Properties

Label 99.3.k.c.46.2
Level $99$
Weight $3$
Character 99.46
Analytic conductor $2.698$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,3,Mod(19,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.k (of order \(10\), degree \(4\), 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: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + 1868 x^{7} - 1619 x^{6} - 16804 x^{5} + 32427 x^{4} + 43316 x^{3} + \cdots + 83521 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 46.2
Root \(0.988132 + 0.846795i\) of defining polynomial
Character \(\chi\) \(=\) 99.46
Dual form 99.3.k.c.28.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28981 - 0.419086i) q^{2} +(-1.74808 - 1.27006i) q^{4} +(-0.708979 - 2.18201i) q^{5} +(-5.74346 + 7.90520i) q^{7} +(4.91103 + 6.75946i) q^{8} +O(q^{10})\) \(q+(-1.28981 - 0.419086i) q^{2} +(-1.74808 - 1.27006i) q^{4} +(-0.708979 - 2.18201i) q^{5} +(-5.74346 + 7.90520i) q^{7} +(4.91103 + 6.75946i) q^{8} +3.11151i q^{10} +(-10.3340 + 3.76954i) q^{11} +(-14.6363 - 4.75561i) q^{13} +(10.7210 - 7.78923i) q^{14} +(-0.830695 - 2.55662i) q^{16} +(-11.2386 + 3.65165i) q^{17} +(7.10329 + 9.77683i) q^{19} +(-1.53192 + 4.71477i) q^{20} +(14.9086 - 0.531195i) q^{22} -16.6610 q^{23} +(15.9669 - 11.6006i) q^{25} +(16.8850 + 12.2677i) q^{26} +(20.0801 - 6.52441i) q^{28} +(15.6013 - 21.4734i) q^{29} +(1.28594 - 3.95770i) q^{31} -29.7749i q^{32} +16.0261 q^{34} +(21.3212 + 6.92769i) q^{35} +(-54.4646 - 39.5709i) q^{37} +(-5.06458 - 15.5872i) q^{38} +(11.2674 - 15.5082i) q^{40} +(10.6080 + 14.6006i) q^{41} +46.3735i q^{43} +(22.8521 + 6.53522i) q^{44} +(21.4896 + 6.98238i) q^{46} +(49.2812 - 35.8049i) q^{47} +(-14.3630 - 44.2047i) q^{49} +(-25.4560 + 8.27115i) q^{50} +(19.5455 + 26.9020i) q^{52} +(-31.2773 + 96.2616i) q^{53} +(15.5517 + 19.8763i) q^{55} -81.6412 q^{56} +(-29.1220 + 21.1584i) q^{58} +(-78.7122 - 57.1878i) q^{59} +(1.19706 - 0.388949i) q^{61} +(-3.31724 + 4.56578i) q^{62} +(-15.8010 + 48.6305i) q^{64} +35.3081i q^{65} -55.1168 q^{67} +(24.2838 + 7.89030i) q^{68} +(-24.5971 - 17.8709i) q^{70} +(4.62167 + 14.2240i) q^{71} +(-44.6021 + 61.3895i) q^{73} +(53.6656 + 73.8644i) q^{74} -26.1123i q^{76} +(29.5537 - 103.342i) q^{77} +(27.7900 + 9.02950i) q^{79} +(-4.98962 + 3.62517i) q^{80} +(-7.56341 - 23.2778i) q^{82} +(6.06044 - 1.96915i) q^{83} +(15.9359 + 21.9339i) q^{85} +(19.4345 - 59.8133i) q^{86} +(-76.2304 - 51.3395i) q^{88} +3.95503 q^{89} +(121.657 - 88.3889i) q^{91} +(29.1247 + 21.1604i) q^{92} +(-78.5689 + 25.5286i) q^{94} +(16.2971 - 22.4310i) q^{95} +(-10.2392 + 31.5131i) q^{97} +63.0352i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28981 0.419086i −0.644907 0.209543i −0.0317398 0.999496i \(-0.510105\pi\)
−0.613167 + 0.789953i \(0.710105\pi\)
\(3\) 0 0
\(4\) −1.74808 1.27006i −0.437020 0.317514i
\(5\) −0.708979 2.18201i −0.141796 0.436402i 0.854789 0.518975i \(-0.173686\pi\)
−0.996585 + 0.0825729i \(0.973686\pi\)
\(6\) 0 0
\(7\) −5.74346 + 7.90520i −0.820495 + 1.12931i 0.169123 + 0.985595i \(0.445906\pi\)
−0.989618 + 0.143720i \(0.954094\pi\)
\(8\) 4.91103 + 6.75946i 0.613879 + 0.844932i
\(9\) 0 0
\(10\) 3.11151i 0.311151i
\(11\) −10.3340 + 3.76954i −0.939450 + 0.342686i
\(12\) 0 0
\(13\) −14.6363 4.75561i −1.12587 0.365816i −0.313862 0.949468i \(-0.601623\pi\)
−0.812004 + 0.583652i \(0.801623\pi\)
\(14\) 10.7210 7.78923i 0.765783 0.556374i
\(15\) 0 0
\(16\) −0.830695 2.55662i −0.0519184 0.159789i
\(17\) −11.2386 + 3.65165i −0.661096 + 0.214803i −0.620300 0.784364i \(-0.712989\pi\)
−0.0407956 + 0.999168i \(0.512989\pi\)
\(18\) 0 0
\(19\) 7.10329 + 9.77683i 0.373857 + 0.514570i 0.953944 0.299984i \(-0.0969814\pi\)
−0.580087 + 0.814555i \(0.696981\pi\)
\(20\) −1.53192 + 4.71477i −0.0765962 + 0.235739i
\(21\) 0 0
\(22\) 14.9086 0.531195i 0.677665 0.0241452i
\(23\) −16.6610 −0.724390 −0.362195 0.932102i \(-0.617973\pi\)
−0.362195 + 0.932102i \(0.617973\pi\)
\(24\) 0 0
\(25\) 15.9669 11.6006i 0.638676 0.464025i
\(26\) 16.8850 + 12.2677i 0.649425 + 0.471835i
\(27\) 0 0
\(28\) 20.0801 6.52441i 0.717146 0.233015i
\(29\) 15.6013 21.4734i 0.537977 0.740462i −0.450343 0.892856i \(-0.648698\pi\)
0.988320 + 0.152394i \(0.0486981\pi\)
\(30\) 0 0
\(31\) 1.28594 3.95770i 0.0414818 0.127668i −0.928171 0.372154i \(-0.878619\pi\)
0.969653 + 0.244486i \(0.0786193\pi\)
\(32\) 29.7749i 0.930466i
\(33\) 0 0
\(34\) 16.0261 0.471356
\(35\) 21.3212 + 6.92769i 0.609178 + 0.197934i
\(36\) 0 0
\(37\) −54.4646 39.5709i −1.47202 1.06948i −0.980023 0.198884i \(-0.936268\pi\)
−0.491994 0.870599i \(-0.663732\pi\)
\(38\) −5.06458 15.5872i −0.133279 0.410189i
\(39\) 0 0
\(40\) 11.2674 15.5082i 0.281685 0.387706i
\(41\) 10.6080 + 14.6006i 0.258731 + 0.356113i 0.918545 0.395316i \(-0.129365\pi\)
−0.659814 + 0.751429i \(0.729365\pi\)
\(42\) 0 0
\(43\) 46.3735i 1.07845i 0.842160 + 0.539227i \(0.181284\pi\)
−0.842160 + 0.539227i \(0.818716\pi\)
\(44\) 22.8521 + 6.53522i 0.519366 + 0.148528i
\(45\) 0 0
\(46\) 21.4896 + 6.98238i 0.467164 + 0.151791i
\(47\) 49.2812 35.8049i 1.04854 0.761806i 0.0766030 0.997062i \(-0.475593\pi\)
0.971934 + 0.235255i \(0.0755926\pi\)
\(48\) 0 0
\(49\) −14.3630 44.2047i −0.293122 0.902137i
\(50\) −25.4560 + 8.27115i −0.509120 + 0.165423i
\(51\) 0 0
\(52\) 19.5455 + 26.9020i 0.375875 + 0.517347i
\(53\) −31.2773 + 96.2616i −0.590138 + 1.81626i −0.0125594 + 0.999921i \(0.503998\pi\)
−0.577578 + 0.816335i \(0.696002\pi\)
\(54\) 0 0
\(55\) 15.5517 + 19.8763i 0.282759 + 0.361387i
\(56\) −81.6412 −1.45788
\(57\) 0 0
\(58\) −29.1220 + 21.1584i −0.502104 + 0.364800i
\(59\) −78.7122 57.1878i −1.33411 0.969284i −0.999639 0.0268769i \(-0.991444\pi\)
−0.334467 0.942408i \(-0.608556\pi\)
\(60\) 0 0
\(61\) 1.19706 0.388949i 0.0196240 0.00637621i −0.299189 0.954194i \(-0.596716\pi\)
0.318813 + 0.947818i \(0.396716\pi\)
\(62\) −3.31724 + 4.56578i −0.0535038 + 0.0736416i
\(63\) 0 0
\(64\) −15.8010 + 48.6305i −0.246891 + 0.759852i
\(65\) 35.3081i 0.543202i
\(66\) 0 0
\(67\) −55.1168 −0.822638 −0.411319 0.911491i \(-0.634932\pi\)
−0.411319 + 0.911491i \(0.634932\pi\)
\(68\) 24.2838 + 7.89030i 0.357115 + 0.116034i
\(69\) 0 0
\(70\) −24.5971 17.8709i −0.351388 0.255298i
\(71\) 4.62167 + 14.2240i 0.0650939 + 0.200338i 0.978314 0.207129i \(-0.0664120\pi\)
−0.913220 + 0.407467i \(0.866412\pi\)
\(72\) 0 0
\(73\) −44.6021 + 61.3895i −0.610987 + 0.840952i −0.996658 0.0816847i \(-0.973970\pi\)
0.385671 + 0.922636i \(0.373970\pi\)
\(74\) 53.6656 + 73.8644i 0.725211 + 0.998168i
\(75\) 0 0
\(76\) 26.1123i 0.343582i
\(77\) 29.5537 103.342i 0.383814 1.34211i
\(78\) 0 0
\(79\) 27.7900 + 9.02950i 0.351772 + 0.114298i 0.479572 0.877502i \(-0.340792\pi\)
−0.127801 + 0.991800i \(0.540792\pi\)
\(80\) −4.98962 + 3.62517i −0.0623703 + 0.0453147i
\(81\) 0 0
\(82\) −7.56341 23.2778i −0.0922367 0.283875i
\(83\) 6.06044 1.96915i 0.0730173 0.0237248i −0.272281 0.962218i \(-0.587778\pi\)
0.345298 + 0.938493i \(0.387778\pi\)
\(84\) 0 0
\(85\) 15.9359 + 21.9339i 0.187481 + 0.258046i
\(86\) 19.4345 59.8133i 0.225983 0.695503i
\(87\) 0 0
\(88\) −76.2304 51.3395i −0.866255 0.583404i
\(89\) 3.95503 0.0444385 0.0222193 0.999753i \(-0.492927\pi\)
0.0222193 + 0.999753i \(0.492927\pi\)
\(90\) 0 0
\(91\) 121.657 88.3889i 1.33689 0.971306i
\(92\) 29.1247 + 21.1604i 0.316573 + 0.230004i
\(93\) 0 0
\(94\) −78.5689 + 25.5286i −0.835840 + 0.271581i
\(95\) 16.2971 22.4310i 0.171548 0.236116i
\(96\) 0 0
\(97\) −10.2392 + 31.5131i −0.105559 + 0.324877i −0.989861 0.142038i \(-0.954635\pi\)
0.884302 + 0.466915i \(0.154635\pi\)
\(98\) 63.0352i 0.643216i
\(99\) 0 0
\(100\) −42.6449 −0.426449
\(101\) −92.3279 29.9992i −0.914138 0.297021i −0.186078 0.982535i \(-0.559578\pi\)
−0.728060 + 0.685514i \(0.759578\pi\)
\(102\) 0 0
\(103\) 150.522 + 109.361i 1.46138 + 1.06175i 0.983001 + 0.183602i \(0.0587757\pi\)
0.478380 + 0.878153i \(0.341224\pi\)
\(104\) −39.7338 122.288i −0.382056 1.17585i
\(105\) 0 0
\(106\) 80.6838 111.052i 0.761168 1.04766i
\(107\) 112.786 + 155.236i 1.05407 + 1.45081i 0.885224 + 0.465165i \(0.154005\pi\)
0.168849 + 0.985642i \(0.445995\pi\)
\(108\) 0 0
\(109\) 113.760i 1.04367i −0.853047 0.521834i \(-0.825248\pi\)
0.853047 0.521834i \(-0.174752\pi\)
\(110\) −11.7290 32.1542i −0.106627 0.292311i
\(111\) 0 0
\(112\) 24.9816 + 8.11703i 0.223050 + 0.0724734i
\(113\) 13.2504 9.62696i 0.117260 0.0851944i −0.527610 0.849487i \(-0.676912\pi\)
0.644870 + 0.764293i \(0.276912\pi\)
\(114\) 0 0
\(115\) 11.8123 + 36.3544i 0.102715 + 0.316125i
\(116\) −54.5448 + 17.7227i −0.470214 + 0.152782i
\(117\) 0 0
\(118\) 77.5575 + 106.749i 0.657267 + 0.904651i
\(119\) 35.6816 109.817i 0.299846 0.922830i
\(120\) 0 0
\(121\) 92.5811 77.9085i 0.765133 0.643872i
\(122\) −1.70699 −0.0139917
\(123\) 0 0
\(124\) −7.27442 + 5.28518i −0.0586647 + 0.0426224i
\(125\) −83.0361 60.3293i −0.664289 0.482634i
\(126\) 0 0
\(127\) 5.31423 1.72670i 0.0418443 0.0135960i −0.288020 0.957624i \(-0.592997\pi\)
0.329864 + 0.944028i \(0.392997\pi\)
\(128\) −29.2442 + 40.2512i −0.228471 + 0.314463i
\(129\) 0 0
\(130\) 14.7971 45.5409i 0.113824 0.350315i
\(131\) 225.713i 1.72300i 0.507758 + 0.861500i \(0.330474\pi\)
−0.507758 + 0.861500i \(0.669526\pi\)
\(132\) 0 0
\(133\) −118.085 −0.887860
\(134\) 71.0904 + 23.0987i 0.530525 + 0.172378i
\(135\) 0 0
\(136\) −79.8765 58.0336i −0.587327 0.426718i
\(137\) −16.1770 49.7877i −0.118080 0.363414i 0.874497 0.485031i \(-0.161192\pi\)
−0.992577 + 0.121618i \(0.961192\pi\)
\(138\) 0 0
\(139\) 16.4968 22.7058i 0.118682 0.163351i −0.745543 0.666458i \(-0.767810\pi\)
0.864224 + 0.503106i \(0.167810\pi\)
\(140\) −28.4727 39.1893i −0.203376 0.279924i
\(141\) 0 0
\(142\) 20.2832i 0.142840i
\(143\) 169.177 6.02777i 1.18305 0.0421523i
\(144\) 0 0
\(145\) −57.9162 18.8181i −0.399422 0.129780i
\(146\) 83.2558 60.4889i 0.570245 0.414308i
\(147\) 0 0
\(148\) 44.9514 + 138.346i 0.303726 + 0.934771i
\(149\) −10.6920 + 3.47406i −0.0717587 + 0.0233158i −0.344676 0.938722i \(-0.612011\pi\)
0.272918 + 0.962037i \(0.412011\pi\)
\(150\) 0 0
\(151\) −59.4636 81.8446i −0.393799 0.542018i 0.565375 0.824834i \(-0.308731\pi\)
−0.959174 + 0.282816i \(0.908731\pi\)
\(152\) −31.2016 + 96.0287i −0.205274 + 0.631768i
\(153\) 0 0
\(154\) −81.4280 + 120.907i −0.528753 + 0.785108i
\(155\) −9.54745 −0.0615965
\(156\) 0 0
\(157\) −15.4295 + 11.2102i −0.0982772 + 0.0714025i −0.635839 0.771822i \(-0.719346\pi\)
0.537561 + 0.843225i \(0.319346\pi\)
\(158\) −32.0597 23.2928i −0.202910 0.147423i
\(159\) 0 0
\(160\) −64.9692 + 21.1098i −0.406057 + 0.131936i
\(161\) 95.6917 131.708i 0.594358 0.818064i
\(162\) 0 0
\(163\) −4.46584 + 13.7444i −0.0273978 + 0.0843217i −0.963820 0.266552i \(-0.914115\pi\)
0.936423 + 0.350874i \(0.114115\pi\)
\(164\) 38.9958i 0.237779i
\(165\) 0 0
\(166\) −8.64208 −0.0520607
\(167\) −125.427 40.7538i −0.751062 0.244035i −0.0916237 0.995794i \(-0.529206\pi\)
−0.659438 + 0.751759i \(0.729206\pi\)
\(168\) 0 0
\(169\) 54.8803 + 39.8729i 0.324736 + 0.235934i
\(170\) −11.3622 34.9691i −0.0668362 0.205701i
\(171\) 0 0
\(172\) 58.8970 81.0647i 0.342424 0.471306i
\(173\) 20.6503 + 28.4227i 0.119366 + 0.164293i 0.864519 0.502601i \(-0.167623\pi\)
−0.745153 + 0.666894i \(0.767623\pi\)
\(174\) 0 0
\(175\) 192.849i 1.10200i
\(176\) 18.2216 + 23.2886i 0.103532 + 0.132322i
\(177\) 0 0
\(178\) −5.10125 1.65750i −0.0286587 0.00931178i
\(179\) −146.405 + 106.370i −0.817907 + 0.594244i −0.916112 0.400922i \(-0.868690\pi\)
0.0982054 + 0.995166i \(0.468690\pi\)
\(180\) 0 0
\(181\) 6.29265 + 19.3668i 0.0347660 + 0.106999i 0.966934 0.255028i \(-0.0820848\pi\)
−0.932168 + 0.362027i \(0.882085\pi\)
\(182\) −193.957 + 63.0205i −1.06570 + 0.346267i
\(183\) 0 0
\(184\) −81.8226 112.619i −0.444688 0.612060i
\(185\) −47.7298 + 146.897i −0.257999 + 0.794040i
\(186\) 0 0
\(187\) 102.374 80.1005i 0.547457 0.428345i
\(188\) −131.622 −0.700116
\(189\) 0 0
\(190\) −30.4207 + 22.1020i −0.160109 + 0.116326i
\(191\) 48.1778 + 35.0032i 0.252240 + 0.183263i 0.706719 0.707495i \(-0.250175\pi\)
−0.454479 + 0.890757i \(0.650175\pi\)
\(192\) 0 0
\(193\) −235.929 + 76.6578i −1.22243 + 0.397191i −0.847965 0.530051i \(-0.822173\pi\)
−0.374462 + 0.927242i \(0.622173\pi\)
\(194\) 26.4134 36.3549i 0.136151 0.187396i
\(195\) 0 0
\(196\) −31.0348 + 95.5152i −0.158341 + 0.487323i
\(197\) 166.342i 0.844374i −0.906509 0.422187i \(-0.861263\pi\)
0.906509 0.422187i \(-0.138737\pi\)
\(198\) 0 0
\(199\) 97.9933 0.492429 0.246214 0.969215i \(-0.420813\pi\)
0.246214 + 0.969215i \(0.420813\pi\)
\(200\) 156.828 + 50.9565i 0.784140 + 0.254782i
\(201\) 0 0
\(202\) 106.514 + 77.3866i 0.527295 + 0.383102i
\(203\) 80.1458 + 246.664i 0.394807 + 1.21509i
\(204\) 0 0
\(205\) 24.3379 33.4983i 0.118722 0.163406i
\(206\) −148.314 204.137i −0.719971 0.990955i
\(207\) 0 0
\(208\) 41.3698i 0.198893i
\(209\) −110.259 74.2572i −0.527556 0.355298i
\(210\) 0 0
\(211\) −11.0358 3.58574i −0.0523023 0.0169940i 0.282749 0.959194i \(-0.408754\pi\)
−0.335051 + 0.942200i \(0.608754\pi\)
\(212\) 176.933 128.549i 0.834589 0.606364i
\(213\) 0 0
\(214\) −80.4153 247.493i −0.375773 1.15651i
\(215\) 101.188 32.8778i 0.470640 0.152920i
\(216\) 0 0
\(217\) 23.9007 + 32.8965i 0.110142 + 0.151597i
\(218\) −47.6751 + 146.729i −0.218693 + 0.673069i
\(219\) 0 0
\(220\) −1.94172 54.4969i −0.00882602 0.247713i
\(221\) 181.857 0.822884
\(222\) 0 0
\(223\) −252.345 + 183.339i −1.13159 + 0.822149i −0.985926 0.167185i \(-0.946532\pi\)
−0.145666 + 0.989334i \(0.546532\pi\)
\(224\) 235.377 + 171.011i 1.05079 + 0.763442i
\(225\) 0 0
\(226\) −21.1251 + 6.86395i −0.0934737 + 0.0303714i
\(227\) 5.60519 7.71488i 0.0246925 0.0339863i −0.796492 0.604649i \(-0.793314\pi\)
0.821185 + 0.570662i \(0.193314\pi\)
\(228\) 0 0
\(229\) 62.0564 190.990i 0.270989 0.834017i −0.719264 0.694737i \(-0.755521\pi\)
0.990253 0.139281i \(-0.0444791\pi\)
\(230\) 51.8408i 0.225395i
\(231\) 0 0
\(232\) 221.767 0.955893
\(233\) −228.533 74.2548i −0.980827 0.318690i −0.225648 0.974209i \(-0.572450\pi\)
−0.755179 + 0.655519i \(0.772450\pi\)
\(234\) 0 0
\(235\) −113.066 82.1473i −0.481132 0.349563i
\(236\) 64.9637 + 199.938i 0.275270 + 0.847194i
\(237\) 0 0
\(238\) −92.0453 + 126.690i −0.386745 + 0.532309i
\(239\) −47.4322 65.2848i −0.198461 0.273158i 0.698174 0.715928i \(-0.253996\pi\)
−0.896636 + 0.442769i \(0.853996\pi\)
\(240\) 0 0
\(241\) 153.259i 0.635928i 0.948103 + 0.317964i \(0.102999\pi\)
−0.948103 + 0.317964i \(0.897001\pi\)
\(242\) −152.063 + 61.6881i −0.628359 + 0.254909i
\(243\) 0 0
\(244\) −2.58655 0.840420i −0.0106006 0.00344435i
\(245\) −86.2722 + 62.6804i −0.352131 + 0.255838i
\(246\) 0 0
\(247\) −57.4707 176.877i −0.232675 0.716100i
\(248\) 33.0672 10.7442i 0.133335 0.0433233i
\(249\) 0 0
\(250\) 81.8180 + 112.613i 0.327272 + 0.450451i
\(251\) 108.893 335.138i 0.433836 1.33521i −0.460439 0.887691i \(-0.652308\pi\)
0.894275 0.447518i \(-0.147692\pi\)
\(252\) 0 0
\(253\) 172.174 62.8042i 0.680528 0.248238i
\(254\) −7.57800 −0.0298347
\(255\) 0 0
\(256\) 220.059 159.882i 0.859605 0.624539i
\(257\) 104.897 + 76.2121i 0.408159 + 0.296545i 0.772856 0.634581i \(-0.218827\pi\)
−0.364697 + 0.931126i \(0.618827\pi\)
\(258\) 0 0
\(259\) 625.631 203.280i 2.41557 0.784865i
\(260\) 44.8432 61.7214i 0.172474 0.237390i
\(261\) 0 0
\(262\) 94.5931 291.128i 0.361042 1.11117i
\(263\) 180.174i 0.685072i −0.939505 0.342536i \(-0.888714\pi\)
0.939505 0.342536i \(-0.111286\pi\)
\(264\) 0 0
\(265\) 232.219 0.876297
\(266\) 152.308 + 49.4879i 0.572587 + 0.186045i
\(267\) 0 0
\(268\) 96.3485 + 70.0013i 0.359509 + 0.261199i
\(269\) −103.985 320.033i −0.386561 1.18971i −0.935342 0.353746i \(-0.884908\pi\)
0.548781 0.835966i \(-0.315092\pi\)
\(270\) 0 0
\(271\) −129.003 + 177.557i −0.476026 + 0.655193i −0.977735 0.209843i \(-0.932705\pi\)
0.501709 + 0.865036i \(0.332705\pi\)
\(272\) 18.6717 + 25.6995i 0.0686461 + 0.0944833i
\(273\) 0 0
\(274\) 70.9964i 0.259111i
\(275\) −121.272 + 180.068i −0.440989 + 0.654794i
\(276\) 0 0
\(277\) −232.844 75.6555i −0.840591 0.273125i −0.143091 0.989709i \(-0.545704\pi\)
−0.697500 + 0.716585i \(0.745704\pi\)
\(278\) −30.7934 + 22.3727i −0.110768 + 0.0804775i
\(279\) 0 0
\(280\) 57.8819 + 178.142i 0.206721 + 0.636222i
\(281\) 328.343 106.685i 1.16848 0.379662i 0.340404 0.940279i \(-0.389436\pi\)
0.828075 + 0.560617i \(0.189436\pi\)
\(282\) 0 0
\(283\) −136.711 188.166i −0.483077 0.664898i 0.496016 0.868313i \(-0.334796\pi\)
−0.979093 + 0.203415i \(0.934796\pi\)
\(284\) 9.98625 30.7345i 0.0351629 0.108220i
\(285\) 0 0
\(286\) −220.733 63.1249i −0.771793 0.220717i
\(287\) −176.348 −0.614452
\(288\) 0 0
\(289\) −120.834 + 87.7908i −0.418110 + 0.303774i
\(290\) 66.8148 + 48.5438i 0.230396 + 0.167392i
\(291\) 0 0
\(292\) 155.936 50.6667i 0.534027 0.173516i
\(293\) −313.718 + 431.796i −1.07071 + 1.47371i −0.201355 + 0.979518i \(0.564535\pi\)
−0.869355 + 0.494188i \(0.835465\pi\)
\(294\) 0 0
\(295\) −68.9791 + 212.296i −0.233828 + 0.719647i
\(296\) 562.485i 1.90029i
\(297\) 0 0
\(298\) 15.2467 0.0511633
\(299\) 243.854 + 79.2331i 0.815566 + 0.264993i
\(300\) 0 0
\(301\) −366.592 266.345i −1.21791 0.884867i
\(302\) 42.3971 + 130.485i 0.140388 + 0.432069i
\(303\) 0 0
\(304\) 19.0950 26.2819i 0.0628123 0.0864538i
\(305\) −1.69738 2.33625i −0.00556519 0.00765982i
\(306\) 0 0
\(307\) 142.846i 0.465296i −0.972561 0.232648i \(-0.925261\pi\)
0.972561 0.232648i \(-0.0747389\pi\)
\(308\) −182.913 + 143.116i −0.593872 + 0.464661i
\(309\) 0 0
\(310\) 12.3144 + 4.00120i 0.0397240 + 0.0129071i
\(311\) −37.1343 + 26.9797i −0.119403 + 0.0867514i −0.645884 0.763435i \(-0.723511\pi\)
0.526481 + 0.850187i \(0.323511\pi\)
\(312\) 0 0
\(313\) 110.168 + 339.062i 0.351975 + 1.08327i 0.957743 + 0.287625i \(0.0928658\pi\)
−0.605768 + 0.795641i \(0.707134\pi\)
\(314\) 24.5992 7.99278i 0.0783415 0.0254547i
\(315\) 0 0
\(316\) −37.1111 51.0791i −0.117440 0.161643i
\(317\) 19.1154 58.8312i 0.0603010 0.185587i −0.916368 0.400336i \(-0.868893\pi\)
0.976669 + 0.214749i \(0.0688933\pi\)
\(318\) 0 0
\(319\) −80.2786 + 280.715i −0.251657 + 0.879985i
\(320\) 117.315 0.366609
\(321\) 0 0
\(322\) −178.622 + 129.776i −0.554726 + 0.403032i
\(323\) −115.533 83.9395i −0.357687 0.259875i
\(324\) 0 0
\(325\) −288.864 + 93.8575i −0.888812 + 0.288792i
\(326\) 11.5202 15.8562i 0.0353380 0.0486386i
\(327\) 0 0
\(328\) −46.5962 + 143.408i −0.142062 + 0.437221i
\(329\) 595.222i 1.80919i
\(330\) 0 0
\(331\) −339.961 −1.02707 −0.513536 0.858068i \(-0.671665\pi\)
−0.513536 + 0.858068i \(0.671665\pi\)
\(332\) −13.0951 4.25485i −0.0394430 0.0128158i
\(333\) 0 0
\(334\) 144.699 + 105.130i 0.433229 + 0.314759i
\(335\) 39.0766 + 120.265i 0.116647 + 0.359001i
\(336\) 0 0
\(337\) −175.877 + 242.074i −0.521890 + 0.718320i −0.985868 0.167527i \(-0.946422\pi\)
0.463977 + 0.885847i \(0.346422\pi\)
\(338\) −54.0753 74.4282i −0.159986 0.220202i
\(339\) 0 0
\(340\) 58.5817i 0.172299i
\(341\) 1.62993 + 45.7461i 0.00477986 + 0.134153i
\(342\) 0 0
\(343\) −23.4224 7.61041i −0.0682870 0.0221878i
\(344\) −313.460 + 227.742i −0.911221 + 0.662041i
\(345\) 0 0
\(346\) −14.7235 45.3143i −0.0425535 0.130966i
\(347\) −202.617 + 65.8344i −0.583912 + 0.189724i −0.586052 0.810273i \(-0.699319\pi\)
0.00214053 + 0.999998i \(0.499319\pi\)
\(348\) 0 0
\(349\) −44.0593 60.6425i −0.126245 0.173761i 0.741216 0.671266i \(-0.234249\pi\)
−0.867461 + 0.497506i \(0.834249\pi\)
\(350\) 80.8205 248.740i 0.230916 0.710685i
\(351\) 0 0
\(352\) 112.238 + 307.692i 0.318857 + 0.874126i
\(353\) 372.860 1.05626 0.528130 0.849164i \(-0.322893\pi\)
0.528130 + 0.849164i \(0.322893\pi\)
\(354\) 0 0
\(355\) 27.7603 20.1691i 0.0781981 0.0568142i
\(356\) −6.91371 5.02310i −0.0194205 0.0141098i
\(357\) 0 0
\(358\) 233.414 75.8407i 0.651993 0.211846i
\(359\) −156.070 + 214.812i −0.434736 + 0.598363i −0.969032 0.246934i \(-0.920577\pi\)
0.534296 + 0.845297i \(0.320577\pi\)
\(360\) 0 0
\(361\) 66.4253 204.436i 0.184004 0.566305i
\(362\) 27.6167i 0.0762892i
\(363\) 0 0
\(364\) −324.925 −0.892651
\(365\) 165.574 + 53.7984i 0.453629 + 0.147393i
\(366\) 0 0
\(367\) −80.4998 58.4866i −0.219346 0.159364i 0.472686 0.881231i \(-0.343284\pi\)
−0.692032 + 0.721867i \(0.743284\pi\)
\(368\) 13.8402 + 42.5957i 0.0376092 + 0.115749i
\(369\) 0 0
\(370\) 123.125 169.467i 0.332771 0.458020i
\(371\) −581.327 800.128i −1.56692 2.15668i
\(372\) 0 0
\(373\) 469.949i 1.25992i −0.776629 0.629959i \(-0.783072\pi\)
0.776629 0.629959i \(-0.216928\pi\)
\(374\) −165.613 + 60.4111i −0.442815 + 0.161527i
\(375\) 0 0
\(376\) 484.043 + 157.275i 1.28735 + 0.418285i
\(377\) −330.464 + 240.096i −0.876563 + 0.636861i
\(378\) 0 0
\(379\) 89.1943 + 274.512i 0.235341 + 0.724305i 0.997076 + 0.0764166i \(0.0243479\pi\)
−0.761735 + 0.647889i \(0.775652\pi\)
\(380\) −56.9773 + 18.5130i −0.149940 + 0.0487185i
\(381\) 0 0
\(382\) −47.4710 65.3382i −0.124270 0.171042i
\(383\) 60.7882 187.087i 0.158716 0.488477i −0.839803 0.542892i \(-0.817329\pi\)
0.998518 + 0.0544147i \(0.0173293\pi\)
\(384\) 0 0
\(385\) −246.447 + 8.78090i −0.640122 + 0.0228075i
\(386\) 336.430 0.871581
\(387\) 0 0
\(388\) 57.9223 42.0830i 0.149284 0.108461i
\(389\) −363.076 263.790i −0.933358 0.678124i 0.0134546 0.999909i \(-0.495717\pi\)
−0.946813 + 0.321785i \(0.895717\pi\)
\(390\) 0 0
\(391\) 187.247 60.8401i 0.478891 0.155601i
\(392\) 228.263 314.177i 0.582303 0.801471i
\(393\) 0 0
\(394\) −69.7115 + 214.550i −0.176933 + 0.544543i
\(395\) 67.0397i 0.169721i
\(396\) 0 0
\(397\) 608.594 1.53298 0.766491 0.642255i \(-0.222001\pi\)
0.766491 + 0.642255i \(0.222001\pi\)
\(398\) −126.393 41.0676i −0.317571 0.103185i
\(399\) 0 0
\(400\) −42.9220 31.1847i −0.107305 0.0779616i
\(401\) 80.0898 + 246.491i 0.199725 + 0.614691i 0.999889 + 0.0149093i \(0.00474596\pi\)
−0.800164 + 0.599782i \(0.795254\pi\)
\(402\) 0 0
\(403\) −37.6426 + 51.8105i −0.0934059 + 0.128562i
\(404\) 123.296 + 169.702i 0.305188 + 0.420056i
\(405\) 0 0
\(406\) 351.738i 0.866350i
\(407\) 711.999 + 203.617i 1.74938 + 0.500287i
\(408\) 0 0
\(409\) 249.341 + 81.0159i 0.609637 + 0.198083i 0.597534 0.801844i \(-0.296147\pi\)
0.0121029 + 0.999927i \(0.496147\pi\)
\(410\) −45.4301 + 33.0069i −0.110805 + 0.0805046i
\(411\) 0 0
\(412\) −124.231 382.343i −0.301531 0.928017i
\(413\) 904.162 293.780i 2.18925 0.711332i
\(414\) 0 0
\(415\) −8.59344 11.8279i −0.0207071 0.0285008i
\(416\) −141.598 + 435.793i −0.340379 + 1.04758i
\(417\) 0 0
\(418\) 111.094 + 141.986i 0.265774 + 0.339680i
\(419\) 650.465 1.55242 0.776211 0.630473i \(-0.217139\pi\)
0.776211 + 0.630473i \(0.217139\pi\)
\(420\) 0 0
\(421\) 508.799 369.664i 1.20855 0.878062i 0.213450 0.976954i \(-0.431530\pi\)
0.995098 + 0.0988920i \(0.0315298\pi\)
\(422\) 12.7314 + 9.24988i 0.0301691 + 0.0219191i
\(423\) 0 0
\(424\) −804.280 + 261.326i −1.89689 + 0.616336i
\(425\) −137.085 + 188.681i −0.322552 + 0.443955i
\(426\) 0 0
\(427\) −3.80056 + 11.6969i −0.00890062 + 0.0273933i
\(428\) 414.610i 0.968715i
\(429\) 0 0
\(430\) −144.292 −0.335562
\(431\) −560.194 182.018i −1.29975 0.422316i −0.424258 0.905541i \(-0.639465\pi\)
−0.875496 + 0.483225i \(0.839465\pi\)
\(432\) 0 0
\(433\) 126.292 + 91.7565i 0.291668 + 0.211909i 0.723990 0.689810i \(-0.242306\pi\)
−0.432323 + 0.901719i \(0.642306\pi\)
\(434\) −17.0410 52.4468i −0.0392650 0.120845i
\(435\) 0 0
\(436\) −144.481 + 198.861i −0.331379 + 0.456104i
\(437\) −118.348 162.892i −0.270818 0.372750i
\(438\) 0 0
\(439\) 209.017i 0.476121i 0.971250 + 0.238060i \(0.0765116\pi\)
−0.971250 + 0.238060i \(0.923488\pi\)
\(440\) −57.9777 + 202.734i −0.131768 + 0.460760i
\(441\) 0 0
\(442\) −234.562 76.2138i −0.530683 0.172430i
\(443\) 276.987 201.242i 0.625252 0.454272i −0.229500 0.973309i \(-0.573709\pi\)
0.854752 + 0.519037i \(0.173709\pi\)
\(444\) 0 0
\(445\) −2.80403 8.62992i −0.00630119 0.0193931i
\(446\) 402.313 130.719i 0.902047 0.293093i
\(447\) 0 0
\(448\) −293.682 404.218i −0.655539 0.902273i
\(449\) −17.7730 + 54.6996i −0.0395835 + 0.121825i −0.968896 0.247470i \(-0.920401\pi\)
0.929312 + 0.369295i \(0.120401\pi\)
\(450\) 0 0
\(451\) −164.660 110.895i −0.365100 0.245887i
\(452\) −35.3895 −0.0782954
\(453\) 0 0
\(454\) −10.4629 + 7.60171i −0.0230459 + 0.0167438i
\(455\) −279.118 202.791i −0.613445 0.445694i
\(456\) 0 0
\(457\) 608.260 197.636i 1.33098 0.432463i 0.444731 0.895664i \(-0.353299\pi\)
0.886253 + 0.463201i \(0.153299\pi\)
\(458\) −160.082 + 220.335i −0.349525 + 0.481080i
\(459\) 0 0
\(460\) 25.5233 78.5527i 0.0554855 0.170767i
\(461\) 492.084i 1.06743i 0.845666 + 0.533713i \(0.179204\pi\)
−0.845666 + 0.533713i \(0.820796\pi\)
\(462\) 0 0
\(463\) 366.054 0.790614 0.395307 0.918549i \(-0.370638\pi\)
0.395307 + 0.918549i \(0.370638\pi\)
\(464\) −67.8592 22.0488i −0.146248 0.0475190i
\(465\) 0 0
\(466\) 263.646 + 191.550i 0.565763 + 0.411051i
\(467\) −100.584 309.566i −0.215383 0.662882i −0.999126 0.0417963i \(-0.986692\pi\)
0.783743 0.621086i \(-0.213308\pi\)
\(468\) 0 0
\(469\) 316.561 435.709i 0.674970 0.929017i
\(470\) 111.407 + 153.339i 0.237037 + 0.326253i
\(471\) 0 0
\(472\) 812.903i 1.72225i
\(473\) −174.807 479.222i −0.369571 1.01315i
\(474\) 0 0
\(475\) 226.835 + 73.7031i 0.477547 + 0.155165i
\(476\) −201.848 + 146.651i −0.424050 + 0.308090i
\(477\) 0 0
\(478\) 33.8188 + 104.083i 0.0707506 + 0.217748i
\(479\) −312.398 + 101.504i −0.652187 + 0.211908i −0.616378 0.787450i \(-0.711401\pi\)
−0.0358087 + 0.999359i \(0.511401\pi\)
\(480\) 0 0
\(481\) 608.975 + 838.182i 1.26606 + 1.74258i
\(482\) 64.2285 197.675i 0.133254 0.410114i
\(483\) 0 0
\(484\) −260.787 + 18.6073i −0.538817 + 0.0384449i
\(485\) 76.0213 0.156745
\(486\) 0 0
\(487\) −260.740 + 189.439i −0.535400 + 0.388991i −0.822374 0.568947i \(-0.807351\pi\)
0.286974 + 0.957938i \(0.407351\pi\)
\(488\) 8.50789 + 6.18135i 0.0174342 + 0.0126667i
\(489\) 0 0
\(490\) 137.544 44.6906i 0.280701 0.0912053i
\(491\) −454.813 + 625.997i −0.926300 + 1.27494i 0.0349859 + 0.999388i \(0.488861\pi\)
−0.961286 + 0.275554i \(0.911139\pi\)
\(492\) 0 0
\(493\) −96.9243 + 298.302i −0.196601 + 0.605076i
\(494\) 252.223i 0.510573i
\(495\) 0 0
\(496\) −11.1865 −0.0225535
\(497\) −138.988 45.1600i −0.279654 0.0908652i
\(498\) 0 0
\(499\) 41.3425 + 30.0371i 0.0828507 + 0.0601946i 0.628440 0.777858i \(-0.283694\pi\)
−0.545589 + 0.838053i \(0.683694\pi\)
\(500\) 68.5324 + 210.921i 0.137065 + 0.421842i
\(501\) 0 0
\(502\) −280.903 + 386.630i −0.559568 + 0.770179i
\(503\) 244.325 + 336.284i 0.485735 + 0.668557i 0.979594 0.200985i \(-0.0644141\pi\)
−0.493859 + 0.869542i \(0.664414\pi\)
\(504\) 0 0
\(505\) 222.729i 0.441048i
\(506\) −248.392 + 8.85022i −0.490894 + 0.0174906i
\(507\) 0 0
\(508\) −11.4827 3.73096i −0.0226038 0.00734441i
\(509\) 270.522 196.546i 0.531478 0.386141i −0.289433 0.957198i \(-0.593467\pi\)
0.820910 + 0.571057i \(0.193467\pi\)
\(510\) 0 0
\(511\) −229.126 705.177i −0.448387 1.37999i
\(512\) −161.567 + 52.4962i −0.315560 + 0.102532i
\(513\) 0 0
\(514\) −103.358 142.260i −0.201086 0.276771i
\(515\) 131.909 405.976i 0.256135 0.788302i
\(516\) 0 0
\(517\) −374.302 + 555.774i −0.723988 + 1.07500i
\(518\) −892.140 −1.72228
\(519\) 0 0
\(520\) −238.664 + 173.399i −0.458968 + 0.333460i
\(521\) 700.990 + 509.299i 1.34547 + 0.977541i 0.999224 + 0.0393970i \(0.0125437\pi\)
0.346246 + 0.938144i \(0.387456\pi\)
\(522\) 0 0
\(523\) −415.392 + 134.969i −0.794248 + 0.258067i −0.677912 0.735143i \(-0.737115\pi\)
−0.116336 + 0.993210i \(0.537115\pi\)
\(524\) 286.668 394.564i 0.547076 0.752986i
\(525\) 0 0
\(526\) −75.5083 + 232.391i −0.143552 + 0.441808i
\(527\) 49.1749i 0.0933111i
\(528\) 0 0
\(529\) −251.412 −0.475259
\(530\) −299.519 97.3197i −0.565130 0.183622i
\(531\) 0 0
\(532\) 206.423 + 149.975i 0.388013 + 0.281908i
\(533\) −85.8263 264.146i −0.161025 0.495584i
\(534\) 0 0
\(535\) 258.765 356.159i 0.483672 0.665718i
\(536\) −270.680 372.559i −0.505000 0.695073i
\(537\) 0 0
\(538\) 456.361i 0.848255i
\(539\) 315.058 + 402.668i 0.584523 + 0.747064i
\(540\) 0 0
\(541\) −738.226 239.864i −1.36456 0.443372i −0.466996 0.884259i \(-0.654664\pi\)
−0.897562 + 0.440888i \(0.854664\pi\)
\(542\) 240.802 174.953i 0.444283 0.322791i
\(543\) 0 0
\(544\) 108.728 + 334.629i 0.199867 + 0.615127i
\(545\) −248.225 + 80.6533i −0.455459 + 0.147988i
\(546\) 0 0
\(547\) −466.258 641.749i −0.852391 1.17322i −0.983331 0.181825i \(-0.941800\pi\)
0.130940 0.991390i \(-0.458200\pi\)
\(548\) −34.9544 + 107.579i −0.0637854 + 0.196311i
\(549\) 0 0
\(550\) 231.883 181.431i 0.421605 0.329875i
\(551\) 320.763 0.582147
\(552\) 0 0
\(553\) −230.991 + 167.825i −0.417705 + 0.303480i
\(554\) 268.619 + 195.163i 0.484872 + 0.352280i
\(555\) 0 0
\(556\) −57.6753 + 18.7399i −0.103733 + 0.0337048i
\(557\) 390.960 538.111i 0.701904 0.966088i −0.298030 0.954557i \(-0.596329\pi\)
0.999934 0.0115312i \(-0.00367058\pi\)
\(558\) 0 0
\(559\) 220.534 678.735i 0.394516 1.21420i
\(560\) 60.2650i 0.107616i
\(561\) 0 0
\(562\) −468.211 −0.833116
\(563\) 375.847 + 122.120i 0.667579 + 0.216910i 0.623149 0.782103i \(-0.285853\pi\)
0.0444299 + 0.999013i \(0.485853\pi\)
\(564\) 0 0
\(565\) −30.4004 22.0872i −0.0538060 0.0390923i
\(566\) 97.4736 + 299.993i 0.172215 + 0.530023i
\(567\) 0 0
\(568\) −73.4495 + 101.095i −0.129313 + 0.177983i
\(569\) 31.1806 + 42.9165i 0.0547990 + 0.0754244i 0.835537 0.549434i \(-0.185157\pi\)
−0.780738 + 0.624858i \(0.785157\pi\)
\(570\) 0 0
\(571\) 878.429i 1.53840i 0.639005 + 0.769202i \(0.279346\pi\)
−0.639005 + 0.769202i \(0.720654\pi\)
\(572\) −303.390 204.327i −0.530403 0.357215i
\(573\) 0 0
\(574\) 227.456 + 73.9048i 0.396264 + 0.128754i
\(575\) −266.024 + 193.278i −0.462651 + 0.336135i
\(576\) 0 0
\(577\) 334.518 + 1029.54i 0.579755 + 1.78430i 0.619385 + 0.785087i \(0.287382\pi\)
−0.0396306 + 0.999214i \(0.512618\pi\)
\(578\) 192.645 62.5941i 0.333296 0.108294i
\(579\) 0 0
\(580\) 77.3422 + 106.452i 0.133349 + 0.183539i
\(581\) −19.2413 + 59.2187i −0.0331176 + 0.101926i
\(582\) 0 0
\(583\) −39.6442 1112.66i −0.0680004 1.90851i
\(584\) −634.002 −1.08562
\(585\) 0 0
\(586\) 585.598 425.462i 0.999313 0.726044i
\(587\) 12.3428 + 8.96760i 0.0210270 + 0.0152770i 0.598249 0.801310i \(-0.295863\pi\)
−0.577222 + 0.816587i \(0.695863\pi\)
\(588\) 0 0
\(589\) 47.8282 15.5403i 0.0812023 0.0263842i
\(590\) 177.940 244.914i 0.301594 0.415109i
\(591\) 0 0
\(592\) −55.9240 + 172.116i −0.0944663 + 0.290737i
\(593\) 214.000i 0.360877i 0.983586 + 0.180439i \(0.0577517\pi\)
−0.983586 + 0.180439i \(0.942248\pi\)
\(594\) 0 0
\(595\) −264.919 −0.445242
\(596\) 23.1028 + 7.50655i 0.0387631 + 0.0125949i
\(597\) 0 0
\(598\) −281.321 204.392i −0.470437 0.341792i
\(599\) −192.777 593.308i −0.321832 0.990498i −0.972850 0.231435i \(-0.925658\pi\)
0.651018 0.759062i \(-0.274342\pi\)
\(600\) 0 0
\(601\) 237.449 326.821i 0.395090 0.543795i −0.564413 0.825493i \(-0.690897\pi\)
0.959503 + 0.281698i \(0.0908975\pi\)
\(602\) 361.214 + 497.169i 0.600024 + 0.825862i
\(603\) 0 0
\(604\) 218.593i 0.361909i
\(605\) −235.635 146.778i −0.389480 0.242607i
\(606\) 0 0
\(607\) −349.561 113.579i −0.575882 0.187115i 0.00657281 0.999978i \(-0.497908\pi\)
−0.582455 + 0.812863i \(0.697908\pi\)
\(608\) 291.104 211.500i 0.478790 0.347861i
\(609\) 0 0
\(610\) 1.21022 + 3.72467i 0.00198397 + 0.00610602i
\(611\) −891.567 + 289.688i −1.45919 + 0.474120i
\(612\) 0 0
\(613\) 286.364 + 394.147i 0.467152 + 0.642980i 0.975973 0.217893i \(-0.0699183\pi\)
−0.508820 + 0.860873i \(0.669918\pi\)
\(614\) −59.8646 + 184.244i −0.0974994 + 0.300072i
\(615\) 0 0
\(616\) 843.676 307.750i 1.36960 0.499594i
\(617\) −455.862 −0.738836 −0.369418 0.929263i \(-0.620443\pi\)
−0.369418 + 0.929263i \(0.620443\pi\)
\(618\) 0 0
\(619\) −463.020 + 336.404i −0.748013 + 0.543463i −0.895210 0.445644i \(-0.852975\pi\)
0.147197 + 0.989107i \(0.452975\pi\)
\(620\) 16.6897 + 12.1258i 0.0269189 + 0.0195577i
\(621\) 0 0
\(622\) 59.2032 19.2363i 0.0951820 0.0309265i
\(623\) −22.7156 + 31.2653i −0.0364616 + 0.0501851i
\(624\) 0 0
\(625\) 79.7020 245.297i 0.127523 0.392476i
\(626\) 483.497i 0.772360i
\(627\) 0 0
\(628\) 41.2096 0.0656204
\(629\) 756.607 + 245.836i 1.20287 + 0.390837i
\(630\) 0 0
\(631\) −181.250 131.686i −0.287243 0.208694i 0.434828 0.900514i \(-0.356809\pi\)
−0.722070 + 0.691820i \(0.756809\pi\)
\(632\) 75.4428 + 232.189i 0.119372 + 0.367388i
\(633\) 0 0
\(634\) −49.3106 + 67.8703i −0.0777770 + 0.107051i
\(635\) −7.53535 10.3715i −0.0118667 0.0163331i
\(636\) 0 0
\(637\) 715.296i 1.12291i
\(638\) 221.188 328.427i 0.346690 0.514775i
\(639\) 0 0
\(640\) 108.562 + 35.2740i 0.169628 + 0.0551156i
\(641\) −383.601 + 278.702i −0.598441 + 0.434793i −0.845325 0.534252i \(-0.820593\pi\)
0.246884 + 0.969045i \(0.420593\pi\)
\(642\) 0 0
\(643\) −255.732 787.063i −0.397717 1.22405i −0.926825 0.375493i \(-0.877473\pi\)
0.529108 0.848554i \(-0.322527\pi\)
\(644\) −334.554 + 108.703i −0.519493 + 0.168794i
\(645\) 0 0
\(646\) 113.838 + 156.685i 0.176220 + 0.242546i
\(647\) −153.080 + 471.133i −0.236600 + 0.728181i 0.760305 + 0.649567i \(0.225050\pi\)
−0.996905 + 0.0786144i \(0.974950\pi\)
\(648\) 0 0
\(649\) 1028.98 + 294.267i 1.58549 + 0.453415i
\(650\) 411.915 0.633715
\(651\) 0 0
\(652\) 25.2628 18.3545i 0.0387467 0.0281511i
\(653\) −543.344 394.762i −0.832073 0.604536i 0.0880721 0.996114i \(-0.471929\pi\)
−0.920145 + 0.391578i \(0.871929\pi\)
\(654\) 0 0
\(655\) 492.508 160.026i 0.751921 0.244314i
\(656\) 28.5162 39.2492i 0.0434699 0.0598312i
\(657\) 0 0
\(658\) 249.449 767.726i 0.379102 1.16676i
\(659\) 59.3106i 0.0900009i −0.998987 0.0450004i \(-0.985671\pi\)
0.998987 0.0450004i \(-0.0143289\pi\)
\(660\) 0 0
\(661\) 604.118 0.913946 0.456973 0.889481i \(-0.348934\pi\)
0.456973 + 0.889481i \(0.348934\pi\)
\(662\) 438.486 + 142.473i 0.662366 + 0.215216i
\(663\) 0 0
\(664\) 43.0734 + 31.2947i 0.0648696 + 0.0471305i
\(665\) 83.7200 + 257.664i 0.125895 + 0.387464i
\(666\) 0 0
\(667\) −259.934 + 357.768i −0.389705 + 0.536384i
\(668\) 167.498 + 230.541i 0.250745 + 0.345121i
\(669\) 0 0
\(670\) 171.496i 0.255965i
\(671\) −10.9042 + 8.53176i −0.0162507 + 0.0127150i
\(672\) 0 0
\(673\) 96.0114 + 31.1960i 0.142662 + 0.0463536i 0.379477 0.925201i \(-0.376104\pi\)
−0.236816 + 0.971555i \(0.576104\pi\)
\(674\) 328.298 238.523i 0.487090 0.353891i
\(675\) 0 0
\(676\) −45.2945 139.402i −0.0670037 0.206216i
\(677\) −191.488 + 62.2184i −0.282849 + 0.0919031i −0.447006 0.894531i \(-0.647510\pi\)
0.164157 + 0.986434i \(0.447510\pi\)
\(678\) 0 0
\(679\) −190.309 261.937i −0.280278 0.385769i
\(680\) −69.9994 + 215.436i −0.102940 + 0.316818i
\(681\) 0 0
\(682\) 17.0692 59.6870i 0.0250282 0.0875176i
\(683\) −381.312 −0.558290 −0.279145 0.960249i \(-0.590051\pi\)
−0.279145 + 0.960249i \(0.590051\pi\)
\(684\) 0 0
\(685\) −97.1682 + 70.5968i −0.141851 + 0.103061i
\(686\) 27.0212 + 19.6320i 0.0393895 + 0.0286181i
\(687\) 0 0
\(688\) 118.559 38.5223i 0.172325 0.0559917i
\(689\) 915.565 1260.17i 1.32883 1.82898i
\(690\) 0 0
\(691\) −353.424 + 1087.73i −0.511468 + 1.57414i 0.278150 + 0.960538i \(0.410279\pi\)
−0.789618 + 0.613598i \(0.789721\pi\)
\(692\) 75.9123i 0.109700i
\(693\) 0 0
\(694\) 288.929 0.416324
\(695\) −61.2403 19.8982i −0.0881155 0.0286305i
\(696\) 0 0
\(697\) −172.536 125.355i −0.247541 0.179849i
\(698\) 31.4139 + 96.6822i 0.0450056 + 0.138513i
\(699\) 0 0
\(700\) 244.929 337.116i 0.349899 0.481595i
\(701\) 302.844 + 416.829i 0.432017 + 0.594620i 0.968415 0.249345i \(-0.0802153\pi\)
−0.536398 + 0.843965i \(0.680215\pi\)
\(702\) 0 0
\(703\) 813.575i 1.15729i
\(704\) −20.0279 562.108i −0.0284488 0.798449i
\(705\) 0 0
\(706\) −480.920 156.260i −0.681189 0.221332i
\(707\) 767.431 557.572i 1.08548 0.788644i
\(708\) 0 0
\(709\) −276.488 850.942i −0.389969 1.20020i −0.932811 0.360366i \(-0.882652\pi\)
0.542842 0.839835i \(-0.317348\pi\)
\(710\) −44.2582 + 14.3804i −0.0623355 + 0.0202540i
\(711\) 0 0
\(712\) 19.4233 + 26.7338i 0.0272799 + 0.0375475i
\(713\) −21.4249 + 65.9392i −0.0300490 + 0.0924813i
\(714\) 0 0
\(715\) −133.095 364.872i −0.186147 0.510311i
\(716\) 391.024 0.546122
\(717\) 0 0
\(718\) 291.326 211.661i 0.405747 0.294793i
\(719\) 126.704 + 92.0559i 0.176223 + 0.128033i 0.672400 0.740188i \(-0.265263\pi\)
−0.496177 + 0.868221i \(0.665263\pi\)
\(720\) 0 0
\(721\) −1729.04 + 561.798i −2.39811 + 0.779193i
\(722\) −171.353 + 235.847i −0.237330 + 0.326657i
\(723\) 0 0
\(724\) 13.5968 41.8467i 0.0187801 0.0577993i
\(725\) 523.849i 0.722551i
\(726\) 0 0
\(727\) 28.5853 0.0393195 0.0196598 0.999807i \(-0.493742\pi\)
0.0196598 + 0.999807i \(0.493742\pi\)
\(728\) 1194.92 + 388.254i 1.64138 + 0.533315i
\(729\) 0 0
\(730\) −191.014 138.780i −0.261663 0.190109i
\(731\) −169.340 521.175i −0.231655 0.712962i
\(732\) 0 0
\(733\) 317.269 436.684i 0.432837 0.595749i −0.535765 0.844367i \(-0.679977\pi\)
0.968601 + 0.248619i \(0.0799766\pi\)
\(734\) 79.3189 + 109.173i 0.108064 + 0.148737i
\(735\) 0 0
\(736\) 496.079i 0.674020i
\(737\) 569.574 207.765i 0.772827 0.281906i
\(738\) 0 0
\(739\) 337.414 + 109.632i 0.456582 + 0.148352i 0.528273 0.849074i \(-0.322840\pi\)
−0.0716913 + 0.997427i \(0.522840\pi\)
\(740\) 270.003 196.169i 0.364869 0.265093i
\(741\) 0 0
\(742\) 414.481 + 1275.64i 0.558600 + 1.71920i
\(743\) −820.225 + 266.507i −1.10394 + 0.358691i −0.803617 0.595147i \(-0.797094\pi\)
−0.300321 + 0.953838i \(0.597094\pi\)
\(744\) 0 0
\(745\) 15.1609 + 20.8671i 0.0203501 + 0.0280096i
\(746\) −196.949 + 606.147i −0.264007 + 0.812529i
\(747\) 0 0
\(748\) −280.691 + 10.0010i −0.375255 + 0.0133703i
\(749\) −1874.96 −2.50328
\(750\) 0 0
\(751\) −15.0547 + 10.9379i −0.0200462 + 0.0145644i −0.597763 0.801673i \(-0.703944\pi\)
0.577717 + 0.816237i \(0.303944\pi\)
\(752\) −132.477 96.2502i −0.176166 0.127992i
\(753\) 0 0
\(754\) 526.859 171.187i 0.698752 0.227038i
\(755\) −136.428 + 187.776i −0.180699 + 0.248710i
\(756\) 0 0
\(757\) 194.396 598.290i 0.256798 0.790343i −0.736672 0.676250i \(-0.763604\pi\)
0.993470 0.114093i \(-0.0363962\pi\)
\(758\) 391.449i 0.516424i
\(759\) 0 0
\(760\) 231.657 0.304812
\(761\) −897.680 291.674i −1.17961 0.383277i −0.347385 0.937722i \(-0.612930\pi\)
−0.832220 + 0.554445i \(0.812930\pi\)
\(762\) 0 0
\(763\) 899.294 + 653.376i 1.17863 + 0.856324i
\(764\) −39.7626 122.377i −0.0520453 0.160179i
\(765\) 0 0
\(766\) −156.811 + 215.832i −0.204714 + 0.281765i
\(767\) 880.090 + 1211.34i 1.14744 + 1.57932i
\(768\) 0 0
\(769\) 332.508i 0.432390i 0.976350 + 0.216195i \(0.0693646\pi\)
−0.976350 + 0.216195i \(0.930635\pi\)
\(770\) 321.550 + 91.9567i 0.417598 + 0.119424i
\(771\) 0 0
\(772\) 509.782 + 165.638i 0.660339 + 0.214557i
\(773\) −747.482 + 543.077i −0.966988 + 0.702558i −0.954763 0.297368i \(-0.903891\pi\)
−0.0122246 + 0.999925i \(0.503891\pi\)
\(774\) 0 0
\(775\) −25.3794 78.1099i −0.0327477 0.100787i
\(776\) −263.296 + 85.5502i −0.339300 + 0.110245i
\(777\) 0 0
\(778\) 357.750 + 492.401i 0.459833 + 0.632906i
\(779\) −67.3965 + 207.425i −0.0865167 + 0.266271i
\(780\) 0 0
\(781\) −101.378 129.569i −0.129806 0.165901i
\(782\) −267.010 −0.341445
\(783\) 0 0
\(784\) −101.083 + 73.4413i −0.128933 + 0.0936751i
\(785\) 35.4000 + 25.7196i 0.0450955 + 0.0327638i
\(786\) 0 0
\(787\) −1224.73 + 397.937i −1.55619 + 0.505638i −0.955788 0.294057i \(-0.904995\pi\)
−0.600407 + 0.799695i \(0.704995\pi\)
\(788\) −211.263 + 290.779i −0.268100 + 0.369009i
\(789\) 0 0
\(790\) −28.0954 + 86.4688i −0.0355638 + 0.109454i
\(791\) 160.039i 0.202325i
\(792\) 0 0
\(793\) −19.3702 −0.0244265
\(794\) −784.973 255.053i −0.988630 0.321225i
\(795\) 0 0
\(796\) −171.300 124.457i −0.215201 0.156353i
\(797\) 67.4452 + 207.575i 0.0846239 + 0.260445i 0.984411 0.175884i \(-0.0562783\pi\)
−0.899787 + 0.436329i \(0.856278\pi\)
\(798\) 0 0
\(799\) −423.106 + 582.356i −0.529545 + 0.728856i
\(800\) −345.408 475.413i −0.431760 0.594266i
\(801\) 0 0
\(802\) 351.492i 0.438270i
\(803\) 229.505 802.525i 0.285810 0.999409i
\(804\) 0 0
\(805\) −355.232 115.422i −0.441283 0.143381i
\(806\) 70.2650 51.0505i 0.0871774 0.0633381i
\(807\) 0 0
\(808\) −250.647 771.413i −0.310207 0.954719i
\(809\) 733.095 238.197i 0.906174 0.294434i 0.181391 0.983411i \(-0.441940\pi\)
0.724783 + 0.688977i \(0.241940\pi\)
\(810\) 0 0
\(811\) 929.155 + 1278.87i 1.14569 + 1.57691i 0.754088 + 0.656773i \(0.228079\pi\)
0.391602 + 0.920135i \(0.371921\pi\)
\(812\) 173.175 532.977i 0.213270 0.656376i
\(813\) 0 0
\(814\) −833.013 561.016i −1.02336 0.689209i
\(815\) 33.1567 0.0406831
\(816\) 0 0
\(817\) −453.387 + 329.405i −0.554941 + 0.403188i
\(818\) −287.651 208.991i −0.351652 0.255490i
\(819\) 0 0
\(820\) −85.0894 + 27.6472i −0.103768 + 0.0337161i
\(821\) −116.880 + 160.872i −0.142364 + 0.195947i −0.874245 0.485486i \(-0.838643\pi\)
0.731881 + 0.681433i \(0.238643\pi\)
\(822\) 0 0
\(823\) 41.5286 127.812i 0.0504600 0.155300i −0.922651 0.385635i \(-0.873982\pi\)
0.973111 + 0.230335i \(0.0739823\pi\)
\(824\) 1554.52i 1.88656i
\(825\) 0 0
\(826\) −1289.32 −1.56092
\(827\) −1136.57 369.292i −1.37432 0.446545i −0.473524 0.880781i \(-0.657018\pi\)
−0.900799 + 0.434236i \(0.857018\pi\)
\(828\) 0 0
\(829\) −1155.60 839.591i −1.39397 1.01278i −0.995417 0.0956281i \(-0.969514\pi\)
−0.398549 0.917147i \(-0.630486\pi\)
\(830\) 6.12705 + 18.8571i 0.00738199 + 0.0227194i
\(831\) 0 0
\(832\) 462.536 636.626i 0.555932 0.765175i
\(833\) 322.841 + 444.352i 0.387564 + 0.533436i
\(834\) 0 0
\(835\) 302.577i 0.362368i
\(836\) 98.4313 + 269.843i 0.117741 + 0.322779i
\(837\) 0 0
\(838\) −838.979 272.601i −1.00117 0.325299i
\(839\) 771.245 560.342i 0.919243 0.667869i −0.0240928 0.999710i \(-0.507670\pi\)
0.943335 + 0.331841i \(0.107670\pi\)
\(840\) 0 0
\(841\) 42.1780 + 129.810i 0.0501522 + 0.154353i
\(842\) −811.177 + 263.567i −0.963393 + 0.313025i
\(843\) 0 0
\(844\) 14.7373 + 20.2842i 0.0174613 + 0.0240334i
\(845\) 48.0941 148.019i 0.0569162 0.175170i
\(846\) 0 0
\(847\) 84.1464 + 1179.34i 0.0993464 + 1.39237i
\(848\) 272.086 0.320856
\(849\) 0 0
\(850\) 255.887 185.913i 0.301044 0.218721i
\(851\) 907.434 + 659.289i 1.06631 + 0.774723i
\(852\) 0 0
\(853\) 926.904 301.170i 1.08664 0.353071i 0.289693 0.957120i \(-0.406447\pi\)
0.796947 + 0.604049i \(0.206447\pi\)
\(854\) 9.80404 13.4941i 0.0114801 0.0158011i
\(855\) 0 0
\(856\) −495.419 + 1524.74i −0.578760 + 1.78124i
\(857\) 1571.80i 1.83407i 0.398805 + 0.917036i \(0.369425\pi\)
−0.398805 + 0.917036i \(0.630575\pi\)
\(858\) 0 0
\(859\) −740.779 −0.862373 −0.431187 0.902263i \(-0.641905\pi\)
−0.431187 + 0.902263i \(0.641905\pi\)
\(860\) −218.641 71.0407i −0.254234 0.0826055i
\(861\) 0 0
\(862\) 646.265 + 469.539i 0.749727 + 0.544709i
\(863\) −105.378 324.320i −0.122106 0.375805i 0.871256 0.490828i \(-0.163306\pi\)
−0.993363 + 0.115023i \(0.963306\pi\)
\(864\) 0 0
\(865\) 47.3781 65.2103i 0.0547723 0.0753877i
\(866\) −124.439 171.276i −0.143694 0.197778i
\(867\) 0 0
\(868\) 87.8610i 0.101222i
\(869\) −321.217 + 11.4450i −0.369640 + 0.0131703i
\(870\) 0 0
\(871\) 806.703 + 262.114i 0.926180 + 0.300934i
\(872\) 768.955 558.678i 0.881829 0.640686i
\(873\) 0 0
\(874\) 84.3809 + 259.698i 0.0965456 + 0.297137i
\(875\) 953.830 309.918i 1.09009 0.354192i
\(876\) 0 0
\(877\) −601.554 827.969i −0.685923 0.944092i 0.314063 0.949402i \(-0.398310\pi\)
−0.999986 + 0.00531028i \(0.998310\pi\)
\(878\) 87.5961 269.593i 0.0997678 0.307054i
\(879\) 0 0
\(880\) 37.8973 56.2709i 0.0430651 0.0639443i
\(881\) 1023.93 1.16224 0.581121 0.813817i \(-0.302614\pi\)
0.581121 + 0.813817i \(0.302614\pi\)
\(882\) 0 0
\(883\) 1348.73 979.908i 1.52744 1.10975i 0.569795 0.821787i \(-0.307022\pi\)
0.957642 0.287961i \(-0.0929775\pi\)
\(884\) −317.901 230.969i −0.359617 0.261277i
\(885\) 0 0
\(886\) −441.599 + 143.484i −0.498419 + 0.161946i
\(887\) −408.038 + 561.617i −0.460021 + 0.633164i −0.974513 0.224331i \(-0.927980\pi\)
0.514492 + 0.857495i \(0.327980\pi\)
\(888\) 0 0
\(889\) −16.8722 + 51.9273i −0.0189789 + 0.0584109i
\(890\) 12.3061i 0.0138271i
\(891\) 0 0
\(892\) 673.970 0.755572
\(893\) 700.117 + 227.482i 0.784006 + 0.254739i
\(894\) 0 0
\(895\) 335.898 + 244.044i 0.375305 + 0.272675i
\(896\) −150.231 462.363i −0.167668 0.516030i
\(897\) 0 0
\(898\) 45.8477 63.1039i 0.0510553 0.0702717i
\(899\) −64.9230 89.3589i −0.0722169 0.0993981i
\(900\) 0 0
\(901\) 1196.06i 1.32748i
\(902\) 165.906 + 212.041i 0.183932 + 0.235078i
\(903\) 0 0
\(904\) 130.146 + 42.2870i 0.143967 + 0.0467777i
\(905\) 37.7972 27.4613i 0.0417648 0.0303439i
\(906\) 0 0
\(907\) −249.523 767.953i −0.275108 0.846696i −0.989191 0.146635i \(-0.953156\pi\)
0.714083 0.700062i \(-0.246844\pi\)
\(908\) −19.5967 + 6.36734i −0.0215822 + 0.00701249i
\(909\) 0 0
\(910\) 275.023 + 378.537i 0.302223 + 0.415974i
\(911\) 282.696 870.047i 0.310313 0.955046i −0.667327 0.744765i \(-0.732562\pi\)
0.977641 0.210282i \(-0.0674382\pi\)
\(912\) 0 0
\(913\) −55.2054 + 43.1942i −0.0604660 + 0.0473102i
\(914\) −867.368 −0.948981
\(915\) 0 0
\(916\) −351.047 + 255.051i −0.383240 + 0.278440i
\(917\) −1784.31 1296.37i −1.94581 1.41371i
\(918\) 0 0
\(919\) 960.986 312.243i 1.04569 0.339764i 0.264712 0.964327i \(-0.414723\pi\)
0.780974 + 0.624563i \(0.214723\pi\)
\(920\) −187.726 + 258.382i −0.204050 + 0.280850i
\(921\) 0 0
\(922\) 206.225 634.696i 0.223672 0.688391i
\(923\) 230.165i 0.249367i
\(924\) 0 0
\(925\) −1328.68 −1.43641
\(926\) −472.142 153.408i −0.509872 0.165668i
\(927\) 0 0
\(928\) −639.369 464.528i −0.688975 0.500569i
\(929\) 76.5132 + 235.483i 0.0823608 + 0.253480i 0.983754 0.179521i \(-0.0574547\pi\)
−0.901393 + 0.433001i \(0.857455\pi\)
\(930\) 0 0
\(931\) 330.158 454.423i 0.354627 0.488102i
\(932\) 305.186 + 420.053i 0.327453 + 0.450700i
\(933\) 0 0
\(934\) 441.436i 0.472629i
\(935\) −247.361 166.593i −0.264558 0.178174i
\(936\) 0 0
\(937\) 1221.51 + 396.891i 1.30363 + 0.423576i 0.876844 0.480774i \(-0.159644\pi\)
0.426790 + 0.904351i \(0.359644\pi\)
\(938\) −590.904 + 429.317i −0.629962 + 0.457694i
\(939\) 0 0
\(940\) 93.3170 + 287.200i 0.0992734 + 0.305532i
\(941\) 1665.76 541.238i 1.77020 0.575173i 0.772027 0.635590i \(-0.219243\pi\)
0.998173 + 0.0604169i \(0.0192430\pi\)
\(942\) 0 0
\(943\) −176.739 243.261i −0.187422 0.257965i
\(944\) −80.8214 + 248.743i −0.0856159 + 0.263498i
\(945\) 0 0
\(946\) 24.6334 + 691.366i 0.0260395 + 0.730831i
\(947\) 87.2570 0.0921405 0.0460702 0.998938i \(-0.485330\pi\)
0.0460702 + 0.998938i \(0.485330\pi\)
\(948\) 0 0
\(949\) 944.752 686.402i 0.995523 0.723290i
\(950\) −261.687 190.127i −0.275460 0.200133i
\(951\) 0 0
\(952\) 917.535 298.125i 0.963798 0.313157i
\(953\) 758.674 1044.23i 0.796090 1.09572i −0.197233 0.980357i \(-0.563195\pi\)
0.993323 0.115368i \(-0.0368046\pi\)
\(954\) 0 0
\(955\) 42.2204 129.941i 0.0442098 0.136064i
\(956\) 174.365i 0.182390i
\(957\) 0 0
\(958\) 445.474 0.465004
\(959\) 486.494 + 158.071i 0.507293 + 0.164829i
\(960\) 0 0
\(961\) 763.456 + 554.683i 0.794439 + 0.577193i
\(962\) −434.194 1336.31i −0.451345 1.38910i
\(963\) 0 0
\(964\) 194.647 267.908i 0.201916 0.277913i
\(965\) 334.536 + 460.450i 0.346670 + 0.477150i
\(966\) 0 0
\(967\) 321.693i 0.332671i −0.986069 0.166336i \(-0.946806\pi\)
0.986069 0.166336i \(-0.0531935\pi\)
\(968\) 981.288 + 243.187i 1.01373 + 0.251226i
\(969\) 0 0
\(970\) −98.0533 31.8595i −0.101086 0.0328448i
\(971\) 101.171 73.5048i 0.104192 0.0757001i −0.534469 0.845188i \(-0.679488\pi\)
0.638661 + 0.769488i \(0.279488\pi\)
\(972\) 0 0
\(973\) 84.7457 + 260.820i 0.0870973 + 0.268058i
\(974\) 415.697 135.068i 0.426794 0.138674i
\(975\) 0 0
\(976\) −1.98879 2.73733i −0.00203769 0.00280464i
\(977\) −435.482 + 1340.28i −0.445734 + 1.37183i 0.435943 + 0.899974i \(0.356415\pi\)
−0.881677 + 0.471854i \(0.843585\pi\)
\(978\) 0 0
\(979\) −40.8711 + 14.9086i −0.0417478 + 0.0152284i
\(980\) 230.418 0.235121
\(981\) 0 0
\(982\) 848.971 616.813i 0.864532 0.628119i
\(983\) 14.9478 + 10.8602i 0.0152063 + 0.0110480i 0.595362 0.803457i \(-0.297008\pi\)
−0.580156 + 0.814505i \(0.697008\pi\)
\(984\) 0 0
\(985\) −362.960 + 117.933i −0.368487 + 0.119729i
\(986\) 250.029 344.135i 0.253579 0.349021i
\(987\) 0 0
\(988\) −124.180 + 382.186i −0.125688 + 0.386828i
\(989\) 772.628i 0.781222i
\(990\) 0 0
\(991\) −212.736 −0.214668 −0.107334 0.994223i \(-0.534231\pi\)
−0.107334 + 0.994223i \(0.534231\pi\)
\(992\) −117.840 38.2886i −0.118791 0.0385974i
\(993\) 0 0
\(994\) 160.343 + 116.496i 0.161311 + 0.117199i
\(995\) −69.4751 213.822i −0.0698242 0.214897i
\(996\) 0 0
\(997\) −206.481 + 284.197i −0.207103 + 0.285052i −0.899915 0.436066i \(-0.856372\pi\)
0.692812 + 0.721118i \(0.256372\pi\)
\(998\) −40.7360 56.0683i −0.0408177 0.0561807i
\(999\) 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 99.3.k.c.46.2 16
3.2 odd 2 33.3.g.a.13.3 16
11.4 even 5 1089.3.c.m.604.6 16
11.6 odd 10 inner 99.3.k.c.28.2 16
11.7 odd 10 1089.3.c.m.604.11 16
12.11 even 2 528.3.bf.b.145.2 16
33.2 even 10 363.3.g.a.118.3 16
33.5 odd 10 363.3.g.f.94.2 16
33.8 even 10 363.3.g.g.40.2 16
33.14 odd 10 363.3.g.a.40.3 16
33.17 even 10 33.3.g.a.28.3 yes 16
33.20 odd 10 363.3.g.g.118.2 16
33.26 odd 10 363.3.c.e.241.11 16
33.29 even 10 363.3.c.e.241.6 16
33.32 even 2 363.3.g.f.112.2 16
132.83 odd 10 528.3.bf.b.193.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.3.g.a.13.3 16 3.2 odd 2
33.3.g.a.28.3 yes 16 33.17 even 10
99.3.k.c.28.2 16 11.6 odd 10 inner
99.3.k.c.46.2 16 1.1 even 1 trivial
363.3.c.e.241.6 16 33.29 even 10
363.3.c.e.241.11 16 33.26 odd 10
363.3.g.a.40.3 16 33.14 odd 10
363.3.g.a.118.3 16 33.2 even 10
363.3.g.f.94.2 16 33.5 odd 10
363.3.g.f.112.2 16 33.32 even 2
363.3.g.g.40.2 16 33.8 even 10
363.3.g.g.118.2 16 33.20 odd 10
528.3.bf.b.145.2 16 12.11 even 2
528.3.bf.b.193.2 16 132.83 odd 10
1089.3.c.m.604.6 16 11.4 even 5
1089.3.c.m.604.11 16 11.7 odd 10