 2.57538
\(71\) −6.18168 −0.733630 −0.366815 0.930294i \(-0.619552\pi\)
−0.366815 + 0.930294i \(0.619552\pi\)
\(72\) −51.0007 −6.01049
\(73\) 8.98494 1.05161 0.525804 0.850606i \(-0.323765\pi\)
0.525804 + 0.850606i \(0.323765\pi\)
\(74\) 8.03327 0.933849
\(75\) −5.88576 −0.679629
\(76\) 25.3169 2.90404
\(77\) −7.93246 −0.903987
\(78\) −19.3743 −2.19371
\(79\) 4.34119 0.488422 0.244211 0.969722i \(-0.421471\pi\)
0.244211 + 0.969722i \(0.421471\pi\)
\(80\) 34.4104 3.84720
\(81\) 7.56686 0.840763
\(82\) 30.6783 3.38786
\(83\) 0.593632 0.0651596 0.0325798 0.999469i \(-0.489628\pi\)
0.0325798 + 0.999469i \(0.489628\pi\)
\(84\) 47.2495 5.15534
\(85\) 4.55711 0.494288
\(86\) −18.7244 −2.01910
\(87\) 7.44789 0.798497
\(88\) −22.8717 −2.43813
\(89\) −11.4237 −1.21091 −0.605454 0.795881i \(-0.707008\pi\)
−0.605454 + 0.795881i \(0.707008\pi\)
\(90\) −41.5155 −4.37612
\(91\) 7.33584 0.769005
\(92\) 6.53770 0.681602
\(93\) 4.81267 0.499050
\(94\) −1.17973 −0.121679
\(95\) 12.7509 1.30822
\(96\) 52.2831 5.33612
\(97\) −13.0544 −1.32547 −0.662735 0.748854i \(-0.730604\pi\)
−0.662735 + 0.748854i \(0.730604\pi\)
\(98\) −5.86932 −0.592891
\(99\) 15.2837 1.53607
\(100\) 10.3853 1.03853
\(101\) −10.0747 −1.00247 −0.501235 0.865311i \(-0.667121\pi\)
−0.501235 + 0.865311i \(0.667121\pi\)
\(102\) 13.8031 1.36671
\(103\) −15.1778 −1.49551 −0.747757 0.663973i \(-0.768869\pi\)
−0.747757 + 0.663973i \(0.768869\pi\)
\(104\) 21.1515 2.07407
\(105\) 23.7973 2.32238
\(106\) −2.69176 −0.261446
\(107\) −3.44767 −0.333298 −0.166649 0.986016i \(-0.553295\pi\)
−0.166649 + 0.986016i \(0.553295\pi\)
\(108\) −44.2540 −4.25834
\(109\) 3.68422 0.352884 0.176442 0.984311i \(-0.443541\pi\)
0.176442 + 0.984311i \(0.443541\pi\)
\(110\) −18.6180 −1.77516
\(111\) 8.87217 0.842109
\(112\) −39.4639 −3.72899
\(113\) −10.6508 −1.00195 −0.500973 0.865463i \(-0.667024\pi\)
−0.500973 + 0.865463i \(0.667024\pi\)
\(114\) 38.6214 3.61722
\(115\) 3.29273 0.307049
\(116\) −13.1417 −1.22017
\(117\) −14.1341 −1.30670
\(118\) −25.7133 −2.36710
\(119\) −5.22636 −0.479100
\(120\) 68.6151 6.26367
\(121\) −4.14591 −0.376900
\(122\) −30.1347 −2.72827
\(123\) 33.8820 3.05504
\(124\) −8.49188 −0.762593
\(125\) −7.97908 −0.713671
\(126\) 47.6125 4.24165
\(127\) −6.13403 −0.544307 −0.272153 0.962254i \(-0.587736\pi\)
−0.272153 + 0.962254i \(0.587736\pi\)
\(128\) −22.1341 −1.95639
\(129\) −20.6797 −1.82075
\(130\) 17.2177 1.51009
\(131\) 1.18583 0.103606 0.0518032 0.998657i \(-0.483503\pi\)
0.0518032 + 0.998657i \(0.483503\pi\)
\(132\) −40.8262 −3.55347
\(133\) −14.6235 −1.26802
\(134\) −9.58643 −0.828141
\(135\) −22.2887 −1.91830
\(136\) −15.0692 −1.29217
\(137\) 18.9855 1.62204 0.811022 0.585016i \(-0.198912\pi\)
0.811022 + 0.585016i \(0.198912\pi\)
\(138\) 9.97339 0.848991
\(139\) −3.15838 −0.267891 −0.133945 0.990989i \(-0.542765\pi\)
−0.133945 + 0.990989i \(0.542765\pi\)
\(140\) −41.9900 −3.54881
\(141\) −1.30292 −0.109726
\(142\) 16.6396 1.39636
\(143\) −6.33858 −0.530059
\(144\) 76.0361 6.33634
\(145\) −6.61885 −0.549666
\(146\) −24.1853 −2.00159
\(147\) −6.48224 −0.534646
\(148\) −15.6548 −1.28682
\(149\) 4.75810 0.389799 0.194899 0.980823i \(-0.437562\pi\)
0.194899 + 0.980823i \(0.437562\pi\)
\(150\) 15.8430 1.29358
\(151\) 1.00000 0.0813788
\(152\) −42.1641 −3.41996
\(153\) 10.0698 0.814091
\(154\) 21.3522 1.72061
\(155\) −4.27696 −0.343534
\(156\) 37.7556 3.02287
\(157\) −22.3291 −1.78205 −0.891026 0.453951i \(-0.850014\pi\)
−0.891026 + 0.453951i \(0.850014\pi\)
\(158\) −11.6854 −0.929643
\(159\) −2.97285 −0.235762
\(160\) −46.4633 −3.67325
\(161\) −3.77630 −0.297614
\(162\) −20.3682 −1.60027
\(163\) −4.54889 −0.356296 −0.178148 0.984004i \(-0.557011\pi\)
−0.178148 + 0.984004i \(0.557011\pi\)
\(164\) −59.7843 −4.66837
\(165\) −20.5623 −1.60077
\(166\) −1.59791 −0.124022
\(167\) 23.4645 1.81574 0.907869 0.419253i \(-0.137708\pi\)
0.907869 + 0.419253i \(0.137708\pi\)
\(168\) −78.6918 −6.07121
\(169\) −7.13816 −0.549089
\(170\) −12.2666 −0.940807
\(171\) 28.1755 2.15463
\(172\) 36.4891 2.78227
\(173\) 20.9127 1.58996 0.794980 0.606636i \(-0.207481\pi\)
0.794980 + 0.606636i \(0.207481\pi\)
\(174\) −20.0479 −1.51983
\(175\) −5.99877 −0.453464
\(176\) 34.0991 2.57031
\(177\) −28.3985 −2.13456
\(178\) 30.7497 2.30479
\(179\) 16.5057 1.23369 0.616846 0.787084i \(-0.288410\pi\)
0.616846 + 0.787084i \(0.288410\pi\)
\(180\) 80.9032 6.03017
\(181\) −10.3592 −0.769995 −0.384997 0.922918i \(-0.625798\pi\)
−0.384997 + 0.922918i \(0.625798\pi\)
\(182\) −19.7463 −1.46369
\(183\) −33.2816 −2.46025
\(184\) −10.8882 −0.802692
\(185\) −7.88459 −0.579687
\(186\) −12.9545 −0.949872
\(187\) 4.51587 0.330233
\(188\) 2.29899 0.167671
\(189\) 25.5619 1.85936
\(190\) −34.3224 −2.49001
\(191\) −18.2427 −1.31999 −0.659996 0.751269i \(-0.729442\pi\)
−0.659996 + 0.751269i \(0.729442\pi\)
\(192\) −63.2923 −4.56773
\(193\) −9.91795 −0.713909 −0.356955 0.934122i \(-0.616185\pi\)
−0.356955 + 0.934122i \(0.616185\pi\)
\(194\) 35.1392 2.52284
\(195\) 19.0157 1.36174
\(196\) 11.4378 0.816987
\(197\) −14.2158 −1.01283 −0.506417 0.862289i \(-0.669030\pi\)
−0.506417 + 0.862289i \(0.669030\pi\)
\(198\) −41.1399 −2.92368
\(199\) 2.31605 0.164180 0.0820901 0.996625i \(-0.473840\pi\)
0.0820901 + 0.996625i \(0.473840\pi\)
\(200\) −17.2963 −1.22303
\(201\) −10.5875 −0.746786
\(202\) 27.1186 1.90806
\(203\) 7.59089 0.532776
\(204\) −26.8987 −1.88328
\(205\) −30.1106 −2.10301
\(206\) 40.8549 2.84650
\(207\) 7.27589 0.505709
\(208\) −31.5344 −2.18652
\(209\) 12.6355 0.874019
\(210\) −64.0566 −4.42033
\(211\) −4.69874 −0.323475 −0.161737 0.986834i \(-0.551710\pi\)
−0.161737 + 0.986834i \(0.551710\pi\)
\(212\) 5.24555 0.360266
\(213\) 18.3772 1.25918
\(214\) 9.28028 0.634387
\(215\) 18.3778 1.25336
\(216\) 73.7030 5.01485
\(217\) 4.90507 0.332978
\(218\) −9.91701 −0.671665
\(219\) −26.7109 −1.80495
\(220\) 36.2818 2.44612
\(221\) −4.17622 −0.280923
\(222\) −23.8817 −1.60284
\(223\) −2.58590 −0.173165 −0.0865825 0.996245i \(-0.527595\pi\)
−0.0865825 + 0.996245i \(0.527595\pi\)
\(224\) 53.2869 3.56038
\(225\) 11.5580 0.770532
\(226\) 28.6694 1.90706
\(227\) −11.1406 −0.739426 −0.369713 0.929146i \(-0.620544\pi\)
−0.369713 + 0.929146i \(0.620544\pi\)
\(228\) −75.2633 −4.98443
\(229\) 16.6802 1.10226 0.551129 0.834420i \(-0.314197\pi\)
0.551129 + 0.834420i \(0.314197\pi\)
\(230\) −8.86323 −0.584424
\(231\) 23.5820 1.55158
\(232\) 21.8869 1.43694
\(233\) −10.6844 −0.699958 −0.349979 0.936757i \(-0.613811\pi\)
−0.349979 + 0.936757i \(0.613811\pi\)
\(234\) 38.0457 2.48712
\(235\) 1.15789 0.0755326
\(236\) 50.1087 3.26180
\(237\) −12.9057 −0.838317
\(238\) 14.0681 0.911899
\(239\) 0.889072 0.0575093 0.0287546 0.999586i \(-0.490846\pi\)
0.0287546 + 0.999586i \(0.490846\pi\)
\(240\) −102.297 −6.60325
\(241\) 7.96341 0.512968 0.256484 0.966548i \(-0.417436\pi\)
0.256484 + 0.966548i \(0.417436\pi\)
\(242\) 11.1598 0.717377
\(243\) 2.81428 0.180536
\(244\) 58.7249 3.75948
\(245\) 5.76069 0.368037
\(246\) −91.2021 −5.81483
\(247\) −11.6852 −0.743511
\(248\) 14.1428 0.898071
\(249\) −1.76478 −0.111838
\(250\) 21.4777 1.35837
\(251\) 15.4113 0.972753 0.486377 0.873749i \(-0.338318\pi\)
0.486377 + 0.873749i \(0.338318\pi\)
\(252\) −92.7846 −5.84488
\(253\) 3.26294 0.205139
\(254\) 16.5113 1.03601
\(255\) −13.5476 −0.848384
\(256\) 16.9993 1.06246
\(257\) −7.51205 −0.468589 −0.234294 0.972166i \(-0.575278\pi\)
−0.234294 + 0.972166i \(0.575278\pi\)
\(258\) 55.6648 3.46554
\(259\) 9.04252 0.561875
\(260\) −33.5530 −2.08087
\(261\) −14.6256 −0.905299
\(262\) −3.19196 −0.197200
\(263\) −12.0556 −0.743382 −0.371691 0.928357i \(-0.621222\pi\)
−0.371691 + 0.928357i \(0.621222\pi\)
\(264\) 67.9942 4.18476
\(265\) 2.64194 0.162293
\(266\) 39.3629 2.41350
\(267\) 33.9609 2.07837
\(268\) 18.6815 1.14116
\(269\) 16.7234 1.01964 0.509822 0.860280i \(-0.329711\pi\)
0.509822 + 0.860280i \(0.329711\pi\)
\(270\) 59.9956 3.65122
\(271\) −8.03520 −0.488103 −0.244052 0.969762i \(-0.578477\pi\)
−0.244052 + 0.969762i \(0.578477\pi\)
\(272\) 22.4664 1.36223
\(273\) −21.8084 −1.31990
\(274\) −51.1044 −3.08733
\(275\) 5.18328 0.312563
\(276\) −19.4356 −1.16989
\(277\) 23.2451 1.39666 0.698330 0.715776i \(-0.253927\pi\)
0.698330 + 0.715776i \(0.253927\pi\)
\(278\) 8.50160 0.509892
\(279\) −9.45072 −0.565800
\(280\) 69.9325 4.17927
\(281\) −16.8127 −1.00296 −0.501480 0.865169i \(-0.667211\pi\)
−0.501480 + 0.865169i \(0.667211\pi\)
\(282\) 3.50715 0.208848
\(283\) 6.77640 0.402815 0.201408 0.979508i \(-0.435448\pi\)
0.201408 + 0.979508i \(0.435448\pi\)
\(284\) −32.4263 −1.92415
\(285\) −37.9066 −2.24539
\(286\) 17.0619 1.00889
\(287\) 34.5326 2.03839
\(288\) −102.669 −6.04984
\(289\) −14.0247 −0.824981
\(290\) 17.8163 1.04621
\(291\) 38.8087 2.27500
\(292\) 47.1310 2.75813
\(293\) 1.55060 0.0905869 0.0452935 0.998974i \(-0.485578\pi\)
0.0452935 + 0.998974i \(0.485578\pi\)
\(294\) 17.4486 1.01762
\(295\) 25.2374 1.46938
\(296\) 26.0724 1.51543
\(297\) −22.0870 −1.28162
\(298\) −12.8076 −0.741927
\(299\) −3.01753 −0.174508
\(300\) −30.8740 −1.78251
\(301\) −21.0768 −1.21485
\(302\) −2.69176 −0.154893
\(303\) 29.9506 1.72062
\(304\) 62.8618 3.60537
\(305\) 29.5770 1.69357
\(306\) −27.1053 −1.54951
\(307\) 3.98608 0.227498 0.113749 0.993510i \(-0.463714\pi\)
0.113749 + 0.993510i \(0.463714\pi\)
\(308\) −41.6101 −2.37096
\(309\) 45.1214 2.56686
\(310\) 11.5125 0.653868
\(311\) 10.9908 0.623229 0.311614 0.950209i \(-0.399130\pi\)
0.311614 + 0.950209i \(0.399130\pi\)
\(312\) −62.8802 −3.55989
\(313\) −14.4532 −0.816941 −0.408470 0.912772i \(-0.633938\pi\)
−0.408470 + 0.912772i \(0.633938\pi\)
\(314\) 60.1044 3.39189
\(315\) −46.7313 −2.63301
\(316\) 22.7719 1.28102
\(317\) 19.1325 1.07459 0.537294 0.843395i \(-0.319446\pi\)
0.537294 + 0.843395i \(0.319446\pi\)
\(318\) 8.00219 0.448740
\(319\) −6.55896 −0.367231
\(320\) 56.2471 3.14431
\(321\) 10.2494 0.572066
\(322\) 10.1649 0.566466
\(323\) 8.32503 0.463217
\(324\) 39.6924 2.20513
\(325\) −4.79343 −0.265892
\(326\) 12.2445 0.678160
\(327\) −10.9526 −0.605682
\(328\) 99.5681 5.49773
\(329\) −1.32794 −0.0732117
\(330\) 55.3486 3.04684
\(331\) 32.6928 1.79696 0.898479 0.439017i \(-0.144673\pi\)
0.898479 + 0.439017i \(0.144673\pi\)
\(332\) 3.11393 0.170899
\(333\) −17.4224 −0.954744
\(334\) −63.1608 −3.45600
\(335\) 9.40901 0.514069
\(336\) 117.320 6.40035
\(337\) −1.54569 −0.0841989 −0.0420994 0.999113i \(-0.513405\pi\)
−0.0420994 + 0.999113i \(0.513405\pi\)
\(338\) 19.2142 1.04511
\(339\) 31.6633 1.71972
\(340\) 23.9045 1.29641
\(341\) −4.23826 −0.229515
\(342\) −75.8415 −4.10104
\(343\) 14.6028 0.788478
\(344\) −60.7709 −3.27655
\(345\) −9.78880 −0.527011
\(346\) −56.2918 −3.02626
\(347\) 10.3814 0.557300 0.278650 0.960393i \(-0.410113\pi\)
0.278650 + 0.960393i \(0.410113\pi\)
\(348\) 39.0683 2.09428
\(349\) 2.33316 0.124891 0.0624456 0.998048i \(-0.480110\pi\)
0.0624456 + 0.998048i \(0.480110\pi\)
\(350\) 16.1472 0.863105
\(351\) 20.4258 1.09025
\(352\) −46.0429 −2.45410
\(353\) 20.8199 1.10813 0.554066 0.832473i \(-0.313076\pi\)
0.554066 + 0.832473i \(0.313076\pi\)
\(354\) 76.4418 4.06284
\(355\) −16.3316 −0.866792
\(356\) −59.9235 −3.17594
\(357\) 15.5372 0.822315
\(358\) −44.4292 −2.34816
\(359\) 25.1936 1.32967 0.664834 0.746991i \(-0.268502\pi\)
0.664834 + 0.746991i \(0.268502\pi\)
\(360\) −134.741 −7.10146
\(361\) 4.29368 0.225983
\(362\) 27.8845 1.46558
\(363\) 12.3252 0.646903
\(364\) 38.4805 2.01693
\(365\) 23.7377 1.24249
\(366\) 89.5860 4.68273
\(367\) −32.4969 −1.69632 −0.848162 0.529738i \(-0.822290\pi\)
−0.848162 + 0.529738i \(0.822290\pi\)
\(368\) 16.2331 0.846209
\(369\) −66.5347 −3.46366
\(370\) 21.2234 1.10335
\(371\) −3.02993 −0.157306
\(372\) 25.2451 1.30890
\(373\) −23.9888 −1.24210 −0.621048 0.783773i \(-0.713293\pi\)
−0.621048 + 0.783773i \(0.713293\pi\)
\(374\) −12.1556 −0.628553
\(375\) 23.7206 1.22493
\(376\) −3.82886 −0.197458
\(377\) 6.06565 0.312397
\(378\) −68.8065 −3.53902
\(379\) −8.35439 −0.429136 −0.214568 0.976709i \(-0.568834\pi\)
−0.214568 + 0.976709i \(0.568834\pi\)
\(380\) 66.8856 3.43116
\(381\) 18.2355 0.934235
\(382\) 49.1048 2.51242
\(383\) −16.6276 −0.849632 −0.424816 0.905280i \(-0.639661\pi\)
−0.424816 + 0.905280i \(0.639661\pi\)
\(384\) 65.8012 3.35791
\(385\) −20.9571 −1.06807
\(386\) 26.6967 1.35883
\(387\) 40.6092 2.06428
\(388\) −68.4773 −3.47641
\(389\) 10.1342 0.513822 0.256911 0.966435i \(-0.417295\pi\)
0.256911 + 0.966435i \(0.417295\pi\)
\(390\) −51.1857 −2.59189
\(391\) 2.14981 0.108721
\(392\) −19.0492 −0.962128
\(393\) −3.52529 −0.177828
\(394\) 38.2655 1.92779
\(395\) 11.4692 0.577076
\(396\) 80.1712 4.02875
\(397\) −4.78968 −0.240387 −0.120194 0.992750i \(-0.538352\pi\)
−0.120194 + 0.992750i \(0.538352\pi\)
\(398\) −6.23424 −0.312494
\(399\) 43.4735 2.17640
\(400\) 25.7868 1.28934
\(401\) 17.1178 0.854823 0.427411 0.904057i \(-0.359426\pi\)
0.427411 + 0.904057i \(0.359426\pi\)
\(402\) 28.4990 1.42140
\(403\) 3.91949 0.195244
\(404\) −52.8474 −2.62925
\(405\) 19.9912 0.993370
\(406\) −20.4328 −1.01406
\(407\) −7.81325 −0.387288
\(408\) 44.7985 2.21786
\(409\) 2.15727 0.106670 0.0533350 0.998577i \(-0.483015\pi\)
0.0533350 + 0.998577i \(0.483015\pi\)
\(410\) 81.0503 4.00279
\(411\) −56.4412 −2.78404
\(412\) −79.6159 −3.92240
\(413\) −28.9438 −1.42423
\(414\) −19.5849 −0.962546
\(415\) 1.56834 0.0769868
\(416\) 42.5799 2.08765
\(417\) 9.38940 0.459801
\(418\) −34.0118 −1.66357
\(419\) 27.2992 1.33365 0.666827 0.745212i \(-0.267652\pi\)
0.666827 + 0.745212i \(0.267652\pi\)
\(420\) 124.830 6.09109
\(421\) −6.95347 −0.338892 −0.169446 0.985540i \(-0.554198\pi\)
−0.169446 + 0.985540i \(0.554198\pi\)
\(422\) 12.6479 0.615688
\(423\) 2.55857 0.124402
\(424\) −8.73623 −0.424269
\(425\) 3.41504 0.165654
\(426\) −49.4669 −2.39668
\(427\) −33.9206 −1.64153
\(428\) −18.0849 −0.874167
\(429\) 18.8437 0.909780
\(430\) −49.4687 −2.38559
\(431\) −21.9338 −1.05651 −0.528257 0.849084i \(-0.677154\pi\)
−0.528257 + 0.849084i \(0.677154\pi\)
\(432\) −109.883 −5.28673
\(433\) 2.44060 0.117288 0.0586438 0.998279i \(-0.481322\pi\)
0.0586438 + 0.998279i \(0.481322\pi\)
\(434\) −13.2033 −0.633777
\(435\) 19.6769 0.943433
\(436\) 19.3257 0.925535
\(437\) 6.01524 0.287748
\(438\) 71.8992 3.43548
\(439\) −36.4387 −1.73913 −0.869563 0.493822i \(-0.835599\pi\)
−0.869563 + 0.493822i \(0.835599\pi\)
\(440\) −60.4257 −2.88068
\(441\) 12.7293 0.606157
\(442\) 11.2414 0.534698
\(443\) 18.4596 0.877044 0.438522 0.898721i \(-0.355502\pi\)
0.438522 + 0.898721i \(0.355502\pi\)
\(444\) 46.5394 2.20866
\(445\) −30.1806 −1.43070
\(446\) 6.96062 0.329595
\(447\) −14.1451 −0.669041
\(448\) −64.5075 −3.04769
\(449\) −2.50709 −0.118317 −0.0591586 0.998249i \(-0.518842\pi\)
−0.0591586 + 0.998249i \(0.518842\pi\)
\(450\) −31.1112 −1.46660
\(451\) −29.8381 −1.40502
\(452\) −55.8694 −2.62788
\(453\) −2.97285 −0.139677
\(454\) 29.9877 1.40739
\(455\) 19.3808 0.908587
\(456\) 125.348 5.86994
\(457\) −16.6574 −0.779203 −0.389601 0.920984i \(-0.627387\pi\)
−0.389601 + 0.920984i \(0.627387\pi\)
\(458\) −44.8990 −2.09799
\(459\) −14.5522 −0.679237
\(460\) 17.2722 0.805320
\(461\) −17.2981 −0.805652 −0.402826 0.915277i \(-0.631972\pi\)
−0.402826 + 0.915277i \(0.631972\pi\)
\(462\) −63.4770 −2.95322
\(463\) 16.9080 0.785783 0.392891 0.919585i \(-0.371475\pi\)
0.392891 + 0.919585i \(0.371475\pi\)
\(464\) −32.6308 −1.51485
\(465\) 12.7148 0.589633
\(466\) 28.7598 1.33227
\(467\) −19.1393 −0.885662 −0.442831 0.896605i \(-0.646026\pi\)
−0.442831 + 0.896605i \(0.646026\pi\)
\(468\) −74.1413 −3.42718
\(469\) −10.7908 −0.498273
\(470\) −3.11676 −0.143766
\(471\) 66.3810 3.05867
\(472\) −83.4538 −3.84127
\(473\) 18.2115 0.837368
\(474\) 34.7390 1.59562
\(475\) 9.55539 0.438431
\(476\) −27.4151 −1.25657
\(477\) 5.83784 0.267296
\(478\) −2.39316 −0.109461
\(479\) −11.6466 −0.532147 −0.266074 0.963953i \(-0.585726\pi\)
−0.266074 + 0.963953i \(0.585726\pi\)
\(480\) 138.129 6.30468
\(481\) 7.22560 0.329459
\(482\) −21.4356 −0.976363
\(483\) 11.2264 0.510818
\(484\) −21.7476 −0.988525
\(485\) −34.4888 −1.56606
\(486\) −7.57534 −0.343625
\(487\) 27.9471 1.26640 0.633201 0.773987i \(-0.281740\pi\)
0.633201 + 0.773987i \(0.281740\pi\)
\(488\) −97.8037 −4.42736
\(489\) 13.5232 0.611538
\(490\) −15.5064 −0.700507
\(491\) −4.45926 −0.201244 −0.100622 0.994925i \(-0.532083\pi\)
−0.100622 + 0.994925i \(0.532083\pi\)
\(492\) 177.730 8.01268
\(493\) −4.32142 −0.194627
\(494\) 31.4537 1.41517
\(495\) 40.3785 1.81488
\(496\) −21.0853 −0.946759
\(497\) 18.7300 0.840158
\(498\) 4.75036 0.212869
\(499\) 8.77067 0.392629 0.196315 0.980541i \(-0.437103\pi\)
0.196315 + 0.980541i \(0.437103\pi\)
\(500\) −41.8547 −1.87180
\(501\) −69.7565 −3.11649
\(502\) −41.4835 −1.85150
\(503\) 23.8303 1.06254 0.531271 0.847202i \(-0.321715\pi\)
0.531271 + 0.847202i \(0.321715\pi\)
\(504\) 154.529 6.88325
\(505\) −26.6167 −1.18443
\(506\) −8.78303 −0.390453
\(507\) 21.2207 0.942443
\(508\) −32.1763 −1.42759
\(509\) 2.76276 0.122457 0.0612286 0.998124i \(-0.480498\pi\)
0.0612286 + 0.998124i \(0.480498\pi\)
\(510\) 36.4668 1.61478
\(511\) −27.2238 −1.20431
\(512\) −1.48982 −0.0658414
\(513\) −40.7174 −1.79772
\(514\) 20.2206 0.891892
\(515\) −40.0988 −1.76697
\(516\) −108.477 −4.77541
\(517\) 1.14742 0.0504633
\(518\) −24.3403 −1.06945
\(519\) −62.1702 −2.72897
\(520\) 55.8809 2.45054
\(521\) 27.7695 1.21661 0.608303 0.793705i \(-0.291851\pi\)
0.608303 + 0.793705i \(0.291851\pi\)
\(522\) 39.3684 1.72311
\(523\) 8.27930 0.362028 0.181014 0.983480i \(-0.442062\pi\)
0.181014 + 0.983480i \(0.442062\pi\)
\(524\) 6.22033 0.271736
\(525\) 17.8334 0.778315
\(526\) 32.4508 1.41492
\(527\) −2.79241 −0.121639
\(528\) −101.371 −4.41163
\(529\) −21.4467 −0.932463
\(530\) −7.11145 −0.308902
\(531\) 55.7667 2.42007
\(532\) −76.7084 −3.32573
\(533\) 27.5939 1.19523
\(534\) −91.4144 −3.95589
\(535\) −9.10852 −0.393796
\(536\) −31.1132 −1.34389
\(537\) −49.0689 −2.11748
\(538\) −45.0153 −1.94075
\(539\) 5.70856 0.245885
\(540\) −116.916 −5.03127
\(541\) −13.1169 −0.563938 −0.281969 0.959424i \(-0.590987\pi\)
−0.281969 + 0.959424i \(0.590987\pi\)
\(542\) 21.6288 0.929036
\(543\) 30.7964 1.32160
\(544\) −30.3357 −1.30063
\(545\) 9.73347 0.416936
\(546\) 58.7028 2.51225
\(547\) −18.4250 −0.787796 −0.393898 0.919154i \(-0.628874\pi\)
−0.393898 + 0.919154i \(0.628874\pi\)
\(548\) 99.5896 4.25426
\(549\) 65.3557 2.78931
\(550\) −13.9521 −0.594920
\(551\) −12.0915 −0.515114
\(552\) 32.3691 1.37772
\(553\) −13.1535 −0.559344
\(554\) −62.5700 −2.65835
\(555\) 23.4397 0.994961
\(556\) −16.5675 −0.702617
\(557\) 30.0796 1.27451 0.637257 0.770652i \(-0.280069\pi\)
0.637257 + 0.770652i \(0.280069\pi\)
\(558\) 25.4390 1.07692
\(559\) −16.8418 −0.712333
\(560\) −104.261 −4.40584
\(561\) −13.4250 −0.566805
\(562\) 45.2556 1.90899
\(563\) 17.0639 0.719157 0.359578 0.933115i \(-0.382921\pi\)
0.359578 + 0.933115i \(0.382921\pi\)
\(564\) −6.83455 −0.287786
\(565\) −28.1388 −1.18381
\(566\) −18.2404 −0.766702
\(567\) −22.9271 −0.962847
\(568\) 54.0045 2.26598
\(569\) −25.7629 −1.08004 −0.540018 0.841654i \(-0.681582\pi\)
−0.540018 + 0.841654i \(0.681582\pi\)
\(570\) 102.035 4.27379
\(571\) 18.8520 0.788931 0.394466 0.918911i \(-0.370930\pi\)
0.394466 + 0.918911i \(0.370930\pi\)
\(572\) −33.2494 −1.39023
\(573\) 54.2327 2.26560
\(574\) −92.9532 −3.87979
\(575\) 2.46753 0.102903
\(576\) 124.288 5.17867
\(577\) −3.45021 −0.143634 −0.0718170 0.997418i \(-0.522880\pi\)
−0.0718170 + 0.997418i \(0.522880\pi\)
\(578\) 37.7510 1.57024
\(579\) 29.4846 1.22534
\(580\) −34.7195 −1.44165
\(581\) −1.79866 −0.0746212
\(582\) −104.463 −4.33015
\(583\) 2.61803 0.108428
\(584\) −78.4945 −3.24813
\(585\) −37.3415 −1.54388
\(586\) −4.17383 −0.172419
\(587\) −46.2270 −1.90799 −0.953996 0.299820i \(-0.903073\pi\)
−0.953996 + 0.299820i \(0.903073\pi\)
\(588\) −34.0029 −1.40226
\(589\) −7.81325 −0.321939
\(590\) −67.9330 −2.79676
\(591\) 42.2615 1.73840
\(592\) −38.8709 −1.59758
\(593\) 35.0539 1.43949 0.719745 0.694239i \(-0.244259\pi\)
0.719745 + 0.694239i \(0.244259\pi\)
\(594\) 59.4527 2.43938
\(595\) −13.8077 −0.566061
\(596\) 24.9588 1.02235
\(597\) −6.88526 −0.281795
\(598\) 8.12244 0.332151
\(599\) 43.1300 1.76224 0.881122 0.472889i \(-0.156789\pi\)
0.881122 + 0.472889i \(0.156789\pi\)
\(600\) 51.4193 2.09919
\(601\) 1.49611 0.0610276 0.0305138 0.999534i \(-0.490286\pi\)
0.0305138 + 0.999534i \(0.490286\pi\)
\(602\) 56.7336 2.31229
\(603\) 20.7909 0.846671
\(604\) 5.24555 0.213438
\(605\) −10.9532 −0.445312
\(606\) −80.6197 −3.27495
\(607\) 37.5771 1.52521 0.762604 0.646866i \(-0.223921\pi\)
0.762604 + 0.646866i \(0.223921\pi\)
\(608\) −84.8803 −3.44235
\(609\) −22.5666 −0.914444
\(610\) −79.6140 −3.22348
\(611\) −1.06112 −0.0429281
\(612\) 52.8214 2.13518
\(613\) 6.77752 0.273742 0.136871 0.990589i \(-0.456295\pi\)
0.136871 + 0.990589i \(0.456295\pi\)
\(614\) −10.7296 −0.433010
\(615\) 89.5142 3.60956
\(616\) 69.2998 2.79217
\(617\) −13.4229 −0.540385 −0.270192 0.962806i \(-0.587087\pi\)
−0.270192 + 0.962806i \(0.587087\pi\)
\(618\) −121.456 −4.88566
\(619\) −31.4297 −1.26327 −0.631634 0.775267i \(-0.717615\pi\)
−0.631634 + 0.775267i \(0.717615\pi\)
\(620\) −22.4350 −0.901012
\(621\) −10.5147 −0.421939
\(622\) −29.5845 −1.18623
\(623\) 34.6129 1.38674
\(624\) 93.7471 3.75289
\(625\) −30.9794 −1.23918
\(626\) 38.9044 1.55493
\(627\) −37.5636 −1.50015
\(628\) −117.128 −4.67392
\(629\) −5.14782 −0.205257
\(630\) 125.789 5.01156
\(631\) −21.8255 −0.868858 −0.434429 0.900706i \(-0.643050\pi\)
−0.434429 + 0.900706i \(0.643050\pi\)
\(632\) −37.9257 −1.50860
\(633\) 13.9687 0.555204
\(634\) −51.5000 −2.04533
\(635\) −16.2057 −0.643104
\(636\) −15.5942 −0.618352
\(637\) −5.27921 −0.209170
\(638\) 17.6551 0.698973
\(639\) −36.0876 −1.42761
\(640\) −58.4768 −2.31150
\(641\) 22.8259 0.901570 0.450785 0.892633i \(-0.351144\pi\)
0.450785 + 0.892633i \(0.351144\pi\)
\(642\) −27.5889 −1.08885
\(643\) −36.2852 −1.43095 −0.715474 0.698640i \(-0.753789\pi\)
−0.715474 + 0.698640i \(0.753789\pi\)
\(644\) −19.8088 −0.780575
\(645\) −54.6346 −2.15123
\(646\) −22.4089 −0.881668
\(647\) −46.2899 −1.81984 −0.909922 0.414780i \(-0.863858\pi\)
−0.909922 + 0.414780i \(0.863858\pi\)
\(648\) −66.1058 −2.59688
\(649\) 25.0091 0.981692
\(650\) 12.9028 0.506088
\(651\) −14.5820 −0.571516
\(652\) −23.8614 −0.934485
\(653\) −5.97064 −0.233649 −0.116825 0.993153i \(-0.537272\pi\)
−0.116825 + 0.993153i \(0.537272\pi\)
\(654\) 29.4818 1.15283
\(655\) 3.13289 0.122412
\(656\) −148.444 −5.79578
\(657\) 52.4527 2.04637
\(658\) 3.57449 0.139348
\(659\) 39.3638 1.53340 0.766699 0.642007i \(-0.221898\pi\)
0.766699 + 0.642007i \(0.221898\pi\)
\(660\) −107.860 −4.19846
\(661\) −0.773148 −0.0300720 −0.0150360 0.999887i \(-0.504786\pi\)
−0.0150360 + 0.999887i \(0.504786\pi\)
\(662\) −88.0010 −3.42026
\(663\) 12.4153 0.482170
\(664\) −5.18611 −0.201260
\(665\) −38.6344 −1.49818
\(666\) 46.8970 1.81722
\(667\) −3.12244 −0.120901
\(668\) 123.084 4.76227
\(669\) 7.68751 0.297216
\(670\) −25.3267 −0.978458
\(671\) 29.3094 1.13147
\(672\) −158.414 −6.11095
\(673\) 16.0619 0.619139 0.309570 0.950877i \(-0.399815\pi\)
0.309570 + 0.950877i \(0.399815\pi\)
\(674\) 4.16061 0.160261
\(675\) −16.7029 −0.642893
\(676\) −37.4436 −1.44014
\(677\) 28.6621 1.10157 0.550786 0.834646i \(-0.314328\pi\)
0.550786 + 0.834646i \(0.314328\pi\)
\(678\) −85.2299 −3.27324
\(679\) 39.5538 1.51794
\(680\) −39.8119 −1.52672
\(681\) 33.1193 1.26913
\(682\) 11.4084 0.436849
\(683\) 21.4561 0.820995 0.410498 0.911862i \(-0.365355\pi\)
0.410498 + 0.911862i \(0.365355\pi\)
\(684\) 147.796 5.65112
\(685\) 50.1586 1.91646
\(686\) −39.3072 −1.50076
\(687\) −49.5877 −1.89189
\(688\) 90.6023 3.45418
\(689\) −2.42112 −0.0922375
\(690\) 26.3491 1.00309
\(691\) −47.6507 −1.81272 −0.906359 0.422508i \(-0.861150\pi\)
−0.906359 + 0.422508i \(0.861150\pi\)
\(692\) 109.698 4.17011
\(693\) −46.3084 −1.75911
\(694\) −27.9441 −1.06074
\(695\) −8.34425 −0.316516
\(696\) −65.0664 −2.46634
\(697\) −19.6591 −0.744640
\(698\) −6.28029 −0.237713
\(699\) 31.7631 1.20139
\(700\) −31.4668 −1.18933
\(701\) 24.4697 0.924208 0.462104 0.886826i \(-0.347095\pi\)
0.462104 + 0.886826i \(0.347095\pi\)
\(702\) −54.9812 −2.07513
\(703\) −14.4038 −0.543248
\(704\) 55.7382 2.10071
\(705\) −3.44224 −0.129642
\(706\) −56.0421 −2.10917
\(707\) 30.5257 1.14804
\(708\) −148.966 −5.59848
\(709\) −8.28446 −0.311130 −0.155565 0.987826i \(-0.549720\pi\)
−0.155565 + 0.987826i \(0.549720\pi\)
\(710\) 43.9607 1.64982
\(711\) 25.3432 0.950444
\(712\) 99.7998 3.74016
\(713\) −2.01765 −0.0755617
\(714\) −41.8223 −1.56516
\(715\) −16.7461 −0.626270
\(716\) 86.5813 3.23570
\(717\) −2.64308 −0.0987075
\(718\) −67.8151 −2.53084
\(719\) −12.4288 −0.463515 −0.231758 0.972774i \(-0.574448\pi\)
−0.231758 + 0.972774i \(0.574448\pi\)
\(720\) 200.883 7.48645
\(721\) 45.9877 1.71267
\(722\) −11.5575 −0.430127
\(723\) −23.6740 −0.880447
\(724\) −54.3398 −2.01952
\(725\) −4.96009 −0.184213
\(726\) −33.1763 −1.23129
\(727\) 41.9968 1.55758 0.778788 0.627287i \(-0.215835\pi\)
0.778788 + 0.627287i \(0.215835\pi\)
\(728\) −64.0876 −2.37524
\(729\) −31.0670 −1.15063
\(730\) −63.8960 −2.36490
\(731\) 11.9988 0.443792
\(732\) −174.580 −6.45267
\(733\) −33.7036 −1.24487 −0.622436 0.782671i \(-0.713857\pi\)
−0.622436 + 0.782671i \(0.713857\pi\)
\(734\) 87.4737 3.22871
\(735\) −17.1257 −0.631690
\(736\) −21.9190 −0.807947
\(737\) 9.32387 0.343449
\(738\) 179.095 6.59259
\(739\) 27.4557 1.00998 0.504988 0.863127i \(-0.331497\pi\)
0.504988 + 0.863127i \(0.331497\pi\)
\(740\) −41.3590 −1.52039
\(741\) 34.7384 1.27615
\(742\) 8.15583 0.299410
\(743\) −4.71004 −0.172795 −0.0863973 0.996261i \(-0.527535\pi\)
−0.0863973 + 0.996261i \(0.527535\pi\)
\(744\) −42.0446 −1.54143
\(745\) 12.5706 0.460551
\(746\) 64.5721 2.36415
\(747\) 3.46553 0.126797
\(748\) 23.6882 0.866128
\(749\) 10.4462 0.381695
\(750\) −63.8501 −2.33148
\(751\) 42.8360 1.56311 0.781554 0.623838i \(-0.214428\pi\)
0.781554 + 0.623838i \(0.214428\pi\)
\(752\) 5.70838 0.208163
\(753\) −45.8155 −1.66961
\(754\) −16.3272 −0.594603
\(755\) 2.64194 0.0961500
\(756\) 134.086 4.87668
\(757\) −20.9901 −0.762897 −0.381449 0.924390i \(-0.624575\pi\)
−0.381449 + 0.924390i \(0.624575\pi\)
\(758\) 22.4880 0.816800
\(759\) −9.70023 −0.352096
\(760\) −111.395 −4.04072
\(761\) −10.0006 −0.362521 −0.181261 0.983435i \(-0.558018\pi\)
−0.181261 + 0.983435i \(0.558018\pi\)
\(762\) −49.0856 −1.77818
\(763\) −11.1629 −0.404125
\(764\) −95.6927 −3.46204
\(765\) 26.6037 0.961858
\(766\) 44.7575 1.61715
\(767\) −23.1281 −0.835106
\(768\) −50.5363 −1.82357
\(769\) −27.1420 −0.978765 −0.489382 0.872069i \(-0.662778\pi\)
−0.489382 + 0.872069i \(0.662778\pi\)
\(770\) 56.4113 2.03292
\(771\) 22.3322 0.804274
\(772\) −52.0251 −1.87242
\(773\) −8.70667 −0.313157 −0.156579 0.987665i \(-0.550046\pi\)
−0.156579 + 0.987665i \(0.550046\pi\)
\(774\) −109.310 −3.92907
\(775\) −3.20511 −0.115131
\(776\) 114.046 4.09401
\(777\) −26.8821 −0.964388
\(778\) −27.2787 −0.977988
\(779\) −55.0066 −1.97082
\(780\) 99.7479 3.57155
\(781\) −16.1838 −0.579103
\(782\) −5.78677 −0.206934
\(783\) 21.1359 0.755336
\(784\) 28.4001 1.01429
\(785\) −58.9920 −2.10551
\(786\) 9.48923 0.338470
\(787\) 16.7454 0.596910 0.298455 0.954424i \(-0.403529\pi\)
0.298455 + 0.954424i \(0.403529\pi\)
\(788\) −74.5697 −2.65644
\(789\) 35.8396 1.27592
\(790\) −30.8722 −1.09838
\(791\) 32.2713 1.14743
\(792\) −133.522 −4.74448
\(793\) −27.1049 −0.962524
\(794\) 12.8926 0.457543
\(795\) −7.85409 −0.278556
\(796\) 12.1489 0.430608
\(797\) 29.5969 1.04838 0.524188 0.851603i \(-0.324369\pi\)
0.524188 + 0.851603i \(0.324369\pi\)
\(798\) −117.020 −4.14247
\(799\) 0.755983 0.0267448
\(800\) −34.8191 −1.23104
\(801\) −66.6896 −2.35636
\(802\) −46.0770 −1.62703
\(803\) 23.5229 0.830104
\(804\) −55.5374 −1.95865
\(805\) −9.97675 −0.351634
\(806\) −10.5503 −0.371619
\(807\) −49.7162 −1.75009
\(808\) 88.0149 3.09635
\(809\) −7.92377 −0.278585 −0.139292 0.990251i \(-0.544483\pi\)
−0.139292 + 0.990251i \(0.544483\pi\)
\(810\) −53.8114 −1.89074
\(811\) −54.0967 −1.89959 −0.949796 0.312869i \(-0.898710\pi\)
−0.949796 + 0.312869i \(0.898710\pi\)
\(812\) 39.8184 1.39735
\(813\) 23.8874 0.837769
\(814\) 21.0314 0.737149
\(815\) −12.0179 −0.420968
\(816\) −66.7894 −2.33810
\(817\) 33.5731 1.17457
\(818\) −5.80684 −0.203031
\(819\) 42.8255 1.49644
\(820\) −157.946 −5.51573
\(821\) −10.9468 −0.382047 −0.191024 0.981585i \(-0.561181\pi\)
−0.191024 + 0.981585i \(0.561181\pi\)
\(822\) 151.926 5.29902
\(823\) 31.7095 1.10532 0.552662 0.833405i \(-0.313612\pi\)
0.552662 + 0.833405i \(0.313612\pi\)
\(824\) 132.597 4.61923
\(825\) −15.4091 −0.536476
\(826\) 77.9095 2.71082
\(827\) −32.1987 −1.11966 −0.559829 0.828608i \(-0.689133\pi\)
−0.559829 + 0.828608i \(0.689133\pi\)
\(828\) 38.1660 1.32636
\(829\) −11.0284 −0.383031 −0.191515 0.981490i \(-0.561340\pi\)
−0.191515 + 0.981490i \(0.561340\pi\)
\(830\) −4.22159 −0.146533
\(831\) −69.1041 −2.39719
\(832\) −51.5460 −1.78703
\(833\) 3.76113 0.130315
\(834\) −25.2740 −0.875166
\(835\) 61.9918 2.14531
\(836\) 66.2804 2.29236
\(837\) 13.6576 0.472075
\(838\) −73.4828 −2.53842
\(839\) −47.2253 −1.63040 −0.815200 0.579180i \(-0.803373\pi\)
−0.815200 + 0.579180i \(0.803373\pi\)
\(840\) −207.899 −7.17320
\(841\) −22.7235 −0.783568
\(842\) 18.7171 0.645032
\(843\) 49.9816 1.72146
\(844\) −24.6475 −0.848401
\(845\) −18.8586 −0.648754
\(846\) −6.88705 −0.236782
\(847\) 12.5618 0.431629
\(848\) 13.0247 0.447270
\(849\) −20.1452 −0.691382
\(850\) −9.19246 −0.315299
\(851\) −3.71955 −0.127505
\(852\) 96.3985 3.30256
\(853\) 16.4614 0.563627 0.281813 0.959469i \(-0.409064\pi\)
0.281813 + 0.959469i \(0.409064\pi\)
\(854\) 91.3060 3.12443
\(855\) 74.4379 2.54572
\(856\) 30.1196 1.02947
\(857\) −4.59033 −0.156803 −0.0784014 0.996922i \(-0.524982\pi\)
−0.0784014 + 0.996922i \(0.524982\pi\)
\(858\) −50.7225 −1.73164
\(859\) −19.6684 −0.671077 −0.335538 0.942027i \(-0.608918\pi\)
−0.335538 + 0.942027i \(0.608918\pi\)
\(860\) 96.4019 3.28728
\(861\) −102.660 −3.49865
\(862\) 59.0405 2.01093
\(863\) 1.50286 0.0511580 0.0255790 0.999673i \(-0.491857\pi\)
0.0255790 + 0.999673i \(0.491857\pi\)
\(864\) 148.371 5.04768
\(865\) 55.2499 1.87855
\(866\) −6.56950 −0.223241
\(867\) 41.6933 1.41598
\(868\) 25.7298 0.873326
\(869\) 11.3654 0.385544
\(870\) −52.9653 −1.79569
\(871\) −8.62260 −0.292166
\(872\) −32.1862 −1.08996
\(873\) −76.2093 −2.57929
\(874\) −16.1916 −0.547687
\(875\) 24.1761 0.817300
\(876\) −140.113 −4.73399
\(877\) 14.4133 0.486703 0.243351 0.969938i \(-0.421753\pi\)
0.243351 + 0.969938i \(0.421753\pi\)
\(878\) 98.0842 3.31018
\(879\) −4.60970 −0.155481
\(880\) 90.0876 3.03685
\(881\) −18.0613 −0.608501 −0.304251 0.952592i \(-0.598406\pi\)
−0.304251 + 0.952592i \(0.598406\pi\)
\(882\) −34.2641 −1.15373
\(883\) 16.8264 0.566253 0.283127 0.959083i \(-0.408628\pi\)
0.283127 + 0.959083i \(0.408628\pi\)
\(884\) −21.9066 −0.736798
\(885\) −75.0271 −2.52201
\(886\) −49.6888 −1.66933
\(887\) 15.5878 0.523386 0.261693 0.965151i \(-0.415719\pi\)
0.261693 + 0.965151i \(0.415719\pi\)
\(888\) −77.5093 −2.60104
\(889\) 18.5857 0.623343
\(890\) 81.2389 2.72313
\(891\) 19.8103 0.663670
\(892\) −13.5645 −0.454173
\(893\) 2.11526 0.0707846
\(894\) 38.0752 1.27342
\(895\) 43.6070 1.45762
\(896\) 67.0647 2.24047
\(897\) 8.97065 0.299521
\(898\) 6.74849 0.225200
\(899\) 4.05577 0.135267
\(900\) 60.6279 2.02093
\(901\) 1.72491 0.0574651
\(902\) 80.3169 2.67426
\(903\) 62.6581 2.08513
\(904\) 93.0481 3.09473
\(905\) −27.3684 −0.909757
\(906\) 8.00219 0.265855
\(907\) 49.1215 1.63105 0.815527 0.578719i \(-0.196447\pi\)
0.815527 + 0.578719i \(0.196447\pi\)
\(908\) −58.4384 −1.93935
\(909\) −58.8145 −1.95075
\(910\) −52.1685 −1.72937
\(911\) −1.94257 −0.0643601 −0.0321800 0.999482i \(-0.510245\pi\)
−0.0321800 + 0.999482i \(0.510245\pi\)
\(912\) −186.879 −6.18817
\(913\) 1.55415 0.0514348
\(914\) 44.8378 1.48310
\(915\) −87.9279 −2.90681
\(916\) 87.4968 2.89097
\(917\) −3.59298 −0.118651
\(918\) 39.1709 1.29283
\(919\) −43.6065 −1.43844 −0.719222 0.694780i \(-0.755502\pi\)
−0.719222 + 0.694780i \(0.755502\pi\)
\(920\) −28.7661 −0.948389
\(921\) −11.8500 −0.390472
\(922\) 46.5622 1.53344
\(923\) 14.9666 0.492632
\(924\) 123.701 4.06945
\(925\) −5.90862 −0.194274
\(926\) −45.5123 −1.49563
\(927\) −88.6056 −2.91019
\(928\) 44.0603 1.44635
\(929\) −56.3550 −1.84895 −0.924474 0.381246i \(-0.875495\pi\)
−0.924474 + 0.381246i \(0.875495\pi\)
\(930\) −34.2251 −1.12228
\(931\) 10.5238 0.344902
\(932\) −56.0456 −1.83583
\(933\) −32.6739 −1.06970
\(934\) 51.5184 1.68573
\(935\) 11.9307 0.390174
\(936\) 123.479 4.03604
\(937\) 10.7476 0.351108 0.175554 0.984470i \(-0.443828\pi\)
0.175554 + 0.984470i \(0.443828\pi\)
\(938\) 29.0462 0.948392
\(939\) 42.9671 1.40218
\(940\) 6.07378 0.198105
\(941\) −45.6863 −1.48933 −0.744665 0.667438i \(-0.767391\pi\)
−0.744665 + 0.667438i \(0.767391\pi\)
\(942\) −178.681 −5.82175
\(943\) −14.2046 −0.462566
\(944\) 124.420 4.04952
\(945\) 67.5331 2.19685
\(946\) −49.0210 −1.59381
\(947\) −60.7725 −1.97484 −0.987420 0.158117i \(-0.949458\pi\)
−0.987420 + 0.158117i \(0.949458\pi\)
\(948\) −67.6976 −2.19872
\(949\) −21.7537 −0.706154
\(950\) −25.7208 −0.834492
\(951\) −56.8781 −1.84440
\(952\) 45.6587 1.47981
\(953\) −33.9325 −1.09918 −0.549590 0.835435i \(-0.685216\pi\)
−0.549590 + 0.835435i \(0.685216\pi\)
\(954\) −15.7140 −0.508761
\(955\) −48.1960 −1.55958
\(956\) 4.66367 0.150834
\(957\) 19.4988 0.630307
\(958\) 31.3498 1.01287
\(959\) −57.5249 −1.85757
\(960\) −167.214 −5.39682
\(961\) −28.3793 −0.915460
\(962\) −19.4495 −0.627079
\(963\) −20.1269 −0.648581
\(964\) 41.7725 1.34540
\(965\) −26.2026 −0.843492
\(966\) −30.2187 −0.972270
\(967\) 24.4574 0.786498 0.393249 0.919432i \(-0.371351\pi\)
0.393249 + 0.919432i \(0.371351\pi\)
\(968\) 36.2196 1.16414
\(969\) −24.7491 −0.795055
\(970\) 92.8355 2.98077
\(971\) −52.9047 −1.69779 −0.848896 0.528560i \(-0.822732\pi\)
−0.848896 + 0.528560i \(0.822732\pi\)
\(972\) 14.7624 0.473505
\(973\) 9.56968 0.306790
\(974\) −75.2267 −2.41042
\(975\) 14.2502 0.456370
\(976\) 145.814 4.66739
\(977\) −44.9071 −1.43671 −0.718353 0.695679i \(-0.755104\pi\)
−0.718353 + 0.695679i \(0.755104\pi\)
\(978\) −36.4010 −1.16398
\(979\) −29.9076 −0.955849
\(980\) 30.2180 0.965278
\(981\) 21.5079 0.686694
\(982\) 12.0033 0.383039
\(983\) −21.1991 −0.676147 −0.338074 0.941120i \(-0.609775\pi\)
−0.338074 + 0.941120i \(0.609775\pi\)
\(984\) −296.001 −9.43617
\(985\) −37.5573 −1.19667
\(986\) 11.6322 0.370445
\(987\) 3.94777 0.125659
\(988\) −61.2953 −1.95006
\(989\) 8.66973 0.275681
\(990\) −108.689 −3.45436
\(991\) −32.2621 −1.02484 −0.512419 0.858735i \(-0.671251\pi\)
−0.512419 + 0.858735i \(0.671251\pi\)
\(992\) 28.4709 0.903951
\(993\) −97.1908 −3.08426
\(994\) −50.4167 −1.59912
\(995\) 6.11885 0.193981
\(996\) −9.25724 −0.293327
\(997\) −30.5309 −0.966922 −0.483461 0.875366i \(-0.660620\pi\)
−0.483461 + 0.875366i \(0.660620\pi\)
\(998\) −23.6085 −0.747314
\(999\) 25.1778 0.796591
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 8003.2.a.a.1.5 147
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.a.1.5 147 1.1 even 1 trivial