Properties

Label 1050.2.o.c.499.2
Level $1050$
Weight $2$
Character 1050.499
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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 499.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.499
Dual form 1050.2.o.c.949.2

$q$-expansion

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

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 \(-0.756123\pi\)
0.720577 0.693375i \(-0.243877\pi\)
\(14\) 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 \(-0.945720\pi\)
−0.639713 0.768613i \(-0.720947\pi\)
\(24\) −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 0.569495 0.821995i \(-0.307139\pi\)
−0.427121 + 0.904194i \(0.640472\pi\)
\(38\) 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 \(-0.791172\pi\)
0.792406 0.609994i \(-0.208828\pi\)
\(44\) 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 0.298401 0.954441i \(-0.403547\pi\)
−0.677369 + 0.735643i \(0.736880\pi\)
\(48\) 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 −0.310835 0.950464i \(-0.600609\pi\)
0.667708 + 0.744423i \(0.267275\pi\)
\(54\) −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 −0.0130248 0.999915i \(-0.504146\pi\)
0.859440 + 0.511237i \(0.170813\pi\)
\(68\) 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 −0.597924 0.801553i \(-0.704008\pi\)
0.395203 + 0.918594i \(0.370674\pi\)
\(74\) 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 \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 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 0.800855 0.598858i \(-0.204379\pi\)
−0.118199 + 0.992990i \(0.537712\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) −5.19615 3.00000i −0.502331 0.290021i 0.227345 0.973814i \(-0.426996\pi\)
−0.729676 + 0.683793i \(0.760329\pi\)
\(108\) −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 \(0.321383\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) −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 \(-0.804308\pi\)
0.816898 0.576782i \(-0.195692\pi\)
\(128\) −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 −0.985577 0.169226i \(-0.945873\pi\)
−0.346235 + 0.938148i \(0.612540\pi\)
\(138\) 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 −0.317156 0.948373i \(-0.602728\pi\)
0.662738 + 0.748852i \(0.269394\pi\)
\(158\) 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 −0.152992 0.988227i \(-0.548891\pi\)
−0.932326 + 0.361619i \(0.882224\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) 0 0
\(166\) 0 0
\(167\) 3.00000i 0.232147i −0.993241 0.116073i \(-0.962969\pi\)
0.993241 0.116073i \(-0.0370308\pi\)
\(168\) −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 0.766119 0.642699i \(-0.222185\pi\)
−0.173534 + 0.984828i \(0.555519\pi\)
\(174\) 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 −0.154805 0.987945i \(-0.549475\pi\)
0.778183 + 0.628037i \(0.216141\pi\)
\(194\) −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 \(0.179445\pi\)
−0.845262 + 0.534353i \(0.820555\pi\)
\(198\) −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 \(0.386874\pi\)
−0.347960 + 0.937509i \(0.613126\pi\)
\(224\) −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 0.320043 0.947403i \(-0.396303\pi\)
−0.660454 + 0.750867i \(0.729636\pi\)
\(234\) −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 0.787787 0.615948i \(-0.211227\pi\)
−0.139533 + 0.990217i \(0.544560\pi\)
\(258\) 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 0.304487 0.952517i \(-0.401515\pi\)
0.977147 + 0.212565i \(0.0681817\pi\)
\(264\) −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 0.364241 0.931305i \(-0.381328\pi\)
0.988654 + 0.150210i \(0.0479951\pi\)
\(278\) −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 0.187980 0.982173i \(-0.439806\pi\)
0.944577 + 0.328291i \(0.106473\pi\)
\(284\) −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 \(0.210205\pi\)
−0.789760 + 0.613417i \(0.789795\pi\)
\(294\) 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 \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) −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 0.398894 0.916997i \(-0.369394\pi\)
−0.594696 + 0.803951i \(0.702728\pi\)
\(314\) 5.00000 0.282166
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 15.5885 + 9.00000i 0.875535 + 0.505490i 0.869184 0.494489i \(-0.164645\pi\)
0.00635137 + 0.999980i \(0.497978\pi\)
\(318\) −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 \(0.183370\pi\)
−0.838608 + 0.544735i \(0.816630\pi\)
\(338\) −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 0.400887 0.916127i \(-0.368702\pi\)
0.993833 + 0.110885i \(0.0353686\pi\)
\(348\) 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 −0.937856 0.347024i \(-0.887192\pi\)
−0.168397 + 0.985719i \(0.553859\pi\)
\(354\) −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 −0.863649 0.504093i \(-0.831827\pi\)
0.00473247 + 0.999989i \(0.498494\pi\)
\(368\) 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 0.258748 0.965945i \(-0.416690\pi\)
−0.707159 + 0.707055i \(0.750023\pi\)
\(374\) 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 0.959391 0.282079i \(-0.0910240\pi\)
0.235408 + 0.971897i \(0.424357\pi\)
\(384\) 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 0.163876 0.986481i \(-0.447600\pi\)
−0.772380 + 0.635161i \(0.780934\pi\)
\(398\) 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 \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) 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 −0.0829786 0.996551i \(-0.526443\pi\)
−0.904528 + 0.426414i \(0.859777\pi\)
\(444\) −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 0.688686 0.725059i \(-0.258188\pi\)
−0.283577 + 0.958950i \(0.591521\pi\)
\(458\) 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 \(0.00739722\pi\)
−0.999730 + 0.0232370i \(0.992603\pi\)
\(464\) 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 \(0.694428\pi\)
−0.996199 + 0.0871056i \(0.972238\pi\)
\(488\) −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 \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) 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 0.0218062 0.999762i \(-0.493058\pi\)
−0.854916 + 0.518766i \(0.826392\pi\)
\(524\) 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 \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) −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 0.433888 0.900967i \(-0.357141\pi\)
0.997204 + 0.0747252i \(0.0238080\pi\)
\(558\) 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 −0.386492 0.922293i \(-0.626313\pi\)
0.605483 + 0.795858i \(0.292980\pi\)
\(564\) 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 −0.841077 0.540916i \(-0.818078\pi\)
0.0479084 + 0.998852i \(0.484744\pi\)
\(578\) −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 \(-0.666197\pi\)
0.498721 0.866763i \(-0.333803\pi\)
\(588\) −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 0.861838 0.507184i \(-0.169314\pi\)
−0.00831589 + 0.999965i \(0.502647\pi\)
\(594\) 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 0.870253 0.492604i \(-0.163955\pi\)
0.00851879 + 0.999964i \(0.497288\pi\)
\(608\) 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 −0.679888 0.733316i \(-0.737972\pi\)
0.295126 + 0.955458i \(0.404638\pi\)
\(614\) 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 \(0.0776561\pi\)
−0.970388 + 0.241551i \(0.922344\pi\)
\(618\) −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 \(0.233884\pi\)
−0.741987 + 0.670415i \(0.766116\pi\)
\(644\) −18.0000 15.5885i −0.709299 0.614271i
\(645\) 0 0
\(646\) 0 0
\(647\) −7.79423 + 4.50000i −0.306423 + 0.176913i −0.645325 0.763908i \(-0.723278\pi\)
0.338902 + 0.940822i \(0.389945\pi\)
\(648\) 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 0.984003 0.178154i \(-0.0570127\pi\)
0.337715 + 0.941248i \(0.390346\pi\)
\(654\) −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 \(-0.874039\pi\)
0.922720 0.385472i \(-0.125961\pi\)
\(674\) −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 0.449242 0.893410i \(-0.351694\pi\)
−0.549095 + 0.835760i \(0.685027\pi\)
\(678\) 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 −0.287819 0.957685i \(-0.592930\pi\)
0.685470 + 0.728101i \(0.259597\pi\)
\(684\) 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 \(0.140258\pi\)
−0.904482 + 0.426511i \(0.859742\pi\)
\(728\) 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 0.483921 0.875112i \(-0.339212\pi\)
−0.515908 + 0.856644i \(0.672546\pi\)
\(734\) −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 \(0.253749\pi\)
−0.698730 + 0.715386i \(0.746251\pi\)
\(744\) 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 \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 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 −0.916385 0.400298i \(-0.868907\pi\)
−0.111524 + 0.993762i \(0.535573\pi\)
\(774\) −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 −0.268091 0.963394i \(-0.586393\pi\)
0.700278 + 0.713871i \(0.253059\pi\)
\(788\)