Properties

Label 6028.2.a.f.1.12
Level $6028$
Weight $2$
Character 6028.1
Self dual yes
Analytic conductor $48.134$
Analytic rank $0$
Dimension $29$
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] = [6028,2,Mod(1,6028)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6028, 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("6028.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6028 = 2^{2} \cdot 11 \cdot 137 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6028.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: \(48.1338223384\)
Analytic rank: \(0\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 6028.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.191141 q^{3} -3.65958 q^{5} +2.84676 q^{7} -2.96346 q^{9} +O(q^{10})\) \(q-0.191141 q^{3} -3.65958 q^{5} +2.84676 q^{7} -2.96346 q^{9} +1.00000 q^{11} +2.64616 q^{13} +0.699498 q^{15} +3.79088 q^{17} -0.211026 q^{19} -0.544135 q^{21} +6.37500 q^{23} +8.39255 q^{25} +1.13987 q^{27} -1.95225 q^{29} -2.76637 q^{31} -0.191141 q^{33} -10.4180 q^{35} -5.91058 q^{37} -0.505791 q^{39} -9.71559 q^{41} -7.53429 q^{43} +10.8450 q^{45} +12.2920 q^{47} +1.10407 q^{49} -0.724595 q^{51} +5.38024 q^{53} -3.65958 q^{55} +0.0403359 q^{57} +0.674804 q^{59} -5.33389 q^{61} -8.43629 q^{63} -9.68384 q^{65} -12.6147 q^{67} -1.21853 q^{69} +3.49942 q^{71} +2.90946 q^{73} -1.60416 q^{75} +2.84676 q^{77} +0.712964 q^{79} +8.67252 q^{81} -15.7980 q^{83} -13.8730 q^{85} +0.373156 q^{87} +1.85344 q^{89} +7.53299 q^{91} +0.528768 q^{93} +0.772268 q^{95} +18.5406 q^{97} -2.96346 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 29 q + 14 q^{3} + 9 q^{5} + 14 q^{7} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 29 q + 14 q^{3} + 9 q^{5} + 14 q^{7} + 43 q^{9} + 29 q^{11} + 10 q^{15} + 29 q^{17} + 7 q^{19} + 2 q^{21} + 36 q^{23} + 36 q^{25} + 50 q^{27} + 9 q^{29} + 28 q^{31} + 14 q^{33} + 15 q^{35} + 25 q^{37} + 9 q^{39} + 19 q^{41} + 23 q^{43} + 5 q^{45} + 27 q^{47} + 27 q^{49} + 13 q^{51} + 4 q^{53} + 9 q^{55} + 14 q^{57} + 40 q^{59} + 20 q^{61} - 17 q^{63} + 9 q^{65} + 59 q^{67} + 30 q^{69} + 29 q^{71} - 5 q^{73} + 46 q^{75} + 14 q^{77} + 29 q^{79} + 61 q^{81} + 35 q^{83} - 57 q^{85} + 45 q^{87} + 39 q^{89} + 45 q^{91} - 8 q^{93} + q^{95} + 55 q^{97} + 43 q^{99}+O(q^{100}) \) 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
\(3\) −0.191141 −0.110356 −0.0551778 0.998477i \(-0.517573\pi\)
−0.0551778 + 0.998477i \(0.517573\pi\)
\(4\) 0 0
\(5\) −3.65958 −1.63662 −0.818308 0.574780i \(-0.805087\pi\)
−0.818308 + 0.574780i \(0.805087\pi\)
\(6\) 0 0
\(7\) 2.84676 1.07598 0.537988 0.842953i \(-0.319185\pi\)
0.537988 + 0.842953i \(0.319185\pi\)
\(8\) 0 0
\(9\) −2.96346 −0.987822
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 2.64616 0.733912 0.366956 0.930238i \(-0.380400\pi\)
0.366956 + 0.930238i \(0.380400\pi\)
\(14\) 0 0
\(15\) 0.699498 0.180610
\(16\) 0 0
\(17\) 3.79088 0.919424 0.459712 0.888068i \(-0.347953\pi\)
0.459712 + 0.888068i \(0.347953\pi\)
\(18\) 0 0
\(19\) −0.211026 −0.0484127 −0.0242064 0.999707i \(-0.507706\pi\)
−0.0242064 + 0.999707i \(0.507706\pi\)
\(20\) 0 0
\(21\) −0.544135 −0.118740
\(22\) 0 0
\(23\) 6.37500 1.32928 0.664640 0.747164i \(-0.268585\pi\)
0.664640 + 0.747164i \(0.268585\pi\)
\(24\) 0 0
\(25\) 8.39255 1.67851
\(26\) 0 0
\(27\) 1.13987 0.219367
\(28\) 0 0
\(29\) −1.95225 −0.362524 −0.181262 0.983435i \(-0.558018\pi\)
−0.181262 + 0.983435i \(0.558018\pi\)
\(30\) 0 0
\(31\) −2.76637 −0.496855 −0.248428 0.968650i \(-0.579914\pi\)
−0.248428 + 0.968650i \(0.579914\pi\)
\(32\) 0 0
\(33\) −0.191141 −0.0332735
\(34\) 0 0
\(35\) −10.4180 −1.76096
\(36\) 0 0
\(37\) −5.91058 −0.971693 −0.485847 0.874044i \(-0.661489\pi\)
−0.485847 + 0.874044i \(0.661489\pi\)
\(38\) 0 0
\(39\) −0.505791 −0.0809913
\(40\) 0 0
\(41\) −9.71559 −1.51732 −0.758660 0.651486i \(-0.774146\pi\)
−0.758660 + 0.651486i \(0.774146\pi\)
\(42\) 0 0
\(43\) −7.53429 −1.14897 −0.574484 0.818516i \(-0.694797\pi\)
−0.574484 + 0.818516i \(0.694797\pi\)
\(44\) 0 0
\(45\) 10.8450 1.61668
\(46\) 0 0
\(47\) 12.2920 1.79297 0.896486 0.443073i \(-0.146112\pi\)
0.896486 + 0.443073i \(0.146112\pi\)
\(48\) 0 0
\(49\) 1.10407 0.157724
\(50\) 0 0
\(51\) −0.724595 −0.101464
\(52\) 0 0
\(53\) 5.38024 0.739032 0.369516 0.929224i \(-0.379523\pi\)
0.369516 + 0.929224i \(0.379523\pi\)
\(54\) 0 0
\(55\) −3.65958 −0.493458
\(56\) 0 0
\(57\) 0.0403359 0.00534261
\(58\) 0 0
\(59\) 0.674804 0.0878520 0.0439260 0.999035i \(-0.486013\pi\)
0.0439260 + 0.999035i \(0.486013\pi\)
\(60\) 0 0
\(61\) −5.33389 −0.682934 −0.341467 0.939894i \(-0.610924\pi\)
−0.341467 + 0.939894i \(0.610924\pi\)
\(62\) 0 0
\(63\) −8.43629 −1.06287
\(64\) 0 0
\(65\) −9.68384 −1.20113
\(66\) 0 0
\(67\) −12.6147 −1.54113 −0.770566 0.637360i \(-0.780026\pi\)
−0.770566 + 0.637360i \(0.780026\pi\)
\(68\) 0 0
\(69\) −1.21853 −0.146693
\(70\) 0 0
\(71\) 3.49942 0.415304 0.207652 0.978203i \(-0.433418\pi\)
0.207652 + 0.978203i \(0.433418\pi\)
\(72\) 0 0
\(73\) 2.90946 0.340527 0.170263 0.985399i \(-0.445538\pi\)
0.170263 + 0.985399i \(0.445538\pi\)
\(74\) 0 0
\(75\) −1.60416 −0.185233
\(76\) 0 0
\(77\) 2.84676 0.324419
\(78\) 0 0
\(79\) 0.712964 0.0802147 0.0401074 0.999195i \(-0.487230\pi\)
0.0401074 + 0.999195i \(0.487230\pi\)
\(80\) 0 0
\(81\) 8.67252 0.963613
\(82\) 0 0
\(83\) −15.7980 −1.73406 −0.867031 0.498255i \(-0.833974\pi\)
−0.867031 + 0.498255i \(0.833974\pi\)
\(84\) 0 0
\(85\) −13.8730 −1.50474
\(86\) 0 0
\(87\) 0.373156 0.0400065
\(88\) 0 0
\(89\) 1.85344 0.196464 0.0982321 0.995164i \(-0.468681\pi\)
0.0982321 + 0.995164i \(0.468681\pi\)
\(90\) 0 0
\(91\) 7.53299 0.789672
\(92\) 0 0
\(93\) 0.528768 0.0548307
\(94\) 0 0
\(95\) 0.772268 0.0792330
\(96\) 0 0
\(97\) 18.5406 1.88252 0.941259 0.337686i \(-0.109644\pi\)
0.941259 + 0.337686i \(0.109644\pi\)
\(98\) 0 0
\(99\) −2.96346 −0.297839
\(100\) 0 0
\(101\) 13.4478 1.33810 0.669052 0.743216i \(-0.266700\pi\)
0.669052 + 0.743216i \(0.266700\pi\)
\(102\) 0 0
\(103\) −13.8383 −1.36353 −0.681765 0.731571i \(-0.738787\pi\)
−0.681765 + 0.731571i \(0.738787\pi\)
\(104\) 0 0
\(105\) 1.99131 0.194332
\(106\) 0 0
\(107\) 1.10269 0.106601 0.0533006 0.998579i \(-0.483026\pi\)
0.0533006 + 0.998579i \(0.483026\pi\)
\(108\) 0 0
\(109\) 8.29086 0.794121 0.397060 0.917792i \(-0.370030\pi\)
0.397060 + 0.917792i \(0.370030\pi\)
\(110\) 0 0
\(111\) 1.12976 0.107232
\(112\) 0 0
\(113\) 3.72302 0.350232 0.175116 0.984548i \(-0.443970\pi\)
0.175116 + 0.984548i \(0.443970\pi\)
\(114\) 0 0
\(115\) −23.3298 −2.17552
\(116\) 0 0
\(117\) −7.84180 −0.724974
\(118\) 0 0
\(119\) 10.7917 0.989278
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 1.85705 0.167445
\(124\) 0 0
\(125\) −12.4153 −1.11046
\(126\) 0 0
\(127\) 9.32564 0.827517 0.413758 0.910387i \(-0.364216\pi\)
0.413758 + 0.910387i \(0.364216\pi\)
\(128\) 0 0
\(129\) 1.44012 0.126795
\(130\) 0 0
\(131\) 16.6262 1.45264 0.726318 0.687359i \(-0.241230\pi\)
0.726318 + 0.687359i \(0.241230\pi\)
\(132\) 0 0
\(133\) −0.600742 −0.0520909
\(134\) 0 0
\(135\) −4.17143 −0.359020
\(136\) 0 0
\(137\) 1.00000 0.0854358
\(138\) 0 0
\(139\) 3.57515 0.303241 0.151620 0.988439i \(-0.451551\pi\)
0.151620 + 0.988439i \(0.451551\pi\)
\(140\) 0 0
\(141\) −2.34951 −0.197864
\(142\) 0 0
\(143\) 2.64616 0.221283
\(144\) 0 0
\(145\) 7.14442 0.593312
\(146\) 0 0
\(147\) −0.211033 −0.0174057
\(148\) 0 0
\(149\) 7.84531 0.642713 0.321356 0.946958i \(-0.395861\pi\)
0.321356 + 0.946958i \(0.395861\pi\)
\(150\) 0 0
\(151\) 12.1896 0.991979 0.495989 0.868329i \(-0.334805\pi\)
0.495989 + 0.868329i \(0.334805\pi\)
\(152\) 0 0
\(153\) −11.2341 −0.908227
\(154\) 0 0
\(155\) 10.1238 0.813161
\(156\) 0 0
\(157\) 16.9694 1.35431 0.677154 0.735842i \(-0.263213\pi\)
0.677154 + 0.735842i \(0.263213\pi\)
\(158\) 0 0
\(159\) −1.02839 −0.0815563
\(160\) 0 0
\(161\) 18.1481 1.43027
\(162\) 0 0
\(163\) −0.337480 −0.0264335 −0.0132167 0.999913i \(-0.504207\pi\)
−0.0132167 + 0.999913i \(0.504207\pi\)
\(164\) 0 0
\(165\) 0.699498 0.0544558
\(166\) 0 0
\(167\) 0.251999 0.0195003 0.00975014 0.999952i \(-0.496896\pi\)
0.00975014 + 0.999952i \(0.496896\pi\)
\(168\) 0 0
\(169\) −5.99785 −0.461373
\(170\) 0 0
\(171\) 0.625369 0.0478231
\(172\) 0 0
\(173\) 13.1881 1.00267 0.501337 0.865252i \(-0.332842\pi\)
0.501337 + 0.865252i \(0.332842\pi\)
\(174\) 0 0
\(175\) 23.8916 1.80604
\(176\) 0 0
\(177\) −0.128983 −0.00969496
\(178\) 0 0
\(179\) 24.0856 1.80024 0.900120 0.435643i \(-0.143479\pi\)
0.900120 + 0.435643i \(0.143479\pi\)
\(180\) 0 0
\(181\) −15.0171 −1.11621 −0.558106 0.829770i \(-0.688472\pi\)
−0.558106 + 0.829770i \(0.688472\pi\)
\(182\) 0 0
\(183\) 1.01953 0.0753656
\(184\) 0 0
\(185\) 21.6303 1.59029
\(186\) 0 0
\(187\) 3.79088 0.277217
\(188\) 0 0
\(189\) 3.24493 0.236034
\(190\) 0 0
\(191\) 6.10029 0.441401 0.220701 0.975342i \(-0.429166\pi\)
0.220701 + 0.975342i \(0.429166\pi\)
\(192\) 0 0
\(193\) 10.5020 0.755947 0.377973 0.925816i \(-0.376621\pi\)
0.377973 + 0.925816i \(0.376621\pi\)
\(194\) 0 0
\(195\) 1.85098 0.132552
\(196\) 0 0
\(197\) 3.85868 0.274920 0.137460 0.990507i \(-0.456106\pi\)
0.137460 + 0.990507i \(0.456106\pi\)
\(198\) 0 0
\(199\) −4.33355 −0.307197 −0.153599 0.988133i \(-0.549086\pi\)
−0.153599 + 0.988133i \(0.549086\pi\)
\(200\) 0 0
\(201\) 2.41119 0.170072
\(202\) 0 0
\(203\) −5.55759 −0.390067
\(204\) 0 0
\(205\) 35.5550 2.48327
\(206\) 0 0
\(207\) −18.8921 −1.31309
\(208\) 0 0
\(209\) −0.211026 −0.0145970
\(210\) 0 0
\(211\) −14.9057 −1.02615 −0.513074 0.858345i \(-0.671493\pi\)
−0.513074 + 0.858345i \(0.671493\pi\)
\(212\) 0 0
\(213\) −0.668884 −0.0458312
\(214\) 0 0
\(215\) 27.5724 1.88042
\(216\) 0 0
\(217\) −7.87521 −0.534604
\(218\) 0 0
\(219\) −0.556119 −0.0375790
\(220\) 0 0
\(221\) 10.0313 0.674776
\(222\) 0 0
\(223\) −17.8953 −1.19836 −0.599179 0.800615i \(-0.704506\pi\)
−0.599179 + 0.800615i \(0.704506\pi\)
\(224\) 0 0
\(225\) −24.8710 −1.65807
\(226\) 0 0
\(227\) −18.3987 −1.22117 −0.610583 0.791953i \(-0.709065\pi\)
−0.610583 + 0.791953i \(0.709065\pi\)
\(228\) 0 0
\(229\) 12.6620 0.836728 0.418364 0.908280i \(-0.362604\pi\)
0.418364 + 0.908280i \(0.362604\pi\)
\(230\) 0 0
\(231\) −0.544135 −0.0358014
\(232\) 0 0
\(233\) 18.7145 1.22603 0.613014 0.790072i \(-0.289957\pi\)
0.613014 + 0.790072i \(0.289957\pi\)
\(234\) 0 0
\(235\) −44.9836 −2.93440
\(236\) 0 0
\(237\) −0.136277 −0.00885214
\(238\) 0 0
\(239\) 1.91435 0.123829 0.0619146 0.998081i \(-0.480279\pi\)
0.0619146 + 0.998081i \(0.480279\pi\)
\(240\) 0 0
\(241\) 22.2997 1.43645 0.718226 0.695810i \(-0.244954\pi\)
0.718226 + 0.695810i \(0.244954\pi\)
\(242\) 0 0
\(243\) −5.07727 −0.325707
\(244\) 0 0
\(245\) −4.04043 −0.258133
\(246\) 0 0
\(247\) −0.558409 −0.0355307
\(248\) 0 0
\(249\) 3.01966 0.191363
\(250\) 0 0
\(251\) 1.62088 0.102309 0.0511546 0.998691i \(-0.483710\pi\)
0.0511546 + 0.998691i \(0.483710\pi\)
\(252\) 0 0
\(253\) 6.37500 0.400793
\(254\) 0 0
\(255\) 2.65171 0.166057
\(256\) 0 0
\(257\) 6.37871 0.397893 0.198946 0.980010i \(-0.436248\pi\)
0.198946 + 0.980010i \(0.436248\pi\)
\(258\) 0 0
\(259\) −16.8260 −1.04552
\(260\) 0 0
\(261\) 5.78542 0.358109
\(262\) 0 0
\(263\) 0.257630 0.0158862 0.00794308 0.999968i \(-0.497472\pi\)
0.00794308 + 0.999968i \(0.497472\pi\)
\(264\) 0 0
\(265\) −19.6894 −1.20951
\(266\) 0 0
\(267\) −0.354269 −0.0216809
\(268\) 0 0
\(269\) −16.8603 −1.02799 −0.513996 0.857792i \(-0.671835\pi\)
−0.513996 + 0.857792i \(0.671835\pi\)
\(270\) 0 0
\(271\) −7.26050 −0.441044 −0.220522 0.975382i \(-0.570776\pi\)
−0.220522 + 0.975382i \(0.570776\pi\)
\(272\) 0 0
\(273\) −1.43987 −0.0871447
\(274\) 0 0
\(275\) 8.39255 0.506090
\(276\) 0 0
\(277\) −15.5461 −0.934072 −0.467036 0.884238i \(-0.654678\pi\)
−0.467036 + 0.884238i \(0.654678\pi\)
\(278\) 0 0
\(279\) 8.19805 0.490804
\(280\) 0 0
\(281\) 5.48160 0.327005 0.163503 0.986543i \(-0.447721\pi\)
0.163503 + 0.986543i \(0.447721\pi\)
\(282\) 0 0
\(283\) 31.8976 1.89612 0.948058 0.318098i \(-0.103044\pi\)
0.948058 + 0.318098i \(0.103044\pi\)
\(284\) 0 0
\(285\) −0.147612 −0.00874380
\(286\) 0 0
\(287\) −27.6580 −1.63260
\(288\) 0 0
\(289\) −2.62922 −0.154660
\(290\) 0 0
\(291\) −3.54389 −0.207746
\(292\) 0 0
\(293\) −9.40112 −0.549219 −0.274610 0.961556i \(-0.588549\pi\)
−0.274610 + 0.961556i \(0.588549\pi\)
\(294\) 0 0
\(295\) −2.46950 −0.143780
\(296\) 0 0
\(297\) 1.13987 0.0661417
\(298\) 0 0
\(299\) 16.8693 0.975574
\(300\) 0 0
\(301\) −21.4484 −1.23626
\(302\) 0 0
\(303\) −2.57043 −0.147667
\(304\) 0 0
\(305\) 19.5198 1.11770
\(306\) 0 0
\(307\) 3.40735 0.194468 0.0972339 0.995262i \(-0.469000\pi\)
0.0972339 + 0.995262i \(0.469000\pi\)
\(308\) 0 0
\(309\) 2.64508 0.150473
\(310\) 0 0
\(311\) 23.1348 1.31186 0.655928 0.754823i \(-0.272277\pi\)
0.655928 + 0.754823i \(0.272277\pi\)
\(312\) 0 0
\(313\) 3.00793 0.170018 0.0850092 0.996380i \(-0.472908\pi\)
0.0850092 + 0.996380i \(0.472908\pi\)
\(314\) 0 0
\(315\) 30.8733 1.73951
\(316\) 0 0
\(317\) −18.7809 −1.05484 −0.527419 0.849605i \(-0.676840\pi\)
−0.527419 + 0.849605i \(0.676840\pi\)
\(318\) 0 0
\(319\) −1.95225 −0.109305
\(320\) 0 0
\(321\) −0.210770 −0.0117640
\(322\) 0 0
\(323\) −0.799975 −0.0445118
\(324\) 0 0
\(325\) 22.2080 1.23188
\(326\) 0 0
\(327\) −1.58473 −0.0876357
\(328\) 0 0
\(329\) 34.9924 1.92919
\(330\) 0 0
\(331\) 25.1658 1.38324 0.691618 0.722264i \(-0.256898\pi\)
0.691618 + 0.722264i \(0.256898\pi\)
\(332\) 0 0
\(333\) 17.5158 0.959860
\(334\) 0 0
\(335\) 46.1646 2.52224
\(336\) 0 0
\(337\) 12.4772 0.679676 0.339838 0.940484i \(-0.389628\pi\)
0.339838 + 0.940484i \(0.389628\pi\)
\(338\) 0 0
\(339\) −0.711624 −0.0386501
\(340\) 0 0
\(341\) −2.76637 −0.149807
\(342\) 0 0
\(343\) −16.7843 −0.906269
\(344\) 0 0
\(345\) 4.45930 0.240081
\(346\) 0 0
\(347\) −6.49616 −0.348732 −0.174366 0.984681i \(-0.555788\pi\)
−0.174366 + 0.984681i \(0.555788\pi\)
\(348\) 0 0
\(349\) 23.7997 1.27397 0.636983 0.770878i \(-0.280182\pi\)
0.636983 + 0.770878i \(0.280182\pi\)
\(350\) 0 0
\(351\) 3.01626 0.160996
\(352\) 0 0
\(353\) −8.41945 −0.448122 −0.224061 0.974575i \(-0.571932\pi\)
−0.224061 + 0.974575i \(0.571932\pi\)
\(354\) 0 0
\(355\) −12.8064 −0.679694
\(356\) 0 0
\(357\) −2.06275 −0.109172
\(358\) 0 0
\(359\) 22.1786 1.17054 0.585271 0.810838i \(-0.300988\pi\)
0.585271 + 0.810838i \(0.300988\pi\)
\(360\) 0 0
\(361\) −18.9555 −0.997656
\(362\) 0 0
\(363\) −0.191141 −0.0100323
\(364\) 0 0
\(365\) −10.6474 −0.557311
\(366\) 0 0
\(367\) −10.3739 −0.541516 −0.270758 0.962647i \(-0.587274\pi\)
−0.270758 + 0.962647i \(0.587274\pi\)
\(368\) 0 0
\(369\) 28.7918 1.49884
\(370\) 0 0
\(371\) 15.3163 0.795181
\(372\) 0 0
\(373\) −8.49700 −0.439958 −0.219979 0.975505i \(-0.570599\pi\)
−0.219979 + 0.975505i \(0.570599\pi\)
\(374\) 0 0
\(375\) 2.37308 0.122545
\(376\) 0 0
\(377\) −5.16596 −0.266061
\(378\) 0 0
\(379\) 31.7991 1.63341 0.816704 0.577057i \(-0.195799\pi\)
0.816704 + 0.577057i \(0.195799\pi\)
\(380\) 0 0
\(381\) −1.78252 −0.0913211
\(382\) 0 0
\(383\) 11.2404 0.574358 0.287179 0.957877i \(-0.407283\pi\)
0.287179 + 0.957877i \(0.407283\pi\)
\(384\) 0 0
\(385\) −10.4180 −0.530949
\(386\) 0 0
\(387\) 22.3276 1.13498
\(388\) 0 0
\(389\) 21.9964 1.11526 0.557630 0.830090i \(-0.311711\pi\)
0.557630 + 0.830090i \(0.311711\pi\)
\(390\) 0 0
\(391\) 24.1669 1.22217
\(392\) 0 0
\(393\) −3.17795 −0.160306
\(394\) 0 0
\(395\) −2.60915 −0.131281
\(396\) 0 0
\(397\) −23.3947 −1.17414 −0.587072 0.809534i \(-0.699720\pi\)
−0.587072 + 0.809534i \(0.699720\pi\)
\(398\) 0 0
\(399\) 0.114827 0.00574852
\(400\) 0 0
\(401\) 3.57728 0.178641 0.0893205 0.996003i \(-0.471530\pi\)
0.0893205 + 0.996003i \(0.471530\pi\)
\(402\) 0 0
\(403\) −7.32026 −0.364648
\(404\) 0 0
\(405\) −31.7378 −1.57706
\(406\) 0 0
\(407\) −5.91058 −0.292977
\(408\) 0 0
\(409\) −12.6237 −0.624202 −0.312101 0.950049i \(-0.601033\pi\)
−0.312101 + 0.950049i \(0.601033\pi\)
\(410\) 0 0
\(411\) −0.191141 −0.00942831
\(412\) 0 0
\(413\) 1.92101 0.0945266
\(414\) 0 0
\(415\) 57.8143 2.83799
\(416\) 0 0
\(417\) −0.683360 −0.0334643
\(418\) 0 0
\(419\) 14.0823 0.687966 0.343983 0.938976i \(-0.388224\pi\)
0.343983 + 0.938976i \(0.388224\pi\)
\(420\) 0 0
\(421\) 26.9202 1.31201 0.656004 0.754757i \(-0.272245\pi\)
0.656004 + 0.754757i \(0.272245\pi\)
\(422\) 0 0
\(423\) −36.4269 −1.77114
\(424\) 0 0
\(425\) 31.8152 1.54326
\(426\) 0 0
\(427\) −15.1843 −0.734821
\(428\) 0 0
\(429\) −0.505791 −0.0244198
\(430\) 0 0
\(431\) −23.7618 −1.14457 −0.572284 0.820056i \(-0.693942\pi\)
−0.572284 + 0.820056i \(0.693942\pi\)
\(432\) 0 0
\(433\) 21.2300 1.02025 0.510125 0.860101i \(-0.329599\pi\)
0.510125 + 0.860101i \(0.329599\pi\)
\(434\) 0 0
\(435\) −1.36559 −0.0654753
\(436\) 0 0
\(437\) −1.34529 −0.0643540
\(438\) 0 0
\(439\) −16.5133 −0.788139 −0.394069 0.919081i \(-0.628933\pi\)
−0.394069 + 0.919081i \(0.628933\pi\)
\(440\) 0 0
\(441\) −3.27186 −0.155803
\(442\) 0 0
\(443\) 3.90666 0.185611 0.0928054 0.995684i \(-0.470417\pi\)
0.0928054 + 0.995684i \(0.470417\pi\)
\(444\) 0 0
\(445\) −6.78281 −0.321536
\(446\) 0 0
\(447\) −1.49956 −0.0709270
\(448\) 0 0
\(449\) 21.2784 1.00419 0.502095 0.864812i \(-0.332563\pi\)
0.502095 + 0.864812i \(0.332563\pi\)
\(450\) 0 0
\(451\) −9.71559 −0.457489
\(452\) 0 0
\(453\) −2.32995 −0.109470
\(454\) 0 0
\(455\) −27.5676 −1.29239
\(456\) 0 0
\(457\) 19.4251 0.908668 0.454334 0.890831i \(-0.349877\pi\)
0.454334 + 0.890831i \(0.349877\pi\)
\(458\) 0 0
\(459\) 4.32109 0.201691
\(460\) 0 0
\(461\) −5.47388 −0.254944 −0.127472 0.991842i \(-0.540686\pi\)
−0.127472 + 0.991842i \(0.540686\pi\)
\(462\) 0 0
\(463\) −36.1130 −1.67831 −0.839156 0.543890i \(-0.816951\pi\)
−0.839156 + 0.543890i \(0.816951\pi\)
\(464\) 0 0
\(465\) −1.93507 −0.0897368
\(466\) 0 0
\(467\) 19.1946 0.888219 0.444110 0.895972i \(-0.353520\pi\)
0.444110 + 0.895972i \(0.353520\pi\)
\(468\) 0 0
\(469\) −35.9111 −1.65822
\(470\) 0 0
\(471\) −3.24356 −0.149455
\(472\) 0 0
\(473\) −7.53429 −0.346427
\(474\) 0 0
\(475\) −1.77105 −0.0812612
\(476\) 0 0
\(477\) −15.9441 −0.730032
\(478\) 0 0
\(479\) −1.14526 −0.0523281 −0.0261640 0.999658i \(-0.508329\pi\)
−0.0261640 + 0.999658i \(0.508329\pi\)
\(480\) 0 0
\(481\) −15.6403 −0.713138
\(482\) 0 0
\(483\) −3.46886 −0.157839
\(484\) 0 0
\(485\) −67.8510 −3.08096
\(486\) 0 0
\(487\) 32.5610 1.47548 0.737739 0.675086i \(-0.235893\pi\)
0.737739 + 0.675086i \(0.235893\pi\)
\(488\) 0 0
\(489\) 0.0645064 0.00291708
\(490\) 0 0
\(491\) 0.129597 0.00584862 0.00292431 0.999996i \(-0.499069\pi\)
0.00292431 + 0.999996i \(0.499069\pi\)
\(492\) 0 0
\(493\) −7.40075 −0.333313
\(494\) 0 0
\(495\) 10.8450 0.487449
\(496\) 0 0
\(497\) 9.96202 0.446857
\(498\) 0 0
\(499\) −30.3346 −1.35796 −0.678982 0.734155i \(-0.737579\pi\)
−0.678982 + 0.734155i \(0.737579\pi\)
\(500\) 0 0
\(501\) −0.0481675 −0.00215196
\(502\) 0 0
\(503\) −3.62787 −0.161759 −0.0808794 0.996724i \(-0.525773\pi\)
−0.0808794 + 0.996724i \(0.525773\pi\)
\(504\) 0 0
\(505\) −49.2133 −2.18996
\(506\) 0 0
\(507\) 1.14644 0.0509151
\(508\) 0 0
\(509\) −12.2882 −0.544667 −0.272333 0.962203i \(-0.587795\pi\)
−0.272333 + 0.962203i \(0.587795\pi\)
\(510\) 0 0
\(511\) 8.28255 0.366398
\(512\) 0 0
\(513\) −0.240541 −0.0106202
\(514\) 0 0
\(515\) 50.6425 2.23157
\(516\) 0 0
\(517\) 12.2920 0.540601
\(518\) 0 0
\(519\) −2.52080 −0.110651
\(520\) 0 0
\(521\) 4.02854 0.176493 0.0882467 0.996099i \(-0.471874\pi\)
0.0882467 + 0.996099i \(0.471874\pi\)
\(522\) 0 0
\(523\) −31.7789 −1.38960 −0.694798 0.719205i \(-0.744506\pi\)
−0.694798 + 0.719205i \(0.744506\pi\)
\(524\) 0 0
\(525\) −4.56668 −0.199306
\(526\) 0 0
\(527\) −10.4870 −0.456820
\(528\) 0 0
\(529\) 17.6406 0.766984
\(530\) 0 0
\(531\) −1.99976 −0.0867821
\(532\) 0 0
\(533\) −25.7090 −1.11358
\(534\) 0 0
\(535\) −4.03539 −0.174465
\(536\) 0 0
\(537\) −4.60375 −0.198666
\(538\) 0 0
\(539\) 1.10407 0.0475555
\(540\) 0 0
\(541\) 13.7235 0.590018 0.295009 0.955495i \(-0.404677\pi\)
0.295009 + 0.955495i \(0.404677\pi\)
\(542\) 0 0
\(543\) 2.87039 0.123180
\(544\) 0 0
\(545\) −30.3411 −1.29967
\(546\) 0 0
\(547\) −1.56232 −0.0668000 −0.0334000 0.999442i \(-0.510634\pi\)
−0.0334000 + 0.999442i \(0.510634\pi\)
\(548\) 0 0
\(549\) 15.8068 0.674617
\(550\) 0 0
\(551\) 0.411976 0.0175508
\(552\) 0 0
\(553\) 2.02964 0.0863091
\(554\) 0 0
\(555\) −4.13444 −0.175497
\(556\) 0 0
\(557\) 4.03434 0.170941 0.0854703 0.996341i \(-0.472761\pi\)
0.0854703 + 0.996341i \(0.472761\pi\)
\(558\) 0 0
\(559\) −19.9369 −0.843242
\(560\) 0 0
\(561\) −0.724595 −0.0305924
\(562\) 0 0
\(563\) −5.04172 −0.212483 −0.106242 0.994340i \(-0.533882\pi\)
−0.106242 + 0.994340i \(0.533882\pi\)
\(564\) 0 0
\(565\) −13.6247 −0.573196
\(566\) 0 0
\(567\) 24.6886 1.03682
\(568\) 0 0
\(569\) 9.97227 0.418059 0.209030 0.977909i \(-0.432969\pi\)
0.209030 + 0.977909i \(0.432969\pi\)
\(570\) 0 0
\(571\) −11.0679 −0.463176 −0.231588 0.972814i \(-0.574392\pi\)
−0.231588 + 0.972814i \(0.574392\pi\)
\(572\) 0 0
\(573\) −1.16602 −0.0487111
\(574\) 0 0
\(575\) 53.5025 2.23121
\(576\) 0 0
\(577\) −37.3322 −1.55416 −0.777081 0.629401i \(-0.783300\pi\)
−0.777081 + 0.629401i \(0.783300\pi\)
\(578\) 0 0
\(579\) −2.00736 −0.0834230
\(580\) 0 0
\(581\) −44.9733 −1.86581
\(582\) 0 0
\(583\) 5.38024 0.222827
\(584\) 0 0
\(585\) 28.6977 1.18650
\(586\) 0 0
\(587\) 26.3727 1.08852 0.544259 0.838917i \(-0.316811\pi\)
0.544259 + 0.838917i \(0.316811\pi\)
\(588\) 0 0
\(589\) 0.583777 0.0240541
\(590\) 0 0
\(591\) −0.737554 −0.0303389
\(592\) 0 0
\(593\) 18.1058 0.743517 0.371758 0.928329i \(-0.378755\pi\)
0.371758 + 0.928329i \(0.378755\pi\)
\(594\) 0 0
\(595\) −39.4933 −1.61907
\(596\) 0 0
\(597\) 0.828321 0.0339009
\(598\) 0 0
\(599\) 14.3505 0.586344 0.293172 0.956060i \(-0.405289\pi\)
0.293172 + 0.956060i \(0.405289\pi\)
\(600\) 0 0
\(601\) 12.7363 0.519525 0.259762 0.965673i \(-0.416356\pi\)
0.259762 + 0.965673i \(0.416356\pi\)
\(602\) 0 0
\(603\) 37.3832 1.52236
\(604\) 0 0
\(605\) −3.65958 −0.148783
\(606\) 0 0
\(607\) 30.6628 1.24456 0.622282 0.782794i \(-0.286206\pi\)
0.622282 + 0.782794i \(0.286206\pi\)
\(608\) 0 0
\(609\) 1.06229 0.0430460
\(610\) 0 0
\(611\) 32.5266 1.31588
\(612\) 0 0
\(613\) 32.1110 1.29695 0.648476 0.761235i \(-0.275407\pi\)
0.648476 + 0.761235i \(0.275407\pi\)
\(614\) 0 0
\(615\) −6.79604 −0.274043
\(616\) 0 0
\(617\) 9.45258 0.380547 0.190273 0.981731i \(-0.439063\pi\)
0.190273 + 0.981731i \(0.439063\pi\)
\(618\) 0 0
\(619\) 30.8478 1.23988 0.619939 0.784650i \(-0.287157\pi\)
0.619939 + 0.784650i \(0.287157\pi\)
\(620\) 0 0
\(621\) 7.26664 0.291600
\(622\) 0 0
\(623\) 5.27630 0.211391
\(624\) 0 0
\(625\) 3.47212 0.138885
\(626\) 0 0
\(627\) 0.0403359 0.00161086
\(628\) 0 0
\(629\) −22.4063 −0.893398
\(630\) 0 0
\(631\) 9.99764 0.398000 0.199000 0.980000i \(-0.436231\pi\)
0.199000 + 0.980000i \(0.436231\pi\)
\(632\) 0 0
\(633\) 2.84909 0.113241
\(634\) 0 0
\(635\) −34.1280 −1.35433
\(636\) 0 0
\(637\) 2.92154 0.115756
\(638\) 0 0
\(639\) −10.3704 −0.410247
\(640\) 0 0
\(641\) −1.67922 −0.0663251 −0.0331625 0.999450i \(-0.510558\pi\)
−0.0331625 + 0.999450i \(0.510558\pi\)
\(642\) 0 0
\(643\) 4.23418 0.166980 0.0834899 0.996509i \(-0.473393\pi\)
0.0834899 + 0.996509i \(0.473393\pi\)
\(644\) 0 0
\(645\) −5.27022 −0.207515
\(646\) 0 0
\(647\) 15.0959 0.593481 0.296741 0.954958i \(-0.404100\pi\)
0.296741 + 0.954958i \(0.404100\pi\)
\(648\) 0 0
\(649\) 0.674804 0.0264884
\(650\) 0 0
\(651\) 1.50528 0.0589965
\(652\) 0 0
\(653\) 11.2754 0.441242 0.220621 0.975360i \(-0.429192\pi\)
0.220621 + 0.975360i \(0.429192\pi\)
\(654\) 0 0
\(655\) −60.8449 −2.37741
\(656\) 0 0
\(657\) −8.62209 −0.336380
\(658\) 0 0
\(659\) 18.2708 0.711730 0.355865 0.934537i \(-0.384186\pi\)
0.355865 + 0.934537i \(0.384186\pi\)
\(660\) 0 0
\(661\) 20.2041 0.785847 0.392924 0.919571i \(-0.371464\pi\)
0.392924 + 0.919571i \(0.371464\pi\)
\(662\) 0 0
\(663\) −1.91739 −0.0744653
\(664\) 0 0
\(665\) 2.19846 0.0852528
\(666\) 0 0
\(667\) −12.4456 −0.481895
\(668\) 0 0
\(669\) 3.42054 0.132246
\(670\) 0 0
\(671\) −5.33389 −0.205912
\(672\) 0 0
\(673\) −21.3590 −0.823328 −0.411664 0.911336i \(-0.635052\pi\)
−0.411664 + 0.911336i \(0.635052\pi\)
\(674\) 0 0
\(675\) 9.56637 0.368210
\(676\) 0 0
\(677\) 35.3233 1.35758 0.678792 0.734331i \(-0.262504\pi\)
0.678792 + 0.734331i \(0.262504\pi\)
\(678\) 0 0
\(679\) 52.7809 2.02554
\(680\) 0 0
\(681\) 3.51676 0.134762
\(682\) 0 0
\(683\) −5.07478 −0.194181 −0.0970905 0.995276i \(-0.530954\pi\)
−0.0970905 + 0.995276i \(0.530954\pi\)
\(684\) 0 0
\(685\) −3.65958 −0.139825
\(686\) 0 0
\(687\) −2.42023 −0.0923375
\(688\) 0 0
\(689\) 14.2370 0.542385
\(690\) 0 0
\(691\) 4.74824 0.180631 0.0903157 0.995913i \(-0.471212\pi\)
0.0903157 + 0.995913i \(0.471212\pi\)
\(692\) 0 0
\(693\) −8.43629 −0.320468
\(694\) 0 0
\(695\) −13.0836 −0.496288
\(696\) 0 0
\(697\) −36.8307 −1.39506
\(698\) 0 0
\(699\) −3.57712 −0.135299
\(700\) 0 0
\(701\) −38.9423 −1.47083 −0.735416 0.677616i \(-0.763013\pi\)
−0.735416 + 0.677616i \(0.763013\pi\)
\(702\) 0 0
\(703\) 1.24729 0.0470423
\(704\) 0 0
\(705\) 8.59823 0.323828
\(706\) 0 0
\(707\) 38.2827 1.43977
\(708\) 0 0
\(709\) −51.2779 −1.92578 −0.962890 0.269893i \(-0.913012\pi\)
−0.962890 + 0.269893i \(0.913012\pi\)
\(710\) 0 0
\(711\) −2.11284 −0.0792378
\(712\) 0 0
\(713\) −17.6356 −0.660459
\(714\) 0 0
\(715\) −9.68384 −0.362155
\(716\) 0 0
\(717\) −0.365913 −0.0136653
\(718\) 0 0
\(719\) 16.5913 0.618749 0.309375 0.950940i \(-0.399880\pi\)
0.309375 + 0.950940i \(0.399880\pi\)
\(720\) 0 0
\(721\) −39.3944 −1.46712
\(722\) 0 0
\(723\) −4.26241 −0.158521
\(724\) 0 0
\(725\) −16.3843 −0.608499
\(726\) 0 0
\(727\) 33.7610 1.25213 0.626063 0.779773i \(-0.284665\pi\)
0.626063 + 0.779773i \(0.284665\pi\)
\(728\) 0 0
\(729\) −25.0471 −0.927670
\(730\) 0 0
\(731\) −28.5616 −1.05639
\(732\) 0 0
\(733\) −25.1316 −0.928256 −0.464128 0.885768i \(-0.653632\pi\)
−0.464128 + 0.885768i \(0.653632\pi\)
\(734\) 0 0
\(735\) 0.772293 0.0284865
\(736\) 0 0
\(737\) −12.6147 −0.464669
\(738\) 0 0
\(739\) −5.55248 −0.204251 −0.102126 0.994771i \(-0.532564\pi\)
−0.102126 + 0.994771i \(0.532564\pi\)
\(740\) 0 0
\(741\) 0.106735 0.00392101
\(742\) 0 0
\(743\) 21.7155 0.796664 0.398332 0.917241i \(-0.369589\pi\)
0.398332 + 0.917241i \(0.369589\pi\)
\(744\) 0 0
\(745\) −28.7106 −1.05187
\(746\) 0 0
\(747\) 46.8170 1.71294
\(748\) 0 0
\(749\) 3.13910 0.114700
\(750\) 0 0
\(751\) −2.44058 −0.0890580 −0.0445290 0.999008i \(-0.514179\pi\)
−0.0445290 + 0.999008i \(0.514179\pi\)
\(752\) 0 0
\(753\) −0.309818 −0.0112904
\(754\) 0 0
\(755\) −44.6090 −1.62349
\(756\) 0 0
\(757\) −38.1738 −1.38745 −0.693726 0.720239i \(-0.744032\pi\)
−0.693726 + 0.720239i \(0.744032\pi\)
\(758\) 0 0
\(759\) −1.21853 −0.0442297
\(760\) 0 0
\(761\) −36.2672 −1.31469 −0.657343 0.753592i \(-0.728320\pi\)
−0.657343 + 0.753592i \(0.728320\pi\)
\(762\) 0 0
\(763\) 23.6021 0.854455
\(764\) 0 0
\(765\) 41.1123 1.48642
\(766\) 0 0
\(767\) 1.78564 0.0644757
\(768\) 0 0
\(769\) −25.6865 −0.926277 −0.463139 0.886286i \(-0.653277\pi\)
−0.463139 + 0.886286i \(0.653277\pi\)
\(770\) 0 0
\(771\) −1.21924 −0.0439097
\(772\) 0 0
\(773\) −20.6836 −0.743936 −0.371968 0.928246i \(-0.621317\pi\)
−0.371968 + 0.928246i \(0.621317\pi\)
\(774\) 0 0
\(775\) −23.2169 −0.833976
\(776\) 0 0
\(777\) 3.21615 0.115379
\(778\) 0 0
\(779\) 2.05024 0.0734576
\(780\) 0 0
\(781\) 3.49942 0.125219
\(782\) 0 0
\(783\) −2.22530 −0.0795258
\(784\) 0 0
\(785\) −62.1010 −2.21648
\(786\) 0 0
\(787\) −25.7277 −0.917092 −0.458546 0.888671i \(-0.651630\pi\)
−0.458546 + 0.888671i \(0.651630\pi\)
\(788\) 0 0
\(789\) −0.0492438 −0.00175313
\(790\) 0 0
\(791\) 10.5986 0.376842
\(792\) 0 0
\(793\) −14.1143 −0.501214
\(794\) 0 0
\(795\) 3.76346 0.133476
\(796\) 0 0
\(797\) 10.0793 0.357026 0.178513 0.983938i \(-0.442871\pi\)
0.178513 + 0.983938i \(0.442871\pi\)
\(798\) 0 0
\(799\) 46.5975 1.64850
\(800\) 0 0
\(801\) −5.49260 −0.194072
\(802\) 0 0
\(803\) 2.90946 0.102673
\(804\) 0 0
\(805\) −66.4146 −2.34081
\(806\) 0 0
\(807\) 3.22271 0.113445
\(808\) 0 0
\(809\) 52.3577 1.84080 0.920400 0.390978i \(-0.127863\pi\)
0.920400 + 0.390978i \(0.127863\pi\)
\(810\) 0 0
\(811\) 36.4110 1.27856 0.639282 0.768972i \(-0.279232\pi\)
0.639282 + 0.768972i \(0.279232\pi\)
\(812\) 0 0
\(813\) 1.38778 0.0486717
\(814\) 0 0
\(815\) 1.23504 0.0432614
\(816\) 0 0
\(817\) 1.58993 0.0556247
\(818\) 0 0
\(819\) −22.3237 −0.780055
\(820\) 0 0
\(821\) −30.9504 −1.08018 −0.540088 0.841608i \(-0.681609\pi\)
−0.540088 + 0.841608i \(0.681609\pi\)
\(822\) 0 0
\(823\) −6.21942 −0.216795 −0.108398 0.994108i \(-0.534572\pi\)
−0.108398 + 0.994108i \(0.534572\pi\)
\(824\) 0 0
\(825\) −1.60416 −0.0558498
\(826\) 0 0
\(827\) 42.5570 1.47985 0.739925 0.672689i \(-0.234861\pi\)
0.739925 + 0.672689i \(0.234861\pi\)
\(828\) 0 0
\(829\) 48.9373 1.69966 0.849832 0.527053i \(-0.176703\pi\)
0.849832 + 0.527053i \(0.176703\pi\)
\(830\) 0 0
\(831\) 2.97150 0.103080
\(832\) 0 0
\(833\) 4.18539 0.145015
\(834\) 0 0
\(835\) −0.922212 −0.0319145
\(836\) 0 0
\(837\) −3.15329 −0.108994
\(838\) 0 0
\(839\) 15.3258 0.529105 0.264552 0.964371i \(-0.414776\pi\)
0.264552 + 0.964371i \(0.414776\pi\)
\(840\) 0 0
\(841\) −25.1887 −0.868577
\(842\) 0 0
\(843\) −1.04776 −0.0360868
\(844\) 0 0
\(845\) 21.9496 0.755090
\(846\) 0 0
\(847\) 2.84676 0.0978160
\(848\) 0 0
\(849\) −6.09695 −0.209247
\(850\) 0 0
\(851\) −37.6799 −1.29165
\(852\) 0 0
\(853\) 43.0565 1.47423 0.737113 0.675770i \(-0.236189\pi\)
0.737113 + 0.675770i \(0.236189\pi\)
\(854\) 0 0
\(855\) −2.28859 −0.0782681
\(856\) 0 0
\(857\) 52.7997 1.80360 0.901801 0.432152i \(-0.142245\pi\)
0.901801 + 0.432152i \(0.142245\pi\)
\(858\) 0 0
\(859\) 40.8128 1.39251 0.696257 0.717793i \(-0.254847\pi\)
0.696257 + 0.717793i \(0.254847\pi\)
\(860\) 0 0
\(861\) 5.28659 0.180167
\(862\) 0 0
\(863\) −15.8251 −0.538694 −0.269347 0.963043i \(-0.586808\pi\)
−0.269347 + 0.963043i \(0.586808\pi\)
\(864\) 0 0
\(865\) −48.2630 −1.64099
\(866\) 0 0
\(867\) 0.502552 0.0170676
\(868\) 0 0
\(869\) 0.712964 0.0241856
\(870\) 0 0
\(871\) −33.3805 −1.13106
\(872\) 0 0
\(873\) −54.9446 −1.85959
\(874\) 0 0
\(875\) −35.3435 −1.19483
\(876\) 0 0
\(877\) −30.7156 −1.03719 −0.518596 0.855020i \(-0.673545\pi\)
−0.518596 + 0.855020i \(0.673545\pi\)
\(878\) 0 0
\(879\) 1.79694 0.0606094
\(880\) 0 0
\(881\) 14.1326 0.476138 0.238069 0.971248i \(-0.423486\pi\)
0.238069 + 0.971248i \(0.423486\pi\)
\(882\) 0 0
\(883\) −26.9330 −0.906368 −0.453184 0.891417i \(-0.649712\pi\)
−0.453184 + 0.891417i \(0.649712\pi\)
\(884\) 0 0
\(885\) 0.472024 0.0158669
\(886\) 0 0
\(887\) −12.9362 −0.434354 −0.217177 0.976132i \(-0.569685\pi\)
−0.217177 + 0.976132i \(0.569685\pi\)
\(888\) 0 0
\(889\) 26.5479 0.890388
\(890\) 0 0
\(891\) 8.67252 0.290540
\(892\) 0 0
\(893\) −2.59393 −0.0868026
\(894\) 0 0
\(895\) −88.1431 −2.94630
\(896\) 0 0
\(897\) −3.22441 −0.107660
\(898\) 0 0
\(899\) 5.40065 0.180122
\(900\) 0 0
\(901\) 20.3958 0.679484
\(902\) 0 0
\(903\) 4.09967 0.136428
\(904\) 0 0
\(905\) 54.9563 1.82681
\(906\) 0 0
\(907\) −13.4277 −0.445861 −0.222930 0.974834i \(-0.571562\pi\)
−0.222930 + 0.974834i \(0.571562\pi\)
\(908\) 0 0
\(909\) −39.8520 −1.32181
\(910\) 0 0
\(911\) 3.16499 0.104861 0.0524303 0.998625i \(-0.483303\pi\)
0.0524303 + 0.998625i \(0.483303\pi\)
\(912\) 0 0
\(913\) −15.7980 −0.522839
\(914\) 0 0
\(915\) −3.73104 −0.123344
\(916\) 0 0
\(917\) 47.3308 1.56300
\(918\) 0 0
\(919\) 23.2242 0.766096 0.383048 0.923728i \(-0.374874\pi\)
0.383048 + 0.923728i \(0.374874\pi\)
\(920\) 0 0
\(921\) −0.651286 −0.0214606
\(922\) 0 0
\(923\) 9.26001 0.304797
\(924\) 0 0
\(925\) −49.6048 −1.63100
\(926\) 0 0
\(927\) 41.0094 1.34692
\(928\) 0 0
\(929\) −38.8402 −1.27431 −0.637153 0.770738i \(-0.719888\pi\)
−0.637153 + 0.770738i \(0.719888\pi\)
\(930\) 0 0
\(931\) −0.232987 −0.00763584
\(932\) 0 0
\(933\) −4.42203 −0.144771
\(934\) 0 0
\(935\) −13.8730 −0.453697
\(936\) 0 0
\(937\) 37.8486 1.23646 0.618230 0.785997i \(-0.287850\pi\)
0.618230 + 0.785997i \(0.287850\pi\)
\(938\) 0 0
\(939\) −0.574941 −0.0187625
\(940\) 0 0
\(941\) 31.3035 1.02046 0.510232 0.860037i \(-0.329559\pi\)
0.510232 + 0.860037i \(0.329559\pi\)
\(942\) 0 0
\(943\) −61.9369 −2.01694
\(944\) 0 0
\(945\) −11.8751 −0.386297
\(946\) 0 0
\(947\) 49.9866 1.62435 0.812173 0.583417i \(-0.198285\pi\)
0.812173 + 0.583417i \(0.198285\pi\)
\(948\) 0 0
\(949\) 7.69889 0.249917
\(950\) 0 0
\(951\) 3.58980 0.116407
\(952\) 0 0
\(953\) −32.2830 −1.04575 −0.522875 0.852410i \(-0.675140\pi\)
−0.522875 + 0.852410i \(0.675140\pi\)
\(954\) 0 0
\(955\) −22.3245 −0.722404
\(956\) 0 0
\(957\) 0.373156 0.0120624
\(958\) 0 0
\(959\) 2.84676 0.0919268
\(960\) 0 0
\(961\) −23.3472 −0.753135
\(962\) 0 0
\(963\) −3.26779 −0.105303
\(964\) 0 0
\(965\) −38.4328 −1.23719
\(966\) 0 0
\(967\) −21.3221 −0.685673 −0.342836 0.939395i \(-0.611388\pi\)
−0.342836 + 0.939395i \(0.611388\pi\)
\(968\) 0 0
\(969\) 0.152908 0.00491213
\(970\) 0 0
\(971\) −5.24615 −0.168357 −0.0841785 0.996451i \(-0.526827\pi\)
−0.0841785 + 0.996451i \(0.526827\pi\)
\(972\) 0 0
\(973\) 10.1776 0.326279
\(974\) 0 0
\(975\) −4.24487 −0.135945
\(976\) 0 0
\(977\) −11.8270 −0.378380 −0.189190 0.981941i \(-0.560586\pi\)
−0.189190 + 0.981941i \(0.560586\pi\)
\(978\) 0 0
\(979\) 1.85344 0.0592362
\(980\) 0 0
\(981\) −24.5697 −0.784450
\(982\) 0 0
\(983\) 32.0570 1.02246 0.511230 0.859444i \(-0.329190\pi\)
0.511230 + 0.859444i \(0.329190\pi\)
\(984\) 0 0
\(985\) −14.1212 −0.449938
\(986\) 0 0
\(987\) −6.68850 −0.212897
\(988\) 0 0
\(989\) −48.0311 −1.52730
\(990\) 0 0
\(991\) 27.2771 0.866484 0.433242 0.901278i \(-0.357369\pi\)
0.433242 + 0.901278i \(0.357369\pi\)
\(992\) 0 0
\(993\) −4.81022 −0.152648
\(994\) 0 0
\(995\) 15.8590 0.502764
\(996\) 0 0
\(997\) −62.2844 −1.97257 −0.986283 0.165062i \(-0.947218\pi\)
−0.986283 + 0.165062i \(0.947218\pi\)
\(998\) 0 0
\(999\) −6.73726 −0.213158
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 6028.2.a.f.1.12 29
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6028.2.a.f.1.12 29 1.1 even 1 trivial