Properties

Label 288.3.u.a.19.6
Level $288$
Weight $3$
Character 288.19
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
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] = [288,3,Mod(19,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 7, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), 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: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 19.6
Character \(\chi\) \(=\) 288.19
Dual form 288.3.u.a.91.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.62478 - 1.16623i) q^{2} +(1.27980 - 3.78974i) q^{4} +(4.51028 - 1.86822i) q^{5} +(-3.85317 - 3.85317i) q^{7} +(-2.34032 - 7.65003i) q^{8} +O(q^{10})\) \(q+(1.62478 - 1.16623i) q^{2} +(1.27980 - 3.78974i) q^{4} +(4.51028 - 1.86822i) q^{5} +(-3.85317 - 3.85317i) q^{7} +(-2.34032 - 7.65003i) q^{8} +(5.14942 - 8.29547i) q^{10} +(4.56441 - 1.89064i) q^{11} +(-5.58307 - 2.31258i) q^{13} +(-10.7542 - 1.76685i) q^{14} +(-12.7242 - 9.70024i) q^{16} +25.0539i q^{17} +(6.43433 - 15.5338i) q^{19} +(-1.30778 - 19.4837i) q^{20} +(5.21122 - 8.39503i) q^{22} +(26.9024 - 26.9024i) q^{23} +(-0.825315 + 0.825315i) q^{25} +(-11.7682 + 2.75372i) q^{26} +(-19.5338 + 9.67119i) q^{28} +(0.210028 - 0.507052i) q^{29} +15.8372i q^{31} +(-31.9867 - 0.921357i) q^{32} +(29.2186 + 40.7070i) q^{34} +(-24.5774 - 10.1803i) q^{35} +(-2.18606 + 0.905498i) q^{37} +(-7.66172 - 32.7430i) q^{38} +(-24.8474 - 30.1315i) q^{40} +(31.1517 + 31.1517i) q^{41} +(12.9078 - 5.34659i) q^{43} +(-1.32348 - 19.7175i) q^{44} +(12.3360 - 75.0848i) q^{46} -15.0033 q^{47} -19.3062i q^{49} +(-0.378444 + 2.30346i) q^{50} +(-15.9093 + 18.1987i) q^{52} +(15.4409 + 37.2776i) q^{53} +(17.0546 - 17.0546i) q^{55} +(-20.4592 + 38.4945i) q^{56} +(-0.250092 - 1.06879i) q^{58} +(14.7242 + 35.5473i) q^{59} +(-15.4603 + 37.3243i) q^{61} +(18.4698 + 25.7319i) q^{62} +(-53.0458 + 35.8070i) q^{64} -29.5016 q^{65} +(61.3598 + 25.4161i) q^{67} +(94.9476 + 32.0641i) q^{68} +(-51.8054 + 12.1223i) q^{70} +(51.7789 + 51.7789i) q^{71} +(64.9440 + 64.9440i) q^{73} +(-2.49585 + 4.02069i) q^{74} +(-50.6345 - 44.2647i) q^{76} +(-24.8724 - 10.3025i) q^{77} -38.1202 q^{79} +(-75.5118 - 19.9792i) q^{80} +(86.9447 + 14.2845i) q^{82} +(-15.9782 + 38.5748i) q^{83} +(46.8061 + 113.000i) q^{85} +(14.7370 - 23.7405i) q^{86} +(-25.1456 - 30.4932i) q^{88} +(-23.7666 + 23.7666i) q^{89} +(12.6017 + 30.4233i) q^{91} +(-67.5231 - 136.383i) q^{92} +(-24.3771 + 17.4974i) q^{94} -82.0827i q^{95} -118.710 q^{97} +(-22.5155 - 31.3682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.62478 1.16623i 0.812389 0.583116i
\(3\) 0 0
\(4\) 1.27980 3.78974i 0.319951 0.947434i
\(5\) 4.51028 1.86822i 0.902055 0.373644i 0.117045 0.993127i \(-0.462658\pi\)
0.785010 + 0.619483i \(0.212658\pi\)
\(6\) 0 0
\(7\) −3.85317 3.85317i −0.550453 0.550453i 0.376119 0.926571i \(-0.377258\pi\)
−0.926571 + 0.376119i \(0.877258\pi\)
\(8\) −2.34032 7.65003i −0.292539 0.956253i
\(9\) 0 0
\(10\) 5.14942 8.29547i 0.514942 0.829547i
\(11\) 4.56441 1.89064i 0.414946 0.171876i −0.165436 0.986221i \(-0.552903\pi\)
0.580382 + 0.814344i \(0.302903\pi\)
\(12\) 0 0
\(13\) −5.58307 2.31258i −0.429467 0.177891i 0.157470 0.987524i \(-0.449666\pi\)
−0.586937 + 0.809633i \(0.699666\pi\)
\(14\) −10.7542 1.76685i −0.768159 0.126204i
\(15\) 0 0
\(16\) −12.7242 9.70024i −0.795263 0.606265i
\(17\) 25.0539i 1.47376i 0.676025 + 0.736879i \(0.263701\pi\)
−0.676025 + 0.736879i \(0.736299\pi\)
\(18\) 0 0
\(19\) 6.43433 15.5338i 0.338649 0.817571i −0.659197 0.751970i \(-0.729104\pi\)
0.997846 0.0656005i \(-0.0208963\pi\)
\(20\) −1.30778 19.4837i −0.0653891 0.974186i
\(21\) 0 0
\(22\) 5.21122 8.39503i 0.236874 0.381592i
\(23\) 26.9024 26.9024i 1.16967 1.16967i 0.187381 0.982287i \(-0.440000\pi\)
0.982287 0.187381i \(-0.0600000\pi\)
\(24\) 0 0
\(25\) −0.825315 + 0.825315i −0.0330126 + 0.0330126i
\(26\) −11.7682 + 2.75372i −0.452625 + 0.105912i
\(27\) 0 0
\(28\) −19.5338 + 9.67119i −0.697636 + 0.345400i
\(29\) 0.210028 0.507052i 0.00724234 0.0174846i −0.920217 0.391409i \(-0.871988\pi\)
0.927459 + 0.373924i \(0.121988\pi\)
\(30\) 0 0
\(31\) 15.8372i 0.510877i 0.966825 + 0.255438i \(0.0822198\pi\)
−0.966825 + 0.255438i \(0.917780\pi\)
\(32\) −31.9867 0.921357i −0.999585 0.0287924i
\(33\) 0 0
\(34\) 29.2186 + 40.7070i 0.859372 + 1.19726i
\(35\) −24.5774 10.1803i −0.702212 0.290866i
\(36\) 0 0
\(37\) −2.18606 + 0.905498i −0.0590828 + 0.0244729i −0.412029 0.911171i \(-0.635180\pi\)
0.352946 + 0.935644i \(0.385180\pi\)
\(38\) −7.66172 32.7430i −0.201624 0.861657i
\(39\) 0 0
\(40\) −24.8474 30.1315i −0.621185 0.753288i
\(41\) 31.1517 + 31.1517i 0.759798 + 0.759798i 0.976285 0.216488i \(-0.0694601\pi\)
−0.216488 + 0.976285i \(0.569460\pi\)
\(42\) 0 0
\(43\) 12.9078 5.34659i 0.300182 0.124339i −0.227509 0.973776i \(-0.573058\pi\)
0.527691 + 0.849437i \(0.323058\pi\)
\(44\) −1.32348 19.7175i −0.0300790 0.448126i
\(45\) 0 0
\(46\) 12.3360 75.0848i 0.268173 1.63228i
\(47\) −15.0033 −0.319220 −0.159610 0.987180i \(-0.551024\pi\)
−0.159610 + 0.987180i \(0.551024\pi\)
\(48\) 0 0
\(49\) 19.3062i 0.394004i
\(50\) −0.378444 + 2.30346i −0.00756888 + 0.0460692i
\(51\) 0 0
\(52\) −15.9093 + 18.1987i −0.305948 + 0.349975i
\(53\) 15.4409 + 37.2776i 0.291338 + 0.703352i 0.999998 0.00219873i \(-0.000699877\pi\)
−0.708660 + 0.705550i \(0.750700\pi\)
\(54\) 0 0
\(55\) 17.0546 17.0546i 0.310084 0.310084i
\(56\) −20.4592 + 38.4945i −0.365343 + 0.687401i
\(57\) 0 0
\(58\) −0.250092 1.06879i −0.00431193 0.0184274i
\(59\) 14.7242 + 35.5473i 0.249562 + 0.602496i 0.998167 0.0605202i \(-0.0192760\pi\)
−0.748605 + 0.663016i \(0.769276\pi\)
\(60\) 0 0
\(61\) −15.4603 + 37.3243i −0.253447 + 0.611875i −0.998478 0.0551552i \(-0.982435\pi\)
0.745031 + 0.667030i \(0.232435\pi\)
\(62\) 18.4698 + 25.7319i 0.297900 + 0.415030i
\(63\) 0 0
\(64\) −53.0458 + 35.8070i −0.828841 + 0.559484i
\(65\) −29.5016 −0.453870
\(66\) 0 0
\(67\) 61.3598 + 25.4161i 0.915818 + 0.379344i 0.790281 0.612745i \(-0.209935\pi\)
0.125537 + 0.992089i \(0.459935\pi\)
\(68\) 94.9476 + 32.0641i 1.39629 + 0.471530i
\(69\) 0 0
\(70\) −51.8054 + 12.1223i −0.740077 + 0.173175i
\(71\) 51.7789 + 51.7789i 0.729281 + 0.729281i 0.970477 0.241196i \(-0.0775395\pi\)
−0.241196 + 0.970477i \(0.577540\pi\)
\(72\) 0 0
\(73\) 64.9440 + 64.9440i 0.889643 + 0.889643i 0.994489 0.104845i \(-0.0334347\pi\)
−0.104845 + 0.994489i \(0.533435\pi\)
\(74\) −2.49585 + 4.02069i −0.0337277 + 0.0543337i
\(75\) 0 0
\(76\) −50.6345 44.2647i −0.666243 0.582430i
\(77\) −24.8724 10.3025i −0.323018 0.133798i
\(78\) 0 0
\(79\) −38.1202 −0.482535 −0.241267 0.970459i \(-0.577563\pi\)
−0.241267 + 0.970459i \(0.577563\pi\)
\(80\) −75.5118 19.9792i −0.943898 0.249740i
\(81\) 0 0
\(82\) 86.9447 + 14.2845i 1.06030 + 0.174201i
\(83\) −15.9782 + 38.5748i −0.192509 + 0.464757i −0.990432 0.138002i \(-0.955932\pi\)
0.797923 + 0.602759i \(0.205932\pi\)
\(84\) 0 0
\(85\) 46.8061 + 113.000i 0.550660 + 1.32941i
\(86\) 14.7370 23.7405i 0.171360 0.276053i
\(87\) 0 0
\(88\) −25.1456 30.4932i −0.285745 0.346513i
\(89\) −23.7666 + 23.7666i −0.267040 + 0.267040i −0.827906 0.560866i \(-0.810468\pi\)
0.560866 + 0.827906i \(0.310468\pi\)
\(90\) 0 0
\(91\) 12.6017 + 30.4233i 0.138481 + 0.334322i
\(92\) −67.5231 136.383i −0.733947 1.48242i
\(93\) 0 0
\(94\) −24.3771 + 17.4974i −0.259331 + 0.186142i
\(95\) 82.0827i 0.864028i
\(96\) 0 0
\(97\) −118.710 −1.22382 −0.611908 0.790929i \(-0.709598\pi\)
−0.611908 + 0.790929i \(0.709598\pi\)
\(98\) −22.5155 31.3682i −0.229750 0.320084i
\(99\) 0 0
\(100\) 2.07148 + 4.18397i 0.0207148 + 0.0418397i
\(101\) 182.236 75.4846i 1.80432 0.747372i 0.819665 0.572844i \(-0.194160\pi\)
0.984652 0.174529i \(-0.0558402\pi\)
\(102\) 0 0
\(103\) −80.3171 80.3171i −0.779777 0.779777i 0.200016 0.979793i \(-0.435901\pi\)
−0.979793 + 0.200016i \(0.935901\pi\)
\(104\) −4.62518 + 48.1228i −0.0444728 + 0.462719i
\(105\) 0 0
\(106\) 68.5624 + 42.5602i 0.646815 + 0.401511i
\(107\) −22.6854 + 9.39659i −0.212013 + 0.0878186i −0.486162 0.873868i \(-0.661604\pi\)
0.274150 + 0.961687i \(0.411604\pi\)
\(108\) 0 0
\(109\) 181.428 + 75.1501i 1.66448 + 0.689450i 0.998406 0.0564360i \(-0.0179737\pi\)
0.666074 + 0.745886i \(0.267974\pi\)
\(110\) 7.82031 47.5996i 0.0710937 0.432724i
\(111\) 0 0
\(112\) 11.6518 + 86.4052i 0.104034 + 0.771475i
\(113\) 32.7876i 0.290156i 0.989420 + 0.145078i \(0.0463433\pi\)
−0.989420 + 0.145078i \(0.953657\pi\)
\(114\) 0 0
\(115\) 71.0777 171.597i 0.618067 1.49214i
\(116\) −1.65280 1.44488i −0.0142483 0.0124558i
\(117\) 0 0
\(118\) 65.3799 + 40.5846i 0.554067 + 0.343937i
\(119\) 96.5368 96.5368i 0.811234 0.811234i
\(120\) 0 0
\(121\) −68.3006 + 68.3006i −0.564468 + 0.564468i
\(122\) 18.4094 + 78.6740i 0.150897 + 0.644869i
\(123\) 0 0
\(124\) 60.0187 + 20.2685i 0.484022 + 0.163456i
\(125\) −48.8860 + 118.021i −0.391088 + 0.944169i
\(126\) 0 0
\(127\) 130.165i 1.02492i −0.858710 0.512462i \(-0.828734\pi\)
0.858710 0.512462i \(-0.171266\pi\)
\(128\) −44.4285 + 120.042i −0.347097 + 0.937829i
\(129\) 0 0
\(130\) −47.9335 + 34.4057i −0.368719 + 0.264659i
\(131\) −24.3356 10.0801i −0.185768 0.0769476i 0.287861 0.957672i \(-0.407056\pi\)
−0.473628 + 0.880725i \(0.657056\pi\)
\(132\) 0 0
\(133\) −84.6471 + 35.0620i −0.636444 + 0.263624i
\(134\) 129.337 30.2643i 0.965202 0.225853i
\(135\) 0 0
\(136\) 191.663 58.6340i 1.40929 0.431132i
\(137\) −147.886 147.886i −1.07946 1.07946i −0.996557 0.0829047i \(-0.973580\pi\)
−0.0829047 0.996557i \(-0.526420\pi\)
\(138\) 0 0
\(139\) −206.929 + 85.7129i −1.48870 + 0.616639i −0.971033 0.238944i \(-0.923199\pi\)
−0.517666 + 0.855583i \(0.673199\pi\)
\(140\) −70.0349 + 80.1131i −0.500249 + 0.572237i
\(141\) 0 0
\(142\) 144.516 + 23.7430i 1.01772 + 0.167204i
\(143\) −29.8556 −0.208781
\(144\) 0 0
\(145\) 2.67932i 0.0184781i
\(146\) 181.259 + 29.7797i 1.24150 + 0.203971i
\(147\) 0 0
\(148\) 0.633863 + 9.44347i 0.00428286 + 0.0638072i
\(149\) 20.4247 + 49.3095i 0.137078 + 0.330936i 0.977480 0.211028i \(-0.0676810\pi\)
−0.840402 + 0.541964i \(0.817681\pi\)
\(150\) 0 0
\(151\) 180.137 180.137i 1.19296 1.19296i 0.216726 0.976232i \(-0.430462\pi\)
0.976232 0.216726i \(-0.0695379\pi\)
\(152\) −133.893 12.8687i −0.880873 0.0846624i
\(153\) 0 0
\(154\) −52.4272 + 12.2677i −0.340436 + 0.0796607i
\(155\) 29.5873 + 71.4300i 0.190886 + 0.460839i
\(156\) 0 0
\(157\) −60.3999 + 145.818i −0.384713 + 0.928779i 0.606327 + 0.795215i \(0.292642\pi\)
−0.991040 + 0.133564i \(0.957358\pi\)
\(158\) −61.9369 + 44.4571i −0.392006 + 0.281374i
\(159\) 0 0
\(160\) −145.990 + 55.6026i −0.912439 + 0.347516i
\(161\) −207.319 −1.28769
\(162\) 0 0
\(163\) −152.162 63.0277i −0.933512 0.386673i −0.136502 0.990640i \(-0.543586\pi\)
−0.797010 + 0.603966i \(0.793586\pi\)
\(164\) 157.925 78.1887i 0.962956 0.476760i
\(165\) 0 0
\(166\) 19.0262 + 81.3099i 0.114615 + 0.489818i
\(167\) −94.8188 94.8188i −0.567777 0.567777i 0.363728 0.931505i \(-0.381504\pi\)
−0.931505 + 0.363728i \(0.881504\pi\)
\(168\) 0 0
\(169\) −93.6785 93.6785i −0.554310 0.554310i
\(170\) 207.834 + 129.013i 1.22255 + 0.758900i
\(171\) 0 0
\(172\) −3.74270 55.7598i −0.0217599 0.324185i
\(173\) 107.416 + 44.4930i 0.620900 + 0.257185i 0.670881 0.741565i \(-0.265916\pi\)
−0.0499813 + 0.998750i \(0.515916\pi\)
\(174\) 0 0
\(175\) 6.36016 0.0363437
\(176\) −76.4181 20.2190i −0.434194 0.114881i
\(177\) 0 0
\(178\) −10.8981 + 66.3328i −0.0612250 + 0.372656i
\(179\) −54.7154 + 132.095i −0.305673 + 0.737959i 0.694163 + 0.719818i \(0.255775\pi\)
−0.999835 + 0.0181410i \(0.994225\pi\)
\(180\) 0 0
\(181\) −128.496 310.218i −0.709925 1.71391i −0.700189 0.713957i \(-0.746901\pi\)
−0.00973575 0.999953i \(-0.503099\pi\)
\(182\) 55.9556 + 34.7345i 0.307448 + 0.190849i
\(183\) 0 0
\(184\) −268.764 142.844i −1.46067 0.776325i
\(185\) −8.16809 + 8.16809i −0.0441518 + 0.0441518i
\(186\) 0 0
\(187\) 47.3678 + 114.356i 0.253304 + 0.611530i
\(188\) −19.2013 + 56.8587i −0.102135 + 0.302440i
\(189\) 0 0
\(190\) −95.7274 133.366i −0.503829 0.701927i
\(191\) 312.806i 1.63773i −0.573986 0.818865i \(-0.694604\pi\)
0.573986 0.818865i \(-0.305396\pi\)
\(192\) 0 0
\(193\) −70.6708 −0.366170 −0.183085 0.983097i \(-0.558608\pi\)
−0.183085 + 0.983097i \(0.558608\pi\)
\(194\) −192.878 + 138.444i −0.994215 + 0.713627i
\(195\) 0 0
\(196\) −73.1653 24.7081i −0.373292 0.126062i
\(197\) −81.5762 + 33.7900i −0.414092 + 0.171523i −0.579996 0.814619i \(-0.696946\pi\)
0.165904 + 0.986142i \(0.446946\pi\)
\(198\) 0 0
\(199\) 102.666 + 102.666i 0.515910 + 0.515910i 0.916331 0.400421i \(-0.131136\pi\)
−0.400421 + 0.916331i \(0.631136\pi\)
\(200\) 8.24518 + 4.38218i 0.0412259 + 0.0219109i
\(201\) 0 0
\(202\) 208.060 335.175i 1.03000 1.65928i
\(203\) −2.76303 + 1.14449i −0.0136110 + 0.00563786i
\(204\) 0 0
\(205\) 198.701 + 82.3046i 0.969273 + 0.401486i
\(206\) −224.166 36.8290i −1.08818 0.178782i
\(207\) 0 0
\(208\) 48.6075 + 83.5828i 0.233690 + 0.401841i
\(209\) 83.0678i 0.397454i
\(210\) 0 0
\(211\) 8.35160 20.1625i 0.0395810 0.0955571i −0.902853 0.429950i \(-0.858531\pi\)
0.942434 + 0.334393i \(0.108531\pi\)
\(212\) 161.034 10.8089i 0.759593 0.0509852i
\(213\) 0 0
\(214\) −25.9001 + 41.7238i −0.121028 + 0.194971i
\(215\) 48.2292 48.2292i 0.224322 0.224322i
\(216\) 0 0
\(217\) 61.0233 61.0233i 0.281213 0.281213i
\(218\) 382.423 89.4854i 1.75423 0.410484i
\(219\) 0 0
\(220\) −42.8059 86.4591i −0.194572 0.392996i
\(221\) 57.9391 139.877i 0.262168 0.632930i
\(222\) 0 0
\(223\) 131.685i 0.590516i −0.955418 0.295258i \(-0.904594\pi\)
0.955418 0.295258i \(-0.0954056\pi\)
\(224\) 119.700 + 126.800i 0.534376 + 0.566073i
\(225\) 0 0
\(226\) 38.2380 + 53.2726i 0.169194 + 0.235719i
\(227\) −60.7552 25.1656i −0.267644 0.110862i 0.244825 0.969567i \(-0.421269\pi\)
−0.512470 + 0.858705i \(0.671269\pi\)
\(228\) 0 0
\(229\) 123.210 51.0352i 0.538035 0.222861i −0.0970835 0.995276i \(-0.530951\pi\)
0.635118 + 0.772415i \(0.280951\pi\)
\(230\) −84.6362 361.699i −0.367983 1.57261i
\(231\) 0 0
\(232\) −4.37050 0.420057i −0.0188383 0.00181059i
\(233\) −110.005 110.005i −0.472124 0.472124i 0.430477 0.902601i \(-0.358345\pi\)
−0.902601 + 0.430477i \(0.858345\pi\)
\(234\) 0 0
\(235\) −67.6692 + 28.0295i −0.287954 + 0.119274i
\(236\) 153.559 10.3071i 0.650673 0.0436743i
\(237\) 0 0
\(238\) 44.2665 269.435i 0.185994 1.13208i
\(239\) −277.831 −1.16247 −0.581236 0.813735i \(-0.697431\pi\)
−0.581236 + 0.813735i \(0.697431\pi\)
\(240\) 0 0
\(241\) 52.0006i 0.215770i 0.994163 + 0.107885i \(0.0344079\pi\)
−0.994163 + 0.107885i \(0.965592\pi\)
\(242\) −31.3189 + 190.628i −0.129417 + 0.787718i
\(243\) 0 0
\(244\) 121.663 + 106.358i 0.498620 + 0.435894i
\(245\) −36.0681 87.0762i −0.147217 0.355413i
\(246\) 0 0
\(247\) −71.8466 + 71.8466i −0.290877 + 0.290877i
\(248\) 121.155 37.0640i 0.488528 0.149452i
\(249\) 0 0
\(250\) 58.2113 + 248.771i 0.232845 + 0.995082i
\(251\) −28.7912 69.5080i −0.114706 0.276924i 0.856092 0.516823i \(-0.172886\pi\)
−0.970798 + 0.239899i \(0.922886\pi\)
\(252\) 0 0
\(253\) 71.9307 173.656i 0.284311 0.686388i
\(254\) −151.803 211.490i −0.597650 0.832637i
\(255\) 0 0
\(256\) 67.8107 + 246.856i 0.264885 + 0.964280i
\(257\) −241.501 −0.939692 −0.469846 0.882748i \(-0.655691\pi\)
−0.469846 + 0.882748i \(0.655691\pi\)
\(258\) 0 0
\(259\) 11.9123 + 4.93424i 0.0459935 + 0.0190511i
\(260\) −37.7562 + 111.803i −0.145216 + 0.430012i
\(261\) 0 0
\(262\) −51.2957 + 12.0030i −0.195785 + 0.0458129i
\(263\) 118.637 + 118.637i 0.451090 + 0.451090i 0.895716 0.444626i \(-0.146664\pi\)
−0.444626 + 0.895716i \(0.646664\pi\)
\(264\) 0 0
\(265\) 139.285 + 139.285i 0.525606 + 0.525606i
\(266\) −96.6423 + 155.686i −0.363317 + 0.585286i
\(267\) 0 0
\(268\) 174.849 200.010i 0.652420 0.746305i
\(269\) 231.194 + 95.7638i 0.859459 + 0.355999i 0.768496 0.639855i \(-0.221006\pi\)
0.0909629 + 0.995854i \(0.471006\pi\)
\(270\) 0 0
\(271\) −2.13724 −0.00788650 −0.00394325 0.999992i \(-0.501255\pi\)
−0.00394325 + 0.999992i \(0.501255\pi\)
\(272\) 243.029 318.791i 0.893488 1.17202i
\(273\) 0 0
\(274\) −412.752 67.8126i −1.50639 0.247491i
\(275\) −2.20670 + 5.32745i −0.00802437 + 0.0193725i
\(276\) 0 0
\(277\) −177.679 428.955i −0.641441 1.54857i −0.824737 0.565517i \(-0.808677\pi\)
0.183296 0.983058i \(-0.441323\pi\)
\(278\) −236.253 + 380.592i −0.849830 + 1.36904i
\(279\) 0 0
\(280\) −20.3606 + 211.843i −0.0727166 + 0.756582i
\(281\) 261.664 261.664i 0.931188 0.931188i −0.0665922 0.997780i \(-0.521213\pi\)
0.997780 + 0.0665922i \(0.0212126\pi\)
\(282\) 0 0
\(283\) 160.904 + 388.456i 0.568564 + 1.37264i 0.902765 + 0.430134i \(0.141534\pi\)
−0.334201 + 0.942502i \(0.608466\pi\)
\(284\) 262.495 129.962i 0.924280 0.457611i
\(285\) 0 0
\(286\) −48.5088 + 34.8186i −0.169611 + 0.121743i
\(287\) 240.066i 0.836465i
\(288\) 0 0
\(289\) −338.697 −1.17196
\(290\) −3.12471 4.35331i −0.0107749 0.0150114i
\(291\) 0 0
\(292\) 329.236 163.005i 1.12752 0.558236i
\(293\) 141.895 58.7749i 0.484284 0.200597i −0.127164 0.991882i \(-0.540587\pi\)
0.611448 + 0.791285i \(0.290587\pi\)
\(294\) 0 0
\(295\) 132.820 + 132.820i 0.450238 + 0.450238i
\(296\) 12.0432 + 14.6043i 0.0406864 + 0.0493389i
\(297\) 0 0
\(298\) 90.6919 + 56.2971i 0.304335 + 0.188916i
\(299\) −212.412 + 87.9838i −0.710407 + 0.294260i
\(300\) 0 0
\(301\) −70.3373 29.1347i −0.233679 0.0967929i
\(302\) 82.6009 502.764i 0.273513 1.66478i
\(303\) 0 0
\(304\) −232.554 + 135.241i −0.764979 + 0.444872i
\(305\) 197.226i 0.646643i
\(306\) 0 0
\(307\) −36.1806 + 87.3476i −0.117852 + 0.284520i −0.971787 0.235860i \(-0.924209\pi\)
0.853935 + 0.520379i \(0.174209\pi\)
\(308\) −70.8755 + 81.0746i −0.230115 + 0.263229i
\(309\) 0 0
\(310\) 131.377 + 81.5523i 0.423796 + 0.263072i
\(311\) −221.462 + 221.462i −0.712098 + 0.712098i −0.966974 0.254876i \(-0.917965\pi\)
0.254876 + 0.966974i \(0.417965\pi\)
\(312\) 0 0
\(313\) 280.384 280.384i 0.895795 0.895795i −0.0992662 0.995061i \(-0.531650\pi\)
0.995061 + 0.0992662i \(0.0316495\pi\)
\(314\) 71.9216 + 307.363i 0.229050 + 0.978862i
\(315\) 0 0
\(316\) −48.7864 + 144.466i −0.154387 + 0.457170i
\(317\) −155.972 + 376.549i −0.492024 + 1.18785i 0.461665 + 0.887055i \(0.347252\pi\)
−0.953688 + 0.300796i \(0.902748\pi\)
\(318\) 0 0
\(319\) 2.71148i 0.00849994i
\(320\) −172.356 + 260.600i −0.538613 + 0.814376i
\(321\) 0 0
\(322\) −336.847 + 241.782i −1.04611 + 0.750875i
\(323\) 389.183 + 161.205i 1.20490 + 0.499086i
\(324\) 0 0
\(325\) 6.51640 2.69918i 0.0200505 0.00830517i
\(326\) −320.735 + 75.0507i −0.983850 + 0.230217i
\(327\) 0 0
\(328\) 165.407 311.216i 0.504288 0.948830i
\(329\) 57.8104 + 57.8104i 0.175715 + 0.175715i
\(330\) 0 0
\(331\) −418.148 + 173.202i −1.26329 + 0.523270i −0.910917 0.412591i \(-0.864624\pi\)
−0.352370 + 0.935861i \(0.614624\pi\)
\(332\) 125.739 + 109.921i 0.378733 + 0.331089i
\(333\) 0 0
\(334\) −264.640 43.4787i −0.792336 0.130176i
\(335\) 324.232 0.967857
\(336\) 0 0
\(337\) 38.1203i 0.113116i −0.998399 0.0565582i \(-0.981987\pi\)
0.998399 0.0565582i \(-0.0180127\pi\)
\(338\) −261.457 42.9558i −0.773543 0.127088i
\(339\) 0 0
\(340\) 488.142 32.7650i 1.43571 0.0963676i
\(341\) 29.9424 + 72.2873i 0.0878076 + 0.211986i
\(342\) 0 0
\(343\) −263.195 + 263.195i −0.767333 + 0.767333i
\(344\) −71.1100 86.2324i −0.206715 0.250676i
\(345\) 0 0
\(346\) 226.416 52.9803i 0.654381 0.153122i
\(347\) 201.452 + 486.348i 0.580553 + 1.40158i 0.892313 + 0.451418i \(0.149082\pi\)
−0.311760 + 0.950161i \(0.600918\pi\)
\(348\) 0 0
\(349\) −53.2160 + 128.475i −0.152481 + 0.368122i −0.981600 0.190951i \(-0.938843\pi\)
0.829118 + 0.559073i \(0.188843\pi\)
\(350\) 10.3338 7.41742i 0.0295253 0.0211926i
\(351\) 0 0
\(352\) −147.742 + 56.2699i −0.419723 + 0.159858i
\(353\) 223.875 0.634208 0.317104 0.948391i \(-0.397290\pi\)
0.317104 + 0.948391i \(0.397290\pi\)
\(354\) 0 0
\(355\) 330.272 + 136.803i 0.930343 + 0.385361i
\(356\) 59.6525 + 120.486i 0.167563 + 0.338443i
\(357\) 0 0
\(358\) 65.1527 + 278.435i 0.181991 + 0.777752i
\(359\) 44.5652 + 44.5652i 0.124137 + 0.124137i 0.766446 0.642309i \(-0.222023\pi\)
−0.642309 + 0.766446i \(0.722023\pi\)
\(360\) 0 0
\(361\) 55.3658 + 55.3658i 0.153368 + 0.153368i
\(362\) −570.564 354.178i −1.57614 0.978393i
\(363\) 0 0
\(364\) 131.424 8.82141i 0.361055 0.0242346i
\(365\) 414.245 + 171.586i 1.13492 + 0.470098i
\(366\) 0 0
\(367\) −294.972 −0.803739 −0.401869 0.915697i \(-0.631639\pi\)
−0.401869 + 0.915697i \(0.631639\pi\)
\(368\) −603.271 + 81.3518i −1.63932 + 0.221065i
\(369\) 0 0
\(370\) −3.74544 + 22.7972i −0.0101228 + 0.0616141i
\(371\) 84.1406 203.133i 0.226794 0.547529i
\(372\) 0 0
\(373\) 96.5187 + 233.017i 0.258763 + 0.624710i 0.998857 0.0477936i \(-0.0152190\pi\)
−0.740094 + 0.672504i \(0.765219\pi\)
\(374\) 210.328 + 130.561i 0.562374 + 0.349094i
\(375\) 0 0
\(376\) 35.1125 + 114.776i 0.0933844 + 0.305255i
\(377\) −2.34520 + 2.34520i −0.00622069 + 0.00622069i
\(378\) 0 0
\(379\) −70.2002 169.478i −0.185225 0.447172i 0.803804 0.594894i \(-0.202806\pi\)
−0.989029 + 0.147722i \(0.952806\pi\)
\(380\) −311.072 105.050i −0.818609 0.276447i
\(381\) 0 0
\(382\) −364.805 508.241i −0.954987 1.33047i
\(383\) 519.043i 1.35520i 0.735429 + 0.677602i \(0.236981\pi\)
−0.735429 + 0.677602i \(0.763019\pi\)
\(384\) 0 0
\(385\) −131.429 −0.341373
\(386\) −114.824 + 82.4186i −0.297473 + 0.213520i
\(387\) 0 0
\(388\) −151.926 + 449.880i −0.391561 + 1.15949i
\(389\) −52.0121 + 21.5441i −0.133707 + 0.0553834i −0.448534 0.893766i \(-0.648054\pi\)
0.314827 + 0.949149i \(0.398054\pi\)
\(390\) 0 0
\(391\) 674.009 + 674.009i 1.72381 + 1.72381i
\(392\) −147.693 + 45.1826i −0.376767 + 0.115262i
\(393\) 0 0
\(394\) −93.1362 + 150.038i −0.236386 + 0.380807i
\(395\) −171.933 + 71.2169i −0.435273 + 0.180296i
\(396\) 0 0
\(397\) 138.533 + 57.3823i 0.348950 + 0.144540i 0.550272 0.834985i \(-0.314524\pi\)
−0.201322 + 0.979525i \(0.564524\pi\)
\(398\) 286.542 + 47.0770i 0.719955 + 0.118284i
\(399\) 0 0
\(400\) 18.5072 2.49572i 0.0462681 0.00623930i
\(401\) 11.3014i 0.0281830i 0.999901 + 0.0140915i \(0.00448560\pi\)
−0.999901 + 0.0140915i \(0.995514\pi\)
\(402\) 0 0
\(403\) 36.6248 88.4200i 0.0908803 0.219404i
\(404\) −52.8404 787.232i −0.130793 1.94859i
\(405\) 0 0
\(406\) −3.15458 + 5.08187i −0.00776989 + 0.0125169i
\(407\) −8.26612 + 8.26612i −0.0203099 + 0.0203099i
\(408\) 0 0
\(409\) 188.958 188.958i 0.462001 0.462001i −0.437310 0.899311i \(-0.644069\pi\)
0.899311 + 0.437310i \(0.144069\pi\)
\(410\) 418.831 98.0048i 1.02154 0.239036i
\(411\) 0 0
\(412\) −407.171 + 201.590i −0.988278 + 0.489297i
\(413\) 80.2350 193.704i 0.194274 0.469018i
\(414\) 0 0
\(415\) 203.834i 0.491166i
\(416\) 176.453 + 79.1159i 0.424167 + 0.190183i
\(417\) 0 0
\(418\) −96.8763 134.967i −0.231762 0.322887i
\(419\) 238.026 + 98.5936i 0.568081 + 0.235307i 0.648189 0.761479i \(-0.275527\pi\)
−0.0801080 + 0.996786i \(0.525527\pi\)
\(420\) 0 0
\(421\) 324.923 134.588i 0.771790 0.319686i 0.0381925 0.999270i \(-0.487840\pi\)
0.733597 + 0.679585i \(0.237840\pi\)
\(422\) −9.94472 42.4995i −0.0235657 0.100710i
\(423\) 0 0
\(424\) 249.038 205.365i 0.587355 0.484351i
\(425\) −20.6773 20.6773i −0.0486526 0.0486526i
\(426\) 0 0
\(427\) 203.388 84.2461i 0.476318 0.197298i
\(428\) 6.57776 + 97.9973i 0.0153686 + 0.228966i
\(429\) 0 0
\(430\) 22.1153 134.608i 0.0514309 0.313042i
\(431\) 16.1400 0.0374479 0.0187239 0.999825i \(-0.494040\pi\)
0.0187239 + 0.999825i \(0.494040\pi\)
\(432\) 0 0
\(433\) 732.781i 1.69233i 0.532918 + 0.846167i \(0.321095\pi\)
−0.532918 + 0.846167i \(0.678905\pi\)
\(434\) 27.9819 170.317i 0.0644745 0.392435i
\(435\) 0 0
\(436\) 516.992 591.388i 1.18576 1.35639i
\(437\) −244.799 590.996i −0.560180 1.35239i
\(438\) 0 0
\(439\) 460.630 460.630i 1.04927 1.04927i 0.0505487 0.998722i \(-0.483903\pi\)
0.998722 0.0505487i \(-0.0160970\pi\)
\(440\) −170.381 90.5551i −0.387231 0.205807i
\(441\) 0 0
\(442\) −68.9914 294.840i −0.156089 0.667059i
\(443\) 55.5453 + 134.098i 0.125384 + 0.302705i 0.974090 0.226161i \(-0.0726175\pi\)
−0.848705 + 0.528866i \(0.822618\pi\)
\(444\) 0 0
\(445\) −62.7927 + 151.595i −0.141107 + 0.340663i
\(446\) −153.575 213.959i −0.344339 0.479728i
\(447\) 0 0
\(448\) 342.365 + 66.4243i 0.764207 + 0.148269i
\(449\) −731.262 −1.62865 −0.814323 0.580412i \(-0.802892\pi\)
−0.814323 + 0.580412i \(0.802892\pi\)
\(450\) 0 0
\(451\) 201.086 + 83.2924i 0.445866 + 0.184684i
\(452\) 124.256 + 41.9617i 0.274903 + 0.0928356i
\(453\) 0 0
\(454\) −128.063 + 29.9662i −0.282077 + 0.0660047i
\(455\) 113.675 + 113.675i 0.249834 + 0.249834i
\(456\) 0 0
\(457\) −332.873 332.873i −0.728388 0.728388i 0.241911 0.970298i \(-0.422226\pi\)
−0.970298 + 0.241911i \(0.922226\pi\)
\(458\) 140.670 226.612i 0.307139 0.494787i
\(459\) 0 0
\(460\) −559.341 488.976i −1.21596 1.06299i
\(461\) 132.650 + 54.9455i 0.287744 + 0.119188i 0.521887 0.853015i \(-0.325228\pi\)
−0.234143 + 0.972202i \(0.575228\pi\)
\(462\) 0 0
\(463\) −873.591 −1.88680 −0.943402 0.331650i \(-0.892395\pi\)
−0.943402 + 0.331650i \(0.892395\pi\)
\(464\) −7.59097 + 4.41452i −0.0163598 + 0.00951404i
\(465\) 0 0
\(466\) −307.025 50.4422i −0.658852 0.108245i
\(467\) 135.550 327.247i 0.290258 0.700744i −0.709735 0.704468i \(-0.751186\pi\)
0.999993 + 0.00372448i \(0.00118554\pi\)
\(468\) 0 0
\(469\) −138.497 334.362i −0.295303 0.712925i
\(470\) −77.2585 + 124.460i −0.164380 + 0.264808i
\(471\) 0 0
\(472\) 237.478 195.832i 0.503132 0.414899i
\(473\) 48.8081 48.8081i 0.103188 0.103188i
\(474\) 0 0
\(475\) 7.50997 + 18.1307i 0.0158105 + 0.0381698i
\(476\) −242.301 489.397i −0.509035 1.02815i
\(477\) 0 0
\(478\) −451.413 + 324.015i −0.944379 + 0.677856i
\(479\) 296.032i 0.618021i 0.951059 + 0.309011i \(0.0999979\pi\)
−0.951059 + 0.309011i \(0.900002\pi\)
\(480\) 0 0
\(481\) 14.2990 0.0297276
\(482\) 60.6448 + 84.4895i 0.125819 + 0.175289i
\(483\) 0 0
\(484\) 171.430 + 346.253i 0.354194 + 0.715398i
\(485\) −535.416 + 221.777i −1.10395 + 0.457271i
\(486\) 0 0
\(487\) −232.632 232.632i −0.477683 0.477683i 0.426707 0.904390i \(-0.359674\pi\)
−0.904390 + 0.426707i \(0.859674\pi\)
\(488\) 321.714 + 30.9206i 0.659250 + 0.0633618i
\(489\) 0 0
\(490\) −160.154 99.4156i −0.326844 0.202889i
\(491\) −217.435 + 90.0644i −0.442840 + 0.183430i −0.592951 0.805239i \(-0.702037\pi\)
0.150110 + 0.988669i \(0.452037\pi\)
\(492\) 0 0
\(493\) 12.7036 + 5.26201i 0.0257680 + 0.0106735i
\(494\) −32.9449 + 200.524i −0.0666901 + 0.405920i
\(495\) 0 0
\(496\) 153.624 201.515i 0.309727 0.406281i
\(497\) 399.026i 0.802869i
\(498\) 0 0
\(499\) 64.7699 156.368i 0.129799 0.313364i −0.845597 0.533822i \(-0.820755\pi\)
0.975396 + 0.220458i \(0.0707553\pi\)
\(500\) 384.705 + 336.309i 0.769409 + 0.672618i
\(501\) 0 0
\(502\) −127.842 79.3579i −0.254665 0.158083i
\(503\) 612.203 612.203i 1.21710 1.21710i 0.248460 0.968642i \(-0.420075\pi\)
0.968642 0.248460i \(-0.0799246\pi\)
\(504\) 0 0
\(505\) 680.913 680.913i 1.34834 1.34834i
\(506\) −85.6520 366.041i −0.169273 0.723400i
\(507\) 0 0
\(508\) −493.292 166.586i −0.971048 0.327925i
\(509\) 273.870 661.182i 0.538056 1.29898i −0.388022 0.921650i \(-0.626842\pi\)
0.926078 0.377332i \(-0.123158\pi\)
\(510\) 0 0
\(511\) 500.480i 0.979413i
\(512\) 398.068 + 322.003i 0.777477 + 0.628911i
\(513\) 0 0
\(514\) −392.385 + 281.646i −0.763395 + 0.547950i
\(515\) −512.302 212.202i −0.994761 0.412043i
\(516\) 0 0
\(517\) −68.4813 + 28.3659i −0.132459 + 0.0548663i
\(518\) 25.1093 5.87548i 0.0484736 0.0113426i
\(519\) 0 0
\(520\) 69.0430 + 225.688i 0.132775 + 0.434015i
\(521\) 527.816 + 527.816i 1.01308 + 1.01308i 0.999913 + 0.0131690i \(0.00419195\pi\)
0.0131690 + 0.999913i \(0.495808\pi\)
\(522\) 0 0
\(523\) 5.01268 2.07632i 0.00958447 0.00397002i −0.377886 0.925852i \(-0.623349\pi\)
0.387471 + 0.921882i \(0.373349\pi\)
\(524\) −69.3458 + 79.3249i −0.132339 + 0.151383i
\(525\) 0 0
\(526\) 331.116 + 54.4002i 0.629498 + 0.103423i
\(527\) −396.783 −0.752908
\(528\) 0 0
\(529\) 918.476i 1.73625i
\(530\) 388.747 + 63.8687i 0.733485 + 0.120507i
\(531\) 0 0
\(532\) 24.5439 + 365.663i 0.0461352 + 0.687336i
\(533\) −101.881 245.963i −0.191147 0.461469i
\(534\) 0 0
\(535\) −84.7624 + 84.7624i −0.158434 + 0.158434i
\(536\) 50.8322 528.886i 0.0948363 0.986727i
\(537\) 0 0
\(538\) 487.322 114.031i 0.905804 0.211954i
\(539\) −36.5010 88.1213i −0.0677199 0.163490i
\(540\) 0 0
\(541\) −229.279 + 553.528i −0.423806 + 1.02316i 0.557409 + 0.830238i \(0.311796\pi\)
−0.981215 + 0.192919i \(0.938204\pi\)
\(542\) −3.47254 + 2.49252i −0.00640691 + 0.00459875i
\(543\) 0 0
\(544\) 23.0836 801.392i 0.0424330 1.47315i
\(545\) 958.688 1.75906
\(546\) 0 0
\(547\) −391.381 162.115i −0.715504 0.296371i −0.00492387 0.999988i \(-0.501567\pi\)
−0.710580 + 0.703617i \(0.751567\pi\)
\(548\) −749.716 + 371.185i −1.36809 + 0.677344i
\(549\) 0 0
\(550\) 2.62764 + 11.2294i 0.00477753 + 0.0204172i
\(551\) −6.52508 6.52508i −0.0118423 0.0118423i
\(552\) 0 0
\(553\) 146.884 + 146.884i 0.265613 + 0.265613i
\(554\) −788.950 489.742i −1.42410 0.884010i
\(555\) 0 0
\(556\) 60.0003 + 893.903i 0.107914 + 1.60774i
\(557\) −364.486 150.975i −0.654374 0.271050i 0.0306953 0.999529i \(-0.490228\pi\)
−0.685069 + 0.728478i \(0.740228\pi\)
\(558\) 0 0
\(559\) −84.4296 −0.151037
\(560\) 213.977 + 367.943i 0.382101 + 0.657041i
\(561\) 0 0
\(562\) 119.985 730.306i 0.213496 1.29948i
\(563\) −114.762 + 277.059i −0.203840 + 0.492113i −0.992431 0.122805i \(-0.960811\pi\)
0.788591 + 0.614918i \(0.210811\pi\)
\(564\) 0 0
\(565\) 61.2544 + 147.881i 0.108415 + 0.261736i
\(566\) 714.463 + 443.503i 1.26230 + 0.783575i
\(567\) 0 0
\(568\) 274.931 517.289i 0.484034 0.910721i
\(569\) −172.424 + 172.424i −0.303029 + 0.303029i −0.842198 0.539169i \(-0.818739\pi\)
0.539169 + 0.842198i \(0.318739\pi\)
\(570\) 0 0
\(571\) 295.206 + 712.690i 0.516998 + 1.24814i 0.939739 + 0.341894i \(0.111068\pi\)
−0.422740 + 0.906251i \(0.638932\pi\)
\(572\) −38.2094 + 113.145i −0.0667996 + 0.197806i
\(573\) 0 0
\(574\) −279.972 390.053i −0.487757 0.679535i
\(575\) 44.4059i 0.0772276i
\(576\) 0 0
\(577\) −756.330 −1.31080 −0.655398 0.755283i \(-0.727499\pi\)
−0.655398 + 0.755283i \(0.727499\pi\)
\(578\) −550.307 + 394.999i −0.952088 + 0.683389i
\(579\) 0 0
\(580\) −10.1539 3.42901i −0.0175068 0.00591209i
\(581\) 210.202 87.0686i 0.361794 0.149860i
\(582\) 0 0
\(583\) 140.957 + 140.957i 0.241779 + 0.241779i
\(584\) 344.834 648.813i 0.590469 1.11098i
\(585\) 0 0
\(586\) 162.003 260.979i 0.276455 0.445356i
\(587\) −736.720 + 305.159i −1.25506 + 0.519863i −0.908390 0.418125i \(-0.862688\pi\)
−0.346670 + 0.937987i \(0.612688\pi\)
\(588\) 0 0
\(589\) 246.012 + 101.902i 0.417678 + 0.173008i
\(590\) 370.702 + 60.9040i 0.628309 + 0.103227i
\(591\) 0 0
\(592\) 36.5995 + 9.68362i 0.0618234 + 0.0163575i
\(593\) 76.7003i 0.129343i −0.997907 0.0646714i \(-0.979400\pi\)
0.997907 0.0646714i \(-0.0205999\pi\)
\(594\) 0 0
\(595\) 255.056 615.759i 0.428665 1.03489i
\(596\) 213.010 14.2976i 0.357399 0.0239892i
\(597\) 0 0
\(598\) −242.512 + 390.676i −0.405539 + 0.653304i
\(599\) −34.1251 + 34.1251i −0.0569702 + 0.0569702i −0.735018 0.678048i \(-0.762826\pi\)
0.678048 + 0.735018i \(0.262826\pi\)
\(600\) 0 0
\(601\) 212.552 212.552i 0.353664 0.353664i −0.507807 0.861471i \(-0.669544\pi\)
0.861471 + 0.507807i \(0.169544\pi\)
\(602\) −148.260 + 34.6923i −0.246280 + 0.0576284i
\(603\) 0 0
\(604\) −452.131 913.211i −0.748561 1.51194i
\(605\) −180.454 + 435.655i −0.298271 + 0.720091i
\(606\) 0 0
\(607\) 56.8377i 0.0936371i 0.998903 + 0.0468186i \(0.0149083\pi\)
−0.998903 + 0.0468186i \(0.985092\pi\)
\(608\) −220.125 + 490.949i −0.362048 + 0.807481i
\(609\) 0 0
\(610\) 230.012 + 320.449i 0.377068 + 0.525326i
\(611\) 83.7646 + 34.6964i 0.137094 + 0.0567863i
\(612\) 0 0
\(613\) −7.45320 + 3.08722i −0.0121586 + 0.00503624i −0.388754 0.921341i \(-0.627095\pi\)
0.376596 + 0.926378i \(0.377095\pi\)
\(614\) 43.0822 + 184.115i 0.0701665 + 0.299862i
\(615\) 0 0
\(616\) −20.6050 + 214.386i −0.0334497 + 0.348028i
\(617\) 325.733 + 325.733i 0.527931 + 0.527931i 0.919955 0.392024i \(-0.128225\pi\)
−0.392024 + 0.919955i \(0.628225\pi\)
\(618\) 0 0
\(619\) 76.1643 31.5483i 0.123044 0.0509665i −0.320312 0.947312i \(-0.603788\pi\)
0.443356 + 0.896346i \(0.353788\pi\)
\(620\) 308.567 20.7116i 0.497689 0.0334058i
\(621\) 0 0
\(622\) −101.551 + 618.104i −0.163265 + 0.993736i
\(623\) 183.153 0.293986
\(624\) 0 0
\(625\) 594.458i 0.951133i
\(626\) 128.569 782.554i 0.205381 1.25009i
\(627\) 0 0
\(628\) 475.313 + 415.519i 0.756868 + 0.661654i
\(629\) −22.6862 54.7694i −0.0360671 0.0870738i
\(630\) 0 0
\(631\) 70.1301 70.1301i 0.111141 0.111141i −0.649349 0.760490i \(-0.724959\pi\)
0.760490 + 0.649349i \(0.224959\pi\)
\(632\) 89.2134 + 291.621i 0.141160 + 0.461425i
\(633\) 0 0
\(634\) 185.724 + 793.707i 0.292940 + 1.25190i
\(635\) −243.177 587.082i −0.382956 0.924538i
\(636\) 0 0
\(637\) −44.6471 + 107.788i −0.0700897 + 0.169211i
\(638\) −3.16222 4.40555i −0.00495645 0.00690526i
\(639\) 0 0
\(640\) 23.8802 + 624.425i 0.0373128 + 0.975664i
\(641\) −458.396 −0.715126 −0.357563 0.933889i \(-0.616392\pi\)
−0.357563 + 0.933889i \(0.616392\pi\)
\(642\) 0 0
\(643\) −882.443 365.520i −1.37238 0.568460i −0.429950 0.902853i \(-0.641469\pi\)
−0.942434 + 0.334393i \(0.891469\pi\)
\(644\) −265.327 + 785.684i −0.411999 + 1.22001i
\(645\) 0 0
\(646\) 820.338 191.956i 1.26987 0.297145i
\(647\) 130.433 + 130.433i 0.201597 + 0.201597i 0.800684 0.599087i \(-0.204470\pi\)
−0.599087 + 0.800684i \(0.704470\pi\)
\(648\) 0 0
\(649\) 134.414 + 134.414i 0.207110 + 0.207110i
\(650\) 7.43982 11.9852i 0.0114459 0.0184388i
\(651\) 0 0
\(652\) −433.597 + 495.992i −0.665026 + 0.760724i
\(653\) −989.811 409.993i −1.51579 0.627861i −0.539047 0.842275i \(-0.681216\pi\)
−0.976743 + 0.214415i \(0.931216\pi\)
\(654\) 0 0
\(655\) −128.592 −0.196324
\(656\) −94.2016 698.560i −0.143600 1.06488i
\(657\) 0 0
\(658\) 161.349 + 26.5087i 0.245212 + 0.0402867i
\(659\) 457.745 1105.09i 0.694605 1.67693i −0.0406841 0.999172i \(-0.512954\pi\)
0.735289 0.677753i \(-0.237046\pi\)
\(660\) 0 0
\(661\) −96.2729 232.423i −0.145647 0.351624i 0.834173 0.551502i \(-0.185945\pi\)
−0.979821 + 0.199879i \(0.935945\pi\)
\(662\) −477.403 + 769.073i −0.721152 + 1.16174i
\(663\) 0 0
\(664\) 332.493 + 31.9565i 0.500742 + 0.0481273i
\(665\) −316.278 + 316.278i −0.475607 + 0.475607i
\(666\) 0 0
\(667\) −7.99066 19.2912i −0.0119800 0.0289223i
\(668\) −480.688 + 237.989i −0.719592 + 0.356271i
\(669\) 0 0
\(670\) 526.805 378.130i 0.786277 0.564373i
\(671\) 199.593i 0.297456i
\(672\) 0 0
\(673\) −135.640 −0.201545 −0.100772 0.994910i \(-0.532131\pi\)
−0.100772 + 0.994910i \(0.532131\pi\)
\(674\) −44.4571 61.9369i −0.0659601 0.0918946i
\(675\) 0 0
\(676\) −474.907 + 235.127i −0.702525 + 0.347820i
\(677\) 348.196 144.228i 0.514322 0.213039i −0.110399 0.993887i \(-0.535213\pi\)
0.624721 + 0.780848i \(0.285213\pi\)
\(678\) 0 0
\(679\) 457.411 + 457.411i 0.673653 + 0.673653i
\(680\) 754.911 622.523i 1.11016 0.915476i
\(681\) 0 0
\(682\) 132.954 + 82.5310i 0.194947 + 0.121013i
\(683\) 812.940 336.731i 1.19025 0.493017i 0.302413 0.953177i \(-0.402208\pi\)
0.887836 + 0.460159i \(0.152208\pi\)
\(684\) 0 0
\(685\) −943.292 390.724i −1.37707 0.570400i
\(686\) −120.687 + 734.581i −0.175928 + 1.07082i
\(687\) 0 0
\(688\) −216.105 57.1778i −0.314106 0.0831073i
\(689\) 243.832i 0.353892i
\(690\) 0 0
\(691\) −78.3893 + 189.249i −0.113443 + 0.273876i −0.970396 0.241518i \(-0.922355\pi\)
0.856953 + 0.515395i \(0.172355\pi\)
\(692\) 306.088 350.135i 0.442323 0.505975i
\(693\) 0 0
\(694\) 894.509 + 555.267i 1.28892 + 0.800097i
\(695\) −773.177 + 773.177i −1.11249 + 1.11249i
\(696\) 0 0
\(697\) −780.471 + 780.471i −1.11976 + 1.11976i
\(698\) 63.3672 + 270.805i 0.0907840 + 0.387973i
\(699\) 0 0
\(700\) 8.13975 24.1033i 0.0116282 0.0344333i
\(701\) −432.140 + 1043.28i −0.616463 + 1.48827i 0.239322 + 0.970940i \(0.423075\pi\)
−0.855785 + 0.517332i \(0.826925\pi\)
\(702\) 0 0
\(703\) 39.7843i 0.0565921i
\(704\) −174.425 + 263.728i −0.247762 + 0.374614i
\(705\) 0 0
\(706\) 363.748 261.091i 0.515223 0.369817i
\(707\) −993.041 411.331i −1.40458 0.581798i
\(708\) 0 0
\(709\) 367.507 152.226i 0.518345 0.214706i −0.108145 0.994135i \(-0.534491\pi\)
0.626490 + 0.779430i \(0.284491\pi\)
\(710\) 696.162 162.899i 0.980510 0.229435i
\(711\) 0 0
\(712\) 237.436 + 126.194i 0.333478 + 0.177238i
\(713\) 426.058 + 426.058i 0.597556 + 0.597556i
\(714\) 0 0
\(715\) −134.657 + 55.7768i −0.188332 + 0.0780096i
\(716\) 430.579 + 376.412i 0.601367 + 0.525715i
\(717\) 0 0
\(718\) 124.382 + 20.4352i 0.173234 + 0.0284612i
\(719\) 100.566 0.139869 0.0699344 0.997552i \(-0.477721\pi\)
0.0699344 + 0.997552i \(0.477721\pi\)
\(720\) 0 0
\(721\) 618.950i 0.858461i
\(722\) 154.527 + 25.3877i 0.214026 + 0.0351631i
\(723\) 0 0
\(724\) −1340.09 + 89.9495i −1.85096 + 0.124240i
\(725\) 0.245139 + 0.591817i 0.000338122 + 0.000816300i
\(726\) 0 0
\(727\) −332.402 + 332.402i −0.457224 + 0.457224i −0.897743 0.440519i \(-0.854794\pi\)
0.440519 + 0.897743i \(0.354794\pi\)
\(728\) 203.247 167.604i 0.279185 0.230225i
\(729\) 0 0
\(730\) 873.164 204.317i 1.19612 0.279886i
\(731\) 133.953 + 323.391i 0.183246 + 0.442395i
\(732\) 0 0
\(733\) −166.189 + 401.215i −0.226724 + 0.547360i −0.995775 0.0918276i \(-0.970729\pi\)
0.769051 + 0.639187i \(0.220729\pi\)
\(734\) −479.264 + 344.006i −0.652948 + 0.468673i
\(735\) 0 0
\(736\) −885.306 + 835.733i −1.20286 + 1.13551i
\(737\) 328.124 0.445215
\(738\) 0 0
\(739\) 1011.25 + 418.874i 1.36840 + 0.566812i 0.941355 0.337417i \(-0.109553\pi\)
0.427049 + 0.904229i \(0.359553\pi\)
\(740\) 20.5014 + 41.4085i 0.0277045 + 0.0559574i
\(741\) 0 0
\(742\) −100.191 428.174i −0.135028 0.577054i
\(743\) −458.897 458.897i −0.617627 0.617627i 0.327295 0.944922i \(-0.393863\pi\)
−0.944922 + 0.327295i \(0.893863\pi\)
\(744\) 0 0
\(745\) 184.242 + 184.242i 0.247304 + 0.247304i
\(746\) 428.573 + 266.037i 0.574495 + 0.356618i
\(747\) 0 0
\(748\) 494.001 33.1582i 0.660429 0.0443292i
\(749\) 123.617 + 51.2039i 0.165043 + 0.0683630i
\(750\) 0 0
\(751\) −636.920 −0.848096 −0.424048 0.905640i \(-0.639391\pi\)
−0.424048 + 0.905640i \(0.639391\pi\)
\(752\) 190.905 + 145.536i 0.253864 + 0.193532i
\(753\) 0 0
\(754\) −1.07538 + 6.54548i −0.00142623 + 0.00868100i
\(755\) 475.932 1149.00i 0.630373 1.52186i
\(756\) 0 0
\(757\) −414.804 1001.43i −0.547958 1.32289i −0.918995 0.394269i \(-0.870998\pi\)
0.371038 0.928618i \(-0.379002\pi\)
\(758\) −311.711 193.495i −0.411228 0.255270i
\(759\) 0 0
\(760\) −627.935 + 192.099i −0.826230 + 0.252762i
\(761\) 520.779 520.779i 0.684334 0.684334i −0.276639 0.960974i \(-0.589221\pi\)
0.960974 + 0.276639i \(0.0892207\pi\)
\(762\) 0 0
\(763\) −409.508 988.640i −0.536708 1.29573i
\(764\) −1185.45 400.331i −1.55164 0.523993i
\(765\) 0 0
\(766\) 605.325 + 843.330i 0.790241 + 1.10095i
\(767\) 232.514i 0.303147i
\(768\) 0 0
\(769\) 973.035 1.26533 0.632663 0.774427i \(-0.281962\pi\)
0.632663 + 0.774427i \(0.281962\pi\)
\(770\) −213.542 + 153.276i −0.277328 + 0.199060i
\(771\) 0 0
\(772\) −90.4448 + 267.824i −0.117157 + 0.346922i
\(773\) −959.578 + 397.470i −1.24137 + 0.514192i −0.904142 0.427232i \(-0.859489\pi\)
−0.337227 + 0.941423i \(0.609489\pi\)
\(774\) 0 0
\(775\) −13.0707 13.0707i −0.0168654 0.0168654i
\(776\) 277.819 + 908.136i 0.358015 + 1.17028i
\(777\) 0 0
\(778\) −59.3827 + 95.6626i −0.0763273 + 0.122960i
\(779\) 684.346 283.465i 0.878493 0.363884i
\(780\) 0 0
\(781\) 334.236 + 138.445i 0.427958 + 0.177266i
\(782\) 1881.17 + 309.064i 2.40558 + 0.395222i
\(783\) 0 0
\(784\) −187.275 + 245.656i −0.238871 + 0.313336i
\(785\) 770.521i 0.981556i
\(786\) 0 0
\(787\) 412.612 996.133i 0.524284 1.26573i −0.410935 0.911665i \(-0.634798\pi\)
0.935219 0.354070i \(-0.115202\pi\)
\(788\) 23.6535 + 352.397i 0.0300171 + 0.447204i
\(789\) 0 0
\(790\) −196.297 + 316.225i −0.248477 + 0.400285i
\(791\) 126.336 126.336i 0.159717 0.159717i
\(792\) 0 0
\(793\) 172.631 172.631i 0.217694 0.217694i
\(794\) 292.006 68.3283i 0.367766 0.0860558i
\(795\) 0 0
\(796\) 520.470 257.685i 0.653856 0.323725i
\(797\) 46.5600 112.406i 0.0584191 0.141036i −0.891975 0.452085i \(-0.850680\pi\)
0.950394 + 0.311049i \(0.100680\pi\)
\(798\) 0 0
\(799\) 375.892i 0.470453i
\(800\) 27.1595 25.6387i 0.0339494 0.0320484i
\(801\) 0 0
\(802\) 13.1800 + 18.3622i 0.0164339 + 0.0228955i
\(803\) 419.216 + 173.645i 0.522063 + 0.216245i
\(804\) 0 0
\(805\) −935.065 + 387.317i −1.16157 + 0.481139i
\(806\) −43.6112 186.376i −0.0541082 0.231236i
\(807\) 0 0
\(808\) −1003.95 1217.45i −1.24251 1.50675i
\(809\) 80.8371 + 80.8371i 0.0999222 + 0.0999222i 0.755301 0.655378i \(-0.227491\pi\)
−0.655378 + 0.755301i \(0.727491\pi\)
\(810\) 0 0
\(811\) 1277.99 529.360i 1.57582 0.652725i 0.588074 0.808807i \(-0.299886\pi\)
0.987744 + 0.156082i \(0.0498865\pi\)
\(812\) 0.801157 + 11.9359i 0.000986647 + 0.0146994i
\(813\) 0 0
\(814\) −3.79039 + 23.0708i −0.00465650 + 0.0283425i
\(815\) −804.044 −0.986557
\(816\) 0 0
\(817\) 234.910i 0.287527i
\(818\) 86.6459 527.384i 0.105924 0.644724i
\(819\) 0 0
\(820\) 566.211 647.690i 0.690501 0.789866i
\(821\) −83.7084 202.090i −0.101959 0.246151i 0.864666 0.502348i \(-0.167530\pi\)
−0.966625 + 0.256197i \(0.917530\pi\)
\(822\) 0 0
\(823\) 588.539 588.539i 0.715114 0.715114i −0.252486 0.967601i \(-0.581248\pi\)
0.967601 + 0.252486i \(0.0812482\pi\)
\(824\) −426.460 + 802.395i −0.517549 + 0.973780i
\(825\) 0 0
\(826\) −95.5403 408.299i −0.115666 0.494309i
\(827\) −281.470 679.529i −0.340351 0.821679i −0.997680 0.0680759i \(-0.978314\pi\)
0.657329 0.753603i \(-0.271686\pi\)
\(828\) 0 0
\(829\) 6.83745 16.5071i 0.00824783 0.0199120i −0.919702 0.392617i \(-0.871570\pi\)
0.927950 + 0.372705i \(0.121570\pi\)
\(830\) 237.718 + 331.185i 0.286407 + 0.399018i
\(831\) 0 0
\(832\) 378.965 77.2398i 0.455487 0.0928363i
\(833\) 483.695 0.580666
\(834\) 0 0
\(835\) −604.801 250.517i −0.724313 0.300020i
\(836\) −314.805 106.311i −0.376561 0.127166i
\(837\) 0 0
\(838\) 501.723 117.401i 0.598714 0.140097i
\(839\) 358.991 + 358.991i 0.427879 + 0.427879i 0.887905 0.460026i \(-0.152160\pi\)
−0.460026 + 0.887905i \(0.652160\pi\)
\(840\) 0 0
\(841\) 594.464 + 594.464i 0.706854 + 0.706854i
\(842\) 370.968 597.611i 0.440579 0.709752i
\(843\) 0 0
\(844\) −65.7223 57.4545i −0.0778700 0.0680740i
\(845\) −597.527 247.504i −0.707133 0.292904i
\(846\) 0 0
\(847\) 526.348 0.621426
\(848\) 165.129 624.109i 0.194727 0.735977i
\(849\) 0 0
\(850\) −57.7107 9.48150i −0.0678949 0.0111547i
\(851\) −34.4503 + 83.1704i −0.0404821 + 0.0977325i
\(852\) 0 0
\(853\) 545.396 + 1316.70i 0.639386 + 1.54361i 0.827499 + 0.561467i \(0.189763\pi\)
−0.188114 + 0.982147i \(0.560237\pi\)
\(854\) 232.210 374.079i 0.271908 0.438031i
\(855\) 0 0
\(856\) 124.975 + 151.553i 0.145999 + 0.177048i
\(857\) −157.052 + 157.052i −0.183258 + 0.183258i −0.792774 0.609516i \(-0.791364\pi\)
0.609516 + 0.792774i \(0.291364\pi\)
\(858\) 0 0
\(859\) 17.7307 + 42.8057i 0.0206411 + 0.0498321i 0.933864 0.357628i \(-0.116414\pi\)
−0.913223 + 0.407460i \(0.866414\pi\)
\(860\) −121.052 244.500i −0.140758 0.284302i
\(861\) 0 0
\(862\) 26.2240 18.8230i 0.0304222 0.0218365i
\(863\) 186.088i 0.215629i −0.994171 0.107815i \(-0.965615\pi\)
0.994171 0.107815i \(-0.0343853\pi\)
\(864\) 0 0
\(865\) 567.597 0.656181
\(866\) 854.592 + 1190.61i 0.986827 + 1.37483i
\(867\) 0 0
\(868\) −153.164 309.360i −0.176457 0.356406i
\(869\) −173.996 + 72.0716i −0.200226 + 0.0829363i
\(870\) 0 0
\(871\) −283.799 283.799i −0.325831 0.325831i
\(872\) 150.301 1563.81i 0.172363 1.79336i
\(873\) 0 0
\(874\) −1086.98 674.745i −1.24369 0.772020i
\(875\) 643.121 266.390i 0.734996 0.304445i
\(876\) 0 0
\(877\) −216.654 89.7412i −0.247040 0.102328i 0.255728 0.966749i \(-0.417685\pi\)
−0.502768 + 0.864421i \(0.667685\pi\)
\(878\) 211.220 1285.62i 0.240569 1.46426i
\(879\) 0 0
\(880\) −382.440 + 51.5725i −0.434591 + 0.0586051i
\(881\) 47.9671i 0.0544462i −0.999629 0.0272231i \(-0.991334\pi\)
0.999629 0.0272231i \(-0.00866645\pi\)
\(882\) 0 0
\(883\) 115.380 278.551i 0.130668 0.315460i −0.844982 0.534795i \(-0.820389\pi\)
0.975650 + 0.219335i \(0.0703888\pi\)
\(884\) −455.948 398.590i −0.515778 0.450893i
\(885\) 0 0
\(886\) 246.639 + 153.101i 0.278373 + 0.172800i
\(887\) −233.227 + 233.227i −0.262939 + 0.262939i −0.826247 0.563308i \(-0.809528\pi\)
0.563308 + 0.826247i \(0.309528\pi\)
\(888\) 0 0
\(889\) −501.549 + 501.549i −0.564172 + 0.564172i
\(890\) 74.7708 + 319.539i 0.0840122 + 0.359033i
\(891\) 0 0
\(892\) −499.052 168.531i −0.559475 0.188936i
\(893\) −96.5364 + 233.059i −0.108103 + 0.260985i
\(894\) 0 0
\(895\) 698.004i 0.779892i
\(896\) 633.733 291.352i 0.707291 0.325170i
\(897\) 0 0
\(898\) −1188.14 + 852.821i −1.32309 + 0.949690i
\(899\) 8.03028 + 3.32625i 0.00893246 + 0.00369994i
\(900\) 0 0
\(901\) −933.949 + 386.854i −1.03657 + 0.429361i
\(902\) 423.858 99.1810i 0.469909 0.109957i
\(903\) 0 0
\(904\) 250.826 76.7333i 0.277462 0.0848820i
\(905\) −1159.11 1159.11i −1.28078 1.28078i
\(906\) 0 0
\(907\) −827.946 + 342.947i −0.912841 + 0.378111i −0.789143 0.614209i \(-0.789475\pi\)
−0.123697 + 0.992320i \(0.539475\pi\)
\(908\) −173.126 + 198.039i −0.190667 + 0.218105i
\(909\) 0 0
\(910\) 317.267 + 52.1249i 0.348645 + 0.0572801i
\(911\) −1321.92 −1.45107 −0.725534 0.688186i \(-0.758407\pi\)
−0.725534 + 0.688186i \(0.758407\pi\)
\(912\) 0 0
\(913\) 206.280i 0.225937i
\(914\) −929.052 152.637i −1.01647 0.166999i
\(915\) 0 0
\(916\) −35.7255 532.248i −0.0390016 0.581057i
\(917\) 54.9287 + 132.610i 0.0599004 + 0.144612i
\(918\) 0 0
\(919\) −717.026 + 717.026i −0.780224 + 0.780224i −0.979868 0.199645i \(-0.936021\pi\)
0.199645 + 0.979868i \(0.436021\pi\)
\(920\) −1479.06 142.156i −1.60768 0.154517i
\(921\) 0 0
\(922\) 279.606 65.4267i 0.303260 0.0709617i
\(923\) −169.342 408.828i −0.183469 0.442934i
\(924\) 0 0
\(925\) 1.05687 2.55151i 0.00114256 0.00275839i
\(926\) −1419.39 + 1018.81i −1.53282 + 1.10023i
\(927\) 0 0
\(928\) −7.18528 + 16.0254i −0.00774276 + 0.0172688i
\(929\) 430.578 0.463485 0.231743 0.972777i \(-0.425557\pi\)
0.231743 + 0.972777i \(0.425557\pi\)
\(930\) 0 0
\(931\) −299.899 124.222i −0.322126 0.133429i
\(932\) −557.674 + 276.105i −0.598363 + 0.296250i
\(933\) 0 0
\(934\) −161.407 689.787i −0.172813 0.738530i
\(935\) 427.284 + 427.284i 0.456988 + 0.456988i
\(936\) 0 0
\(937\) 752.850 + 752.850i 0.803469 + 0.803469i 0.983636 0.180167i \(-0.0576639\pi\)
−0.180167 + 0.983636i \(0.557664\pi\)
\(938\) −614.971 381.744i −0.655619 0.406976i
\(939\) 0 0
\(940\) 19.6211 + 292.321i 0.0208735 + 0.310979i
\(941\) 1482.20 + 613.948i 1.57513 + 0.652442i 0.987633 0.156781i \(-0.0501118\pi\)
0.587501 + 0.809223i \(0.300112\pi\)
\(942\) 0 0
\(943\) 1676.11 1.77742
\(944\) 157.464 595.139i 0.166805 0.630444i
\(945\) 0 0
\(946\) 22.3807 136.224i 0.0236582 0.144000i
\(947\) −528.730 + 1276.47i −0.558321 + 1.34791i 0.352773 + 0.935709i \(0.385239\pi\)
−0.911094 + 0.412198i \(0.864761\pi\)
\(948\) 0 0
\(949\) −212.398 512.775i −0.223813 0.540332i
\(950\) 33.3466 + 20.6999i 0.0351017 + 0.0217894i
\(951\) 0 0
\(952\) −964.436 512.583i −1.01306 0.538427i
\(953\) 538.112 538.112i 0.564650 0.564650i −0.365975 0.930625i \(-0.619264\pi\)
0.930625 + 0.365975i \(0.119264\pi\)
\(954\) 0 0
\(955\) −584.391 1410.84i −0.611927 1.47732i
\(956\) −355.569 + 1052.91i −0.371934 + 1.10137i
\(957\) 0 0
\(958\) 345.242 + 480.987i 0.360378 + 0.502074i
\(959\) 1139.66i 1.18839i
\(960\) 0 0
\(961\) 710.184 0.739005
\(962\) 23.2327 16.6759i 0.0241504 0.0173347i
\(963\) 0 0
\(964\) 197.069 + 66.5506i 0.204428 + 0.0690359i
\(965\) −318.745 + 132.028i −0.330306 + 0.136817i
\(966\) 0 0
\(967\) −380.769 380.769i −0.393763 0.393763i 0.482263 0.876026i \(-0.339815\pi\)
−0.876026 + 0.482263i \(0.839815\pi\)
\(968\) 682.347 + 362.657i 0.704904 + 0.374645i
\(969\) 0 0
\(970\) −611.289 + 984.757i −0.630195 + 1.01521i
\(971\) 1000.67 414.490i 1.03055 0.426869i 0.197642 0.980274i \(-0.436672\pi\)
0.832912 + 0.553405i \(0.186672\pi\)
\(972\) 0 0
\(973\) 1127.60 + 467.067i 1.15889 + 0.480028i
\(974\) −649.277 106.672i −0.666609 0.109520i
\(975\) 0 0
\(976\) 558.775 324.954i 0.572515 0.332945i
\(977\) 920.476i 0.942145i 0.882095 + 0.471072i \(0.156133\pi\)
−0.882095 + 0.471072i \(0.843867\pi\)
\(978\) 0 0
\(979\) −63.5463 + 153.414i −0.0649094 + 0.156705i
\(980\) −376.156 + 25.2483i −0.383833 + 0.0257635i
\(981\) 0 0
\(982\) −248.247 + 399.914i −0.252797 + 0.407244i
\(983\) −465.265 + 465.265i −0.473312 + 0.473312i −0.902985 0.429673i \(-0.858629\pi\)
0.429673 + 0.902985i \(0.358629\pi\)
\(984\) 0 0
\(985\) −304.804 + 304.804i −0.309446 + 0.309446i
\(986\) 26.7773 6.26578i 0.0271575 0.00635474i
\(987\) 0 0
\(988\) 180.330 + 364.229i 0.182520 + 0.368653i
\(989\) 203.415 491.087i 0.205677 0.496549i
\(990\) 0 0
\(991\) 365.984i 0.369307i −0.982804 0.184654i \(-0.940884\pi\)
0.982804 0.184654i \(-0.0591164\pi\)
\(992\) 14.5917 506.580i 0.0147094 0.510665i
\(993\) 0 0
\(994\) −465.357 648.329i −0.468166 0.652242i
\(995\) 654.855 + 271.250i 0.658146 + 0.272613i
\(996\) 0 0
\(997\) −77.3922 + 32.0569i −0.0776251 + 0.0321534i −0.421158 0.906987i \(-0.638376\pi\)
0.343533 + 0.939141i \(0.388376\pi\)
\(998\) −77.1252 329.601i −0.0772798 0.330261i
\(999\) 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 288.3.u.a.19.6 28
3.2 odd 2 32.3.h.a.19.2 28
12.11 even 2 128.3.h.a.111.7 28
24.5 odd 2 256.3.h.b.223.7 28
24.11 even 2 256.3.h.a.223.1 28
32.27 odd 8 inner 288.3.u.a.91.6 28
96.5 odd 8 128.3.h.a.15.7 28
96.11 even 8 256.3.h.b.31.7 28
96.53 odd 8 256.3.h.a.31.1 28
96.59 even 8 32.3.h.a.27.2 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.3.h.a.19.2 28 3.2 odd 2
32.3.h.a.27.2 yes 28 96.59 even 8
128.3.h.a.15.7 28 96.5 odd 8
128.3.h.a.111.7 28 12.11 even 2
256.3.h.a.31.1 28 96.53 odd 8
256.3.h.a.223.1 28 24.11 even 2
256.3.h.b.31.7 28 96.11 even 8
256.3.h.b.223.7 28 24.5 odd 2
288.3.u.a.19.6 28 1.1 even 1 trivial
288.3.u.a.91.6 28 32.27 odd 8 inner