Properties

Label 8026.2.a.d.1.12
Level $8026$
Weight $2$
Character 8026.1
Self dual yes
Analytic conductor $64.088$
Analytic rank $0$
Dimension $96$
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] = [8026,2,Mod(1,8026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.0879326623\)
Analytic rank: \(0\)
Dimension: \(96\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 8026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.75991 q^{3} +1.00000 q^{4} +1.94869 q^{5} -2.75991 q^{6} -1.07781 q^{7} +1.00000 q^{8} +4.61711 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.75991 q^{3} +1.00000 q^{4} +1.94869 q^{5} -2.75991 q^{6} -1.07781 q^{7} +1.00000 q^{8} +4.61711 q^{9} +1.94869 q^{10} -0.979671 q^{11} -2.75991 q^{12} +2.80600 q^{13} -1.07781 q^{14} -5.37822 q^{15} +1.00000 q^{16} +6.13809 q^{17} +4.61711 q^{18} -5.84597 q^{19} +1.94869 q^{20} +2.97467 q^{21} -0.979671 q^{22} +0.812960 q^{23} -2.75991 q^{24} -1.20259 q^{25} +2.80600 q^{26} -4.46309 q^{27} -1.07781 q^{28} +6.89766 q^{29} -5.37822 q^{30} +2.82331 q^{31} +1.00000 q^{32} +2.70381 q^{33} +6.13809 q^{34} -2.10033 q^{35} +4.61711 q^{36} +2.48058 q^{37} -5.84597 q^{38} -7.74430 q^{39} +1.94869 q^{40} +9.53441 q^{41} +2.97467 q^{42} -11.3478 q^{43} -0.979671 q^{44} +8.99734 q^{45} +0.812960 q^{46} +6.34815 q^{47} -2.75991 q^{48} -5.83832 q^{49} -1.20259 q^{50} -16.9406 q^{51} +2.80600 q^{52} -2.87238 q^{53} -4.46309 q^{54} -1.90908 q^{55} -1.07781 q^{56} +16.1344 q^{57} +6.89766 q^{58} -11.5474 q^{59} -5.37822 q^{60} -1.18561 q^{61} +2.82331 q^{62} -4.97639 q^{63} +1.00000 q^{64} +5.46803 q^{65} +2.70381 q^{66} +12.4222 q^{67} +6.13809 q^{68} -2.24370 q^{69} -2.10033 q^{70} +0.804562 q^{71} +4.61711 q^{72} -1.00335 q^{73} +2.48058 q^{74} +3.31904 q^{75} -5.84597 q^{76} +1.05590 q^{77} -7.74430 q^{78} +17.3763 q^{79} +1.94869 q^{80} -1.53360 q^{81} +9.53441 q^{82} -13.6050 q^{83} +2.97467 q^{84} +11.9613 q^{85} -11.3478 q^{86} -19.0369 q^{87} -0.979671 q^{88} +4.49866 q^{89} +8.99734 q^{90} -3.02434 q^{91} +0.812960 q^{92} -7.79208 q^{93} +6.34815 q^{94} -11.3920 q^{95} -2.75991 q^{96} +6.91840 q^{97} -5.83832 q^{98} -4.52325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.75991 −1.59344 −0.796718 0.604351i \(-0.793432\pi\)
−0.796718 + 0.604351i \(0.793432\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.94869 0.871483 0.435741 0.900072i \(-0.356486\pi\)
0.435741 + 0.900072i \(0.356486\pi\)
\(6\) −2.75991 −1.12673
\(7\) −1.07781 −0.407375 −0.203688 0.979036i \(-0.565293\pi\)
−0.203688 + 0.979036i \(0.565293\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.61711 1.53904
\(10\) 1.94869 0.616231
\(11\) −0.979671 −0.295382 −0.147691 0.989034i \(-0.547184\pi\)
−0.147691 + 0.989034i \(0.547184\pi\)
\(12\) −2.75991 −0.796718
\(13\) 2.80600 0.778243 0.389122 0.921186i \(-0.372779\pi\)
0.389122 + 0.921186i \(0.372779\pi\)
\(14\) −1.07781 −0.288058
\(15\) −5.37822 −1.38865
\(16\) 1.00000 0.250000
\(17\) 6.13809 1.48870 0.744352 0.667787i \(-0.232758\pi\)
0.744352 + 0.667787i \(0.232758\pi\)
\(18\) 4.61711 1.08826
\(19\) −5.84597 −1.34116 −0.670579 0.741839i \(-0.733954\pi\)
−0.670579 + 0.741839i \(0.733954\pi\)
\(20\) 1.94869 0.435741
\(21\) 2.97467 0.649127
\(22\) −0.979671 −0.208867
\(23\) 0.812960 0.169514 0.0847569 0.996402i \(-0.472989\pi\)
0.0847569 + 0.996402i \(0.472989\pi\)
\(24\) −2.75991 −0.563365
\(25\) −1.20259 −0.240518
\(26\) 2.80600 0.550301
\(27\) −4.46309 −0.858922
\(28\) −1.07781 −0.203688
\(29\) 6.89766 1.28086 0.640431 0.768016i \(-0.278756\pi\)
0.640431 + 0.768016i \(0.278756\pi\)
\(30\) −5.37822 −0.981925
\(31\) 2.82331 0.507081 0.253540 0.967325i \(-0.418405\pi\)
0.253540 + 0.967325i \(0.418405\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.70381 0.470672
\(34\) 6.13809 1.05267
\(35\) −2.10033 −0.355021
\(36\) 4.61711 0.769519
\(37\) 2.48058 0.407804 0.203902 0.978991i \(-0.434638\pi\)
0.203902 + 0.978991i \(0.434638\pi\)
\(38\) −5.84597 −0.948341
\(39\) −7.74430 −1.24008
\(40\) 1.94869 0.308116
\(41\) 9.53441 1.48903 0.744513 0.667608i \(-0.232682\pi\)
0.744513 + 0.667608i \(0.232682\pi\)
\(42\) 2.97467 0.459002
\(43\) −11.3478 −1.73052 −0.865261 0.501321i \(-0.832848\pi\)
−0.865261 + 0.501321i \(0.832848\pi\)
\(44\) −0.979671 −0.147691
\(45\) 8.99734 1.34124
\(46\) 0.812960 0.119864
\(47\) 6.34815 0.925973 0.462986 0.886365i \(-0.346778\pi\)
0.462986 + 0.886365i \(0.346778\pi\)
\(48\) −2.75991 −0.398359
\(49\) −5.83832 −0.834045
\(50\) −1.20259 −0.170072
\(51\) −16.9406 −2.37216
\(52\) 2.80600 0.389122
\(53\) −2.87238 −0.394551 −0.197276 0.980348i \(-0.563209\pi\)
−0.197276 + 0.980348i \(0.563209\pi\)
\(54\) −4.46309 −0.607350
\(55\) −1.90908 −0.257420
\(56\) −1.07781 −0.144029
\(57\) 16.1344 2.13705
\(58\) 6.89766 0.905707
\(59\) −11.5474 −1.50334 −0.751670 0.659539i \(-0.770751\pi\)
−0.751670 + 0.659539i \(0.770751\pi\)
\(60\) −5.37822 −0.694326
\(61\) −1.18561 −0.151802 −0.0759009 0.997115i \(-0.524183\pi\)
−0.0759009 + 0.997115i \(0.524183\pi\)
\(62\) 2.82331 0.358560
\(63\) −4.97639 −0.626966
\(64\) 1.00000 0.125000
\(65\) 5.46803 0.678225
\(66\) 2.70381 0.332816
\(67\) 12.4222 1.51761 0.758806 0.651317i \(-0.225783\pi\)
0.758806 + 0.651317i \(0.225783\pi\)
\(68\) 6.13809 0.744352
\(69\) −2.24370 −0.270109
\(70\) −2.10033 −0.251037
\(71\) 0.804562 0.0954840 0.0477420 0.998860i \(-0.484797\pi\)
0.0477420 + 0.998860i \(0.484797\pi\)
\(72\) 4.61711 0.544132
\(73\) −1.00335 −0.117433 −0.0587165 0.998275i \(-0.518701\pi\)
−0.0587165 + 0.998275i \(0.518701\pi\)
\(74\) 2.48058 0.288361
\(75\) 3.31904 0.383250
\(76\) −5.84597 −0.670579
\(77\) 1.05590 0.120331
\(78\) −7.74430 −0.876870
\(79\) 17.3763 1.95499 0.977494 0.210965i \(-0.0676605\pi\)
0.977494 + 0.210965i \(0.0676605\pi\)
\(80\) 1.94869 0.217871
\(81\) −1.53360 −0.170400
\(82\) 9.53441 1.05290
\(83\) −13.6050 −1.49334 −0.746672 0.665193i \(-0.768349\pi\)
−0.746672 + 0.665193i \(0.768349\pi\)
\(84\) 2.97467 0.324563
\(85\) 11.9613 1.29738
\(86\) −11.3478 −1.22366
\(87\) −19.0369 −2.04097
\(88\) −0.979671 −0.104433
\(89\) 4.49866 0.476857 0.238429 0.971160i \(-0.423368\pi\)
0.238429 + 0.971160i \(0.423368\pi\)
\(90\) 8.99734 0.948403
\(91\) −3.02434 −0.317037
\(92\) 0.812960 0.0847569
\(93\) −7.79208 −0.808001
\(94\) 6.34815 0.654762
\(95\) −11.3920 −1.16879
\(96\) −2.75991 −0.281682
\(97\) 6.91840 0.702457 0.351228 0.936290i \(-0.385764\pi\)
0.351228 + 0.936290i \(0.385764\pi\)
\(98\) −5.83832 −0.589759
\(99\) −4.52325 −0.454604
\(100\) −1.20259 −0.120259
\(101\) 15.8733 1.57946 0.789728 0.613457i \(-0.210222\pi\)
0.789728 + 0.613457i \(0.210222\pi\)
\(102\) −16.9406 −1.67737
\(103\) −6.02551 −0.593711 −0.296855 0.954922i \(-0.595938\pi\)
−0.296855 + 0.954922i \(0.595938\pi\)
\(104\) 2.80600 0.275151
\(105\) 5.79673 0.565703
\(106\) −2.87238 −0.278990
\(107\) 3.14456 0.303996 0.151998 0.988381i \(-0.451429\pi\)
0.151998 + 0.988381i \(0.451429\pi\)
\(108\) −4.46309 −0.429461
\(109\) 5.80426 0.555947 0.277974 0.960589i \(-0.410337\pi\)
0.277974 + 0.960589i \(0.410337\pi\)
\(110\) −1.90908 −0.182024
\(111\) −6.84617 −0.649810
\(112\) −1.07781 −0.101844
\(113\) 6.71337 0.631541 0.315771 0.948836i \(-0.397737\pi\)
0.315771 + 0.948836i \(0.397737\pi\)
\(114\) 16.1344 1.51112
\(115\) 1.58421 0.147728
\(116\) 6.89766 0.640431
\(117\) 12.9556 1.19775
\(118\) −11.5474 −1.06302
\(119\) −6.61572 −0.606462
\(120\) −5.37822 −0.490962
\(121\) −10.0402 −0.912749
\(122\) −1.18561 −0.107340
\(123\) −26.3141 −2.37267
\(124\) 2.82331 0.253540
\(125\) −12.0870 −1.08109
\(126\) −4.97639 −0.443332
\(127\) 10.3462 0.918075 0.459038 0.888417i \(-0.348194\pi\)
0.459038 + 0.888417i \(0.348194\pi\)
\(128\) 1.00000 0.0883883
\(129\) 31.3189 2.75748
\(130\) 5.46803 0.479578
\(131\) −20.9417 −1.82968 −0.914841 0.403815i \(-0.867684\pi\)
−0.914841 + 0.403815i \(0.867684\pi\)
\(132\) 2.70381 0.235336
\(133\) 6.30087 0.546354
\(134\) 12.4222 1.07311
\(135\) −8.69720 −0.748536
\(136\) 6.13809 0.526337
\(137\) −13.9708 −1.19360 −0.596801 0.802389i \(-0.703562\pi\)
−0.596801 + 0.802389i \(0.703562\pi\)
\(138\) −2.24370 −0.190996
\(139\) 11.5737 0.981668 0.490834 0.871253i \(-0.336692\pi\)
0.490834 + 0.871253i \(0.336692\pi\)
\(140\) −2.10033 −0.177510
\(141\) −17.5203 −1.47548
\(142\) 0.804562 0.0675174
\(143\) −2.74895 −0.229879
\(144\) 4.61711 0.384759
\(145\) 13.4414 1.11625
\(146\) −1.00335 −0.0830377
\(147\) 16.1132 1.32900
\(148\) 2.48058 0.203902
\(149\) −20.9446 −1.71585 −0.857925 0.513774i \(-0.828247\pi\)
−0.857925 + 0.513774i \(0.828247\pi\)
\(150\) 3.31904 0.270999
\(151\) 16.3586 1.33124 0.665621 0.746290i \(-0.268167\pi\)
0.665621 + 0.746290i \(0.268167\pi\)
\(152\) −5.84597 −0.474171
\(153\) 28.3402 2.29117
\(154\) 1.05590 0.0850871
\(155\) 5.50176 0.441912
\(156\) −7.74430 −0.620040
\(157\) 10.0426 0.801484 0.400742 0.916191i \(-0.368752\pi\)
0.400742 + 0.916191i \(0.368752\pi\)
\(158\) 17.3763 1.38238
\(159\) 7.92750 0.628692
\(160\) 1.94869 0.154058
\(161\) −0.876220 −0.0690558
\(162\) −1.53360 −0.120491
\(163\) 11.6883 0.915502 0.457751 0.889081i \(-0.348655\pi\)
0.457751 + 0.889081i \(0.348655\pi\)
\(164\) 9.53441 0.744513
\(165\) 5.26889 0.410183
\(166\) −13.6050 −1.05595
\(167\) 8.90188 0.688848 0.344424 0.938814i \(-0.388074\pi\)
0.344424 + 0.938814i \(0.388074\pi\)
\(168\) 2.97467 0.229501
\(169\) −5.12639 −0.394337
\(170\) 11.9613 0.917386
\(171\) −26.9915 −2.06409
\(172\) −11.3478 −0.865261
\(173\) −23.5687 −1.79190 −0.895949 0.444156i \(-0.853504\pi\)
−0.895949 + 0.444156i \(0.853504\pi\)
\(174\) −19.0369 −1.44319
\(175\) 1.29617 0.0979812
\(176\) −0.979671 −0.0738455
\(177\) 31.8697 2.39548
\(178\) 4.49866 0.337189
\(179\) −0.131051 −0.00979525 −0.00489762 0.999988i \(-0.501559\pi\)
−0.00489762 + 0.999988i \(0.501559\pi\)
\(180\) 8.99734 0.670622
\(181\) 2.51657 0.187055 0.0935274 0.995617i \(-0.470186\pi\)
0.0935274 + 0.995617i \(0.470186\pi\)
\(182\) −3.02434 −0.224179
\(183\) 3.27218 0.241886
\(184\) 0.812960 0.0599322
\(185\) 4.83388 0.355394
\(186\) −7.79208 −0.571343
\(187\) −6.01331 −0.439737
\(188\) 6.34815 0.462986
\(189\) 4.81038 0.349904
\(190\) −11.3920 −0.826463
\(191\) 7.60721 0.550438 0.275219 0.961382i \(-0.411250\pi\)
0.275219 + 0.961382i \(0.411250\pi\)
\(192\) −2.75991 −0.199179
\(193\) 8.64913 0.622578 0.311289 0.950315i \(-0.399239\pi\)
0.311289 + 0.950315i \(0.399239\pi\)
\(194\) 6.91840 0.496712
\(195\) −15.0913 −1.08071
\(196\) −5.83832 −0.417023
\(197\) −3.46928 −0.247176 −0.123588 0.992334i \(-0.539440\pi\)
−0.123588 + 0.992334i \(0.539440\pi\)
\(198\) −4.52325 −0.321454
\(199\) −6.46451 −0.458257 −0.229128 0.973396i \(-0.573588\pi\)
−0.229128 + 0.973396i \(0.573588\pi\)
\(200\) −1.20259 −0.0850360
\(201\) −34.2842 −2.41822
\(202\) 15.8733 1.11684
\(203\) −7.43439 −0.521792
\(204\) −16.9406 −1.18608
\(205\) 18.5797 1.29766
\(206\) −6.02551 −0.419817
\(207\) 3.75353 0.260888
\(208\) 2.80600 0.194561
\(209\) 5.72713 0.396154
\(210\) 5.79673 0.400012
\(211\) 20.1627 1.38806 0.694030 0.719946i \(-0.255833\pi\)
0.694030 + 0.719946i \(0.255833\pi\)
\(212\) −2.87238 −0.197276
\(213\) −2.22052 −0.152148
\(214\) 3.14456 0.214958
\(215\) −22.1134 −1.50812
\(216\) −4.46309 −0.303675
\(217\) −3.04300 −0.206572
\(218\) 5.80426 0.393114
\(219\) 2.76915 0.187122
\(220\) −1.90908 −0.128710
\(221\) 17.2234 1.15857
\(222\) −6.84617 −0.459485
\(223\) −2.31323 −0.154905 −0.0774525 0.996996i \(-0.524679\pi\)
−0.0774525 + 0.996996i \(0.524679\pi\)
\(224\) −1.07781 −0.0720145
\(225\) −5.55250 −0.370167
\(226\) 6.71337 0.446567
\(227\) 19.3373 1.28346 0.641731 0.766929i \(-0.278216\pi\)
0.641731 + 0.766929i \(0.278216\pi\)
\(228\) 16.1344 1.06852
\(229\) −24.3476 −1.60894 −0.804469 0.593995i \(-0.797550\pi\)
−0.804469 + 0.593995i \(0.797550\pi\)
\(230\) 1.58421 0.104460
\(231\) −2.91420 −0.191740
\(232\) 6.89766 0.452853
\(233\) 17.8808 1.17141 0.585706 0.810523i \(-0.300817\pi\)
0.585706 + 0.810523i \(0.300817\pi\)
\(234\) 12.9556 0.846934
\(235\) 12.3706 0.806969
\(236\) −11.5474 −0.751670
\(237\) −47.9571 −3.11515
\(238\) −6.61572 −0.428833
\(239\) −2.47497 −0.160093 −0.0800464 0.996791i \(-0.525507\pi\)
−0.0800464 + 0.996791i \(0.525507\pi\)
\(240\) −5.37822 −0.347163
\(241\) 16.3687 1.05440 0.527199 0.849742i \(-0.323242\pi\)
0.527199 + 0.849742i \(0.323242\pi\)
\(242\) −10.0402 −0.645411
\(243\) 17.6219 1.13044
\(244\) −1.18561 −0.0759009
\(245\) −11.3771 −0.726856
\(246\) −26.3141 −1.67773
\(247\) −16.4038 −1.04375
\(248\) 2.82331 0.179280
\(249\) 37.5486 2.37955
\(250\) −12.0870 −0.764446
\(251\) −17.8088 −1.12408 −0.562042 0.827109i \(-0.689984\pi\)
−0.562042 + 0.827109i \(0.689984\pi\)
\(252\) −4.97639 −0.313483
\(253\) −0.796433 −0.0500713
\(254\) 10.3462 0.649177
\(255\) −33.0120 −2.06729
\(256\) 1.00000 0.0625000
\(257\) 8.77644 0.547460 0.273730 0.961807i \(-0.411743\pi\)
0.273730 + 0.961807i \(0.411743\pi\)
\(258\) 31.3189 1.94983
\(259\) −2.67360 −0.166129
\(260\) 5.46803 0.339113
\(261\) 31.8473 1.97130
\(262\) −20.9417 −1.29378
\(263\) −5.38526 −0.332070 −0.166035 0.986120i \(-0.553096\pi\)
−0.166035 + 0.986120i \(0.553096\pi\)
\(264\) 2.70381 0.166408
\(265\) −5.59738 −0.343844
\(266\) 6.30087 0.386331
\(267\) −12.4159 −0.759842
\(268\) 12.4222 0.758806
\(269\) −4.20717 −0.256516 −0.128258 0.991741i \(-0.540939\pi\)
−0.128258 + 0.991741i \(0.540939\pi\)
\(270\) −8.69720 −0.529295
\(271\) 27.9024 1.69495 0.847474 0.530836i \(-0.178122\pi\)
0.847474 + 0.530836i \(0.178122\pi\)
\(272\) 6.13809 0.372176
\(273\) 8.34692 0.505178
\(274\) −13.9708 −0.844004
\(275\) 1.17814 0.0710447
\(276\) −2.24370 −0.135055
\(277\) −5.19763 −0.312295 −0.156148 0.987734i \(-0.549908\pi\)
−0.156148 + 0.987734i \(0.549908\pi\)
\(278\) 11.5737 0.694144
\(279\) 13.0355 0.780417
\(280\) −2.10033 −0.125519
\(281\) 0.149335 0.00890861 0.00445430 0.999990i \(-0.498582\pi\)
0.00445430 + 0.999990i \(0.498582\pi\)
\(282\) −17.5203 −1.04332
\(283\) 3.98574 0.236928 0.118464 0.992958i \(-0.462203\pi\)
0.118464 + 0.992958i \(0.462203\pi\)
\(284\) 0.804562 0.0477420
\(285\) 31.4409 1.86240
\(286\) −2.74895 −0.162549
\(287\) −10.2763 −0.606592
\(288\) 4.61711 0.272066
\(289\) 20.6761 1.21624
\(290\) 13.4414 0.789307
\(291\) −19.0942 −1.11932
\(292\) −1.00335 −0.0587165
\(293\) 13.0709 0.763611 0.381805 0.924243i \(-0.375302\pi\)
0.381805 + 0.924243i \(0.375302\pi\)
\(294\) 16.1132 0.939743
\(295\) −22.5023 −1.31013
\(296\) 2.48058 0.144181
\(297\) 4.37236 0.253710
\(298\) −20.9446 −1.21329
\(299\) 2.28116 0.131923
\(300\) 3.31904 0.191625
\(301\) 12.2308 0.704973
\(302\) 16.3586 0.941331
\(303\) −43.8090 −2.51676
\(304\) −5.84597 −0.335289
\(305\) −2.31039 −0.132293
\(306\) 28.3402 1.62010
\(307\) 26.2437 1.49781 0.748905 0.662678i \(-0.230580\pi\)
0.748905 + 0.662678i \(0.230580\pi\)
\(308\) 1.05590 0.0601657
\(309\) 16.6299 0.946040
\(310\) 5.50176 0.312479
\(311\) 16.4523 0.932923 0.466461 0.884542i \(-0.345529\pi\)
0.466461 + 0.884542i \(0.345529\pi\)
\(312\) −7.74430 −0.438435
\(313\) −12.2007 −0.689624 −0.344812 0.938672i \(-0.612057\pi\)
−0.344812 + 0.938672i \(0.612057\pi\)
\(314\) 10.0426 0.566735
\(315\) −9.69746 −0.546390
\(316\) 17.3763 0.977494
\(317\) 1.51828 0.0852749 0.0426374 0.999091i \(-0.486424\pi\)
0.0426374 + 0.999091i \(0.486424\pi\)
\(318\) 7.92750 0.444552
\(319\) −6.75743 −0.378344
\(320\) 1.94869 0.108935
\(321\) −8.67871 −0.484399
\(322\) −0.876220 −0.0488298
\(323\) −35.8831 −1.99659
\(324\) −1.53360 −0.0852002
\(325\) −3.37446 −0.187182
\(326\) 11.6883 0.647357
\(327\) −16.0192 −0.885866
\(328\) 9.53441 0.526450
\(329\) −6.84213 −0.377219
\(330\) 5.26889 0.290043
\(331\) 29.2707 1.60886 0.804432 0.594045i \(-0.202470\pi\)
0.804432 + 0.594045i \(0.202470\pi\)
\(332\) −13.6050 −0.746672
\(333\) 11.4531 0.627626
\(334\) 8.90188 0.487089
\(335\) 24.2071 1.32257
\(336\) 2.97467 0.162282
\(337\) −16.3957 −0.893131 −0.446565 0.894751i \(-0.647353\pi\)
−0.446565 + 0.894751i \(0.647353\pi\)
\(338\) −5.12639 −0.278839
\(339\) −18.5283 −1.00632
\(340\) 11.9613 0.648690
\(341\) −2.76591 −0.149783
\(342\) −26.9915 −1.45953
\(343\) 13.8373 0.747145
\(344\) −11.3478 −0.611832
\(345\) −4.37228 −0.235396
\(346\) −23.5687 −1.26706
\(347\) 32.4629 1.74270 0.871349 0.490664i \(-0.163246\pi\)
0.871349 + 0.490664i \(0.163246\pi\)
\(348\) −19.0369 −1.02049
\(349\) 9.69041 0.518716 0.259358 0.965781i \(-0.416489\pi\)
0.259358 + 0.965781i \(0.416489\pi\)
\(350\) 1.29617 0.0692832
\(351\) −12.5234 −0.668450
\(352\) −0.979671 −0.0522166
\(353\) 17.9689 0.956389 0.478195 0.878254i \(-0.341291\pi\)
0.478195 + 0.878254i \(0.341291\pi\)
\(354\) 31.8697 1.69386
\(355\) 1.56785 0.0832126
\(356\) 4.49866 0.238429
\(357\) 18.2588 0.966358
\(358\) −0.131051 −0.00692628
\(359\) 1.40738 0.0742787 0.0371394 0.999310i \(-0.488175\pi\)
0.0371394 + 0.999310i \(0.488175\pi\)
\(360\) 8.99734 0.474202
\(361\) 15.1753 0.798702
\(362\) 2.51657 0.132268
\(363\) 27.7102 1.45441
\(364\) −3.02434 −0.158519
\(365\) −1.95522 −0.102341
\(366\) 3.27218 0.171040
\(367\) −0.423661 −0.0221149 −0.0110575 0.999939i \(-0.503520\pi\)
−0.0110575 + 0.999939i \(0.503520\pi\)
\(368\) 0.812960 0.0423785
\(369\) 44.0215 2.29167
\(370\) 4.83388 0.251302
\(371\) 3.09589 0.160730
\(372\) −7.79208 −0.404000
\(373\) 6.59142 0.341291 0.170645 0.985332i \(-0.445415\pi\)
0.170645 + 0.985332i \(0.445415\pi\)
\(374\) −6.01331 −0.310941
\(375\) 33.3589 1.72265
\(376\) 6.34815 0.327381
\(377\) 19.3548 0.996823
\(378\) 4.81038 0.247419
\(379\) 10.1493 0.521334 0.260667 0.965429i \(-0.416057\pi\)
0.260667 + 0.965429i \(0.416057\pi\)
\(380\) −11.3920 −0.584397
\(381\) −28.5546 −1.46289
\(382\) 7.60721 0.389219
\(383\) −30.9076 −1.57931 −0.789653 0.613554i \(-0.789739\pi\)
−0.789653 + 0.613554i \(0.789739\pi\)
\(384\) −2.75991 −0.140841
\(385\) 2.05763 0.104867
\(386\) 8.64913 0.440229
\(387\) −52.3941 −2.66334
\(388\) 6.91840 0.351228
\(389\) 22.0663 1.11880 0.559402 0.828897i \(-0.311031\pi\)
0.559402 + 0.828897i \(0.311031\pi\)
\(390\) −15.0913 −0.764176
\(391\) 4.99002 0.252356
\(392\) −5.83832 −0.294880
\(393\) 57.7971 2.91548
\(394\) −3.46928 −0.174780
\(395\) 33.8611 1.70374
\(396\) −4.52325 −0.227302
\(397\) 20.6663 1.03721 0.518607 0.855013i \(-0.326451\pi\)
0.518607 + 0.855013i \(0.326451\pi\)
\(398\) −6.46451 −0.324037
\(399\) −17.3898 −0.870581
\(400\) −1.20259 −0.0601295
\(401\) 12.1495 0.606715 0.303357 0.952877i \(-0.401892\pi\)
0.303357 + 0.952877i \(0.401892\pi\)
\(402\) −34.2842 −1.70994
\(403\) 7.92219 0.394632
\(404\) 15.8733 0.789728
\(405\) −2.98852 −0.148501
\(406\) −7.43439 −0.368963
\(407\) −2.43015 −0.120458
\(408\) −16.9406 −0.838684
\(409\) −2.08319 −0.103007 −0.0515037 0.998673i \(-0.516401\pi\)
−0.0515037 + 0.998673i \(0.516401\pi\)
\(410\) 18.5797 0.917584
\(411\) 38.5580 1.90193
\(412\) −6.02551 −0.296855
\(413\) 12.4459 0.612424
\(414\) 3.75353 0.184476
\(415\) −26.5120 −1.30142
\(416\) 2.80600 0.137575
\(417\) −31.9424 −1.56422
\(418\) 5.72713 0.280123
\(419\) −30.5228 −1.49113 −0.745567 0.666430i \(-0.767821\pi\)
−0.745567 + 0.666430i \(0.767821\pi\)
\(420\) 5.79673 0.282851
\(421\) −34.4862 −1.68075 −0.840377 0.542003i \(-0.817666\pi\)
−0.840377 + 0.542003i \(0.817666\pi\)
\(422\) 20.1627 0.981507
\(423\) 29.3101 1.42511
\(424\) −2.87238 −0.139495
\(425\) −7.38161 −0.358060
\(426\) −2.22052 −0.107585
\(427\) 1.27787 0.0618403
\(428\) 3.14456 0.151998
\(429\) 7.58687 0.366297
\(430\) −22.1134 −1.06640
\(431\) −0.285310 −0.0137429 −0.00687145 0.999976i \(-0.502187\pi\)
−0.00687145 + 0.999976i \(0.502187\pi\)
\(432\) −4.46309 −0.214731
\(433\) 9.69131 0.465735 0.232867 0.972509i \(-0.425189\pi\)
0.232867 + 0.972509i \(0.425189\pi\)
\(434\) −3.04300 −0.146069
\(435\) −37.0971 −1.77867
\(436\) 5.80426 0.277974
\(437\) −4.75254 −0.227345
\(438\) 2.76915 0.132315
\(439\) −20.4018 −0.973727 −0.486863 0.873478i \(-0.661859\pi\)
−0.486863 + 0.873478i \(0.661859\pi\)
\(440\) −1.90908 −0.0910118
\(441\) −26.9562 −1.28363
\(442\) 17.2234 0.819236
\(443\) 16.8381 0.800004 0.400002 0.916514i \(-0.369009\pi\)
0.400002 + 0.916514i \(0.369009\pi\)
\(444\) −6.84617 −0.324905
\(445\) 8.76652 0.415573
\(446\) −2.31323 −0.109534
\(447\) 57.8053 2.73410
\(448\) −1.07781 −0.0509219
\(449\) −31.2864 −1.47649 −0.738247 0.674530i \(-0.764346\pi\)
−0.738247 + 0.674530i \(0.764346\pi\)
\(450\) −5.55250 −0.261747
\(451\) −9.34059 −0.439831
\(452\) 6.71337 0.315771
\(453\) −45.1483 −2.12125
\(454\) 19.3373 0.907545
\(455\) −5.89352 −0.276292
\(456\) 16.1344 0.755560
\(457\) −20.5708 −0.962260 −0.481130 0.876649i \(-0.659774\pi\)
−0.481130 + 0.876649i \(0.659774\pi\)
\(458\) −24.3476 −1.13769
\(459\) −27.3948 −1.27868
\(460\) 1.58421 0.0738642
\(461\) 38.1200 1.77543 0.887713 0.460398i \(-0.152293\pi\)
0.887713 + 0.460398i \(0.152293\pi\)
\(462\) −2.91420 −0.135581
\(463\) 4.21206 0.195751 0.0978754 0.995199i \(-0.468795\pi\)
0.0978754 + 0.995199i \(0.468795\pi\)
\(464\) 6.89766 0.320216
\(465\) −15.1844 −0.704159
\(466\) 17.8808 0.828314
\(467\) 0.467726 0.0216438 0.0108219 0.999941i \(-0.496555\pi\)
0.0108219 + 0.999941i \(0.496555\pi\)
\(468\) 12.9556 0.598873
\(469\) −13.3888 −0.618238
\(470\) 12.3706 0.570613
\(471\) −27.7166 −1.27711
\(472\) −11.5474 −0.531511
\(473\) 11.1171 0.511165
\(474\) −47.9571 −2.20274
\(475\) 7.03031 0.322573
\(476\) −6.61572 −0.303231
\(477\) −13.2621 −0.607229
\(478\) −2.47497 −0.113203
\(479\) 27.3789 1.25098 0.625488 0.780234i \(-0.284900\pi\)
0.625488 + 0.780234i \(0.284900\pi\)
\(480\) −5.37822 −0.245481
\(481\) 6.96048 0.317371
\(482\) 16.3687 0.745572
\(483\) 2.41829 0.110036
\(484\) −10.0402 −0.456375
\(485\) 13.4818 0.612179
\(486\) 17.6219 0.799345
\(487\) 20.9230 0.948112 0.474056 0.880495i \(-0.342789\pi\)
0.474056 + 0.880495i \(0.342789\pi\)
\(488\) −1.18561 −0.0536700
\(489\) −32.2588 −1.45879
\(490\) −11.3771 −0.513965
\(491\) 31.5076 1.42192 0.710959 0.703234i \(-0.248261\pi\)
0.710959 + 0.703234i \(0.248261\pi\)
\(492\) −26.3141 −1.18633
\(493\) 42.3384 1.90683
\(494\) −16.4038 −0.738040
\(495\) −8.81444 −0.396179
\(496\) 2.82331 0.126770
\(497\) −0.867169 −0.0388978
\(498\) 37.5486 1.68259
\(499\) −1.46096 −0.0654016 −0.0327008 0.999465i \(-0.510411\pi\)
−0.0327008 + 0.999465i \(0.510411\pi\)
\(500\) −12.0870 −0.540545
\(501\) −24.5684 −1.09763
\(502\) −17.8088 −0.794847
\(503\) −9.96582 −0.444354 −0.222177 0.975006i \(-0.571316\pi\)
−0.222177 + 0.975006i \(0.571316\pi\)
\(504\) −4.97639 −0.221666
\(505\) 30.9323 1.37647
\(506\) −0.796433 −0.0354058
\(507\) 14.1484 0.628351
\(508\) 10.3462 0.459038
\(509\) 4.10846 0.182104 0.0910522 0.995846i \(-0.470977\pi\)
0.0910522 + 0.995846i \(0.470977\pi\)
\(510\) −33.0120 −1.46180
\(511\) 1.08142 0.0478393
\(512\) 1.00000 0.0441942
\(513\) 26.0911 1.15195
\(514\) 8.77644 0.387112
\(515\) −11.7419 −0.517409
\(516\) 31.3189 1.37874
\(517\) −6.21910 −0.273516
\(518\) −2.67360 −0.117471
\(519\) 65.0477 2.85528
\(520\) 5.46803 0.239789
\(521\) 28.5129 1.24917 0.624585 0.780957i \(-0.285268\pi\)
0.624585 + 0.780957i \(0.285268\pi\)
\(522\) 31.8473 1.39392
\(523\) 42.9607 1.87854 0.939270 0.343178i \(-0.111503\pi\)
0.939270 + 0.343178i \(0.111503\pi\)
\(524\) −20.9417 −0.914841
\(525\) −3.57731 −0.156127
\(526\) −5.38526 −0.234809
\(527\) 17.3297 0.754894
\(528\) 2.70381 0.117668
\(529\) −22.3391 −0.971265
\(530\) −5.59738 −0.243135
\(531\) −53.3155 −2.31370
\(532\) 6.30087 0.273177
\(533\) 26.7535 1.15882
\(534\) −12.4159 −0.537289
\(535\) 6.12779 0.264927
\(536\) 12.4222 0.536557
\(537\) 0.361690 0.0156081
\(538\) −4.20717 −0.181384
\(539\) 5.71963 0.246362
\(540\) −8.69720 −0.374268
\(541\) 41.8976 1.80132 0.900658 0.434528i \(-0.143085\pi\)
0.900658 + 0.434528i \(0.143085\pi\)
\(542\) 27.9024 1.19851
\(543\) −6.94550 −0.298060
\(544\) 6.13809 0.263168
\(545\) 11.3107 0.484498
\(546\) 8.34692 0.357215
\(547\) 2.45563 0.104995 0.0524975 0.998621i \(-0.483282\pi\)
0.0524975 + 0.998621i \(0.483282\pi\)
\(548\) −13.9708 −0.596801
\(549\) −5.47410 −0.233629
\(550\) 1.17814 0.0502362
\(551\) −40.3235 −1.71784
\(552\) −2.24370 −0.0954981
\(553\) −18.7284 −0.796414
\(554\) −5.19763 −0.220826
\(555\) −13.3411 −0.566298
\(556\) 11.5737 0.490834
\(557\) −38.0194 −1.61093 −0.805466 0.592642i \(-0.798085\pi\)
−0.805466 + 0.592642i \(0.798085\pi\)
\(558\) 13.0355 0.551838
\(559\) −31.8419 −1.34677
\(560\) −2.10033 −0.0887552
\(561\) 16.5962 0.700692
\(562\) 0.149335 0.00629934
\(563\) 15.7669 0.664495 0.332247 0.943192i \(-0.392193\pi\)
0.332247 + 0.943192i \(0.392193\pi\)
\(564\) −17.5203 −0.737739
\(565\) 13.0823 0.550377
\(566\) 3.98574 0.167533
\(567\) 1.65294 0.0694169
\(568\) 0.804562 0.0337587
\(569\) 22.1317 0.927809 0.463905 0.885885i \(-0.346448\pi\)
0.463905 + 0.885885i \(0.346448\pi\)
\(570\) 31.4409 1.31692
\(571\) 10.2704 0.429804 0.214902 0.976636i \(-0.431057\pi\)
0.214902 + 0.976636i \(0.431057\pi\)
\(572\) −2.74895 −0.114940
\(573\) −20.9952 −0.877088
\(574\) −10.2763 −0.428926
\(575\) −0.977658 −0.0407712
\(576\) 4.61711 0.192380
\(577\) 20.6211 0.858467 0.429234 0.903193i \(-0.358784\pi\)
0.429234 + 0.903193i \(0.358784\pi\)
\(578\) 20.6761 0.860013
\(579\) −23.8708 −0.992038
\(580\) 13.4414 0.558125
\(581\) 14.6637 0.608352
\(582\) −19.0942 −0.791479
\(583\) 2.81398 0.116543
\(584\) −1.00335 −0.0415189
\(585\) 25.2465 1.04381
\(586\) 13.0709 0.539954
\(587\) −9.44050 −0.389651 −0.194826 0.980838i \(-0.562414\pi\)
−0.194826 + 0.980838i \(0.562414\pi\)
\(588\) 16.1132 0.664499
\(589\) −16.5050 −0.680075
\(590\) −22.5023 −0.926405
\(591\) 9.57490 0.393859
\(592\) 2.48058 0.101951
\(593\) 24.9189 1.02330 0.511648 0.859195i \(-0.329035\pi\)
0.511648 + 0.859195i \(0.329035\pi\)
\(594\) 4.37236 0.179400
\(595\) −12.8920 −0.528521
\(596\) −20.9446 −0.857925
\(597\) 17.8415 0.730203
\(598\) 2.28116 0.0932836
\(599\) 38.5056 1.57329 0.786647 0.617402i \(-0.211815\pi\)
0.786647 + 0.617402i \(0.211815\pi\)
\(600\) 3.31904 0.135499
\(601\) 17.6057 0.718151 0.359076 0.933308i \(-0.383092\pi\)
0.359076 + 0.933308i \(0.383092\pi\)
\(602\) 12.2308 0.498491
\(603\) 57.3547 2.33566
\(604\) 16.3586 0.665621
\(605\) −19.5654 −0.795445
\(606\) −43.8090 −1.77962
\(607\) 19.4163 0.788085 0.394042 0.919092i \(-0.371076\pi\)
0.394042 + 0.919092i \(0.371076\pi\)
\(608\) −5.84597 −0.237085
\(609\) 20.5183 0.831442
\(610\) −2.31039 −0.0935450
\(611\) 17.8129 0.720632
\(612\) 28.3402 1.14559
\(613\) −45.5552 −1.83996 −0.919978 0.391971i \(-0.871793\pi\)
−0.919978 + 0.391971i \(0.871793\pi\)
\(614\) 26.2437 1.05911
\(615\) −51.2782 −2.06774
\(616\) 1.05590 0.0425436
\(617\) −12.7964 −0.515164 −0.257582 0.966256i \(-0.582926\pi\)
−0.257582 + 0.966256i \(0.582926\pi\)
\(618\) 16.6299 0.668951
\(619\) −8.36623 −0.336267 −0.168134 0.985764i \(-0.553774\pi\)
−0.168134 + 0.985764i \(0.553774\pi\)
\(620\) 5.50176 0.220956
\(621\) −3.62831 −0.145599
\(622\) 16.4523 0.659676
\(623\) −4.84872 −0.194260
\(624\) −7.74430 −0.310020
\(625\) −17.5408 −0.701633
\(626\) −12.2007 −0.487638
\(627\) −15.8064 −0.631245
\(628\) 10.0426 0.400742
\(629\) 15.2260 0.607100
\(630\) −9.69746 −0.386356
\(631\) −21.0840 −0.839339 −0.419670 0.907677i \(-0.637854\pi\)
−0.419670 + 0.907677i \(0.637854\pi\)
\(632\) 17.3763 0.691192
\(633\) −55.6474 −2.21178
\(634\) 1.51828 0.0602985
\(635\) 20.1615 0.800087
\(636\) 7.92750 0.314346
\(637\) −16.3823 −0.649090
\(638\) −6.75743 −0.267529
\(639\) 3.71476 0.146953
\(640\) 1.94869 0.0770289
\(641\) 15.0917 0.596084 0.298042 0.954553i \(-0.403666\pi\)
0.298042 + 0.954553i \(0.403666\pi\)
\(642\) −8.67871 −0.342521
\(643\) −11.5376 −0.454999 −0.227499 0.973778i \(-0.573055\pi\)
−0.227499 + 0.973778i \(0.573055\pi\)
\(644\) −0.876220 −0.0345279
\(645\) 61.0310 2.40309
\(646\) −35.8831 −1.41180
\(647\) 13.0312 0.512311 0.256155 0.966636i \(-0.417544\pi\)
0.256155 + 0.966636i \(0.417544\pi\)
\(648\) −1.53360 −0.0602456
\(649\) 11.3126 0.444060
\(650\) −3.37446 −0.132357
\(651\) 8.39841 0.329160
\(652\) 11.6883 0.457751
\(653\) 29.3440 1.14832 0.574160 0.818743i \(-0.305329\pi\)
0.574160 + 0.818743i \(0.305329\pi\)
\(654\) −16.0192 −0.626402
\(655\) −40.8089 −1.59454
\(656\) 9.53441 0.372256
\(657\) −4.63257 −0.180734
\(658\) −6.84213 −0.266734
\(659\) −22.3510 −0.870673 −0.435336 0.900268i \(-0.643371\pi\)
−0.435336 + 0.900268i \(0.643371\pi\)
\(660\) 5.26889 0.205091
\(661\) 1.02423 0.0398377 0.0199189 0.999802i \(-0.493659\pi\)
0.0199189 + 0.999802i \(0.493659\pi\)
\(662\) 29.2707 1.13764
\(663\) −47.5352 −1.84611
\(664\) −13.6050 −0.527977
\(665\) 12.2785 0.476138
\(666\) 11.4531 0.443799
\(667\) 5.60752 0.217124
\(668\) 8.90188 0.344424
\(669\) 6.38430 0.246831
\(670\) 24.2071 0.935200
\(671\) 1.16151 0.0448395
\(672\) 2.97467 0.114750
\(673\) −35.7299 −1.37729 −0.688644 0.725099i \(-0.741794\pi\)
−0.688644 + 0.725099i \(0.741794\pi\)
\(674\) −16.3957 −0.631539
\(675\) 5.36727 0.206586
\(676\) −5.12639 −0.197169
\(677\) 1.99090 0.0765166 0.0382583 0.999268i \(-0.487819\pi\)
0.0382583 + 0.999268i \(0.487819\pi\)
\(678\) −18.5283 −0.711576
\(679\) −7.45675 −0.286164
\(680\) 11.9613 0.458693
\(681\) −53.3693 −2.04512
\(682\) −2.76591 −0.105912
\(683\) 13.3001 0.508913 0.254456 0.967084i \(-0.418103\pi\)
0.254456 + 0.967084i \(0.418103\pi\)
\(684\) −26.9915 −1.03205
\(685\) −27.2247 −1.04020
\(686\) 13.8373 0.528311
\(687\) 67.1973 2.56374
\(688\) −11.3478 −0.432631
\(689\) −8.05987 −0.307057
\(690\) −4.37228 −0.166450
\(691\) 47.1513 1.79372 0.896861 0.442313i \(-0.145842\pi\)
0.896861 + 0.442313i \(0.145842\pi\)
\(692\) −23.5687 −0.895949
\(693\) 4.87523 0.185195
\(694\) 32.4629 1.23227
\(695\) 22.5536 0.855506
\(696\) −19.0369 −0.721593
\(697\) 58.5231 2.21672
\(698\) 9.69041 0.366788
\(699\) −49.3495 −1.86657
\(700\) 1.29617 0.0489906
\(701\) −3.19487 −0.120668 −0.0603342 0.998178i \(-0.519217\pi\)
−0.0603342 + 0.998178i \(0.519217\pi\)
\(702\) −12.5234 −0.472666
\(703\) −14.5014 −0.546929
\(704\) −0.979671 −0.0369227
\(705\) −34.1418 −1.28585
\(706\) 17.9689 0.676269
\(707\) −17.1085 −0.643431
\(708\) 31.8697 1.19774
\(709\) −9.31234 −0.349732 −0.174866 0.984592i \(-0.555949\pi\)
−0.174866 + 0.984592i \(0.555949\pi\)
\(710\) 1.56785 0.0588402
\(711\) 80.2284 3.00880
\(712\) 4.49866 0.168595
\(713\) 2.29523 0.0859572
\(714\) 18.2588 0.683318
\(715\) −5.35687 −0.200336
\(716\) −0.131051 −0.00489762
\(717\) 6.83071 0.255098
\(718\) 1.40738 0.0525230
\(719\) 14.4611 0.539308 0.269654 0.962957i \(-0.413091\pi\)
0.269654 + 0.962957i \(0.413091\pi\)
\(720\) 8.99734 0.335311
\(721\) 6.49438 0.241863
\(722\) 15.1753 0.564768
\(723\) −45.1760 −1.68012
\(724\) 2.51657 0.0935274
\(725\) −8.29506 −0.308071
\(726\) 27.7102 1.02842
\(727\) −39.3755 −1.46036 −0.730179 0.683256i \(-0.760563\pi\)
−0.730179 + 0.683256i \(0.760563\pi\)
\(728\) −3.02434 −0.112090
\(729\) −44.0340 −1.63089
\(730\) −1.95522 −0.0723659
\(731\) −69.6538 −2.57624
\(732\) 3.27218 0.120943
\(733\) 8.91663 0.329343 0.164672 0.986348i \(-0.447344\pi\)
0.164672 + 0.986348i \(0.447344\pi\)
\(734\) −0.423661 −0.0156376
\(735\) 31.3998 1.15820
\(736\) 0.812960 0.0299661
\(737\) −12.1697 −0.448275
\(738\) 44.0215 1.62045
\(739\) −7.35201 −0.270448 −0.135224 0.990815i \(-0.543175\pi\)
−0.135224 + 0.990815i \(0.543175\pi\)
\(740\) 4.83388 0.177697
\(741\) 45.2729 1.66314
\(742\) 3.09589 0.113654
\(743\) −38.1743 −1.40048 −0.700240 0.713907i \(-0.746924\pi\)
−0.700240 + 0.713907i \(0.746924\pi\)
\(744\) −7.79208 −0.285671
\(745\) −40.8147 −1.49533
\(746\) 6.59142 0.241329
\(747\) −62.8159 −2.29831
\(748\) −6.01331 −0.219868
\(749\) −3.38925 −0.123841
\(750\) 33.3589 1.21810
\(751\) −39.9738 −1.45867 −0.729333 0.684159i \(-0.760169\pi\)
−0.729333 + 0.684159i \(0.760169\pi\)
\(752\) 6.34815 0.231493
\(753\) 49.1508 1.79116
\(754\) 19.3548 0.704860
\(755\) 31.8779 1.16015
\(756\) 4.81038 0.174952
\(757\) −40.3248 −1.46563 −0.732815 0.680428i \(-0.761794\pi\)
−0.732815 + 0.680428i \(0.761794\pi\)
\(758\) 10.1493 0.368639
\(759\) 2.19809 0.0797855
\(760\) −11.3920 −0.413231
\(761\) 23.9110 0.866772 0.433386 0.901208i \(-0.357319\pi\)
0.433386 + 0.901208i \(0.357319\pi\)
\(762\) −28.5546 −1.03442
\(763\) −6.25591 −0.226479
\(764\) 7.60721 0.275219
\(765\) 55.2265 1.99672
\(766\) −30.9076 −1.11674
\(767\) −32.4019 −1.16996
\(768\) −2.75991 −0.0995897
\(769\) 35.6971 1.28727 0.643636 0.765332i \(-0.277425\pi\)
0.643636 + 0.765332i \(0.277425\pi\)
\(770\) 2.05763 0.0741519
\(771\) −24.2222 −0.872342
\(772\) 8.64913 0.311289
\(773\) −45.7212 −1.64448 −0.822239 0.569143i \(-0.807275\pi\)
−0.822239 + 0.569143i \(0.807275\pi\)
\(774\) −52.3941 −1.88327
\(775\) −3.39528 −0.121962
\(776\) 6.91840 0.248356
\(777\) 7.37890 0.264717
\(778\) 22.0663 0.791114
\(779\) −55.7379 −1.99702
\(780\) −15.0913 −0.540354
\(781\) −0.788207 −0.0282042
\(782\) 4.99002 0.178443
\(783\) −30.7849 −1.10016
\(784\) −5.83832 −0.208511
\(785\) 19.5699 0.698479
\(786\) 57.7971 2.06156
\(787\) 18.9694 0.676187 0.338093 0.941113i \(-0.390218\pi\)
0.338093 + 0.941113i \(0.390218\pi\)
\(788\) −3.46928 −0.123588
\(789\) 14.8629 0.529131
\(790\) 33.8611 1.20472
\(791\) −7.23577 −0.257274
\(792\) −4.52325 −0.160727
\(793\) −3.32682 −0.118139
\(794\) 20.6663 0.733420
\(795\) 15.4483 0.547894
\(796\) −6.46451 −0.229128
\(797\) −0.359493 −0.0127339 −0.00636696 0.999980i \(-0.502027\pi\)
−0.00636696 + 0.999980i \(0.502027\pi\)
\(798\) −17.3898 −0.615594
\(799\) 38.9655 1.37850
\(800\) −1.20259 −0.0425180
\(801\) 20.7708 0.733902
\(802\) 12.1495 0.429012
\(803\) 0.982952 0.0346876
\(804\) −34.2842 −1.20911
\(805\) −1.70748 −0.0601809
\(806\) 7.92219 0.279047
\(807\) 11.6114 0.408742
\(808\) 15.8733 0.558422
\(809\) −17.9681 −0.631725 −0.315863 0.948805i \(-0.602294\pi\)
−0.315863 + 0.948805i \(0.602294\pi\)
\(810\) −2.98852 −0.105006
\(811\) −25.8396 −0.907351 −0.453676 0.891167i \(-0.649887\pi\)
−0.453676 + 0.891167i \(0.649887\pi\)
\(812\) −7.43439 −0.260896
\(813\) −77.0081 −2.70079
\(814\) −2.43015 −0.0851766
\(815\) 22.7770 0.797844
\(816\) −16.9406 −0.593039
\(817\) 66.3389 2.32090
\(818\) −2.08319 −0.0728372
\(819\) −13.9637 −0.487932
\(820\) 18.5797 0.648830
\(821\) 15.3699 0.536413 0.268207 0.963361i \(-0.413569\pi\)
0.268207 + 0.963361i \(0.413569\pi\)
\(822\) 38.5580 1.34487
\(823\) −48.7044 −1.69773 −0.848865 0.528610i \(-0.822713\pi\)
−0.848865 + 0.528610i \(0.822713\pi\)
\(824\) −6.02551 −0.209908
\(825\) −3.25157 −0.113205
\(826\) 12.4459 0.433049
\(827\) −52.6902 −1.83222 −0.916110 0.400928i \(-0.868688\pi\)
−0.916110 + 0.400928i \(0.868688\pi\)
\(828\) 3.75353 0.130444
\(829\) −20.4754 −0.711141 −0.355570 0.934650i \(-0.615713\pi\)
−0.355570 + 0.934650i \(0.615713\pi\)
\(830\) −26.5120 −0.920245
\(831\) 14.3450 0.497622
\(832\) 2.80600 0.0972804
\(833\) −35.8361 −1.24165
\(834\) −31.9424 −1.10607
\(835\) 17.3470 0.600319
\(836\) 5.72713 0.198077
\(837\) −12.6007 −0.435543
\(838\) −30.5228 −1.05439
\(839\) 44.4620 1.53500 0.767499 0.641050i \(-0.221501\pi\)
0.767499 + 0.641050i \(0.221501\pi\)
\(840\) 5.79673 0.200006
\(841\) 18.5776 0.640609
\(842\) −34.4862 −1.18847
\(843\) −0.412153 −0.0141953
\(844\) 20.1627 0.694030
\(845\) −9.98976 −0.343658
\(846\) 29.3101 1.00770
\(847\) 10.8215 0.371832
\(848\) −2.87238 −0.0986378
\(849\) −11.0003 −0.377529
\(850\) −7.38161 −0.253187
\(851\) 2.01661 0.0691284
\(852\) −2.22052 −0.0760738
\(853\) −41.1419 −1.40867 −0.704336 0.709867i \(-0.748755\pi\)
−0.704336 + 0.709867i \(0.748755\pi\)
\(854\) 1.27787 0.0437277
\(855\) −52.5982 −1.79882
\(856\) 3.14456 0.107479
\(857\) 25.7476 0.879521 0.439761 0.898115i \(-0.355063\pi\)
0.439761 + 0.898115i \(0.355063\pi\)
\(858\) 7.58687 0.259011
\(859\) 13.4030 0.457306 0.228653 0.973508i \(-0.426568\pi\)
0.228653 + 0.973508i \(0.426568\pi\)
\(860\) −22.1134 −0.754060
\(861\) 28.3618 0.966566
\(862\) −0.285310 −0.00971769
\(863\) 25.0039 0.851142 0.425571 0.904925i \(-0.360073\pi\)
0.425571 + 0.904925i \(0.360073\pi\)
\(864\) −4.46309 −0.151837
\(865\) −45.9283 −1.56161
\(866\) 9.69131 0.329324
\(867\) −57.0642 −1.93800
\(868\) −3.04300 −0.103286
\(869\) −17.0231 −0.577468
\(870\) −37.0971 −1.25771
\(871\) 34.8566 1.18107
\(872\) 5.80426 0.196557
\(873\) 31.9430 1.08111
\(874\) −4.75254 −0.160757
\(875\) 13.0275 0.440410
\(876\) 2.76915 0.0935610
\(877\) 9.80661 0.331146 0.165573 0.986198i \(-0.447053\pi\)
0.165573 + 0.986198i \(0.447053\pi\)
\(878\) −20.4018 −0.688529
\(879\) −36.0746 −1.21676
\(880\) −1.90908 −0.0643551
\(881\) 15.3207 0.516167 0.258083 0.966123i \(-0.416909\pi\)
0.258083 + 0.966123i \(0.416909\pi\)
\(882\) −26.9562 −0.907661
\(883\) −36.2701 −1.22058 −0.610292 0.792176i \(-0.708948\pi\)
−0.610292 + 0.792176i \(0.708948\pi\)
\(884\) 17.2234 0.579287
\(885\) 62.1044 2.08762
\(886\) 16.8381 0.565688
\(887\) −6.41568 −0.215417 −0.107709 0.994183i \(-0.534351\pi\)
−0.107709 + 0.994183i \(0.534351\pi\)
\(888\) −6.84617 −0.229742
\(889\) −11.1513 −0.374001
\(890\) 8.76652 0.293854
\(891\) 1.50243 0.0503332
\(892\) −2.31323 −0.0774525
\(893\) −37.1111 −1.24187
\(894\) 57.8053 1.93330
\(895\) −0.255379 −0.00853639
\(896\) −1.07781 −0.0360072
\(897\) −6.29581 −0.210211
\(898\) −31.2864 −1.04404
\(899\) 19.4742 0.649501
\(900\) −5.55250 −0.185083
\(901\) −17.6309 −0.587370
\(902\) −9.34059 −0.311008
\(903\) −33.7560 −1.12333
\(904\) 6.71337 0.223284
\(905\) 4.90402 0.163015
\(906\) −45.1483 −1.49995
\(907\) −45.8274 −1.52167 −0.760837 0.648942i \(-0.775212\pi\)
−0.760837 + 0.648942i \(0.775212\pi\)
\(908\) 19.3373 0.641731
\(909\) 73.2890 2.43084
\(910\) −5.89352 −0.195368
\(911\) −38.5475 −1.27714 −0.638568 0.769565i \(-0.720473\pi\)
−0.638568 + 0.769565i \(0.720473\pi\)
\(912\) 16.1344 0.534262
\(913\) 13.3284 0.441107
\(914\) −20.5708 −0.680421
\(915\) 6.37648 0.210800
\(916\) −24.3476 −0.804469
\(917\) 22.5712 0.745367
\(918\) −27.3948 −0.904164
\(919\) 12.0676 0.398072 0.199036 0.979992i \(-0.436219\pi\)
0.199036 + 0.979992i \(0.436219\pi\)
\(920\) 1.58421 0.0522299
\(921\) −72.4304 −2.38666
\(922\) 38.1200 1.25542
\(923\) 2.25760 0.0743098
\(924\) −2.91420 −0.0958702
\(925\) −2.98312 −0.0980843
\(926\) 4.21206 0.138417
\(927\) −27.8204 −0.913743
\(928\) 6.89766 0.226427
\(929\) −19.4079 −0.636753 −0.318377 0.947964i \(-0.603138\pi\)
−0.318377 + 0.947964i \(0.603138\pi\)
\(930\) −15.1844 −0.497915
\(931\) 34.1306 1.11859
\(932\) 17.8808 0.585706
\(933\) −45.4068 −1.48655
\(934\) 0.467726 0.0153044
\(935\) −11.7181 −0.383223
\(936\) 12.9556 0.423467
\(937\) 10.0986 0.329908 0.164954 0.986301i \(-0.447252\pi\)
0.164954 + 0.986301i \(0.447252\pi\)
\(938\) −13.3888 −0.437160
\(939\) 33.6728 1.09887
\(940\) 12.3706 0.403485
\(941\) 11.8119 0.385058 0.192529 0.981291i \(-0.438331\pi\)
0.192529 + 0.981291i \(0.438331\pi\)
\(942\) −27.7166 −0.903055
\(943\) 7.75109 0.252410
\(944\) −11.5474 −0.375835
\(945\) 9.37396 0.304935
\(946\) 11.1171 0.361448
\(947\) −51.4580 −1.67216 −0.836080 0.548607i \(-0.815158\pi\)
−0.836080 + 0.548607i \(0.815158\pi\)
\(948\) −47.9571 −1.55757
\(949\) −2.81539 −0.0913915
\(950\) 7.03031 0.228093
\(951\) −4.19031 −0.135880
\(952\) −6.61572 −0.214417
\(953\) 45.8690 1.48584 0.742922 0.669378i \(-0.233439\pi\)
0.742922 + 0.669378i \(0.233439\pi\)
\(954\) −13.2621 −0.429376
\(955\) 14.8241 0.479697
\(956\) −2.47497 −0.0800464
\(957\) 18.6499 0.602866
\(958\) 27.3789 0.884573
\(959\) 15.0579 0.486244
\(960\) −5.37822 −0.173581
\(961\) −23.0289 −0.742869
\(962\) 6.96048 0.224415
\(963\) 14.5188 0.467862
\(964\) 16.3687 0.527199
\(965\) 16.8545 0.542566
\(966\) 2.41829 0.0778072
\(967\) −36.9900 −1.18952 −0.594760 0.803904i \(-0.702753\pi\)
−0.594760 + 0.803904i \(0.702753\pi\)
\(968\) −10.0402 −0.322706
\(969\) 99.0341 3.18143
\(970\) 13.4818 0.432876
\(971\) −7.18233 −0.230492 −0.115246 0.993337i \(-0.536766\pi\)
−0.115246 + 0.993337i \(0.536766\pi\)
\(972\) 17.6219 0.565222
\(973\) −12.4743 −0.399907
\(974\) 20.9230 0.670416
\(975\) 9.31323 0.298262
\(976\) −1.18561 −0.0379504
\(977\) 19.0271 0.608731 0.304365 0.952555i \(-0.401556\pi\)
0.304365 + 0.952555i \(0.401556\pi\)
\(978\) −32.2588 −1.03152
\(979\) −4.40721 −0.140855
\(980\) −11.3771 −0.363428
\(981\) 26.7989 0.855624
\(982\) 31.5076 1.00545
\(983\) −19.3901 −0.618447 −0.309223 0.950989i \(-0.600069\pi\)
−0.309223 + 0.950989i \(0.600069\pi\)
\(984\) −26.3141 −0.838864
\(985\) −6.76056 −0.215409
\(986\) 42.3384 1.34833
\(987\) 18.8837 0.601074
\(988\) −16.4038 −0.521873
\(989\) −9.22530 −0.293348
\(990\) −8.81444 −0.280141
\(991\) −15.8049 −0.502059 −0.251030 0.967979i \(-0.580769\pi\)
−0.251030 + 0.967979i \(0.580769\pi\)
\(992\) 2.82331 0.0896401
\(993\) −80.7846 −2.56362
\(994\) −0.867169 −0.0275049
\(995\) −12.5974 −0.399363
\(996\) 37.5486 1.18977
\(997\) −6.20291 −0.196448 −0.0982241 0.995164i \(-0.531316\pi\)
−0.0982241 + 0.995164i \(0.531316\pi\)
\(998\) −1.46096 −0.0462459
\(999\) −11.0710 −0.350272
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 8026.2.a.d.1.12 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8026.2.a.d.1.12 96 1.1 even 1 trivial