Properties

Label 2900.2.c.f.349.4
Level $2900$
Weight $2$
Character 2900.349
Analytic conductor $23.157$
Analytic rank $0$
Dimension $6$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2900,2,Mod(349,2900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2900.349");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2900.c (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(23.1566165862\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5089536.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 580)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.4
Root \(0.675970 - 0.675970i\) of defining polynomial
Character \(\chi\) \(=\) 2900.349
Dual form 2900.2.c.f.349.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.35194i q^{3} +0.648061i q^{7} +1.17226 q^{9} +O(q^{10})\) \(q+1.35194i q^{3} +0.648061i q^{7} +1.17226 q^{9} +3.35194 q^{11} +4.17226i q^{13} -4.82032i q^{17} -6.82032 q^{19} -0.876139 q^{21} +5.52420i q^{23} +5.64064i q^{27} +1.00000 q^{29} -2.82032 q^{31} +4.53162i q^{33} +10.2281i q^{37} -5.64064 q^{39} +8.17226 q^{41} -5.69646i q^{43} +2.64806i q^{47} +6.58002 q^{49} +6.51678 q^{51} -2.87614i q^{53} -9.22066i q^{57} +13.2207 q^{59} -1.12386 q^{61} +0.759696i q^{63} -1.52420i q^{67} -7.46838 q^{69} -8.87614 q^{71} +9.69646i q^{73} +2.17226i q^{77} -8.99258 q^{79} -4.10902 q^{81} +1.94418i q^{83} +1.35194i q^{87} -17.0484 q^{89} -2.70388 q^{91} -3.81290i q^{93} +13.3519i q^{97} +3.92935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 22 q^{9} + 16 q^{11} - 16 q^{19} + 32 q^{21} + 6 q^{29} + 8 q^{31} + 16 q^{39} + 20 q^{41} - 6 q^{49} - 48 q^{51} - 16 q^{59} - 44 q^{61} - 24 q^{69} - 16 q^{71} + 46 q^{81} - 36 q^{89} - 8 q^{91} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times\).

\(n\) \(901\) \(1277\) \(1451\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 1.35194i 0.780542i 0.920700 + 0.390271i \(0.127619\pi\)
−0.920700 + 0.390271i \(0.872381\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.648061i 0.244944i 0.992472 + 0.122472i \(0.0390822\pi\)
−0.992472 + 0.122472i \(0.960918\pi\)
\(8\) 0 0
\(9\) 1.17226 0.390753
\(10\) 0 0
\(11\) 3.35194 1.01065 0.505324 0.862930i \(-0.331373\pi\)
0.505324 + 0.862930i \(0.331373\pi\)
\(12\) 0 0
\(13\) 4.17226i 1.15718i 0.815620 + 0.578588i \(0.196396\pi\)
−0.815620 + 0.578588i \(0.803604\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 4.82032i − 1.16910i −0.811358 0.584550i \(-0.801271\pi\)
0.811358 0.584550i \(-0.198729\pi\)
\(18\) 0 0
\(19\) −6.82032 −1.56469 −0.782344 0.622846i \(-0.785976\pi\)
−0.782344 + 0.622846i \(0.785976\pi\)
\(20\) 0 0
\(21\) −0.876139 −0.191189
\(22\) 0 0
\(23\) 5.52420i 1.15188i 0.817494 + 0.575938i \(0.195363\pi\)
−0.817494 + 0.575938i \(0.804637\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.64064i 1.08554i
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −2.82032 −0.506545 −0.253272 0.967395i \(-0.581507\pi\)
−0.253272 + 0.967395i \(0.581507\pi\)
\(32\) 0 0
\(33\) 4.53162i 0.788853i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.2281i 1.68149i 0.541435 + 0.840743i \(0.317881\pi\)
−0.541435 + 0.840743i \(0.682119\pi\)
\(38\) 0 0
\(39\) −5.64064 −0.903226
\(40\) 0 0
\(41\) 8.17226 1.27629 0.638146 0.769915i \(-0.279701\pi\)
0.638146 + 0.769915i \(0.279701\pi\)
\(42\) 0 0
\(43\) − 5.69646i − 0.868702i −0.900744 0.434351i \(-0.856978\pi\)
0.900744 0.434351i \(-0.143022\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.64806i 0.386259i 0.981173 + 0.193130i \(0.0618638\pi\)
−0.981173 + 0.193130i \(0.938136\pi\)
\(48\) 0 0
\(49\) 6.58002 0.940002
\(50\) 0 0
\(51\) 6.51678 0.912532
\(52\) 0 0
\(53\) − 2.87614i − 0.395068i −0.980296 0.197534i \(-0.936707\pi\)
0.980296 0.197534i \(-0.0632933\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) − 9.22066i − 1.22131i
\(58\) 0 0
\(59\) 13.2207 1.72118 0.860592 0.509296i \(-0.170094\pi\)
0.860592 + 0.509296i \(0.170094\pi\)
\(60\) 0 0
\(61\) −1.12386 −0.143896 −0.0719478 0.997408i \(-0.522922\pi\)
−0.0719478 + 0.997408i \(0.522922\pi\)
\(62\) 0 0
\(63\) 0.759696i 0.0957127i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 1.52420i − 0.186211i −0.995656 0.0931053i \(-0.970321\pi\)
0.995656 0.0931053i \(-0.0296793\pi\)
\(68\) 0 0
\(69\) −7.46838 −0.899088
\(70\) 0 0
\(71\) −8.87614 −1.05340 −0.526702 0.850050i \(-0.676572\pi\)
−0.526702 + 0.850050i \(0.676572\pi\)
\(72\) 0 0
\(73\) 9.69646i 1.13488i 0.823413 + 0.567442i \(0.192067\pi\)
−0.823413 + 0.567442i \(0.807933\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.17226i 0.247552i
\(78\) 0 0
\(79\) −8.99258 −1.01174 −0.505872 0.862608i \(-0.668829\pi\)
−0.505872 + 0.862608i \(0.668829\pi\)
\(80\) 0 0
\(81\) −4.10902 −0.456558
\(82\) 0 0
\(83\) 1.94418i 0.213402i 0.994291 + 0.106701i \(0.0340287\pi\)
−0.994291 + 0.106701i \(0.965971\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.35194i 0.144943i
\(88\) 0 0
\(89\) −17.0484 −1.80713 −0.903563 0.428455i \(-0.859058\pi\)
−0.903563 + 0.428455i \(0.859058\pi\)
\(90\) 0 0
\(91\) −2.70388 −0.283443
\(92\) 0 0
\(93\) − 3.81290i − 0.395380i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.3519i 1.35568i 0.735208 + 0.677842i \(0.237085\pi\)
−0.735208 + 0.677842i \(0.762915\pi\)
\(98\) 0 0
\(99\) 3.92935 0.394914
\(100\) 0 0
\(101\) 18.4562 1.83646 0.918228 0.396052i \(-0.129620\pi\)
0.918228 + 0.396052i \(0.129620\pi\)
\(102\) 0 0
\(103\) − 14.8203i − 1.46029i −0.683292 0.730145i \(-0.739453\pi\)
0.683292 0.730145i \(-0.260547\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.35194i 0.324044i 0.986787 + 0.162022i \(0.0518016\pi\)
−0.986787 + 0.162022i \(0.948198\pi\)
\(108\) 0 0
\(109\) −2.76450 −0.264791 −0.132396 0.991197i \(-0.542267\pi\)
−0.132396 + 0.991197i \(0.542267\pi\)
\(110\) 0 0
\(111\) −13.8277 −1.31247
\(112\) 0 0
\(113\) 7.94418i 0.747326i 0.927565 + 0.373663i \(0.121898\pi\)
−0.927565 + 0.373663i \(0.878102\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.89098i 0.452171i
\(118\) 0 0
\(119\) 3.12386 0.286364
\(120\) 0 0
\(121\) 0.235496 0.0214088
\(122\) 0 0
\(123\) 11.0484i 0.996201i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 17.6965i 1.57031i 0.619301 + 0.785153i \(0.287416\pi\)
−0.619301 + 0.785153i \(0.712584\pi\)
\(128\) 0 0
\(129\) 7.70127 0.678059
\(130\) 0 0
\(131\) 5.52420 0.482652 0.241326 0.970444i \(-0.422418\pi\)
0.241326 + 0.970444i \(0.422418\pi\)
\(132\) 0 0
\(133\) − 4.41998i − 0.383261i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.86872i 0.330527i 0.986249 + 0.165264i \(0.0528475\pi\)
−0.986249 + 0.165264i \(0.947153\pi\)
\(138\) 0 0
\(139\) −5.64064 −0.478433 −0.239217 0.970966i \(-0.576891\pi\)
−0.239217 + 0.970966i \(0.576891\pi\)
\(140\) 0 0
\(141\) −3.58002 −0.301492
\(142\) 0 0
\(143\) 13.9852i 1.16950i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 8.89578i 0.733712i
\(148\) 0 0
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) −17.2207 −1.40140 −0.700699 0.713457i \(-0.747128\pi\)
−0.700699 + 0.713457i \(0.747128\pi\)
\(152\) 0 0
\(153\) − 5.65067i − 0.456830i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.69646i 0.454627i 0.973822 + 0.227314i \(0.0729942\pi\)
−0.973822 + 0.227314i \(0.927006\pi\)
\(158\) 0 0
\(159\) 3.88836 0.308367
\(160\) 0 0
\(161\) −3.58002 −0.282145
\(162\) 0 0
\(163\) 16.4003i 1.28457i 0.766464 + 0.642287i \(0.222014\pi\)
−0.766464 + 0.642287i \(0.777986\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 23.2765i 1.80119i 0.434661 + 0.900594i \(0.356868\pi\)
−0.434661 + 0.900594i \(0.643132\pi\)
\(168\) 0 0
\(169\) −4.40776 −0.339058
\(170\) 0 0
\(171\) −7.99519 −0.611408
\(172\) 0 0
\(173\) − 13.9245i − 1.05866i −0.848415 0.529332i \(-0.822443\pi\)
0.848415 0.529332i \(-0.177557\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.8735i 1.34346i
\(178\) 0 0
\(179\) 4.34452 0.324725 0.162362 0.986731i \(-0.448089\pi\)
0.162362 + 0.986731i \(0.448089\pi\)
\(180\) 0 0
\(181\) 20.5168 1.52500 0.762500 0.646988i \(-0.223972\pi\)
0.762500 + 0.646988i \(0.223972\pi\)
\(182\) 0 0
\(183\) − 1.51939i − 0.112317i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) − 16.1574i − 1.18155i
\(188\) 0 0
\(189\) −3.65548 −0.265897
\(190\) 0 0
\(191\) −9.10422 −0.658758 −0.329379 0.944198i \(-0.606839\pi\)
−0.329379 + 0.944198i \(0.606839\pi\)
\(192\) 0 0
\(193\) − 25.1648i − 1.81140i −0.423914 0.905702i \(-0.639344\pi\)
0.423914 0.905702i \(-0.360656\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.703878i 0.0501493i 0.999686 + 0.0250746i \(0.00798234\pi\)
−0.999686 + 0.0250746i \(0.992018\pi\)
\(198\) 0 0
\(199\) 5.22066 0.370083 0.185041 0.982731i \(-0.440758\pi\)
0.185041 + 0.982731i \(0.440758\pi\)
\(200\) 0 0
\(201\) 2.06063 0.145345
\(202\) 0 0
\(203\) 0.648061i 0.0454850i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.47580i 0.450099i
\(208\) 0 0
\(209\) −22.8613 −1.58135
\(210\) 0 0
\(211\) −13.1042 −0.902131 −0.451066 0.892491i \(-0.648956\pi\)
−0.451066 + 0.892491i \(0.648956\pi\)
\(212\) 0 0
\(213\) − 12.0000i − 0.822226i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) − 1.82774i − 0.124075i
\(218\) 0 0
\(219\) −13.1090 −0.885826
\(220\) 0 0
\(221\) 20.1116 1.35285
\(222\) 0 0
\(223\) − 20.5726i − 1.37764i −0.724931 0.688822i \(-0.758128\pi\)
0.724931 0.688822i \(-0.241872\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.41256i 0.624734i 0.949962 + 0.312367i \(0.101122\pi\)
−0.949962 + 0.312367i \(0.898878\pi\)
\(228\) 0 0
\(229\) −2.00000 −0.132164 −0.0660819 0.997814i \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) 0 0
\(231\) −2.93676 −0.193225
\(232\) 0 0
\(233\) 10.3445i 0.677692i 0.940842 + 0.338846i \(0.110037\pi\)
−0.940842 + 0.338846i \(0.889963\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) − 12.1574i − 0.789710i
\(238\) 0 0
\(239\) −20.8761 −1.35037 −0.675183 0.737651i \(-0.735935\pi\)
−0.675183 + 0.737651i \(0.735935\pi\)
\(240\) 0 0
\(241\) 21.1600 1.36304 0.681519 0.731801i \(-0.261320\pi\)
0.681519 + 0.731801i \(0.261320\pi\)
\(242\) 0 0
\(243\) 11.3668i 0.729179i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 28.4562i − 1.81062i
\(248\) 0 0
\(249\) −2.62842 −0.166569
\(250\) 0 0
\(251\) −8.64806 −0.545861 −0.272930 0.962034i \(-0.587993\pi\)
−0.272930 + 0.962034i \(0.587993\pi\)
\(252\) 0 0
\(253\) 18.5168i 1.16414i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 27.4535i − 1.71251i −0.516557 0.856253i \(-0.672787\pi\)
0.516557 0.856253i \(-0.327213\pi\)
\(258\) 0 0
\(259\) −6.62842 −0.411870
\(260\) 0 0
\(261\) 1.17226 0.0725611
\(262\) 0 0
\(263\) − 11.3371i − 0.699076i −0.936922 0.349538i \(-0.886339\pi\)
0.936922 0.349538i \(-0.113661\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 23.0484i − 1.41054i
\(268\) 0 0
\(269\) 20.1723 1.22992 0.614962 0.788557i \(-0.289171\pi\)
0.614962 + 0.788557i \(0.289171\pi\)
\(270\) 0 0
\(271\) −10.7449 −0.652704 −0.326352 0.945248i \(-0.605819\pi\)
−0.326352 + 0.945248i \(0.605819\pi\)
\(272\) 0 0
\(273\) − 3.65548i − 0.221240i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 12.6284i 0.758768i 0.925239 + 0.379384i \(0.123864\pi\)
−0.925239 + 0.379384i \(0.876136\pi\)
\(278\) 0 0
\(279\) −3.30615 −0.197934
\(280\) 0 0
\(281\) 6.76450 0.403536 0.201768 0.979433i \(-0.435331\pi\)
0.201768 + 0.979433i \(0.435331\pi\)
\(282\) 0 0
\(283\) 1.06804i 0.0634886i 0.999496 + 0.0317443i \(0.0101062\pi\)
−0.999496 + 0.0317443i \(0.989894\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.29612i 0.312620i
\(288\) 0 0
\(289\) −6.23550 −0.366794
\(290\) 0 0
\(291\) −18.0510 −1.05817
\(292\) 0 0
\(293\) 5.46357i 0.319185i 0.987183 + 0.159593i \(0.0510181\pi\)
−0.987183 + 0.159593i \(0.948982\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 18.9071i 1.09710i
\(298\) 0 0
\(299\) −23.0484 −1.33292
\(300\) 0 0
\(301\) 3.69165 0.212783
\(302\) 0 0
\(303\) 24.9516i 1.43343i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 6.30354i − 0.359762i −0.983688 0.179881i \(-0.942429\pi\)
0.983688 0.179881i \(-0.0575713\pi\)
\(308\) 0 0
\(309\) 20.0362 1.13982
\(310\) 0 0
\(311\) 24.6842 1.39971 0.699857 0.714283i \(-0.253247\pi\)
0.699857 + 0.714283i \(0.253247\pi\)
\(312\) 0 0
\(313\) − 24.1723i − 1.36630i −0.730280 0.683148i \(-0.760610\pi\)
0.730280 0.683148i \(-0.239390\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 1.42740i − 0.0801708i −0.999196 0.0400854i \(-0.987237\pi\)
0.999196 0.0400854i \(-0.0127630\pi\)
\(318\) 0 0
\(319\) 3.35194 0.187673
\(320\) 0 0
\(321\) −4.53162 −0.252930
\(322\) 0 0
\(323\) 32.8761i 1.82928i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 3.73744i − 0.206681i
\(328\) 0 0
\(329\) −1.71610 −0.0946119
\(330\) 0 0
\(331\) 34.2132 1.88053 0.940265 0.340444i \(-0.110577\pi\)
0.940265 + 0.340444i \(0.110577\pi\)
\(332\) 0 0
\(333\) 11.9900i 0.657046i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 4.40034i − 0.239702i −0.992792 0.119851i \(-0.961758\pi\)
0.992792 0.119851i \(-0.0382416\pi\)
\(338\) 0 0
\(339\) −10.7401 −0.583320
\(340\) 0 0
\(341\) −9.45355 −0.511938
\(342\) 0 0
\(343\) 8.80068i 0.475192i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 12.9926i − 0.697478i −0.937220 0.348739i \(-0.886610\pi\)
0.937220 0.348739i \(-0.113390\pi\)
\(348\) 0 0
\(349\) 20.0968 1.07576 0.537878 0.843022i \(-0.319226\pi\)
0.537878 + 0.843022i \(0.319226\pi\)
\(350\) 0 0
\(351\) −23.5342 −1.25616
\(352\) 0 0
\(353\) − 17.8129i − 0.948085i −0.880502 0.474043i \(-0.842794\pi\)
0.880502 0.474043i \(-0.157206\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 4.22327i 0.223519i
\(358\) 0 0
\(359\) −5.52420 −0.291556 −0.145778 0.989317i \(-0.546569\pi\)
−0.145778 + 0.989317i \(0.546569\pi\)
\(360\) 0 0
\(361\) 27.5168 1.44825
\(362\) 0 0
\(363\) 0.318377i 0.0167104i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 20.0558i 1.04691i 0.852055 + 0.523453i \(0.175356\pi\)
−0.852055 + 0.523453i \(0.824644\pi\)
\(368\) 0 0
\(369\) 9.58002 0.498716
\(370\) 0 0
\(371\) 1.86391 0.0967695
\(372\) 0 0
\(373\) − 1.88836i − 0.0977758i −0.998804 0.0488879i \(-0.984432\pi\)
0.998804 0.0488879i \(-0.0155677\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.17226i 0.214882i
\(378\) 0 0
\(379\) 15.0894 0.775089 0.387545 0.921851i \(-0.373323\pi\)
0.387545 + 0.921851i \(0.373323\pi\)
\(380\) 0 0
\(381\) −23.9245 −1.22569
\(382\) 0 0
\(383\) 17.3371i 0.885885i 0.896550 + 0.442942i \(0.146065\pi\)
−0.896550 + 0.442942i \(0.853935\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 6.67773i − 0.339448i
\(388\) 0 0
\(389\) 0.890976 0.0451743 0.0225871 0.999745i \(-0.492810\pi\)
0.0225871 + 0.999745i \(0.492810\pi\)
\(390\) 0 0
\(391\) 26.6284 1.34666
\(392\) 0 0
\(393\) 7.46838i 0.376730i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) − 5.39292i − 0.270663i −0.990800 0.135331i \(-0.956790\pi\)
0.990800 0.135331i \(-0.0432099\pi\)
\(398\) 0 0
\(399\) 5.97555 0.299152
\(400\) 0 0
\(401\) 5.23550 0.261448 0.130724 0.991419i \(-0.458270\pi\)
0.130724 + 0.991419i \(0.458270\pi\)
\(402\) 0 0
\(403\) − 11.7671i − 0.586162i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 34.2839i 1.69939i
\(408\) 0 0
\(409\) 16.0606 0.794147 0.397073 0.917787i \(-0.370026\pi\)
0.397073 + 0.917787i \(0.370026\pi\)
\(410\) 0 0
\(411\) −5.23027 −0.257990
\(412\) 0 0
\(413\) 8.56779i 0.421593i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) − 7.62581i − 0.373437i
\(418\) 0 0
\(419\) 19.9245 0.973377 0.486689 0.873575i \(-0.338205\pi\)
0.486689 + 0.873575i \(0.338205\pi\)
\(420\) 0 0
\(421\) −15.5652 −0.758600 −0.379300 0.925274i \(-0.623835\pi\)
−0.379300 + 0.925274i \(0.623835\pi\)
\(422\) 0 0
\(423\) 3.10422i 0.150932i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) − 0.728330i − 0.0352464i
\(428\) 0 0
\(429\) −18.9071 −0.912843
\(430\) 0 0
\(431\) −13.4078 −0.645829 −0.322914 0.946428i \(-0.604663\pi\)
−0.322914 + 0.946428i \(0.604663\pi\)
\(432\) 0 0
\(433\) − 34.6842i − 1.66682i −0.552657 0.833409i \(-0.686386\pi\)
0.552657 0.833409i \(-0.313614\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 37.6768i − 1.80233i
\(438\) 0 0
\(439\) 15.2355 0.727151 0.363575 0.931565i \(-0.381556\pi\)
0.363575 + 0.931565i \(0.381556\pi\)
\(440\) 0 0
\(441\) 7.71349 0.367309
\(442\) 0 0
\(443\) 5.00742i 0.237910i 0.992900 + 0.118955i \(0.0379544\pi\)
−0.992900 + 0.118955i \(0.962046\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 24.3349i − 1.15100i
\(448\) 0 0
\(449\) 17.8129 0.840643 0.420321 0.907375i \(-0.361917\pi\)
0.420321 + 0.907375i \(0.361917\pi\)
\(450\) 0 0
\(451\) 27.3929 1.28988
\(452\) 0 0
\(453\) − 23.2813i − 1.09385i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) − 24.4051i − 1.14162i −0.821081 0.570812i \(-0.806628\pi\)
0.821081 0.570812i \(-0.193372\pi\)
\(458\) 0 0
\(459\) 27.1897 1.26911
\(460\) 0 0
\(461\) −7.98516 −0.371906 −0.185953 0.982559i \(-0.559537\pi\)
−0.185953 + 0.982559i \(0.559537\pi\)
\(462\) 0 0
\(463\) 11.6210i 0.540074i 0.962850 + 0.270037i \(0.0870359\pi\)
−0.962850 + 0.270037i \(0.912964\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 1.24030i − 0.0573944i −0.999588 0.0286972i \(-0.990864\pi\)
0.999588 0.0286972i \(-0.00913586\pi\)
\(468\) 0 0
\(469\) 0.987774 0.0456112
\(470\) 0 0
\(471\) −7.70127 −0.354856
\(472\) 0 0
\(473\) − 19.0942i − 0.877952i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) − 3.37158i − 0.154374i
\(478\) 0 0
\(479\) −19.6965 −0.899954 −0.449977 0.893040i \(-0.648568\pi\)
−0.449977 + 0.893040i \(0.648568\pi\)
\(480\) 0 0
\(481\) −42.6742 −1.94578
\(482\) 0 0
\(483\) − 4.83997i − 0.220226i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 15.0894i 0.683765i 0.939743 + 0.341883i \(0.111064\pi\)
−0.939743 + 0.341883i \(0.888936\pi\)
\(488\) 0 0
\(489\) −22.1723 −1.00266
\(490\) 0 0
\(491\) −12.2281 −0.551845 −0.275923 0.961180i \(-0.588983\pi\)
−0.275923 + 0.961180i \(0.588983\pi\)
\(492\) 0 0
\(493\) − 4.82032i − 0.217096i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 5.75228i − 0.258025i
\(498\) 0 0
\(499\) 5.52901 0.247512 0.123756 0.992313i \(-0.460506\pi\)
0.123756 + 0.992313i \(0.460506\pi\)
\(500\) 0 0
\(501\) −31.4684 −1.40590
\(502\) 0 0
\(503\) 24.2887i 1.08298i 0.840707 + 0.541490i \(0.182140\pi\)
−0.840707 + 0.541490i \(0.817860\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 5.95902i − 0.264649i
\(508\) 0 0
\(509\) 9.58002 0.424627 0.212313 0.977202i \(-0.431900\pi\)
0.212313 + 0.977202i \(0.431900\pi\)
\(510\) 0 0
\(511\) −6.28390 −0.277983
\(512\) 0 0
\(513\) − 38.4710i − 1.69854i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 8.87614i 0.390372i
\(518\) 0 0
\(519\) 18.8251 0.826331
\(520\) 0 0
\(521\) −21.5800 −0.945438 −0.472719 0.881213i \(-0.656727\pi\)
−0.472719 + 0.881213i \(0.656727\pi\)
\(522\) 0 0
\(523\) − 42.2132i − 1.84586i −0.384972 0.922928i \(-0.625789\pi\)
0.384972 0.922928i \(-0.374211\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 13.5949i 0.592201i
\(528\) 0 0
\(529\) −7.51678 −0.326817
\(530\) 0 0
\(531\) 15.4981 0.672558
\(532\) 0 0
\(533\) 34.0968i 1.47690i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 5.87353i 0.253461i
\(538\) 0 0
\(539\) 22.0558 0.950011
\(540\) 0 0
\(541\) 36.5530 1.57153 0.785767 0.618522i \(-0.212268\pi\)
0.785767 + 0.618522i \(0.212268\pi\)
\(542\) 0 0
\(543\) 27.7374i 1.19033i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 26.6236i − 1.13834i −0.822219 0.569172i \(-0.807264\pi\)
0.822219 0.569172i \(-0.192736\pi\)
\(548\) 0 0
\(549\) −1.31746 −0.0562277
\(550\) 0 0
\(551\) −6.82032 −0.290555
\(552\) 0 0
\(553\) − 5.82774i − 0.247821i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 22.2233i − 0.941630i −0.882232 0.470815i \(-0.843960\pi\)
0.882232 0.470815i \(-0.156040\pi\)
\(558\) 0 0
\(559\) 23.7671 1.00524
\(560\) 0 0
\(561\) 21.8439 0.922248
\(562\) 0 0
\(563\) 1.11905i 0.0471625i 0.999722 + 0.0235812i \(0.00750684\pi\)
−0.999722 + 0.0235812i \(0.992493\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 2.66290i − 0.111831i
\(568\) 0 0
\(569\) 10.5316 0.441508 0.220754 0.975329i \(-0.429148\pi\)
0.220754 + 0.975329i \(0.429148\pi\)
\(570\) 0 0
\(571\) −1.18449 −0.0495692 −0.0247846 0.999693i \(-0.507890\pi\)
−0.0247846 + 0.999693i \(0.507890\pi\)
\(572\) 0 0
\(573\) − 12.3083i − 0.514189i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) − 11.8687i − 0.494101i −0.969003 0.247051i \(-0.920539\pi\)
0.969003 0.247051i \(-0.0794614\pi\)
\(578\) 0 0
\(579\) 34.0213 1.41388
\(580\) 0 0
\(581\) −1.25995 −0.0522715
\(582\) 0 0
\(583\) − 9.64064i − 0.399275i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 32.4610i − 1.33981i −0.742448 0.669904i \(-0.766335\pi\)
0.742448 0.669904i \(-0.233665\pi\)
\(588\) 0 0
\(589\) 19.2355 0.792585
\(590\) 0 0
\(591\) −0.951601 −0.0391436
\(592\) 0 0
\(593\) 9.12386i 0.374672i 0.982296 + 0.187336i \(0.0599853\pi\)
−0.982296 + 0.187336i \(0.940015\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.05801i 0.288865i
\(598\) 0 0
\(599\) 30.2887 1.23756 0.618781 0.785563i \(-0.287627\pi\)
0.618781 + 0.785563i \(0.287627\pi\)
\(600\) 0 0
\(601\) 20.5168 0.836897 0.418448 0.908241i \(-0.362574\pi\)
0.418448 + 0.908241i \(0.362574\pi\)
\(602\) 0 0
\(603\) − 1.78676i − 0.0727624i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 13.9293i 0.565375i 0.959212 + 0.282687i \(0.0912259\pi\)
−0.959212 + 0.282687i \(0.908774\pi\)
\(608\) 0 0
\(609\) −0.876139 −0.0355029
\(610\) 0 0
\(611\) −11.0484 −0.446970
\(612\) 0 0
\(613\) 19.7523i 0.797787i 0.916997 + 0.398893i \(0.130606\pi\)
−0.916997 + 0.398893i \(0.869394\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.2010i 1.49766i 0.662764 + 0.748828i \(0.269383\pi\)
−0.662764 + 0.748828i \(0.730617\pi\)
\(618\) 0 0
\(619\) −7.46357 −0.299986 −0.149993 0.988687i \(-0.547925\pi\)
−0.149993 + 0.988687i \(0.547925\pi\)
\(620\) 0 0
\(621\) −31.1600 −1.25041
\(622\) 0 0
\(623\) − 11.0484i − 0.442645i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) − 30.9071i − 1.23431i
\(628\) 0 0
\(629\) 49.3026 1.96582
\(630\) 0 0
\(631\) 44.4562 1.76977 0.884886 0.465808i \(-0.154236\pi\)
0.884886 + 0.465808i \(0.154236\pi\)
\(632\) 0 0
\(633\) − 17.7161i − 0.704152i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 27.4535i 1.08775i
\(638\) 0 0
\(639\) −10.4051 −0.411621
\(640\) 0 0
\(641\) −40.7401 −1.60914 −0.804568 0.593861i \(-0.797603\pi\)
−0.804568 + 0.593861i \(0.797603\pi\)
\(642\) 0 0
\(643\) 20.3493i 0.802499i 0.915969 + 0.401250i \(0.131424\pi\)
−0.915969 + 0.401250i \(0.868576\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 41.7933i − 1.64306i −0.570163 0.821531i \(-0.693120\pi\)
0.570163 0.821531i \(-0.306880\pi\)
\(648\) 0 0
\(649\) 44.3148 1.73951
\(650\) 0 0
\(651\) 2.47099 0.0968458
\(652\) 0 0
\(653\) 23.7933i 0.931102i 0.885021 + 0.465551i \(0.154144\pi\)
−0.885021 + 0.465551i \(0.845856\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 11.3668i 0.443460i
\(658\) 0 0
\(659\) −7.50936 −0.292523 −0.146262 0.989246i \(-0.546724\pi\)
−0.146262 + 0.989246i \(0.546724\pi\)
\(660\) 0 0
\(661\) 45.9245 1.78626 0.893129 0.449801i \(-0.148505\pi\)
0.893129 + 0.449801i \(0.148505\pi\)
\(662\) 0 0
\(663\) 27.1897i 1.05596i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 5.52420i 0.213898i
\(668\) 0 0
\(669\) 27.8129 1.07531
\(670\) 0 0
\(671\) −3.76711 −0.145428
\(672\) 0 0
\(673\) 7.29612i 0.281245i 0.990063 + 0.140622i \(0.0449104\pi\)
−0.990063 + 0.140622i \(0.955090\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 36.2494i − 1.39318i −0.717470 0.696589i \(-0.754700\pi\)
0.717470 0.696589i \(-0.245300\pi\)
\(678\) 0 0
\(679\) −8.65287 −0.332067
\(680\) 0 0
\(681\) −12.7252 −0.487631
\(682\) 0 0
\(683\) − 5.40295i − 0.206738i −0.994643 0.103369i \(-0.967038\pi\)
0.994643 0.103369i \(-0.0329623\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) − 2.70388i − 0.103159i
\(688\) 0 0
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) −36.0458 −1.37125 −0.685623 0.727957i \(-0.740470\pi\)
−0.685623 + 0.727957i \(0.740470\pi\)
\(692\) 0 0
\(693\) 2.54645i 0.0967318i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) − 39.3929i − 1.49211i
\(698\) 0 0
\(699\) −13.9852 −0.528967
\(700\) 0 0
\(701\) 3.33229 0.125859 0.0629295 0.998018i \(-0.479956\pi\)
0.0629295 + 0.998018i \(0.479956\pi\)
\(702\) 0 0
\(703\) − 69.7588i − 2.63100i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 11.9607i 0.449829i
\(708\) 0 0
\(709\) −7.48322 −0.281038 −0.140519 0.990078i \(-0.544877\pi\)
−0.140519 + 0.990078i \(0.544877\pi\)
\(710\) 0 0
\(711\) −10.5416 −0.395343
\(712\) 0 0
\(713\) − 15.5800i − 0.583476i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) − 28.2233i − 1.05402i
\(718\) 0 0
\(719\) 39.6620 1.47914 0.739571 0.673078i \(-0.235028\pi\)
0.739571 + 0.673078i \(0.235028\pi\)
\(720\) 0 0
\(721\) 9.60447 0.357689
\(722\) 0 0
\(723\) 28.6071i 1.06391i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 8.05582i 0.298774i 0.988779 + 0.149387i \(0.0477300\pi\)
−0.988779 + 0.149387i \(0.952270\pi\)
\(728\) 0 0
\(729\) −27.6943 −1.02571
\(730\) 0 0
\(731\) −27.4588 −1.01560
\(732\) 0 0
\(733\) − 28.9320i − 1.06863i −0.845287 0.534313i \(-0.820570\pi\)
0.845287 0.534313i \(-0.179430\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 5.10902i − 0.188193i
\(738\) 0 0
\(739\) −36.0772 −1.32712 −0.663560 0.748123i \(-0.730955\pi\)
−0.663560 + 0.748123i \(0.730955\pi\)
\(740\) 0 0
\(741\) 38.4710 1.41327
\(742\) 0 0
\(743\) − 40.9681i − 1.50297i −0.659747 0.751487i \(-0.729337\pi\)
0.659747 0.751487i \(-0.270663\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.27909i 0.0833875i
\(748\) 0 0
\(749\) −2.17226 −0.0793727
\(750\) 0 0
\(751\) 23.2861 0.849722 0.424861 0.905259i \(-0.360323\pi\)
0.424861 + 0.905259i \(0.360323\pi\)
\(752\) 0 0
\(753\) − 11.6917i − 0.426067i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 27.3275i − 0.993234i −0.867970 0.496617i \(-0.834575\pi\)
0.867970 0.496617i \(-0.165425\pi\)
\(758\) 0 0
\(759\) −25.0336 −0.908661
\(760\) 0 0
\(761\) 44.5626 1.61539 0.807696 0.589599i \(-0.200714\pi\)
0.807696 + 0.589599i \(0.200714\pi\)
\(762\) 0 0
\(763\) − 1.79157i − 0.0648591i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 55.1600i 1.99171i
\(768\) 0 0
\(769\) −51.6110 −1.86114 −0.930570 0.366115i \(-0.880688\pi\)
−0.930570 + 0.366115i \(0.880688\pi\)
\(770\) 0 0
\(771\) 37.1155 1.33668
\(772\) 0 0
\(773\) − 19.6358i − 0.706252i −0.935576 0.353126i \(-0.885119\pi\)
0.935576 0.353126i \(-0.114881\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) − 8.96122i − 0.321482i
\(778\) 0 0
\(779\) −55.7374 −1.99700
\(780\) 0 0
\(781\) −29.7523 −1.06462
\(782\) 0 0
\(783\) 5.64064i 0.201580i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 37.3371i − 1.33092i −0.746432 0.665462i \(-0.768235\pi\)
0.746432 0.665462i \(-0.231765\pi\)
\(788\) 0 0
\(789\) 15.3271 0.545658
\(790\) 0 0
\(791\) −5.14831 −0.183053
\(792\) 0 0
\(793\) − 4.68904i − 0.166513i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.2159i 0.397286i 0.980072 + 0.198643i \(0.0636534\pi\)
−0.980072 + 0.198643i \(0.936347\pi\)
\(798\) 0 0
\(799\) 12.7645 0.451576
\(800\) 0 0
\(801\) −19.9852 −0.706141
\(802\) 0 0
\(803\) 32.5019i 1.14697i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 27.2717i 0.960008i
\(808\) 0 0
\(809\) −11.1749 −0.392888 −0.196444 0.980515i \(-0.562939\pi\)
−0.196444 + 0.980515i \(0.562939\pi\)
\(810\) 0 0
\(811\) 17.6406 0.619447 0.309723 0.950827i \(-0.399764\pi\)
0.309723 + 0.950827i \(0.399764\pi\)
\(812\) 0 0
\(813\) − 14.5264i − 0.509463i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 38.8517i 1.35925i
\(818\) 0 0
\(819\) −3.16965 −0.110757
\(820\) 0 0
\(821\) 24.2477 0.846251 0.423126 0.906071i \(-0.360933\pi\)
0.423126 + 0.906071i \(0.360933\pi\)
\(822\) 0 0
\(823\) 16.9777i 0.591807i 0.955218 + 0.295903i \(0.0956207\pi\)
−0.955218 + 0.295903i \(0.904379\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 5.58482i 0.194203i 0.995274 + 0.0971017i \(0.0309572\pi\)
−0.995274 + 0.0971017i \(0.969043\pi\)
\(828\) 0 0
\(829\) −18.6136 −0.646476 −0.323238 0.946318i \(-0.604771\pi\)
−0.323238 + 0.946318i \(0.604771\pi\)
\(830\) 0 0
\(831\) −17.0729 −0.592251
\(832\) 0 0
\(833\) − 31.7178i − 1.09896i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) − 15.9084i − 0.549876i
\(838\) 0 0
\(839\) 15.9293 0.549942 0.274971 0.961453i \(-0.411332\pi\)
0.274971 + 0.961453i \(0.411332\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 9.14520i 0.314977i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0.152616i 0.00524395i
\(848\) 0 0
\(849\) −1.44393 −0.0495555
\(850\) 0 0
\(851\) −56.5019 −1.93686
\(852\) 0 0
\(853\) − 27.0288i − 0.925447i −0.886503 0.462723i \(-0.846872\pi\)
0.886503 0.462723i \(-0.153128\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 30.2691i − 1.03397i −0.855994 0.516986i \(-0.827054\pi\)
0.855994 0.516986i \(-0.172946\pi\)
\(858\) 0 0
\(859\) 41.4487 1.41421 0.707106 0.707107i \(-0.250000\pi\)
0.707106 + 0.707107i \(0.250000\pi\)
\(860\) 0 0
\(861\) −7.16003 −0.244013
\(862\) 0 0
\(863\) 42.2494i 1.43819i 0.694913 + 0.719093i \(0.255443\pi\)
−0.694913 + 0.719093i \(0.744557\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) − 8.43001i − 0.286298i
\(868\) 0 0
\(869\) −30.1426 −1.02252
\(870\) 0 0
\(871\) 6.35936 0.215479
\(872\) 0 0
\(873\) 15.6519i 0.529738i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 37.8129i − 1.27685i −0.769684 0.638426i \(-0.779586\pi\)
0.769684 0.638426i \(-0.220414\pi\)
\(878\) 0 0
\(879\) −7.38642 −0.249138
\(880\) 0 0
\(881\) −5.35675 −0.180473 −0.0902367 0.995920i \(-0.528762\pi\)
−0.0902367 + 0.995920i \(0.528762\pi\)
\(882\) 0 0
\(883\) 8.53643i 0.287274i 0.989630 + 0.143637i \(0.0458797\pi\)
−0.989630 + 0.143637i \(0.954120\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 22.7597i 0.764196i 0.924122 + 0.382098i \(0.124798\pi\)
−0.924122 + 0.382098i \(0.875202\pi\)
\(888\) 0 0
\(889\) −11.4684 −0.384637
\(890\) 0 0
\(891\) −13.7732 −0.461420
\(892\) 0 0
\(893\) − 18.0606i − 0.604376i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) − 31.1600i − 1.04040i
\(898\) 0 0
\(899\) −2.82032 −0.0940630
\(900\) 0 0
\(901\) −13.8639 −0.461874
\(902\) 0 0
\(903\) 4.99089i 0.166086i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) − 3.94418i − 0.130964i −0.997854 0.0654822i \(-0.979141\pi\)
0.997854 0.0654822i \(-0.0208586\pi\)
\(908\) 0 0
\(909\) 21.6354 0.717602
\(910\) 0 0
\(911\) −40.6546 −1.34695 −0.673473 0.739212i \(-0.735198\pi\)
−0.673473 + 0.739212i \(0.735198\pi\)
\(912\) 0 0
\(913\) 6.51678i 0.215674i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.58002i 0.118223i
\(918\) 0 0
\(919\) −27.3471 −0.902099 −0.451049 0.892499i \(-0.648950\pi\)
−0.451049 + 0.892499i \(0.648950\pi\)
\(920\) 0 0
\(921\) 8.52200 0.280810
\(922\) 0 0
\(923\) − 37.0336i − 1.21897i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 17.3733i − 0.570613i
\(928\) 0 0
\(929\) −20.9368 −0.686913 −0.343456 0.939169i \(-0.611598\pi\)
−0.343456 + 0.939169i \(0.611598\pi\)
\(930\) 0 0
\(931\) −44.8778 −1.47081
\(932\) 0 0
\(933\) 33.3716i 1.09254i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 36.4051i − 1.18930i −0.803983 0.594652i \(-0.797290\pi\)
0.803983 0.594652i \(-0.202710\pi\)
\(938\) 0 0
\(939\) 32.6794 1.06645
\(940\) 0 0
\(941\) 28.0968 0.915929 0.457965 0.888970i \(-0.348579\pi\)
0.457965 + 0.888970i \(0.348579\pi\)
\(942\) 0 0
\(943\) 45.1452i 1.47013i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 10.8809i 0.353583i 0.984248 + 0.176792i \(0.0565719\pi\)
−0.984248 + 0.176792i \(0.943428\pi\)
\(948\) 0 0
\(949\) −40.4562 −1.31326
\(950\) 0 0
\(951\) 1.92976 0.0625767
\(952\) 0 0
\(953\) 38.8103i 1.25719i 0.777733 + 0.628594i \(0.216369\pi\)
−0.777733 + 0.628594i \(0.783631\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 4.53162i 0.146486i
\(958\) 0 0
\(959\) −2.50717 −0.0809606
\(960\) 0 0
\(961\) −23.0458 −0.743413
\(962\) 0 0
\(963\) 3.92935i 0.126621i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 47.1862i − 1.51741i −0.651437 0.758703i \(-0.725834\pi\)
0.651437 0.758703i \(-0.274166\pi\)
\(968\) 0 0
\(969\) −44.4465 −1.42783
\(970\) 0 0
\(971\) 40.0772 1.28614 0.643069 0.765809i \(-0.277661\pi\)
0.643069 + 0.765809i \(0.277661\pi\)
\(972\) 0 0
\(973\) − 3.65548i − 0.117189i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 2.29873i − 0.0735430i −0.999324 0.0367715i \(-0.988293\pi\)
0.999324 0.0367715i \(-0.0117074\pi\)
\(978\) 0 0
\(979\) −57.1452 −1.82637
\(980\) 0 0
\(981\) −3.24072 −0.103468
\(982\) 0 0
\(983\) − 8.89578i − 0.283731i −0.989886 0.141866i \(-0.954690\pi\)
0.989886 0.141866i \(-0.0453101\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) − 2.32007i − 0.0738486i
\(988\) 0 0
\(989\) 31.4684 1.00064
\(990\) 0 0
\(991\) 37.5652 1.19330 0.596649 0.802503i \(-0.296499\pi\)
0.596649 + 0.802503i \(0.296499\pi\)
\(992\) 0 0
\(993\) 46.2542i 1.46783i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 25.8081i 0.817351i 0.912680 + 0.408675i \(0.134009\pi\)
−0.912680 + 0.408675i \(0.865991\pi\)
\(998\) 0 0
\(999\) −57.6929 −1.82532
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 2900.2.c.f.349.4 6
5.2 odd 4 580.2.a.c.1.2 3
5.3 odd 4 2900.2.a.g.1.2 3
5.4 even 2 inner 2900.2.c.f.349.3 6
15.2 even 4 5220.2.a.x.1.2 3
20.7 even 4 2320.2.a.m.1.2 3
40.27 even 4 9280.2.a.bw.1.2 3
40.37 odd 4 9280.2.a.bk.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.2.a.c.1.2 3 5.2 odd 4
2320.2.a.m.1.2 3 20.7 even 4
2900.2.a.g.1.2 3 5.3 odd 4
2900.2.c.f.349.3 6 5.4 even 2 inner
2900.2.c.f.349.4 6 1.1 even 1 trivial
5220.2.a.x.1.2 3 15.2 even 4
9280.2.a.bk.1.2 3 40.37 odd 4
9280.2.a.bw.1.2 3 40.27 even 4