Properties

Label 6008.2.a.d.1.7
Level $6008$
Weight $2$
Character 6008.1
Self dual yes
Analytic conductor $47.974$
Analytic rank $0$
Dimension $49$
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] = [6008,2,Mod(1,6008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6008, 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("6008.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6008.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: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(49\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 6008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.35470 q^{3} +0.425735 q^{5} -0.578482 q^{7} +2.54461 q^{9} +O(q^{10})\) \(q-2.35470 q^{3} +0.425735 q^{5} -0.578482 q^{7} +2.54461 q^{9} -4.03768 q^{11} -3.33254 q^{13} -1.00248 q^{15} -7.84439 q^{17} -2.14927 q^{19} +1.36215 q^{21} -0.686334 q^{23} -4.81875 q^{25} +1.07231 q^{27} -3.07780 q^{29} -3.74521 q^{31} +9.50752 q^{33} -0.246280 q^{35} -5.44935 q^{37} +7.84714 q^{39} -2.94114 q^{41} +10.8673 q^{43} +1.08333 q^{45} -4.16598 q^{47} -6.66536 q^{49} +18.4712 q^{51} -10.0788 q^{53} -1.71898 q^{55} +5.06088 q^{57} +8.27982 q^{59} -12.2143 q^{61} -1.47201 q^{63} -1.41878 q^{65} -7.40169 q^{67} +1.61611 q^{69} -1.81940 q^{71} +11.6016 q^{73} +11.3467 q^{75} +2.33573 q^{77} +15.2276 q^{79} -10.1588 q^{81} +7.49183 q^{83} -3.33963 q^{85} +7.24729 q^{87} -0.487590 q^{89} +1.92782 q^{91} +8.81886 q^{93} -0.915018 q^{95} +5.00611 q^{97} -10.2743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 49 q + 14 q^{3} - 7 q^{5} + 22 q^{7} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 49 q + 14 q^{3} - 7 q^{5} + 22 q^{7} + 59 q^{9} + 19 q^{11} + 15 q^{13} + 17 q^{15} + 14 q^{17} + 24 q^{19} - 8 q^{21} + 28 q^{23} + 72 q^{25} + 62 q^{27} - 35 q^{29} + 51 q^{31} + 28 q^{33} + 23 q^{35} + 19 q^{37} + 34 q^{39} + 12 q^{41} + 37 q^{43} - 20 q^{45} + 54 q^{47} + 65 q^{49} + 43 q^{51} - 17 q^{53} + 57 q^{55} + 19 q^{57} + 52 q^{59} - 16 q^{61} + 41 q^{63} + 13 q^{65} + 44 q^{67} - 4 q^{69} + 52 q^{71} + 58 q^{73} + 81 q^{75} - 27 q^{77} + 43 q^{79} + 73 q^{81} + 51 q^{83} - 16 q^{85} + 41 q^{87} + 40 q^{89} + 73 q^{91} + 22 q^{93} + 70 q^{95} + 96 q^{97} + 78 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.35470 −1.35949 −0.679743 0.733450i \(-0.737909\pi\)
−0.679743 + 0.733450i \(0.737909\pi\)
\(4\) 0 0
\(5\) 0.425735 0.190394 0.0951971 0.995458i \(-0.469652\pi\)
0.0951971 + 0.995458i \(0.469652\pi\)
\(6\) 0 0
\(7\) −0.578482 −0.218646 −0.109323 0.994006i \(-0.534868\pi\)
−0.109323 + 0.994006i \(0.534868\pi\)
\(8\) 0 0
\(9\) 2.54461 0.848203
\(10\) 0 0
\(11\) −4.03768 −1.21741 −0.608703 0.793398i \(-0.708310\pi\)
−0.608703 + 0.793398i \(0.708310\pi\)
\(12\) 0 0
\(13\) −3.33254 −0.924281 −0.462141 0.886807i \(-0.652918\pi\)
−0.462141 + 0.886807i \(0.652918\pi\)
\(14\) 0 0
\(15\) −1.00248 −0.258838
\(16\) 0 0
\(17\) −7.84439 −1.90254 −0.951271 0.308355i \(-0.900222\pi\)
−0.951271 + 0.308355i \(0.900222\pi\)
\(18\) 0 0
\(19\) −2.14927 −0.493076 −0.246538 0.969133i \(-0.579293\pi\)
−0.246538 + 0.969133i \(0.579293\pi\)
\(20\) 0 0
\(21\) 1.36215 0.297246
\(22\) 0 0
\(23\) −0.686334 −0.143111 −0.0715553 0.997437i \(-0.522796\pi\)
−0.0715553 + 0.997437i \(0.522796\pi\)
\(24\) 0 0
\(25\) −4.81875 −0.963750
\(26\) 0 0
\(27\) 1.07231 0.206365
\(28\) 0 0
\(29\) −3.07780 −0.571533 −0.285766 0.958299i \(-0.592248\pi\)
−0.285766 + 0.958299i \(0.592248\pi\)
\(30\) 0 0
\(31\) −3.74521 −0.672660 −0.336330 0.941744i \(-0.609186\pi\)
−0.336330 + 0.941744i \(0.609186\pi\)
\(32\) 0 0
\(33\) 9.50752 1.65505
\(34\) 0 0
\(35\) −0.246280 −0.0416289
\(36\) 0 0
\(37\) −5.44935 −0.895867 −0.447934 0.894067i \(-0.647840\pi\)
−0.447934 + 0.894067i \(0.647840\pi\)
\(38\) 0 0
\(39\) 7.84714 1.25655
\(40\) 0 0
\(41\) −2.94114 −0.459328 −0.229664 0.973270i \(-0.573763\pi\)
−0.229664 + 0.973270i \(0.573763\pi\)
\(42\) 0 0
\(43\) 10.8673 1.65725 0.828627 0.559801i \(-0.189122\pi\)
0.828627 + 0.559801i \(0.189122\pi\)
\(44\) 0 0
\(45\) 1.08333 0.161493
\(46\) 0 0
\(47\) −4.16598 −0.607671 −0.303836 0.952724i \(-0.598267\pi\)
−0.303836 + 0.952724i \(0.598267\pi\)
\(48\) 0 0
\(49\) −6.66536 −0.952194
\(50\) 0 0
\(51\) 18.4712 2.58648
\(52\) 0 0
\(53\) −10.0788 −1.38443 −0.692217 0.721689i \(-0.743366\pi\)
−0.692217 + 0.721689i \(0.743366\pi\)
\(54\) 0 0
\(55\) −1.71898 −0.231787
\(56\) 0 0
\(57\) 5.06088 0.670330
\(58\) 0 0
\(59\) 8.27982 1.07794 0.538971 0.842325i \(-0.318813\pi\)
0.538971 + 0.842325i \(0.318813\pi\)
\(60\) 0 0
\(61\) −12.2143 −1.56388 −0.781939 0.623355i \(-0.785769\pi\)
−0.781939 + 0.623355i \(0.785769\pi\)
\(62\) 0 0
\(63\) −1.47201 −0.185456
\(64\) 0 0
\(65\) −1.41878 −0.175978
\(66\) 0 0
\(67\) −7.40169 −0.904261 −0.452130 0.891952i \(-0.649336\pi\)
−0.452130 + 0.891952i \(0.649336\pi\)
\(68\) 0 0
\(69\) 1.61611 0.194557
\(70\) 0 0
\(71\) −1.81940 −0.215923 −0.107962 0.994155i \(-0.534432\pi\)
−0.107962 + 0.994155i \(0.534432\pi\)
\(72\) 0 0
\(73\) 11.6016 1.35787 0.678934 0.734199i \(-0.262442\pi\)
0.678934 + 0.734199i \(0.262442\pi\)
\(74\) 0 0
\(75\) 11.3467 1.31021
\(76\) 0 0
\(77\) 2.33573 0.266181
\(78\) 0 0
\(79\) 15.2276 1.71324 0.856620 0.515947i \(-0.172560\pi\)
0.856620 + 0.515947i \(0.172560\pi\)
\(80\) 0 0
\(81\) −10.1588 −1.12875
\(82\) 0 0
\(83\) 7.49183 0.822335 0.411167 0.911560i \(-0.365121\pi\)
0.411167 + 0.911560i \(0.365121\pi\)
\(84\) 0 0
\(85\) −3.33963 −0.362233
\(86\) 0 0
\(87\) 7.24729 0.776991
\(88\) 0 0
\(89\) −0.487590 −0.0516844 −0.0258422 0.999666i \(-0.508227\pi\)
−0.0258422 + 0.999666i \(0.508227\pi\)
\(90\) 0 0
\(91\) 1.92782 0.202090
\(92\) 0 0
\(93\) 8.81886 0.914473
\(94\) 0 0
\(95\) −0.915018 −0.0938789
\(96\) 0 0
\(97\) 5.00611 0.508293 0.254147 0.967166i \(-0.418205\pi\)
0.254147 + 0.967166i \(0.418205\pi\)
\(98\) 0 0
\(99\) −10.2743 −1.03261
\(100\) 0 0
\(101\) 0.389675 0.0387741 0.0193871 0.999812i \(-0.493829\pi\)
0.0193871 + 0.999812i \(0.493829\pi\)
\(102\) 0 0
\(103\) 2.42326 0.238771 0.119386 0.992848i \(-0.461908\pi\)
0.119386 + 0.992848i \(0.461908\pi\)
\(104\) 0 0
\(105\) 0.579915 0.0565939
\(106\) 0 0
\(107\) −6.95974 −0.672823 −0.336412 0.941715i \(-0.609213\pi\)
−0.336412 + 0.941715i \(0.609213\pi\)
\(108\) 0 0
\(109\) 7.29549 0.698781 0.349390 0.936977i \(-0.386389\pi\)
0.349390 + 0.936977i \(0.386389\pi\)
\(110\) 0 0
\(111\) 12.8316 1.21792
\(112\) 0 0
\(113\) 9.84270 0.925924 0.462962 0.886378i \(-0.346787\pi\)
0.462962 + 0.886378i \(0.346787\pi\)
\(114\) 0 0
\(115\) −0.292196 −0.0272474
\(116\) 0 0
\(117\) −8.48002 −0.783978
\(118\) 0 0
\(119\) 4.53784 0.415983
\(120\) 0 0
\(121\) 5.30284 0.482077
\(122\) 0 0
\(123\) 6.92549 0.624450
\(124\) 0 0
\(125\) −4.18018 −0.373887
\(126\) 0 0
\(127\) −17.2346 −1.52932 −0.764661 0.644433i \(-0.777094\pi\)
−0.764661 + 0.644433i \(0.777094\pi\)
\(128\) 0 0
\(129\) −25.5893 −2.25302
\(130\) 0 0
\(131\) −13.3091 −1.16282 −0.581411 0.813610i \(-0.697499\pi\)
−0.581411 + 0.813610i \(0.697499\pi\)
\(132\) 0 0
\(133\) 1.24331 0.107809
\(134\) 0 0
\(135\) 0.456518 0.0392908
\(136\) 0 0
\(137\) −3.83442 −0.327596 −0.163798 0.986494i \(-0.552375\pi\)
−0.163798 + 0.986494i \(0.552375\pi\)
\(138\) 0 0
\(139\) −15.7402 −1.33507 −0.667534 0.744579i \(-0.732650\pi\)
−0.667534 + 0.744579i \(0.732650\pi\)
\(140\) 0 0
\(141\) 9.80964 0.826121
\(142\) 0 0
\(143\) 13.4557 1.12523
\(144\) 0 0
\(145\) −1.31032 −0.108817
\(146\) 0 0
\(147\) 15.6949 1.29449
\(148\) 0 0
\(149\) −6.24421 −0.511546 −0.255773 0.966737i \(-0.582330\pi\)
−0.255773 + 0.966737i \(0.582330\pi\)
\(150\) 0 0
\(151\) 5.44920 0.443450 0.221725 0.975109i \(-0.428831\pi\)
0.221725 + 0.975109i \(0.428831\pi\)
\(152\) 0 0
\(153\) −19.9609 −1.61374
\(154\) 0 0
\(155\) −1.59447 −0.128071
\(156\) 0 0
\(157\) 0.764245 0.0609934 0.0304967 0.999535i \(-0.490291\pi\)
0.0304967 + 0.999535i \(0.490291\pi\)
\(158\) 0 0
\(159\) 23.7326 1.88212
\(160\) 0 0
\(161\) 0.397032 0.0312905
\(162\) 0 0
\(163\) −17.1108 −1.34022 −0.670111 0.742261i \(-0.733754\pi\)
−0.670111 + 0.742261i \(0.733754\pi\)
\(164\) 0 0
\(165\) 4.04768 0.315111
\(166\) 0 0
\(167\) 5.81723 0.450151 0.225075 0.974341i \(-0.427737\pi\)
0.225075 + 0.974341i \(0.427737\pi\)
\(168\) 0 0
\(169\) −1.89416 −0.145704
\(170\) 0 0
\(171\) −5.46905 −0.418229
\(172\) 0 0
\(173\) −24.4925 −1.86213 −0.931064 0.364857i \(-0.881118\pi\)
−0.931064 + 0.364857i \(0.881118\pi\)
\(174\) 0 0
\(175\) 2.78756 0.210720
\(176\) 0 0
\(177\) −19.4965 −1.46545
\(178\) 0 0
\(179\) −24.9428 −1.86431 −0.932155 0.362059i \(-0.882074\pi\)
−0.932155 + 0.362059i \(0.882074\pi\)
\(180\) 0 0
\(181\) −5.82699 −0.433117 −0.216559 0.976270i \(-0.569483\pi\)
−0.216559 + 0.976270i \(0.569483\pi\)
\(182\) 0 0
\(183\) 28.7610 2.12607
\(184\) 0 0
\(185\) −2.31997 −0.170568
\(186\) 0 0
\(187\) 31.6731 2.31617
\(188\) 0 0
\(189\) −0.620310 −0.0451209
\(190\) 0 0
\(191\) −13.8190 −0.999907 −0.499953 0.866052i \(-0.666650\pi\)
−0.499953 + 0.866052i \(0.666650\pi\)
\(192\) 0 0
\(193\) −5.49356 −0.395435 −0.197718 0.980259i \(-0.563353\pi\)
−0.197718 + 0.980259i \(0.563353\pi\)
\(194\) 0 0
\(195\) 3.34080 0.239239
\(196\) 0 0
\(197\) 5.80083 0.413292 0.206646 0.978416i \(-0.433745\pi\)
0.206646 + 0.978416i \(0.433745\pi\)
\(198\) 0 0
\(199\) 13.5121 0.957845 0.478923 0.877857i \(-0.341027\pi\)
0.478923 + 0.877857i \(0.341027\pi\)
\(200\) 0 0
\(201\) 17.4288 1.22933
\(202\) 0 0
\(203\) 1.78045 0.124963
\(204\) 0 0
\(205\) −1.25214 −0.0874535
\(206\) 0 0
\(207\) −1.74645 −0.121387
\(208\) 0 0
\(209\) 8.67806 0.600274
\(210\) 0 0
\(211\) 0.955150 0.0657552 0.0328776 0.999459i \(-0.489533\pi\)
0.0328776 + 0.999459i \(0.489533\pi\)
\(212\) 0 0
\(213\) 4.28414 0.293545
\(214\) 0 0
\(215\) 4.62660 0.315532
\(216\) 0 0
\(217\) 2.16654 0.147074
\(218\) 0 0
\(219\) −27.3183 −1.84600
\(220\) 0 0
\(221\) 26.1418 1.75848
\(222\) 0 0
\(223\) 20.9958 1.40598 0.702992 0.711197i \(-0.251847\pi\)
0.702992 + 0.711197i \(0.251847\pi\)
\(224\) 0 0
\(225\) −12.2618 −0.817456
\(226\) 0 0
\(227\) −4.92570 −0.326930 −0.163465 0.986549i \(-0.552267\pi\)
−0.163465 + 0.986549i \(0.552267\pi\)
\(228\) 0 0
\(229\) 21.7148 1.43495 0.717477 0.696583i \(-0.245297\pi\)
0.717477 + 0.696583i \(0.245297\pi\)
\(230\) 0 0
\(231\) −5.49993 −0.361869
\(232\) 0 0
\(233\) 17.5291 1.14837 0.574184 0.818727i \(-0.305320\pi\)
0.574184 + 0.818727i \(0.305320\pi\)
\(234\) 0 0
\(235\) −1.77360 −0.115697
\(236\) 0 0
\(237\) −35.8565 −2.32913
\(238\) 0 0
\(239\) 2.69333 0.174217 0.0871086 0.996199i \(-0.472237\pi\)
0.0871086 + 0.996199i \(0.472237\pi\)
\(240\) 0 0
\(241\) −28.4270 −1.83115 −0.915573 0.402152i \(-0.868262\pi\)
−0.915573 + 0.402152i \(0.868262\pi\)
\(242\) 0 0
\(243\) 20.7040 1.32816
\(244\) 0 0
\(245\) −2.83767 −0.181292
\(246\) 0 0
\(247\) 7.16253 0.455741
\(248\) 0 0
\(249\) −17.6410 −1.11795
\(250\) 0 0
\(251\) −9.30627 −0.587407 −0.293703 0.955897i \(-0.594888\pi\)
−0.293703 + 0.955897i \(0.594888\pi\)
\(252\) 0 0
\(253\) 2.77120 0.174224
\(254\) 0 0
\(255\) 7.86382 0.492451
\(256\) 0 0
\(257\) 25.6483 1.59990 0.799950 0.600067i \(-0.204859\pi\)
0.799950 + 0.600067i \(0.204859\pi\)
\(258\) 0 0
\(259\) 3.15235 0.195878
\(260\) 0 0
\(261\) −7.83179 −0.484776
\(262\) 0 0
\(263\) 20.3920 1.25743 0.628713 0.777637i \(-0.283582\pi\)
0.628713 + 0.777637i \(0.283582\pi\)
\(264\) 0 0
\(265\) −4.29091 −0.263588
\(266\) 0 0
\(267\) 1.14813 0.0702642
\(268\) 0 0
\(269\) −0.377432 −0.0230124 −0.0115062 0.999934i \(-0.503663\pi\)
−0.0115062 + 0.999934i \(0.503663\pi\)
\(270\) 0 0
\(271\) 12.4554 0.756609 0.378304 0.925681i \(-0.376507\pi\)
0.378304 + 0.925681i \(0.376507\pi\)
\(272\) 0 0
\(273\) −4.53943 −0.274739
\(274\) 0 0
\(275\) 19.4566 1.17327
\(276\) 0 0
\(277\) −5.69975 −0.342465 −0.171233 0.985231i \(-0.554775\pi\)
−0.171233 + 0.985231i \(0.554775\pi\)
\(278\) 0 0
\(279\) −9.53011 −0.570553
\(280\) 0 0
\(281\) 2.53871 0.151447 0.0757233 0.997129i \(-0.475873\pi\)
0.0757233 + 0.997129i \(0.475873\pi\)
\(282\) 0 0
\(283\) −13.5674 −0.806496 −0.403248 0.915091i \(-0.632119\pi\)
−0.403248 + 0.915091i \(0.632119\pi\)
\(284\) 0 0
\(285\) 2.15459 0.127627
\(286\) 0 0
\(287\) 1.70139 0.100430
\(288\) 0 0
\(289\) 44.5344 2.61967
\(290\) 0 0
\(291\) −11.7879 −0.691018
\(292\) 0 0
\(293\) −10.7111 −0.625747 −0.312874 0.949795i \(-0.601292\pi\)
−0.312874 + 0.949795i \(0.601292\pi\)
\(294\) 0 0
\(295\) 3.52501 0.205234
\(296\) 0 0
\(297\) −4.32963 −0.251230
\(298\) 0 0
\(299\) 2.28724 0.132274
\(300\) 0 0
\(301\) −6.28657 −0.362352
\(302\) 0 0
\(303\) −0.917568 −0.0527129
\(304\) 0 0
\(305\) −5.20004 −0.297753
\(306\) 0 0
\(307\) 11.2690 0.643154 0.321577 0.946883i \(-0.395787\pi\)
0.321577 + 0.946883i \(0.395787\pi\)
\(308\) 0 0
\(309\) −5.70606 −0.324606
\(310\) 0 0
\(311\) 17.1837 0.974396 0.487198 0.873292i \(-0.338019\pi\)
0.487198 + 0.873292i \(0.338019\pi\)
\(312\) 0 0
\(313\) 15.7705 0.891403 0.445702 0.895182i \(-0.352954\pi\)
0.445702 + 0.895182i \(0.352954\pi\)
\(314\) 0 0
\(315\) −0.626686 −0.0353098
\(316\) 0 0
\(317\) −12.5078 −0.702506 −0.351253 0.936281i \(-0.614244\pi\)
−0.351253 + 0.936281i \(0.614244\pi\)
\(318\) 0 0
\(319\) 12.4272 0.695787
\(320\) 0 0
\(321\) 16.3881 0.914694
\(322\) 0 0
\(323\) 16.8597 0.938099
\(324\) 0 0
\(325\) 16.0587 0.890776
\(326\) 0 0
\(327\) −17.1787 −0.949983
\(328\) 0 0
\(329\) 2.40995 0.132865
\(330\) 0 0
\(331\) 3.56009 0.195680 0.0978401 0.995202i \(-0.468807\pi\)
0.0978401 + 0.995202i \(0.468807\pi\)
\(332\) 0 0
\(333\) −13.8665 −0.759877
\(334\) 0 0
\(335\) −3.15116 −0.172166
\(336\) 0 0
\(337\) 14.9049 0.811922 0.405961 0.913890i \(-0.366937\pi\)
0.405961 + 0.913890i \(0.366937\pi\)
\(338\) 0 0
\(339\) −23.1766 −1.25878
\(340\) 0 0
\(341\) 15.1220 0.818901
\(342\) 0 0
\(343\) 7.90517 0.426839
\(344\) 0 0
\(345\) 0.688034 0.0370425
\(346\) 0 0
\(347\) 3.75308 0.201476 0.100738 0.994913i \(-0.467880\pi\)
0.100738 + 0.994913i \(0.467880\pi\)
\(348\) 0 0
\(349\) 17.0028 0.910138 0.455069 0.890456i \(-0.349615\pi\)
0.455069 + 0.890456i \(0.349615\pi\)
\(350\) 0 0
\(351\) −3.57351 −0.190740
\(352\) 0 0
\(353\) 6.57205 0.349795 0.174897 0.984587i \(-0.444041\pi\)
0.174897 + 0.984587i \(0.444041\pi\)
\(354\) 0 0
\(355\) −0.774582 −0.0411105
\(356\) 0 0
\(357\) −10.6852 −0.565523
\(358\) 0 0
\(359\) −21.3117 −1.12479 −0.562394 0.826870i \(-0.690119\pi\)
−0.562394 + 0.826870i \(0.690119\pi\)
\(360\) 0 0
\(361\) −14.3806 −0.756876
\(362\) 0 0
\(363\) −12.4866 −0.655377
\(364\) 0 0
\(365\) 4.93921 0.258530
\(366\) 0 0
\(367\) 9.23696 0.482165 0.241083 0.970505i \(-0.422498\pi\)
0.241083 + 0.970505i \(0.422498\pi\)
\(368\) 0 0
\(369\) −7.48404 −0.389604
\(370\) 0 0
\(371\) 5.83043 0.302701
\(372\) 0 0
\(373\) 24.7862 1.28338 0.641689 0.766965i \(-0.278234\pi\)
0.641689 + 0.766965i \(0.278234\pi\)
\(374\) 0 0
\(375\) 9.84307 0.508294
\(376\) 0 0
\(377\) 10.2569 0.528257
\(378\) 0 0
\(379\) −16.9546 −0.870898 −0.435449 0.900213i \(-0.643410\pi\)
−0.435449 + 0.900213i \(0.643410\pi\)
\(380\) 0 0
\(381\) 40.5823 2.07909
\(382\) 0 0
\(383\) 14.2009 0.725631 0.362816 0.931861i \(-0.381816\pi\)
0.362816 + 0.931861i \(0.381816\pi\)
\(384\) 0 0
\(385\) 0.994399 0.0506793
\(386\) 0 0
\(387\) 27.6532 1.40569
\(388\) 0 0
\(389\) 5.27384 0.267394 0.133697 0.991022i \(-0.457315\pi\)
0.133697 + 0.991022i \(0.457315\pi\)
\(390\) 0 0
\(391\) 5.38387 0.272274
\(392\) 0 0
\(393\) 31.3389 1.58084
\(394\) 0 0
\(395\) 6.48292 0.326191
\(396\) 0 0
\(397\) 23.4577 1.17731 0.588655 0.808384i \(-0.299658\pi\)
0.588655 + 0.808384i \(0.299658\pi\)
\(398\) 0 0
\(399\) −2.92763 −0.146565
\(400\) 0 0
\(401\) 11.2981 0.564199 0.282100 0.959385i \(-0.408969\pi\)
0.282100 + 0.959385i \(0.408969\pi\)
\(402\) 0 0
\(403\) 12.4811 0.621727
\(404\) 0 0
\(405\) −4.32495 −0.214908
\(406\) 0 0
\(407\) 22.0027 1.09063
\(408\) 0 0
\(409\) −11.1786 −0.552748 −0.276374 0.961050i \(-0.589133\pi\)
−0.276374 + 0.961050i \(0.589133\pi\)
\(410\) 0 0
\(411\) 9.02890 0.445363
\(412\) 0 0
\(413\) −4.78973 −0.235687
\(414\) 0 0
\(415\) 3.18953 0.156568
\(416\) 0 0
\(417\) 37.0635 1.81501
\(418\) 0 0
\(419\) 18.0526 0.881925 0.440963 0.897525i \(-0.354637\pi\)
0.440963 + 0.897525i \(0.354637\pi\)
\(420\) 0 0
\(421\) −5.48272 −0.267211 −0.133606 0.991035i \(-0.542656\pi\)
−0.133606 + 0.991035i \(0.542656\pi\)
\(422\) 0 0
\(423\) −10.6008 −0.515429
\(424\) 0 0
\(425\) 37.8001 1.83358
\(426\) 0 0
\(427\) 7.06574 0.341935
\(428\) 0 0
\(429\) −31.6842 −1.52973
\(430\) 0 0
\(431\) −6.95184 −0.334858 −0.167429 0.985884i \(-0.553547\pi\)
−0.167429 + 0.985884i \(0.553547\pi\)
\(432\) 0 0
\(433\) −12.1796 −0.585316 −0.292658 0.956217i \(-0.594540\pi\)
−0.292658 + 0.956217i \(0.594540\pi\)
\(434\) 0 0
\(435\) 3.08542 0.147935
\(436\) 0 0
\(437\) 1.47512 0.0705645
\(438\) 0 0
\(439\) 30.1095 1.43705 0.718523 0.695503i \(-0.244818\pi\)
0.718523 + 0.695503i \(0.244818\pi\)
\(440\) 0 0
\(441\) −16.9607 −0.807654
\(442\) 0 0
\(443\) −0.472461 −0.0224473 −0.0112236 0.999937i \(-0.503573\pi\)
−0.0112236 + 0.999937i \(0.503573\pi\)
\(444\) 0 0
\(445\) −0.207584 −0.00984041
\(446\) 0 0
\(447\) 14.7032 0.695440
\(448\) 0 0
\(449\) 4.38542 0.206961 0.103480 0.994631i \(-0.467002\pi\)
0.103480 + 0.994631i \(0.467002\pi\)
\(450\) 0 0
\(451\) 11.8754 0.559189
\(452\) 0 0
\(453\) −12.8312 −0.602864
\(454\) 0 0
\(455\) 0.820738 0.0384768
\(456\) 0 0
\(457\) 23.8117 1.11387 0.556933 0.830558i \(-0.311978\pi\)
0.556933 + 0.830558i \(0.311978\pi\)
\(458\) 0 0
\(459\) −8.41158 −0.392619
\(460\) 0 0
\(461\) −29.3553 −1.36721 −0.683607 0.729850i \(-0.739590\pi\)
−0.683607 + 0.729850i \(0.739590\pi\)
\(462\) 0 0
\(463\) −30.1192 −1.39976 −0.699880 0.714261i \(-0.746763\pi\)
−0.699880 + 0.714261i \(0.746763\pi\)
\(464\) 0 0
\(465\) 3.75449 0.174110
\(466\) 0 0
\(467\) −24.7073 −1.14332 −0.571659 0.820491i \(-0.693700\pi\)
−0.571659 + 0.820491i \(0.693700\pi\)
\(468\) 0 0
\(469\) 4.28175 0.197713
\(470\) 0 0
\(471\) −1.79957 −0.0829197
\(472\) 0 0
\(473\) −43.8788 −2.01755
\(474\) 0 0
\(475\) 10.3568 0.475202
\(476\) 0 0
\(477\) −25.6467 −1.17428
\(478\) 0 0
\(479\) −27.5561 −1.25907 −0.629536 0.776971i \(-0.716755\pi\)
−0.629536 + 0.776971i \(0.716755\pi\)
\(480\) 0 0
\(481\) 18.1602 0.828033
\(482\) 0 0
\(483\) −0.934892 −0.0425391
\(484\) 0 0
\(485\) 2.13127 0.0967761
\(486\) 0 0
\(487\) −25.6362 −1.16169 −0.580844 0.814015i \(-0.697277\pi\)
−0.580844 + 0.814015i \(0.697277\pi\)
\(488\) 0 0
\(489\) 40.2908 1.82201
\(490\) 0 0
\(491\) 1.23326 0.0556562 0.0278281 0.999613i \(-0.491141\pi\)
0.0278281 + 0.999613i \(0.491141\pi\)
\(492\) 0 0
\(493\) 24.1434 1.08737
\(494\) 0 0
\(495\) −4.37413 −0.196603
\(496\) 0 0
\(497\) 1.05249 0.0472107
\(498\) 0 0
\(499\) 14.0051 0.626955 0.313478 0.949596i \(-0.398506\pi\)
0.313478 + 0.949596i \(0.398506\pi\)
\(500\) 0 0
\(501\) −13.6978 −0.611974
\(502\) 0 0
\(503\) 20.1129 0.896791 0.448395 0.893835i \(-0.351996\pi\)
0.448395 + 0.893835i \(0.351996\pi\)
\(504\) 0 0
\(505\) 0.165898 0.00738237
\(506\) 0 0
\(507\) 4.46017 0.198083
\(508\) 0 0
\(509\) −40.4957 −1.79494 −0.897469 0.441077i \(-0.854597\pi\)
−0.897469 + 0.441077i \(0.854597\pi\)
\(510\) 0 0
\(511\) −6.71134 −0.296892
\(512\) 0 0
\(513\) −2.30468 −0.101754
\(514\) 0 0
\(515\) 1.03167 0.0454607
\(516\) 0 0
\(517\) 16.8209 0.739782
\(518\) 0 0
\(519\) 57.6724 2.53154
\(520\) 0 0
\(521\) 11.5074 0.504146 0.252073 0.967708i \(-0.418888\pi\)
0.252073 + 0.967708i \(0.418888\pi\)
\(522\) 0 0
\(523\) −15.5286 −0.679018 −0.339509 0.940603i \(-0.610261\pi\)
−0.339509 + 0.940603i \(0.610261\pi\)
\(524\) 0 0
\(525\) −6.56387 −0.286471
\(526\) 0 0
\(527\) 29.3789 1.27977
\(528\) 0 0
\(529\) −22.5289 −0.979519
\(530\) 0 0
\(531\) 21.0689 0.914313
\(532\) 0 0
\(533\) 9.80146 0.424548
\(534\) 0 0
\(535\) −2.96300 −0.128102
\(536\) 0 0
\(537\) 58.7327 2.53451
\(538\) 0 0
\(539\) 26.9126 1.15921
\(540\) 0 0
\(541\) −12.8592 −0.552859 −0.276430 0.961034i \(-0.589151\pi\)
−0.276430 + 0.961034i \(0.589151\pi\)
\(542\) 0 0
\(543\) 13.7208 0.588817
\(544\) 0 0
\(545\) 3.10594 0.133044
\(546\) 0 0
\(547\) 3.01903 0.129085 0.0645423 0.997915i \(-0.479441\pi\)
0.0645423 + 0.997915i \(0.479441\pi\)
\(548\) 0 0
\(549\) −31.0806 −1.32649
\(550\) 0 0
\(551\) 6.61502 0.281809
\(552\) 0 0
\(553\) −8.80891 −0.374593
\(554\) 0 0
\(555\) 5.46284 0.231885
\(556\) 0 0
\(557\) −37.7793 −1.60076 −0.800379 0.599494i \(-0.795369\pi\)
−0.800379 + 0.599494i \(0.795369\pi\)
\(558\) 0 0
\(559\) −36.2159 −1.53177
\(560\) 0 0
\(561\) −74.5806 −3.14880
\(562\) 0 0
\(563\) 7.09824 0.299155 0.149578 0.988750i \(-0.452209\pi\)
0.149578 + 0.988750i \(0.452209\pi\)
\(564\) 0 0
\(565\) 4.19038 0.176291
\(566\) 0 0
\(567\) 5.87668 0.246797
\(568\) 0 0
\(569\) 29.2532 1.22636 0.613180 0.789943i \(-0.289890\pi\)
0.613180 + 0.789943i \(0.289890\pi\)
\(570\) 0 0
\(571\) 27.5640 1.15352 0.576760 0.816914i \(-0.304317\pi\)
0.576760 + 0.816914i \(0.304317\pi\)
\(572\) 0 0
\(573\) 32.5396 1.35936
\(574\) 0 0
\(575\) 3.30727 0.137923
\(576\) 0 0
\(577\) 21.0184 0.875008 0.437504 0.899216i \(-0.355863\pi\)
0.437504 + 0.899216i \(0.355863\pi\)
\(578\) 0 0
\(579\) 12.9357 0.537589
\(580\) 0 0
\(581\) −4.33389 −0.179800
\(582\) 0 0
\(583\) 40.6951 1.68542
\(584\) 0 0
\(585\) −3.61024 −0.149265
\(586\) 0 0
\(587\) 41.0366 1.69376 0.846881 0.531782i \(-0.178477\pi\)
0.846881 + 0.531782i \(0.178477\pi\)
\(588\) 0 0
\(589\) 8.04948 0.331673
\(590\) 0 0
\(591\) −13.6592 −0.561865
\(592\) 0 0
\(593\) −39.9158 −1.63915 −0.819573 0.572975i \(-0.805789\pi\)
−0.819573 + 0.572975i \(0.805789\pi\)
\(594\) 0 0
\(595\) 1.93191 0.0792008
\(596\) 0 0
\(597\) −31.8169 −1.30218
\(598\) 0 0
\(599\) 15.4693 0.632060 0.316030 0.948749i \(-0.397650\pi\)
0.316030 + 0.948749i \(0.397650\pi\)
\(600\) 0 0
\(601\) −32.2013 −1.31352 −0.656759 0.754100i \(-0.728073\pi\)
−0.656759 + 0.754100i \(0.728073\pi\)
\(602\) 0 0
\(603\) −18.8344 −0.766997
\(604\) 0 0
\(605\) 2.25760 0.0917846
\(606\) 0 0
\(607\) −11.7254 −0.475918 −0.237959 0.971275i \(-0.576478\pi\)
−0.237959 + 0.971275i \(0.576478\pi\)
\(608\) 0 0
\(609\) −4.19243 −0.169886
\(610\) 0 0
\(611\) 13.8833 0.561659
\(612\) 0 0
\(613\) −36.9557 −1.49263 −0.746313 0.665596i \(-0.768178\pi\)
−0.746313 + 0.665596i \(0.768178\pi\)
\(614\) 0 0
\(615\) 2.94842 0.118892
\(616\) 0 0
\(617\) −12.2797 −0.494360 −0.247180 0.968970i \(-0.579504\pi\)
−0.247180 + 0.968970i \(0.579504\pi\)
\(618\) 0 0
\(619\) −10.0383 −0.403475 −0.201738 0.979440i \(-0.564659\pi\)
−0.201738 + 0.979440i \(0.564659\pi\)
\(620\) 0 0
\(621\) −0.735961 −0.0295331
\(622\) 0 0
\(623\) 0.282062 0.0113006
\(624\) 0 0
\(625\) 22.3141 0.892564
\(626\) 0 0
\(627\) −20.4342 −0.816064
\(628\) 0 0
\(629\) 42.7468 1.70443
\(630\) 0 0
\(631\) 25.4380 1.01267 0.506335 0.862337i \(-0.331000\pi\)
0.506335 + 0.862337i \(0.331000\pi\)
\(632\) 0 0
\(633\) −2.24909 −0.0893934
\(634\) 0 0
\(635\) −7.33736 −0.291174
\(636\) 0 0
\(637\) 22.2126 0.880095
\(638\) 0 0
\(639\) −4.62967 −0.183147
\(640\) 0 0
\(641\) −44.7497 −1.76751 −0.883753 0.467955i \(-0.844991\pi\)
−0.883753 + 0.467955i \(0.844991\pi\)
\(642\) 0 0
\(643\) −39.8475 −1.57143 −0.785717 0.618587i \(-0.787706\pi\)
−0.785717 + 0.618587i \(0.787706\pi\)
\(644\) 0 0
\(645\) −10.8943 −0.428961
\(646\) 0 0
\(647\) −43.2531 −1.70045 −0.850226 0.526417i \(-0.823535\pi\)
−0.850226 + 0.526417i \(0.823535\pi\)
\(648\) 0 0
\(649\) −33.4313 −1.31229
\(650\) 0 0
\(651\) −5.10155 −0.199946
\(652\) 0 0
\(653\) 1.39120 0.0544420 0.0272210 0.999629i \(-0.491334\pi\)
0.0272210 + 0.999629i \(0.491334\pi\)
\(654\) 0 0
\(655\) −5.66615 −0.221395
\(656\) 0 0
\(657\) 29.5216 1.15175
\(658\) 0 0
\(659\) −18.5780 −0.723694 −0.361847 0.932237i \(-0.617854\pi\)
−0.361847 + 0.932237i \(0.617854\pi\)
\(660\) 0 0
\(661\) −30.6574 −1.19243 −0.596217 0.802823i \(-0.703330\pi\)
−0.596217 + 0.802823i \(0.703330\pi\)
\(662\) 0 0
\(663\) −61.5560 −2.39064
\(664\) 0 0
\(665\) 0.529322 0.0205262
\(666\) 0 0
\(667\) 2.11240 0.0817924
\(668\) 0 0
\(669\) −49.4389 −1.91142
\(670\) 0 0
\(671\) 49.3173 1.90387
\(672\) 0 0
\(673\) 7.17390 0.276533 0.138267 0.990395i \(-0.455847\pi\)
0.138267 + 0.990395i \(0.455847\pi\)
\(674\) 0 0
\(675\) −5.16718 −0.198885
\(676\) 0 0
\(677\) 39.7193 1.52654 0.763269 0.646081i \(-0.223593\pi\)
0.763269 + 0.646081i \(0.223593\pi\)
\(678\) 0 0
\(679\) −2.89595 −0.111136
\(680\) 0 0
\(681\) 11.5985 0.444457
\(682\) 0 0
\(683\) −10.0188 −0.383359 −0.191680 0.981458i \(-0.561393\pi\)
−0.191680 + 0.981458i \(0.561393\pi\)
\(684\) 0 0
\(685\) −1.63244 −0.0623724
\(686\) 0 0
\(687\) −51.1318 −1.95080
\(688\) 0 0
\(689\) 33.5882 1.27961
\(690\) 0 0
\(691\) 17.0164 0.647333 0.323667 0.946171i \(-0.395084\pi\)
0.323667 + 0.946171i \(0.395084\pi\)
\(692\) 0 0
\(693\) 5.94351 0.225775
\(694\) 0 0
\(695\) −6.70115 −0.254189
\(696\) 0 0
\(697\) 23.0714 0.873892
\(698\) 0 0
\(699\) −41.2757 −1.56119
\(700\) 0 0
\(701\) 16.0982 0.608019 0.304010 0.952669i \(-0.401675\pi\)
0.304010 + 0.952669i \(0.401675\pi\)
\(702\) 0 0
\(703\) 11.7121 0.441731
\(704\) 0 0
\(705\) 4.17630 0.157289
\(706\) 0 0
\(707\) −0.225420 −0.00847780
\(708\) 0 0
\(709\) −43.6319 −1.63863 −0.819316 0.573343i \(-0.805646\pi\)
−0.819316 + 0.573343i \(0.805646\pi\)
\(710\) 0 0
\(711\) 38.7484 1.45318
\(712\) 0 0
\(713\) 2.57047 0.0962649
\(714\) 0 0
\(715\) 5.72857 0.214236
\(716\) 0 0
\(717\) −6.34199 −0.236846
\(718\) 0 0
\(719\) 40.5782 1.51331 0.756656 0.653813i \(-0.226832\pi\)
0.756656 + 0.653813i \(0.226832\pi\)
\(720\) 0 0
\(721\) −1.40181 −0.0522063
\(722\) 0 0
\(723\) 66.9371 2.48942
\(724\) 0 0
\(725\) 14.8311 0.550815
\(726\) 0 0
\(727\) 12.0836 0.448155 0.224078 0.974571i \(-0.428063\pi\)
0.224078 + 0.974571i \(0.428063\pi\)
\(728\) 0 0
\(729\) −18.2753 −0.676862
\(730\) 0 0
\(731\) −85.2476 −3.15300
\(732\) 0 0
\(733\) 3.78346 0.139745 0.0698726 0.997556i \(-0.477741\pi\)
0.0698726 + 0.997556i \(0.477741\pi\)
\(734\) 0 0
\(735\) 6.68187 0.246464
\(736\) 0 0
\(737\) 29.8857 1.10085
\(738\) 0 0
\(739\) −18.6879 −0.687444 −0.343722 0.939072i \(-0.611688\pi\)
−0.343722 + 0.939072i \(0.611688\pi\)
\(740\) 0 0
\(741\) −16.8656 −0.619574
\(742\) 0 0
\(743\) −34.4136 −1.26251 −0.631256 0.775574i \(-0.717460\pi\)
−0.631256 + 0.775574i \(0.717460\pi\)
\(744\) 0 0
\(745\) −2.65838 −0.0973954
\(746\) 0 0
\(747\) 19.0638 0.697507
\(748\) 0 0
\(749\) 4.02609 0.147110
\(750\) 0 0
\(751\) 1.00000 0.0364905
\(752\) 0 0
\(753\) 21.9135 0.798571
\(754\) 0 0
\(755\) 2.31991 0.0844303
\(756\) 0 0
\(757\) −3.83996 −0.139566 −0.0697829 0.997562i \(-0.522231\pi\)
−0.0697829 + 0.997562i \(0.522231\pi\)
\(758\) 0 0
\(759\) −6.52534 −0.236855
\(760\) 0 0
\(761\) 9.05432 0.328219 0.164109 0.986442i \(-0.447525\pi\)
0.164109 + 0.986442i \(0.447525\pi\)
\(762\) 0 0
\(763\) −4.22031 −0.152785
\(764\) 0 0
\(765\) −8.49805 −0.307247
\(766\) 0 0
\(767\) −27.5929 −0.996321
\(768\) 0 0
\(769\) −11.7040 −0.422057 −0.211028 0.977480i \(-0.567681\pi\)
−0.211028 + 0.977480i \(0.567681\pi\)
\(770\) 0 0
\(771\) −60.3941 −2.17504
\(772\) 0 0
\(773\) 15.1490 0.544871 0.272435 0.962174i \(-0.412171\pi\)
0.272435 + 0.962174i \(0.412171\pi\)
\(774\) 0 0
\(775\) 18.0473 0.648276
\(776\) 0 0
\(777\) −7.42284 −0.266293
\(778\) 0 0
\(779\) 6.32129 0.226484
\(780\) 0 0
\(781\) 7.34615 0.262866
\(782\) 0 0
\(783\) −3.30034 −0.117945
\(784\) 0 0
\(785\) 0.325365 0.0116128
\(786\) 0 0
\(787\) 45.4277 1.61932 0.809661 0.586898i \(-0.199651\pi\)
0.809661 + 0.586898i \(0.199651\pi\)
\(788\) 0 0
\(789\) −48.0171 −1.70945
\(790\) 0 0
\(791\) −5.69383 −0.202449
\(792\) 0 0
\(793\) 40.7046 1.44546
\(794\) 0 0
\(795\) 10.1038 0.358345
\(796\) 0 0
\(797\) 8.95885 0.317339 0.158669 0.987332i \(-0.449280\pi\)
0.158669 + 0.987332i \(0.449280\pi\)
\(798\) 0 0
\(799\) 32.6796 1.15612
\(800\) 0 0
\(801\) −1.24073 −0.0438389
\(802\) 0 0
\(803\) −46.8436 −1.65308
\(804\) 0 0
\(805\) 0.169030 0.00595754
\(806\) 0 0
\(807\) 0.888738 0.0312851
\(808\) 0 0
\(809\) −32.2722 −1.13463 −0.567314 0.823501i \(-0.692017\pi\)
−0.567314 + 0.823501i \(0.692017\pi\)
\(810\) 0 0
\(811\) 23.4792 0.824466 0.412233 0.911078i \(-0.364749\pi\)
0.412233 + 0.911078i \(0.364749\pi\)
\(812\) 0 0
\(813\) −29.3286 −1.02860
\(814\) 0 0
\(815\) −7.28466 −0.255171
\(816\) 0 0
\(817\) −23.3569 −0.817153
\(818\) 0 0
\(819\) 4.90554 0.171414
\(820\) 0 0
\(821\) −35.7928 −1.24918 −0.624589 0.780954i \(-0.714733\pi\)
−0.624589 + 0.780954i \(0.714733\pi\)
\(822\) 0 0
\(823\) 15.0590 0.524922 0.262461 0.964943i \(-0.415466\pi\)
0.262461 + 0.964943i \(0.415466\pi\)
\(824\) 0 0
\(825\) −45.8144 −1.59505
\(826\) 0 0
\(827\) −8.12303 −0.282465 −0.141233 0.989976i \(-0.545107\pi\)
−0.141233 + 0.989976i \(0.545107\pi\)
\(828\) 0 0
\(829\) 29.7777 1.03422 0.517112 0.855918i \(-0.327007\pi\)
0.517112 + 0.855918i \(0.327007\pi\)
\(830\) 0 0
\(831\) 13.4212 0.465577
\(832\) 0 0
\(833\) 52.2856 1.81159
\(834\) 0 0
\(835\) 2.47659 0.0857061
\(836\) 0 0
\(837\) −4.01602 −0.138814
\(838\) 0 0
\(839\) −22.1416 −0.764412 −0.382206 0.924077i \(-0.624836\pi\)
−0.382206 + 0.924077i \(0.624836\pi\)
\(840\) 0 0
\(841\) −19.5272 −0.673351
\(842\) 0 0
\(843\) −5.97790 −0.205890
\(844\) 0 0
\(845\) −0.806408 −0.0277413
\(846\) 0 0
\(847\) −3.06760 −0.105404
\(848\) 0 0
\(849\) 31.9471 1.09642
\(850\) 0 0
\(851\) 3.74007 0.128208
\(852\) 0 0
\(853\) 47.6944 1.63302 0.816512 0.577328i \(-0.195905\pi\)
0.816512 + 0.577328i \(0.195905\pi\)
\(854\) 0 0
\(855\) −2.32836 −0.0796284
\(856\) 0 0
\(857\) −1.64474 −0.0561831 −0.0280916 0.999605i \(-0.508943\pi\)
−0.0280916 + 0.999605i \(0.508943\pi\)
\(858\) 0 0
\(859\) −28.7961 −0.982510 −0.491255 0.871016i \(-0.663462\pi\)
−0.491255 + 0.871016i \(0.663462\pi\)
\(860\) 0 0
\(861\) −4.00627 −0.136533
\(862\) 0 0
\(863\) 47.0031 1.60000 0.800002 0.599998i \(-0.204832\pi\)
0.800002 + 0.599998i \(0.204832\pi\)
\(864\) 0 0
\(865\) −10.4273 −0.354538
\(866\) 0 0
\(867\) −104.865 −3.56141
\(868\) 0 0
\(869\) −61.4842 −2.08571
\(870\) 0 0
\(871\) 24.6665 0.835791
\(872\) 0 0
\(873\) 12.7386 0.431136
\(874\) 0 0
\(875\) 2.41816 0.0817488
\(876\) 0 0
\(877\) −1.87569 −0.0633375 −0.0316688 0.999498i \(-0.510082\pi\)
−0.0316688 + 0.999498i \(0.510082\pi\)
\(878\) 0 0
\(879\) 25.2213 0.850695
\(880\) 0 0
\(881\) 19.8497 0.668754 0.334377 0.942439i \(-0.391474\pi\)
0.334377 + 0.942439i \(0.391474\pi\)
\(882\) 0 0
\(883\) −0.442016 −0.0148750 −0.00743751 0.999972i \(-0.502367\pi\)
−0.00743751 + 0.999972i \(0.502367\pi\)
\(884\) 0 0
\(885\) −8.30033 −0.279013
\(886\) 0 0
\(887\) −33.8829 −1.13768 −0.568839 0.822449i \(-0.692607\pi\)
−0.568839 + 0.822449i \(0.692607\pi\)
\(888\) 0 0
\(889\) 9.96990 0.334380
\(890\) 0 0
\(891\) 41.0179 1.37415
\(892\) 0 0
\(893\) 8.95382 0.299628
\(894\) 0 0
\(895\) −10.6190 −0.354954
\(896\) 0 0
\(897\) −5.38576 −0.179825
\(898\) 0 0
\(899\) 11.5270 0.384447
\(900\) 0 0
\(901\) 79.0623 2.63395
\(902\) 0 0
\(903\) 14.8030 0.492612
\(904\) 0 0
\(905\) −2.48075 −0.0824630
\(906\) 0 0
\(907\) −23.9331 −0.794687 −0.397343 0.917670i \(-0.630068\pi\)
−0.397343 + 0.917670i \(0.630068\pi\)
\(908\) 0 0
\(909\) 0.991571 0.0328883
\(910\) 0 0
\(911\) −31.6188 −1.04758 −0.523789 0.851848i \(-0.675482\pi\)
−0.523789 + 0.851848i \(0.675482\pi\)
\(912\) 0 0
\(913\) −30.2496 −1.00112
\(914\) 0 0
\(915\) 12.2445 0.404792
\(916\) 0 0
\(917\) 7.69908 0.254246
\(918\) 0 0
\(919\) 2.83120 0.0933926 0.0466963 0.998909i \(-0.485131\pi\)
0.0466963 + 0.998909i \(0.485131\pi\)
\(920\) 0 0
\(921\) −26.5350 −0.874359
\(922\) 0 0
\(923\) 6.06323 0.199574
\(924\) 0 0
\(925\) 26.2590 0.863392
\(926\) 0 0
\(927\) 6.16626 0.202527
\(928\) 0 0
\(929\) −55.1741 −1.81021 −0.905103 0.425193i \(-0.860206\pi\)
−0.905103 + 0.425193i \(0.860206\pi\)
\(930\) 0 0
\(931\) 14.3257 0.469504
\(932\) 0 0
\(933\) −40.4624 −1.32468
\(934\) 0 0
\(935\) 13.4843 0.440985
\(936\) 0 0
\(937\) 8.60307 0.281050 0.140525 0.990077i \(-0.455121\pi\)
0.140525 + 0.990077i \(0.455121\pi\)
\(938\) 0 0
\(939\) −37.1349 −1.21185
\(940\) 0 0
\(941\) −26.5099 −0.864197 −0.432098 0.901826i \(-0.642227\pi\)
−0.432098 + 0.901826i \(0.642227\pi\)
\(942\) 0 0
\(943\) 2.01860 0.0657347
\(944\) 0 0
\(945\) −0.264087 −0.00859077
\(946\) 0 0
\(947\) 22.8199 0.741549 0.370774 0.928723i \(-0.379092\pi\)
0.370774 + 0.928723i \(0.379092\pi\)
\(948\) 0 0
\(949\) −38.6629 −1.25505
\(950\) 0 0
\(951\) 29.4520 0.955047
\(952\) 0 0
\(953\) −30.5763 −0.990463 −0.495232 0.868761i \(-0.664917\pi\)
−0.495232 + 0.868761i \(0.664917\pi\)
\(954\) 0 0
\(955\) −5.88322 −0.190376
\(956\) 0 0
\(957\) −29.2622 −0.945913
\(958\) 0 0
\(959\) 2.21814 0.0716275
\(960\) 0 0
\(961\) −16.9734 −0.547528
\(962\) 0 0
\(963\) −17.7098 −0.570691
\(964\) 0 0
\(965\) −2.33880 −0.0752886
\(966\) 0 0
\(967\) −34.9697 −1.12455 −0.562275 0.826950i \(-0.690074\pi\)
−0.562275 + 0.826950i \(0.690074\pi\)
\(968\) 0 0
\(969\) −39.6995 −1.27533
\(970\) 0 0
\(971\) 8.89375 0.285414 0.142707 0.989765i \(-0.454419\pi\)
0.142707 + 0.989765i \(0.454419\pi\)
\(972\) 0 0
\(973\) 9.10544 0.291907
\(974\) 0 0
\(975\) −37.8134 −1.21100
\(976\) 0 0
\(977\) 28.0338 0.896881 0.448440 0.893813i \(-0.351980\pi\)
0.448440 + 0.893813i \(0.351980\pi\)
\(978\) 0 0
\(979\) 1.96873 0.0629209
\(980\) 0 0
\(981\) 18.5642 0.592708
\(982\) 0 0
\(983\) 16.7595 0.534546 0.267273 0.963621i \(-0.413878\pi\)
0.267273 + 0.963621i \(0.413878\pi\)
\(984\) 0 0
\(985\) 2.46961 0.0786885
\(986\) 0 0
\(987\) −5.67470 −0.180628
\(988\) 0 0
\(989\) −7.45863 −0.237171
\(990\) 0 0
\(991\) 28.9457 0.919491 0.459745 0.888051i \(-0.347941\pi\)
0.459745 + 0.888051i \(0.347941\pi\)
\(992\) 0 0
\(993\) −8.38294 −0.266025
\(994\) 0 0
\(995\) 5.75255 0.182368
\(996\) 0 0
\(997\) 43.2081 1.36841 0.684207 0.729288i \(-0.260148\pi\)
0.684207 + 0.729288i \(0.260148\pi\)
\(998\) 0 0
\(999\) −5.84337 −0.184876
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 6008.2.a.d.1.7 49
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.d.1.7 49 1.1 even 1 trivial