Properties

Label 1950.2.bc.g.901.4
Level $1950$
Weight $2$
Character 1950.901
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.bc (of order \(6\), degree \(2\), 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 901.4
Root \(-1.80668 + 1.80668i\) of defining polynomial
Character \(\chi\) \(=\) 1950.901
Dual form 1950.2.bc.g.751.4

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) 2.01141 1.16129i 0.760243 0.438926i −0.0691402 0.997607i \(-0.522026\pi\)
0.829383 + 0.558681i \(0.188692\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 4.62926 + 2.67270i 1.39577 + 0.805850i 0.993946 0.109865i \(-0.0350420\pi\)
0.401827 + 0.915716i \(0.368375\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.60194 0.161290i 0.998999 0.0447338i
\(14\) 2.32258 0.620736
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.48387 + 2.01141i −0.799254 + 0.461450i −0.843210 0.537584i \(-0.819337\pi\)
0.0439559 + 0.999033i \(0.486004\pi\)
\(20\) 0 0
\(21\) 2.32258i 0.506828i
\(22\) 2.67270 + 4.62926i 0.569822 + 0.986961i
\(23\) 2.46797 4.27464i 0.514607 0.891325i −0.485250 0.874376i \(-0.661271\pi\)
0.999856 0.0169494i \(-0.00539541\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) 3.20002 + 1.66129i 0.627575 + 0.325806i
\(27\) −1.00000 −0.192450
\(28\) 2.01141 + 1.16129i 0.380121 + 0.219463i
\(29\) −2.14539 + 3.71592i −0.398388 + 0.690029i −0.993527 0.113594i \(-0.963764\pi\)
0.595139 + 0.803623i \(0.297097\pi\)
\(30\) 0 0
\(31\) 3.47183i 0.623560i 0.950154 + 0.311780i \(0.100925\pi\)
−0.950154 + 0.311780i \(0.899075\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 4.62926 2.67270i 0.805850 0.465258i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 2.72733 + 1.57463i 0.448371 + 0.258867i 0.707142 0.707072i \(-0.249984\pi\)
−0.258771 + 0.965939i \(0.583318\pi\)
\(38\) −4.02283 −0.652589
\(39\) 1.66129 3.20002i 0.266019 0.512413i
\(40\) 0 0
\(41\) 2.29078 + 1.32258i 0.357759 + 0.206552i 0.668097 0.744074i \(-0.267109\pi\)
−0.310338 + 0.950626i \(0.600442\pi\)
\(42\) 1.16129 2.01141i 0.179191 0.310368i
\(43\) −6.12539 10.6095i −0.934113 1.61793i −0.776207 0.630478i \(-0.782859\pi\)
−0.157906 0.987454i \(-0.550474\pi\)
\(44\) 5.34541i 0.805850i
\(45\) 0 0
\(46\) 4.27464 2.46797i 0.630262 0.363882i
\(47\) 1.81894i 0.265320i 0.991162 + 0.132660i \(0.0423518\pi\)
−0.991162 + 0.132660i \(0.957648\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −0.802812 + 1.39051i −0.114687 + 0.198644i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 1.94065 + 3.03873i 0.269120 + 0.421396i
\(53\) 5.48693 0.753687 0.376844 0.926277i \(-0.377009\pi\)
0.376844 + 0.926277i \(0.377009\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.16129 + 2.01141i 0.155184 + 0.268786i
\(57\) 4.02283i 0.532836i
\(58\) −3.71592 + 2.14539i −0.487924 + 0.281703i
\(59\) 5.87744 3.39334i 0.765177 0.441775i −0.0659742 0.997821i \(-0.521016\pi\)
0.831152 + 0.556046i \(0.187682\pi\)
\(60\) 0 0
\(61\) −0.267949 0.464102i −0.0343074 0.0594221i 0.848362 0.529417i \(-0.177589\pi\)
−0.882669 + 0.469995i \(0.844256\pi\)
\(62\) −1.73592 + 3.00670i −0.220462 + 0.381851i
\(63\) −2.01141 1.16129i −0.253414 0.146309i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 5.34541 0.657974
\(67\) −3.55872 2.05463i −0.434767 0.251013i 0.266608 0.963805i \(-0.414097\pi\)
−0.701376 + 0.712792i \(0.747430\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) −2.46797 4.27464i −0.297108 0.514607i
\(70\) 0 0
\(71\) 13.7454 7.93593i 1.63128 0.941822i 0.647586 0.761992i \(-0.275779\pi\)
0.983698 0.179830i \(-0.0575547\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 13.5734i 1.58864i 0.607498 + 0.794321i \(0.292173\pi\)
−0.607498 + 0.794321i \(0.707827\pi\)
\(74\) 1.57463 + 2.72733i 0.183047 + 0.317046i
\(75\) 0 0
\(76\) −3.48387 2.01141i −0.399627 0.230725i
\(77\) 12.4151 1.41484
\(78\) 3.03873 1.94065i 0.344068 0.219736i
\(79\) −7.96774 −0.896441 −0.448220 0.893923i \(-0.647942\pi\)
−0.448220 + 0.893923i \(0.647942\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.32258 + 2.29078i 0.146054 + 0.252974i
\(83\) 11.3360i 1.24428i 0.782904 + 0.622142i \(0.213737\pi\)
−0.782904 + 0.622142i \(0.786263\pi\)
\(84\) 2.01141 1.16129i 0.219463 0.126707i
\(85\) 0 0
\(86\) 12.2508i 1.32104i
\(87\) 2.14539 + 3.71592i 0.230010 + 0.398388i
\(88\) −2.67270 + 4.62926i −0.284911 + 0.493480i
\(89\) −1.50670 0.869891i −0.159709 0.0922083i 0.418015 0.908440i \(-0.362726\pi\)
−0.577725 + 0.816232i \(0.696059\pi\)
\(90\) 0 0
\(91\) 7.05769 4.50732i 0.739847 0.472495i
\(92\) 4.93593 0.514607
\(93\) 3.00670 + 1.73592i 0.311780 + 0.180006i
\(94\) −0.909471 + 1.57525i −0.0938048 + 0.162475i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 13.9510 8.05463i 1.41651 0.817824i 0.420522 0.907282i \(-0.361847\pi\)
0.995991 + 0.0894586i \(0.0285137\pi\)
\(98\) −1.39051 + 0.802812i −0.140463 + 0.0810962i
\(99\) 5.34541i 0.537233i
\(100\) 0 0
\(101\) 6.34541 10.9906i 0.631391 1.09360i −0.355876 0.934533i \(-0.615817\pi\)
0.987267 0.159069i \(-0.0508492\pi\)
\(102\) −3.46410 2.00000i −0.342997 0.198030i
\(103\) 4.79612 0.472575 0.236288 0.971683i \(-0.424069\pi\)
0.236288 + 0.971683i \(0.424069\pi\)
\(104\) 0.161290 + 3.60194i 0.0158158 + 0.353199i
\(105\) 0 0
\(106\) 4.75182 + 2.74346i 0.461537 + 0.266469i
\(107\) 1.53590 2.66025i 0.148481 0.257176i −0.782185 0.623046i \(-0.785895\pi\)
0.930666 + 0.365869i \(0.119228\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 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
\(112\) 2.32258i 0.219463i
\(113\) −3.55486 6.15720i −0.334413 0.579220i 0.648959 0.760823i \(-0.275205\pi\)
−0.983372 + 0.181603i \(0.941871\pi\)
\(114\) −2.01141 + 3.48387i −0.188386 + 0.326294i
\(115\) 0 0
\(116\) −4.29078 −0.398388
\(117\) −1.94065 3.03873i −0.179413 0.280931i
\(118\) 6.78668 0.624765
\(119\) −8.04565 4.64516i −0.737544 0.425821i
\(120\) 0 0
\(121\) 8.78668 + 15.2190i 0.798789 + 1.38354i
\(122\) 0.535898i 0.0485180i
\(123\) 2.29078 1.32258i 0.206552 0.119253i
\(124\) −3.00670 + 1.73592i −0.270009 + 0.155890i
\(125\) 0 0
\(126\) −1.16129 2.01141i −0.103456 0.179191i
\(127\) 1.06604 1.84644i 0.0945961 0.163845i −0.814844 0.579680i \(-0.803177\pi\)
0.909440 + 0.415835i \(0.136511\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −12.2508 −1.07862
\(130\) 0 0
\(131\) 1.25851 0.109957 0.0549785 0.998488i \(-0.482491\pi\)
0.0549785 + 0.998488i \(0.482491\pi\)
\(132\) 4.62926 + 2.67270i 0.402925 + 0.232629i
\(133\) −4.67167 + 8.09156i −0.405085 + 0.701628i
\(134\) −2.05463 3.55872i −0.177493 0.307427i
\(135\) 0 0
\(136\) 3.46410 2.00000i 0.297044 0.171499i
\(137\) −17.0736 + 9.85744i −1.45870 + 0.842178i −0.998947 0.0458713i \(-0.985394\pi\)
−0.459748 + 0.888049i \(0.652060\pi\)
\(138\) 4.93593i 0.420175i
\(139\) −2.83871 4.91679i −0.240776 0.417037i 0.720159 0.693809i \(-0.244069\pi\)
−0.960936 + 0.276772i \(0.910735\pi\)
\(140\) 0 0
\(141\) 1.57525 + 0.909471i 0.132660 + 0.0765913i
\(142\) 15.8719 1.33194
\(143\) 17.1054 + 8.88027i 1.43043 + 0.742605i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −6.78668 + 11.7549i −0.561670 + 0.972841i
\(147\) 0.802812 + 1.39051i 0.0662148 + 0.114687i
\(148\) 3.14925i 0.258867i
\(149\) −16.8680 + 9.73875i −1.38188 + 0.797829i −0.992382 0.123198i \(-0.960685\pi\)
−0.389499 + 0.921027i \(0.627352\pi\)
\(150\) 0 0
\(151\) 14.5170i 1.18138i 0.806899 + 0.590690i \(0.201144\pi\)
−0.806899 + 0.590690i \(0.798856\pi\)
\(152\) −2.01141 3.48387i −0.163147 0.282579i
\(153\) −2.00000 + 3.46410i −0.161690 + 0.280056i
\(154\) 10.7518 + 6.20757i 0.866406 + 0.500220i
\(155\) 0 0
\(156\) 3.60194 0.161290i 0.288386 0.0129135i
\(157\) −24.3829 −1.94596 −0.972982 0.230879i \(-0.925840\pi\)
−0.972982 + 0.230879i \(0.925840\pi\)
\(158\) −6.90026 3.98387i −0.548956 0.316940i
\(159\) 2.74346 4.75182i 0.217571 0.376844i
\(160\) 0 0
\(161\) 11.4641i 0.903498i
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) −20.4614 + 11.8134i −1.60266 + 0.925295i −0.611704 + 0.791086i \(0.709516\pi\)
−0.990953 + 0.134208i \(0.957151\pi\)
\(164\) 2.64516i 0.206552i
\(165\) 0 0
\(166\) −5.66799 + 9.81724i −0.439921 + 0.761966i
\(167\) −14.5035 8.37357i −1.12231 0.647967i −0.180321 0.983608i \(-0.557714\pi\)
−0.941990 + 0.335641i \(0.891047\pi\)
\(168\) 2.32258 0.179191
\(169\) 12.9480 1.16191i 0.995998 0.0893780i
\(170\) 0 0
\(171\) 3.48387 + 2.01141i 0.266418 + 0.153817i
\(172\) 6.12539 10.6095i 0.467057 0.808966i
\(173\) −8.06604 13.9708i −0.613250 1.06218i −0.990689 0.136146i \(-0.956529\pi\)
0.377439 0.926034i \(-0.376805\pi\)
\(174\) 4.29078i 0.325283i
\(175\) 0 0
\(176\) −4.62926 + 2.67270i −0.348943 + 0.201463i
\(177\) 6.78668i 0.510118i
\(178\) −0.869891 1.50670i −0.0652011 0.112932i
\(179\) 3.66412 6.34644i 0.273869 0.474355i −0.695980 0.718061i \(-0.745030\pi\)
0.969849 + 0.243706i \(0.0783631\pi\)
\(180\) 0 0
\(181\) −19.5734 −1.45488 −0.727438 0.686173i \(-0.759289\pi\)
−0.727438 + 0.686173i \(0.759289\pi\)
\(182\) 8.36580 0.374609i 0.620114 0.0277678i
\(183\) −0.535898 −0.0396147
\(184\) 4.27464 + 2.46797i 0.315131 + 0.181941i
\(185\) 0 0
\(186\) 1.73592 + 3.00670i 0.127284 + 0.220462i
\(187\) 21.3816i 1.56358i
\(188\) −1.57525 + 0.909471i −0.114887 + 0.0663300i
\(189\) −2.01141 + 1.16129i −0.146309 + 0.0844714i
\(190\) 0 0
\(191\) 8.51873 + 14.7549i 0.616394 + 1.06763i 0.990138 + 0.140094i \(0.0447404\pi\)
−0.373744 + 0.927532i \(0.621926\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −5.33031 3.07746i −0.383684 0.221520i 0.295736 0.955270i \(-0.404435\pi\)
−0.679420 + 0.733750i \(0.737769\pi\)
\(194\) 16.1093 1.15658
\(195\) 0 0
\(196\) −1.60562 −0.114687
\(197\) 11.9396 + 6.89334i 0.850662 + 0.491130i 0.860874 0.508818i \(-0.169917\pi\)
−0.0102119 + 0.999948i \(0.503251\pi\)
\(198\) 2.67270 4.62926i 0.189941 0.328987i
\(199\) 1.14152 + 1.97717i 0.0809203 + 0.140158i 0.903646 0.428281i \(-0.140881\pi\)
−0.822725 + 0.568439i \(0.807547\pi\)
\(200\) 0 0
\(201\) −3.55872 + 2.05463i −0.251013 + 0.144922i
\(202\) 10.9906 6.34541i 0.773293 0.446461i
\(203\) 9.96567i 0.699453i
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) 0 0
\(206\) 4.15356 + 2.39806i 0.289392 + 0.167081i
\(207\) −4.93593 −0.343071
\(208\) −1.66129 + 3.20002i −0.115190 + 0.221881i
\(209\) −21.5036 −1.48744
\(210\) 0 0
\(211\) −11.2387 + 19.4661i −0.773707 + 1.34010i 0.161811 + 0.986822i \(0.448267\pi\)
−0.935518 + 0.353278i \(0.885067\pi\)
\(212\) 2.74346 + 4.75182i 0.188422 + 0.326356i
\(213\) 15.8719i 1.08752i
\(214\) 2.66025 1.53590i 0.181851 0.104992i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 4.03180 + 6.98329i 0.273697 + 0.474057i
\(218\) 3.34541 5.79441i 0.226579 0.392447i
\(219\) 11.7549 + 6.78668i 0.794321 + 0.458601i
\(220\) 0 0
\(221\) −7.76261 12.1549i −0.522170 0.817628i
\(222\) 3.14925 0.211364
\(223\) −1.19417 0.689457i −0.0799678 0.0461694i 0.459483 0.888187i \(-0.348035\pi\)
−0.539451 + 0.842017i \(0.681368\pi\)
\(224\) −1.16129 + 2.01141i −0.0775919 + 0.134393i
\(225\) 0 0
\(226\) 7.10972i 0.472931i
\(227\) 16.7321 9.66025i 1.11055 0.641174i 0.171575 0.985171i \(-0.445115\pi\)
0.938971 + 0.343998i \(0.111781\pi\)
\(228\) −3.48387 + 2.01141i −0.230725 + 0.133209i
\(229\) 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
\(232\) −3.71592 2.14539i −0.243962 0.140852i
\(233\) 16.5549 1.08455 0.542275 0.840201i \(-0.317563\pi\)
0.542275 + 0.840201i \(0.317563\pi\)
\(234\) −0.161290 3.60194i −0.0105438 0.235466i
\(235\) 0 0
\(236\) 5.87744 + 3.39334i 0.382589 + 0.220888i
\(237\) −3.98387 + 6.90026i −0.258780 + 0.448220i
\(238\) −4.64516 8.04565i −0.301101 0.521522i
\(239\) 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 −0.868351 0.495950i \(-0.834820\pi\)
−0.00466988 + 0.999989i \(0.501486\pi\)
\(242\) 17.5734i 1.12966i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0.267949 0.464102i 0.0171537 0.0297111i
\(245\) 0 0
\(246\) 2.64516 0.168649
\(247\) −12.2243 + 7.80691i −0.777812 + 0.496742i
\(248\) −3.47183 −0.220462
\(249\) 9.81724 + 5.66799i 0.622142 + 0.359194i
\(250\) 0 0
\(251\) −14.1708 24.5446i −0.894454 1.54924i −0.834479 0.551040i \(-0.814231\pi\)
−0.0599750 0.998200i \(-0.519102\pi\)
\(252\) 2.32258i 0.146309i
\(253\) 22.8497 13.1923i 1.43655 0.829392i
\(254\) 1.84644 1.06604i 0.115856 0.0668895i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.25465 10.8334i 0.390154 0.675767i −0.602315 0.798258i \(-0.705755\pi\)
0.992470 + 0.122491i \(0.0390883\pi\)
\(258\) −10.6095 6.12539i −0.660518 0.381350i
\(259\) 7.31439 0.454494
\(260\) 0 0
\(261\) 4.29078 0.265592
\(262\) 1.08991 + 0.629257i 0.0673346 + 0.0388756i
\(263\) −5.35295 + 9.27159i −0.330077 + 0.571711i −0.982527 0.186122i \(-0.940408\pi\)
0.652449 + 0.757832i \(0.273741\pi\)
\(264\) 2.67270 + 4.62926i 0.164493 + 0.284911i
\(265\) 0 0
\(266\) −8.09156 + 4.67167i −0.496126 + 0.286438i
\(267\) −1.50670 + 0.869891i −0.0922083 + 0.0532365i
\(268\) 4.10926i 0.251013i
\(269\) −3.76261 6.51703i −0.229410 0.397350i 0.728223 0.685340i \(-0.240346\pi\)
−0.957633 + 0.287990i \(0.907013\pi\)
\(270\) 0 0
\(271\) 8.52920 + 4.92434i 0.518112 + 0.299132i 0.736162 0.676805i \(-0.236636\pi\)
−0.218050 + 0.975938i \(0.569970\pi\)
\(272\) 4.00000 0.242536
\(273\) −0.374609 8.36580i −0.0226723 0.506321i
\(274\) −19.7149 −1.19102
\(275\) 0 0
\(276\) 2.46797 4.27464i 0.148554 0.257303i
\(277\) −0.476550 0.825410i −0.0286331 0.0495941i 0.851354 0.524592i \(-0.175782\pi\)
−0.879987 + 0.474998i \(0.842449\pi\)
\(278\) 5.67742i 0.340509i
\(279\) 3.00670 1.73592i 0.180006 0.103927i
\(280\) 0 0
\(281\) 5.57336i 0.332479i −0.986085 0.166239i \(-0.946838\pi\)
0.986085 0.166239i \(-0.0531625\pi\)
\(282\) 0.909471 + 1.57525i 0.0541582 + 0.0938048i
\(283\) −11.0067 + 19.0642i −0.654280 + 1.13325i 0.327794 + 0.944749i \(0.393695\pi\)
−0.982074 + 0.188497i \(0.939638\pi\)
\(284\) 13.7454 + 7.93593i 0.815642 + 0.470911i
\(285\) 0 0
\(286\) 10.3736 + 16.2432i 0.613402 + 0.960483i
\(287\) 6.14359 0.362645
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 16.1093i 0.944342i
\(292\) −11.7549 + 6.78668i −0.687902 + 0.397160i
\(293\) −5.92623 + 3.42151i −0.346214 + 0.199887i −0.663016 0.748605i \(-0.730724\pi\)
0.316803 + 0.948491i \(0.397391\pi\)
\(294\) 1.60562i 0.0936419i
\(295\) 0 0
\(296\) −1.57463 + 2.72733i −0.0915233 + 0.158523i
\(297\) −4.62926 2.67270i −0.268617 0.155086i
\(298\) −19.4775 −1.12830
\(299\) 8.20002 15.7951i 0.474219 0.913453i
\(300\) 0 0
\(301\) −24.6414 14.2267i −1.42031 0.820014i
\(302\) −7.25851 + 12.5721i −0.417681 + 0.723444i
\(303\) −6.34541 10.9906i −0.364534 0.631391i
\(304\) 4.02283i 0.230725i
\(305\) 0 0
\(306\) −3.46410 + 2.00000i −0.198030 + 0.114332i
\(307\) 4.75442i 0.271349i 0.990753 + 0.135675i \(0.0433202\pi\)
−0.990753 + 0.135675i \(0.956680\pi\)
\(308\) 6.20757 + 10.7518i 0.353709 + 0.612642i
\(309\) 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 \(0.482516\pi\)
\(312\) 3.20002 + 1.66129i 0.181165 + 0.0940520i
\(313\) −25.5545 −1.44443 −0.722213 0.691671i \(-0.756875\pi\)
−0.722213 + 0.691671i \(0.756875\pi\)
\(314\) −21.1162 12.1914i −1.19166 0.688002i
\(315\) 0 0
\(316\) −3.98387 6.90026i −0.224110 0.388170i
\(317\) 12.6667i 0.711435i 0.934594 + 0.355717i \(0.115763\pi\)
−0.934594 + 0.355717i \(0.884237\pi\)
\(318\) 4.75182 2.74346i 0.266469 0.153846i
\(319\) −19.8631 + 11.4680i −1.11212 + 0.642083i
\(320\) 0 0
\(321\) −1.53590 2.66025i −0.0857255 0.148481i
\(322\) 5.73205 9.92820i 0.319435 0.553277i
\(323\) 13.9355 + 8.04565i 0.775391 + 0.447672i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −23.6267 −1.30856
\(327\) −5.79441 3.34541i −0.320432 0.185001i
\(328\) −1.32258 + 2.29078i −0.0730272 + 0.126487i
\(329\) 2.11232 + 3.65864i 0.116456 + 0.201708i
\(330\) 0 0
\(331\) −20.5231 + 11.8490i −1.12805 + 0.651282i −0.943445 0.331530i \(-0.892435\pi\)
−0.184609 + 0.982812i \(0.559102\pi\)
\(332\) −9.81724 + 5.66799i −0.538791 + 0.311071i
\(333\) 3.14925i 0.172578i
\(334\) −8.37357 14.5035i −0.458182 0.793594i
\(335\) 0 0
\(336\) 2.01141 + 1.16129i 0.109732 + 0.0633536i
\(337\) −19.5554 −1.06525 −0.532625 0.846351i \(-0.678795\pi\)
−0.532625 + 0.846351i \(0.678795\pi\)
\(338\) 11.7942 + 5.46774i 0.641521 + 0.297406i
\(339\) −7.10972 −0.386147
\(340\) 0 0
\(341\) −9.27918 + 16.0720i −0.502496 + 0.870348i
\(342\) 2.01141 + 3.48387i 0.108765 + 0.188386i
\(343\) 19.9872i 1.07921i
\(344\) 10.6095 6.12539i 0.572025 0.330259i
\(345\) 0 0
\(346\) 16.1321i 0.867266i
\(347\) −11.5187 19.9510i −0.618358 1.07103i −0.989785 0.142565i \(-0.954465\pi\)
0.371427 0.928462i \(-0.378868\pi\)
\(348\) −2.14539 + 3.71592i −0.115005 + 0.199194i
\(349\) 13.2679 + 7.66025i 0.710217 + 0.410044i 0.811141 0.584850i \(-0.198847\pi\)
−0.100924 + 0.994894i \(0.532180\pi\)
\(350\) 0 0
\(351\) −3.60194 + 0.161290i −0.192257 + 0.00860902i
\(352\) −5.34541 −0.284911
\(353\) −24.6018 14.2039i −1.30942 0.755996i −0.327424 0.944877i \(-0.606181\pi\)
−0.982000 + 0.188881i \(0.939514\pi\)
\(354\) 3.39334 5.87744i 0.180354 0.312382i
\(355\) 0 0
\(356\) 1.73978i 0.0922083i
\(357\) −8.04565 + 4.64516i −0.425821 + 0.245848i
\(358\) 6.34644 3.66412i 0.335420 0.193655i
\(359\) 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
\(362\) −16.9510 9.78668i −0.890926 0.514377i
\(363\) 17.5734 0.922362
\(364\) 7.43230 + 3.85848i 0.389558 + 0.202239i
\(365\) 0 0
\(366\) −0.464102 0.267949i −0.0242590 0.0140059i
\(367\) 13.7454 23.8078i 0.717506 1.24276i −0.244479 0.969655i \(-0.578617\pi\)
0.961985 0.273103i \(-0.0880498\pi\)
\(368\) 2.46797 + 4.27464i 0.128652 + 0.222831i
\(369\) 2.64516i 0.137701i
\(370\) 0 0
\(371\) 11.0365 6.37191i 0.572985 0.330813i
\(372\) 3.47183i 0.180006i
\(373\) 13.1710 + 22.8129i 0.681971 + 1.18121i 0.974379 + 0.224914i \(0.0722102\pi\)
−0.292408 + 0.956294i \(0.594456\pi\)
\(374\) 10.6908 18.5170i 0.552809 0.957493i
\(375\) 0 0
\(376\) −1.81894 −0.0938048
\(377\) −7.12822 + 13.7306i −0.367122 + 0.707160i
\(378\) −2.32258 −0.119461
\(379\) 0.388456 + 0.224275i 0.0199537 + 0.0115202i 0.509944 0.860208i \(-0.329666\pi\)
−0.489990 + 0.871728i \(0.663000\pi\)
\(380\) 0 0
\(381\) −1.06604 1.84644i −0.0546151 0.0945961i
\(382\) 17.0375i 0.871713i
\(383\) −10.4985 + 6.06133i −0.536450 + 0.309719i −0.743639 0.668582i \(-0.766902\pi\)
0.207189 + 0.978301i \(0.433568\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) −3.07746 5.33031i −0.156638 0.271306i
\(387\) −6.12539 + 10.6095i −0.311371 + 0.539311i
\(388\) 13.9510 + 8.05463i 0.708256 + 0.408912i
\(389\) 18.6195 0.944045 0.472022 0.881587i \(-0.343524\pi\)
0.472022 + 0.881587i \(0.343524\pi\)
\(390\) 0 0
\(391\) −19.7437 −0.998484
\(392\) −1.39051 0.802812i −0.0702314 0.0405481i
\(393\) 0.629257 1.08991i 0.0317418 0.0549785i
\(394\) 6.89334 + 11.9396i 0.347281 + 0.601509i
\(395\) 0 0
\(396\) 4.62926 2.67270i 0.232629 0.134308i
\(397\) −9.78970 + 5.65208i −0.491331 + 0.283670i −0.725126 0.688616i \(-0.758219\pi\)
0.233796 + 0.972286i \(0.424885\pi\)
\(398\) 2.28304i 0.114439i
\(399\) 4.67167 + 8.09156i 0.233876 + 0.405085i
\(400\) 0 0
\(401\) −1.30406 0.752899i −0.0651216 0.0375980i 0.467086 0.884212i \(-0.345304\pi\)
−0.532207 + 0.846614i \(0.678637\pi\)
\(402\) −4.10926 −0.204951
\(403\) 0.559971 + 12.5053i 0.0278942 + 0.622935i
\(404\) 12.6908 0.631391
\(405\) 0 0
\(406\) −4.98283 + 8.63052i −0.247294 + 0.428326i
\(407\) 8.41702 + 14.5787i 0.417216 + 0.722640i
\(408\) 4.00000i 0.198030i
\(409\) 9.64697 5.56968i 0.477012 0.275403i −0.242158 0.970237i \(-0.577855\pi\)
0.719170 + 0.694834i \(0.244522\pi\)
\(410\) 0 0
\(411\) 19.7149i 0.972464i
\(412\) 2.39806 + 4.15356i 0.118144 + 0.204631i
\(413\) 7.88130 13.6508i 0.387814 0.671713i
\(414\) −4.27464 2.46797i −0.210087 0.121294i
\(415\) 0 0
\(416\) −3.03873 + 1.94065i −0.148986 + 0.0951483i
\(417\) −5.67742 −0.278024
\(418\) −18.6227 10.7518i −0.910866 0.525889i
\(419\) 7.75488 13.4318i 0.378851 0.656188i −0.612045 0.790823i \(-0.709653\pi\)
0.990895 + 0.134635i \(0.0429861\pi\)
\(420\) 0 0
\(421\) 39.4452i 1.92244i −0.275778 0.961221i \(-0.588935\pi\)
0.275778 0.961221i \(-0.411065\pi\)
\(422\) −19.4661 + 11.2387i −0.947594 + 0.547094i
\(423\) 1.57525 0.909471i 0.0765913 0.0442200i
\(424\) 5.48693i 0.266469i
\(425\) 0 0
\(426\) 7.93593 13.7454i 0.384497 0.665969i
\(427\) −1.07791 0.622333i −0.0521639 0.0301168i
\(428\) 3.07180 0.148481
\(429\) 16.2432 10.3736i 0.784231 0.500841i
\(430\) 0 0
\(431\) 1.86621 + 1.07746i 0.0898921 + 0.0518993i 0.544272 0.838909i \(-0.316806\pi\)
−0.454380 + 0.890808i \(0.650139\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −0.669689 1.15994i −0.0321832 0.0557429i 0.849485 0.527612i \(-0.176913\pi\)
−0.881668 + 0.471870i \(0.843579\pi\)
\(434\) 8.06361i 0.387066i
\(435\) 0 0
\(436\) 5.79441 3.34541i 0.277502 0.160216i
\(437\) 19.8564i 0.949861i
\(438\) 6.78668 + 11.7549i 0.324280 + 0.561670i
\(439\) −15.8490 + 27.4513i −0.756434 + 1.31018i 0.188225 + 0.982126i \(0.439727\pi\)
−0.944658 + 0.328055i \(0.893607\pi\)
\(440\) 0 0
\(441\) 1.60562 0.0764583
\(442\) −0.645159 14.4078i −0.0306871 0.685308i
\(443\) 28.0904 1.33461 0.667307 0.744782i \(-0.267447\pi\)
0.667307 + 0.744782i \(0.267447\pi\)
\(444\) 2.72733 + 1.57463i 0.129434 + 0.0747285i
\(445\) 0 0
\(446\) −0.689457 1.19417i −0.0326467 0.0565458i
\(447\) 19.4775i 0.921254i
\(448\) −2.01141 + 1.16129i −0.0950303 + 0.0548658i
\(449\) 25.0426 14.4583i 1.18183 0.682332i 0.225395 0.974267i \(-0.427633\pi\)
0.956438 + 0.291936i \(0.0942994\pi\)
\(450\) 0 0
\(451\) 7.06973 + 12.2451i 0.332900 + 0.576600i
\(452\) 3.55486 6.15720i 0.167206 0.289610i
\(453\) 12.5721 + 7.25851i 0.590690 + 0.341035i
\(454\) 19.3205 0.906756
\(455\) 0 0
\(456\) −4.02283 −0.188386
\(457\) −8.39958 4.84950i −0.392916 0.226850i 0.290507 0.956873i \(-0.406176\pi\)
−0.683423 + 0.730023i \(0.739509\pi\)
\(458\) 7.88130 13.6508i 0.368269 0.637861i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 0 0
\(461\) 10.3905 5.99896i 0.483934 0.279400i −0.238120 0.971236i \(-0.576531\pi\)
0.722055 + 0.691836i \(0.243198\pi\)
\(462\) 10.7518 6.20757i 0.500220 0.288802i
\(463\) 6.42664i 0.298671i −0.988787 0.149336i \(-0.952287\pi\)
0.988787 0.149336i \(-0.0477135\pi\)
\(464\) −2.14539 3.71592i −0.0995971 0.172507i
\(465\) 0 0
\(466\) 14.3370 + 8.27747i 0.664149 + 0.383447i
\(467\) −26.2642 −1.21536 −0.607681 0.794182i \(-0.707900\pi\)
−0.607681 + 0.794182i \(0.707900\pi\)
\(468\) 1.66129 3.20002i 0.0767932 0.147921i
\(469\) −9.54409 −0.440705
\(470\) 0 0
\(471\) −12.1914 + 21.1162i −0.561752 + 0.972982i
\(472\) 3.39334 + 5.87744i 0.156191 + 0.270531i
\(473\) 65.4854i 3.01102i
\(474\) −6.90026 + 3.98387i −0.316940 + 0.182985i
\(475\) 0 0
\(476\) 9.29032i 0.425821i
\(477\) −2.74346 4.75182i −0.125615 0.217571i
\(478\) −13.1003 + 22.6904i −0.599193 + 1.03783i
\(479\) −22.2418 12.8413i −1.01625 0.586735i −0.103237 0.994657i \(-0.532920\pi\)
−0.913017 + 0.407922i \(0.866253\pi\)
\(480\) 0 0
\(481\) 10.0777 + 5.23182i 0.459502 + 0.238551i
\(482\) −15.6496 −0.712818
\(483\) −9.92820 5.73205i −0.451749 0.260817i
\(484\) −8.78668 + 15.2190i −0.399395 + 0.691772i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 8.12238 4.68946i 0.368060 0.212500i −0.304551 0.952496i \(-0.598506\pi\)
0.672611 + 0.739997i \(0.265173\pi\)
\(488\) 0.464102 0.267949i 0.0210089 0.0121295i
\(489\) 23.6267i 1.06844i
\(490\) 0 0
\(491\) −3.86927 + 6.70177i −0.174618 + 0.302447i −0.940029 0.341095i \(-0.889202\pi\)
0.765411 + 0.643541i \(0.222536\pi\)
\(492\) 2.29078 + 1.32258i 0.103276 + 0.0596265i
\(493\) 17.1631 0.772987
\(494\) −14.4900 + 0.648841i −0.651935 + 0.0291927i
\(495\) 0 0
\(496\) −3.00670 1.73592i −0.135005 0.0779450i
\(497\) 18.4318 31.9249i 0.826781 1.43203i
\(498\) 5.66799 + 9.81724i 0.253989 + 0.439921i
\(499\) 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
\(502\) 28.3416i 1.26495i
\(503\) −17.5379 30.3765i −0.781975 1.35442i −0.930789 0.365556i \(-0.880879\pi\)
0.148814 0.988865i \(-0.452454\pi\)
\(504\) 1.16129 2.01141i 0.0517280 0.0895955i
\(505\) 0 0
\(506\) 26.3846 1.17294
\(507\) 5.46774 11.7942i 0.242831 0.523800i
\(508\) 2.13209 0.0945961
\(509\) −16.2697 9.39334i −0.721144 0.416353i 0.0940298 0.995569i \(-0.470025\pi\)
−0.815173 + 0.579217i \(0.803358\pi\)
\(510\) 0 0
\(511\) 15.7626 + 27.3016i 0.697297 + 1.20775i
\(512\) 1.00000i 0.0441942i
\(513\) 3.48387 2.01141i 0.153817 0.0888061i
\(514\) 10.8334 6.25465i 0.477839 0.275881i
\(515\) 0 0
\(516\) −6.12539 10.6095i −0.269655 0.467057i
\(517\) −4.86149 + 8.42035i −0.213808 + 0.370327i
\(518\) 6.33445 + 3.65720i 0.278320 + 0.160688i
\(519\) −16.1321 −0.708120
\(520\) 0 0
\(521\) 5.28512 0.231545 0.115773 0.993276i \(-0.463066\pi\)
0.115773 + 0.993276i \(0.463066\pi\)
\(522\) 3.71592 + 2.14539i 0.162641 + 0.0939011i
\(523\) −10.3762 + 17.9721i −0.453718 + 0.785863i −0.998614 0.0526409i \(-0.983236\pi\)
0.544895 + 0.838504i \(0.316569\pi\)
\(524\) 0.629257 + 1.08991i 0.0274892 + 0.0476127i
\(525\) 0 0
\(526\) −9.27159 + 5.35295i −0.404260 + 0.233400i
\(527\) 12.0268 6.94367i 0.523895 0.302471i
\(528\) 5.34541i 0.232629i
\(529\) −0.681725 1.18078i −0.0296402 0.0513384i
\(530\) 0 0
\(531\) −5.87744 3.39334i −0.255059 0.147258i
\(532\) −9.34333 −0.405085
\(533\) 8.46456 + 4.39438i 0.366641 + 0.190342i
\(534\) −1.73978 −0.0752877
\(535\) 0 0
\(536\) 2.05463 3.55872i 0.0887465 0.153713i
\(537\) −3.66412 6.34644i −0.158118 0.273869i
\(538\) 7.52522i 0.324435i
\(539\) −7.43284 + 4.29135i −0.320155 + 0.184842i
\(540\) 0 0
\(541\) 28.7365i 1.23548i −0.786384 0.617739i \(-0.788049\pi\)
0.786384 0.617739i \(-0.211951\pi\)
\(542\) 4.92434 + 8.52920i 0.211518 + 0.366361i
\(543\) −9.78668 + 16.9510i −0.419987 + 0.727438i
\(544\) 3.46410 + 2.00000i 0.148522 + 0.0857493i
\(545\) 0 0
\(546\) 3.85848 7.43230i 0.165128 0.318073i
\(547\) −18.3768 −0.785737 −0.392869 0.919595i \(-0.628517\pi\)
−0.392869 + 0.919595i \(0.628517\pi\)
\(548\) −17.0736 9.85744i −0.729348 0.421089i
\(549\) −0.267949 + 0.464102i −0.0114358 + 0.0198074i
\(550\) 0 0
\(551\) 17.2610i 0.735345i
\(552\) 4.27464 2.46797i 0.181941 0.105044i
\(553\) −16.0264 + 9.25285i −0.681512 + 0.393471i
\(554\) 0.953101i 0.0404934i
\(555\) 0 0
\(556\) 2.83871 4.91679i 0.120388 0.208518i
\(557\) −22.9831 13.2693i −0.973826 0.562238i −0.0734252 0.997301i \(-0.523393\pi\)
−0.900400 + 0.435062i \(0.856726\pi\)
\(558\) 3.47183 0.146974
\(559\) −23.7745 37.2268i −1.00555 1.57453i
\(560\) 0 0
\(561\) −18.5170 10.6908i −0.781790 0.451366i
\(562\) 2.78668 4.82667i 0.117549 0.203601i
\(563\) 3.03056 + 5.24908i 0.127723 + 0.221222i 0.922794 0.385294i \(-0.125900\pi\)
−0.795071 + 0.606516i \(0.792567\pi\)
\(564\) 1.81894i 0.0765913i
\(565\) 0 0
\(566\) −19.0642 + 11.0067i −0.801326 + 0.462646i
\(567\) 2.32258i 0.0975392i
\(568\) 7.93593 + 13.7454i 0.332984 + 0.576746i
\(569\) −7.24818 + 12.5542i −0.303860 + 0.526300i −0.977007 0.213208i \(-0.931609\pi\)
0.673147 + 0.739509i \(0.264942\pi\)
\(570\) 0 0
\(571\) −2.90413 −0.121534 −0.0607670 0.998152i \(-0.519355\pi\)
−0.0607670 + 0.998152i \(0.519355\pi\)
\(572\) 0.862160 + 19.2538i 0.0360487 + 0.805044i
\(573\) 17.0375 0.711750
\(574\) 5.32051 + 3.07180i 0.222074 + 0.128214i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 18.8180i 0.783405i 0.920092 + 0.391702i \(0.128114\pi\)
−0.920092 + 0.391702i \(0.871886\pi\)
\(578\) 0.866025 0.500000i 0.0360219 0.0207973i
\(579\) −5.33031 + 3.07746i −0.221520 + 0.127895i
\(580\) 0 0
\(581\) 13.1643 + 22.8013i 0.546149 + 0.945958i
\(582\) 8.05463 13.9510i 0.333875 0.578289i
\(583\) 25.4004 + 14.6649i 1.05198 + 0.607359i
\(584\) −13.5734 −0.561670
\(585\) 0 0
\(586\) −6.84302 −0.282682
\(587\) 3.40901 + 1.96820i 0.140705 + 0.0812361i 0.568700 0.822545i \(-0.307447\pi\)
−0.427995 + 0.903781i \(0.640780\pi\)
\(588\) −0.802812 + 1.39051i −0.0331074 + 0.0573437i
\(589\) −6.98329 12.0954i −0.287741 0.498383i
\(590\) 0 0
\(591\) 11.9396 6.89334i 0.491130 0.283554i
\(592\) −2.72733 + 1.57463i −0.112093 + 0.0647168i
\(593\) 20.1227i 0.826338i −0.910654 0.413169i \(-0.864422\pi\)
0.910654 0.413169i \(-0.135578\pi\)
\(594\) −2.67270 4.62926i −0.109662 0.189941i
\(595\) 0 0
\(596\) −16.8680 9.73875i −0.690940 0.398915i
\(597\) 2.28304 0.0934388
\(598\) 14.9990 9.57893i 0.613353 0.391712i
\(599\) 48.1172 1.96601 0.983007 0.183567i \(-0.0587644\pi\)
0.983007 + 0.183567i \(0.0587644\pi\)
\(600\) 0 0
\(601\) 2.12109 3.67383i 0.0865209 0.149859i −0.819517 0.573054i \(-0.805758\pi\)
0.906038 + 0.423196i \(0.139092\pi\)
\(602\) −14.2267 24.6414i −0.579837 1.00431i
\(603\) 4.10926i 0.167342i
\(604\) −12.5721 + 7.25851i −0.511552 + 0.295345i
\(605\) 0 0
\(606\) 12.6908i 0.515529i
\(607\) 6.03424 + 10.4516i 0.244922 + 0.424218i 0.962110 0.272663i \(-0.0879042\pi\)
−0.717188 + 0.696880i \(0.754571\pi\)
\(608\) 2.01141 3.48387i 0.0815736 0.141290i
\(609\) 8.63052 + 4.98283i 0.349726 + 0.201915i
\(610\) 0 0
\(611\) 0.293377 + 6.55172i 0.0118688 + 0.265054i
\(612\) −4.00000 −0.161690
\(613\) −36.1497 20.8711i −1.46007 0.842974i −0.461060 0.887369i \(-0.652531\pi\)
−0.999014 + 0.0443946i \(0.985864\pi\)
\(614\) −2.37721 + 4.11745i −0.0959364 + 0.166167i
\(615\) 0 0
\(616\) 12.4151i 0.500220i
\(617\) 28.9760 16.7293i 1.16653 0.673497i 0.213670 0.976906i \(-0.431458\pi\)
0.952860 + 0.303409i \(0.0981249\pi\)
\(618\) 4.15356 2.39806i 0.167081 0.0964640i
\(619\) 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
\(622\) 1.67696 + 0.968196i 0.0672401 + 0.0388211i
\(623\) −4.04078 −0.161891
\(624\) 1.94065 + 3.03873i 0.0776883 + 0.121646i
\(625\) 0 0
\(626\) −22.1308 12.7772i −0.884526 0.510681i
\(627\) −10.7518 + 18.6227i −0.429386 + 0.743719i
\(628\) −12.1914 21.1162i −0.486491 0.842628i
\(629\) 12.5970i 0.502276i
\(630\) 0 0
\(631\) −21.4775 + 12.4000i −0.855005 + 0.493638i −0.862337 0.506335i \(-0.831000\pi\)
0.00733109 + 0.999973i \(0.497666\pi\)
\(632\) 7.96774i 0.316940i
\(633\) 11.2387 + 19.4661i 0.446700 + 0.773707i
\(634\) −6.33337 + 10.9697i −0.251530 + 0.435663i
\(635\) 0 0
\(636\) 5.48693 0.217571
\(637\) −2.66741 + 5.13802i −0.105686 + 0.203576i
\(638\) −22.9359 −0.908042
\(639\) −13.7454 7.93593i −0.543761 0.313941i
\(640\) 0 0
\(641\) 2.04259 + 3.53788i 0.0806776 + 0.139738i 0.903541 0.428501i \(-0.140958\pi\)
−0.822864 + 0.568239i \(0.807625\pi\)
\(642\) 3.07180i 0.121234i
\(643\) 31.6806 18.2908i 1.24936 0.721318i 0.278377 0.960472i \(-0.410203\pi\)
0.970982 + 0.239154i \(0.0768701\pi\)
\(644\) 9.92820 5.73205i 0.391226 0.225874i
\(645\) 0 0
\(646\) 8.04565 + 13.9355i 0.316552 + 0.548284i
\(647\) −8.61704 + 14.9251i −0.338771 + 0.586768i −0.984202 0.177050i \(-0.943344\pi\)
0.645431 + 0.763818i \(0.276678\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 36.2776 1.42402
\(650\) 0 0
\(651\) 8.06361 0.316038
\(652\) −20.4614 11.8134i −0.801329 0.462647i
\(653\) −10.9637 + 18.9897i −0.429042 + 0.743123i −0.996788 0.0800806i \(-0.974482\pi\)
0.567746 + 0.823204i \(0.307816\pi\)
\(654\) −3.34541 5.79441i −0.130816 0.226579i
\(655\) 0 0
\(656\) −2.29078 + 1.32258i −0.0894397 + 0.0516381i
\(657\) 11.7549 6.78668i 0.458601 0.264774i
\(658\) 4.22464i 0.164694i
\(659\) 24.2379 + 41.9813i 0.944176 + 1.63536i 0.757393 + 0.652960i \(0.226473\pi\)
0.186783 + 0.982401i \(0.440194\pi\)
\(660\) 0 0
\(661\) −25.8267 14.9110i −1.00454 0.579972i −0.0949524 0.995482i \(-0.530270\pi\)
−0.909589 + 0.415510i \(0.863603\pi\)
\(662\) −23.6981 −0.921052
\(663\) −14.4078 + 0.645159i −0.559551 + 0.0250559i
\(664\) −11.3360 −0.439921
\(665\) 0 0
\(666\) 1.57463 2.72733i 0.0610155 0.105682i
\(667\) 10.5895 + 18.3415i 0.410027 + 0.710187i
\(668\) 16.7471i 0.647967i
\(669\) −1.19417 + 0.689457i −0.0461694 + 0.0266559i
\(670\) 0 0
\(671\) 2.86459i 0.110586i
\(672\) 1.16129 + 2.01141i 0.0447977 + 0.0775919i
\(673\) 15.3360 26.5627i 0.591158 1.02392i −0.402919 0.915236i \(-0.632004\pi\)
0.994077 0.108680i \(-0.0346625\pi\)
\(674\) −16.9355 9.77770i −0.652330 0.376623i
\(675\) 0 0
\(676\) 7.48023 + 10.6323i 0.287701 + 0.408935i
\(677\) −21.0831 −0.810290 −0.405145 0.914252i \(-0.632779\pi\)
−0.405145 + 0.914252i \(0.632779\pi\)
\(678\) −6.15720 3.55486i −0.236466 0.136524i
\(679\) 18.7075 32.4024i 0.717929 1.24349i
\(680\) 0 0
\(681\) 19.3205i 0.740363i
\(682\) −16.0720 + 9.27918i −0.615429 + 0.355318i
\(683\) 11.5493 6.66799i 0.441921 0.255143i −0.262491 0.964934i \(-0.584544\pi\)
0.704412 + 0.709791i \(0.251211\pi\)
\(684\) 4.02283i 0.153817i
\(685\) 0 0
\(686\) −9.99362 + 17.3095i −0.381558 + 0.660878i
\(687\) −13.6508 7.88130i −0.520811 0.300691i
\(688\) 12.2508 0.467057
\(689\) 19.7636 0.884986i 0.752933 0.0337153i
\(690\) 0 0
\(691\) −30.2289 17.4527i −1.14996 0.663932i −0.201085 0.979574i \(-0.564447\pi\)
−0.948878 + 0.315642i \(0.897780\pi\)
\(692\) 8.06604 13.9708i 0.306625 0.531090i
\(693\) −6.20757 10.7518i −0.235806 0.408428i
\(694\) 23.0375i 0.874490i
\(695\) 0 0
\(696\) −3.71592 + 2.14539i −0.140852 + 0.0813207i
\(697\) 10.5806i 0.400770i
\(698\) 7.66025 + 13.2679i 0.289945 + 0.502199i
\(699\) 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 \(0.230445\pi\)
\(702\) −3.20002 1.66129i −0.120777 0.0627013i
\(703\) −12.6689 −0.477817
\(704\) −4.62926 2.67270i −0.174472 0.100731i
\(705\) 0 0
\(706\) −14.2039 24.6018i −0.534570 0.925903i
\(707\) 29.4754i 1.10854i
\(708\) 5.87744 3.39334i 0.220888 0.127530i
\(709\) 2.45467 1.41720i 0.0921869 0.0532242i −0.453198 0.891410i \(-0.649717\pi\)
0.545385 + 0.838186i \(0.316384\pi\)
\(710\) 0 0
\(711\) 3.98387 + 6.90026i 0.149407 + 0.258780i
\(712\) 0.869891 1.50670i 0.0326005 0.0564658i
\(713\) 14.8409 + 8.56837i 0.555794 + 0.320888i
\(714\) −9.29032 −0.347681
\(715\) 0 0
\(716\) 7.32824 0.273869
\(717\) 22.6904 + 13.1003i 0.847387 + 0.489239i
\(718\) −11.7867 + 20.4151i −0.439875 + 0.761886i
\(719\) −21.8564 37.8564i −0.815106 1.41181i −0.909251 0.416247i \(-0.863345\pi\)
0.0941451 0.995558i \(-0.469988\pi\)
\(720\) 0 0
\(721\) 9.64697 5.56968i 0.359272 0.207426i
\(722\) −2.43948 + 1.40844i −0.0907881 + 0.0524165i
\(723\) 15.6496i 0.582014i
\(724\) −9.78668 16.9510i −0.363719 0.629980i
\(725\) 0 0
\(726\) 15.2190 + 8.78668i 0.564829 + 0.326104i
\(727\) 16.2568 0.602932 0.301466 0.953477i \(-0.402524\pi\)
0.301466 + 0.953477i \(0.402524\pi\)
\(728\) 4.50732 + 7.05769i 0.167052 + 0.261575i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −24.5016 + 42.4380i −0.906223 + 1.56962i
\(732\) −0.267949 0.464102i −0.00990369 0.0171537i
\(733\) 4.96774i 0.183488i −0.995783 0.0917438i \(-0.970756\pi\)
0.995783 0.0917438i \(-0.0292441\pi\)
\(734\) 23.8078 13.7454i 0.878762 0.507354i
\(735\) 0 0
\(736\) 4.93593i 0.181941i
\(737\) −10.9828 19.0228i −0.404558 0.700715i
\(738\) 1.32258 2.29078i 0.0486848 0.0843246i
\(739\) 43.0306 + 24.8437i 1.58291 + 0.913892i 0.994432 + 0.105377i \(0.0336048\pi\)
0.588475 + 0.808515i \(0.299729\pi\)
\(740\) 0 0
\(741\) 0.648841 + 14.4900i 0.0238358 + 0.532303i
\(742\) 12.7438 0.467841
\(743\) −18.6559 10.7710i −0.684420 0.395150i 0.117098 0.993120i \(-0.462641\pi\)
−0.801518 + 0.597970i \(0.795974\pi\)
\(744\) −1.73592 + 3.00670i −0.0636418 + 0.110231i
\(745\) 0 0
\(746\) 26.3421i 0.964452i
\(747\) 9.81724 5.66799i 0.359194 0.207381i
\(748\) 18.5170 10.6908i 0.677050 0.390895i
\(749\) 7.13449i 0.260689i
\(750\) 0 0
\(751\) −3.17436 + 5.49816i −0.115834 + 0.200631i −0.918113 0.396319i \(-0.870287\pi\)
0.802279 + 0.596950i \(0.203621\pi\)
\(752\) −1.57525 0.909471i −0.0574435 0.0331650i
\(753\) −28.3416 −1.03283
\(754\) −13.0385 + 8.32690i −0.474834 + 0.303248i
\(755\) 0 0
\(756\) −2.01141 1.16129i −0.0731544 0.0422357i
\(757\) −24.0554 + 41.6651i −0.874307 + 1.51434i −0.0168078 + 0.999859i \(0.505350\pi\)
−0.857499 + 0.514485i \(0.827983\pi\)
\(758\) 0.224275 + 0.388456i 0.00814604 + 0.0141094i
\(759\) 26.3846i 0.957699i
\(760\) 0 0
\(761\) 29.1734 16.8433i 1.05754 0.610569i 0.132786 0.991145i \(-0.457608\pi\)
0.924750 + 0.380576i \(0.124274\pi\)
\(762\) 2.13209i 0.0772374i
\(763\) −7.76997 13.4580i −0.281292 0.487212i
\(764\) −8.51873 + 14.7549i −0.308197 + 0.533813i
\(765\) 0 0
\(766\) −12.1227 −0.438009
\(767\) 20.6229 13.1706i 0.744649 0.475562i
\(768\) −1.00000 −0.0360844
\(769\) −5.18651 2.99443i −0.187030 0.107982i 0.403561 0.914953i \(-0.367772\pi\)
−0.590592 + 0.806971i \(0.701106\pi\)
\(770\) 0 0
\(771\) −6.25465 10.8334i −0.225256 0.390154i
\(772\) 6.15491i 0.221520i
\(773\) −11.6811 + 6.74409i −0.420140 + 0.242568i −0.695137 0.718877i \(-0.744656\pi\)
0.274997 + 0.961445i \(0.411323\pi\)
\(774\) −10.6095 + 6.12539i −0.381350 + 0.220173i
\(775\) 0 0
\(776\) 8.05463 + 13.9510i 0.289144 + 0.500813i
\(777\) 3.65720 6.33445i 0.131201 0.227247i
\(778\) 16.1249 + 9.30974i 0.578107 + 0.333770i
\(779\) −10.6410 −0.381254
\(780\) 0 0
\(781\) 84.8416 3.03587
\(782\) −17.0986 9.87187i −0.611444 0.353017i
\(783\) 2.14539 3.71592i 0.0766699 0.132796i
\(784\) −0.802812 1.39051i −0.0286718 0.0496611i
\(785\)