Properties

Label 1620.3.o.g.1241.4
Level $1620$
Weight $3$
Character 1620.1241
Analytic conductor $44.142$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1620,3,Mod(701,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1620.701");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1620.o (of order \(6\), degree \(2\), 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: \(44.1418028264\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1241.4
Character \(\chi\) \(=\) 1620.1241
Dual form 1620.3.o.g.701.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.93649 + 1.11803i) q^{5} +(3.57283 - 6.18832i) q^{7} +O(q^{10})\) \(q+(-1.93649 + 1.11803i) q^{5} +(3.57283 - 6.18832i) q^{7} +(2.20431 + 1.27266i) q^{11} +(-5.57892 - 9.66297i) q^{13} +2.05814i q^{17} -19.3781 q^{19} +(10.4254 - 6.01908i) q^{23} +(2.50000 - 4.33013i) q^{25} +(19.3077 + 11.1473i) q^{29} +(-7.08342 - 12.2689i) q^{31} +15.9782i q^{35} -46.3319 q^{37} +(-15.0752 + 8.70366i) q^{41} +(-13.5098 + 23.3997i) q^{43} +(-42.2514 - 24.3938i) q^{47} +(-1.03020 - 1.78437i) q^{49} -9.84048i q^{53} -5.69151 q^{55} +(76.1103 - 43.9423i) q^{59} +(-29.9240 + 51.8300i) q^{61} +(21.6071 + 12.4748i) q^{65} +(3.85720 + 6.68087i) q^{67} +79.5282i q^{71} -6.01802 q^{73} +(15.7513 - 9.09400i) q^{77} +(8.46386 - 14.6598i) q^{79} +(-127.148 - 73.4091i) q^{83} +(-2.30107 - 3.98557i) q^{85} +100.304i q^{89} -79.7301 q^{91} +(37.5255 - 21.6653i) q^{95} +(-36.3075 + 62.8865i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{7} + 40 q^{13} + 112 q^{19} + 80 q^{25} + 64 q^{31} - 176 q^{37} - 128 q^{43} - 216 q^{49} - 8 q^{61} + 40 q^{67} + 112 q^{73} + 136 q^{79} - 784 q^{91} - 128 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0
\(4\) 0 0
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) 0 0
\(7\) 3.57283 6.18832i 0.510404 0.884046i −0.489523 0.871990i \(-0.662829\pi\)
0.999927 0.0120555i \(-0.00383748\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.20431 + 1.27266i 0.200392 + 0.115696i 0.596838 0.802361i \(-0.296423\pi\)
−0.396446 + 0.918058i \(0.629757\pi\)
\(12\) 0 0
\(13\) −5.57892 9.66297i −0.429147 0.743305i 0.567650 0.823270i \(-0.307853\pi\)
−0.996798 + 0.0799646i \(0.974519\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.05814i 0.121067i 0.998166 + 0.0605335i \(0.0192802\pi\)
−0.998166 + 0.0605335i \(0.980720\pi\)
\(18\) 0 0
\(19\) −19.3781 −1.01990 −0.509949 0.860204i \(-0.670336\pi\)
−0.509949 + 0.860204i \(0.670336\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 10.4254 6.01908i 0.453276 0.261699i −0.255937 0.966694i \(-0.582384\pi\)
0.709213 + 0.704994i \(0.249051\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 19.3077 + 11.1473i 0.665782 + 0.384390i 0.794477 0.607295i \(-0.207745\pi\)
−0.128694 + 0.991684i \(0.541079\pi\)
\(30\) 0 0
\(31\) −7.08342 12.2689i −0.228498 0.395769i 0.728865 0.684657i \(-0.240048\pi\)
−0.957363 + 0.288888i \(0.906715\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 15.9782i 0.456519i
\(36\) 0 0
\(37\) −46.3319 −1.25221 −0.626107 0.779737i \(-0.715353\pi\)
−0.626107 + 0.779737i \(0.715353\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −15.0752 + 8.70366i −0.367687 + 0.212284i −0.672448 0.740145i \(-0.734757\pi\)
0.304760 + 0.952429i \(0.401424\pi\)
\(42\) 0 0
\(43\) −13.5098 + 23.3997i −0.314183 + 0.544180i −0.979263 0.202591i \(-0.935064\pi\)
0.665081 + 0.746771i \(0.268397\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −42.2514 24.3938i −0.898965 0.519018i −0.0221009 0.999756i \(-0.507036\pi\)
−0.876864 + 0.480738i \(0.840369\pi\)
\(48\) 0 0
\(49\) −1.03020 1.78437i −0.0210246 0.0364157i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.84048i 0.185670i −0.995682 0.0928348i \(-0.970407\pi\)
0.995682 0.0928348i \(-0.0295928\pi\)
\(54\) 0 0
\(55\) −5.69151 −0.103482
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 76.1103 43.9423i 1.29001 0.744785i 0.311350 0.950295i \(-0.399219\pi\)
0.978655 + 0.205510i \(0.0658854\pi\)
\(60\) 0 0
\(61\) −29.9240 + 51.8300i −0.490558 + 0.849672i −0.999941 0.0108684i \(-0.996540\pi\)
0.509383 + 0.860540i \(0.329874\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 21.6071 + 12.4748i 0.332416 + 0.191921i
\(66\) 0 0
\(67\) 3.85720 + 6.68087i 0.0575701 + 0.0997144i 0.893374 0.449314i \(-0.148331\pi\)
−0.835804 + 0.549028i \(0.814998\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 79.5282i 1.12012i 0.828453 + 0.560058i \(0.189221\pi\)
−0.828453 + 0.560058i \(0.810779\pi\)
\(72\) 0 0
\(73\) −6.01802 −0.0824387 −0.0412193 0.999150i \(-0.513124\pi\)
−0.0412193 + 0.999150i \(0.513124\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 15.7513 9.09400i 0.204562 0.118104i
\(78\) 0 0
\(79\) 8.46386 14.6598i 0.107137 0.185568i −0.807472 0.589906i \(-0.799165\pi\)
0.914609 + 0.404338i \(0.132498\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −127.148 73.4091i −1.53191 0.884447i −0.999274 0.0381001i \(-0.987869\pi\)
−0.532633 0.846347i \(-0.678797\pi\)
\(84\) 0 0
\(85\) −2.30107 3.98557i −0.0270714 0.0468890i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 100.304i 1.12701i 0.826113 + 0.563504i \(0.190547\pi\)
−0.826113 + 0.563504i \(0.809453\pi\)
\(90\) 0 0
\(91\) −79.7301 −0.876154
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 37.5255 21.6653i 0.395005 0.228056i
\(96\) 0 0
\(97\) −36.3075 + 62.8865i −0.374304 + 0.648314i −0.990223 0.139496i \(-0.955452\pi\)
0.615918 + 0.787810i \(0.288785\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −128.595 74.2442i −1.27321 0.735091i −0.297623 0.954683i \(-0.596194\pi\)
−0.975592 + 0.219593i \(0.929527\pi\)
\(102\) 0 0
\(103\) −70.9917 122.961i −0.689240 1.19380i −0.972084 0.234633i \(-0.924611\pi\)
0.282844 0.959166i \(-0.408722\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.62138i 0.0338447i −0.999857 0.0169224i \(-0.994613\pi\)
0.999857 0.0169224i \(-0.00538681\pi\)
\(108\) 0 0
\(109\) −193.000 −1.77064 −0.885320 0.464983i \(-0.846060\pi\)
−0.885320 + 0.464983i \(0.846060\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 75.2851 43.4659i 0.666240 0.384654i −0.128411 0.991721i \(-0.540988\pi\)
0.794650 + 0.607067i \(0.207654\pi\)
\(114\) 0 0
\(115\) −13.4591 + 23.3118i −0.117035 + 0.202711i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 12.7364 + 7.35337i 0.107029 + 0.0617931i
\(120\) 0 0
\(121\) −57.2607 99.1784i −0.473229 0.819656i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.1803i 0.0894427i
\(126\) 0 0
\(127\) −83.5634 −0.657979 −0.328990 0.944334i \(-0.606708\pi\)
−0.328990 + 0.944334i \(0.606708\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −19.2345 + 11.1050i −0.146828 + 0.0847712i −0.571614 0.820522i \(-0.693683\pi\)
0.424786 + 0.905294i \(0.360349\pi\)
\(132\) 0 0
\(133\) −69.2345 + 119.918i −0.520560 + 0.901637i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.28159 5.35873i −0.0677489 0.0391148i 0.465743 0.884920i \(-0.345787\pi\)
−0.533492 + 0.845805i \(0.679120\pi\)
\(138\) 0 0
\(139\) 21.2704 + 36.8414i 0.153025 + 0.265046i 0.932338 0.361588i \(-0.117765\pi\)
−0.779313 + 0.626634i \(0.784432\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 28.4003i 0.198603i
\(144\) 0 0
\(145\) −49.8522 −0.343808
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −84.7559 + 48.9338i −0.568831 + 0.328415i −0.756682 0.653783i \(-0.773181\pi\)
0.187851 + 0.982198i \(0.439848\pi\)
\(150\) 0 0
\(151\) 2.06713 3.58037i 0.0136896 0.0237111i −0.859099 0.511809i \(-0.828976\pi\)
0.872789 + 0.488098i \(0.162309\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 27.4340 + 15.8390i 0.176993 + 0.102187i
\(156\) 0 0
\(157\) −115.393 199.866i −0.734986 1.27303i −0.954730 0.297475i \(-0.903855\pi\)
0.219744 0.975558i \(-0.429478\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 86.0205i 0.534289i
\(162\) 0 0
\(163\) −76.8009 −0.471171 −0.235586 0.971854i \(-0.575701\pi\)
−0.235586 + 0.971854i \(0.575701\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 83.0831 47.9680i 0.497503 0.287234i −0.230179 0.973148i \(-0.573931\pi\)
0.727682 + 0.685915i \(0.240598\pi\)
\(168\) 0 0
\(169\) 22.2514 38.5405i 0.131665 0.228050i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 88.2873 + 50.9727i 0.510331 + 0.294640i 0.732970 0.680261i \(-0.238134\pi\)
−0.222639 + 0.974901i \(0.571467\pi\)
\(174\) 0 0
\(175\) −17.8641 30.9416i −0.102081 0.176809i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 174.549i 0.975131i 0.873086 + 0.487566i \(0.162115\pi\)
−0.873086 + 0.487566i \(0.837885\pi\)
\(180\) 0 0
\(181\) −299.220 −1.65315 −0.826575 0.562827i \(-0.809714\pi\)
−0.826575 + 0.562827i \(0.809714\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 89.7214 51.8006i 0.484980 0.280003i
\(186\) 0 0
\(187\) −2.61931 + 4.53678i −0.0140070 + 0.0242609i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −123.233 71.1486i −0.645199 0.372506i 0.141415 0.989950i \(-0.454835\pi\)
−0.786615 + 0.617444i \(0.788168\pi\)
\(192\) 0 0
\(193\) −111.425 192.995i −0.577334 0.999972i −0.995784 0.0917319i \(-0.970760\pi\)
0.418450 0.908240i \(-0.362574\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 270.569i 1.37345i 0.726919 + 0.686723i \(0.240952\pi\)
−0.726919 + 0.686723i \(0.759048\pi\)
\(198\) 0 0
\(199\) −140.476 −0.705912 −0.352956 0.935640i \(-0.614823\pi\)
−0.352956 + 0.935640i \(0.614823\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 137.966 79.6548i 0.679636 0.392388i
\(204\) 0 0
\(205\) 19.4620 33.7091i 0.0949365 0.164435i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −42.7154 24.6617i −0.204380 0.117999i
\(210\) 0 0
\(211\) 103.996 + 180.127i 0.492874 + 0.853682i 0.999966 0.00820932i \(-0.00261314\pi\)
−0.507093 + 0.861892i \(0.669280\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 60.4179i 0.281013i
\(216\) 0 0
\(217\) −101.231 −0.466504
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 19.8877 11.4822i 0.0899897 0.0519556i
\(222\) 0 0
\(223\) −110.548 + 191.476i −0.495733 + 0.858635i −0.999988 0.00491996i \(-0.998434\pi\)
0.504255 + 0.863555i \(0.331767\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −151.949 87.7280i −0.669380 0.386467i 0.126461 0.991972i \(-0.459638\pi\)
−0.795842 + 0.605505i \(0.792971\pi\)
\(228\) 0 0
\(229\) −107.009 185.344i −0.467287 0.809364i 0.532015 0.846735i \(-0.321435\pi\)
−0.999301 + 0.0373707i \(0.988102\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.77506i 0.0419530i −0.999780 0.0209765i \(-0.993322\pi\)
0.999780 0.0209765i \(-0.00667752\pi\)
\(234\) 0 0
\(235\) 109.093 0.464224
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 248.842 143.669i 1.04118 0.601125i 0.121012 0.992651i \(-0.461386\pi\)
0.920167 + 0.391526i \(0.128053\pi\)
\(240\) 0 0
\(241\) 163.672 283.488i 0.679137 1.17630i −0.296105 0.955155i \(-0.595688\pi\)
0.975241 0.221143i \(-0.0709789\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.98997 + 2.30361i 0.0162856 + 0.00940248i
\(246\) 0 0
\(247\) 108.109 + 187.250i 0.437687 + 0.758096i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 290.903i 1.15897i 0.814981 + 0.579487i \(0.196747\pi\)
−0.814981 + 0.579487i \(0.803253\pi\)
\(252\) 0 0
\(253\) 30.6410 0.121111
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −276.077 + 159.393i −1.07423 + 0.620207i −0.929334 0.369240i \(-0.879618\pi\)
−0.144896 + 0.989447i \(0.546285\pi\)
\(258\) 0 0
\(259\) −165.536 + 286.717i −0.639135 + 1.10701i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 145.630 + 84.0798i 0.553728 + 0.319695i 0.750624 0.660729i \(-0.229753\pi\)
−0.196896 + 0.980424i \(0.563086\pi\)
\(264\) 0 0
\(265\) 11.0020 + 19.0560i 0.0415170 + 0.0719095i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 129.572i 0.481679i −0.970565 0.240839i \(-0.922577\pi\)
0.970565 0.240839i \(-0.0774227\pi\)
\(270\) 0 0
\(271\) −15.6638 −0.0578000 −0.0289000 0.999582i \(-0.509200\pi\)
−0.0289000 + 0.999582i \(0.509200\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.0216 6.36331i 0.0400784 0.0231393i
\(276\) 0 0
\(277\) 46.1348 79.9078i 0.166552 0.288476i −0.770654 0.637254i \(-0.780070\pi\)
0.937205 + 0.348778i \(0.113403\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −72.8094 42.0365i −0.259108 0.149596i 0.364819 0.931078i \(-0.381131\pi\)
−0.623928 + 0.781482i \(0.714464\pi\)
\(282\) 0 0
\(283\) 131.855 + 228.380i 0.465920 + 0.806996i 0.999243 0.0389154i \(-0.0123903\pi\)
−0.533323 + 0.845912i \(0.679057\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 124.387i 0.433403i
\(288\) 0 0
\(289\) 284.764 0.985343
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 475.043 274.266i 1.62131 0.936061i 0.634735 0.772730i \(-0.281109\pi\)
0.986571 0.163331i \(-0.0522239\pi\)
\(294\) 0 0
\(295\) −98.2580 + 170.188i −0.333078 + 0.576908i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −116.324 67.1599i −0.389045 0.224615i
\(300\) 0 0
\(301\) 96.5367 + 167.207i 0.320720 + 0.555503i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 133.824i 0.438769i
\(306\) 0 0
\(307\) −192.466 −0.626926 −0.313463 0.949600i \(-0.601489\pi\)
−0.313463 + 0.949600i \(0.601489\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −392.392 + 226.548i −1.26171 + 0.728449i −0.973405 0.229090i \(-0.926425\pi\)
−0.288305 + 0.957539i \(0.593092\pi\)
\(312\) 0 0
\(313\) 32.8644 56.9228i 0.104998 0.181862i −0.808739 0.588167i \(-0.799850\pi\)
0.913737 + 0.406305i \(0.133183\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.16081 + 2.40225i 0.0131256 + 0.00757806i 0.506548 0.862212i \(-0.330921\pi\)
−0.493423 + 0.869790i \(0.664254\pi\)
\(318\) 0 0
\(319\) 28.3735 + 49.1443i 0.0889450 + 0.154057i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 39.8827i 0.123476i
\(324\) 0 0
\(325\) −55.7892 −0.171659
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −301.914 + 174.310i −0.917671 + 0.529818i
\(330\) 0 0
\(331\) −72.6006 + 125.748i −0.219337 + 0.379903i −0.954605 0.297873i \(-0.903723\pi\)
0.735268 + 0.677776i \(0.237056\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −14.9389 8.62496i −0.0445936 0.0257462i
\(336\) 0 0
\(337\) 72.8538 + 126.187i 0.216183 + 0.374441i 0.953638 0.300956i \(-0.0973057\pi\)
−0.737455 + 0.675397i \(0.763972\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 36.0592i 0.105745i
\(342\) 0 0
\(343\) 335.414 0.977884
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −161.823 + 93.4285i −0.466349 + 0.269246i −0.714710 0.699421i \(-0.753441\pi\)
0.248361 + 0.968667i \(0.420108\pi\)
\(348\) 0 0
\(349\) 90.7738 157.225i 0.260097 0.450501i −0.706171 0.708042i \(-0.749579\pi\)
0.966267 + 0.257541i \(0.0829122\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 584.949 + 337.721i 1.65708 + 0.956715i 0.974052 + 0.226322i \(0.0726703\pi\)
0.683027 + 0.730393i \(0.260663\pi\)
\(354\) 0 0
\(355\) −88.9153 154.006i −0.250466 0.433819i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 361.492i 1.00694i −0.864012 0.503471i \(-0.832056\pi\)
0.864012 0.503471i \(-0.167944\pi\)
\(360\) 0 0
\(361\) 14.5096 0.0401929
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11.6539 6.72836i 0.0319284 0.0184339i
\(366\) 0 0
\(367\) 47.6816 82.5869i 0.129923 0.225033i −0.793724 0.608278i \(-0.791860\pi\)
0.923646 + 0.383246i \(0.125194\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −60.8961 35.1584i −0.164140 0.0947665i
\(372\) 0 0
\(373\) −296.189 513.014i −0.794071 1.37537i −0.923427 0.383774i \(-0.874624\pi\)
0.129356 0.991598i \(-0.458709\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 248.759i 0.659839i
\(378\) 0 0
\(379\) 289.491 0.763830 0.381915 0.924198i \(-0.375265\pi\)
0.381915 + 0.924198i \(0.375265\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 543.273 313.659i 1.41847 0.818953i 0.422304 0.906454i \(-0.361221\pi\)
0.996164 + 0.0875011i \(0.0278881\pi\)
\(384\) 0 0
\(385\) −20.3348 + 35.2209i −0.0528177 + 0.0914829i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −345.046 199.212i −0.887008 0.512114i −0.0140453 0.999901i \(-0.504471\pi\)
−0.872963 + 0.487787i \(0.837804\pi\)
\(390\) 0 0
\(391\) 12.3881 + 21.4568i 0.0316831 + 0.0548767i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 37.8515i 0.0958267i
\(396\) 0 0
\(397\) 101.894 0.256660 0.128330 0.991731i \(-0.459038\pi\)
0.128330 + 0.991731i \(0.459038\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −445.055 + 256.953i −1.10986 + 0.640779i −0.938794 0.344480i \(-0.888055\pi\)
−0.171069 + 0.985259i \(0.554722\pi\)
\(402\) 0 0
\(403\) −79.0357 + 136.894i −0.196118 + 0.339687i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −102.130 58.9648i −0.250934 0.144877i
\(408\) 0 0
\(409\) −87.3358 151.270i −0.213535 0.369854i 0.739283 0.673394i \(-0.235164\pi\)
−0.952818 + 0.303541i \(0.901831\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 627.993i 1.52056i
\(414\) 0 0
\(415\) 328.295 0.791073
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −404.169 + 233.347i −0.964604 + 0.556914i −0.897587 0.440837i \(-0.854682\pi\)
−0.0670171 + 0.997752i \(0.521348\pi\)
\(420\) 0 0
\(421\) 335.886 581.771i 0.797828 1.38188i −0.123200 0.992382i \(-0.539316\pi\)
0.921028 0.389497i \(-0.127351\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.91200 + 5.14534i 0.0209694 + 0.0121067i
\(426\) 0 0
\(427\) 213.827 + 370.359i 0.500766 + 0.867352i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 690.758i 1.60269i 0.598204 + 0.801344i \(0.295881\pi\)
−0.598204 + 0.801344i \(0.704119\pi\)
\(432\) 0 0
\(433\) 418.521 0.966562 0.483281 0.875465i \(-0.339445\pi\)
0.483281 + 0.875465i \(0.339445\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −202.023 + 116.638i −0.462296 + 0.266906i
\(438\) 0 0
\(439\) 180.726 313.027i 0.411677 0.713045i −0.583397 0.812187i \(-0.698277\pi\)
0.995073 + 0.0991427i \(0.0316100\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 579.959 + 334.839i 1.30916 + 0.755845i 0.981956 0.189108i \(-0.0605595\pi\)
0.327206 + 0.944953i \(0.393893\pi\)
\(444\) 0 0
\(445\) −112.143 194.237i −0.252007 0.436489i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 236.187i 0.526028i −0.964792 0.263014i \(-0.915283\pi\)
0.964792 0.263014i \(-0.0847166\pi\)
\(450\) 0 0
\(451\) −44.3072 −0.0982422
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 154.397 89.1409i 0.339333 0.195914i
\(456\) 0 0
\(457\) 346.900 600.848i 0.759080 1.31477i −0.184240 0.982881i \(-0.558982\pi\)
0.943320 0.331884i \(-0.107684\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 290.417 + 167.672i 0.629971 + 0.363714i 0.780741 0.624855i \(-0.214842\pi\)
−0.150770 + 0.988569i \(0.548175\pi\)
\(462\) 0 0
\(463\) 180.088 + 311.922i 0.388960 + 0.673698i 0.992310 0.123778i \(-0.0395012\pi\)
−0.603350 + 0.797476i \(0.706168\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 679.050i 1.45407i −0.686602 0.727034i \(-0.740898\pi\)
0.686602 0.727034i \(-0.259102\pi\)
\(468\) 0 0
\(469\) 55.1245 0.117536
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −59.5599 + 34.3869i −0.125919 + 0.0726996i
\(474\) 0 0
\(475\) −48.4452 + 83.9095i −0.101990 + 0.176652i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −188.160 108.634i −0.392818 0.226794i 0.290562 0.956856i \(-0.406158\pi\)
−0.683381 + 0.730062i \(0.739491\pi\)
\(480\) 0 0
\(481\) 258.482 + 447.704i 0.537384 + 0.930777i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 162.372i 0.334788i
\(486\) 0 0
\(487\) 737.594 1.51457 0.757283 0.653086i \(-0.226526\pi\)
0.757283 + 0.653086i \(0.226526\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −657.536 + 379.629i −1.33918 + 0.773175i −0.986685 0.162640i \(-0.947999\pi\)
−0.352492 + 0.935815i \(0.614666\pi\)
\(492\) 0 0
\(493\) −22.9427 + 39.7379i −0.0465369 + 0.0806042i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 492.146 + 284.141i 0.990234 + 0.571712i
\(498\) 0 0
\(499\) 333.289 + 577.274i 0.667915 + 1.15686i 0.978486 + 0.206312i \(0.0661462\pi\)
−0.310572 + 0.950550i \(0.600520\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 180.800i 0.359444i 0.983717 + 0.179722i \(0.0575199\pi\)
−0.983717 + 0.179722i \(0.942480\pi\)
\(504\) 0 0
\(505\) 332.030 0.657485
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −318.561 + 183.921i −0.625856 + 0.361338i −0.779146 0.626843i \(-0.784347\pi\)
0.153289 + 0.988181i \(0.451013\pi\)
\(510\) 0 0
\(511\) −21.5014 + 37.2415i −0.0420770 + 0.0728796i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 274.950 + 158.742i 0.533883 + 0.308238i
\(516\) 0 0
\(517\) −62.0902 107.543i −0.120097 0.208014i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 428.171i 0.821825i −0.911675 0.410913i \(-0.865210\pi\)
0.911675 0.410913i \(-0.134790\pi\)
\(522\) 0 0
\(523\) 742.878 1.42042 0.710208 0.703992i \(-0.248601\pi\)
0.710208 + 0.703992i \(0.248601\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 25.2510 14.5787i 0.0479146 0.0276635i
\(528\) 0 0
\(529\) −192.041 + 332.625i −0.363027 + 0.628782i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 168.206 + 97.1140i 0.315584 + 0.182203i
\(534\) 0 0
\(535\) 4.04883 + 7.01278i 0.00756791 + 0.0131080i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5.24441i 0.00972989i
\(540\) 0 0
\(541\) −431.532 −0.797656 −0.398828 0.917026i \(-0.630583\pi\)
−0.398828 + 0.917026i \(0.630583\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 373.742 215.780i 0.685766 0.395927i
\(546\) 0 0
\(547\) −72.9216 + 126.304i −0.133312 + 0.230903i −0.924951 0.380086i \(-0.875895\pi\)
0.791639 + 0.610989i \(0.209228\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −374.146 216.013i −0.679030 0.392038i
\(552\) 0 0
\(553\) −60.4799 104.754i −0.109367 0.189429i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 680.396i 1.22154i 0.791809 + 0.610769i \(0.209140\pi\)
−0.791809 + 0.610769i \(0.790860\pi\)
\(558\) 0 0
\(559\) 301.481 0.539323
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 797.888 460.661i 1.41721 0.818226i 0.421155 0.906988i \(-0.361625\pi\)
0.996053 + 0.0887629i \(0.0282914\pi\)
\(564\) 0 0
\(565\) −97.1926 + 168.343i −0.172022 + 0.297951i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 685.403 + 395.717i 1.20457 + 0.695461i 0.961569 0.274564i \(-0.0885335\pi\)
0.243005 + 0.970025i \(0.421867\pi\)
\(570\) 0 0
\(571\) 529.700 + 917.468i 0.927672 + 1.60677i 0.787207 + 0.616688i \(0.211526\pi\)
0.140464 + 0.990086i \(0.455141\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 60.1908i 0.104680i
\(576\) 0 0
\(577\) −526.293 −0.912119 −0.456060 0.889949i \(-0.650740\pi\)
−0.456060 + 0.889949i \(0.650740\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −908.558 + 524.556i −1.56378 + 0.902850i
\(582\) 0 0
\(583\) 12.5236 21.6915i 0.0214813 0.0372067i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −808.682 466.893i −1.37765 0.795388i −0.385776 0.922592i \(-0.626066\pi\)
−0.991877 + 0.127204i \(0.959400\pi\)
\(588\) 0 0
\(589\) 137.263 + 237.747i 0.233044 + 0.403645i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 686.623i 1.15788i −0.815370 0.578940i \(-0.803467\pi\)
0.815370 0.578940i \(-0.196533\pi\)
\(594\) 0 0
\(595\) −32.8853 −0.0552694
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 217.781 125.736i 0.363574 0.209910i −0.307073 0.951686i \(-0.599350\pi\)
0.670647 + 0.741776i \(0.266016\pi\)
\(600\) 0 0
\(601\) 304.733 527.812i 0.507043 0.878223i −0.492924 0.870072i \(-0.664072\pi\)
0.999967 0.00815116i \(-0.00259462\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 221.770 + 128.039i 0.366561 + 0.211634i
\(606\) 0 0
\(607\) 414.080 + 717.208i 0.682175 + 1.18156i 0.974316 + 0.225187i \(0.0722993\pi\)
−0.292140 + 0.956375i \(0.594367\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 544.365i 0.890941i
\(612\) 0 0
\(613\) 534.809 0.872445 0.436223 0.899839i \(-0.356316\pi\)
0.436223 + 0.899839i \(0.356316\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −384.859 + 222.199i −0.623759 + 0.360127i −0.778331 0.627854i \(-0.783933\pi\)
0.154572 + 0.987982i \(0.450600\pi\)
\(618\) 0 0
\(619\) 149.322 258.633i 0.241231 0.417824i −0.719834 0.694146i \(-0.755782\pi\)
0.961065 + 0.276322i \(0.0891156\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 620.712 + 358.368i 0.996327 + 0.575230i
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 95.3574i 0.151602i
\(630\) 0 0
\(631\) 1154.93 1.83031 0.915155 0.403103i \(-0.132068\pi\)
0.915155 + 0.403103i \(0.132068\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 161.820 93.4267i 0.254834 0.147129i
\(636\) 0 0
\(637\) −11.4949 + 19.9097i −0.0180453 + 0.0312554i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −588.759 339.920i −0.918502 0.530297i −0.0353448 0.999375i \(-0.511253\pi\)
−0.883157 + 0.469078i \(0.844586\pi\)
\(642\) 0 0
\(643\) −217.288 376.354i −0.337929 0.585310i 0.646114 0.763241i \(-0.276393\pi\)
−0.984043 + 0.177931i \(0.943060\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 222.972i 0.344625i 0.985042 + 0.172312i \(0.0551239\pi\)
−0.985042 + 0.172312i \(0.944876\pi\)
\(648\) 0 0
\(649\) 223.695 0.344676
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 453.763 261.980i 0.694889 0.401194i −0.110552 0.993870i \(-0.535262\pi\)
0.805441 + 0.592676i \(0.201929\pi\)
\(654\) 0 0
\(655\) 24.8316 43.0096i 0.0379109 0.0656635i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 249.789 + 144.216i 0.379043 + 0.218841i 0.677402 0.735613i \(-0.263106\pi\)
−0.298359 + 0.954454i \(0.596439\pi\)
\(660\) 0 0
\(661\) −24.7991 42.9533i −0.0375176 0.0649823i 0.846657 0.532139i \(-0.178612\pi\)
−0.884174 + 0.467157i \(0.845278\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 309.626i 0.465603i
\(666\) 0 0
\(667\) 268.386 0.402378
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −131.924 + 76.1664i −0.196608 + 0.113512i
\(672\) 0 0
\(673\) −306.034 + 530.066i −0.454731 + 0.787617i −0.998673 0.0515058i \(-0.983598\pi\)
0.543942 + 0.839123i \(0.316931\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 931.146 + 537.597i 1.37540 + 0.794087i 0.991602 0.129330i \(-0.0412825\pi\)
0.383798 + 0.923417i \(0.374616\pi\)
\(678\) 0 0
\(679\) 259.441 + 449.365i 0.382093 + 0.661804i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 718.621i 1.05215i −0.850437 0.526077i \(-0.823663\pi\)
0.850437 0.526077i \(-0.176337\pi\)
\(684\) 0 0
\(685\) 23.9650 0.0349854
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −95.0883 + 54.8992i −0.138009 + 0.0796796i
\(690\) 0 0
\(691\) 420.368 728.099i 0.608347 1.05369i −0.383165 0.923680i \(-0.625166\pi\)
0.991513 0.130009i \(-0.0415006\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −82.3800 47.5621i −0.118532 0.0684347i
\(696\) 0 0
\(697\) −17.9133 31.0268i −0.0257006 0.0445148i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 614.419i 0.876490i −0.898856 0.438245i \(-0.855600\pi\)
0.898856 0.438245i \(-0.144400\pi\)
\(702\) 0 0
\(703\) 897.823 1.27713
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −918.893 + 530.523i −1.29971 + 0.750387i
\(708\) 0 0
\(709\) 434.681 752.890i 0.613091 1.06190i −0.377625 0.925958i \(-0.623259\pi\)
0.990716 0.135946i \(-0.0434074\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −147.694 85.2714i −0.207145 0.119595i
\(714\) 0 0
\(715\) 31.7525 + 54.9969i 0.0444091 + 0.0769188i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1307.10i 1.81794i 0.416859 + 0.908971i \(0.363131\pi\)
−0.416859 + 0.908971i \(0.636869\pi\)
\(720\) 0 0
\(721\) −1014.57 −1.40716
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 96.5384 55.7365i 0.133156 0.0768779i
\(726\) 0 0
\(727\) 112.223 194.376i 0.154365 0.267367i −0.778463 0.627691i \(-0.784000\pi\)
0.932827 + 0.360323i \(0.117334\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −48.1599 27.8051i −0.0658822 0.0380371i
\(732\) 0 0
\(733\) −571.310 989.538i −0.779413 1.34998i −0.932280 0.361737i \(-0.882184\pi\)
0.152867 0.988247i \(-0.451149\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19.6356i 0.0266427i
\(738\) 0 0
\(739\) −450.991 −0.610272 −0.305136 0.952309i \(-0.598702\pi\)
−0.305136 + 0.952309i \(0.598702\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1074.55 620.394i 1.44624 0.834985i 0.447983 0.894042i \(-0.352143\pi\)
0.998255 + 0.0590568i \(0.0188093\pi\)
\(744\) 0 0
\(745\) 109.419 189.520i 0.146872 0.254389i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −22.4103 12.9386i −0.0299203 0.0172745i
\(750\) 0 0
\(751\) 226.995 + 393.168i 0.302257 + 0.523525i 0.976647 0.214850i \(-0.0689264\pi\)
−0.674389 + 0.738376i \(0.735593\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.24448i 0.0122443i
\(756\) 0 0
\(757\) −18.7572 −0.0247784 −0.0123892 0.999923i \(-0.503944\pi\)
−0.0123892 + 0.999923i \(0.503944\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −655.215 + 378.289i −0.860992 + 0.497094i −0.864344 0.502900i \(-0.832266\pi\)
0.00335213 + 0.999994i \(0.498933\pi\)
\(762\) 0 0
\(763\) −689.555 + 1194.34i −0.903742 + 1.56533i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −849.226 490.301i −1.10721 0.639245i
\(768\) 0 0
\(769\) −583.868 1011.29i −0.759257 1.31507i −0.943230 0.332140i \(-0.892229\pi\)
0.183974 0.982931i \(-0.441104\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 763.809i 0.988110i −0.869431 0.494055i \(-0.835514\pi\)
0.869431 0.494055i \(-0.164486\pi\)
\(774\) 0 0
\(775\) −70.8342 −0.0913990
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 292.128 168.660i 0.375004 0.216509i
\(780\) 0 0
\(781\) −101.213 + 175.305i −0.129594 + 0.224463i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 446.914 + 258.026i 0.569318 + 0.328696i
\(786\) 0 0
\(787\) −248.732 430.817i −0.316051 0.547416i 0.663609 0.748079i \(-0.269024\pi\)
−0.979660 + 0.200663i \(0.935690\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 621.184i 0.785315i
\(792\) 0 0
\(793\) 667.775 0.842087
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1163.28 + 671.621i −1.45958 + 0.842686i −0.998990 0.0449296i \(-0.985694\pi\)
−0.460585 + 0.887616i \(0.652360\pi\)
\(798\) 0 0
\(799\) 50.2059 86.9591i 0.0628359 0.108835i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −13.2656 7.65891i −0.0165201 0.00953787i
\(804\) 0 0
\(805\) 96.1739 + 166.578i 0.119471 + 0.206929i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 244.633i 0.302389i −0.988504 0.151195i \(-0.951688\pi\)
0.988504 0.151195i \(-0.0483120\pi\)
\(810\) 0 0
\(811\) −1182.65 −1.45827 −0.729133 0.684372i \(-0.760076\pi\)
−0.729133 + 0.684372i \(0.760076\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 148.724 85.8660i 0.182484 0.105357i
\(816\) 0 0
\(817\) 261.795 453.442i 0.320434 0.555008i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −795.256 459.141i −0.968643 0.559246i −0.0698205 0.997560i \(-0.522243\pi\)
−0.898822 + 0.438313i \(0.855576\pi\)
\(822\) 0 0
\(823\) −406.279 703.695i −0.493656 0.855037i 0.506318 0.862347i \(-0.331006\pi\)
−0.999973 + 0.00731049i \(0.997673\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 476.892i 0.576653i 0.957532 + 0.288327i \(0.0930989\pi\)
−0.957532 + 0.288327i \(0.906901\pi\)
\(828\) 0 0
\(829\) −369.534 −0.445758 −0.222879 0.974846i \(-0.571546\pi\)
−0.222879 + 0.974846i \(0.571546\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.67247 2.12030i 0.00440873 0.00254538i
\(834\) 0 0
\(835\) −107.260 + 185.779i −0.128455 + 0.222490i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 728.282 + 420.474i 0.868036 + 0.501161i 0.866695 0.498838i \(-0.166240\pi\)
0.00134090 + 0.999999i \(0.499573\pi\)
\(840\) 0 0
\(841\) −171.976 297.870i −0.204489 0.354186i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 99.5111i 0.117765i
\(846\) 0 0
\(847\) −818.330 −0.966151
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −483.026 + 278.875i −0.567599 + 0.327703i
\(852\) 0 0
\(853\) −362.604 + 628.048i −0.425092 + 0.736282i −0.996429 0.0844341i \(-0.973092\pi\)
0.571337 + 0.820716i \(0.306425\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −732.868 423.121i −0.855155 0.493724i 0.00723204 0.999974i \(-0.497698\pi\)
−0.862387 + 0.506250i \(0.831031\pi\)
\(858\) 0 0
\(859\) 352.776 + 611.025i 0.410682 + 0.711321i 0.994964 0.100229i \(-0.0319574\pi\)
−0.584283 + 0.811550i \(0.698624\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 626.198i 0.725606i −0.931866 0.362803i \(-0.881820\pi\)
0.931866 0.362803i \(-0.118180\pi\)
\(864\) 0 0
\(865\) −227.957 −0.263534
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 37.3140 21.5433i 0.0429390 0.0247909i
\(870\) 0 0
\(871\) 43.0380 74.5440i 0.0494122 0.0855844i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 69.1875 + 39.9454i 0.0790715 + 0.0456519i
\(876\) 0 0
\(877\) 288.812 + 500.237i 0.329318 + 0.570395i 0.982377 0.186912i \(-0.0598479\pi\)
−0.653059 + 0.757307i \(0.726515\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1719.11i 1.95131i 0.219306 + 0.975656i \(0.429621\pi\)
−0.219306 + 0.975656i \(0.570379\pi\)
\(882\) 0 0
\(883\) −356.656 −0.403914 −0.201957 0.979394i \(-0.564730\pi\)
−0.201957 + 0.979394i \(0.564730\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 428.591 247.447i 0.483192 0.278971i −0.238554 0.971129i \(-0.576673\pi\)
0.721746 + 0.692158i \(0.243340\pi\)
\(888\) 0 0
\(889\) −298.558 + 517.117i −0.335835 + 0.581684i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 818.750 + 472.705i 0.916853 + 0.529345i
\(894\) 0 0
\(895\) −195.151 338.012i −0.218046 0.377667i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 315.844i 0.351328i
\(900\) 0 0
\(901\) 20.2531 0.0224784
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 579.437 334.538i 0.640262 0.369655i
\(906\) 0 0
\(907\) −311.723 + 539.919i −0.343685 + 0.595280i −0.985114 0.171902i \(-0.945009\pi\)
0.641429 + 0.767183i \(0.278342\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1527.46 881.879i −1.67668 0.968034i −0.963752 0.266800i \(-0.914034\pi\)
−0.712931 0.701234i \(-0.752633\pi\)
\(912\) 0 0
\(913\) −186.850 323.633i −0.204655 0.354472i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 158.705i 0.173070i
\(918\) 0 0
\(919\) −540.616 −0.588266 −0.294133 0.955765i \(-0.595031\pi\)
−0.294133 + 0.955765i \(0.595031\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 768.479 443.682i 0.832588 0.480695i
\(924\) 0 0
\(925\) −115.830 + 200.623i −0.125221 + 0.216890i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 206.950 + 119.482i 0.222766 + 0.128614i 0.607230 0.794526i \(-0.292281\pi\)
−0.384464 + 0.923140i \(0.625614\pi\)
\(930\) 0 0
\(931\) 19.9634 + 34.5776i 0.0214429 + 0.0371403i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 11.7139i 0.0125283i
\(936\) 0 0
\(937\) −75.1773 −0.0802320 −0.0401160 0.999195i \(-0.512773\pi\)
−0.0401160 + 0.999195i \(0.512773\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 57.3372 33.1037i 0.0609322 0.0351792i −0.469224 0.883079i \(-0.655466\pi\)
0.530157 + 0.847900i \(0.322133\pi\)
\(942\) 0 0
\(943\) −104.776 + 181.477i −0.111109 + 0.192447i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −225.603 130.252i −0.238230 0.137542i 0.376133 0.926566i \(-0.377254\pi\)
−0.614363 + 0.789024i \(0.710587\pi\)
\(948\) 0 0
\(949\) 33.5741 + 58.1520i 0.0353784 + 0.0612771i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 502.854i 0.527654i 0.964570 + 0.263827i \(0.0849847\pi\)
−0.964570 + 0.263827i \(0.915015\pi\)
\(954\) 0 0
\(955\) 318.186 0.333179
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −66.3231 + 38.2917i −0.0691586 + 0.0399287i
\(960\) 0 0
\(961\) 380.150 658.439i 0.395578 0.685161i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 431.549 + 249.155i 0.447201 + 0.258192i
\(966\) 0 0
\(967\) −308.935 535.091i −0.319478 0.553352i 0.660901 0.750473i \(-0.270174\pi\)
−0.980379 + 0.197121i \(0.936841\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 240.669i 0.247856i 0.992291 + 0.123928i \(0.0395492\pi\)
−0.992291 + 0.123928i \(0.960451\pi\)
\(972\) 0 0
\(973\) 303.982 0.312417
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1293.59 746.857i 1.32405 0.764439i 0.339675 0.940543i \(-0.389683\pi\)
0.984372 + 0.176104i \(0.0563494\pi\)
\(978\) 0 0
\(979\) −127.653 + 221.101i −0.130391 + 0.225844i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −674.535 389.443i −0.686200 0.396178i 0.115987 0.993251i \(-0.462997\pi\)
−0.802187 + 0.597073i \(0.796330\pi\)
\(984\) 0 0
\(985\) −302.505 523.955i −0.307112 0.531934i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 325.267i 0.328885i
\(990\) 0 0
\(991\) −703.289 −0.709676 −0.354838 0.934928i \(-0.615464\pi\)
−0.354838 + 0.934928i \(0.615464\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 272.032 157.057i 0.273399 0.157847i
\(996\) 0 0
\(997\) 293.948 509.133i 0.294833 0.510665i −0.680113 0.733107i \(-0.738069\pi\)
0.974946 + 0.222442i \(0.0714027\pi\)
\(998\) 0 0
\(999\) 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 1620.3.o.g.1241.4 32
3.2 odd 2 inner 1620.3.o.g.1241.12 32
9.2 odd 6 1620.3.g.c.161.10 yes 16
9.4 even 3 inner 1620.3.o.g.701.12 32
9.5 odd 6 inner 1620.3.o.g.701.4 32
9.7 even 3 1620.3.g.c.161.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1620.3.g.c.161.2 16 9.7 even 3
1620.3.g.c.161.10 yes 16 9.2 odd 6
1620.3.o.g.701.4 32 9.5 odd 6 inner
1620.3.o.g.701.12 32 9.4 even 3 inner
1620.3.o.g.1241.4 32 1.1 even 1 trivial
1620.3.o.g.1241.12 32 3.2 odd 2 inner