Properties

Label 690.3.k.a.553.6
Level $690$
Weight $3$
Character 690.553
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 553.6
Character \(\chi\) \(=\) 690.553
Dual form 690.3.k.a.277.6

$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 −0.693698 0.720266i \(-0.744020\pi\)
0.720266 + 0.693698i \(0.244020\pi\)
\(8\) −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 0.933829 + 0.357719i \(0.116446\pi\)
0.357719 + 0.933829i \(0.383554\pi\)
\(14\) 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 0.181758 0.983343i \(-0.441821\pi\)
0.983343 0.181758i \(-0.0581786\pi\)
\(18\) 3.00000 + 3.00000i 0.166667 + 0.166667i
\(19\) 16.2208i 0.853727i −0.904316 0.426863i \(-0.859618\pi\)
0.904316 0.426863i \(-0.140382\pi\)
\(20\) −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 \(0.0326649\pi\)
−0.994739 + 0.102440i \(0.967335\pi\)
\(30\) −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 −0.281353 + 0.959604i \(0.590783\pi\)
−0.959604 + 0.281353i \(0.909217\pi\)
\(38\) −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 0.361453 0.932390i \(-0.382281\pi\)
−0.932390 + 0.361453i \(0.882281\pi\)
\(44\) 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 −0.309734 0.950823i \(-0.600240\pi\)
0.950823 + 0.309734i \(0.100240\pi\)
\(48\) 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 −0.999598 0.0283437i \(-0.990977\pi\)
−0.0283437 0.999598i \(-0.509023\pi\)
\(54\) 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 \(0.266881\pi\)
−0.668631 + 0.743594i \(0.733119\pi\)
\(60\) 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 −0.668512 0.743701i \(-0.733069\pi\)
0.743701 + 0.668512i \(0.233069\pi\)
\(68\) −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 0.860025 0.510252i \(-0.170448\pi\)
−0.510252 + 0.860025i \(0.670448\pi\)
\(74\) 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 \(-0.817246\pi\)
0.839660 0.543113i \(-0.182754\pi\)
\(80\) −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 0.346713 0.937971i \(-0.387298\pi\)
−0.937971 + 0.346713i \(0.887298\pi\)
\(84\) 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 \(0.118712\pi\)
−0.931259 + 0.364358i \(0.881288\pi\)
\(90\) 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 −0.954868 0.297032i \(-0.904003\pi\)
0.297032 + 0.954868i \(0.404003\pi\)
\(98\) 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 0.485556 0.874206i \(-0.338617\pi\)
−0.874206 + 0.485556i \(0.838617\pi\)
\(104\) 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 −0.755794 0.654810i \(-0.772749\pi\)
0.654810 + 0.755794i \(0.272749\pi\)
\(108\) −7.34847 7.34847i −0.0680414 0.0680414i
\(109\) 159.431i 1.46267i −0.682019 0.731334i \(-0.738898\pi\)
0.682019 0.731334i \(-0.261102\pi\)
\(110\) −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 0.618058 0.786133i \(-0.287920\pi\)
−0.786133 + 0.618058i \(0.787920\pi\)
\(114\) 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 −0.425706 0.904862i \(-0.639974\pi\)
0.904862 + 0.425706i \(0.139974\pi\)
\(128\) 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 −0.0269071 + 0.999638i \(0.508566\pi\)
−0.999638 + 0.0269071i \(0.991434\pi\)
\(138\) −8.30662 8.30662i −0.0601929 0.0601929i
\(139\) 96.0813i 0.691232i 0.938376 + 0.345616i \(0.112330\pi\)
−0.938376 + 0.345616i \(0.887670\pi\)
\(140\) −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 \(-0.963394\pi\)
0.993394 0.114749i \(-0.0366065\pi\)
\(150\) 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 −0.889448 0.457037i \(-0.848911\pi\)
0.457037 + 0.889448i \(0.348911\pi\)
\(158\) −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 0.284726 0.958609i \(-0.408098\pi\)
−0.958609 + 0.284726i \(0.908098\pi\)
\(164\) 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 −0.636415 0.771347i \(-0.719583\pi\)
0.771347 + 0.636415i \(0.219583\pi\)
\(168\) 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 0.677948 0.735110i \(-0.262869\pi\)
−0.735110 + 0.677948i \(0.762869\pi\)
\(174\) 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 \(0.294563\pi\)
−0.601517 + 0.798860i \(0.705437\pi\)
\(180\) 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 0.788167 0.615461i \(-0.211030\pi\)
−0.615461 + 0.788167i \(0.711030\pi\)
\(194\) 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 −0.995930 0.0901317i \(-0.971271\pi\)
0.0901317 + 0.995930i \(0.471271\pi\)
\(198\) 52.9075 + 52.9075i 0.267210 + 0.267210i
\(199\) 91.0351i 0.457463i −0.973490 0.228731i \(-0.926542\pi\)
0.973490 0.228731i \(-0.0734578\pi\)
\(200\) −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 −0.982126 0.188223i \(-0.939727\pi\)
−0.188223 0.982126i \(-0.560273\pi\)
\(224\) 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 −0.567701 0.823234i \(-0.692167\pi\)
0.823234 + 0.567701i \(0.192167\pi\)
\(228\) 39.7327 + 39.7327i 0.174266 + 0.174266i
\(229\) 55.6940i 0.243205i 0.992579 + 0.121603i \(0.0388033\pi\)
−0.992579 + 0.121603i \(0.961197\pi\)
\(230\) 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 0.958018 0.286708i \(-0.0925609\pi\)
−0.286708 + 0.958018i \(0.592561\pi\)
\(234\) 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 \(0.215730\pi\)
−0.778995 + 0.627031i \(0.784270\pi\)
\(240\) 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 −0.344784 + 0.938682i \(0.612048\pi\)
−0.938682 + 0.344784i \(0.887952\pi\)
\(258\) 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 0.754403 0.656411i \(-0.227926\pi\)
−0.656411 + 0.754403i \(0.727926\pi\)
\(264\) 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 \(0.224826\pi\)
−0.760761 + 0.649032i \(0.775174\pi\)
\(270\) −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 −0.648206 0.761465i \(-0.724480\pi\)
0.761465 + 0.648206i \(0.224480\pi\)
\(278\) 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 0.375913 0.926655i \(-0.377329\pi\)
−0.926655 + 0.375913i \(0.877329\pi\)
\(284\) 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 0.509448 0.860502i \(-0.329850\pi\)
−0.860502 + 0.509448i \(0.829850\pi\)
\(294\) 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 −0.383876 0.923385i \(-0.625411\pi\)
0.923385 + 0.383876i \(0.125411\pi\)
\(308\) −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 0.725479 0.688244i \(-0.241618\pi\)
−0.688244 + 0.725479i \(0.741618\pi\)
\(314\) 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 −0.967043 0.254612i \(-0.918052\pi\)
0.254612 + 0.967043i \(0.418052\pi\)
\(318\) 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 −0.222346 0.974968i \(-0.571371\pi\)
0.974968 + 0.222346i \(0.0713715\pi\)
\(338\) 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 −0.778351 0.627830i \(-0.783943\pi\)
0.627830 + 0.778351i \(0.283943\pi\)
\(348\) −14.5537 14.5537i −0.0418209 0.0418209i
\(349\) 413.853i 1.18583i 0.805266 + 0.592913i \(0.202022\pi\)
−0.805266 + 0.592913i \(0.797978\pi\)
\(350\) −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 0.576130 0.817358i \(-0.304562\pi\)
−0.817358 + 0.576130i \(0.804562\pi\)
\(354\) 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 \(-0.704708\pi\)
0.599686 0.800236i \(-0.295292\pi\)
\(360\) −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 −0.965882 0.258981i \(-0.916613\pi\)
0.258981 + 0.965882i \(0.416613\pi\)
\(368\) −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 0.806330 0.591466i \(-0.201451\pi\)
−0.591466 + 0.806330i \(0.701451\pi\)
\(374\) 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 \(0.392814\pi\)
−0.330407 + 0.943838i \(0.607186\pi\)
\(380\) −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 0.961164 0.275977i \(-0.0890015\pi\)
−0.275977 + 0.961164i \(0.589001\pi\)
\(384\) 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 \(0.234962\pi\)
−0.739712 + 0.672924i \(0.765038\pi\)
\(390\) −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 −0.277831 0.960630i \(-0.589616\pi\)
0.960630 + 0.277831i \(0.0896155\pi\)
\(398\) −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 \(0.0342926\pi\)
−0.994202 + 0.107525i \(0.965707\pi\)
\(410\) 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 \(-0.772518\pi\)
0.755319 0.655358i \(-0.227482\pi\)
\(420\) 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 0.986744 0.162282i \(-0.0518855\pi\)
−0.162282 + 0.986744i \(0.551886\pi\)
\(434\) 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 \(-0.965323\pi\)
0.994072 0.108725i \(-0.0346768\pi\)
\(440\) −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 0.597252 0.802054i \(-0.296259\pi\)
−0.802054 + 0.597252i \(0.796259\pi\)
\(444\) 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 \(0.276427\pi\)
−0.646033 + 0.763310i \(0.723573\pi\)
\(450\) 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 −0.684018 0.729465i \(-0.739769\pi\)
0.729465 + 0.684018i \(0.239769\pi\)
\(458\) 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 −0.999229 0.0392698i \(-0.987497\pi\)
−0.0392698 0.999229i \(-0.512503\pi\)
\(464\) 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 0.00649415 0.999979i \(-0.497933\pi\)
0.999979 0.00649415i \(-0.00206717\pi\)
\(468\) 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 \(0.0685465\pi\)
−0.976903 + 0.213685i \(0.931453\pi\)
\(480\) 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 −0.310838 0.950463i \(-0.600610\pi\)
0.950463 + 0.310838i \(0.100610\pi\)
\(488\) −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 \(-0.951826\pi\)
0.988569 0.150768i \(-0.0481745\pi\)
\(500\) −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 −0.986881 0.161446i \(-0.948384\pi\)
−0.161446 0.986881i \(-0.551616\pi\)
\(504\) 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 \(-0.994051\pi\)
0.999825 0.0186888i \(-0.00594918\pi\)
\(510\) 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 0.655685 0.755034i \(-0.272380\pi\)
−0.755034 + 0.655685i \(0.772380\pi\)
\(524\) 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 0.0508772 0.998705i \(-0.483798\pi\)
0.998705 0.0508772i \(-0.0162017\pi\)
\(548\) 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 −0.803386 0.595458i \(-0.796970\pi\)
0.595458 + 0.803386i \(0.296970\pi\)
\(558\) −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 0.994882 + 0.101040i \(0.0322169\pi\)
0.101040 + 0.994882i \(0.467783\pi\)
\(564\) 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 \(0.0373122\pi\)
−0.993138 + 0.116951i \(0.962688\pi\)
\(570\) 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 −0.0291673 + 0.999575i \(0.509286\pi\)
−0.999575 + 0.0291673i \(0.990714\pi\)
\(578\) −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 −0.0334516 0.999440i \(-0.510650\pi\)
0.999440 + 0.0334516i \(0.0106500\pi\)
\(588\) −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 0.665755 0.746170i \(-0.268110\pi\)
−0.746170 + 0.665755i \(0.768110\pi\)
\(594\) 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 \(-0.769646\pi\)
0.749376 0.662145i \(-0.230354\pi\)
\(600\) 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 −0.0615699 + 0.998103i \(0.519611\pi\)
−0.998103 + 0.0615699i \(0.980389\pi\)
\(608\) 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 0.391914 0.920002i \(-0.371813\pi\)
−0.920002 + 0.391914i \(0.871813\pi\)
\(614\) 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 −0.455949 0.890006i \(-0.650700\pi\)
0.890006 + 0.455949i \(0.150700\pi\)
\(618\) 98.0554 + 98.0554i 0.158666 + 0.158666i
\(619\) 508.117i 0.820867i 0.911890 + 0.410434i \(0.134623\pi\)
−0.911890 + 0.410434i \(0.865377\pi\)
\(620\) 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 0.988631 + 0.150364i \(0.0480447\pi\)
0.150364 + 0.988631i \(0.451955\pi\)
\(644\) 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 0.344286 0.938865i \(-0.388121\pi\)
0.938865 0.344286i \(-0.111879\pi\)
\(648\) 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 0.826168 0.563423i \(-0.190516\pi\)
−0.563423 + 0.826168i \(0.690516\pi\)
\(654\) 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 \(-0.791870\pi\)
0.793742 0.608255i \(-0.208130\pi\)
\(660\) 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 0.906801 0.421558i \(-0.138517\pi\)
−0.421558 + 0.906801i \(0.638517\pi\)
\(674\) 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 −0.000685886 1.00000i \(-0.500218\pi\)
1.00000 0.000685886i \(0.000218324\pi\)
\(678\) 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 0.788411 0.615149i \(-0.210904\pi\)
−0.615149 + 0.788411i \(0.710904\pi\)
\(684\) 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 \(0.0675443\pi\)
−0.977571 + 0.210608i \(0.932456\pi\)
\(710\) −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 \(0.0906415\pi\)
−0.959729 + 0.280926i \(0.909359\pi\)
\(720\) −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 −0.163497 + 0.986544i \(0.552277\pi\)
−0.986544 + 0.163497i \(0.947723\pi\)
\(728\) −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 −0.999986 0.00521382i \(-0.998340\pi\)
−0.00521382 0.999986i \(-0.501660\pi\)
\(734\) 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 \(-0.946161\pi\)
0.985730 0.168335i \(-0.0538391\pi\)
\(740\) 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 0.787949 0.615741i \(-0.211143\pi\)
−0.615741 + 0.787949i \(0.711143\pi\)
\(744\) 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 −0.593687 0.804696i \(-0.702328\pi\)
0.804696 + 0.593687i \(0.202328\pi\)
\(758\) 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 \(-0.863750\pi\)
0.909780 0.415091i \(-0.136250\pi\)
\(770\) −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 0.697011 0.717061i \(-0.254513\pi\)
−0.717061 + 0.697011i \(0.754513\pi\)
\(774\) 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