Properties

Label 690.3.k.a.277.20
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 277.20
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(1.06006 + 4.88634i) q^{5} +2.44949 q^{6} +(6.77823 + 6.77823i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(1.06006 + 4.88634i) q^{5} +2.44949 q^{6} +(6.77823 + 6.77823i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-3.82628 + 5.94639i) q^{10} +6.48073 q^{11} +(2.44949 + 2.44949i) q^{12} +(7.70435 - 7.70435i) q^{13} +13.5565i q^{14} +(7.28281 + 4.68622i) q^{15} -4.00000 q^{16} +(0.781759 + 0.781759i) q^{17} +(3.00000 - 3.00000i) q^{18} -0.529087i q^{19} +(-9.77267 + 2.12011i) q^{20} +16.6032 q^{21} +(6.48073 + 6.48073i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(-22.7526 + 10.3596i) q^{25} +15.4087 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-13.5565 + 13.5565i) q^{28} +22.8105i q^{29} +(2.59660 + 11.9690i) q^{30} -24.3355 q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.93724 - 7.93724i) q^{33} +1.56352i q^{34} +(-25.9354 + 40.3060i) q^{35} +6.00000 q^{36} +(6.38099 + 6.38099i) q^{37} +(0.529087 - 0.529087i) q^{38} -18.8717i q^{39} +(-11.8928 - 7.65256i) q^{40} +16.5189 q^{41} +(16.6032 + 16.6032i) q^{42} +(11.3582 - 11.3582i) q^{43} +12.9615i q^{44} +(14.6590 - 3.18017i) q^{45} -6.78233 q^{46} +(-19.1854 - 19.1854i) q^{47} +(-4.89898 + 4.89898i) q^{48} +42.8889i q^{49} +(-33.1121 - 12.3930i) q^{50} +1.91491 q^{51} +(15.4087 + 15.4087i) q^{52} +(-7.76688 + 7.76688i) q^{53} -7.34847i q^{54} +(6.86994 + 31.6670i) q^{55} -27.1129 q^{56} +(-0.647996 - 0.647996i) q^{57} +(-22.8105 + 22.8105i) q^{58} +62.7613i q^{59} +(-9.37243 + 14.5656i) q^{60} +37.8465 q^{61} +(-24.3355 - 24.3355i) q^{62} +(20.3347 - 20.3347i) q^{63} -8.00000i q^{64} +(45.8131 + 29.4790i) q^{65} +15.8745 q^{66} +(-23.8308 - 23.8308i) q^{67} +(-1.56352 + 1.56352i) q^{68} +8.30662i q^{69} +(-66.2415 + 14.3706i) q^{70} +82.9169 q^{71} +(6.00000 + 6.00000i) q^{72} +(32.9265 - 32.9265i) q^{73} +12.7620i q^{74} +(-15.1782 + 40.5539i) q^{75} +1.05817 q^{76} +(43.9279 + 43.9279i) q^{77} +(18.8717 - 18.8717i) q^{78} -55.5424i q^{79} +(-4.24022 - 19.5453i) q^{80} -9.00000 q^{81} +(16.5189 + 16.5189i) q^{82} +(-53.8067 + 53.8067i) q^{83} +33.2064i q^{84} +(-2.99123 + 4.64864i) q^{85} +22.7164 q^{86} +(27.9371 + 27.9371i) q^{87} +(-12.9615 + 12.9615i) q^{88} +9.20780i q^{89} +(17.8392 + 11.4788i) q^{90} +104.444 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-29.8048 + 29.8048i) q^{93} -38.3707i q^{94} +(2.58529 - 0.560862i) q^{95} -9.79796 q^{96} +(79.6850 + 79.6850i) q^{97} +(-42.8889 + 42.8889i) q^{98} -19.4422i 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
\(5\) 1.06006 + 4.88634i 0.212011 + 0.977267i
\(6\) 2.44949 0.408248
\(7\) 6.77823 + 6.77823i 0.968319 + 0.968319i 0.999513 0.0311941i \(-0.00993100\pi\)
−0.0311941 + 0.999513i \(0.509931\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −3.82628 + 5.94639i −0.382628 + 0.594639i
\(11\) 6.48073 0.589157 0.294579 0.955627i \(-0.404821\pi\)
0.294579 + 0.955627i \(0.404821\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 7.70435 7.70435i 0.592642 0.592642i −0.345702 0.938344i \(-0.612359\pi\)
0.938344 + 0.345702i \(0.112359\pi\)
\(14\) 13.5565i 0.968319i
\(15\) 7.28281 + 4.68622i 0.485521 + 0.312414i
\(16\) −4.00000 −0.250000
\(17\) 0.781759 + 0.781759i 0.0459858 + 0.0459858i 0.729726 0.683740i \(-0.239648\pi\)
−0.683740 + 0.729726i \(0.739648\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 0.529087i 0.0278467i −0.999903 0.0139233i \(-0.995568\pi\)
0.999903 0.0139233i \(-0.00443208\pi\)
\(20\) −9.77267 + 2.12011i −0.488634 + 0.106006i
\(21\) 16.6032 0.790629
\(22\) 6.48073 + 6.48073i 0.294579 + 0.294579i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −22.7526 + 10.3596i −0.910102 + 0.414383i
\(26\) 15.4087 0.592642
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −13.5565 + 13.5565i −0.484160 + 0.484160i
\(29\) 22.8105i 0.786570i 0.919417 + 0.393285i \(0.128662\pi\)
−0.919417 + 0.393285i \(0.871338\pi\)
\(30\) 2.59660 + 11.9690i 0.0865532 + 0.398968i
\(31\) −24.3355 −0.785017 −0.392508 0.919748i \(-0.628393\pi\)
−0.392508 + 0.919748i \(0.628393\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 7.93724 7.93724i 0.240522 0.240522i
\(34\) 1.56352i 0.0459858i
\(35\) −25.9354 + 40.3060i −0.741012 + 1.15160i
\(36\) 6.00000 0.166667
\(37\) 6.38099 + 6.38099i 0.172459 + 0.172459i 0.788059 0.615600i \(-0.211086\pi\)
−0.615600 + 0.788059i \(0.711086\pi\)
\(38\) 0.529087 0.529087i 0.0139233 0.0139233i
\(39\) 18.8717i 0.483890i
\(40\) −11.8928 7.65256i −0.297320 0.191314i
\(41\) 16.5189 0.402899 0.201450 0.979499i \(-0.435435\pi\)
0.201450 + 0.979499i \(0.435435\pi\)
\(42\) 16.6032 + 16.6032i 0.395315 + 0.395315i
\(43\) 11.3582 11.3582i 0.264144 0.264144i −0.562591 0.826735i \(-0.690195\pi\)
0.826735 + 0.562591i \(0.190195\pi\)
\(44\) 12.9615i 0.294579i
\(45\) 14.6590 3.18017i 0.325756 0.0706704i
\(46\) −6.78233 −0.147442
\(47\) −19.1854 19.1854i −0.408199 0.408199i 0.472911 0.881110i \(-0.343203\pi\)
−0.881110 + 0.472911i \(0.843203\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 42.8889i 0.875284i
\(50\) −33.1121 12.3930i −0.662243 0.247860i
\(51\) 1.91491 0.0375473
\(52\) 15.4087 + 15.4087i 0.296321 + 0.296321i
\(53\) −7.76688 + 7.76688i −0.146545 + 0.146545i −0.776573 0.630028i \(-0.783043\pi\)
0.630028 + 0.776573i \(0.283043\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 6.86994 + 31.6670i 0.124908 + 0.575764i
\(56\) −27.1129 −0.484160
\(57\) −0.647996 0.647996i −0.0113684 0.0113684i
\(58\) −22.8105 + 22.8105i −0.393285 + 0.393285i
\(59\) 62.7613i 1.06375i 0.846822 + 0.531876i \(0.178513\pi\)
−0.846822 + 0.531876i \(0.821487\pi\)
\(60\) −9.37243 + 14.5656i −0.156207 + 0.242760i
\(61\) 37.8465 0.620435 0.310218 0.950666i \(-0.399598\pi\)
0.310218 + 0.950666i \(0.399598\pi\)
\(62\) −24.3355 24.3355i −0.392508 0.392508i
\(63\) 20.3347 20.3347i 0.322773 0.322773i
\(64\) 8.00000i 0.125000i
\(65\) 45.8131 + 29.4790i 0.704817 + 0.453523i
\(66\) 15.8745 0.240522
\(67\) −23.8308 23.8308i −0.355683 0.355683i 0.506536 0.862219i \(-0.330926\pi\)
−0.862219 + 0.506536i \(0.830926\pi\)
\(68\) −1.56352 + 1.56352i −0.0229929 + 0.0229929i
\(69\) 8.30662i 0.120386i
\(70\) −66.2415 + 14.3706i −0.946307 + 0.205295i
\(71\) 82.9169 1.16784 0.583922 0.811810i \(-0.301517\pi\)
0.583922 + 0.811810i \(0.301517\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 32.9265 32.9265i 0.451048 0.451048i −0.444654 0.895702i \(-0.646674\pi\)
0.895702 + 0.444654i \(0.146674\pi\)
\(74\) 12.7620i 0.172459i
\(75\) −15.1782 + 40.5539i −0.202377 + 0.540719i
\(76\) 1.05817 0.0139233
\(77\) 43.9279 + 43.9279i 0.570492 + 0.570492i
\(78\) 18.8717 18.8717i 0.241945 0.241945i
\(79\) 55.5424i 0.703069i −0.936175 0.351534i \(-0.885660\pi\)
0.936175 0.351534i \(-0.114340\pi\)
\(80\) −4.24022 19.5453i −0.0530028 0.244317i
\(81\) −9.00000 −0.111111
\(82\) 16.5189 + 16.5189i 0.201450 + 0.201450i
\(83\) −53.8067 + 53.8067i −0.648274 + 0.648274i −0.952576 0.304302i \(-0.901577\pi\)
0.304302 + 0.952576i \(0.401577\pi\)
\(84\) 33.2064i 0.395315i
\(85\) −2.99123 + 4.64864i −0.0351909 + 0.0546899i
\(86\) 22.7164 0.264144
\(87\) 27.9371 + 27.9371i 0.321116 + 0.321116i
\(88\) −12.9615 + 12.9615i −0.147289 + 0.147289i
\(89\) 9.20780i 0.103458i 0.998661 + 0.0517292i \(0.0164733\pi\)
−0.998661 + 0.0517292i \(0.983527\pi\)
\(90\) 17.8392 + 11.4788i 0.198213 + 0.127543i
\(91\) 104.444 1.14773
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) −29.8048 + 29.8048i −0.320482 + 0.320482i
\(94\) 38.3707i 0.408199i
\(95\) 2.58529 0.560862i 0.0272136 0.00590381i
\(96\) −9.79796 −0.102062
\(97\) 79.6850 + 79.6850i 0.821495 + 0.821495i 0.986322 0.164828i \(-0.0527068\pi\)
−0.164828 + 0.986322i \(0.552707\pi\)
\(98\) −42.8889 + 42.8889i −0.437642 + 0.437642i
\(99\) 19.4422i 0.196386i
\(100\) −20.7192 45.5051i −0.207192 0.455051i
\(101\) −139.733 −1.38350 −0.691749 0.722138i \(-0.743160\pi\)
−0.691749 + 0.722138i \(0.743160\pi\)
\(102\) 1.91491 + 1.91491i 0.0187736 + 0.0187736i
\(103\) 98.3312 98.3312i 0.954672 0.954672i −0.0443444 0.999016i \(-0.514120\pi\)
0.999016 + 0.0443444i \(0.0141199\pi\)
\(104\) 30.8174i 0.296321i
\(105\) 17.6003 + 81.1289i 0.167622 + 0.772656i
\(106\) −15.5338 −0.146545
\(107\) −11.4279 11.4279i −0.106803 0.106803i 0.651686 0.758489i \(-0.274062\pi\)
−0.758489 + 0.651686i \(0.774062\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 79.8261i 0.732350i −0.930546 0.366175i \(-0.880667\pi\)
0.930546 0.366175i \(-0.119333\pi\)
\(110\) −24.7971 + 38.5370i −0.225428 + 0.350336i
\(111\) 15.6302 0.140812
\(112\) −27.1129 27.1129i −0.242080 0.242080i
\(113\) 80.7359 80.7359i 0.714477 0.714477i −0.252992 0.967468i \(-0.581415\pi\)
0.967468 + 0.252992i \(0.0814145\pi\)
\(114\) 1.29599i 0.0113684i
\(115\) −20.1652 12.9755i −0.175350 0.112831i
\(116\) −45.6211 −0.393285
\(117\) −23.1130 23.1130i −0.197547 0.197547i
\(118\) −62.7613 + 62.7613i −0.531876 + 0.531876i
\(119\) 10.5979i 0.0890579i
\(120\) −23.9381 + 5.19319i −0.199484 + 0.0432766i
\(121\) −79.0002 −0.652894
\(122\) 37.8465 + 37.8465i 0.310218 + 0.310218i
\(123\) 20.2314 20.2314i 0.164483 0.164483i
\(124\) 48.6710i 0.392508i
\(125\) −74.7394 100.195i −0.597915 0.801559i
\(126\) 40.6694 0.322773
\(127\) −130.755 130.755i −1.02957 1.02957i −0.999549 0.0300209i \(-0.990443\pi\)
−0.0300209 0.999549i \(-0.509557\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 27.8218i 0.215673i
\(130\) 16.3341 + 75.2921i 0.125647 + 0.579170i
\(131\) 38.3122 0.292459 0.146230 0.989251i \(-0.453286\pi\)
0.146230 + 0.989251i \(0.453286\pi\)
\(132\) 15.8745 + 15.8745i 0.120261 + 0.120261i
\(133\) 3.58627 3.58627i 0.0269645 0.0269645i
\(134\) 47.6616i 0.355683i
\(135\) 14.0587 21.8484i 0.104138 0.161840i
\(136\) −3.12703 −0.0229929
\(137\) −43.2358 43.2358i −0.315589 0.315589i 0.531481 0.847070i \(-0.321636\pi\)
−0.847070 + 0.531481i \(0.821636\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 113.502i 0.816562i −0.912856 0.408281i \(-0.866128\pi\)
0.912856 0.408281i \(-0.133872\pi\)
\(140\) −80.6121 51.8708i −0.575801 0.370506i
\(141\) −46.9944 −0.333293
\(142\) 82.9169 + 82.9169i 0.583922 + 0.583922i
\(143\) 49.9298 49.9298i 0.349159 0.349159i
\(144\) 12.0000i 0.0833333i
\(145\) −111.460 + 24.1805i −0.768690 + 0.166762i
\(146\) 65.8530 0.451048
\(147\) 52.5280 + 52.5280i 0.357333 + 0.357333i
\(148\) −12.7620 + 12.7620i −0.0862295 + 0.0862295i
\(149\) 80.8820i 0.542832i −0.962462 0.271416i \(-0.912508\pi\)
0.962462 0.271416i \(-0.0874920\pi\)
\(150\) −55.7322 + 25.3757i −0.371548 + 0.169171i
\(151\) −54.8655 −0.363348 −0.181674 0.983359i \(-0.558152\pi\)
−0.181674 + 0.983359i \(0.558152\pi\)
\(152\) 1.05817 + 1.05817i 0.00696167 + 0.00696167i
\(153\) 2.34528 2.34528i 0.0153286 0.0153286i
\(154\) 87.8558i 0.570492i
\(155\) −25.7970 118.912i −0.166432 0.767171i
\(156\) 37.7434 0.241945
\(157\) −143.794 143.794i −0.915885 0.915885i 0.0808422 0.996727i \(-0.474239\pi\)
−0.996727 + 0.0808422i \(0.974239\pi\)
\(158\) 55.5424 55.5424i 0.351534 0.351534i
\(159\) 19.0249i 0.119653i
\(160\) 15.3051 23.7856i 0.0956570 0.148660i
\(161\) −45.9722 −0.285542
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 108.194 108.194i 0.663769 0.663769i −0.292497 0.956266i \(-0.594486\pi\)
0.956266 + 0.292497i \(0.0944862\pi\)
\(164\) 33.0377i 0.201450i
\(165\) 47.1979 + 30.3701i 0.286048 + 0.184061i
\(166\) −107.613 −0.648274
\(167\) 178.168 + 178.168i 1.06688 + 1.06688i 0.997597 + 0.0692787i \(0.0220698\pi\)
0.0692787 + 0.997597i \(0.477930\pi\)
\(168\) −33.2064 + 33.2064i −0.197657 + 0.197657i
\(169\) 50.2860i 0.297550i
\(170\) −7.63987 + 1.65742i −0.0449404 + 0.00974951i
\(171\) −1.58726 −0.00928222
\(172\) 22.7164 + 22.7164i 0.132072 + 0.132072i
\(173\) −12.0550 + 12.0550i −0.0696822 + 0.0696822i −0.741089 0.671407i \(-0.765690\pi\)
0.671407 + 0.741089i \(0.265690\pi\)
\(174\) 55.8742i 0.321116i
\(175\) −224.442 84.0025i −1.28253 0.480014i
\(176\) −25.9229 −0.147289
\(177\) 76.8666 + 76.8666i 0.434275 + 0.434275i
\(178\) −9.20780 + 9.20780i −0.0517292 + 0.0517292i
\(179\) 47.2728i 0.264094i 0.991243 + 0.132047i \(0.0421550\pi\)
−0.991243 + 0.132047i \(0.957845\pi\)
\(180\) 6.36034 + 29.3180i 0.0353352 + 0.162878i
\(181\) −47.4383 −0.262090 −0.131045 0.991376i \(-0.541833\pi\)
−0.131045 + 0.991376i \(0.541833\pi\)
\(182\) 104.444 + 104.444i 0.573867 + 0.573867i
\(183\) 46.3524 46.3524i 0.253292 0.253292i
\(184\) 13.5647i 0.0737210i
\(185\) −24.4154 + 37.9438i −0.131975 + 0.205102i
\(186\) −59.6096 −0.320482
\(187\) 5.06637 + 5.06637i 0.0270929 + 0.0270929i
\(188\) 38.3707 38.3707i 0.204100 0.204100i
\(189\) 49.8097i 0.263543i
\(190\) 3.14616 + 2.02443i 0.0165587 + 0.0106549i
\(191\) 126.903 0.664416 0.332208 0.943206i \(-0.392206\pi\)
0.332208 + 0.943206i \(0.392206\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −148.959 + 148.959i −0.771811 + 0.771811i −0.978423 0.206612i \(-0.933756\pi\)
0.206612 + 0.978423i \(0.433756\pi\)
\(194\) 159.370i 0.821495i
\(195\) 92.2136 20.0051i 0.472890 0.102590i
\(196\) −85.7779 −0.437642
\(197\) 10.2081 + 10.2081i 0.0518175 + 0.0518175i 0.732541 0.680723i \(-0.238334\pi\)
−0.680723 + 0.732541i \(0.738334\pi\)
\(198\) 19.4422 19.4422i 0.0981929 0.0981929i
\(199\) 365.840i 1.83839i −0.393803 0.919195i \(-0.628841\pi\)
0.393803 0.919195i \(-0.371159\pi\)
\(200\) 24.7860 66.2243i 0.123930 0.331121i
\(201\) −58.3732 −0.290414
\(202\) −139.733 139.733i −0.691749 0.691749i
\(203\) −154.615 + 154.615i −0.761651 + 0.761651i
\(204\) 3.82982i 0.0187736i
\(205\) 17.5109 + 80.7167i 0.0854192 + 0.393740i
\(206\) 196.662 0.954672
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −30.8174 + 30.8174i −0.148161 + 0.148161i
\(209\) 3.42887i 0.0164061i
\(210\) −63.5286 + 98.7292i −0.302517 + 0.470139i
\(211\) 52.5021 0.248825 0.124413 0.992231i \(-0.460295\pi\)
0.124413 + 0.992231i \(0.460295\pi\)
\(212\) −15.5338 15.5338i −0.0732724 0.0732724i
\(213\) 101.552 101.552i 0.476770 0.476770i
\(214\) 22.8558i 0.106803i
\(215\) 67.5403 + 43.4596i 0.314141 + 0.202138i
\(216\) 14.6969 0.0680414
\(217\) −164.952 164.952i −0.760147 0.760147i
\(218\) 79.8261 79.8261i 0.366175 0.366175i
\(219\) 80.6531i 0.368279i
\(220\) −63.3340 + 13.7399i −0.287882 + 0.0624540i
\(221\) 12.0459 0.0545063
\(222\) 15.6302 + 15.6302i 0.0704061 + 0.0704061i
\(223\) −20.5666 + 20.5666i −0.0922271 + 0.0922271i −0.751715 0.659488i \(-0.770773\pi\)
0.659488 + 0.751715i \(0.270773\pi\)
\(224\) 54.2259i 0.242080i
\(225\) 31.0787 + 68.2577i 0.138128 + 0.303367i
\(226\) 161.472 0.714477
\(227\) 233.250 + 233.250i 1.02753 + 1.02753i 0.999610 + 0.0279229i \(0.00888930\pi\)
0.0279229 + 0.999610i \(0.491111\pi\)
\(228\) 1.29599 1.29599i 0.00568418 0.00568418i
\(229\) 407.228i 1.77829i −0.457629 0.889143i \(-0.651301\pi\)
0.457629 0.889143i \(-0.348699\pi\)
\(230\) −7.18965 33.1407i −0.0312594 0.144090i
\(231\) 107.601 0.465805
\(232\) −45.6211 45.6211i −0.196643 0.196643i
\(233\) 67.8138 67.8138i 0.291046 0.291046i −0.546447 0.837494i \(-0.684020\pi\)
0.837494 + 0.546447i \(0.184020\pi\)
\(234\) 46.2261i 0.197547i
\(235\) 73.4086 114.084i 0.312377 0.485463i
\(236\) −125.523 −0.531876
\(237\) −68.0253 68.0253i −0.287027 0.287027i
\(238\) −10.5979 + 10.5979i −0.0445289 + 0.0445289i
\(239\) 126.104i 0.527630i −0.964573 0.263815i \(-0.915019\pi\)
0.964573 0.263815i \(-0.0849808\pi\)
\(240\) −29.1313 18.7449i −0.121380 0.0781036i
\(241\) 169.295 0.702467 0.351234 0.936288i \(-0.385762\pi\)
0.351234 + 0.936288i \(0.385762\pi\)
\(242\) −79.0002 79.0002i −0.326447 0.326447i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 75.6931i 0.310218i
\(245\) −209.570 + 45.4647i −0.855387 + 0.185570i
\(246\) 40.4628 0.164483
\(247\) −4.07627 4.07627i −0.0165031 0.0165031i
\(248\) 48.6710 48.6710i 0.196254 0.196254i
\(249\) 131.799i 0.529313i
\(250\) 25.4555 174.934i 0.101822 0.699737i
\(251\) 352.257 1.40341 0.701707 0.712466i \(-0.252422\pi\)
0.701707 + 0.712466i \(0.252422\pi\)
\(252\) 40.6694 + 40.6694i 0.161387 + 0.161387i
\(253\) −21.9772 + 21.9772i −0.0868665 + 0.0868665i
\(254\) 261.511i 1.02957i
\(255\) 2.02991 + 9.35689i 0.00796044 + 0.0366937i
\(256\) 16.0000 0.0625000
\(257\) 36.1183 + 36.1183i 0.140538 + 0.140538i 0.773876 0.633338i \(-0.218316\pi\)
−0.633338 + 0.773876i \(0.718316\pi\)
\(258\) 27.8218 27.8218i 0.107836 0.107836i
\(259\) 86.5037i 0.333991i
\(260\) −58.9580 + 91.6262i −0.226762 + 0.352408i
\(261\) 68.4316 0.262190
\(262\) 38.3122 + 38.3122i 0.146230 + 0.146230i
\(263\) −217.636 + 217.636i −0.827513 + 0.827513i −0.987172 0.159660i \(-0.948960\pi\)
0.159660 + 0.987172i \(0.448960\pi\)
\(264\) 31.7490i 0.120261i
\(265\) −46.1849 29.7182i −0.174283 0.112144i
\(266\) 7.17255 0.0269645
\(267\) 11.2772 + 11.2772i 0.0422367 + 0.0422367i
\(268\) 47.6616 47.6616i 0.177842 0.177842i
\(269\) 525.831i 1.95476i −0.211488 0.977381i \(-0.567831\pi\)
0.211488 0.977381i \(-0.432169\pi\)
\(270\) 35.9071 7.78979i 0.132989 0.0288511i
\(271\) 518.661 1.91388 0.956939 0.290289i \(-0.0937514\pi\)
0.956939 + 0.290289i \(0.0937514\pi\)
\(272\) −3.12703 3.12703i −0.0114965 0.0114965i
\(273\) 127.917 127.917i 0.468560 0.468560i
\(274\) 86.4715i 0.315589i
\(275\) −147.453 + 67.1376i −0.536193 + 0.244137i
\(276\) −16.6132 −0.0601929
\(277\) −223.617 223.617i −0.807281 0.807281i 0.176940 0.984222i \(-0.443380\pi\)
−0.984222 + 0.176940i \(0.943380\pi\)
\(278\) 113.502 113.502i 0.408281 0.408281i
\(279\) 73.0066i 0.261672i
\(280\) −28.7412 132.483i −0.102647 0.473153i
\(281\) 425.954 1.51585 0.757926 0.652341i \(-0.226213\pi\)
0.757926 + 0.652341i \(0.226213\pi\)
\(282\) −46.9944 46.9944i −0.166647 0.166647i
\(283\) 30.5658 30.5658i 0.108006 0.108006i −0.651038 0.759045i \(-0.725666\pi\)
0.759045 + 0.651038i \(0.225666\pi\)
\(284\) 165.834i 0.583922i
\(285\) 2.47941 3.85324i 0.00869970 0.0135201i
\(286\) 99.8596 0.349159
\(287\) 111.969 + 111.969i 0.390135 + 0.390135i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 287.778i 0.995771i
\(290\) −135.640 87.2795i −0.467726 0.300964i
\(291\) 195.188 0.670748
\(292\) 65.8530 + 65.8530i 0.225524 + 0.225524i
\(293\) −237.549 + 237.549i −0.810749 + 0.810749i −0.984746 0.173997i \(-0.944332\pi\)
0.173997 + 0.984746i \(0.444332\pi\)
\(294\) 105.056i 0.357333i
\(295\) −306.673 + 66.5305i −1.03957 + 0.225527i
\(296\) −25.5239 −0.0862295
\(297\) −23.8117 23.8117i −0.0801741 0.0801741i
\(298\) 80.8820 80.8820i 0.271416 0.271416i
\(299\) 52.2534i 0.174761i
\(300\) −81.1079 30.3565i −0.270360 0.101188i
\(301\) 153.977 0.511552
\(302\) −54.8655 54.8655i −0.181674 0.181674i
\(303\) −171.138 + 171.138i −0.564811 + 0.564811i
\(304\) 2.11635i 0.00696167i
\(305\) 40.1195 + 184.931i 0.131539 + 0.606331i
\(306\) 4.69055 0.0153286
\(307\) −237.912 237.912i −0.774959 0.774959i 0.204010 0.978969i \(-0.434602\pi\)
−0.978969 + 0.204010i \(0.934602\pi\)
\(308\) −87.8558 + 87.8558i −0.285246 + 0.285246i
\(309\) 240.861i 0.779486i
\(310\) 93.1145 144.709i 0.300369 0.466802i
\(311\) −81.3114 −0.261452 −0.130726 0.991419i \(-0.541731\pi\)
−0.130726 + 0.991419i \(0.541731\pi\)
\(312\) 37.7434 + 37.7434i 0.120973 + 0.120973i
\(313\) −327.200 + 327.200i −1.04537 + 1.04537i −0.0464467 + 0.998921i \(0.514790\pi\)
−0.998921 + 0.0464467i \(0.985210\pi\)
\(314\) 287.588i 0.915885i
\(315\) 120.918 + 77.8063i 0.383867 + 0.247004i
\(316\) 111.085 0.351534
\(317\) 274.470 + 274.470i 0.865837 + 0.865837i 0.992008 0.126171i \(-0.0402690\pi\)
−0.126171 + 0.992008i \(0.540269\pi\)
\(318\) −19.0249 + 19.0249i −0.0598267 + 0.0598267i
\(319\) 147.829i 0.463414i
\(320\) 39.0907 8.48045i 0.122158 0.0265014i
\(321\) −27.9925 −0.0872040
\(322\) −45.9722 45.9722i −0.142771 0.142771i
\(323\) 0.413618 0.413618i 0.00128055 0.00128055i
\(324\) 18.0000i 0.0555556i
\(325\) −95.4798 + 255.108i −0.293784 + 0.784946i
\(326\) 216.389 0.663769
\(327\) −97.7666 97.7666i −0.298981 0.298981i
\(328\) −33.0377 + 33.0377i −0.100725 + 0.100725i
\(329\) 260.086i 0.790535i
\(330\) 16.8278 + 77.5680i 0.0509934 + 0.235055i
\(331\) 209.454 0.632791 0.316396 0.948627i \(-0.397527\pi\)
0.316396 + 0.948627i \(0.397527\pi\)
\(332\) −107.613 107.613i −0.324137 0.324137i
\(333\) 19.1430 19.1430i 0.0574864 0.0574864i
\(334\) 356.337i 1.06688i
\(335\) 91.1832 141.707i 0.272189 0.423006i
\(336\) −66.4129 −0.197657
\(337\) −267.075 267.075i −0.792506 0.792506i 0.189395 0.981901i \(-0.439347\pi\)
−0.981901 + 0.189395i \(0.939347\pi\)
\(338\) −50.2860 + 50.2860i −0.148775 + 0.148775i
\(339\) 197.762i 0.583368i
\(340\) −9.29729 5.98246i −0.0273450 0.0175955i
\(341\) −157.712 −0.462498
\(342\) −1.58726 1.58726i −0.00464111 0.00464111i
\(343\) 41.4222 41.4222i 0.120765 0.120765i
\(344\) 45.4328i 0.132072i
\(345\) −40.5890 + 8.80549i −0.117649 + 0.0255232i
\(346\) −24.1100 −0.0696822
\(347\) 302.377 + 302.377i 0.871403 + 0.871403i 0.992625 0.121222i \(-0.0386813\pi\)
−0.121222 + 0.992625i \(0.538681\pi\)
\(348\) −55.8742 + 55.8742i −0.160558 + 0.160558i
\(349\) 38.7883i 0.111141i −0.998455 0.0555706i \(-0.982302\pi\)
0.998455 0.0555706i \(-0.0176978\pi\)
\(350\) −140.439 308.444i −0.401255 0.881270i
\(351\) −56.6152 −0.161297
\(352\) −25.9229 25.9229i −0.0736446 0.0736446i
\(353\) 228.425 228.425i 0.647096 0.647096i −0.305194 0.952290i \(-0.598721\pi\)
0.952290 + 0.305194i \(0.0987213\pi\)
\(354\) 153.733i 0.434275i
\(355\) 87.8966 + 405.160i 0.247596 + 1.14130i
\(356\) −18.4156 −0.0517292
\(357\) 12.9797 + 12.9797i 0.0363577 + 0.0363577i
\(358\) −47.2728 + 47.2728i −0.132047 + 0.132047i
\(359\) 572.493i 1.59469i 0.603525 + 0.797344i \(0.293762\pi\)
−0.603525 + 0.797344i \(0.706238\pi\)
\(360\) −22.9577 + 35.6784i −0.0637713 + 0.0991065i
\(361\) 360.720 0.999225
\(362\) −47.4383 47.4383i −0.131045 0.131045i
\(363\) −96.7550 + 96.7550i −0.266543 + 0.266543i
\(364\) 208.888i 0.573867i
\(365\) 195.794 + 125.986i 0.536421 + 0.345167i
\(366\) 92.7047 0.253292
\(367\) −156.250 156.250i −0.425750 0.425750i 0.461428 0.887178i \(-0.347337\pi\)
−0.887178 + 0.461428i \(0.847337\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 49.5566i 0.134300i
\(370\) −62.3593 + 13.5284i −0.168539 + 0.0365633i
\(371\) −105.291 −0.283804
\(372\) −59.6096 59.6096i −0.160241 0.160241i
\(373\) 14.7884 14.7884i 0.0396472 0.0396472i −0.687005 0.726652i \(-0.741075\pi\)
0.726652 + 0.687005i \(0.241075\pi\)
\(374\) 10.1327i 0.0270929i
\(375\) −214.250 31.1765i −0.571333 0.0831374i
\(376\) 76.7415 0.204100
\(377\) 175.740 + 175.740i 0.466155 + 0.466155i
\(378\) 49.8097 49.8097i 0.131772 0.131772i
\(379\) 39.4302i 0.104038i 0.998646 + 0.0520188i \(0.0165656\pi\)
−0.998646 + 0.0520188i \(0.983434\pi\)
\(380\) 1.12172 + 5.17059i 0.00295190 + 0.0136068i
\(381\) −320.284 −0.840640
\(382\) 126.903 + 126.903i 0.332208 + 0.332208i
\(383\) −262.977 + 262.977i −0.686624 + 0.686624i −0.961484 0.274860i \(-0.911368\pi\)
0.274860 + 0.961484i \(0.411368\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −168.080 + 261.213i −0.436573 + 0.678474i
\(386\) −297.919 −0.771811
\(387\) −34.0746 34.0746i −0.0880480 0.0880480i
\(388\) −159.370 + 159.370i −0.410747 + 0.410747i
\(389\) 412.312i 1.05993i −0.848021 0.529963i \(-0.822206\pi\)
0.848021 0.529963i \(-0.177794\pi\)
\(390\) 112.219 + 72.2085i 0.287740 + 0.185150i
\(391\) −5.30215 −0.0135605
\(392\) −85.7779 85.7779i −0.218821 0.218821i
\(393\) 46.9226 46.9226i 0.119396 0.119396i
\(394\) 20.4161i 0.0518175i
\(395\) 271.399 58.8781i 0.687086 0.149058i
\(396\) 38.8844 0.0981929
\(397\) 79.4123 + 79.4123i 0.200031 + 0.200031i 0.800013 0.599982i \(-0.204826\pi\)
−0.599982 + 0.800013i \(0.704826\pi\)
\(398\) 365.840 365.840i 0.919195 0.919195i
\(399\) 8.78454i 0.0220164i
\(400\) 91.0102 41.4383i 0.227526 0.103596i
\(401\) −604.333 −1.50706 −0.753532 0.657411i \(-0.771651\pi\)
−0.753532 + 0.657411i \(0.771651\pi\)
\(402\) −58.3732 58.3732i −0.145207 0.145207i
\(403\) −187.489 + 187.489i −0.465234 + 0.465234i
\(404\) 279.467i 0.691749i
\(405\) −9.54051 43.9770i −0.0235568 0.108585i
\(406\) −309.230 −0.761651
\(407\) 41.3534 + 41.3534i 0.101606 + 0.101606i
\(408\) −3.82982 + 3.82982i −0.00938681 + 0.00938681i
\(409\) 31.8712i 0.0779247i −0.999241 0.0389624i \(-0.987595\pi\)
0.999241 0.0389624i \(-0.0124052\pi\)
\(410\) −63.2058 + 98.2277i −0.154161 + 0.239580i
\(411\) −105.906 −0.257678
\(412\) 196.662 + 196.662i 0.477336 + 0.477336i
\(413\) −425.411 + 425.411i −1.03005 + 1.03005i
\(414\) 20.3470i 0.0491473i
\(415\) −319.956 205.880i −0.770978 0.496095i
\(416\) −61.6348 −0.148161
\(417\) −139.011 139.011i −0.333360 0.333360i
\(418\) 3.42887 3.42887i 0.00820303 0.00820303i
\(419\) 542.434i 1.29459i −0.762239 0.647296i \(-0.775900\pi\)
0.762239 0.647296i \(-0.224100\pi\)
\(420\) −162.258 + 35.2007i −0.386328 + 0.0838112i
\(421\) −377.783 −0.897347 −0.448673 0.893696i \(-0.648103\pi\)
−0.448673 + 0.893696i \(0.648103\pi\)
\(422\) 52.5021 + 52.5021i 0.124413 + 0.124413i
\(423\) −57.5561 + 57.5561i −0.136066 + 0.136066i
\(424\) 31.0675i 0.0732724i
\(425\) −25.8857 9.68832i −0.0609075 0.0227960i
\(426\) 203.104 0.476770
\(427\) 256.533 + 256.533i 0.600779 + 0.600779i
\(428\) 22.8558 22.8558i 0.0534013 0.0534013i
\(429\) 122.303i 0.285087i
\(430\) 24.0807 + 111.000i 0.0560015 + 0.258139i
\(431\) −380.401 −0.882600 −0.441300 0.897360i \(-0.645483\pi\)
−0.441300 + 0.897360i \(0.645483\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −520.972 + 520.972i −1.20317 + 1.20317i −0.229972 + 0.973197i \(0.573863\pi\)
−0.973197 + 0.229972i \(0.926137\pi\)
\(434\) 329.904i 0.760147i
\(435\) −106.895 + 166.125i −0.245736 + 0.381896i
\(436\) 159.652 0.366175
\(437\) 1.79422 + 1.79422i 0.00410577 + 0.00410577i
\(438\) 80.6531 80.6531i 0.184139 0.184139i
\(439\) 62.4039i 0.142150i −0.997471 0.0710750i \(-0.977357\pi\)
0.997471 0.0710750i \(-0.0226430\pi\)
\(440\) −77.0739 49.5942i −0.175168 0.112714i
\(441\) 128.667 0.291761
\(442\) 12.0459 + 12.0459i 0.0272531 + 0.0272531i
\(443\) 3.05050 3.05050i 0.00688601 0.00688601i −0.703655 0.710541i \(-0.748450\pi\)
0.710541 + 0.703655i \(0.248450\pi\)
\(444\) 31.2603i 0.0704061i
\(445\) −44.9924 + 9.76079i −0.101107 + 0.0219344i
\(446\) −41.1333 −0.0922271
\(447\) −99.0598 99.0598i −0.221610 0.221610i
\(448\) 54.2259 54.2259i 0.121040 0.121040i
\(449\) 122.374i 0.272547i 0.990671 + 0.136274i \(0.0435127\pi\)
−0.990671 + 0.136274i \(0.956487\pi\)
\(450\) −37.1789 + 99.3364i −0.0826199 + 0.220748i
\(451\) 107.054 0.237371
\(452\) 161.472 + 161.472i 0.357238 + 0.357238i
\(453\) −67.1963 + 67.1963i −0.148336 + 0.148336i
\(454\) 466.500i 1.02753i
\(455\) 110.716 + 510.347i 0.243332 + 1.12164i
\(456\) 2.59198 0.00568418
\(457\) 191.581 + 191.581i 0.419213 + 0.419213i 0.884933 0.465719i \(-0.154204\pi\)
−0.465719 + 0.884933i \(0.654204\pi\)
\(458\) 407.228 407.228i 0.889143 0.889143i
\(459\) 5.74473i 0.0125158i
\(460\) 25.9511 40.3304i 0.0564154 0.0876748i
\(461\) −69.9790 −0.151798 −0.0758992 0.997115i \(-0.524183\pi\)
−0.0758992 + 0.997115i \(0.524183\pi\)
\(462\) 107.601 + 107.601i 0.232902 + 0.232902i
\(463\) −506.603 + 506.603i −1.09417 + 1.09417i −0.0990971 + 0.995078i \(0.531595\pi\)
−0.995078 + 0.0990971i \(0.968405\pi\)
\(464\) 91.2422i 0.196643i
\(465\) −177.231 114.042i −0.381142 0.245251i
\(466\) 135.628 0.291046
\(467\) 361.691 + 361.691i 0.774498 + 0.774498i 0.978889 0.204391i \(-0.0655215\pi\)
−0.204391 + 0.978889i \(0.565521\pi\)
\(468\) 46.2261 46.2261i 0.0987737 0.0987737i
\(469\) 323.061i 0.688830i
\(470\) 187.492 40.6751i 0.398920 0.0865429i
\(471\) −352.222 −0.747817
\(472\) −125.523 125.523i −0.265938 0.265938i
\(473\) 73.6094 73.6094i 0.155622 0.155622i
\(474\) 136.051i 0.287027i
\(475\) 5.48112 + 12.0381i 0.0115392 + 0.0253433i
\(476\) −21.1958 −0.0445289
\(477\) 23.3006 + 23.3006i 0.0488483 + 0.0488483i
\(478\) 126.104 126.104i 0.263815 0.263815i
\(479\) 472.746i 0.986945i 0.869762 + 0.493472i \(0.164273\pi\)
−0.869762 + 0.493472i \(0.835727\pi\)
\(480\) −10.3864 47.8761i −0.0216383 0.0997419i
\(481\) 98.3227 0.204413
\(482\) 169.295 + 169.295i 0.351234 + 0.351234i
\(483\) −56.3042 + 56.3042i −0.116572 + 0.116572i
\(484\) 158.000i 0.326447i
\(485\) −304.897 + 473.838i −0.628654 + 0.976986i
\(486\) −22.0454 −0.0453609
\(487\) −245.070 245.070i −0.503224 0.503224i 0.409214 0.912438i \(-0.365803\pi\)
−0.912438 + 0.409214i \(0.865803\pi\)
\(488\) −75.6931 + 75.6931i −0.155109 + 0.155109i
\(489\) 265.021i 0.541965i
\(490\) −255.034 164.105i −0.520478 0.334908i
\(491\) −89.9842 −0.183267 −0.0916336 0.995793i \(-0.529209\pi\)
−0.0916336 + 0.995793i \(0.529209\pi\)
\(492\) 40.4628 + 40.4628i 0.0822415 + 0.0822415i
\(493\) −17.8323 + 17.8323i −0.0361711 + 0.0361711i
\(494\) 8.15254i 0.0165031i
\(495\) 95.0011 20.6098i 0.191921 0.0416360i
\(496\) 97.3421 0.196254
\(497\) 562.030 + 562.030i 1.13085 + 1.13085i
\(498\) −131.799 + 131.799i −0.264657 + 0.264657i
\(499\) 823.542i 1.65038i 0.564852 + 0.825192i \(0.308933\pi\)
−0.564852 + 0.825192i \(0.691067\pi\)
\(500\) 200.390 149.479i 0.400780 0.298958i
\(501\) 436.421 0.871101
\(502\) 352.257 + 352.257i 0.701707 + 0.701707i
\(503\) −141.332 + 141.332i −0.280978 + 0.280978i −0.833499 0.552521i \(-0.813666\pi\)
0.552521 + 0.833499i \(0.313666\pi\)
\(504\) 81.3388i 0.161387i
\(505\) −148.125 682.784i −0.293317 1.35205i
\(506\) −43.9544 −0.0868665
\(507\) 61.5875 + 61.5875i 0.121474 + 0.121474i
\(508\) 261.511 261.511i 0.514785 0.514785i
\(509\) 565.134i 1.11028i −0.831756 0.555141i \(-0.812664\pi\)
0.831756 0.555141i \(-0.187336\pi\)
\(510\) −7.32698 + 11.3868i −0.0143666 + 0.0223271i
\(511\) 446.367 0.873517
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −1.94399 + 1.94399i −0.00378945 + 0.00378945i
\(514\) 72.2366i 0.140538i
\(515\) 584.716 + 376.243i 1.13537 + 0.730568i
\(516\) 55.6436 0.107836
\(517\) −124.335 124.335i −0.240494 0.240494i
\(518\) −86.5037 + 86.5037i −0.166995 + 0.166995i
\(519\) 29.5286i 0.0568953i
\(520\) −150.584 + 32.6682i −0.289585 + 0.0628234i
\(521\) −355.537 −0.682413 −0.341206 0.939988i \(-0.610835\pi\)
−0.341206 + 0.939988i \(0.610835\pi\)
\(522\) 68.4316 + 68.4316i 0.131095 + 0.131095i
\(523\) −325.412 + 325.412i −0.622204 + 0.622204i −0.946094 0.323891i \(-0.895009\pi\)
0.323891 + 0.946094i \(0.395009\pi\)
\(524\) 76.6244i 0.146230i
\(525\) −377.766 + 172.002i −0.719554 + 0.327624i
\(526\) −435.272 −0.827513
\(527\) −19.0245 19.0245i −0.0360996 0.0360996i
\(528\) −31.7490 + 31.7490i −0.0601306 + 0.0601306i
\(529\) 23.0000i 0.0434783i
\(530\) −16.4666 75.9031i −0.0310691 0.143213i
\(531\) 188.284 0.354584
\(532\) 7.17255 + 7.17255i 0.0134822 + 0.0134822i
\(533\) 127.267 127.267i 0.238775 0.238775i
\(534\) 22.5544i 0.0422367i
\(535\) 43.7263 67.9546i 0.0817313 0.127018i
\(536\) 95.3231 0.177842
\(537\) 57.8971 + 57.8971i 0.107816 + 0.107816i
\(538\) 525.831 525.831i 0.977381 0.977381i
\(539\) 277.952i 0.515680i
\(540\) 43.6969 + 28.1173i 0.0809202 + 0.0520691i
\(541\) 862.324 1.59394 0.796972 0.604016i \(-0.206434\pi\)
0.796972 + 0.604016i \(0.206434\pi\)
\(542\) 518.661 + 518.661i 0.956939 + 0.956939i
\(543\) −58.0998 + 58.0998i −0.106998 + 0.106998i
\(544\) 6.25407i 0.0114965i
\(545\) 390.057 84.6202i 0.715701 0.155266i
\(546\) 255.834 0.468560
\(547\) 530.824 + 530.824i 0.970429 + 0.970429i 0.999575 0.0291465i \(-0.00927895\pi\)
−0.0291465 + 0.999575i \(0.509279\pi\)
\(548\) 86.4715 86.4715i 0.157795 0.157795i
\(549\) 113.540i 0.206812i
\(550\) −214.591 80.3155i −0.390165 0.146028i
\(551\) 12.0688 0.0219034
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 376.480 376.480i 0.680795 0.680795i
\(554\) 447.234i 0.807281i
\(555\) 16.5688 + 76.3742i 0.0298538 + 0.137611i
\(556\) 227.004 0.408281
\(557\) 82.0074 + 82.0074i 0.147230 + 0.147230i 0.776880 0.629649i \(-0.216801\pi\)
−0.629649 + 0.776880i \(0.716801\pi\)
\(558\) −73.0066 + 73.0066i −0.130836 + 0.130836i
\(559\) 175.015i 0.313086i
\(560\) 103.742 161.224i 0.185253 0.287900i
\(561\) 12.4100 0.0221212
\(562\) 425.954 + 425.954i 0.757926 + 0.757926i
\(563\) −467.229 + 467.229i −0.829892 + 0.829892i −0.987501 0.157610i \(-0.949621\pi\)
0.157610 + 0.987501i \(0.449621\pi\)
\(564\) 93.9887i 0.166647i
\(565\) 480.087 + 308.918i 0.849712 + 0.546758i
\(566\) 61.1315 0.108006
\(567\) −61.0041 61.0041i −0.107591 0.107591i
\(568\) −165.834 + 165.834i −0.291961 + 0.291961i
\(569\) 571.773i 1.00487i −0.864614 0.502437i \(-0.832437\pi\)
0.864614 0.502437i \(-0.167563\pi\)
\(570\) 6.33265 1.37382i 0.0111099 0.00241022i
\(571\) 303.885 0.532197 0.266099 0.963946i \(-0.414265\pi\)
0.266099 + 0.963946i \(0.414265\pi\)
\(572\) 99.8596 + 99.8596i 0.174580 + 0.174580i
\(573\) 155.424 155.424i 0.271247 0.271247i
\(574\) 223.938i 0.390135i
\(575\) 42.0266 112.289i 0.0730898 0.195285i
\(576\) −24.0000 −0.0416667
\(577\) 334.483 + 334.483i 0.579693 + 0.579693i 0.934819 0.355126i \(-0.115562\pi\)
−0.355126 + 0.934819i \(0.615562\pi\)
\(578\) 287.778 287.778i 0.497885 0.497885i
\(579\) 364.875i 0.630181i
\(580\) −48.3609 222.920i −0.0833809 0.384345i
\(581\) −729.429 −1.25547
\(582\) 195.188 + 195.188i 0.335374 + 0.335374i
\(583\) −50.3350 + 50.3350i −0.0863379 + 0.0863379i
\(584\) 131.706i 0.225524i
\(585\) 88.4370 137.439i 0.151174 0.234939i
\(586\) −475.099 −0.810749
\(587\) 102.989 + 102.989i 0.175450 + 0.175450i 0.789369 0.613919i \(-0.210408\pi\)
−0.613919 + 0.789369i \(0.710408\pi\)
\(588\) −105.056 + 105.056i −0.178667 + 0.178667i
\(589\) 12.8756i 0.0218601i
\(590\) −373.204 240.142i −0.632548 0.407021i
\(591\) 25.0045 0.0423088
\(592\) −25.5239 25.5239i −0.0431148 0.0431148i
\(593\) −798.294 + 798.294i −1.34620 + 1.34620i −0.456444 + 0.889752i \(0.650877\pi\)
−0.889752 + 0.456444i \(0.849123\pi\)
\(594\) 47.6234i 0.0801741i
\(595\) −51.7848 + 11.2344i −0.0870333 + 0.0188813i
\(596\) 161.764 0.271416
\(597\) −448.060 448.060i −0.750520 0.750520i
\(598\) −52.2534 + 52.2534i −0.0873803 + 0.0873803i
\(599\) 176.987i 0.295471i 0.989027 + 0.147736i \(0.0471984\pi\)
−0.989027 + 0.147736i \(0.952802\pi\)
\(600\) −50.7514 111.464i −0.0845856 0.185774i
\(601\) −879.913 −1.46408 −0.732041 0.681261i \(-0.761432\pi\)
−0.732041 + 0.681261i \(0.761432\pi\)
\(602\) 153.977 + 153.977i 0.255776 + 0.255776i
\(603\) −71.4923 + 71.4923i −0.118561 + 0.118561i
\(604\) 109.731i 0.181674i
\(605\) −83.7446 386.021i −0.138421 0.638052i
\(606\) −342.275 −0.564811
\(607\) 80.2035 + 80.2035i 0.132131 + 0.132131i 0.770079 0.637948i \(-0.220217\pi\)
−0.637948 + 0.770079i \(0.720217\pi\)
\(608\) −2.11635 + 2.11635i −0.00348083 + 0.00348083i
\(609\) 378.728i 0.621886i
\(610\) −144.811 + 225.050i −0.237396 + 0.368935i
\(611\) −295.622 −0.483832
\(612\) 4.69055 + 4.69055i 0.00766430 + 0.00766430i
\(613\) −619.641 + 619.641i −1.01083 + 1.01083i −0.0108925 + 0.999941i \(0.503467\pi\)
−0.999941 + 0.0108925i \(0.996533\pi\)
\(614\) 475.825i 0.774959i
\(615\) 120.304 + 77.4110i 0.195616 + 0.125872i
\(616\) −175.712 −0.285246
\(617\) −29.7434 29.7434i −0.0482065 0.0482065i 0.682593 0.730799i \(-0.260852\pi\)
−0.730799 + 0.682593i \(0.760852\pi\)
\(618\) 240.861 240.861i 0.389743 0.389743i
\(619\) 220.508i 0.356233i 0.984009 + 0.178116i \(0.0570004\pi\)
−0.984009 + 0.178116i \(0.943000\pi\)
\(620\) 237.823 51.5940i 0.383586 0.0832162i
\(621\) 24.9199 0.0401286
\(622\) −81.3114 81.3114i −0.130726 0.130726i
\(623\) −62.4127 + 62.4127i −0.100181 + 0.100181i
\(624\) 75.4869i 0.120973i
\(625\) 410.358 471.414i 0.656573 0.754262i
\(626\) −654.400 −1.04537
\(627\) −4.19949 4.19949i −0.00669775 0.00669775i
\(628\) 287.588 287.588i 0.457942 0.457942i
\(629\) 9.97678i 0.0158613i
\(630\) 43.1119 + 198.724i 0.0684315 + 0.315436i
\(631\) 716.316 1.13521 0.567604 0.823302i \(-0.307871\pi\)
0.567604 + 0.823302i \(0.307871\pi\)
\(632\) 111.085 + 111.085i 0.175767 + 0.175767i
\(633\) 64.3017 64.3017i 0.101582 0.101582i
\(634\) 548.941i 0.865837i
\(635\) 500.307 777.523i 0.787885 1.22445i
\(636\) −38.0498 −0.0598267
\(637\) 330.431 + 330.431i 0.518730 + 0.518730i
\(638\) −147.829 + 147.829i −0.231707 + 0.231707i
\(639\) 248.751i 0.389281i
\(640\) 47.5711 + 30.6102i 0.0743299 + 0.0478285i
\(641\) −969.601 −1.51264 −0.756319 0.654203i \(-0.773004\pi\)
−0.756319 + 0.654203i \(0.773004\pi\)
\(642\) −27.9925 27.9925i −0.0436020 0.0436020i
\(643\) 373.341 373.341i 0.580623 0.580623i −0.354451 0.935075i \(-0.615332\pi\)
0.935075 + 0.354451i \(0.115332\pi\)
\(644\) 91.9445i 0.142771i
\(645\) 135.947 29.4927i 0.210770 0.0457250i
\(646\) 0.827236 0.00128055
\(647\) −695.075 695.075i −1.07430 1.07430i −0.997008 0.0772961i \(-0.975371\pi\)
−0.0772961 0.997008i \(-0.524629\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 406.739i 0.626717i
\(650\) −350.587 + 159.628i −0.539365 + 0.245581i
\(651\) −404.048 −0.620657
\(652\) 216.389 + 216.389i 0.331885 + 0.331885i
\(653\) 42.2499 42.2499i 0.0647012 0.0647012i −0.674016 0.738717i \(-0.735432\pi\)
0.738717 + 0.674016i \(0.235432\pi\)
\(654\) 195.533i 0.298981i
\(655\) 40.6131 + 187.206i 0.0620047 + 0.285811i
\(656\) −66.0755 −0.100725
\(657\) −98.7795 98.7795i −0.150349 0.150349i
\(658\) 260.086 260.086i 0.395267 0.395267i
\(659\) 961.226i 1.45861i −0.684187 0.729307i \(-0.739843\pi\)
0.684187 0.729307i \(-0.260157\pi\)
\(660\) −60.7402 + 94.3959i −0.0920306 + 0.143024i
\(661\) 163.994 0.248100 0.124050 0.992276i \(-0.460412\pi\)
0.124050 + 0.992276i \(0.460412\pi\)
\(662\) 209.454 + 209.454i 0.316396 + 0.316396i
\(663\) 14.7531 14.7531i 0.0222521 0.0222521i
\(664\) 215.227i 0.324137i
\(665\) 21.3254 + 13.7221i 0.0320683 + 0.0206347i
\(666\) 38.2859 0.0574864
\(667\) −77.3543 77.3543i −0.115973 0.115973i
\(668\) −356.337 + 356.337i −0.533438 + 0.533438i
\(669\) 50.3778i 0.0753031i
\(670\) 232.890 50.5239i 0.347598 0.0754088i
\(671\) 245.273 0.365534
\(672\) −66.4129 66.4129i −0.0988287 0.0988287i
\(673\) 171.550 171.550i 0.254904 0.254904i −0.568074 0.822978i \(-0.692311\pi\)
0.822978 + 0.568074i \(0.192311\pi\)
\(674\) 534.149i 0.792506i
\(675\) 121.662 + 45.5347i 0.180240 + 0.0674588i
\(676\) −100.572 −0.148775
\(677\) −164.860 164.860i −0.243516 0.243516i 0.574787 0.818303i \(-0.305085\pi\)
−0.818303 + 0.574787i \(0.805085\pi\)
\(678\) 197.762 197.762i 0.291684 0.291684i
\(679\) 1080.25i 1.59094i
\(680\) −3.31483 15.2797i −0.00487475 0.0224702i
\(681\) 571.343 0.838977
\(682\) −157.712 157.712i −0.231249 0.231249i
\(683\) 16.9389 16.9389i 0.0248007 0.0248007i −0.694598 0.719398i \(-0.744418\pi\)
0.719398 + 0.694598i \(0.244418\pi\)
\(684\) 3.17452i 0.00464111i
\(685\) 165.432 257.097i 0.241507 0.375324i
\(686\) 82.8445 0.120765
\(687\) −498.750 498.750i −0.725982 0.725982i
\(688\) −45.4328 + 45.4328i −0.0660360 + 0.0660360i
\(689\) 119.677i 0.173697i
\(690\) −49.3944 31.7835i −0.0715862 0.0460630i
\(691\) 1270.25 1.83828 0.919141 0.393928i \(-0.128884\pi\)
0.919141 + 0.393928i \(0.128884\pi\)
\(692\) −24.1100 24.1100i −0.0348411 0.0348411i
\(693\) 131.784 131.784i 0.190164 0.190164i
\(694\) 604.754i 0.871403i
\(695\) 554.609 120.319i 0.797999 0.173120i
\(696\) −111.748 −0.160558
\(697\) 12.9138 + 12.9138i 0.0185276 + 0.0185276i
\(698\) 38.7883 38.7883i 0.0555706 0.0555706i
\(699\) 166.109i 0.237638i
\(700\) 168.005 448.884i 0.240007 0.641263i
\(701\) −1394.68 −1.98956 −0.994781 0.102031i \(-0.967466\pi\)
−0.994781 + 0.102031i \(0.967466\pi\)
\(702\) −56.6152 56.6152i −0.0806484 0.0806484i
\(703\) 3.37609 3.37609i 0.00480241 0.00480241i
\(704\) 51.8458i 0.0736446i
\(705\) −49.8167 229.630i −0.0706620 0.325717i
\(706\) 456.850 0.647096
\(707\) −947.145 947.145i −1.33967 1.33967i
\(708\) −153.733 + 153.733i −0.217137 + 0.217137i
\(709\) 842.555i 1.18837i −0.804328 0.594185i \(-0.797475\pi\)
0.804328 0.594185i \(-0.202525\pi\)
\(710\) −317.263 + 493.057i −0.446850 + 0.694446i
\(711\) −166.627 −0.234356
\(712\) −18.4156 18.4156i −0.0258646 0.0258646i
\(713\) 82.5258 82.5258i 0.115744 0.115744i
\(714\) 25.9594i 0.0363577i
\(715\) 296.902 + 191.045i 0.415248 + 0.267196i
\(716\) −94.5456 −0.132047
\(717\) −154.445 154.445i −0.215404 0.215404i
\(718\) −572.493 + 572.493i −0.797344 + 0.797344i
\(719\) 685.162i 0.952937i 0.879191 + 0.476469i \(0.158083\pi\)
−0.879191 + 0.476469i \(0.841917\pi\)
\(720\) −58.6360 + 12.7207i −0.0814389 + 0.0176676i
\(721\) 1333.02 1.84885
\(722\) 360.720 + 360.720i 0.499612 + 0.499612i
\(723\) 207.343 207.343i 0.286781 0.286781i
\(724\) 94.8765i 0.131045i
\(725\) −236.308 518.998i −0.325942 0.715860i
\(726\) −193.510 −0.266543
\(727\) 752.841 + 752.841i 1.03554 + 1.03554i 0.999345 + 0.0361997i \(0.0115252\pi\)
0.0361997 + 0.999345i \(0.488475\pi\)
\(728\) −208.888 + 208.888i −0.286933 + 0.286933i
\(729\) 27.0000i 0.0370370i
\(730\) 69.8079 + 321.780i 0.0956272 + 0.440794i
\(731\) 17.7587 0.0242938
\(732\) 92.7047 + 92.7047i 0.126646 + 0.126646i
\(733\) −232.917 + 232.917i −0.317758 + 0.317758i −0.847905 0.530148i \(-0.822137\pi\)
0.530148 + 0.847905i \(0.322137\pi\)
\(734\) 312.501i 0.425750i
\(735\) −200.987 + 312.352i −0.273451 + 0.424969i
\(736\) 27.1293 0.0368605
\(737\) −154.441 154.441i −0.209553 0.209553i
\(738\) 49.5566 49.5566i 0.0671499 0.0671499i
\(739\) 135.488i 0.183339i −0.995789 0.0916696i \(-0.970780\pi\)
0.995789 0.0916696i \(-0.0292204\pi\)
\(740\) −75.8877 48.8309i −0.102551 0.0659877i
\(741\) −9.98478 −0.0134747
\(742\) −105.291 105.291i −0.141902 0.141902i
\(743\) 726.590 726.590i 0.977914 0.977914i −0.0218472 0.999761i \(-0.506955\pi\)
0.999761 + 0.0218472i \(0.00695474\pi\)
\(744\) 119.219i 0.160241i
\(745\) 395.217 85.7395i 0.530492 0.115087i
\(746\) 29.5768 0.0396472
\(747\) 161.420 + 161.420i 0.216091 + 0.216091i
\(748\) −10.1327 + 10.1327i −0.0135464 + 0.0135464i
\(749\) 154.922i 0.206838i
\(750\) −183.073 245.426i −0.244098 0.327235i
\(751\) −1008.88 −1.34339 −0.671694 0.740829i \(-0.734433\pi\)
−0.671694 + 0.740829i \(0.734433\pi\)
\(752\) 76.7415 + 76.7415i 0.102050 + 0.102050i
\(753\) 431.425 431.425i 0.572941 0.572941i
\(754\) 351.481i 0.466155i
\(755\) −58.1605 268.091i −0.0770338 0.355088i
\(756\) 99.6193 0.131772
\(757\) 570.746 + 570.746i 0.753958 + 0.753958i 0.975215 0.221257i \(-0.0710161\pi\)
−0.221257 + 0.975215i \(0.571016\pi\)
\(758\) −39.4302 + 39.4302i −0.0520188 + 0.0520188i
\(759\) 53.8330i 0.0709262i
\(760\) −4.04887 + 6.29231i −0.00532746 + 0.00827936i
\(761\) −1183.62 −1.55535 −0.777675 0.628667i \(-0.783601\pi\)
−0.777675 + 0.628667i \(0.783601\pi\)
\(762\) −320.284 320.284i −0.420320 0.420320i
\(763\) 541.080 541.080i 0.709148 0.709148i
\(764\) 253.807i 0.332208i
\(765\) 13.9459 + 8.97368i 0.0182300 + 0.0117303i
\(766\) −525.954 −0.686624
\(767\) 483.535 + 483.535i 0.630424 + 0.630424i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 363.068i 0.472130i −0.971737 0.236065i \(-0.924142\pi\)
0.971737 0.236065i \(-0.0758578\pi\)
\(770\) −429.293 + 93.1321i −0.557523 + 0.120951i
\(771\) 88.4714 0.114749
\(772\) −297.919 297.919i −0.385905 0.385905i
\(773\) −1014.90 + 1014.90i −1.31293 + 1.31293i −0.393693 + 0.919242i \(0.628803\pi\)
−0.919242 + 0.393693i \(0.871197\pi\)
\(774\) 68.1492i 0.0880480i
\(775\) 553.695 252.106i 0.714446 0.325298i
\(776\) −318.740 −0.410747
\(777\) 105.945 + 105.945i 0.136351 + 0.136351i
\(778\) 412.312 412.312i 0.529963 0.529963i
\(779\) 8.73991i