Properties

Label 1441.2.a.e.1.22
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $0$
Dimension $28$
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] = [1441,2,Mod(1,1441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1441, 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("1441.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.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: \(11.5064429313\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) \(=\) 1441.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.07554 q^{2} -2.88027 q^{3} +2.30788 q^{4} -3.62707 q^{5} -5.97813 q^{6} -5.05987 q^{7} +0.639017 q^{8} +5.29598 q^{9} +O(q^{10})\) \(q+2.07554 q^{2} -2.88027 q^{3} +2.30788 q^{4} -3.62707 q^{5} -5.97813 q^{6} -5.05987 q^{7} +0.639017 q^{8} +5.29598 q^{9} -7.52814 q^{10} +1.00000 q^{11} -6.64733 q^{12} +0.599325 q^{13} -10.5020 q^{14} +10.4470 q^{15} -3.28945 q^{16} -3.13619 q^{17} +10.9920 q^{18} +3.58210 q^{19} -8.37084 q^{20} +14.5738 q^{21} +2.07554 q^{22} +6.21835 q^{23} -1.84055 q^{24} +8.15564 q^{25} +1.24393 q^{26} -6.61305 q^{27} -11.6776 q^{28} +1.58591 q^{29} +21.6831 q^{30} -1.68617 q^{31} -8.10543 q^{32} -2.88027 q^{33} -6.50930 q^{34} +18.3525 q^{35} +12.2225 q^{36} +0.605232 q^{37} +7.43481 q^{38} -1.72622 q^{39} -2.31776 q^{40} -10.4360 q^{41} +30.2486 q^{42} +0.0776603 q^{43} +2.30788 q^{44} -19.2089 q^{45} +12.9065 q^{46} -2.17142 q^{47} +9.47452 q^{48} +18.6023 q^{49} +16.9274 q^{50} +9.03309 q^{51} +1.38317 q^{52} -0.650569 q^{53} -13.7257 q^{54} -3.62707 q^{55} -3.23334 q^{56} -10.3174 q^{57} +3.29163 q^{58} +12.5623 q^{59} +24.1103 q^{60} -10.8256 q^{61} -3.49971 q^{62} -26.7970 q^{63} -10.2443 q^{64} -2.17380 q^{65} -5.97813 q^{66} -13.6832 q^{67} -7.23795 q^{68} -17.9106 q^{69} +38.0914 q^{70} +15.3074 q^{71} +3.38422 q^{72} +9.83072 q^{73} +1.25618 q^{74} -23.4905 q^{75} +8.26707 q^{76} -5.05987 q^{77} -3.58285 q^{78} +1.02929 q^{79} +11.9311 q^{80} +3.15947 q^{81} -21.6604 q^{82} -3.03240 q^{83} +33.6346 q^{84} +11.3752 q^{85} +0.161187 q^{86} -4.56787 q^{87} +0.639017 q^{88} -7.74657 q^{89} -39.8689 q^{90} -3.03251 q^{91} +14.3512 q^{92} +4.85663 q^{93} -4.50687 q^{94} -12.9925 q^{95} +23.3459 q^{96} -7.34334 q^{97} +38.6098 q^{98} +5.29598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.07554 1.46763 0.733815 0.679349i \(-0.237738\pi\)
0.733815 + 0.679349i \(0.237738\pi\)
\(3\) −2.88027 −1.66293 −0.831464 0.555579i \(-0.812497\pi\)
−0.831464 + 0.555579i \(0.812497\pi\)
\(4\) 2.30788 1.15394
\(5\) −3.62707 −1.62208 −0.811038 0.584994i \(-0.801097\pi\)
−0.811038 + 0.584994i \(0.801097\pi\)
\(6\) −5.97813 −2.44056
\(7\) −5.05987 −1.91245 −0.956225 0.292631i \(-0.905469\pi\)
−0.956225 + 0.292631i \(0.905469\pi\)
\(8\) 0.639017 0.225927
\(9\) 5.29598 1.76533
\(10\) −7.52814 −2.38061
\(11\) 1.00000 0.301511
\(12\) −6.64733 −1.91892
\(13\) 0.599325 0.166223 0.0831115 0.996540i \(-0.473514\pi\)
0.0831115 + 0.996540i \(0.473514\pi\)
\(14\) −10.5020 −2.80677
\(15\) 10.4470 2.69739
\(16\) −3.28945 −0.822363
\(17\) −3.13619 −0.760638 −0.380319 0.924855i \(-0.624186\pi\)
−0.380319 + 0.924855i \(0.624186\pi\)
\(18\) 10.9920 2.59085
\(19\) 3.58210 0.821791 0.410896 0.911682i \(-0.365216\pi\)
0.410896 + 0.911682i \(0.365216\pi\)
\(20\) −8.37084 −1.87178
\(21\) 14.5738 3.18027
\(22\) 2.07554 0.442507
\(23\) 6.21835 1.29662 0.648308 0.761378i \(-0.275477\pi\)
0.648308 + 0.761378i \(0.275477\pi\)
\(24\) −1.84055 −0.375700
\(25\) 8.15564 1.63113
\(26\) 1.24393 0.243954
\(27\) −6.61305 −1.27268
\(28\) −11.6776 −2.20685
\(29\) 1.58591 0.294497 0.147248 0.989100i \(-0.452958\pi\)
0.147248 + 0.989100i \(0.452958\pi\)
\(30\) 21.6831 3.95878
\(31\) −1.68617 −0.302845 −0.151422 0.988469i \(-0.548385\pi\)
−0.151422 + 0.988469i \(0.548385\pi\)
\(32\) −8.10543 −1.43285
\(33\) −2.88027 −0.501391
\(34\) −6.50930 −1.11634
\(35\) 18.3525 3.10214
\(36\) 12.2225 2.03708
\(37\) 0.605232 0.0994995 0.0497497 0.998762i \(-0.484158\pi\)
0.0497497 + 0.998762i \(0.484158\pi\)
\(38\) 7.43481 1.20609
\(39\) −1.72622 −0.276417
\(40\) −2.31776 −0.366470
\(41\) −10.4360 −1.62983 −0.814916 0.579579i \(-0.803217\pi\)
−0.814916 + 0.579579i \(0.803217\pi\)
\(42\) 30.2486 4.66746
\(43\) 0.0776603 0.0118431 0.00592154 0.999982i \(-0.498115\pi\)
0.00592154 + 0.999982i \(0.498115\pi\)
\(44\) 2.30788 0.347926
\(45\) −19.2089 −2.86349
\(46\) 12.9065 1.90295
\(47\) −2.17142 −0.316734 −0.158367 0.987380i \(-0.550623\pi\)
−0.158367 + 0.987380i \(0.550623\pi\)
\(48\) 9.47452 1.36753
\(49\) 18.6023 2.65747
\(50\) 16.9274 2.39389
\(51\) 9.03309 1.26489
\(52\) 1.38317 0.191811
\(53\) −0.650569 −0.0893625 −0.0446813 0.999001i \(-0.514227\pi\)
−0.0446813 + 0.999001i \(0.514227\pi\)
\(54\) −13.7257 −1.86783
\(55\) −3.62707 −0.489074
\(56\) −3.23334 −0.432074
\(57\) −10.3174 −1.36658
\(58\) 3.29163 0.432213
\(59\) 12.5623 1.63547 0.817737 0.575592i \(-0.195228\pi\)
0.817737 + 0.575592i \(0.195228\pi\)
\(60\) 24.1103 3.11263
\(61\) −10.8256 −1.38608 −0.693038 0.720901i \(-0.743728\pi\)
−0.693038 + 0.720901i \(0.743728\pi\)
\(62\) −3.49971 −0.444464
\(63\) −26.7970 −3.37610
\(64\) −10.2443 −1.28053
\(65\) −2.17380 −0.269626
\(66\) −5.97813 −0.735857
\(67\) −13.6832 −1.67167 −0.835836 0.548980i \(-0.815016\pi\)
−0.835836 + 0.548980i \(0.815016\pi\)
\(68\) −7.23795 −0.877731
\(69\) −17.9106 −2.15618
\(70\) 38.0914 4.55279
\(71\) 15.3074 1.81666 0.908330 0.418255i \(-0.137358\pi\)
0.908330 + 0.418255i \(0.137358\pi\)
\(72\) 3.38422 0.398835
\(73\) 9.83072 1.15060 0.575299 0.817943i \(-0.304886\pi\)
0.575299 + 0.817943i \(0.304886\pi\)
\(74\) 1.25618 0.146028
\(75\) −23.4905 −2.71245
\(76\) 8.26707 0.948297
\(77\) −5.05987 −0.576626
\(78\) −3.58285 −0.405678
\(79\) 1.02929 0.115804 0.0579021 0.998322i \(-0.481559\pi\)
0.0579021 + 0.998322i \(0.481559\pi\)
\(80\) 11.9311 1.33393
\(81\) 3.15947 0.351052
\(82\) −21.6604 −2.39199
\(83\) −3.03240 −0.332850 −0.166425 0.986054i \(-0.553222\pi\)
−0.166425 + 0.986054i \(0.553222\pi\)
\(84\) 33.6346 3.66984
\(85\) 11.3752 1.23381
\(86\) 0.161187 0.0173813
\(87\) −4.56787 −0.489727
\(88\) 0.639017 0.0681195
\(89\) −7.74657 −0.821135 −0.410567 0.911830i \(-0.634669\pi\)
−0.410567 + 0.911830i \(0.634669\pi\)
\(90\) −39.8689 −4.20255
\(91\) −3.03251 −0.317893
\(92\) 14.3512 1.49622
\(93\) 4.85663 0.503609
\(94\) −4.50687 −0.464849
\(95\) −12.9925 −1.33301
\(96\) 23.3459 2.38273
\(97\) −7.34334 −0.745603 −0.372801 0.927911i \(-0.621603\pi\)
−0.372801 + 0.927911i \(0.621603\pi\)
\(98\) 38.6098 3.90018
\(99\) 5.29598 0.532266
\(100\) 18.8222 1.88222
\(101\) 19.8066 1.97083 0.985416 0.170165i \(-0.0544300\pi\)
0.985416 + 0.170165i \(0.0544300\pi\)
\(102\) 18.7486 1.85639
\(103\) 8.56496 0.843931 0.421966 0.906612i \(-0.361340\pi\)
0.421966 + 0.906612i \(0.361340\pi\)
\(104\) 0.382979 0.0375542
\(105\) −52.8602 −5.15863
\(106\) −1.35028 −0.131151
\(107\) 1.50416 0.145413 0.0727065 0.997353i \(-0.476836\pi\)
0.0727065 + 0.997353i \(0.476836\pi\)
\(108\) −15.2621 −1.46860
\(109\) 4.72854 0.452912 0.226456 0.974021i \(-0.427286\pi\)
0.226456 + 0.974021i \(0.427286\pi\)
\(110\) −7.52814 −0.717780
\(111\) −1.74323 −0.165460
\(112\) 16.6442 1.57273
\(113\) −17.8995 −1.68385 −0.841923 0.539597i \(-0.818576\pi\)
−0.841923 + 0.539597i \(0.818576\pi\)
\(114\) −21.4143 −2.00563
\(115\) −22.5544 −2.10321
\(116\) 3.66010 0.339832
\(117\) 3.17402 0.293438
\(118\) 26.0736 2.40027
\(119\) 15.8687 1.45468
\(120\) 6.67579 0.609413
\(121\) 1.00000 0.0909091
\(122\) −22.4690 −2.03425
\(123\) 30.0586 2.71029
\(124\) −3.89147 −0.349464
\(125\) −11.4457 −1.02374
\(126\) −55.6183 −4.95487
\(127\) 22.0619 1.95768 0.978839 0.204634i \(-0.0656004\pi\)
0.978839 + 0.204634i \(0.0656004\pi\)
\(128\) −5.05157 −0.446500
\(129\) −0.223683 −0.0196942
\(130\) −4.51181 −0.395712
\(131\) −1.00000 −0.0873704
\(132\) −6.64733 −0.578576
\(133\) −18.1250 −1.57163
\(134\) −28.4001 −2.45340
\(135\) 23.9860 2.06439
\(136\) −2.00408 −0.171849
\(137\) 18.1008 1.54646 0.773229 0.634127i \(-0.218641\pi\)
0.773229 + 0.634127i \(0.218641\pi\)
\(138\) −37.1741 −3.16447
\(139\) 6.83730 0.579932 0.289966 0.957037i \(-0.406356\pi\)
0.289966 + 0.957037i \(0.406356\pi\)
\(140\) 42.3554 3.57968
\(141\) 6.25428 0.526706
\(142\) 31.7713 2.66618
\(143\) 0.599325 0.0501181
\(144\) −17.4209 −1.45174
\(145\) −5.75222 −0.477696
\(146\) 20.4041 1.68865
\(147\) −53.5797 −4.41918
\(148\) 1.39680 0.114816
\(149\) −1.95100 −0.159832 −0.0799161 0.996802i \(-0.525465\pi\)
−0.0799161 + 0.996802i \(0.525465\pi\)
\(150\) −48.7555 −3.98087
\(151\) 7.09464 0.577353 0.288677 0.957427i \(-0.406785\pi\)
0.288677 + 0.957427i \(0.406785\pi\)
\(152\) 2.28903 0.185665
\(153\) −16.6092 −1.34277
\(154\) −10.5020 −0.846273
\(155\) 6.11585 0.491237
\(156\) −3.98391 −0.318968
\(157\) 4.14969 0.331182 0.165591 0.986195i \(-0.447047\pi\)
0.165591 + 0.986195i \(0.447047\pi\)
\(158\) 2.13634 0.169958
\(159\) 1.87382 0.148603
\(160\) 29.3990 2.32419
\(161\) −31.4640 −2.47971
\(162\) 6.55762 0.515215
\(163\) −13.9793 −1.09494 −0.547472 0.836824i \(-0.684410\pi\)
−0.547472 + 0.836824i \(0.684410\pi\)
\(164\) −24.0851 −1.88073
\(165\) 10.4470 0.813295
\(166\) −6.29389 −0.488500
\(167\) 11.5905 0.896904 0.448452 0.893807i \(-0.351976\pi\)
0.448452 + 0.893807i \(0.351976\pi\)
\(168\) 9.31292 0.718507
\(169\) −12.6408 −0.972370
\(170\) 23.6097 1.81078
\(171\) 18.9708 1.45073
\(172\) 0.179231 0.0136662
\(173\) −11.7666 −0.894600 −0.447300 0.894384i \(-0.647614\pi\)
−0.447300 + 0.894384i \(0.647614\pi\)
\(174\) −9.48081 −0.718738
\(175\) −41.2665 −3.11945
\(176\) −3.28945 −0.247952
\(177\) −36.1829 −2.71967
\(178\) −16.0783 −1.20512
\(179\) −11.0446 −0.825509 −0.412754 0.910842i \(-0.635433\pi\)
−0.412754 + 0.910842i \(0.635433\pi\)
\(180\) −44.3318 −3.30430
\(181\) −17.9824 −1.33662 −0.668311 0.743882i \(-0.732982\pi\)
−0.668311 + 0.743882i \(0.732982\pi\)
\(182\) −6.29410 −0.466550
\(183\) 31.1807 2.30494
\(184\) 3.97363 0.292940
\(185\) −2.19522 −0.161396
\(186\) 10.0801 0.739111
\(187\) −3.13619 −0.229341
\(188\) −5.01137 −0.365492
\(189\) 33.4612 2.43394
\(190\) −26.9666 −1.95636
\(191\) 17.6166 1.27469 0.637345 0.770579i \(-0.280033\pi\)
0.637345 + 0.770579i \(0.280033\pi\)
\(192\) 29.5063 2.12944
\(193\) 9.99634 0.719552 0.359776 0.933039i \(-0.382853\pi\)
0.359776 + 0.933039i \(0.382853\pi\)
\(194\) −15.2414 −1.09427
\(195\) 6.26113 0.448369
\(196\) 42.9318 3.06656
\(197\) −10.6889 −0.761552 −0.380776 0.924667i \(-0.624343\pi\)
−0.380776 + 0.924667i \(0.624343\pi\)
\(198\) 10.9920 0.781170
\(199\) 9.24682 0.655490 0.327745 0.944766i \(-0.393711\pi\)
0.327745 + 0.944766i \(0.393711\pi\)
\(200\) 5.21160 0.368516
\(201\) 39.4114 2.77987
\(202\) 41.1095 2.89245
\(203\) −8.02452 −0.563211
\(204\) 20.8473 1.45960
\(205\) 37.8522 2.64371
\(206\) 17.7770 1.23858
\(207\) 32.9323 2.28895
\(208\) −1.97145 −0.136696
\(209\) 3.58210 0.247779
\(210\) −109.714 −7.57097
\(211\) 19.4129 1.33644 0.668220 0.743963i \(-0.267056\pi\)
0.668220 + 0.743963i \(0.267056\pi\)
\(212\) −1.50143 −0.103119
\(213\) −44.0896 −3.02097
\(214\) 3.12196 0.213413
\(215\) −0.281679 −0.0192104
\(216\) −4.22586 −0.287533
\(217\) 8.53179 0.579175
\(218\) 9.81428 0.664707
\(219\) −28.3152 −1.91336
\(220\) −8.37084 −0.564362
\(221\) −1.87960 −0.126436
\(222\) −3.61816 −0.242835
\(223\) 1.53370 0.102704 0.0513519 0.998681i \(-0.483647\pi\)
0.0513519 + 0.998681i \(0.483647\pi\)
\(224\) 41.0124 2.74026
\(225\) 43.1921 2.87947
\(226\) −37.1513 −2.47126
\(227\) −1.49973 −0.0995409 −0.0497704 0.998761i \(-0.515849\pi\)
−0.0497704 + 0.998761i \(0.515849\pi\)
\(228\) −23.8114 −1.57695
\(229\) 4.15251 0.274405 0.137203 0.990543i \(-0.456189\pi\)
0.137203 + 0.990543i \(0.456189\pi\)
\(230\) −46.8126 −3.08673
\(231\) 14.5738 0.958886
\(232\) 1.01343 0.0665347
\(233\) 16.0967 1.05453 0.527266 0.849700i \(-0.323217\pi\)
0.527266 + 0.849700i \(0.323217\pi\)
\(234\) 6.58781 0.430658
\(235\) 7.87589 0.513766
\(236\) 28.9923 1.88724
\(237\) −2.96464 −0.192574
\(238\) 32.9362 2.13494
\(239\) 11.9835 0.775147 0.387573 0.921839i \(-0.373313\pi\)
0.387573 + 0.921839i \(0.373313\pi\)
\(240\) −34.3648 −2.21824
\(241\) 20.3342 1.30984 0.654920 0.755698i \(-0.272702\pi\)
0.654920 + 0.755698i \(0.272702\pi\)
\(242\) 2.07554 0.133421
\(243\) 10.7390 0.688909
\(244\) −24.9842 −1.59945
\(245\) −67.4718 −4.31061
\(246\) 62.3879 3.97771
\(247\) 2.14685 0.136601
\(248\) −1.07749 −0.0684207
\(249\) 8.73416 0.553505
\(250\) −23.7561 −1.50247
\(251\) 0.584210 0.0368750 0.0184375 0.999830i \(-0.494131\pi\)
0.0184375 + 0.999830i \(0.494131\pi\)
\(252\) −61.8442 −3.89582
\(253\) 6.21835 0.390944
\(254\) 45.7904 2.87315
\(255\) −32.7637 −2.05174
\(256\) 10.0038 0.625238
\(257\) −21.9099 −1.36670 −0.683352 0.730089i \(-0.739479\pi\)
−0.683352 + 0.730089i \(0.739479\pi\)
\(258\) −0.464263 −0.0289038
\(259\) −3.06239 −0.190288
\(260\) −5.01686 −0.311132
\(261\) 8.39897 0.519883
\(262\) −2.07554 −0.128227
\(263\) −9.59178 −0.591455 −0.295727 0.955272i \(-0.595562\pi\)
−0.295727 + 0.955272i \(0.595562\pi\)
\(264\) −1.84055 −0.113278
\(265\) 2.35966 0.144953
\(266\) −37.6192 −2.30658
\(267\) 22.3122 1.36549
\(268\) −31.5792 −1.92901
\(269\) 25.2765 1.54113 0.770567 0.637359i \(-0.219973\pi\)
0.770567 + 0.637359i \(0.219973\pi\)
\(270\) 49.7840 3.02976
\(271\) −6.16044 −0.374220 −0.187110 0.982339i \(-0.559912\pi\)
−0.187110 + 0.982339i \(0.559912\pi\)
\(272\) 10.3163 0.625520
\(273\) 8.73446 0.528633
\(274\) 37.5690 2.26963
\(275\) 8.15564 0.491804
\(276\) −41.3354 −2.48810
\(277\) −8.89641 −0.534534 −0.267267 0.963623i \(-0.586121\pi\)
−0.267267 + 0.963623i \(0.586121\pi\)
\(278\) 14.1911 0.851126
\(279\) −8.92991 −0.534620
\(280\) 11.7276 0.700856
\(281\) 15.8974 0.948360 0.474180 0.880428i \(-0.342745\pi\)
0.474180 + 0.880428i \(0.342745\pi\)
\(282\) 12.9810 0.773009
\(283\) −31.7367 −1.88655 −0.943277 0.332007i \(-0.892274\pi\)
−0.943277 + 0.332007i \(0.892274\pi\)
\(284\) 35.3277 2.09632
\(285\) 37.4221 2.21669
\(286\) 1.24393 0.0735549
\(287\) 52.8049 3.11697
\(288\) −42.9262 −2.52945
\(289\) −7.16430 −0.421430
\(290\) −11.9390 −0.701081
\(291\) 21.1508 1.23988
\(292\) 22.6881 1.32772
\(293\) 10.0739 0.588524 0.294262 0.955725i \(-0.404926\pi\)
0.294262 + 0.955725i \(0.404926\pi\)
\(294\) −111.207 −6.48572
\(295\) −45.5644 −2.65286
\(296\) 0.386753 0.0224796
\(297\) −6.61305 −0.383728
\(298\) −4.04939 −0.234575
\(299\) 3.72682 0.215527
\(300\) −54.2132 −3.13000
\(301\) −0.392951 −0.0226493
\(302\) 14.7252 0.847342
\(303\) −57.0485 −3.27735
\(304\) −11.7832 −0.675810
\(305\) 39.2652 2.24832
\(306\) −34.4731 −1.97070
\(307\) 26.5321 1.51427 0.757135 0.653259i \(-0.226599\pi\)
0.757135 + 0.653259i \(0.226599\pi\)
\(308\) −11.6776 −0.665391
\(309\) −24.6694 −1.40340
\(310\) 12.6937 0.720954
\(311\) −11.8642 −0.672758 −0.336379 0.941727i \(-0.609202\pi\)
−0.336379 + 0.941727i \(0.609202\pi\)
\(312\) −1.10309 −0.0624499
\(313\) 2.21275 0.125072 0.0625362 0.998043i \(-0.480081\pi\)
0.0625362 + 0.998043i \(0.480081\pi\)
\(314\) 8.61287 0.486052
\(315\) 97.1945 5.47629
\(316\) 2.37548 0.133631
\(317\) −4.67660 −0.262664 −0.131332 0.991338i \(-0.541925\pi\)
−0.131332 + 0.991338i \(0.541925\pi\)
\(318\) 3.88919 0.218095
\(319\) 1.58591 0.0887941
\(320\) 37.1567 2.07712
\(321\) −4.33241 −0.241811
\(322\) −65.3050 −3.63930
\(323\) −11.2342 −0.625086
\(324\) 7.29168 0.405093
\(325\) 4.88788 0.271131
\(326\) −29.0147 −1.60697
\(327\) −13.6195 −0.753159
\(328\) −6.66879 −0.368223
\(329\) 10.9871 0.605738
\(330\) 21.6831 1.19362
\(331\) −25.5661 −1.40524 −0.702620 0.711565i \(-0.747987\pi\)
−0.702620 + 0.711565i \(0.747987\pi\)
\(332\) −6.99842 −0.384088
\(333\) 3.20529 0.175649
\(334\) 24.0567 1.31632
\(335\) 49.6300 2.71158
\(336\) −47.9398 −2.61533
\(337\) −1.59339 −0.0867976 −0.0433988 0.999058i \(-0.513819\pi\)
−0.0433988 + 0.999058i \(0.513819\pi\)
\(338\) −26.2365 −1.42708
\(339\) 51.5556 2.80011
\(340\) 26.2526 1.42375
\(341\) −1.68617 −0.0913111
\(342\) 39.3746 2.12914
\(343\) −58.7060 −3.16983
\(344\) 0.0496263 0.00267567
\(345\) 64.9628 3.49748
\(346\) −24.4221 −1.31294
\(347\) 25.0492 1.34471 0.672356 0.740228i \(-0.265283\pi\)
0.672356 + 0.740228i \(0.265283\pi\)
\(348\) −10.5421 −0.565115
\(349\) 9.93581 0.531852 0.265926 0.963993i \(-0.414322\pi\)
0.265926 + 0.963993i \(0.414322\pi\)
\(350\) −85.6503 −4.57820
\(351\) −3.96337 −0.211549
\(352\) −8.10543 −0.432021
\(353\) 12.0578 0.641771 0.320885 0.947118i \(-0.396020\pi\)
0.320885 + 0.947118i \(0.396020\pi\)
\(354\) −75.0992 −3.99148
\(355\) −55.5212 −2.94676
\(356\) −17.8781 −0.947540
\(357\) −45.7063 −2.41903
\(358\) −22.9235 −1.21154
\(359\) 24.1797 1.27615 0.638077 0.769972i \(-0.279730\pi\)
0.638077 + 0.769972i \(0.279730\pi\)
\(360\) −12.2748 −0.646940
\(361\) −6.16853 −0.324659
\(362\) −37.3233 −1.96167
\(363\) −2.88027 −0.151175
\(364\) −6.99866 −0.366830
\(365\) −35.6567 −1.86636
\(366\) 64.7169 3.38281
\(367\) 2.94826 0.153898 0.0769490 0.997035i \(-0.475482\pi\)
0.0769490 + 0.997035i \(0.475482\pi\)
\(368\) −20.4550 −1.06629
\(369\) −55.2689 −2.87719
\(370\) −4.55627 −0.236869
\(371\) 3.29179 0.170901
\(372\) 11.2085 0.581134
\(373\) −29.6265 −1.53400 −0.767002 0.641645i \(-0.778252\pi\)
−0.767002 + 0.641645i \(0.778252\pi\)
\(374\) −6.50930 −0.336588
\(375\) 32.9668 1.70240
\(376\) −1.38757 −0.0715587
\(377\) 0.950479 0.0489521
\(378\) 69.4501 3.57213
\(379\) 0.0207330 0.00106498 0.000532491 1.00000i \(-0.499831\pi\)
0.000532491 1.00000i \(0.499831\pi\)
\(380\) −29.9852 −1.53821
\(381\) −63.5443 −3.25547
\(382\) 36.5639 1.87077
\(383\) 21.6673 1.10715 0.553573 0.832801i \(-0.313264\pi\)
0.553573 + 0.832801i \(0.313264\pi\)
\(384\) 14.5499 0.742496
\(385\) 18.3525 0.935330
\(386\) 20.7478 1.05604
\(387\) 0.411287 0.0209069
\(388\) −16.9475 −0.860381
\(389\) −4.78430 −0.242573 −0.121287 0.992618i \(-0.538702\pi\)
−0.121287 + 0.992618i \(0.538702\pi\)
\(390\) 12.9952 0.658040
\(391\) −19.5019 −0.986255
\(392\) 11.8872 0.600393
\(393\) 2.88027 0.145291
\(394\) −22.1853 −1.11768
\(395\) −3.73331 −0.187843
\(396\) 12.2225 0.614203
\(397\) 25.9260 1.30119 0.650596 0.759424i \(-0.274519\pi\)
0.650596 + 0.759424i \(0.274519\pi\)
\(398\) 19.1922 0.962017
\(399\) 52.2049 2.61351
\(400\) −26.8276 −1.34138
\(401\) 12.7727 0.637840 0.318920 0.947782i \(-0.396680\pi\)
0.318920 + 0.947782i \(0.396680\pi\)
\(402\) 81.8001 4.07982
\(403\) −1.01056 −0.0503397
\(404\) 45.7113 2.27422
\(405\) −11.4596 −0.569433
\(406\) −16.6552 −0.826585
\(407\) 0.605232 0.0300002
\(408\) 5.77230 0.285772
\(409\) −21.3764 −1.05699 −0.528497 0.848935i \(-0.677244\pi\)
−0.528497 + 0.848935i \(0.677244\pi\)
\(410\) 78.5638 3.87999
\(411\) −52.1353 −2.57165
\(412\) 19.7669 0.973846
\(413\) −63.5637 −3.12776
\(414\) 68.3523 3.35933
\(415\) 10.9987 0.539907
\(416\) −4.85779 −0.238173
\(417\) −19.6933 −0.964384
\(418\) 7.43481 0.363649
\(419\) −20.2058 −0.987117 −0.493558 0.869713i \(-0.664304\pi\)
−0.493558 + 0.869713i \(0.664304\pi\)
\(420\) −121.995 −5.95275
\(421\) −16.3870 −0.798652 −0.399326 0.916809i \(-0.630756\pi\)
−0.399326 + 0.916809i \(0.630756\pi\)
\(422\) 40.2924 1.96140
\(423\) −11.4998 −0.559139
\(424\) −0.415725 −0.0201894
\(425\) −25.5776 −1.24070
\(426\) −91.5099 −4.43367
\(427\) 54.7761 2.65080
\(428\) 3.47143 0.167798
\(429\) −1.72622 −0.0833428
\(430\) −0.584637 −0.0281937
\(431\) 23.0721 1.11135 0.555673 0.831401i \(-0.312461\pi\)
0.555673 + 0.831401i \(0.312461\pi\)
\(432\) 21.7533 1.04661
\(433\) −36.0195 −1.73099 −0.865494 0.500920i \(-0.832995\pi\)
−0.865494 + 0.500920i \(0.832995\pi\)
\(434\) 17.7081 0.850016
\(435\) 16.5680 0.794374
\(436\) 10.9129 0.522633
\(437\) 22.2748 1.06555
\(438\) −58.7694 −2.80811
\(439\) 20.5470 0.980654 0.490327 0.871538i \(-0.336877\pi\)
0.490327 + 0.871538i \(0.336877\pi\)
\(440\) −2.31776 −0.110495
\(441\) 98.5173 4.69130
\(442\) −3.90119 −0.185561
\(443\) −15.5511 −0.738854 −0.369427 0.929260i \(-0.620446\pi\)
−0.369427 + 0.929260i \(0.620446\pi\)
\(444\) −4.02317 −0.190931
\(445\) 28.0974 1.33194
\(446\) 3.18325 0.150731
\(447\) 5.61942 0.265789
\(448\) 51.8347 2.44896
\(449\) 0.180417 0.00851440 0.00425720 0.999991i \(-0.498645\pi\)
0.00425720 + 0.999991i \(0.498645\pi\)
\(450\) 89.6471 4.22601
\(451\) −10.4360 −0.491413
\(452\) −41.3100 −1.94306
\(453\) −20.4345 −0.960097
\(454\) −3.11276 −0.146089
\(455\) 10.9991 0.515647
\(456\) −6.59303 −0.308747
\(457\) 13.4260 0.628040 0.314020 0.949416i \(-0.398324\pi\)
0.314020 + 0.949416i \(0.398324\pi\)
\(458\) 8.61871 0.402726
\(459\) 20.7398 0.968051
\(460\) −52.0528 −2.42698
\(461\) 1.01035 0.0470567 0.0235284 0.999723i \(-0.492510\pi\)
0.0235284 + 0.999723i \(0.492510\pi\)
\(462\) 30.2486 1.40729
\(463\) 4.58674 0.213164 0.106582 0.994304i \(-0.466009\pi\)
0.106582 + 0.994304i \(0.466009\pi\)
\(464\) −5.21679 −0.242183
\(465\) −17.6153 −0.816891
\(466\) 33.4095 1.54766
\(467\) −8.75168 −0.404979 −0.202490 0.979284i \(-0.564903\pi\)
−0.202490 + 0.979284i \(0.564903\pi\)
\(468\) 7.32525 0.338610
\(469\) 69.2353 3.19699
\(470\) 16.3468 0.754019
\(471\) −11.9523 −0.550731
\(472\) 8.02754 0.369497
\(473\) 0.0776603 0.00357082
\(474\) −6.15323 −0.282627
\(475\) 29.2144 1.34045
\(476\) 36.6231 1.67862
\(477\) −3.44540 −0.157754
\(478\) 24.8722 1.13763
\(479\) 38.4992 1.75907 0.879536 0.475832i \(-0.157853\pi\)
0.879536 + 0.475832i \(0.157853\pi\)
\(480\) −84.6771 −3.86496
\(481\) 0.362731 0.0165391
\(482\) 42.2045 1.92236
\(483\) 90.6251 4.12358
\(484\) 2.30788 0.104904
\(485\) 26.6348 1.20942
\(486\) 22.2893 1.01106
\(487\) 18.8334 0.853422 0.426711 0.904388i \(-0.359672\pi\)
0.426711 + 0.904388i \(0.359672\pi\)
\(488\) −6.91775 −0.313152
\(489\) 40.2642 1.82081
\(490\) −140.041 −6.32639
\(491\) 13.9059 0.627566 0.313783 0.949495i \(-0.398404\pi\)
0.313783 + 0.949495i \(0.398404\pi\)
\(492\) 69.3716 3.12751
\(493\) −4.97373 −0.224006
\(494\) 4.45587 0.200479
\(495\) −19.2089 −0.863376
\(496\) 5.54657 0.249048
\(497\) −77.4536 −3.47427
\(498\) 18.1281 0.812340
\(499\) 12.3494 0.552836 0.276418 0.961038i \(-0.410853\pi\)
0.276418 + 0.961038i \(0.410853\pi\)
\(500\) −26.4154 −1.18133
\(501\) −33.3840 −1.49149
\(502\) 1.21255 0.0541189
\(503\) −28.0862 −1.25230 −0.626150 0.779703i \(-0.715370\pi\)
−0.626150 + 0.779703i \(0.715370\pi\)
\(504\) −17.1237 −0.762752
\(505\) −71.8400 −3.19684
\(506\) 12.9065 0.573762
\(507\) 36.4090 1.61698
\(508\) 50.9162 2.25904
\(509\) 32.1680 1.42582 0.712911 0.701255i \(-0.247376\pi\)
0.712911 + 0.701255i \(0.247376\pi\)
\(510\) −68.0024 −3.01120
\(511\) −49.7422 −2.20046
\(512\) 30.8665 1.36412
\(513\) −23.6887 −1.04588
\(514\) −45.4750 −2.00582
\(515\) −31.0657 −1.36892
\(516\) −0.516233 −0.0227259
\(517\) −2.17142 −0.0954989
\(518\) −6.35613 −0.279272
\(519\) 33.8911 1.48766
\(520\) −1.38909 −0.0609158
\(521\) 28.3236 1.24088 0.620439 0.784255i \(-0.286954\pi\)
0.620439 + 0.784255i \(0.286954\pi\)
\(522\) 17.4324 0.762996
\(523\) 28.0700 1.22741 0.613707 0.789534i \(-0.289677\pi\)
0.613707 + 0.789534i \(0.289677\pi\)
\(524\) −2.30788 −0.100820
\(525\) 118.859 5.18742
\(526\) −19.9082 −0.868037
\(527\) 5.28814 0.230355
\(528\) 9.47452 0.412326
\(529\) 15.6679 0.681212
\(530\) 4.89758 0.212737
\(531\) 66.5298 2.88715
\(532\) −41.8303 −1.81357
\(533\) −6.25457 −0.270915
\(534\) 46.3100 2.00403
\(535\) −5.45571 −0.235871
\(536\) −8.74382 −0.377675
\(537\) 31.8114 1.37276
\(538\) 52.4624 2.26182
\(539\) 18.6023 0.801257
\(540\) 55.3568 2.38218
\(541\) 2.37442 0.102084 0.0510420 0.998697i \(-0.483746\pi\)
0.0510420 + 0.998697i \(0.483746\pi\)
\(542\) −12.7863 −0.549217
\(543\) 51.7943 2.22271
\(544\) 25.4202 1.08988
\(545\) −17.1507 −0.734657
\(546\) 18.1287 0.775839
\(547\) −35.7363 −1.52797 −0.763987 0.645231i \(-0.776761\pi\)
−0.763987 + 0.645231i \(0.776761\pi\)
\(548\) 41.7745 1.78452
\(549\) −57.3322 −2.44688
\(550\) 16.9274 0.721786
\(551\) 5.68091 0.242015
\(552\) −11.4452 −0.487138
\(553\) −5.20807 −0.221470
\(554\) −18.4649 −0.784498
\(555\) 6.32283 0.268389
\(556\) 15.7797 0.669206
\(557\) −12.6279 −0.535059 −0.267530 0.963550i \(-0.586207\pi\)
−0.267530 + 0.963550i \(0.586207\pi\)
\(558\) −18.5344 −0.784624
\(559\) 0.0465438 0.00196859
\(560\) −60.3697 −2.55108
\(561\) 9.03309 0.381377
\(562\) 32.9958 1.39184
\(563\) −15.0992 −0.636354 −0.318177 0.948031i \(-0.603071\pi\)
−0.318177 + 0.948031i \(0.603071\pi\)
\(564\) 14.4341 0.607787
\(565\) 64.9229 2.73133
\(566\) −65.8710 −2.76876
\(567\) −15.9865 −0.671370
\(568\) 9.78172 0.410432
\(569\) −29.9217 −1.25438 −0.627191 0.778866i \(-0.715795\pi\)
−0.627191 + 0.778866i \(0.715795\pi\)
\(570\) 77.6712 3.25329
\(571\) −39.6674 −1.66003 −0.830015 0.557740i \(-0.811668\pi\)
−0.830015 + 0.557740i \(0.811668\pi\)
\(572\) 1.38317 0.0578333
\(573\) −50.7405 −2.11972
\(574\) 109.599 4.57456
\(575\) 50.7146 2.11495
\(576\) −54.2535 −2.26056
\(577\) 9.08201 0.378089 0.189044 0.981969i \(-0.439461\pi\)
0.189044 + 0.981969i \(0.439461\pi\)
\(578\) −14.8698 −0.618503
\(579\) −28.7922 −1.19656
\(580\) −13.2754 −0.551232
\(581\) 15.3436 0.636559
\(582\) 43.8995 1.81969
\(583\) −0.650569 −0.0269438
\(584\) 6.28200 0.259951
\(585\) −11.5124 −0.475978
\(586\) 20.9088 0.863736
\(587\) −36.2095 −1.49453 −0.747264 0.664527i \(-0.768633\pi\)
−0.747264 + 0.664527i \(0.768633\pi\)
\(588\) −123.655 −5.09946
\(589\) −6.04003 −0.248875
\(590\) −94.5709 −3.89342
\(591\) 30.7869 1.26641
\(592\) −1.99088 −0.0818246
\(593\) 13.6094 0.558871 0.279435 0.960164i \(-0.409853\pi\)
0.279435 + 0.960164i \(0.409853\pi\)
\(594\) −13.7257 −0.563172
\(595\) −57.5570 −2.35961
\(596\) −4.50268 −0.184437
\(597\) −26.6334 −1.09003
\(598\) 7.73517 0.316314
\(599\) −40.8257 −1.66809 −0.834047 0.551694i \(-0.813982\pi\)
−0.834047 + 0.551694i \(0.813982\pi\)
\(600\) −15.0108 −0.612814
\(601\) −13.9254 −0.568029 −0.284015 0.958820i \(-0.591666\pi\)
−0.284015 + 0.958820i \(0.591666\pi\)
\(602\) −0.815586 −0.0332408
\(603\) −72.4661 −2.95105
\(604\) 16.3736 0.666231
\(605\) −3.62707 −0.147461
\(606\) −118.407 −4.80994
\(607\) 15.5306 0.630368 0.315184 0.949031i \(-0.397934\pi\)
0.315184 + 0.949031i \(0.397934\pi\)
\(608\) −29.0345 −1.17750
\(609\) 23.1128 0.936578
\(610\) 81.4966 3.29970
\(611\) −1.30139 −0.0526485
\(612\) −38.3321 −1.54948
\(613\) −9.02158 −0.364378 −0.182189 0.983264i \(-0.558318\pi\)
−0.182189 + 0.983264i \(0.558318\pi\)
\(614\) 55.0686 2.22239
\(615\) −109.025 −4.39630
\(616\) −3.23334 −0.130275
\(617\) 17.7311 0.713827 0.356914 0.934137i \(-0.383829\pi\)
0.356914 + 0.934137i \(0.383829\pi\)
\(618\) −51.2025 −2.05967
\(619\) 29.7961 1.19760 0.598802 0.800897i \(-0.295643\pi\)
0.598802 + 0.800897i \(0.295643\pi\)
\(620\) 14.1146 0.566858
\(621\) −41.1223 −1.65018
\(622\) −24.6247 −0.987360
\(623\) 39.1966 1.57038
\(624\) 5.67832 0.227315
\(625\) 0.736272 0.0294509
\(626\) 4.59267 0.183560
\(627\) −10.3174 −0.412039
\(628\) 9.57699 0.382164
\(629\) −1.89812 −0.0756831
\(630\) 201.731 8.03717
\(631\) 10.9697 0.436696 0.218348 0.975871i \(-0.429933\pi\)
0.218348 + 0.975871i \(0.429933\pi\)
\(632\) 0.657734 0.0261633
\(633\) −55.9146 −2.22240
\(634\) −9.70648 −0.385493
\(635\) −80.0201 −3.17550
\(636\) 4.32454 0.171479
\(637\) 11.1488 0.441732
\(638\) 3.29163 0.130317
\(639\) 81.0679 3.20700
\(640\) 18.3224 0.724256
\(641\) 40.1623 1.58632 0.793158 0.609016i \(-0.208436\pi\)
0.793158 + 0.609016i \(0.208436\pi\)
\(642\) −8.99210 −0.354890
\(643\) 20.2220 0.797476 0.398738 0.917065i \(-0.369448\pi\)
0.398738 + 0.917065i \(0.369448\pi\)
\(644\) −72.6152 −2.86144
\(645\) 0.811314 0.0319454
\(646\) −23.3170 −0.917395
\(647\) 19.8737 0.781315 0.390658 0.920536i \(-0.372248\pi\)
0.390658 + 0.920536i \(0.372248\pi\)
\(648\) 2.01896 0.0793121
\(649\) 12.5623 0.493114
\(650\) 10.1450 0.397920
\(651\) −24.5739 −0.963127
\(652\) −32.2626 −1.26350
\(653\) −31.5604 −1.23505 −0.617527 0.786550i \(-0.711865\pi\)
−0.617527 + 0.786550i \(0.711865\pi\)
\(654\) −28.2678 −1.10536
\(655\) 3.62707 0.141721
\(656\) 34.3288 1.34031
\(657\) 52.0633 2.03118
\(658\) 22.8042 0.889000
\(659\) 30.4814 1.18739 0.593694 0.804691i \(-0.297669\pi\)
0.593694 + 0.804691i \(0.297669\pi\)
\(660\) 24.1103 0.938493
\(661\) 36.8905 1.43487 0.717436 0.696624i \(-0.245315\pi\)
0.717436 + 0.696624i \(0.245315\pi\)
\(662\) −53.0636 −2.06237
\(663\) 5.41376 0.210253
\(664\) −1.93776 −0.0751996
\(665\) 65.7406 2.54931
\(666\) 6.65273 0.257788
\(667\) 9.86177 0.381849
\(668\) 26.7496 1.03497
\(669\) −4.41746 −0.170789
\(670\) 103.009 3.97959
\(671\) −10.8256 −0.417918
\(672\) −118.127 −4.55685
\(673\) 47.7316 1.83992 0.919958 0.392017i \(-0.128222\pi\)
0.919958 + 0.392017i \(0.128222\pi\)
\(674\) −3.30715 −0.127387
\(675\) −53.9337 −2.07591
\(676\) −29.1735 −1.12206
\(677\) −21.6364 −0.831555 −0.415777 0.909466i \(-0.636490\pi\)
−0.415777 + 0.909466i \(0.636490\pi\)
\(678\) 107.006 4.10953
\(679\) 37.1563 1.42593
\(680\) 7.26894 0.278751
\(681\) 4.31965 0.165529
\(682\) −3.49971 −0.134011
\(683\) −31.0578 −1.18840 −0.594198 0.804319i \(-0.702530\pi\)
−0.594198 + 0.804319i \(0.702530\pi\)
\(684\) 43.7822 1.67405
\(685\) −65.6529 −2.50847
\(686\) −121.847 −4.65213
\(687\) −11.9604 −0.456316
\(688\) −0.255460 −0.00973931
\(689\) −0.389903 −0.0148541
\(690\) 134.833 5.13301
\(691\) 6.36017 0.241952 0.120976 0.992655i \(-0.461398\pi\)
0.120976 + 0.992655i \(0.461398\pi\)
\(692\) −27.1560 −1.03231
\(693\) −26.7970 −1.01793
\(694\) 51.9907 1.97354
\(695\) −24.7994 −0.940693
\(696\) −2.91895 −0.110642
\(697\) 32.7293 1.23971
\(698\) 20.6222 0.780562
\(699\) −46.3630 −1.75361
\(700\) −95.2381 −3.59966
\(701\) 29.4627 1.11279 0.556395 0.830918i \(-0.312184\pi\)
0.556395 + 0.830918i \(0.312184\pi\)
\(702\) −8.22615 −0.310476
\(703\) 2.16800 0.0817678
\(704\) −10.2443 −0.386096
\(705\) −22.6847 −0.854356
\(706\) 25.0264 0.941882
\(707\) −100.219 −3.76912
\(708\) −83.5058 −3.13834
\(709\) −19.6700 −0.738723 −0.369361 0.929286i \(-0.620424\pi\)
−0.369361 + 0.929286i \(0.620424\pi\)
\(710\) −115.237 −4.32475
\(711\) 5.45110 0.204432
\(712\) −4.95019 −0.185516
\(713\) −10.4852 −0.392673
\(714\) −94.8653 −3.55025
\(715\) −2.17380 −0.0812954
\(716\) −25.4895 −0.952588
\(717\) −34.5157 −1.28901
\(718\) 50.1860 1.87292
\(719\) 13.4191 0.500447 0.250224 0.968188i \(-0.419496\pi\)
0.250224 + 0.968188i \(0.419496\pi\)
\(720\) 63.1867 2.35483
\(721\) −43.3376 −1.61398
\(722\) −12.8031 −0.476480
\(723\) −58.5681 −2.17817
\(724\) −41.5012 −1.54238
\(725\) 12.9341 0.480362
\(726\) −5.97813 −0.221869
\(727\) −23.7914 −0.882373 −0.441186 0.897415i \(-0.645442\pi\)
−0.441186 + 0.897415i \(0.645442\pi\)
\(728\) −1.93783 −0.0718206
\(729\) −40.4097 −1.49666
\(730\) −74.0071 −2.73912
\(731\) −0.243557 −0.00900830
\(732\) 71.9613 2.65977
\(733\) −35.5237 −1.31210 −0.656049 0.754718i \(-0.727774\pi\)
−0.656049 + 0.754718i \(0.727774\pi\)
\(734\) 6.11924 0.225865
\(735\) 194.337 7.16824
\(736\) −50.4024 −1.85786
\(737\) −13.6832 −0.504028
\(738\) −114.713 −4.22265
\(739\) −15.1272 −0.556462 −0.278231 0.960514i \(-0.589748\pi\)
−0.278231 + 0.960514i \(0.589748\pi\)
\(740\) −5.06630 −0.186241
\(741\) −6.18351 −0.227157
\(742\) 6.83226 0.250820
\(743\) 46.1710 1.69385 0.846925 0.531713i \(-0.178451\pi\)
0.846925 + 0.531713i \(0.178451\pi\)
\(744\) 3.10347 0.113779
\(745\) 7.07642 0.259260
\(746\) −61.4912 −2.25135
\(747\) −16.0596 −0.587588
\(748\) −7.23795 −0.264646
\(749\) −7.61088 −0.278095
\(750\) 68.4241 2.49850
\(751\) −14.2430 −0.519736 −0.259868 0.965644i \(-0.583679\pi\)
−0.259868 + 0.965644i \(0.583679\pi\)
\(752\) 7.14278 0.260470
\(753\) −1.68269 −0.0613205
\(754\) 1.97276 0.0718437
\(755\) −25.7328 −0.936511
\(756\) 77.2244 2.80862
\(757\) 7.19531 0.261518 0.130759 0.991414i \(-0.458259\pi\)
0.130759 + 0.991414i \(0.458259\pi\)
\(758\) 0.0430322 0.00156300
\(759\) −17.9106 −0.650112
\(760\) −8.30246 −0.301162
\(761\) −2.94531 −0.106767 −0.0533837 0.998574i \(-0.517001\pi\)
−0.0533837 + 0.998574i \(0.517001\pi\)
\(762\) −131.889 −4.77783
\(763\) −23.9258 −0.866171
\(764\) 40.6569 1.47091
\(765\) 60.2428 2.17808
\(766\) 44.9714 1.62488
\(767\) 7.52892 0.271853
\(768\) −28.8137 −1.03972
\(769\) 31.7843 1.14617 0.573086 0.819495i \(-0.305746\pi\)
0.573086 + 0.819495i \(0.305746\pi\)
\(770\) 38.0914 1.37272
\(771\) 63.1066 2.27273
\(772\) 23.0703 0.830320
\(773\) 6.99225 0.251494 0.125747 0.992062i \(-0.459867\pi\)
0.125747 + 0.992062i \(0.459867\pi\)
\(774\) 0.853644 0.0306836
\(775\) −13.7518 −0.493978
\(776\) −4.69252 −0.168452
\(777\) 8.82053 0.316435
\(778\) −9.93001 −0.356008
\(779\) −37.3829 −1.33938
\(780\) 14.4499 0.517391
\(781\) 15.3074 0.547743
\(782\) −40.4771 −1.44746
\(783\) −10.4877 −0.374801
\(784\) −61.1913 −2.18540
\(785\) −15.0512 −0.537201
\(786\) 5.97813 0.213233
\(787\) 30.0445 1.07097 0.535486 0.844544i \(-0.320128\pi\)
0.535486 + 0.844544i \(0.320128\pi\)
\(788\) −24.6687 −0.878785
\(789\) 27.6270 0.983546
\(790\) −7.74864 −0.275684
\(791\) 90.5693 3.22027
\(792\) 3.38422 0.120253
\(793\) −6.48806 −0.230398
\(794\) 53.8106 1.90967
\(795\) −6.79647 −0.241046
\(796\) 21.3405 0.756396
\(797\) 42.2552 1.49675 0.748377 0.663273i \(-0.230833\pi\)
0.748377 + 0.663273i \(0.230833\pi\)
\(798\) 108.354 3.83567
\(799\) 6.80999 0.240920
\(800\) −66.1050 −2.33716
\(801\) −41.0257 −1.44957
\(802\) 26.5104 0.936113
\(803\) 9.83072 0.346919
\(804\) 90.9568 3.20780
\(805\) 114.122 4.02228
\(806\) −2.09747 −0.0738801
\(807\) −72.8032 −2.56279
\(808\) 12.6568 0.445264
\(809\) 14.6690 0.515734 0.257867 0.966180i \(-0.416980\pi\)
0.257867 + 0.966180i \(0.416980\pi\)
\(810\) −23.7849 −0.835718
\(811\) −9.66211 −0.339283 −0.169641 0.985506i \(-0.554261\pi\)
−0.169641 + 0.985506i \(0.554261\pi\)
\(812\) −18.5196 −0.649911
\(813\) 17.7438 0.622301
\(814\) 1.25618 0.0440292
\(815\) 50.7039 1.77608
\(816\) −29.7139 −1.04019
\(817\) 0.278187 0.00973254
\(818\) −44.3676 −1.55128
\(819\) −16.0601 −0.561186
\(820\) 87.3582 3.05068
\(821\) 11.0306 0.384971 0.192486 0.981300i \(-0.438345\pi\)
0.192486 + 0.981300i \(0.438345\pi\)
\(822\) −108.209 −3.77423
\(823\) −7.76970 −0.270835 −0.135417 0.990789i \(-0.543238\pi\)
−0.135417 + 0.990789i \(0.543238\pi\)
\(824\) 5.47316 0.190667
\(825\) −23.4905 −0.817834
\(826\) −131.929 −4.59040
\(827\) 56.4825 1.96409 0.982044 0.188653i \(-0.0604123\pi\)
0.982044 + 0.188653i \(0.0604123\pi\)
\(828\) 76.0037 2.64131
\(829\) −29.3697 −1.02005 −0.510026 0.860159i \(-0.670364\pi\)
−0.510026 + 0.860159i \(0.670364\pi\)
\(830\) 22.8284 0.792384
\(831\) 25.6241 0.888891
\(832\) −6.13965 −0.212854
\(833\) −58.3403 −2.02137
\(834\) −40.8743 −1.41536
\(835\) −42.0397 −1.45485
\(836\) 8.26707 0.285922
\(837\) 11.1507 0.385425
\(838\) −41.9380 −1.44872
\(839\) 22.8663 0.789432 0.394716 0.918803i \(-0.370843\pi\)
0.394716 + 0.918803i \(0.370843\pi\)
\(840\) −33.7786 −1.16547
\(841\) −26.4849 −0.913272
\(842\) −34.0119 −1.17213
\(843\) −45.7889 −1.57705
\(844\) 44.8027 1.54217
\(845\) 45.8491 1.57726
\(846\) −23.8683 −0.820610
\(847\) −5.05987 −0.173859
\(848\) 2.14001 0.0734884
\(849\) 91.4105 3.13720
\(850\) −53.0875 −1.82089
\(851\) 3.76354 0.129013
\(852\) −101.754 −3.48602
\(853\) −19.9206 −0.682067 −0.341033 0.940051i \(-0.610777\pi\)
−0.341033 + 0.940051i \(0.610777\pi\)
\(854\) 113.690 3.89040
\(855\) −68.8083 −2.35319
\(856\) 0.961187 0.0328527
\(857\) 3.07747 0.105124 0.0525622 0.998618i \(-0.483261\pi\)
0.0525622 + 0.998618i \(0.483261\pi\)
\(858\) −3.58285 −0.122316
\(859\) −21.9826 −0.750035 −0.375018 0.927018i \(-0.622363\pi\)
−0.375018 + 0.927018i \(0.622363\pi\)
\(860\) −0.650082 −0.0221676
\(861\) −152.092 −5.18330
\(862\) 47.8872 1.63105
\(863\) 44.5908 1.51789 0.758944 0.651156i \(-0.225716\pi\)
0.758944 + 0.651156i \(0.225716\pi\)
\(864\) 53.6017 1.82357
\(865\) 42.6784 1.45111
\(866\) −74.7600 −2.54045
\(867\) 20.6352 0.700807
\(868\) 19.6903 0.668334
\(869\) 1.02929 0.0349163
\(870\) 34.3876 1.16585
\(871\) −8.20070 −0.277870
\(872\) 3.02162 0.102325
\(873\) −38.8902 −1.31623
\(874\) 46.2323 1.56383
\(875\) 57.9139 1.95785
\(876\) −65.3480 −2.20790
\(877\) 19.8995 0.671958 0.335979 0.941869i \(-0.390933\pi\)
0.335979 + 0.941869i \(0.390933\pi\)
\(878\) 42.6462 1.43924
\(879\) −29.0156 −0.978673
\(880\) 11.9311 0.402196
\(881\) 38.9192 1.31122 0.655611 0.755099i \(-0.272411\pi\)
0.655611 + 0.755099i \(0.272411\pi\)
\(882\) 204.477 6.88509
\(883\) 21.5851 0.726397 0.363198 0.931712i \(-0.381685\pi\)
0.363198 + 0.931712i \(0.381685\pi\)
\(884\) −4.33789 −0.145899
\(885\) 131.238 4.41152
\(886\) −32.2770 −1.08437
\(887\) −7.59618 −0.255055 −0.127527 0.991835i \(-0.540704\pi\)
−0.127527 + 0.991835i \(0.540704\pi\)
\(888\) −1.11396 −0.0373819
\(889\) −111.630 −3.74396
\(890\) 58.3173 1.95480
\(891\) 3.15947 0.105846
\(892\) 3.53959 0.118514
\(893\) −7.77825 −0.260289
\(894\) 11.6633 0.390081
\(895\) 40.0594 1.33904
\(896\) 25.5603 0.853909
\(897\) −10.7343 −0.358406
\(898\) 0.374463 0.0124960
\(899\) −2.67412 −0.0891868
\(900\) 99.6822 3.32274
\(901\) 2.04031 0.0679725
\(902\) −21.6604 −0.721212
\(903\) 1.13181 0.0376641
\(904\) −11.4381 −0.380426
\(905\) 65.2235 2.16810
\(906\) −42.4127 −1.40907
\(907\) −19.1778 −0.636788 −0.318394 0.947958i \(-0.603144\pi\)
−0.318394 + 0.947958i \(0.603144\pi\)
\(908\) −3.46121 −0.114864
\(909\) 104.895 3.47916
\(910\) 22.8292 0.756779
\(911\) −52.0752 −1.72533 −0.862665 0.505776i \(-0.831206\pi\)
−0.862665 + 0.505776i \(0.831206\pi\)
\(912\) 33.9387 1.12382
\(913\) −3.03240 −0.100358
\(914\) 27.8662 0.921731
\(915\) −113.095 −3.73879
\(916\) 9.58348 0.316647
\(917\) 5.05987 0.167092
\(918\) 43.0464 1.42074
\(919\) −25.4213 −0.838570 −0.419285 0.907855i \(-0.637719\pi\)
−0.419285 + 0.907855i \(0.637719\pi\)
\(920\) −14.4126 −0.475171
\(921\) −76.4199 −2.51812
\(922\) 2.09703 0.0690619
\(923\) 9.17414 0.301970
\(924\) 33.6346 1.10650
\(925\) 4.93605 0.162296
\(926\) 9.51999 0.312846
\(927\) 45.3599 1.48981
\(928\) −12.8545 −0.421970
\(929\) −42.7304 −1.40194 −0.700969 0.713192i \(-0.747249\pi\)
−0.700969 + 0.713192i \(0.747249\pi\)
\(930\) −36.5614 −1.19889
\(931\) 66.6353 2.18388
\(932\) 37.1493 1.21687
\(933\) 34.1722 1.11875
\(934\) −18.1645 −0.594360
\(935\) 11.3752 0.372008
\(936\) 2.02825 0.0662955
\(937\) 20.6902 0.675921 0.337960 0.941160i \(-0.390263\pi\)
0.337960 + 0.941160i \(0.390263\pi\)
\(938\) 143.701 4.69200
\(939\) −6.37334 −0.207986
\(940\) 18.1766 0.592856
\(941\) 21.3223 0.695089 0.347544 0.937664i \(-0.387016\pi\)
0.347544 + 0.937664i \(0.387016\pi\)
\(942\) −24.8074 −0.808269
\(943\) −64.8948 −2.11326
\(944\) −41.3231 −1.34495
\(945\) −121.366 −3.94804
\(946\) 0.161187 0.00524065
\(947\) −12.7588 −0.414604 −0.207302 0.978277i \(-0.566468\pi\)
−0.207302 + 0.978277i \(0.566468\pi\)
\(948\) −6.84203 −0.222219
\(949\) 5.89180 0.191256
\(950\) 60.6357 1.96728
\(951\) 13.4699 0.436791
\(952\) 10.1404 0.328652
\(953\) 1.98491 0.0642974 0.0321487 0.999483i \(-0.489765\pi\)
0.0321487 + 0.999483i \(0.489765\pi\)
\(954\) −7.15108 −0.231525
\(955\) −63.8965 −2.06764
\(956\) 27.6564 0.894473
\(957\) −4.56787 −0.147658
\(958\) 79.9067 2.58167
\(959\) −91.5878 −2.95752
\(960\) −107.021 −3.45410
\(961\) −28.1568 −0.908285
\(962\) 0.752863 0.0242733
\(963\) 7.96603 0.256702
\(964\) 46.9289 1.51148
\(965\) −36.2574 −1.16717
\(966\) 188.096 6.05190
\(967\) 43.8337 1.40960 0.704799 0.709407i \(-0.251037\pi\)
0.704799 + 0.709407i \(0.251037\pi\)
\(968\) 0.639017 0.0205388
\(969\) 32.3575 1.03947
\(970\) 55.2817 1.77499
\(971\) −28.8723 −0.926555 −0.463277 0.886213i \(-0.653327\pi\)
−0.463277 + 0.886213i \(0.653327\pi\)
\(972\) 24.7844 0.794959
\(973\) −34.5958 −1.10909
\(974\) 39.0895 1.25251
\(975\) −14.0784 −0.450871
\(976\) 35.6103 1.13986
\(977\) 61.5281 1.96846 0.984229 0.176897i \(-0.0566061\pi\)
0.984229 + 0.176897i \(0.0566061\pi\)
\(978\) 83.5702 2.67228
\(979\) −7.74657 −0.247581
\(980\) −155.717 −4.97419
\(981\) 25.0422 0.799537
\(982\) 28.8624 0.921035
\(983\) 4.64930 0.148290 0.0741448 0.997247i \(-0.476377\pi\)
0.0741448 + 0.997247i \(0.476377\pi\)
\(984\) 19.2080 0.612327
\(985\) 38.7694 1.23529
\(986\) −10.3232 −0.328757
\(987\) −31.6459 −1.00730
\(988\) 4.95466 0.157629
\(989\) 0.482919 0.0153559
\(990\) −39.8689 −1.26712
\(991\) 43.7093 1.38847 0.694235 0.719748i \(-0.255743\pi\)
0.694235 + 0.719748i \(0.255743\pi\)
\(992\) 13.6671 0.433931
\(993\) 73.6374 2.33681
\(994\) −160.758 −5.09895
\(995\) −33.5389 −1.06325
\(996\) 20.1574 0.638711
\(997\) −32.7113 −1.03598 −0.517988 0.855388i \(-0.673319\pi\)
−0.517988 + 0.855388i \(0.673319\pi\)
\(998\) 25.6317 0.811359
\(999\) −4.00243 −0.126631
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 1441.2.a.e.1.22 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.e.1.22 28 1.1 even 1 trivial