Properties

Label 300.3.f.b.199.10
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $16$
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] = [300,3,Mod(199,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.199");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\), degree \(1\), 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: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.10
Root \(0.957636 + 1.04064i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.b.199.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.169449 + 1.99281i) q^{2} -1.73205 q^{3} +(-3.94257 + 0.675358i) q^{4} +(-0.293494 - 3.45165i) q^{6} +12.3959 q^{7} +(-2.01392 - 7.74236i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(0.169449 + 1.99281i) q^{2} -1.73205 q^{3} +(-3.94257 + 0.675358i) q^{4} +(-0.293494 - 3.45165i) q^{6} +12.3959 q^{7} +(-2.01392 - 7.74236i) q^{8} +3.00000 q^{9} +11.0403i q^{11} +(6.82874 - 1.16975i) q^{12} +2.82009i q^{13} +(2.10047 + 24.7027i) q^{14} +(15.0878 - 5.32529i) q^{16} -6.52606i q^{17} +(0.508346 + 5.97843i) q^{18} +27.9928i q^{19} -21.4703 q^{21} +(-22.0012 + 1.87077i) q^{22} +7.90421 q^{23} +(3.48822 + 13.4102i) q^{24} +(-5.61989 + 0.477860i) q^{26} -5.19615 q^{27} +(-48.8718 + 8.37167i) q^{28} -50.7169 q^{29} +36.3467i q^{31} +(13.1689 + 29.1647i) q^{32} -19.1224i q^{33} +(13.0052 - 1.10583i) q^{34} +(-11.8277 + 2.02607i) q^{36} +18.9279i q^{37} +(-55.7842 + 4.74333i) q^{38} -4.88453i q^{39} +5.30410 q^{41} +(-3.63812 - 42.7863i) q^{42} +45.5870 q^{43} +(-7.45616 - 43.5273i) q^{44} +(1.33936 + 15.7516i) q^{46} +11.7246 q^{47} +(-26.1328 + 9.22368i) q^{48} +104.658 q^{49} +11.3035i q^{51} +(-1.90457 - 11.1184i) q^{52} +41.1680i q^{53} +(-0.880481 - 10.3549i) q^{54} +(-24.9644 - 95.9735i) q^{56} -48.4849i q^{57} +(-8.59391 - 101.069i) q^{58} -10.7008i q^{59} +56.1297 q^{61} +(-72.4319 + 6.15889i) q^{62} +37.1877 q^{63} +(-55.8882 + 31.1850i) q^{64} +(38.1073 - 3.24026i) q^{66} -16.1709 q^{67} +(4.40743 + 25.7295i) q^{68} -13.6905 q^{69} +66.1617i q^{71} +(-6.04177 - 23.2271i) q^{72} +15.6330i q^{73} +(-37.7198 + 3.20731i) q^{74} +(-18.9051 - 110.363i) q^{76} +136.855i q^{77} +(9.73394 - 0.827677i) q^{78} -123.057i q^{79} +9.00000 q^{81} +(0.898773 + 10.5701i) q^{82} +99.6700 q^{83} +(84.6484 - 14.5002i) q^{84} +(7.72465 + 90.8461i) q^{86} +87.8443 q^{87} +(85.4781 - 22.2343i) q^{88} -101.083 q^{89} +34.9575i q^{91} +(-31.1629 + 5.33817i) q^{92} -62.9543i q^{93} +(1.98672 + 23.3649i) q^{94} +(-22.8092 - 50.5148i) q^{96} -127.293i q^{97} +(17.7342 + 208.564i) q^{98} +33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9} + 40 q^{14} + 68 q^{16} - 96 q^{21} - 36 q^{24} - 72 q^{26} - 128 q^{29} + 184 q^{34} - 60 q^{36} - 32 q^{41} - 344 q^{44} + 304 q^{46} + 112 q^{49} - 36 q^{54} + 232 q^{56} - 352 q^{61} + 220 q^{64} + 216 q^{66} + 192 q^{69} - 264 q^{74} - 48 q^{76} + 144 q^{81} + 72 q^{84} - 400 q^{86} - 160 q^{89} + 192 q^{94} - 348 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.169449 + 1.99281i 0.0847243 + 0.996404i
\(3\) −1.73205 −0.577350
\(4\) −3.94257 + 0.675358i −0.985644 + 0.168839i
\(5\) 0 0
\(6\) −0.293494 3.45165i −0.0489156 0.575274i
\(7\) 12.3959 1.77084 0.885422 0.464789i \(-0.153870\pi\)
0.885422 + 0.464789i \(0.153870\pi\)
\(8\) −2.01392 7.74236i −0.251740 0.967795i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 11.0403i 1.00366i 0.864965 + 0.501832i \(0.167341\pi\)
−0.864965 + 0.501832i \(0.832659\pi\)
\(12\) 6.82874 1.16975i 0.569062 0.0974795i
\(13\) 2.82009i 0.216930i 0.994100 + 0.108465i \(0.0345935\pi\)
−0.994100 + 0.108465i \(0.965407\pi\)
\(14\) 2.10047 + 24.7027i 0.150034 + 1.76448i
\(15\) 0 0
\(16\) 15.0878 5.32529i 0.942987 0.332831i
\(17\) 6.52606i 0.383886i −0.981406 0.191943i \(-0.938521\pi\)
0.981406 0.191943i \(-0.0614789\pi\)
\(18\) 0.508346 + 5.97843i 0.0282414 + 0.332135i
\(19\) 27.9928i 1.47330i 0.676273 + 0.736651i \(0.263594\pi\)
−0.676273 + 0.736651i \(0.736406\pi\)
\(20\) 0 0
\(21\) −21.4703 −1.02240
\(22\) −22.0012 + 1.87077i −1.00006 + 0.0850348i
\(23\) 7.90421 0.343661 0.171831 0.985126i \(-0.445032\pi\)
0.171831 + 0.985126i \(0.445032\pi\)
\(24\) 3.48822 + 13.4102i 0.145342 + 0.558757i
\(25\) 0 0
\(26\) −5.61989 + 0.477860i −0.216150 + 0.0183792i
\(27\) −5.19615 −0.192450
\(28\) −48.8718 + 8.37167i −1.74542 + 0.298988i
\(29\) −50.7169 −1.74886 −0.874429 0.485153i \(-0.838764\pi\)
−0.874429 + 0.485153i \(0.838764\pi\)
\(30\) 0 0
\(31\) 36.3467i 1.17247i 0.810140 + 0.586236i \(0.199391\pi\)
−0.810140 + 0.586236i \(0.800609\pi\)
\(32\) 13.1689 + 29.1647i 0.411528 + 0.911397i
\(33\) 19.1224i 0.579466i
\(34\) 13.0052 1.10583i 0.382506 0.0325245i
\(35\) 0 0
\(36\) −11.8277 + 2.02607i −0.328548 + 0.0562798i
\(37\) 18.9279i 0.511566i 0.966734 + 0.255783i \(0.0823332\pi\)
−0.966734 + 0.255783i \(0.917667\pi\)
\(38\) −55.7842 + 4.74333i −1.46801 + 0.124825i
\(39\) 4.88453i 0.125244i
\(40\) 0 0
\(41\) 5.30410 0.129368 0.0646842 0.997906i \(-0.479396\pi\)
0.0646842 + 0.997906i \(0.479396\pi\)
\(42\) −3.63812 42.7863i −0.0866219 1.01872i
\(43\) 45.5870 1.06016 0.530081 0.847947i \(-0.322162\pi\)
0.530081 + 0.847947i \(0.322162\pi\)
\(44\) −7.45616 43.5273i −0.169458 0.989256i
\(45\) 0 0
\(46\) 1.33936 + 15.7516i 0.0291165 + 0.342426i
\(47\) 11.7246 0.249460 0.124730 0.992191i \(-0.460194\pi\)
0.124730 + 0.992191i \(0.460194\pi\)
\(48\) −26.1328 + 9.22368i −0.544434 + 0.192160i
\(49\) 104.658 2.13589
\(50\) 0 0
\(51\) 11.3035i 0.221637i
\(52\) −1.90457 11.1184i −0.0366263 0.213815i
\(53\) 41.1680i 0.776755i 0.921500 + 0.388378i \(0.126964\pi\)
−0.921500 + 0.388378i \(0.873036\pi\)
\(54\) −0.880481 10.3549i −0.0163052 0.191758i
\(55\) 0 0
\(56\) −24.9644 95.9735i −0.445793 1.71381i
\(57\) 48.4849i 0.850612i
\(58\) −8.59391 101.069i −0.148171 1.74257i
\(59\) 10.7008i 0.181370i −0.995880 0.0906848i \(-0.971094\pi\)
0.995880 0.0906848i \(-0.0289056\pi\)
\(60\) 0 0
\(61\) 56.1297 0.920159 0.460080 0.887878i \(-0.347821\pi\)
0.460080 + 0.887878i \(0.347821\pi\)
\(62\) −72.4319 + 6.15889i −1.16826 + 0.0993370i
\(63\) 37.1877 0.590281
\(64\) −55.8882 + 31.1850i −0.873254 + 0.487266i
\(65\) 0 0
\(66\) 38.1073 3.24026i 0.577383 0.0490949i
\(67\) −16.1709 −0.241357 −0.120679 0.992692i \(-0.538507\pi\)
−0.120679 + 0.992692i \(0.538507\pi\)
\(68\) 4.40743 + 25.7295i 0.0648151 + 0.378375i
\(69\) −13.6905 −0.198413
\(70\) 0 0
\(71\) 66.1617i 0.931855i 0.884823 + 0.465928i \(0.154279\pi\)
−0.884823 + 0.465928i \(0.845721\pi\)
\(72\) −6.04177 23.2271i −0.0839134 0.322598i
\(73\) 15.6330i 0.214150i 0.994251 + 0.107075i \(0.0341485\pi\)
−0.994251 + 0.107075i \(0.965851\pi\)
\(74\) −37.7198 + 3.20731i −0.509727 + 0.0433421i
\(75\) 0 0
\(76\) −18.9051 110.363i −0.248752 1.45215i
\(77\) 136.855i 1.77733i
\(78\) 9.73394 0.827677i 0.124794 0.0106112i
\(79\) 123.057i 1.55768i −0.627223 0.778840i \(-0.715809\pi\)
0.627223 0.778840i \(-0.284191\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 0.898773 + 10.5701i 0.0109606 + 0.128903i
\(83\) 99.6700 1.20084 0.600422 0.799684i \(-0.294999\pi\)
0.600422 + 0.799684i \(0.294999\pi\)
\(84\) 84.6484 14.5002i 1.00772 0.172621i
\(85\) 0 0
\(86\) 7.72465 + 90.8461i 0.0898215 + 1.05635i
\(87\) 87.8443 1.00970
\(88\) 85.4781 22.2343i 0.971342 0.252663i
\(89\) −101.083 −1.13576 −0.567881 0.823110i \(-0.692237\pi\)
−0.567881 + 0.823110i \(0.692237\pi\)
\(90\) 0 0
\(91\) 34.9575i 0.384148i
\(92\) −31.1629 + 5.33817i −0.338728 + 0.0580236i
\(93\) 62.9543i 0.676927i
\(94\) 1.98672 + 23.3649i 0.0211353 + 0.248563i
\(95\) 0 0
\(96\) −22.8092 50.5148i −0.237596 0.526195i
\(97\) 127.293i 1.31230i −0.754630 0.656151i \(-0.772183\pi\)
0.754630 0.656151i \(-0.227817\pi\)
\(98\) 17.7342 + 208.564i 0.180962 + 2.12821i
\(99\) 33.1209i 0.334555i
\(100\) 0 0
\(101\) −94.3535 −0.934193 −0.467096 0.884206i \(-0.654700\pi\)
−0.467096 + 0.884206i \(0.654700\pi\)
\(102\) −22.5257 + 1.91536i −0.220840 + 0.0187780i
\(103\) 31.8455 0.309180 0.154590 0.987979i \(-0.450594\pi\)
0.154590 + 0.987979i \(0.450594\pi\)
\(104\) 21.8341 5.67943i 0.209943 0.0546099i
\(105\) 0 0
\(106\) −82.0400 + 6.97587i −0.773962 + 0.0658101i
\(107\) 33.7912 0.315805 0.157903 0.987455i \(-0.449527\pi\)
0.157903 + 0.987455i \(0.449527\pi\)
\(108\) 20.4862 3.50926i 0.189687 0.0324932i
\(109\) 83.4266 0.765382 0.382691 0.923876i \(-0.374997\pi\)
0.382691 + 0.923876i \(0.374997\pi\)
\(110\) 0 0
\(111\) 32.7842i 0.295353i
\(112\) 187.027 66.0118i 1.66988 0.589391i
\(113\) 111.796i 0.989342i −0.869080 0.494671i \(-0.835289\pi\)
0.869080 0.494671i \(-0.164711\pi\)
\(114\) 96.6211 8.21569i 0.847553 0.0720675i
\(115\) 0 0
\(116\) 199.955 34.2520i 1.72375 0.295276i
\(117\) 8.46026i 0.0723099i
\(118\) 21.3247 1.81324i 0.180717 0.0153664i
\(119\) 80.8964i 0.679802i
\(120\) 0 0
\(121\) −0.888544 −0.00734334
\(122\) 9.51110 + 111.856i 0.0779599 + 0.916851i
\(123\) −9.18697 −0.0746908
\(124\) −24.5470 143.299i −0.197960 1.15564i
\(125\) 0 0
\(126\) 6.30141 + 74.1080i 0.0500112 + 0.588159i
\(127\) 16.6855 0.131382 0.0656909 0.997840i \(-0.479075\pi\)
0.0656909 + 0.997840i \(0.479075\pi\)
\(128\) −71.6160 106.090i −0.559500 0.828831i
\(129\) −78.9589 −0.612085
\(130\) 0 0
\(131\) 196.418i 1.49937i −0.661794 0.749686i \(-0.730204\pi\)
0.661794 0.749686i \(-0.269796\pi\)
\(132\) 12.9144 + 75.3914i 0.0978367 + 0.571147i
\(133\) 346.995i 2.60899i
\(134\) −2.74015 32.2256i −0.0204488 0.240490i
\(135\) 0 0
\(136\) −50.5271 + 13.1430i −0.371523 + 0.0966396i
\(137\) 117.127i 0.854942i 0.904029 + 0.427471i \(0.140595\pi\)
−0.904029 + 0.427471i \(0.859405\pi\)
\(138\) −2.31984 27.2825i −0.0168104 0.197700i
\(139\) 187.238i 1.34704i 0.739170 + 0.673519i \(0.235218\pi\)
−0.739170 + 0.673519i \(0.764782\pi\)
\(140\) 0 0
\(141\) −20.3076 −0.144026
\(142\) −131.848 + 11.2110i −0.928505 + 0.0789508i
\(143\) −31.1346 −0.217725
\(144\) 45.2634 15.9759i 0.314329 0.110944i
\(145\) 0 0
\(146\) −31.1535 + 2.64899i −0.213380 + 0.0181437i
\(147\) −181.274 −1.23315
\(148\) −12.7831 74.6248i −0.0863725 0.504222i
\(149\) 50.2274 0.337096 0.168548 0.985693i \(-0.446092\pi\)
0.168548 + 0.985693i \(0.446092\pi\)
\(150\) 0 0
\(151\) 213.160i 1.41166i −0.708382 0.705829i \(-0.750575\pi\)
0.708382 0.705829i \(-0.249425\pi\)
\(152\) 216.730 56.3752i 1.42585 0.370890i
\(153\) 19.5782i 0.127962i
\(154\) −272.725 + 23.1898i −1.77094 + 0.150583i
\(155\) 0 0
\(156\) 3.29880 + 19.2576i 0.0211462 + 0.123446i
\(157\) 203.918i 1.29884i −0.760431 0.649419i \(-0.775012\pi\)
0.760431 0.649419i \(-0.224988\pi\)
\(158\) 245.228 20.8518i 1.55208 0.131973i
\(159\) 71.3051i 0.448460i
\(160\) 0 0
\(161\) 97.9798 0.608570
\(162\) 1.52504 + 17.9353i 0.00941381 + 0.110712i
\(163\) −215.898 −1.32452 −0.662262 0.749272i \(-0.730404\pi\)
−0.662262 + 0.749272i \(0.730404\pi\)
\(164\) −20.9118 + 3.58216i −0.127511 + 0.0218425i
\(165\) 0 0
\(166\) 16.8889 + 198.623i 0.101741 + 1.19653i
\(167\) −255.029 −1.52712 −0.763560 0.645737i \(-0.776550\pi\)
−0.763560 + 0.645737i \(0.776550\pi\)
\(168\) 43.2396 + 166.231i 0.257378 + 0.989470i
\(169\) 161.047 0.952942
\(170\) 0 0
\(171\) 83.9783i 0.491101i
\(172\) −179.730 + 30.7875i −1.04494 + 0.178997i
\(173\) 235.426i 1.36084i −0.732822 0.680421i \(-0.761797\pi\)
0.732822 0.680421i \(-0.238203\pi\)
\(174\) 14.8851 + 175.057i 0.0855465 + 1.00607i
\(175\) 0 0
\(176\) 58.7929 + 166.574i 0.334051 + 0.946443i
\(177\) 18.5343i 0.104714i
\(178\) −17.1284 201.439i −0.0962267 1.13168i
\(179\) 102.669i 0.573572i 0.957995 + 0.286786i \(0.0925869\pi\)
−0.957995 + 0.286786i \(0.907413\pi\)
\(180\) 0 0
\(181\) −56.8222 −0.313935 −0.156967 0.987604i \(-0.550172\pi\)
−0.156967 + 0.987604i \(0.550172\pi\)
\(182\) −69.6636 + 5.92350i −0.382767 + 0.0325467i
\(183\) −97.2195 −0.531254
\(184\) −15.9185 61.1972i −0.0865134 0.332594i
\(185\) 0 0
\(186\) 125.456 10.6675i 0.674493 0.0573522i
\(187\) 72.0498 0.385293
\(188\) −46.2251 + 7.91830i −0.245878 + 0.0421186i
\(189\) −64.4110 −0.340799
\(190\) 0 0
\(191\) 158.493i 0.829808i 0.909865 + 0.414904i \(0.136185\pi\)
−0.909865 + 0.414904i \(0.863815\pi\)
\(192\) 96.8013 54.0140i 0.504173 0.281323i
\(193\) 156.732i 0.812084i −0.913854 0.406042i \(-0.866909\pi\)
0.913854 0.406042i \(-0.133091\pi\)
\(194\) 253.671 21.5697i 1.30758 0.111184i
\(195\) 0 0
\(196\) −412.624 + 70.6819i −2.10522 + 0.360622i
\(197\) 260.127i 1.32044i −0.751072 0.660221i \(-0.770463\pi\)
0.751072 0.660221i \(-0.229537\pi\)
\(198\) −66.0037 + 5.61230i −0.333352 + 0.0283449i
\(199\) 14.0326i 0.0705157i 0.999378 + 0.0352579i \(0.0112253\pi\)
−0.999378 + 0.0352579i \(0.988775\pi\)
\(200\) 0 0
\(201\) 28.0089 0.139348
\(202\) −15.9881 188.028i −0.0791489 0.930834i
\(203\) −628.682 −3.09696
\(204\) −7.63389 44.5648i −0.0374210 0.218455i
\(205\) 0 0
\(206\) 5.39618 + 63.4620i 0.0261950 + 0.308068i
\(207\) 23.7126 0.114554
\(208\) 15.0178 + 42.5488i 0.0722009 + 0.204562i
\(209\) −309.049 −1.47870
\(210\) 0 0
\(211\) 74.4941i 0.353052i 0.984296 + 0.176526i \(0.0564860\pi\)
−0.984296 + 0.176526i \(0.943514\pi\)
\(212\) −27.8031 162.308i −0.131147 0.765604i
\(213\) 114.595i 0.538007i
\(214\) 5.72587 + 67.3393i 0.0267564 + 0.314670i
\(215\) 0 0
\(216\) 10.4646 + 40.2305i 0.0484474 + 0.186252i
\(217\) 450.550i 2.07627i
\(218\) 14.1365 + 166.253i 0.0648465 + 0.762630i
\(219\) 27.0771i 0.123640i
\(220\) 0 0
\(221\) 18.4041 0.0832763
\(222\) 65.3326 5.55523i 0.294291 0.0250236i
\(223\) −159.996 −0.717471 −0.358736 0.933439i \(-0.616792\pi\)
−0.358736 + 0.933439i \(0.616792\pi\)
\(224\) 163.240 + 361.523i 0.728752 + 1.61394i
\(225\) 0 0
\(226\) 222.787 18.9436i 0.985784 0.0838213i
\(227\) 175.978 0.775236 0.387618 0.921820i \(-0.373298\pi\)
0.387618 + 0.921820i \(0.373298\pi\)
\(228\) 32.7446 + 191.155i 0.143617 + 0.838400i
\(229\) 114.170 0.498560 0.249280 0.968431i \(-0.419806\pi\)
0.249280 + 0.968431i \(0.419806\pi\)
\(230\) 0 0
\(231\) 237.039i 1.02614i
\(232\) 102.140 + 392.668i 0.440258 + 1.69254i
\(233\) 260.062i 1.11615i 0.829792 + 0.558073i \(0.188459\pi\)
−0.829792 + 0.558073i \(0.811541\pi\)
\(234\) −16.8597 + 1.43358i −0.0720499 + 0.00612641i
\(235\) 0 0
\(236\) 7.22687 + 42.1887i 0.0306223 + 0.178766i
\(237\) 213.140i 0.899327i
\(238\) 161.211 13.7078i 0.677358 0.0575958i
\(239\) 140.089i 0.586147i 0.956090 + 0.293073i \(0.0946780\pi\)
−0.956090 + 0.293073i \(0.905322\pi\)
\(240\) 0 0
\(241\) 105.920 0.439503 0.219752 0.975556i \(-0.429475\pi\)
0.219752 + 0.975556i \(0.429475\pi\)
\(242\) −0.150563 1.77070i −0.000622159 0.00731693i
\(243\) −15.5885 −0.0641500
\(244\) −221.296 + 37.9076i −0.906949 + 0.155359i
\(245\) 0 0
\(246\) −1.55672 18.3079i −0.00632813 0.0744223i
\(247\) −78.9419 −0.319603
\(248\) 281.409 73.1993i 1.13471 0.295159i
\(249\) −172.633 −0.693307
\(250\) 0 0
\(251\) 167.879i 0.668839i −0.942424 0.334420i \(-0.891460\pi\)
0.942424 0.334420i \(-0.108540\pi\)
\(252\) −146.615 + 25.1150i −0.581807 + 0.0996627i
\(253\) 87.2650i 0.344921i
\(254\) 2.82733 + 33.2510i 0.0111312 + 0.130909i
\(255\) 0 0
\(256\) 199.282 160.694i 0.778447 0.627710i
\(257\) 198.849i 0.773732i −0.922136 0.386866i \(-0.873558\pi\)
0.922136 0.386866i \(-0.126442\pi\)
\(258\) −13.3795 157.350i −0.0518585 0.609884i
\(259\) 234.629i 0.905903i
\(260\) 0 0
\(261\) −152.151 −0.582953
\(262\) 391.423 33.2827i 1.49398 0.127033i
\(263\) 480.528 1.82710 0.913552 0.406722i \(-0.133328\pi\)
0.913552 + 0.406722i \(0.133328\pi\)
\(264\) −148.052 + 38.5110i −0.560804 + 0.145875i
\(265\) 0 0
\(266\) −691.496 + 58.7979i −2.59961 + 0.221045i
\(267\) 175.081 0.655733
\(268\) 63.7552 10.9212i 0.237892 0.0407506i
\(269\) 291.496 1.08363 0.541815 0.840498i \(-0.317737\pi\)
0.541815 + 0.840498i \(0.317737\pi\)
\(270\) 0 0
\(271\) 174.063i 0.642299i −0.947029 0.321150i \(-0.895931\pi\)
0.947029 0.321150i \(-0.104069\pi\)
\(272\) −34.7532 98.4638i −0.127769 0.361999i
\(273\) 60.5482i 0.221788i
\(274\) −233.412 + 19.8470i −0.851868 + 0.0724344i
\(275\) 0 0
\(276\) 53.9758 9.24598i 0.195564 0.0334999i
\(277\) 50.5203i 0.182384i 0.995833 + 0.0911918i \(0.0290676\pi\)
−0.995833 + 0.0911918i \(0.970932\pi\)
\(278\) −373.130 + 31.7273i −1.34219 + 0.114127i
\(279\) 109.040i 0.390824i
\(280\) 0 0
\(281\) −66.0514 −0.235058 −0.117529 0.993069i \(-0.537497\pi\)
−0.117529 + 0.993069i \(0.537497\pi\)
\(282\) −3.44110 40.4692i −0.0122025 0.143508i
\(283\) −116.934 −0.413196 −0.206598 0.978426i \(-0.566239\pi\)
−0.206598 + 0.978426i \(0.566239\pi\)
\(284\) −44.6828 260.848i −0.157334 0.918477i
\(285\) 0 0
\(286\) −5.27572 62.0454i −0.0184466 0.216942i
\(287\) 65.7491 0.229091
\(288\) 39.5067 + 87.4941i 0.137176 + 0.303799i
\(289\) 246.411 0.852631
\(290\) 0 0
\(291\) 220.478i 0.757658i
\(292\) −10.5578 61.6341i −0.0361570 0.211076i
\(293\) 68.3732i 0.233356i −0.993170 0.116678i \(-0.962776\pi\)
0.993170 0.116678i \(-0.0372245\pi\)
\(294\) −30.7166 361.244i −0.104478 1.22872i
\(295\) 0 0
\(296\) 146.547 38.1194i 0.495091 0.128782i
\(297\) 57.3672i 0.193155i
\(298\) 8.51096 + 100.094i 0.0285603 + 0.335884i
\(299\) 22.2905i 0.0745503i
\(300\) 0 0
\(301\) 565.092 1.87738
\(302\) 424.788 36.1197i 1.40658 0.119602i
\(303\) 163.425 0.539356
\(304\) 149.070 + 422.349i 0.490361 + 1.38930i
\(305\) 0 0
\(306\) 39.0156 3.31750i 0.127502 0.0108415i
\(307\) −369.497 −1.20357 −0.601786 0.798657i \(-0.705544\pi\)
−0.601786 + 0.798657i \(0.705544\pi\)
\(308\) −92.4258 539.560i −0.300084 1.75182i
\(309\) −55.1580 −0.178505
\(310\) 0 0
\(311\) 303.446i 0.975712i −0.872924 0.487856i \(-0.837779\pi\)
0.872924 0.487856i \(-0.162221\pi\)
\(312\) −37.8178 + 9.83707i −0.121211 + 0.0315291i
\(313\) 297.693i 0.951097i 0.879689 + 0.475549i \(0.157750\pi\)
−0.879689 + 0.475549i \(0.842250\pi\)
\(314\) 406.369 34.5536i 1.29417 0.110043i
\(315\) 0 0
\(316\) 83.1072 + 485.160i 0.262998 + 1.53532i
\(317\) 264.678i 0.834948i −0.908689 0.417474i \(-0.862916\pi\)
0.908689 0.417474i \(-0.137084\pi\)
\(318\) 142.097 12.0826i 0.446847 0.0379955i
\(319\) 559.931i 1.75527i
\(320\) 0 0
\(321\) −58.5280 −0.182330
\(322\) 16.6026 + 195.255i 0.0515607 + 0.606382i
\(323\) 182.682 0.565580
\(324\) −35.4832 + 6.07822i −0.109516 + 0.0187599i
\(325\) 0 0
\(326\) −36.5835 430.243i −0.112219 1.31976i
\(327\) −144.499 −0.441893
\(328\) −10.6820 41.0663i −0.0325672 0.125202i
\(329\) 145.337 0.441754
\(330\) 0 0
\(331\) 473.426i 1.43029i 0.698976 + 0.715145i \(0.253639\pi\)
−0.698976 + 0.715145i \(0.746361\pi\)
\(332\) −392.956 + 67.3129i −1.18360 + 0.202750i
\(333\) 56.7838i 0.170522i
\(334\) −43.2143 508.224i −0.129384 1.52163i
\(335\) 0 0
\(336\) −323.940 + 114.336i −0.964107 + 0.340285i
\(337\) 29.7588i 0.0883051i −0.999025 0.0441526i \(-0.985941\pi\)
0.999025 0.0441526i \(-0.0140588\pi\)
\(338\) 27.2892 + 320.936i 0.0807373 + 0.949515i
\(339\) 193.636i 0.571197i
\(340\) 0 0
\(341\) −401.278 −1.17677
\(342\) −167.353 + 14.2300i −0.489335 + 0.0416082i
\(343\) 689.937 2.01148
\(344\) −91.8086 352.951i −0.266885 1.02602i
\(345\) 0 0
\(346\) 469.158 39.8925i 1.35595 0.115296i
\(347\) 306.190 0.882391 0.441195 0.897411i \(-0.354555\pi\)
0.441195 + 0.897411i \(0.354555\pi\)
\(348\) −346.333 + 59.3263i −0.995208 + 0.170478i
\(349\) −649.149 −1.86002 −0.930012 0.367528i \(-0.880204\pi\)
−0.930012 + 0.367528i \(0.880204\pi\)
\(350\) 0 0
\(351\) 14.6536i 0.0417481i
\(352\) −321.988 + 145.389i −0.914737 + 0.413036i
\(353\) 275.547i 0.780587i −0.920691 0.390293i \(-0.872374\pi\)
0.920691 0.390293i \(-0.127626\pi\)
\(354\) −36.9354 + 3.14062i −0.104337 + 0.00887181i
\(355\) 0 0
\(356\) 398.527 68.2671i 1.11946 0.191761i
\(357\) 140.117i 0.392484i
\(358\) −204.600 + 17.3972i −0.571510 + 0.0485955i
\(359\) 507.672i 1.41413i −0.707149 0.707065i \(-0.750019\pi\)
0.707149 0.707065i \(-0.249981\pi\)
\(360\) 0 0
\(361\) −422.594 −1.17062
\(362\) −9.62845 113.236i −0.0265979 0.312806i
\(363\) 1.53900 0.00423968
\(364\) −23.6088 137.823i −0.0648594 0.378633i
\(365\) 0 0
\(366\) −16.4737 193.740i −0.0450102 0.529344i
\(367\) −62.7671 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(368\) 119.257 42.0923i 0.324068 0.114381i
\(369\) 15.9123 0.0431228
\(370\) 0 0
\(371\) 510.315i 1.37551i
\(372\) 42.5166 + 248.202i 0.114292 + 0.667209i
\(373\) 272.776i 0.731302i −0.930752 0.365651i \(-0.880846\pi\)
0.930752 0.365651i \(-0.119154\pi\)
\(374\) 12.2087 + 143.581i 0.0326437 + 0.383908i
\(375\) 0 0
\(376\) −23.6124 90.7761i −0.0627990 0.241426i
\(377\) 143.026i 0.379379i
\(378\) −10.9144 128.359i −0.0288740 0.339574i
\(379\) 376.828i 0.994270i −0.867673 0.497135i \(-0.834385\pi\)
0.867673 0.497135i \(-0.165615\pi\)
\(380\) 0 0
\(381\) −28.9001 −0.0758533
\(382\) −315.847 + 26.8565i −0.826825 + 0.0703049i
\(383\) 412.206 1.07625 0.538127 0.842864i \(-0.319132\pi\)
0.538127 + 0.842864i \(0.319132\pi\)
\(384\) 124.042 + 183.754i 0.323027 + 0.478526i
\(385\) 0 0
\(386\) 312.337 26.5581i 0.809164 0.0688032i
\(387\) 136.761 0.353387
\(388\) 85.9685 + 501.863i 0.221568 + 1.29346i
\(389\) 161.289 0.414623 0.207312 0.978275i \(-0.433529\pi\)
0.207312 + 0.978275i \(0.433529\pi\)
\(390\) 0 0
\(391\) 51.5834i 0.131927i
\(392\) −210.774 810.303i −0.537689 2.06710i
\(393\) 340.206i 0.865663i
\(394\) 518.383 44.0782i 1.31569 0.111874i
\(395\) 0 0
\(396\) −22.3685 130.582i −0.0564861 0.329752i
\(397\) 186.505i 0.469785i 0.972021 + 0.234893i \(0.0754738\pi\)
−0.972021 + 0.234893i \(0.924526\pi\)
\(398\) −27.9643 + 2.37781i −0.0702622 + 0.00597440i
\(399\) 601.014i 1.50630i
\(400\) 0 0
\(401\) 239.061 0.596162 0.298081 0.954541i \(-0.403653\pi\)
0.298081 + 0.954541i \(0.403653\pi\)
\(402\) 4.74607 + 55.8164i 0.0118061 + 0.138847i
\(403\) −102.501 −0.254344
\(404\) 371.996 63.7223i 0.920781 0.157729i
\(405\) 0 0
\(406\) −106.529 1252.84i −0.262387 3.08582i
\(407\) −208.970 −0.513441
\(408\) 87.5155 22.7643i 0.214499 0.0557949i
\(409\) −47.8016 −0.116874 −0.0584372 0.998291i \(-0.518612\pi\)
−0.0584372 + 0.998291i \(0.518612\pi\)
\(410\) 0 0
\(411\) 202.870i 0.493601i
\(412\) −125.553 + 21.5071i −0.304741 + 0.0522017i
\(413\) 132.646i 0.321177i
\(414\) 4.01807 + 47.2547i 0.00970549 + 0.114142i
\(415\) 0 0
\(416\) −82.2470 + 37.1374i −0.197709 + 0.0892726i
\(417\) 324.306i 0.777713i
\(418\) −52.3679 615.875i −0.125282 1.47339i
\(419\) 239.009i 0.570428i 0.958464 + 0.285214i \(0.0920647\pi\)
−0.958464 + 0.285214i \(0.907935\pi\)
\(420\) 0 0
\(421\) −257.592 −0.611857 −0.305929 0.952054i \(-0.598967\pi\)
−0.305929 + 0.952054i \(0.598967\pi\)
\(422\) −148.452 + 12.6229i −0.351783 + 0.0299121i
\(423\) 35.1738 0.0831532
\(424\) 318.738 82.9092i 0.751740 0.195541i
\(425\) 0 0
\(426\) 228.367 19.4181i 0.536073 0.0455823i
\(427\) 695.779 1.62946
\(428\) −133.224 + 22.8211i −0.311271 + 0.0533204i
\(429\) 53.9268 0.125703
\(430\) 0 0
\(431\) 343.164i 0.796205i 0.917341 + 0.398103i \(0.130331\pi\)
−0.917341 + 0.398103i \(0.869669\pi\)
\(432\) −78.3984 + 27.6710i −0.181478 + 0.0640533i
\(433\) 234.760i 0.542171i −0.962555 0.271085i \(-0.912617\pi\)
0.962555 0.271085i \(-0.0873826\pi\)
\(434\) −897.859 + 76.3450i −2.06880 + 0.175910i
\(435\) 0 0
\(436\) −328.916 + 56.3428i −0.754394 + 0.129227i
\(437\) 221.261i 0.506317i
\(438\) 53.9595 4.58818i 0.123195 0.0104753i
\(439\) 374.473i 0.853013i 0.904484 + 0.426507i \(0.140256\pi\)
−0.904484 + 0.426507i \(0.859744\pi\)
\(440\) 0 0
\(441\) 313.975 0.711962
\(442\) 3.11854 + 36.6758i 0.00705553 + 0.0829768i
\(443\) −108.557 −0.245050 −0.122525 0.992465i \(-0.539099\pi\)
−0.122525 + 0.992465i \(0.539099\pi\)
\(444\) 22.1410 + 129.254i 0.0498672 + 0.291113i
\(445\) 0 0
\(446\) −27.1111 318.842i −0.0607873 0.714891i
\(447\) −86.9963 −0.194623
\(448\) −692.785 + 386.566i −1.54640 + 0.862872i
\(449\) 431.511 0.961050 0.480525 0.876981i \(-0.340446\pi\)
0.480525 + 0.876981i \(0.340446\pi\)
\(450\) 0 0
\(451\) 58.5589i 0.129842i
\(452\) 75.5020 + 440.762i 0.167040 + 0.975138i
\(453\) 369.205i 0.815021i
\(454\) 29.8193 + 350.692i 0.0656813 + 0.772448i
\(455\) 0 0
\(456\) −375.387 + 97.6448i −0.823218 + 0.214133i
\(457\) 219.747i 0.480847i −0.970668 0.240424i \(-0.922714\pi\)
0.970668 0.240424i \(-0.0772864\pi\)
\(458\) 19.3460 + 227.520i 0.0422402 + 0.496768i
\(459\) 33.9104i 0.0738789i
\(460\) 0 0
\(461\) 223.434 0.484673 0.242337 0.970192i \(-0.422086\pi\)
0.242337 + 0.970192i \(0.422086\pi\)
\(462\) 472.374 40.1660i 1.02245 0.0869394i
\(463\) 740.855 1.60012 0.800059 0.599921i \(-0.204802\pi\)
0.800059 + 0.599921i \(0.204802\pi\)
\(464\) −765.206 + 270.082i −1.64915 + 0.582074i
\(465\) 0 0
\(466\) −518.254 + 44.0672i −1.11213 + 0.0945648i
\(467\) −249.381 −0.534007 −0.267004 0.963696i \(-0.586034\pi\)
−0.267004 + 0.963696i \(0.586034\pi\)
\(468\) −5.71370 33.3552i −0.0122088 0.0712718i
\(469\) −200.454 −0.427406
\(470\) 0 0
\(471\) 353.196i 0.749885i
\(472\) −82.8495 + 21.5506i −0.175529 + 0.0456580i
\(473\) 503.294i 1.06405i
\(474\) −424.748 + 36.1164i −0.896093 + 0.0761948i
\(475\) 0 0
\(476\) 54.6340 + 318.940i 0.114777 + 0.670043i
\(477\) 123.504i 0.258918i
\(478\) −279.171 + 23.7379i −0.584039 + 0.0496609i
\(479\) 210.915i 0.440324i −0.975463 0.220162i \(-0.929341\pi\)
0.975463 0.220162i \(-0.0706587\pi\)
\(480\) 0 0
\(481\) −53.3784 −0.110974
\(482\) 17.9480 + 211.079i 0.0372366 + 0.437923i
\(483\) −169.706 −0.351358
\(484\) 3.50315 0.600085i 0.00723791 0.00123984i
\(485\) 0 0
\(486\) −2.64144 31.0648i −0.00543507 0.0639194i
\(487\) 710.541 1.45902 0.729508 0.683972i \(-0.239749\pi\)
0.729508 + 0.683972i \(0.239749\pi\)
\(488\) −113.041 434.576i −0.231641 0.890525i
\(489\) 373.946 0.764715
\(490\) 0 0
\(491\) 697.876i 1.42134i 0.703528 + 0.710668i \(0.251607\pi\)
−0.703528 + 0.710668i \(0.748393\pi\)
\(492\) 36.2203 6.20449i 0.0736185 0.0126108i
\(493\) 330.982i 0.671363i
\(494\) −13.3766 157.316i −0.0270781 0.318454i
\(495\) 0 0
\(496\) 193.557 + 548.390i 0.390235 + 1.10563i
\(497\) 820.135i 1.65017i
\(498\) −29.2525 344.025i −0.0587400 0.690814i
\(499\) 875.602i 1.75471i 0.479838 + 0.877357i \(0.340695\pi\)
−0.479838 + 0.877357i \(0.659305\pi\)
\(500\) 0 0
\(501\) 441.723 0.881683
\(502\) 334.550 28.4468i 0.666434 0.0566670i
\(503\) −142.849 −0.283995 −0.141997 0.989867i \(-0.545352\pi\)
−0.141997 + 0.989867i \(0.545352\pi\)
\(504\) −74.8932 287.921i −0.148598 0.571271i
\(505\) 0 0
\(506\) −173.902 + 14.7869i −0.343681 + 0.0292232i
\(507\) −278.942 −0.550181
\(508\) −65.7837 + 11.2687i −0.129496 + 0.0221824i
\(509\) 147.662 0.290102 0.145051 0.989424i \(-0.453665\pi\)
0.145051 + 0.989424i \(0.453665\pi\)
\(510\) 0 0
\(511\) 193.785i 0.379227i
\(512\) 354.000 + 369.903i 0.691407 + 0.722466i
\(513\) 145.455i 0.283537i
\(514\) 396.268 33.6947i 0.770950 0.0655539i
\(515\) 0 0
\(516\) 311.301 53.3255i 0.603297 0.103344i
\(517\) 129.443i 0.250374i
\(518\) −467.571 + 39.7576i −0.902646 + 0.0767520i
\(519\) 407.769i 0.785682i
\(520\) 0 0
\(521\) −348.592 −0.669082 −0.334541 0.942381i \(-0.608581\pi\)
−0.334541 + 0.942381i \(0.608581\pi\)
\(522\) −25.7817 303.207i −0.0493903 0.580857i
\(523\) −370.317 −0.708063 −0.354032 0.935233i \(-0.615189\pi\)
−0.354032 + 0.935233i \(0.615189\pi\)
\(524\) 132.652 + 774.392i 0.253153 + 1.47785i
\(525\) 0 0
\(526\) 81.4249 + 957.601i 0.154800 + 1.82053i
\(527\) 237.201 0.450096
\(528\) −101.832 288.514i −0.192864 0.546429i
\(529\) −466.523 −0.881897
\(530\) 0 0
\(531\) 32.1024i 0.0604565i
\(532\) −234.346 1368.06i −0.440500 2.57153i
\(533\) 14.9580i 0.0280638i
\(534\) 29.6672 + 348.902i 0.0555565 + 0.653375i
\(535\) 0 0
\(536\) 32.5670 + 125.201i 0.0607594 + 0.233584i
\(537\) 177.829i 0.331152i
\(538\) 49.3937 + 580.897i 0.0918098 + 1.07973i
\(539\) 1155.46i 2.14371i
\(540\) 0 0
\(541\) −279.719 −0.517041 −0.258520 0.966006i \(-0.583235\pi\)
−0.258520 + 0.966006i \(0.583235\pi\)
\(542\) 346.874 29.4947i 0.639990 0.0544183i
\(543\) 98.4190 0.181250
\(544\) 190.331 85.9411i 0.349873 0.157980i
\(545\) 0 0
\(546\) 120.661 10.2598i 0.220991 0.0187909i
\(547\) −387.716 −0.708804 −0.354402 0.935093i \(-0.615315\pi\)
−0.354402 + 0.935093i \(0.615315\pi\)
\(548\) −79.1026 461.782i −0.144348 0.842668i
\(549\) 168.389 0.306720
\(550\) 0 0
\(551\) 1419.71i 2.57660i
\(552\) 27.5716 + 105.997i 0.0499485 + 0.192023i
\(553\) 1525.40i 2.75841i
\(554\) −100.677 + 8.56059i −0.181728 + 0.0154523i
\(555\) 0 0
\(556\) −126.453 738.201i −0.227433 1.32770i
\(557\) 43.5564i 0.0781983i −0.999235 0.0390991i \(-0.987551\pi\)
0.999235 0.0390991i \(-0.0124488\pi\)
\(558\) −217.296 + 18.4767i −0.389419 + 0.0331123i
\(559\) 128.559i 0.229981i
\(560\) 0 0
\(561\) −124.794 −0.222449
\(562\) −11.1923 131.628i −0.0199152 0.234213i
\(563\) 361.646 0.642355 0.321178 0.947019i \(-0.395921\pi\)
0.321178 + 0.947019i \(0.395921\pi\)
\(564\) 80.0642 13.7149i 0.141958 0.0243172i
\(565\) 0 0
\(566\) −19.8144 233.028i −0.0350078 0.411710i
\(567\) 111.563 0.196760
\(568\) 512.248 133.245i 0.901845 0.234586i
\(569\) −888.559 −1.56161 −0.780807 0.624772i \(-0.785192\pi\)
−0.780807 + 0.624772i \(0.785192\pi\)
\(570\) 0 0
\(571\) 447.745i 0.784142i −0.919935 0.392071i \(-0.871759\pi\)
0.919935 0.392071i \(-0.128241\pi\)
\(572\) 122.751 21.0270i 0.214599 0.0367605i
\(573\) 274.519i 0.479090i
\(574\) 11.1411 + 131.025i 0.0194096 + 0.228267i
\(575\) 0 0
\(576\) −167.665 + 93.5551i −0.291085 + 0.162422i
\(577\) 1069.90i 1.85425i −0.374756 0.927124i \(-0.622273\pi\)
0.374756 0.927124i \(-0.377727\pi\)
\(578\) 41.7539 + 491.049i 0.0722386 + 0.849566i
\(579\) 271.468i 0.468857i
\(580\) 0 0
\(581\) 1235.50 2.12651
\(582\) −439.371 + 37.3598i −0.754934 + 0.0641921i
\(583\) −454.508 −0.779602
\(584\) 121.036 31.4836i 0.207253 0.0539102i
\(585\) 0 0
\(586\) 136.255 11.5857i 0.232517 0.0197709i
\(587\) −129.637 −0.220847 −0.110424 0.993885i \(-0.535221\pi\)
−0.110424 + 0.993885i \(0.535221\pi\)
\(588\) 714.685 122.425i 1.21545 0.208205i
\(589\) −1017.44 −1.72741
\(590\) 0 0
\(591\) 450.553i 0.762357i
\(592\) 100.797 + 285.581i 0.170265 + 0.482400i
\(593\) 892.757i 1.50549i 0.658311 + 0.752746i \(0.271271\pi\)
−0.658311 + 0.752746i \(0.728729\pi\)
\(594\) 114.322 9.72079i 0.192461 0.0163650i
\(595\) 0 0
\(596\) −198.025 + 33.9214i −0.332257 + 0.0569151i
\(597\) 24.3052i 0.0407123i
\(598\) −44.4208 + 3.77710i −0.0742823 + 0.00631623i
\(599\) 1030.62i 1.72057i −0.509816 0.860284i \(-0.670286\pi\)
0.509816 0.860284i \(-0.329714\pi\)
\(600\) 0 0
\(601\) −815.961 −1.35767 −0.678836 0.734289i \(-0.737515\pi\)
−0.678836 + 0.734289i \(0.737515\pi\)
\(602\) 95.7540 + 1126.12i 0.159060 + 1.87063i
\(603\) −48.5128 −0.0804525
\(604\) 143.959 + 840.401i 0.238343 + 1.39139i
\(605\) 0 0
\(606\) 27.6921 + 325.675i 0.0456966 + 0.537417i
\(607\) −842.678 −1.38827 −0.694133 0.719847i \(-0.744212\pi\)
−0.694133 + 0.719847i \(0.744212\pi\)
\(608\) −816.400 + 368.634i −1.34276 + 0.606305i
\(609\) 1088.91 1.78803
\(610\) 0 0
\(611\) 33.0644i 0.0541152i
\(612\) 13.2223 + 77.1885i 0.0216050 + 0.126125i
\(613\) 731.088i 1.19264i −0.802747 0.596320i \(-0.796629\pi\)
0.802747 0.596320i \(-0.203371\pi\)
\(614\) −62.6107 736.336i −0.101972 1.19924i
\(615\) 0 0
\(616\) 1059.58 275.615i 1.72009 0.447426i
\(617\) 919.609i 1.49045i 0.666812 + 0.745226i \(0.267658\pi\)
−0.666812 + 0.745226i \(0.732342\pi\)
\(618\) −9.34645 109.919i −0.0151237 0.177863i
\(619\) 688.974i 1.11304i −0.830833 0.556522i \(-0.812135\pi\)
0.830833 0.556522i \(-0.187865\pi\)
\(620\) 0 0
\(621\) −41.0715 −0.0661377
\(622\) 604.711 51.4186i 0.972203 0.0826665i
\(623\) −1253.01 −2.01126
\(624\) −26.0116 73.6968i −0.0416852 0.118104i
\(625\) 0 0
\(626\) −593.246 + 50.4438i −0.947678 + 0.0805811i
\(627\) 535.288 0.853729
\(628\) 137.717 + 803.960i 0.219295 + 1.28019i
\(629\) 123.525 0.196383
\(630\) 0 0
\(631\) 418.968i 0.663975i 0.943284 + 0.331987i \(0.107719\pi\)
−0.943284 + 0.331987i \(0.892281\pi\)
\(632\) −952.749 + 247.827i −1.50751 + 0.392131i
\(633\) 129.027i 0.203835i
\(634\) 527.454 44.8494i 0.831946 0.0707404i
\(635\) 0 0
\(636\) 48.1565 + 281.126i 0.0757177 + 0.442022i
\(637\) 295.146i 0.463337i
\(638\) 1115.83 94.8795i 1.74896 0.148714i
\(639\) 198.485i 0.310618i
\(640\) 0 0
\(641\) −47.2426 −0.0737014 −0.0368507 0.999321i \(-0.511733\pi\)
−0.0368507 + 0.999321i \(0.511733\pi\)
\(642\) −9.91749 116.635i −0.0154478 0.181675i
\(643\) −710.880 −1.10557 −0.552784 0.833325i \(-0.686435\pi\)
−0.552784 + 0.833325i \(0.686435\pi\)
\(644\) −386.293 + 66.1714i −0.599834 + 0.102751i
\(645\) 0 0
\(646\) 30.9553 + 364.051i 0.0479184 + 0.563547i
\(647\) 468.195 0.723641 0.361820 0.932248i \(-0.382155\pi\)
0.361820 + 0.932248i \(0.382155\pi\)
\(648\) −18.1253 69.6812i −0.0279711 0.107533i
\(649\) 118.140 0.182034
\(650\) 0 0
\(651\) 780.375i 1.19873i
\(652\) 851.192 145.808i 1.30551 0.223632i
\(653\) 551.066i 0.843900i 0.906619 + 0.421950i \(0.138654\pi\)
−0.906619 + 0.421950i \(0.861346\pi\)
\(654\) −24.4852 287.959i −0.0374391 0.440304i
\(655\) 0 0
\(656\) 80.0271 28.2459i 0.121993 0.0430578i
\(657\) 46.8989i 0.0713834i
\(658\) 24.6272 + 289.629i 0.0374273 + 0.440165i
\(659\) 158.259i 0.240151i 0.992765 + 0.120075i \(0.0383136\pi\)
−0.992765 + 0.120075i \(0.961686\pi\)
\(660\) 0 0
\(661\) 92.4953 0.139932 0.0699662 0.997549i \(-0.477711\pi\)
0.0699662 + 0.997549i \(0.477711\pi\)
\(662\) −943.447 + 80.2214i −1.42515 + 0.121180i
\(663\) −31.8768 −0.0480796
\(664\) −200.728 771.681i −0.302301 1.16217i
\(665\) 0 0
\(666\) −113.159 + 9.62194i −0.169909 + 0.0144474i
\(667\) −400.877 −0.601015
\(668\) 1005.47 172.236i 1.50520 0.257838i
\(669\) 277.121 0.414232
\(670\) 0 0
\(671\) 619.690i 0.923532i
\(672\) −282.741 626.176i −0.420745 0.931810i
\(673\) 956.062i 1.42060i 0.703900 + 0.710299i \(0.251440\pi\)
−0.703900 + 0.710299i \(0.748560\pi\)
\(674\) 59.3037 5.04259i 0.0879876 0.00748159i
\(675\) 0 0
\(676\) −634.940 + 108.764i −0.939261 + 0.160894i
\(677\) 1116.67i 1.64944i −0.565543 0.824719i \(-0.691333\pi\)
0.565543 0.824719i \(-0.308667\pi\)
\(678\) −385.879 + 32.8113i −0.569143 + 0.0483942i
\(679\) 1577.92i 2.32388i
\(680\) 0 0
\(681\) −304.804 −0.447583
\(682\) −67.9961 799.671i −0.0997010 1.17254i
\(683\) −826.776 −1.21051 −0.605254 0.796033i \(-0.706928\pi\)
−0.605254 + 0.796033i \(0.706928\pi\)
\(684\) −56.7153 331.090i −0.0829172 0.484050i
\(685\) 0 0
\(686\) 116.909 + 1374.91i 0.170421 + 2.00424i
\(687\) −197.749 −0.287844
\(688\) 687.806 242.764i 0.999718 0.352855i
\(689\) −116.097 −0.168501
\(690\) 0 0
\(691\) 965.432i 1.39715i −0.715536 0.698576i \(-0.753818\pi\)
0.715536 0.698576i \(-0.246182\pi\)
\(692\) 158.996 + 928.183i 0.229764 + 1.34130i
\(693\) 410.564i 0.592444i
\(694\) 51.8834 + 610.177i 0.0747600 + 0.879218i
\(695\) 0 0
\(696\) −176.912 680.122i −0.254183 0.977186i
\(697\) 34.6149i 0.0496627i
\(698\) −109.997 1293.63i −0.157589 1.85334i
\(699\) 450.441i 0.644408i
\(700\) 0 0
\(701\) −1109.94 −1.58337 −0.791686 0.610928i \(-0.790797\pi\)
−0.791686 + 0.610928i \(0.790797\pi\)
\(702\) 29.2018 2.48303i 0.0415980 0.00353708i
\(703\) −529.845 −0.753691
\(704\) −344.292 617.024i −0.489052 0.876454i
\(705\) 0 0
\(706\) 549.113 46.6911i 0.777780 0.0661347i
\(707\) −1169.60 −1.65431
\(708\) −12.5173 73.0730i −0.0176798 0.103210i
\(709\) 964.244 1.36001 0.680003 0.733210i \(-0.261979\pi\)
0.680003 + 0.733210i \(0.261979\pi\)
\(710\) 0 0
\(711\) 369.170i 0.519226i
\(712\) 203.573 + 782.620i 0.285917 + 1.09919i
\(713\) 287.292i 0.402934i
\(714\) −279.226 + 23.7426i −0.391073 + 0.0332529i
\(715\) 0 0
\(716\) −69.3385 404.782i −0.0968415 0.565338i
\(717\) 242.641i 0.338412i
\(718\) 1011.69 86.0244i 1.40904 0.119811i
\(719\) 190.820i 0.265396i 0.991157 + 0.132698i \(0.0423641\pi\)
−0.991157 + 0.132698i \(0.957636\pi\)
\(720\) 0 0
\(721\) 394.754 0.547509
\(722\) −71.6080 842.149i −0.0991801 1.16641i
\(723\) −183.459 −0.253747
\(724\) 224.026 38.3753i 0.309428 0.0530046i
\(725\) 0 0
\(726\) 0.260782 + 3.06694i 0.000359204 + 0.00422443i
\(727\) −202.134 −0.278039 −0.139019 0.990290i \(-0.544395\pi\)
−0.139019 + 0.990290i \(0.544395\pi\)
\(728\) 270.654 70.4017i 0.371777 0.0967056i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 297.503i 0.406981i
\(732\) 383.295 65.6579i 0.523627 0.0896966i
\(733\) 962.435i 1.31301i −0.754322 0.656504i \(-0.772034\pi\)
0.754322 0.656504i \(-0.227966\pi\)
\(734\) −10.6358 125.083i −0.0144902 0.170413i
\(735\) 0 0
\(736\) 104.090 + 230.524i 0.141426 + 0.313212i
\(737\) 178.532i 0.242242i
\(738\) 2.69632 + 31.7102i 0.00365355 + 0.0429677i
\(739\) 932.112i 1.26132i 0.776061 + 0.630658i \(0.217215\pi\)
−0.776061 + 0.630658i \(0.782785\pi\)
\(740\) 0 0
\(741\) 136.731 0.184523
\(742\) −1016.96 + 86.4722i −1.37057 + 0.116539i
\(743\) 1153.70 1.55276 0.776379 0.630266i \(-0.217054\pi\)
0.776379 + 0.630266i \(0.217054\pi\)
\(744\) −487.414 + 126.785i −0.655127 + 0.170410i
\(745\) 0 0
\(746\) 543.590 46.2215i 0.728672 0.0619591i
\(747\) 299.010 0.400281
\(748\) −284.062 + 48.6594i −0.379762 + 0.0650526i
\(749\) 418.872 0.559242
\(750\) 0 0
\(751\) 204.359i 0.272116i −0.990701 0.136058i \(-0.956557\pi\)
0.990701 0.136058i \(-0.0434434\pi\)
\(752\) 176.898 62.4369i 0.235237 0.0830279i
\(753\) 290.774i 0.386155i
\(754\) 285.023 24.2356i 0.378015 0.0321427i
\(755\) 0 0
\(756\) 253.945 43.5005i 0.335906 0.0575403i
\(757\) 216.739i 0.286314i 0.989700 + 0.143157i \(0.0457253\pi\)
−0.989700 + 0.143157i \(0.954275\pi\)
\(758\) 750.947 63.8530i 0.990695 0.0842388i
\(759\) 151.147i 0.199140i
\(760\) 0 0
\(761\) 1324.78 1.74085 0.870424 0.492303i \(-0.163845\pi\)
0.870424 + 0.492303i \(0.163845\pi\)
\(762\) −4.89708 57.5924i −0.00642662 0.0755805i
\(763\) 1034.15 1.35537
\(764\) −107.040 624.872i −0.140104 0.817895i
\(765\) 0 0
\(766\) 69.8477 + 821.447i 0.0911849 + 1.07238i
\(767\) 30.1772 0.0393444
\(768\) −345.167 + 278.330i −0.449437 + 0.362409i
\(769\) −444.088 −0.577488 −0.288744 0.957406i \(-0.593238\pi\)
−0.288744 + 0.957406i \(0.593238\pi\)
\(770\) 0 0
\(771\) 344.417i 0.446714i
\(772\) 105.850 + 617.928i 0.137112 + 0.800425i
\(773\) 751.987i 0.972817i −0.873732 0.486408i \(-0.838307\pi\)
0.873732 0.486408i \(-0.161693\pi\)
\(774\) 23.1739 + 272.538i 0.0299405 + 0.352117i
\(775\) 0 0
\(776\) −985.550 + 256.359i −1.27004 + 0.330359i
\(777\) 406.389i 0.523023i
\(778\) 27.3301 + 321.417i 0.0351287 + 0.413133i
\(779\) 148.476i 0.190599i
\(780\) 0 0
\(781\) −730.446 −0.935271
\(782\) 102.796 8.74073i 0.131452 0.0111774i
\(783\) 263.533 0.336568
\(784\) 1579.06 557.337i 2.01411 0.710889i
\(785\) 0 0
\(786\) −677.965 + 57.6474i −0.862550 + 0.0733427i
\(787\) 442.296 0.562002 0.281001 0.959707i \(-0.409334\pi\)
0.281001 + 0.959707i \(0.409334\pi\)
\(788\) 175.679 + 1025.57i 0.222943 + 1.30148i
\(789\) −832.299 −1.05488
\(790\) 0 0
\(791\) 1385.81i 1.75197i
\(792\) 256.434 66.7030i 0.323781 0.0842210i
\(793\) 158.291i 0.199610i
\(794\) −371.668 + 31.6030i −0.468096 + 0.0398022i
\(795\) 0 0
\(796\) −9.47704 55.3247i −0.0119058 0.0695034i
\(797\) 56.2072i 0.0705235i 0.999378 + 0.0352618i \(0.0112265\pi\)
−0.999378 + 0.0352618i \(0.988774\pi\)
\(798\) 1197.71 101.841i 1.50088 0.127620i
\(799\) 76.5155i 0.0957641i
\(800\) 0 0
\(801\) −303.249 −0.378588
\(802\) 40.5086 + 476.403i 0.0505094 + 0.594019i
\(803\) −172.593 −0.214935
\(804\) −110.427 + 18.9160i −0.137347 + 0.0235274i
\(805\) 0 0
\(806\) −17.3686 204.264i −0.0215491 0.253430i
\(807\) −504.887 −0.625634
\(808\) 190.021 + 730.518i 0.235174 + 0.904107i
\(809\) −1522.16 −1.88153 −0.940765 0.339060i \(-0.889891\pi\)
−0.940765 + 0.339060i \(0.889891\pi\)
\(810\) 0 0
\(811\) 930.734i 1.14764i −0.818982 0.573819i \(-0.805461\pi\)
0.818982 0.573819i \(-0.194539\pi\)
\(812\) 2478.63 424.585i 3.05249 0.522888i
\(813\) 301.486i 0.370832i
\(814\) −35.4098 416.438i −0.0435009 0.511595i
\(815\) 0 0
\(816\) 60.1943 + 170.544i 0.0737676 + 0.209000i
\(817\) 1276.10i 1.56194i
\(818\) −8.09992 95.2595i −0.00990210 0.116454i
\(819\) 104.873i 0.128049i
\(820\) 0 0
\(821\) 349.814 0.426083 0.213041 0.977043i \(-0.431663\pi\)
0.213041 + 0.977043i \(0.431663\pi\)
\(822\) 404.281 34.3761i 0.491826 0.0418200i
\(823\) 61.2187 0.0743849 0.0371924 0.999308i \(-0.488159\pi\)
0.0371924 + 0.999308i \(0.488159\pi\)
\(824\) −64.1344 246.559i −0.0778330 0.299222i
\(825\) 0 0
\(826\) 264.338 22.4767i 0.320022 0.0272115i
\(827\) −46.2063 −0.0558721 −0.0279361 0.999610i \(-0.508893\pi\)
−0.0279361 + 0.999610i \(0.508893\pi\)
\(828\) −93.4888 + 16.0145i −0.112909 + 0.0193412i
\(829\) −223.832 −0.270002 −0.135001 0.990845i \(-0.543104\pi\)
−0.135001 + 0.990845i \(0.543104\pi\)
\(830\) 0 0
\(831\) 87.5037i 0.105299i
\(832\) −87.9444 157.610i −0.105702 0.189435i
\(833\) 683.007i 0.819937i
\(834\) 646.280 54.9532i 0.774916 0.0658912i
\(835\) 0 0
\(836\) 1218.45 208.718i 1.45747 0.249663i
\(837\) 188.863i 0.225642i
\(838\) −476.300 + 40.4998i −0.568377 + 0.0483291i
\(839\) 361.794i 0.431220i −0.976480 0.215610i \(-0.930826\pi\)
0.976480 0.215610i \(-0.0691740\pi\)
\(840\) 0 0
\(841\) 1731.20 2.05851
\(842\) −43.6486 513.332i −0.0518392 0.609657i
\(843\) 114.404 0.135711
\(844\) −50.3101 293.698i −0.0596092 0.347984i
\(845\) 0 0
\(846\) 5.96015 + 70.0947i 0.00704510 + 0.0828542i
\(847\) −11.0143 −0.0130039
\(848\) 219.232 + 621.134i 0.258528 + 0.732470i
\(849\) 202.536 0.238559
\(850\) 0 0
\(851\) 149.610i 0.175805i
\(852\) 77.3929 + 451.801i 0.0908368 + 0.530283i
\(853\) 844.503i 0.990039i −0.868882 0.495019i \(-0.835161\pi\)
0.868882 0.495019i \(-0.164839\pi\)
\(854\) 117.899 + 1386.55i 0.138055 + 1.62360i
\(855\) 0 0
\(856\) −68.0528 261.623i −0.0795009 0.305635i
\(857\) 1389.51i 1.62137i 0.585482 + 0.810685i \(0.300905\pi\)
−0.585482 + 0.810685i \(0.699095\pi\)
\(858\) 9.13782 + 107.466i 0.0106501 + 0.125251i
\(859\) 1205.45i 1.40332i 0.712512 + 0.701660i \(0.247558\pi\)
−0.712512 + 0.701660i \(0.752442\pi\)
\(860\) 0 0
\(861\) −113.881 −0.132266
\(862\) −683.861 + 58.1487i −0.793342 + 0.0674579i
\(863\) 258.868 0.299963 0.149981 0.988689i \(-0.452079\pi\)
0.149981 + 0.988689i \(0.452079\pi\)
\(864\) −68.4276 151.544i −0.0791986 0.175398i
\(865\) 0 0
\(866\) 467.832 39.7798i 0.540222 0.0459351i
\(867\) −426.796 −0.492267
\(868\) −304.282 1776.33i −0.350555 2.04646i
\(869\) 1358.58 1.56339
\(870\) 0 0
\(871\) 45.6035i 0.0523576i
\(872\) −168.015 645.919i −0.192677 0.740732i
\(873\) 381.880i 0.437434i
\(874\) −440.930 + 37.4923i −0.504497 + 0.0428974i
\(875\) 0 0
\(876\) 18.2867 + 106.753i 0.0208752 + 0.121865i
\(877\) 156.268i 0.178185i 0.996023 + 0.0890926i \(0.0283967\pi\)
−0.996023 + 0.0890926i \(0.971603\pi\)
\(878\) −746.253 + 63.4539i −0.849946 + 0.0722710i
\(879\) 118.426i 0.134728i
\(880\) 0 0
\(881\) −1343.58 −1.52507 −0.762533 0.646950i \(-0.776044\pi\)
−0.762533 + 0.646950i \(0.776044\pi\)
\(882\) 53.2027 + 625.693i 0.0603205 + 0.709402i
\(883\) 149.478 0.169284 0.0846420 0.996411i \(-0.473025\pi\)
0.0846420 + 0.996411i \(0.473025\pi\)
\(884\) −72.5594 + 12.4293i −0.0820807 + 0.0140603i
\(885\) 0 0
\(886\) −18.3949 216.334i −0.0207617 0.244169i
\(887\) 1532.07 1.72725 0.863626 0.504134i \(-0.168188\pi\)
0.863626 + 0.504134i \(0.168188\pi\)
\(888\) −253.827 + 66.0247i −0.285841 + 0.0743522i
\(889\) 206.832 0.232656
\(890\) 0 0
\(891\) 99.3628i 0.111518i
\(892\) 630.796 108.055i 0.707171 0.121137i
\(893\) 328.204i 0.367529i
\(894\) −14.7414 173.367i −0.0164893 0.193923i
\(895\) 0 0
\(896\) −887.745 1315.09i −0.990786 1.46773i
\(897\) 38.6084i 0.0430417i
\(898\) 73.1190 + 859.919i 0.0814243 + 0.957594i
\(899\) 1843.39i 2.05049i
\(900\) 0 0
\(901\) 268.665 0.298186
\(902\) −116.697 + 9.92273i −0.129376 + 0.0110008i
\(903\) −978.767 −1.08391
\(904\) −865.562 + 225.148i −0.957480 + 0.249057i
\(905\) 0 0
\(906\) −735.754 + 62.5612i −0.812091 + 0.0690521i
\(907\) 1245.02 1.37268 0.686341 0.727280i \(-0.259216\pi\)
0.686341 + 0.727280i \(0.259216\pi\)
\(908\) −693.808 + 118.848i −0.764106 + 0.130890i
\(909\) −283.060 −0.311398
\(910\) 0 0
\(911\) 173.681i 0.190649i 0.995446 + 0.0953245i \(0.0303889\pi\)
−0.995446 + 0.0953245i \(0.969611\pi\)
\(912\) −258.196 731.529i −0.283110 0.802115i
\(913\) 1100.39i 1.20524i
\(914\) 437.914 37.2359i 0.479118 0.0407395i
\(915\) 0 0
\(916\) −450.125 + 77.1058i −0.491403 + 0.0841766i
\(917\) 2434.78i 2.65515i
\(918\) −67.5770 + 5.74607i −0.0736133 + 0.00625934i
\(919\) 874.426i 0.951498i 0.879581 + 0.475749i \(0.157823\pi\)
−0.879581 + 0.475749i \(0.842177\pi\)
\(920\) 0 0
\(921\) 639.987 0.694882
\(922\) 37.8607 + 445.262i 0.0410636 + 0.482931i
\(923\) −186.582 −0.202147
\(924\) 160.086 + 934.545i 0.173254 + 1.01141i
\(925\) 0 0
\(926\) 125.537 + 1476.38i 0.135569 + 1.59436i
\(927\) 95.5365 0.103060
\(928\) −667.886 1479.14i −0.719705 1.59390i
\(929\) 1564.05 1.68358 0.841792 0.539803i \(-0.181501\pi\)
0.841792 + 0.539803i \(0.181501\pi\)
\(930\) 0 0
\(931\) 2929.68i 3.14681i
\(932\) −175.635 1025.31i −0.188450 1.10012i
\(933\) 525.584i 0.563327i
\(934\) −42.2573 496.970i −0.0452434 0.532087i
\(935\) 0 0
\(936\) 65.5023 17.0383i 0.0699811 0.0182033i
\(937\) 958.621i 1.02308i −0.859261 0.511538i \(-0.829076\pi\)
0.859261 0.511538i \(-0.170924\pi\)
\(938\) −33.9666 399.466i −0.0362117 0.425869i
\(939\) 515.620i 0.549116i
\(940\) 0 0
\(941\) −752.357 −0.799529 −0.399765 0.916618i \(-0.630908\pi\)
−0.399765 + 0.916618i \(0.630908\pi\)
\(942\) −703.852 + 59.8485i −0.747188 + 0.0635335i
\(943\) 41.9247 0.0444589
\(944\) −56.9849 161.451i −0.0603654 0.171029i
\(945\) 0 0
\(946\) −1002.97 + 85.2825i −1.06022 + 0.0901507i
\(947\) −1013.16 −1.06986 −0.534932 0.844895i \(-0.679663\pi\)
−0.534932 + 0.844895i \(0.679663\pi\)
\(948\) −143.946 840.322i −0.151842 0.886415i
\(949\) −44.0863 −0.0464555
\(950\) 0 0
\(951\) 458.436i 0.482057i
\(952\) −626.329 + 162.919i −0.657909 + 0.171134i
\(953\) 21.5482i 0.0226109i −0.999936 0.0113054i \(-0.996401\pi\)
0.999936 0.0113054i \(-0.00359871\pi\)
\(954\) −246.120 + 20.9276i −0.257987 + 0.0219367i
\(955\) 0 0
\(956\) −94.6102 552.312i −0.0989646 0.577732i
\(957\) 969.828i 1.01340i
\(958\) 420.314 35.7393i 0.438741 0.0373062i
\(959\) 1451.90i 1.51397i
\(960\) 0 0
\(961\) −360.079 −0.374692
\(962\) −9.04490 106.373i −0.00940218 0.110575i
\(963\) 101.373 0.105268
\(964\) −417.599 + 71.5340i −0.433193 + 0.0742054i
\(965\) 0 0
\(966\) −28.7565 338.192i −0.0297686 0.350095i
\(967\) −303.965 −0.314338 −0.157169 0.987572i \(-0.550237\pi\)
−0.157169 + 0.987572i \(0.550237\pi\)
\(968\) 1.78946 + 6.87942i 0.00184861 + 0.00710684i
\(969\) −316.415 −0.326538
\(970\) 0 0
\(971\) 356.162i 0.366799i 0.983038 + 0.183399i \(0.0587101\pi\)
−0.983038 + 0.183399i \(0.941290\pi\)
\(972\) 61.4587 10.5278i 0.0632291 0.0108311i
\(973\) 2320.99i 2.38539i
\(974\) 120.400 + 1415.97i 0.123614 + 1.45377i
\(975\) 0 0
\(976\) 846.873 298.907i 0.867698 0.306257i
\(977\) 1845.09i 1.88852i 0.329194 + 0.944262i \(0.393223\pi\)
−0.329194 + 0.944262i \(0.606777\pi\)
\(978\) 63.3646 + 745.202i 0.0647899 + 0.761965i
\(979\) 1115.99i 1.13993i
\(980\) 0 0
\(981\) 250.280 0.255127
\(982\) −1390.73 + 118.254i −1.41623 + 0.120422i
\(983\) −289.444 −0.294449 −0.147225 0.989103i \(-0.547034\pi\)
−0.147225 + 0.989103i \(0.547034\pi\)
\(984\) 18.5019 + 71.1288i 0.0188027 + 0.0722854i
\(985\) 0 0
\(986\) −659.583 + 56.0844i −0.668949 + 0.0568807i
\(987\) −251.731 −0.255047
\(988\) 311.234 53.3140i 0.315015 0.0539616i
\(989\) 360.329 0.364337
\(990\) 0 0
\(991\) 441.980i 0.445994i 0.974819 + 0.222997i \(0.0715840\pi\)
−0.974819 + 0.222997i \(0.928416\pi\)
\(992\) −1060.04 + 478.645i −1.06859 + 0.482505i
\(993\) 819.998i 0.825778i
\(994\) −1634.37 + 138.971i −1.64424 + 0.139810i
\(995\) 0 0
\(996\) 680.620 116.589i 0.683354 0.117058i
\(997\) 1045.42i 1.04856i 0.851545 + 0.524282i \(0.175666\pi\)
−0.851545 + 0.524282i \(0.824334\pi\)
\(998\) −1744.91 + 148.370i −1.74841 + 0.148667i
\(999\) 98.3525i 0.0984509i
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 300.3.f.b.199.10 16
3.2 odd 2 900.3.f.f.199.7 16
4.3 odd 2 inner 300.3.f.b.199.8 16
5.2 odd 4 60.3.c.a.31.2 yes 8
5.3 odd 4 300.3.c.d.151.7 8
5.4 even 2 inner 300.3.f.b.199.7 16
12.11 even 2 900.3.f.f.199.9 16
15.2 even 4 180.3.c.b.91.7 8
15.8 even 4 900.3.c.u.451.2 8
15.14 odd 2 900.3.f.f.199.10 16
20.3 even 4 300.3.c.d.151.8 8
20.7 even 4 60.3.c.a.31.1 8
20.19 odd 2 inner 300.3.f.b.199.9 16
40.27 even 4 960.3.e.c.511.7 8
40.37 odd 4 960.3.e.c.511.4 8
60.23 odd 4 900.3.c.u.451.1 8
60.47 odd 4 180.3.c.b.91.8 8
60.59 even 2 900.3.f.f.199.8 16
120.77 even 4 2880.3.e.j.2431.4 8
120.107 odd 4 2880.3.e.j.2431.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.c.a.31.1 8 20.7 even 4
60.3.c.a.31.2 yes 8 5.2 odd 4
180.3.c.b.91.7 8 15.2 even 4
180.3.c.b.91.8 8 60.47 odd 4
300.3.c.d.151.7 8 5.3 odd 4
300.3.c.d.151.8 8 20.3 even 4
300.3.f.b.199.7 16 5.4 even 2 inner
300.3.f.b.199.8 16 4.3 odd 2 inner
300.3.f.b.199.9 16 20.19 odd 2 inner
300.3.f.b.199.10 16 1.1 even 1 trivial
900.3.c.u.451.1 8 60.23 odd 4
900.3.c.u.451.2 8 15.8 even 4
900.3.f.f.199.7 16 3.2 odd 2
900.3.f.f.199.8 16 60.59 even 2
900.3.f.f.199.9 16 12.11 even 2
900.3.f.f.199.10 16 15.14 odd 2
960.3.e.c.511.4 8 40.37 odd 4
960.3.e.c.511.7 8 40.27 even 4
2880.3.e.j.2431.1 8 120.107 odd 4
2880.3.e.j.2431.4 8 120.77 even 4