Properties

Label 690.2.j.a.643.8
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 643.8
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.a.367.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.57090 - 1.59131i) q^{5} -1.00000 q^{6} +(-1.37926 - 1.37926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.57090 - 1.59131i) q^{5} -1.00000 q^{6} +(-1.37926 - 1.37926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-2.23602 - 0.0144369i) q^{10} -0.0288739i q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.711585 + 0.711585i) q^{13} -1.95057 q^{14} +(-0.0144369 + 2.23602i) q^{15} -1.00000 q^{16} +(-0.438634 - 0.438634i) q^{17} +(0.707107 + 0.707107i) q^{18} -7.23057 q^{19} +(-1.59131 + 1.57090i) q^{20} +1.95057i q^{21} +(-0.0204169 - 0.0204169i) q^{22} +(3.06679 + 3.68711i) q^{23} +1.00000i q^{24} +(-0.0645626 + 4.99958i) q^{25} +1.00633 q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.37926 + 1.37926i) q^{28} -3.97284i q^{29} +(1.57090 + 1.59131i) q^{30} -5.20915 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0204169 + 0.0204169i) q^{33} -0.620322 q^{34} +(-0.0281603 + 4.36152i) q^{35} +1.00000 q^{36} +(1.46265 + 1.46265i) q^{37} +(-5.11278 + 5.11278i) q^{38} -1.00633i q^{39} +(-0.0144369 + 2.23602i) q^{40} -7.17074 q^{41} +(1.37926 + 1.37926i) q^{42} +(-5.83089 + 5.83089i) q^{43} -0.0288739 q^{44} +(1.59131 - 1.57090i) q^{45} +(4.77573 + 0.438634i) q^{46} +(6.90153 - 6.90153i) q^{47} +(0.707107 + 0.707107i) q^{48} -3.19528i q^{49} +(3.48959 + 3.58089i) q^{50} +0.620322i q^{51} +(0.711585 - 0.711585i) q^{52} +(2.73811 - 2.73811i) q^{53} -1.00000i q^{54} +(-0.0459474 + 0.0453579i) q^{55} +1.95057i q^{56} +(5.11278 + 5.11278i) q^{57} +(-2.80922 - 2.80922i) q^{58} -5.73861i q^{59} +(2.23602 + 0.0144369i) q^{60} -5.09237i q^{61} +(-3.68342 + 3.68342i) q^{62} +(1.37926 - 1.37926i) q^{63} +1.00000i q^{64} +(0.0145284 - 2.25018i) q^{65} +0.0288739i q^{66} +(-4.63966 - 4.63966i) q^{67} +(-0.438634 + 0.438634i) q^{68} +(0.438634 - 4.77573i) q^{69} +(3.06415 + 3.10397i) q^{70} -5.47777 q^{71} +(0.707107 - 0.707107i) q^{72} +(-0.908695 - 0.908695i) q^{73} +2.06849 q^{74} +(3.58089 - 3.48959i) q^{75} +7.23057i q^{76} +(-0.0398246 + 0.0398246i) q^{77} +(-0.711585 - 0.711585i) q^{78} -5.20235 q^{79} +(1.57090 + 1.59131i) q^{80} -1.00000 q^{81} +(-5.07048 + 5.07048i) q^{82} +(9.95414 - 9.95414i) q^{83} +1.95057 q^{84} +(-0.00895556 + 1.38705i) q^{85} +8.24612i q^{86} +(-2.80922 + 2.80922i) q^{87} +(-0.0204169 + 0.0204169i) q^{88} +10.5118 q^{89} +(0.0144369 - 2.23602i) q^{90} -1.96292i q^{91} +(3.68711 - 3.06679i) q^{92} +(3.68342 + 3.68342i) q^{93} -9.76024i q^{94} +(11.3585 + 11.5061i) q^{95} +1.00000 q^{96} +(-0.850780 - 0.850780i) q^{97} +(-2.25940 - 2.25940i) q^{98} +0.0288739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{6} + O(q^{10}) \) \( 24q - 24q^{6} - 24q^{16} - 8q^{23} - 16q^{25} - 16q^{26} + 16q^{31} - 16q^{35} + 24q^{36} - 8q^{46} - 8q^{47} + 24q^{50} + 24q^{55} + 16q^{58} - 56q^{62} - 32q^{70} - 16q^{71} - 48q^{73} - 24q^{81} + 24q^{82} + 16q^{87} - 8q^{92} + 56q^{93} + 24q^{95} + 24q^{96} - 32q^{98} + O(q^{100}) \)

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
\(5\) −1.57090 1.59131i −0.702527 0.711657i
\(6\) −1.00000 −0.408248
\(7\) −1.37926 1.37926i −0.521312 0.521312i 0.396656 0.917967i \(-0.370171\pi\)
−0.917967 + 0.396656i \(0.870171\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −2.23602 0.0144369i −0.707092 0.00456536i
\(11\) 0.0288739i 0.00870580i −0.999991 0.00435290i \(-0.998614\pi\)
0.999991 0.00435290i \(-0.00138558\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 0.711585 + 0.711585i 0.197358 + 0.197358i 0.798866 0.601508i \(-0.205433\pi\)
−0.601508 + 0.798866i \(0.705433\pi\)
\(14\) −1.95057 −0.521312
\(15\) −0.0144369 + 2.23602i −0.00372760 + 0.577338i
\(16\) −1.00000 −0.250000
\(17\) −0.438634 0.438634i −0.106384 0.106384i 0.651911 0.758295i \(-0.273968\pi\)
−0.758295 + 0.651911i \(0.773968\pi\)
\(18\) 0.707107 + 0.707107i 0.166667 + 0.166667i
\(19\) −7.23057 −1.65881 −0.829403 0.558651i \(-0.811319\pi\)
−0.829403 + 0.558651i \(0.811319\pi\)
\(20\) −1.59131 + 1.57090i −0.355829 + 0.351263i
\(21\) 1.95057i 0.425649i
\(22\) −0.0204169 0.0204169i −0.00435290 0.00435290i
\(23\) 3.06679 + 3.68711i 0.639470 + 0.768816i
\(24\) 1.00000i 0.204124i
\(25\) −0.0645626 + 4.99958i −0.0129125 + 0.999917i
\(26\) 1.00633 0.197358
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −1.37926 + 1.37926i −0.260656 + 0.260656i
\(29\) 3.97284i 0.737738i −0.929481 0.368869i \(-0.879745\pi\)
0.929481 0.368869i \(-0.120255\pi\)
\(30\) 1.57090 + 1.59131i 0.286805 + 0.290533i
\(31\) −5.20915 −0.935591 −0.467795 0.883837i \(-0.654952\pi\)
−0.467795 + 0.883837i \(0.654952\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −0.0204169 + 0.0204169i −0.00355413 + 0.00355413i
\(34\) −0.620322 −0.106384
\(35\) −0.0281603 + 4.36152i −0.00475995 + 0.737231i
\(36\) 1.00000 0.166667
\(37\) 1.46265 + 1.46265i 0.240457 + 0.240457i 0.817039 0.576582i \(-0.195614\pi\)
−0.576582 + 0.817039i \(0.695614\pi\)
\(38\) −5.11278 + 5.11278i −0.829403 + 0.829403i
\(39\) 1.00633i 0.161142i
\(40\) −0.0144369 + 2.23602i −0.00228268 + 0.353546i
\(41\) −7.17074 −1.11988 −0.559941 0.828533i \(-0.689176\pi\)
−0.559941 + 0.828533i \(0.689176\pi\)
\(42\) 1.37926 + 1.37926i 0.212825 + 0.212825i
\(43\) −5.83089 + 5.83089i −0.889202 + 0.889202i −0.994446 0.105244i \(-0.966438\pi\)
0.105244 + 0.994446i \(0.466438\pi\)
\(44\) −0.0288739 −0.00435290
\(45\) 1.59131 1.57090i 0.237219 0.234176i
\(46\) 4.77573 + 0.438634i 0.704143 + 0.0646731i
\(47\) 6.90153 6.90153i 1.00669 1.00669i 0.00671393 0.999977i \(-0.497863\pi\)
0.999977 0.00671393i \(-0.00213713\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 3.19528i 0.456468i
\(50\) 3.48959 + 3.58089i 0.493502 + 0.506415i
\(51\) 0.620322i 0.0868625i
\(52\) 0.711585 0.711585i 0.0986790 0.0986790i
\(53\) 2.73811 2.73811i 0.376108 0.376108i −0.493588 0.869696i \(-0.664315\pi\)
0.869696 + 0.493588i \(0.164315\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −0.0459474 + 0.0453579i −0.00619555 + 0.00611606i
\(56\) 1.95057i 0.260656i
\(57\) 5.11278 + 5.11278i 0.677205 + 0.677205i
\(58\) −2.80922 2.80922i −0.368869 0.368869i
\(59\) 5.73861i 0.747104i −0.927609 0.373552i \(-0.878140\pi\)
0.927609 0.373552i \(-0.121860\pi\)
\(60\) 2.23602 + 0.0144369i 0.288669 + 0.00186380i
\(61\) 5.09237i 0.652011i −0.945368 0.326005i \(-0.894297\pi\)
0.945368 0.326005i \(-0.105703\pi\)
\(62\) −3.68342 + 3.68342i −0.467795 + 0.467795i
\(63\) 1.37926 1.37926i 0.173771 0.173771i
\(64\) 1.00000i 0.125000i
\(65\) 0.0145284 2.25018i 0.00180202 0.279101i
\(66\) 0.0288739i 0.00355413i
\(67\) −4.63966 4.63966i −0.566825 0.566825i 0.364413 0.931238i \(-0.381270\pi\)
−0.931238 + 0.364413i \(0.881270\pi\)
\(68\) −0.438634 + 0.438634i −0.0531922 + 0.0531922i
\(69\) 0.438634 4.77573i 0.0528053 0.574930i
\(70\) 3.06415 + 3.10397i 0.366235 + 0.370995i
\(71\) −5.47777 −0.650092 −0.325046 0.945698i \(-0.605380\pi\)
−0.325046 + 0.945698i \(0.605380\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) −0.908695 0.908695i −0.106355 0.106355i 0.651927 0.758282i \(-0.273961\pi\)
−0.758282 + 0.651927i \(0.773961\pi\)
\(74\) 2.06849 0.240457
\(75\) 3.58089 3.48959i 0.413486 0.402943i
\(76\) 7.23057i 0.829403i
\(77\) −0.0398246 + 0.0398246i −0.00453844 + 0.00453844i
\(78\) −0.711585 0.711585i −0.0805711 0.0805711i
\(79\) −5.20235 −0.585310 −0.292655 0.956218i \(-0.594539\pi\)
−0.292655 + 0.956218i \(0.594539\pi\)
\(80\) 1.57090 + 1.59131i 0.175632 + 0.177914i
\(81\) −1.00000 −0.111111
\(82\) −5.07048 + 5.07048i −0.559941 + 0.559941i
\(83\) 9.95414 9.95414i 1.09261 1.09261i 0.0973599 0.995249i \(-0.468960\pi\)
0.995249 0.0973599i \(-0.0310398\pi\)
\(84\) 1.95057 0.212825
\(85\) −0.00895556 + 1.38705i −0.000971366 + 0.150447i
\(86\) 8.24612i 0.889202i
\(87\) −2.80922 + 2.80922i −0.301180 + 0.301180i
\(88\) −0.0204169 + 0.0204169i −0.00217645 + 0.00217645i
\(89\) 10.5118 1.11425 0.557123 0.830430i \(-0.311905\pi\)
0.557123 + 0.830430i \(0.311905\pi\)
\(90\) 0.0144369 2.23602i 0.00152179 0.235697i
\(91\) 1.96292i 0.205770i
\(92\) 3.68711 3.06679i 0.384408 0.319735i
\(93\) 3.68342 + 3.68342i 0.381953 + 0.381953i
\(94\) 9.76024i 1.00669i
\(95\) 11.3585 + 11.5061i 1.16536 + 1.18050i
\(96\) 1.00000 0.102062
\(97\) −0.850780 0.850780i −0.0863836 0.0863836i 0.662595 0.748978i \(-0.269455\pi\)
−0.748978 + 0.662595i \(0.769455\pi\)
\(98\) −2.25940 2.25940i −0.228234 0.228234i
\(99\) 0.0288739 0.00290193
\(100\) 4.99958 + 0.0645626i 0.499958 + 0.00645626i
\(101\) −15.2097 −1.51342 −0.756712 0.653748i \(-0.773196\pi\)
−0.756712 + 0.653748i \(0.773196\pi\)
\(102\) 0.438634 + 0.438634i 0.0434313 + 0.0434313i
\(103\) −2.54161 + 2.54161i −0.250432 + 0.250432i −0.821148 0.570715i \(-0.806666\pi\)
0.570715 + 0.821148i \(0.306666\pi\)
\(104\) 1.00633i 0.0986790i
\(105\) 3.10397 3.06415i 0.302916 0.299030i
\(106\) 3.87227i 0.376108i
\(107\) −7.38286 7.38286i −0.713728 0.713728i 0.253585 0.967313i \(-0.418390\pi\)
−0.967313 + 0.253585i \(0.918390\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 1.23206 0.118010 0.0590049 0.998258i \(-0.481207\pi\)
0.0590049 + 0.998258i \(0.481207\pi\)
\(110\) −0.000416850 0.0645626i −3.97451e−5 0.00615580i
\(111\) 2.06849i 0.196333i
\(112\) 1.37926 + 1.37926i 0.130328 + 0.130328i
\(113\) 10.6065 10.6065i 0.997771 0.997771i −0.00222660 0.999998i \(-0.500709\pi\)
0.999998 + 0.00222660i \(0.000708750\pi\)
\(114\) 7.23057 0.677205
\(115\) 1.04974 10.6723i 0.0978890 0.995197i
\(116\) −3.97284 −0.368869
\(117\) −0.711585 + 0.711585i −0.0657860 + 0.0657860i
\(118\) −4.05781 4.05781i −0.373552 0.373552i
\(119\) 1.20998i 0.110919i
\(120\) 1.59131 1.57090i 0.145266 0.143403i
\(121\) 10.9992 0.999924
\(122\) −3.60085 3.60085i −0.326005 0.326005i
\(123\) 5.07048 + 5.07048i 0.457190 + 0.457190i
\(124\) 5.20915i 0.467795i
\(125\) 8.05733 7.75109i 0.720669 0.693279i
\(126\) 1.95057i 0.173771i
\(127\) −6.45653 + 6.45653i −0.572925 + 0.572925i −0.932945 0.360020i \(-0.882770\pi\)
0.360020 + 0.932945i \(0.382770\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 8.24612 0.726030
\(130\) −1.58085 1.60139i −0.138649 0.140451i
\(131\) −14.1312 −1.23465 −0.617323 0.786710i \(-0.711783\pi\)
−0.617323 + 0.786710i \(0.711783\pi\)
\(132\) 0.0204169 + 0.0204169i 0.00177706 + 0.00177706i
\(133\) 9.97284 + 9.97284i 0.864755 + 0.864755i
\(134\) −6.56147 −0.566825
\(135\) −2.23602 0.0144369i −0.192446 0.00124253i
\(136\) 0.620322i 0.0531922i
\(137\) 9.99147 + 9.99147i 0.853629 + 0.853629i 0.990578 0.136949i \(-0.0437296\pi\)
−0.136949 + 0.990578i \(0.543730\pi\)
\(138\) −3.06679 3.68711i −0.261063 0.313868i
\(139\) 11.0483i 0.937102i −0.883436 0.468551i \(-0.844776\pi\)
0.883436 0.468551i \(-0.155224\pi\)
\(140\) 4.36152 + 0.0281603i 0.368615 + 0.00237998i
\(141\) −9.76024 −0.821960
\(142\) −3.87337 + 3.87337i −0.325046 + 0.325046i
\(143\) 0.0205462 0.0205462i 0.00171816 0.00171816i
\(144\) 1.00000i 0.0833333i
\(145\) −6.32204 + 6.24092i −0.525017 + 0.518281i
\(146\) −1.28509 −0.106355
\(147\) −2.25940 + 2.25940i −0.186352 + 0.186352i
\(148\) 1.46265 1.46265i 0.120229 0.120229i
\(149\) 13.0448 1.06867 0.534336 0.845272i \(-0.320562\pi\)
0.534336 + 0.845272i \(0.320562\pi\)
\(150\) 0.0645626 4.99958i 0.00527152 0.408214i
\(151\) 2.16088 0.175850 0.0879250 0.996127i \(-0.471976\pi\)
0.0879250 + 0.996127i \(0.471976\pi\)
\(152\) 5.11278 + 5.11278i 0.414701 + 0.414701i
\(153\) 0.438634 0.438634i 0.0354615 0.0354615i
\(154\) 0.0563205i 0.00453844i
\(155\) 8.18304 + 8.28939i 0.657277 + 0.665820i
\(156\) −1.00633 −0.0805711
\(157\) −13.4623 13.4623i −1.07441 1.07441i −0.996999 0.0774088i \(-0.975335\pi\)
−0.0774088 0.996999i \(-0.524665\pi\)
\(158\) −3.67862 + 3.67862i −0.292655 + 0.292655i
\(159\) −3.87227 −0.307091
\(160\) 2.23602 + 0.0144369i 0.176773 + 0.00114134i
\(161\) 0.855587 9.31540i 0.0674297 0.734156i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) −0.576831 0.576831i −0.0451809 0.0451809i 0.684155 0.729336i \(-0.260171\pi\)
−0.729336 + 0.684155i \(0.760171\pi\)
\(164\) 7.17074i 0.559941i
\(165\) 0.0645626 0.000416850i 0.00502619 3.24518e-5i
\(166\) 14.0773i 1.09261i
\(167\) 4.06044 4.06044i 0.314206 0.314206i −0.532331 0.846537i \(-0.678684\pi\)
0.846537 + 0.532331i \(0.178684\pi\)
\(168\) 1.37926 1.37926i 0.106412 0.106412i
\(169\) 11.9873i 0.922100i
\(170\) 0.974463 + 0.987128i 0.0747379 + 0.0757092i
\(171\) 7.23057i 0.552935i
\(172\) 5.83089 + 5.83089i 0.444601 + 0.444601i
\(173\) 12.1320 + 12.1320i 0.922379 + 0.922379i 0.997197 0.0748182i \(-0.0238377\pi\)
−0.0748182 + 0.997197i \(0.523838\pi\)
\(174\) 3.97284i 0.301180i
\(175\) 6.98478 6.80668i 0.528000 0.514537i
\(176\) 0.0288739i 0.00217645i
\(177\) −4.05781 + 4.05781i −0.305004 + 0.305004i
\(178\) 7.43295 7.43295i 0.557123 0.557123i
\(179\) 16.6646i 1.24557i −0.782393 0.622785i \(-0.786001\pi\)
0.782393 0.622785i \(-0.213999\pi\)
\(180\) −1.57090 1.59131i −0.117088 0.118610i
\(181\) 6.69613i 0.497719i 0.968540 + 0.248860i \(0.0800558\pi\)
−0.968540 + 0.248860i \(0.919944\pi\)
\(182\) −1.38800 1.38800i −0.102885 0.102885i
\(183\) −3.60085 + 3.60085i −0.266182 + 0.266182i
\(184\) 0.438634 4.77573i 0.0323365 0.352072i
\(185\) 0.0298627 4.62519i 0.00219555 0.340051i
\(186\) 5.20915 0.381953
\(187\) −0.0126651 + 0.0126651i −0.000926162 + 0.000926162i
\(188\) −6.90153 6.90153i −0.503346 0.503346i
\(189\) −1.95057 −0.141883
\(190\) 16.1677 + 0.104387i 1.17293 + 0.00757305i
\(191\) 7.32933i 0.530332i 0.964203 + 0.265166i \(0.0854267\pi\)
−0.964203 + 0.265166i \(0.914573\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −5.03982 5.03982i −0.362775 0.362775i 0.502059 0.864833i \(-0.332576\pi\)
−0.864833 + 0.502059i \(0.832576\pi\)
\(194\) −1.20318 −0.0863836
\(195\) −1.60139 + 1.58085i −0.114678 + 0.113207i
\(196\) −3.19528 −0.228234
\(197\) 6.17707 6.17707i 0.440098 0.440098i −0.451947 0.892045i \(-0.649270\pi\)
0.892045 + 0.451947i \(0.149270\pi\)
\(198\) 0.0204169 0.0204169i 0.00145097 0.00145097i
\(199\) −20.6272 −1.46222 −0.731111 0.682258i \(-0.760998\pi\)
−0.731111 + 0.682258i \(0.760998\pi\)
\(200\) 3.58089 3.48959i 0.253207 0.246751i
\(201\) 6.56147i 0.462811i
\(202\) −10.7549 + 10.7549i −0.756712 + 0.756712i
\(203\) −5.47959 + 5.47959i −0.384592 + 0.384592i
\(204\) 0.620322 0.0434313
\(205\) 11.2645 + 11.4109i 0.786747 + 0.796972i
\(206\) 3.59438i 0.250432i
\(207\) −3.68711 + 3.06679i −0.256272 + 0.213157i
\(208\) −0.711585 0.711585i −0.0493395 0.0493395i
\(209\) 0.208774i 0.0144412i
\(210\) 0.0281603 4.36152i 0.00194324 0.300973i
\(211\) −25.2880 −1.74090 −0.870448 0.492261i \(-0.836171\pi\)
−0.870448 + 0.492261i \(0.836171\pi\)
\(212\) −2.73811 2.73811i −0.188054 0.188054i
\(213\) 3.87337 + 3.87337i 0.265399 + 0.265399i
\(214\) −10.4409 −0.713728
\(215\) 18.4385 + 0.119049i 1.25750 + 0.00811906i
\(216\) −1.00000 −0.0680414
\(217\) 7.18478 + 7.18478i 0.487735 + 0.487735i
\(218\) 0.871197 0.871197i 0.0590049 0.0590049i
\(219\) 1.28509i 0.0868382i
\(220\) 0.0453579 + 0.0459474i 0.00305803 + 0.00309777i
\(221\) 0.624251i 0.0419916i
\(222\) −1.46265 1.46265i −0.0981663 0.0981663i
\(223\) 6.36523 + 6.36523i 0.426247 + 0.426247i 0.887348 0.461101i \(-0.152545\pi\)
−0.461101 + 0.887348i \(0.652545\pi\)
\(224\) 1.95057 0.130328
\(225\) −4.99958 0.0645626i −0.333306 0.00430417i
\(226\) 14.9998i 0.997771i
\(227\) 12.2183 + 12.2183i 0.810956 + 0.810956i 0.984777 0.173822i \(-0.0556116\pi\)
−0.173822 + 0.984777i \(0.555612\pi\)
\(228\) 5.11278 5.11278i 0.338602 0.338602i
\(229\) 20.2222 1.33632 0.668162 0.744016i \(-0.267081\pi\)
0.668162 + 0.744016i \(0.267081\pi\)
\(230\) −6.80418 8.28874i −0.448654 0.546543i
\(231\) 0.0563205 0.00370562
\(232\) −2.80922 + 2.80922i −0.184434 + 0.184434i
\(233\) −2.91503 2.91503i −0.190970 0.190970i 0.605145 0.796115i \(-0.293115\pi\)
−0.796115 + 0.605145i \(0.793115\pi\)
\(234\) 1.00633i 0.0657860i
\(235\) −21.8241 0.140908i −1.42365 0.00919182i
\(236\) −5.73861 −0.373552
\(237\) 3.67862 + 3.67862i 0.238952 + 0.238952i
\(238\) 0.855587 + 0.855587i 0.0554594 + 0.0554594i
\(239\) 8.30821i 0.537413i 0.963222 + 0.268707i \(0.0865962\pi\)
−0.963222 + 0.268707i \(0.913404\pi\)
\(240\) 0.0144369 2.23602i 0.000931900 0.144335i
\(241\) 14.5130i 0.934862i 0.884030 + 0.467431i \(0.154820\pi\)
−0.884030 + 0.467431i \(0.845180\pi\)
\(242\) 7.77759 7.77759i 0.499962 0.499962i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) −5.09237 −0.326005
\(245\) −5.08469 + 5.01945i −0.324849 + 0.320681i
\(246\) 7.17074 0.457190
\(247\) −5.14516 5.14516i −0.327379 0.327379i
\(248\) 3.68342 + 3.68342i 0.233898 + 0.233898i
\(249\) −14.0773 −0.892112
\(250\) 0.216542 11.1782i 0.0136953 0.706974i
\(251\) 14.3863i 0.908054i −0.890988 0.454027i \(-0.849987\pi\)
0.890988 0.454027i \(-0.150013\pi\)
\(252\) −1.37926 1.37926i −0.0868853 0.0868853i
\(253\) 0.106461 0.0885501i 0.00669316 0.00556710i
\(254\) 9.13091i 0.572925i
\(255\) 0.987128 0.974463i 0.0618163 0.0610232i
\(256\) 1.00000 0.0625000
\(257\) 3.82209 3.82209i 0.238416 0.238416i −0.577778 0.816194i \(-0.696080\pi\)
0.816194 + 0.577778i \(0.196080\pi\)
\(258\) 5.83089 5.83089i 0.363015 0.363015i
\(259\) 4.03474i 0.250707i
\(260\) −2.25018 0.0145284i −0.139550 0.000901011i
\(261\) 3.97284 0.245913
\(262\) −9.99224 + 9.99224i −0.617323 + 0.617323i
\(263\) −19.6268 + 19.6268i −1.21024 + 1.21024i −0.239296 + 0.970947i \(0.576917\pi\)
−0.970947 + 0.239296i \(0.923083\pi\)
\(264\) 0.0288739 0.00177706
\(265\) −8.65847 0.0559037i −0.531886 0.00343414i
\(266\) 14.1037 0.864755
\(267\) −7.43295 7.43295i −0.454889 0.454889i
\(268\) −4.63966 + 4.63966i −0.283413 + 0.283413i
\(269\) 1.94226i 0.118422i −0.998245 0.0592110i \(-0.981142\pi\)
0.998245 0.0592110i \(-0.0188585\pi\)
\(270\) −1.59131 + 1.57090i −0.0968443 + 0.0956018i
\(271\) 5.65568 0.343558 0.171779 0.985136i \(-0.445049\pi\)
0.171779 + 0.985136i \(0.445049\pi\)
\(272\) 0.438634 + 0.438634i 0.0265961 + 0.0265961i
\(273\) −1.38800 + 1.38800i −0.0840053 + 0.0840053i
\(274\) 14.1301 0.853629
\(275\) 0.144357 + 0.00186417i 0.00870508 + 0.000112414i
\(276\) −4.77573 0.438634i −0.287465 0.0264027i
\(277\) −6.03861 + 6.03861i −0.362825 + 0.362825i −0.864852 0.502027i \(-0.832588\pi\)
0.502027 + 0.864852i \(0.332588\pi\)
\(278\) −7.81231 7.81231i −0.468551 0.468551i
\(279\) 5.20915i 0.311864i
\(280\) 3.10397 3.06415i 0.185498 0.183118i
\(281\) 19.0527i 1.13659i 0.822825 + 0.568294i \(0.192396\pi\)
−0.822825 + 0.568294i \(0.807604\pi\)
\(282\) −6.90153 + 6.90153i −0.410980 + 0.410980i
\(283\) 3.82033 3.82033i 0.227095 0.227095i −0.584383 0.811478i \(-0.698663\pi\)
0.811478 + 0.584383i \(0.198663\pi\)
\(284\) 5.47777i 0.325046i
\(285\) 0.104387 16.1677i 0.00618337 0.957692i
\(286\) 0.0290567i 0.00171816i
\(287\) 9.89032 + 9.89032i 0.583807 + 0.583807i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) 16.6152i 0.977365i
\(290\) −0.0573557 + 8.88336i −0.00336804 + 0.521649i
\(291\) 1.20318i 0.0705319i
\(292\) −0.908695 + 0.908695i −0.0531773 + 0.0531773i
\(293\) 2.20441 2.20441i 0.128783 0.128783i −0.639777 0.768560i \(-0.720973\pi\)
0.768560 + 0.639777i \(0.220973\pi\)
\(294\) 3.19528i 0.186352i
\(295\) −9.13194 + 9.01477i −0.531682 + 0.524860i
\(296\) 2.06849i 0.120229i
\(297\) −0.0204169 0.0204169i −0.00118471 0.00118471i
\(298\) 9.22408 9.22408i 0.534336 0.534336i
\(299\) −0.441412 + 4.80597i −0.0255275 + 0.277937i
\(300\) −3.48959 3.58089i −0.201471 0.206743i
\(301\) 16.0846 0.927103
\(302\) 1.52797 1.52797i 0.0879250 0.0879250i
\(303\) 10.7549 + 10.7549i 0.617853 + 0.617853i
\(304\) 7.23057 0.414701
\(305\) −8.10355 + 7.99958i −0.464008 + 0.458055i
\(306\) 0.620322i 0.0354615i
\(307\) −13.5388 + 13.5388i −0.772700 + 0.772700i −0.978578 0.205878i \(-0.933995\pi\)
0.205878 + 0.978578i \(0.433995\pi\)
\(308\) 0.0398246 + 0.0398246i 0.00226922 + 0.00226922i
\(309\) 3.59438 0.204477
\(310\) 11.6478 + 0.0752042i 0.661549 + 0.00427131i
\(311\) −32.1959 −1.82566 −0.912831 0.408337i \(-0.866109\pi\)
−0.912831 + 0.408337i \(0.866109\pi\)
\(312\) −0.711585 + 0.711585i −0.0402855 + 0.0402855i
\(313\) 19.4438 19.4438i 1.09903 1.09903i 0.104502 0.994525i \(-0.466675\pi\)
0.994525 0.104502i \(-0.0333247\pi\)
\(314\) −19.0386 −1.07441
\(315\) −4.36152 0.0281603i −0.245744 0.00158665i
\(316\) 5.20235i 0.292655i
\(317\) −1.40155 + 1.40155i −0.0787188 + 0.0787188i −0.745370 0.666651i \(-0.767727\pi\)
0.666651 + 0.745370i \(0.267727\pi\)
\(318\) −2.73811 + 2.73811i −0.153545 + 0.153545i
\(319\) −0.114711 −0.00642260
\(320\) 1.59131 1.57090i 0.0889572 0.0878158i
\(321\) 10.4409i 0.582756i
\(322\) −5.98199 7.19197i −0.333363 0.400793i
\(323\) 3.17157 + 3.17157i 0.176471 + 0.176471i
\(324\) 1.00000i 0.0555556i
\(325\) −3.60357 + 3.51168i −0.199890 + 0.194793i
\(326\) −0.815762 −0.0451809
\(327\) −0.871197 0.871197i −0.0481773 0.0481773i
\(328\) 5.07048 + 5.07048i 0.279970 + 0.279970i
\(329\) −19.0380 −1.04960
\(330\) 0.0459474 0.0453579i 0.00252932 0.00249687i
\(331\) 29.9547 1.64646 0.823229 0.567709i \(-0.192170\pi\)
0.823229 + 0.567709i \(0.192170\pi\)
\(332\) −9.95414 9.95414i −0.546305 0.546305i
\(333\) −1.46265 + 1.46265i −0.0801525 + 0.0801525i
\(334\) 5.74232i 0.314206i
\(335\) −0.0947276 + 14.6716i −0.00517552 + 0.801595i
\(336\) 1.95057i 0.106412i
\(337\) 9.66919 + 9.66919i 0.526714 + 0.526714i 0.919591 0.392877i \(-0.128520\pi\)
−0.392877 + 0.919591i \(0.628520\pi\)
\(338\) −8.47630 8.47630i −0.461050 0.461050i
\(339\) −14.9998 −0.814677
\(340\) 1.38705 + 0.00895556i 0.0752236 + 0.000485683i
\(341\) 0.150408i 0.00814507i
\(342\) −5.11278 5.11278i −0.276468 0.276468i
\(343\) −14.0620 + 14.0620i −0.759274 + 0.759274i
\(344\) 8.24612 0.444601
\(345\) −8.28874 + 6.80418i −0.446251 + 0.366325i
\(346\) 17.1572 0.922379
\(347\) 5.75653 5.75653i 0.309026 0.309026i −0.535505 0.844532i \(-0.679879\pi\)
0.844532 + 0.535505i \(0.179879\pi\)
\(348\) 2.80922 + 2.80922i 0.150590 + 0.150590i
\(349\) 15.4579i 0.827443i 0.910404 + 0.413721i \(0.135771\pi\)
−0.910404 + 0.413721i \(0.864229\pi\)
\(350\) 0.125934 9.75204i 0.00673145 0.521268i
\(351\) 1.00633 0.0537141
\(352\) 0.0204169 + 0.0204169i 0.00108823 + 0.00108823i
\(353\) 0.0222101 + 0.0222101i 0.00118213 + 0.00118213i 0.707698 0.706515i \(-0.249734\pi\)
−0.706515 + 0.707698i \(0.749734\pi\)
\(354\) 5.73861i 0.305004i
\(355\) 8.60501 + 8.71685i 0.456707 + 0.462643i
\(356\) 10.5118i 0.557123i
\(357\) 0.855587 0.855587i 0.0452824 0.0452824i
\(358\) −11.7837 11.7837i −0.622785 0.622785i
\(359\) 32.6259 1.72193 0.860964 0.508666i \(-0.169861\pi\)
0.860964 + 0.508666i \(0.169861\pi\)
\(360\) −2.23602 0.0144369i −0.117849 0.000760894i
\(361\) 33.2811 1.75164
\(362\) 4.73488 + 4.73488i 0.248860 + 0.248860i
\(363\) −7.77759 7.77759i −0.408217 0.408217i
\(364\) −1.96292 −0.102885
\(365\) −0.0185527 + 2.87348i −0.000971095 + 0.150405i
\(366\) 5.09237i 0.266182i
\(367\) 15.1093 + 15.1093i 0.788701 + 0.788701i 0.981281 0.192580i \(-0.0616854\pi\)
−0.192580 + 0.981281i \(0.561685\pi\)
\(368\) −3.06679 3.68711i −0.159867 0.192204i
\(369\) 7.17074i 0.373294i
\(370\) −3.24939 3.29162i −0.168928 0.171123i
\(371\) −7.55313 −0.392139
\(372\) 3.68342 3.68342i 0.190977 0.190977i
\(373\) −9.38306 + 9.38306i −0.485836 + 0.485836i −0.906990 0.421153i \(-0.861625\pi\)
0.421153 + 0.906990i \(0.361625\pi\)
\(374\) 0.0179111i 0.000926162i
\(375\) −11.1782 0.216542i −0.577242 0.0111822i
\(376\) −9.76024 −0.503346
\(377\) 2.82701 2.82701i 0.145599 0.145599i
\(378\) −1.37926 + 1.37926i −0.0709416 + 0.0709416i
\(379\) 14.3962 0.739483 0.369741 0.929135i \(-0.379446\pi\)
0.369741 + 0.929135i \(0.379446\pi\)
\(380\) 11.5061 11.3585i 0.590251 0.582678i
\(381\) 9.13091 0.467791
\(382\) 5.18262 + 5.18262i 0.265166 + 0.265166i
\(383\) −6.21540 + 6.21540i −0.317592 + 0.317592i −0.847842 0.530249i \(-0.822098\pi\)
0.530249 + 0.847842i \(0.322098\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0.125934 0.000813096i 0.00641819 4.14392e-5i
\(386\) −7.12739 −0.362775
\(387\) −5.83089 5.83089i −0.296401 0.296401i
\(388\) −0.850780 + 0.850780i −0.0431918 + 0.0431918i
\(389\) −23.6231 −1.19774 −0.598869 0.800847i \(-0.704383\pi\)
−0.598869 + 0.800847i \(0.704383\pi\)
\(390\) −0.0145284 + 2.25018i −0.000735672 + 0.113942i
\(391\) 0.272095 2.96249i 0.0137604 0.149820i
\(392\) −2.25940 + 2.25940i −0.114117 + 0.114117i
\(393\) 9.99224 + 9.99224i 0.504042 + 0.504042i
\(394\) 8.73570i 0.440098i
\(395\) 8.17236 + 8.27858i 0.411196 + 0.416540i
\(396\) 0.0288739i 0.00145097i
\(397\) −4.91069 + 4.91069i −0.246461 + 0.246461i −0.819516 0.573056i \(-0.805758\pi\)
0.573056 + 0.819516i \(0.305758\pi\)
\(398\) −14.5856 + 14.5856i −0.731111 + 0.731111i
\(399\) 14.1037i 0.706069i
\(400\) 0.0645626 4.99958i 0.00322813 0.249979i
\(401\) 14.4696i 0.722575i −0.932454 0.361288i \(-0.882337\pi\)
0.932454 0.361288i \(-0.117663\pi\)
\(402\) 4.63966 + 4.63966i 0.231405 + 0.231405i
\(403\) −3.70675 3.70675i −0.184646 0.184646i
\(404\) 15.2097i 0.756712i
\(405\) 1.57090 + 1.59131i 0.0780585 + 0.0790730i
\(406\) 7.74930i 0.384592i
\(407\) 0.0422322 0.0422322i 0.00209337 0.00209337i
\(408\) 0.438634 0.438634i 0.0217156 0.0217156i
\(409\) 22.5518i 1.11512i −0.830138 0.557558i \(-0.811738\pi\)
0.830138 0.557558i \(-0.188262\pi\)
\(410\) 16.0339 + 0.103524i 0.791859 + 0.00511266i
\(411\) 14.1301i 0.696985i
\(412\) 2.54161 + 2.54161i 0.125216 + 0.125216i
\(413\) −7.91505 + 7.91505i −0.389474 + 0.389474i
\(414\) −0.438634 + 4.77573i −0.0215577 + 0.234714i
\(415\) −31.4771 0.203233i −1.54515 0.00997631i
\(416\) −1.00633 −0.0493395
\(417\) −7.81231 + 7.81231i −0.382570 + 0.382570i
\(418\) 0.147626 + 0.147626i 0.00722062 + 0.00722062i
\(419\) −30.0512 −1.46810 −0.734049 0.679097i \(-0.762372\pi\)
−0.734049 + 0.679097i \(0.762372\pi\)
\(420\) −3.06415 3.10397i −0.149515 0.151458i
\(421\) 21.5409i 1.04984i 0.851152 + 0.524919i \(0.175905\pi\)
−0.851152 + 0.524919i \(0.824095\pi\)
\(422\) −17.8813 + 17.8813i −0.870448 + 0.870448i
\(423\) 6.90153 + 6.90153i 0.335564 + 0.335564i
\(424\) −3.87227 −0.188054
\(425\) 2.22131 2.16467i 0.107749 0.105002i
\(426\) 5.47777 0.265399
\(427\) −7.02370 + 7.02370i −0.339901 + 0.339901i
\(428\) −7.38286 + 7.38286i −0.356864 + 0.356864i
\(429\) −0.0290567 −0.00140287
\(430\) 13.1222 12.9538i 0.632807 0.624688i
\(431\) 15.6022i 0.751529i 0.926715 + 0.375765i \(0.122620\pi\)
−0.926715 + 0.375765i \(0.877380\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −11.2969 + 11.2969i −0.542893 + 0.542893i −0.924376 0.381483i \(-0.875414\pi\)
0.381483 + 0.924376i \(0.375414\pi\)
\(434\) 10.1608 0.487735
\(435\) 8.88336 + 0.0573557i 0.425924 + 0.00274999i
\(436\) 1.23206i 0.0590049i
\(437\) −22.1746 26.6599i −1.06076 1.27532i
\(438\) 0.908695 + 0.908695i 0.0434191 + 0.0434191i
\(439\) 3.20333i 0.152887i −0.997074 0.0764433i \(-0.975644\pi\)
0.997074 0.0764433i \(-0.0243564\pi\)
\(440\) 0.0645626 0.000416850i 0.00307790 1.98726e-5i
\(441\) 3.19528 0.152156
\(442\) −0.441412 0.441412i −0.0209958 0.0209958i
\(443\) −15.6087 15.6087i −0.741590 0.741590i 0.231294 0.972884i \(-0.425704\pi\)
−0.972884 + 0.231294i \(0.925704\pi\)
\(444\) −2.06849 −0.0981663
\(445\) −16.5129 16.7275i −0.782788 0.792961i
\(446\) 9.00179 0.426247
\(447\) −9.22408 9.22408i −0.436284 0.436284i
\(448\) 1.37926 1.37926i 0.0651640 0.0651640i
\(449\) 11.2112i 0.529087i 0.964374 + 0.264543i \(0.0852213\pi\)
−0.964374 + 0.264543i \(0.914779\pi\)
\(450\) −3.58089 + 3.48959i −0.168805 + 0.164501i
\(451\) 0.207047i 0.00974947i
\(452\) −10.6065 10.6065i −0.498885 0.498885i
\(453\) −1.52797 1.52797i −0.0717904 0.0717904i
\(454\) 17.2793 0.810956
\(455\) −3.12363 + 3.08355i −0.146438 + 0.144559i
\(456\) 7.23057i 0.338602i
\(457\) 17.6613 + 17.6613i 0.826163 + 0.826163i 0.986984 0.160821i \(-0.0514141\pi\)
−0.160821 + 0.986984i \(0.551414\pi\)
\(458\) 14.2993 14.2993i 0.668162 0.668162i
\(459\) −0.620322 −0.0289542
\(460\) −10.6723 1.04974i −0.497599 0.0489445i
\(461\) 19.3119 0.899444 0.449722 0.893169i \(-0.351523\pi\)
0.449722 + 0.893169i \(0.351523\pi\)
\(462\) 0.0398246 0.0398246i 0.00185281 0.00185281i
\(463\) 12.6411 + 12.6411i 0.587484 + 0.587484i 0.936949 0.349465i \(-0.113637\pi\)
−0.349465 + 0.936949i \(0.613637\pi\)
\(464\) 3.97284i 0.184434i
\(465\) 0.0752042 11.6478i 0.00348751 0.540152i
\(466\) −4.12247 −0.190970
\(467\) −27.3483 27.3483i −1.26553 1.26553i −0.948373 0.317157i \(-0.897272\pi\)
−0.317157 0.948373i \(-0.602728\pi\)
\(468\) 0.711585 + 0.711585i 0.0328930 + 0.0328930i
\(469\) 12.7986i 0.590985i
\(470\) −15.5316 + 15.3323i −0.716419 + 0.707228i
\(471\) 19.0386i 0.877251i
\(472\) −4.05781 + 4.05781i −0.186776 + 0.186776i
\(473\) 0.168360 + 0.168360i 0.00774122 + 0.00774122i
\(474\) 5.20235 0.238952
\(475\) 0.466824 36.1498i 0.0214194 1.65867i
\(476\) 1.20998 0.0554594
\(477\) 2.73811 + 2.73811i 0.125369 + 0.125369i
\(478\) 5.87479 + 5.87479i 0.268707 + 0.268707i
\(479\) −26.9547 −1.23159 −0.615796 0.787906i \(-0.711165\pi\)
−0.615796 + 0.787906i \(0.711165\pi\)
\(480\) −1.57090 1.59131i −0.0717013 0.0726332i
\(481\) 2.08159i 0.0949124i
\(482\) 10.2622 + 10.2622i 0.467431 + 0.467431i
\(483\) −7.19197 + 5.98199i −0.327246 + 0.272190i
\(484\) 10.9992i 0.499962i
\(485\) −0.0173703 + 2.69035i −0.000788745 + 0.122162i
\(486\) 1.00000 0.0453609
\(487\) 28.7208 28.7208i 1.30146 1.30146i 0.374058 0.927405i \(-0.377966\pi\)
0.927405 0.374058i \(-0.122034\pi\)
\(488\) −3.60085 + 3.60085i −0.163003 + 0.163003i
\(489\) 0.815762i 0.0368900i
\(490\) −0.0461300 + 7.14470i −0.00208394 + 0.322765i
\(491\) 2.65360 0.119755 0.0598777 0.998206i \(-0.480929\pi\)
0.0598777 + 0.998206i \(0.480929\pi\)
\(492\) 5.07048 5.07048i 0.228595 0.228595i
\(493\) −1.74262 + 1.74262i −0.0784838 + 0.0784838i
\(494\) −7.27635 −0.327379
\(495\) −0.0453579 0.0459474i −0.00203869 0.00206518i
\(496\) 5.20915 0.233898
\(497\) 7.55528 + 7.55528i 0.338900 + 0.338900i
\(498\) −9.95414 + 9.95414i −0.446056 + 0.446056i
\(499\) 9.11525i 0.408055i 0.978965 + 0.204027i \(0.0654032\pi\)
−0.978965 + 0.204027i \(0.934597\pi\)
\(500\) −7.75109 8.05733i −0.346639 0.360335i
\(501\) −5.74232 −0.256548
\(502\) −10.1726 10.1726i −0.454027 0.454027i
\(503\) 17.5461 17.5461i 0.782343 0.782343i −0.197883 0.980226i \(-0.563407\pi\)
0.980226 + 0.197883i \(0.0634065\pi\)
\(504\) −1.95057 −0.0868853
\(505\) 23.8929 + 24.2035i 1.06322 + 1.07704i
\(506\) 0.0126651 0.137894i 0.000563031 0.00613013i
\(507\) −8.47630 + 8.47630i −0.376446 + 0.376446i
\(508\) 6.45653 + 6.45653i 0.286462 + 0.286462i
\(509\) 23.7897i 1.05446i −0.849722 0.527231i \(-0.823230\pi\)
0.849722 0.527231i \(-0.176770\pi\)
\(510\) 0.00895556 1.38705i 0.000396559 0.0614198i
\(511\) 2.50666i 0.110888i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −5.11278 + 5.11278i −0.225735 + 0.225735i
\(514\) 5.40526i 0.238416i
\(515\) 8.03712 + 0.0518919i 0.354158 + 0.00228663i
\(516\) 8.24612i 0.363015i
\(517\) −0.199274 0.199274i −0.00876406 0.00876406i
\(518\) −2.85299 2.85299i −0.125353 0.125353i
\(519\) 17.1572i 0.753119i
\(520\) −1.60139 + 1.58085i −0.0702257 + 0.0693246i
\(521\) 34.3911i 1.50670i −0.657619 0.753351i \(-0.728436\pi\)
0.657619 0.753351i \(-0.271564\pi\)
\(522\) 2.80922 2.80922i 0.122956 0.122956i
\(523\) 7.14069 7.14069i 0.312240 0.312240i −0.533537 0.845777i \(-0.679137\pi\)
0.845777 + 0.533537i \(0.179137\pi\)
\(524\) 14.1312i 0.617323i
\(525\) −9.75204 0.125934i −0.425614 0.00549621i
\(526\) 27.7565i 1.21024i
\(527\) 2.28491 + 2.28491i 0.0995323 + 0.0995323i
\(528\) 0.0204169 0.0204169i 0.000888532 0.000888532i
\(529\) −4.18960 + 22.6152i −0.182156 + 0.983270i
\(530\) −6.16199 + 6.08293i −0.267660 + 0.264226i
\(531\) 5.73861 0.249035
\(532\) 9.97284 9.97284i 0.432377 0.432377i
\(533\) −5.10259 5.10259i −0.221018 0.221018i
\(534\) −10.5118 −0.454889
\(535\) −0.150735 + 23.3462i −0.00651685 + 1.00934i
\(536\) 6.56147i 0.283413i
\(537\) −11.7837 + 11.7837i −0.508502 + 0.508502i
\(538\) −1.37339 1.37339i −0.0592110 0.0592110i
\(539\) −0.0922600 −0.00397392
\(540\) −0.0144369 + 2.23602i −0.000621267 + 0.0962230i
\(541\) 8.24675 0.354555 0.177278 0.984161i \(-0.443271\pi\)
0.177278 + 0.984161i \(0.443271\pi\)
\(542\) 3.99917 3.99917i 0.171779 0.171779i
\(543\) 4.73488 4.73488i 0.203193 0.203193i
\(544\) 0.620322 0.0265961
\(545\) −1.93544 1.96059i −0.0829050 0.0839825i
\(546\) 1.96292i 0.0840053i
\(547\) 11.4282 11.4282i 0.488633 0.488633i −0.419242 0.907875i \(-0.637704\pi\)
0.907875 + 0.419242i \(0.137704\pi\)
\(548\) 9.99147 9.99147i 0.426815 0.426815i
\(549\) 5.09237 0.217337
\(550\) 0.103394 0.100758i 0.00440875 0.00429633i
\(551\) 28.7259i 1.22376i
\(552\) −3.68711 + 3.06679i −0.156934 + 0.130531i
\(553\) 7.17540 + 7.17540i 0.305129 + 0.305129i
\(554\) 8.53988i 0.362825i
\(555\) −3.29162 + 3.24939i −0.139722 + 0.137929i
\(556\) −11.0483 −0.468551
\(557\) −28.6684 28.6684i −1.21472 1.21472i −0.969456 0.245264i \(-0.921125\pi\)
−0.245264 0.969456i \(-0.578875\pi\)
\(558\) −3.68342 3.68342i −0.155932 0.155932i
\(559\) −8.29834 −0.350982
\(560\) 0.0281603 4.36152i 0.00118999 0.184308i
\(561\) 0.0179111 0.000756208
\(562\) 13.4723 + 13.4723i 0.568294 + 0.568294i
\(563\) 6.96259 6.96259i 0.293438 0.293438i −0.544999 0.838437i \(-0.683470\pi\)
0.838437 + 0.544999i \(0.183470\pi\)
\(564\) 9.76024i 0.410980i
\(565\) −33.5398 0.216551i −1.41103 0.00911037i
\(566\) 5.40276i 0.227095i
\(567\) 1.37926 + 1.37926i 0.0579235 + 0.0579235i
\(568\) 3.87337 + 3.87337i 0.162523 + 0.162523i
\(569\) 14.2217 0.596204 0.298102 0.954534i \(-0.403647\pi\)
0.298102 + 0.954534i \(0.403647\pi\)
\(570\) −11.3585 11.5061i −0.475754 0.481938i
\(571\) 35.8009i 1.49822i −0.662444 0.749111i \(-0.730481\pi\)
0.662444 0.749111i \(-0.269519\pi\)
\(572\) −0.0205462 0.0205462i −0.000859080 0.000859080i
\(573\) 5.18262 5.18262i 0.216507 0.216507i
\(574\) 13.9870 0.583807
\(575\) −18.6320 + 15.0946i −0.777009 + 0.629489i
\(576\) −1.00000 −0.0416667
\(577\) −27.3402 + 27.3402i −1.13819 + 1.13819i −0.149414 + 0.988775i \(0.547739\pi\)
−0.988775 + 0.149414i \(0.952261\pi\)
\(578\) −11.7487 11.7487i −0.488682 0.488682i
\(579\) 7.12739i 0.296204i
\(580\) 6.24092 + 6.32204i 0.259140 + 0.262508i
\(581\) −27.4587 −1.13918
\(582\) 0.850780 + 0.850780i 0.0352660 + 0.0352660i
\(583\) −0.0790597 0.0790597i −0.00327432 0.00327432i
\(584\) 1.28509i 0.0531773i
\(585\) 2.25018 + 0.0145284i 0.0930335 + 0.000600674i
\(586\) 3.11750i 0.128783i
\(587\) 20.3799 20.3799i 0.841168 0.841168i −0.147843 0.989011i \(-0.547233\pi\)
0.989011 + 0.147843i \(0.0472330\pi\)
\(588\) 2.25940 + 2.25940i 0.0931761 + 0.0931761i
\(589\) 37.6651 1.55196
\(590\) −0.0828480 + 12.8317i −0.00341080 + 0.528271i
\(591\) −8.73570 −0.359339
\(592\) −1.46265 1.46265i −0.0601144 0.0601144i
\(593\) 25.3498 + 25.3498i 1.04099 + 1.04099i 0.999123 + 0.0418694i \(0.0133313\pi\)
0.0418694 + 0.999123i \(0.486669\pi\)
\(594\) −0.0288739 −0.00118471
\(595\) 1.92546 1.90076i 0.0789363 0.0779235i
\(596\) 13.0448i 0.534336i
\(597\) 14.5856 + 14.5856i 0.596950 + 0.596950i
\(598\) 3.08621 + 3.71046i 0.126205 + 0.151732i
\(599\) 10.3371i 0.422363i 0.977447 + 0.211182i \(0.0677311\pi\)
−0.977447 + 0.211182i \(0.932269\pi\)
\(600\) −4.99958 0.0645626i −0.204107 0.00263576i
\(601\) −4.83569 −0.197252 −0.0986259 0.995125i \(-0.531445\pi\)
−0.0986259 + 0.995125i \(0.531445\pi\)
\(602\) 11.3736 11.3736i 0.463552 0.463552i
\(603\) 4.63966 4.63966i 0.188942 0.188942i
\(604\) 2.16088i 0.0879250i
\(605\) −17.2786 17.5031i −0.702473 0.711603i
\(606\) 15.2097 0.617853
\(607\) 25.7553 25.7553i 1.04538 1.04538i 0.0464558 0.998920i \(-0.485207\pi\)
0.998920 0.0464558i \(-0.0147927\pi\)
\(608\) 5.11278 5.11278i 0.207351 0.207351i
\(609\) 7.74930 0.314018
\(610\) −0.0735182 + 11.3866i −0.00297666 + 0.461031i
\(611\) 9.82204 0.397357
\(612\) −0.438634 0.438634i −0.0177307 0.0177307i
\(613\) 16.7564 16.7564i 0.676784 0.676784i −0.282487 0.959271i \(-0.591159\pi\)
0.959271 + 0.282487i \(0.0911593\pi\)
\(614\) 19.1467i 0.772700i
\(615\) 0.103524 16.0339i 0.00417447 0.646550i
\(616\) 0.0563205 0.00226922
\(617\) 3.44309 + 3.44309i 0.138614 + 0.138614i 0.773009 0.634395i \(-0.218751\pi\)
−0.634395 + 0.773009i \(0.718751\pi\)
\(618\) 2.54161 2.54161i 0.102239 0.102239i
\(619\) 41.6136 1.67259 0.836296 0.548278i \(-0.184716\pi\)
0.836296 + 0.548278i \(0.184716\pi\)
\(620\) 8.28939 8.18304i 0.332910 0.328639i
\(621\) 4.77573 + 0.438634i 0.191643 + 0.0176018i
\(622\) −22.7659 + 22.7659i −0.912831 + 0.912831i
\(623\) −14.4985 14.4985i −0.580870 0.580870i
\(624\) 1.00633i 0.0402855i
\(625\) −24.9917 0.645572i −0.999667 0.0258229i
\(626\) 27.4976i 1.09903i
\(627\) 0.147626 0.147626i 0.00589561 0.00589561i
\(628\) −13.4623 + 13.4623i −0.537204 + 0.537204i
\(629\) 1.28313i 0.0511618i
\(630\) −3.10397 + 3.06415i −0.123665 + 0.122078i
\(631\) 6.27086i 0.249639i 0.992179 + 0.124820i \(0.0398352\pi\)
−0.992179 + 0.124820i \(0.960165\pi\)
\(632\) 3.67862 + 3.67862i 0.146328 + 0.146328i
\(633\) 17.8813 + 17.8813i 0.710718 + 0.710718i
\(634\) 1.98209i 0.0787188i
\(635\) 20.4169 + 0.131822i 0.810221 + 0.00523121i
\(636\) 3.87227i 0.153545i
\(637\) 2.27371 2.27371i 0.0900876 0.0900876i
\(638\) −0.0811132 + 0.0811132i −0.00321130 + 0.00321130i
\(639\) 5.47777i 0.216697i
\(640\) 0.0144369 2.23602i 0.000570670 0.0883865i
\(641\) 21.1913i 0.837007i 0.908215 + 0.418504i \(0.137445\pi\)
−0.908215 + 0.418504i \(0.862555\pi\)
\(642\) 7.38286 + 7.38286i 0.291378 + 0.291378i
\(643\) 25.8131 25.8131i 1.01797 1.01797i 0.0181324 0.999836i \(-0.494228\pi\)
0.999836 0.0181324i \(-0.00577205\pi\)
\(644\) −9.31540 0.855587i −0.367078 0.0337148i
\(645\) −12.9538 13.1222i −0.510056 0.516685i
\(646\) 4.48528 0.176471
\(647\) 33.5677 33.5677i 1.31968 1.31968i 0.405654 0.914027i \(-0.367044\pi\)
0.914027 0.405654i \(-0.132956\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) −0.165696 −0.00650414
\(650\) −0.0649715 + 5.03124i −0.00254839 + 0.197342i
\(651\) 10.1608i 0.398234i
\(652\) −0.576831 + 0.576831i −0.0225904 + 0.0225904i
\(653\) −13.1083 13.1083i −0.512967 0.512967i 0.402467 0.915434i \(-0.368153\pi\)
−0.915434 + 0.402467i \(0.868153\pi\)
\(654\) −1.23206 −0.0481773
\(655\) 22.1986 + 22.4871i 0.867372 + 0.878645i
\(656\) 7.17074 0.279970
\(657\) 0.908695 0.908695i 0.0354516 0.0354516i
\(658\) −13.4619 + 13.4619i −0.524800 + 0.524800i
\(659\) 13.3409 0.519688 0.259844 0.965651i \(-0.416329\pi\)
0.259844 + 0.965651i \(0.416329\pi\)
\(660\) 0.000416850 0.0645626i 1.62259e−5 0.00251310i
\(661\) 42.1609i 1.63987i −0.572459 0.819934i \(-0.694010\pi\)
0.572459 0.819934i \(-0.305990\pi\)
\(662\) 21.1812 21.1812i 0.823229 0.823229i
\(663\) −0.441412 + 0.441412i −0.0171430 + 0.0171430i
\(664\) −14.0773 −0.546305
\(665\) 0.203615 31.5362i 0.00789584 1.22292i
\(666\) 2.06849i 0.0801525i
\(667\) 14.6483 12.1839i 0.567185 0.471761i
\(668\) −4.06044 4.06044i −0.157103 0.157103i
\(669\) 9.00179i 0.348029i
\(670\) 10.3074 + 10.4414i 0.398210 + 0.403385i
\(671\) −0.147036 −0.00567627
\(672\) −1.37926 1.37926i −0.0532062 0.0532062i
\(673\) −8.80148 8.80148i −0.339272 0.339272i 0.516821 0.856093i \(-0.327115\pi\)
−0.856093 + 0.516821i \(0.827115\pi\)
\(674\) 13.6743 0.526714
\(675\) 3.48959 + 3.58089i 0.134314 + 0.137829i
\(676\) −11.9873 −0.461050
\(677\) 1.46521 + 1.46521i 0.0563127 + 0.0563127i 0.734702 0.678390i \(-0.237322\pi\)
−0.678390 + 0.734702i \(0.737322\pi\)
\(678\) −10.6065 + 10.6065i −0.407338 + 0.407338i
\(679\) 2.34690i 0.0900656i
\(680\) 0.987128 0.974463i 0.0378546 0.0373689i
\(681\) 17.2793i 0.662142i
\(682\) 0.106355 + 0.106355i 0.00407253 + 0.00407253i
\(683\) −8.63814 8.63814i −0.330529 0.330529i 0.522258 0.852787i \(-0.325090\pi\)
−0.852787 + 0.522258i \(0.825090\pi\)
\(684\) −7.23057 −0.276468
\(685\) 0.203995 31.5952i 0.00779425 1.20719i
\(686\) 19.8866i 0.759274i
\(687\) −14.2993 14.2993i −0.545552 0.545552i
\(688\) 5.83089 5.83089i 0.222300 0.222300i
\(689\) 3.89679 0.148456
\(690\) −1.04974 + 10.6723i −0.0399630 + 0.406288i
\(691\) −3.45873 −0.131576 −0.0657882 0.997834i \(-0.520956\pi\)
−0.0657882 + 0.997834i \(0.520956\pi\)
\(692\) 12.1320 12.1320i 0.461189 0.461189i
\(693\) −0.0398246 0.0398246i −0.00151281 0.00151281i
\(694\) 8.14096i 0.309026i
\(695\) −17.5813 + 17.3557i −0.666895 + 0.658339i
\(696\) 3.97284 0.150590
\(697\) 3.14533 + 3.14533i 0.119138 + 0.119138i
\(698\) 10.9304 + 10.9304i 0.413721 + 0.413721i
\(699\) 4.12247i 0.155926i
\(700\) −6.80668 6.98478i −0.257268 0.264000i
\(701\) 27.3257i 1.03208i −0.856565 0.516039i \(-0.827406\pi\)
0.856565 0.516039i \(-0.172594\pi\)
\(702\) 0.711585 0.711585i 0.0268570 0.0268570i
\(703\) −10.5758 10.5758i −0.398872 0.398872i
\(704\) 0.0288739 0.00108823
\(705\) 15.3323 + 15.5316i 0.577449 + 0.584954i
\(706\) 0.0314099 0.00118213
\(707\) 20.9782 + 20.9782i 0.788966 + 0.788966i
\(708\) 4.05781 + 4.05781i 0.152502 + 0.152502i
\(709\) −16.0144 −0.601435 −0.300717 0.953713i \(-0.597226\pi\)
−0.300717 + 0.953713i \(0.597226\pi\)
\(710\) 12.2484 + 0.0790822i 0.459675 + 0.00296790i
\(711\) 5.20235i 0.195103i
\(712\) −7.43295 7.43295i −0.278562 0.278562i
\(713\) −15.9754 19.2067i −0.598282 0.719297i
\(714\) 1.20998i 0.0452824i
\(715\) −0.0649715 0.000419490i −0.00242979 1.56880e-5i
\(716\) −16.6646 −0.622785
\(717\) 5.87479 5.87479i 0.219398 0.219398i
\(718\) 23.0700 23.0700i 0.860964 0.860964i
\(719\) 19.1306i 0.713451i 0.934209 + 0.356726i \(0.116107\pi\)
−0.934209 + 0.356726i \(0.883893\pi\)
\(720\) −1.59131 + 1.57090i −0.0593048 + 0.0585439i
\(721\) 7.01110 0.261107
\(722\) 23.5333 23.5333i 0.875818 0.875818i
\(723\) 10.2622 10.2622i 0.381656 0.381656i
\(724\) 6.69613 0.248860
\(725\) 19.8625 + 0.256497i 0.737676 + 0.00952606i
\(726\) −10.9992 −0.408217
\(727\) 19.9934 + 19.9934i 0.741513 + 0.741513i 0.972869 0.231356i \(-0.0743162\pi\)
−0.231356 + 0.972869i \(0.574316\pi\)
\(728\) −1.38800 + 1.38800i −0.0514425 + 0.0514425i
\(729\) 1.00000i 0.0370370i
\(730\) 2.01874 + 2.04498i 0.0747170 + 0.0756881i
\(731\) 5.11525 0.189194
\(732\) 3.60085 + 3.60085i 0.133091 + 0.133091i
\(733\) 24.0119 24.0119i 0.886899 0.886899i −0.107325 0.994224i \(-0.534229\pi\)
0.994224 + 0.107325i \(0.0342286\pi\)
\(734\) 21.3678 0.788701
\(735\) 7.14470 + 0.0461300i 0.263536 + 0.00170153i
\(736\) −4.77573 0.438634i −0.176036 0.0161683i
\(737\) −0.133965 + 0.133965i −0.00493467 + 0.00493467i
\(738\) −5.07048 5.07048i −0.186647 0.186647i
\(739\) 34.2178i 1.25872i 0.777114 + 0.629360i \(0.216683\pi\)
−0.777114 + 0.629360i \(0.783317\pi\)
\(740\) −4.62519 0.0298627i −0.170026 0.00109777i
\(741\) 7.27635i 0.267304i
\(742\) −5.34087 + 5.34087i −0.196069 + 0.196069i
\(743\) 4.18125 4.18125i 0.153395 0.153395i −0.626237 0.779633i \(-0.715406\pi\)
0.779633 + 0.626237i \(0.215406\pi\)
\(744\) 5.20915i 0.190977i
\(745\) −20.4921 20.7584i −0.750771 0.760529i
\(746\) 13.2696i 0.485836i
\(747\) 9.95414 + 9.95414i 0.364203 + 0.364203i
\(748\) 0.0126651 + 0.0126651i 0.000463081 + 0.000463081i
\(749\) 20.3658i 0.744150i
\(750\) −8.05733 + 7.75109i −0.294212 + 0.283030i
\(751\) 27.8901i 1.01772i −0.860848 0.508861i \(-0.830067\pi\)
0.860848 0.508861i \(-0.169933\pi\)
\(752\) −6.90153 + 6.90153i −0.251673 + 0.251673i
\(753\) −10.1726 + 10.1726i −0.370712 + 0.370712i
\(754\) 3.99800i 0.145599i
\(755\) −3.39452 3.43864i −0.123539 0.125145i
\(756\) 1.95057i 0.0709416i
\(757\) 24.9495 + 24.9495i 0.906806 + 0.906806i 0.996013 0.0892070i \(-0.0284333\pi\)
−0.0892070 + 0.996013i \(0.528433\pi\)
\(758\) 10.1796 10.1796i 0.369741 0.369741i
\(759\) −0.137894 0.0126651i −0.00500523 0.000459713i
\(760\) 0.104387 16.1677i 0.00378652 0.586464i
\(761\) 13.0514 0.473115 0.236557 0.971618i \(-0.423981\pi\)
0.236557 + 0.971618i \(0.423981\pi\)
\(762\) 6.45653 6.45653i 0.233895 0.233895i
\(763\) −1.69933 1.69933i −0.0615199 0.0615199i
\(764\) 7.32933 0.265166
\(765\) −1.38705 0.00895556i −0.0501490 0.000323789i
\(766\) 8.78991i 0.317592i
\(767\) 4.08351 4.08351i 0.147447 0.147447i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) −50.0583 −1.80515 −0.902574 0.430536i \(-0.858325\pi\)
−0.902574 + 0.430536i \(0.858325\pi\)
\(770\) 0.0896237 0.0884738i 0.00322981 0.00318837i
\(771\) −5.40526 −0.194666
\(772\) −5.03982 + 5.03982i −0.181387 + 0.181387i
\(773\) 4.59947 4.59947i 0.165431 0.165431i −0.619537 0.784968i \(-0.712679\pi\)
0.784968 + 0.619537i \(0.212679\pi\)
\(774\) −8.24612 −0.296401
\(775\) 0.336316 26.0436i 0.0120808 0.935513i
\(776\) 1.20318i 0.0431918i
\(777\) −2.85299 + 2.85299i −0.102351 + 0.102351i
\(778\) −16.7040 + 16.7040i −0.598869 + 0.598869i
\(779\) 51.8485 1.85767
\(780\)