Properties

Label 1950.2.z.o.1849.2
Level $1950$
Weight $2$
Character 1950.1849
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 1849.2
Root \(-2.15988 - 0.578737i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1849
Dual form 1950.2.z.o.1699.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + 4q^{6} + 4q^{9} + O(q^{10}) \) \( 8q + 4q^{4} + 4q^{6} + 4q^{9} - 12q^{11} - 4q^{16} - 4q^{24} - 8q^{29} + 48q^{31} - 32q^{34} - 4q^{36} - 24q^{44} + 4q^{46} + 12q^{49} - 32q^{51} - 4q^{54} - 24q^{59} - 20q^{61} - 8q^{64} - 24q^{66} + 4q^{69} + 44q^{71} + 4q^{74} - 48q^{79} - 4q^{81} + 16q^{86} - 16q^{89} + 40q^{91} + 24q^{94} - 8q^{96} - 24q^{99} + O(q^{100}) \)

Character values

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

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

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 \(-0.129449\pi\)
0.116657 + 0.993172i \(0.462782\pi\)
\(8\) 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 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 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 \(-0.300941\pi\)
−0.409435 + 0.912339i \(0.634274\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.58114 + 2.73861i −0.362738 + 0.628281i −0.988410 0.151805i \(-0.951491\pi\)
0.625672 + 0.780086i \(0.284825\pi\)
\(20\) 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 \(-0.594287\pi\)
0.682360 + 0.731016i \(0.260954\pi\)
\(24\) −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 0.993910 0.110193i \(-0.0351470\pi\)
−0.592385 + 0.805655i \(0.701814\pi\)
\(30\) 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 \(-0.420912\pi\)
0.962388 + 0.271678i \(0.0875787\pi\)
\(38\) 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 −0.952133 0.305685i \(-0.901115\pi\)
0.211336 0.977414i \(-0.432219\pi\)
\(42\) 2.73861 1.58114i 0.422577 0.243975i
\(43\) 1.00656 + 0.581139i 0.153499 + 0.0886228i 0.574782 0.818306i \(-0.305087\pi\)
−0.421283 + 0.906929i \(0.638420\pi\)
\(44\) −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 −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) 0 0
\(61\) 2.24342 3.88571i 0.287240 0.497514i −0.685910 0.727686i \(-0.740596\pi\)
0.973150 + 0.230172i \(0.0739289\pi\)
\(62\) −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 \(-0.745238\pi\)
0.273241 + 0.961946i \(0.411904\pi\)
\(68\) 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 −0.0492001 0.998789i \(-0.515667\pi\)
0.889577 0.456786i \(-0.150999\pi\)
\(72\) 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 0.842972 0.537958i \(-0.180804\pi\)
−0.887371 + 0.461056i \(0.847471\pi\)
\(90\) 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 0.999618 + 0.0276537i \(0.00880356\pi\)
0.523758 + 0.851867i \(0.324530\pi\)
\(98\) −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 0.566590 0.824000i \(-0.308262\pi\)
−0.996900 + 0.0786819i \(0.974929\pi\)
\(102\) 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 \(-0.573004\pi\)
0.729676 + 0.683793i \(0.239671\pi\)
\(108\) 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 \(-0.171925\pi\)
−0.0165186 + 0.999864i \(0.505258\pi\)
\(114\) 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 −0.564822 + 0.825213i \(0.691055\pi\)
−0.997066 + 0.0765432i \(0.975612\pi\)
\(128\) 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 \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) 2.16228i 0.184065i
\(139\) −2.83772 + 4.91508i −0.240692 + 0.416892i −0.960912 0.276855i \(-0.910708\pi\)
0.720219 + 0.693747i \(0.244041\pi\)
\(140\) 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 −0.971405 0.237428i \(-0.923696\pi\)
0.691321 + 0.722548i \(0.257029\pi\)
\(150\) 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 \(-0.120782\pi\)
0.143654 + 0.989628i \(0.454115\pi\)
\(164\) −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 \(-0.564391\pi\)
0.747909 + 0.663801i \(0.231058\pi\)
\(168\) 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 \(-0.353620\pi\)
−0.554143 + 0.832422i \(0.686954\pi\)
\(174\) 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 0.847073 + 0.531477i \(0.178363\pi\)
0.0367358 + 0.999325i \(0.488304\pi\)
\(180\) 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 0.423268 + 0.906004i \(0.360883\pi\)
−0.996257 + 0.0864411i \(0.972451\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 15.0035 8.66228i 1.07998 0.623524i 0.149086 0.988824i \(-0.452367\pi\)
0.930890 + 0.365300i \(0.119034\pi\)
\(194\) −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 \(-0.735232\pi\)
0.303340 + 0.952882i \(0.401898\pi\)
\(198\) 2.59808 1.50000i 0.184637 0.106600i
\(199\) 4.41886 7.65369i 0.313245 0.542556i −0.665818 0.746114i \(-0.731917\pi\)
0.979063 + 0.203558i \(0.0652506\pi\)
\(200\) 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 0.545510 0.838104i \(-0.316336\pi\)
−0.998575 + 0.0533737i \(0.983003\pi\)
\(212\) 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 −0.515881 + 0.856660i \(0.672535\pi\)
−0.999830 + 0.0184358i \(0.994131\pi\)
\(224\) 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 \(-0.593451\pi\)
−0.973663 + 0.227991i \(0.926784\pi\)
\(228\) −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 −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) 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 −0.999536 0.0304521i \(-0.990305\pi\)
0.526140 + 0.850398i \(0.323639\pi\)
\(252\) 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 \(-0.964520\pi\)
−0.400567 + 0.916267i \(0.631187\pi\)
\(258\) 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 \(-0.661889\pi\)
0.512942 + 0.858423i \(0.328555\pi\)
\(264\) −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 −0.992630 0.121186i \(-0.961330\pi\)
0.601265 + 0.799050i \(0.294664\pi\)
\(270\) 0 0
\(271\) −0.162278 0.281073i −0.00985767 0.0170740i 0.861054 0.508513i \(-0.169805\pi\)
−0.870912 + 0.491439i \(0.836471\pi\)
\(272\) 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 \(-0.248056\pi\)
−0.252916 + 0.967488i \(0.581390\pi\)
\(278\) 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 \(-0.470037\pi\)
0.909187 + 0.416387i \(0.136704\pi\)
\(284\) −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 \(-0.117356\pi\)
0.154297 + 0.988025i \(0.450689\pi\)
\(294\) 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 −0.578908 0.815393i \(-0.696521\pi\)
0.995605 + 0.0936524i \(0.0298543\pi\)
\(332\) 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 \(-0.344653\pi\)
−0.530474 + 0.847701i \(0.677986\pi\)
\(348\) −3.74517 + 2.16228i −0.200762 + 0.115910i
\(349\) −17.7302 30.7097i −0.949078 1.64385i −0.747372 0.664406i \(-0.768685\pi\)
−0.201707 0.979446i \(-0.564649\pi\)
\(350\) 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 \(-0.489898\pi\)
0.881454 + 0.472270i \(0.156565\pi\)
\(354\) 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 \(-0.828480\pi\)
0.0152467 + 0.999884i \(0.495147\pi\)
\(368\) −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 \(-0.420851\pi\)
−0.716341 + 0.697751i \(0.754184\pi\)
\(374\) 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 0.890565 0.454855i \(-0.150309\pi\)
−0.839199 + 0.543825i \(0.816976\pi\)
\(380\) 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 \(-0.350927\pi\)
−0.547079 + 0.837081i \(0.684260\pi\)
\(384\) −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 \(-0.238684\pi\)
−0.224324 + 0.974515i \(0.572017\pi\)
\(398\) 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 0.587016 0.809575i \(-0.300303\pi\)
−0.994621 + 0.103583i \(0.966969\pi\)
\(402\) 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 −0.198227 0.980156i \(-0.563518\pi\)
0.947954 0.318408i \(-0.103148\pi\)
\(410\) 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 0.954759 0.297382i \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) 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 0.994266 + 0.106939i \(0.0341049\pi\)
−0.404521 + 0.914529i \(0.632562\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) −29.9842 17.3114i −1.44095 0.831932i −0.443036 0.896504i \(-0.646099\pi\)
−0.997913 + 0.0645717i \(0.979432\pi\)
\(434\) −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 −0.857206 0.514974i \(-0.827802\pi\)
−0.0173773 0.999849i \(-0.505532\pi\)
\(440\) 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 −0.834850 0.550477i \(-0.814446\pi\)
0.894152 + 0.447763i \(0.147779\pi\)
\(450\) 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 \(-0.744502\pi\)
0.275464 + 0.961311i \(0.411169\pi\)
\(458\) −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 −0.594021 0.804450i \(-0.702460\pi\)
0.993684 + 0.112212i \(0.0357937\pi\)
\(462\) −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 0.666463 0.745538i \(-0.267807\pi\)
−0.978886 + 0.204405i \(0.934474\pi\)
\(480\) 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 \(-0.310507\pi\)
−0.436666 + 0.899624i \(0.643841\pi\)
\(488\) 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 0.999988 0.00480977i \(-0.00153100\pi\)
−0.504160 + 0.863611i \(0.668198\pi\)
\(492\) 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 \(-0.455619\pi\)
−0.788133 + 0.615504i \(0.788952\pi\)
\(504\) 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 −0.993741 0.111709i \(-0.964368\pi\)
0.400128 0.916459i \(-0.368966\pi\)
\(510\) 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 \(-0.922947\pi\)
−0.277824 + 0.960632i \(0.589613\pi\)
\(524\) 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 \(-0.534992\pi\)
0.805943 + 0.591994i \(0.201659\pi\)
\(558\) 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 \(-0.0793456\pi\)
0.270899 + 0.962608i \(0.412679\pi\)
\(564\) 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 0.783635 0.621221i \(-0.213363\pi\)
−0.929811 + 0.368038i \(0.880030\pi\)
\(570\) 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 \(-0.809346\pi\)
0.0752860 + 0.997162i \(0.476013\pi\)
\(588\) −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 −0.847892 0.530169i \(-0.822129\pi\)
−0.0351935 0.999381i \(-0.511205\pi\)
\(602\) −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 \(-0.597178\pi\)
−0.976266 + 0.216574i \(0.930512\pi\)
\(608\) −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 \(-0.992948\pi\)
−0.480692 + 0.876889i \(0.659615\pi\)
\(614\) −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 0.977452 + 0.211158i \(0.0677236\pi\)
0.671594 + 0.740919i \(0.265610\pi\)
\(618\) −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 −0.672645 0.739965i \(-0.734842\pi\)
0.977151 + 0.212545i \(0.0681752\pi\)
\(632\) 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 0.487467 + 0.873141i \(0.337921\pi\)
−0.999896 + 0.0144117i \(0.995412\pi\)
\(642\) 6.00000i 0.236801i
\(643\) −10.1112 5.83772i −0.398748 0.230217i 0.287196 0.957872i \(-0.407277\pi\)
−0.685944 + 0.727655i \(0.740610\pi\)
\(644\) 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 \(-0.819606\pi\)
0.0431121 + 0.999070i \(0.486273\pi\)
\(648\) 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 \(-0.607236\pi\)
0.652066 + 0.758162i \(0.273903\pi\)
\(654\) 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 −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) 0 0
\(661\) −13.0000 22.5167i −0.505641 0.875797i −0.999979 0.00652642i \(-0.997923\pi\)
0.494337 0.869270i \(-0.335411\pi\)
\(662\) 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 \(-0.644261\pi\)
0.559671 + 0.828715i \(0.310928\pi\)
\(674\) 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 \(-0.520164\pi\)
−0.895940 + 0.444175i \(0.853497\pi\)
\(684\) 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 0.998717 0.0506436i \(-0.0161273\pi\)
−0.543217 + 0.839592i \(0.682794\pi\)
\(692\) −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 −0.851469 0.524405i \(-0.824288\pi\)
0.879883 + 0.475191i \(0.157621\pi\)
\(710\) 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 −0.0138864 + 0.999904i \(0.504420\pi\)
−0.858999 + 0.511978i \(0.828913\pi\)
\(720\) 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 0.987109 0.160049i \(-0.0511651\pi\)
−0.632161 + 0.774837i \(0.717832\pi\)
\(740\) 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 \(-0.361191\pi\)
0.996173 + 0.0874050i \(0.0278574\pi\)
\(744\) −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 0.981002 0.193999i \(-0.0621458\pi\)
−0.658509 + 0.752573i \(0.728812\pi\)
\(752\) −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 \(-0.730573\pi\)
0.317252 + 0.948341i \(0.397240\pi\)
\(758\) −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 −0.0460237 0.998940i \(-0.514655\pi\)
0.888120 0.459613i \(-0.152012\pi\)
\(762\) 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 0.968857 0.247621i \(-0.0796489\pi\)
−0.698875 + 0.715244i \(0.746316\pi\)
\(770\) 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 \(-0.387117\pi\)
−0.638514 + 0.769610i \(0.720451\pi\)
\(774\) −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
\(784\) 1.50000 2.59808i 0.0535714 0.0927884i