Properties

Label 8041.2.a.c.1.19
Level $8041$
Weight $2$
Character 8041.1
Self dual yes
Analytic conductor $64.208$
Analytic rank $1$
Dimension $60$
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] = [8041,2,Mod(1,8041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8041.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(60\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 8041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.32373 q^{2} -3.06819 q^{3} -0.247749 q^{4} +3.29067 q^{5} +4.06144 q^{6} -2.61144 q^{7} +2.97540 q^{8} +6.41379 q^{9} +O(q^{10})\) \(q-1.32373 q^{2} -3.06819 q^{3} -0.247749 q^{4} +3.29067 q^{5} +4.06144 q^{6} -2.61144 q^{7} +2.97540 q^{8} +6.41379 q^{9} -4.35594 q^{10} +1.00000 q^{11} +0.760142 q^{12} +5.06631 q^{13} +3.45683 q^{14} -10.0964 q^{15} -3.44312 q^{16} +1.00000 q^{17} -8.49010 q^{18} +5.54578 q^{19} -0.815260 q^{20} +8.01240 q^{21} -1.32373 q^{22} +1.26421 q^{23} -9.12911 q^{24} +5.82848 q^{25} -6.70641 q^{26} -10.4742 q^{27} +0.646983 q^{28} -5.31625 q^{29} +13.3649 q^{30} +5.32587 q^{31} -1.39306 q^{32} -3.06819 q^{33} -1.32373 q^{34} -8.59338 q^{35} -1.58901 q^{36} +11.0730 q^{37} -7.34109 q^{38} -15.5444 q^{39} +9.79106 q^{40} -7.71007 q^{41} -10.6062 q^{42} -1.00000 q^{43} -0.247749 q^{44} +21.1056 q^{45} -1.67347 q^{46} -7.04648 q^{47} +10.5642 q^{48} -0.180376 q^{49} -7.71531 q^{50} -3.06819 q^{51} -1.25517 q^{52} -2.42816 q^{53} +13.8649 q^{54} +3.29067 q^{55} -7.77009 q^{56} -17.0155 q^{57} +7.03725 q^{58} +0.973284 q^{59} +2.50137 q^{60} -8.10682 q^{61} -7.04999 q^{62} -16.7492 q^{63} +8.73027 q^{64} +16.6715 q^{65} +4.06144 q^{66} -10.8514 q^{67} -0.247749 q^{68} -3.87884 q^{69} +11.3753 q^{70} -12.4014 q^{71} +19.0836 q^{72} +10.2699 q^{73} -14.6576 q^{74} -17.8829 q^{75} -1.37396 q^{76} -2.61144 q^{77} +20.5765 q^{78} -4.52430 q^{79} -11.3302 q^{80} +12.8954 q^{81} +10.2060 q^{82} -15.1729 q^{83} -1.98507 q^{84} +3.29067 q^{85} +1.32373 q^{86} +16.3113 q^{87} +2.97540 q^{88} -16.7185 q^{89} -27.9381 q^{90} -13.2304 q^{91} -0.313207 q^{92} -16.3408 q^{93} +9.32761 q^{94} +18.2493 q^{95} +4.27417 q^{96} +0.313815 q^{97} +0.238768 q^{98} +6.41379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32373 −0.936016 −0.468008 0.883724i \(-0.655028\pi\)
−0.468008 + 0.883724i \(0.655028\pi\)
\(3\) −3.06819 −1.77142 −0.885710 0.464238i \(-0.846328\pi\)
−0.885710 + 0.464238i \(0.846328\pi\)
\(4\) −0.247749 −0.123875
\(5\) 3.29067 1.47163 0.735815 0.677182i \(-0.236799\pi\)
0.735815 + 0.677182i \(0.236799\pi\)
\(6\) 4.06144 1.65808
\(7\) −2.61144 −0.987032 −0.493516 0.869737i \(-0.664289\pi\)
−0.493516 + 0.869737i \(0.664289\pi\)
\(8\) 2.97540 1.05196
\(9\) 6.41379 2.13793
\(10\) −4.35594 −1.37747
\(11\) 1.00000 0.301511
\(12\) 0.760142 0.219434
\(13\) 5.06631 1.40514 0.702571 0.711614i \(-0.252035\pi\)
0.702571 + 0.711614i \(0.252035\pi\)
\(14\) 3.45683 0.923877
\(15\) −10.0964 −2.60688
\(16\) −3.44312 −0.860780
\(17\) 1.00000 0.242536
\(18\) −8.49010 −2.00114
\(19\) 5.54578 1.27229 0.636145 0.771570i \(-0.280528\pi\)
0.636145 + 0.771570i \(0.280528\pi\)
\(20\) −0.815260 −0.182298
\(21\) 8.01240 1.74845
\(22\) −1.32373 −0.282219
\(23\) 1.26421 0.263606 0.131803 0.991276i \(-0.457923\pi\)
0.131803 + 0.991276i \(0.457923\pi\)
\(24\) −9.12911 −1.86347
\(25\) 5.82848 1.16570
\(26\) −6.70641 −1.31523
\(27\) −10.4742 −2.01575
\(28\) 0.646983 0.122268
\(29\) −5.31625 −0.987202 −0.493601 0.869688i \(-0.664320\pi\)
−0.493601 + 0.869688i \(0.664320\pi\)
\(30\) 13.3649 2.44008
\(31\) 5.32587 0.956554 0.478277 0.878209i \(-0.341261\pi\)
0.478277 + 0.878209i \(0.341261\pi\)
\(32\) −1.39306 −0.246260
\(33\) −3.06819 −0.534103
\(34\) −1.32373 −0.227017
\(35\) −8.59338 −1.45255
\(36\) −1.58901 −0.264835
\(37\) 11.0730 1.82039 0.910193 0.414183i \(-0.135933\pi\)
0.910193 + 0.414183i \(0.135933\pi\)
\(38\) −7.34109 −1.19088
\(39\) −15.5444 −2.48910
\(40\) 9.79106 1.54810
\(41\) −7.71007 −1.20411 −0.602055 0.798454i \(-0.705651\pi\)
−0.602055 + 0.798454i \(0.705651\pi\)
\(42\) −10.6062 −1.63658
\(43\) −1.00000 −0.152499
\(44\) −0.247749 −0.0373496
\(45\) 21.1056 3.14624
\(46\) −1.67347 −0.246739
\(47\) −7.04648 −1.02783 −0.513917 0.857840i \(-0.671806\pi\)
−0.513917 + 0.857840i \(0.671806\pi\)
\(48\) 10.5642 1.52480
\(49\) −0.180376 −0.0257679
\(50\) −7.71531 −1.09111
\(51\) −3.06819 −0.429633
\(52\) −1.25517 −0.174061
\(53\) −2.42816 −0.333533 −0.166767 0.985996i \(-0.553333\pi\)
−0.166767 + 0.985996i \(0.553333\pi\)
\(54\) 13.8649 1.88678
\(55\) 3.29067 0.443713
\(56\) −7.77009 −1.03832
\(57\) −17.0155 −2.25376
\(58\) 7.03725 0.924037
\(59\) 0.973284 0.126711 0.0633554 0.997991i \(-0.479820\pi\)
0.0633554 + 0.997991i \(0.479820\pi\)
\(60\) 2.50137 0.322926
\(61\) −8.10682 −1.03797 −0.518986 0.854783i \(-0.673690\pi\)
−0.518986 + 0.854783i \(0.673690\pi\)
\(62\) −7.04999 −0.895350
\(63\) −16.7492 −2.11021
\(64\) 8.73027 1.09128
\(65\) 16.6715 2.06785
\(66\) 4.06144 0.499929
\(67\) −10.8514 −1.32571 −0.662854 0.748749i \(-0.730655\pi\)
−0.662854 + 0.748749i \(0.730655\pi\)
\(68\) −0.247749 −0.0300440
\(69\) −3.87884 −0.466957
\(70\) 11.3753 1.35961
\(71\) −12.4014 −1.47178 −0.735890 0.677101i \(-0.763236\pi\)
−0.735890 + 0.677101i \(0.763236\pi\)
\(72\) 19.0836 2.24903
\(73\) 10.2699 1.20200 0.601000 0.799249i \(-0.294769\pi\)
0.601000 + 0.799249i \(0.294769\pi\)
\(74\) −14.6576 −1.70391
\(75\) −17.8829 −2.06494
\(76\) −1.37396 −0.157604
\(77\) −2.61144 −0.297601
\(78\) 20.5765 2.32983
\(79\) −4.52430 −0.509024 −0.254512 0.967070i \(-0.581915\pi\)
−0.254512 + 0.967070i \(0.581915\pi\)
\(80\) −11.3302 −1.26675
\(81\) 12.8954 1.43282
\(82\) 10.2060 1.12707
\(83\) −15.1729 −1.66544 −0.832721 0.553693i \(-0.813218\pi\)
−0.832721 + 0.553693i \(0.813218\pi\)
\(84\) −1.98507 −0.216588
\(85\) 3.29067 0.356923
\(86\) 1.32373 0.142741
\(87\) 16.3113 1.74875
\(88\) 2.97540 0.317179
\(89\) −16.7185 −1.77216 −0.886079 0.463533i \(-0.846581\pi\)
−0.886079 + 0.463533i \(0.846581\pi\)
\(90\) −27.9381 −2.94493
\(91\) −13.2304 −1.38692
\(92\) −0.313207 −0.0326541
\(93\) −16.3408 −1.69446
\(94\) 9.32761 0.962069
\(95\) 18.2493 1.87234
\(96\) 4.27417 0.436231
\(97\) 0.313815 0.0318631 0.0159316 0.999873i \(-0.494929\pi\)
0.0159316 + 0.999873i \(0.494929\pi\)
\(98\) 0.238768 0.0241192
\(99\) 6.41379 0.644610
\(100\) −1.44400 −0.144400
\(101\) −7.44088 −0.740395 −0.370198 0.928953i \(-0.620710\pi\)
−0.370198 + 0.928953i \(0.620710\pi\)
\(102\) 4.06144 0.402143
\(103\) −1.17331 −0.115610 −0.0578049 0.998328i \(-0.518410\pi\)
−0.0578049 + 0.998328i \(0.518410\pi\)
\(104\) 15.0743 1.47816
\(105\) 26.3661 2.57307
\(106\) 3.21422 0.312193
\(107\) −11.4399 −1.10594 −0.552970 0.833201i \(-0.686505\pi\)
−0.552970 + 0.833201i \(0.686505\pi\)
\(108\) 2.59497 0.249701
\(109\) 9.33134 0.893780 0.446890 0.894589i \(-0.352532\pi\)
0.446890 + 0.894589i \(0.352532\pi\)
\(110\) −4.35594 −0.415323
\(111\) −33.9740 −3.22467
\(112\) 8.99151 0.849618
\(113\) −12.7753 −1.20180 −0.600898 0.799326i \(-0.705190\pi\)
−0.600898 + 0.799326i \(0.705190\pi\)
\(114\) 22.5239 2.10955
\(115\) 4.16009 0.387930
\(116\) 1.31710 0.122289
\(117\) 32.4943 3.00410
\(118\) −1.28836 −0.118603
\(119\) −2.61144 −0.239390
\(120\) −30.0408 −2.74234
\(121\) 1.00000 0.0909091
\(122\) 10.7312 0.971558
\(123\) 23.6560 2.13299
\(124\) −1.31948 −0.118493
\(125\) 2.72625 0.243843
\(126\) 22.1714 1.97519
\(127\) −3.00321 −0.266492 −0.133246 0.991083i \(-0.542540\pi\)
−0.133246 + 0.991083i \(0.542540\pi\)
\(128\) −8.77037 −0.775199
\(129\) 3.06819 0.270139
\(130\) −22.0685 −1.93554
\(131\) 8.95047 0.782006 0.391003 0.920389i \(-0.372128\pi\)
0.391003 + 0.920389i \(0.372128\pi\)
\(132\) 0.760142 0.0661619
\(133\) −14.4825 −1.25579
\(134\) 14.3643 1.24088
\(135\) −34.4670 −2.96645
\(136\) 2.97540 0.255139
\(137\) −14.4207 −1.23204 −0.616020 0.787731i \(-0.711256\pi\)
−0.616020 + 0.787731i \(0.711256\pi\)
\(138\) 5.13452 0.437079
\(139\) −21.3866 −1.81399 −0.906994 0.421144i \(-0.861629\pi\)
−0.906994 + 0.421144i \(0.861629\pi\)
\(140\) 2.12900 0.179934
\(141\) 21.6199 1.82073
\(142\) 16.4161 1.37761
\(143\) 5.06631 0.423666
\(144\) −22.0835 −1.84029
\(145\) −17.4940 −1.45280
\(146\) −13.5945 −1.12509
\(147\) 0.553427 0.0456458
\(148\) −2.74332 −0.225500
\(149\) 14.6922 1.20363 0.601816 0.798634i \(-0.294444\pi\)
0.601816 + 0.798634i \(0.294444\pi\)
\(150\) 23.6720 1.93281
\(151\) −0.122631 −0.00997955 −0.00498977 0.999988i \(-0.501588\pi\)
−0.00498977 + 0.999988i \(0.501588\pi\)
\(152\) 16.5009 1.33840
\(153\) 6.41379 0.518524
\(154\) 3.45683 0.278560
\(155\) 17.5257 1.40769
\(156\) 3.85112 0.308336
\(157\) −10.0524 −0.802266 −0.401133 0.916020i \(-0.631384\pi\)
−0.401133 + 0.916020i \(0.631384\pi\)
\(158\) 5.98894 0.476454
\(159\) 7.45006 0.590828
\(160\) −4.58409 −0.362404
\(161\) −3.30141 −0.260187
\(162\) −17.0699 −1.34114
\(163\) −5.30239 −0.415316 −0.207658 0.978202i \(-0.566584\pi\)
−0.207658 + 0.978202i \(0.566584\pi\)
\(164\) 1.91016 0.149159
\(165\) −10.0964 −0.786003
\(166\) 20.0848 1.55888
\(167\) 12.9321 1.00071 0.500356 0.865820i \(-0.333202\pi\)
0.500356 + 0.865820i \(0.333202\pi\)
\(168\) 23.8401 1.83931
\(169\) 12.6675 0.974424
\(170\) −4.35594 −0.334085
\(171\) 35.5695 2.72007
\(172\) 0.247749 0.0188907
\(173\) −3.39988 −0.258488 −0.129244 0.991613i \(-0.541255\pi\)
−0.129244 + 0.991613i \(0.541255\pi\)
\(174\) −21.5916 −1.63686
\(175\) −15.2207 −1.15058
\(176\) −3.44312 −0.259535
\(177\) −2.98622 −0.224458
\(178\) 22.1307 1.65877
\(179\) −5.87314 −0.438979 −0.219490 0.975615i \(-0.570439\pi\)
−0.219490 + 0.975615i \(0.570439\pi\)
\(180\) −5.22891 −0.389740
\(181\) −1.69841 −0.126242 −0.0631208 0.998006i \(-0.520105\pi\)
−0.0631208 + 0.998006i \(0.520105\pi\)
\(182\) 17.5134 1.29818
\(183\) 24.8733 1.83868
\(184\) 3.76153 0.277304
\(185\) 36.4375 2.67894
\(186\) 21.6307 1.58604
\(187\) 1.00000 0.0731272
\(188\) 1.74576 0.127323
\(189\) 27.3527 1.98961
\(190\) −24.1571 −1.75254
\(191\) −8.94524 −0.647255 −0.323627 0.946185i \(-0.604902\pi\)
−0.323627 + 0.946185i \(0.604902\pi\)
\(192\) −26.7861 −1.93312
\(193\) 8.63763 0.621750 0.310875 0.950451i \(-0.399378\pi\)
0.310875 + 0.950451i \(0.399378\pi\)
\(194\) −0.415406 −0.0298244
\(195\) −51.1514 −3.66303
\(196\) 0.0446879 0.00319199
\(197\) 0.920019 0.0655487 0.0327743 0.999463i \(-0.489566\pi\)
0.0327743 + 0.999463i \(0.489566\pi\)
\(198\) −8.49010 −0.603365
\(199\) 5.49924 0.389831 0.194915 0.980820i \(-0.437557\pi\)
0.194915 + 0.980820i \(0.437557\pi\)
\(200\) 17.3421 1.22627
\(201\) 33.2941 2.34839
\(202\) 9.84968 0.693021
\(203\) 13.8831 0.974400
\(204\) 0.760142 0.0532206
\(205\) −25.3713 −1.77201
\(206\) 1.55314 0.108213
\(207\) 8.10838 0.563571
\(208\) −17.4439 −1.20952
\(209\) 5.54578 0.383610
\(210\) −34.9015 −2.40843
\(211\) −20.5953 −1.41784 −0.708921 0.705288i \(-0.750818\pi\)
−0.708921 + 0.705288i \(0.750818\pi\)
\(212\) 0.601575 0.0413163
\(213\) 38.0500 2.60714
\(214\) 15.1433 1.03518
\(215\) −3.29067 −0.224422
\(216\) −31.1649 −2.12050
\(217\) −13.9082 −0.944150
\(218\) −12.3521 −0.836592
\(219\) −31.5100 −2.12925
\(220\) −0.815260 −0.0549648
\(221\) 5.06631 0.340797
\(222\) 44.9723 3.01834
\(223\) −12.5594 −0.841040 −0.420520 0.907283i \(-0.638152\pi\)
−0.420520 + 0.907283i \(0.638152\pi\)
\(224\) 3.63789 0.243067
\(225\) 37.3827 2.49218
\(226\) 16.9109 1.12490
\(227\) −19.5012 −1.29434 −0.647169 0.762347i \(-0.724047\pi\)
−0.647169 + 0.762347i \(0.724047\pi\)
\(228\) 4.21558 0.279184
\(229\) 6.23187 0.411814 0.205907 0.978572i \(-0.433986\pi\)
0.205907 + 0.978572i \(0.433986\pi\)
\(230\) −5.50682 −0.363109
\(231\) 8.01240 0.527177
\(232\) −15.8180 −1.03850
\(233\) 3.71757 0.243546 0.121773 0.992558i \(-0.461142\pi\)
0.121773 + 0.992558i \(0.461142\pi\)
\(234\) −43.0135 −2.81188
\(235\) −23.1876 −1.51259
\(236\) −0.241130 −0.0156962
\(237\) 13.8814 0.901695
\(238\) 3.45683 0.224073
\(239\) −3.50632 −0.226805 −0.113403 0.993549i \(-0.536175\pi\)
−0.113403 + 0.993549i \(0.536175\pi\)
\(240\) 34.7631 2.24395
\(241\) −3.37137 −0.217169 −0.108585 0.994087i \(-0.534632\pi\)
−0.108585 + 0.994087i \(0.534632\pi\)
\(242\) −1.32373 −0.0850923
\(243\) −8.14291 −0.522368
\(244\) 2.00846 0.128578
\(245\) −0.593556 −0.0379209
\(246\) −31.3140 −1.99651
\(247\) 28.0966 1.78775
\(248\) 15.8466 1.00626
\(249\) 46.5533 2.95020
\(250\) −3.60881 −0.228241
\(251\) 0.348846 0.0220190 0.0110095 0.999939i \(-0.496496\pi\)
0.0110095 + 0.999939i \(0.496496\pi\)
\(252\) 4.14961 0.261401
\(253\) 1.26421 0.0794802
\(254\) 3.97542 0.249440
\(255\) −10.0964 −0.632260
\(256\) −5.85097 −0.365686
\(257\) 20.2449 1.26284 0.631422 0.775439i \(-0.282472\pi\)
0.631422 + 0.775439i \(0.282472\pi\)
\(258\) −4.06144 −0.252854
\(259\) −28.9164 −1.79678
\(260\) −4.13036 −0.256154
\(261\) −34.0973 −2.11057
\(262\) −11.8480 −0.731970
\(263\) −13.3935 −0.825877 −0.412939 0.910759i \(-0.635498\pi\)
−0.412939 + 0.910759i \(0.635498\pi\)
\(264\) −9.12911 −0.561858
\(265\) −7.99026 −0.490838
\(266\) 19.1708 1.17544
\(267\) 51.2956 3.13924
\(268\) 2.68842 0.164222
\(269\) 10.5138 0.641040 0.320520 0.947242i \(-0.396142\pi\)
0.320520 + 0.947242i \(0.396142\pi\)
\(270\) 45.6248 2.77664
\(271\) −16.3128 −0.990930 −0.495465 0.868628i \(-0.665002\pi\)
−0.495465 + 0.868628i \(0.665002\pi\)
\(272\) −3.44312 −0.208770
\(273\) 40.5933 2.45682
\(274\) 19.0890 1.15321
\(275\) 5.82848 0.351471
\(276\) 0.960979 0.0578441
\(277\) 26.7626 1.60801 0.804003 0.594625i \(-0.202699\pi\)
0.804003 + 0.594625i \(0.202699\pi\)
\(278\) 28.3100 1.69792
\(279\) 34.1590 2.04505
\(280\) −25.5688 −1.52803
\(281\) −2.21316 −0.132026 −0.0660131 0.997819i \(-0.521028\pi\)
−0.0660131 + 0.997819i \(0.521028\pi\)
\(282\) −28.6189 −1.70423
\(283\) −2.87234 −0.170743 −0.0853715 0.996349i \(-0.527208\pi\)
−0.0853715 + 0.996349i \(0.527208\pi\)
\(284\) 3.07245 0.182316
\(285\) −55.9924 −3.31670
\(286\) −6.70641 −0.396558
\(287\) 20.1344 1.18850
\(288\) −8.93479 −0.526487
\(289\) 1.00000 0.0588235
\(290\) 23.1572 1.35984
\(291\) −0.962845 −0.0564430
\(292\) −2.54436 −0.148897
\(293\) 12.6167 0.737078 0.368539 0.929612i \(-0.379858\pi\)
0.368539 + 0.929612i \(0.379858\pi\)
\(294\) −0.732585 −0.0427252
\(295\) 3.20275 0.186471
\(296\) 32.9466 1.91498
\(297\) −10.4742 −0.607773
\(298\) −19.4485 −1.12662
\(299\) 6.40488 0.370404
\(300\) 4.43047 0.255793
\(301\) 2.61144 0.150521
\(302\) 0.162330 0.00934101
\(303\) 22.8300 1.31155
\(304\) −19.0948 −1.09516
\(305\) −26.6768 −1.52751
\(306\) −8.49010 −0.485347
\(307\) 28.9978 1.65499 0.827496 0.561471i \(-0.189764\pi\)
0.827496 + 0.561471i \(0.189764\pi\)
\(308\) 0.646983 0.0368653
\(309\) 3.59994 0.204794
\(310\) −23.1992 −1.31762
\(311\) −9.26842 −0.525564 −0.262782 0.964855i \(-0.584640\pi\)
−0.262782 + 0.964855i \(0.584640\pi\)
\(312\) −46.2509 −2.61844
\(313\) 9.89724 0.559425 0.279713 0.960084i \(-0.409761\pi\)
0.279713 + 0.960084i \(0.409761\pi\)
\(314\) 13.3066 0.750934
\(315\) −55.1162 −3.10544
\(316\) 1.12089 0.0630551
\(317\) 21.2221 1.19195 0.595976 0.803002i \(-0.296765\pi\)
0.595976 + 0.803002i \(0.296765\pi\)
\(318\) −9.86184 −0.553024
\(319\) −5.31625 −0.297653
\(320\) 28.7284 1.60597
\(321\) 35.0999 1.95908
\(322\) 4.37016 0.243540
\(323\) 5.54578 0.308575
\(324\) −3.19481 −0.177490
\(325\) 29.5289 1.63797
\(326\) 7.01892 0.388742
\(327\) −28.6303 −1.58326
\(328\) −22.9406 −1.26668
\(329\) 18.4015 1.01451
\(330\) 13.3649 0.735711
\(331\) −30.1059 −1.65477 −0.827384 0.561637i \(-0.810172\pi\)
−0.827384 + 0.561637i \(0.810172\pi\)
\(332\) 3.75907 0.206306
\(333\) 71.0198 3.89186
\(334\) −17.1185 −0.936683
\(335\) −35.7083 −1.95095
\(336\) −27.5877 −1.50503
\(337\) 12.3346 0.671909 0.335955 0.941878i \(-0.390941\pi\)
0.335955 + 0.941878i \(0.390941\pi\)
\(338\) −16.7683 −0.912076
\(339\) 39.1969 2.12889
\(340\) −0.815260 −0.0442137
\(341\) 5.32587 0.288412
\(342\) −47.0843 −2.54602
\(343\) 18.7511 1.01247
\(344\) −2.97540 −0.160423
\(345\) −12.7640 −0.687188
\(346\) 4.50051 0.241949
\(347\) −28.4883 −1.52933 −0.764666 0.644426i \(-0.777096\pi\)
−0.764666 + 0.644426i \(0.777096\pi\)
\(348\) −4.04110 −0.216626
\(349\) −2.57991 −0.138100 −0.0690498 0.997613i \(-0.521997\pi\)
−0.0690498 + 0.997613i \(0.521997\pi\)
\(350\) 20.1481 1.07696
\(351\) −53.0654 −2.83242
\(352\) −1.39306 −0.0742503
\(353\) −24.8428 −1.32225 −0.661123 0.750277i \(-0.729920\pi\)
−0.661123 + 0.750277i \(0.729920\pi\)
\(354\) 3.95294 0.210096
\(355\) −40.8090 −2.16592
\(356\) 4.14200 0.219526
\(357\) 8.01240 0.424061
\(358\) 7.77443 0.410891
\(359\) −24.8131 −1.30959 −0.654794 0.755808i \(-0.727245\pi\)
−0.654794 + 0.755808i \(0.727245\pi\)
\(360\) 62.7978 3.30974
\(361\) 11.7557 0.618720
\(362\) 2.24823 0.118164
\(363\) −3.06819 −0.161038
\(364\) 3.27781 0.171804
\(365\) 33.7948 1.76890
\(366\) −32.9254 −1.72104
\(367\) 37.4816 1.95653 0.978263 0.207370i \(-0.0664903\pi\)
0.978263 + 0.207370i \(0.0664903\pi\)
\(368\) −4.35283 −0.226907
\(369\) −49.4508 −2.57431
\(370\) −48.2332 −2.50753
\(371\) 6.34100 0.329208
\(372\) 4.04842 0.209901
\(373\) −21.4703 −1.11169 −0.555845 0.831286i \(-0.687605\pi\)
−0.555845 + 0.831286i \(0.687605\pi\)
\(374\) −1.32373 −0.0684482
\(375\) −8.36466 −0.431949
\(376\) −20.9661 −1.08125
\(377\) −26.9338 −1.38716
\(378\) −36.2074 −1.86231
\(379\) 22.6124 1.16152 0.580762 0.814074i \(-0.302755\pi\)
0.580762 + 0.814074i \(0.302755\pi\)
\(380\) −4.52125 −0.231935
\(381\) 9.21441 0.472069
\(382\) 11.8410 0.605841
\(383\) 5.48800 0.280424 0.140212 0.990122i \(-0.455222\pi\)
0.140212 + 0.990122i \(0.455222\pi\)
\(384\) 26.9092 1.37320
\(385\) −8.59338 −0.437959
\(386\) −11.4339 −0.581968
\(387\) −6.41379 −0.326031
\(388\) −0.0777475 −0.00394703
\(389\) 22.9128 1.16173 0.580864 0.814001i \(-0.302715\pi\)
0.580864 + 0.814001i \(0.302715\pi\)
\(390\) 67.7105 3.42865
\(391\) 1.26421 0.0639338
\(392\) −0.536690 −0.0271069
\(393\) −27.4617 −1.38526
\(394\) −1.21785 −0.0613546
\(395\) −14.8880 −0.749095
\(396\) −1.58901 −0.0798509
\(397\) −3.77228 −0.189325 −0.0946627 0.995509i \(-0.530177\pi\)
−0.0946627 + 0.995509i \(0.530177\pi\)
\(398\) −7.27949 −0.364888
\(399\) 44.4350 2.22453
\(400\) −20.0682 −1.00341
\(401\) 9.10387 0.454626 0.227313 0.973822i \(-0.427006\pi\)
0.227313 + 0.973822i \(0.427006\pi\)
\(402\) −44.0723 −2.19813
\(403\) 26.9825 1.34409
\(404\) 1.84347 0.0917162
\(405\) 42.4343 2.10858
\(406\) −18.3774 −0.912054
\(407\) 11.0730 0.548867
\(408\) −9.12911 −0.451958
\(409\) −20.6221 −1.01970 −0.509849 0.860264i \(-0.670299\pi\)
−0.509849 + 0.860264i \(0.670299\pi\)
\(410\) 33.5846 1.65863
\(411\) 44.2453 2.18246
\(412\) 0.290687 0.0143211
\(413\) −2.54167 −0.125068
\(414\) −10.7333 −0.527512
\(415\) −49.9289 −2.45091
\(416\) −7.05767 −0.346031
\(417\) 65.6182 3.21334
\(418\) −7.34109 −0.359065
\(419\) −29.5803 −1.44509 −0.722546 0.691323i \(-0.757028\pi\)
−0.722546 + 0.691323i \(0.757028\pi\)
\(420\) −6.53219 −0.318738
\(421\) −40.1253 −1.95559 −0.977795 0.209564i \(-0.932796\pi\)
−0.977795 + 0.209564i \(0.932796\pi\)
\(422\) 27.2626 1.32712
\(423\) −45.1947 −2.19744
\(424\) −7.22476 −0.350865
\(425\) 5.82848 0.282723
\(426\) −50.3678 −2.44033
\(427\) 21.1705 1.02451
\(428\) 2.83423 0.136998
\(429\) −15.5444 −0.750491
\(430\) 4.35594 0.210062
\(431\) 2.21544 0.106714 0.0533571 0.998575i \(-0.483008\pi\)
0.0533571 + 0.998575i \(0.483008\pi\)
\(432\) 36.0638 1.73512
\(433\) −18.2480 −0.876944 −0.438472 0.898745i \(-0.644480\pi\)
−0.438472 + 0.898745i \(0.644480\pi\)
\(434\) 18.4106 0.883739
\(435\) 53.6749 2.57351
\(436\) −2.31183 −0.110717
\(437\) 7.01103 0.335383
\(438\) 41.7106 1.99301
\(439\) 18.4083 0.878578 0.439289 0.898346i \(-0.355230\pi\)
0.439289 + 0.898346i \(0.355230\pi\)
\(440\) 9.79106 0.466771
\(441\) −1.15689 −0.0550901
\(442\) −6.70641 −0.318991
\(443\) −18.7295 −0.889863 −0.444932 0.895564i \(-0.646772\pi\)
−0.444932 + 0.895564i \(0.646772\pi\)
\(444\) 8.41704 0.399455
\(445\) −55.0150 −2.60796
\(446\) 16.6252 0.787226
\(447\) −45.0785 −2.13214
\(448\) −22.7986 −1.07713
\(449\) −12.3196 −0.581400 −0.290700 0.956814i \(-0.593888\pi\)
−0.290700 + 0.956814i \(0.593888\pi\)
\(450\) −49.4844 −2.33272
\(451\) −7.71007 −0.363053
\(452\) 3.16506 0.148872
\(453\) 0.376255 0.0176780
\(454\) 25.8142 1.21152
\(455\) −43.5367 −2.04103
\(456\) −50.6280 −2.37087
\(457\) −26.0552 −1.21881 −0.609407 0.792858i \(-0.708592\pi\)
−0.609407 + 0.792858i \(0.708592\pi\)
\(458\) −8.24929 −0.385464
\(459\) −10.4742 −0.488892
\(460\) −1.03066 −0.0480547
\(461\) −10.8724 −0.506380 −0.253190 0.967417i \(-0.581480\pi\)
−0.253190 + 0.967417i \(0.581480\pi\)
\(462\) −10.6062 −0.493446
\(463\) 35.0402 1.62846 0.814229 0.580544i \(-0.197160\pi\)
0.814229 + 0.580544i \(0.197160\pi\)
\(464\) 18.3045 0.849764
\(465\) −53.7720 −2.49362
\(466\) −4.92104 −0.227963
\(467\) −14.1930 −0.656773 −0.328386 0.944543i \(-0.606505\pi\)
−0.328386 + 0.944543i \(0.606505\pi\)
\(468\) −8.05043 −0.372131
\(469\) 28.3377 1.30852
\(470\) 30.6940 1.41581
\(471\) 30.8426 1.42115
\(472\) 2.89591 0.133295
\(473\) −1.00000 −0.0459800
\(474\) −18.3752 −0.844001
\(475\) 32.3235 1.48310
\(476\) 0.646983 0.0296544
\(477\) −15.5737 −0.713071
\(478\) 4.64141 0.212293
\(479\) −3.57255 −0.163234 −0.0816171 0.996664i \(-0.526008\pi\)
−0.0816171 + 0.996664i \(0.526008\pi\)
\(480\) 14.0649 0.641970
\(481\) 56.0992 2.55790
\(482\) 4.46277 0.203274
\(483\) 10.1294 0.460901
\(484\) −0.247749 −0.0112613
\(485\) 1.03266 0.0468907
\(486\) 10.7790 0.488945
\(487\) 38.9110 1.76323 0.881613 0.471972i \(-0.156458\pi\)
0.881613 + 0.471972i \(0.156458\pi\)
\(488\) −24.1211 −1.09191
\(489\) 16.2688 0.735699
\(490\) 0.785705 0.0354945
\(491\) −24.3200 −1.09755 −0.548773 0.835972i \(-0.684905\pi\)
−0.548773 + 0.835972i \(0.684905\pi\)
\(492\) −5.86075 −0.264223
\(493\) −5.31625 −0.239432
\(494\) −37.1923 −1.67336
\(495\) 21.1056 0.948628
\(496\) −18.3376 −0.823383
\(497\) 32.3856 1.45269
\(498\) −61.6239 −2.76143
\(499\) −33.9940 −1.52178 −0.760891 0.648880i \(-0.775238\pi\)
−0.760891 + 0.648880i \(0.775238\pi\)
\(500\) −0.675427 −0.0302060
\(501\) −39.6780 −1.77268
\(502\) −0.461776 −0.0206101
\(503\) −9.22831 −0.411470 −0.205735 0.978608i \(-0.565958\pi\)
−0.205735 + 0.978608i \(0.565958\pi\)
\(504\) −49.8358 −2.21986
\(505\) −24.4854 −1.08959
\(506\) −1.67347 −0.0743947
\(507\) −38.8663 −1.72611
\(508\) 0.744042 0.0330115
\(509\) −27.6150 −1.22401 −0.612006 0.790853i \(-0.709637\pi\)
−0.612006 + 0.790853i \(0.709637\pi\)
\(510\) 13.3649 0.591806
\(511\) −26.8192 −1.18641
\(512\) 25.2858 1.11749
\(513\) −58.0874 −2.56462
\(514\) −26.7987 −1.18204
\(515\) −3.86097 −0.170135
\(516\) −0.760142 −0.0334634
\(517\) −7.04648 −0.309904
\(518\) 38.2774 1.68181
\(519\) 10.4315 0.457891
\(520\) 49.6046 2.17530
\(521\) −43.3674 −1.89996 −0.949980 0.312310i \(-0.898897\pi\)
−0.949980 + 0.312310i \(0.898897\pi\)
\(522\) 45.1355 1.97553
\(523\) −0.658755 −0.0288054 −0.0144027 0.999896i \(-0.504585\pi\)
−0.0144027 + 0.999896i \(0.504585\pi\)
\(524\) −2.21747 −0.0968707
\(525\) 46.7001 2.03816
\(526\) 17.7293 0.773034
\(527\) 5.32587 0.231998
\(528\) 10.5642 0.459746
\(529\) −21.4018 −0.930512
\(530\) 10.5769 0.459432
\(531\) 6.24244 0.270899
\(532\) 3.58802 0.155561
\(533\) −39.0616 −1.69195
\(534\) −67.9013 −2.93838
\(535\) −37.6450 −1.62753
\(536\) −32.2873 −1.39460
\(537\) 18.0199 0.777617
\(538\) −13.9174 −0.600023
\(539\) −0.180376 −0.00776932
\(540\) 8.53917 0.367467
\(541\) −3.01235 −0.129511 −0.0647555 0.997901i \(-0.520627\pi\)
−0.0647555 + 0.997901i \(0.520627\pi\)
\(542\) 21.5936 0.927526
\(543\) 5.21104 0.223627
\(544\) −1.39306 −0.0597269
\(545\) 30.7063 1.31531
\(546\) −53.7344 −2.29962
\(547\) 27.7750 1.18757 0.593786 0.804623i \(-0.297633\pi\)
0.593786 + 0.804623i \(0.297633\pi\)
\(548\) 3.57271 0.152618
\(549\) −51.9954 −2.21911
\(550\) −7.71531 −0.328982
\(551\) −29.4827 −1.25601
\(552\) −11.5411 −0.491222
\(553\) 11.8150 0.502423
\(554\) −35.4263 −1.50512
\(555\) −111.797 −4.74552
\(556\) 5.29851 0.224707
\(557\) −4.19375 −0.177695 −0.0888474 0.996045i \(-0.528318\pi\)
−0.0888474 + 0.996045i \(0.528318\pi\)
\(558\) −45.2172 −1.91420
\(559\) −5.06631 −0.214282
\(560\) 29.5881 1.25032
\(561\) −3.06819 −0.129539
\(562\) 2.92962 0.123579
\(563\) −9.14152 −0.385269 −0.192635 0.981271i \(-0.561703\pi\)
−0.192635 + 0.981271i \(0.561703\pi\)
\(564\) −5.35632 −0.225542
\(565\) −42.0391 −1.76860
\(566\) 3.80220 0.159818
\(567\) −33.6755 −1.41424
\(568\) −36.8993 −1.54826
\(569\) 21.5988 0.905469 0.452735 0.891645i \(-0.350448\pi\)
0.452735 + 0.891645i \(0.350448\pi\)
\(570\) 74.1185 3.10448
\(571\) 32.2692 1.35042 0.675211 0.737624i \(-0.264052\pi\)
0.675211 + 0.737624i \(0.264052\pi\)
\(572\) −1.25517 −0.0524815
\(573\) 27.4457 1.14656
\(574\) −26.6524 −1.11245
\(575\) 7.36842 0.307284
\(576\) 55.9941 2.33309
\(577\) 15.1275 0.629767 0.314883 0.949130i \(-0.398035\pi\)
0.314883 + 0.949130i \(0.398035\pi\)
\(578\) −1.32373 −0.0550597
\(579\) −26.5019 −1.10138
\(580\) 4.33412 0.179965
\(581\) 39.6231 1.64384
\(582\) 1.27454 0.0528315
\(583\) −2.42816 −0.100564
\(584\) 30.5571 1.26446
\(585\) 106.928 4.42092
\(586\) −16.7011 −0.689917
\(587\) 31.5834 1.30359 0.651793 0.758397i \(-0.274017\pi\)
0.651793 + 0.758397i \(0.274017\pi\)
\(588\) −0.137111 −0.00565436
\(589\) 29.5361 1.21701
\(590\) −4.23957 −0.174540
\(591\) −2.82279 −0.116114
\(592\) −38.1256 −1.56695
\(593\) 14.2537 0.585329 0.292665 0.956215i \(-0.405458\pi\)
0.292665 + 0.956215i \(0.405458\pi\)
\(594\) 13.8649 0.568885
\(595\) −8.59338 −0.352294
\(596\) −3.63998 −0.149100
\(597\) −16.8727 −0.690554
\(598\) −8.47831 −0.346704
\(599\) 12.4437 0.508436 0.254218 0.967147i \(-0.418182\pi\)
0.254218 + 0.967147i \(0.418182\pi\)
\(600\) −53.2088 −2.17224
\(601\) 44.3406 1.80869 0.904346 0.426801i \(-0.140359\pi\)
0.904346 + 0.426801i \(0.140359\pi\)
\(602\) −3.45683 −0.140890
\(603\) −69.5985 −2.83427
\(604\) 0.0303817 0.00123621
\(605\) 3.29067 0.133785
\(606\) −30.2207 −1.22763
\(607\) −26.9200 −1.09265 −0.546325 0.837574i \(-0.683973\pi\)
−0.546325 + 0.837574i \(0.683973\pi\)
\(608\) −7.72560 −0.313314
\(609\) −42.5959 −1.72607
\(610\) 35.3128 1.42977
\(611\) −35.6997 −1.44425
\(612\) −1.58901 −0.0642320
\(613\) −27.2210 −1.09945 −0.549724 0.835346i \(-0.685267\pi\)
−0.549724 + 0.835346i \(0.685267\pi\)
\(614\) −38.3852 −1.54910
\(615\) 77.8439 3.13897
\(616\) −7.77009 −0.313066
\(617\) 14.3210 0.576543 0.288271 0.957549i \(-0.406919\pi\)
0.288271 + 0.957549i \(0.406919\pi\)
\(618\) −4.76534 −0.191690
\(619\) −45.7670 −1.83953 −0.919766 0.392468i \(-0.871621\pi\)
−0.919766 + 0.392468i \(0.871621\pi\)
\(620\) −4.34197 −0.174378
\(621\) −13.2415 −0.531365
\(622\) 12.2689 0.491936
\(623\) 43.6594 1.74918
\(624\) 53.5213 2.14257
\(625\) −20.1712 −0.806849
\(626\) −13.1012 −0.523631
\(627\) −17.0155 −0.679534
\(628\) 2.49047 0.0993804
\(629\) 11.0730 0.441509
\(630\) 72.9587 2.90674
\(631\) 25.6636 1.02165 0.510825 0.859685i \(-0.329340\pi\)
0.510825 + 0.859685i \(0.329340\pi\)
\(632\) −13.4616 −0.535475
\(633\) 63.1904 2.51159
\(634\) −28.0922 −1.11569
\(635\) −9.88255 −0.392177
\(636\) −1.84575 −0.0731886
\(637\) −0.913839 −0.0362076
\(638\) 7.03725 0.278607
\(639\) −79.5403 −3.14657
\(640\) −28.8604 −1.14081
\(641\) −14.6785 −0.579767 −0.289883 0.957062i \(-0.593617\pi\)
−0.289883 + 0.957062i \(0.593617\pi\)
\(642\) −46.4626 −1.83373
\(643\) −6.69048 −0.263847 −0.131923 0.991260i \(-0.542115\pi\)
−0.131923 + 0.991260i \(0.542115\pi\)
\(644\) 0.817922 0.0322306
\(645\) 10.0964 0.397545
\(646\) −7.34109 −0.288831
\(647\) 1.06123 0.0417211 0.0208605 0.999782i \(-0.493359\pi\)
0.0208605 + 0.999782i \(0.493359\pi\)
\(648\) 38.3689 1.50727
\(649\) 0.973284 0.0382047
\(650\) −39.0882 −1.53316
\(651\) 42.6730 1.67249
\(652\) 1.31366 0.0514471
\(653\) 27.2507 1.06640 0.533201 0.845988i \(-0.320989\pi\)
0.533201 + 0.845988i \(0.320989\pi\)
\(654\) 37.8987 1.48196
\(655\) 29.4530 1.15082
\(656\) 26.5467 1.03648
\(657\) 65.8690 2.56979
\(658\) −24.3585 −0.949593
\(659\) 3.12236 0.121630 0.0608149 0.998149i \(-0.480630\pi\)
0.0608149 + 0.998149i \(0.480630\pi\)
\(660\) 2.50137 0.0973658
\(661\) −27.4025 −1.06584 −0.532918 0.846167i \(-0.678904\pi\)
−0.532918 + 0.846167i \(0.678904\pi\)
\(662\) 39.8519 1.54889
\(663\) −15.5444 −0.603695
\(664\) −45.1455 −1.75199
\(665\) −47.6570 −1.84806
\(666\) −94.0108 −3.64284
\(667\) −6.72085 −0.260232
\(668\) −3.20391 −0.123963
\(669\) 38.5346 1.48983
\(670\) 47.2680 1.82612
\(671\) −8.10682 −0.312960
\(672\) −11.1617 −0.430573
\(673\) −28.4613 −1.09710 −0.548551 0.836117i \(-0.684820\pi\)
−0.548551 + 0.836117i \(0.684820\pi\)
\(674\) −16.3276 −0.628917
\(675\) −61.0485 −2.34976
\(676\) −3.13837 −0.120706
\(677\) −12.2744 −0.471744 −0.235872 0.971784i \(-0.575795\pi\)
−0.235872 + 0.971784i \(0.575795\pi\)
\(678\) −51.8860 −1.99267
\(679\) −0.819510 −0.0314499
\(680\) 9.79106 0.375470
\(681\) 59.8333 2.29282
\(682\) −7.04999 −0.269958
\(683\) 40.6350 1.55486 0.777428 0.628972i \(-0.216524\pi\)
0.777428 + 0.628972i \(0.216524\pi\)
\(684\) −8.81231 −0.336947
\(685\) −47.4535 −1.81311
\(686\) −24.8214 −0.947684
\(687\) −19.1206 −0.729495
\(688\) 3.44312 0.131268
\(689\) −12.3018 −0.468662
\(690\) 16.8960 0.643219
\(691\) −3.97248 −0.151120 −0.0755601 0.997141i \(-0.524074\pi\)
−0.0755601 + 0.997141i \(0.524074\pi\)
\(692\) 0.842318 0.0320201
\(693\) −16.7492 −0.636251
\(694\) 37.7107 1.43148
\(695\) −70.3762 −2.66952
\(696\) 48.5326 1.83962
\(697\) −7.71007 −0.292040
\(698\) 3.41510 0.129263
\(699\) −11.4062 −0.431422
\(700\) 3.77093 0.142528
\(701\) 13.2868 0.501837 0.250919 0.968008i \(-0.419267\pi\)
0.250919 + 0.968008i \(0.419267\pi\)
\(702\) 70.2440 2.65119
\(703\) 61.4083 2.31606
\(704\) 8.73027 0.329034
\(705\) 71.1440 2.67944
\(706\) 32.8850 1.23764
\(707\) 19.4314 0.730794
\(708\) 0.739834 0.0278047
\(709\) −7.95956 −0.298928 −0.149464 0.988767i \(-0.547755\pi\)
−0.149464 + 0.988767i \(0.547755\pi\)
\(710\) 54.0199 2.02733
\(711\) −29.0179 −1.08826
\(712\) −49.7443 −1.86425
\(713\) 6.73301 0.252153
\(714\) −10.6062 −0.396928
\(715\) 16.6715 0.623480
\(716\) 1.45507 0.0543784
\(717\) 10.7581 0.401767
\(718\) 32.8458 1.22579
\(719\) 12.5936 0.469662 0.234831 0.972036i \(-0.424546\pi\)
0.234831 + 0.972036i \(0.424546\pi\)
\(720\) −72.6693 −2.70823
\(721\) 3.06403 0.114111
\(722\) −15.5613 −0.579131
\(723\) 10.3440 0.384698
\(724\) 0.420779 0.0156381
\(725\) −30.9856 −1.15078
\(726\) 4.06144 0.150734
\(727\) 47.9025 1.77661 0.888303 0.459257i \(-0.151884\pi\)
0.888303 + 0.459257i \(0.151884\pi\)
\(728\) −39.3657 −1.45899
\(729\) −13.7021 −0.507484
\(730\) −44.7350 −1.65572
\(731\) −1.00000 −0.0369863
\(732\) −6.16233 −0.227766
\(733\) 28.5751 1.05545 0.527723 0.849416i \(-0.323046\pi\)
0.527723 + 0.849416i \(0.323046\pi\)
\(734\) −49.6154 −1.83134
\(735\) 1.82114 0.0671738
\(736\) −1.76112 −0.0649157
\(737\) −10.8514 −0.399716
\(738\) 65.4593 2.40959
\(739\) −53.8455 −1.98074 −0.990368 0.138457i \(-0.955786\pi\)
−0.990368 + 0.138457i \(0.955786\pi\)
\(740\) −9.02736 −0.331852
\(741\) −86.2059 −3.16685
\(742\) −8.39374 −0.308144
\(743\) −25.5932 −0.938924 −0.469462 0.882953i \(-0.655552\pi\)
−0.469462 + 0.882953i \(0.655552\pi\)
\(744\) −48.6204 −1.78251
\(745\) 48.3472 1.77130
\(746\) 28.4208 1.04056
\(747\) −97.3158 −3.56060
\(748\) −0.247749 −0.00905861
\(749\) 29.8747 1.09160
\(750\) 11.0725 0.404311
\(751\) −22.3213 −0.814514 −0.407257 0.913314i \(-0.633515\pi\)
−0.407257 + 0.913314i \(0.633515\pi\)
\(752\) 24.2619 0.884740
\(753\) −1.07033 −0.0390048
\(754\) 35.6529 1.29840
\(755\) −0.403537 −0.0146862
\(756\) −6.77660 −0.246463
\(757\) −33.2148 −1.20721 −0.603606 0.797283i \(-0.706270\pi\)
−0.603606 + 0.797283i \(0.706270\pi\)
\(758\) −29.9327 −1.08720
\(759\) −3.87884 −0.140793
\(760\) 54.2991 1.96963
\(761\) −33.1364 −1.20119 −0.600597 0.799552i \(-0.705070\pi\)
−0.600597 + 0.799552i \(0.705070\pi\)
\(762\) −12.1974 −0.441864
\(763\) −24.3682 −0.882190
\(764\) 2.21618 0.0801785
\(765\) 21.1056 0.763076
\(766\) −7.26461 −0.262481
\(767\) 4.93096 0.178047
\(768\) 17.9519 0.647783
\(769\) −29.2335 −1.05419 −0.527093 0.849807i \(-0.676718\pi\)
−0.527093 + 0.849807i \(0.676718\pi\)
\(770\) 11.3753 0.409937
\(771\) −62.1153 −2.23703
\(772\) −2.13997 −0.0770190
\(773\) 13.6889 0.492354 0.246177 0.969225i \(-0.420825\pi\)
0.246177 + 0.969225i \(0.420825\pi\)
\(774\) 8.49010 0.305171
\(775\) 31.0417 1.11505
\(776\) 0.933728 0.0335189
\(777\) 88.7211 3.18285
\(778\) −30.3303 −1.08739
\(779\) −42.7584 −1.53198
\(780\) 12.6727 0.453757
\(781\) −12.4014 −0.443759
\(782\) −1.67347 −0.0598431
\(783\) 55.6832 1.98996
\(784\) 0.621055 0.0221805
\(785\) −33.0790 −1.18064
\(786\) 36.3518 1.29663
\(787\) −3.01198 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(788\) −0.227934 −0.00811981
\(789\) 41.0937 1.46298
\(790\) 19.7076 0.701165
\(791\) 33.3618 1.18621
\(792\) 19.0836 0.678107
\(793\) −41.0717 −1.45850
\(794\) 4.99347 0.177212
\(795\) 24.5157 0.869481
\(796\) −1.36243 −0.0482901
\(797\) −27.4119 −0.970981 −0.485490 0.874242i \(-0.661359\pi\)
−0.485490 + 0.874242i \(0.661359\pi\)
\(798\) −58.8198 −2.08220
\(799\) −7.04648 −0.249287
\(800\) −8.11941 −0.287065
\(801\) −107.229 −3.78875
\(802\) −12.0510 −0.425537
\(803\) 10.2699 0.362417
\(804\) −8.24859 −0.290905
\(805\) −10.8638 −0.382900
\(806\) −35.7175 −1.25809
\(807\) −32.2584 −1.13555
\(808\) −22.1396 −0.778869
\(809\) 29.0679 1.02197 0.510986 0.859589i \(-0.329280\pi\)
0.510986 + 0.859589i \(0.329280\pi\)
\(810\) −56.1714 −1.97366
\(811\) −45.1234 −1.58450 −0.792249 0.610198i \(-0.791090\pi\)
−0.792249 + 0.610198i \(0.791090\pi\)
\(812\) −3.43952 −0.120703
\(813\) 50.0507 1.75535
\(814\) −14.6576 −0.513748
\(815\) −17.4484 −0.611191
\(816\) 10.5642 0.369819
\(817\) −5.54578 −0.194022
\(818\) 27.2980 0.954453
\(819\) −84.8569 −2.96514
\(820\) 6.28571 0.219507
\(821\) 14.8790 0.519279 0.259640 0.965706i \(-0.416396\pi\)
0.259640 + 0.965706i \(0.416396\pi\)
\(822\) −58.5687 −2.04282
\(823\) 49.1389 1.71287 0.856437 0.516251i \(-0.172673\pi\)
0.856437 + 0.516251i \(0.172673\pi\)
\(824\) −3.49107 −0.121617
\(825\) −17.8829 −0.622602
\(826\) 3.36448 0.117065
\(827\) 35.6216 1.23868 0.619342 0.785121i \(-0.287399\pi\)
0.619342 + 0.785121i \(0.287399\pi\)
\(828\) −2.00884 −0.0698122
\(829\) −18.2847 −0.635052 −0.317526 0.948249i \(-0.602852\pi\)
−0.317526 + 0.948249i \(0.602852\pi\)
\(830\) 66.0922 2.29409
\(831\) −82.1127 −2.84846
\(832\) 44.2303 1.53341
\(833\) −0.180376 −0.00624964
\(834\) −86.8605 −3.00773
\(835\) 42.5551 1.47268
\(836\) −1.37396 −0.0475195
\(837\) −55.7840 −1.92818
\(838\) 39.1562 1.35263
\(839\) 50.2858 1.73606 0.868029 0.496514i \(-0.165387\pi\)
0.868029 + 0.496514i \(0.165387\pi\)
\(840\) 78.4499 2.70678
\(841\) −0.737536 −0.0254323
\(842\) 53.1150 1.83046
\(843\) 6.79040 0.233874
\(844\) 5.10248 0.175635
\(845\) 41.6845 1.43399
\(846\) 59.8254 2.05684
\(847\) −2.61144 −0.0897302
\(848\) 8.36045 0.287099
\(849\) 8.81290 0.302458
\(850\) −7.71531 −0.264633
\(851\) 13.9986 0.479865
\(852\) −9.42686 −0.322959
\(853\) 40.6167 1.39069 0.695345 0.718676i \(-0.255252\pi\)
0.695345 + 0.718676i \(0.255252\pi\)
\(854\) −28.0239 −0.958959
\(855\) 117.047 4.00293
\(856\) −34.0384 −1.16341
\(857\) −19.3959 −0.662550 −0.331275 0.943534i \(-0.607479\pi\)
−0.331275 + 0.943534i \(0.607479\pi\)
\(858\) 20.5765 0.702471
\(859\) 11.5975 0.395701 0.197851 0.980232i \(-0.436604\pi\)
0.197851 + 0.980232i \(0.436604\pi\)
\(860\) 0.815260 0.0278001
\(861\) −61.7762 −2.10533
\(862\) −2.93264 −0.0998861
\(863\) −22.9365 −0.780769 −0.390385 0.920652i \(-0.627658\pi\)
−0.390385 + 0.920652i \(0.627658\pi\)
\(864\) 14.5911 0.496400
\(865\) −11.1879 −0.380399
\(866\) 24.1554 0.820834
\(867\) −3.06819 −0.104201
\(868\) 3.44574 0.116956
\(869\) −4.52430 −0.153476
\(870\) −71.0508 −2.40885
\(871\) −54.9765 −1.86281
\(872\) 27.7645 0.940225
\(873\) 2.01275 0.0681212
\(874\) −9.28068 −0.313924
\(875\) −7.11945 −0.240681
\(876\) 7.80658 0.263760
\(877\) 3.94279 0.133139 0.0665694 0.997782i \(-0.478795\pi\)
0.0665694 + 0.997782i \(0.478795\pi\)
\(878\) −24.3675 −0.822363
\(879\) −38.7106 −1.30568
\(880\) −11.3302 −0.381940
\(881\) 23.1435 0.779725 0.389863 0.920873i \(-0.372522\pi\)
0.389863 + 0.920873i \(0.372522\pi\)
\(882\) 1.53141 0.0515652
\(883\) 27.3514 0.920447 0.460223 0.887803i \(-0.347769\pi\)
0.460223 + 0.887803i \(0.347769\pi\)
\(884\) −1.25517 −0.0422161
\(885\) −9.82665 −0.330319
\(886\) 24.7927 0.832926
\(887\) −5.94032 −0.199457 −0.0997283 0.995015i \(-0.531797\pi\)
−0.0997283 + 0.995015i \(0.531797\pi\)
\(888\) −101.086 −3.39224
\(889\) 7.84270 0.263036
\(890\) 72.8248 2.44109
\(891\) 12.8954 0.432011
\(892\) 3.11158 0.104183
\(893\) −39.0782 −1.30770
\(894\) 59.6716 1.99572
\(895\) −19.3265 −0.646015
\(896\) 22.9033 0.765146
\(897\) −19.6514 −0.656141
\(898\) 16.3078 0.544199
\(899\) −28.3136 −0.944312
\(900\) −9.26153 −0.308718
\(901\) −2.42816 −0.0808937
\(902\) 10.2060 0.339823
\(903\) −8.01240 −0.266636
\(904\) −38.0116 −1.26425
\(905\) −5.58889 −0.185781
\(906\) −0.498058 −0.0165469
\(907\) −41.4801 −1.37732 −0.688662 0.725082i \(-0.741802\pi\)
−0.688662 + 0.725082i \(0.741802\pi\)
\(908\) 4.83140 0.160336
\(909\) −47.7242 −1.58291
\(910\) 57.6307 1.91044
\(911\) −38.2395 −1.26693 −0.633466 0.773770i \(-0.718368\pi\)
−0.633466 + 0.773770i \(0.718368\pi\)
\(912\) 58.5865 1.93999
\(913\) −15.1729 −0.502150
\(914\) 34.4900 1.14083
\(915\) 81.8496 2.70586
\(916\) −1.54394 −0.0510133
\(917\) −23.3736 −0.771865
\(918\) 13.8649 0.457611
\(919\) 52.5976 1.73503 0.867517 0.497407i \(-0.165715\pi\)
0.867517 + 0.497407i \(0.165715\pi\)
\(920\) 12.3780 0.408089
\(921\) −88.9708 −2.93169
\(922\) 14.3921 0.473979
\(923\) −62.8296 −2.06806
\(924\) −1.98507 −0.0653039
\(925\) 64.5387 2.12202
\(926\) −46.3837 −1.52426
\(927\) −7.52537 −0.247166
\(928\) 7.40584 0.243109
\(929\) −7.29117 −0.239215 −0.119608 0.992821i \(-0.538164\pi\)
−0.119608 + 0.992821i \(0.538164\pi\)
\(930\) 71.1795 2.33407
\(931\) −1.00032 −0.0327843
\(932\) −0.921024 −0.0301691
\(933\) 28.4373 0.930995
\(934\) 18.7876 0.614750
\(935\) 3.29067 0.107616
\(936\) 96.6836 3.16020
\(937\) −22.6136 −0.738756 −0.369378 0.929279i \(-0.620429\pi\)
−0.369378 + 0.929279i \(0.620429\pi\)
\(938\) −37.5114 −1.22479
\(939\) −30.3666 −0.990977
\(940\) 5.74471 0.187372
\(941\) 44.6558 1.45574 0.727868 0.685717i \(-0.240511\pi\)
0.727868 + 0.685717i \(0.240511\pi\)
\(942\) −40.8271 −1.33022
\(943\) −9.74715 −0.317411
\(944\) −3.35113 −0.109070
\(945\) 90.0085 2.92798
\(946\) 1.32373 0.0430380
\(947\) 6.21336 0.201907 0.100953 0.994891i \(-0.467811\pi\)
0.100953 + 0.994891i \(0.467811\pi\)
\(948\) −3.43911 −0.111697
\(949\) 52.0305 1.68898
\(950\) −42.7874 −1.38821
\(951\) −65.1134 −2.11145
\(952\) −7.77009 −0.251830
\(953\) −8.97776 −0.290818 −0.145409 0.989372i \(-0.546450\pi\)
−0.145409 + 0.989372i \(0.546450\pi\)
\(954\) 20.6153 0.667446
\(955\) −29.4358 −0.952520
\(956\) 0.868689 0.0280954
\(957\) 16.3113 0.527268
\(958\) 4.72908 0.152790
\(959\) 37.6587 1.21606
\(960\) −88.1442 −2.84484
\(961\) −2.63512 −0.0850039
\(962\) −74.2599 −2.39424
\(963\) −73.3733 −2.36442
\(964\) 0.835255 0.0269017
\(965\) 28.4235 0.914986
\(966\) −13.4085 −0.431411
\(967\) 32.1152 1.03275 0.516377 0.856361i \(-0.327280\pi\)
0.516377 + 0.856361i \(0.327280\pi\)
\(968\) 2.97540 0.0956331
\(969\) −17.0155 −0.546617
\(970\) −1.36696 −0.0438905
\(971\) −25.3868 −0.814702 −0.407351 0.913272i \(-0.633547\pi\)
−0.407351 + 0.913272i \(0.633547\pi\)
\(972\) 2.01740 0.0647082
\(973\) 55.8499 1.79046
\(974\) −51.5075 −1.65041
\(975\) −90.6003 −2.90153
\(976\) 27.9128 0.893466
\(977\) 60.5451 1.93701 0.968505 0.248994i \(-0.0801000\pi\)
0.968505 + 0.248994i \(0.0801000\pi\)
\(978\) −21.5354 −0.688625
\(979\) −16.7185 −0.534326
\(980\) 0.147053 0.00469743
\(981\) 59.8493 1.91084
\(982\) 32.1930 1.02732
\(983\) 4.25333 0.135660 0.0678301 0.997697i \(-0.478392\pi\)
0.0678301 + 0.997697i \(0.478392\pi\)
\(984\) 70.3861 2.24383
\(985\) 3.02748 0.0964634
\(986\) 7.03725 0.224112
\(987\) −56.4592 −1.79712
\(988\) −6.96092 −0.221456
\(989\) −1.26421 −0.0401995
\(990\) −27.9381 −0.887931
\(991\) −5.11660 −0.162534 −0.0812671 0.996692i \(-0.525897\pi\)
−0.0812671 + 0.996692i \(0.525897\pi\)
\(992\) −7.41925 −0.235561
\(993\) 92.3705 2.93129
\(994\) −42.8697 −1.35974
\(995\) 18.0962 0.573687
\(996\) −11.5336 −0.365455
\(997\) 23.4779 0.743553 0.371777 0.928322i \(-0.378749\pi\)
0.371777 + 0.928322i \(0.378749\pi\)
\(998\) 44.9988 1.42441
\(999\) −115.980 −3.66945
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 8041.2.a.c.1.19 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8041.2.a.c.1.19 60 1.1 even 1 trivial