Properties

Label 1950.2.z.o.1849.1
Level $1950$
Weight $2$
Character 1950.1849
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 1849.1
Root \(2.15988 + 0.578737i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1849
Dual form 1950.2.z.o.1699.1

$q$-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} +(-1.87259 - 3.08114i) q^{13} +3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.20271 + 3.58114i) q^{17} +1.00000i q^{18} +(1.58114 - 2.73861i) q^{19} +3.16228 q^{21} +(2.59808 + 1.50000i) q^{22} +(-3.60464 + 2.08114i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.16228 + 1.73205i) q^{26} +1.00000i q^{27} +(-2.73861 + 1.58114i) q^{28} +(-4.16228 - 7.20928i) q^{29} +9.16228 q^{31} +(0.866025 + 0.500000i) q^{32} +(2.59808 + 1.50000i) q^{33} -7.16228 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-9.08186 + 5.24342i) q^{37} +3.16228i q^{38} +(3.16228 + 1.73205i) q^{39} +(4.74342 + 8.21584i) q^{41} +(-2.73861 + 1.58114i) q^{42} +(-4.47066 - 2.58114i) q^{43} -3.00000 q^{44} +(2.08114 - 3.60464i) q^{46} -6.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(1.50000 + 2.59808i) q^{49} -7.16228 q^{51} +(-3.60464 + 0.0811388i) q^{52} +7.16228i q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.58114 - 2.73861i) q^{56} +3.16228i q^{57} +(7.20928 + 4.16228i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-7.24342 + 12.5460i) q^{61} +(-7.93477 + 4.58114i) q^{62} +(-2.73861 + 1.58114i) q^{63} -1.00000 q^{64} -3.00000 q^{66} +(-3.46410 + 2.00000i) q^{67} +(6.20271 - 3.58114i) q^{68} +(2.08114 - 3.60464i) q^{69} +(3.91886 - 6.78767i) q^{71} +(0.866025 + 0.500000i) q^{72} -1.32456i q^{73} +(5.24342 - 9.08186i) q^{74} +(-1.58114 - 2.73861i) q^{76} +9.48683i q^{77} +(-3.60464 + 0.0811388i) q^{78} -9.16228 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.21584 - 4.74342i) q^{82} -13.6491i q^{83} +(1.58114 - 2.73861i) q^{84} +5.16228 q^{86} +(7.20928 + 4.16228i) q^{87} +(2.59808 - 1.50000i) q^{88} +(-3.58114 - 6.20271i) q^{89} +(0.256584 + 11.3989i) q^{91} +4.16228i q^{92} +(-7.93477 + 4.58114i) q^{93} +(3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(4.04905 + 2.33772i) 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 −0.116657 0.993172i \(-0.537218\pi\)
−0.918441 + 0.395558i \(0.870551\pi\)
\(8\) 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
\(13\) −1.87259 3.08114i −0.519362 0.854554i
\(14\) 3.16228 0.845154
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 6.20271 + 3.58114i 1.50438 + 0.868554i 0.999987 + 0.00507902i \(0.00161671\pi\)
0.504392 + 0.863475i \(0.331717\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.58114 2.73861i 0.362738 0.628281i −0.625672 0.780086i \(-0.715175\pi\)
0.988410 + 0.151805i \(0.0485086\pi\)
\(20\) 0 0
\(21\) 3.16228 0.690066
\(22\) 2.59808 + 1.50000i 0.553912 + 0.319801i
\(23\) −3.60464 + 2.08114i −0.751619 + 0.433947i −0.826279 0.563262i \(-0.809546\pi\)
0.0746596 + 0.997209i \(0.476213\pi\)
\(24\) −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
\(29\) −4.16228 7.20928i −0.772916 1.33873i −0.935959 0.352110i \(-0.885464\pi\)
0.163043 0.986619i \(-0.447869\pi\)
\(30\) 0 0
\(31\) 9.16228 1.64559 0.822797 0.568336i \(-0.192412\pi\)
0.822797 + 0.568336i \(0.192412\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 2.59808 + 1.50000i 0.452267 + 0.261116i
\(34\) −7.16228 −1.22832
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −9.08186 + 5.24342i −1.49305 + 0.862012i −0.999968 0.00797106i \(-0.997463\pi\)
−0.493081 + 0.869983i \(0.664129\pi\)
\(38\) 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 \(0.0988854\pi\)
−0.211336 + 0.977414i \(0.567781\pi\)
\(42\) −2.73861 + 1.58114i −0.422577 + 0.243975i
\(43\) −4.47066 2.58114i −0.681770 0.393620i 0.118752 0.992924i \(-0.462111\pi\)
−0.800522 + 0.599304i \(0.795444\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) 2.08114 3.60464i 0.306847 0.531475i
\(47\) 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
\(51\) −7.16228 −1.00292
\(52\) −3.60464 + 0.0811388i −0.499873 + 0.0112519i
\(53\) 7.16228i 0.983814i 0.870648 + 0.491907i \(0.163700\pi\)
−0.870648 + 0.491907i \(0.836300\pi\)
\(54\) −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
\(58\) 7.20928 + 4.16228i 0.946624 + 0.546534i
\(59\) −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
\(61\) −7.24342 + 12.5460i −0.927424 + 1.60635i −0.139810 + 0.990178i \(0.544649\pi\)
−0.787615 + 0.616168i \(0.788684\pi\)
\(62\) −7.93477 + 4.58114i −1.00772 + 0.581805i
\(63\) −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 \(0.411904\pi\)
\(68\) 6.20271 3.58114i 0.752190 0.434277i
\(69\) 2.08114 3.60464i 0.250540 0.433947i
\(70\) 0 0
\(71\) 3.91886 6.78767i 0.465083 0.805548i −0.534122 0.845407i \(-0.679358\pi\)
0.999205 + 0.0398596i \(0.0126911\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 1.32456i 0.155027i −0.996991 0.0775137i \(-0.975302\pi\)
0.996991 0.0775137i \(-0.0246982\pi\)
\(74\) 5.24342 9.08186i 0.609535 1.05575i
\(75\) 0 0
\(76\) −1.58114 2.73861i −0.181369 0.314140i
\(77\) 9.48683i 1.08112i
\(78\) −3.60464 + 0.0811388i −0.408145 + 0.00918716i
\(79\) −9.16228 −1.03084 −0.515418 0.856939i \(-0.672363\pi\)
−0.515418 + 0.856939i \(0.672363\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −8.21584 4.74342i −0.907288 0.523823i
\(83\) 13.6491i 1.49818i −0.662466 0.749092i \(-0.730490\pi\)
0.662466 0.749092i \(-0.269510\pi\)
\(84\) 1.58114 2.73861i 0.172516 0.298807i
\(85\) 0 0
\(86\) 5.16228 0.556663
\(87\) 7.20928 + 4.16228i 0.772916 + 0.446243i
\(88\) 2.59808 1.50000i 0.276956 0.159901i
\(89\) −3.58114 6.20271i −0.379600 0.657486i 0.611404 0.791319i \(-0.290605\pi\)
−0.991004 + 0.133832i \(0.957272\pi\)
\(90\) 0 0
\(91\) 0.256584 + 11.3989i 0.0268973 + 1.19493i
\(92\) 4.16228i 0.433947i
\(93\) −7.93477 + 4.58114i −0.822797 + 0.475042i
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 4.04905 + 2.33772i 0.411119 + 0.237360i 0.691270 0.722596i \(-0.257051\pi\)
−0.280151 + 0.959956i \(0.590385\pi\)
\(98\) −2.59808 1.50000i −0.262445 0.151523i
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 8.32456 + 14.4186i 0.828324 + 1.43470i 0.899352 + 0.437225i \(0.144039\pi\)
−0.0710278 + 0.997474i \(0.522628\pi\)
\(102\) 6.20271 3.58114i 0.614160 0.354586i
\(103\) 13.4868i 1.32890i 0.747334 + 0.664449i \(0.231334\pi\)
−0.747334 + 0.664449i \(0.768666\pi\)
\(104\) 3.08114 1.87259i 0.302131 0.183622i
\(105\) 0 0
\(106\) −3.58114 6.20271i −0.347831 0.602461i
\(107\) 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
\(109\) −8.48683 −0.812891 −0.406446 0.913675i \(-0.633232\pi\)
−0.406446 + 0.913675i \(0.633232\pi\)
\(110\) 0 0
\(111\) 5.24342 9.08186i 0.497683 0.862012i
\(112\) 3.16228i 0.298807i
\(113\) −2.01312 1.16228i −0.189379 0.109338i 0.402313 0.915502i \(-0.368206\pi\)
−0.591692 + 0.806164i \(0.701540\pi\)
\(114\) −1.58114 2.73861i −0.148087 0.256495i
\(115\) 0 0
\(116\) −8.32456 −0.772916
\(117\) −3.60464 + 0.0811388i −0.333249 + 0.00750129i
\(118\) 6.00000i 0.552345i
\(119\) −11.3246 19.6147i −1.03812 1.79808i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 14.4868i 1.31158i
\(123\) −8.21584 4.74342i −0.740797 0.427699i
\(124\) 4.58114 7.93477i 0.411398 0.712563i
\(125\) 0 0
\(126\) 1.58114 2.73861i 0.140859 0.243975i
\(127\) −6.64713 + 3.83772i −0.589837 + 0.340543i −0.765033 0.643991i \(-0.777277\pi\)
0.175196 + 0.984534i \(0.443944\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 5.16228 0.454513
\(130\) 0 0
\(131\) 3.67544 0.321125 0.160563 0.987026i \(-0.448669\pi\)
0.160563 + 0.987026i \(0.448669\pi\)
\(132\) 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
\(136\) −3.58114 + 6.20271i −0.307080 + 0.531878i
\(137\) 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) 4.16228i 0.354317i
\(139\) −9.16228 + 15.8695i −0.777134 + 1.34604i 0.156453 + 0.987685i \(0.449994\pi\)
−0.933587 + 0.358351i \(0.883339\pi\)
\(140\) 0 0
\(141\) 3.00000 + 5.19615i 0.252646 + 0.437595i
\(142\) 7.83772i 0.657727i
\(143\) −5.19615 + 9.48683i −0.434524 + 0.793329i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 0.662278 + 1.14710i 0.0548105 + 0.0949346i
\(147\) −2.59808 1.50000i −0.214286 0.123718i
\(148\) 10.4868i 0.862012i
\(149\) −6.58114 + 11.3989i −0.539148 + 0.933832i 0.459802 + 0.888021i \(0.347920\pi\)
−0.998950 + 0.0458102i \(0.985413\pi\)
\(150\) 0 0
\(151\) −21.8114 −1.77499 −0.887493 0.460822i \(-0.847555\pi\)
−0.887493 + 0.460822i \(0.847555\pi\)
\(152\) 2.73861 + 1.58114i 0.222131 + 0.128247i
\(153\) 6.20271 3.58114i 0.501460 0.289518i
\(154\) −4.74342 8.21584i −0.382235 0.662051i
\(155\) 0 0
\(156\) 3.08114 1.87259i 0.246689 0.149927i
\(157\) 9.83772i 0.785136i 0.919723 + 0.392568i \(0.128413\pi\)
−0.919723 + 0.392568i \(0.871587\pi\)
\(158\) 7.93477 4.58114i 0.631256 0.364456i
\(159\) −3.58114 6.20271i −0.284003 0.491907i
\(160\) 0 0
\(161\) 13.1623 1.03733
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) −13.6931 7.90569i −1.07252 0.619222i −0.143654 0.989628i \(-0.545885\pi\)
−0.928870 + 0.370406i \(0.879218\pi\)
\(164\) 9.48683 0.740797
\(165\) 0 0
\(166\) 6.82456 + 11.8205i 0.529688 + 0.917447i
\(167\) 1.59151 0.918861i 0.123155 0.0711036i −0.437157 0.899385i \(-0.644015\pi\)
0.560312 + 0.828282i \(0.310681\pi\)
\(168\) 3.16228i 0.243975i
\(169\) −5.98683 + 11.5394i −0.460526 + 0.887646i
\(170\) 0 0
\(171\) −1.58114 2.73861i −0.120913 0.209427i
\(172\) −4.47066 + 2.58114i −0.340885 + 0.196810i
\(173\) −12.4054 7.16228i −0.943167 0.544538i −0.0522155 0.998636i \(-0.516628\pi\)
−0.890952 + 0.454098i \(0.849962\pi\)
\(174\) −8.32456 −0.631083
\(175\) 0 0
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) 6.00000i 0.450988i
\(178\) 6.20271 + 3.58114i 0.464913 + 0.268418i
\(179\) −0.824555 1.42817i −0.0616302 0.106747i 0.833564 0.552423i \(-0.186297\pi\)
−0.895194 + 0.445676i \(0.852963\pi\)
\(180\) 0 0
\(181\) −18.8114 −1.39824 −0.699120 0.715005i \(-0.746425\pi\)
−0.699120 + 0.715005i \(0.746425\pi\)
\(182\) −5.92164 9.74342i −0.438941 0.722230i
\(183\) 14.4868i 1.07090i
\(184\) −2.08114 3.60464i −0.153424 0.265737i
\(185\) 0 0
\(186\) 4.58114 7.93477i 0.335905 0.581805i
\(187\) 21.4868i 1.57127i
\(188\) −5.19615 3.00000i −0.378968 0.218797i
\(189\) 1.58114 2.73861i 0.115011 0.199205i
\(190\) 0 0
\(191\) −11.0811 + 19.1931i −0.801803 + 1.38876i 0.116625 + 0.993176i \(0.462792\pi\)
−0.918428 + 0.395588i \(0.870541\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 4.04905 2.33772i 0.291457 0.168273i −0.347142 0.937813i \(-0.612848\pi\)
0.638599 + 0.769540i \(0.279514\pi\)
\(194\) −4.67544 −0.335677
\(195\) 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
\(199\) 7.58114 13.1309i 0.537413 0.930826i −0.461630 0.887073i \(-0.652735\pi\)
0.999042 0.0437533i \(-0.0139316\pi\)
\(200\) 0 0
\(201\) 2.00000 3.46410i 0.141069 0.244339i
\(202\) −14.4186 8.32456i −1.01449 0.585714i
\(203\) 26.3246i 1.84762i
\(204\) −3.58114 + 6.20271i −0.250730 + 0.434277i
\(205\) 0 0
\(206\) −6.74342 11.6799i −0.469836 0.813780i
\(207\) 4.16228i 0.289298i
\(208\) −1.73205 + 3.16228i −0.120096 + 0.219265i
\(209\) −9.48683 −0.656218
\(210\) 0 0
\(211\) −3.41886 5.92164i −0.235364 0.407663i 0.724014 0.689785i \(-0.242295\pi\)
−0.959378 + 0.282122i \(0.908962\pi\)
\(212\) 6.20271 + 3.58114i 0.426004 + 0.245954i
\(213\) 7.83772i 0.537032i
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −25.0919 14.4868i −1.70335 0.983430i
\(218\) 7.34981 4.24342i 0.497792 0.287400i
\(219\) 0.662278 + 1.14710i 0.0447526 + 0.0775137i
\(220\) 0 0
\(221\) −0.581139 25.8174i −0.0390916 1.73667i
\(222\) 10.4868i 0.703830i
\(223\) 15.7062 9.06797i 1.05176 0.607236i 0.128621 0.991694i \(-0.458945\pi\)
0.923143 + 0.384457i \(0.125611\pi\)
\(224\) −1.58114 2.73861i −0.105644 0.182981i
\(225\) 0 0
\(226\) 2.32456 0.154627
\(227\) 13.8336 + 7.98683i 0.918168 + 0.530105i 0.883050 0.469278i \(-0.155486\pi\)
0.0351181 + 0.999383i \(0.488819\pi\)
\(228\) 2.73861 + 1.58114i 0.181369 + 0.104713i
\(229\) −2.48683 −0.164335 −0.0821673 0.996619i \(-0.526184\pi\)
−0.0821673 + 0.996619i \(0.526184\pi\)
\(230\) 0 0
\(231\) −4.74342 8.21584i −0.312094 0.540562i
\(232\) 7.20928 4.16228i 0.473312 0.273267i
\(233\) 26.3246i 1.72458i −0.506416 0.862289i \(-0.669030\pi\)
0.506416 0.862289i \(-0.330970\pi\)
\(234\) 3.08114 1.87259i 0.201420 0.122415i
\(235\) 0 0
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) 7.93477 4.58114i 0.515418 0.297577i
\(238\) 19.6147 + 11.3246i 1.27143 + 0.734062i
\(239\) 0.486833 0.0314906 0.0157453 0.999876i \(-0.494988\pi\)
0.0157453 + 0.999876i \(0.494988\pi\)
\(240\) 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
\(244\) 7.24342 + 12.5460i 0.463712 + 0.803173i
\(245\) 0 0
\(246\) 9.48683 0.604858
\(247\) −11.3989 + 0.256584i −0.725293 + 0.0163260i
\(248\) 9.16228i 0.581805i
\(249\) 6.82456 + 11.8205i 0.432489 + 0.749092i
\(250\) 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
\(253\) 10.8139 + 6.24342i 0.679865 + 0.392520i
\(254\) 3.83772 6.64713i 0.240800 0.417078i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.03281 2.90569i 0.313938 0.181252i −0.334749 0.942307i \(-0.608652\pi\)
0.648687 + 0.761055i \(0.275318\pi\)
\(258\) −4.47066 + 2.58114i −0.278331 + 0.160695i
\(259\) 33.1623 2.06060
\(260\) 0 0
\(261\) −8.32456 −0.515277
\(262\) −3.18303 + 1.83772i −0.196648 + 0.113535i
\(263\) −16.0101 + 9.24342i −0.987223 + 0.569973i −0.904443 0.426594i \(-0.859713\pi\)
−0.0827800 + 0.996568i \(0.526380\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 0 0
\(266\) 5.00000 8.66025i 0.306570 0.530994i
\(267\) 6.20271 + 3.58114i 0.379600 + 0.219162i
\(268\) 4.00000i 0.244339i
\(269\) −9.58114 + 16.5950i −0.584172 + 1.01182i 0.410806 + 0.911723i \(0.365247\pi\)
−0.994978 + 0.100093i \(0.968086\pi\)
\(270\) 0 0
\(271\) 6.16228 + 10.6734i 0.374332 + 0.648362i 0.990227 0.139467i \(-0.0445388\pi\)
−0.615895 + 0.787828i \(0.711205\pi\)
\(272\) 7.16228i 0.434277i
\(273\) −5.92164 9.74342i −0.358394 0.589698i
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) −2.08114 3.60464i −0.125270 0.216974i
\(277\) −19.7552 11.4057i −1.18698 0.685302i −0.229359 0.973342i \(-0.573663\pi\)
−0.957618 + 0.288040i \(0.906996\pi\)
\(278\) 18.3246i 1.09903i
\(279\) 4.58114 7.93477i 0.274266 0.475042i
\(280\) 0 0
\(281\) −2.51317 −0.149923 −0.0749615 0.997186i \(-0.523883\pi\)
−0.0749615 + 0.997186i \(0.523883\pi\)
\(282\) −5.19615 3.00000i −0.309426 0.178647i
\(283\) 0.444416 0.256584i 0.0264178 0.0152523i −0.486733 0.873551i \(-0.661812\pi\)
0.513151 + 0.858299i \(0.328478\pi\)
\(284\) −3.91886 6.78767i −0.232542 0.402774i
\(285\) 0 0
\(286\) −0.243416 10.8139i −0.0143935 0.639440i
\(287\) 30.0000i 1.77084i
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 17.1491 + 29.7031i 1.00877 + 1.74724i
\(290\) 0 0
\(291\) −4.67544 −0.274079
\(292\) −1.14710 0.662278i −0.0671289 0.0387569i
\(293\) 2.17647 + 1.25658i 0.127151 + 0.0734104i 0.562226 0.826984i \(-0.309945\pi\)
−0.435076 + 0.900394i \(0.643278\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) −5.24342 9.08186i −0.304767 0.527873i
\(297\) 2.59808 1.50000i 0.150756 0.0870388i
\(298\) 13.1623i 0.762470i
\(299\) 13.1623 + 7.20928i 0.761194 + 0.416923i
\(300\) 0 0
\(301\) 8.16228 + 14.1375i 0.470466 + 0.814871i
\(302\) 18.8892 10.9057i 1.08695 0.627552i
\(303\) −14.4186 8.32456i −0.828324 0.478233i
\(304\) −3.16228 −0.181369
\(305\) 0 0
\(306\) −3.58114 + 6.20271i −0.204720 + 0.354586i
\(307\) 8.64911i 0.493631i −0.969063 0.246815i \(-0.920616\pi\)
0.969063 0.246815i \(-0.0793841\pi\)
\(308\) 8.21584 + 4.74342i 0.468141 + 0.270281i
\(309\) −6.74342 11.6799i −0.383620 0.664449i
\(310\) 0 0
\(311\) 12.4868 0.708063 0.354032 0.935233i \(-0.384811\pi\)
0.354032 + 0.935233i \(0.384811\pi\)
\(312\) −1.73205 + 3.16228i −0.0980581 + 0.179029i
\(313\) 17.6491i 0.997587i 0.866721 + 0.498793i \(0.166223\pi\)
−0.866721 + 0.498793i \(0.833777\pi\)
\(314\) −4.91886 8.51972i −0.277587 0.480795i
\(315\) 0 0
\(316\) −4.58114 + 7.93477i −0.257709 + 0.446365i
\(317\) 0.188612i 0.0105935i −0.999986 0.00529674i \(-0.998314\pi\)
0.999986 0.00529674i \(-0.00168601\pi\)
\(318\) 6.20271 + 3.58114i 0.347831 + 0.200820i
\(319\) −12.4868 + 21.6278i −0.699128 + 1.21093i
\(320\) 0 0
\(321\) −3.00000 + 5.19615i −0.167444 + 0.290021i
\(322\) −11.3989 + 6.58114i −0.635234 + 0.366753i
\(323\) 19.6147 11.3246i 1.09139 0.630115i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 15.8114 0.875712
\(327\) 7.34981 4.24342i 0.406446 0.234661i
\(328\) −8.21584 + 4.74342i −0.453644 + 0.261911i
\(329\) −9.48683 + 16.4317i −0.523026 + 0.905908i
\(330\) 0 0
\(331\) 4.41886 7.65369i 0.242883 0.420685i −0.718652 0.695370i \(-0.755240\pi\)
0.961534 + 0.274685i \(0.0885737\pi\)
\(332\) −11.8205 6.82456i −0.648733 0.374546i
\(333\) 10.4868i 0.574675i
\(334\) −0.918861 + 1.59151i −0.0502778 + 0.0870838i
\(335\) 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 \(-0.0347479\pi\)
\(338\) −0.584952 12.9868i −0.0318172 0.706391i
\(339\) 2.32456 0.126253
\(340\) 0 0
\(341\) −13.7434 23.8043i −0.744248 1.28907i
\(342\) 2.73861 + 1.58114i 0.148087 + 0.0854982i
\(343\) 12.6491i 0.682988i
\(344\) 2.58114 4.47066i 0.139166 0.241042i
\(345\) 0 0
\(346\) 14.3246 0.770093
\(347\) 9.80735 + 5.66228i 0.526486 + 0.303967i 0.739584 0.673064i \(-0.235022\pi\)
−0.213098 + 0.977031i \(0.568355\pi\)
\(348\) 7.20928 4.16228i 0.386458 0.223122i
\(349\) 10.7302 + 18.5853i 0.574377 + 0.994850i 0.996109 + 0.0881297i \(0.0280890\pi\)
−0.421732 + 0.906721i \(0.638578\pi\)
\(350\) 0 0
\(351\) 3.08114 1.87259i 0.164459 0.0999513i
\(352\) 3.00000i 0.159901i
\(353\) −10.2290 + 5.90569i −0.544433 + 0.314328i −0.746874 0.664966i \(-0.768446\pi\)
0.202441 + 0.979295i \(0.435113\pi\)
\(354\) 3.00000 + 5.19615i 0.159448 + 0.276172i
\(355\) 0 0
\(356\) −7.16228 −0.379600
\(357\) 19.6147 + 11.3246i 1.03812 + 0.599359i
\(358\) 1.42817 + 0.824555i 0.0754812 + 0.0435791i
\(359\) 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
\(362\) 16.2911 9.40569i 0.856243 0.494352i
\(363\) 2.00000i 0.104973i
\(364\) 10.0000 + 5.47723i 0.524142 + 0.287085i
\(365\) 0 0
\(366\) 7.24342 + 12.5460i 0.378619 + 0.655788i
\(367\) 5.75830 3.32456i 0.300581 0.173540i −0.342123 0.939655i \(-0.611146\pi\)
0.642704 + 0.766115i \(0.277813\pi\)
\(368\) 3.60464 + 2.08114i 0.187905 + 0.108487i
\(369\) 9.48683 0.493865
\(370\) 0 0
\(371\) 11.3246 19.6147i 0.587942 1.01834i
\(372\) 9.16228i 0.475042i
\(373\) 7.34981 + 4.24342i 0.380559 + 0.219716i 0.678061 0.735005i \(-0.262820\pi\)
−0.297503 + 0.954721i \(0.596154\pi\)
\(374\) 10.7434 + 18.6081i 0.555529 + 0.962204i
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −14.4186 + 26.3246i −0.742593 + 1.35578i
\(378\) 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
\(381\) 3.83772 6.64713i 0.196612 0.340543i
\(382\) 22.1623i 1.13392i
\(383\) 3.60464 + 2.08114i 0.184188 + 0.106341i 0.589259 0.807944i \(-0.299420\pi\)
−0.405071 + 0.914285i \(0.632753\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −2.33772 + 4.04905i −0.118987 + 0.206091i
\(387\) −4.47066 + 2.58114i −0.227257 + 0.131207i
\(388\) 4.04905 2.33772i 0.205560 0.118680i
\(389\) 15.6754 0.794777 0.397388 0.917651i \(-0.369917\pi\)
0.397388 + 0.917651i \(0.369917\pi\)
\(390\) 0 0
\(391\) −29.8114 −1.50763
\(392\) −2.59808 + 1.50000i −0.131223 + 0.0757614i
\(393\) −3.18303 + 1.83772i −0.160563 + 0.0927008i
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 0 0
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) 21.0657 + 12.1623i 1.05726 + 0.610407i 0.924672 0.380765i \(-0.124339\pi\)
0.132584 + 0.991172i \(0.457672\pi\)
\(398\) 15.1623i 0.760016i
\(399\) 5.00000 8.66025i 0.250313 0.433555i
\(400\) 0 0
\(401\) −1.83772 3.18303i −0.0917715 0.158953i 0.816485 0.577366i \(-0.195920\pi\)
−0.908257 + 0.418414i \(0.862586\pi\)
\(402\) 4.00000i 0.199502i
\(403\) −17.1572 28.2302i −0.854659 1.40625i
\(404\) 16.6491 0.828324
\(405\) 0 0
\(406\) −13.1623 22.7977i −0.653233 1.13143i
\(407\) 27.2456 + 15.7302i 1.35051 + 0.779720i
\(408\) 7.16228i 0.354586i
\(409\) 8.83772 15.3074i 0.436997 0.756901i −0.560459 0.828182i \(-0.689375\pi\)
0.997456 + 0.0712807i \(0.0227086\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 11.6799 + 6.74342i 0.575429 + 0.332224i
\(413\) 16.4317 9.48683i 0.808550 0.466817i
\(414\) −2.08114 3.60464i −0.102282 0.177158i
\(415\) 0 0
\(416\) −0.0811388 3.60464i −0.00397816 0.176732i
\(417\) 18.3246i 0.897357i
\(418\) 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
\(421\) 21.8377 1.06431 0.532153 0.846648i \(-0.321383\pi\)
0.532153 + 0.846648i \(0.321383\pi\)
\(422\) 5.92164 + 3.41886i 0.288261 + 0.166428i
\(423\) −5.19615 3.00000i −0.252646 0.145865i
\(424\) −7.16228 −0.347831
\(425\) 0 0
\(426\) −3.91886 6.78767i −0.189869 0.328864i
\(427\) 39.6738 22.9057i 1.91995 1.10848i
\(428\) 6.00000i 0.290021i
\(429\) −0.243416 10.8139i −0.0117523 0.522101i
\(430\) 0 0
\(431\) 2.75658 + 4.77454i 0.132780 + 0.229982i 0.924747 0.380582i \(-0.124276\pi\)
−0.791967 + 0.610564i \(0.790943\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 24.7881 + 14.3114i 1.19124 + 0.687761i 0.958587 0.284799i \(-0.0919269\pi\)
0.232650 + 0.972560i \(0.425260\pi\)
\(434\) 28.9737 1.39078
\(435\) 0 0
\(436\) −4.24342 + 7.34981i −0.203223 + 0.351992i
\(437\) 13.1623i 0.629637i
\(438\) −1.14710 0.662278i −0.0548105 0.0316449i
\(439\) −5.67544 9.83016i −0.270874 0.469168i 0.698212 0.715891i \(-0.253979\pi\)
−0.969086 + 0.246723i \(0.920646\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 13.4120 + 22.0680i 0.637943 + 1.04967i
\(443\) 9.00000i 0.427603i 0.976877 + 0.213801i \(0.0685846\pi\)
−0.976877 + 0.213801i \(0.931415\pi\)
\(444\) −5.24342 9.08186i −0.248842 0.431006i
\(445\) 0 0
\(446\) −9.06797 + 15.7062i −0.429381 + 0.743710i
\(447\) 13.1623i 0.622554i
\(448\) 2.73861 + 1.58114i 0.129387 + 0.0747018i
\(449\) 10.7434 18.6081i 0.507013 0.878173i −0.492954 0.870055i \(-0.664083\pi\)
0.999967 0.00811713i \(-0.00258379\pi\)
\(450\) 0 0
\(451\) 14.2302 24.6475i 0.670076 1.16061i
\(452\) −2.01312 + 1.16228i −0.0946894 + 0.0546689i
\(453\) 18.8892 10.9057i 0.887493 0.512394i
\(454\) −15.9737 −0.749681
\(455\) 0 0
\(456\) −3.16228 −0.148087
\(457\) −30.8730 + 17.8246i −1.44418 + 0.833798i −0.998125 0.0612082i \(-0.980505\pi\)
−0.446055 + 0.895006i \(0.647171\pi\)
\(458\) 2.15366 1.24342i 0.100634 0.0581010i
\(459\) −3.58114 + 6.20271i −0.167153 + 0.289518i
\(460\) 0 0
\(461\) 5.41886 9.38574i 0.252382 0.437138i −0.711799 0.702383i \(-0.752120\pi\)
0.964181 + 0.265245i \(0.0854529\pi\)
\(462\) 8.21584 + 4.74342i 0.382235 + 0.220684i
\(463\) 23.4868i 1.09153i −0.837940 0.545763i \(-0.816240\pi\)
0.837940 0.545763i \(-0.183760\pi\)
\(464\) −4.16228 + 7.20928i −0.193229 + 0.334682i
\(465\) 0 0
\(466\) 13.1623 + 22.7977i 0.609731 + 1.05608i
\(467\) 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
\(471\) −4.91886 8.51972i −0.226649 0.392568i
\(472\) −5.19615 3.00000i −0.239172 0.138086i
\(473\) 15.4868i 0.712085i
\(474\) −4.58114 + 7.93477i −0.210419 + 0.364456i
\(475\) 0 0
\(476\) −22.6491 −1.03812
\(477\) 6.20271 + 3.58114i 0.284003 + 0.163969i
\(478\) −0.421610 + 0.243416i −0.0192840 + 0.0111336i
\(479\) −13.1623 22.7977i −0.601400 1.04166i −0.992609 0.121353i \(-0.961277\pi\)
0.391210 0.920302i \(-0.372057\pi\)
\(480\) 0 0
\(481\) 33.1623 + 18.1637i 1.51207 + 0.828195i
\(482\) 8.00000i 0.364390i
\(483\) −11.3989 + 6.58114i −0.518666 + 0.299452i
\(484\) −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 0.436666 0.899624i \(-0.356159\pi\)
−0.560764 + 0.827976i \(0.689493\pi\)
\(488\) −12.5460 7.24342i −0.567929 0.327894i
\(489\) 15.8114 0.715016
\(490\) 0 0
\(491\) −7.98683 13.8336i −0.360441 0.624302i 0.627593 0.778542i \(-0.284040\pi\)
−0.988033 + 0.154240i \(0.950707\pi\)
\(492\) −8.21584 + 4.74342i −0.370399 + 0.213850i
\(493\) 59.6228i 2.68527i
\(494\) 9.74342 5.92164i 0.438377 0.266427i
\(495\) 0 0
\(496\) −4.58114 7.93477i −0.205699 0.356281i
\(497\) −21.4645 + 12.3925i −0.962814 + 0.555881i
\(498\) −11.8205 6.82456i −0.529688 0.305816i
\(499\) −8.18861 −0.366573 −0.183286 0.983060i \(-0.558674\pi\)
−0.183286 + 0.983060i \(0.558674\pi\)
\(500\) 0 0
\(501\) −0.918861 + 1.59151i −0.0410517 + 0.0711036i
\(502\) 15.0000i 0.669483i
\(503\) 12.8270 + 7.40569i 0.571929 + 0.330204i 0.757920 0.652348i \(-0.226216\pi\)
−0.185990 + 0.982552i \(0.559549\pi\)
\(504\) −1.58114 2.73861i −0.0704295 0.121988i
\(505\) 0 0
\(506\) −12.4868 −0.555107
\(507\) −0.584952 12.9868i −0.0259786 0.576766i
\(508\) 7.67544i 0.340543i
\(509\) 21.3925 + 37.0529i 0.948207 + 1.64234i 0.749199 + 0.662345i \(0.230439\pi\)
0.199008 + 0.979998i \(0.436228\pi\)
\(510\) 0 0
\(511\) −2.09431 + 3.62744i −0.0926466 + 0.160469i
\(512\) 1.00000i 0.0441942i
\(513\) 2.73861 + 1.58114i 0.120913 + 0.0698090i
\(514\) −2.90569 + 5.03281i −0.128165 + 0.221988i
\(515\) 0 0
\(516\) 2.58114 4.47066i 0.113628 0.196810i
\(517\) −15.5885 + 9.00000i −0.685580 + 0.395820i
\(518\) −28.7194 + 16.5811i −1.26186 + 0.728533i
\(519\) 14.3246 0.628778
\(520\) 0 0
\(521\) 4.64911 0.203681 0.101841 0.994801i \(-0.467527\pi\)
0.101841 + 0.994801i \(0.467527\pi\)
\(522\) 7.20928 4.16228i 0.315541 0.182178i
\(523\) 4.30732 2.48683i 0.188346 0.108742i −0.402862 0.915261i \(-0.631985\pi\)
0.591208 + 0.806519i \(0.298651\pi\)
\(524\) 1.83772 3.18303i 0.0802813 0.139051i
\(525\) 0 0
\(526\) 9.24342 16.0101i 0.403032 0.698072i
\(527\) 56.8310 + 32.8114i 2.47560 + 1.42929i
\(528\) 3.00000i 0.130558i
\(529\) −2.83772 + 4.91508i −0.123379 + 0.213699i
\(530\) 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
\(534\) −7.16228 −0.309942
\(535\) 0 0
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 1.42817 + 0.824555i 0.0616302 + 0.0355822i
\(538\) 19.1623i 0.826144i
\(539\) 4.50000 7.79423i 0.193829 0.335721i
\(540\) 0 0
\(541\) −0.811388 −0.0348843 −0.0174422 0.999848i \(-0.505552\pi\)
−0.0174422 + 0.999848i \(0.505552\pi\)
\(542\) −10.6734 6.16228i −0.458461 0.264692i
\(543\) 16.2911 9.40569i 0.699120 0.403637i
\(544\) 3.58114 + 6.20271i 0.153540 + 0.265939i
\(545\) 0 0
\(546\) 10.0000 + 5.47723i 0.427960 + 0.234404i
\(547\) 30.1359i 1.28852i −0.764807 0.644260i \(-0.777165\pi\)
0.764807 0.644260i \(-0.222835\pi\)
\(548\) 10.3923 6.00000i 0.443937 0.256307i
\(549\) 7.24342 + 12.5460i 0.309141 + 0.535449i
\(550\) 0 0
\(551\) −26.3246 −1.12146
\(552\) 3.60464 + 2.08114i 0.153424 + 0.0885792i
\(553\) 25.0919 + 14.4868i 1.06702 + 0.616043i
\(554\) 22.8114 0.969163
\(555\) 0 0
\(556\) 9.16228 + 15.8695i 0.388567 + 0.673018i
\(557\) −16.4317 + 9.48683i −0.696232 + 0.401970i −0.805943 0.591994i \(-0.798341\pi\)
0.109710 + 0.993964i \(0.465008\pi\)
\(558\) 9.16228i 0.387870i
\(559\) 0.418861 + 18.6081i 0.0177159 + 0.787041i
\(560\) 0 0
\(561\) 10.7434 + 18.6081i 0.453587 + 0.785636i
\(562\) 2.17647 1.25658i 0.0918087 0.0530058i
\(563\) −3.44130 1.98683i −0.145033 0.0837350i 0.425727 0.904851i \(-0.360018\pi\)
−0.570761 + 0.821116i \(0.693352\pi\)
\(564\) 6.00000 0.252646
\(565\) 0 0
\(566\) −0.256584 + 0.444416i −0.0107850 + 0.0186802i
\(567\) 3.16228i 0.132803i
\(568\) 6.78767 + 3.91886i 0.284804 + 0.164432i
\(569\) 15.4868 + 26.8240i 0.649242 + 1.12452i 0.983304 + 0.181969i \(0.0582470\pi\)
−0.334062 + 0.942551i \(0.608420\pi\)
\(570\) 0 0
\(571\) −19.6754 −0.823392 −0.411696 0.911321i \(-0.635063\pi\)
−0.411696 + 0.911321i \(0.635063\pi\)
\(572\) 5.61776 + 9.24342i 0.234890 + 0.386487i
\(573\) 22.1623i 0.925842i
\(574\) 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 \(-0.352865\pi\)
\(578\) −29.7031 17.1491i −1.23549 0.713309i
\(579\) −2.33772 + 4.04905i −0.0971524 + 0.168273i
\(580\) 0 0
\(581\) −21.5811 + 37.3796i −0.895337 + 1.55077i
\(582\) 4.04905 2.33772i 0.167839 0.0969017i
\(583\) 18.6081 10.7434i 0.770671 0.444947i
\(584\) 1.32456 0.0548105
\(585\) 0 0
\(586\) −2.51317 −0.103818
\(587\) −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
\(589\) 14.4868 25.0919i 0.596920 1.03389i
\(590\) 0 0
\(591\) 3.00000 5.19615i 0.123404 0.213741i
\(592\) 9.08186 + 5.24342i 0.373262 + 0.215503i
\(593\) 1.16228i 0.0477290i −0.999715 0.0238645i \(-0.992403\pi\)
0.999715 0.0238645i \(-0.00759703\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) 0 0
\(596\) 6.58114 + 11.3989i 0.269574 + 0.466916i
\(597\) 15.1623i 0.620551i
\(598\) −15.0035 + 0.337722i −0.613539 + 0.0138105i
\(599\) −32.8114 −1.34064 −0.670318 0.742074i \(-0.733843\pi\)
−0.670318 + 0.742074i \(0.733843\pi\)
\(600\) 0 0
\(601\) 3.64911 + 6.32045i 0.148850 + 0.257816i 0.930803 0.365522i \(-0.119109\pi\)
−0.781952 + 0.623338i \(0.785776\pi\)
\(602\) −14.1375 8.16228i −0.576201 0.332670i
\(603\) 4.00000i 0.162893i
\(604\) −10.9057 + 18.8892i −0.443746 + 0.768591i
\(605\) 0 0
\(606\) 16.6491 0.676324
\(607\) −20.5035 11.8377i −0.832213 0.480478i 0.0223969 0.999749i \(-0.492870\pi\)
−0.854610 + 0.519271i \(0.826204\pi\)
\(608\) 2.73861 1.58114i 0.111065 0.0641236i
\(609\) −13.1623 22.7977i −0.533362 0.923811i
\(610\) 0 0
\(611\) −18.4868 + 11.2355i −0.747897 + 0.454541i
\(612\) 7.16228i 0.289518i
\(613\) −25.6997 + 14.8377i −1.03800 + 0.599290i −0.919266 0.393636i \(-0.871217\pi\)
−0.118734 + 0.992926i \(0.537884\pi\)
\(614\) 4.32456 + 7.49035i 0.174525 + 0.302286i
\(615\) 0 0
\(616\) −9.48683 −0.382235
\(617\) −2.85634 1.64911i −0.114992 0.0663907i 0.441401 0.897310i \(-0.354482\pi\)
−0.556393 + 0.830919i \(0.687815\pi\)
\(618\) 11.6799 + 6.74342i 0.469836 + 0.271260i
\(619\) −8.00000 −0.321547 −0.160774 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(620\) 0 0
\(621\) −2.08114 3.60464i −0.0835132 0.144649i
\(622\) −10.8139 + 6.24342i −0.433598 + 0.250338i
\(623\) 22.6491i 0.907417i
\(624\) −0.0811388 3.60464i −0.00324815 0.144301i
\(625\) 0 0
\(626\) −8.82456 15.2846i −0.352700 0.610895i
\(627\) 8.21584 4.74342i 0.328109 0.189434i
\(628\) 8.51972 + 4.91886i 0.339974 + 0.196284i
\(629\) −75.1096 −2.99482
\(630\) 0 0
\(631\) −17.6491 + 30.5692i −0.702600 + 1.21694i 0.264951 + 0.964262i \(0.414644\pi\)
−0.967551 + 0.252677i \(0.918689\pi\)
\(632\) 9.16228i 0.364456i
\(633\) 5.92164 + 3.41886i 0.235364 + 0.135888i
\(634\) 0.0943058 + 0.163343i 0.00374536 + 0.00648716i
\(635\) 0 0
\(636\) −7.16228 −0.284003
\(637\) 5.19615 9.48683i 0.205879 0.375882i
\(638\) 24.9737i 0.988717i
\(639\) −3.91886 6.78767i −0.155028 0.268516i
\(640\) 0 0
\(641\) 24.9737 43.2557i 0.986400 1.70850i 0.350861 0.936428i \(-0.385889\pi\)
0.635540 0.772068i \(-0.280778\pi\)
\(642\) 6.00000i 0.236801i
\(643\) −21.0657 12.1623i −0.830749 0.479633i 0.0233598 0.999727i \(-0.492564\pi\)
−0.854109 + 0.520094i \(0.825897\pi\)
\(644\) 6.58114 11.3989i 0.259333 0.449178i
\(645\) 0 0
\(646\) −11.3246 + 19.6147i −0.445559 + 0.771730i
\(647\) −36.7947 + 21.2434i −1.44655 + 0.835165i −0.998274 0.0587312i \(-0.981295\pi\)
−0.448274 + 0.893896i \(0.647961\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 18.0000 0.706562
\(650\) 0 0
\(651\) 28.9737 1.13557
\(652\) −13.6931 + 7.90569i −0.536262 + 0.309611i
\(653\) −8.21584 + 4.74342i −0.321511 + 0.185624i −0.652066 0.758162i \(-0.726097\pi\)
0.330555 + 0.943787i \(0.392764\pi\)
\(654\) −4.24342 + 7.34981i −0.165931 + 0.287400i
\(655\) 0 0
\(656\) 4.74342 8.21584i 0.185199 0.320775i
\(657\) −1.14710 0.662278i −0.0447526 0.0258379i
\(658\) 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 \(-0.335411\pi\)
\(662\) 8.83772i 0.343488i
\(663\) 13.4120 + 22.0680i 0.520879 + 0.857049i
\(664\) 13.6491 0.529688
\(665\) 0 0
\(666\) −5.24342 9.08186i −0.203178 0.351915i
\(667\) 30.0070 + 17.3246i 1.16188 + 0.670809i
\(668\) 1.83772i 0.0711036i
\(669\) −9.06797 + 15.7062i −0.350588 + 0.607236i
\(670\) 0 0
\(671\) 43.4605 1.67777
\(672\) 2.73861 + 1.58114i 0.105644 + 0.0609938i
\(673\) −18.7487 + 10.8246i −0.722708 + 0.417256i −0.815749 0.578406i \(-0.803675\pi\)
0.0930403 + 0.995662i \(0.470341\pi\)
\(674\) 2.00000 + 3.46410i 0.0770371 + 0.133432i
\(675\) 0 0
\(676\) 7.00000 + 10.9545i 0.269231 + 0.421325i
\(677\) 7.35089i 0.282518i −0.989973 0.141259i \(-0.954885\pi\)
0.989973 0.141259i \(-0.0451150\pi\)
\(678\) −2.01312 + 1.16228i −0.0773136 + 0.0446370i
\(679\) −7.39253 12.8042i −0.283699 0.491381i
\(680\) 0 0
\(681\) −15.9737 −0.612112
\(682\) 23.8043 + 13.7434i 0.911514 + 0.526263i
\(683\) 40.6576 + 23.4737i 1.55572 + 0.898195i 0.997658 + 0.0683948i \(0.0217878\pi\)
0.558061 + 0.829800i \(0.311546\pi\)
\(684\) −3.16228 −0.120913
\(685\) 0 0
\(686\) −6.32456 10.9545i −0.241473 0.418243i
\(687\) 2.15366 1.24342i 0.0821673 0.0474393i
\(688\) 5.16228i 0.196810i
\(689\) 22.0680 13.4120i 0.840723 0.510956i
\(690\) 0 0
\(691\) −25.9737 44.9877i −0.988085 1.71141i −0.627333 0.778751i \(-0.715853\pi\)
−0.360752 0.932662i \(-0.617480\pi\)
\(692\) −12.4054 + 7.16228i −0.471584 + 0.272269i
\(693\) 8.21584 + 4.74342i 0.312094 + 0.180187i
\(694\) −11.3246 −0.429874
\(695\) 0 0
\(696\) −4.16228 + 7.20928i −0.157771 + 0.273267i
\(697\) 67.9473i 2.57369i
\(698\) −18.5853 10.7302i −0.703465 0.406146i
\(699\) 13.1623 + 22.7977i 0.497843 + 0.862289i
\(700\) 0 0
\(701\) 34.4605 1.30156 0.650778 0.759268i \(-0.274443\pi\)
0.650778 + 0.759268i \(0.274443\pi\)
\(702\) −1.73205 + 3.16228i −0.0653720 + 0.119352i
\(703\) 33.1623i 1.25074i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 5.90569 10.2290i 0.222264 0.384972i
\(707\) 52.6491i 1.98007i
\(708\) −5.19615 3.00000i −0.195283 0.112747i
\(709\) 10.2434 17.7421i 0.384700 0.666319i −0.607028 0.794681i \(-0.707638\pi\)
0.991727 + 0.128361i \(0.0409717\pi\)
\(710\) 0 0
\(711\) −4.58114 + 7.93477i −0.171806 + 0.297577i
\(712\) 6.20271 3.58114i 0.232457 0.134209i
\(713\) −33.0267 + 19.0680i −1.23686 + 0.714101i
\(714\) −22.6491 −0.847622
\(715\) 0 0
\(716\) −1.64911 −0.0616302
\(717\) −0.421610 + 0.243416i −0.0157453 + 0.00909056i
\(718\) −10.3923 + 6.00000i −0.387837 + 0.223918i
\(719\) −7.59431 + 13.1537i −0.283220 + 0.490551i −0.972176 0.234252i \(-0.924736\pi\)
0.688956 + 0.724803i \(0.258069\pi\)
\(720\) 0 0
\(721\) 21.3246 36.9352i 0.794168 1.37554i
\(722\) −7.79423 4.50000i −0.290071 0.167473i
\(723\) 8.00000i 0.297523i
\(724\) −9.40569 + 16.2911i −0.349560 + 0.605455i
\(725\) 0 0
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) 0.324555i 0.0120371i −0.999982 0.00601855i \(-0.998084\pi\)
0.999982 0.00601855i \(-0.00191577\pi\)
\(728\) −11.3989 + 0.256584i −0.422470 + 0.00950962i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −18.4868 32.0201i −0.683760 1.18431i
\(732\) −12.5460 7.24342i −0.463712 0.267724i
\(733\) 38.4868i 1.42154i −0.703423 0.710772i \(-0.748346\pi\)
0.703423 0.710772i \(-0.251654\pi\)
\(734\) −3.32456 + 5.75830i −0.122712 + 0.212543i
\(735\) 0 0
\(736\) −4.16228 −0.153424
\(737\) 10.3923 + 6.00000i 0.382805 + 0.221013i
\(738\) −8.21584 + 4.74342i −0.302429 + 0.174608i
\(739\) −15.6491 27.1051i −0.575662 0.997076i −0.995969 0.0896938i \(-0.971411\pi\)
0.420308 0.907382i \(-0.361922\pi\)
\(740\) 0 0
\(741\) 9.74342 5.92164i 0.357933 0.217537i
\(742\) 22.6491i 0.831475i
\(743\) 16.7584 9.67544i 0.614805 0.354958i −0.160039 0.987111i \(-0.551162\pi\)
0.774844 + 0.632153i \(0.217829\pi\)
\(744\) −4.58114 7.93477i −0.167953 0.290903i
\(745\) 0 0
\(746\) −8.48683 −0.310725
\(747\) −11.8205 6.82456i −0.432489 0.249697i
\(748\) −18.6081 10.7434i −0.680381 0.392818i
\(749\) −18.9737 −0.693283
\(750\) 0 0
\(751\) 15.1623 + 26.2618i 0.553279 + 0.958308i 0.998035 + 0.0626561i \(0.0199571\pi\)
−0.444756 + 0.895652i \(0.646710\pi\)
\(752\) −5.19615 + 3.00000i −0.189484 + 0.109399i
\(753\) 15.0000i 0.546630i
\(754\) −0.675445 30.0070i −0.0245982 1.09279i
\(755\) 0 0
\(756\) −1.58114 2.73861i −0.0575055 0.0996024i
\(757\) 23.3599 13.4868i 0.849029 0.490187i −0.0112939 0.999936i \(-0.503595\pi\)
0.860323 + 0.509749i \(0.170262\pi\)
\(758\) −1.73205 1.00000i −0.0629109 0.0363216i
\(759\) −12.4868 −0.453243
\(760\) 0 0
\(761\) −5.23025 + 9.05906i −0.189596 + 0.328391i −0.945116 0.326736i \(-0.894051\pi\)
0.755519 + 0.655126i \(0.227385\pi\)
\(762\) 7.67544i 0.278052i
\(763\) 23.2421 + 13.4189i 0.841422 + 0.485795i
\(764\) 11.0811 + 19.1931i 0.400902 + 0.694382i
\(765\) 0 0
\(766\) −4.16228 −0.150389
\(767\) 21.6278 0.486833i 0.780936 0.0175785i
\(768\) 1.00000i 0.0360844i
\(769\) −11.4868 19.8958i −0.414226 0.717460i 0.581121 0.813817i \(-0.302614\pi\)
−0.995347 + 0.0963570i \(0.969281\pi\)
\(770\) 0 0
\(771\) −2.90569 + 5.03281i −0.104646 + 0.181252i
\(772\) 4.67544i 0.168273i
\(773\) −30.0070 17.3246i −1.07928 0.623121i −0.148576 0.988901i \(-0.547469\pi\)
−0.930701 + 0.365780i \(0.880802\pi\)
\(774\) 2.58114 4.47066i 0.0927771 0.160695i
\(775\) 0 0
\(776\) −2.33772 + 4.04905i −0.0839193 + 0.145353i
\(777\) −28.7194 + 16.5811i −1.03030 + 0.594845i
\(778\) −13.5753 + 7.83772i −0.486699 + 0.280996i
\(779\) 30.0000 1.07486
\(780\) 0 0
\(781\) −23.5132 −0.841367
\(782\) 25.8174 14.9057i 0.923229 0.533027i
\(783\) 7.20928 4.16228i 0.257639 0.148748i
\(784\) 1.50000 2.59808i 0.0535714 0.0927884i