Properties

Label 324.3.j.a.19.3
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 19.3
Character \(\chi\) \(=\) 324.19
Dual form 324.3.j.a.307.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.97794 + 0.296237i) q^{2} +(3.82449 - 1.17188i) q^{4} +(0.00321173 + 0.0182146i) q^{5} +(0.446686 - 0.532339i) q^{7} +(-7.21745 + 3.45086i) q^{8} +O(q^{10})\) \(q+(-1.97794 + 0.296237i) q^{2} +(3.82449 - 1.17188i) q^{4} +(0.00321173 + 0.0182146i) q^{5} +(0.446686 - 0.532339i) q^{7} +(-7.21745 + 3.45086i) q^{8} +(-0.0117484 - 0.0350759i) q^{10} +(5.71885 + 1.00839i) q^{11} +(6.99816 + 2.54712i) q^{13} +(-0.725818 + 1.18526i) q^{14} +(13.2534 - 8.96367i) q^{16} +(4.38388 + 7.59310i) q^{17} +(-17.1217 - 9.88523i) q^{19} +(0.0336285 + 0.0658977i) q^{20} +(-11.6103 - 0.300393i) q^{22} +(7.15027 + 8.52136i) q^{23} +(23.4920 - 8.55039i) q^{25} +(-14.5965 - 2.96494i) q^{26} +(1.08451 - 2.55939i) q^{28} +(21.1363 - 7.69297i) q^{29} +(-20.2667 - 24.1529i) q^{31} +(-23.5590 + 21.6557i) q^{32} +(-10.9204 - 13.7200i) q^{34} +(0.0111310 + 0.00642647i) q^{35} +(26.7594 + 46.3486i) q^{37} +(36.7941 + 14.4803i) q^{38} +(-0.0860365 - 0.120380i) q^{40} +(52.8679 + 19.2423i) q^{41} +(70.5871 + 12.4464i) q^{43} +(23.0534 - 2.84523i) q^{44} +(-16.6671 - 14.7366i) q^{46} +(43.9159 - 52.3369i) q^{47} +(8.42490 + 47.7800i) q^{49} +(-43.9328 + 23.8713i) q^{50} +(29.7493 + 1.54044i) q^{52} +41.1446 q^{53} +0.107405i q^{55} +(-1.38690 + 5.38358i) q^{56} +(-39.5273 + 21.4776i) q^{58} +(-50.0926 + 8.83268i) q^{59} +(28.9297 + 24.2749i) q^{61} +(47.2413 + 41.7693i) q^{62} +(40.1831 - 49.8128i) q^{64} +(-0.0239186 + 0.135649i) q^{65} +(14.8206 - 40.7193i) q^{67} +(25.6643 + 23.9023i) q^{68} +(-0.0239202 - 0.00941376i) q^{70} +(-49.5059 + 28.5822i) q^{71} +(14.6051 - 25.2968i) q^{73} +(-66.6587 - 83.7477i) q^{74} +(-77.0661 - 17.7414i) q^{76} +(3.09133 - 2.59394i) q^{77} +(46.0077 + 126.405i) q^{79} +(0.205836 + 0.212617i) q^{80} +(-110.270 - 22.3987i) q^{82} +(-49.0991 - 134.899i) q^{83} +(-0.124225 + 0.104237i) q^{85} +(-143.304 - 3.70771i) q^{86} +(-44.7553 + 12.4570i) q^{88} +(29.5539 - 51.1889i) q^{89} +(4.48191 - 2.58763i) q^{91} +(37.3321 + 24.2106i) q^{92} +(-71.3588 + 116.529i) q^{94} +(0.125065 - 0.343614i) q^{95} +(6.63733 - 37.6422i) q^{97} +(-30.8182 - 92.0102i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97794 + 0.296237i −0.988970 + 0.148119i
\(3\) 0 0
\(4\) 3.82449 1.17188i 0.956122 0.292970i
\(5\) 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 −0.733194 0.680019i \(-0.761971\pi\)
0.797006 + 0.603971i \(0.206416\pi\)
\(8\) −7.21745 + 3.45086i −0.902181 + 0.431358i
\(9\) 0 0
\(10\) −0.0117484 0.0350759i −0.00117484 0.00350759i
\(11\) 5.71885 + 1.00839i 0.519896 + 0.0916716i 0.427437 0.904045i \(-0.359416\pi\)
0.0924582 + 0.995717i \(0.470528\pi\)
\(12\) 0 0
\(13\) 6.99816 + 2.54712i 0.538320 + 0.195933i 0.596850 0.802353i \(-0.296419\pi\)
−0.0585294 + 0.998286i \(0.518641\pi\)
\(14\) −0.725818 + 1.18526i −0.0518442 + 0.0846614i
\(15\) 0 0
\(16\) 13.2534 8.96367i 0.828338 0.560229i
\(17\) 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 −0.0235724 0.999722i \(-0.507504\pi\)
−0.877571 + 0.479447i \(0.840837\pi\)
\(20\) 0.0336285 + 0.0658977i 0.00168143 + 0.00329489i
\(21\) 0 0
\(22\) −11.6103 0.300393i −0.527739 0.0136542i
\(23\) 7.15027 + 8.52136i 0.310881 + 0.370494i 0.898749 0.438463i \(-0.144477\pi\)
−0.587868 + 0.808957i \(0.700033\pi\)
\(24\) 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 0.332712 0.943029i \(-0.392036\pi\)
−0.986477 + 0.163902i \(0.947592\pi\)
\(32\) −23.5590 + 21.6557i −0.736220 + 0.676742i
\(33\) 0 0
\(34\) −10.9204 13.7200i −0.321188 0.403530i
\(35\) 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 \(0.575991\pi\)
\(38\) 36.7941 + 14.4803i 0.968266 + 0.381060i
\(39\) 0 0
\(40\) −0.0860365 0.120380i −0.00215091 0.00300949i
\(41\) 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 0.916740 0.399485i \(-0.130811\pi\)
0.724822 + 0.688936i \(0.241922\pi\)
\(44\) 23.0534 2.84523i 0.523941 0.0646644i
\(45\) 0 0
\(46\) −16.6671 14.7366i −0.362329 0.320360i
\(47\) 43.9159 52.3369i 0.934381 1.11355i −0.0589506 0.998261i \(-0.518775\pi\)
0.993332 0.115291i \(-0.0367801\pi\)
\(48\) 0 0
\(49\) 8.42490 + 47.7800i 0.171937 + 0.975102i
\(50\) −43.9328 + 23.8713i −0.878656 + 0.477427i
\(51\) 0 0
\(52\) 29.7493 + 1.54044i 0.572102 + 0.0296238i
\(53\) 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
\(56\) −1.38690 + 5.38358i −0.0247661 + 0.0961354i
\(57\) 0 0
\(58\) −39.5273 + 21.4776i −0.681505 + 0.370303i
\(59\) −50.0926 + 8.83268i −0.849027 + 0.149706i −0.581200 0.813761i \(-0.697417\pi\)
−0.267827 + 0.963467i \(0.586306\pi\)
\(60\) 0 0
\(61\) 28.9297 + 24.2749i 0.474258 + 0.397949i 0.848345 0.529444i \(-0.177599\pi\)
−0.374087 + 0.927394i \(0.622044\pi\)
\(62\) 47.2413 + 41.7693i 0.761957 + 0.673698i
\(63\) 0 0
\(64\) 40.1831 49.8128i 0.627861 0.778325i
\(65\) −0.0239186 + 0.135649i −0.000367979 + 0.00208691i
\(66\) 0 0
\(67\) 14.8206 40.7193i 0.221203 0.607751i −0.778601 0.627519i \(-0.784070\pi\)
0.999805 + 0.0197678i \(0.00629269\pi\)
\(68\) 25.6643 + 23.9023i 0.377416 + 0.351505i
\(69\) 0 0
\(70\) −0.0239202 0.00941376i −0.000341717 0.000134482i
\(71\) −49.5059 + 28.5822i −0.697266 + 0.402567i −0.806328 0.591468i \(-0.798549\pi\)
0.109062 + 0.994035i \(0.465215\pi\)
\(72\) 0 0
\(73\) 14.6051 25.2968i 0.200070 0.346532i −0.748481 0.663157i \(-0.769216\pi\)
0.948551 + 0.316625i \(0.102550\pi\)
\(74\) −66.6587 83.7477i −0.900793 1.13173i
\(75\) 0 0
\(76\) −77.0661 17.7414i −1.01403 0.233439i
\(77\) 3.09133 2.59394i 0.0401472 0.0336875i
\(78\) 0 0
\(79\) 46.0077 + 126.405i 0.582376 + 1.60007i 0.784107 + 0.620625i \(0.213121\pi\)
−0.201731 + 0.979441i \(0.564657\pi\)
\(80\) 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 \(-0.778559\pi\)
0.176064 0.984379i \(-0.443663\pi\)
\(84\) 0 0
\(85\) −0.124225 + 0.104237i −0.00146148 + 0.00122632i
\(86\) −143.304 3.70771i −1.66633 0.0431129i
\(87\) 0 0
\(88\) −44.7553 + 12.4570i −0.508583 + 0.141557i
\(89\) 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
\(92\) 37.3321 + 24.2106i 0.405784 + 0.263159i
\(93\) 0 0
\(94\) −71.3588 + 116.529i −0.759137 + 1.23967i
\(95\) 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 \(-0.00757248\pi\)
\(98\) −30.8182 92.0102i −0.314471 0.938879i
\(99\) 0 0
\(100\) 79.8248 60.2306i 0.798248 0.602306i
\(101\) −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 −0.404210 0.914666i \(-0.632453\pi\)
−0.0669984 + 0.997753i \(0.521342\pi\)
\(104\) −59.2986 + 5.76595i −0.570179 + 0.0554419i
\(105\) 0 0
\(106\) −81.3815 + 12.1886i −0.767750 + 0.114986i
\(107\) 171.403i 1.60189i 0.598736 + 0.800946i \(0.295670\pi\)
−0.598736 + 0.800946i \(0.704330\pi\)
\(108\) 0 0
\(109\) −117.306 −1.07620 −0.538100 0.842881i \(-0.680858\pi\)
−0.538100 + 0.842881i \(0.680858\pi\)
\(110\) −0.0318174 0.212441i −0.000289249 0.00193128i
\(111\) 0 0
\(112\) 1.14839 11.0593i 0.0102535 0.0987433i
\(113\) −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
\(116\) 71.8201 54.1908i 0.619139 0.467162i
\(117\) 0 0
\(118\) 96.4636 32.3098i 0.817488 0.273812i
\(119\) 6.00032 + 1.05802i 0.0504229 + 0.00889091i
\(120\) 0 0
\(121\) −82.0144 29.8508i −0.677805 0.246701i
\(122\) −64.4123 39.4442i −0.527970 0.323313i
\(123\) 0 0
\(124\) −105.814 68.6224i −0.853339 0.553406i
\(125\) 0.462387 + 0.800877i 0.00369909 + 0.00640702i
\(126\) 0 0
\(127\) −168.353 97.1989i −1.32562 0.765346i −0.340999 0.940064i \(-0.610765\pi\)
−0.984618 + 0.174718i \(0.944099\pi\)
\(128\) −64.7234 + 110.430i −0.505651 + 0.862738i
\(129\) 0 0
\(130\) 0.00712522 0.275392i 5.48094e−5 0.00211840i
\(131\) 57.8214 + 68.9089i 0.441385 + 0.526022i 0.940171 0.340703i \(-0.110665\pi\)
−0.498786 + 0.866725i \(0.666221\pi\)
\(132\) 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 0.520905 0.853615i \(-0.325595\pi\)
−0.931101 + 0.364762i \(0.881150\pi\)
\(140\) 0.0501013 + 0.0115338i 0.000357867 + 8.23843e-5i
\(141\) 0 0
\(142\) 89.4525 71.1994i 0.629947 0.501404i
\(143\) 37.4530 + 21.6235i 0.261909 + 0.151213i
\(144\) 0 0
\(145\) 0.208008 + 0.360281i 0.00143454 + 0.00248470i
\(146\) −21.3942 + 54.3621i −0.146535 + 0.372343i
\(147\) 0 0
\(148\) 156.656 + 145.901i 1.05849 + 0.985818i
\(149\) −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 0.478210 0.878246i \(-0.341286\pi\)
0.148993 + 0.988838i \(0.452397\pi\)
\(152\) 157.688 + 12.2615i 1.03742 + 0.0806676i
\(153\) 0 0
\(154\) −5.34605 + 6.04642i −0.0347146 + 0.0392625i
\(155\) 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 \(0.857420\pi\)
\(158\) −128.446 236.393i −0.812952 1.49616i
\(159\) 0 0
\(160\) −0.470116 0.359566i −0.00293822 0.00224729i
\(161\) 7.73018 0.0480135
\(162\) 0 0
\(163\) 61.7577i 0.378882i 0.981892 + 0.189441i \(0.0606675\pi\)
−0.981892 + 0.189441i \(0.939332\pi\)
\(164\) 224.742 + 11.6373i 1.37038 + 0.0709592i
\(165\) 0 0
\(166\) 137.077 + 252.276i 0.825765 + 1.51974i
\(167\) 295.731 52.1454i 1.77085 0.312248i 0.809404 0.587252i \(-0.199790\pi\)
0.961443 + 0.275004i \(0.0886792\pi\)
\(168\) 0 0
\(169\) −86.9751 72.9808i −0.514645 0.431839i
\(170\) 0.214831 0.242976i 0.00126371 0.00142927i
\(171\) 0 0
\(172\) 284.545 35.1184i 1.65433 0.204177i
\(173\) −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
\(176\) 84.8331 37.8973i 0.482006 0.215326i
\(177\) 0 0
\(178\) −43.2918 + 110.004i −0.243212 + 0.617997i
\(179\) −187.706 + 108.372i −1.04864 + 0.605431i −0.922267 0.386553i \(-0.873666\pi\)
−0.126369 + 0.991983i \(0.540332\pi\)
\(180\) 0 0
\(181\) 15.1790 26.2908i 0.0838619 0.145253i −0.821044 0.570865i \(-0.806608\pi\)
0.904906 + 0.425612i \(0.139941\pi\)
\(182\) −8.09840 + 6.44589i −0.0444967 + 0.0354170i
\(183\) 0 0
\(184\) −81.0128 36.8279i −0.440287 0.200152i
\(185\) −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 \(-0.858962\pi\)
0.416491 0.909140i \(-0.363260\pi\)
\(192\) 0 0
\(193\) 203.137 170.452i 1.05252 0.883172i 0.0591665 0.998248i \(-0.481156\pi\)
0.993357 + 0.115076i \(0.0367113\pi\)
\(194\) −1.97722 + 76.4202i −0.0101919 + 0.393918i
\(195\) 0 0
\(196\) 88.2133 + 172.861i 0.450068 + 0.881944i
\(197\) −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 −0.738203 0.674579i \(-0.764325\pi\)
0.215101 + 0.976592i \(0.430992\pi\)
\(200\) −140.046 + 142.780i −0.700230 + 0.713898i
\(201\) 0 0
\(202\) 229.863 + 140.761i 1.13794 + 0.696839i
\(203\) 5.34600 14.6880i 0.0263350 0.0723547i
\(204\) 0 0
\(205\) −0.180694 + 1.02477i −0.000881435 + 0.00499887i
\(206\) 93.4629 31.3048i 0.453704 0.151965i
\(207\) 0 0
\(208\) 115.581 28.9712i 0.555678 0.139285i
\(209\) −87.9484 73.7975i −0.420806 0.353098i
\(210\) 0 0
\(211\) 273.456 48.2177i 1.29600 0.228520i 0.517239 0.855841i \(-0.326960\pi\)
0.778761 + 0.627321i \(0.215849\pi\)
\(212\) 157.357 48.2165i 0.742250 0.227436i
\(213\) 0 0
\(214\) −50.7758 339.024i −0.237270 1.58422i
\(215\) 1.32569i 0.00616600i
\(216\) 0 0
\(217\) −21.9104 −0.100970
\(218\) 232.024 34.7504i 1.06433 0.159405i
\(219\) 0 0
\(220\) 0.125866 + 0.410770i 0.000572118 + 0.00186714i
\(221\) 11.3385 + 64.3040i 0.0513056 + 0.290968i
\(222\) 0 0
\(223\) −23.5366 + 28.0498i −0.105545 + 0.125784i −0.816231 0.577726i \(-0.803940\pi\)
0.710686 + 0.703510i \(0.248385\pi\)
\(224\) 1.00471 + 22.2147i 0.00448533 + 0.0991729i
\(225\) 0 0
\(226\) 21.4814 + 64.1344i 0.0950504 + 0.283781i
\(227\) 33.4702 + 5.90171i 0.147446 + 0.0259987i 0.246884 0.969045i \(-0.420593\pi\)
−0.0994379 + 0.995044i \(0.531704\pi\)
\(228\) 0 0
\(229\) −285.636 103.963i −1.24732 0.453986i −0.367823 0.929896i \(-0.619897\pi\)
−0.879494 + 0.475909i \(0.842119\pi\)
\(230\) 0.214890 0.350915i 0.000934305 0.00152572i
\(231\) 0 0
\(232\) −126.003 + 128.462i −0.543114 + 0.553715i
\(233\) 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
\(236\) −181.228 + 92.4829i −0.767914 + 0.391877i
\(237\) 0 0
\(238\) −12.1817 0.315177i −0.0511836 0.00132427i
\(239\) 83.2205 + 99.1783i 0.348203 + 0.414972i 0.911511 0.411275i \(-0.134916\pi\)
−0.563309 + 0.826247i \(0.690472\pi\)
\(240\) 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
\(248\) 229.622 + 104.385i 0.925896 + 0.420907i
\(249\) 0 0
\(250\) −1.15182 1.44711i −0.00460729 0.00578844i
\(251\) −178.915 103.297i −0.712810 0.411541i 0.0992905 0.995058i \(-0.468343\pi\)
−0.812101 + 0.583517i \(0.801676\pi\)
\(252\) 0 0
\(253\) 32.2985 + 55.9427i 0.127662 + 0.221117i
\(254\) 361.787 + 142.381i 1.42436 + 0.560555i
\(255\) 0 0
\(256\) 95.3052 237.598i 0.372286 0.928118i
\(257\) −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
\(260\) 0.0674881 + 0.546819i 0.000259570 + 0.00210315i
\(261\) 0 0
\(262\) −134.781 119.169i −0.514430 0.454842i
\(263\) −110.483 + 131.668i −0.420087 + 0.500640i −0.934035 0.357181i \(-0.883738\pi\)
0.513948 + 0.857821i \(0.328182\pi\)
\(264\) 0 0
\(265\) 0.132145 + 0.749432i 0.000498661 + 0.00282805i
\(266\) 24.1438 13.1188i 0.0907663 0.0493188i
\(267\) 0 0
\(268\) 8.96317 173.099i 0.0334447 0.645890i
\(269\) −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 \(0.153113\pi\)
−0.886524 + 0.462682i \(0.846887\pi\)
\(272\) 126.163 + 61.3387i 0.463836 + 0.225510i
\(273\) 0 0
\(274\) −105.499 + 57.3239i −0.385032 + 0.209211i
\(275\) 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 \(0.703089\pi\)
\(278\) 132.906 + 117.511i 0.478079 + 0.422703i
\(279\) 0 0
\(280\) −0.102514 0.00797129i −0.000366122 2.84689e-5i
\(281\) −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 \(-0.675024\pi\)
0.948347 0.317234i \(-0.102754\pi\)
\(284\) −155.840 + 167.327i −0.548731 + 0.589181i
\(285\) 0 0
\(286\) −80.4854 31.6750i −0.281417 0.110752i
\(287\) 33.8588 19.5484i 0.117975 0.0681128i
\(288\) 0 0
\(289\) 106.063 183.707i 0.367001 0.635664i
\(290\) −0.518156 0.650994i −0.00178675 0.00224481i
\(291\) 0 0
\(292\) 26.2123 113.863i 0.0897681 0.389941i
\(293\) −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
\(302\) −192.273 4.97468i −0.636665 0.0164725i
\(303\) 0 0
\(304\) −315.529 + 22.4605i −1.03792 + 0.0738834i
\(305\) −0.349243 + 0.604907i −0.00114506 + 0.00198330i
\(306\) 0 0
\(307\) −345.391 + 199.412i −1.12505 + 0.649549i −0.942686 0.333681i \(-0.891709\pi\)
−0.182366 + 0.983231i \(0.558376\pi\)
\(308\) 8.78299 13.5431i 0.0285162 0.0439713i
\(309\) 0 0
\(310\) −0.609084 + 0.994633i −0.00196479 + 0.00320849i
\(311\) −82.2845 + 226.075i −0.264580 + 0.726928i 0.734264 + 0.678864i \(0.237527\pi\)
−0.998844 + 0.0480643i \(0.984695\pi\)
\(312\) 0 0
\(313\) 21.6287 122.662i 0.0691012 0.391892i −0.930567 0.366122i \(-0.880685\pi\)
0.999668 0.0257700i \(-0.00820376\pi\)
\(314\) −53.8528 160.782i −0.171506 0.512044i
\(315\) 0 0
\(316\) 324.088 + 429.520i 1.02559 + 1.35924i
\(317\) −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
\(320\) 1.03638 + 0.571934i 0.00323868 + 0.00178729i
\(321\) 0 0
\(322\) −15.2898 + 2.28997i −0.0474839 + 0.00711170i
\(323\) 173.343i 0.536664i
\(324\) 0 0
\(325\) 186.180 0.572861
\(326\) −18.2949 122.153i −0.0561195 0.374703i
\(327\) 0 0
\(328\) −447.974 + 43.5591i −1.36577 + 0.132802i
\(329\) −8.24440 46.7563i −0.0250590 0.142117i
\(330\) 0 0
\(331\) −30.9734 + 36.9126i −0.0935751 + 0.111518i −0.810800 0.585323i \(-0.800968\pi\)
0.717225 + 0.696842i \(0.245412\pi\)
\(332\) −345.864 458.380i −1.04176 1.38066i
\(333\) 0 0
\(334\) −569.491 + 190.747i −1.70506 + 0.571099i
\(335\) 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 \(0.930718\pi\)
\(338\) 193.651 + 118.586i 0.572932 + 0.350847i
\(339\) 0 0
\(340\) −0.352945 + 0.544232i −0.00103807 + 0.00160068i
\(341\) −91.5468 158.564i −0.268466 0.464996i
\(342\) 0 0
\(343\) 58.6875 + 33.8833i 0.171101 + 0.0987850i
\(344\) −552.410 + 153.755i −1.60584 + 0.446962i
\(345\) 0 0
\(346\) 15.8188 611.403i 0.0457192 1.76706i
\(347\) 74.5764 + 88.8767i 0.214918 + 0.256129i 0.862723 0.505677i \(-0.168757\pi\)
−0.647805 + 0.761806i \(0.724313\pi\)
\(348\) 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
\(356\) 53.0414 230.405i 0.148993 0.647205i
\(357\) 0 0
\(358\) 339.167 269.959i 0.947394 0.754075i
\(359\) −284.704 164.374i −0.793046 0.457866i 0.0479875 0.998848i \(-0.484719\pi\)
−0.841034 + 0.540982i \(0.818053\pi\)
\(360\) 0 0
\(361\) 14.9356 + 25.8692i 0.0413728 + 0.0716599i
\(362\) −22.2348 + 56.4982i −0.0614222 + 0.156072i
\(363\) 0 0
\(364\) 14.1086 15.1486i 0.0387600 0.0416171i
\(365\) 0.507679 + 0.184780i 0.00139090 + 0.000506246i
\(366\) 0 0
\(367\) −108.149 19.0695i −0.294683 0.0519605i 0.0243522 0.999703i \(-0.492248\pi\)
−0.319035 + 0.947743i \(0.603359\pi\)
\(368\) 171.148 + 48.8444i 0.465076 + 0.132729i
\(369\) 0 0
\(370\) 1.31134 1.48314i 0.00354416 0.00400847i
\(371\) 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 \(0.556572\pi\)
\(374\) −48.6170 89.4747i −0.129992 0.239237i
\(375\) 0 0
\(376\) −136.353 + 529.287i −0.362642 + 1.40768i
\(377\) 167.510 0.444323
\(378\) 0 0
\(379\) 138.113i 0.364413i 0.983260 + 0.182207i \(0.0583239\pi\)
−0.983260 + 0.182207i \(0.941676\pi\)
\(380\) 0.0756365 1.46071i 0.000199044 0.00384397i
\(381\) 0 0
\(382\) 259.659 + 477.876i 0.679735 + 1.25098i
\(383\) 37.4599 6.60520i 0.0978067 0.0172460i −0.124531 0.992216i \(-0.539743\pi\)
0.222337 + 0.974970i \(0.428631\pi\)
\(384\) 0 0
\(385\) 0.0571760 + 0.0479764i 0.000148509 + 0.000124614i
\(386\) −351.298 + 397.321i −0.910099 + 1.02933i
\(387\) 0 0
\(388\) −18.7277 151.740i −0.0482672 0.391083i
\(389\) 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
\(392\) −225.688 315.777i −0.575736 0.805552i
\(393\) 0 0
\(394\) 123.705 314.332i 0.313973 0.797798i
\(395\) −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 \(0.825006\pi\)
\(398\) 188.094 149.713i 0.472598 0.376163i
\(399\) 0 0
\(400\) 234.706 323.896i 0.586765 0.809740i
\(401\) 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 \(-0.0268992\pi\)
\(410\) 0.0538277 2.08046i 0.000131287 0.00507429i
\(411\) 0 0
\(412\) −175.590 + 89.6061i −0.426190 + 0.217491i
\(413\) −17.6737 + 30.6117i −0.0427934 + 0.0741204i
\(414\) 0 0
\(415\) 2.29943 1.32758i 0.00554080 0.00319898i
\(416\) −220.030 + 91.5426i −0.528918 + 0.220054i
\(417\) 0 0
\(418\) 195.818 + 119.913i 0.468465 + 0.286874i
\(419\) 114.302 314.043i 0.272798 0.749507i −0.725333 0.688398i \(-0.758314\pi\)
0.998131 0.0611085i \(-0.0194636\pi\)
\(420\) 0 0
\(421\) −86.2197 + 488.976i −0.204797 + 1.16146i 0.692961 + 0.720975i \(0.256306\pi\)
−0.897758 + 0.440488i \(0.854805\pi\)
\(422\) −526.595 + 176.379i −1.24786 + 0.417961i
\(423\) 0 0
\(424\) −296.959 + 141.984i −0.700375 + 0.334868i
\(425\) 167.910 + 140.893i 0.395082 + 0.331513i
\(426\) 0 0
\(427\) 25.8450 4.55717i 0.0605269 0.0106725i
\(428\) 200.863 + 655.527i 0.469306 + 1.53160i
\(429\) 0 0
\(430\) −0.392719 2.62214i −0.000913300 0.00609799i
\(431\) 406.367i 0.942847i −0.881907 0.471424i \(-0.843740\pi\)
0.881907 0.471424i \(-0.156260\pi\)
\(432\) 0 0
\(433\) 313.745 0.724584 0.362292 0.932065i \(-0.381994\pi\)
0.362292 + 0.932065i \(0.381994\pi\)
\(434\) 43.3374 6.49068i 0.0998558 0.0149555i
\(435\) 0 0
\(436\) −448.635 + 137.468i −1.02898 + 0.315294i
\(437\) −38.1893 216.583i −0.0873898 0.495612i
\(438\) 0 0
\(439\) 291.034 346.841i 0.662948 0.790070i −0.324858 0.945763i \(-0.605317\pi\)
0.987806 + 0.155693i \(0.0497610\pi\)
\(440\) −0.370641 0.775192i −0.000842365 0.00176180i
\(441\) 0 0
\(442\) −41.4762 123.830i −0.0938375 0.280159i
\(443\) 230.762 + 40.6896i 0.520908 + 0.0918502i 0.427919 0.903817i \(-0.359247\pi\)
0.0929890 + 0.995667i \(0.470358\pi\)
\(444\) 0 0
\(445\) 1.02730 + 0.373908i 0.00230855 + 0.000840243i
\(446\) 38.2446 62.4533i 0.0857502 0.140030i
\(447\) 0 0
\(448\) −8.56809 43.6417i −0.0191252 0.0974146i
\(449\) 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
\(452\) −61.4879 120.490i −0.136035 0.266572i
\(453\) 0 0
\(454\) −67.9504 1.75808i −0.149671 0.00387243i
\(455\) 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 0.898207 0.439574i \(-0.144870\pi\)
−0.588867 + 0.808230i \(0.700426\pi\)
\(464\) 211.170 291.416i 0.455108 0.628053i
\(465\) 0 0
\(466\) −124.522 156.445i −0.267214 0.335718i
\(467\) 385.006 + 222.284i 0.824425 + 0.475982i 0.851940 0.523639i \(-0.175426\pi\)
−0.0275151 + 0.999621i \(0.508759\pi\)
\(468\) 0 0
\(469\) −15.0563 26.0783i −0.0321031 0.0556042i
\(470\) −2.35171 0.925514i −0.00500364 0.00196918i
\(471\) 0 0
\(472\) 331.061 236.612i 0.701399 0.501297i
\(473\) 391.127 + 142.358i 0.826906 + 0.300969i
\(474\) 0 0
\(475\) −486.746 85.8264i −1.02473 0.180687i
\(476\) 24.1880 2.98527i 0.0508152 0.00627158i
\(477\) 0 0
\(478\) −193.985 171.516i −0.405827 0.358819i
\(479\) −365.461 + 435.539i −0.762966 + 0.909268i −0.998032 0.0627117i \(-0.980025\pi\)
0.235065 + 0.971980i \(0.424470\pi\)
\(480\) 0 0
\(481\) 69.2109 + 392.515i 0.143890 + 0.816039i
\(482\) −104.510 + 56.7864i −0.216825 + 0.117814i
\(483\) 0 0
\(484\) −348.644 18.0531i −0.720340 0.0372997i
\(485\) 0.706954 0.00145764
\(486\) 0 0
\(487\) 927.501i 1.90452i −0.305288 0.952260i \(-0.598753\pi\)
0.305288 0.952260i \(-0.401247\pi\)
\(488\) −292.568 75.3705i −0.599525 0.154448i
\(489\) 0 0
\(490\) 1.57695 0.856852i 0.00321826 0.00174868i
\(491\) −538.209 + 94.9007i −1.09615 + 0.193281i −0.692346 0.721566i \(-0.743423\pi\)
−0.403802 + 0.914846i \(0.632312\pi\)
\(492\) 0 0
\(493\) 151.072 + 126.765i 0.306435 + 0.257129i
\(494\) 220.608 + 195.055i 0.446575 + 0.394847i
\(495\) 0 0
\(496\) −485.102 138.444i −0.978027 0.279121i
\(497\) −6.89813 + 39.1212i −0.0138795 + 0.0787147i
\(498\) 0 0
\(499\) −263.489 + 723.929i −0.528034 + 1.45076i 0.333349 + 0.942804i \(0.391821\pi\)
−0.861382 + 0.507957i \(0.830401\pi\)
\(500\) 2.70692 + 2.52108i 0.00541384 + 0.00504217i
\(501\) 0 0
\(502\) 384.484 + 151.313i 0.765905 + 0.301421i
\(503\) 367.090 211.939i 0.729801 0.421351i −0.0885483 0.996072i \(-0.528223\pi\)
0.818349 + 0.574721i \(0.194889\pi\)
\(504\) 0 0
\(505\) 1.24632 2.15868i 0.00246795 0.00427462i
\(506\) −80.4568 101.083i −0.159006 0.199769i
\(507\) 0 0
\(508\) −757.771 174.446i −1.49167 0.343398i
\(509\) −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
\(518\) −74.3577 1.92386i −0.143548 0.00371401i
\(519\) 0 0
\(520\) −0.295475 1.06158i −0.000568222 0.00204150i
\(521\) 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 0.0908806 0.995862i \(-0.471032\pi\)
0.907882 + 0.419226i \(0.137699\pi\)
\(524\) 301.890 + 195.781i 0.576126 + 0.373629i
\(525\) 0 0
\(526\) 179.523 293.161i 0.341299 0.557340i
\(527\) 94.5487 259.770i 0.179409 0.492923i
\(528\) 0 0
\(529\) 70.3727 399.103i 0.133030 0.754448i
\(530\) −0.483385 1.44318i −0.000912047 0.00272299i
\(531\) 0 0
\(532\) −43.8688 + 33.1005i −0.0824601 + 0.0622190i
\(533\) 320.965 + 269.322i 0.602186 + 0.505294i
\(534\) 0 0
\(535\) −3.12203 + 0.550498i −0.00583557 + 0.00102897i
\(536\) 33.5496 + 345.034i 0.0625926 + 0.643719i
\(537\) 0 0
\(538\) 435.115 65.1675i 0.808765 0.121129i
\(539\) 281.742i 0.522713i
\(540\) 0 0
\(541\) 406.606 0.751582 0.375791 0.926705i \(-0.377371\pi\)
0.375791 + 0.926705i \(0.377371\pi\)
\(542\) −74.2886 496.015i −0.137064 0.915158i
\(543\) 0 0
\(544\) −267.714 83.9500i −0.492122 0.154320i
\(545\) −0.376754 2.13668i −0.000691292 0.00392051i
\(546\) 0 0
\(547\) −342.420 + 408.080i −0.625996 + 0.746032i −0.982089 0.188418i \(-0.939664\pi\)
0.356093 + 0.934450i \(0.384108\pi\)
\(548\) 191.689 144.636i 0.349797 0.263934i
\(549\) 0 0
\(550\) −275.317 + 92.2154i −0.500576 + 0.167664i
\(551\) −437.936 77.2199i −0.794802 0.140145i
\(552\) 0 0
\(553\) 87.8415 + 31.9717i 0.158845 + 0.0578150i
\(554\) −56.7625 34.7597i −0.102459 0.0627431i
\(555\) 0 0
\(556\) −297.691 193.058i −0.535416 0.347228i
\(557\) −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
\(560\) 0.205128 0.0146018i 0.000366300 2.60746e-5i
\(561\) 0 0
\(562\) 8.21032 317.331i 0.0146091 0.564646i
\(563\) −670.430 798.988i −1.19082 1.41916i −0.884060 0.467373i \(-0.845200\pi\)
−0.306758 0.951788i \(-0.599244\pi\)
\(564\) 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 0.762151 0.647400i \(-0.224144\pi\)
−0.769910 + 0.638152i \(0.779699\pi\)
\(572\) 168.578 + 38.8084i 0.294718 + 0.0678468i
\(573\) 0 0
\(574\) −61.1796 + 48.6957i −0.106585 + 0.0848358i
\(575\) 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 \(-0.488683\pi\)
\(578\) −155.366 + 394.781i −0.268799 + 0.683012i
\(579\) 0 0
\(580\) 1.21773 + 1.13413i 0.00209953 + 0.00195539i
\(581\) −93.7437 34.1199i −0.161349 0.0587262i
\(582\) 0 0
\(583\) 235.300 + 41.4897i 0.403602 + 0.0711659i
\(584\) −18.1159 + 232.979i −0.0310204 + 0.398936i
\(585\) 0 0
\(586\) 36.8122 41.6349i 0.0628195 0.0710493i
\(587\) 222.285 264.909i 0.378680 0.451293i −0.542717 0.839915i \(-0.682605\pi\)
0.921397 + 0.388623i \(0.127049\pi\)
\(588\) 0 0
\(589\) 108.244 + 613.881i 0.183775 + 1.04224i
\(590\) 0.898325 + 1.65328i 0.00152258 + 0.00280216i
\(591\) 0 0
\(592\) 770.107 + 374.415i 1.30086 + 0.632457i
\(593\) 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
\(596\) −563.290 29.1676i −0.945118 0.0489389i
\(597\) 0 0
\(598\) −79.1036 145.582i −0.132280 0.243448i
\(599\) −873.003 + 153.934i −1.45743 + 0.256985i −0.845522 0.533941i \(-0.820710\pi\)
−0.611912 + 0.790926i \(0.709599\pi\)
\(600\) 0 0
\(601\) 417.266 + 350.128i 0.694287 + 0.582576i 0.920142 0.391585i \(-0.128073\pi\)
−0.225855 + 0.974161i \(0.572518\pi\)
\(602\) −65.9857 + 74.6303i −0.109611 + 0.123971i
\(603\) 0 0
\(604\) 381.778 47.1188i 0.632082 0.0780112i
\(605\) 0.280313 1.58973i 0.000463327 0.00262766i
\(606\) 0 0
\(607\) −334.605 + 919.318i −0.551243 + 1.51453i 0.280772 + 0.959775i \(0.409410\pi\)
−0.832015 + 0.554753i \(0.812813\pi\)
\(608\) 617.444 137.897i 1.01553 0.226804i
\(609\) 0 0
\(610\) 0.511586 1.29993i 0.000838666 0.00213103i
\(611\) 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 \(0.107132\pi\)
\(614\) 624.089 496.742i 1.01643 0.809026i
\(615\) 0 0
\(616\) −13.3602 + 29.3894i −0.0216887 + 0.0477100i
\(617\) −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 \(-0.866388\pi\)
0.437584 0.899178i \(-0.355834\pi\)
\(620\) 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
\(626\) −6.44305 + 249.026i −0.0102924 + 0.397805i
\(627\) 0 0
\(628\) 154.147 + 302.064i 0.245457 + 0.480993i
\(629\) −234.620 + 406.373i −0.373004 + 0.646063i
\(630\) 0 0
\(631\) 901.462 520.459i 1.42862 0.824817i 0.431612 0.902059i \(-0.357945\pi\)
0.997012 + 0.0772427i \(0.0246116\pi\)
\(632\) −768.265 753.557i −1.21561 1.19234i
\(633\) 0 0
\(634\) 668.427 + 409.325i 1.05430 + 0.645623i
\(635\) 1.22973 3.37867i 0.00193659 0.00532073i
\(636\) 0 0
\(637\) −62.7427 + 355.831i −0.0984972 + 0.558605i
\(638\) −247.708 + 82.9682i −0.388258 + 0.130044i
\(639\) 0 0
\(640\) −2.21932 0.824238i −0.00346769 0.00128787i
\(641\) −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 −0.421403 0.906873i \(-0.638462\pi\)
−0.0858206 + 0.996311i \(0.527351\pi\)
\(644\) 29.5640 9.05884i 0.0459068 0.0140665i
\(645\) 0 0
\(646\) 51.3505 + 342.861i 0.0794900 + 0.530745i
\(647\) 302.985i 0.468293i 0.972201 + 0.234146i \(0.0752295\pi\)
−0.972201 + 0.234146i \(0.924771\pi\)
\(648\) 0 0
\(649\) −295.379 −0.455129
\(650\) −368.252 + 55.1534i −0.566542 + 0.0848513i
\(651\) 0 0
\(652\) 72.3726 + 236.192i 0.111001 + 0.362257i
\(653\) 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
\(656\) 873.161 218.864i 1.33104 0.333634i
\(657\) 0 0
\(658\) 30.1579 + 90.0389i 0.0458327 + 0.136837i
\(659\) 969.694 + 170.983i 1.47146 + 0.259459i 0.851161 0.524904i \(-0.175899\pi\)
0.620302 + 0.784363i \(0.287010\pi\)
\(660\) 0 0
\(661\) −708.366 257.824i −1.07166 0.390052i −0.254862 0.966978i \(-0.582030\pi\)
−0.816797 + 0.576926i \(0.804252\pi\)
\(662\) 50.3285 82.1864i 0.0760250 0.124149i
\(663\) 0 0
\(664\) 819.887 + 804.190i 1.23477 + 1.21113i
\(665\) −0.127054 0.220065i −0.000191059 0.000330924i
\(666\) 0 0
\(667\) 216.685 + 125.103i 0.324864 + 0.187561i
\(668\) 1069.91 545.991i 1.60167 0.817352i
\(669\) 0 0
\(670\) −1.60239 0.0414586i −0.00239162 6.18786e-5i
\(671\) 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
\(680\) 0.536881 1.18101i 0.000789531 0.00173678i
\(681\) 0 0
\(682\) 228.046 + 286.510i 0.334379 + 0.420102i
\(683\) 709.493 + 409.626i 1.03879 + 0.599745i 0.919490 0.393113i \(-0.128602\pi\)
0.119299 + 0.992858i \(0.461935\pi\)
\(684\) 0 0
\(685\) 0.555176 + 0.961594i 0.000810476 + 0.00140379i
\(686\) −126.118 49.6336i −0.183845 0.0723522i
\(687\) 0 0
\(688\) 1047.09 467.763i 1.52193 0.679887i
\(689\) 287.936 + 104.800i 0.417905 + 0.152105i
\(690\) 0 0
\(691\) −540.831 95.3631i −0.782679 0.138007i −0.231990 0.972718i \(-0.574524\pi\)
−0.550689 + 0.834711i \(0.685635\pi\)
\(692\) 149.832 + 1214.00i 0.216520 + 1.75434i
\(693\) 0 0
\(694\) −173.836 153.700i −0.250484 0.221470i
\(695\) 1.05457 1.25678i 0.00151736 0.00180832i
\(696\) 0 0
\(697\) 85.6573 + 485.787i 0.122894 + 0.696968i
\(698\) 290.822 158.021i 0.416650 0.226391i
\(699\) 0 0
\(700\) 3.59348 69.3980i 0.00513354 0.0991401i
\(701\) −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
\(704\) 280.032 244.352i 0.397773 0.347091i
\(705\) 0 0
\(706\) −1128.57 + 613.218i −1.59853 + 0.868581i
\(707\) −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 \(0.929438\pi\)
\(710\) 1.58417 + 1.40067i 0.00223122 + 0.00197277i
\(711\) 0 0
\(712\) −36.6582 + 471.440i −0.0514862 + 0.662135i
\(713\) 60.9033 345.400i 0.0854184 0.484432i
\(714\) 0 0
\(715\) −0.273574 + 0.751639i −0.000382621 + 0.00105124i
\(716\) −590.880 + 634.436i −0.825251 + 0.886084i
\(717\) 0 0
\(718\) 611.820 + 240.781i 0.852117 + 0.335350i
\(719\) 464.412 268.129i 0.645914 0.372919i −0.140975 0.990013i \(-0.545024\pi\)
0.786889 + 0.617094i \(0.211690\pi\)
\(720\) 0 0
\(721\) −17.1239 + 29.6595i −0.0237502 + 0.0411366i
\(722\) −37.2051 46.7433i −0.0515307 0.0647413i
\(723\) 0 0
\(724\) 27.2423 118.337i 0.0376274 0.163449i
\(725\) 430.755 361.446i 0.594145 0.498547i
\(726\) 0 0
\(727\) 169.632 + 466.059i 0.233331 + 0.641071i 1.00000 0.000971702i \(-0.000309302\pi\)
−0.766669 + 0.642043i \(0.778087\pi\)
\(728\) −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 \(0.207262\pi\)
\(734\) 219.560 + 5.68070i 0.299129 + 0.00773937i
\(735\) 0 0
\(736\) −352.990 45.9107i −0.479606 0.0623787i
\(737\) 125.818 217.923i 0.170716 0.295689i
\(738\) 0 0
\(739\) −163.942 + 94.6517i −0.221842 + 0.128081i −0.606803 0.794852i \(-0.707548\pi\)
0.384961 + 0.922933i \(0.374215\pi\)
\(740\) −2.15439 + 3.32202i −0.00291134 + 0.00448922i
\(741\) 0 0
\(742\) −29.8635 + 48.7670i −0.0402473 + 0.0657237i
\(743\) −215.502 + 592.087i −0.290043 + 0.796886i 0.706016 + 0.708196i \(0.250491\pi\)
−0.996059 + 0.0886907i \(0.971732\pi\)
\(744\) 0 0
\(745\) 0.452889 2.56846i 0.000607905 0.00344760i
\(746\) −444.764 1327.88i −0.596198 1.78000i
\(747\) 0 0
\(748\) 122.667 + 162.573i 0.163994 + 0.217344i
\(749\) 91.2443 + 76.5631i 0.121821 + 0.102220i
\(750\) 0 0
\(751\) −1238.93 + 218.457i −1.64971 + 0.290888i −0.919721 0.392572i \(-0.871585\pi\)
−0.729988 + 0.683460i \(0.760474\pi\)
\(752\) 112.904 1087.29i 0.150138 1.44586i
\(753\) 0 0
\(754\) −331.324 + 49.6227i −0.439422 + 0.0658126i
\(755\) 1.77869i 0.00235589i
\(756\) 0 0
\(757\) −1329.08 −1.75572 −0.877859 0.478919i \(-0.841029\pi\)
−0.877859 + 0.478919i \(0.841029\pi\)
\(758\) −40.9141 273.178i −0.0539764 0.360393i
\(759\) 0 0
\(760\) 0.283112 + 2.91160i 0.000372516 + 0.00383105i
\(761\) −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
\(764\) −655.154 868.289i −0.857532 1.13650i
\(765\) 0 0
\(766\) −72.1368 + 24.1617i −0.0941734 + 0.0315427i
\(767\) −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 \(0.773710\pi\)
\(770\) −0.127303 0.0779567i −0.000165329 0.000101242i
\(771\) 0 0
\(772\) 577.145 889.944i 0.747598 1.15278i
\(773\) −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
\(776\) 81.9933 + 294.585i 0.105661 + 0.379620i
\(777\) 0 0
\(778\) −2.33029 + 90.0663i −0.00299523 + 0.115766i
\(779\) −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 0.858227 0.513271i \(-0.171566\pi\)
−0.654503 + 0.756060i \(0.727122\pi\)
\(788\) −151.565 + 658.377i −0.192341 + 0.835503i
\(789\) 0 0
\(790\) 3.89326 3.09883i 0.00492818 0.00392257i
\(791\) −20.3524 11.7505i −0.0257300 0.0148552i
\(792\) 0 0
\(793\) 140.624 + 243.567i 0.177331 + 0.307147i
\(794\) 511.064 1298.60i 0.643658 1.63552i
\(795\) 0 0
\(796\) −327.688 + 351.843i −0.411669 + 0.442014i
\(797\) −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
\(800\) −368.284 + 710.176i −0.460355 + 0.887719i
\(801\) 0 0
\(802\) −799.505 + 904.246i −0.996889 + 1.12749i
\(803\) 109.033 129.941i 0.135783 0.161820i
\(804\) 0 0
\(805\) 0.0248272 + 0.140802i 3.08413e−5 + 0.000174910i
\(806\) 224.211 + 412.637i 0.278177 + 0.511957i
\(807\) 0 0
\(808\) 1044.06 + 268.969i 1.29216 + 0.332882i
\(809\) −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 \(0.184437\pi\)
−0.836777 + 0.547543i \(0.815563\pi\)
\(812\) 3.23313 62.4389i 0.00398169 0.0768952i
\(813\) 0 0
\(814\) −296.761 546.158i −0.364571 0.670956i
\(815\) −1.12489 + 0.198349i −0.00138024 + 0.000243373i
\(816\) 0 0
\(817\) −1085.54 910.874i −1.32869 1.11490i
\(818\) −885.966 + 1002.03i −1.08309 + 1.22498i
\(819\) 0 0
\(820\) 0.509841 + 4.13096i 0.000621757 + 0.00503776i
\(821\) 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 \(0.243918\pi\)
−0.997678 + 0.0681051i \(0.978305\pi\)
\(824\) 320.762 229.252i 0.389275 0.278218i
\(825\) 0 0
\(826\) 25.8891 65.7837i 0.0313428 0.0796413i
\(827\) −537.817 + 310.509i −0.650322 + 0.375464i −0.788580 0.614933i \(-0.789183\pi\)
0.138257 + 0.990396i \(0.455850\pi\)
\(828\) 0 0
\(829\) 155.530 269.386i 0.187612 0.324953i −0.756842 0.653598i \(-0.773259\pi\)
0.944453 + 0.328645i \(0.106592\pi\)
\(830\) −4.15486 + 3.30705i −0.00500585 + 0.00398439i
\(831\) 0 0
\(832\) 408.087 246.247i 0.490490 0.295970i
\(833\) −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 \(0.144970\pi\)
−0.405228 + 0.914216i \(0.632808\pi\)
\(840\) 0 0
\(841\) −256.684 + 215.383i −0.305212 + 0.256104i
\(842\) 25.6843 992.707i 0.0305040 1.17899i
\(843\) 0 0
\(844\) 989.324 504.865i 1.17218 0.598181i
\(845\) 1.04998 1.81861i 0.00124257 0.00215220i
\(846\) 0 0
\(847\) −52.5254 + 30.3256i −0.0620135 + 0.0358035i
\(848\) 545.306 368.806i 0.643049 0.434913i
\(849\) 0 0
\(850\) −373.853 228.937i −0.439828 0.269338i
\(851\) −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 \(-0.159649\pi\)
\(854\) −49.7698 + 16.6700i −0.0582785 + 0.0195200i
\(855\) 0 0
\(856\) −591.486 1237.09i −0.690988 1.44520i
\(857\) 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 0.397535 0.917587i \(-0.369866\pi\)
0.687394 + 0.726285i \(0.258755\pi\)
\(860\) 1.55355 + 5.07009i 0.00180645 + 0.00589545i
\(861\) 0 0
\(862\) 120.381 + 803.770i 0.139653 + 0.932447i
\(863\) 1407.68i 1.63114i −0.578657 0.815571i \(-0.696423\pi\)
0.578657 0.815571i \(-0.303577\pi\)
\(864\) 0 0
\(865\) −5.65602 −0.00653875
\(866\) −620.568 + 92.9429i −0.716592 + 0.107324i
\(867\) 0 0
\(868\) −83.7960 + 25.6763i −0.0965392 + 0.0295810i
\(869\) 135.646 + 769.286i 0.156094 + 0.885255i
\(870\) 0 0
\(871\) 207.434 247.211i 0.238156 0.283824i
\(872\) 846.649 404.806i 0.970928 0.464227i
\(873\) 0 0
\(874\) 139.696 + 417.074i 0.159835 + 0.477201i
\(875\) 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 \(0.667285\pi\)
\(878\) −472.900 + 772.245i −0.538611 + 0.879550i
\(879\) 0 0
\(880\) 0.962745 + 1.42348i 0.00109403 + 0.00161760i
\(881\) −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 0.631896 0.775053i \(-0.282277\pi\)
−0.355268 + 0.934765i \(0.615610\pi\)
\(884\) 118.721 + 232.642i 0.134299 + 0.263170i
\(885\) 0 0
\(886\) −468.488 12.1212i −0.528767 0.0136808i
\(887\) 224.634 + 267.708i 0.253251 + 0.301813i 0.877659 0.479285i \(-0.159104\pi\)
−0.624408 + 0.781099i \(0.714660\pi\)
\(888\) 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
\(896\) 29.8755 + 83.7825i 0.0333432 + 0.0935073i
\(897\) 0 0
\(898\) −199.914 251.165i −0.222621 0.279694i
\(899\) −614.170 354.591i −0.683170 0.394429i
\(900\) 0 0
\(901\) 180.373 + 312.415i 0.200192 + 0.346742i
\(902\) −608.030 239.290i −0.674090 0.265288i
\(903\) 0 0
\(904\) 157.313 + 220.108i 0.174019 + 0.243482i
\(905\) 0.527627 + 0.192041i 0.000583014 + 0.000212200i
\(906\) 0 0
\(907\) −268.404 47.3268i −0.295925 0.0521795i 0.0237146 0.999719i \(-0.492451\pi\)
−0.319639 + 0.947539i \(0.603562\pi\)
\(908\) 134.923 16.6521i 0.148593 0.0183393i
\(909\) 0 0
\(910\) −0.143419 0.126807i −0.000157603 0.000139348i
\(911\) 31.4750 37.5105i 0.0345500 0.0411750i −0.748493 0.663143i \(-0.769222\pi\)
0.783043 + 0.621968i \(0.213667\pi\)
\(912\) 0 0
\(913\) −144.760 820.976i −0.158555 0.899207i
\(914\) −160.596 + 87.2615i −0.175707 + 0.0954721i
\(915\) 0 0
\(916\) −1214.24 62.8743i −1.32559 0.0686401i
\(917\) 62.5109 0.0681689
\(918\) 0 0
\(919\) 710.873i 0.773529i 0.922179 + 0.386764i \(0.126407\pi\)
−0.922179 + 0.386764i \(0.873593\pi\)
\(920\) 0.410615 1.59390i 0.000446320 0.00173250i
\(921\) 0 0
\(922\) −231.909 + 126.010i −0.251528 + 0.136670i
\(923\) −419.253 + 73.9256i −0.454228 + 0.0800927i
\(924\) 0 0
\(925\) 1024.93 + 860.019i 1.10803 + 0.929750i
\(926\) −333.852 295.182i −0.360532 0.318771i
\(927\) 0 0
\(928\) −331.353 + 638.960i −0.357062 + 0.688535i
\(929\) 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
\(932\) 292.641 + 272.550i 0.313992 + 0.292436i
\(933\) 0 0
\(934\) −827.368 325.610i −0.885833 0.348619i
\(935\) −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 \(0.0520831\pi\)
\(938\) 37.5059 + 47.1211i 0.0399850 + 0.0502358i
\(939\) 0 0
\(940\) 4.92571 + 1.13395i 0.00524012 + 0.00120633i
\(941\) 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 0.791565 0.611085i \(-0.209267\pi\)
−0.999172 + 0.0406899i \(0.987044\pi\)
\(948\) 0 0
\(949\) 166.643 139.830i 0.175599 0.147345i
\(950\) 988.179 + 25.5672i 1.04019 + 0.0269128i
\(951\) 0 0
\(952\) −46.9581 + 13.0701i −0.0493257 + 0.0137291i
\(953\) −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
\(956\) 434.501 + 281.782i 0.454498 + 0.294751i
\(957\) 0 0
\(958\) 593.836 969.733i 0.619871 1.01225i
\(959\) 14.2685 39.2025i 0.0148785 0.0408785i
\(960\) 0 0
\(961\) −5.74824 + 32.5999i −0.00598152 + 0.0339229i
\(962\) −253.173 755.867i −0.263173 0.785725i
\(963\) 0 0
\(964\) 189.891 143.280i 0.196983 0.148630i
\(965\) 3.75714 + 3.15261i 0.00389341 + 0.00326696i
\(966\) 0 0
\(967\) 40.1386 7.07751i 0.0415083 0.00731904i −0.152855 0.988249i \(-0.548847\pi\)
0.194364 + 0.980930i \(0.437736\pi\)
\(968\) 694.946 67.5736i 0.717919 0.0698075i
\(969\) 0 0
\(970\) −1.39831 + 0.209426i −0.00144156 + 0.000215903i
\(971\) 1253.25i 1.29068i 0.763895 + 0.645341i \(0.223285\pi\)
−0.763895 + 0.645341i \(0.776715\pi\)
\(972\) 0 0
\(973\) −61.6415 −0.0633520
\(974\) 274.760 + 1834.54i 0.282095 + 1.88351i
\(975\) 0 0
\(976\) 601.009 + 62.4087i 0.615788 + 0.0639434i
\(977\) −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
\(980\) −2.86528 + 2.16195i −0.00292375 + 0.00220607i
\(981\) 0 0
\(982\) 1036.43 347.145i 1.05543 0.353509i
\(983\) −964.524 170.072i −0.981204 0.173013i −0.340035 0.940413i \(-0.610439\pi\)
−0.641169 + 0.767400i \(0.721550\pi\)
\(984\) 0 0
\(985\) −2.93550 1.06843i −0.00298020 0.00108470i
\(986\) −336.364 205.980i −0.341140 0.208904i
\(987\) 0 0
\(988\) −494.132 320.454i −0.500133 0.324346i
\(989\) 398.657 + 690.494i 0.403091 + 0.698174i
\(990\) 0 0
\(991\) −574.931 331.937i −0.580153 0.334951i 0.181041 0.983475i \(-0.442053\pi\)
−0.761194 + 0.648524i \(0.775387\pi\)
\(992\) 1000.51 + 130.129i 1.00858 + 0.131179i
\(993\) 0 0
\(994\) 2.05491 79.4229i 0.00206731 0.0799023i
\(995\) −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.19.3 204
3.2 odd 2 108.3.j.a.7.32 yes 204
4.3 odd 2 inner 324.3.j.a.19.5 204
12.11 even 2 108.3.j.a.7.30 204
27.4 even 9 inner 324.3.j.a.307.5 204
27.23 odd 18 108.3.j.a.31.30 yes 204
108.23 even 18 108.3.j.a.31.32 yes 204
108.31 odd 18 inner 324.3.j.a.307.3 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.7.30 204 12.11 even 2
108.3.j.a.7.32 yes 204 3.2 odd 2
108.3.j.a.31.30 yes 204 27.23 odd 18
108.3.j.a.31.32 yes 204 108.23 even 18
324.3.j.a.19.3 204 1.1 even 1 trivial
324.3.j.a.19.5 204 4.3 odd 2 inner
324.3.j.a.307.3 204 108.31 odd 18 inner
324.3.j.a.307.5 204 27.4 even 9 inner