Properties

Label 324.3.j.a.19.5
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 19.5
Character \(\chi\) \(=\) 324.19
Dual form 324.3.j.a.307.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.70561 + 1.04446i) q^{2} +(1.81819 - 3.56289i) q^{4} +(0.00321173 + 0.0182146i) q^{5} +(-0.446686 + 0.532339i) q^{7} +(0.620191 + 7.97592i) q^{8} +O(q^{10})\) \(q+(-1.70561 + 1.04446i) q^{2} +(1.81819 - 3.56289i) q^{4} +(0.00321173 + 0.0182146i) q^{5} +(-0.446686 + 0.532339i) q^{7} +(0.620191 + 7.97592i) q^{8} +(-0.0245024 - 0.0277124i) q^{10} +(-5.71885 - 1.00839i) q^{11} +(6.99816 + 2.54712i) q^{13} +(0.205861 - 1.37451i) q^{14} +(-9.38837 - 12.9560i) q^{16} +(4.38388 + 7.59310i) q^{17} +(17.1217 + 9.88523i) q^{19} +(0.0707361 + 0.0216746i) q^{20} +(10.8073 - 4.25322i) q^{22} +(-7.15027 - 8.52136i) q^{23} +(23.4920 - 8.55039i) q^{25} +(-14.5965 + 2.96494i) q^{26} +(1.08451 + 2.55939i) q^{28} +(21.1363 - 7.69297i) q^{29} +(20.2667 + 24.1529i) q^{31} +(29.5450 + 12.2921i) q^{32} +(-15.4079 - 8.37204i) q^{34} +(-0.0111310 - 0.00642647i) q^{35} +(26.7594 + 46.3486i) q^{37} +(-39.5277 + 1.02270i) q^{38} +(-0.143286 + 0.0369130i) q^{40} +(52.8679 + 19.2423i) q^{41} +(-70.5871 - 12.4464i) q^{43} +(-13.9907 + 18.5422i) q^{44} +(21.0958 + 7.06589i) q^{46} +(-43.9159 + 52.3369i) q^{47} +(8.42490 + 47.7800i) q^{49} +(-31.1375 + 39.1201i) q^{50} +(21.7991 - 20.3025i) q^{52} +41.1446 q^{53} -0.107405i q^{55} +(-4.52293 - 3.23258i) q^{56} +(-28.0151 + 35.1972i) q^{58} +(50.0926 - 8.83268i) q^{59} +(28.9297 + 24.2749i) q^{61} +(-59.7939 - 20.0275i) q^{62} +(-63.2307 + 9.89320i) q^{64} +(-0.0239186 + 0.135649i) q^{65} +(-14.8206 + 40.7193i) q^{67} +(35.0241 - 1.81357i) q^{68} +(0.0256973 - 0.000664867i) q^{70} +(49.5059 - 28.5822i) q^{71} +(14.6051 - 25.2968i) q^{73} +(-94.0505 - 51.1033i) q^{74} +(66.3505 - 43.0296i) q^{76} +(3.09133 - 2.59394i) q^{77} +(-46.0077 - 126.405i) q^{79} +(0.205836 - 0.212617i) q^{80} +(-110.270 + 22.3987i) q^{82} +(49.0991 + 134.899i) q^{83} +(-0.124225 + 0.104237i) q^{85} +(133.394 - 52.4970i) q^{86} +(4.49604 - 46.2385i) q^{88} +(29.5539 - 51.1889i) q^{89} +(-4.48191 + 2.58763i) q^{91} +(-43.3612 + 9.98217i) q^{92} +(20.2392 - 135.135i) q^{94} +(-0.125065 + 0.343614i) q^{95} +(6.63733 - 37.6422i) q^{97} +(-64.2741 - 72.6944i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70561 + 1.04446i −0.852803 + 0.522232i
\(3\) 0 0
\(4\) 1.81819 3.56289i 0.454548 0.890722i
\(5\) 0.00321173 + 0.0182146i 0.000642345 + 0.00364292i 0.985127 0.171826i \(-0.0549668\pi\)
−0.984485 + 0.175469i \(0.943856\pi\)
\(6\) 0 0
\(7\) −0.446686 + 0.532339i −0.0638123 + 0.0760485i −0.797006 0.603971i \(-0.793584\pi\)
0.733194 + 0.680019i \(0.238029\pi\)
\(8\) 0.620191 + 7.97592i 0.0775239 + 0.996990i
\(9\) 0 0
\(10\) −0.0245024 0.0277124i −0.00245024 0.00277124i
\(11\) −5.71885 1.00839i −0.519896 0.0916716i −0.0924582 0.995717i \(-0.529472\pi\)
−0.427437 + 0.904045i \(0.640584\pi\)
\(12\) 0 0
\(13\) 6.99816 + 2.54712i 0.538320 + 0.195933i 0.596850 0.802353i \(-0.296419\pi\)
−0.0585294 + 0.998286i \(0.518641\pi\)
\(14\) 0.205861 1.37451i 0.0147044 0.0981792i
\(15\) 0 0
\(16\) −9.38837 12.9560i −0.586773 0.809752i
\(17\) 4.38388 + 7.59310i 0.257875 + 0.446653i 0.965672 0.259763i \(-0.0836444\pi\)
−0.707797 + 0.706416i \(0.750311\pi\)
\(18\) 0 0
\(19\) 17.1217 + 9.88523i 0.901143 + 0.520275i 0.877571 0.479447i \(-0.159163\pi\)
0.0235724 + 0.999722i \(0.492496\pi\)
\(20\) 0.0707361 + 0.0216746i 0.00353681 + 0.00108373i
\(21\) 0 0
\(22\) 10.8073 4.25322i 0.491243 0.193328i
\(23\) −7.15027 8.52136i −0.310881 0.370494i 0.587868 0.808957i \(-0.299967\pi\)
−0.898749 + 0.438463i \(0.855523\pi\)
\(24\) 0 0
\(25\) 23.4920 8.55039i 0.939680 0.342015i
\(26\) −14.5965 + 2.96494i −0.561404 + 0.114036i
\(27\) 0 0
\(28\) 1.08451 + 2.55939i 0.0387324 + 0.0914067i
\(29\) 21.1363 7.69297i 0.728837 0.265275i 0.0491643 0.998791i \(-0.484344\pi\)
0.679672 + 0.733516i \(0.262122\pi\)
\(30\) 0 0
\(31\) 20.2667 + 24.1529i 0.653765 + 0.779126i 0.986477 0.163902i \(-0.0524081\pi\)
−0.332712 + 0.943029i \(0.607964\pi\)
\(32\) 29.5450 + 12.2921i 0.923280 + 0.384127i
\(33\) 0 0
\(34\) −15.4079 8.37204i −0.453173 0.246236i
\(35\) −0.0111310 0.00642647i −0.000318028 0.000183614i
\(36\) 0 0
\(37\) 26.7594 + 46.3486i 0.723227 + 1.25267i 0.959700 + 0.281028i \(0.0906753\pi\)
−0.236473 + 0.971638i \(0.575991\pi\)
\(38\) −39.5277 + 1.02270i −1.04020 + 0.0269132i
\(39\) 0 0
\(40\) −0.143286 + 0.0369130i −0.00358216 + 0.000922825i
\(41\) 52.8679 + 19.2423i 1.28946 + 0.469325i 0.893550 0.448964i \(-0.148207\pi\)
0.395910 + 0.918289i \(0.370429\pi\)
\(42\) 0 0
\(43\) −70.5871 12.4464i −1.64156 0.289452i −0.724822 0.688936i \(-0.758078\pi\)
−0.916740 + 0.399485i \(0.869189\pi\)
\(44\) −13.9907 + 18.5422i −0.317971 + 0.421414i
\(45\) 0 0
\(46\) 21.0958 + 7.06589i 0.458605 + 0.153606i
\(47\) −43.9159 + 52.3369i −0.934381 + 1.11355i 0.0589506 + 0.998261i \(0.481225\pi\)
−0.993332 + 0.115291i \(0.963220\pi\)
\(48\) 0 0
\(49\) 8.42490 + 47.7800i 0.171937 + 0.975102i
\(50\) −31.1375 + 39.1201i −0.622751 + 0.782403i
\(51\) 0 0
\(52\) 21.7991 20.3025i 0.419214 0.390433i
\(53\) 41.1446 0.776313 0.388156 0.921594i \(-0.373112\pi\)
0.388156 + 0.921594i \(0.373112\pi\)
\(54\) 0 0
\(55\) 0.107405i 0.00195282i
\(56\) −4.52293 3.23258i −0.0807666 0.0577246i
\(57\) 0 0
\(58\) −28.0151 + 35.1972i −0.483019 + 0.606849i
\(59\) 50.0926 8.83268i 0.849027 0.149706i 0.267827 0.963467i \(-0.413694\pi\)
0.581200 + 0.813761i \(0.302583\pi\)
\(60\) 0 0
\(61\) 28.9297 + 24.2749i 0.474258 + 0.397949i 0.848345 0.529444i \(-0.177599\pi\)
−0.374087 + 0.927394i \(0.622044\pi\)
\(62\) −59.7939 20.0275i −0.964417 0.323025i
\(63\) 0 0
\(64\) −63.2307 + 9.89320i −0.987980 + 0.154581i
\(65\) −0.0239186 + 0.135649i −0.000367979 + 0.00208691i
\(66\) 0 0
\(67\) −14.8206 + 40.7193i −0.221203 + 0.607751i −0.999805 0.0197678i \(-0.993707\pi\)
0.778601 + 0.627519i \(0.215930\pi\)
\(68\) 35.0241 1.81357i 0.515060 0.0266702i
\(69\) 0 0
\(70\) 0.0256973 0.000664867i 0.000367104 9.49810e-6i
\(71\) 49.5059 28.5822i 0.697266 0.402567i −0.109062 0.994035i \(-0.534785\pi\)
0.806328 + 0.591468i \(0.201451\pi\)
\(72\) 0 0
\(73\) 14.6051 25.2968i 0.200070 0.346532i −0.748481 0.663157i \(-0.769216\pi\)
0.948551 + 0.316625i \(0.102550\pi\)
\(74\) −94.0505 51.1033i −1.27095 0.690586i
\(75\) 0 0
\(76\) 66.3505 43.0296i 0.873033 0.566179i
\(77\) 3.09133 2.59394i 0.0401472 0.0336875i
\(78\) 0 0
\(79\) −46.0077 126.405i −0.582376 1.60007i −0.784107 0.620625i \(-0.786879\pi\)
0.201731 0.979441i \(-0.435343\pi\)
\(80\) 0.205836 0.212617i 0.00257295 0.00265771i
\(81\) 0 0
\(82\) −110.270 + 22.3987i −1.34475 + 0.273155i
\(83\) 49.0991 + 134.899i 0.591555 + 1.62528i 0.767619 + 0.640906i \(0.221441\pi\)
−0.176064 + 0.984379i \(0.556337\pi\)
\(84\) 0 0
\(85\) −0.124225 + 0.104237i −0.00146148 + 0.00122632i
\(86\) 133.394 52.4970i 1.55109 0.610431i
\(87\) 0 0
\(88\) 4.49604 46.2385i 0.0510914 0.525438i
\(89\) 29.5539 51.1889i 0.332067 0.575156i −0.650850 0.759206i \(-0.725587\pi\)
0.982917 + 0.184050i \(0.0589208\pi\)
\(90\) 0 0
\(91\) −4.48191 + 2.58763i −0.0492518 + 0.0284355i
\(92\) −43.3612 + 9.98217i −0.471318 + 0.108502i
\(93\) 0 0
\(94\) 20.2392 135.135i 0.215311 1.43760i
\(95\) −0.125065 + 0.343614i −0.00131648 + 0.00361699i
\(96\) 0 0
\(97\) 6.63733 37.6422i 0.0684261 0.388064i −0.931291 0.364276i \(-0.881316\pi\)
0.999717 0.0237874i \(-0.00757248\pi\)
\(98\) −64.2741 72.6944i −0.655858 0.741780i
\(99\) 0 0
\(100\) 12.2488 99.2456i 0.122488 0.992456i
\(101\) −103.239 86.6279i −1.02217 0.857702i −0.0322707 0.999479i \(-0.510274\pi\)
−0.989899 + 0.141777i \(0.954718\pi\)
\(102\) 0 0
\(103\) 48.5344 8.55793i 0.471208 0.0830867i 0.0669984 0.997753i \(-0.478658\pi\)
0.404210 + 0.914666i \(0.367547\pi\)
\(104\) −15.9755 + 57.3965i −0.153610 + 0.551890i
\(105\) 0 0
\(106\) −70.1765 + 42.9740i −0.662042 + 0.405415i
\(107\) 171.403i 1.60189i −0.598736 0.800946i \(-0.704330\pi\)
0.598736 0.800946i \(-0.295670\pi\)
\(108\) 0 0
\(109\) −117.306 −1.07620 −0.538100 0.842881i \(-0.680858\pi\)
−0.538100 + 0.842881i \(0.680858\pi\)
\(110\) 0.112181 + 0.183191i 0.00101983 + 0.00166537i
\(111\) 0 0
\(112\) 11.0907 + 0.789474i 0.0990237 + 0.00704888i
\(113\) −5.87247 33.3044i −0.0519687 0.294729i 0.947735 0.319058i \(-0.103366\pi\)
−0.999704 + 0.0243284i \(0.992255\pi\)
\(114\) 0 0
\(115\) 0.132248 0.157608i 0.00114999 0.00137050i
\(116\) 11.0205 89.2934i 0.0950047 0.769771i
\(117\) 0 0
\(118\) −76.2129 + 67.3850i −0.645872 + 0.571059i
\(119\) −6.00032 1.05802i −0.0504229 0.00889091i
\(120\) 0 0
\(121\) −82.0144 29.8508i −0.677805 0.246701i
\(122\) −74.6970 11.1874i −0.612270 0.0917002i
\(123\) 0 0
\(124\) 122.903 28.2934i 0.991153 0.228173i
\(125\) 0.462387 + 0.800877i 0.00369909 + 0.00640702i
\(126\) 0 0
\(127\) 168.353 + 97.1989i 1.32562 + 0.765346i 0.984618 0.174718i \(-0.0559014\pi\)
0.340999 + 0.940064i \(0.389235\pi\)
\(128\) 97.5137 82.9161i 0.761826 0.647782i
\(129\) 0 0
\(130\) −0.100885 0.256347i −0.000776039 0.00197190i
\(131\) −57.8214 68.9089i −0.441385 0.526022i 0.498786 0.866725i \(-0.333779\pi\)
−0.940171 + 0.340703i \(0.889335\pi\)
\(132\) 0 0
\(133\) −12.9103 + 4.69897i −0.0970701 + 0.0353306i
\(134\) −17.2517 84.9308i −0.128744 0.633812i
\(135\) 0 0
\(136\) −57.8431 + 39.6746i −0.425317 + 0.291725i
\(137\) 56.4129 20.5326i 0.411773 0.149873i −0.127823 0.991797i \(-0.540799\pi\)
0.539596 + 0.841924i \(0.318577\pi\)
\(138\) 0 0
\(139\) 57.0172 + 67.9505i 0.410196 + 0.488852i 0.931101 0.364762i \(-0.118850\pi\)
−0.520905 + 0.853615i \(0.674405\pi\)
\(140\) −0.0431351 + 0.0279739i −0.000308108 + 0.000199814i
\(141\) 0 0
\(142\) −54.5845 + 100.457i −0.384398 + 0.707445i
\(143\) −37.4530 21.6235i −0.261909 0.151213i
\(144\) 0 0
\(145\) 0.208008 + 0.360281i 0.00143454 + 0.00248470i
\(146\) 1.51101 + 58.4009i 0.0103494 + 0.400006i
\(147\) 0 0
\(148\) 213.789 11.0701i 1.44452 0.0747982i
\(149\) −132.507 48.2287i −0.889310 0.323682i −0.143349 0.989672i \(-0.545787\pi\)
−0.745961 + 0.665990i \(0.768009\pi\)
\(150\) 0 0
\(151\) −94.7076 16.6995i −0.627203 0.110593i −0.148993 0.988838i \(-0.547603\pi\)
−0.478210 + 0.878246i \(0.658714\pi\)
\(152\) −68.2251 + 142.692i −0.448849 + 0.938765i
\(153\) 0 0
\(154\) −2.56333 + 7.65302i −0.0166450 + 0.0496950i
\(155\) −0.374845 + 0.446722i −0.00241835 + 0.00288208i
\(156\) 0 0
\(157\) 14.7220 + 83.4925i 0.0937706 + 0.531799i 0.995117 + 0.0987008i \(0.0314687\pi\)
−0.901347 + 0.433099i \(0.857420\pi\)
\(158\) 210.497 + 167.544i 1.33226 + 1.06041i
\(159\) 0 0
\(160\) −0.129005 + 0.577628i −0.000806281 + 0.00361018i
\(161\) 7.73018 0.0480135
\(162\) 0 0
\(163\) 61.7577i 0.378882i −0.981892 0.189441i \(-0.939332\pi\)
0.981892 0.189441i \(-0.0606675\pi\)
\(164\) 164.682 153.376i 1.00416 0.935220i
\(165\) 0 0
\(166\) −224.640 178.802i −1.35326 1.07712i
\(167\) −295.731 + 52.1454i −1.77085 + 0.312248i −0.961443 0.275004i \(-0.911321\pi\)
−0.809404 + 0.587252i \(0.800210\pi\)
\(168\) 0 0
\(169\) −86.9751 72.9808i −0.514645 0.431839i
\(170\) 0.103007 0.307537i 0.000605926 0.00180904i
\(171\) 0 0
\(172\) −172.686 + 228.864i −1.00399 + 1.33061i
\(173\) −53.1023 + 301.158i −0.306950 + 1.74080i 0.307234 + 0.951634i \(0.400597\pi\)
−0.614183 + 0.789163i \(0.710514\pi\)
\(174\) 0 0
\(175\) −5.94183 + 16.3250i −0.0339533 + 0.0932860i
\(176\) 40.6260 + 83.5607i 0.230829 + 0.474777i
\(177\) 0 0
\(178\) 3.05758 + 118.176i 0.0171774 + 0.663911i
\(179\) 187.706 108.372i 1.04864 0.605431i 0.126369 0.991983i \(-0.459668\pi\)
0.922267 + 0.386553i \(0.126334\pi\)
\(180\) 0 0
\(181\) 15.1790 26.2908i 0.0838619 0.145253i −0.821044 0.570865i \(-0.806608\pi\)
0.904906 + 0.425612i \(0.139941\pi\)
\(182\) 4.94169 9.09468i 0.0271522 0.0499708i
\(183\) 0 0
\(184\) 63.5312 62.3149i 0.345278 0.338668i
\(185\) −0.758278 + 0.636271i −0.00409880 + 0.00343930i
\(186\) 0 0
\(187\) −17.4140 47.8444i −0.0931227 0.255853i
\(188\) 106.623 + 251.626i 0.567145 + 1.33844i
\(189\) 0 0
\(190\) −0.145580 0.716697i −0.000766212 0.00377209i
\(191\) 93.0062 + 255.533i 0.486944 + 1.33787i 0.903434 + 0.428727i \(0.141038\pi\)
−0.416491 + 0.909140i \(0.636740\pi\)
\(192\) 0 0
\(193\) 203.137 170.452i 1.05252 0.883172i 0.0591665 0.998248i \(-0.481156\pi\)
0.993357 + 0.115076i \(0.0367113\pi\)
\(194\) 27.9952 + 71.1352i 0.144305 + 0.366676i
\(195\) 0 0
\(196\) 185.553 + 56.8561i 0.946699 + 0.290082i
\(197\) −84.4497 + 146.271i −0.428678 + 0.742493i −0.996756 0.0804822i \(-0.974354\pi\)
0.568078 + 0.822975i \(0.307687\pi\)
\(198\) 0 0
\(199\) 104.097 60.1006i 0.523102 0.302013i −0.215101 0.976592i \(-0.569008\pi\)
0.738203 + 0.674579i \(0.235675\pi\)
\(200\) 82.7668 + 182.067i 0.413834 + 0.910337i
\(201\) 0 0
\(202\) 266.565 + 39.9236i 1.31963 + 0.197642i
\(203\) −5.34600 + 14.6880i −0.0263350 + 0.0723547i
\(204\) 0 0
\(205\) −0.180694 + 1.02477i −0.000881435 + 0.00499887i
\(206\) −73.8422 + 65.2889i −0.358457 + 0.316936i
\(207\) 0 0
\(208\) −32.7007 114.582i −0.157215 0.550873i
\(209\) −87.9484 73.7975i −0.420806 0.353098i
\(210\) 0 0
\(211\) −273.456 + 48.2177i −1.29600 + 0.228520i −0.778761 0.627321i \(-0.784151\pi\)
−0.517239 + 0.855841i \(0.673040\pi\)
\(212\) 74.8087 146.594i 0.352871 0.691479i
\(213\) 0 0
\(214\) 179.024 + 292.345i 0.836559 + 1.36610i
\(215\) 1.32569i 0.00616600i
\(216\) 0 0
\(217\) −21.9104 −0.100970
\(218\) 200.078 122.522i 0.917788 0.562026i
\(219\) 0 0
\(220\) −0.382673 0.195283i −0.00173942 0.000887651i
\(221\) 11.3385 + 64.3040i 0.0513056 + 0.290968i
\(222\) 0 0
\(223\) 23.5366 28.0498i 0.105545 0.125784i −0.710686 0.703510i \(-0.751615\pi\)
0.816231 + 0.577726i \(0.196060\pi\)
\(224\) −19.7409 + 10.2373i −0.0881289 + 0.0457020i
\(225\) 0 0
\(226\) 44.8014 + 50.6707i 0.198236 + 0.224206i
\(227\) −33.4702 5.90171i −0.147446 0.0259987i 0.0994379 0.995044i \(-0.468296\pi\)
−0.246884 + 0.969045i \(0.579407\pi\)
\(228\) 0 0
\(229\) −285.636 103.963i −1.24732 0.453986i −0.367823 0.929896i \(-0.619897\pi\)
−0.879494 + 0.475909i \(0.842119\pi\)
\(230\) −0.0609485 + 0.406945i −0.000264993 + 0.00176933i
\(231\) 0 0
\(232\) 74.4671 + 163.810i 0.320979 + 0.706078i
\(233\) 49.9878 + 86.5815i 0.214540 + 0.371594i 0.953130 0.302560i \(-0.0978414\pi\)
−0.738590 + 0.674155i \(0.764508\pi\)
\(234\) 0 0
\(235\) −1.09434 0.631819i −0.00465678 0.00268859i
\(236\) 59.6081 194.534i 0.252577 0.824297i
\(237\) 0 0
\(238\) 11.3392 4.46255i 0.0476439 0.0187502i
\(239\) −83.2205 99.1783i −0.348203 0.414972i 0.563309 0.826247i \(-0.309528\pi\)
−0.911511 + 0.411275i \(0.865084\pi\)
\(240\) 0 0
\(241\) 55.8840 20.3401i 0.231884 0.0843987i −0.223465 0.974712i \(-0.571737\pi\)
0.455349 + 0.890313i \(0.349515\pi\)
\(242\) 171.062 34.7473i 0.706869 0.143584i
\(243\) 0 0
\(244\) 139.089 58.9370i 0.570035 0.241545i
\(245\) −0.843235 + 0.306912i −0.00344178 + 0.00125270i
\(246\) 0 0
\(247\) 94.6417 + 112.790i 0.383165 + 0.456638i
\(248\) −180.073 + 176.625i −0.726099 + 0.712198i
\(249\) 0 0
\(250\) −1.62514 0.883035i −0.00650055 0.00353214i
\(251\) 178.915 + 103.297i 0.712810 + 0.411541i 0.812101 0.583517i \(-0.198324\pi\)
−0.0992905 + 0.995058i \(0.531657\pi\)
\(252\) 0 0
\(253\) 32.2985 + 55.9427i 0.127662 + 0.221117i
\(254\) −388.665 + 10.0560i −1.53018 + 0.0395904i
\(255\) 0 0
\(256\) −79.7171 + 243.272i −0.311395 + 0.950281i
\(257\) −5.94379 2.16336i −0.0231276 0.00841775i 0.330430 0.943830i \(-0.392806\pi\)
−0.353558 + 0.935413i \(0.615028\pi\)
\(258\) 0 0
\(259\) −36.6262 6.45820i −0.141414 0.0249351i
\(260\) 0.439815 + 0.331856i 0.00169160 + 0.00127637i
\(261\) 0 0
\(262\) 170.593 + 57.1391i 0.651120 + 0.218088i
\(263\) 110.483 131.668i 0.420087 0.500640i −0.513948 0.857821i \(-0.671818\pi\)
0.934035 + 0.357181i \(0.116262\pi\)
\(264\) 0 0
\(265\) 0.132145 + 0.749432i 0.000498661 + 0.00282805i
\(266\) 17.1120 21.4990i 0.0643310 0.0808232i
\(267\) 0 0
\(268\) 118.132 + 126.840i 0.440790 + 0.473283i
\(269\) −219.984 −0.817785 −0.408893 0.912582i \(-0.634085\pi\)
−0.408893 + 0.912582i \(0.634085\pi\)
\(270\) 0 0
\(271\) 250.774i 0.925365i −0.886524 0.462682i \(-0.846887\pi\)
0.886524 0.462682i \(-0.153113\pi\)
\(272\) 57.2189 128.084i 0.210364 0.470898i
\(273\) 0 0
\(274\) −74.7727 + 93.9419i −0.272893 + 0.342853i
\(275\) −142.969 + 25.2094i −0.519889 + 0.0916704i
\(276\) 0 0
\(277\) 25.4939 + 21.3919i 0.0920358 + 0.0772272i 0.687645 0.726047i \(-0.258645\pi\)
−0.595609 + 0.803275i \(0.703089\pi\)
\(278\) −168.221 56.3444i −0.605111 0.202678i
\(279\) 0 0
\(280\) 0.0443537 0.0927655i 0.000158406 0.000331305i
\(281\) −27.5612 + 156.307i −0.0980826 + 0.556254i 0.895677 + 0.444706i \(0.146692\pi\)
−0.993759 + 0.111548i \(0.964419\pi\)
\(282\) 0 0
\(283\) −120.497 + 331.063i −0.425785 + 1.16984i 0.522562 + 0.852601i \(0.324976\pi\)
−0.948347 + 0.317234i \(0.897246\pi\)
\(284\) −11.8242 228.352i −0.0416346 0.804056i
\(285\) 0 0
\(286\) 86.4650 2.23711i 0.302325 0.00782207i
\(287\) −33.8588 + 19.5484i −0.117975 + 0.0681128i
\(288\) 0 0
\(289\) 106.063 183.707i 0.367001 0.635664i
\(290\) −0.731081 0.397240i −0.00252097 0.00136979i
\(291\) 0 0
\(292\) −63.5748 98.0308i −0.217722 0.335722i
\(293\) −21.2865 + 17.8615i −0.0726503 + 0.0609608i −0.678390 0.734702i \(-0.737322\pi\)
0.605739 + 0.795663i \(0.292877\pi\)
\(294\) 0 0
\(295\) 0.321767 + 0.884049i 0.00109074 + 0.00299678i
\(296\) −353.077 + 242.176i −1.19283 + 0.818162i
\(297\) 0 0
\(298\) 276.378 56.1398i 0.927444 0.188389i
\(299\) −28.3338 77.8465i −0.0947619 0.260356i
\(300\) 0 0
\(301\) 38.1560 32.0167i 0.126764 0.106368i
\(302\) 178.976 70.4359i 0.592636 0.233231i
\(303\) 0 0
\(304\) −32.6717 314.636i −0.107473 1.03499i
\(305\) −0.349243 + 0.604907i −0.00114506 + 0.00198330i
\(306\) 0 0
\(307\) 345.391 199.412i 1.12505 0.649549i 0.182366 0.983231i \(-0.441624\pi\)
0.942686 + 0.333681i \(0.108291\pi\)
\(308\) −3.62128 15.7304i −0.0117574 0.0510726i
\(309\) 0 0
\(310\) 0.172752 1.15344i 0.000557265 0.00372079i
\(311\) 82.2845 226.075i 0.264580 0.726928i −0.734264 0.678864i \(-0.762473\pi\)
0.998844 0.0480643i \(-0.0153052\pi\)
\(312\) 0 0
\(313\) 21.6287 122.662i 0.0691012 0.391892i −0.930567 0.366122i \(-0.880685\pi\)
0.999668 0.0257700i \(-0.00820376\pi\)
\(314\) −112.315 127.029i −0.357690 0.404550i
\(315\) 0 0
\(316\) −534.019 65.9083i −1.68993 0.208570i
\(317\) −300.212 251.908i −0.947043 0.794663i 0.0317545 0.999496i \(-0.489891\pi\)
−0.978797 + 0.204833i \(0.934335\pi\)
\(318\) 0 0
\(319\) −128.633 + 22.6814i −0.403237 + 0.0711016i
\(320\) −0.383280 1.11995i −0.00119775 0.00349984i
\(321\) 0 0
\(322\) −13.1847 + 8.07390i −0.0409461 + 0.0250742i
\(323\) 173.343i 0.536664i
\(324\) 0 0
\(325\) 186.180 0.572861
\(326\) 64.5037 + 105.334i 0.197864 + 0.323112i
\(327\) 0 0
\(328\) −120.687 + 433.604i −0.367949 + 1.32196i
\(329\) −8.24440 46.7563i −0.0250590 0.142117i
\(330\) 0 0
\(331\) 30.9734 36.9126i 0.0935751 0.111518i −0.717225 0.696842i \(-0.754588\pi\)
0.810800 + 0.585323i \(0.199032\pi\)
\(332\) 569.900 + 70.3368i 1.71657 + 0.211858i
\(333\) 0 0
\(334\) 449.938 397.820i 1.34712 1.19108i
\(335\) −0.789286 0.139172i −0.00235608 0.000415440i
\(336\) 0 0
\(337\) −534.338 194.483i −1.58557 0.577101i −0.609166 0.793043i \(-0.708496\pi\)
−0.976406 + 0.215941i \(0.930718\pi\)
\(338\) 224.571 + 33.6342i 0.664411 + 0.0995093i
\(339\) 0 0
\(340\) 0.145521 + 0.632125i 0.000428004 + 0.00185919i
\(341\) −91.5468 158.564i −0.268466 0.464996i
\(342\) 0 0
\(343\) −58.6875 33.8833i −0.171101 0.0987850i
\(344\) 55.4942 570.717i 0.161320 1.65906i
\(345\) 0 0
\(346\) −223.977 569.121i −0.647332 1.64486i
\(347\) −74.5764 88.8767i −0.214918 0.256129i 0.647805 0.761806i \(-0.275687\pi\)
−0.862723 + 0.505677i \(0.831243\pi\)
\(348\) 0 0
\(349\) −155.510 + 56.6009i −0.445587 + 0.162180i −0.555062 0.831809i \(-0.687305\pi\)
0.109475 + 0.993990i \(0.465083\pi\)
\(350\) −6.91649 34.0501i −0.0197614 0.0972861i
\(351\) 0 0
\(352\) −156.568 100.089i −0.444796 0.284345i
\(353\) 603.473 219.646i 1.70956 0.622227i 0.712700 0.701469i \(-0.247472\pi\)
0.996855 + 0.0792417i \(0.0252499\pi\)
\(354\) 0 0
\(355\) 0.679613 + 0.809932i 0.00191440 + 0.00228150i
\(356\) −128.646 198.369i −0.361365 0.557215i
\(357\) 0 0
\(358\) −206.962 + 380.892i −0.578106 + 1.06394i
\(359\) 284.704 + 164.374i 0.793046 + 0.457866i 0.841034 0.540982i \(-0.181947\pi\)
−0.0479875 + 0.998848i \(0.515281\pi\)
\(360\) 0 0
\(361\) 14.9356 + 25.8692i 0.0413728 + 0.0716599i
\(362\) 1.57038 + 60.6957i 0.00433807 + 0.167668i
\(363\) 0 0
\(364\) 1.07048 + 20.6734i 0.00294089 + 0.0567950i
\(365\) 0.507679 + 0.184780i 0.00139090 + 0.000506246i
\(366\) 0 0
\(367\) 108.149 + 19.0695i 0.294683 + 0.0519605i 0.319035 0.947743i \(-0.396641\pi\)
−0.0243522 + 0.999703i \(0.507752\pi\)
\(368\) −43.2736 + 172.641i −0.117591 + 0.469133i
\(369\) 0 0
\(370\) 0.628762 1.87722i 0.00169936 0.00507357i
\(371\) −18.3787 + 21.9029i −0.0495383 + 0.0590374i
\(372\) 0 0
\(373\) 121.587 + 689.555i 0.325971 + 1.84867i 0.502763 + 0.864425i \(0.332317\pi\)
−0.176792 + 0.984248i \(0.556572\pi\)
\(374\) 79.6732 + 63.4156i 0.213030 + 0.169560i
\(375\) 0 0
\(376\) −444.672 317.811i −1.18264 0.845242i
\(377\) 167.510 0.444323
\(378\) 0 0
\(379\) 138.113i 0.364413i −0.983260 0.182207i \(-0.941676\pi\)
0.983260 0.182207i \(-0.0583239\pi\)
\(380\) 0.996866 + 1.07035i 0.00262333 + 0.00281671i
\(381\) 0 0
\(382\) −425.527 338.696i −1.11394 0.886640i
\(383\) −37.4599 + 6.60520i −0.0978067 + 0.0172460i −0.222337 0.974970i \(-0.571369\pi\)
0.124531 + 0.992216i \(0.460257\pi\)
\(384\) 0 0
\(385\) 0.0571760 + 0.0479764i 0.000148509 + 0.000124614i
\(386\) −168.441 + 502.894i −0.436375 + 1.30283i
\(387\) 0 0
\(388\) −122.047 92.0887i −0.314554 0.237342i
\(389\) 7.82254 44.3639i 0.0201094 0.114046i −0.973101 0.230380i \(-0.926003\pi\)
0.993210 + 0.116334i \(0.0371143\pi\)
\(390\) 0 0
\(391\) 33.3576 91.6493i 0.0853136 0.234397i
\(392\) −375.865 + 96.8291i −0.958838 + 0.247013i
\(393\) 0 0
\(394\) −8.73695 337.686i −0.0221750 0.857070i
\(395\) 2.15466 1.24399i 0.00545483 0.00314935i
\(396\) 0 0
\(397\) −348.887 + 604.290i −0.878809 + 1.52214i −0.0261596 + 0.999658i \(0.508328\pi\)
−0.852649 + 0.522484i \(0.825006\pi\)
\(398\) −114.776 + 211.234i −0.288382 + 0.530738i
\(399\) 0 0
\(400\) −331.330 224.089i −0.828326 0.560222i
\(401\) 462.311 387.925i 1.15289 0.967394i 0.153112 0.988209i \(-0.451071\pi\)
0.999783 + 0.0208151i \(0.00662614\pi\)
\(402\) 0 0
\(403\) 80.3092 + 220.648i 0.199279 + 0.547513i
\(404\) −496.354 + 210.324i −1.22860 + 0.520603i
\(405\) 0 0
\(406\) −6.22292 30.6357i −0.0153274 0.0754573i
\(407\) −106.296 292.045i −0.261169 0.717555i
\(408\) 0 0
\(409\) 512.307 429.876i 1.25258 1.05104i 0.256152 0.966637i \(-0.417545\pi\)
0.996431 0.0844058i \(-0.0268992\pi\)
\(410\) −0.762140 1.93658i −0.00185888 0.00472337i
\(411\) 0 0
\(412\) 57.7539 188.483i 0.140179 0.457482i
\(413\) −17.6737 + 30.6117i −0.0427934 + 0.0741204i
\(414\) 0 0
\(415\) −2.29943 + 1.32758i −0.00554080 + 0.00319898i
\(416\) 175.451 + 161.277i 0.421757 + 0.387684i
\(417\) 0 0
\(418\) 227.084 + 34.0106i 0.543264 + 0.0813650i
\(419\) −114.302 + 314.043i −0.272798 + 0.749507i 0.725333 + 0.688398i \(0.241686\pi\)
−0.998131 + 0.0611085i \(0.980536\pi\)
\(420\) 0 0
\(421\) −86.2197 + 488.976i −0.204797 + 1.16146i 0.692961 + 0.720975i \(0.256306\pi\)
−0.897758 + 0.440488i \(0.854805\pi\)
\(422\) 416.047 367.855i 0.985893 0.871695i
\(423\) 0 0
\(424\) 25.5175 + 328.166i 0.0601828 + 0.773977i
\(425\) 167.910 + 140.893i 0.395082 + 0.331513i
\(426\) 0 0
\(427\) −25.8450 + 4.55717i −0.0605269 + 0.0106725i
\(428\) −610.688 311.642i −1.42684 0.728136i
\(429\) 0 0
\(430\) 1.38464 + 2.26111i 0.00322008 + 0.00525839i
\(431\) 406.367i 0.942847i 0.881907 + 0.471424i \(0.156260\pi\)
−0.881907 + 0.471424i \(0.843740\pi\)
\(432\) 0 0
\(433\) 313.745 0.724584 0.362292 0.932065i \(-0.381994\pi\)
0.362292 + 0.932065i \(0.381994\pi\)
\(434\) 37.3705 22.8846i 0.0861072 0.0527295i
\(435\) 0 0
\(436\) −213.284 + 417.948i −0.489184 + 0.958596i
\(437\) −38.1893 216.583i −0.0873898 0.495612i
\(438\) 0 0
\(439\) −291.034 + 346.841i −0.662948 + 0.790070i −0.987806 0.155693i \(-0.950239\pi\)
0.324858 + 0.945763i \(0.394683\pi\)
\(440\) 0.856656 0.0666118i 0.00194695 0.000151390i
\(441\) 0 0
\(442\) −86.5023 97.8347i −0.195706 0.221345i
\(443\) −230.762 40.6896i −0.520908 0.0918502i −0.0929890 0.995667i \(-0.529642\pi\)
−0.427919 + 0.903817i \(0.640753\pi\)
\(444\) 0 0
\(445\) 1.02730 + 0.373908i 0.00230855 + 0.000840243i
\(446\) −10.8472 + 72.4251i −0.0243210 + 0.162388i
\(447\) 0 0
\(448\) 22.9777 38.0794i 0.0512896 0.0849986i
\(449\) 80.2533 + 139.003i 0.178738 + 0.309583i 0.941449 0.337157i \(-0.109465\pi\)
−0.762711 + 0.646740i \(0.776132\pi\)
\(450\) 0 0
\(451\) −282.940 163.355i −0.627361 0.362207i
\(452\) −129.337 39.6308i −0.286144 0.0876788i
\(453\) 0 0
\(454\) 63.2512 24.8925i 0.139320 0.0548292i
\(455\) −0.0615274 0.0733255i −0.000135225 0.000161155i
\(456\) 0 0
\(457\) 85.8747 31.2559i 0.187910 0.0683935i −0.246351 0.969181i \(-0.579232\pi\)
0.434261 + 0.900787i \(0.357010\pi\)
\(458\) 595.768 121.016i 1.30080 0.264228i
\(459\) 0 0
\(460\) −0.321086 0.757747i −0.000698012 0.00164728i
\(461\) 124.007 45.1350i 0.268997 0.0979068i −0.204000 0.978971i \(-0.565394\pi\)
0.472997 + 0.881064i \(0.343172\pi\)
\(462\) 0 0
\(463\) −143.224 170.688i −0.309339 0.368656i 0.588867 0.808230i \(-0.299574\pi\)
−0.898207 + 0.439574i \(0.855130\pi\)
\(464\) −298.105 201.617i −0.642468 0.434520i
\(465\) 0 0
\(466\) −175.691 95.4635i −0.377019 0.204857i
\(467\) −385.006 222.284i −0.824425 0.475982i 0.0275151 0.999621i \(-0.491241\pi\)
−0.851940 + 0.523639i \(0.824574\pi\)
\(468\) 0 0
\(469\) −15.0563 26.0783i −0.0321031 0.0556042i
\(470\) 2.52643 0.0653664i 0.00537538 0.000139077i
\(471\) 0 0
\(472\) 101.516 + 394.057i 0.215076 + 0.834866i
\(473\) 391.127 + 142.358i 0.826906 + 0.300969i
\(474\) 0 0
\(475\) 486.746 + 85.8264i 1.02473 + 0.180687i
\(476\) −14.6793 + 19.4548i −0.0308389 + 0.0408714i
\(477\) 0 0
\(478\) 245.530 + 82.2384i 0.513660 + 0.172047i
\(479\) 365.461 435.539i 0.762966 0.909268i −0.235065 0.971980i \(-0.575530\pi\)
0.998032 + 0.0627117i \(0.0199749\pi\)
\(480\) 0 0
\(481\) 69.2109 + 392.515i 0.143890 + 0.816039i
\(482\) −74.0716 + 93.0610i −0.153675 + 0.193073i
\(483\) 0 0
\(484\) −255.473 + 237.934i −0.527837 + 0.491599i
\(485\) 0.706954 0.00145764
\(486\) 0 0
\(487\) 927.501i 1.90452i 0.305288 + 0.952260i \(0.401247\pi\)
−0.305288 + 0.952260i \(0.598753\pi\)
\(488\) −175.673 + 245.796i −0.359985 + 0.503681i
\(489\) 0 0
\(490\) 1.11767 1.40420i 0.00228096 0.00286572i
\(491\) 538.209 94.9007i 1.09615 0.193281i 0.403802 0.914846i \(-0.367688\pi\)
0.692346 + 0.721566i \(0.256577\pi\)
\(492\) 0 0
\(493\) 151.072 + 126.765i 0.306435 + 0.257129i
\(494\) −279.226 93.5249i −0.565235 0.189322i
\(495\) 0 0
\(496\) 122.655 489.332i 0.247287 0.986557i
\(497\) −6.89813 + 39.1212i −0.0138795 + 0.0787147i
\(498\) 0 0
\(499\) 263.489 723.929i 0.528034 1.45076i −0.333349 0.942804i \(-0.608179\pi\)
0.861382 0.507957i \(-0.169599\pi\)
\(500\) 3.69414 0.191285i 0.00738829 0.000382571i
\(501\) 0 0
\(502\) −413.049 + 10.6868i −0.822807 + 0.0212885i
\(503\) −367.090 + 211.939i −0.729801 + 0.421351i −0.818349 0.574721i \(-0.805111\pi\)
0.0885483 + 0.996072i \(0.471777\pi\)
\(504\) 0 0
\(505\) 1.24632 2.15868i 0.00246795 0.00427462i
\(506\) −113.519 61.6816i −0.224345 0.121900i
\(507\) 0 0
\(508\) 652.407 423.099i 1.28427 0.832871i
\(509\) −530.899 + 445.477i −1.04302 + 0.875200i −0.992343 0.123514i \(-0.960583\pi\)
−0.0506806 + 0.998715i \(0.516139\pi\)
\(510\) 0 0
\(511\) 6.94259 + 19.0746i 0.0135863 + 0.0373280i
\(512\) −118.123 498.188i −0.230708 0.973023i
\(513\) 0 0
\(514\) 12.3973 2.51823i 0.0241193 0.00489928i
\(515\) 0.311758 + 0.856549i 0.000605356 + 0.00166320i
\(516\) 0 0
\(517\) 303.925 255.023i 0.587862 0.493275i
\(518\) 69.2153 27.2396i 0.133620 0.0525862i
\(519\) 0 0
\(520\) −1.09676 0.106645i −0.00210916 0.000205086i
\(521\) 304.376 527.195i 0.584215 1.01189i −0.410758 0.911744i \(-0.634736\pi\)
0.994973 0.100145i \(-0.0319308\pi\)
\(522\) 0 0
\(523\) −522.353 + 301.581i −0.998762 + 0.576636i −0.907882 0.419226i \(-0.862301\pi\)
−0.0908806 + 0.995862i \(0.528968\pi\)
\(524\) −350.645 + 80.7218i −0.669170 + 0.154049i
\(525\) 0 0
\(526\) −50.9175 + 339.970i −0.0968013 + 0.646330i
\(527\) −94.5487 + 259.770i −0.179409 + 0.492923i
\(528\) 0 0
\(529\) 70.3727 399.103i 0.133030 0.754448i
\(530\) −1.00814 1.14022i −0.00190216 0.00215135i
\(531\) 0 0
\(532\) −6.73150 + 54.5417i −0.0126532 + 0.102522i
\(533\) 320.965 + 269.322i 0.602186 + 0.505294i
\(534\) 0 0
\(535\) 3.12203 0.550498i 0.00583557 0.00102897i
\(536\) −333.966 92.9544i −0.623071 0.173422i
\(537\) 0 0
\(538\) 375.207 229.766i 0.697410 0.427074i
\(539\) 281.742i 0.522713i
\(540\) 0 0
\(541\) 406.606 0.751582 0.375791 0.926705i \(-0.377371\pi\)
0.375791 + 0.926705i \(0.377371\pi\)
\(542\) 261.924 + 427.722i 0.483255 + 0.789154i
\(543\) 0 0
\(544\) 36.1866 + 278.225i 0.0665194 + 0.511442i
\(545\) −0.376754 2.13668i −0.000691292 0.00392051i
\(546\) 0 0
\(547\) 342.420 408.080i 0.625996 0.746032i −0.356093 0.934450i \(-0.615892\pi\)
0.982089 + 0.188418i \(0.0603359\pi\)
\(548\) 29.4140 238.325i 0.0536751 0.434900i
\(549\) 0 0
\(550\) 217.519 192.324i 0.395490 0.349679i
\(551\) 437.936 + 77.2199i 0.794802 + 0.140145i
\(552\) 0 0
\(553\) 87.8415 + 31.9717i 0.158845 + 0.0578150i
\(554\) −65.8257 9.85876i −0.118819 0.0177956i
\(555\) 0 0
\(556\) 345.768 79.5992i 0.621885 0.143164i
\(557\) −42.5317 73.6671i −0.0763586 0.132257i 0.825318 0.564669i \(-0.190996\pi\)
−0.901676 + 0.432412i \(0.857663\pi\)
\(558\) 0 0
\(559\) −462.278 266.896i −0.826973 0.477453i
\(560\) 0.0212402 + 0.204547i 3.79289e−5 + 0.000365263i
\(561\) 0 0
\(562\) −116.249 295.386i −0.206848 0.525597i
\(563\) 670.430 + 798.988i 1.19082 + 1.41916i 0.884060 + 0.467373i \(0.154800\pi\)
0.306758 + 0.951788i \(0.400756\pi\)
\(564\) 0 0
\(565\) 0.587766 0.213929i 0.00104029 0.000378636i
\(566\) −140.263 690.519i −0.247814 1.22000i
\(567\) 0 0
\(568\) 258.673 + 377.129i 0.455410 + 0.663959i
\(569\) −233.686 + 85.0548i −0.410696 + 0.149481i −0.539102 0.842241i \(-0.681236\pi\)
0.128406 + 0.991722i \(0.459014\pi\)
\(570\) 0 0
\(571\) 4.43075 + 5.28036i 0.00775963 + 0.00924757i 0.769910 0.638152i \(-0.220301\pi\)
−0.762151 + 0.647400i \(0.775856\pi\)
\(572\) −145.139 + 94.1252i −0.253739 + 0.164555i
\(573\) 0 0
\(574\) 37.3322 68.7061i 0.0650387 0.119697i
\(575\) −240.835 139.046i −0.418844 0.241819i
\(576\) 0 0
\(577\) −489.126 847.191i −0.847705 1.46827i −0.883251 0.468901i \(-0.844650\pi\)
0.0355453 0.999368i \(-0.488683\pi\)
\(578\) 10.9730 + 424.111i 0.0189845 + 0.733756i
\(579\) 0 0
\(580\) 1.66184 0.0860512i 0.00286524 0.000148364i
\(581\) −93.7437 34.1199i −0.161349 0.0587262i
\(582\) 0 0
\(583\) −235.300 41.4897i −0.403602 0.0711659i
\(584\) 210.823 + 100.800i 0.360999 + 0.172604i
\(585\) 0 0
\(586\) 17.6508 52.6978i 0.0301207 0.0899279i
\(587\) −222.285 + 264.909i −0.378680 + 0.451293i −0.921397 0.388623i \(-0.872951\pi\)
0.542717 + 0.839915i \(0.317395\pi\)
\(588\) 0 0
\(589\) 108.244 + 613.881i 0.183775 + 1.04224i
\(590\) −1.47217 1.17177i −0.00249520 0.00198604i
\(591\) 0 0
\(592\) 349.267 781.833i 0.589978 1.32066i
\(593\) 555.768 0.937214 0.468607 0.883407i \(-0.344756\pi\)
0.468607 + 0.883407i \(0.344756\pi\)
\(594\) 0 0
\(595\) 0.112691i 0.000189397i
\(596\) −412.757 + 384.420i −0.692545 + 0.644999i
\(597\) 0 0
\(598\) 129.634 + 103.182i 0.216780 + 0.172545i
\(599\) 873.003 153.934i 1.45743 0.256985i 0.611912 0.790926i \(-0.290401\pi\)
0.845522 + 0.533941i \(0.179290\pi\)
\(600\) 0 0
\(601\) 417.266 + 350.128i 0.694287 + 0.582576i 0.920142 0.391585i \(-0.128073\pi\)
−0.225855 + 0.974161i \(0.572518\pi\)
\(602\) −31.6389 + 94.4604i −0.0525563 + 0.156911i
\(603\) 0 0
\(604\) −231.695 + 307.070i −0.383601 + 0.508394i
\(605\) 0.280313 1.58973i 0.000463327 0.00262766i
\(606\) 0 0
\(607\) 334.605 919.318i 0.551243 1.51453i −0.280772 0.959775i \(-0.590590\pi\)
0.832015 0.554753i \(-0.187187\pi\)
\(608\) 384.351 + 502.520i 0.632156 + 0.826514i
\(609\) 0 0
\(610\) −0.0361319 1.39651i −5.92326e−5 0.00228935i
\(611\) −440.639 + 254.403i −0.721177 + 0.416372i
\(612\) 0 0
\(613\) 113.985 197.428i 0.185947 0.322069i −0.757949 0.652314i \(-0.773798\pi\)
0.943895 + 0.330245i \(0.107132\pi\)
\(614\) −380.823 + 700.866i −0.620233 + 1.14148i
\(615\) 0 0
\(616\) 22.6063 + 23.0475i 0.0366985 + 0.0374148i
\(617\) −490.000 + 411.159i −0.794165 + 0.666384i −0.946773 0.321903i \(-0.895677\pi\)
0.152607 + 0.988287i \(0.451233\pi\)
\(618\) 0 0
\(619\) 294.399 + 808.856i 0.475605 + 1.30671i 0.913189 + 0.407536i \(0.133612\pi\)
−0.437584 + 0.899178i \(0.644166\pi\)
\(620\) 0.910084 + 2.14776i 0.00146788 + 0.00346412i
\(621\) 0 0
\(622\) 95.7819 + 471.538i 0.153990 + 0.758099i
\(623\) 14.0486 + 38.5981i 0.0225498 + 0.0619552i
\(624\) 0 0
\(625\) 478.758 401.726i 0.766013 0.642761i
\(626\) 91.2264 + 231.804i 0.145729 + 0.370294i
\(627\) 0 0
\(628\) 324.242 + 99.3525i 0.516309 + 0.158205i
\(629\) −234.620 + 406.373i −0.373004 + 0.646063i
\(630\) 0 0
\(631\) −901.462 + 520.459i −1.42862 + 0.824817i −0.997012 0.0772427i \(-0.975388\pi\)
−0.431612 + 0.902059i \(0.642055\pi\)
\(632\) 979.665 445.350i 1.55010 0.704667i
\(633\) 0 0
\(634\) 775.154 + 116.095i 1.22264 + 0.183116i
\(635\) −1.22973 + 3.37867i −0.00193659 + 0.00532073i
\(636\) 0 0
\(637\) −62.7427 + 355.831i −0.0984972 + 0.558605i
\(638\) 195.707 173.038i 0.306750 0.271219i
\(639\) 0 0
\(640\) 1.82347 + 1.50987i 0.00284917 + 0.00235917i
\(641\) −207.258 173.910i −0.323336 0.271311i 0.466642 0.884446i \(-0.345464\pi\)
−0.789978 + 0.613135i \(0.789908\pi\)
\(642\) 0 0
\(643\) 326.145 57.5082i 0.507224 0.0894373i 0.0858206 0.996311i \(-0.472649\pi\)
0.421403 + 0.906873i \(0.361538\pi\)
\(644\) 14.0549 27.5418i 0.0218244 0.0427667i
\(645\) 0 0
\(646\) −181.050 295.654i −0.280263 0.457669i
\(647\) 302.985i 0.468293i −0.972201 0.234146i \(-0.924771\pi\)
0.972201 0.234146i \(-0.0752295\pi\)
\(648\) 0 0
\(649\) −295.379 −0.455129
\(650\) −317.549 + 194.458i −0.488537 + 0.299166i
\(651\) 0 0
\(652\) −220.036 112.287i −0.337478 0.172220i
\(653\) 108.363 + 614.557i 0.165946 + 0.941129i 0.948083 + 0.318022i \(0.103019\pi\)
−0.782137 + 0.623107i \(0.785870\pi\)
\(654\) 0 0
\(655\) 1.06944 1.27451i 0.00163273 0.00194582i
\(656\) −247.039 865.611i −0.376584 1.31953i
\(657\) 0 0
\(658\) 62.8970 + 71.1370i 0.0955882 + 0.108111i
\(659\) −969.694 170.983i −1.47146 0.259459i −0.620302 0.784363i \(-0.712990\pi\)
−0.851161 + 0.524904i \(0.824101\pi\)
\(660\) 0 0
\(661\) −708.366 257.824i −1.07166 0.390052i −0.254862 0.966978i \(-0.582030\pi\)
−0.816797 + 0.576926i \(0.804252\pi\)
\(662\) −14.2745 + 95.3090i −0.0215627 + 0.143971i
\(663\) 0 0
\(664\) −1045.49 + 475.274i −1.57453 + 0.715773i
\(665\) −0.127054 0.220065i −0.000191059 0.000330924i
\(666\) 0 0
\(667\) −216.685 125.103i −0.324864 0.187561i
\(668\) −351.908 + 1148.47i −0.526808 + 1.71926i
\(669\) 0 0
\(670\) 1.49157 0.587007i 0.00222623 0.000876130i
\(671\) −140.966 167.997i −0.210084 0.250368i
\(672\) 0 0
\(673\) 120.292 43.7828i 0.178740 0.0650562i −0.251100 0.967961i \(-0.580792\pi\)
0.429840 + 0.902905i \(0.358570\pi\)
\(674\) 1114.50 226.385i 1.65356 0.335883i
\(675\) 0 0
\(676\) −418.160 + 177.190i −0.618579 + 0.262115i
\(677\) −795.059 + 289.378i −1.17439 + 0.427441i −0.854216 0.519919i \(-0.825962\pi\)
−0.320170 + 0.947360i \(0.603740\pi\)
\(678\) 0 0
\(679\) 17.0736 + 20.3475i 0.0251452 + 0.0299669i
\(680\) −0.908434 0.926165i −0.00133593 0.00136201i
\(681\) 0 0
\(682\) 321.757 + 174.830i 0.471784 + 0.256349i
\(683\) −709.493 409.626i −1.03879 0.599745i −0.119299 0.992858i \(-0.538065\pi\)
−0.919490 + 0.393113i \(0.871398\pi\)
\(684\) 0 0
\(685\) 0.555176 + 0.961594i 0.000810476 + 0.00140379i
\(686\) 135.488 3.50548i 0.197504 0.00511003i
\(687\) 0 0
\(688\) 501.442 + 1031.38i 0.728840 + 1.49910i
\(689\) 287.936 + 104.800i 0.417905 + 0.152105i
\(690\) 0 0
\(691\) 540.831 + 95.3631i 0.782679 + 0.138007i 0.550689 0.834711i \(-0.314365\pi\)
0.231990 + 0.972718i \(0.425476\pi\)
\(692\) 976.443 + 736.760i 1.41104 + 1.06468i
\(693\) 0 0
\(694\) 220.027 + 73.6964i 0.317041 + 0.106191i
\(695\) −1.05457 + 1.25678i −0.00151736 + 0.00180832i
\(696\) 0 0
\(697\) 85.6573 + 485.787i 0.122894 + 0.696968i
\(698\) 206.121 258.963i 0.295302 0.371008i
\(699\) 0 0
\(700\) 47.3610 + 50.8521i 0.0676585 + 0.0726459i
\(701\) −378.016 −0.539253 −0.269626 0.962965i \(-0.586900\pi\)
−0.269626 + 0.962965i \(0.586900\pi\)
\(702\) 0 0
\(703\) 1058.09i 1.50511i
\(704\) 371.583 + 7.18337i 0.527817 + 0.0102036i
\(705\) 0 0
\(706\) −799.875 + 1004.94i −1.13297 + 1.42342i
\(707\) 92.2309 16.2628i 0.130454 0.0230025i
\(708\) 0 0
\(709\) −658.239 552.328i −0.928404 0.779024i 0.0471258 0.998889i \(-0.484994\pi\)
−0.975530 + 0.219865i \(0.929438\pi\)
\(710\) −2.00510 0.671594i −0.00282408 0.000945906i
\(711\) 0 0
\(712\) 426.608 + 203.973i 0.599169 + 0.286479i
\(713\) 60.9033 345.400i 0.0854184 0.484432i
\(714\) 0 0
\(715\) 0.273574 0.751639i 0.000382621 0.00105124i
\(716\) −44.8326 865.817i −0.0626154 1.20924i
\(717\) 0 0
\(718\) −657.275 + 17.0057i −0.915425 + 0.0236848i
\(719\) −464.412 + 268.129i −0.645914 + 0.372919i −0.786889 0.617094i \(-0.788310\pi\)
0.140975 + 0.990013i \(0.454976\pi\)
\(720\) 0 0
\(721\) −17.1239 + 29.6595i −0.0237502 + 0.0411366i
\(722\) −52.4937 28.5230i −0.0727060 0.0395056i
\(723\) 0 0
\(724\) −66.0729 101.883i −0.0912609 0.140722i
\(725\) 430.755 361.446i 0.594145 0.498547i
\(726\) 0 0
\(727\) −169.632 466.059i −0.233331 0.641071i 0.766669 0.642043i \(-0.221913\pi\)
−1.00000 0.000971702i \(0.999691\pi\)
\(728\) −23.4184 34.1426i −0.0321681 0.0468991i
\(729\) 0 0
\(730\) −1.05890 + 0.215090i −0.00145054 + 0.000294644i
\(731\) −214.938 590.539i −0.294033 0.807850i
\(732\) 0 0
\(733\) 246.754 207.051i 0.336635 0.282471i −0.458762 0.888559i \(-0.651707\pi\)
0.795397 + 0.606089i \(0.207262\pi\)
\(734\) −204.376 + 80.4322i −0.278442 + 0.109581i
\(735\) 0 0
\(736\) −106.509 339.655i −0.144714 0.461488i
\(737\) 125.818 217.923i 0.170716 0.295689i
\(738\) 0 0
\(739\) 163.942 94.6517i 0.221842 0.128081i −0.384961 0.922933i \(-0.625785\pi\)
0.606803 + 0.794852i \(0.292452\pi\)
\(740\) 0.888269 + 3.85852i 0.00120036 + 0.00521422i
\(741\) 0 0
\(742\) 8.47007 56.5536i 0.0114152 0.0762178i
\(743\) 215.502 592.087i 0.290043 0.796886i −0.706016 0.708196i \(-0.749509\pi\)
0.996059 0.0886907i \(-0.0282683\pi\)
\(744\) 0 0
\(745\) 0.452889 2.56846i 0.000607905 0.00344760i
\(746\) −927.595 1049.12i −1.24343 1.40632i
\(747\) 0 0
\(748\) −202.126 24.9463i −0.270222 0.0333507i
\(749\) 91.2443 + 76.5631i 0.121821 + 0.102220i
\(750\) 0 0
\(751\) 1238.93 218.457i 1.64971 0.290888i 0.729988 0.683460i \(-0.239526\pi\)
0.919721 + 0.392572i \(0.128415\pi\)
\(752\) 1090.38 + 77.6172i 1.44997 + 0.103214i
\(753\) 0 0
\(754\) −285.706 + 174.958i −0.378921 + 0.232040i
\(755\) 1.77869i 0.00235589i
\(756\) 0 0
\(757\) −1329.08 −1.75572 −0.877859 0.478919i \(-0.841029\pi\)
−0.877859 + 0.478919i \(0.841029\pi\)
\(758\) 144.254 + 235.566i 0.190308 + 0.310773i
\(759\) 0 0
\(760\) −2.81820 0.784405i −0.00370816 0.00103211i
\(761\) −42.4342 240.656i −0.0557611 0.316237i 0.944151 0.329514i \(-0.106885\pi\)
−0.999912 + 0.0132768i \(0.995774\pi\)
\(762\) 0 0
\(763\) 52.3989 62.4465i 0.0686748 0.0818434i
\(764\) 1079.54 + 133.236i 1.41301 + 0.174392i
\(765\) 0 0
\(766\) 56.9931 50.3914i 0.0744035 0.0657852i
\(767\) 373.054 + 65.7795i 0.486381 + 0.0857621i
\(768\) 0 0
\(769\) −706.569 257.170i −0.918815 0.334421i −0.161048 0.986947i \(-0.551487\pi\)
−0.757767 + 0.652525i \(0.773710\pi\)
\(770\) −0.147629 0.0221106i −0.000191727 2.87150e-5i
\(771\) 0 0
\(772\) −237.961 1033.67i −0.308239 1.33895i
\(773\) −152.659 264.413i −0.197489 0.342061i 0.750225 0.661183i \(-0.229945\pi\)
−0.947714 + 0.319122i \(0.896612\pi\)
\(774\) 0 0
\(775\) 682.622 + 394.112i 0.880803 + 0.508532i
\(776\) 304.348 + 29.5935i 0.392200 + 0.0381359i
\(777\) 0 0
\(778\) 32.9943 + 83.8377i 0.0424091 + 0.107760i
\(779\) 714.974 + 852.073i 0.917810 + 1.09380i
\(780\) 0 0
\(781\) −311.939 + 113.536i −0.399410 + 0.145373i
\(782\) 38.8294 + 191.159i 0.0496540 + 0.244448i
\(783\) 0 0
\(784\) 539.943 557.729i 0.688703 0.711390i
\(785\) −1.47350 + 0.536310i −0.00187707 + 0.000683197i
\(786\) 0 0
\(787\) −160.331 191.075i −0.203724 0.242789i 0.654503 0.756060i \(-0.272878\pi\)
−0.858227 + 0.513271i \(0.828434\pi\)
\(788\) 367.602 + 566.833i 0.466500 + 0.719332i
\(789\) 0 0
\(790\) −2.37569 + 4.37222i −0.00300721 + 0.00553446i
\(791\) 20.3524 + 11.7505i 0.0257300 + 0.0148552i
\(792\) 0 0
\(793\) 140.624 + 243.567i 0.177331 + 0.307147i
\(794\) −36.0950 1395.08i −0.0454597 1.75703i
\(795\) 0 0
\(796\) −24.8631 480.162i −0.0312351 0.603218i
\(797\) −1423.05 517.950i −1.78551 0.649874i −0.999498 0.0316673i \(-0.989918\pi\)
−0.786016 0.618207i \(-0.787859\pi\)
\(798\) 0 0
\(799\) −589.921 104.019i −0.738325 0.130187i
\(800\) 799.172 + 36.1445i 0.998965 + 0.0451806i
\(801\) 0 0
\(802\) −383.347 + 1144.51i −0.477989 + 1.42708i
\(803\) −109.033 + 129.941i −0.135783 + 0.161820i
\(804\) 0 0
\(805\) 0.0248272 + 0.140802i 3.08413e−5 + 0.000174910i
\(806\) −367.435 292.458i −0.455874 0.362852i
\(807\) 0 0
\(808\) 626.909 877.153i 0.775878 1.08559i
\(809\) −1163.03 −1.43761 −0.718806 0.695211i \(-0.755311\pi\)
−0.718806 + 0.695211i \(0.755311\pi\)
\(810\) 0 0
\(811\) 888.115i 1.09509i −0.836777 0.547543i \(-0.815563\pi\)
0.836777 0.547543i \(-0.184437\pi\)
\(812\) 42.6117 + 45.7528i 0.0524775 + 0.0563458i
\(813\) 0 0
\(814\) 486.329 + 387.092i 0.597456 + 0.475543i
\(815\) 1.12489 0.198349i 0.00138024 0.000243373i
\(816\) 0 0
\(817\) −1085.54 910.874i −1.32869 1.11490i
\(818\) −424.803 + 1268.29i −0.519320 + 1.55047i
\(819\) 0 0
\(820\) 3.32260 + 2.50702i 0.00405195 + 0.00305734i
\(821\) 167.273 948.650i 0.203742 1.15548i −0.695664 0.718367i \(-0.744890\pi\)
0.899406 0.437113i \(-0.143999\pi\)
\(822\) 0 0
\(823\) 228.127 626.774i 0.277189 0.761572i −0.720489 0.693467i \(-0.756082\pi\)
0.997678 0.0681051i \(-0.0216953\pi\)
\(824\) 98.3580 + 381.799i 0.119366 + 0.463349i
\(825\) 0 0
\(826\) −1.82847 70.6711i −0.00221365 0.0855582i
\(827\) 537.817 310.509i 0.650322 0.375464i −0.138257 0.990396i \(-0.544150\pi\)
0.788580 + 0.614933i \(0.210817\pi\)
\(828\) 0 0
\(829\) 155.530 269.386i 0.187612 0.324953i −0.756842 0.653598i \(-0.773259\pi\)
0.944453 + 0.328645i \(0.106592\pi\)
\(830\) 2.53532 4.66600i 0.00305460 0.00562169i
\(831\) 0 0
\(832\) −467.698 91.8222i −0.562137 0.110363i
\(833\) −325.864 + 273.433i −0.391194 + 0.328251i
\(834\) 0 0
\(835\) −1.89962 5.21915i −0.00227499 0.00625048i
\(836\) −422.839 + 179.173i −0.505789 + 0.214321i
\(837\) 0 0
\(838\) −133.052 655.019i −0.158773 0.781646i
\(839\) −413.494 1136.06i −0.492841 1.35407i −0.898069 0.439854i \(-0.855030\pi\)
0.405228 0.914216i \(-0.367192\pi\)
\(840\) 0 0
\(841\) −256.684 + 215.383i −0.305212 + 0.256104i
\(842\) −363.661 924.055i −0.431901 1.09745i
\(843\) 0 0
\(844\) −325.401 + 1061.96i −0.385546 + 1.25825i
\(845\) 1.04998 1.81861i 0.00124257 0.00215220i
\(846\) 0 0
\(847\) 52.5254 30.3256i 0.0620135 0.0358035i
\(848\) −386.280 533.070i −0.455519 0.628621i
\(849\) 0 0
\(850\) −433.546 64.9325i −0.510054 0.0763912i
\(851\) 203.617 559.432i 0.239267 0.657382i
\(852\) 0 0
\(853\) 185.373 1051.30i 0.217319 1.23248i −0.659519 0.751688i \(-0.729240\pi\)
0.876837 0.480787i \(-0.159649\pi\)
\(854\) 39.3216 34.7669i 0.0460440 0.0407106i
\(855\) 0 0
\(856\) 1367.09 106.302i 1.59707 0.124185i
\(857\) 518.525 + 435.094i 0.605047 + 0.507695i 0.893063 0.449931i \(-0.148551\pi\)
−0.288017 + 0.957625i \(0.592996\pi\)
\(858\) 0 0
\(859\) −931.954 + 164.329i −1.08493 + 0.191302i −0.687394 0.726285i \(-0.741245\pi\)
−0.397535 + 0.917587i \(0.630134\pi\)
\(860\) −4.72329 2.41036i −0.00549220 0.00280274i
\(861\) 0 0
\(862\) −424.436 693.103i −0.492385 0.804064i
\(863\) 1407.68i 1.63114i 0.578657 + 0.815571i \(0.303577\pi\)
−0.578657 + 0.815571i \(0.696423\pi\)
\(864\) 0 0
\(865\) −5.65602 −0.00653875
\(866\) −535.125 + 327.695i −0.617928 + 0.378401i
\(867\) 0 0
\(868\) −39.8373 + 78.0643i −0.0458955 + 0.0899359i
\(869\) 135.646 + 769.286i 0.156094 + 0.885255i
\(870\) 0 0
\(871\) −207.434 + 247.211i −0.238156 + 0.283824i
\(872\) −72.7521 935.623i −0.0834313 1.07296i
\(873\) 0 0
\(874\) 291.349 + 329.517i 0.333351 + 0.377022i
\(875\) −0.632880 0.111594i −0.000723291 0.000127536i
\(876\) 0 0
\(877\) −289.362 105.319i −0.329946 0.120090i 0.171735 0.985143i \(-0.445063\pi\)
−0.501681 + 0.865053i \(0.667285\pi\)
\(878\) 134.127 895.548i 0.152764 1.01999i
\(879\) 0 0
\(880\) −1.39155 + 1.00836i −0.00158130 + 0.00114586i
\(881\) −308.635 534.572i −0.350324 0.606778i 0.635982 0.771704i \(-0.280595\pi\)
−0.986306 + 0.164925i \(0.947262\pi\)
\(882\) 0 0
\(883\) −244.263 141.025i −0.276629 0.159712i 0.355268 0.934765i \(-0.384390\pi\)
−0.631896 + 0.775053i \(0.717723\pi\)
\(884\) 249.724 + 76.5190i 0.282493 + 0.0865599i
\(885\) 0 0
\(886\) 436.089 171.622i 0.492200 0.193705i
\(887\) −224.634 267.708i −0.253251 0.301813i 0.624408 0.781099i \(-0.285340\pi\)
−0.877659 + 0.479285i \(0.840896\pi\)
\(888\) 0 0
\(889\) −126.944 + 46.2038i −0.142794 + 0.0519728i
\(890\) −2.14271 + 0.435242i −0.00240754 + 0.000489036i
\(891\) 0 0
\(892\) −57.1444 134.858i −0.0640633 0.151186i
\(893\) −1269.28 + 461.980i −1.42136 + 0.517335i
\(894\) 0 0
\(895\) 2.57681 + 3.07093i 0.00287912 + 0.00343120i
\(896\) 0.581539 + 88.9478i 0.000649039 + 0.0992721i
\(897\) 0 0
\(898\) −282.064 153.263i −0.314103 0.170671i
\(899\) 614.170 + 354.591i 0.683170 + 0.394429i
\(900\) 0 0
\(901\) 180.373 + 312.415i 0.200192 + 0.346742i
\(902\) 653.203 16.9003i 0.724172 0.0187365i
\(903\) 0 0
\(904\) 261.991 67.4934i 0.289813 0.0746609i
\(905\) 0.527627 + 0.192041i 0.000583014 + 0.000212200i
\(906\) 0 0
\(907\) 268.404 + 47.3268i 0.295925 + 0.0521795i 0.319639 0.947539i \(-0.396438\pi\)
−0.0237146 + 0.999719i \(0.507549\pi\)
\(908\) −81.8824 + 108.520i −0.0901789 + 0.119516i
\(909\) 0 0
\(910\) 0.181527 + 0.0608013i 0.000199481 + 6.68146e-5i
\(911\) −31.4750 + 37.5105i −0.0345500 + 0.0411750i −0.783043 0.621968i \(-0.786333\pi\)
0.748493 + 0.663143i \(0.230778\pi\)
\(912\) 0 0
\(913\) −144.760 820.976i −0.158555 0.899207i
\(914\) −113.823 + 143.003i −0.124533 + 0.156459i
\(915\) 0 0
\(916\) −889.748 + 828.664i −0.971341 + 0.904655i
\(917\) 62.5109 0.0681689
\(918\) 0 0
\(919\) 710.873i 0.773529i −0.922179 0.386764i \(-0.873593\pi\)
0.922179 0.386764i \(-0.126407\pi\)
\(920\) 1.33909 + 0.957057i 0.00145553 + 0.00104028i
\(921\) 0 0
\(922\) −164.366 + 206.504i −0.178271 + 0.223974i
\(923\) 419.253 73.9256i 0.454228 0.0800927i
\(924\) 0 0
\(925\) 1024.93 + 860.019i 1.10803 + 0.929750i
\(926\) 422.561 + 141.534i 0.456329 + 0.152844i
\(927\) 0 0
\(928\) 719.033 + 32.5200i 0.774820 + 0.0350431i
\(929\) 147.173 834.661i 0.158421 0.898451i −0.797170 0.603755i \(-0.793670\pi\)
0.955591 0.294696i \(-0.0952184\pi\)
\(930\) 0 0
\(931\) −328.068 + 901.358i −0.352382 + 0.968161i
\(932\) 399.368 20.6795i 0.428506 0.0221884i
\(933\) 0 0
\(934\) 888.837 22.9969i 0.951645 0.0246220i
\(935\) 0.815538 0.470851i 0.000872234 0.000503584i
\(936\) 0 0
\(937\) 330.059 571.679i 0.352251 0.610116i −0.634393 0.773011i \(-0.718750\pi\)
0.986643 + 0.162895i \(0.0520831\pi\)
\(938\) 52.9181 + 28.7536i 0.0564159 + 0.0306542i
\(939\) 0 0
\(940\) −4.24082 + 2.75025i −0.00451151 + 0.00292580i
\(941\) 711.987 597.428i 0.756628 0.634886i −0.180619 0.983553i \(-0.557810\pi\)
0.937247 + 0.348667i \(0.113366\pi\)
\(942\) 0 0
\(943\) −214.049 588.094i −0.226987 0.623642i
\(944\) −584.724 566.077i −0.619411 0.599658i
\(945\) 0 0
\(946\) −815.797 + 165.710i −0.862364 + 0.175169i
\(947\) 196.604 + 540.164i 0.207607 + 0.570395i 0.999172 0.0406899i \(-0.0129556\pi\)
−0.791565 + 0.611085i \(0.790733\pi\)
\(948\) 0 0
\(949\) 166.643 139.830i 0.175599 0.147345i
\(950\) −919.840 + 362.002i −0.968253 + 0.381055i
\(951\) 0 0
\(952\) 4.71733 48.5143i 0.00495518 0.0509604i
\(953\) −747.116 + 1294.04i −0.783962 + 1.35786i 0.145655 + 0.989335i \(0.453471\pi\)
−0.929617 + 0.368527i \(0.879862\pi\)
\(954\) 0 0
\(955\) −4.35571 + 2.51477i −0.00456095 + 0.00263327i
\(956\) −504.672 + 116.180i −0.527900 + 0.121528i
\(957\) 0 0
\(958\) −168.428 + 1124.57i −0.175812 + 1.17387i
\(959\) −14.2685 + 39.2025i −0.0148785 + 0.0408785i
\(960\) 0 0
\(961\) −5.74824 + 32.5999i −0.00598152 + 0.0339229i
\(962\) −528.014 597.188i −0.548871 0.620777i
\(963\) 0 0
\(964\) 29.1382 236.091i 0.0302263 0.244907i
\(965\) 3.75714 + 3.15261i 0.00389341 + 0.00326696i
\(966\) 0 0
\(967\) −40.1386 + 7.07751i −0.0415083 + 0.00731904i −0.194364 0.980930i \(-0.562264\pi\)
0.152855 + 0.988249i \(0.451153\pi\)
\(968\) 187.223 672.654i 0.193412 0.694890i
\(969\) 0 0
\(970\) −1.20579 + 0.738388i −0.00124308 + 0.000761225i
\(971\) 1253.25i 1.29068i −0.763895 0.645341i \(-0.776715\pi\)
0.763895 0.645341i \(-0.223285\pi\)
\(972\) 0 0
\(973\) −61.6415 −0.0633520
\(974\) −968.742 1581.95i −0.994601 1.62418i
\(975\) 0 0
\(976\) 42.9036 602.716i 0.0439586 0.617537i
\(977\) −87.2483 494.810i −0.0893023 0.506458i −0.996345 0.0854199i \(-0.972777\pi\)
0.907043 0.421039i \(-0.138334\pi\)
\(978\) 0 0
\(979\) −220.633 + 262.940i −0.225366 + 0.268580i
\(980\) −0.439667 + 3.56238i −0.000448639 + 0.00363508i
\(981\) 0 0
\(982\) −818.852 + 724.003i −0.833862 + 0.737274i
\(983\) 964.524 + 170.072i 0.981204 + 0.173013i 0.641169 0.767400i \(-0.278450\pi\)
0.340035 + 0.940413i \(0.389561\pi\)
\(984\) 0 0
\(985\) −2.93550 1.06843i −0.00298020 0.00108470i
\(986\) −390.071 58.4212i −0.395609 0.0592507i
\(987\) 0 0
\(988\) 573.933 132.125i 0.580904 0.133730i
\(989\) 398.657 + 690.494i 0.403091 + 0.698174i
\(990\) 0 0
\(991\) 574.931 + 331.937i 0.580153 + 0.334951i 0.761194 0.648524i \(-0.224613\pi\)
−0.181041 + 0.983475i \(0.557947\pi\)
\(992\) 301.890 + 962.717i 0.304324 + 0.970481i
\(993\) 0 0
\(994\) −29.0952 73.9303i −0.0292708 0.0743765i
\(995\) 1.42904 + 1.70306i 0.00143622 + 0.00171162i
\(996\) 0 0
\(997\) 147.082 53.5333i 0.147524 0.0536944i −0.267203 0.963640i \(-0.586099\pi\)
0.414727 + 0.909946i \(0.363877\pi\)
\(998\) 306.710 + 1509.94i 0.307325 + 1.51297i
\(999\) 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.19.5 204
3.2 odd 2 108.3.j.a.7.30 204
4.3 odd 2 inner 324.3.j.a.19.3 204
12.11 even 2 108.3.j.a.7.32 yes 204
27.4 even 9 inner 324.3.j.a.307.3 204
27.23 odd 18 108.3.j.a.31.32 yes 204
108.23 even 18 108.3.j.a.31.30 yes 204
108.31 odd 18 inner 324.3.j.a.307.5 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.7.30 204 3.2 odd 2
108.3.j.a.7.32 yes 204 12.11 even 2
108.3.j.a.31.30 yes 204 108.23 even 18
108.3.j.a.31.32 yes 204 27.23 odd 18
324.3.j.a.19.3 204 4.3 odd 2 inner
324.3.j.a.19.5 204 1.1 even 1 trivial
324.3.j.a.307.3 204 27.4 even 9 inner
324.3.j.a.307.5 204 108.31 odd 18 inner