Properties

Label 690.2.j.b.643.5
Level $690$
Weight $2$
Character 690.643
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 643.5
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.b.367.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.07661 + 1.95982i) q^{5} +1.00000 q^{6} +(-3.43458 - 3.43458i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.07661 + 1.95982i) q^{5} +1.00000 q^{6} +(-3.43458 - 3.43458i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-2.14708 - 0.624526i) q^{10} +1.77870i q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.21834 + 1.21834i) q^{13} +4.85722 q^{14} +(0.624526 - 2.14708i) q^{15} -1.00000 q^{16} +(1.12442 + 1.12442i) q^{17} +(-0.707107 - 0.707107i) q^{18} +2.57499 q^{19} +(1.95982 - 1.07661i) q^{20} +4.85722i q^{21} +(-1.25773 - 1.25773i) q^{22} +(-0.510395 + 4.76859i) q^{23} -1.00000i q^{24} +(-2.68182 + 4.21993i) q^{25} -1.72299 q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.43458 + 3.43458i) q^{28} +3.23574i q^{29} +(1.07661 + 1.95982i) q^{30} +6.41786 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.25773 - 1.25773i) q^{33} -1.59016 q^{34} +(3.03346 - 10.4289i) q^{35} +1.00000 q^{36} +(-0.321856 - 0.321856i) q^{37} +(-1.82079 + 1.82079i) q^{38} -1.72299i q^{39} +(-0.624526 + 2.14708i) q^{40} +10.2290 q^{41} +(-3.43458 - 3.43458i) q^{42} +(-6.47101 + 6.47101i) q^{43} +1.77870 q^{44} +(-1.95982 + 1.07661i) q^{45} +(-3.01100 - 3.73281i) q^{46} +(9.10509 - 9.10509i) q^{47} +(0.707107 + 0.707107i) q^{48} +16.5926i q^{49} +(-1.08761 - 4.88028i) q^{50} -1.59016i q^{51} +(1.21834 - 1.21834i) q^{52} +(-6.42643 + 6.42643i) q^{53} +1.00000i q^{54} +(-3.48594 + 1.91497i) q^{55} -4.85722i q^{56} +(-1.82079 - 1.82079i) q^{57} +(-2.28801 - 2.28801i) q^{58} +10.4081i q^{59} +(-2.14708 - 0.624526i) q^{60} +14.4727i q^{61} +(-4.53812 + 4.53812i) q^{62} +(3.43458 - 3.43458i) q^{63} +1.00000i q^{64} +(-1.07605 + 3.69940i) q^{65} +1.77870i q^{66} +(-0.586681 - 0.586681i) q^{67} +(1.12442 - 1.12442i) q^{68} +(3.73281 - 3.01100i) q^{69} +(5.22934 + 9.51930i) q^{70} -13.3156 q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.84689 + 3.84689i) q^{73} +0.455173 q^{74} +(4.88028 - 1.08761i) q^{75} -2.57499i q^{76} +(6.10909 - 6.10909i) q^{77} +(1.21834 + 1.21834i) q^{78} +6.55768 q^{79} +(-1.07661 - 1.95982i) q^{80} -1.00000 q^{81} +(-7.23299 + 7.23299i) q^{82} +(2.56461 - 2.56461i) q^{83} +4.85722 q^{84} +(-0.993099 + 3.41421i) q^{85} -9.15139i q^{86} +(2.28801 - 2.28801i) q^{87} +(-1.25773 + 1.25773i) q^{88} +3.44952 q^{89} +(0.624526 - 2.14708i) q^{90} -8.36895i q^{91} +(4.76859 + 0.510395i) q^{92} +(-4.53812 - 4.53812i) q^{93} +12.8765i q^{94} +(2.77226 + 5.04652i) q^{95} -1.00000 q^{96} +(-7.79375 - 7.79375i) q^{97} +(-11.7328 - 11.7328i) q^{98} -1.77870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{6} + O(q^{10}) \) \( 24q + 24q^{6} + 16q^{13} - 24q^{16} + 16q^{23} - 16q^{25} + 16q^{31} + 24q^{36} + 8q^{46} + 40q^{47} - 8q^{50} + 16q^{52} - 56q^{55} - 16q^{58} - 8q^{62} + 32q^{70} + 64q^{71} - 16q^{73} + 32q^{75} + 16q^{77} + 16q^{78} - 24q^{81} + 24q^{82} - 48q^{85} + 16q^{87} + 16q^{92} - 8q^{93} + 24q^{95} - 24q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 1.07661 + 1.95982i 0.481475 + 0.876460i
\(6\) 1.00000 0.408248
\(7\) −3.43458 3.43458i −1.29815 1.29815i −0.929615 0.368533i \(-0.879860\pi\)
−0.368533 0.929615i \(-0.620140\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −2.14708 0.624526i −0.678967 0.197492i
\(11\) 1.77870i 0.536299i 0.963377 + 0.268149i \(0.0864121\pi\)
−0.963377 + 0.268149i \(0.913588\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 1.21834 + 1.21834i 0.337906 + 0.337906i 0.855579 0.517673i \(-0.173202\pi\)
−0.517673 + 0.855579i \(0.673202\pi\)
\(14\) 4.85722 1.29815
\(15\) 0.624526 2.14708i 0.161252 0.554375i
\(16\) −1.00000 −0.250000
\(17\) 1.12442 + 1.12442i 0.272711 + 0.272711i 0.830191 0.557480i \(-0.188232\pi\)
−0.557480 + 0.830191i \(0.688232\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 2.57499 0.590742 0.295371 0.955383i \(-0.404557\pi\)
0.295371 + 0.955383i \(0.404557\pi\)
\(20\) 1.95982 1.07661i 0.438230 0.240737i
\(21\) 4.85722i 1.05993i
\(22\) −1.25773 1.25773i −0.268149 0.268149i
\(23\) −0.510395 + 4.76859i −0.106425 + 0.994321i
\(24\) 1.00000i 0.204124i
\(25\) −2.68182 + 4.21993i −0.536364 + 0.843987i
\(26\) −1.72299 −0.337906
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −3.43458 + 3.43458i −0.649074 + 0.649074i
\(29\) 3.23574i 0.600862i 0.953804 + 0.300431i \(0.0971305\pi\)
−0.953804 + 0.300431i \(0.902870\pi\)
\(30\) 1.07661 + 1.95982i 0.196561 + 0.357813i
\(31\) 6.41786 1.15268 0.576341 0.817209i \(-0.304480\pi\)
0.576341 + 0.817209i \(0.304480\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 1.25773 1.25773i 0.218943 0.218943i
\(34\) −1.59016 −0.272711
\(35\) 3.03346 10.4289i 0.512749 1.76280i
\(36\) 1.00000 0.166667
\(37\) −0.321856 0.321856i −0.0529127 0.0529127i 0.680155 0.733068i \(-0.261912\pi\)
−0.733068 + 0.680155i \(0.761912\pi\)
\(38\) −1.82079 + 1.82079i −0.295371 + 0.295371i
\(39\) 1.72299i 0.275899i
\(40\) −0.624526 + 2.14708i −0.0987462 + 0.339484i
\(41\) 10.2290 1.59750 0.798750 0.601663i \(-0.205495\pi\)
0.798750 + 0.601663i \(0.205495\pi\)
\(42\) −3.43458 3.43458i −0.529967 0.529967i
\(43\) −6.47101 + 6.47101i −0.986820 + 0.986820i −0.999914 0.0130943i \(-0.995832\pi\)
0.0130943 + 0.999914i \(0.495832\pi\)
\(44\) 1.77870 0.268149
\(45\) −1.95982 + 1.07661i −0.292153 + 0.160492i
\(46\) −3.01100 3.73281i −0.443948 0.550373i
\(47\) 9.10509 9.10509i 1.32811 1.32811i 0.421100 0.907014i \(-0.361644\pi\)
0.907014 0.421100i \(-0.138356\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 16.5926i 2.37038i
\(50\) −1.08761 4.88028i −0.153812 0.690175i
\(51\) 1.59016i 0.222667i
\(52\) 1.21834 1.21834i 0.168953 0.168953i
\(53\) −6.42643 + 6.42643i −0.882738 + 0.882738i −0.993812 0.111074i \(-0.964571\pi\)
0.111074 + 0.993812i \(0.464571\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −3.48594 + 1.91497i −0.470044 + 0.258214i
\(56\) 4.85722i 0.649074i
\(57\) −1.82079 1.82079i −0.241170 0.241170i
\(58\) −2.28801 2.28801i −0.300431 0.300431i
\(59\) 10.4081i 1.35502i 0.735514 + 0.677510i \(0.236941\pi\)
−0.735514 + 0.677510i \(0.763059\pi\)
\(60\) −2.14708 0.624526i −0.277187 0.0806260i
\(61\) 14.4727i 1.85303i 0.376252 + 0.926517i \(0.377213\pi\)
−0.376252 + 0.926517i \(0.622787\pi\)
\(62\) −4.53812 + 4.53812i −0.576341 + 0.576341i
\(63\) 3.43458 3.43458i 0.432716 0.432716i
\(64\) 1.00000i 0.125000i
\(65\) −1.07605 + 3.69940i −0.133468 + 0.458854i
\(66\) 1.77870i 0.218943i
\(67\) −0.586681 0.586681i −0.0716745 0.0716745i 0.670361 0.742035i \(-0.266139\pi\)
−0.742035 + 0.670361i \(0.766139\pi\)
\(68\) 1.12442 1.12442i 0.136355 0.136355i
\(69\) 3.73281 3.01100i 0.449377 0.362482i
\(70\) 5.22934 + 9.51930i 0.625026 + 1.13777i
\(71\) −13.3156 −1.58027 −0.790137 0.612931i \(-0.789990\pi\)
−0.790137 + 0.612931i \(0.789990\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) 3.84689 + 3.84689i 0.450245 + 0.450245i 0.895436 0.445191i \(-0.146864\pi\)
−0.445191 + 0.895436i \(0.646864\pi\)
\(74\) 0.455173 0.0529127
\(75\) 4.88028 1.08761i 0.563526 0.125587i
\(76\) 2.57499i 0.295371i
\(77\) 6.10909 6.10909i 0.696195 0.696195i
\(78\) 1.21834 + 1.21834i 0.137950 + 0.137950i
\(79\) 6.55768 0.737796 0.368898 0.929470i \(-0.379735\pi\)
0.368898 + 0.929470i \(0.379735\pi\)
\(80\) −1.07661 1.95982i −0.120369 0.219115i
\(81\) −1.00000 −0.111111
\(82\) −7.23299 + 7.23299i −0.798750 + 0.798750i
\(83\) 2.56461 2.56461i 0.281502 0.281502i −0.552206 0.833708i \(-0.686214\pi\)
0.833708 + 0.552206i \(0.186214\pi\)
\(84\) 4.85722 0.529967
\(85\) −0.993099 + 3.41421i −0.107717 + 0.370323i
\(86\) 9.15139i 0.986820i
\(87\) 2.28801 2.28801i 0.245301 0.245301i
\(88\) −1.25773 + 1.25773i −0.134075 + 0.134075i
\(89\) 3.44952 0.365648 0.182824 0.983146i \(-0.441476\pi\)
0.182824 + 0.983146i \(0.441476\pi\)
\(90\) 0.624526 2.14708i 0.0658308 0.226322i
\(91\) 8.36895i 0.877304i
\(92\) 4.76859 + 0.510395i 0.497160 + 0.0532123i
\(93\) −4.53812 4.53812i −0.470581 0.470581i
\(94\) 12.8765i 1.32811i
\(95\) 2.77226 + 5.04652i 0.284428 + 0.517762i
\(96\) −1.00000 −0.102062
\(97\) −7.79375 7.79375i −0.791335 0.791335i 0.190376 0.981711i \(-0.439029\pi\)
−0.981711 + 0.190376i \(0.939029\pi\)
\(98\) −11.7328 11.7328i −1.18519 1.18519i
\(99\) −1.77870 −0.178766
\(100\) 4.21993 + 2.68182i 0.421993 + 0.268182i
\(101\) 0.109089 0.0108547 0.00542736 0.999985i \(-0.498272\pi\)
0.00542736 + 0.999985i \(0.498272\pi\)
\(102\) 1.12442 + 1.12442i 0.111334 + 0.111334i
\(103\) 0.451663 0.451663i 0.0445037 0.0445037i −0.684505 0.729008i \(-0.739981\pi\)
0.729008 + 0.684505i \(0.239981\pi\)
\(104\) 1.72299i 0.168953i
\(105\) −9.51930 + 5.22934i −0.928989 + 0.510331i
\(106\) 9.08835i 0.882738i
\(107\) 5.06879 + 5.06879i 0.490018 + 0.490018i 0.908312 0.418293i \(-0.137372\pi\)
−0.418293 + 0.908312i \(0.637372\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −7.67531 −0.735161 −0.367581 0.929992i \(-0.619814\pi\)
−0.367581 + 0.929992i \(0.619814\pi\)
\(110\) 1.11085 3.81902i 0.105915 0.364129i
\(111\) 0.455173i 0.0432031i
\(112\) 3.43458 + 3.43458i 0.324537 + 0.324537i
\(113\) 10.3565 10.3565i 0.974254 0.974254i −0.0254229 0.999677i \(-0.508093\pi\)
0.999677 + 0.0254229i \(0.00809325\pi\)
\(114\) 2.57499 0.241170
\(115\) −9.89510 + 4.13364i −0.922723 + 0.385464i
\(116\) 3.23574 0.300431
\(117\) −1.21834 + 1.21834i −0.112635 + 0.112635i
\(118\) −7.35964 7.35964i −0.677510 0.677510i
\(119\) 7.72378i 0.708038i
\(120\) 1.95982 1.07661i 0.178907 0.0982807i
\(121\) 7.83622 0.712384
\(122\) −10.2337 10.2337i −0.926517 0.926517i
\(123\) −7.23299 7.23299i −0.652177 0.652177i
\(124\) 6.41786i 0.576341i
\(125\) −11.1576 0.712667i −0.997966 0.0637429i
\(126\) 4.85722i 0.432716i
\(127\) 8.30451 8.30451i 0.736906 0.736906i −0.235072 0.971978i \(-0.575533\pi\)
0.971978 + 0.235072i \(0.0755326\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 9.15139 0.805735
\(130\) −1.85499 3.37676i −0.162693 0.296161i
\(131\) −12.6605 −1.10615 −0.553077 0.833130i \(-0.686546\pi\)
−0.553077 + 0.833130i \(0.686546\pi\)
\(132\) −1.25773 1.25773i −0.109472 0.109472i
\(133\) −8.84399 8.84399i −0.766871 0.766871i
\(134\) 0.829692 0.0716745
\(135\) 2.14708 + 0.624526i 0.184792 + 0.0537506i
\(136\) 1.59016i 0.136355i
\(137\) 1.04108 + 1.04108i 0.0889456 + 0.0889456i 0.750180 0.661234i \(-0.229967\pi\)
−0.661234 + 0.750180i \(0.729967\pi\)
\(138\) −0.510395 + 4.76859i −0.0434477 + 0.405930i
\(139\) 8.89535i 0.754494i −0.926113 0.377247i \(-0.876871\pi\)
0.926113 0.377247i \(-0.123129\pi\)
\(140\) −10.4289 3.03346i −0.881400 0.256374i
\(141\) −12.8765 −1.08440
\(142\) 9.41557 9.41557i 0.790137 0.790137i
\(143\) −2.16706 + 2.16706i −0.181219 + 0.181219i
\(144\) 1.00000i 0.0833333i
\(145\) −6.34148 + 3.48363i −0.526631 + 0.289300i
\(146\) −5.44033 −0.450245
\(147\) 11.7328 11.7328i 0.967702 0.967702i
\(148\) −0.321856 + 0.321856i −0.0264564 + 0.0264564i
\(149\) 11.3358 0.928666 0.464333 0.885661i \(-0.346294\pi\)
0.464333 + 0.885661i \(0.346294\pi\)
\(150\) −2.68182 + 4.21993i −0.218970 + 0.344556i
\(151\) −8.75190 −0.712219 −0.356110 0.934444i \(-0.615897\pi\)
−0.356110 + 0.934444i \(0.615897\pi\)
\(152\) 1.82079 + 1.82079i 0.147686 + 0.147686i
\(153\) −1.12442 + 1.12442i −0.0909036 + 0.0909036i
\(154\) 8.63956i 0.696195i
\(155\) 6.90954 + 12.5779i 0.554988 + 1.01028i
\(156\) −1.72299 −0.137950
\(157\) −14.2015 14.2015i −1.13340 1.13340i −0.989608 0.143791i \(-0.954071\pi\)
−0.143791 0.989608i \(-0.545929\pi\)
\(158\) −4.63698 + 4.63698i −0.368898 + 0.368898i
\(159\) 9.08835 0.720753
\(160\) 2.14708 + 0.624526i 0.169742 + 0.0493731i
\(161\) 18.1311 14.6251i 1.42893 1.15262i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −3.88265 3.88265i −0.304113 0.304113i 0.538508 0.842621i \(-0.318988\pi\)
−0.842621 + 0.538508i \(0.818988\pi\)
\(164\) 10.2290i 0.798750i
\(165\) 3.81902 + 1.11085i 0.297310 + 0.0864792i
\(166\) 3.62690i 0.281502i
\(167\) −6.37019 + 6.37019i −0.492940 + 0.492940i −0.909231 0.416291i \(-0.863330\pi\)
0.416291 + 0.909231i \(0.363330\pi\)
\(168\) −3.43458 + 3.43458i −0.264983 + 0.264983i
\(169\) 10.0313i 0.771639i
\(170\) −1.71199 3.11644i −0.131303 0.239020i
\(171\) 2.57499i 0.196914i
\(172\) 6.47101 + 6.47101i 0.493410 + 0.493410i
\(173\) 6.60779 + 6.60779i 0.502381 + 0.502381i 0.912177 0.409796i \(-0.134400\pi\)
−0.409796 + 0.912177i \(0.634400\pi\)
\(174\) 3.23574i 0.245301i
\(175\) 23.7046 5.28277i 1.79190 0.399340i
\(176\) 1.77870i 0.134075i
\(177\) 7.35964 7.35964i 0.553184 0.553184i
\(178\) −2.43918 + 2.43918i −0.182824 + 0.182824i
\(179\) 0.676121i 0.0505357i 0.999681 + 0.0252678i \(0.00804386\pi\)
−0.999681 + 0.0252678i \(0.991956\pi\)
\(180\) 1.07661 + 1.95982i 0.0802458 + 0.146077i
\(181\) 17.9595i 1.33492i −0.744647 0.667458i \(-0.767382\pi\)
0.744647 0.667458i \(-0.232618\pi\)
\(182\) 5.91774 + 5.91774i 0.438652 + 0.438652i
\(183\) 10.2337 10.2337i 0.756498 0.756498i
\(184\) −3.73281 + 3.01100i −0.275186 + 0.221974i
\(185\) 0.284267 0.977294i 0.0208997 0.0718521i
\(186\) 6.41786 0.470581
\(187\) −2.00000 + 2.00000i −0.146254 + 0.146254i
\(188\) −9.10509 9.10509i −0.664057 0.664057i
\(189\) −4.85722 −0.353311
\(190\) −5.52871 1.60815i −0.401095 0.116667i
\(191\) 12.7383i 0.921709i −0.887476 0.460855i \(-0.847543\pi\)
0.887476 0.460855i \(-0.152457\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −1.84399 1.84399i −0.132733 0.132733i 0.637619 0.770352i \(-0.279919\pi\)
−0.770352 + 0.637619i \(0.779919\pi\)
\(194\) 11.0220 0.791335
\(195\) 3.37676 1.85499i 0.241814 0.132838i
\(196\) 16.5926 1.18519
\(197\) −12.1629 + 12.1629i −0.866568 + 0.866568i −0.992091 0.125523i \(-0.959939\pi\)
0.125523 + 0.992091i \(0.459939\pi\)
\(198\) 1.25773 1.25773i 0.0893831 0.0893831i
\(199\) 5.37229 0.380832 0.190416 0.981704i \(-0.439016\pi\)
0.190416 + 0.981704i \(0.439016\pi\)
\(200\) −4.88028 + 1.08761i −0.345088 + 0.0769058i
\(201\) 0.829692i 0.0585219i
\(202\) −0.0771372 + 0.0771372i −0.00542736 + 0.00542736i
\(203\) 11.1134 11.1134i 0.780007 0.780007i
\(204\) −1.59016 −0.111334
\(205\) 11.0126 + 20.0470i 0.769156 + 1.40014i
\(206\) 0.638749i 0.0445037i
\(207\) −4.76859 0.510395i −0.331440 0.0354749i
\(208\) −1.21834 1.21834i −0.0844765 0.0844765i
\(209\) 4.58013i 0.316814i
\(210\) 3.03346 10.4289i 0.209329 0.719660i
\(211\) 8.05312 0.554400 0.277200 0.960812i \(-0.410594\pi\)
0.277200 + 0.960812i \(0.410594\pi\)
\(212\) 6.42643 + 6.42643i 0.441369 + 0.441369i
\(213\) 9.41557 + 9.41557i 0.645144 + 0.645144i
\(214\) −7.16835 −0.490018
\(215\) −19.6488 5.71528i −1.34004 0.389779i
\(216\) 1.00000 0.0680414
\(217\) −22.0426 22.0426i −1.49635 1.49635i
\(218\) 5.42726 5.42726i 0.367581 0.367581i
\(219\) 5.44033i 0.367623i
\(220\) 1.91497 + 3.48594i 0.129107 + 0.235022i
\(221\) 2.73983i 0.184301i
\(222\) −0.321856 0.321856i −0.0216015 0.0216015i
\(223\) 7.99544 + 7.99544i 0.535414 + 0.535414i 0.922179 0.386764i \(-0.126407\pi\)
−0.386764 + 0.922179i \(0.626407\pi\)
\(224\) −4.85722 −0.324537
\(225\) −4.21993 2.68182i −0.281329 0.178788i
\(226\) 14.6462i 0.974254i
\(227\) 13.1571 + 13.1571i 0.873268 + 0.873268i 0.992827 0.119559i \(-0.0381481\pi\)
−0.119559 + 0.992827i \(0.538148\pi\)
\(228\) −1.82079 + 1.82079i −0.120585 + 0.120585i
\(229\) 6.27877 0.414913 0.207456 0.978244i \(-0.433482\pi\)
0.207456 + 0.978244i \(0.433482\pi\)
\(230\) 4.07397 9.91982i 0.268630 0.654093i
\(231\) −8.63956 −0.568441
\(232\) −2.28801 + 2.28801i −0.150215 + 0.150215i
\(233\) 11.9743 + 11.9743i 0.784465 + 0.784465i 0.980581 0.196116i \(-0.0628329\pi\)
−0.196116 + 0.980581i \(0.562833\pi\)
\(234\) 1.72299i 0.112635i
\(235\) 27.6470 + 8.04174i 1.80349 + 0.524585i
\(236\) 10.4081 0.677510
\(237\) −4.63698 4.63698i −0.301204 0.301204i
\(238\) 5.46154 + 5.46154i 0.354019 + 0.354019i
\(239\) 4.39325i 0.284176i 0.989854 + 0.142088i \(0.0453816\pi\)
−0.989854 + 0.142088i \(0.954618\pi\)
\(240\) −0.624526 + 2.14708i −0.0403130 + 0.138594i
\(241\) 7.44107i 0.479321i −0.970857 0.239661i \(-0.922964\pi\)
0.970857 0.239661i \(-0.0770362\pi\)
\(242\) −5.54104 + 5.54104i −0.356192 + 0.356192i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 14.4727 0.926517
\(245\) −32.5186 + 17.8638i −2.07754 + 1.14128i
\(246\) 10.2290 0.652177
\(247\) 3.13720 + 3.13720i 0.199615 + 0.199615i
\(248\) 4.53812 + 4.53812i 0.288171 + 0.288171i
\(249\) −3.62690 −0.229845
\(250\) 8.39355 7.38569i 0.530855 0.467112i
\(251\) 12.7768i 0.806466i 0.915097 + 0.403233i \(0.132114\pi\)
−0.915097 + 0.403233i \(0.867886\pi\)
\(252\) −3.43458 3.43458i −0.216358 0.216358i
\(253\) −8.48191 0.907840i −0.533253 0.0570754i
\(254\) 11.7443i 0.736906i
\(255\) 3.11644 1.71199i 0.195159 0.107209i
\(256\) 1.00000 0.0625000
\(257\) −12.2990 + 12.2990i −0.767192 + 0.767192i −0.977611 0.210420i \(-0.932517\pi\)
0.210420 + 0.977611i \(0.432517\pi\)
\(258\) −6.47101 + 6.47101i −0.402868 + 0.402868i
\(259\) 2.21088i 0.137377i
\(260\) 3.69940 + 1.07605i 0.229427 + 0.0667339i
\(261\) −3.23574 −0.200287
\(262\) 8.95233 8.95233i 0.553077 0.553077i
\(263\) −0.838721 + 0.838721i −0.0517177 + 0.0517177i −0.732493 0.680775i \(-0.761643\pi\)
0.680775 + 0.732493i \(0.261643\pi\)
\(264\) 1.77870 0.109472
\(265\) −19.5134 5.67591i −1.19870 0.348668i
\(266\) 12.5073 0.766871
\(267\) −2.43918 2.43918i −0.149275 0.149275i
\(268\) −0.586681 + 0.586681i −0.0358372 + 0.0358372i
\(269\) 25.8476i 1.57595i −0.615704 0.787977i \(-0.711128\pi\)
0.615704 0.787977i \(-0.288872\pi\)
\(270\) −1.95982 + 1.07661i −0.119271 + 0.0655204i
\(271\) −32.0433 −1.94649 −0.973246 0.229764i \(-0.926205\pi\)
−0.973246 + 0.229764i \(0.926205\pi\)
\(272\) −1.12442 1.12442i −0.0681777 0.0681777i
\(273\) −5.91774 + 5.91774i −0.358158 + 0.358158i
\(274\) −1.47231 −0.0889456
\(275\) −7.50601 4.77016i −0.452629 0.287651i
\(276\) −3.01100 3.73281i −0.181241 0.224689i
\(277\) −18.2414 + 18.2414i −1.09602 + 1.09602i −0.101147 + 0.994871i \(0.532251\pi\)
−0.994871 + 0.101147i \(0.967749\pi\)
\(278\) 6.28997 + 6.28997i 0.377247 + 0.377247i
\(279\) 6.41786i 0.384227i
\(280\) 9.51930 5.22934i 0.568887 0.312513i
\(281\) 3.19489i 0.190591i −0.995449 0.0952954i \(-0.969620\pi\)
0.995449 0.0952954i \(-0.0303796\pi\)
\(282\) 9.10509 9.10509i 0.542200 0.542200i
\(283\) −22.6171 + 22.6171i −1.34444 + 1.34444i −0.452865 + 0.891579i \(0.649598\pi\)
−0.891579 + 0.452865i \(0.850402\pi\)
\(284\) 13.3156i 0.790137i
\(285\) 1.60815 5.52871i 0.0952583 0.327493i
\(286\) 3.06468i 0.181219i
\(287\) −35.1323 35.1323i −2.07379 2.07379i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 14.4714i 0.851258i
\(290\) 2.02080 6.94740i 0.118666 0.407965i
\(291\) 11.0220i 0.646123i
\(292\) 3.84689 3.84689i 0.225122 0.225122i
\(293\) 2.26468 2.26468i 0.132304 0.132304i −0.637854 0.770158i \(-0.720177\pi\)
0.770158 + 0.637854i \(0.220177\pi\)
\(294\) 16.5926i 0.967702i
\(295\) −20.3981 + 11.2055i −1.18762 + 0.652408i
\(296\) 0.455173i 0.0264564i
\(297\) 1.25773 + 1.25773i 0.0729810 + 0.0729810i
\(298\) −8.01563 + 8.01563i −0.464333 + 0.464333i
\(299\) −6.43159 + 5.18792i −0.371948 + 0.300025i
\(300\) −1.08761 4.88028i −0.0627933 0.281763i
\(301\) 44.4504 2.56208
\(302\) 6.18852 6.18852i 0.356110 0.356110i
\(303\) −0.0771372 0.0771372i −0.00443142 0.00443142i
\(304\) −2.57499 −0.147686
\(305\) −28.3639 + 15.5814i −1.62411 + 0.892190i
\(306\) 1.59016i 0.0909036i
\(307\) 6.36515 6.36515i 0.363278 0.363278i −0.501740 0.865018i \(-0.667307\pi\)
0.865018 + 0.501740i \(0.167307\pi\)
\(308\) −6.10909 6.10909i −0.348098 0.348098i
\(309\) −0.638749 −0.0363371
\(310\) −13.7797 4.00812i −0.782634 0.227646i
\(311\) 11.5795 0.656615 0.328307 0.944571i \(-0.393522\pi\)
0.328307 + 0.944571i \(0.393522\pi\)
\(312\) 1.21834 1.21834i 0.0689748 0.0689748i
\(313\) −0.636677 + 0.636677i −0.0359871 + 0.0359871i −0.724871 0.688884i \(-0.758101\pi\)
0.688884 + 0.724871i \(0.258101\pi\)
\(314\) 20.0839 1.13340
\(315\) 10.4289 + 3.03346i 0.587600 + 0.170916i
\(316\) 6.55768i 0.368898i
\(317\) 16.8675 16.8675i 0.947373 0.947373i −0.0513100 0.998683i \(-0.516340\pi\)
0.998683 + 0.0513100i \(0.0163396\pi\)
\(318\) −6.42643 + 6.42643i −0.360376 + 0.360376i
\(319\) −5.75542 −0.322241
\(320\) −1.95982 + 1.07661i −0.109557 + 0.0601844i
\(321\) 7.16835i 0.400098i
\(322\) −2.47910 + 23.1621i −0.138155 + 1.29078i
\(323\) 2.89535 + 2.89535i 0.161102 + 0.161102i
\(324\) 1.00000i 0.0555556i
\(325\) −8.40866 + 1.87394i −0.466429 + 0.103948i
\(326\) 5.49090 0.304113
\(327\) 5.42726 + 5.42726i 0.300128 + 0.300128i
\(328\) 7.23299 + 7.23299i 0.399375 + 0.399375i
\(329\) −62.5443 −3.44818
\(330\) −3.48594 + 1.91497i −0.191895 + 0.105416i
\(331\) −9.50258 −0.522309 −0.261155 0.965297i \(-0.584103\pi\)
−0.261155 + 0.965297i \(0.584103\pi\)
\(332\) −2.56461 2.56461i −0.140751 0.140751i
\(333\) 0.321856 0.321856i 0.0176376 0.0176376i
\(334\) 9.00881i 0.492940i
\(335\) 0.518164 1.78142i 0.0283103 0.0973292i
\(336\) 4.85722i 0.264983i
\(337\) 12.5879 + 12.5879i 0.685708 + 0.685708i 0.961280 0.275572i \(-0.0888673\pi\)
−0.275572 + 0.961280i \(0.588867\pi\)
\(338\) 7.09321 + 7.09321i 0.385820 + 0.385820i
\(339\) −14.6462 −0.795475
\(340\) 3.41421 + 0.993099i 0.185162 + 0.0538583i
\(341\) 11.4155i 0.618182i
\(342\) −1.82079 1.82079i −0.0984571 0.0984571i
\(343\) 32.9466 32.9466i 1.77895 1.77895i
\(344\) −9.15139 −0.493410
\(345\) 9.91982 + 4.07397i 0.534065 + 0.219335i
\(346\) −9.34483 −0.502381
\(347\) −17.5983 + 17.5983i −0.944725 + 0.944725i −0.998550 0.0538250i \(-0.982859\pi\)
0.0538250 + 0.998550i \(0.482859\pi\)
\(348\) −2.28801 2.28801i −0.122650 0.122650i
\(349\) 21.7045i 1.16181i 0.813970 + 0.580907i \(0.197302\pi\)
−0.813970 + 0.580907i \(0.802698\pi\)
\(350\) −13.0262 + 20.4972i −0.696280 + 1.09562i
\(351\) 1.72299 0.0919664
\(352\) 1.25773 + 1.25773i 0.0670374 + 0.0670374i
\(353\) 13.2550 + 13.2550i 0.705492 + 0.705492i 0.965584 0.260092i \(-0.0837528\pi\)
−0.260092 + 0.965584i \(0.583753\pi\)
\(354\) 10.4081i 0.553184i
\(355\) −14.3357 26.0963i −0.760862 1.38505i
\(356\) 3.44952i 0.182824i
\(357\) −5.46154 + 5.46154i −0.289055 + 0.289055i
\(358\) −0.478090 0.478090i −0.0252678 0.0252678i
\(359\) 9.12191 0.481436 0.240718 0.970595i \(-0.422617\pi\)
0.240718 + 0.970595i \(0.422617\pi\)
\(360\) −2.14708 0.624526i −0.113161 0.0329154i
\(361\) −12.3694 −0.651023
\(362\) 12.6993 + 12.6993i 0.667458 + 0.667458i
\(363\) −5.54104 5.54104i −0.290829 0.290829i
\(364\) −8.36895 −0.438652
\(365\) −3.39762 + 11.6808i −0.177840 + 0.611403i
\(366\) 14.4727i 0.756498i
\(367\) 14.3884 + 14.3884i 0.751067 + 0.751067i 0.974678 0.223611i \(-0.0717846\pi\)
−0.223611 + 0.974678i \(0.571785\pi\)
\(368\) 0.510395 4.76859i 0.0266062 0.248580i
\(369\) 10.2290i 0.532500i
\(370\) 0.490044 + 0.892058i 0.0254762 + 0.0463759i
\(371\) 44.1441 2.29185
\(372\) −4.53812 + 4.53812i −0.235290 + 0.235290i
\(373\) 2.31754 2.31754i 0.119998 0.119998i −0.644558 0.764556i \(-0.722959\pi\)
0.764556 + 0.644558i \(0.222959\pi\)
\(374\) 2.82843i 0.146254i
\(375\) 7.38569 + 8.39355i 0.381395 + 0.433441i
\(376\) 12.8765 0.664057
\(377\) −3.94222 + 3.94222i −0.203035 + 0.203035i
\(378\) 3.43458 3.43458i 0.176656 0.176656i
\(379\) 29.3993 1.51014 0.755070 0.655644i \(-0.227603\pi\)
0.755070 + 0.655644i \(0.227603\pi\)
\(380\) 5.04652 2.77226i 0.258881 0.142214i
\(381\) −11.7443 −0.601681
\(382\) 9.00732 + 9.00732i 0.460855 + 0.460855i
\(383\) −8.99894 + 8.99894i −0.459824 + 0.459824i −0.898598 0.438773i \(-0.855413\pi\)
0.438773 + 0.898598i \(0.355413\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 18.5498 + 5.39563i 0.945388 + 0.274987i
\(386\) 2.60779 0.132733
\(387\) −6.47101 6.47101i −0.328940 0.328940i
\(388\) −7.79375 + 7.79375i −0.395668 + 0.395668i
\(389\) 28.2251 1.43107 0.715534 0.698578i \(-0.246183\pi\)
0.715534 + 0.698578i \(0.246183\pi\)
\(390\) −1.07605 + 3.69940i −0.0544880 + 0.187326i
\(391\) −5.93578 + 4.78799i −0.300185 + 0.242139i
\(392\) −11.7328 + 11.7328i −0.592594 + 0.592594i
\(393\) 8.95233 + 8.95233i 0.451585 + 0.451585i
\(394\) 17.2009i 0.866568i
\(395\) 7.06007 + 12.8519i 0.355230 + 0.646649i
\(396\) 1.77870i 0.0893831i
\(397\) 8.54761 8.54761i 0.428992 0.428992i −0.459293 0.888285i \(-0.651897\pi\)
0.888285 + 0.459293i \(0.151897\pi\)
\(398\) −3.79878 + 3.79878i −0.190416 + 0.190416i
\(399\) 12.5073i 0.626147i
\(400\) 2.68182 4.21993i 0.134091 0.210997i
\(401\) 38.2744i 1.91133i 0.294451 + 0.955667i \(0.404863\pi\)
−0.294451 + 0.955667i \(0.595137\pi\)
\(402\) −0.586681 0.586681i −0.0292610 0.0292610i
\(403\) 7.81912 + 7.81912i 0.389498 + 0.389498i
\(404\) 0.109089i 0.00542736i
\(405\) −1.07661 1.95982i −0.0534972 0.0973844i
\(406\) 15.7167i 0.780007i
\(407\) 0.572485 0.572485i 0.0283770 0.0283770i
\(408\) 1.12442 1.12442i 0.0556669 0.0556669i
\(409\) 32.8990i 1.62675i 0.581738 + 0.813376i \(0.302373\pi\)
−0.581738 + 0.813376i \(0.697627\pi\)
\(410\) −21.9625 6.38827i −1.08465 0.315494i
\(411\) 1.47231i 0.0726238i
\(412\) −0.451663 0.451663i −0.0222519 0.0222519i
\(413\) 35.7474 35.7474i 1.75902 1.75902i
\(414\) 3.73281 3.01100i 0.183458 0.147983i
\(415\) 7.78726 + 2.26509i 0.382261 + 0.111189i
\(416\) 1.72299 0.0844765
\(417\) −6.28997 + 6.28997i −0.308021 + 0.308021i
\(418\) −3.23864 3.23864i −0.158407 0.158407i
\(419\) −22.0511 −1.07727 −0.538634 0.842540i \(-0.681059\pi\)
−0.538634 + 0.842540i \(0.681059\pi\)
\(420\) 5.22934 + 9.51930i 0.255166 + 0.464495i
\(421\) 36.8446i 1.79570i −0.440305 0.897848i \(-0.645130\pi\)
0.440305 0.897848i \(-0.354870\pi\)
\(422\) −5.69442 + 5.69442i −0.277200 + 0.277200i
\(423\) 9.10509 + 9.10509i 0.442705 + 0.442705i
\(424\) −9.08835 −0.441369
\(425\) −7.76044 + 1.72948i −0.376437 + 0.0838921i
\(426\) −13.3156 −0.645144
\(427\) 49.7075 49.7075i 2.40551 2.40551i
\(428\) 5.06879 5.06879i 0.245009 0.245009i
\(429\) 3.06468 0.147964
\(430\) 17.9351 9.85249i 0.864908 0.475129i
\(431\) 32.4060i 1.56094i −0.625192 0.780471i \(-0.714979\pi\)
0.625192 0.780471i \(-0.285021\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 1.69960 1.69960i 0.0816773 0.0816773i −0.665088 0.746765i \(-0.731606\pi\)
0.746765 + 0.665088i \(0.231606\pi\)
\(434\) 31.1730 1.49635
\(435\) 6.94740 + 2.02080i 0.333102 + 0.0968901i
\(436\) 7.67531i 0.367581i
\(437\) −1.31426 + 12.2791i −0.0628695 + 0.587387i
\(438\) 3.84689 + 3.84689i 0.183812 + 0.183812i
\(439\) 33.8924i 1.61760i −0.588085 0.808799i \(-0.700118\pi\)
0.588085 0.808799i \(-0.299882\pi\)
\(440\) −3.81902 1.11085i −0.182065 0.0529575i
\(441\) −16.5926 −0.790125
\(442\) −1.93736 1.93736i −0.0921506 0.0921506i
\(443\) 2.44684 + 2.44684i 0.116253 + 0.116253i 0.762840 0.646587i \(-0.223804\pi\)
−0.646587 + 0.762840i \(0.723804\pi\)
\(444\) 0.455173 0.0216015
\(445\) 3.71379 + 6.76045i 0.176050 + 0.320476i
\(446\) −11.3073 −0.535414
\(447\) −8.01563 8.01563i −0.379126 0.379126i
\(448\) 3.43458 3.43458i 0.162268 0.162268i
\(449\) 4.49307i 0.212041i 0.994364 + 0.106021i \(0.0338110\pi\)
−0.994364 + 0.106021i \(0.966189\pi\)
\(450\) 4.88028 1.08761i 0.230058 0.0512705i
\(451\) 18.1943i 0.856738i
\(452\) −10.3565 10.3565i −0.487127 0.487127i
\(453\) 6.18852 + 6.18852i 0.290762 + 0.290762i
\(454\) −18.6070 −0.873268
\(455\) 16.4017 9.01010i 0.768922 0.422400i
\(456\) 2.57499i 0.120585i
\(457\) 1.48242 + 1.48242i 0.0693445 + 0.0693445i 0.740928 0.671584i \(-0.234386\pi\)
−0.671584 + 0.740928i \(0.734386\pi\)
\(458\) −4.43976 + 4.43976i −0.207456 + 0.207456i
\(459\) 1.59016 0.0742225
\(460\) 4.13364 + 9.89510i 0.192732 + 0.461362i
\(461\) −0.0650793 −0.00303104 −0.00151552 0.999999i \(-0.500482\pi\)
−0.00151552 + 0.999999i \(0.500482\pi\)
\(462\) 6.10909 6.10909i 0.284221 0.284221i
\(463\) −8.88726 8.88726i −0.413026 0.413026i 0.469765 0.882791i \(-0.344338\pi\)
−0.882791 + 0.469765i \(0.844338\pi\)
\(464\) 3.23574i 0.150215i
\(465\) 4.00812 13.7797i 0.185872 0.639018i
\(466\) −16.9343 −0.784465
\(467\) 4.47713 + 4.47713i 0.207177 + 0.207177i 0.803066 0.595889i \(-0.203200\pi\)
−0.595889 + 0.803066i \(0.703200\pi\)
\(468\) 1.21834 + 1.21834i 0.0563177 + 0.0563177i
\(469\) 4.03000i 0.186088i
\(470\) −25.2358 + 13.8630i −1.16404 + 0.639454i
\(471\) 20.0839i 0.925417i
\(472\) −7.35964 + 7.35964i −0.338755 + 0.338755i
\(473\) −11.5100 11.5100i −0.529230 0.529230i
\(474\) 6.55768 0.301204
\(475\) −6.90565 + 10.8663i −0.316853 + 0.498579i
\(476\) −7.72378 −0.354019
\(477\) −6.42643 6.42643i −0.294246 0.294246i
\(478\) −3.10650 3.10650i −0.142088 0.142088i
\(479\) −33.4775 −1.52962 −0.764812 0.644253i \(-0.777168\pi\)
−0.764812 + 0.644253i \(0.777168\pi\)
\(480\) −1.07661 1.95982i −0.0491403 0.0894533i
\(481\) 0.784258i 0.0357591i
\(482\) 5.26163 + 5.26163i 0.239661 + 0.239661i
\(483\) −23.1621 2.47910i −1.05391 0.112803i
\(484\) 7.83622i 0.356192i
\(485\) 6.88354 23.6652i 0.312566 1.07458i
\(486\) −1.00000 −0.0453609
\(487\) −0.188074 + 0.188074i −0.00852246 + 0.00852246i −0.711355 0.702833i \(-0.751918\pi\)
0.702833 + 0.711355i \(0.251918\pi\)
\(488\) −10.2337 + 10.2337i −0.463259 + 0.463259i
\(489\) 5.49090i 0.248307i
\(490\) 10.3625 35.6258i 0.468131 1.60941i
\(491\) −15.9414 −0.719427 −0.359713 0.933063i \(-0.617126\pi\)
−0.359713 + 0.933063i \(0.617126\pi\)
\(492\) −7.23299 + 7.23299i −0.326088 + 0.326088i
\(493\) −3.63831 + 3.63831i −0.163861 + 0.163861i
\(494\) −4.43667 −0.199615
\(495\) −1.91497 3.48594i −0.0860715 0.156681i
\(496\) −6.41786 −0.288171
\(497\) 45.7335 + 45.7335i 2.05143 + 2.05143i
\(498\) 2.56461 2.56461i 0.114923 0.114923i
\(499\) 23.4075i 1.04786i −0.851761 0.523931i \(-0.824465\pi\)
0.851761 0.523931i \(-0.175535\pi\)
\(500\) −0.712667 + 11.1576i −0.0318714 + 0.498983i
\(501\) 9.00881 0.402484
\(502\) −9.03458 9.03458i −0.403233 0.403233i
\(503\) 11.3295 11.3295i 0.505158 0.505158i −0.407878 0.913036i \(-0.633731\pi\)
0.913036 + 0.407878i \(0.133731\pi\)
\(504\) 4.85722 0.216358
\(505\) 0.117446 + 0.213794i 0.00522627 + 0.00951372i
\(506\) 6.63956 5.35568i 0.295164 0.238089i
\(507\) −7.09321 + 7.09321i −0.315020 + 0.315020i
\(508\) −8.30451 8.30451i −0.368453 0.368453i
\(509\) 21.9841i 0.974429i −0.873282 0.487214i \(-0.838013\pi\)
0.873282 0.487214i \(-0.161987\pi\)
\(510\) −0.993099 + 3.41421i −0.0439751 + 0.151184i
\(511\) 26.4249i 1.16897i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 1.82079 1.82079i 0.0803898 0.0803898i
\(514\) 17.3934i 0.767192i
\(515\) 1.37145 + 0.398915i 0.0604332 + 0.0175783i
\(516\) 9.15139i 0.402868i
\(517\) 16.1952 + 16.1952i 0.712266 + 0.712266i
\(518\) −1.56333 1.56333i −0.0686886 0.0686886i
\(519\) 9.34483i 0.410192i
\(520\) −3.37676 + 1.85499i −0.148081 + 0.0813466i
\(521\) 6.76810i 0.296516i −0.988949 0.148258i \(-0.952633\pi\)
0.988949 0.148258i \(-0.0473665\pi\)
\(522\) 2.28801 2.28801i 0.100144 0.100144i
\(523\) −12.2965 + 12.2965i −0.537690 + 0.537690i −0.922850 0.385160i \(-0.874146\pi\)
0.385160 + 0.922850i \(0.374146\pi\)
\(524\) 12.6605i 0.553077i
\(525\) −20.4972 13.0262i −0.894570 0.568510i
\(526\) 1.18613i 0.0517177i
\(527\) 7.21634 + 7.21634i 0.314349 + 0.314349i
\(528\) −1.25773 + 1.25773i −0.0547358 + 0.0547358i
\(529\) −22.4790 4.86773i −0.977348 0.211640i
\(530\) 17.8116 9.78461i 0.773685 0.425016i
\(531\) −10.4081 −0.451673
\(532\) −8.84399 + 8.84399i −0.383435 + 0.383435i
\(533\) 12.4624 + 12.4624i 0.539805 + 0.539805i
\(534\) 3.44952 0.149275
\(535\) −4.47682 + 15.3911i −0.193550 + 0.665413i
\(536\) 0.829692i 0.0358372i
\(537\) 0.478090 0.478090i 0.0206311 0.0206311i
\(538\) 18.2770 + 18.2770i 0.787977 + 0.787977i
\(539\) −29.5133 −1.27123
\(540\) 0.624526 2.14708i 0.0268753 0.0923958i
\(541\) −11.2899 −0.485390 −0.242695 0.970103i \(-0.578031\pi\)
−0.242695 + 0.970103i \(0.578031\pi\)
\(542\) 22.6580 22.6580i 0.973246 0.973246i
\(543\) −12.6993 + 12.6993i −0.544977 + 0.544977i
\(544\) 1.59016 0.0681777
\(545\) −8.26332 15.0423i −0.353962 0.644339i
\(546\) 8.36895i 0.358158i
\(547\) 3.14045 3.14045i 0.134276 0.134276i −0.636774 0.771050i \(-0.719732\pi\)
0.771050 + 0.636774i \(0.219732\pi\)
\(548\) 1.04108 1.04108i 0.0444728 0.0444728i
\(549\) −14.4727 −0.617678
\(550\) 8.68056 1.93454i 0.370140 0.0824889i
\(551\) 8.33198i 0.354954i
\(552\) 4.76859 + 0.510395i 0.202965 + 0.0217238i
\(553\) −22.5228 22.5228i −0.957769 0.957769i
\(554\) 25.7972i 1.09602i
\(555\) −0.892058 + 0.490044i −0.0378658 + 0.0208012i
\(556\) −8.89535 −0.377247
\(557\) 11.8068 + 11.8068i 0.500272 + 0.500272i 0.911522 0.411251i \(-0.134908\pi\)
−0.411251 + 0.911522i \(0.634908\pi\)
\(558\) −4.53812 4.53812i −0.192114 0.192114i
\(559\) −15.7677 −0.666905
\(560\) −3.03346 + 10.4289i −0.128187 + 0.440700i
\(561\) 2.82843 0.119416
\(562\) 2.25912 + 2.25912i 0.0952954 + 0.0952954i
\(563\) 28.7684 28.7684i 1.21244 1.21244i 0.242221 0.970221i \(-0.422124\pi\)
0.970221 0.242221i \(-0.0778758\pi\)
\(564\) 12.8765i 0.542200i
\(565\) 31.4467 + 9.14696i 1.32297 + 0.384816i
\(566\) 31.9853i 1.34444i
\(567\) 3.43458 + 3.43458i 0.144239 + 0.144239i
\(568\) −9.41557 9.41557i −0.395068 0.395068i
\(569\) 21.2280 0.889925 0.444963 0.895549i \(-0.353217\pi\)
0.444963 + 0.895549i \(0.353217\pi\)
\(570\) 2.77226 + 5.04652i 0.116117 + 0.211375i
\(571\) 22.5582i 0.944030i 0.881591 + 0.472015i \(0.156473\pi\)
−0.881591 + 0.472015i \(0.843527\pi\)
\(572\) 2.16706 + 2.16706i 0.0906093 + 0.0906093i
\(573\) −9.00732 + 9.00732i −0.376286 + 0.376286i
\(574\) 49.6845 2.07379
\(575\) −18.7544 14.9423i −0.782111 0.623139i
\(576\) −1.00000 −0.0416667
\(577\) 17.1528 17.1528i 0.714078 0.714078i −0.253307 0.967386i \(-0.581518\pi\)
0.967386 + 0.253307i \(0.0815184\pi\)
\(578\) 10.2328 + 10.2328i 0.425629 + 0.425629i
\(579\) 2.60779i 0.108376i
\(580\) 3.48363 + 6.34148i 0.144650 + 0.263316i
\(581\) −17.6167 −0.730863
\(582\) −7.79375 7.79375i −0.323061 0.323061i
\(583\) −11.4307 11.4307i −0.473412 0.473412i
\(584\) 5.44033i 0.225122i
\(585\) −3.69940 1.07605i −0.152951 0.0444893i
\(586\) 3.20275i 0.132304i
\(587\) −18.6292 + 18.6292i −0.768907 + 0.768907i −0.977914 0.209007i \(-0.932977\pi\)
0.209007 + 0.977914i \(0.432977\pi\)
\(588\) −11.7328 11.7328i −0.483851 0.483851i
\(589\) 16.5259 0.680938
\(590\) 6.50013 22.3471i 0.267606 0.920014i
\(591\) 17.2009 0.707550
\(592\) 0.321856 + 0.321856i 0.0132282 + 0.0132282i
\(593\) 4.49108 + 4.49108i 0.184427 + 0.184427i 0.793282 0.608855i \(-0.208371\pi\)
−0.608855 + 0.793282i \(0.708371\pi\)
\(594\) −1.77870 −0.0729810
\(595\) 15.1373 8.31550i 0.620567 0.340902i
\(596\) 11.3358i 0.464333i
\(597\) −3.79878 3.79878i −0.155474 0.155474i
\(598\) 0.879404 8.21624i 0.0359615 0.335987i
\(599\) 22.1900i 0.906660i −0.891343 0.453330i \(-0.850236\pi\)
0.891343 0.453330i \(-0.149764\pi\)
\(600\) 4.21993 + 2.68182i 0.172278 + 0.109485i
\(601\) −15.6107 −0.636776 −0.318388 0.947961i \(-0.603141\pi\)
−0.318388 + 0.947961i \(0.603141\pi\)
\(602\) −31.4312 + 31.4312i −1.28104 + 1.28104i
\(603\) 0.586681 0.586681i 0.0238915 0.0238915i
\(604\) 8.75190i 0.356110i
\(605\) 8.43656 + 15.3576i 0.342995 + 0.624376i
\(606\) 0.109089 0.00443142
\(607\) 1.06267 1.06267i 0.0431325 0.0431325i −0.685212 0.728344i \(-0.740290\pi\)
0.728344 + 0.685212i \(0.240290\pi\)
\(608\) 1.82079 1.82079i 0.0738428 0.0738428i
\(609\) −15.7167 −0.636873
\(610\) 9.03856 31.0740i 0.365960 1.25815i
\(611\) 22.1861 0.897555
\(612\) 1.12442 + 1.12442i 0.0454518 + 0.0454518i
\(613\) 14.1331 14.1331i 0.570829 0.570829i −0.361531 0.932360i \(-0.617746\pi\)
0.932360 + 0.361531i \(0.117746\pi\)
\(614\) 9.00168i 0.363278i
\(615\) 6.38827 21.9625i 0.257600 0.885614i
\(616\) 8.63956 0.348098
\(617\) 19.3155 + 19.3155i 0.777614 + 0.777614i 0.979425 0.201811i \(-0.0646826\pi\)
−0.201811 + 0.979425i \(0.564683\pi\)
\(618\) 0.451663 0.451663i 0.0181686 0.0181686i
\(619\) 42.0979 1.69206 0.846028 0.533138i \(-0.178988\pi\)
0.846028 + 0.533138i \(0.178988\pi\)
\(620\) 12.5779 6.90954i 0.505140 0.277494i
\(621\) 3.01100 + 3.73281i 0.120827 + 0.149792i
\(622\) −8.18796 + 8.18796i −0.328307 + 0.328307i
\(623\) −11.8476 11.8476i −0.474666 0.474666i
\(624\) 1.72299i 0.0689748i
\(625\) −10.6157 22.6342i −0.424628 0.905368i
\(626\) 0.900397i 0.0359871i
\(627\) 3.23864 3.23864i 0.129339 0.129339i
\(628\) −14.2015 + 14.2015i −0.566700 + 0.566700i
\(629\) 0.723799i 0.0288598i
\(630\) −9.51930 + 5.22934i −0.379258 + 0.208342i
\(631\) 16.9667i 0.675434i 0.941248 + 0.337717i \(0.109655\pi\)
−0.941248 + 0.337717i \(0.890345\pi\)
\(632\) 4.63698 + 4.63698i 0.184449 + 0.184449i
\(633\) −5.69442 5.69442i −0.226333 0.226333i
\(634\) 23.8542i 0.947373i
\(635\) 25.2161 + 7.33465i 1.00067 + 0.291067i
\(636\) 9.08835i 0.360376i
\(637\) −20.2154 + 20.2154i −0.800964 + 0.800964i
\(638\) 4.06969 4.06969i 0.161121 0.161121i
\(639\) 13.3156i 0.526758i
\(640\) 0.624526 2.14708i 0.0246866 0.0848709i
\(641\) 5.44396i 0.215023i 0.994204 + 0.107512i \(0.0342883\pi\)
−0.994204 + 0.107512i \(0.965712\pi\)
\(642\) 5.06879 + 5.06879i 0.200049 + 0.200049i
\(643\) −4.81939 + 4.81939i −0.190058 + 0.190058i −0.795721 0.605663i \(-0.792908\pi\)
0.605663 + 0.795721i \(0.292908\pi\)
\(644\) −14.6251 18.1311i −0.576310 0.714465i
\(645\) 9.85249 + 17.9351i 0.387941 + 0.706194i
\(646\) −4.09465 −0.161102
\(647\) −8.57433 + 8.57433i −0.337092 + 0.337092i −0.855272 0.518180i \(-0.826610\pi\)
0.518180 + 0.855272i \(0.326610\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) −18.5129 −0.726696
\(650\) 4.62075 7.27090i 0.181241 0.285188i
\(651\) 31.1730i 1.22177i
\(652\) −3.88265 + 3.88265i −0.152056 + 0.152056i
\(653\) 11.9157 + 11.9157i 0.466297 + 0.466297i 0.900713 0.434416i \(-0.143045\pi\)
−0.434416 + 0.900713i \(0.643045\pi\)
\(654\) −7.67531 −0.300128
\(655\) −13.6304 24.8124i −0.532585 0.969499i
\(656\) −10.2290 −0.399375
\(657\) −3.84689 + 3.84689i −0.150082 + 0.150082i
\(658\) 44.2255 44.2255i 1.72409 1.72409i
\(659\) −0.738479 −0.0287670 −0.0143835 0.999897i \(-0.504579\pi\)
−0.0143835 + 0.999897i \(0.504579\pi\)
\(660\) 1.11085 3.81902i 0.0432396 0.148655i
\(661\) 8.03867i 0.312668i 0.987704 + 0.156334i \(0.0499676\pi\)
−0.987704 + 0.156334i \(0.950032\pi\)
\(662\) 6.71934 6.71934i 0.261155 0.261155i
\(663\) 1.93736 1.93736i 0.0752407 0.0752407i
\(664\) 3.62690 0.140751
\(665\) 7.81113 26.8542i 0.302902 1.04136i
\(666\) 0.455173i 0.0176376i
\(667\) −15.4299 1.65150i −0.597449 0.0639465i
\(668\) 6.37019 + 6.37019i 0.246470 + 0.246470i
\(669\) 11.3073i 0.437164i
\(670\) 0.893255 + 1.62605i 0.0345095 + 0.0628198i
\(671\) −25.7426 −0.993780
\(672\) 3.43458 + 3.43458i 0.132492 + 0.132492i
\(673\) −32.1774 32.1774i −1.24035 1.24035i −0.959857 0.280488i \(-0.909504\pi\)
−0.280488 0.959857i \(-0.590496\pi\)
\(674\) −17.8020 −0.685708
\(675\) 1.08761 + 4.88028i 0.0418622 + 0.187842i
\(676\) −10.0313 −0.385820
\(677\) −12.9663 12.9663i −0.498335 0.498335i 0.412585 0.910919i \(-0.364626\pi\)
−0.910919 + 0.412585i \(0.864626\pi\)
\(678\) 10.3565 10.3565i 0.397737 0.397737i
\(679\) 53.5365i 2.05454i
\(680\) −3.11644 + 1.71199i −0.119510 + 0.0656517i
\(681\) 18.6070i 0.713020i
\(682\) −8.07196 8.07196i −0.309091 0.309091i
\(683\) 27.7204 + 27.7204i 1.06069 + 1.06069i 0.998035 + 0.0626558i \(0.0199570\pi\)
0.0626558 + 0.998035i \(0.480043\pi\)
\(684\) 2.57499 0.0984571
\(685\) −0.919497 + 3.16118i −0.0351322 + 0.120782i
\(686\) 46.5936i 1.77895i
\(687\) −4.43976 4.43976i −0.169387 0.169387i
\(688\) 6.47101 6.47101i 0.246705 0.246705i
\(689\) −15.6591 −0.596565
\(690\) −9.89510 + 4.13364i −0.376700 + 0.157365i
\(691\) 23.1360 0.880137 0.440068 0.897964i \(-0.354954\pi\)
0.440068 + 0.897964i \(0.354954\pi\)
\(692\) 6.60779 6.60779i 0.251191 0.251191i
\(693\) 6.10909 + 6.10909i 0.232065 + 0.232065i
\(694\) 24.8877i 0.944725i
\(695\) 17.4333 9.57683i 0.661284 0.363270i
\(696\) 3.23574 0.122650
\(697\) 11.5016 + 11.5016i 0.435656 + 0.435656i
\(698\) −15.3474 15.3474i −0.580907 0.580907i
\(699\) 16.9343i 0.640513i
\(700\) −5.28277 23.7046i −0.199670 0.895950i
\(701\) 27.0938i 1.02332i −0.859189 0.511659i \(-0.829031\pi\)
0.859189 0.511659i \(-0.170969\pi\)
\(702\) −1.21834 + 1.21834i −0.0459832 + 0.0459832i
\(703\) −0.828774 0.828774i −0.0312578 0.0312578i
\(704\) −1.77870 −0.0670374
\(705\) −13.8630 25.2358i −0.522112 0.950434i
\(706\) −18.7454 −0.705492
\(707\) −0.374673 0.374673i −0.0140910 0.0140910i
\(708\) −7.35964 7.35964i −0.276592 0.276592i
\(709\) −7.87786 −0.295859 −0.147930 0.988998i \(-0.547261\pi\)
−0.147930 + 0.988998i \(0.547261\pi\)
\(710\) 28.5897 + 8.31595i 1.07295 + 0.312092i
\(711\) 6.55768i 0.245932i
\(712\) 2.43918 + 2.43918i 0.0914121 + 0.0914121i
\(713\) −3.27564 + 30.6042i −0.122674 + 1.14614i
\(714\) 7.72378i 0.289055i
\(715\) −6.58013 1.91398i −0.246083 0.0715786i
\(716\) 0.676121 0.0252678
\(717\) 3.10650 3.10650i 0.116014 0.116014i
\(718\) −6.45016 + 6.45016i −0.240718 + 0.240718i
\(719\) 18.0186i 0.671980i −0.941865 0.335990i \(-0.890929\pi\)
0.941865 0.335990i \(-0.109071\pi\)
\(720\) 1.95982 1.07661i 0.0730383 0.0401229i
\(721\) −3.10255 −0.115545
\(722\) 8.74652 8.74652i 0.325512 0.325512i
\(723\) −5.26163 + 5.26163i −0.195682 + 0.195682i
\(724\) −17.9595 −0.667458
\(725\) −13.6546 8.67767i −0.507119 0.322280i
\(726\) 7.83622 0.290829
\(727\) −19.6163 19.6163i −0.727530 0.727530i 0.242598 0.970127i \(-0.422001\pi\)
−0.970127 + 0.242598i \(0.922001\pi\)
\(728\) 5.91774 5.91774i 0.219326 0.219326i
\(729\) 1.00000i 0.0370370i
\(730\) −5.85711 10.6621i −0.216781 0.394621i
\(731\) −14.5522 −0.538233
\(732\) −10.2337 10.2337i −0.378249 0.378249i
\(733\) 16.5747 16.5747i 0.612200 0.612200i −0.331319 0.943519i \(-0.607494\pi\)
0.943519 + 0.331319i \(0.107494\pi\)
\(734\) −20.3482 −0.751067
\(735\) 35.6258 + 10.3625i 1.31408 + 0.382228i
\(736\) 3.01100 + 3.73281i 0.110987 + 0.137593i
\(737\) 1.04353 1.04353i 0.0384389 0.0384389i
\(738\) −7.23299 7.23299i −0.266250 0.266250i
\(739\) 45.4934i 1.67350i −0.547585 0.836750i \(-0.684453\pi\)
0.547585 0.836750i \(-0.315547\pi\)
\(740\) −0.977294 0.284267i −0.0359260 0.0104499i
\(741\) 4.43667i 0.162985i
\(742\) −31.2146 + 31.2146i −1.14592 + 1.14592i
\(743\) −4.79938 + 4.79938i −0.176072 + 0.176072i −0.789641 0.613569i \(-0.789733\pi\)
0.613569 + 0.789641i \(0.289733\pi\)
\(744\) 6.41786i 0.235290i
\(745\) 12.2043 + 22.2162i 0.447129 + 0.813938i
\(746\) 3.27750i 0.119998i
\(747\) 2.56461 + 2.56461i 0.0938340 + 0.0938340i
\(748\) 2.00000 + 2.00000i 0.0731272 + 0.0731272i
\(749\) 34.8183i 1.27223i
\(750\) −11.1576 0.712667i −0.407418 0.0260229i
\(751\) 48.8764i 1.78352i 0.452505 + 0.891762i \(0.350531\pi\)
−0.452505 + 0.891762i \(0.649469\pi\)
\(752\) −9.10509 + 9.10509i −0.332029 + 0.332029i
\(753\) 9.03458 9.03458i 0.329238 0.329238i
\(754\) 5.57514i 0.203035i
\(755\) −9.42238 17.1522i −0.342916 0.624231i
\(756\) 4.85722i 0.176656i
\(757\) −7.64728 7.64728i −0.277945 0.277945i 0.554343 0.832288i \(-0.312970\pi\)
−0.832288 + 0.554343i \(0.812970\pi\)
\(758\) −20.7884 + 20.7884i −0.755070 + 0.755070i
\(759\) 5.35568 + 6.63956i 0.194399 + 0.241001i
\(760\) −1.60815 + 5.52871i −0.0583336 + 0.200547i
\(761\) 31.0826 1.12674 0.563372 0.826203i \(-0.309504\pi\)
0.563372 + 0.826203i \(0.309504\pi\)
\(762\) 8.30451 8.30451i 0.300841 0.300841i
\(763\) 26.3614 + 26.3614i 0.954348 + 0.954348i
\(764\) −12.7383 −0.460855
\(765\) −3.41421 0.993099i −0.123441 0.0359056i
\(766\) 12.7264i 0.459824i
\(767\) −12.6806 + 12.6806i −0.457869 + 0.457869i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) −13.6176 −0.491062 −0.245531 0.969389i \(-0.578962\pi\)
−0.245531 + 0.969389i \(0.578962\pi\)
\(770\) −16.9320 + 9.30144i −0.610187 + 0.335201i
\(771\) 17.3934 0.626409
\(772\) −1.84399 + 1.84399i −0.0663665 + 0.0663665i
\(773\) −6.20764 + 6.20764i −0.223273 + 0.223273i −0.809875 0.586602i \(-0.800465\pi\)
0.586602 + 0.809875i \(0.300465\pi\)
\(774\) 9.15139 0.328940
\(775\) −17.2116 + 27.0830i −0.618257 + 0.972849i
\(776\) 11.0220i 0.395668i
\(777\) 1.56333 1.56333i 0.0560840 0.0560840i
\(778\) −19.9581 + 19.9581i −0.715534 + 0.715534i
\(779\) 26.3395 0.943711
\(780\) −1.85499