Properties

Label 6029.2.a.a.1.15
Level $6029$
Weight $2$
Character 6029.1
Self dual yes
Analytic conductor $48.142$
Analytic rank $1$
Dimension $234$
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] = [6029,2,Mod(1,6029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6029 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6029.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: \(48.1418073786\)
Analytic rank: \(1\)
Dimension: \(234\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 6029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.51561 q^{2} +0.109654 q^{3} +4.32830 q^{4} -3.06491 q^{5} -0.275847 q^{6} +2.34212 q^{7} -5.85711 q^{8} -2.98798 q^{9} +O(q^{10})\) \(q-2.51561 q^{2} +0.109654 q^{3} +4.32830 q^{4} -3.06491 q^{5} -0.275847 q^{6} +2.34212 q^{7} -5.85711 q^{8} -2.98798 q^{9} +7.71012 q^{10} +5.97568 q^{11} +0.474617 q^{12} +1.37139 q^{13} -5.89186 q^{14} -0.336080 q^{15} +6.07760 q^{16} +1.44330 q^{17} +7.51659 q^{18} -7.12936 q^{19} -13.2659 q^{20} +0.256823 q^{21} -15.0325 q^{22} +0.0744293 q^{23} -0.642256 q^{24} +4.39366 q^{25} -3.44989 q^{26} -0.656607 q^{27} +10.1374 q^{28} +4.48625 q^{29} +0.845447 q^{30} +2.15670 q^{31} -3.57468 q^{32} +0.655258 q^{33} -3.63077 q^{34} -7.17838 q^{35} -12.9329 q^{36} -9.59831 q^{37} +17.9347 q^{38} +0.150379 q^{39} +17.9515 q^{40} +8.99353 q^{41} -0.646067 q^{42} -3.85591 q^{43} +25.8646 q^{44} +9.15787 q^{45} -0.187235 q^{46} +3.94668 q^{47} +0.666435 q^{48} -1.51449 q^{49} -11.0528 q^{50} +0.158264 q^{51} +5.93580 q^{52} +3.97955 q^{53} +1.65177 q^{54} -18.3149 q^{55} -13.7180 q^{56} -0.781765 q^{57} -11.2857 q^{58} -11.3592 q^{59} -1.45466 q^{60} -12.8104 q^{61} -5.42541 q^{62} -6.99819 q^{63} -3.16271 q^{64} -4.20319 q^{65} -1.64838 q^{66} -2.39098 q^{67} +6.24703 q^{68} +0.00816148 q^{69} +18.0580 q^{70} -3.03894 q^{71} +17.5009 q^{72} +2.90445 q^{73} +24.1456 q^{74} +0.481784 q^{75} -30.8580 q^{76} +13.9957 q^{77} -0.378295 q^{78} +13.4125 q^{79} -18.6273 q^{80} +8.89193 q^{81} -22.6242 q^{82} -13.7443 q^{83} +1.11161 q^{84} -4.42357 q^{85} +9.69996 q^{86} +0.491936 q^{87} -35.0002 q^{88} -0.765554 q^{89} -23.0377 q^{90} +3.21196 q^{91} +0.322153 q^{92} +0.236491 q^{93} -9.92830 q^{94} +21.8508 q^{95} -0.391978 q^{96} +16.1047 q^{97} +3.80986 q^{98} -17.8552 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51561 −1.77881 −0.889403 0.457124i \(-0.848880\pi\)
−0.889403 + 0.457124i \(0.848880\pi\)
\(3\) 0.109654 0.0633089 0.0316544 0.999499i \(-0.489922\pi\)
0.0316544 + 0.999499i \(0.489922\pi\)
\(4\) 4.32830 2.16415
\(5\) −3.06491 −1.37067 −0.685334 0.728229i \(-0.740344\pi\)
−0.685334 + 0.728229i \(0.740344\pi\)
\(6\) −0.275847 −0.112614
\(7\) 2.34212 0.885237 0.442619 0.896710i \(-0.354050\pi\)
0.442619 + 0.896710i \(0.354050\pi\)
\(8\) −5.85711 −2.07080
\(9\) −2.98798 −0.995992
\(10\) 7.71012 2.43815
\(11\) 5.97568 1.80174 0.900868 0.434094i \(-0.142931\pi\)
0.900868 + 0.434094i \(0.142931\pi\)
\(12\) 0.474617 0.137010
\(13\) 1.37139 0.380355 0.190178 0.981750i \(-0.439094\pi\)
0.190178 + 0.981750i \(0.439094\pi\)
\(14\) −5.89186 −1.57467
\(15\) −0.336080 −0.0867755
\(16\) 6.07760 1.51940
\(17\) 1.44330 0.350051 0.175025 0.984564i \(-0.443999\pi\)
0.175025 + 0.984564i \(0.443999\pi\)
\(18\) 7.51659 1.77168
\(19\) −7.12936 −1.63559 −0.817794 0.575511i \(-0.804803\pi\)
−0.817794 + 0.575511i \(0.804803\pi\)
\(20\) −13.2659 −2.96634
\(21\) 0.256823 0.0560434
\(22\) −15.0325 −3.20494
\(23\) 0.0744293 0.0155196 0.00775979 0.999970i \(-0.497530\pi\)
0.00775979 + 0.999970i \(0.497530\pi\)
\(24\) −0.642256 −0.131100
\(25\) 4.39366 0.878733
\(26\) −3.44989 −0.676578
\(27\) −0.656607 −0.126364
\(28\) 10.1374 1.91579
\(29\) 4.48625 0.833075 0.416538 0.909119i \(-0.363243\pi\)
0.416538 + 0.909119i \(0.363243\pi\)
\(30\) 0.845447 0.154357
\(31\) 2.15670 0.387354 0.193677 0.981065i \(-0.437959\pi\)
0.193677 + 0.981065i \(0.437959\pi\)
\(32\) −3.57468 −0.631920
\(33\) 0.655258 0.114066
\(34\) −3.63077 −0.622673
\(35\) −7.17838 −1.21337
\(36\) −12.9329 −2.15548
\(37\) −9.59831 −1.57795 −0.788976 0.614424i \(-0.789389\pi\)
−0.788976 + 0.614424i \(0.789389\pi\)
\(38\) 17.9347 2.90939
\(39\) 0.150379 0.0240799
\(40\) 17.9515 2.83838
\(41\) 8.99353 1.40455 0.702276 0.711904i \(-0.252167\pi\)
0.702276 + 0.711904i \(0.252167\pi\)
\(42\) −0.646067 −0.0996903
\(43\) −3.85591 −0.588020 −0.294010 0.955802i \(-0.594990\pi\)
−0.294010 + 0.955802i \(0.594990\pi\)
\(44\) 25.8646 3.89923
\(45\) 9.15787 1.36518
\(46\) −0.187235 −0.0276063
\(47\) 3.94668 0.575682 0.287841 0.957678i \(-0.407063\pi\)
0.287841 + 0.957678i \(0.407063\pi\)
\(48\) 0.666435 0.0961916
\(49\) −1.51449 −0.216355
\(50\) −11.0528 −1.56310
\(51\) 0.158264 0.0221613
\(52\) 5.93580 0.823147
\(53\) 3.97955 0.546633 0.273317 0.961924i \(-0.411879\pi\)
0.273317 + 0.961924i \(0.411879\pi\)
\(54\) 1.65177 0.224777
\(55\) −18.3149 −2.46958
\(56\) −13.7180 −1.83315
\(57\) −0.781765 −0.103547
\(58\) −11.2857 −1.48188
\(59\) −11.3592 −1.47884 −0.739418 0.673246i \(-0.764899\pi\)
−0.739418 + 0.673246i \(0.764899\pi\)
\(60\) −1.45466 −0.187795
\(61\) −12.8104 −1.64021 −0.820105 0.572213i \(-0.806085\pi\)
−0.820105 + 0.572213i \(0.806085\pi\)
\(62\) −5.42541 −0.689028
\(63\) −6.99819 −0.881689
\(64\) −3.16271 −0.395338
\(65\) −4.20319 −0.521341
\(66\) −1.64838 −0.202901
\(67\) −2.39098 −0.292104 −0.146052 0.989277i \(-0.546657\pi\)
−0.146052 + 0.989277i \(0.546657\pi\)
\(68\) 6.24703 0.757563
\(69\) 0.00816148 0.000982527 0
\(70\) 18.0580 2.15834
\(71\) −3.03894 −0.360656 −0.180328 0.983607i \(-0.557716\pi\)
−0.180328 + 0.983607i \(0.557716\pi\)
\(72\) 17.5009 2.06250
\(73\) 2.90445 0.339940 0.169970 0.985449i \(-0.445633\pi\)
0.169970 + 0.985449i \(0.445633\pi\)
\(74\) 24.1456 2.80687
\(75\) 0.481784 0.0556316
\(76\) −30.8580 −3.53966
\(77\) 13.9957 1.59496
\(78\) −0.378295 −0.0428334
\(79\) 13.4125 1.50902 0.754512 0.656287i \(-0.227874\pi\)
0.754512 + 0.656287i \(0.227874\pi\)
\(80\) −18.6273 −2.08260
\(81\) 8.89193 0.987992
\(82\) −22.6242 −2.49843
\(83\) −13.7443 −1.50863 −0.754315 0.656512i \(-0.772031\pi\)
−0.754315 + 0.656512i \(0.772031\pi\)
\(84\) 1.11161 0.121286
\(85\) −4.42357 −0.479804
\(86\) 9.69996 1.04597
\(87\) 0.491936 0.0527410
\(88\) −35.0002 −3.73103
\(89\) −0.765554 −0.0811486 −0.0405743 0.999177i \(-0.512919\pi\)
−0.0405743 + 0.999177i \(0.512919\pi\)
\(90\) −23.0377 −2.42838
\(91\) 3.21196 0.336705
\(92\) 0.322153 0.0335867
\(93\) 0.236491 0.0245230
\(94\) −9.92830 −1.02403
\(95\) 21.8508 2.24185
\(96\) −0.391978 −0.0400061
\(97\) 16.1047 1.63518 0.817591 0.575800i \(-0.195309\pi\)
0.817591 + 0.575800i \(0.195309\pi\)
\(98\) 3.80986 0.384854
\(99\) −17.8552 −1.79451
\(100\) 19.0171 1.90171
\(101\) 2.41605 0.240406 0.120203 0.992749i \(-0.461645\pi\)
0.120203 + 0.992749i \(0.461645\pi\)
\(102\) −0.398130 −0.0394207
\(103\) −12.8673 −1.26786 −0.633929 0.773391i \(-0.718559\pi\)
−0.633929 + 0.773391i \(0.718559\pi\)
\(104\) −8.03238 −0.787640
\(105\) −0.787139 −0.0768169
\(106\) −10.0110 −0.972354
\(107\) −3.77762 −0.365196 −0.182598 0.983188i \(-0.558451\pi\)
−0.182598 + 0.983188i \(0.558451\pi\)
\(108\) −2.84199 −0.273471
\(109\) −14.1078 −1.35129 −0.675643 0.737229i \(-0.736134\pi\)
−0.675643 + 0.737229i \(0.736134\pi\)
\(110\) 46.0732 4.39291
\(111\) −1.05250 −0.0998984
\(112\) 14.2345 1.34503
\(113\) 5.62655 0.529301 0.264650 0.964344i \(-0.414743\pi\)
0.264650 + 0.964344i \(0.414743\pi\)
\(114\) 1.96662 0.184190
\(115\) −0.228119 −0.0212722
\(116\) 19.4178 1.80290
\(117\) −4.09768 −0.378831
\(118\) 28.5752 2.63056
\(119\) 3.38037 0.309878
\(120\) 1.96846 0.179695
\(121\) 24.7088 2.24625
\(122\) 32.2261 2.91762
\(123\) 0.986178 0.0889207
\(124\) 9.33484 0.838293
\(125\) 1.85836 0.166217
\(126\) 17.6047 1.56835
\(127\) −4.50963 −0.400165 −0.200082 0.979779i \(-0.564121\pi\)
−0.200082 + 0.979779i \(0.564121\pi\)
\(128\) 15.1055 1.33515
\(129\) −0.422816 −0.0372269
\(130\) 10.5736 0.927365
\(131\) −9.42940 −0.823851 −0.411925 0.911218i \(-0.635144\pi\)
−0.411925 + 0.911218i \(0.635144\pi\)
\(132\) 2.83616 0.246856
\(133\) −16.6978 −1.44788
\(134\) 6.01477 0.519597
\(135\) 2.01244 0.173203
\(136\) −8.45354 −0.724885
\(137\) 11.2200 0.958592 0.479296 0.877653i \(-0.340892\pi\)
0.479296 + 0.877653i \(0.340892\pi\)
\(138\) −0.0205311 −0.00174773
\(139\) 20.5009 1.73886 0.869432 0.494052i \(-0.164485\pi\)
0.869432 + 0.494052i \(0.164485\pi\)
\(140\) −31.0702 −2.62591
\(141\) 0.432769 0.0364458
\(142\) 7.64480 0.641537
\(143\) 8.19499 0.685300
\(144\) −18.1597 −1.51331
\(145\) −13.7499 −1.14187
\(146\) −7.30646 −0.604687
\(147\) −0.166070 −0.0136972
\(148\) −41.5444 −3.41493
\(149\) −0.179490 −0.0147044 −0.00735218 0.999973i \(-0.502340\pi\)
−0.00735218 + 0.999973i \(0.502340\pi\)
\(150\) −1.21198 −0.0989578
\(151\) 7.30082 0.594132 0.297066 0.954857i \(-0.403992\pi\)
0.297066 + 0.954857i \(0.403992\pi\)
\(152\) 41.7575 3.38698
\(153\) −4.31254 −0.348648
\(154\) −35.2079 −2.83713
\(155\) −6.61008 −0.530934
\(156\) 0.650885 0.0521125
\(157\) −2.39448 −0.191101 −0.0955503 0.995425i \(-0.530461\pi\)
−0.0955503 + 0.995425i \(0.530461\pi\)
\(158\) −33.7406 −2.68426
\(159\) 0.436374 0.0346067
\(160\) 10.9561 0.866153
\(161\) 0.174322 0.0137385
\(162\) −22.3686 −1.75745
\(163\) −11.5948 −0.908171 −0.454086 0.890958i \(-0.650034\pi\)
−0.454086 + 0.890958i \(0.650034\pi\)
\(164\) 38.9267 3.03967
\(165\) −2.00831 −0.156346
\(166\) 34.5753 2.68356
\(167\) −15.7489 −1.21869 −0.609343 0.792907i \(-0.708567\pi\)
−0.609343 + 0.792907i \(0.708567\pi\)
\(168\) −1.50424 −0.116055
\(169\) −11.1193 −0.855330
\(170\) 11.1280 0.853478
\(171\) 21.3024 1.62903
\(172\) −16.6895 −1.27256
\(173\) 10.3400 0.786134 0.393067 0.919510i \(-0.371414\pi\)
0.393067 + 0.919510i \(0.371414\pi\)
\(174\) −1.23752 −0.0938161
\(175\) 10.2905 0.777887
\(176\) 36.3178 2.73756
\(177\) −1.24558 −0.0936235
\(178\) 1.92584 0.144348
\(179\) −1.71846 −0.128444 −0.0642220 0.997936i \(-0.520457\pi\)
−0.0642220 + 0.997936i \(0.520457\pi\)
\(180\) 39.6381 2.95445
\(181\) −6.60119 −0.490662 −0.245331 0.969439i \(-0.578897\pi\)
−0.245331 + 0.969439i \(0.578897\pi\)
\(182\) −8.08004 −0.598932
\(183\) −1.40472 −0.103840
\(184\) −0.435940 −0.0321380
\(185\) 29.4179 2.16285
\(186\) −0.594919 −0.0436216
\(187\) 8.62468 0.630699
\(188\) 17.0824 1.24586
\(189\) −1.53785 −0.111862
\(190\) −54.9682 −3.98782
\(191\) 9.45777 0.684340 0.342170 0.939638i \(-0.388838\pi\)
0.342170 + 0.939638i \(0.388838\pi\)
\(192\) −0.346804 −0.0250284
\(193\) 23.2393 1.67280 0.836399 0.548121i \(-0.184657\pi\)
0.836399 + 0.548121i \(0.184657\pi\)
\(194\) −40.5131 −2.90867
\(195\) −0.460897 −0.0330055
\(196\) −6.55516 −0.468225
\(197\) −1.04491 −0.0744467 −0.0372234 0.999307i \(-0.511851\pi\)
−0.0372234 + 0.999307i \(0.511851\pi\)
\(198\) 44.9167 3.19209
\(199\) −26.9437 −1.90999 −0.954994 0.296626i \(-0.904138\pi\)
−0.954994 + 0.296626i \(0.904138\pi\)
\(200\) −25.7342 −1.81968
\(201\) −0.262181 −0.0184928
\(202\) −6.07784 −0.427635
\(203\) 10.5073 0.737469
\(204\) 0.685013 0.0479605
\(205\) −27.5643 −1.92518
\(206\) 32.3693 2.25527
\(207\) −0.222393 −0.0154574
\(208\) 8.33477 0.577912
\(209\) −42.6028 −2.94690
\(210\) 1.98014 0.136642
\(211\) −16.5729 −1.14093 −0.570463 0.821323i \(-0.693236\pi\)
−0.570463 + 0.821323i \(0.693236\pi\)
\(212\) 17.2247 1.18300
\(213\) −0.333233 −0.0228327
\(214\) 9.50303 0.649613
\(215\) 11.8180 0.805981
\(216\) 3.84582 0.261675
\(217\) 5.05124 0.342900
\(218\) 35.4898 2.40368
\(219\) 0.318485 0.0215212
\(220\) −79.2725 −5.34455
\(221\) 1.97932 0.133144
\(222\) 2.64767 0.177700
\(223\) 3.08329 0.206472 0.103236 0.994657i \(-0.467080\pi\)
0.103236 + 0.994657i \(0.467080\pi\)
\(224\) −8.37232 −0.559399
\(225\) −13.1282 −0.875211
\(226\) −14.1542 −0.941524
\(227\) 3.64014 0.241605 0.120802 0.992677i \(-0.461453\pi\)
0.120802 + 0.992677i \(0.461453\pi\)
\(228\) −3.38371 −0.224092
\(229\) −8.09614 −0.535008 −0.267504 0.963557i \(-0.586199\pi\)
−0.267504 + 0.963557i \(0.586199\pi\)
\(230\) 0.573859 0.0378391
\(231\) 1.53469 0.100975
\(232\) −26.2764 −1.72513
\(233\) −28.9808 −1.89860 −0.949298 0.314378i \(-0.898204\pi\)
−0.949298 + 0.314378i \(0.898204\pi\)
\(234\) 10.3082 0.673867
\(235\) −12.0962 −0.789069
\(236\) −49.1659 −3.20043
\(237\) 1.47074 0.0955346
\(238\) −8.50370 −0.551213
\(239\) 27.9834 1.81009 0.905047 0.425312i \(-0.139836\pi\)
0.905047 + 0.425312i \(0.139836\pi\)
\(240\) −2.04256 −0.131847
\(241\) 14.9674 0.964137 0.482068 0.876134i \(-0.339886\pi\)
0.482068 + 0.876134i \(0.339886\pi\)
\(242\) −62.1577 −3.99565
\(243\) 2.94486 0.188913
\(244\) −55.4475 −3.54966
\(245\) 4.64176 0.296551
\(246\) −2.48084 −0.158173
\(247\) −9.77714 −0.622105
\(248\) −12.6320 −0.802133
\(249\) −1.50712 −0.0955097
\(250\) −4.67492 −0.295668
\(251\) 12.3891 0.781991 0.390996 0.920393i \(-0.372131\pi\)
0.390996 + 0.920393i \(0.372131\pi\)
\(252\) −30.2903 −1.90811
\(253\) 0.444766 0.0279622
\(254\) 11.3445 0.711816
\(255\) −0.485063 −0.0303758
\(256\) −31.6742 −1.97963
\(257\) −6.37361 −0.397575 −0.198788 0.980043i \(-0.563700\pi\)
−0.198788 + 0.980043i \(0.563700\pi\)
\(258\) 1.06364 0.0662194
\(259\) −22.4804 −1.39686
\(260\) −18.1927 −1.12826
\(261\) −13.4048 −0.829736
\(262\) 23.7207 1.46547
\(263\) 28.2867 1.74423 0.872116 0.489299i \(-0.162747\pi\)
0.872116 + 0.489299i \(0.162747\pi\)
\(264\) −3.83792 −0.236208
\(265\) −12.1970 −0.749253
\(266\) 42.0052 2.57550
\(267\) −0.0839463 −0.00513743
\(268\) −10.3489 −0.632158
\(269\) −13.8923 −0.847026 −0.423513 0.905890i \(-0.639203\pi\)
−0.423513 + 0.905890i \(0.639203\pi\)
\(270\) −5.06252 −0.308095
\(271\) 22.1281 1.34419 0.672093 0.740467i \(-0.265396\pi\)
0.672093 + 0.740467i \(0.265396\pi\)
\(272\) 8.77179 0.531868
\(273\) 0.352205 0.0213164
\(274\) −28.2252 −1.70515
\(275\) 26.2551 1.58324
\(276\) 0.0353254 0.00212634
\(277\) −5.50198 −0.330582 −0.165291 0.986245i \(-0.552856\pi\)
−0.165291 + 0.986245i \(0.552856\pi\)
\(278\) −51.5723 −3.09310
\(279\) −6.44416 −0.385802
\(280\) 42.0445 2.51264
\(281\) −24.7559 −1.47682 −0.738408 0.674354i \(-0.764422\pi\)
−0.738408 + 0.674354i \(0.764422\pi\)
\(282\) −1.08868 −0.0648300
\(283\) 18.0241 1.07142 0.535710 0.844402i \(-0.320044\pi\)
0.535710 + 0.844402i \(0.320044\pi\)
\(284\) −13.1535 −0.780515
\(285\) 2.39604 0.141929
\(286\) −20.6154 −1.21902
\(287\) 21.0639 1.24336
\(288\) 10.6811 0.629387
\(289\) −14.9169 −0.877464
\(290\) 34.5895 2.03117
\(291\) 1.76594 0.103521
\(292\) 12.5713 0.735681
\(293\) 16.4441 0.960677 0.480338 0.877083i \(-0.340514\pi\)
0.480338 + 0.877083i \(0.340514\pi\)
\(294\) 0.417767 0.0243647
\(295\) 34.8148 2.02700
\(296\) 56.2184 3.26763
\(297\) −3.92367 −0.227675
\(298\) 0.451526 0.0261562
\(299\) 0.102072 0.00590296
\(300\) 2.08531 0.120395
\(301\) −9.03098 −0.520537
\(302\) −18.3660 −1.05685
\(303\) 0.264930 0.0152198
\(304\) −43.3295 −2.48511
\(305\) 39.2628 2.24818
\(306\) 10.8487 0.620177
\(307\) −7.36738 −0.420479 −0.210239 0.977650i \(-0.567424\pi\)
−0.210239 + 0.977650i \(0.567424\pi\)
\(308\) 60.5778 3.45174
\(309\) −1.41096 −0.0802666
\(310\) 16.6284 0.944429
\(311\) −4.52462 −0.256568 −0.128284 0.991737i \(-0.540947\pi\)
−0.128284 + 0.991737i \(0.540947\pi\)
\(312\) −0.880785 −0.0498646
\(313\) 11.3604 0.642130 0.321065 0.947057i \(-0.395959\pi\)
0.321065 + 0.947057i \(0.395959\pi\)
\(314\) 6.02359 0.339931
\(315\) 21.4488 1.20850
\(316\) 58.0533 3.26576
\(317\) 5.13238 0.288263 0.144131 0.989559i \(-0.453961\pi\)
0.144131 + 0.989559i \(0.453961\pi\)
\(318\) −1.09775 −0.0615587
\(319\) 26.8084 1.50098
\(320\) 9.69340 0.541878
\(321\) −0.414232 −0.0231202
\(322\) −0.438527 −0.0244381
\(323\) −10.2898 −0.572539
\(324\) 38.4870 2.13816
\(325\) 6.02543 0.334231
\(326\) 29.1679 1.61546
\(327\) −1.54698 −0.0855484
\(328\) −52.6761 −2.90855
\(329\) 9.24358 0.509615
\(330\) 5.05212 0.278110
\(331\) −13.9866 −0.768771 −0.384386 0.923173i \(-0.625587\pi\)
−0.384386 + 0.923173i \(0.625587\pi\)
\(332\) −59.4894 −3.26491
\(333\) 28.6795 1.57163
\(334\) 39.6181 2.16781
\(335\) 7.32813 0.400378
\(336\) 1.56087 0.0851524
\(337\) 22.5592 1.22888 0.614438 0.788965i \(-0.289383\pi\)
0.614438 + 0.788965i \(0.289383\pi\)
\(338\) 27.9718 1.52147
\(339\) 0.616974 0.0335094
\(340\) −19.1466 −1.03837
\(341\) 12.8877 0.697910
\(342\) −53.5885 −2.89773
\(343\) −19.9419 −1.07676
\(344\) 22.5845 1.21767
\(345\) −0.0250142 −0.00134672
\(346\) −26.0114 −1.39838
\(347\) −32.9515 −1.76893 −0.884464 0.466609i \(-0.845476\pi\)
−0.884464 + 0.466609i \(0.845476\pi\)
\(348\) 2.12925 0.114140
\(349\) −19.1978 −1.02763 −0.513817 0.857900i \(-0.671769\pi\)
−0.513817 + 0.857900i \(0.671769\pi\)
\(350\) −25.8868 −1.38371
\(351\) −0.900464 −0.0480632
\(352\) −21.3611 −1.13855
\(353\) −18.1307 −0.964998 −0.482499 0.875897i \(-0.660271\pi\)
−0.482499 + 0.875897i \(0.660271\pi\)
\(354\) 3.13339 0.166538
\(355\) 9.31408 0.494340
\(356\) −3.31355 −0.175618
\(357\) 0.370672 0.0196180
\(358\) 4.32299 0.228477
\(359\) 33.5414 1.77025 0.885125 0.465353i \(-0.154073\pi\)
0.885125 + 0.465353i \(0.154073\pi\)
\(360\) −53.6387 −2.82701
\(361\) 31.8278 1.67515
\(362\) 16.6060 0.872793
\(363\) 2.70942 0.142208
\(364\) 13.9023 0.728680
\(365\) −8.90186 −0.465945
\(366\) 3.53373 0.184711
\(367\) −9.55097 −0.498557 −0.249278 0.968432i \(-0.580193\pi\)
−0.249278 + 0.968432i \(0.580193\pi\)
\(368\) 0.452352 0.0235805
\(369\) −26.8724 −1.39892
\(370\) −74.0041 −3.84729
\(371\) 9.32057 0.483900
\(372\) 1.02360 0.0530714
\(373\) 20.9958 1.08712 0.543560 0.839370i \(-0.317076\pi\)
0.543560 + 0.839370i \(0.317076\pi\)
\(374\) −21.6963 −1.12189
\(375\) 0.203777 0.0105230
\(376\) −23.1161 −1.19212
\(377\) 6.15240 0.316865
\(378\) 3.86863 0.198981
\(379\) −24.0977 −1.23782 −0.618909 0.785463i \(-0.712425\pi\)
−0.618909 + 0.785463i \(0.712425\pi\)
\(380\) 94.5771 4.85170
\(381\) −0.494500 −0.0253340
\(382\) −23.7921 −1.21731
\(383\) −29.8732 −1.52645 −0.763225 0.646133i \(-0.776385\pi\)
−0.763225 + 0.646133i \(0.776385\pi\)
\(384\) 1.65638 0.0845268
\(385\) −42.8957 −2.18617
\(386\) −58.4609 −2.97558
\(387\) 11.5214 0.585663
\(388\) 69.7059 3.53878
\(389\) −25.5557 −1.29572 −0.647862 0.761758i \(-0.724336\pi\)
−0.647862 + 0.761758i \(0.724336\pi\)
\(390\) 1.15944 0.0587104
\(391\) 0.107424 0.00543264
\(392\) 8.87051 0.448028
\(393\) −1.03397 −0.0521571
\(394\) 2.62859 0.132426
\(395\) −41.1081 −2.06837
\(396\) −77.2827 −3.88360
\(397\) 1.03331 0.0518603 0.0259301 0.999664i \(-0.491745\pi\)
0.0259301 + 0.999664i \(0.491745\pi\)
\(398\) 67.7799 3.39750
\(399\) −1.83098 −0.0916639
\(400\) 26.7030 1.33515
\(401\) 0.885632 0.0442264 0.0221132 0.999755i \(-0.492961\pi\)
0.0221132 + 0.999755i \(0.492961\pi\)
\(402\) 0.659545 0.0328951
\(403\) 2.95767 0.147332
\(404\) 10.4574 0.520275
\(405\) −27.2529 −1.35421
\(406\) −26.4323 −1.31181
\(407\) −57.3564 −2.84305
\(408\) −0.926967 −0.0458917
\(409\) −29.9718 −1.48201 −0.741004 0.671501i \(-0.765650\pi\)
−0.741004 + 0.671501i \(0.765650\pi\)
\(410\) 69.3412 3.42452
\(411\) 1.23032 0.0606874
\(412\) −55.6938 −2.74384
\(413\) −26.6045 −1.30912
\(414\) 0.559454 0.0274957
\(415\) 42.1250 2.06783
\(416\) −4.90228 −0.240354
\(417\) 2.24801 0.110086
\(418\) 107.172 5.24196
\(419\) −12.9675 −0.633505 −0.316753 0.948508i \(-0.602592\pi\)
−0.316753 + 0.948508i \(0.602592\pi\)
\(420\) −3.40698 −0.166243
\(421\) 21.3185 1.03900 0.519501 0.854470i \(-0.326118\pi\)
0.519501 + 0.854470i \(0.326118\pi\)
\(422\) 41.6910 2.02949
\(423\) −11.7926 −0.573374
\(424\) −23.3086 −1.13197
\(425\) 6.34136 0.307601
\(426\) 0.838284 0.0406150
\(427\) −30.0036 −1.45197
\(428\) −16.3507 −0.790340
\(429\) 0.898615 0.0433856
\(430\) −29.7295 −1.43368
\(431\) 5.94836 0.286522 0.143261 0.989685i \(-0.454241\pi\)
0.143261 + 0.989685i \(0.454241\pi\)
\(432\) −3.99060 −0.191998
\(433\) 14.2140 0.683082 0.341541 0.939867i \(-0.389051\pi\)
0.341541 + 0.939867i \(0.389051\pi\)
\(434\) −12.7070 −0.609953
\(435\) −1.50774 −0.0722905
\(436\) −61.0630 −2.92439
\(437\) −0.530633 −0.0253836
\(438\) −0.801184 −0.0382820
\(439\) 3.57191 0.170478 0.0852391 0.996361i \(-0.472835\pi\)
0.0852391 + 0.996361i \(0.472835\pi\)
\(440\) 107.272 5.11401
\(441\) 4.52525 0.215488
\(442\) −4.97921 −0.236837
\(443\) 21.2486 1.00955 0.504775 0.863251i \(-0.331576\pi\)
0.504775 + 0.863251i \(0.331576\pi\)
\(444\) −4.55552 −0.216195
\(445\) 2.34635 0.111228
\(446\) −7.75635 −0.367274
\(447\) −0.0196818 −0.000930917 0
\(448\) −7.40743 −0.349968
\(449\) −9.34568 −0.441050 −0.220525 0.975381i \(-0.570777\pi\)
−0.220525 + 0.975381i \(0.570777\pi\)
\(450\) 33.0254 1.55683
\(451\) 53.7424 2.53063
\(452\) 24.3534 1.14549
\(453\) 0.800565 0.0376138
\(454\) −9.15719 −0.429768
\(455\) −9.84436 −0.461511
\(456\) 4.57888 0.214426
\(457\) −18.4164 −0.861483 −0.430742 0.902475i \(-0.641748\pi\)
−0.430742 + 0.902475i \(0.641748\pi\)
\(458\) 20.3668 0.951676
\(459\) −0.947678 −0.0442338
\(460\) −0.987368 −0.0460363
\(461\) −31.8181 −1.48192 −0.740959 0.671550i \(-0.765629\pi\)
−0.740959 + 0.671550i \(0.765629\pi\)
\(462\) −3.86069 −0.179616
\(463\) 8.98406 0.417525 0.208762 0.977966i \(-0.433056\pi\)
0.208762 + 0.977966i \(0.433056\pi\)
\(464\) 27.2656 1.26578
\(465\) −0.724823 −0.0336128
\(466\) 72.9045 3.37723
\(467\) −3.05723 −0.141472 −0.0707358 0.997495i \(-0.522535\pi\)
−0.0707358 + 0.997495i \(0.522535\pi\)
\(468\) −17.7360 −0.819848
\(469\) −5.59995 −0.258582
\(470\) 30.4293 1.40360
\(471\) −0.262565 −0.0120984
\(472\) 66.5318 3.06238
\(473\) −23.0417 −1.05946
\(474\) −3.69980 −0.169938
\(475\) −31.3240 −1.43724
\(476\) 14.6313 0.670623
\(477\) −11.8908 −0.544442
\(478\) −70.3953 −3.21981
\(479\) −10.4524 −0.477581 −0.238790 0.971071i \(-0.576751\pi\)
−0.238790 + 0.971071i \(0.576751\pi\)
\(480\) 1.20138 0.0548352
\(481\) −13.1630 −0.600183
\(482\) −37.6522 −1.71501
\(483\) 0.0191152 0.000869770 0
\(484\) 106.947 4.86123
\(485\) −49.3593 −2.24129
\(486\) −7.40812 −0.336039
\(487\) −34.8112 −1.57745 −0.788723 0.614749i \(-0.789257\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(488\) 75.0322 3.39655
\(489\) −1.27141 −0.0574953
\(490\) −11.6769 −0.527507
\(491\) 10.6515 0.480694 0.240347 0.970687i \(-0.422739\pi\)
0.240347 + 0.970687i \(0.422739\pi\)
\(492\) 4.26848 0.192438
\(493\) 6.47498 0.291619
\(494\) 24.5955 1.10660
\(495\) 54.7245 2.45968
\(496\) 13.1075 0.588546
\(497\) −7.11756 −0.319266
\(498\) 3.79132 0.169893
\(499\) 27.4772 1.23005 0.615023 0.788509i \(-0.289147\pi\)
0.615023 + 0.788509i \(0.289147\pi\)
\(500\) 8.04357 0.359719
\(501\) −1.72693 −0.0771537
\(502\) −31.1661 −1.39101
\(503\) −23.3475 −1.04101 −0.520507 0.853857i \(-0.674257\pi\)
−0.520507 + 0.853857i \(0.674257\pi\)
\(504\) 40.9892 1.82580
\(505\) −7.40497 −0.329517
\(506\) −1.11886 −0.0497393
\(507\) −1.21928 −0.0541500
\(508\) −19.5190 −0.866018
\(509\) −25.7282 −1.14038 −0.570191 0.821512i \(-0.693131\pi\)
−0.570191 + 0.821512i \(0.693131\pi\)
\(510\) 1.22023 0.0540327
\(511\) 6.80255 0.300927
\(512\) 49.4689 2.18624
\(513\) 4.68119 0.206679
\(514\) 16.0335 0.707209
\(515\) 39.4372 1.73781
\(516\) −1.83008 −0.0805646
\(517\) 23.5841 1.03723
\(518\) 56.5519 2.48475
\(519\) 1.13382 0.0497693
\(520\) 24.6185 1.07959
\(521\) −22.5748 −0.989021 −0.494510 0.869172i \(-0.664653\pi\)
−0.494510 + 0.869172i \(0.664653\pi\)
\(522\) 33.7213 1.47594
\(523\) −25.6577 −1.12193 −0.560967 0.827838i \(-0.689571\pi\)
−0.560967 + 0.827838i \(0.689571\pi\)
\(524\) −40.8133 −1.78294
\(525\) 1.12839 0.0492471
\(526\) −71.1583 −3.10265
\(527\) 3.11275 0.135594
\(528\) 3.98240 0.173312
\(529\) −22.9945 −0.999759
\(530\) 30.6828 1.33278
\(531\) 33.9409 1.47291
\(532\) −72.2732 −3.13344
\(533\) 12.3336 0.534229
\(534\) 0.211176 0.00913849
\(535\) 11.5781 0.500563
\(536\) 14.0042 0.604890
\(537\) −0.188437 −0.00813164
\(538\) 34.9476 1.50670
\(539\) −9.05009 −0.389815
\(540\) 8.71045 0.374838
\(541\) −25.9268 −1.11468 −0.557341 0.830284i \(-0.688178\pi\)
−0.557341 + 0.830284i \(0.688178\pi\)
\(542\) −55.6657 −2.39105
\(543\) −0.723848 −0.0310633
\(544\) −5.15932 −0.221204
\(545\) 43.2392 1.85217
\(546\) −0.886010 −0.0379177
\(547\) 15.3858 0.657849 0.328925 0.944356i \(-0.393314\pi\)
0.328925 + 0.944356i \(0.393314\pi\)
\(548\) 48.5637 2.07454
\(549\) 38.2773 1.63364
\(550\) −66.0477 −2.81628
\(551\) −31.9841 −1.36257
\(552\) −0.0478027 −0.00203462
\(553\) 31.4136 1.33584
\(554\) 13.8409 0.588041
\(555\) 3.22580 0.136928
\(556\) 88.7342 3.76317
\(557\) 29.7817 1.26189 0.630946 0.775827i \(-0.282667\pi\)
0.630946 + 0.775827i \(0.282667\pi\)
\(558\) 16.2110 0.686266
\(559\) −5.28795 −0.223657
\(560\) −43.6273 −1.84359
\(561\) 0.945732 0.0399288
\(562\) 62.2764 2.62697
\(563\) 39.0349 1.64512 0.822562 0.568675i \(-0.192544\pi\)
0.822562 + 0.568675i \(0.192544\pi\)
\(564\) 1.87316 0.0788742
\(565\) −17.2448 −0.725496
\(566\) −45.3415 −1.90585
\(567\) 20.8259 0.874607
\(568\) 17.7994 0.746847
\(569\) 36.9995 1.55110 0.775550 0.631286i \(-0.217473\pi\)
0.775550 + 0.631286i \(0.217473\pi\)
\(570\) −6.02750 −0.252464
\(571\) 6.04832 0.253114 0.126557 0.991959i \(-0.459607\pi\)
0.126557 + 0.991959i \(0.459607\pi\)
\(572\) 35.4704 1.48309
\(573\) 1.03708 0.0433248
\(574\) −52.9886 −2.21170
\(575\) 0.327017 0.0136376
\(576\) 9.45009 0.393754
\(577\) −38.2544 −1.59255 −0.796276 0.604933i \(-0.793200\pi\)
−0.796276 + 0.604933i \(0.793200\pi\)
\(578\) 37.5251 1.56084
\(579\) 2.54828 0.105903
\(580\) −59.5139 −2.47118
\(581\) −32.1907 −1.33550
\(582\) −4.44243 −0.184145
\(583\) 23.7805 0.984888
\(584\) −17.0117 −0.703947
\(585\) 12.5590 0.519252
\(586\) −41.3671 −1.70886
\(587\) 33.9792 1.40247 0.701236 0.712929i \(-0.252632\pi\)
0.701236 + 0.712929i \(0.252632\pi\)
\(588\) −0.718800 −0.0296428
\(589\) −15.3759 −0.633552
\(590\) −87.5805 −3.60563
\(591\) −0.114579 −0.00471314
\(592\) −58.3347 −2.39754
\(593\) −18.4718 −0.758546 −0.379273 0.925285i \(-0.623826\pi\)
−0.379273 + 0.925285i \(0.623826\pi\)
\(594\) 9.87044 0.404989
\(595\) −10.3605 −0.424740
\(596\) −0.776886 −0.0318225
\(597\) −2.95449 −0.120919
\(598\) −0.256773 −0.0105002
\(599\) −34.0234 −1.39016 −0.695079 0.718934i \(-0.744630\pi\)
−0.695079 + 0.718934i \(0.744630\pi\)
\(600\) −2.82186 −0.115202
\(601\) −13.1688 −0.537168 −0.268584 0.963256i \(-0.586556\pi\)
−0.268584 + 0.963256i \(0.586556\pi\)
\(602\) 22.7185 0.925935
\(603\) 7.14419 0.290934
\(604\) 31.6002 1.28579
\(605\) −75.7301 −3.07887
\(606\) −0.666461 −0.0270731
\(607\) −21.0334 −0.853719 −0.426860 0.904318i \(-0.640380\pi\)
−0.426860 + 0.904318i \(0.640380\pi\)
\(608\) 25.4852 1.03356
\(609\) 1.15217 0.0466883
\(610\) −98.7701 −3.99908
\(611\) 5.41243 0.218964
\(612\) −18.6660 −0.754527
\(613\) −30.8704 −1.24684 −0.623422 0.781885i \(-0.714258\pi\)
−0.623422 + 0.781885i \(0.714258\pi\)
\(614\) 18.5335 0.747950
\(615\) −3.02254 −0.121881
\(616\) −81.9746 −3.30285
\(617\) 32.8924 1.32420 0.662100 0.749416i \(-0.269666\pi\)
0.662100 + 0.749416i \(0.269666\pi\)
\(618\) 3.54942 0.142779
\(619\) 23.1323 0.929767 0.464884 0.885372i \(-0.346096\pi\)
0.464884 + 0.885372i \(0.346096\pi\)
\(620\) −28.6104 −1.14902
\(621\) −0.0488708 −0.00196112
\(622\) 11.3822 0.456385
\(623\) −1.79302 −0.0718358
\(624\) 0.913943 0.0365870
\(625\) −27.6640 −1.10656
\(626\) −28.5785 −1.14223
\(627\) −4.67158 −0.186565
\(628\) −10.3641 −0.413571
\(629\) −13.8532 −0.552364
\(630\) −53.9569 −2.14969
\(631\) −19.9797 −0.795377 −0.397689 0.917520i \(-0.630188\pi\)
−0.397689 + 0.917520i \(0.630188\pi\)
\(632\) −78.5584 −3.12489
\(633\) −1.81729 −0.0722308
\(634\) −12.9111 −0.512764
\(635\) 13.8216 0.548494
\(636\) 1.88876 0.0748942
\(637\) −2.07695 −0.0822918
\(638\) −67.4395 −2.66995
\(639\) 9.08029 0.359211
\(640\) −46.2970 −1.83005
\(641\) −41.7437 −1.64878 −0.824388 0.566025i \(-0.808480\pi\)
−0.824388 + 0.566025i \(0.808480\pi\)
\(642\) 1.04205 0.0411263
\(643\) −17.2286 −0.679431 −0.339716 0.940528i \(-0.610331\pi\)
−0.339716 + 0.940528i \(0.610331\pi\)
\(644\) 0.754519 0.0297322
\(645\) 1.29589 0.0510257
\(646\) 25.8851 1.01844
\(647\) −30.4198 −1.19593 −0.597963 0.801524i \(-0.704023\pi\)
−0.597963 + 0.801524i \(0.704023\pi\)
\(648\) −52.0810 −2.04593
\(649\) −67.8787 −2.66447
\(650\) −15.1576 −0.594532
\(651\) 0.553889 0.0217086
\(652\) −50.1856 −1.96542
\(653\) 11.3656 0.444769 0.222385 0.974959i \(-0.428616\pi\)
0.222385 + 0.974959i \(0.428616\pi\)
\(654\) 3.89161 0.152174
\(655\) 28.9003 1.12923
\(656\) 54.6591 2.13408
\(657\) −8.67841 −0.338577
\(658\) −23.2533 −0.906506
\(659\) −38.4595 −1.49817 −0.749085 0.662474i \(-0.769506\pi\)
−0.749085 + 0.662474i \(0.769506\pi\)
\(660\) −8.69256 −0.338358
\(661\) −19.1525 −0.744948 −0.372474 0.928043i \(-0.621490\pi\)
−0.372474 + 0.928043i \(0.621490\pi\)
\(662\) 35.1848 1.36750
\(663\) 0.217041 0.00842918
\(664\) 80.5017 3.12407
\(665\) 51.1772 1.98457
\(666\) −72.1466 −2.79562
\(667\) 0.333908 0.0129290
\(668\) −68.1660 −2.63742
\(669\) 0.338095 0.0130715
\(670\) −18.4347 −0.712196
\(671\) −76.5511 −2.95522
\(672\) −0.918060 −0.0354149
\(673\) −3.04424 −0.117347 −0.0586734 0.998277i \(-0.518687\pi\)
−0.0586734 + 0.998277i \(0.518687\pi\)
\(674\) −56.7501 −2.18593
\(675\) −2.88491 −0.111040
\(676\) −48.1277 −1.85106
\(677\) 35.6688 1.37086 0.685432 0.728137i \(-0.259613\pi\)
0.685432 + 0.728137i \(0.259613\pi\)
\(678\) −1.55207 −0.0596068
\(679\) 37.7190 1.44752
\(680\) 25.9093 0.993578
\(681\) 0.399157 0.0152957
\(682\) −32.4205 −1.24145
\(683\) −9.68229 −0.370482 −0.185241 0.982693i \(-0.559307\pi\)
−0.185241 + 0.982693i \(0.559307\pi\)
\(684\) 92.2031 3.52547
\(685\) −34.3884 −1.31391
\(686\) 50.1661 1.91535
\(687\) −0.887776 −0.0338708
\(688\) −23.4347 −0.893438
\(689\) 5.45752 0.207915
\(690\) 0.0629260 0.00239555
\(691\) −25.1219 −0.955680 −0.477840 0.878447i \(-0.658580\pi\)
−0.477840 + 0.878447i \(0.658580\pi\)
\(692\) 44.7546 1.70131
\(693\) −41.8190 −1.58857
\(694\) 82.8931 3.14658
\(695\) −62.8334 −2.38341
\(696\) −2.88132 −0.109216
\(697\) 12.9803 0.491665
\(698\) 48.2942 1.82796
\(699\) −3.17787 −0.120198
\(700\) 44.5403 1.68347
\(701\) −27.2124 −1.02780 −0.513899 0.857851i \(-0.671799\pi\)
−0.513899 + 0.857851i \(0.671799\pi\)
\(702\) 2.26522 0.0854952
\(703\) 68.4299 2.58088
\(704\) −18.8993 −0.712295
\(705\) −1.32640 −0.0499551
\(706\) 45.6097 1.71654
\(707\) 5.65867 0.212816
\(708\) −5.39125 −0.202615
\(709\) −44.8116 −1.68293 −0.841467 0.540309i \(-0.818307\pi\)
−0.841467 + 0.540309i \(0.818307\pi\)
\(710\) −23.4306 −0.879335
\(711\) −40.0762 −1.50298
\(712\) 4.48394 0.168043
\(713\) 0.160521 0.00601157
\(714\) −0.932466 −0.0348967
\(715\) −25.1169 −0.939319
\(716\) −7.43803 −0.277972
\(717\) 3.06849 0.114595
\(718\) −84.3773 −3.14893
\(719\) −27.3245 −1.01903 −0.509515 0.860462i \(-0.670175\pi\)
−0.509515 + 0.860462i \(0.670175\pi\)
\(720\) 55.6579 2.07425
\(721\) −30.1368 −1.12235
\(722\) −80.0664 −2.97976
\(723\) 1.64124 0.0610384
\(724\) −28.5719 −1.06187
\(725\) 19.7111 0.732050
\(726\) −6.81585 −0.252960
\(727\) 8.10796 0.300708 0.150354 0.988632i \(-0.451959\pi\)
0.150354 + 0.988632i \(0.451959\pi\)
\(728\) −18.8128 −0.697248
\(729\) −26.3529 −0.976032
\(730\) 22.3936 0.828825
\(731\) −5.56522 −0.205837
\(732\) −6.08005 −0.224725
\(733\) 15.4156 0.569389 0.284694 0.958618i \(-0.408108\pi\)
0.284694 + 0.958618i \(0.408108\pi\)
\(734\) 24.0265 0.886836
\(735\) 0.508989 0.0187743
\(736\) −0.266061 −0.00980713
\(737\) −14.2877 −0.526295
\(738\) 67.6006 2.48841
\(739\) −30.0721 −1.10622 −0.553111 0.833108i \(-0.686559\pi\)
−0.553111 + 0.833108i \(0.686559\pi\)
\(740\) 127.330 4.68074
\(741\) −1.07210 −0.0393847
\(742\) −23.4469 −0.860764
\(743\) −20.6158 −0.756322 −0.378161 0.925740i \(-0.623443\pi\)
−0.378161 + 0.925740i \(0.623443\pi\)
\(744\) −1.38515 −0.0507821
\(745\) 0.550119 0.0201548
\(746\) −52.8172 −1.93378
\(747\) 41.0676 1.50258
\(748\) 37.3302 1.36493
\(749\) −8.84763 −0.323285
\(750\) −0.512625 −0.0187184
\(751\) 26.8436 0.979537 0.489768 0.871853i \(-0.337081\pi\)
0.489768 + 0.871853i \(0.337081\pi\)
\(752\) 23.9863 0.874691
\(753\) 1.35851 0.0495070
\(754\) −15.4770 −0.563641
\(755\) −22.3763 −0.814358
\(756\) −6.65628 −0.242087
\(757\) −24.1265 −0.876892 −0.438446 0.898758i \(-0.644471\pi\)
−0.438446 + 0.898758i \(0.644471\pi\)
\(758\) 60.6206 2.20184
\(759\) 0.0487704 0.00177025
\(760\) −127.983 −4.64242
\(761\) 28.1515 1.02049 0.510245 0.860029i \(-0.329555\pi\)
0.510245 + 0.860029i \(0.329555\pi\)
\(762\) 1.24397 0.0450643
\(763\) −33.0422 −1.19621
\(764\) 40.9361 1.48102
\(765\) 13.2175 0.477881
\(766\) 75.1494 2.71526
\(767\) −15.5778 −0.562483
\(768\) −3.47320 −0.125328
\(769\) −2.87899 −0.103819 −0.0519096 0.998652i \(-0.516531\pi\)
−0.0519096 + 0.998652i \(0.516531\pi\)
\(770\) 107.909 3.88877
\(771\) −0.698893 −0.0251700
\(772\) 100.587 3.62019
\(773\) 5.87427 0.211283 0.105641 0.994404i \(-0.466310\pi\)
0.105641 + 0.994404i \(0.466310\pi\)
\(774\) −28.9833 −1.04178
\(775\) 9.47580 0.340381
\(776\) −94.3268 −3.38613
\(777\) −2.46507 −0.0884338
\(778\) 64.2881 2.30484
\(779\) −64.1181 −2.29727
\(780\) −1.99490 −0.0714290
\(781\) −18.1598 −0.649807
\(782\) −0.270236 −0.00966362
\(783\) −2.94570 −0.105271
\(784\) −9.20445 −0.328730
\(785\) 7.33887 0.261936
\(786\) 2.60108 0.0927773
\(787\) 1.10544 0.0394046 0.0197023 0.999806i \(-0.493728\pi\)
0.0197023 + 0.999806i \(0.493728\pi\)
\(788\) −4.52268 −0.161114
\(789\) 3.10175 0.110425
\(790\) 103.412 3.67923
\(791\) 13.1780 0.468557
\(792\) 104.580 3.71608
\(793\) −17.5681 −0.623862
\(794\) −2.59940 −0.0922494
\(795\) −1.33745 −0.0474344
\(796\) −116.620 −4.13350
\(797\) −40.5711 −1.43710 −0.718551 0.695474i \(-0.755194\pi\)
−0.718551 + 0.695474i \(0.755194\pi\)
\(798\) 4.60605 0.163052
\(799\) 5.69622 0.201518
\(800\) −15.7059 −0.555289
\(801\) 2.28746 0.0808234
\(802\) −2.22791 −0.0786701
\(803\) 17.3560 0.612481
\(804\) −1.13480 −0.0400212
\(805\) −0.534281 −0.0188309
\(806\) −7.44036 −0.262075
\(807\) −1.52335 −0.0536243
\(808\) −14.1511 −0.497833
\(809\) 37.6019 1.32201 0.661007 0.750380i \(-0.270129\pi\)
0.661007 + 0.750380i \(0.270129\pi\)
\(810\) 68.5578 2.40888
\(811\) −35.4190 −1.24373 −0.621864 0.783125i \(-0.713624\pi\)
−0.621864 + 0.783125i \(0.713624\pi\)
\(812\) 45.4789 1.59599
\(813\) 2.42644 0.0850989
\(814\) 144.287 5.05724
\(815\) 35.5369 1.24480
\(816\) 0.961863 0.0336719
\(817\) 27.4902 0.961759
\(818\) 75.3973 2.63621
\(819\) −9.59725 −0.335355
\(820\) −119.307 −4.16637
\(821\) −25.1654 −0.878278 −0.439139 0.898419i \(-0.644716\pi\)
−0.439139 + 0.898419i \(0.644716\pi\)
\(822\) −3.09502 −0.107951
\(823\) 16.2066 0.564926 0.282463 0.959278i \(-0.408849\pi\)
0.282463 + 0.959278i \(0.408849\pi\)
\(824\) 75.3655 2.62548
\(825\) 2.87899 0.100233
\(826\) 66.9266 2.32867
\(827\) 10.5401 0.366516 0.183258 0.983065i \(-0.441336\pi\)
0.183258 + 0.983065i \(0.441336\pi\)
\(828\) −0.962584 −0.0334521
\(829\) −30.8998 −1.07319 −0.536597 0.843838i \(-0.680291\pi\)
−0.536597 + 0.843838i \(0.680291\pi\)
\(830\) −105.970 −3.67827
\(831\) −0.603315 −0.0209288
\(832\) −4.33731 −0.150369
\(833\) −2.18585 −0.0757353
\(834\) −5.65512 −0.195821
\(835\) 48.2689 1.67042
\(836\) −184.398 −6.37753
\(837\) −1.41610 −0.0489476
\(838\) 32.6213 1.12688
\(839\) −25.6649 −0.886051 −0.443025 0.896509i \(-0.646095\pi\)
−0.443025 + 0.896509i \(0.646095\pi\)
\(840\) 4.61036 0.159072
\(841\) −8.87359 −0.305986
\(842\) −53.6291 −1.84818
\(843\) −2.71459 −0.0934956
\(844\) −71.7326 −2.46914
\(845\) 34.0796 1.17237
\(846\) 29.6655 1.01992
\(847\) 57.8708 1.98846
\(848\) 24.1861 0.830555
\(849\) 1.97641 0.0678303
\(850\) −15.9524 −0.547163
\(851\) −0.714396 −0.0244892
\(852\) −1.44233 −0.0494135
\(853\) 47.9373 1.64134 0.820670 0.571402i \(-0.193600\pi\)
0.820670 + 0.571402i \(0.193600\pi\)
\(854\) 75.4773 2.58278
\(855\) −65.2898 −2.23286
\(856\) 22.1259 0.756249
\(857\) −21.2849 −0.727077 −0.363539 0.931579i \(-0.618432\pi\)
−0.363539 + 0.931579i \(0.618432\pi\)
\(858\) −2.26057 −0.0771745
\(859\) −2.47244 −0.0843585 −0.0421792 0.999110i \(-0.513430\pi\)
−0.0421792 + 0.999110i \(0.513430\pi\)
\(860\) 51.1519 1.74426
\(861\) 2.30974 0.0787159
\(862\) −14.9638 −0.509668
\(863\) −13.3682 −0.455058 −0.227529 0.973771i \(-0.573065\pi\)
−0.227529 + 0.973771i \(0.573065\pi\)
\(864\) 2.34716 0.0798519
\(865\) −31.6911 −1.07753
\(866\) −35.7570 −1.21507
\(867\) −1.63570 −0.0555513
\(868\) 21.8633 0.742088
\(869\) 80.1488 2.71886
\(870\) 3.79288 0.128591
\(871\) −3.27897 −0.111104
\(872\) 82.6311 2.79824
\(873\) −48.1204 −1.62863
\(874\) 1.33487 0.0451526
\(875\) 4.35251 0.147142
\(876\) 1.37850 0.0465751
\(877\) 48.4913 1.63744 0.818718 0.574195i \(-0.194685\pi\)
0.818718 + 0.574195i \(0.194685\pi\)
\(878\) −8.98555 −0.303248
\(879\) 1.80317 0.0608194
\(880\) −111.311 −3.75229
\(881\) 38.7922 1.30694 0.653471 0.756952i \(-0.273312\pi\)
0.653471 + 0.756952i \(0.273312\pi\)
\(882\) −11.3838 −0.383311
\(883\) −59.3659 −1.99782 −0.998911 0.0466624i \(-0.985141\pi\)
−0.998911 + 0.0466624i \(0.985141\pi\)
\(884\) 8.56711 0.288143
\(885\) 3.81759 0.128327
\(886\) −53.4531 −1.79579
\(887\) −33.5285 −1.12578 −0.562888 0.826533i \(-0.690310\pi\)
−0.562888 + 0.826533i \(0.690310\pi\)
\(888\) 6.16458 0.206870
\(889\) −10.5621 −0.354241
\(890\) −5.90252 −0.197853
\(891\) 53.1353 1.78010
\(892\) 13.3454 0.446837
\(893\) −28.1373 −0.941578
\(894\) 0.0495118 0.00165592
\(895\) 5.26693 0.176054
\(896\) 35.3788 1.18192
\(897\) 0.0111926 0.000373709 0
\(898\) 23.5101 0.784542
\(899\) 9.67547 0.322695
\(900\) −56.8227 −1.89409
\(901\) 5.74367 0.191349
\(902\) −135.195 −4.50151
\(903\) −0.990285 −0.0329546
\(904\) −32.9553 −1.09608
\(905\) 20.2320 0.672536
\(906\) −2.01391 −0.0669077
\(907\) −4.45849 −0.148042 −0.0740209 0.997257i \(-0.523583\pi\)
−0.0740209 + 0.997257i \(0.523583\pi\)
\(908\) 15.7556 0.522869
\(909\) −7.21910 −0.239442
\(910\) 24.7646 0.820938
\(911\) −12.1205 −0.401570 −0.200785 0.979635i \(-0.564349\pi\)
−0.200785 + 0.979635i \(0.564349\pi\)
\(912\) −4.75126 −0.157330
\(913\) −82.1314 −2.71815
\(914\) 46.3285 1.53241
\(915\) 4.30534 0.142330
\(916\) −35.0426 −1.15784
\(917\) −22.0848 −0.729303
\(918\) 2.38399 0.0786834
\(919\) −33.1316 −1.09291 −0.546455 0.837488i \(-0.684023\pi\)
−0.546455 + 0.837488i \(0.684023\pi\)
\(920\) 1.33612 0.0440505
\(921\) −0.807864 −0.0266200
\(922\) 80.0421 2.63605
\(923\) −4.16758 −0.137177
\(924\) 6.64261 0.218526
\(925\) −42.1718 −1.38660
\(926\) −22.6004 −0.742696
\(927\) 38.4473 1.26278
\(928\) −16.0369 −0.526437
\(929\) −19.9837 −0.655644 −0.327822 0.944739i \(-0.606315\pi\)
−0.327822 + 0.944739i \(0.606315\pi\)
\(930\) 1.82337 0.0597907
\(931\) 10.7973 0.353868
\(932\) −125.438 −4.10885
\(933\) −0.496144 −0.0162430
\(934\) 7.69080 0.251651
\(935\) −26.4339 −0.864479
\(936\) 24.0006 0.784483
\(937\) 53.3853 1.74402 0.872011 0.489487i \(-0.162816\pi\)
0.872011 + 0.489487i \(0.162816\pi\)
\(938\) 14.0873 0.459967
\(939\) 1.24572 0.0406525
\(940\) −52.3560 −1.70766
\(941\) −14.4740 −0.471839 −0.235920 0.971773i \(-0.575810\pi\)
−0.235920 + 0.971773i \(0.575810\pi\)
\(942\) 0.660512 0.0215206
\(943\) 0.669382 0.0217981
\(944\) −69.0365 −2.24695
\(945\) 4.71337 0.153326
\(946\) 57.9639 1.88457
\(947\) 18.5202 0.601827 0.300913 0.953651i \(-0.402708\pi\)
0.300913 + 0.953651i \(0.402708\pi\)
\(948\) 6.36579 0.206751
\(949\) 3.98313 0.129298
\(950\) 78.7991 2.55658
\(951\) 0.562786 0.0182496
\(952\) −19.7992 −0.641696
\(953\) −54.7246 −1.77270 −0.886352 0.463012i \(-0.846769\pi\)
−0.886352 + 0.463012i \(0.846769\pi\)
\(954\) 29.9126 0.968457
\(955\) −28.9872 −0.938003
\(956\) 121.121 3.91732
\(957\) 2.93965 0.0950254
\(958\) 26.2941 0.849524
\(959\) 26.2786 0.848581
\(960\) 1.06292 0.0343057
\(961\) −26.3487 −0.849957
\(962\) 33.1131 1.06761
\(963\) 11.2874 0.363733
\(964\) 64.7836 2.08654
\(965\) −71.2262 −2.29285
\(966\) −0.0480863 −0.00154715
\(967\) −14.1338 −0.454511 −0.227255 0.973835i \(-0.572975\pi\)
−0.227255 + 0.973835i \(0.572975\pi\)
\(968\) −144.722 −4.65154
\(969\) −1.12832 −0.0362468
\(970\) 124.169 3.98682
\(971\) 45.2229 1.45127 0.725636 0.688078i \(-0.241546\pi\)
0.725636 + 0.688078i \(0.241546\pi\)
\(972\) 12.7462 0.408836
\(973\) 48.0155 1.53931
\(974\) 87.5715 2.80597
\(975\) 0.660714 0.0211598
\(976\) −77.8568 −2.49214
\(977\) −9.71934 −0.310949 −0.155475 0.987840i \(-0.549691\pi\)
−0.155475 + 0.987840i \(0.549691\pi\)
\(978\) 3.19838 0.102273
\(979\) −4.57471 −0.146208
\(980\) 20.0910 0.641782
\(981\) 42.1539 1.34587
\(982\) −26.7950 −0.855062
\(983\) 36.4697 1.16320 0.581602 0.813474i \(-0.302426\pi\)
0.581602 + 0.813474i \(0.302426\pi\)
\(984\) −5.77615 −0.184137
\(985\) 3.20255 0.102042
\(986\) −16.2885 −0.518733
\(987\) 1.01360 0.0322631
\(988\) −42.3184 −1.34633
\(989\) −0.286992 −0.00912583
\(990\) −137.666 −4.37530
\(991\) 40.8078 1.29630 0.648151 0.761512i \(-0.275543\pi\)
0.648151 + 0.761512i \(0.275543\pi\)
\(992\) −7.70950 −0.244777
\(993\) −1.53369 −0.0486700
\(994\) 17.9050 0.567913
\(995\) 82.5799 2.61796
\(996\) −6.52326 −0.206697
\(997\) −17.1690 −0.543749 −0.271874 0.962333i \(-0.587644\pi\)
−0.271874 + 0.962333i \(0.587644\pi\)
\(998\) −69.1219 −2.18801
\(999\) 6.30232 0.199396
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 6029.2.a.a.1.15 234
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6029.2.a.a.1.15 234 1.1 even 1 trivial