Properties

Label 1950.2.y.j.49.2
Level $1950$
Weight $2$
Character 1950.49
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
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.y (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: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.2
Root \(3.17270 + 3.17270i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.j.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(1.16129 - 2.01141i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(1.16129 - 2.01141i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(4.62926 - 2.67270i) q^{11} -1.00000i q^{12} +(-0.161290 + 3.60194i) q^{13} -2.32258 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.46410 + 2.00000i) q^{17} -1.00000 q^{18} +(3.48387 + 2.01141i) q^{19} +2.32258i q^{21} +(-4.62926 - 2.67270i) q^{22} +(-4.27464 + 2.46797i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.20002 - 1.66129i) q^{26} +1.00000i q^{27} +(1.16129 + 2.01141i) q^{28} +(2.14539 + 3.71592i) q^{29} -3.47183i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.67270 + 4.62926i) q^{33} -4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(-1.57463 - 2.72733i) q^{37} -4.02283i q^{38} +(-1.66129 - 3.20002i) q^{39} +(2.29078 - 1.32258i) q^{41} +(2.01141 - 1.16129i) q^{42} +(-10.6095 - 6.12539i) q^{43} +5.34541i q^{44} +(4.27464 + 2.46797i) q^{46} -1.81894 q^{47} +(0.866025 + 0.500000i) q^{48} +(0.802812 + 1.39051i) q^{49} -4.00000 q^{51} +(-3.03873 - 1.94065i) q^{52} +5.48693i q^{53} +(0.866025 - 0.500000i) q^{54} +(1.16129 - 2.01141i) q^{56} -4.02283 q^{57} +(2.14539 - 3.71592i) q^{58} +(-5.87744 - 3.39334i) q^{59} +(-0.267949 + 0.464102i) q^{61} +(-3.00670 + 1.73592i) q^{62} +(-1.16129 - 2.01141i) q^{63} +1.00000 q^{64} +5.34541 q^{66} +(2.05463 + 3.55872i) q^{67} +(-3.46410 + 2.00000i) q^{68} +(2.46797 - 4.27464i) q^{69} +(13.7454 + 7.93593i) q^{71} +(0.500000 - 0.866025i) q^{72} +13.5734 q^{73} +(-1.57463 + 2.72733i) q^{74} +(-3.48387 + 2.01141i) q^{76} -12.4151i q^{77} +(-1.94065 + 3.03873i) q^{78} +7.96774 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.29078 - 1.32258i) q^{82} +11.3360 q^{83} +(-2.01141 - 1.16129i) q^{84} +12.2508i q^{86} +(-3.71592 - 2.14539i) q^{87} +(4.62926 - 2.67270i) q^{88} +(1.50670 - 0.869891i) q^{89} +(7.05769 + 4.50732i) q^{91} -4.93593i q^{92} +(1.73592 + 3.00670i) q^{93} +(0.909471 + 1.57525i) q^{94} -1.00000i q^{96} +(8.05463 - 13.9510i) q^{97} +(0.802812 - 1.39051i) q^{98} -5.34541i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + 6q^{11} + 6q^{13} - 4q^{14} - 4q^{16} - 8q^{18} + 6q^{19} - 6q^{22} + 6q^{23} - 12q^{26} + 2q^{28} + 8q^{29} - 4q^{32} + 2q^{33} + 4q^{36} - 10q^{37} - 6q^{39} - 48q^{43} - 6q^{46} - 16q^{47} - 14q^{49} - 32q^{51} + 6q^{52} + 2q^{56} + 8q^{58} - 24q^{59} - 16q^{61} + 30q^{62} - 2q^{63} + 8q^{64} - 4q^{66} - 12q^{67} - 4q^{69} - 12q^{71} + 4q^{72} + 24q^{73} - 10q^{74} - 6q^{76} - 6q^{78} + 20q^{79} - 4q^{81} - 32q^{83} + 6q^{87} + 6q^{88} - 42q^{89} - 10q^{91} + 4q^{93} + 8q^{94} + 36q^{97} - 14q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) 1.16129 2.01141i 0.438926 0.760243i −0.558681 0.829383i \(-0.688692\pi\)
0.997607 + 0.0691402i \(0.0220256\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 4.62926 2.67270i 1.39577 0.805850i 0.401827 0.915716i \(-0.368375\pi\)
0.993946 + 0.109865i \(0.0350420\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −0.161290 + 3.60194i −0.0447338 + 0.998999i
\(14\) −2.32258 −0.620736
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.46410 + 2.00000i 0.840168 + 0.485071i 0.857321 0.514782i \(-0.172127\pi\)
−0.0171533 + 0.999853i \(0.505460\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.48387 + 2.01141i 0.799254 + 0.461450i 0.843210 0.537584i \(-0.180663\pi\)
−0.0439559 + 0.999033i \(0.513996\pi\)
\(20\) 0 0
\(21\) 2.32258i 0.506828i
\(22\) −4.62926 2.67270i −0.986961 0.569822i
\(23\) −4.27464 + 2.46797i −0.891325 + 0.514607i −0.874376 0.485250i \(-0.838729\pi\)
−0.0169494 + 0.999856i \(0.505395\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) 3.20002 1.66129i 0.627575 0.325806i
\(27\) 1.00000i 0.192450i
\(28\) 1.16129 + 2.01141i 0.219463 + 0.380121i
\(29\) 2.14539 + 3.71592i 0.398388 + 0.690029i 0.993527 0.113594i \(-0.0362363\pi\)
−0.595139 + 0.803623i \(0.702903\pi\)
\(30\) 0 0
\(31\) 3.47183i 0.623560i −0.950154 0.311780i \(-0.899075\pi\)
0.950154 0.311780i \(-0.100925\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.67270 + 4.62926i −0.465258 + 0.805850i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −1.57463 2.72733i −0.258867 0.448371i 0.707072 0.707142i \(-0.250016\pi\)
−0.965939 + 0.258771i \(0.916682\pi\)
\(38\) 4.02283i 0.652589i
\(39\) −1.66129 3.20002i −0.266019 0.512413i
\(40\) 0 0
\(41\) 2.29078 1.32258i 0.357759 0.206552i −0.310338 0.950626i \(-0.600442\pi\)
0.668097 + 0.744074i \(0.267109\pi\)
\(42\) 2.01141 1.16129i 0.310368 0.179191i
\(43\) −10.6095 6.12539i −1.61793 0.934113i −0.987454 0.157906i \(-0.949526\pi\)
−0.630478 0.776207i \(-0.717141\pi\)
\(44\) 5.34541i 0.805850i
\(45\) 0 0
\(46\) 4.27464 + 2.46797i 0.630262 + 0.363882i
\(47\) −1.81894 −0.265320 −0.132660 0.991162i \(-0.542352\pi\)
−0.132660 + 0.991162i \(0.542352\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) 0.802812 + 1.39051i 0.114687 + 0.198644i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) −3.03873 1.94065i −0.421396 0.269120i
\(53\) 5.48693i 0.753687i 0.926277 + 0.376844i \(0.122991\pi\)
−0.926277 + 0.376844i \(0.877009\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.16129 2.01141i 0.155184 0.268786i
\(57\) −4.02283 −0.532836
\(58\) 2.14539 3.71592i 0.281703 0.487924i
\(59\) −5.87744 3.39334i −0.765177 0.441775i 0.0659742 0.997821i \(-0.478984\pi\)
−0.831152 + 0.556046i \(0.812318\pi\)
\(60\) 0 0
\(61\) −0.267949 + 0.464102i −0.0343074 + 0.0594221i −0.882669 0.469995i \(-0.844256\pi\)
0.848362 + 0.529417i \(0.177589\pi\)
\(62\) −3.00670 + 1.73592i −0.381851 + 0.220462i
\(63\) −1.16129 2.01141i −0.146309 0.253414i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 5.34541 0.657974
\(67\) 2.05463 + 3.55872i 0.251013 + 0.434767i 0.963805 0.266608i \(-0.0859030\pi\)
−0.712792 + 0.701376i \(0.752570\pi\)
\(68\) −3.46410 + 2.00000i −0.420084 + 0.242536i
\(69\) 2.46797 4.27464i 0.297108 0.514607i
\(70\) 0 0
\(71\) 13.7454 + 7.93593i 1.63128 + 0.941822i 0.983698 + 0.179830i \(0.0575547\pi\)
0.647586 + 0.761992i \(0.275779\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 13.5734 1.58864 0.794321 0.607498i \(-0.207827\pi\)
0.794321 + 0.607498i \(0.207827\pi\)
\(74\) −1.57463 + 2.72733i −0.183047 + 0.317046i
\(75\) 0 0
\(76\) −3.48387 + 2.01141i −0.399627 + 0.230725i
\(77\) 12.4151i 1.41484i
\(78\) −1.94065 + 3.03873i −0.219736 + 0.344068i
\(79\) 7.96774 0.896441 0.448220 0.893923i \(-0.352058\pi\)
0.448220 + 0.893923i \(0.352058\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.29078 1.32258i −0.252974 0.146054i
\(83\) 11.3360 1.24428 0.622142 0.782904i \(-0.286263\pi\)
0.622142 + 0.782904i \(0.286263\pi\)
\(84\) −2.01141 1.16129i −0.219463 0.126707i
\(85\) 0 0
\(86\) 12.2508i 1.32104i
\(87\) −3.71592 2.14539i −0.398388 0.230010i
\(88\) 4.62926 2.67270i 0.493480 0.284911i
\(89\) 1.50670 0.869891i 0.159709 0.0922083i −0.418015 0.908440i \(-0.637274\pi\)
0.577725 + 0.816232i \(0.303941\pi\)
\(90\) 0 0
\(91\) 7.05769 + 4.50732i 0.739847 + 0.472495i
\(92\) 4.93593i 0.514607i
\(93\) 1.73592 + 3.00670i 0.180006 + 0.311780i
\(94\) 0.909471 + 1.57525i 0.0938048 + 0.162475i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 8.05463 13.9510i 0.817824 1.41651i −0.0894586 0.995991i \(-0.528514\pi\)
0.907282 0.420522i \(-0.138153\pi\)
\(98\) 0.802812 1.39051i 0.0810962 0.140463i
\(99\) 5.34541i 0.537233i
\(100\) 0 0
\(101\) 6.34541 + 10.9906i 0.631391 + 1.09360i 0.987267 + 0.159069i \(0.0508492\pi\)
−0.355876 + 0.934533i \(0.615817\pi\)
\(102\) 2.00000 + 3.46410i 0.198030 + 0.342997i
\(103\) 4.79612i 0.472575i 0.971683 + 0.236288i \(0.0759308\pi\)
−0.971683 + 0.236288i \(0.924069\pi\)
\(104\) −0.161290 + 3.60194i −0.0158158 + 0.353199i
\(105\) 0 0
\(106\) 4.75182 2.74346i 0.461537 0.266469i
\(107\) 2.66025 1.53590i 0.257176 0.148481i −0.365869 0.930666i \(-0.619228\pi\)
0.623046 + 0.782185i \(0.285895\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 6.69081i 0.640864i −0.947272 0.320432i \(-0.896172\pi\)
0.947272 0.320432i \(-0.103828\pi\)
\(110\) 0 0
\(111\) 2.72733 + 1.57463i 0.258867 + 0.149457i
\(112\) −2.32258 −0.219463
\(113\) −6.15720 3.55486i −0.579220 0.334413i 0.181603 0.983372i \(-0.441871\pi\)
−0.760823 + 0.648959i \(0.775205\pi\)
\(114\) 2.01141 + 3.48387i 0.188386 + 0.326294i
\(115\) 0 0
\(116\) −4.29078 −0.398388
\(117\) 3.03873 + 1.94065i 0.280931 + 0.179413i
\(118\) 6.78668i 0.624765i
\(119\) 8.04565 4.64516i 0.737544 0.425821i
\(120\) 0 0
\(121\) 8.78668 15.2190i 0.798789 1.38354i
\(122\) 0.535898 0.0485180
\(123\) −1.32258 + 2.29078i −0.119253 + 0.206552i
\(124\) 3.00670 + 1.73592i 0.270009 + 0.155890i
\(125\) 0 0
\(126\) −1.16129 + 2.01141i −0.103456 + 0.179191i
\(127\) 1.84644 1.06604i 0.163845 0.0945961i −0.415835 0.909440i \(-0.636511\pi\)
0.579680 + 0.814844i \(0.303177\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 12.2508 1.07862
\(130\) 0 0
\(131\) 1.25851 0.109957 0.0549785 0.998488i \(-0.482491\pi\)
0.0549785 + 0.998488i \(0.482491\pi\)
\(132\) −2.67270 4.62926i −0.232629 0.402925i
\(133\) 8.09156 4.67167i 0.701628 0.405085i
\(134\) 2.05463 3.55872i 0.177493 0.307427i
\(135\) 0 0
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) −9.85744 + 17.0736i −0.842178 + 1.45870i 0.0458713 + 0.998947i \(0.485394\pi\)
−0.888049 + 0.459748i \(0.847940\pi\)
\(138\) −4.93593 −0.420175
\(139\) 2.83871 4.91679i 0.240776 0.417037i −0.720159 0.693809i \(-0.755931\pi\)
0.960936 + 0.276772i \(0.0892647\pi\)
\(140\) 0 0
\(141\) 1.57525 0.909471i 0.132660 0.0765913i
\(142\) 15.8719i 1.33194i
\(143\) 8.88027 + 17.1054i 0.742605 + 1.43043i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −6.78668 11.7549i −0.561670 0.972841i
\(147\) −1.39051 0.802812i −0.114687 0.0662148i
\(148\) 3.14925 0.258867
\(149\) 16.8680 + 9.73875i 1.38188 + 0.797829i 0.992382 0.123198i \(-0.0393150\pi\)
0.389499 + 0.921027i \(0.372648\pi\)
\(150\) 0 0
\(151\) 14.5170i 1.18138i −0.806899 0.590690i \(-0.798856\pi\)
0.806899 0.590690i \(-0.201144\pi\)
\(152\) 3.48387 + 2.01141i 0.282579 + 0.163147i
\(153\) 3.46410 2.00000i 0.280056 0.161690i
\(154\) −10.7518 + 6.20757i −0.866406 + 0.500220i
\(155\) 0 0
\(156\) 3.60194 + 0.161290i 0.288386 + 0.0129135i
\(157\) 24.3829i 1.94596i 0.230879 + 0.972982i \(0.425840\pi\)
−0.230879 + 0.972982i \(0.574160\pi\)
\(158\) −3.98387 6.90026i −0.316940 0.548956i
\(159\) −2.74346 4.75182i −0.217571 0.376844i
\(160\) 0 0
\(161\) 11.4641i 0.903498i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 11.8134 20.4614i 0.925295 1.60266i 0.134208 0.990953i \(-0.457151\pi\)
0.791086 0.611704i \(-0.209516\pi\)
\(164\) 2.64516i 0.206552i
\(165\) 0 0
\(166\) −5.66799 9.81724i −0.439921 0.761966i
\(167\) 8.37357 + 14.5035i 0.647967 + 1.12231i 0.983608 + 0.180321i \(0.0577137\pi\)
−0.335641 + 0.941990i \(0.608953\pi\)
\(168\) 2.32258i 0.179191i
\(169\) −12.9480 1.16191i −0.995998 0.0893780i
\(170\) 0 0
\(171\) 3.48387 2.01141i 0.266418 0.153817i
\(172\) 10.6095 6.12539i 0.808966 0.467057i
\(173\) −13.9708 8.06604i −1.06218 0.613250i −0.136146 0.990689i \(-0.543471\pi\)
−0.926034 + 0.377439i \(0.876805\pi\)
\(174\) 4.29078i 0.325283i
\(175\) 0 0
\(176\) −4.62926 2.67270i −0.348943 0.201463i
\(177\) 6.78668 0.510118
\(178\) −1.50670 0.869891i −0.112932 0.0652011i
\(179\) −3.66412 6.34644i −0.273869 0.474355i 0.695980 0.718061i \(-0.254970\pi\)
−0.969849 + 0.243706i \(0.921637\pi\)
\(180\) 0 0
\(181\) −19.5734 −1.45488 −0.727438 0.686173i \(-0.759289\pi\)
−0.727438 + 0.686173i \(0.759289\pi\)
\(182\) 0.374609 8.36580i 0.0277678 0.620114i
\(183\) 0.535898i 0.0396147i
\(184\) −4.27464 + 2.46797i −0.315131 + 0.181941i
\(185\) 0 0
\(186\) 1.73592 3.00670i 0.127284 0.220462i
\(187\) 21.3816 1.56358
\(188\) 0.909471 1.57525i 0.0663300 0.114887i
\(189\) 2.01141 + 1.16129i 0.146309 + 0.0844714i
\(190\) 0 0
\(191\) 8.51873 14.7549i 0.616394 1.06763i −0.373744 0.927532i \(-0.621926\pi\)
0.990138 0.140094i \(-0.0447404\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −3.07746 5.33031i −0.221520 0.383684i 0.733750 0.679420i \(-0.237769\pi\)
−0.955270 + 0.295736i \(0.904435\pi\)
\(194\) −16.1093 −1.15658
\(195\) 0 0
\(196\) −1.60562 −0.114687
\(197\) −6.89334 11.9396i −0.491130 0.850662i 0.508818 0.860874i \(-0.330083\pi\)
−0.999948 + 0.0102119i \(0.996749\pi\)
\(198\) −4.62926 + 2.67270i −0.328987 + 0.189941i
\(199\) −1.14152 + 1.97717i −0.0809203 + 0.140158i −0.903646 0.428281i \(-0.859119\pi\)
0.822725 + 0.568439i \(0.192453\pi\)
\(200\) 0 0
\(201\) −3.55872 2.05463i −0.251013 0.144922i
\(202\) 6.34541 10.9906i 0.446461 0.773293i
\(203\) 9.96567 0.699453
\(204\) 2.00000 3.46410i 0.140028 0.242536i
\(205\) 0 0
\(206\) 4.15356 2.39806i 0.289392 0.167081i
\(207\) 4.93593i 0.343071i
\(208\) 3.20002 1.66129i 0.221881 0.115190i
\(209\) 21.5036 1.48744
\(210\) 0 0
\(211\) −11.2387 19.4661i −0.773707 1.34010i −0.935518 0.353278i \(-0.885067\pi\)
0.161811 0.986822i \(-0.448267\pi\)
\(212\) −4.75182 2.74346i −0.326356 0.188422i
\(213\) −15.8719 −1.08752
\(214\) −2.66025 1.53590i −0.181851 0.104992i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −6.98329 4.03180i −0.474057 0.273697i
\(218\) −5.79441 + 3.34541i −0.392447 + 0.226579i
\(219\) −11.7549 + 6.78668i −0.794321 + 0.458601i
\(220\) 0 0
\(221\) −7.76261 + 12.1549i −0.522170 + 0.817628i
\(222\) 3.14925i 0.211364i
\(223\) −0.689457 1.19417i −0.0461694 0.0799678i 0.842017 0.539451i \(-0.181368\pi\)
−0.888187 + 0.459483i \(0.848035\pi\)
\(224\) 1.16129 + 2.01141i 0.0775919 + 0.134393i
\(225\) 0 0
\(226\) 7.10972i 0.472931i
\(227\) 9.66025 16.7321i 0.641174 1.11055i −0.343998 0.938971i \(-0.611781\pi\)
0.985171 0.171575i \(-0.0548855\pi\)
\(228\) 2.01141 3.48387i 0.133209 0.230725i
\(229\) 15.7626i 1.04162i −0.853672 0.520811i \(-0.825630\pi\)
0.853672 0.520811i \(-0.174370\pi\)
\(230\) 0 0
\(231\) 6.20757 + 10.7518i 0.408428 + 0.707418i
\(232\) 2.14539 + 3.71592i 0.140852 + 0.243962i
\(233\) 16.5549i 1.08455i 0.840201 + 0.542275i \(0.182437\pi\)
−0.840201 + 0.542275i \(0.817563\pi\)
\(234\) 0.161290 3.60194i 0.0105438 0.235466i
\(235\) 0 0
\(236\) 5.87744 3.39334i 0.382589 0.220888i
\(237\) −6.90026 + 3.98387i −0.448220 + 0.258780i
\(238\) −8.04565 4.64516i −0.521522 0.301101i
\(239\) 26.2006i 1.69477i 0.530976 + 0.847387i \(0.321825\pi\)
−0.530976 + 0.847387i \(0.678175\pi\)
\(240\) 0 0
\(241\) −13.5529 7.82479i −0.873021 0.504039i −0.00466988 0.999989i \(-0.501486\pi\)
−0.868351 + 0.495950i \(0.834820\pi\)
\(242\) −17.5734 −1.12966
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −0.267949 0.464102i −0.0171537 0.0297111i
\(245\) 0 0
\(246\) 2.64516 0.168649
\(247\) −7.80691 + 12.2243i −0.496742 + 0.777812i
\(248\) 3.47183i 0.220462i
\(249\) −9.81724 + 5.66799i −0.622142 + 0.359194i
\(250\) 0 0
\(251\) −14.1708 + 24.5446i −0.894454 + 1.54924i −0.0599750 + 0.998200i \(0.519102\pi\)
−0.834479 + 0.551040i \(0.814231\pi\)
\(252\) 2.32258 0.146309
\(253\) −13.1923 + 22.8497i −0.829392 + 1.43655i
\(254\) −1.84644 1.06604i −0.115856 0.0668895i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.8334 6.25465i 0.675767 0.390154i −0.122491 0.992470i \(-0.539088\pi\)
0.798258 + 0.602315i \(0.205755\pi\)
\(258\) −6.12539 10.6095i −0.381350 0.660518i
\(259\) −7.31439 −0.454494
\(260\) 0 0
\(261\) 4.29078 0.265592
\(262\) −0.629257 1.08991i −0.0388756 0.0673346i
\(263\) 9.27159 5.35295i 0.571711 0.330077i −0.186122 0.982527i \(-0.559592\pi\)
0.757832 + 0.652449i \(0.226259\pi\)
\(264\) −2.67270 + 4.62926i −0.164493 + 0.284911i
\(265\) 0 0
\(266\) −8.09156 4.67167i −0.496126 0.286438i
\(267\) −0.869891 + 1.50670i −0.0532365 + 0.0922083i
\(268\) −4.10926 −0.251013
\(269\) 3.76261 6.51703i 0.229410 0.397350i −0.728223 0.685340i \(-0.759654\pi\)
0.957633 + 0.287990i \(0.0929869\pi\)
\(270\) 0 0
\(271\) 8.52920 4.92434i 0.518112 0.299132i −0.218050 0.975938i \(-0.569970\pi\)
0.736162 + 0.676805i \(0.236636\pi\)
\(272\) 4.00000i 0.242536i
\(273\) −8.36580 0.374609i −0.506321 0.0226723i
\(274\) 19.7149 1.19102
\(275\) 0 0
\(276\) 2.46797 + 4.27464i 0.148554 + 0.257303i
\(277\) 0.825410 + 0.476550i 0.0495941 + 0.0286331i 0.524592 0.851354i \(-0.324218\pi\)
−0.474998 + 0.879987i \(0.657551\pi\)
\(278\) −5.67742 −0.340509
\(279\) −3.00670 1.73592i −0.180006 0.103927i
\(280\) 0 0
\(281\) 5.57336i 0.332479i 0.986085 + 0.166239i \(0.0531625\pi\)
−0.986085 + 0.166239i \(0.946838\pi\)
\(282\) −1.57525 0.909471i −0.0938048 0.0541582i
\(283\) 19.0642 11.0067i 1.13325 0.654280i 0.188497 0.982074i \(-0.439638\pi\)
0.944749 + 0.327794i \(0.106305\pi\)
\(284\) −13.7454 + 7.93593i −0.815642 + 0.470911i
\(285\) 0 0
\(286\) 10.3736 16.2432i 0.613402 0.960483i
\(287\) 6.14359i 0.362645i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) 16.1093i 0.944342i
\(292\) −6.78668 + 11.7549i −0.397160 + 0.687902i
\(293\) 3.42151 5.92623i 0.199887 0.346214i −0.748605 0.663016i \(-0.769276\pi\)
0.948491 + 0.316803i \(0.102609\pi\)
\(294\) 1.60562i 0.0936419i
\(295\) 0 0
\(296\) −1.57463 2.72733i −0.0915233 0.158523i
\(297\) 2.67270 + 4.62926i 0.155086 + 0.268617i
\(298\) 19.4775i 1.12830i
\(299\) −8.20002 15.7951i −0.474219 0.913453i
\(300\) 0 0
\(301\) −24.6414 + 14.2267i −1.42031 + 0.820014i
\(302\) −12.5721 + 7.25851i −0.723444 + 0.417681i
\(303\) −10.9906 6.34541i −0.631391 0.364534i
\(304\) 4.02283i 0.230725i
\(305\) 0 0
\(306\) −3.46410 2.00000i −0.198030 0.114332i
\(307\) −4.75442 −0.271349 −0.135675 0.990753i \(-0.543320\pi\)
−0.135675 + 0.990753i \(0.543320\pi\)
\(308\) 10.7518 + 6.20757i 0.612642 + 0.353709i
\(309\) −2.39806 4.15356i −0.136421 0.236288i
\(310\) 0 0
\(311\) 1.93639 0.109803 0.0549013 0.998492i \(-0.482516\pi\)
0.0549013 + 0.998492i \(0.482516\pi\)
\(312\) −1.66129 3.20002i −0.0940520 0.181165i
\(313\) 25.5545i 1.44443i −0.691671 0.722213i \(-0.743125\pi\)
0.691671 0.722213i \(-0.256875\pi\)
\(314\) 21.1162 12.1914i 1.19166 0.688002i
\(315\) 0 0
\(316\) −3.98387 + 6.90026i −0.224110 + 0.388170i
\(317\) −12.6667 −0.711435 −0.355717 0.934594i \(-0.615763\pi\)
−0.355717 + 0.934594i \(0.615763\pi\)
\(318\) −2.74346 + 4.75182i −0.153846 + 0.266469i
\(319\) 19.8631 + 11.4680i 1.11212 + 0.642083i
\(320\) 0 0
\(321\) −1.53590 + 2.66025i −0.0857255 + 0.148481i
\(322\) 9.92820 5.73205i 0.553277 0.319435i
\(323\) 8.04565 + 13.9355i 0.447672 + 0.775391i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −23.6267 −1.30856
\(327\) 3.34541 + 5.79441i 0.185001 + 0.320432i
\(328\) 2.29078 1.32258i 0.126487 0.0730272i
\(329\) −2.11232 + 3.65864i −0.116456 + 0.201708i
\(330\) 0 0
\(331\) −20.5231 11.8490i −1.12805 0.651282i −0.184609 0.982812i \(-0.559102\pi\)
−0.943445 + 0.331530i \(0.892435\pi\)
\(332\) −5.66799 + 9.81724i −0.311071 + 0.538791i
\(333\) −3.14925 −0.172578
\(334\) 8.37357 14.5035i 0.458182 0.793594i
\(335\) 0 0
\(336\) 2.01141 1.16129i 0.109732 0.0633536i
\(337\) 19.5554i 1.06525i 0.846351 + 0.532625i \(0.178795\pi\)
−0.846351 + 0.532625i \(0.821205\pi\)
\(338\) 5.46774 + 11.7942i 0.297406 + 0.641521i
\(339\) 7.10972 0.386147
\(340\) 0 0
\(341\) −9.27918 16.0720i −0.502496 0.870348i
\(342\) −3.48387 2.01141i −0.188386 0.108765i
\(343\) 19.9872 1.07921
\(344\) −10.6095 6.12539i −0.572025 0.330259i
\(345\) 0 0
\(346\) 16.1321i 0.867266i
\(347\) 19.9510 + 11.5187i 1.07103 + 0.618358i 0.928462 0.371427i \(-0.121132\pi\)
0.142565 + 0.989785i \(0.454465\pi\)
\(348\) 3.71592 2.14539i 0.199194 0.115005i
\(349\) −13.2679 + 7.66025i −0.710217 + 0.410044i −0.811141 0.584850i \(-0.801153\pi\)
0.100924 + 0.994894i \(0.467820\pi\)
\(350\) 0 0
\(351\) −3.60194 0.161290i −0.192257 0.00860902i
\(352\) 5.34541i 0.284911i
\(353\) −14.2039 24.6018i −0.755996 1.30942i −0.944877 0.327424i \(-0.893819\pi\)
0.188881 0.982000i \(-0.439514\pi\)
\(354\) −3.39334 5.87744i −0.180354 0.312382i
\(355\) 0 0
\(356\) 1.73978i 0.0922083i
\(357\) −4.64516 + 8.04565i −0.245848 + 0.425821i
\(358\) −3.66412 + 6.34644i −0.193655 + 0.335420i
\(359\) 23.5734i 1.24415i 0.782956 + 0.622077i \(0.213711\pi\)
−0.782956 + 0.622077i \(0.786289\pi\)
\(360\) 0 0
\(361\) −1.40844 2.43948i −0.0741282 0.128394i
\(362\) 9.78668 + 16.9510i 0.514377 + 0.890926i
\(363\) 17.5734i 0.922362i
\(364\) −7.43230 + 3.85848i −0.389558 + 0.202239i
\(365\) 0 0
\(366\) −0.464102 + 0.267949i −0.0242590 + 0.0140059i
\(367\) 23.8078 13.7454i 1.24276 0.717506i 0.273103 0.961985i \(-0.411950\pi\)
0.969655 + 0.244479i \(0.0786168\pi\)
\(368\) 4.27464 + 2.46797i 0.222831 + 0.128652i
\(369\) 2.64516i 0.137701i
\(370\) 0 0
\(371\) 11.0365 + 6.37191i 0.572985 + 0.330813i
\(372\) −3.47183 −0.180006
\(373\) 22.8129 + 13.1710i 1.18121 + 0.681971i 0.956294 0.292408i \(-0.0944564\pi\)
0.224914 + 0.974379i \(0.427790\pi\)
\(374\) −10.6908 18.5170i −0.552809 0.957493i
\(375\) 0 0
\(376\) −1.81894 −0.0938048
\(377\) −13.7306 + 7.12822i −0.707160 + 0.367122i
\(378\) 2.32258i 0.119461i
\(379\) −0.388456 + 0.224275i −0.0199537 + 0.0115202i −0.509944 0.860208i \(-0.670334\pi\)
0.489990 + 0.871728i \(0.337000\pi\)
\(380\) 0 0
\(381\) −1.06604 + 1.84644i −0.0546151 + 0.0945961i
\(382\) −17.0375 −0.871713
\(383\) 6.06133 10.4985i 0.309719 0.536450i −0.668582 0.743639i \(-0.733098\pi\)
0.978301 + 0.207189i \(0.0664316\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) −3.07746 + 5.33031i −0.156638 + 0.271306i
\(387\) −10.6095 + 6.12539i −0.539311 + 0.311371i
\(388\) 8.05463 + 13.9510i 0.408912 + 0.708256i
\(389\) −18.6195 −0.944045 −0.472022 0.881587i \(-0.656476\pi\)
−0.472022 + 0.881587i \(0.656476\pi\)
\(390\) 0 0
\(391\) −19.7437 −0.998484
\(392\) 0.802812 + 1.39051i 0.0405481 + 0.0702314i
\(393\) −1.08991 + 0.629257i −0.0549785 + 0.0317418i
\(394\) −6.89334 + 11.9396i −0.347281 + 0.601509i
\(395\) 0 0
\(396\) 4.62926 + 2.67270i 0.232629 + 0.134308i
\(397\) −5.65208 + 9.78970i −0.283670 + 0.491331i −0.972286 0.233796i \(-0.924885\pi\)
0.688616 + 0.725126i \(0.258219\pi\)
\(398\) 2.28304 0.114439
\(399\) −4.67167 + 8.09156i −0.233876 + 0.405085i
\(400\) 0 0
\(401\) −1.30406 + 0.752899i −0.0651216 + 0.0375980i −0.532207 0.846614i \(-0.678637\pi\)
0.467086 + 0.884212i \(0.345304\pi\)
\(402\) 4.10926i 0.204951i
\(403\) 12.5053 + 0.559971i 0.622935 + 0.0278942i
\(404\) −12.6908 −0.631391
\(405\) 0 0
\(406\) −4.98283 8.63052i −0.247294 0.428326i
\(407\) −14.5787 8.41702i −0.722640 0.417216i
\(408\) −4.00000 −0.198030
\(409\) −9.64697 5.56968i −0.477012 0.275403i 0.242158 0.970237i \(-0.422145\pi\)
−0.719170 + 0.694834i \(0.755478\pi\)
\(410\) 0 0
\(411\) 19.7149i 0.972464i
\(412\) −4.15356 2.39806i −0.204631 0.118144i
\(413\) −13.6508 + 7.88130i −0.671713 + 0.387814i
\(414\) 4.27464 2.46797i 0.210087 0.121294i
\(415\) 0 0
\(416\) −3.03873 1.94065i −0.148986 0.0951483i
\(417\) 5.67742i 0.278024i
\(418\) −10.7518 18.6227i −0.525889 0.910866i
\(419\) −7.75488 13.4318i −0.378851 0.656188i 0.612045 0.790823i \(-0.290347\pi\)
−0.990895 + 0.134635i \(0.957014\pi\)
\(420\) 0 0
\(421\) 39.4452i 1.92244i 0.275778 + 0.961221i \(0.411065\pi\)
−0.275778 + 0.961221i \(0.588935\pi\)
\(422\) −11.2387 + 19.4661i −0.547094 + 0.947594i
\(423\) −0.909471 + 1.57525i −0.0442200 + 0.0765913i
\(424\) 5.48693i 0.266469i
\(425\) 0 0
\(426\) 7.93593 + 13.7454i 0.384497 + 0.665969i
\(427\) 0.622333 + 1.07791i 0.0301168 + 0.0521639i
\(428\) 3.07180i 0.148481i
\(429\) −16.2432 10.3736i −0.784231 0.500841i
\(430\) 0 0
\(431\) 1.86621 1.07746i 0.0898921 0.0518993i −0.454380 0.890808i \(-0.650139\pi\)
0.544272 + 0.838909i \(0.316806\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) −1.15994 0.669689i −0.0557429 0.0321832i 0.471870 0.881668i \(-0.343579\pi\)
−0.527612 + 0.849485i \(0.676913\pi\)
\(434\) 8.06361i 0.387066i
\(435\) 0 0
\(436\) 5.79441 + 3.34541i 0.277502 + 0.160216i
\(437\) −19.8564 −0.949861
\(438\) 11.7549 + 6.78668i 0.561670 + 0.324280i
\(439\) 15.8490 + 27.4513i 0.756434 + 1.31018i 0.944658 + 0.328055i \(0.106393\pi\)
−0.188225 + 0.982126i \(0.560273\pi\)
\(440\) 0 0
\(441\) 1.60562 0.0764583
\(442\) 14.4078 + 0.645159i 0.685308 + 0.0306871i
\(443\) 28.0904i 1.33461i 0.744782 + 0.667307i \(0.232553\pi\)
−0.744782 + 0.667307i \(0.767447\pi\)
\(444\) −2.72733 + 1.57463i −0.129434 + 0.0747285i
\(445\) 0 0
\(446\) −0.689457 + 1.19417i −0.0326467 + 0.0565458i
\(447\) −19.4775 −0.921254
\(448\) 1.16129 2.01141i 0.0548658 0.0950303i
\(449\) −25.0426 14.4583i −1.18183 0.682332i −0.225395 0.974267i \(-0.572367\pi\)
−0.956438 + 0.291936i \(0.905701\pi\)
\(450\) 0 0
\(451\) 7.06973 12.2451i 0.332900 0.576600i
\(452\) 6.15720 3.55486i 0.289610 0.167206i
\(453\) 7.25851 + 12.5721i 0.341035 + 0.590690i
\(454\) −19.3205 −0.906756
\(455\) 0 0
\(456\) −4.02283 −0.188386
\(457\) 4.84950 + 8.39958i 0.226850 + 0.392916i 0.956873 0.290507i \(-0.0938239\pi\)
−0.730023 + 0.683423i \(0.760491\pi\)
\(458\) −13.6508 + 7.88130i −0.637861 + 0.368269i
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) 0 0
\(461\) 10.3905 + 5.99896i 0.483934 + 0.279400i 0.722055 0.691836i \(-0.243198\pi\)
−0.238120 + 0.971236i \(0.576531\pi\)
\(462\) 6.20757 10.7518i 0.288802 0.500220i
\(463\) −6.42664 −0.298671 −0.149336 0.988787i \(-0.547713\pi\)
−0.149336 + 0.988787i \(0.547713\pi\)
\(464\) 2.14539 3.71592i 0.0995971 0.172507i
\(465\) 0 0
\(466\) 14.3370 8.27747i 0.664149 0.383447i
\(467\) 26.2642i 1.21536i 0.794182 + 0.607681i \(0.207900\pi\)
−0.794182 + 0.607681i \(0.792100\pi\)
\(468\) −3.20002 + 1.66129i −0.147921 + 0.0767932i
\(469\) 9.54409 0.440705
\(470\) 0 0
\(471\) −12.1914 21.1162i −0.561752 0.972982i
\(472\) −5.87744 3.39334i −0.270531 0.156191i
\(473\) −65.4854 −3.01102
\(474\) 6.90026 + 3.98387i 0.316940 + 0.182985i
\(475\) 0 0
\(476\) 9.29032i 0.425821i
\(477\) 4.75182 + 2.74346i 0.217571 + 0.125615i
\(478\) 22.6904 13.1003i 1.03783 0.599193i
\(479\) 22.2418 12.8413i 1.01625 0.586735i 0.103237 0.994657i \(-0.467080\pi\)
0.913017 + 0.407922i \(0.133747\pi\)
\(480\) 0 0
\(481\) 10.0777 5.23182i 0.459502 0.238551i
\(482\) 15.6496i 0.712818i
\(483\) −5.73205 9.92820i −0.260817 0.451749i
\(484\) 8.78668 + 15.2190i 0.399395 + 0.691772i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 4.68946 8.12238i 0.212500 0.368060i −0.739997 0.672611i \(-0.765173\pi\)
0.952496 + 0.304551i \(0.0985063\pi\)
\(488\) −0.267949 + 0.464102i −0.0121295 + 0.0210089i
\(489\) 23.6267i 1.06844i
\(490\) 0 0
\(491\) −3.86927 6.70177i −0.174618 0.302447i 0.765411 0.643541i \(-0.222536\pi\)
−0.940029 + 0.341095i \(0.889202\pi\)
\(492\) −1.32258 2.29078i −0.0596265 0.103276i
\(493\) 17.1631i 0.772987i
\(494\) 14.4900 + 0.648841i 0.651935 + 0.0291927i
\(495\) 0 0
\(496\) −3.00670 + 1.73592i −0.135005 + 0.0779450i
\(497\) 31.9249 18.4318i 1.43203 0.826781i
\(498\) 9.81724 + 5.66799i 0.439921 + 0.253989i
\(499\) 3.18106i 0.142404i 0.997462 + 0.0712019i \(0.0226834\pi\)
−0.997462 + 0.0712019i \(0.977317\pi\)
\(500\) 0 0
\(501\) −14.5035 8.37357i −0.647967 0.374104i
\(502\) 28.3416 1.26495
\(503\) −30.3765 17.5379i −1.35442 0.781975i −0.365556 0.930789i \(-0.619121\pi\)
−0.988865 + 0.148814i \(0.952454\pi\)
\(504\) −1.16129 2.01141i −0.0517280 0.0895955i
\(505\) 0 0
\(506\) 26.3846 1.17294
\(507\) 11.7942 5.46774i 0.523800 0.242831i
\(508\) 2.13209i 0.0945961i
\(509\) 16.2697 9.39334i 0.721144 0.416353i −0.0940298 0.995569i \(-0.529975\pi\)
0.815173 + 0.579217i \(0.196642\pi\)
\(510\) 0 0
\(511\) 15.7626 27.3016i 0.697297 1.20775i
\(512\) 1.00000 0.0441942
\(513\) −2.01141 + 3.48387i −0.0888061 + 0.153817i
\(514\) −10.8334 6.25465i −0.477839 0.275881i
\(515\) 0 0
\(516\) −6.12539 + 10.6095i −0.269655 + 0.467057i
\(517\) −8.42035 + 4.86149i −0.370327 + 0.213808i
\(518\) 3.65720 + 6.33445i 0.160688 + 0.278320i
\(519\) 16.1321 0.708120
\(520\) 0 0
\(521\) 5.28512 0.231545 0.115773 0.993276i \(-0.463066\pi\)
0.115773 + 0.993276i \(0.463066\pi\)
\(522\) −2.14539 3.71592i −0.0939011 0.162641i
\(523\) 17.9721 10.3762i 0.785863 0.453718i −0.0526409 0.998614i \(-0.516764\pi\)
0.838504 + 0.544895i \(0.183431\pi\)
\(524\) −0.629257 + 1.08991i −0.0274892 + 0.0476127i
\(525\) 0 0
\(526\) −9.27159 5.35295i −0.404260 0.233400i
\(527\) 6.94367 12.0268i 0.302471 0.523895i
\(528\) 5.34541 0.232629
\(529\) 0.681725 1.18078i 0.0296402 0.0513384i
\(530\) 0 0
\(531\) −5.87744 + 3.39334i −0.255059 + 0.147258i
\(532\) 9.34333i 0.405085i
\(533\) 4.39438 + 8.46456i 0.190342 + 0.366641i
\(534\) 1.73978 0.0752877
\(535\) 0 0
\(536\) 2.05463 + 3.55872i 0.0887465 + 0.153713i
\(537\) 6.34644 + 3.66412i 0.273869 + 0.158118i
\(538\) −7.52522 −0.324435
\(539\) 7.43284 + 4.29135i 0.320155 + 0.184842i
\(540\) 0 0
\(541\) 28.7365i 1.23548i 0.786384 + 0.617739i \(0.211951\pi\)
−0.786384 + 0.617739i \(0.788049\pi\)
\(542\) −8.52920 4.92434i −0.366361 0.211518i
\(543\) 16.9510 9.78668i 0.727438 0.419987i
\(544\) −3.46410 + 2.00000i −0.148522 + 0.0857493i
\(545\) 0 0
\(546\) 3.85848 + 7.43230i 0.165128 + 0.318073i
\(547\) 18.3768i 0.785737i 0.919595 + 0.392869i \(0.128517\pi\)
−0.919595 + 0.392869i \(0.871483\pi\)
\(548\) −9.85744 17.0736i −0.421089 0.729348i
\(549\) 0.267949 + 0.464102i 0.0114358 + 0.0198074i
\(550\) 0 0
\(551\) 17.2610i 0.735345i
\(552\) 2.46797 4.27464i 0.105044 0.181941i
\(553\) 9.25285 16.0264i 0.393471 0.681512i
\(554\) 0.953101i 0.0404934i
\(555\) 0 0
\(556\) 2.83871 + 4.91679i 0.120388 + 0.208518i
\(557\) 13.2693 + 22.9831i 0.562238 + 0.973826i 0.997301 + 0.0734252i \(0.0233930\pi\)
−0.435062 + 0.900400i \(0.643274\pi\)
\(558\) 3.47183i 0.146974i
\(559\) 23.7745 37.2268i 1.00555 1.57453i
\(560\) 0 0
\(561\) −18.5170 + 10.6908i −0.781790 + 0.451366i
\(562\) 4.82667 2.78668i 0.203601 0.117549i
\(563\) 5.24908 + 3.03056i 0.221222 + 0.127723i 0.606516 0.795071i \(-0.292567\pi\)
−0.385294 + 0.922794i \(0.625900\pi\)
\(564\) 1.81894i 0.0765913i
\(565\) 0 0
\(566\) −19.0642 11.0067i −0.801326 0.462646i
\(567\) −2.32258 −0.0975392
\(568\) 13.7454 + 7.93593i 0.576746 + 0.332984i
\(569\) 7.24818 + 12.5542i 0.303860 + 0.526300i 0.977007 0.213208i \(-0.0683913\pi\)
−0.673147 + 0.739509i \(0.735058\pi\)
\(570\) 0 0
\(571\) −2.90413 −0.121534 −0.0607670 0.998152i \(-0.519355\pi\)
−0.0607670 + 0.998152i \(0.519355\pi\)
\(572\) −19.2538 0.862160i −0.805044 0.0360487i
\(573\) 17.0375i 0.711750i
\(574\) −5.32051 + 3.07180i −0.222074 + 0.128214i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −18.8180 −0.783405 −0.391702 0.920092i \(-0.628114\pi\)
−0.391702 + 0.920092i \(0.628114\pi\)
\(578\) −0.500000 + 0.866025i −0.0207973 + 0.0360219i
\(579\) 5.33031 + 3.07746i 0.221520 + 0.127895i
\(580\) 0 0
\(581\) 13.1643 22.8013i 0.546149 0.945958i
\(582\) 13.9510 8.05463i 0.578289 0.333875i
\(583\) 14.6649 + 25.4004i 0.607359 + 1.05198i
\(584\) 13.5734 0.561670
\(585\) 0 0
\(586\) −6.84302 −0.282682
\(587\) −1.96820 3.40901i −0.0812361 0.140705i 0.822545 0.568700i \(-0.192553\pi\)
−0.903781 + 0.427995i \(0.859220\pi\)
\(588\) 1.39051 0.802812i 0.0573437 0.0331074i
\(589\) 6.98329 12.0954i 0.287741 0.498383i
\(590\) 0 0
\(591\) 11.9396 + 6.89334i 0.491130 + 0.283554i
\(592\) −1.57463 + 2.72733i −0.0647168 + 0.112093i
\(593\) −20.1227 −0.826338 −0.413169 0.910654i \(-0.635578\pi\)
−0.413169 + 0.910654i \(0.635578\pi\)
\(594\) 2.67270 4.62926i 0.109662 0.189941i
\(595\) 0 0
\(596\) −16.8680 + 9.73875i −0.690940 + 0.398915i
\(597\) 2.28304i 0.0934388i
\(598\) −9.57893 + 14.9990i −0.391712 + 0.613353i
\(599\) −48.1172 −1.96601 −0.983007 0.183567i \(-0.941236\pi\)
−0.983007 + 0.183567i \(0.941236\pi\)
\(600\) 0 0
\(601\) 2.12109 + 3.67383i 0.0865209 + 0.149859i 0.906038 0.423196i \(-0.139092\pi\)
−0.819517 + 0.573054i \(0.805758\pi\)
\(602\) 24.6414 + 14.2267i 1.00431 + 0.579837i
\(603\) 4.10926 0.167342
\(604\) 12.5721 + 7.25851i 0.511552 + 0.295345i
\(605\) 0 0
\(606\) 12.6908i 0.515529i
\(607\) −10.4516 6.03424i −0.424218 0.244922i 0.272663 0.962110i \(-0.412096\pi\)
−0.696880 + 0.717188i \(0.745429\pi\)
\(608\) −3.48387 + 2.01141i −0.141290 + 0.0815736i
\(609\) −8.63052 + 4.98283i −0.349726 + 0.201915i
\(610\) 0 0
\(611\) 0.293377 6.55172i 0.0118688 0.265054i
\(612\) 4.00000i 0.161690i
\(613\) −20.8711 36.1497i −0.842974 1.46007i −0.887369 0.461060i \(-0.847469\pi\)
0.0443946 0.999014i \(-0.485864\pi\)
\(614\) 2.37721 + 4.11745i 0.0959364 + 0.166167i
\(615\) 0 0
\(616\) 12.4151i 0.500220i
\(617\) 16.7293 28.9760i 0.673497 1.16653i −0.303409 0.952860i \(-0.598125\pi\)
0.976906 0.213670i \(-0.0685418\pi\)
\(618\) −2.39806 + 4.15356i −0.0964640 + 0.167081i
\(619\) 38.0978i 1.53128i 0.643270 + 0.765639i \(0.277577\pi\)
−0.643270 + 0.765639i \(0.722423\pi\)
\(620\) 0 0
\(621\) −2.46797 4.27464i −0.0990361 0.171536i
\(622\) −0.968196 1.67696i −0.0388211 0.0672401i
\(623\) 4.04078i 0.161891i
\(624\) −1.94065 + 3.03873i −0.0776883 + 0.121646i
\(625\) 0 0
\(626\) −22.1308 + 12.7772i −0.884526 + 0.510681i
\(627\) −18.6227 + 10.7518i −0.743719 + 0.429386i
\(628\) −21.1162 12.1914i −0.842628 0.486491i
\(629\) 12.5970i 0.502276i
\(630\) 0 0
\(631\) −21.4775 12.4000i −0.855005 0.493638i 0.00733109 0.999973i \(-0.497666\pi\)
−0.862337 + 0.506335i \(0.831000\pi\)
\(632\) 7.96774 0.316940
\(633\) 19.4661 + 11.2387i 0.773707 + 0.446700i
\(634\) 6.33337 + 10.9697i 0.251530 + 0.435663i
\(635\) 0 0
\(636\) 5.48693 0.217571
\(637\) −5.13802 + 2.66741i −0.203576 + 0.105686i
\(638\) 22.9359i 0.908042i
\(639\) 13.7454 7.93593i 0.543761 0.313941i
\(640\) 0 0
\(641\) 2.04259 3.53788i 0.0806776 0.139738i −0.822864 0.568239i \(-0.807625\pi\)
0.903541 + 0.428501i \(0.140958\pi\)
\(642\) 3.07180 0.121234
\(643\) −18.2908 + 31.6806i −0.721318 + 1.24936i 0.239154 + 0.970982i \(0.423130\pi\)
−0.960472 + 0.278377i \(0.910203\pi\)
\(644\) −9.92820 5.73205i −0.391226 0.225874i
\(645\) 0 0
\(646\) 8.04565 13.9355i 0.316552 0.548284i
\(647\) −14.9251 + 8.61704i −0.586768 + 0.338771i −0.763818 0.645431i \(-0.776678\pi\)
0.177050 + 0.984202i \(0.443344\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −36.2776 −1.42402
\(650\) 0 0
\(651\) 8.06361 0.316038
\(652\) 11.8134 + 20.4614i 0.462647 + 0.801329i
\(653\) 18.9897 10.9637i 0.743123 0.429042i −0.0800806 0.996788i \(-0.525518\pi\)
0.823204 + 0.567746i \(0.192184\pi\)
\(654\) 3.34541 5.79441i 0.130816 0.226579i
\(655\) 0 0
\(656\) −2.29078 1.32258i −0.0894397 0.0516381i
\(657\) 6.78668 11.7549i 0.264774 0.458601i
\(658\) 4.22464 0.164694
\(659\) −24.2379 + 41.9813i −0.944176 + 1.63536i −0.186783 + 0.982401i \(0.559806\pi\)
−0.757393 + 0.652960i \(0.773527\pi\)
\(660\) 0 0
\(661\) −25.8267 + 14.9110i −1.00454 + 0.579972i −0.909589 0.415510i \(-0.863603\pi\)
−0.0949524 + 0.995482i \(0.530270\pi\)
\(662\) 23.6981i 0.921052i
\(663\) 0.645159 14.4078i 0.0250559 0.559551i
\(664\) 11.3360 0.439921
\(665\) 0 0
\(666\) 1.57463 + 2.72733i 0.0610155 + 0.105682i
\(667\) −18.3415 10.5895i −0.710187 0.410027i
\(668\) −16.7471 −0.647967
\(669\) 1.19417 + 0.689457i 0.0461694 + 0.0266559i
\(670\) 0 0
\(671\) 2.86459i 0.110586i
\(672\) −2.01141 1.16129i −0.0775919 0.0447977i
\(673\) −26.5627 + 15.3360i −1.02392 + 0.591158i −0.915236 0.402919i \(-0.867996\pi\)
−0.108680 + 0.994077i \(0.534662\pi\)
\(674\) 16.9355 9.77770i 0.652330 0.376623i
\(675\) 0 0
\(676\) 7.48023 10.6323i 0.287701 0.408935i
\(677\) 21.0831i 0.810290i 0.914252 + 0.405145i \(0.132779\pi\)
−0.914252 + 0.405145i \(0.867221\pi\)
\(678\) −3.55486 6.15720i −0.136524 0.236466i
\(679\) −18.7075 32.4024i −0.717929 1.24349i
\(680\) 0 0
\(681\) 19.3205i 0.740363i
\(682\) −9.27918 + 16.0720i −0.355318 + 0.615429i
\(683\) −6.66799 + 11.5493i −0.255143 + 0.441921i −0.964934 0.262491i \(-0.915456\pi\)
0.709791 + 0.704412i \(0.248789\pi\)
\(684\) 4.02283i 0.153817i
\(685\) 0 0
\(686\) −9.99362 17.3095i −0.381558 0.660878i
\(687\) 7.88130 + 13.6508i 0.300691 + 0.520811i
\(688\) 12.2508i 0.467057i
\(689\) −19.7636 0.884986i −0.752933 0.0337153i
\(690\) 0 0
\(691\) −30.2289 + 17.4527i −1.14996 + 0.663932i −0.948878 0.315642i \(-0.897780\pi\)
−0.201085 + 0.979574i \(0.564447\pi\)
\(692\) 13.9708 8.06604i 0.531090 0.306625i
\(693\) −10.7518 6.20757i −0.408428 0.235806i
\(694\) 23.0375i 0.874490i
\(695\) 0 0
\(696\) −3.71592 2.14539i −0.140852 0.0813207i
\(697\) 10.5806 0.400770
\(698\) 13.2679 + 7.66025i 0.502199 + 0.289945i
\(699\) −8.27747 14.3370i −0.313083 0.542275i
\(700\) 0 0
\(701\) 39.6715 1.49837 0.749186 0.662360i \(-0.230445\pi\)
0.749186 + 0.662360i \(0.230445\pi\)
\(702\) 1.66129 + 3.20002i 0.0627013 + 0.120777i
\(703\) 12.6689i 0.477817i
\(704\) 4.62926 2.67270i 0.174472 0.100731i
\(705\) 0 0
\(706\) −14.2039 + 24.6018i −0.534570 + 0.925903i
\(707\) 29.4754 1.10854
\(708\) −3.39334 + 5.87744i −0.127530 + 0.220888i
\(709\) −2.45467 1.41720i −0.0921869 0.0532242i 0.453198 0.891410i \(-0.350283\pi\)
−0.545385 + 0.838186i \(0.683616\pi\)
\(710\) 0 0
\(711\) 3.98387 6.90026i 0.149407 0.258780i
\(712\) 1.50670 0.869891i 0.0564658 0.0326005i
\(713\) 8.56837 + 14.8409i 0.320888 + 0.555794i
\(714\) 9.29032 0.347681
\(715\) 0 0
\(716\) 7.32824 0.273869
\(717\) −13.1003 22.6904i −0.489239 0.847387i
\(718\) 20.4151 11.7867i 0.761886 0.439875i
\(719\) 21.8564 37.8564i 0.815106 1.41181i −0.0941451 0.995558i \(-0.530012\pi\)
0.909251 0.416247i \(-0.136655\pi\)
\(720\) 0 0
\(721\) 9.64697 + 5.56968i 0.359272 + 0.207426i
\(722\) −1.40844 + 2.43948i −0.0524165 + 0.0907881i
\(723\) 15.6496 0.582014
\(724\) 9.78668 16.9510i 0.363719 0.629980i
\(725\) 0 0
\(726\) 15.2190 8.78668i 0.564829 0.326104i
\(727\) 16.2568i 0.602932i −0.953477 0.301466i \(-0.902524\pi\)
0.953477 0.301466i \(-0.0974759\pi\)
\(728\) 7.05769 + 4.50732i 0.261575 + 0.167052i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −24.5016 42.4380i −0.906223 1.56962i
\(732\) 0.464102 + 0.267949i 0.0171537 + 0.00990369i
\(733\) −4.96774 −0.183488 −0.0917438 0.995783i \(-0.529244\pi\)
−0.0917438 + 0.995783i \(0.529244\pi\)
\(734\) −23.8078 13.7454i −0.878762 0.507354i
\(735\) 0 0
\(736\) 4.93593i 0.181941i
\(737\) 19.0228 + 10.9828i 0.700715 + 0.404558i
\(738\) −2.29078 + 1.32258i −0.0843246 + 0.0486848i
\(739\) −43.0306 + 24.8437i −1.58291 + 0.913892i −0.588475 + 0.808515i \(0.700271\pi\)
−0.994432 + 0.105377i \(0.966395\pi\)
\(740\) 0 0
\(741\) 0.648841 14.4900i 0.0238358 0.532303i
\(742\) 12.7438i 0.467841i
\(743\) −10.7710 18.6559i −0.395150 0.684420i 0.597970 0.801518i \(-0.295974\pi\)
−0.993120 + 0.117098i \(0.962641\pi\)
\(744\) 1.73592 + 3.00670i 0.0636418 + 0.110231i
\(745\) 0 0
\(746\) 26.3421i 0.964452i
\(747\) 5.66799 9.81724i 0.207381 0.359194i
\(748\) −10.6908 + 18.5170i −0.390895 + 0.677050i
\(749\) 7.13449i 0.260689i
\(750\) 0 0
\(751\) −3.17436 5.49816i −0.115834 0.200631i 0.802279 0.596950i \(-0.203621\pi\)
−0.918113 + 0.396319i \(0.870287\pi\)
\(752\) 0.909471 + 1.57525i 0.0331650 + 0.0574435i
\(753\) 28.3416i 1.03283i
\(754\) 13.0385 + 8.32690i 0.474834 + 0.303248i
\(755\) 0 0
\(756\) −2.01141 + 1.16129i −0.0731544 + 0.0422357i
\(757\) −41.6651 + 24.0554i −1.51434 + 0.874307i −0.514485 + 0.857499i \(0.672017\pi\)
−0.999859 + 0.0168078i \(0.994650\pi\)
\(758\) 0.388456 + 0.224275i 0.0141094 + 0.00814604i
\(759\) 26.3846i 0.957699i
\(760\) 0 0
\(761\) 29.1734 + 16.8433i 1.05754 + 0.610569i 0.924750 0.380576i \(-0.124274\pi\)
0.132786 + 0.991145i \(0.457608\pi\)
\(762\) 2.13209 0.0772374
\(763\) −13.4580 7.76997i −0.487212 0.281292i
\(764\) 8.51873 + 14.7549i 0.308197 + 0.533813i
\(765\) 0 0
\(766\) −12.1227 −0.438009
\(767\) 13.1706 20.6229i 0.475562 0.744649i
\(768\) 1.00000i 0.0360844i
\(769\) 5.18651 2.99443i 0.187030 0.107982i −0.403561 0.914953i \(-0.632228\pi\)
0.590592 + 0.806971i \(0.298894\pi\)
\(770\) 0 0
\(771\) −6.25465 + 10.8334i −0.225256 + 0.390154i
\(772\) 6.15491 0.221520
\(773\) 6.74409 11.6811i 0.242568 0.420140i −0.718877 0.695137i \(-0.755344\pi\)
0.961445 + 0.274997i \(0.0886769\pi\)
\(774\) 10.6095 + 6.12539i 0.381350 + 0.220173i
\(775\) 0 0
\(776\) 8.05463 13.9510i 0.289144 0.500813i
\(777\) 6.33445 3.65720i 0.227247 0.131201i
\(778\) 9.30974 + 16.1249i 0.333770 + 0.578107i
\(779\) 10.6410 0.381254
\(780\) 0 0
\(781\) 84.8416 3.03587
\(782\) 9.87187 + 17.0986i 0.353017 + 0.611444i
\(783\) −3.71592 + 2.14539i −0.132796 + 0.0766699i
\(784\) 0.802812 1.39051i 0.0286718 0.0496611i
\(785\) <