Properties

Label 1950.2.i.ba.451.2
Level $1950$
Weight $2$
Character 1950.451
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{10})\)
Defining polynomial: \(x^{4} + 10 x^{2} + 100\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.2
Root \(1.58114 + 2.73861i\) of defining polynomial
Character \(\chi\) \(=\) 1950.451
Dual form 1950.2.i.ba.601.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.58114 + 2.73861i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.58114 + 2.73861i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(-3.08114 - 1.87259i) q^{13} -3.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.58114 - 6.20271i) q^{17} +1.00000 q^{18} +(-1.58114 - 2.73861i) q^{19} +3.16228 q^{21} +(-1.50000 - 2.59808i) q^{22} +(2.08114 - 3.60464i) q^{23} +(0.500000 - 0.866025i) q^{24} +(3.16228 - 1.73205i) q^{26} -1.00000 q^{27} +(1.58114 - 2.73861i) q^{28} +(4.16228 - 7.20928i) q^{29} +9.16228 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +7.16228 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-5.24342 + 9.08186i) q^{37} +3.16228 q^{38} +(-3.16228 + 1.73205i) q^{39} +(4.74342 - 8.21584i) q^{41} +(-1.58114 + 2.73861i) q^{42} +(-2.58114 - 4.47066i) q^{43} +3.00000 q^{44} +(2.08114 + 3.60464i) q^{46} +6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} -7.16228 q^{51} +(-0.0811388 + 3.60464i) q^{52} +7.16228 q^{53} +(0.500000 - 0.866025i) q^{54} +(1.58114 + 2.73861i) q^{56} -3.16228 q^{57} +(4.16228 + 7.20928i) q^{58} +(3.00000 + 5.19615i) q^{59} +(-7.24342 - 12.5460i) q^{61} +(-4.58114 + 7.93477i) q^{62} +(1.58114 - 2.73861i) q^{63} +1.00000 q^{64} -3.00000 q^{66} +(-2.00000 + 3.46410i) q^{67} +(-3.58114 + 6.20271i) q^{68} +(-2.08114 - 3.60464i) q^{69} +(3.91886 + 6.78767i) q^{71} +(-0.500000 - 0.866025i) q^{72} -1.32456 q^{73} +(-5.24342 - 9.08186i) q^{74} +(-1.58114 + 2.73861i) q^{76} -9.48683 q^{77} +(0.0811388 - 3.60464i) q^{78} +9.16228 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.74342 + 8.21584i) q^{82} -13.6491 q^{83} +(-1.58114 - 2.73861i) q^{84} +5.16228 q^{86} +(-4.16228 - 7.20928i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(3.58114 - 6.20271i) q^{89} +(0.256584 - 11.3989i) q^{91} -4.16228 q^{92} +(4.58114 - 7.93477i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-2.33772 - 4.04905i) q^{97} +(-1.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} + 4 q^{8} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} + 4 q^{8} - 2 q^{9} - 6 q^{11} - 4 q^{12} - 6 q^{13} - 2 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{22} + 2 q^{23} + 2 q^{24} - 4 q^{27} + 4 q^{29} + 24 q^{31} - 2 q^{32} + 6 q^{33} + 16 q^{34} - 2 q^{36} - 2 q^{37} - 4 q^{43} + 12 q^{44} + 2 q^{46} + 24 q^{47} + 2 q^{48} - 6 q^{49} - 16 q^{51} + 6 q^{52} + 16 q^{53} + 2 q^{54} + 4 q^{58} + 12 q^{59} - 10 q^{61} - 12 q^{62} + 4 q^{64} - 12 q^{66} - 8 q^{67} - 8 q^{68} - 2 q^{69} + 22 q^{71} - 2 q^{72} + 20 q^{73} - 2 q^{74} - 6 q^{78} + 24 q^{79} - 2 q^{81} - 4 q^{83} + 8 q^{86} - 4 q^{87} - 6 q^{88} + 8 q^{89} + 20 q^{91} - 4 q^{92} + 12 q^{93} - 12 q^{94} - 4 q^{96} - 22 q^{97} - 6 q^{98} + 12 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 1.58114 + 2.73861i 0.597614 + 1.03510i 0.993172 + 0.116657i \(0.0372179\pi\)
−0.395558 + 0.918441i \(0.629449\pi\)
\(8\) 1.00000 0.353553
\(9\) −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 \(0.316051\pi\)
\(12\) −1.00000 −0.288675
\(13\) −3.08114 1.87259i −0.854554 0.519362i
\(14\) −3.16228 −0.845154
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.58114 6.20271i −0.868554 1.50438i −0.863475 0.504392i \(-0.831717\pi\)
−0.00507902 0.999987i \(-0.501617\pi\)
\(18\) 1.00000 0.235702
\(19\) −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
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 2.08114 3.60464i 0.433947 0.751619i −0.563262 0.826279i \(-0.690454\pi\)
0.997209 + 0.0746596i \(0.0237870\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) 3.16228 1.73205i 0.620174 0.339683i
\(27\) −1.00000 −0.192450
\(28\) 1.58114 2.73861i 0.298807 0.517549i
\(29\) 4.16228 7.20928i 0.772916 1.33873i −0.163043 0.986619i \(-0.552131\pi\)
0.935959 0.352110i \(-0.114536\pi\)
\(30\) 0 0
\(31\) 9.16228 1.64559 0.822797 0.568336i \(-0.192412\pi\)
0.822797 + 0.568336i \(0.192412\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 7.16228 1.22832
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −5.24342 + 9.08186i −0.862012 + 1.49305i 0.00797106 + 0.999968i \(0.497463\pi\)
−0.869983 + 0.493081i \(0.835871\pi\)
\(38\) 3.16228 0.512989
\(39\) −3.16228 + 1.73205i −0.506370 + 0.277350i
\(40\) 0 0
\(41\) 4.74342 8.21584i 0.740797 1.28310i −0.211336 0.977414i \(-0.567781\pi\)
0.952133 0.305685i \(-0.0988854\pi\)
\(42\) −1.58114 + 2.73861i −0.243975 + 0.422577i
\(43\) −2.58114 4.47066i −0.393620 0.681770i 0.599304 0.800522i \(-0.295444\pi\)
−0.992924 + 0.118752i \(0.962111\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) 2.08114 + 3.60464i 0.306847 + 0.531475i
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) 0 0
\(51\) −7.16228 −1.00292
\(52\) −0.0811388 + 3.60464i −0.0112519 + 0.499873i
\(53\) 7.16228 0.983814 0.491907 0.870648i \(-0.336300\pi\)
0.491907 + 0.870648i \(0.336300\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 1.58114 + 2.73861i 0.211289 + 0.365963i
\(57\) −3.16228 −0.418854
\(58\) 4.16228 + 7.20928i 0.546534 + 0.946624i
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) −7.24342 12.5460i −0.927424 1.60635i −0.787615 0.616168i \(-0.788684\pi\)
−0.139810 0.990178i \(-0.544649\pi\)
\(62\) −4.58114 + 7.93477i −0.581805 + 1.00772i
\(63\) 1.58114 2.73861i 0.199205 0.345033i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 −0.369274
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) −3.58114 + 6.20271i −0.434277 + 0.752190i
\(69\) −2.08114 3.60464i −0.250540 0.433947i
\(70\) 0 0
\(71\) 3.91886 + 6.78767i 0.465083 + 0.805548i 0.999205 0.0398596i \(-0.0126911\pi\)
−0.534122 + 0.845407i \(0.679358\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −1.32456 −0.155027 −0.0775137 0.996991i \(-0.524698\pi\)
−0.0775137 + 0.996991i \(0.524698\pi\)
\(74\) −5.24342 9.08186i −0.609535 1.05575i
\(75\) 0 0
\(76\) −1.58114 + 2.73861i −0.181369 + 0.314140i
\(77\) −9.48683 −1.08112
\(78\) 0.0811388 3.60464i 0.00918716 0.408145i
\(79\) 9.16228 1.03084 0.515418 0.856939i \(-0.327637\pi\)
0.515418 + 0.856939i \(0.327637\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.74342 + 8.21584i 0.523823 + 0.907288i
\(83\) −13.6491 −1.49818 −0.749092 0.662466i \(-0.769510\pi\)
−0.749092 + 0.662466i \(0.769510\pi\)
\(84\) −1.58114 2.73861i −0.172516 0.298807i
\(85\) 0 0
\(86\) 5.16228 0.556663
\(87\) −4.16228 7.20928i −0.446243 0.772916i
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) 3.58114 6.20271i 0.379600 0.657486i −0.611404 0.791319i \(-0.709395\pi\)
0.991004 + 0.133832i \(0.0427283\pi\)
\(90\) 0 0
\(91\) 0.256584 11.3989i 0.0268973 1.19493i
\(92\) −4.16228 −0.433947
\(93\) 4.58114 7.93477i 0.475042 0.822797i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −2.33772 4.04905i −0.237360 0.411119i 0.722596 0.691270i \(-0.242949\pi\)
−0.959956 + 0.280151i \(0.909615\pi\)
\(98\) −1.50000 2.59808i −0.151523 0.262445i
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) 8.32456 14.4186i 0.828324 1.43470i −0.0710278 0.997474i \(-0.522628\pi\)
0.899352 0.437225i \(-0.144039\pi\)
\(102\) 3.58114 6.20271i 0.354586 0.614160i
\(103\) 13.4868 1.32890 0.664449 0.747334i \(-0.268666\pi\)
0.664449 + 0.747334i \(0.268666\pi\)
\(104\) −3.08114 1.87259i −0.302131 0.183622i
\(105\) 0 0
\(106\) −3.58114 + 6.20271i −0.347831 + 0.602461i
\(107\) 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i \(-0.739671\pi\)
0.973814 + 0.227345i \(0.0730044\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 8.48683 0.812891 0.406446 0.913675i \(-0.366768\pi\)
0.406446 + 0.913675i \(0.366768\pi\)
\(110\) 0 0
\(111\) 5.24342 + 9.08186i 0.497683 + 0.862012i
\(112\) −3.16228 −0.298807
\(113\) −1.16228 2.01312i −0.109338 0.189379i 0.806164 0.591692i \(-0.201540\pi\)
−0.915502 + 0.402313i \(0.868206\pi\)
\(114\) 1.58114 2.73861i 0.148087 0.256495i
\(115\) 0 0
\(116\) −8.32456 −0.772916
\(117\) −0.0811388 + 3.60464i −0.00750129 + 0.333249i
\(118\) −6.00000 −0.552345
\(119\) 11.3246 19.6147i 1.03812 1.79808i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 14.4868 1.31158
\(123\) −4.74342 8.21584i −0.427699 0.740797i
\(124\) −4.58114 7.93477i −0.411398 0.712563i
\(125\) 0 0
\(126\) 1.58114 + 2.73861i 0.140859 + 0.243975i
\(127\) −3.83772 + 6.64713i −0.340543 + 0.589837i −0.984534 0.175196i \(-0.943944\pi\)
0.643991 + 0.765033i \(0.277277\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −5.16228 −0.454513
\(130\) 0 0
\(131\) 3.67544 0.321125 0.160563 0.987026i \(-0.448669\pi\)
0.160563 + 0.987026i \(0.448669\pi\)
\(132\) 1.50000 2.59808i 0.130558 0.226134i
\(133\) 5.00000 8.66025i 0.433555 0.750939i
\(134\) −2.00000 3.46410i −0.172774 0.299253i
\(135\) 0 0
\(136\) −3.58114 6.20271i −0.307080 0.531878i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 4.16228 0.354317
\(139\) 9.16228 + 15.8695i 0.777134 + 1.34604i 0.933587 + 0.358351i \(0.116661\pi\)
−0.156453 + 0.987685i \(0.550006\pi\)
\(140\) 0 0
\(141\) 3.00000 5.19615i 0.252646 0.437595i
\(142\) −7.83772 −0.657727
\(143\) 9.48683 5.19615i 0.793329 0.434524i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 0.662278 1.14710i 0.0548105 0.0949346i
\(147\) 1.50000 + 2.59808i 0.123718 + 0.214286i
\(148\) 10.4868 0.862012
\(149\) 6.58114 + 11.3989i 0.539148 + 0.933832i 0.998950 + 0.0458102i \(0.0145870\pi\)
−0.459802 + 0.888021i \(0.652080\pi\)
\(150\) 0 0
\(151\) −21.8114 −1.77499 −0.887493 0.460822i \(-0.847555\pi\)
−0.887493 + 0.460822i \(0.847555\pi\)
\(152\) −1.58114 2.73861i −0.128247 0.222131i
\(153\) −3.58114 + 6.20271i −0.289518 + 0.501460i
\(154\) 4.74342 8.21584i 0.382235 0.662051i
\(155\) 0 0
\(156\) 3.08114 + 1.87259i 0.246689 + 0.149927i
\(157\) −9.83772 −0.785136 −0.392568 0.919723i \(-0.628413\pi\)
−0.392568 + 0.919723i \(0.628413\pi\)
\(158\) −4.58114 + 7.93477i −0.364456 + 0.631256i
\(159\) 3.58114 6.20271i 0.284003 0.491907i
\(160\) 0 0
\(161\) 13.1623 1.03733
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −7.90569 13.6931i −0.619222 1.07252i −0.989628 0.143654i \(-0.954115\pi\)
0.370406 0.928870i \(-0.379218\pi\)
\(164\) −9.48683 −0.740797
\(165\) 0 0
\(166\) 6.82456 11.8205i 0.529688 0.917447i
\(167\) 0.918861 1.59151i 0.0711036 0.123155i −0.828282 0.560312i \(-0.810681\pi\)
0.899385 + 0.437157i \(0.144015\pi\)
\(168\) 3.16228 0.243975
\(169\) 5.98683 + 11.5394i 0.460526 + 0.887646i
\(170\) 0 0
\(171\) −1.58114 + 2.73861i −0.120913 + 0.209427i
\(172\) −2.58114 + 4.47066i −0.196810 + 0.340885i
\(173\) −7.16228 12.4054i −0.544538 0.943167i −0.998636 0.0522155i \(-0.983372\pi\)
0.454098 0.890952i \(-0.349962\pi\)
\(174\) 8.32456 0.631083
\(175\) 0 0
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 6.00000 0.450988
\(178\) 3.58114 + 6.20271i 0.268418 + 0.464913i
\(179\) 0.824555 1.42817i 0.0616302 0.106747i −0.833564 0.552423i \(-0.813703\pi\)
0.895194 + 0.445676i \(0.147037\pi\)
\(180\) 0 0
\(181\) −18.8114 −1.39824 −0.699120 0.715005i \(-0.746425\pi\)
−0.699120 + 0.715005i \(0.746425\pi\)
\(182\) 9.74342 + 5.92164i 0.722230 + 0.438941i
\(183\) −14.4868 −1.07090
\(184\) 2.08114 3.60464i 0.153424 0.265737i
\(185\) 0 0
\(186\) 4.58114 + 7.93477i 0.335905 + 0.581805i
\(187\) 21.4868 1.57127
\(188\) −3.00000 5.19615i −0.218797 0.378968i
\(189\) −1.58114 2.73861i −0.115011 0.199205i
\(190\) 0 0
\(191\) −11.0811 19.1931i −0.801803 1.38876i −0.918428 0.395588i \(-0.870541\pi\)
0.116625 0.993176i \(-0.462792\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −2.33772 + 4.04905i −0.168273 + 0.291457i −0.937813 0.347142i \(-0.887152\pi\)
0.769540 + 0.638599i \(0.220486\pi\)
\(194\) 4.67544 0.335677
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) −3.00000 + 5.19615i −0.213741 + 0.370211i −0.952882 0.303340i \(-0.901898\pi\)
0.739141 + 0.673550i \(0.235232\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) −7.58114 13.1309i −0.537413 0.930826i −0.999042 0.0437533i \(-0.986068\pi\)
0.461630 0.887073i \(-0.347265\pi\)
\(200\) 0 0
\(201\) 2.00000 + 3.46410i 0.141069 + 0.244339i
\(202\) 8.32456 + 14.4186i 0.585714 + 1.01449i
\(203\) 26.3246 1.84762
\(204\) 3.58114 + 6.20271i 0.250730 + 0.434277i
\(205\) 0 0
\(206\) −6.74342 + 11.6799i −0.469836 + 0.813780i
\(207\) −4.16228 −0.289298
\(208\) 3.16228 1.73205i 0.219265 0.120096i
\(209\) 9.48683 0.656218
\(210\) 0 0
\(211\) −3.41886 + 5.92164i −0.235364 + 0.407663i −0.959378 0.282122i \(-0.908962\pi\)
0.724014 + 0.689785i \(0.242295\pi\)
\(212\) −3.58114 6.20271i −0.245954 0.426004i
\(213\) 7.83772 0.537032
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 14.4868 + 25.0919i 0.983430 + 1.70335i
\(218\) −4.24342 + 7.34981i −0.287400 + 0.497792i
\(219\) −0.662278 + 1.14710i −0.0447526 + 0.0775137i
\(220\) 0 0
\(221\) −0.581139 + 25.8174i −0.0390916 + 1.73667i
\(222\) −10.4868 −0.703830
\(223\) −9.06797 + 15.7062i −0.607236 + 1.05176i 0.384457 + 0.923143i \(0.374389\pi\)
−0.991694 + 0.128621i \(0.958945\pi\)
\(224\) 1.58114 2.73861i 0.105644 0.182981i
\(225\) 0 0
\(226\) 2.32456 0.154627
\(227\) −7.98683 13.8336i −0.530105 0.918168i −0.999383 0.0351181i \(-0.988819\pi\)
0.469278 0.883050i \(-0.344514\pi\)
\(228\) 1.58114 + 2.73861i 0.104713 + 0.181369i
\(229\) 2.48683 0.164335 0.0821673 0.996619i \(-0.473816\pi\)
0.0821673 + 0.996619i \(0.473816\pi\)
\(230\) 0 0
\(231\) −4.74342 + 8.21584i −0.312094 + 0.540562i
\(232\) 4.16228 7.20928i 0.273267 0.473312i
\(233\) −26.3246 −1.72458 −0.862289 0.506416i \(-0.830970\pi\)
−0.862289 + 0.506416i \(0.830970\pi\)
\(234\) −3.08114 1.87259i −0.201420 0.122415i
\(235\) 0 0
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) 4.58114 7.93477i 0.297577 0.515418i
\(238\) 11.3246 + 19.6147i 0.734062 + 1.27143i
\(239\) −0.486833 −0.0314906 −0.0157453 0.999876i \(-0.505012\pi\)
−0.0157453 + 0.999876i \(0.505012\pi\)
\(240\) 0 0
\(241\) −4.00000 6.92820i −0.257663 0.446285i 0.707953 0.706260i \(-0.249619\pi\)
−0.965615 + 0.259975i \(0.916286\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −7.24342 + 12.5460i −0.463712 + 0.803173i
\(245\) 0 0
\(246\) 9.48683 0.604858
\(247\) −0.256584 + 11.3989i −0.0163260 + 0.725293i
\(248\) 9.16228 0.581805
\(249\) −6.82456 + 11.8205i −0.432489 + 0.749092i
\(250\) 0 0
\(251\) −7.50000 12.9904i −0.473396 0.819946i 0.526140 0.850398i \(-0.323639\pi\)
−0.999536 + 0.0304521i \(0.990305\pi\)
\(252\) −3.16228 −0.199205
\(253\) 6.24342 + 10.8139i 0.392520 + 0.679865i
\(254\) −3.83772 6.64713i −0.240800 0.417078i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.90569 5.03281i 0.181252 0.313938i −0.761055 0.648687i \(-0.775318\pi\)
0.942307 + 0.334749i \(0.108652\pi\)
\(258\) 2.58114 4.47066i 0.160695 0.278331i
\(259\) −33.1623 −2.06060
\(260\) 0 0
\(261\) −8.32456 −0.515277
\(262\) −1.83772 + 3.18303i −0.113535 + 0.196648i
\(263\) 9.24342 16.0101i 0.569973 0.987223i −0.426594 0.904443i \(-0.640287\pi\)
0.996568 0.0827800i \(-0.0263799\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) 0 0
\(266\) 5.00000 + 8.66025i 0.306570 + 0.530994i
\(267\) −3.58114 6.20271i −0.219162 0.379600i
\(268\) 4.00000 0.244339
\(269\) 9.58114 + 16.5950i 0.584172 + 1.01182i 0.994978 + 0.100093i \(0.0319141\pi\)
−0.410806 + 0.911723i \(0.634753\pi\)
\(270\) 0 0
\(271\) 6.16228 10.6734i 0.374332 0.648362i −0.615895 0.787828i \(-0.711205\pi\)
0.990227 + 0.139467i \(0.0445388\pi\)
\(272\) 7.16228 0.434277
\(273\) −9.74342 5.92164i −0.589698 0.358394i
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) −2.08114 + 3.60464i −0.125270 + 0.216974i
\(277\) 11.4057 + 19.7552i 0.685302 + 1.18698i 0.973342 + 0.229359i \(0.0736630\pi\)
−0.288040 + 0.957618i \(0.593004\pi\)
\(278\) −18.3246 −1.09903
\(279\) −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 \(0.523883\pi\)
\(282\) 3.00000 + 5.19615i 0.178647 + 0.309426i
\(283\) −0.256584 + 0.444416i −0.0152523 + 0.0264178i −0.873551 0.486733i \(-0.838188\pi\)
0.858299 + 0.513151i \(0.171522\pi\)
\(284\) 3.91886 6.78767i 0.232542 0.402774i
\(285\) 0 0
\(286\) −0.243416 + 10.8139i −0.0143935 + 0.639440i
\(287\) 30.0000 1.77084
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −17.1491 + 29.7031i −1.00877 + 1.74724i
\(290\) 0 0
\(291\) −4.67544 −0.274079
\(292\) 0.662278 + 1.14710i 0.0387569 + 0.0671289i
\(293\) 1.25658 + 2.17647i 0.0734104 + 0.127151i 0.900394 0.435076i \(-0.143278\pi\)
−0.826984 + 0.562226i \(0.809945\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) −5.24342 + 9.08186i −0.304767 + 0.527873i
\(297\) 1.50000 2.59808i 0.0870388 0.150756i
\(298\) −13.1623 −0.762470
\(299\) −13.1623 + 7.20928i −0.761194 + 0.416923i
\(300\) 0 0
\(301\) 8.16228 14.1375i 0.470466 0.814871i
\(302\) 10.9057 18.8892i 0.627552 1.08695i
\(303\) −8.32456 14.4186i −0.478233 0.828324i
\(304\) 3.16228 0.181369
\(305\) 0 0
\(306\) −3.58114 6.20271i −0.204720 0.354586i
\(307\) 8.64911 0.493631 0.246815 0.969063i \(-0.420616\pi\)
0.246815 + 0.969063i \(0.420616\pi\)
\(308\) 4.74342 + 8.21584i 0.270281 + 0.468141i
\(309\) 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 \(0.384811\pi\)
\(312\) −3.16228 + 1.73205i −0.179029 + 0.0980581i
\(313\) 17.6491 0.997587 0.498793 0.866721i \(-0.333777\pi\)
0.498793 + 0.866721i \(0.333777\pi\)
\(314\) 4.91886 8.51972i 0.277587 0.480795i
\(315\) 0 0
\(316\) −4.58114 7.93477i −0.257709 0.446365i
\(317\) 0.188612 0.0105935 0.00529674 0.999986i \(-0.498314\pi\)
0.00529674 + 0.999986i \(0.498314\pi\)
\(318\) 3.58114 + 6.20271i 0.200820 + 0.347831i
\(319\) 12.4868 + 21.6278i 0.699128 + 1.21093i
\(320\) 0 0
\(321\) −3.00000 5.19615i −0.167444 0.290021i
\(322\) −6.58114 + 11.3989i −0.366753 + 0.635234i
\(323\) −11.3246 + 19.6147i −0.630115 + 1.09139i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 15.8114 0.875712
\(327\) 4.24342 7.34981i 0.234661 0.406446i
\(328\) 4.74342 8.21584i 0.261911 0.453644i
\(329\) 9.48683 + 16.4317i 0.523026 + 0.905908i
\(330\) 0 0
\(331\) 4.41886 + 7.65369i 0.242883 + 0.420685i 0.961534 0.274685i \(-0.0885737\pi\)
−0.718652 + 0.695370i \(0.755240\pi\)
\(332\) 6.82456 + 11.8205i 0.374546 + 0.648733i
\(333\) 10.4868 0.574675
\(334\) 0.918861 + 1.59151i 0.0502778 + 0.0870838i
\(335\) 0 0
\(336\) −1.58114 + 2.73861i −0.0862582 + 0.149404i
\(337\) 4.00000 0.217894 0.108947 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) −12.9868 0.584952i −0.706391 0.0318172i
\(339\) −2.32456 −0.126253
\(340\) 0 0
\(341\) −13.7434 + 23.8043i −0.744248 + 1.28907i
\(342\) −1.58114 2.73861i −0.0854982 0.148087i
\(343\) 12.6491 0.682988
\(344\) −2.58114 4.47066i −0.139166 0.241042i
\(345\) 0 0
\(346\) 14.3246 0.770093
\(347\) −5.66228 9.80735i −0.303967 0.526486i 0.673064 0.739584i \(-0.264978\pi\)
−0.977031 + 0.213098i \(0.931645\pi\)
\(348\) −4.16228 + 7.20928i −0.223122 + 0.386458i
\(349\) −10.7302 + 18.5853i −0.574377 + 0.994850i 0.421732 + 0.906721i \(0.361422\pi\)
−0.996109 + 0.0881297i \(0.971911\pi\)
\(350\) 0 0
\(351\) 3.08114 + 1.87259i 0.164459 + 0.0999513i
\(352\) 3.00000 0.159901
\(353\) 5.90569 10.2290i 0.314328 0.544433i −0.664966 0.746874i \(-0.731554\pi\)
0.979295 + 0.202441i \(0.0648874\pi\)
\(354\) −3.00000 + 5.19615i −0.159448 + 0.276172i
\(355\) 0 0
\(356\) −7.16228 −0.379600
\(357\) −11.3246 19.6147i −0.599359 1.03812i
\(358\) 0.824555 + 1.42817i 0.0435791 + 0.0754812i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) 4.50000 7.79423i 0.236842 0.410223i
\(362\) 9.40569 16.2911i 0.494352 0.856243i
\(363\) 2.00000 0.104973
\(364\) −10.0000 + 5.47723i −0.524142 + 0.287085i
\(365\) 0 0
\(366\) 7.24342 12.5460i 0.378619 0.655788i
\(367\) 3.32456 5.75830i 0.173540 0.300581i −0.766115 0.642704i \(-0.777813\pi\)
0.939655 + 0.342123i \(0.111146\pi\)
\(368\) 2.08114 + 3.60464i 0.108487 + 0.187905i
\(369\) −9.48683 −0.493865
\(370\) 0 0
\(371\) 11.3246 + 19.6147i 0.587942 + 1.01834i
\(372\) −9.16228 −0.475042
\(373\) 4.24342 + 7.34981i 0.219716 + 0.380559i 0.954721 0.297503i \(-0.0961537\pi\)
−0.735005 + 0.678061i \(0.762820\pi\)
\(374\) −10.7434 + 18.6081i −0.555529 + 0.962204i
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −26.3246 + 14.4186i −1.35578 + 0.742593i
\(378\) 3.16228 0.162650
\(379\) −1.00000 + 1.73205i −0.0513665 + 0.0889695i −0.890565 0.454855i \(-0.849691\pi\)
0.839199 + 0.543825i \(0.183024\pi\)
\(380\) 0 0
\(381\) 3.83772 + 6.64713i 0.196612 + 0.340543i
\(382\) 22.1623 1.13392
\(383\) 2.08114 + 3.60464i 0.106341 + 0.184188i 0.914285 0.405071i \(-0.132753\pi\)
−0.807944 + 0.589259i \(0.799420\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −2.33772 4.04905i −0.118987 0.206091i
\(387\) −2.58114 + 4.47066i −0.131207 + 0.227257i
\(388\) −2.33772 + 4.04905i −0.118680 + 0.205560i
\(389\) −15.6754 −0.794777 −0.397388 0.917651i \(-0.630083\pi\)
−0.397388 + 0.917651i \(0.630083\pi\)
\(390\) 0 0
\(391\) −29.8114 −1.50763
\(392\) −1.50000 + 2.59808i −0.0757614 + 0.131223i
\(393\) 1.83772 3.18303i 0.0927008 0.160563i
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) −12.1623 21.0657i −0.610407 1.05726i −0.991172 0.132584i \(-0.957672\pi\)
0.380765 0.924672i \(-0.375661\pi\)
\(398\) 15.1623 0.760016
\(399\) −5.00000 8.66025i −0.250313 0.433555i
\(400\) 0 0
\(401\) −1.83772 + 3.18303i −0.0917715 + 0.158953i −0.908257 0.418414i \(-0.862586\pi\)
0.816485 + 0.577366i \(0.195920\pi\)
\(402\) −4.00000 −0.199502
\(403\) −28.2302 17.1572i −1.40625 0.854659i
\(404\) −16.6491 −0.828324
\(405\) 0 0
\(406\) −13.1623 + 22.7977i −0.653233 + 1.13143i
\(407\) −15.7302 27.2456i −0.779720 1.35051i
\(408\) −7.16228 −0.354586
\(409\) −8.83772 15.3074i −0.436997 0.756901i 0.560459 0.828182i \(-0.310625\pi\)
−0.997456 + 0.0712807i \(0.977291\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) −6.74342 11.6799i −0.332224 0.575429i
\(413\) −9.48683 + 16.4317i −0.466817 + 0.808550i
\(414\) 2.08114 3.60464i 0.102282 0.177158i
\(415\) 0 0
\(416\) −0.0811388 + 3.60464i −0.00397816 + 0.176732i
\(417\) 18.3246 0.897357
\(418\) −4.74342 + 8.21584i −0.232008 + 0.401850i
\(419\) −4.50000 + 7.79423i −0.219839 + 0.380773i −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 0 0
\(421\) 21.8377 1.06431 0.532153 0.846648i \(-0.321383\pi\)
0.532153 + 0.846648i \(0.321383\pi\)
\(422\) −3.41886 5.92164i −0.166428 0.288261i
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 7.16228 0.347831
\(425\) 0 0
\(426\) −3.91886 + 6.78767i −0.189869 + 0.328864i
\(427\) 22.9057 39.6738i 1.10848 1.91995i
\(428\) −6.00000 −0.290021
\(429\) 0.243416 10.8139i 0.0117523 0.522101i
\(430\) 0 0
\(431\) 2.75658 4.77454i 0.132780 0.229982i −0.791967 0.610564i \(-0.790943\pi\)
0.924747 + 0.380582i \(0.124276\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 14.3114 + 24.7881i 0.687761 + 1.19124i 0.972560 + 0.232650i \(0.0747398\pi\)
−0.284799 + 0.958587i \(0.591927\pi\)
\(434\) −28.9737 −1.39078
\(435\) 0 0
\(436\) −4.24342 7.34981i −0.203223 0.351992i
\(437\) −13.1623 −0.629637
\(438\) −0.662278 1.14710i −0.0316449 0.0548105i
\(439\) 5.67544 9.83016i 0.270874 0.469168i −0.698212 0.715891i \(-0.746021\pi\)
0.969086 + 0.246723i \(0.0793539\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) −22.0680 13.4120i −1.04967 0.637943i
\(443\) 9.00000 0.427603 0.213801 0.976877i \(-0.431415\pi\)
0.213801 + 0.976877i \(0.431415\pi\)
\(444\) 5.24342 9.08186i 0.248842 0.431006i
\(445\) 0 0
\(446\) −9.06797 15.7062i −0.429381 0.743710i
\(447\) 13.1623 0.622554
\(448\) 1.58114 + 2.73861i 0.0747018 + 0.129387i
\(449\) −10.7434 18.6081i −0.507013 0.878173i −0.999967 0.00811713i \(-0.997416\pi\)
0.492954 0.870055i \(-0.335917\pi\)
\(450\) 0 0
\(451\) 14.2302 + 24.6475i 0.670076 + 1.16061i
\(452\) −1.16228 + 2.01312i −0.0546689 + 0.0946894i
\(453\) −10.9057 + 18.8892i −0.512394 + 0.887493i
\(454\) 15.9737 0.749681
\(455\) 0 0
\(456\) −3.16228 −0.148087
\(457\) −17.8246 + 30.8730i −0.833798 + 1.44418i 0.0612082 + 0.998125i \(0.480505\pi\)
−0.895006 + 0.446055i \(0.852829\pi\)
\(458\) −1.24342 + 2.15366i −0.0581010 + 0.100634i
\(459\) 3.58114 + 6.20271i 0.167153 + 0.289518i
\(460\) 0 0
\(461\) 5.41886 + 9.38574i 0.252382 + 0.437138i 0.964181 0.265245i \(-0.0854529\pi\)
−0.711799 + 0.702383i \(0.752120\pi\)
\(462\) −4.74342 8.21584i −0.220684 0.382235i
\(463\) −23.4868 −1.09153 −0.545763 0.837940i \(-0.683760\pi\)
−0.545763 + 0.837940i \(0.683760\pi\)
\(464\) 4.16228 + 7.20928i 0.193229 + 0.334682i
\(465\) 0 0
\(466\) 13.1623 22.7977i 0.609731 1.05608i
\(467\) 3.00000 0.138823 0.0694117 0.997588i \(-0.477888\pi\)
0.0694117 + 0.997588i \(0.477888\pi\)
\(468\) 3.16228 1.73205i 0.146176 0.0800641i
\(469\) −12.6491 −0.584082
\(470\) 0 0
\(471\) −4.91886 + 8.51972i −0.226649 + 0.392568i
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) 15.4868 0.712085
\(474\) 4.58114 + 7.93477i 0.210419 + 0.364456i
\(475\) 0 0
\(476\) −22.6491 −1.03812
\(477\) −3.58114 6.20271i −0.163969 0.284003i
\(478\) 0.243416 0.421610i 0.0111336 0.0192840i
\(479\) 13.1623 22.7977i 0.601400 1.04166i −0.391210 0.920302i \(-0.627943\pi\)
0.992609 0.121353i \(-0.0387234\pi\)
\(480\) 0 0
\(481\) 33.1623 18.1637i 1.51207 0.828195i
\(482\) 8.00000 0.364390
\(483\) 6.58114 11.3989i 0.299452 0.518666i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 1.58114 + 2.73861i 0.0716482 + 0.124098i 0.899624 0.436666i \(-0.143841\pi\)
−0.827976 + 0.560764i \(0.810507\pi\)
\(488\) −7.24342 12.5460i −0.327894 0.567929i
\(489\) −15.8114 −0.715016
\(490\) 0 0
\(491\) −7.98683 + 13.8336i −0.360441 + 0.624302i −0.988033 0.154240i \(-0.950707\pi\)
0.627593 + 0.778542i \(0.284040\pi\)
\(492\) −4.74342 + 8.21584i −0.213850 + 0.370399i
\(493\) −59.6228 −2.68527
\(494\) −9.74342 5.92164i −0.438377 0.266427i
\(495\) 0 0
\(496\) −4.58114 + 7.93477i −0.205699 + 0.356281i
\(497\) −12.3925 + 21.4645i −0.555881 + 0.962814i
\(498\) −6.82456 11.8205i −0.305816 0.529688i
\(499\) 8.18861 0.366573 0.183286 0.983060i \(-0.441326\pi\)
0.183286 + 0.983060i \(0.441326\pi\)
\(500\) 0 0
\(501\) −0.918861 1.59151i −0.0410517 0.0711036i
\(502\) 15.0000 0.669483
\(503\) 7.40569 + 12.8270i 0.330204 + 0.571929i 0.982552 0.185990i \(-0.0595493\pi\)
−0.652348 + 0.757920i \(0.726216\pi\)
\(504\) 1.58114 2.73861i 0.0704295 0.121988i
\(505\) 0 0
\(506\) −12.4868 −0.555107
\(507\) 12.9868 + 0.584952i 0.576766 + 0.0259786i
\(508\) 7.67544 0.340543
\(509\) −21.3925 + 37.0529i −0.948207 + 1.64234i −0.199008 + 0.979998i \(0.563772\pi\)
−0.749199 + 0.662345i \(0.769561\pi\)
\(510\) 0 0
\(511\) −2.09431 3.62744i −0.0926466 0.160469i
\(512\) 1.00000 0.0441942
\(513\) 1.58114 + 2.73861i 0.0698090 + 0.120913i
\(514\) 2.90569 + 5.03281i 0.128165 + 0.221988i
\(515\) 0 0
\(516\) 2.58114 + 4.47066i 0.113628 + 0.196810i
\(517\) −9.00000 + 15.5885i −0.395820 + 0.685580i
\(518\) 16.5811 28.7194i 0.728533 1.26186i
\(519\) −14.3246 −0.628778
\(520\) 0 0
\(521\) 4.64911 0.203681 0.101841 0.994801i \(-0.467527\pi\)
0.101841 + 0.994801i \(0.467527\pi\)
\(522\) 4.16228 7.20928i 0.182178 0.315541i
\(523\) −2.48683 + 4.30732i −0.108742 + 0.188346i −0.915261 0.402862i \(-0.868015\pi\)
0.806519 + 0.591208i \(0.201349\pi\)
\(524\) −1.83772 3.18303i −0.0802813 0.139051i
\(525\) 0 0
\(526\) 9.24342 + 16.0101i 0.403032 + 0.698072i
\(527\) −32.8114 56.8310i −1.42929 2.47560i
\(528\) −3.00000 −0.130558
\(529\) 2.83772 + 4.91508i 0.123379 + 0.213699i
\(530\) 0 0
\(531\) 3.00000 5.19615i 0.130189 0.225494i
\(532\) −10.0000 −0.433555
\(533\) −30.0000 + 16.4317i −1.29944 + 0.711735i
\(534\) 7.16228 0.309942
\(535\) 0 0
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) −0.824555 1.42817i −0.0355822 0.0616302i
\(538\) −19.1623 −0.826144
\(539\) −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 \(0.505552\pi\)
\(542\) 6.16228 + 10.6734i 0.264692 + 0.458461i
\(543\) −9.40569 + 16.2911i −0.403637 + 0.699120i
\(544\) −3.58114 + 6.20271i −0.153540 + 0.265939i
\(545\) 0 0
\(546\) 10.0000 5.47723i 0.427960 0.234404i
\(547\) 30.1359 1.28852 0.644260 0.764807i \(-0.277165\pi\)
0.644260 + 0.764807i \(0.277165\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) −7.24342 + 12.5460i −0.309141 + 0.535449i
\(550\) 0 0
\(551\) −26.3246 −1.12146
\(552\) −2.08114 3.60464i −0.0885792 0.153424i
\(553\) 14.4868 + 25.0919i 0.616043 + 1.06702i
\(554\) −22.8114 −0.969163
\(555\) 0 0
\(556\) 9.16228 15.8695i 0.388567 0.673018i
\(557\) −9.48683 + 16.4317i −0.401970 + 0.696232i −0.993964 0.109710i \(-0.965008\pi\)
0.591994 + 0.805943i \(0.298341\pi\)
\(558\) 9.16228 0.387870
\(559\) −0.418861 + 18.6081i −0.0177159 + 0.787041i
\(560\) 0 0
\(561\) 10.7434 18.6081i 0.453587 0.785636i
\(562\) 1.25658 2.17647i 0.0530058 0.0918087i
\(563\) −1.98683 3.44130i −0.0837350 0.145033i 0.821116 0.570761i \(-0.193352\pi\)
−0.904851 + 0.425727i \(0.860018\pi\)
\(564\) −6.00000 −0.252646
\(565\) 0 0
\(566\) −0.256584 0.444416i −0.0107850 0.0186802i
\(567\) −3.16228 −0.132803
\(568\) 3.91886 + 6.78767i 0.164432 + 0.284804i
\(569\) −15.4868 + 26.8240i −0.649242 + 1.12452i 0.334062 + 0.942551i \(0.391580\pi\)
−0.983304 + 0.181969i \(0.941753\pi\)
\(570\) 0 0
\(571\) −19.6754 −0.823392 −0.411696 0.911321i \(-0.635063\pi\)
−0.411696 + 0.911321i \(0.635063\pi\)
\(572\) −9.24342 5.61776i −0.386487 0.234890i
\(573\) −22.1623 −0.925842
\(574\) −15.0000 + 25.9808i −0.626088 + 1.08442i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 43.0000 1.79011 0.895057 0.445952i \(-0.147135\pi\)
0.895057 + 0.445952i \(0.147135\pi\)
\(578\) −17.1491 29.7031i −0.713309 1.23549i
\(579\) 2.33772 + 4.04905i 0.0971524 + 0.168273i
\(580\) 0 0
\(581\) −21.5811 37.3796i −0.895337 1.55077i
\(582\) 2.33772 4.04905i 0.0969017 0.167839i
\(583\) −10.7434 + 18.6081i −0.444947 + 0.770671i
\(584\) −1.32456 −0.0548105
\(585\) 0 0
\(586\) −2.51317 −0.103818
\(587\) −10.5000 + 18.1865i −0.433381 + 0.750639i −0.997162 0.0752860i \(-0.976013\pi\)
0.563781 + 0.825925i \(0.309346\pi\)
\(588\) 1.50000 2.59808i 0.0618590 0.107143i
\(589\) −14.4868 25.0919i −0.596920 1.03389i
\(590\) 0 0
\(591\) 3.00000 + 5.19615i 0.123404 + 0.213741i
\(592\) −5.24342 9.08186i −0.215503 0.373262i
\(593\) −1.16228 −0.0477290 −0.0238645 0.999715i \(-0.507597\pi\)
−0.0238645 + 0.999715i \(0.507597\pi\)
\(594\) 1.50000 + 2.59808i 0.0615457 + 0.106600i
\(595\) 0 0
\(596\) 6.58114 11.3989i 0.269574 0.466916i
\(597\) −15.1623 −0.620551
\(598\) 0.337722 15.0035i 0.0138105 0.613539i
\(599\) 32.8114 1.34064 0.670318 0.742074i \(-0.266157\pi\)
0.670318 + 0.742074i \(0.266157\pi\)
\(600\) 0 0
\(601\) 3.64911 6.32045i 0.148850 0.257816i −0.781952 0.623338i \(-0.785776\pi\)
0.930803 + 0.365522i \(0.119109\pi\)
\(602\) 8.16228 + 14.1375i 0.332670 + 0.576201i
\(603\) 4.00000 0.162893
\(604\) 10.9057 + 18.8892i 0.443746 + 0.768591i
\(605\) 0 0
\(606\) 16.6491 0.676324
\(607\) 11.8377 + 20.5035i 0.480478 + 0.832213i 0.999749 0.0223969i \(-0.00712974\pi\)
−0.519271 + 0.854610i \(0.673796\pi\)
\(608\) −1.58114 + 2.73861i −0.0641236 + 0.111065i
\(609\) 13.1623 22.7977i 0.533362 0.923811i
\(610\) 0 0
\(611\) −18.4868 11.2355i −0.747897 0.454541i
\(612\) 7.16228 0.289518
\(613\) 14.8377 25.6997i 0.599290 1.03800i −0.393636 0.919266i \(-0.628783\pi\)
0.992926 0.118734i \(-0.0378837\pi\)
\(614\) −4.32456 + 7.49035i −0.174525 + 0.302286i
\(615\) 0 0
\(616\) −9.48683 −0.382235
\(617\) 1.64911 + 2.85634i 0.0663907 + 0.114992i 0.897310 0.441401i \(-0.145518\pi\)
−0.830919 + 0.556393i \(0.812185\pi\)
\(618\) 6.74342 + 11.6799i 0.271260 + 0.469836i
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 0 0
\(621\) −2.08114 + 3.60464i −0.0835132 + 0.144649i
\(622\) −6.24342 + 10.8139i −0.250338 + 0.433598i
\(623\) 22.6491 0.907417
\(624\) 0.0811388 3.60464i 0.00324815 0.144301i
\(625\) 0 0
\(626\) −8.82456 + 15.2846i −0.352700 + 0.610895i
\(627\) 4.74342 8.21584i 0.189434 0.328109i
\(628\) 4.91886 + 8.51972i 0.196284 + 0.339974i
\(629\) 75.1096 2.99482
\(630\) 0 0
\(631\) −17.6491 30.5692i −0.702600 1.21694i −0.967551 0.252677i \(-0.918689\pi\)
0.264951 0.964262i \(-0.414644\pi\)
\(632\) 9.16228 0.364456
\(633\) 3.41886 + 5.92164i 0.135888 + 0.235364i
\(634\) −0.0943058 + 0.163343i −0.00374536 + 0.00648716i
\(635\) 0 0
\(636\) −7.16228 −0.284003
\(637\) 9.48683 5.19615i 0.375882 0.205879i
\(638\) −24.9737 −0.988717
\(639\) 3.91886 6.78767i 0.155028 0.268516i
\(640\) 0 0
\(641\) 24.9737 + 43.2557i 0.986400 + 1.70850i 0.635540 + 0.772068i \(0.280778\pi\)
0.350861 + 0.936428i \(0.385889\pi\)
\(642\) 6.00000 0.236801
\(643\) −12.1623 21.0657i −0.479633 0.830749i 0.520094 0.854109i \(-0.325897\pi\)
−0.999727 + 0.0233598i \(0.992564\pi\)
\(644\) −6.58114 11.3989i −0.259333 0.449178i
\(645\) 0 0
\(646\) −11.3246 19.6147i −0.445559 0.771730i
\(647\) −21.2434 + 36.7947i −0.835165 + 1.44655i 0.0587312 + 0.998274i \(0.481295\pi\)
−0.893896 + 0.448274i \(0.852039\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −18.0000 −0.706562
\(650\) 0 0
\(651\) 28.9737 1.13557
\(652\) −7.90569 + 13.6931i −0.309611 + 0.536262i
\(653\) 4.74342 8.21584i 0.185624 0.321511i −0.758162 0.652066i \(-0.773903\pi\)
0.943787 + 0.330555i \(0.107236\pi\)
\(654\) 4.24342 + 7.34981i 0.165931 + 0.287400i
\(655\) 0 0
\(656\) 4.74342 + 8.21584i 0.185199 + 0.320775i
\(657\) 0.662278 + 1.14710i 0.0258379 + 0.0447526i
\(658\) −18.9737 −0.739671
\(659\) 7.50000 + 12.9904i 0.292159 + 0.506033i 0.974320 0.225168i \(-0.0722932\pi\)
−0.682161 + 0.731202i \(0.738960\pi\)
\(660\) 0 0
\(661\) −13.0000 + 22.5167i −0.505641 + 0.875797i 0.494337 + 0.869270i \(0.335411\pi\)
−0.999979 + 0.00652642i \(0.997923\pi\)
\(662\) −8.83772 −0.343488
\(663\) 22.0680 + 13.4120i 0.857049 + 0.520879i
\(664\) −13.6491 −0.529688
\(665\) 0 0
\(666\) −5.24342 + 9.08186i −0.203178 + 0.351915i
\(667\) −17.3246 30.0070i −0.670809 1.16188i
\(668\) −1.83772 −0.0711036
\(669\) 9.06797 + 15.7062i 0.350588 + 0.607236i
\(670\) 0 0
\(671\) 43.4605 1.67777
\(672\) −1.58114 2.73861i −0.0609938 0.105644i
\(673\) 10.8246 18.7487i 0.417256 0.722708i −0.578406 0.815749i \(-0.696325\pi\)
0.995662 + 0.0930403i \(0.0296585\pi\)
\(674\) −2.00000 + 3.46410i −0.0770371 + 0.133432i
\(675\) 0 0
\(676\) 7.00000 10.9545i 0.269231 0.421325i
\(677\) 7.35089 0.282518 0.141259 0.989973i \(-0.454885\pi\)
0.141259 + 0.989973i \(0.454885\pi\)
\(678\) 1.16228 2.01312i 0.0446370 0.0773136i
\(679\) 7.39253 12.8042i 0.283699 0.491381i
\(680\) 0 0
\(681\) −15.9737 −0.612112
\(682\) −13.7434 23.8043i −0.526263 0.911514i
\(683\) 23.4737 + 40.6576i 0.898195 + 1.55572i 0.829800 + 0.558061i \(0.188454\pi\)
0.0683948 + 0.997658i \(0.478212\pi\)
\(684\) 3.16228 0.120913
\(685\) 0 0
\(686\) −6.32456 + 10.9545i −0.241473 + 0.418243i
\(687\) 1.24342 2.15366i 0.0474393 0.0821673i
\(688\) 5.16228 0.196810
\(689\) −22.0680 13.4120i −0.840723 0.510956i
\(690\) 0 0
\(691\) −25.9737 + 44.9877i −0.988085 + 1.71141i −0.360752 + 0.932662i \(0.617480\pi\)
−0.627333 + 0.778751i \(0.715853\pi\)
\(692\) −7.16228 + 12.4054i −0.272269 + 0.471584i
\(693\) 4.74342 + 8.21584i 0.180187 + 0.312094i
\(694\) 11.3246 0.429874
\(695\) 0 0
\(696\) −4.16228 7.20928i −0.157771 0.273267i
\(697\) −67.9473 −2.57369
\(698\) −10.7302 18.5853i −0.406146 0.703465i
\(699\) −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 \(0.274443\pi\)
\(702\) −3.16228 + 1.73205i −0.119352 + 0.0653720i
\(703\) 33.1623 1.25074
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 5.90569 + 10.2290i 0.222264 + 0.384972i
\(707\) 52.6491 1.98007
\(708\) −3.00000 5.19615i −0.112747 0.195283i
\(709\) −10.2434 17.7421i −0.384700 0.666319i 0.607028 0.794681i \(-0.292362\pi\)
−0.991727 + 0.128361i \(0.959028\pi\)
\(710\) 0 0
\(711\) −4.58114 7.93477i −0.171806 0.297577i
\(712\) 3.58114 6.20271i 0.134209 0.232457i
\(713\) 19.0680 33.0267i 0.714101 1.23686i
\(714\) 22.6491 0.847622
\(715\) 0 0
\(716\) −1.64911 −0.0616302
\(717\) −0.243416 + 0.421610i −0.00909056 + 0.0157453i
\(718\) 6.00000 10.3923i 0.223918 0.387837i
\(719\) 7.59431 + 13.1537i 0.283220 + 0.490551i 0.972176 0.234252i \(-0.0752641\pi\)
−0.688956 + 0.724803i \(0.741931\pi\)
\(720\) 0 0
\(721\) 21.3246 + 36.9352i 0.794168 + 1.37554i
\(722\) 4.50000 + 7.79423i 0.167473 + 0.290071i
\(723\) −8.00000 −0.297523
\(724\) 9.40569 + 16.2911i 0.349560 + 0.605455i
\(725\) 0 0
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) 0.324555 0.0120371 0.00601855 0.999982i \(-0.498084\pi\)
0.00601855 + 0.999982i \(0.498084\pi\)
\(728\) 0.256584 11.3989i 0.00950962 0.422470i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −18.4868 + 32.0201i −0.683760 + 1.18431i
\(732\) 7.24342 + 12.5460i 0.267724 + 0.463712i
\(733\) −38.4868 −1.42154 −0.710772 0.703423i \(-0.751654\pi\)
−0.710772 + 0.703423i \(0.751654\pi\)
\(734\) 3.32456 + 5.75830i 0.122712 + 0.212543i
\(735\) 0 0
\(736\) −4.16228 −0.153424
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) 4.74342 8.21584i 0.174608 0.302429i
\(739\) 15.6491 27.1051i 0.575662 0.997076i −0.420308 0.907382i \(-0.638078\pi\)
0.995969 0.0896938i \(-0.0285889\pi\)
\(740\) 0 0
\(741\) 9.74342 + 5.92164i 0.357933 + 0.217537i
\(742\) −22.6491 −0.831475
\(743\) −9.67544 + 16.7584i −0.354958 + 0.614805i −0.987111 0.160039i \(-0.948838\pi\)
0.632153 + 0.774844i \(0.282171\pi\)
\(744\) 4.58114 7.93477i 0.167953 0.290903i
\(745\) 0 0
\(746\) −8.48683 −0.310725
\(747\) 6.82456 + 11.8205i 0.249697 + 0.432489i
\(748\) −10.7434 18.6081i −0.392818 0.680381i
\(749\) 18.9737 0.693283
\(750\) 0 0
\(751\) 15.1623 26.2618i 0.553279 0.958308i −0.444756 0.895652i \(-0.646710\pi\)
0.998035 0.0626561i \(-0.0199571\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) −15.0000 −0.546630
\(754\) 0.675445 30.0070i 0.0245982 1.09279i
\(755\) 0 0
\(756\) −1.58114 + 2.73861i −0.0575055 + 0.0996024i
\(757\) 13.4868 23.3599i 0.490187 0.849029i −0.509749 0.860323i \(-0.670262\pi\)
0.999936 + 0.0112939i \(0.00359505\pi\)
\(758\) −1.00000 1.73205i −0.0363216 0.0629109i
\(759\) 12.4868 0.453243
\(760\) 0 0
\(761\) −5.23025 9.05906i −0.189596 0.328391i 0.755519 0.655126i \(-0.227385\pi\)
−0.945116 + 0.326736i \(0.894051\pi\)
\(762\) −7.67544 −0.278052
\(763\) 13.4189 + 23.2421i 0.485795 + 0.841422i
\(764\) −11.0811 + 19.1931i −0.400902 + 0.694382i
\(765\) 0 0
\(766\) −4.16228 −0.150389
\(767\) 0.486833 21.6278i 0.0175785 0.780936i
\(768\) −1.00000 −0.0360844
\(769\) 11.4868 19.8958i 0.414226 0.717460i −0.581121 0.813817i \(-0.697386\pi\)
0.995347 + 0.0963570i \(0.0307191\pi\)
\(770\) 0 0
\(771\) −2.90569 5.03281i −0.104646 0.181252i
\(772\) 4.67544 0.168273
\(773\) −17.3246 30.0070i −0.623121 1.07928i −0.988901 0.148576i \(-0.952531\pi\)
0.365780 0.930701i \(-0.380802\pi\)
\(774\) −2.58114 4.47066i −0.0927771 0.160695i
\(775\) 0 0
\(776\) −2.33772 4.04905i −0.0839193 0.145353i
\(777\) −16.5811 + 28.7194i −0.594845 + 1.03030i
\(778\) 7.83772 13.5753i 0.280996 0.486699i
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) −23.5132 −0.841367
\(782\) 14.9057 25.8174i 0.533027 0.923229i
\(783\) −4.16228 + 7.20928i −0.148748 + 0.257639i
\(784\) −1.50000 2.59808i −0.0535714 0.0927884i
\(785\) 0 0
\(786\)