Properties

Label 1950.2.i.ba.451.1
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 451.1
Root \(-1.58114 - 2.73861i\) of defining polynomial
Character \(\chi\) \(=\) 1950.451
Dual form 1950.2.i.ba.601.1

$q$-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} +(0.0811388 + 3.60464i) q^{13} +3.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.418861 - 0.725489i) q^{17} +1.00000 q^{18} +(1.58114 + 2.73861i) q^{19} -3.16228 q^{21} +(-1.50000 - 2.59808i) q^{22} +(-1.08114 + 1.87259i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.16228 - 1.73205i) q^{26} -1.00000 q^{27} +(-1.58114 + 2.73861i) q^{28} +(-2.16228 + 3.74517i) q^{29} +2.83772 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +0.837722 q^{34} +(-0.500000 + 0.866025i) q^{36} +(4.24342 - 7.34981i) q^{37} -3.16228 q^{38} +(3.16228 + 1.73205i) q^{39} +(-4.74342 + 8.21584i) q^{41} +(1.58114 - 2.73861i) q^{42} +(0.581139 + 1.00656i) q^{43} +3.00000 q^{44} +(-1.08114 - 1.87259i) q^{46} +6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} -0.837722 q^{51} +(3.08114 - 1.87259i) q^{52} +0.837722 q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.58114 - 2.73861i) q^{56} +3.16228 q^{57} +(-2.16228 - 3.74517i) q^{58} +(3.00000 + 5.19615i) q^{59} +(2.24342 + 3.88571i) q^{61} +(-1.41886 + 2.45754i) q^{62} +(-1.58114 + 2.73861i) q^{63} +1.00000 q^{64} -3.00000 q^{66} +(-2.00000 + 3.46410i) q^{67} +(-0.418861 + 0.725489i) q^{68} +(1.08114 + 1.87259i) q^{69} +(7.08114 + 12.2649i) q^{71} +(-0.500000 - 0.866025i) q^{72} +11.3246 q^{73} +(4.24342 + 7.34981i) q^{74} +(1.58114 - 2.73861i) q^{76} +9.48683 q^{77} +(-3.08114 + 1.87259i) q^{78} +2.83772 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.74342 - 8.21584i) q^{82} +11.6491 q^{83} +(1.58114 + 2.73861i) q^{84} -1.16228 q^{86} +(2.16228 + 3.74517i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(0.418861 - 0.725489i) q^{89} +(9.74342 - 5.92164i) q^{91} +2.16228 q^{92} +(1.41886 - 2.45754i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-8.66228 - 15.0035i) 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 \(-0.962782\pi\)
0.395558 0.918441i \(-0.370551\pi\)
\(8\) 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
\(13\) 0.0811388 + 3.60464i 0.0225039 + 0.999747i
\(14\) 3.16228 0.845154
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.418861 0.725489i −0.101589 0.175957i 0.810751 0.585392i \(-0.199059\pi\)
−0.912339 + 0.409435i \(0.865726\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.58114 + 2.73861i 0.362738 + 0.628281i 0.988410 0.151805i \(-0.0485086\pi\)
−0.625672 + 0.780086i \(0.715175\pi\)
\(20\) 0 0
\(21\) −3.16228 −0.690066
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) −1.08114 + 1.87259i −0.225433 + 0.390461i −0.956449 0.291899i \(-0.905713\pi\)
0.731016 + 0.682360i \(0.239046\pi\)
\(24\) 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
\(29\) −2.16228 + 3.74517i −0.401525 + 0.695461i −0.993910 0.110193i \(-0.964853\pi\)
0.592385 + 0.805655i \(0.298186\pi\)
\(30\) 0 0
\(31\) 2.83772 0.509670 0.254835 0.966985i \(-0.417979\pi\)
0.254835 + 0.966985i \(0.417979\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 0.837722 0.143668
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 4.24342 7.34981i 0.697613 1.20830i −0.271678 0.962388i \(-0.587579\pi\)
0.969292 0.245914i \(-0.0790880\pi\)
\(38\) −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 \(0.432219\pi\)
−0.952133 + 0.305685i \(0.901115\pi\)
\(42\) 1.58114 2.73861i 0.243975 0.422577i
\(43\) 0.581139 + 1.00656i 0.0886228 + 0.153499i 0.906929 0.421283i \(-0.138420\pi\)
−0.818306 + 0.574782i \(0.805087\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) −1.08114 1.87259i −0.159405 0.276098i
\(47\) 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
\(51\) −0.837722 −0.117305
\(52\) 3.08114 1.87259i 0.427277 0.259681i
\(53\) 0.837722 0.115070 0.0575350 0.998343i \(-0.481676\pi\)
0.0575350 + 0.998343i \(0.481676\pi\)
\(54\) 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
\(58\) −2.16228 3.74517i −0.283921 0.491766i
\(59\) 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
\(61\) 2.24342 + 3.88571i 0.287240 + 0.497514i 0.973150 0.230172i \(-0.0739289\pi\)
−0.685910 + 0.727686i \(0.740596\pi\)
\(62\) −1.41886 + 2.45754i −0.180196 + 0.312108i
\(63\) −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 \(0.245238\pi\)
\(68\) −0.418861 + 0.725489i −0.0507944 + 0.0879784i
\(69\) 1.08114 + 1.87259i 0.130154 + 0.225433i
\(70\) 0 0
\(71\) 7.08114 + 12.2649i 0.840377 + 1.45557i 0.889577 + 0.456786i \(0.150999\pi\)
−0.0492001 + 0.998789i \(0.515667\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 11.3246 1.32544 0.662719 0.748868i \(-0.269402\pi\)
0.662719 + 0.748868i \(0.269402\pi\)
\(74\) 4.24342 + 7.34981i 0.493287 + 0.854398i
\(75\) 0 0
\(76\) 1.58114 2.73861i 0.181369 0.314140i
\(77\) 9.48683 1.08112
\(78\) −3.08114 + 1.87259i −0.348870 + 0.212029i
\(79\) 2.83772 0.319269 0.159634 0.987176i \(-0.448968\pi\)
0.159634 + 0.987176i \(0.448968\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.74342 8.21584i −0.523823 0.907288i
\(83\) 11.6491 1.27866 0.639328 0.768934i \(-0.279213\pi\)
0.639328 + 0.768934i \(0.279213\pi\)
\(84\) 1.58114 + 2.73861i 0.172516 + 0.298807i
\(85\) 0 0
\(86\) −1.16228 −0.125332
\(87\) 2.16228 + 3.74517i 0.231820 + 0.401525i
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) 0.418861 0.725489i 0.0443992 0.0769017i −0.842972 0.537958i \(-0.819196\pi\)
0.887371 + 0.461056i \(0.152529\pi\)
\(90\) 0 0
\(91\) 9.74342 5.92164i 1.02139 0.620757i
\(92\) 2.16228 0.225433
\(93\) 1.41886 2.45754i 0.147129 0.254835i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −8.66228 15.0035i −0.879521 1.52338i −0.851867 0.523758i \(-0.824530\pi\)
−0.0276537 0.999618i \(-0.508804\pi\)
\(98\) −1.50000 2.59808i −0.151523 0.262445i
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) −4.32456 + 7.49035i −0.430309 + 0.745318i −0.996900 0.0786819i \(-0.974929\pi\)
0.566590 + 0.824000i \(0.308262\pi\)
\(102\) 0.418861 0.725489i 0.0414734 0.0718341i
\(103\) −5.48683 −0.540634 −0.270317 0.962771i \(-0.587128\pi\)
−0.270317 + 0.962771i \(0.587128\pi\)
\(104\) 0.0811388 + 3.60464i 0.00795632 + 0.353464i
\(105\) 0 0
\(106\) −0.418861 + 0.725489i −0.0406834 + 0.0704657i
\(107\) 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
\(109\) −10.4868 −1.00446 −0.502228 0.864735i \(-0.667486\pi\)
−0.502228 + 0.864735i \(0.667486\pi\)
\(110\) 0 0
\(111\) −4.24342 7.34981i −0.402767 0.697613i
\(112\) 3.16228 0.298807
\(113\) 5.16228 + 8.94133i 0.485626 + 0.841129i 0.999864 0.0165186i \(-0.00525828\pi\)
−0.514237 + 0.857648i \(0.671925\pi\)
\(114\) −1.58114 + 2.73861i −0.148087 + 0.256495i
\(115\) 0 0
\(116\) 4.32456 0.401525
\(117\) 3.08114 1.87259i 0.284851 0.173121i
\(118\) −6.00000 −0.552345
\(119\) −1.32456 + 2.29420i −0.121422 + 0.210309i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −4.48683 −0.406219
\(123\) 4.74342 + 8.21584i 0.427699 + 0.740797i
\(124\) −1.41886 2.45754i −0.127417 0.220694i
\(125\) 0 0
\(126\) −1.58114 2.73861i −0.140859 0.243975i
\(127\) −10.1623 + 17.6016i −0.901756 + 1.56189i −0.0765432 + 0.997066i \(0.524388\pi\)
−0.825213 + 0.564822i \(0.808945\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 1.16228 0.102333
\(130\) 0 0
\(131\) 16.3246 1.42628 0.713142 0.701020i \(-0.247272\pi\)
0.713142 + 0.701020i \(0.247272\pi\)
\(132\) 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
\(136\) −0.418861 0.725489i −0.0359170 0.0622102i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) −2.16228 −0.184065
\(139\) 2.83772 + 4.91508i 0.240692 + 0.416892i 0.960912 0.276855i \(-0.0892921\pi\)
−0.720219 + 0.693747i \(0.755959\pi\)
\(140\) 0 0
\(141\) 3.00000 5.19615i 0.252646 0.437595i
\(142\) −14.1623 −1.18847
\(143\) −9.48683 5.19615i −0.793329 0.434524i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −5.66228 + 9.80735i −0.468613 + 0.811662i
\(147\) 1.50000 + 2.59808i 0.123718 + 0.214286i
\(148\) −8.48683 −0.697613
\(149\) 3.41886 + 5.92164i 0.280084 + 0.485120i 0.971405 0.237428i \(-0.0763043\pi\)
−0.691321 + 0.722548i \(0.742971\pi\)
\(150\) 0 0
\(151\) 9.81139 0.798439 0.399220 0.916855i \(-0.369281\pi\)
0.399220 + 0.916855i \(0.369281\pi\)
\(152\) 1.58114 + 2.73861i 0.128247 + 0.222131i
\(153\) −0.418861 + 0.725489i −0.0338629 + 0.0586523i
\(154\) −4.74342 + 8.21584i −0.382235 + 0.662051i
\(155\) 0 0
\(156\) −0.0811388 3.60464i −0.00649631 0.288602i
\(157\) −16.1623 −1.28989 −0.644945 0.764229i \(-0.723120\pi\)
−0.644945 + 0.764229i \(0.723120\pi\)
\(158\) −1.41886 + 2.45754i −0.112879 + 0.195511i
\(159\) 0.418861 0.725489i 0.0332179 0.0575350i
\(160\) 0 0
\(161\) 6.83772 0.538888
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 7.90569 + 13.6931i 0.619222 + 1.07252i 0.989628 + 0.143654i \(0.0458851\pi\)
−0.370406 + 0.928870i \(0.620782\pi\)
\(164\) 9.48683 0.740797
\(165\) 0 0
\(166\) −5.82456 + 10.0884i −0.452073 + 0.783014i
\(167\) 4.08114 7.06874i 0.315808 0.546996i −0.663801 0.747909i \(-0.731058\pi\)
0.979609 + 0.200914i \(0.0643911\pi\)
\(168\) −3.16228 −0.243975
\(169\) −12.9868 + 0.584952i −0.998987 + 0.0449963i
\(170\) 0 0
\(171\) 1.58114 2.73861i 0.120913 0.209427i
\(172\) 0.581139 1.00656i 0.0443114 0.0767496i
\(173\) −0.837722 1.45098i −0.0636909 0.110316i 0.832422 0.554143i \(-0.186954\pi\)
−0.896113 + 0.443827i \(0.853620\pi\)
\(174\) −4.32456 −0.327844
\(175\) 0 0
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 6.00000 0.450988
\(178\) 0.418861 + 0.725489i 0.0313950 + 0.0543777i
\(179\) −11.8246 + 20.4807i −0.883809 + 1.53080i −0.0367358 + 0.999325i \(0.511696\pi\)
−0.847073 + 0.531477i \(0.821637\pi\)
\(180\) 0 0
\(181\) 12.8114 0.952263 0.476131 0.879374i \(-0.342039\pi\)
0.476131 + 0.879374i \(0.342039\pi\)
\(182\) 0.256584 + 11.3989i 0.0190192 + 0.844940i
\(183\) 4.48683 0.331676
\(184\) −1.08114 + 1.87259i −0.0797026 + 0.138049i
\(185\) 0 0
\(186\) 1.41886 + 2.45754i 0.104036 + 0.180196i
\(187\) 2.51317 0.183781
\(188\) −3.00000 5.19615i −0.218797 0.378968i
\(189\) 1.58114 + 2.73861i 0.115011 + 0.199205i
\(190\) 0 0
\(191\) −7.91886 13.7159i −0.572989 0.992446i −0.996257 0.0864411i \(-0.972451\pi\)
0.423268 0.906004i \(-0.360883\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −8.66228 + 15.0035i −0.623524 + 1.07998i 0.365300 + 0.930890i \(0.380966\pi\)
−0.988824 + 0.149086i \(0.952367\pi\)
\(194\) 17.3246 1.24383
\(195\) 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
\(199\) −4.41886 7.65369i −0.313245 0.542556i 0.665818 0.746114i \(-0.268083\pi\)
−0.979063 + 0.203558i \(0.934749\pi\)
\(200\) 0 0
\(201\) 2.00000 + 3.46410i 0.141069 + 0.244339i
\(202\) −4.32456 7.49035i −0.304275 0.527019i
\(203\) 13.6754 0.959828
\(204\) 0.418861 + 0.725489i 0.0293261 + 0.0507944i
\(205\) 0 0
\(206\) 2.74342 4.75174i 0.191143 0.331069i
\(207\) 2.16228 0.150289
\(208\) −3.16228 1.73205i −0.219265 0.120096i
\(209\) −9.48683 −0.656218
\(210\) 0 0
\(211\) −6.58114 + 11.3989i −0.453064 + 0.784730i −0.998575 0.0533737i \(-0.983003\pi\)
0.545510 + 0.838104i \(0.316336\pi\)
\(212\) −0.418861 0.725489i −0.0287675 0.0498268i
\(213\) 14.1623 0.970383
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −4.48683 7.77142i −0.304586 0.527559i
\(218\) 5.24342 9.08186i 0.355129 0.615101i
\(219\) 5.66228 9.80735i 0.382621 0.662719i
\(220\) 0 0
\(221\) 2.58114 1.56871i 0.173626 0.105523i
\(222\) 8.48683 0.569599
\(223\) 13.0680 22.6344i 0.875096 1.51571i 0.0184358 0.999830i \(-0.494131\pi\)
0.856660 0.515881i \(-0.172535\pi\)
\(224\) −1.58114 + 2.73861i −0.105644 + 0.182981i
\(225\) 0 0
\(226\) −10.3246 −0.686779
\(227\) 10.9868 + 19.0298i 0.729222 + 1.26305i 0.957213 + 0.289386i \(0.0934510\pi\)
−0.227991 + 0.973663i \(0.573216\pi\)
\(228\) −1.58114 2.73861i −0.104713 0.181369i
\(229\) −16.4868 −1.08948 −0.544740 0.838605i \(-0.683372\pi\)
−0.544740 + 0.838605i \(0.683372\pi\)
\(230\) 0 0
\(231\) 4.74342 8.21584i 0.312094 0.540562i
\(232\) −2.16228 + 3.74517i −0.141960 + 0.245883i
\(233\) −13.6754 −0.895908 −0.447954 0.894057i \(-0.647847\pi\)
−0.447954 + 0.894057i \(0.647847\pi\)
\(234\) 0.0811388 + 3.60464i 0.00530421 + 0.235643i
\(235\) 0 0
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) 1.41886 2.45754i 0.0921649 0.159634i
\(238\) −1.32456 2.29420i −0.0858582 0.148711i
\(239\) 18.4868 1.19581 0.597907 0.801566i \(-0.295999\pi\)
0.597907 + 0.801566i \(0.295999\pi\)
\(240\) 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
\(244\) 2.24342 3.88571i 0.143620 0.248757i
\(245\) 0 0
\(246\) −9.48683 −0.604858
\(247\) −9.74342 + 5.92164i −0.619959 + 0.376785i
\(248\) 2.83772 0.180196
\(249\) 5.82456 10.0884i 0.369116 0.639328i
\(250\) 0 0
\(251\) −7.50000 12.9904i −0.473396 0.819946i 0.526140 0.850398i \(-0.323639\pi\)
−0.999536 + 0.0304521i \(0.990305\pi\)
\(252\) 3.16228 0.199205
\(253\) −3.24342 5.61776i −0.203912 0.353186i
\(254\) −10.1623 17.6016i −0.637638 1.10442i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −12.9057 + 22.3533i −0.805035 + 1.39436i 0.111232 + 0.993794i \(0.464520\pi\)
−0.916267 + 0.400567i \(0.868813\pi\)
\(258\) −0.581139 + 1.00656i −0.0361801 + 0.0626658i
\(259\) −26.8377 −1.66761
\(260\) 0 0
\(261\) 4.32456 0.267683
\(262\) −8.16228 + 14.1375i −0.504267 + 0.873416i
\(263\) −0.243416 + 0.421610i −0.0150097 + 0.0259976i −0.873433 0.486945i \(-0.838111\pi\)
0.858423 + 0.512942i \(0.171445\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) 0 0
\(266\) 5.00000 + 8.66025i 0.306570 + 0.530994i
\(267\) −0.418861 0.725489i −0.0256339 0.0443992i
\(268\) 4.00000 0.244339
\(269\) 6.41886 + 11.1178i 0.391365 + 0.677864i 0.992630 0.121186i \(-0.0386697\pi\)
−0.601265 + 0.799050i \(0.705336\pi\)
\(270\) 0 0
\(271\) −0.162278 + 0.281073i −0.00985767 + 0.0170740i −0.870912 0.491439i \(-0.836471\pi\)
0.861054 + 0.508513i \(0.169805\pi\)
\(272\) 0.837722 0.0507944
\(273\) −0.256584 11.3989i −0.0155291 0.689891i
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 1.08114 1.87259i 0.0650769 0.112717i
\(277\) −4.40569 7.63089i −0.264713 0.458496i 0.702776 0.711411i \(-0.251944\pi\)
−0.967488 + 0.252916i \(0.918610\pi\)
\(278\) −5.67544 −0.340391
\(279\) −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 \(0.721438\pi\)
\(282\) 3.00000 + 5.19615i 0.178647 + 0.309426i
\(283\) −9.74342 + 16.8761i −0.579186 + 1.00318i 0.416387 + 0.909187i \(0.363296\pi\)
−0.995573 + 0.0939921i \(0.970037\pi\)
\(284\) 7.08114 12.2649i 0.420188 0.727787i
\(285\) 0 0
\(286\) 9.24342 5.61776i 0.546575 0.332185i
\(287\) 30.0000 1.77084
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 8.14911 14.1147i 0.479359 0.830275i
\(290\) 0 0
\(291\) −17.3246 −1.01558
\(292\) −5.66228 9.80735i −0.331360 0.573932i
\(293\) 10.7434 + 18.6081i 0.627637 + 1.08710i 0.988025 + 0.154297i \(0.0493111\pi\)
−0.360387 + 0.932803i \(0.617356\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) 4.24342 7.34981i 0.246644 0.427199i
\(297\) 1.50000 2.59808i 0.0870388 0.150756i
\(298\) −6.83772 −0.396099
\(299\) −6.83772 3.74517i −0.395436 0.216589i
\(300\) 0 0
\(301\) 1.83772 3.18303i 0.105925 0.183467i
\(302\) −4.90569 + 8.49691i −0.282291 + 0.488942i
\(303\) 4.32456 + 7.49035i 0.248439 + 0.430309i
\(304\) −3.16228 −0.181369
\(305\) 0 0
\(306\) −0.418861 0.725489i −0.0239447 0.0414734i
\(307\) −16.6491 −0.950215 −0.475107 0.879928i \(-0.657591\pi\)
−0.475107 + 0.879928i \(0.657591\pi\)
\(308\) −4.74342 8.21584i −0.270281 0.468141i
\(309\) −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 \(0.558878\pi\)
\(312\) 3.16228 + 1.73205i 0.179029 + 0.0980581i
\(313\) −7.64911 −0.432353 −0.216177 0.976354i \(-0.569359\pi\)
−0.216177 + 0.976354i \(0.569359\pi\)
\(314\) 8.08114 13.9969i 0.456045 0.789893i
\(315\) 0 0
\(316\) −1.41886 2.45754i −0.0798172 0.138247i
\(317\) 31.8114 1.78671 0.893353 0.449356i \(-0.148347\pi\)
0.893353 + 0.449356i \(0.148347\pi\)
\(318\) 0.418861 + 0.725489i 0.0234886 + 0.0406834i
\(319\) −6.48683 11.2355i −0.363193 0.629069i
\(320\) 0 0
\(321\) −3.00000 5.19615i −0.167444 0.290021i
\(322\) −3.41886 + 5.92164i −0.190526 + 0.330000i
\(323\) 1.32456 2.29420i 0.0737002 0.127653i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −15.8114 −0.875712
\(327\) −5.24342 + 9.08186i −0.289962 + 0.502228i
\(328\) −4.74342 + 8.21584i −0.261911 + 0.453644i
\(329\) −9.48683 16.4317i −0.523026 0.905908i
\(330\) 0 0
\(331\) 7.58114 + 13.1309i 0.416697 + 0.721741i 0.995605 0.0936524i \(-0.0298543\pi\)
−0.578908 + 0.815393i \(0.696521\pi\)
\(332\) −5.82456 10.0884i −0.319664 0.553674i
\(333\) −8.48683 −0.465076
\(334\) 4.08114 + 7.06874i 0.223310 + 0.386784i
\(335\) 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 \(0.465252\pi\)
\(338\) 5.98683 11.5394i 0.325641 0.627661i
\(339\) 10.3246 0.560753
\(340\) 0 0
\(341\) −4.25658 + 7.37262i −0.230507 + 0.399250i
\(342\) 1.58114 + 2.73861i 0.0854982 + 0.148087i
\(343\) −12.6491 −0.682988
\(344\) 0.581139 + 1.00656i 0.0313329 + 0.0542702i
\(345\) 0 0
\(346\) 1.67544 0.0900725
\(347\) 0.662278 + 1.14710i 0.0355529 + 0.0615795i 0.883254 0.468894i \(-0.155347\pi\)
−0.847701 + 0.530474i \(0.822014\pi\)
\(348\) 2.16228 3.74517i 0.115910 0.200762i
\(349\) 17.7302 30.7097i 0.949078 1.64385i 0.201707 0.979446i \(-0.435351\pi\)
0.747372 0.664406i \(-0.231315\pi\)
\(350\) 0 0
\(351\) −0.0811388 3.60464i −0.00433087 0.192401i
\(352\) 3.00000 0.159901
\(353\) −9.90569 + 17.1572i −0.527227 + 0.913184i 0.472270 + 0.881454i \(0.343435\pi\)
−0.999496 + 0.0317296i \(0.989898\pi\)
\(354\) −3.00000 + 5.19615i −0.159448 + 0.276172i
\(355\) 0 0
\(356\) −0.837722 −0.0443992
\(357\) 1.32456 + 2.29420i 0.0701029 + 0.121422i
\(358\) −11.8246 20.4807i −0.624947 1.08244i
\(359\) −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
\(362\) −6.40569 + 11.0950i −0.336676 + 0.583140i
\(363\) 2.00000 0.104973
\(364\) −10.0000 5.47723i −0.524142 0.287085i
\(365\) 0 0
\(366\) −2.24342 + 3.88571i −0.117265 + 0.203109i
\(367\) −9.32456 + 16.1506i −0.486738 + 0.843055i −0.999884 0.0152467i \(-0.995147\pi\)
0.513146 + 0.858301i \(0.328480\pi\)
\(368\) −1.08114 1.87259i −0.0563583 0.0976154i
\(369\) 9.48683 0.493865
\(370\) 0 0
\(371\) −1.32456 2.29420i −0.0687675 0.119109i
\(372\) −2.83772 −0.147129
\(373\) −5.24342 9.08186i −0.271494 0.470241i 0.697751 0.716341i \(-0.254184\pi\)
−0.969245 + 0.246100i \(0.920851\pi\)
\(374\) −1.25658 + 2.17647i −0.0649764 + 0.112542i
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −13.6754 7.49035i −0.704321 0.385773i
\(378\) −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
\(381\) 10.1623 + 17.6016i 0.520629 + 0.901756i
\(382\) 15.8377 0.810328
\(383\) −1.08114 1.87259i −0.0552436 0.0956847i 0.837081 0.547079i \(-0.184260\pi\)
−0.892325 + 0.451394i \(0.850927\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −8.66228 15.0035i −0.440898 0.763658i
\(387\) 0.581139 1.00656i 0.0295409 0.0511664i
\(388\) −8.66228 + 15.0035i −0.439761 + 0.761688i
\(389\) −28.3246 −1.43611 −0.718056 0.695985i \(-0.754968\pi\)
−0.718056 + 0.695985i \(0.754968\pi\)
\(390\) 0 0
\(391\) 1.81139 0.0916058
\(392\) −1.50000 + 2.59808i −0.0757614 + 0.131223i
\(393\) 8.16228 14.1375i 0.411732 0.713142i
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) −5.83772 10.1112i −0.292987 0.507468i 0.681528 0.731792i \(-0.261316\pi\)
−0.974515 + 0.224324i \(0.927983\pi\)
\(398\) 8.83772 0.442995
\(399\) −5.00000 8.66025i −0.250313 0.433555i
\(400\) 0 0
\(401\) −8.16228 + 14.1375i −0.407605 + 0.705992i −0.994621 0.103583i \(-0.966969\pi\)
0.587016 + 0.809575i \(0.300303\pi\)
\(402\) −4.00000 −0.199502
\(403\) 0.230249 + 10.2290i 0.0114695 + 0.509541i
\(404\) 8.64911 0.430309
\(405\) 0 0
\(406\) −6.83772 + 11.8433i −0.339350 + 0.587772i
\(407\) 12.7302 + 22.0494i 0.631015 + 1.09295i
\(408\) −0.837722 −0.0414734
\(409\) −15.1623 26.2618i −0.749726 1.29856i −0.947954 0.318408i \(-0.896852\pi\)
0.198227 0.980156i \(-0.436482\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 2.74342 + 4.75174i 0.135158 + 0.234101i
\(413\) 9.48683 16.4317i 0.466817 0.808550i
\(414\) −1.08114 + 1.87259i −0.0531351 + 0.0920326i
\(415\) 0 0
\(416\) 3.08114 1.87259i 0.151065 0.0918112i
\(417\) 5.67544 0.277928
\(418\) 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
\(421\) 28.1623 1.37255 0.686273 0.727344i \(-0.259246\pi\)
0.686273 + 0.727344i \(0.259246\pi\)
\(422\) −6.58114 11.3989i −0.320365 0.554888i
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 0.837722 0.0406834
\(425\) 0 0
\(426\) −7.08114 + 12.2649i −0.343082 + 0.594236i
\(427\) 7.09431 12.2877i 0.343318 0.594643i
\(428\) −6.00000 −0.290021
\(429\) −9.24342 + 5.61776i −0.446276 + 0.271228i
\(430\) 0 0
\(431\) 12.2434 21.2062i 0.589745 1.02147i −0.404521 0.914529i \(-0.632562\pi\)
0.994266 0.106939i \(-0.0341049\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −17.3114 29.9842i −0.831932 1.44095i −0.896504 0.443036i \(-0.853901\pi\)
0.0645717 0.997913i \(-0.479432\pi\)
\(434\) 8.97367 0.430750
\(435\) 0 0
\(436\) 5.24342 + 9.08186i 0.251114 + 0.434942i
\(437\) −6.83772 −0.327093
\(438\) 5.66228 + 9.80735i 0.270554 + 0.468613i
\(439\) 18.3246 31.7391i 0.874583 1.51482i 0.0173773 0.999849i \(-0.494468\pi\)
0.857206 0.514974i \(-0.172198\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 0.0679718 + 3.01969i 0.00323309 + 0.143632i
\(443\) 9.00000 0.427603 0.213801 0.976877i \(-0.431415\pi\)
0.213801 + 0.976877i \(0.431415\pi\)
\(444\) −4.24342 + 7.34981i −0.201384 + 0.348807i
\(445\) 0 0
\(446\) 13.0680 + 22.6344i 0.618786 + 1.07177i
\(447\) 6.83772 0.323413
\(448\) −1.58114 2.73861i −0.0747018 0.129387i
\(449\) −1.25658 2.17647i −0.0593018 0.102714i 0.834850 0.550477i \(-0.185554\pi\)
−0.894152 + 0.447763i \(0.852221\pi\)
\(450\) 0 0
\(451\) −14.2302 24.6475i −0.670076 1.16061i
\(452\) 5.16228 8.94133i 0.242813 0.420565i
\(453\) 4.90569 8.49691i 0.230490 0.399220i
\(454\) −21.9737 −1.03128
\(455\) 0 0
\(456\) 3.16228 0.148087
\(457\) −5.17544 + 8.96413i −0.242097 + 0.419324i −0.961311 0.275464i \(-0.911169\pi\)
0.719214 + 0.694788i \(0.244502\pi\)
\(458\) 8.24342 14.2780i 0.385190 0.667168i
\(459\) 0.418861 + 0.725489i 0.0195508 + 0.0338629i
\(460\) 0 0
\(461\) 8.58114 + 14.8630i 0.399663 + 0.692237i 0.993684 0.112212i \(-0.0357937\pi\)
−0.594021 + 0.804450i \(0.702460\pi\)
\(462\) 4.74342 + 8.21584i 0.220684 + 0.382235i
\(463\) −4.51317 −0.209745 −0.104872 0.994486i \(-0.533443\pi\)
−0.104872 + 0.994486i \(0.533443\pi\)
\(464\) −2.16228 3.74517i −0.100381 0.173865i
\(465\) 0 0
\(466\) 6.83772 11.8433i 0.316751 0.548629i
\(467\) 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
\(471\) −8.08114 + 13.9969i −0.372359 + 0.644945i
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) −3.48683 −0.160325
\(474\) 1.41886 + 2.45754i 0.0651705 + 0.112879i
\(475\) 0 0
\(476\) 2.64911 0.121422
\(477\) −0.418861 0.725489i −0.0191783 0.0332179i
\(478\) −9.24342 + 16.0101i −0.422784 + 0.732283i
\(479\) 6.83772 11.8433i 0.312424 0.541133i −0.666463 0.745538i \(-0.732193\pi\)
0.978886 + 0.204405i \(0.0655259\pi\)
\(480\) 0 0
\(481\) 26.8377 + 14.6996i 1.22369 + 0.670245i
\(482\) 8.00000 0.364390
\(483\) 3.41886 5.92164i 0.155564 0.269444i
\(484\) 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 0.827976 0.560764i \(-0.189493\pi\)
−0.899624 + 0.436666i \(0.856159\pi\)
\(488\) 2.24342 + 3.88571i 0.101555 + 0.175898i
\(489\) 15.8114 0.715016
\(490\) 0 0
\(491\) 10.9868 19.0298i 0.495829 0.858801i −0.504160 0.863611i \(-0.668198\pi\)
0.999988 + 0.00480977i \(0.00153100\pi\)
\(492\) 4.74342 8.21584i 0.213850 0.370399i
\(493\) 3.62278 0.163162
\(494\) −0.256584 11.3989i −0.0115442 0.512859i
\(495\) 0 0
\(496\) −1.41886 + 2.45754i −0.0637087 + 0.110347i
\(497\) 22.3925 38.7850i 1.00444 1.73974i
\(498\) 5.82456 + 10.0884i 0.261005 + 0.452073i
\(499\) 39.8114 1.78220 0.891101 0.453805i \(-0.149934\pi\)
0.891101 + 0.453805i \(0.149934\pi\)
\(500\) 0 0
\(501\) −4.08114 7.06874i −0.182332 0.315808i
\(502\) 15.0000 0.669483
\(503\) −8.40569 14.5591i −0.374791 0.649158i 0.615504 0.788133i \(-0.288952\pi\)
−0.990296 + 0.138976i \(0.955619\pi\)
\(504\) −1.58114 + 2.73861i −0.0704295 + 0.121988i
\(505\) 0 0
\(506\) 6.48683 0.288375
\(507\) −5.98683 + 11.5394i −0.265885 + 0.512483i
\(508\) 20.3246 0.901756
\(509\) 13.3925 23.1965i 0.593613 1.02817i −0.400128 0.916459i \(-0.631034\pi\)
0.993741 0.111709i \(-0.0356325\pi\)
\(510\) 0 0
\(511\) −17.9057 31.0136i −0.792101 1.37196i
\(512\) 1.00000 0.0441942
\(513\) −1.58114 2.73861i −0.0698090 0.120913i
\(514\) −12.9057 22.3533i −0.569246 0.985963i
\(515\) 0 0
\(516\) −0.581139 1.00656i −0.0255832 0.0443114i
\(517\) −9.00000 + 15.5885i −0.395820 + 0.685580i
\(518\) 13.4189 23.2421i 0.589591 1.02120i
\(519\) −1.67544 −0.0735439
\(520\) 0 0
\(521\) −20.6491 −0.904654 −0.452327 0.891852i \(-0.649406\pi\)
−0.452327 + 0.891852i \(0.649406\pi\)
\(522\) −2.16228 + 3.74517i −0.0946403 + 0.163922i
\(523\) 16.4868 28.5560i 0.720919 1.24867i −0.239713 0.970844i \(-0.577053\pi\)
0.960632 0.277824i \(-0.0896133\pi\)
\(524\) −8.16228 14.1375i −0.356571 0.617599i
\(525\) 0 0
\(526\) −0.243416 0.421610i −0.0106135 0.0183831i
\(527\) −1.18861 2.05874i −0.0517767 0.0896799i
\(528\) −3.00000 −0.130558
\(529\) 9.16228 + 15.8695i 0.398360 + 0.689980i
\(530\) 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
\(534\) 0.837722 0.0362518
\(535\) 0 0
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) 11.8246 + 20.4807i 0.510267 + 0.883809i
\(538\) −12.8377 −0.553474
\(539\) −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 \(0.269562\pi\)
\(542\) −0.162278 0.281073i −0.00697042 0.0120731i
\(543\) 6.40569 11.0950i 0.274895 0.476131i
\(544\) −0.418861 + 0.725489i −0.0179585 + 0.0311051i
\(545\) 0 0
\(546\) 10.0000 + 5.47723i 0.427960 + 0.234404i
\(547\) −14.1359 −0.604409 −0.302205 0.953243i \(-0.597723\pi\)
−0.302205 + 0.953243i \(0.597723\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) 2.24342 3.88571i 0.0957467 0.165838i
\(550\) 0 0
\(551\) −13.6754 −0.582594
\(552\) 1.08114 + 1.87259i 0.0460163 + 0.0797026i
\(553\) −4.48683 7.77142i −0.190800 0.330475i
\(554\) 8.81139 0.374360
\(555\) 0 0
\(556\) 2.83772 4.91508i 0.120346 0.208446i
\(557\) 9.48683 16.4317i 0.401970 0.696232i −0.591994 0.805943i \(-0.701659\pi\)
0.993964 + 0.109710i \(0.0349923\pi\)
\(558\) 2.83772 0.120130
\(559\) −3.58114 + 2.17647i −0.151466 + 0.0920547i
\(560\) 0 0
\(561\) 1.25658 2.17647i 0.0530530 0.0918905i
\(562\) 10.7434 18.6081i 0.453184 0.784937i
\(563\) 16.9868 + 29.4221i 0.715910 + 1.23999i 0.962608 + 0.270899i \(0.0873211\pi\)
−0.246698 + 0.969092i \(0.579346\pi\)
\(564\) −6.00000 −0.252646
\(565\) 0 0
\(566\) −9.74342 16.8761i −0.409546 0.709355i
\(567\) 3.16228 0.132803
\(568\) 7.08114 + 12.2649i 0.297118 + 0.514623i
\(569\) 3.48683 6.03937i 0.146176 0.253184i −0.783635 0.621221i \(-0.786637\pi\)
0.929811 + 0.368038i \(0.119970\pi\)
\(570\) 0 0
\(571\) −32.3246 −1.35274 −0.676370 0.736562i \(-0.736448\pi\)
−0.676370 + 0.736562i \(0.736448\pi\)
\(572\) 0.243416 + 10.8139i 0.0101778 + 0.452152i
\(573\) −15.8377 −0.661630
\(574\) −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 \(0.147135\pi\)
\(578\) 8.14911 + 14.1147i 0.338958 + 0.587093i
\(579\) 8.66228 + 15.0035i 0.359992 + 0.623524i
\(580\) 0 0
\(581\) −18.4189 31.9024i −0.764143 1.32353i
\(582\) 8.66228 15.0035i 0.359063 0.621915i
\(583\) −1.25658 + 2.17647i −0.0520424 + 0.0901400i
\(584\) 11.3246 0.468613
\(585\) 0 0
\(586\) −21.4868 −0.887613
\(587\) −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
\(589\) 4.48683 + 7.77142i 0.184877 + 0.320216i
\(590\) 0 0
\(591\) 3.00000 + 5.19615i 0.123404 + 0.213741i
\(592\) 4.24342 + 7.34981i 0.174403 + 0.302075i
\(593\) 5.16228 0.211989 0.105995 0.994367i \(-0.466197\pi\)
0.105995 + 0.994367i \(0.466197\pi\)
\(594\) 1.50000 + 2.59808i 0.0615457 + 0.106600i
\(595\) 0 0
\(596\) 3.41886 5.92164i 0.140042 0.242560i
\(597\) −8.83772 −0.361704
\(598\) 6.66228 4.04905i 0.272441 0.165578i
\(599\) 1.18861 0.0485654 0.0242827 0.999705i \(-0.492270\pi\)
0.0242827 + 0.999705i \(0.492270\pi\)
\(600\) 0 0
\(601\) −21.6491 + 37.4974i −0.883086 + 1.52955i −0.0351935 + 0.999381i \(0.511205\pi\)
−0.847892 + 0.530169i \(0.822129\pi\)
\(602\) 1.83772 + 3.18303i 0.0749000 + 0.129731i
\(603\) 4.00000 0.162893
\(604\) −4.90569 8.49691i −0.199610 0.345734i
\(605\) 0 0
\(606\) −8.64911 −0.351346
\(607\) 18.1623 + 31.4580i 0.737184 + 1.27684i 0.953758 + 0.300574i \(0.0971783\pi\)
−0.216574 + 0.976266i \(0.569488\pi\)
\(608\) 1.58114 2.73861i 0.0641236 0.111065i
\(609\) 6.83772 11.8433i 0.277078 0.479914i
\(610\) 0 0
\(611\) 0.486833 + 21.6278i 0.0196952 + 0.874968i
\(612\) 0.837722 0.0338629
\(613\) 21.1623 36.6541i 0.854736 1.48045i −0.0221531 0.999755i \(-0.507052\pi\)
0.876889 0.480692i \(-0.159615\pi\)
\(614\) 8.32456 14.4186i 0.335952 0.581885i
\(615\) 0 0
\(616\) 9.48683 0.382235
\(617\) −23.6491 40.9615i −0.952077 1.64905i −0.740919 0.671594i \(-0.765610\pi\)
−0.211158 0.977452i \(-0.567724\pi\)
\(618\) −2.74342 4.75174i −0.110356 0.191143i
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 0 0
\(621\) 1.08114 1.87259i 0.0433846 0.0751443i
\(622\) 3.24342 5.61776i 0.130049 0.225252i
\(623\) −2.64911 −0.106134
\(624\) −3.08114 + 1.87259i −0.123344 + 0.0749635i
\(625\) 0 0
\(626\) 3.82456 6.62432i 0.152860 0.264761i
\(627\) −4.74342 + 8.21584i −0.189434 + 0.328109i
\(628\) 8.08114 + 13.9969i 0.322473 + 0.558539i
\(629\) −7.10961 −0.283479
\(630\) 0 0
\(631\) 7.64911 + 13.2486i 0.304506 + 0.527420i 0.977151 0.212545i \(-0.0681752\pi\)
−0.672645 + 0.739965i \(0.734842\pi\)
\(632\) 2.83772 0.112879
\(633\) 6.58114 + 11.3989i 0.261577 + 0.453064i
\(634\) −15.9057 + 27.5495i −0.631696 + 1.09413i
\(635\) 0 0
\(636\) −0.837722 −0.0332179
\(637\) −9.48683 5.19615i −0.375882 0.205879i
\(638\) 12.9737 0.513632
\(639\) 7.08114 12.2649i 0.280126 0.485192i
\(640\) 0 0
\(641\) −12.9737 22.4710i −0.512429 0.887553i −0.999896 0.0144117i \(-0.995412\pi\)
0.487467 0.873141i \(-0.337921\pi\)
\(642\) 6.00000 0.236801
\(643\) −5.83772 10.1112i −0.230217 0.398748i 0.727655 0.685944i \(-0.240610\pi\)
−0.957872 + 0.287196i \(0.907277\pi\)
\(644\) −3.41886 5.92164i −0.134722 0.233345i
\(645\) 0 0
\(646\) 1.32456 + 2.29420i 0.0521139 + 0.0902640i
\(647\) −11.7566 + 20.3630i −0.462199 + 0.800552i −0.999070 0.0431121i \(-0.986273\pi\)
0.536871 + 0.843664i \(0.319606\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −18.0000 −0.706562
\(650\) 0 0
\(651\) −8.97367 −0.351706
\(652\) 7.90569 13.6931i 0.309611 0.536262i
\(653\) −4.74342 + 8.21584i −0.185624 + 0.321511i −0.943787 0.330555i \(-0.892764\pi\)
0.758162 + 0.652066i \(0.226097\pi\)
\(654\) −5.24342 9.08186i −0.205034 0.355129i
\(655\) 0 0
\(656\) −4.74342 8.21584i −0.185199 0.320775i
\(657\) −5.66228 9.80735i −0.220906 0.382621i
\(658\) 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 \(0.997923\pi\)
\(662\) −15.1623 −0.589299
\(663\) −0.0679718 3.01969i −0.00263981 0.117275i
\(664\) 11.6491 0.452073
\(665\) 0 0
\(666\) 4.24342 7.34981i 0.164429 0.284799i
\(667\) −4.67544 8.09811i −0.181034 0.313560i
\(668\) −8.16228 −0.315808
\(669\) −13.0680 22.6344i −0.505237 0.875096i
\(670\) 0 0
\(671\) −13.4605 −0.519637
\(672\) 1.58114 + 2.73861i 0.0609938 + 0.105644i
\(673\) −1.82456 + 3.16022i −0.0703314 + 0.121818i −0.899047 0.437853i \(-0.855739\pi\)
0.828715 + 0.559671i \(0.189072\pi\)
\(674\) −2.00000 + 3.46410i −0.0770371 + 0.133432i
\(675\) 0 0
\(676\) 7.00000 + 10.9545i 0.269231 + 0.421325i
\(677\) 32.6491 1.25481 0.627404 0.778694i \(-0.284118\pi\)
0.627404 + 0.778694i \(0.284118\pi\)
\(678\) −5.16228 + 8.94133i −0.198256 + 0.343390i
\(679\) −27.3925 + 47.4452i −1.05123 + 1.82078i
\(680\) 0 0
\(681\) 21.9737 0.842033
\(682\) −4.25658 7.37262i −0.162993 0.282312i
\(683\) −14.4737 25.0691i −0.553819 0.959243i −0.997994 0.0633033i \(-0.979836\pi\)
0.444175 0.895940i \(-0.353497\pi\)
\(684\) −3.16228 −0.120913
\(685\) 0 0
\(686\) 6.32456 10.9545i 0.241473 0.418243i
\(687\) −8.24342 + 14.2780i −0.314506 + 0.544740i
\(688\) −1.16228 −0.0443114
\(689\) 0.0679718 + 3.01969i 0.00258952 + 0.115041i
\(690\) 0 0
\(691\) 11.9737 20.7390i 0.455500 0.788949i −0.543217 0.839592i \(-0.682794\pi\)
0.998717 + 0.0506436i \(0.0161273\pi\)
\(692\) −0.837722 + 1.45098i −0.0318454 + 0.0551579i
\(693\) −4.74342 8.21584i −0.180187 0.312094i
\(694\) −1.32456 −0.0502794
\(695\) 0 0
\(696\) 2.16228 + 3.74517i 0.0819609 + 0.141960i
\(697\) 7.94733 0.301027
\(698\) 17.7302 + 30.7097i 0.671100 + 1.16238i
\(699\) −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 \(0.639431\pi\)
\(702\) 3.16228 + 1.73205i 0.119352 + 0.0653720i
\(703\) 26.8377 1.01220
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −9.90569 17.1572i −0.372806 0.645718i
\(707\) 27.3509 1.02864
\(708\) −3.00000 5.19615i −0.112747 0.195283i
\(709\) −0.756584 1.31044i −0.0284141 0.0492146i 0.851469 0.524405i \(-0.175712\pi\)
−0.879883 + 0.475191i \(0.842379\pi\)
\(710\) 0 0
\(711\) −1.41886 2.45754i −0.0532115 0.0921649i
\(712\) 0.418861 0.725489i 0.0156975 0.0271888i
\(713\) −3.06797 + 5.31388i −0.114896 + 0.199006i
\(714\) −2.64911 −0.0991405
\(715\) 0 0
\(716\) 23.6491 0.883809
\(717\) 9.24342 16.0101i 0.345202 0.597907i
\(718\) 6.00000 10.3923i 0.223918 0.387837i
\(719\) 23.4057 + 40.5399i 0.872885 + 1.51188i 0.858999 + 0.511978i \(0.171087\pi\)
0.0138864 + 0.999904i \(0.495580\pi\)
\(720\) 0 0
\(721\) 8.67544 + 15.0263i 0.323090 + 0.559609i
\(722\) 4.50000 + 7.79423i 0.167473 + 0.290071i
\(723\) −8.00000 −0.297523
\(724\) −6.40569 11.0950i −0.238066 0.412342i
\(725\) 0 0
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) −12.3246 −0.457092 −0.228546 0.973533i \(-0.573397\pi\)
−0.228546 + 0.973533i \(0.573397\pi\)
\(728\) 9.74342 5.92164i 0.361115 0.219471i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.486833 0.843219i 0.0180062 0.0311876i
\(732\) −2.24342 3.88571i −0.0829191 0.143620i
\(733\) −19.5132 −0.720735 −0.360368 0.932810i \(-0.617349\pi\)
−0.360368 + 0.932810i \(0.617349\pi\)
\(734\) −9.32456 16.1506i −0.344176 0.596130i
\(735\) 0 0
\(736\) 2.16228 0.0797026
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) −4.74342 + 8.21584i −0.174608 + 0.302429i
\(739\) −9.64911 + 16.7127i −0.354948 + 0.614788i −0.987109 0.160049i \(-0.948835\pi\)
0.632161 + 0.774837i \(0.282168\pi\)
\(740\) 0 0
\(741\) 0.256584 + 11.3989i 0.00942583 + 0.418748i
\(742\) 2.64911 0.0972519
\(743\) −22.3246 + 38.6673i −0.819009 + 1.41856i 0.0874050 + 0.996173i \(0.472143\pi\)
−0.906414 + 0.422391i \(0.861191\pi\)
\(744\) 1.41886 2.45754i 0.0520180 0.0900978i
\(745\) 0 0
\(746\) 10.4868 0.383950
\(747\) −5.82456 10.0884i −0.213109 0.369116i
\(748\) −1.25658 2.17647i −0.0459452 0.0795795i
\(749\) −18.9737 −0.693283
\(750\) 0 0
\(751\) 8.83772 15.3074i 0.322493 0.558574i −0.658509 0.752573i \(-0.728812\pi\)
0.981002 + 0.193999i \(0.0621458\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) −15.0000 −0.546630
\(754\) 13.3246 8.09811i 0.485252 0.294916i
\(755\) 0 0
\(756\) 1.58114 2.73861i 0.0575055 0.0996024i
\(757\) −5.48683 + 9.50347i −0.199422 + 0.345410i −0.948341 0.317252i \(-0.897240\pi\)
0.748919 + 0.662662i \(0.230573\pi\)
\(758\) −1.00000 1.73205i −0.0363216 0.0629109i
\(759\) −6.48683 −0.235457
\(760\) 0 0
\(761\) 23.2302 + 40.2360i 0.842096 + 1.45855i 0.888120 + 0.459613i \(0.152012\pi\)
−0.0460237 + 0.998940i \(0.514655\pi\)
\(762\) −20.3246 −0.736281
\(763\) 16.5811 + 28.7194i 0.600278 + 1.03971i
\(764\) −7.91886 + 13.7159i −0.286494 + 0.496223i
\(765\) 0 0
\(766\) 2.16228 0.0781263
\(767\) −18.4868 + 11.2355i −0.667521 + 0.405691i
\(768\) −1.00000 −0.0360844
\(769\) −7.48683 + 12.9676i −0.269982 + 0.467623i −0.968857 0.247621i \(-0.920351\pi\)
0.698875 + 0.715244i \(0.253684\pi\)
\(770\) 0 0
\(771\) 12.9057 + 22.3533i 0.464787 + 0.805035i
\(772\) 17.3246 0.623524
\(773\) −4.67544 8.09811i −0.168164 0.291269i 0.769610 0.638514i \(-0.220451\pi\)
−0.937774 + 0.347245i \(0.887117\pi\)
\(774\) 0.581139 + 1.00656i 0.0208886 + 0.0361801i
\(775\) 0 0
\(776\) −8.66228 15.0035i −0.310958 0.538594i
\(777\) −13.4189 + 23.2421i −0.481399 + 0.833807i
\(778\) 14.1623 24.5298i 0.507742 0.879435i
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) −42.4868 −1.52030
\(782\) −0.905694 + 1.56871i −0.0323876 + 0.0560969i
\(783\) 2.16228 3.74517i 0.0772735 0.133842i
\(784\) −1.50000 2.59808i −0.0535714 0.0927884i
\(785\) 0 0