Properties

Label 1050.3.q.b.199.7
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
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] = [1050,3,Mod(199,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.199");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), 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: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.22986704741655040229376.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.7
Root \(0.337183 + 1.25838i\) of defining polynomial
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.b.649.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.64728 + 2.85317i) q^{11} +(-1.73205 - 3.00000i) q^{12} -7.72850 q^{13} +(-4.24500 + 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-6.30929 + 10.9280i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-1.54304 + 0.890872i) q^{19} +(0.974040 + 12.0852i) q^{21} +4.65921i q^{22} +(-5.85120 + 3.37819i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-9.46544 + 5.46488i) q^{26} -5.19615 q^{27} +(1.12472 + 13.9547i) q^{28} -39.2933 q^{29} +(9.46751 + 5.46607i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(2.85317 + 4.94184i) q^{33} +17.8454i q^{34} -6.00000 q^{36} +(-29.7883 + 17.1983i) q^{37} +(-1.25988 + 2.18218i) q^{38} +(-6.69308 + 11.5928i) q^{39} +18.8536i q^{41} +(9.73845 + 14.1125i) q^{42} +77.4197i q^{43} +(3.29456 + 5.70635i) q^{44} +(-4.77748 + 8.27485i) q^{46} +(-6.44335 - 11.1602i) q^{47} -6.92820 q^{48} +(17.3875 - 45.8113i) q^{49} +(10.9280 + 18.9279i) q^{51} +(-7.72850 + 13.3862i) q^{52} +(44.7631 + 25.8440i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} +3.08607i q^{57} +(-48.1243 + 27.7846i) q^{58} +(-97.7973 - 56.4633i) q^{59} +(-22.7184 + 13.1165i) q^{61} +15.4604 q^{62} +(18.9713 + 9.00500i) q^{63} -8.00000 q^{64} +(6.98882 + 4.03500i) q^{66} +(-17.2453 - 9.95656i) q^{67} +(12.6186 + 21.8560i) q^{68} +11.7024i q^{69} +87.4319 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-30.4575 + 52.7540i) q^{73} +(-24.3220 + 42.1270i) q^{74} +3.56349i q^{76} +(-1.85274 - 22.9874i) q^{77} +18.9309i q^{78} +(-17.7888 - 30.8112i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(13.3315 + 23.0909i) q^{82} -46.6773 q^{83} +(21.9062 + 10.3981i) q^{84} +(54.7440 + 94.8194i) q^{86} +(-34.0290 + 58.9399i) q^{87} +(8.06999 + 4.65921i) q^{88} +(47.4706 - 27.4072i) q^{89} +(44.5270 - 30.7263i) q^{91} +13.5128i q^{92} +(16.3982 - 9.46751i) q^{93} +(-15.7829 - 9.11228i) q^{94} +(-8.48528 + 4.89898i) q^{96} -45.7447 q^{97} +(-11.0982 - 68.4020i) q^{98} +9.88368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.612372 0.353553i
\(3\) 0.866025 1.50000i 0.288675 0.500000i
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −5.76140 + 3.97571i −0.823057 + 0.567958i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) −1.64728 + 2.85317i −0.149753 + 0.259379i −0.931136 0.364672i \(-0.881181\pi\)
0.781383 + 0.624051i \(0.214514\pi\)
\(12\) −1.73205 3.00000i −0.144338 0.250000i
\(13\) −7.72850 −0.594500 −0.297250 0.954800i \(-0.596069\pi\)
−0.297250 + 0.954800i \(0.596069\pi\)
\(14\) −4.24500 + 8.94315i −0.303214 + 0.638797i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −6.30929 + 10.9280i −0.371135 + 0.642824i −0.989740 0.142877i \(-0.954365\pi\)
0.618606 + 0.785702i \(0.287698\pi\)
\(18\) −3.67423 2.12132i −0.204124 0.117851i
\(19\) −1.54304 + 0.890872i −0.0812124 + 0.0468880i −0.540056 0.841629i \(-0.681597\pi\)
0.458844 + 0.888517i \(0.348264\pi\)
\(20\) 0 0
\(21\) 0.974040 + 12.0852i 0.0463829 + 0.575484i
\(22\) 4.65921i 0.211782i
\(23\) −5.85120 + 3.37819i −0.254400 + 0.146878i −0.621777 0.783194i \(-0.713589\pi\)
0.367377 + 0.930072i \(0.380256\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 0 0
\(26\) −9.46544 + 5.46488i −0.364055 + 0.210188i
\(27\) −5.19615 −0.192450
\(28\) 1.12472 + 13.9547i 0.0401687 + 0.498384i
\(29\) −39.2933 −1.35494 −0.677471 0.735550i \(-0.736924\pi\)
−0.677471 + 0.735550i \(0.736924\pi\)
\(30\) 0 0
\(31\) 9.46751 + 5.46607i 0.305404 + 0.176325i 0.644868 0.764294i \(-0.276912\pi\)
−0.339464 + 0.940619i \(0.610246\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) 2.85317 + 4.94184i 0.0864598 + 0.149753i
\(34\) 17.8454i 0.524864i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −29.7883 + 17.1983i −0.805089 + 0.464818i −0.845248 0.534375i \(-0.820547\pi\)
0.0401585 + 0.999193i \(0.487214\pi\)
\(38\) −1.25988 + 2.18218i −0.0331548 + 0.0574258i
\(39\) −6.69308 + 11.5928i −0.171617 + 0.297250i
\(40\) 0 0
\(41\) 18.8536i 0.459844i 0.973209 + 0.229922i \(0.0738472\pi\)
−0.973209 + 0.229922i \(0.926153\pi\)
\(42\) 9.73845 + 14.1125i 0.231868 + 0.336012i
\(43\) 77.4197i 1.80046i 0.435416 + 0.900229i \(0.356601\pi\)
−0.435416 + 0.900229i \(0.643399\pi\)
\(44\) 3.29456 + 5.70635i 0.0748764 + 0.129690i
\(45\) 0 0
\(46\) −4.77748 + 8.27485i −0.103858 + 0.179888i
\(47\) −6.44335 11.1602i −0.137093 0.237451i 0.789302 0.614005i \(-0.210442\pi\)
−0.926395 + 0.376553i \(0.877109\pi\)
\(48\) −6.92820 −0.144338
\(49\) 17.3875 45.8113i 0.354847 0.934924i
\(50\) 0 0
\(51\) 10.9280 + 18.9279i 0.214275 + 0.371135i
\(52\) −7.72850 + 13.3862i −0.148625 + 0.257426i
\(53\) 44.7631 + 25.8440i 0.844586 + 0.487622i 0.858821 0.512276i \(-0.171198\pi\)
−0.0142341 + 0.999899i \(0.504531\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 11.2450 + 16.2957i 0.200804 + 0.290995i
\(57\) 3.08607i 0.0541416i
\(58\) −48.1243 + 27.7846i −0.829729 + 0.479044i
\(59\) −97.7973 56.4633i −1.65758 0.957005i −0.973827 0.227292i \(-0.927013\pi\)
−0.683754 0.729713i \(-0.739654\pi\)
\(60\) 0 0
\(61\) −22.7184 + 13.1165i −0.372432 + 0.215024i −0.674521 0.738256i \(-0.735650\pi\)
0.302088 + 0.953280i \(0.402316\pi\)
\(62\) 15.4604 0.249361
\(63\) 18.9713 + 9.00500i 0.301132 + 0.142937i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 6.98882 + 4.03500i 0.105891 + 0.0611363i
\(67\) −17.2453 9.95656i −0.257392 0.148605i 0.365752 0.930712i \(-0.380812\pi\)
−0.623144 + 0.782107i \(0.714145\pi\)
\(68\) 12.6186 + 21.8560i 0.185567 + 0.321412i
\(69\) 11.7024i 0.169600i
\(70\) 0 0
\(71\) 87.4319 1.23144 0.615718 0.787967i \(-0.288866\pi\)
0.615718 + 0.787967i \(0.288866\pi\)
\(72\) −7.34847 + 4.24264i −0.102062 + 0.0589256i
\(73\) −30.4575 + 52.7540i −0.417226 + 0.722657i −0.995659 0.0930727i \(-0.970331\pi\)
0.578433 + 0.815730i \(0.303664\pi\)
\(74\) −24.3220 + 42.1270i −0.328676 + 0.569284i
\(75\) 0 0
\(76\) 3.56349i 0.0468880i
\(77\) −1.85274 22.9874i −0.0240615 0.298537i
\(78\) 18.9309i 0.242704i
\(79\) −17.7888 30.8112i −0.225175 0.390015i 0.731197 0.682167i \(-0.238962\pi\)
−0.956372 + 0.292152i \(0.905629\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 13.3315 + 23.0909i 0.162580 + 0.281596i
\(83\) −46.6773 −0.562377 −0.281188 0.959653i \(-0.590729\pi\)
−0.281188 + 0.959653i \(0.590729\pi\)
\(84\) 21.9062 + 10.3981i 0.260788 + 0.123787i
\(85\) 0 0
\(86\) 54.7440 + 94.8194i 0.636558 + 1.10255i
\(87\) −34.0290 + 58.9399i −0.391138 + 0.677471i
\(88\) 8.06999 + 4.65921i 0.0917044 + 0.0529456i
\(89\) 47.4706 27.4072i 0.533378 0.307946i −0.209013 0.977913i \(-0.567025\pi\)
0.742391 + 0.669967i \(0.233692\pi\)
\(90\) 0 0
\(91\) 44.5270 30.7263i 0.489308 0.337651i
\(92\) 13.5128i 0.146878i
\(93\) 16.3982 9.46751i 0.176325 0.101801i
\(94\) −15.7829 9.11228i −0.167903 0.0969391i
\(95\) 0 0
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) −45.7447 −0.471595 −0.235798 0.971802i \(-0.575770\pi\)
−0.235798 + 0.971802i \(0.575770\pi\)
\(98\) −11.0982 68.4020i −0.113247 0.697979i
\(99\) 9.88368 0.0998352
\(100\) 0 0
\(101\) 79.2589 + 45.7601i 0.784741 + 0.453071i 0.838108 0.545504i \(-0.183662\pi\)
−0.0533667 + 0.998575i \(0.516995\pi\)
\(102\) 26.7681 + 15.4545i 0.262432 + 0.151515i
\(103\) −25.2541 43.7414i −0.245186 0.424674i 0.716998 0.697075i \(-0.245516\pi\)
−0.962184 + 0.272401i \(0.912182\pi\)
\(104\) 21.8595i 0.210188i
\(105\) 0 0
\(106\) 73.0978 0.689602
\(107\) −81.3626 + 46.9747i −0.760398 + 0.439016i −0.829439 0.558598i \(-0.811340\pi\)
0.0690404 + 0.997614i \(0.478006\pi\)
\(108\) −5.19615 + 9.00000i −0.0481125 + 0.0833333i
\(109\) 60.3052 104.452i 0.553258 0.958272i −0.444778 0.895641i \(-0.646718\pi\)
0.998037 0.0626310i \(-0.0199491\pi\)
\(110\) 0 0
\(111\) 59.5766i 0.536726i
\(112\) 25.2951 + 12.0067i 0.225849 + 0.107202i
\(113\) 10.7318i 0.0949713i −0.998872 0.0474856i \(-0.984879\pi\)
0.998872 0.0474856i \(-0.0151208\pi\)
\(114\) 2.18218 + 3.77965i 0.0191419 + 0.0331548i
\(115\) 0 0
\(116\) −39.2933 + 68.0580i −0.338735 + 0.586707i
\(117\) 11.5928 + 20.0792i 0.0990834 + 0.171617i
\(118\) −159.702 −1.35341
\(119\) −7.09622 88.0446i −0.0596321 0.739870i
\(120\) 0 0
\(121\) 55.0729 + 95.3891i 0.455148 + 0.788340i
\(122\) −18.5495 + 32.1286i −0.152045 + 0.263349i
\(123\) 28.2804 + 16.3277i 0.229922 + 0.132746i
\(124\) 18.9350 10.9321i 0.152702 0.0881624i
\(125\) 0 0
\(126\) 29.6025 2.38590i 0.234940 0.0189357i
\(127\) 117.281i 0.923476i −0.887016 0.461738i \(-0.847226\pi\)
0.887016 0.461738i \(-0.152774\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) 116.130 + 67.0475i 0.900229 + 0.519748i
\(130\) 0 0
\(131\) 80.2758 46.3473i 0.612792 0.353796i −0.161265 0.986911i \(-0.551557\pi\)
0.774058 + 0.633115i \(0.218224\pi\)
\(132\) 11.4127 0.0864598
\(133\) 5.34820 11.2673i 0.0402120 0.0847168i
\(134\) −28.1614 −0.210160
\(135\) 0 0
\(136\) 30.9091 + 17.8454i 0.227273 + 0.131216i
\(137\) −23.7932 13.7370i −0.173673 0.100270i 0.410644 0.911796i \(-0.365304\pi\)
−0.584317 + 0.811526i \(0.698637\pi\)
\(138\) 8.27485 + 14.3325i 0.0599626 + 0.103858i
\(139\) 67.0127i 0.482106i −0.970512 0.241053i \(-0.922507\pi\)
0.970512 0.241053i \(-0.0774928\pi\)
\(140\) 0 0
\(141\) −22.3204 −0.158301
\(142\) 107.082 61.8237i 0.754097 0.435378i
\(143\) 12.7310 22.0507i 0.0890280 0.154201i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 86.1469i 0.590047i
\(147\) −53.6589 65.7550i −0.365027 0.447313i
\(148\) 68.7931i 0.464818i
\(149\) 25.5567 + 44.2656i 0.171522 + 0.297084i 0.938952 0.344048i \(-0.111798\pi\)
−0.767430 + 0.641132i \(0.778465\pi\)
\(150\) 0 0
\(151\) 82.6090 143.083i 0.547079 0.947569i −0.451394 0.892325i \(-0.649073\pi\)
0.998473 0.0552442i \(-0.0175937\pi\)
\(152\) 2.51977 + 4.36436i 0.0165774 + 0.0287129i
\(153\) 37.8558 0.247423
\(154\) −18.5237 26.8436i −0.120284 0.174309i
\(155\) 0 0
\(156\) 13.3862 + 23.1855i 0.0858087 + 0.148625i
\(157\) −95.4059 + 165.248i −0.607681 + 1.05253i 0.383941 + 0.923358i \(0.374567\pi\)
−0.991622 + 0.129176i \(0.958767\pi\)
\(158\) −43.5736 25.1572i −0.275782 0.159223i
\(159\) 77.5319 44.7631i 0.487622 0.281529i
\(160\) 0 0
\(161\) 20.2804 42.7258i 0.125965 0.265377i
\(162\) 12.7279i 0.0785674i
\(163\) −214.949 + 124.101i −1.31871 + 0.761356i −0.983521 0.180796i \(-0.942133\pi\)
−0.335186 + 0.942152i \(0.608799\pi\)
\(164\) 32.6554 + 18.8536i 0.199118 + 0.114961i
\(165\) 0 0
\(166\) −57.1678 + 33.0058i −0.344384 + 0.198830i
\(167\) −29.2974 −0.175433 −0.0877167 0.996145i \(-0.527957\pi\)
−0.0877167 + 0.996145i \(0.527957\pi\)
\(168\) 34.1820 2.75500i 0.203464 0.0163988i
\(169\) −109.270 −0.646570
\(170\) 0 0
\(171\) 4.62911 + 2.67262i 0.0270708 + 0.0156293i
\(172\) 134.095 + 77.4197i 0.779622 + 0.450115i
\(173\) 11.5460 + 19.9982i 0.0667397 + 0.115597i 0.897464 0.441087i \(-0.145407\pi\)
−0.830725 + 0.556683i \(0.812074\pi\)
\(174\) 96.2485i 0.553152i
\(175\) 0 0
\(176\) 13.1782 0.0748764
\(177\) −169.390 + 97.7973i −0.957005 + 0.552527i
\(178\) 38.7596 67.1336i 0.217751 0.377155i
\(179\) −104.717 + 181.376i −0.585014 + 1.01327i 0.409860 + 0.912148i \(0.365577\pi\)
−0.994874 + 0.101125i \(0.967756\pi\)
\(180\) 0 0
\(181\) 243.667i 1.34622i −0.739540 0.673112i \(-0.764957\pi\)
0.739540 0.673112i \(-0.235043\pi\)
\(182\) 32.8075 69.1172i 0.180261 0.379765i
\(183\) 45.4367i 0.248288i
\(184\) 9.55497 + 16.5497i 0.0519292 + 0.0899440i
\(185\) 0 0
\(186\) 13.3891 23.1906i 0.0719843 0.124681i
\(187\) −20.7863 36.0030i −0.111157 0.192529i
\(188\) −25.7734 −0.137093
\(189\) 29.9371 20.6584i 0.158397 0.109304i
\(190\) 0 0
\(191\) 118.423 + 205.114i 0.620014 + 1.07390i 0.989483 + 0.144653i \(0.0462064\pi\)
−0.369468 + 0.929243i \(0.620460\pi\)
\(192\) −6.92820 + 12.0000i −0.0360844 + 0.0625000i
\(193\) −115.088 66.4460i −0.596310 0.344280i 0.171278 0.985223i \(-0.445210\pi\)
−0.767589 + 0.640943i \(0.778544\pi\)
\(194\) −56.0256 + 32.3464i −0.288792 + 0.166734i
\(195\) 0 0
\(196\) −61.9600 75.9273i −0.316122 0.387384i
\(197\) 105.779i 0.536950i −0.963287 0.268475i \(-0.913480\pi\)
0.963287 0.268475i \(-0.0865197\pi\)
\(198\) 12.1050 6.98882i 0.0611363 0.0352971i
\(199\) −174.541 100.771i −0.877091 0.506389i −0.00739279 0.999973i \(-0.502353\pi\)
−0.869698 + 0.493584i \(0.835687\pi\)
\(200\) 0 0
\(201\) −29.8697 + 17.2453i −0.148605 + 0.0857973i
\(202\) 129.429 0.640739
\(203\) 226.384 156.219i 1.11519 0.769550i
\(204\) 43.7121 0.214275
\(205\) 0 0
\(206\) −61.8597 35.7147i −0.300290 0.173372i
\(207\) 17.5536 + 10.1346i 0.0848000 + 0.0489593i
\(208\) 15.4570 + 26.7723i 0.0743125 + 0.128713i
\(209\) 5.87006i 0.0280864i
\(210\) 0 0
\(211\) 29.6045 0.140306 0.0701528 0.997536i \(-0.477651\pi\)
0.0701528 + 0.997536i \(0.477651\pi\)
\(212\) 89.5262 51.6880i 0.422293 0.243811i
\(213\) 75.7183 131.148i 0.355485 0.615718i
\(214\) −66.4323 + 115.064i −0.310431 + 0.537683i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −76.2777 + 6.14783i −0.351510 + 0.0283310i
\(218\) 170.569i 0.782426i
\(219\) 52.7540 + 91.3726i 0.240886 + 0.417226i
\(220\) 0 0
\(221\) 48.7614 84.4572i 0.220640 0.382159i
\(222\) 42.1270 + 72.9661i 0.189761 + 0.328676i
\(223\) −328.532 −1.47324 −0.736620 0.676307i \(-0.763579\pi\)
−0.736620 + 0.676307i \(0.763579\pi\)
\(224\) 39.4700 3.18120i 0.176205 0.0142018i
\(225\) 0 0
\(226\) −7.58850 13.1437i −0.0335774 0.0581578i
\(227\) −182.228 + 315.628i −0.802766 + 1.39043i 0.115023 + 0.993363i \(0.463306\pi\)
−0.917789 + 0.397069i \(0.870028\pi\)
\(228\) 5.34523 + 3.08607i 0.0234440 + 0.0135354i
\(229\) 260.716 150.525i 1.13850 0.657313i 0.192441 0.981309i \(-0.438360\pi\)
0.946059 + 0.323996i \(0.105026\pi\)
\(230\) 0 0
\(231\) −36.0856 17.1285i −0.156215 0.0741496i
\(232\) 111.138i 0.479044i
\(233\) 244.241 141.013i 1.04824 0.605204i 0.126087 0.992019i \(-0.459758\pi\)
0.922157 + 0.386815i \(0.126425\pi\)
\(234\) 28.3963 + 16.3946i 0.121352 + 0.0700625i
\(235\) 0 0
\(236\) −195.595 + 112.927i −0.828790 + 0.478502i
\(237\) −61.6224 −0.260010
\(238\) −70.9480 102.814i −0.298101 0.431993i
\(239\) −83.0347 −0.347425 −0.173713 0.984796i \(-0.555576\pi\)
−0.173713 + 0.984796i \(0.555576\pi\)
\(240\) 0 0
\(241\) −287.369 165.912i −1.19240 0.688433i −0.233551 0.972345i \(-0.575035\pi\)
−0.958851 + 0.283911i \(0.908368\pi\)
\(242\) 134.901 + 77.8849i 0.557440 + 0.321838i
\(243\) 7.79423 + 13.5000i 0.0320750 + 0.0555556i
\(244\) 52.4658i 0.215024i
\(245\) 0 0
\(246\) 46.1817 0.187731
\(247\) 11.9254 6.88511i 0.0482808 0.0278749i
\(248\) 15.4604 26.7782i 0.0623403 0.107977i
\(249\) −40.4237 + 70.0159i −0.162344 + 0.281188i
\(250\) 0 0
\(251\) 419.075i 1.66962i −0.550537 0.834811i \(-0.685577\pi\)
0.550537 0.834811i \(-0.314423\pi\)
\(252\) 34.5684 23.8542i 0.137176 0.0946597i
\(253\) 22.2593i 0.0879815i
\(254\) −82.9305 143.640i −0.326498 0.565511i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −166.979 289.215i −0.649722 1.12535i −0.983189 0.182590i \(-0.941552\pi\)
0.333467 0.942762i \(-0.391781\pi\)
\(258\) 189.639 0.735034
\(259\) 103.247 217.516i 0.398637 0.839829i
\(260\) 0 0
\(261\) 58.9399 + 102.087i 0.225824 + 0.391138i
\(262\) 65.5449 113.527i 0.250171 0.433310i
\(263\) 176.995 + 102.188i 0.672986 + 0.388549i 0.797207 0.603706i \(-0.206310\pi\)
−0.124221 + 0.992255i \(0.539643\pi\)
\(264\) 13.9776 8.06999i 0.0529456 0.0305681i
\(265\) 0 0
\(266\) −1.41702 17.5814i −0.00532715 0.0660953i
\(267\) 94.9412i 0.355585i
\(268\) −34.4905 + 19.9131i −0.128696 + 0.0743027i
\(269\) 120.768 + 69.7257i 0.448953 + 0.259203i 0.707388 0.706825i \(-0.249873\pi\)
−0.258435 + 0.966029i \(0.583207\pi\)
\(270\) 0 0
\(271\) −323.213 + 186.607i −1.19267 + 0.688586i −0.958910 0.283709i \(-0.908435\pi\)
−0.233756 + 0.972295i \(0.575102\pi\)
\(272\) 50.4743 0.185567
\(273\) −7.52787 93.4002i −0.0275746 0.342125i
\(274\) −38.8542 −0.141804
\(275\) 0 0
\(276\) 20.2691 + 11.7024i 0.0734389 + 0.0424000i
\(277\) 430.851 + 248.752i 1.55542 + 0.898022i 0.997685 + 0.0680029i \(0.0216627\pi\)
0.557735 + 0.830019i \(0.311671\pi\)
\(278\) −47.3852 82.0735i −0.170450 0.295228i
\(279\) 32.7964i 0.117550i
\(280\) 0 0
\(281\) 292.779 1.04192 0.520959 0.853582i \(-0.325574\pi\)
0.520959 + 0.853582i \(0.325574\pi\)
\(282\) −27.3368 + 15.7829i −0.0969391 + 0.0559678i
\(283\) −138.383 + 239.686i −0.488986 + 0.846949i −0.999920 0.0126714i \(-0.995966\pi\)
0.510934 + 0.859620i \(0.329300\pi\)
\(284\) 87.4319 151.437i 0.307859 0.533227i
\(285\) 0 0
\(286\) 36.0087i 0.125905i
\(287\) −74.9565 108.623i −0.261172 0.378478i
\(288\) 16.9706i 0.0589256i
\(289\) 64.8857 + 112.385i 0.224518 + 0.388876i
\(290\) 0 0
\(291\) −39.6161 + 68.6171i −0.136138 + 0.235798i
\(292\) 60.9150 + 105.508i 0.208613 + 0.361329i
\(293\) 375.299 1.28088 0.640442 0.768006i \(-0.278751\pi\)
0.640442 + 0.768006i \(0.278751\pi\)
\(294\) −112.214 42.5905i −0.381681 0.144866i
\(295\) 0 0
\(296\) 48.6441 + 84.2540i 0.164338 + 0.284642i
\(297\) 8.55952 14.8255i 0.0288199 0.0499176i
\(298\) 62.6009 + 36.1427i 0.210070 + 0.121284i
\(299\) 45.2210 26.1084i 0.151241 0.0873189i
\(300\) 0 0
\(301\) −307.798 446.046i −1.02259 1.48188i
\(302\) 233.653i 0.773687i
\(303\) 137.280 79.2589i 0.453071 0.261580i
\(304\) 6.17214 + 3.56349i 0.0203031 + 0.0117220i
\(305\) 0 0
\(306\) 46.3636 26.7681i 0.151515 0.0874773i
\(307\) 107.784 0.351088 0.175544 0.984472i \(-0.443832\pi\)
0.175544 + 0.984472i \(0.443832\pi\)
\(308\) −41.6680 19.7783i −0.135286 0.0642154i
\(309\) −87.4828 −0.283116
\(310\) 0 0
\(311\) −499.771 288.543i −1.60698 0.927791i −0.990041 0.140780i \(-0.955039\pi\)
−0.616940 0.787010i \(-0.711628\pi\)
\(312\) 32.7893 + 18.9309i 0.105094 + 0.0606759i
\(313\) −198.637 344.050i −0.634624 1.09920i −0.986595 0.163190i \(-0.947822\pi\)
0.351971 0.936011i \(-0.385512\pi\)
\(314\) 269.849i 0.859390i
\(315\) 0 0
\(316\) −71.1554 −0.225175
\(317\) 69.6026 40.1851i 0.219566 0.126767i −0.386183 0.922422i \(-0.626207\pi\)
0.605749 + 0.795655i \(0.292873\pi\)
\(318\) 63.3046 109.647i 0.199071 0.344801i
\(319\) 64.7271 112.111i 0.202906 0.351444i
\(320\) 0 0
\(321\) 162.725i 0.506932i
\(322\) −5.37336 66.6686i −0.0166874 0.207045i
\(323\) 22.4831i 0.0696071i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −175.505 + 303.984i −0.538360 + 0.932467i
\(327\) −104.452 180.915i −0.319424 0.553258i
\(328\) 53.3261 0.162580
\(329\) 81.4925 + 38.6816i 0.247698 + 0.117573i
\(330\) 0 0
\(331\) −246.021 426.121i −0.743266 1.28737i −0.951000 0.309189i \(-0.899942\pi\)
0.207734 0.978185i \(-0.433391\pi\)
\(332\) −46.6773 + 80.8474i −0.140594 + 0.243516i
\(333\) 89.3649 + 51.5948i 0.268363 + 0.154939i
\(334\) −35.8818 + 20.7164i −0.107431 + 0.0620251i
\(335\) 0 0
\(336\) 39.9162 27.5445i 0.118798 0.0819777i
\(337\) 630.123i 1.86980i −0.354910 0.934901i \(-0.615488\pi\)
0.354910 0.934901i \(-0.384512\pi\)
\(338\) −133.828 + 77.2657i −0.395941 + 0.228597i
\(339\) −16.0976 9.29397i −0.0474856 0.0274159i
\(340\) 0 0
\(341\) −31.1913 + 18.0083i −0.0914701 + 0.0528103i
\(342\) 7.55930 0.0221032
\(343\) 81.9559 + 333.065i 0.238938 + 0.971035i
\(344\) 218.976 0.636558
\(345\) 0 0
\(346\) 28.2817 + 16.3285i 0.0817391 + 0.0471921i
\(347\) 372.514 + 215.071i 1.07353 + 0.619802i 0.929143 0.369720i \(-0.120546\pi\)
0.144385 + 0.989522i \(0.453880\pi\)
\(348\) 68.0580 + 117.880i 0.195569 + 0.338735i
\(349\) 95.1819i 0.272727i 0.990659 + 0.136364i \(0.0435416\pi\)
−0.990659 + 0.136364i \(0.956458\pi\)
\(350\) 0 0
\(351\) 40.1585 0.114412
\(352\) 16.1400 9.31842i 0.0458522 0.0264728i
\(353\) 131.469 227.710i 0.372432 0.645071i −0.617507 0.786565i \(-0.711857\pi\)
0.989939 + 0.141494i \(0.0451906\pi\)
\(354\) −138.306 + 239.553i −0.390696 + 0.676704i
\(355\) 0 0
\(356\) 109.629i 0.307946i
\(357\) −138.212 65.6045i −0.387150 0.183766i
\(358\) 296.186i 0.827334i
\(359\) 149.386 + 258.743i 0.416116 + 0.720734i 0.995545 0.0942890i \(-0.0300578\pi\)
−0.579429 + 0.815023i \(0.696724\pi\)
\(360\) 0 0
\(361\) −178.913 + 309.886i −0.495603 + 0.858410i
\(362\) −172.298 298.429i −0.475962 0.824391i
\(363\) 190.778 0.525560
\(364\) −8.69244 107.849i −0.0238803 0.296289i
\(365\) 0 0
\(366\) 32.1286 + 55.6484i 0.0877831 + 0.152045i
\(367\) 66.0380 114.381i 0.179940 0.311665i −0.761920 0.647671i \(-0.775743\pi\)
0.941860 + 0.336006i \(0.109076\pi\)
\(368\) 23.4048 + 13.5128i 0.0636000 + 0.0367195i
\(369\) 48.9831 28.2804i 0.132746 0.0766407i
\(370\) 0 0
\(371\) −360.646 + 29.0674i −0.972092 + 0.0783487i
\(372\) 37.8701i 0.101801i
\(373\) −9.25597 + 5.34394i −0.0248149 + 0.0143269i −0.512356 0.858773i \(-0.671227\pi\)
0.487541 + 0.873100i \(0.337894\pi\)
\(374\) −50.9159 29.3963i −0.136139 0.0785998i
\(375\) 0 0
\(376\) −31.5659 + 18.2246i −0.0839517 + 0.0484696i
\(377\) 303.678 0.805513
\(378\) 22.0577 46.4700i 0.0583536 0.122936i
\(379\) −142.918 −0.377092 −0.188546 0.982064i \(-0.560378\pi\)
−0.188546 + 0.982064i \(0.560378\pi\)
\(380\) 0 0
\(381\) −175.922 101.569i −0.461738 0.266585i
\(382\) 290.075 + 167.475i 0.759359 + 0.438416i
\(383\) 308.507 + 534.349i 0.805500 + 1.39517i 0.915953 + 0.401286i \(0.131437\pi\)
−0.110452 + 0.993881i \(0.535230\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −187.938 −0.486885
\(387\) 201.142 116.130i 0.519748 0.300076i
\(388\) −45.7447 + 79.2322i −0.117899 + 0.204207i
\(389\) −346.969 + 600.968i −0.891951 + 1.54490i −0.0544171 + 0.998518i \(0.517330\pi\)
−0.837534 + 0.546386i \(0.816003\pi\)
\(390\) 0 0
\(391\) 85.2560i 0.218046i
\(392\) −129.574 49.1793i −0.330546 0.125457i
\(393\) 160.552i 0.408528i
\(394\) −74.7972 129.553i −0.189841 0.328814i
\(395\) 0 0
\(396\) 9.88368 17.1190i 0.0249588 0.0432299i
\(397\) −279.776 484.587i −0.704726 1.22062i −0.966790 0.255571i \(-0.917737\pi\)
0.262065 0.965050i \(-0.415597\pi\)
\(398\) −285.024 −0.716142
\(399\) −12.2693 17.7801i −0.0307502 0.0445616i
\(400\) 0 0
\(401\) 80.6033 + 139.609i 0.201006 + 0.348152i 0.948853 0.315719i \(-0.102246\pi\)
−0.747847 + 0.663871i \(0.768912\pi\)
\(402\) −24.3885 + 42.2421i −0.0606679 + 0.105080i
\(403\) −73.1697 42.2445i −0.181563 0.104825i
\(404\) 158.518 91.5203i 0.392371 0.226535i
\(405\) 0 0
\(406\) 166.800 351.406i 0.410837 0.865532i
\(407\) 113.322i 0.278431i
\(408\) 53.5361 30.9091i 0.131216 0.0757576i
\(409\) −398.217 229.911i −0.973637 0.562129i −0.0732937 0.997310i \(-0.523351\pi\)
−0.900343 + 0.435181i \(0.856684\pi\)
\(410\) 0 0
\(411\) −41.2111 + 23.7932i −0.100270 + 0.0578911i
\(412\) −101.016 −0.245186
\(413\) 787.931 63.5056i 1.90782 0.153767i
\(414\) 28.6649 0.0692389
\(415\) 0 0
\(416\) 37.8618 + 21.8595i 0.0910139 + 0.0525469i
\(417\) −100.519 58.0347i −0.241053 0.139172i
\(418\) −4.15076 7.18933i −0.00993005 0.0171994i
\(419\) 93.5818i 0.223346i −0.993745 0.111673i \(-0.964379\pi\)
0.993745 0.111673i \(-0.0356208\pi\)
\(420\) 0 0
\(421\) 162.957 0.387072 0.193536 0.981093i \(-0.438004\pi\)
0.193536 + 0.981093i \(0.438004\pi\)
\(422\) 36.2579 20.9335i 0.0859193 0.0496055i
\(423\) −19.3301 + 33.4806i −0.0456975 + 0.0791504i
\(424\) 73.0978 126.609i 0.172400 0.298606i
\(425\) 0 0
\(426\) 214.164i 0.502731i
\(427\) 78.7425 165.891i 0.184409 0.388503i
\(428\) 187.899i 0.439016i
\(429\) −22.0507 38.1930i −0.0514003 0.0890280i
\(430\) 0 0
\(431\) 165.543 286.728i 0.384090 0.665263i −0.607553 0.794279i \(-0.707849\pi\)
0.991642 + 0.129016i \(0.0411820\pi\)
\(432\) 10.3923 + 18.0000i 0.0240563 + 0.0416667i
\(433\) −88.4130 −0.204187 −0.102094 0.994775i \(-0.532554\pi\)
−0.102094 + 0.994775i \(0.532554\pi\)
\(434\) −89.0735 + 61.4660i −0.205238 + 0.141627i
\(435\) 0 0
\(436\) −120.610 208.903i −0.276629 0.479136i
\(437\) 6.01907 10.4253i 0.0137736 0.0238566i
\(438\) 129.220 + 74.6054i 0.295024 + 0.170332i
\(439\) 60.4608 34.9070i 0.137724 0.0795149i −0.429555 0.903041i \(-0.641330\pi\)
0.567279 + 0.823526i \(0.307996\pi\)
\(440\) 0 0
\(441\) −145.102 + 23.5429i −0.329031 + 0.0533852i
\(442\) 137.918i 0.312032i
\(443\) −571.953 + 330.217i −1.29109 + 0.745411i −0.978847 0.204592i \(-0.934413\pi\)
−0.312242 + 0.950003i \(0.601080\pi\)
\(444\) 103.190 + 59.5766i 0.232409 + 0.134182i
\(445\) 0 0
\(446\) −402.368 + 232.307i −0.902171 + 0.520869i
\(447\) 88.5311 0.198056
\(448\) 46.0912 31.8057i 0.102882 0.0709948i
\(449\) 560.274 1.24783 0.623913 0.781493i \(-0.285542\pi\)
0.623913 + 0.781493i \(0.285542\pi\)
\(450\) 0 0
\(451\) −53.7926 31.0572i −0.119274 0.0688629i
\(452\) −18.5879 10.7318i −0.0411238 0.0237428i
\(453\) −143.083 247.827i −0.315856 0.547079i
\(454\) 515.418i 1.13528i
\(455\) 0 0
\(456\) 8.72873 0.0191419
\(457\) 159.158 91.8900i 0.348267 0.201072i −0.315655 0.948874i \(-0.602224\pi\)
0.663922 + 0.747802i \(0.268891\pi\)
\(458\) 212.874 368.709i 0.464790 0.805041i
\(459\) 32.7840 56.7836i 0.0714249 0.123712i
\(460\) 0 0
\(461\) 28.4330i 0.0616767i 0.999524 + 0.0308384i \(0.00981771\pi\)
−0.999524 + 0.0308384i \(0.990182\pi\)
\(462\) −56.3073 + 4.53826i −0.121877 + 0.00982307i
\(463\) 269.931i 0.583005i 0.956570 + 0.291503i \(0.0941552\pi\)
−0.956570 + 0.291503i \(0.905845\pi\)
\(464\) 78.5866 + 136.116i 0.169368 + 0.293353i
\(465\) 0 0
\(466\) 199.422 345.409i 0.427944 0.741221i
\(467\) 167.166 + 289.539i 0.357956 + 0.619999i 0.987619 0.156870i \(-0.0501403\pi\)
−0.629663 + 0.776868i \(0.716807\pi\)
\(468\) 46.3710 0.0990834
\(469\) 138.941 11.1984i 0.296250 0.0238772i
\(470\) 0 0
\(471\) 165.248 + 286.218i 0.350845 + 0.607681i
\(472\) −159.702 + 276.612i −0.338352 + 0.586043i
\(473\) −220.892 127.532i −0.467002 0.269624i
\(474\) −75.4717 + 43.5736i −0.159223 + 0.0919274i
\(475\) 0 0
\(476\) −159.594 75.7536i −0.335281 0.159146i
\(477\) 155.064i 0.325081i
\(478\) −101.696 + 58.7144i −0.212754 + 0.122833i
\(479\) −114.560 66.1412i −0.239165 0.138082i 0.375628 0.926771i \(-0.377427\pi\)
−0.614793 + 0.788689i \(0.710760\pi\)
\(480\) 0 0
\(481\) 230.219 132.917i 0.478626 0.276335i
\(482\) −469.271 −0.973592
\(483\) −46.5253 67.4222i −0.0963257 0.139591i
\(484\) 220.292 0.455148
\(485\) 0 0
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) 447.970 + 258.635i 0.919856 + 0.531079i 0.883589 0.468263i \(-0.155120\pi\)
0.0362667 + 0.999342i \(0.488453\pi\)
\(488\) 37.0989 + 64.2573i 0.0760224 + 0.131675i
\(489\) 429.898i 0.879138i
\(490\) 0 0
\(491\) 484.805 0.987383 0.493692 0.869637i \(-0.335647\pi\)
0.493692 + 0.869637i \(0.335647\pi\)
\(492\) 56.5609 32.6554i 0.114961 0.0663728i
\(493\) 247.913 429.398i 0.502866 0.870989i
\(494\) 9.73701 16.8650i 0.0197105 0.0341397i
\(495\) 0 0
\(496\) 43.7286i 0.0881624i
\(497\) −503.730 + 347.604i −1.01354 + 0.699404i
\(498\) 114.336i 0.229589i
\(499\) −64.6450 111.968i −0.129549 0.224385i 0.793953 0.607979i \(-0.208020\pi\)
−0.923502 + 0.383594i \(0.874686\pi\)
\(500\) 0 0
\(501\) −25.3723 + 43.9461i −0.0506432 + 0.0877167i
\(502\) −296.331 513.260i −0.590300 1.02243i
\(503\) −160.905 −0.319890 −0.159945 0.987126i \(-0.551132\pi\)
−0.159945 + 0.987126i \(0.551132\pi\)
\(504\) 25.4700 53.6589i 0.0505357 0.106466i
\(505\) 0 0
\(506\) −15.7397 27.2620i −0.0311061 0.0538774i
\(507\) −94.6308 + 163.905i −0.186649 + 0.323285i
\(508\) −203.137 117.281i −0.399877 0.230869i
\(509\) 320.453 185.014i 0.629575 0.363485i −0.151013 0.988532i \(-0.548253\pi\)
0.780587 + 0.625047i \(0.214920\pi\)
\(510\) 0 0
\(511\) −34.2563 425.027i −0.0670378 0.831755i
\(512\) 22.6274i 0.0441942i
\(513\) 8.01785 4.62911i 0.0156293 0.00902360i
\(514\) −409.012 236.143i −0.795744 0.459423i
\(515\) 0 0
\(516\) 232.259 134.095i 0.450115 0.259874i
\(517\) 42.4560 0.0821200
\(518\) −27.3556 339.408i −0.0528101 0.655228i
\(519\) 39.9964 0.0770644
\(520\) 0 0
\(521\) 65.1395 + 37.6083i 0.125028 + 0.0721849i 0.561210 0.827674i \(-0.310336\pi\)
−0.436182 + 0.899859i \(0.643670\pi\)
\(522\) 144.373 + 83.3537i 0.276576 + 0.159681i
\(523\) −468.058 810.701i −0.894949 1.55010i −0.833867 0.551965i \(-0.813878\pi\)
−0.0610819 0.998133i \(-0.519455\pi\)
\(524\) 185.389i 0.353796i
\(525\) 0 0
\(526\) 289.032 0.549491
\(527\) −119.467 + 68.9741i −0.226692 + 0.130881i
\(528\) 11.4127 19.7674i 0.0216149 0.0374382i
\(529\) −241.676 + 418.594i −0.456854 + 0.791294i
\(530\) 0 0
\(531\) 338.780i 0.638003i
\(532\) −14.1674 20.5307i −0.0266304 0.0385915i
\(533\) 145.710i 0.273377i
\(534\) −67.1336 116.279i −0.125718 0.217751i
\(535\) 0 0
\(536\) −28.1614 + 48.7770i −0.0525399 + 0.0910018i
\(537\) 181.376 + 314.152i 0.337758 + 0.585014i
\(538\) 197.214 0.366569
\(539\) 102.065 + 125.074i 0.189361 + 0.232047i
\(540\) 0 0
\(541\) 304.692 + 527.742i 0.563201 + 0.975493i 0.997215 + 0.0745867i \(0.0237638\pi\)
−0.434013 + 0.900906i \(0.642903\pi\)
\(542\) −263.902 + 457.092i −0.486904 + 0.843343i
\(543\) −365.500 211.021i −0.673112 0.388622i
\(544\) 61.8182 35.6907i 0.113636 0.0656080i
\(545\) 0 0
\(546\) −75.2637 109.068i −0.137846 0.199759i
\(547\) 491.361i 0.898283i −0.893461 0.449141i \(-0.851730\pi\)
0.893461 0.449141i \(-0.148270\pi\)
\(548\) −47.5865 + 27.4741i −0.0868366 + 0.0501351i
\(549\) 68.1551 + 39.3494i 0.124144 + 0.0716746i
\(550\) 0 0
\(551\) 60.6310 35.0053i 0.110038 0.0635305i
\(552\) 33.0994 0.0599626
\(553\) 224.985 + 106.792i 0.406844 + 0.193115i
\(554\) 703.577 1.27000
\(555\) 0 0
\(556\) −116.069 67.0127i −0.208758 0.120527i
\(557\) 911.250 + 526.110i 1.63600 + 0.944543i 0.982192 + 0.187878i \(0.0601610\pi\)
0.653803 + 0.756665i \(0.273172\pi\)
\(558\) −23.1906 40.1673i −0.0415602 0.0719843i
\(559\) 598.339i 1.07037i
\(560\) 0 0
\(561\) −72.0060 −0.128353
\(562\) 358.580 207.026i 0.638042 0.368374i
\(563\) −387.269 + 670.769i −0.687866 + 1.19142i 0.284661 + 0.958628i \(0.408119\pi\)
−0.972527 + 0.232791i \(0.925214\pi\)
\(564\) −22.3204 + 38.6601i −0.0395752 + 0.0685463i
\(565\) 0 0
\(566\) 391.406i 0.691531i
\(567\) −5.06126 62.7964i −0.00892639 0.110752i
\(568\) 247.295i 0.435378i
\(569\) 156.525 + 271.109i 0.275088 + 0.476466i 0.970157 0.242477i \(-0.0779598\pi\)
−0.695070 + 0.718942i \(0.744626\pi\)
\(570\) 0 0
\(571\) −324.711 + 562.416i −0.568670 + 0.984966i 0.428027 + 0.903766i \(0.359209\pi\)
−0.996698 + 0.0812002i \(0.974125\pi\)
\(572\) −25.4620 44.1015i −0.0445140 0.0771005i
\(573\) 410.228 0.715931
\(574\) −168.611 80.0336i −0.293747 0.139431i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −514.893 + 891.822i −0.892363 + 1.54562i −0.0553284 + 0.998468i \(0.517621\pi\)
−0.837035 + 0.547150i \(0.815713\pi\)
\(578\) 158.937 + 91.7622i 0.274977 + 0.158758i
\(579\) −199.338 + 115.088i −0.344280 + 0.198770i
\(580\) 0 0
\(581\) 268.927 185.575i 0.462868 0.319406i
\(582\) 112.051i 0.192528i
\(583\) −147.475 + 85.1445i −0.252958 + 0.146046i
\(584\) 149.211 + 86.1469i 0.255498 + 0.147512i
\(585\) 0 0
\(586\) 459.646 265.376i 0.784378 0.452861i
\(587\) 791.817 1.34892 0.674461 0.738311i \(-0.264376\pi\)
0.674461 + 0.738311i \(0.264376\pi\)
\(588\) −167.550 + 27.1850i −0.284949 + 0.0462329i
\(589\) −19.4783 −0.0330701
\(590\) 0 0
\(591\) −158.669 91.6075i −0.268475 0.155004i
\(592\) 119.153 + 68.7931i 0.201272 + 0.116205i
\(593\) 42.2509 + 73.1807i 0.0712494 + 0.123408i 0.899449 0.437025i \(-0.143968\pi\)
−0.828200 + 0.560433i \(0.810635\pi\)
\(594\) 24.2100i 0.0407575i
\(595\) 0 0
\(596\) 102.227 0.171522
\(597\) −302.314 + 174.541i −0.506389 + 0.292364i
\(598\) 36.9228 63.9522i 0.0617438 0.106943i
\(599\) −233.463 + 404.369i −0.389754 + 0.675074i −0.992416 0.122922i \(-0.960773\pi\)
0.602662 + 0.797997i \(0.294107\pi\)
\(600\) 0 0
\(601\) 1095.93i 1.82351i 0.410733 + 0.911756i \(0.365273\pi\)
−0.410733 + 0.911756i \(0.634727\pi\)
\(602\) −692.377 328.647i −1.15013 0.545925i
\(603\) 59.7394i 0.0990702i
\(604\) −165.218 286.166i −0.273540 0.473785i
\(605\) 0 0
\(606\) 112.089 194.144i 0.184965 0.320369i
\(607\) −179.449 310.815i −0.295633 0.512051i 0.679499 0.733676i \(-0.262197\pi\)
−0.975132 + 0.221625i \(0.928864\pi\)
\(608\) 10.0791 0.0165774
\(609\) −38.2733 474.866i −0.0628461 0.779747i
\(610\) 0 0
\(611\) 49.7975 + 86.2517i 0.0815016 + 0.141165i
\(612\) 37.8558 65.5681i 0.0618558 0.107137i
\(613\) −400.154 231.029i −0.652780 0.376883i 0.136741 0.990607i \(-0.456337\pi\)
−0.789520 + 0.613724i \(0.789671\pi\)
\(614\) 132.008 76.2148i 0.214996 0.124128i
\(615\) 0 0
\(616\) −65.0181 + 5.24033i −0.105549 + 0.00850703i
\(617\) 219.440i 0.355656i 0.984062 + 0.177828i \(0.0569071\pi\)
−0.984062 + 0.177828i \(0.943093\pi\)
\(618\) −107.144 + 61.8597i −0.173372 + 0.100097i
\(619\) −832.792 480.813i −1.34538 0.776757i −0.357791 0.933802i \(-0.616470\pi\)
−0.987592 + 0.157044i \(0.949803\pi\)
\(620\) 0 0
\(621\) 30.4037 17.5536i 0.0489593 0.0282667i
\(622\) −816.123 −1.31209
\(623\) −164.534 + 346.633i −0.264100 + 0.556393i
\(624\) 53.5446 0.0858087
\(625\) 0 0
\(626\) −486.560 280.915i −0.777252 0.448747i
\(627\) −8.80509 5.08362i −0.0140432 0.00810785i
\(628\) 190.812 + 330.496i 0.303840 + 0.526267i
\(629\) 434.036i 0.690041i
\(630\) 0 0
\(631\) 584.721 0.926658 0.463329 0.886186i \(-0.346655\pi\)
0.463329 + 0.886186i \(0.346655\pi\)
\(632\) −87.1472 + 50.3144i −0.137891 + 0.0796115i
\(633\) 25.6382 44.4067i 0.0405027 0.0701528i
\(634\) 56.8303 98.4329i 0.0896376 0.155257i
\(635\) 0 0
\(636\) 179.052i 0.281529i
\(637\) −134.379 + 354.053i −0.210957 + 0.555813i
\(638\) 183.076i 0.286953i
\(639\) −131.148 227.155i −0.205239 0.355485i
\(640\) 0 0
\(641\) −269.518 + 466.819i −0.420465 + 0.728268i −0.995985 0.0895205i \(-0.971467\pi\)
0.575520 + 0.817788i \(0.304800\pi\)
\(642\) 115.064 + 199.297i 0.179228 + 0.310431i
\(643\) 150.959 0.234773 0.117386 0.993086i \(-0.462548\pi\)
0.117386 + 0.993086i \(0.462548\pi\)
\(644\) −53.7228 77.8525i −0.0834205 0.120889i
\(645\) 0 0
\(646\) −15.8979 27.5360i −0.0246098 0.0426255i
\(647\) −225.808 + 391.111i −0.349008 + 0.604499i −0.986073 0.166310i \(-0.946815\pi\)
0.637066 + 0.770809i \(0.280148\pi\)
\(648\) 22.0454 + 12.7279i 0.0340207 + 0.0196419i
\(649\) 322.199 186.022i 0.496454 0.286628i
\(650\) 0 0
\(651\) −56.8366 + 119.741i −0.0873067 + 0.183933i
\(652\) 496.404i 0.761356i
\(653\) −373.860 + 215.848i −0.572526 + 0.330548i −0.758158 0.652071i \(-0.773900\pi\)
0.185631 + 0.982619i \(0.440567\pi\)
\(654\) −255.853 147.717i −0.391213 0.225867i
\(655\) 0 0
\(656\) 65.3108 37.7072i 0.0995592 0.0574805i
\(657\) 182.745 0.278151
\(658\) 127.160 10.2488i 0.193252 0.0155757i
\(659\) 195.185 0.296184 0.148092 0.988974i \(-0.452687\pi\)
0.148092 + 0.988974i \(0.452687\pi\)
\(660\) 0 0
\(661\) 596.305 + 344.277i 0.902126 + 0.520843i 0.877889 0.478863i \(-0.158951\pi\)
0.0242368 + 0.999706i \(0.492284\pi\)
\(662\) −602.626 347.926i −0.910311 0.525569i
\(663\) −84.4572 146.284i −0.127386 0.220640i
\(664\) 132.023i 0.198830i
\(665\) 0 0
\(666\) 145.932 0.219118
\(667\) 229.913 132.740i 0.344697 0.199011i
\(668\) −29.2974 + 50.7445i −0.0438583 + 0.0759649i
\(669\) −284.517 + 492.799i −0.425288 + 0.736620i
\(670\) 0 0
\(671\) 86.4259i 0.128802i
\(672\) 29.4102 61.9600i 0.0437652 0.0922024i
\(673\) 200.020i 0.297206i −0.988897 0.148603i \(-0.952522\pi\)
0.988897 0.148603i \(-0.0474777\pi\)
\(674\) −445.564 771.740i −0.661075 1.14501i
\(675\) 0 0
\(676\) −109.270 + 189.262i −0.161642 + 0.279973i
\(677\) 424.807 + 735.787i 0.627484 + 1.08683i 0.988055 + 0.154103i \(0.0492486\pi\)
−0.360571 + 0.932732i \(0.617418\pi\)
\(678\) −26.2873 −0.0387719
\(679\) 263.554 181.868i 0.388150 0.267846i
\(680\) 0 0
\(681\) 315.628 + 546.684i 0.463477 + 0.802766i
\(682\) −25.4676 + 44.1111i −0.0373425 + 0.0646791i
\(683\) −387.988 224.005i −0.568064 0.327972i 0.188311 0.982109i \(-0.439699\pi\)
−0.756376 + 0.654137i \(0.773032\pi\)
\(684\) 9.25821 5.34523i 0.0135354 0.00781467i
\(685\) 0 0
\(686\) 335.888 + 349.968i 0.489632 + 0.510157i
\(687\) 521.433i 0.759000i
\(688\) 268.190 154.839i 0.389811 0.225057i
\(689\) −345.952 199.735i −0.502107 0.289891i
\(690\) 0 0
\(691\) −337.930 + 195.104i −0.489044 + 0.282350i −0.724178 0.689613i \(-0.757781\pi\)
0.235134 + 0.971963i \(0.424447\pi\)
\(692\) 46.1839 0.0667397
\(693\) −56.9439 + 39.2946i −0.0821701 + 0.0567022i
\(694\) 608.313 0.876532
\(695\) 0 0
\(696\) 166.707 + 96.2485i 0.239522 + 0.138288i
\(697\) −206.033 118.953i −0.295599 0.170664i
\(698\) 67.3038 + 116.574i 0.0964237 + 0.167011i
\(699\) 488.482i 0.698830i
\(700\) 0 0
\(701\) 989.018 1.41087 0.705434 0.708776i \(-0.250752\pi\)
0.705434 + 0.708776i \(0.250752\pi\)
\(702\) 49.1839 28.3963i 0.0700625 0.0404506i
\(703\) 30.6429 53.0751i 0.0435888 0.0754980i
\(704\) 13.1782 22.8254i 0.0187191 0.0324224i
\(705\) 0 0
\(706\) 371.849i 0.526699i
\(707\) −638.571 + 51.4676i −0.903212 + 0.0727971i
\(708\) 391.189i 0.552527i
\(709\) 554.927 + 961.161i 0.782689 + 1.35566i 0.930370 + 0.366623i \(0.119486\pi\)
−0.147680 + 0.989035i \(0.547181\pi\)
\(710\) 0 0
\(711\) −53.3665 + 92.4335i −0.0750584 + 0.130005i
\(712\) −77.5192 134.267i −0.108875 0.188578i
\(713\) −73.8617 −0.103593
\(714\) −215.664 + 17.3821i −0.302051 + 0.0243447i
\(715\) 0 0
\(716\) 209.435 + 362.752i 0.292507 + 0.506637i
\(717\) −71.9101 + 124.552i −0.100293 + 0.173713i
\(718\) 365.918 + 211.263i 0.509636 + 0.294238i
\(719\) −936.393 + 540.627i −1.30235 + 0.751915i −0.980807 0.194979i \(-0.937536\pi\)
−0.321547 + 0.946894i \(0.604203\pi\)
\(720\) 0 0
\(721\) 319.402 + 151.609i 0.442999 + 0.210276i
\(722\) 506.042i 0.700889i
\(723\) −497.737 + 287.369i −0.688433 + 0.397467i
\(724\) −422.043 243.667i −0.582932 0.336556i
\(725\) 0 0
\(726\) 233.655 134.901i 0.321838 0.185813i
\(727\) 491.493 0.676056 0.338028 0.941136i \(-0.390240\pi\)
0.338028 + 0.941136i \(0.390240\pi\)
\(728\) −86.9070 125.941i −0.119378 0.172996i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −846.044 488.464i −1.15738 0.668213i
\(732\) 78.6988 + 45.4367i 0.107512 + 0.0620721i
\(733\) 23.3826 + 40.4999i 0.0318999 + 0.0552522i 0.881535 0.472119i \(-0.156511\pi\)
−0.849635 + 0.527372i \(0.823178\pi\)
\(734\) 186.784i 0.254474i
\(735\) 0 0
\(736\) 38.2199 0.0519292
\(737\) 56.8156 32.8025i 0.0770903 0.0445081i
\(738\) 39.9946 69.2726i 0.0541932 0.0938653i
\(739\) −368.856 + 638.878i −0.499129 + 0.864517i −0.999999 0.00100544i \(-0.999680\pi\)
0.500870 + 0.865522i \(0.333013\pi\)
\(740\) 0 0
\(741\) 23.8507i 0.0321872i
\(742\) −421.146 + 290.615i −0.567582 + 0.391665i
\(743\) 258.593i 0.348039i 0.984742 + 0.174020i \(0.0556757\pi\)
−0.984742 + 0.174020i \(0.944324\pi\)
\(744\) −26.7782 46.3812i −0.0359922 0.0623403i
\(745\) 0 0
\(746\) −7.55747 + 13.0899i −0.0101307 + 0.0175468i
\(747\) 70.0159 + 121.271i 0.0937295 + 0.162344i
\(748\) −83.1454 −0.111157
\(749\) 282.005 594.114i 0.376509 0.793210i
\(750\) 0 0
\(751\) −175.310 303.645i −0.233435 0.404321i 0.725382 0.688347i \(-0.241663\pi\)
−0.958817 + 0.284025i \(0.908330\pi\)
\(752\) −25.7734 + 44.6409i −0.0342731 + 0.0593628i
\(753\) −628.613 362.930i −0.834811 0.481978i
\(754\) 371.928 214.733i 0.493274 0.284792i
\(755\) 0 0
\(756\) −5.84424 72.5110i −0.00773048 0.0959140i
\(757\) 907.187i 1.19840i 0.800600 + 0.599199i \(0.204514\pi\)
−0.800600 + 0.599199i \(0.795486\pi\)
\(758\) −175.038 + 101.058i −0.230921 + 0.133322i
\(759\) −33.3890 19.2771i −0.0439907 0.0253981i
\(760\) 0 0
\(761\) 1067.66 616.416i 1.40297 0.810007i 0.408277 0.912858i \(-0.366130\pi\)
0.994697 + 0.102851i \(0.0327965\pi\)
\(762\) −287.280 −0.377008
\(763\) 67.8267 + 841.543i 0.0888948 + 1.10294i
\(764\) 473.691 0.620014
\(765\) 0 0
\(766\) 755.684 + 436.294i 0.986532 + 0.569575i
\(767\) 755.826 + 436.376i 0.985432 + 0.568939i
\(768\) 13.8564 + 24.0000i 0.0180422 + 0.0312500i
\(769\) 685.828i 0.891844i 0.895072 + 0.445922i \(0.147124\pi\)
−0.895072 + 0.445922i \(0.852876\pi\)
\(770\) 0 0
\(771\) −578.431 −0.750235
\(772\) −230.176 + 132.892i −0.298155 + 0.172140i
\(773\) 193.077 334.420i 0.249776 0.432625i −0.713687 0.700465i \(-0.752976\pi\)
0.963464 + 0.267839i \(0.0863095\pi\)
\(774\) 164.232 284.458i 0.212186 0.367517i
\(775\) 0 0
\(776\) 129.386i 0.166734i
\(777\) −236.859 343.245i −0.304838 0.441756i
\(778\) 981.376i 1.26141i
\(779\) −16.7962 29.0918i −0.0215612 0.0373451i
\(780\) 0 0
\(781\) −144.025 + 249.458i −0.184411 + 0.319409i
\(782\) −60.2851 104.417i −0.0770909 0.133525i
\(783\) 204.174 0.260759
\(784\) −193.470 + 31.3905i −0.246773 + 0.0400389i
\(785\) 0 0
\(786\) −113.527 196.635i −0.144437 0.250171i
\(787\) −614.543 + 1064.42i −0.780867 + 1.35250i 0.150570 + 0.988599i \(0.451889\pi\)
−0.931437 + 0.363902i \(0.881444\pi\)
\(788\) −183.215 105.779i −0.232506 0.134238i
\(789\) 306.565 176.995i 0.388549 0.224329i
\(790\) 0 0
\(791\) 42.6663 + 61.8300i 0.0539397 + 0.0781668i
\(792\) 27.9553i 0.0352971i
\(793\) 175.579 101.371i 0.221411 0.127832i
\(794\) −685.309 395.663i −0.863109 0.498316i
\(795\) 0 0
\(796\) −349.082 + 201.543i −0.438545 + 0.253194i
\(797\) 821.718 1.03101 0.515507 0.856886i \(-0.327604\pi\)
0.515507 + 0.856886i \(0.327604\pi\)
\(798\) −27.5992 13.1004i −0.0345855 0.0164165i
\(799\) 162.612 0.203519
\(800\) 0 0
\(801\) −142.412 82.2215i −0.177793 0.102649i
\(802\) 197.437 + 113.990i 0.246181 + 0.142132i
\(803\) −100.344 173.801i −0.124962 0.216440i
\(804\) 68.9811i 0.0857973i
\(805\) 0 0
\(806\) −119.486 −0.148245
\(807\) 209.177 120.768i 0.259203 0.149651i
\(808\) 129.429 224.178i 0.160185 0.277448i
\(809\) −216.809 + 375.524i −0.267996 + 0.464184i −0.968344 0.249618i \(-0.919695\pi\)
0.700348 + 0.713802i \(0.253028\pi\)
\(810\) 0 0
\(811\) 1618.04i 1.99512i 0.0698416 + 0.997558i \(0.477751\pi\)
−0.0698416 + 0.997558i \(0.522249\pi\)
\(812\) −44.1941 548.328i −0.0544263 0.675281i
\(813\) 646.425i 0.795111i
\(814\) −80.1304 138.790i −0.0984403 0.170504i
\(815\) 0 0
\(816\) 43.7121 75.7115i 0.0535687 0.0927837i
\(817\) −68.9711 119.461i −0.0844199 0.146220i
\(818\) −650.286 −0.794971
\(819\) −146.620 69.5952i −0.179023 0.0849758i
\(820\) 0 0
\(821\) 429.043 + 743.125i 0.522586 + 0.905146i 0.999655 + 0.0262799i \(0.00836612\pi\)
−0.477068 + 0.878866i \(0.658301\pi\)
\(822\) −33.6487 + 58.2813i −0.0409352 + 0.0709018i
\(823\) −679.461 392.287i −0.825591 0.476655i 0.0267498 0.999642i \(-0.491484\pi\)
−0.852341 + 0.522987i \(0.824818\pi\)
\(824\) −123.719 + 71.4294i −0.150145 + 0.0866862i
\(825\) 0 0
\(826\) 920.109 634.929i 1.11393 0.768680i
\(827\) 773.795i 0.935665i −0.883817 0.467833i \(-0.845035\pi\)
0.883817 0.467833i \(-0.154965\pi\)
\(828\) 35.1072 20.2691i 0.0424000 0.0244796i
\(829\) 573.640 + 331.191i 0.691966 + 0.399507i 0.804348 0.594158i \(-0.202515\pi\)
−0.112382 + 0.993665i \(0.535848\pi\)
\(830\) 0 0
\(831\) 746.256 430.851i 0.898022 0.518473i
\(832\) 61.8280 0.0743125
\(833\) 390.924 + 479.048i 0.469296 + 0.575087i
\(834\) −164.147 −0.196819
\(835\) 0 0
\(836\) −10.1672 5.87006i −0.0121618 0.00702161i
\(837\) −49.1946 28.4025i −0.0587750 0.0339337i
\(838\) −66.1723 114.614i −0.0789646 0.136771i
\(839\) 359.133i 0.428049i −0.976828 0.214024i \(-0.931343\pi\)
0.976828 0.214024i \(-0.0686572\pi\)
\(840\) 0 0
\(841\) 702.963 0.835866
\(842\) 199.581 115.228i 0.237032 0.136851i
\(843\) 253.554 439.169i 0.300776 0.520959i
\(844\) 29.6045 51.2764i 0.0350764 0.0607541i
\(845\) 0 0
\(846\) 54.6737i 0.0646261i
\(847\) −696.537 330.621i −0.822357 0.390344i
\(848\) 206.752i 0.243811i
\(849\) 239.686 + 415.149i 0.282316 + 0.488986i
\(850\) 0 0
\(851\) 116.198 201.261i 0.136543 0.236500i
\(852\) −151.437 262.296i −0.177742 0.307859i
\(853\) 1089.78 1.27758 0.638792 0.769379i \(-0.279434\pi\)
0.638792 + 0.769379i \(0.279434\pi\)
\(854\) −20.8631 258.853i −0.0244298 0.303107i
\(855\) 0 0
\(856\) 132.865 + 230.128i 0.155216 + 0.268841i
\(857\) 32.4560 56.2155i 0.0378717 0.0655956i −0.846468 0.532439i \(-0.821276\pi\)
0.884340 + 0.466843i \(0.154609\pi\)
\(858\) −54.0131 31.1845i −0.0629523 0.0363455i
\(859\) −250.689 + 144.735i −0.291838 + 0.168493i −0.638770 0.769397i \(-0.720557\pi\)
0.346933 + 0.937890i \(0.387223\pi\)
\(860\) 0 0
\(861\) −227.849 + 18.3642i −0.264633 + 0.0213289i
\(862\) 468.225i 0.543185i
\(863\) −812.738 + 469.234i −0.941759 + 0.543725i −0.890511 0.454961i \(-0.849653\pi\)
−0.0512476 + 0.998686i \(0.516320\pi\)
\(864\) 25.4558 + 14.6969i 0.0294628 + 0.0170103i
\(865\) 0 0
\(866\) −108.283 + 62.5174i −0.125038 + 0.0721910i
\(867\) 224.771 0.259251
\(868\) −65.6293 + 138.265i −0.0756098 + 0.159291i
\(869\) 117.213 0.134882
\(870\) 0 0
\(871\) 133.280 + 76.9493i 0.153020 + 0.0883459i
\(872\) −295.434 170.569i −0.338800 0.195606i
\(873\) 68.6171 + 118.848i 0.0785992 + 0.136138i
\(874\) 17.0245i 0.0194788i
\(875\) 0 0
\(876\) 211.016 0.240886
\(877\) 191.465 110.543i 0.218318 0.126046i −0.386853 0.922141i \(-0.626438\pi\)
0.605171 + 0.796095i \(0.293105\pi\)
\(878\) 49.3660 85.5044i 0.0562255 0.0973855i
\(879\) 325.019 562.949i 0.369759 0.640442i
\(880\) 0 0
\(881\) 154.796i 0.175704i 0.996134 + 0.0878522i \(0.0280003\pi\)
−0.996134 + 0.0878522i \(0.972000\pi\)
\(882\) −161.066 + 131.437i −0.182615 + 0.149022i
\(883\) 1267.40i 1.43534i 0.696385 + 0.717668i \(0.254791\pi\)
−0.696385 + 0.717668i \(0.745209\pi\)
\(884\) −97.5227 168.914i −0.110320 0.191080i
\(885\) 0 0
\(886\) −466.997 + 808.863i −0.527085 + 0.912938i
\(887\) −828.399 1434.83i −0.933934 1.61762i −0.776524 0.630087i \(-0.783019\pi\)
−0.157410 0.987533i \(-0.550314\pi\)
\(888\) 168.508 0.189761
\(889\) 466.277 + 675.706i 0.524496 + 0.760074i
\(890\) 0 0
\(891\) −14.8255 25.6786i −0.0166392 0.0288199i
\(892\) −328.532 + 569.035i −0.368310 + 0.637931i
\(893\) 19.8846 + 11.4804i 0.0222672 + 0.0128560i
\(894\) 108.428 62.6009i 0.121284 0.0700234i
\(895\) 0 0
\(896\) 33.9600 71.5452i 0.0379018 0.0798496i
\(897\) 90.4420i 0.100827i
\(898\) 686.193 396.174i 0.764135 0.441173i
\(899\) −372.010 214.780i −0.413804 0.238910i
\(900\) 0 0
\(901\) −564.847 + 326.114i −0.626911 + 0.361947i
\(902\) −87.8430 −0.0973869
\(903\) −935.630 + 75.4099i −1.03614 + 0.0835105i
\(904\) −30.3540 −0.0335774
\(905\) 0 0
\(906\) −350.480 202.350i −0.386844 0.223344i
\(907\) 637.793 + 368.230i 0.703190 + 0.405987i 0.808534 0.588449i \(-0.200261\pi\)
−0.105345 + 0.994436i \(0.533595\pi\)
\(908\) 364.456 + 631.256i 0.401383 + 0.695216i
\(909\) 274.561i 0.302047i
\(910\) 0 0
\(911\) 197.935 0.217273 0.108636 0.994082i \(-0.465352\pi\)
0.108636 + 0.994082i \(0.465352\pi\)
\(912\) 10.6905 6.17214i 0.0117220 0.00676770i
\(913\) 76.8905 133.178i 0.0842175 0.145869i
\(914\) 129.952 225.084i 0.142180 0.246262i
\(915\) 0 0
\(916\) 602.099i 0.657313i
\(917\) −278.238 + 586.178i −0.303422 + 0.639235i
\(918\) 92.7273i 0.101010i
\(919\) 821.091 + 1422.17i 0.893462 + 1.54752i 0.835697 + 0.549191i \(0.185064\pi\)
0.0577645 + 0.998330i \(0.481603\pi\)
\(920\) 0 0
\(921\) 93.3436 161.676i 0.101350 0.175544i
\(922\) 20.1051 + 34.8231i 0.0218060 + 0.0377691i
\(923\) −675.718 −0.732089
\(924\) −65.7531 + 45.3735i −0.0711614 + 0.0491055i
\(925\) 0 0
\(926\) 190.870 + 330.597i 0.206123 + 0.357016i
\(927\) −75.7623 + 131.224i −0.0817285 + 0.141558i
\(928\) 192.497 + 111.138i 0.207432 + 0.119761i
\(929\) −1317.18 + 760.473i −1.41784 + 0.818593i −0.996109 0.0881263i \(-0.971912\pi\)
−0.421735 + 0.906719i \(0.638579\pi\)
\(930\) 0 0
\(931\) 13.9825 + 86.1785i 0.0150188 + 0.0925655i
\(932\) 564.050i 0.605204i
\(933\) −865.629 + 499.771i −0.927791 + 0.535660i
\(934\) 409.471 + 236.408i 0.438405 + 0.253113i
\(935\) 0 0
\(936\) 56.7927 32.7893i 0.0606759 0.0350313i
\(937\) −682.636 −0.728534 −0.364267 0.931295i \(-0.618680\pi\)
−0.364267 + 0.931295i \(0.618680\pi\)
\(938\) 162.249 111.961i 0.172974 0.119362i
\(939\) −688.100 −0.732800
\(940\) 0 0
\(941\) −248.545 143.497i −0.264129 0.152495i 0.362088 0.932144i \(-0.382064\pi\)
−0.626216 + 0.779649i \(0.715397\pi\)
\(942\) 404.773 + 233.696i 0.429695 + 0.248085i
\(943\) −63.6911 110.316i −0.0675410 0.116984i
\(944\) 451.706i 0.478502i
\(945\) 0 0
\(946\) −360.715 −0.381305
\(947\) 415.790 240.057i 0.439061 0.253492i −0.264139 0.964485i \(-0.585088\pi\)
0.703199 + 0.710993i \(0.251754\pi\)
\(948\) −61.6224 + 106.733i −0.0650025 + 0.112588i
\(949\) 235.391 407.709i 0.248041 0.429620i
\(950\) 0 0
\(951\) 139.205i 0.146378i
\(952\) −249.028 + 20.0711i −0.261584 + 0.0210831i
\(953\) 1147.30i 1.20388i −0.798540 0.601941i \(-0.794394\pi\)
0.798540 0.601941i \(-0.205606\pi\)
\(954\) −109.647 189.914i −0.114934 0.199071i
\(955\) 0 0
\(956\) −83.0347 + 143.820i −0.0868563 + 0.150440i
\(957\) −112.111 194.181i −0.117148 0.202906i
\(958\) −187.076 −0.195277
\(959\) 191.697 15.4504i 0.199892 0.0161109i
\(960\) 0 0
\(961\) −420.744 728.750i −0.437819 0.758325i
\(962\) 187.973 325.579i 0.195398 0.338439i
\(963\) 244.088 + 140.924i 0.253466 + 0.146339i
\(964\) −574.737 + 331.825i −0.596201 + 0.344217i
\(965\) 0 0
\(966\) −104.656 49.6767i −0.108340 0.0514251i
\(967\) 1400.07i 1.44785i −0.689881 0.723923i \(-0.742337\pi\)
0.689881 0.723923i \(-0.257663\pi\)
\(968\) 269.801 155.770i 0.278720 0.160919i
\(969\) −33.7246 19.4709i −0.0348035 0.0200938i
\(970\) 0 0
\(971\) 226.263 130.633i 0.233020 0.134534i −0.378944 0.925419i \(-0.623713\pi\)
0.611965 + 0.790885i \(0.290379\pi\)
\(972\) 31.1769 0.0320750
\(973\) 266.423 + 386.087i 0.273816 + 0.396801i
\(974\) 731.532 0.751059
\(975\) 0 0
\(976\) 90.8735 + 52.4658i 0.0931081 + 0.0537560i
\(977\) −675.019 389.723i −0.690910 0.398897i 0.113043 0.993590i \(-0.463940\pi\)
−0.803953 + 0.594693i \(0.797274\pi\)
\(978\) 303.984 + 526.516i 0.310822 + 0.538360i
\(979\) 180.589i 0.184463i
\(980\) 0 0
\(981\) −361.831 −0.368839
\(982\) 593.763 342.809i 0.604646 0.349093i
\(983\) −769.118 + 1332.15i −0.782419 + 1.35519i 0.148110 + 0.988971i \(0.452681\pi\)
−0.930529 + 0.366219i \(0.880652\pi\)
\(984\) 46.1817 79.9891i 0.0469327 0.0812898i
\(985\) 0 0
\(986\) 701.204i 0.711160i
\(987\) 128.597 88.7395i 0.130291 0.0899083i
\(988\) 27.5404i 0.0278749i
\(989\) −261.539 452.998i −0.264448 0.458037i
\(990\) 0 0
\(991\) −482.270 + 835.316i −0.486650 + 0.842902i −0.999882 0.0153476i \(-0.995115\pi\)
0.513233 + 0.858250i \(0.328448\pi\)
\(992\) −30.9208 53.5563i −0.0311701 0.0539883i
\(993\) −852.242 −0.858250
\(994\) −371.148 + 781.917i −0.373389 + 0.786637i
\(995\) 0 0
\(996\) 80.8474 + 140.032i 0.0811721 + 0.140594i
\(997\) −208.868 + 361.770i −0.209496 + 0.362858i −0.951556 0.307476i \(-0.900516\pi\)
0.742060 + 0.670334i \(0.233849\pi\)
\(998\) −158.347 91.4218i −0.158664 0.0916050i
\(999\) 154.785 89.3649i 0.154939 0.0894543i
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 1050.3.q.b.199.7 16
5.2 odd 4 1050.3.p.c.451.3 8
5.3 odd 4 1050.3.p.d.451.2 yes 8
5.4 even 2 inner 1050.3.q.b.199.2 16
7.5 odd 6 inner 1050.3.q.b.649.2 16
35.12 even 12 1050.3.p.c.901.3 yes 8
35.19 odd 6 inner 1050.3.q.b.649.7 16
35.33 even 12 1050.3.p.d.901.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.3.p.c.451.3 8 5.2 odd 4
1050.3.p.c.901.3 yes 8 35.12 even 12
1050.3.p.d.451.2 yes 8 5.3 odd 4
1050.3.p.d.901.2 yes 8 35.33 even 12
1050.3.q.b.199.2 16 5.4 even 2 inner
1050.3.q.b.199.7 16 1.1 even 1 trivial
1050.3.q.b.649.2 16 7.5 odd 6 inner
1050.3.q.b.649.7 16 35.19 odd 6 inner