Properties

Label 1859.2.a.s.1.1
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1859,2,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, 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("1859.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1859.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.68791 q^{2} -2.90985 q^{3} +5.22486 q^{4} -3.09378 q^{5} +7.82142 q^{6} -1.70397 q^{7} -8.66813 q^{8} +5.46725 q^{9} +O(q^{10})\) \(q-2.68791 q^{2} -2.90985 q^{3} +5.22486 q^{4} -3.09378 q^{5} +7.82142 q^{6} -1.70397 q^{7} -8.66813 q^{8} +5.46725 q^{9} +8.31580 q^{10} -1.00000 q^{11} -15.2036 q^{12} +4.58011 q^{14} +9.00245 q^{15} +12.8494 q^{16} +1.04237 q^{17} -14.6955 q^{18} +0.291109 q^{19} -16.1646 q^{20} +4.95829 q^{21} +2.68791 q^{22} -7.88320 q^{23} +25.2230 q^{24} +4.57148 q^{25} -7.17933 q^{27} -8.90299 q^{28} -0.935722 q^{29} -24.1978 q^{30} -1.01935 q^{31} -17.2019 q^{32} +2.90985 q^{33} -2.80179 q^{34} +5.27170 q^{35} +28.5656 q^{36} +6.79609 q^{37} -0.782475 q^{38} +26.8173 q^{40} -4.76040 q^{41} -13.3274 q^{42} -10.1591 q^{43} -5.22486 q^{44} -16.9145 q^{45} +21.1893 q^{46} -2.04588 q^{47} -37.3900 q^{48} -4.09650 q^{49} -12.2877 q^{50} -3.03314 q^{51} -4.76011 q^{53} +19.2974 q^{54} +3.09378 q^{55} +14.7702 q^{56} -0.847085 q^{57} +2.51514 q^{58} -11.6149 q^{59} +47.0365 q^{60} +9.48390 q^{61} +2.73991 q^{62} -9.31601 q^{63} +20.5382 q^{64} -7.82142 q^{66} -9.43031 q^{67} +5.44623 q^{68} +22.9389 q^{69} -14.1699 q^{70} -0.582928 q^{71} -47.3908 q^{72} -15.8198 q^{73} -18.2673 q^{74} -13.3023 q^{75} +1.52100 q^{76} +1.70397 q^{77} -12.2976 q^{79} -39.7533 q^{80} +4.48905 q^{81} +12.7955 q^{82} +10.5008 q^{83} +25.9064 q^{84} -3.22486 q^{85} +27.3069 q^{86} +2.72281 q^{87} +8.66813 q^{88} -5.79180 q^{89} +45.4646 q^{90} -41.1886 q^{92} +2.96615 q^{93} +5.49914 q^{94} -0.900628 q^{95} +50.0549 q^{96} +0.922801 q^{97} +11.0110 q^{98} -5.46725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68791 −1.90064 −0.950320 0.311276i \(-0.899244\pi\)
−0.950320 + 0.311276i \(0.899244\pi\)
\(3\) −2.90985 −1.68000 −0.840002 0.542583i \(-0.817446\pi\)
−0.840002 + 0.542583i \(0.817446\pi\)
\(4\) 5.22486 2.61243
\(5\) −3.09378 −1.38358 −0.691790 0.722098i \(-0.743178\pi\)
−0.691790 + 0.722098i \(0.743178\pi\)
\(6\) 7.82142 3.19308
\(7\) −1.70397 −0.644039 −0.322020 0.946733i \(-0.604362\pi\)
−0.322020 + 0.946733i \(0.604362\pi\)
\(8\) −8.66813 −3.06465
\(9\) 5.46725 1.82242
\(10\) 8.31580 2.62969
\(11\) −1.00000 −0.301511
\(12\) −15.2036 −4.38889
\(13\) 0 0
\(14\) 4.58011 1.22409
\(15\) 9.00245 2.32442
\(16\) 12.8494 3.21236
\(17\) 1.04237 0.252811 0.126406 0.991979i \(-0.459656\pi\)
0.126406 + 0.991979i \(0.459656\pi\)
\(18\) −14.6955 −3.46375
\(19\) 0.291109 0.0667850 0.0333925 0.999442i \(-0.489369\pi\)
0.0333925 + 0.999442i \(0.489369\pi\)
\(20\) −16.1646 −3.61451
\(21\) 4.95829 1.08199
\(22\) 2.68791 0.573064
\(23\) −7.88320 −1.64376 −0.821880 0.569661i \(-0.807075\pi\)
−0.821880 + 0.569661i \(0.807075\pi\)
\(24\) 25.2230 5.14862
\(25\) 4.57148 0.914296
\(26\) 0 0
\(27\) −7.17933 −1.38166
\(28\) −8.90299 −1.68251
\(29\) −0.935722 −0.173759 −0.0868796 0.996219i \(-0.527690\pi\)
−0.0868796 + 0.996219i \(0.527690\pi\)
\(30\) −24.1978 −4.41789
\(31\) −1.01935 −0.183080 −0.0915399 0.995801i \(-0.529179\pi\)
−0.0915399 + 0.995801i \(0.529179\pi\)
\(32\) −17.2019 −3.04089
\(33\) 2.90985 0.506540
\(34\) −2.80179 −0.480503
\(35\) 5.27170 0.891080
\(36\) 28.5656 4.76093
\(37\) 6.79609 1.11727 0.558635 0.829414i \(-0.311325\pi\)
0.558635 + 0.829414i \(0.311325\pi\)
\(38\) −0.782475 −0.126934
\(39\) 0 0
\(40\) 26.8173 4.24019
\(41\) −4.76040 −0.743450 −0.371725 0.928343i \(-0.621234\pi\)
−0.371725 + 0.928343i \(0.621234\pi\)
\(42\) −13.3274 −2.05647
\(43\) −10.1591 −1.54926 −0.774628 0.632418i \(-0.782063\pi\)
−0.774628 + 0.632418i \(0.782063\pi\)
\(44\) −5.22486 −0.787677
\(45\) −16.9145 −2.52146
\(46\) 21.1893 3.12419
\(47\) −2.04588 −0.298422 −0.149211 0.988805i \(-0.547673\pi\)
−0.149211 + 0.988805i \(0.547673\pi\)
\(48\) −37.3900 −5.39678
\(49\) −4.09650 −0.585214
\(50\) −12.2877 −1.73775
\(51\) −3.03314 −0.424724
\(52\) 0 0
\(53\) −4.76011 −0.653851 −0.326926 0.945050i \(-0.606013\pi\)
−0.326926 + 0.945050i \(0.606013\pi\)
\(54\) 19.2974 2.62604
\(55\) 3.09378 0.417165
\(56\) 14.7702 1.97375
\(57\) −0.847085 −0.112199
\(58\) 2.51514 0.330254
\(59\) −11.6149 −1.51212 −0.756062 0.654500i \(-0.772879\pi\)
−0.756062 + 0.654500i \(0.772879\pi\)
\(60\) 47.0365 6.07239
\(61\) 9.48390 1.21429 0.607145 0.794591i \(-0.292315\pi\)
0.607145 + 0.794591i \(0.292315\pi\)
\(62\) 2.73991 0.347969
\(63\) −9.31601 −1.17371
\(64\) 20.5382 2.56727
\(65\) 0 0
\(66\) −7.82142 −0.962751
\(67\) −9.43031 −1.15210 −0.576048 0.817416i \(-0.695406\pi\)
−0.576048 + 0.817416i \(0.695406\pi\)
\(68\) 5.44623 0.660452
\(69\) 22.9389 2.76152
\(70\) −14.1699 −1.69362
\(71\) −0.582928 −0.0691808 −0.0345904 0.999402i \(-0.511013\pi\)
−0.0345904 + 0.999402i \(0.511013\pi\)
\(72\) −47.3908 −5.58506
\(73\) −15.8198 −1.85157 −0.925784 0.378053i \(-0.876594\pi\)
−0.925784 + 0.378053i \(0.876594\pi\)
\(74\) −18.2673 −2.12353
\(75\) −13.3023 −1.53602
\(76\) 1.52100 0.174471
\(77\) 1.70397 0.194185
\(78\) 0 0
\(79\) −12.2976 −1.38358 −0.691792 0.722097i \(-0.743179\pi\)
−0.691792 + 0.722097i \(0.743179\pi\)
\(80\) −39.7533 −4.44456
\(81\) 4.48905 0.498783
\(82\) 12.7955 1.41303
\(83\) 10.5008 1.15261 0.576305 0.817235i \(-0.304494\pi\)
0.576305 + 0.817235i \(0.304494\pi\)
\(84\) 25.9064 2.82662
\(85\) −3.22486 −0.349785
\(86\) 27.3069 2.94458
\(87\) 2.72281 0.291916
\(88\) 8.66813 0.924026
\(89\) −5.79180 −0.613930 −0.306965 0.951721i \(-0.599313\pi\)
−0.306965 + 0.951721i \(0.599313\pi\)
\(90\) 45.4646 4.79238
\(91\) 0 0
\(92\) −41.1886 −4.29421
\(93\) 2.96615 0.307575
\(94\) 5.49914 0.567193
\(95\) −0.900628 −0.0924025
\(96\) 50.0549 5.10870
\(97\) 0.922801 0.0936963 0.0468481 0.998902i \(-0.485082\pi\)
0.0468481 + 0.998902i \(0.485082\pi\)
\(98\) 11.0110 1.11228
\(99\) −5.46725 −0.549479
\(100\) 23.8853 2.38853
\(101\) −12.8629 −1.27990 −0.639951 0.768415i \(-0.721046\pi\)
−0.639951 + 0.768415i \(0.721046\pi\)
\(102\) 8.15280 0.807248
\(103\) −16.8954 −1.66475 −0.832377 0.554210i \(-0.813021\pi\)
−0.832377 + 0.554210i \(0.813021\pi\)
\(104\) 0 0
\(105\) −15.3399 −1.49702
\(106\) 12.7947 1.24274
\(107\) 4.69227 0.453619 0.226809 0.973939i \(-0.427171\pi\)
0.226809 + 0.973939i \(0.427171\pi\)
\(108\) −37.5110 −3.60949
\(109\) −13.7724 −1.31916 −0.659580 0.751634i \(-0.729266\pi\)
−0.659580 + 0.751634i \(0.729266\pi\)
\(110\) −8.31580 −0.792881
\(111\) −19.7756 −1.87702
\(112\) −21.8950 −2.06888
\(113\) −8.36051 −0.786491 −0.393245 0.919434i \(-0.628648\pi\)
−0.393245 + 0.919434i \(0.628648\pi\)
\(114\) 2.27689 0.213250
\(115\) 24.3889 2.27428
\(116\) −4.88902 −0.453934
\(117\) 0 0
\(118\) 31.2197 2.87400
\(119\) −1.77616 −0.162820
\(120\) −78.0344 −7.12353
\(121\) 1.00000 0.0909091
\(122\) −25.4919 −2.30793
\(123\) 13.8521 1.24900
\(124\) −5.32594 −0.478283
\(125\) 1.32574 0.118578
\(126\) 25.0406 2.23079
\(127\) −4.09166 −0.363076 −0.181538 0.983384i \(-0.558107\pi\)
−0.181538 + 0.983384i \(0.558107\pi\)
\(128\) −20.8010 −1.83857
\(129\) 29.5616 2.60276
\(130\) 0 0
\(131\) −1.63924 −0.143221 −0.0716104 0.997433i \(-0.522814\pi\)
−0.0716104 + 0.997433i \(0.522814\pi\)
\(132\) 15.2036 1.32330
\(133\) −0.496041 −0.0430122
\(134\) 25.3478 2.18972
\(135\) 22.2113 1.91164
\(136\) −9.03538 −0.774778
\(137\) −7.27779 −0.621783 −0.310892 0.950445i \(-0.600628\pi\)
−0.310892 + 0.950445i \(0.600628\pi\)
\(138\) −61.6578 −5.24866
\(139\) 11.0849 0.940212 0.470106 0.882610i \(-0.344216\pi\)
0.470106 + 0.882610i \(0.344216\pi\)
\(140\) 27.5439 2.32788
\(141\) 5.95321 0.501351
\(142\) 1.56686 0.131488
\(143\) 0 0
\(144\) 70.2510 5.85425
\(145\) 2.89492 0.240410
\(146\) 42.5222 3.51916
\(147\) 11.9202 0.983162
\(148\) 35.5086 2.91879
\(149\) −0.116636 −0.00955523 −0.00477761 0.999989i \(-0.501521\pi\)
−0.00477761 + 0.999989i \(0.501521\pi\)
\(150\) 35.7555 2.91942
\(151\) 9.89456 0.805208 0.402604 0.915374i \(-0.368105\pi\)
0.402604 + 0.915374i \(0.368105\pi\)
\(152\) −2.52337 −0.204673
\(153\) 5.69888 0.460727
\(154\) −4.58011 −0.369076
\(155\) 3.15363 0.253306
\(156\) 0 0
\(157\) 7.33594 0.585472 0.292736 0.956193i \(-0.405434\pi\)
0.292736 + 0.956193i \(0.405434\pi\)
\(158\) 33.0547 2.62969
\(159\) 13.8512 1.09847
\(160\) 53.2188 4.20731
\(161\) 13.4327 1.05865
\(162\) −12.0661 −0.948006
\(163\) 20.1802 1.58064 0.790318 0.612696i \(-0.209915\pi\)
0.790318 + 0.612696i \(0.209915\pi\)
\(164\) −24.8724 −1.94221
\(165\) −9.00245 −0.700840
\(166\) −28.2251 −2.19069
\(167\) 4.95156 0.383163 0.191582 0.981477i \(-0.438638\pi\)
0.191582 + 0.981477i \(0.438638\pi\)
\(168\) −42.9791 −3.31591
\(169\) 0 0
\(170\) 8.66813 0.664815
\(171\) 1.59157 0.121710
\(172\) −53.0801 −4.04732
\(173\) 21.1077 1.60479 0.802394 0.596795i \(-0.203560\pi\)
0.802394 + 0.596795i \(0.203560\pi\)
\(174\) −7.31868 −0.554828
\(175\) −7.78965 −0.588842
\(176\) −12.8494 −0.968562
\(177\) 33.7975 2.54038
\(178\) 15.5678 1.16686
\(179\) 1.06432 0.0795513 0.0397757 0.999209i \(-0.487336\pi\)
0.0397757 + 0.999209i \(0.487336\pi\)
\(180\) −88.3757 −6.58713
\(181\) 18.7869 1.39642 0.698210 0.715893i \(-0.253980\pi\)
0.698210 + 0.715893i \(0.253980\pi\)
\(182\) 0 0
\(183\) −27.5968 −2.04001
\(184\) 68.3326 5.03754
\(185\) −21.0256 −1.54583
\(186\) −7.97273 −0.584589
\(187\) −1.04237 −0.0762255
\(188\) −10.6894 −0.779608
\(189\) 12.2333 0.889844
\(190\) 2.42081 0.175624
\(191\) −19.2897 −1.39575 −0.697876 0.716219i \(-0.745871\pi\)
−0.697876 + 0.716219i \(0.745871\pi\)
\(192\) −59.7630 −4.31303
\(193\) −10.4036 −0.748864 −0.374432 0.927254i \(-0.622162\pi\)
−0.374432 + 0.927254i \(0.622162\pi\)
\(194\) −2.48041 −0.178083
\(195\) 0 0
\(196\) −21.4036 −1.52883
\(197\) −9.93369 −0.707746 −0.353873 0.935293i \(-0.615136\pi\)
−0.353873 + 0.935293i \(0.615136\pi\)
\(198\) 14.6955 1.04436
\(199\) −12.7227 −0.901886 −0.450943 0.892553i \(-0.648912\pi\)
−0.450943 + 0.892553i \(0.648912\pi\)
\(200\) −39.6262 −2.80199
\(201\) 27.4408 1.93553
\(202\) 34.5742 2.43263
\(203\) 1.59444 0.111908
\(204\) −15.8477 −1.10956
\(205\) 14.7276 1.02862
\(206\) 45.4133 3.16410
\(207\) −43.0994 −2.99561
\(208\) 0 0
\(209\) −0.291109 −0.0201364
\(210\) 41.2322 2.84529
\(211\) 2.00015 0.137696 0.0688480 0.997627i \(-0.478068\pi\)
0.0688480 + 0.997627i \(0.478068\pi\)
\(212\) −24.8709 −1.70814
\(213\) 1.69623 0.116224
\(214\) −12.6124 −0.862166
\(215\) 31.4302 2.14352
\(216\) 62.2313 4.23431
\(217\) 1.73693 0.117911
\(218\) 37.0191 2.50725
\(219\) 46.0333 3.11064
\(220\) 16.1646 1.08981
\(221\) 0 0
\(222\) 53.1551 3.56753
\(223\) 3.25053 0.217672 0.108836 0.994060i \(-0.465288\pi\)
0.108836 + 0.994060i \(0.465288\pi\)
\(224\) 29.3114 1.95845
\(225\) 24.9934 1.66623
\(226\) 22.4723 1.49483
\(227\) 17.3081 1.14878 0.574388 0.818583i \(-0.305240\pi\)
0.574388 + 0.818583i \(0.305240\pi\)
\(228\) −4.42590 −0.293112
\(229\) 12.2229 0.807712 0.403856 0.914822i \(-0.367670\pi\)
0.403856 + 0.914822i \(0.367670\pi\)
\(230\) −65.5551 −4.32258
\(231\) −4.95829 −0.326232
\(232\) 8.11096 0.532511
\(233\) 0.275611 0.0180558 0.00902792 0.999959i \(-0.497126\pi\)
0.00902792 + 0.999959i \(0.497126\pi\)
\(234\) 0 0
\(235\) 6.32951 0.412892
\(236\) −60.6860 −3.95032
\(237\) 35.7841 2.32443
\(238\) 4.77416 0.309463
\(239\) −22.4425 −1.45168 −0.725841 0.687863i \(-0.758549\pi\)
−0.725841 + 0.687863i \(0.758549\pi\)
\(240\) 115.676 7.46688
\(241\) 17.7396 1.14271 0.571353 0.820705i \(-0.306419\pi\)
0.571353 + 0.820705i \(0.306419\pi\)
\(242\) −2.68791 −0.172785
\(243\) 8.47551 0.543704
\(244\) 49.5521 3.17225
\(245\) 12.6737 0.809691
\(246\) −37.2331 −2.37390
\(247\) 0 0
\(248\) 8.83582 0.561075
\(249\) −30.5557 −1.93639
\(250\) −3.56348 −0.225374
\(251\) −20.5224 −1.29537 −0.647683 0.761910i \(-0.724262\pi\)
−0.647683 + 0.761910i \(0.724262\pi\)
\(252\) −48.6748 −3.06623
\(253\) 7.88320 0.495612
\(254\) 10.9980 0.690076
\(255\) 9.38387 0.587641
\(256\) 14.8350 0.927185
\(257\) −10.1295 −0.631862 −0.315931 0.948782i \(-0.602317\pi\)
−0.315931 + 0.948782i \(0.602317\pi\)
\(258\) −79.4590 −4.94690
\(259\) −11.5803 −0.719565
\(260\) 0 0
\(261\) −5.11583 −0.316662
\(262\) 4.40612 0.272211
\(263\) 0.0974277 0.00600765 0.00300383 0.999995i \(-0.499044\pi\)
0.00300383 + 0.999995i \(0.499044\pi\)
\(264\) −25.2230 −1.55237
\(265\) 14.7267 0.904656
\(266\) 1.33331 0.0817506
\(267\) 16.8533 1.03140
\(268\) −49.2721 −3.00977
\(269\) −3.50796 −0.213884 −0.106942 0.994265i \(-0.534106\pi\)
−0.106942 + 0.994265i \(0.534106\pi\)
\(270\) −59.7019 −3.63334
\(271\) −15.3135 −0.930230 −0.465115 0.885250i \(-0.653987\pi\)
−0.465115 + 0.885250i \(0.653987\pi\)
\(272\) 13.3938 0.812121
\(273\) 0 0
\(274\) 19.5620 1.18179
\(275\) −4.57148 −0.275671
\(276\) 119.853 7.21429
\(277\) −20.6695 −1.24191 −0.620954 0.783847i \(-0.713255\pi\)
−0.620954 + 0.783847i \(0.713255\pi\)
\(278\) −29.7953 −1.78700
\(279\) −5.57301 −0.333648
\(280\) −45.6958 −2.73085
\(281\) 28.7750 1.71657 0.858286 0.513172i \(-0.171530\pi\)
0.858286 + 0.513172i \(0.171530\pi\)
\(282\) −16.0017 −0.952887
\(283\) −30.2757 −1.79971 −0.899853 0.436193i \(-0.856326\pi\)
−0.899853 + 0.436193i \(0.856326\pi\)
\(284\) −3.04571 −0.180730
\(285\) 2.62070 0.155237
\(286\) 0 0
\(287\) 8.11157 0.478811
\(288\) −94.0468 −5.54176
\(289\) −15.9135 −0.936086
\(290\) −7.78128 −0.456933
\(291\) −2.68522 −0.157410
\(292\) −82.6562 −4.83709
\(293\) 11.0766 0.647100 0.323550 0.946211i \(-0.395124\pi\)
0.323550 + 0.946211i \(0.395124\pi\)
\(294\) −32.0404 −1.86864
\(295\) 35.9338 2.09215
\(296\) −58.9094 −3.42404
\(297\) 7.17933 0.416587
\(298\) 0.313508 0.0181610
\(299\) 0 0
\(300\) −69.5028 −4.01275
\(301\) 17.3108 0.997781
\(302\) −26.5957 −1.53041
\(303\) 37.4291 2.15024
\(304\) 3.74059 0.214537
\(305\) −29.3411 −1.68007
\(306\) −15.3181 −0.875677
\(307\) 5.13474 0.293055 0.146528 0.989207i \(-0.453190\pi\)
0.146528 + 0.989207i \(0.453190\pi\)
\(308\) 8.90299 0.507295
\(309\) 49.1632 2.79679
\(310\) −8.47668 −0.481443
\(311\) 21.3788 1.21228 0.606141 0.795357i \(-0.292717\pi\)
0.606141 + 0.795357i \(0.292717\pi\)
\(312\) 0 0
\(313\) 1.92078 0.108569 0.0542845 0.998526i \(-0.482712\pi\)
0.0542845 + 0.998526i \(0.482712\pi\)
\(314\) −19.7183 −1.11277
\(315\) 28.8217 1.62392
\(316\) −64.2530 −3.61452
\(317\) −8.45359 −0.474801 −0.237400 0.971412i \(-0.576295\pi\)
−0.237400 + 0.971412i \(0.576295\pi\)
\(318\) −37.2308 −2.08780
\(319\) 0.935722 0.0523904
\(320\) −63.5406 −3.55203
\(321\) −13.6538 −0.762082
\(322\) −36.1059 −2.01210
\(323\) 0.303443 0.0168840
\(324\) 23.4546 1.30303
\(325\) 0 0
\(326\) −54.2426 −3.00422
\(327\) 40.0758 2.21619
\(328\) 41.2638 2.27841
\(329\) 3.48611 0.192196
\(330\) 24.1978 1.33204
\(331\) −24.7021 −1.35775 −0.678874 0.734255i \(-0.737532\pi\)
−0.678874 + 0.734255i \(0.737532\pi\)
\(332\) 54.8651 3.01111
\(333\) 37.1559 2.03613
\(334\) −13.3093 −0.728255
\(335\) 29.1753 1.59402
\(336\) 63.7113 3.47573
\(337\) 25.8404 1.40762 0.703809 0.710389i \(-0.251481\pi\)
0.703809 + 0.710389i \(0.251481\pi\)
\(338\) 0 0
\(339\) 24.3279 1.32131
\(340\) −16.8494 −0.913789
\(341\) 1.01935 0.0552007
\(342\) −4.27799 −0.231327
\(343\) 18.9081 1.02094
\(344\) 88.0608 4.74792
\(345\) −70.9681 −3.82079
\(346\) −56.7355 −3.05012
\(347\) 1.98790 0.106716 0.0533580 0.998575i \(-0.483008\pi\)
0.0533580 + 0.998575i \(0.483008\pi\)
\(348\) 14.2263 0.762611
\(349\) 9.65372 0.516752 0.258376 0.966044i \(-0.416813\pi\)
0.258376 + 0.966044i \(0.416813\pi\)
\(350\) 20.9379 1.11918
\(351\) 0 0
\(352\) 17.2019 0.916862
\(353\) −4.97653 −0.264874 −0.132437 0.991191i \(-0.542280\pi\)
−0.132437 + 0.991191i \(0.542280\pi\)
\(354\) −90.8447 −4.82834
\(355\) 1.80345 0.0957172
\(356\) −30.2614 −1.60385
\(357\) 5.16837 0.273539
\(358\) −2.86081 −0.151198
\(359\) −15.8428 −0.836149 −0.418075 0.908413i \(-0.637295\pi\)
−0.418075 + 0.908413i \(0.637295\pi\)
\(360\) 146.617 7.72738
\(361\) −18.9153 −0.995540
\(362\) −50.4975 −2.65409
\(363\) −2.90985 −0.152728
\(364\) 0 0
\(365\) 48.9430 2.56179
\(366\) 74.1776 3.87733
\(367\) −4.23360 −0.220992 −0.110496 0.993877i \(-0.535244\pi\)
−0.110496 + 0.993877i \(0.535244\pi\)
\(368\) −101.295 −5.28035
\(369\) −26.0263 −1.35488
\(370\) 56.5149 2.93807
\(371\) 8.11107 0.421106
\(372\) 15.4977 0.803518
\(373\) −3.24566 −0.168054 −0.0840269 0.996463i \(-0.526778\pi\)
−0.0840269 + 0.996463i \(0.526778\pi\)
\(374\) 2.80179 0.144877
\(375\) −3.85772 −0.199212
\(376\) 17.7340 0.914559
\(377\) 0 0
\(378\) −32.8821 −1.69127
\(379\) −20.8566 −1.07133 −0.535666 0.844430i \(-0.679940\pi\)
−0.535666 + 0.844430i \(0.679940\pi\)
\(380\) −4.70565 −0.241395
\(381\) 11.9061 0.609969
\(382\) 51.8489 2.65282
\(383\) −25.6788 −1.31213 −0.656063 0.754706i \(-0.727780\pi\)
−0.656063 + 0.754706i \(0.727780\pi\)
\(384\) 60.5279 3.08880
\(385\) −5.27170 −0.268671
\(386\) 27.9638 1.42332
\(387\) −55.5426 −2.82339
\(388\) 4.82151 0.244775
\(389\) 16.8280 0.853214 0.426607 0.904437i \(-0.359709\pi\)
0.426607 + 0.904437i \(0.359709\pi\)
\(390\) 0 0
\(391\) −8.21719 −0.415561
\(392\) 35.5090 1.79347
\(393\) 4.76994 0.240611
\(394\) 26.7009 1.34517
\(395\) 38.0460 1.91430
\(396\) −28.5656 −1.43547
\(397\) −3.41837 −0.171563 −0.0857817 0.996314i \(-0.527339\pi\)
−0.0857817 + 0.996314i \(0.527339\pi\)
\(398\) 34.1974 1.71416
\(399\) 1.44341 0.0722606
\(400\) 58.7409 2.93705
\(401\) 5.82738 0.291005 0.145503 0.989358i \(-0.453520\pi\)
0.145503 + 0.989358i \(0.453520\pi\)
\(402\) −73.7585 −3.67874
\(403\) 0 0
\(404\) −67.2067 −3.34366
\(405\) −13.8881 −0.690106
\(406\) −4.28571 −0.212696
\(407\) −6.79609 −0.336870
\(408\) 26.2916 1.30163
\(409\) 13.4473 0.664927 0.332464 0.943116i \(-0.392120\pi\)
0.332464 + 0.943116i \(0.392120\pi\)
\(410\) −39.5866 −1.95504
\(411\) 21.1773 1.04460
\(412\) −88.2761 −4.34905
\(413\) 19.7913 0.973867
\(414\) 115.847 5.69358
\(415\) −32.4871 −1.59473
\(416\) 0 0
\(417\) −32.2555 −1.57956
\(418\) 0.782475 0.0382721
\(419\) −25.5596 −1.24867 −0.624335 0.781157i \(-0.714630\pi\)
−0.624335 + 0.781157i \(0.714630\pi\)
\(420\) −80.1487 −3.91086
\(421\) −30.5005 −1.48650 −0.743251 0.669013i \(-0.766717\pi\)
−0.743251 + 0.669013i \(0.766717\pi\)
\(422\) −5.37622 −0.261710
\(423\) −11.1853 −0.543850
\(424\) 41.2613 2.00382
\(425\) 4.76517 0.231145
\(426\) −4.55932 −0.220900
\(427\) −16.1603 −0.782050
\(428\) 24.5164 1.18505
\(429\) 0 0
\(430\) −84.4815 −4.07406
\(431\) 9.03274 0.435092 0.217546 0.976050i \(-0.430195\pi\)
0.217546 + 0.976050i \(0.430195\pi\)
\(432\) −92.2503 −4.43839
\(433\) −20.8135 −1.00023 −0.500116 0.865958i \(-0.666709\pi\)
−0.500116 + 0.865958i \(0.666709\pi\)
\(434\) −4.66872 −0.224106
\(435\) −8.42379 −0.403890
\(436\) −71.9590 −3.44621
\(437\) −2.29487 −0.109779
\(438\) −123.733 −5.91221
\(439\) 25.1827 1.20191 0.600953 0.799284i \(-0.294788\pi\)
0.600953 + 0.799284i \(0.294788\pi\)
\(440\) −26.8173 −1.27846
\(441\) −22.3966 −1.06650
\(442\) 0 0
\(443\) 37.6126 1.78703 0.893513 0.449037i \(-0.148233\pi\)
0.893513 + 0.449037i \(0.148233\pi\)
\(444\) −103.325 −4.90358
\(445\) 17.9186 0.849422
\(446\) −8.73714 −0.413715
\(447\) 0.339395 0.0160528
\(448\) −34.9964 −1.65342
\(449\) −9.31247 −0.439482 −0.219741 0.975558i \(-0.570521\pi\)
−0.219741 + 0.975558i \(0.570521\pi\)
\(450\) −67.1800 −3.16690
\(451\) 4.76040 0.224159
\(452\) −43.6825 −2.05465
\(453\) −28.7917 −1.35275
\(454\) −46.5225 −2.18341
\(455\) 0 0
\(456\) 7.34264 0.343851
\(457\) 24.0367 1.12439 0.562194 0.827005i \(-0.309957\pi\)
0.562194 + 0.827005i \(0.309957\pi\)
\(458\) −32.8541 −1.53517
\(459\) −7.48350 −0.349300
\(460\) 127.428 5.94138
\(461\) 26.9815 1.25665 0.628327 0.777949i \(-0.283740\pi\)
0.628327 + 0.777949i \(0.283740\pi\)
\(462\) 13.3274 0.620049
\(463\) −32.5496 −1.51271 −0.756355 0.654161i \(-0.773022\pi\)
−0.756355 + 0.654161i \(0.773022\pi\)
\(464\) −12.0235 −0.558177
\(465\) −9.17661 −0.425555
\(466\) −0.740816 −0.0343177
\(467\) −20.5962 −0.953077 −0.476538 0.879154i \(-0.658109\pi\)
−0.476538 + 0.879154i \(0.658109\pi\)
\(468\) 0 0
\(469\) 16.0689 0.741995
\(470\) −17.0131 −0.784758
\(471\) −21.3465 −0.983595
\(472\) 100.679 4.63413
\(473\) 10.1591 0.467118
\(474\) −96.1845 −4.41790
\(475\) 1.33080 0.0610613
\(476\) −9.28019 −0.425357
\(477\) −26.0247 −1.19159
\(478\) 60.3233 2.75912
\(479\) −11.7511 −0.536923 −0.268461 0.963290i \(-0.586515\pi\)
−0.268461 + 0.963290i \(0.586515\pi\)
\(480\) −154.859 −7.06830
\(481\) 0 0
\(482\) −47.6823 −2.17187
\(483\) −39.0872 −1.77853
\(484\) 5.22486 0.237494
\(485\) −2.85495 −0.129636
\(486\) −22.7814 −1.03339
\(487\) −9.45558 −0.428473 −0.214237 0.976782i \(-0.568726\pi\)
−0.214237 + 0.976782i \(0.568726\pi\)
\(488\) −82.2077 −3.72137
\(489\) −58.7215 −2.65548
\(490\) −34.0657 −1.53893
\(491\) 16.0978 0.726482 0.363241 0.931695i \(-0.381670\pi\)
0.363241 + 0.931695i \(0.381670\pi\)
\(492\) 72.3751 3.26292
\(493\) −0.975367 −0.0439283
\(494\) 0 0
\(495\) 16.9145 0.760249
\(496\) −13.0980 −0.588118
\(497\) 0.993290 0.0445551
\(498\) 82.1310 3.68038
\(499\) −30.5933 −1.36954 −0.684772 0.728758i \(-0.740098\pi\)
−0.684772 + 0.728758i \(0.740098\pi\)
\(500\) 6.92683 0.309777
\(501\) −14.4083 −0.643716
\(502\) 55.1625 2.46202
\(503\) 26.5348 1.18313 0.591563 0.806259i \(-0.298511\pi\)
0.591563 + 0.806259i \(0.298511\pi\)
\(504\) 80.7524 3.59700
\(505\) 39.7949 1.77085
\(506\) −21.1893 −0.941980
\(507\) 0 0
\(508\) −21.3783 −0.948510
\(509\) −22.5513 −0.999570 −0.499785 0.866149i \(-0.666588\pi\)
−0.499785 + 0.866149i \(0.666588\pi\)
\(510\) −25.2230 −1.11689
\(511\) 26.9564 1.19248
\(512\) 1.72704 0.0763250
\(513\) −2.08997 −0.0922743
\(514\) 27.2272 1.20094
\(515\) 52.2707 2.30332
\(516\) 154.455 6.79952
\(517\) 2.04588 0.0899777
\(518\) 31.1268 1.36763
\(519\) −61.4203 −2.69605
\(520\) 0 0
\(521\) 16.4510 0.720732 0.360366 0.932811i \(-0.382652\pi\)
0.360366 + 0.932811i \(0.382652\pi\)
\(522\) 13.7509 0.601859
\(523\) −10.0678 −0.440234 −0.220117 0.975473i \(-0.570644\pi\)
−0.220117 + 0.975473i \(0.570644\pi\)
\(524\) −8.56478 −0.374154
\(525\) 22.6667 0.989258
\(526\) −0.261877 −0.0114184
\(527\) −1.06253 −0.0462847
\(528\) 37.3900 1.62719
\(529\) 39.1448 1.70195
\(530\) −39.5841 −1.71943
\(531\) −63.5013 −2.75572
\(532\) −2.59174 −0.112366
\(533\) 0 0
\(534\) −45.3001 −1.96033
\(535\) −14.5169 −0.627618
\(536\) 81.7432 3.53077
\(537\) −3.09703 −0.133647
\(538\) 9.42909 0.406517
\(539\) 4.09650 0.176449
\(540\) 116.051 4.99403
\(541\) −3.30312 −0.142012 −0.0710060 0.997476i \(-0.522621\pi\)
−0.0710060 + 0.997476i \(0.522621\pi\)
\(542\) 41.1614 1.76803
\(543\) −54.6672 −2.34599
\(544\) −17.9307 −0.768771
\(545\) 42.6089 1.82516
\(546\) 0 0
\(547\) 4.05777 0.173498 0.0867489 0.996230i \(-0.472352\pi\)
0.0867489 + 0.996230i \(0.472352\pi\)
\(548\) −38.0254 −1.62436
\(549\) 51.8508 2.21294
\(550\) 12.2877 0.523950
\(551\) −0.272397 −0.0116045
\(552\) −198.838 −8.46310
\(553\) 20.9546 0.891082
\(554\) 55.5577 2.36042
\(555\) 61.1814 2.59701
\(556\) 57.9172 2.45624
\(557\) 6.10464 0.258662 0.129331 0.991601i \(-0.458717\pi\)
0.129331 + 0.991601i \(0.458717\pi\)
\(558\) 14.9798 0.634144
\(559\) 0 0
\(560\) 67.7384 2.86247
\(561\) 3.03314 0.128059
\(562\) −77.3446 −3.26258
\(563\) −17.0418 −0.718225 −0.359112 0.933294i \(-0.616921\pi\)
−0.359112 + 0.933294i \(0.616921\pi\)
\(564\) 31.1047 1.30974
\(565\) 25.8656 1.08817
\(566\) 81.3785 3.42059
\(567\) −7.64919 −0.321236
\(568\) 5.05289 0.212015
\(569\) −7.42389 −0.311226 −0.155613 0.987818i \(-0.549735\pi\)
−0.155613 + 0.987818i \(0.549735\pi\)
\(570\) −7.04419 −0.295049
\(571\) 10.9772 0.459382 0.229691 0.973264i \(-0.426228\pi\)
0.229691 + 0.973264i \(0.426228\pi\)
\(572\) 0 0
\(573\) 56.1301 2.34487
\(574\) −21.8032 −0.910047
\(575\) −36.0379 −1.50288
\(576\) 112.287 4.67863
\(577\) 3.74826 0.156042 0.0780211 0.996952i \(-0.475140\pi\)
0.0780211 + 0.996952i \(0.475140\pi\)
\(578\) 42.7740 1.77916
\(579\) 30.2728 1.25810
\(580\) 15.1255 0.628054
\(581\) −17.8930 −0.742326
\(582\) 7.21762 0.299180
\(583\) 4.76011 0.197144
\(584\) 137.128 5.67440
\(585\) 0 0
\(586\) −29.7728 −1.22990
\(587\) −20.5788 −0.849377 −0.424688 0.905340i \(-0.639616\pi\)
−0.424688 + 0.905340i \(0.639616\pi\)
\(588\) 62.2814 2.56844
\(589\) −0.296741 −0.0122270
\(590\) −96.5868 −3.97642
\(591\) 28.9056 1.18902
\(592\) 87.3258 3.58907
\(593\) −6.50155 −0.266986 −0.133493 0.991050i \(-0.542619\pi\)
−0.133493 + 0.991050i \(0.542619\pi\)
\(594\) −19.2974 −0.791781
\(595\) 5.49505 0.225275
\(596\) −0.609409 −0.0249624
\(597\) 37.0211 1.51517
\(598\) 0 0
\(599\) −22.5421 −0.921045 −0.460522 0.887648i \(-0.652338\pi\)
−0.460522 + 0.887648i \(0.652338\pi\)
\(600\) 115.306 4.70736
\(601\) 42.5783 1.73680 0.868402 0.495860i \(-0.165147\pi\)
0.868402 + 0.495860i \(0.165147\pi\)
\(602\) −46.5300 −1.89642
\(603\) −51.5578 −2.09960
\(604\) 51.6977 2.10355
\(605\) −3.09378 −0.125780
\(606\) −100.606 −4.08684
\(607\) 25.3486 1.02887 0.514434 0.857530i \(-0.328002\pi\)
0.514434 + 0.857530i \(0.328002\pi\)
\(608\) −5.00762 −0.203086
\(609\) −4.63959 −0.188006
\(610\) 78.8663 3.19320
\(611\) 0 0
\(612\) 29.7759 1.20362
\(613\) −16.9842 −0.685985 −0.342992 0.939338i \(-0.611441\pi\)
−0.342992 + 0.939338i \(0.611441\pi\)
\(614\) −13.8017 −0.556992
\(615\) −42.8553 −1.72809
\(616\) −14.7702 −0.595109
\(617\) 44.9940 1.81139 0.905695 0.423929i \(-0.139350\pi\)
0.905695 + 0.423929i \(0.139350\pi\)
\(618\) −132.146 −5.31570
\(619\) 11.3275 0.455292 0.227646 0.973744i \(-0.426897\pi\)
0.227646 + 0.973744i \(0.426897\pi\)
\(620\) 16.4773 0.661744
\(621\) 56.5960 2.27112
\(622\) −57.4644 −2.30411
\(623\) 9.86904 0.395395
\(624\) 0 0
\(625\) −26.9590 −1.07836
\(626\) −5.16289 −0.206351
\(627\) 0.847085 0.0338293
\(628\) 38.3293 1.52950
\(629\) 7.08402 0.282459
\(630\) −77.4701 −3.08648
\(631\) 3.00798 0.119746 0.0598730 0.998206i \(-0.480930\pi\)
0.0598730 + 0.998206i \(0.480930\pi\)
\(632\) 106.597 4.24020
\(633\) −5.82014 −0.231330
\(634\) 22.7225 0.902425
\(635\) 12.6587 0.502345
\(636\) 72.3707 2.86968
\(637\) 0 0
\(638\) −2.51514 −0.0995752
\(639\) −3.18701 −0.126076
\(640\) 64.3538 2.54381
\(641\) −15.0695 −0.595208 −0.297604 0.954689i \(-0.596188\pi\)
−0.297604 + 0.954689i \(0.596188\pi\)
\(642\) 36.7002 1.44844
\(643\) 16.4528 0.648833 0.324417 0.945914i \(-0.394832\pi\)
0.324417 + 0.945914i \(0.394832\pi\)
\(644\) 70.1840 2.76564
\(645\) −91.4572 −3.60112
\(646\) −0.815627 −0.0320904
\(647\) 30.2788 1.19038 0.595191 0.803585i \(-0.297077\pi\)
0.595191 + 0.803585i \(0.297077\pi\)
\(648\) −38.9116 −1.52859
\(649\) 11.6149 0.455923
\(650\) 0 0
\(651\) −5.05422 −0.198090
\(652\) 105.439 4.12930
\(653\) 23.8518 0.933394 0.466697 0.884417i \(-0.345444\pi\)
0.466697 + 0.884417i \(0.345444\pi\)
\(654\) −107.720 −4.21219
\(655\) 5.07144 0.198157
\(656\) −61.1685 −2.38823
\(657\) −86.4908 −3.37433
\(658\) −9.37036 −0.365295
\(659\) −11.9043 −0.463727 −0.231863 0.972748i \(-0.574482\pi\)
−0.231863 + 0.972748i \(0.574482\pi\)
\(660\) −47.0365 −1.83089
\(661\) 4.50059 0.175053 0.0875263 0.996162i \(-0.472104\pi\)
0.0875263 + 0.996162i \(0.472104\pi\)
\(662\) 66.3969 2.58059
\(663\) 0 0
\(664\) −91.0221 −3.53234
\(665\) 1.53464 0.0595108
\(666\) −99.8717 −3.86995
\(667\) 7.37648 0.285619
\(668\) 25.8712 1.00099
\(669\) −9.45857 −0.365690
\(670\) −78.4206 −3.02965
\(671\) −9.48390 −0.366122
\(672\) −85.2918 −3.29020
\(673\) −9.30191 −0.358562 −0.179281 0.983798i \(-0.557377\pi\)
−0.179281 + 0.983798i \(0.557377\pi\)
\(674\) −69.4568 −2.67538
\(675\) −32.8202 −1.26325
\(676\) 0 0
\(677\) 44.0200 1.69183 0.845913 0.533322i \(-0.179056\pi\)
0.845913 + 0.533322i \(0.179056\pi\)
\(678\) −65.3911 −2.51133
\(679\) −1.57242 −0.0603441
\(680\) 27.9535 1.07197
\(681\) −50.3639 −1.92995
\(682\) −2.73991 −0.104917
\(683\) −17.7684 −0.679891 −0.339945 0.940445i \(-0.610409\pi\)
−0.339945 + 0.940445i \(0.610409\pi\)
\(684\) 8.31571 0.317959
\(685\) 22.5159 0.860287
\(686\) −50.8232 −1.94044
\(687\) −35.5669 −1.35696
\(688\) −130.539 −4.97676
\(689\) 0 0
\(690\) 190.756 7.26195
\(691\) −6.75142 −0.256836 −0.128418 0.991720i \(-0.540990\pi\)
−0.128418 + 0.991720i \(0.540990\pi\)
\(692\) 110.285 4.19239
\(693\) 9.31601 0.353886
\(694\) −5.34329 −0.202829
\(695\) −34.2943 −1.30086
\(696\) −23.6017 −0.894621
\(697\) −4.96209 −0.187953
\(698\) −25.9483 −0.982159
\(699\) −0.801986 −0.0303339
\(700\) −40.6998 −1.53831
\(701\) −10.2838 −0.388412 −0.194206 0.980961i \(-0.562213\pi\)
−0.194206 + 0.980961i \(0.562213\pi\)
\(702\) 0 0
\(703\) 1.97840 0.0746169
\(704\) −20.5382 −0.774061
\(705\) −18.4179 −0.693660
\(706\) 13.3765 0.503430
\(707\) 21.9179 0.824307
\(708\) 176.587 6.63655
\(709\) 26.3616 0.990029 0.495015 0.868885i \(-0.335163\pi\)
0.495015 + 0.868885i \(0.335163\pi\)
\(710\) −4.84751 −0.181924
\(711\) −67.2338 −2.52147
\(712\) 50.2041 1.88148
\(713\) 8.03570 0.300939
\(714\) −13.8921 −0.519899
\(715\) 0 0
\(716\) 5.56094 0.207822
\(717\) 65.3043 2.43883
\(718\) 42.5839 1.58922
\(719\) 31.9625 1.19200 0.596000 0.802984i \(-0.296756\pi\)
0.596000 + 0.802984i \(0.296756\pi\)
\(720\) −217.341 −8.09983
\(721\) 28.7892 1.07217
\(722\) 50.8425 1.89216
\(723\) −51.6195 −1.91975
\(724\) 98.1590 3.64805
\(725\) −4.27764 −0.158867
\(726\) 7.82142 0.290280
\(727\) −6.35132 −0.235557 −0.117779 0.993040i \(-0.537577\pi\)
−0.117779 + 0.993040i \(0.537577\pi\)
\(728\) 0 0
\(729\) −38.1296 −1.41221
\(730\) −131.554 −4.86905
\(731\) −10.5896 −0.391669
\(732\) −144.189 −5.32939
\(733\) −33.9768 −1.25496 −0.627481 0.778632i \(-0.715914\pi\)
−0.627481 + 0.778632i \(0.715914\pi\)
\(734\) 11.3795 0.420026
\(735\) −36.8785 −1.36028
\(736\) 135.606 4.99849
\(737\) 9.43031 0.347370
\(738\) 69.9563 2.57513
\(739\) −31.1540 −1.14602 −0.573009 0.819549i \(-0.694224\pi\)
−0.573009 + 0.819549i \(0.694224\pi\)
\(740\) −109.856 −4.03838
\(741\) 0 0
\(742\) −21.8018 −0.800370
\(743\) 39.1173 1.43507 0.717537 0.696520i \(-0.245269\pi\)
0.717537 + 0.696520i \(0.245269\pi\)
\(744\) −25.7109 −0.942609
\(745\) 0.360847 0.0132204
\(746\) 8.72403 0.319410
\(747\) 57.4103 2.10053
\(748\) −5.44623 −0.199134
\(749\) −7.99547 −0.292148
\(750\) 10.3692 0.378630
\(751\) −2.15947 −0.0788001 −0.0394000 0.999224i \(-0.512545\pi\)
−0.0394000 + 0.999224i \(0.512545\pi\)
\(752\) −26.2884 −0.958640
\(753\) 59.7173 2.17622
\(754\) 0 0
\(755\) −30.6116 −1.11407
\(756\) 63.9174 2.32466
\(757\) −0.315358 −0.0114619 −0.00573094 0.999984i \(-0.501824\pi\)
−0.00573094 + 0.999984i \(0.501824\pi\)
\(758\) 56.0607 2.03622
\(759\) −22.9389 −0.832631
\(760\) 7.80676 0.283181
\(761\) 20.6516 0.748622 0.374311 0.927303i \(-0.377879\pi\)
0.374311 + 0.927303i \(0.377879\pi\)
\(762\) −32.0026 −1.15933
\(763\) 23.4678 0.849590
\(764\) −100.786 −3.64630
\(765\) −17.6311 −0.637454
\(766\) 69.0223 2.49388
\(767\) 0 0
\(768\) −43.1675 −1.55767
\(769\) −12.7162 −0.458559 −0.229280 0.973361i \(-0.573637\pi\)
−0.229280 + 0.973361i \(0.573637\pi\)
\(770\) 14.1699 0.510646
\(771\) 29.4754 1.06153
\(772\) −54.3571 −1.95635
\(773\) 8.70103 0.312954 0.156477 0.987682i \(-0.449986\pi\)
0.156477 + 0.987682i \(0.449986\pi\)
\(774\) 149.293 5.36624
\(775\) −4.65992 −0.167389
\(776\) −7.99896 −0.287146
\(777\) 33.6970 1.20887
\(778\) −45.2322 −1.62165
\(779\) −1.38580 −0.0496513
\(780\) 0 0
\(781\) 0.582928 0.0208588
\(782\) 22.0871 0.789832
\(783\) 6.71786 0.240077
\(784\) −52.6376 −1.87992
\(785\) −22.6958 −0.810048
\(786\) −12.8212 −0.457316
\(787\) −36.4098 −1.29787 −0.648934 0.760845i \(-0.724785\pi\)
−0.648934 + 0.760845i \(0.724785\pi\)
\(788\) −51.9021 −1.84894
\(789\) −0.283500 −0.0100929
\(790\) −102.264 −3.63840
\(791\) 14.2460 0.506531
\(792\) 47.3908 1.68396
\(793\) 0 0
\(794\) 9.18828 0.326080
\(795\) −42.8527 −1.51983
\(796\) −66.4741 −2.35611
\(797\) 3.32151 0.117654 0.0588270 0.998268i \(-0.481264\pi\)
0.0588270 + 0.998268i \(0.481264\pi\)
\(798\) −3.87974 −0.137341
\(799\) −2.13256 −0.0754446
\(800\) −78.6379 −2.78027
\(801\) −31.6652 −1.11884
\(802\) −15.6635 −0.553096
\(803\) 15.8198 0.558269
\(804\) 143.374 5.05643
\(805\) −41.5579 −1.46472
\(806\) 0 0
\(807\) 10.2077 0.359327
\(808\) 111.497 3.92245
\(809\) 7.94177 0.279218 0.139609 0.990207i \(-0.455415\pi\)
0.139609 + 0.990207i \(0.455415\pi\)
\(810\) 37.3300 1.31164
\(811\) −18.5407 −0.651052 −0.325526 0.945533i \(-0.605541\pi\)
−0.325526 + 0.945533i \(0.605541\pi\)
\(812\) 8.33072 0.292351
\(813\) 44.5601 1.56279
\(814\) 18.2673 0.640267
\(815\) −62.4332 −2.18694
\(816\) −38.9741 −1.36437
\(817\) −2.95742 −0.103467
\(818\) −36.1452 −1.26379
\(819\) 0 0
\(820\) 76.9499 2.68721
\(821\) −26.9214 −0.939565 −0.469782 0.882782i \(-0.655668\pi\)
−0.469782 + 0.882782i \(0.655668\pi\)
\(822\) −56.9226 −1.98541
\(823\) −48.5760 −1.69325 −0.846626 0.532188i \(-0.821370\pi\)
−0.846626 + 0.532188i \(0.821370\pi\)
\(824\) 146.452 5.10188
\(825\) 13.3023 0.463128
\(826\) −53.1973 −1.85097
\(827\) 47.6008 1.65524 0.827621 0.561287i \(-0.189694\pi\)
0.827621 + 0.561287i \(0.189694\pi\)
\(828\) −225.188 −7.82583
\(829\) −3.40020 −0.118094 −0.0590470 0.998255i \(-0.518806\pi\)
−0.0590470 + 0.998255i \(0.518806\pi\)
\(830\) 87.3224 3.03100
\(831\) 60.1451 2.08641
\(832\) 0 0
\(833\) −4.27006 −0.147949
\(834\) 86.6999 3.00217
\(835\) −15.3190 −0.530137
\(836\) −1.52100 −0.0526050
\(837\) 7.31822 0.252955
\(838\) 68.7020 2.37327
\(839\) 42.8825 1.48047 0.740233 0.672350i \(-0.234715\pi\)
0.740233 + 0.672350i \(0.234715\pi\)
\(840\) 132.968 4.58783
\(841\) −28.1244 −0.969808
\(842\) 81.9825 2.82530
\(843\) −83.7310 −2.88385
\(844\) 10.4505 0.359721
\(845\) 0 0
\(846\) 30.0652 1.03366
\(847\) −1.70397 −0.0585490
\(848\) −61.1647 −2.10040
\(849\) 88.0980 3.02351
\(850\) −12.8083 −0.439322
\(851\) −53.5749 −1.83652
\(852\) 8.86258 0.303627
\(853\) 41.0285 1.40479 0.702395 0.711787i \(-0.252114\pi\)
0.702395 + 0.711787i \(0.252114\pi\)
\(854\) 43.4373 1.48639
\(855\) −4.92396 −0.168396
\(856\) −40.6732 −1.39018
\(857\) −46.7316 −1.59632 −0.798161 0.602444i \(-0.794194\pi\)
−0.798161 + 0.602444i \(0.794194\pi\)
\(858\) 0 0
\(859\) 5.18746 0.176994 0.0884970 0.996076i \(-0.471794\pi\)
0.0884970 + 0.996076i \(0.471794\pi\)
\(860\) 164.218 5.59979
\(861\) −23.6035 −0.804405
\(862\) −24.2792 −0.826953
\(863\) 44.3316 1.50907 0.754533 0.656262i \(-0.227864\pi\)
0.754533 + 0.656262i \(0.227864\pi\)
\(864\) 123.498 4.20148
\(865\) −65.3025 −2.22035
\(866\) 55.9448 1.90108
\(867\) 46.3059 1.57263
\(868\) 9.07522 0.308033
\(869\) 12.2976 0.417166
\(870\) 22.6424 0.767649
\(871\) 0 0
\(872\) 119.381 4.04276
\(873\) 5.04518 0.170754
\(874\) 6.16841 0.208649
\(875\) −2.25902 −0.0763690
\(876\) 240.518 8.12633
\(877\) −28.7343 −0.970288 −0.485144 0.874434i \(-0.661233\pi\)
−0.485144 + 0.874434i \(0.661233\pi\)
\(878\) −67.6889 −2.28439
\(879\) −32.2312 −1.08713
\(880\) 39.7533 1.34008
\(881\) 3.46294 0.116669 0.0583347 0.998297i \(-0.481421\pi\)
0.0583347 + 0.998297i \(0.481421\pi\)
\(882\) 60.1999 2.02704
\(883\) −25.7431 −0.866326 −0.433163 0.901316i \(-0.642602\pi\)
−0.433163 + 0.901316i \(0.642602\pi\)
\(884\) 0 0
\(885\) −104.562 −3.51482
\(886\) −101.099 −3.39649
\(887\) 56.3033 1.89048 0.945240 0.326375i \(-0.105827\pi\)
0.945240 + 0.326375i \(0.105827\pi\)
\(888\) 171.418 5.75240
\(889\) 6.97205 0.233835
\(890\) −48.1635 −1.61444
\(891\) −4.48905 −0.150389
\(892\) 16.9836 0.568652
\(893\) −0.595575 −0.0199302
\(894\) −0.912263 −0.0305106
\(895\) −3.29279 −0.110066
\(896\) 35.4443 1.18411
\(897\) 0 0
\(898\) 25.0311 0.835298
\(899\) 0.953825 0.0318118
\(900\) 130.587 4.35290
\(901\) −4.96179 −0.165301
\(902\) −12.7955 −0.426045
\(903\) −50.3720 −1.67628
\(904\) 72.4700 2.41032
\(905\) −58.1226 −1.93206
\(906\) 77.3896 2.57110
\(907\) 25.6494 0.851676 0.425838 0.904799i \(-0.359979\pi\)
0.425838 + 0.904799i \(0.359979\pi\)
\(908\) 90.4322 3.00110
\(909\) −70.3245 −2.33251
\(910\) 0 0
\(911\) 35.7349 1.18395 0.591975 0.805957i \(-0.298349\pi\)
0.591975 + 0.805957i \(0.298349\pi\)
\(912\) −10.8846 −0.360424
\(913\) −10.5008 −0.347525
\(914\) −64.6084 −2.13706
\(915\) 85.3784 2.82252
\(916\) 63.8630 2.11009
\(917\) 2.79320 0.0922397
\(918\) 20.1150 0.663893
\(919\) −7.42382 −0.244889 −0.122445 0.992475i \(-0.539073\pi\)
−0.122445 + 0.992475i \(0.539073\pi\)
\(920\) −211.406 −6.96985
\(921\) −14.9414 −0.492334
\(922\) −72.5238 −2.38845
\(923\) 0 0
\(924\) −25.9064 −0.852258
\(925\) 31.0682 1.02152
\(926\) 87.4905 2.87512
\(927\) −92.3714 −3.03387
\(928\) 16.0962 0.528382
\(929\) −28.5106 −0.935403 −0.467702 0.883886i \(-0.654918\pi\)
−0.467702 + 0.883886i \(0.654918\pi\)
\(930\) 24.6659 0.808827
\(931\) −1.19253 −0.0390835
\(932\) 1.44003 0.0471696
\(933\) −62.2093 −2.03664
\(934\) 55.3606 1.81146
\(935\) 3.22486 0.105464
\(936\) 0 0
\(937\) 14.3343 0.468280 0.234140 0.972203i \(-0.424773\pi\)
0.234140 + 0.972203i \(0.424773\pi\)
\(938\) −43.1919 −1.41026
\(939\) −5.58920 −0.182396
\(940\) 33.0708 1.07865
\(941\) 26.5519 0.865568 0.432784 0.901498i \(-0.357531\pi\)
0.432784 + 0.901498i \(0.357531\pi\)
\(942\) 57.3775 1.86946
\(943\) 37.5272 1.22205
\(944\) −149.244 −4.85749
\(945\) −37.8473 −1.23117
\(946\) −27.3069 −0.887823
\(947\) −51.3198 −1.66767 −0.833835 0.552013i \(-0.813860\pi\)
−0.833835 + 0.552013i \(0.813860\pi\)
\(948\) 186.967 6.07240
\(949\) 0 0
\(950\) −3.57707 −0.116055
\(951\) 24.5987 0.797668
\(952\) 15.3960 0.498987
\(953\) 32.8316 1.06352 0.531759 0.846895i \(-0.321531\pi\)
0.531759 + 0.846895i \(0.321531\pi\)
\(954\) 69.9520 2.26478
\(955\) 59.6780 1.93113
\(956\) −117.259 −3.79242
\(957\) −2.72281 −0.0880161
\(958\) 31.5860 1.02050
\(959\) 12.4011 0.400453
\(960\) 184.894 5.96742
\(961\) −29.9609 −0.966482
\(962\) 0 0
\(963\) 25.6538 0.826682
\(964\) 92.6867 2.98524
\(965\) 32.1863 1.03611
\(966\) 105.063 3.38034
\(967\) 26.5335 0.853259 0.426630 0.904426i \(-0.359701\pi\)
0.426630 + 0.904426i \(0.359701\pi\)
\(968\) −8.66813 −0.278604
\(969\) −0.882975 −0.0283652
\(970\) 7.67384 0.246392
\(971\) 0.504385 0.0161865 0.00809324 0.999967i \(-0.497424\pi\)
0.00809324 + 0.999967i \(0.497424\pi\)
\(972\) 44.2834 1.42039
\(973\) −18.8884 −0.605533
\(974\) 25.4157 0.814373
\(975\) 0 0
\(976\) 121.863 3.90073
\(977\) −19.3758 −0.619886 −0.309943 0.950755i \(-0.600310\pi\)
−0.309943 + 0.950755i \(0.600310\pi\)
\(978\) 157.838 5.04710
\(979\) 5.79180 0.185107
\(980\) 66.2181 2.11526
\(981\) −75.2973 −2.40406
\(982\) −43.2693 −1.38078
\(983\) 10.6735 0.340432 0.170216 0.985407i \(-0.445554\pi\)
0.170216 + 0.985407i \(0.445554\pi\)
\(984\) −120.072 −3.82774
\(985\) 30.7327 0.979224
\(986\) 2.62170 0.0834919
\(987\) −10.1441 −0.322890
\(988\) 0 0
\(989\) 80.0865 2.54660
\(990\) −45.4646 −1.44496
\(991\) −8.52193 −0.270708 −0.135354 0.990797i \(-0.543217\pi\)
−0.135354 + 0.990797i \(0.543217\pi\)
\(992\) 17.5346 0.556725
\(993\) 71.8794 2.28102
\(994\) −2.66987 −0.0846832
\(995\) 39.3611 1.24783
\(996\) −159.649 −5.05868
\(997\) −35.8287 −1.13471 −0.567354 0.823474i \(-0.692033\pi\)
−0.567354 + 0.823474i \(0.692033\pi\)
\(998\) 82.2320 2.60301
\(999\) −48.7913 −1.54369
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 1859.2.a.s.1.1 21
13.12 even 2 1859.2.a.t.1.21 yes 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.1 21 1.1 even 1 trivial
1859.2.a.t.1.21 yes 21 13.12 even 2