Properties

Label 9280.2.a.bj.1.2
Level $9280$
Weight $2$
Character 9280.1
Self dual yes
Analytic conductor $74.101$
Analytic rank $0$
Dimension $3$
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] = [9280,2,Mod(1,9280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("9280.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9280 = 2^{6} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9280.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: \(74.1011730757\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 145)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 9280.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.806063 q^{3} -1.00000 q^{5} +1.19394 q^{7} -2.35026 q^{9} +O(q^{10})\) \(q-0.806063 q^{3} -1.00000 q^{5} +1.19394 q^{7} -2.35026 q^{9} -4.15633 q^{11} -2.96239 q^{13} +0.806063 q^{15} +5.50659 q^{17} +3.19394 q^{19} -0.962389 q^{21} +1.84367 q^{23} +1.00000 q^{25} +4.31265 q^{27} +1.00000 q^{29} -4.80606 q^{31} +3.35026 q^{33} -1.19394 q^{35} +9.50659 q^{37} +2.38787 q^{39} -11.2750 q^{41} +0.0303172 q^{43} +2.35026 q^{45} +4.80606 q^{47} -5.57452 q^{49} -4.43866 q^{51} +1.35026 q^{53} +4.15633 q^{55} -2.57452 q^{57} -13.2750 q^{59} -8.88717 q^{61} -2.80606 q^{63} +2.96239 q^{65} -5.84367 q^{67} -1.48612 q^{69} -1.27504 q^{71} -15.2447 q^{73} -0.806063 q^{75} -4.96239 q^{77} -4.93207 q^{79} +3.57452 q^{81} -4.41819 q^{83} -5.50659 q^{85} -0.806063 q^{87} -3.61213 q^{89} -3.53690 q^{91} +3.87399 q^{93} -3.19394 q^{95} -1.38058 q^{97} +9.76845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} - 3 q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{3} - 3 q^{5} + 4 q^{7} + 3 q^{9} - 2 q^{11} + 2 q^{13} + 2 q^{15} - 4 q^{17} + 10 q^{19} + 8 q^{21} + 16 q^{23} + 3 q^{25} - 8 q^{27} + 3 q^{29} - 14 q^{31} - 4 q^{35} + 8 q^{37} + 8 q^{39} - 2 q^{41} - 2 q^{43} - 3 q^{45} + 14 q^{47} - 5 q^{49} + 16 q^{51} - 6 q^{53} + 2 q^{55} + 4 q^{57} - 8 q^{59} + 6 q^{61} - 8 q^{63} - 2 q^{65} - 28 q^{67} - 12 q^{69} + 28 q^{71} - 16 q^{73} - 2 q^{75} - 4 q^{77} - 6 q^{79} - q^{81} - 12 q^{83} + 4 q^{85} - 2 q^{87} - 10 q^{89} + 12 q^{91} + 20 q^{93} - 10 q^{95} + 8 q^{97} + 18 q^{99}+O(q^{100}) \) 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
\(3\) −0.806063 −0.465381 −0.232690 0.972551i \(-0.574753\pi\)
−0.232690 + 0.972551i \(0.574753\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.19394 0.451266 0.225633 0.974212i \(-0.427555\pi\)
0.225633 + 0.974212i \(0.427555\pi\)
\(8\) 0 0
\(9\) −2.35026 −0.783421
\(10\) 0 0
\(11\) −4.15633 −1.25318 −0.626590 0.779349i \(-0.715550\pi\)
−0.626590 + 0.779349i \(0.715550\pi\)
\(12\) 0 0
\(13\) −2.96239 −0.821619 −0.410809 0.911721i \(-0.634754\pi\)
−0.410809 + 0.911721i \(0.634754\pi\)
\(14\) 0 0
\(15\) 0.806063 0.208125
\(16\) 0 0
\(17\) 5.50659 1.33554 0.667772 0.744366i \(-0.267248\pi\)
0.667772 + 0.744366i \(0.267248\pi\)
\(18\) 0 0
\(19\) 3.19394 0.732739 0.366370 0.930469i \(-0.380601\pi\)
0.366370 + 0.930469i \(0.380601\pi\)
\(20\) 0 0
\(21\) −0.962389 −0.210010
\(22\) 0 0
\(23\) 1.84367 0.384433 0.192216 0.981353i \(-0.438432\pi\)
0.192216 + 0.981353i \(0.438432\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 4.31265 0.829970
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −4.80606 −0.863194 −0.431597 0.902066i \(-0.642050\pi\)
−0.431597 + 0.902066i \(0.642050\pi\)
\(32\) 0 0
\(33\) 3.35026 0.583206
\(34\) 0 0
\(35\) −1.19394 −0.201812
\(36\) 0 0
\(37\) 9.50659 1.56287 0.781437 0.623985i \(-0.214487\pi\)
0.781437 + 0.623985i \(0.214487\pi\)
\(38\) 0 0
\(39\) 2.38787 0.382366
\(40\) 0 0
\(41\) −11.2750 −1.76087 −0.880433 0.474171i \(-0.842748\pi\)
−0.880433 + 0.474171i \(0.842748\pi\)
\(42\) 0 0
\(43\) 0.0303172 0.00462332 0.00231166 0.999997i \(-0.499264\pi\)
0.00231166 + 0.999997i \(0.499264\pi\)
\(44\) 0 0
\(45\) 2.35026 0.350356
\(46\) 0 0
\(47\) 4.80606 0.701036 0.350518 0.936556i \(-0.386005\pi\)
0.350518 + 0.936556i \(0.386005\pi\)
\(48\) 0 0
\(49\) −5.57452 −0.796359
\(50\) 0 0
\(51\) −4.43866 −0.621536
\(52\) 0 0
\(53\) 1.35026 0.185473 0.0927364 0.995691i \(-0.470439\pi\)
0.0927364 + 0.995691i \(0.470439\pi\)
\(54\) 0 0
\(55\) 4.15633 0.560439
\(56\) 0 0
\(57\) −2.57452 −0.341003
\(58\) 0 0
\(59\) −13.2750 −1.72826 −0.864131 0.503266i \(-0.832132\pi\)
−0.864131 + 0.503266i \(0.832132\pi\)
\(60\) 0 0
\(61\) −8.88717 −1.13788 −0.568942 0.822377i \(-0.692647\pi\)
−0.568942 + 0.822377i \(0.692647\pi\)
\(62\) 0 0
\(63\) −2.80606 −0.353531
\(64\) 0 0
\(65\) 2.96239 0.367439
\(66\) 0 0
\(67\) −5.84367 −0.713919 −0.356959 0.934120i \(-0.616187\pi\)
−0.356959 + 0.934120i \(0.616187\pi\)
\(68\) 0 0
\(69\) −1.48612 −0.178908
\(70\) 0 0
\(71\) −1.27504 −0.151319 −0.0756596 0.997134i \(-0.524106\pi\)
−0.0756596 + 0.997134i \(0.524106\pi\)
\(72\) 0 0
\(73\) −15.2447 −1.78426 −0.892130 0.451779i \(-0.850790\pi\)
−0.892130 + 0.451779i \(0.850790\pi\)
\(74\) 0 0
\(75\) −0.806063 −0.0930762
\(76\) 0 0
\(77\) −4.96239 −0.565517
\(78\) 0 0
\(79\) −4.93207 −0.554901 −0.277451 0.960740i \(-0.589490\pi\)
−0.277451 + 0.960740i \(0.589490\pi\)
\(80\) 0 0
\(81\) 3.57452 0.397168
\(82\) 0 0
\(83\) −4.41819 −0.484959 −0.242480 0.970156i \(-0.577961\pi\)
−0.242480 + 0.970156i \(0.577961\pi\)
\(84\) 0 0
\(85\) −5.50659 −0.597273
\(86\) 0 0
\(87\) −0.806063 −0.0864191
\(88\) 0 0
\(89\) −3.61213 −0.382885 −0.191442 0.981504i \(-0.561316\pi\)
−0.191442 + 0.981504i \(0.561316\pi\)
\(90\) 0 0
\(91\) −3.53690 −0.370768
\(92\) 0 0
\(93\) 3.87399 0.401714
\(94\) 0 0
\(95\) −3.19394 −0.327691
\(96\) 0 0
\(97\) −1.38058 −0.140177 −0.0700883 0.997541i \(-0.522328\pi\)
−0.0700883 + 0.997541i \(0.522328\pi\)
\(98\) 0 0
\(99\) 9.76845 0.981766
\(100\) 0 0
\(101\) 13.0132 1.29486 0.647430 0.762125i \(-0.275844\pi\)
0.647430 + 0.762125i \(0.275844\pi\)
\(102\) 0 0
\(103\) 5.31994 0.524190 0.262095 0.965042i \(-0.415587\pi\)
0.262095 + 0.965042i \(0.415587\pi\)
\(104\) 0 0
\(105\) 0.962389 0.0939195
\(106\) 0 0
\(107\) 13.8192 1.33596 0.667978 0.744181i \(-0.267160\pi\)
0.667978 + 0.744181i \(0.267160\pi\)
\(108\) 0 0
\(109\) 1.87399 0.179496 0.0897479 0.995965i \(-0.471394\pi\)
0.0897479 + 0.995965i \(0.471394\pi\)
\(110\) 0 0
\(111\) −7.66291 −0.727331
\(112\) 0 0
\(113\) −11.7685 −1.10708 −0.553541 0.832822i \(-0.686724\pi\)
−0.553541 + 0.832822i \(0.686724\pi\)
\(114\) 0 0
\(115\) −1.84367 −0.171924
\(116\) 0 0
\(117\) 6.96239 0.643673
\(118\) 0 0
\(119\) 6.57452 0.602685
\(120\) 0 0
\(121\) 6.27504 0.570458
\(122\) 0 0
\(123\) 9.08840 0.819473
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 14.2677 1.26606 0.633029 0.774128i \(-0.281811\pi\)
0.633029 + 0.774128i \(0.281811\pi\)
\(128\) 0 0
\(129\) −0.0244376 −0.00215161
\(130\) 0 0
\(131\) −5.89446 −0.515001 −0.257501 0.966278i \(-0.582899\pi\)
−0.257501 + 0.966278i \(0.582899\pi\)
\(132\) 0 0
\(133\) 3.81336 0.330660
\(134\) 0 0
\(135\) −4.31265 −0.371174
\(136\) 0 0
\(137\) 18.2823 1.56197 0.780983 0.624553i \(-0.214719\pi\)
0.780983 + 0.624553i \(0.214719\pi\)
\(138\) 0 0
\(139\) 11.5369 0.978547 0.489274 0.872130i \(-0.337262\pi\)
0.489274 + 0.872130i \(0.337262\pi\)
\(140\) 0 0
\(141\) −3.87399 −0.326249
\(142\) 0 0
\(143\) 12.3127 1.02964
\(144\) 0 0
\(145\) −1.00000 −0.0830455
\(146\) 0 0
\(147\) 4.49341 0.370610
\(148\) 0 0
\(149\) −2.77575 −0.227398 −0.113699 0.993515i \(-0.536270\pi\)
−0.113699 + 0.993515i \(0.536270\pi\)
\(150\) 0 0
\(151\) 1.79877 0.146382 0.0731909 0.997318i \(-0.476682\pi\)
0.0731909 + 0.997318i \(0.476682\pi\)
\(152\) 0 0
\(153\) −12.9419 −1.04629
\(154\) 0 0
\(155\) 4.80606 0.386032
\(156\) 0 0
\(157\) −3.76845 −0.300755 −0.150378 0.988629i \(-0.548049\pi\)
−0.150378 + 0.988629i \(0.548049\pi\)
\(158\) 0 0
\(159\) −1.08840 −0.0863155
\(160\) 0 0
\(161\) 2.20123 0.173481
\(162\) 0 0
\(163\) −1.64244 −0.128646 −0.0643231 0.997929i \(-0.520489\pi\)
−0.0643231 + 0.997929i \(0.520489\pi\)
\(164\) 0 0
\(165\) −3.35026 −0.260818
\(166\) 0 0
\(167\) 8.08110 0.625334 0.312667 0.949863i \(-0.398778\pi\)
0.312667 + 0.949863i \(0.398778\pi\)
\(168\) 0 0
\(169\) −4.22425 −0.324943
\(170\) 0 0
\(171\) −7.50659 −0.574043
\(172\) 0 0
\(173\) 7.73813 0.588320 0.294160 0.955756i \(-0.404960\pi\)
0.294160 + 0.955756i \(0.404960\pi\)
\(174\) 0 0
\(175\) 1.19394 0.0902531
\(176\) 0 0
\(177\) 10.7005 0.804301
\(178\) 0 0
\(179\) 21.4010 1.59959 0.799795 0.600274i \(-0.204942\pi\)
0.799795 + 0.600274i \(0.204942\pi\)
\(180\) 0 0
\(181\) −15.2750 −1.13538 −0.567692 0.823241i \(-0.692164\pi\)
−0.567692 + 0.823241i \(0.692164\pi\)
\(182\) 0 0
\(183\) 7.16362 0.529550
\(184\) 0 0
\(185\) −9.50659 −0.698938
\(186\) 0 0
\(187\) −22.8872 −1.67368
\(188\) 0 0
\(189\) 5.14903 0.374537
\(190\) 0 0
\(191\) 3.31994 0.240223 0.120111 0.992760i \(-0.461675\pi\)
0.120111 + 0.992760i \(0.461675\pi\)
\(192\) 0 0
\(193\) −4.88129 −0.351363 −0.175681 0.984447i \(-0.556213\pi\)
−0.175681 + 0.984447i \(0.556213\pi\)
\(194\) 0 0
\(195\) −2.38787 −0.170999
\(196\) 0 0
\(197\) 24.2374 1.72685 0.863423 0.504481i \(-0.168316\pi\)
0.863423 + 0.504481i \(0.168316\pi\)
\(198\) 0 0
\(199\) 16.7513 1.18747 0.593734 0.804661i \(-0.297653\pi\)
0.593734 + 0.804661i \(0.297653\pi\)
\(200\) 0 0
\(201\) 4.71037 0.332244
\(202\) 0 0
\(203\) 1.19394 0.0837979
\(204\) 0 0
\(205\) 11.2750 0.787483
\(206\) 0 0
\(207\) −4.33312 −0.301173
\(208\) 0 0
\(209\) −13.2750 −0.918254
\(210\) 0 0
\(211\) 25.3054 1.74209 0.871046 0.491201i \(-0.163442\pi\)
0.871046 + 0.491201i \(0.163442\pi\)
\(212\) 0 0
\(213\) 1.02776 0.0704211
\(214\) 0 0
\(215\) −0.0303172 −0.00206761
\(216\) 0 0
\(217\) −5.73813 −0.389530
\(218\) 0 0
\(219\) 12.2882 0.830360
\(220\) 0 0
\(221\) −16.3127 −1.09731
\(222\) 0 0
\(223\) 17.6932 1.18483 0.592413 0.805634i \(-0.298175\pi\)
0.592413 + 0.805634i \(0.298175\pi\)
\(224\) 0 0
\(225\) −2.35026 −0.156684
\(226\) 0 0
\(227\) −26.8423 −1.78158 −0.890792 0.454412i \(-0.849849\pi\)
−0.890792 + 0.454412i \(0.849849\pi\)
\(228\) 0 0
\(229\) 17.2243 1.13821 0.569105 0.822265i \(-0.307290\pi\)
0.569105 + 0.822265i \(0.307290\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) 0 0
\(233\) −9.07381 −0.594445 −0.297222 0.954808i \(-0.596060\pi\)
−0.297222 + 0.954808i \(0.596060\pi\)
\(234\) 0 0
\(235\) −4.80606 −0.313513
\(236\) 0 0
\(237\) 3.97556 0.258241
\(238\) 0 0
\(239\) 20.4993 1.32599 0.662995 0.748624i \(-0.269285\pi\)
0.662995 + 0.748624i \(0.269285\pi\)
\(240\) 0 0
\(241\) 5.47627 0.352758 0.176379 0.984322i \(-0.443562\pi\)
0.176379 + 0.984322i \(0.443562\pi\)
\(242\) 0 0
\(243\) −15.8192 −1.01480
\(244\) 0 0
\(245\) 5.57452 0.356143
\(246\) 0 0
\(247\) −9.46168 −0.602032
\(248\) 0 0
\(249\) 3.56134 0.225691
\(250\) 0 0
\(251\) 29.6180 1.86947 0.934736 0.355343i \(-0.115636\pi\)
0.934736 + 0.355343i \(0.115636\pi\)
\(252\) 0 0
\(253\) −7.66291 −0.481763
\(254\) 0 0
\(255\) 4.43866 0.277960
\(256\) 0 0
\(257\) 17.6629 1.10178 0.550891 0.834577i \(-0.314288\pi\)
0.550891 + 0.834577i \(0.314288\pi\)
\(258\) 0 0
\(259\) 11.3503 0.705271
\(260\) 0 0
\(261\) −2.35026 −0.145478
\(262\) 0 0
\(263\) 27.3561 1.68685 0.843426 0.537245i \(-0.180535\pi\)
0.843426 + 0.537245i \(0.180535\pi\)
\(264\) 0 0
\(265\) −1.35026 −0.0829459
\(266\) 0 0
\(267\) 2.91160 0.178187
\(268\) 0 0
\(269\) −10.4993 −0.640153 −0.320077 0.947392i \(-0.603709\pi\)
−0.320077 + 0.947392i \(0.603709\pi\)
\(270\) 0 0
\(271\) −9.61801 −0.584252 −0.292126 0.956380i \(-0.594363\pi\)
−0.292126 + 0.956380i \(0.594363\pi\)
\(272\) 0 0
\(273\) 2.85097 0.172548
\(274\) 0 0
\(275\) −4.15633 −0.250636
\(276\) 0 0
\(277\) −13.3503 −0.802139 −0.401070 0.916048i \(-0.631362\pi\)
−0.401070 + 0.916048i \(0.631362\pi\)
\(278\) 0 0
\(279\) 11.2955 0.676244
\(280\) 0 0
\(281\) 20.4241 1.21840 0.609199 0.793017i \(-0.291491\pi\)
0.609199 + 0.793017i \(0.291491\pi\)
\(282\) 0 0
\(283\) 8.02047 0.476767 0.238384 0.971171i \(-0.423382\pi\)
0.238384 + 0.971171i \(0.423382\pi\)
\(284\) 0 0
\(285\) 2.57452 0.152501
\(286\) 0 0
\(287\) −13.4617 −0.794618
\(288\) 0 0
\(289\) 13.3225 0.783676
\(290\) 0 0
\(291\) 1.11283 0.0652355
\(292\) 0 0
\(293\) 23.3054 1.36151 0.680757 0.732510i \(-0.261651\pi\)
0.680757 + 0.732510i \(0.261651\pi\)
\(294\) 0 0
\(295\) 13.2750 0.772903
\(296\) 0 0
\(297\) −17.9248 −1.04010
\(298\) 0 0
\(299\) −5.46168 −0.315857
\(300\) 0 0
\(301\) 0.0361968 0.00208635
\(302\) 0 0
\(303\) −10.4894 −0.602603
\(304\) 0 0
\(305\) 8.88717 0.508878
\(306\) 0 0
\(307\) 6.73084 0.384149 0.192075 0.981380i \(-0.438478\pi\)
0.192075 + 0.981380i \(0.438478\pi\)
\(308\) 0 0
\(309\) −4.28821 −0.243948
\(310\) 0 0
\(311\) −22.0567 −1.25072 −0.625359 0.780337i \(-0.715048\pi\)
−0.625359 + 0.780337i \(0.715048\pi\)
\(312\) 0 0
\(313\) 5.03761 0.284743 0.142371 0.989813i \(-0.454527\pi\)
0.142371 + 0.989813i \(0.454527\pi\)
\(314\) 0 0
\(315\) 2.80606 0.158104
\(316\) 0 0
\(317\) −34.2941 −1.92615 −0.963074 0.269237i \(-0.913229\pi\)
−0.963074 + 0.269237i \(0.913229\pi\)
\(318\) 0 0
\(319\) −4.15633 −0.232710
\(320\) 0 0
\(321\) −11.1392 −0.621729
\(322\) 0 0
\(323\) 17.5877 0.978605
\(324\) 0 0
\(325\) −2.96239 −0.164324
\(326\) 0 0
\(327\) −1.51056 −0.0835340
\(328\) 0 0
\(329\) 5.73813 0.316354
\(330\) 0 0
\(331\) 34.8324 1.91456 0.957281 0.289159i \(-0.0933755\pi\)
0.957281 + 0.289159i \(0.0933755\pi\)
\(332\) 0 0
\(333\) −22.3430 −1.22439
\(334\) 0 0
\(335\) 5.84367 0.319274
\(336\) 0 0
\(337\) −17.6326 −0.960509 −0.480254 0.877129i \(-0.659456\pi\)
−0.480254 + 0.877129i \(0.659456\pi\)
\(338\) 0 0
\(339\) 9.48612 0.515215
\(340\) 0 0
\(341\) 19.9756 1.08174
\(342\) 0 0
\(343\) −15.0132 −0.810635
\(344\) 0 0
\(345\) 1.48612 0.0800099
\(346\) 0 0
\(347\) 3.11871 0.167421 0.0837107 0.996490i \(-0.473323\pi\)
0.0837107 + 0.996490i \(0.473323\pi\)
\(348\) 0 0
\(349\) 13.0738 0.699825 0.349912 0.936782i \(-0.386211\pi\)
0.349912 + 0.936782i \(0.386211\pi\)
\(350\) 0 0
\(351\) −12.7757 −0.681919
\(352\) 0 0
\(353\) 5.19982 0.276758 0.138379 0.990379i \(-0.455811\pi\)
0.138379 + 0.990379i \(0.455811\pi\)
\(354\) 0 0
\(355\) 1.27504 0.0676720
\(356\) 0 0
\(357\) −5.29948 −0.280478
\(358\) 0 0
\(359\) 30.4182 1.60541 0.802705 0.596376i \(-0.203393\pi\)
0.802705 + 0.596376i \(0.203393\pi\)
\(360\) 0 0
\(361\) −8.79877 −0.463093
\(362\) 0 0
\(363\) −5.05808 −0.265480
\(364\) 0 0
\(365\) 15.2447 0.797945
\(366\) 0 0
\(367\) 20.6556 1.07821 0.539107 0.842237i \(-0.318762\pi\)
0.539107 + 0.842237i \(0.318762\pi\)
\(368\) 0 0
\(369\) 26.4993 1.37950
\(370\) 0 0
\(371\) 1.61213 0.0836975
\(372\) 0 0
\(373\) −11.0884 −0.574135 −0.287068 0.957910i \(-0.592680\pi\)
−0.287068 + 0.957910i \(0.592680\pi\)
\(374\) 0 0
\(375\) 0.806063 0.0416249
\(376\) 0 0
\(377\) −2.96239 −0.152571
\(378\) 0 0
\(379\) −10.0811 −0.517831 −0.258916 0.965900i \(-0.583365\pi\)
−0.258916 + 0.965900i \(0.583365\pi\)
\(380\) 0 0
\(381\) −11.5007 −0.589199
\(382\) 0 0
\(383\) 16.3576 0.835832 0.417916 0.908486i \(-0.362761\pi\)
0.417916 + 0.908486i \(0.362761\pi\)
\(384\) 0 0
\(385\) 4.96239 0.252907
\(386\) 0 0
\(387\) −0.0712533 −0.00362201
\(388\) 0 0
\(389\) −31.9003 −1.61741 −0.808706 0.588213i \(-0.799831\pi\)
−0.808706 + 0.588213i \(0.799831\pi\)
\(390\) 0 0
\(391\) 10.1524 0.513427
\(392\) 0 0
\(393\) 4.75131 0.239672
\(394\) 0 0
\(395\) 4.93207 0.248159
\(396\) 0 0
\(397\) −2.98683 −0.149905 −0.0749523 0.997187i \(-0.523880\pi\)
−0.0749523 + 0.997187i \(0.523880\pi\)
\(398\) 0 0
\(399\) −3.07381 −0.153883
\(400\) 0 0
\(401\) −21.9756 −1.09741 −0.548704 0.836017i \(-0.684878\pi\)
−0.548704 + 0.836017i \(0.684878\pi\)
\(402\) 0 0
\(403\) 14.2374 0.709217
\(404\) 0 0
\(405\) −3.57452 −0.177619
\(406\) 0 0
\(407\) −39.5125 −1.95856
\(408\) 0 0
\(409\) −22.4387 −1.10952 −0.554760 0.832010i \(-0.687190\pi\)
−0.554760 + 0.832010i \(0.687190\pi\)
\(410\) 0 0
\(411\) −14.7367 −0.726909
\(412\) 0 0
\(413\) −15.8496 −0.779906
\(414\) 0 0
\(415\) 4.41819 0.216880
\(416\) 0 0
\(417\) −9.29948 −0.455397
\(418\) 0 0
\(419\) −10.3634 −0.506287 −0.253143 0.967429i \(-0.581464\pi\)
−0.253143 + 0.967429i \(0.581464\pi\)
\(420\) 0 0
\(421\) −34.0362 −1.65882 −0.829411 0.558638i \(-0.811324\pi\)
−0.829411 + 0.558638i \(0.811324\pi\)
\(422\) 0 0
\(423\) −11.2955 −0.549206
\(424\) 0 0
\(425\) 5.50659 0.267109
\(426\) 0 0
\(427\) −10.6107 −0.513488
\(428\) 0 0
\(429\) −9.92478 −0.479173
\(430\) 0 0
\(431\) 25.7743 1.24151 0.620753 0.784006i \(-0.286827\pi\)
0.620753 + 0.784006i \(0.286827\pi\)
\(432\) 0 0
\(433\) 2.18076 0.104801 0.0524004 0.998626i \(-0.483313\pi\)
0.0524004 + 0.998626i \(0.483313\pi\)
\(434\) 0 0
\(435\) 0.806063 0.0386478
\(436\) 0 0
\(437\) 5.88858 0.281689
\(438\) 0 0
\(439\) −35.5125 −1.69492 −0.847459 0.530861i \(-0.821869\pi\)
−0.847459 + 0.530861i \(0.821869\pi\)
\(440\) 0 0
\(441\) 13.1016 0.623884
\(442\) 0 0
\(443\) 4.34297 0.206341 0.103170 0.994664i \(-0.467101\pi\)
0.103170 + 0.994664i \(0.467101\pi\)
\(444\) 0 0
\(445\) 3.61213 0.171231
\(446\) 0 0
\(447\) 2.23743 0.105827
\(448\) 0 0
\(449\) 31.3357 1.47882 0.739411 0.673254i \(-0.235104\pi\)
0.739411 + 0.673254i \(0.235104\pi\)
\(450\) 0 0
\(451\) 46.8627 2.20668
\(452\) 0 0
\(453\) −1.44992 −0.0681233
\(454\) 0 0
\(455\) 3.53690 0.165813
\(456\) 0 0
\(457\) 34.3488 1.60677 0.803386 0.595459i \(-0.203030\pi\)
0.803386 + 0.595459i \(0.203030\pi\)
\(458\) 0 0
\(459\) 23.7480 1.10846
\(460\) 0 0
\(461\) −11.8641 −0.552568 −0.276284 0.961076i \(-0.589103\pi\)
−0.276284 + 0.961076i \(0.589103\pi\)
\(462\) 0 0
\(463\) 40.4953 1.88198 0.940989 0.338438i \(-0.109899\pi\)
0.940989 + 0.338438i \(0.109899\pi\)
\(464\) 0 0
\(465\) −3.87399 −0.179652
\(466\) 0 0
\(467\) 30.2071 1.39782 0.698909 0.715210i \(-0.253669\pi\)
0.698909 + 0.715210i \(0.253669\pi\)
\(468\) 0 0
\(469\) −6.97698 −0.322167
\(470\) 0 0
\(471\) 3.03761 0.139966
\(472\) 0 0
\(473\) −0.126008 −0.00579385
\(474\) 0 0
\(475\) 3.19394 0.146548
\(476\) 0 0
\(477\) −3.17347 −0.145303
\(478\) 0 0
\(479\) 0.0547547 0.00250181 0.00125090 0.999999i \(-0.499602\pi\)
0.00125090 + 0.999999i \(0.499602\pi\)
\(480\) 0 0
\(481\) −28.1622 −1.28409
\(482\) 0 0
\(483\) −1.77433 −0.0807349
\(484\) 0 0
\(485\) 1.38058 0.0626889
\(486\) 0 0
\(487\) −0.881286 −0.0399349 −0.0199674 0.999801i \(-0.506356\pi\)
−0.0199674 + 0.999801i \(0.506356\pi\)
\(488\) 0 0
\(489\) 1.32391 0.0598695
\(490\) 0 0
\(491\) −41.0698 −1.85346 −0.926728 0.375733i \(-0.877391\pi\)
−0.926728 + 0.375733i \(0.877391\pi\)
\(492\) 0 0
\(493\) 5.50659 0.248004
\(494\) 0 0
\(495\) −9.76845 −0.439059
\(496\) 0 0
\(497\) −1.52232 −0.0682852
\(498\) 0 0
\(499\) −12.3733 −0.553904 −0.276952 0.960884i \(-0.589324\pi\)
−0.276952 + 0.960884i \(0.589324\pi\)
\(500\) 0 0
\(501\) −6.51388 −0.291019
\(502\) 0 0
\(503\) −2.26774 −0.101114 −0.0505569 0.998721i \(-0.516100\pi\)
−0.0505569 + 0.998721i \(0.516100\pi\)
\(504\) 0 0
\(505\) −13.0132 −0.579079
\(506\) 0 0
\(507\) 3.40502 0.151222
\(508\) 0 0
\(509\) 10.9018 0.483212 0.241606 0.970374i \(-0.422326\pi\)
0.241606 + 0.970374i \(0.422326\pi\)
\(510\) 0 0
\(511\) −18.2012 −0.805175
\(512\) 0 0
\(513\) 13.7743 0.608152
\(514\) 0 0
\(515\) −5.31994 −0.234425
\(516\) 0 0
\(517\) −19.9756 −0.878524
\(518\) 0 0
\(519\) −6.23743 −0.273793
\(520\) 0 0
\(521\) −4.72496 −0.207004 −0.103502 0.994629i \(-0.533005\pi\)
−0.103502 + 0.994629i \(0.533005\pi\)
\(522\) 0 0
\(523\) 1.06793 0.0466973 0.0233486 0.999727i \(-0.492567\pi\)
0.0233486 + 0.999727i \(0.492567\pi\)
\(524\) 0 0
\(525\) −0.962389 −0.0420021
\(526\) 0 0
\(527\) −26.4650 −1.15283
\(528\) 0 0
\(529\) −19.6009 −0.852211
\(530\) 0 0
\(531\) 31.1998 1.35396
\(532\) 0 0
\(533\) 33.4010 1.44676
\(534\) 0 0
\(535\) −13.8192 −0.597458
\(536\) 0 0
\(537\) −17.2506 −0.744418
\(538\) 0 0
\(539\) 23.1695 0.997981
\(540\) 0 0
\(541\) 7.46168 0.320803 0.160401 0.987052i \(-0.448721\pi\)
0.160401 + 0.987052i \(0.448721\pi\)
\(542\) 0 0
\(543\) 12.3127 0.528386
\(544\) 0 0
\(545\) −1.87399 −0.0802730
\(546\) 0 0
\(547\) 38.9683 1.66616 0.833081 0.553150i \(-0.186575\pi\)
0.833081 + 0.553150i \(0.186575\pi\)
\(548\) 0 0
\(549\) 20.8872 0.891443
\(550\) 0 0
\(551\) 3.19394 0.136066
\(552\) 0 0
\(553\) −5.88858 −0.250408
\(554\) 0 0
\(555\) 7.66291 0.325273
\(556\) 0 0
\(557\) 22.9986 0.974481 0.487241 0.873268i \(-0.338003\pi\)
0.487241 + 0.873268i \(0.338003\pi\)
\(558\) 0 0
\(559\) −0.0898112 −0.00379861
\(560\) 0 0
\(561\) 18.4485 0.778897
\(562\) 0 0
\(563\) −11.6688 −0.491781 −0.245890 0.969298i \(-0.579080\pi\)
−0.245890 + 0.969298i \(0.579080\pi\)
\(564\) 0 0
\(565\) 11.7685 0.495102
\(566\) 0 0
\(567\) 4.26774 0.179228
\(568\) 0 0
\(569\) 11.3357 0.475216 0.237608 0.971361i \(-0.423637\pi\)
0.237608 + 0.971361i \(0.423637\pi\)
\(570\) 0 0
\(571\) −27.1754 −1.13725 −0.568627 0.822595i \(-0.692525\pi\)
−0.568627 + 0.822595i \(0.692525\pi\)
\(572\) 0 0
\(573\) −2.67609 −0.111795
\(574\) 0 0
\(575\) 1.84367 0.0768866
\(576\) 0 0
\(577\) 22.5950 0.940641 0.470321 0.882496i \(-0.344138\pi\)
0.470321 + 0.882496i \(0.344138\pi\)
\(578\) 0 0
\(579\) 3.93463 0.163517
\(580\) 0 0
\(581\) −5.27504 −0.218845
\(582\) 0 0
\(583\) −5.61213 −0.232431
\(584\) 0 0
\(585\) −6.96239 −0.287859
\(586\) 0 0
\(587\) −9.31994 −0.384675 −0.192338 0.981329i \(-0.561607\pi\)
−0.192338 + 0.981329i \(0.561607\pi\)
\(588\) 0 0
\(589\) −15.3503 −0.632497
\(590\) 0 0
\(591\) −19.5369 −0.803641
\(592\) 0 0
\(593\) −15.1246 −0.621093 −0.310546 0.950558i \(-0.600512\pi\)
−0.310546 + 0.950558i \(0.600512\pi\)
\(594\) 0 0
\(595\) −6.57452 −0.269529
\(596\) 0 0
\(597\) −13.5026 −0.552625
\(598\) 0 0
\(599\) 4.09569 0.167345 0.0836727 0.996493i \(-0.473335\pi\)
0.0836727 + 0.996493i \(0.473335\pi\)
\(600\) 0 0
\(601\) 22.2276 0.906682 0.453341 0.891337i \(-0.350232\pi\)
0.453341 + 0.891337i \(0.350232\pi\)
\(602\) 0 0
\(603\) 13.7342 0.559298
\(604\) 0 0
\(605\) −6.27504 −0.255117
\(606\) 0 0
\(607\) −48.2941 −1.96020 −0.980098 0.198512i \(-0.936389\pi\)
−0.980098 + 0.198512i \(0.936389\pi\)
\(608\) 0 0
\(609\) −0.962389 −0.0389980
\(610\) 0 0
\(611\) −14.2374 −0.575985
\(612\) 0 0
\(613\) 9.74798 0.393717 0.196859 0.980432i \(-0.436926\pi\)
0.196859 + 0.980432i \(0.436926\pi\)
\(614\) 0 0
\(615\) −9.08840 −0.366480
\(616\) 0 0
\(617\) 18.2170 0.733387 0.366694 0.930342i \(-0.380490\pi\)
0.366694 + 0.930342i \(0.380490\pi\)
\(618\) 0 0
\(619\) −25.0943 −1.00862 −0.504312 0.863521i \(-0.668254\pi\)
−0.504312 + 0.863521i \(0.668254\pi\)
\(620\) 0 0
\(621\) 7.95112 0.319068
\(622\) 0 0
\(623\) −4.31265 −0.172783
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 10.7005 0.427338
\(628\) 0 0
\(629\) 52.3488 2.08729
\(630\) 0 0
\(631\) 21.4617 0.854376 0.427188 0.904163i \(-0.359504\pi\)
0.427188 + 0.904163i \(0.359504\pi\)
\(632\) 0 0
\(633\) −20.3977 −0.810737
\(634\) 0 0
\(635\) −14.2677 −0.566198
\(636\) 0 0
\(637\) 16.5139 0.654304
\(638\) 0 0
\(639\) 2.99668 0.118547
\(640\) 0 0
\(641\) 3.17347 0.125344 0.0626722 0.998034i \(-0.480038\pi\)
0.0626722 + 0.998034i \(0.480038\pi\)
\(642\) 0 0
\(643\) 2.74069 0.108082 0.0540411 0.998539i \(-0.482790\pi\)
0.0540411 + 0.998539i \(0.482790\pi\)
\(644\) 0 0
\(645\) 0.0244376 0.000962228 0
\(646\) 0 0
\(647\) 6.34297 0.249368 0.124684 0.992197i \(-0.460208\pi\)
0.124684 + 0.992197i \(0.460208\pi\)
\(648\) 0 0
\(649\) 55.1754 2.16582
\(650\) 0 0
\(651\) 4.62530 0.181280
\(652\) 0 0
\(653\) −4.08110 −0.159706 −0.0798529 0.996807i \(-0.525445\pi\)
−0.0798529 + 0.996807i \(0.525445\pi\)
\(654\) 0 0
\(655\) 5.89446 0.230316
\(656\) 0 0
\(657\) 35.8291 1.39783
\(658\) 0 0
\(659\) −9.58181 −0.373254 −0.186627 0.982431i \(-0.559756\pi\)
−0.186627 + 0.982431i \(0.559756\pi\)
\(660\) 0 0
\(661\) 27.5271 1.07068 0.535339 0.844637i \(-0.320184\pi\)
0.535339 + 0.844637i \(0.320184\pi\)
\(662\) 0 0
\(663\) 13.1490 0.510666
\(664\) 0 0
\(665\) −3.81336 −0.147876
\(666\) 0 0
\(667\) 1.84367 0.0713874
\(668\) 0 0
\(669\) −14.2619 −0.551396
\(670\) 0 0
\(671\) 36.9380 1.42597
\(672\) 0 0
\(673\) 3.13727 0.120933 0.0604665 0.998170i \(-0.480741\pi\)
0.0604665 + 0.998170i \(0.480741\pi\)
\(674\) 0 0
\(675\) 4.31265 0.165994
\(676\) 0 0
\(677\) 46.2579 1.77784 0.888918 0.458067i \(-0.151458\pi\)
0.888918 + 0.458067i \(0.151458\pi\)
\(678\) 0 0
\(679\) −1.64832 −0.0632569
\(680\) 0 0
\(681\) 21.6366 0.829115
\(682\) 0 0
\(683\) 9.01905 0.345104 0.172552 0.985000i \(-0.444799\pi\)
0.172552 + 0.985000i \(0.444799\pi\)
\(684\) 0 0
\(685\) −18.2823 −0.698532
\(686\) 0 0
\(687\) −13.8838 −0.529702
\(688\) 0 0
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) 50.0625 1.90447 0.952234 0.305368i \(-0.0987794\pi\)
0.952234 + 0.305368i \(0.0987794\pi\)
\(692\) 0 0
\(693\) 11.6629 0.443037
\(694\) 0 0
\(695\) −11.5369 −0.437620
\(696\) 0 0
\(697\) −62.0870 −2.35171
\(698\) 0 0
\(699\) 7.31406 0.276643
\(700\) 0 0
\(701\) −45.3014 −1.71101 −0.855505 0.517795i \(-0.826753\pi\)
−0.855505 + 0.517795i \(0.826753\pi\)
\(702\) 0 0
\(703\) 30.3634 1.14518
\(704\) 0 0
\(705\) 3.87399 0.145903
\(706\) 0 0
\(707\) 15.5369 0.584325
\(708\) 0 0
\(709\) 3.27504 0.122997 0.0614983 0.998107i \(-0.480412\pi\)
0.0614983 + 0.998107i \(0.480412\pi\)
\(710\) 0 0
\(711\) 11.5917 0.434721
\(712\) 0 0
\(713\) −8.86082 −0.331840
\(714\) 0 0
\(715\) −12.3127 −0.460467
\(716\) 0 0
\(717\) −16.5237 −0.617090
\(718\) 0 0
\(719\) 27.7235 1.03391 0.516957 0.856011i \(-0.327065\pi\)
0.516957 + 0.856011i \(0.327065\pi\)
\(720\) 0 0
\(721\) 6.35168 0.236549
\(722\) 0 0
\(723\) −4.41422 −0.164167
\(724\) 0 0
\(725\) 1.00000 0.0371391
\(726\) 0 0
\(727\) −26.8930 −0.997408 −0.498704 0.866772i \(-0.666190\pi\)
−0.498704 + 0.866772i \(0.666190\pi\)
\(728\) 0 0
\(729\) 2.02776 0.0751023
\(730\) 0 0
\(731\) 0.166944 0.00617465
\(732\) 0 0
\(733\) −3.17935 −0.117432 −0.0587160 0.998275i \(-0.518701\pi\)
−0.0587160 + 0.998275i \(0.518701\pi\)
\(734\) 0 0
\(735\) −4.49341 −0.165742
\(736\) 0 0
\(737\) 24.2882 0.894668
\(738\) 0 0
\(739\) 29.7440 1.09415 0.547076 0.837083i \(-0.315741\pi\)
0.547076 + 0.837083i \(0.315741\pi\)
\(740\) 0 0
\(741\) 7.62672 0.280174
\(742\) 0 0
\(743\) −4.34297 −0.159328 −0.0796640 0.996822i \(-0.525385\pi\)
−0.0796640 + 0.996822i \(0.525385\pi\)
\(744\) 0 0
\(745\) 2.77575 0.101695
\(746\) 0 0
\(747\) 10.3839 0.379927
\(748\) 0 0
\(749\) 16.4993 0.602871
\(750\) 0 0
\(751\) 22.5804 0.823970 0.411985 0.911191i \(-0.364836\pi\)
0.411985 + 0.911191i \(0.364836\pi\)
\(752\) 0 0
\(753\) −23.8740 −0.870017
\(754\) 0 0
\(755\) −1.79877 −0.0654639
\(756\) 0 0
\(757\) −9.88461 −0.359262 −0.179631 0.983734i \(-0.557490\pi\)
−0.179631 + 0.983734i \(0.557490\pi\)
\(758\) 0 0
\(759\) 6.17679 0.224203
\(760\) 0 0
\(761\) 13.6991 0.496592 0.248296 0.968684i \(-0.420129\pi\)
0.248296 + 0.968684i \(0.420129\pi\)
\(762\) 0 0
\(763\) 2.23743 0.0810003
\(764\) 0 0
\(765\) 12.9419 0.467916
\(766\) 0 0
\(767\) 39.3258 1.41997
\(768\) 0 0
\(769\) 25.0132 0.901998 0.450999 0.892524i \(-0.351068\pi\)
0.450999 + 0.892524i \(0.351068\pi\)
\(770\) 0 0
\(771\) −14.2374 −0.512748
\(772\) 0 0
\(773\) 35.9062 1.29146 0.645728 0.763567i \(-0.276554\pi\)
0.645728 + 0.763567i \(0.276554\pi\)
\(774\) 0 0
\(775\) −4.80606 −0.172639
\(776\) 0 0
\(777\) −9.14903 −0.328220
\(778\) 0 0
\(779\) −36.0118 −1.29026
\(780\) 0 0
\(781\) 5.29948 0.189630
\(782\) 0 0
\(783\) 4.31265 0.154122
\(784\) 0 0
\(785\) 3.76845 0.134502
\(786\) 0 0
\(787\) −50.3839 −1.79599 −0.897996 0.440003i \(-0.854977\pi\)
−0.897996 + 0.440003i \(0.854977\pi\)
\(788\) 0 0
\(789\) −22.0508 −0.785029
\(790\) 0 0
\(791\) −14.0508 −0.499588
\(792\) 0 0
\(793\) 26.3272 0.934908
\(794\) 0 0
\(795\) 1.08840 0.0386014
\(796\) 0 0
\(797\) 5.69323 0.201665 0.100832 0.994903i \(-0.467849\pi\)
0.100832 + 0.994903i \(0.467849\pi\)
\(798\) 0 0
\(799\) 26.4650 0.936265
\(800\) 0 0
\(801\) 8.48944 0.299960
\(802\) 0 0
\(803\) 63.3620 2.23600
\(804\) 0 0
\(805\) −2.20123 −0.0775832
\(806\) 0 0
\(807\) 8.46310 0.297915
\(808\) 0 0
\(809\) −7.76257 −0.272918 −0.136459 0.990646i \(-0.543572\pi\)
−0.136459 + 0.990646i \(0.543572\pi\)
\(810\) 0 0
\(811\) 26.4894 0.930170 0.465085 0.885266i \(-0.346024\pi\)
0.465085 + 0.885266i \(0.346024\pi\)
\(812\) 0 0
\(813\) 7.75272 0.271900
\(814\) 0 0
\(815\) 1.64244 0.0575323
\(816\) 0 0
\(817\) 0.0968311 0.00338769
\(818\) 0 0
\(819\) 8.31265 0.290468
\(820\) 0 0
\(821\) −25.4763 −0.889128 −0.444564 0.895747i \(-0.646641\pi\)
−0.444564 + 0.895747i \(0.646641\pi\)
\(822\) 0 0
\(823\) −9.22028 −0.321399 −0.160699 0.987003i \(-0.551375\pi\)
−0.160699 + 0.987003i \(0.551375\pi\)
\(824\) 0 0
\(825\) 3.35026 0.116641
\(826\) 0 0
\(827\) −24.5343 −0.853143 −0.426571 0.904454i \(-0.640279\pi\)
−0.426571 + 0.904454i \(0.640279\pi\)
\(828\) 0 0
\(829\) −0.201231 −0.00698903 −0.00349452 0.999994i \(-0.501112\pi\)
−0.00349452 + 0.999994i \(0.501112\pi\)
\(830\) 0 0
\(831\) 10.7612 0.373300
\(832\) 0 0
\(833\) −30.6966 −1.06357
\(834\) 0 0
\(835\) −8.08110 −0.279658
\(836\) 0 0
\(837\) −20.7269 −0.716425
\(838\) 0 0
\(839\) 1.45580 0.0502599 0.0251299 0.999684i \(-0.492000\pi\)
0.0251299 + 0.999684i \(0.492000\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −16.4631 −0.567019
\(844\) 0 0
\(845\) 4.22425 0.145319
\(846\) 0 0
\(847\) 7.49200 0.257428
\(848\) 0 0
\(849\) −6.46501 −0.221878
\(850\) 0 0
\(851\) 17.5271 0.600820
\(852\) 0 0
\(853\) −43.1793 −1.47843 −0.739216 0.673468i \(-0.764804\pi\)
−0.739216 + 0.673468i \(0.764804\pi\)
\(854\) 0 0
\(855\) 7.50659 0.256720
\(856\) 0 0
\(857\) −20.9887 −0.716962 −0.358481 0.933537i \(-0.616705\pi\)
−0.358481 + 0.933537i \(0.616705\pi\)
\(858\) 0 0
\(859\) 49.4069 1.68574 0.842871 0.538115i \(-0.180863\pi\)
0.842871 + 0.538115i \(0.180863\pi\)
\(860\) 0 0
\(861\) 10.8510 0.369800
\(862\) 0 0
\(863\) 56.6820 1.92948 0.964738 0.263211i \(-0.0847816\pi\)
0.964738 + 0.263211i \(0.0847816\pi\)
\(864\) 0 0
\(865\) −7.73813 −0.263104
\(866\) 0 0
\(867\) −10.7388 −0.364708
\(868\) 0 0
\(869\) 20.4993 0.695391
\(870\) 0 0
\(871\) 17.3112 0.586569
\(872\) 0 0
\(873\) 3.24472 0.109817
\(874\) 0 0
\(875\) −1.19394 −0.0403624
\(876\) 0 0
\(877\) 13.1998 0.445726 0.222863 0.974850i \(-0.428460\pi\)
0.222863 + 0.974850i \(0.428460\pi\)
\(878\) 0 0
\(879\) −18.7856 −0.633622
\(880\) 0 0
\(881\) 6.37802 0.214881 0.107441 0.994212i \(-0.465734\pi\)
0.107441 + 0.994212i \(0.465734\pi\)
\(882\) 0 0
\(883\) −48.6213 −1.63624 −0.818119 0.575049i \(-0.804983\pi\)
−0.818119 + 0.575049i \(0.804983\pi\)
\(884\) 0 0
\(885\) −10.7005 −0.359694
\(886\) 0 0
\(887\) −15.0317 −0.504716 −0.252358 0.967634i \(-0.581206\pi\)
−0.252358 + 0.967634i \(0.581206\pi\)
\(888\) 0 0
\(889\) 17.0348 0.571328
\(890\) 0 0
\(891\) −14.8568 −0.497723
\(892\) 0 0
\(893\) 15.3503 0.513677
\(894\) 0 0
\(895\) −21.4010 −0.715358
\(896\) 0 0
\(897\) 4.40246 0.146994
\(898\) 0 0
\(899\) −4.80606 −0.160291
\(900\) 0 0
\(901\) 7.43533 0.247707
\(902\) 0 0
\(903\) −0.0291769 −0.000970946 0
\(904\) 0 0
\(905\) 15.2750 0.507759
\(906\) 0 0
\(907\) 0.342968 0.0113880 0.00569402 0.999984i \(-0.498188\pi\)
0.00569402 + 0.999984i \(0.498188\pi\)
\(908\) 0 0
\(909\) −30.5844 −1.01442
\(910\) 0 0
\(911\) 20.9076 0.692701 0.346350 0.938105i \(-0.387421\pi\)
0.346350 + 0.938105i \(0.387421\pi\)
\(912\) 0 0
\(913\) 18.3634 0.607741
\(914\) 0 0
\(915\) −7.16362 −0.236822
\(916\) 0 0
\(917\) −7.03761 −0.232402
\(918\) 0 0
\(919\) −1.90034 −0.0626864 −0.0313432 0.999509i \(-0.509978\pi\)
−0.0313432 + 0.999509i \(0.509978\pi\)
\(920\) 0 0
\(921\) −5.42548 −0.178776
\(922\) 0 0
\(923\) 3.77716 0.124327
\(924\) 0 0
\(925\) 9.50659 0.312575
\(926\) 0 0
\(927\) −12.5033 −0.410661
\(928\) 0 0
\(929\) 39.3522 1.29110 0.645551 0.763717i \(-0.276628\pi\)
0.645551 + 0.763717i \(0.276628\pi\)
\(930\) 0 0
\(931\) −17.8046 −0.583524
\(932\) 0 0
\(933\) 17.7791 0.582061
\(934\) 0 0
\(935\) 22.8872 0.748490
\(936\) 0 0
\(937\) −6.37802 −0.208361 −0.104180 0.994558i \(-0.533222\pi\)
−0.104180 + 0.994558i \(0.533222\pi\)
\(938\) 0 0
\(939\) −4.06063 −0.132514
\(940\) 0 0
\(941\) 26.6253 0.867960 0.433980 0.900923i \(-0.357109\pi\)
0.433980 + 0.900923i \(0.357109\pi\)
\(942\) 0 0
\(943\) −20.7875 −0.676934
\(944\) 0 0
\(945\) −5.14903 −0.167498
\(946\) 0 0
\(947\) 12.2823 0.399122 0.199561 0.979885i \(-0.436048\pi\)
0.199561 + 0.979885i \(0.436048\pi\)
\(948\) 0 0
\(949\) 45.1608 1.46598
\(950\) 0 0
\(951\) 27.6432 0.896393
\(952\) 0 0
\(953\) 0.821792 0.0266205 0.0133102 0.999911i \(-0.495763\pi\)
0.0133102 + 0.999911i \(0.495763\pi\)
\(954\) 0 0
\(955\) −3.31994 −0.107431
\(956\) 0 0
\(957\) 3.35026 0.108299
\(958\) 0 0
\(959\) 21.8279 0.704861
\(960\) 0 0
\(961\) −7.90175 −0.254895
\(962\) 0 0
\(963\) −32.4788 −1.04662
\(964\) 0 0
\(965\) 4.88129 0.157134
\(966\) 0 0
\(967\) −37.4314 −1.20371 −0.601856 0.798605i \(-0.705572\pi\)
−0.601856 + 0.798605i \(0.705572\pi\)
\(968\) 0 0
\(969\) −14.1768 −0.455424
\(970\) 0 0
\(971\) 8.71625 0.279718 0.139859 0.990171i \(-0.455335\pi\)
0.139859 + 0.990171i \(0.455335\pi\)
\(972\) 0 0
\(973\) 13.7743 0.441585
\(974\) 0 0
\(975\) 2.38787 0.0764731
\(976\) 0 0
\(977\) −33.7645 −1.08022 −0.540111 0.841594i \(-0.681618\pi\)
−0.540111 + 0.841594i \(0.681618\pi\)
\(978\) 0 0
\(979\) 15.0132 0.479823
\(980\) 0 0
\(981\) −4.40437 −0.140621
\(982\) 0 0
\(983\) 43.6082 1.39088 0.695442 0.718582i \(-0.255209\pi\)
0.695442 + 0.718582i \(0.255209\pi\)
\(984\) 0 0
\(985\) −24.2374 −0.772269
\(986\) 0 0
\(987\) −4.62530 −0.147225
\(988\) 0 0
\(989\) 0.0558950 0.00177736
\(990\) 0 0
\(991\) −52.9741 −1.68278 −0.841390 0.540429i \(-0.818262\pi\)
−0.841390 + 0.540429i \(0.818262\pi\)
\(992\) 0 0
\(993\) −28.0771 −0.891001
\(994\) 0 0
\(995\) −16.7513 −0.531052
\(996\) 0 0
\(997\) −13.6326 −0.431749 −0.215874 0.976421i \(-0.569260\pi\)
−0.215874 + 0.976421i \(0.569260\pi\)
\(998\) 0 0
\(999\) 40.9986 1.29714
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 9280.2.a.bj.1.2 3
4.3 odd 2 9280.2.a.br.1.2 3
8.3 odd 2 2320.2.a.n.1.2 3
8.5 even 2 145.2.a.c.1.1 3
24.5 odd 2 1305.2.a.p.1.3 3
40.13 odd 4 725.2.b.e.349.5 6
40.29 even 2 725.2.a.e.1.3 3
40.37 odd 4 725.2.b.e.349.2 6
56.13 odd 2 7105.2.a.o.1.1 3
120.29 odd 2 6525.2.a.be.1.1 3
232.173 even 2 4205.2.a.f.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
145.2.a.c.1.1 3 8.5 even 2
725.2.a.e.1.3 3 40.29 even 2
725.2.b.e.349.2 6 40.37 odd 4
725.2.b.e.349.5 6 40.13 odd 4
1305.2.a.p.1.3 3 24.5 odd 2
2320.2.a.n.1.2 3 8.3 odd 2
4205.2.a.f.1.3 3 232.173 even 2
6525.2.a.be.1.1 3 120.29 odd 2
7105.2.a.o.1.1 3 56.13 odd 2
9280.2.a.bj.1.2 3 1.1 even 1 trivial
9280.2.a.br.1.2 3 4.3 odd 2