Properties

Label 1170.2.bs.f.901.3
Level $1170$
Weight $2$
Character 1170.901
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
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 901.3
Root \(3.17270 - 3.17270i\) of defining polynomial
Character \(\chi\) \(=\) 1170.901
Dual form 1170.2.bs.f.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.01141 + 1.16129i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.01141 + 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(-4.62926 - 2.67270i) q^{11} +(-3.60194 + 0.161290i) q^{13} -2.32258 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-3.48387 + 2.01141i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-2.67270 - 4.62926i) q^{22} +(2.46797 - 4.27464i) q^{23} -1.00000 q^{25} +(-3.20002 - 1.66129i) q^{26} +(-2.01141 - 1.16129i) q^{28} +(2.14539 - 3.71592i) q^{29} +3.47183i q^{31} +(-0.866025 + 0.500000i) q^{32} -4.00000i q^{34} +(-1.16129 - 2.01141i) q^{35} +(-2.72733 - 1.57463i) q^{37} -4.02283 q^{38} -1.00000 q^{40} +(-2.29078 - 1.32258i) q^{41} +(6.12539 + 10.6095i) q^{43} -5.34541i q^{44} +(4.27464 - 2.46797i) q^{46} +1.81894i q^{47} +(-0.802812 + 1.39051i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-1.94065 - 3.03873i) q^{52} +5.48693 q^{53} +(2.67270 - 4.62926i) q^{55} +(-1.16129 - 2.01141i) q^{56} +(3.71592 - 2.14539i) q^{58} +(-5.87744 + 3.39334i) q^{59} +(-0.267949 - 0.464102i) q^{61} +(-1.73592 + 3.00670i) q^{62} -1.00000 q^{64} +(-0.161290 - 3.60194i) q^{65} +(3.55872 + 2.05463i) q^{67} +(2.00000 - 3.46410i) q^{68} -2.32258i q^{70} +(-13.7454 + 7.93593i) q^{71} -13.5734i q^{73} +(-1.57463 - 2.72733i) q^{74} +(-3.48387 - 2.01141i) q^{76} +12.4151 q^{77} -7.96774 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-1.32258 - 2.29078i) q^{82} +11.3360i q^{83} +(3.46410 - 2.00000i) q^{85} +12.2508i q^{86} +(2.67270 - 4.62926i) q^{88} +(1.50670 + 0.869891i) q^{89} +(7.05769 - 4.50732i) q^{91} +4.93593 q^{92} +(-0.909471 + 1.57525i) q^{94} +(-2.01141 - 3.48387i) q^{95} +(-13.9510 + 8.05463i) q^{97} +(-1.39051 + 0.802812i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{10} - 6q^{11} - 12q^{13} - 4q^{14} - 4q^{16} - 16q^{17} - 6q^{19} + 2q^{22} - 4q^{23} - 8q^{25} + 12q^{26} + 8q^{29} - 2q^{35} + 30q^{37} - 8q^{40} + 14q^{43} - 6q^{46} + 14q^{49} - 6q^{52} - 16q^{53} - 2q^{55} - 2q^{56} - 6q^{58} - 24q^{59} - 16q^{61} - 4q^{62} - 8q^{64} + 6q^{65} + 24q^{67} + 16q^{68} + 12q^{71} - 10q^{74} - 6q^{76} - 16q^{77} - 20q^{79} + 4q^{82} - 2q^{88} - 42q^{89} - 10q^{91} - 8q^{92} - 8q^{94} - 24q^{97} - 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −2.01141 + 1.16129i −0.760243 + 0.438926i −0.829383 0.558681i \(-0.811308\pi\)
0.0691402 + 0.997607i \(0.477974\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −4.62926 2.67270i −1.39577 0.805850i −0.401827 0.915716i \(-0.631625\pi\)
−0.993946 + 0.109865i \(0.964958\pi\)
\(12\) 0 0
\(13\) −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 \(0.994540\pi\)
\(18\) 0 0
\(19\) −3.48387 + 2.01141i −0.799254 + 0.461450i −0.843210 0.537584i \(-0.819337\pi\)
0.0439559 + 0.999033i \(0.486004\pi\)
\(20\) −0.866025 + 0.500000i −0.193649 + 0.111803i
\(21\) 0 0
\(22\) −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 0
\(25\) −1.00000 −0.200000
\(26\) −3.20002 1.66129i −0.627575 0.325806i
\(27\) 0 0
\(28\) −2.01141 1.16129i −0.380121 0.219463i
\(29\) 2.14539 3.71592i 0.398388 0.690029i −0.595139 0.803623i \(-0.702903\pi\)
0.993527 + 0.113594i \(0.0362363\pi\)
\(30\) 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
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) −1.16129 2.01141i −0.196294 0.339991i
\(36\) 0 0
\(37\) −2.72733 1.57463i −0.448371 0.258867i 0.258771 0.965939i \(-0.416682\pi\)
−0.707142 + 0.707072i \(0.750016\pi\)
\(38\) −4.02283 −0.652589
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −2.29078 1.32258i −0.357759 0.206552i 0.310338 0.950626i \(-0.399558\pi\)
−0.668097 + 0.744074i \(0.732891\pi\)
\(42\) 0 0
\(43\) 6.12539 + 10.6095i 0.934113 + 1.61793i 0.776207 + 0.630478i \(0.217141\pi\)
0.157906 + 0.987454i \(0.449526\pi\)
\(44\) 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 0
\(49\) −0.802812 + 1.39051i −0.114687 + 0.198644i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 0 0
\(52\) −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 0
\(55\) 2.67270 4.62926i 0.360387 0.624209i
\(56\) −1.16129 2.01141i −0.155184 0.268786i
\(57\) 0 0
\(58\) 3.71592 2.14539i 0.487924 0.281703i
\(59\) −5.87744 + 3.39334i −0.765177 + 0.441775i −0.831152 0.556046i \(-0.812318\pi\)
0.0659742 + 0.997821i \(0.478984\pi\)
\(60\) 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
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.161290 3.60194i −0.0200055 0.446766i
\(66\) 0 0
\(67\) 3.55872 + 2.05463i 0.434767 + 0.251013i 0.701376 0.712792i \(-0.252570\pi\)
−0.266608 + 0.963805i \(0.585903\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 0 0
\(70\) 2.32258i 0.277601i
\(71\) −13.7454 + 7.93593i −1.63128 + 0.941822i −0.647586 + 0.761992i \(0.724221\pi\)
−0.983698 + 0.179830i \(0.942445\pi\)
\(72\) 0 0
\(73\) 13.5734i 1.58864i −0.607498 0.794321i \(-0.707827\pi\)
0.607498 0.794321i \(-0.292173\pi\)
\(74\) −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
\(78\) 0 0
\(79\) −7.96774 −0.896441 −0.448220 0.893923i \(-0.647942\pi\)
−0.448220 + 0.893923i \(0.647942\pi\)
\(80\) −0.866025 0.500000i −0.0968246 0.0559017i
\(81\) 0 0
\(82\) −1.32258 2.29078i −0.146054 0.252974i
\(83\) 11.3360i 1.24428i 0.782904 + 0.622142i \(0.213737\pi\)
−0.782904 + 0.622142i \(0.786263\pi\)
\(84\) 0 0
\(85\) 3.46410 2.00000i 0.375735 0.216930i
\(86\) 12.2508i 1.32104i
\(87\) 0 0
\(88\) 2.67270 4.62926i 0.284911 0.493480i
\(89\) 1.50670 + 0.869891i 0.159709 + 0.0922083i 0.577725 0.816232i \(-0.303941\pi\)
−0.418015 + 0.908440i \(0.637274\pi\)
\(90\) 0 0
\(91\) 7.05769 4.50732i 0.739847 0.472495i
\(92\) 4.93593 0.514607
\(93\) 0 0
\(94\) −0.909471 + 1.57525i −0.0938048 + 0.162475i
\(95\) −2.01141 3.48387i −0.206367 0.357437i
\(96\) 0 0
\(97\) −13.9510 + 8.05463i −1.41651 + 0.817824i −0.995991 0.0894586i \(-0.971486\pi\)
−0.420522 + 0.907282i \(0.638153\pi\)
\(98\) −1.39051 + 0.802812i −0.140463 + 0.0810962i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −6.34541 + 10.9906i −0.631391 + 1.09360i 0.355876 + 0.934533i \(0.384183\pi\)
−0.987267 + 0.159069i \(0.949151\pi\)
\(102\) 0 0
\(103\) −4.79612 −0.472575 −0.236288 0.971683i \(-0.575931\pi\)
−0.236288 + 0.971683i \(0.575931\pi\)
\(104\) −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 0
\(109\) 6.69081i 0.640864i −0.947272 0.320432i \(-0.896172\pi\)
0.947272 0.320432i \(-0.103828\pi\)
\(110\) 4.62926 2.67270i 0.441382 0.254832i
\(111\) 0 0
\(112\) 2.32258i 0.219463i
\(113\) −3.55486 6.15720i −0.334413 0.579220i 0.648959 0.760823i \(-0.275205\pi\)
−0.983372 + 0.181603i \(0.941871\pi\)
\(114\) 0 0
\(115\) 4.27464 + 2.46797i 0.398613 + 0.230139i
\(116\) 4.29078 0.398388
\(117\) 0 0
\(118\) −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
\(123\) 0 0
\(124\) −3.00670 + 1.73592i −0.270009 + 0.155890i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −1.06604 + 1.84644i −0.0945961 + 0.163845i −0.909440 0.415835i \(-0.863489\pi\)
0.814844 + 0.579680i \(0.196823\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 1.66129 3.20002i 0.145705 0.280660i
\(131\) −1.25851 −0.109957 −0.0549785 0.998488i \(-0.517509\pi\)
−0.0549785 + 0.998488i \(0.517509\pi\)
\(132\) 0 0
\(133\) 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 \(0.652060\pi\)
\(138\) 0 0
\(139\) −2.83871 4.91679i −0.240776 0.417037i 0.720159 0.693809i \(-0.244069\pi\)
−0.960936 + 0.276772i \(0.910735\pi\)
\(140\) 1.16129 2.01141i 0.0981469 0.169995i
\(141\) 0 0
\(142\) −15.8719 −1.33194
\(143\) 17.1054 + 8.88027i 1.43043 + 0.742605i
\(144\) 0 0
\(145\) 3.71592 + 2.14539i 0.308590 + 0.178165i
\(146\) 6.78668 11.7549i 0.561670 0.972841i
\(147\) 0 0
\(148\) 3.14925i 0.258867i
\(149\) 16.8680 9.73875i 1.38188 0.797829i 0.389499 0.921027i \(-0.372648\pi\)
0.992382 + 0.123198i \(0.0393150\pi\)
\(150\) 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
\(153\) 0 0
\(154\) 10.7518 + 6.20757i 0.866406 + 0.500220i
\(155\) −3.47183 −0.278864
\(156\) 0 0
\(157\) 24.3829 1.94596 0.972982 0.230879i \(-0.0741602\pi\)
0.972982 + 0.230879i \(0.0741602\pi\)
\(158\) −6.90026 3.98387i −0.548956 0.316940i
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 11.4641i 0.903498i
\(162\) 0 0
\(163\) 20.4614 11.8134i 1.60266 0.925295i 0.611704 0.791086i \(-0.290484\pi\)
0.990953 0.134208i \(-0.0428492\pi\)
\(164\) 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 \(0.891047\pi\)
\(168\) 0 0
\(169\) 12.9480 1.16191i 0.995998 0.0893780i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) −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 \(-0.376805\pi\)
\(174\) 0 0
\(175\) 2.01141 1.16129i 0.152049 0.0877853i
\(176\) 4.62926 2.67270i 0.348943 0.201463i
\(177\) 0 0
\(178\) 0.869891 + 1.50670i 0.0652011 + 0.112932i
\(179\) −3.66412 + 6.34644i −0.273869 + 0.474355i −0.969849 0.243706i \(-0.921637\pi\)
0.695980 + 0.718061i \(0.254970\pi\)
\(180\) 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 0
\(184\) 4.27464 + 2.46797i 0.315131 + 0.181941i
\(185\) 1.57463 2.72733i 0.115769 0.200518i
\(186\) 0 0
\(187\) 21.3816i 1.56358i
\(188\) −1.57525 + 0.909471i −0.114887 + 0.0663300i
\(189\) 0 0
\(190\) 4.02283i 0.291846i
\(191\) −8.51873 14.7549i −0.616394 1.06763i −0.990138 0.140094i \(-0.955260\pi\)
0.373744 0.927532i \(-0.378074\pi\)
\(192\) 0 0
\(193\) 5.33031 + 3.07746i 0.383684 + 0.221520i 0.679420 0.733750i \(-0.262231\pi\)
−0.295736 + 0.955270i \(0.595565\pi\)
\(194\) −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 \(0.503251\pi\)
\(198\) 0 0
\(199\) 1.14152 + 1.97717i 0.0809203 + 0.140158i 0.903646 0.428281i \(-0.140881\pi\)
−0.822725 + 0.568439i \(0.807547\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) −10.9906 + 6.34541i −0.773293 + 0.446461i
\(203\) 9.96567i 0.699453i
\(204\) 0 0
\(205\) 1.32258 2.29078i 0.0923730 0.159995i
\(206\) −4.15356 2.39806i −0.289392 0.167081i
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) 2.66025 1.53590i 0.181851 0.104992i
\(215\) −10.6095 + 6.12539i −0.723561 + 0.417748i
\(216\) 0 0
\(217\) −4.03180 6.98329i −0.273697 0.474057i
\(218\) 3.34541 5.79441i 0.226579 0.392447i
\(219\) 0 0
\(220\) 5.34541 0.360387
\(221\) 7.76261 + 12.1549i 0.522170 + 0.817628i
\(222\) 0 0
\(223\) 1.19417 + 0.689457i 0.0799678 + 0.0461694i 0.539451 0.842017i \(-0.318632\pi\)
−0.459483 + 0.888187i \(0.651965\pi\)
\(224\) 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 \(0.111781\pi\)
\(228\) 0 0
\(229\) 15.7626i 1.04162i −0.853672 0.520811i \(-0.825630\pi\)
0.853672 0.520811i \(-0.174370\pi\)
\(230\) 2.46797 + 4.27464i 0.162733 + 0.281862i
\(231\) 0 0
\(232\) 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 0
\(235\) −1.81894 −0.118655
\(236\) −5.87744 3.39334i −0.382589 0.220888i
\(237\) 0 0
\(238\) 4.64516 + 8.04565i 0.301101 + 0.521522i
\(239\) 26.2006i 1.69477i −0.530976 0.847387i \(-0.678175\pi\)
0.530976 0.847387i \(-0.321825\pi\)
\(240\) 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 0
\(244\) 0.267949 0.464102i 0.0171537 0.0297111i
\(245\) −1.39051 0.802812i −0.0888365 0.0512898i
\(246\) 0 0
\(247\) 12.2243 7.80691i 0.777812 0.496742i
\(248\) −3.47183 −0.220462
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 14.1708 + 24.5446i 0.894454 + 1.54924i 0.834479 + 0.551040i \(0.185769\pi\)
0.0599750 + 0.998200i \(0.480898\pi\)
\(252\) 0 0
\(253\) −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 \(0.0390883\pi\)
\(258\) 0 0
\(259\) 7.31439 0.454494
\(260\) 3.03873 1.94065i 0.188454 0.120354i
\(261\) 0 0
\(262\) −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 \(0.273741\pi\)
\(264\) 0 0
\(265\) 5.48693i 0.337059i
\(266\) 8.09156 4.67167i 0.496126 0.286438i
\(267\) 0 0
\(268\) 4.10926i 0.251013i
\(269\) 3.76261 + 6.51703i 0.229410 + 0.397350i 0.957633 0.287990i \(-0.0929869\pi\)
−0.728223 + 0.685340i \(0.759654\pi\)
\(270\) 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 0
\(274\) −19.7149 −1.19102
\(275\) 4.62926 + 2.67270i 0.279155 + 0.161170i
\(276\) 0 0
\(277\) 0.476550 + 0.825410i 0.0286331 + 0.0495941i 0.879987 0.474998i \(-0.157551\pi\)
−0.851354 + 0.524592i \(0.824218\pi\)
\(278\) 5.67742i 0.340509i
\(279\) 0 0
\(280\) 2.01141 1.16129i 0.120205 0.0694003i
\(281\) 5.57336i 0.332479i 0.986085 + 0.166239i \(0.0531625\pi\)
−0.986085 + 0.166239i \(0.946838\pi\)
\(282\) 0 0
\(283\) 11.0067 19.0642i 0.654280 1.13325i −0.327794 0.944749i \(-0.606305\pi\)
0.982074 0.188497i \(-0.0603616\pi\)
\(284\) −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 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 2.14539 + 3.71592i 0.125981 + 0.218206i
\(291\) 0 0
\(292\) 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 \(0.397391\pi\)
\(294\) 0 0
\(295\) −3.39334 5.87744i −0.197568 0.342198i
\(296\) 1.57463 2.72733i 0.0915233 0.158523i
\(297\) 0 0
\(298\) 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
\(303\) 0 0
\(304\) 4.02283i 0.230725i
\(305\) 0.464102 0.267949i 0.0265744 0.0153427i
\(306\) 0 0
\(307\) 4.75442i 0.271349i −0.990753 0.135675i \(-0.956680\pi\)
0.990753 0.135675i \(-0.0433202\pi\)
\(308\) 6.20757 + 10.7518i 0.353709 + 0.612642i
\(309\) 0 0
\(310\) −3.00670 1.73592i −0.170769 0.0985934i
\(311\) −1.93639 −0.109803 −0.0549013 0.998492i \(-0.517484\pi\)
−0.0549013 + 0.998492i \(0.517484\pi\)
\(312\) 0 0
\(313\) 25.5545 1.44443 0.722213 0.691671i \(-0.243125\pi\)
0.722213 + 0.691671i \(0.243125\pi\)
\(314\) 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 \(0.884237\pi\)
\(318\) 0 0
\(319\) −19.8631 + 11.4680i −1.11212 + 0.642083i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −5.73205 + 9.92820i −0.319435 + 0.553277i
\(323\) 13.9355 + 8.04565i 0.775391 + 0.447672i
\(324\) 0 0
\(325\) 3.60194 0.161290i 0.199800 0.00894675i
\(326\) 23.6267 1.30856
\(327\) 0 0
\(328\) 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
\(333\) 0 0
\(334\) −8.37357 14.5035i −0.458182 0.793594i
\(335\) −2.05463 + 3.55872i −0.112256 + 0.194434i
\(336\) 0 0
\(337\) 19.5554 1.06525 0.532625 0.846351i \(-0.321205\pi\)
0.532625 + 0.846351i \(0.321205\pi\)
\(338\) 11.7942 + 5.46774i 0.641521 + 0.297406i
\(339\) 0 0
\(340\) 3.46410 + 2.00000i 0.187867 + 0.108465i
\(341\) 9.27918 16.0720i 0.502496 0.870348i
\(342\) 0 0
\(343\) 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 \(-0.378868\pi\)
\(348\) 0 0
\(349\) 13.2679 + 7.66025i 0.710217 + 0.410044i 0.811141 0.584850i \(-0.198847\pi\)
−0.100924 + 0.994894i \(0.532180\pi\)
\(350\) 2.32258 0.124147
\(351\) 0 0
\(352\) 5.34541 0.284911
\(353\) −24.6018 14.2039i −1.30942 0.755996i −0.327424 0.944877i \(-0.606181\pi\)
−0.982000 + 0.188881i \(0.939514\pi\)
\(354\) 0 0
\(355\) −7.93593 13.7454i −0.421196 0.729532i
\(356\) 1.73978i 0.0922083i
\(357\) 0 0
\(358\) −6.34644 + 3.66412i −0.335420 + 0.193655i
\(359\) 23.5734i 1.24415i −0.782956 0.622077i \(-0.786289\pi\)
0.782956 0.622077i \(-0.213711\pi\)
\(360\) 0 0
\(361\) −1.40844 + 2.43948i −0.0741282 + 0.128394i
\(362\) −16.9510 9.78668i −0.890926 0.514377i
\(363\) 0 0
\(364\) 7.43230 + 3.85848i 0.389558 + 0.202239i
\(365\) 13.5734 0.710462
\(366\) 0 0
\(367\) −13.7454 + 23.8078i −0.717506 + 1.24276i 0.244479 + 0.969655i \(0.421383\pi\)
−0.961985 + 0.273103i \(0.911950\pi\)
\(368\) 2.46797 + 4.27464i 0.128652 + 0.222831i
\(369\) 0 0
\(370\) 2.72733 1.57463i 0.141787 0.0818609i
\(371\) −11.0365 + 6.37191i −0.572985 + 0.330813i
\(372\) 0 0
\(373\) −13.1710 22.8129i −0.681971 1.18121i −0.974379 0.224914i \(-0.927790\pi\)
0.292408 0.956294i \(-0.405544\pi\)
\(374\) −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
\(378\) 0 0
\(379\) 0.388456 + 0.224275i 0.0199537 + 0.0115202i 0.509944 0.860208i \(-0.329666\pi\)
−0.489990 + 0.871728i \(0.663000\pi\)
\(380\) 2.01141 3.48387i 0.103183 0.178719i
\(381\) 0 0
\(382\) 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 0
\(385\) 12.4151i 0.632734i
\(386\) 3.07746 + 5.33031i 0.156638 + 0.271306i
\(387\) 0 0
\(388\) −13.9510 8.05463i −0.708256 0.408912i
\(389\) −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
\(392\) −1.39051 0.802812i −0.0702314 0.0405481i
\(393\) 0 0
\(394\) 6.89334 + 11.9396i 0.347281 + 0.601509i
\(395\) 7.96774i 0.400900i
\(396\) 0 0
\(397\) 9.78970 5.65208i 0.491331 0.283670i −0.233796 0.972286i \(-0.575115\pi\)
0.725126 + 0.688616i \(0.241781\pi\)
\(398\) 2.28304i 0.114439i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 1.30406 + 0.752899i 0.0651216 + 0.0375980i 0.532207 0.846614i \(-0.321363\pi\)
−0.467086 + 0.884212i \(0.654696\pi\)
\(402\) 0 0
\(403\) −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
\(408\) 0 0
\(409\) 9.64697 5.56968i 0.477012 0.275403i −0.242158 0.970237i \(-0.577855\pi\)
0.719170 + 0.694834i \(0.244522\pi\)
\(410\) 2.29078 1.32258i 0.113133 0.0653176i
\(411\) 0 0
\(412\) −2.39806 4.15356i −0.118144 0.204631i
\(413\) 7.88130 13.6508i 0.387814 0.671713i
\(414\) 0 0
\(415\) −11.3360 −0.556461
\(416\) 3.03873 1.94065i 0.148986 0.0951483i
\(417\) 0 0
\(418\) 18.6227 + 10.7518i 0.910866 + 0.525889i
\(419\) −7.75488 + 13.4318i −0.378851 + 0.656188i −0.990895 0.134635i \(-0.957014\pi\)
0.612045 + 0.790823i \(0.290347\pi\)
\(420\) 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
\(423\) 0 0
\(424\) 5.48693i 0.266469i
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0 0
\(427\) 1.07791 + 0.622333i 0.0521639 + 0.0301168i
\(428\) 3.07180 0.148481
\(429\) 0 0
\(430\) −12.2508 −0.590785
\(431\) −1.86621 1.07746i −0.0898921 0.0518993i 0.454380 0.890808i \(-0.349861\pi\)
−0.544272 + 0.838909i \(0.683194\pi\)
\(432\) 0 0
\(433\) 0.669689 + 1.15994i 0.0321832 + 0.0557429i 0.881668 0.471870i \(-0.156421\pi\)
−0.849485 + 0.527612i \(0.823087\pi\)
\(434\) 8.06361i 0.387066i
\(435\) 0 0
\(436\) 5.79441 3.34541i 0.277502 0.160216i
\(437\) 19.8564i 0.949861i
\(438\) 0 0
\(439\) −15.8490 + 27.4513i −0.756434 + 1.31018i 0.188225 + 0.982126i \(0.439727\pi\)
−0.944658 + 0.328055i \(0.893607\pi\)
\(440\) 4.62926 + 2.67270i 0.220691 + 0.127416i
\(441\) 0 0
\(442\) 0.645159 + 14.4078i 0.0306871 + 0.685308i
\(443\) 28.0904 1.33461 0.667307 0.744782i \(-0.267447\pi\)
0.667307 + 0.744782i \(0.267447\pi\)
\(444\) 0 0
\(445\) −0.869891 + 1.50670i −0.0412368 + 0.0714242i
\(446\) 0.689457 + 1.19417i 0.0326467 + 0.0565458i
\(447\) 0 0
\(448\) 2.01141 1.16129i 0.0950303 0.0548658i
\(449\) −25.0426 + 14.4583i −1.18183 + 0.682332i −0.956438 0.291936i \(-0.905701\pi\)
−0.225395 + 0.974267i \(0.572367\pi\)
\(450\) 0 0
\(451\) 7.06973 + 12.2451i 0.332900 + 0.576600i
\(452\) 3.55486 6.15720i 0.167206 0.289610i
\(453\) 0 0
\(454\) 19.3205 0.906756
\(455\) 4.50732 + 7.05769i 0.211306 + 0.330870i
\(456\) 0 0
\(457\) 8.39958 + 4.84950i 0.392916 + 0.226850i 0.683423 0.730023i \(-0.260491\pi\)
−0.290507 + 0.956873i \(0.593824\pi\)
\(458\) 7.88130 13.6508i 0.368269 0.637861i
\(459\) 0 0
\(460\) 4.93593i 0.230139i
\(461\) −10.3905 + 5.99896i −0.483934 + 0.279400i −0.722055 0.691836i \(-0.756802\pi\)
0.238120 + 0.971236i \(0.423469\pi\)
\(462\) 0 0
\(463\) 6.42664i 0.298671i 0.988787 + 0.149336i \(0.0477135\pi\)
−0.988787 + 0.149336i \(0.952287\pi\)
\(464\) 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 \(0.707900\pi\)
\(468\) 0 0
\(469\) −9.54409 −0.440705
\(470\) −1.57525 0.909471i −0.0726609 0.0419508i
\(471\) 0 0
\(472\) −3.39334 5.87744i −0.156191 0.270531i
\(473\) 65.4854i 3.01102i
\(474\) 0 0
\(475\) 3.48387 2.01141i 0.159851 0.0922900i
\(476\) 9.29032i 0.425821i
\(477\) 0 0
\(478\) 13.1003 22.6904i 0.599193 1.03783i
\(479\) 22.2418 + 12.8413i 1.01625 + 0.586735i 0.913017 0.407922i \(-0.133747\pi\)
0.103237 + 0.994657i \(0.467080\pi\)
\(480\) 0 0
\(481\) 10.0777 + 5.23182i 0.459502 + 0.238551i
\(482\) −15.6496 −0.712818
\(483\) 0 0
\(484\) −8.78668 + 15.2190i −0.399395 + 0.691772i
\(485\) −8.05463 13.9510i −0.365742 0.633484i
\(486\) 0 0
\(487\) −8.12238 + 4.68946i −0.368060 + 0.212500i −0.672611 0.739997i \(-0.734827\pi\)
0.304551 + 0.952496i \(0.401494\pi\)
\(488\) 0.464102 0.267949i 0.0210089 0.0121295i
\(489\) 0 0
\(490\) −0.802812 1.39051i −0.0362673 0.0628169i
\(491\) 3.86927 6.70177i 0.174618 0.302447i −0.765411 0.643541i \(-0.777464\pi\)
0.940029 + 0.341095i \(0.110798\pi\)
\(492\) 0 0
\(493\) −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
\(498\) 0 0
\(499\) 3.18106i 0.142404i 0.997462 + 0.0712019i \(0.0226834\pi\)
−0.997462 + 0.0712019i \(0.977317\pi\)
\(500\) 0.866025 0.500000i 0.0387298 0.0223607i
\(501\) 0 0
\(502\) 28.3416i 1.26495i
\(503\) −17.5379 30.3765i −0.781975 1.35442i −0.930789 0.365556i \(-0.880879\pi\)
0.148814 0.988865i \(-0.452454\pi\)
\(504\) 0 0
\(505\) −10.9906 6.34541i −0.489074 0.282367i
\(506\) −26.3846 −1.17294
\(507\) 0 0
\(508\) −2.13209 −0.0945961
\(509\) 16.2697 + 9.39334i 0.721144 + 0.416353i 0.815173 0.579217i \(-0.196642\pi\)
−0.0940298 + 0.995569i \(0.529975\pi\)
\(510\) 0 0
\(511\) 15.7626 + 27.3016i 0.697297 + 1.20775i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 10.8334 6.25465i 0.477839 0.275881i
\(515\) 4.79612i 0.211342i
\(516\) 0 0
\(517\) 4.86149 8.42035i 0.213808 0.370327i
\(518\) 6.33445 + 3.65720i 0.278320 + 0.160688i
\(519\) 0 0
\(520\) 3.60194 0.161290i 0.157956 0.00707303i
\(521\) −5.28512 −0.231545 −0.115773 0.993276i \(-0.536934\pi\)
−0.115773 + 0.993276i \(0.536934\pi\)
\(522\) 0 0
\(523\) 10.3762 17.9721i 0.453718 0.785863i −0.544895 0.838504i \(-0.683431\pi\)
0.998614 + 0.0526409i \(0.0167639\pi\)
\(524\) −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
\(528\) 0 0
\(529\) −0.681725 1.18078i −0.0296402 0.0513384i
\(530\) −2.74346 + 4.75182i −0.119168 + 0.206406i
\(531\) 0 0
\(532\) 9.34333 0.405085
\(533\) 8.46456 + 4.39438i 0.366641 + 0.190342i
\(534\) 0 0
\(535\) 2.66025 + 1.53590i 0.115013 + 0.0664027i
\(536\) −2.05463 + 3.55872i −0.0887465 + 0.153713i
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) 3.46410 + 2.00000i 0.148522 + 0.0857493i
\(545\) 6.69081 0.286603
\(546\) 0 0
\(547\) 18.3768 0.785737 0.392869 0.919595i \(-0.371483\pi\)
0.392869 + 0.919595i \(0.371483\pi\)
\(548\) −17.0736 9.85744i −0.729348 0.421089i
\(549\) 0 0
\(550\) 2.67270 + 4.62926i 0.113964 + 0.197392i
\(551\) 17.2610i 0.735345i
\(552\) 0 0
\(553\) 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 \(0.856726\pi\)
\(558\) 0 0
\(559\) −23.7745 37.2268i −1.00555 1.57453i
\(560\) 2.32258 0.0981469
\(561\) 0 0
\(562\) −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 \(0.792567\pi\)
\(564\) 0 0
\(565\) 6.15720 3.55486i 0.259035 0.149554i
\(566\) 19.0642 11.0067i 0.801326 0.462646i
\(567\) 0 0
\(568\) −7.93593 13.7454i −0.332984 0.576746i
\(569\) 7.24818 12.5542i 0.303860 0.526300i −0.673147 0.739509i \(-0.735058\pi\)
0.977007 + 0.213208i \(0.0683913\pi\)
\(570\) 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
\(573\) 0 0
\(574\) 5.32051 + 3.07180i 0.222074 + 0.128214i
\(575\) −2.46797 + 4.27464i −0.102921 + 0.178265i
\(576\) 0 0
\(577\) 18.8180i 0.783405i −0.920092 0.391702i \(-0.871886\pi\)
0.920092 0.391702i \(-0.128114\pi\)
\(578\) 0.866025 0.500000i 0.0360219 0.0207973i
\(579\) 0 0
\(580\) 4.29078i 0.178165i
\(581\) −13.1643 22.8013i −0.546149 0.945958i
\(582\) 0 0
\(583\) −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 0
\(589\) −6.98329 12.0954i −0.287741 0.498383i
\(590\) 6.78668i 0.279403i
\(591\) 0 0
\(592\) 2.72733 1.57463i 0.112093 0.0647168i
\(593\) 20.1227i 0.826338i −0.910654 0.413169i \(-0.864422\pi\)
0.910654 0.413169i \(-0.135578\pi\)
\(594\) 0 0
\(595\) −4.64516 + 8.04565i −0.190433 + 0.329840i
\(596\) 16.8680 + 9.73875i 0.690940 + 0.398915i
\(597\) 0 0
\(598\) −14.9990 + 9.57893i −0.613353 + 0.391712i
\(599\) −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 −0.819517 0.573054i \(-0.805758\pi\)
0.906038 + 0.423196i \(0.139092\pi\)
\(602\) −14.2267 24.6414i −0.579837 1.00431i
\(603\) 0 0
\(604\) −12.5721 + 7.25851i −0.511552 + 0.295345i
\(605\) −15.2190 + 8.78668i −0.618739 + 0.357229i
\(606\) 0 0
\(607\) −6.03424 10.4516i −0.244922 0.424218i 0.717188 0.696880i \(-0.245429\pi\)
−0.962110 + 0.272663i \(0.912096\pi\)
\(608\) 2.01141 3.48387i 0.0815736 0.141290i
\(609\) 0 0
\(610\) 0.535898 0.0216979
\(611\) −0.293377 6.55172i −0.0118688 0.265054i
\(612\) 0 0
\(613\) 36.1497 + 20.8711i 1.46007 + 0.842974i 0.999014 0.0443946i \(-0.0141359\pi\)
0.461060 + 0.887369i \(0.347469\pi\)
\(614\) 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 \(0.0981249\pi\)
\(618\) 0 0
\(619\) 38.0978i 1.53128i 0.643270 + 0.765639i \(0.277577\pi\)
−0.643270 + 0.765639i \(0.722423\pi\)
\(620\) −1.73592 3.00670i −0.0697161 0.120752i
\(621\) 0 0
\(622\) −1.67696 0.968196i −0.0672401 0.0388211i
\(623\) −4.04078 −0.161891
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 22.1308 + 12.7772i 0.884526 + 0.510681i
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) −6.33337 + 10.9697i −0.251530 + 0.435663i
\(635\) −1.84644 1.06604i −0.0732738 0.0423046i
\(636\) 0 0
\(637\) 2.66741 5.13802i 0.105686 0.203576i
\(638\) −22.9359 −0.908042
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −2.04259 3.53788i −0.0806776 0.139738i 0.822864 0.568239i \(-0.192375\pi\)
−0.903541 + 0.428501i \(0.859042\pi\)
\(642\) 0 0
\(643\) −31.6806 + 18.2908i −1.24936 + 0.721318i −0.970982 0.239154i \(-0.923130\pi\)
−0.278377 + 0.960472i \(0.589797\pi\)
\(644\) −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 0
\(649\) 36.2776 1.42402
\(650\) 3.20002 + 1.66129i 0.125515 + 0.0651611i
\(651\) 0 0
\(652\) 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 \(0.307816\pi\)
\(654\) 0 0
\(655\) 1.25851i 0.0491742i
\(656\) 2.29078 1.32258i 0.0894397 0.0516381i
\(657\) 0 0
\(658\) 4.22464i 0.164694i
\(659\) −24.2379 41.9813i −0.944176 1.63536i −0.757393 0.652960i \(-0.773527\pi\)
−0.186783 0.982401i \(-0.559806\pi\)
\(660\) 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
\(663\) 0 0
\(664\) −11.3360 −0.439921
\(665\) 8.09156 + 4.67167i 0.313777 + 0.181159i
\(666\) 0 0
\(667\) −10.5895 18.3415i −0.410027 0.710187i
\(668\) 16.7471i 0.647967i
\(669\) 0 0
\(670\) −3.55872 + 2.05463i −0.137486 + 0.0793773i
\(671\) 2.86459i 0.110586i
\(672\) 0 0
\(673\) −15.3360 + 26.5627i −0.591158 + 1.02392i 0.402919 + 0.915236i \(0.367996\pi\)
−0.994077 + 0.108680i \(0.965338\pi\)
\(674\) 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 \(0.632779\pi\)
\(678\) 0 0
\(679\) 18.7075 32.4024i 0.717929 1.24349i
\(680\) 2.00000 + 3.46410i 0.0766965 + 0.132842i
\(681\) 0 0
\(682\) 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 \(0.251211\pi\)
\(684\) 0 0
\(685\) −9.85744 17.0736i −0.376634 0.652348i
\(686\) 9.99362 17.3095i 0.381558 0.660878i
\(687\) 0 0
\(688\) −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
\(693\) 0 0
\(694\) 23.0375i 0.874490i
\(695\) 4.91679 2.83871i 0.186504 0.107678i
\(696\) 0 0
\(697\) 10.5806i 0.400770i
\(698\) 7.66025 + 13.2679i 0.289945 + 0.502199i
\(699\) 0 0
\(700\) 2.01141 + 1.16129i 0.0760243 + 0.0438926i
\(701\) −39.6715 −1.49837 −0.749186 0.662360i \(-0.769555\pi\)
−0.749186 + 0.662360i \(0.769555\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) 2.45467 1.41720i 0.0921869 0.0532242i −0.453198 0.891410i \(-0.649717\pi\)
0.545385 + 0.838186i \(0.316384\pi\)
\(710\) 15.8719i 0.595661i
\(711\) 0 0
\(712\) −0.869891 + 1.50670i −0.0326005 + 0.0564658i
\(713\) 14.8409 + 8.56837i 0.555794 + 0.320888i
\(714\) 0 0
\(715\) −8.88027 + 17.1054i −0.332103 + 0.639706i
\(716\) −7.32824 −0.273869
\(717\) 0 0
\(718\) 11.7867 20.4151i 0.439875 0.761886i
\(719\) 21.8564 + 37.8564i 0.815106 + 1.41181i 0.909251 + 0.416247i \(0.136655\pi\)
−0.0941451 + 0.995558i \(0.530012\pi\)
\(720\) 0 0
\(721\) 9.64697 5.56968i 0.359272 0.207426i
\(722\) −2.43948 + 1.40844i −0.0907881 + 0.0524165i
\(723\) 0 0
\(724\) −9.78668 16.9510i −0.363719 0.629980i
\(725\) −2.14539 + 3.71592i −0.0796777 + 0.138006i
\(726\) 0 0
\(727\) −16.2568 −0.602932 −0.301466 0.953477i \(-0.597476\pi\)
−0.301466 + 0.953477i \(0.597476\pi\)
\(728\) 4.50732 + 7.05769i 0.167052 + 0.261575i
\(729\) 0 0
\(730\) 11.7549 + 6.78668i 0.435068 + 0.251186i
\(731\) 24.5016 42.4380i 0.906223 1.56962i
\(732\) 0 0
\(733\) 4.96774i 0.183488i 0.995783 + 0.0917438i \(0.0292441\pi\)
−0.995783 + 0.0917438i \(0.970756\pi\)
\(734\) −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
\(738\) 0 0
\(739\) 43.0306 + 24.8437i 1.58291 + 0.913892i 0.994432 + 0.105377i \(0.0336048\pi\)
0.588475 + 0.808515i \(0.299729\pi\)
\(740\) 3.14925 0.115769
\(741\) 0 0
\(742\) −12.7438 −0.467841
\(743\) −18.6559 10.7710i −0.684420 0.395150i 0.117098 0.993120i \(-0.462641\pi\)
−0.801518 + 0.597970i \(0.795974\pi\)
\(744\) 0 0
\(745\) 9.73875 + 16.8680i 0.356800 + 0.617996i
\(746\) 26.3421i 0.964452i
\(747\) 0 0
\(748\) −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
\(753\) 0 0
\(754\) −13.0385 + 8.32690i −0.474834 + 0.303248i
\(755\) −14.5170 −0.528329
\(756\) 0 0
\(757\) 24.0554 41.6651i 0.874307 1.51434i 0.0168078 0.999859i \(-0.494650\pi\)
0.857499 0.514485i \(-0.172017\pi\)
\(758\) 0.224275 + 0.388456i 0.00814604 + 0.0141094i
\(759\) 0 0
\(760\) 3.48387 2.01141i 0.126373 0.0729616i
\(761\) −29.1734 + 16.8433i −1.05754 + 0.610569i −0.924750 0.380576i \(-0.875726\pi\)
−0.132786 + 0.991145i \(0.542392\pi\)
\(762\) 0 0
\(763\) 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
\(768\) 0 0
\(769\) −5.18651 2.99443i −0.187030 0.107982i 0.403561 0.914953i \(-0.367772\pi\)
−0.590592 + 0.806971i \(0.701106\pi\)
\(770\) −6.20757 + 10.7518i −0.223705 + 0.387469i
\(771\) 0 0
\(772\) 6.15491i 0.221520i
\(773\) −11.6811 + 6.74409i −0.420140 + 0.242568i −0.695137 0.718877i \(-0.744656\pi\)
0.274997 + 0.961445i \(0.411323\pi\)
\(774\) 0 0
\(775\) 3.47183i 0.124712i
\(776\) −8.05463 13.9510i −0.289144 0.500813i
\(777\) 0 0
\(778\) −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
\(783\) 0 0
\(784\) −0.802812 1.39051i −0.0286718 0.0496611i
\(785\) 24.3829i 0.870262i
\(786\) 0 0
\(787\) −47.3272 + 27.3244i −1.68703 + 0.974009i −0.730261 + 0.683168i \(0.760602\pi\)
−0.956772 + 0.290841i \(0.906065\pi\)
\(788\) 13.7867i 0.491130i
\(789\) 0 0