Properties

Label 1050.2.o.l.949.1
Level $1050$
Weight $2$
Character 1050.949
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.l.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} +(-0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 - 1.50000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(3.00000 + 5.19615i) q^{19} +(-2.00000 + 1.73205i) q^{21} +4.00000i q^{22} +(-6.06218 + 3.50000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(-1.73205 - 2.00000i) q^{28} -4.00000 q^{29} +(2.50000 - 4.33013i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.46410 + 2.00000i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(1.73205 - 1.00000i) q^{37} +(-5.19615 - 3.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +7.00000 q^{41} +(0.866025 - 2.50000i) q^{42} -2.00000i q^{43} +(-2.00000 - 3.46410i) q^{44} +(3.50000 - 6.06218i) q^{46} +(0.866025 - 0.500000i) q^{47} +1.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(1.50000 + 2.59808i) q^{51} +(-3.46410 - 2.00000i) q^{52} +(-1.73205 - 1.00000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} -6.00000i q^{57} +(3.46410 - 2.00000i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-6.00000 - 10.3923i) q^{61} +5.00000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(2.00000 - 3.46410i) q^{66} +(-10.3923 - 6.00000i) q^{67} +(-2.59808 + 1.50000i) q^{68} +7.00000 q^{69} -9.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.19615 + 3.00000i) q^{73} +(-1.00000 + 1.73205i) q^{74} +6.00000 q^{76} +(-6.92820 - 8.00000i) q^{77} -4.00000i q^{78} +(-8.50000 - 14.7224i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-6.06218 + 3.50000i) q^{82} +4.00000i q^{83} +(0.500000 + 2.59808i) q^{84} +(1.00000 + 1.73205i) q^{86} +(3.46410 + 2.00000i) q^{87} +(3.46410 + 2.00000i) q^{88} +(-3.50000 - 6.06218i) q^{89} +(-10.0000 - 3.46410i) q^{91} +7.00000i q^{92} +(-4.33013 + 2.50000i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(-0.500000 - 0.866025i) q^{96} -7.00000i q^{97} +(6.92820 + 1.00000i) q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + 8q^{11} + 2q^{14} - 2q^{16} + 12q^{19} - 8q^{21} + 2q^{24} + 8q^{26} - 16q^{29} + 10q^{31} + 12q^{34} + 4q^{36} - 8q^{39} + 28q^{41} - 8q^{44} + 14q^{46} - 22q^{49} + 6q^{51} + 2q^{54} + 10q^{56} - 28q^{59} - 24q^{61} - 4q^{64} + 8q^{66} + 28q^{69} - 36q^{71} - 4q^{74} + 24q^{76} - 34q^{79} - 2q^{81} + 2q^{84} + 4q^{86} - 14q^{89} - 40q^{91} - 2q^{94} - 2q^{96} + 16q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 0.866025 2.50000i 0.327327 0.944911i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.59808 1.50000i −0.630126 0.363803i 0.150675 0.988583i \(-0.451855\pi\)
−0.780801 + 0.624780i \(0.785189\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 4.00000i 0.852803i
\(23\) −6.06218 + 3.50000i −1.26405 + 0.729800i −0.973856 0.227167i \(-0.927054\pi\)
−0.290196 + 0.956967i \(0.593720\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) 2.00000 + 3.46410i 0.392232 + 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) −1.73205 2.00000i −0.327327 0.377964i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i \(-0.685109\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −3.46410 + 2.00000i −0.603023 + 0.348155i
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 1.73205 1.00000i 0.284747 0.164399i −0.350823 0.936442i \(-0.614098\pi\)
0.635571 + 0.772043i \(0.280765\pi\)
\(38\) −5.19615 3.00000i −0.842927 0.486664i
\(39\) −2.00000 + 3.46410i −0.320256 + 0.554700i
\(40\) 0 0
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) 0.866025 2.50000i 0.133631 0.385758i
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) 0 0
\(46\) 3.50000 6.06218i 0.516047 0.893819i
\(47\) 0.866025 0.500000i 0.126323 0.0729325i −0.435507 0.900185i \(-0.643431\pi\)
0.561830 + 0.827253i \(0.310098\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) 0 0
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) −3.46410 2.00000i −0.480384 0.277350i
\(53\) −1.73205 1.00000i −0.237915 0.137361i 0.376303 0.926497i \(-0.377195\pi\)
−0.614218 + 0.789136i \(0.710529\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 6.00000i 0.794719i
\(58\) 3.46410 2.00000i 0.454859 0.262613i
\(59\) −7.00000 + 12.1244i −0.911322 + 1.57846i −0.0991242 + 0.995075i \(0.531604\pi\)
−0.812198 + 0.583382i \(0.801729\pi\)
\(60\) 0 0
\(61\) −6.00000 10.3923i −0.768221 1.33060i −0.938527 0.345207i \(-0.887809\pi\)
0.170305 0.985391i \(-0.445525\pi\)
\(62\) 5.00000i 0.635001i
\(63\) 2.59808 0.500000i 0.327327 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 2.00000 3.46410i 0.246183 0.426401i
\(67\) −10.3923 6.00000i −1.26962 0.733017i −0.294706 0.955588i \(-0.595222\pi\)
−0.974916 + 0.222571i \(0.928555\pi\)
\(68\) −2.59808 + 1.50000i −0.315063 + 0.181902i
\(69\) 7.00000 0.842701
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 5.19615 + 3.00000i 0.608164 + 0.351123i 0.772246 0.635323i \(-0.219133\pi\)
−0.164083 + 0.986447i \(0.552466\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 0 0
\(76\) 6.00000 0.688247
\(77\) −6.92820 8.00000i −0.789542 0.911685i
\(78\) 4.00000i 0.452911i
\(79\) −8.50000 14.7224i −0.956325 1.65640i −0.731307 0.682048i \(-0.761089\pi\)
−0.225018 0.974355i \(-0.572244\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −6.06218 + 3.50000i −0.669456 + 0.386510i
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0.500000 + 2.59808i 0.0545545 + 0.283473i
\(85\) 0 0
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 3.46410 + 2.00000i 0.371391 + 0.214423i
\(88\) 3.46410 + 2.00000i 0.369274 + 0.213201i
\(89\) −3.50000 6.06218i −0.370999 0.642590i 0.618720 0.785611i \(-0.287651\pi\)
−0.989720 + 0.143022i \(0.954318\pi\)
\(90\) 0 0
\(91\) −10.0000 3.46410i −1.04828 0.363137i
\(92\) 7.00000i 0.729800i
\(93\) −4.33013 + 2.50000i −0.449013 + 0.259238i
\(94\) −0.500000 + 0.866025i −0.0515711 + 0.0893237i
\(95\) 0 0
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 7.00000i 0.710742i −0.934725 0.355371i \(-0.884354\pi\)
0.934725 0.355371i \(-0.115646\pi\)
\(98\) 6.92820 + 1.00000i 0.699854 + 0.101015i
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) −2.59808 1.50000i −0.257248 0.148522i
\(103\) 6.06218 3.50000i 0.597324 0.344865i −0.170664 0.985329i \(-0.554591\pi\)
0.767988 + 0.640464i \(0.221258\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 12.1244 7.00000i 1.17211 0.676716i 0.217931 0.975964i \(-0.430069\pi\)
0.954175 + 0.299249i \(0.0967360\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 3.00000 5.19615i 0.287348 0.497701i −0.685828 0.727764i \(-0.740560\pi\)
0.973176 + 0.230063i \(0.0738931\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) −2.59808 + 0.500000i −0.245495 + 0.0472456i
\(113\) 3.00000i 0.282216i 0.989994 + 0.141108i \(0.0450665\pi\)
−0.989994 + 0.141108i \(0.954933\pi\)
\(114\) 3.00000 + 5.19615i 0.280976 + 0.486664i
\(115\) 0 0
\(116\) −2.00000 + 3.46410i −0.185695 + 0.321634i
\(117\) 3.46410 2.00000i 0.320256 0.184900i
\(118\) 14.0000i 1.28880i
\(119\) −6.00000 + 5.19615i −0.550019 + 0.476331i
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 10.3923 + 6.00000i 0.940875 + 0.543214i
\(123\) −6.06218 3.50000i −0.546608 0.315584i
\(124\) −2.50000 4.33013i −0.224507 0.388857i
\(125\) 0 0
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) 16.0000i 1.41977i 0.704317 + 0.709885i \(0.251253\pi\)
−0.704317 + 0.709885i \(0.748747\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −1.00000 + 1.73205i −0.0880451 + 0.152499i
\(130\) 0 0
\(131\) 4.00000 + 6.92820i 0.349482 + 0.605320i 0.986157 0.165812i \(-0.0530244\pi\)
−0.636676 + 0.771132i \(0.719691\pi\)
\(132\) 4.00000i 0.348155i
\(133\) 15.5885 3.00000i 1.35169 0.260133i
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) −12.9904 7.50000i −1.10984 0.640768i −0.171054 0.985262i \(-0.554717\pi\)
−0.938789 + 0.344493i \(0.888051\pi\)
\(138\) −6.06218 + 3.50000i −0.516047 + 0.297940i
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −1.00000 −0.0842152
\(142\) 7.79423 4.50000i 0.654077 0.377632i
\(143\) −13.8564 8.00000i −1.15873 0.668994i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) 2.59808 + 6.50000i 0.214286 + 0.536111i
\(148\) 2.00000i 0.164399i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −12.0000 + 20.7846i −0.976546 + 1.69143i −0.301811 + 0.953368i \(0.597591\pi\)
−0.674735 + 0.738060i \(0.735742\pi\)
\(152\) −5.19615 + 3.00000i −0.421464 + 0.243332i
\(153\) 3.00000i 0.242536i
\(154\) 10.0000 + 3.46410i 0.805823 + 0.279145i
\(155\) 0 0
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) 3.46410 + 2.00000i 0.276465 + 0.159617i 0.631822 0.775113i \(-0.282307\pi\)
−0.355357 + 0.934731i \(0.615641\pi\)
\(158\) 14.7224 + 8.50000i 1.17125 + 0.676224i
\(159\) 1.00000 + 1.73205i 0.0793052 + 0.137361i
\(160\) 0 0
\(161\) 3.50000 + 18.1865i 0.275839 + 1.43330i
\(162\) 1.00000i 0.0785674i
\(163\) 6.92820 4.00000i 0.542659 0.313304i −0.203497 0.979076i \(-0.565231\pi\)
0.746156 + 0.665771i \(0.231897\pi\)
\(164\) 3.50000 6.06218i 0.273304 0.473377i
\(165\) 0 0
\(166\) −2.00000 3.46410i −0.155230 0.268866i
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) −1.73205 2.00000i −0.133631 0.154303i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) −3.00000 + 5.19615i −0.229416 + 0.397360i
\(172\) −1.73205 1.00000i −0.132068 0.0762493i
\(173\) −5.19615 + 3.00000i −0.395056 + 0.228086i −0.684349 0.729155i \(-0.739913\pi\)
0.289292 + 0.957241i \(0.406580\pi\)
\(174\) −4.00000 −0.303239
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 12.1244 7.00000i 0.911322 0.526152i
\(178\) 6.06218 + 3.50000i 0.454379 + 0.262336i
\(179\) 1.00000 1.73205i 0.0747435 0.129460i −0.826231 0.563331i \(-0.809520\pi\)
0.900975 + 0.433872i \(0.142853\pi\)
\(180\) 0 0
\(181\) 12.0000 0.891953 0.445976 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 10.3923 2.00000i 0.770329 0.148250i
\(183\) 12.0000i 0.887066i
\(184\) −3.50000 6.06218i −0.258023 0.446910i
\(185\) 0 0
\(186\) 2.50000 4.33013i 0.183309 0.317500i
\(187\) −10.3923 + 6.00000i −0.759961 + 0.438763i
\(188\) 1.00000i 0.0729325i
\(189\) −2.50000 0.866025i −0.181848 0.0629941i
\(190\) 0 0
\(191\) −7.50000 12.9904i −0.542681 0.939951i −0.998749 0.0500060i \(-0.984076\pi\)
0.456068 0.889945i \(-0.349257\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 21.6506 + 12.5000i 1.55845 + 0.899770i 0.997406 + 0.0719816i \(0.0229323\pi\)
0.561041 + 0.827788i \(0.310401\pi\)
\(194\) 3.50000 + 6.06218i 0.251285 + 0.435239i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 20.0000i 1.42494i 0.701702 + 0.712470i \(0.252424\pi\)
−0.701702 + 0.712470i \(0.747576\pi\)
\(198\) −3.46410 + 2.00000i −0.246183 + 0.142134i
\(199\) 7.50000 12.9904i 0.531661 0.920864i −0.467656 0.883911i \(-0.654901\pi\)
0.999317 0.0369532i \(-0.0117652\pi\)
\(200\) 0 0
\(201\) 6.00000 + 10.3923i 0.423207 + 0.733017i
\(202\) 18.0000i 1.26648i
\(203\) −3.46410 + 10.0000i −0.243132 + 0.701862i
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) −3.50000 + 6.06218i −0.243857 + 0.422372i
\(207\) −6.06218 3.50000i −0.421350 0.243267i
\(208\) −3.46410 + 2.00000i −0.240192 + 0.138675i
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) −1.73205 + 1.00000i −0.118958 + 0.0686803i
\(213\) 7.79423 + 4.50000i 0.534052 + 0.308335i
\(214\) −7.00000 + 12.1244i −0.478510 + 0.828804i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −8.66025 10.0000i −0.587896 0.678844i
\(218\) 6.00000i 0.406371i
\(219\) −3.00000 5.19615i −0.202721 0.351123i
\(220\) 0 0
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) 1.73205 1.00000i 0.116248 0.0671156i
\(223\) 9.00000i 0.602685i −0.953516 0.301342i \(-0.902565\pi\)
0.953516 0.301342i \(-0.0974347\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 0 0
\(226\) −1.50000 2.59808i −0.0997785 0.172821i
\(227\) 19.0526 + 11.0000i 1.26456 + 0.730096i 0.973954 0.226746i \(-0.0728088\pi\)
0.290609 + 0.956842i \(0.406142\pi\)
\(228\) −5.19615 3.00000i −0.344124 0.198680i
\(229\) 4.00000 + 6.92820i 0.264327 + 0.457829i 0.967387 0.253302i \(-0.0815167\pi\)
−0.703060 + 0.711131i \(0.748183\pi\)
\(230\) 0 0
\(231\) 2.00000 + 10.3923i 0.131590 + 0.683763i
\(232\) 4.00000i 0.262613i
\(233\) 5.19615 3.00000i 0.340411 0.196537i −0.320043 0.947403i \(-0.603697\pi\)
0.660454 + 0.750867i \(0.270364\pi\)
\(234\) −2.00000 + 3.46410i −0.130744 + 0.226455i
\(235\) 0 0
\(236\) 7.00000 + 12.1244i 0.455661 + 0.789228i
\(237\) 17.0000i 1.10427i
\(238\) 2.59808 7.50000i 0.168408 0.486153i
\(239\) −3.00000 −0.194054 −0.0970269 0.995282i \(-0.530933\pi\)
−0.0970269 + 0.995282i \(0.530933\pi\)
\(240\) 0 0
\(241\) 1.00000 1.73205i 0.0644157 0.111571i −0.832019 0.554747i \(-0.812815\pi\)
0.896435 + 0.443176i \(0.146148\pi\)
\(242\) 4.33013 + 2.50000i 0.278351 + 0.160706i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −12.0000 −0.768221
\(245\) 0 0
\(246\) 7.00000 0.446304
\(247\) 20.7846 12.0000i 1.32249 0.763542i
\(248\) 4.33013 + 2.50000i 0.274963 + 0.158750i
\(249\) 2.00000 3.46410i 0.126745 0.219529i
\(250\) 0 0
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 0.866025 2.50000i 0.0545545 0.157485i
\(253\) 28.0000i 1.76034i
\(254\) −8.00000 13.8564i −0.501965 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.73205 + 1.00000i −0.108042 + 0.0623783i −0.553047 0.833150i \(-0.686535\pi\)
0.445005 + 0.895528i \(0.353202\pi\)
\(258\) 2.00000i 0.124515i
\(259\) −1.00000 5.19615i −0.0621370 0.322873i
\(260\) 0 0
\(261\) −2.00000 3.46410i −0.123797 0.214423i
\(262\) −6.92820 4.00000i −0.428026 0.247121i
\(263\) −23.3827 13.5000i −1.44184 0.832446i −0.443866 0.896093i \(-0.646393\pi\)
−0.997972 + 0.0636476i \(0.979727\pi\)
\(264\) −2.00000 3.46410i −0.123091 0.213201i
\(265\) 0 0
\(266\) −12.0000 + 10.3923i −0.735767 + 0.637193i
\(267\) 7.00000i 0.428393i
\(268\) −10.3923 + 6.00000i −0.634811 + 0.366508i
\(269\) −5.00000 + 8.66025i −0.304855 + 0.528025i −0.977229 0.212187i \(-0.931941\pi\)
0.672374 + 0.740212i \(0.265275\pi\)
\(270\) 0 0
\(271\) −2.50000 4.33013i −0.151864 0.263036i 0.780049 0.625719i \(-0.215194\pi\)
−0.931913 + 0.362682i \(0.881861\pi\)
\(272\) 3.00000i 0.181902i
\(273\) 6.92820 + 8.00000i 0.419314 + 0.484182i
\(274\) 15.0000 0.906183
\(275\) 0 0
\(276\) 3.50000 6.06218i 0.210675 0.364900i
\(277\) 13.8564 + 8.00000i 0.832551 + 0.480673i 0.854725 0.519081i \(-0.173726\pi\)
−0.0221745 + 0.999754i \(0.507059\pi\)
\(278\) 1.73205 1.00000i 0.103882 0.0599760i
\(279\) 5.00000 0.299342
\(280\) 0 0
\(281\) 17.0000 1.01413 0.507067 0.861906i \(-0.330729\pi\)
0.507067 + 0.861906i \(0.330729\pi\)
\(282\) 0.866025 0.500000i 0.0515711 0.0297746i
\(283\) −6.92820 4.00000i −0.411839 0.237775i 0.279741 0.960076i \(-0.409752\pi\)
−0.691580 + 0.722300i \(0.743085\pi\)
\(284\) −4.50000 + 7.79423i −0.267026 + 0.462502i
\(285\) 0 0
\(286\) 16.0000 0.946100
\(287\) 6.06218 17.5000i 0.357839 1.03299i
\(288\) 1.00000i 0.0589256i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) 0 0
\(291\) −3.50000 + 6.06218i −0.205174 + 0.355371i
\(292\) 5.19615 3.00000i 0.304082 0.175562i
\(293\) 12.0000i 0.701047i 0.936554 + 0.350524i \(0.113996\pi\)
−0.936554 + 0.350524i \(0.886004\pi\)
\(294\) −5.50000 4.33013i −0.320767 0.252538i
\(295\) 0 0
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) −3.46410 2.00000i −0.201008 0.116052i
\(298\) 5.19615 + 3.00000i 0.301005 + 0.173785i
\(299\) 14.0000 + 24.2487i 0.809641 + 1.40234i
\(300\) 0 0
\(301\) −5.00000 1.73205i −0.288195 0.0998337i
\(302\) 24.0000i 1.38104i
\(303\) −15.5885 + 9.00000i −0.895533 + 0.517036i
\(304\) 3.00000 5.19615i 0.172062 0.298020i
\(305\) 0 0
\(306\) 1.50000 + 2.59808i 0.0857493 + 0.148522i
\(307\) 20.0000i 1.14146i 0.821138 + 0.570730i \(0.193340\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(308\) −10.3923 + 2.00000i −0.592157 + 0.113961i
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) −10.5000 + 18.1865i −0.595400 + 1.03126i 0.398090 + 0.917346i \(0.369673\pi\)
−0.993490 + 0.113917i \(0.963660\pi\)
\(312\) −3.46410 2.00000i −0.196116 0.113228i
\(313\) 23.3827 13.5000i 1.32167 0.763065i 0.337673 0.941263i \(-0.390360\pi\)
0.983995 + 0.178198i \(0.0570269\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −17.0000 −0.956325
\(317\) 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i \(-0.497978\pi\)
0.869184 + 0.494489i \(0.164645\pi\)
\(318\) −1.73205 1.00000i −0.0971286 0.0560772i
\(319\) −8.00000 + 13.8564i −0.447914 + 0.775810i
\(320\) 0 0
\(321\) −14.0000 −0.781404
\(322\) −12.1244 14.0000i −0.675664 0.780189i
\(323\) 18.0000i 1.00155i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) −5.19615 + 3.00000i −0.287348 + 0.165900i
\(328\) 7.00000i 0.386510i
\(329\) −0.500000 2.59808i −0.0275659 0.143237i
\(330\) 0 0
\(331\) 17.0000 + 29.4449i 0.934405 + 1.61844i 0.775692 + 0.631111i \(0.217401\pi\)
0.158712 + 0.987325i \(0.449266\pi\)
\(332\) 3.46410 + 2.00000i 0.190117 + 0.109764i
\(333\) 1.73205 + 1.00000i 0.0949158 + 0.0547997i
\(334\) 0 0
\(335\) 0 0
\(336\) 2.50000 + 0.866025i 0.136386 + 0.0472456i
\(337\) 3.00000i 0.163420i 0.996656 + 0.0817102i \(0.0260382\pi\)
−0.996656 + 0.0817102i \(0.973962\pi\)
\(338\) 2.59808 1.50000i 0.141317 0.0815892i
\(339\) 1.50000 2.59808i 0.0814688 0.141108i
\(340\) 0 0
\(341\) −10.0000 17.3205i −0.541530 0.937958i
\(342\) 6.00000i 0.324443i
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −27.7128 16.0000i −1.48770 0.858925i −0.487800 0.872955i \(-0.662201\pi\)
−0.999902 + 0.0140303i \(0.995534\pi\)
\(348\) 3.46410 2.00000i 0.185695 0.107211i
\(349\) 18.0000 0.963518 0.481759 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 3.46410 2.00000i 0.184637 0.106600i
\(353\) −12.9904 7.50000i −0.691408 0.399185i 0.112731 0.993626i \(-0.464040\pi\)
−0.804139 + 0.594441i \(0.797373\pi\)
\(354\) −7.00000 + 12.1244i −0.372046 + 0.644402i
\(355\) 0 0
\(356\) −7.00000 −0.370999
\(357\) 7.79423 1.50000i 0.412514 0.0793884i
\(358\) 2.00000i 0.105703i
\(359\) 2.00000 + 3.46410i 0.105556 + 0.182828i 0.913965 0.405793i \(-0.133004\pi\)
−0.808409 + 0.588621i \(0.799671\pi\)
\(360\) 0 0
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −10.3923 + 6.00000i −0.546207 + 0.315353i
\(363\) 5.00000i 0.262432i
\(364\) −8.00000 + 6.92820i −0.419314 + 0.363137i
\(365\) 0 0
\(366\) −6.00000 10.3923i −0.313625 0.543214i
\(367\) 27.7128 + 16.0000i 1.44660 + 0.835193i 0.998277 0.0586798i \(-0.0186891\pi\)
0.448320 + 0.893873i \(0.352022\pi\)
\(368\) 6.06218 + 3.50000i 0.316013 + 0.182450i
\(369\) 3.50000 + 6.06218i 0.182203 + 0.315584i
\(370\) 0 0
\(371\) −4.00000 + 3.46410i −0.207670 + 0.179847i
\(372\) 5.00000i 0.259238i
\(373\) −10.3923 + 6.00000i −0.538093 + 0.310668i −0.744306 0.667839i \(-0.767219\pi\)
0.206213 + 0.978507i \(0.433886\pi\)
\(374\) 6.00000 10.3923i 0.310253 0.537373i
\(375\) 0 0
\(376\) 0.500000 + 0.866025i 0.0257855 + 0.0446619i
\(377\) 16.0000i 0.824042i
\(378\) 2.59808 0.500000i 0.133631 0.0257172i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 8.00000 13.8564i 0.409852 0.709885i
\(382\) 12.9904 + 7.50000i 0.664646 + 0.383733i
\(383\) 26.8468 15.5000i 1.37181 0.792013i 0.380651 0.924719i \(-0.375700\pi\)
0.991155 + 0.132706i \(0.0423665\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −25.0000 −1.27247
\(387\) 1.73205 1.00000i 0.0880451 0.0508329i
\(388\) −6.06218 3.50000i −0.307760 0.177686i
\(389\) 5.00000 8.66025i 0.253510 0.439092i −0.710980 0.703213i \(-0.751748\pi\)
0.964490 + 0.264120i \(0.0850816\pi\)
\(390\) 0 0
\(391\) 21.0000 1.06202
\(392\) 4.33013 5.50000i 0.218704 0.277792i
\(393\) 8.00000i 0.403547i
\(394\) −10.0000 17.3205i −0.503793 0.872595i
\(395\) 0 0
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) −19.0526 + 11.0000i −0.956221 + 0.552074i −0.895008 0.446051i \(-0.852830\pi\)
−0.0612128 + 0.998125i \(0.519497\pi\)
\(398\) 15.0000i 0.751882i
\(399\) −15.0000 5.19615i −0.750939 0.260133i
\(400\) 0 0
\(401\) −17.0000 29.4449i −0.848939 1.47041i −0.882156 0.470958i \(-0.843908\pi\)
0.0332161 0.999448i \(-0.489425\pi\)
\(402\) −10.3923 6.00000i −0.518321 0.299253i
\(403\) −17.3205 10.0000i −0.862796 0.498135i
\(404\) −9.00000 15.5885i −0.447767 0.775555i
\(405\) 0 0
\(406\) −2.00000 10.3923i −0.0992583 0.515761i
\(407\) 8.00000i 0.396545i
\(408\) −2.59808 + 1.50000i −0.128624 + 0.0742611i
\(409\) 14.5000 25.1147i 0.716979 1.24184i −0.245212 0.969469i \(-0.578858\pi\)
0.962191 0.272374i \(-0.0878089\pi\)
\(410\) 0 0
\(411\) 7.50000 + 12.9904i 0.369948 + 0.640768i
\(412\) 7.00000i 0.344865i
\(413\) 24.2487 + 28.0000i 1.19320 + 1.37779i
\(414\) 7.00000 0.344031
\(415\) 0 0
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 1.73205 + 1.00000i 0.0848189 + 0.0489702i
\(418\) −20.7846 + 12.0000i −1.01661 + 0.586939i
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) 0 0
\(421\) 16.0000 0.779792 0.389896 0.920859i \(-0.372511\pi\)
0.389896 + 0.920859i \(0.372511\pi\)
\(422\) 19.0526 11.0000i 0.927464 0.535472i
\(423\) 0.866025 + 0.500000i 0.0421076 + 0.0243108i
\(424\) 1.00000 1.73205i 0.0485643 0.0841158i
\(425\) 0 0
\(426\) −9.00000 −0.436051
\(427\) −31.1769 + 6.00000i −1.50876 + 0.290360i
\(428\) 14.0000i 0.676716i
\(429\) 8.00000 + 13.8564i 0.386244 + 0.668994i
\(430\) 0 0
\(431\) 19.5000 33.7750i 0.939282 1.62688i 0.172468 0.985015i \(-0.444826\pi\)
0.766814 0.641869i \(-0.221841\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 37.0000i 1.77811i −0.457804 0.889053i \(-0.651364\pi\)
0.457804 0.889053i \(-0.348636\pi\)
\(434\) 12.5000 + 4.33013i 0.600019 + 0.207853i
\(435\) 0 0
\(436\) −3.00000 5.19615i −0.143674 0.248851i
\(437\) −36.3731 21.0000i −1.73996 1.00457i
\(438\) 5.19615 + 3.00000i 0.248282 + 0.143346i
\(439\) 8.50000 + 14.7224i 0.405683 + 0.702663i 0.994401 0.105675i \(-0.0337004\pi\)
−0.588718 + 0.808339i \(0.700367\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 12.0000i 0.570782i
\(443\) 22.5167 13.0000i 1.06980 0.617649i 0.141672 0.989914i \(-0.454752\pi\)
0.928126 + 0.372265i \(0.121419\pi\)
\(444\) −1.00000 + 1.73205i −0.0474579 + 0.0821995i
\(445\) 0 0
\(446\) 4.50000 + 7.79423i 0.213081 + 0.369067i
\(447\) 6.00000i 0.283790i
\(448\) −0.866025 + 2.50000i −0.0409159 + 0.118114i
\(449\) 13.0000 0.613508 0.306754 0.951789i \(-0.400757\pi\)
0.306754 + 0.951789i \(0.400757\pi\)
\(450\) 0 0
\(451\) 14.0000 24.2487i 0.659234 1.14183i
\(452\) 2.59808 + 1.50000i 0.122203 + 0.0705541i
\(453\) 20.7846 12.0000i 0.976546 0.563809i
\(454\) −22.0000 −1.03251
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) 15.5885 9.00000i 0.729197 0.421002i −0.0889312 0.996038i \(-0.528345\pi\)
0.818128 + 0.575036i \(0.195012\pi\)
\(458\) −6.92820 4.00000i −0.323734 0.186908i
\(459\) −1.50000 + 2.59808i −0.0700140 + 0.121268i
\(460\) 0 0
\(461\) 36.0000 1.67669 0.838344 0.545142i \(-0.183524\pi\)
0.838344 + 0.545142i \(0.183524\pi\)
\(462\) −6.92820 8.00000i −0.322329 0.372194i
\(463\) 7.00000i 0.325318i 0.986682 + 0.162659i \(0.0520070\pi\)
−0.986682 + 0.162659i \(0.947993\pi\)
\(464\) 2.00000 + 3.46410i 0.0928477 + 0.160817i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 4.00000i 0.184900i
\(469\) −24.0000 + 20.7846i −1.10822 + 0.959744i
\(470\) 0 0
\(471\) −2.00000 3.46410i −0.0921551 0.159617i
\(472\) −12.1244 7.00000i −0.558069 0.322201i
\(473\) −6.92820 4.00000i −0.318559 0.183920i
\(474\) −8.50000 14.7224i −0.390418 0.676224i
\(475\) 0 0
\(476\) 1.50000 + 7.79423i 0.0687524 + 0.357248i
\(477\) 2.00000i 0.0915737i
\(478\) 2.59808 1.50000i 0.118833 0.0686084i
\(479\) 0.500000 0.866025i 0.0228456 0.0395697i −0.854377 0.519654i \(-0.826061\pi\)
0.877222 + 0.480085i \(0.159394\pi\)
\(480\) 0 0
\(481\) −4.00000 6.92820i −0.182384 0.315899i
\(482\) 2.00000i 0.0910975i
\(483\) 6.06218 17.5000i 0.275839 0.796278i
\(484\) −5.00000 −0.227273
\(485\) 0 0
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −4.33013 2.50000i −0.196217 0.113286i 0.398673 0.917093i \(-0.369471\pi\)
−0.594890 + 0.803807i \(0.702804\pi\)
\(488\) 10.3923 6.00000i 0.470438 0.271607i
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) 38.0000 1.71492 0.857458 0.514554i \(-0.172042\pi\)
0.857458 + 0.514554i \(0.172042\pi\)
\(492\) −6.06218 + 3.50000i −0.273304 + 0.157792i
\(493\) 10.3923 + 6.00000i 0.468046 + 0.270226i
\(494\) −12.0000 + 20.7846i −0.539906 + 0.935144i
\(495\) 0 0
\(496\) −5.00000 −0.224507
\(497\) −7.79423 + 22.5000i −0.349619 + 1.00926i
\(498\) 4.00000i 0.179244i
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −3.46410 + 2.00000i −0.154610 + 0.0892644i
\(503\) 36.0000i 1.60516i −0.596544 0.802580i \(-0.703460\pi\)
0.596544 0.802580i \(-0.296540\pi\)
\(504\) 0.500000 + 2.59808i 0.0222718 + 0.115728i
\(505\) 0 0
\(506\) −14.0000 24.2487i −0.622376 1.07799i
\(507\) 2.59808 + 1.50000i 0.115385 + 0.0666173i
\(508\) 13.8564 + 8.00000i 0.614779 + 0.354943i
\(509\) −8.00000 13.8564i −0.354594 0.614174i 0.632455 0.774597i \(-0.282047\pi\)
−0.987048 + 0.160423i \(0.948714\pi\)
\(510\) 0 0
\(511\) 12.0000 10.3923i 0.530849 0.459728i
\(512\) 1.00000i 0.0441942i
\(513\) 5.19615 3.00000i 0.229416 0.132453i
\(514\) 1.00000 1.73205i 0.0441081 0.0763975i
\(515\) 0 0
\(516\) 1.00000 + 1.73205i 0.0440225 + 0.0762493i
\(517\) 4.00000i 0.175920i
\(518\) 3.46410 + 4.00000i 0.152204 + 0.175750i
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 4.50000 7.79423i 0.197149 0.341471i −0.750454 0.660922i \(-0.770165\pi\)
0.947603 + 0.319451i \(0.103499\pi\)
\(522\) 3.46410 + 2.00000i 0.151620 + 0.0875376i
\(523\) −38.1051 + 22.0000i −1.66622 + 0.961993i −0.696573 + 0.717486i \(0.745293\pi\)
−0.969648 + 0.244507i \(0.921374\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) 27.0000 1.17726
\(527\) −12.9904 + 7.50000i −0.565870 + 0.326705i
\(528\) 3.46410 + 2.00000i 0.150756 + 0.0870388i
\(529\) 13.0000 22.5167i 0.565217 0.978985i
\(530\) 0 0
\(531\) −14.0000 −0.607548
\(532\) 5.19615 15.0000i 0.225282 0.650332i
\(533\) 28.0000i 1.21281i
\(534\) −3.50000 6.06218i −0.151460 0.262336i
\(535\) 0 0
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −1.73205 + 1.00000i −0.0747435 + 0.0431532i
\(538\) 10.0000i 0.431131i
\(539\) −26.0000 + 10.3923i −1.11990 + 0.447628i
\(540\) 0 0
\(541\) −16.0000 27.7128i −0.687894 1.19147i −0.972518 0.232828i \(-0.925202\pi\)
0.284624 0.958639i \(-0.408131\pi\)
\(542\) 4.33013 + 2.50000i 0.185995 + 0.107384i
\(543\) −10.3923 6.00000i −0.445976 0.257485i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 0 0
\(546\) −10.0000 3.46410i −0.427960 0.148250i
\(547\) 22.0000i 0.940652i 0.882493 + 0.470326i \(0.155864\pi\)
−0.882493 + 0.470326i \(0.844136\pi\)
\(548\) −12.9904 + 7.50000i −0.554922 + 0.320384i
\(549\) 6.00000 10.3923i 0.256074 0.443533i
\(550\) 0 0
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 7.00000i 0.297940i
\(553\) −44.1673 + 8.50000i −1.87818 + 0.361457i
\(554\) −16.0000 −0.679775
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) −25.9808 15.0000i −1.10084 0.635570i −0.164399 0.986394i \(-0.552568\pi\)
−0.936442 + 0.350824i \(0.885902\pi\)
\(558\) −4.33013 + 2.50000i −0.183309 + 0.105833i
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) −14.7224 + 8.50000i −0.621028 + 0.358551i
\(563\) −1.73205 1.00000i −0.0729972 0.0421450i 0.463057 0.886328i \(-0.346752\pi\)
−0.536054 + 0.844183i \(0.680086\pi\)
\(564\) −0.500000 + 0.866025i −0.0210538 + 0.0364662i
\(565\) 0 0
\(566\) 8.00000 0.336265
\(567\) 1.73205 + 2.00000i 0.0727393 + 0.0839921i
\(568\) 9.00000i 0.377632i
\(569\) −22.5000 38.9711i −0.943249 1.63376i −0.759220 0.650835i \(-0.774419\pi\)
−0.184030 0.982921i \(-0.558914\pi\)
\(570\) 0 0
\(571\) −20.0000 + 34.6410i −0.836974 + 1.44968i 0.0554391 + 0.998462i \(0.482344\pi\)
−0.892413 + 0.451219i \(0.850989\pi\)
\(572\) −13.8564 + 8.00000i −0.579365 + 0.334497i
\(573\) 15.0000i 0.626634i
\(574\) 3.50000 + 18.1865i 0.146087 + 0.759091i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 1.73205 + 1.00000i 0.0721062 + 0.0416305i 0.535620 0.844459i \(-0.320078\pi\)
−0.463513 + 0.886090i \(0.653411\pi\)
\(578\) 6.92820 + 4.00000i 0.288175 + 0.166378i
\(579\) −12.5000 21.6506i −0.519482 0.899770i
\(580\) 0 0
\(581\) 10.0000 + 3.46410i 0.414870 + 0.143715i
\(582\) 7.00000i 0.290159i
\(583\) −6.92820 + 4.00000i −0.286937 + 0.165663i
\(584\) −3.00000 + 5.19615i −0.124141 + 0.215018i
\(585\) 0 0
\(586\) −6.00000 10.3923i −0.247858 0.429302i
\(587\) 42.0000i 1.73353i 0.498721 + 0.866763i \(0.333803\pi\)
−0.498721 + 0.866763i \(0.666197\pi\)
\(588\) 6.92820 + 1.00000i 0.285714 + 0.0412393i
\(589\) 30.0000 1.23613
\(590\) 0 0
\(591\) 10.0000 17.3205i 0.411345 0.712470i
\(592\) −1.73205 1.00000i −0.0711868 0.0410997i
\(593\) −11.2583 + 6.50000i −0.462324 + 0.266923i −0.713021 0.701143i \(-0.752674\pi\)
0.250697 + 0.968066i \(0.419340\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −12.9904 + 7.50000i −0.531661 + 0.306955i
\(598\) −24.2487 14.0000i −0.991604 0.572503i
\(599\) −15.5000 + 26.8468i −0.633313 + 1.09693i 0.353557 + 0.935413i \(0.384972\pi\)
−0.986870 + 0.161517i \(0.948361\pi\)
\(600\) 0 0
\(601\) 46.0000 1.87638 0.938190 0.346122i \(-0.112502\pi\)
0.938190 + 0.346122i \(0.112502\pi\)
\(602\) 5.19615 1.00000i 0.211779 0.0407570i
\(603\) 12.0000i 0.488678i
\(604\) 12.0000 + 20.7846i 0.488273 + 0.845714i
\(605\) 0 0
\(606\) 9.00000 15.5885i 0.365600 0.633238i
\(607\) 25.1147 14.5000i 1.01938 0.588537i 0.105453 0.994424i \(-0.466371\pi\)
0.913923 + 0.405887i \(0.133038\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 8.00000 6.92820i 0.324176 0.280745i
\(610\) 0 0
\(611\) −2.00000 3.46410i −0.0809113 0.140143i
\(612\) −2.59808 1.50000i −0.105021 0.0606339i
\(613\) 3.46410 + 2.00000i 0.139914 + 0.0807792i 0.568323 0.822806i \(-0.307592\pi\)
−0.428409 + 0.903585i \(0.640926\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 0 0
\(616\) 8.00000 6.92820i 0.322329 0.279145i
\(617\) 1.00000i 0.0402585i 0.999797 + 0.0201292i \(0.00640777\pi\)
−0.999797 + 0.0201292i \(0.993592\pi\)
\(618\) 6.06218 3.50000i 0.243857 0.140791i
\(619\) −8.00000 + 13.8564i −0.321547 + 0.556936i −0.980807 0.194979i \(-0.937536\pi\)
0.659260 + 0.751915i \(0.270870\pi\)
\(620\) 0 0
\(621\) 3.50000 + 6.06218i 0.140450 + 0.243267i
\(622\) 21.0000i 0.842023i
\(623\) −18.1865 + 3.50000i −0.728628 + 0.140225i
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) −13.5000 + 23.3827i −0.539569 + 0.934560i
\(627\) −20.7846 12.0000i −0.830057 0.479234i
\(628\) 3.46410 2.00000i 0.138233 0.0798087i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) 14.7224 8.50000i 0.585627 0.338112i
\(633\) 19.0526 + 11.0000i 0.757271 + 0.437211i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 0 0
\(636\) 2.00000 0.0793052
\(637\) −17.3205 + 22.0000i −0.686264 + 0.871672i
\(638\) 16.0000i 0.633446i
\(639\) −4.50000 7.79423i −0.178017 0.308335i
\(640\) 0 0
\(641\) 4.50000 7.79423i 0.177739 0.307854i −0.763367 0.645966i \(-0.776455\pi\)
0.941106 + 0.338112i \(0.109788\pi\)
\(642\) 12.1244 7.00000i 0.478510 0.276268i
\(643\) 14.0000i 0.552106i −0.961142 0.276053i \(-0.910973\pi\)
0.961142 0.276053i \(-0.0890266\pi\)
\(644\) 17.5000 + 6.06218i 0.689597 + 0.238883i
\(645\) 0 0
\(646\) 9.00000 + 15.5885i 0.354100 + 0.613320i
\(647\) 27.7128 + 16.0000i 1.08950 + 0.629025i 0.933444 0.358723i \(-0.116788\pi\)
0.156059 + 0.987748i \(0.450121\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 28.0000 + 48.4974i 1.09910 + 1.90369i
\(650\) 0 0
\(651\) 2.50000 + 12.9904i 0.0979827 + 0.509133i
\(652\) 8.00000i 0.313304i
\(653\) −13.8564 + 8.00000i −0.542243 + 0.313064i −0.745988 0.665960i \(-0.768022\pi\)
0.203744 + 0.979024i \(0.434689\pi\)
\(654\) 3.00000 5.19615i 0.117309 0.203186i
\(655\) 0 0
\(656\) −3.50000 6.06218i −0.136652 0.236688i
\(657\) 6.00000i 0.234082i
\(658\) 1.73205 + 2.00000i 0.0675224 + 0.0779681i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −15.0000 + 25.9808i −0.583432 + 1.01053i 0.411636 + 0.911348i \(0.364957\pi\)
−0.995069 + 0.0991864i \(0.968376\pi\)
\(662\) −29.4449 17.0000i −1.14441 0.660724i
\(663\) 10.3923 6.00000i 0.403604 0.233021i
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 24.2487 14.0000i 0.938914 0.542082i
\(668\) 0 0
\(669\) −4.50000 + 7.79423i −0.173980 + 0.301342i
\(670\) 0 0
\(671\) −48.0000 −1.85302
\(672\) −2.59808 + 0.500000i −0.100223 + 0.0192879i
\(673\) 11.0000i 0.424019i 0.977268 + 0.212009i \(0.0680008\pi\)
−0.977268 + 0.212009i \(0.931999\pi\)
\(674\) −1.50000 2.59808i −0.0577778 0.100074i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) 27.7128 16.0000i 1.06509 0.614930i 0.138254 0.990397i \(-0.455851\pi\)
0.926836 + 0.375467i \(0.122518\pi\)
\(678\) 3.00000i 0.115214i
\(679\) −17.5000 6.06218i −0.671588 0.232645i
\(680\) 0 0
\(681\) −11.0000 19.0526i −0.421521 0.730096i
\(682\) 17.3205 + 10.0000i 0.663237 + 0.382920i
\(683\) 19.0526 + 11.0000i 0.729026 + 0.420903i 0.818066 0.575125i \(-0.195047\pi\)
−0.0890398 + 0.996028i \(0.528380\pi\)
\(684\) 3.00000 + 5.19615i 0.114708 + 0.198680i
\(685\) 0 0
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 8.00000i 0.305219i
\(688\) −1.73205 + 1.00000i −0.0660338 + 0.0381246i
\(689\) −4.00000 + 6.92820i −0.152388 + 0.263944i
\(690\) 0 0
\(691\) 12.0000 + 20.7846i 0.456502 + 0.790684i 0.998773 0.0495194i \(-0.0157690\pi\)
−0.542272 + 0.840203i \(0.682436\pi\)
\(692\) 6.00000i 0.228086i
\(693\) 3.46410 10.0000i 0.131590 0.379869i
\(694\) 32.0000 1.21470
\(695\) 0 0
\(696\) −2.00000 + 3.46410i −0.0758098 + 0.131306i
\(697\) −18.1865 10.5000i −0.688864 0.397716i
\(698\) −15.5885 + 9.00000i −0.590032 + 0.340655i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 3.46410 2.00000i 0.130744 0.0754851i
\(703\) 10.3923 + 6.00000i 0.391953 + 0.226294i
\(704\) −2.00000 + 3.46410i −0.0753778 + 0.130558i
\(705\) 0 0
\(706\) 15.0000 0.564532
\(707\) −31.1769 36.0000i −1.17253 1.35392i
\(708\) 14.0000i 0.526152i
\(709\) 7.00000 + 12.1244i 0.262891 + 0.455340i 0.967009 0.254743i \(-0.0819909\pi\)
−0.704118 + 0.710083i \(0.748658\pi\)
\(710\) 0 0
\(711\) 8.50000 14.7224i 0.318775 0.552134i
\(712\) 6.06218 3.50000i 0.227190 0.131168i
\(713\) 35.0000i 1.31076i
\(714\) −6.00000 + 5.19615i −0.224544 + 0.194461i
\(715\) 0 0
\(716\) −1.00000 1.73205i −0.0373718 0.0647298i
\(717\) 2.59808 + 1.50000i 0.0970269 + 0.0560185i
\(718\) −3.46410 2.00000i −0.129279 0.0746393i
\(719\) −3.50000 6.06218i −0.130528 0.226081i 0.793352 0.608763i \(-0.208334\pi\)
−0.923880 + 0.382682i \(0.875001\pi\)
\(720\) 0 0
\(721\) −3.50000 18.1865i −0.130347 0.677302i
\(722\) 17.0000i 0.632674i
\(723\) −1.73205 + 1.00000i −0.0644157 + 0.0371904i
\(724\) 6.00000 10.3923i 0.222988 0.386227i
\(725\) 0 0
\(726\) −2.50000 4.33013i −0.0927837 0.160706i
\(727\) 49.0000i 1.81731i −0.417548 0.908655i \(-0.637111\pi\)
0.417548 0.908655i \(-0.362889\pi\)
\(728\) 3.46410 10.0000i 0.128388 0.370625i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −3.00000 + 5.19615i −0.110959 + 0.192187i
\(732\) 10.3923 + 6.00000i 0.384111 + 0.221766i
\(733\) 8.66025 5.00000i 0.319874 0.184679i −0.331463 0.943468i \(-0.607542\pi\)
0.651336 + 0.758789i \(0.274209\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) −41.5692 + 24.0000i −1.53122 + 0.884051i
\(738\) −6.06218 3.50000i −0.223152 0.128837i
\(739\) 7.00000 12.1244i 0.257499 0.446002i −0.708072 0.706140i \(-0.750435\pi\)
0.965571 + 0.260138i \(0.0837682\pi\)
\(740\) 0 0
\(741\) −24.0000 −0.881662
\(742\) 1.73205 5.00000i 0.0635856 0.183556i
\(743\) 1.00000i 0.0366864i −0.999832 0.0183432i \(-0.994161\pi\)
0.999832 0.0183432i \(-0.00583916\pi\)
\(744\) −2.50000 4.33013i −0.0916544 0.158750i
\(745\) 0 0
\(746\) 6.00000 10.3923i 0.219676 0.380489i
\(747\) −3.46410 + 2.00000i −0.126745 + 0.0731762i
\(748\) 12.0000i 0.438763i
\(749\) −7.00000 36.3731i −0.255774 1.32904i
\(750\) 0 0
\(751\) 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) −0.866025 0.500000i −0.0315807 0.0182331i
\(753\) −3.46410 2.00000i −0.126239 0.0728841i
\(754\) −8.00000 13.8564i −0.291343 0.504621i
\(755\) 0 0
\(756\) −2.00000 + 1.73205i −0.0727393 + 0.0629941i
\(757\) 16.0000i 0.581530i −0.956795 0.290765i \(-0.906090\pi\)
0.956795 0.290765i \(-0.0939098\pi\)
\(758\) 17.3205 10.0000i 0.629109 0.363216i
\(759\) 14.0000 24.2487i 0.508168 0.880172i
\(760\) 0 0
\(761\) 10.5000 + 18.1865i 0.380625 + 0.659261i 0.991152 0.132734i \(-0.0423756\pi\)
−0.610527 + 0.791995i \(0.709042\pi\)
\(762\) 16.0000i 0.579619i
\(763\) −10.3923 12.0000i −0.376227 0.434429i
\(764\) −15.0000 −0.542681
\(765\) 0 0
\(766\) −15.5000 + 26.8468i −0.560038 + 0.970014i
\(767\) 48.4974 + 28.0000i 1.75114 + 1.01102i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 2.00000 0.0720282
\(772\) 21.6506 12.5000i 0.779223 0.449885i
\(773\) −15.5885 9.00000i −0.560678 0.323708i 0.192740 0.981250i \(-0.438263\pi\)
−0.753418 + 0.657542i \(0.771596\pi\)
\(774\) −1.00000 + 1.73205i −0.0359443 + 0.0622573i
\(775\) 0 0
\(776\) 7.00000 0.251285
\(777\) −1.73205 + 5.00000i −0.0621370 + 0.179374i
\(778\) 10.0000i 0.358517i
\(779\) 21.0000 + 36.3731i 0.752403 + 1.30320i
\(780\) 0 0
\(781\) −18.0000 + 31.1769i −0.644091 + 1.11560i
\(782\) −18.1865 + 10.5000i −0.650349 + 0.375479i
\(783\) 4.00000i 0.142948i
\(784\) −1.00000