Properties

Label 252.4.b.e.55.11
Level $252$
Weight $4$
Character 252.55
Analytic conductor $14.868$
Analytic rank $0$
Dimension $12$
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] = [252,4,Mod(55,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.55");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.b (of order \(2\), degree \(1\), 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: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.11
Root \(-2.78362 + 0.501431i\) of defining polynomial
Character \(\chi\) \(=\) 252.55
Dual form 252.4.b.e.55.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.78362 - 0.501431i) q^{2} +(7.49713 - 2.79159i) q^{4} +4.57514i q^{5} +(-2.93118 - 18.2868i) q^{7} +(19.4694 - 11.5300i) q^{8} +O(q^{10})\) \(q+(2.78362 - 0.501431i) q^{2} +(7.49713 - 2.79159i) q^{4} +4.57514i q^{5} +(-2.93118 - 18.2868i) q^{7} +(19.4694 - 11.5300i) q^{8} +(2.29411 + 12.7355i) q^{10} -26.0206i q^{11} -75.0905i q^{13} +(-17.3289 - 49.4339i) q^{14} +(48.4141 - 41.8578i) q^{16} +115.976i q^{17} +119.051 q^{19} +(12.7719 + 34.3004i) q^{20} +(-13.0475 - 72.4315i) q^{22} -61.4339i q^{23} +104.068 q^{25} +(-37.6527 - 209.024i) q^{26} +(-73.0248 - 128.916i) q^{28} +71.9146 q^{29} -231.587 q^{31} +(113.778 - 140.793i) q^{32} +(58.1538 + 322.833i) q^{34} +(83.6647 - 13.4106i) q^{35} +13.3306 q^{37} +(331.392 - 59.6956i) q^{38} +(52.7515 + 89.0753i) q^{40} -144.133i q^{41} +288.638i q^{43} +(-72.6387 - 195.080i) q^{44} +(-30.8049 - 171.009i) q^{46} -343.549 q^{47} +(-325.816 + 107.204i) q^{49} +(289.687 - 52.1829i) q^{50} +(-209.622 - 562.963i) q^{52} -142.666 q^{53} +119.048 q^{55} +(-267.916 - 322.237i) q^{56} +(200.183 - 36.0602i) q^{58} +403.919 q^{59} -21.7765i q^{61} +(-644.651 + 116.125i) q^{62} +(246.117 - 448.966i) q^{64} +343.549 q^{65} +598.674i q^{67} +(323.757 + 869.486i) q^{68} +(226.167 - 79.2821i) q^{70} +589.524i q^{71} +6.85314i q^{73} +(37.1075 - 6.68439i) q^{74} +(892.538 - 332.340i) q^{76} +(-475.834 + 76.2711i) q^{77} +972.231i q^{79} +(191.505 + 221.501i) q^{80} +(-72.2726 - 401.212i) q^{82} -429.745 q^{83} -530.605 q^{85} +(144.732 + 803.461i) q^{86} +(-300.018 - 506.605i) q^{88} -1083.91i q^{89} +(-1373.17 + 220.104i) q^{91} +(-171.498 - 460.578i) q^{92} +(-956.312 + 172.266i) q^{94} +544.673i q^{95} +1031.01i q^{97} +(-853.195 + 461.790i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8} - 56 q^{10} - 101 q^{14} + 41 q^{16} + 84 q^{19} + 172 q^{20} - 182 q^{22} - 216 q^{25} + 300 q^{26} - 379 q^{28} - 200 q^{29} + 384 q^{31} + 159 q^{32} + 164 q^{34} + 84 q^{35} - 244 q^{37} + 268 q^{38} + 316 q^{40} - 190 q^{44} + 894 q^{46} + 280 q^{47} - 424 q^{49} + 1771 q^{50} + 796 q^{52} + 16 q^{53} - 212 q^{55} + 1759 q^{56} - 570 q^{58} + 1168 q^{59} - 384 q^{62} + 2705 q^{64} - 280 q^{65} + 1552 q^{68} + 2592 q^{70} - 1622 q^{74} + 788 q^{76} - 968 q^{77} - 3060 q^{80} + 2540 q^{82} - 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} - 1648 q^{91} - 4298 q^{92} - 4256 q^{94} - 3137 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.78362 0.501431i 0.984160 0.177282i
\(3\) 0 0
\(4\) 7.49713 2.79159i 0.937142 0.348949i
\(5\) 4.57514i 0.409213i 0.978844 + 0.204606i \(0.0655914\pi\)
−0.978844 + 0.204606i \(0.934409\pi\)
\(6\) 0 0
\(7\) −2.93118 18.2868i −0.158269 0.987396i
\(8\) 19.4694 11.5300i 0.860435 0.509560i
\(9\) 0 0
\(10\) 2.29411 + 12.7355i 0.0725462 + 0.402731i
\(11\) 26.0206i 0.713227i −0.934252 0.356613i \(-0.883931\pi\)
0.934252 0.356613i \(-0.116069\pi\)
\(12\) 0 0
\(13\) 75.0905i 1.60203i −0.598647 0.801013i \(-0.704295\pi\)
0.598647 0.801013i \(-0.295705\pi\)
\(14\) −17.3289 49.4339i −0.330810 0.943697i
\(15\) 0 0
\(16\) 48.4141 41.8578i 0.756470 0.654029i
\(17\) 115.976i 1.65460i 0.561758 + 0.827302i \(0.310125\pi\)
−0.561758 + 0.827302i \(0.689875\pi\)
\(18\) 0 0
\(19\) 119.051 1.43748 0.718739 0.695280i \(-0.244720\pi\)
0.718739 + 0.695280i \(0.244720\pi\)
\(20\) 12.7719 + 34.3004i 0.142794 + 0.383490i
\(21\) 0 0
\(22\) −13.0475 72.4315i −0.126443 0.701929i
\(23\) 61.4339i 0.556950i −0.960443 0.278475i \(-0.910171\pi\)
0.960443 0.278475i \(-0.0898290\pi\)
\(24\) 0 0
\(25\) 104.068 0.832545
\(26\) −37.6527 209.024i −0.284011 1.57665i
\(27\) 0 0
\(28\) −73.0248 128.916i −0.492871 0.870102i
\(29\) 71.9146 0.460490 0.230245 0.973133i \(-0.426047\pi\)
0.230245 + 0.973133i \(0.426047\pi\)
\(30\) 0 0
\(31\) −231.587 −1.34175 −0.670875 0.741571i \(-0.734081\pi\)
−0.670875 + 0.741571i \(0.734081\pi\)
\(32\) 113.778 140.793i 0.628539 0.777778i
\(33\) 0 0
\(34\) 58.1538 + 322.833i 0.293332 + 1.62839i
\(35\) 83.6647 13.4106i 0.404055 0.0647657i
\(36\) 0 0
\(37\) 13.3306 0.0592309 0.0296155 0.999561i \(-0.490572\pi\)
0.0296155 + 0.999561i \(0.490572\pi\)
\(38\) 331.392 59.6956i 1.41471 0.254840i
\(39\) 0 0
\(40\) 52.7515 + 89.0753i 0.208518 + 0.352101i
\(41\) 144.133i 0.549018i −0.961584 0.274509i \(-0.911485\pi\)
0.961584 0.274509i \(-0.0885154\pi\)
\(42\) 0 0
\(43\) 288.638i 1.02365i 0.859090 + 0.511825i \(0.171030\pi\)
−0.859090 + 0.511825i \(0.828970\pi\)
\(44\) −72.6387 195.080i −0.248880 0.668395i
\(45\) 0 0
\(46\) −30.8049 171.009i −0.0987376 0.548128i
\(47\) −343.549 −1.06621 −0.533104 0.846050i \(-0.678975\pi\)
−0.533104 + 0.846050i \(0.678975\pi\)
\(48\) 0 0
\(49\) −325.816 + 107.204i −0.949902 + 0.312548i
\(50\) 289.687 52.1829i 0.819357 0.147596i
\(51\) 0 0
\(52\) −209.622 562.963i −0.559025 1.50133i
\(53\) −142.666 −0.369749 −0.184875 0.982762i \(-0.559188\pi\)
−0.184875 + 0.982762i \(0.559188\pi\)
\(54\) 0 0
\(55\) 119.048 0.291861
\(56\) −267.916 322.237i −0.639318 0.768943i
\(57\) 0 0
\(58\) 200.183 36.0602i 0.453196 0.0816368i
\(59\) 403.919 0.891284 0.445642 0.895211i \(-0.352975\pi\)
0.445642 + 0.895211i \(0.352975\pi\)
\(60\) 0 0
\(61\) 21.7765i 0.0457082i −0.999739 0.0228541i \(-0.992725\pi\)
0.999739 0.0228541i \(-0.00727532\pi\)
\(62\) −644.651 + 116.125i −1.32050 + 0.237869i
\(63\) 0 0
\(64\) 246.117 448.966i 0.480697 0.876887i
\(65\) 343.549 0.655570
\(66\) 0 0
\(67\) 598.674i 1.09164i 0.837904 + 0.545818i \(0.183781\pi\)
−0.837904 + 0.545818i \(0.816219\pi\)
\(68\) 323.757 + 869.486i 0.577372 + 1.55060i
\(69\) 0 0
\(70\) 226.167 79.2821i 0.386173 0.135372i
\(71\) 589.524i 0.985403i 0.870198 + 0.492701i \(0.163991\pi\)
−0.870198 + 0.492701i \(0.836009\pi\)
\(72\) 0 0
\(73\) 6.85314i 0.0109877i 0.999985 + 0.00549383i \(0.00174875\pi\)
−0.999985 + 0.00549383i \(0.998251\pi\)
\(74\) 37.1075 6.68439i 0.0582927 0.0105006i
\(75\) 0 0
\(76\) 892.538 332.340i 1.34712 0.501606i
\(77\) −475.834 + 76.2711i −0.704237 + 0.112882i
\(78\) 0 0
\(79\) 972.231i 1.38461i 0.721603 + 0.692307i \(0.243406\pi\)
−0.721603 + 0.692307i \(0.756594\pi\)
\(80\) 191.505 + 221.501i 0.267637 + 0.309557i
\(81\) 0 0
\(82\) −72.2726 401.212i −0.0973313 0.540322i
\(83\) −429.745 −0.568321 −0.284161 0.958777i \(-0.591715\pi\)
−0.284161 + 0.958777i \(0.591715\pi\)
\(84\) 0 0
\(85\) −530.605 −0.677085
\(86\) 144.732 + 803.461i 0.181475 + 1.00743i
\(87\) 0 0
\(88\) −300.018 506.605i −0.363432 0.613685i
\(89\) 1083.91i 1.29095i −0.763781 0.645476i \(-0.776659\pi\)
0.763781 0.645476i \(-0.223341\pi\)
\(90\) 0 0
\(91\) −1373.17 + 220.104i −1.58183 + 0.253551i
\(92\) −171.498 460.578i −0.194347 0.521942i
\(93\) 0 0
\(94\) −956.312 + 172.266i −1.04932 + 0.189020i
\(95\) 544.673i 0.588234i
\(96\) 0 0
\(97\) 1031.01i 1.07921i 0.841920 + 0.539603i \(0.181426\pi\)
−0.841920 + 0.539603i \(0.818574\pi\)
\(98\) −853.195 + 461.790i −0.879446 + 0.475999i
\(99\) 0 0
\(100\) 780.213 290.515i 0.780213 0.290515i
\(101\) 207.988i 0.204907i 0.994738 + 0.102454i \(0.0326693\pi\)
−0.994738 + 0.102454i \(0.967331\pi\)
\(102\) 0 0
\(103\) 1229.81 1.17647 0.588237 0.808689i \(-0.299822\pi\)
0.588237 + 0.808689i \(0.299822\pi\)
\(104\) −865.795 1461.97i −0.816329 1.37844i
\(105\) 0 0
\(106\) −397.129 + 71.5372i −0.363892 + 0.0655500i
\(107\) 1502.68i 1.35766i 0.734294 + 0.678832i \(0.237513\pi\)
−0.734294 + 0.678832i \(0.762487\pi\)
\(108\) 0 0
\(109\) 579.301 0.509055 0.254527 0.967066i \(-0.418080\pi\)
0.254527 + 0.967066i \(0.418080\pi\)
\(110\) 331.384 59.6941i 0.287238 0.0517419i
\(111\) 0 0
\(112\) −907.358 762.647i −0.765511 0.643423i
\(113\) −614.637 −0.511683 −0.255842 0.966719i \(-0.582353\pi\)
−0.255842 + 0.966719i \(0.582353\pi\)
\(114\) 0 0
\(115\) 281.069 0.227911
\(116\) 539.153 200.756i 0.431544 0.160687i
\(117\) 0 0
\(118\) 1124.36 202.537i 0.877166 0.158009i
\(119\) 2120.83 339.946i 1.63375 0.261873i
\(120\) 0 0
\(121\) 653.930 0.491308
\(122\) −10.9194 60.6177i −0.00810327 0.0449842i
\(123\) 0 0
\(124\) −1736.24 + 646.496i −1.25741 + 0.468202i
\(125\) 1048.02i 0.749901i
\(126\) 0 0
\(127\) 273.874i 0.191358i −0.995412 0.0956788i \(-0.969498\pi\)
0.995412 0.0956788i \(-0.0305022\pi\)
\(128\) 459.972 1373.16i 0.317626 0.948216i
\(129\) 0 0
\(130\) 956.312 172.266i 0.645185 0.116221i
\(131\) −2187.84 −1.45918 −0.729591 0.683884i \(-0.760290\pi\)
−0.729591 + 0.683884i \(0.760290\pi\)
\(132\) 0 0
\(133\) −348.959 2177.06i −0.227508 1.41936i
\(134\) 300.193 + 1666.48i 0.193528 + 1.07434i
\(135\) 0 0
\(136\) 1337.20 + 2257.98i 0.843120 + 1.42368i
\(137\) 2535.39 1.58112 0.790558 0.612388i \(-0.209791\pi\)
0.790558 + 0.612388i \(0.209791\pi\)
\(138\) 0 0
\(139\) −1007.32 −0.614675 −0.307338 0.951601i \(-0.599438\pi\)
−0.307338 + 0.951601i \(0.599438\pi\)
\(140\) 589.809 334.098i 0.356057 0.201689i
\(141\) 0 0
\(142\) 295.605 + 1641.01i 0.174695 + 0.969794i
\(143\) −1953.90 −1.14261
\(144\) 0 0
\(145\) 329.019i 0.188438i
\(146\) 3.43637 + 19.0766i 0.00194792 + 0.0108136i
\(147\) 0 0
\(148\) 99.9416 37.2137i 0.0555078 0.0206686i
\(149\) −2342.59 −1.28800 −0.644002 0.765024i \(-0.722727\pi\)
−0.644002 + 0.765024i \(0.722727\pi\)
\(150\) 0 0
\(151\) 561.022i 0.302353i 0.988507 + 0.151177i \(0.0483062\pi\)
−0.988507 + 0.151177i \(0.951694\pi\)
\(152\) 2317.85 1372.66i 1.23686 0.732481i
\(153\) 0 0
\(154\) −1286.30 + 450.908i −0.673070 + 0.235943i
\(155\) 1059.54i 0.549061i
\(156\) 0 0
\(157\) 459.220i 0.233438i −0.993165 0.116719i \(-0.962762\pi\)
0.993165 0.116719i \(-0.0372377\pi\)
\(158\) 487.506 + 2706.33i 0.245468 + 1.36268i
\(159\) 0 0
\(160\) 644.146 + 520.549i 0.318277 + 0.257206i
\(161\) −1123.43 + 180.074i −0.549931 + 0.0881480i
\(162\) 0 0
\(163\) 558.186i 0.268224i 0.990966 + 0.134112i \(0.0428182\pi\)
−0.990966 + 0.134112i \(0.957182\pi\)
\(164\) −402.359 1080.58i −0.191579 0.514508i
\(165\) 0 0
\(166\) −1196.25 + 215.487i −0.559319 + 0.100753i
\(167\) 2494.32 1.15579 0.577893 0.816113i \(-0.303875\pi\)
0.577893 + 0.816113i \(0.303875\pi\)
\(168\) 0 0
\(169\) −3441.58 −1.56649
\(170\) −1477.01 + 266.062i −0.666360 + 0.120035i
\(171\) 0 0
\(172\) 805.760 + 2163.96i 0.357201 + 0.959305i
\(173\) 2881.62i 1.26639i 0.773993 + 0.633195i \(0.218257\pi\)
−0.773993 + 0.633195i \(0.781743\pi\)
\(174\) 0 0
\(175\) −305.043 1903.08i −0.131766 0.822052i
\(176\) −1089.16 1259.76i −0.466471 0.539534i
\(177\) 0 0
\(178\) −543.508 3017.21i −0.228863 1.27050i
\(179\) 2072.63i 0.865452i 0.901525 + 0.432726i \(0.142448\pi\)
−0.901525 + 0.432726i \(0.857552\pi\)
\(180\) 0 0
\(181\) 2764.12i 1.13511i −0.823335 0.567556i \(-0.807889\pi\)
0.823335 0.567556i \(-0.192111\pi\)
\(182\) −3712.01 + 1301.23i −1.51183 + 0.529967i
\(183\) 0 0
\(184\) −708.335 1196.08i −0.283800 0.479220i
\(185\) 60.9895i 0.0242380i
\(186\) 0 0
\(187\) 3017.76 1.18011
\(188\) −2575.63 + 959.048i −0.999188 + 0.372052i
\(189\) 0 0
\(190\) 273.115 + 1516.16i 0.104284 + 0.578916i
\(191\) 4118.94i 1.56040i −0.625530 0.780200i \(-0.715117\pi\)
0.625530 0.780200i \(-0.284883\pi\)
\(192\) 0 0
\(193\) 4537.82 1.69243 0.846216 0.532840i \(-0.178875\pi\)
0.846216 + 0.532840i \(0.178875\pi\)
\(194\) 516.979 + 2869.94i 0.191324 + 1.06211i
\(195\) 0 0
\(196\) −2143.42 + 1713.27i −0.781129 + 0.624369i
\(197\) −846.178 −0.306029 −0.153014 0.988224i \(-0.548898\pi\)
−0.153014 + 0.988224i \(0.548898\pi\)
\(198\) 0 0
\(199\) 1218.87 0.434188 0.217094 0.976151i \(-0.430342\pi\)
0.217094 + 0.976151i \(0.430342\pi\)
\(200\) 2026.15 1199.91i 0.716351 0.424232i
\(201\) 0 0
\(202\) 104.292 + 578.962i 0.0363265 + 0.201661i
\(203\) −210.795 1315.09i −0.0728813 0.454686i
\(204\) 0 0
\(205\) 659.427 0.224665
\(206\) 3423.33 616.664i 1.15784 0.208568i
\(207\) 0 0
\(208\) −3143.12 3635.43i −1.04777 1.21188i
\(209\) 3097.76i 1.02525i
\(210\) 0 0
\(211\) 5064.81i 1.65249i −0.563308 0.826247i \(-0.690472\pi\)
0.563308 0.826247i \(-0.309528\pi\)
\(212\) −1069.59 + 398.265i −0.346507 + 0.129023i
\(213\) 0 0
\(214\) 753.492 + 4182.91i 0.240690 + 1.33616i
\(215\) −1320.56 −0.418890
\(216\) 0 0
\(217\) 678.824 + 4234.99i 0.212357 + 1.32484i
\(218\) 1612.56 290.479i 0.500992 0.0902465i
\(219\) 0 0
\(220\) 892.516 332.332i 0.273516 0.101845i
\(221\) 8708.67 2.65072
\(222\) 0 0
\(223\) −3894.06 −1.16935 −0.584676 0.811267i \(-0.698778\pi\)
−0.584676 + 0.811267i \(0.698778\pi\)
\(224\) −2908.16 1667.95i −0.867453 0.497519i
\(225\) 0 0
\(226\) −1710.92 + 308.198i −0.503578 + 0.0907124i
\(227\) 1165.95 0.340910 0.170455 0.985365i \(-0.445476\pi\)
0.170455 + 0.985365i \(0.445476\pi\)
\(228\) 0 0
\(229\) 2537.92i 0.732361i 0.930544 + 0.366181i \(0.119335\pi\)
−0.930544 + 0.366181i \(0.880665\pi\)
\(230\) 782.390 140.936i 0.224301 0.0404047i
\(231\) 0 0
\(232\) 1400.14 829.177i 0.396221 0.234647i
\(233\) −1345.53 −0.378321 −0.189160 0.981946i \(-0.560577\pi\)
−0.189160 + 0.981946i \(0.560577\pi\)
\(234\) 0 0
\(235\) 1571.78i 0.436306i
\(236\) 3028.24 1127.58i 0.835260 0.311012i
\(237\) 0 0
\(238\) 5733.13 2009.73i 1.56144 0.547360i
\(239\) 6239.81i 1.68878i −0.535725 0.844392i \(-0.679962\pi\)
0.535725 0.844392i \(-0.320038\pi\)
\(240\) 0 0
\(241\) 4546.01i 1.21508i 0.794289 + 0.607540i \(0.207844\pi\)
−0.794289 + 0.607540i \(0.792156\pi\)
\(242\) 1820.30 327.901i 0.483525 0.0871002i
\(243\) 0 0
\(244\) −60.7912 163.262i −0.0159498 0.0428351i
\(245\) −490.474 1490.65i −0.127899 0.388712i
\(246\) 0 0
\(247\) 8939.56i 2.30288i
\(248\) −4508.86 + 2670.20i −1.15449 + 0.683702i
\(249\) 0 0
\(250\) 525.508 + 2917.29i 0.132944 + 0.738022i
\(251\) 6775.91 1.70395 0.851976 0.523582i \(-0.175404\pi\)
0.851976 + 0.523582i \(0.175404\pi\)
\(252\) 0 0
\(253\) −1598.55 −0.397232
\(254\) −137.329 762.363i −0.0339243 0.188326i
\(255\) 0 0
\(256\) 591.842 4053.02i 0.144493 0.989506i
\(257\) 7170.16i 1.74032i −0.492770 0.870160i \(-0.664016\pi\)
0.492770 0.870160i \(-0.335984\pi\)
\(258\) 0 0
\(259\) −39.0746 243.775i −0.00937442 0.0584844i
\(260\) 2575.63 959.048i 0.614362 0.228760i
\(261\) 0 0
\(262\) −6090.14 + 1097.05i −1.43607 + 0.258687i
\(263\) 2093.31i 0.490795i −0.969422 0.245398i \(-0.921081\pi\)
0.969422 0.245398i \(-0.0789185\pi\)
\(264\) 0 0
\(265\) 652.717i 0.151306i
\(266\) −2063.01 5885.13i −0.475532 1.35654i
\(267\) 0 0
\(268\) 1671.25 + 4488.34i 0.380925 + 1.02302i
\(269\) 1573.92i 0.356742i −0.983963 0.178371i \(-0.942917\pi\)
0.983963 0.178371i \(-0.0570828\pi\)
\(270\) 0 0
\(271\) 1974.18 0.442519 0.221260 0.975215i \(-0.428983\pi\)
0.221260 + 0.975215i \(0.428983\pi\)
\(272\) 4854.50 + 5614.86i 1.08216 + 1.25166i
\(273\) 0 0
\(274\) 7057.57 1271.32i 1.55607 0.280304i
\(275\) 2707.91i 0.593793i
\(276\) 0 0
\(277\) 4758.46 1.03216 0.516079 0.856541i \(-0.327391\pi\)
0.516079 + 0.856541i \(0.327391\pi\)
\(278\) −2804.00 + 505.102i −0.604939 + 0.108971i
\(279\) 0 0
\(280\) 1474.28 1225.75i 0.314661 0.261617i
\(281\) −1753.46 −0.372252 −0.186126 0.982526i \(-0.559593\pi\)
−0.186126 + 0.982526i \(0.559593\pi\)
\(282\) 0 0
\(283\) 3603.19 0.756846 0.378423 0.925633i \(-0.376466\pi\)
0.378423 + 0.925633i \(0.376466\pi\)
\(284\) 1645.71 + 4419.74i 0.343855 + 0.923462i
\(285\) 0 0
\(286\) −5438.91 + 979.743i −1.12451 + 0.202564i
\(287\) −2635.73 + 422.480i −0.542099 + 0.0868926i
\(288\) 0 0
\(289\) −8537.38 −1.73771
\(290\) 164.980 + 915.865i 0.0334068 + 0.185453i
\(291\) 0 0
\(292\) 19.1311 + 51.3789i 0.00383413 + 0.0102970i
\(293\) 8854.04i 1.76539i 0.469949 + 0.882693i \(0.344272\pi\)
−0.469949 + 0.882693i \(0.655728\pi\)
\(294\) 0 0
\(295\) 1847.98i 0.364725i
\(296\) 259.540 153.703i 0.0509644 0.0301817i
\(297\) 0 0
\(298\) −6520.90 + 1174.65i −1.26760 + 0.228341i
\(299\) −4613.10 −0.892249
\(300\) 0 0
\(301\) 5278.28 846.052i 1.01075 0.162012i
\(302\) 281.314 + 1561.68i 0.0536019 + 0.297564i
\(303\) 0 0
\(304\) 5763.72 4983.20i 1.08741 0.940152i
\(305\) 99.6307 0.0187044
\(306\) 0 0
\(307\) −4372.30 −0.812836 −0.406418 0.913687i \(-0.633222\pi\)
−0.406418 + 0.913687i \(0.633222\pi\)
\(308\) −3354.47 + 1900.15i −0.620580 + 0.351529i
\(309\) 0 0
\(310\) −531.287 2949.37i −0.0973389 0.540364i
\(311\) −1956.21 −0.356676 −0.178338 0.983969i \(-0.557072\pi\)
−0.178338 + 0.983969i \(0.557072\pi\)
\(312\) 0 0
\(313\) 6314.07i 1.14023i −0.821565 0.570115i \(-0.806899\pi\)
0.821565 0.570115i \(-0.193101\pi\)
\(314\) −230.267 1278.30i −0.0413844 0.229740i
\(315\) 0 0
\(316\) 2714.07 + 7288.95i 0.483159 + 1.29758i
\(317\) −4962.78 −0.879298 −0.439649 0.898170i \(-0.644897\pi\)
−0.439649 + 0.898170i \(0.644897\pi\)
\(318\) 0 0
\(319\) 1871.26i 0.328434i
\(320\) 2054.08 + 1126.02i 0.358833 + 0.196707i
\(321\) 0 0
\(322\) −3036.92 + 1064.58i −0.525593 + 0.184245i
\(323\) 13807.0i 2.37846i
\(324\) 0 0
\(325\) 7814.52i 1.33376i
\(326\) 279.892 + 1553.78i 0.0475514 + 0.263976i
\(327\) 0 0
\(328\) −1661.86 2806.18i −0.279758 0.472395i
\(329\) 1007.01 + 6282.42i 0.168748 + 1.05277i
\(330\) 0 0
\(331\) 6941.96i 1.15276i 0.817181 + 0.576381i \(0.195536\pi\)
−0.817181 + 0.576381i \(0.804464\pi\)
\(332\) −3221.86 + 1199.67i −0.532598 + 0.198315i
\(333\) 0 0
\(334\) 6943.25 1250.73i 1.13748 0.204900i
\(335\) −2739.01 −0.446711
\(336\) 0 0
\(337\) −1809.91 −0.292558 −0.146279 0.989243i \(-0.546730\pi\)
−0.146279 + 0.989243i \(0.546730\pi\)
\(338\) −9580.06 + 1725.71i −1.54168 + 0.277711i
\(339\) 0 0
\(340\) −3978.02 + 1481.23i −0.634524 + 0.236268i
\(341\) 6026.02i 0.956972i
\(342\) 0 0
\(343\) 2915.45 + 5643.91i 0.458949 + 0.888463i
\(344\) 3328.01 + 5619.62i 0.521611 + 0.880784i
\(345\) 0 0
\(346\) 1444.93 + 8021.34i 0.224509 + 1.24633i
\(347\) 3542.86i 0.548100i 0.961716 + 0.274050i \(0.0883633\pi\)
−0.961716 + 0.274050i \(0.911637\pi\)
\(348\) 0 0
\(349\) 1318.04i 0.202158i 0.994878 + 0.101079i \(0.0322295\pi\)
−0.994878 + 0.101079i \(0.967771\pi\)
\(350\) −1803.39 5144.49i −0.275414 0.785671i
\(351\) 0 0
\(352\) −3663.51 2960.56i −0.554732 0.448291i
\(353\) 1254.21i 0.189107i −0.995520 0.0945534i \(-0.969858\pi\)
0.995520 0.0945534i \(-0.0301423\pi\)
\(354\) 0 0
\(355\) −2697.15 −0.403239
\(356\) −3025.84 8126.25i −0.450476 1.20980i
\(357\) 0 0
\(358\) 1039.28 + 5769.44i 0.153430 + 0.851743i
\(359\) 2350.70i 0.345585i 0.984958 + 0.172793i \(0.0552791\pi\)
−0.984958 + 0.172793i \(0.944721\pi\)
\(360\) 0 0
\(361\) 7314.03 1.06634
\(362\) −1386.01 7694.26i −0.201235 1.11713i
\(363\) 0 0
\(364\) −9680.37 + 5483.47i −1.39393 + 0.789593i
\(365\) −31.3540 −0.00449629
\(366\) 0 0
\(367\) −2941.18 −0.418333 −0.209167 0.977880i \(-0.567075\pi\)
−0.209167 + 0.977880i \(0.567075\pi\)
\(368\) −2571.49 2974.27i −0.364262 0.421316i
\(369\) 0 0
\(370\) 30.5820 + 169.772i 0.00429698 + 0.0238541i
\(371\) 418.181 + 2608.91i 0.0585198 + 0.365089i
\(372\) 0 0
\(373\) −7367.26 −1.02269 −0.511343 0.859377i \(-0.670852\pi\)
−0.511343 + 0.859377i \(0.670852\pi\)
\(374\) 8400.30 1513.19i 1.16141 0.209212i
\(375\) 0 0
\(376\) −6688.70 + 3961.13i −0.917403 + 0.543297i
\(377\) 5400.10i 0.737717i
\(378\) 0 0
\(379\) 8022.57i 1.08731i 0.839308 + 0.543657i \(0.182961\pi\)
−0.839308 + 0.543657i \(0.817039\pi\)
\(380\) 1520.50 + 4083.48i 0.205263 + 0.551259i
\(381\) 0 0
\(382\) −2065.36 11465.6i −0.276632 1.53568i
\(383\) 13469.5 1.79702 0.898511 0.438950i \(-0.144650\pi\)
0.898511 + 0.438950i \(0.144650\pi\)
\(384\) 0 0
\(385\) −348.950 2177.00i −0.0461926 0.288183i
\(386\) 12631.6 2275.40i 1.66562 0.300039i
\(387\) 0 0
\(388\) 2878.15 + 7729.61i 0.376588 + 1.01137i
\(389\) 642.221 0.0837067 0.0418533 0.999124i \(-0.486674\pi\)
0.0418533 + 0.999124i \(0.486674\pi\)
\(390\) 0 0
\(391\) 7124.85 0.921532
\(392\) −5107.39 + 5843.87i −0.658067 + 0.752960i
\(393\) 0 0
\(394\) −2355.44 + 424.299i −0.301181 + 0.0542535i
\(395\) −4448.09 −0.566602
\(396\) 0 0
\(397\) 6101.12i 0.771301i 0.922645 + 0.385650i \(0.126023\pi\)
−0.922645 + 0.385650i \(0.873977\pi\)
\(398\) 3392.88 611.179i 0.427311 0.0769740i
\(399\) 0 0
\(400\) 5038.36 4356.07i 0.629795 0.544508i
\(401\) −6300.98 −0.784679 −0.392339 0.919821i \(-0.628334\pi\)
−0.392339 + 0.919821i \(0.628334\pi\)
\(402\) 0 0
\(403\) 17390.0i 2.14952i
\(404\) 580.618 + 1559.32i 0.0715021 + 0.192027i
\(405\) 0 0
\(406\) −1246.20 3555.02i −0.152335 0.434563i
\(407\) 346.871i 0.0422451i
\(408\) 0 0
\(409\) 897.858i 0.108548i −0.998526 0.0542741i \(-0.982716\pi\)
0.998526 0.0542741i \(-0.0172845\pi\)
\(410\) 1835.60 330.657i 0.221107 0.0398292i
\(411\) 0 0
\(412\) 9220.05 3433.12i 1.10252 0.410529i
\(413\) −1183.96 7386.40i −0.141063 0.880051i
\(414\) 0 0
\(415\) 1966.14i 0.232564i
\(416\) −10572.2 8543.63i −1.24602 1.00694i
\(417\) 0 0
\(418\) −1553.31 8623.01i −0.181758 1.00901i
\(419\) −8654.42 −1.00906 −0.504530 0.863394i \(-0.668334\pi\)
−0.504530 + 0.863394i \(0.668334\pi\)
\(420\) 0 0
\(421\) −13325.5 −1.54263 −0.771313 0.636456i \(-0.780400\pi\)
−0.771313 + 0.636456i \(0.780400\pi\)
\(422\) −2539.65 14098.5i −0.292958 1.62632i
\(423\) 0 0
\(424\) −2777.63 + 1644.94i −0.318145 + 0.188409i
\(425\) 12069.4i 1.37753i
\(426\) 0 0
\(427\) −398.224 + 63.8311i −0.0451321 + 0.00723420i
\(428\) 4194.88 + 11265.8i 0.473755 + 1.27232i
\(429\) 0 0
\(430\) −3675.94 + 662.169i −0.412255 + 0.0742619i
\(431\) 4512.65i 0.504332i 0.967684 + 0.252166i \(0.0811428\pi\)
−0.967684 + 0.252166i \(0.918857\pi\)
\(432\) 0 0
\(433\) 4597.71i 0.510282i 0.966904 + 0.255141i \(0.0821219\pi\)
−0.966904 + 0.255141i \(0.917878\pi\)
\(434\) 4013.15 + 11448.2i 0.443864 + 1.26621i
\(435\) 0 0
\(436\) 4343.10 1617.17i 0.477057 0.177634i
\(437\) 7313.74i 0.800604i
\(438\) 0 0
\(439\) −14584.7 −1.58562 −0.792811 0.609467i \(-0.791383\pi\)
−0.792811 + 0.609467i \(0.791383\pi\)
\(440\) 2317.79 1372.62i 0.251128 0.148721i
\(441\) 0 0
\(442\) 24241.7 4366.80i 2.60873 0.469926i
\(443\) 10578.3i 1.13452i 0.823539 + 0.567259i \(0.191996\pi\)
−0.823539 + 0.567259i \(0.808004\pi\)
\(444\) 0 0
\(445\) 4959.06 0.528274
\(446\) −10839.6 + 1952.60i −1.15083 + 0.207306i
\(447\) 0 0
\(448\) −8931.58 3184.69i −0.941914 0.335854i
\(449\) 833.584 0.0876152 0.0438076 0.999040i \(-0.486051\pi\)
0.0438076 + 0.999040i \(0.486051\pi\)
\(450\) 0 0
\(451\) −3750.42 −0.391575
\(452\) −4608.02 + 1715.81i −0.479520 + 0.178551i
\(453\) 0 0
\(454\) 3245.56 584.642i 0.335510 0.0604375i
\(455\) −1007.01 6282.42i −0.103756 0.647307i
\(456\) 0 0
\(457\) −6462.47 −0.661492 −0.330746 0.943720i \(-0.607300\pi\)
−0.330746 + 0.943720i \(0.607300\pi\)
\(458\) 1272.59 + 7064.63i 0.129835 + 0.720761i
\(459\) 0 0
\(460\) 2107.21 784.628i 0.213585 0.0795293i
\(461\) 10142.3i 1.02467i −0.858786 0.512334i \(-0.828781\pi\)
0.858786 0.512334i \(-0.171219\pi\)
\(462\) 0 0
\(463\) 1428.43i 0.143380i 0.997427 + 0.0716898i \(0.0228391\pi\)
−0.997427 + 0.0716898i \(0.977161\pi\)
\(464\) 3481.68 3010.19i 0.348346 0.301173i
\(465\) 0 0
\(466\) −3745.46 + 674.691i −0.372328 + 0.0670697i
\(467\) 2039.86 0.202128 0.101064 0.994880i \(-0.467775\pi\)
0.101064 + 0.994880i \(0.467775\pi\)
\(468\) 0 0
\(469\) 10947.8 1754.82i 1.07788 0.172772i
\(470\) −788.141 4375.26i −0.0773494 0.429395i
\(471\) 0 0
\(472\) 7864.07 4657.20i 0.766892 0.454163i
\(473\) 7510.53 0.730094
\(474\) 0 0
\(475\) 12389.4 1.19676
\(476\) 14951.2 8469.11i 1.43967 0.815506i
\(477\) 0 0
\(478\) −3128.83 17369.3i −0.299392 1.66203i
\(479\) 13044.0 1.24425 0.622126 0.782917i \(-0.286269\pi\)
0.622126 + 0.782917i \(0.286269\pi\)
\(480\) 0 0
\(481\) 1001.00i 0.0948895i
\(482\) 2279.51 + 12654.4i 0.215412 + 1.19583i
\(483\) 0 0
\(484\) 4902.60 1825.51i 0.460425 0.171441i
\(485\) −4717.00 −0.441625
\(486\) 0 0
\(487\) 6444.14i 0.599614i −0.954000 0.299807i \(-0.903078\pi\)
0.954000 0.299807i \(-0.0969223\pi\)
\(488\) −251.084 423.977i −0.0232911 0.0393289i
\(489\) 0 0
\(490\) −2112.75 3903.48i −0.194785 0.359880i
\(491\) 8032.35i 0.738279i −0.929374 0.369140i \(-0.879652\pi\)
0.929374 0.369140i \(-0.120348\pi\)
\(492\) 0 0
\(493\) 8340.35i 0.761928i
\(494\) −4482.57 24884.4i −0.408260 2.26640i
\(495\) 0 0
\(496\) −11212.1 + 9693.73i −1.01499 + 0.877543i
\(497\) 10780.5 1728.00i 0.972983 0.155959i
\(498\) 0 0
\(499\) 1184.12i 0.106230i −0.998588 0.0531148i \(-0.983085\pi\)
0.998588 0.0531148i \(-0.0169149\pi\)
\(500\) 2925.64 + 7857.13i 0.261677 + 0.702763i
\(501\) 0 0
\(502\) 18861.6 3397.65i 1.67696 0.302081i
\(503\) −19759.9 −1.75159 −0.875794 0.482684i \(-0.839662\pi\)
−0.875794 + 0.482684i \(0.839662\pi\)
\(504\) 0 0
\(505\) −951.576 −0.0838506
\(506\) −4449.75 + 801.560i −0.390940 + 0.0704223i
\(507\) 0 0
\(508\) −764.544 2053.27i −0.0667740 0.179329i
\(509\) 14150.4i 1.23223i −0.787654 0.616117i \(-0.788705\pi\)
0.787654 0.616117i \(-0.211295\pi\)
\(510\) 0 0
\(511\) 125.322 20.0878i 0.0108492 0.00173901i
\(512\) −384.840 11578.8i −0.0332182 0.999448i
\(513\) 0 0
\(514\) −3595.34 19959.0i −0.308528 1.71275i
\(515\) 5626.55i 0.481428i
\(516\) 0 0
\(517\) 8939.34i 0.760448i
\(518\) −231.005 658.986i −0.0195942 0.0558961i
\(519\) 0 0
\(520\) 6688.70 3961.13i 0.564075 0.334052i
\(521\) 18031.5i 1.51626i 0.652101 + 0.758132i \(0.273888\pi\)
−0.652101 + 0.758132i \(0.726112\pi\)
\(522\) 0 0
\(523\) −5733.64 −0.479378 −0.239689 0.970850i \(-0.577045\pi\)
−0.239689 + 0.970850i \(0.577045\pi\)
\(524\) −16402.6 + 6107.56i −1.36746 + 0.509180i
\(525\) 0 0
\(526\) −1049.65 5827.00i −0.0870094 0.483021i
\(527\) 26858.5i 2.22006i
\(528\) 0 0
\(529\) 8392.87 0.689806
\(530\) −327.292 1816.92i −0.0268239 0.148909i
\(531\) 0 0
\(532\) −8693.64 15347.5i −0.708491 1.25075i
\(533\) −10823.0 −0.879542
\(534\) 0 0
\(535\) −6874.99 −0.555573
\(536\) 6902.73 + 11655.8i 0.556254 + 0.939282i
\(537\) 0 0
\(538\) −789.213 4381.21i −0.0632442 0.351092i
\(539\) 2789.51 + 8477.92i 0.222918 + 0.677495i
\(540\) 0 0
\(541\) −3887.89 −0.308971 −0.154486 0.987995i \(-0.549372\pi\)
−0.154486 + 0.987995i \(0.549372\pi\)
\(542\) 5495.37 989.913i 0.435510 0.0784509i
\(543\) 0 0
\(544\) 16328.6 + 13195.5i 1.28691 + 1.03998i
\(545\) 2650.38i 0.208312i
\(546\) 0 0
\(547\) 4722.04i 0.369104i −0.982823 0.184552i \(-0.940917\pi\)
0.982823 0.184552i \(-0.0590834\pi\)
\(548\) 19008.1 7077.76i 1.48173 0.551728i
\(549\) 0 0
\(550\) −1357.83 7537.81i −0.105269 0.584388i
\(551\) 8561.47 0.661943
\(552\) 0 0
\(553\) 17779.0 2849.79i 1.36716 0.219142i
\(554\) 13245.8 2386.04i 1.01581 0.182984i
\(555\) 0 0
\(556\) −7552.02 + 2812.03i −0.576038 + 0.214490i
\(557\) 13987.0 1.06400 0.532000 0.846745i \(-0.321441\pi\)
0.532000 + 0.846745i \(0.321441\pi\)
\(558\) 0 0
\(559\) 21674.0 1.63991
\(560\) 3489.21 4151.29i 0.263297 0.313257i
\(561\) 0 0
\(562\) −4880.98 + 879.240i −0.366356 + 0.0659938i
\(563\) 6757.50 0.505852 0.252926 0.967486i \(-0.418607\pi\)
0.252926 + 0.967486i \(0.418607\pi\)
\(564\) 0 0
\(565\) 2812.05i 0.209387i
\(566\) 10029.9 1806.75i 0.744858 0.134176i
\(567\) 0 0
\(568\) 6797.23 + 11477.7i 0.502122 + 0.847875i
\(569\) 7220.86 0.532011 0.266005 0.963972i \(-0.414296\pi\)
0.266005 + 0.963972i \(0.414296\pi\)
\(570\) 0 0
\(571\) 365.261i 0.0267700i 0.999910 + 0.0133850i \(0.00426071\pi\)
−0.999910 + 0.0133850i \(0.995739\pi\)
\(572\) −14648.6 + 5454.48i −1.07079 + 0.398712i
\(573\) 0 0
\(574\) −7125.04 + 2497.66i −0.518107 + 0.181621i
\(575\) 6393.31i 0.463686i
\(576\) 0 0
\(577\) 2258.22i 0.162931i 0.996676 + 0.0814653i \(0.0259600\pi\)
−0.996676 + 0.0814653i \(0.974040\pi\)
\(578\) −23764.9 + 4280.90i −1.71019 + 0.308066i
\(579\) 0 0
\(580\) 918.486 + 2466.70i 0.0657553 + 0.176593i
\(581\) 1259.66 + 7858.68i 0.0899477 + 0.561158i
\(582\) 0 0
\(583\) 3712.25i 0.263715i
\(584\) 79.0169 + 133.427i 0.00559887 + 0.00945417i
\(585\) 0 0
\(586\) 4439.69 + 24646.3i 0.312972 + 1.73742i
\(587\) 1086.09 0.0763677 0.0381839 0.999271i \(-0.487843\pi\)
0.0381839 + 0.999271i \(0.487843\pi\)
\(588\) 0 0
\(589\) −27570.6 −1.92873
\(590\) 926.636 + 5144.10i 0.0646593 + 0.358948i
\(591\) 0 0
\(592\) 645.391 557.992i 0.0448064 0.0387387i
\(593\) 7013.68i 0.485695i −0.970064 0.242848i \(-0.921919\pi\)
0.970064 0.242848i \(-0.0780815\pi\)
\(594\) 0 0
\(595\) 1555.30 + 9703.08i 0.107162 + 0.668551i
\(596\) −17562.7 + 6539.56i −1.20704 + 0.449447i
\(597\) 0 0
\(598\) −12841.1 + 2313.15i −0.878116 + 0.158180i
\(599\) 25452.7i 1.73618i −0.496409 0.868089i \(-0.665348\pi\)
0.496409 0.868089i \(-0.334652\pi\)
\(600\) 0 0
\(601\) 26422.8i 1.79336i −0.442682 0.896679i \(-0.645973\pi\)
0.442682 0.896679i \(-0.354027\pi\)
\(602\) 14268.5 5001.78i 0.966015 0.338634i
\(603\) 0 0
\(604\) 1566.14 + 4206.06i 0.105506 + 0.283348i
\(605\) 2991.82i 0.201049i
\(606\) 0 0
\(607\) −6179.28 −0.413195 −0.206597 0.978426i \(-0.566239\pi\)
−0.206597 + 0.978426i \(0.566239\pi\)
\(608\) 13545.3 16761.5i 0.903511 1.11804i
\(609\) 0 0
\(610\) 277.334 49.9579i 0.0184081 0.00331596i
\(611\) 25797.3i 1.70809i
\(612\) 0 0
\(613\) −6512.10 −0.429072 −0.214536 0.976716i \(-0.568824\pi\)
−0.214536 + 0.976716i \(0.568824\pi\)
\(614\) −12170.9 + 2192.41i −0.799960 + 0.144102i
\(615\) 0 0
\(616\) −8384.80 + 6971.33i −0.548430 + 0.455979i
\(617\) −15211.8 −0.992551 −0.496275 0.868165i \(-0.665299\pi\)
−0.496275 + 0.868165i \(0.665299\pi\)
\(618\) 0 0
\(619\) −11712.0 −0.760496 −0.380248 0.924885i \(-0.624161\pi\)
−0.380248 + 0.924885i \(0.624161\pi\)
\(620\) −2957.81 7943.53i −0.191594 0.514548i
\(621\) 0 0
\(622\) −5445.35 + 980.902i −0.351027 + 0.0632325i
\(623\) −19821.4 + 3177.15i −1.27468 + 0.204318i
\(624\) 0 0
\(625\) 8213.69 0.525676
\(626\) −3166.07 17576.0i −0.202143 1.12217i
\(627\) 0 0
\(628\) −1281.95 3442.83i −0.0814578 0.218764i
\(629\) 1546.03i 0.0980037i
\(630\) 0 0
\(631\) 16130.7i 1.01768i −0.860862 0.508839i \(-0.830075\pi\)
0.860862 0.508839i \(-0.169925\pi\)
\(632\) 11209.9 + 18928.8i 0.705544 + 1.19137i
\(633\) 0 0
\(634\) −13814.5 + 2488.49i −0.865370 + 0.155884i
\(635\) 1253.01 0.0783059
\(636\) 0 0
\(637\) 8050.01 + 24465.7i 0.500711 + 1.52177i
\(638\) −938.306 5208.88i −0.0582255 0.323231i
\(639\) 0 0
\(640\) 6282.41 + 2104.43i 0.388022 + 0.129977i
\(641\) −20295.1 −1.25056 −0.625280 0.780401i \(-0.715015\pi\)
−0.625280 + 0.780401i \(0.715015\pi\)
\(642\) 0 0
\(643\) −10255.3 −0.628976 −0.314488 0.949262i \(-0.601833\pi\)
−0.314488 + 0.949262i \(0.601833\pi\)
\(644\) −7919.83 + 4486.20i −0.484604 + 0.274505i
\(645\) 0 0
\(646\) 6923.24 + 38433.5i 0.421658 + 2.34078i
\(647\) 15162.9 0.921352 0.460676 0.887568i \(-0.347607\pi\)
0.460676 + 0.887568i \(0.347607\pi\)
\(648\) 0 0
\(649\) 10510.2i 0.635688i
\(650\) −3918.44 21752.7i −0.236452 1.31263i
\(651\) 0 0
\(652\) 1558.23 + 4184.80i 0.0935965 + 0.251364i
\(653\) 7126.05 0.427050 0.213525 0.976938i \(-0.431505\pi\)
0.213525 + 0.976938i \(0.431505\pi\)
\(654\) 0 0
\(655\) 10009.7i 0.597116i
\(656\) −6033.09 6978.05i −0.359074 0.415316i
\(657\) 0 0
\(658\) 5953.33 + 16983.0i 0.352712 + 1.00618i
\(659\) 2646.23i 0.156422i −0.996937 0.0782112i \(-0.975079\pi\)
0.996937 0.0782112i \(-0.0249208\pi\)
\(660\) 0 0
\(661\) 13839.8i 0.814381i −0.913343 0.407191i \(-0.866508\pi\)
0.913343 0.407191i \(-0.133492\pi\)
\(662\) 3480.91 + 19323.8i 0.204365 + 1.13450i
\(663\) 0 0
\(664\) −8366.89 + 4954.98i −0.489004 + 0.289594i
\(665\) 9960.33 1596.54i 0.580820 0.0930992i
\(666\) 0 0
\(667\) 4417.99i 0.256470i
\(668\) 18700.2 6963.11i 1.08313 0.403310i
\(669\) 0 0
\(670\) −7624.39 + 1373.43i −0.439636 + 0.0791941i
\(671\) −566.638 −0.0326003
\(672\) 0 0
\(673\) −32235.3 −1.84633 −0.923165 0.384404i \(-0.874407\pi\)
−0.923165 + 0.384404i \(0.874407\pi\)
\(674\) −5038.11 + 907.544i −0.287924 + 0.0518654i
\(675\) 0 0
\(676\) −25802.0 + 9607.47i −1.46802 + 0.546624i
\(677\) 9.30221i 0.000528084i 1.00000 0.000264042i \(8.40472e-5\pi\)
−1.00000 0.000264042i \(0.999916\pi\)
\(678\) 0 0
\(679\) 18853.9 3022.07i 1.06560 0.170805i
\(680\) −10330.6 + 6117.89i −0.582587 + 0.345015i
\(681\) 0 0
\(682\) 3021.63 + 16774.2i 0.169654 + 0.941813i
\(683\) 26622.3i 1.49147i 0.666244 + 0.745734i \(0.267901\pi\)
−0.666244 + 0.745734i \(0.732099\pi\)
\(684\) 0 0
\(685\) 11599.7i 0.647012i
\(686\) 10945.6 + 14248.6i 0.609188 + 0.793026i
\(687\) 0 0
\(688\) 12081.8 + 13974.2i 0.669496 + 0.774360i
\(689\) 10712.9i 0.592348i
\(690\) 0 0
\(691\) 20064.5 1.10462 0.552309 0.833639i \(-0.313747\pi\)
0.552309 + 0.833639i \(0.313747\pi\)
\(692\) 8044.29 + 21603.9i 0.441905 + 1.18679i
\(693\) 0 0
\(694\) 1776.50 + 9861.98i 0.0971684 + 0.539418i
\(695\) 4608.63i 0.251533i
\(696\) 0 0
\(697\) 16715.9 0.908408
\(698\) 660.906 + 3668.93i 0.0358390 + 0.198956i
\(699\) 0 0
\(700\) −7599.55 13416.1i −0.410337 0.724399i
\(701\) −32384.8 −1.74487 −0.872436 0.488728i \(-0.837461\pi\)
−0.872436 + 0.488728i \(0.837461\pi\)
\(702\) 0 0
\(703\) 1587.02 0.0851431
\(704\) −11682.3 6404.10i −0.625419 0.342846i
\(705\) 0 0
\(706\) −628.898 3491.24i −0.0335253 0.186111i
\(707\) 3803.45 609.652i 0.202325 0.0324305i
\(708\) 0 0
\(709\) 34258.5 1.81468 0.907338 0.420403i \(-0.138111\pi\)
0.907338 + 0.420403i \(0.138111\pi\)
\(710\) −7507.86 + 1352.43i −0.396852 + 0.0714873i
\(711\) 0 0
\(712\) −12497.6 21103.2i −0.657818 1.11078i
\(713\) 14227.3i 0.747288i
\(714\) 0 0
\(715\) 8939.34i 0.467570i
\(716\) 5785.94 + 15538.8i 0.301998 + 0.811051i
\(717\) 0 0
\(718\) 1178.71 + 6543.46i 0.0612662 + 0.340111i
\(719\) 10303.7 0.534443 0.267221 0.963635i \(-0.413895\pi\)
0.267221 + 0.963635i \(0.413895\pi\)
\(720\) 0 0
\(721\) −3604.80 22489.3i −0.186199 1.16165i
\(722\) 20359.5 3667.48i 1.04945 0.189044i
\(723\) 0 0
\(724\) −7716.28 20722.9i −0.396095 1.06376i
\(725\) 7484.01 0.383378
\(726\) 0 0
\(727\) 1468.60 0.0749209 0.0374605 0.999298i \(-0.488073\pi\)
0.0374605 + 0.999298i \(0.488073\pi\)
\(728\) −24197.0 + 20117.9i −1.23187 + 1.02420i
\(729\) 0 0
\(730\) −87.2779 + 15.7219i −0.00442507 + 0.000797113i
\(731\) −33475.1 −1.69373
\(732\) 0 0
\(733\) 5917.44i 0.298179i −0.988824 0.149090i \(-0.952366\pi\)
0.988824 0.149090i \(-0.0476343\pi\)
\(734\) −8187.14 + 1474.80i −0.411707 + 0.0741631i
\(735\) 0 0
\(736\) −8649.46 6989.82i −0.433184 0.350065i
\(737\) 15577.8 0.778584
\(738\) 0 0
\(739\) 8120.94i 0.404240i −0.979361 0.202120i \(-0.935217\pi\)
0.979361 0.202120i \(-0.0647831\pi\)
\(740\) 170.258 + 457.247i 0.00845783 + 0.0227145i
\(741\) 0 0
\(742\) 2472.25 + 7052.54i 0.122317 + 0.348931i
\(743\) 7975.20i 0.393784i −0.980425 0.196892i \(-0.936915\pi\)
0.980425 0.196892i \(-0.0630849\pi\)
\(744\) 0 0
\(745\) 10717.7i 0.527068i
\(746\) −20507.7 + 3694.17i −1.00649 + 0.181304i
\(747\) 0 0
\(748\) 22624.5 8424.33i 1.10593 0.411797i
\(749\) 27479.3 4404.65i 1.34055 0.214876i
\(750\) 0 0
\(751\) 7417.00i 0.360387i −0.983631 0.180193i \(-0.942328\pi\)
0.983631 0.180193i \(-0.0576723\pi\)
\(752\) −16632.6 + 14380.2i −0.806554 + 0.697331i
\(753\) 0 0
\(754\) −2707.77 15031.8i −0.130784 0.726031i
\(755\) −2566.75 −0.123727
\(756\) 0 0
\(757\) 2056.45 0.0987358 0.0493679 0.998781i \(-0.484279\pi\)
0.0493679 + 0.998781i \(0.484279\pi\)
\(758\) 4022.76 + 22331.8i 0.192762 + 1.07009i
\(759\) 0 0
\(760\) 6280.09 + 10604.5i 0.299741 + 0.506137i
\(761\) 28244.9i 1.34544i 0.739898 + 0.672719i \(0.234874\pi\)
−0.739898 + 0.672719i \(0.765126\pi\)
\(762\) 0 0
\(763\) −1698.04 10593.6i −0.0805676 0.502639i
\(764\) −11498.4 30880.3i −0.544499 1.46232i
\(765\) 0 0
\(766\) 37494.1 6754.02i 1.76856 0.318581i
\(767\) 30330.5i 1.42786i
\(768\) 0 0
\(769\) 27026.1i 1.26734i 0.773603 + 0.633671i \(0.218453\pi\)
−0.773603 + 0.633671i \(0.781547\pi\)
\(770\) −2062.96 5884.99i −0.0965507 0.275429i
\(771\) 0 0
\(772\) 34020.6 12667.7i 1.58605 0.590572i
\(773\) 21487.5i 0.999810i −0.866080 0.499905i \(-0.833368\pi\)
0.866080 0.499905i \(-0.166632\pi\)
\(774\) 0 0
\(775\) −24100.8 −1.11707
\(776\) 11887.6 + 20073.1i 0.549921 + 0.928587i
\(777\) 0 0
\(778\) 1787.70 322.029i 0.0823808 0.0148397i
\(779\) 17159.1i 0.789202i
\(780\) 0 0
\(781\) 15339.7 0.702816
\(782\) 19832.9 3572.62i 0.906935 0.163372i
\(783\) 0 0
\(784\) −11286.8 + 18828.2i −0.514156 + 0.857697i
\(785\) 2100.99 0.0955257
\(786\) 0 0
\(787\) 13905.7 0.629843 0.314921 0.949118i \(-0.398022\pi\)
0.314921 + 0.949118i \(0.398022\pi\)
\(788\) −6343.91 + 2362.18i −0.286792 + 0.106788i
\(789\) 0 0
\(790\) −12381.8 + 2230.41i −0.557627 + 0.100449i
\(791\) 1801.61 + 11239.8i 0.0809836 + 0.505234i
\(792\) 0 0
\(793\) −1635.21 −0.0732258
\(794\) 3059.29 + 16983.2i 0.136738 + 0.759083i
\(795\) 0 0
\(796\) 9138.04 3402.59i 0.406896 0.151509i
\(797\) 21571.7i 0.958730i −0.877616 0.479365i \(-0.840867\pi\)
0.877616 0.479365i \(-0.159133\pi\)
\(798\) 0 0
\(799\) 39843.4i 1.76415i
\(800\) 11840.6 14652.0i 0.523287 0.647535i
\(801\) 0 0
\(802\) −17539.6 + 3159.51i −0.772249 + 0.139110i
\(803\) 178.323 0.00783669
\(804\) 0 0
\(805\) −823.864 5139.85i −0.0360713 0.225039i
\(806\) 8719.86 + 48407.2i 0.381072 + 2.11547i
\(807\) 0 0
\(808\) 2398.11 + 4049.42i 0.104413 + 0.176309i
\(809\) −33518.7 −1.45668 −0.728339 0.685217i \(-0.759708\pi\)
−0.728339 + 0.685217i \(0.759708\pi\)
\(810\) 0 0
\(811\) −35133.3 −1.52120 −0.760602 0.649218i \(-0.775096\pi\)
−0.760602 + 0.649218i \(0.775096\pi\)
\(812\) −5251.55 9270.95i −0.226962 0.400673i
\(813\) 0 0
\(814\) −173.932 965.558i −0.00748931 0.0415759i
\(815\) −2553.78 −0.109761
\(816\) 0 0
\(817\) 34362.5i 1.47147i
\(818\) −450.214 2499.30i −0.0192437 0.106829i
\(819\) 0 0
\(820\) 4943.81 1840.85i 0.210543 0.0783967i
\(821\) 21025.2 0.893768 0.446884 0.894592i \(-0.352534\pi\)
0.446884 + 0.894592i \(0.352534\pi\)
\(822\) 0 0
\(823\) 20491.2i 0.867894i 0.900938 + 0.433947i \(0.142880\pi\)
−0.900938 + 0.433947i \(0.857120\pi\)
\(824\) 23943.7 14179.7i 1.01228 0.599484i
\(825\) 0 0
\(826\) −6999.47 19967.3i −0.294846 0.841103i
\(827\) 18080.6i 0.760245i 0.924936 + 0.380122i \(0.124118\pi\)
−0.924936 + 0.380122i \(0.875882\pi\)
\(828\) 0 0
\(829\) 38666.1i 1.61994i 0.586471 + 0.809970i \(0.300517\pi\)
−0.586471 + 0.809970i \(0.699483\pi\)
\(830\) −985.885 5473.01i −0.0412296 0.228881i
\(831\) 0 0
\(832\) −33713.1 18481.0i −1.40480 0.770089i
\(833\) −12433.1 37786.8i −0.517144 1.57171i
\(834\) 0 0
\(835\) 11411.8i 0.472962i
\(836\) −8647.68 23224.3i −0.357759 0.960802i
\(837\) 0 0
\(838\) −24090.6 + 4339.59i −0.993076 + 0.178889i
\(839\) 36214.5 1.49018 0.745091 0.666962i \(-0.232406\pi\)
0.745091 + 0.666962i \(0.232406\pi\)
\(840\) 0 0
\(841\) −19217.3 −0.787949
\(842\) −37093.2 + 6681.82i −1.51819 + 0.273481i
\(843\) 0 0
\(844\) −14138.9 37971.6i −0.576635 1.54862i
\(845\) 15745.7i 0.641027i
\(846\) 0 0
\(847\) −1916.79 11958.3i −0.0777588 0.485115i
\(848\) −6907.05 + 5971.70i −0.279704 + 0.241827i
\(849\) 0 0
\(850\) 6051.96 + 33596.6i 0.244212 + 1.35571i
\(851\) 818.954i 0.0329887i
\(852\) 0 0
\(853\) 1180.57i 0.0473881i −0.999719 0.0236941i \(-0.992457\pi\)
0.999719 0.0236941i \(-0.00754276\pi\)
\(854\) −1076.50 + 377.363i −0.0431347 + 0.0151207i
\(855\) 0 0
\(856\) 17326.0 + 29256.4i 0.691811 + 1.16818i
\(857\) 29570.1i 1.17864i −0.807900 0.589320i \(-0.799396\pi\)
0.807900 0.589320i \(-0.200604\pi\)
\(858\) 0 0
\(859\) 18516.7 0.735483 0.367742 0.929928i \(-0.380131\pi\)
0.367742 + 0.929928i \(0.380131\pi\)
\(860\) −9900.41 + 3686.46i −0.392560 + 0.146171i
\(861\) 0 0
\(862\) 2262.78 + 12561.5i 0.0894092 + 0.496343i
\(863\) 35215.9i 1.38907i 0.719461 + 0.694533i \(0.244389\pi\)
−0.719461 + 0.694533i \(0.755611\pi\)
\(864\) 0 0
\(865\) −13183.8 −0.518223
\(866\) 2305.43 + 12798.3i 0.0904640 + 0.502199i
\(867\) 0 0
\(868\) 16911.6 + 29855.3i 0.661310 + 1.16746i
\(869\) 25298.0 0.987544
\(870\) 0 0
\(871\) 44954.7 1.74883
\(872\) 11278.7 6679.36i 0.438009 0.259394i
\(873\) 0 0
\(874\) −3667.33 20358.7i −0.141933 0.787922i
\(875\) 19164.9 3071.93i 0.740449 0.118686i
\(876\) 0 0
\(877\) −20910.2 −0.805115 −0.402558 0.915395i \(-0.631879\pi\)
−0.402558 + 0.915395i \(0.631879\pi\)
\(878\) −40598.3 + 7313.20i −1.56051 + 0.281103i
\(879\) 0 0
\(880\) 5763.58 4983.08i 0.220784 0.190886i
\(881\) 19841.3i 0.758762i 0.925241 + 0.379381i \(0.123863\pi\)
−0.925241 + 0.379381i \(0.876137\pi\)
\(882\) 0 0
\(883\) 37682.4i 1.43614i 0.695971 + 0.718070i \(0.254974\pi\)
−0.695971 + 0.718070i \(0.745026\pi\)
\(884\) 65290.1 24311.0i 2.48410 0.924965i
\(885\) 0 0
\(886\) 5304.30 + 29446.1i 0.201130 + 1.11655i
\(887\) −16665.2 −0.630850 −0.315425 0.948950i \(-0.602147\pi\)
−0.315425 + 0.948950i \(0.602147\pi\)
\(888\) 0 0
\(889\) −5008.29 + 802.776i −0.188946 + 0.0302860i
\(890\) 13804.2 2486.62i 0.519906 0.0936537i
\(891\) 0 0
\(892\) −29194.3 + 10870.6i −1.09585 + 0.408044i
\(893\) −40899.7 −1.53265
\(894\) 0 0
\(895\) −9482.58 −0.354154
\(896\) −26459.1 4386.43i −0.986535 0.163549i
\(897\) 0 0
\(898\) 2320.38 417.984i 0.0862274 0.0155326i
\(899\) −16654.5 −0.617862
\(900\) 0 0
\(901\) 16545.8i 0.611788i
\(902\) −10439.7 + 1880.57i −0.385372 + 0.0694193i
\(903\) 0 0
\(904\) −11966.6 + 7086.78i −0.440270 + 0.260733i
\(905\) 12646.2 0.464502
\(906\) 0 0
\(907\) 20577.7i 0.753331i −0.926349 0.376665i \(-0.877071\pi\)
0.926349 0.376665i \(-0.122929\pi\)
\(908\) 8741.27 3254.85i 0.319481 0.118960i
\(909\) 0 0
\(910\) −5953.33 16983.0i −0.216869 0.618659i
\(911\) 35684.4i 1.29778i −0.760883 0.648889i \(-0.775234\pi\)
0.760883 0.648889i \(-0.224766\pi\)
\(912\) 0 0
\(913\) 11182.2i 0.405342i
\(914\) −17989.1 + 3240.48i −0.651013 + 0.117271i
\(915\) 0 0
\(916\) 7084.84 + 19027.2i 0.255556 + 0.686326i
\(917\) 6412.97 + 40008.7i 0.230943 + 1.44079i
\(918\) 0 0
\(919\) 2549.71i 0.0915205i 0.998952 + 0.0457602i \(0.0145710\pi\)
−0.998952 + 0.0457602i \(0.985429\pi\)
\(920\) 5472.24 3240.73i 0.196103 0.116134i
\(921\) 0 0
\(922\) −5085.64 28232.2i −0.181656 1.00844i
\(923\) 44267.6 1.57864
\(924\) 0 0
\(925\) 1387.30 0.0493124
\(926\) 716.258 + 3976.21i 0.0254187 + 0.141108i
\(927\) 0 0
\(928\) 8182.28 10125.1i 0.289436 0.358159i
\(929\) 24991.8i 0.882620i −0.897355 0.441310i \(-0.854514\pi\)
0.897355 0.441310i \(-0.145486\pi\)
\(930\) 0 0
\(931\) −38788.6 + 12762.7i −1.36546 + 0.449281i
\(932\) −10087.6 + 3756.18i −0.354540 + 0.132015i
\(933\) 0 0
\(934\) 5678.21 1022.85i 0.198926 0.0358337i
\(935\) 13806.6i 0.482915i
\(936\) 0 0
\(937\) 36329.3i 1.26662i −0.773896 0.633312i \(-0.781695\pi\)
0.773896 0.633312i \(-0.218305\pi\)
\(938\) 29594.8 10374.4i 1.03017 0.361124i
\(939\) 0 0
\(940\) −4387.78 11783.9i −0.152248 0.408881i
\(941\) 21505.5i 0.745015i 0.928029 + 0.372507i \(0.121502\pi\)
−0.928029 + 0.372507i \(0.878498\pi\)
\(942\) 0 0
\(943\) −8854.64 −0.305776
\(944\) 19555.4 16907.2i 0.674230 0.582926i
\(945\) 0 0
\(946\) 20906.5 3766.01i 0.718530 0.129433i
\(947\) 17365.5i 0.595886i 0.954584 + 0.297943i \(0.0963005\pi\)
−0.954584 + 0.297943i \(0.903699\pi\)
\(948\) 0 0
\(949\) 514.605 0.0176025
\(950\) 34487.4 6212.41i 1.17781 0.212165i
\(951\) 0 0
\(952\) 37371.7 31071.8i 1.27229 1.05782i
\(953\) −22686.6 −0.771133 −0.385566 0.922680i \(-0.625994\pi\)
−0.385566 + 0.922680i \(0.625994\pi\)
\(954\) 0 0
\(955\) 18844.7 0.638535
\(956\) −17419.0 46780.7i −0.589299 1.58263i
\(957\) 0 0
\(958\) 36309.7 6540.68i 1.22454 0.220584i
\(959\) −7431.69 46364.2i −0.250242 1.56119i
\(960\) 0 0
\(961\) 23841.5 0.800293
\(962\) −501.934 2786.42i −0.0168222 0.0933865i
\(963\) 0 0
\(964\) 12690.6 + 34082.1i 0.424001 + 1.13870i
\(965\) 20761.1i 0.692565i
\(966\) 0 0
\(967\) 30178.5i 1.00359i 0.864985 + 0.501797i \(0.167328\pi\)
−0.864985 + 0.501797i \(0.832672\pi\)
\(968\) 12731.6 7539.84i 0.422738 0.250351i
\(969\) 0 0
\(970\) −13130.4 + 2365.25i −0.434630 + 0.0782924i
\(971\) −54731.9 −1.80889 −0.904445 0.426591i \(-0.859714\pi\)
−0.904445 + 0.426591i \(0.859714\pi\)
\(972\) 0 0
\(973\) 2952.64 + 18420.7i 0.0972841 + 0.606928i
\(974\) −3231.29 17938.1i −0.106301 0.590116i
\(975\) 0 0
\(976\) −911.519 1054.29i −0.0298945 0.0345769i
\(977\) 29860.7 0.977817 0.488908 0.872335i \(-0.337395\pi\)
0.488908 + 0.872335i \(0.337395\pi\)
\(978\) 0 0
\(979\) −28204.1 −0.920741
\(980\) −7838.44 9806.43i −0.255500 0.319648i
\(981\) 0 0
\(982\) −4027.67 22359.1i −0.130884 0.726585i
\(983\) −10417.7 −0.338018 −0.169009 0.985615i \(-0.554057\pi\)
−0.169009 + 0.985615i \(0.554057\pi\)
\(984\) 0 0
\(985\) 3871.38i 0.125231i
\(986\) 4182.11 + 23216.4i 0.135076 + 0.749859i
\(987\) 0 0
\(988\) −24955.6 67021.1i −0.803586 2.15812i
\(989\) 17732.2 0.570122
\(990\) 0 0
\(991\) 3803.09i 0.121906i −0.998141 0.0609531i \(-0.980586\pi\)
0.998141 0.0609531i \(-0.0194140\pi\)
\(992\) −26349.4 + 32605.8i −0.843343 + 1.04358i
\(993\) 0 0
\(994\) 29142.5 10215.8i 0.929922 0.325981i
\(995\) 5576.50i 0.177675i
\(996\) 0 0
\(997\) 53386.9i 1.69587i −0.530103 0.847933i \(-0.677847\pi\)
0.530103 0.847933i \(-0.322153\pi\)
\(998\) −593.755 3296.15i −0.0188327 0.104547i
\(999\) 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 252.4.b.e.55.11 12
3.2 odd 2 84.4.b.b.55.2 yes 12
4.3 odd 2 252.4.b.f.55.12 12
7.6 odd 2 252.4.b.f.55.11 12
12.11 even 2 84.4.b.a.55.1 12
21.20 even 2 84.4.b.a.55.2 yes 12
24.5 odd 2 1344.4.b.g.895.8 12
24.11 even 2 1344.4.b.h.895.8 12
28.27 even 2 inner 252.4.b.e.55.12 12
84.83 odd 2 84.4.b.b.55.1 yes 12
168.83 odd 2 1344.4.b.g.895.5 12
168.125 even 2 1344.4.b.h.895.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.4.b.a.55.1 12 12.11 even 2
84.4.b.a.55.2 yes 12 21.20 even 2
84.4.b.b.55.1 yes 12 84.83 odd 2
84.4.b.b.55.2 yes 12 3.2 odd 2
252.4.b.e.55.11 12 1.1 even 1 trivial
252.4.b.e.55.12 12 28.27 even 2 inner
252.4.b.f.55.11 12 7.6 odd 2
252.4.b.f.55.12 12 4.3 odd 2
1344.4.b.g.895.5 12 168.83 odd 2
1344.4.b.g.895.8 12 24.5 odd 2
1344.4.b.h.895.5 12 168.125 even 2
1344.4.b.h.895.8 12 24.11 even 2