Properties

Label 8027.2.a.d.1.9
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $1$
Dimension $149$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(1\)
Dimension: \(149\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.55845 q^{2} -2.16736 q^{3} +4.54566 q^{4} +2.09071 q^{5} +5.54507 q^{6} -1.08828 q^{7} -6.51294 q^{8} +1.69743 q^{9} +O(q^{10})\) \(q-2.55845 q^{2} -2.16736 q^{3} +4.54566 q^{4} +2.09071 q^{5} +5.54507 q^{6} -1.08828 q^{7} -6.51294 q^{8} +1.69743 q^{9} -5.34897 q^{10} -0.572630 q^{11} -9.85206 q^{12} +6.70474 q^{13} +2.78431 q^{14} -4.53131 q^{15} +7.57170 q^{16} +4.32748 q^{17} -4.34279 q^{18} +7.81314 q^{19} +9.50365 q^{20} +2.35870 q^{21} +1.46504 q^{22} -1.00000 q^{23} +14.1158 q^{24} -0.628931 q^{25} -17.1537 q^{26} +2.82313 q^{27} -4.94696 q^{28} +0.377519 q^{29} +11.5931 q^{30} +2.85397 q^{31} -6.34592 q^{32} +1.24109 q^{33} -11.0716 q^{34} -2.27528 q^{35} +7.71594 q^{36} -10.7375 q^{37} -19.9895 q^{38} -14.5315 q^{39} -13.6167 q^{40} +1.13241 q^{41} -6.03460 q^{42} -11.9714 q^{43} -2.60298 q^{44} +3.54883 q^{45} +2.55845 q^{46} +5.19986 q^{47} -16.4106 q^{48} -5.81564 q^{49} +1.60909 q^{50} -9.37918 q^{51} +30.4774 q^{52} -12.3033 q^{53} -7.22284 q^{54} -1.19720 q^{55} +7.08792 q^{56} -16.9339 q^{57} -0.965864 q^{58} +11.8731 q^{59} -20.5978 q^{60} -4.91632 q^{61} -7.30172 q^{62} -1.84728 q^{63} +1.09232 q^{64} +14.0177 q^{65} -3.17527 q^{66} +9.03085 q^{67} +19.6712 q^{68} +2.16736 q^{69} +5.82120 q^{70} -3.28754 q^{71} -11.0553 q^{72} -10.7068 q^{73} +27.4713 q^{74} +1.36312 q^{75} +35.5159 q^{76} +0.623183 q^{77} +37.1782 q^{78} -2.73419 q^{79} +15.8302 q^{80} -11.2110 q^{81} -2.89721 q^{82} -5.15394 q^{83} +10.7218 q^{84} +9.04750 q^{85} +30.6281 q^{86} -0.818219 q^{87} +3.72950 q^{88} +8.87297 q^{89} -9.07951 q^{90} -7.29665 q^{91} -4.54566 q^{92} -6.18556 q^{93} -13.3036 q^{94} +16.3350 q^{95} +13.7539 q^{96} -3.08901 q^{97} +14.8790 q^{98} -0.971999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55845 −1.80910 −0.904548 0.426372i \(-0.859792\pi\)
−0.904548 + 0.426372i \(0.859792\pi\)
\(3\) −2.16736 −1.25132 −0.625662 0.780095i \(-0.715171\pi\)
−0.625662 + 0.780095i \(0.715171\pi\)
\(4\) 4.54566 2.27283
\(5\) 2.09071 0.934994 0.467497 0.883995i \(-0.345156\pi\)
0.467497 + 0.883995i \(0.345156\pi\)
\(6\) 5.54507 2.26376
\(7\) −1.08828 −0.411332 −0.205666 0.978622i \(-0.565936\pi\)
−0.205666 + 0.978622i \(0.565936\pi\)
\(8\) −6.51294 −2.30267
\(9\) 1.69743 0.565810
\(10\) −5.34897 −1.69149
\(11\) −0.572630 −0.172654 −0.0863272 0.996267i \(-0.527513\pi\)
−0.0863272 + 0.996267i \(0.527513\pi\)
\(12\) −9.85206 −2.84404
\(13\) 6.70474 1.85956 0.929780 0.368116i \(-0.119997\pi\)
0.929780 + 0.368116i \(0.119997\pi\)
\(14\) 2.78431 0.744139
\(15\) −4.53131 −1.16998
\(16\) 7.57170 1.89292
\(17\) 4.32748 1.04957 0.524784 0.851236i \(-0.324146\pi\)
0.524784 + 0.851236i \(0.324146\pi\)
\(18\) −4.34279 −1.02360
\(19\) 7.81314 1.79246 0.896229 0.443592i \(-0.146296\pi\)
0.896229 + 0.443592i \(0.146296\pi\)
\(20\) 9.50365 2.12508
\(21\) 2.35870 0.514709
\(22\) 1.46504 0.312348
\(23\) −1.00000 −0.208514
\(24\) 14.1158 2.88139
\(25\) −0.628931 −0.125786
\(26\) −17.1537 −3.36412
\(27\) 2.82313 0.543312
\(28\) −4.94696 −0.934888
\(29\) 0.377519 0.0701036 0.0350518 0.999385i \(-0.488840\pi\)
0.0350518 + 0.999385i \(0.488840\pi\)
\(30\) 11.5931 2.11661
\(31\) 2.85397 0.512587 0.256294 0.966599i \(-0.417499\pi\)
0.256294 + 0.966599i \(0.417499\pi\)
\(32\) −6.34592 −1.12181
\(33\) 1.24109 0.216046
\(34\) −11.0716 −1.89877
\(35\) −2.27528 −0.384593
\(36\) 7.71594 1.28599
\(37\) −10.7375 −1.76523 −0.882615 0.470097i \(-0.844219\pi\)
−0.882615 + 0.470097i \(0.844219\pi\)
\(38\) −19.9895 −3.24273
\(39\) −14.5315 −2.32691
\(40\) −13.6167 −2.15298
\(41\) 1.13241 0.176853 0.0884264 0.996083i \(-0.471816\pi\)
0.0884264 + 0.996083i \(0.471816\pi\)
\(42\) −6.03460 −0.931159
\(43\) −11.9714 −1.82562 −0.912809 0.408387i \(-0.866091\pi\)
−0.912809 + 0.408387i \(0.866091\pi\)
\(44\) −2.60298 −0.392414
\(45\) 3.54883 0.529029
\(46\) 2.55845 0.377223
\(47\) 5.19986 0.758478 0.379239 0.925299i \(-0.376186\pi\)
0.379239 + 0.925299i \(0.376186\pi\)
\(48\) −16.4106 −2.36866
\(49\) −5.81564 −0.830806
\(50\) 1.60909 0.227559
\(51\) −9.37918 −1.31335
\(52\) 30.4774 4.22646
\(53\) −12.3033 −1.68999 −0.844994 0.534776i \(-0.820396\pi\)
−0.844994 + 0.534776i \(0.820396\pi\)
\(54\) −7.22284 −0.982904
\(55\) −1.19720 −0.161431
\(56\) 7.08792 0.947163
\(57\) −16.9339 −2.24294
\(58\) −0.965864 −0.126824
\(59\) 11.8731 1.54575 0.772875 0.634558i \(-0.218818\pi\)
0.772875 + 0.634558i \(0.218818\pi\)
\(60\) −20.5978 −2.65916
\(61\) −4.91632 −0.629471 −0.314735 0.949179i \(-0.601916\pi\)
−0.314735 + 0.949179i \(0.601916\pi\)
\(62\) −7.30172 −0.927320
\(63\) −1.84728 −0.232736
\(64\) 1.09232 0.136540
\(65\) 14.0177 1.73868
\(66\) −3.17527 −0.390849
\(67\) 9.03085 1.10329 0.551647 0.834078i \(-0.314000\pi\)
0.551647 + 0.834078i \(0.314000\pi\)
\(68\) 19.6712 2.38549
\(69\) 2.16736 0.260919
\(70\) 5.82120 0.695766
\(71\) −3.28754 −0.390159 −0.195079 0.980787i \(-0.562496\pi\)
−0.195079 + 0.980787i \(0.562496\pi\)
\(72\) −11.0553 −1.30287
\(73\) −10.7068 −1.25313 −0.626566 0.779368i \(-0.715540\pi\)
−0.626566 + 0.779368i \(0.715540\pi\)
\(74\) 27.4713 3.19347
\(75\) 1.36312 0.157399
\(76\) 35.5159 4.07395
\(77\) 0.623183 0.0710183
\(78\) 37.1782 4.20960
\(79\) −2.73419 −0.307620 −0.153810 0.988100i \(-0.549154\pi\)
−0.153810 + 0.988100i \(0.549154\pi\)
\(80\) 15.8302 1.76987
\(81\) −11.2110 −1.24567
\(82\) −2.89721 −0.319944
\(83\) −5.15394 −0.565718 −0.282859 0.959161i \(-0.591283\pi\)
−0.282859 + 0.959161i \(0.591283\pi\)
\(84\) 10.7218 1.16985
\(85\) 9.04750 0.981339
\(86\) 30.6281 3.30272
\(87\) −0.818219 −0.0877223
\(88\) 3.72950 0.397566
\(89\) 8.87297 0.940533 0.470267 0.882524i \(-0.344158\pi\)
0.470267 + 0.882524i \(0.344158\pi\)
\(90\) −9.07951 −0.957064
\(91\) −7.29665 −0.764897
\(92\) −4.54566 −0.473918
\(93\) −6.18556 −0.641413
\(94\) −13.3036 −1.37216
\(95\) 16.3350 1.67594
\(96\) 13.7539 1.40375
\(97\) −3.08901 −0.313642 −0.156821 0.987627i \(-0.550125\pi\)
−0.156821 + 0.987627i \(0.550125\pi\)
\(98\) 14.8790 1.50301
\(99\) −0.971999 −0.0976895
\(100\) −2.85891 −0.285891
\(101\) −3.85148 −0.383237 −0.191618 0.981470i \(-0.561374\pi\)
−0.191618 + 0.981470i \(0.561374\pi\)
\(102\) 23.9962 2.37597
\(103\) −14.9638 −1.47443 −0.737215 0.675658i \(-0.763860\pi\)
−0.737215 + 0.675658i \(0.763860\pi\)
\(104\) −43.6675 −4.28195
\(105\) 4.93135 0.481250
\(106\) 31.4773 3.05735
\(107\) 3.30099 0.319118 0.159559 0.987188i \(-0.448993\pi\)
0.159559 + 0.987188i \(0.448993\pi\)
\(108\) 12.8330 1.23486
\(109\) −12.7781 −1.22392 −0.611959 0.790890i \(-0.709618\pi\)
−0.611959 + 0.790890i \(0.709618\pi\)
\(110\) 3.06298 0.292044
\(111\) 23.2719 2.20887
\(112\) −8.24014 −0.778620
\(113\) −15.1681 −1.42690 −0.713449 0.700707i \(-0.752868\pi\)
−0.713449 + 0.700707i \(0.752868\pi\)
\(114\) 43.3244 4.05770
\(115\) −2.09071 −0.194960
\(116\) 1.71607 0.159334
\(117\) 11.3808 1.05216
\(118\) −30.3768 −2.79641
\(119\) −4.70952 −0.431721
\(120\) 29.5121 2.69408
\(121\) −10.6721 −0.970190
\(122\) 12.5782 1.13877
\(123\) −2.45434 −0.221300
\(124\) 12.9732 1.16502
\(125\) −11.7685 −1.05260
\(126\) 4.72618 0.421041
\(127\) −0.0914164 −0.00811190 −0.00405595 0.999992i \(-0.501291\pi\)
−0.00405595 + 0.999992i \(0.501291\pi\)
\(128\) 9.89720 0.874797
\(129\) 25.9462 2.28444
\(130\) −35.8635 −3.14543
\(131\) −12.4632 −1.08892 −0.544459 0.838787i \(-0.683265\pi\)
−0.544459 + 0.838787i \(0.683265\pi\)
\(132\) 5.64158 0.491037
\(133\) −8.50291 −0.737296
\(134\) −23.1050 −1.99597
\(135\) 5.90235 0.507994
\(136\) −28.1846 −2.41681
\(137\) −12.0257 −1.02743 −0.513714 0.857962i \(-0.671731\pi\)
−0.513714 + 0.857962i \(0.671731\pi\)
\(138\) −5.54507 −0.472027
\(139\) −19.9830 −1.69494 −0.847470 0.530843i \(-0.821875\pi\)
−0.847470 + 0.530843i \(0.821875\pi\)
\(140\) −10.3427 −0.874114
\(141\) −11.2700 −0.949101
\(142\) 8.41099 0.705835
\(143\) −3.83933 −0.321061
\(144\) 12.8524 1.07103
\(145\) 0.789284 0.0655465
\(146\) 27.3927 2.26704
\(147\) 12.6046 1.03961
\(148\) −48.8089 −4.01206
\(149\) −18.5822 −1.52231 −0.761155 0.648570i \(-0.775368\pi\)
−0.761155 + 0.648570i \(0.775368\pi\)
\(150\) −3.48747 −0.284750
\(151\) −5.46717 −0.444912 −0.222456 0.974943i \(-0.571407\pi\)
−0.222456 + 0.974943i \(0.571407\pi\)
\(152\) −50.8865 −4.12744
\(153\) 7.34559 0.593856
\(154\) −1.59438 −0.128479
\(155\) 5.96682 0.479266
\(156\) −66.0555 −5.28867
\(157\) 10.4416 0.833333 0.416666 0.909059i \(-0.363198\pi\)
0.416666 + 0.909059i \(0.363198\pi\)
\(158\) 6.99528 0.556514
\(159\) 26.6656 2.11472
\(160\) −13.2675 −1.04889
\(161\) 1.08828 0.0857687
\(162\) 28.6828 2.25354
\(163\) −10.9470 −0.857437 −0.428719 0.903438i \(-0.641035\pi\)
−0.428719 + 0.903438i \(0.641035\pi\)
\(164\) 5.14755 0.401956
\(165\) 2.59476 0.202002
\(166\) 13.1861 1.02344
\(167\) 8.40690 0.650546 0.325273 0.945620i \(-0.394544\pi\)
0.325273 + 0.945620i \(0.394544\pi\)
\(168\) −15.3620 −1.18521
\(169\) 31.9535 2.45796
\(170\) −23.1476 −1.77534
\(171\) 13.2623 1.01419
\(172\) −54.4178 −4.14932
\(173\) 8.06123 0.612884 0.306442 0.951889i \(-0.400861\pi\)
0.306442 + 0.951889i \(0.400861\pi\)
\(174\) 2.09337 0.158698
\(175\) 0.684455 0.0517399
\(176\) −4.33578 −0.326822
\(177\) −25.7333 −1.93423
\(178\) −22.7010 −1.70151
\(179\) 18.0151 1.34651 0.673255 0.739410i \(-0.264896\pi\)
0.673255 + 0.739410i \(0.264896\pi\)
\(180\) 16.1318 1.20239
\(181\) −10.1670 −0.755708 −0.377854 0.925865i \(-0.623338\pi\)
−0.377854 + 0.925865i \(0.623338\pi\)
\(182\) 18.6681 1.38377
\(183\) 10.6554 0.787671
\(184\) 6.51294 0.480140
\(185\) −22.4489 −1.65048
\(186\) 15.8254 1.16038
\(187\) −2.47804 −0.181212
\(188\) 23.6368 1.72389
\(189\) −3.07237 −0.223482
\(190\) −41.7923 −3.03193
\(191\) −18.0265 −1.30435 −0.652176 0.758067i \(-0.726144\pi\)
−0.652176 + 0.758067i \(0.726144\pi\)
\(192\) −2.36744 −0.170855
\(193\) −17.4815 −1.25835 −0.629174 0.777264i \(-0.716607\pi\)
−0.629174 + 0.777264i \(0.716607\pi\)
\(194\) 7.90308 0.567408
\(195\) −30.3813 −2.17565
\(196\) −26.4359 −1.88828
\(197\) 2.27470 0.162066 0.0810330 0.996711i \(-0.474178\pi\)
0.0810330 + 0.996711i \(0.474178\pi\)
\(198\) 2.48681 0.176730
\(199\) 16.5889 1.17596 0.587978 0.808877i \(-0.299924\pi\)
0.587978 + 0.808877i \(0.299924\pi\)
\(200\) 4.09619 0.289644
\(201\) −19.5731 −1.38058
\(202\) 9.85381 0.693312
\(203\) −0.410848 −0.0288359
\(204\) −42.6346 −2.98502
\(205\) 2.36754 0.165356
\(206\) 38.2842 2.66739
\(207\) −1.69743 −0.117980
\(208\) 50.7662 3.52000
\(209\) −4.47404 −0.309476
\(210\) −12.6166 −0.870628
\(211\) 0.486380 0.0334838 0.0167419 0.999860i \(-0.494671\pi\)
0.0167419 + 0.999860i \(0.494671\pi\)
\(212\) −55.9266 −3.84105
\(213\) 7.12526 0.488215
\(214\) −8.44540 −0.577316
\(215\) −25.0287 −1.70694
\(216\) −18.3869 −1.25107
\(217\) −3.10592 −0.210844
\(218\) 32.6920 2.21418
\(219\) 23.2054 1.56807
\(220\) −5.44208 −0.366905
\(221\) 29.0146 1.95173
\(222\) −59.5400 −3.99606
\(223\) −13.9279 −0.932683 −0.466342 0.884605i \(-0.654428\pi\)
−0.466342 + 0.884605i \(0.654428\pi\)
\(224\) 6.90615 0.461437
\(225\) −1.06757 −0.0711711
\(226\) 38.8069 2.58140
\(227\) −4.44523 −0.295040 −0.147520 0.989059i \(-0.547129\pi\)
−0.147520 + 0.989059i \(0.547129\pi\)
\(228\) −76.9755 −5.09783
\(229\) 20.0929 1.32777 0.663887 0.747833i \(-0.268906\pi\)
0.663887 + 0.747833i \(0.268906\pi\)
\(230\) 5.34897 0.352701
\(231\) −1.35066 −0.0888668
\(232\) −2.45876 −0.161426
\(233\) 21.3391 1.39797 0.698986 0.715136i \(-0.253635\pi\)
0.698986 + 0.715136i \(0.253635\pi\)
\(234\) −29.1172 −1.90345
\(235\) 10.8714 0.709172
\(236\) 53.9712 3.51323
\(237\) 5.92595 0.384932
\(238\) 12.0491 0.781025
\(239\) 17.5715 1.13661 0.568303 0.822819i \(-0.307600\pi\)
0.568303 + 0.822819i \(0.307600\pi\)
\(240\) −34.3097 −2.21468
\(241\) −0.237506 −0.0152991 −0.00764957 0.999971i \(-0.502435\pi\)
−0.00764957 + 0.999971i \(0.502435\pi\)
\(242\) 27.3040 1.75517
\(243\) 15.8289 1.01542
\(244\) −22.3479 −1.43068
\(245\) −12.1588 −0.776798
\(246\) 6.27929 0.400353
\(247\) 52.3851 3.33318
\(248\) −18.5877 −1.18032
\(249\) 11.1704 0.707896
\(250\) 30.1090 1.90426
\(251\) 4.70249 0.296819 0.148409 0.988926i \(-0.452585\pi\)
0.148409 + 0.988926i \(0.452585\pi\)
\(252\) −8.39712 −0.528969
\(253\) 0.572630 0.0360009
\(254\) 0.233884 0.0146752
\(255\) −19.6092 −1.22797
\(256\) −27.5061 −1.71913
\(257\) 4.32883 0.270025 0.135012 0.990844i \(-0.456893\pi\)
0.135012 + 0.990844i \(0.456893\pi\)
\(258\) −66.3821 −4.13277
\(259\) 11.6854 0.726095
\(260\) 63.7195 3.95172
\(261\) 0.640813 0.0396653
\(262\) 31.8866 1.96996
\(263\) −7.77504 −0.479429 −0.239715 0.970843i \(-0.577054\pi\)
−0.239715 + 0.970843i \(0.577054\pi\)
\(264\) −8.08315 −0.497484
\(265\) −25.7226 −1.58013
\(266\) 21.7543 1.33384
\(267\) −19.2309 −1.17691
\(268\) 41.0512 2.50760
\(269\) −30.9948 −1.88978 −0.944892 0.327383i \(-0.893833\pi\)
−0.944892 + 0.327383i \(0.893833\pi\)
\(270\) −15.1009 −0.919009
\(271\) 14.8952 0.904821 0.452410 0.891810i \(-0.350564\pi\)
0.452410 + 0.891810i \(0.350564\pi\)
\(272\) 32.7663 1.98675
\(273\) 15.8144 0.957133
\(274\) 30.7672 1.85872
\(275\) 0.360145 0.0217175
\(276\) 9.85206 0.593024
\(277\) −15.2531 −0.916468 −0.458234 0.888832i \(-0.651518\pi\)
−0.458234 + 0.888832i \(0.651518\pi\)
\(278\) 51.1256 3.06631
\(279\) 4.84441 0.290027
\(280\) 14.8188 0.885591
\(281\) 7.74032 0.461749 0.230874 0.972984i \(-0.425841\pi\)
0.230874 + 0.972984i \(0.425841\pi\)
\(282\) 28.8336 1.71702
\(283\) −27.5054 −1.63503 −0.817513 0.575910i \(-0.804648\pi\)
−0.817513 + 0.575910i \(0.804648\pi\)
\(284\) −14.9440 −0.886764
\(285\) −35.4038 −2.09714
\(286\) 9.82273 0.580830
\(287\) −1.23238 −0.0727453
\(288\) −10.7717 −0.634731
\(289\) 1.72706 0.101592
\(290\) −2.01934 −0.118580
\(291\) 6.69499 0.392467
\(292\) −48.6693 −2.84816
\(293\) −12.0116 −0.701726 −0.350863 0.936427i \(-0.614112\pi\)
−0.350863 + 0.936427i \(0.614112\pi\)
\(294\) −32.2481 −1.88075
\(295\) 24.8233 1.44527
\(296\) 69.9325 4.06474
\(297\) −1.61661 −0.0938052
\(298\) 47.5415 2.75401
\(299\) −6.70474 −0.387745
\(300\) 6.19627 0.357742
\(301\) 13.0282 0.750935
\(302\) 13.9875 0.804888
\(303\) 8.34753 0.479553
\(304\) 59.1587 3.39299
\(305\) −10.2786 −0.588551
\(306\) −18.7933 −1.07434
\(307\) −8.23444 −0.469965 −0.234982 0.972000i \(-0.575503\pi\)
−0.234982 + 0.972000i \(0.575503\pi\)
\(308\) 2.83278 0.161412
\(309\) 32.4320 1.84499
\(310\) −15.2658 −0.867039
\(311\) −6.20525 −0.351868 −0.175934 0.984402i \(-0.556294\pi\)
−0.175934 + 0.984402i \(0.556294\pi\)
\(312\) 94.6431 5.35811
\(313\) −11.6970 −0.661153 −0.330576 0.943779i \(-0.607243\pi\)
−0.330576 + 0.943779i \(0.607243\pi\)
\(314\) −26.7144 −1.50758
\(315\) −3.86213 −0.217607
\(316\) −12.4287 −0.699168
\(317\) 9.01989 0.506608 0.253304 0.967387i \(-0.418483\pi\)
0.253304 + 0.967387i \(0.418483\pi\)
\(318\) −68.2226 −3.82573
\(319\) −0.216179 −0.0121037
\(320\) 2.28372 0.127664
\(321\) −7.15441 −0.399320
\(322\) −2.78431 −0.155164
\(323\) 33.8112 1.88131
\(324\) −50.9615 −2.83119
\(325\) −4.21682 −0.233907
\(326\) 28.0074 1.55119
\(327\) 27.6946 1.53152
\(328\) −7.37532 −0.407234
\(329\) −5.65892 −0.311986
\(330\) −6.63857 −0.365441
\(331\) 27.3403 1.50276 0.751379 0.659871i \(-0.229389\pi\)
0.751379 + 0.659871i \(0.229389\pi\)
\(332\) −23.4280 −1.28578
\(333\) −18.2261 −0.998784
\(334\) −21.5086 −1.17690
\(335\) 18.8809 1.03157
\(336\) 17.8593 0.974306
\(337\) −33.8605 −1.84450 −0.922250 0.386595i \(-0.873651\pi\)
−0.922250 + 0.386595i \(0.873651\pi\)
\(338\) −81.7514 −4.44669
\(339\) 32.8747 1.78551
\(340\) 41.1269 2.23042
\(341\) −1.63427 −0.0885005
\(342\) −33.9308 −1.83477
\(343\) 13.9470 0.753069
\(344\) 77.9688 4.20380
\(345\) 4.53131 0.243958
\(346\) −20.6242 −1.10877
\(347\) 1.64263 0.0881809 0.0440904 0.999028i \(-0.485961\pi\)
0.0440904 + 0.999028i \(0.485961\pi\)
\(348\) −3.71934 −0.199378
\(349\) −1.00000 −0.0535288
\(350\) −1.75114 −0.0936025
\(351\) 18.9284 1.01032
\(352\) 3.63386 0.193685
\(353\) 2.92348 0.155601 0.0778004 0.996969i \(-0.475210\pi\)
0.0778004 + 0.996969i \(0.475210\pi\)
\(354\) 65.8373 3.49921
\(355\) −6.87328 −0.364796
\(356\) 40.3335 2.13767
\(357\) 10.2072 0.540222
\(358\) −46.0906 −2.43597
\(359\) −17.8603 −0.942631 −0.471316 0.881965i \(-0.656221\pi\)
−0.471316 + 0.881965i \(0.656221\pi\)
\(360\) −23.1133 −1.21818
\(361\) 42.0452 2.21291
\(362\) 26.0118 1.36715
\(363\) 23.1302 1.21402
\(364\) −33.1681 −1.73848
\(365\) −22.3848 −1.17167
\(366\) −27.2613 −1.42497
\(367\) −18.0746 −0.943489 −0.471744 0.881735i \(-0.656375\pi\)
−0.471744 + 0.881735i \(0.656375\pi\)
\(368\) −7.57170 −0.394702
\(369\) 1.92219 0.100065
\(370\) 57.4344 2.98587
\(371\) 13.3895 0.695146
\(372\) −28.1174 −1.45782
\(373\) −33.4792 −1.73349 −0.866745 0.498752i \(-0.833792\pi\)
−0.866745 + 0.498752i \(0.833792\pi\)
\(374\) 6.33994 0.327831
\(375\) 25.5064 1.31715
\(376\) −33.8664 −1.74653
\(377\) 2.53117 0.130362
\(378\) 7.86049 0.404300
\(379\) 32.9058 1.69026 0.845130 0.534561i \(-0.179523\pi\)
0.845130 + 0.534561i \(0.179523\pi\)
\(380\) 74.2534 3.80912
\(381\) 0.198132 0.0101506
\(382\) 46.1199 2.35970
\(383\) −32.9753 −1.68496 −0.842479 0.538730i \(-0.818904\pi\)
−0.842479 + 0.538730i \(0.818904\pi\)
\(384\) −21.4508 −1.09465
\(385\) 1.30289 0.0664017
\(386\) 44.7256 2.27647
\(387\) −20.3206 −1.03295
\(388\) −14.0416 −0.712854
\(389\) 27.3377 1.38608 0.693038 0.720901i \(-0.256272\pi\)
0.693038 + 0.720901i \(0.256272\pi\)
\(390\) 77.7289 3.93596
\(391\) −4.32748 −0.218850
\(392\) 37.8769 1.91307
\(393\) 27.0123 1.36259
\(394\) −5.81971 −0.293193
\(395\) −5.71639 −0.287623
\(396\) −4.41837 −0.222032
\(397\) −2.63299 −0.132146 −0.0660730 0.997815i \(-0.521047\pi\)
−0.0660730 + 0.997815i \(0.521047\pi\)
\(398\) −42.4418 −2.12742
\(399\) 18.4288 0.922595
\(400\) −4.76208 −0.238104
\(401\) −7.71959 −0.385498 −0.192749 0.981248i \(-0.561740\pi\)
−0.192749 + 0.981248i \(0.561740\pi\)
\(402\) 50.0767 2.49760
\(403\) 19.1351 0.953187
\(404\) −17.5075 −0.871031
\(405\) −23.4390 −1.16469
\(406\) 1.05113 0.0521669
\(407\) 6.14859 0.304775
\(408\) 61.0860 3.02421
\(409\) 6.19025 0.306088 0.153044 0.988219i \(-0.451092\pi\)
0.153044 + 0.988219i \(0.451092\pi\)
\(410\) −6.05723 −0.299146
\(411\) 26.0640 1.28564
\(412\) −68.0205 −3.35113
\(413\) −12.9213 −0.635817
\(414\) 4.34279 0.213436
\(415\) −10.7754 −0.528943
\(416\) −42.5477 −2.08607
\(417\) 43.3104 2.12092
\(418\) 11.4466 0.559871
\(419\) 0.119648 0.00584518 0.00292259 0.999996i \(-0.499070\pi\)
0.00292259 + 0.999996i \(0.499070\pi\)
\(420\) 22.4162 1.09380
\(421\) 35.3432 1.72252 0.861260 0.508165i \(-0.169676\pi\)
0.861260 + 0.508165i \(0.169676\pi\)
\(422\) −1.24438 −0.0605753
\(423\) 8.82640 0.429154
\(424\) 80.1306 3.89149
\(425\) −2.72169 −0.132021
\(426\) −18.2296 −0.883227
\(427\) 5.35035 0.258922
\(428\) 15.0052 0.725302
\(429\) 8.32120 0.401751
\(430\) 64.0346 3.08802
\(431\) −35.4439 −1.70727 −0.853636 0.520870i \(-0.825608\pi\)
−0.853636 + 0.520870i \(0.825608\pi\)
\(432\) 21.3759 1.02845
\(433\) −31.0338 −1.49139 −0.745694 0.666289i \(-0.767882\pi\)
−0.745694 + 0.666289i \(0.767882\pi\)
\(434\) 7.94634 0.381437
\(435\) −1.71066 −0.0820198
\(436\) −58.0848 −2.78176
\(437\) −7.81314 −0.373753
\(438\) −59.3698 −2.83680
\(439\) 12.8352 0.612590 0.306295 0.951937i \(-0.400911\pi\)
0.306295 + 0.951937i \(0.400911\pi\)
\(440\) 7.79731 0.371722
\(441\) −9.87164 −0.470078
\(442\) −74.2324 −3.53087
\(443\) 40.8922 1.94285 0.971424 0.237351i \(-0.0762791\pi\)
0.971424 + 0.237351i \(0.0762791\pi\)
\(444\) 105.786 5.02039
\(445\) 18.5508 0.879393
\(446\) 35.6339 1.68731
\(447\) 40.2742 1.90490
\(448\) −1.18875 −0.0561631
\(449\) −15.8681 −0.748863 −0.374432 0.927255i \(-0.622162\pi\)
−0.374432 + 0.927255i \(0.622162\pi\)
\(450\) 2.73131 0.128755
\(451\) −0.648452 −0.0305344
\(452\) −68.9492 −3.24310
\(453\) 11.8493 0.556728
\(454\) 11.3729 0.533756
\(455\) −15.2552 −0.715174
\(456\) 110.289 5.16476
\(457\) −6.44894 −0.301669 −0.150834 0.988559i \(-0.548196\pi\)
−0.150834 + 0.988559i \(0.548196\pi\)
\(458\) −51.4065 −2.40207
\(459\) 12.2170 0.570243
\(460\) −9.50365 −0.443110
\(461\) 26.6938 1.24326 0.621628 0.783313i \(-0.286472\pi\)
0.621628 + 0.783313i \(0.286472\pi\)
\(462\) 3.45559 0.160769
\(463\) 24.0380 1.11714 0.558570 0.829457i \(-0.311350\pi\)
0.558570 + 0.829457i \(0.311350\pi\)
\(464\) 2.85846 0.132701
\(465\) −12.9322 −0.599717
\(466\) −54.5950 −2.52906
\(467\) −3.66311 −0.169509 −0.0847543 0.996402i \(-0.527011\pi\)
−0.0847543 + 0.996402i \(0.527011\pi\)
\(468\) 51.7333 2.39137
\(469\) −9.82812 −0.453820
\(470\) −27.8139 −1.28296
\(471\) −22.6307 −1.04277
\(472\) −77.3290 −3.55935
\(473\) 6.85517 0.315201
\(474\) −15.1612 −0.696379
\(475\) −4.91393 −0.225467
\(476\) −21.4079 −0.981228
\(477\) −20.8840 −0.956212
\(478\) −44.9558 −2.05623
\(479\) 34.5023 1.57645 0.788224 0.615388i \(-0.211001\pi\)
0.788224 + 0.615388i \(0.211001\pi\)
\(480\) 28.7553 1.31250
\(481\) −71.9919 −3.28255
\(482\) 0.607648 0.0276776
\(483\) −2.35870 −0.107324
\(484\) −48.5117 −2.20508
\(485\) −6.45823 −0.293253
\(486\) −40.4973 −1.83700
\(487\) −38.9746 −1.76611 −0.883054 0.469272i \(-0.844516\pi\)
−0.883054 + 0.469272i \(0.844516\pi\)
\(488\) 32.0197 1.44946
\(489\) 23.7261 1.07293
\(490\) 31.1077 1.40530
\(491\) 30.1341 1.35993 0.679966 0.733244i \(-0.261994\pi\)
0.679966 + 0.733244i \(0.261994\pi\)
\(492\) −11.1566 −0.502977
\(493\) 1.63371 0.0735785
\(494\) −134.025 −6.03005
\(495\) −2.03217 −0.0913391
\(496\) 21.6094 0.970289
\(497\) 3.57777 0.160485
\(498\) −28.5789 −1.28065
\(499\) −6.41075 −0.286985 −0.143492 0.989651i \(-0.545833\pi\)
−0.143492 + 0.989651i \(0.545833\pi\)
\(500\) −53.4954 −2.39239
\(501\) −18.2207 −0.814043
\(502\) −12.0311 −0.536973
\(503\) −8.29640 −0.369918 −0.184959 0.982746i \(-0.559215\pi\)
−0.184959 + 0.982746i \(0.559215\pi\)
\(504\) 12.0312 0.535914
\(505\) −8.05233 −0.358324
\(506\) −1.46504 −0.0651291
\(507\) −69.2546 −3.07571
\(508\) −0.415548 −0.0184370
\(509\) −1.52084 −0.0674099 −0.0337050 0.999432i \(-0.510731\pi\)
−0.0337050 + 0.999432i \(0.510731\pi\)
\(510\) 50.1690 2.22152
\(511\) 11.6520 0.515454
\(512\) 50.5786 2.23528
\(513\) 22.0575 0.973864
\(514\) −11.0751 −0.488501
\(515\) −31.2850 −1.37858
\(516\) 117.943 5.19214
\(517\) −2.97760 −0.130955
\(518\) −29.8965 −1.31358
\(519\) −17.4715 −0.766916
\(520\) −91.2961 −4.00360
\(521\) −2.10526 −0.0922333 −0.0461166 0.998936i \(-0.514685\pi\)
−0.0461166 + 0.998936i \(0.514685\pi\)
\(522\) −1.63949 −0.0717584
\(523\) 27.1481 1.18710 0.593552 0.804796i \(-0.297725\pi\)
0.593552 + 0.804796i \(0.297725\pi\)
\(524\) −56.6537 −2.47493
\(525\) −1.48346 −0.0647434
\(526\) 19.8920 0.867334
\(527\) 12.3505 0.537995
\(528\) 9.39717 0.408959
\(529\) 1.00000 0.0434783
\(530\) 65.8100 2.85860
\(531\) 20.1538 0.874601
\(532\) −38.6513 −1.67575
\(533\) 7.59252 0.328868
\(534\) 49.2012 2.12915
\(535\) 6.90141 0.298374
\(536\) −58.8174 −2.54052
\(537\) −39.0451 −1.68492
\(538\) 79.2985 3.41880
\(539\) 3.33021 0.143442
\(540\) 26.8301 1.15458
\(541\) 13.6886 0.588519 0.294259 0.955726i \(-0.404927\pi\)
0.294259 + 0.955726i \(0.404927\pi\)
\(542\) −38.1087 −1.63691
\(543\) 22.0355 0.945635
\(544\) −27.4618 −1.17742
\(545\) −26.7152 −1.14436
\(546\) −40.4604 −1.73155
\(547\) 18.2783 0.781522 0.390761 0.920492i \(-0.372212\pi\)
0.390761 + 0.920492i \(0.372212\pi\)
\(548\) −54.6649 −2.33517
\(549\) −8.34511 −0.356161
\(550\) −0.921412 −0.0392891
\(551\) 2.94961 0.125658
\(552\) −14.1158 −0.600810
\(553\) 2.97557 0.126534
\(554\) 39.0242 1.65798
\(555\) 48.6548 2.06528
\(556\) −90.8361 −3.85231
\(557\) −27.5191 −1.16602 −0.583010 0.812465i \(-0.698125\pi\)
−0.583010 + 0.812465i \(0.698125\pi\)
\(558\) −12.3942 −0.524687
\(559\) −80.2649 −3.39485
\(560\) −17.2278 −0.728005
\(561\) 5.37080 0.226755
\(562\) −19.8032 −0.835348
\(563\) 2.09577 0.0883262 0.0441631 0.999024i \(-0.485938\pi\)
0.0441631 + 0.999024i \(0.485938\pi\)
\(564\) −51.2294 −2.15714
\(565\) −31.7122 −1.33414
\(566\) 70.3712 2.95792
\(567\) 12.2008 0.512384
\(568\) 21.4115 0.898407
\(569\) −14.4176 −0.604417 −0.302208 0.953242i \(-0.597724\pi\)
−0.302208 + 0.953242i \(0.597724\pi\)
\(570\) 90.5788 3.79393
\(571\) −16.6303 −0.695954 −0.347977 0.937503i \(-0.613131\pi\)
−0.347977 + 0.937503i \(0.613131\pi\)
\(572\) −17.4523 −0.729717
\(573\) 39.0699 1.63217
\(574\) 3.15299 0.131603
\(575\) 0.628931 0.0262282
\(576\) 1.85413 0.0772554
\(577\) 44.5377 1.85413 0.927064 0.374904i \(-0.122324\pi\)
0.927064 + 0.374904i \(0.122324\pi\)
\(578\) −4.41860 −0.183790
\(579\) 37.8887 1.57460
\(580\) 3.58781 0.148976
\(581\) 5.60894 0.232698
\(582\) −17.1288 −0.710011
\(583\) 7.04523 0.291784
\(584\) 69.7325 2.88555
\(585\) 23.7940 0.983761
\(586\) 30.7311 1.26949
\(587\) 39.7683 1.64142 0.820708 0.571348i \(-0.193579\pi\)
0.820708 + 0.571348i \(0.193579\pi\)
\(588\) 57.2960 2.36285
\(589\) 22.2984 0.918791
\(590\) −63.5091 −2.61463
\(591\) −4.93009 −0.202797
\(592\) −81.3008 −3.34144
\(593\) 33.6019 1.37987 0.689933 0.723874i \(-0.257640\pi\)
0.689933 + 0.723874i \(0.257640\pi\)
\(594\) 4.13601 0.169703
\(595\) −9.84624 −0.403656
\(596\) −84.4682 −3.45995
\(597\) −35.9540 −1.47150
\(598\) 17.1537 0.701468
\(599\) −17.6751 −0.722186 −0.361093 0.932530i \(-0.617596\pi\)
−0.361093 + 0.932530i \(0.617596\pi\)
\(600\) −8.87790 −0.362439
\(601\) −4.34564 −0.177262 −0.0886311 0.996065i \(-0.528249\pi\)
−0.0886311 + 0.996065i \(0.528249\pi\)
\(602\) −33.3321 −1.35851
\(603\) 15.3292 0.624255
\(604\) −24.8519 −1.01121
\(605\) −22.3123 −0.907122
\(606\) −21.3567 −0.867557
\(607\) −17.5745 −0.713329 −0.356664 0.934233i \(-0.616086\pi\)
−0.356664 + 0.934233i \(0.616086\pi\)
\(608\) −49.5816 −2.01080
\(609\) 0.890453 0.0360830
\(610\) 26.2973 1.06475
\(611\) 34.8637 1.41044
\(612\) 33.3905 1.34973
\(613\) −6.27729 −0.253538 −0.126769 0.991932i \(-0.540461\pi\)
−0.126769 + 0.991932i \(0.540461\pi\)
\(614\) 21.0674 0.850211
\(615\) −5.13131 −0.206914
\(616\) −4.05875 −0.163532
\(617\) 27.3866 1.10254 0.551272 0.834326i \(-0.314143\pi\)
0.551272 + 0.834326i \(0.314143\pi\)
\(618\) −82.9755 −3.33776
\(619\) 17.5376 0.704897 0.352449 0.935831i \(-0.385349\pi\)
0.352449 + 0.935831i \(0.385349\pi\)
\(620\) 27.1231 1.08929
\(621\) −2.82313 −0.113288
\(622\) 15.8758 0.636562
\(623\) −9.65630 −0.386871
\(624\) −110.028 −4.40466
\(625\) −21.4598 −0.858392
\(626\) 29.9261 1.19609
\(627\) 9.69683 0.387254
\(628\) 47.4641 1.89402
\(629\) −46.4662 −1.85273
\(630\) 9.88107 0.393671
\(631\) 47.8209 1.90372 0.951859 0.306535i \(-0.0991695\pi\)
0.951859 + 0.306535i \(0.0991695\pi\)
\(632\) 17.8076 0.708348
\(633\) −1.05416 −0.0418990
\(634\) −23.0769 −0.916502
\(635\) −0.191125 −0.00758458
\(636\) 121.213 4.80640
\(637\) −38.9923 −1.54493
\(638\) 0.553083 0.0218967
\(639\) −5.58036 −0.220756
\(640\) 20.6922 0.817930
\(641\) −10.1589 −0.401251 −0.200626 0.979668i \(-0.564297\pi\)
−0.200626 + 0.979668i \(0.564297\pi\)
\(642\) 18.3042 0.722409
\(643\) 16.9046 0.666651 0.333326 0.942812i \(-0.391829\pi\)
0.333326 + 0.942812i \(0.391829\pi\)
\(644\) 4.94696 0.194938
\(645\) 54.2460 2.13594
\(646\) −86.5042 −3.40346
\(647\) 15.7257 0.618242 0.309121 0.951023i \(-0.399965\pi\)
0.309121 + 0.951023i \(0.399965\pi\)
\(648\) 73.0167 2.86837
\(649\) −6.79891 −0.266880
\(650\) 10.7885 0.423160
\(651\) 6.73164 0.263834
\(652\) −49.7614 −1.94881
\(653\) −32.5049 −1.27202 −0.636008 0.771683i \(-0.719415\pi\)
−0.636008 + 0.771683i \(0.719415\pi\)
\(654\) −70.8553 −2.77066
\(655\) −26.0570 −1.01813
\(656\) 8.57427 0.334769
\(657\) −18.1740 −0.709035
\(658\) 14.4781 0.564413
\(659\) −12.7285 −0.495833 −0.247917 0.968781i \(-0.579746\pi\)
−0.247917 + 0.968781i \(0.579746\pi\)
\(660\) 11.7949 0.459116
\(661\) −15.7884 −0.614097 −0.307048 0.951694i \(-0.599341\pi\)
−0.307048 + 0.951694i \(0.599341\pi\)
\(662\) −69.9487 −2.71863
\(663\) −62.8850 −2.44225
\(664\) 33.5673 1.30266
\(665\) −17.7771 −0.689367
\(666\) 46.6305 1.80690
\(667\) −0.377519 −0.0146176
\(668\) 38.2149 1.47858
\(669\) 30.1868 1.16709
\(670\) −48.3058 −1.86622
\(671\) 2.81523 0.108681
\(672\) −14.9681 −0.577407
\(673\) −14.1982 −0.547299 −0.273649 0.961830i \(-0.588231\pi\)
−0.273649 + 0.961830i \(0.588231\pi\)
\(674\) 86.6304 3.33688
\(675\) −1.77556 −0.0683412
\(676\) 145.250 5.58653
\(677\) −3.23792 −0.124443 −0.0622216 0.998062i \(-0.519819\pi\)
−0.0622216 + 0.998062i \(0.519819\pi\)
\(678\) −84.1083 −3.23016
\(679\) 3.36172 0.129011
\(680\) −58.9258 −2.25970
\(681\) 9.63439 0.369190
\(682\) 4.18118 0.160106
\(683\) −10.9123 −0.417547 −0.208774 0.977964i \(-0.566947\pi\)
−0.208774 + 0.977964i \(0.566947\pi\)
\(684\) 60.2857 2.30508
\(685\) −25.1423 −0.960638
\(686\) −35.6828 −1.36237
\(687\) −43.5484 −1.66147
\(688\) −90.6436 −3.45576
\(689\) −82.4904 −3.14263
\(690\) −11.5931 −0.441343
\(691\) 26.7202 1.01648 0.508242 0.861214i \(-0.330296\pi\)
0.508242 + 0.861214i \(0.330296\pi\)
\(692\) 36.6436 1.39298
\(693\) 1.05781 0.0401828
\(694\) −4.20258 −0.159528
\(695\) −41.7788 −1.58476
\(696\) 5.32901 0.201996
\(697\) 4.90048 0.185619
\(698\) 2.55845 0.0968387
\(699\) −46.2494 −1.74931
\(700\) 3.11130 0.117596
\(701\) 11.4647 0.433018 0.216509 0.976281i \(-0.430533\pi\)
0.216509 + 0.976281i \(0.430533\pi\)
\(702\) −48.4273 −1.82777
\(703\) −83.8934 −3.16410
\(704\) −0.625493 −0.0235741
\(705\) −23.5622 −0.887404
\(706\) −7.47956 −0.281497
\(707\) 4.19150 0.157638
\(708\) −116.975 −4.39618
\(709\) 32.2851 1.21249 0.606247 0.795277i \(-0.292674\pi\)
0.606247 + 0.795277i \(0.292674\pi\)
\(710\) 17.5849 0.659951
\(711\) −4.64109 −0.174054
\(712\) −57.7891 −2.16574
\(713\) −2.85397 −0.106882
\(714\) −26.1146 −0.977314
\(715\) −8.02693 −0.300190
\(716\) 81.8904 3.06039
\(717\) −38.0837 −1.42226
\(718\) 45.6947 1.70531
\(719\) −35.0346 −1.30657 −0.653285 0.757112i \(-0.726609\pi\)
−0.653285 + 0.757112i \(0.726609\pi\)
\(720\) 26.8707 1.00141
\(721\) 16.2849 0.606481
\(722\) −107.570 −4.00336
\(723\) 0.514761 0.0191442
\(724\) −46.2157 −1.71759
\(725\) −0.237434 −0.00881807
\(726\) −59.1775 −2.19628
\(727\) −34.0891 −1.26430 −0.632148 0.774848i \(-0.717827\pi\)
−0.632148 + 0.774848i \(0.717827\pi\)
\(728\) 47.5226 1.76131
\(729\) −0.673720 −0.0249526
\(730\) 57.2702 2.11967
\(731\) −51.8059 −1.91611
\(732\) 48.4359 1.79024
\(733\) 49.8656 1.84183 0.920914 0.389765i \(-0.127444\pi\)
0.920914 + 0.389765i \(0.127444\pi\)
\(734\) 46.2430 1.70686
\(735\) 26.3525 0.972026
\(736\) 6.34592 0.233914
\(737\) −5.17134 −0.190489
\(738\) −4.91782 −0.181027
\(739\) −6.61721 −0.243418 −0.121709 0.992566i \(-0.538837\pi\)
−0.121709 + 0.992566i \(0.538837\pi\)
\(740\) −102.045 −3.75126
\(741\) −113.537 −4.17089
\(742\) −34.2563 −1.25759
\(743\) 43.9946 1.61401 0.807003 0.590547i \(-0.201088\pi\)
0.807003 + 0.590547i \(0.201088\pi\)
\(744\) 40.2861 1.47696
\(745\) −38.8499 −1.42335
\(746\) 85.6549 3.13605
\(747\) −8.74844 −0.320089
\(748\) −11.2643 −0.411865
\(749\) −3.59241 −0.131264
\(750\) −65.2569 −2.38285
\(751\) −30.3461 −1.10734 −0.553672 0.832735i \(-0.686774\pi\)
−0.553672 + 0.832735i \(0.686774\pi\)
\(752\) 39.3718 1.43574
\(753\) −10.1920 −0.371416
\(754\) −6.47587 −0.235837
\(755\) −11.4303 −0.415990
\(756\) −13.9659 −0.507936
\(757\) −22.1165 −0.803839 −0.401919 0.915675i \(-0.631657\pi\)
−0.401919 + 0.915675i \(0.631657\pi\)
\(758\) −84.1879 −3.05784
\(759\) −1.24109 −0.0450488
\(760\) −106.389 −3.85913
\(761\) 50.4559 1.82902 0.914512 0.404559i \(-0.132575\pi\)
0.914512 + 0.404559i \(0.132575\pi\)
\(762\) −0.506910 −0.0183634
\(763\) 13.9062 0.503437
\(764\) −81.9424 −2.96457
\(765\) 15.3575 0.555251
\(766\) 84.3655 3.04825
\(767\) 79.6062 2.87441
\(768\) 59.6155 2.15119
\(769\) −40.6203 −1.46481 −0.732403 0.680871i \(-0.761601\pi\)
−0.732403 + 0.680871i \(0.761601\pi\)
\(770\) −3.33339 −0.120127
\(771\) −9.38211 −0.337888
\(772\) −79.4651 −2.86001
\(773\) −0.554639 −0.0199490 −0.00997448 0.999950i \(-0.503175\pi\)
−0.00997448 + 0.999950i \(0.503175\pi\)
\(774\) 51.9891 1.86871
\(775\) −1.79495 −0.0644764
\(776\) 20.1185 0.722214
\(777\) −25.3264 −0.908580
\(778\) −69.9421 −2.50755
\(779\) 8.84769 0.317001
\(780\) −138.103 −4.94487
\(781\) 1.88254 0.0673626
\(782\) 11.0716 0.395921
\(783\) 1.06579 0.0380881
\(784\) −44.0343 −1.57265
\(785\) 21.8304 0.779161
\(786\) −69.1095 −2.46506
\(787\) −39.8718 −1.42128 −0.710638 0.703558i \(-0.751593\pi\)
−0.710638 + 0.703558i \(0.751593\pi\)
\(788\) 10.3400 0.368348
\(789\) 16.8513 0.599921
\(790\) 14.6251 0.520338
\(791\) 16.5072 0.586929
\(792\) 6.33057 0.224947
\(793\) −32.9627 −1.17054
\(794\) 6.73637 0.239065
\(795\) 55.7501 1.97725
\(796\) 75.4075 2.67275
\(797\) −23.7275 −0.840471 −0.420235 0.907415i \(-0.638052\pi\)
−0.420235 + 0.907415i \(0.638052\pi\)
\(798\) −47.1492 −1.66906
\(799\) 22.5023 0.796074
\(800\) 3.99115 0.141108
\(801\) 15.0612 0.532163
\(802\) 19.7502 0.697403
\(803\) 6.13101 0.216359
\(804\) −88.9725 −3.13782
\(805\) 2.27528 0.0801932
\(806\) −48.9561 −1.72441
\(807\) 67.1767 2.36473
\(808\) 25.0844 0.882468
\(809\) −7.46657 −0.262510 −0.131255 0.991349i \(-0.541901\pi\)
−0.131255 + 0.991349i \(0.541901\pi\)
\(810\) 59.9675 2.10704
\(811\) −1.86543 −0.0655042 −0.0327521 0.999464i \(-0.510427\pi\)
−0.0327521 + 0.999464i \(0.510427\pi\)
\(812\) −1.86757 −0.0655390
\(813\) −32.2833 −1.13222
\(814\) −15.7309 −0.551366
\(815\) −22.8871 −0.801699
\(816\) −71.0163 −2.48607
\(817\) −93.5341 −3.27234
\(818\) −15.8374 −0.553743
\(819\) −12.3855 −0.432786
\(820\) 10.7620 0.375827
\(821\) −8.91557 −0.311156 −0.155578 0.987824i \(-0.549724\pi\)
−0.155578 + 0.987824i \(0.549724\pi\)
\(822\) −66.6835 −2.32585
\(823\) −29.1497 −1.01609 −0.508047 0.861329i \(-0.669632\pi\)
−0.508047 + 0.861329i \(0.669632\pi\)
\(824\) 97.4585 3.39513
\(825\) −0.780562 −0.0271757
\(826\) 33.0585 1.15025
\(827\) −26.8507 −0.933692 −0.466846 0.884339i \(-0.654610\pi\)
−0.466846 + 0.884339i \(0.654610\pi\)
\(828\) −7.71594 −0.268147
\(829\) 0.0673933 0.00234067 0.00117033 0.999999i \(-0.499627\pi\)
0.00117033 + 0.999999i \(0.499627\pi\)
\(830\) 27.5683 0.956909
\(831\) 33.0588 1.14680
\(832\) 7.32369 0.253903
\(833\) −25.1671 −0.871987
\(834\) −110.807 −3.83694
\(835\) 17.5764 0.608256
\(836\) −20.3375 −0.703385
\(837\) 8.05713 0.278495
\(838\) −0.306113 −0.0105745
\(839\) 6.36028 0.219581 0.109791 0.993955i \(-0.464982\pi\)
0.109791 + 0.993955i \(0.464982\pi\)
\(840\) −32.1176 −1.10816
\(841\) −28.8575 −0.995085
\(842\) −90.4236 −3.11620
\(843\) −16.7760 −0.577797
\(844\) 2.21092 0.0761029
\(845\) 66.8055 2.29818
\(846\) −22.5819 −0.776381
\(847\) 11.6143 0.399071
\(848\) −93.1568 −3.19902
\(849\) 59.6140 2.04595
\(850\) 6.96329 0.238839
\(851\) 10.7375 0.368076
\(852\) 32.3890 1.10963
\(853\) −30.8901 −1.05766 −0.528829 0.848728i \(-0.677369\pi\)
−0.528829 + 0.848728i \(0.677369\pi\)
\(854\) −13.6886 −0.468414
\(855\) 27.7275 0.948262
\(856\) −21.4991 −0.734825
\(857\) 1.53183 0.0523264 0.0261632 0.999658i \(-0.491671\pi\)
0.0261632 + 0.999658i \(0.491671\pi\)
\(858\) −21.2894 −0.726807
\(859\) −44.1394 −1.50602 −0.753009 0.658010i \(-0.771398\pi\)
−0.753009 + 0.658010i \(0.771398\pi\)
\(860\) −113.772 −3.87959
\(861\) 2.67101 0.0910278
\(862\) 90.6814 3.08862
\(863\) 1.34221 0.0456894 0.0228447 0.999739i \(-0.492728\pi\)
0.0228447 + 0.999739i \(0.492728\pi\)
\(864\) −17.9154 −0.609493
\(865\) 16.8537 0.573043
\(866\) 79.3983 2.69806
\(867\) −3.74316 −0.127124
\(868\) −14.1185 −0.479212
\(869\) 1.56568 0.0531119
\(870\) 4.37663 0.148382
\(871\) 60.5495 2.05164
\(872\) 83.2228 2.81828
\(873\) −5.24338 −0.177462
\(874\) 19.9895 0.676156
\(875\) 12.8074 0.432970
\(876\) 105.484 3.56396
\(877\) 5.95567 0.201109 0.100554 0.994932i \(-0.467938\pi\)
0.100554 + 0.994932i \(0.467938\pi\)
\(878\) −32.8382 −1.10824
\(879\) 26.0334 0.878086
\(880\) −9.06485 −0.305576
\(881\) 40.3518 1.35949 0.679743 0.733451i \(-0.262091\pi\)
0.679743 + 0.733451i \(0.262091\pi\)
\(882\) 25.2561 0.850417
\(883\) 16.4008 0.551929 0.275965 0.961168i \(-0.411003\pi\)
0.275965 + 0.961168i \(0.411003\pi\)
\(884\) 131.890 4.43596
\(885\) −53.8009 −1.80850
\(886\) −104.621 −3.51480
\(887\) 52.0897 1.74900 0.874500 0.485025i \(-0.161190\pi\)
0.874500 + 0.485025i \(0.161190\pi\)
\(888\) −151.568 −5.08631
\(889\) 0.0994869 0.00333668
\(890\) −47.4613 −1.59091
\(891\) 6.41976 0.215070
\(892\) −63.3116 −2.11983
\(893\) 40.6273 1.35954
\(894\) −103.039 −3.44615
\(895\) 37.6643 1.25898
\(896\) −10.7710 −0.359832
\(897\) 14.5315 0.485194
\(898\) 40.5978 1.35477
\(899\) 1.07743 0.0359342
\(900\) −4.85279 −0.161760
\(901\) −53.2422 −1.77376
\(902\) 1.65903 0.0552397
\(903\) −28.2368 −0.939663
\(904\) 98.7891 3.28568
\(905\) −21.2563 −0.706582
\(906\) −30.3158 −1.00718
\(907\) 0.548629 0.0182169 0.00910847 0.999959i \(-0.497101\pi\)
0.00910847 + 0.999959i \(0.497101\pi\)
\(908\) −20.2065 −0.670576
\(909\) −6.53762 −0.216839
\(910\) 39.0296 1.29382
\(911\) −11.7488 −0.389254 −0.194627 0.980877i \(-0.562350\pi\)
−0.194627 + 0.980877i \(0.562350\pi\)
\(912\) −128.218 −4.24572
\(913\) 2.95130 0.0976737
\(914\) 16.4993 0.545748
\(915\) 22.2774 0.736468
\(916\) 91.3353 3.01780
\(917\) 13.5635 0.447907
\(918\) −31.2567 −1.03162
\(919\) −48.0176 −1.58395 −0.791977 0.610550i \(-0.790948\pi\)
−0.791977 + 0.610550i \(0.790948\pi\)
\(920\) 13.6167 0.448928
\(921\) 17.8470 0.588078
\(922\) −68.2948 −2.24917
\(923\) −22.0421 −0.725523
\(924\) −6.13963 −0.201979
\(925\) 6.75313 0.222042
\(926\) −61.5000 −2.02101
\(927\) −25.4001 −0.834247
\(928\) −2.39571 −0.0786430
\(929\) 1.46111 0.0479376 0.0239688 0.999713i \(-0.492370\pi\)
0.0239688 + 0.999713i \(0.492370\pi\)
\(930\) 33.0864 1.08495
\(931\) −45.4384 −1.48918
\(932\) 97.0003 3.17735
\(933\) 13.4490 0.440300
\(934\) 9.37188 0.306657
\(935\) −5.18087 −0.169433
\(936\) −74.1226 −2.42277
\(937\) −25.4885 −0.832674 −0.416337 0.909210i \(-0.636686\pi\)
−0.416337 + 0.909210i \(0.636686\pi\)
\(938\) 25.1447 0.821005
\(939\) 25.3515 0.827316
\(940\) 49.4177 1.61183
\(941\) −17.7647 −0.579112 −0.289556 0.957161i \(-0.593508\pi\)
−0.289556 + 0.957161i \(0.593508\pi\)
\(942\) 57.8995 1.88647
\(943\) −1.13241 −0.0368764
\(944\) 89.8997 2.92599
\(945\) −6.42343 −0.208954
\(946\) −17.5386 −0.570229
\(947\) −28.2392 −0.917650 −0.458825 0.888527i \(-0.651729\pi\)
−0.458825 + 0.888527i \(0.651729\pi\)
\(948\) 26.9374 0.874885
\(949\) −71.7861 −2.33027
\(950\) 12.5720 0.407891
\(951\) −19.5493 −0.633930
\(952\) 30.6728 0.994111
\(953\) 5.98352 0.193825 0.0969125 0.995293i \(-0.469103\pi\)
0.0969125 + 0.995293i \(0.469103\pi\)
\(954\) 53.4306 1.72988
\(955\) −37.6882 −1.21956
\(956\) 79.8740 2.58331
\(957\) 0.468536 0.0151456
\(958\) −88.2722 −2.85195
\(959\) 13.0874 0.422614
\(960\) −4.94963 −0.159748
\(961\) −22.8549 −0.737254
\(962\) 184.188 5.93845
\(963\) 5.60319 0.180560
\(964\) −1.07962 −0.0347723
\(965\) −36.5488 −1.17655
\(966\) 6.03460 0.194160
\(967\) 16.5491 0.532182 0.266091 0.963948i \(-0.414268\pi\)
0.266091 + 0.963948i \(0.414268\pi\)
\(968\) 69.5067 2.23403
\(969\) −73.2809 −2.35412
\(970\) 16.5231 0.530523
\(971\) −29.7739 −0.955490 −0.477745 0.878499i \(-0.658546\pi\)
−0.477745 + 0.878499i \(0.658546\pi\)
\(972\) 71.9526 2.30788
\(973\) 21.7472 0.697183
\(974\) 99.7145 3.19506
\(975\) 9.13935 0.292693
\(976\) −37.2249 −1.19154
\(977\) −16.2033 −0.518389 −0.259194 0.965825i \(-0.583457\pi\)
−0.259194 + 0.965825i \(0.583457\pi\)
\(978\) −60.7020 −1.94104
\(979\) −5.08093 −0.162387
\(980\) −55.2698 −1.76553
\(981\) −21.6899 −0.692504
\(982\) −77.0965 −2.46025
\(983\) −37.3227 −1.19041 −0.595205 0.803574i \(-0.702929\pi\)
−0.595205 + 0.803574i \(0.702929\pi\)
\(984\) 15.9849 0.509581
\(985\) 4.75575 0.151531
\(986\) −4.17976 −0.133111
\(987\) 12.2649 0.390396
\(988\) 238.125 7.57576
\(989\) 11.9714 0.380668
\(990\) 5.19920 0.165241
\(991\) −35.1627 −1.11698 −0.558490 0.829511i \(-0.688619\pi\)
−0.558490 + 0.829511i \(0.688619\pi\)
\(992\) −18.1110 −0.575026
\(993\) −59.2561 −1.88044
\(994\) −9.15353 −0.290332
\(995\) 34.6826 1.09951
\(996\) 50.7769 1.60893
\(997\) 3.84743 0.121849 0.0609247 0.998142i \(-0.480595\pi\)
0.0609247 + 0.998142i \(0.480595\pi\)
\(998\) 16.4016 0.519183
\(999\) −30.3133 −0.959071
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8027.2.a.d.1.9 149
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.d.1.9 149 1.1 even 1 trivial