Properties

Label 144.4.k.a.109.5
Level $144$
Weight $4$
Character 144.109
Analytic conductor $8.496$
Analytic rank $0$
Dimension $10$
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] = [144,4,Mod(37,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 144.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.49627504083\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 109.5
Root \(1.28199 + 1.53509i\) of defining polynomial
Character \(\chi\) \(=\) 144.109
Dual form 144.4.k.a.37.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.81708 - 0.253099i) q^{2} +(7.87188 - 1.42600i) q^{4} +(4.66372 - 4.66372i) q^{5} -24.8965i q^{7} +(21.8148 - 6.00953i) q^{8} +O(q^{10})\) \(q+(2.81708 - 0.253099i) q^{2} +(7.87188 - 1.42600i) q^{4} +(4.66372 - 4.66372i) q^{5} -24.8965i q^{7} +(21.8148 - 6.00953i) q^{8} +(11.9577 - 14.3185i) q^{10} +(-22.3431 + 22.3431i) q^{11} +(-11.2714 - 11.2714i) q^{13} +(-6.30129 - 70.1355i) q^{14} +(59.9330 - 22.4506i) q^{16} +88.4846 q^{17} +(37.8187 + 37.8187i) q^{19} +(30.0618 - 43.3627i) q^{20} +(-57.2873 + 68.5974i) q^{22} -48.1224i q^{23} +81.4994i q^{25} +(-34.6053 - 28.8997i) q^{26} +(-35.5025 - 195.982i) q^{28} +(-10.4432 - 10.4432i) q^{29} -96.9578 q^{31} +(163.154 - 78.4142i) q^{32} +(249.268 - 22.3954i) q^{34} +(-116.110 - 116.110i) q^{35} +(-163.279 + 163.279i) q^{37} +(116.110 + 96.9665i) q^{38} +(73.7114 - 129.765i) q^{40} +360.519i q^{41} +(-100.249 + 100.249i) q^{43} +(-144.021 + 207.744i) q^{44} +(-12.1797 - 135.565i) q^{46} -220.669 q^{47} -276.837 q^{49} +(20.6274 + 229.590i) q^{50} +(-104.800 - 72.6542i) q^{52} +(175.752 - 175.752i) q^{53} +208.404i q^{55} +(-149.616 - 543.113i) q^{56} +(-32.0624 - 26.7761i) q^{58} +(-405.008 + 405.008i) q^{59} +(664.576 + 664.576i) q^{61} +(-273.138 + 24.5399i) q^{62} +(439.771 - 262.193i) q^{64} -105.133 q^{65} +(-107.377 - 107.377i) q^{67} +(696.540 - 126.179i) q^{68} +(-356.480 - 297.705i) q^{70} -215.050i q^{71} -668.587i q^{73} +(-418.644 + 501.296i) q^{74} +(351.634 + 243.775i) q^{76} +(556.266 + 556.266i) q^{77} -822.956 q^{79} +(174.808 - 384.215i) q^{80} +(91.2471 + 1015.61i) q^{82} +(-326.873 - 326.873i) q^{83} +(412.668 - 412.668i) q^{85} +(-257.037 + 307.783i) q^{86} +(-353.139 + 621.682i) q^{88} +262.733i q^{89} +(-280.619 + 280.619i) q^{91} +(-68.6226 - 378.814i) q^{92} +(-621.643 + 55.8512i) q^{94} +352.752 q^{95} -150.801 q^{97} +(-779.871 + 70.0671i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.81708 0.253099i 0.995988 0.0894841i
\(3\) 0 0
\(4\) 7.87188 1.42600i 0.983985 0.178250i
\(5\) 4.66372 4.66372i 0.417136 0.417136i −0.467079 0.884215i \(-0.654694\pi\)
0.884215 + 0.467079i \(0.154694\pi\)
\(6\) 0 0
\(7\) 24.8965i 1.34429i −0.740422 0.672143i \(-0.765374\pi\)
0.740422 0.672143i \(-0.234626\pi\)
\(8\) 21.8148 6.00953i 0.964087 0.265586i
\(9\) 0 0
\(10\) 11.9577 14.3185i 0.378136 0.452790i
\(11\) −22.3431 + 22.3431i −0.612427 + 0.612427i −0.943578 0.331151i \(-0.892563\pi\)
0.331151 + 0.943578i \(0.392563\pi\)
\(12\) 0 0
\(13\) −11.2714 11.2714i −0.240471 0.240471i 0.576574 0.817045i \(-0.304389\pi\)
−0.817045 + 0.576574i \(0.804389\pi\)
\(14\) −6.30129 70.1355i −0.120292 1.33889i
\(15\) 0 0
\(16\) 59.9330 22.4506i 0.936454 0.350791i
\(17\) 88.4846 1.26239 0.631196 0.775623i \(-0.282564\pi\)
0.631196 + 0.775623i \(0.282564\pi\)
\(18\) 0 0
\(19\) 37.8187 + 37.8187i 0.456643 + 0.456643i 0.897552 0.440909i \(-0.145344\pi\)
−0.440909 + 0.897552i \(0.645344\pi\)
\(20\) 30.0618 43.3627i 0.336101 0.484810i
\(21\) 0 0
\(22\) −57.2873 + 68.5974i −0.555168 + 0.664773i
\(23\) 48.1224i 0.436270i −0.975919 0.218135i \(-0.930003\pi\)
0.975919 0.218135i \(-0.0699973\pi\)
\(24\) 0 0
\(25\) 81.4994i 0.651995i
\(26\) −34.6053 28.8997i −0.261025 0.217988i
\(27\) 0 0
\(28\) −35.5025 195.982i −0.239619 1.32276i
\(29\) −10.4432 10.4432i −0.0668705 0.0668705i 0.672881 0.739751i \(-0.265057\pi\)
−0.739751 + 0.672881i \(0.765057\pi\)
\(30\) 0 0
\(31\) −96.9578 −0.561746 −0.280873 0.959745i \(-0.590624\pi\)
−0.280873 + 0.959745i \(0.590624\pi\)
\(32\) 163.154 78.4142i 0.901307 0.433181i
\(33\) 0 0
\(34\) 249.268 22.3954i 1.25733 0.112964i
\(35\) −116.110 116.110i −0.560750 0.560750i
\(36\) 0 0
\(37\) −163.279 + 163.279i −0.725484 + 0.725484i −0.969717 0.244233i \(-0.921464\pi\)
0.244233 + 0.969717i \(0.421464\pi\)
\(38\) 116.110 + 96.9665i 0.495673 + 0.413949i
\(39\) 0 0
\(40\) 73.7114 129.765i 0.291370 0.512941i
\(41\) 360.519i 1.37326i 0.727008 + 0.686629i \(0.240910\pi\)
−0.727008 + 0.686629i \(0.759090\pi\)
\(42\) 0 0
\(43\) −100.249 + 100.249i −0.355531 + 0.355531i −0.862163 0.506632i \(-0.830890\pi\)
0.506632 + 0.862163i \(0.330890\pi\)
\(44\) −144.021 + 207.744i −0.493454 + 0.711785i
\(45\) 0 0
\(46\) −12.1797 135.565i −0.0390392 0.434520i
\(47\) −220.669 −0.684849 −0.342425 0.939545i \(-0.611248\pi\)
−0.342425 + 0.939545i \(0.611248\pi\)
\(48\) 0 0
\(49\) −276.837 −0.807104
\(50\) 20.6274 + 229.590i 0.0583432 + 0.649379i
\(51\) 0 0
\(52\) −104.800 72.6542i −0.279484 0.193756i
\(53\) 175.752 175.752i 0.455498 0.455498i −0.441676 0.897174i \(-0.645616\pi\)
0.897174 + 0.441676i \(0.145616\pi\)
\(54\) 0 0
\(55\) 208.404i 0.510931i
\(56\) −149.616 543.113i −0.357024 1.29601i
\(57\) 0 0
\(58\) −32.0624 26.7761i −0.0725861 0.0606184i
\(59\) −405.008 + 405.008i −0.893687 + 0.893687i −0.994868 0.101181i \(-0.967738\pi\)
0.101181 + 0.994868i \(0.467738\pi\)
\(60\) 0 0
\(61\) 664.576 + 664.576i 1.39492 + 1.39492i 0.813860 + 0.581061i \(0.197362\pi\)
0.581061 + 0.813860i \(0.302638\pi\)
\(62\) −273.138 + 24.5399i −0.559493 + 0.0502674i
\(63\) 0 0
\(64\) 439.771 262.193i 0.858928 0.512096i
\(65\) −105.133 −0.200619
\(66\) 0 0
\(67\) −107.377 107.377i −0.195794 0.195794i 0.602400 0.798194i \(-0.294211\pi\)
−0.798194 + 0.602400i \(0.794211\pi\)
\(68\) 696.540 126.179i 1.24218 0.225022i
\(69\) 0 0
\(70\) −356.480 297.705i −0.608679 0.508322i
\(71\) 215.050i 0.359461i −0.983716 0.179731i \(-0.942477\pi\)
0.983716 0.179731i \(-0.0575226\pi\)
\(72\) 0 0
\(73\) 668.587i 1.07195i −0.844235 0.535974i \(-0.819945\pi\)
0.844235 0.535974i \(-0.180055\pi\)
\(74\) −418.644 + 501.296i −0.657654 + 0.787492i
\(75\) 0 0
\(76\) 351.634 + 243.775i 0.530726 + 0.367933i
\(77\) 556.266 + 556.266i 0.823277 + 0.823277i
\(78\) 0 0
\(79\) −822.956 −1.17202 −0.586012 0.810303i \(-0.699303\pi\)
−0.586012 + 0.810303i \(0.699303\pi\)
\(80\) 174.808 384.215i 0.244301 0.536956i
\(81\) 0 0
\(82\) 91.2471 + 1015.61i 0.122885 + 1.36775i
\(83\) −326.873 326.873i −0.432277 0.432277i 0.457125 0.889402i \(-0.348879\pi\)
−0.889402 + 0.457125i \(0.848879\pi\)
\(84\) 0 0
\(85\) 412.668 412.668i 0.526589 0.526589i
\(86\) −257.037 + 307.783i −0.322290 + 0.385919i
\(87\) 0 0
\(88\) −353.139 + 621.682i −0.427781 + 0.753086i
\(89\) 262.733i 0.312918i 0.987684 + 0.156459i \(0.0500079\pi\)
−0.987684 + 0.156459i \(0.949992\pi\)
\(90\) 0 0
\(91\) −280.619 + 280.619i −0.323262 + 0.323262i
\(92\) −68.6226 378.814i −0.0777652 0.429283i
\(93\) 0 0
\(94\) −621.643 + 55.8512i −0.682102 + 0.0612831i
\(95\) 352.752 0.380964
\(96\) 0 0
\(97\) −150.801 −0.157850 −0.0789251 0.996881i \(-0.525149\pi\)
−0.0789251 + 0.996881i \(0.525149\pi\)
\(98\) −779.871 + 70.0671i −0.803866 + 0.0722229i
\(99\) 0 0
\(100\) 116.218 + 641.553i 0.116218 + 0.641553i
\(101\) −487.985 + 487.985i −0.480755 + 0.480755i −0.905373 0.424617i \(-0.860409\pi\)
0.424617 + 0.905373i \(0.360409\pi\)
\(102\) 0 0
\(103\) 1840.58i 1.76075i −0.474275 0.880377i \(-0.657290\pi\)
0.474275 0.880377i \(-0.342710\pi\)
\(104\) −313.620 178.148i −0.295701 0.167970i
\(105\) 0 0
\(106\) 450.625 539.590i 0.412911 0.494431i
\(107\) 79.4098 79.4098i 0.0717461 0.0717461i −0.670323 0.742069i \(-0.733845\pi\)
0.742069 + 0.670323i \(0.233845\pi\)
\(108\) 0 0
\(109\) 952.979 + 952.979i 0.837421 + 0.837421i 0.988519 0.151098i \(-0.0482809\pi\)
−0.151098 + 0.988519i \(0.548281\pi\)
\(110\) 52.7469 + 587.091i 0.0457202 + 0.508881i
\(111\) 0 0
\(112\) −558.942 1492.12i −0.471563 1.25886i
\(113\) 720.469 0.599788 0.299894 0.953973i \(-0.403049\pi\)
0.299894 + 0.953973i \(0.403049\pi\)
\(114\) 0 0
\(115\) −224.430 224.430i −0.181984 0.181984i
\(116\) −97.0993 67.3153i −0.0777193 0.0538799i
\(117\) 0 0
\(118\) −1038.43 + 1243.45i −0.810131 + 0.970072i
\(119\) 2202.96i 1.69702i
\(120\) 0 0
\(121\) 332.571i 0.249865i
\(122\) 2040.37 + 1703.96i 1.51415 + 1.26450i
\(123\) 0 0
\(124\) −763.240 + 138.262i −0.552750 + 0.100131i
\(125\) 963.056 + 963.056i 0.689107 + 0.689107i
\(126\) 0 0
\(127\) 2622.35 1.83225 0.916124 0.400895i \(-0.131301\pi\)
0.916124 + 0.400895i \(0.131301\pi\)
\(128\) 1172.51 849.925i 0.809658 0.586902i
\(129\) 0 0
\(130\) −296.169 + 26.6092i −0.199814 + 0.0179522i
\(131\) −657.574 657.574i −0.438569 0.438569i 0.452961 0.891530i \(-0.350368\pi\)
−0.891530 + 0.452961i \(0.850368\pi\)
\(132\) 0 0
\(133\) 941.555 941.555i 0.613858 0.613858i
\(134\) −329.666 275.312i −0.212529 0.177488i
\(135\) 0 0
\(136\) 1930.27 531.751i 1.21706 0.335274i
\(137\) 2511.52i 1.56623i −0.621874 0.783117i \(-0.713629\pi\)
0.621874 0.783117i \(-0.286371\pi\)
\(138\) 0 0
\(139\) −1086.02 + 1086.02i −0.662697 + 0.662697i −0.956015 0.293318i \(-0.905241\pi\)
0.293318 + 0.956015i \(0.405241\pi\)
\(140\) −1079.58 748.434i −0.651723 0.451816i
\(141\) 0 0
\(142\) −54.4290 605.813i −0.0321661 0.358019i
\(143\) 503.677 0.294543
\(144\) 0 0
\(145\) −97.4080 −0.0557882
\(146\) −169.219 1883.46i −0.0959222 1.06765i
\(147\) 0 0
\(148\) −1052.48 + 1518.15i −0.584547 + 0.843183i
\(149\) 2284.63 2284.63i 1.25614 1.25614i 0.303214 0.952922i \(-0.401940\pi\)
0.952922 0.303214i \(-0.0980598\pi\)
\(150\) 0 0
\(151\) 2814.39i 1.51677i −0.651809 0.758383i \(-0.725990\pi\)
0.651809 0.758383i \(-0.274010\pi\)
\(152\) 1052.28 + 597.735i 0.561521 + 0.318965i
\(153\) 0 0
\(154\) 1707.84 + 1426.25i 0.893645 + 0.746304i
\(155\) −452.184 + 452.184i −0.234325 + 0.234325i
\(156\) 0 0
\(157\) −906.308 906.308i −0.460709 0.460709i 0.438179 0.898888i \(-0.355624\pi\)
−0.898888 + 0.438179i \(0.855624\pi\)
\(158\) −2318.33 + 208.290i −1.16732 + 0.104877i
\(159\) 0 0
\(160\) 395.203 1126.61i 0.195272 0.556663i
\(161\) −1198.08 −0.586472
\(162\) 0 0
\(163\) 1392.36 + 1392.36i 0.669067 + 0.669067i 0.957500 0.288433i \(-0.0931342\pi\)
−0.288433 + 0.957500i \(0.593134\pi\)
\(164\) 514.101 + 2837.96i 0.244784 + 1.35127i
\(165\) 0 0
\(166\) −1003.56 838.097i −0.469225 0.391861i
\(167\) 1221.66i 0.566075i 0.959109 + 0.283038i \(0.0913421\pi\)
−0.959109 + 0.283038i \(0.908658\pi\)
\(168\) 0 0
\(169\) 1942.91i 0.884347i
\(170\) 1058.07 1266.96i 0.477356 0.571598i
\(171\) 0 0
\(172\) −646.193 + 932.104i −0.286464 + 0.413211i
\(173\) 563.418 + 563.418i 0.247606 + 0.247606i 0.819988 0.572381i \(-0.193980\pi\)
−0.572381 + 0.819988i \(0.693980\pi\)
\(174\) 0 0
\(175\) 2029.05 0.876468
\(176\) −837.474 + 1840.71i −0.358676 + 0.788344i
\(177\) 0 0
\(178\) 66.4976 + 740.141i 0.0280012 + 0.311662i
\(179\) 2202.23 + 2202.23i 0.919565 + 0.919565i 0.996998 0.0774329i \(-0.0246724\pi\)
−0.0774329 + 0.996998i \(0.524672\pi\)
\(180\) 0 0
\(181\) 121.294 121.294i 0.0498104 0.0498104i −0.681763 0.731573i \(-0.738786\pi\)
0.731573 + 0.681763i \(0.238786\pi\)
\(182\) −719.502 + 861.551i −0.293039 + 0.350892i
\(183\) 0 0
\(184\) −289.193 1049.78i −0.115867 0.420602i
\(185\) 1522.98i 0.605251i
\(186\) 0 0
\(187\) −1977.02 + 1977.02i −0.773124 + 0.773124i
\(188\) −1737.08 + 314.675i −0.673882 + 0.122074i
\(189\) 0 0
\(190\) 993.731 89.2813i 0.379436 0.0340902i
\(191\) −3927.65 −1.48793 −0.743966 0.668218i \(-0.767058\pi\)
−0.743966 + 0.668218i \(0.767058\pi\)
\(192\) 0 0
\(193\) −3249.02 −1.21176 −0.605880 0.795556i \(-0.707179\pi\)
−0.605880 + 0.795556i \(0.707179\pi\)
\(194\) −424.817 + 38.1675i −0.157217 + 0.0141251i
\(195\) 0 0
\(196\) −2179.23 + 394.769i −0.794178 + 0.143866i
\(197\) −2420.90 + 2420.90i −0.875545 + 0.875545i −0.993070 0.117525i \(-0.962504\pi\)
0.117525 + 0.993070i \(0.462504\pi\)
\(198\) 0 0
\(199\) 1371.30i 0.488488i 0.969714 + 0.244244i \(0.0785397\pi\)
−0.969714 + 0.244244i \(0.921460\pi\)
\(200\) 489.773 + 1777.89i 0.173161 + 0.628580i
\(201\) 0 0
\(202\) −1251.18 + 1498.20i −0.435807 + 0.521847i
\(203\) −259.998 + 259.998i −0.0898931 + 0.0898931i
\(204\) 0 0
\(205\) 1681.36 + 1681.36i 0.572836 + 0.572836i
\(206\) −465.849 5185.06i −0.157559 1.75369i
\(207\) 0 0
\(208\) −928.580 422.480i −0.309546 0.140835i
\(209\) −1689.98 −0.559321
\(210\) 0 0
\(211\) −1620.50 1620.50i −0.528719 0.528719i 0.391471 0.920190i \(-0.371966\pi\)
−0.920190 + 0.391471i \(0.871966\pi\)
\(212\) 1132.88 1634.12i 0.367011 0.529396i
\(213\) 0 0
\(214\) 203.605 243.802i 0.0650382 0.0778784i
\(215\) 935.068i 0.296610i
\(216\) 0 0
\(217\) 2413.91i 0.755148i
\(218\) 2925.82 + 2443.42i 0.908997 + 0.759125i
\(219\) 0 0
\(220\) 297.185 + 1640.53i 0.0910736 + 0.502749i
\(221\) −997.347 997.347i −0.303569 0.303569i
\(222\) 0 0
\(223\) −419.617 −0.126007 −0.0630036 0.998013i \(-0.520068\pi\)
−0.0630036 + 0.998013i \(0.520068\pi\)
\(224\) −1952.24 4061.97i −0.582320 1.21161i
\(225\) 0 0
\(226\) 2029.62 182.350i 0.597381 0.0536714i
\(227\) 2133.64 + 2133.64i 0.623853 + 0.623853i 0.946515 0.322661i \(-0.104577\pi\)
−0.322661 + 0.946515i \(0.604577\pi\)
\(228\) 0 0
\(229\) −1574.42 + 1574.42i −0.454325 + 0.454325i −0.896787 0.442462i \(-0.854105\pi\)
0.442462 + 0.896787i \(0.354105\pi\)
\(230\) −689.039 575.433i −0.197539 0.164969i
\(231\) 0 0
\(232\) −290.574 165.057i −0.0822289 0.0467091i
\(233\) 1194.86i 0.335957i −0.985791 0.167978i \(-0.946276\pi\)
0.985791 0.167978i \(-0.0537239\pi\)
\(234\) 0 0
\(235\) −1029.14 + 1029.14i −0.285675 + 0.285675i
\(236\) −2610.63 + 3765.71i −0.720075 + 1.03867i
\(237\) 0 0
\(238\) −557.567 6205.91i −0.151856 1.69021i
\(239\) 4241.03 1.14782 0.573911 0.818917i \(-0.305425\pi\)
0.573911 + 0.818917i \(0.305425\pi\)
\(240\) 0 0
\(241\) −5571.19 −1.48910 −0.744548 0.667569i \(-0.767335\pi\)
−0.744548 + 0.667569i \(0.767335\pi\)
\(242\) 84.1734 + 936.878i 0.0223590 + 0.248863i
\(243\) 0 0
\(244\) 6179.15 + 4283.77i 1.62123 + 1.12394i
\(245\) −1291.09 + 1291.09i −0.336672 + 0.336672i
\(246\) 0 0
\(247\) 852.541i 0.219619i
\(248\) −2115.12 + 582.671i −0.541572 + 0.149192i
\(249\) 0 0
\(250\) 2956.75 + 2469.26i 0.748006 + 0.624678i
\(251\) 482.728 482.728i 0.121393 0.121393i −0.643801 0.765193i \(-0.722643\pi\)
0.765193 + 0.643801i \(0.222643\pi\)
\(252\) 0 0
\(253\) 1075.20 + 1075.20i 0.267184 + 0.267184i
\(254\) 7387.36 663.713i 1.82490 0.163957i
\(255\) 0 0
\(256\) 3087.94 2691.07i 0.753891 0.656999i
\(257\) −8093.12 −1.96434 −0.982169 0.188002i \(-0.939799\pi\)
−0.982169 + 0.188002i \(0.939799\pi\)
\(258\) 0 0
\(259\) 4065.08 + 4065.08i 0.975257 + 0.975257i
\(260\) −827.598 + 149.921i −0.197406 + 0.0357603i
\(261\) 0 0
\(262\) −2018.87 1686.01i −0.476054 0.397564i
\(263\) 410.300i 0.0961984i 0.998843 + 0.0480992i \(0.0153164\pi\)
−0.998843 + 0.0480992i \(0.984684\pi\)
\(264\) 0 0
\(265\) 1639.32i 0.380009i
\(266\) 2414.13 2890.74i 0.556465 0.666326i
\(267\) 0 0
\(268\) −998.378 692.139i −0.227558 0.157758i
\(269\) 4.77962 + 4.77962i 0.00108334 + 0.00108334i 0.707648 0.706565i \(-0.249756\pi\)
−0.706565 + 0.707648i \(0.749756\pi\)
\(270\) 0 0
\(271\) −2833.98 −0.635247 −0.317623 0.948217i \(-0.602885\pi\)
−0.317623 + 0.948217i \(0.602885\pi\)
\(272\) 5303.15 1986.54i 1.18217 0.442836i
\(273\) 0 0
\(274\) −635.665 7075.17i −0.140153 1.55995i
\(275\) −1820.95 1820.95i −0.399300 0.399300i
\(276\) 0 0
\(277\) 1525.80 1525.80i 0.330962 0.330962i −0.521989 0.852952i \(-0.674810\pi\)
0.852952 + 0.521989i \(0.174810\pi\)
\(278\) −2784.53 + 3334.27i −0.600738 + 0.719339i
\(279\) 0 0
\(280\) −3230.70 1835.16i −0.689539 0.391684i
\(281\) 4750.23i 1.00845i −0.863572 0.504226i \(-0.831778\pi\)
0.863572 0.504226i \(-0.168222\pi\)
\(282\) 0 0
\(283\) 644.104 644.104i 0.135293 0.135293i −0.636217 0.771510i \(-0.719502\pi\)
0.771510 + 0.636217i \(0.219502\pi\)
\(284\) −306.662 1692.85i −0.0640740 0.353705i
\(285\) 0 0
\(286\) 1418.90 127.480i 0.293361 0.0263569i
\(287\) 8975.67 1.84605
\(288\) 0 0
\(289\) 2916.53 0.593635
\(290\) −274.406 + 24.6539i −0.0555644 + 0.00499216i
\(291\) 0 0
\(292\) −953.405 5263.03i −0.191075 1.05478i
\(293\) 1433.16 1433.16i 0.285755 0.285755i −0.549644 0.835399i \(-0.685237\pi\)
0.835399 + 0.549644i \(0.185237\pi\)
\(294\) 0 0
\(295\) 3777.69i 0.745578i
\(296\) −2580.67 + 4543.13i −0.506751 + 0.892108i
\(297\) 0 0
\(298\) 5857.75 7014.23i 1.13869 1.36350i
\(299\) −542.407 + 542.407i −0.104910 + 0.104910i
\(300\) 0 0
\(301\) 2495.85 + 2495.85i 0.477935 + 0.477935i
\(302\) −712.319 7928.36i −0.135726 1.51068i
\(303\) 0 0
\(304\) 3115.65 + 1417.54i 0.587811 + 0.267439i
\(305\) 6198.79 1.16374
\(306\) 0 0
\(307\) −231.211 231.211i −0.0429834 0.0429834i 0.685288 0.728272i \(-0.259676\pi\)
−0.728272 + 0.685288i \(0.759676\pi\)
\(308\) 5172.09 + 3585.62i 0.956842 + 0.663343i
\(309\) 0 0
\(310\) −1159.39 + 1388.29i −0.212416 + 0.254353i
\(311\) 871.410i 0.158885i −0.996839 0.0794423i \(-0.974686\pi\)
0.996839 0.0794423i \(-0.0253140\pi\)
\(312\) 0 0
\(313\) 3515.02i 0.634762i −0.948298 0.317381i \(-0.897197\pi\)
0.948298 0.317381i \(-0.102803\pi\)
\(314\) −2782.53 2323.76i −0.500087 0.417634i
\(315\) 0 0
\(316\) −6478.22 + 1173.54i −1.15325 + 0.208913i
\(317\) −4723.77 4723.77i −0.836951 0.836951i 0.151506 0.988456i \(-0.451588\pi\)
−0.988456 + 0.151506i \(0.951588\pi\)
\(318\) 0 0
\(319\) 466.665 0.0819067
\(320\) 828.174 3273.77i 0.144676 0.571904i
\(321\) 0 0
\(322\) −3375.09 + 303.233i −0.584119 + 0.0524799i
\(323\) 3346.38 + 3346.38i 0.576462 + 0.576462i
\(324\) 0 0
\(325\) 918.613 918.613i 0.156786 0.156786i
\(326\) 4274.79 + 3569.98i 0.726254 + 0.606512i
\(327\) 0 0
\(328\) 2166.55 + 7864.65i 0.364718 + 1.32394i
\(329\) 5493.90i 0.920633i
\(330\) 0 0
\(331\) −1820.26 + 1820.26i −0.302268 + 0.302268i −0.841901 0.539633i \(-0.818563\pi\)
0.539633 + 0.841901i \(0.318563\pi\)
\(332\) −3039.23 2106.99i −0.502408 0.348301i
\(333\) 0 0
\(334\) 309.200 + 3441.50i 0.0506547 + 0.563804i
\(335\) −1001.55 −0.163345
\(336\) 0 0
\(337\) 74.0970 0.0119772 0.00598861 0.999982i \(-0.498094\pi\)
0.00598861 + 0.999982i \(0.498094\pi\)
\(338\) −491.749 5473.33i −0.0791350 0.880799i
\(339\) 0 0
\(340\) 2660.01 3836.94i 0.424292 0.612021i
\(341\) 2166.34 2166.34i 0.344029 0.344029i
\(342\) 0 0
\(343\) 1647.24i 0.259307i
\(344\) −1584.46 + 2789.36i −0.248339 + 0.437187i
\(345\) 0 0
\(346\) 1729.80 + 1444.59i 0.268770 + 0.224456i
\(347\) −2102.73 + 2102.73i −0.325305 + 0.325305i −0.850798 0.525493i \(-0.823881\pi\)
0.525493 + 0.850798i \(0.323881\pi\)
\(348\) 0 0
\(349\) −6612.85 6612.85i −1.01426 1.01426i −0.999897 0.0143661i \(-0.995427\pi\)
−0.0143661 0.999897i \(-0.504573\pi\)
\(350\) 5716.00 513.551i 0.872951 0.0784299i
\(351\) 0 0
\(352\) −1893.35 + 5397.38i −0.286693 + 0.817277i
\(353\) −2216.90 −0.334259 −0.167130 0.985935i \(-0.553450\pi\)
−0.167130 + 0.985935i \(0.553450\pi\)
\(354\) 0 0
\(355\) −1002.93 1002.93i −0.149944 0.149944i
\(356\) 374.658 + 2068.21i 0.0557776 + 0.307906i
\(357\) 0 0
\(358\) 6761.23 + 5646.46i 0.998162 + 0.833589i
\(359\) 2082.23i 0.306117i 0.988217 + 0.153059i \(0.0489123\pi\)
−0.988217 + 0.153059i \(0.951088\pi\)
\(360\) 0 0
\(361\) 3998.49i 0.582955i
\(362\) 310.995 372.393i 0.0451533 0.0540678i
\(363\) 0 0
\(364\) −1808.84 + 2609.16i −0.260464 + 0.375707i
\(365\) −3118.10 3118.10i −0.447148 0.447148i
\(366\) 0 0
\(367\) 4509.22 0.641360 0.320680 0.947188i \(-0.396089\pi\)
0.320680 + 0.947188i \(0.396089\pi\)
\(368\) −1080.38 2884.12i −0.153040 0.408547i
\(369\) 0 0
\(370\) 385.464 + 4290.34i 0.0541603 + 0.602823i
\(371\) −4375.61 4375.61i −0.612320 0.612320i
\(372\) 0 0
\(373\) −8661.56 + 8661.56i −1.20236 + 1.20236i −0.228908 + 0.973448i \(0.573515\pi\)
−0.973448 + 0.228908i \(0.926485\pi\)
\(374\) −5069.05 + 6069.81i −0.700840 + 0.839205i
\(375\) 0 0
\(376\) −4813.86 + 1326.12i −0.660254 + 0.181886i
\(377\) 235.418i 0.0321609i
\(378\) 0 0
\(379\) 3522.46 3522.46i 0.477405 0.477405i −0.426896 0.904301i \(-0.640393\pi\)
0.904301 + 0.426896i \(0.140393\pi\)
\(380\) 2776.82 503.025i 0.374863 0.0679069i
\(381\) 0 0
\(382\) −11064.5 + 994.086i −1.48196 + 0.133146i
\(383\) −3044.88 −0.406229 −0.203115 0.979155i \(-0.565106\pi\)
−0.203115 + 0.979155i \(0.565106\pi\)
\(384\) 0 0
\(385\) 5188.54 0.686837
\(386\) −9152.75 + 822.325i −1.20690 + 0.108433i
\(387\) 0 0
\(388\) −1187.08 + 215.042i −0.155322 + 0.0281368i
\(389\) −1932.73 + 1932.73i −0.251911 + 0.251911i −0.821754 0.569843i \(-0.807004\pi\)
0.569843 + 0.821754i \(0.307004\pi\)
\(390\) 0 0
\(391\) 4258.09i 0.550744i
\(392\) −6039.14 + 1663.66i −0.778119 + 0.214356i
\(393\) 0 0
\(394\) −6207.15 + 7432.61i −0.793685 + 0.950379i
\(395\) −3838.04 + 3838.04i −0.488893 + 0.488893i
\(396\) 0 0
\(397\) −672.457 672.457i −0.0850117 0.0850117i 0.663322 0.748334i \(-0.269146\pi\)
−0.748334 + 0.663322i \(0.769146\pi\)
\(398\) 347.075 + 3863.07i 0.0437119 + 0.486528i
\(399\) 0 0
\(400\) 1829.71 + 4884.51i 0.228714 + 0.610563i
\(401\) 7606.74 0.947288 0.473644 0.880716i \(-0.342938\pi\)
0.473644 + 0.880716i \(0.342938\pi\)
\(402\) 0 0
\(403\) 1092.85 + 1092.85i 0.135084 + 0.135084i
\(404\) −3145.49 + 4537.23i −0.387361 + 0.558751i
\(405\) 0 0
\(406\) −666.631 + 798.241i −0.0814885 + 0.0975765i
\(407\) 7296.32i 0.888612i
\(408\) 0 0
\(409\) 4981.58i 0.602257i 0.953584 + 0.301129i \(0.0973634\pi\)
−0.953584 + 0.301129i \(0.902637\pi\)
\(410\) 5162.08 + 4310.98i 0.621797 + 0.519278i
\(411\) 0 0
\(412\) −2624.67 14488.8i −0.313855 1.73256i
\(413\) 10083.3 + 10083.3i 1.20137 + 1.20137i
\(414\) 0 0
\(415\) −3048.89 −0.360637
\(416\) −2722.81 955.136i −0.320906 0.112571i
\(417\) 0 0
\(418\) −4760.80 + 427.732i −0.557077 + 0.0500503i
\(419\) 3433.38 + 3433.38i 0.400314 + 0.400314i 0.878344 0.478030i \(-0.158649\pi\)
−0.478030 + 0.878344i \(0.658649\pi\)
\(420\) 0 0
\(421\) 7973.72 7973.72i 0.923077 0.923077i −0.0741686 0.997246i \(-0.523630\pi\)
0.997246 + 0.0741686i \(0.0236303\pi\)
\(422\) −4975.22 4154.93i −0.573910 0.479286i
\(423\) 0 0
\(424\) 2777.81 4890.18i 0.318166 0.560114i
\(425\) 7211.44i 0.823074i
\(426\) 0 0
\(427\) 16545.6 16545.6i 1.87517 1.87517i
\(428\) 511.866 738.343i 0.0578084 0.0833859i
\(429\) 0 0
\(430\) 236.665 + 2634.16i 0.0265418 + 0.295420i
\(431\) −4800.16 −0.536463 −0.268232 0.963354i \(-0.586439\pi\)
−0.268232 + 0.963354i \(0.586439\pi\)
\(432\) 0 0
\(433\) 6242.32 0.692810 0.346405 0.938085i \(-0.387402\pi\)
0.346405 + 0.938085i \(0.387402\pi\)
\(434\) 610.959 + 6800.18i 0.0675737 + 0.752118i
\(435\) 0 0
\(436\) 8860.69 + 6142.79i 0.973280 + 0.674739i
\(437\) 1819.93 1819.93i 0.199220 0.199220i
\(438\) 0 0
\(439\) 4929.27i 0.535903i 0.963432 + 0.267951i \(0.0863466\pi\)
−0.963432 + 0.267951i \(0.913653\pi\)
\(440\) 1252.41 + 4546.30i 0.135696 + 0.492582i
\(441\) 0 0
\(442\) −3062.03 2557.18i −0.329516 0.275187i
\(443\) 7670.67 7670.67i 0.822674 0.822674i −0.163817 0.986491i \(-0.552381\pi\)
0.986491 + 0.163817i \(0.0523807\pi\)
\(444\) 0 0
\(445\) 1225.32 + 1225.32i 0.130529 + 0.130529i
\(446\) −1182.09 + 106.205i −0.125502 + 0.0112756i
\(447\) 0 0
\(448\) −6527.70 10948.8i −0.688404 1.15464i
\(449\) 11515.2 1.21032 0.605162 0.796102i \(-0.293108\pi\)
0.605162 + 0.796102i \(0.293108\pi\)
\(450\) 0 0
\(451\) −8055.12 8055.12i −0.841021 0.841021i
\(452\) 5671.44 1027.39i 0.590182 0.106912i
\(453\) 0 0
\(454\) 6550.66 + 5470.61i 0.677176 + 0.565526i
\(455\) 2617.46i 0.269689i
\(456\) 0 0
\(457\) 4829.89i 0.494383i 0.968967 + 0.247191i \(0.0795076\pi\)
−0.968967 + 0.247191i \(0.920492\pi\)
\(458\) −4036.78 + 4833.74i −0.411848 + 0.493157i
\(459\) 0 0
\(460\) −2086.72 1446.65i −0.211508 0.146631i
\(461\) −8265.79 8265.79i −0.835090 0.835090i 0.153118 0.988208i \(-0.451069\pi\)
−0.988208 + 0.153118i \(0.951069\pi\)
\(462\) 0 0
\(463\) −5043.86 −0.506281 −0.253141 0.967430i \(-0.581464\pi\)
−0.253141 + 0.967430i \(0.581464\pi\)
\(464\) −860.346 391.435i −0.0860788 0.0391636i
\(465\) 0 0
\(466\) −302.418 3366.02i −0.0300628 0.334609i
\(467\) −12438.8 12438.8i −1.23255 1.23255i −0.962982 0.269564i \(-0.913120\pi\)
−0.269564 0.962982i \(-0.586880\pi\)
\(468\) 0 0
\(469\) −2673.31 + 2673.31i −0.263203 + 0.263203i
\(470\) −2638.70 + 3159.64i −0.258966 + 0.310093i
\(471\) 0 0
\(472\) −6401.26 + 11269.1i −0.624241 + 1.09894i
\(473\) 4479.75i 0.435474i
\(474\) 0 0
\(475\) −3082.20 + 3082.20i −0.297729 + 0.297729i
\(476\) −3141.42 17341.4i −0.302493 1.66984i
\(477\) 0 0
\(478\) 11947.3 1073.40i 1.14322 0.102712i
\(479\) −13059.7 −1.24575 −0.622875 0.782321i \(-0.714036\pi\)
−0.622875 + 0.782321i \(0.714036\pi\)
\(480\) 0 0
\(481\) 3680.77 0.348916
\(482\) −15694.5 + 1410.06i −1.48312 + 0.133250i
\(483\) 0 0
\(484\) 474.246 + 2617.96i 0.0445385 + 0.245864i
\(485\) −703.292 + 703.292i −0.0658450 + 0.0658450i
\(486\) 0 0
\(487\) 15549.3i 1.44683i 0.690414 + 0.723414i \(0.257428\pi\)
−0.690414 + 0.723414i \(0.742572\pi\)
\(488\) 18491.4 + 10503.8i 1.71530 + 0.974354i
\(489\) 0 0
\(490\) −3310.33 + 3963.88i −0.305195 + 0.365448i
\(491\) 8628.34 8628.34i 0.793058 0.793058i −0.188932 0.981990i \(-0.560503\pi\)
0.981990 + 0.188932i \(0.0605027\pi\)
\(492\) 0 0
\(493\) −924.059 924.059i −0.0844169 0.0844169i
\(494\) −215.777 2401.68i −0.0196524 0.218738i
\(495\) 0 0
\(496\) −5810.98 + 2176.76i −0.526049 + 0.197056i
\(497\) −5354.00 −0.483219
\(498\) 0 0
\(499\) 1732.42 + 1732.42i 0.155418 + 0.155418i 0.780533 0.625115i \(-0.214948\pi\)
−0.625115 + 0.780533i \(0.714948\pi\)
\(500\) 8954.38 + 6207.74i 0.800904 + 0.555237i
\(501\) 0 0
\(502\) 1237.71 1482.06i 0.110043 0.131768i
\(503\) 16579.6i 1.46968i 0.678241 + 0.734839i \(0.262742\pi\)
−0.678241 + 0.734839i \(0.737258\pi\)
\(504\) 0 0
\(505\) 4551.65i 0.401081i
\(506\) 3301.07 + 2756.80i 0.290021 + 0.242203i
\(507\) 0 0
\(508\) 20642.8 3739.47i 1.80291 0.326599i
\(509\) 7830.92 + 7830.92i 0.681924 + 0.681924i 0.960434 0.278509i \(-0.0898403\pi\)
−0.278509 + 0.960434i \(0.589840\pi\)
\(510\) 0 0
\(511\) −16645.5 −1.44100
\(512\) 8017.86 8362.51i 0.692076 0.721825i
\(513\) 0 0
\(514\) −22799.0 + 2048.36i −1.95646 + 0.175777i
\(515\) −8583.95 8583.95i −0.734474 0.734474i
\(516\) 0 0
\(517\) 4930.44 4930.44i 0.419420 0.419420i
\(518\) 12480.5 + 10422.8i 1.05861 + 0.884075i
\(519\) 0 0
\(520\) −2293.47 + 631.803i −0.193414 + 0.0532815i
\(521\) 3400.02i 0.285907i 0.989729 + 0.142953i \(0.0456599\pi\)
−0.989729 + 0.142953i \(0.954340\pi\)
\(522\) 0 0
\(523\) −2019.50 + 2019.50i −0.168847 + 0.168847i −0.786472 0.617626i \(-0.788095\pi\)
0.617626 + 0.786472i \(0.288095\pi\)
\(524\) −6114.05 4238.64i −0.509720 0.353370i
\(525\) 0 0
\(526\) 103.847 + 1155.85i 0.00860822 + 0.0958124i
\(527\) −8579.28 −0.709144
\(528\) 0 0
\(529\) 9851.23 0.809668
\(530\) −414.910 4618.09i −0.0340048 0.378485i
\(531\) 0 0
\(532\) 6069.15 8754.47i 0.494607 0.713448i
\(533\) 4063.56 4063.56i 0.330229 0.330229i
\(534\) 0 0
\(535\) 740.691i 0.0598558i
\(536\) −2987.69 1697.12i −0.240762 0.136762i
\(537\) 0 0
\(538\) 14.6743 + 12.2548i 0.00117594 + 0.000982052i
\(539\) 6185.39 6185.39i 0.494293 0.494293i
\(540\) 0 0
\(541\) −13432.6 13432.6i −1.06749 1.06749i −0.997551 0.0699388i \(-0.977720\pi\)
−0.0699388 0.997551i \(-0.522280\pi\)
\(542\) −7983.54 + 717.278i −0.632699 + 0.0568445i
\(543\) 0 0
\(544\) 14436.6 6938.45i 1.13780 0.546845i
\(545\) 8888.86 0.698637
\(546\) 0 0
\(547\) −5376.46 5376.46i −0.420257 0.420257i 0.465035 0.885292i \(-0.346042\pi\)
−0.885292 + 0.465035i \(0.846042\pi\)
\(548\) −3581.44 19770.4i −0.279181 1.54115i
\(549\) 0 0
\(550\) −5590.64 4668.88i −0.433429 0.361967i
\(551\) 789.894i 0.0610719i
\(552\) 0 0
\(553\) 20488.7i 1.57553i
\(554\) 3912.13 4684.49i 0.300019 0.359251i
\(555\) 0 0
\(556\) −7000.34 + 10097.7i −0.533958 + 0.770210i
\(557\) 2076.28 + 2076.28i 0.157944 + 0.157944i 0.781655 0.623711i \(-0.214376\pi\)
−0.623711 + 0.781655i \(0.714376\pi\)
\(558\) 0 0
\(559\) 2259.90 0.170990
\(560\) −9565.61 4352.10i −0.721823 0.328410i
\(561\) 0 0
\(562\) −1202.28 13381.8i −0.0902405 1.00441i
\(563\) 16643.1 + 16643.1i 1.24587 + 1.24587i 0.957528 + 0.288339i \(0.0931031\pi\)
0.288339 + 0.957528i \(0.406897\pi\)
\(564\) 0 0
\(565\) 3360.07 3360.07i 0.250193 0.250193i
\(566\) 1651.47 1977.51i 0.122644 0.146857i
\(567\) 0 0
\(568\) −1292.35 4691.28i −0.0954679 0.346552i
\(569\) 5659.60i 0.416982i −0.978024 0.208491i \(-0.933145\pi\)
0.978024 0.208491i \(-0.0668551\pi\)
\(570\) 0 0
\(571\) 4872.67 4872.67i 0.357119 0.357119i −0.505631 0.862750i \(-0.668740\pi\)
0.862750 + 0.505631i \(0.168740\pi\)
\(572\) 3964.89 718.244i 0.289825 0.0525023i
\(573\) 0 0
\(574\) 25285.2 2271.73i 1.83865 0.165192i
\(575\) 3921.95 0.284446
\(576\) 0 0
\(577\) 10652.2 0.768556 0.384278 0.923217i \(-0.374450\pi\)
0.384278 + 0.923217i \(0.374450\pi\)
\(578\) 8216.10 738.171i 0.591254 0.0531209i
\(579\) 0 0
\(580\) −766.784 + 138.904i −0.0548948 + 0.00994426i
\(581\) −8138.01 + 8138.01i −0.581104 + 0.581104i
\(582\) 0 0
\(583\) 7853.69i 0.557919i
\(584\) −4017.89 14585.1i −0.284694 1.03345i
\(585\) 0 0
\(586\) 3674.61 4400.07i 0.259039 0.310180i
\(587\) −9903.95 + 9903.95i −0.696388 + 0.696388i −0.963630 0.267242i \(-0.913888\pi\)
0.267242 + 0.963630i \(0.413888\pi\)
\(588\) 0 0
\(589\) −3666.82 3666.82i −0.256517 0.256517i
\(590\) 956.129 + 10642.0i 0.0667173 + 0.742587i
\(591\) 0 0
\(592\) −6120.09 + 13451.5i −0.424889 + 0.933875i
\(593\) 3528.04 0.244316 0.122158 0.992511i \(-0.461019\pi\)
0.122158 + 0.992511i \(0.461019\pi\)
\(594\) 0 0
\(595\) −10274.0 10274.0i −0.707887 0.707887i
\(596\) 14726.5 21242.2i 1.01211 1.45993i
\(597\) 0 0
\(598\) −1390.72 + 1665.29i −0.0951018 + 0.113877i
\(599\) 19024.9i 1.29772i −0.760907 0.648861i \(-0.775246\pi\)
0.760907 0.648861i \(-0.224754\pi\)
\(600\) 0 0
\(601\) 1065.92i 0.0723460i 0.999346 + 0.0361730i \(0.0115167\pi\)
−0.999346 + 0.0361730i \(0.988483\pi\)
\(602\) 7662.72 + 6399.32i 0.518786 + 0.433250i
\(603\) 0 0
\(604\) −4013.32 22154.5i −0.270364 1.49248i
\(605\) 1551.02 + 1551.02i 0.104228 + 0.104228i
\(606\) 0 0
\(607\) 12909.7 0.863242 0.431621 0.902055i \(-0.357942\pi\)
0.431621 + 0.902055i \(0.357942\pi\)
\(608\) 9135.80 + 3204.75i 0.609384 + 0.213766i
\(609\) 0 0
\(610\) 17462.5 1568.91i 1.15908 0.104137i
\(611\) 2487.25 + 2487.25i 0.164687 + 0.164687i
\(612\) 0 0
\(613\) −8763.41 + 8763.41i −0.577408 + 0.577408i −0.934188 0.356781i \(-0.883874\pi\)
0.356781 + 0.934188i \(0.383874\pi\)
\(614\) −709.859 592.820i −0.0466573 0.0389646i
\(615\) 0 0
\(616\) 15477.7 + 8791.93i 1.01236 + 0.575060i
\(617\) 18921.2i 1.23459i 0.786733 + 0.617293i \(0.211771\pi\)
−0.786733 + 0.617293i \(0.788229\pi\)
\(618\) 0 0
\(619\) −15116.6 + 15116.6i −0.981565 + 0.981565i −0.999833 0.0182677i \(-0.994185\pi\)
0.0182677 + 0.999833i \(0.494185\pi\)
\(620\) −2914.73 + 4204.36i −0.188804 + 0.272340i
\(621\) 0 0
\(622\) −220.553 2454.83i −0.0142176 0.158247i
\(623\) 6541.15 0.420651
\(624\) 0 0
\(625\) −1204.57 −0.0770926
\(626\) −889.648 9902.09i −0.0568011 0.632216i
\(627\) 0 0
\(628\) −8426.75 5841.95i −0.535452 0.371209i
\(629\) −14447.7 + 14447.7i −0.915845 + 0.915845i
\(630\) 0 0
\(631\) 9602.80i 0.605834i −0.953017 0.302917i \(-0.902039\pi\)
0.953017 0.302917i \(-0.0979605\pi\)
\(632\) −17952.6 + 4945.58i −1.12993 + 0.311273i
\(633\) 0 0
\(634\) −14502.8 12111.7i −0.908487 0.758699i
\(635\) 12229.9 12229.9i 0.764297 0.764297i
\(636\) 0 0
\(637\) 3120.34 + 3120.34i 0.194085 + 0.194085i
\(638\) 1314.63 118.113i 0.0815781 0.00732935i
\(639\) 0 0
\(640\) 1504.44 9432.08i 0.0929194 0.582556i
\(641\) −4450.84 −0.274256 −0.137128 0.990553i \(-0.543787\pi\)
−0.137128 + 0.990553i \(0.543787\pi\)
\(642\) 0 0
\(643\) 6491.27 + 6491.27i 0.398119 + 0.398119i 0.877569 0.479450i \(-0.159164\pi\)
−0.479450 + 0.877569i \(0.659164\pi\)
\(644\) −9431.15 + 1708.46i −0.577080 + 0.104539i
\(645\) 0 0
\(646\) 10274.0 + 8580.05i 0.625734 + 0.522566i
\(647\) 5546.17i 0.337005i 0.985701 + 0.168503i \(0.0538932\pi\)
−0.985701 + 0.168503i \(0.946107\pi\)
\(648\) 0 0
\(649\) 18098.3i 1.09464i
\(650\) 2355.31 2820.31i 0.142127 0.170187i
\(651\) 0 0
\(652\) 12946.0 + 8974.98i 0.777613 + 0.539091i
\(653\) −6327.58 6327.58i −0.379200 0.379200i 0.491614 0.870813i \(-0.336407\pi\)
−0.870813 + 0.491614i \(0.836407\pi\)
\(654\) 0 0
\(655\) −6133.49 −0.365886
\(656\) 8093.88 + 21607.0i 0.481727 + 1.28599i
\(657\) 0 0
\(658\) 1390.50 + 15476.7i 0.0823820 + 0.916940i
\(659\) −15135.2 15135.2i −0.894663 0.894663i 0.100294 0.994958i \(-0.468022\pi\)
−0.994958 + 0.100294i \(0.968022\pi\)
\(660\) 0 0
\(661\) −23460.1 + 23460.1i −1.38047 + 1.38047i −0.536694 + 0.843777i \(0.680327\pi\)
−0.843777 + 0.536694i \(0.819673\pi\)
\(662\) −4667.12 + 5588.53i −0.274007 + 0.328103i
\(663\) 0 0
\(664\) −9095.03 5166.32i −0.531560 0.301946i
\(665\) 8782.30i 0.512125i
\(666\) 0 0
\(667\) −502.550 + 502.550i −0.0291736 + 0.0291736i
\(668\) 1742.08 + 9616.73i 0.100903 + 0.557009i
\(669\) 0 0
\(670\) −2821.45 + 253.492i −0.162690 + 0.0146168i
\(671\) −29697.4 −1.70858
\(672\) 0 0
\(673\) 30638.5 1.75487 0.877436 0.479694i \(-0.159252\pi\)
0.877436 + 0.479694i \(0.159252\pi\)
\(674\) 208.737 18.7539i 0.0119292 0.00107177i
\(675\) 0 0
\(676\) −2770.59 15294.4i −0.157635 0.870184i
\(677\) 12468.9 12468.9i 0.707855 0.707855i −0.258229 0.966084i \(-0.583139\pi\)
0.966084 + 0.258229i \(0.0831388\pi\)
\(678\) 0 0
\(679\) 3754.41i 0.212196i
\(680\) 6522.33 11482.2i 0.367823 0.647533i
\(681\) 0 0
\(682\) 5554.45 6651.05i 0.311864 0.373434i
\(683\) −13838.5 + 13838.5i −0.775280 + 0.775280i −0.979024 0.203744i \(-0.934689\pi\)
0.203744 + 0.979024i \(0.434689\pi\)
\(684\) 0 0
\(685\) −11713.1 11713.1i −0.653333 0.653333i
\(686\) −416.914 4640.40i −0.0232039 0.258267i
\(687\) 0 0
\(688\) −3757.58 + 8258.89i −0.208221 + 0.457656i
\(689\) −3961.95 −0.219068
\(690\) 0 0
\(691\) −106.012 106.012i −0.00583628 0.00583628i 0.704183 0.710019i \(-0.251314\pi\)
−0.710019 + 0.704183i \(0.751314\pi\)
\(692\) 5238.60 + 3631.73i 0.287777 + 0.199505i
\(693\) 0 0
\(694\) −5391.37 + 6455.77i −0.294890 + 0.353109i
\(695\) 10129.8i 0.552870i
\(696\) 0 0
\(697\) 31900.4i 1.73359i
\(698\) −20302.6 16955.2i −1.10095 0.919434i
\(699\) 0 0
\(700\) 15972.4 2893.43i 0.862431 0.156231i
\(701\) −7839.35 7839.35i −0.422380 0.422380i 0.463643 0.886022i \(-0.346542\pi\)
−0.886022 + 0.463643i \(0.846542\pi\)
\(702\) 0 0
\(703\) −12350.0 −0.662574
\(704\) −3967.64 + 15684.1i −0.212409 + 0.839653i
\(705\) 0 0
\(706\) −6245.17 + 561.095i −0.332918 + 0.0299109i
\(707\) 12149.1 + 12149.1i 0.646273 + 0.646273i
\(708\) 0 0
\(709\) 2728.30 2728.30i 0.144518 0.144518i −0.631146 0.775664i \(-0.717415\pi\)
0.775664 + 0.631146i \(0.217415\pi\)
\(710\) −3079.19 2571.50i −0.162760 0.135925i
\(711\) 0 0
\(712\) 1578.90 + 5731.48i 0.0831066 + 0.301680i
\(713\) 4665.84i 0.245073i
\(714\) 0 0
\(715\) 2349.01 2349.01i 0.122864 0.122864i
\(716\) 20476.0 + 14195.3i 1.06875 + 0.740925i
\(717\) 0 0
\(718\) 527.011 + 5865.82i 0.0273926 + 0.304889i
\(719\) 32717.8 1.69704 0.848519 0.529166i \(-0.177495\pi\)
0.848519 + 0.529166i \(0.177495\pi\)
\(720\) 0 0
\(721\) −45824.0 −2.36696
\(722\) −1012.01 11264.1i −0.0521652 0.580616i
\(723\) 0 0
\(724\) 781.844 1127.77i 0.0401340 0.0578914i
\(725\) 851.111 851.111i 0.0435993 0.0435993i
\(726\) 0 0
\(727\) 25847.2i 1.31859i 0.751883 + 0.659297i \(0.229146\pi\)
−0.751883 + 0.659297i \(0.770854\pi\)
\(728\) −4435.26 + 7808.03i −0.225799 + 0.397507i
\(729\) 0 0
\(730\) −9573.13 7994.75i −0.485366 0.405341i
\(731\) −8870.50 + 8870.50i −0.448820 + 0.448820i
\(732\) 0 0
\(733\) 10131.9 + 10131.9i 0.510547 + 0.510547i 0.914694 0.404147i \(-0.132432\pi\)
−0.404147 + 0.914694i \(0.632432\pi\)
\(734\) 12702.8 1141.28i 0.638787 0.0573915i
\(735\) 0 0
\(736\) −3773.48 7851.36i −0.188984 0.393213i
\(737\) 4798.27 0.239819
\(738\) 0 0
\(739\) 19163.7 + 19163.7i 0.953921 + 0.953921i 0.998984 0.0450633i \(-0.0143490\pi\)
−0.0450633 + 0.998984i \(0.514349\pi\)
\(740\) 2171.76 + 11988.7i 0.107886 + 0.595558i
\(741\) 0 0
\(742\) −13433.9 11219.0i −0.664656 0.555070i
\(743\) 23322.1i 1.15155i 0.817607 + 0.575777i \(0.195301\pi\)
−0.817607 + 0.575777i \(0.804699\pi\)
\(744\) 0 0
\(745\) 21309.8i 1.04796i
\(746\) −22208.1 + 26592.5i −1.08994 + 1.30512i
\(747\) 0 0
\(748\) −12743.6 + 18382.1i −0.622933 + 0.898552i
\(749\) −1977.03 1977.03i −0.0964473 0.0964473i
\(750\) 0 0
\(751\) 25994.0 1.26303 0.631515 0.775364i \(-0.282434\pi\)
0.631515 + 0.775364i \(0.282434\pi\)
\(752\) −13225.4 + 4954.16i −0.641330 + 0.240239i
\(753\) 0 0
\(754\) 59.5842 + 663.192i 0.00287789 + 0.0320319i
\(755\) −13125.5 13125.5i −0.632698 0.632698i
\(756\) 0 0
\(757\) 22145.0 22145.0i 1.06324 1.06324i 0.0653808 0.997860i \(-0.479174\pi\)
0.997860 0.0653808i \(-0.0208262\pi\)
\(758\) 9031.52 10814.6i 0.432770 0.518210i
\(759\) 0 0
\(760\) 7695.22 2119.87i 0.367283 0.101179i
\(761\) 16497.5i 0.785853i −0.919570 0.392926i \(-0.871463\pi\)
0.919570 0.392926i \(-0.128537\pi\)
\(762\) 0 0
\(763\) 23725.9 23725.9i 1.12573 1.12573i
\(764\) −30918.0 + 5600.84i −1.46410 + 0.265224i
\(765\) 0 0
\(766\) −8577.66 + 770.656i −0.404600 + 0.0363511i
\(767\) 9130.02 0.429812
\(768\) 0 0
\(769\) −24867.3 −1.16611 −0.583055 0.812433i \(-0.698143\pi\)
−0.583055 + 0.812433i \(0.698143\pi\)
\(770\) 14616.5 1313.21i 0.684082 0.0614610i
\(771\) 0 0
\(772\) −25575.9 + 4633.11i −1.19235 + 0.215996i
\(773\) −1881.72 + 1881.72i −0.0875559 + 0.0875559i −0.749528 0.661972i \(-0.769720\pi\)
0.661972 + 0.749528i \(0.269720\pi\)
\(774\) 0 0
\(775\) 7902.00i 0.366256i
\(776\) −3289.68 + 906.240i −0.152181 + 0.0419228i
\(777\) 0 0
\(778\) −4955.49 + 5933.84i −0.228359 + 0.273443i
\(779\) −13634.4 + 13634.4i −0.627089 + 0.627089i
\(780\) 0 0
\(781\) 4804.89 + 4804.89i 0.220144 + 0.220144i
\(782\) −1077.72 11995.4i −0.0492828 0.548535i
\(783\) 0 0
\(784\) −16591.7 + 6215.16i −0.755815 + 0.283125i
\(785\) −8453.54 −0.384356
\(786\) 0 0
\(787\) −7790.94 7790.94i −0.352881 0.352881i 0.508300 0.861180i \(-0.330274\pi\)
−0.861180 + 0.508300i \(0.830274\pi\)
\(788\) −15604.9 + 22509.3i −0.705457 + 1.01759i
\(789\) 0 0
\(790\) −9840.66 + 11783.5i −0.443184 + 0.530680i
\(791\) 17937.2i 0.806286i
\(792\) 0 0
\(793\) 14981.4i 0.670877i
\(794\) −2064.56 1724.17i −0.0922778 0.0770634i
\(795\) 0 0
\(796\) 1955.48 + 10794.7i 0.0870730 + 0.480665i
\(797\) 4209.84 + 4209.84i 0.187102 + 0.187102i 0.794442 0.607340i \(-0.207763\pi\)
−0.607340 + 0.794442i \(0.707763\pi\)
\(798\) 0 0
\(799\) −19525.8 −0.864549
\(800\) 6390.71 + 13296.9i 0.282432 + 0.587648i
\(801\) 0 0
\(802\) 21428.8 1925.26i 0.943488 0.0847672i
\(803\) 14938.3 + 14938.3i 0.656490 + 0.656490i
\(804\) 0 0
\(805\) −5587.51 + 5587.51i −0.244639 + 0.244639i
\(806\) 3355.25 + 2802.05i 0.146630 + 0.122454i
\(807\) 0 0
\(808\) −7712.73 + 13577.8i −0.335808 + 0.591172i
\(809\) 27554.3i 1.19747i −0.800946 0.598737i \(-0.795670\pi\)
0.800946 0.598737i \(-0.204330\pi\)
\(810\) 0 0
\(811\) 3406.54 3406.54i 0.147497 0.147497i −0.629502 0.776999i \(-0.716741\pi\)
0.776999 + 0.629502i \(0.216741\pi\)
\(812\) −1675.92 + 2417.43i −0.0724300 + 0.104477i
\(813\) 0 0
\(814\) −1846.69 20554.3i −0.0795166 0.885047i
\(815\) 12987.1 0.558184
\(816\) 0 0
\(817\) −7582.59 −0.324701
\(818\) 1260.83 + 14033.5i 0.0538924 + 0.599841i
\(819\) 0 0
\(820\) 15633.1 + 10837.8i 0.665770 + 0.461554i
\(821\) 9839.14 9839.14i 0.418256 0.418256i −0.466346 0.884602i \(-0.654430\pi\)
0.884602 + 0.466346i \(0.154430\pi\)
\(822\) 0 0
\(823\) 36653.5i 1.55244i −0.630461 0.776221i \(-0.717134\pi\)
0.630461 0.776221i \(-0.282866\pi\)
\(824\) −11061.0 40151.9i −0.467632 1.69752i
\(825\) 0 0
\(826\) 30957.5 + 25853.3i 1.30405 + 1.08905i
\(827\) 22223.2 22223.2i 0.934431 0.934431i −0.0635475 0.997979i \(-0.520241\pi\)
0.997979 + 0.0635475i \(0.0202414\pi\)
\(828\) 0 0
\(829\) 14715.5 + 14715.5i 0.616516 + 0.616516i 0.944636 0.328120i \(-0.106415\pi\)
−0.328120 + 0.944636i \(0.606415\pi\)
\(830\) −8588.98 + 771.672i −0.359190 + 0.0322713i
\(831\) 0 0
\(832\) −7912.13 2001.55i −0.329692 0.0834031i
\(833\) −24495.8 −1.01888
\(834\) 0 0
\(835\) 5697.46 + 5697.46i 0.236130 + 0.236130i
\(836\) −13303.3 + 2409.91i −0.550364 + 0.0996991i
\(837\) 0 0
\(838\) 10541.1 + 8803.12i 0.434530 + 0.362886i
\(839\) 11010.0i 0.453050i 0.974005 + 0.226525i \(0.0727365\pi\)
−0.974005 + 0.226525i \(0.927263\pi\)
\(840\) 0 0
\(841\) 24170.9i 0.991057i
\(842\) 20444.5 24480.8i 0.836773 1.00197i
\(843\) 0 0
\(844\) −15067.2 10445.5i −0.614496 0.426007i
\(845\) −9061.20 9061.20i −0.368893 0.368893i
\(846\) 0 0
\(847\) 8279.85 0.335890
\(848\) 6587.61 14479.1i 0.266768 0.586338i
\(849\) 0 0
\(850\) 1825.21 + 20315.2i 0.0736520 + 0.819772i
\(851\) 7857.37 + 7857.37i 0.316507 + 0.316507i
\(852\) 0 0
\(853\) 12809.9 12809.9i 0.514190 0.514190i −0.401617 0.915808i \(-0.631552\pi\)
0.915808 + 0.401617i \(0.131552\pi\)
\(854\) 42422.7 50798.0i 1.69985 2.03545i
\(855\) 0 0
\(856\) 1255.09 2209.52i 0.0501147 0.0882243i
\(857\) 38510.8i 1.53501i 0.641043 + 0.767505i \(0.278502\pi\)
−0.641043 + 0.767505i \(0.721498\pi\)
\(858\) 0 0
\(859\) 23234.6 23234.6i 0.922882 0.922882i −0.0743503 0.997232i \(-0.523688\pi\)
0.997232 + 0.0743503i \(0.0236883\pi\)
\(860\) 1333.41 + 7360.74i 0.0528707 + 0.291860i
\(861\) 0 0
\(862\) −13522.4 + 1214.92i −0.534311 + 0.0480049i
\(863\) 22079.5 0.870911 0.435456 0.900210i \(-0.356587\pi\)
0.435456 + 0.900210i \(0.356587\pi\)
\(864\) 0 0
\(865\) 5255.26 0.206571
\(866\) 17585.1 1579.93i 0.690031 0.0619955i
\(867\) 0 0
\(868\) 3442.24 + 19002.0i 0.134605 + 0.743054i
\(869\) 18387.4 18387.4i 0.717779 0.717779i
\(870\) 0 0
\(871\) 2420.58i 0.0941656i
\(872\) 26516.0 + 15062.1i 1.02975 + 0.584939i
\(873\) 0 0
\(874\) 4666.26 5587.51i 0.180593 0.216247i
\(875\) 23976.7 23976.7i 0.926356 0.926356i
\(876\) 0 0
\(877\) 4082.13 + 4082.13i 0.157176 + 0.157176i 0.781314 0.624138i \(-0.214550\pi\)
−0.624138 + 0.781314i \(0.714550\pi\)
\(878\) 1247.59 + 13886.2i 0.0479547 + 0.533753i
\(879\) 0 0
\(880\) 4678.80 + 12490.3i 0.179230 + 0.478463i
\(881\) −7132.59 −0.272762 −0.136381 0.990656i \(-0.543547\pi\)
−0.136381 + 0.990656i \(0.543547\pi\)
\(882\) 0 0
\(883\) 19170.0 + 19170.0i 0.730601 + 0.730601i 0.970739 0.240138i \(-0.0771926\pi\)
−0.240138 + 0.970739i \(0.577193\pi\)
\(884\) −9273.21 6428.78i −0.352819 0.244596i
\(885\) 0 0
\(886\) 19667.4 23550.3i 0.745757 0.892989i
\(887\) 45045.7i 1.70517i −0.522589 0.852585i \(-0.675034\pi\)
0.522589 0.852585i \(-0.324966\pi\)
\(888\) 0 0
\(889\) 65287.3i 2.46306i
\(890\) 3761.94 + 3141.69i 0.141686 + 0.118325i
\(891\) 0 0
\(892\) −3303.17 + 598.374i −0.123989 + 0.0224608i
\(893\) −8345.43 8345.43i −0.312731 0.312731i
\(894\) 0 0
\(895\) 20541.1 0.767167
\(896\) −21160.2 29191.4i −0.788964 1.08841i
\(897\) 0 0
\(898\) 32439.2 2914.49i 1.20547 0.108305i
\(899\) 1012.55 + 1012.55i 0.0375643 + 0.0375643i
\(900\) 0 0
\(901\) 15551.4 15551.4i 0.575017 0.575017i
\(902\) −24730.6 20653.2i −0.912905 0.762389i
\(903\) 0 0
\(904\) 15716.9 4329.68i 0.578247 0.159295i
\(905\) 1131.36i 0.0415554i
\(906\) 0 0
\(907\) −33658.2 + 33658.2i −1.23220 + 1.23220i −0.269079 + 0.963118i \(0.586719\pi\)
−0.963118 + 0.269079i \(0.913281\pi\)
\(908\) 19838.3 + 13753.2i 0.725065 + 0.502661i
\(909\) 0 0
\(910\) 662.476 + 7373.59i 0.0241328 + 0.268607i
\(911\) 42503.8 1.54579 0.772895 0.634534i \(-0.218808\pi\)
0.772895 + 0.634534i \(0.218808\pi\)
\(912\) 0 0
\(913\) 14606.7 0.529477
\(914\) 1222.44 + 13606.2i 0.0442394 + 0.492399i
\(915\) 0 0
\(916\) −10148.5 + 14638.7i −0.366066 + 0.528033i
\(917\) −16371.3 + 16371.3i −0.589562 + 0.589562i
\(918\) 0 0
\(919\) 8819.41i 0.316568i 0.987394 + 0.158284i \(0.0505961\pi\)
−0.987394 + 0.158284i \(0.949404\pi\)
\(920\) −6244.60 3547.17i −0.223781 0.127116i
\(921\) 0 0
\(922\) −25377.5 21193.3i −0.906467 0.757012i
\(923\) −2423.92 + 2423.92i −0.0864402 + 0.0864402i
\(924\) 0 0
\(925\) −13307.1 13307.1i −0.473012 0.473012i
\(926\) −14209.0 + 1276.60i −0.504250 + 0.0453041i
\(927\) 0 0
\(928\) −2522.73 884.950i −0.0892380 0.0313038i
\(929\) 14155.6 0.499925 0.249963 0.968256i \(-0.419582\pi\)
0.249963 + 0.968256i \(0.419582\pi\)
\(930\) 0 0
\(931\) −10469.6 10469.6i −0.368558 0.368558i
\(932\) −1703.87 9405.80i −0.0598844 0.330577i
\(933\) 0 0
\(934\) −38189.4 31892.9i −1.33790 1.11731i
\(935\) 18440.6i 0.644996i
\(936\) 0 0
\(937\) 38518.7i 1.34296i 0.741023 + 0.671479i \(0.234341\pi\)
−0.741023 + 0.671479i \(0.765659\pi\)
\(938\) −6854.32 + 8207.55i −0.238594 + 0.285699i
\(939\) 0 0
\(940\) −6633.71 + 9568.82i −0.230179 + 0.332022i
\(941\) −27998.2 27998.2i −0.969942 0.969942i 0.0296196 0.999561i \(-0.490570\pi\)
−0.999561 + 0.0296196i \(0.990570\pi\)
\(942\) 0 0
\(943\) 17349.0 0.599112
\(944\) −15180.7 + 33366.0i −0.523399 + 1.15039i
\(945\) 0 0
\(946\) −1133.82 12619.8i −0.0389680 0.433727i
\(947\) 32839.5 + 32839.5i 1.12687 + 1.12687i 0.990684 + 0.136181i \(0.0434829\pi\)
0.136181 + 0.990684i \(0.456517\pi\)
\(948\) 0 0
\(949\) −7535.92 + 7535.92i −0.257773 + 0.257773i
\(950\) −7902.71 + 9462.92i −0.269892 + 0.323176i
\(951\) 0 0
\(952\) −13238.7 48057.1i −0.450704 1.63607i
\(953\) 20600.1i 0.700211i −0.936710 0.350106i \(-0.886146\pi\)
0.936710 0.350106i \(-0.113854\pi\)
\(954\) 0 0
\(955\) −18317.5 + 18317.5i −0.620670 + 0.620670i
\(956\) 33384.9 6047.72i 1.12944 0.204600i
\(957\) 0 0
\(958\) −36790.3 + 3305.41i −1.24075 + 0.111475i
\(959\) −62528.2 −2.10547
\(960\) 0 0
\(961\) −20390.2 −0.684441
\(962\) 10369.0 931.599i 0.347516 0.0312224i
\(963\) 0 0
\(964\) −43855.8 + 7944.53i −1.46525 + 0.265432i
\(965\) −15152.5 + 15152.5i −0.505469 + 0.505469i
\(966\) 0 0
\(967\) 38210.9i 1.27071i −0.772219 0.635356i \(-0.780853\pi\)
0.772219 0.635356i \(-0.219147\pi\)
\(968\) 1998.59 + 7254.96i 0.0663607 + 0.240892i
\(969\) 0 0
\(970\) −1803.23 + 2159.23i −0.0596888 + 0.0714730i
\(971\) −37224.9 + 37224.9i −1.23028 + 1.23028i −0.266427 + 0.963855i \(0.585843\pi\)
−0.963855 + 0.266427i \(0.914157\pi\)
\(972\) 0 0
\(973\) 27038.1 + 27038.1i 0.890854 + 0.890854i
\(974\) 3935.51 + 43803.6i 0.129468 + 1.44102i
\(975\) 0 0
\(976\) 54750.2 + 24909.9i 1.79560 + 0.816953i
\(977\) −7985.95 −0.261508 −0.130754 0.991415i \(-0.541740\pi\)
−0.130754 + 0.991415i \(0.541740\pi\)
\(978\) 0 0
\(979\) −5870.28 5870.28i −0.191639 0.191639i
\(980\) −8322.21 + 12004.4i −0.271269 + 0.391292i
\(981\) 0 0
\(982\) 22122.9 26490.5i 0.718910 0.860842i
\(983\) 10703.1i 0.347279i −0.984809 0.173639i \(-0.944447\pi\)
0.984809 0.173639i \(-0.0555527\pi\)
\(984\) 0 0
\(985\) 22580.9i 0.730442i
\(986\) −2837.03 2369.27i −0.0916322 0.0765243i
\(987\) 0 0
\(988\) −1215.72 6711.10i −0.0391471 0.216102i
\(989\) 4824.23 + 4824.23i 0.155108 + 0.155108i
\(990\) 0 0
\(991\) −23945.4 −0.767558 −0.383779 0.923425i \(-0.625377\pi\)
−0.383779 + 0.923425i \(0.625377\pi\)
\(992\) −15819.0 + 7602.87i −0.506306 + 0.243338i
\(993\) 0 0
\(994\) −15082.6 + 1355.09i −0.481280 + 0.0432404i
\(995\) 6395.37 + 6395.37i 0.203766 + 0.203766i
\(996\) 0 0
\(997\) −14292.5 + 14292.5i −0.454010 + 0.454010i −0.896683 0.442673i \(-0.854030\pi\)
0.442673 + 0.896683i \(0.354030\pi\)
\(998\) 5318.83 + 4441.88i 0.168702 + 0.140887i
\(999\) 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 144.4.k.a.109.5 10
3.2 odd 2 16.4.e.a.13.1 yes 10
4.3 odd 2 576.4.k.a.145.4 10
12.11 even 2 64.4.e.a.17.1 10
16.5 even 4 inner 144.4.k.a.37.5 10
16.11 odd 4 576.4.k.a.433.4 10
24.5 odd 2 128.4.e.b.33.1 10
24.11 even 2 128.4.e.a.33.5 10
48.5 odd 4 16.4.e.a.5.1 10
48.11 even 4 64.4.e.a.49.1 10
48.29 odd 4 128.4.e.b.97.1 10
48.35 even 4 128.4.e.a.97.5 10
96.5 odd 8 1024.4.a.n.1.2 10
96.11 even 8 1024.4.a.m.1.2 10
96.29 odd 8 1024.4.b.j.513.9 10
96.35 even 8 1024.4.b.k.513.2 10
96.53 odd 8 1024.4.a.n.1.9 10
96.59 even 8 1024.4.a.m.1.9 10
96.77 odd 8 1024.4.b.j.513.2 10
96.83 even 8 1024.4.b.k.513.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.4.e.a.5.1 10 48.5 odd 4
16.4.e.a.13.1 yes 10 3.2 odd 2
64.4.e.a.17.1 10 12.11 even 2
64.4.e.a.49.1 10 48.11 even 4
128.4.e.a.33.5 10 24.11 even 2
128.4.e.a.97.5 10 48.35 even 4
128.4.e.b.33.1 10 24.5 odd 2
128.4.e.b.97.1 10 48.29 odd 4
144.4.k.a.37.5 10 16.5 even 4 inner
144.4.k.a.109.5 10 1.1 even 1 trivial
576.4.k.a.145.4 10 4.3 odd 2
576.4.k.a.433.4 10 16.11 odd 4
1024.4.a.m.1.2 10 96.11 even 8
1024.4.a.m.1.9 10 96.59 even 8
1024.4.a.n.1.2 10 96.5 odd 8
1024.4.a.n.1.9 10 96.53 odd 8
1024.4.b.j.513.2 10 96.77 odd 8
1024.4.b.j.513.9 10 96.29 odd 8
1024.4.b.k.513.2 10 96.35 even 8
1024.4.b.k.513.9 10 96.83 even 8