Properties

Label 1050.2.o.b.949.2
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: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.b.499.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-0.500000 + 2.59808i) q^{21} +3.00000i q^{22} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(-2.59808 - 0.500000i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.59808 - 1.50000i) q^{33} +1.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(-3.46410 - 2.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +(0.866025 + 2.50000i) q^{42} -10.0000i q^{43} +(1.50000 + 2.59808i) q^{44} +(5.19615 - 3.00000i) q^{47} +1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(-3.46410 - 2.00000i) q^{52} +(2.59808 + 1.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.50000 + 0.866025i) q^{56} +4.00000i q^{57} +(-7.79423 + 4.50000i) q^{58} +(1.50000 - 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} -1.00000i q^{62} +(1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(-8.66025 - 5.00000i) q^{67} -6.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(7.79423 + 1.50000i) q^{77} +4.00000i q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -9.00000i q^{83} +(2.00000 + 1.73205i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(7.79423 + 4.50000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-0.866025 + 0.500000i) q^{93} +(3.00000 - 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000i q^{97} +(-2.59808 + 6.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} - 6q^{11} - 8q^{14} - 2q^{16} - 8q^{19} - 2q^{21} - 2q^{24} - 8q^{26} - 36q^{29} + 2q^{31} + 4q^{36} - 8q^{39} + 6q^{44} - 22q^{49} - 2q^{54} - 10q^{56} + 6q^{59} + 20q^{61} - 4q^{64} + 6q^{66} - 24q^{71} - 16q^{74} - 16q^{76} - 2q^{79} - 2q^{81} + 8q^{84} - 20q^{86} + 12q^{89} - 40q^{91} + 12q^{94} + 2q^{96} - 12q^{99} + O(q^{100}) \)

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
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) −2.00000 1.73205i −0.534522 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 0 0
\(21\) −0.500000 + 2.59808i −0.109109 + 0.566947i
\(22\) 3.00000i 0.639602i
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) −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
\(28\) −2.59808 0.500000i −0.490990 0.0944911i
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 2.59808 1.50000i 0.452267 0.261116i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −6.92820 + 4.00000i −1.13899 + 0.657596i −0.946180 0.323640i \(-0.895093\pi\)
−0.192809 + 0.981236i \(0.561760\pi\)
\(38\) −3.46410 2.00000i −0.561951 0.324443i
\(39\) −2.00000 + 3.46410i −0.320256 + 0.554700i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0.866025 + 2.50000i 0.133631 + 0.385758i
\(43\) 10.0000i 1.52499i −0.646997 0.762493i \(-0.723975\pi\)
0.646997 0.762493i \(-0.276025\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 0 0
\(46\) 0 0
\(47\) 5.19615 3.00000i 0.757937 0.437595i −0.0706177 0.997503i \(-0.522497\pi\)
0.828554 + 0.559908i \(0.189164\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.46410 2.00000i −0.480384 0.277350i
\(53\) 2.59808 + 1.50000i 0.356873 + 0.206041i 0.667708 0.744423i \(-0.267275\pi\)
−0.310835 + 0.950464i \(0.600609\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) 4.00000i 0.529813i
\(58\) −7.79423 + 4.50000i −1.02343 + 0.590879i
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 1.00000i 0.127000i
\(63\) 1.73205 2.00000i 0.218218 0.251976i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 1.50000 2.59808i 0.184637 0.319801i
\(67\) −8.66025 5.00000i −1.05802 0.610847i −0.133135 0.991098i \(-0.542504\pi\)
−0.924883 + 0.380251i \(0.875838\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) −1.73205 1.00000i −0.202721 0.117041i 0.395203 0.918594i \(-0.370674\pi\)
−0.597924 + 0.801553i \(0.704008\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 7.79423 + 1.50000i 0.888235 + 0.170941i
\(78\) 4.00000i 0.452911i
\(79\) −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i \(-0.184582\pi\)
−0.892781 + 0.450490i \(0.851249\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 9.00000i 0.987878i −0.869496 0.493939i \(-0.835557\pi\)
0.869496 0.493939i \(-0.164443\pi\)
\(84\) 2.00000 + 1.73205i 0.218218 + 0.188982i
\(85\) 0 0
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 7.79423 + 4.50000i 0.835629 + 0.482451i
\(88\) 2.59808 + 1.50000i 0.276956 + 0.159901i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) −10.0000 + 3.46410i −1.04828 + 0.363137i
\(92\) 0 0
\(93\) −0.866025 + 0.500000i −0.0898027 + 0.0518476i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 1.00000i 0.101535i 0.998711 + 0.0507673i \(0.0161667\pi\)
−0.998711 + 0.0507673i \(0.983833\pi\)
\(98\) −2.59808 + 6.50000i −0.262445 + 0.656599i
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 0 0
\(103\) 6.92820 4.00000i 0.682656 0.394132i −0.118199 0.992990i \(-0.537712\pi\)
0.800855 + 0.598858i \(0.204379\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) 2.59808 1.50000i 0.251166 0.145010i −0.369132 0.929377i \(-0.620345\pi\)
0.620298 + 0.784366i \(0.287012\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 7.00000 12.1244i 0.670478 1.16130i −0.307290 0.951616i \(-0.599422\pi\)
0.977769 0.209687i \(-0.0672444\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) −1.73205 + 2.00000i −0.163663 + 0.188982i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) 0 0
\(116\) −4.50000 + 7.79423i −0.417815 + 0.723676i
\(117\) 3.46410 2.00000i 0.320256 0.184900i
\(118\) 3.00000i 0.276172i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 8.66025 + 5.00000i 0.784063 + 0.452679i
\(123\) 0 0
\(124\) −0.500000 0.866025i −0.0449013 0.0777714i
\(125\) 0 0
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) 5.00000i 0.443678i −0.975083 0.221839i \(-0.928794\pi\)
0.975083 0.221839i \(-0.0712060\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −5.00000 + 8.66025i −0.440225 + 0.762493i
\(130\) 0 0
\(131\) 4.50000 + 7.79423i 0.393167 + 0.680985i 0.992865 0.119241i \(-0.0380462\pi\)
−0.599699 + 0.800226i \(0.704713\pi\)
\(132\) 3.00000i 0.261116i
\(133\) −6.92820 + 8.00000i −0.600751 + 0.693688i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) 15.5885 + 9.00000i 1.33181 + 0.768922i 0.985577 0.169226i \(-0.0541268\pi\)
0.346235 + 0.938148i \(0.387460\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −5.19615 + 3.00000i −0.436051 + 0.251754i
\(143\) 10.3923 + 6.00000i 0.869048 + 0.501745i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 6.92820 1.00000i 0.571429 0.0824786i
\(148\) 8.00000i 0.657596i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i \(-0.820378\pi\)
0.885653 + 0.464348i \(0.153711\pi\)
\(152\) −3.46410 + 2.00000i −0.280976 + 0.162221i
\(153\) 0 0
\(154\) 7.50000 2.59808i 0.604367 0.209359i
\(155\) 0 0
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) −3.46410 2.00000i −0.276465 0.159617i 0.355357 0.934731i \(-0.384359\pi\)
−0.631822 + 0.775113i \(0.717693\pi\)
\(158\) −0.866025 0.500000i −0.0688973 0.0397779i
\(159\) −1.50000 2.59808i −0.118958 0.206041i
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) −13.8564 + 8.00000i −1.08532 + 0.626608i −0.932326 0.361619i \(-0.882224\pi\)
−0.152992 + 0.988227i \(0.548891\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) 6.00000i 0.464294i −0.972681 0.232147i \(-0.925425\pi\)
0.972681 0.232147i \(-0.0745750\pi\)
\(168\) 2.59808 + 0.500000i 0.200446 + 0.0385758i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) −8.66025 5.00000i −0.660338 0.381246i
\(173\) 15.5885 9.00000i 1.18517 0.684257i 0.227964 0.973670i \(-0.426793\pi\)
0.957205 + 0.289412i \(0.0934598\pi\)
\(174\) 9.00000 0.682288
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) −2.59808 + 1.50000i −0.195283 + 0.112747i
\(178\) 5.19615 + 3.00000i 0.389468 + 0.224860i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −6.92820 + 8.00000i −0.513553 + 0.592999i
\(183\) 10.0000i 0.739221i
\(184\) 0 0
\(185\) 0 0
\(186\) −0.500000 + 0.866025i −0.0366618 + 0.0635001i
\(187\) 0 0
\(188\) 6.00000i 0.437595i
\(189\) −2.50000 + 0.866025i −0.181848 + 0.0629941i
\(190\) 0 0
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 16.4545 + 9.50000i 1.18442 + 0.683825i 0.957033 0.289980i \(-0.0936485\pi\)
0.227387 + 0.973805i \(0.426982\pi\)
\(194\) 0.500000 + 0.866025i 0.0358979 + 0.0621770i
\(195\) 0 0
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) 6.00000i 0.427482i −0.976890 0.213741i \(-0.931435\pi\)
0.976890 0.213741i \(-0.0685649\pi\)
\(198\) −2.59808 + 1.50000i −0.184637 + 0.106600i
\(199\) 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i \(-0.582534\pi\)
0.965272 0.261245i \(-0.0841331\pi\)
\(200\) 0 0
\(201\) 5.00000 + 8.66025i 0.352673 + 0.610847i
\(202\) 18.0000i 1.26648i
\(203\) 7.79423 + 22.5000i 0.547048 + 1.57919i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 0 0
\(208\) −3.46410 + 2.00000i −0.240192 + 0.138675i
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 2.59808 1.50000i 0.178437 0.103020i
\(213\) 5.19615 + 3.00000i 0.356034 + 0.205557i
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −2.59808 0.500000i −0.176369 0.0339422i
\(218\) 14.0000i 0.948200i
\(219\) 1.00000 + 1.73205i 0.0675737 + 0.117041i
\(220\) 0 0
\(221\) 0 0
\(222\) 6.92820 4.00000i 0.464991 0.268462i
\(223\) 19.0000i 1.27233i −0.771551 0.636167i \(-0.780519\pi\)
0.771551 0.636167i \(-0.219481\pi\)
\(224\) −0.500000 + 2.59808i −0.0334077 + 0.173591i
\(225\) 0 0
\(226\) 0 0
\(227\) −23.3827 13.5000i −1.55196 0.896026i −0.997982 0.0634974i \(-0.979775\pi\)
−0.553981 0.832529i \(-0.686892\pi\)
\(228\) 3.46410 + 2.00000i 0.229416 + 0.132453i
\(229\) −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i \(-0.208859\pi\)
−0.924510 + 0.381157i \(0.875526\pi\)
\(230\) 0 0
\(231\) −6.00000 5.19615i −0.394771 0.341882i
\(232\) 9.00000i 0.590879i
\(233\) −20.7846 + 12.0000i −1.36165 + 0.786146i −0.989843 0.142166i \(-0.954593\pi\)
−0.371802 + 0.928312i \(0.621260\pi\)
\(234\) 2.00000 3.46410i 0.130744 0.226455i
\(235\) 0 0
\(236\) −1.50000 2.59808i −0.0976417 0.169120i
\(237\) 1.00000i 0.0649570i
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 1.73205 + 1.00000i 0.111340 + 0.0642824i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 10.0000 0.640184
\(245\) 0 0
\(246\) 0 0
\(247\) −13.8564 + 8.00000i −0.881662 + 0.509028i
\(248\) −0.866025 0.500000i −0.0549927 0.0317500i
\(249\) −4.50000 + 7.79423i −0.285176 + 0.493939i
\(250\) 0 0
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) −0.866025 2.50000i −0.0545545 0.157485i
\(253\) 0 0
\(254\) −2.50000 4.33013i −0.156864 0.271696i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.19615 + 3.00000i −0.324127 + 0.187135i −0.653231 0.757159i \(-0.726587\pi\)
0.329104 + 0.944294i \(0.393253\pi\)
\(258\) 10.0000i 0.622573i
\(259\) 16.0000 + 13.8564i 0.994192 + 0.860995i
\(260\) 0 0
\(261\) −4.50000 7.79423i −0.278543 0.482451i
\(262\) 7.79423 + 4.50000i 0.481529 + 0.278011i
\(263\) 5.19615 + 3.00000i 0.320408 + 0.184988i 0.651575 0.758585i \(-0.274109\pi\)
−0.331166 + 0.943572i \(0.607442\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) 0 0
\(266\) −2.00000 + 10.3923i −0.122628 + 0.637193i
\(267\) 6.00000i 0.367194i
\(268\) −8.66025 + 5.00000i −0.529009 + 0.305424i
\(269\) 10.5000 18.1865i 0.640196 1.10885i −0.345192 0.938532i \(-0.612186\pi\)
0.985389 0.170321i \(-0.0544803\pi\)
\(270\) 0 0
\(271\) −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i \(-0.275099\pi\)
−0.983312 + 0.181928i \(0.941766\pi\)
\(272\) 0 0
\(273\) 10.3923 + 2.00000i 0.628971 + 0.121046i
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) 6.92820 + 4.00000i 0.416275 + 0.240337i 0.693482 0.720473i \(-0.256075\pi\)
−0.277207 + 0.960810i \(0.589409\pi\)
\(278\) −1.73205 + 1.00000i −0.103882 + 0.0599760i
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) −5.19615 + 3.00000i −0.309426 + 0.178647i
\(283\) −12.1244 7.00000i −0.720718 0.416107i 0.0942988 0.995544i \(-0.469939\pi\)
−0.815017 + 0.579437i \(0.803272\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −8.50000 14.7224i −0.500000 0.866025i
\(290\) 0 0
\(291\) 0.500000 0.866025i 0.0293105 0.0507673i
\(292\) −1.73205 + 1.00000i −0.101361 + 0.0585206i
\(293\) 33.0000i 1.92788i 0.266119 + 0.963940i \(0.414259\pi\)
−0.266119 + 0.963940i \(0.585741\pi\)
\(294\) 5.50000 4.33013i 0.320767 0.252538i
\(295\) 0 0
\(296\) 4.00000 + 6.92820i 0.232495 + 0.402694i
\(297\) 2.59808 + 1.50000i 0.150756 + 0.0870388i
\(298\) 15.5885 + 9.00000i 0.903015 + 0.521356i
\(299\) 0 0
\(300\) 0 0
\(301\) −25.0000 + 8.66025i −1.44098 + 0.499169i
\(302\) 1.00000i 0.0575435i
\(303\) −15.5885 + 9.00000i −0.895533 + 0.517036i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) 8.00000i 0.456584i −0.973593 0.228292i \(-0.926686\pi\)
0.973593 0.228292i \(-0.0733141\pi\)
\(308\) 5.19615 6.00000i 0.296078 0.341882i
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 3.46410 + 2.00000i 0.196116 + 0.113228i
\(313\) −26.8468 + 15.5000i −1.51747 + 0.876112i −0.517681 + 0.855574i \(0.673205\pi\)
−0.999789 + 0.0205381i \(0.993462\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) −7.79423 + 4.50000i −0.437767 + 0.252745i −0.702650 0.711535i \(-0.748000\pi\)
0.264883 + 0.964281i \(0.414667\pi\)
\(318\) −2.59808 1.50000i −0.145693 0.0841158i
\(319\) 13.5000 23.3827i 0.755855 1.30918i
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −8.00000 + 13.8564i −0.443079 + 0.767435i
\(327\) −12.1244 + 7.00000i −0.670478 + 0.387101i
\(328\) 0 0
\(329\) −12.0000 10.3923i −0.661581 0.572946i
\(330\) 0 0
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) −7.79423 4.50000i −0.427764 0.246970i
\(333\) −6.92820 4.00000i −0.379663 0.219199i
\(334\) −3.00000 5.19615i −0.164153 0.284321i
\(335\) 0 0
\(336\) 2.50000 0.866025i 0.136386 0.0472456i
\(337\) 7.00000i 0.381314i 0.981657 + 0.190657i \(0.0610619\pi\)
−0.981657 + 0.190657i \(0.938938\pi\)
\(338\) −2.59808 + 1.50000i −0.141317 + 0.0815892i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.50000 + 2.59808i 0.0812296 + 0.140694i
\(342\) 4.00000i 0.216295i
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 9.00000 15.5885i 0.483843 0.838041i
\(347\) 10.3923 + 6.00000i 0.557888 + 0.322097i 0.752297 0.658824i \(-0.228946\pi\)
−0.194409 + 0.980921i \(0.562279\pi\)
\(348\) 7.79423 4.50000i 0.417815 0.241225i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 2.59808 1.50000i 0.138478 0.0799503i
\(353\) −20.7846 12.0000i −1.10625 0.638696i −0.168397 0.985719i \(-0.553859\pi\)
−0.937856 + 0.347024i \(0.887192\pi\)
\(354\) −1.50000 + 2.59808i −0.0797241 + 0.138086i
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 12.0000i 0.634220i
\(359\) 15.0000 + 25.9808i 0.791670 + 1.37121i 0.924932 + 0.380131i \(0.124121\pi\)
−0.133263 + 0.991081i \(0.542545\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 6.92820 4.00000i 0.364138 0.210235i
\(363\) 2.00000i 0.104973i
\(364\) −2.00000 + 10.3923i −0.104828 + 0.544705i
\(365\) 0 0
\(366\) −5.00000 8.66025i −0.261354 0.452679i
\(367\) −16.4545 9.50000i −0.858917 0.495896i 0.00473247 0.999989i \(-0.498494\pi\)
−0.863649 + 0.504093i \(0.831827\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.50000 7.79423i 0.0778761 0.404656i
\(372\) 1.00000i 0.0518476i
\(373\) 6.92820 4.00000i 0.358729 0.207112i −0.309794 0.950804i \(-0.600260\pi\)
0.668523 + 0.743691i \(0.266927\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) 36.0000i 1.85409i
\(378\) −1.73205 + 2.00000i −0.0890871 + 0.102869i
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 0 0
\(381\) −2.50000 + 4.33013i −0.128079 + 0.221839i
\(382\) 0 0
\(383\) 15.5885 9.00000i 0.796533 0.459879i −0.0457244 0.998954i \(-0.514560\pi\)
0.842257 + 0.539076i \(0.181226\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 19.0000 0.967075
\(387\) 8.66025 5.00000i 0.440225 0.254164i
\(388\) 0.866025 + 0.500000i 0.0439658 + 0.0253837i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 4.33013 + 5.50000i 0.218704 + 0.277792i
\(393\) 9.00000i 0.453990i
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) 0 0
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) 3.46410 2.00000i 0.173858 0.100377i −0.410546 0.911840i \(-0.634662\pi\)
0.584404 + 0.811463i \(0.301328\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 10.0000 3.46410i 0.500626 0.173422i
\(400\) 0 0
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 8.66025 + 5.00000i 0.431934 + 0.249377i
\(403\) −3.46410 2.00000i −0.172559 0.0996271i
\(404\) −9.00000 15.5885i −0.447767 0.775555i
\(405\) 0 0
\(406\) 18.0000 + 15.5885i 0.893325 + 0.773642i
\(407\) 24.0000i 1.18964i
\(408\) 0 0
\(409\) −12.5000 + 21.6506i −0.618085 + 1.07056i 0.371750 + 0.928333i \(0.378758\pi\)
−0.989835 + 0.142222i \(0.954575\pi\)
\(410\) 0 0
\(411\) −9.00000 15.5885i −0.443937 0.768922i
\(412\) 8.00000i 0.394132i
\(413\) −7.79423 1.50000i −0.383529 0.0738102i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.00000 + 3.46410i −0.0980581 + 0.169842i
\(417\) 1.73205 + 1.00000i 0.0848189 + 0.0489702i
\(418\) 10.3923 6.00000i 0.508304 0.293470i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 12.1244 7.00000i 0.590204 0.340755i
\(423\) 5.19615 + 3.00000i 0.252646 + 0.145865i
\(424\) 1.50000 2.59808i 0.0728464 0.126174i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) 17.3205 20.0000i 0.838198 0.967868i
\(428\) 3.00000i 0.145010i
\(429\) −6.00000 10.3923i −0.289683 0.501745i
\(430\) 0 0
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 34.0000i 1.63394i −0.576683 0.816968i \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) −2.50000 + 0.866025i −0.120004 + 0.0415705i
\(435\) 0 0
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) 0 0
\(438\) 1.73205 + 1.00000i 0.0827606 + 0.0477818i
\(439\) 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i \(0.147999\pi\)
−0.0586141 + 0.998281i \(0.518668\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 0 0
\(443\) −28.5788 + 16.5000i −1.35782 + 0.783939i −0.989330 0.145692i \(-0.953459\pi\)
−0.368492 + 0.929631i \(0.620126\pi\)
\(444\) 4.00000 6.92820i 0.189832 0.328798i
\(445\) 0 0
\(446\) −9.50000 16.4545i −0.449838 0.779142i
\(447\) 18.0000i 0.851371i
\(448\) 0.866025 + 2.50000i 0.0409159 + 0.118114i
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.866025 + 0.500000i −0.0406894 + 0.0234920i
\(454\) −27.0000 −1.26717
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 0.866025 0.500000i 0.0405110 0.0233890i −0.479608 0.877483i \(-0.659221\pi\)
0.520119 + 0.854094i \(0.325888\pi\)
\(458\) −3.46410 2.00000i −0.161867 0.0934539i
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) −7.79423 1.50000i −0.362620 0.0697863i
\(463\) 8.00000i 0.371792i 0.982569 + 0.185896i \(0.0595187\pi\)
−0.982569 + 0.185896i \(0.940481\pi\)
\(464\) 4.50000 + 7.79423i 0.208907 + 0.361838i
\(465\) 0 0
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) −31.1769 + 18.0000i −1.44270 + 0.832941i −0.998029 0.0627555i \(-0.980011\pi\)
−0.444667 + 0.895696i \(0.646678\pi\)
\(468\) 4.00000i 0.184900i
\(469\) −5.00000 + 25.9808i −0.230879 + 1.19968i
\(470\) 0 0
\(471\) 2.00000 + 3.46410i 0.0921551 + 0.159617i
\(472\) −2.59808 1.50000i −0.119586 0.0690431i
\(473\) 25.9808 + 15.0000i 1.19460 + 0.689701i
\(474\) 0.500000 + 0.866025i 0.0229658 + 0.0397779i
\(475\) 0 0
\(476\) 0 0
\(477\) 3.00000i 0.137361i
\(478\) 20.7846 12.0000i 0.950666 0.548867i
\(479\) −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i \(-0.968231\pi\)
0.583803 + 0.811895i \(0.301564\pi\)
\(480\) 0 0
\(481\) 16.0000 + 27.7128i 0.729537 + 1.26360i
\(482\) 1.00000i 0.0455488i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 35.5070 + 20.5000i 1.60898 + 0.928944i 0.989599 + 0.143851i \(0.0459486\pi\)
0.619378 + 0.785093i \(0.287385\pi\)
\(488\) 8.66025 5.00000i 0.392031 0.226339i
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) −33.0000 −1.48927 −0.744635 0.667472i \(-0.767376\pi\)
−0.744635 + 0.667472i \(0.767376\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −8.00000 + 13.8564i −0.359937 + 0.623429i
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 5.19615 + 15.0000i 0.233079 + 0.672842i
\(498\) 9.00000i 0.403300i
\(499\) 1.00000 + 1.73205i 0.0447661 + 0.0775372i 0.887540 0.460730i \(-0.152412\pi\)
−0.842774 + 0.538267i \(0.819079\pi\)
\(500\) 0 0
\(501\) −3.00000 + 5.19615i −0.134030 + 0.232147i
\(502\) 23.3827 13.5000i 1.04362 0.602534i
\(503\) 12.0000i 0.535054i −0.963550 0.267527i \(-0.913794\pi\)
0.963550 0.267527i \(-0.0862064\pi\)
\(504\) −2.00000 1.73205i −0.0890871 0.0771517i
\(505\) 0 0
\(506\) 0 0
\(507\) 2.59808 + 1.50000i 0.115385 + 0.0666173i
\(508\) −4.33013 2.50000i −0.192118 0.110920i
\(509\) −1.50000 2.59808i −0.0664863 0.115158i 0.830866 0.556473i \(-0.187846\pi\)
−0.897352 + 0.441315i \(0.854512\pi\)
\(510\) 0 0
\(511\) −1.00000 + 5.19615i −0.0442374 + 0.229864i
\(512\) 1.00000i 0.0441942i
\(513\) −3.46410 + 2.00000i −0.152944 + 0.0883022i
\(514\) −3.00000 + 5.19615i −0.132324 + 0.229192i
\(515\) 0 0
\(516\) 5.00000 + 8.66025i 0.220113 + 0.381246i
\(517\) 18.0000i 0.791639i
\(518\) 20.7846 + 4.00000i 0.913223 + 0.175750i
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) −7.79423 4.50000i −0.341144 0.196960i
\(523\) −3.46410 + 2.00000i −0.151475 + 0.0874539i −0.573822 0.818980i \(-0.694540\pi\)
0.422347 + 0.906434i \(0.361206\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 6.00000 0.261612
\(527\) 0 0
\(528\) −2.59808 1.50000i −0.113067 0.0652791i
\(529\) −11.5000 + 19.9186i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) 3.00000 0.130189
\(532\) 3.46410 + 10.0000i 0.150188 + 0.433555i
\(533\) 0 0
\(534\) −3.00000 5.19615i −0.129823 0.224860i
\(535\) 0 0
\(536\) −5.00000 + 8.66025i −0.215967 + 0.374066i
\(537\) −10.3923 + 6.00000i −0.448461 + 0.258919i
\(538\) 21.0000i 0.905374i
\(539\) −3.00000 20.7846i −0.129219 0.895257i
\(540\) 0 0
\(541\) −13.0000 22.5167i −0.558914 0.968067i −0.997587 0.0694205i \(-0.977885\pi\)
0.438674 0.898646i \(-0.355448\pi\)
\(542\) −9.52628 5.50000i −0.409189 0.236245i
\(543\) −6.92820 4.00000i −0.297318 0.171656i
\(544\) 0 0
\(545\) 0 0
\(546\) 10.0000 3.46410i 0.427960 0.148250i
\(547\) 8.00000i 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) 15.5885 9.00000i 0.665906 0.384461i
\(549\) −5.00000 + 8.66025i −0.213395 + 0.369611i
\(550\) 0 0
\(551\) 18.0000 + 31.1769i 0.766826 + 1.32818i
\(552\) 0 0
\(553\) −1.73205 + 2.00000i −0.0736543 + 0.0850487i
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) 2.59808 + 1.50000i 0.110084 + 0.0635570i 0.554031 0.832496i \(-0.313089\pi\)
−0.443947 + 0.896053i \(0.646422\pi\)
\(558\) 0.866025 0.500000i 0.0366618 0.0211667i
\(559\) −40.0000 −1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) 5.19615 3.00000i 0.219186 0.126547i
\(563\) −33.7750 19.5000i −1.42345 0.821827i −0.426855 0.904320i \(-0.640378\pi\)
−0.996592 + 0.0824933i \(0.973712\pi\)
\(564\) −3.00000 + 5.19615i −0.126323 + 0.218797i
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) 2.59808 + 0.500000i 0.109109 + 0.0209980i
\(568\) 6.00000i 0.251754i
\(569\) −18.0000 31.1769i −0.754599 1.30700i −0.945573 0.325409i \(-0.894498\pi\)
0.190974 0.981595i \(-0.438835\pi\)
\(570\) 0 0
\(571\) 17.0000 29.4449i 0.711428 1.23223i −0.252893 0.967494i \(-0.581382\pi\)
0.964321 0.264735i \(-0.0852845\pi\)
\(572\) 10.3923 6.00000i 0.434524 0.250873i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 19.9186 + 11.5000i 0.829222 + 0.478751i 0.853586 0.520952i \(-0.174423\pi\)
−0.0243645 + 0.999703i \(0.507756\pi\)
\(578\) −14.7224 8.50000i −0.612372 0.353553i
\(579\) −9.50000 16.4545i −0.394807 0.683825i
\(580\) 0 0
\(581\) −22.5000 + 7.79423i −0.933457 + 0.323359i
\(582\) 1.00000i 0.0414513i
\(583\) −7.79423 + 4.50000i −0.322804 + 0.186371i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) 16.5000 + 28.5788i 0.681609 + 1.18058i
\(587\) 21.0000i 0.866763i −0.901211 0.433381i \(-0.857320\pi\)
0.901211 0.433381i \(-0.142680\pi\)
\(588\) 2.59808 6.50000i 0.107143 0.268055i
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) 6.92820 + 4.00000i 0.284747 + 0.164399i
\(593\) 20.7846 12.0000i 0.853522 0.492781i −0.00831589 0.999965i \(-0.502647\pi\)
0.861838 + 0.507184i \(0.169314\pi\)
\(594\) 3.00000 0.123091
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) −17.3205 + 10.0000i −0.708881 + 0.409273i
\(598\) 0 0
\(599\) −9.00000 + 15.5885i −0.367730 + 0.636927i −0.989210 0.146503i \(-0.953198\pi\)
0.621480 + 0.783430i \(0.286532\pi\)
\(600\) 0 0
\(601\) 11.0000 0.448699 0.224350 0.974509i \(-0.427974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(602\) −17.3205 + 20.0000i −0.705931 + 0.815139i
\(603\) 10.0000i 0.407231i
\(604\) −0.500000 0.866025i −0.0203447 0.0352381i
\(605\) 0 0
\(606\) −9.00000 + 15.5885i −0.365600 + 0.633238i
\(607\) 6.06218 3.50000i 0.246056 0.142061i −0.371901 0.928272i \(-0.621294\pi\)
0.617957 + 0.786212i \(0.287961\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 4.50000 23.3827i 0.182349 0.947514i
\(610\) 0 0
\(611\) −12.0000 20.7846i −0.485468 0.840855i
\(612\) 0 0
\(613\) 13.8564 + 8.00000i 0.559655 + 0.323117i 0.753007 0.658012i \(-0.228603\pi\)
−0.193352 + 0.981129i \(0.561936\pi\)
\(614\) −4.00000 6.92820i −0.161427 0.279600i
\(615\) 0 0
\(616\) 1.50000 7.79423i 0.0604367 0.314038i
\(617\) 6.00000i 0.241551i 0.992680 + 0.120775i \(0.0385381\pi\)
−0.992680 + 0.120775i \(0.961462\pi\)
\(618\) −6.92820 + 4.00000i −0.278693 + 0.160904i
\(619\) −17.0000 + 29.4449i −0.683288 + 1.18349i 0.290684 + 0.956819i \(0.406117\pi\)
−0.973972 + 0.226670i \(0.927216\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000i 0.962312i
\(623\) 10.3923 12.0000i 0.416359 0.480770i
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) −15.5000 + 26.8468i −0.619505 + 1.07301i
\(627\) −10.3923 6.00000i −0.415029 0.239617i
\(628\) −3.46410 + 2.00000i −0.138233 + 0.0798087i
\(629\) 0 0
\(630\) 0 0
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) −0.866025 + 0.500000i −0.0344486 + 0.0198889i
\(633\) −12.1244 7.00000i −0.481900 0.278225i
\(634\) −4.50000 + 7.79423i −0.178718 + 0.309548i
\(635\) 0 0
\(636\) −3.00000 −0.118958
\(637\) 17.3205 + 22.0000i 0.686264 + 0.871672i
\(638\) 27.0000i 1.06894i
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0 0
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) −2.59808 + 1.50000i −0.102538 + 0.0592003i
\(643\) 34.0000i 1.34083i −0.741987 0.670415i \(-0.766116\pi\)
0.741987 0.670415i \(-0.233884\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.5885 9.00000i −0.612845 0.353827i 0.161233 0.986916i \(-0.448453\pi\)
−0.774078 + 0.633090i \(0.781786\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 4.50000 + 7.79423i 0.176640 + 0.305950i
\(650\) 0 0
\(651\) 2.00000 + 1.73205i 0.0783862 + 0.0678844i
\(652\) 16.0000i 0.626608i
\(653\) 2.59808 1.50000i 0.101671 0.0586995i −0.448303 0.893882i \(-0.647971\pi\)
0.549973 + 0.835182i \(0.314638\pi\)
\(654\) −7.00000 + 12.1244i −0.273722 + 0.474100i
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000i 0.0780274i
\(658\) −15.5885 3.00000i −0.607701 0.116952i
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) −17.3205 10.0000i −0.673181 0.388661i
\(663\) 0 0
\(664\) −9.00000 −0.349268
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) 0 0
\(668\) −5.19615 3.00000i −0.201045 0.116073i
\(669\) −9.50000 + 16.4545i −0.367291 + 0.636167i
\(670\) 0 0
\(671\) −30.0000 −1.15814
\(672\) 1.73205 2.00000i 0.0668153 0.0771517i
\(673\) 29.0000i 1.11787i 0.829212 + 0.558934i \(0.188789\pi\)
−0.829212 + 0.558934i \(0.811211\pi\)
\(674\) 3.50000 + 6.06218i 0.134815 + 0.233506i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) 28.5788 16.5000i 1.09837 0.634147i 0.162581 0.986695i \(-0.448018\pi\)
0.935793 + 0.352549i \(0.114685\pi\)
\(678\) 0 0
\(679\) 2.50000 0.866025i 0.0959412 0.0332350i
\(680\) 0 0
\(681\) 13.5000 + 23.3827i 0.517321 + 0.896026i
\(682\) 2.59808 + 1.50000i 0.0994855 + 0.0574380i
\(683\) −28.5788 16.5000i −1.09354 0.631355i −0.159022 0.987275i \(-0.550834\pi\)
−0.934516 + 0.355920i \(0.884168\pi\)
\(684\) −2.00000 3.46410i −0.0764719 0.132453i
\(685\) 0 0
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) 4.00000i 0.152610i
\(688\) −8.66025 + 5.00000i −0.330169 + 0.190623i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 2.59808 + 7.50000i 0.0986928 + 0.284901i
\(694\) 12.0000 0.455514
\(695\) 0 0
\(696\) 4.50000 7.79423i 0.170572 0.295439i
\(697\) 0 0
\(698\) −22.5167 + 13.0000i −0.852268 + 0.492057i
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) −3.46410 + 2.00000i −0.130744 + 0.0754851i
\(703\) 27.7128 + 16.0000i 1.04521 + 0.603451i
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) −46.7654 9.00000i −1.75879 0.338480i
\(708\) 3.00000i 0.112747i
\(709\) −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) 0 0
\(711\) 0.500000 0.866025i 0.0187515 0.0324785i
\(712\) 5.19615 3.00000i 0.194734 0.112430i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) −20.7846 12.0000i −0.776215 0.448148i
\(718\) 25.9808 + 15.0000i 0.969593 + 0.559795i
\(719\) −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) 0 0
\(721\) −16.0000 13.8564i −0.595871 0.516040i
\(722\) 3.00000i 0.111648i
\(723\) −0.866025 + 0.500000i −0.0322078 + 0.0185952i
\(724\) 4.00000 6.92820i 0.148659 0.257485i
\(725\) 0 0
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) 13.0000i 0.482143i 0.970507 + 0.241072i \(0.0774989\pi\)
−0.970507 + 0.241072i \(0.922501\pi\)
\(728\) 3.46410 + 10.0000i 0.128388 + 0.370625i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) −8.66025 5.00000i −0.320092 0.184805i
\(733\) −8.66025 + 5.00000i −0.319874 + 0.184679i −0.651336 0.758789i \(-0.725791\pi\)
0.331463 + 0.943468i \(0.392458\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) 0 0
\(737\) 25.9808 15.0000i 0.957014 0.552532i
\(738\) 0 0
\(739\) 25.0000 43.3013i 0.919640 1.59286i 0.119677 0.992813i \(-0.461814\pi\)
0.799962 0.600050i \(-0.204853\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) −2.59808 7.50000i −0.0953784 0.275334i
\(743\) 42.0000i 1.54083i 0.637542 + 0.770415i \(0.279951\pi\)
−0.637542 + 0.770415i \(0.720049\pi\)
\(744\) 0.500000 + 0.866025i 0.0183309 + 0.0317500i
\(745\) 0 0
\(746\) 4.00000 6.92820i 0.146450 0.253660i
\(747\) 7.79423 4.50000i 0.285176 0.164646i
\(748\) 0 0
\(749\) −6.00000 5.19615i −0.219235 0.189863i
\(750\) 0 0
\(751\) 3.50000 + 6.06218i 0.127717 + 0.221212i 0.922792 0.385299i \(-0.125902\pi\)
−0.795075 + 0.606511i \(0.792568\pi\)
\(752\) −5.19615 3.00000i −0.189484 0.109399i
\(753\) −23.3827 13.5000i −0.852112 0.491967i
\(754\) 18.0000 + 31.1769i 0.655521 + 1.13540i
\(755\) 0 0
\(756\) −0.500000 + 2.59808i −0.0181848 + 0.0944911i
\(757\) 38.0000i 1.38113i −0.723269 0.690567i \(-0.757361\pi\)
0.723269 0.690567i \(-0.242639\pi\)
\(758\) −6.92820 + 4.00000i −0.251644 + 0.145287i
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 10.3923i −0.217500 0.376721i 0.736543 0.676391i \(-0.236457\pi\)
−0.954043 + 0.299670i \(0.903123\pi\)
\(762\) 5.00000i 0.181131i
\(763\) −36.3731 7.00000i −1.31679 0.253417i
\(764\) 0 0
\(765\) 0 0
\(766\) 9.00000 15.5885i 0.325183 0.563234i
\(767\) −10.3923 6.00000i −0.375244 0.216647i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) 19.0000 0.685158 0.342579 0.939489i \(-0.388700\pi\)
0.342579 + 0.939489i \(0.388700\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) 16.4545 9.50000i 0.592210 0.341912i
\(773\) −5.19615 3.00000i −0.186893 0.107903i 0.403634 0.914920i \(-0.367747\pi\)
−0.590527 + 0.807018i \(0.701080\pi\)
\(774\) 5.00000 8.66025i 0.179721 0.311286i
\(775\) 0 0
\(776\) 1.00000 0.0358979
\(777\) −6.92820 20.0000i −0.248548 0.717496i
\(778\) 6.00000i 0.215110i
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 15.5885i 0.322045 0.557799i
\(782\) 0 0
\(783\) 9.00000i 0.321634i
\(784\) 6.50000 + 2.59808i 0.232143 + 0.0927884i
\(785\) 0 0
\(786\) −4.50000 7.79423i −0.160510 0.278011i
\(787\) 43.3013 + 25.0000i 1.54352 + 0.891154i 0.998613 + 0.0526599i \(0.0167699\pi\)
0.544911 + 0.838494i