Properties

Label 1050.2.o.c.499.1
Level $1050$
Weight $2$
Character 1050.499
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 499.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.499
Dual form 1050.2.o.c.949.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(0.866025 + 0.500000i) q^{12} +5.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.866025 + 0.500000i) q^{18} +(2.50000 - 4.33013i) q^{19} +(-0.500000 + 2.59808i) q^{21} +3.00000i q^{22} +(7.79423 + 4.50000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{26} -1.00000i q^{27} +(-2.59808 - 0.500000i) q^{28} +(5.00000 + 8.66025i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} +1.00000 q^{36} +(-0.866025 - 0.500000i) q^{37} +(-4.33013 + 2.50000i) q^{38} +(2.50000 + 4.33013i) q^{39} +9.00000 q^{41} +(1.73205 - 2.00000i) q^{42} +8.00000i q^{43} +(1.50000 - 2.59808i) q^{44} +(-4.50000 - 7.79423i) q^{46} +(2.59808 + 1.50000i) q^{47} +1.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(-4.33013 + 2.50000i) q^{52} +(-2.59808 + 1.50000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.00000 + 1.73205i) q^{56} -5.00000i q^{57} +(6.00000 + 10.3923i) q^{59} +(-4.00000 + 6.92820i) q^{61} -10.0000i q^{62} +(0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(-6.92820 + 4.00000i) q^{67} +9.00000 q^{69} -6.00000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(1.73205 - 1.00000i) q^{73} +(0.500000 + 0.866025i) q^{74} +5.00000 q^{76} +(7.79423 + 1.50000i) q^{77} -5.00000i q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-7.79423 - 4.50000i) q^{82} +(-2.50000 + 0.866025i) q^{84} +(4.00000 - 6.92820i) q^{86} +(-2.59808 + 1.50000i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-10.0000 - 8.66025i) q^{91} +9.00000i q^{92} +(8.66025 + 5.00000i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} -8.00000i q^{97} +(-2.59808 + 6.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} - 6q^{11} + 10q^{14} - 2q^{16} + 10q^{19} - 2q^{21} - 2q^{24} + 10q^{26} + 20q^{31} + 4q^{36} + 10q^{39} + 36q^{41} + 6q^{44} - 18q^{46} - 4q^{49} - 2q^{54} + 8q^{56} + 24q^{59} - 16q^{61} - 4q^{64} + 6q^{66} + 36q^{69} - 24q^{71} + 2q^{74} + 20q^{76} + 16q^{79} - 2q^{81} - 10q^{84} + 16q^{86} + 12q^{89} - 40q^{91} - 6q^{94} + 2q^{96} - 12q^{99} + O(q^{100}) \)

Character values

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

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

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
\(7\) −1.73205 + 2.00000i −0.654654 + 0.755929i
\(8\) 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 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) 5.00000i 1.38675i 0.720577 + 0.693375i \(0.243877\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 2.50000 0.866025i 0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) −0.500000 + 2.59808i −0.109109 + 0.566947i
\(22\) 3.00000i 0.639602i
\(23\) 7.79423 + 4.50000i 1.62521 + 0.938315i 0.985496 + 0.169701i \(0.0542803\pi\)
0.639713 + 0.768613i \(0.279053\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) 2.50000 4.33013i 0.490290 0.849208i
\(27\) 1.00000i 0.192450i
\(28\) −2.59808 0.500000i −0.490990 0.0944911i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 5.00000 + 8.66025i 0.898027 + 1.55543i 0.830014 + 0.557743i \(0.188333\pi\)
0.0680129 + 0.997684i \(0.478334\pi\)
\(32\) 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
\(37\) −0.866025 0.500000i −0.142374 0.0821995i 0.427121 0.904194i \(-0.359528\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(38\) −4.33013 + 2.50000i −0.702439 + 0.405554i
\(39\) 2.50000 + 4.33013i 0.400320 + 0.693375i
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 1.73205 2.00000i 0.267261 0.308607i
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) −4.50000 7.79423i −0.663489 1.14920i
\(47\) 2.59808 + 1.50000i 0.378968 + 0.218797i 0.677369 0.735643i \(-0.263120\pi\)
−0.298401 + 0.954441i \(0.596453\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) −4.33013 + 2.50000i −0.600481 + 0.346688i
\(53\) −2.59808 + 1.50000i −0.356873 + 0.206041i −0.667708 0.744423i \(-0.732725\pi\)
0.310835 + 0.950464i \(0.399391\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) 5.00000i 0.662266i
\(58\) 0 0
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 10.0000i 1.27000i
\(63\) 0.866025 + 2.50000i 0.109109 + 0.314970i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 1.50000 + 2.59808i 0.184637 + 0.319801i
\(67\) −6.92820 + 4.00000i −0.846415 + 0.488678i −0.859440 0.511237i \(-0.829187\pi\)
0.0130248 + 0.999915i \(0.495854\pi\)
\(68\) 0 0
\(69\) 9.00000 1.08347
\(70\) 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 \(-0.629326\pi\)
0.597924 + 0.801553i \(0.295992\pi\)
\(74\) 0.500000 + 0.866025i 0.0581238 + 0.100673i
\(75\) 0 0
\(76\) 5.00000 0.573539
\(77\) 7.79423 + 1.50000i 0.888235 + 0.170941i
\(78\) 5.00000i 0.566139i
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −7.79423 4.50000i −0.860729 0.496942i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −2.50000 + 0.866025i −0.272772 + 0.0944911i
\(85\) 0 0
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 0 0
\(88\) −2.59808 + 1.50000i −0.276956 + 0.159901i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) −10.0000 8.66025i −1.04828 0.907841i
\(92\) 9.00000i 0.938315i
\(93\) 8.66025 + 5.00000i 0.898027 + 0.518476i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 8.00000i 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) −2.59808 + 6.50000i −0.262445 + 0.656599i
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) −6.92820 4.00000i −0.682656 0.394132i 0.118199 0.992990i \(-0.462288\pi\)
−0.800855 + 0.598858i \(0.795621\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) 5.19615 + 3.00000i 0.502331 + 0.290021i 0.729676 0.683793i \(-0.239671\pi\)
−0.227345 + 0.973814i \(0.573004\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i \(0.0672444\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) −0.866025 2.50000i −0.0818317 0.236228i
\(113\) 18.0000i 1.69330i −0.532152 0.846649i \(-0.678617\pi\)
0.532152 0.846649i \(-0.321383\pi\)
\(114\) −2.50000 + 4.33013i −0.234146 + 0.405554i
\(115\) 0 0
\(116\) 0 0
\(117\) 4.33013 + 2.50000i 0.400320 + 0.231125i
\(118\) 12.0000i 1.10469i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 6.92820 4.00000i 0.627250 0.362143i
\(123\) 7.79423 4.50000i 0.702782 0.405751i
\(124\) −5.00000 + 8.66025i −0.449013 + 0.777714i
\(125\) 0 0
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) 13.0000i 1.15356i 0.816898 + 0.576782i \(0.195692\pi\)
−0.816898 + 0.576782i \(0.804308\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 4.00000 + 6.92820i 0.352180 + 0.609994i
\(130\) 0 0
\(131\) 4.50000 7.79423i 0.393167 0.680985i −0.599699 0.800226i \(-0.704713\pi\)
0.992865 + 0.119241i \(0.0380462\pi\)
\(132\) 3.00000i 0.261116i
\(133\) 4.33013 + 12.5000i 0.375470 + 1.08389i
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 0 0
\(137\) 15.5885 9.00000i 1.33181 0.768922i 0.346235 0.938148i \(-0.387460\pi\)
0.985577 + 0.169226i \(0.0541268\pi\)
\(138\) −7.79423 4.50000i −0.663489 0.383065i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 5.19615 + 3.00000i 0.436051 + 0.251754i
\(143\) 12.9904 7.50000i 1.08631 0.627182i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −4.33013 5.50000i −0.357143 0.453632i
\(148\) 1.00000i 0.0821995i
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0 0
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) −4.33013 2.50000i −0.351220 0.202777i
\(153\) 0 0
\(154\) −6.00000 5.19615i −0.483494 0.418718i
\(155\) 0 0
\(156\) −2.50000 + 4.33013i −0.200160 + 0.346688i
\(157\) −4.33013 + 2.50000i −0.345582 + 0.199522i −0.662738 0.748852i \(-0.730606\pi\)
0.317156 + 0.948373i \(0.397272\pi\)
\(158\) −6.92820 + 4.00000i −0.551178 + 0.318223i
\(159\) −1.50000 + 2.59808i −0.118958 + 0.206041i
\(160\) 0 0
\(161\) −22.5000 + 7.79423i −1.77325 + 0.614271i
\(162\) 1.00000i 0.0785674i
\(163\) 13.8564 + 8.00000i 1.08532 + 0.626608i 0.932326 0.361619i \(-0.117776\pi\)
0.152992 + 0.988227i \(0.451109\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) 0 0
\(166\) 0 0
\(167\) 3.00000i 0.232147i 0.993241 + 0.116073i \(0.0370308\pi\)
−0.993241 + 0.116073i \(0.962969\pi\)
\(168\) 2.59808 + 0.500000i 0.200446 + 0.0385758i
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −2.50000 4.33013i −0.191180 0.331133i
\(172\) −6.92820 + 4.00000i −0.528271 + 0.304997i
\(173\) −7.79423 4.50000i −0.592584 0.342129i 0.173534 0.984828i \(-0.444481\pi\)
−0.766119 + 0.642699i \(0.777815\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) 10.3923 + 6.00000i 0.781133 + 0.450988i
\(178\) −5.19615 + 3.00000i −0.389468 + 0.224860i
\(179\) −7.50000 12.9904i −0.560576 0.970947i −0.997446 0.0714220i \(-0.977246\pi\)
0.436870 0.899525i \(-0.356087\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 4.33013 + 12.5000i 0.320970 + 0.926562i
\(183\) 8.00000i 0.591377i
\(184\) 4.50000 7.79423i 0.331744 0.574598i
\(185\) 0 0
\(186\) −5.00000 8.66025i −0.366618 0.635001i
\(187\) 0 0
\(188\) 3.00000i 0.218797i
\(189\) 2.00000 + 1.73205i 0.145479 + 0.125988i
\(190\) 0 0
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −8.66025 + 5.00000i −0.623379 + 0.359908i −0.778183 0.628037i \(-0.783859\pi\)
0.154805 + 0.987945i \(0.450525\pi\)
\(194\) −4.00000 + 6.92820i −0.287183 + 0.497416i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 15.0000i 1.06871i −0.845262 0.534353i \(-0.820555\pi\)
0.845262 0.534353i \(-0.179445\pi\)
\(198\) 2.59808 + 1.50000i 0.184637 + 0.106600i
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 0 0
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 7.79423 4.50000i 0.541736 0.312772i
\(208\) −4.33013 2.50000i −0.300240 0.173344i
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) −2.59808 1.50000i −0.178437 0.103020i
\(213\) −5.19615 + 3.00000i −0.356034 + 0.205557i
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −25.9808 5.00000i −1.76369 0.339422i
\(218\) 14.0000i 0.948200i
\(219\) 1.00000 1.73205i 0.0675737 0.117041i
\(220\) 0 0
\(221\) 0 0
\(222\) 0.866025 + 0.500000i 0.0581238 + 0.0335578i
\(223\) 28.0000i 1.87502i −0.347960 0.937509i \(-0.613126\pi\)
0.347960 0.937509i \(-0.386874\pi\)
\(224\) −0.500000 + 2.59808i −0.0334077 + 0.173591i
\(225\) 0 0
\(226\) −9.00000 + 15.5885i −0.598671 + 1.03693i
\(227\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) 4.33013 2.50000i 0.286770 0.165567i
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) 0 0
\(231\) 7.50000 2.59808i 0.493464 0.170941i
\(232\) 0 0
\(233\) 5.19615 + 3.00000i 0.340411 + 0.196537i 0.660454 0.750867i \(-0.270364\pi\)
−0.320043 + 0.947403i \(0.603697\pi\)
\(234\) −2.50000 4.33013i −0.163430 0.283069i
\(235\) 0 0
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) 8.00000i 0.519656i
\(238\) 0 0
\(239\) −30.0000 −1.94054 −0.970269 0.242028i \(-0.922188\pi\)
−0.970269 + 0.242028i \(0.922188\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) −1.73205 + 1.00000i −0.111340 + 0.0642824i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) 21.6506 + 12.5000i 1.37760 + 0.795356i
\(248\) 8.66025 5.00000i 0.549927 0.317500i
\(249\) 0 0
\(250\) 0 0
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) −1.73205 + 2.00000i −0.109109 + 0.125988i
\(253\) 27.0000i 1.69748i
\(254\) 6.50000 11.2583i 0.407846 0.706410i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.3923 6.00000i −0.648254 0.374270i 0.139533 0.990217i \(-0.455440\pi\)
−0.787787 + 0.615948i \(0.788773\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 2.50000 0.866025i 0.155342 0.0538122i
\(260\) 0 0
\(261\) 0 0
\(262\) −7.79423 + 4.50000i −0.481529 + 0.278011i
\(263\) −20.7846 + 12.0000i −1.28163 + 0.739952i −0.977147 0.212565i \(-0.931818\pi\)
−0.304487 + 0.952517i \(0.598485\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 0 0
\(266\) 2.50000 12.9904i 0.153285 0.796491i
\(267\) 6.00000i 0.367194i
\(268\) −6.92820 4.00000i −0.423207 0.244339i
\(269\) 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 0 0
\(273\) −12.9904 2.50000i −0.786214 0.151307i
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 4.50000 + 7.79423i 0.270868 + 0.469157i
\(277\) −22.5167 + 13.0000i −1.35290 + 0.781094i −0.988654 0.150210i \(-0.952005\pi\)
−0.364241 + 0.931305i \(0.618672\pi\)
\(278\) 17.3205 + 10.0000i 1.03882 + 0.599760i
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) −21.0000 −1.25275 −0.626377 0.779520i \(-0.715463\pi\)
−0.626377 + 0.779520i \(0.715463\pi\)
\(282\) −2.59808 1.50000i −0.154713 0.0893237i
\(283\) −19.0526 + 11.0000i −1.13256 + 0.653882i −0.944577 0.328291i \(-0.893527\pi\)
−0.187980 + 0.982173i \(0.560194\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0 0
\(286\) −15.0000 −0.886969
\(287\) −15.5885 + 18.0000i −0.920158 + 1.06251i
\(288\) 1.00000i 0.0589256i
\(289\) −8.50000 + 14.7224i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) −4.00000 6.92820i −0.234484 0.406138i
\(292\) 1.73205 + 1.00000i 0.101361 + 0.0585206i
\(293\) 21.0000i 1.22683i −0.789760 0.613417i \(-0.789795\pi\)
0.789760 0.613417i \(-0.210205\pi\)
\(294\) 1.00000 + 6.92820i 0.0583212 + 0.404061i
\(295\) 0 0
\(296\) −0.500000 + 0.866025i −0.0290619 + 0.0503367i
\(297\) −2.59808 + 1.50000i −0.150756 + 0.0870388i
\(298\) 0 0
\(299\) −22.5000 + 38.9711i −1.30121 + 2.25376i
\(300\) 0 0
\(301\) −16.0000 13.8564i −0.922225 0.798670i
\(302\) 10.0000i 0.575435i
\(303\) 0 0
\(304\) 2.50000 + 4.33013i 0.143385 + 0.248350i
\(305\) 0 0
\(306\) 0 0
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 2.59808 + 7.50000i 0.148039 + 0.427352i
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i \(-0.0561621\pi\)
−0.644246 + 0.764818i \(0.722829\pi\)
\(312\) 4.33013 2.50000i 0.245145 0.141535i
\(313\) 3.46410 + 2.00000i 0.195803 + 0.113047i 0.594696 0.803951i \(-0.297272\pi\)
−0.398894 + 0.916997i \(0.630606\pi\)
\(314\) 5.00000 0.282166
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −15.5885 9.00000i −0.875535 0.505490i −0.00635137 0.999980i \(-0.502022\pi\)
−0.869184 + 0.494489i \(0.835355\pi\)
\(318\) 2.59808 1.50000i 0.145693 0.0841158i
\(319\) 0 0
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 23.3827 + 4.50000i 1.30307 + 0.250775i
\(323\) 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
\(328\) 9.00000i 0.496942i
\(329\) −7.50000 + 2.59808i −0.413488 + 0.143237i
\(330\) 0 0
\(331\) −5.50000 + 9.52628i −0.302307 + 0.523612i −0.976658 0.214799i \(-0.931090\pi\)
0.674351 + 0.738411i \(0.264424\pi\)
\(332\) 0 0
\(333\) −0.866025 + 0.500000i −0.0474579 + 0.0273998i
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) 0 0
\(336\) −2.00000 1.73205i −0.109109 0.0944911i
\(337\) 20.0000i 1.08947i −0.838608 0.544735i \(-0.816630\pi\)
0.838608 0.544735i \(-0.183370\pi\)
\(338\) 10.3923 + 6.00000i 0.565267 + 0.326357i
\(339\) −9.00000 15.5885i −0.488813 0.846649i
\(340\) 0 0
\(341\) 15.0000 25.9808i 0.812296 1.40694i
\(342\) 5.00000i 0.270369i
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 4.50000 + 7.79423i 0.241921 + 0.419020i
\(347\) −25.9808 + 15.0000i −1.39472 + 0.805242i −0.993833 0.110885i \(-0.964631\pi\)
−0.400887 + 0.916127i \(0.631298\pi\)
\(348\) 0 0
\(349\) 28.0000 1.49881 0.749403 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) −2.59808 1.50000i −0.138478 0.0799503i
\(353\) 20.7846 12.0000i 1.10625 0.638696i 0.168397 0.985719i \(-0.446141\pi\)
0.937856 + 0.347024i \(0.112808\pi\)
\(354\) −6.00000 10.3923i −0.318896 0.552345i
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 15.0000i 0.792775i
\(359\) 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i \(-0.730769\pi\)
0.979791 + 0.200026i \(0.0641026\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) −6.92820 4.00000i −0.364138 0.210235i
\(363\) 2.00000i 0.104973i
\(364\) 2.50000 12.9904i 0.131036 0.680881i
\(365\) 0 0
\(366\) 4.00000 6.92820i 0.209083 0.362143i
\(367\) 16.4545 9.50000i 0.858917 0.495896i −0.00473247 0.999989i \(-0.501506\pi\)
0.863649 + 0.504093i \(0.168173\pi\)
\(368\) −7.79423 + 4.50000i −0.406302 + 0.234579i
\(369\) 4.50000 7.79423i 0.234261 0.405751i
\(370\) 0 0
\(371\) 1.50000 7.79423i 0.0778761 0.404656i
\(372\) 10.0000i 0.518476i
\(373\) 8.66025 + 5.00000i 0.448411 + 0.258890i 0.707159 0.707055i \(-0.249977\pi\)
−0.258748 + 0.965945i \(0.583310\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) 0 0
\(378\) −0.866025 2.50000i −0.0445435 0.128586i
\(379\) 19.0000 0.975964 0.487982 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(380\) 0 0
\(381\) 6.50000 + 11.2583i 0.333005 + 0.576782i
\(382\) 15.5885 9.00000i 0.797575 0.460480i
\(383\) −23.3827 13.5000i −1.19480 0.689818i −0.235408 0.971897i \(-0.575643\pi\)
−0.959391 + 0.282079i \(0.908976\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 6.92820 + 4.00000i 0.352180 + 0.203331i
\(388\) 6.92820 4.00000i 0.351726 0.203069i
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −6.92820 + 1.00000i −0.349927 + 0.0505076i
\(393\) 9.00000i 0.453990i
\(394\) −7.50000 + 12.9904i −0.377845 + 0.654446i
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) 12.1244 + 7.00000i 0.608504 + 0.351320i 0.772380 0.635161i \(-0.219066\pi\)
−0.163876 + 0.986481i \(0.552400\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 10.0000 + 8.66025i 0.500626 + 0.433555i
\(400\) 0 0
\(401\) −7.50000 + 12.9904i −0.374532 + 0.648709i −0.990257 0.139253i \(-0.955530\pi\)
0.615725 + 0.787961i \(0.288863\pi\)
\(402\) 6.92820 4.00000i 0.345547 0.199502i
\(403\) −43.3013 + 25.0000i −2.15699 + 1.24534i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) 1.00000 + 1.73205i 0.0494468 + 0.0856444i 0.889689 0.456566i \(-0.150921\pi\)
−0.840243 + 0.542211i \(0.817588\pi\)
\(410\) 0 0
\(411\) 9.00000 15.5885i 0.443937 0.768922i
\(412\) 8.00000i 0.394132i
\(413\) −31.1769 6.00000i −1.53412 0.295241i
\(414\) −9.00000 −0.442326
\(415\) 0 0
\(416\) 2.50000 + 4.33013i 0.122573 + 0.212302i
\(417\) −17.3205 + 10.0000i −0.848189 + 0.489702i
\(418\) 12.9904 + 7.50000i 0.635380 + 0.366837i
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 14.0000 0.682318 0.341159 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) −4.33013 2.50000i −0.210787 0.121698i
\(423\) 2.59808 1.50000i 0.126323 0.0729325i
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) −6.92820 20.0000i −0.335279 0.967868i
\(428\) 6.00000i 0.290021i
\(429\) 7.50000 12.9904i 0.362103 0.627182i
\(430\) 0 0
\(431\) 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i \(0.0295076\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 16.0000i 0.768911i −0.923144 0.384455i \(-0.874389\pi\)
0.923144 0.384455i \(-0.125611\pi\)
\(434\) 20.0000 + 17.3205i 0.960031 + 0.831411i
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 38.9711 22.5000i 1.86424 1.07632i
\(438\) −1.73205 + 1.00000i −0.0827606 + 0.0477818i
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 0 0
\(443\) 20.7846 + 12.0000i 0.987507 + 0.570137i 0.904528 0.426414i \(-0.140223\pi\)
0.0829786 + 0.996551i \(0.473557\pi\)
\(444\) −0.500000 0.866025i −0.0237289 0.0410997i
\(445\) 0 0
\(446\) −14.0000 + 24.2487i −0.662919 + 1.14821i
\(447\) 0 0
\(448\) 1.73205 2.00000i 0.0818317 0.0944911i
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) −13.5000 23.3827i −0.635690 1.10105i
\(452\) 15.5885 9.00000i 0.733219 0.423324i
\(453\) 8.66025 + 5.00000i 0.406894 + 0.234920i
\(454\) 0 0
\(455\) 0 0
\(456\) −5.00000 −0.234146
\(457\) −8.66025 5.00000i −0.405110 0.233890i 0.283577 0.958950i \(-0.408479\pi\)
−0.688686 + 0.725059i \(0.741812\pi\)
\(458\) −12.1244 + 7.00000i −0.566534 + 0.327089i
\(459\) 0 0
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) −7.79423 1.50000i −0.362620 0.0697863i
\(463\) 1.00000i 0.0464739i −0.999730 0.0232370i \(-0.992603\pi\)
0.999730 0.0232370i \(-0.00739722\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 5.00000i 0.231125i
\(469\) 4.00000 20.7846i 0.184703 0.959744i
\(470\) 0 0
\(471\) −2.50000 + 4.33013i −0.115194 + 0.199522i
\(472\) 10.3923 6.00000i 0.478345 0.276172i
\(473\) 20.7846 12.0000i 0.955677 0.551761i
\(474\) −4.00000 + 6.92820i −0.183726 + 0.318223i
\(475\) 0 0
\(476\) 0 0
\(477\) 3.00000i 0.137361i
\(478\) 25.9808 + 15.0000i 1.18833 + 0.686084i
\(479\) −9.00000 15.5885i −0.411220 0.712255i 0.583803 0.811895i \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) 0 0
\(481\) 2.50000 4.33013i 0.113990 0.197437i
\(482\) 1.00000i 0.0455488i
\(483\) −15.5885 + 18.0000i −0.709299 + 0.819028i
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 34.6410 20.0000i 1.56973 0.906287i 0.573535 0.819181i \(-0.305572\pi\)
0.996199 0.0871056i \(-0.0277618\pi\)
\(488\) 6.92820 + 4.00000i 0.313625 + 0.181071i
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 7.79423 + 4.50000i 0.351391 + 0.202876i
\(493\) 0 0
\(494\) −12.5000 21.6506i −0.562402 0.974108i
\(495\) 0 0
\(496\) −10.0000 −0.449013
\(497\) 10.3923 12.0000i 0.466159 0.538274i
\(498\) 0 0
\(499\) −8.00000 + 13.8564i −0.358129 + 0.620298i −0.987648 0.156687i \(-0.949919\pi\)
0.629519 + 0.776985i \(0.283252\pi\)
\(500\) 0 0
\(501\) 1.50000 + 2.59808i 0.0670151 + 0.116073i
\(502\) −7.79423 4.50000i −0.347873 0.200845i
\(503\) 12.0000i 0.535054i −0.963550 0.267527i \(-0.913794\pi\)
0.963550 0.267527i \(-0.0862064\pi\)
\(504\) 2.50000 0.866025i 0.111359 0.0385758i
\(505\) 0 0
\(506\) −13.5000 + 23.3827i −0.600148 + 1.03949i
\(507\) −10.3923 + 6.00000i −0.461538 + 0.266469i
\(508\) −11.2583 + 6.50000i −0.499508 + 0.288391i
\(509\) 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) 0 0
\(511\) −1.00000 + 5.19615i −0.0442374 + 0.229864i
\(512\) 1.00000i 0.0441942i
\(513\) −4.33013 2.50000i −0.191180 0.110378i
\(514\) 6.00000 + 10.3923i 0.264649 + 0.458385i
\(515\) 0 0
\(516\) −4.00000 + 6.92820i −0.176090 + 0.304997i
\(517\) 9.00000i 0.395820i
\(518\) −2.59808 0.500000i −0.114153 0.0219687i
\(519\) −9.00000 −0.395056
\(520\) 0 0
\(521\) −13.5000 23.3827i −0.591446 1.02441i −0.994038 0.109035i \(-0.965224\pi\)
0.402592 0.915379i \(-0.368109\pi\)
\(522\) 0 0
\(523\) 19.0526 + 11.0000i 0.833110 + 0.480996i 0.854916 0.518766i \(-0.173608\pi\)
−0.0218062 + 0.999762i \(0.506942\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 2.59808 1.50000i 0.113067 0.0652791i
\(529\) 29.0000 + 50.2295i 1.26087 + 2.18389i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) −8.66025 + 10.0000i −0.375470 + 0.433555i
\(533\) 45.0000i 1.94917i
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 0 0
\(536\) 4.00000 + 6.92820i 0.172774 + 0.299253i
\(537\) −12.9904 7.50000i −0.560576 0.323649i
\(538\) 12.0000i 0.517357i
\(539\) −16.5000 + 12.9904i −0.710705 + 0.559535i
\(540\) 0 0
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) −13.8564 + 8.00000i −0.595184 + 0.343629i
\(543\) 6.92820 4.00000i 0.297318 0.171656i
\(544\) 0 0
\(545\) 0 0
\(546\) 10.0000 + 8.66025i 0.427960 + 0.370625i
\(547\) 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
\(549\) 4.00000 + 6.92820i 0.170716 + 0.295689i
\(550\) 0 0
\(551\) 0 0
\(552\) 9.00000i 0.383065i
\(553\) 6.92820 + 20.0000i 0.294617 + 0.850487i
\(554\) 26.0000 1.10463
\(555\) 0 0
\(556\) −10.0000 17.3205i −0.424094 0.734553i
\(557\) −33.7750 + 19.5000i −1.43109 + 0.826242i −0.997204 0.0747252i \(-0.976192\pi\)
−0.433888 + 0.900967i \(0.642859\pi\)
\(558\) −8.66025 5.00000i −0.366618 0.211667i
\(559\) −40.0000 −1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) 18.1865 + 10.5000i 0.767153 + 0.442916i
\(563\) −5.19615 + 3.00000i −0.218992 + 0.126435i −0.605483 0.795858i \(-0.707020\pi\)
0.386492 + 0.922293i \(0.373687\pi\)
\(564\) 1.50000 + 2.59808i 0.0631614 + 0.109399i
\(565\) 0 0
\(566\) 22.0000 0.924729
\(567\) 2.59808 + 0.500000i 0.109109 + 0.0209980i
\(568\) 6.00000i 0.251754i
\(569\) 13.5000 23.3827i 0.565949 0.980253i −0.431011 0.902347i \(-0.641843\pi\)
0.996961 0.0779066i \(-0.0248236\pi\)
\(570\) 0 0
\(571\) 8.00000 + 13.8564i 0.334790 + 0.579873i 0.983444 0.181210i \(-0.0580014\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) 12.9904 + 7.50000i 0.543155 + 0.313591i
\(573\) 18.0000i 0.751961i
\(574\) 22.5000 7.79423i 0.939132 0.325325i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 19.0526 11.0000i 0.793168 0.457936i −0.0479084 0.998852i \(-0.515256\pi\)
0.841077 + 0.540916i \(0.181922\pi\)
\(578\) 14.7224 8.50000i 0.612372 0.353553i
\(579\) −5.00000 + 8.66025i −0.207793 + 0.359908i
\(580\) 0 0
\(581\) 0 0
\(582\) 8.00000i 0.331611i
\(583\) 7.79423 + 4.50000i 0.322804 + 0.186371i
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) 0 0
\(586\) −10.5000 + 18.1865i −0.433751 + 0.751279i
\(587\) 42.0000i 1.73353i 0.498721 + 0.866763i \(0.333803\pi\)
−0.498721 + 0.866763i \(0.666197\pi\)
\(588\) 2.59808 6.50000i 0.107143 0.268055i
\(589\) 50.0000 2.06021
\(590\) 0 0
\(591\) −7.50000 12.9904i −0.308509 0.534353i
\(592\) 0.866025 0.500000i 0.0355934 0.0205499i
\(593\) −20.7846 12.0000i −0.853522 0.492781i 0.00831589 0.999965i \(-0.497353\pi\)
−0.861838 + 0.507184i \(0.830686\pi\)
\(594\) 3.00000 0.123091
\(595\) 0 0
\(596\) 0 0
\(597\) −13.8564 8.00000i −0.567105 0.327418i
\(598\) 38.9711 22.5000i 1.59365 0.920093i
\(599\) 9.00000 + 15.5885i 0.367730 + 0.636927i 0.989210 0.146503i \(-0.0468017\pi\)
−0.621480 + 0.783430i \(0.713468\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 6.92820 + 20.0000i 0.282372 + 0.815139i
\(603\) 8.00000i 0.325785i
\(604\) −5.00000 + 8.66025i −0.203447 + 0.352381i
\(605\) 0 0
\(606\) 0 0
\(607\) −21.6506 12.5000i −0.878772 0.507359i −0.00851879 0.999964i \(-0.502712\pi\)
−0.870253 + 0.492604i \(0.836045\pi\)
\(608\) 5.00000i 0.202777i
\(609\) 0 0
\(610\) 0 0
\(611\) −7.50000 + 12.9904i −0.303418 + 0.525535i
\(612\) 0 0
\(613\) 9.52628 5.50000i 0.384763 0.222143i −0.295126 0.955458i \(-0.595362\pi\)
0.679888 + 0.733316i \(0.262028\pi\)
\(614\) 14.0000 24.2487i 0.564994 0.978598i
\(615\) 0 0
\(616\) 1.50000 7.79423i 0.0604367 0.314038i
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 6.92820 + 4.00000i 0.278693 + 0.160904i
\(619\) 14.5000 + 25.1147i 0.582804 + 1.00945i 0.995145 + 0.0984169i \(0.0313779\pi\)
−0.412341 + 0.911030i \(0.635289\pi\)
\(620\) 0 0
\(621\) 4.50000 7.79423i 0.180579 0.312772i
\(622\) 12.0000i 0.481156i
\(623\) 5.19615 + 15.0000i 0.208179 + 0.600962i
\(624\) −5.00000 −0.200160
\(625\) 0 0
\(626\) −2.00000 3.46410i −0.0799361 0.138453i
\(627\) −12.9904 + 7.50000i −0.518786 + 0.299521i
\(628\) −4.33013 2.50000i −0.172791 0.0997609i
\(629\) 0 0
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) −6.92820 4.00000i −0.275589 0.159111i
\(633\) 4.33013 2.50000i 0.172107 0.0993661i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 0 0
\(636\) −3.00000 −0.118958
\(637\) 34.6410 5.00000i 1.37253 0.198107i
\(638\) 0 0
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) −5.19615 3.00000i −0.205076 0.118401i
\(643\) 34.0000i 1.34083i −0.741987 0.670415i \(-0.766116\pi\)
0.741987 0.670415i \(-0.233884\pi\)
\(644\) −18.0000 15.5885i −0.709299 0.614271i
\(645\) 0 0
\(646\) 0 0
\(647\) 7.79423 4.50000i 0.306423 0.176913i −0.338902 0.940822i \(-0.610055\pi\)
0.645325 + 0.763908i \(0.276722\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 18.0000 31.1769i 0.706562 1.22380i
\(650\) 0 0
\(651\) −25.0000 + 8.66025i −0.979827 + 0.339422i
\(652\) 16.0000i 0.626608i
\(653\) −33.7750 19.5000i −1.32172 0.763094i −0.337715 0.941248i \(-0.609654\pi\)
−0.984003 + 0.178154i \(0.942987\pi\)
\(654\) −7.00000 12.1244i −0.273722 0.474100i
\(655\) 0 0
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) 2.00000i 0.0780274i
\(658\) 7.79423 + 1.50000i 0.303851 + 0.0584761i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 20.0000 + 34.6410i 0.777910 + 1.34738i 0.933144 + 0.359502i \(0.117053\pi\)
−0.155235 + 0.987878i \(0.549613\pi\)
\(662\) 9.52628 5.50000i 0.370249 0.213764i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) −2.59808 + 1.50000i −0.100523 + 0.0580367i
\(669\) −14.0000 24.2487i −0.541271 0.937509i
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) 0.866025 + 2.50000i 0.0334077 + 0.0964396i
\(673\) 20.0000i 0.770943i 0.922720 + 0.385472i \(0.125961\pi\)
−0.922720 + 0.385472i \(0.874039\pi\)
\(674\) −10.0000 + 17.3205i −0.385186 + 0.667161i
\(675\) 0 0
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) 2.59808 + 1.50000i 0.0998522 + 0.0576497i 0.549095 0.835760i \(-0.314973\pi\)
−0.449242 + 0.893410i \(0.648306\pi\)
\(678\) 18.0000i 0.691286i
\(679\) 16.0000 + 13.8564i 0.614024 + 0.531760i
\(680\) 0 0
\(681\) 0 0
\(682\) −25.9808 + 15.0000i −0.994855 + 0.574380i
\(683\) −10.3923 + 6.00000i −0.397650 + 0.229584i −0.685470 0.728101i \(-0.740403\pi\)
0.287819 + 0.957685i \(0.407070\pi\)
\(684\) 2.50000 4.33013i 0.0955899 0.165567i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 14.0000i 0.534133i
\(688\) −6.92820 4.00000i −0.264135 0.152499i
\(689\) −7.50000 12.9904i −0.285727 0.494894i
\(690\) 0 0
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) 9.00000i 0.342129i
\(693\) 5.19615 6.00000i 0.197386 0.227921i
\(694\) 30.0000 1.13878
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −24.2487 14.0000i −0.917827 0.529908i
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) −4.33013 2.50000i −0.163430 0.0943564i
\(703\) −4.33013 + 2.50000i −0.163314 + 0.0942893i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) 12.0000i 0.450988i
\(709\) −14.0000 + 24.2487i −0.525781 + 0.910679i 0.473768 + 0.880650i \(0.342894\pi\)
−0.999549 + 0.0300298i \(0.990440\pi\)
\(710\) 0 0
\(711\) −4.00000 6.92820i −0.150012 0.259828i
\(712\) −5.19615 3.00000i −0.194734 0.112430i
\(713\) 90.0000i 3.37053i
\(714\) 0 0
\(715\) 0 0
\(716\) 7.50000 12.9904i 0.280288 0.485473i
\(717\) −25.9808 + 15.0000i −0.970269 + 0.560185i
\(718\) −10.3923 + 6.00000i −0.387837 + 0.223918i
\(719\) 9.00000 15.5885i 0.335643 0.581351i −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 0 0
\(721\) 20.0000 6.92820i 0.744839 0.258020i
\(722\) 6.00000i 0.223297i
\(723\) 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
\(727\) 23.0000i 0.853023i −0.904482 0.426511i \(-0.859742\pi\)
0.904482 0.426511i \(-0.140258\pi\)
\(728\) −8.66025 + 10.0000i −0.320970 + 0.370625i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) −6.92820 + 4.00000i −0.256074 + 0.147844i
\(733\) 0.866025 + 0.500000i 0.0319874 + 0.0184679i 0.515908 0.856644i \(-0.327454\pi\)
−0.483921 + 0.875112i \(0.660788\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) 9.00000 0.331744
\(737\) 20.7846 + 12.0000i 0.765611 + 0.442026i
\(738\) −7.79423 + 4.50000i −0.286910 + 0.165647i
\(739\) 2.50000 + 4.33013i 0.0919640 + 0.159286i 0.908337 0.418238i \(-0.137352\pi\)
−0.816373 + 0.577524i \(0.804019\pi\)
\(740\) 0 0
\(741\) 25.0000 0.918398
\(742\) −5.19615 + 6.00000i −0.190757 + 0.220267i
\(743\) 39.0000i 1.43077i −0.698730 0.715386i \(-0.746251\pi\)
0.698730 0.715386i \(-0.253749\pi\)
\(744\) 5.00000 8.66025i 0.183309 0.317500i
\(745\) 0 0
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) 0 0
\(748\) 0 0
\(749\) −15.0000 + 5.19615i −0.548088 + 0.189863i
\(750\) 0 0
\(751\) −1.00000 + 1.73205i −0.0364905 + 0.0632034i −0.883694 0.468065i \(-0.844951\pi\)
0.847203 + 0.531269i \(0.178285\pi\)
\(752\) −2.59808 + 1.50000i −0.0947421 + 0.0546994i
\(753\) 7.79423 4.50000i 0.284037 0.163989i
\(754\) 0 0
\(755\) 0 0
\(756\) −0.500000 + 2.59808i −0.0181848 + 0.0944911i
\(757\) 2.00000i 0.0726912i −0.999339 0.0363456i \(-0.988428\pi\)
0.999339 0.0363456i \(-0.0115717\pi\)
\(758\) −16.4545 9.50000i −0.597654 0.345056i
\(759\) −13.5000 23.3827i −0.490019 0.848738i
\(760\) 0 0
\(761\) 16.5000 28.5788i 0.598125 1.03598i −0.394973 0.918693i \(-0.629246\pi\)
0.993098 0.117289i \(-0.0374205\pi\)
\(762\) 13.0000i 0.470940i
\(763\) −36.3731 7.00000i −1.31679 0.253417i
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) 13.5000 + 23.3827i 0.487775 + 0.844851i
\(767\) −51.9615 + 30.0000i −1.87622 + 1.08324i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) −35.0000 −1.26213 −0.631066 0.775729i \(-0.717382\pi\)
−0.631066 + 0.775729i \(0.717382\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) −8.66025 5.00000i −0.311689 0.179954i
\(773\) 28.5788 16.5000i 1.02791 0.593464i 0.111524 0.993762i \(-0.464427\pi\)
0.916385 + 0.400298i \(0.131093\pi\)
\(774\) −4.00000 6.92820i −0.143777 0.249029i
\(775\) 0 0
\(776\) −8.00000 −0.287183
\(777\) 1.73205 2.00000i 0.0621370 0.0717496i
\(778\) 6.00000i 0.215110i
\(779\) 22.5000 38.9711i 0.806146 1.39629i
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) 0 0
\(783\) 0 0
\(784\) 6.50000 + 2.59808i 0.232143 + 0.0927884i
\(785\) 0 0
\(786\) −4.50000 + 7.79423i −0.160510 + 0.278011i
\(787\) −12.1244 + 7.00000i −0.432187 + 0.249523i −0.700278 0.713871i \(-0.746941\pi\)
0.268091 + 0.963394i \(0.413607\pi\)