Properties

Label 1950.2.z.o.1699.3
Level $1950$
Weight $2$
Character 1950.1699
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.3317760000.2
Defining polynomial: \(x^{8} - 25 x^{4} + 625\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1699.3
Root \(0.578737 + 2.15988i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1699
Dual form 1950.2.z.o.1849.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.73861 + 1.58114i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.73861 + 1.58114i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +1.00000i q^{12} +(-3.60464 + 0.0811388i) q^{13} -3.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.725489 + 0.418861i) q^{17} +1.00000i q^{18} +(-1.58114 - 2.73861i) q^{19} -3.16228 q^{21} +(-2.59808 + 1.50000i) q^{22} +(-1.87259 - 1.08114i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.16228 - 1.73205i) q^{26} +1.00000i q^{27} +(-2.73861 - 1.58114i) q^{28} +(2.16228 - 3.74517i) q^{29} +2.83772 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.59808 + 1.50000i) q^{33} -0.837722 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-7.34981 - 4.24342i) q^{37} -3.16228i q^{38} +(-3.16228 - 1.73205i) q^{39} +(-4.74342 + 8.21584i) q^{41} +(-2.73861 - 1.58114i) q^{42} +(-1.00656 + 0.581139i) q^{43} -3.00000 q^{44} +(-1.08114 - 1.87259i) q^{46} -6.00000i q^{47} +(-0.866025 + 0.500000i) q^{48} +(1.50000 - 2.59808i) q^{49} -0.837722 q^{51} +(-1.87259 - 3.08114i) q^{52} +0.837722i q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.58114 - 2.73861i) q^{56} -3.16228i q^{57} +(3.74517 - 2.16228i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(2.24342 + 3.88571i) q^{61} +(2.45754 + 1.41886i) q^{62} +(-2.73861 - 1.58114i) q^{63} -1.00000 q^{64} -3.00000 q^{66} +(3.46410 + 2.00000i) q^{67} +(-0.725489 - 0.418861i) q^{68} +(-1.08114 - 1.87259i) q^{69} +(7.08114 + 12.2649i) q^{71} +(-0.866025 + 0.500000i) q^{72} +11.3246i q^{73} +(-4.24342 - 7.34981i) q^{74} +(1.58114 - 2.73861i) q^{76} -9.48683i q^{77} +(-1.87259 - 3.08114i) q^{78} -2.83772 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-8.21584 + 4.74342i) q^{82} +11.6491i q^{83} +(-1.58114 - 2.73861i) q^{84} -1.16228 q^{86} +(3.74517 - 2.16228i) q^{87} +(-2.59808 - 1.50000i) q^{88} +(-0.418861 + 0.725489i) q^{89} +(9.74342 - 5.92164i) q^{91} -2.16228i q^{92} +(2.45754 + 1.41886i) q^{93} +(3.00000 - 5.19615i) q^{94} -1.00000 q^{96} +(-15.0035 + 8.66228i) q^{97} +(2.59808 - 1.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9} - 12 q^{11} - 4 q^{16} - 4 q^{24} - 8 q^{29} + 48 q^{31} - 32 q^{34} - 4 q^{36} - 24 q^{44} + 4 q^{46} + 12 q^{49} - 32 q^{51} - 4 q^{54} - 24 q^{59} - 20 q^{61} - 8 q^{64} - 24 q^{66} + 4 q^{69} + 44 q^{71} + 4 q^{74} - 48 q^{79} - 4 q^{81} + 16 q^{86} - 16 q^{89} + 40 q^{91} + 24 q^{94} - 8 q^{96} - 24 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −2.73861 + 1.58114i −1.03510 + 0.597614i −0.918441 0.395558i \(-0.870551\pi\)
−0.116657 + 0.993172i \(0.537218\pi\)
\(8\) 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 \(0.316051\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.60464 + 0.0811388i −0.999747 + 0.0225039i
\(14\) −3.16228 −0.845154
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.725489 + 0.418861i −0.175957 + 0.101589i −0.585392 0.810751i \(-0.699059\pi\)
0.409435 + 0.912339i \(0.365726\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.58114 2.73861i −0.362738 0.628281i 0.625672 0.780086i \(-0.284825\pi\)
−0.988410 + 0.151805i \(0.951491\pi\)
\(20\) 0 0
\(21\) −3.16228 −0.690066
\(22\) −2.59808 + 1.50000i −0.553912 + 0.319801i
\(23\) −1.87259 1.08114i −0.390461 0.225433i 0.291899 0.956449i \(-0.405713\pi\)
−0.682360 + 0.731016i \(0.739046\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) −3.16228 1.73205i −0.620174 0.339683i
\(27\) 1.00000i 0.192450i
\(28\) −2.73861 1.58114i −0.517549 0.298807i
\(29\) 2.16228 3.74517i 0.401525 0.695461i −0.592385 0.805655i \(-0.701814\pi\)
0.993910 + 0.110193i \(0.0351470\pi\)
\(30\) 0 0
\(31\) 2.83772 0.509670 0.254835 0.966985i \(-0.417979\pi\)
0.254835 + 0.966985i \(0.417979\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −2.59808 + 1.50000i −0.452267 + 0.261116i
\(34\) −0.837722 −0.143668
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −7.34981 4.24342i −1.20830 0.697613i −0.245914 0.969292i \(-0.579088\pi\)
−0.962388 + 0.271678i \(0.912421\pi\)
\(38\) 3.16228i 0.512989i
\(39\) −3.16228 1.73205i −0.506370 0.277350i
\(40\) 0 0
\(41\) −4.74342 + 8.21584i −0.740797 + 1.28310i 0.211336 + 0.977414i \(0.432219\pi\)
−0.952133 + 0.305685i \(0.901115\pi\)
\(42\) −2.73861 1.58114i −0.422577 0.243975i
\(43\) −1.00656 + 0.581139i −0.153499 + 0.0886228i −0.574782 0.818306i \(-0.694913\pi\)
0.421283 + 0.906929i \(0.361580\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −1.08114 1.87259i −0.159405 0.276098i
\(47\) 6.00000i 0.875190i −0.899172 0.437595i \(-0.855830\pi\)
0.899172 0.437595i \(-0.144170\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0 0
\(51\) −0.837722 −0.117305
\(52\) −1.87259 3.08114i −0.259681 0.427277i
\(53\) 0.837722i 0.115070i 0.998343 + 0.0575350i \(0.0183241\pi\)
−0.998343 + 0.0575350i \(0.981676\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −1.58114 2.73861i −0.211289 0.365963i
\(57\) 3.16228i 0.418854i
\(58\) 3.74517 2.16228i 0.491766 0.283921i
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) 2.24342 + 3.88571i 0.287240 + 0.497514i 0.973150 0.230172i \(-0.0739289\pi\)
−0.685910 + 0.727686i \(0.740596\pi\)
\(62\) 2.45754 + 1.41886i 0.312108 + 0.180196i
\(63\) −2.73861 1.58114i −0.345033 0.199205i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −3.00000 −0.369274
\(67\) 3.46410 + 2.00000i 0.423207 + 0.244339i 0.696449 0.717607i \(-0.254762\pi\)
−0.273241 + 0.961946i \(0.588096\pi\)
\(68\) −0.725489 0.418861i −0.0879784 0.0507944i
\(69\) −1.08114 1.87259i −0.130154 0.225433i
\(70\) 0 0
\(71\) 7.08114 + 12.2649i 0.840377 + 1.45557i 0.889577 + 0.456786i \(0.150999\pi\)
−0.0492001 + 0.998789i \(0.515667\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 11.3246i 1.32544i 0.748868 + 0.662719i \(0.230598\pi\)
−0.748868 + 0.662719i \(0.769402\pi\)
\(74\) −4.24342 7.34981i −0.493287 0.854398i
\(75\) 0 0
\(76\) 1.58114 2.73861i 0.181369 0.314140i
\(77\) 9.48683i 1.08112i
\(78\) −1.87259 3.08114i −0.212029 0.348870i
\(79\) −2.83772 −0.319269 −0.159634 0.987176i \(-0.551032\pi\)
−0.159634 + 0.987176i \(0.551032\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −8.21584 + 4.74342i −0.907288 + 0.523823i
\(83\) 11.6491i 1.27866i 0.768934 + 0.639328i \(0.220787\pi\)
−0.768934 + 0.639328i \(0.779213\pi\)
\(84\) −1.58114 2.73861i −0.172516 0.298807i
\(85\) 0 0
\(86\) −1.16228 −0.125332
\(87\) 3.74517 2.16228i 0.401525 0.231820i
\(88\) −2.59808 1.50000i −0.276956 0.159901i
\(89\) −0.418861 + 0.725489i −0.0443992 + 0.0769017i −0.887371 0.461056i \(-0.847471\pi\)
0.842972 + 0.537958i \(0.180804\pi\)
\(90\) 0 0
\(91\) 9.74342 5.92164i 1.02139 0.620757i
\(92\) 2.16228i 0.225433i
\(93\) 2.45754 + 1.41886i 0.254835 + 0.147129i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −15.0035 + 8.66228i −1.52338 + 0.879521i −0.523758 + 0.851867i \(0.675470\pi\)
−0.999618 + 0.0276537i \(0.991196\pi\)
\(98\) 2.59808 1.50000i 0.262445 0.151523i
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) −4.32456 + 7.49035i −0.430309 + 0.745318i −0.996900 0.0786819i \(-0.974929\pi\)
0.566590 + 0.824000i \(0.308262\pi\)
\(102\) −0.725489 0.418861i −0.0718341 0.0414734i
\(103\) 5.48683i 0.540634i −0.962771 0.270317i \(-0.912872\pi\)
0.962771 0.270317i \(-0.0871285\pi\)
\(104\) −0.0811388 3.60464i −0.00795632 0.353464i
\(105\) 0 0
\(106\) −0.418861 + 0.725489i −0.0406834 + 0.0704657i
\(107\) −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
\(109\) 10.4868 1.00446 0.502228 0.864735i \(-0.332514\pi\)
0.502228 + 0.864735i \(0.332514\pi\)
\(110\) 0 0
\(111\) −4.24342 7.34981i −0.402767 0.697613i
\(112\) 3.16228i 0.298807i
\(113\) −8.94133 + 5.16228i −0.841129 + 0.485626i −0.857648 0.514237i \(-0.828075\pi\)
0.0165186 + 0.999864i \(0.494742\pi\)
\(114\) 1.58114 2.73861i 0.148087 0.256495i
\(115\) 0 0
\(116\) 4.32456 0.401525
\(117\) −1.87259 3.08114i −0.173121 0.284851i
\(118\) 6.00000i 0.552345i
\(119\) 1.32456 2.29420i 0.121422 0.210309i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 4.48683i 0.406219i
\(123\) −8.21584 + 4.74342i −0.740797 + 0.427699i
\(124\) 1.41886 + 2.45754i 0.127417 + 0.220694i
\(125\) 0 0
\(126\) −1.58114 2.73861i −0.140859 0.243975i
\(127\) 17.6016 + 10.1623i 1.56189 + 0.901756i 0.997066 + 0.0765432i \(0.0243883\pi\)
0.564822 + 0.825213i \(0.308945\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −1.16228 −0.102333
\(130\) 0 0
\(131\) 16.3246 1.42628 0.713142 0.701020i \(-0.247272\pi\)
0.713142 + 0.701020i \(0.247272\pi\)
\(132\) −2.59808 1.50000i −0.226134 0.130558i
\(133\) 8.66025 + 5.00000i 0.750939 + 0.433555i
\(134\) 2.00000 + 3.46410i 0.172774 + 0.299253i
\(135\) 0 0
\(136\) −0.418861 0.725489i −0.0359170 0.0622102i
\(137\) −10.3923 + 6.00000i −0.887875 + 0.512615i −0.873247 0.487278i \(-0.837990\pi\)
−0.0146279 + 0.999893i \(0.504656\pi\)
\(138\) 2.16228i 0.184065i
\(139\) −2.83772 4.91508i −0.240692 0.416892i 0.720219 0.693747i \(-0.244041\pi\)
−0.960912 + 0.276855i \(0.910708\pi\)
\(140\) 0 0
\(141\) 3.00000 5.19615i 0.252646 0.437595i
\(142\) 14.1623i 1.18847i
\(143\) 5.19615 9.48683i 0.434524 0.793329i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −5.66228 + 9.80735i −0.468613 + 0.811662i
\(147\) 2.59808 1.50000i 0.214286 0.123718i
\(148\) 8.48683i 0.697613i
\(149\) −3.41886 5.92164i −0.280084 0.485120i 0.691321 0.722548i \(-0.257029\pi\)
−0.971405 + 0.237428i \(0.923696\pi\)
\(150\) 0 0
\(151\) 9.81139 0.798439 0.399220 0.916855i \(-0.369281\pi\)
0.399220 + 0.916855i \(0.369281\pi\)
\(152\) 2.73861 1.58114i 0.222131 0.128247i
\(153\) −0.725489 0.418861i −0.0586523 0.0338629i
\(154\) 4.74342 8.21584i 0.382235 0.662051i
\(155\) 0 0
\(156\) −0.0811388 3.60464i −0.00649631 0.288602i
\(157\) 16.1623i 1.28989i 0.764229 + 0.644945i \(0.223120\pi\)
−0.764229 + 0.644945i \(0.776880\pi\)
\(158\) −2.45754 1.41886i −0.195511 0.112879i
\(159\) −0.418861 + 0.725489i −0.0332179 + 0.0575350i
\(160\) 0 0
\(161\) 6.83772 0.538888
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) −13.6931 + 7.90569i −1.07252 + 0.619222i −0.928870 0.370406i \(-0.879218\pi\)
−0.143654 + 0.989628i \(0.545885\pi\)
\(164\) −9.48683 −0.740797
\(165\) 0 0
\(166\) −5.82456 + 10.0884i −0.452073 + 0.783014i
\(167\) −7.06874 4.08114i −0.546996 0.315808i 0.200914 0.979609i \(-0.435609\pi\)
−0.747909 + 0.663801i \(0.768942\pi\)
\(168\) 3.16228i 0.243975i
\(169\) 12.9868 0.584952i 0.998987 0.0449963i
\(170\) 0 0
\(171\) 1.58114 2.73861i 0.120913 0.209427i
\(172\) −1.00656 0.581139i −0.0767496 0.0443114i
\(173\) 1.45098 0.837722i 0.110316 0.0636909i −0.443827 0.896113i \(-0.646380\pi\)
0.554143 + 0.832422i \(0.313046\pi\)
\(174\) 4.32456 0.327844
\(175\) 0 0
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 6.00000i 0.450988i
\(178\) −0.725489 + 0.418861i −0.0543777 + 0.0313950i
\(179\) 11.8246 20.4807i 0.883809 1.53080i 0.0367358 0.999325i \(-0.488304\pi\)
0.847073 0.531477i \(-0.178363\pi\)
\(180\) 0 0
\(181\) 12.8114 0.952263 0.476131 0.879374i \(-0.342039\pi\)
0.476131 + 0.879374i \(0.342039\pi\)
\(182\) 11.3989 0.256584i 0.844940 0.0190192i
\(183\) 4.48683i 0.331676i
\(184\) 1.08114 1.87259i 0.0797026 0.138049i
\(185\) 0 0
\(186\) 1.41886 + 2.45754i 0.104036 + 0.180196i
\(187\) 2.51317i 0.183781i
\(188\) 5.19615 3.00000i 0.378968 0.218797i
\(189\) −1.58114 2.73861i −0.115011 0.199205i
\(190\) 0 0
\(191\) −7.91886 13.7159i −0.572989 0.992446i −0.996257 0.0864411i \(-0.972451\pi\)
0.423268 0.906004i \(-0.360883\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −15.0035 8.66228i −1.07998 0.623524i −0.149086 0.988824i \(-0.547633\pi\)
−0.930890 + 0.365300i \(0.880966\pi\)
\(194\) −17.3246 −1.24383
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) 5.19615 + 3.00000i 0.370211 + 0.213741i 0.673550 0.739141i \(-0.264768\pi\)
−0.303340 + 0.952882i \(0.598102\pi\)
\(198\) −2.59808 1.50000i −0.184637 0.106600i
\(199\) 4.41886 + 7.65369i 0.313245 + 0.542556i 0.979063 0.203558i \(-0.0652506\pi\)
−0.665818 + 0.746114i \(0.731917\pi\)
\(200\) 0 0
\(201\) 2.00000 + 3.46410i 0.141069 + 0.244339i
\(202\) −7.49035 + 4.32456i −0.527019 + 0.304275i
\(203\) 13.6754i 0.959828i
\(204\) −0.418861 0.725489i −0.0293261 0.0507944i
\(205\) 0 0
\(206\) 2.74342 4.75174i 0.191143 0.331069i
\(207\) 2.16228i 0.150289i
\(208\) 1.73205 3.16228i 0.120096 0.219265i
\(209\) 9.48683 0.656218
\(210\) 0 0
\(211\) −6.58114 + 11.3989i −0.453064 + 0.784730i −0.998575 0.0533737i \(-0.983003\pi\)
0.545510 + 0.838104i \(0.316336\pi\)
\(212\) −0.725489 + 0.418861i −0.0498268 + 0.0287675i
\(213\) 14.1623i 0.970383i
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −7.77142 + 4.48683i −0.527559 + 0.304586i
\(218\) 9.08186 + 5.24342i 0.615101 + 0.355129i
\(219\) −5.66228 + 9.80735i −0.382621 + 0.662719i
\(220\) 0 0
\(221\) 2.58114 1.56871i 0.173626 0.105523i
\(222\) 8.48683i 0.569599i
\(223\) 22.6344 + 13.0680i 1.51571 + 0.875096i 0.999830 + 0.0184358i \(0.00586863\pi\)
0.515881 + 0.856660i \(0.327465\pi\)
\(224\) 1.58114 2.73861i 0.105644 0.182981i
\(225\) 0 0
\(226\) −10.3246 −0.686779
\(227\) 19.0298 10.9868i 1.26305 0.729222i 0.289386 0.957213i \(-0.406549\pi\)
0.973663 + 0.227991i \(0.0732156\pi\)
\(228\) 2.73861 1.58114i 0.181369 0.104713i
\(229\) 16.4868 1.08948 0.544740 0.838605i \(-0.316628\pi\)
0.544740 + 0.838605i \(0.316628\pi\)
\(230\) 0 0
\(231\) 4.74342 8.21584i 0.312094 0.540562i
\(232\) 3.74517 + 2.16228i 0.245883 + 0.141960i
\(233\) 13.6754i 0.895908i −0.894057 0.447954i \(-0.852153\pi\)
0.894057 0.447954i \(-0.147847\pi\)
\(234\) −0.0811388 3.60464i −0.00530421 0.235643i
\(235\) 0 0
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) −2.45754 1.41886i −0.159634 0.0921649i
\(238\) 2.29420 1.32456i 0.148711 0.0858582i
\(239\) −18.4868 −1.19581 −0.597907 0.801566i \(-0.704001\pi\)
−0.597907 + 0.801566i \(0.704001\pi\)
\(240\) 0 0
\(241\) −4.00000 6.92820i −0.257663 0.446285i 0.707953 0.706260i \(-0.249619\pi\)
−0.965615 + 0.259975i \(0.916286\pi\)
\(242\) 2.00000i 0.128565i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −2.24342 + 3.88571i −0.143620 + 0.248757i
\(245\) 0 0
\(246\) −9.48683 −0.604858
\(247\) 5.92164 + 9.74342i 0.376785 + 0.619959i
\(248\) 2.83772i 0.180196i
\(249\) −5.82456 + 10.0884i −0.369116 + 0.639328i
\(250\) 0 0
\(251\) −7.50000 12.9904i −0.473396 0.819946i 0.526140 0.850398i \(-0.323639\pi\)
−0.999536 + 0.0304521i \(0.990305\pi\)
\(252\) 3.16228i 0.199205i
\(253\) 5.61776 3.24342i 0.353186 0.203912i
\(254\) 10.1623 + 17.6016i 0.637638 + 1.10442i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 22.3533 + 12.9057i 1.39436 + 0.805035i 0.993794 0.111232i \(-0.0354798\pi\)
0.400567 + 0.916267i \(0.368813\pi\)
\(258\) −1.00656 0.581139i −0.0626658 0.0361801i
\(259\) 26.8377 1.66761
\(260\) 0 0
\(261\) 4.32456 0.267683
\(262\) 14.1375 + 8.16228i 0.873416 + 0.504267i
\(263\) −0.421610 0.243416i −0.0259976 0.0150097i 0.486945 0.873433i \(-0.338111\pi\)
−0.512942 + 0.858423i \(0.671445\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) 0 0
\(266\) 5.00000 + 8.66025i 0.306570 + 0.530994i
\(267\) −0.725489 + 0.418861i −0.0443992 + 0.0256339i
\(268\) 4.00000i 0.244339i
\(269\) −6.41886 11.1178i −0.391365 0.677864i 0.601265 0.799050i \(-0.294664\pi\)
−0.992630 + 0.121186i \(0.961330\pi\)
\(270\) 0 0
\(271\) −0.162278 + 0.281073i −0.00985767 + 0.0170740i −0.870912 0.491439i \(-0.836471\pi\)
0.861054 + 0.508513i \(0.169805\pi\)
\(272\) 0.837722i 0.0507944i
\(273\) 11.3989 0.256584i 0.689891 0.0155291i
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 1.08114 1.87259i 0.0650769 0.112717i
\(277\) −7.63089 + 4.40569i −0.458496 + 0.264713i −0.711411 0.702776i \(-0.751944\pi\)
0.252916 + 0.967488i \(0.418610\pi\)
\(278\) 5.67544i 0.340391i
\(279\) 1.41886 + 2.45754i 0.0849450 + 0.147129i
\(280\) 0 0
\(281\) −21.4868 −1.28180 −0.640898 0.767626i \(-0.721438\pi\)
−0.640898 + 0.767626i \(0.721438\pi\)
\(282\) 5.19615 3.00000i 0.309426 0.178647i
\(283\) −16.8761 9.74342i −1.00318 0.579186i −0.0939921 0.995573i \(-0.529963\pi\)
−0.909187 + 0.416387i \(0.863296\pi\)
\(284\) −7.08114 + 12.2649i −0.420188 + 0.727787i
\(285\) 0 0
\(286\) 9.24342 5.61776i 0.546575 0.332185i
\(287\) 30.0000i 1.77084i
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) −8.14911 + 14.1147i −0.479359 + 0.830275i
\(290\) 0 0
\(291\) −17.3246 −1.01558
\(292\) −9.80735 + 5.66228i −0.573932 + 0.331360i
\(293\) −18.6081 + 10.7434i −1.08710 + 0.627637i −0.932803 0.360387i \(-0.882644\pi\)
−0.154297 + 0.988025i \(0.549311\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) 4.24342 7.34981i 0.246644 0.427199i
\(297\) −2.59808 1.50000i −0.150756 0.0870388i
\(298\) 6.83772i 0.396099i
\(299\) 6.83772 + 3.74517i 0.395436 + 0.216589i
\(300\) 0 0
\(301\) 1.83772 3.18303i 0.105925 0.183467i
\(302\) 8.49691 + 4.90569i 0.488942 + 0.282291i
\(303\) −7.49035 + 4.32456i −0.430309 + 0.248439i
\(304\) 3.16228 0.181369
\(305\) 0 0
\(306\) −0.418861 0.725489i −0.0239447 0.0414734i
\(307\) 16.6491i 0.950215i 0.879928 + 0.475107i \(0.157591\pi\)
−0.879928 + 0.475107i \(0.842409\pi\)
\(308\) 8.21584 4.74342i 0.468141 0.270281i
\(309\) 2.74342 4.75174i 0.156068 0.270317i
\(310\) 0 0
\(311\) −6.48683 −0.367835 −0.183917 0.982942i \(-0.558878\pi\)
−0.183917 + 0.982942i \(0.558878\pi\)
\(312\) 1.73205 3.16228i 0.0980581 0.179029i
\(313\) 7.64911i 0.432353i −0.976354 0.216177i \(-0.930641\pi\)
0.976354 0.216177i \(-0.0693587\pi\)
\(314\) −8.08114 + 13.9969i −0.456045 + 0.789893i
\(315\) 0 0
\(316\) −1.41886 2.45754i −0.0798172 0.138247i
\(317\) 31.8114i 1.78671i −0.449356 0.893353i \(-0.648347\pi\)
0.449356 0.893353i \(-0.351653\pi\)
\(318\) −0.725489 + 0.418861i −0.0406834 + 0.0234886i
\(319\) 6.48683 + 11.2355i 0.363193 + 0.629069i
\(320\) 0 0
\(321\) −3.00000 5.19615i −0.167444 0.290021i
\(322\) 5.92164 + 3.41886i 0.330000 + 0.190526i
\(323\) 2.29420 + 1.32456i 0.127653 + 0.0737002i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −15.8114 −0.875712
\(327\) 9.08186 + 5.24342i 0.502228 + 0.289962i
\(328\) −8.21584 4.74342i −0.453644 0.261911i
\(329\) 9.48683 + 16.4317i 0.523026 + 0.905908i
\(330\) 0 0
\(331\) 7.58114 + 13.1309i 0.416697 + 0.721741i 0.995605 0.0936524i \(-0.0298543\pi\)
−0.578908 + 0.815393i \(0.696521\pi\)
\(332\) −10.0884 + 5.82456i −0.553674 + 0.319664i
\(333\) 8.48683i 0.465076i
\(334\) −4.08114 7.06874i −0.223310 0.386784i
\(335\) 0 0
\(336\) 1.58114 2.73861i 0.0862582 0.149404i
\(337\) 4.00000i 0.217894i −0.994048 0.108947i \(-0.965252\pi\)
0.994048 0.108947i \(-0.0347479\pi\)
\(338\) 11.5394 + 5.98683i 0.627661 + 0.325641i
\(339\) −10.3246 −0.560753
\(340\) 0 0
\(341\) −4.25658 + 7.37262i −0.230507 + 0.399250i
\(342\) 2.73861 1.58114i 0.148087 0.0854982i
\(343\) 12.6491i 0.682988i
\(344\) −0.581139 1.00656i −0.0313329 0.0542702i
\(345\) 0 0
\(346\) 1.67544 0.0900725
\(347\) 1.14710 0.662278i 0.0615795 0.0355529i −0.468894 0.883254i \(-0.655347\pi\)
0.530474 + 0.847701i \(0.322014\pi\)
\(348\) 3.74517 + 2.16228i 0.200762 + 0.115910i
\(349\) −17.7302 + 30.7097i −0.949078 + 1.64385i −0.201707 + 0.979446i \(0.564649\pi\)
−0.747372 + 0.664406i \(0.768685\pi\)
\(350\) 0 0
\(351\) −0.0811388 3.60464i −0.00433087 0.192401i
\(352\) 3.00000i 0.159901i
\(353\) −17.1572 9.90569i −0.913184 0.527227i −0.0317296 0.999496i \(-0.510102\pi\)
−0.881454 + 0.472270i \(0.843435\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) 0 0
\(356\) −0.837722 −0.0443992
\(357\) 2.29420 1.32456i 0.121422 0.0701029i
\(358\) 20.4807 11.8246i 1.08244 0.624947i
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) 4.50000 7.79423i 0.236842 0.410223i
\(362\) 11.0950 + 6.40569i 0.583140 + 0.336676i
\(363\) 2.00000i 0.104973i
\(364\) 10.0000 + 5.47723i 0.524142 + 0.287085i
\(365\) 0 0
\(366\) −2.24342 + 3.88571i −0.117265 + 0.203109i
\(367\) 16.1506 + 9.32456i 0.843055 + 0.486738i 0.858301 0.513146i \(-0.171520\pi\)
−0.0152467 + 0.999884i \(0.504853\pi\)
\(368\) 1.87259 1.08114i 0.0976154 0.0563583i
\(369\) −9.48683 −0.493865
\(370\) 0 0
\(371\) −1.32456 2.29420i −0.0687675 0.119109i
\(372\) 2.83772i 0.147129i
\(373\) 9.08186 5.24342i 0.470241 0.271494i −0.246100 0.969245i \(-0.579149\pi\)
0.716341 + 0.697751i \(0.245816\pi\)
\(374\) 1.25658 2.17647i 0.0649764 0.112542i
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −7.49035 + 13.6754i −0.385773 + 0.704321i
\(378\) 3.16228i 0.162650i
\(379\) 1.00000 1.73205i 0.0513665 0.0889695i −0.839199 0.543825i \(-0.816976\pi\)
0.890565 + 0.454855i \(0.150309\pi\)
\(380\) 0 0
\(381\) 10.1623 + 17.6016i 0.520629 + 0.901756i
\(382\) 15.8377i 0.810328i
\(383\) 1.87259 1.08114i 0.0956847 0.0552436i −0.451394 0.892325i \(-0.649073\pi\)
0.547079 + 0.837081i \(0.315740\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) −8.66228 15.0035i −0.440898 0.763658i
\(387\) −1.00656 0.581139i −0.0511664 0.0295409i
\(388\) −15.0035 8.66228i −0.761688 0.439761i
\(389\) 28.3246 1.43611 0.718056 0.695985i \(-0.245032\pi\)
0.718056 + 0.695985i \(0.245032\pi\)
\(390\) 0 0
\(391\) 1.81139 0.0916058
\(392\) 2.59808 + 1.50000i 0.131223 + 0.0757614i
\(393\) 14.1375 + 8.16228i 0.713142 + 0.411732i
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) −10.1112 + 5.83772i −0.507468 + 0.292987i −0.731792 0.681528i \(-0.761316\pi\)
0.224324 + 0.974515i \(0.427983\pi\)
\(398\) 8.83772i 0.442995i
\(399\) 5.00000 + 8.66025i 0.250313 + 0.433555i
\(400\) 0 0
\(401\) −8.16228 + 14.1375i −0.407605 + 0.705992i −0.994621 0.103583i \(-0.966969\pi\)
0.587016 + 0.809575i \(0.300303\pi\)
\(402\) 4.00000i 0.199502i
\(403\) −10.2290 + 0.230249i −0.509541 + 0.0114695i
\(404\) −8.64911 −0.430309
\(405\) 0 0
\(406\) −6.83772 + 11.8433i −0.339350 + 0.587772i
\(407\) 22.0494 12.7302i 1.09295 0.631015i
\(408\) 0.837722i 0.0414734i
\(409\) 15.1623 + 26.2618i 0.749726 + 1.29856i 0.947954 + 0.318408i \(0.103148\pi\)
−0.198227 + 0.980156i \(0.563518\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 4.75174 2.74342i 0.234101 0.135158i
\(413\) 16.4317 + 9.48683i 0.808550 + 0.466817i
\(414\) 1.08114 1.87259i 0.0531351 0.0920326i
\(415\) 0 0
\(416\) 3.08114 1.87259i 0.151065 0.0918112i
\(417\) 5.67544i 0.277928i
\(418\) 8.21584 + 4.74342i 0.401850 + 0.232008i
\(419\) 4.50000 7.79423i 0.219839 0.380773i −0.734919 0.678155i \(-0.762780\pi\)
0.954759 + 0.297382i \(0.0961133\pi\)
\(420\) 0 0
\(421\) 28.1623 1.37255 0.686273 0.727344i \(-0.259246\pi\)
0.686273 + 0.727344i \(0.259246\pi\)
\(422\) −11.3989 + 6.58114i −0.554888 + 0.320365i
\(423\) 5.19615 3.00000i 0.252646 0.145865i
\(424\) −0.837722 −0.0406834
\(425\) 0 0
\(426\) −7.08114 + 12.2649i −0.343082 + 0.594236i
\(427\) −12.2877 7.09431i −0.594643 0.343318i
\(428\) 6.00000i 0.290021i
\(429\) 9.24342 5.61776i 0.446276 0.271228i
\(430\) 0 0
\(431\) 12.2434 21.2062i 0.589745 1.02147i −0.404521 0.914529i \(-0.632562\pi\)
0.994266 0.106939i \(-0.0341049\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 29.9842 17.3114i 1.44095 0.831932i 0.443036 0.896504i \(-0.353901\pi\)
0.997913 + 0.0645717i \(0.0205681\pi\)
\(434\) −8.97367 −0.430750
\(435\) 0 0
\(436\) 5.24342 + 9.08186i 0.251114 + 0.434942i
\(437\) 6.83772i 0.327093i
\(438\) −9.80735 + 5.66228i −0.468613 + 0.270554i
\(439\) −18.3246 + 31.7391i −0.874583 + 1.51482i −0.0173773 + 0.999849i \(0.505532\pi\)
−0.857206 + 0.514974i \(0.827802\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 3.01969 0.0679718i 0.143632 0.00323309i
\(443\) 9.00000i 0.427603i 0.976877 + 0.213801i \(0.0685846\pi\)
−0.976877 + 0.213801i \(0.931415\pi\)
\(444\) 4.24342 7.34981i 0.201384 0.348807i
\(445\) 0 0
\(446\) 13.0680 + 22.6344i 0.618786 + 1.07177i
\(447\) 6.83772i 0.323413i
\(448\) 2.73861 1.58114i 0.129387 0.0747018i
\(449\) 1.25658 + 2.17647i 0.0593018 + 0.102714i 0.894152 0.447763i \(-0.147779\pi\)
−0.834850 + 0.550477i \(0.814446\pi\)
\(450\) 0 0
\(451\) −14.2302 24.6475i −0.670076 1.16061i
\(452\) −8.94133 5.16228i −0.420565 0.242813i
\(453\) 8.49691 + 4.90569i 0.399220 + 0.230490i
\(454\) 21.9737 1.03128
\(455\) 0 0
\(456\) 3.16228 0.148087
\(457\) 8.96413 + 5.17544i 0.419324 + 0.242097i 0.694788 0.719214i \(-0.255498\pi\)
−0.275464 + 0.961311i \(0.588831\pi\)
\(458\) 14.2780 + 8.24342i 0.667168 + 0.385190i
\(459\) −0.418861 0.725489i −0.0195508 0.0338629i
\(460\) 0 0
\(461\) 8.58114 + 14.8630i 0.399663 + 0.692237i 0.993684 0.112212i \(-0.0357937\pi\)
−0.594021 + 0.804450i \(0.702460\pi\)
\(462\) 8.21584 4.74342i 0.382235 0.220684i
\(463\) 4.51317i 0.209745i −0.994486 0.104872i \(-0.966557\pi\)
0.994486 0.104872i \(-0.0334434\pi\)
\(464\) 2.16228 + 3.74517i 0.100381 + 0.173865i
\(465\) 0 0
\(466\) 6.83772 11.8433i 0.316751 0.548629i
\(467\) 3.00000i 0.138823i −0.997588 0.0694117i \(-0.977888\pi\)
0.997588 0.0694117i \(-0.0221122\pi\)
\(468\) 1.73205 3.16228i 0.0800641 0.146176i
\(469\) −12.6491 −0.584082
\(470\) 0 0
\(471\) −8.08114 + 13.9969i −0.372359 + 0.644945i
\(472\) 5.19615 3.00000i 0.239172 0.138086i
\(473\) 3.48683i 0.160325i
\(474\) −1.41886 2.45754i −0.0651705 0.112879i
\(475\) 0 0
\(476\) 2.64911 0.121422
\(477\) −0.725489 + 0.418861i −0.0332179 + 0.0191783i
\(478\) −16.0101 9.24342i −0.732283 0.422784i
\(479\) −6.83772 + 11.8433i −0.312424 + 0.541133i −0.978886 0.204405i \(-0.934474\pi\)
0.666463 + 0.745538i \(0.267807\pi\)
\(480\) 0 0
\(481\) 26.8377 + 14.6996i 1.22369 + 0.670245i
\(482\) 8.00000i 0.364390i
\(483\) 5.92164 + 3.41886i 0.269444 + 0.155564i
\(484\) −1.00000 + 1.73205i −0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −2.73861 + 1.58114i −0.124098 + 0.0716482i −0.560764 0.827976i \(-0.689493\pi\)
0.436666 + 0.899624i \(0.356159\pi\)
\(488\) −3.88571 + 2.24342i −0.175898 + 0.101555i
\(489\) −15.8114 −0.715016
\(490\) 0 0
\(491\) 10.9868 19.0298i 0.495829 0.858801i −0.504160 0.863611i \(-0.668198\pi\)
0.999988 + 0.00480977i \(0.00153100\pi\)
\(492\) −8.21584 4.74342i −0.370399 0.213850i
\(493\) 3.62278i 0.163162i
\(494\) 0.256584 + 11.3989i 0.0115442 + 0.512859i
\(495\) 0 0
\(496\) −1.41886 + 2.45754i −0.0637087 + 0.110347i
\(497\) −38.7850 22.3925i −1.73974 1.00444i
\(498\) −10.0884 + 5.82456i −0.452073 + 0.261005i
\(499\) −39.8114 −1.78220 −0.891101 0.453805i \(-0.850066\pi\)
−0.891101 + 0.453805i \(0.850066\pi\)
\(500\) 0 0
\(501\) −4.08114 7.06874i −0.182332 0.315808i
\(502\) 15.0000i 0.669483i
\(503\) 14.5591 8.40569i 0.649158 0.374791i −0.138976 0.990296i \(-0.544381\pi\)
0.788133 + 0.615504i \(0.211048\pi\)
\(504\) 1.58114 2.73861i 0.0704295 0.121988i
\(505\) 0 0
\(506\) 6.48683 0.288375
\(507\) 11.5394 + 5.98683i 0.512483 + 0.265885i
\(508\) 20.3246i 0.901756i
\(509\) −13.3925 + 23.1965i −0.593613 + 1.02817i 0.400128 + 0.916459i \(0.368966\pi\)
−0.993741 + 0.111709i \(0.964368\pi\)
\(510\) 0 0
\(511\) −17.9057 31.0136i −0.792101 1.37196i
\(512\) 1.00000i 0.0441942i
\(513\) 2.73861 1.58114i 0.120913 0.0698090i
\(514\) 12.9057 + 22.3533i 0.569246 + 0.985963i
\(515\) 0 0
\(516\) −0.581139 1.00656i −0.0255832 0.0443114i
\(517\) 15.5885 + 9.00000i 0.685580 + 0.395820i
\(518\) 23.2421 + 13.4189i 1.02120 + 0.589591i
\(519\) 1.67544 0.0735439
\(520\) 0 0
\(521\) −20.6491 −0.904654 −0.452327 0.891852i \(-0.649406\pi\)
−0.452327 + 0.891852i \(0.649406\pi\)
\(522\) 3.74517 + 2.16228i 0.163922 + 0.0946403i
\(523\) 28.5560 + 16.4868i 1.24867 + 0.720919i 0.970844 0.239713i \(-0.0770534\pi\)
0.277824 + 0.960632i \(0.410387\pi\)
\(524\) 8.16228 + 14.1375i 0.356571 + 0.617599i
\(525\) 0 0
\(526\) −0.243416 0.421610i −0.0106135 0.0183831i
\(527\) −2.05874 + 1.18861i −0.0896799 + 0.0517767i
\(528\) 3.00000i 0.130558i
\(529\) −9.16228 15.8695i −0.398360 0.689980i
\(530\) 0 0
\(531\) 3.00000 5.19615i 0.130189 0.225494i
\(532\) 10.0000i 0.433555i
\(533\) 16.4317 30.0000i 0.711735 1.29944i
\(534\) −0.837722 −0.0362518
\(535\) 0 0
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) 20.4807 11.8246i 0.883809 0.510267i
\(538\) 12.8377i 0.553474i
\(539\) 4.50000 + 7.79423i 0.193829 + 0.335721i
\(540\) 0 0
\(541\) 30.8114 1.32469 0.662343 0.749201i \(-0.269562\pi\)
0.662343 + 0.749201i \(0.269562\pi\)
\(542\) −0.281073 + 0.162278i −0.0120731 + 0.00697042i
\(543\) 11.0950 + 6.40569i 0.476131 + 0.274895i
\(544\) 0.418861 0.725489i 0.0179585 0.0311051i
\(545\) 0 0
\(546\) 10.0000 + 5.47723i 0.427960 + 0.234404i
\(547\) 14.1359i 0.604409i 0.953243 + 0.302205i \(0.0977226\pi\)
−0.953243 + 0.302205i \(0.902277\pi\)
\(548\) −10.3923 6.00000i −0.443937 0.256307i
\(549\) −2.24342 + 3.88571i −0.0957467 + 0.165838i
\(550\) 0 0
\(551\) −13.6754 −0.582594
\(552\) 1.87259 1.08114i 0.0797026 0.0460163i
\(553\) 7.77142 4.48683i 0.330475 0.190800i
\(554\) −8.81139 −0.374360
\(555\) 0 0
\(556\) 2.83772 4.91508i 0.120346 0.208446i
\(557\) −16.4317 9.48683i −0.696232 0.401970i 0.109710 0.993964i \(-0.465008\pi\)
−0.805943 + 0.591994i \(0.798341\pi\)
\(558\) 2.83772i 0.120130i
\(559\) 3.58114 2.17647i 0.151466 0.0920547i
\(560\) 0 0
\(561\) 1.25658 2.17647i 0.0530530 0.0918905i
\(562\) −18.6081 10.7434i −0.784937 0.453184i
\(563\) −29.4221 + 16.9868i −1.23999 + 0.715910i −0.969092 0.246698i \(-0.920654\pi\)
−0.270899 + 0.962608i \(0.587321\pi\)
\(564\) 6.00000 0.252646
\(565\) 0 0
\(566\) −9.74342 16.8761i −0.409546 0.709355i
\(567\) 3.16228i 0.132803i
\(568\) −12.2649 + 7.08114i −0.514623 + 0.297118i
\(569\) −3.48683 + 6.03937i −0.146176 + 0.253184i −0.929811 0.368038i \(-0.880030\pi\)
0.783635 + 0.621221i \(0.213363\pi\)
\(570\) 0 0
\(571\) −32.3246 −1.35274 −0.676370 0.736562i \(-0.736448\pi\)
−0.676370 + 0.736562i \(0.736448\pi\)
\(572\) 10.8139 0.243416i 0.452152 0.0101778i
\(573\) 15.8377i 0.661630i
\(574\) 15.0000 25.9808i 0.626088 1.08442i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 43.0000i 1.79011i −0.445952 0.895057i \(-0.647135\pi\)
0.445952 0.895057i \(-0.352865\pi\)
\(578\) −14.1147 + 8.14911i −0.587093 + 0.338958i
\(579\) −8.66228 15.0035i −0.359992 0.623524i
\(580\) 0 0
\(581\) −18.4189 31.9024i −0.764143 1.32353i
\(582\) −15.0035 8.66228i −0.621915 0.359063i
\(583\) −2.17647 1.25658i −0.0901400 0.0520424i
\(584\) −11.3246 −0.468613
\(585\) 0 0
\(586\) −21.4868 −0.887613
\(587\) 18.1865 + 10.5000i 0.750639 + 0.433381i 0.825925 0.563781i \(-0.190654\pi\)
−0.0752860 + 0.997162i \(0.523987\pi\)
\(588\) 2.59808 + 1.50000i 0.107143 + 0.0618590i
\(589\) −4.48683 7.77142i −0.184877 0.320216i
\(590\) 0 0
\(591\) 3.00000 + 5.19615i 0.123404 + 0.213741i
\(592\) 7.34981 4.24342i 0.302075 0.174403i
\(593\) 5.16228i 0.211989i 0.994367 + 0.105995i \(0.0338026\pi\)
−0.994367 + 0.105995i \(0.966197\pi\)
\(594\) −1.50000 2.59808i −0.0615457 0.106600i
\(595\) 0 0
\(596\) 3.41886 5.92164i 0.140042 0.242560i
\(597\) 8.83772i 0.361704i
\(598\) 4.04905 + 6.66228i 0.165578 + 0.272441i
\(599\) −1.18861 −0.0485654 −0.0242827 0.999705i \(-0.507730\pi\)
−0.0242827 + 0.999705i \(0.507730\pi\)
\(600\) 0 0
\(601\) −21.6491 + 37.4974i −0.883086 + 1.52955i −0.0351935 + 0.999381i \(0.511205\pi\)
−0.847892 + 0.530169i \(0.822129\pi\)
\(602\) 3.18303 1.83772i 0.129731 0.0749000i
\(603\) 4.00000i 0.162893i
\(604\) 4.90569 + 8.49691i 0.199610 + 0.345734i
\(605\) 0 0
\(606\) −8.64911 −0.351346
\(607\) 31.4580 18.1623i 1.27684 0.737184i 0.300574 0.953758i \(-0.402822\pi\)
0.976266 + 0.216574i \(0.0694884\pi\)
\(608\) 2.73861 + 1.58114i 0.111065 + 0.0641236i
\(609\) −6.83772 + 11.8433i −0.277078 + 0.479914i
\(610\) 0 0
\(611\) 0.486833 + 21.6278i 0.0196952 + 0.874968i
\(612\) 0.837722i 0.0338629i
\(613\) 36.6541 + 21.1623i 1.48045 + 0.854736i 0.999755 0.0221531i \(-0.00705211\pi\)
0.480692 + 0.876889i \(0.340385\pi\)
\(614\) −8.32456 + 14.4186i −0.335952 + 0.581885i
\(615\) 0 0
\(616\) 9.48683 0.382235
\(617\) −40.9615 + 23.6491i −1.64905 + 0.952077i −0.671594 + 0.740919i \(0.734390\pi\)
−0.977452 + 0.211158i \(0.932276\pi\)
\(618\) 4.75174 2.74342i 0.191143 0.110356i
\(619\) −8.00000 −0.321547 −0.160774 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(620\) 0 0
\(621\) 1.08114 1.87259i 0.0433846 0.0751443i
\(622\) −5.61776 3.24342i −0.225252 0.130049i
\(623\) 2.64911i 0.106134i
\(624\) 3.08114 1.87259i 0.123344 0.0749635i
\(625\) 0 0
\(626\) 3.82456 6.62432i 0.152860 0.264761i
\(627\) 8.21584 + 4.74342i 0.328109 + 0.189434i
\(628\) −13.9969 + 8.08114i −0.558539 + 0.322473i
\(629\) 7.10961 0.283479
\(630\) 0 0
\(631\) 7.64911 + 13.2486i 0.304506 + 0.527420i 0.977151 0.212545i \(-0.0681752\pi\)
−0.672645 + 0.739965i \(0.734842\pi\)
\(632\) 2.83772i 0.112879i
\(633\) −11.3989 + 6.58114i −0.453064 + 0.261577i
\(634\) 15.9057 27.5495i 0.631696 1.09413i
\(635\) 0 0
\(636\) −0.837722 −0.0332179
\(637\) −5.19615 + 9.48683i −0.205879 + 0.375882i
\(638\) 12.9737i 0.513632i
\(639\) −7.08114 + 12.2649i −0.280126 + 0.485192i
\(640\) 0 0
\(641\) −12.9737 22.4710i −0.512429 0.887553i −0.999896 0.0144117i \(-0.995412\pi\)
0.487467 0.873141i \(-0.337921\pi\)
\(642\) 6.00000i 0.236801i
\(643\) 10.1112 5.83772i 0.398748 0.230217i −0.287196 0.957872i \(-0.592723\pi\)
0.685944 + 0.727655i \(0.259390\pi\)
\(644\) 3.41886 + 5.92164i 0.134722 + 0.233345i
\(645\) 0 0
\(646\) 1.32456 + 2.29420i 0.0521139 + 0.0902640i
\(647\) 20.3630 + 11.7566i 0.800552 + 0.462199i 0.843664 0.536871i \(-0.180394\pi\)
−0.0431121 + 0.999070i \(0.513727\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 18.0000 0.706562
\(650\) 0 0
\(651\) −8.97367 −0.351706
\(652\) −13.6931 7.90569i −0.536262 0.309611i
\(653\) −8.21584 4.74342i −0.321511 0.185624i 0.330555 0.943787i \(-0.392764\pi\)
−0.652066 + 0.758162i \(0.726097\pi\)
\(654\) 5.24342 + 9.08186i 0.205034 + 0.355129i
\(655\) 0 0
\(656\) −4.74342 8.21584i −0.185199 0.320775i
\(657\) −9.80735 + 5.66228i −0.382621 + 0.220906i
\(658\) 18.9737i 0.739671i
\(659\) −7.50000 12.9904i −0.292159 0.506033i 0.682161 0.731202i \(-0.261040\pi\)
−0.974320 + 0.225168i \(0.927707\pi\)
\(660\) 0 0
\(661\) −13.0000 + 22.5167i −0.505641 + 0.875797i 0.494337 + 0.869270i \(0.335411\pi\)
−0.999979 + 0.00652642i \(0.997923\pi\)
\(662\) 15.1623i 0.589299i
\(663\) 3.01969 0.0679718i 0.117275 0.00263981i
\(664\) −11.6491 −0.452073
\(665\) 0 0
\(666\) 4.24342 7.34981i 0.164429 0.284799i
\(667\) −8.09811 + 4.67544i −0.313560 + 0.181034i
\(668\) 8.16228i 0.315808i
\(669\) 13.0680 + 22.6344i 0.505237 + 0.875096i
\(670\) 0 0
\(671\) −13.4605 −0.519637
\(672\) 2.73861 1.58114i 0.105644 0.0609938i
\(673\) −3.16022 1.82456i −0.121818 0.0703314i 0.437853 0.899047i \(-0.355739\pi\)
−0.559671 + 0.828715i \(0.689072\pi\)
\(674\) 2.00000 3.46410i 0.0770371 0.133432i
\(675\) 0 0
\(676\) 7.00000 + 10.9545i 0.269231 + 0.421325i
\(677\) 32.6491i 1.25481i −0.778694 0.627404i \(-0.784118\pi\)
0.778694 0.627404i \(-0.215882\pi\)
\(678\) −8.94133 5.16228i −0.343390 0.198256i
\(679\) 27.3925 47.4452i 1.05123 1.82078i
\(680\) 0 0
\(681\) 21.9737 0.842033
\(682\) −7.37262 + 4.25658i −0.282312 + 0.162993i
\(683\) 25.0691 14.4737i 0.959243 0.553819i 0.0633033 0.997994i \(-0.479836\pi\)
0.895940 + 0.444175i \(0.146503\pi\)
\(684\) 3.16228 0.120913
\(685\) 0 0
\(686\) 6.32456 10.9545i 0.241473 0.418243i
\(687\) 14.2780 + 8.24342i 0.544740 + 0.314506i
\(688\) 1.16228i 0.0443114i
\(689\) −0.0679718 3.01969i −0.00258952 0.115041i
\(690\) 0 0
\(691\) 11.9737 20.7390i 0.455500 0.788949i −0.543217 0.839592i \(-0.682794\pi\)
0.998717 + 0.0506436i \(0.0161273\pi\)
\(692\) 1.45098 + 0.837722i 0.0551579 + 0.0318454i
\(693\) 8.21584 4.74342i 0.312094 0.180187i
\(694\) 1.32456 0.0502794
\(695\) 0 0
\(696\) 2.16228 + 3.74517i 0.0819609 + 0.141960i
\(697\) 7.94733i 0.301027i
\(698\) −30.7097 + 17.7302i −1.16238 + 0.671100i
\(699\) 6.83772 11.8433i 0.258626 0.447954i
\(700\) 0 0
\(701\) −22.4605 −0.848321 −0.424161 0.905587i \(-0.639431\pi\)
−0.424161 + 0.905587i \(0.639431\pi\)
\(702\) 1.73205 3.16228i 0.0653720 0.119352i
\(703\) 26.8377i 1.01220i
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) −9.90569 17.1572i −0.372806 0.645718i
\(707\) 27.3509i 1.02864i
\(708\) 5.19615 3.00000i 0.195283 0.112747i
\(709\) 0.756584 + 1.31044i 0.0284141 + 0.0492146i 0.879883 0.475191i \(-0.157621\pi\)
−0.851469 + 0.524405i \(0.824288\pi\)
\(710\) 0 0
\(711\) −1.41886 2.45754i −0.0532115 0.0921649i
\(712\) −0.725489 0.418861i −0.0271888 0.0156975i
\(713\) −5.31388 3.06797i −0.199006 0.114896i
\(714\) 2.64911 0.0991405
\(715\) 0 0
\(716\) 23.6491 0.883809
\(717\) −16.0101 9.24342i −0.597907 0.345202i
\(718\) 10.3923 + 6.00000i 0.387837 + 0.223918i
\(719\) −23.4057 40.5399i −0.872885 1.51188i −0.858999 0.511978i \(-0.828913\pi\)
−0.0138864 0.999904i \(-0.504420\pi\)
\(720\) 0 0
\(721\) 8.67544 + 15.0263i 0.323090 + 0.559609i
\(722\) 7.79423 4.50000i 0.290071 0.167473i
\(723\) 8.00000i 0.297523i
\(724\) 6.40569 + 11.0950i 0.238066 + 0.412342i
\(725\) 0 0
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) 12.3246i 0.457092i 0.973533 + 0.228546i \(0.0733972\pi\)
−0.973533 + 0.228546i \(0.926603\pi\)
\(728\) 5.92164 + 9.74342i 0.219471 + 0.361115i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0.486833 0.843219i 0.0180062 0.0311876i
\(732\) −3.88571 + 2.24342i −0.143620 + 0.0829191i
\(733\) 19.5132i 0.720735i −0.932810 0.360368i \(-0.882651\pi\)
0.932810 0.360368i \(-0.117349\pi\)
\(734\) 9.32456 + 16.1506i 0.344176 + 0.596130i
\(735\) 0 0
\(736\) 2.16228 0.0797026
\(737\) −10.3923 + 6.00000i −0.382805 + 0.221013i
\(738\) −8.21584 4.74342i −0.302429 0.174608i
\(739\) 9.64911 16.7127i 0.354948 0.614788i −0.632161 0.774837i \(-0.717832\pi\)
0.987109 + 0.160049i \(0.0511651\pi\)
\(740\) 0 0
\(741\) 0.256584 + 11.3989i 0.00942583 + 0.418748i
\(742\) 2.64911i 0.0972519i
\(743\) −38.6673 22.3246i −1.41856 0.819009i −0.422391 0.906414i \(-0.638809\pi\)
−0.996173 + 0.0874050i \(0.972143\pi\)
\(744\) −1.41886 + 2.45754i −0.0520180 + 0.0900978i
\(745\) 0 0
\(746\) 10.4868 0.383950
\(747\) −10.0884 + 5.82456i −0.369116 + 0.213109i
\(748\) 2.17647 1.25658i 0.0795795 0.0459452i
\(749\) 18.9737 0.693283
\(750\) 0 0
\(751\) 8.83772 15.3074i 0.322493 0.558574i −0.658509 0.752573i \(-0.728812\pi\)
0.981002 + 0.193999i \(0.0621458\pi\)
\(752\) 5.19615 + 3.00000i 0.189484 + 0.109399i
\(753\) 15.0000i 0.546630i
\(754\) −13.3246 + 8.09811i −0.485252 + 0.294916i
\(755\) 0 0
\(756\) 1.58114 2.73861i 0.0575055 0.0996024i
\(757\) 9.50347 + 5.48683i 0.345410 + 0.199422i 0.662662 0.748919i \(-0.269427\pi\)
−0.317252 + 0.948341i \(0.602760\pi\)
\(758\) 1.73205 1.00000i 0.0629109 0.0363216i
\(759\) 6.48683 0.235457
\(760\) 0 0
\(761\) 23.2302 + 40.2360i 0.842096 + 1.45855i 0.888120 + 0.459613i \(0.152012\pi\)
−0.0460237 + 0.998940i \(0.514655\pi\)
\(762\) 20.3246i 0.736281i
\(763\) −28.7194 + 16.5811i −1.03971 + 0.600278i
\(764\) 7.91886 13.7159i 0.286494 0.496223i
\(765\) 0 0
\(766\) 2.16228 0.0781263
\(767\) 11.2355 + 18.4868i 0.405691 + 0.667521i
\(768\) 1.00000i 0.0360844i
\(769\) 7.48683 12.9676i 0.269982 0.467623i −0.698875 0.715244i \(-0.746316\pi\)
0.968857 + 0.247621i \(0.0796489\pi\)
\(770\) 0 0
\(771\) 12.9057 + 22.3533i 0.464787 + 0.805035i
\(772\) 17.3246i 0.623524i
\(773\) 8.09811 4.67544i 0.291269 0.168164i −0.347245 0.937774i \(-0.612883\pi\)
0.638514 + 0.769610i \(0.279549\pi\)
\(774\) −0.581139 1.00656i −0.0208886 0.0361801i
\(775\) 0 0
\(776\) −8.66228 15.0035i −0.310958 0.538594i
\(777\) 23.2421 + 13.4189i 0.833807 + 0.481399i
\(778\) 24.5298 + 14.1623i 0.879435 + 0.507742i
\(779\) 30.0000 1.07486
\(780\) 0 0
\(781\) −42.4868 −1.52030
\(782\) 1.56871 + 0.905694i 0.0560969 + 0.0323876i
\(783\) 3.74517 + 2.16228i 0.133842 + 0.0772735i
\(784\)