Properties

Label 1638.2.y.c.827.7
Level $1638$
Weight $2$
Character 1638.827
Analytic conductor $13.079$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1638,2,Mod(827,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.827");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.y (of order \(4\), degree \(2\), 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: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 20 x^{14} - 12 x^{13} + 40 x^{12} + 40 x^{11} + 82 x^{10} + 104 x^{9} + 537 x^{8} - 2528 x^{7} + 5494 x^{6} - 7284 x^{5} + 6002 x^{4} - 2984 x^{3} + 1000 x^{2} + \cdots + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 827.7
Root \(-1.90660 - 0.789738i\) of defining polynomial
Character \(\chi\) \(=\) 1638.827
Dual form 1638.2.y.c.1331.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.746053 - 0.746053i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.746053 - 0.746053i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.05508i q^{10} +(3.35792 + 3.35792i) q^{11} +(-1.20860 + 3.39695i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +2.02598 q^{17} +(5.03497 + 5.03497i) q^{19} +(-0.746053 - 0.746053i) q^{20} +4.74881 q^{22} -2.39154 q^{23} +3.88681i q^{25} +(1.54740 + 3.25662i) q^{26} +(0.707107 + 0.707107i) q^{28} +8.46166i q^{29} +(-5.55035 - 5.55035i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.43258 - 1.43258i) q^{34} +1.05508i q^{35} +(6.97346 - 6.97346i) q^{37} +7.12053 q^{38} -1.05508 q^{40} +(2.39122 - 2.39122i) q^{41} -9.24408i q^{43} +(3.35792 - 3.35792i) q^{44} +(-1.69107 + 1.69107i) q^{46} +(3.48199 + 3.48199i) q^{47} -1.00000i q^{49} +(2.74839 + 2.74839i) q^{50} +(3.39695 + 1.20860i) q^{52} +1.35557i q^{53} +5.01037 q^{55} +1.00000 q^{56} +(5.98330 + 5.98330i) q^{58} +(4.49527 + 4.49527i) q^{59} -1.56297 q^{61} -7.84938 q^{62} +1.00000i q^{64} +(1.63263 + 3.43599i) q^{65} +(-1.78711 - 1.78711i) q^{67} -2.02598i q^{68} +(0.746053 + 0.746053i) q^{70} +(9.95954 - 9.95954i) q^{71} +(-3.90170 + 3.90170i) q^{73} -9.86196i q^{74} +(5.03497 - 5.03497i) q^{76} -4.74881 q^{77} +10.2625 q^{79} +(-0.746053 + 0.746053i) q^{80} -3.38170i q^{82} +(-10.2261 + 10.2261i) q^{83} +(1.51149 - 1.51149i) q^{85} +(-6.53655 - 6.53655i) q^{86} -4.74881i q^{88} +(-4.40919 - 4.40919i) q^{89} +(-1.54740 - 3.25662i) q^{91} +2.39154i q^{92} +4.92428 q^{94} +7.51271 q^{95} +(-11.0928 - 11.0928i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{5} + 8 q^{11} + 4 q^{13} - 16 q^{16} + 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} - 24 q^{23} - 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} - 16 q^{38} + 16 q^{41} + 8 q^{44} - 4 q^{47} + 16 q^{50} - 16 q^{55} + 16 q^{56} + 4 q^{58} + 8 q^{59} - 40 q^{61} - 24 q^{62} - 56 q^{65} - 4 q^{67} - 4 q^{70} + 24 q^{71} - 12 q^{73} + 16 q^{76} + 8 q^{77} + 16 q^{79} + 4 q^{80} + 8 q^{85} - 24 q^{86} - 16 q^{89} + 8 q^{91} - 8 q^{94} + 40 q^{95} - 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0.746053 0.746053i 0.333645 0.333645i −0.520324 0.853969i \(-0.674189\pi\)
0.853969 + 0.520324i \(0.174189\pi\)
\(6\) 0 0
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) 1.05508i 0.333645i
\(11\) 3.35792 + 3.35792i 1.01245 + 1.01245i 0.999922 + 0.0125287i \(0.00398811\pi\)
0.0125287 + 0.999922i \(0.496012\pi\)
\(12\) 0 0
\(13\) −1.20860 + 3.39695i −0.335206 + 0.942145i
\(14\) 1.00000i 0.267261i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 2.02598 0.491372 0.245686 0.969349i \(-0.420987\pi\)
0.245686 + 0.969349i \(0.420987\pi\)
\(18\) 0 0
\(19\) 5.03497 + 5.03497i 1.15510 + 1.15510i 0.985515 + 0.169586i \(0.0542432\pi\)
0.169586 + 0.985515i \(0.445757\pi\)
\(20\) −0.746053 0.746053i −0.166823 0.166823i
\(21\) 0 0
\(22\) 4.74881 1.01245
\(23\) −2.39154 −0.498670 −0.249335 0.968417i \(-0.580212\pi\)
−0.249335 + 0.968417i \(0.580212\pi\)
\(24\) 0 0
\(25\) 3.88681i 0.777362i
\(26\) 1.54740 + 3.25662i 0.303470 + 0.638675i
\(27\) 0 0
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) 8.46166i 1.57129i 0.618677 + 0.785645i \(0.287669\pi\)
−0.618677 + 0.785645i \(0.712331\pi\)
\(30\) 0 0
\(31\) −5.55035 5.55035i −0.996872 0.996872i 0.00312287 0.999995i \(-0.499006\pi\)
−0.999995 + 0.00312287i \(0.999006\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) 1.43258 1.43258i 0.245686 0.245686i
\(35\) 1.05508i 0.178341i
\(36\) 0 0
\(37\) 6.97346 6.97346i 1.14643 1.14643i 0.159180 0.987250i \(-0.449115\pi\)
0.987250 0.159180i \(-0.0508849\pi\)
\(38\) 7.12053 1.15510
\(39\) 0 0
\(40\) −1.05508 −0.166823
\(41\) 2.39122 2.39122i 0.373446 0.373446i −0.495285 0.868731i \(-0.664936\pi\)
0.868731 + 0.495285i \(0.164936\pi\)
\(42\) 0 0
\(43\) 9.24408i 1.40971i −0.709352 0.704855i \(-0.751012\pi\)
0.709352 0.704855i \(-0.248988\pi\)
\(44\) 3.35792 3.35792i 0.506225 0.506225i
\(45\) 0 0
\(46\) −1.69107 + 1.69107i −0.249335 + 0.249335i
\(47\) 3.48199 + 3.48199i 0.507901 + 0.507901i 0.913882 0.405981i \(-0.133070\pi\)
−0.405981 + 0.913882i \(0.633070\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 2.74839 + 2.74839i 0.388681 + 0.388681i
\(51\) 0 0
\(52\) 3.39695 + 1.20860i 0.471072 + 0.167603i
\(53\) 1.35557i 0.186202i 0.995657 + 0.0931011i \(0.0296780\pi\)
−0.995657 + 0.0931011i \(0.970322\pi\)
\(54\) 0 0
\(55\) 5.01037 0.675598
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) 5.98330 + 5.98330i 0.785645 + 0.785645i
\(59\) 4.49527 + 4.49527i 0.585235 + 0.585235i 0.936337 0.351103i \(-0.114193\pi\)
−0.351103 + 0.936337i \(0.614193\pi\)
\(60\) 0 0
\(61\) −1.56297 −0.200118 −0.100059 0.994982i \(-0.531903\pi\)
−0.100059 + 0.994982i \(0.531903\pi\)
\(62\) −7.84938 −0.996872
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 1.63263 + 3.43599i 0.202502 + 0.426182i
\(66\) 0 0
\(67\) −1.78711 1.78711i −0.218331 0.218331i 0.589464 0.807795i \(-0.299339\pi\)
−0.807795 + 0.589464i \(0.799339\pi\)
\(68\) 2.02598i 0.245686i
\(69\) 0 0
\(70\) 0.746053 + 0.746053i 0.0891704 + 0.0891704i
\(71\) 9.95954 9.95954i 1.18198 1.18198i 0.202749 0.979231i \(-0.435013\pi\)
0.979231 0.202749i \(-0.0649875\pi\)
\(72\) 0 0
\(73\) −3.90170 + 3.90170i −0.456659 + 0.456659i −0.897557 0.440898i \(-0.854660\pi\)
0.440898 + 0.897557i \(0.354660\pi\)
\(74\) 9.86196i 1.14643i
\(75\) 0 0
\(76\) 5.03497 5.03497i 0.577551 0.577551i
\(77\) −4.74881 −0.541177
\(78\) 0 0
\(79\) 10.2625 1.15463 0.577313 0.816523i \(-0.304101\pi\)
0.577313 + 0.816523i \(0.304101\pi\)
\(80\) −0.746053 + 0.746053i −0.0834113 + 0.0834113i
\(81\) 0 0
\(82\) 3.38170i 0.373446i
\(83\) −10.2261 + 10.2261i −1.12246 + 1.12246i −0.131088 + 0.991371i \(0.541847\pi\)
−0.991371 + 0.131088i \(0.958153\pi\)
\(84\) 0 0
\(85\) 1.51149 1.51149i 0.163944 0.163944i
\(86\) −6.53655 6.53655i −0.704855 0.704855i
\(87\) 0 0
\(88\) 4.74881i 0.506225i
\(89\) −4.40919 4.40919i −0.467373 0.467373i 0.433690 0.901062i \(-0.357211\pi\)
−0.901062 + 0.433690i \(0.857211\pi\)
\(90\) 0 0
\(91\) −1.54740 3.25662i −0.162211 0.341386i
\(92\) 2.39154i 0.249335i
\(93\) 0 0
\(94\) 4.92428 0.507901
\(95\) 7.51271 0.770788
\(96\) 0 0
\(97\) −11.0928 11.0928i −1.12630 1.12630i −0.990773 0.135531i \(-0.956726\pi\)
−0.135531 0.990773i \(-0.543274\pi\)
\(98\) −0.707107 0.707107i −0.0714286 0.0714286i
\(99\) 0 0
\(100\) 3.88681 0.388681
\(101\) 4.43684 0.441482 0.220741 0.975332i \(-0.429152\pi\)
0.220741 + 0.975332i \(0.429152\pi\)
\(102\) 0 0
\(103\) 9.93465i 0.978890i −0.872034 0.489445i \(-0.837199\pi\)
0.872034 0.489445i \(-0.162801\pi\)
\(104\) 3.25662 1.54740i 0.319338 0.151735i
\(105\) 0 0
\(106\) 0.958534 + 0.958534i 0.0931011 + 0.0931011i
\(107\) 12.0250i 1.16250i 0.813725 + 0.581250i \(0.197436\pi\)
−0.813725 + 0.581250i \(0.802564\pi\)
\(108\) 0 0
\(109\) 2.47819 + 2.47819i 0.237367 + 0.237367i 0.815759 0.578392i \(-0.196320\pi\)
−0.578392 + 0.815759i \(0.696320\pi\)
\(110\) 3.54287 3.54287i 0.337799 0.337799i
\(111\) 0 0
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) 19.4049i 1.82546i 0.408561 + 0.912731i \(0.366031\pi\)
−0.408561 + 0.912731i \(0.633969\pi\)
\(114\) 0 0
\(115\) −1.78421 + 1.78421i −0.166379 + 0.166379i
\(116\) 8.46166 0.785645
\(117\) 0 0
\(118\) 6.35727 0.585235
\(119\) −1.43258 + 1.43258i −0.131325 + 0.131325i
\(120\) 0 0
\(121\) 11.5512i 1.05011i
\(122\) −1.10519 + 1.10519i −0.100059 + 0.100059i
\(123\) 0 0
\(124\) −5.55035 + 5.55035i −0.498436 + 0.498436i
\(125\) 6.63003 + 6.63003i 0.593008 + 0.593008i
\(126\) 0 0
\(127\) 14.6946i 1.30393i −0.758248 0.651966i \(-0.773944\pi\)
0.758248 0.651966i \(-0.226056\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 3.58405 + 1.27517i 0.314342 + 0.111840i
\(131\) 2.22152i 0.194095i 0.995280 + 0.0970477i \(0.0309399\pi\)
−0.995280 + 0.0970477i \(0.969060\pi\)
\(132\) 0 0
\(133\) −7.12053 −0.617428
\(134\) −2.52736 −0.218331
\(135\) 0 0
\(136\) −1.43258 1.43258i −0.122843 0.122843i
\(137\) 0.387266 + 0.387266i 0.0330864 + 0.0330864i 0.723456 0.690370i \(-0.242552\pi\)
−0.690370 + 0.723456i \(0.742552\pi\)
\(138\) 0 0
\(139\) −2.80074 −0.237556 −0.118778 0.992921i \(-0.537898\pi\)
−0.118778 + 0.992921i \(0.537898\pi\)
\(140\) 1.05508 0.0891704
\(141\) 0 0
\(142\) 14.0849i 1.18198i
\(143\) −15.4651 + 7.34830i −1.29325 + 0.614496i
\(144\) 0 0
\(145\) 6.31285 + 6.31285i 0.524253 + 0.524253i
\(146\) 5.51784i 0.456659i
\(147\) 0 0
\(148\) −6.97346 6.97346i −0.573215 0.573215i
\(149\) 0.866918 0.866918i 0.0710207 0.0710207i −0.670704 0.741725i \(-0.734008\pi\)
0.741725 + 0.670704i \(0.234008\pi\)
\(150\) 0 0
\(151\) 14.7845 14.7845i 1.20315 1.20315i 0.229945 0.973204i \(-0.426145\pi\)
0.973204 0.229945i \(-0.0738546\pi\)
\(152\) 7.12053i 0.577551i
\(153\) 0 0
\(154\) −3.35792 + 3.35792i −0.270589 + 0.270589i
\(155\) −8.28171 −0.665203
\(156\) 0 0
\(157\) 15.2471 1.21685 0.608424 0.793612i \(-0.291802\pi\)
0.608424 + 0.793612i \(0.291802\pi\)
\(158\) 7.25671 7.25671i 0.577313 0.577313i
\(159\) 0 0
\(160\) 1.05508i 0.0834113i
\(161\) 1.69107 1.69107i 0.133275 0.133275i
\(162\) 0 0
\(163\) −16.2208 + 16.2208i −1.27051 + 1.27051i −0.324693 + 0.945819i \(0.605261\pi\)
−0.945819 + 0.324693i \(0.894739\pi\)
\(164\) −2.39122 2.39122i −0.186723 0.186723i
\(165\) 0 0
\(166\) 14.4619i 1.12246i
\(167\) −17.0656 17.0656i −1.32058 1.32058i −0.913308 0.407269i \(-0.866481\pi\)
−0.407269 0.913308i \(-0.633519\pi\)
\(168\) 0 0
\(169\) −10.0786 8.21112i −0.775274 0.631625i
\(170\) 2.13757i 0.163944i
\(171\) 0 0
\(172\) −9.24408 −0.704855
\(173\) 8.52210 0.647923 0.323961 0.946070i \(-0.394985\pi\)
0.323961 + 0.946070i \(0.394985\pi\)
\(174\) 0 0
\(175\) −2.74839 2.74839i −0.207759 0.207759i
\(176\) −3.35792 3.35792i −0.253113 0.253113i
\(177\) 0 0
\(178\) −6.23553 −0.467373
\(179\) −3.46058 −0.258656 −0.129328 0.991602i \(-0.541282\pi\)
−0.129328 + 0.991602i \(0.541282\pi\)
\(180\) 0 0
\(181\) 24.8236i 1.84513i 0.385846 + 0.922563i \(0.373910\pi\)
−0.385846 + 0.922563i \(0.626090\pi\)
\(182\) −3.39695 1.20860i −0.251799 0.0895875i
\(183\) 0 0
\(184\) 1.69107 + 1.69107i 0.124668 + 0.124668i
\(185\) 10.4051i 0.765001i
\(186\) 0 0
\(187\) 6.80307 + 6.80307i 0.497490 + 0.497490i
\(188\) 3.48199 3.48199i 0.253951 0.253951i
\(189\) 0 0
\(190\) 5.31229 5.31229i 0.385394 0.385394i
\(191\) 7.86219i 0.568888i 0.958693 + 0.284444i \(0.0918090\pi\)
−0.958693 + 0.284444i \(0.908191\pi\)
\(192\) 0 0
\(193\) 4.85067 4.85067i 0.349159 0.349159i −0.510637 0.859796i \(-0.670591\pi\)
0.859796 + 0.510637i \(0.170591\pi\)
\(194\) −15.6876 −1.12630
\(195\) 0 0
\(196\) −1.00000 −0.0714286
\(197\) 9.34718 9.34718i 0.665959 0.665959i −0.290819 0.956778i \(-0.593928\pi\)
0.956778 + 0.290819i \(0.0939278\pi\)
\(198\) 0 0
\(199\) 23.0454i 1.63365i −0.576887 0.816824i \(-0.695733\pi\)
0.576887 0.816824i \(-0.304267\pi\)
\(200\) 2.74839 2.74839i 0.194340 0.194340i
\(201\) 0 0
\(202\) 3.13732 3.13732i 0.220741 0.220741i
\(203\) −5.98330 5.98330i −0.419945 0.419945i
\(204\) 0 0
\(205\) 3.56796i 0.249197i
\(206\) −7.02486 7.02486i −0.489445 0.489445i
\(207\) 0 0
\(208\) 1.20860 3.39695i 0.0838014 0.235536i
\(209\) 33.8140i 2.33897i
\(210\) 0 0
\(211\) −0.931807 −0.0641482 −0.0320741 0.999485i \(-0.510211\pi\)
−0.0320741 + 0.999485i \(0.510211\pi\)
\(212\) 1.35557 0.0931011
\(213\) 0 0
\(214\) 8.50295 + 8.50295i 0.581250 + 0.581250i
\(215\) −6.89658 6.89658i −0.470343 0.470343i
\(216\) 0 0
\(217\) 7.84938 0.532851
\(218\) 3.50468 0.237367
\(219\) 0 0
\(220\) 5.01037i 0.337799i
\(221\) −2.44860 + 6.88216i −0.164711 + 0.462944i
\(222\) 0 0
\(223\) −0.806330 0.806330i −0.0539959 0.0539959i 0.679593 0.733589i \(-0.262156\pi\)
−0.733589 + 0.679593i \(0.762156\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 0 0
\(226\) 13.7214 + 13.7214i 0.912731 + 0.912731i
\(227\) 2.04742 2.04742i 0.135892 0.135892i −0.635889 0.771781i \(-0.719366\pi\)
0.771781 + 0.635889i \(0.219366\pi\)
\(228\) 0 0
\(229\) −12.3112 + 12.3112i −0.813549 + 0.813549i −0.985164 0.171615i \(-0.945101\pi\)
0.171615 + 0.985164i \(0.445101\pi\)
\(230\) 2.52326i 0.166379i
\(231\) 0 0
\(232\) 5.98330 5.98330i 0.392823 0.392823i
\(233\) 24.7227 1.61964 0.809818 0.586682i \(-0.199566\pi\)
0.809818 + 0.586682i \(0.199566\pi\)
\(234\) 0 0
\(235\) 5.19550 0.338917
\(236\) 4.49527 4.49527i 0.292617 0.292617i
\(237\) 0 0
\(238\) 2.02598i 0.131325i
\(239\) −1.69453 + 1.69453i −0.109610 + 0.109610i −0.759785 0.650175i \(-0.774696\pi\)
0.650175 + 0.759785i \(0.274696\pi\)
\(240\) 0 0
\(241\) 4.52253 4.52253i 0.291322 0.291322i −0.546281 0.837602i \(-0.683957\pi\)
0.837602 + 0.546281i \(0.183957\pi\)
\(242\) 8.16794 + 8.16794i 0.525055 + 0.525055i
\(243\) 0 0
\(244\) 1.56297i 0.100059i
\(245\) −0.746053 0.746053i −0.0476636 0.0476636i
\(246\) 0 0
\(247\) −23.1888 + 11.0183i −1.47547 + 0.701077i
\(248\) 7.84938i 0.498436i
\(249\) 0 0
\(250\) 9.37628 0.593008
\(251\) −27.3370 −1.72549 −0.862747 0.505636i \(-0.831258\pi\)
−0.862747 + 0.505636i \(0.831258\pi\)
\(252\) 0 0
\(253\) −8.03059 8.03059i −0.504879 0.504879i
\(254\) −10.3906 10.3906i −0.651966 0.651966i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −27.6049 −1.72195 −0.860975 0.508648i \(-0.830145\pi\)
−0.860975 + 0.508648i \(0.830145\pi\)
\(258\) 0 0
\(259\) 9.86196i 0.612792i
\(260\) 3.43599 1.63263i 0.213091 0.101251i
\(261\) 0 0
\(262\) 1.57085 + 1.57085i 0.0970477 + 0.0970477i
\(263\) 26.9692i 1.66299i −0.555529 0.831497i \(-0.687484\pi\)
0.555529 0.831497i \(-0.312516\pi\)
\(264\) 0 0
\(265\) 1.01133 + 1.01133i 0.0621254 + 0.0621254i
\(266\) −5.03497 + 5.03497i −0.308714 + 0.308714i
\(267\) 0 0
\(268\) −1.78711 + 1.78711i −0.109165 + 0.109165i
\(269\) 15.1618i 0.924433i −0.886767 0.462217i \(-0.847054\pi\)
0.886767 0.462217i \(-0.152946\pi\)
\(270\) 0 0
\(271\) −17.8111 + 17.8111i −1.08195 + 1.08195i −0.0856179 + 0.996328i \(0.527286\pi\)
−0.996328 + 0.0856179i \(0.972714\pi\)
\(272\) −2.02598 −0.122843
\(273\) 0 0
\(274\) 0.547677 0.0330864
\(275\) −13.0516 + 13.0516i −0.787040 + 0.787040i
\(276\) 0 0
\(277\) 3.04741i 0.183101i −0.995800 0.0915507i \(-0.970818\pi\)
0.995800 0.0915507i \(-0.0291823\pi\)
\(278\) −1.98042 + 1.98042i −0.118778 + 0.118778i
\(279\) 0 0
\(280\) 0.746053 0.746053i 0.0445852 0.0445852i
\(281\) 10.5654 + 10.5654i 0.630278 + 0.630278i 0.948138 0.317859i \(-0.102964\pi\)
−0.317859 + 0.948138i \(0.602964\pi\)
\(282\) 0 0
\(283\) 21.8771i 1.30046i −0.759738 0.650229i \(-0.774673\pi\)
0.759738 0.650229i \(-0.225327\pi\)
\(284\) −9.95954 9.95954i −0.590990 0.590990i
\(285\) 0 0
\(286\) −5.73942 + 16.1315i −0.339379 + 0.953875i
\(287\) 3.38170i 0.199615i
\(288\) 0 0
\(289\) −12.8954 −0.758553
\(290\) 8.92771 0.524253
\(291\) 0 0
\(292\) 3.90170 + 3.90170i 0.228330 + 0.228330i
\(293\) 9.78815 + 9.78815i 0.571830 + 0.571830i 0.932640 0.360809i \(-0.117500\pi\)
−0.360809 + 0.932640i \(0.617500\pi\)
\(294\) 0 0
\(295\) 6.70742 0.390521
\(296\) −9.86196 −0.573215
\(297\) 0 0
\(298\) 1.22601i 0.0710207i
\(299\) 2.89042 8.12394i 0.167157 0.469820i
\(300\) 0 0
\(301\) 6.53655 + 6.53655i 0.376761 + 0.376761i
\(302\) 20.9085i 1.20315i
\(303\) 0 0
\(304\) −5.03497 5.03497i −0.288775 0.288775i
\(305\) −1.16606 + 1.16606i −0.0667684 + 0.0667684i
\(306\) 0 0
\(307\) −12.3093 + 12.3093i −0.702527 + 0.702527i −0.964952 0.262425i \(-0.915478\pi\)
0.262425 + 0.964952i \(0.415478\pi\)
\(308\) 4.74881i 0.270589i
\(309\) 0 0
\(310\) −5.85605 + 5.85605i −0.332601 + 0.332601i
\(311\) −2.57110 −0.145794 −0.0728968 0.997339i \(-0.523224\pi\)
−0.0728968 + 0.997339i \(0.523224\pi\)
\(312\) 0 0
\(313\) 1.14291 0.0646013 0.0323006 0.999478i \(-0.489717\pi\)
0.0323006 + 0.999478i \(0.489717\pi\)
\(314\) 10.7813 10.7813i 0.608424 0.608424i
\(315\) 0 0
\(316\) 10.2625i 0.577313i
\(317\) 9.45116 9.45116i 0.530830 0.530830i −0.389989 0.920819i \(-0.627521\pi\)
0.920819 + 0.389989i \(0.127521\pi\)
\(318\) 0 0
\(319\) −28.4136 + 28.4136i −1.59085 + 1.59085i
\(320\) 0.746053 + 0.746053i 0.0417056 + 0.0417056i
\(321\) 0 0
\(322\) 2.39154i 0.133275i
\(323\) 10.2008 + 10.2008i 0.567585 + 0.567585i
\(324\) 0 0
\(325\) −13.2033 4.69760i −0.732388 0.260576i
\(326\) 22.9397i 1.27051i
\(327\) 0 0
\(328\) −3.38170 −0.186723
\(329\) −4.92428 −0.271485
\(330\) 0 0
\(331\) 8.76490 + 8.76490i 0.481763 + 0.481763i 0.905694 0.423932i \(-0.139350\pi\)
−0.423932 + 0.905694i \(0.639350\pi\)
\(332\) 10.2261 + 10.2261i 0.561229 + 0.561229i
\(333\) 0 0
\(334\) −24.1344 −1.32058
\(335\) −2.66656 −0.145690
\(336\) 0 0
\(337\) 31.8297i 1.73387i −0.498418 0.866937i \(-0.666086\pi\)
0.498418 0.866937i \(-0.333914\pi\)
\(338\) −12.9328 + 1.32048i −0.703449 + 0.0718249i
\(339\) 0 0
\(340\) −1.51149 1.51149i −0.0819720 0.0819720i
\(341\) 37.2752i 2.01857i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −6.53655 + 6.53655i −0.352427 + 0.352427i
\(345\) 0 0
\(346\) 6.02603 6.02603i 0.323961 0.323961i
\(347\) 20.0727i 1.07756i −0.842447 0.538780i \(-0.818886\pi\)
0.842447 0.538780i \(-0.181114\pi\)
\(348\) 0 0
\(349\) −8.88355 + 8.88355i −0.475525 + 0.475525i −0.903697 0.428172i \(-0.859158\pi\)
0.428172 + 0.903697i \(0.359158\pi\)
\(350\) −3.88681 −0.207759
\(351\) 0 0
\(352\) −4.74881 −0.253113
\(353\) −12.9241 + 12.9241i −0.687878 + 0.687878i −0.961763 0.273884i \(-0.911691\pi\)
0.273884 + 0.961763i \(0.411691\pi\)
\(354\) 0 0
\(355\) 14.8607i 0.788723i
\(356\) −4.40919 + 4.40919i −0.233686 + 0.233686i
\(357\) 0 0
\(358\) −2.44700 + 2.44700i −0.129328 + 0.129328i
\(359\) −10.7224 10.7224i −0.565907 0.565907i 0.365072 0.930979i \(-0.381044\pi\)
−0.930979 + 0.365072i \(0.881044\pi\)
\(360\) 0 0
\(361\) 31.7019i 1.66852i
\(362\) 17.5530 + 17.5530i 0.922563 + 0.922563i
\(363\) 0 0
\(364\) −3.25662 + 1.54740i −0.170693 + 0.0811057i
\(365\) 5.82175i 0.304724i
\(366\) 0 0
\(367\) −14.5681 −0.760447 −0.380224 0.924895i \(-0.624153\pi\)
−0.380224 + 0.924895i \(0.624153\pi\)
\(368\) 2.39154 0.124668
\(369\) 0 0
\(370\) −7.35754 7.35754i −0.382500 0.382500i
\(371\) −0.958534 0.958534i −0.0497646 0.0497646i
\(372\) 0 0
\(373\) −4.64322 −0.240417 −0.120208 0.992749i \(-0.538356\pi\)
−0.120208 + 0.992749i \(0.538356\pi\)
\(374\) 9.62100 0.497490
\(375\) 0 0
\(376\) 4.92428i 0.253951i
\(377\) −28.7438 10.2268i −1.48038 0.526705i
\(378\) 0 0
\(379\) −6.74493 6.74493i −0.346464 0.346464i 0.512327 0.858791i \(-0.328784\pi\)
−0.858791 + 0.512327i \(0.828784\pi\)
\(380\) 7.51271i 0.385394i
\(381\) 0 0
\(382\) 5.55941 + 5.55941i 0.284444 + 0.284444i
\(383\) 1.32694 1.32694i 0.0678037 0.0678037i −0.672392 0.740195i \(-0.734733\pi\)
0.740195 + 0.672392i \(0.234733\pi\)
\(384\) 0 0
\(385\) −3.54287 + 3.54287i −0.180561 + 0.180561i
\(386\) 6.85988i 0.349159i
\(387\) 0 0
\(388\) −11.0928 + 11.0928i −0.563152 + 0.563152i
\(389\) 25.9151 1.31395 0.656974 0.753913i \(-0.271836\pi\)
0.656974 + 0.753913i \(0.271836\pi\)
\(390\) 0 0
\(391\) −4.84521 −0.245033
\(392\) −0.707107 + 0.707107i −0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 13.2189i 0.665959i
\(395\) 7.65639 7.65639i 0.385235 0.385235i
\(396\) 0 0
\(397\) −21.1031 + 21.1031i −1.05913 + 1.05913i −0.0609954 + 0.998138i \(0.519427\pi\)
−0.998138 + 0.0609954i \(0.980573\pi\)
\(398\) −16.2956 16.2956i −0.816824 0.816824i
\(399\) 0 0
\(400\) 3.88681i 0.194340i
\(401\) 18.9302 + 18.9302i 0.945332 + 0.945332i 0.998581 0.0532497i \(-0.0169579\pi\)
−0.0532497 + 0.998581i \(0.516958\pi\)
\(402\) 0 0
\(403\) 25.5624 12.1461i 1.27336 0.605041i
\(404\) 4.43684i 0.220741i
\(405\) 0 0
\(406\) −8.46166 −0.419945
\(407\) 46.8326 2.32141
\(408\) 0 0
\(409\) −10.4950 10.4950i −0.518945 0.518945i 0.398307 0.917252i \(-0.369598\pi\)
−0.917252 + 0.398307i \(0.869598\pi\)
\(410\) −2.52293 2.52293i −0.124598 0.124598i
\(411\) 0 0
\(412\) −9.93465 −0.489445
\(413\) −6.35727 −0.312821
\(414\) 0 0
\(415\) 15.2584i 0.749005i
\(416\) −1.54740 3.25662i −0.0758674 0.159669i
\(417\) 0 0
\(418\) 23.9101 + 23.9101i 1.16948 + 1.16948i
\(419\) 22.9538i 1.12136i −0.828031 0.560682i \(-0.810539\pi\)
0.828031 0.560682i \(-0.189461\pi\)
\(420\) 0 0
\(421\) 20.3182 + 20.3182i 0.990247 + 0.990247i 0.999953 0.00970630i \(-0.00308966\pi\)
−0.00970630 + 0.999953i \(0.503090\pi\)
\(422\) −0.658887 + 0.658887i −0.0320741 + 0.0320741i
\(423\) 0 0
\(424\) 0.958534 0.958534i 0.0465505 0.0465505i
\(425\) 7.87460i 0.381974i
\(426\) 0 0
\(427\) 1.10519 1.10519i 0.0534838 0.0534838i
\(428\) 12.0250 0.581250
\(429\) 0 0
\(430\) −9.75323 −0.470343
\(431\) −0.553365 + 0.553365i −0.0266547 + 0.0266547i −0.720309 0.693654i \(-0.756000\pi\)
0.693654 + 0.720309i \(0.256000\pi\)
\(432\) 0 0
\(433\) 1.38424i 0.0665222i −0.999447 0.0332611i \(-0.989411\pi\)
0.999447 0.0332611i \(-0.0105893\pi\)
\(434\) 5.55035 5.55035i 0.266425 0.266425i
\(435\) 0 0
\(436\) 2.47819 2.47819i 0.118684 0.118684i
\(437\) −12.0413 12.0413i −0.576015 0.576015i
\(438\) 0 0
\(439\) 14.3680i 0.685746i −0.939382 0.342873i \(-0.888600\pi\)
0.939382 0.342873i \(-0.111400\pi\)
\(440\) −3.54287 3.54287i −0.168899 0.168899i
\(441\) 0 0
\(442\) 3.13500 + 6.59784i 0.149117 + 0.313827i
\(443\) 7.27225i 0.345515i −0.984964 0.172758i \(-0.944732\pi\)
0.984964 0.172758i \(-0.0552677\pi\)
\(444\) 0 0
\(445\) −6.57897 −0.311873
\(446\) −1.14032 −0.0539959
\(447\) 0 0
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) −11.1201 11.1201i −0.524789 0.524789i 0.394225 0.919014i \(-0.371013\pi\)
−0.919014 + 0.394225i \(0.871013\pi\)
\(450\) 0 0
\(451\) 16.0591 0.756191
\(452\) 19.4049 0.912731
\(453\) 0 0
\(454\) 2.89548i 0.135892i
\(455\) −3.58405 1.27517i −0.168023 0.0597808i
\(456\) 0 0
\(457\) 7.25037 + 7.25037i 0.339158 + 0.339158i 0.856050 0.516892i \(-0.172911\pi\)
−0.516892 + 0.856050i \(0.672911\pi\)
\(458\) 17.4107i 0.813549i
\(459\) 0 0
\(460\) 1.78421 + 1.78421i 0.0831894 + 0.0831894i
\(461\) 20.4191 20.4191i 0.951011 0.951011i −0.0478439 0.998855i \(-0.515235\pi\)
0.998855 + 0.0478439i \(0.0152350\pi\)
\(462\) 0 0
\(463\) 5.16963 5.16963i 0.240253 0.240253i −0.576702 0.816955i \(-0.695661\pi\)
0.816955 + 0.576702i \(0.195661\pi\)
\(464\) 8.46166i 0.392823i
\(465\) 0 0
\(466\) 17.4816 17.4816i 0.809818 0.809818i
\(467\) −16.6030 −0.768293 −0.384147 0.923272i \(-0.625504\pi\)
−0.384147 + 0.923272i \(0.625504\pi\)
\(468\) 0 0
\(469\) 2.52736 0.116703
\(470\) 3.67378 3.67378i 0.169459 0.169459i
\(471\) 0 0
\(472\) 6.35727i 0.292617i
\(473\) 31.0409 31.0409i 1.42726 1.42726i
\(474\) 0 0
\(475\) −19.5700 + 19.5700i −0.897932 + 0.897932i
\(476\) 1.43258 + 1.43258i 0.0656624 + 0.0656624i
\(477\) 0 0
\(478\) 2.39642i 0.109610i
\(479\) 20.7447 + 20.7447i 0.947851 + 0.947851i 0.998706 0.0508550i \(-0.0161946\pi\)
−0.0508550 + 0.998706i \(0.516195\pi\)
\(480\) 0 0
\(481\) 15.2604 + 32.1166i 0.695813 + 1.46439i
\(482\) 6.39582i 0.291322i
\(483\) 0 0
\(484\) 11.5512 0.525055
\(485\) −16.5516 −0.751572
\(486\) 0 0
\(487\) −5.21573 5.21573i −0.236347 0.236347i 0.578989 0.815336i \(-0.303448\pi\)
−0.815336 + 0.578989i \(0.803448\pi\)
\(488\) 1.10519 + 1.10519i 0.0500295 + 0.0500295i
\(489\) 0 0
\(490\) −1.05508 −0.0476636
\(491\) −11.0398 −0.498220 −0.249110 0.968475i \(-0.580138\pi\)
−0.249110 + 0.968475i \(0.580138\pi\)
\(492\) 0 0
\(493\) 17.1431i 0.772089i
\(494\) −8.60587 + 24.1881i −0.387197 + 1.08827i
\(495\) 0 0
\(496\) 5.55035 + 5.55035i 0.249218 + 0.249218i
\(497\) 14.0849i 0.631795i
\(498\) 0 0
\(499\) 3.56893 + 3.56893i 0.159767 + 0.159767i 0.782464 0.622696i \(-0.213963\pi\)
−0.622696 + 0.782464i \(0.713963\pi\)
\(500\) 6.63003 6.63003i 0.296504 0.296504i
\(501\) 0 0
\(502\) −19.3302 + 19.3302i −0.862747 + 0.862747i
\(503\) 36.7436i 1.63832i 0.573566 + 0.819159i \(0.305559\pi\)
−0.573566 + 0.819159i \(0.694441\pi\)
\(504\) 0 0
\(505\) 3.31012 3.31012i 0.147298 0.147298i
\(506\) −11.3570 −0.504879
\(507\) 0 0
\(508\) −14.6946 −0.651966
\(509\) 8.92586 8.92586i 0.395632 0.395632i −0.481057 0.876689i \(-0.659747\pi\)
0.876689 + 0.481057i \(0.159747\pi\)
\(510\) 0 0
\(511\) 5.51784i 0.244095i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) −19.5196 + 19.5196i −0.860975 + 0.860975i
\(515\) −7.41178 7.41178i −0.326602 0.326602i
\(516\) 0 0
\(517\) 23.3845i 1.02845i
\(518\) 6.97346 + 6.97346i 0.306396 + 0.306396i
\(519\) 0 0
\(520\) 1.27517 3.58405i 0.0559198 0.157171i
\(521\) 11.5826i 0.507445i 0.967277 + 0.253722i \(0.0816550\pi\)
−0.967277 + 0.253722i \(0.918345\pi\)
\(522\) 0 0
\(523\) 31.9601 1.39752 0.698758 0.715358i \(-0.253737\pi\)
0.698758 + 0.715358i \(0.253737\pi\)
\(524\) 2.22152 0.0970477
\(525\) 0 0
\(526\) −19.0701 19.0701i −0.831497 0.831497i
\(527\) −11.2449 11.2449i −0.489835 0.489835i
\(528\) 0 0
\(529\) −17.2805 −0.751328
\(530\) 1.43023 0.0621254
\(531\) 0 0
\(532\) 7.12053i 0.308714i
\(533\) 5.23283 + 11.0129i 0.226659 + 0.477022i
\(534\) 0 0
\(535\) 8.97127 + 8.97127i 0.387862 + 0.387862i
\(536\) 2.52736i 0.109165i
\(537\) 0 0
\(538\) −10.7210 10.7210i −0.462217 0.462217i
\(539\) 3.35792 3.35792i 0.144636 0.144636i
\(540\) 0 0
\(541\) 3.83741 3.83741i 0.164983 0.164983i −0.619787 0.784770i \(-0.712781\pi\)
0.784770 + 0.619787i \(0.212781\pi\)
\(542\) 25.1887i 1.08195i
\(543\) 0 0
\(544\) −1.43258 + 1.43258i −0.0614215 + 0.0614215i
\(545\) 3.69772 0.158393
\(546\) 0 0
\(547\) −10.7371 −0.459087 −0.229544 0.973298i \(-0.573723\pi\)
−0.229544 + 0.973298i \(0.573723\pi\)
\(548\) 0.387266 0.387266i 0.0165432 0.0165432i
\(549\) 0 0
\(550\) 18.4577i 0.787040i
\(551\) −42.6042 + 42.6042i −1.81500 + 1.81500i
\(552\) 0 0
\(553\) −7.25671 + 7.25671i −0.308587 + 0.308587i
\(554\) −2.15485 2.15485i −0.0915507 0.0915507i
\(555\) 0 0
\(556\) 2.80074i 0.118778i
\(557\) −5.56727 5.56727i −0.235893 0.235893i 0.579254 0.815147i \(-0.303344\pi\)
−0.815147 + 0.579254i \(0.803344\pi\)
\(558\) 0 0
\(559\) 31.4017 + 11.1724i 1.32815 + 0.472543i
\(560\) 1.05508i 0.0445852i
\(561\) 0 0
\(562\) 14.9417 0.630278
\(563\) −35.8520 −1.51098 −0.755491 0.655159i \(-0.772601\pi\)
−0.755491 + 0.655159i \(0.772601\pi\)
\(564\) 0 0
\(565\) 14.4771 + 14.4771i 0.609056 + 0.609056i
\(566\) −15.4694 15.4694i −0.650229 0.650229i
\(567\) 0 0
\(568\) −14.0849 −0.590990
\(569\) 11.7932 0.494398 0.247199 0.968965i \(-0.420490\pi\)
0.247199 + 0.968965i \(0.420490\pi\)
\(570\) 0 0
\(571\) 36.8437i 1.54186i −0.636920 0.770930i \(-0.719792\pi\)
0.636920 0.770930i \(-0.280208\pi\)
\(572\) 7.34830 + 15.4651i 0.307248 + 0.646627i
\(573\) 0 0
\(574\) 2.39122 + 2.39122i 0.0998077 + 0.0998077i
\(575\) 9.29545i 0.387647i
\(576\) 0 0
\(577\) −2.65397 2.65397i −0.110486 0.110486i 0.649702 0.760189i \(-0.274893\pi\)
−0.760189 + 0.649702i \(0.774893\pi\)
\(578\) −9.11843 + 9.11843i −0.379277 + 0.379277i
\(579\) 0 0
\(580\) 6.31285 6.31285i 0.262127 0.262127i
\(581\) 14.4619i 0.599979i
\(582\) 0 0
\(583\) −4.55190 + 4.55190i −0.188520 + 0.188520i
\(584\) 5.51784 0.228330
\(585\) 0 0
\(586\) 13.8425 0.571830
\(587\) −8.67198 + 8.67198i −0.357931 + 0.357931i −0.863050 0.505119i \(-0.831449\pi\)
0.505119 + 0.863050i \(0.331449\pi\)
\(588\) 0 0
\(589\) 55.8917i 2.30298i
\(590\) 4.74286 4.74286i 0.195261 0.195261i
\(591\) 0 0
\(592\) −6.97346 + 6.97346i −0.286607 + 0.286607i
\(593\) 23.0726 + 23.0726i 0.947478 + 0.947478i 0.998688 0.0512098i \(-0.0163077\pi\)
−0.0512098 + 0.998688i \(0.516308\pi\)
\(594\) 0 0
\(595\) 2.13757i 0.0876317i
\(596\) −0.866918 0.866918i −0.0355103 0.0355103i
\(597\) 0 0
\(598\) −3.70066 7.78833i −0.151331 0.318488i
\(599\) 12.1997i 0.498465i −0.968444 0.249232i \(-0.919822\pi\)
0.968444 0.249232i \(-0.0801783\pi\)
\(600\) 0 0
\(601\) −0.975365 −0.0397860 −0.0198930 0.999802i \(-0.506333\pi\)
−0.0198930 + 0.999802i \(0.506333\pi\)
\(602\) 9.24408 0.376761
\(603\) 0 0
\(604\) −14.7845 14.7845i −0.601574 0.601574i
\(605\) 8.61782 + 8.61782i 0.350364 + 0.350364i
\(606\) 0 0
\(607\) −21.1566 −0.858721 −0.429360 0.903133i \(-0.641261\pi\)
−0.429360 + 0.903133i \(0.641261\pi\)
\(608\) −7.12053 −0.288775
\(609\) 0 0
\(610\) 1.64906i 0.0667684i
\(611\) −16.0365 + 7.61983i −0.648768 + 0.308265i
\(612\) 0 0
\(613\) −3.67466 3.67466i −0.148418 0.148418i 0.628993 0.777411i \(-0.283467\pi\)
−0.777411 + 0.628993i \(0.783467\pi\)
\(614\) 17.4079i 0.702527i
\(615\) 0 0
\(616\) 3.35792 + 3.35792i 0.135294 + 0.135294i
\(617\) 28.6513 28.6513i 1.15346 1.15346i 0.167604 0.985854i \(-0.446397\pi\)
0.985854 0.167604i \(-0.0536031\pi\)
\(618\) 0 0
\(619\) 20.2324 20.2324i 0.813211 0.813211i −0.171903 0.985114i \(-0.554992\pi\)
0.985114 + 0.171903i \(0.0549916\pi\)
\(620\) 8.28171i 0.332601i
\(621\) 0 0
\(622\) −1.81804 + 1.81804i −0.0728968 + 0.0728968i
\(623\) 6.23553 0.249821
\(624\) 0 0
\(625\) −9.54134 −0.381654
\(626\) 0.808162 0.808162i 0.0323006 0.0323006i
\(627\) 0 0
\(628\) 15.2471i 0.608424i
\(629\) 14.1281 14.1281i 0.563324 0.563324i
\(630\) 0 0
\(631\) 15.8814 15.8814i 0.632228 0.632228i −0.316398 0.948626i \(-0.602474\pi\)
0.948626 + 0.316398i \(0.102474\pi\)
\(632\) −7.25671 7.25671i −0.288656 0.288656i
\(633\) 0 0
\(634\) 13.3660i 0.530830i
\(635\) −10.9629 10.9629i −0.435051 0.435051i
\(636\) 0 0
\(637\) 3.39695 + 1.20860i 0.134592 + 0.0478865i
\(638\) 40.1828i 1.59085i
\(639\) 0 0
\(640\) 1.05508 0.0417056
\(641\) 35.2108 1.39074 0.695371 0.718651i \(-0.255240\pi\)
0.695371 + 0.718651i \(0.255240\pi\)
\(642\) 0 0
\(643\) −19.8170 19.8170i −0.781505 0.781505i 0.198580 0.980085i \(-0.436367\pi\)
−0.980085 + 0.198580i \(0.936367\pi\)
\(644\) −1.69107 1.69107i −0.0666376 0.0666376i
\(645\) 0 0
\(646\) 14.4260 0.567585
\(647\) 11.6901 0.459585 0.229793 0.973240i \(-0.426195\pi\)
0.229793 + 0.973240i \(0.426195\pi\)
\(648\) 0 0
\(649\) 30.1895i 1.18504i
\(650\) −12.6579 + 6.01444i −0.496482 + 0.235906i
\(651\) 0 0
\(652\) 16.2208 + 16.2208i 0.635256 + 0.635256i
\(653\) 34.8963i 1.36560i −0.730606 0.682800i \(-0.760762\pi\)
0.730606 0.682800i \(-0.239238\pi\)
\(654\) 0 0
\(655\) 1.65737 + 1.65737i 0.0647590 + 0.0647590i
\(656\) −2.39122 + 2.39122i −0.0933616 + 0.0933616i
\(657\) 0 0
\(658\) −3.48199 + 3.48199i −0.135742 + 0.135742i
\(659\) 10.9137i 0.425136i 0.977146 + 0.212568i \(0.0681828\pi\)
−0.977146 + 0.212568i \(0.931817\pi\)
\(660\) 0 0
\(661\) 17.9445 17.9445i 0.697959 0.697959i −0.266011 0.963970i \(-0.585706\pi\)
0.963970 + 0.266011i \(0.0857056\pi\)
\(662\) 12.3954 0.481763
\(663\) 0 0
\(664\) 14.4619 0.561229
\(665\) −5.31229 + 5.31229i −0.206002 + 0.206002i
\(666\) 0 0
\(667\) 20.2364i 0.783556i
\(668\) −17.0656 + 17.0656i −0.660289 + 0.660289i
\(669\) 0 0
\(670\) −1.88554 + 1.88554i −0.0728449 + 0.0728449i
\(671\) −5.24833 5.24833i −0.202610 0.202610i
\(672\) 0 0
\(673\) 44.1565i 1.70211i −0.525078 0.851054i \(-0.675964\pi\)
0.525078 0.851054i \(-0.324036\pi\)
\(674\) −22.5070 22.5070i −0.866937 0.866937i
\(675\) 0 0
\(676\) −8.21112 + 10.0786i −0.315812 + 0.387637i
\(677\) 14.9679i 0.575262i −0.957741 0.287631i \(-0.907132\pi\)
0.957741 0.287631i \(-0.0928676\pi\)
\(678\) 0 0
\(679\) 15.6876 0.602035
\(680\) −2.13757 −0.0819720
\(681\) 0 0
\(682\) −26.3576 26.3576i −1.00928 1.00928i
\(683\) 9.38498 + 9.38498i 0.359106 + 0.359106i 0.863483 0.504377i \(-0.168278\pi\)
−0.504377 + 0.863483i \(0.668278\pi\)
\(684\) 0 0
\(685\) 0.577842 0.0220782
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) 9.24408i 0.352427i
\(689\) −4.60481 1.63835i −0.175429 0.0624160i
\(690\) 0 0
\(691\) −15.2672 15.2672i −0.580793 0.580793i 0.354328 0.935121i \(-0.384710\pi\)
−0.935121 + 0.354328i \(0.884710\pi\)
\(692\) 8.52210i 0.323961i
\(693\) 0 0
\(694\) −14.1935 14.1935i −0.538780 0.538780i
\(695\) −2.08950 + 2.08950i −0.0792594 + 0.0792594i
\(696\) 0 0
\(697\) 4.84457 4.84457i 0.183501 0.183501i
\(698\) 12.5632i 0.475525i
\(699\) 0 0
\(700\) −2.74839 + 2.74839i −0.103879 + 0.103879i
\(701\) −1.91734 −0.0724168 −0.0362084 0.999344i \(-0.511528\pi\)
−0.0362084 + 0.999344i \(0.511528\pi\)
\(702\) 0 0
\(703\) 70.2223 2.64848
\(704\) −3.35792 + 3.35792i −0.126556 + 0.126556i
\(705\) 0 0
\(706\) 18.2774i 0.687878i
\(707\) −3.13732 + 3.13732i −0.117991 + 0.117991i
\(708\) 0 0
\(709\) −35.5754 + 35.5754i −1.33606 + 1.33606i −0.436222 + 0.899839i \(0.643684\pi\)
−0.899839 + 0.436222i \(0.856316\pi\)
\(710\) −10.5081 10.5081i −0.394362 0.394362i
\(711\) 0 0
\(712\) 6.23553i 0.233686i
\(713\) 13.2739 + 13.2739i 0.497110 + 0.497110i
\(714\) 0 0
\(715\) −6.05554 + 17.0200i −0.226464 + 0.636511i
\(716\) 3.46058i 0.129328i
\(717\) 0 0
\(718\) −15.1638 −0.565907
\(719\) −3.52562 −0.131484 −0.0657418 0.997837i \(-0.520941\pi\)
−0.0657418 + 0.997837i \(0.520941\pi\)
\(720\) 0 0
\(721\) 7.02486 + 7.02486i 0.261619 + 0.261619i
\(722\) 22.4166 + 22.4166i 0.834260 + 0.834260i
\(723\) 0 0
\(724\) 24.8236 0.922563
\(725\) −32.8889 −1.22146
\(726\) 0 0
\(727\) 20.5218i 0.761112i −0.924758 0.380556i \(-0.875733\pi\)
0.924758 0.380556i \(-0.124267\pi\)
\(728\) −1.20860 + 3.39695i −0.0447937 + 0.125899i
\(729\) 0 0
\(730\) 4.11660 + 4.11660i 0.152362 + 0.152362i
\(731\) 18.7283i 0.692692i
\(732\) 0 0
\(733\) 7.62778 + 7.62778i 0.281739 + 0.281739i 0.833802 0.552064i \(-0.186159\pi\)
−0.552064 + 0.833802i \(0.686159\pi\)
\(734\) −10.3012 + 10.3012i −0.380224 + 0.380224i
\(735\) 0 0
\(736\) 1.69107 1.69107i 0.0623338 0.0623338i
\(737\) 12.0020i 0.442098i
\(738\) 0 0
\(739\) 22.0350 22.0350i 0.810572 0.810572i −0.174148 0.984720i \(-0.555717\pi\)
0.984720 + 0.174148i \(0.0557170\pi\)
\(740\) −10.4051 −0.382500
\(741\) 0 0
\(742\) −1.35557 −0.0497646
\(743\) 7.44855 7.44855i 0.273261 0.273261i −0.557151 0.830411i \(-0.688105\pi\)
0.830411 + 0.557151i \(0.188105\pi\)
\(744\) 0 0
\(745\) 1.29353i 0.0473914i
\(746\) −3.28325 + 3.28325i −0.120208 + 0.120208i
\(747\) 0 0
\(748\) 6.80307 6.80307i 0.248745 0.248745i
\(749\) −8.50295 8.50295i −0.310691 0.310691i
\(750\) 0 0
\(751\) 9.76517i 0.356336i 0.984000 + 0.178168i \(0.0570171\pi\)
−0.984000 + 0.178168i \(0.942983\pi\)
\(752\) −3.48199 3.48199i −0.126975 0.126975i
\(753\) 0 0
\(754\) −27.5564 + 13.0936i −1.00354 + 0.476839i
\(755\) 22.0601i 0.802849i
\(756\) 0 0
\(757\) 23.6708 0.860329 0.430165 0.902750i \(-0.358456\pi\)
0.430165 + 0.902750i \(0.358456\pi\)
\(758\) −9.53877 −0.346464
\(759\) 0 0
\(760\) −5.31229 5.31229i −0.192697 0.192697i
\(761\) −20.9560 20.9560i −0.759656 0.759656i 0.216604 0.976260i \(-0.430502\pi\)
−0.976260 + 0.216604i \(0.930502\pi\)
\(762\) 0 0
\(763\) −3.50468 −0.126878
\(764\) 7.86219 0.284444
\(765\) 0 0
\(766\) 1.87658i 0.0678037i
\(767\) −20.7032 + 9.83723i −0.747550 + 0.355202i
\(768\) 0 0
\(769\) 26.9775 + 26.9775i 0.972835 + 0.972835i 0.999641 0.0268055i \(-0.00853346\pi\)
−0.0268055 + 0.999641i \(0.508533\pi\)
\(770\) 5.01037i 0.180561i
\(771\) 0 0
\(772\) −4.85067 4.85067i −0.174579 0.174579i
\(773\) 22.9037 22.9037i 0.823788 0.823788i −0.162861 0.986649i \(-0.552072\pi\)
0.986649 + 0.162861i \(0.0520722\pi\)
\(774\) 0 0
\(775\) 21.5732 21.5732i 0.774931 0.774931i
\(776\) 15.6876i 0.563152i
\(777\) 0 0
\(778\) 18.3247 18.3247i 0.656974 0.656974i
\(779\) 24.0795 0.862737
\(780\) 0 0
\(781\) 66.8866 2.39339
\(782\) −3.42608 + 3.42608i −0.122516 + 0.122516i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 11.3751 11.3751i 0.405995 0.405995i
\(786\) 0 0
\(787\) 7.47326 7.47326i 0.266393 0.266393i −0.561252 0.827645i \(-0.689680\pi\)
0.827645 + 0.561252i \(0.189680\pi\)
\(788\) −9.34718 9.34718i −0.332979 0.332979i
\(789\) 0 0
\(790\) 10.8278i 0.385235i
\(791\) −13.7214 13.7214i −0.487875 0.487875i
\(792\) 0 0
\(793\) 1.88901 5.30934i 0.0670807 0.188540i
\(794\) 29.8443i 1.05913i
\(795\) 0 0
\(796\) −23.0454 −0.816824
\(797\) 23.7417 0.840973 0.420487 0.907299i \(-0.361859\pi\)
0.420487 + 0.907299i \(0.361859\pi\)
\(798\) 0 0
\(799\) 7.05445 + 7.05445i 0.249569 + 0.249569i
\(800\) −2.74839 2.74839i −0.0971702 0.0971702i
\(801\) 0 0
\(802\) 26.7714 0.945332
\(803\) −26.2032 −0.924690
\(804\) 0 0
\(805\) 2.52326i 0.0889332i
\(806\) 9.48677 26.6640i 0.334157 0.939198i
\(807\) 0 0
\(808\) −3.13732 3.13732i −0.110371 0.110371i
\(809\) 28.8848i 1.01553i 0.861494 + 0.507767i \(0.169529\pi\)
−0.861494 + 0.507767i \(0.830471\pi\)
\(810\) 0 0
\(811\) 19.3037 + 19.3037i 0.677845 + 0.677845i 0.959512 0.281667i \(-0.0908873\pi\)
−0.281667 + 0.959512i \(0.590887\pi\)
\(812\) −5.98330 + 5.98330i −0.209973 + 0.209973i
\(813\) 0 0
\(814\) 33.1156 33.1156i 1.16070 1.16070i
\(815\) 24.2032i 0.847800i
\(816\) 0 0
\(817\) 46.5437 46.5437i 1.62836 1.62836i
\(818\) −14.8422 −0.518945
\(819\) 0 0
\(820\) −3.56796 −0.124598
\(821\) −31.2406 + 31.2406i −1.09030 + 1.09030i −0.0948096 + 0.995495i \(0.530224\pi\)
−0.995495 + 0.0948096i \(0.969776\pi\)
\(822\) 0 0
\(823\) 19.6275i 0.684173i 0.939668 + 0.342086i \(0.111134\pi\)
−0.939668 + 0.342086i \(0.888866\pi\)
\(824\) −7.02486 + 7.02486i −0.244723 + 0.244723i
\(825\) 0 0
\(826\) −4.49527 + 4.49527i −0.156411 + 0.156411i
\(827\) 24.2147 + 24.2147i 0.842026 + 0.842026i 0.989122 0.147096i \(-0.0469927\pi\)
−0.147096 + 0.989122i \(0.546993\pi\)
\(828\) 0 0
\(829\) 29.0909i 1.01037i −0.863012 0.505184i \(-0.831425\pi\)
0.863012 0.505184i \(-0.168575\pi\)
\(830\) 10.7893 + 10.7893i 0.374503 + 0.374503i
\(831\) 0 0
\(832\) −3.39695 1.20860i −0.117768 0.0419007i
\(833\) 2.02598i 0.0701960i
\(834\) 0 0
\(835\) −25.4637 −0.881208
\(836\) 33.8140 1.16948
\(837\) 0 0
\(838\) −16.2308 16.2308i −0.560682 0.560682i
\(839\) −13.2912 13.2912i −0.458863 0.458863i 0.439419 0.898282i \(-0.355184\pi\)
−0.898282 + 0.439419i \(0.855184\pi\)
\(840\) 0 0
\(841\) −42.5997 −1.46895
\(842\) 28.7342 0.990247
\(843\) 0 0
\(844\) 0.931807i 0.0320741i
\(845\) −13.6451 + 1.39321i −0.469405 + 0.0479280i
\(846\) 0 0
\(847\) −8.16794 8.16794i −0.280654 0.280654i
\(848\) 1.35557i 0.0465505i
\(849\) 0 0
\(850\) 5.56818 + 5.56818i 0.190987 + 0.190987i
\(851\) −16.6773 + 16.6773i −0.571690 + 0.571690i
\(852\) 0 0
\(853\) −15.3079 + 15.3079i −0.524133 + 0.524133i −0.918817 0.394684i \(-0.870854\pi\)
0.394684 + 0.918817i \(0.370854\pi\)
\(854\) 1.56297i 0.0534838i
\(855\) 0 0
\(856\) 8.50295 8.50295i 0.290625 0.290625i
\(857\) 37.8080 1.29150 0.645749 0.763550i \(-0.276545\pi\)
0.645749 + 0.763550i \(0.276545\pi\)
\(858\) 0 0
\(859\) 22.6413 0.772512 0.386256 0.922392i \(-0.373768\pi\)
0.386256 + 0.922392i \(0.373768\pi\)
\(860\) −6.89658 + 6.89658i −0.235171 + 0.235171i
\(861\) 0 0
\(862\) 0.782576i 0.0266547i
\(863\) −29.0990 + 29.0990i −0.990543 + 0.990543i −0.999956 0.00941262i \(-0.997004\pi\)
0.00941262 + 0.999956i \(0.497004\pi\)
\(864\) 0 0
\(865\) 6.35793 6.35793i 0.216176 0.216176i
\(866\) −0.978804 0.978804i −0.0332611 0.0332611i
\(867\) 0 0
\(868\) 7.84938i 0.266425i
\(869\) 34.4607 + 34.4607i 1.16900 + 1.16900i
\(870\) 0 0
\(871\) 8.23064 3.91083i 0.278885 0.132513i
\(872\) 3.50468i 0.118684i
\(873\) 0 0
\(874\) −17.0290 −0.576015
\(875\) −9.37628 −0.316976
\(876\) 0 0
\(877\) −19.6423 19.6423i −0.663273 0.663273i 0.292877 0.956150i \(-0.405387\pi\)
−0.956150 + 0.292877i \(0.905387\pi\)
\(878\) −10.1597 10.1597i −0.342873 0.342873i
\(879\) 0 0
\(880\) −5.01037 −0.168899
\(881\) −19.3210 −0.650942 −0.325471 0.945552i \(-0.605523\pi\)
−0.325471 + 0.945552i \(0.605523\pi\)
\(882\) 0 0
\(883\) 15.1008i 0.508181i −0.967180 0.254090i \(-0.918224\pi\)
0.967180 0.254090i \(-0.0817761\pi\)
\(884\) 6.88216 + 2.44860i 0.231472 + 0.0823554i
\(885\) 0 0
\(886\) −5.14226 5.14226i −0.172758 0.172758i
\(887\) 51.8363i 1.74049i −0.492617 0.870246i \(-0.663960\pi\)
0.492617 0.870246i \(-0.336040\pi\)
\(888\) 0 0
\(889\) 10.3906 + 10.3906i 0.348491 + 0.348491i
\(890\) −4.65204 + 4.65204i −0.155937 + 0.155937i
\(891\) 0 0
\(892\) −0.806330 + 0.806330i −0.0269979 + 0.0269979i
\(893\) 35.0635i 1.17335i
\(894\) 0 0
\(895\) −2.58178 + 2.58178i −0.0862993 + 0.0862993i
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −15.7262 −0.524789
\(899\) 46.9652 46.9652i 1.56638 1.56638i
\(900\) 0 0
\(901\) 2.74636i 0.0914946i
\(902\) 11.3555 11.3555i 0.378096 0.378096i
\(903\) 0 0
\(904\) 13.7214 13.7214i 0.456365 0.456365i
\(905\) 18.5197 + 18.5197i 0.615617 + 0.615617i
\(906\) 0 0
\(907\) 50.0706i 1.66257i −0.555848 0.831284i \(-0.687606\pi\)
0.555848 0.831284i \(-0.312394\pi\)
\(908\) −2.04742 2.04742i −0.0679459 0.0679459i
\(909\) 0 0
\(910\) −3.43599 + 1.63263i −0.113902 + 0.0541210i
\(911\) 4.50281i 0.149185i 0.997214 + 0.0745924i \(0.0237656\pi\)
−0.997214 + 0.0745924i \(0.976234\pi\)
\(912\) 0 0
\(913\) −68.6767 −2.27287
\(914\) 10.2536 0.339158
\(915\) 0 0
\(916\) 12.3112 + 12.3112i 0.406774 + 0.406774i
\(917\) −1.57085 1.57085i −0.0518742 0.0518742i
\(918\) 0 0
\(919\) −18.6075 −0.613806 −0.306903 0.951741i \(-0.599293\pi\)
−0.306903 + 0.951741i \(0.599293\pi\)
\(920\) 2.52326 0.0831894
\(921\) 0 0
\(922\) 28.8769i 0.951011i
\(923\) 21.7950 + 45.8692i 0.717390 + 1.50980i
\(924\) 0 0
\(925\) 27.1045 + 27.1045i 0.891191 + 0.891191i
\(926\) 7.31096i 0.240253i
\(927\) 0 0
\(928\) −5.98330 5.98330i −0.196411 0.196411i
\(929\) 31.8475 31.8475i 1.04488 1.04488i 0.0459383 0.998944i \(-0.485372\pi\)
0.998944 0.0459383i \(-0.0146278\pi\)
\(930\) 0 0
\(931\) 5.03497 5.03497i 0.165015 0.165015i
\(932\) 24.7227i 0.809818i
\(933\) 0 0
\(934\) −11.7401 + 11.7401i −0.384147 + 0.384147i
\(935\) 10.1509 0.331970
\(936\) 0 0
\(937\) 20.3250 0.663987 0.331994 0.943282i \(-0.392279\pi\)
0.331994 + 0.943282i \(0.392279\pi\)
\(938\) 1.78711 1.78711i 0.0583513 0.0583513i
\(939\) 0 0
\(940\) 5.19550i 0.169459i
\(941\) −32.4919 + 32.4919i −1.05921 + 1.05921i −0.0610727 + 0.998133i \(0.519452\pi\)
−0.998133 + 0.0610727i \(0.980548\pi\)
\(942\) 0 0
\(943\) −5.71870 + 5.71870i −0.186226 + 0.186226i
\(944\) −4.49527 4.49527i −0.146309 0.146309i
\(945\) 0 0
\(946\) 43.8984i 1.42726i
\(947\) 14.9562 + 14.9562i 0.486013 + 0.486013i 0.907045 0.421033i \(-0.138332\pi\)
−0.421033 + 0.907045i \(0.638332\pi\)
\(948\) 0 0
\(949\) −8.53829 17.9695i −0.277165 0.583314i
\(950\) 27.6761i 0.897932i
\(951\) 0 0
\(952\) 2.02598 0.0656624
\(953\) 4.44039 0.143838 0.0719192 0.997410i \(-0.477088\pi\)
0.0719192 + 0.997410i \(0.477088\pi\)
\(954\) 0 0
\(955\) 5.86561 + 5.86561i 0.189807 + 0.189807i
\(956\) 1.69453 + 1.69453i 0.0548050 + 0.0548050i
\(957\) 0 0
\(958\) 29.3375 0.947851
\(959\) −0.547677 −0.0176854
\(960\) 0 0
\(961\) 30.6128i 0.987509i
\(962\) 33.5006 + 11.9192i 1.08010 + 0.384290i
\(963\) 0 0
\(964\) −4.52253 4.52253i −0.145661 0.145661i
\(965\) 7.23771i 0.232990i
\(966\) 0 0
\(967\) 13.2096 + 13.2096i 0.424792 + 0.424792i 0.886850 0.462058i \(-0.152889\pi\)
−0.462058 + 0.886850i \(0.652889\pi\)
\(968\) 8.16794 8.16794i 0.262528 0.262528i
\(969\) 0 0
\(970\) −11.7038 + 11.7038i −0.375786 + 0.375786i
\(971\) 26.3005i 0.844025i −0.906590 0.422012i \(-0.861324\pi\)
0.906590 0.422012i \(-0.138676\pi\)
\(972\) 0 0
\(973\) 1.98042 1.98042i 0.0634895 0.0634895i
\(974\) −7.37615 −0.236347
\(975\) 0 0
\(976\) 1.56297 0.0500295
\(977\) −35.2572 + 35.2572i −1.12798 + 1.12798i −0.137470 + 0.990506i \(0.543897\pi\)
−0.990506 + 0.137470i \(0.956103\pi\)
\(978\) 0 0
\(979\) 29.6114i 0.946383i
\(980\) −0.746053 + 0.746053i −0.0238318 + 0.0238318i
\(981\) 0 0
\(982\) −7.80634 + 7.80634i −0.249110 + 0.249110i
\(983\) −20.2759 20.2759i −0.646699 0.646699i 0.305494 0.952194i \(-0.401178\pi\)
−0.952194 + 0.305494i \(0.901178\pi\)
\(984\) 0 0
\(985\) 13.9470i 0.444388i
\(986\) 12.1220 + 12.1220i 0.386044 + 0.386044i
\(987\) 0 0
\(988\) 11.0183 + 23.1888i 0.350538 + 0.737735i
\(989\) 22.1076i 0.702980i
\(990\) 0 0
\(991\) −3.24098 −0.102953 −0.0514765 0.998674i \(-0.516393\pi\)
−0.0514765 + 0.998674i \(0.516393\pi\)
\(992\) 7.84938 0.249218
\(993\) 0 0
\(994\) 9.95954 + 9.95954i 0.315897 + 0.315897i
\(995\) −17.1931 17.1931i −0.545059 0.545059i
\(996\) 0 0
\(997\) 19.8807 0.629629 0.314814 0.949153i \(-0.398058\pi\)
0.314814 + 0.949153i \(0.398058\pi\)
\(998\) 5.04723 0.159767
\(999\) 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 1638.2.y.c.827.7 16
3.2 odd 2 1638.2.y.d.827.2 yes 16
13.5 odd 4 1638.2.y.d.1331.2 yes 16
39.5 even 4 inner 1638.2.y.c.1331.7 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1638.2.y.c.827.7 16 1.1 even 1 trivial
1638.2.y.c.1331.7 yes 16 39.5 even 4 inner
1638.2.y.d.827.2 yes 16 3.2 odd 2
1638.2.y.d.1331.2 yes 16 13.5 odd 4