Properties

Label 1339.2.a.g.1.1
Level $1339$
Weight $2$
Character 1339.1
Self dual yes
Analytic conductor $10.692$
Analytic rank $0$
Dimension $30$
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] = [1339,2,Mod(1,1339)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1339, 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("1339.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.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: \(10.6919688306\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1339.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.71030 q^{2} -2.41604 q^{3} +5.34571 q^{4} +3.72865 q^{5} +6.54819 q^{6} -2.88700 q^{7} -9.06786 q^{8} +2.83725 q^{9} +O(q^{10})\) \(q-2.71030 q^{2} -2.41604 q^{3} +5.34571 q^{4} +3.72865 q^{5} +6.54819 q^{6} -2.88700 q^{7} -9.06786 q^{8} +2.83725 q^{9} -10.1057 q^{10} -4.46651 q^{11} -12.9155 q^{12} -1.00000 q^{13} +7.82461 q^{14} -9.00857 q^{15} +13.8852 q^{16} -1.88158 q^{17} -7.68980 q^{18} -8.12116 q^{19} +19.9323 q^{20} +6.97510 q^{21} +12.1056 q^{22} -2.19223 q^{23} +21.9083 q^{24} +8.90282 q^{25} +2.71030 q^{26} +0.393202 q^{27} -15.4330 q^{28} +8.82158 q^{29} +24.4159 q^{30} +5.98295 q^{31} -19.4972 q^{32} +10.7913 q^{33} +5.09965 q^{34} -10.7646 q^{35} +15.1671 q^{36} -9.44386 q^{37} +22.0108 q^{38} +2.41604 q^{39} -33.8109 q^{40} -6.21801 q^{41} -18.9046 q^{42} -0.0964750 q^{43} -23.8767 q^{44} +10.5791 q^{45} +5.94159 q^{46} +4.49548 q^{47} -33.5472 q^{48} +1.33474 q^{49} -24.1293 q^{50} +4.54598 q^{51} -5.34571 q^{52} +1.45631 q^{53} -1.06569 q^{54} -16.6540 q^{55} +26.1789 q^{56} +19.6211 q^{57} -23.9091 q^{58} +8.09604 q^{59} -48.1572 q^{60} +1.81432 q^{61} -16.2156 q^{62} -8.19114 q^{63} +25.0729 q^{64} -3.72865 q^{65} -29.2475 q^{66} +7.20656 q^{67} -10.0584 q^{68} +5.29652 q^{69} +29.1752 q^{70} +10.0084 q^{71} -25.7278 q^{72} -3.27988 q^{73} +25.5957 q^{74} -21.5096 q^{75} -43.4134 q^{76} +12.8948 q^{77} -6.54819 q^{78} -2.69531 q^{79} +51.7730 q^{80} -9.46175 q^{81} +16.8526 q^{82} -8.82524 q^{83} +37.2868 q^{84} -7.01576 q^{85} +0.261476 q^{86} -21.3133 q^{87} +40.5017 q^{88} +11.4254 q^{89} -28.6726 q^{90} +2.88700 q^{91} -11.7190 q^{92} -14.4550 q^{93} -12.1841 q^{94} -30.2810 q^{95} +47.1061 q^{96} -3.79001 q^{97} -3.61755 q^{98} -12.6726 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71030 −1.91647 −0.958235 0.285983i \(-0.907680\pi\)
−0.958235 + 0.285983i \(0.907680\pi\)
\(3\) −2.41604 −1.39490 −0.697451 0.716633i \(-0.745682\pi\)
−0.697451 + 0.716633i \(0.745682\pi\)
\(4\) 5.34571 2.67285
\(5\) 3.72865 1.66750 0.833751 0.552140i \(-0.186189\pi\)
0.833751 + 0.552140i \(0.186189\pi\)
\(6\) 6.54819 2.67329
\(7\) −2.88700 −1.09118 −0.545591 0.838052i \(-0.683695\pi\)
−0.545591 + 0.838052i \(0.683695\pi\)
\(8\) −9.06786 −3.20597
\(9\) 2.83725 0.945751
\(10\) −10.1057 −3.19572
\(11\) −4.46651 −1.34670 −0.673352 0.739322i \(-0.735146\pi\)
−0.673352 + 0.739322i \(0.735146\pi\)
\(12\) −12.9155 −3.72837
\(13\) −1.00000 −0.277350
\(14\) 7.82461 2.09122
\(15\) −9.00857 −2.32600
\(16\) 13.8852 3.47130
\(17\) −1.88158 −0.456351 −0.228175 0.973620i \(-0.573276\pi\)
−0.228175 + 0.973620i \(0.573276\pi\)
\(18\) −7.68980 −1.81250
\(19\) −8.12116 −1.86312 −0.931561 0.363584i \(-0.881553\pi\)
−0.931561 + 0.363584i \(0.881553\pi\)
\(20\) 19.9323 4.45699
\(21\) 6.97510 1.52209
\(22\) 12.1056 2.58092
\(23\) −2.19223 −0.457112 −0.228556 0.973531i \(-0.573400\pi\)
−0.228556 + 0.973531i \(0.573400\pi\)
\(24\) 21.9083 4.47202
\(25\) 8.90282 1.78056
\(26\) 2.71030 0.531533
\(27\) 0.393202 0.0756717
\(28\) −15.4330 −2.91657
\(29\) 8.82158 1.63813 0.819063 0.573703i \(-0.194494\pi\)
0.819063 + 0.573703i \(0.194494\pi\)
\(30\) 24.4159 4.45771
\(31\) 5.98295 1.07457 0.537285 0.843401i \(-0.319450\pi\)
0.537285 + 0.843401i \(0.319450\pi\)
\(32\) −19.4972 −3.44666
\(33\) 10.7913 1.87852
\(34\) 5.09965 0.874583
\(35\) −10.7646 −1.81955
\(36\) 15.1671 2.52786
\(37\) −9.44386 −1.55256 −0.776281 0.630387i \(-0.782896\pi\)
−0.776281 + 0.630387i \(0.782896\pi\)
\(38\) 22.0108 3.57062
\(39\) 2.41604 0.386876
\(40\) −33.8109 −5.34597
\(41\) −6.21801 −0.971089 −0.485545 0.874212i \(-0.661379\pi\)
−0.485545 + 0.874212i \(0.661379\pi\)
\(42\) −18.9046 −2.91704
\(43\) −0.0964750 −0.0147123 −0.00735615 0.999973i \(-0.502342\pi\)
−0.00735615 + 0.999973i \(0.502342\pi\)
\(44\) −23.8767 −3.59954
\(45\) 10.5791 1.57704
\(46\) 5.94159 0.876040
\(47\) 4.49548 0.655733 0.327866 0.944724i \(-0.393670\pi\)
0.327866 + 0.944724i \(0.393670\pi\)
\(48\) −33.5472 −4.84212
\(49\) 1.33474 0.190678
\(50\) −24.1293 −3.41240
\(51\) 4.54598 0.636565
\(52\) −5.34571 −0.741316
\(53\) 1.45631 0.200040 0.100020 0.994985i \(-0.468109\pi\)
0.100020 + 0.994985i \(0.468109\pi\)
\(54\) −1.06569 −0.145023
\(55\) −16.6540 −2.24563
\(56\) 26.1789 3.49830
\(57\) 19.6211 2.59887
\(58\) −23.9091 −3.13942
\(59\) 8.09604 1.05402 0.527008 0.849861i \(-0.323314\pi\)
0.527008 + 0.849861i \(0.323314\pi\)
\(60\) −48.1572 −6.21707
\(61\) 1.81432 0.232299 0.116150 0.993232i \(-0.462945\pi\)
0.116150 + 0.993232i \(0.462945\pi\)
\(62\) −16.2156 −2.05938
\(63\) −8.19114 −1.03199
\(64\) 25.0729 3.13412
\(65\) −3.72865 −0.462482
\(66\) −29.2475 −3.60012
\(67\) 7.20656 0.880422 0.440211 0.897894i \(-0.354904\pi\)
0.440211 + 0.897894i \(0.354904\pi\)
\(68\) −10.0584 −1.21976
\(69\) 5.29652 0.637626
\(70\) 29.1752 3.48711
\(71\) 10.0084 1.18778 0.593889 0.804547i \(-0.297592\pi\)
0.593889 + 0.804547i \(0.297592\pi\)
\(72\) −25.7278 −3.03205
\(73\) −3.27988 −0.383881 −0.191940 0.981407i \(-0.561478\pi\)
−0.191940 + 0.981407i \(0.561478\pi\)
\(74\) 25.5957 2.97544
\(75\) −21.5096 −2.48371
\(76\) −43.4134 −4.97986
\(77\) 12.8948 1.46950
\(78\) −6.54819 −0.741436
\(79\) −2.69531 −0.303246 −0.151623 0.988438i \(-0.548450\pi\)
−0.151623 + 0.988438i \(0.548450\pi\)
\(80\) 51.7730 5.78839
\(81\) −9.46175 −1.05131
\(82\) 16.8526 1.86106
\(83\) −8.82524 −0.968696 −0.484348 0.874875i \(-0.660943\pi\)
−0.484348 + 0.874875i \(0.660943\pi\)
\(84\) 37.2868 4.06833
\(85\) −7.01576 −0.760966
\(86\) 0.261476 0.0281957
\(87\) −21.3133 −2.28503
\(88\) 40.5017 4.31750
\(89\) 11.4254 1.21109 0.605545 0.795811i \(-0.292955\pi\)
0.605545 + 0.795811i \(0.292955\pi\)
\(90\) −28.6726 −3.02235
\(91\) 2.88700 0.302639
\(92\) −11.7190 −1.22179
\(93\) −14.4550 −1.49892
\(94\) −12.1841 −1.25669
\(95\) −30.2810 −3.10676
\(96\) 47.1061 4.80775
\(97\) −3.79001 −0.384817 −0.192409 0.981315i \(-0.561630\pi\)
−0.192409 + 0.981315i \(0.561630\pi\)
\(98\) −3.61755 −0.365428
\(99\) −12.6726 −1.27365
\(100\) 47.5919 4.75919
\(101\) 17.7796 1.76914 0.884570 0.466407i \(-0.154452\pi\)
0.884570 + 0.466407i \(0.154452\pi\)
\(102\) −12.3210 −1.21996
\(103\) 1.00000 0.0985329
\(104\) 9.06786 0.889177
\(105\) 26.0077 2.53809
\(106\) −3.94704 −0.383370
\(107\) 5.63431 0.544690 0.272345 0.962200i \(-0.412201\pi\)
0.272345 + 0.962200i \(0.412201\pi\)
\(108\) 2.10194 0.202259
\(109\) 8.39968 0.804543 0.402272 0.915520i \(-0.368221\pi\)
0.402272 + 0.915520i \(0.368221\pi\)
\(110\) 45.1374 4.30368
\(111\) 22.8168 2.16567
\(112\) −40.0865 −3.78781
\(113\) 1.62078 0.152470 0.0762352 0.997090i \(-0.475710\pi\)
0.0762352 + 0.997090i \(0.475710\pi\)
\(114\) −53.1789 −4.98066
\(115\) −8.17406 −0.762235
\(116\) 47.1576 4.37847
\(117\) −2.83725 −0.262304
\(118\) −21.9427 −2.01999
\(119\) 5.43212 0.497962
\(120\) 81.6885 7.45710
\(121\) 8.94971 0.813610
\(122\) −4.91733 −0.445195
\(123\) 15.0230 1.35457
\(124\) 31.9831 2.87217
\(125\) 14.5522 1.30159
\(126\) 22.2004 1.97777
\(127\) −8.95322 −0.794470 −0.397235 0.917717i \(-0.630030\pi\)
−0.397235 + 0.917717i \(0.630030\pi\)
\(128\) −28.9606 −2.55978
\(129\) 0.233088 0.0205222
\(130\) 10.1057 0.886332
\(131\) 4.50594 0.393686 0.196843 0.980435i \(-0.436931\pi\)
0.196843 + 0.980435i \(0.436931\pi\)
\(132\) 57.6870 5.02101
\(133\) 23.4458 2.03301
\(134\) −19.5319 −1.68730
\(135\) 1.46611 0.126183
\(136\) 17.0619 1.46305
\(137\) −11.9373 −1.01987 −0.509935 0.860213i \(-0.670331\pi\)
−0.509935 + 0.860213i \(0.670331\pi\)
\(138\) −14.3551 −1.22199
\(139\) −12.6510 −1.07304 −0.536520 0.843888i \(-0.680261\pi\)
−0.536520 + 0.843888i \(0.680261\pi\)
\(140\) −57.5444 −4.86339
\(141\) −10.8613 −0.914683
\(142\) −27.1257 −2.27634
\(143\) 4.46651 0.373508
\(144\) 39.3958 3.28298
\(145\) 32.8926 2.73158
\(146\) 8.88945 0.735696
\(147\) −3.22479 −0.265977
\(148\) −50.4842 −4.14977
\(149\) −3.00561 −0.246229 −0.123115 0.992392i \(-0.539288\pi\)
−0.123115 + 0.992392i \(0.539288\pi\)
\(150\) 58.2973 4.75996
\(151\) −12.6213 −1.02711 −0.513554 0.858057i \(-0.671671\pi\)
−0.513554 + 0.858057i \(0.671671\pi\)
\(152\) 73.6416 5.97312
\(153\) −5.33853 −0.431594
\(154\) −34.9487 −2.81625
\(155\) 22.3083 1.79185
\(156\) 12.9155 1.03406
\(157\) −1.39969 −0.111707 −0.0558536 0.998439i \(-0.517788\pi\)
−0.0558536 + 0.998439i \(0.517788\pi\)
\(158\) 7.30509 0.581161
\(159\) −3.51851 −0.279036
\(160\) −72.6984 −5.74731
\(161\) 6.32896 0.498792
\(162\) 25.6442 2.01480
\(163\) 22.1668 1.73624 0.868118 0.496358i \(-0.165330\pi\)
0.868118 + 0.496358i \(0.165330\pi\)
\(164\) −33.2397 −2.59558
\(165\) 40.2369 3.13244
\(166\) 23.9190 1.85648
\(167\) 23.6661 1.83134 0.915668 0.401934i \(-0.131662\pi\)
0.915668 + 0.401934i \(0.131662\pi\)
\(168\) −63.2492 −4.87979
\(169\) 1.00000 0.0769231
\(170\) 19.0148 1.45837
\(171\) −23.0418 −1.76205
\(172\) −0.515727 −0.0393238
\(173\) 22.0669 1.67771 0.838857 0.544351i \(-0.183224\pi\)
0.838857 + 0.544351i \(0.183224\pi\)
\(174\) 57.7654 4.37918
\(175\) −25.7024 −1.94292
\(176\) −62.0183 −4.67481
\(177\) −19.5604 −1.47025
\(178\) −30.9662 −2.32102
\(179\) 16.2811 1.21691 0.608453 0.793590i \(-0.291790\pi\)
0.608453 + 0.793590i \(0.291790\pi\)
\(180\) 56.5529 4.21520
\(181\) −14.4397 −1.07329 −0.536646 0.843808i \(-0.680309\pi\)
−0.536646 + 0.843808i \(0.680309\pi\)
\(182\) −7.82461 −0.579999
\(183\) −4.38346 −0.324035
\(184\) 19.8788 1.46549
\(185\) −35.2129 −2.58890
\(186\) 39.1775 2.87263
\(187\) 8.40411 0.614569
\(188\) 24.0315 1.75268
\(189\) −1.13517 −0.0825716
\(190\) 82.0704 5.95401
\(191\) 8.61603 0.623434 0.311717 0.950175i \(-0.399096\pi\)
0.311717 + 0.950175i \(0.399096\pi\)
\(192\) −60.5773 −4.37179
\(193\) 13.6430 0.982045 0.491022 0.871147i \(-0.336623\pi\)
0.491022 + 0.871147i \(0.336623\pi\)
\(194\) 10.2721 0.737490
\(195\) 9.00857 0.645117
\(196\) 7.13515 0.509653
\(197\) −16.9346 −1.20654 −0.603269 0.797538i \(-0.706135\pi\)
−0.603269 + 0.797538i \(0.706135\pi\)
\(198\) 34.3466 2.44090
\(199\) 6.04968 0.428850 0.214425 0.976740i \(-0.431212\pi\)
0.214425 + 0.976740i \(0.431212\pi\)
\(200\) −80.7296 −5.70844
\(201\) −17.4114 −1.22810
\(202\) −48.1881 −3.39050
\(203\) −25.4679 −1.78749
\(204\) 24.3015 1.70144
\(205\) −23.1848 −1.61929
\(206\) −2.71030 −0.188835
\(207\) −6.21991 −0.432314
\(208\) −13.8852 −0.962764
\(209\) 36.2733 2.50907
\(210\) −70.4886 −4.86417
\(211\) −1.32862 −0.0914657 −0.0457328 0.998954i \(-0.514562\pi\)
−0.0457328 + 0.998954i \(0.514562\pi\)
\(212\) 7.78502 0.534677
\(213\) −24.1807 −1.65683
\(214\) −15.2707 −1.04388
\(215\) −0.359721 −0.0245328
\(216\) −3.56550 −0.242602
\(217\) −17.2727 −1.17255
\(218\) −22.7656 −1.54188
\(219\) 7.92433 0.535476
\(220\) −89.0277 −6.00224
\(221\) 1.88158 0.126569
\(222\) −61.8402 −4.15044
\(223\) −21.5713 −1.44452 −0.722261 0.691620i \(-0.756897\pi\)
−0.722261 + 0.691620i \(0.756897\pi\)
\(224\) 56.2885 3.76093
\(225\) 25.2596 1.68397
\(226\) −4.39280 −0.292205
\(227\) 10.9540 0.727041 0.363521 0.931586i \(-0.381575\pi\)
0.363521 + 0.931586i \(0.381575\pi\)
\(228\) 104.888 6.94641
\(229\) −12.8148 −0.846825 −0.423412 0.905937i \(-0.639168\pi\)
−0.423412 + 0.905937i \(0.639168\pi\)
\(230\) 22.1541 1.46080
\(231\) −31.1544 −2.04981
\(232\) −79.9929 −5.25179
\(233\) 7.56663 0.495706 0.247853 0.968798i \(-0.420275\pi\)
0.247853 + 0.968798i \(0.420275\pi\)
\(234\) 7.68980 0.502698
\(235\) 16.7621 1.09344
\(236\) 43.2791 2.81723
\(237\) 6.51198 0.422998
\(238\) −14.7227 −0.954328
\(239\) 5.69918 0.368649 0.184325 0.982865i \(-0.440990\pi\)
0.184325 + 0.982865i \(0.440990\pi\)
\(240\) −125.086 −8.07424
\(241\) 15.1300 0.974612 0.487306 0.873231i \(-0.337980\pi\)
0.487306 + 0.873231i \(0.337980\pi\)
\(242\) −24.2564 −1.55926
\(243\) 21.6804 1.39080
\(244\) 9.69880 0.620902
\(245\) 4.97679 0.317955
\(246\) −40.7167 −2.59600
\(247\) 8.12116 0.516737
\(248\) −54.2526 −3.44504
\(249\) 21.3222 1.35124
\(250\) −39.4409 −2.49446
\(251\) −24.2446 −1.53031 −0.765153 0.643849i \(-0.777336\pi\)
−0.765153 + 0.643849i \(0.777336\pi\)
\(252\) −43.7874 −2.75835
\(253\) 9.79162 0.615594
\(254\) 24.2659 1.52258
\(255\) 16.9504 1.06147
\(256\) 28.3460 1.77163
\(257\) 18.4097 1.14837 0.574184 0.818726i \(-0.305319\pi\)
0.574184 + 0.818726i \(0.305319\pi\)
\(258\) −0.631736 −0.0393302
\(259\) 27.2644 1.69413
\(260\) −19.9323 −1.23615
\(261\) 25.0291 1.54926
\(262\) −12.2124 −0.754487
\(263\) 21.0436 1.29760 0.648802 0.760957i \(-0.275270\pi\)
0.648802 + 0.760957i \(0.275270\pi\)
\(264\) −97.8538 −6.02248
\(265\) 5.43007 0.333567
\(266\) −63.5450 −3.89619
\(267\) −27.6042 −1.68935
\(268\) 38.5242 2.35324
\(269\) −29.0529 −1.77139 −0.885694 0.464269i \(-0.846317\pi\)
−0.885694 + 0.464269i \(0.846317\pi\)
\(270\) −3.97360 −0.241825
\(271\) 21.6941 1.31782 0.658912 0.752220i \(-0.271017\pi\)
0.658912 + 0.752220i \(0.271017\pi\)
\(272\) −26.1261 −1.58413
\(273\) −6.97510 −0.422152
\(274\) 32.3536 1.95455
\(275\) −39.7645 −2.39789
\(276\) 28.3136 1.70428
\(277\) 3.12197 0.187581 0.0937904 0.995592i \(-0.470102\pi\)
0.0937904 + 0.995592i \(0.470102\pi\)
\(278\) 34.2879 2.05645
\(279\) 16.9751 1.01628
\(280\) 97.6119 5.83342
\(281\) −23.0923 −1.37757 −0.688785 0.724965i \(-0.741856\pi\)
−0.688785 + 0.724965i \(0.741856\pi\)
\(282\) 29.4372 1.75296
\(283\) 19.4513 1.15626 0.578131 0.815944i \(-0.303782\pi\)
0.578131 + 0.815944i \(0.303782\pi\)
\(284\) 53.5019 3.17476
\(285\) 73.1600 4.33363
\(286\) −12.1056 −0.715817
\(287\) 17.9514 1.05964
\(288\) −55.3186 −3.25968
\(289\) −13.4596 −0.791744
\(290\) −89.1487 −5.23499
\(291\) 9.15682 0.536782
\(292\) −17.5333 −1.02606
\(293\) 10.1827 0.594882 0.297441 0.954740i \(-0.403867\pi\)
0.297441 + 0.954740i \(0.403867\pi\)
\(294\) 8.74015 0.509736
\(295\) 30.1873 1.75757
\(296\) 85.6357 4.97747
\(297\) −1.75624 −0.101907
\(298\) 8.14609 0.471890
\(299\) 2.19223 0.126780
\(300\) −114.984 −6.63860
\(301\) 0.278523 0.0160538
\(302\) 34.2075 1.96842
\(303\) −42.9563 −2.46778
\(304\) −112.764 −6.46745
\(305\) 6.76495 0.387360
\(306\) 14.4690 0.827138
\(307\) 0.443021 0.0252845 0.0126423 0.999920i \(-0.495976\pi\)
0.0126423 + 0.999920i \(0.495976\pi\)
\(308\) 68.9318 3.92775
\(309\) −2.41604 −0.137444
\(310\) −60.4621 −3.43402
\(311\) 24.7475 1.40330 0.701650 0.712522i \(-0.252447\pi\)
0.701650 + 0.712522i \(0.252447\pi\)
\(312\) −21.9083 −1.24031
\(313\) −10.8305 −0.612173 −0.306087 0.952004i \(-0.599020\pi\)
−0.306087 + 0.952004i \(0.599020\pi\)
\(314\) 3.79357 0.214084
\(315\) −30.5419 −1.72084
\(316\) −14.4083 −0.810532
\(317\) 27.3315 1.53509 0.767544 0.640997i \(-0.221479\pi\)
0.767544 + 0.640997i \(0.221479\pi\)
\(318\) 9.53620 0.534764
\(319\) −39.4017 −2.20607
\(320\) 93.4882 5.22615
\(321\) −13.6127 −0.759789
\(322\) −17.1534 −0.955919
\(323\) 15.2806 0.850238
\(324\) −50.5798 −2.80999
\(325\) −8.90282 −0.493840
\(326\) −60.0785 −3.32744
\(327\) −20.2940 −1.12226
\(328\) 56.3840 3.11329
\(329\) −12.9784 −0.715524
\(330\) −109.054 −6.00322
\(331\) 14.4478 0.794123 0.397061 0.917792i \(-0.370030\pi\)
0.397061 + 0.917792i \(0.370030\pi\)
\(332\) −47.1772 −2.58918
\(333\) −26.7946 −1.46834
\(334\) −64.1421 −3.50970
\(335\) 26.8707 1.46811
\(336\) 96.8505 5.28363
\(337\) 14.3299 0.780599 0.390300 0.920688i \(-0.372371\pi\)
0.390300 + 0.920688i \(0.372371\pi\)
\(338\) −2.71030 −0.147421
\(339\) −3.91588 −0.212681
\(340\) −37.5042 −2.03395
\(341\) −26.7229 −1.44713
\(342\) 62.4501 3.37692
\(343\) 16.3556 0.883118
\(344\) 0.874822 0.0471672
\(345\) 19.7489 1.06324
\(346\) −59.8078 −3.21529
\(347\) 31.1467 1.67204 0.836020 0.548699i \(-0.184877\pi\)
0.836020 + 0.548699i \(0.184877\pi\)
\(348\) −113.935 −6.10754
\(349\) 2.40158 0.128554 0.0642769 0.997932i \(-0.479526\pi\)
0.0642769 + 0.997932i \(0.479526\pi\)
\(350\) 69.6611 3.72354
\(351\) −0.393202 −0.0209876
\(352\) 87.0846 4.64163
\(353\) 20.4095 1.08629 0.543144 0.839640i \(-0.317234\pi\)
0.543144 + 0.839640i \(0.317234\pi\)
\(354\) 53.0144 2.81768
\(355\) 37.3178 1.98062
\(356\) 61.0768 3.23707
\(357\) −13.1242 −0.694608
\(358\) −44.1266 −2.33216
\(359\) −30.6694 −1.61867 −0.809334 0.587349i \(-0.800172\pi\)
−0.809334 + 0.587349i \(0.800172\pi\)
\(360\) −95.9300 −5.05596
\(361\) 46.9533 2.47123
\(362\) 39.1357 2.05693
\(363\) −21.6229 −1.13491
\(364\) 15.4330 0.808911
\(365\) −12.2295 −0.640122
\(366\) 11.8805 0.621003
\(367\) −0.968271 −0.0505433 −0.0252717 0.999681i \(-0.508045\pi\)
−0.0252717 + 0.999681i \(0.508045\pi\)
\(368\) −30.4395 −1.58677
\(369\) −17.6421 −0.918409
\(370\) 95.4373 4.96155
\(371\) −4.20436 −0.218280
\(372\) −77.2725 −4.00639
\(373\) 20.0505 1.03817 0.519087 0.854721i \(-0.326272\pi\)
0.519087 + 0.854721i \(0.326272\pi\)
\(374\) −22.7776 −1.17780
\(375\) −35.1588 −1.81559
\(376\) −40.7644 −2.10226
\(377\) −8.82158 −0.454335
\(378\) 3.07665 0.158246
\(379\) −4.26123 −0.218884 −0.109442 0.993993i \(-0.534906\pi\)
−0.109442 + 0.993993i \(0.534906\pi\)
\(380\) −161.873 −8.30392
\(381\) 21.6313 1.10821
\(382\) −23.3520 −1.19479
\(383\) −6.57977 −0.336210 −0.168105 0.985769i \(-0.553765\pi\)
−0.168105 + 0.985769i \(0.553765\pi\)
\(384\) 69.9701 3.57065
\(385\) 48.0802 2.45039
\(386\) −36.9766 −1.88206
\(387\) −0.273724 −0.0139142
\(388\) −20.2603 −1.02856
\(389\) 14.0220 0.710941 0.355471 0.934687i \(-0.384321\pi\)
0.355471 + 0.934687i \(0.384321\pi\)
\(390\) −24.4159 −1.23635
\(391\) 4.12486 0.208603
\(392\) −12.1033 −0.611307
\(393\) −10.8865 −0.549153
\(394\) 45.8977 2.31229
\(395\) −10.0499 −0.505663
\(396\) −67.7441 −3.40427
\(397\) −18.0146 −0.904125 −0.452063 0.891986i \(-0.649312\pi\)
−0.452063 + 0.891986i \(0.649312\pi\)
\(398\) −16.3964 −0.821878
\(399\) −56.6459 −2.83584
\(400\) 123.617 6.18087
\(401\) −35.9551 −1.79551 −0.897755 0.440495i \(-0.854803\pi\)
−0.897755 + 0.440495i \(0.854803\pi\)
\(402\) 47.1899 2.35362
\(403\) −5.98295 −0.298032
\(404\) 95.0448 4.72866
\(405\) −35.2796 −1.75305
\(406\) 69.0255 3.42568
\(407\) 42.1811 2.09084
\(408\) −41.2223 −2.04081
\(409\) 13.3433 0.659786 0.329893 0.944018i \(-0.392987\pi\)
0.329893 + 0.944018i \(0.392987\pi\)
\(410\) 62.8376 3.10333
\(411\) 28.8410 1.42262
\(412\) 5.34571 0.263364
\(413\) −23.3732 −1.15012
\(414\) 16.8578 0.828516
\(415\) −32.9062 −1.61530
\(416\) 19.4972 0.955931
\(417\) 30.5652 1.49679
\(418\) −98.3113 −4.80856
\(419\) −15.5375 −0.759058 −0.379529 0.925180i \(-0.623914\pi\)
−0.379529 + 0.925180i \(0.623914\pi\)
\(420\) 139.030 6.78395
\(421\) 4.30962 0.210038 0.105019 0.994470i \(-0.466510\pi\)
0.105019 + 0.994470i \(0.466510\pi\)
\(422\) 3.60094 0.175291
\(423\) 12.7548 0.620160
\(424\) −13.2056 −0.641322
\(425\) −16.7514 −0.812562
\(426\) 65.5368 3.17527
\(427\) −5.23792 −0.253481
\(428\) 30.1194 1.45588
\(429\) −10.7913 −0.521007
\(430\) 0.974952 0.0470163
\(431\) −20.3114 −0.978366 −0.489183 0.872181i \(-0.662705\pi\)
−0.489183 + 0.872181i \(0.662705\pi\)
\(432\) 5.45968 0.262679
\(433\) 18.7669 0.901878 0.450939 0.892555i \(-0.351089\pi\)
0.450939 + 0.892555i \(0.351089\pi\)
\(434\) 46.8143 2.24716
\(435\) −79.4698 −3.81029
\(436\) 44.9022 2.15043
\(437\) 17.8035 0.851655
\(438\) −21.4773 −1.02622
\(439\) 23.3941 1.11654 0.558269 0.829660i \(-0.311466\pi\)
0.558269 + 0.829660i \(0.311466\pi\)
\(440\) 151.017 7.19943
\(441\) 3.78701 0.180334
\(442\) −5.09965 −0.242566
\(443\) −25.8019 −1.22588 −0.612942 0.790128i \(-0.710014\pi\)
−0.612942 + 0.790128i \(0.710014\pi\)
\(444\) 121.972 5.78852
\(445\) 42.6013 2.01949
\(446\) 58.4647 2.76838
\(447\) 7.26167 0.343465
\(448\) −72.3855 −3.41989
\(449\) 8.48971 0.400654 0.200327 0.979729i \(-0.435800\pi\)
0.200327 + 0.979729i \(0.435800\pi\)
\(450\) −68.4609 −3.22728
\(451\) 27.7728 1.30777
\(452\) 8.66423 0.407531
\(453\) 30.4936 1.43271
\(454\) −29.6885 −1.39335
\(455\) 10.7646 0.504652
\(456\) −177.921 −8.33192
\(457\) 13.6623 0.639096 0.319548 0.947570i \(-0.396469\pi\)
0.319548 + 0.947570i \(0.396469\pi\)
\(458\) 34.7319 1.62291
\(459\) −0.739842 −0.0345329
\(460\) −43.6961 −2.03734
\(461\) −22.8686 −1.06510 −0.532549 0.846399i \(-0.678766\pi\)
−0.532549 + 0.846399i \(0.678766\pi\)
\(462\) 84.4375 3.92839
\(463\) 3.21950 0.149623 0.0748115 0.997198i \(-0.476164\pi\)
0.0748115 + 0.997198i \(0.476164\pi\)
\(464\) 122.489 5.68642
\(465\) −53.8978 −2.49945
\(466\) −20.5078 −0.950006
\(467\) 26.8827 1.24398 0.621991 0.783025i \(-0.286324\pi\)
0.621991 + 0.783025i \(0.286324\pi\)
\(468\) −15.1671 −0.701101
\(469\) −20.8053 −0.960700
\(470\) −45.4302 −2.09554
\(471\) 3.38170 0.155821
\(472\) −73.4138 −3.37915
\(473\) 0.430906 0.0198131
\(474\) −17.6494 −0.810663
\(475\) −72.3013 −3.31741
\(476\) 29.0385 1.33098
\(477\) 4.13192 0.189188
\(478\) −15.4465 −0.706505
\(479\) −18.2753 −0.835021 −0.417511 0.908672i \(-0.637097\pi\)
−0.417511 + 0.908672i \(0.637097\pi\)
\(480\) 175.642 8.01693
\(481\) 9.44386 0.430603
\(482\) −41.0069 −1.86781
\(483\) −15.2910 −0.695766
\(484\) 47.8425 2.17466
\(485\) −14.1316 −0.641684
\(486\) −58.7603 −2.66542
\(487\) 26.4880 1.20028 0.600142 0.799894i \(-0.295111\pi\)
0.600142 + 0.799894i \(0.295111\pi\)
\(488\) −16.4520 −0.744746
\(489\) −53.5558 −2.42188
\(490\) −13.4886 −0.609352
\(491\) 21.4783 0.969301 0.484650 0.874708i \(-0.338947\pi\)
0.484650 + 0.874708i \(0.338947\pi\)
\(492\) 80.3084 3.62058
\(493\) −16.5985 −0.747561
\(494\) −22.0108 −0.990311
\(495\) −47.2518 −2.12381
\(496\) 83.0743 3.73015
\(497\) −28.8942 −1.29608
\(498\) −57.7894 −2.58960
\(499\) 10.4746 0.468908 0.234454 0.972127i \(-0.424670\pi\)
0.234454 + 0.972127i \(0.424670\pi\)
\(500\) 77.7921 3.47897
\(501\) −57.1782 −2.55454
\(502\) 65.7100 2.93278
\(503\) −15.8868 −0.708358 −0.354179 0.935178i \(-0.615240\pi\)
−0.354179 + 0.935178i \(0.615240\pi\)
\(504\) 74.2761 3.30852
\(505\) 66.2940 2.95005
\(506\) −26.5382 −1.17977
\(507\) −2.41604 −0.107300
\(508\) −47.8613 −2.12350
\(509\) 18.2970 0.811002 0.405501 0.914095i \(-0.367097\pi\)
0.405501 + 0.914095i \(0.367097\pi\)
\(510\) −45.9405 −2.03428
\(511\) 9.46900 0.418884
\(512\) −18.9049 −0.835487
\(513\) −3.19326 −0.140986
\(514\) −49.8958 −2.20081
\(515\) 3.72865 0.164304
\(516\) 1.24602 0.0548529
\(517\) −20.0791 −0.883078
\(518\) −73.8946 −3.24674
\(519\) −53.3145 −2.34025
\(520\) 33.8109 1.48271
\(521\) −13.4600 −0.589695 −0.294847 0.955544i \(-0.595269\pi\)
−0.294847 + 0.955544i \(0.595269\pi\)
\(522\) −67.8362 −2.96911
\(523\) −36.0870 −1.57798 −0.788988 0.614409i \(-0.789395\pi\)
−0.788988 + 0.614409i \(0.789395\pi\)
\(524\) 24.0874 1.05226
\(525\) 62.0981 2.71018
\(526\) −57.0344 −2.48682
\(527\) −11.2574 −0.490381
\(528\) 149.839 6.52090
\(529\) −18.1941 −0.791049
\(530\) −14.7171 −0.639270
\(531\) 22.9705 0.996836
\(532\) 125.334 5.43393
\(533\) 6.21801 0.269332
\(534\) 74.8156 3.23759
\(535\) 21.0084 0.908271
\(536\) −65.3481 −2.82261
\(537\) −39.3358 −1.69746
\(538\) 78.7421 3.39481
\(539\) −5.96164 −0.256786
\(540\) 7.83740 0.337268
\(541\) −11.2553 −0.483901 −0.241951 0.970289i \(-0.577787\pi\)
−0.241951 + 0.970289i \(0.577787\pi\)
\(542\) −58.7975 −2.52557
\(543\) 34.8868 1.49714
\(544\) 36.6857 1.57289
\(545\) 31.3194 1.34158
\(546\) 18.9046 0.809042
\(547\) −22.0034 −0.940798 −0.470399 0.882454i \(-0.655890\pi\)
−0.470399 + 0.882454i \(0.655890\pi\)
\(548\) −63.8132 −2.72597
\(549\) 5.14767 0.219697
\(550\) 107.774 4.59549
\(551\) −71.6415 −3.05203
\(552\) −48.0281 −2.04421
\(553\) 7.78134 0.330896
\(554\) −8.46145 −0.359493
\(555\) 85.0757 3.61126
\(556\) −67.6283 −2.86808
\(557\) 20.2468 0.857886 0.428943 0.903331i \(-0.358886\pi\)
0.428943 + 0.903331i \(0.358886\pi\)
\(558\) −46.0077 −1.94766
\(559\) 0.0964750 0.00408046
\(560\) −149.468 −6.31619
\(561\) −20.3047 −0.857264
\(562\) 62.5870 2.64007
\(563\) 24.4794 1.03169 0.515843 0.856683i \(-0.327479\pi\)
0.515843 + 0.856683i \(0.327479\pi\)
\(564\) −58.0611 −2.44481
\(565\) 6.04333 0.254245
\(566\) −52.7189 −2.21594
\(567\) 27.3160 1.14717
\(568\) −90.7547 −3.80798
\(569\) 13.1464 0.551125 0.275563 0.961283i \(-0.411136\pi\)
0.275563 + 0.961283i \(0.411136\pi\)
\(570\) −198.285 −8.30526
\(571\) −32.5556 −1.36241 −0.681205 0.732092i \(-0.738544\pi\)
−0.681205 + 0.732092i \(0.738544\pi\)
\(572\) 23.8767 0.998333
\(573\) −20.8167 −0.869629
\(574\) −48.6535 −2.03076
\(575\) −19.5170 −0.813917
\(576\) 71.1383 2.96410
\(577\) −36.0583 −1.50113 −0.750564 0.660798i \(-0.770218\pi\)
−0.750564 + 0.660798i \(0.770218\pi\)
\(578\) 36.4796 1.51735
\(579\) −32.9621 −1.36986
\(580\) 175.834 7.30112
\(581\) 25.4784 1.05702
\(582\) −24.8177 −1.02873
\(583\) −6.50463 −0.269394
\(584\) 29.7415 1.23071
\(585\) −10.5791 −0.437393
\(586\) −27.5983 −1.14007
\(587\) −29.2925 −1.20903 −0.604516 0.796593i \(-0.706633\pi\)
−0.604516 + 0.796593i \(0.706633\pi\)
\(588\) −17.2388 −0.710917
\(589\) −48.5885 −2.00205
\(590\) −81.8166 −3.36833
\(591\) 40.9146 1.68300
\(592\) −131.130 −5.38940
\(593\) 14.8347 0.609190 0.304595 0.952482i \(-0.401479\pi\)
0.304595 + 0.952482i \(0.401479\pi\)
\(594\) 4.75993 0.195302
\(595\) 20.2545 0.830352
\(596\) −16.0671 −0.658134
\(597\) −14.6163 −0.598204
\(598\) −5.94159 −0.242970
\(599\) −23.5377 −0.961724 −0.480862 0.876796i \(-0.659676\pi\)
−0.480862 + 0.876796i \(0.659676\pi\)
\(600\) 195.046 7.96272
\(601\) 15.2715 0.622936 0.311468 0.950257i \(-0.399179\pi\)
0.311468 + 0.950257i \(0.399179\pi\)
\(602\) −0.754880 −0.0307666
\(603\) 20.4469 0.832660
\(604\) −67.4698 −2.74531
\(605\) 33.3703 1.35670
\(606\) 116.424 4.72942
\(607\) 14.1425 0.574026 0.287013 0.957927i \(-0.407338\pi\)
0.287013 + 0.957927i \(0.407338\pi\)
\(608\) 158.340 6.42155
\(609\) 61.5314 2.49338
\(610\) −18.3350 −0.742363
\(611\) −4.49548 −0.181868
\(612\) −28.5382 −1.15359
\(613\) 13.6543 0.551493 0.275747 0.961230i \(-0.411075\pi\)
0.275747 + 0.961230i \(0.411075\pi\)
\(614\) −1.20072 −0.0484570
\(615\) 56.0153 2.25876
\(616\) −116.928 −4.71117
\(617\) −20.9206 −0.842231 −0.421116 0.907007i \(-0.638361\pi\)
−0.421116 + 0.907007i \(0.638361\pi\)
\(618\) 6.54819 0.263407
\(619\) 45.8833 1.84421 0.922104 0.386943i \(-0.126469\pi\)
0.922104 + 0.386943i \(0.126469\pi\)
\(620\) 119.254 4.78935
\(621\) −0.861989 −0.0345904
\(622\) −67.0730 −2.68938
\(623\) −32.9851 −1.32152
\(624\) 33.5472 1.34296
\(625\) 9.74611 0.389844
\(626\) 29.3537 1.17321
\(627\) −87.6377 −3.49991
\(628\) −7.48233 −0.298577
\(629\) 17.7694 0.708513
\(630\) 82.7776 3.29794
\(631\) −10.8853 −0.433336 −0.216668 0.976245i \(-0.569519\pi\)
−0.216668 + 0.976245i \(0.569519\pi\)
\(632\) 24.4407 0.972198
\(633\) 3.20999 0.127586
\(634\) −74.0763 −2.94195
\(635\) −33.3834 −1.32478
\(636\) −18.8089 −0.745822
\(637\) −1.33474 −0.0528845
\(638\) 106.790 4.22787
\(639\) 28.3963 1.12334
\(640\) −107.984 −4.26844
\(641\) −2.82436 −0.111555 −0.0557777 0.998443i \(-0.517764\pi\)
−0.0557777 + 0.998443i \(0.517764\pi\)
\(642\) 36.8945 1.45611
\(643\) −37.6914 −1.48640 −0.743202 0.669067i \(-0.766694\pi\)
−0.743202 + 0.669067i \(0.766694\pi\)
\(644\) 33.8328 1.33320
\(645\) 0.869101 0.0342208
\(646\) −41.4151 −1.62945
\(647\) 3.17982 0.125012 0.0625059 0.998045i \(-0.480091\pi\)
0.0625059 + 0.998045i \(0.480091\pi\)
\(648\) 85.7979 3.37046
\(649\) −36.1611 −1.41945
\(650\) 24.1293 0.946428
\(651\) 41.7317 1.63559
\(652\) 118.497 4.64071
\(653\) −7.12183 −0.278699 −0.139349 0.990243i \(-0.544501\pi\)
−0.139349 + 0.990243i \(0.544501\pi\)
\(654\) 55.0027 2.15077
\(655\) 16.8011 0.656472
\(656\) −86.3382 −3.37094
\(657\) −9.30585 −0.363056
\(658\) 35.1754 1.37128
\(659\) 17.8612 0.695775 0.347887 0.937536i \(-0.386899\pi\)
0.347887 + 0.937536i \(0.386899\pi\)
\(660\) 215.095 8.37254
\(661\) 6.58887 0.256277 0.128139 0.991756i \(-0.459100\pi\)
0.128139 + 0.991756i \(0.459100\pi\)
\(662\) −39.1578 −1.52191
\(663\) −4.54598 −0.176551
\(664\) 80.0261 3.10562
\(665\) 87.4210 3.39004
\(666\) 72.6214 2.81402
\(667\) −19.3389 −0.748807
\(668\) 126.512 4.89490
\(669\) 52.1172 2.01497
\(670\) −72.8277 −2.81358
\(671\) −8.10366 −0.312838
\(672\) −135.995 −5.24613
\(673\) 11.4750 0.442328 0.221164 0.975237i \(-0.429014\pi\)
0.221164 + 0.975237i \(0.429014\pi\)
\(674\) −38.8383 −1.49599
\(675\) 3.50060 0.134738
\(676\) 5.34571 0.205604
\(677\) −35.1193 −1.34974 −0.674872 0.737934i \(-0.735801\pi\)
−0.674872 + 0.737934i \(0.735801\pi\)
\(678\) 10.6132 0.407597
\(679\) 10.9417 0.419906
\(680\) 63.6180 2.43964
\(681\) −26.4653 −1.01415
\(682\) 72.4270 2.77337
\(683\) −5.01898 −0.192046 −0.0960230 0.995379i \(-0.530612\pi\)
−0.0960230 + 0.995379i \(0.530612\pi\)
\(684\) −123.175 −4.70970
\(685\) −44.5099 −1.70064
\(686\) −44.3285 −1.69247
\(687\) 30.9610 1.18124
\(688\) −1.33957 −0.0510707
\(689\) −1.45631 −0.0554810
\(690\) −53.5253 −2.03767
\(691\) 12.4329 0.472968 0.236484 0.971635i \(-0.424005\pi\)
0.236484 + 0.971635i \(0.424005\pi\)
\(692\) 117.963 4.48429
\(693\) 36.5858 1.38978
\(694\) −84.4167 −3.20441
\(695\) −47.1710 −1.78930
\(696\) 193.266 7.32573
\(697\) 11.6997 0.443158
\(698\) −6.50900 −0.246369
\(699\) −18.2813 −0.691462
\(700\) −137.398 −5.19314
\(701\) 3.05709 0.115465 0.0577323 0.998332i \(-0.481613\pi\)
0.0577323 + 0.998332i \(0.481613\pi\)
\(702\) 1.06569 0.0402220
\(703\) 76.6952 2.89261
\(704\) −111.989 −4.22073
\(705\) −40.4978 −1.52524
\(706\) −55.3158 −2.08184
\(707\) −51.3298 −1.93045
\(708\) −104.564 −3.92976
\(709\) 15.7066 0.589874 0.294937 0.955517i \(-0.404701\pi\)
0.294937 + 0.955517i \(0.404701\pi\)
\(710\) −101.142 −3.79580
\(711\) −7.64727 −0.286795
\(712\) −103.604 −3.88272
\(713\) −13.1160 −0.491198
\(714\) 35.5706 1.33119
\(715\) 16.6540 0.622826
\(716\) 87.0340 3.25261
\(717\) −13.7695 −0.514230
\(718\) 83.1231 3.10213
\(719\) 20.0098 0.746238 0.373119 0.927784i \(-0.378288\pi\)
0.373119 + 0.927784i \(0.378288\pi\)
\(720\) 146.893 5.47438
\(721\) −2.88700 −0.107517
\(722\) −127.257 −4.73603
\(723\) −36.5548 −1.35949
\(724\) −77.1902 −2.86875
\(725\) 78.5370 2.91679
\(726\) 58.6044 2.17501
\(727\) 8.61430 0.319487 0.159743 0.987159i \(-0.448933\pi\)
0.159743 + 0.987159i \(0.448933\pi\)
\(728\) −26.1789 −0.970254
\(729\) −23.9954 −0.888719
\(730\) 33.1456 1.22678
\(731\) 0.181526 0.00671397
\(732\) −23.4327 −0.866098
\(733\) −8.17582 −0.301981 −0.150990 0.988535i \(-0.548246\pi\)
−0.150990 + 0.988535i \(0.548246\pi\)
\(734\) 2.62430 0.0968648
\(735\) −12.0241 −0.443517
\(736\) 42.7424 1.57551
\(737\) −32.1882 −1.18567
\(738\) 47.8152 1.76010
\(739\) 15.1353 0.556759 0.278380 0.960471i \(-0.410203\pi\)
0.278380 + 0.960471i \(0.410203\pi\)
\(740\) −188.238 −6.91975
\(741\) −19.6211 −0.720798
\(742\) 11.3951 0.418326
\(743\) −40.8558 −1.49885 −0.749426 0.662088i \(-0.769671\pi\)
−0.749426 + 0.662088i \(0.769671\pi\)
\(744\) 131.076 4.80549
\(745\) −11.2069 −0.410587
\(746\) −54.3427 −1.98963
\(747\) −25.0395 −0.916146
\(748\) 44.9259 1.64265
\(749\) −16.2662 −0.594355
\(750\) 95.2908 3.47953
\(751\) −8.91979 −0.325488 −0.162744 0.986668i \(-0.552034\pi\)
−0.162744 + 0.986668i \(0.552034\pi\)
\(752\) 62.4205 2.27624
\(753\) 58.5759 2.13463
\(754\) 23.9091 0.870718
\(755\) −47.0604 −1.71270
\(756\) −6.06830 −0.220702
\(757\) −6.76209 −0.245772 −0.122886 0.992421i \(-0.539215\pi\)
−0.122886 + 0.992421i \(0.539215\pi\)
\(758\) 11.5492 0.419485
\(759\) −23.6570 −0.858693
\(760\) 274.584 9.96020
\(761\) −42.8735 −1.55416 −0.777081 0.629401i \(-0.783300\pi\)
−0.777081 + 0.629401i \(0.783300\pi\)
\(762\) −58.6274 −2.12385
\(763\) −24.2498 −0.877903
\(764\) 46.0588 1.66635
\(765\) −19.9055 −0.719685
\(766\) 17.8331 0.644337
\(767\) −8.09604 −0.292331
\(768\) −68.4852 −2.47125
\(769\) 3.60879 0.130136 0.0650681 0.997881i \(-0.479274\pi\)
0.0650681 + 0.997881i \(0.479274\pi\)
\(770\) −130.311 −4.69610
\(771\) −44.4787 −1.60186
\(772\) 72.9315 2.62486
\(773\) −23.6267 −0.849794 −0.424897 0.905242i \(-0.639690\pi\)
−0.424897 + 0.905242i \(0.639690\pi\)
\(774\) 0.741873 0.0266661
\(775\) 53.2651 1.91334
\(776\) 34.3673 1.23371
\(777\) −65.8719 −2.36314
\(778\) −38.0036 −1.36250
\(779\) 50.4974 1.80926
\(780\) 48.1572 1.72430
\(781\) −44.7026 −1.59958
\(782\) −11.1796 −0.399782
\(783\) 3.46866 0.123960
\(784\) 18.5332 0.661898
\(785\) −5.21895 −0.186272
\(786\) 29.5057 1.05243
\(787\) 13.7575 0.490401 0.245201 0.969472i \(-0.421146\pi\)
0.245201 + 0.969472i \(0.421146\pi\)
\(788\) −90.5272 −3.22490
\(789\) −50.8422 −1.81003
\(790\) 27.2381 0.969088
\(791\) −4.67919 −0.166373
\(792\) 114.914 4.08328
\(793\) −1.81432 −0.0644282
\(794\) 48.8248 1.73273
\(795\) −13.1193 −0.465293
\(796\) 32.3398 1.14625
\(797\) 20.2972 0.718965 0.359483 0.933152i \(-0.382953\pi\)
0.359483 + 0.933152i \(0.382953\pi\)
\(798\) 153.527 5.43481
\(799\) −8.45862 −0.299244
\(800\) −173.580 −6.13700
\(801\) 32.4168 1.14539
\(802\) 97.4489 3.44104
\(803\) 14.6496 0.516974
\(804\) −93.0760 −3.28254
\(805\) 23.5985 0.831737
\(806\) 16.2156 0.571169
\(807\) 70.1931 2.47091
\(808\) −161.223 −5.67182
\(809\) 22.4195 0.788229 0.394114 0.919061i \(-0.371051\pi\)
0.394114 + 0.919061i \(0.371051\pi\)
\(810\) 95.6181 3.35968
\(811\) −30.0963 −1.05682 −0.528412 0.848988i \(-0.677213\pi\)
−0.528412 + 0.848988i \(0.677213\pi\)
\(812\) −136.144 −4.77771
\(813\) −52.4139 −1.83824
\(814\) −114.323 −4.00703
\(815\) 82.6521 2.89518
\(816\) 63.1218 2.20970
\(817\) 0.783489 0.0274108
\(818\) −36.1644 −1.26446
\(819\) 8.19114 0.286222
\(820\) −123.939 −4.32814
\(821\) −46.3978 −1.61929 −0.809647 0.586917i \(-0.800342\pi\)
−0.809647 + 0.586917i \(0.800342\pi\)
\(822\) −78.1676 −2.72641
\(823\) 4.02324 0.140241 0.0701206 0.997539i \(-0.477662\pi\)
0.0701206 + 0.997539i \(0.477662\pi\)
\(824\) −9.06786 −0.315894
\(825\) 96.0727 3.34482
\(826\) 63.3484 2.20417
\(827\) 50.0728 1.74120 0.870600 0.491991i \(-0.163731\pi\)
0.870600 + 0.491991i \(0.163731\pi\)
\(828\) −33.2498 −1.15551
\(829\) 32.1441 1.11641 0.558206 0.829703i \(-0.311490\pi\)
0.558206 + 0.829703i \(0.311490\pi\)
\(830\) 89.1857 3.09568
\(831\) −7.54280 −0.261657
\(832\) −25.0729 −0.869248
\(833\) −2.51143 −0.0870159
\(834\) −82.8409 −2.86854
\(835\) 88.2425 3.05376
\(836\) 193.906 6.70639
\(837\) 2.35251 0.0813145
\(838\) 42.1113 1.45471
\(839\) 34.0270 1.17474 0.587371 0.809318i \(-0.300163\pi\)
0.587371 + 0.809318i \(0.300163\pi\)
\(840\) −235.834 −8.13705
\(841\) 48.8203 1.68346
\(842\) −11.6803 −0.402531
\(843\) 55.7919 1.92158
\(844\) −7.10239 −0.244474
\(845\) 3.72865 0.128269
\(846\) −34.5693 −1.18852
\(847\) −25.8378 −0.887796
\(848\) 20.2212 0.694397
\(849\) −46.9952 −1.61287
\(850\) 45.4013 1.55725
\(851\) 20.7031 0.709694
\(852\) −129.263 −4.42847
\(853\) −25.1406 −0.860796 −0.430398 0.902639i \(-0.641627\pi\)
−0.430398 + 0.902639i \(0.641627\pi\)
\(854\) 14.1963 0.485788
\(855\) −85.9148 −2.93822
\(856\) −51.0912 −1.74626
\(857\) −4.22334 −0.144266 −0.0721332 0.997395i \(-0.522981\pi\)
−0.0721332 + 0.997395i \(0.522981\pi\)
\(858\) 29.2475 0.998495
\(859\) −2.87834 −0.0982077 −0.0491038 0.998794i \(-0.515637\pi\)
−0.0491038 + 0.998794i \(0.515637\pi\)
\(860\) −1.92297 −0.0655726
\(861\) −43.3712 −1.47809
\(862\) 55.0500 1.87501
\(863\) −6.79893 −0.231438 −0.115719 0.993282i \(-0.536917\pi\)
−0.115719 + 0.993282i \(0.536917\pi\)
\(864\) −7.66635 −0.260815
\(865\) 82.2797 2.79759
\(866\) −50.8638 −1.72842
\(867\) 32.5191 1.10440
\(868\) −92.3351 −3.13406
\(869\) 12.0386 0.408382
\(870\) 215.387 7.30230
\(871\) −7.20656 −0.244185
\(872\) −76.1671 −2.57934
\(873\) −10.7532 −0.363941
\(874\) −48.2527 −1.63217
\(875\) −42.0123 −1.42027
\(876\) 42.3611 1.43125
\(877\) 7.24349 0.244595 0.122298 0.992493i \(-0.460974\pi\)
0.122298 + 0.992493i \(0.460974\pi\)
\(878\) −63.4049 −2.13981
\(879\) −24.6019 −0.829802
\(880\) −231.244 −7.79525
\(881\) −40.3317 −1.35881 −0.679406 0.733763i \(-0.737762\pi\)
−0.679406 + 0.733763i \(0.737762\pi\)
\(882\) −10.2639 −0.345604
\(883\) 10.4924 0.353097 0.176548 0.984292i \(-0.443507\pi\)
0.176548 + 0.984292i \(0.443507\pi\)
\(884\) 10.0584 0.338300
\(885\) −72.9338 −2.45164
\(886\) 69.9308 2.34937
\(887\) −20.6936 −0.694823 −0.347411 0.937713i \(-0.612939\pi\)
−0.347411 + 0.937713i \(0.612939\pi\)
\(888\) −206.899 −6.94309
\(889\) 25.8479 0.866911
\(890\) −115.462 −3.87030
\(891\) 42.2610 1.41580
\(892\) −115.314 −3.86100
\(893\) −36.5085 −1.22171
\(894\) −19.6813 −0.658241
\(895\) 60.7065 2.02919
\(896\) 83.6092 2.79319
\(897\) −5.29652 −0.176846
\(898\) −23.0096 −0.767841
\(899\) 52.7791 1.76028
\(900\) 135.030 4.50101
\(901\) −2.74017 −0.0912883
\(902\) −75.2725 −2.50630
\(903\) −0.672923 −0.0223935
\(904\) −14.6970 −0.488816
\(905\) −53.8404 −1.78972
\(906\) −82.6467 −2.74575
\(907\) 8.46304 0.281011 0.140505 0.990080i \(-0.455127\pi\)
0.140505 + 0.990080i \(0.455127\pi\)
\(908\) 58.5568 1.94328
\(909\) 50.4454 1.67317
\(910\) −29.1752 −0.967150
\(911\) −31.2749 −1.03618 −0.518091 0.855325i \(-0.673357\pi\)
−0.518091 + 0.855325i \(0.673357\pi\)
\(912\) 272.442 9.02146
\(913\) 39.4180 1.30455
\(914\) −37.0289 −1.22481
\(915\) −16.3444 −0.540329
\(916\) −68.5041 −2.26344
\(917\) −13.0086 −0.429583
\(918\) 2.00519 0.0661812
\(919\) −17.9054 −0.590645 −0.295323 0.955398i \(-0.595427\pi\)
−0.295323 + 0.955398i \(0.595427\pi\)
\(920\) 74.1212 2.44370
\(921\) −1.07036 −0.0352694
\(922\) 61.9808 2.04123
\(923\) −10.0084 −0.329430
\(924\) −166.542 −5.47883
\(925\) −84.0770 −2.76444
\(926\) −8.72581 −0.286748
\(927\) 2.83725 0.0931876
\(928\) −171.997 −5.64606
\(929\) 35.9314 1.17887 0.589436 0.807815i \(-0.299350\pi\)
0.589436 + 0.807815i \(0.299350\pi\)
\(930\) 146.079 4.79012
\(931\) −10.8397 −0.355256
\(932\) 40.4490 1.32495
\(933\) −59.7909 −1.95747
\(934\) −72.8600 −2.38405
\(935\) 31.3360 1.02480
\(936\) 25.7278 0.840940
\(937\) 35.2537 1.15169 0.575845 0.817559i \(-0.304673\pi\)
0.575845 + 0.817559i \(0.304673\pi\)
\(938\) 56.3886 1.84115
\(939\) 26.1668 0.853922
\(940\) 89.6051 2.92260
\(941\) 43.7224 1.42531 0.712654 0.701515i \(-0.247493\pi\)
0.712654 + 0.701515i \(0.247493\pi\)
\(942\) −9.16542 −0.298626
\(943\) 13.6313 0.443896
\(944\) 112.415 3.65880
\(945\) −4.23266 −0.137688
\(946\) −1.16788 −0.0379712
\(947\) −3.03635 −0.0986680 −0.0493340 0.998782i \(-0.515710\pi\)
−0.0493340 + 0.998782i \(0.515710\pi\)
\(948\) 34.8111 1.13061
\(949\) 3.27988 0.106469
\(950\) 195.958 6.35771
\(951\) −66.0339 −2.14130
\(952\) −49.2577 −1.59645
\(953\) 44.3886 1.43789 0.718944 0.695068i \(-0.244626\pi\)
0.718944 + 0.695068i \(0.244626\pi\)
\(954\) −11.1987 −0.362573
\(955\) 32.1261 1.03958
\(956\) 30.4662 0.985346
\(957\) 95.1961 3.07725
\(958\) 49.5316 1.60029
\(959\) 34.4629 1.11286
\(960\) −225.871 −7.28997
\(961\) 4.79567 0.154699
\(962\) −25.5957 −0.825238
\(963\) 15.9860 0.515141
\(964\) 80.8808 2.60500
\(965\) 50.8700 1.63756
\(966\) 41.4432 1.33341
\(967\) −6.85729 −0.220516 −0.110258 0.993903i \(-0.535168\pi\)
−0.110258 + 0.993903i \(0.535168\pi\)
\(968\) −81.1548 −2.60841
\(969\) −36.9187 −1.18600
\(970\) 38.3009 1.22977
\(971\) 34.8877 1.11960 0.559799 0.828628i \(-0.310878\pi\)
0.559799 + 0.828628i \(0.310878\pi\)
\(972\) 115.897 3.71740
\(973\) 36.5233 1.17088
\(974\) −71.7902 −2.30031
\(975\) 21.5096 0.688858
\(976\) 25.1921 0.806380
\(977\) 12.7827 0.408954 0.204477 0.978871i \(-0.434451\pi\)
0.204477 + 0.978871i \(0.434451\pi\)
\(978\) 145.152 4.64146
\(979\) −51.0316 −1.63098
\(980\) 26.6045 0.849848
\(981\) 23.8320 0.760898
\(982\) −58.2125 −1.85764
\(983\) −26.7457 −0.853054 −0.426527 0.904475i \(-0.640263\pi\)
−0.426527 + 0.904475i \(0.640263\pi\)
\(984\) −136.226 −4.34273
\(985\) −63.1430 −2.01190
\(986\) 44.9870 1.43268
\(987\) 31.3564 0.998085
\(988\) 43.4134 1.38116
\(989\) 0.211495 0.00672516
\(990\) 128.066 4.07021
\(991\) −58.9088 −1.87130 −0.935649 0.352931i \(-0.885185\pi\)
−0.935649 + 0.352931i \(0.885185\pi\)
\(992\) −116.651 −3.70367
\(993\) −34.9065 −1.10772
\(994\) 78.3118 2.48390
\(995\) 22.5571 0.715109
\(996\) 113.982 3.61166
\(997\) 22.9734 0.727574 0.363787 0.931482i \(-0.381484\pi\)
0.363787 + 0.931482i \(0.381484\pi\)
\(998\) −28.3893 −0.898648
\(999\) −3.71334 −0.117485
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 1339.2.a.g.1.1 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1339.2.a.g.1.1 30 1.1 even 1 trivial