Properties

Label 690.3.k.a.277.6
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.6
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.62353 + 4.25642i) q^{5} -2.44949 q^{6} +(0.185981 + 0.185981i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(2.62353 + 4.25642i) q^{5} -2.44949 q^{6} +(0.185981 + 0.185981i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.63289 + 6.87995i) q^{10} +17.6358 q^{11} +(-2.44949 - 2.44949i) q^{12} +(16.7901 - 16.7901i) q^{13} +0.371963i q^{14} +(-8.42618 - 1.99988i) q^{15} -4.00000 q^{16} +(19.8067 + 19.8067i) q^{17} +(3.00000 - 3.00000i) q^{18} +16.2208i q^{19} +(-8.51284 + 5.24705i) q^{20} -0.455559 q^{21} +(17.6358 + 17.6358i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-11.2342 + 22.3337i) q^{25} +33.5803 q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.371963 + 0.371963i) q^{28} -5.94151i q^{29} +(-6.42630 - 10.4261i) q^{30} -4.19616 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-21.5994 + 21.5994i) q^{33} +39.6134i q^{34} +(-0.303688 + 1.27954i) q^{35} +6.00000 q^{36} +(-45.9154 - 45.9154i) q^{37} +(-16.2208 + 16.2208i) q^{38} +41.1273i q^{39} +(-13.7599 - 3.26579i) q^{40} -37.8568 q^{41} +(-0.455559 - 0.455559i) q^{42} +(-24.5503 + 24.5503i) q^{43} +35.2717i q^{44} +(12.7693 - 7.87058i) q^{45} +6.78233 q^{46} +(30.1312 + 30.1312i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.9308i q^{49} +(-33.5679 + 11.0994i) q^{50} -48.5163 q^{51} +(33.5803 + 33.5803i) q^{52} +(-54.4809 + 54.4809i) q^{53} +7.34847i q^{54} +(46.2681 + 75.0656i) q^{55} -0.743925 q^{56} +(-19.8664 - 19.8664i) q^{57} +(5.94151 - 5.94151i) q^{58} -87.7441i q^{59} +(3.99976 - 16.8524i) q^{60} +20.2409 q^{61} +(-4.19616 - 4.19616i) q^{62} +(0.557944 - 0.557944i) q^{63} -8.00000i q^{64} +(115.515 + 27.4165i) q^{65} -43.1988 q^{66} +(5.03763 + 5.03763i) q^{67} +(-39.6134 + 39.6134i) q^{68} +8.30662i q^{69} +(-1.58323 + 0.975853i) q^{70} +42.6028 q^{71} +(6.00000 + 6.00000i) q^{72} +(25.5335 - 25.5335i) q^{73} -91.8308i q^{74} +(-13.5940 - 41.1121i) q^{75} -32.4416 q^{76} +(3.27994 + 3.27994i) q^{77} +(-41.1273 + 41.1273i) q^{78} +85.8118i q^{79} +(-10.4941 - 17.0257i) q^{80} -9.00000 q^{81} +(-37.8568 - 37.8568i) q^{82} +(-49.0744 + 49.0744i) q^{83} -0.911118i q^{84} +(-32.3423 + 136.269i) q^{85} -49.1006 q^{86} +(7.27683 + 7.27683i) q^{87} +(-35.2717 + 35.2717i) q^{88} -64.8558i q^{89} +(20.6398 + 4.89868i) q^{90} +6.24530 q^{91} +(6.78233 + 6.78233i) q^{92} +(5.13922 - 5.13922i) q^{93} +60.2624i q^{94} +(-69.0426 + 42.5557i) q^{95} +9.79796 q^{96} +(-63.8100 - 63.8100i) q^{97} +(48.9308 - 48.9308i) q^{98} -52.9075i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 2.62353 + 4.25642i 0.524705 + 0.851284i
\(6\) −2.44949 −0.408248
\(7\) 0.185981 + 0.185981i 0.0265688 + 0.0265688i 0.720266 0.693698i \(-0.244020\pi\)
−0.693698 + 0.720266i \(0.744020\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −1.63289 + 6.87995i −0.163289 + 0.687995i
\(11\) 17.6358 1.60326 0.801629 0.597821i \(-0.203967\pi\)
0.801629 + 0.597821i \(0.203967\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 16.7901 16.7901i 1.29155 1.29155i 0.357719 0.933829i \(-0.383554\pi\)
0.933829 0.357719i \(-0.116446\pi\)
\(14\) 0.371963i 0.0265688i
\(15\) −8.42618 1.99988i −0.561745 0.133325i
\(16\) −4.00000 −0.250000
\(17\) 19.8067 + 19.8067i 1.16510 + 1.16510i 0.983343 + 0.181758i \(0.0581786\pi\)
0.181758 + 0.983343i \(0.441821\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 16.2208i 0.853727i 0.904316 + 0.426863i \(0.140382\pi\)
−0.904316 + 0.426863i \(0.859618\pi\)
\(20\) −8.51284 + 5.24705i −0.425642 + 0.262353i
\(21\) −0.455559 −0.0216933
\(22\) 17.6358 + 17.6358i 0.801629 + 0.801629i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −11.2342 + 22.3337i −0.449369 + 0.893346i
\(26\) 33.5803 1.29155
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −0.371963 + 0.371963i −0.0132844 + 0.0132844i
\(29\) 5.94151i 0.204880i −0.994739 0.102440i \(-0.967335\pi\)
0.994739 0.102440i \(-0.0326649\pi\)
\(30\) −6.42630 10.4261i −0.214210 0.347535i
\(31\) −4.19616 −0.135360 −0.0676799 0.997707i \(-0.521560\pi\)
−0.0676799 + 0.997707i \(0.521560\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −21.5994 + 21.5994i −0.654528 + 0.654528i
\(34\) 39.6134i 1.16510i
\(35\) −0.303688 + 1.27954i −0.00867680 + 0.0365583i
\(36\) 6.00000 0.166667
\(37\) −45.9154 45.9154i −1.24096 1.24096i −0.959604 0.281353i \(-0.909217\pi\)
−0.281353 0.959604i \(-0.590783\pi\)
\(38\) −16.2208 + 16.2208i −0.426863 + 0.426863i
\(39\) 41.1273i 1.05454i
\(40\) −13.7599 3.26579i −0.343997 0.0816447i
\(41\) −37.8568 −0.923336 −0.461668 0.887053i \(-0.652749\pi\)
−0.461668 + 0.887053i \(0.652749\pi\)
\(42\) −0.455559 0.455559i −0.0108466 0.0108466i
\(43\) −24.5503 + 24.5503i −0.570937 + 0.570937i −0.932390 0.361453i \(-0.882281\pi\)
0.361453 + 0.932390i \(0.382281\pi\)
\(44\) 35.2717i 0.801629i
\(45\) 12.7693 7.87058i 0.283761 0.174902i
\(46\) 6.78233 0.147442
\(47\) 30.1312 + 30.1312i 0.641089 + 0.641089i 0.950823 0.309734i \(-0.100240\pi\)
−0.309734 + 0.950823i \(0.600240\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 48.9308i 0.998588i
\(50\) −33.5679 + 11.0994i −0.671358 + 0.221989i
\(51\) −48.5163 −0.951301
\(52\) 33.5803 + 33.5803i 0.645774 + 0.645774i
\(53\) −54.4809 + 54.4809i −1.02794 + 1.02794i −0.0283437 + 0.999598i \(0.509023\pi\)
−0.999598 + 0.0283437i \(0.990977\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 46.2681 + 75.0656i 0.841238 + 1.36483i
\(56\) −0.743925 −0.0132844
\(57\) −19.8664 19.8664i −0.348533 0.348533i
\(58\) 5.94151 5.94151i 0.102440 0.102440i
\(59\) 87.7441i 1.48719i −0.668631 0.743594i \(-0.733119\pi\)
0.668631 0.743594i \(-0.266881\pi\)
\(60\) 3.99976 16.8524i 0.0666627 0.280873i
\(61\) 20.2409 0.331818 0.165909 0.986141i \(-0.446944\pi\)
0.165909 + 0.986141i \(0.446944\pi\)
\(62\) −4.19616 4.19616i −0.0676799 0.0676799i
\(63\) 0.557944 0.557944i 0.00885625 0.00885625i
\(64\) 8.00000i 0.125000i
\(65\) 115.515 + 27.4165i 1.77716 + 0.421793i
\(66\) −43.1988 −0.654528
\(67\) 5.03763 + 5.03763i 0.0751885 + 0.0751885i 0.743701 0.668512i \(-0.233069\pi\)
−0.668512 + 0.743701i \(0.733069\pi\)
\(68\) −39.6134 + 39.6134i −0.582550 + 0.582550i
\(69\) 8.30662i 0.120386i
\(70\) −1.58323 + 0.975853i −0.0226176 + 0.0139408i
\(71\) 42.6028 0.600039 0.300020 0.953933i \(-0.403007\pi\)
0.300020 + 0.953933i \(0.403007\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 25.5335 25.5335i 0.349773 0.349773i −0.510252 0.860025i \(-0.670448\pi\)
0.860025 + 0.510252i \(0.170448\pi\)
\(74\) 91.8308i 1.24096i
\(75\) −13.5940 41.1121i −0.181253 0.548161i
\(76\) −32.4416 −0.426863
\(77\) 3.27994 + 3.27994i 0.0425966 + 0.0425966i
\(78\) −41.1273 + 41.1273i −0.527272 + 0.527272i
\(79\) 85.8118i 1.08623i 0.839660 + 0.543113i \(0.182754\pi\)
−0.839660 + 0.543113i \(0.817246\pi\)
\(80\) −10.4941 17.0257i −0.131176 0.212821i
\(81\) −9.00000 −0.111111
\(82\) −37.8568 37.8568i −0.461668 0.461668i
\(83\) −49.0744 + 49.0744i −0.591258 + 0.591258i −0.937971 0.346713i \(-0.887298\pi\)
0.346713 + 0.937971i \(0.387298\pi\)
\(84\) 0.911118i 0.0108466i
\(85\) −32.3423 + 136.269i −0.380497 + 1.60317i
\(86\) −49.1006 −0.570937
\(87\) 7.27683 + 7.27683i 0.0836418 + 0.0836418i
\(88\) −35.2717 + 35.2717i −0.400815 + 0.400815i
\(89\) 64.8558i 0.728717i −0.931259 0.364358i \(-0.881288\pi\)
0.931259 0.364358i \(-0.118712\pi\)
\(90\) 20.6398 + 4.89868i 0.229332 + 0.0544298i
\(91\) 6.24530 0.0686297
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 5.13922 5.13922i 0.0552604 0.0552604i
\(94\) 60.2624i 0.641089i
\(95\) −69.0426 + 42.5557i −0.726764 + 0.447955i
\(96\) 9.79796 0.102062
\(97\) −63.8100 63.8100i −0.657835 0.657835i 0.297032 0.954868i \(-0.404003\pi\)
−0.954868 + 0.297032i \(0.904003\pi\)
\(98\) 48.9308 48.9308i 0.499294 0.499294i
\(99\) 52.9075i 0.534420i
\(100\) −44.6673 22.4685i −0.446673 0.224685i
\(101\) 193.561 1.91645 0.958224 0.286017i \(-0.0923315\pi\)
0.958224 + 0.286017i \(0.0923315\pi\)
\(102\) −48.5163 48.5163i −0.475650 0.475650i
\(103\) −40.0309 + 40.0309i −0.388650 + 0.388650i −0.874206 0.485556i \(-0.838617\pi\)
0.485556 + 0.874206i \(0.338617\pi\)
\(104\) 67.1605i 0.645774i
\(105\) −1.19517 1.93905i −0.0113826 0.0184672i
\(106\) −108.962 −1.02794
\(107\) −10.8053 10.8053i −0.100984 0.100984i 0.654810 0.755794i \(-0.272749\pi\)
−0.755794 + 0.654810i \(0.772749\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 159.431i 1.46267i 0.682019 + 0.731334i \(0.261102\pi\)
−0.682019 + 0.731334i \(0.738898\pi\)
\(110\) −28.7975 + 121.334i −0.261795 + 1.10303i
\(111\) 112.469 1.01324
\(112\) −0.743925 0.743925i −0.00664219 0.00664219i
\(113\) −18.9925 + 18.9925i −0.168075 + 0.168075i −0.786133 0.618058i \(-0.787920\pi\)
0.618058 + 0.786133i \(0.287920\pi\)
\(114\) 39.7327i 0.348533i
\(115\) 23.3310 + 5.53742i 0.202879 + 0.0481514i
\(116\) 11.8830 0.102440
\(117\) −50.3704 50.3704i −0.430516 0.430516i
\(118\) 87.7441 87.7441i 0.743594 0.743594i
\(119\) 7.36736i 0.0619106i
\(120\) 20.8521 12.8526i 0.173768 0.107105i
\(121\) 190.023 1.57044
\(122\) 20.2409 + 20.2409i 0.165909 + 0.165909i
\(123\) 46.3649 46.3649i 0.376950 0.376950i
\(124\) 8.39231i 0.0676799i
\(125\) −124.535 + 10.7753i −0.996278 + 0.0862025i
\(126\) 1.11589 0.00885625
\(127\) 60.8528 + 60.8528i 0.479156 + 0.479156i 0.904862 0.425706i \(-0.139974\pi\)
−0.425706 + 0.904862i \(0.639974\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 60.1357i 0.466168i
\(130\) 88.0987 + 142.932i 0.677682 + 1.09947i
\(131\) −51.5356 −0.393401 −0.196701 0.980464i \(-0.563023\pi\)
−0.196701 + 0.980464i \(0.563023\pi\)
\(132\) −43.1988 43.1988i −0.327264 0.327264i
\(133\) −3.01677 + 3.01677i −0.0226825 + 0.0226825i
\(134\) 10.0753i 0.0751885i
\(135\) −5.99964 + 25.2785i −0.0444418 + 0.187248i
\(136\) −79.2269 −0.582550
\(137\) −140.637 140.637i −1.02655 1.02655i −0.999638 0.0269071i \(-0.991434\pi\)
−0.0269071 0.999638i \(-0.508566\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 96.0813i 0.691232i −0.938376 0.345616i \(-0.887670\pi\)
0.938376 0.345616i \(-0.112330\pi\)
\(140\) −2.55908 0.607376i −0.0182792 0.00433840i
\(141\) −73.8061 −0.523447
\(142\) 42.6028 + 42.6028i 0.300020 + 0.300020i
\(143\) 296.108 296.108i 2.07069 2.07069i
\(144\) 12.0000i 0.0833333i
\(145\) 25.2896 15.5877i 0.174411 0.107501i
\(146\) 51.0669 0.349773
\(147\) 59.9278 + 59.9278i 0.407672 + 0.407672i
\(148\) 91.8308 91.8308i 0.620479 0.620479i
\(149\) 34.1953i 0.229499i 0.993394 + 0.114749i \(0.0366065\pi\)
−0.993394 + 0.114749i \(0.963394\pi\)
\(150\) 27.5181 54.7061i 0.183454 0.364707i
\(151\) 182.642 1.20955 0.604776 0.796395i \(-0.293263\pi\)
0.604776 + 0.796395i \(0.293263\pi\)
\(152\) −32.4416 32.4416i −0.213432 0.213432i
\(153\) 59.4201 59.4201i 0.388367 0.388367i
\(154\) 6.55987i 0.0425966i
\(155\) −11.0087 17.8606i −0.0710240 0.115230i
\(156\) −82.2545 −0.527272
\(157\) −67.8885 67.8885i −0.432411 0.432411i 0.457037 0.889448i \(-0.348911\pi\)
−0.889448 + 0.457037i \(0.848911\pi\)
\(158\) −85.8118 + 85.8118i −0.543113 + 0.543113i
\(159\) 133.450i 0.839311i
\(160\) 6.53158 27.5198i 0.0408224 0.171999i
\(161\) 1.26139 0.00783470
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −109.843 + 109.843i −0.673883 + 0.673883i −0.958609 0.284726i \(-0.908098\pi\)
0.284726 + 0.958609i \(0.408098\pi\)
\(164\) 75.7135i 0.461668i
\(165\) −148.603 35.2696i −0.900623 0.213755i
\(166\) −98.1488 −0.591258
\(167\) 22.5337 + 22.5337i 0.134932 + 0.134932i 0.771347 0.636415i \(-0.219583\pi\)
−0.636415 + 0.771347i \(0.719583\pi\)
\(168\) 0.911118 0.911118i 0.00542332 0.00542332i
\(169\) 394.817i 2.33620i
\(170\) −168.611 + 103.927i −0.991832 + 0.611334i
\(171\) 48.6624 0.284576
\(172\) −49.1006 49.1006i −0.285469 0.285469i
\(173\) −9.88896 + 9.88896i −0.0571616 + 0.0571616i −0.735110 0.677948i \(-0.762869\pi\)
0.677948 + 0.735110i \(0.262869\pi\)
\(174\) 14.5537i 0.0836418i
\(175\) −6.24300 + 2.06429i −0.0356743 + 0.0117959i
\(176\) −70.5434 −0.400815
\(177\) 107.464 + 107.464i 0.607142 + 0.607142i
\(178\) 64.8558 64.8558i 0.364358 0.364358i
\(179\) 285.992i 1.59772i −0.601517 0.798860i \(-0.705437\pi\)
0.601517 0.798860i \(-0.294563\pi\)
\(180\) 15.7412 + 25.5385i 0.0874508 + 0.141881i
\(181\) −133.675 −0.738539 −0.369269 0.929322i \(-0.620392\pi\)
−0.369269 + 0.929322i \(0.620392\pi\)
\(182\) 6.24530 + 6.24530i 0.0343148 + 0.0343148i
\(183\) −24.7900 + 24.7900i −0.135464 + 0.135464i
\(184\) 13.5647i 0.0737210i
\(185\) 74.9751 315.896i 0.405271 1.70754i
\(186\) 10.2784 0.0552604
\(187\) 349.308 + 349.308i 1.86796 + 1.86796i
\(188\) −60.2624 + 60.2624i −0.320545 + 0.320545i
\(189\) 1.36668i 0.00723110i
\(190\) −111.598 26.4869i −0.587360 0.139405i
\(191\) 106.774 0.559028 0.279514 0.960142i \(-0.409827\pi\)
0.279514 + 0.960142i \(0.409827\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 33.3322 33.3322i 0.172706 0.172706i −0.615461 0.788167i \(-0.711030\pi\)
0.788167 + 0.615461i \(0.211030\pi\)
\(194\) 127.620i 0.657835i
\(195\) −175.055 + 107.898i −0.897717 + 0.553325i
\(196\) 97.8616 0.499294
\(197\) −178.442 178.442i −0.905798 0.905798i 0.0901317 0.995930i \(-0.471271\pi\)
−0.995930 + 0.0901317i \(0.971271\pi\)
\(198\) 52.9075 52.9075i 0.267210 0.267210i
\(199\) 91.0351i 0.457463i 0.973490 + 0.228731i \(0.0734578\pi\)
−0.973490 + 0.228731i \(0.926542\pi\)
\(200\) −22.1989 67.1358i −0.110994 0.335679i
\(201\) −12.3396 −0.0613912
\(202\) 193.561 + 193.561i 0.958224 + 0.958224i
\(203\) 1.10501 1.10501i 0.00544340 0.00544340i
\(204\) 97.0327i 0.475650i
\(205\) −99.3182 161.134i −0.484479 0.786021i
\(206\) −80.0619 −0.388650
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) −67.1605 + 67.1605i −0.322887 + 0.322887i
\(209\) 286.068i 1.36875i
\(210\) 0.743880 3.13422i 0.00354229 0.0149249i
\(211\) 384.346 1.82154 0.910772 0.412909i \(-0.135487\pi\)
0.910772 + 0.412909i \(0.135487\pi\)
\(212\) −108.962 108.962i −0.513971 0.513971i
\(213\) −52.1775 + 52.1775i −0.244965 + 0.244965i
\(214\) 21.6106i 0.100984i
\(215\) −168.905 40.0881i −0.785603 0.186456i
\(216\) −14.6969 −0.0680414
\(217\) −0.780406 0.780406i −0.00359634 0.00359634i
\(218\) −159.431 + 159.431i −0.731334 + 0.731334i
\(219\) 62.5439i 0.285589i
\(220\) −150.131 + 92.5362i −0.682414 + 0.420619i
\(221\) 665.115 3.00957
\(222\) 112.469 + 112.469i 0.506619 + 0.506619i
\(223\) −260.988 + 260.988i −1.17035 + 1.17035i −0.188223 + 0.982126i \(0.560273\pi\)
−0.982126 + 0.188223i \(0.939727\pi\)
\(224\) 1.48785i 0.00664219i
\(225\) 67.0010 + 33.7027i 0.297782 + 0.149790i
\(226\) −37.9849 −0.168075
\(227\) 58.0060 + 58.0060i 0.255533 + 0.255533i 0.823234 0.567701i \(-0.192167\pi\)
−0.567701 + 0.823234i \(0.692167\pi\)
\(228\) 39.7327 39.7327i 0.174266 0.174266i
\(229\) 55.6940i 0.243205i −0.992579 0.121603i \(-0.961197\pi\)
0.992579 0.121603i \(-0.0388033\pi\)
\(230\) 17.7936 + 28.8684i 0.0773635 + 0.125515i
\(231\) −8.03417 −0.0347800
\(232\) 11.8830 + 11.8830i 0.0512199 + 0.0512199i
\(233\) 156.415 156.415i 0.671310 0.671310i −0.286708 0.958018i \(-0.592561\pi\)
0.958018 + 0.286708i \(0.0925609\pi\)
\(234\) 100.741i 0.430516i
\(235\) −49.2011 + 207.301i −0.209366 + 0.882132i
\(236\) 175.488 0.743594
\(237\) −105.098 105.098i −0.443450 0.443450i
\(238\) −7.36736 + 7.36736i −0.0309553 + 0.0309553i
\(239\) 299.721i 1.25406i −0.778995 0.627031i \(-0.784270\pi\)
0.778995 0.627031i \(-0.215730\pi\)
\(240\) 33.7047 + 7.99952i 0.140436 + 0.0333313i
\(241\) 317.414 1.31707 0.658536 0.752549i \(-0.271176\pi\)
0.658536 + 0.752549i \(0.271176\pi\)
\(242\) 190.023 + 190.023i 0.785219 + 0.785219i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 40.4819i 0.165909i
\(245\) 208.270 128.371i 0.850082 0.523964i
\(246\) 92.7298 0.376950
\(247\) 272.350 + 272.350i 1.10263 + 1.10263i
\(248\) 8.39231 8.39231i 0.0338400 0.0338400i
\(249\) 120.207i 0.482760i
\(250\) −135.310 113.759i −0.541240 0.455038i
\(251\) 178.565 0.711416 0.355708 0.934597i \(-0.384240\pi\)
0.355708 + 0.934597i \(0.384240\pi\)
\(252\) 1.11589 + 1.11589i 0.00442813 + 0.00442813i
\(253\) 59.8061 59.8061i 0.236388 0.236388i
\(254\) 121.706i 0.479156i
\(255\) −127.284 206.506i −0.499152 0.809827i
\(256\) 16.0000 0.0625000
\(257\) −329.851 329.851i −1.28347 1.28347i −0.938682 0.344784i \(-0.887952\pi\)
−0.344784 0.938682i \(-0.612048\pi\)
\(258\) 60.1357 60.1357i 0.233084 0.233084i
\(259\) 17.0788i 0.0659414i
\(260\) −54.8330 + 231.030i −0.210896 + 0.888578i
\(261\) −17.8245 −0.0682932
\(262\) −51.5356 51.5356i −0.196701 0.196701i
\(263\) 25.7719 25.7719i 0.0979919 0.0979919i −0.656411 0.754403i \(-0.727926\pi\)
0.754403 + 0.656411i \(0.227926\pi\)
\(264\) 86.3976i 0.327264i
\(265\) −374.826 88.9616i −1.41444 0.335704i
\(266\) −6.03353 −0.0226825
\(267\) 79.4318 + 79.4318i 0.297497 + 0.297497i
\(268\) −10.0753 + 10.0753i −0.0375943 + 0.0375943i
\(269\) 349.179i 1.29806i −0.760761 0.649032i \(-0.775174\pi\)
0.760761 0.649032i \(-0.224826\pi\)
\(270\) −31.2782 + 19.2789i −0.115845 + 0.0714033i
\(271\) −479.592 −1.76971 −0.884856 0.465866i \(-0.845743\pi\)
−0.884856 + 0.465866i \(0.845743\pi\)
\(272\) −79.2269 79.2269i −0.291275 0.291275i
\(273\) −7.64890 + 7.64890i −0.0280179 + 0.0280179i
\(274\) 281.273i 1.02655i
\(275\) −198.125 + 393.873i −0.720455 + 1.43227i
\(276\) −16.6132 −0.0601929
\(277\) 31.3729 + 31.3729i 0.113260 + 0.113260i 0.761465 0.648206i \(-0.224480\pi\)
−0.648206 + 0.761465i \(0.724480\pi\)
\(278\) 96.0813 96.0813i 0.345616 0.345616i
\(279\) 12.5885i 0.0451199i
\(280\) −1.95171 3.16646i −0.00697038 0.0113088i
\(281\) −398.612 −1.41855 −0.709275 0.704932i \(-0.750977\pi\)
−0.709275 + 0.704932i \(0.750977\pi\)
\(282\) −73.8061 73.8061i −0.261724 0.261724i
\(283\) −155.860 + 155.860i −0.550741 + 0.550741i −0.926655 0.375913i \(-0.877329\pi\)
0.375913 + 0.926655i \(0.377329\pi\)
\(284\) 85.2056i 0.300020i
\(285\) 32.4397 136.679i 0.113823 0.479577i
\(286\) 592.216 2.07069
\(287\) −7.04065 7.04065i −0.0245319 0.0245319i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 495.612i 1.71492i
\(290\) 40.8773 + 9.70186i 0.140956 + 0.0334547i
\(291\) 156.302 0.537120
\(292\) 51.0669 + 51.0669i 0.174887 + 0.174887i
\(293\) −102.859 + 102.859i −0.351054 + 0.351054i −0.860502 0.509448i \(-0.829850\pi\)
0.509448 + 0.860502i \(0.329850\pi\)
\(294\) 119.856i 0.407672i
\(295\) 373.476 230.199i 1.26602 0.780335i
\(296\) 183.662 0.620479
\(297\) 64.7982 + 64.7982i 0.218176 + 0.218176i
\(298\) −34.1953 + 34.1953i −0.114749 + 0.114749i
\(299\) 113.876i 0.380857i
\(300\) 82.2242 27.1879i 0.274081 0.0906264i
\(301\) −9.13179 −0.0303382
\(302\) 182.642 + 182.642i 0.604776 + 0.604776i
\(303\) −237.063 + 237.063i −0.782387 + 0.782387i
\(304\) 64.8833i 0.213432i
\(305\) 53.1026 + 86.1539i 0.174107 + 0.282472i
\(306\) 118.840 0.388367
\(307\) 165.629 + 165.629i 0.539508 + 0.539508i 0.923385 0.383876i \(-0.125411\pi\)
−0.383876 + 0.923385i \(0.625411\pi\)
\(308\) −6.55987 + 6.55987i −0.0212983 + 0.0212983i
\(309\) 98.0554i 0.317331i
\(310\) 6.85188 28.8693i 0.0221028 0.0931268i
\(311\) −176.951 −0.568974 −0.284487 0.958680i \(-0.591823\pi\)
−0.284487 + 0.958680i \(0.591823\pi\)
\(312\) −82.2545 82.2545i −0.263636 0.263636i
\(313\) 11.6544 11.6544i 0.0372345 0.0372345i −0.688244 0.725479i \(-0.741618\pi\)
0.725479 + 0.688244i \(0.241618\pi\)
\(314\) 135.777i 0.432411i
\(315\) 3.83862 + 0.911064i 0.0121861 + 0.00289227i
\(316\) −171.624 −0.543113
\(317\) −225.841 225.841i −0.712431 0.712431i 0.254612 0.967043i \(-0.418052\pi\)
−0.967043 + 0.254612i \(0.918052\pi\)
\(318\) 133.450 133.450i 0.419656 0.419656i
\(319\) 104.784i 0.328475i
\(320\) 34.0514 20.9882i 0.106411 0.0655881i
\(321\) 26.4675 0.0824533
\(322\) 1.26139 + 1.26139i 0.00391735 + 0.00391735i
\(323\) −321.281 + 321.281i −0.994678 + 0.994678i
\(324\) 18.0000i 0.0555556i
\(325\) 186.361 + 563.609i 0.573418 + 1.73418i
\(326\) −219.686 −0.673883
\(327\) −195.262 195.262i −0.597132 0.597132i
\(328\) 75.7135 75.7135i 0.230834 0.230834i
\(329\) 11.2077i 0.0340659i
\(330\) −113.333 183.872i −0.343434 0.557189i
\(331\) −217.937 −0.658421 −0.329211 0.944257i \(-0.606783\pi\)
−0.329211 + 0.944257i \(0.606783\pi\)
\(332\) −98.1488 98.1488i −0.295629 0.295629i
\(333\) −137.746 + 137.746i −0.413652 + 0.413652i
\(334\) 45.0674i 0.134932i
\(335\) −8.22592 + 34.6586i −0.0245550 + 0.103459i
\(336\) 1.82224 0.00542332
\(337\) 253.634 + 253.634i 0.752622 + 0.752622i 0.974968 0.222346i \(-0.0713715\pi\)
−0.222346 + 0.974968i \(0.571371\pi\)
\(338\) 394.817 394.817i 1.16810 1.16810i
\(339\) 46.5219i 0.137233i
\(340\) −272.538 64.6846i −0.801583 0.190249i
\(341\) −74.0027 −0.217017
\(342\) 48.6624 + 48.6624i 0.142288 + 0.142288i
\(343\) 18.2133 18.2133i 0.0531000 0.0531000i
\(344\) 98.2012i 0.285469i
\(345\) −35.3565 + 21.7926i −0.102483 + 0.0631671i
\(346\) −19.7779 −0.0571616
\(347\) −52.2309 52.2309i −0.150521 0.150521i 0.627830 0.778351i \(-0.283943\pi\)
−0.778351 + 0.627830i \(0.783943\pi\)
\(348\) −14.5537 + 14.5537i −0.0418209 + 0.0418209i
\(349\) 413.853i 1.18583i −0.805266 0.592913i \(-0.797978\pi\)
0.805266 0.592913i \(-0.202022\pi\)
\(350\) −8.30728 4.17871i −0.0237351 0.0119392i
\(351\) 123.382 0.351515
\(352\) −70.5434 70.5434i −0.200407 0.200407i
\(353\) −85.1537 + 85.1537i −0.241229 + 0.241229i −0.817358 0.576130i \(-0.804562\pi\)
0.576130 + 0.817358i \(0.304562\pi\)
\(354\) 214.928i 0.607142i
\(355\) 111.770 + 181.335i 0.314844 + 0.510804i
\(356\) 129.712 0.364358
\(357\) −9.02313 9.02313i −0.0252749 0.0252749i
\(358\) 285.992 285.992i 0.798860 0.798860i
\(359\) 574.569i 1.60047i 0.599686 + 0.800236i \(0.295292\pi\)
−0.599686 + 0.800236i \(0.704708\pi\)
\(360\) −9.79737 + 41.2797i −0.0272149 + 0.114666i
\(361\) 97.8852 0.271150
\(362\) −133.675 133.675i −0.369269 0.369269i
\(363\) −232.730 + 232.730i −0.641129 + 0.641129i
\(364\) 12.4906i 0.0343148i
\(365\) 175.669 + 41.6934i 0.481284 + 0.114229i
\(366\) −49.5799 −0.135464
\(367\) −259.433 259.433i −0.706902 0.706902i 0.258981 0.965882i \(-0.416613\pi\)
−0.965882 + 0.258981i \(0.916613\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 113.570i 0.307779i
\(370\) 390.871 240.921i 1.05641 0.651137i
\(371\) −20.2649 −0.0546223
\(372\) 10.2784 + 10.2784i 0.0276302 + 0.0276302i
\(373\) 80.1444 80.1444i 0.214864 0.214864i −0.591466 0.806330i \(-0.701451\pi\)
0.806330 + 0.591466i \(0.201451\pi\)
\(374\) 698.616i 1.86796i
\(375\) 139.326 165.720i 0.371537 0.441921i
\(376\) −120.525 −0.320545
\(377\) −99.7587 99.7587i −0.264612 0.264612i
\(378\) −1.36668 + 1.36668i −0.00361555 + 0.00361555i
\(379\) 715.430i 1.88768i −0.330407 0.943838i \(-0.607186\pi\)
0.330407 0.943838i \(-0.392814\pi\)
\(380\) −85.1114 138.085i −0.223977 0.363382i
\(381\) −149.058 −0.391229
\(382\) 106.774 + 106.774i 0.279514 + 0.279514i
\(383\) 262.427 262.427i 0.685187 0.685187i −0.275977 0.961164i \(-0.589001\pi\)
0.961164 + 0.275977i \(0.0890015\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −5.35579 + 22.5658i −0.0139111 + 0.0586124i
\(386\) 66.6643 0.172706
\(387\) 73.6509 + 73.6509i 0.190312 + 0.190312i
\(388\) 127.620 127.620i 0.328918 0.328918i
\(389\) 523.535i 1.34585i −0.739712 0.672924i \(-0.765038\pi\)
0.739712 0.672924i \(-0.234962\pi\)
\(390\) −282.953 67.1565i −0.725521 0.172196i
\(391\) 134.336 0.343570
\(392\) 97.8616 + 97.8616i 0.249647 + 0.249647i
\(393\) 63.1179 63.1179i 0.160605 0.160605i
\(394\) 356.884i 0.905798i
\(395\) −365.251 + 225.129i −0.924686 + 0.569948i
\(396\) 105.815 0.267210
\(397\) 271.071 + 271.071i 0.682799 + 0.682799i 0.960630 0.277831i \(-0.0896155\pi\)
−0.277831 + 0.960630i \(0.589616\pi\)
\(398\) −91.0351 + 91.0351i −0.228731 + 0.228731i
\(399\) 7.38954i 0.0185202i
\(400\) 44.9369 89.3346i 0.112342 0.223337i
\(401\) 275.406 0.686799 0.343399 0.939189i \(-0.388422\pi\)
0.343399 + 0.939189i \(0.388422\pi\)
\(402\) −12.3396 12.3396i −0.0306956 0.0306956i
\(403\) −70.4540 + 70.4540i −0.174824 + 0.174824i
\(404\) 387.123i 0.958224i
\(405\) −23.6117 38.3078i −0.0583006 0.0945871i
\(406\) 2.21002 0.00544340
\(407\) −809.757 809.757i −1.98958 1.98958i
\(408\) 97.0327 97.0327i 0.237825 0.237825i
\(409\) 87.9556i 0.215050i −0.994202 0.107525i \(-0.965707\pi\)
0.994202 0.107525i \(-0.0342926\pi\)
\(410\) 61.8161 260.453i 0.150771 0.635250i
\(411\) 344.488 0.838171
\(412\) −80.0619 80.0619i −0.194325 0.194325i
\(413\) 16.3188 16.3188i 0.0395127 0.0395127i
\(414\) 20.3470i 0.0491473i
\(415\) −337.629 80.1333i −0.813564 0.193092i
\(416\) −134.321 −0.322887
\(417\) 117.675 + 117.675i 0.282194 + 0.282194i
\(418\) −286.068 + 286.068i −0.684373 + 0.684373i
\(419\) 549.190i 1.31072i 0.755319 + 0.655358i \(0.227482\pi\)
−0.755319 + 0.655358i \(0.772518\pi\)
\(420\) 3.87810 2.39034i 0.00923358 0.00569129i
\(421\) −579.831 −1.37727 −0.688636 0.725107i \(-0.741790\pi\)
−0.688636 + 0.725107i \(0.741790\pi\)
\(422\) 384.346 + 384.346i 0.910772 + 0.910772i
\(423\) 90.3936 90.3936i 0.213696 0.213696i
\(424\) 217.924i 0.513971i
\(425\) −664.870 + 219.843i −1.56440 + 0.517278i
\(426\) −104.355 −0.244965
\(427\) 3.76443 + 3.76443i 0.00881600 + 0.00881600i
\(428\) 21.6106 21.6106i 0.0504921 0.0504921i
\(429\) 725.314i 1.69071i
\(430\) −128.817 208.993i −0.299574 0.486030i
\(431\) 422.783 0.980935 0.490467 0.871460i \(-0.336826\pi\)
0.490467 + 0.871460i \(0.336826\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 356.992 356.992i 0.824462 0.824462i −0.162282 0.986744i \(-0.551886\pi\)
0.986744 + 0.162282i \(0.0518855\pi\)
\(434\) 1.56081i 0.00359634i
\(435\) −11.8823 + 50.0642i −0.0273156 + 0.115090i
\(436\) −318.862 −0.731334
\(437\) 55.0075 + 55.0075i 0.125875 + 0.125875i
\(438\) −62.5439 + 62.5439i −0.142794 + 0.142794i
\(439\) 95.4606i 0.217450i 0.994072 + 0.108725i \(0.0346768\pi\)
−0.994072 + 0.108725i \(0.965323\pi\)
\(440\) −242.667 57.5950i −0.551517 0.130898i
\(441\) −146.792 −0.332863
\(442\) 665.115 + 665.115i 1.50478 + 1.50478i
\(443\) −90.7273 + 90.7273i −0.204802 + 0.204802i −0.802054 0.597252i \(-0.796259\pi\)
0.597252 + 0.802054i \(0.296259\pi\)
\(444\) 224.939i 0.506619i
\(445\) 276.053 170.151i 0.620345 0.382361i
\(446\) −521.976 −1.17035
\(447\) −41.8805 41.8805i −0.0936924 0.0936924i
\(448\) 1.48785 1.48785i 0.00332109 0.00332109i
\(449\) 685.452i 1.52662i −0.646033 0.763310i \(-0.723573\pi\)
0.646033 0.763310i \(-0.276427\pi\)
\(450\) 33.2983 + 100.704i 0.0739962 + 0.223786i
\(451\) −667.636 −1.48035
\(452\) −37.9849 37.9849i −0.0840375 0.0840375i
\(453\) −223.690 + 223.690i −0.493798 + 0.493798i
\(454\) 116.012i 0.255533i
\(455\) 16.3847 + 26.5826i 0.0360103 + 0.0584233i
\(456\) 79.4654 0.174266
\(457\) 20.7695 + 20.7695i 0.0454474 + 0.0454474i 0.729465 0.684018i \(-0.239769\pi\)
−0.684018 + 0.729465i \(0.739769\pi\)
\(458\) 55.6940 55.6940i 0.121603 0.121603i
\(459\) 145.549i 0.317100i
\(460\) −11.0748 + 46.6621i −0.0240757 + 0.101439i
\(461\) 413.944 0.897926 0.448963 0.893550i \(-0.351794\pi\)
0.448963 + 0.893550i \(0.351794\pi\)
\(462\) −8.03417 8.03417i −0.0173900 0.0173900i
\(463\) −480.825 + 480.825i −1.03850 + 1.03850i −0.0392698 + 0.999229i \(0.512503\pi\)
−0.999229 + 0.0392698i \(0.987497\pi\)
\(464\) 23.7660i 0.0512199i
\(465\) 35.3576 + 8.39181i 0.0760377 + 0.0180469i
\(466\) 312.831 0.671310
\(467\) 470.023 + 470.023i 1.00647 + 1.00647i 0.999979 + 0.00649415i \(0.00206717\pi\)
0.00649415 + 0.999979i \(0.497933\pi\)
\(468\) 100.741 100.741i 0.215258 0.215258i
\(469\) 1.87381i 0.00399533i
\(470\) −256.502 + 158.100i −0.545749 + 0.336383i
\(471\) 166.292 0.353062
\(472\) 175.488 + 175.488i 0.371797 + 0.371797i
\(473\) −432.965 + 432.965i −0.915360 + 0.915360i
\(474\) 210.195i 0.443450i
\(475\) −362.270 182.228i −0.762674 0.383639i
\(476\) −14.7347 −0.0309553
\(477\) 163.443 + 163.443i 0.342647 + 0.342647i
\(478\) 299.721 299.721i 0.627031 0.627031i
\(479\) 204.710i 0.427370i −0.976903 0.213685i \(-0.931453\pi\)
0.976903 0.213685i \(-0.0685465\pi\)
\(480\) 25.7052 + 41.7042i 0.0535525 + 0.0868838i
\(481\) −1541.85 −3.20551
\(482\) 317.414 + 317.414i 0.658536 + 0.658536i
\(483\) −1.54488 + 1.54488i −0.00319850 + 0.00319850i
\(484\) 380.046i 0.785219i
\(485\) 104.195 439.010i 0.214835 0.905174i
\(486\) 22.0454 0.0453609
\(487\) 311.497 + 311.497i 0.639625 + 0.639625i 0.950463 0.310838i \(-0.100610\pi\)
−0.310838 + 0.950463i \(0.600610\pi\)
\(488\) −40.4819 + 40.4819i −0.0829546 + 0.0829546i
\(489\) 269.059i 0.550224i
\(490\) 336.641 + 79.8989i 0.687023 + 0.163059i
\(491\) 356.163 0.725383 0.362691 0.931909i \(-0.381858\pi\)
0.362691 + 0.931909i \(0.381858\pi\)
\(492\) 92.7298 + 92.7298i 0.188475 + 0.188475i
\(493\) 117.682 117.682i 0.238706 0.238706i
\(494\) 544.699i 1.10263i
\(495\) 225.197 138.804i 0.454943 0.280413i
\(496\) 16.7846 0.0338400
\(497\) 7.92332 + 7.92332i 0.0159423 + 0.0159423i
\(498\) 120.207 120.207i 0.241380 0.241380i
\(499\) 150.466i 0.301535i 0.988569 + 0.150768i \(0.0481745\pi\)
−0.988569 + 0.150768i \(0.951826\pi\)
\(500\) −21.5506 249.069i −0.0431013 0.498139i
\(501\) −55.1961 −0.110172
\(502\) 178.565 + 178.565i 0.355708 + 0.355708i
\(503\) −577.609 + 577.609i −1.14833 + 1.14833i −0.161446 + 0.986881i \(0.551616\pi\)
−0.986881 + 0.161446i \(0.948384\pi\)
\(504\) 2.23178i 0.00442813i
\(505\) 507.813 + 823.878i 1.00557 + 1.63144i
\(506\) 119.612 0.236388
\(507\) 483.550 + 483.550i 0.953748 + 0.953748i
\(508\) −121.706 + 121.706i −0.239578 + 0.239578i
\(509\) 19.0252i 0.0373776i 0.999825 + 0.0186888i \(0.00594918\pi\)
−0.999825 + 0.0186888i \(0.994051\pi\)
\(510\) 79.2221 333.790i 0.155337 0.654490i
\(511\) 9.49749 0.0185861
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −59.5991 + 59.5991i −0.116178 + 0.116178i
\(514\) 659.701i 1.28347i
\(515\) −275.411 65.3663i −0.534778 0.126925i
\(516\) 120.271 0.233084
\(517\) 531.389 + 531.389i 1.02783 + 1.02783i
\(518\) 17.0788 17.0788i 0.0329707 0.0329707i
\(519\) 24.2229i 0.0466723i
\(520\) −285.863 + 176.197i −0.549737 + 0.338841i
\(521\) 320.453 0.615072 0.307536 0.951536i \(-0.400496\pi\)
0.307536 + 0.951536i \(0.400496\pi\)
\(522\) −17.8245 17.8245i −0.0341466 0.0341466i
\(523\) −51.9595 + 51.9595i −0.0993490 + 0.0993490i −0.755034 0.655685i \(-0.772380\pi\)
0.655685 + 0.755034i \(0.272380\pi\)
\(524\) 103.071i 0.196701i
\(525\) 5.11786 10.1743i 0.00974830 0.0193796i
\(526\) 51.5438 0.0979919
\(527\) −83.1121 83.1121i −0.157708 0.157708i
\(528\) 86.3976 86.3976i 0.163632 0.163632i
\(529\) 23.0000i 0.0434783i
\(530\) −285.864 463.787i −0.539366 0.875071i
\(531\) −263.232 −0.495730
\(532\) −6.03353 6.03353i −0.0113412 0.0113412i
\(533\) −635.620 + 635.620i −1.19253 + 1.19253i
\(534\) 158.864i 0.297497i
\(535\) 17.6439 74.3400i 0.0329793 0.138953i
\(536\) −20.1505 −0.0375943
\(537\) 350.267 + 350.267i 0.652266 + 0.652266i
\(538\) 349.179 349.179i 0.649032 0.649032i
\(539\) 862.936i 1.60100i
\(540\) −50.5571 11.9993i −0.0936242 0.0222209i
\(541\) 179.611 0.331999 0.165999 0.986126i \(-0.446915\pi\)
0.165999 + 0.986126i \(0.446915\pi\)
\(542\) −479.592 479.592i −0.884856 0.884856i
\(543\) 163.718 163.718i 0.301507 0.301507i
\(544\) 158.454i 0.291275i
\(545\) −678.605 + 418.271i −1.24515 + 0.767470i
\(546\) −15.2978 −0.0280179
\(547\) 574.121 + 574.121i 1.04958 + 1.04958i 0.998705 + 0.0508772i \(0.0162017\pi\)
0.0508772 + 0.998705i \(0.483798\pi\)
\(548\) 281.273 281.273i 0.513273 0.513273i
\(549\) 60.7228i 0.110606i
\(550\) −591.998 + 195.748i −1.07636 + 0.355905i
\(551\) 96.3761 0.174911
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) −15.9594 + 15.9594i −0.0288597 + 0.0288597i
\(554\) 62.7459i 0.113260i
\(555\) 295.066 + 478.717i 0.531651 + 0.862553i
\(556\) 192.163 0.345616
\(557\) −115.816 115.816i −0.207928 0.207928i 0.595458 0.803386i \(-0.296970\pi\)
−0.803386 + 0.595458i \(0.796970\pi\)
\(558\) −12.5885 + 12.5885i −0.0225600 + 0.0225600i
\(559\) 824.405i 1.47479i
\(560\) 1.21475 5.11816i 0.00216920 0.00913958i
\(561\) −855.627 −1.52518
\(562\) −398.612 398.612i −0.709275 0.709275i
\(563\) 617.004 617.004i 1.09592 1.09592i 0.101040 0.994882i \(-0.467783\pi\)
0.994882 0.101040i \(-0.0322169\pi\)
\(564\) 147.612i 0.261724i
\(565\) −130.667 31.0127i −0.231269 0.0548898i
\(566\) −311.720 −0.550741
\(567\) −1.67383 1.67383i −0.00295208 0.00295208i
\(568\) −85.2056 + 85.2056i −0.150010 + 0.150010i
\(569\) 133.091i 0.233903i −0.993138 0.116951i \(-0.962688\pi\)
0.993138 0.116951i \(-0.0373122\pi\)
\(570\) 169.119 104.240i 0.296700 0.182877i
\(571\) −70.1411 −0.122839 −0.0614195 0.998112i \(-0.519563\pi\)
−0.0614195 + 0.998112i \(0.519563\pi\)
\(572\) 592.216 + 592.216i 1.03534 + 1.03534i
\(573\) −130.771 + 130.771i −0.228222 + 0.228222i
\(574\) 14.0813i 0.0245319i
\(575\) 37.6400 + 113.834i 0.0654608 + 0.197973i
\(576\) −24.0000 −0.0416667
\(577\) −593.584 593.584i −1.02874 1.02874i −0.999575 0.0291673i \(-0.990714\pi\)
−0.0291673 0.999575i \(-0.509286\pi\)
\(578\) −495.612 + 495.612i −0.857460 + 0.857460i
\(579\) 81.6468i 0.141014i
\(580\) 31.1754 + 50.5791i 0.0537507 + 0.0872054i
\(581\) −18.2538 −0.0314180
\(582\) 156.302 + 156.302i 0.268560 + 0.268560i
\(583\) −960.817 + 960.817i −1.64806 + 1.64806i
\(584\) 102.134i 0.174887i
\(585\) 82.2496 346.546i 0.140598 0.592386i
\(586\) −205.717 −0.351054
\(587\) 567.035 + 567.035i 0.965989 + 0.965989i 0.999440 0.0334516i \(-0.0106500\pi\)
−0.0334516 + 0.999440i \(0.510650\pi\)
\(588\) −119.856 + 119.856i −0.203836 + 0.203836i
\(589\) 68.0650i 0.115560i
\(590\) 603.675 + 143.277i 1.02318 + 0.242842i
\(591\) 437.092 0.739581
\(592\) 183.662 + 183.662i 0.310239 + 0.310239i
\(593\) −47.6862 + 47.6862i −0.0804152 + 0.0804152i −0.746170 0.665755i \(-0.768110\pi\)
0.665755 + 0.746170i \(0.268110\pi\)
\(594\) 129.596i 0.218176i
\(595\) −31.3586 + 19.3284i −0.0527035 + 0.0324848i
\(596\) −68.3906 −0.114749
\(597\) −111.495 111.495i −0.186758 0.186758i
\(598\) 113.876 113.876i 0.190428 0.190428i
\(599\) 793.250i 1.32429i 0.749376 + 0.662145i \(0.230354\pi\)
−0.749376 + 0.662145i \(0.769646\pi\)
\(600\) 109.412 + 55.0363i 0.182354 + 0.0917271i
\(601\) −234.950 −0.390931 −0.195465 0.980711i \(-0.562622\pi\)
−0.195465 + 0.980711i \(0.562622\pi\)
\(602\) −9.13179 9.13179i −0.0151691 0.0151691i
\(603\) 15.1129 15.1129i 0.0250628 0.0250628i
\(604\) 365.285i 0.604776i
\(605\) 498.530 + 808.818i 0.824017 + 1.33689i
\(606\) −474.127 −0.782387
\(607\) −643.221 643.221i −1.05967 1.05967i −0.998103 0.0615699i \(-0.980389\pi\)
−0.0615699 0.998103i \(-0.519611\pi\)
\(608\) 64.8833 64.8833i 0.106716 0.106716i
\(609\) 2.70671i 0.00444452i
\(610\) −33.0513 + 139.256i −0.0541825 + 0.228289i
\(611\) 1011.81 1.65600
\(612\) 118.840 + 118.840i 0.194183 + 0.194183i
\(613\) −323.718 + 323.718i −0.528088 + 0.528088i −0.920002 0.391914i \(-0.871813\pi\)
0.391914 + 0.920002i \(0.371813\pi\)
\(614\) 331.258i 0.539508i
\(615\) 318.988 + 75.7090i 0.518680 + 0.123104i
\(616\) −13.1197 −0.0212983
\(617\) 267.813 + 267.813i 0.434057 + 0.434057i 0.890006 0.455949i \(-0.150700\pi\)
−0.455949 + 0.890006i \(0.650700\pi\)
\(618\) 98.0554 98.0554i 0.158666 0.158666i
\(619\) 508.117i 0.820867i −0.911890 0.410434i \(-0.865377\pi\)
0.911890 0.410434i \(-0.134623\pi\)
\(620\) 35.7212 22.0174i 0.0576148 0.0355120i
\(621\) 24.9199 0.0401286
\(622\) −176.951 176.951i −0.284487 0.284487i
\(623\) 12.0620 12.0620i 0.0193611 0.0193611i
\(624\) 164.509i 0.263636i
\(625\) −372.584 501.803i −0.596135 0.802884i
\(626\) 23.3088 0.0372345
\(627\) −350.360 350.360i −0.558788 0.558788i
\(628\) 135.777 135.777i 0.216205 0.216205i
\(629\) 1818.87i 2.89168i
\(630\) 2.92756 + 4.74969i 0.00464692 + 0.00753919i
\(631\) −15.4171 −0.0244327 −0.0122164 0.999925i \(-0.503889\pi\)
−0.0122164 + 0.999925i \(0.503889\pi\)
\(632\) −171.624 171.624i −0.271556 0.271556i
\(633\) −470.726 + 470.726i −0.743643 + 0.743643i
\(634\) 451.681i 0.712431i
\(635\) −99.3662 + 418.664i −0.156482 + 0.659313i
\(636\) 266.901 0.419656
\(637\) −821.555 821.555i −1.28973 1.28973i
\(638\) 104.784 104.784i 0.164238 0.164238i
\(639\) 127.808i 0.200013i
\(640\) 55.0396 + 13.0632i 0.0859993 + 0.0204112i
\(641\) 127.618 0.199091 0.0995456 0.995033i \(-0.468261\pi\)
0.0995456 + 0.995033i \(0.468261\pi\)
\(642\) 26.4675 + 26.4675i 0.0412267 + 0.0412267i
\(643\) 732.374 732.374i 1.13899 1.13899i 0.150364 0.988631i \(-0.451955\pi\)
0.988631 0.150364i \(-0.0480447\pi\)
\(644\) 2.52277i 0.00391735i
\(645\) 255.963 157.768i 0.396842 0.244601i
\(646\) −642.562 −0.994678
\(647\) 830.198 + 830.198i 1.28315 + 1.28315i 0.938865 + 0.344286i \(0.111879\pi\)
0.344286 + 0.938865i \(0.388121\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 1547.44i 2.38435i
\(650\) −377.248 + 749.970i −0.580382 + 1.15380i
\(651\) 1.91160 0.00293640
\(652\) −219.686 219.686i −0.336942 0.336942i
\(653\) 171.573 171.573i 0.262745 0.262745i −0.563423 0.826168i \(-0.690516\pi\)
0.826168 + 0.563423i \(0.190516\pi\)
\(654\) 390.524i 0.597132i
\(655\) −135.205 219.357i −0.206420 0.334896i
\(656\) 151.427 0.230834
\(657\) −76.6004 76.6004i −0.116591 0.116591i
\(658\) −11.2077 + 11.2077i −0.0170329 + 0.0170329i
\(659\) 801.680i 1.21651i 0.793742 + 0.608255i \(0.208130\pi\)
−0.793742 + 0.608255i \(0.791870\pi\)
\(660\) 70.5391 297.206i 0.106877 0.450311i
\(661\) −960.626 −1.45329 −0.726646 0.687012i \(-0.758922\pi\)
−0.726646 + 0.687012i \(0.758922\pi\)
\(662\) −217.937 217.937i −0.329211 0.329211i
\(663\) −814.596 + 814.596i −1.22865 + 1.22865i
\(664\) 196.298i 0.295629i
\(665\) −20.7552 4.92606i −0.0312108 0.00740761i
\(666\) −275.493 −0.413652
\(667\) −20.1486 20.1486i −0.0302079 0.0302079i
\(668\) −45.0674 + 45.0674i −0.0674662 + 0.0674662i
\(669\) 639.287i 0.955586i
\(670\) −42.8845 + 26.4327i −0.0640068 + 0.0394518i
\(671\) 356.966 0.531991
\(672\) 1.82224 + 1.82224i 0.00271166 + 0.00271166i
\(673\) 326.569 326.569i 0.485243 0.485243i −0.421558 0.906801i \(-0.638517\pi\)
0.906801 + 0.421558i \(0.138517\pi\)
\(674\) 507.267i 0.752622i
\(675\) −123.336 + 40.7819i −0.182720 + 0.0604176i
\(676\) 789.634 1.16810
\(677\) 676.535 + 676.535i 0.999314 + 0.999314i 1.00000 0.000685886i \(-0.000218324\pi\)
−0.000685886 1.00000i \(0.500218\pi\)
\(678\) 46.5219 46.5219i 0.0686163 0.0686163i
\(679\) 23.7349i 0.0349557i
\(680\) −207.854 337.223i −0.305667 0.495916i
\(681\) −142.085 −0.208642
\(682\) −74.0027 74.0027i −0.108508 0.108508i
\(683\) 118.338 118.338i 0.173262 0.173262i −0.615149 0.788411i \(-0.710904\pi\)
0.788411 + 0.615149i \(0.210904\pi\)
\(684\) 97.3249i 0.142288i
\(685\) 229.645 967.573i 0.335248 1.41251i
\(686\) 36.4266 0.0531000
\(687\) 68.2109 + 68.2109i 0.0992880 + 0.0992880i
\(688\) 98.2012 98.2012i 0.142734 0.142734i
\(689\) 1829.48i 2.65527i
\(690\) −57.1491 13.5638i −0.0828248 0.0196577i
\(691\) 1096.90 1.58741 0.793705 0.608302i \(-0.208149\pi\)
0.793705 + 0.608302i \(0.208149\pi\)
\(692\) −19.7779 19.7779i −0.0285808 0.0285808i
\(693\) 9.83981 9.83981i 0.0141989 0.0141989i
\(694\) 104.462i 0.150521i
\(695\) 408.962 252.072i 0.588435 0.362693i
\(696\) −29.1073 −0.0418209
\(697\) −749.818 749.818i −1.07578 1.07578i
\(698\) 413.853 413.853i 0.592913 0.592913i
\(699\) 383.138i 0.548122i
\(700\) −4.12857 12.4860i −0.00589796 0.0178371i
\(701\) 1131.15 1.61362 0.806809 0.590813i \(-0.201193\pi\)
0.806809 + 0.590813i \(0.201193\pi\)
\(702\) 123.382 + 123.382i 0.175757 + 0.175757i
\(703\) 744.785 744.785i 1.05944 1.05944i
\(704\) 141.087i 0.200407i
\(705\) −193.632 314.150i −0.274655 0.445602i
\(706\) −170.307 −0.241229
\(707\) 35.9988 + 35.9988i 0.0509177 + 0.0509177i
\(708\) −214.928 + 214.928i −0.303571 + 0.303571i
\(709\) 298.642i 0.421215i −0.977571 0.210608i \(-0.932456\pi\)
0.977571 0.210608i \(-0.0675443\pi\)
\(710\) −69.5659 + 293.105i −0.0979801 + 0.412824i
\(711\) 257.435 0.362075
\(712\) 129.712 + 129.712i 0.182179 + 0.182179i
\(713\) −14.2299 + 14.2299i −0.0199577 + 0.0199577i
\(714\) 18.0463i 0.0252749i
\(715\) 2037.21 + 483.513i 2.84924 + 0.676243i
\(716\) 571.984 0.798860
\(717\) 367.081 + 367.081i 0.511968 + 0.511968i
\(718\) −574.569 + 574.569i −0.800236 + 0.800236i
\(719\) 403.971i 0.561852i −0.959729 0.280926i \(-0.909359\pi\)
0.959729 0.280926i \(-0.0906415\pi\)
\(720\) −51.0770 + 31.4823i −0.0709403 + 0.0437254i
\(721\) −14.8900 −0.0206519
\(722\) 97.8852 + 97.8852i 0.135575 + 0.135575i
\(723\) −388.752 + 388.752i −0.537693 + 0.537693i
\(724\) 267.351i 0.369269i
\(725\) 132.696 + 66.7483i 0.183028 + 0.0920666i
\(726\) −465.460 −0.641129
\(727\) −836.080 836.080i −1.15004 1.15004i −0.986544 0.163497i \(-0.947723\pi\)
−0.163497 0.986544i \(-0.552277\pi\)
\(728\) −12.4906 + 12.4906i −0.0171574 + 0.0171574i
\(729\) 27.0000i 0.0370370i
\(730\) 133.975 + 217.362i 0.183528 + 0.297756i
\(731\) −972.522 −1.33040
\(732\) −49.5799 49.5799i −0.0677322 0.0677322i
\(733\) −736.812 + 736.812i −1.00520 + 1.00520i −0.00521382 + 0.999986i \(0.501660\pi\)
−0.999986 + 0.00521382i \(0.998340\pi\)
\(734\) 518.866i 0.706902i
\(735\) −97.8558 + 412.300i −0.133137 + 0.560952i
\(736\) −27.1293 −0.0368605
\(737\) 88.8429 + 88.8429i 0.120547 + 0.120547i
\(738\) −113.570 + 113.570i −0.153889 + 0.153889i
\(739\) 248.799i 0.336670i 0.985730 + 0.168335i \(0.0538391\pi\)
−0.985730 + 0.168335i \(0.946161\pi\)
\(740\) 631.791 + 149.950i 0.853772 + 0.202635i
\(741\) −667.117 −0.900293
\(742\) −20.2649 20.2649i −0.0273111 0.0273111i
\(743\) 127.951 127.951i 0.172208 0.172208i −0.615741 0.787949i \(-0.711143\pi\)
0.787949 + 0.615741i \(0.211143\pi\)
\(744\) 20.5569i 0.0276302i
\(745\) −145.550 + 89.7122i −0.195368 + 0.120419i
\(746\) 160.289 0.214864
\(747\) 147.223 + 147.223i 0.197086 + 0.197086i
\(748\) −698.616 + 698.616i −0.933979 + 0.933979i
\(749\) 4.01917i 0.00536605i
\(750\) 305.046 26.3940i 0.406729 0.0351920i
\(751\) 267.001 0.355527 0.177764 0.984073i \(-0.443114\pi\)
0.177764 + 0.984073i \(0.443114\pi\)
\(752\) −120.525 120.525i −0.160272 0.160272i
\(753\) −218.697 + 218.697i −0.290434 + 0.290434i
\(754\) 199.517i 0.264612i
\(755\) 479.167 + 777.403i 0.634658 + 1.02967i
\(756\) −2.73336 −0.00361555
\(757\) 159.734 + 159.734i 0.211009 + 0.211009i 0.804696 0.593687i \(-0.202328\pi\)
−0.593687 + 0.804696i \(0.702328\pi\)
\(758\) 715.430 715.430i 0.943838 0.943838i
\(759\) 146.494i 0.193010i
\(760\) 52.9738 223.197i 0.0697023 0.293680i
\(761\) −913.192 −1.19999 −0.599995 0.800004i \(-0.704831\pi\)
−0.599995 + 0.800004i \(0.704831\pi\)
\(762\) −149.058 149.058i −0.195615 0.195615i
\(763\) −29.6512 + 29.6512i −0.0388613 + 0.0388613i
\(764\) 213.549i 0.279514i
\(765\) 408.807 + 97.0269i 0.534389 + 0.126832i
\(766\) 524.853 0.685187
\(767\) −1473.24 1473.24i −1.92078 1.92078i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 638.410i 0.830182i 0.909780 + 0.415091i \(0.136250\pi\)
−0.909780 + 0.415091i \(0.863750\pi\)
\(770\) −27.9216 + 17.2100i −0.0362618 + 0.0223506i
\(771\) 807.966 1.04795
\(772\) 66.6643 + 66.6643i 0.0863528 + 0.0863528i
\(773\) −15.4984 + 15.4984i −0.0200496 + 0.0200496i −0.717061 0.697011i \(-0.754513\pi\)
0.697011 + 0.717061i \(0.254513\pi\)
\(774\) 147.302i 0.190312i
\(775\) 47.1406 93.7155i 0.0608265 0.120923i
\(776\) 255.240 0.328918
\(777\) 20.9172 + 20.9172i 0.0269205 + 0.0269205i
\(778\) 523.535 523.535i 0.672924 0.672924i