Properties

Label 354.4.c.a.353.14
Level $354$
Weight $4$
Character 354.353
Analytic conductor $20.887$
Analytic rank $0$
Dimension $30$
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] = [354,4,Mod(353,354)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(354, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("354.353");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 354.c (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: \(20.8866761420\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 353.14
Character \(\chi\) \(=\) 354.353
Dual form 354.4.c.a.353.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +(-1.46648 + 4.98492i) q^{3} +4.00000 q^{4} +18.9931i q^{5} +(2.93296 - 9.96984i) q^{6} -10.1890 q^{7} -8.00000 q^{8} +(-22.6989 - 14.6206i) q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +(-1.46648 + 4.98492i) q^{3} +4.00000 q^{4} +18.9931i q^{5} +(2.93296 - 9.96984i) q^{6} -10.1890 q^{7} -8.00000 q^{8} +(-22.6989 - 14.6206i) q^{9} -37.9861i q^{10} -10.1714 q^{11} +(-5.86593 + 19.9397i) q^{12} -82.2827i q^{13} +20.3780 q^{14} +(-94.6789 - 27.8530i) q^{15} +16.0000 q^{16} -92.4725i q^{17} +(45.3977 + 29.2412i) q^{18} +23.3309 q^{19} +75.9722i q^{20} +(14.9420 - 50.7914i) q^{21} +20.3427 q^{22} +39.6956 q^{23} +(11.7319 - 39.8794i) q^{24} -235.736 q^{25} +164.565i q^{26} +(106.170 - 91.7112i) q^{27} -40.7560 q^{28} +118.325i q^{29} +(189.358 + 55.7060i) q^{30} +30.7291i q^{31} -32.0000 q^{32} +(14.9161 - 50.7034i) q^{33} +184.945i q^{34} -193.520i q^{35} +(-90.7954 - 58.4824i) q^{36} +221.478i q^{37} -46.6619 q^{38} +(410.173 + 120.666i) q^{39} -151.944i q^{40} -63.0445i q^{41} +(-29.8840 + 101.583i) q^{42} +147.338i q^{43} -40.6854 q^{44} +(277.690 - 431.121i) q^{45} -79.3912 q^{46} -37.8072 q^{47} +(-23.4637 + 79.7587i) q^{48} -239.184 q^{49} +471.472 q^{50} +(460.968 + 135.609i) q^{51} -329.131i q^{52} +409.038i q^{53} +(-212.340 + 183.422i) q^{54} -193.185i q^{55} +81.5120 q^{56} +(-34.2144 + 116.303i) q^{57} -236.651i q^{58} +(170.128 - 420.042i) q^{59} +(-378.715 - 111.412i) q^{60} -709.628i q^{61} -61.4582i q^{62} +(231.279 + 148.969i) q^{63} +64.0000 q^{64} +1562.80 q^{65} +(-29.8322 + 101.407i) q^{66} -1044.75i q^{67} -369.890i q^{68} +(-58.2129 + 197.880i) q^{69} +387.041i q^{70} +361.984i q^{71} +(181.591 + 116.965i) q^{72} -327.686i q^{73} -442.955i q^{74} +(345.703 - 1175.13i) q^{75} +93.3238 q^{76} +103.636 q^{77} +(-820.345 - 241.332i) q^{78} -238.712 q^{79} +303.889i q^{80} +(301.476 + 663.742i) q^{81} +126.089i q^{82} -156.436 q^{83} +(59.7680 - 203.165i) q^{84} +1756.34 q^{85} -294.677i q^{86} +(-589.843 - 173.522i) q^{87} +81.3709 q^{88} -1097.96 q^{89} +(-555.379 + 862.241i) q^{90} +838.379i q^{91} +158.782 q^{92} +(-153.182 - 45.0637i) q^{93} +75.6143 q^{94} +443.126i q^{95} +(46.9274 - 159.517i) q^{96} +1334.04i q^{97} +478.368 q^{98} +(230.878 + 148.711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −1.46648 + 4.98492i −0.282225 + 0.959348i
\(4\) 4.00000 0.500000
\(5\) 18.9931i 1.69879i 0.527757 + 0.849395i \(0.323033\pi\)
−0.527757 + 0.849395i \(0.676967\pi\)
\(6\) 2.93296 9.96984i 0.199563 0.678362i
\(7\) −10.1890 −0.550154 −0.275077 0.961422i \(-0.588703\pi\)
−0.275077 + 0.961422i \(0.588703\pi\)
\(8\) −8.00000 −0.353553
\(9\) −22.6989 14.6206i −0.840699 0.541503i
\(10\) 37.9861i 1.20123i
\(11\) −10.1714 −0.278798 −0.139399 0.990236i \(-0.544517\pi\)
−0.139399 + 0.990236i \(0.544517\pi\)
\(12\) −5.86593 + 19.9397i −0.141112 + 0.479674i
\(13\) 82.2827i 1.75547i −0.479146 0.877735i \(-0.659054\pi\)
0.479146 0.877735i \(-0.340946\pi\)
\(14\) 20.3780 0.389018
\(15\) −94.6789 27.8530i −1.62973 0.479441i
\(16\) 16.0000 0.250000
\(17\) 92.4725i 1.31929i −0.751579 0.659644i \(-0.770707\pi\)
0.751579 0.659644i \(-0.229293\pi\)
\(18\) 45.3977 + 29.2412i 0.594464 + 0.382901i
\(19\) 23.3309 0.281710 0.140855 0.990030i \(-0.455015\pi\)
0.140855 + 0.990030i \(0.455015\pi\)
\(20\) 75.9722i 0.849395i
\(21\) 14.9420 50.7914i 0.155267 0.527790i
\(22\) 20.3427 0.197140
\(23\) 39.6956 0.359874 0.179937 0.983678i \(-0.442411\pi\)
0.179937 + 0.983678i \(0.442411\pi\)
\(24\) 11.7319 39.8794i 0.0997815 0.339181i
\(25\) −235.736 −1.88589
\(26\) 164.565i 1.24131i
\(27\) 106.170 91.7112i 0.756756 0.653697i
\(28\) −40.7560 −0.275077
\(29\) 118.325i 0.757672i 0.925464 + 0.378836i \(0.123675\pi\)
−0.925464 + 0.378836i \(0.876325\pi\)
\(30\) 189.358 + 55.7060i 1.15239 + 0.339016i
\(31\) 30.7291i 0.178036i 0.996030 + 0.0890179i \(0.0283728\pi\)
−0.996030 + 0.0890179i \(0.971627\pi\)
\(32\) −32.0000 −0.176777
\(33\) 14.9161 50.7034i 0.0786837 0.267465i
\(34\) 184.945i 0.932877i
\(35\) 193.520i 0.934597i
\(36\) −90.7954 58.4824i −0.420349 0.270752i
\(37\) 221.478i 0.984073i 0.870575 + 0.492036i \(0.163747\pi\)
−0.870575 + 0.492036i \(0.836253\pi\)
\(38\) −46.6619 −0.199199
\(39\) 410.173 + 120.666i 1.68411 + 0.495437i
\(40\) 151.944i 0.600613i
\(41\) 63.0445i 0.240144i −0.992765 0.120072i \(-0.961687\pi\)
0.992765 0.120072i \(-0.0383125\pi\)
\(42\) −29.8840 + 101.583i −0.109790 + 0.373204i
\(43\) 147.338i 0.522532i 0.965267 + 0.261266i \(0.0841400\pi\)
−0.965267 + 0.261266i \(0.915860\pi\)
\(44\) −40.6854 −0.139399
\(45\) 277.690 431.121i 0.919901 1.42817i
\(46\) −79.3912 −0.254470
\(47\) −37.8072 −0.117335 −0.0586675 0.998278i \(-0.518685\pi\)
−0.0586675 + 0.998278i \(0.518685\pi\)
\(48\) −23.4637 + 79.7587i −0.0705562 + 0.239837i
\(49\) −239.184 −0.697330
\(50\) 471.472 1.33353
\(51\) 460.968 + 135.609i 1.26566 + 0.372335i
\(52\) 329.131i 0.877735i
\(53\) 409.038i 1.06011i 0.847964 + 0.530054i \(0.177828\pi\)
−0.847964 + 0.530054i \(0.822172\pi\)
\(54\) −212.340 + 183.422i −0.535108 + 0.462234i
\(55\) 193.185i 0.473620i
\(56\) 81.5120 0.194509
\(57\) −34.2144 + 116.303i −0.0795054 + 0.270258i
\(58\) 236.651i 0.535755i
\(59\) 170.128 420.042i 0.375403 0.926862i
\(60\) −378.715 111.412i −0.814866 0.239720i
\(61\) 709.628i 1.48949i −0.667352 0.744743i \(-0.732572\pi\)
0.667352 0.744743i \(-0.267428\pi\)
\(62\) 61.4582i 0.125890i
\(63\) 231.279 + 148.969i 0.462514 + 0.297911i
\(64\) 64.0000 0.125000
\(65\) 1562.80 2.98218
\(66\) −29.8322 + 101.407i −0.0556378 + 0.189126i
\(67\) 1044.75i 1.90502i −0.304513 0.952508i \(-0.598494\pi\)
0.304513 0.952508i \(-0.401506\pi\)
\(68\) 369.890i 0.659644i
\(69\) −58.2129 + 197.880i −0.101565 + 0.345245i
\(70\) 387.041i 0.660860i
\(71\) 361.984i 0.605064i 0.953139 + 0.302532i \(0.0978319\pi\)
−0.953139 + 0.302532i \(0.902168\pi\)
\(72\) 181.591 + 116.965i 0.297232 + 0.191450i
\(73\) 327.686i 0.525380i −0.964880 0.262690i \(-0.915390\pi\)
0.964880 0.262690i \(-0.0846097\pi\)
\(74\) 442.955i 0.695844i
\(75\) 345.703 1175.13i 0.532244 1.80922i
\(76\) 93.3238 0.140855
\(77\) 103.636 0.153382
\(78\) −820.345 241.332i −1.19084 0.350327i
\(79\) −238.712 −0.339964 −0.169982 0.985447i \(-0.554371\pi\)
−0.169982 + 0.985447i \(0.554371\pi\)
\(80\) 303.889i 0.424698i
\(81\) 301.476 + 663.742i 0.413548 + 0.910482i
\(82\) 126.089i 0.169807i
\(83\) −156.436 −0.206880 −0.103440 0.994636i \(-0.532985\pi\)
−0.103440 + 0.994636i \(0.532985\pi\)
\(84\) 59.7680 203.165i 0.0776336 0.263895i
\(85\) 1756.34 2.24119
\(86\) 294.677i 0.369486i
\(87\) −589.843 173.522i −0.726871 0.213834i
\(88\) 81.3709 0.0985701
\(89\) −1097.96 −1.30768 −0.653838 0.756634i \(-0.726842\pi\)
−0.653838 + 0.756634i \(0.726842\pi\)
\(90\) −555.379 + 862.241i −0.650468 + 1.00987i
\(91\) 838.379i 0.965780i
\(92\) 158.782 0.179937
\(93\) −153.182 45.0637i −0.170798 0.0502461i
\(94\) 75.6143 0.0829683
\(95\) 443.126i 0.478566i
\(96\) 46.9274 159.517i 0.0498907 0.169590i
\(97\) 1334.04i 1.39640i 0.715902 + 0.698201i \(0.246016\pi\)
−0.715902 + 0.698201i \(0.753984\pi\)
\(98\) 478.368 0.493087
\(99\) 230.878 + 148.711i 0.234385 + 0.150970i
\(100\) −942.945 −0.942945
\(101\) 807.886 0.795917 0.397958 0.917403i \(-0.369719\pi\)
0.397958 + 0.917403i \(0.369719\pi\)
\(102\) −921.936 271.219i −0.894954 0.263281i
\(103\) 1915.68i 1.83260i −0.400492 0.916300i \(-0.631161\pi\)
0.400492 0.916300i \(-0.368839\pi\)
\(104\) 658.262i 0.620653i
\(105\) 964.683 + 283.794i 0.896604 + 0.263766i
\(106\) 818.076i 0.749609i
\(107\) 1003.68i 0.906815i −0.891303 0.453407i \(-0.850208\pi\)
0.891303 0.453407i \(-0.149792\pi\)
\(108\) 424.680 366.845i 0.378378 0.326849i
\(109\) 1972.94i 1.73370i −0.498567 0.866851i \(-0.666140\pi\)
0.498567 0.866851i \(-0.333860\pi\)
\(110\) 386.370i 0.334900i
\(111\) −1104.05 324.793i −0.944069 0.277730i
\(112\) −163.024 −0.137539
\(113\) 524.671 0.436787 0.218393 0.975861i \(-0.429918\pi\)
0.218393 + 0.975861i \(0.429918\pi\)
\(114\) 68.4288 232.606i 0.0562188 0.191101i
\(115\) 753.941i 0.611351i
\(116\) 473.302i 0.378836i
\(117\) −1203.02 + 1867.72i −0.950593 + 1.47582i
\(118\) −340.256 + 840.084i −0.265450 + 0.655390i
\(119\) 942.203i 0.725812i
\(120\) 757.431 + 222.824i 0.576197 + 0.169508i
\(121\) −1227.54 −0.922272
\(122\) 1419.26i 1.05322i
\(123\) 314.272 + 92.4537i 0.230382 + 0.0677745i
\(124\) 122.916i 0.0890179i
\(125\) 2103.22i 1.50494i
\(126\) −462.558 297.939i −0.327047 0.210655i
\(127\) 1399.78 0.978037 0.489018 0.872273i \(-0.337355\pi\)
0.489018 + 0.872273i \(0.337355\pi\)
\(128\) −128.000 −0.0883883
\(129\) −734.470 216.069i −0.501291 0.147472i
\(130\) −3125.60 −2.10872
\(131\) −2065.19 −1.37738 −0.688689 0.725057i \(-0.741813\pi\)
−0.688689 + 0.725057i \(0.741813\pi\)
\(132\) 59.6645 202.814i 0.0393419 0.133732i
\(133\) −237.719 −0.154984
\(134\) 2089.49i 1.34705i
\(135\) 1741.88 + 2016.49i 1.11049 + 1.28557i
\(136\) 739.780i 0.466438i
\(137\) 438.983i 0.273758i −0.990588 0.136879i \(-0.956293\pi\)
0.990588 0.136879i \(-0.0437071\pi\)
\(138\) 116.426 395.759i 0.0718176 0.244125i
\(139\) 2717.07 1.65798 0.828989 0.559266i \(-0.188917\pi\)
0.828989 + 0.559266i \(0.188917\pi\)
\(140\) 774.081i 0.467299i
\(141\) 55.4435 188.466i 0.0331148 0.112565i
\(142\) 723.967i 0.427845i
\(143\) 836.927i 0.489422i
\(144\) −363.182 233.929i −0.210175 0.135376i
\(145\) −2247.36 −1.28713
\(146\) 655.372i 0.371500i
\(147\) 350.759 1192.31i 0.196804 0.668982i
\(148\) 885.910i 0.492036i
\(149\) −2675.78 −1.47120 −0.735600 0.677417i \(-0.763099\pi\)
−0.735600 + 0.677417i \(0.763099\pi\)
\(150\) −691.406 + 2350.25i −0.376354 + 1.27932i
\(151\) 2596.05i 1.39910i −0.714585 0.699548i \(-0.753385\pi\)
0.714585 0.699548i \(-0.246615\pi\)
\(152\) −186.648 −0.0995995
\(153\) −1352.00 + 2099.02i −0.714399 + 1.10912i
\(154\) −207.272 −0.108458
\(155\) −583.639 −0.302445
\(156\) 1640.69 + 482.664i 0.842054 + 0.247719i
\(157\) 1973.10i 1.00300i 0.865158 + 0.501499i \(0.167218\pi\)
−0.865158 + 0.501499i \(0.832782\pi\)
\(158\) 477.423 0.240391
\(159\) −2039.02 599.847i −1.01701 0.299189i
\(160\) 607.778i 0.300307i
\(161\) −404.459 −0.197986
\(162\) −602.953 1327.48i −0.292423 0.643808i
\(163\) 1338.42 0.643150 0.321575 0.946884i \(-0.395788\pi\)
0.321575 + 0.946884i \(0.395788\pi\)
\(164\) 252.178i 0.120072i
\(165\) 963.013 + 283.303i 0.454366 + 0.133667i
\(166\) 312.872 0.146286
\(167\) 916.784i 0.424808i 0.977182 + 0.212404i \(0.0681292\pi\)
−0.977182 + 0.212404i \(0.931871\pi\)
\(168\) −119.536 + 406.331i −0.0548952 + 0.186602i
\(169\) −4573.44 −2.08168
\(170\) −3512.67 −1.58476
\(171\) −529.586 341.112i −0.236833 0.152547i
\(172\) 589.354i 0.261266i
\(173\) 1781.69 0.783004 0.391502 0.920177i \(-0.371956\pi\)
0.391502 + 0.920177i \(0.371956\pi\)
\(174\) 1179.69 + 347.044i 0.513975 + 0.151203i
\(175\) 2401.92 1.03753
\(176\) −162.742 −0.0696996
\(177\) 1844.39 + 1464.06i 0.783235 + 0.621725i
\(178\) 2195.91 0.924667
\(179\) −870.852 −0.363634 −0.181817 0.983332i \(-0.558198\pi\)
−0.181817 + 0.983332i \(0.558198\pi\)
\(180\) 1110.76 1724.48i 0.459950 0.714085i
\(181\) −3247.54 −1.33364 −0.666818 0.745221i \(-0.732344\pi\)
−0.666818 + 0.745221i \(0.732344\pi\)
\(182\) 1676.76i 0.682910i
\(183\) 3537.44 + 1040.66i 1.42894 + 0.420369i
\(184\) −317.565 −0.127235
\(185\) −4206.54 −1.67173
\(186\) 306.364 + 90.1273i 0.120773 + 0.0355293i
\(187\) 940.572i 0.367815i
\(188\) −151.229 −0.0586675
\(189\) −1081.77 + 934.445i −0.416333 + 0.359634i
\(190\) 886.252i 0.338397i
\(191\) 1580.55 0.598766 0.299383 0.954133i \(-0.403219\pi\)
0.299383 + 0.954133i \(0.403219\pi\)
\(192\) −93.8549 + 319.035i −0.0352781 + 0.119919i
\(193\) 1657.33 0.618120 0.309060 0.951043i \(-0.399986\pi\)
0.309060 + 0.951043i \(0.399986\pi\)
\(194\) 2668.08i 0.987405i
\(195\) −2291.82 + 7790.43i −0.841644 + 2.86095i
\(196\) −956.737 −0.348665
\(197\) 1740.87i 0.629602i −0.949158 0.314801i \(-0.898062\pi\)
0.949158 0.314801i \(-0.101938\pi\)
\(198\) −461.757 297.423i −0.165735 0.106752i
\(199\) 614.923 0.219049 0.109524 0.993984i \(-0.465067\pi\)
0.109524 + 0.993984i \(0.465067\pi\)
\(200\) 1885.89 0.666763
\(201\) 5207.98 + 1532.10i 1.82757 + 0.537643i
\(202\) −1615.77 −0.562798
\(203\) 1205.62i 0.416836i
\(204\) 1843.87 + 542.437i 0.632828 + 0.186168i
\(205\) 1197.41 0.407954
\(206\) 3831.37i 1.29584i
\(207\) −901.045 580.374i −0.302546 0.194873i
\(208\) 1316.52i 0.438868i
\(209\) −237.308 −0.0785402
\(210\) −1929.37 567.588i −0.633995 0.186511i
\(211\) 3523.30i 1.14954i −0.818313 0.574772i \(-0.805091\pi\)
0.818313 0.574772i \(-0.194909\pi\)
\(212\) 1636.15i 0.530054i
\(213\) −1804.46 530.842i −0.580467 0.170764i
\(214\) 2007.36i 0.641215i
\(215\) −2798.41 −0.887673
\(216\) −849.360 + 733.689i −0.267554 + 0.231117i
\(217\) 313.099i 0.0979471i
\(218\) 3945.88i 1.22591i
\(219\) 1633.49 + 480.546i 0.504022 + 0.148275i
\(220\) 772.741i 0.236810i
\(221\) −7608.89 −2.31597
\(222\) 2208.10 + 649.586i 0.667557 + 0.196384i
\(223\) 4805.24 1.44297 0.721485 0.692430i \(-0.243460\pi\)
0.721485 + 0.692430i \(0.243460\pi\)
\(224\) 326.048 0.0972545
\(225\) 5350.94 + 3446.60i 1.58546 + 1.02122i
\(226\) −1049.34 −0.308855
\(227\) 4618.27 1.35033 0.675166 0.737665i \(-0.264072\pi\)
0.675166 + 0.737665i \(0.264072\pi\)
\(228\) −136.858 + 465.212i −0.0397527 + 0.135129i
\(229\) 3653.07i 1.05415i −0.849817 0.527077i \(-0.823288\pi\)
0.849817 0.527077i \(-0.176712\pi\)
\(230\) 1507.88i 0.432291i
\(231\) −151.980 + 516.617i −0.0432882 + 0.147147i
\(232\) 946.603i 0.267877i
\(233\) 1303.90 0.366615 0.183307 0.983056i \(-0.441320\pi\)
0.183307 + 0.983056i \(0.441320\pi\)
\(234\) 2406.04 3735.45i 0.672171 1.04356i
\(235\) 718.074i 0.199327i
\(236\) 680.512 1680.17i 0.187702 0.463431i
\(237\) 350.066 1189.96i 0.0959462 0.326144i
\(238\) 1884.41i 0.513226i
\(239\) 6935.79i 1.87715i 0.345073 + 0.938576i \(0.387854\pi\)
−0.345073 + 0.938576i \(0.612146\pi\)
\(240\) −1514.86 445.648i −0.407433 0.119860i
\(241\) 974.319 0.260421 0.130210 0.991486i \(-0.458435\pi\)
0.130210 + 0.991486i \(0.458435\pi\)
\(242\) 2455.09 0.652144
\(243\) −3750.81 + 529.471i −0.990183 + 0.139776i
\(244\) 2838.51i 0.744743i
\(245\) 4542.84i 1.18462i
\(246\) −628.544 184.907i −0.162904 0.0479238i
\(247\) 1919.73i 0.494533i
\(248\) 245.833i 0.0629451i
\(249\) 229.410 779.820i 0.0583867 0.198470i
\(250\) 4206.44i 1.06415i
\(251\) 2287.55i 0.575254i −0.957742 0.287627i \(-0.907134\pi\)
0.957742 0.287627i \(-0.0928664\pi\)
\(252\) 925.115 + 595.877i 0.231257 + 0.148955i
\(253\) −403.759 −0.100332
\(254\) −2799.57 −0.691577
\(255\) −2575.64 + 8755.19i −0.632520 + 2.15008i
\(256\) 256.000 0.0625000
\(257\) 6990.89i 1.69681i −0.529349 0.848404i \(-0.677564\pi\)
0.529349 0.848404i \(-0.322436\pi\)
\(258\) 1468.94 + 432.138i 0.354466 + 0.104278i
\(259\) 2256.64i 0.541392i
\(260\) 6251.20 1.49109
\(261\) 1729.99 2685.85i 0.410282 0.636973i
\(262\) 4130.38 0.973953
\(263\) 2946.13i 0.690747i −0.938465 0.345373i \(-0.887752\pi\)
0.938465 0.345373i \(-0.112248\pi\)
\(264\) −119.329 + 405.627i −0.0278189 + 0.0945630i
\(265\) −7768.89 −1.80090
\(266\) 475.438 0.109590
\(267\) 1610.13 5473.23i 0.369059 1.25452i
\(268\) 4178.99i 0.952508i
\(269\) −1274.53 −0.288882 −0.144441 0.989513i \(-0.546138\pi\)
−0.144441 + 0.989513i \(0.546138\pi\)
\(270\) −3483.75 4032.98i −0.785238 0.909036i
\(271\) −4929.25 −1.10491 −0.552455 0.833543i \(-0.686309\pi\)
−0.552455 + 0.833543i \(0.686309\pi\)
\(272\) 1479.56i 0.329822i
\(273\) −4179.25 1229.47i −0.926519 0.272567i
\(274\) 877.966i 0.193576i
\(275\) 2397.76 0.525783
\(276\) −232.852 + 791.518i −0.0507827 + 0.172622i
\(277\) −6811.99 −1.47759 −0.738796 0.673929i \(-0.764605\pi\)
−0.738796 + 0.673929i \(0.764605\pi\)
\(278\) −5434.14 −1.17237
\(279\) 449.278 697.515i 0.0964070 0.149674i
\(280\) 1548.16i 0.330430i
\(281\) 4763.12i 1.01119i −0.862771 0.505594i \(-0.831273\pi\)
0.862771 0.505594i \(-0.168727\pi\)
\(282\) −110.887 + 376.931i −0.0234157 + 0.0795955i
\(283\) 6042.10i 1.26914i −0.772867 0.634568i \(-0.781178\pi\)
0.772867 0.634568i \(-0.218822\pi\)
\(284\) 1447.93i 0.302532i
\(285\) −2208.95 649.836i −0.459111 0.135063i
\(286\) 1673.85i 0.346074i
\(287\) 642.361i 0.132116i
\(288\) 726.364 + 467.859i 0.148616 + 0.0957252i
\(289\) −3638.17 −0.740519
\(290\) 4494.72 0.910135
\(291\) −6650.07 1956.34i −1.33964 0.394099i
\(292\) 1310.74i 0.262690i
\(293\) 1472.96i 0.293691i 0.989159 + 0.146845i \(0.0469120\pi\)
−0.989159 + 0.146845i \(0.953088\pi\)
\(294\) −701.519 + 2384.63i −0.139161 + 0.473042i
\(295\) 7977.89 + 3231.25i 1.57454 + 0.637731i
\(296\) 1771.82i 0.347922i
\(297\) −1079.89 + 932.827i −0.210982 + 0.182250i
\(298\) 5351.57 1.04029
\(299\) 3266.26i 0.631749i
\(300\) 1382.81 4700.50i 0.266122 0.904612i
\(301\) 1501.23i 0.287474i
\(302\) 5192.10i 0.989311i
\(303\) −1184.75 + 4027.24i −0.224627 + 0.763562i
\(304\) 373.295 0.0704275
\(305\) 13478.0 2.53032
\(306\) 2704.01 4198.04i 0.505156 0.784268i
\(307\) 2075.53 0.385852 0.192926 0.981213i \(-0.438202\pi\)
0.192926 + 0.981213i \(0.438202\pi\)
\(308\) 414.544 0.0766911
\(309\) 9549.53 + 2809.31i 1.75810 + 0.517205i
\(310\) 1167.28 0.213861
\(311\) 5120.23i 0.933575i −0.884370 0.466787i \(-0.845411\pi\)
0.884370 0.466787i \(-0.154589\pi\)
\(312\) −3281.38 965.329i −0.595422 0.175163i
\(313\) 4181.55i 0.755128i −0.925984 0.377564i \(-0.876762\pi\)
0.925984 0.377564i \(-0.123238\pi\)
\(314\) 3946.21i 0.709227i
\(315\) −2829.38 + 4392.69i −0.506088 + 0.785714i
\(316\) −954.846 −0.169982
\(317\) 5414.77i 0.959380i 0.877438 + 0.479690i \(0.159251\pi\)
−0.877438 + 0.479690i \(0.840749\pi\)
\(318\) 4078.05 + 1199.69i 0.719137 + 0.211558i
\(319\) 1203.53i 0.211238i
\(320\) 1215.56i 0.212349i
\(321\) 5003.25 + 1471.88i 0.869951 + 0.255925i
\(322\) 808.918 0.139998
\(323\) 2157.47i 0.371656i
\(324\) 1205.91 + 2654.97i 0.206774 + 0.455241i
\(325\) 19397.0i 3.31062i
\(326\) −2676.85 −0.454776
\(327\) 9834.96 + 2893.28i 1.66322 + 0.489293i
\(328\) 504.356i 0.0849037i
\(329\) 385.217 0.0645523
\(330\) −1926.03 566.605i −0.321286 0.0945170i
\(331\) 1106.67 0.183770 0.0918852 0.995770i \(-0.470711\pi\)
0.0918852 + 0.995770i \(0.470711\pi\)
\(332\) −625.743 −0.103440
\(333\) 3238.13 5027.29i 0.532879 0.827308i
\(334\) 1833.57i 0.300384i
\(335\) 19842.9 3.23622
\(336\) 239.072 812.662i 0.0388168 0.131947i
\(337\) 8283.09i 1.33890i 0.742858 + 0.669449i \(0.233470\pi\)
−0.742858 + 0.669449i \(0.766530\pi\)
\(338\) 9146.89 1.47197
\(339\) −769.421 + 2615.44i −0.123272 + 0.419031i
\(340\) 7025.34 1.12060
\(341\) 312.557i 0.0496360i
\(342\) 1059.17 + 682.225i 0.167466 + 0.107867i
\(343\) 5931.88 0.933794
\(344\) 1178.71i 0.184743i
\(345\) −3758.34 1105.64i −0.586499 0.172538i
\(346\) −3563.39 −0.553668
\(347\) −3871.50 −0.598943 −0.299471 0.954105i \(-0.596810\pi\)
−0.299471 + 0.954105i \(0.596810\pi\)
\(348\) −2359.37 694.088i −0.363435 0.106917i
\(349\) 10305.7i 1.58067i 0.612678 + 0.790333i \(0.290092\pi\)
−0.612678 + 0.790333i \(0.709908\pi\)
\(350\) −4803.83 −0.733645
\(351\) −7546.24 8735.95i −1.14755 1.32846i
\(352\) 325.484 0.0492850
\(353\) −5062.97 −0.763385 −0.381692 0.924289i \(-0.624659\pi\)
−0.381692 + 0.924289i \(0.624659\pi\)
\(354\) −3688.77 2928.12i −0.553831 0.439626i
\(355\) −6875.17 −1.02788
\(356\) −4391.83 −0.653838
\(357\) −4696.81 1381.72i −0.696306 0.204842i
\(358\) 1741.70 0.257128
\(359\) 7093.69i 1.04287i 0.853291 + 0.521435i \(0.174603\pi\)
−0.853291 + 0.521435i \(0.825397\pi\)
\(360\) −2221.52 + 3448.97i −0.325234 + 0.504935i
\(361\) −6314.67 −0.920640
\(362\) 6495.09 0.943022
\(363\) 1800.17 6119.21i 0.260288 0.884780i
\(364\) 3353.52i 0.482890i
\(365\) 6223.76 0.892511
\(366\) −7074.88 2081.31i −1.01041 0.297246i
\(367\) 7928.64i 1.12772i 0.825872 + 0.563858i \(0.190683\pi\)
−0.825872 + 0.563858i \(0.809317\pi\)
\(368\) 635.130 0.0899686
\(369\) −921.749 + 1431.04i −0.130039 + 0.201889i
\(370\) 8413.07 1.18209
\(371\) 4167.69i 0.583223i
\(372\) −612.728 180.255i −0.0853991 0.0251230i
\(373\) −8719.31 −1.21037 −0.605186 0.796084i \(-0.706901\pi\)
−0.605186 + 0.796084i \(0.706901\pi\)
\(374\) 1881.14i 0.260084i
\(375\) 10484.4 + 3084.33i 1.44376 + 0.424731i
\(376\) 302.457 0.0414842
\(377\) 9736.13 1.33007
\(378\) 2163.53 1868.89i 0.294392 0.254300i
\(379\) −789.446 −0.106995 −0.0534975 0.998568i \(-0.517037\pi\)
−0.0534975 + 0.998568i \(0.517037\pi\)
\(380\) 1772.50i 0.239283i
\(381\) −2052.76 + 6977.81i −0.276026 + 0.938278i
\(382\) −3161.09 −0.423392
\(383\) 4907.40i 0.654717i −0.944900 0.327359i \(-0.893842\pi\)
0.944900 0.327359i \(-0.106158\pi\)
\(384\) 187.710 638.070i 0.0249454 0.0847952i
\(385\) 1968.37i 0.260564i
\(386\) −3314.66 −0.437077
\(387\) 2154.17 3344.41i 0.282953 0.439292i
\(388\) 5336.15i 0.698201i
\(389\) 2497.38i 0.325507i 0.986667 + 0.162754i \(0.0520376\pi\)
−0.986667 + 0.162754i \(0.947962\pi\)
\(390\) 4583.64 15580.9i 0.595132 2.02299i
\(391\) 3670.75i 0.474778i
\(392\) 1913.47 0.246543
\(393\) 3028.56 10294.8i 0.388730 1.32139i
\(394\) 3481.73i 0.445196i
\(395\) 4533.86i 0.577527i
\(396\) 923.513 + 594.845i 0.117193 + 0.0754851i
\(397\) 6068.25i 0.767145i −0.923511 0.383573i \(-0.874694\pi\)
0.923511 0.383573i \(-0.125306\pi\)
\(398\) −1229.85 −0.154891
\(399\) 348.611 1185.01i 0.0437403 0.148684i
\(400\) −3771.78 −0.471472
\(401\) −9709.46 −1.20915 −0.604573 0.796550i \(-0.706656\pi\)
−0.604573 + 0.796550i \(0.706656\pi\)
\(402\) −10416.0 3064.20i −1.29229 0.380171i
\(403\) 2528.47 0.312536
\(404\) 3231.54 0.397958
\(405\) −12606.5 + 5725.96i −1.54672 + 0.702531i
\(406\) 2411.24i 0.294748i
\(407\) 2252.73i 0.274358i
\(408\) −3687.75 1084.87i −0.447477 0.131640i
\(409\) 5832.59i 0.705142i 0.935785 + 0.352571i \(0.114693\pi\)
−0.935785 + 0.352571i \(0.885307\pi\)
\(410\) −2394.82 −0.288467
\(411\) 2188.29 + 643.761i 0.262629 + 0.0772612i
\(412\) 7662.73i 0.916300i
\(413\) −1733.43 + 4279.81i −0.206530 + 0.509917i
\(414\) 1802.09 + 1160.75i 0.213932 + 0.137796i
\(415\) 2971.19i 0.351446i
\(416\) 2633.05i 0.310326i
\(417\) −3984.53 + 13544.4i −0.467922 + 1.59058i
\(418\) 474.615 0.0555363
\(419\) −6572.59 −0.766330 −0.383165 0.923680i \(-0.625166\pi\)
−0.383165 + 0.923680i \(0.625166\pi\)
\(420\) 3858.73 + 1135.18i 0.448302 + 0.131883i
\(421\) 8822.88i 1.02138i −0.859765 0.510690i \(-0.829390\pi\)
0.859765 0.510690i \(-0.170610\pi\)
\(422\) 7046.60i 0.812851i
\(423\) 858.179 + 552.763i 0.0986433 + 0.0635373i
\(424\) 3272.31i 0.374805i
\(425\) 21799.1i 2.48803i
\(426\) 3608.92 + 1061.68i 0.410452 + 0.120748i
\(427\) 7230.40i 0.819447i
\(428\) 4014.71i 0.453407i
\(429\) −4172.02 1227.34i −0.469526 0.138127i
\(430\) 5596.81 0.627680
\(431\) −9519.82 −1.06393 −0.531965 0.846767i \(-0.678546\pi\)
−0.531965 + 0.846767i \(0.678546\pi\)
\(432\) 1698.72 1467.38i 0.189189 0.163424i
\(433\) −4618.05 −0.512539 −0.256269 0.966605i \(-0.582493\pi\)
−0.256269 + 0.966605i \(0.582493\pi\)
\(434\) 626.198i 0.0692591i
\(435\) 3295.71 11202.9i 0.363258 1.23480i
\(436\) 7891.77i 0.866851i
\(437\) 926.136 0.101380
\(438\) −3266.98 961.091i −0.356398 0.104846i
\(439\) −6509.93 −0.707749 −0.353875 0.935293i \(-0.615136\pi\)
−0.353875 + 0.935293i \(0.615136\pi\)
\(440\) 1545.48i 0.167450i
\(441\) 5429.21 + 3497.02i 0.586244 + 0.377607i
\(442\) 15217.8 1.63764
\(443\) −13277.5 −1.42401 −0.712003 0.702176i \(-0.752212\pi\)
−0.712003 + 0.702176i \(0.752212\pi\)
\(444\) −4416.19 1299.17i −0.472034 0.138865i
\(445\) 20853.6i 2.22147i
\(446\) −9610.47 −1.02033
\(447\) 3923.99 13338.6i 0.415209 1.41139i
\(448\) −652.096 −0.0687693
\(449\) 12397.8i 1.30310i 0.758607 + 0.651548i \(0.225880\pi\)
−0.758607 + 0.651548i \(0.774120\pi\)
\(450\) −10701.9 6893.21i −1.12109 0.722108i
\(451\) 641.249i 0.0669517i
\(452\) 2098.69 0.218393
\(453\) 12941.1 + 3807.06i 1.34222 + 0.394860i
\(454\) −9236.55 −0.954829
\(455\) −15923.4 −1.64066
\(456\) 273.715 930.423i 0.0281094 0.0955506i
\(457\) 2877.48i 0.294536i 0.989097 + 0.147268i \(0.0470479\pi\)
−0.989097 + 0.147268i \(0.952952\pi\)
\(458\) 7306.13i 0.745400i
\(459\) −8480.76 9817.81i −0.862414 0.998379i
\(460\) 3015.76i 0.305676i
\(461\) 5221.95i 0.527571i −0.964581 0.263786i \(-0.915029\pi\)
0.964581 0.263786i \(-0.0849712\pi\)
\(462\) 303.961 1033.23i 0.0306094 0.104049i
\(463\) 16063.6i 1.61240i 0.591645 + 0.806198i \(0.298479\pi\)
−0.591645 + 0.806198i \(0.701521\pi\)
\(464\) 1893.21i 0.189418i
\(465\) 855.897 2909.40i 0.0853575 0.290150i
\(466\) −2607.80 −0.259236
\(467\) −19210.6 −1.90356 −0.951778 0.306787i \(-0.900746\pi\)
−0.951778 + 0.306787i \(0.900746\pi\)
\(468\) −4812.09 + 7470.89i −0.475297 + 0.737911i
\(469\) 10644.9i 1.04805i
\(470\) 1436.15i 0.140946i
\(471\) −9835.76 2893.52i −0.962225 0.283071i
\(472\) −1361.02 + 3360.34i −0.132725 + 0.327695i
\(473\) 1498.63i 0.145681i
\(474\) −700.132 + 2379.92i −0.0678442 + 0.230618i
\(475\) −5499.95 −0.531273
\(476\) 3768.81i 0.362906i
\(477\) 5980.38 9284.70i 0.574052 0.891231i
\(478\) 13871.6i 1.32735i
\(479\) 11153.0i 1.06387i −0.846786 0.531934i \(-0.821466\pi\)
0.846786 0.531934i \(-0.178534\pi\)
\(480\) 3029.72 + 891.295i 0.288099 + 0.0847539i
\(481\) 18223.8 1.72751
\(482\) −1948.64 −0.184145
\(483\) 593.132 2016.20i 0.0558767 0.189938i
\(484\) −4910.17 −0.461136
\(485\) −25337.4 −2.37219
\(486\) 7501.62 1058.94i 0.700165 0.0988366i
\(487\) 7355.98 0.684459 0.342229 0.939616i \(-0.388818\pi\)
0.342229 + 0.939616i \(0.388818\pi\)
\(488\) 5677.03i 0.526612i
\(489\) −1962.77 + 6671.94i −0.181513 + 0.617005i
\(490\) 9085.68i 0.837651i
\(491\) 2400.04i 0.220596i −0.993899 0.110298i \(-0.964820\pi\)
0.993899 0.110298i \(-0.0351805\pi\)
\(492\) 1257.09 + 369.815i 0.115191 + 0.0338873i
\(493\) 10941.8 0.999586
\(494\) 3839.47i 0.349688i
\(495\) −2824.48 + 4385.08i −0.256467 + 0.398172i
\(496\) 491.665i 0.0445089i
\(497\) 3688.25i 0.332879i
\(498\) −458.821 + 1559.64i −0.0412856 + 0.140340i
\(499\) 18219.5 1.63450 0.817252 0.576280i \(-0.195496\pi\)
0.817252 + 0.576280i \(0.195496\pi\)
\(500\) 8412.87i 0.752470i
\(501\) −4570.09 1344.45i −0.407538 0.119891i
\(502\) 4575.10i 0.406766i
\(503\) −812.931 −0.0720612 −0.0360306 0.999351i \(-0.511471\pi\)
−0.0360306 + 0.999351i \(0.511471\pi\)
\(504\) −1850.23 1191.75i −0.163523 0.105327i
\(505\) 15344.2i 1.35210i
\(506\) 807.517 0.0709457
\(507\) 6706.87 22798.3i 0.587500 1.99705i
\(508\) 5599.13 0.489018
\(509\) −7475.46 −0.650971 −0.325485 0.945547i \(-0.605528\pi\)
−0.325485 + 0.945547i \(0.605528\pi\)
\(510\) 5151.27 17510.4i 0.447259 1.52034i
\(511\) 3338.79i 0.289040i
\(512\) −512.000 −0.0441942
\(513\) 2477.05 2139.71i 0.213186 0.184153i
\(514\) 13981.8i 1.19983i
\(515\) 36384.7 3.11320
\(516\) −2937.88 864.277i −0.250645 0.0737358i
\(517\) 384.550 0.0327128
\(518\) 4513.27i 0.382822i
\(519\) −2612.82 + 8881.61i −0.220983 + 0.751174i
\(520\) −12502.4 −1.05436
\(521\) 13918.5i 1.17041i 0.810886 + 0.585204i \(0.198986\pi\)
−0.810886 + 0.585204i \(0.801014\pi\)
\(522\) −3459.98 + 5371.70i −0.290113 + 0.450408i
\(523\) 10698.0 0.894438 0.447219 0.894425i \(-0.352415\pi\)
0.447219 + 0.894425i \(0.352415\pi\)
\(524\) −8260.76 −0.688689
\(525\) −3522.37 + 11973.4i −0.292817 + 0.995353i
\(526\) 5892.27i 0.488432i
\(527\) 2841.60 0.234880
\(528\) 238.658 811.255i 0.0196709 0.0668662i
\(529\) −10591.3 −0.870490
\(530\) 15537.8 1.27343
\(531\) −10003.0 + 7047.11i −0.817500 + 0.575929i
\(532\) −950.876 −0.0774920
\(533\) −5187.48 −0.421566
\(534\) −3220.27 + 10946.5i −0.260964 + 0.887078i
\(535\) 19062.9 1.54049
\(536\) 8357.97i 0.673525i
\(537\) 1277.09 4341.13i 0.102627 0.348852i
\(538\) 2549.06 0.204271
\(539\) 2432.83 0.194414
\(540\) 6967.50 + 8065.97i 0.555247 + 0.642785i
\(541\) 11634.8i 0.924616i −0.886720 0.462308i \(-0.847022\pi\)
0.886720 0.462308i \(-0.152978\pi\)
\(542\) 9858.49 0.781289
\(543\) 4762.46 16188.7i 0.376385 1.27942i
\(544\) 2959.12i 0.233219i
\(545\) 37472.2 2.94520
\(546\) 8358.50 + 2458.94i 0.655148 + 0.192734i
\(547\) −19199.4 −1.50074 −0.750371 0.661016i \(-0.770125\pi\)
−0.750371 + 0.661016i \(0.770125\pi\)
\(548\) 1755.93i 0.136879i
\(549\) −10375.2 + 16107.8i −0.806561 + 1.25221i
\(550\) −4795.52 −0.371784
\(551\) 2760.64i 0.213444i
\(552\) 465.703 1583.04i 0.0359088 0.122062i
\(553\) 2432.23 0.187033
\(554\) 13624.0 1.04482
\(555\) 6168.81 20969.2i 0.471804 1.60377i
\(556\) 10868.3 0.828989
\(557\) 12237.1i 0.930883i −0.885079 0.465442i \(-0.845896\pi\)
0.885079 0.465442i \(-0.154104\pi\)
\(558\) −898.555 + 1395.03i −0.0681700 + 0.105836i
\(559\) 12123.4 0.917290
\(560\) 3096.32i 0.233649i
\(561\) −4688.67 1379.33i −0.352863 0.103806i
\(562\) 9526.24i 0.715018i
\(563\) −1826.20 −0.136705 −0.0683527 0.997661i \(-0.521774\pi\)
−0.0683527 + 0.997661i \(0.521774\pi\)
\(564\) 221.774 753.863i 0.0165574 0.0562825i
\(565\) 9965.11i 0.742010i
\(566\) 12084.2i 0.897415i
\(567\) −3071.74 6762.87i −0.227515 0.500906i
\(568\) 2895.87i 0.213922i
\(569\) −4352.74 −0.320696 −0.160348 0.987061i \(-0.551262\pi\)
−0.160348 + 0.987061i \(0.551262\pi\)
\(570\) 4417.90 + 1299.67i 0.324641 + 0.0955040i
\(571\) 5189.16i 0.380315i 0.981754 + 0.190157i \(0.0608998\pi\)
−0.981754 + 0.190157i \(0.939100\pi\)
\(572\) 3347.71i 0.244711i
\(573\) −2317.84 + 7878.90i −0.168987 + 0.574426i
\(574\) 1284.72i 0.0934203i
\(575\) −9357.69 −0.678683
\(576\) −1452.73 935.718i −0.105087 0.0676879i
\(577\) 9056.33 0.653414 0.326707 0.945126i \(-0.394061\pi\)
0.326707 + 0.945126i \(0.394061\pi\)
\(578\) 7276.34 0.523626
\(579\) −2430.44 + 8261.66i −0.174449 + 0.592993i
\(580\) −8989.44 −0.643563
\(581\) 1593.93 0.113816
\(582\) 13300.1 + 3912.68i 0.947266 + 0.278670i
\(583\) 4160.48i 0.295556i
\(584\) 2621.49i 0.185750i
\(585\) −35473.8 22849.1i −2.50711 1.61486i
\(586\) 2945.93i 0.207671i
\(587\) −25369.7 −1.78385 −0.891925 0.452183i \(-0.850645\pi\)
−0.891925 + 0.452183i \(0.850645\pi\)
\(588\) 1403.04 4769.26i 0.0984019 0.334491i
\(589\) 716.939i 0.0501544i
\(590\) −15955.8 6462.50i −1.11337 0.450944i
\(591\) 8678.08 + 2552.95i 0.604008 + 0.177689i
\(592\) 3543.64i 0.246018i
\(593\) 556.620i 0.0385457i 0.999814 + 0.0192729i \(0.00613512\pi\)
−0.999814 + 0.0192729i \(0.993865\pi\)
\(594\) 2159.79 1865.65i 0.149187 0.128870i
\(595\) −17895.3 −1.23300
\(596\) −10703.1 −0.735600
\(597\) −901.773 + 3065.34i −0.0618210 + 0.210144i
\(598\) 6532.53i 0.446714i
\(599\) 15541.0i 1.06008i −0.847973 0.530039i \(-0.822177\pi\)
0.847973 0.530039i \(-0.177823\pi\)
\(600\) −2765.62 + 9401.01i −0.188177 + 0.639658i
\(601\) 3882.45i 0.263508i −0.991282 0.131754i \(-0.957939\pi\)
0.991282 0.131754i \(-0.0420609\pi\)
\(602\) 3002.46i 0.203275i
\(603\) −15274.8 + 23714.6i −1.03157 + 1.60154i
\(604\) 10384.2i 0.699548i
\(605\) 23314.8i 1.56675i
\(606\) 2369.50 8054.49i 0.158836 0.539920i
\(607\) −2132.51 −0.142596 −0.0712982 0.997455i \(-0.522714\pi\)
−0.0712982 + 0.997455i \(0.522714\pi\)
\(608\) −746.590 −0.0497997
\(609\) 6009.91 + 1768.02i 0.399891 + 0.117642i
\(610\) −26956.0 −1.78921
\(611\) 3110.88i 0.205978i
\(612\) −5408.01 + 8396.08i −0.357199 + 0.554561i
\(613\) 842.437i 0.0555069i −0.999615 0.0277534i \(-0.991165\pi\)
0.999615 0.0277534i \(-0.00883533\pi\)
\(614\) −4151.05 −0.272838
\(615\) −1755.98 + 5968.99i −0.115135 + 0.391370i
\(616\) −829.088 −0.0542288
\(617\) 22352.9i 1.45850i −0.684250 0.729248i \(-0.739870\pi\)
0.684250 0.729248i \(-0.260130\pi\)
\(618\) −19099.1 5618.63i −1.24317 0.365719i
\(619\) −12127.3 −0.787458 −0.393729 0.919227i \(-0.628815\pi\)
−0.393729 + 0.919227i \(0.628815\pi\)
\(620\) −2334.56 −0.151223
\(621\) 4214.48 3640.53i 0.272337 0.235249i
\(622\) 10240.5i 0.660137i
\(623\) 11187.1 0.719424
\(624\) 6562.76 + 1930.66i 0.421027 + 0.123859i
\(625\) 10479.5 0.670689
\(626\) 8363.09i 0.533956i
\(627\) 348.007 1182.96i 0.0221660 0.0753474i
\(628\) 7892.41i 0.501499i
\(629\) 20480.6 1.29827
\(630\) 5658.76 8785.38i 0.357858 0.555584i
\(631\) 18241.3 1.15083 0.575414 0.817862i \(-0.304841\pi\)
0.575414 + 0.817862i \(0.304841\pi\)
\(632\) 1909.69 0.120195
\(633\) 17563.4 + 5166.86i 1.10281 + 0.324430i
\(634\) 10829.5i 0.678384i
\(635\) 26586.2i 1.66148i
\(636\) −8156.09 2399.39i −0.508506 0.149594i
\(637\) 19680.7i 1.22414i
\(638\) 2407.06i 0.149367i
\(639\) 5292.41 8216.61i 0.327644 0.508676i
\(640\) 2431.11i 0.150153i
\(641\) 27962.8i 1.72303i 0.507728 + 0.861517i \(0.330485\pi\)
−0.507728 + 0.861517i \(0.669515\pi\)
\(642\) −10006.5 2943.75i −0.615148 0.180967i
\(643\) 2162.12 0.132606 0.0663031 0.997800i \(-0.478880\pi\)
0.0663031 + 0.997800i \(0.478880\pi\)
\(644\) −1617.84 −0.0989932
\(645\) 4103.81 13949.8i 0.250523 0.851588i
\(646\) 4314.94i 0.262801i
\(647\) 1584.19i 0.0962614i −0.998841 0.0481307i \(-0.984674\pi\)
0.998841 0.0481307i \(-0.0153264\pi\)
\(648\) −2411.81 5309.93i −0.146211 0.321904i
\(649\) −1730.43 + 4272.40i −0.104662 + 0.258407i
\(650\) 38794.0i 2.34096i
\(651\) 1560.77 + 459.154i 0.0939654 + 0.0276431i
\(652\) 5353.69 0.321575
\(653\) 31720.4i 1.90094i −0.310814 0.950471i \(-0.600602\pi\)
0.310814 0.950471i \(-0.399398\pi\)
\(654\) −19669.9 5786.57i −1.17608 0.345983i
\(655\) 39224.3i 2.33988i
\(656\) 1008.71i 0.0600360i
\(657\) −4790.96 + 7438.10i −0.284495 + 0.441686i
\(658\) −770.435 −0.0456454
\(659\) −1761.47 −0.104123 −0.0520615 0.998644i \(-0.516579\pi\)
−0.0520615 + 0.998644i \(0.516579\pi\)
\(660\) 3852.05 + 1133.21i 0.227183 + 0.0668336i
\(661\) 22221.3 1.30758 0.653788 0.756677i \(-0.273179\pi\)
0.653788 + 0.756677i \(0.273179\pi\)
\(662\) −2213.34 −0.129945
\(663\) 11158.3 37929.7i 0.653624 2.22182i
\(664\) 1251.49 0.0731432
\(665\) 4515.01i 0.263285i
\(666\) −6476.27 + 10054.6i −0.376802 + 0.584995i
\(667\) 4697.00i 0.272667i
\(668\) 3667.13i 0.212404i
\(669\) −7046.79 + 23953.7i −0.407242 + 1.38431i
\(670\) −39685.9 −2.28836
\(671\) 7217.89i 0.415266i
\(672\) −478.144 + 1625.32i −0.0274476 + 0.0933009i
\(673\) 18991.3i 1.08776i −0.839163 0.543880i \(-0.816955\pi\)
0.839163 0.543880i \(-0.183045\pi\)
\(674\) 16566.2i 0.946744i
\(675\) −25028.1 + 21619.6i −1.42716 + 1.23280i
\(676\) −18293.8 −1.04084
\(677\) 26193.0i 1.48697i 0.668754 + 0.743484i \(0.266828\pi\)
−0.668754 + 0.743484i \(0.733172\pi\)
\(678\) 1538.84 5230.89i 0.0871665 0.296300i
\(679\) 13592.5i 0.768237i
\(680\) −14050.7 −0.792381
\(681\) −6772.61 + 23021.7i −0.381097 + 1.29544i
\(682\) 625.113i 0.0350980i
\(683\) 29944.8 1.67761 0.838803 0.544435i \(-0.183256\pi\)
0.838803 + 0.544435i \(0.183256\pi\)
\(684\) −2118.34 1364.45i −0.118417 0.0762734i
\(685\) 8337.63 0.465057
\(686\) −11863.8 −0.660292
\(687\) 18210.2 + 5357.16i 1.01130 + 0.297508i
\(688\) 2357.41i 0.130633i
\(689\) 33656.8 1.86099
\(690\) 7516.67 + 2211.28i 0.414717 + 0.122003i
\(691\) 4559.60i 0.251021i 0.992092 + 0.125510i \(0.0400568\pi\)
−0.992092 + 0.125510i \(0.959943\pi\)
\(692\) 7126.78 0.391502
\(693\) −2352.42 1515.22i −0.128948 0.0830569i
\(694\) 7743.00 0.423516
\(695\) 51605.5i 2.81656i
\(696\) 4718.74 + 1388.18i 0.256988 + 0.0756016i
\(697\) −5829.89 −0.316819
\(698\) 20611.4i 1.11770i
\(699\) −1912.14 + 6499.83i −0.103468 + 0.351711i
\(700\) 9607.67 0.518765
\(701\) −23909.3 −1.28822 −0.644109 0.764934i \(-0.722772\pi\)
−0.644109 + 0.764934i \(0.722772\pi\)
\(702\) 15092.5 + 17471.9i 0.811438 + 0.939365i
\(703\) 5167.28i 0.277223i
\(704\) −650.967 −0.0348498
\(705\) 3579.54 + 1053.04i 0.191224 + 0.0562551i
\(706\) 10125.9 0.539794
\(707\) −8231.55 −0.437877
\(708\) 7377.55 + 5856.24i 0.391618 + 0.310863i
\(709\) 7047.67 0.373316 0.186658 0.982425i \(-0.440234\pi\)
0.186658 + 0.982425i \(0.440234\pi\)
\(710\) 13750.3 0.726819
\(711\) 5418.48 + 3490.10i 0.285807 + 0.184092i
\(712\) 8783.66 0.462334
\(713\) 1219.81i 0.0640705i
\(714\) 9393.61 + 2763.45i 0.492363 + 0.144845i
\(715\) −15895.8 −0.831426
\(716\) −3483.41 −0.181817
\(717\) −34574.4 10171.2i −1.80084 0.529778i
\(718\) 14187.4i 0.737421i
\(719\) 11771.4 0.610567 0.305283 0.952262i \(-0.401249\pi\)
0.305283 + 0.952262i \(0.401249\pi\)
\(720\) 4443.04 6897.93i 0.229975 0.357043i
\(721\) 19518.9i 1.00821i
\(722\) 12629.3 0.650990
\(723\) −1428.82 + 4856.90i −0.0734972 + 0.249834i
\(724\) −12990.2 −0.666818
\(725\) 27893.6i 1.42888i
\(726\) −3600.34 + 12238.4i −0.184051 + 0.625634i
\(727\) 29044.3 1.48170 0.740848 0.671673i \(-0.234424\pi\)
0.740848 + 0.671673i \(0.234424\pi\)
\(728\) 6707.03i 0.341455i
\(729\) 2861.12 19473.9i 0.145360 0.989379i
\(730\) −12447.5 −0.631100
\(731\) 13624.8 0.689370
\(732\) 14149.8 + 4162.63i 0.714468 + 0.210185i
\(733\) −2188.98 −0.110303 −0.0551514 0.998478i \(-0.517564\pi\)
−0.0551514 + 0.998478i \(0.517564\pi\)
\(734\) 15857.3i 0.797416i
\(735\) 22645.7 + 6661.99i 1.13646 + 0.334328i
\(736\) −1270.26 −0.0636174
\(737\) 10626.5i 0.531115i
\(738\) 1843.50 2862.08i 0.0919513 0.142757i
\(739\) 21285.6i 1.05955i 0.848140 + 0.529773i \(0.177723\pi\)
−0.848140 + 0.529773i \(0.822277\pi\)
\(740\) −16826.1 −0.835867
\(741\) 9569.72 + 2815.25i 0.474430 + 0.139569i
\(742\) 8335.38i 0.412401i
\(743\) 28955.4i 1.42971i −0.699275 0.714853i \(-0.746494\pi\)
0.699275 0.714853i \(-0.253506\pi\)
\(744\) 1225.46 + 360.509i 0.0603863 + 0.0177647i
\(745\) 50821.3i 2.49926i
\(746\) 17438.6 0.855862
\(747\) 3550.92 + 2287.19i 0.173924 + 0.112026i
\(748\) 3762.29i 0.183907i
\(749\) 10226.5i 0.498888i
\(750\) −20968.7 6168.66i −1.02089 0.300330i
\(751\) 31748.3i 1.54263i −0.636456 0.771313i \(-0.719600\pi\)
0.636456 0.771313i \(-0.280400\pi\)
\(752\) −604.915 −0.0293337
\(753\) 11403.3 + 3354.65i 0.551869 + 0.162351i
\(754\) −19472.3 −0.940502
\(755\) 49306.9 2.37677
\(756\) −4327.06 + 3737.78i −0.208166 + 0.179817i
\(757\) −16734.2 −0.803453 −0.401727 0.915760i \(-0.631590\pi\)
−0.401727 + 0.915760i \(0.631590\pi\)
\(758\) 1578.89 0.0756569
\(759\) 592.105 2012.70i 0.0283163 0.0962537i
\(760\) 3545.01i 0.169199i
\(761\) 25291.3i 1.20474i −0.798216 0.602371i \(-0.794223\pi\)
0.798216 0.602371i \(-0.205777\pi\)
\(762\) 4105.51 13955.6i 0.195180 0.663463i
\(763\) 20102.3i 0.953804i
\(764\) 6322.19 0.299383
\(765\) −39866.8 25678.7i −1.88417 1.21361i
\(766\) 9814.81i 0.462955i
\(767\) −34562.2 13998.6i −1.62708 0.659009i
\(768\) −375.419 + 1276.14i −0.0176390 + 0.0599593i
\(769\) 18921.8i 0.887307i −0.896198 0.443653i \(-0.853682\pi\)
0.896198 0.443653i \(-0.146318\pi\)
\(770\) 3936.73i 0.184247i
\(771\) 34849.0 + 10252.0i 1.62783 + 0.478881i
\(772\) 6629.32 0.309060
\(773\) 29323.8 1.36443 0.682215 0.731152i \(-0.261017\pi\)
0.682215 + 0.731152i \(0.261017\pi\)
\(774\) −4308.35 + 6688.83i −0.200078 + 0.310627i
\(775\) 7243.96i 0.335756i
\(776\) 10672.3i 0.493703i
\(777\) 11249.1 + 3309.32i 0.519384 + 0.152794i
\(778\) 4994.77i 0.230169i
\(779\) 1470.89i 0.0676509i
\(780\) −9167.27 + 31161.7i −0.420822 + 1.43047i
\(781\) 3681.87i 0.168691i
\(782\) 7341.51i 0.335718i
\(783\) 10851.8 + 12562.6i 0.495288 + 0.573373i
\(784\) −3826.95 −0.174333
\(785\) −37475.3 −1.70388
\(786\) −6057.13 + 20589.6i −0.274874 + 0.934360i
\(787\) 29548.3 1.33835 0.669177 0.743103i \(-0.266647\pi\)
0.669177 + 0.743103i \(0.266647\pi\)
\(788\) 6963.47i 0.314801i
\(789\) 14686.2 + 4320.45i 0.662667 + 0.194946i
\(790\) 9067.72i 0.408374i
\(791\) −5345.88 −0.240300
\(792\) −1847.03 1189.69i −0.0828677 0.0533760i
\(793\) −58390.1 −2.61475
\(794\) 12136.5i 0.542454i
\(795\) 11392.9 38727.3i 0.508259 1.72769i
\(796\) 2459.69 0.109524
\(797\) −22579.7 −1.00353 −0.501765 0.865004i \(-0.667316\pi\)
−0.501765 + 0.865004i \(0.667316\pi\)
\(798\) −697.222 + 2370.02i −0.0309290 + 0.105135i
\(799\) 3496.12i 0.154798i
\(800\) 7543.56 0.333381
\(801\) 24922.4 + 16052.8i 1.09936 + 0.708111i
\(802\) 19418.9 0.854995
\(803\) 3333.01i 0.146475i
\(804\) 20831.9 + 6128.41i 0.913787 + 0.268821i
\(805\) 7681.91i 0.336338i
\(806\) −5056.95 −0.220997
\(807\) 1869.07 6353.42i 0.0815297 0.277139i
\(808\) −6463.08 −0.281399
\(809\) −11940.1 −0.518902 −0.259451 0.965756i \(-0.583542\pi\)
−0.259451 + 0.965756i \(0.583542\pi\)
\(810\) 25213.0 11451.9i 1.09370 0.496765i
\(811\) 3871.63i 0.167634i −0.996481 0.0838171i \(-0.973289\pi\)
0.996481 0.0838171i \(-0.0267111\pi\)
\(812\) 4822.47i 0.208418i
\(813\) 7228.65 24571.9i 0.311833 1.05999i
\(814\) 4505.46i 0.194000i
\(815\) 25420.8i 1.09258i
\(816\) 7375.49 + 2169.75i 0.316414 + 0.0930838i
\(817\) 3437.54i 0.147203i
\(818\) 11665.2i 0.498611i
\(819\) 12257.6 19030.2i 0.522973 0.811930i
\(820\) 4789.63 0.203977
\(821\) −1641.98 −0.0697996 −0.0348998 0.999391i \(-0.511111\pi\)
−0.0348998 + 0.999391i \(0.511111\pi\)
\(822\) −4376.59 1287.52i −0.185707 0.0546319i
\(823\) 34300.1i 1.45277i 0.687289 + 0.726384i \(0.258801\pi\)
−0.687289 + 0.726384i \(0.741199\pi\)
\(824\) 15325.5i 0.647922i
\(825\) −3516.27 + 11952.6i −0.148389 + 0.504409i
\(826\) 3466.87 8559.62i 0.146039 0.360566i
\(827\) 33600.0i 1.41280i 0.707812 + 0.706401i \(0.249682\pi\)
−0.707812 + 0.706401i \(0.750318\pi\)
\(828\) −3604.18 2321.49i −0.151273 0.0974366i
\(829\) −27672.8 −1.15937 −0.579684 0.814841i \(-0.696824\pi\)
−0.579684 + 0.814841i \(0.696824\pi\)
\(830\) 5942.39i 0.248510i
\(831\) 9989.67 33957.2i 0.417013 1.41753i
\(832\) 5266.09i 0.219434i
\(833\) 22118.0i 0.919979i
\(834\) 7969.07 27088.7i 0.330871 1.12471i
\(835\) −17412.5 −0.721659
\(836\) −949.230 −0.0392701
\(837\) 2818.20 + 3262.51i 0.116381 + 0.134730i
\(838\) 13145.2 0.541877
\(839\) −22478.3 −0.924956 −0.462478 0.886631i \(-0.653040\pi\)
−0.462478 + 0.886631i \(0.653040\pi\)
\(840\) −7717.47 2270.35i −0.316997 0.0932555i
\(841\) 10388.1 0.425934
\(842\) 17645.8i 0.722224i
\(843\) 23743.8 + 6985.03i 0.970082 + 0.285382i
\(844\) 14093.2i 0.574772i
\(845\) 86863.7i 3.53633i
\(846\) −1716.36 1105.53i −0.0697513 0.0449276i
\(847\) 12507.4 0.507392
\(848\) 6544.61i 0.265027i
\(849\) 30119.4 + 8860.63i 1.21754 + 0.358181i
\(850\) 43598.2i 1.75930i
\(851\) 8791.69i 0.354143i
\(852\) −7217.84 2123.37i −0.290234 0.0853820i
\(853\) 35718.4 1.43373 0.716866 0.697211i \(-0.245576\pi\)
0.716866 + 0.697211i \(0.245576\pi\)
\(854\) 14460.8i 0.579436i
\(855\) 6478.76 10058.5i 0.259145 0.402330i
\(856\) 8029.42i 0.320607i
\(857\) −27395.6 −1.09197 −0.545984 0.837796i \(-0.683844\pi\)
−0.545984 + 0.837796i \(0.683844\pi\)
\(858\) 8344.03 + 2454.68i 0.332005 + 0.0976705i
\(859\) 32403.6i 1.28707i −0.765415 0.643536i \(-0.777466\pi\)
0.765415 0.643536i \(-0.222534\pi\)
\(860\) −11193.6 −0.443837
\(861\) −3202.12 942.011i −0.126746 0.0372865i
\(862\) 19039.6 0.752312
\(863\) 21545.2 0.849835 0.424917 0.905232i \(-0.360303\pi\)
0.424917 + 0.905232i \(0.360303\pi\)
\(864\) −3397.44 + 2934.76i −0.133777 + 0.115558i
\(865\) 33839.8i 1.33016i
\(866\) 9236.10 0.362420
\(867\) 5335.31 18136.0i 0.208993 0.710415i
\(868\) 1252.40i 0.0489736i
\(869\) 2428.02 0.0947813
\(870\) −6591.43 + 22405.8i −0.256863 + 0.873137i
\(871\) −85964.6 −3.34420
\(872\) 15783.5i 0.612956i
\(873\) 19504.4 30281.1i 0.756156 1.17395i
\(874\) −1852.27 −0.0716866
\(875\) 21429.7i 0.827950i
\(876\) 6533.95 + 1922.18i 0.252011 + 0.0741376i
\(877\) −21365.2 −0.822635 −0.411318 0.911492i \(-0.634931\pi\)
−0.411318 + 0.911492i \(0.634931\pi\)
\(878\) 13019.9 0.500454
\(879\) −7342.60 2160.07i −0.281752 0.0828868i
\(880\) 3090.96i 0.118405i
\(881\) −39856.6 −1.52418 −0.762091 0.647470i \(-0.775827\pi\)
−0.762091 + 0.647470i \(0.775827\pi\)
\(882\) −10858.4 6994.03i −0.414537 0.267008i
\(883\) 3668.31 0.139806 0.0699028 0.997554i \(-0.477731\pi\)
0.0699028 + 0.997554i \(0.477731\pi\)
\(884\) −30435.6 −1.15798
\(885\) −27807.0 + 35030.5i −1.05618 + 1.33055i
\(886\) 26555.1 1.00692
\(887\) 33102.6 1.25308 0.626538 0.779391i \(-0.284471\pi\)
0.626538 + 0.779391i \(0.284471\pi\)
\(888\) 8832.38 + 2598.34i 0.333779 + 0.0981922i
\(889\) −14262.4 −0.538071
\(890\) 41707.1i 1.57082i
\(891\) −3066.43 6751.16i −0.115296 0.253841i
\(892\) 19220.9 0.721485
\(893\) −882.077 −0.0330544
\(894\) −7847.98 + 26677.1i −0.293597 + 0.998005i
\(895\) 16540.1i 0.617738i
\(896\) 1304.19 0.0486272
\(897\) 16282.1 + 4789.92i 0.606067 + 0.178295i
\(898\) 24795.7i 0.921429i
\(899\) −3636.03 −0.134893
\(900\) 21403.8 + 13786.4i 0.792732 + 0.510608i
\(901\) 37824.8 1.39859
\(902\) 1282.50i 0.0473420i
\(903\) 7483.52 + 2201.53i 0.275787 + 0.0811321i
\(904\) −4197.37 −0.154428
\(905\) 61680.8i 2.26557i
\(906\) −25882.2 7614.12i −0.949094 0.279208i
\(907\) −17757.5 −0.650084 −0.325042 0.945700i \(-0.605378\pi\)
−0.325042 + 0.945700i \(0.605378\pi\)
\(908\) 18473.1 0.675166
\(909\) −18338.1 11811.8i −0.669126 0.430992i
\(910\) 31846.7 1.16012
\(911\) 32005.8i 1.16400i −0.813190 0.581998i \(-0.802271\pi\)
0.813190 0.581998i \(-0.197729\pi\)
\(912\) −547.431 + 1860.85i −0.0198764 + 0.0675645i
\(913\) 1591.17 0.0576779
\(914\) 5754.96i 0.208268i
\(915\) −19765.3 + 67186.8i −0.714120 + 2.42746i
\(916\) 14612.3i 0.527077i
\(917\) 21042.2 0.757771
\(918\) 16961.5 + 19635.6i 0.609819 + 0.705960i
\(919\) 33130.1i 1.18919i 0.804027 + 0.594593i \(0.202687\pi\)
−0.804027 + 0.594593i \(0.797313\pi\)
\(920\) 6031.53i 0.216145i
\(921\) −3043.72 + 10346.3i −0.108897 + 0.370166i
\(922\) 10443.9i 0.373049i
\(923\) 29785.0 1.06217
\(924\) −607.922 + 2066.47i −0.0216441 + 0.0735734i
\(925\) 52210.3i 1.85585i
\(926\) 32127.2i 1.14014i
\(927\) −28008.4 + 43483.8i −0.992359 + 1.54066i
\(928\) 3786.41i 0.133939i
\(929\) −6394.41 −0.225827 −0.112914 0.993605i \(-0.536018\pi\)
−0.112914 + 0.993605i \(0.536018\pi\)
\(930\) −1711.79 + 5818.79i −0.0603569 + 0.205167i
\(931\) −5580.39 −0.196445
\(932\) 5215.59 0.183307
\(933\) 25524.0 + 7508.73i 0.895623 + 0.263478i
\(934\) 38421.2 1.34602
\(935\) −17864.3 −0.624841
\(936\) 9624.18 14941.8i 0.336086 0.521782i
\(937\) 30950.9i 1.07910i 0.841952 + 0.539552i \(0.181406\pi\)
−0.841952 + 0.539552i \(0.818594\pi\)
\(938\) 21289.9i 0.741086i
\(939\) 20844.7 + 6132.16i 0.724431 + 0.213116i
\(940\) 2872.29i 0.0996637i
\(941\) −6243.39 −0.216290 −0.108145 0.994135i \(-0.534491\pi\)
−0.108145 + 0.994135i \(0.534491\pi\)
\(942\) 19671.5 + 5787.04i 0.680396 + 0.200161i
\(943\) 2502.59i 0.0864216i
\(944\) 2722.05 6720.68i 0.0938508 0.231715i
\(945\) −17748.0 20546.0i −0.610944 0.707262i
\(946\) 2997.26i 0.103012i
\(947\) 43732.9i 1.50067i 0.661061 + 0.750333i \(0.270107\pi\)
−0.661061 + 0.750333i \(0.729893\pi\)
\(948\) 1400.26 4759.83i 0.0479731 0.163072i
\(949\) −26962.9 −0.922289
\(950\) 10999.9 0.375667
\(951\) −26992.2 7940.66i −0.920380 0.270761i
\(952\) 7537.62i 0.256613i
\(953\) 8829.30i 0.300114i 0.988677 + 0.150057i \(0.0479458\pi\)
−0.988677 + 0.150057i \(0.952054\pi\)
\(954\) −11960.8 + 18569.4i −0.405916 + 0.630196i
\(955\) 30019.4i 1.01718i
\(956\) 27743.2i 0.938576i
\(957\) 5999.50 + 1764.96i 0.202650 + 0.0596164i
\(958\) 22306.0i 0.752268i
\(959\) 4472.80i 0.150609i
\(960\) −6059.45 1782.59i −0.203716 0.0599301i
\(961\) 28846.7 0.968303
\(962\) −36447.5 −1.22153
\(963\) −14674.4 + 22782.3i −0.491043 + 0.762358i
\(964\) 3897.28 0.130210
\(965\) 31477.8i 1.05006i
\(966\) −1186.26 + 4032.39i −0.0395108 + 0.134306i
\(967\) 28794.6i 0.957572i −0.877932 0.478786i \(-0.841077\pi\)
0.877932 0.478786i \(-0.158923\pi\)
\(968\) 9820.35 0.326072
\(969\) 10754.8 + 3163.89i 0.356548 + 0.104891i
\(970\) 50674.9 1.67739
\(971\) 55951.4i 1.84919i 0.380947 + 0.924597i \(0.375598\pi\)
−0.380947 + 0.924597i \(0.624402\pi\)
\(972\) −15003.2 + 2117.88i −0.495092 + 0.0698880i
\(973\) −27684.2 −0.912144
\(974\) −14712.0 −0.483986
\(975\) −96692.5 28445.4i −3.17604 0.934339i
\(976\) 11354.1i 0.372371i
\(977\) −5523.97 −0.180888 −0.0904440 0.995902i \(-0.528829\pi\)
−0.0904440 + 0.995902i \(0.528829\pi\)
\(978\) 3925.55 13343.9i 0.128349 0.436288i
\(979\) 11167.7 0.364578
\(980\) 18171.4i 0.592309i
\(981\) −28845.6 + 44783.5i −0.938806 + 1.45752i
\(982\) 4800.09i 0.155985i
\(983\) 22325.7 0.724394 0.362197 0.932101i \(-0.382027\pi\)
0.362197 + 0.932101i \(0.382027\pi\)
\(984\) −2514.18 739.630i −0.0814522 0.0239619i
\(985\) 33064.4 1.06956
\(986\) −21883.7 −0.706814
\(987\) −564.914 + 1920.28i −0.0182183 + 0.0619282i
\(988\) 7678.93i 0.247267i
\(989\) 5848.69i 0.188046i
\(990\) 5648.97 8770.17i 0.181349 0.281550i
\(991\) 16996.5i 0.544816i −0.962182 0.272408i \(-0.912180\pi\)
0.962182 0.272408i \(-0.0878201\pi\)
\(992\) 983.331i 0.0314726i
\(993\) −1622.91 + 5516.66i −0.0518645 + 0.176300i
\(994\) 7376.50i 0.235381i
\(995\) 11679.3i 0.372118i
\(996\) 917.642 3119.28i 0.0291934 0.0992351i
\(997\) −19053.3 −0.605241 −0.302621 0.953111i \(-0.597861\pi\)
−0.302621 + 0.953111i \(0.597861\pi\)
\(998\) −36439.0 −1.15577
\(999\) 20312.0 + 23514.3i 0.643285 + 0.744703i
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 354.4.c.a.353.14 yes 30
3.2 odd 2 354.4.c.b.353.13 yes 30
59.58 odd 2 354.4.c.b.353.14 yes 30
177.176 even 2 inner 354.4.c.a.353.13 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.4.c.a.353.13 30 177.176 even 2 inner
354.4.c.a.353.14 yes 30 1.1 even 1 trivial
354.4.c.b.353.13 yes 30 3.2 odd 2
354.4.c.b.353.14 yes 30 59.58 odd 2