Properties

Label 6003.2.a.w.1.5
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $0$
Dimension $30$
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] = [6003,2,Mod(1,6003)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6003, 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("6003.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.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: \(47.9341963334\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 6003.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.23657 q^{2} +3.00224 q^{4} -0.453557 q^{5} +2.23602 q^{7} -2.24159 q^{8} +O(q^{10})\) \(q-2.23657 q^{2} +3.00224 q^{4} -0.453557 q^{5} +2.23602 q^{7} -2.24159 q^{8} +1.01441 q^{10} -2.98485 q^{11} +0.660563 q^{13} -5.00102 q^{14} -0.991020 q^{16} -2.90682 q^{17} +5.95647 q^{19} -1.36169 q^{20} +6.67583 q^{22} -1.00000 q^{23} -4.79429 q^{25} -1.47739 q^{26} +6.71308 q^{28} +1.00000 q^{29} +1.21096 q^{31} +6.69966 q^{32} +6.50131 q^{34} -1.01416 q^{35} -2.58687 q^{37} -13.3221 q^{38} +1.01669 q^{40} -4.93674 q^{41} +4.83954 q^{43} -8.96125 q^{44} +2.23657 q^{46} +3.25072 q^{47} -2.00021 q^{49} +10.7228 q^{50} +1.98317 q^{52} -11.3487 q^{53} +1.35380 q^{55} -5.01224 q^{56} -2.23657 q^{58} +9.01149 q^{59} -6.99942 q^{61} -2.70840 q^{62} -13.0022 q^{64} -0.299603 q^{65} +5.10792 q^{67} -8.72699 q^{68} +2.26825 q^{70} +6.78368 q^{71} -3.70604 q^{73} +5.78571 q^{74} +17.8828 q^{76} -6.67419 q^{77} +9.99775 q^{79} +0.449484 q^{80} +11.0414 q^{82} +9.24765 q^{83} +1.31841 q^{85} -10.8240 q^{86} +6.69081 q^{88} -6.86790 q^{89} +1.47703 q^{91} -3.00224 q^{92} -7.27047 q^{94} -2.70160 q^{95} +16.0800 q^{97} +4.47360 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + q^{2} + 37 q^{4} + 10 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + q^{2} + 37 q^{4} + 10 q^{7} + 6 q^{8} + 8 q^{10} + 36 q^{13} + 7 q^{14} + 47 q^{16} + 18 q^{17} + 16 q^{19} + 25 q^{22} - 30 q^{23} + 56 q^{25} + 11 q^{26} + 27 q^{28} + 30 q^{29} + 14 q^{31} - 7 q^{32} + 3 q^{34} - 22 q^{35} + 40 q^{37} + 6 q^{38} + 30 q^{40} + 14 q^{41} + 34 q^{43} + 5 q^{44} - q^{46} - 2 q^{47} + 74 q^{49} - 21 q^{50} + 71 q^{52} + 16 q^{53} + 22 q^{55} + 14 q^{56} + q^{58} - 32 q^{59} + 46 q^{61} + 20 q^{62} + 68 q^{64} + 12 q^{65} + 14 q^{67} + 27 q^{68} - 32 q^{71} + 50 q^{73} - 26 q^{74} + 56 q^{76} + 34 q^{77} + 16 q^{79} + 2 q^{80} + 38 q^{82} - 14 q^{83} + 38 q^{85} + 10 q^{86} + 40 q^{88} - 2 q^{89} + 32 q^{91} - 37 q^{92} + 29 q^{94} - 28 q^{95} + 56 q^{97} + 8 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23657 −1.58149 −0.790747 0.612143i \(-0.790308\pi\)
−0.790747 + 0.612143i \(0.790308\pi\)
\(3\) 0 0
\(4\) 3.00224 1.50112
\(5\) −0.453557 −0.202837 −0.101418 0.994844i \(-0.532338\pi\)
−0.101418 + 0.994844i \(0.532338\pi\)
\(6\) 0 0
\(7\) 2.23602 0.845137 0.422568 0.906331i \(-0.361129\pi\)
0.422568 + 0.906331i \(0.361129\pi\)
\(8\) −2.24159 −0.792521
\(9\) 0 0
\(10\) 1.01441 0.320785
\(11\) −2.98485 −0.899967 −0.449983 0.893037i \(-0.648570\pi\)
−0.449983 + 0.893037i \(0.648570\pi\)
\(12\) 0 0
\(13\) 0.660563 0.183207 0.0916036 0.995796i \(-0.470801\pi\)
0.0916036 + 0.995796i \(0.470801\pi\)
\(14\) −5.00102 −1.33658
\(15\) 0 0
\(16\) −0.991020 −0.247755
\(17\) −2.90682 −0.705008 −0.352504 0.935810i \(-0.614670\pi\)
−0.352504 + 0.935810i \(0.614670\pi\)
\(18\) 0 0
\(19\) 5.95647 1.36651 0.683254 0.730181i \(-0.260564\pi\)
0.683254 + 0.730181i \(0.260564\pi\)
\(20\) −1.36169 −0.304483
\(21\) 0 0
\(22\) 6.67583 1.42329
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −4.79429 −0.958857
\(26\) −1.47739 −0.289741
\(27\) 0 0
\(28\) 6.71308 1.26865
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 1.21096 0.217495 0.108748 0.994069i \(-0.465316\pi\)
0.108748 + 0.994069i \(0.465316\pi\)
\(32\) 6.69966 1.18434
\(33\) 0 0
\(34\) 6.50131 1.11497
\(35\) −1.01416 −0.171425
\(36\) 0 0
\(37\) −2.58687 −0.425278 −0.212639 0.977131i \(-0.568206\pi\)
−0.212639 + 0.977131i \(0.568206\pi\)
\(38\) −13.3221 −2.16112
\(39\) 0 0
\(40\) 1.01669 0.160753
\(41\) −4.93674 −0.770989 −0.385494 0.922710i \(-0.625969\pi\)
−0.385494 + 0.922710i \(0.625969\pi\)
\(42\) 0 0
\(43\) 4.83954 0.738023 0.369012 0.929425i \(-0.379696\pi\)
0.369012 + 0.929425i \(0.379696\pi\)
\(44\) −8.96125 −1.35096
\(45\) 0 0
\(46\) 2.23657 0.329764
\(47\) 3.25072 0.474167 0.237083 0.971489i \(-0.423809\pi\)
0.237083 + 0.971489i \(0.423809\pi\)
\(48\) 0 0
\(49\) −2.00021 −0.285744
\(50\) 10.7228 1.51643
\(51\) 0 0
\(52\) 1.98317 0.275016
\(53\) −11.3487 −1.55886 −0.779432 0.626487i \(-0.784492\pi\)
−0.779432 + 0.626487i \(0.784492\pi\)
\(54\) 0 0
\(55\) 1.35380 0.182546
\(56\) −5.01224 −0.669789
\(57\) 0 0
\(58\) −2.23657 −0.293676
\(59\) 9.01149 1.17320 0.586598 0.809878i \(-0.300467\pi\)
0.586598 + 0.809878i \(0.300467\pi\)
\(60\) 0 0
\(61\) −6.99942 −0.896184 −0.448092 0.893987i \(-0.647896\pi\)
−0.448092 + 0.893987i \(0.647896\pi\)
\(62\) −2.70840 −0.343967
\(63\) 0 0
\(64\) −13.0022 −1.62528
\(65\) −0.299603 −0.0371612
\(66\) 0 0
\(67\) 5.10792 0.624031 0.312016 0.950077i \(-0.398996\pi\)
0.312016 + 0.950077i \(0.398996\pi\)
\(68\) −8.72699 −1.05830
\(69\) 0 0
\(70\) 2.26825 0.271107
\(71\) 6.78368 0.805075 0.402537 0.915404i \(-0.368128\pi\)
0.402537 + 0.915404i \(0.368128\pi\)
\(72\) 0 0
\(73\) −3.70604 −0.433759 −0.216879 0.976198i \(-0.569588\pi\)
−0.216879 + 0.976198i \(0.569588\pi\)
\(74\) 5.78571 0.672575
\(75\) 0 0
\(76\) 17.8828 2.05130
\(77\) −6.67419 −0.760595
\(78\) 0 0
\(79\) 9.99775 1.12483 0.562417 0.826854i \(-0.309872\pi\)
0.562417 + 0.826854i \(0.309872\pi\)
\(80\) 0.449484 0.0502539
\(81\) 0 0
\(82\) 11.0414 1.21931
\(83\) 9.24765 1.01506 0.507531 0.861634i \(-0.330558\pi\)
0.507531 + 0.861634i \(0.330558\pi\)
\(84\) 0 0
\(85\) 1.31841 0.143002
\(86\) −10.8240 −1.16718
\(87\) 0 0
\(88\) 6.69081 0.713243
\(89\) −6.86790 −0.727996 −0.363998 0.931400i \(-0.618589\pi\)
−0.363998 + 0.931400i \(0.618589\pi\)
\(90\) 0 0
\(91\) 1.47703 0.154835
\(92\) −3.00224 −0.313006
\(93\) 0 0
\(94\) −7.27047 −0.749892
\(95\) −2.70160 −0.277178
\(96\) 0 0
\(97\) 16.0800 1.63268 0.816340 0.577571i \(-0.195999\pi\)
0.816340 + 0.577571i \(0.195999\pi\)
\(98\) 4.47360 0.451902
\(99\) 0 0
\(100\) −14.3936 −1.43936
\(101\) 5.32290 0.529649 0.264824 0.964297i \(-0.414686\pi\)
0.264824 + 0.964297i \(0.414686\pi\)
\(102\) 0 0
\(103\) 8.88241 0.875210 0.437605 0.899167i \(-0.355827\pi\)
0.437605 + 0.899167i \(0.355827\pi\)
\(104\) −1.48071 −0.145196
\(105\) 0 0
\(106\) 25.3822 2.46533
\(107\) −9.48454 −0.916905 −0.458452 0.888719i \(-0.651596\pi\)
−0.458452 + 0.888719i \(0.651596\pi\)
\(108\) 0 0
\(109\) 3.68396 0.352860 0.176430 0.984313i \(-0.443545\pi\)
0.176430 + 0.984313i \(0.443545\pi\)
\(110\) −3.02787 −0.288696
\(111\) 0 0
\(112\) −2.21594 −0.209387
\(113\) −0.789297 −0.0742508 −0.0371254 0.999311i \(-0.511820\pi\)
−0.0371254 + 0.999311i \(0.511820\pi\)
\(114\) 0 0
\(115\) 0.453557 0.0422944
\(116\) 3.00224 0.278751
\(117\) 0 0
\(118\) −20.1548 −1.85540
\(119\) −6.49972 −0.595828
\(120\) 0 0
\(121\) −2.09066 −0.190060
\(122\) 15.6547 1.41731
\(123\) 0 0
\(124\) 3.63561 0.326487
\(125\) 4.44227 0.397329
\(126\) 0 0
\(127\) 9.73448 0.863796 0.431898 0.901923i \(-0.357844\pi\)
0.431898 + 0.901923i \(0.357844\pi\)
\(128\) 15.6810 1.38602
\(129\) 0 0
\(130\) 0.670083 0.0587702
\(131\) 4.79840 0.419238 0.209619 0.977783i \(-0.432778\pi\)
0.209619 + 0.977783i \(0.432778\pi\)
\(132\) 0 0
\(133\) 13.3188 1.15489
\(134\) −11.4242 −0.986901
\(135\) 0 0
\(136\) 6.51590 0.558734
\(137\) 10.5960 0.905274 0.452637 0.891695i \(-0.350483\pi\)
0.452637 + 0.891695i \(0.350483\pi\)
\(138\) 0 0
\(139\) 4.96119 0.420803 0.210401 0.977615i \(-0.432523\pi\)
0.210401 + 0.977615i \(0.432523\pi\)
\(140\) −3.04477 −0.257330
\(141\) 0 0
\(142\) −15.1722 −1.27322
\(143\) −1.97168 −0.164880
\(144\) 0 0
\(145\) −0.453557 −0.0376659
\(146\) 8.28881 0.685987
\(147\) 0 0
\(148\) −7.76641 −0.638395
\(149\) 4.11712 0.337287 0.168644 0.985677i \(-0.446061\pi\)
0.168644 + 0.985677i \(0.446061\pi\)
\(150\) 0 0
\(151\) 17.2586 1.40449 0.702244 0.711936i \(-0.252182\pi\)
0.702244 + 0.711936i \(0.252182\pi\)
\(152\) −13.3520 −1.08299
\(153\) 0 0
\(154\) 14.9273 1.20288
\(155\) −0.549241 −0.0441161
\(156\) 0 0
\(157\) −17.8082 −1.42125 −0.710625 0.703571i \(-0.751588\pi\)
−0.710625 + 0.703571i \(0.751588\pi\)
\(158\) −22.3607 −1.77892
\(159\) 0 0
\(160\) −3.03868 −0.240229
\(161\) −2.23602 −0.176223
\(162\) 0 0
\(163\) −10.0763 −0.789241 −0.394620 0.918844i \(-0.629124\pi\)
−0.394620 + 0.918844i \(0.629124\pi\)
\(164\) −14.8213 −1.15735
\(165\) 0 0
\(166\) −20.6830 −1.60531
\(167\) 18.2564 1.41272 0.706361 0.707852i \(-0.250336\pi\)
0.706361 + 0.707852i \(0.250336\pi\)
\(168\) 0 0
\(169\) −12.5637 −0.966435
\(170\) −2.94872 −0.226156
\(171\) 0 0
\(172\) 14.5295 1.10786
\(173\) −10.6770 −0.811756 −0.405878 0.913927i \(-0.633034\pi\)
−0.405878 + 0.913927i \(0.633034\pi\)
\(174\) 0 0
\(175\) −10.7201 −0.810365
\(176\) 2.95805 0.222971
\(177\) 0 0
\(178\) 15.3605 1.15132
\(179\) −10.0442 −0.750740 −0.375370 0.926875i \(-0.622484\pi\)
−0.375370 + 0.926875i \(0.622484\pi\)
\(180\) 0 0
\(181\) −4.44665 −0.330517 −0.165259 0.986250i \(-0.552846\pi\)
−0.165259 + 0.986250i \(0.552846\pi\)
\(182\) −3.30349 −0.244871
\(183\) 0 0
\(184\) 2.24159 0.165252
\(185\) 1.17329 0.0862622
\(186\) 0 0
\(187\) 8.67644 0.634484
\(188\) 9.75946 0.711782
\(189\) 0 0
\(190\) 6.04232 0.438356
\(191\) −10.1295 −0.732944 −0.366472 0.930429i \(-0.619435\pi\)
−0.366472 + 0.930429i \(0.619435\pi\)
\(192\) 0 0
\(193\) 6.54906 0.471412 0.235706 0.971824i \(-0.424260\pi\)
0.235706 + 0.971824i \(0.424260\pi\)
\(194\) −35.9641 −2.58207
\(195\) 0 0
\(196\) −6.00511 −0.428936
\(197\) 14.8397 1.05728 0.528641 0.848845i \(-0.322702\pi\)
0.528641 + 0.848845i \(0.322702\pi\)
\(198\) 0 0
\(199\) 4.83719 0.342899 0.171450 0.985193i \(-0.445155\pi\)
0.171450 + 0.985193i \(0.445155\pi\)
\(200\) 10.7468 0.759914
\(201\) 0 0
\(202\) −11.9050 −0.837636
\(203\) 2.23602 0.156938
\(204\) 0 0
\(205\) 2.23909 0.156385
\(206\) −19.8661 −1.38414
\(207\) 0 0
\(208\) −0.654631 −0.0453905
\(209\) −17.7792 −1.22981
\(210\) 0 0
\(211\) 21.8458 1.50393 0.751965 0.659203i \(-0.229106\pi\)
0.751965 + 0.659203i \(0.229106\pi\)
\(212\) −34.0716 −2.34004
\(213\) 0 0
\(214\) 21.2128 1.45008
\(215\) −2.19501 −0.149698
\(216\) 0 0
\(217\) 2.70774 0.183813
\(218\) −8.23944 −0.558045
\(219\) 0 0
\(220\) 4.06444 0.274025
\(221\) −1.92014 −0.129163
\(222\) 0 0
\(223\) −21.0488 −1.40953 −0.704766 0.709440i \(-0.748948\pi\)
−0.704766 + 0.709440i \(0.748948\pi\)
\(224\) 14.9806 1.00093
\(225\) 0 0
\(226\) 1.76532 0.117427
\(227\) −4.78355 −0.317495 −0.158748 0.987319i \(-0.550746\pi\)
−0.158748 + 0.987319i \(0.550746\pi\)
\(228\) 0 0
\(229\) 19.9948 1.32130 0.660648 0.750696i \(-0.270281\pi\)
0.660648 + 0.750696i \(0.270281\pi\)
\(230\) −1.01441 −0.0668883
\(231\) 0 0
\(232\) −2.24159 −0.147167
\(233\) −2.20911 −0.144724 −0.0723618 0.997378i \(-0.523054\pi\)
−0.0723618 + 0.997378i \(0.523054\pi\)
\(234\) 0 0
\(235\) −1.47439 −0.0961785
\(236\) 27.0547 1.76111
\(237\) 0 0
\(238\) 14.5371 0.942299
\(239\) −0.518959 −0.0335687 −0.0167843 0.999859i \(-0.505343\pi\)
−0.0167843 + 0.999859i \(0.505343\pi\)
\(240\) 0 0
\(241\) −15.2652 −0.983318 −0.491659 0.870788i \(-0.663609\pi\)
−0.491659 + 0.870788i \(0.663609\pi\)
\(242\) 4.67590 0.300578
\(243\) 0 0
\(244\) −21.0140 −1.34528
\(245\) 0.907208 0.0579594
\(246\) 0 0
\(247\) 3.93462 0.250354
\(248\) −2.71448 −0.172370
\(249\) 0 0
\(250\) −9.93544 −0.628373
\(251\) 5.84986 0.369240 0.184620 0.982810i \(-0.440895\pi\)
0.184620 + 0.982810i \(0.440895\pi\)
\(252\) 0 0
\(253\) 2.98485 0.187656
\(254\) −21.7718 −1.36609
\(255\) 0 0
\(256\) −9.06731 −0.566707
\(257\) 20.4478 1.27550 0.637751 0.770243i \(-0.279865\pi\)
0.637751 + 0.770243i \(0.279865\pi\)
\(258\) 0 0
\(259\) −5.78429 −0.359418
\(260\) −0.899481 −0.0557835
\(261\) 0 0
\(262\) −10.7320 −0.663022
\(263\) −1.65230 −0.101885 −0.0509426 0.998702i \(-0.516223\pi\)
−0.0509426 + 0.998702i \(0.516223\pi\)
\(264\) 0 0
\(265\) 5.14728 0.316195
\(266\) −29.7884 −1.82645
\(267\) 0 0
\(268\) 15.3352 0.936747
\(269\) −15.5998 −0.951137 −0.475568 0.879679i \(-0.657758\pi\)
−0.475568 + 0.879679i \(0.657758\pi\)
\(270\) 0 0
\(271\) 3.71144 0.225454 0.112727 0.993626i \(-0.464041\pi\)
0.112727 + 0.993626i \(0.464041\pi\)
\(272\) 2.88072 0.174669
\(273\) 0 0
\(274\) −23.6986 −1.43169
\(275\) 14.3102 0.862940
\(276\) 0 0
\(277\) −31.7396 −1.90705 −0.953523 0.301320i \(-0.902573\pi\)
−0.953523 + 0.301320i \(0.902573\pi\)
\(278\) −11.0960 −0.665497
\(279\) 0 0
\(280\) 2.27334 0.135858
\(281\) 16.7174 0.997276 0.498638 0.866810i \(-0.333834\pi\)
0.498638 + 0.866810i \(0.333834\pi\)
\(282\) 0 0
\(283\) 10.1798 0.605128 0.302564 0.953129i \(-0.402157\pi\)
0.302564 + 0.953129i \(0.402157\pi\)
\(284\) 20.3663 1.20851
\(285\) 0 0
\(286\) 4.40981 0.260757
\(287\) −11.0386 −0.651591
\(288\) 0 0
\(289\) −8.55038 −0.502963
\(290\) 1.01441 0.0595683
\(291\) 0 0
\(292\) −11.1264 −0.651125
\(293\) 4.30025 0.251223 0.125612 0.992079i \(-0.459911\pi\)
0.125612 + 0.992079i \(0.459911\pi\)
\(294\) 0 0
\(295\) −4.08723 −0.237967
\(296\) 5.79869 0.337042
\(297\) 0 0
\(298\) −9.20822 −0.533418
\(299\) −0.660563 −0.0382013
\(300\) 0 0
\(301\) 10.8213 0.623731
\(302\) −38.6001 −2.22119
\(303\) 0 0
\(304\) −5.90298 −0.338559
\(305\) 3.17464 0.181779
\(306\) 0 0
\(307\) 7.72908 0.441122 0.220561 0.975373i \(-0.429211\pi\)
0.220561 + 0.975373i \(0.429211\pi\)
\(308\) −20.0376 −1.14175
\(309\) 0 0
\(310\) 1.22842 0.0697693
\(311\) −8.91470 −0.505506 −0.252753 0.967531i \(-0.581336\pi\)
−0.252753 + 0.967531i \(0.581336\pi\)
\(312\) 0 0
\(313\) −8.83299 −0.499270 −0.249635 0.968340i \(-0.580311\pi\)
−0.249635 + 0.968340i \(0.580311\pi\)
\(314\) 39.8293 2.24770
\(315\) 0 0
\(316\) 30.0157 1.68851
\(317\) 8.44890 0.474538 0.237269 0.971444i \(-0.423748\pi\)
0.237269 + 0.971444i \(0.423748\pi\)
\(318\) 0 0
\(319\) −2.98485 −0.167120
\(320\) 5.89725 0.329666
\(321\) 0 0
\(322\) 5.00102 0.278696
\(323\) −17.3144 −0.963399
\(324\) 0 0
\(325\) −3.16693 −0.175670
\(326\) 22.5365 1.24818
\(327\) 0 0
\(328\) 11.0661 0.611025
\(329\) 7.26869 0.400736
\(330\) 0 0
\(331\) 3.42025 0.187994 0.0939969 0.995572i \(-0.470036\pi\)
0.0939969 + 0.995572i \(0.470036\pi\)
\(332\) 27.7637 1.52373
\(333\) 0 0
\(334\) −40.8317 −2.23421
\(335\) −2.31673 −0.126577
\(336\) 0 0
\(337\) 11.1876 0.609429 0.304714 0.952444i \(-0.401439\pi\)
0.304714 + 0.952444i \(0.401439\pi\)
\(338\) 28.0995 1.52841
\(339\) 0 0
\(340\) 3.95819 0.214663
\(341\) −3.61454 −0.195739
\(342\) 0 0
\(343\) −20.1247 −1.08663
\(344\) −10.8483 −0.584899
\(345\) 0 0
\(346\) 23.8798 1.28379
\(347\) 1.74483 0.0936673 0.0468337 0.998903i \(-0.485087\pi\)
0.0468337 + 0.998903i \(0.485087\pi\)
\(348\) 0 0
\(349\) 19.3270 1.03455 0.517275 0.855820i \(-0.326947\pi\)
0.517275 + 0.855820i \(0.326947\pi\)
\(350\) 23.9763 1.28159
\(351\) 0 0
\(352\) −19.9975 −1.06587
\(353\) 29.0440 1.54586 0.772928 0.634494i \(-0.218791\pi\)
0.772928 + 0.634494i \(0.218791\pi\)
\(354\) 0 0
\(355\) −3.07679 −0.163299
\(356\) −20.6191 −1.09281
\(357\) 0 0
\(358\) 22.4646 1.18729
\(359\) 16.7914 0.886214 0.443107 0.896469i \(-0.353876\pi\)
0.443107 + 0.896469i \(0.353876\pi\)
\(360\) 0 0
\(361\) 16.4795 0.867344
\(362\) 9.94525 0.522711
\(363\) 0 0
\(364\) 4.43441 0.232426
\(365\) 1.68090 0.0879823
\(366\) 0 0
\(367\) 2.56298 0.133787 0.0668933 0.997760i \(-0.478691\pi\)
0.0668933 + 0.997760i \(0.478691\pi\)
\(368\) 0.991020 0.0516605
\(369\) 0 0
\(370\) −2.62415 −0.136423
\(371\) −25.3759 −1.31745
\(372\) 0 0
\(373\) 11.8875 0.615512 0.307756 0.951465i \(-0.400422\pi\)
0.307756 + 0.951465i \(0.400422\pi\)
\(374\) −19.4055 −1.00343
\(375\) 0 0
\(376\) −7.28678 −0.375787
\(377\) 0.660563 0.0340207
\(378\) 0 0
\(379\) −10.1944 −0.523652 −0.261826 0.965115i \(-0.584325\pi\)
−0.261826 + 0.965115i \(0.584325\pi\)
\(380\) −8.11086 −0.416078
\(381\) 0 0
\(382\) 22.6553 1.15915
\(383\) −9.63108 −0.492125 −0.246063 0.969254i \(-0.579137\pi\)
−0.246063 + 0.969254i \(0.579137\pi\)
\(384\) 0 0
\(385\) 3.02713 0.154277
\(386\) −14.6474 −0.745535
\(387\) 0 0
\(388\) 48.2762 2.45085
\(389\) 33.0169 1.67402 0.837012 0.547184i \(-0.184300\pi\)
0.837012 + 0.547184i \(0.184300\pi\)
\(390\) 0 0
\(391\) 2.90682 0.147004
\(392\) 4.48364 0.226458
\(393\) 0 0
\(394\) −33.1900 −1.67209
\(395\) −4.53455 −0.228158
\(396\) 0 0
\(397\) −30.6212 −1.53683 −0.768416 0.639951i \(-0.778955\pi\)
−0.768416 + 0.639951i \(0.778955\pi\)
\(398\) −10.8187 −0.542293
\(399\) 0 0
\(400\) 4.75123 0.237562
\(401\) 9.63167 0.480983 0.240491 0.970651i \(-0.422691\pi\)
0.240491 + 0.970651i \(0.422691\pi\)
\(402\) 0 0
\(403\) 0.799917 0.0398467
\(404\) 15.9806 0.795067
\(405\) 0 0
\(406\) −5.00102 −0.248196
\(407\) 7.72142 0.382736
\(408\) 0 0
\(409\) −20.8897 −1.03293 −0.516464 0.856309i \(-0.672752\pi\)
−0.516464 + 0.856309i \(0.672752\pi\)
\(410\) −5.00788 −0.247322
\(411\) 0 0
\(412\) 26.6672 1.31380
\(413\) 20.1499 0.991511
\(414\) 0 0
\(415\) −4.19434 −0.205892
\(416\) 4.42555 0.216980
\(417\) 0 0
\(418\) 39.7644 1.94494
\(419\) −35.6859 −1.74337 −0.871686 0.490065i \(-0.836973\pi\)
−0.871686 + 0.490065i \(0.836973\pi\)
\(420\) 0 0
\(421\) 9.67002 0.471288 0.235644 0.971839i \(-0.424280\pi\)
0.235644 + 0.971839i \(0.424280\pi\)
\(422\) −48.8597 −2.37846
\(423\) 0 0
\(424\) 25.4391 1.23543
\(425\) 13.9361 0.676002
\(426\) 0 0
\(427\) −15.6509 −0.757398
\(428\) −28.4749 −1.37639
\(429\) 0 0
\(430\) 4.90929 0.236747
\(431\) 14.4851 0.697721 0.348860 0.937175i \(-0.386569\pi\)
0.348860 + 0.937175i \(0.386569\pi\)
\(432\) 0 0
\(433\) −15.7872 −0.758684 −0.379342 0.925256i \(-0.623850\pi\)
−0.379342 + 0.925256i \(0.623850\pi\)
\(434\) −6.05605 −0.290700
\(435\) 0 0
\(436\) 11.0602 0.529685
\(437\) −5.95647 −0.284937
\(438\) 0 0
\(439\) 3.56024 0.169921 0.0849605 0.996384i \(-0.472924\pi\)
0.0849605 + 0.996384i \(0.472924\pi\)
\(440\) −3.03466 −0.144672
\(441\) 0 0
\(442\) 4.29453 0.204270
\(443\) 13.7694 0.654205 0.327102 0.944989i \(-0.393928\pi\)
0.327102 + 0.944989i \(0.393928\pi\)
\(444\) 0 0
\(445\) 3.11499 0.147665
\(446\) 47.0771 2.22916
\(447\) 0 0
\(448\) −29.0732 −1.37358
\(449\) 22.2348 1.04933 0.524663 0.851310i \(-0.324191\pi\)
0.524663 + 0.851310i \(0.324191\pi\)
\(450\) 0 0
\(451\) 14.7354 0.693864
\(452\) −2.36966 −0.111459
\(453\) 0 0
\(454\) 10.6987 0.502117
\(455\) −0.669919 −0.0314063
\(456\) 0 0
\(457\) 22.6394 1.05903 0.529513 0.848302i \(-0.322375\pi\)
0.529513 + 0.848302i \(0.322375\pi\)
\(458\) −44.7199 −2.08962
\(459\) 0 0
\(460\) 1.36169 0.0634891
\(461\) 7.28173 0.339144 0.169572 0.985518i \(-0.445761\pi\)
0.169572 + 0.985518i \(0.445761\pi\)
\(462\) 0 0
\(463\) −14.2864 −0.663946 −0.331973 0.943289i \(-0.607714\pi\)
−0.331973 + 0.943289i \(0.607714\pi\)
\(464\) −0.991020 −0.0460069
\(465\) 0 0
\(466\) 4.94083 0.228879
\(467\) 38.3371 1.77403 0.887015 0.461742i \(-0.152775\pi\)
0.887015 + 0.461742i \(0.152775\pi\)
\(468\) 0 0
\(469\) 11.4214 0.527392
\(470\) 3.29757 0.152106
\(471\) 0 0
\(472\) −20.2000 −0.929783
\(473\) −14.4453 −0.664197
\(474\) 0 0
\(475\) −28.5570 −1.31029
\(476\) −19.5137 −0.894411
\(477\) 0 0
\(478\) 1.16069 0.0530887
\(479\) 21.0038 0.959688 0.479844 0.877354i \(-0.340693\pi\)
0.479844 + 0.877354i \(0.340693\pi\)
\(480\) 0 0
\(481\) −1.70879 −0.0779141
\(482\) 34.1417 1.55511
\(483\) 0 0
\(484\) −6.27666 −0.285303
\(485\) −7.29322 −0.331168
\(486\) 0 0
\(487\) 23.2968 1.05568 0.527839 0.849345i \(-0.323003\pi\)
0.527839 + 0.849345i \(0.323003\pi\)
\(488\) 15.6898 0.710245
\(489\) 0 0
\(490\) −2.02903 −0.0916624
\(491\) 7.19117 0.324533 0.162266 0.986747i \(-0.448120\pi\)
0.162266 + 0.986747i \(0.448120\pi\)
\(492\) 0 0
\(493\) −2.90682 −0.130917
\(494\) −8.80006 −0.395933
\(495\) 0 0
\(496\) −1.20009 −0.0538856
\(497\) 15.1685 0.680398
\(498\) 0 0
\(499\) −24.7979 −1.11011 −0.555053 0.831815i \(-0.687302\pi\)
−0.555053 + 0.831815i \(0.687302\pi\)
\(500\) 13.3368 0.596439
\(501\) 0 0
\(502\) −13.0836 −0.583950
\(503\) −42.0808 −1.87629 −0.938145 0.346243i \(-0.887457\pi\)
−0.938145 + 0.346243i \(0.887457\pi\)
\(504\) 0 0
\(505\) −2.41424 −0.107432
\(506\) −6.67583 −0.296777
\(507\) 0 0
\(508\) 29.2253 1.29666
\(509\) 22.7171 1.00692 0.503459 0.864019i \(-0.332061\pi\)
0.503459 + 0.864019i \(0.332061\pi\)
\(510\) 0 0
\(511\) −8.28678 −0.366585
\(512\) −11.0824 −0.489778
\(513\) 0 0
\(514\) −45.7330 −2.01720
\(515\) −4.02868 −0.177525
\(516\) 0 0
\(517\) −9.70293 −0.426734
\(518\) 12.9370 0.568418
\(519\) 0 0
\(520\) 0.671586 0.0294510
\(521\) −26.9094 −1.17892 −0.589462 0.807796i \(-0.700660\pi\)
−0.589462 + 0.807796i \(0.700660\pi\)
\(522\) 0 0
\(523\) 26.4973 1.15865 0.579323 0.815098i \(-0.303317\pi\)
0.579323 + 0.815098i \(0.303317\pi\)
\(524\) 14.4060 0.629327
\(525\) 0 0
\(526\) 3.69548 0.161131
\(527\) −3.52005 −0.153336
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −11.5123 −0.500061
\(531\) 0 0
\(532\) 39.9863 1.73362
\(533\) −3.26102 −0.141251
\(534\) 0 0
\(535\) 4.30178 0.185982
\(536\) −11.4498 −0.494558
\(537\) 0 0
\(538\) 34.8901 1.50422
\(539\) 5.97032 0.257160
\(540\) 0 0
\(541\) 18.7935 0.807994 0.403997 0.914760i \(-0.367621\pi\)
0.403997 + 0.914760i \(0.367621\pi\)
\(542\) −8.30089 −0.356554
\(543\) 0 0
\(544\) −19.4747 −0.834972
\(545\) −1.67089 −0.0715729
\(546\) 0 0
\(547\) 5.46597 0.233708 0.116854 0.993149i \(-0.462719\pi\)
0.116854 + 0.993149i \(0.462719\pi\)
\(548\) 31.8117 1.35893
\(549\) 0 0
\(550\) −32.0058 −1.36473
\(551\) 5.95647 0.253754
\(552\) 0 0
\(553\) 22.3552 0.950639
\(554\) 70.9878 3.01598
\(555\) 0 0
\(556\) 14.8947 0.631676
\(557\) 2.16854 0.0918841 0.0459420 0.998944i \(-0.485371\pi\)
0.0459420 + 0.998944i \(0.485371\pi\)
\(558\) 0 0
\(559\) 3.19682 0.135211
\(560\) 1.00506 0.0424714
\(561\) 0 0
\(562\) −37.3896 −1.57719
\(563\) 39.9355 1.68308 0.841540 0.540194i \(-0.181649\pi\)
0.841540 + 0.540194i \(0.181649\pi\)
\(564\) 0 0
\(565\) 0.357991 0.0150608
\(566\) −22.7679 −0.957006
\(567\) 0 0
\(568\) −15.2062 −0.638038
\(569\) −5.04467 −0.211484 −0.105742 0.994394i \(-0.533722\pi\)
−0.105742 + 0.994394i \(0.533722\pi\)
\(570\) 0 0
\(571\) −11.9257 −0.499076 −0.249538 0.968365i \(-0.580279\pi\)
−0.249538 + 0.968365i \(0.580279\pi\)
\(572\) −5.91947 −0.247506
\(573\) 0 0
\(574\) 24.6887 1.03049
\(575\) 4.79429 0.199936
\(576\) 0 0
\(577\) 23.7255 0.987704 0.493852 0.869546i \(-0.335588\pi\)
0.493852 + 0.869546i \(0.335588\pi\)
\(578\) 19.1235 0.795433
\(579\) 0 0
\(580\) −1.36169 −0.0565411
\(581\) 20.6780 0.857866
\(582\) 0 0
\(583\) 33.8742 1.40293
\(584\) 8.30741 0.343763
\(585\) 0 0
\(586\) −9.61781 −0.397308
\(587\) 38.7609 1.59983 0.799916 0.600112i \(-0.204877\pi\)
0.799916 + 0.600112i \(0.204877\pi\)
\(588\) 0 0
\(589\) 7.21306 0.297209
\(590\) 9.14136 0.376344
\(591\) 0 0
\(592\) 2.56364 0.105365
\(593\) 13.5642 0.557016 0.278508 0.960434i \(-0.410160\pi\)
0.278508 + 0.960434i \(0.410160\pi\)
\(594\) 0 0
\(595\) 2.94799 0.120856
\(596\) 12.3606 0.506310
\(597\) 0 0
\(598\) 1.47739 0.0604152
\(599\) 30.4692 1.24494 0.622469 0.782645i \(-0.286130\pi\)
0.622469 + 0.782645i \(0.286130\pi\)
\(600\) 0 0
\(601\) 18.9846 0.774397 0.387199 0.921996i \(-0.373443\pi\)
0.387199 + 0.921996i \(0.373443\pi\)
\(602\) −24.2026 −0.986426
\(603\) 0 0
\(604\) 51.8146 2.10831
\(605\) 0.948232 0.0385511
\(606\) 0 0
\(607\) 36.3484 1.47534 0.737669 0.675163i \(-0.235927\pi\)
0.737669 + 0.675163i \(0.235927\pi\)
\(608\) 39.9063 1.61842
\(609\) 0 0
\(610\) −7.10030 −0.287483
\(611\) 2.14731 0.0868708
\(612\) 0 0
\(613\) 0.882083 0.0356270 0.0178135 0.999841i \(-0.494329\pi\)
0.0178135 + 0.999841i \(0.494329\pi\)
\(614\) −17.2866 −0.697631
\(615\) 0 0
\(616\) 14.9608 0.602788
\(617\) −1.04758 −0.0421742 −0.0210871 0.999778i \(-0.506713\pi\)
−0.0210871 + 0.999778i \(0.506713\pi\)
\(618\) 0 0
\(619\) −26.9392 −1.08278 −0.541389 0.840772i \(-0.682101\pi\)
−0.541389 + 0.840772i \(0.682101\pi\)
\(620\) −1.64895 −0.0662236
\(621\) 0 0
\(622\) 19.9383 0.799454
\(623\) −15.3568 −0.615256
\(624\) 0 0
\(625\) 21.9566 0.878264
\(626\) 19.7556 0.789592
\(627\) 0 0
\(628\) −53.4646 −2.13347
\(629\) 7.51957 0.299825
\(630\) 0 0
\(631\) −26.5512 −1.05698 −0.528492 0.848938i \(-0.677242\pi\)
−0.528492 + 0.848938i \(0.677242\pi\)
\(632\) −22.4108 −0.891455
\(633\) 0 0
\(634\) −18.8966 −0.750478
\(635\) −4.41514 −0.175210
\(636\) 0 0
\(637\) −1.32126 −0.0523503
\(638\) 6.67583 0.264299
\(639\) 0 0
\(640\) −7.11225 −0.281136
\(641\) −4.68929 −0.185216 −0.0926080 0.995703i \(-0.529520\pi\)
−0.0926080 + 0.995703i \(0.529520\pi\)
\(642\) 0 0
\(643\) −15.6616 −0.617634 −0.308817 0.951122i \(-0.599933\pi\)
−0.308817 + 0.951122i \(0.599933\pi\)
\(644\) −6.71308 −0.264532
\(645\) 0 0
\(646\) 38.7249 1.52361
\(647\) −37.3920 −1.47003 −0.735015 0.678050i \(-0.762825\pi\)
−0.735015 + 0.678050i \(0.762825\pi\)
\(648\) 0 0
\(649\) −26.8980 −1.05584
\(650\) 7.08305 0.277820
\(651\) 0 0
\(652\) −30.2517 −1.18475
\(653\) −5.61580 −0.219763 −0.109882 0.993945i \(-0.535047\pi\)
−0.109882 + 0.993945i \(0.535047\pi\)
\(654\) 0 0
\(655\) −2.17635 −0.0850370
\(656\) 4.89240 0.191016
\(657\) 0 0
\(658\) −16.2569 −0.633761
\(659\) 22.2009 0.864825 0.432412 0.901676i \(-0.357663\pi\)
0.432412 + 0.901676i \(0.357663\pi\)
\(660\) 0 0
\(661\) 22.6255 0.880028 0.440014 0.897991i \(-0.354973\pi\)
0.440014 + 0.897991i \(0.354973\pi\)
\(662\) −7.64962 −0.297311
\(663\) 0 0
\(664\) −20.7294 −0.804458
\(665\) −6.04084 −0.234254
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 54.8101 2.12067
\(669\) 0 0
\(670\) 5.18153 0.200180
\(671\) 20.8922 0.806536
\(672\) 0 0
\(673\) −21.6175 −0.833294 −0.416647 0.909068i \(-0.636795\pi\)
−0.416647 + 0.909068i \(0.636795\pi\)
\(674\) −25.0219 −0.963807
\(675\) 0 0
\(676\) −37.7192 −1.45074
\(677\) 17.2957 0.664729 0.332365 0.943151i \(-0.392154\pi\)
0.332365 + 0.943151i \(0.392154\pi\)
\(678\) 0 0
\(679\) 35.9553 1.37984
\(680\) −2.95533 −0.113332
\(681\) 0 0
\(682\) 8.08418 0.309559
\(683\) 30.8022 1.17862 0.589308 0.807909i \(-0.299401\pi\)
0.589308 + 0.807909i \(0.299401\pi\)
\(684\) 0 0
\(685\) −4.80587 −0.183623
\(686\) 45.0102 1.71850
\(687\) 0 0
\(688\) −4.79608 −0.182849
\(689\) −7.49653 −0.285595
\(690\) 0 0
\(691\) −23.3225 −0.887230 −0.443615 0.896217i \(-0.646304\pi\)
−0.443615 + 0.896217i \(0.646304\pi\)
\(692\) −32.0549 −1.21854
\(693\) 0 0
\(694\) −3.90243 −0.148134
\(695\) −2.25018 −0.0853543
\(696\) 0 0
\(697\) 14.3502 0.543553
\(698\) −43.2261 −1.63613
\(699\) 0 0
\(700\) −32.1844 −1.21646
\(701\) −14.4108 −0.544287 −0.272143 0.962257i \(-0.587732\pi\)
−0.272143 + 0.962257i \(0.587732\pi\)
\(702\) 0 0
\(703\) −15.4086 −0.581146
\(704\) 38.8097 1.46270
\(705\) 0 0
\(706\) −64.9589 −2.44476
\(707\) 11.9021 0.447625
\(708\) 0 0
\(709\) −25.3763 −0.953026 −0.476513 0.879168i \(-0.658099\pi\)
−0.476513 + 0.879168i \(0.658099\pi\)
\(710\) 6.88145 0.258256
\(711\) 0 0
\(712\) 15.3950 0.576952
\(713\) −1.21096 −0.0453509
\(714\) 0 0
\(715\) 0.894271 0.0334438
\(716\) −30.1552 −1.12695
\(717\) 0 0
\(718\) −37.5550 −1.40154
\(719\) 2.41527 0.0900742 0.0450371 0.998985i \(-0.485659\pi\)
0.0450371 + 0.998985i \(0.485659\pi\)
\(720\) 0 0
\(721\) 19.8613 0.739672
\(722\) −36.8576 −1.37170
\(723\) 0 0
\(724\) −13.3499 −0.496147
\(725\) −4.79429 −0.178055
\(726\) 0 0
\(727\) 31.7792 1.17863 0.589313 0.807905i \(-0.299398\pi\)
0.589313 + 0.807905i \(0.299398\pi\)
\(728\) −3.31090 −0.122710
\(729\) 0 0
\(730\) −3.75945 −0.139143
\(731\) −14.0677 −0.520313
\(732\) 0 0
\(733\) 21.3148 0.787279 0.393639 0.919265i \(-0.371216\pi\)
0.393639 + 0.919265i \(0.371216\pi\)
\(734\) −5.73229 −0.211583
\(735\) 0 0
\(736\) −6.69966 −0.246953
\(737\) −15.2464 −0.561607
\(738\) 0 0
\(739\) 7.18650 0.264360 0.132180 0.991226i \(-0.457802\pi\)
0.132180 + 0.991226i \(0.457802\pi\)
\(740\) 3.52251 0.129490
\(741\) 0 0
\(742\) 56.7551 2.08354
\(743\) 47.3808 1.73823 0.869117 0.494606i \(-0.164688\pi\)
0.869117 + 0.494606i \(0.164688\pi\)
\(744\) 0 0
\(745\) −1.86735 −0.0684144
\(746\) −26.5872 −0.973428
\(747\) 0 0
\(748\) 26.0488 0.952438
\(749\) −21.2076 −0.774910
\(750\) 0 0
\(751\) 5.17198 0.188728 0.0943641 0.995538i \(-0.469918\pi\)
0.0943641 + 0.995538i \(0.469918\pi\)
\(752\) −3.22153 −0.117477
\(753\) 0 0
\(754\) −1.47739 −0.0538035
\(755\) −7.82778 −0.284882
\(756\) 0 0
\(757\) 2.36910 0.0861063 0.0430532 0.999073i \(-0.486292\pi\)
0.0430532 + 0.999073i \(0.486292\pi\)
\(758\) 22.8005 0.828153
\(759\) 0 0
\(760\) 6.05587 0.219670
\(761\) −25.8371 −0.936593 −0.468297 0.883571i \(-0.655132\pi\)
−0.468297 + 0.883571i \(0.655132\pi\)
\(762\) 0 0
\(763\) 8.23742 0.298215
\(764\) −30.4112 −1.10024
\(765\) 0 0
\(766\) 21.5406 0.778293
\(767\) 5.95266 0.214938
\(768\) 0 0
\(769\) 42.7704 1.54234 0.771170 0.636629i \(-0.219672\pi\)
0.771170 + 0.636629i \(0.219672\pi\)
\(770\) −6.77038 −0.243988
\(771\) 0 0
\(772\) 19.6619 0.707646
\(773\) −4.78538 −0.172118 −0.0860591 0.996290i \(-0.527427\pi\)
−0.0860591 + 0.996290i \(0.527427\pi\)
\(774\) 0 0
\(775\) −5.80570 −0.208547
\(776\) −36.0448 −1.29393
\(777\) 0 0
\(778\) −73.8446 −2.64746
\(779\) −29.4055 −1.05356
\(780\) 0 0
\(781\) −20.2483 −0.724540
\(782\) −6.50131 −0.232486
\(783\) 0 0
\(784\) 1.98225 0.0707945
\(785\) 8.07704 0.288282
\(786\) 0 0
\(787\) 41.5741 1.48196 0.740978 0.671529i \(-0.234362\pi\)
0.740978 + 0.671529i \(0.234362\pi\)
\(788\) 44.5523 1.58711
\(789\) 0 0
\(790\) 10.1418 0.360830
\(791\) −1.76488 −0.0627521
\(792\) 0 0
\(793\) −4.62356 −0.164187
\(794\) 68.4864 2.43049
\(795\) 0 0
\(796\) 14.5224 0.514734
\(797\) 8.27869 0.293246 0.146623 0.989192i \(-0.453160\pi\)
0.146623 + 0.989192i \(0.453160\pi\)
\(798\) 0 0
\(799\) −9.44928 −0.334291
\(800\) −32.1201 −1.13562
\(801\) 0 0
\(802\) −21.5419 −0.760671
\(803\) 11.0620 0.390369
\(804\) 0 0
\(805\) 1.01416 0.0357446
\(806\) −1.78907 −0.0630173
\(807\) 0 0
\(808\) −11.9318 −0.419758
\(809\) 47.8198 1.68125 0.840627 0.541614i \(-0.182187\pi\)
0.840627 + 0.541614i \(0.182187\pi\)
\(810\) 0 0
\(811\) −46.1665 −1.62112 −0.810562 0.585653i \(-0.800838\pi\)
−0.810562 + 0.585653i \(0.800838\pi\)
\(812\) 6.71308 0.235583
\(813\) 0 0
\(814\) −17.2695 −0.605295
\(815\) 4.57020 0.160087
\(816\) 0 0
\(817\) 28.8266 1.00851
\(818\) 46.7212 1.63357
\(819\) 0 0
\(820\) 6.72230 0.234753
\(821\) −7.48770 −0.261323 −0.130661 0.991427i \(-0.541710\pi\)
−0.130661 + 0.991427i \(0.541710\pi\)
\(822\) 0 0
\(823\) 44.5952 1.55449 0.777245 0.629198i \(-0.216616\pi\)
0.777245 + 0.629198i \(0.216616\pi\)
\(824\) −19.9107 −0.693622
\(825\) 0 0
\(826\) −45.0666 −1.56807
\(827\) 27.9479 0.971842 0.485921 0.874003i \(-0.338484\pi\)
0.485921 + 0.874003i \(0.338484\pi\)
\(828\) 0 0
\(829\) 11.6817 0.405723 0.202862 0.979207i \(-0.434976\pi\)
0.202862 + 0.979207i \(0.434976\pi\)
\(830\) 9.38093 0.325617
\(831\) 0 0
\(832\) −8.58878 −0.297762
\(833\) 5.81425 0.201452
\(834\) 0 0
\(835\) −8.28032 −0.286552
\(836\) −53.3774 −1.84610
\(837\) 0 0
\(838\) 79.8140 2.75713
\(839\) 0.687980 0.0237517 0.0118759 0.999929i \(-0.496220\pi\)
0.0118759 + 0.999929i \(0.496220\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −21.6277 −0.745339
\(843\) 0 0
\(844\) 65.5865 2.25758
\(845\) 5.69834 0.196029
\(846\) 0 0
\(847\) −4.67475 −0.160626
\(848\) 11.2468 0.386216
\(849\) 0 0
\(850\) −31.1692 −1.06909
\(851\) 2.58687 0.0886767
\(852\) 0 0
\(853\) 49.2306 1.68562 0.842812 0.538208i \(-0.180898\pi\)
0.842812 + 0.538208i \(0.180898\pi\)
\(854\) 35.0042 1.19782
\(855\) 0 0
\(856\) 21.2604 0.726666
\(857\) 46.7516 1.59701 0.798503 0.601991i \(-0.205626\pi\)
0.798503 + 0.601991i \(0.205626\pi\)
\(858\) 0 0
\(859\) 17.6789 0.603196 0.301598 0.953435i \(-0.402480\pi\)
0.301598 + 0.953435i \(0.402480\pi\)
\(860\) −6.58995 −0.224716
\(861\) 0 0
\(862\) −32.3968 −1.10344
\(863\) 56.7921 1.93323 0.966613 0.256242i \(-0.0824843\pi\)
0.966613 + 0.256242i \(0.0824843\pi\)
\(864\) 0 0
\(865\) 4.84262 0.164654
\(866\) 35.3092 1.19985
\(867\) 0 0
\(868\) 8.12929 0.275926
\(869\) −29.8418 −1.01231
\(870\) 0 0
\(871\) 3.37410 0.114327
\(872\) −8.25793 −0.279649
\(873\) 0 0
\(874\) 13.3221 0.450625
\(875\) 9.93301 0.335797
\(876\) 0 0
\(877\) −37.4597 −1.26492 −0.632462 0.774591i \(-0.717956\pi\)
−0.632462 + 0.774591i \(0.717956\pi\)
\(878\) −7.96272 −0.268729
\(879\) 0 0
\(880\) −1.34164 −0.0452268
\(881\) −11.5175 −0.388035 −0.194018 0.980998i \(-0.562152\pi\)
−0.194018 + 0.980998i \(0.562152\pi\)
\(882\) 0 0
\(883\) −3.51176 −0.118180 −0.0590900 0.998253i \(-0.518820\pi\)
−0.0590900 + 0.998253i \(0.518820\pi\)
\(884\) −5.76473 −0.193889
\(885\) 0 0
\(886\) −30.7963 −1.03462
\(887\) −16.0468 −0.538800 −0.269400 0.963028i \(-0.586825\pi\)
−0.269400 + 0.963028i \(0.586825\pi\)
\(888\) 0 0
\(889\) 21.7665 0.730025
\(890\) −6.96688 −0.233530
\(891\) 0 0
\(892\) −63.1936 −2.11588
\(893\) 19.3628 0.647953
\(894\) 0 0
\(895\) 4.55562 0.152278
\(896\) 35.0632 1.17138
\(897\) 0 0
\(898\) −49.7297 −1.65950
\(899\) 1.21096 0.0403879
\(900\) 0 0
\(901\) 32.9887 1.09901
\(902\) −32.9568 −1.09734
\(903\) 0 0
\(904\) 1.76928 0.0588453
\(905\) 2.01681 0.0670411
\(906\) 0 0
\(907\) 33.5760 1.11487 0.557436 0.830220i \(-0.311785\pi\)
0.557436 + 0.830220i \(0.311785\pi\)
\(908\) −14.3614 −0.476599
\(909\) 0 0
\(910\) 1.49832 0.0496688
\(911\) 37.9612 1.25771 0.628855 0.777523i \(-0.283524\pi\)
0.628855 + 0.777523i \(0.283524\pi\)
\(912\) 0 0
\(913\) −27.6029 −0.913522
\(914\) −50.6346 −1.67484
\(915\) 0 0
\(916\) 60.0294 1.98343
\(917\) 10.7293 0.354314
\(918\) 0 0
\(919\) −21.7984 −0.719062 −0.359531 0.933133i \(-0.617063\pi\)
−0.359531 + 0.933133i \(0.617063\pi\)
\(920\) −1.01669 −0.0335192
\(921\) 0 0
\(922\) −16.2861 −0.536354
\(923\) 4.48105 0.147495
\(924\) 0 0
\(925\) 12.4022 0.407781
\(926\) 31.9526 1.05003
\(927\) 0 0
\(928\) 6.69966 0.219927
\(929\) 26.7546 0.877790 0.438895 0.898538i \(-0.355370\pi\)
0.438895 + 0.898538i \(0.355370\pi\)
\(930\) 0 0
\(931\) −11.9142 −0.390471
\(932\) −6.63228 −0.217248
\(933\) 0 0
\(934\) −85.7436 −2.80562
\(935\) −3.93526 −0.128697
\(936\) 0 0
\(937\) 21.0999 0.689305 0.344652 0.938730i \(-0.387997\pi\)
0.344652 + 0.938730i \(0.387997\pi\)
\(938\) −25.5448 −0.834066
\(939\) 0 0
\(940\) −4.42647 −0.144376
\(941\) 20.5081 0.668545 0.334273 0.942476i \(-0.391509\pi\)
0.334273 + 0.942476i \(0.391509\pi\)
\(942\) 0 0
\(943\) 4.93674 0.160762
\(944\) −8.93057 −0.290665
\(945\) 0 0
\(946\) 32.3080 1.05042
\(947\) 58.6897 1.90716 0.953580 0.301141i \(-0.0973675\pi\)
0.953580 + 0.301141i \(0.0973675\pi\)
\(948\) 0 0
\(949\) −2.44807 −0.0794677
\(950\) 63.8698 2.07221
\(951\) 0 0
\(952\) 14.5697 0.472206
\(953\) −22.6328 −0.733149 −0.366574 0.930389i \(-0.619469\pi\)
−0.366574 + 0.930389i \(0.619469\pi\)
\(954\) 0 0
\(955\) 4.59430 0.148668
\(956\) −1.55804 −0.0503907
\(957\) 0 0
\(958\) −46.9764 −1.51774
\(959\) 23.6928 0.765080
\(960\) 0 0
\(961\) −29.5336 −0.952696
\(962\) 3.82183 0.123221
\(963\) 0 0
\(964\) −45.8298 −1.47608
\(965\) −2.97037 −0.0956197
\(966\) 0 0
\(967\) 50.9635 1.63887 0.819437 0.573169i \(-0.194286\pi\)
0.819437 + 0.573169i \(0.194286\pi\)
\(968\) 4.68639 0.150626
\(969\) 0 0
\(970\) 16.3118 0.523740
\(971\) −23.2567 −0.746344 −0.373172 0.927762i \(-0.621730\pi\)
−0.373172 + 0.927762i \(0.621730\pi\)
\(972\) 0 0
\(973\) 11.0933 0.355636
\(974\) −52.1048 −1.66955
\(975\) 0 0
\(976\) 6.93657 0.222034
\(977\) −48.6497 −1.55644 −0.778221 0.627990i \(-0.783878\pi\)
−0.778221 + 0.627990i \(0.783878\pi\)
\(978\) 0 0
\(979\) 20.4997 0.655173
\(980\) 2.72366 0.0870041
\(981\) 0 0
\(982\) −16.0835 −0.513247
\(983\) −15.9161 −0.507646 −0.253823 0.967251i \(-0.581688\pi\)
−0.253823 + 0.967251i \(0.581688\pi\)
\(984\) 0 0
\(985\) −6.73064 −0.214456
\(986\) 6.50131 0.207044
\(987\) 0 0
\(988\) 11.8127 0.375812
\(989\) −4.83954 −0.153889
\(990\) 0 0
\(991\) 17.6468 0.560570 0.280285 0.959917i \(-0.409571\pi\)
0.280285 + 0.959917i \(0.409571\pi\)
\(992\) 8.11304 0.257589
\(993\) 0 0
\(994\) −33.9253 −1.07605
\(995\) −2.19394 −0.0695526
\(996\) 0 0
\(997\) −28.2198 −0.893730 −0.446865 0.894601i \(-0.647460\pi\)
−0.446865 + 0.894601i \(0.647460\pi\)
\(998\) 55.4622 1.75563
\(999\) 0 0
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 6003.2.a.w.1.5 yes 30
3.2 odd 2 6003.2.a.v.1.26 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6003.2.a.v.1.26 30 3.2 odd 2
6003.2.a.w.1.5 yes 30 1.1 even 1 trivial