Properties

Label 1050.2.o.b.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: no (minimal twist has level 42)
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.b.499.1

$q$-expansion

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

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 \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) −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 0.192809 0.981236i \(-0.438240\pi\)
0.946180 + 0.323640i \(0.104907\pi\)
\(38\) 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 \(0.276025\pi\)
−0.646997 + 0.762493i \(0.723975\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 0 0
\(46\) 0 0
\(47\) −5.19615 + 3.00000i −0.757937 + 0.437595i −0.828554 0.559908i \(-0.810836\pi\)
0.0706177 + 0.997503i \(0.477503\pi\)
\(48\) 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 0.310835 0.950464i \(-0.399391\pi\)
−0.667708 + 0.744423i \(0.732725\pi\)
\(54\) −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 0.924883 0.380251i \(-0.124162\pi\)
0.133135 + 0.991098i \(0.457496\pi\)
\(68\) 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 0.597924 0.801553i \(-0.295992\pi\)
−0.395203 + 0.918594i \(0.629326\pi\)
\(74\) −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 \(0.164443\pi\)
−0.869496 + 0.493939i \(0.835557\pi\)
\(84\) 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 \(-0.983833\pi\)
0.998711 0.0507673i \(-0.0161667\pi\)
\(98\) 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 −0.800855 0.598858i \(-0.795621\pi\)
0.118199 + 0.992990i \(0.462288\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) −2.59808 + 1.50000i −0.251166 + 0.145010i −0.620298 0.784366i \(-0.712988\pi\)
0.369132 + 0.929377i \(0.379655\pi\)
\(108\) 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 \(0.0712060\pi\)
−0.975083 + 0.221839i \(0.928794\pi\)
\(128\) 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 −0.346235 0.938148i \(-0.612540\pi\)
−0.985577 + 0.169226i \(0.945873\pi\)
\(138\) 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 0.631822 0.775113i \(-0.282307\pi\)
−0.355357 + 0.934731i \(0.615641\pi\)
\(158\) 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 0.152992 0.988227i \(-0.451109\pi\)
0.932326 + 0.361619i \(0.117776\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) 6.00000i 0.464294i 0.972681 + 0.232147i \(0.0745750\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(168\) −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 −0.957205 0.289412i \(-0.906540\pi\)
−0.227964 + 0.973670i \(0.573207\pi\)
\(174\) 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 −0.227387 0.973805i \(-0.573018\pi\)
−0.957033 + 0.289980i \(0.906351\pi\)
\(194\) 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 \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) 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 \(0.219481\pi\)
−0.771551 + 0.636167i \(0.780519\pi\)
\(224\) −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 \(0.0202255\pi\)
0.553981 + 0.832529i \(0.313108\pi\)
\(228\) −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 0.371802 0.928312i \(-0.378740\pi\)
0.989843 + 0.142166i \(0.0454066\pi\)
\(234\) 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 −0.329104 0.944294i \(-0.606747\pi\)
0.653231 + 0.757159i \(0.273413\pi\)
\(258\) 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 0.331166 0.943572i \(-0.392558\pi\)
−0.651575 + 0.758585i \(0.725891\pi\)
\(264\) −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 0.277207 0.960810i \(-0.410591\pi\)
−0.693482 + 0.720473i \(0.743925\pi\)
\(278\) 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 0.815017 0.579437i \(-0.196728\pi\)
−0.0942988 + 0.995544i \(0.530061\pi\)
\(284\) −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 \(-0.585741\pi\)
0.266119 0.963940i \(-0.414259\pi\)
\(294\) 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 \(0.0733141\pi\)
−0.973593 + 0.228292i \(0.926686\pi\)
\(308\) −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 \(-0.326795\pi\)
0.999789 0.0205381i \(-0.00653795\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) 7.79423 4.50000i 0.437767 0.252745i −0.264883 0.964281i \(-0.585333\pi\)
0.702650 + 0.711535i \(0.252000\pi\)
\(318\) 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 \(-0.938938\pi\)
0.981657 0.190657i \(-0.0610619\pi\)
\(338\) 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 0.194409 0.980921i \(-0.437721\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(348\) −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 0.937856 0.347024i \(-0.112808\pi\)
0.168397 + 0.985719i \(0.446141\pi\)
\(354\) −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 0.863649 0.504093i \(-0.168173\pi\)
−0.00473247 + 0.999989i \(0.501506\pi\)
\(368\) 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 −0.668523 0.743691i \(-0.733073\pi\)
0.309794 + 0.950804i \(0.399740\pi\)
\(374\) 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 −0.842257 0.539076i \(-0.818774\pi\)
0.0457244 + 0.998954i \(0.485440\pi\)
\(384\) 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 −0.584404 0.811463i \(-0.698672\pi\)
0.410546 + 0.911840i \(0.365338\pi\)
\(398\) 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 \(0.304347\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) −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 0.368492 0.929631i \(-0.379874\pi\)
0.989330 + 0.145692i \(0.0465410\pi\)
\(444\) 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 −0.520119 0.854094i \(-0.674112\pi\)
0.479608 + 0.877483i \(0.340779\pi\)
\(458\) 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 \(-0.940481\pi\)
0.982569 0.185896i \(-0.0595187\pi\)
\(464\) 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 0.444667 0.895696i \(-0.353322\pi\)
0.998029 + 0.0627555i \(0.0199888\pi\)
\(468\) 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 \(-0.954051\pi\)
−0.619378 0.785093i \(-0.712615\pi\)
\(488\) −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 \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) −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 −0.422347 0.906434i \(-0.638794\pi\)
0.573822 + 0.818980i \(0.305460\pi\)
\(524\) 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 \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) −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 0.443947 0.896053i \(-0.353578\pi\)
−0.554031 + 0.832496i \(0.686911\pi\)
\(558\) −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 0.996592 0.0824933i \(-0.0262883\pi\)
0.426855 + 0.904320i \(0.359622\pi\)
\(564\) −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 0.0243645 0.999703i \(-0.492244\pi\)
−0.853586 + 0.520952i \(0.825577\pi\)
\(578\) 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 \(0.142680\pi\)
−0.901211 + 0.433381i \(0.857320\pi\)
\(588\) −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 −0.861838 0.507184i \(-0.830686\pi\)
0.00831589 + 0.999965i \(0.497353\pi\)
\(594\) 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 −0.617957 0.786212i \(-0.712039\pi\)
0.371901 + 0.928272i \(0.378706\pi\)
\(608\) 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 0.193352 0.981129i \(-0.438064\pi\)
−0.753007 + 0.658012i \(0.771397\pi\)
\(614\) −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 \(-0.961462\pi\)
0.992680 0.120775i \(-0.0385381\pi\)
\(618\) 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 \(0.233884\pi\)
−0.741987 + 0.670415i \(0.766116\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.5885 + 9.00000i 0.612845 + 0.353827i 0.774078 0.633090i \(-0.218214\pi\)
−0.161233 + 0.986916i \(0.551547\pi\)
\(648\) −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 −0.549973 0.835182i \(-0.685362\pi\)
0.448303 + 0.893882i \(0.352029\pi\)
\(654\) −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 \(-0.811211\pi\)
0.829212 0.558934i \(-0.188789\pi\)
\(674\) 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 −0.935793 0.352549i \(-0.885315\pi\)
−0.162581 + 0.986695i \(0.551982\pi\)
\(678\) 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 0.934516 0.355920i \(-0.115832\pi\)
0.159022 + 0.987275i \(0.449166\pi\)
\(684\) −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 \(-0.922501\pi\)
0.970507 0.241072i \(-0.0774989\pi\)
\(728\) −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 −0.331463 0.943468i \(-0.607542\pi\)
0.651336 + 0.758789i \(0.274209\pi\)
\(734\) −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 \(-0.720049\pi\)
0.637542 0.770415i \(-0.279951\pi\)
\(744\) 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 \(0.242639\pi\)
−0.723269 + 0.690567i \(0.757361\pi\)
\(758\) 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 0.590527 0.807018i \(-0.298920\pi\)
−0.403634 + 0.914920i \(0.632253\pi\)
\(774\) 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 \(-0.983230\pi\)
−0.544911 0.838494i \(-0.683437\pi\)