Properties

Label 1441.2.a.f.1.19
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $0$
Dimension $31$
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] = [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: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
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)
 
\(f(q)\) \(=\) \(q+0.867375 q^{2} +0.595469 q^{3} -1.24766 q^{4} +3.84366 q^{5} +0.516495 q^{6} +1.26797 q^{7} -2.81694 q^{8} -2.64542 q^{9} +O(q^{10})\) \(q+0.867375 q^{2} +0.595469 q^{3} -1.24766 q^{4} +3.84366 q^{5} +0.516495 q^{6} +1.26797 q^{7} -2.81694 q^{8} -2.64542 q^{9} +3.33390 q^{10} -1.00000 q^{11} -0.742944 q^{12} +5.03984 q^{13} +1.09981 q^{14} +2.28878 q^{15} +0.0519793 q^{16} -3.67254 q^{17} -2.29457 q^{18} +3.68668 q^{19} -4.79559 q^{20} +0.755038 q^{21} -0.867375 q^{22} +5.90488 q^{23} -1.67740 q^{24} +9.77374 q^{25} +4.37143 q^{26} -3.36167 q^{27} -1.58200 q^{28} +8.38794 q^{29} +1.98523 q^{30} +4.86681 q^{31} +5.67896 q^{32} -0.595469 q^{33} -3.18547 q^{34} +4.87366 q^{35} +3.30058 q^{36} -2.88281 q^{37} +3.19773 q^{38} +3.00107 q^{39} -10.8274 q^{40} -1.35972 q^{41} +0.654901 q^{42} -7.22890 q^{43} +1.24766 q^{44} -10.1681 q^{45} +5.12175 q^{46} -2.45880 q^{47} +0.0309521 q^{48} -5.39225 q^{49} +8.47750 q^{50} -2.18688 q^{51} -6.28802 q^{52} +2.17735 q^{53} -2.91583 q^{54} -3.84366 q^{55} -3.57180 q^{56} +2.19531 q^{57} +7.27548 q^{58} +9.50732 q^{59} -2.85562 q^{60} -3.72670 q^{61} +4.22135 q^{62} -3.35431 q^{63} +4.82183 q^{64} +19.3715 q^{65} -0.516495 q^{66} +4.48935 q^{67} +4.58208 q^{68} +3.51618 q^{69} +4.22729 q^{70} -4.16560 q^{71} +7.45198 q^{72} -7.67820 q^{73} -2.50047 q^{74} +5.81996 q^{75} -4.59973 q^{76} -1.26797 q^{77} +2.60305 q^{78} +5.11376 q^{79} +0.199791 q^{80} +5.93448 q^{81} -1.17939 q^{82} -4.45753 q^{83} -0.942032 q^{84} -14.1160 q^{85} -6.27016 q^{86} +4.99476 q^{87} +2.81694 q^{88} -15.0346 q^{89} -8.81954 q^{90} +6.39038 q^{91} -7.36729 q^{92} +2.89804 q^{93} -2.13271 q^{94} +14.1704 q^{95} +3.38165 q^{96} -2.95569 q^{97} -4.67710 q^{98} +2.64542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.867375 0.613327 0.306663 0.951818i \(-0.400787\pi\)
0.306663 + 0.951818i \(0.400787\pi\)
\(3\) 0.595469 0.343794 0.171897 0.985115i \(-0.445010\pi\)
0.171897 + 0.985115i \(0.445010\pi\)
\(4\) −1.24766 −0.623830
\(5\) 3.84366 1.71894 0.859469 0.511188i \(-0.170794\pi\)
0.859469 + 0.511188i \(0.170794\pi\)
\(6\) 0.516495 0.210858
\(7\) 1.26797 0.479248 0.239624 0.970866i \(-0.422976\pi\)
0.239624 + 0.970866i \(0.422976\pi\)
\(8\) −2.81694 −0.995938
\(9\) −2.64542 −0.881805
\(10\) 3.33390 1.05427
\(11\) −1.00000 −0.301511
\(12\) −0.742944 −0.214469
\(13\) 5.03984 1.39780 0.698901 0.715219i \(-0.253673\pi\)
0.698901 + 0.715219i \(0.253673\pi\)
\(14\) 1.09981 0.293936
\(15\) 2.28878 0.590961
\(16\) 0.0519793 0.0129948
\(17\) −3.67254 −0.890722 −0.445361 0.895351i \(-0.646925\pi\)
−0.445361 + 0.895351i \(0.646925\pi\)
\(18\) −2.29457 −0.540835
\(19\) 3.68668 0.845783 0.422891 0.906180i \(-0.361015\pi\)
0.422891 + 0.906180i \(0.361015\pi\)
\(20\) −4.79559 −1.07233
\(21\) 0.755038 0.164763
\(22\) −0.867375 −0.184925
\(23\) 5.90488 1.23125 0.615627 0.788038i \(-0.288903\pi\)
0.615627 + 0.788038i \(0.288903\pi\)
\(24\) −1.67740 −0.342398
\(25\) 9.77374 1.95475
\(26\) 4.37143 0.857309
\(27\) −3.36167 −0.646954
\(28\) −1.58200 −0.298970
\(29\) 8.38794 1.55760 0.778800 0.627272i \(-0.215829\pi\)
0.778800 + 0.627272i \(0.215829\pi\)
\(30\) 1.98523 0.362452
\(31\) 4.86681 0.874105 0.437053 0.899436i \(-0.356022\pi\)
0.437053 + 0.899436i \(0.356022\pi\)
\(32\) 5.67896 1.00391
\(33\) −0.595469 −0.103658
\(34\) −3.18547 −0.546303
\(35\) 4.87366 0.823798
\(36\) 3.30058 0.550097
\(37\) −2.88281 −0.473931 −0.236965 0.971518i \(-0.576153\pi\)
−0.236965 + 0.971518i \(0.576153\pi\)
\(38\) 3.19773 0.518741
\(39\) 3.00107 0.480556
\(40\) −10.8274 −1.71196
\(41\) −1.35972 −0.212352 −0.106176 0.994347i \(-0.533861\pi\)
−0.106176 + 0.994347i \(0.533861\pi\)
\(42\) 0.654901 0.101053
\(43\) −7.22890 −1.10240 −0.551198 0.834374i \(-0.685829\pi\)
−0.551198 + 0.834374i \(0.685829\pi\)
\(44\) 1.24766 0.188092
\(45\) −10.1681 −1.51577
\(46\) 5.12175 0.755160
\(47\) −2.45880 −0.358653 −0.179327 0.983790i \(-0.557392\pi\)
−0.179327 + 0.983790i \(0.557392\pi\)
\(48\) 0.0309521 0.00446755
\(49\) −5.39225 −0.770321
\(50\) 8.47750 1.19890
\(51\) −2.18688 −0.306225
\(52\) −6.28802 −0.871991
\(53\) 2.17735 0.299082 0.149541 0.988756i \(-0.452220\pi\)
0.149541 + 0.988756i \(0.452220\pi\)
\(54\) −2.91583 −0.396794
\(55\) −3.84366 −0.518279
\(56\) −3.57180 −0.477302
\(57\) 2.19531 0.290775
\(58\) 7.27548 0.955318
\(59\) 9.50732 1.23775 0.618874 0.785490i \(-0.287589\pi\)
0.618874 + 0.785490i \(0.287589\pi\)
\(60\) −2.85562 −0.368660
\(61\) −3.72670 −0.477155 −0.238577 0.971123i \(-0.576681\pi\)
−0.238577 + 0.971123i \(0.576681\pi\)
\(62\) 4.22135 0.536112
\(63\) −3.35431 −0.422604
\(64\) 4.82183 0.602729
\(65\) 19.3715 2.40273
\(66\) −0.516495 −0.0635761
\(67\) 4.48935 0.548462 0.274231 0.961664i \(-0.411577\pi\)
0.274231 + 0.961664i \(0.411577\pi\)
\(68\) 4.58208 0.555659
\(69\) 3.51618 0.423298
\(70\) 4.22729 0.505257
\(71\) −4.16560 −0.494366 −0.247183 0.968969i \(-0.579505\pi\)
−0.247183 + 0.968969i \(0.579505\pi\)
\(72\) 7.45198 0.878224
\(73\) −7.67820 −0.898665 −0.449333 0.893365i \(-0.648338\pi\)
−0.449333 + 0.893365i \(0.648338\pi\)
\(74\) −2.50047 −0.290674
\(75\) 5.81996 0.672031
\(76\) −4.59973 −0.527625
\(77\) −1.26797 −0.144499
\(78\) 2.60305 0.294738
\(79\) 5.11376 0.575343 0.287672 0.957729i \(-0.407119\pi\)
0.287672 + 0.957729i \(0.407119\pi\)
\(80\) 0.199791 0.0223373
\(81\) 5.93448 0.659386
\(82\) −1.17939 −0.130241
\(83\) −4.45753 −0.489277 −0.244639 0.969614i \(-0.578669\pi\)
−0.244639 + 0.969614i \(0.578669\pi\)
\(84\) −0.942032 −0.102784
\(85\) −14.1160 −1.53110
\(86\) −6.27016 −0.676129
\(87\) 4.99476 0.535494
\(88\) 2.81694 0.300287
\(89\) −15.0346 −1.59367 −0.796833 0.604199i \(-0.793493\pi\)
−0.796833 + 0.604199i \(0.793493\pi\)
\(90\) −8.81954 −0.929661
\(91\) 6.39038 0.669894
\(92\) −7.36729 −0.768093
\(93\) 2.89804 0.300512
\(94\) −2.13271 −0.219972
\(95\) 14.1704 1.45385
\(96\) 3.38165 0.345138
\(97\) −2.95569 −0.300105 −0.150052 0.988678i \(-0.547944\pi\)
−0.150052 + 0.988678i \(0.547944\pi\)
\(98\) −4.67710 −0.472458
\(99\) 2.64542 0.265874
\(100\) −12.1943 −1.21943
\(101\) 10.3820 1.03305 0.516524 0.856273i \(-0.327226\pi\)
0.516524 + 0.856273i \(0.327226\pi\)
\(102\) −1.89685 −0.187816
\(103\) −1.30158 −0.128249 −0.0641243 0.997942i \(-0.520425\pi\)
−0.0641243 + 0.997942i \(0.520425\pi\)
\(104\) −14.1969 −1.39212
\(105\) 2.90211 0.283217
\(106\) 1.88858 0.183435
\(107\) −5.63697 −0.544947 −0.272473 0.962163i \(-0.587842\pi\)
−0.272473 + 0.962163i \(0.587842\pi\)
\(108\) 4.19423 0.403590
\(109\) 2.62758 0.251676 0.125838 0.992051i \(-0.459838\pi\)
0.125838 + 0.992051i \(0.459838\pi\)
\(110\) −3.33390 −0.317875
\(111\) −1.71662 −0.162935
\(112\) 0.0659083 0.00622775
\(113\) 1.54047 0.144915 0.0724575 0.997371i \(-0.476916\pi\)
0.0724575 + 0.997371i \(0.476916\pi\)
\(114\) 1.90415 0.178340
\(115\) 22.6964 2.11645
\(116\) −10.4653 −0.971679
\(117\) −13.3325 −1.23259
\(118\) 8.24641 0.759144
\(119\) −4.65668 −0.426877
\(120\) −6.44736 −0.588561
\(121\) 1.00000 0.0909091
\(122\) −3.23244 −0.292652
\(123\) −0.809671 −0.0730055
\(124\) −6.07213 −0.545294
\(125\) 18.3486 1.64115
\(126\) −2.90945 −0.259194
\(127\) −10.8282 −0.960843 −0.480422 0.877038i \(-0.659516\pi\)
−0.480422 + 0.877038i \(0.659516\pi\)
\(128\) −7.17559 −0.634239
\(129\) −4.30459 −0.378998
\(130\) 16.8023 1.47366
\(131\) 1.00000 0.0873704
\(132\) 0.742944 0.0646649
\(133\) 4.67461 0.405340
\(134\) 3.89395 0.336386
\(135\) −12.9211 −1.11207
\(136\) 10.3453 0.887104
\(137\) 1.62529 0.138858 0.0694289 0.997587i \(-0.477882\pi\)
0.0694289 + 0.997587i \(0.477882\pi\)
\(138\) 3.04984 0.259620
\(139\) 16.9885 1.44095 0.720473 0.693483i \(-0.243925\pi\)
0.720473 + 0.693483i \(0.243925\pi\)
\(140\) −6.08067 −0.513910
\(141\) −1.46414 −0.123303
\(142\) −3.61314 −0.303208
\(143\) −5.03984 −0.421453
\(144\) −0.137507 −0.0114589
\(145\) 32.2404 2.67742
\(146\) −6.65988 −0.551175
\(147\) −3.21092 −0.264832
\(148\) 3.59677 0.295652
\(149\) 1.64713 0.134938 0.0674690 0.997721i \(-0.478508\pi\)
0.0674690 + 0.997721i \(0.478508\pi\)
\(150\) 5.04809 0.412175
\(151\) −13.9952 −1.13892 −0.569458 0.822021i \(-0.692847\pi\)
−0.569458 + 0.822021i \(0.692847\pi\)
\(152\) −10.3852 −0.842347
\(153\) 9.71540 0.785443
\(154\) −1.09981 −0.0886250
\(155\) 18.7064 1.50253
\(156\) −3.74432 −0.299786
\(157\) −16.6427 −1.32824 −0.664118 0.747628i \(-0.731193\pi\)
−0.664118 + 0.747628i \(0.731193\pi\)
\(158\) 4.43555 0.352873
\(159\) 1.29654 0.102823
\(160\) 21.8280 1.72566
\(161\) 7.48723 0.590076
\(162\) 5.14742 0.404419
\(163\) 14.7990 1.15914 0.579572 0.814921i \(-0.303220\pi\)
0.579572 + 0.814921i \(0.303220\pi\)
\(164\) 1.69647 0.132472
\(165\) −2.28878 −0.178181
\(166\) −3.86635 −0.300087
\(167\) 2.68372 0.207672 0.103836 0.994594i \(-0.466888\pi\)
0.103836 + 0.994594i \(0.466888\pi\)
\(168\) −2.12690 −0.164094
\(169\) 12.4000 0.953849
\(170\) −12.2439 −0.939061
\(171\) −9.75281 −0.745816
\(172\) 9.01921 0.687708
\(173\) −22.9315 −1.74345 −0.871724 0.489998i \(-0.836997\pi\)
−0.871724 + 0.489998i \(0.836997\pi\)
\(174\) 4.33233 0.328433
\(175\) 12.3928 0.936810
\(176\) −0.0519793 −0.00391809
\(177\) 5.66132 0.425531
\(178\) −13.0407 −0.977438
\(179\) −10.7008 −0.799814 −0.399907 0.916556i \(-0.630958\pi\)
−0.399907 + 0.916556i \(0.630958\pi\)
\(180\) 12.6863 0.945583
\(181\) −12.8845 −0.957698 −0.478849 0.877897i \(-0.658946\pi\)
−0.478849 + 0.877897i \(0.658946\pi\)
\(182\) 5.54286 0.410864
\(183\) −2.21913 −0.164043
\(184\) −16.6337 −1.22625
\(185\) −11.0805 −0.814657
\(186\) 2.51368 0.184312
\(187\) 3.67254 0.268563
\(188\) 3.06775 0.223739
\(189\) −4.26251 −0.310052
\(190\) 12.2910 0.891684
\(191\) 5.67609 0.410708 0.205354 0.978688i \(-0.434165\pi\)
0.205354 + 0.978688i \(0.434165\pi\)
\(192\) 2.87125 0.207215
\(193\) 6.16025 0.443424 0.221712 0.975112i \(-0.428835\pi\)
0.221712 + 0.975112i \(0.428835\pi\)
\(194\) −2.56369 −0.184062
\(195\) 11.5351 0.826046
\(196\) 6.72770 0.480550
\(197\) −15.2154 −1.08405 −0.542026 0.840362i \(-0.682342\pi\)
−0.542026 + 0.840362i \(0.682342\pi\)
\(198\) 2.29457 0.163068
\(199\) −19.4965 −1.38207 −0.691036 0.722821i \(-0.742845\pi\)
−0.691036 + 0.722821i \(0.742845\pi\)
\(200\) −27.5320 −1.94681
\(201\) 2.67327 0.188558
\(202\) 9.00509 0.633596
\(203\) 10.6357 0.746478
\(204\) 2.72849 0.191032
\(205\) −5.22630 −0.365021
\(206\) −1.12896 −0.0786583
\(207\) −15.6209 −1.08573
\(208\) 0.261968 0.0181642
\(209\) −3.68668 −0.255013
\(210\) 2.51722 0.173705
\(211\) −12.9329 −0.890338 −0.445169 0.895446i \(-0.646856\pi\)
−0.445169 + 0.895446i \(0.646856\pi\)
\(212\) −2.71659 −0.186576
\(213\) −2.48049 −0.169960
\(214\) −4.88937 −0.334230
\(215\) −27.7854 −1.89495
\(216\) 9.46963 0.644326
\(217\) 6.17098 0.418914
\(218\) 2.27909 0.154360
\(219\) −4.57213 −0.308956
\(220\) 4.79559 0.323318
\(221\) −18.5090 −1.24505
\(222\) −1.48896 −0.0999321
\(223\) 23.7404 1.58977 0.794886 0.606759i \(-0.207531\pi\)
0.794886 + 0.606759i \(0.207531\pi\)
\(224\) 7.20077 0.481122
\(225\) −25.8556 −1.72371
\(226\) 1.33616 0.0888802
\(227\) 1.00908 0.0669749 0.0334874 0.999439i \(-0.489339\pi\)
0.0334874 + 0.999439i \(0.489339\pi\)
\(228\) −2.73900 −0.181394
\(229\) −4.62476 −0.305613 −0.152806 0.988256i \(-0.548831\pi\)
−0.152806 + 0.988256i \(0.548831\pi\)
\(230\) 19.6863 1.29807
\(231\) −0.755038 −0.0496779
\(232\) −23.6283 −1.55127
\(233\) −22.3623 −1.46500 −0.732501 0.680766i \(-0.761647\pi\)
−0.732501 + 0.680766i \(0.761647\pi\)
\(234\) −11.5643 −0.755980
\(235\) −9.45081 −0.616503
\(236\) −11.8619 −0.772145
\(237\) 3.04509 0.197800
\(238\) −4.03908 −0.261815
\(239\) 18.2618 1.18125 0.590627 0.806944i \(-0.298880\pi\)
0.590627 + 0.806944i \(0.298880\pi\)
\(240\) 0.118969 0.00767944
\(241\) −27.7795 −1.78943 −0.894717 0.446634i \(-0.852623\pi\)
−0.894717 + 0.446634i \(0.852623\pi\)
\(242\) 0.867375 0.0557570
\(243\) 13.6188 0.873647
\(244\) 4.64965 0.297664
\(245\) −20.7260 −1.32413
\(246\) −0.702288 −0.0447762
\(247\) 18.5803 1.18224
\(248\) −13.7095 −0.870555
\(249\) −2.65432 −0.168211
\(250\) 15.9152 1.00656
\(251\) −17.1272 −1.08106 −0.540529 0.841325i \(-0.681776\pi\)
−0.540529 + 0.841325i \(0.681776\pi\)
\(252\) 4.18505 0.263633
\(253\) −5.90488 −0.371237
\(254\) −9.39207 −0.589311
\(255\) −8.40564 −0.526382
\(256\) −15.8676 −0.991725
\(257\) 29.3116 1.82841 0.914203 0.405258i \(-0.132818\pi\)
0.914203 + 0.405258i \(0.132818\pi\)
\(258\) −3.73369 −0.232449
\(259\) −3.65532 −0.227130
\(260\) −24.1690 −1.49890
\(261\) −22.1896 −1.37350
\(262\) 0.867375 0.0535866
\(263\) 0.190663 0.0117568 0.00587839 0.999983i \(-0.498129\pi\)
0.00587839 + 0.999983i \(0.498129\pi\)
\(264\) 1.67740 0.103237
\(265\) 8.36900 0.514103
\(266\) 4.05464 0.248606
\(267\) −8.95265 −0.547893
\(268\) −5.60119 −0.342147
\(269\) 20.9533 1.27755 0.638774 0.769395i \(-0.279442\pi\)
0.638774 + 0.769395i \(0.279442\pi\)
\(270\) −11.2075 −0.682065
\(271\) −30.2804 −1.83940 −0.919701 0.392619i \(-0.871569\pi\)
−0.919701 + 0.392619i \(0.871569\pi\)
\(272\) −0.190896 −0.0115748
\(273\) 3.80528 0.230306
\(274\) 1.40973 0.0851652
\(275\) −9.77374 −0.589379
\(276\) −4.38699 −0.264066
\(277\) 9.93007 0.596640 0.298320 0.954466i \(-0.403574\pi\)
0.298320 + 0.954466i \(0.403574\pi\)
\(278\) 14.7354 0.883771
\(279\) −12.8747 −0.770791
\(280\) −13.7288 −0.820452
\(281\) −20.0093 −1.19366 −0.596829 0.802369i \(-0.703573\pi\)
−0.596829 + 0.802369i \(0.703573\pi\)
\(282\) −1.26996 −0.0756250
\(283\) 29.5664 1.75754 0.878769 0.477248i \(-0.158366\pi\)
0.878769 + 0.477248i \(0.158366\pi\)
\(284\) 5.19726 0.308401
\(285\) 8.43801 0.499825
\(286\) −4.37143 −0.258488
\(287\) −1.72409 −0.101770
\(288\) −15.0232 −0.885252
\(289\) −3.51246 −0.206615
\(290\) 27.9645 1.64213
\(291\) −1.76002 −0.103174
\(292\) 9.57979 0.560615
\(293\) 0.259296 0.0151482 0.00757412 0.999971i \(-0.497589\pi\)
0.00757412 + 0.999971i \(0.497589\pi\)
\(294\) −2.78507 −0.162429
\(295\) 36.5429 2.12761
\(296\) 8.12069 0.472006
\(297\) 3.36167 0.195064
\(298\) 1.42868 0.0827611
\(299\) 29.7597 1.72105
\(300\) −7.26134 −0.419234
\(301\) −9.16604 −0.528322
\(302\) −12.1391 −0.698527
\(303\) 6.18216 0.355156
\(304\) 0.191631 0.0109908
\(305\) −14.3242 −0.820199
\(306\) 8.42689 0.481733
\(307\) −10.4703 −0.597570 −0.298785 0.954320i \(-0.596581\pi\)
−0.298785 + 0.954320i \(0.596581\pi\)
\(308\) 1.58200 0.0901428
\(309\) −0.775052 −0.0440912
\(310\) 16.2254 0.921543
\(311\) 20.6984 1.17370 0.586849 0.809696i \(-0.300368\pi\)
0.586849 + 0.809696i \(0.300368\pi\)
\(312\) −8.45384 −0.478604
\(313\) −32.4711 −1.83537 −0.917686 0.397306i \(-0.869945\pi\)
−0.917686 + 0.397306i \(0.869945\pi\)
\(314\) −14.4355 −0.814642
\(315\) −12.8929 −0.726430
\(316\) −6.38024 −0.358917
\(317\) 7.29773 0.409882 0.204941 0.978774i \(-0.434300\pi\)
0.204941 + 0.978774i \(0.434300\pi\)
\(318\) 1.12459 0.0630639
\(319\) −8.38794 −0.469634
\(320\) 18.5335 1.03605
\(321\) −3.35664 −0.187350
\(322\) 6.49423 0.361909
\(323\) −13.5395 −0.753357
\(324\) −7.40421 −0.411345
\(325\) 49.2581 2.73235
\(326\) 12.8362 0.710934
\(327\) 1.56464 0.0865248
\(328\) 3.83024 0.211490
\(329\) −3.11770 −0.171884
\(330\) −1.98523 −0.109283
\(331\) 24.2183 1.33116 0.665580 0.746327i \(-0.268184\pi\)
0.665580 + 0.746327i \(0.268184\pi\)
\(332\) 5.56148 0.305226
\(333\) 7.62622 0.417915
\(334\) 2.32779 0.127371
\(335\) 17.2556 0.942772
\(336\) 0.0392464 0.00214107
\(337\) −33.0504 −1.80037 −0.900184 0.435510i \(-0.856568\pi\)
−0.900184 + 0.435510i \(0.856568\pi\)
\(338\) 10.7555 0.585021
\(339\) 0.917301 0.0498210
\(340\) 17.6120 0.955144
\(341\) −4.86681 −0.263553
\(342\) −8.45934 −0.457429
\(343\) −15.7130 −0.848424
\(344\) 20.3634 1.09792
\(345\) 13.5150 0.727623
\(346\) −19.8902 −1.06930
\(347\) −8.92109 −0.478909 −0.239454 0.970908i \(-0.576969\pi\)
−0.239454 + 0.970908i \(0.576969\pi\)
\(348\) −6.23176 −0.334058
\(349\) 22.1550 1.18593 0.592965 0.805228i \(-0.297957\pi\)
0.592965 + 0.805228i \(0.297957\pi\)
\(350\) 10.7492 0.574570
\(351\) −16.9423 −0.904313
\(352\) −5.67896 −0.302690
\(353\) 26.3039 1.40002 0.700009 0.714134i \(-0.253179\pi\)
0.700009 + 0.714134i \(0.253179\pi\)
\(354\) 4.91049 0.260989
\(355\) −16.0112 −0.849785
\(356\) 18.7581 0.994178
\(357\) −2.77291 −0.146758
\(358\) −9.28158 −0.490547
\(359\) −33.2141 −1.75297 −0.876487 0.481425i \(-0.840119\pi\)
−0.876487 + 0.481425i \(0.840119\pi\)
\(360\) 28.6429 1.50961
\(361\) −5.40838 −0.284652
\(362\) −11.1757 −0.587382
\(363\) 0.595469 0.0312540
\(364\) −7.97303 −0.417900
\(365\) −29.5124 −1.54475
\(366\) −1.92482 −0.100612
\(367\) −18.6855 −0.975377 −0.487689 0.873018i \(-0.662160\pi\)
−0.487689 + 0.873018i \(0.662160\pi\)
\(368\) 0.306932 0.0159999
\(369\) 3.59702 0.187253
\(370\) −9.61098 −0.499651
\(371\) 2.76082 0.143335
\(372\) −3.61577 −0.187469
\(373\) −28.8666 −1.49465 −0.747327 0.664457i \(-0.768663\pi\)
−0.747327 + 0.664457i \(0.768663\pi\)
\(374\) 3.18547 0.164717
\(375\) 10.9261 0.564219
\(376\) 6.92630 0.357197
\(377\) 42.2739 2.17722
\(378\) −3.69719 −0.190163
\(379\) 16.2912 0.836824 0.418412 0.908257i \(-0.362587\pi\)
0.418412 + 0.908257i \(0.362587\pi\)
\(380\) −17.6798 −0.906955
\(381\) −6.44783 −0.330333
\(382\) 4.92330 0.251898
\(383\) −6.93561 −0.354393 −0.177197 0.984175i \(-0.556703\pi\)
−0.177197 + 0.984175i \(0.556703\pi\)
\(384\) −4.27284 −0.218048
\(385\) −4.87366 −0.248385
\(386\) 5.34324 0.271964
\(387\) 19.1234 0.972099
\(388\) 3.68770 0.187214
\(389\) −6.63758 −0.336539 −0.168269 0.985741i \(-0.553818\pi\)
−0.168269 + 0.985741i \(0.553818\pi\)
\(390\) 10.0053 0.506636
\(391\) −21.6859 −1.09670
\(392\) 15.1896 0.767192
\(393\) 0.595469 0.0300374
\(394\) −13.1974 −0.664877
\(395\) 19.6556 0.988979
\(396\) −3.30058 −0.165861
\(397\) 38.5529 1.93491 0.967457 0.253034i \(-0.0814283\pi\)
0.967457 + 0.253034i \(0.0814283\pi\)
\(398\) −16.9108 −0.847661
\(399\) 2.78359 0.139354
\(400\) 0.508032 0.0254016
\(401\) −29.5892 −1.47762 −0.738808 0.673916i \(-0.764611\pi\)
−0.738808 + 0.673916i \(0.764611\pi\)
\(402\) 2.31873 0.115648
\(403\) 24.5280 1.22183
\(404\) −12.9532 −0.644447
\(405\) 22.8101 1.13344
\(406\) 9.22511 0.457835
\(407\) 2.88281 0.142895
\(408\) 6.16032 0.304981
\(409\) 28.4586 1.40719 0.703594 0.710602i \(-0.251577\pi\)
0.703594 + 0.710602i \(0.251577\pi\)
\(410\) −4.53316 −0.223877
\(411\) 0.967810 0.0477385
\(412\) 1.62393 0.0800054
\(413\) 12.0550 0.593189
\(414\) −13.5492 −0.665904
\(415\) −17.1332 −0.841037
\(416\) 28.6211 1.40326
\(417\) 10.1161 0.495389
\(418\) −3.19773 −0.156406
\(419\) 26.4337 1.29137 0.645685 0.763604i \(-0.276572\pi\)
0.645685 + 0.763604i \(0.276572\pi\)
\(420\) −3.62085 −0.176680
\(421\) 2.61960 0.127672 0.0638358 0.997960i \(-0.479667\pi\)
0.0638358 + 0.997960i \(0.479667\pi\)
\(422\) −11.2177 −0.546068
\(423\) 6.50456 0.316263
\(424\) −6.13346 −0.297867
\(425\) −35.8944 −1.74114
\(426\) −2.15151 −0.104241
\(427\) −4.72535 −0.228676
\(428\) 7.03303 0.339954
\(429\) −3.00107 −0.144893
\(430\) −24.1004 −1.16222
\(431\) −12.5844 −0.606169 −0.303084 0.952964i \(-0.598016\pi\)
−0.303084 + 0.952964i \(0.598016\pi\)
\(432\) −0.174737 −0.00840706
\(433\) −1.91400 −0.0919811 −0.0459906 0.998942i \(-0.514644\pi\)
−0.0459906 + 0.998942i \(0.514644\pi\)
\(434\) 5.35256 0.256931
\(435\) 19.1982 0.920481
\(436\) −3.27832 −0.157003
\(437\) 21.7694 1.04137
\(438\) −3.96575 −0.189491
\(439\) −15.4552 −0.737634 −0.368817 0.929502i \(-0.620237\pi\)
−0.368817 + 0.929502i \(0.620237\pi\)
\(440\) 10.8274 0.516174
\(441\) 14.2647 0.679273
\(442\) −16.0543 −0.763624
\(443\) 23.3994 1.11174 0.555870 0.831269i \(-0.312385\pi\)
0.555870 + 0.831269i \(0.312385\pi\)
\(444\) 2.14176 0.101644
\(445\) −57.7880 −2.73941
\(446\) 20.5918 0.975049
\(447\) 0.980815 0.0463909
\(448\) 6.11395 0.288857
\(449\) 7.91672 0.373613 0.186807 0.982397i \(-0.440186\pi\)
0.186807 + 0.982397i \(0.440186\pi\)
\(450\) −22.4265 −1.05720
\(451\) 1.35972 0.0640266
\(452\) −1.92198 −0.0904024
\(453\) −8.33373 −0.391553
\(454\) 0.875249 0.0410775
\(455\) 24.5625 1.15151
\(456\) −6.18404 −0.289594
\(457\) −5.17072 −0.241876 −0.120938 0.992660i \(-0.538590\pi\)
−0.120938 + 0.992660i \(0.538590\pi\)
\(458\) −4.01140 −0.187440
\(459\) 12.3459 0.576256
\(460\) −28.3174 −1.32030
\(461\) −23.3908 −1.08942 −0.544708 0.838626i \(-0.683360\pi\)
−0.544708 + 0.838626i \(0.683360\pi\)
\(462\) −0.654901 −0.0304688
\(463\) 23.3101 1.08331 0.541656 0.840600i \(-0.317797\pi\)
0.541656 + 0.840600i \(0.317797\pi\)
\(464\) 0.435999 0.0202408
\(465\) 11.1391 0.516562
\(466\) −19.3965 −0.898525
\(467\) 1.40125 0.0648420 0.0324210 0.999474i \(-0.489678\pi\)
0.0324210 + 0.999474i \(0.489678\pi\)
\(468\) 16.6344 0.768926
\(469\) 5.69238 0.262849
\(470\) −8.19740 −0.378118
\(471\) −9.91024 −0.456640
\(472\) −26.7816 −1.23272
\(473\) 7.22890 0.332385
\(474\) 2.64123 0.121316
\(475\) 36.0327 1.65329
\(476\) 5.80995 0.266299
\(477\) −5.76000 −0.263732
\(478\) 15.8398 0.724495
\(479\) 7.91235 0.361524 0.180762 0.983527i \(-0.442144\pi\)
0.180762 + 0.983527i \(0.442144\pi\)
\(480\) 12.9979 0.593271
\(481\) −14.5289 −0.662461
\(482\) −24.0952 −1.09751
\(483\) 4.45841 0.202865
\(484\) −1.24766 −0.0567119
\(485\) −11.3607 −0.515861
\(486\) 11.8126 0.535831
\(487\) −38.7460 −1.75575 −0.877874 0.478892i \(-0.841038\pi\)
−0.877874 + 0.478892i \(0.841038\pi\)
\(488\) 10.4979 0.475217
\(489\) 8.81233 0.398507
\(490\) −17.9772 −0.812127
\(491\) 28.8886 1.30372 0.651861 0.758338i \(-0.273989\pi\)
0.651861 + 0.758338i \(0.273989\pi\)
\(492\) 1.01019 0.0455431
\(493\) −30.8050 −1.38739
\(494\) 16.1161 0.725097
\(495\) 10.1681 0.457022
\(496\) 0.252974 0.0113589
\(497\) −5.28187 −0.236924
\(498\) −2.30229 −0.103168
\(499\) 36.1054 1.61630 0.808149 0.588978i \(-0.200469\pi\)
0.808149 + 0.588978i \(0.200469\pi\)
\(500\) −22.8929 −1.02380
\(501\) 1.59807 0.0713966
\(502\) −14.8557 −0.663042
\(503\) 5.13330 0.228882 0.114441 0.993430i \(-0.463492\pi\)
0.114441 + 0.993430i \(0.463492\pi\)
\(504\) 9.44890 0.420887
\(505\) 39.9049 1.77575
\(506\) −5.12175 −0.227689
\(507\) 7.38384 0.327928
\(508\) 13.5099 0.599403
\(509\) 12.0429 0.533793 0.266896 0.963725i \(-0.414002\pi\)
0.266896 + 0.963725i \(0.414002\pi\)
\(510\) −7.29084 −0.322844
\(511\) −9.73574 −0.430684
\(512\) 0.588034 0.0259877
\(513\) −12.3934 −0.547182
\(514\) 25.4241 1.12141
\(515\) −5.00284 −0.220451
\(516\) 5.37066 0.236430
\(517\) 2.45880 0.108138
\(518\) −3.17053 −0.139305
\(519\) −13.6550 −0.599387
\(520\) −54.5682 −2.39298
\(521\) −25.0171 −1.09602 −0.548009 0.836473i \(-0.684614\pi\)
−0.548009 + 0.836473i \(0.684614\pi\)
\(522\) −19.2467 −0.842405
\(523\) 32.1032 1.40378 0.701888 0.712287i \(-0.252341\pi\)
0.701888 + 0.712287i \(0.252341\pi\)
\(524\) −1.24766 −0.0545043
\(525\) 7.37955 0.322070
\(526\) 0.165376 0.00721075
\(527\) −17.8736 −0.778584
\(528\) −0.0309521 −0.00134702
\(529\) 11.8676 0.515984
\(530\) 7.25906 0.315313
\(531\) −25.1508 −1.09145
\(532\) −5.83233 −0.252863
\(533\) −6.85277 −0.296826
\(534\) −7.76531 −0.336038
\(535\) −21.6666 −0.936730
\(536\) −12.6462 −0.546234
\(537\) −6.37198 −0.274971
\(538\) 18.1744 0.783554
\(539\) 5.39225 0.232261
\(540\) 16.1212 0.693746
\(541\) 1.16455 0.0500678 0.0250339 0.999687i \(-0.492031\pi\)
0.0250339 + 0.999687i \(0.492031\pi\)
\(542\) −26.2644 −1.12815
\(543\) −7.67233 −0.329251
\(544\) −20.8562 −0.894203
\(545\) 10.0995 0.432616
\(546\) 3.30060 0.141253
\(547\) −15.6353 −0.668518 −0.334259 0.942481i \(-0.608486\pi\)
−0.334259 + 0.942481i \(0.608486\pi\)
\(548\) −2.02781 −0.0866237
\(549\) 9.85867 0.420758
\(550\) −8.47750 −0.361482
\(551\) 30.9236 1.31739
\(552\) −9.90485 −0.421579
\(553\) 6.48411 0.275732
\(554\) 8.61309 0.365935
\(555\) −6.59812 −0.280075
\(556\) −21.1959 −0.898906
\(557\) −15.3129 −0.648828 −0.324414 0.945915i \(-0.605167\pi\)
−0.324414 + 0.945915i \(0.605167\pi\)
\(558\) −11.1672 −0.472747
\(559\) −36.4325 −1.54093
\(560\) 0.253329 0.0107051
\(561\) 2.18688 0.0923303
\(562\) −17.3556 −0.732102
\(563\) 33.3451 1.40533 0.702664 0.711522i \(-0.251994\pi\)
0.702664 + 0.711522i \(0.251994\pi\)
\(564\) 1.82675 0.0769202
\(565\) 5.92104 0.249100
\(566\) 25.6451 1.07794
\(567\) 7.52475 0.316010
\(568\) 11.7343 0.492358
\(569\) −15.0210 −0.629714 −0.314857 0.949139i \(-0.601957\pi\)
−0.314857 + 0.949139i \(0.601957\pi\)
\(570\) 7.31892 0.306556
\(571\) 9.46964 0.396292 0.198146 0.980173i \(-0.436508\pi\)
0.198146 + 0.980173i \(0.436508\pi\)
\(572\) 6.28802 0.262915
\(573\) 3.37994 0.141199
\(574\) −1.49543 −0.0624180
\(575\) 57.7128 2.40679
\(576\) −12.7558 −0.531490
\(577\) −30.5253 −1.27079 −0.635393 0.772189i \(-0.719162\pi\)
−0.635393 + 0.772189i \(0.719162\pi\)
\(578\) −3.04662 −0.126723
\(579\) 3.66824 0.152447
\(580\) −40.2251 −1.67026
\(581\) −5.65202 −0.234485
\(582\) −1.52660 −0.0632795
\(583\) −2.17735 −0.0901766
\(584\) 21.6290 0.895015
\(585\) −51.2456 −2.11874
\(586\) 0.224907 0.00929082
\(587\) 3.21876 0.132853 0.0664263 0.997791i \(-0.478840\pi\)
0.0664263 + 0.997791i \(0.478840\pi\)
\(588\) 4.00614 0.165210
\(589\) 17.9424 0.739303
\(590\) 31.6964 1.30492
\(591\) −9.06029 −0.372691
\(592\) −0.149846 −0.00615865
\(593\) −42.3987 −1.74111 −0.870553 0.492075i \(-0.836239\pi\)
−0.870553 + 0.492075i \(0.836239\pi\)
\(594\) 2.91583 0.119638
\(595\) −17.8987 −0.733775
\(596\) −2.05506 −0.0841785
\(597\) −11.6096 −0.475148
\(598\) 25.8128 1.05556
\(599\) 12.7398 0.520532 0.260266 0.965537i \(-0.416190\pi\)
0.260266 + 0.965537i \(0.416190\pi\)
\(600\) −16.3945 −0.669302
\(601\) 9.94914 0.405834 0.202917 0.979196i \(-0.434958\pi\)
0.202917 + 0.979196i \(0.434958\pi\)
\(602\) −7.95039 −0.324034
\(603\) −11.8762 −0.483637
\(604\) 17.4613 0.710490
\(605\) 3.84366 0.156267
\(606\) 5.36225 0.217827
\(607\) 28.2258 1.14565 0.572825 0.819678i \(-0.305847\pi\)
0.572825 + 0.819678i \(0.305847\pi\)
\(608\) 20.9365 0.849088
\(609\) 6.33321 0.256635
\(610\) −12.4244 −0.503050
\(611\) −12.3920 −0.501326
\(612\) −12.1215 −0.489983
\(613\) 15.4348 0.623407 0.311704 0.950179i \(-0.399100\pi\)
0.311704 + 0.950179i \(0.399100\pi\)
\(614\) −9.08165 −0.366506
\(615\) −3.11210 −0.125492
\(616\) 3.57180 0.143912
\(617\) 37.2977 1.50155 0.750774 0.660559i \(-0.229681\pi\)
0.750774 + 0.660559i \(0.229681\pi\)
\(618\) −0.672260 −0.0270423
\(619\) 34.9963 1.40662 0.703311 0.710883i \(-0.251704\pi\)
0.703311 + 0.710883i \(0.251704\pi\)
\(620\) −23.3392 −0.937326
\(621\) −19.8503 −0.796564
\(622\) 17.9533 0.719860
\(623\) −19.0635 −0.763762
\(624\) 0.155994 0.00624475
\(625\) 21.6573 0.866292
\(626\) −28.1646 −1.12568
\(627\) −2.19531 −0.0876720
\(628\) 20.7645 0.828594
\(629\) 10.5872 0.422140
\(630\) −11.1829 −0.445539
\(631\) −30.5790 −1.21733 −0.608665 0.793427i \(-0.708295\pi\)
−0.608665 + 0.793427i \(0.708295\pi\)
\(632\) −14.4052 −0.573006
\(633\) −7.70115 −0.306093
\(634\) 6.32987 0.251391
\(635\) −41.6198 −1.65163
\(636\) −1.61765 −0.0641439
\(637\) −27.1761 −1.07676
\(638\) −7.27548 −0.288039
\(639\) 11.0198 0.435935
\(640\) −27.5806 −1.09022
\(641\) −1.66285 −0.0656785 −0.0328392 0.999461i \(-0.510455\pi\)
−0.0328392 + 0.999461i \(0.510455\pi\)
\(642\) −2.91147 −0.114907
\(643\) −16.9066 −0.666730 −0.333365 0.942798i \(-0.608184\pi\)
−0.333365 + 0.942798i \(0.608184\pi\)
\(644\) −9.34152 −0.368107
\(645\) −16.5454 −0.651473
\(646\) −11.7438 −0.462054
\(647\) 47.7281 1.87639 0.938193 0.346112i \(-0.112498\pi\)
0.938193 + 0.346112i \(0.112498\pi\)
\(648\) −16.7171 −0.656708
\(649\) −9.50732 −0.373195
\(650\) 42.7253 1.67582
\(651\) 3.67463 0.144020
\(652\) −18.4641 −0.723109
\(653\) 7.82868 0.306360 0.153180 0.988198i \(-0.451049\pi\)
0.153180 + 0.988198i \(0.451049\pi\)
\(654\) 1.35713 0.0530680
\(655\) 3.84366 0.150184
\(656\) −0.0706772 −0.00275948
\(657\) 20.3120 0.792448
\(658\) −2.70421 −0.105421
\(659\) 27.2725 1.06238 0.531192 0.847251i \(-0.321744\pi\)
0.531192 + 0.847251i \(0.321744\pi\)
\(660\) 2.85562 0.111155
\(661\) 31.7462 1.23478 0.617392 0.786656i \(-0.288189\pi\)
0.617392 + 0.786656i \(0.288189\pi\)
\(662\) 21.0064 0.816436
\(663\) −11.0216 −0.428042
\(664\) 12.5566 0.487290
\(665\) 17.9676 0.696754
\(666\) 6.61480 0.256318
\(667\) 49.5298 1.91780
\(668\) −3.34837 −0.129552
\(669\) 14.1366 0.546554
\(670\) 14.9670 0.578227
\(671\) 3.72670 0.143868
\(672\) 4.28784 0.165407
\(673\) 21.8473 0.842153 0.421077 0.907025i \(-0.361652\pi\)
0.421077 + 0.907025i \(0.361652\pi\)
\(674\) −28.6670 −1.10421
\(675\) −32.8561 −1.26463
\(676\) −15.4710 −0.595040
\(677\) −23.9730 −0.921356 −0.460678 0.887567i \(-0.652394\pi\)
−0.460678 + 0.887567i \(0.652394\pi\)
\(678\) 0.795644 0.0305565
\(679\) −3.74773 −0.143825
\(680\) 39.7639 1.52488
\(681\) 0.600875 0.0230256
\(682\) −4.22135 −0.161644
\(683\) 3.72529 0.142544 0.0712722 0.997457i \(-0.477294\pi\)
0.0712722 + 0.997457i \(0.477294\pi\)
\(684\) 12.1682 0.465263
\(685\) 6.24706 0.238688
\(686\) −13.6291 −0.520361
\(687\) −2.75390 −0.105068
\(688\) −0.375753 −0.0143255
\(689\) 10.9735 0.418057
\(690\) 11.7226 0.446270
\(691\) −27.1674 −1.03350 −0.516748 0.856138i \(-0.672857\pi\)
−0.516748 + 0.856138i \(0.672857\pi\)
\(692\) 28.6107 1.08762
\(693\) 3.35431 0.127420
\(694\) −7.73793 −0.293728
\(695\) 65.2981 2.47690
\(696\) −14.0699 −0.533319
\(697\) 4.99362 0.189147
\(698\) 19.2167 0.727363
\(699\) −13.3161 −0.503659
\(700\) −15.4620 −0.584411
\(701\) 27.5977 1.04235 0.521176 0.853450i \(-0.325494\pi\)
0.521176 + 0.853450i \(0.325494\pi\)
\(702\) −14.6953 −0.554639
\(703\) −10.6280 −0.400842
\(704\) −4.82183 −0.181730
\(705\) −5.62767 −0.211950
\(706\) 22.8154 0.858668
\(707\) 13.1641 0.495087
\(708\) −7.06341 −0.265459
\(709\) 5.35679 0.201178 0.100589 0.994928i \(-0.467927\pi\)
0.100589 + 0.994928i \(0.467927\pi\)
\(710\) −13.8877 −0.521196
\(711\) −13.5280 −0.507341
\(712\) 42.3516 1.58719
\(713\) 28.7380 1.07624
\(714\) −2.40515 −0.0900105
\(715\) −19.3715 −0.724452
\(716\) 13.3509 0.498948
\(717\) 10.8743 0.406109
\(718\) −28.8091 −1.07515
\(719\) −36.4342 −1.35877 −0.679383 0.733783i \(-0.737753\pi\)
−0.679383 + 0.733783i \(0.737753\pi\)
\(720\) −0.528530 −0.0196972
\(721\) −1.65037 −0.0614630
\(722\) −4.69110 −0.174585
\(723\) −16.5418 −0.615197
\(724\) 16.0755 0.597441
\(725\) 81.9815 3.04472
\(726\) 0.516495 0.0191689
\(727\) −13.4891 −0.500282 −0.250141 0.968209i \(-0.580477\pi\)
−0.250141 + 0.968209i \(0.580477\pi\)
\(728\) −18.0013 −0.667173
\(729\) −9.69385 −0.359031
\(730\) −25.5983 −0.947436
\(731\) 26.5484 0.981928
\(732\) 2.76873 0.102335
\(733\) −41.1742 −1.52080 −0.760402 0.649452i \(-0.774998\pi\)
−0.760402 + 0.649452i \(0.774998\pi\)
\(734\) −16.2074 −0.598225
\(735\) −12.3417 −0.455230
\(736\) 33.5336 1.23607
\(737\) −4.48935 −0.165367
\(738\) 3.11997 0.114848
\(739\) 0.159177 0.00585542 0.00292771 0.999996i \(-0.499068\pi\)
0.00292771 + 0.999996i \(0.499068\pi\)
\(740\) 13.8248 0.508208
\(741\) 11.0640 0.406446
\(742\) 2.39466 0.0879109
\(743\) 4.13854 0.151828 0.0759142 0.997114i \(-0.475812\pi\)
0.0759142 + 0.997114i \(0.475812\pi\)
\(744\) −8.16359 −0.299292
\(745\) 6.33101 0.231950
\(746\) −25.0381 −0.916711
\(747\) 11.7920 0.431447
\(748\) −4.58208 −0.167538
\(749\) −7.14753 −0.261165
\(750\) 9.47698 0.346051
\(751\) −7.06567 −0.257830 −0.128915 0.991656i \(-0.541149\pi\)
−0.128915 + 0.991656i \(0.541149\pi\)
\(752\) −0.127807 −0.00466064
\(753\) −10.1987 −0.371662
\(754\) 36.6673 1.33534
\(755\) −53.7929 −1.95772
\(756\) 5.31816 0.193420
\(757\) 1.70590 0.0620021 0.0310010 0.999519i \(-0.490130\pi\)
0.0310010 + 0.999519i \(0.490130\pi\)
\(758\) 14.1306 0.513246
\(759\) −3.51618 −0.127629
\(760\) −39.9170 −1.44794
\(761\) 35.5762 1.28964 0.644819 0.764336i \(-0.276933\pi\)
0.644819 + 0.764336i \(0.276933\pi\)
\(762\) −5.59269 −0.202602
\(763\) 3.33169 0.120615
\(764\) −7.08184 −0.256212
\(765\) 37.3427 1.35013
\(766\) −6.01578 −0.217359
\(767\) 47.9154 1.73013
\(768\) −9.44866 −0.340949
\(769\) 18.6049 0.670908 0.335454 0.942057i \(-0.391110\pi\)
0.335454 + 0.942057i \(0.391110\pi\)
\(770\) −4.22729 −0.152341
\(771\) 17.4541 0.628595
\(772\) −7.68590 −0.276621
\(773\) 29.5051 1.06122 0.530612 0.847615i \(-0.321962\pi\)
0.530612 + 0.847615i \(0.321962\pi\)
\(774\) 16.5872 0.596214
\(775\) 47.5670 1.70866
\(776\) 8.32599 0.298886
\(777\) −2.17663 −0.0780862
\(778\) −5.75727 −0.206408
\(779\) −5.01285 −0.179604
\(780\) −14.3919 −0.515313
\(781\) 4.16560 0.149057
\(782\) −18.8098 −0.672638
\(783\) −28.1975 −1.00770
\(784\) −0.280285 −0.0100102
\(785\) −63.9691 −2.28315
\(786\) 0.516495 0.0184228
\(787\) −40.5428 −1.44520 −0.722598 0.691269i \(-0.757052\pi\)
−0.722598 + 0.691269i \(0.757052\pi\)
\(788\) 18.9836 0.676264
\(789\) 0.113534 0.00404191
\(790\) 17.0487 0.606567
\(791\) 1.95327 0.0694503
\(792\) −7.45198 −0.264794
\(793\) −18.7820 −0.666968
\(794\) 33.4398 1.18673
\(795\) 4.98348 0.176746
\(796\) 24.3250 0.862178
\(797\) 49.5865 1.75644 0.878221 0.478255i \(-0.158730\pi\)
0.878221 + 0.478255i \(0.158730\pi\)
\(798\) 2.41441 0.0854693
\(799\) 9.03006 0.319460
\(800\) 55.5047 1.96239
\(801\) 39.7728 1.40530
\(802\) −25.6650 −0.906261
\(803\) 7.67820 0.270958
\(804\) −3.33534 −0.117628
\(805\) 28.7784 1.01430
\(806\) 21.2750 0.749378
\(807\) 12.4771 0.439214
\(808\) −29.2455 −1.02885
\(809\) −12.6206 −0.443718 −0.221859 0.975079i \(-0.571212\pi\)
−0.221859 + 0.975079i \(0.571212\pi\)
\(810\) 19.7849 0.695172
\(811\) 17.1042 0.600609 0.300305 0.953843i \(-0.402912\pi\)
0.300305 + 0.953843i \(0.402912\pi\)
\(812\) −13.2697 −0.465675
\(813\) −18.0310 −0.632376
\(814\) 2.50047 0.0876416
\(815\) 56.8822 1.99250
\(816\) −0.113673 −0.00397934
\(817\) −26.6506 −0.932388
\(818\) 24.6843 0.863066
\(819\) −16.9052 −0.590716
\(820\) 6.52065 0.227711
\(821\) −20.7235 −0.723255 −0.361628 0.932323i \(-0.617779\pi\)
−0.361628 + 0.932323i \(0.617779\pi\)
\(822\) 0.839454 0.0292793
\(823\) −6.01068 −0.209519 −0.104760 0.994498i \(-0.533407\pi\)
−0.104760 + 0.994498i \(0.533407\pi\)
\(824\) 3.66648 0.127728
\(825\) −5.81996 −0.202625
\(826\) 10.4562 0.363818
\(827\) −5.08408 −0.176791 −0.0883954 0.996085i \(-0.528174\pi\)
−0.0883954 + 0.996085i \(0.528174\pi\)
\(828\) 19.4896 0.677309
\(829\) −13.4710 −0.467866 −0.233933 0.972253i \(-0.575160\pi\)
−0.233933 + 0.972253i \(0.575160\pi\)
\(830\) −14.8609 −0.515831
\(831\) 5.91305 0.205122
\(832\) 24.3013 0.842496
\(833\) 19.8032 0.686142
\(834\) 8.77448 0.303835
\(835\) 10.3153 0.356976
\(836\) 4.59973 0.159085
\(837\) −16.3606 −0.565506
\(838\) 22.9279 0.792032
\(839\) −30.1935 −1.04240 −0.521198 0.853436i \(-0.674515\pi\)
−0.521198 + 0.853436i \(0.674515\pi\)
\(840\) −8.17508 −0.282067
\(841\) 41.3575 1.42612
\(842\) 2.27218 0.0783044
\(843\) −11.9149 −0.410373
\(844\) 16.1359 0.555420
\(845\) 47.6616 1.63961
\(846\) 5.64189 0.193972
\(847\) 1.26797 0.0435680
\(848\) 0.113177 0.00388652
\(849\) 17.6059 0.604231
\(850\) −31.1339 −1.06789
\(851\) −17.0226 −0.583528
\(852\) 3.09481 0.106026
\(853\) 8.80353 0.301427 0.150714 0.988577i \(-0.451843\pi\)
0.150714 + 0.988577i \(0.451843\pi\)
\(854\) −4.09865 −0.140253
\(855\) −37.4865 −1.28201
\(856\) 15.8790 0.542733
\(857\) 20.4733 0.699354 0.349677 0.936870i \(-0.386291\pi\)
0.349677 + 0.936870i \(0.386291\pi\)
\(858\) −2.60305 −0.0888668
\(859\) −33.7758 −1.15241 −0.576207 0.817304i \(-0.695468\pi\)
−0.576207 + 0.817304i \(0.695468\pi\)
\(860\) 34.6668 1.18213
\(861\) −1.02664 −0.0349878
\(862\) −10.9154 −0.371779
\(863\) 47.5170 1.61750 0.808748 0.588155i \(-0.200146\pi\)
0.808748 + 0.588155i \(0.200146\pi\)
\(864\) −19.0908 −0.649483
\(865\) −88.1408 −2.99688
\(866\) −1.66016 −0.0564145
\(867\) −2.09156 −0.0710331
\(868\) −7.69929 −0.261331
\(869\) −5.11376 −0.173472
\(870\) 16.6520 0.564556
\(871\) 22.6256 0.766641
\(872\) −7.40172 −0.250654
\(873\) 7.81902 0.264634
\(874\) 18.8822 0.638701
\(875\) 23.2656 0.786520
\(876\) 5.70447 0.192736
\(877\) −52.2233 −1.76346 −0.881728 0.471759i \(-0.843619\pi\)
−0.881728 + 0.471759i \(0.843619\pi\)
\(878\) −13.4054 −0.452411
\(879\) 0.154403 0.00520788
\(880\) −0.199791 −0.00673495
\(881\) −38.5855 −1.29998 −0.649990 0.759943i \(-0.725227\pi\)
−0.649990 + 0.759943i \(0.725227\pi\)
\(882\) 12.3729 0.416616
\(883\) 44.7200 1.50495 0.752474 0.658622i \(-0.228860\pi\)
0.752474 + 0.658622i \(0.228860\pi\)
\(884\) 23.0930 0.776701
\(885\) 21.7602 0.731461
\(886\) 20.2961 0.681859
\(887\) −15.2555 −0.512229 −0.256114 0.966646i \(-0.582442\pi\)
−0.256114 + 0.966646i \(0.582442\pi\)
\(888\) 4.83562 0.162273
\(889\) −13.7298 −0.460483
\(890\) −50.1239 −1.68016
\(891\) −5.93448 −0.198812
\(892\) −29.6199 −0.991748
\(893\) −9.06483 −0.303343
\(894\) 0.850734 0.0284528
\(895\) −41.1302 −1.37483
\(896\) −9.09845 −0.303958
\(897\) 17.7210 0.591686
\(898\) 6.86676 0.229147
\(899\) 40.8225 1.36151
\(900\) 32.2590 1.07530
\(901\) −7.99640 −0.266399
\(902\) 1.17939 0.0392692
\(903\) −5.45809 −0.181634
\(904\) −4.33940 −0.144326
\(905\) −49.5237 −1.64622
\(906\) −7.22846 −0.240150
\(907\) −29.7506 −0.987853 −0.493927 0.869504i \(-0.664439\pi\)
−0.493927 + 0.869504i \(0.664439\pi\)
\(908\) −1.25899 −0.0417810
\(909\) −27.4647 −0.910947
\(910\) 21.3049 0.706250
\(911\) −36.9951 −1.22570 −0.612851 0.790199i \(-0.709977\pi\)
−0.612851 + 0.790199i \(0.709977\pi\)
\(912\) 0.114110 0.00377858
\(913\) 4.45753 0.147523
\(914\) −4.48496 −0.148349
\(915\) −8.52960 −0.281980
\(916\) 5.77013 0.190651
\(917\) 1.26797 0.0418721
\(918\) 10.7085 0.353433
\(919\) −36.0714 −1.18989 −0.594943 0.803768i \(-0.702825\pi\)
−0.594943 + 0.803768i \(0.702825\pi\)
\(920\) −63.9343 −2.10785
\(921\) −6.23473 −0.205441
\(922\) −20.2886 −0.668168
\(923\) −20.9940 −0.691026
\(924\) 0.942032 0.0309906
\(925\) −28.1758 −0.926415
\(926\) 20.2186 0.664424
\(927\) 3.44323 0.113090
\(928\) 47.6348 1.56369
\(929\) 46.8108 1.53581 0.767906 0.640563i \(-0.221299\pi\)
0.767906 + 0.640563i \(0.221299\pi\)
\(930\) 9.66175 0.316821
\(931\) −19.8795 −0.651524
\(932\) 27.9005 0.913913
\(933\) 12.3253 0.403511
\(934\) 1.21541 0.0397693
\(935\) 14.1160 0.461643
\(936\) 37.5568 1.22758
\(937\) −11.8377 −0.386720 −0.193360 0.981128i \(-0.561938\pi\)
−0.193360 + 0.981128i \(0.561938\pi\)
\(938\) 4.93742 0.161213
\(939\) −19.3355 −0.630991
\(940\) 11.7914 0.384593
\(941\) −5.97152 −0.194666 −0.0973330 0.995252i \(-0.531031\pi\)
−0.0973330 + 0.995252i \(0.531031\pi\)
\(942\) −8.59589 −0.280069
\(943\) −8.02898 −0.261459
\(944\) 0.494184 0.0160843
\(945\) −16.3836 −0.532960
\(946\) 6.27016 0.203861
\(947\) 34.7025 1.12768 0.563840 0.825884i \(-0.309323\pi\)
0.563840 + 0.825884i \(0.309323\pi\)
\(948\) −3.79924 −0.123393
\(949\) −38.6969 −1.25616
\(950\) 31.2538 1.01401
\(951\) 4.34558 0.140915
\(952\) 13.1176 0.425143
\(953\) −26.9293 −0.872325 −0.436162 0.899868i \(-0.643663\pi\)
−0.436162 + 0.899868i \(0.643663\pi\)
\(954\) −4.99608 −0.161754
\(955\) 21.8170 0.705981
\(956\) −22.7845 −0.736903
\(957\) −4.99476 −0.161458
\(958\) 6.86297 0.221733
\(959\) 2.06082 0.0665474
\(960\) 11.0361 0.356189
\(961\) −7.31414 −0.235940
\(962\) −12.6020 −0.406305
\(963\) 14.9121 0.480537
\(964\) 34.6594 1.11630
\(965\) 23.6779 0.762219
\(966\) 3.86712 0.124422
\(967\) −16.8814 −0.542868 −0.271434 0.962457i \(-0.587498\pi\)
−0.271434 + 0.962457i \(0.587498\pi\)
\(968\) −2.81694 −0.0905399
\(969\) −8.06234 −0.259000
\(970\) −9.85395 −0.316391
\(971\) −42.9313 −1.37773 −0.688865 0.724889i \(-0.741891\pi\)
−0.688865 + 0.724889i \(0.741891\pi\)
\(972\) −16.9917 −0.545008
\(973\) 21.5410 0.690571
\(974\) −33.6073 −1.07685
\(975\) 29.3317 0.939366
\(976\) −0.193711 −0.00620054
\(977\) 27.0054 0.863979 0.431990 0.901879i \(-0.357812\pi\)
0.431990 + 0.901879i \(0.357812\pi\)
\(978\) 7.64359 0.244415
\(979\) 15.0346 0.480509
\(980\) 25.8590 0.826035
\(981\) −6.95103 −0.221929
\(982\) 25.0572 0.799607
\(983\) −44.2278 −1.41065 −0.705324 0.708885i \(-0.749198\pi\)
−0.705324 + 0.708885i \(0.749198\pi\)
\(984\) 2.28079 0.0727090
\(985\) −58.4828 −1.86342
\(986\) −26.7195 −0.850922
\(987\) −1.85649 −0.0590928
\(988\) −23.1819 −0.737515
\(989\) −42.6858 −1.35733
\(990\) 8.81954 0.280303
\(991\) 42.8353 1.36071 0.680355 0.732883i \(-0.261826\pi\)
0.680355 + 0.732883i \(0.261826\pi\)
\(992\) 27.6385 0.877522
\(993\) 14.4213 0.457645
\(994\) −4.58136 −0.145312
\(995\) −74.9380 −2.37570
\(996\) 3.31169 0.104935
\(997\) 44.7819 1.41826 0.709128 0.705080i \(-0.249089\pi\)
0.709128 + 0.705080i \(0.249089\pi\)
\(998\) 31.3169 0.991319
\(999\) 9.69105 0.306611
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.f.1.19 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.f.1.19 31 1.1 even 1 trivial