Properties

Label 1950.2.y.k.49.3
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 49.3
Root \(3.17270 + 3.17270i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.k.199.3

$q$-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 −0.997607 0.0691402i \(-0.977974\pi\)
0.558681 + 0.829383i \(0.311308\pi\)
\(8\) −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 0.0171533 0.999853i \(-0.494540\pi\)
−0.857321 + 0.514782i \(0.827873\pi\)
\(18\) 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 0.0169494 0.999856i \(-0.494605\pi\)
0.874376 + 0.485250i \(0.161271\pi\)
\(24\) −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 0.965939 0.258771i \(-0.0833175\pi\)
−0.707072 + 0.707142i \(0.749984\pi\)
\(38\) 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 \(0.0504744\pi\)
0.630478 + 0.776207i \(0.282859\pi\)
\(44\) 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 \(-0.457648\pi\)
0.132660 + 0.991162i \(0.457648\pi\)
\(48\) −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 \(-0.877009\pi\)
0.926277 0.376844i \(-0.122991\pi\)
\(54\) 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 0.712792 0.701376i \(-0.247430\pi\)
−0.963805 + 0.266608i \(0.914097\pi\)
\(68\) 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 \(-0.792173\pi\)
−0.794321 + 0.607498i \(0.792173\pi\)
\(74\) −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 \(-0.713737\pi\)
−0.622142 + 0.782904i \(0.713737\pi\)
\(84\) −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 \(0.471486\pi\)
−0.907282 + 0.420522i \(0.861847\pi\)
\(98\) −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 \(-0.924069\pi\)
0.971683 0.236288i \(-0.0759308\pi\)
\(104\) −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 −0.623046 0.782185i \(-0.714105\pi\)
0.365869 + 0.930666i \(0.380772\pi\)
\(108\) 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 0.760823 0.648959i \(-0.224795\pi\)
−0.181603 + 0.983372i \(0.558129\pi\)
\(114\) 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 −0.579680 0.814844i \(-0.696823\pi\)
0.415835 + 0.909440i \(0.363489\pi\)
\(128\) 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 \(-0.514606\pi\)
0.888049 0.459748i \(-0.152060\pi\)
\(138\) 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 \(-0.574160\pi\)
0.230879 0.972982i \(-0.425840\pi\)
\(158\) 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 \(0.542849\pi\)
−0.791086 + 0.611704i \(0.790484\pi\)
\(164\) 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 \(-0.942286\pi\)
0.335641 0.941990i \(-0.391047\pi\)
\(168\) 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 0.926034 0.377439i \(-0.123195\pi\)
0.136146 + 0.990689i \(0.456529\pi\)
\(174\) 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 0.955270 0.295736i \(-0.0955648\pi\)
−0.733750 + 0.679420i \(0.762231\pi\)
\(194\) −16.1093 −1.15658
\(195\) 0 0
\(196\) −1.60562 −0.114687
\(197\) 6.89334 + 11.9396i 0.491130 + 0.850662i 0.999948 0.0102119i \(-0.00325060\pi\)
−0.508818 + 0.860874i \(0.669917\pi\)
\(198\) 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 0.888187 0.459483i \(-0.151965\pi\)
−0.842017 + 0.539451i \(0.818632\pi\)
\(224\) 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 \(0.388219\pi\)
−0.985171 + 0.171575i \(0.945115\pi\)
\(228\) −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 \(-0.817563\pi\)
0.840201 0.542275i \(-0.182437\pi\)
\(234\) 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 −0.798258 0.602315i \(-0.794245\pi\)
0.122491 + 0.992470i \(0.460912\pi\)
\(258\) 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 −0.757832 0.652449i \(-0.773741\pi\)
0.186122 + 0.982527i \(0.440408\pi\)
\(264\) −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 0.474998 0.879987i \(-0.342449\pi\)
−0.524592 + 0.851354i \(0.675782\pi\)
\(278\) 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 −0.944749 0.327794i \(-0.893695\pi\)
−0.188497 + 0.982074i \(0.560362\pi\)
\(284\) −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 −0.948491 0.316803i \(-0.897391\pi\)
0.748605 + 0.663016i \(0.230724\pi\)
\(294\) 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 \(-0.456680\pi\)
0.135675 + 0.990753i \(0.456680\pi\)
\(308\) −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 \(0.256875\pi\)
−0.691671 + 0.722213i \(0.743125\pi\)
\(314\) 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 \(-0.384237\pi\)
0.355717 + 0.934594i \(0.384237\pi\)
\(318\) 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 \(-0.821205\pi\)
0.846351 0.532625i \(-0.178795\pi\)
\(338\) −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 −0.142565 0.989785i \(-0.545535\pi\)
−0.928462 + 0.371427i \(0.878868\pi\)
\(348\) −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 \(0.106181\pi\)
−0.188881 + 0.982000i \(0.560486\pi\)
\(354\) −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 −0.969655 0.244479i \(-0.921383\pi\)
−0.273103 + 0.961985i \(0.588050\pi\)
\(368\) −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 −0.224914 0.974379i \(-0.572210\pi\)
−0.956294 + 0.292408i \(0.905544\pi\)
\(374\) −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 −0.978301 0.207189i \(-0.933568\pi\)
0.668582 + 0.743639i \(0.266902\pi\)
\(384\) 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 −0.688616 0.725126i \(-0.741781\pi\)
0.972286 + 0.233796i \(0.0751147\pi\)
\(398\) −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 0.527612 0.849485i \(-0.323087\pi\)
−0.471870 + 0.881668i \(0.656421\pi\)
\(434\) 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 \(-0.767447\pi\)
0.744782 0.667307i \(-0.232553\pi\)
\(444\) −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 0.730023 0.683423i \(-0.239509\pi\)
−0.956873 + 0.290507i \(0.906176\pi\)
\(458\) 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 \(-0.452287\pi\)
0.149336 + 0.988787i \(0.452287\pi\)
\(464\) 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 \(-0.792100\pi\)
0.794182 0.607681i \(-0.207900\pi\)
\(468\) 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 −0.952496 0.304551i \(-0.901494\pi\)
0.739997 + 0.672611i \(0.234827\pi\)
\(488\) 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 0.988865 0.148814i \(-0.0475456\pi\)
0.365556 + 0.930789i \(0.380879\pi\)
\(504\) −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 −0.838504 0.544895i \(-0.816569\pi\)
0.0526409 + 0.998614i \(0.483236\pi\)
\(524\) −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 \(-0.871483\pi\)
0.919595 0.392869i \(-0.128517\pi\)
\(548\) 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 \(-0.976607\pi\)
0.435062 0.900400i \(-0.356726\pi\)
\(558\) 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 0.385294 0.922794i \(-0.374100\pi\)
−0.606516 + 0.795071i \(0.707433\pi\)
\(564\) 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 \(-0.371886\pi\)
0.391702 + 0.920092i \(0.371886\pi\)
\(578\) 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 0.903781 0.427995i \(-0.140780\pi\)
−0.822545 + 0.568700i \(0.807447\pi\)
\(588\) −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 \(-0.364422\pi\)
0.413169 + 0.910654i \(0.364422\pi\)
\(594\) 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 0.696880 0.717188i \(-0.254571\pi\)
−0.272663 + 0.962110i \(0.587904\pi\)
\(608\) 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 \(0.152531\pi\)
−0.0443946 + 0.999014i \(0.514136\pi\)
\(614\) 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 \(0.401875\pi\)
−0.976906 + 0.213670i \(0.931458\pi\)
\(618\) 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 \(-0.576870\pi\)
0.960472 0.278377i \(-0.0897966\pi\)
\(644\) −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 −0.177050 0.984202i \(-0.556656\pi\)
0.763818 + 0.645431i \(0.223322\pi\)
\(648\) 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 −0.823204 0.567746i \(-0.807816\pi\)
0.0800806 + 0.996788i \(0.474482\pi\)
\(654\) 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 0.108680 0.994077i \(-0.465338\pi\)
0.915236 + 0.402919i \(0.132004\pi\)
\(674\) 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 \(-0.867221\pi\)
0.914252 0.405145i \(-0.132779\pi\)
\(678\) 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 −0.709791 0.704412i \(-0.751211\pi\)
0.964934 + 0.262491i \(0.0845440\pi\)
\(684\) 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 \(0.0974759\pi\)
−0.953477 + 0.301466i \(0.902524\pi\)
\(728\) −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 \(-0.470756\pi\)
0.0917438 + 0.995783i \(0.470756\pi\)
\(734\) −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 0.993120 0.117098i \(-0.0373593\pi\)
−0.597970 + 0.801518i \(0.704026\pi\)
\(744\) 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 \(-0.327983\pi\)
0.999859 0.0168078i \(-0.00535036\pi\)
\(758\) −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 −0.961445 0.274997i \(-0.911323\pi\)
0.718877 + 0.695137i \(0.244656\pi\)
\(774\) 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