Properties

Label 1441.2.a.d.1.19
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $1$
Dimension $23$
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: \(1\)
Dimension: \(23\)
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)
 
\(f(q)\) \(=\) \(q+1.54502 q^{2} +2.73368 q^{3} +0.387096 q^{4} -3.25406 q^{5} +4.22360 q^{6} -3.29481 q^{7} -2.49197 q^{8} +4.47303 q^{9} +O(q^{10})\) \(q+1.54502 q^{2} +2.73368 q^{3} +0.387096 q^{4} -3.25406 q^{5} +4.22360 q^{6} -3.29481 q^{7} -2.49197 q^{8} +4.47303 q^{9} -5.02759 q^{10} -1.00000 q^{11} +1.05820 q^{12} -5.51417 q^{13} -5.09056 q^{14} -8.89556 q^{15} -4.62435 q^{16} +0.673006 q^{17} +6.91093 q^{18} +3.11070 q^{19} -1.25963 q^{20} -9.00696 q^{21} -1.54502 q^{22} +0.320864 q^{23} -6.81227 q^{24} +5.58889 q^{25} -8.51952 q^{26} +4.02679 q^{27} -1.27541 q^{28} -1.44518 q^{29} -13.7438 q^{30} -1.86574 q^{31} -2.16078 q^{32} -2.73368 q^{33} +1.03981 q^{34} +10.7215 q^{35} +1.73149 q^{36} -5.81490 q^{37} +4.80611 q^{38} -15.0740 q^{39} +8.10903 q^{40} -2.70144 q^{41} -13.9160 q^{42} +7.48431 q^{43} -0.387096 q^{44} -14.5555 q^{45} +0.495742 q^{46} +10.5675 q^{47} -12.6415 q^{48} +3.85576 q^{49} +8.63496 q^{50} +1.83979 q^{51} -2.13451 q^{52} -1.04762 q^{53} +6.22148 q^{54} +3.25406 q^{55} +8.21058 q^{56} +8.50368 q^{57} -2.23283 q^{58} -5.63765 q^{59} -3.44344 q^{60} +4.55464 q^{61} -2.88260 q^{62} -14.7378 q^{63} +5.91025 q^{64} +17.9434 q^{65} -4.22360 q^{66} -15.7868 q^{67} +0.260518 q^{68} +0.877141 q^{69} +16.5650 q^{70} -7.75176 q^{71} -11.1467 q^{72} +2.58126 q^{73} -8.98415 q^{74} +15.2783 q^{75} +1.20414 q^{76} +3.29481 q^{77} -23.2897 q^{78} +16.3556 q^{79} +15.0479 q^{80} -2.41112 q^{81} -4.17378 q^{82} +4.48950 q^{83} -3.48656 q^{84} -2.19000 q^{85} +11.5634 q^{86} -3.95065 q^{87} +2.49197 q^{88} -10.2834 q^{89} -22.4886 q^{90} +18.1681 q^{91} +0.124205 q^{92} -5.10033 q^{93} +16.3270 q^{94} -10.1224 q^{95} -5.90688 q^{96} -18.8099 q^{97} +5.95725 q^{98} -4.47303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.54502 1.09250 0.546248 0.837623i \(-0.316056\pi\)
0.546248 + 0.837623i \(0.316056\pi\)
\(3\) 2.73368 1.57829 0.789146 0.614205i \(-0.210523\pi\)
0.789146 + 0.614205i \(0.210523\pi\)
\(4\) 0.387096 0.193548
\(5\) −3.25406 −1.45526 −0.727629 0.685970i \(-0.759378\pi\)
−0.727629 + 0.685970i \(0.759378\pi\)
\(6\) 4.22360 1.72428
\(7\) −3.29481 −1.24532 −0.622660 0.782492i \(-0.713948\pi\)
−0.622660 + 0.782492i \(0.713948\pi\)
\(8\) −2.49197 −0.881046
\(9\) 4.47303 1.49101
\(10\) −5.02759 −1.58986
\(11\) −1.00000 −0.301511
\(12\) 1.05820 0.305475
\(13\) −5.51417 −1.52936 −0.764678 0.644412i \(-0.777102\pi\)
−0.764678 + 0.644412i \(0.777102\pi\)
\(14\) −5.09056 −1.36051
\(15\) −8.89556 −2.29682
\(16\) −4.62435 −1.15609
\(17\) 0.673006 0.163228 0.0816140 0.996664i \(-0.473993\pi\)
0.0816140 + 0.996664i \(0.473993\pi\)
\(18\) 6.91093 1.62892
\(19\) 3.11070 0.713644 0.356822 0.934172i \(-0.383860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(20\) −1.25963 −0.281662
\(21\) −9.00696 −1.96548
\(22\) −1.54502 −0.329400
\(23\) 0.320864 0.0669048 0.0334524 0.999440i \(-0.489350\pi\)
0.0334524 + 0.999440i \(0.489350\pi\)
\(24\) −6.81227 −1.39055
\(25\) 5.58889 1.11778
\(26\) −8.51952 −1.67082
\(27\) 4.02679 0.774955
\(28\) −1.27541 −0.241029
\(29\) −1.44518 −0.268362 −0.134181 0.990957i \(-0.542840\pi\)
−0.134181 + 0.990957i \(0.542840\pi\)
\(30\) −13.7438 −2.50927
\(31\) −1.86574 −0.335096 −0.167548 0.985864i \(-0.553585\pi\)
−0.167548 + 0.985864i \(0.553585\pi\)
\(32\) −2.16078 −0.381975
\(33\) −2.73368 −0.475873
\(34\) 1.03981 0.178326
\(35\) 10.7215 1.81226
\(36\) 1.73149 0.288582
\(37\) −5.81490 −0.955963 −0.477982 0.878370i \(-0.658631\pi\)
−0.477982 + 0.878370i \(0.658631\pi\)
\(38\) 4.80611 0.779654
\(39\) −15.0740 −2.41377
\(40\) 8.10903 1.28215
\(41\) −2.70144 −0.421893 −0.210947 0.977498i \(-0.567655\pi\)
−0.210947 + 0.977498i \(0.567655\pi\)
\(42\) −13.9160 −2.14728
\(43\) 7.48431 1.14135 0.570673 0.821177i \(-0.306682\pi\)
0.570673 + 0.821177i \(0.306682\pi\)
\(44\) −0.387096 −0.0583569
\(45\) −14.5555 −2.16980
\(46\) 0.495742 0.0730932
\(47\) 10.5675 1.54142 0.770712 0.637184i \(-0.219901\pi\)
0.770712 + 0.637184i \(0.219901\pi\)
\(48\) −12.6415 −1.82464
\(49\) 3.85576 0.550824
\(50\) 8.63496 1.22117
\(51\) 1.83979 0.257622
\(52\) −2.13451 −0.296004
\(53\) −1.04762 −0.143902 −0.0719510 0.997408i \(-0.522923\pi\)
−0.0719510 + 0.997408i \(0.522923\pi\)
\(54\) 6.22148 0.846636
\(55\) 3.25406 0.438777
\(56\) 8.21058 1.09718
\(57\) 8.50368 1.12634
\(58\) −2.23283 −0.293185
\(59\) −5.63765 −0.733959 −0.366980 0.930229i \(-0.619608\pi\)
−0.366980 + 0.930229i \(0.619608\pi\)
\(60\) −3.44344 −0.444546
\(61\) 4.55464 0.583161 0.291581 0.956546i \(-0.405819\pi\)
0.291581 + 0.956546i \(0.405819\pi\)
\(62\) −2.88260 −0.366091
\(63\) −14.7378 −1.85678
\(64\) 5.91025 0.738781
\(65\) 17.9434 2.22561
\(66\) −4.22360 −0.519890
\(67\) −15.7868 −1.92866 −0.964332 0.264696i \(-0.914728\pi\)
−0.964332 + 0.264696i \(0.914728\pi\)
\(68\) 0.260518 0.0315924
\(69\) 0.877141 0.105595
\(70\) 16.5650 1.97989
\(71\) −7.75176 −0.919965 −0.459982 0.887928i \(-0.652144\pi\)
−0.459982 + 0.887928i \(0.652144\pi\)
\(72\) −11.1467 −1.31365
\(73\) 2.58126 0.302114 0.151057 0.988525i \(-0.451732\pi\)
0.151057 + 0.988525i \(0.451732\pi\)
\(74\) −8.98415 −1.04439
\(75\) 15.2783 1.76418
\(76\) 1.20414 0.138124
\(77\) 3.29481 0.375478
\(78\) −23.2897 −2.63704
\(79\) 16.3556 1.84015 0.920073 0.391748i \(-0.128129\pi\)
0.920073 + 0.391748i \(0.128129\pi\)
\(80\) 15.0479 1.68241
\(81\) −2.41112 −0.267902
\(82\) −4.17378 −0.460917
\(83\) 4.48950 0.492787 0.246393 0.969170i \(-0.420754\pi\)
0.246393 + 0.969170i \(0.420754\pi\)
\(84\) −3.48656 −0.380415
\(85\) −2.19000 −0.237539
\(86\) 11.5634 1.24692
\(87\) −3.95065 −0.423554
\(88\) 2.49197 0.265645
\(89\) −10.2834 −1.09003 −0.545017 0.838425i \(-0.683477\pi\)
−0.545017 + 0.838425i \(0.683477\pi\)
\(90\) −22.4886 −2.37050
\(91\) 18.1681 1.90454
\(92\) 0.124205 0.0129493
\(93\) −5.10033 −0.528880
\(94\) 16.3270 1.68400
\(95\) −10.1224 −1.03854
\(96\) −5.90688 −0.602868
\(97\) −18.8099 −1.90985 −0.954926 0.296844i \(-0.904066\pi\)
−0.954926 + 0.296844i \(0.904066\pi\)
\(98\) 5.95725 0.601773
\(99\) −4.47303 −0.449556
\(100\) 2.16344 0.216344
\(101\) −7.92610 −0.788676 −0.394338 0.918965i \(-0.629026\pi\)
−0.394338 + 0.918965i \(0.629026\pi\)
\(102\) 2.84251 0.281451
\(103\) −10.0377 −0.989049 −0.494524 0.869164i \(-0.664658\pi\)
−0.494524 + 0.869164i \(0.664658\pi\)
\(104\) 13.7412 1.34743
\(105\) 29.3092 2.86028
\(106\) −1.61860 −0.157212
\(107\) 9.78669 0.946115 0.473057 0.881032i \(-0.343150\pi\)
0.473057 + 0.881032i \(0.343150\pi\)
\(108\) 1.55875 0.149991
\(109\) −5.84952 −0.560283 −0.280141 0.959959i \(-0.590381\pi\)
−0.280141 + 0.959959i \(0.590381\pi\)
\(110\) 5.02759 0.479362
\(111\) −15.8961 −1.50879
\(112\) 15.2363 1.43970
\(113\) −4.16421 −0.391735 −0.195868 0.980630i \(-0.562752\pi\)
−0.195868 + 0.980630i \(0.562752\pi\)
\(114\) 13.1384 1.23052
\(115\) −1.04411 −0.0973637
\(116\) −0.559421 −0.0519410
\(117\) −24.6650 −2.28028
\(118\) −8.71029 −0.801848
\(119\) −2.21743 −0.203271
\(120\) 22.1675 2.02361
\(121\) 1.00000 0.0909091
\(122\) 7.03702 0.637102
\(123\) −7.38487 −0.665871
\(124\) −0.722219 −0.0648571
\(125\) −1.91628 −0.171397
\(126\) −22.7702 −2.02853
\(127\) −16.6543 −1.47783 −0.738917 0.673796i \(-0.764663\pi\)
−0.738917 + 0.673796i \(0.764663\pi\)
\(128\) 13.4530 1.18909
\(129\) 20.4597 1.80138
\(130\) 27.7230 2.43147
\(131\) −1.00000 −0.0873704
\(132\) −1.05820 −0.0921043
\(133\) −10.2492 −0.888716
\(134\) −24.3910 −2.10706
\(135\) −13.1034 −1.12776
\(136\) −1.67711 −0.143811
\(137\) 12.0488 1.02940 0.514699 0.857371i \(-0.327904\pi\)
0.514699 + 0.857371i \(0.327904\pi\)
\(138\) 1.35520 0.115362
\(139\) 12.0168 1.01925 0.509626 0.860396i \(-0.329784\pi\)
0.509626 + 0.860396i \(0.329784\pi\)
\(140\) 4.15025 0.350760
\(141\) 28.8881 2.43282
\(142\) −11.9766 −1.00506
\(143\) 5.51417 0.461118
\(144\) −20.6848 −1.72374
\(145\) 4.70268 0.390537
\(146\) 3.98811 0.330058
\(147\) 10.5404 0.869361
\(148\) −2.25092 −0.185025
\(149\) 5.85354 0.479541 0.239770 0.970830i \(-0.422928\pi\)
0.239770 + 0.970830i \(0.422928\pi\)
\(150\) 23.6053 1.92736
\(151\) 2.52100 0.205156 0.102578 0.994725i \(-0.467291\pi\)
0.102578 + 0.994725i \(0.467291\pi\)
\(152\) −7.75179 −0.628753
\(153\) 3.01038 0.243374
\(154\) 5.09056 0.410209
\(155\) 6.07121 0.487651
\(156\) −5.83508 −0.467181
\(157\) 20.3807 1.62656 0.813279 0.581874i \(-0.197680\pi\)
0.813279 + 0.581874i \(0.197680\pi\)
\(158\) 25.2697 2.01035
\(159\) −2.86387 −0.227120
\(160\) 7.03129 0.555872
\(161\) −1.05719 −0.0833179
\(162\) −3.72523 −0.292682
\(163\) 12.1542 0.951988 0.475994 0.879449i \(-0.342088\pi\)
0.475994 + 0.879449i \(0.342088\pi\)
\(164\) −1.04571 −0.0816566
\(165\) 8.89556 0.692519
\(166\) 6.93638 0.538368
\(167\) 5.33778 0.413050 0.206525 0.978441i \(-0.433785\pi\)
0.206525 + 0.978441i \(0.433785\pi\)
\(168\) 22.4451 1.73168
\(169\) 17.4061 1.33893
\(170\) −3.38360 −0.259510
\(171\) 13.9143 1.06405
\(172\) 2.89715 0.220905
\(173\) −4.53547 −0.344825 −0.172413 0.985025i \(-0.555156\pi\)
−0.172413 + 0.985025i \(0.555156\pi\)
\(174\) −6.10385 −0.462731
\(175\) −18.4143 −1.39199
\(176\) 4.62435 0.348573
\(177\) −15.4115 −1.15840
\(178\) −15.8880 −1.19086
\(179\) −22.3191 −1.66820 −0.834102 0.551610i \(-0.814014\pi\)
−0.834102 + 0.551610i \(0.814014\pi\)
\(180\) −5.63437 −0.419961
\(181\) −1.86197 −0.138399 −0.0691995 0.997603i \(-0.522045\pi\)
−0.0691995 + 0.997603i \(0.522045\pi\)
\(182\) 28.0702 2.08070
\(183\) 12.4509 0.920400
\(184\) −0.799585 −0.0589462
\(185\) 18.9220 1.39117
\(186\) −7.88013 −0.577799
\(187\) −0.673006 −0.0492151
\(188\) 4.09062 0.298339
\(189\) −13.2675 −0.965068
\(190\) −15.6393 −1.13460
\(191\) −16.4987 −1.19380 −0.596900 0.802315i \(-0.703601\pi\)
−0.596900 + 0.802315i \(0.703601\pi\)
\(192\) 16.1567 1.16601
\(193\) −11.3043 −0.813702 −0.406851 0.913495i \(-0.633373\pi\)
−0.406851 + 0.913495i \(0.633373\pi\)
\(194\) −29.0617 −2.08651
\(195\) 49.0517 3.51266
\(196\) 1.49255 0.106611
\(197\) −15.1553 −1.07977 −0.539885 0.841739i \(-0.681532\pi\)
−0.539885 + 0.841739i \(0.681532\pi\)
\(198\) −6.91093 −0.491138
\(199\) −14.9645 −1.06081 −0.530403 0.847745i \(-0.677959\pi\)
−0.530403 + 0.847745i \(0.677959\pi\)
\(200\) −13.9274 −0.984814
\(201\) −43.1561 −3.04400
\(202\) −12.2460 −0.861626
\(203\) 4.76158 0.334197
\(204\) 0.712174 0.0498621
\(205\) 8.79063 0.613964
\(206\) −15.5085 −1.08053
\(207\) 1.43523 0.0997556
\(208\) 25.4995 1.76807
\(209\) −3.11070 −0.215172
\(210\) 45.2834 3.12485
\(211\) −3.96743 −0.273129 −0.136565 0.990631i \(-0.543606\pi\)
−0.136565 + 0.990631i \(0.543606\pi\)
\(212\) −0.405531 −0.0278520
\(213\) −21.1909 −1.45197
\(214\) 15.1207 1.03363
\(215\) −24.3544 −1.66095
\(216\) −10.0346 −0.682771
\(217\) 6.14724 0.417302
\(218\) −9.03765 −0.612107
\(219\) 7.05635 0.476824
\(220\) 1.25963 0.0849244
\(221\) −3.71107 −0.249634
\(222\) −24.5598 −1.64835
\(223\) 10.1257 0.678070 0.339035 0.940774i \(-0.389900\pi\)
0.339035 + 0.940774i \(0.389900\pi\)
\(224\) 7.11935 0.475681
\(225\) 24.9992 1.66662
\(226\) −6.43379 −0.427969
\(227\) 0.0578550 0.00383997 0.00191999 0.999998i \(-0.499389\pi\)
0.00191999 + 0.999998i \(0.499389\pi\)
\(228\) 3.29174 0.218001
\(229\) −11.2902 −0.746074 −0.373037 0.927816i \(-0.621684\pi\)
−0.373037 + 0.927816i \(0.621684\pi\)
\(230\) −1.61317 −0.106370
\(231\) 9.00696 0.592615
\(232\) 3.60134 0.236439
\(233\) −13.7996 −0.904044 −0.452022 0.892007i \(-0.649297\pi\)
−0.452022 + 0.892007i \(0.649297\pi\)
\(234\) −38.1080 −2.49120
\(235\) −34.3871 −2.24317
\(236\) −2.18231 −0.142056
\(237\) 44.7110 2.90429
\(238\) −3.42598 −0.222073
\(239\) −8.61019 −0.556947 −0.278474 0.960444i \(-0.589828\pi\)
−0.278474 + 0.960444i \(0.589828\pi\)
\(240\) 41.1362 2.65533
\(241\) 8.68434 0.559408 0.279704 0.960086i \(-0.409764\pi\)
0.279704 + 0.960086i \(0.409764\pi\)
\(242\) 1.54502 0.0993178
\(243\) −18.6716 −1.19778
\(244\) 1.76308 0.112870
\(245\) −12.5469 −0.801591
\(246\) −11.4098 −0.727462
\(247\) −17.1530 −1.09142
\(248\) 4.64936 0.295235
\(249\) 12.2729 0.777762
\(250\) −2.96070 −0.187251
\(251\) 7.94755 0.501645 0.250822 0.968033i \(-0.419299\pi\)
0.250822 + 0.968033i \(0.419299\pi\)
\(252\) −5.70493 −0.359377
\(253\) −0.320864 −0.0201725
\(254\) −25.7313 −1.61453
\(255\) −5.98677 −0.374906
\(256\) 8.96473 0.560296
\(257\) 15.2272 0.949849 0.474925 0.880027i \(-0.342475\pi\)
0.474925 + 0.880027i \(0.342475\pi\)
\(258\) 31.6108 1.96800
\(259\) 19.1590 1.19048
\(260\) 6.94583 0.430762
\(261\) −6.46431 −0.400130
\(262\) −1.54502 −0.0954518
\(263\) −17.9040 −1.10401 −0.552003 0.833842i \(-0.686136\pi\)
−0.552003 + 0.833842i \(0.686136\pi\)
\(264\) 6.81227 0.419266
\(265\) 3.40903 0.209415
\(266\) −15.8352 −0.970919
\(267\) −28.1115 −1.72039
\(268\) −6.11100 −0.373289
\(269\) −25.9932 −1.58484 −0.792418 0.609979i \(-0.791178\pi\)
−0.792418 + 0.609979i \(0.791178\pi\)
\(270\) −20.2450 −1.23207
\(271\) 19.0435 1.15681 0.578404 0.815751i \(-0.303676\pi\)
0.578404 + 0.815751i \(0.303676\pi\)
\(272\) −3.11222 −0.188706
\(273\) 49.6660 3.00592
\(274\) 18.6157 1.12461
\(275\) −5.58889 −0.337023
\(276\) 0.339537 0.0204378
\(277\) 21.0210 1.26303 0.631516 0.775363i \(-0.282433\pi\)
0.631516 + 0.775363i \(0.282433\pi\)
\(278\) 18.5662 1.11353
\(279\) −8.34548 −0.499631
\(280\) −26.7177 −1.59669
\(281\) 0.480384 0.0286573 0.0143287 0.999897i \(-0.495439\pi\)
0.0143287 + 0.999897i \(0.495439\pi\)
\(282\) 44.6328 2.65784
\(283\) 18.7058 1.11194 0.555972 0.831201i \(-0.312346\pi\)
0.555972 + 0.831201i \(0.312346\pi\)
\(284\) −3.00067 −0.178057
\(285\) −27.6715 −1.63912
\(286\) 8.51952 0.503770
\(287\) 8.90072 0.525393
\(288\) −9.66521 −0.569528
\(289\) −16.5471 −0.973357
\(290\) 7.26575 0.426660
\(291\) −51.4202 −3.01431
\(292\) 0.999196 0.0584735
\(293\) −28.9779 −1.69291 −0.846453 0.532463i \(-0.821266\pi\)
−0.846453 + 0.532463i \(0.821266\pi\)
\(294\) 16.2852 0.949773
\(295\) 18.3452 1.06810
\(296\) 14.4906 0.842247
\(297\) −4.02679 −0.233658
\(298\) 9.04385 0.523896
\(299\) −1.76930 −0.102321
\(300\) 5.91415 0.341454
\(301\) −24.6594 −1.42134
\(302\) 3.89500 0.224132
\(303\) −21.6674 −1.24476
\(304\) −14.3850 −0.825035
\(305\) −14.8210 −0.848651
\(306\) 4.65110 0.265886
\(307\) 23.7743 1.35687 0.678435 0.734661i \(-0.262659\pi\)
0.678435 + 0.734661i \(0.262659\pi\)
\(308\) 1.27541 0.0726730
\(309\) −27.4400 −1.56101
\(310\) 9.38016 0.532757
\(311\) 5.85577 0.332050 0.166025 0.986122i \(-0.446907\pi\)
0.166025 + 0.986122i \(0.446907\pi\)
\(312\) 37.5640 2.12664
\(313\) −25.9307 −1.46569 −0.732845 0.680395i \(-0.761808\pi\)
−0.732845 + 0.680395i \(0.761808\pi\)
\(314\) 31.4887 1.77701
\(315\) 47.9575 2.70210
\(316\) 6.33117 0.356156
\(317\) −4.87657 −0.273896 −0.136948 0.990578i \(-0.543729\pi\)
−0.136948 + 0.990578i \(0.543729\pi\)
\(318\) −4.42474 −0.248127
\(319\) 1.44518 0.0809143
\(320\) −19.2323 −1.07512
\(321\) 26.7537 1.49325
\(322\) −1.63338 −0.0910245
\(323\) 2.09352 0.116487
\(324\) −0.933334 −0.0518519
\(325\) −30.8181 −1.70948
\(326\) 18.7785 1.04004
\(327\) −15.9907 −0.884290
\(328\) 6.73191 0.371707
\(329\) −34.8178 −1.91957
\(330\) 13.7438 0.756574
\(331\) 11.1378 0.612188 0.306094 0.952001i \(-0.400978\pi\)
0.306094 + 0.952001i \(0.400978\pi\)
\(332\) 1.73787 0.0953779
\(333\) −26.0102 −1.42535
\(334\) 8.24699 0.451255
\(335\) 51.3711 2.80670
\(336\) 41.6513 2.27227
\(337\) 18.2130 0.992128 0.496064 0.868286i \(-0.334778\pi\)
0.496064 + 0.868286i \(0.334778\pi\)
\(338\) 26.8928 1.46278
\(339\) −11.3836 −0.618273
\(340\) −0.847741 −0.0459752
\(341\) 1.86574 0.101035
\(342\) 21.4978 1.16247
\(343\) 10.3597 0.559369
\(344\) −18.6507 −1.00558
\(345\) −2.85427 −0.153668
\(346\) −7.00740 −0.376720
\(347\) 24.3068 1.30486 0.652429 0.757850i \(-0.273750\pi\)
0.652429 + 0.757850i \(0.273750\pi\)
\(348\) −1.52928 −0.0819781
\(349\) −34.2737 −1.83463 −0.917314 0.398165i \(-0.869647\pi\)
−0.917314 + 0.398165i \(0.869647\pi\)
\(350\) −28.4505 −1.52075
\(351\) −22.2044 −1.18518
\(352\) 2.16078 0.115170
\(353\) −13.3932 −0.712847 −0.356424 0.934324i \(-0.616004\pi\)
−0.356424 + 0.934324i \(0.616004\pi\)
\(354\) −23.8112 −1.26555
\(355\) 25.2247 1.33879
\(356\) −3.98065 −0.210974
\(357\) −6.06174 −0.320822
\(358\) −34.4835 −1.82251
\(359\) 5.57906 0.294452 0.147226 0.989103i \(-0.452966\pi\)
0.147226 + 0.989103i \(0.452966\pi\)
\(360\) 36.2719 1.91170
\(361\) −9.32353 −0.490712
\(362\) −2.87679 −0.151200
\(363\) 2.73368 0.143481
\(364\) 7.03281 0.368620
\(365\) −8.39957 −0.439654
\(366\) 19.2370 1.00553
\(367\) 26.1407 1.36453 0.682265 0.731105i \(-0.260995\pi\)
0.682265 + 0.731105i \(0.260995\pi\)
\(368\) −1.48379 −0.0773477
\(369\) −12.0836 −0.629047
\(370\) 29.2349 1.51985
\(371\) 3.45172 0.179204
\(372\) −1.97432 −0.102364
\(373\) −24.7201 −1.27996 −0.639980 0.768392i \(-0.721057\pi\)
−0.639980 + 0.768392i \(0.721057\pi\)
\(374\) −1.03981 −0.0537673
\(375\) −5.23850 −0.270515
\(376\) −26.3339 −1.35806
\(377\) 7.96895 0.410422
\(378\) −20.4986 −1.05433
\(379\) 14.5359 0.746661 0.373330 0.927699i \(-0.378216\pi\)
0.373330 + 0.927699i \(0.378216\pi\)
\(380\) −3.91834 −0.201007
\(381\) −45.5277 −2.33246
\(382\) −25.4908 −1.30422
\(383\) −24.6096 −1.25749 −0.628745 0.777612i \(-0.716431\pi\)
−0.628745 + 0.777612i \(0.716431\pi\)
\(384\) 36.7763 1.87673
\(385\) −10.7215 −0.546418
\(386\) −17.4654 −0.888966
\(387\) 33.4775 1.70176
\(388\) −7.28122 −0.369648
\(389\) 14.4517 0.732733 0.366366 0.930471i \(-0.380602\pi\)
0.366366 + 0.930471i \(0.380602\pi\)
\(390\) 75.7860 3.83757
\(391\) 0.215944 0.0109207
\(392\) −9.60847 −0.485301
\(393\) −2.73368 −0.137896
\(394\) −23.4153 −1.17965
\(395\) −53.2220 −2.67789
\(396\) −1.73149 −0.0870106
\(397\) 9.96478 0.500118 0.250059 0.968231i \(-0.419550\pi\)
0.250059 + 0.968231i \(0.419550\pi\)
\(398\) −23.1205 −1.15893
\(399\) −28.0180 −1.40265
\(400\) −25.8450 −1.29225
\(401\) −12.1122 −0.604856 −0.302428 0.953172i \(-0.597797\pi\)
−0.302428 + 0.953172i \(0.597797\pi\)
\(402\) −66.6772 −3.32555
\(403\) 10.2880 0.512481
\(404\) −3.06816 −0.152647
\(405\) 7.84592 0.389867
\(406\) 7.35674 0.365109
\(407\) 5.81490 0.288234
\(408\) −4.58470 −0.226976
\(409\) −10.6917 −0.528668 −0.264334 0.964431i \(-0.585152\pi\)
−0.264334 + 0.964431i \(0.585152\pi\)
\(410\) 13.5817 0.670753
\(411\) 32.9376 1.62469
\(412\) −3.88557 −0.191428
\(413\) 18.5750 0.914015
\(414\) 2.21747 0.108983
\(415\) −14.6091 −0.717132
\(416\) 11.9149 0.584176
\(417\) 32.8501 1.60868
\(418\) −4.80611 −0.235074
\(419\) 31.3600 1.53203 0.766017 0.642820i \(-0.222236\pi\)
0.766017 + 0.642820i \(0.222236\pi\)
\(420\) 11.3455 0.553602
\(421\) −22.1870 −1.08133 −0.540665 0.841238i \(-0.681827\pi\)
−0.540665 + 0.841238i \(0.681827\pi\)
\(422\) −6.12977 −0.298393
\(423\) 47.2686 2.29828
\(424\) 2.61065 0.126784
\(425\) 3.76136 0.182453
\(426\) −32.7404 −1.58628
\(427\) −15.0067 −0.726223
\(428\) 3.78839 0.183119
\(429\) 15.0740 0.727780
\(430\) −37.6281 −1.81459
\(431\) −29.2280 −1.40786 −0.703931 0.710269i \(-0.748573\pi\)
−0.703931 + 0.710269i \(0.748573\pi\)
\(432\) −18.6213 −0.895916
\(433\) 13.1577 0.632317 0.316158 0.948706i \(-0.397607\pi\)
0.316158 + 0.948706i \(0.397607\pi\)
\(434\) 9.49763 0.455901
\(435\) 12.8556 0.616381
\(436\) −2.26433 −0.108442
\(437\) 0.998112 0.0477462
\(438\) 10.9022 0.520928
\(439\) −32.0762 −1.53091 −0.765456 0.643488i \(-0.777487\pi\)
−0.765456 + 0.643488i \(0.777487\pi\)
\(440\) −8.10903 −0.386583
\(441\) 17.2469 0.821283
\(442\) −5.73369 −0.272724
\(443\) 31.8373 1.51264 0.756318 0.654204i \(-0.226996\pi\)
0.756318 + 0.654204i \(0.226996\pi\)
\(444\) −6.15331 −0.292023
\(445\) 33.4626 1.58628
\(446\) 15.6445 0.740788
\(447\) 16.0017 0.756856
\(448\) −19.4731 −0.920019
\(449\) −17.2091 −0.812146 −0.406073 0.913841i \(-0.633102\pi\)
−0.406073 + 0.913841i \(0.633102\pi\)
\(450\) 38.6244 1.82077
\(451\) 2.70144 0.127206
\(452\) −1.61195 −0.0758196
\(453\) 6.89162 0.323796
\(454\) 0.0893873 0.00419516
\(455\) −59.1202 −2.77160
\(456\) −21.1909 −0.992357
\(457\) 4.79162 0.224143 0.112071 0.993700i \(-0.464251\pi\)
0.112071 + 0.993700i \(0.464251\pi\)
\(458\) −17.4435 −0.815083
\(459\) 2.71005 0.126494
\(460\) −0.404171 −0.0188445
\(461\) 33.8620 1.57711 0.788554 0.614965i \(-0.210830\pi\)
0.788554 + 0.614965i \(0.210830\pi\)
\(462\) 13.9160 0.647429
\(463\) 5.82989 0.270938 0.135469 0.990782i \(-0.456746\pi\)
0.135469 + 0.990782i \(0.456746\pi\)
\(464\) 6.68299 0.310250
\(465\) 16.5968 0.769657
\(466\) −21.3208 −0.987665
\(467\) 36.3416 1.68169 0.840844 0.541277i \(-0.182059\pi\)
0.840844 + 0.541277i \(0.182059\pi\)
\(468\) −9.54773 −0.441344
\(469\) 52.0145 2.40180
\(470\) −53.1289 −2.45066
\(471\) 55.7144 2.56719
\(472\) 14.0489 0.646652
\(473\) −7.48431 −0.344129
\(474\) 69.0795 3.17292
\(475\) 17.3854 0.797696
\(476\) −0.858357 −0.0393427
\(477\) −4.68604 −0.214559
\(478\) −13.3029 −0.608463
\(479\) −15.9821 −0.730243 −0.365121 0.930960i \(-0.618972\pi\)
−0.365121 + 0.930960i \(0.618972\pi\)
\(480\) 19.2213 0.877329
\(481\) 32.0643 1.46201
\(482\) 13.4175 0.611151
\(483\) −2.89001 −0.131500
\(484\) 0.387096 0.0175953
\(485\) 61.2084 2.77933
\(486\) −28.8480 −1.30857
\(487\) 30.7826 1.39489 0.697447 0.716636i \(-0.254319\pi\)
0.697447 + 0.716636i \(0.254319\pi\)
\(488\) −11.3500 −0.513792
\(489\) 33.2256 1.50252
\(490\) −19.3852 −0.875735
\(491\) −30.3735 −1.37074 −0.685369 0.728196i \(-0.740359\pi\)
−0.685369 + 0.728196i \(0.740359\pi\)
\(492\) −2.85865 −0.128878
\(493\) −0.972612 −0.0438042
\(494\) −26.5017 −1.19237
\(495\) 14.5555 0.654220
\(496\) 8.62781 0.387400
\(497\) 25.5406 1.14565
\(498\) 18.9619 0.849702
\(499\) 0.397630 0.0178004 0.00890019 0.999960i \(-0.497167\pi\)
0.00890019 + 0.999960i \(0.497167\pi\)
\(500\) −0.741784 −0.0331736
\(501\) 14.5918 0.651913
\(502\) 12.2791 0.548045
\(503\) −7.83869 −0.349510 −0.174755 0.984612i \(-0.555913\pi\)
−0.174755 + 0.984612i \(0.555913\pi\)
\(504\) 36.7261 1.63591
\(505\) 25.7920 1.14773
\(506\) −0.495742 −0.0220384
\(507\) 47.5828 2.11323
\(508\) −6.44683 −0.286032
\(509\) −21.1021 −0.935334 −0.467667 0.883905i \(-0.654905\pi\)
−0.467667 + 0.883905i \(0.654905\pi\)
\(510\) −9.24970 −0.409584
\(511\) −8.50476 −0.376229
\(512\) −13.0553 −0.576969
\(513\) 12.5261 0.553042
\(514\) 23.5264 1.03771
\(515\) 32.6634 1.43932
\(516\) 7.91988 0.348653
\(517\) −10.5675 −0.464757
\(518\) 29.6010 1.30060
\(519\) −12.3985 −0.544235
\(520\) −44.7146 −1.96086
\(521\) 44.7251 1.95944 0.979722 0.200364i \(-0.0642125\pi\)
0.979722 + 0.200364i \(0.0642125\pi\)
\(522\) −9.98750 −0.437141
\(523\) 11.3957 0.498299 0.249150 0.968465i \(-0.419849\pi\)
0.249150 + 0.968465i \(0.419849\pi\)
\(524\) −0.387096 −0.0169104
\(525\) −50.3389 −2.19697
\(526\) −27.6621 −1.20612
\(527\) −1.25565 −0.0546971
\(528\) 12.6415 0.550151
\(529\) −22.8970 −0.995524
\(530\) 5.26702 0.228785
\(531\) −25.2173 −1.09434
\(532\) −3.96741 −0.172009
\(533\) 14.8962 0.645225
\(534\) −43.4328 −1.87952
\(535\) −31.8464 −1.37684
\(536\) 39.3403 1.69924
\(537\) −61.0133 −2.63292
\(538\) −40.1601 −1.73143
\(539\) −3.85576 −0.166080
\(540\) −5.07227 −0.218276
\(541\) 37.4149 1.60859 0.804296 0.594229i \(-0.202543\pi\)
0.804296 + 0.594229i \(0.202543\pi\)
\(542\) 29.4226 1.26381
\(543\) −5.09003 −0.218434
\(544\) −1.45422 −0.0623490
\(545\) 19.0347 0.815356
\(546\) 76.7350 3.28396
\(547\) 12.5850 0.538095 0.269048 0.963127i \(-0.413291\pi\)
0.269048 + 0.963127i \(0.413291\pi\)
\(548\) 4.66404 0.199238
\(549\) 20.3730 0.869499
\(550\) −8.63496 −0.368196
\(551\) −4.49551 −0.191515
\(552\) −2.18581 −0.0930343
\(553\) −53.8885 −2.29157
\(554\) 32.4780 1.37986
\(555\) 51.7268 2.19568
\(556\) 4.65165 0.197274
\(557\) 6.13432 0.259920 0.129960 0.991519i \(-0.458515\pi\)
0.129960 + 0.991519i \(0.458515\pi\)
\(558\) −12.8940 −0.545845
\(559\) −41.2698 −1.74553
\(560\) −49.5799 −2.09513
\(561\) −1.83979 −0.0776758
\(562\) 0.742205 0.0313080
\(563\) −15.4142 −0.649630 −0.324815 0.945778i \(-0.605302\pi\)
−0.324815 + 0.945778i \(0.605302\pi\)
\(564\) 11.1825 0.470867
\(565\) 13.5506 0.570076
\(566\) 28.9009 1.21479
\(567\) 7.94417 0.333624
\(568\) 19.3172 0.810531
\(569\) −13.6152 −0.570780 −0.285390 0.958411i \(-0.592123\pi\)
−0.285390 + 0.958411i \(0.592123\pi\)
\(570\) −42.7530 −1.79073
\(571\) −36.9828 −1.54768 −0.773842 0.633379i \(-0.781667\pi\)
−0.773842 + 0.633379i \(0.781667\pi\)
\(572\) 2.13451 0.0892485
\(573\) −45.1021 −1.88417
\(574\) 13.7518 0.573989
\(575\) 1.79327 0.0747847
\(576\) 26.4367 1.10153
\(577\) −33.1889 −1.38167 −0.690836 0.723011i \(-0.742758\pi\)
−0.690836 + 0.723011i \(0.742758\pi\)
\(578\) −25.5656 −1.06339
\(579\) −30.9024 −1.28426
\(580\) 1.82039 0.0755875
\(581\) −14.7921 −0.613678
\(582\) −79.4454 −3.29312
\(583\) 1.04762 0.0433881
\(584\) −6.43244 −0.266176
\(585\) 80.2614 3.31840
\(586\) −44.7715 −1.84949
\(587\) −36.7254 −1.51582 −0.757910 0.652359i \(-0.773779\pi\)
−0.757910 + 0.652359i \(0.773779\pi\)
\(588\) 4.08016 0.168263
\(589\) −5.80375 −0.239139
\(590\) 28.3438 1.16690
\(591\) −41.4298 −1.70419
\(592\) 26.8901 1.10518
\(593\) −43.7224 −1.79546 −0.897731 0.440544i \(-0.854786\pi\)
−0.897731 + 0.440544i \(0.854786\pi\)
\(594\) −6.22148 −0.255270
\(595\) 7.21564 0.295812
\(596\) 2.26588 0.0928141
\(597\) −40.9083 −1.67426
\(598\) −2.73361 −0.111786
\(599\) 26.6179 1.08758 0.543789 0.839222i \(-0.316989\pi\)
0.543789 + 0.839222i \(0.316989\pi\)
\(600\) −38.0730 −1.55432
\(601\) 19.3001 0.787267 0.393634 0.919267i \(-0.371218\pi\)
0.393634 + 0.919267i \(0.371218\pi\)
\(602\) −38.0993 −1.55281
\(603\) −70.6147 −2.87565
\(604\) 0.975869 0.0397075
\(605\) −3.25406 −0.132296
\(606\) −33.4767 −1.35990
\(607\) 42.2893 1.71647 0.858235 0.513256i \(-0.171561\pi\)
0.858235 + 0.513256i \(0.171561\pi\)
\(608\) −6.72153 −0.272594
\(609\) 13.0166 0.527461
\(610\) −22.8989 −0.927148
\(611\) −58.2709 −2.35739
\(612\) 1.16530 0.0471046
\(613\) 42.5174 1.71726 0.858630 0.512596i \(-0.171316\pi\)
0.858630 + 0.512596i \(0.171316\pi\)
\(614\) 36.7318 1.48237
\(615\) 24.0308 0.969015
\(616\) −8.21058 −0.330814
\(617\) 41.2254 1.65967 0.829835 0.558008i \(-0.188434\pi\)
0.829835 + 0.558008i \(0.188434\pi\)
\(618\) −42.3955 −1.70540
\(619\) 28.9911 1.16525 0.582625 0.812741i \(-0.302026\pi\)
0.582625 + 0.812741i \(0.302026\pi\)
\(620\) 2.35014 0.0943839
\(621\) 1.29205 0.0518482
\(622\) 9.04730 0.362764
\(623\) 33.8817 1.35744
\(624\) 69.7074 2.79053
\(625\) −21.7088 −0.868350
\(626\) −40.0635 −1.60126
\(627\) −8.50368 −0.339604
\(628\) 7.88929 0.314817
\(629\) −3.91346 −0.156040
\(630\) 74.0955 2.95203
\(631\) −15.7533 −0.627131 −0.313565 0.949567i \(-0.601523\pi\)
−0.313565 + 0.949567i \(0.601523\pi\)
\(632\) −40.7577 −1.62125
\(633\) −10.8457 −0.431078
\(634\) −7.53442 −0.299230
\(635\) 54.1942 2.15063
\(636\) −1.10859 −0.0439585
\(637\) −21.2614 −0.842406
\(638\) 2.23283 0.0883985
\(639\) −34.6738 −1.37168
\(640\) −43.7769 −1.73043
\(641\) −2.16918 −0.0856773 −0.0428387 0.999082i \(-0.513640\pi\)
−0.0428387 + 0.999082i \(0.513640\pi\)
\(642\) 41.3351 1.63137
\(643\) 32.1923 1.26954 0.634771 0.772701i \(-0.281095\pi\)
0.634771 + 0.772701i \(0.281095\pi\)
\(644\) −0.409232 −0.0161260
\(645\) −66.5771 −2.62147
\(646\) 3.23454 0.127261
\(647\) 7.84217 0.308308 0.154154 0.988047i \(-0.450735\pi\)
0.154154 + 0.988047i \(0.450735\pi\)
\(648\) 6.00844 0.236034
\(649\) 5.63765 0.221297
\(650\) −47.6147 −1.86760
\(651\) 16.8046 0.658625
\(652\) 4.70483 0.184255
\(653\) 11.1317 0.435617 0.217808 0.975992i \(-0.430109\pi\)
0.217808 + 0.975992i \(0.430109\pi\)
\(654\) −24.7061 −0.966084
\(655\) 3.25406 0.127147
\(656\) 12.4924 0.487746
\(657\) 11.5460 0.450454
\(658\) −53.7943 −2.09712
\(659\) −12.4652 −0.485576 −0.242788 0.970079i \(-0.578062\pi\)
−0.242788 + 0.970079i \(0.578062\pi\)
\(660\) 3.44344 0.134036
\(661\) 32.4838 1.26348 0.631738 0.775182i \(-0.282342\pi\)
0.631738 + 0.775182i \(0.282342\pi\)
\(662\) 17.2081 0.668813
\(663\) −10.1449 −0.393995
\(664\) −11.1877 −0.434168
\(665\) 33.3514 1.29331
\(666\) −40.1863 −1.55719
\(667\) −0.463705 −0.0179547
\(668\) 2.06623 0.0799449
\(669\) 27.6806 1.07019
\(670\) 79.3696 3.06631
\(671\) −4.55464 −0.175830
\(672\) 19.4620 0.750764
\(673\) −7.39051 −0.284883 −0.142442 0.989803i \(-0.545495\pi\)
−0.142442 + 0.989803i \(0.545495\pi\)
\(674\) 28.1396 1.08390
\(675\) 22.5053 0.866228
\(676\) 6.73783 0.259147
\(677\) 41.6597 1.60111 0.800557 0.599257i \(-0.204537\pi\)
0.800557 + 0.599257i \(0.204537\pi\)
\(678\) −17.5880 −0.675461
\(679\) 61.9749 2.37838
\(680\) 5.45743 0.209283
\(681\) 0.158157 0.00606060
\(682\) 2.88260 0.110381
\(683\) −41.3039 −1.58045 −0.790224 0.612817i \(-0.790036\pi\)
−0.790224 + 0.612817i \(0.790036\pi\)
\(684\) 5.38615 0.205945
\(685\) −39.2075 −1.49804
\(686\) 16.0059 0.611108
\(687\) −30.8637 −1.17752
\(688\) −34.6101 −1.31950
\(689\) 5.77677 0.220078
\(690\) −4.40991 −0.167882
\(691\) −13.2163 −0.502772 −0.251386 0.967887i \(-0.580886\pi\)
−0.251386 + 0.967887i \(0.580886\pi\)
\(692\) −1.75566 −0.0667402
\(693\) 14.7378 0.559841
\(694\) 37.5546 1.42555
\(695\) −39.1034 −1.48328
\(696\) 9.84492 0.373171
\(697\) −1.81808 −0.0688648
\(698\) −52.9536 −2.00432
\(699\) −37.7238 −1.42685
\(700\) −7.12811 −0.269417
\(701\) 42.7837 1.61592 0.807960 0.589238i \(-0.200572\pi\)
0.807960 + 0.589238i \(0.200572\pi\)
\(702\) −34.3063 −1.29481
\(703\) −18.0884 −0.682217
\(704\) −5.91025 −0.222751
\(705\) −94.0036 −3.54038
\(706\) −20.6928 −0.778783
\(707\) 26.1150 0.982155
\(708\) −5.96574 −0.224206
\(709\) −7.91729 −0.297340 −0.148670 0.988887i \(-0.547499\pi\)
−0.148670 + 0.988887i \(0.547499\pi\)
\(710\) 38.9727 1.46262
\(711\) 73.1589 2.74367
\(712\) 25.6259 0.960370
\(713\) −0.598647 −0.0224195
\(714\) −9.36553 −0.350496
\(715\) −17.9434 −0.671046
\(716\) −8.63962 −0.322878
\(717\) −23.5375 −0.879026
\(718\) 8.61978 0.321687
\(719\) −47.9553 −1.78843 −0.894215 0.447639i \(-0.852265\pi\)
−0.894215 + 0.447639i \(0.852265\pi\)
\(720\) 67.3096 2.50848
\(721\) 33.0725 1.23168
\(722\) −14.4051 −0.536101
\(723\) 23.7402 0.882909
\(724\) −0.720761 −0.0267869
\(725\) −8.07692 −0.299969
\(726\) 4.22360 0.156753
\(727\) −5.77077 −0.214026 −0.107013 0.994258i \(-0.534129\pi\)
−0.107013 + 0.994258i \(0.534129\pi\)
\(728\) −45.2745 −1.67799
\(729\) −43.8089 −1.62255
\(730\) −12.9775 −0.480320
\(731\) 5.03699 0.186300
\(732\) 4.81971 0.178141
\(733\) 5.15826 0.190525 0.0952623 0.995452i \(-0.469631\pi\)
0.0952623 + 0.995452i \(0.469631\pi\)
\(734\) 40.3879 1.49074
\(735\) −34.2992 −1.26515
\(736\) −0.693315 −0.0255559
\(737\) 15.7868 0.581514
\(738\) −18.6694 −0.687231
\(739\) −35.4979 −1.30581 −0.652906 0.757439i \(-0.726450\pi\)
−0.652906 + 0.757439i \(0.726450\pi\)
\(740\) 7.32463 0.269259
\(741\) −46.8907 −1.72257
\(742\) 5.33298 0.195780
\(743\) 22.4474 0.823514 0.411757 0.911294i \(-0.364915\pi\)
0.411757 + 0.911294i \(0.364915\pi\)
\(744\) 12.7099 0.465967
\(745\) −19.0478 −0.697856
\(746\) −38.1932 −1.39835
\(747\) 20.0817 0.734749
\(748\) −0.260518 −0.00952548
\(749\) −32.2453 −1.17822
\(750\) −8.09361 −0.295537
\(751\) 28.4385 1.03774 0.518868 0.854854i \(-0.326354\pi\)
0.518868 + 0.854854i \(0.326354\pi\)
\(752\) −48.8677 −1.78202
\(753\) 21.7261 0.791742
\(754\) 12.3122 0.448384
\(755\) −8.20348 −0.298555
\(756\) −5.13579 −0.186787
\(757\) −2.12328 −0.0771720 −0.0385860 0.999255i \(-0.512285\pi\)
−0.0385860 + 0.999255i \(0.512285\pi\)
\(758\) 22.4583 0.815724
\(759\) −0.877141 −0.0318382
\(760\) 25.2248 0.914999
\(761\) −1.92689 −0.0698498 −0.0349249 0.999390i \(-0.511119\pi\)
−0.0349249 + 0.999390i \(0.511119\pi\)
\(762\) −70.3414 −2.54820
\(763\) 19.2731 0.697732
\(764\) −6.38656 −0.231058
\(765\) −9.79593 −0.354173
\(766\) −38.0223 −1.37380
\(767\) 31.0870 1.12249
\(768\) 24.5067 0.884311
\(769\) −4.44718 −0.160370 −0.0801848 0.996780i \(-0.525551\pi\)
−0.0801848 + 0.996780i \(0.525551\pi\)
\(770\) −16.5650 −0.596960
\(771\) 41.6265 1.49914
\(772\) −4.37585 −0.157490
\(773\) 13.4750 0.484663 0.242331 0.970194i \(-0.422088\pi\)
0.242331 + 0.970194i \(0.422088\pi\)
\(774\) 51.7235 1.85916
\(775\) −10.4274 −0.374563
\(776\) 46.8737 1.68267
\(777\) 52.3746 1.87893
\(778\) 22.3283 0.800508
\(779\) −8.40336 −0.301082
\(780\) 18.9877 0.679869
\(781\) 7.75176 0.277380
\(782\) 0.333638 0.0119309
\(783\) −5.81941 −0.207969
\(784\) −17.8304 −0.636800
\(785\) −66.3200 −2.36706
\(786\) −4.22360 −0.150651
\(787\) 6.72808 0.239830 0.119915 0.992784i \(-0.461738\pi\)
0.119915 + 0.992784i \(0.461738\pi\)
\(788\) −5.86655 −0.208987
\(789\) −48.9438 −1.74245
\(790\) −82.2292 −2.92558
\(791\) 13.7203 0.487836
\(792\) 11.1467 0.396079
\(793\) −25.1151 −0.891862
\(794\) 15.3958 0.546377
\(795\) 9.31920 0.330518
\(796\) −5.79270 −0.205317
\(797\) −39.5004 −1.39918 −0.699588 0.714547i \(-0.746633\pi\)
−0.699588 + 0.714547i \(0.746633\pi\)
\(798\) −43.2884 −1.53239
\(799\) 7.11197 0.251604
\(800\) −12.0763 −0.426963
\(801\) −45.9977 −1.62525
\(802\) −18.7137 −0.660803
\(803\) −2.58126 −0.0910907
\(804\) −16.7055 −0.589159
\(805\) 3.44014 0.121249
\(806\) 15.8952 0.559884
\(807\) −71.0573 −2.50133
\(808\) 19.7516 0.694860
\(809\) −48.8110 −1.71610 −0.858051 0.513564i \(-0.828325\pi\)
−0.858051 + 0.513564i \(0.828325\pi\)
\(810\) 12.1221 0.425928
\(811\) −32.6211 −1.14548 −0.572741 0.819737i \(-0.694120\pi\)
−0.572741 + 0.819737i \(0.694120\pi\)
\(812\) 1.84319 0.0646832
\(813\) 52.0588 1.82578
\(814\) 8.98415 0.314894
\(815\) −39.5504 −1.38539
\(816\) −8.50781 −0.297833
\(817\) 23.2815 0.814515
\(818\) −16.5189 −0.577568
\(819\) 81.2666 2.83968
\(820\) 3.40282 0.118831
\(821\) −46.6063 −1.62657 −0.813286 0.581865i \(-0.802323\pi\)
−0.813286 + 0.581865i \(0.802323\pi\)
\(822\) 50.8893 1.77497
\(823\) −35.0927 −1.22325 −0.611627 0.791147i \(-0.709485\pi\)
−0.611627 + 0.791147i \(0.709485\pi\)
\(824\) 25.0138 0.871397
\(825\) −15.2783 −0.531921
\(826\) 28.6988 0.998557
\(827\) −53.4331 −1.85805 −0.929026 0.370015i \(-0.879353\pi\)
−0.929026 + 0.370015i \(0.879353\pi\)
\(828\) 0.555573 0.0193075
\(829\) 30.7341 1.06744 0.533719 0.845662i \(-0.320794\pi\)
0.533719 + 0.845662i \(0.320794\pi\)
\(830\) −22.5714 −0.783464
\(831\) 57.4649 1.99343
\(832\) −32.5901 −1.12986
\(833\) 2.59495 0.0899098
\(834\) 50.7542 1.75747
\(835\) −17.3694 −0.601094
\(836\) −1.20414 −0.0416461
\(837\) −7.51292 −0.259684
\(838\) 48.4519 1.67374
\(839\) 49.3178 1.70264 0.851319 0.524648i \(-0.175803\pi\)
0.851319 + 0.524648i \(0.175803\pi\)
\(840\) −73.0377 −2.52004
\(841\) −26.9115 −0.927982
\(842\) −34.2795 −1.18135
\(843\) 1.31322 0.0452297
\(844\) −1.53578 −0.0528636
\(845\) −56.6405 −1.94849
\(846\) 73.0310 2.51086
\(847\) −3.29481 −0.113211
\(848\) 4.84457 0.166363
\(849\) 51.1357 1.75497
\(850\) 5.81139 0.199329
\(851\) −1.86579 −0.0639585
\(852\) −8.20289 −0.281026
\(853\) −0.819663 −0.0280647 −0.0140324 0.999902i \(-0.504467\pi\)
−0.0140324 + 0.999902i \(0.504467\pi\)
\(854\) −23.1856 −0.793396
\(855\) −45.2778 −1.54847
\(856\) −24.3882 −0.833571
\(857\) 3.01099 0.102853 0.0514267 0.998677i \(-0.483623\pi\)
0.0514267 + 0.998677i \(0.483623\pi\)
\(858\) 23.2897 0.795097
\(859\) −4.77571 −0.162945 −0.0814726 0.996676i \(-0.525962\pi\)
−0.0814726 + 0.996676i \(0.525962\pi\)
\(860\) −9.42748 −0.321474
\(861\) 24.3317 0.829223
\(862\) −45.1579 −1.53808
\(863\) 3.01791 0.102731 0.0513655 0.998680i \(-0.483643\pi\)
0.0513655 + 0.998680i \(0.483643\pi\)
\(864\) −8.70099 −0.296014
\(865\) 14.7587 0.501810
\(866\) 20.3289 0.690804
\(867\) −45.2344 −1.53624
\(868\) 2.37957 0.0807679
\(869\) −16.3556 −0.554825
\(870\) 19.8623 0.673394
\(871\) 87.0511 2.94961
\(872\) 14.5769 0.493635
\(873\) −84.1370 −2.84761
\(874\) 1.54211 0.0521625
\(875\) 6.31378 0.213445
\(876\) 2.73148 0.0922883
\(877\) 34.4673 1.16388 0.581939 0.813232i \(-0.302294\pi\)
0.581939 + 0.813232i \(0.302294\pi\)
\(878\) −49.5584 −1.67252
\(879\) −79.2164 −2.67190
\(880\) −15.0479 −0.507264
\(881\) −16.4588 −0.554510 −0.277255 0.960796i \(-0.589425\pi\)
−0.277255 + 0.960796i \(0.589425\pi\)
\(882\) 26.6469 0.897248
\(883\) 42.6507 1.43531 0.717656 0.696398i \(-0.245215\pi\)
0.717656 + 0.696398i \(0.245215\pi\)
\(884\) −1.43654 −0.0483161
\(885\) 50.1500 1.68578
\(886\) 49.1893 1.65255
\(887\) −1.57557 −0.0529024 −0.0264512 0.999650i \(-0.508421\pi\)
−0.0264512 + 0.999650i \(0.508421\pi\)
\(888\) 39.6126 1.32931
\(889\) 54.8729 1.84038
\(890\) 51.7006 1.73301
\(891\) 2.41112 0.0807755
\(892\) 3.91963 0.131239
\(893\) 32.8723 1.10003
\(894\) 24.7230 0.826862
\(895\) 72.6275 2.42767
\(896\) −44.3251 −1.48080
\(897\) −4.83670 −0.161493
\(898\) −26.5884 −0.887266
\(899\) 2.69632 0.0899271
\(900\) 9.67710 0.322570
\(901\) −0.705057 −0.0234889
\(902\) 4.17378 0.138972
\(903\) −67.4109 −2.24329
\(904\) 10.3771 0.345137
\(905\) 6.05895 0.201406
\(906\) 10.6477 0.353746
\(907\) −46.0305 −1.52842 −0.764209 0.644968i \(-0.776871\pi\)
−0.764209 + 0.644968i \(0.776871\pi\)
\(908\) 0.0223954 0.000743219 0
\(909\) −35.4536 −1.17592
\(910\) −91.3420 −3.02796
\(911\) −52.6729 −1.74513 −0.872565 0.488498i \(-0.837545\pi\)
−0.872565 + 0.488498i \(0.837545\pi\)
\(912\) −39.3240 −1.30215
\(913\) −4.48950 −0.148581
\(914\) 7.40317 0.244875
\(915\) −40.5161 −1.33942
\(916\) −4.37037 −0.144401
\(917\) 3.29481 0.108804
\(918\) 4.18709 0.138195
\(919\) 14.4730 0.477421 0.238710 0.971091i \(-0.423275\pi\)
0.238710 + 0.971091i \(0.423275\pi\)
\(920\) 2.60189 0.0857819
\(921\) 64.9913 2.14154
\(922\) 52.3175 1.72299
\(923\) 42.7445 1.40695
\(924\) 3.48656 0.114699
\(925\) −32.4988 −1.06855
\(926\) 9.00732 0.295999
\(927\) −44.8991 −1.47468
\(928\) 3.12270 0.102508
\(929\) 20.0925 0.659213 0.329606 0.944118i \(-0.393084\pi\)
0.329606 + 0.944118i \(0.393084\pi\)
\(930\) 25.6424 0.840847
\(931\) 11.9941 0.393092
\(932\) −5.34178 −0.174976
\(933\) 16.0078 0.524073
\(934\) 56.1486 1.83724
\(935\) 2.19000 0.0716207
\(936\) 61.4646 2.00903
\(937\) −6.25372 −0.204300 −0.102150 0.994769i \(-0.532572\pi\)
−0.102150 + 0.994769i \(0.532572\pi\)
\(938\) 80.3635 2.62396
\(939\) −70.8863 −2.31329
\(940\) −13.3111 −0.434161
\(941\) 16.4267 0.535494 0.267747 0.963489i \(-0.413721\pi\)
0.267747 + 0.963489i \(0.413721\pi\)
\(942\) 86.0801 2.80464
\(943\) −0.866793 −0.0282267
\(944\) 26.0704 0.848521
\(945\) 43.1732 1.40442
\(946\) −11.5634 −0.375960
\(947\) −26.6074 −0.864623 −0.432312 0.901724i \(-0.642302\pi\)
−0.432312 + 0.901724i \(0.642302\pi\)
\(948\) 17.3074 0.562119
\(949\) −14.2335 −0.462040
\(950\) 26.8608 0.871479
\(951\) −13.3310 −0.432288
\(952\) 5.52577 0.179091
\(953\) −34.3273 −1.11197 −0.555986 0.831192i \(-0.687659\pi\)
−0.555986 + 0.831192i \(0.687659\pi\)
\(954\) −7.24005 −0.234405
\(955\) 53.6876 1.73729
\(956\) −3.33297 −0.107796
\(957\) 3.95065 0.127706
\(958\) −24.6928 −0.797787
\(959\) −39.6985 −1.28193
\(960\) −52.5750 −1.69685
\(961\) −27.5190 −0.887711
\(962\) 49.5401 1.59724
\(963\) 43.7761 1.41067
\(964\) 3.36167 0.108272
\(965\) 36.7849 1.18415
\(966\) −4.46513 −0.143663
\(967\) −41.5468 −1.33605 −0.668027 0.744137i \(-0.732861\pi\)
−0.668027 + 0.744137i \(0.732861\pi\)
\(968\) −2.49197 −0.0800951
\(969\) 5.72303 0.183850
\(970\) 94.5683 3.03641
\(971\) −12.7640 −0.409615 −0.204808 0.978802i \(-0.565657\pi\)
−0.204808 + 0.978802i \(0.565657\pi\)
\(972\) −7.22770 −0.231828
\(973\) −39.5931 −1.26930
\(974\) 47.5599 1.52392
\(975\) −84.2469 −2.69806
\(976\) −21.0622 −0.674185
\(977\) −5.30707 −0.169788 −0.0848941 0.996390i \(-0.527055\pi\)
−0.0848941 + 0.996390i \(0.527055\pi\)
\(978\) 51.3344 1.64149
\(979\) 10.2834 0.328658
\(980\) −4.85685 −0.155146
\(981\) −26.1651 −0.835386
\(982\) −46.9278 −1.49753
\(983\) −28.1899 −0.899120 −0.449560 0.893250i \(-0.648419\pi\)
−0.449560 + 0.893250i \(0.648419\pi\)
\(984\) 18.4029 0.586663
\(985\) 49.3162 1.57135
\(986\) −1.50271 −0.0478560
\(987\) −95.1808 −3.02964
\(988\) −6.63984 −0.211241
\(989\) 2.40145 0.0763615
\(990\) 22.4886 0.714733
\(991\) 41.8088 1.32810 0.664050 0.747688i \(-0.268836\pi\)
0.664050 + 0.747688i \(0.268836\pi\)
\(992\) 4.03144 0.127998
\(993\) 30.4472 0.966212
\(994\) 39.4608 1.25162
\(995\) 48.6954 1.54375
\(996\) 4.75078 0.150534
\(997\) −0.0216208 −0.000684737 0 −0.000342368 1.00000i \(-0.500109\pi\)
−0.000342368 1.00000i \(0.500109\pi\)
\(998\) 0.614348 0.0194468
\(999\) −23.4153 −0.740829
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.d.1.19 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.d.1.19 23 1.1 even 1 trivial