Properties

Label 690.3.k.b.277.16
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.16
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.16

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.93589 - 3.08362i) q^{5} -2.44949 q^{6} +(-1.42240 - 1.42240i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.93589 - 3.08362i) q^{5} -2.44949 q^{6} +(-1.42240 - 1.42240i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-7.01952 - 0.852269i) q^{10} +3.13344 q^{11} +(2.44949 + 2.44949i) q^{12} +(-8.16946 + 8.16946i) q^{13} +2.84480i q^{14} +(1.04381 - 8.59712i) q^{15} -4.00000 q^{16} +(-8.80764 - 8.80764i) q^{17} +(-3.00000 + 3.00000i) q^{18} -33.0294i q^{19} +(6.16725 + 7.87179i) q^{20} -3.48416 q^{21} +(-3.13344 - 3.13344i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(5.98252 - 24.2736i) q^{25} +16.3389 q^{26} +(-3.67423 - 3.67423i) q^{27} +(2.84480 - 2.84480i) q^{28} +8.67288i q^{29} +(-9.64093 + 7.55331i) q^{30} -47.5546 q^{31} +(4.00000 + 4.00000i) q^{32} +(3.83766 - 3.83766i) q^{33} +17.6153i q^{34} +(-9.98457 - 1.21227i) q^{35} +6.00000 q^{36} +(18.6967 + 18.6967i) q^{37} +(-33.0294 + 33.0294i) q^{38} +20.0110i q^{39} +(1.70454 - 14.0390i) q^{40} +21.0080 q^{41} +(3.48416 + 3.48416i) q^{42} +(37.8115 - 37.8115i) q^{43} +6.26687i q^{44} +(-9.25087 - 11.8077i) q^{45} -6.78233 q^{46} +(-4.90320 - 4.90320i) q^{47} +(-4.89898 + 4.89898i) q^{48} -44.9536i q^{49} +(-30.2562 + 18.2911i) q^{50} -21.5742 q^{51} +(-16.3389 - 16.3389i) q^{52} +(6.02763 - 6.02763i) q^{53} +7.34847i q^{54} +(12.3329 - 9.66234i) q^{55} -5.68960 q^{56} +(-40.4526 - 40.4526i) q^{57} +(8.67288 - 8.67288i) q^{58} -91.3726i q^{59} +(17.1942 + 2.08762i) q^{60} -76.7830 q^{61} +(47.5546 + 47.5546i) q^{62} +(-4.26720 + 4.26720i) q^{63} -8.00000i q^{64} +(-6.96258 + 57.3457i) q^{65} -7.67532 q^{66} +(79.6346 + 79.6346i) q^{67} +(17.6153 - 17.6153i) q^{68} -8.30662i q^{69} +(8.77230 + 11.1968i) q^{70} -123.580 q^{71} +(-6.00000 - 6.00000i) q^{72} +(89.3944 - 89.3944i) q^{73} -37.3933i q^{74} +(-22.4020 - 37.0561i) q^{75} +66.0589 q^{76} +(-4.45700 - 4.45700i) q^{77} +(20.0110 - 20.0110i) q^{78} +43.8149i q^{79} +(-15.7436 + 12.3345i) q^{80} -9.00000 q^{81} +(-21.0080 - 21.0080i) q^{82} +(-72.8343 + 72.8343i) q^{83} -6.96831i q^{84} +(-61.8254 - 7.50647i) q^{85} -75.6230 q^{86} +(10.6221 + 10.6221i) q^{87} +(6.26687 - 6.26687i) q^{88} +85.1273i q^{89} +(-2.55681 + 21.0586i) q^{90} +23.2405 q^{91} +(6.78233 + 6.78233i) q^{92} +(-58.2422 + 58.2422i) q^{93} +9.80641i q^{94} +(-101.850 - 130.000i) q^{95} +9.79796 q^{96} +(-104.892 - 104.892i) q^{97} +(-44.9536 + 44.9536i) q^{98} -9.40031i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

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
\(5\) 3.93589 3.08362i 0.787179 0.616725i
\(6\) −2.44949 −0.408248
\(7\) −1.42240 1.42240i −0.203200 0.203200i 0.598170 0.801370i \(-0.295895\pi\)
−0.801370 + 0.598170i \(0.795895\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −7.01952 0.852269i −0.701952 0.0852269i
\(11\) 3.13344 0.284858 0.142429 0.989805i \(-0.454509\pi\)
0.142429 + 0.989805i \(0.454509\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −8.16946 + 8.16946i −0.628420 + 0.628420i −0.947670 0.319250i \(-0.896569\pi\)
0.319250 + 0.947670i \(0.396569\pi\)
\(14\) 2.84480i 0.203200i
\(15\) 1.04381 8.59712i 0.0695874 0.573141i
\(16\) −4.00000 −0.250000
\(17\) −8.80764 8.80764i −0.518096 0.518096i 0.398899 0.916995i \(-0.369393\pi\)
−0.916995 + 0.398899i \(0.869393\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 33.0294i 1.73839i −0.494469 0.869196i \(-0.664637\pi\)
0.494469 0.869196i \(-0.335363\pi\)
\(20\) 6.16725 + 7.87179i 0.308362 + 0.393589i
\(21\) −3.48416 −0.165912
\(22\) −3.13344 3.13344i −0.142429 0.142429i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 5.98252 24.2736i 0.239301 0.970946i
\(26\) 16.3389 0.628420
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 2.84480 2.84480i 0.101600 0.101600i
\(29\) 8.67288i 0.299065i 0.988757 + 0.149532i \(0.0477769\pi\)
−0.988757 + 0.149532i \(0.952223\pi\)
\(30\) −9.64093 + 7.55331i −0.321364 + 0.251777i
\(31\) −47.5546 −1.53402 −0.767010 0.641636i \(-0.778256\pi\)
−0.767010 + 0.641636i \(0.778256\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 3.83766 3.83766i 0.116293 0.116293i
\(34\) 17.6153i 0.518096i
\(35\) −9.98457 1.21227i −0.285273 0.0346362i
\(36\) 6.00000 0.166667
\(37\) 18.6967 + 18.6967i 0.505315 + 0.505315i 0.913085 0.407770i \(-0.133693\pi\)
−0.407770 + 0.913085i \(0.633693\pi\)
\(38\) −33.0294 + 33.0294i −0.869196 + 0.869196i
\(39\) 20.0110i 0.513103i
\(40\) 1.70454 14.0390i 0.0426134 0.350976i
\(41\) 21.0080 0.512390 0.256195 0.966625i \(-0.417531\pi\)
0.256195 + 0.966625i \(0.417531\pi\)
\(42\) 3.48416 + 3.48416i 0.0829561 + 0.0829561i
\(43\) 37.8115 37.8115i 0.879337 0.879337i −0.114129 0.993466i \(-0.536408\pi\)
0.993466 + 0.114129i \(0.0364076\pi\)
\(44\) 6.26687i 0.142429i
\(45\) −9.25087 11.8077i −0.205575 0.262393i
\(46\) −6.78233 −0.147442
\(47\) −4.90320 4.90320i −0.104323 0.104323i 0.653018 0.757342i \(-0.273502\pi\)
−0.757342 + 0.653018i \(0.773502\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 44.9536i 0.917419i
\(50\) −30.2562 + 18.2911i −0.605123 + 0.365822i
\(51\) −21.5742 −0.423024
\(52\) −16.3389 16.3389i −0.314210 0.314210i
\(53\) 6.02763 6.02763i 0.113729 0.113729i −0.647952 0.761681i \(-0.724374\pi\)
0.761681 + 0.647952i \(0.224374\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 12.3329 9.66234i 0.224234 0.175679i
\(56\) −5.68960 −0.101600
\(57\) −40.4526 40.4526i −0.709695 0.709695i
\(58\) 8.67288 8.67288i 0.149532 0.149532i
\(59\) 91.3726i 1.54869i −0.632765 0.774344i \(-0.718080\pi\)
0.632765 0.774344i \(-0.281920\pi\)
\(60\) 17.1942 + 2.08762i 0.286571 + 0.0347937i
\(61\) −76.7830 −1.25874 −0.629369 0.777107i \(-0.716687\pi\)
−0.629369 + 0.777107i \(0.716687\pi\)
\(62\) 47.5546 + 47.5546i 0.767010 + 0.767010i
\(63\) −4.26720 + 4.26720i −0.0677334 + 0.0677334i
\(64\) 8.00000i 0.125000i
\(65\) −6.96258 + 57.3457i −0.107117 + 0.882242i
\(66\) −7.67532 −0.116293
\(67\) 79.6346 + 79.6346i 1.18858 + 1.18858i 0.977461 + 0.211114i \(0.0677093\pi\)
0.211114 + 0.977461i \(0.432291\pi\)
\(68\) 17.6153 17.6153i 0.259048 0.259048i
\(69\) 8.30662i 0.120386i
\(70\) 8.77230 + 11.1968i 0.125319 + 0.159955i
\(71\) −123.580 −1.74057 −0.870283 0.492552i \(-0.836064\pi\)
−0.870283 + 0.492552i \(0.836064\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 89.3944 89.3944i 1.22458 1.22458i 0.258596 0.965986i \(-0.416740\pi\)
0.965986 0.258596i \(-0.0832598\pi\)
\(74\) 37.3933i 0.505315i
\(75\) −22.4020 37.0561i −0.298693 0.494081i
\(76\) 66.0589 0.869196
\(77\) −4.45700 4.45700i −0.0578831 0.0578831i
\(78\) 20.0110 20.0110i 0.256552 0.256552i
\(79\) 43.8149i 0.554618i 0.960781 + 0.277309i \(0.0894427\pi\)
−0.960781 + 0.277309i \(0.910557\pi\)
\(80\) −15.7436 + 12.3345i −0.196795 + 0.154181i
\(81\) −9.00000 −0.111111
\(82\) −21.0080 21.0080i −0.256195 0.256195i
\(83\) −72.8343 + 72.8343i −0.877522 + 0.877522i −0.993278 0.115756i \(-0.963071\pi\)
0.115756 + 0.993278i \(0.463071\pi\)
\(84\) 6.96831i 0.0829561i
\(85\) −61.8254 7.50647i −0.727357 0.0883115i
\(86\) −75.6230 −0.879337
\(87\) 10.6221 + 10.6221i 0.122093 + 0.122093i
\(88\) 6.26687 6.26687i 0.0712145 0.0712145i
\(89\) 85.1273i 0.956487i 0.878227 + 0.478243i \(0.158726\pi\)
−0.878227 + 0.478243i \(0.841274\pi\)
\(90\) −2.55681 + 21.0586i −0.0284090 + 0.233984i
\(91\) 23.2405 0.255390
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −58.2422 + 58.2422i −0.626261 + 0.626261i
\(94\) 9.80641i 0.104323i
\(95\) −101.850 130.000i −1.07211 1.36842i
\(96\) 9.79796 0.102062
\(97\) −104.892 104.892i −1.08136 1.08136i −0.996383 0.0849800i \(-0.972917\pi\)
−0.0849800 0.996383i \(-0.527083\pi\)
\(98\) −44.9536 + 44.9536i −0.458710 + 0.458710i
\(99\) 9.40031i 0.0949526i
\(100\) 48.5473 + 11.9650i 0.485473 + 0.119650i
\(101\) −161.022 −1.59428 −0.797138 0.603798i \(-0.793654\pi\)
−0.797138 + 0.603798i \(0.793654\pi\)
\(102\) 21.5742 + 21.5742i 0.211512 + 0.211512i
\(103\) 51.2006 51.2006i 0.497094 0.497094i −0.413438 0.910532i \(-0.635672\pi\)
0.910532 + 0.413438i \(0.135672\pi\)
\(104\) 32.6779i 0.314210i
\(105\) −13.7133 + 10.7438i −0.130603 + 0.102322i
\(106\) −12.0553 −0.113729
\(107\) 88.6095 + 88.6095i 0.828127 + 0.828127i 0.987257 0.159131i \(-0.0508692\pi\)
−0.159131 + 0.987257i \(0.550869\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 45.9965i 0.421986i −0.977488 0.210993i \(-0.932330\pi\)
0.977488 0.210993i \(-0.0676698\pi\)
\(110\) −21.9952 2.67053i −0.199957 0.0242775i
\(111\) 45.7973 0.412588
\(112\) 5.68960 + 5.68960i 0.0508000 + 0.0508000i
\(113\) −100.216 + 100.216i −0.886871 + 0.886871i −0.994221 0.107350i \(-0.965763\pi\)
0.107350 + 0.994221i \(0.465763\pi\)
\(114\) 80.9052i 0.709695i
\(115\) 2.89018 23.8043i 0.0251320 0.206994i
\(116\) −17.3458 −0.149532
\(117\) 24.5084 + 24.5084i 0.209473 + 0.209473i
\(118\) −91.3726 + 91.3726i −0.774344 + 0.774344i
\(119\) 25.0560i 0.210554i
\(120\) −15.1066 19.2819i −0.125888 0.160682i
\(121\) −111.182 −0.918856
\(122\) 76.7830 + 76.7830i 0.629369 + 0.629369i
\(123\) 25.7294 25.7294i 0.209182 0.209182i
\(124\) 95.1092i 0.767010i
\(125\) −51.3042 113.986i −0.410434 0.911890i
\(126\) 8.53440 0.0677334
\(127\) 17.0379 + 17.0379i 0.134157 + 0.134157i 0.770996 0.636840i \(-0.219759\pi\)
−0.636840 + 0.770996i \(0.719759\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 92.6189i 0.717976i
\(130\) 64.3083 50.3831i 0.494679 0.387563i
\(131\) 226.477 1.72884 0.864418 0.502774i \(-0.167687\pi\)
0.864418 + 0.502774i \(0.167687\pi\)
\(132\) 7.67532 + 7.67532i 0.0581464 + 0.0581464i
\(133\) −46.9811 + 46.9811i −0.353241 + 0.353241i
\(134\) 159.269i 1.18858i
\(135\) −25.7914 3.13144i −0.191047 0.0231958i
\(136\) −35.2306 −0.259048
\(137\) −13.3335 13.3335i −0.0973250 0.0973250i 0.656768 0.754093i \(-0.271923\pi\)
−0.754093 + 0.656768i \(0.771923\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 136.577i 0.982566i −0.871000 0.491283i \(-0.836528\pi\)
0.871000 0.491283i \(-0.163472\pi\)
\(140\) 2.42453 19.9691i 0.0173181 0.142637i
\(141\) −12.0103 −0.0851798
\(142\) 123.580 + 123.580i 0.870283 + 0.870283i
\(143\) −25.5985 + 25.5985i −0.179011 + 0.179011i
\(144\) 12.0000i 0.0833333i
\(145\) 26.7439 + 34.1355i 0.184441 + 0.235418i
\(146\) −178.789 −1.22458
\(147\) −55.0566 55.0566i −0.374535 0.374535i
\(148\) −37.3933 + 37.3933i −0.252658 + 0.252658i
\(149\) 21.6052i 0.145001i −0.997368 0.0725006i \(-0.976902\pi\)
0.997368 0.0725006i \(-0.0230979\pi\)
\(150\) −14.6541 + 59.4580i −0.0976941 + 0.396387i
\(151\) 283.184 1.87539 0.937695 0.347459i \(-0.112955\pi\)
0.937695 + 0.347459i \(0.112955\pi\)
\(152\) −66.0589 66.0589i −0.434598 0.434598i
\(153\) −26.4229 + 26.4229i −0.172699 + 0.172699i
\(154\) 8.91400i 0.0578831i
\(155\) −187.170 + 146.641i −1.20755 + 0.946068i
\(156\) −40.0220 −0.256552
\(157\) 124.318 + 124.318i 0.791832 + 0.791832i 0.981792 0.189960i \(-0.0608357\pi\)
−0.189960 + 0.981792i \(0.560836\pi\)
\(158\) 43.8149 43.8149i 0.277309 0.277309i
\(159\) 14.7646i 0.0928592i
\(160\) 28.0781 + 3.40907i 0.175488 + 0.0213067i
\(161\) −9.64719 −0.0599204
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 72.7999 72.7999i 0.446625 0.446625i −0.447606 0.894231i \(-0.647723\pi\)
0.894231 + 0.447606i \(0.147723\pi\)
\(164\) 42.0160i 0.256195i
\(165\) 3.27072 26.9385i 0.0198225 0.163264i
\(166\) 145.669 0.877522
\(167\) 60.4809 + 60.4809i 0.362161 + 0.362161i 0.864608 0.502447i \(-0.167567\pi\)
−0.502447 + 0.864608i \(0.667567\pi\)
\(168\) −6.96831 + 6.96831i −0.0414780 + 0.0414780i
\(169\) 35.5197i 0.210176i
\(170\) 54.3189 + 69.3319i 0.319523 + 0.407834i
\(171\) −99.0883 −0.579464
\(172\) 75.6230 + 75.6230i 0.439669 + 0.439669i
\(173\) 96.5087 96.5087i 0.557854 0.557854i −0.370842 0.928696i \(-0.620931\pi\)
0.928696 + 0.370842i \(0.120931\pi\)
\(174\) 21.2441i 0.122093i
\(175\) −43.0364 + 26.0173i −0.245922 + 0.148670i
\(176\) −12.5337 −0.0712145
\(177\) −111.908 111.908i −0.632249 0.632249i
\(178\) 85.1273 85.1273i 0.478243 0.478243i
\(179\) 115.452i 0.644983i −0.946572 0.322491i \(-0.895480\pi\)
0.946572 0.322491i \(-0.104520\pi\)
\(180\) 23.6154 18.5017i 0.131196 0.102787i
\(181\) 182.511 1.00835 0.504174 0.863602i \(-0.331797\pi\)
0.504174 + 0.863602i \(0.331797\pi\)
\(182\) −23.2405 23.2405i −0.127695 0.127695i
\(183\) −94.0396 + 94.0396i −0.513878 + 0.513878i
\(184\) 13.5647i 0.0737210i
\(185\) 131.242 + 15.9346i 0.709414 + 0.0861329i
\(186\) 116.484 0.626261
\(187\) −27.5982 27.5982i −0.147584 0.147584i
\(188\) 9.80641 9.80641i 0.0521617 0.0521617i
\(189\) 10.4525i 0.0553040i
\(190\) −28.1499 + 231.851i −0.148158 + 1.22027i
\(191\) −126.245 −0.660969 −0.330485 0.943811i \(-0.607212\pi\)
−0.330485 + 0.943811i \(0.607212\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −104.990 + 104.990i −0.543989 + 0.543989i −0.924696 0.380707i \(-0.875681\pi\)
0.380707 + 0.924696i \(0.375681\pi\)
\(194\) 209.784i 1.08136i
\(195\) 61.7065 + 78.7612i 0.316443 + 0.403904i
\(196\) 89.9071 0.458710
\(197\) 189.425 + 189.425i 0.961546 + 0.961546i 0.999288 0.0377412i \(-0.0120163\pi\)
−0.0377412 + 0.999288i \(0.512016\pi\)
\(198\) −9.40031 + 9.40031i −0.0474763 + 0.0474763i
\(199\) 140.728i 0.707178i −0.935401 0.353589i \(-0.884961\pi\)
0.935401 0.353589i \(-0.115039\pi\)
\(200\) −36.5822 60.5123i −0.182911 0.302562i
\(201\) 195.064 0.970468
\(202\) 161.022 + 161.022i 0.797138 + 0.797138i
\(203\) 12.3363 12.3363i 0.0607700 0.0607700i
\(204\) 43.1484i 0.211512i
\(205\) 82.6853 64.7808i 0.403343 0.316004i
\(206\) −102.401 −0.497094
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 32.6779 32.6779i 0.157105 0.157105i
\(209\) 103.496i 0.495194i
\(210\) 24.4571 + 2.96944i 0.116462 + 0.0141402i
\(211\) 84.3383 0.399707 0.199854 0.979826i \(-0.435953\pi\)
0.199854 + 0.979826i \(0.435953\pi\)
\(212\) 12.0553 + 12.0553i 0.0568644 + 0.0568644i
\(213\) −151.354 + 151.354i −0.710583 + 0.710583i
\(214\) 177.219i 0.828127i
\(215\) 32.2256 265.419i 0.149886 1.23450i
\(216\) −14.6969 −0.0680414
\(217\) 67.6417 + 67.6417i 0.311713 + 0.311713i
\(218\) −45.9965 + 45.9965i −0.210993 + 0.210993i
\(219\) 218.971i 0.999867i
\(220\) 19.3247 + 24.6657i 0.0878395 + 0.112117i
\(221\) 143.907 0.651165
\(222\) −45.7973 45.7973i −0.206294 0.206294i
\(223\) 178.882 178.882i 0.802163 0.802163i −0.181270 0.983433i \(-0.558021\pi\)
0.983433 + 0.181270i \(0.0580209\pi\)
\(224\) 11.3792i 0.0508000i
\(225\) −72.8209 17.9475i −0.323649 0.0797669i
\(226\) 200.433 0.886871
\(227\) 159.186 + 159.186i 0.701259 + 0.701259i 0.964681 0.263422i \(-0.0848510\pi\)
−0.263422 + 0.964681i \(0.584851\pi\)
\(228\) 80.9052 80.9052i 0.354848 0.354848i
\(229\) 139.731i 0.610178i −0.952324 0.305089i \(-0.901314\pi\)
0.952324 0.305089i \(-0.0986862\pi\)
\(230\) −26.6945 + 20.9142i −0.116063 + 0.0909311i
\(231\) −10.9174 −0.0472614
\(232\) 17.3458 + 17.3458i 0.0747662 + 0.0747662i
\(233\) 63.6155 63.6155i 0.273028 0.273028i −0.557290 0.830318i \(-0.688159\pi\)
0.830318 + 0.557290i \(0.188159\pi\)
\(234\) 49.0168i 0.209473i
\(235\) −34.4181 4.17885i −0.146460 0.0177823i
\(236\) 182.745 0.774344
\(237\) 53.6620 + 53.6620i 0.226422 + 0.226422i
\(238\) 25.0560 25.0560i 0.105277 0.105277i
\(239\) 56.4515i 0.236199i 0.993002 + 0.118099i \(0.0376801\pi\)
−0.993002 + 0.118099i \(0.962320\pi\)
\(240\) −4.17525 + 34.3885i −0.0173969 + 0.143285i
\(241\) 88.4572 0.367042 0.183521 0.983016i \(-0.441250\pi\)
0.183521 + 0.983016i \(0.441250\pi\)
\(242\) 111.182 + 111.182i 0.459428 + 0.459428i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 153.566i 0.629369i
\(245\) −138.620 176.932i −0.565795 0.722173i
\(246\) −51.4589 −0.209182
\(247\) 269.833 + 269.833i 1.09244 + 1.09244i
\(248\) −95.1092 + 95.1092i −0.383505 + 0.383505i
\(249\) 178.407i 0.716493i
\(250\) −62.6820 + 165.291i −0.250728 + 0.661162i
\(251\) 68.5838 0.273242 0.136621 0.990623i \(-0.456376\pi\)
0.136621 + 0.990623i \(0.456376\pi\)
\(252\) −8.53440 8.53440i −0.0338667 0.0338667i
\(253\) 10.6260 10.6260i 0.0420000 0.0420000i
\(254\) 34.0758i 0.134157i
\(255\) −84.9138 + 66.5268i −0.332995 + 0.260889i
\(256\) 16.0000 0.0625000
\(257\) 133.320 + 133.320i 0.518754 + 0.518754i 0.917194 0.398440i \(-0.130448\pi\)
−0.398440 + 0.917194i \(0.630448\pi\)
\(258\) −92.6189 + 92.6189i −0.358988 + 0.358988i
\(259\) 53.1883i 0.205360i
\(260\) −114.691 13.9252i −0.441121 0.0535583i
\(261\) 26.0186 0.0996883
\(262\) −226.477 226.477i −0.864418 0.864418i
\(263\) 269.935 269.935i 1.02637 1.02637i 0.0267265 0.999643i \(-0.491492\pi\)
0.999643 0.0267265i \(-0.00850832\pi\)
\(264\) 15.3506i 0.0581464i
\(265\) 5.13716 42.3110i 0.0193855 0.159664i
\(266\) 93.9621 0.353241
\(267\) 104.259 + 104.259i 0.390484 + 0.390484i
\(268\) −159.269 + 159.269i −0.594288 + 0.594288i
\(269\) 287.611i 1.06919i 0.845109 + 0.534593i \(0.179535\pi\)
−0.845109 + 0.534593i \(0.820465\pi\)
\(270\) 22.6599 + 28.9228i 0.0839256 + 0.107121i
\(271\) 146.523 0.540675 0.270338 0.962766i \(-0.412865\pi\)
0.270338 + 0.962766i \(0.412865\pi\)
\(272\) 35.2306 + 35.2306i 0.129524 + 0.129524i
\(273\) 28.4637 28.4637i 0.104263 0.104263i
\(274\) 26.6670i 0.0973250i
\(275\) 18.7458 76.0599i 0.0681667 0.276582i
\(276\) 16.6132 0.0601929
\(277\) 75.7854 + 75.7854i 0.273594 + 0.273594i 0.830545 0.556951i \(-0.188029\pi\)
−0.556951 + 0.830545i \(0.688029\pi\)
\(278\) −136.577 + 136.577i −0.491283 + 0.491283i
\(279\) 142.664i 0.511340i
\(280\) −22.3937 + 17.5446i −0.0799774 + 0.0626593i
\(281\) 461.843 1.64357 0.821785 0.569798i \(-0.192979\pi\)
0.821785 + 0.569798i \(0.192979\pi\)
\(282\) 12.0103 + 12.0103i 0.0425899 + 0.0425899i
\(283\) 17.7043 17.7043i 0.0625594 0.0625594i −0.675135 0.737694i \(-0.735915\pi\)
0.737694 + 0.675135i \(0.235915\pi\)
\(284\) 247.160i 0.870283i
\(285\) −283.958 34.4765i −0.996344 0.120970i
\(286\) 51.1970 0.179011
\(287\) −29.8818 29.8818i −0.104118 0.104118i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 133.851i 0.463152i
\(290\) 7.39163 60.8795i 0.0254884 0.209929i
\(291\) −256.932 −0.882929
\(292\) 178.789 + 178.789i 0.612291 + 0.612291i
\(293\) −135.640 + 135.640i −0.462934 + 0.462934i −0.899616 0.436682i \(-0.856153\pi\)
0.436682 + 0.899616i \(0.356153\pi\)
\(294\) 110.113i 0.374535i
\(295\) −281.759 359.633i −0.955114 1.21909i
\(296\) 74.7866 0.252658
\(297\) −11.5130 11.5130i −0.0387643 0.0387643i
\(298\) −21.6052 + 21.6052i −0.0725006 + 0.0725006i
\(299\) 55.4080i 0.185311i
\(300\) 74.1121 44.8039i 0.247040 0.149346i
\(301\) −107.566 −0.357363
\(302\) −283.184 283.184i −0.937695 0.937695i
\(303\) −197.211 + 197.211i −0.650860 + 0.650860i
\(304\) 132.118i 0.434598i
\(305\) −302.210 + 236.770i −0.990852 + 0.776295i
\(306\) 52.8458 0.172699
\(307\) −337.020 337.020i −1.09779 1.09779i −0.994669 0.103116i \(-0.967119\pi\)
−0.103116 0.994669i \(-0.532881\pi\)
\(308\) 8.91400 8.91400i 0.0289416 0.0289416i
\(309\) 125.415i 0.405875i
\(310\) 333.810 + 40.5293i 1.07681 + 0.130740i
\(311\) 205.353 0.660298 0.330149 0.943929i \(-0.392901\pi\)
0.330149 + 0.943929i \(0.392901\pi\)
\(312\) 40.0220 + 40.0220i 0.128276 + 0.128276i
\(313\) −51.0361 + 51.0361i −0.163055 + 0.163055i −0.783918 0.620864i \(-0.786782\pi\)
0.620864 + 0.783918i \(0.286782\pi\)
\(314\) 248.635i 0.791832i
\(315\) −3.63680 + 29.9537i −0.0115454 + 0.0950911i
\(316\) −87.6297 −0.277309
\(317\) 415.998 + 415.998i 1.31230 + 1.31230i 0.919718 + 0.392580i \(0.128417\pi\)
0.392580 + 0.919718i \(0.371583\pi\)
\(318\) −14.7646 + 14.7646i −0.0464296 + 0.0464296i
\(319\) 27.1759i 0.0851910i
\(320\) −24.6690 31.4871i −0.0770906 0.0983973i
\(321\) 217.048 0.676162
\(322\) 9.64719 + 9.64719i 0.0299602 + 0.0299602i
\(323\) −290.911 + 290.911i −0.900654 + 0.900654i
\(324\) 18.0000i 0.0555556i
\(325\) 149.429 + 247.177i 0.459781 + 0.760543i
\(326\) −145.600 −0.446625
\(327\) −56.3340 56.3340i −0.172275 0.172275i
\(328\) 42.0160 42.0160i 0.128098 0.128098i
\(329\) 13.9486i 0.0423971i
\(330\) −30.2092 + 23.6678i −0.0915432 + 0.0717206i
\(331\) 624.517 1.88676 0.943379 0.331717i \(-0.107628\pi\)
0.943379 + 0.331717i \(0.107628\pi\)
\(332\) −145.669 145.669i −0.438761 0.438761i
\(333\) 56.0900 56.0900i 0.168438 0.168438i
\(334\) 120.962i 0.362161i
\(335\) 558.996 + 67.8701i 1.66865 + 0.202597i
\(336\) 13.9366 0.0414780
\(337\) −86.5233 86.5233i −0.256746 0.256746i 0.566984 0.823729i \(-0.308110\pi\)
−0.823729 + 0.566984i \(0.808110\pi\)
\(338\) 35.5197 35.5197i 0.105088 0.105088i
\(339\) 245.479i 0.724127i
\(340\) 15.0129 123.651i 0.0441557 0.363679i
\(341\) −149.009 −0.436978
\(342\) 99.0883 + 99.0883i 0.289732 + 0.289732i
\(343\) −133.640 + 133.640i −0.389620 + 0.389620i
\(344\) 151.246i 0.439669i
\(345\) −25.6145 32.6940i −0.0742450 0.0947652i
\(346\) −193.017 −0.557854
\(347\) 382.830 + 382.830i 1.10326 + 1.10326i 0.994015 + 0.109242i \(0.0348423\pi\)
0.109242 + 0.994015i \(0.465158\pi\)
\(348\) −21.2441 + 21.2441i −0.0610464 + 0.0610464i
\(349\) 392.877i 1.12572i 0.826552 + 0.562861i \(0.190299\pi\)
−0.826552 + 0.562861i \(0.809701\pi\)
\(350\) 69.0537 + 17.0191i 0.197296 + 0.0486259i
\(351\) 60.0331 0.171034
\(352\) 12.5337 + 12.5337i 0.0356072 + 0.0356072i
\(353\) −238.494 + 238.494i −0.675620 + 0.675620i −0.959006 0.283386i \(-0.908542\pi\)
0.283386 + 0.959006i \(0.408542\pi\)
\(354\) 223.816i 0.632249i
\(355\) −486.398 + 381.075i −1.37014 + 1.07345i
\(356\) −170.255 −0.478243
\(357\) 30.6872 + 30.6872i 0.0859585 + 0.0859585i
\(358\) −115.452 + 115.452i −0.322491 + 0.322491i
\(359\) 434.304i 1.20976i −0.796316 0.604881i \(-0.793221\pi\)
0.796316 0.604881i \(-0.206779\pi\)
\(360\) −42.1171 5.11361i −0.116992 0.0142045i
\(361\) −729.943 −2.02200
\(362\) −182.511 182.511i −0.504174 0.504174i
\(363\) −136.169 + 136.169i −0.375121 + 0.375121i
\(364\) 46.4810i 0.127695i
\(365\) 76.1881 627.506i 0.208734 1.71919i
\(366\) 188.079 0.513878
\(367\) 139.615 + 139.615i 0.380421 + 0.380421i 0.871254 0.490832i \(-0.163307\pi\)
−0.490832 + 0.871254i \(0.663307\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 63.0240i 0.170797i
\(370\) −115.307 147.176i −0.311640 0.397773i
\(371\) −17.1474 −0.0462194
\(372\) −116.484 116.484i −0.313130 0.313130i
\(373\) −78.8131 + 78.8131i −0.211295 + 0.211295i −0.804817 0.593522i \(-0.797737\pi\)
0.593522 + 0.804817i \(0.297737\pi\)
\(374\) 55.1964i 0.147584i
\(375\) −202.439 76.7695i −0.539837 0.204719i
\(376\) −19.6128 −0.0521617
\(377\) −70.8528 70.8528i −0.187938 0.187938i
\(378\) 10.4525 10.4525i 0.0276520 0.0276520i
\(379\) 59.0081i 0.155694i 0.996965 + 0.0778470i \(0.0248046\pi\)
−0.996965 + 0.0778470i \(0.975195\pi\)
\(380\) 260.001 203.701i 0.684212 0.536055i
\(381\) 41.7342 0.109539
\(382\) 126.245 + 126.245i 0.330485 + 0.330485i
\(383\) 101.487 101.487i 0.264980 0.264980i −0.562094 0.827074i \(-0.690004\pi\)
0.827074 + 0.562094i \(0.190004\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −31.2860 3.79856i −0.0812624 0.00986640i
\(386\) 209.980 0.543989
\(387\) −113.435 113.435i −0.293112 0.293112i
\(388\) 209.784 209.784i 0.540681 0.540681i
\(389\) 276.824i 0.711630i 0.934556 + 0.355815i \(0.115797\pi\)
−0.934556 + 0.355815i \(0.884203\pi\)
\(390\) 17.0548 140.468i 0.0437302 0.360174i
\(391\) −59.7363 −0.152778
\(392\) −89.9071 89.9071i −0.229355 0.229355i
\(393\) 277.377 277.377i 0.705794 0.705794i
\(394\) 378.849i 0.961546i
\(395\) 135.109 + 172.451i 0.342047 + 0.436584i
\(396\) 18.8006 0.0474763
\(397\) −304.445 304.445i −0.766864 0.766864i 0.210689 0.977553i \(-0.432429\pi\)
−0.977553 + 0.210689i \(0.932429\pi\)
\(398\) −140.728 + 140.728i −0.353589 + 0.353589i
\(399\) 115.080i 0.288420i
\(400\) −23.9301 + 97.0946i −0.0598252 + 0.242736i
\(401\) −506.097 −1.26209 −0.631044 0.775747i \(-0.717373\pi\)
−0.631044 + 0.775747i \(0.717373\pi\)
\(402\) −195.064 195.064i −0.485234 0.485234i
\(403\) 388.496 388.496i 0.964009 0.964009i
\(404\) 322.044i 0.797138i
\(405\) −35.4230 + 27.7526i −0.0874643 + 0.0685250i
\(406\) −24.6726 −0.0607700
\(407\) 58.5848 + 58.5848i 0.143943 + 0.143943i
\(408\) −43.1484 + 43.1484i −0.105756 + 0.105756i
\(409\) 65.7017i 0.160640i 0.996769 + 0.0803200i \(0.0255942\pi\)
−0.996769 + 0.0803200i \(0.974406\pi\)
\(410\) −147.466 17.9045i −0.359673 0.0436694i
\(411\) −32.6603 −0.0794655
\(412\) 102.401 + 102.401i 0.248547 + 0.248547i
\(413\) −129.968 + 129.968i −0.314693 + 0.314693i
\(414\) 20.3470i 0.0491473i
\(415\) −62.0744 + 511.262i −0.149577 + 1.23196i
\(416\) −65.3557 −0.157105
\(417\) −167.272 167.272i −0.401131 0.401131i
\(418\) −103.496 + 103.496i −0.247597 + 0.247597i
\(419\) 496.707i 1.18546i −0.805402 0.592729i \(-0.798051\pi\)
0.805402 0.592729i \(-0.201949\pi\)
\(420\) −21.4877 27.4265i −0.0511611 0.0653013i
\(421\) −452.792 −1.07552 −0.537758 0.843099i \(-0.680728\pi\)
−0.537758 + 0.843099i \(0.680728\pi\)
\(422\) −84.3383 84.3383i −0.199854 0.199854i
\(423\) −14.7096 + 14.7096i −0.0347745 + 0.0347745i
\(424\) 24.1105i 0.0568644i
\(425\) −266.485 + 161.102i −0.627024 + 0.379063i
\(426\) 302.708 0.710583
\(427\) 109.216 + 109.216i 0.255776 + 0.255776i
\(428\) −177.219 + 177.219i −0.414063 + 0.414063i
\(429\) 62.7033i 0.146161i
\(430\) −297.644 + 233.193i −0.692196 + 0.542309i
\(431\) 375.766 0.871847 0.435924 0.899984i \(-0.356422\pi\)
0.435924 + 0.899984i \(0.356422\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 463.698 463.698i 1.07090 1.07090i 0.0736079 0.997287i \(-0.476549\pi\)
0.997287 0.0736079i \(-0.0234513\pi\)
\(434\) 135.283i 0.311713i
\(435\) 74.5618 + 9.05286i 0.171406 + 0.0208112i
\(436\) 91.9930 0.210993
\(437\) −112.008 112.008i −0.256312 0.256312i
\(438\) −218.971 + 218.971i −0.499933 + 0.499933i
\(439\) 772.787i 1.76033i −0.474664 0.880167i \(-0.657430\pi\)
0.474664 0.880167i \(-0.342570\pi\)
\(440\) 5.34106 43.9904i 0.0121388 0.0999783i
\(441\) −134.861 −0.305806
\(442\) −143.907 143.907i −0.325582 0.325582i
\(443\) −314.253 + 314.253i −0.709374 + 0.709374i −0.966404 0.257029i \(-0.917256\pi\)
0.257029 + 0.966404i \(0.417256\pi\)
\(444\) 91.5946i 0.206294i
\(445\) 262.501 + 335.052i 0.589889 + 0.752926i
\(446\) −357.765 −0.802163
\(447\) −26.4608 26.4608i −0.0591965 0.0591965i
\(448\) −11.3792 + 11.3792i −0.0254000 + 0.0254000i
\(449\) 123.814i 0.275756i −0.990449 0.137878i \(-0.955972\pi\)
0.990449 0.137878i \(-0.0440281\pi\)
\(450\) 54.8734 + 90.7685i 0.121941 + 0.201708i
\(451\) 65.8273 0.145958
\(452\) −200.433 200.433i −0.443435 0.443435i
\(453\) 346.828 346.828i 0.765625 0.765625i
\(454\) 318.372i 0.701259i
\(455\) 91.4721 71.6650i 0.201038 0.157505i
\(456\) −161.810 −0.354848
\(457\) −83.6198 83.6198i −0.182976 0.182976i 0.609676 0.792651i \(-0.291300\pi\)
−0.792651 + 0.609676i \(0.791300\pi\)
\(458\) −139.731 + 139.731i −0.305089 + 0.305089i
\(459\) 64.7227i 0.141008i
\(460\) 47.6087 + 5.78037i 0.103497 + 0.0125660i
\(461\) −350.628 −0.760582 −0.380291 0.924867i \(-0.624176\pi\)
−0.380291 + 0.924867i \(0.624176\pi\)
\(462\) 10.9174 + 10.9174i 0.0236307 + 0.0236307i
\(463\) −486.539 + 486.539i −1.05084 + 1.05084i −0.0522029 + 0.998636i \(0.516624\pi\)
−0.998636 + 0.0522029i \(0.983376\pi\)
\(464\) 34.6915i 0.0747662i
\(465\) −49.6380 + 408.833i −0.106748 + 0.879210i
\(466\) −127.231 −0.273028
\(467\) −392.159 392.159i −0.839742 0.839742i 0.149083 0.988825i \(-0.452368\pi\)
−0.988825 + 0.149083i \(0.952368\pi\)
\(468\) −49.0168 + 49.0168i −0.104737 + 0.104737i
\(469\) 226.545i 0.483037i
\(470\) 30.2393 + 38.5970i 0.0643389 + 0.0821212i
\(471\) 304.515 0.646528
\(472\) −182.745 182.745i −0.387172 0.387172i
\(473\) 118.480 118.480i 0.250486 0.250486i
\(474\) 107.324i 0.226422i
\(475\) −801.744 197.599i −1.68788 0.415998i
\(476\) −50.1120 −0.105277
\(477\) −18.0829 18.0829i −0.0379096 0.0379096i
\(478\) 56.4515 56.4515i 0.118099 0.118099i
\(479\) 201.795i 0.421283i −0.977563 0.210642i \(-0.932445\pi\)
0.977563 0.210642i \(-0.0675553\pi\)
\(480\) 38.5637 30.2132i 0.0803411 0.0629442i
\(481\) −305.483 −0.635101
\(482\) −88.4572 88.4572i −0.183521 0.183521i
\(483\) −11.8153 + 11.8153i −0.0244624 + 0.0244624i
\(484\) 222.363i 0.459428i
\(485\) −736.293 89.3963i −1.51813 0.184322i
\(486\) 22.0454 0.0453609
\(487\) −406.615 406.615i −0.834939 0.834939i 0.153249 0.988188i \(-0.451026\pi\)
−0.988188 + 0.153249i \(0.951026\pi\)
\(488\) −153.566 + 153.566i −0.314684 + 0.314684i
\(489\) 178.323i 0.364668i
\(490\) −38.3125 + 315.552i −0.0781888 + 0.643984i
\(491\) 128.249 0.261199 0.130599 0.991435i \(-0.458310\pi\)
0.130599 + 0.991435i \(0.458310\pi\)
\(492\) 51.4589 + 51.4589i 0.104591 + 0.104591i
\(493\) 76.3876 76.3876i 0.154944 0.154944i
\(494\) 539.666i 1.09244i
\(495\) −28.9870 36.9986i −0.0585597 0.0747447i
\(496\) 190.218 0.383505
\(497\) 175.780 + 175.780i 0.353683 + 0.353683i
\(498\) 178.407 178.407i 0.358247 0.358247i
\(499\) 395.030i 0.791644i −0.918327 0.395822i \(-0.870460\pi\)
0.918327 0.395822i \(-0.129540\pi\)
\(500\) 227.973 102.608i 0.455945 0.205217i
\(501\) 148.147 0.295703
\(502\) −68.5838 68.5838i −0.136621 0.136621i
\(503\) 194.782 194.782i 0.387241 0.387241i −0.486461 0.873702i \(-0.661713\pi\)
0.873702 + 0.486461i \(0.161713\pi\)
\(504\) 17.0688i 0.0338667i
\(505\) −633.765 + 496.531i −1.25498 + 0.983229i
\(506\) −21.2520 −0.0420000
\(507\) 43.5026 + 43.5026i 0.0858039 + 0.0858039i
\(508\) −34.0758 + 34.0758i −0.0670784 + 0.0670784i
\(509\) 366.809i 0.720646i 0.932828 + 0.360323i \(0.117334\pi\)
−0.932828 + 0.360323i \(0.882666\pi\)
\(510\) 151.441 + 18.3870i 0.296942 + 0.0360530i
\(511\) −254.309 −0.497670
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −121.358 + 121.358i −0.236565 + 0.236565i
\(514\) 266.639i 0.518754i
\(515\) 43.6367 359.404i 0.0847315 0.697872i
\(516\) 185.238 0.358988
\(517\) −15.3639 15.3639i −0.0297174 0.0297174i
\(518\) −53.1883 + 53.1883i −0.102680 + 0.102680i
\(519\) 236.397i 0.455485i
\(520\) 100.766 + 128.617i 0.193781 + 0.247340i
\(521\) 301.749 0.579173 0.289587 0.957152i \(-0.406482\pi\)
0.289587 + 0.957152i \(0.406482\pi\)
\(522\) −26.0186 26.0186i −0.0498442 0.0498442i
\(523\) −323.972 + 323.972i −0.619449 + 0.619449i −0.945390 0.325941i \(-0.894319\pi\)
0.325941 + 0.945390i \(0.394319\pi\)
\(524\) 452.955i 0.864418i
\(525\) −20.8440 + 84.5731i −0.0397029 + 0.161092i
\(526\) −539.870 −1.02637
\(527\) 418.844 + 418.844i 0.794770 + 0.794770i
\(528\) −15.3506 + 15.3506i −0.0290732 + 0.0290732i
\(529\) 23.0000i 0.0434783i
\(530\) −47.4482 + 37.1739i −0.0895249 + 0.0701394i
\(531\) −274.118 −0.516229
\(532\) −93.9621 93.9621i −0.176621 0.176621i
\(533\) −171.624 + 171.624i −0.321996 + 0.321996i
\(534\) 208.519i 0.390484i
\(535\) 621.996 + 75.5191i 1.16261 + 0.141157i
\(536\) 318.538 0.594288
\(537\) −141.399 141.399i −0.263313 0.263313i
\(538\) 287.611 287.611i 0.534593 0.534593i
\(539\) 140.859i 0.261334i
\(540\) 6.26287 51.5827i 0.0115979 0.0955235i
\(541\) −38.7881 −0.0716970 −0.0358485 0.999357i \(-0.511413\pi\)
−0.0358485 + 0.999357i \(0.511413\pi\)
\(542\) −146.523 146.523i −0.270338 0.270338i
\(543\) 223.529 223.529i 0.411656 0.411656i
\(544\) 70.4611i 0.129524i
\(545\) −141.836 181.037i −0.260250 0.332179i
\(546\) −56.9274 −0.104263
\(547\) 539.005 + 539.005i 0.985383 + 0.985383i 0.999895 0.0145113i \(-0.00461926\pi\)
−0.0145113 + 0.999895i \(0.504619\pi\)
\(548\) 26.6670 26.6670i 0.0486625 0.0486625i
\(549\) 230.349i 0.419579i
\(550\) −94.8058 + 57.3141i −0.172374 + 0.104207i
\(551\) 286.460 0.519892
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 62.3223 62.3223i 0.112699 0.112699i
\(554\) 151.571i 0.273594i
\(555\) 180.253 141.222i 0.324781 0.254453i
\(556\) 273.153 0.491283
\(557\) −239.468 239.468i −0.429925 0.429925i 0.458678 0.888603i \(-0.348323\pi\)
−0.888603 + 0.458678i \(0.848323\pi\)
\(558\) 142.664 142.664i 0.255670 0.255670i
\(559\) 617.800i 1.10519i
\(560\) 39.9383 + 4.84907i 0.0713183 + 0.00865905i
\(561\) −67.6015 −0.120502
\(562\) −461.843 461.843i −0.821785 0.821785i
\(563\) 316.131 316.131i 0.561512 0.561512i −0.368225 0.929737i \(-0.620034\pi\)
0.929737 + 0.368225i \(0.120034\pi\)
\(564\) 24.0207i 0.0425899i
\(565\) −85.4113 + 703.471i −0.151170 + 1.24508i
\(566\) −35.4086 −0.0625594
\(567\) 12.8016 + 12.8016i 0.0225778 + 0.0225778i
\(568\) −247.160 + 247.160i −0.435141 + 0.435141i
\(569\) 235.711i 0.414256i 0.978314 + 0.207128i \(0.0664116\pi\)
−0.978314 + 0.207128i \(0.933588\pi\)
\(570\) 249.481 + 318.434i 0.437687 + 0.558657i
\(571\) 930.317 1.62928 0.814638 0.579969i \(-0.196935\pi\)
0.814638 + 0.579969i \(0.196935\pi\)
\(572\) −51.1970 51.1970i −0.0895053 0.0895053i
\(573\) −154.618 + 154.618i −0.269840 + 0.269840i
\(574\) 59.7636i 0.104118i
\(575\) −62.0282 102.604i −0.107875 0.178441i
\(576\) −24.0000 −0.0416667
\(577\) −480.176 480.176i −0.832193 0.832193i 0.155623 0.987816i \(-0.450261\pi\)
−0.987816 + 0.155623i \(0.950261\pi\)
\(578\) −133.851 + 133.851i −0.231576 + 0.231576i
\(579\) 257.172i 0.444165i
\(580\) −68.2711 + 53.4878i −0.117709 + 0.0922204i
\(581\) 207.199 0.356625
\(582\) 256.932 + 256.932i 0.441464 + 0.441464i
\(583\) 18.8872 18.8872i 0.0323966 0.0323966i
\(584\) 357.578i 0.612291i
\(585\) 172.037 + 20.8877i 0.294081 + 0.0357055i
\(586\) 271.279 0.462934
\(587\) 175.266 + 175.266i 0.298579 + 0.298579i 0.840457 0.541878i \(-0.182287\pi\)
−0.541878 + 0.840457i \(0.682287\pi\)
\(588\) 110.113 110.113i 0.187267 0.187267i
\(589\) 1570.70i 2.66673i
\(590\) −77.8740 + 641.391i −0.131990 + 1.08710i
\(591\) 463.994 0.785099
\(592\) −74.7866 74.7866i −0.126329 0.126329i
\(593\) 204.328 204.328i 0.344567 0.344567i −0.513514 0.858081i \(-0.671657\pi\)
0.858081 + 0.513514i \(0.171657\pi\)
\(594\) 23.0260i 0.0387643i
\(595\) 77.2632 + 98.6177i 0.129854 + 0.165744i
\(596\) 43.2103 0.0725006
\(597\) −172.356 172.356i −0.288704 0.288704i
\(598\) 55.4080 55.4080i 0.0926555 0.0926555i
\(599\) 353.006i 0.589326i 0.955601 + 0.294663i \(0.0952074\pi\)
−0.955601 + 0.294663i \(0.904793\pi\)
\(600\) −118.916 29.3082i −0.198193 0.0488470i
\(601\) −377.286 −0.627763 −0.313882 0.949462i \(-0.601630\pi\)
−0.313882 + 0.949462i \(0.601630\pi\)
\(602\) 107.566 + 107.566i 0.178681 + 0.178681i
\(603\) 238.904 238.904i 0.396192 0.396192i
\(604\) 566.368i 0.937695i
\(605\) −437.599 + 342.842i −0.723304 + 0.566681i
\(606\) 394.421 0.650860
\(607\) 582.145 + 582.145i 0.959053 + 0.959053i 0.999194 0.0401409i \(-0.0127807\pi\)
−0.0401409 + 0.999194i \(0.512781\pi\)
\(608\) 132.118 132.118i 0.217299 0.217299i
\(609\) 30.2177i 0.0496185i
\(610\) 538.980 + 65.4397i 0.883573 + 0.107278i
\(611\) 80.1131 0.131118
\(612\) −52.8458 52.8458i −0.0863494 0.0863494i
\(613\) −88.4721 + 88.4721i −0.144326 + 0.144326i −0.775578 0.631252i \(-0.782542\pi\)
0.631252 + 0.775578i \(0.282542\pi\)
\(614\) 674.040i 1.09779i
\(615\) 21.9284 180.608i 0.0356559 0.293672i
\(616\) −17.8280 −0.0289416
\(617\) 604.135 + 604.135i 0.979149 + 0.979149i 0.999787 0.0206376i \(-0.00656963\pi\)
−0.0206376 + 0.999787i \(0.506570\pi\)
\(618\) −125.415 + 125.415i −0.202938 + 0.202938i
\(619\) 822.499i 1.32875i 0.747397 + 0.664377i \(0.231303\pi\)
−0.747397 + 0.664377i \(0.768697\pi\)
\(620\) −293.281 374.340i −0.473034 0.603774i
\(621\) −24.9199 −0.0401286
\(622\) −205.353 205.353i −0.330149 0.330149i
\(623\) 121.085 121.085i 0.194358 0.194358i
\(624\) 80.0441i 0.128276i
\(625\) −553.419 290.435i −0.885470 0.464696i
\(626\) 102.072 0.163055
\(627\) −126.756 126.756i −0.202162 0.202162i
\(628\) −248.635 + 248.635i −0.395916 + 0.395916i
\(629\) 329.347i 0.523604i
\(630\) 33.5905 26.3169i 0.0533183 0.0417728i
\(631\) −190.298 −0.301582 −0.150791 0.988566i \(-0.548182\pi\)
−0.150791 + 0.988566i \(0.548182\pi\)
\(632\) 87.6297 + 87.6297i 0.138655 + 0.138655i
\(633\) 103.293 103.293i 0.163180 0.163180i
\(634\) 831.997i 1.31230i
\(635\) 119.598 + 14.5209i 0.188343 + 0.0228675i
\(636\) 29.5292 0.0464296
\(637\) 367.246 + 367.246i 0.576525 + 0.576525i
\(638\) 27.1759 27.1759i 0.0425955 0.0425955i
\(639\) 370.740i 0.580189i
\(640\) −6.81815 + 56.1561i −0.0106534 + 0.0877440i
\(641\) 490.787 0.765658 0.382829 0.923819i \(-0.374950\pi\)
0.382829 + 0.923819i \(0.374950\pi\)
\(642\) −217.048 217.048i −0.338081 0.338081i
\(643\) 159.376 159.376i 0.247863 0.247863i −0.572230 0.820093i \(-0.693921\pi\)
0.820093 + 0.572230i \(0.193921\pi\)
\(644\) 19.2944i 0.0299602i
\(645\) −285.602 364.538i −0.442794 0.565175i
\(646\) 581.823 0.900654
\(647\) 518.536 + 518.536i 0.801446 + 0.801446i 0.983322 0.181875i \(-0.0582167\pi\)
−0.181875 + 0.983322i \(0.558217\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 286.310i 0.441156i
\(650\) 97.7479 396.605i 0.150381 0.610162i
\(651\) 165.688 0.254512
\(652\) 145.600 + 145.600i 0.223313 + 0.223313i
\(653\) 33.5738 33.5738i 0.0514148 0.0514148i −0.680932 0.732347i \(-0.738425\pi\)
0.732347 + 0.680932i \(0.238425\pi\)
\(654\) 112.668i 0.172275i
\(655\) 891.391 698.372i 1.36090 1.06622i
\(656\) −84.0320 −0.128098
\(657\) −268.183 268.183i −0.408194 0.408194i
\(658\) 13.9486 13.9486i 0.0211985 0.0211985i
\(659\) 69.0686i 0.104808i −0.998626 0.0524041i \(-0.983312\pi\)
0.998626 0.0524041i \(-0.0166884\pi\)
\(660\) 53.8771 + 6.54144i 0.0816319 + 0.00991127i
\(661\) −1025.91 −1.55205 −0.776026 0.630701i \(-0.782768\pi\)
−0.776026 + 0.630701i \(0.782768\pi\)
\(662\) −624.517 624.517i −0.943379 0.943379i
\(663\) 176.250 176.250i 0.265837 0.265837i
\(664\) 291.337i 0.438761i
\(665\) −40.0405 + 329.785i −0.0602113 + 0.495917i
\(666\) −112.180 −0.168438
\(667\) 29.4112 + 29.4112i 0.0440947 + 0.0440947i
\(668\) −120.962 + 120.962i −0.181081 + 0.181081i
\(669\) 438.170i 0.654963i
\(670\) −491.126 626.866i −0.733024 0.935622i
\(671\) −240.595 −0.358561
\(672\) −13.9366 13.9366i −0.0207390 0.0207390i
\(673\) 36.3139 36.3139i 0.0539583 0.0539583i −0.679613 0.733571i \(-0.737852\pi\)
0.733571 + 0.679613i \(0.237852\pi\)
\(674\) 173.047i 0.256746i
\(675\) −111.168 + 67.2059i −0.164694 + 0.0995643i
\(676\) −71.0394 −0.105088
\(677\) 564.145 + 564.145i 0.833302 + 0.833302i 0.987967 0.154665i \(-0.0494299\pi\)
−0.154665 + 0.987967i \(0.549430\pi\)
\(678\) 245.479 245.479i 0.362063 0.362063i
\(679\) 298.397i 0.439466i
\(680\) −138.664 + 108.638i −0.203917 + 0.159761i
\(681\) 389.924 0.572576
\(682\) 149.009 + 149.009i 0.218489 + 0.218489i
\(683\) 120.894 120.894i 0.177005 0.177005i −0.613044 0.790049i \(-0.710055\pi\)
0.790049 + 0.613044i \(0.210055\pi\)
\(684\) 198.177i 0.289732i
\(685\) −93.5949 11.3637i −0.136635 0.0165894i
\(686\) 267.279 0.389620
\(687\) −171.135 171.135i −0.249104 0.249104i
\(688\) −151.246 + 151.246i −0.219834 + 0.219834i
\(689\) 98.4850i 0.142939i
\(690\) −7.07948 + 58.3085i −0.0102601 + 0.0845051i
\(691\) −979.008 −1.41680 −0.708400 0.705812i \(-0.750582\pi\)
−0.708400 + 0.705812i \(0.750582\pi\)
\(692\) 193.017 + 193.017i 0.278927 + 0.278927i
\(693\) −13.3710 + 13.3710i −0.0192944 + 0.0192944i
\(694\) 765.660i 1.10326i
\(695\) −421.151 537.551i −0.605973 0.773455i
\(696\) 42.4883 0.0610464
\(697\) −185.031 185.031i −0.265468 0.265468i
\(698\) 392.877 392.877i 0.562861 0.562861i
\(699\) 155.825i 0.222926i
\(700\) −52.0346 86.0727i −0.0743351 0.122961i
\(701\) −941.739 −1.34342 −0.671711 0.740813i \(-0.734440\pi\)
−0.671711 + 0.740813i \(0.734440\pi\)
\(702\) −60.0331 60.0331i −0.0855172 0.0855172i
\(703\) 617.540 617.540i 0.878435 0.878435i
\(704\) 25.0675i 0.0356072i
\(705\) −47.2714 + 37.0354i −0.0670517 + 0.0525325i
\(706\) 476.988 0.675620
\(707\) 229.037 + 229.037i 0.323957 + 0.323957i
\(708\) 223.816 223.816i 0.316124 0.316124i
\(709\) 754.542i 1.06423i −0.846671 0.532117i \(-0.821397\pi\)
0.846671 0.532117i \(-0.178603\pi\)
\(710\) 867.473 + 105.323i 1.22179 + 0.148343i
\(711\) 131.445 0.184873
\(712\) 170.255 + 170.255i 0.239122 + 0.239122i
\(713\) −161.265 + 161.265i −0.226179 + 0.226179i
\(714\) 61.3744i 0.0859585i
\(715\) −21.8168 + 179.689i −0.0305130 + 0.251314i
\(716\) 230.904 0.322491
\(717\) 69.1386 + 69.1386i 0.0964277 + 0.0964277i
\(718\) −434.304 + 434.304i −0.604881 + 0.604881i
\(719\) 266.966i 0.371302i −0.982616 0.185651i \(-0.940561\pi\)
0.982616 0.185651i \(-0.0594394\pi\)
\(720\) 37.0035 + 47.2307i 0.0513937 + 0.0655982i
\(721\) −145.656 −0.202019
\(722\) 729.943 + 729.943i 1.01100 + 1.01100i
\(723\) 108.337 108.337i 0.149844 0.149844i
\(724\) 365.022i 0.504174i
\(725\) 210.522 + 51.8857i 0.290376 + 0.0715664i
\(726\) 272.338 0.375121
\(727\) −767.189 767.189i −1.05528 1.05528i −0.998380 0.0569010i \(-0.981878\pi\)
−0.0569010 0.998380i \(-0.518122\pi\)
\(728\) 46.4810 46.4810i 0.0638475 0.0638475i
\(729\) 27.0000i 0.0370370i
\(730\) −703.694 + 551.318i −0.963964 + 0.755230i
\(731\) −666.060 −0.911163
\(732\) −188.079 188.079i −0.256939 0.256939i
\(733\) 633.411 633.411i 0.864135 0.864135i −0.127680 0.991815i \(-0.540753\pi\)
0.991815 + 0.127680i \(0.0407531\pi\)
\(734\) 279.229i 0.380421i
\(735\) −386.471 46.9230i −0.525811 0.0638409i
\(736\) 27.1293 0.0368605
\(737\) 249.530 + 249.530i 0.338575 + 0.338575i
\(738\) −63.0240 + 63.0240i −0.0853984 + 0.0853984i
\(739\) 228.825i 0.309641i 0.987943 + 0.154820i \(0.0494799\pi\)
−0.987943 + 0.154820i \(0.950520\pi\)
\(740\) −31.8692 + 262.483i −0.0430664 + 0.354707i
\(741\) 660.953 0.891974
\(742\) 17.1474 + 17.1474i 0.0231097 + 0.0231097i
\(743\) −391.292 + 391.292i −0.526638 + 0.526638i −0.919568 0.392931i \(-0.871461\pi\)
0.392931 + 0.919568i \(0.371461\pi\)
\(744\) 232.969i 0.313130i
\(745\) −66.6222 85.0356i −0.0894258 0.114142i
\(746\) 157.626 0.211295
\(747\) 218.503 + 218.503i 0.292507 + 0.292507i
\(748\) 55.1964 55.1964i 0.0737919 0.0737919i
\(749\) 252.076i 0.336551i
\(750\) 125.669 + 279.208i 0.167559 + 0.372278i
\(751\) 430.557 0.573312 0.286656 0.958034i \(-0.407456\pi\)
0.286656 + 0.958034i \(0.407456\pi\)
\(752\) 19.6128 + 19.6128i 0.0260809 + 0.0260809i
\(753\) 83.9976 83.9976i 0.111551 0.111551i
\(754\) 141.706i 0.187938i
\(755\) 1114.58 873.233i 1.47627 1.15660i
\(756\) −20.9049 −0.0276520
\(757\) −788.836 788.836i −1.04206 1.04206i −0.999076 0.0429790i \(-0.986315\pi\)
−0.0429790 0.999076i \(-0.513685\pi\)
\(758\) 59.0081 59.0081i 0.0778470 0.0778470i
\(759\) 26.0283i 0.0342929i
\(760\) −463.701 56.2999i −0.610133 0.0740788i
\(761\) 1041.88 1.36909 0.684546 0.728969i \(-0.260000\pi\)
0.684546 + 0.728969i \(0.260000\pi\)
\(762\) −41.7342 41.7342i −0.0547693 0.0547693i
\(763\) −65.4255 + 65.4255i −0.0857477 + 0.0857477i
\(764\) 252.490i 0.330485i
\(765\) −22.5194 + 185.476i −0.0294372 + 0.242452i
\(766\) −202.975 −0.264980
\(767\) 746.465 + 746.465i 0.973227 + 0.973227i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 920.965i 1.19761i 0.800893 + 0.598807i \(0.204358\pi\)
−0.800893 + 0.598807i \(0.795642\pi\)
\(770\) 27.4874 + 35.0846i 0.0356980 + 0.0455644i
\(771\) 326.565 0.423561
\(772\) −209.980 209.980i −0.271994 0.271994i
\(773\) 95.8217 95.8217i 0.123961 0.123961i −0.642405 0.766366i \(-0.722063\pi\)
0.766366 + 0.642405i \(0.222063\pi\)
\(774\) 226.869i 0.293112i
\(775\) −284.496 + 1154.32i −0.367092 + 1.48945i
\(776\) −419.569 −0.540681
\(777\) −65.1421 65.1421i −0.0838379 0.0838379i
\(778\) 276.824 276.824i 0.355815 0.355815i