Properties

Label 8009.2.a.b.1.16
Level $8009$
Weight $2$
Character 8009.1
Self dual yes
Analytic conductor $63.952$
Analytic rank $0$
Dimension $361$
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] = [8009,2,Mod(1,8009)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8009, 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("8009.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8009 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8009.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: \(63.9521869788\)
Analytic rank: \(0\)
Dimension: \(361\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 8009.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.64190 q^{2} -1.64895 q^{3} +4.97966 q^{4} -2.14113 q^{5} +4.35636 q^{6} -4.48395 q^{7} -7.87198 q^{8} -0.280971 q^{9} +O(q^{10})\) \(q-2.64190 q^{2} -1.64895 q^{3} +4.97966 q^{4} -2.14113 q^{5} +4.35636 q^{6} -4.48395 q^{7} -7.87198 q^{8} -0.280971 q^{9} +5.65667 q^{10} +0.688916 q^{11} -8.21120 q^{12} -0.730634 q^{13} +11.8462 q^{14} +3.53062 q^{15} +10.8377 q^{16} +4.48164 q^{17} +0.742299 q^{18} -0.881821 q^{19} -10.6621 q^{20} +7.39380 q^{21} -1.82005 q^{22} -0.650746 q^{23} +12.9805 q^{24} -0.415549 q^{25} +1.93027 q^{26} +5.41015 q^{27} -22.3286 q^{28} -2.05320 q^{29} -9.32755 q^{30} -2.91404 q^{31} -12.8882 q^{32} -1.13599 q^{33} -11.8401 q^{34} +9.60074 q^{35} -1.39914 q^{36} +11.0206 q^{37} +2.32969 q^{38} +1.20478 q^{39} +16.8550 q^{40} +1.60820 q^{41} -19.5337 q^{42} -0.0262366 q^{43} +3.43057 q^{44} +0.601597 q^{45} +1.71921 q^{46} -10.8424 q^{47} -17.8708 q^{48} +13.1058 q^{49} +1.09784 q^{50} -7.38999 q^{51} -3.63831 q^{52} -5.29224 q^{53} -14.2931 q^{54} -1.47506 q^{55} +35.2976 q^{56} +1.45408 q^{57} +5.42436 q^{58} +10.9850 q^{59} +17.5813 q^{60} +4.55069 q^{61} +7.69861 q^{62} +1.25986 q^{63} +12.3740 q^{64} +1.56438 q^{65} +3.00117 q^{66} +15.0490 q^{67} +22.3170 q^{68} +1.07305 q^{69} -25.3642 q^{70} +11.6455 q^{71} +2.21180 q^{72} -13.7634 q^{73} -29.1153 q^{74} +0.685218 q^{75} -4.39117 q^{76} -3.08906 q^{77} -3.18291 q^{78} -3.90914 q^{79} -23.2050 q^{80} -8.07814 q^{81} -4.24872 q^{82} -17.6562 q^{83} +36.8186 q^{84} -9.59579 q^{85} +0.0693147 q^{86} +3.38562 q^{87} -5.42313 q^{88} -17.8246 q^{89} -1.58936 q^{90} +3.27613 q^{91} -3.24050 q^{92} +4.80509 q^{93} +28.6447 q^{94} +1.88810 q^{95} +21.2520 q^{96} -7.74103 q^{97} -34.6243 q^{98} -0.193566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9} + 65 q^{10} + 33 q^{11} + 52 q^{12} + 89 q^{13} + 32 q^{14} + 55 q^{15} + 512 q^{16} + 42 q^{17} + 34 q^{18} + 191 q^{19} + 48 q^{20} + 53 q^{21} + 61 q^{22} + 52 q^{23} + 139 q^{24} + 458 q^{25} + 57 q^{26} + 80 q^{27} + 194 q^{28} + 47 q^{29} + 32 q^{30} + 254 q^{31} + 55 q^{32} + 40 q^{33} + 122 q^{34} + 93 q^{35} + 519 q^{36} + 43 q^{37} + 25 q^{38} + 210 q^{39} + 184 q^{40} + 54 q^{41} + 48 q^{42} + 151 q^{43} + 56 q^{44} + 82 q^{45} + 101 q^{46} + 117 q^{47} + 77 q^{48} + 563 q^{49} + 38 q^{50} + 143 q^{51} + 241 q^{52} + 14 q^{53} + 164 q^{54} + 452 q^{55} + 52 q^{56} + 21 q^{57} + 55 q^{58} + 125 q^{59} + 39 q^{60} + 227 q^{61} + 58 q^{62} + 292 q^{63} + 710 q^{64} + 15 q^{65} + 105 q^{66} + 120 q^{67} + 125 q^{68} + 136 q^{69} + 88 q^{70} + 105 q^{71} + 78 q^{72} + 108 q^{73} + 41 q^{74} + 128 q^{75} + 461 q^{76} + 28 q^{77} + 13 q^{78} + 400 q^{79} + 59 q^{80} + 485 q^{81} + 175 q^{82} + 97 q^{83} + 76 q^{84} + 144 q^{85} - 14 q^{86} + 327 q^{87} + 145 q^{88} + 52 q^{89} + 60 q^{90} + 192 q^{91} + 11 q^{92} + 32 q^{93} + 366 q^{94} + 182 q^{95} + 275 q^{96} + 117 q^{97} + 42 q^{98} + 111 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64190 −1.86811 −0.934054 0.357131i \(-0.883755\pi\)
−0.934054 + 0.357131i \(0.883755\pi\)
\(3\) −1.64895 −0.952020 −0.476010 0.879440i \(-0.657917\pi\)
−0.476010 + 0.879440i \(0.657917\pi\)
\(4\) 4.97966 2.48983
\(5\) −2.14113 −0.957544 −0.478772 0.877939i \(-0.658918\pi\)
−0.478772 + 0.877939i \(0.658918\pi\)
\(6\) 4.35636 1.77848
\(7\) −4.48395 −1.69477 −0.847387 0.530976i \(-0.821826\pi\)
−0.847387 + 0.530976i \(0.821826\pi\)
\(8\) −7.87198 −2.78317
\(9\) −0.280971 −0.0936571
\(10\) 5.65667 1.78880
\(11\) 0.688916 0.207716 0.103858 0.994592i \(-0.466881\pi\)
0.103858 + 0.994592i \(0.466881\pi\)
\(12\) −8.21120 −2.37037
\(13\) −0.730634 −0.202641 −0.101321 0.994854i \(-0.532307\pi\)
−0.101321 + 0.994854i \(0.532307\pi\)
\(14\) 11.8462 3.16602
\(15\) 3.53062 0.911601
\(16\) 10.8377 2.70943
\(17\) 4.48164 1.08696 0.543479 0.839423i \(-0.317107\pi\)
0.543479 + 0.839423i \(0.317107\pi\)
\(18\) 0.742299 0.174962
\(19\) −0.881821 −0.202304 −0.101152 0.994871i \(-0.532253\pi\)
−0.101152 + 0.994871i \(0.532253\pi\)
\(20\) −10.6621 −2.38412
\(21\) 7.39380 1.61346
\(22\) −1.82005 −0.388036
\(23\) −0.650746 −0.135690 −0.0678450 0.997696i \(-0.521612\pi\)
−0.0678450 + 0.997696i \(0.521612\pi\)
\(24\) 12.9805 2.64963
\(25\) −0.415549 −0.0831098
\(26\) 1.93027 0.378556
\(27\) 5.41015 1.04118
\(28\) −22.3286 −4.21970
\(29\) −2.05320 −0.381270 −0.190635 0.981661i \(-0.561055\pi\)
−0.190635 + 0.981661i \(0.561055\pi\)
\(30\) −9.32755 −1.70297
\(31\) −2.91404 −0.523376 −0.261688 0.965152i \(-0.584279\pi\)
−0.261688 + 0.965152i \(0.584279\pi\)
\(32\) −12.8882 −2.27834
\(33\) −1.13599 −0.197750
\(34\) −11.8401 −2.03055
\(35\) 9.60074 1.62282
\(36\) −1.39914 −0.233190
\(37\) 11.0206 1.81177 0.905885 0.423523i \(-0.139207\pi\)
0.905885 + 0.423523i \(0.139207\pi\)
\(38\) 2.32969 0.377925
\(39\) 1.20478 0.192919
\(40\) 16.8550 2.66500
\(41\) 1.60820 0.251159 0.125580 0.992084i \(-0.459921\pi\)
0.125580 + 0.992084i \(0.459921\pi\)
\(42\) −19.5337 −3.01412
\(43\) −0.0262366 −0.00400105 −0.00200052 0.999998i \(-0.500637\pi\)
−0.00200052 + 0.999998i \(0.500637\pi\)
\(44\) 3.43057 0.517177
\(45\) 0.601597 0.0896808
\(46\) 1.71921 0.253484
\(47\) −10.8424 −1.58153 −0.790766 0.612119i \(-0.790317\pi\)
−0.790766 + 0.612119i \(0.790317\pi\)
\(48\) −17.8708 −2.57943
\(49\) 13.1058 1.87226
\(50\) 1.09784 0.155258
\(51\) −7.38999 −1.03481
\(52\) −3.63831 −0.504543
\(53\) −5.29224 −0.726945 −0.363473 0.931605i \(-0.618409\pi\)
−0.363473 + 0.931605i \(0.618409\pi\)
\(54\) −14.2931 −1.94504
\(55\) −1.47506 −0.198897
\(56\) 35.2976 4.71684
\(57\) 1.45408 0.192597
\(58\) 5.42436 0.712253
\(59\) 10.9850 1.43013 0.715063 0.699060i \(-0.246398\pi\)
0.715063 + 0.699060i \(0.246398\pi\)
\(60\) 17.5813 2.26973
\(61\) 4.55069 0.582656 0.291328 0.956623i \(-0.405903\pi\)
0.291328 + 0.956623i \(0.405903\pi\)
\(62\) 7.69861 0.977724
\(63\) 1.25986 0.158728
\(64\) 12.3740 1.54675
\(65\) 1.56438 0.194038
\(66\) 3.00117 0.369418
\(67\) 15.0490 1.83853 0.919265 0.393638i \(-0.128784\pi\)
0.919265 + 0.393638i \(0.128784\pi\)
\(68\) 22.3170 2.70634
\(69\) 1.07305 0.129180
\(70\) −25.3642 −3.03161
\(71\) 11.6455 1.38206 0.691032 0.722824i \(-0.257156\pi\)
0.691032 + 0.722824i \(0.257156\pi\)
\(72\) 2.21180 0.260663
\(73\) −13.7634 −1.61088 −0.805441 0.592676i \(-0.798071\pi\)
−0.805441 + 0.592676i \(0.798071\pi\)
\(74\) −29.1153 −3.38458
\(75\) 0.685218 0.0791222
\(76\) −4.39117 −0.503702
\(77\) −3.08906 −0.352032
\(78\) −3.18291 −0.360393
\(79\) −3.90914 −0.439812 −0.219906 0.975521i \(-0.570575\pi\)
−0.219906 + 0.975521i \(0.570575\pi\)
\(80\) −23.2050 −2.59439
\(81\) −8.07814 −0.897571
\(82\) −4.24872 −0.469193
\(83\) −17.6562 −1.93802 −0.969008 0.247028i \(-0.920546\pi\)
−0.969008 + 0.247028i \(0.920546\pi\)
\(84\) 36.8186 4.01724
\(85\) −9.59579 −1.04081
\(86\) 0.0693147 0.00747440
\(87\) 3.38562 0.362977
\(88\) −5.42313 −0.578108
\(89\) −17.8246 −1.88941 −0.944703 0.327927i \(-0.893650\pi\)
−0.944703 + 0.327927i \(0.893650\pi\)
\(90\) −1.58936 −0.167533
\(91\) 3.27613 0.343431
\(92\) −3.24050 −0.337845
\(93\) 4.80509 0.498265
\(94\) 28.6447 2.95447
\(95\) 1.88810 0.193715
\(96\) 21.2520 2.16902
\(97\) −7.74103 −0.785983 −0.392991 0.919542i \(-0.628560\pi\)
−0.392991 + 0.919542i \(0.628560\pi\)
\(98\) −34.6243 −3.49758
\(99\) −0.193566 −0.0194541
\(100\) −2.06929 −0.206929
\(101\) 1.84260 0.183345 0.0916727 0.995789i \(-0.470779\pi\)
0.0916727 + 0.995789i \(0.470779\pi\)
\(102\) 19.5236 1.93313
\(103\) −9.20814 −0.907305 −0.453653 0.891179i \(-0.649879\pi\)
−0.453653 + 0.891179i \(0.649879\pi\)
\(104\) 5.75154 0.563984
\(105\) −15.8311 −1.54496
\(106\) 13.9816 1.35801
\(107\) −14.6432 −1.41561 −0.707805 0.706408i \(-0.750314\pi\)
−0.707805 + 0.706408i \(0.750314\pi\)
\(108\) 26.9407 2.59237
\(109\) 11.2003 1.07280 0.536399 0.843965i \(-0.319784\pi\)
0.536399 + 0.843965i \(0.319784\pi\)
\(110\) 3.89697 0.371561
\(111\) −18.1723 −1.72484
\(112\) −48.5957 −4.59186
\(113\) −19.2501 −1.81089 −0.905447 0.424459i \(-0.860464\pi\)
−0.905447 + 0.424459i \(0.860464\pi\)
\(114\) −3.84153 −0.359793
\(115\) 1.39333 0.129929
\(116\) −10.2242 −0.949297
\(117\) 0.205287 0.0189788
\(118\) −29.0213 −2.67163
\(119\) −20.0955 −1.84215
\(120\) −27.7929 −2.53714
\(121\) −10.5254 −0.956854
\(122\) −12.0225 −1.08846
\(123\) −2.65185 −0.239109
\(124\) −14.5109 −1.30312
\(125\) 11.5954 1.03713
\(126\) −3.32843 −0.296520
\(127\) −0.329290 −0.0292198 −0.0146099 0.999893i \(-0.504651\pi\)
−0.0146099 + 0.999893i \(0.504651\pi\)
\(128\) −6.91459 −0.611169
\(129\) 0.0432628 0.00380908
\(130\) −4.13295 −0.362484
\(131\) 14.4214 1.26001 0.630004 0.776592i \(-0.283053\pi\)
0.630004 + 0.776592i \(0.283053\pi\)
\(132\) −5.65683 −0.492364
\(133\) 3.95404 0.342859
\(134\) −39.7581 −3.43458
\(135\) −11.5839 −0.996979
\(136\) −35.2794 −3.02518
\(137\) −11.2783 −0.963566 −0.481783 0.876290i \(-0.660011\pi\)
−0.481783 + 0.876290i \(0.660011\pi\)
\(138\) −2.83489 −0.241322
\(139\) 21.0454 1.78505 0.892524 0.450999i \(-0.148932\pi\)
0.892524 + 0.450999i \(0.148932\pi\)
\(140\) 47.8084 4.04055
\(141\) 17.8786 1.50565
\(142\) −30.7663 −2.58185
\(143\) −0.503345 −0.0420918
\(144\) −3.04508 −0.253757
\(145\) 4.39618 0.365083
\(146\) 36.3615 3.00930
\(147\) −21.6108 −1.78243
\(148\) 54.8787 4.51100
\(149\) 1.46360 0.119903 0.0599515 0.998201i \(-0.480905\pi\)
0.0599515 + 0.998201i \(0.480905\pi\)
\(150\) −1.81028 −0.147809
\(151\) −1.79920 −0.146417 −0.0732085 0.997317i \(-0.523324\pi\)
−0.0732085 + 0.997317i \(0.523324\pi\)
\(152\) 6.94168 0.563045
\(153\) −1.25921 −0.101801
\(154\) 8.16102 0.657633
\(155\) 6.23934 0.501156
\(156\) 5.99938 0.480335
\(157\) 13.9717 1.11506 0.557532 0.830156i \(-0.311749\pi\)
0.557532 + 0.830156i \(0.311749\pi\)
\(158\) 10.3276 0.821617
\(159\) 8.72663 0.692067
\(160\) 27.5954 2.18161
\(161\) 2.91791 0.229964
\(162\) 21.3417 1.67676
\(163\) −18.3793 −1.43958 −0.719790 0.694192i \(-0.755762\pi\)
−0.719790 + 0.694192i \(0.755762\pi\)
\(164\) 8.00832 0.625344
\(165\) 2.43230 0.189354
\(166\) 46.6459 3.62043
\(167\) 7.13215 0.551902 0.275951 0.961172i \(-0.411007\pi\)
0.275951 + 0.961172i \(0.411007\pi\)
\(168\) −58.2039 −4.49053
\(169\) −12.4662 −0.958936
\(170\) 25.3512 1.94434
\(171\) 0.247766 0.0189472
\(172\) −0.130650 −0.00996194
\(173\) −8.61980 −0.655351 −0.327676 0.944790i \(-0.606265\pi\)
−0.327676 + 0.944790i \(0.606265\pi\)
\(174\) −8.94449 −0.678080
\(175\) 1.86330 0.140852
\(176\) 7.46626 0.562791
\(177\) −18.1137 −1.36151
\(178\) 47.0910 3.52962
\(179\) 23.3760 1.74721 0.873604 0.486638i \(-0.161777\pi\)
0.873604 + 0.486638i \(0.161777\pi\)
\(180\) 2.99575 0.223290
\(181\) −11.0699 −0.822818 −0.411409 0.911451i \(-0.634963\pi\)
−0.411409 + 0.911451i \(0.634963\pi\)
\(182\) −8.65521 −0.641567
\(183\) −7.50385 −0.554700
\(184\) 5.12266 0.377648
\(185\) −23.5965 −1.73485
\(186\) −12.6946 −0.930813
\(187\) 3.08747 0.225778
\(188\) −53.9916 −3.93775
\(189\) −24.2588 −1.76457
\(190\) −4.98817 −0.361880
\(191\) −7.24505 −0.524234 −0.262117 0.965036i \(-0.584421\pi\)
−0.262117 + 0.965036i \(0.584421\pi\)
\(192\) −20.4041 −1.47254
\(193\) −17.0709 −1.22879 −0.614396 0.788998i \(-0.710600\pi\)
−0.614396 + 0.788998i \(0.710600\pi\)
\(194\) 20.4511 1.46830
\(195\) −2.57959 −0.184728
\(196\) 65.2625 4.66161
\(197\) 1.44189 0.102731 0.0513653 0.998680i \(-0.483643\pi\)
0.0513653 + 0.998680i \(0.483643\pi\)
\(198\) 0.511382 0.0363423
\(199\) 5.45280 0.386538 0.193269 0.981146i \(-0.438091\pi\)
0.193269 + 0.981146i \(0.438091\pi\)
\(200\) 3.27119 0.231308
\(201\) −24.8151 −1.75032
\(202\) −4.86797 −0.342509
\(203\) 9.20645 0.646166
\(204\) −36.7996 −2.57649
\(205\) −3.44338 −0.240496
\(206\) 24.3270 1.69494
\(207\) 0.182841 0.0127083
\(208\) −7.91839 −0.549042
\(209\) −0.607501 −0.0420217
\(210\) 41.8243 2.88615
\(211\) 8.89410 0.612295 0.306147 0.951984i \(-0.400960\pi\)
0.306147 + 0.951984i \(0.400960\pi\)
\(212\) −26.3536 −1.80997
\(213\) −19.2028 −1.31575
\(214\) 38.6859 2.64451
\(215\) 0.0561761 0.00383118
\(216\) −42.5886 −2.89779
\(217\) 13.0664 0.887005
\(218\) −29.5902 −2.00410
\(219\) 22.6951 1.53359
\(220\) −7.34530 −0.495220
\(221\) −3.27444 −0.220263
\(222\) 48.0096 3.22219
\(223\) 18.5131 1.23973 0.619865 0.784709i \(-0.287187\pi\)
0.619865 + 0.784709i \(0.287187\pi\)
\(224\) 57.7901 3.86127
\(225\) 0.116757 0.00778382
\(226\) 50.8569 3.38295
\(227\) −14.5643 −0.966666 −0.483333 0.875437i \(-0.660574\pi\)
−0.483333 + 0.875437i \(0.660574\pi\)
\(228\) 7.24081 0.479535
\(229\) −22.4062 −1.48064 −0.740321 0.672253i \(-0.765327\pi\)
−0.740321 + 0.672253i \(0.765327\pi\)
\(230\) −3.68106 −0.242722
\(231\) 5.09371 0.335141
\(232\) 16.1628 1.06114
\(233\) −23.1631 −1.51746 −0.758732 0.651403i \(-0.774181\pi\)
−0.758732 + 0.651403i \(0.774181\pi\)
\(234\) −0.542349 −0.0354545
\(235\) 23.2151 1.51439
\(236\) 54.7016 3.56077
\(237\) 6.44596 0.418710
\(238\) 53.0903 3.44133
\(239\) −25.0004 −1.61714 −0.808570 0.588401i \(-0.799758\pi\)
−0.808570 + 0.588401i \(0.799758\pi\)
\(240\) 38.2638 2.46992
\(241\) −3.08174 −0.198512 −0.0992562 0.995062i \(-0.531646\pi\)
−0.0992562 + 0.995062i \(0.531646\pi\)
\(242\) 27.8071 1.78751
\(243\) −2.91002 −0.186678
\(244\) 22.6609 1.45071
\(245\) −28.0613 −1.79277
\(246\) 7.00592 0.446681
\(247\) 0.644289 0.0409951
\(248\) 22.9392 1.45664
\(249\) 29.1141 1.84503
\(250\) −30.6340 −1.93746
\(251\) −19.3582 −1.22188 −0.610939 0.791678i \(-0.709208\pi\)
−0.610939 + 0.791678i \(0.709208\pi\)
\(252\) 6.27368 0.395205
\(253\) −0.448309 −0.0281850
\(254\) 0.869953 0.0545857
\(255\) 15.8230 0.990872
\(256\) −6.48038 −0.405024
\(257\) 10.2645 0.640282 0.320141 0.947370i \(-0.396270\pi\)
0.320141 + 0.947370i \(0.396270\pi\)
\(258\) −0.114296 −0.00711578
\(259\) −49.4157 −3.07054
\(260\) 7.79010 0.483122
\(261\) 0.576890 0.0357086
\(262\) −38.1001 −2.35383
\(263\) −18.8217 −1.16060 −0.580298 0.814404i \(-0.697064\pi\)
−0.580298 + 0.814404i \(0.697064\pi\)
\(264\) 8.94246 0.550370
\(265\) 11.3314 0.696082
\(266\) −10.4462 −0.640498
\(267\) 29.3919 1.79875
\(268\) 74.9390 4.57763
\(269\) −8.95809 −0.546185 −0.273092 0.961988i \(-0.588046\pi\)
−0.273092 + 0.961988i \(0.588046\pi\)
\(270\) 30.6034 1.86247
\(271\) 30.6870 1.86410 0.932050 0.362330i \(-0.118019\pi\)
0.932050 + 0.362330i \(0.118019\pi\)
\(272\) 48.5707 2.94503
\(273\) −5.40216 −0.326954
\(274\) 29.7961 1.80005
\(275\) −0.286278 −0.0172632
\(276\) 5.34341 0.321635
\(277\) −0.156570 −0.00940736 −0.00470368 0.999989i \(-0.501497\pi\)
−0.00470368 + 0.999989i \(0.501497\pi\)
\(278\) −55.6000 −3.33467
\(279\) 0.818761 0.0490179
\(280\) −75.5768 −4.51658
\(281\) 5.15293 0.307398 0.153699 0.988118i \(-0.450881\pi\)
0.153699 + 0.988118i \(0.450881\pi\)
\(282\) −47.2336 −2.81272
\(283\) 22.9182 1.36235 0.681174 0.732121i \(-0.261470\pi\)
0.681174 + 0.732121i \(0.261470\pi\)
\(284\) 57.9906 3.44111
\(285\) −3.11337 −0.184420
\(286\) 1.32979 0.0786321
\(287\) −7.21111 −0.425658
\(288\) 3.62122 0.213382
\(289\) 3.08510 0.181476
\(290\) −11.6143 −0.682014
\(291\) 12.7646 0.748271
\(292\) −68.5369 −4.01082
\(293\) 10.6272 0.620850 0.310425 0.950598i \(-0.399529\pi\)
0.310425 + 0.950598i \(0.399529\pi\)
\(294\) 57.0937 3.32977
\(295\) −23.5204 −1.36941
\(296\) −86.7537 −5.04246
\(297\) 3.72714 0.216270
\(298\) −3.86670 −0.223992
\(299\) 0.475457 0.0274964
\(300\) 3.41216 0.197001
\(301\) 0.117644 0.00678088
\(302\) 4.75332 0.273523
\(303\) −3.03835 −0.174549
\(304\) −9.55692 −0.548127
\(305\) −9.74363 −0.557919
\(306\) 3.32672 0.190176
\(307\) −4.31153 −0.246072 −0.123036 0.992402i \(-0.539263\pi\)
−0.123036 + 0.992402i \(0.539263\pi\)
\(308\) −15.3825 −0.876499
\(309\) 15.1837 0.863773
\(310\) −16.4837 −0.936214
\(311\) −30.1171 −1.70779 −0.853893 0.520448i \(-0.825765\pi\)
−0.853893 + 0.520448i \(0.825765\pi\)
\(312\) −9.48398 −0.536925
\(313\) 25.9092 1.46448 0.732238 0.681049i \(-0.238476\pi\)
0.732238 + 0.681049i \(0.238476\pi\)
\(314\) −36.9119 −2.08306
\(315\) −2.69753 −0.151989
\(316\) −19.4662 −1.09506
\(317\) −23.8777 −1.34110 −0.670552 0.741862i \(-0.733943\pi\)
−0.670552 + 0.741862i \(0.733943\pi\)
\(318\) −23.0549 −1.29286
\(319\) −1.41448 −0.0791958
\(320\) −26.4945 −1.48108
\(321\) 24.1458 1.34769
\(322\) −7.70885 −0.429598
\(323\) −3.95201 −0.219895
\(324\) −40.2264 −2.23480
\(325\) 0.303614 0.0168415
\(326\) 48.5564 2.68929
\(327\) −18.4688 −1.02133
\(328\) −12.6598 −0.699018
\(329\) 48.6169 2.68034
\(330\) −6.42590 −0.353734
\(331\) −19.9194 −1.09487 −0.547435 0.836848i \(-0.684396\pi\)
−0.547435 + 0.836848i \(0.684396\pi\)
\(332\) −87.9217 −4.82533
\(333\) −3.09646 −0.169685
\(334\) −18.8425 −1.03101
\(335\) −32.2220 −1.76047
\(336\) 80.1318 4.37155
\(337\) 9.09140 0.495240 0.247620 0.968857i \(-0.420351\pi\)
0.247620 + 0.968857i \(0.420351\pi\)
\(338\) 32.9344 1.79140
\(339\) 31.7424 1.72401
\(340\) −47.7838 −2.59144
\(341\) −2.00753 −0.108714
\(342\) −0.654575 −0.0353954
\(343\) −27.3782 −1.47828
\(344\) 0.206534 0.0111356
\(345\) −2.29754 −0.123695
\(346\) 22.7727 1.22427
\(347\) 17.0597 0.915812 0.457906 0.889001i \(-0.348600\pi\)
0.457906 + 0.889001i \(0.348600\pi\)
\(348\) 16.8592 0.903750
\(349\) −22.5647 −1.20786 −0.603929 0.797038i \(-0.706399\pi\)
−0.603929 + 0.797038i \(0.706399\pi\)
\(350\) −4.92266 −0.263127
\(351\) −3.95284 −0.210987
\(352\) −8.87890 −0.473247
\(353\) −1.54051 −0.0819930 −0.0409965 0.999159i \(-0.513053\pi\)
−0.0409965 + 0.999159i \(0.513053\pi\)
\(354\) 47.8547 2.54345
\(355\) −24.9345 −1.32339
\(356\) −88.7606 −4.70430
\(357\) 33.1364 1.75376
\(358\) −61.7573 −3.26397
\(359\) 13.7494 0.725664 0.362832 0.931855i \(-0.381810\pi\)
0.362832 + 0.931855i \(0.381810\pi\)
\(360\) −4.73576 −0.249596
\(361\) −18.2224 −0.959073
\(362\) 29.2456 1.53711
\(363\) 17.3558 0.910945
\(364\) 16.3140 0.855086
\(365\) 29.4692 1.54249
\(366\) 19.8245 1.03624
\(367\) 27.0340 1.41116 0.705581 0.708629i \(-0.250686\pi\)
0.705581 + 0.708629i \(0.250686\pi\)
\(368\) −7.05260 −0.367642
\(369\) −0.451859 −0.0235229
\(370\) 62.3397 3.24089
\(371\) 23.7302 1.23201
\(372\) 23.9277 1.24060
\(373\) 15.0311 0.778282 0.389141 0.921178i \(-0.372772\pi\)
0.389141 + 0.921178i \(0.372772\pi\)
\(374\) −8.15681 −0.421779
\(375\) −19.1202 −0.987364
\(376\) 85.3514 4.40166
\(377\) 1.50014 0.0772610
\(378\) 64.0896 3.29641
\(379\) 11.1260 0.571505 0.285752 0.958304i \(-0.407757\pi\)
0.285752 + 0.958304i \(0.407757\pi\)
\(380\) 9.40208 0.482317
\(381\) 0.542982 0.0278178
\(382\) 19.1407 0.979325
\(383\) −20.0880 −1.02645 −0.513225 0.858254i \(-0.671549\pi\)
−0.513225 + 0.858254i \(0.671549\pi\)
\(384\) 11.4018 0.581845
\(385\) 6.61410 0.337086
\(386\) 45.0998 2.29552
\(387\) 0.00737174 0.000374727 0
\(388\) −38.5477 −1.95696
\(389\) 15.9040 0.806367 0.403184 0.915119i \(-0.367904\pi\)
0.403184 + 0.915119i \(0.367904\pi\)
\(390\) 6.81503 0.345092
\(391\) −2.91641 −0.147489
\(392\) −103.169 −5.21081
\(393\) −23.7802 −1.19955
\(394\) −3.80935 −0.191912
\(395\) 8.36998 0.421140
\(396\) −0.963891 −0.0484373
\(397\) −8.30352 −0.416742 −0.208371 0.978050i \(-0.566816\pi\)
−0.208371 + 0.978050i \(0.566816\pi\)
\(398\) −14.4058 −0.722096
\(399\) −6.52001 −0.326409
\(400\) −4.50360 −0.225180
\(401\) −10.3059 −0.514650 −0.257325 0.966325i \(-0.582841\pi\)
−0.257325 + 0.966325i \(0.582841\pi\)
\(402\) 65.5590 3.26979
\(403\) 2.12909 0.106058
\(404\) 9.17552 0.456499
\(405\) 17.2964 0.859464
\(406\) −24.3226 −1.20711
\(407\) 7.59224 0.376334
\(408\) 58.1739 2.88004
\(409\) 29.7410 1.47060 0.735300 0.677742i \(-0.237041\pi\)
0.735300 + 0.677742i \(0.237041\pi\)
\(410\) 9.09708 0.449273
\(411\) 18.5973 0.917335
\(412\) −45.8534 −2.25904
\(413\) −49.2562 −2.42374
\(414\) −0.483049 −0.0237405
\(415\) 37.8042 1.85574
\(416\) 9.41657 0.461685
\(417\) −34.7028 −1.69940
\(418\) 1.60496 0.0785011
\(419\) −22.4034 −1.09448 −0.547238 0.836977i \(-0.684321\pi\)
−0.547238 + 0.836977i \(0.684321\pi\)
\(420\) −78.8336 −3.84668
\(421\) −1.54300 −0.0752012 −0.0376006 0.999293i \(-0.511971\pi\)
−0.0376006 + 0.999293i \(0.511971\pi\)
\(422\) −23.4974 −1.14383
\(423\) 3.04641 0.148122
\(424\) 41.6604 2.02321
\(425\) −1.86234 −0.0903368
\(426\) 50.7320 2.45797
\(427\) −20.4051 −0.987470
\(428\) −72.9181 −3.52463
\(429\) 0.829990 0.0400723
\(430\) −0.148412 −0.00715706
\(431\) 1.88515 0.0908044 0.0454022 0.998969i \(-0.485543\pi\)
0.0454022 + 0.998969i \(0.485543\pi\)
\(432\) 58.6336 2.82101
\(433\) −9.34449 −0.449067 −0.224534 0.974466i \(-0.572086\pi\)
−0.224534 + 0.974466i \(0.572086\pi\)
\(434\) −34.5202 −1.65702
\(435\) −7.24906 −0.347566
\(436\) 55.7739 2.67108
\(437\) 0.573842 0.0274506
\(438\) −59.9583 −2.86492
\(439\) 14.9511 0.713576 0.356788 0.934185i \(-0.383872\pi\)
0.356788 + 0.934185i \(0.383872\pi\)
\(440\) 11.6116 0.553564
\(441\) −3.68236 −0.175350
\(442\) 8.65075 0.411474
\(443\) 16.1247 0.766110 0.383055 0.923726i \(-0.374872\pi\)
0.383055 + 0.923726i \(0.374872\pi\)
\(444\) −90.4921 −4.29457
\(445\) 38.1649 1.80919
\(446\) −48.9099 −2.31595
\(447\) −2.41341 −0.114150
\(448\) −55.4846 −2.62140
\(449\) 6.79125 0.320499 0.160249 0.987077i \(-0.448770\pi\)
0.160249 + 0.987077i \(0.448770\pi\)
\(450\) −0.308462 −0.0145410
\(451\) 1.10792 0.0521698
\(452\) −95.8588 −4.50882
\(453\) 2.96679 0.139392
\(454\) 38.4775 1.80584
\(455\) −7.01462 −0.328851
\(456\) −11.4465 −0.536030
\(457\) −33.4025 −1.56250 −0.781251 0.624218i \(-0.785418\pi\)
−0.781251 + 0.624218i \(0.785418\pi\)
\(458\) 59.1950 2.76600
\(459\) 24.2463 1.13172
\(460\) 6.93833 0.323501
\(461\) 0.997728 0.0464688 0.0232344 0.999730i \(-0.492604\pi\)
0.0232344 + 0.999730i \(0.492604\pi\)
\(462\) −13.4571 −0.626080
\(463\) −26.8812 −1.24927 −0.624637 0.780916i \(-0.714753\pi\)
−0.624637 + 0.780916i \(0.714753\pi\)
\(464\) −22.2520 −1.03302
\(465\) −10.2883 −0.477111
\(466\) 61.1946 2.83479
\(467\) −30.8270 −1.42650 −0.713251 0.700909i \(-0.752778\pi\)
−0.713251 + 0.700909i \(0.752778\pi\)
\(468\) 1.02226 0.0472540
\(469\) −67.4791 −3.11589
\(470\) −61.3321 −2.82904
\(471\) −23.0386 −1.06156
\(472\) −86.4737 −3.98028
\(473\) −0.0180748 −0.000831082 0
\(474\) −17.0296 −0.782196
\(475\) 0.366440 0.0168134
\(476\) −100.069 −4.58663
\(477\) 1.48697 0.0680836
\(478\) 66.0486 3.02099
\(479\) −29.2170 −1.33496 −0.667480 0.744628i \(-0.732627\pi\)
−0.667480 + 0.744628i \(0.732627\pi\)
\(480\) −45.5033 −2.07693
\(481\) −8.05200 −0.367140
\(482\) 8.14167 0.370843
\(483\) −4.81149 −0.218930
\(484\) −52.4129 −2.38240
\(485\) 16.5746 0.752613
\(486\) 7.68799 0.348734
\(487\) 8.94699 0.405427 0.202713 0.979238i \(-0.435024\pi\)
0.202713 + 0.979238i \(0.435024\pi\)
\(488\) −35.8229 −1.62163
\(489\) 30.3066 1.37051
\(490\) 74.1353 3.34909
\(491\) −13.0312 −0.588088 −0.294044 0.955792i \(-0.595001\pi\)
−0.294044 + 0.955792i \(0.595001\pi\)
\(492\) −13.2053 −0.595341
\(493\) −9.20171 −0.414424
\(494\) −1.70215 −0.0765833
\(495\) 0.414450 0.0186281
\(496\) −31.5815 −1.41805
\(497\) −52.2178 −2.34229
\(498\) −76.9167 −3.44672
\(499\) −28.0640 −1.25632 −0.628159 0.778085i \(-0.716191\pi\)
−0.628159 + 0.778085i \(0.716191\pi\)
\(500\) 57.7412 2.58227
\(501\) −11.7605 −0.525422
\(502\) 51.1425 2.28260
\(503\) −18.2375 −0.813170 −0.406585 0.913613i \(-0.633280\pi\)
−0.406585 + 0.913613i \(0.633280\pi\)
\(504\) −9.91761 −0.441765
\(505\) −3.94525 −0.175561
\(506\) 1.18439 0.0526526
\(507\) 20.5561 0.912927
\(508\) −1.63975 −0.0727523
\(509\) 4.58881 0.203396 0.101698 0.994815i \(-0.467573\pi\)
0.101698 + 0.994815i \(0.467573\pi\)
\(510\) −41.8027 −1.85106
\(511\) 61.7143 2.73008
\(512\) 30.9497 1.36780
\(513\) −4.77079 −0.210635
\(514\) −27.1178 −1.19612
\(515\) 19.7159 0.868784
\(516\) 0.215434 0.00948397
\(517\) −7.46952 −0.328509
\(518\) 130.552 5.73611
\(519\) 14.2136 0.623908
\(520\) −12.3148 −0.540040
\(521\) −9.29839 −0.407370 −0.203685 0.979036i \(-0.565292\pi\)
−0.203685 + 0.979036i \(0.565292\pi\)
\(522\) −1.52409 −0.0667076
\(523\) 33.5669 1.46778 0.733889 0.679269i \(-0.237703\pi\)
0.733889 + 0.679269i \(0.237703\pi\)
\(524\) 71.8139 3.13721
\(525\) −3.07249 −0.134094
\(526\) 49.7252 2.16812
\(527\) −13.0597 −0.568888
\(528\) −12.3115 −0.535788
\(529\) −22.5765 −0.981588
\(530\) −29.9365 −1.30036
\(531\) −3.08647 −0.133941
\(532\) 19.6898 0.853661
\(533\) −1.17501 −0.0508953
\(534\) −77.6505 −3.36027
\(535\) 31.3530 1.35551
\(536\) −118.466 −5.11694
\(537\) −38.5459 −1.66338
\(538\) 23.6664 1.02033
\(539\) 9.02880 0.388898
\(540\) −57.6837 −2.48231
\(541\) −42.7840 −1.83943 −0.919714 0.392589i \(-0.871579\pi\)
−0.919714 + 0.392589i \(0.871579\pi\)
\(542\) −81.0720 −3.48234
\(543\) 18.2537 0.783340
\(544\) −57.7603 −2.47645
\(545\) −23.9814 −1.02725
\(546\) 14.2720 0.610785
\(547\) 11.2899 0.482721 0.241360 0.970436i \(-0.422406\pi\)
0.241360 + 0.970436i \(0.422406\pi\)
\(548\) −56.1619 −2.39912
\(549\) −1.27861 −0.0545699
\(550\) 0.756320 0.0322496
\(551\) 1.81056 0.0771323
\(552\) −8.44700 −0.359528
\(553\) 17.5284 0.745382
\(554\) 0.413642 0.0175740
\(555\) 38.9094 1.65161
\(556\) 104.799 4.44447
\(557\) −13.9568 −0.591367 −0.295683 0.955286i \(-0.595547\pi\)
−0.295683 + 0.955286i \(0.595547\pi\)
\(558\) −2.16309 −0.0915708
\(559\) 0.0191694 0.000810778 0
\(560\) 104.050 4.39691
\(561\) −5.09108 −0.214946
\(562\) −13.6136 −0.574253
\(563\) −26.3118 −1.10891 −0.554455 0.832213i \(-0.687073\pi\)
−0.554455 + 0.832213i \(0.687073\pi\)
\(564\) 89.0294 3.74881
\(565\) 41.2170 1.73401
\(566\) −60.5478 −2.54501
\(567\) 36.2220 1.52118
\(568\) −91.6730 −3.84652
\(569\) 27.1435 1.13792 0.568958 0.822367i \(-0.307347\pi\)
0.568958 + 0.822367i \(0.307347\pi\)
\(570\) 8.22524 0.344517
\(571\) 28.8580 1.20767 0.603834 0.797110i \(-0.293639\pi\)
0.603834 + 0.797110i \(0.293639\pi\)
\(572\) −2.50649 −0.104802
\(573\) 11.9467 0.499081
\(574\) 19.0511 0.795176
\(575\) 0.270417 0.0112772
\(576\) −3.47675 −0.144865
\(577\) −3.64259 −0.151643 −0.0758214 0.997121i \(-0.524158\pi\)
−0.0758214 + 0.997121i \(0.524158\pi\)
\(578\) −8.15053 −0.339017
\(579\) 28.1491 1.16984
\(580\) 21.8915 0.908994
\(581\) 79.1694 3.28450
\(582\) −33.7227 −1.39785
\(583\) −3.64591 −0.150998
\(584\) 108.345 4.48335
\(585\) −0.439547 −0.0181730
\(586\) −28.0762 −1.15982
\(587\) −7.08010 −0.292227 −0.146113 0.989268i \(-0.546676\pi\)
−0.146113 + 0.989268i \(0.546676\pi\)
\(588\) −107.614 −4.43795
\(589\) 2.56966 0.105881
\(590\) 62.1385 2.55820
\(591\) −2.37761 −0.0978017
\(592\) 119.438 4.90886
\(593\) −37.4591 −1.53826 −0.769131 0.639091i \(-0.779311\pi\)
−0.769131 + 0.639091i \(0.779311\pi\)
\(594\) −9.84674 −0.404017
\(595\) 43.0270 1.76394
\(596\) 7.28825 0.298538
\(597\) −8.99138 −0.367993
\(598\) −1.25611 −0.0513663
\(599\) 13.9970 0.571904 0.285952 0.958244i \(-0.407690\pi\)
0.285952 + 0.958244i \(0.407690\pi\)
\(600\) −5.39403 −0.220210
\(601\) 33.7814 1.37797 0.688987 0.724774i \(-0.258056\pi\)
0.688987 + 0.724774i \(0.258056\pi\)
\(602\) −0.310804 −0.0126674
\(603\) −4.22834 −0.172191
\(604\) −8.95942 −0.364553
\(605\) 22.5363 0.916230
\(606\) 8.02703 0.326076
\(607\) 47.5837 1.93136 0.965681 0.259729i \(-0.0836333\pi\)
0.965681 + 0.259729i \(0.0836333\pi\)
\(608\) 11.3651 0.460916
\(609\) −15.1810 −0.615163
\(610\) 25.7417 1.04225
\(611\) 7.92185 0.320484
\(612\) −6.27045 −0.253468
\(613\) 36.2505 1.46414 0.732072 0.681227i \(-0.238553\pi\)
0.732072 + 0.681227i \(0.238553\pi\)
\(614\) 11.3906 0.459689
\(615\) 5.67796 0.228957
\(616\) 24.3171 0.979762
\(617\) 17.3256 0.697501 0.348750 0.937216i \(-0.386606\pi\)
0.348750 + 0.937216i \(0.386606\pi\)
\(618\) −40.1140 −1.61362
\(619\) −1.04685 −0.0420763 −0.0210382 0.999779i \(-0.506697\pi\)
−0.0210382 + 0.999779i \(0.506697\pi\)
\(620\) 31.0698 1.24779
\(621\) −3.52064 −0.141278
\(622\) 79.5666 3.19033
\(623\) 79.9247 3.20212
\(624\) 13.0570 0.522699
\(625\) −22.7496 −0.909983
\(626\) −68.4497 −2.73580
\(627\) 1.00174 0.0400055
\(628\) 69.5743 2.77632
\(629\) 49.3902 1.96932
\(630\) 7.12662 0.283931
\(631\) 18.0332 0.717890 0.358945 0.933359i \(-0.383137\pi\)
0.358945 + 0.933359i \(0.383137\pi\)
\(632\) 30.7726 1.22407
\(633\) −14.6659 −0.582917
\(634\) 63.0826 2.50533
\(635\) 0.705054 0.0279792
\(636\) 43.4557 1.72313
\(637\) −9.57555 −0.379397
\(638\) 3.73693 0.147946
\(639\) −3.27205 −0.129440
\(640\) 14.8051 0.585221
\(641\) −4.89061 −0.193168 −0.0965838 0.995325i \(-0.530792\pi\)
−0.0965838 + 0.995325i \(0.530792\pi\)
\(642\) −63.7910 −2.51763
\(643\) −16.9752 −0.669437 −0.334719 0.942318i \(-0.608641\pi\)
−0.334719 + 0.942318i \(0.608641\pi\)
\(644\) 14.5302 0.572571
\(645\) −0.0926315 −0.00364736
\(646\) 10.4408 0.410789
\(647\) −11.5274 −0.453189 −0.226594 0.973989i \(-0.572759\pi\)
−0.226594 + 0.973989i \(0.572759\pi\)
\(648\) 63.5910 2.49809
\(649\) 7.56774 0.297060
\(650\) −0.802120 −0.0314617
\(651\) −21.5458 −0.844447
\(652\) −91.5229 −3.58431
\(653\) −4.02982 −0.157699 −0.0788495 0.996887i \(-0.525125\pi\)
−0.0788495 + 0.996887i \(0.525125\pi\)
\(654\) 48.7927 1.90795
\(655\) −30.8782 −1.20651
\(656\) 17.4292 0.680498
\(657\) 3.86711 0.150870
\(658\) −128.441 −5.00716
\(659\) −37.3760 −1.45596 −0.727980 0.685598i \(-0.759541\pi\)
−0.727980 + 0.685598i \(0.759541\pi\)
\(660\) 12.1120 0.471460
\(661\) −14.0706 −0.547283 −0.273642 0.961832i \(-0.588228\pi\)
−0.273642 + 0.961832i \(0.588228\pi\)
\(662\) 52.6252 2.04534
\(663\) 5.39938 0.209694
\(664\) 138.989 5.39382
\(665\) −8.46613 −0.328303
\(666\) 8.18056 0.316990
\(667\) 1.33611 0.0517345
\(668\) 35.5157 1.37414
\(669\) −30.5271 −1.18025
\(670\) 85.1273 3.28876
\(671\) 3.13504 0.121027
\(672\) −95.2929 −3.67600
\(673\) 32.1386 1.23885 0.619426 0.785055i \(-0.287366\pi\)
0.619426 + 0.785055i \(0.287366\pi\)
\(674\) −24.0186 −0.925163
\(675\) −2.24818 −0.0865326
\(676\) −62.0773 −2.38759
\(677\) −2.45146 −0.0942174 −0.0471087 0.998890i \(-0.515001\pi\)
−0.0471087 + 0.998890i \(0.515001\pi\)
\(678\) −83.8603 −3.22064
\(679\) 34.7104 1.33206
\(680\) 75.5379 2.89674
\(681\) 24.0158 0.920286
\(682\) 5.30369 0.203089
\(683\) −6.80081 −0.260226 −0.130113 0.991499i \(-0.541534\pi\)
−0.130113 + 0.991499i \(0.541534\pi\)
\(684\) 1.23379 0.0471753
\(685\) 24.1482 0.922657
\(686\) 72.3306 2.76159
\(687\) 36.9466 1.40960
\(688\) −0.284345 −0.0108405
\(689\) 3.86669 0.147309
\(690\) 6.06987 0.231076
\(691\) 37.9471 1.44357 0.721787 0.692115i \(-0.243321\pi\)
0.721787 + 0.692115i \(0.243321\pi\)
\(692\) −42.9237 −1.63171
\(693\) 0.867939 0.0329703
\(694\) −45.0701 −1.71084
\(695\) −45.0610 −1.70926
\(696\) −26.6515 −1.01022
\(697\) 7.20740 0.273000
\(698\) 59.6137 2.25641
\(699\) 38.1947 1.44466
\(700\) 9.27861 0.350698
\(701\) −4.96143 −0.187391 −0.0936953 0.995601i \(-0.529868\pi\)
−0.0936953 + 0.995601i \(0.529868\pi\)
\(702\) 10.4430 0.394147
\(703\) −9.71817 −0.366528
\(704\) 8.52467 0.321285
\(705\) −38.2805 −1.44173
\(706\) 4.06987 0.153172
\(707\) −8.26212 −0.310729
\(708\) −90.2001 −3.38993
\(709\) −43.8791 −1.64791 −0.823956 0.566653i \(-0.808238\pi\)
−0.823956 + 0.566653i \(0.808238\pi\)
\(710\) 65.8747 2.47223
\(711\) 1.09836 0.0411915
\(712\) 140.315 5.25853
\(713\) 1.89630 0.0710169
\(714\) −87.5431 −3.27622
\(715\) 1.07773 0.0403048
\(716\) 116.405 4.35025
\(717\) 41.2243 1.53955
\(718\) −36.3245 −1.35562
\(719\) 46.3143 1.72723 0.863616 0.504150i \(-0.168194\pi\)
0.863616 + 0.504150i \(0.168194\pi\)
\(720\) 6.51993 0.242983
\(721\) 41.2889 1.53768
\(722\) 48.1418 1.79165
\(723\) 5.08163 0.188988
\(724\) −55.1243 −2.04868
\(725\) 0.853205 0.0316872
\(726\) −45.8524 −1.70174
\(727\) 3.06186 0.113558 0.0567790 0.998387i \(-0.481917\pi\)
0.0567790 + 0.998387i \(0.481917\pi\)
\(728\) −25.7896 −0.955826
\(729\) 29.0329 1.07529
\(730\) −77.8549 −2.88154
\(731\) −0.117583 −0.00434897
\(732\) −37.3666 −1.38111
\(733\) 6.95530 0.256900 0.128450 0.991716i \(-0.459000\pi\)
0.128450 + 0.991716i \(0.459000\pi\)
\(734\) −71.4212 −2.63620
\(735\) 46.2716 1.70675
\(736\) 8.38696 0.309147
\(737\) 10.3675 0.381892
\(738\) 1.19377 0.0439433
\(739\) 26.0340 0.957677 0.478839 0.877903i \(-0.341058\pi\)
0.478839 + 0.877903i \(0.341058\pi\)
\(740\) −117.503 −4.31948
\(741\) −1.06240 −0.0390282
\(742\) −62.6928 −2.30153
\(743\) −22.6699 −0.831677 −0.415838 0.909438i \(-0.636512\pi\)
−0.415838 + 0.909438i \(0.636512\pi\)
\(744\) −37.8256 −1.38675
\(745\) −3.13377 −0.114812
\(746\) −39.7108 −1.45392
\(747\) 4.96088 0.181509
\(748\) 15.3746 0.562150
\(749\) 65.6593 2.39914
\(750\) 50.5138 1.84450
\(751\) 18.6786 0.681591 0.340795 0.940137i \(-0.389304\pi\)
0.340795 + 0.940137i \(0.389304\pi\)
\(752\) −117.507 −4.28504
\(753\) 31.9206 1.16325
\(754\) −3.96322 −0.144332
\(755\) 3.85233 0.140201
\(756\) −120.801 −4.39348
\(757\) 22.7767 0.827833 0.413916 0.910315i \(-0.364161\pi\)
0.413916 + 0.910315i \(0.364161\pi\)
\(758\) −29.3938 −1.06763
\(759\) 0.739239 0.0268327
\(760\) −14.8631 −0.539140
\(761\) −19.1047 −0.692544 −0.346272 0.938134i \(-0.612553\pi\)
−0.346272 + 0.938134i \(0.612553\pi\)
\(762\) −1.43451 −0.0519667
\(763\) −50.2218 −1.81815
\(764\) −36.0779 −1.30525
\(765\) 2.69614 0.0974792
\(766\) 53.0706 1.91752
\(767\) −8.02601 −0.289803
\(768\) 10.6858 0.385591
\(769\) 23.1098 0.833361 0.416681 0.909053i \(-0.363193\pi\)
0.416681 + 0.909053i \(0.363193\pi\)
\(770\) −17.4738 −0.629713
\(771\) −16.9256 −0.609561
\(772\) −85.0074 −3.05948
\(773\) 23.5540 0.847178 0.423589 0.905854i \(-0.360770\pi\)
0.423589 + 0.905854i \(0.360770\pi\)
\(774\) −0.0194754 −0.000700030 0
\(775\) 1.21092 0.0434977
\(776\) 60.9372 2.18752
\(777\) 81.4839 2.92322
\(778\) −42.0170 −1.50638
\(779\) −1.41815 −0.0508105
\(780\) −12.8455 −0.459942
\(781\) 8.02276 0.287077
\(782\) 7.70488 0.275526
\(783\) −11.1081 −0.396972
\(784\) 142.037 5.07275
\(785\) −29.9153 −1.06772
\(786\) 62.8251 2.24090
\(787\) −37.8230 −1.34824 −0.674122 0.738620i \(-0.735478\pi\)
−0.674122 + 0.738620i \(0.735478\pi\)
\(788\) 7.18014 0.255782
\(789\) 31.0360 1.10491
\(790\) −22.1127 −0.786734
\(791\) 86.3164 3.06906
\(792\) 1.52374 0.0541439
\(793\) −3.32489 −0.118070
\(794\) 21.9371 0.778519
\(795\) −18.6849 −0.662684
\(796\) 27.1531 0.962415
\(797\) 5.16109 0.182815 0.0914076 0.995814i \(-0.470863\pi\)
0.0914076 + 0.995814i \(0.470863\pi\)
\(798\) 17.2253 0.609767
\(799\) −48.5919 −1.71906
\(800\) 5.35568 0.189352
\(801\) 5.00821 0.176956
\(802\) 27.2271 0.961422
\(803\) −9.48181 −0.334606
\(804\) −123.571 −4.35800
\(805\) −6.24764 −0.220201
\(806\) −5.62486 −0.198127
\(807\) 14.7714 0.519979
\(808\) −14.5049 −0.510281
\(809\) 16.1848 0.569026 0.284513 0.958672i \(-0.408168\pi\)
0.284513 + 0.958672i \(0.408168\pi\)
\(810\) −45.6954 −1.60557
\(811\) −17.3125 −0.607924 −0.303962 0.952684i \(-0.598310\pi\)
−0.303962 + 0.952684i \(0.598310\pi\)
\(812\) 45.8450 1.60884
\(813\) −50.6012 −1.77466
\(814\) −20.0580 −0.703032
\(815\) 39.3526 1.37846
\(816\) −80.0905 −2.80373
\(817\) 0.0231360 0.000809427 0
\(818\) −78.5730 −2.74724
\(819\) −0.920497 −0.0321648
\(820\) −17.1469 −0.598795
\(821\) 30.5927 1.06769 0.533846 0.845582i \(-0.320746\pi\)
0.533846 + 0.845582i \(0.320746\pi\)
\(822\) −49.1322 −1.71368
\(823\) −33.8819 −1.18105 −0.590525 0.807019i \(-0.701079\pi\)
−0.590525 + 0.807019i \(0.701079\pi\)
\(824\) 72.4863 2.52518
\(825\) 0.472058 0.0164349
\(826\) 130.130 4.52781
\(827\) −12.3965 −0.431067 −0.215533 0.976496i \(-0.569149\pi\)
−0.215533 + 0.976496i \(0.569149\pi\)
\(828\) 0.910486 0.0316416
\(829\) 51.9348 1.80377 0.901885 0.431977i \(-0.142184\pi\)
0.901885 + 0.431977i \(0.142184\pi\)
\(830\) −99.8751 −3.46672
\(831\) 0.258175 0.00895600
\(832\) −9.04089 −0.313436
\(833\) 58.7356 2.03507
\(834\) 91.6815 3.17467
\(835\) −15.2709 −0.528471
\(836\) −3.02515 −0.104627
\(837\) −15.7654 −0.544931
\(838\) 59.1876 2.04460
\(839\) 44.0237 1.51987 0.759933 0.650001i \(-0.225232\pi\)
0.759933 + 0.650001i \(0.225232\pi\)
\(840\) 124.622 4.29987
\(841\) −24.7844 −0.854633
\(842\) 4.07646 0.140484
\(843\) −8.49691 −0.292649
\(844\) 44.2896 1.52451
\(845\) 26.6917 0.918224
\(846\) −8.04833 −0.276707
\(847\) 47.1954 1.62165
\(848\) −57.3557 −1.96960
\(849\) −37.7910 −1.29698
\(850\) 4.92013 0.168759
\(851\) −7.17159 −0.245839
\(852\) −95.6234 −3.27600
\(853\) −57.3095 −1.96224 −0.981119 0.193405i \(-0.938047\pi\)
−0.981119 + 0.193405i \(0.938047\pi\)
\(854\) 53.9082 1.84470
\(855\) −0.530501 −0.0181428
\(856\) 115.271 3.93988
\(857\) 23.7996 0.812978 0.406489 0.913656i \(-0.366753\pi\)
0.406489 + 0.913656i \(0.366753\pi\)
\(858\) −2.19275 −0.0748594
\(859\) −42.1637 −1.43861 −0.719303 0.694696i \(-0.755539\pi\)
−0.719303 + 0.694696i \(0.755539\pi\)
\(860\) 0.279738 0.00953899
\(861\) 11.8907 0.405236
\(862\) −4.98038 −0.169632
\(863\) −16.8201 −0.572564 −0.286282 0.958145i \(-0.592419\pi\)
−0.286282 + 0.958145i \(0.592419\pi\)
\(864\) −69.7272 −2.37217
\(865\) 18.4561 0.627528
\(866\) 24.6872 0.838907
\(867\) −5.08716 −0.172769
\(868\) 65.0662 2.20849
\(869\) −2.69307 −0.0913560
\(870\) 19.1513 0.649291
\(871\) −10.9953 −0.372562
\(872\) −88.1688 −2.98577
\(873\) 2.17501 0.0736128
\(874\) −1.51604 −0.0512807
\(875\) −51.9933 −1.75769
\(876\) 113.014 3.81838
\(877\) 13.0362 0.440200 0.220100 0.975477i \(-0.429362\pi\)
0.220100 + 0.975477i \(0.429362\pi\)
\(878\) −39.4993 −1.33304
\(879\) −17.5238 −0.591062
\(880\) −15.9863 −0.538897
\(881\) −45.0853 −1.51896 −0.759481 0.650529i \(-0.774547\pi\)
−0.759481 + 0.650529i \(0.774547\pi\)
\(882\) 9.72844 0.327574
\(883\) 52.7437 1.77497 0.887483 0.460841i \(-0.152452\pi\)
0.887483 + 0.460841i \(0.152452\pi\)
\(884\) −16.3056 −0.548416
\(885\) 38.7838 1.30370
\(886\) −42.6000 −1.43118
\(887\) −8.48029 −0.284740 −0.142370 0.989813i \(-0.545472\pi\)
−0.142370 + 0.989813i \(0.545472\pi\)
\(888\) 143.052 4.80052
\(889\) 1.47652 0.0495209
\(890\) −100.828 −3.37976
\(891\) −5.56516 −0.186440
\(892\) 92.1890 3.08672
\(893\) 9.56109 0.319950
\(894\) 6.37599 0.213245
\(895\) −50.0512 −1.67303
\(896\) 31.0047 1.03579
\(897\) −0.784004 −0.0261771
\(898\) −17.9418 −0.598727
\(899\) 5.98310 0.199548
\(900\) 0.581412 0.0193804
\(901\) −23.7179 −0.790158
\(902\) −2.92701 −0.0974589
\(903\) −0.193988 −0.00645553
\(904\) 151.536 5.04002
\(905\) 23.7021 0.787885
\(906\) −7.83798 −0.260399
\(907\) −26.5487 −0.881534 −0.440767 0.897621i \(-0.645294\pi\)
−0.440767 + 0.897621i \(0.645294\pi\)
\(908\) −72.5252 −2.40683
\(909\) −0.517717 −0.0171716
\(910\) 18.5320 0.614329
\(911\) 16.3174 0.540618 0.270309 0.962774i \(-0.412874\pi\)
0.270309 + 0.962774i \(0.412874\pi\)
\(912\) 15.7589 0.521828
\(913\) −12.1636 −0.402557
\(914\) 88.2461 2.91892
\(915\) 16.0667 0.531150
\(916\) −111.575 −3.68655
\(917\) −64.6651 −2.13543
\(918\) −64.0565 −2.11418
\(919\) 52.9780 1.74758 0.873792 0.486299i \(-0.161654\pi\)
0.873792 + 0.486299i \(0.161654\pi\)
\(920\) −10.9683 −0.361614
\(921\) 7.10949 0.234265
\(922\) −2.63590 −0.0868088
\(923\) −8.50859 −0.280064
\(924\) 25.3649 0.834445
\(925\) −4.57959 −0.150576
\(926\) 71.0175 2.33378
\(927\) 2.58722 0.0849756
\(928\) 26.4621 0.868661
\(929\) 29.6619 0.973174 0.486587 0.873632i \(-0.338242\pi\)
0.486587 + 0.873632i \(0.338242\pi\)
\(930\) 27.1808 0.891294
\(931\) −11.5570 −0.378765
\(932\) −115.344 −3.77823
\(933\) 49.6616 1.62585
\(934\) 81.4419 2.66486
\(935\) −6.61069 −0.216193
\(936\) −1.61602 −0.0528211
\(937\) 5.09150 0.166332 0.0831660 0.996536i \(-0.473497\pi\)
0.0831660 + 0.996536i \(0.473497\pi\)
\(938\) 178.273 5.82083
\(939\) −42.7229 −1.39421
\(940\) 115.603 3.77056
\(941\) 48.4373 1.57901 0.789506 0.613743i \(-0.210337\pi\)
0.789506 + 0.613743i \(0.210337\pi\)
\(942\) 60.8658 1.98312
\(943\) −1.04653 −0.0340798
\(944\) 119.052 3.87482
\(945\) 51.9414 1.68965
\(946\) 0.0477520 0.00155255
\(947\) −3.63858 −0.118238 −0.0591190 0.998251i \(-0.518829\pi\)
−0.0591190 + 0.998251i \(0.518829\pi\)
\(948\) 32.0987 1.04252
\(949\) 10.0560 0.326431
\(950\) −0.968099 −0.0314093
\(951\) 39.3731 1.27676
\(952\) 158.191 5.12700
\(953\) −16.9365 −0.548626 −0.274313 0.961640i \(-0.588450\pi\)
−0.274313 + 0.961640i \(0.588450\pi\)
\(954\) −3.92843 −0.127188
\(955\) 15.5126 0.501977
\(956\) −124.493 −4.02640
\(957\) 2.33241 0.0753960
\(958\) 77.1886 2.49385
\(959\) 50.5711 1.63303
\(960\) 43.6880 1.41002
\(961\) −22.5084 −0.726077
\(962\) 21.2726 0.685857
\(963\) 4.11431 0.132582
\(964\) −15.3460 −0.494262
\(965\) 36.5511 1.17662
\(966\) 12.7115 0.408986
\(967\) −11.0199 −0.354376 −0.177188 0.984177i \(-0.556700\pi\)
−0.177188 + 0.984177i \(0.556700\pi\)
\(968\) 82.8557 2.66308
\(969\) 6.51665 0.209345
\(970\) −43.7885 −1.40596
\(971\) −54.8152 −1.75910 −0.879551 0.475804i \(-0.842157\pi\)
−0.879551 + 0.475804i \(0.842157\pi\)
\(972\) −14.4909 −0.464796
\(973\) −94.3666 −3.02525
\(974\) −23.6371 −0.757381
\(975\) −0.500644 −0.0160334
\(976\) 49.3190 1.57866
\(977\) 0.0948358 0.00303407 0.00151703 0.999999i \(-0.499517\pi\)
0.00151703 + 0.999999i \(0.499517\pi\)
\(978\) −80.0670 −2.56026
\(979\) −12.2797 −0.392460
\(980\) −139.736 −4.46369
\(981\) −3.14697 −0.100475
\(982\) 34.4271 1.09861
\(983\) 31.3305 0.999289 0.499645 0.866231i \(-0.333464\pi\)
0.499645 + 0.866231i \(0.333464\pi\)
\(984\) 20.8753 0.665480
\(985\) −3.08729 −0.0983691
\(986\) 24.3100 0.774189
\(987\) −80.1668 −2.55174
\(988\) 3.20834 0.102071
\(989\) 0.0170734 0.000542902 0
\(990\) −1.09494 −0.0347994
\(991\) 28.7029 0.911778 0.455889 0.890037i \(-0.349321\pi\)
0.455889 + 0.890037i \(0.349321\pi\)
\(992\) 37.5567 1.19243
\(993\) 32.8461 1.04234
\(994\) 137.954 4.37565
\(995\) −11.6752 −0.370128
\(996\) 144.978 4.59382
\(997\) 10.2624 0.325014 0.162507 0.986707i \(-0.448042\pi\)
0.162507 + 0.986707i \(0.448042\pi\)
\(998\) 74.1424 2.34694
\(999\) 59.6229 1.88639
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 8009.2.a.b.1.16 361
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8009.2.a.b.1.16 361 1.1 even 1 trivial