Properties

Label 324.3.j.a.19.9
Level $324$
Weight $3$
Character 324.19
Analytic conductor $8.828$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(19,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.j (of order \(18\), degree \(6\), not 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: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 19.9
Character \(\chi\) \(=\) 324.19
Dual form 324.3.j.a.307.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.43960 - 1.38836i) q^{2} +(0.144916 + 3.99737i) q^{4} +(0.133306 + 0.756014i) q^{5} +(-3.08121 + 3.67204i) q^{7} +(5.34117 - 5.95583i) q^{8} +O(q^{10})\) \(q+(-1.43960 - 1.38836i) q^{2} +(0.144916 + 3.99737i) q^{4} +(0.133306 + 0.756014i) q^{5} +(-3.08121 + 3.67204i) q^{7} +(5.34117 - 5.95583i) q^{8} +(0.857712 - 1.27344i) q^{10} +(-7.79262 - 1.37405i) q^{11} +(7.52188 + 2.73774i) q^{13} +(9.53383 - 1.00846i) q^{14} +(-15.9580 + 1.15857i) q^{16} +(-6.81117 - 11.7973i) q^{17} +(-11.9343 - 6.89025i) q^{19} +(-3.00275 + 0.642431i) q^{20} +(9.31061 + 12.7970i) q^{22} +(-22.4825 - 26.7936i) q^{23} +(22.9385 - 8.34894i) q^{25} +(-7.02756 - 14.3843i) q^{26} +(-15.1250 - 11.7846i) q^{28} +(-38.1507 + 13.8857i) q^{29} +(-14.9912 - 17.8658i) q^{31} +(24.5817 + 20.4876i) q^{32} +(-6.57349 + 26.4398i) q^{34} +(-3.18685 - 1.83993i) q^{35} +(-1.05245 - 1.82290i) q^{37} +(7.61446 + 26.4883i) q^{38} +(5.21470 + 3.24405i) q^{40} +(-14.0090 - 5.09885i) q^{41} +(-57.3675 - 10.1154i) q^{43} +(4.36331 - 31.3491i) q^{44} +(-4.83326 + 69.7860i) q^{46} +(-49.8023 + 59.3520i) q^{47} +(4.51872 + 25.6270i) q^{49} +(-44.6137 - 19.8278i) q^{50} +(-9.85373 + 30.4645i) q^{52} +43.6318 q^{53} -6.07450i q^{55} +(5.41279 + 37.9641i) q^{56} +(74.2002 + 32.9769i) q^{58} +(43.0425 - 7.58956i) q^{59} +(-66.2578 - 55.5969i) q^{61} +(-3.22280 + 46.5329i) q^{62} +(-6.94381 - 63.6222i) q^{64} +(-1.06706 + 6.05160i) q^{65} +(14.0519 - 38.6072i) q^{67} +(46.1711 - 28.9364i) q^{68} +(2.03332 + 7.07327i) q^{70} +(-74.9269 + 43.2591i) q^{71} +(-42.9421 + 74.3779i) q^{73} +(-1.01573 + 4.08544i) q^{74} +(25.8134 - 48.7042i) q^{76} +(29.0562 - 24.3811i) q^{77} +(-7.58889 - 20.8503i) q^{79} +(-3.00319 - 11.9100i) q^{80} +(13.0883 + 26.7898i) q^{82} +(-7.46796 - 20.5180i) q^{83} +(8.01094 - 6.72198i) q^{85} +(68.5425 + 94.2089i) q^{86} +(-49.8053 + 39.0725i) q^{88} +(66.5965 - 115.349i) q^{89} +(-33.2296 + 19.1851i) q^{91} +(103.846 - 93.7538i) q^{92} +(154.097 - 16.2999i) q^{94} +(3.61822 - 9.94098i) q^{95} +(28.3954 - 161.038i) q^{97} +(29.0743 - 43.1663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.43960 1.38836i −0.719802 0.694180i
\(3\) 0 0
\(4\) 0.144916 + 3.99737i 0.0362291 + 0.999344i
\(5\) 0.133306 + 0.756014i 0.0266611 + 0.151203i 0.995232 0.0975344i \(-0.0310956\pi\)
−0.968571 + 0.248737i \(0.919984\pi\)
\(6\) 0 0
\(7\) −3.08121 + 3.67204i −0.440172 + 0.524577i −0.939828 0.341647i \(-0.889015\pi\)
0.499656 + 0.866224i \(0.333460\pi\)
\(8\) 5.34117 5.95583i 0.667646 0.744479i
\(9\) 0 0
\(10\) 0.857712 1.27344i 0.0857712 0.127344i
\(11\) −7.79262 1.37405i −0.708420 0.124914i −0.192183 0.981359i \(-0.561557\pi\)
−0.516237 + 0.856446i \(0.672668\pi\)
\(12\) 0 0
\(13\) 7.52188 + 2.73774i 0.578606 + 0.210595i 0.614711 0.788753i \(-0.289273\pi\)
−0.0361046 + 0.999348i \(0.511495\pi\)
\(14\) 9.53383 1.00846i 0.680988 0.0720327i
\(15\) 0 0
\(16\) −15.9580 + 1.15857i −0.997375 + 0.0724106i
\(17\) −6.81117 11.7973i −0.400657 0.693958i 0.593149 0.805093i \(-0.297885\pi\)
−0.993805 + 0.111135i \(0.964551\pi\)
\(18\) 0 0
\(19\) −11.9343 6.89025i −0.628119 0.362645i 0.151904 0.988395i \(-0.451459\pi\)
−0.780023 + 0.625750i \(0.784793\pi\)
\(20\) −3.00275 + 0.642431i −0.150138 + 0.0321216i
\(21\) 0 0
\(22\) 9.31061 + 12.7970i 0.423210 + 0.581684i
\(23\) −22.4825 26.7936i −0.977500 1.16494i −0.986297 0.164978i \(-0.947245\pi\)
0.00879696 0.999961i \(-0.497200\pi\)
\(24\) 0 0
\(25\) 22.9385 8.34894i 0.917541 0.333958i
\(26\) −7.02756 14.3843i −0.270291 0.553244i
\(27\) 0 0
\(28\) −15.1250 11.7846i −0.540180 0.420878i
\(29\) −38.1507 + 13.8857i −1.31554 + 0.478817i −0.902026 0.431681i \(-0.857921\pi\)
−0.413513 + 0.910498i \(0.635698\pi\)
\(30\) 0 0
\(31\) −14.9912 17.8658i −0.483588 0.576317i 0.467987 0.883735i \(-0.344979\pi\)
−0.951575 + 0.307418i \(0.900535\pi\)
\(32\) 24.5817 + 20.4876i 0.768178 + 0.640236i
\(33\) 0 0
\(34\) −6.57349 + 26.4398i −0.193338 + 0.777640i
\(35\) −3.18685 1.83993i −0.0910530 0.0525695i
\(36\) 0 0
\(37\) −1.05245 1.82290i −0.0284447 0.0492676i 0.851453 0.524431i \(-0.175722\pi\)
−0.879897 + 0.475164i \(0.842389\pi\)
\(38\) 7.61446 + 26.4883i 0.200381 + 0.697060i
\(39\) 0 0
\(40\) 5.21470 + 3.24405i 0.130367 + 0.0811013i
\(41\) −14.0090 5.09885i −0.341683 0.124362i 0.165479 0.986213i \(-0.447083\pi\)
−0.507161 + 0.861851i \(0.669305\pi\)
\(42\) 0 0
\(43\) −57.3675 10.1154i −1.33413 0.235243i −0.539318 0.842102i \(-0.681318\pi\)
−0.794809 + 0.606860i \(0.792429\pi\)
\(44\) 4.36331 31.3491i 0.0991662 0.712481i
\(45\) 0 0
\(46\) −4.83326 + 69.7860i −0.105071 + 1.51709i
\(47\) −49.8023 + 59.3520i −1.05962 + 1.26281i −0.0960456 + 0.995377i \(0.530619\pi\)
−0.963577 + 0.267432i \(0.913825\pi\)
\(48\) 0 0
\(49\) 4.51872 + 25.6270i 0.0922189 + 0.522999i
\(50\) −44.6137 19.8278i −0.892274 0.396555i
\(51\) 0 0
\(52\) −9.85373 + 30.4645i −0.189495 + 0.585856i
\(53\) 43.6318 0.823241 0.411620 0.911355i \(-0.364963\pi\)
0.411620 + 0.911355i \(0.364963\pi\)
\(54\) 0 0
\(55\) 6.07450i 0.110445i
\(56\) 5.41279 + 37.9641i 0.0966570 + 0.677931i
\(57\) 0 0
\(58\) 74.2002 + 32.9769i 1.27931 + 0.568567i
\(59\) 43.0425 7.58956i 0.729534 0.128637i 0.203470 0.979081i \(-0.434778\pi\)
0.526065 + 0.850445i \(0.323667\pi\)
\(60\) 0 0
\(61\) −66.2578 55.5969i −1.08619 0.911425i −0.0897734 0.995962i \(-0.528614\pi\)
−0.996420 + 0.0845375i \(0.973059\pi\)
\(62\) −3.22280 + 46.5329i −0.0519806 + 0.750531i
\(63\) 0 0
\(64\) −6.94381 63.6222i −0.108497 0.994097i
\(65\) −1.06706 + 6.05160i −0.0164163 + 0.0931016i
\(66\) 0 0
\(67\) 14.0519 38.6072i 0.209730 0.576227i −0.789570 0.613661i \(-0.789696\pi\)
0.999299 + 0.0374339i \(0.0119184\pi\)
\(68\) 46.1711 28.9364i 0.678987 0.425535i
\(69\) 0 0
\(70\) 2.03332 + 7.07327i 0.0290474 + 0.101047i
\(71\) −74.9269 + 43.2591i −1.05531 + 0.609283i −0.924131 0.382076i \(-0.875209\pi\)
−0.131178 + 0.991359i \(0.541876\pi\)
\(72\) 0 0
\(73\) −42.9421 + 74.3779i −0.588248 + 1.01888i 0.406214 + 0.913778i \(0.366849\pi\)
−0.994462 + 0.105097i \(0.966485\pi\)
\(74\) −1.01573 + 4.08544i −0.0137261 + 0.0552086i
\(75\) 0 0
\(76\) 25.8134 48.7042i 0.339650 0.640845i
\(77\) 29.0562 24.3811i 0.377354 0.316637i
\(78\) 0 0
\(79\) −7.58889 20.8503i −0.0960619 0.263928i 0.882349 0.470595i \(-0.155961\pi\)
−0.978411 + 0.206667i \(0.933738\pi\)
\(80\) −3.00319 11.9100i −0.0375398 0.148875i
\(81\) 0 0
\(82\) 13.0883 + 26.7898i 0.159614 + 0.326705i
\(83\) −7.46796 20.5180i −0.0899754 0.247205i 0.886540 0.462651i \(-0.153102\pi\)
−0.976516 + 0.215446i \(0.930880\pi\)
\(84\) 0 0
\(85\) 8.01094 6.72198i 0.0942464 0.0790821i
\(86\) 68.5425 + 94.2089i 0.797006 + 1.09545i
\(87\) 0 0
\(88\) −49.8053 + 39.0725i −0.565970 + 0.444006i
\(89\) 66.5965 115.349i 0.748275 1.29605i −0.200373 0.979720i \(-0.564216\pi\)
0.948649 0.316331i \(-0.102451\pi\)
\(90\) 0 0
\(91\) −33.2296 + 19.1851i −0.365160 + 0.210825i
\(92\) 103.846 93.7538i 1.12876 1.01906i
\(93\) 0 0
\(94\) 154.097 16.2999i 1.63933 0.173404i
\(95\) 3.61822 9.94098i 0.0380865 0.104642i
\(96\) 0 0
\(97\) 28.3954 161.038i 0.292736 1.66019i −0.383529 0.923529i \(-0.625291\pi\)
0.676265 0.736659i \(-0.263598\pi\)
\(98\) 29.0743 43.1663i 0.296676 0.440472i
\(99\) 0 0
\(100\) 36.6980 + 90.4840i 0.366980 + 0.904840i
\(101\) 20.6121 + 17.2956i 0.204081 + 0.171244i 0.739100 0.673596i \(-0.235251\pi\)
−0.535019 + 0.844840i \(0.679696\pi\)
\(102\) 0 0
\(103\) 47.0573 8.29747i 0.456867 0.0805580i 0.0595214 0.998227i \(-0.481043\pi\)
0.397346 + 0.917669i \(0.369931\pi\)
\(104\) 56.4812 30.1763i 0.543088 0.290157i
\(105\) 0 0
\(106\) −62.8124 60.5766i −0.592570 0.571477i
\(107\) 61.2748i 0.572661i 0.958131 + 0.286331i \(0.0924356\pi\)
−0.958131 + 0.286331i \(0.907564\pi\)
\(108\) 0 0
\(109\) 193.438 1.77466 0.887331 0.461133i \(-0.152557\pi\)
0.887331 + 0.461133i \(0.152557\pi\)
\(110\) −8.43359 + 8.74487i −0.0766690 + 0.0794988i
\(111\) 0 0
\(112\) 44.9156 62.1682i 0.401032 0.555073i
\(113\) −13.4483 76.2690i −0.119011 0.674947i −0.984686 0.174339i \(-0.944221\pi\)
0.865674 0.500608i \(-0.166890\pi\)
\(114\) 0 0
\(115\) 17.2593 20.5688i 0.150081 0.178859i
\(116\) −61.0350 150.490i −0.526164 1.29733i
\(117\) 0 0
\(118\) −72.5012 48.8325i −0.614417 0.413835i
\(119\) 64.3067 + 11.3390i 0.540392 + 0.0952858i
\(120\) 0 0
\(121\) −54.8659 19.9695i −0.453437 0.165038i
\(122\) 18.1965 + 172.027i 0.149152 + 1.41006i
\(123\) 0 0
\(124\) 69.2440 62.5146i 0.558419 0.504150i
\(125\) 18.9657 + 32.8496i 0.151726 + 0.262797i
\(126\) 0 0
\(127\) 134.077 + 77.4091i 1.05572 + 0.609521i 0.924246 0.381799i \(-0.124695\pi\)
0.131475 + 0.991319i \(0.458029\pi\)
\(128\) −78.3341 + 101.231i −0.611985 + 0.790869i
\(129\) 0 0
\(130\) 9.93794 7.23044i 0.0764457 0.0556188i
\(131\) 56.4836 + 67.3145i 0.431173 + 0.513851i 0.937260 0.348631i \(-0.113353\pi\)
−0.506088 + 0.862482i \(0.668909\pi\)
\(132\) 0 0
\(133\) 62.0732 22.5928i 0.466716 0.169871i
\(134\) −73.8298 + 36.0700i −0.550969 + 0.269179i
\(135\) 0 0
\(136\) −106.642 22.4452i −0.784134 0.165038i
\(137\) −247.706 + 90.1577i −1.80807 + 0.658085i −0.810717 + 0.585438i \(0.800923\pi\)
−0.997358 + 0.0726476i \(0.976855\pi\)
\(138\) 0 0
\(139\) −142.549 169.883i −1.02553 1.22218i −0.974710 0.223475i \(-0.928260\pi\)
−0.0508232 0.998708i \(-0.516184\pi\)
\(140\) 6.89307 13.0057i 0.0492362 0.0928977i
\(141\) 0 0
\(142\) 167.924 + 41.7496i 1.18256 + 0.294011i
\(143\) −54.8534 31.6696i −0.383590 0.221466i
\(144\) 0 0
\(145\) −15.5835 26.9914i −0.107472 0.186147i
\(146\) 165.083 47.4556i 1.13070 0.325038i
\(147\) 0 0
\(148\) 7.13430 4.47121i 0.0482047 0.0302109i
\(149\) −0.892365 0.324794i −0.00598903 0.00217983i 0.339024 0.940778i \(-0.389903\pi\)
−0.345013 + 0.938598i \(0.612125\pi\)
\(150\) 0 0
\(151\) 219.805 + 38.7576i 1.45566 + 0.256673i 0.844808 0.535070i \(-0.179715\pi\)
0.610855 + 0.791743i \(0.290826\pi\)
\(152\) −104.780 + 34.2764i −0.689343 + 0.225503i
\(153\) 0 0
\(154\) −75.6792 5.24142i −0.491423 0.0340352i
\(155\) 11.5084 13.7152i 0.0742478 0.0884851i
\(156\) 0 0
\(157\) 32.0271 + 181.635i 0.203994 + 1.15691i 0.899014 + 0.437919i \(0.144284\pi\)
−0.695020 + 0.718990i \(0.744604\pi\)
\(158\) −18.0227 + 40.5523i −0.114068 + 0.256660i
\(159\) 0 0
\(160\) −12.2120 + 21.3152i −0.0763250 + 0.133220i
\(161\) 167.660 1.04137
\(162\) 0 0
\(163\) 210.034i 1.28855i 0.764793 + 0.644276i \(0.222841\pi\)
−0.764793 + 0.644276i \(0.777159\pi\)
\(164\) 18.3519 56.7381i 0.111902 0.345964i
\(165\) 0 0
\(166\) −17.7355 + 39.9061i −0.106840 + 0.240398i
\(167\) 129.841 22.8945i 0.777493 0.137093i 0.229200 0.973379i \(-0.426389\pi\)
0.548293 + 0.836286i \(0.315278\pi\)
\(168\) 0 0
\(169\) −80.3780 67.4452i −0.475610 0.399084i
\(170\) −20.8651 1.44508i −0.122736 0.00850049i
\(171\) 0 0
\(172\) 32.1217 230.785i 0.186754 1.34177i
\(173\) −35.2162 + 199.721i −0.203562 + 1.15446i 0.696125 + 0.717921i \(0.254906\pi\)
−0.899687 + 0.436536i \(0.856205\pi\)
\(174\) 0 0
\(175\) −40.0207 + 109.956i −0.228690 + 0.628320i
\(176\) 125.947 + 12.8988i 0.715605 + 0.0732886i
\(177\) 0 0
\(178\) −256.018 + 73.5963i −1.43830 + 0.413462i
\(179\) 59.8299 34.5428i 0.334245 0.192976i −0.323479 0.946235i \(-0.604853\pi\)
0.657724 + 0.753259i \(0.271519\pi\)
\(180\) 0 0
\(181\) −44.8622 + 77.7036i −0.247858 + 0.429302i −0.962931 0.269747i \(-0.913060\pi\)
0.715074 + 0.699049i \(0.246393\pi\)
\(182\) 74.4732 + 18.5156i 0.409193 + 0.101734i
\(183\) 0 0
\(184\) −279.661 9.20724i −1.51990 0.0500394i
\(185\) 1.23784 1.03867i 0.00669103 0.00561444i
\(186\) 0 0
\(187\) 36.8668 + 101.291i 0.197149 + 0.541661i
\(188\) −244.469 190.477i −1.30037 1.01318i
\(189\) 0 0
\(190\) −19.0104 + 9.28767i −0.100055 + 0.0488825i
\(191\) −101.142 277.887i −0.529542 1.45490i −0.859612 0.510947i \(-0.829295\pi\)
0.330071 0.943956i \(-0.392927\pi\)
\(192\) 0 0
\(193\) −238.508 + 200.132i −1.23579 + 1.03695i −0.237949 + 0.971278i \(0.576475\pi\)
−0.997841 + 0.0656734i \(0.979080\pi\)
\(194\) −264.457 + 192.408i −1.36318 + 0.991795i
\(195\) 0 0
\(196\) −101.786 + 21.7768i −0.519315 + 0.111106i
\(197\) −72.0482 + 124.791i −0.365727 + 0.633457i −0.988892 0.148633i \(-0.952513\pi\)
0.623166 + 0.782090i \(0.285846\pi\)
\(198\) 0 0
\(199\) −168.765 + 97.4366i −0.848066 + 0.489631i −0.859998 0.510298i \(-0.829535\pi\)
0.0119320 + 0.999929i \(0.496202\pi\)
\(200\) 72.7937 181.211i 0.363969 0.906055i
\(201\) 0 0
\(202\) −5.66075 53.5159i −0.0280235 0.264930i
\(203\) 66.5612 182.875i 0.327888 0.900864i
\(204\) 0 0
\(205\) 1.98733 11.2707i 0.00969428 0.0549790i
\(206\) −79.2637 53.3874i −0.384775 0.259162i
\(207\) 0 0
\(208\) −123.206 34.9742i −0.592337 0.168145i
\(209\) 83.5316 + 70.0914i 0.399673 + 0.335365i
\(210\) 0 0
\(211\) 114.338 20.1608i 0.541884 0.0955488i 0.103995 0.994578i \(-0.466837\pi\)
0.437889 + 0.899029i \(0.355726\pi\)
\(212\) 6.32295 + 174.412i 0.0298252 + 0.822700i
\(213\) 0 0
\(214\) 85.0714 88.2113i 0.397530 0.412203i
\(215\) 44.7190i 0.207996i
\(216\) 0 0
\(217\) 111.795 0.515185
\(218\) −278.474 268.562i −1.27740 1.23193i
\(219\) 0 0
\(220\) 24.2820 0.880293i 0.110373 0.00400133i
\(221\) −18.9349 107.385i −0.0856781 0.485905i
\(222\) 0 0
\(223\) 95.4717 113.779i 0.428124 0.510219i −0.508256 0.861206i \(-0.669710\pi\)
0.936380 + 0.350987i \(0.114154\pi\)
\(224\) −150.972 + 27.1386i −0.673984 + 0.121154i
\(225\) 0 0
\(226\) −86.5286 + 128.468i −0.382870 + 0.568443i
\(227\) 163.627 + 28.8519i 0.720826 + 0.127101i 0.522014 0.852937i \(-0.325181\pi\)
0.198812 + 0.980038i \(0.436292\pi\)
\(228\) 0 0
\(229\) −218.671 79.5896i −0.954894 0.347553i −0.182863 0.983138i \(-0.558537\pi\)
−0.772031 + 0.635585i \(0.780759\pi\)
\(230\) −53.4035 + 5.64885i −0.232189 + 0.0245602i
\(231\) 0 0
\(232\) −121.068 + 301.385i −0.521846 + 1.29907i
\(233\) 102.146 + 176.922i 0.438394 + 0.759320i 0.997566 0.0697314i \(-0.0222142\pi\)
−0.559172 + 0.829052i \(0.688881\pi\)
\(234\) 0 0
\(235\) −51.5099 29.7392i −0.219191 0.126550i
\(236\) 36.5759 + 170.957i 0.154982 + 0.724395i
\(237\) 0 0
\(238\) −76.8335 105.604i −0.322830 0.443716i
\(239\) 59.1551 + 70.4983i 0.247511 + 0.294972i 0.875468 0.483276i \(-0.160553\pi\)
−0.627957 + 0.778248i \(0.716109\pi\)
\(240\) 0 0
\(241\) −194.954 + 70.9574i −0.808938 + 0.294429i −0.713185 0.700976i \(-0.752748\pi\)
−0.0957527 + 0.995405i \(0.530526\pi\)
\(242\) 51.2602 + 104.922i 0.211819 + 0.433561i
\(243\) 0 0
\(244\) 212.640 272.914i 0.871475 1.11850i
\(245\) −18.7720 + 6.83244i −0.0766203 + 0.0278875i
\(246\) 0 0
\(247\) −70.9044 84.5006i −0.287062 0.342108i
\(248\) −186.477 6.13934i −0.751922 0.0247554i
\(249\) 0 0
\(250\) 18.3039 73.6216i 0.0732156 0.294486i
\(251\) 269.842 + 155.793i 1.07507 + 0.620690i 0.929561 0.368667i \(-0.120186\pi\)
0.145505 + 0.989357i \(0.453519\pi\)
\(252\) 0 0
\(253\) 138.382 + 239.684i 0.546964 + 0.947370i
\(254\) −85.5454 297.585i −0.336793 1.17159i
\(255\) 0 0
\(256\) 253.315 36.9769i 0.989513 0.144441i
\(257\) −281.815 102.572i −1.09656 0.399114i −0.270511 0.962717i \(-0.587192\pi\)
−0.826046 + 0.563603i \(0.809415\pi\)
\(258\) 0 0
\(259\) 9.93659 + 1.75209i 0.0383652 + 0.00676482i
\(260\) −24.3452 3.38847i −0.0936352 0.0130326i
\(261\) 0 0
\(262\) 12.1428 175.326i 0.0463465 0.669182i
\(263\) −126.004 + 150.166i −0.479102 + 0.570972i −0.950411 0.310996i \(-0.899337\pi\)
0.471309 + 0.881968i \(0.343782\pi\)
\(264\) 0 0
\(265\) 5.81636 + 32.9862i 0.0219485 + 0.124476i
\(266\) −120.728 53.6552i −0.453864 0.201711i
\(267\) 0 0
\(268\) 156.364 + 50.5758i 0.583447 + 0.188716i
\(269\) 110.390 0.410372 0.205186 0.978723i \(-0.434220\pi\)
0.205186 + 0.978723i \(0.434220\pi\)
\(270\) 0 0
\(271\) 157.984i 0.582967i −0.956576 0.291484i \(-0.905851\pi\)
0.956576 0.291484i \(-0.0941489\pi\)
\(272\) 122.361 + 180.370i 0.449855 + 0.663124i
\(273\) 0 0
\(274\) 481.770 + 214.114i 1.75829 + 0.781438i
\(275\) −190.223 + 33.5415i −0.691720 + 0.121969i
\(276\) 0 0
\(277\) 133.295 + 111.848i 0.481210 + 0.403783i 0.850864 0.525386i \(-0.176079\pi\)
−0.369654 + 0.929170i \(0.620524\pi\)
\(278\) −30.6450 + 442.474i −0.110234 + 1.59163i
\(279\) 0 0
\(280\) −27.9798 + 9.15298i −0.0999280 + 0.0326892i
\(281\) 64.5172 365.895i 0.229599 1.30212i −0.624098 0.781346i \(-0.714533\pi\)
0.853696 0.520772i \(-0.174356\pi\)
\(282\) 0 0
\(283\) −142.624 + 391.857i −0.503973 + 1.38465i 0.383392 + 0.923586i \(0.374756\pi\)
−0.887365 + 0.461068i \(0.847466\pi\)
\(284\) −183.781 293.242i −0.647116 1.03254i
\(285\) 0 0
\(286\) 34.9983 + 121.748i 0.122372 + 0.425692i
\(287\) 61.8878 35.7309i 0.215637 0.124498i
\(288\) 0 0
\(289\) 51.7160 89.5748i 0.178948 0.309947i
\(290\) −15.0397 + 60.4923i −0.0518610 + 0.208594i
\(291\) 0 0
\(292\) −303.539 160.877i −1.03952 0.550949i
\(293\) −33.9075 + 28.4518i −0.115725 + 0.0971050i −0.698814 0.715304i \(-0.746288\pi\)
0.583089 + 0.812408i \(0.301844\pi\)
\(294\) 0 0
\(295\) 11.4756 + 31.5290i 0.0389004 + 0.106878i
\(296\) −16.4782 3.46820i −0.0556697 0.0117169i
\(297\) 0 0
\(298\) 0.833720 + 1.70650i 0.00279772 + 0.00572650i
\(299\) −95.7568 263.090i −0.320257 0.879898i
\(300\) 0 0
\(301\) 213.905 179.488i 0.710649 0.596305i
\(302\) −262.623 360.964i −0.869611 1.19524i
\(303\) 0 0
\(304\) 198.430 + 96.1279i 0.652730 + 0.316210i
\(305\) 33.1995 57.5032i 0.108851 0.188535i
\(306\) 0 0
\(307\) 279.865 161.580i 0.911612 0.526320i 0.0306628 0.999530i \(-0.490238\pi\)
0.880950 + 0.473210i \(0.156905\pi\)
\(308\) 101.671 + 112.615i 0.330101 + 0.365635i
\(309\) 0 0
\(310\) −35.6092 + 3.76662i −0.114868 + 0.0121504i
\(311\) 1.32044 3.62789i 0.00424580 0.0116652i −0.937552 0.347846i \(-0.886913\pi\)
0.941797 + 0.336181i \(0.109135\pi\)
\(312\) 0 0
\(313\) −5.20268 + 29.5059i −0.0166220 + 0.0942679i −0.991990 0.126315i \(-0.959685\pi\)
0.975368 + 0.220583i \(0.0707960\pi\)
\(314\) 206.068 305.947i 0.656268 0.974354i
\(315\) 0 0
\(316\) 82.2467 33.3572i 0.260275 0.105561i
\(317\) 429.901 + 360.730i 1.35615 + 1.13795i 0.977150 + 0.212553i \(0.0681778\pi\)
0.379004 + 0.925395i \(0.376267\pi\)
\(318\) 0 0
\(319\) 316.373 55.7851i 0.991766 0.174875i
\(320\) 47.1736 13.7308i 0.147418 0.0429088i
\(321\) 0 0
\(322\) −241.365 232.773i −0.749579 0.722897i
\(323\) 187.723i 0.581184i
\(324\) 0 0
\(325\) 195.398 0.601225
\(326\) 291.603 302.366i 0.894486 0.927502i
\(327\) 0 0
\(328\) −105.192 + 56.2013i −0.320708 + 0.171345i
\(329\) −64.4919 365.752i −0.196024 1.11171i
\(330\) 0 0
\(331\) −90.3131 + 107.631i −0.272849 + 0.325169i −0.885017 0.465559i \(-0.845853\pi\)
0.612168 + 0.790728i \(0.290298\pi\)
\(332\) 80.9361 32.8256i 0.243783 0.0988723i
\(333\) 0 0
\(334\) −218.706 147.307i −0.654808 0.441040i
\(335\) 31.0608 + 5.47685i 0.0927188 + 0.0163488i
\(336\) 0 0
\(337\) −398.458 145.027i −1.18237 0.430346i −0.325330 0.945601i \(-0.605475\pi\)
−0.857037 + 0.515254i \(0.827697\pi\)
\(338\) 22.0744 + 208.688i 0.0653087 + 0.617420i
\(339\) 0 0
\(340\) 28.0312 + 31.0486i 0.0824447 + 0.0913194i
\(341\) 92.2724 + 159.820i 0.270593 + 0.468682i
\(342\) 0 0
\(343\) −311.440 179.810i −0.907988 0.524227i
\(344\) −366.655 + 287.643i −1.06586 + 0.836170i
\(345\) 0 0
\(346\) 327.982 238.626i 0.947925 0.689672i
\(347\) −73.0006 86.9988i −0.210376 0.250717i 0.650530 0.759481i \(-0.274547\pi\)
−0.860906 + 0.508764i \(0.830103\pi\)
\(348\) 0 0
\(349\) 94.6615 34.4540i 0.271236 0.0987220i −0.202821 0.979216i \(-0.565011\pi\)
0.474058 + 0.880494i \(0.342789\pi\)
\(350\) 210.272 102.730i 0.600778 0.293514i
\(351\) 0 0
\(352\) −163.405 193.428i −0.464219 0.549512i
\(353\) 24.4299 8.89174i 0.0692064 0.0251891i −0.307185 0.951650i \(-0.599387\pi\)
0.376391 + 0.926461i \(0.377165\pi\)
\(354\) 0 0
\(355\) −42.6926 50.8791i −0.120261 0.143321i
\(356\) 470.742 + 249.495i 1.32231 + 0.700829i
\(357\) 0 0
\(358\) −134.089 33.3374i −0.374550 0.0931213i
\(359\) 50.8289 + 29.3461i 0.141585 + 0.0817439i 0.569119 0.822255i \(-0.307284\pi\)
−0.427534 + 0.903999i \(0.640618\pi\)
\(360\) 0 0
\(361\) −85.5489 148.175i −0.236978 0.410457i
\(362\) 172.464 49.5775i 0.476421 0.136955i
\(363\) 0 0
\(364\) −81.5055 130.051i −0.223916 0.357282i
\(365\) −61.9551 22.5498i −0.169740 0.0617803i
\(366\) 0 0
\(367\) 107.710 + 18.9921i 0.293487 + 0.0517497i 0.318453 0.947939i \(-0.396837\pi\)
−0.0249660 + 0.999688i \(0.507948\pi\)
\(368\) 389.818 + 401.525i 1.05929 + 1.09110i
\(369\) 0 0
\(370\) −3.22405 0.223292i −0.00871365 0.000603493i
\(371\) −134.438 + 160.218i −0.362368 + 0.431853i
\(372\) 0 0
\(373\) 11.6320 + 65.9686i 0.0311851 + 0.176859i 0.996422 0.0845170i \(-0.0269347\pi\)
−0.965237 + 0.261376i \(0.915824\pi\)
\(374\) 87.5543 197.003i 0.234102 0.526745i
\(375\) 0 0
\(376\) 87.4882 + 613.623i 0.232681 + 1.63198i
\(377\) −324.980 −0.862016
\(378\) 0 0
\(379\) 276.576i 0.729753i −0.931056 0.364876i \(-0.881111\pi\)
0.931056 0.364876i \(-0.118889\pi\)
\(380\) 40.2621 + 13.0228i 0.105953 + 0.0342704i
\(381\) 0 0
\(382\) −240.201 + 540.468i −0.628800 + 1.41484i
\(383\) −39.6849 + 6.99751i −0.103616 + 0.0182703i −0.225216 0.974309i \(-0.572309\pi\)
0.121600 + 0.992579i \(0.461198\pi\)
\(384\) 0 0
\(385\) 22.3058 + 18.7168i 0.0579371 + 0.0486150i
\(386\) 621.211 + 43.0241i 1.60935 + 0.111461i
\(387\) 0 0
\(388\) 647.845 + 90.1699i 1.66970 + 0.232397i
\(389\) 25.8684 146.707i 0.0664998 0.377139i −0.933336 0.359005i \(-0.883116\pi\)
0.999836 0.0181346i \(-0.00577273\pi\)
\(390\) 0 0
\(391\) −162.960 + 447.728i −0.416777 + 1.14508i
\(392\) 176.765 + 109.965i 0.450931 + 0.280523i
\(393\) 0 0
\(394\) 276.976 79.6209i 0.702984 0.202084i
\(395\) 14.7515 8.51677i 0.0373455 0.0215614i
\(396\) 0 0
\(397\) 373.378 646.710i 0.940499 1.62899i 0.175978 0.984394i \(-0.443691\pi\)
0.764521 0.644598i \(-0.222975\pi\)
\(398\) 378.232 + 94.0366i 0.950331 + 0.236273i
\(399\) 0 0
\(400\) −356.380 + 159.808i −0.890950 + 0.399521i
\(401\) −44.3852 + 37.2436i −0.110686 + 0.0928768i −0.696451 0.717604i \(-0.745239\pi\)
0.585765 + 0.810481i \(0.300794\pi\)
\(402\) 0 0
\(403\) −63.8501 175.427i −0.158437 0.435302i
\(404\) −66.1501 + 84.9009i −0.163738 + 0.210151i
\(405\) 0 0
\(406\) −349.719 + 170.857i −0.861376 + 0.420830i
\(407\) 5.69661 + 15.6513i 0.0139966 + 0.0384553i
\(408\) 0 0
\(409\) 226.059 189.686i 0.552712 0.463780i −0.323146 0.946349i \(-0.604741\pi\)
0.875858 + 0.482569i \(0.160296\pi\)
\(410\) −18.5087 + 13.4662i −0.0451432 + 0.0328444i
\(411\) 0 0
\(412\) 39.9875 + 186.903i 0.0970569 + 0.453648i
\(413\) −104.754 + 181.439i −0.253641 + 0.439319i
\(414\) 0 0
\(415\) 14.5164 8.38105i 0.0349793 0.0201953i
\(416\) 128.811 + 221.403i 0.309642 + 0.532219i
\(417\) 0 0
\(418\) −22.9404 216.876i −0.0548814 0.518841i
\(419\) −150.722 + 414.106i −0.359719 + 0.988320i 0.619408 + 0.785069i \(0.287373\pi\)
−0.979127 + 0.203250i \(0.934849\pi\)
\(420\) 0 0
\(421\) 11.8192 67.0301i 0.0280742 0.159216i −0.967548 0.252688i \(-0.918685\pi\)
0.995622 + 0.0934717i \(0.0297965\pi\)
\(422\) −192.591 129.718i −0.456377 0.307389i
\(423\) 0 0
\(424\) 233.045 259.863i 0.549634 0.612885i
\(425\) −254.733 213.746i −0.599372 0.502933i
\(426\) 0 0
\(427\) 408.308 71.9957i 0.956225 0.168608i
\(428\) −244.938 + 8.87971i −0.572285 + 0.0207470i
\(429\) 0 0
\(430\) −62.0861 + 64.3777i −0.144386 + 0.149716i
\(431\) 53.6108i 0.124387i 0.998064 + 0.0621935i \(0.0198096\pi\)
−0.998064 + 0.0621935i \(0.980190\pi\)
\(432\) 0 0
\(433\) −686.735 −1.58599 −0.792997 0.609226i \(-0.791480\pi\)
−0.792997 + 0.609226i \(0.791480\pi\)
\(434\) −160.941 155.212i −0.370831 0.357631i
\(435\) 0 0
\(436\) 28.0323 + 773.245i 0.0642943 + 1.77350i
\(437\) 83.6975 + 474.672i 0.191527 + 1.08621i
\(438\) 0 0
\(439\) −74.5743 + 88.8742i −0.169873 + 0.202447i −0.844264 0.535928i \(-0.819962\pi\)
0.674391 + 0.738375i \(0.264406\pi\)
\(440\) −36.1787 32.4449i −0.0822242 0.0737385i
\(441\) 0 0
\(442\) −121.830 + 180.880i −0.275634 + 0.409231i
\(443\) −126.688 22.3386i −0.285978 0.0504257i 0.0288188 0.999585i \(-0.490825\pi\)
−0.314797 + 0.949159i \(0.601937\pi\)
\(444\) 0 0
\(445\) 96.0828 + 34.9713i 0.215916 + 0.0785871i
\(446\) −295.407 + 31.2472i −0.662348 + 0.0700611i
\(447\) 0 0
\(448\) 255.018 + 170.535i 0.569238 + 0.380659i
\(449\) −361.840 626.725i −0.805880 1.39583i −0.915695 0.401873i \(-0.868359\pi\)
0.109815 0.993952i \(-0.464974\pi\)
\(450\) 0 0
\(451\) 102.161 + 58.9825i 0.226520 + 0.130782i
\(452\) 302.927 64.8105i 0.670192 0.143386i
\(453\) 0 0
\(454\) −195.502 268.709i −0.430621 0.591870i
\(455\) −18.9339 22.5645i −0.0416129 0.0495924i
\(456\) 0 0
\(457\) 49.8588 18.1471i 0.109100 0.0397092i −0.286893 0.957963i \(-0.592623\pi\)
0.395993 + 0.918253i \(0.370400\pi\)
\(458\) 204.300 + 418.171i 0.446070 + 0.913037i
\(459\) 0 0
\(460\) 84.7224 + 66.0111i 0.184179 + 0.143502i
\(461\) −198.117 + 72.1085i −0.429754 + 0.156418i −0.547835 0.836586i \(-0.684548\pi\)
0.118081 + 0.993004i \(0.462326\pi\)
\(462\) 0 0
\(463\) −407.123 485.190i −0.879315 1.04793i −0.998483 0.0550524i \(-0.982467\pi\)
0.119169 0.992874i \(-0.461977\pi\)
\(464\) 592.720 265.788i 1.27741 0.572819i
\(465\) 0 0
\(466\) 98.5814 396.512i 0.211548 0.850884i
\(467\) −254.886 147.159i −0.545795 0.315115i 0.201629 0.979462i \(-0.435376\pi\)
−0.747424 + 0.664347i \(0.768710\pi\)
\(468\) 0 0
\(469\) 98.4705 + 170.556i 0.209958 + 0.363659i
\(470\) 32.8650 + 114.327i 0.0699256 + 0.243249i
\(471\) 0 0
\(472\) 184.695 296.891i 0.391304 0.629007i
\(473\) 433.144 + 157.651i 0.915737 + 0.333301i
\(474\) 0 0
\(475\) −331.281 58.4137i −0.697433 0.122976i
\(476\) −36.0072 + 258.701i −0.0756453 + 0.543490i
\(477\) 0 0
\(478\) 12.7171 183.618i 0.0266048 0.384138i
\(479\) −349.313 + 416.295i −0.729255 + 0.869092i −0.995495 0.0948146i \(-0.969774\pi\)
0.266240 + 0.963907i \(0.414219\pi\)
\(480\) 0 0
\(481\) −2.92579 16.5930i −0.00608273 0.0344969i
\(482\) 379.171 + 168.516i 0.786662 + 0.349617i
\(483\) 0 0
\(484\) 71.8748 222.213i 0.148502 0.459118i
\(485\) 125.532 0.258830
\(486\) 0 0
\(487\) 168.509i 0.346015i 0.984921 + 0.173007i \(0.0553484\pi\)
−0.984921 + 0.173007i \(0.944652\pi\)
\(488\) −685.020 + 97.6677i −1.40373 + 0.200139i
\(489\) 0 0
\(490\) 36.5101 + 16.2262i 0.0745103 + 0.0331148i
\(491\) −394.774 + 69.6093i −0.804021 + 0.141771i −0.560532 0.828133i \(-0.689403\pi\)
−0.243489 + 0.969904i \(0.578292\pi\)
\(492\) 0 0
\(493\) 423.664 + 355.496i 0.859359 + 0.721088i
\(494\) −15.2429 + 220.088i −0.0308562 + 0.445522i
\(495\) 0 0
\(496\) 259.929 + 267.735i 0.524050 + 0.539788i
\(497\) 72.0163 408.425i 0.144902 0.821780i
\(498\) 0 0
\(499\) 54.0863 148.601i 0.108389 0.297797i −0.873626 0.486598i \(-0.838238\pi\)
0.982015 + 0.188800i \(0.0604599\pi\)
\(500\) −128.564 + 80.5735i −0.257127 + 0.161147i
\(501\) 0 0
\(502\) −172.168 598.918i −0.342964 1.19306i
\(503\) 94.5144 54.5679i 0.187901 0.108485i −0.403098 0.915157i \(-0.632067\pi\)
0.591000 + 0.806672i \(0.298733\pi\)
\(504\) 0 0
\(505\) −10.3280 + 17.8887i −0.0204515 + 0.0354231i
\(506\) 133.553 537.174i 0.263939 1.06161i
\(507\) 0 0
\(508\) −290.003 + 547.172i −0.570873 + 1.07711i
\(509\) 177.370 148.831i 0.348467 0.292399i −0.451707 0.892166i \(-0.649185\pi\)
0.800174 + 0.599768i \(0.204740\pi\)
\(510\) 0 0
\(511\) −140.805 386.859i −0.275548 0.757062i
\(512\) −416.011 298.461i −0.812521 0.582931i
\(513\) 0 0
\(514\) 263.295 + 538.924i 0.512246 + 1.04849i
\(515\) 12.5460 + 34.4699i 0.0243612 + 0.0669318i
\(516\) 0 0
\(517\) 469.643 394.077i 0.908400 0.762238i
\(518\) −11.8722 16.3179i −0.0229193 0.0315017i
\(519\) 0 0
\(520\) 30.3430 + 38.6779i 0.0583518 + 0.0743805i
\(521\) 96.0523 166.367i 0.184361 0.319323i −0.759000 0.651091i \(-0.774312\pi\)
0.943361 + 0.331768i \(0.107645\pi\)
\(522\) 0 0
\(523\) −295.086 + 170.368i −0.564217 + 0.325751i −0.754836 0.655913i \(-0.772284\pi\)
0.190619 + 0.981664i \(0.438950\pi\)
\(524\) −260.896 + 235.541i −0.497893 + 0.449506i
\(525\) 0 0
\(526\) 389.880 41.2402i 0.741216 0.0784035i
\(527\) −108.661 + 298.543i −0.206187 + 0.566495i
\(528\) 0 0
\(529\) −120.574 + 683.812i −0.227929 + 1.29265i
\(530\) 37.4235 55.5623i 0.0706103 0.104834i
\(531\) 0 0
\(532\) 99.3073 + 244.856i 0.186668 + 0.460255i
\(533\) −91.4146 76.7059i −0.171509 0.143914i
\(534\) 0 0
\(535\) −46.3246 + 8.16827i −0.0865880 + 0.0152678i
\(536\) −154.885 289.898i −0.288964 0.540855i
\(537\) 0 0
\(538\) −158.918 153.261i −0.295387 0.284872i
\(539\) 205.910i 0.382022i
\(540\) 0 0
\(541\) −543.807 −1.00519 −0.502595 0.864522i \(-0.667621\pi\)
−0.502595 + 0.864522i \(0.667621\pi\)
\(542\) −219.339 + 227.434i −0.404684 + 0.419621i
\(543\) 0 0
\(544\) 74.2675 429.541i 0.136521 0.789598i
\(545\) 25.7864 + 146.242i 0.0473145 + 0.268334i
\(546\) 0 0
\(547\) 163.630 195.007i 0.299141 0.356502i −0.595447 0.803395i \(-0.703025\pi\)
0.894588 + 0.446893i \(0.147469\pi\)
\(548\) −396.291 977.109i −0.723158 1.78305i
\(549\) 0 0
\(550\) 320.413 + 215.812i 0.582570 + 0.392385i
\(551\) 550.976 + 97.1519i 0.999956 + 0.176319i
\(552\) 0 0
\(553\) 99.9461 + 36.3774i 0.180734 + 0.0657819i
\(554\) −36.6071 346.078i −0.0660777 0.624690i
\(555\) 0 0
\(556\) 658.430 594.441i 1.18423 1.06914i
\(557\) 104.885 + 181.666i 0.188303 + 0.326150i 0.944685 0.327980i \(-0.106368\pi\)
−0.756382 + 0.654131i \(0.773035\pi\)
\(558\) 0 0
\(559\) −403.818 233.144i −0.722393 0.417074i
\(560\) 52.9875 + 25.6694i 0.0946205 + 0.0458383i
\(561\) 0 0
\(562\) −600.873 + 437.171i −1.06917 + 0.777884i
\(563\) −436.787 520.543i −0.775821 0.924588i 0.222916 0.974838i \(-0.428443\pi\)
−0.998737 + 0.0502501i \(0.983998\pi\)
\(564\) 0 0
\(565\) 55.8677 20.3342i 0.0988809 0.0359897i
\(566\) 749.361 366.105i 1.32396 0.646829i
\(567\) 0 0
\(568\) −142.554 + 677.306i −0.250975 + 1.19244i
\(569\) 727.101 264.643i 1.27786 0.465102i 0.388135 0.921603i \(-0.373120\pi\)
0.889723 + 0.456501i \(0.150897\pi\)
\(570\) 0 0
\(571\) −706.930 842.487i −1.23806 1.47546i −0.825377 0.564582i \(-0.809038\pi\)
−0.412679 0.910876i \(-0.635407\pi\)
\(572\) 118.646 223.859i 0.207423 0.391362i
\(573\) 0 0
\(574\) −138.701 34.4841i −0.241640 0.0600768i
\(575\) −739.414 426.901i −1.28594 0.742436i
\(576\) 0 0
\(577\) −26.4305 45.7790i −0.0458068 0.0793398i 0.842213 0.539145i \(-0.181253\pi\)
−0.888020 + 0.459805i \(0.847919\pi\)
\(578\) −198.813 + 57.1518i −0.343967 + 0.0988785i
\(579\) 0 0
\(580\) 105.636 66.2045i 0.182132 0.114146i
\(581\) 98.3534 + 35.7977i 0.169283 + 0.0616139i
\(582\) 0 0
\(583\) −340.006 59.9522i −0.583200 0.102834i
\(584\) 213.621 + 653.021i 0.365789 + 1.11819i
\(585\) 0 0
\(586\) 88.3146 + 6.11653i 0.150707 + 0.0104378i
\(587\) 714.090 851.019i 1.21651 1.44978i 0.360543 0.932743i \(-0.382591\pi\)
0.855965 0.517034i \(-0.172964\pi\)
\(588\) 0 0
\(589\) 55.8091 + 316.509i 0.0947522 + 0.537367i
\(590\) 27.2533 61.3216i 0.0461920 0.103935i
\(591\) 0 0
\(592\) 18.9070 + 27.8705i 0.0319375 + 0.0470786i
\(593\) −1059.78 −1.78715 −0.893575 0.448914i \(-0.851811\pi\)
−0.893575 + 0.448914i \(0.851811\pi\)
\(594\) 0 0
\(595\) 50.1283i 0.0842492i
\(596\) 1.16901 3.61418i 0.00196142 0.00606407i
\(597\) 0 0
\(598\) −227.411 + 511.690i −0.380286 + 0.855668i
\(599\) 771.927 136.112i 1.28869 0.227231i 0.513026 0.858373i \(-0.328524\pi\)
0.775668 + 0.631142i \(0.217413\pi\)
\(600\) 0 0
\(601\) −733.365 615.367i −1.22024 1.02390i −0.998812 0.0487281i \(-0.984483\pi\)
−0.221430 0.975176i \(-0.571072\pi\)
\(602\) −557.132 38.5861i −0.925469 0.0640965i
\(603\) 0 0
\(604\) −123.075 + 884.260i −0.203767 + 1.46401i
\(605\) 7.78332 44.1414i 0.0128650 0.0729610i
\(606\) 0 0
\(607\) −354.168 + 973.069i −0.583473 + 1.60308i 0.198729 + 0.980055i \(0.436319\pi\)
−0.782202 + 0.623025i \(0.785904\pi\)
\(608\) −152.200 413.878i −0.250329 0.680720i
\(609\) 0 0
\(610\) −127.629 + 36.6890i −0.209228 + 0.0601459i
\(611\) −537.097 + 310.093i −0.879046 + 0.507517i
\(612\) 0 0
\(613\) −366.538 + 634.862i −0.597941 + 1.03566i 0.395184 + 0.918602i \(0.370681\pi\)
−0.993125 + 0.117062i \(0.962652\pi\)
\(614\) −627.226 155.942i −1.02154 0.253977i
\(615\) 0 0
\(616\) 9.98476 303.277i 0.0162090 0.492334i
\(617\) 46.7240 39.2061i 0.0757278 0.0635431i −0.604138 0.796880i \(-0.706482\pi\)
0.679866 + 0.733337i \(0.262038\pi\)
\(618\) 0 0
\(619\) 283.250 + 778.223i 0.457593 + 1.25723i 0.927272 + 0.374389i \(0.122148\pi\)
−0.469678 + 0.882838i \(0.655630\pi\)
\(620\) 56.4925 + 44.0159i 0.0911169 + 0.0709933i
\(621\) 0 0
\(622\) −6.93773 + 3.38947i −0.0111539 + 0.00544931i
\(623\) 218.367 + 599.958i 0.350508 + 0.963014i
\(624\) 0 0
\(625\) 445.185 373.555i 0.712296 0.597687i
\(626\) 48.4545 35.2535i 0.0774034 0.0563156i
\(627\) 0 0
\(628\) −721.421 + 154.346i −1.14876 + 0.245774i
\(629\) −14.3369 + 24.8322i −0.0227931 + 0.0394788i
\(630\) 0 0
\(631\) 273.648 157.991i 0.433673 0.250381i −0.267237 0.963631i \(-0.586111\pi\)
0.700910 + 0.713250i \(0.252777\pi\)
\(632\) −164.714 66.1669i −0.260624 0.104694i
\(633\) 0 0
\(634\) −118.064 1116.16i −0.186221 1.76051i
\(635\) −40.6492 + 111.683i −0.0640145 + 0.175878i
\(636\) 0 0
\(637\) −36.1707 + 205.134i −0.0567828 + 0.322031i
\(638\) −532.902 358.931i −0.835269 0.562588i
\(639\) 0 0
\(640\) −86.9746 45.7270i −0.135898 0.0714484i
\(641\) −445.886 374.143i −0.695610 0.583686i 0.224911 0.974379i \(-0.427791\pi\)
−0.920521 + 0.390693i \(0.872235\pi\)
\(642\) 0 0
\(643\) 884.213 155.911i 1.37514 0.242474i 0.563249 0.826287i \(-0.309551\pi\)
0.811888 + 0.583814i \(0.198440\pi\)
\(644\) 24.2967 + 670.201i 0.0377278 + 1.04069i
\(645\) 0 0
\(646\) 260.626 270.246i 0.403446 0.418337i
\(647\) 822.404i 1.27110i −0.772058 0.635552i \(-0.780773\pi\)
0.772058 0.635552i \(-0.219227\pi\)
\(648\) 0 0
\(649\) −345.843 −0.532885
\(650\) −281.296 271.283i −0.432763 0.417358i
\(651\) 0 0
\(652\) −839.584 + 30.4373i −1.28771 + 0.0466830i
\(653\) 199.644 + 1132.24i 0.305734 + 1.73390i 0.620030 + 0.784578i \(0.287120\pi\)
−0.314296 + 0.949325i \(0.601768\pi\)
\(654\) 0 0
\(655\) −43.3611 + 51.6758i −0.0662002 + 0.0788943i
\(656\) 229.463 + 65.1371i 0.349791 + 0.0992944i
\(657\) 0 0
\(658\) −414.952 + 616.075i −0.630626 + 0.936285i
\(659\) −354.825 62.5652i −0.538430 0.0949397i −0.102181 0.994766i \(-0.532582\pi\)
−0.436249 + 0.899826i \(0.643693\pi\)
\(660\) 0 0
\(661\) 766.959 + 279.150i 1.16030 + 0.422315i 0.849205 0.528063i \(-0.177082\pi\)
0.311097 + 0.950378i \(0.399304\pi\)
\(662\) 279.445 29.5589i 0.422123 0.0446508i
\(663\) 0 0
\(664\) −162.090 65.1125i −0.244111 0.0980610i
\(665\) 25.3552 + 43.9164i 0.0381281 + 0.0660398i
\(666\) 0 0
\(667\) 1229.77 + 710.008i 1.84373 + 1.06448i
\(668\) 110.334 + 515.707i 0.165171 + 0.772016i
\(669\) 0 0
\(670\) −37.1114 51.0080i −0.0553901 0.0761314i
\(671\) 439.929 + 524.287i 0.655632 + 0.781352i
\(672\) 0 0
\(673\) −218.010 + 79.3492i −0.323938 + 0.117904i −0.498870 0.866677i \(-0.666252\pi\)
0.174932 + 0.984580i \(0.444029\pi\)
\(674\) 372.272 + 761.983i 0.552332 + 1.13054i
\(675\) 0 0
\(676\) 257.956 331.075i 0.381591 0.489756i
\(677\) 115.647 42.0921i 0.170823 0.0621744i −0.255193 0.966890i \(-0.582139\pi\)
0.426016 + 0.904716i \(0.359917\pi\)
\(678\) 0 0
\(679\) 503.847 + 600.461i 0.742042 + 0.884331i
\(680\) 2.75285 83.6150i 0.00404830 0.122963i
\(681\) 0 0
\(682\) 89.0526 358.185i 0.130576 0.525198i
\(683\) 293.573 + 169.494i 0.429829 + 0.248162i 0.699274 0.714854i \(-0.253507\pi\)
−0.269445 + 0.963016i \(0.586840\pi\)
\(684\) 0 0
\(685\) −101.181 175.251i −0.147710 0.255841i
\(686\) 198.709 + 691.246i 0.289664 + 1.00765i
\(687\) 0 0
\(688\) 927.189 + 94.9579i 1.34766 + 0.138020i
\(689\) 328.193 + 119.452i 0.476332 + 0.173371i
\(690\) 0 0
\(691\) −757.805 133.621i −1.09668 0.193374i −0.404099 0.914715i \(-0.632415\pi\)
−0.692580 + 0.721342i \(0.743526\pi\)
\(692\) −803.463 111.830i −1.16107 0.161603i
\(693\) 0 0
\(694\) −15.6936 + 226.595i −0.0226132 + 0.326505i
\(695\) 109.432 130.415i 0.157456 0.187648i
\(696\) 0 0
\(697\) 35.2649 + 199.997i 0.0505952 + 0.286940i
\(698\) −184.110 81.8241i −0.263767 0.117227i
\(699\) 0 0
\(700\) −445.335 144.043i −0.636193 0.205776i
\(701\) −118.777 −0.169440 −0.0847199 0.996405i \(-0.527000\pi\)
−0.0847199 + 0.996405i \(0.527000\pi\)
\(702\) 0 0
\(703\) 29.0066i 0.0412612i
\(704\) −33.3096 + 505.325i −0.0473147 + 0.717791i
\(705\) 0 0
\(706\) −47.5142 21.1168i −0.0673006 0.0299105i
\(707\) −127.021 + 22.3971i −0.179661 + 0.0316791i
\(708\) 0 0
\(709\) 176.615 + 148.198i 0.249104 + 0.209023i 0.758787 0.651339i \(-0.225793\pi\)
−0.509682 + 0.860363i \(0.670237\pi\)
\(710\) −9.17801 + 132.518i −0.0129268 + 0.186646i
\(711\) 0 0
\(712\) −331.293 1012.73i −0.465299 1.42238i
\(713\) −141.650 + 803.338i −0.198668 + 1.12670i
\(714\) 0 0
\(715\) 16.6304 45.6916i 0.0232593 0.0639044i
\(716\) 146.751 + 234.156i 0.204959 + 0.327034i
\(717\) 0 0
\(718\) −32.4305 112.815i −0.0451679 0.157125i
\(719\) 157.002 90.6454i 0.218362 0.126072i −0.386829 0.922151i \(-0.626430\pi\)
0.605192 + 0.796080i \(0.293096\pi\)
\(720\) 0 0
\(721\) −114.525 + 198.362i −0.158841 + 0.275121i
\(722\) −82.5637 + 332.086i −0.114354 + 0.459953i
\(723\) 0 0
\(724\) −317.112 168.071i −0.438000 0.232142i
\(725\) −759.189 + 637.035i −1.04716 + 0.878669i
\(726\) 0 0
\(727\) −129.850 356.761i −0.178611 0.490730i 0.817788 0.575520i \(-0.195200\pi\)
−0.996399 + 0.0847899i \(0.972978\pi\)
\(728\) −63.2216 + 300.380i −0.0868428 + 0.412610i
\(729\) 0 0
\(730\) 57.8836 + 118.479i 0.0792926 + 0.162300i
\(731\) 271.405 + 745.678i 0.371279 + 1.02008i
\(732\) 0 0
\(733\) 201.798 169.329i 0.275305 0.231008i −0.494672 0.869079i \(-0.664712\pi\)
0.769977 + 0.638071i \(0.220268\pi\)
\(734\) −128.691 176.881i −0.175329 0.240982i
\(735\) 0 0
\(736\) −3.72264 1119.24i −0.00505794 1.52071i
\(737\) −162.549 + 281.543i −0.220555 + 0.382013i
\(738\) 0 0
\(739\) 515.106 297.397i 0.697032 0.402431i −0.109209 0.994019i \(-0.534832\pi\)
0.806241 + 0.591587i \(0.201499\pi\)
\(740\) 4.33134 + 4.79759i 0.00585317 + 0.00648323i
\(741\) 0 0
\(742\) 415.978 44.0008i 0.560617 0.0593003i
\(743\) 364.905 1002.57i 0.491124 1.34935i −0.408528 0.912746i \(-0.633958\pi\)
0.899652 0.436607i \(-0.143820\pi\)
\(744\) 0 0
\(745\) 0.126592 0.717937i 0.000169922 0.000963674i
\(746\) 74.8426 111.118i 0.100325 0.148952i
\(747\) 0 0
\(748\) −399.554 + 162.049i −0.534163 + 0.216643i
\(749\) −225.003 188.800i −0.300405 0.252070i
\(750\) 0 0
\(751\) 923.903 162.909i 1.23023 0.216923i 0.479506 0.877539i \(-0.340816\pi\)
0.750724 + 0.660616i \(0.229705\pi\)
\(752\) 725.981 1004.84i 0.965400 1.33622i
\(753\) 0 0
\(754\) 467.842 + 451.189i 0.620481 + 0.598394i
\(755\) 171.342i 0.226943i
\(756\) 0 0
\(757\) −496.473 −0.655843 −0.327922 0.944705i \(-0.606348\pi\)
−0.327922 + 0.944705i \(0.606348\pi\)
\(758\) −383.987 + 398.160i −0.506580 + 0.525277i
\(759\) 0 0
\(760\) −39.8812 74.6459i −0.0524753 0.0982183i
\(761\) 34.9002 + 197.929i 0.0458610 + 0.260091i 0.999114 0.0420821i \(-0.0133991\pi\)
−0.953253 + 0.302173i \(0.902288\pi\)
\(762\) 0 0
\(763\) −596.023 + 710.312i −0.781157 + 0.930947i
\(764\) 1096.16 444.574i 1.43476 0.581904i
\(765\) 0 0
\(766\) 66.8455 + 45.0232i 0.0872657 + 0.0587770i
\(767\) 344.539 + 60.7515i 0.449203 + 0.0792067i
\(768\) 0 0
\(769\) −608.961 221.644i −0.791886 0.288223i −0.0857663 0.996315i \(-0.527334\pi\)
−0.706120 + 0.708092i \(0.749556\pi\)
\(770\) −6.12587 57.9132i −0.00795568 0.0752119i
\(771\) 0 0
\(772\) −834.564 924.401i −1.08104 1.19741i
\(773\) −581.802 1007.71i −0.752654 1.30364i −0.946532 0.322610i \(-0.895440\pi\)
0.193878 0.981026i \(-0.437893\pi\)
\(774\) 0 0
\(775\) −493.037 284.655i −0.636177 0.367297i
\(776\) −807.452 1029.25i −1.04053 1.32635i
\(777\) 0 0
\(778\) −240.923 + 175.286i −0.309669 + 0.225303i
\(779\) 132.055 + 157.376i 0.169518 + 0.202024i
\(780\) 0 0
\(781\) 643.317 234.148i 0.823710 0.299806i
\(782\) 856.205 418.304i 1.09489 0.534916i
\(783\) 0 0
\(784\) −101.800 403.720i −0.129847 0.514949i
\(785\) −133.049 + 48.4259i −0.169489 + 0.0616890i
\(786\) 0 0
\(787\) 179.534 + 213.961i 0.228125 + 0.271869i 0.867950 0.496652i \(-0.165437\pi\)
−0.639825 + 0.768521i \(0.720993\pi\)
\(788\) −509.277 269.919i −0.646291 0.342537i
\(789\) 0 0
\(790\) −33.0606 8.21958i −0.0418489 0.0104045i
\(791\) 321.500 + 185.618i 0.406447 + 0.234662i
\(792\) 0 0
\(793\) −346.173 599.590i −0.436537 0.756103i
\(794\) −1435.38 + 412.623i −1.80779 + 0.519676i
\(795\) 0 0
\(796\) −413.947 660.497i −0.520034 0.829770i
\(797\) 1142.08 + 415.682i 1.43297 + 0.521558i 0.937781 0.347228i \(-0.112877\pi\)
0.495188 + 0.868786i \(0.335099\pi\)
\(798\) 0 0
\(799\) 1039.40 + 183.275i 1.30088 + 0.229380i
\(800\) 734.917 + 264.723i 0.918647 + 0.330904i
\(801\) 0 0
\(802\) 115.605 + 8.00659i 0.144145 + 0.00998328i
\(803\) 436.830 520.594i 0.543998 0.648312i
\(804\) 0 0
\(805\) 22.3501 + 126.754i 0.0277641 + 0.157458i
\(806\) −151.637 + 341.192i −0.188135 + 0.423315i
\(807\) 0 0
\(808\) 213.103 30.3834i 0.263741 0.0376033i
\(809\) 1111.49 1.37390 0.686952 0.726703i \(-0.258948\pi\)
0.686952 + 0.726703i \(0.258948\pi\)
\(810\) 0 0
\(811\) 553.768i 0.682821i 0.939914 + 0.341411i \(0.110905\pi\)
−0.939914 + 0.341411i \(0.889095\pi\)
\(812\) 740.667 + 239.568i 0.912152 + 0.295035i
\(813\) 0 0
\(814\) 13.5288 30.4406i 0.0166201 0.0373963i
\(815\) −158.789 + 27.9987i −0.194833 + 0.0343542i
\(816\) 0 0
\(817\) 614.940 + 515.996i 0.752681 + 0.631574i
\(818\) −588.788 40.7785i −0.719789 0.0498515i
\(819\) 0 0
\(820\) 45.3412 + 6.31078i 0.0552941 + 0.00769608i
\(821\) 41.0204 232.638i 0.0499639 0.283360i −0.949581 0.313522i \(-0.898491\pi\)
0.999545 + 0.0301620i \(0.00960231\pi\)
\(822\) 0 0
\(823\) −204.440 + 561.693i −0.248408 + 0.682495i 0.751337 + 0.659918i \(0.229409\pi\)
−0.999745 + 0.0225763i \(0.992813\pi\)
\(824\) 201.923 324.583i 0.245052 0.393912i
\(825\) 0 0
\(826\) 402.706 115.764i 0.487538 0.140150i
\(827\) 888.113 512.752i 1.07390 0.620015i 0.144654 0.989482i \(-0.453793\pi\)
0.929244 + 0.369467i \(0.120460\pi\)
\(828\) 0 0
\(829\) 11.4162 19.7735i 0.0137711 0.0238522i −0.859058 0.511879i \(-0.828950\pi\)
0.872829 + 0.488026i \(0.162283\pi\)
\(830\) −32.5338 8.08860i −0.0391973 0.00974530i
\(831\) 0 0
\(832\) 121.951 497.569i 0.146575 0.598040i
\(833\) 271.551 227.858i 0.325991 0.273539i
\(834\) 0 0
\(835\) 34.6172 + 95.1099i 0.0414577 + 0.113904i
\(836\) −268.076 + 344.065i −0.320665 + 0.411561i
\(837\) 0 0
\(838\) 791.908 386.892i 0.944998 0.461685i
\(839\) 217.276 + 596.961i 0.258970 + 0.711515i 0.999232 + 0.0391958i \(0.0124796\pi\)
−0.740261 + 0.672319i \(0.765298\pi\)
\(840\) 0 0
\(841\) 618.416 518.913i 0.735334 0.617019i
\(842\) −110.077 + 80.0875i −0.130733 + 0.0951158i
\(843\) 0 0
\(844\) 97.1596 + 454.128i 0.115118 + 0.538067i
\(845\) 40.2746 69.7577i 0.0476623 0.0825535i
\(846\) 0 0
\(847\) 242.382 139.939i 0.286165 0.165218i
\(848\) −696.275 + 50.5504i −0.821080 + 0.0596113i
\(849\) 0 0
\(850\) 69.9577 + 661.371i 0.0823032 + 0.778083i
\(851\) −25.1803 + 69.1824i −0.0295891 + 0.0812954i
\(852\) 0 0
\(853\) 13.1002 74.2950i 0.0153578 0.0870984i −0.976165 0.217028i \(-0.930364\pi\)
0.991523 + 0.129929i \(0.0414750\pi\)
\(854\) −687.758 463.233i −0.805337 0.542427i
\(855\) 0 0
\(856\) 364.942 + 327.279i 0.426334 + 0.382335i
\(857\) 186.048 + 156.113i 0.217093 + 0.182162i 0.744848 0.667234i \(-0.232522\pi\)
−0.527756 + 0.849396i \(0.676966\pi\)
\(858\) 0 0
\(859\) 832.750 146.836i 0.969442 0.170939i 0.333563 0.942728i \(-0.391749\pi\)
0.635879 + 0.771789i \(0.280638\pi\)
\(860\) 178.759 6.48051i 0.207859 0.00753548i
\(861\) 0 0
\(862\) 74.4310 77.1782i 0.0863469 0.0895339i
\(863\) 411.636i 0.476983i −0.971145 0.238491i \(-0.923347\pi\)
0.971145 0.238491i \(-0.0766529\pi\)
\(864\) 0 0
\(865\) −155.686 −0.179984
\(866\) 988.626 + 953.435i 1.14160 + 1.10096i
\(867\) 0 0
\(868\) 16.2009 + 446.887i 0.0186647 + 0.514847i
\(869\) 30.4880 + 172.906i 0.0350840 + 0.198971i
\(870\) 0 0
\(871\) 211.393 251.928i 0.242702 0.289241i
\(872\) 1033.19 1152.08i 1.18485 1.32120i
\(873\) 0 0
\(874\) 538.524 799.542i 0.616160 0.914807i
\(875\) −179.062 31.5735i −0.204642 0.0360840i
\(876\) 0 0
\(877\) −107.037 38.9581i −0.122049 0.0444221i 0.280274 0.959920i \(-0.409575\pi\)
−0.402322 + 0.915498i \(0.631797\pi\)
\(878\) 230.747 24.4077i 0.262809 0.0277992i
\(879\) 0 0
\(880\) 7.03772 + 96.9368i 0.00799741 + 0.110155i
\(881\) −238.369 412.868i −0.270567 0.468635i 0.698440 0.715668i \(-0.253878\pi\)
−0.969007 + 0.247033i \(0.920544\pi\)
\(882\) 0 0
\(883\) 554.004 + 319.854i 0.627411 + 0.362236i 0.779749 0.626093i \(-0.215347\pi\)
−0.152338 + 0.988328i \(0.548680\pi\)
\(884\) 426.514 91.2516i 0.482482 0.103226i
\(885\) 0 0
\(886\) 151.367 + 208.048i 0.170843 + 0.234817i
\(887\) 106.718 + 127.182i 0.120314 + 0.143384i 0.822839 0.568274i \(-0.192389\pi\)
−0.702525 + 0.711659i \(0.747944\pi\)
\(888\) 0 0
\(889\) −697.367 + 253.821i −0.784440 + 0.285513i
\(890\) −89.7684 183.742i −0.100863 0.206452i
\(891\) 0 0
\(892\) 468.652 + 365.148i 0.525394 + 0.409359i
\(893\) 1003.30 365.173i 1.12352 0.408928i
\(894\) 0 0
\(895\) 34.0905 + 40.6274i 0.0380899 + 0.0453938i
\(896\) −130.361 599.560i −0.145493 0.669152i
\(897\) 0 0
\(898\) −349.214 + 1404.60i −0.388880 + 1.56414i
\(899\) 820.005 + 473.430i 0.912130 + 0.526618i
\(900\) 0 0
\(901\) −297.183 514.736i −0.329837 0.571294i
\(902\) −65.1819 226.747i −0.0722638 0.251382i
\(903\) 0 0
\(904\) −526.075 327.270i −0.581941 0.362025i
\(905\) −64.7254 23.5581i −0.0715198 0.0260311i
\(906\) 0 0
\(907\) −75.7474 13.3563i −0.0835142 0.0147258i 0.131735 0.991285i \(-0.457945\pi\)
−0.215249 + 0.976559i \(0.569056\pi\)
\(908\) −91.6197 + 658.261i −0.100903 + 0.724958i
\(909\) 0 0
\(910\) −4.07038 + 58.7710i −0.00447295 + 0.0645835i
\(911\) −913.726 + 1088.94i −1.00299 + 1.19532i −0.0223018 + 0.999751i \(0.507099\pi\)
−0.980690 + 0.195568i \(0.937345\pi\)
\(912\) 0 0
\(913\) 30.0022 + 170.151i 0.0328611 + 0.186364i
\(914\) −96.9715 43.0972i −0.106096 0.0471523i
\(915\) 0 0
\(916\) 286.461 885.643i 0.312730 0.966859i
\(917\) −421.219 −0.459345
\(918\) 0 0
\(919\) 1228.21i 1.33646i −0.743955 0.668229i \(-0.767052\pi\)
0.743955 0.668229i \(-0.232948\pi\)
\(920\) −30.3196 212.655i −0.0329561 0.231147i
\(921\) 0 0
\(922\) 385.322 + 171.249i 0.417920 + 0.185737i
\(923\) −682.023 + 120.259i −0.738920 + 0.130292i
\(924\) 0 0
\(925\) −39.3610 33.0278i −0.0425524 0.0357057i
\(926\) −87.5228 + 1263.71i −0.0945170 + 1.36470i
\(927\) 0 0
\(928\) −1222.29 440.280i −1.31712 0.474439i
\(929\) 36.4353 206.635i 0.0392200 0.222427i −0.958898 0.283751i \(-0.908421\pi\)
0.998118 + 0.0613236i \(0.0195322\pi\)
\(930\) 0 0
\(931\) 122.649 336.974i 0.131738 0.361948i
\(932\) −692.419 + 433.954i −0.742939 + 0.465615i
\(933\) 0 0
\(934\) 162.626 + 565.724i 0.174118 + 0.605700i
\(935\) −71.6626 + 41.3744i −0.0766445 + 0.0442507i
\(936\) 0 0
\(937\) −227.457 + 393.966i −0.242750 + 0.420455i −0.961497 0.274817i \(-0.911383\pi\)
0.718747 + 0.695272i \(0.244716\pi\)
\(938\) 95.0344 382.245i 0.101316 0.407511i
\(939\) 0 0
\(940\) 111.414 210.214i 0.118526 0.223632i
\(941\) 869.171 729.321i 0.923667 0.775049i −0.0510024 0.998699i \(-0.516242\pi\)
0.974670 + 0.223650i \(0.0717972\pi\)
\(942\) 0 0
\(943\) 178.340 + 489.986i 0.189120 + 0.519604i
\(944\) −678.080 + 170.982i −0.718305 + 0.181125i
\(945\) 0 0
\(946\) −404.678 828.315i −0.427778 0.875597i
\(947\) 4.02952 + 11.0710i 0.00425503 + 0.0116906i 0.941802 0.336168i \(-0.109131\pi\)
−0.937547 + 0.347859i \(0.886909\pi\)
\(948\) 0 0
\(949\) −526.633 + 441.897i −0.554934 + 0.465645i
\(950\) 395.814 + 544.029i 0.416646 + 0.572662i
\(951\) 0 0
\(952\) 411.006 322.436i 0.431729 0.338693i
\(953\) 67.1825 116.364i 0.0704958 0.122102i −0.828623 0.559807i \(-0.810875\pi\)
0.899119 + 0.437705i \(0.144209\pi\)
\(954\) 0 0
\(955\) 196.603 113.509i 0.205867 0.118858i
\(956\) −273.236 + 246.681i −0.285811 + 0.258035i
\(957\) 0 0
\(958\) 1080.84 114.328i 1.12823 0.119340i
\(959\) 432.172 1187.38i 0.450648 1.23815i
\(960\) 0 0
\(961\) 72.4243 410.739i 0.0753635 0.427408i
\(962\) −18.8251 + 27.9494i −0.0195687 + 0.0290534i
\(963\) 0 0
\(964\) −311.895 769.021i −0.323543 0.797740i
\(965\) −183.097 153.636i −0.189737 0.159209i
\(966\) 0 0
\(967\) −946.293 + 166.857i −0.978586 + 0.172551i −0.639992 0.768381i \(-0.721062\pi\)
−0.338594 + 0.940933i \(0.609951\pi\)
\(968\) −411.983 + 220.111i −0.425602 + 0.227387i
\(969\) 0 0
\(970\) −180.717 174.284i −0.186306 0.179674i
\(971\) 1270.91i 1.30887i 0.756118 + 0.654435i \(0.227094\pi\)
−0.756118 + 0.654435i \(0.772906\pi\)
\(972\) 0 0
\(973\) 1063.04 1.09254
\(974\) 233.951 242.586i 0.240196 0.249062i
\(975\) 0 0
\(976\) 1121.75 + 810.451i 1.14934 + 0.830380i
\(977\) −298.940 1695.37i −0.305977 1.73528i −0.618869 0.785494i \(-0.712409\pi\)
0.312892 0.949789i \(-0.398702\pi\)
\(978\) 0 0
\(979\) −677.456 + 807.361i −0.691988 + 0.824679i
\(980\) −30.0322 74.0484i −0.0306451 0.0755596i
\(981\) 0 0
\(982\) 664.961 + 447.879i 0.677150 + 0.456088i
\(983\) −1386.92 244.552i −1.41091 0.248781i −0.584291 0.811544i \(-0.698627\pi\)
−0.826619 + 0.562763i \(0.809739\pi\)
\(984\) 0 0
\(985\) −103.948 37.8340i −0.105531 0.0384102i
\(986\) −116.352 1099.97i −0.118004 1.11559i
\(987\) 0 0
\(988\) 327.505 295.677i 0.331483 0.299268i
\(989\) 1018.74 + 1764.50i 1.03007 + 1.78413i
\(990\) 0 0
\(991\) −918.471 530.279i −0.926812 0.535095i −0.0410102 0.999159i \(-0.513058\pi\)
−0.885802 + 0.464064i \(0.846391\pi\)
\(992\) −2.48224 746.306i −0.00250226 0.752325i
\(993\) 0 0
\(994\) −670.715 + 487.985i −0.674764 + 0.490931i
\(995\) −96.1607 114.600i −0.0966440 0.115176i
\(996\) 0 0
\(997\) −1156.49 + 420.929i −1.15997 + 0.422195i −0.849087 0.528252i \(-0.822847\pi\)
−0.310885 + 0.950448i \(0.600625\pi\)
\(998\) −284.174 + 138.835i −0.284744 + 0.139113i
\(999\) 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 324.3.j.a.19.9 204
3.2 odd 2 108.3.j.a.7.26 yes 204
4.3 odd 2 inner 324.3.j.a.19.17 204
12.11 even 2 108.3.j.a.7.18 204
27.4 even 9 inner 324.3.j.a.307.17 204
27.23 odd 18 108.3.j.a.31.18 yes 204
108.23 even 18 108.3.j.a.31.26 yes 204
108.31 odd 18 inner 324.3.j.a.307.9 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.7.18 204 12.11 even 2
108.3.j.a.7.26 yes 204 3.2 odd 2
108.3.j.a.31.18 yes 204 27.23 odd 18
108.3.j.a.31.26 yes 204 108.23 even 18
324.3.j.a.19.9 204 1.1 even 1 trivial
324.3.j.a.19.17 204 4.3 odd 2 inner
324.3.j.a.307.9 204 108.31 odd 18 inner
324.3.j.a.307.17 204 27.4 even 9 inner