Properties

Label 441.2.f.h.148.11
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.11
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.h.295.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.35757 + 2.35137i) q^{2} +(-0.521588 - 1.65165i) q^{3} +(-2.68597 + 4.65224i) q^{4} +(-0.793197 + 1.37386i) q^{5} +(3.17555 - 3.46867i) q^{6} -9.15528 q^{8} +(-2.45589 + 1.72296i) q^{9} +O(q^{10})\) \(q+(1.35757 + 2.35137i) q^{2} +(-0.521588 - 1.65165i) q^{3} +(-2.68597 + 4.65224i) q^{4} +(-0.793197 + 1.37386i) q^{5} +(3.17555 - 3.46867i) q^{6} -9.15528 q^{8} +(-2.45589 + 1.72296i) q^{9} -4.30727 q^{10} +(0.674376 + 1.16805i) q^{11} +(9.08484 + 2.00973i) q^{12} +(-1.58916 + 2.75251i) q^{13} +(2.68285 + 0.593495i) q^{15} +(-7.05696 - 12.2230i) q^{16} -2.80054 q^{17} +(-7.38536 - 3.43568i) q^{18} -0.625693 q^{19} +(-4.26101 - 7.38028i) q^{20} +(-1.83102 + 3.17142i) q^{22} +(0.142434 - 0.246702i) q^{23} +(4.77529 + 15.1213i) q^{24} +(1.24168 + 2.15065i) q^{25} -8.62957 q^{26} +(4.12669 + 3.15760i) q^{27} +(2.27396 + 3.93861i) q^{29} +(2.24662 + 7.11410i) q^{30} +(3.71502 - 6.43461i) q^{31} +(10.0053 - 17.3297i) q^{32} +(1.57747 - 1.72308i) q^{33} +(-3.80191 - 6.58511i) q^{34} +(-1.41918 - 16.0532i) q^{36} +8.02252 q^{37} +(-0.849420 - 1.47124i) q^{38} +(5.37507 + 1.18906i) q^{39} +(7.26194 - 12.5780i) q^{40} +(-5.01329 + 8.68327i) q^{41} +(-3.12937 - 5.42022i) q^{43} -7.24542 q^{44} +(-0.419098 - 4.74069i) q^{45} +0.773452 q^{46} +(5.57383 + 9.65415i) q^{47} +(-16.5073 + 18.0310i) q^{48} +(-3.37132 + 5.83930i) q^{50} +(1.46073 + 4.62550i) q^{51} +(-8.53689 - 14.7863i) q^{52} +2.78698 q^{53} +(-1.82243 + 13.9900i) q^{54} -2.13965 q^{55} +(0.326354 + 1.03343i) q^{57} +(-6.17410 + 10.6939i) q^{58} +(2.28734 - 3.96180i) q^{59} +(-9.96715 + 10.8872i) q^{60} +(-0.192507 - 0.333432i) q^{61} +20.1736 q^{62} +26.1036 q^{64} +(-2.52104 - 4.36656i) q^{65} +(6.19311 + 1.37003i) q^{66} +(1.26958 - 2.19898i) q^{67} +(7.52217 - 13.0288i) q^{68} +(-0.481757 - 0.106573i) q^{69} -1.45208 q^{71} +(22.4844 - 15.7742i) q^{72} +0.468134 q^{73} +(10.8911 + 18.8639i) q^{74} +(2.90448 - 3.17257i) q^{75} +(1.68059 - 2.91087i) q^{76} +(4.50108 + 14.2530i) q^{78} +(7.85620 + 13.6073i) q^{79} +22.3902 q^{80} +(3.06281 - 8.46281i) q^{81} -27.2235 q^{82} +(6.99338 + 12.1129i) q^{83} +(2.22138 - 3.84754i) q^{85} +(8.49665 - 14.7166i) q^{86} +(5.31914 - 5.81012i) q^{87} +(-6.17410 - 10.6939i) q^{88} +2.58706 q^{89} +(10.5782 - 7.42126i) q^{90} +(0.765146 + 1.32527i) q^{92} +(-12.5654 - 2.77970i) q^{93} +(-15.1337 + 26.2123i) q^{94} +(0.496297 - 0.859612i) q^{95} +(-33.8412 - 7.48628i) q^{96} +(-7.22962 - 12.5221i) q^{97} +(-3.66871 - 1.70669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + 20q^{11} + 4q^{15} - 12q^{16} + 4q^{18} + 32q^{23} - 12q^{25} + 16q^{29} + 48q^{32} - 4q^{36} + 24q^{37} + 32q^{39} - 112q^{44} - 48q^{46} - 4q^{50} - 56q^{51} - 64q^{53} - 12q^{57} - 88q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} + 168q^{72} + 68q^{74} - 60q^{78} + 12q^{79} + 80q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 80q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35757 + 2.35137i 0.959944 + 1.66267i 0.722624 + 0.691241i \(0.242936\pi\)
0.237320 + 0.971432i \(0.423731\pi\)
\(3\) −0.521588 1.65165i −0.301139 0.953580i
\(4\) −2.68597 + 4.65224i −1.34299 + 2.32612i
\(5\) −0.793197 + 1.37386i −0.354728 + 0.614407i −0.987071 0.160281i \(-0.948760\pi\)
0.632343 + 0.774688i \(0.282093\pi\)
\(6\) 3.17555 3.46867i 1.29641 1.41608i
\(7\) 0 0
\(8\) −9.15528 −3.23688
\(9\) −2.45589 + 1.72296i −0.818630 + 0.574321i
\(10\) −4.30727 −1.36208
\(11\) 0.674376 + 1.16805i 0.203332 + 0.352181i 0.949600 0.313464i \(-0.101490\pi\)
−0.746268 + 0.665646i \(0.768156\pi\)
\(12\) 9.08484 + 2.00973i 2.62257 + 0.580159i
\(13\) −1.58916 + 2.75251i −0.440754 + 0.763409i −0.997746 0.0671096i \(-0.978622\pi\)
0.556991 + 0.830518i \(0.311956\pi\)
\(14\) 0 0
\(15\) 2.68285 + 0.593495i 0.692709 + 0.153240i
\(16\) −7.05696 12.2230i −1.76424 3.05575i
\(17\) −2.80054 −0.679230 −0.339615 0.940565i \(-0.610297\pi\)
−0.339615 + 0.940565i \(0.610297\pi\)
\(18\) −7.38536 3.43568i −1.74075 0.809799i
\(19\) −0.625693 −0.143544 −0.0717719 0.997421i \(-0.522865\pi\)
−0.0717719 + 0.997421i \(0.522865\pi\)
\(20\) −4.26101 7.38028i −0.952791 1.65028i
\(21\) 0 0
\(22\) −1.83102 + 3.17142i −0.390375 + 0.676149i
\(23\) 0.142434 0.246702i 0.0296995 0.0514410i −0.850794 0.525500i \(-0.823878\pi\)
0.880493 + 0.474059i \(0.157212\pi\)
\(24\) 4.77529 + 15.1213i 0.974751 + 3.08663i
\(25\) 1.24168 + 2.15065i 0.248336 + 0.430130i
\(26\) −8.62957 −1.69240
\(27\) 4.12669 + 3.15760i 0.794182 + 0.607679i
\(28\) 0 0
\(29\) 2.27396 + 3.93861i 0.422264 + 0.731382i 0.996161 0.0875454i \(-0.0279023\pi\)
−0.573897 + 0.818928i \(0.694569\pi\)
\(30\) 2.24662 + 7.11410i 0.410175 + 1.29885i
\(31\) 3.71502 6.43461i 0.667238 1.15569i −0.311435 0.950267i \(-0.600810\pi\)
0.978673 0.205423i \(-0.0658569\pi\)
\(32\) 10.0053 17.3297i 1.76870 3.06348i
\(33\) 1.57747 1.72308i 0.274602 0.299949i
\(34\) −3.80191 6.58511i −0.652023 1.12934i
\(35\) 0 0
\(36\) −1.41918 16.0532i −0.236529 2.67554i
\(37\) 8.02252 1.31889 0.659447 0.751751i \(-0.270791\pi\)
0.659447 + 0.751751i \(0.270791\pi\)
\(38\) −0.849420 1.47124i −0.137794 0.238666i
\(39\) 5.37507 + 1.18906i 0.860700 + 0.190402i
\(40\) 7.26194 12.5780i 1.14821 1.98876i
\(41\) −5.01329 + 8.68327i −0.782944 + 1.35610i 0.147275 + 0.989096i \(0.452950\pi\)
−0.930219 + 0.367004i \(0.880384\pi\)
\(42\) 0 0
\(43\) −3.12937 5.42022i −0.477224 0.826576i 0.522435 0.852679i \(-0.325024\pi\)
−0.999659 + 0.0261027i \(0.991690\pi\)
\(44\) −7.24542 −1.09229
\(45\) −0.419098 4.74069i −0.0624754 0.706700i
\(46\) 0.773452 0.114039
\(47\) 5.57383 + 9.65415i 0.813026 + 1.40820i 0.910737 + 0.412988i \(0.135515\pi\)
−0.0977106 + 0.995215i \(0.531152\pi\)
\(48\) −16.5073 + 18.0310i −2.38262 + 2.60255i
\(49\) 0 0
\(50\) −3.37132 + 5.83930i −0.476777 + 0.825802i
\(51\) 1.46073 + 4.62550i 0.204543 + 0.647700i
\(52\) −8.53689 14.7863i −1.18385 2.05049i
\(53\) 2.78698 0.382821 0.191410 0.981510i \(-0.438694\pi\)
0.191410 + 0.981510i \(0.438694\pi\)
\(54\) −1.82243 + 13.9900i −0.248001 + 1.90380i
\(55\) −2.13965 −0.288510
\(56\) 0 0
\(57\) 0.326354 + 1.03343i 0.0432266 + 0.136881i
\(58\) −6.17410 + 10.6939i −0.810699 + 1.40417i
\(59\) 2.28734 3.96180i 0.297787 0.515782i −0.677842 0.735207i \(-0.737085\pi\)
0.975629 + 0.219425i \(0.0704182\pi\)
\(60\) −9.96715 + 10.8872i −1.28675 + 1.40553i
\(61\) −0.192507 0.333432i −0.0246480 0.0426916i 0.853438 0.521194i \(-0.174513\pi\)
−0.878086 + 0.478502i \(0.841180\pi\)
\(62\) 20.1736 2.56205
\(63\) 0 0
\(64\) 26.1036 3.26295
\(65\) −2.52104 4.36656i −0.312696 0.541605i
\(66\) 6.19311 + 1.37003i 0.762320 + 0.168639i
\(67\) 1.26958 2.19898i 0.155104 0.268648i −0.777993 0.628273i \(-0.783762\pi\)
0.933097 + 0.359625i \(0.117095\pi\)
\(68\) 7.52217 13.0288i 0.912197 1.57997i
\(69\) −0.481757 0.106573i −0.0579968 0.0128299i
\(70\) 0 0
\(71\) −1.45208 −0.172330 −0.0861651 0.996281i \(-0.527461\pi\)
−0.0861651 + 0.996281i \(0.527461\pi\)
\(72\) 22.4844 15.7742i 2.64981 1.85901i
\(73\) 0.468134 0.0547909 0.0273955 0.999625i \(-0.491279\pi\)
0.0273955 + 0.999625i \(0.491279\pi\)
\(74\) 10.8911 + 18.8639i 1.26606 + 2.19289i
\(75\) 2.90448 3.17257i 0.335380 0.366337i
\(76\) 1.68059 2.91087i 0.192777 0.333900i
\(77\) 0 0
\(78\) 4.50108 + 14.2530i 0.509647 + 1.61384i
\(79\) 7.85620 + 13.6073i 0.883892 + 1.53095i 0.846978 + 0.531627i \(0.178419\pi\)
0.0369135 + 0.999318i \(0.488247\pi\)
\(80\) 22.3902 2.50330
\(81\) 3.06281 8.46281i 0.340312 0.940313i
\(82\) −27.2235 −3.00633
\(83\) 6.99338 + 12.1129i 0.767623 + 1.32956i 0.938848 + 0.344331i \(0.111894\pi\)
−0.171225 + 0.985232i \(0.554772\pi\)
\(84\) 0 0
\(85\) 2.22138 3.84754i 0.240942 0.417324i
\(86\) 8.49665 14.7166i 0.916217 1.58693i
\(87\) 5.31914 5.81012i 0.570272 0.622910i
\(88\) −6.17410 10.6939i −0.658162 1.13997i
\(89\) 2.58706 0.274228 0.137114 0.990555i \(-0.456217\pi\)
0.137114 + 0.990555i \(0.456217\pi\)
\(90\) 10.5782 7.42126i 1.11504 0.782269i
\(91\) 0 0
\(92\) 0.765146 + 1.32527i 0.0797719 + 0.138169i
\(93\) −12.5654 2.77970i −1.30297 0.288241i
\(94\) −15.1337 + 26.2123i −1.56092 + 2.70359i
\(95\) 0.496297 0.859612i 0.0509190 0.0881944i
\(96\) −33.8412 7.48628i −3.45390 0.764065i
\(97\) −7.22962 12.5221i −0.734057 1.27142i −0.955136 0.296168i \(-0.904291\pi\)
0.221079 0.975256i \(-0.429042\pi\)
\(98\) 0 0
\(99\) −3.66871 1.70669i −0.368719 0.171529i
\(100\) −13.3405 −1.33405
\(101\) 4.91888 + 8.51975i 0.489447 + 0.847747i 0.999926 0.0121430i \(-0.00386534\pi\)
−0.510479 + 0.859890i \(0.670532\pi\)
\(102\) −8.89326 + 9.71414i −0.880564 + 0.961844i
\(103\) 5.52897 9.57646i 0.544786 0.943597i −0.453834 0.891086i \(-0.649944\pi\)
0.998620 0.0525110i \(-0.0167225\pi\)
\(104\) 14.5492 25.2000i 1.42667 2.47106i
\(105\) 0 0
\(106\) 3.78350 + 6.55322i 0.367486 + 0.636505i
\(107\) −1.92431 −0.186030 −0.0930149 0.995665i \(-0.529650\pi\)
−0.0930149 + 0.995665i \(0.529650\pi\)
\(108\) −25.7741 + 10.7172i −2.48011 + 1.03126i
\(109\) −18.6068 −1.78221 −0.891105 0.453797i \(-0.850069\pi\)
−0.891105 + 0.453797i \(0.850069\pi\)
\(110\) −2.90472 5.03112i −0.276954 0.479698i
\(111\) −4.18445 13.2504i −0.397170 1.25767i
\(112\) 0 0
\(113\) 1.59338 2.75982i 0.149893 0.259622i −0.781295 0.624162i \(-0.785440\pi\)
0.931188 + 0.364540i \(0.118774\pi\)
\(114\) −1.98692 + 2.17032i −0.186092 + 0.203269i
\(115\) 0.225956 + 0.391367i 0.0210705 + 0.0364951i
\(116\) −24.4312 −2.26838
\(117\) −0.839659 9.49793i −0.0776265 0.878084i
\(118\) 12.4209 1.14344
\(119\) 0 0
\(120\) −24.5623 5.43361i −2.24222 0.496019i
\(121\) 4.59043 7.95086i 0.417312 0.722806i
\(122\) 0.522682 0.905312i 0.0473214 0.0819631i
\(123\) 16.9566 + 3.75110i 1.52892 + 0.338226i
\(124\) 19.9569 + 34.5664i 1.79218 + 3.10415i
\(125\) −11.8715 −1.06182
\(126\) 0 0
\(127\) −8.37387 −0.743061 −0.371530 0.928421i \(-0.621167\pi\)
−0.371530 + 0.928421i \(0.621167\pi\)
\(128\) 15.4267 + 26.7199i 1.36354 + 2.36173i
\(129\) −7.32007 + 7.99574i −0.644496 + 0.703986i
\(130\) 6.84495 11.8558i 0.600341 1.03982i
\(131\) −5.98629 + 10.3686i −0.523024 + 0.905905i 0.476616 + 0.879111i \(0.341863\pi\)
−0.999641 + 0.0267937i \(0.991470\pi\)
\(132\) 3.77913 + 11.9669i 0.328931 + 1.04158i
\(133\) 0 0
\(134\) 6.89415 0.595564
\(135\) −7.61136 + 3.16489i −0.655082 + 0.272390i
\(136\) 25.6397 2.19859
\(137\) −8.27525 14.3332i −0.707003 1.22456i −0.965964 0.258677i \(-0.916714\pi\)
0.258961 0.965888i \(-0.416620\pi\)
\(138\) −0.403424 1.27747i −0.0343417 0.108746i
\(139\) −3.95119 + 6.84367i −0.335136 + 0.580472i −0.983511 0.180849i \(-0.942116\pi\)
0.648375 + 0.761321i \(0.275449\pi\)
\(140\) 0 0
\(141\) 13.0380 14.2415i 1.09800 1.19935i
\(142\) −1.97130 3.41438i −0.165427 0.286529i
\(143\) −4.28677 −0.358478
\(144\) 38.3909 + 17.8595i 3.19924 + 1.48829i
\(145\) −7.21479 −0.599156
\(146\) 0.635523 + 1.10076i 0.0525962 + 0.0910994i
\(147\) 0 0
\(148\) −21.5483 + 37.3227i −1.77126 + 3.06791i
\(149\) 6.83427 11.8373i 0.559885 0.969749i −0.437620 0.899160i \(-0.644179\pi\)
0.997505 0.0705895i \(-0.0224881\pi\)
\(150\) 11.4029 + 2.52253i 0.931045 + 0.205964i
\(151\) −1.94982 3.37718i −0.158674 0.274831i 0.775717 0.631081i \(-0.217389\pi\)
−0.934391 + 0.356250i \(0.884055\pi\)
\(152\) 5.72839 0.464634
\(153\) 6.87781 4.82522i 0.556038 0.390096i
\(154\) 0 0
\(155\) 5.89349 + 10.2078i 0.473376 + 0.819912i
\(156\) −19.9691 + 21.8123i −1.59881 + 1.74638i
\(157\) −0.147176 + 0.254917i −0.0117459 + 0.0203446i −0.871839 0.489793i \(-0.837072\pi\)
0.860093 + 0.510138i \(0.170406\pi\)
\(158\) −21.3306 + 36.9457i −1.69697 + 2.93925i
\(159\) −1.45365 4.60311i −0.115282 0.365050i
\(160\) 15.8723 + 27.4917i 1.25482 + 2.17341i
\(161\) 0 0
\(162\) 24.0572 4.28703i 1.89011 0.336821i
\(163\) 10.7091 0.838802 0.419401 0.907801i \(-0.362240\pi\)
0.419401 + 0.907801i \(0.362240\pi\)
\(164\) −26.9311 46.6461i −2.10297 3.64245i
\(165\) 1.11602 + 3.53395i 0.0868818 + 0.275118i
\(166\) −18.9880 + 32.8881i −1.47375 + 2.55261i
\(167\) −1.59872 + 2.76907i −0.123713 + 0.214277i −0.921229 0.389020i \(-0.872814\pi\)
0.797516 + 0.603298i \(0.206147\pi\)
\(168\) 0 0
\(169\) 1.44913 + 2.50997i 0.111472 + 0.193074i
\(170\) 12.0627 0.925164
\(171\) 1.53663 1.07804i 0.117509 0.0824401i
\(172\) 33.6216 2.56362
\(173\) −5.71875 9.90517i −0.434789 0.753076i 0.562490 0.826804i \(-0.309844\pi\)
−0.997278 + 0.0737284i \(0.976510\pi\)
\(174\) 20.8828 + 4.61966i 1.58312 + 0.350216i
\(175\) 0 0
\(176\) 9.51809 16.4858i 0.717453 1.24266i
\(177\) −7.73655 1.71146i −0.581515 0.128642i
\(178\) 3.51210 + 6.08314i 0.263243 + 0.455951i
\(179\) 1.09855 0.0821095 0.0410547 0.999157i \(-0.486928\pi\)
0.0410547 + 0.999157i \(0.486928\pi\)
\(180\) 23.1805 + 10.7836i 1.72777 + 0.803764i
\(181\) −3.19013 −0.237120 −0.118560 0.992947i \(-0.537828\pi\)
−0.118560 + 0.992947i \(0.537828\pi\)
\(182\) 0 0
\(183\) −0.450303 + 0.491868i −0.0332874 + 0.0363599i
\(184\) −1.30402 + 2.25863i −0.0961336 + 0.166508i
\(185\) −6.36343 + 11.0218i −0.467849 + 0.810338i
\(186\) −10.5223 33.3197i −0.771532 2.44312i
\(187\) −1.88861 3.27118i −0.138109 0.239212i
\(188\) −59.8846 −4.36753
\(189\) 0 0
\(190\) 2.69503 0.195518
\(191\) −1.93407 3.34992i −0.139945 0.242391i 0.787531 0.616275i \(-0.211359\pi\)
−0.927475 + 0.373884i \(0.878026\pi\)
\(192\) −13.6153 43.1139i −0.982601 3.11148i
\(193\) 2.06793 3.58175i 0.148853 0.257820i −0.781951 0.623340i \(-0.785775\pi\)
0.930804 + 0.365520i \(0.119109\pi\)
\(194\) 19.6294 33.9991i 1.40931 2.44099i
\(195\) −5.89709 + 6.44141i −0.422299 + 0.461279i
\(196\) 0 0
\(197\) −0.889267 −0.0633576 −0.0316788 0.999498i \(-0.510085\pi\)
−0.0316788 + 0.999498i \(0.510085\pi\)
\(198\) −0.967449 10.9434i −0.0687536 0.777717i
\(199\) −6.32386 −0.448287 −0.224143 0.974556i \(-0.571958\pi\)
−0.224143 + 0.974556i \(0.571958\pi\)
\(200\) −11.3679 19.6898i −0.803833 1.39228i
\(201\) −4.29414 0.949940i −0.302885 0.0670036i
\(202\) −13.3554 + 23.1323i −0.939684 + 1.62758i
\(203\) 0 0
\(204\) −25.4424 5.62833i −1.78133 0.394062i
\(205\) −7.95305 13.7751i −0.555465 0.962093i
\(206\) 30.0238 2.09186
\(207\) 0.0752570 + 0.851282i 0.00523073 + 0.0591682i
\(208\) 44.8586 3.11038
\(209\) −0.421952 0.730843i −0.0291870 0.0505535i
\(210\) 0 0
\(211\) 5.71291 9.89505i 0.393293 0.681204i −0.599589 0.800308i \(-0.704669\pi\)
0.992882 + 0.119105i \(0.0380025\pi\)
\(212\) −7.48574 + 12.9657i −0.514123 + 0.890487i
\(213\) 0.757388 + 2.39833i 0.0518954 + 0.164331i
\(214\) −2.61237 4.52476i −0.178578 0.309307i
\(215\) 9.92881 0.677139
\(216\) −37.7810 28.9087i −2.57067 1.96699i
\(217\) 0 0
\(218\) −25.2600 43.7516i −1.71082 2.96323i
\(219\) −0.244173 0.773193i −0.0164997 0.0522475i
\(220\) 5.74705 9.95417i 0.387466 0.671110i
\(221\) 4.45051 7.70850i 0.299373 0.518530i
\(222\) 25.4759 27.8275i 1.70983 1.86766i
\(223\) −8.35953 14.4791i −0.559796 0.969595i −0.997513 0.0704822i \(-0.977546\pi\)
0.437717 0.899113i \(-0.355787\pi\)
\(224\) 0 0
\(225\) −6.75492 3.14240i −0.450328 0.209493i
\(226\) 8.65250 0.575555
\(227\) 8.53501 + 14.7831i 0.566489 + 0.981187i 0.996909 + 0.0785588i \(0.0250318\pi\)
−0.430421 + 0.902628i \(0.641635\pi\)
\(228\) −5.68432 1.25747i −0.376453 0.0832783i
\(229\) 9.89471 17.1381i 0.653861 1.13252i −0.328317 0.944567i \(-0.606482\pi\)
0.982178 0.187953i \(-0.0601851\pi\)
\(230\) −0.613500 + 1.06261i −0.0404530 + 0.0700666i
\(231\) 0 0
\(232\) −20.8187 36.0591i −1.36682 2.36740i
\(233\) 5.93159 0.388591 0.194296 0.980943i \(-0.437758\pi\)
0.194296 + 0.980943i \(0.437758\pi\)
\(234\) 21.1933 14.8684i 1.38545 0.971979i
\(235\) −17.6846 −1.15361
\(236\) 12.2875 + 21.2826i 0.799847 + 1.38538i
\(237\) 18.3769 20.0731i 1.19371 1.30389i
\(238\) 0 0
\(239\) −10.0277 + 17.3685i −0.648637 + 1.12347i 0.334812 + 0.942285i \(0.391327\pi\)
−0.983449 + 0.181187i \(0.942006\pi\)
\(240\) −11.6785 36.9808i −0.753842 2.38710i
\(241\) 14.6444 + 25.3648i 0.943326 + 1.63389i 0.759069 + 0.651010i \(0.225654\pi\)
0.184256 + 0.982878i \(0.441012\pi\)
\(242\) 24.9273 1.60239
\(243\) −15.5751 0.644577i −0.999145 0.0413497i
\(244\) 2.06827 0.132408
\(245\) 0 0
\(246\) 14.1995 + 44.9637i 0.905324 + 2.86678i
\(247\) 0.994327 1.72223i 0.0632675 0.109583i
\(248\) −34.0121 + 58.9107i −2.15977 + 3.74083i
\(249\) 16.3586 17.8686i 1.03668 1.13237i
\(250\) −16.1164 27.9144i −1.01929 1.76546i
\(251\) 22.7856 1.43821 0.719106 0.694901i \(-0.244552\pi\)
0.719106 + 0.694901i \(0.244552\pi\)
\(252\) 0 0
\(253\) 0.384215 0.0241554
\(254\) −11.3681 19.6901i −0.713297 1.23547i
\(255\) −7.51342 1.66210i −0.470509 0.104085i
\(256\) −15.7821 + 27.3354i −0.986381 + 1.70846i
\(257\) −12.1444 + 21.0348i −0.757550 + 1.31211i 0.186547 + 0.982446i \(0.440270\pi\)
−0.944097 + 0.329668i \(0.893063\pi\)
\(258\) −28.7385 6.35747i −1.78918 0.395798i
\(259\) 0 0
\(260\) 27.0857 1.67979
\(261\) −12.3707 5.75486i −0.765726 0.356217i
\(262\) −32.5071 −2.00830
\(263\) 4.30578 + 7.45782i 0.265506 + 0.459869i 0.967696 0.252120i \(-0.0811278\pi\)
−0.702190 + 0.711989i \(0.747794\pi\)
\(264\) −14.4422 + 15.7752i −0.888854 + 0.970899i
\(265\) −2.21062 + 3.82890i −0.135797 + 0.235208i
\(266\) 0 0
\(267\) −1.34938 4.27291i −0.0825807 0.261498i
\(268\) 6.82011 + 11.8128i 0.416605 + 0.721581i
\(269\) 15.2312 0.928664 0.464332 0.885661i \(-0.346294\pi\)
0.464332 + 0.885661i \(0.346294\pi\)
\(270\) −17.7748 13.6006i −1.08174 0.827707i
\(271\) 4.67820 0.284181 0.142090 0.989854i \(-0.454618\pi\)
0.142090 + 0.989854i \(0.454618\pi\)
\(272\) 19.7633 + 34.2310i 1.19832 + 2.07556i
\(273\) 0 0
\(274\) 22.4684 38.9164i 1.35737 2.35103i
\(275\) −1.67472 + 2.90069i −0.100989 + 0.174918i
\(276\) 1.78979 1.95500i 0.107733 0.117677i
\(277\) 8.19537 + 14.1948i 0.492412 + 0.852883i 0.999962 0.00873986i \(-0.00278202\pi\)
−0.507550 + 0.861622i \(0.669449\pi\)
\(278\) −21.4560 −1.28685
\(279\) 1.96289 + 22.2035i 0.117515 + 1.32929i
\(280\) 0 0
\(281\) 1.75702 + 3.04325i 0.104815 + 0.181545i 0.913663 0.406473i \(-0.133242\pi\)
−0.808848 + 0.588018i \(0.799908\pi\)
\(282\) 51.1871 + 11.3235i 3.04815 + 0.674305i
\(283\) 13.0354 22.5780i 0.774874 1.34212i −0.159992 0.987118i \(-0.551147\pi\)
0.934865 0.355002i \(-0.115520\pi\)
\(284\) 3.90025 6.75543i 0.231437 0.400861i
\(285\) −1.67864 0.371346i −0.0994341 0.0219966i
\(286\) −5.81958 10.0798i −0.344119 0.596031i
\(287\) 0 0
\(288\) 5.28645 + 59.7985i 0.311507 + 3.52366i
\(289\) −9.15699 −0.538647
\(290\) −9.79455 16.9647i −0.575156 0.996199i
\(291\) −16.9112 + 18.4722i −0.991352 + 1.08286i
\(292\) −1.25740 + 2.17787i −0.0735835 + 0.127450i
\(293\) 9.44192 16.3539i 0.551603 0.955404i −0.446556 0.894756i \(-0.647350\pi\)
0.998159 0.0606487i \(-0.0193169\pi\)
\(294\) 0 0
\(295\) 3.62863 + 6.28497i 0.211267 + 0.365925i
\(296\) −73.4484 −4.26910
\(297\) −0.905298 + 6.94961i −0.0525307 + 0.403257i
\(298\) 37.1119 2.14983
\(299\) 0.452700 + 0.784099i 0.0261803 + 0.0453456i
\(300\) 6.95823 + 22.0338i 0.401733 + 1.27212i
\(301\) 0 0
\(302\) 5.29401 9.16950i 0.304636 0.527645i
\(303\) 11.5060 12.5681i 0.661003 0.722017i
\(304\) 4.41549 + 7.64785i 0.253246 + 0.438634i
\(305\) 0.610783 0.0349734
\(306\) 20.6830 + 9.62176i 1.18237 + 0.550039i
\(307\) 21.6407 1.23510 0.617551 0.786531i \(-0.288125\pi\)
0.617551 + 0.786531i \(0.288125\pi\)
\(308\) 0 0
\(309\) −18.7008 4.13696i −1.06385 0.235343i
\(310\) −16.0016 + 27.7156i −0.908830 + 1.57414i
\(311\) 2.24724 3.89234i 0.127429 0.220714i −0.795251 0.606281i \(-0.792661\pi\)
0.922680 + 0.385567i \(0.125994\pi\)
\(312\) −49.2103 10.8862i −2.78598 0.616309i
\(313\) 4.30102 + 7.44958i 0.243108 + 0.421075i 0.961598 0.274462i \(-0.0884997\pi\)
−0.718490 + 0.695537i \(0.755166\pi\)
\(314\) −0.799206 −0.0451018
\(315\) 0 0
\(316\) −84.4062 −4.74822
\(317\) 4.03128 + 6.98237i 0.226419 + 0.392169i 0.956744 0.290930i \(-0.0939648\pi\)
−0.730325 + 0.683100i \(0.760631\pi\)
\(318\) 8.85019 9.66711i 0.496294 0.542104i
\(319\) −3.06701 + 5.31221i −0.171719 + 0.297427i
\(320\) −20.7053 + 35.8626i −1.15746 + 2.00478i
\(321\) 1.00370 + 3.17828i 0.0560208 + 0.177394i
\(322\) 0 0
\(323\) 1.75228 0.0974992
\(324\) 31.1444 + 36.9798i 1.73025 + 2.05443i
\(325\) −7.89291 −0.437820
\(326\) 14.5383 + 25.1811i 0.805203 + 1.39465i
\(327\) 9.70510 + 30.7319i 0.536693 + 1.69948i
\(328\) 45.8981 79.4978i 2.53430 4.38953i
\(329\) 0 0
\(330\) −6.79458 + 7.42175i −0.374029 + 0.408554i
\(331\) 11.4513 + 19.8342i 0.629419 + 1.09019i 0.987668 + 0.156560i \(0.0500405\pi\)
−0.358249 + 0.933626i \(0.616626\pi\)
\(332\) −75.1361 −4.12363
\(333\) −19.7024 + 13.8225i −1.07969 + 0.757468i
\(334\) −8.68150 −0.475030
\(335\) 2.01405 + 3.48844i 0.110039 + 0.190594i
\(336\) 0 0
\(337\) −6.81891 + 11.8107i −0.371450 + 0.643369i −0.989789 0.142542i \(-0.954472\pi\)
0.618339 + 0.785911i \(0.287806\pi\)
\(338\) −3.93458 + 6.81489i −0.214013 + 0.370681i
\(339\) −5.38935 1.19222i −0.292709 0.0647525i
\(340\) 11.9331 + 20.6688i 0.647164 + 1.12092i
\(341\) 10.0213 0.542683
\(342\) 4.62097 + 2.14968i 0.249873 + 0.116242i
\(343\) 0 0
\(344\) 28.6502 + 49.6237i 1.54472 + 2.67553i
\(345\) 0.528545 0.577332i 0.0284559 0.0310825i
\(346\) 15.5272 26.8938i 0.834746 1.44582i
\(347\) 1.41282 2.44707i 0.0758440 0.131366i −0.825609 0.564243i \(-0.809168\pi\)
0.901453 + 0.432877i \(0.142502\pi\)
\(348\) 12.7430 + 40.3517i 0.683097 + 2.16308i
\(349\) 1.81202 + 3.13851i 0.0969951 + 0.168000i 0.910440 0.413642i \(-0.135744\pi\)
−0.813444 + 0.581643i \(0.802410\pi\)
\(350\) 0 0
\(351\) −15.2493 + 6.34083i −0.813947 + 0.338448i
\(352\) 26.9893 1.43854
\(353\) −1.37701 2.38504i −0.0732907 0.126943i 0.827051 0.562127i \(-0.190017\pi\)
−0.900342 + 0.435184i \(0.856683\pi\)
\(354\) −6.47859 20.5149i −0.344333 1.09036i
\(355\) 1.15179 1.99495i 0.0611304 0.105881i
\(356\) −6.94877 + 12.0356i −0.368284 + 0.637887i
\(357\) 0 0
\(358\) 1.49135 + 2.58310i 0.0788205 + 0.136521i
\(359\) −16.8015 −0.886750 −0.443375 0.896336i \(-0.646219\pi\)
−0.443375 + 0.896336i \(0.646219\pi\)
\(360\) 3.83696 + 43.4024i 0.202226 + 2.28750i
\(361\) −18.6085 −0.979395
\(362\) −4.33081 7.50119i −0.227622 0.394254i
\(363\) −15.5264 3.43471i −0.814922 0.180276i
\(364\) 0 0
\(365\) −0.371322 + 0.643149i −0.0194359 + 0.0336640i
\(366\) −1.76788 0.391087i −0.0924087 0.0204425i
\(367\) −11.9670 20.7274i −0.624670 1.08196i −0.988605 0.150536i \(-0.951900\pi\)
0.363934 0.931425i \(-0.381433\pi\)
\(368\) −4.02059 −0.209588
\(369\) −2.64885 29.9629i −0.137894 1.55981i
\(370\) −34.5551 −1.79644
\(371\) 0 0
\(372\) 46.6822 50.9912i 2.42036 2.64377i
\(373\) 9.58030 16.5936i 0.496049 0.859182i −0.503941 0.863738i \(-0.668117\pi\)
0.999990 + 0.00455622i \(0.00145030\pi\)
\(374\) 5.12784 8.88168i 0.265154 0.459261i
\(375\) 6.19206 + 19.6076i 0.319757 + 1.01253i
\(376\) −51.0299 88.3865i −2.63167 4.55818i
\(377\) −14.4548 −0.744458
\(378\) 0 0
\(379\) 10.0770 0.517622 0.258811 0.965928i \(-0.416669\pi\)
0.258811 + 0.965928i \(0.416669\pi\)
\(380\) 2.66608 + 4.61779i 0.136767 + 0.236888i
\(381\) 4.36771 + 13.8307i 0.223765 + 0.708568i
\(382\) 5.25127 9.09546i 0.268678 0.465364i
\(383\) −10.0718 + 17.4448i −0.514643 + 0.891388i 0.485213 + 0.874396i \(0.338742\pi\)
−0.999856 + 0.0169915i \(0.994591\pi\)
\(384\) 36.0855 39.4164i 1.84148 2.01146i
\(385\) 0 0
\(386\) 11.2294 0.571561
\(387\) 17.0242 + 7.91970i 0.865390 + 0.402581i
\(388\) 77.6743 3.94332
\(389\) −6.69736 11.6002i −0.339570 0.588152i 0.644782 0.764366i \(-0.276948\pi\)
−0.984352 + 0.176215i \(0.943615\pi\)
\(390\) −23.1519 5.12161i −1.17234 0.259343i
\(391\) −0.398891 + 0.690899i −0.0201728 + 0.0349402i
\(392\) 0 0
\(393\) 20.2476 + 4.47913i 1.02136 + 0.225942i
\(394\) −1.20724 2.09100i −0.0608198 0.105343i
\(395\) −24.9261 −1.25417
\(396\) 17.7940 12.4836i 0.894181 0.627324i
\(397\) 18.0133 0.904061 0.452031 0.892002i \(-0.350700\pi\)
0.452031 + 0.892002i \(0.350700\pi\)
\(398\) −8.58506 14.8698i −0.430330 0.745354i
\(399\) 0 0
\(400\) 17.5249 30.3541i 0.876247 1.51770i
\(401\) −14.4337 + 25.0000i −0.720787 + 1.24844i 0.239898 + 0.970798i \(0.422886\pi\)
−0.960685 + 0.277642i \(0.910447\pi\)
\(402\) −3.59591 11.3867i −0.179348 0.567918i
\(403\) 11.8075 + 20.4513i 0.588176 + 1.01875i
\(404\) −52.8479 −2.62928
\(405\) 9.19729 + 10.9205i 0.457017 + 0.542646i
\(406\) 0 0
\(407\) 5.41019 + 9.37073i 0.268173 + 0.464490i
\(408\) −13.3734 42.3478i −0.662080 2.09653i
\(409\) −5.42937 + 9.40395i −0.268465 + 0.464995i −0.968466 0.249147i \(-0.919850\pi\)
0.700000 + 0.714142i \(0.253183\pi\)
\(410\) 21.5936 37.4012i 1.06643 1.84711i
\(411\) −19.3571 + 21.1438i −0.954814 + 1.04295i
\(412\) 29.7014 + 51.4443i 1.46328 + 2.53448i
\(413\) 0 0
\(414\) −1.89951 + 1.33263i −0.0933561 + 0.0654951i
\(415\) −22.1885 −1.08919
\(416\) 31.8001 + 55.0793i 1.55913 + 2.70049i
\(417\) 13.3642 + 2.95641i 0.654449 + 0.144776i
\(418\) 1.14566 1.98434i 0.0560359 0.0970570i
\(419\) 0.247572 0.428807i 0.0120947 0.0209486i −0.859915 0.510438i \(-0.829483\pi\)
0.872009 + 0.489489i \(0.162817\pi\)
\(420\) 0 0
\(421\) 9.50320 + 16.4600i 0.463158 + 0.802212i 0.999116 0.0420318i \(-0.0133831\pi\)
−0.535959 + 0.844244i \(0.680050\pi\)
\(422\) 31.0226 1.51016
\(423\) −30.3224 14.1061i −1.47433 0.685860i
\(424\) −25.5155 −1.23914
\(425\) −3.47737 6.02298i −0.168677 0.292157i
\(426\) −4.61116 + 5.03679i −0.223411 + 0.244033i
\(427\) 0 0
\(428\) 5.16864 8.95234i 0.249835 0.432728i
\(429\) 2.23593 + 7.08024i 0.107952 + 0.341837i
\(430\) 13.4790 + 23.3464i 0.650016 + 1.12586i
\(431\) −16.9215 −0.815078 −0.407539 0.913188i \(-0.633613\pi\)
−0.407539 + 0.913188i \(0.633613\pi\)
\(432\) 9.47342 72.7236i 0.455790 3.49892i
\(433\) 33.4740 1.60866 0.804330 0.594183i \(-0.202524\pi\)
0.804330 + 0.594183i \(0.202524\pi\)
\(434\) 0 0
\(435\) 3.76315 + 11.9163i 0.180429 + 0.571343i
\(436\) 49.9774 86.5634i 2.39348 4.14564i
\(437\) −0.0891197 + 0.154360i −0.00426317 + 0.00738403i
\(438\) 1.48658 1.62380i 0.0710318 0.0775883i
\(439\) 10.4657 + 18.1272i 0.499502 + 0.865163i 1.00000 0.000574559i \(-0.000182888\pi\)
−0.500498 + 0.865738i \(0.666850\pi\)
\(440\) 19.5891 0.933874
\(441\) 0 0
\(442\) 24.1674 1.14953
\(443\) 15.4290 + 26.7238i 0.733054 + 1.26969i 0.955572 + 0.294759i \(0.0952393\pi\)
−0.222517 + 0.974929i \(0.571427\pi\)
\(444\) 72.8833 + 16.1231i 3.45889 + 0.765169i
\(445\) −2.05205 + 3.55425i −0.0972763 + 0.168487i
\(446\) 22.6972 39.3128i 1.07475 1.86151i
\(447\) −23.1157 5.11362i −1.09334 0.241866i
\(448\) 0 0
\(449\) −33.2789 −1.57053 −0.785263 0.619162i \(-0.787472\pi\)
−0.785263 + 0.619162i \(0.787472\pi\)
\(450\) −1.78129 20.1493i −0.0839709 0.949849i
\(451\) −13.5234 −0.636791
\(452\) 8.55957 + 14.8256i 0.402608 + 0.697338i
\(453\) −4.56092 + 4.98191i −0.214291 + 0.234071i
\(454\) −23.1737 + 40.1380i −1.08760 + 1.88377i
\(455\) 0 0
\(456\) −2.98786 9.46130i −0.139919 0.443066i
\(457\) −11.8952 20.6031i −0.556434 0.963772i −0.997790 0.0664402i \(-0.978836\pi\)
0.441356 0.897332i \(-0.354498\pi\)
\(458\) 53.7309 2.51068
\(459\) −11.5570 8.84296i −0.539432 0.412754i
\(460\) −2.42764 −0.113189
\(461\) −8.53122 14.7765i −0.397339 0.688211i 0.596058 0.802941i \(-0.296733\pi\)
−0.993397 + 0.114731i \(0.963400\pi\)
\(462\) 0 0
\(463\) 18.1243 31.3922i 0.842306 1.45892i −0.0456338 0.998958i \(-0.514531\pi\)
0.887940 0.459959i \(-0.152136\pi\)
\(464\) 32.0945 55.5893i 1.48995 2.58067i
\(465\) 13.7858 15.0583i 0.639300 0.698310i
\(466\) 8.05253 + 13.9474i 0.373026 + 0.646100i
\(467\) 8.19160 0.379062 0.189531 0.981875i \(-0.439303\pi\)
0.189531 + 0.981875i \(0.439303\pi\)
\(468\) 46.4420 + 21.6049i 2.14678 + 0.998686i
\(469\) 0 0
\(470\) −24.0080 41.5830i −1.10740 1.91808i
\(471\) 0.497798 + 0.110122i 0.0229373 + 0.00507415i
\(472\) −20.9413 + 36.2714i −0.963900 + 1.66952i
\(473\) 4.22074 7.31054i 0.194070 0.336139i
\(474\) 72.1472 + 15.9603i 3.31383 + 0.733079i
\(475\) −0.776909 1.34565i −0.0356470 0.0617425i
\(476\) 0 0
\(477\) −6.84451 + 4.80185i −0.313389 + 0.219862i
\(478\) −54.4530 −2.49062
\(479\) −12.7775 22.1312i −0.583817 1.01120i −0.995022 0.0996574i \(-0.968225\pi\)
0.411205 0.911543i \(-0.365108\pi\)
\(480\) 37.1278 40.5549i 1.69464 1.85107i
\(481\) −12.7491 + 22.0820i −0.581308 + 1.00685i
\(482\) −39.7614 + 68.8687i −1.81108 + 3.13688i
\(483\) 0 0
\(484\) 24.6596 + 42.7116i 1.12089 + 1.94144i
\(485\) 22.9381 1.04156
\(486\) −19.6286 37.4980i −0.890372 1.70094i
\(487\) −6.92281 −0.313702 −0.156851 0.987622i \(-0.550134\pi\)
−0.156851 + 0.987622i \(0.550134\pi\)
\(488\) 1.76246 + 3.05266i 0.0797826 + 0.138188i
\(489\) −5.58574 17.6877i −0.252596 0.799865i
\(490\) 0 0
\(491\) 18.7262 32.4348i 0.845103 1.46376i −0.0404294 0.999182i \(-0.512873\pi\)
0.885532 0.464578i \(-0.153794\pi\)
\(492\) −62.9960 + 68.8108i −2.84008 + 3.10223i
\(493\) −6.36831 11.0302i −0.286814 0.496777i
\(494\) 5.39946 0.242933
\(495\) 5.25475 3.68654i 0.236183 0.165698i
\(496\) −104.867 −4.70867
\(497\) 0 0
\(498\) 64.2235 + 14.2074i 2.87793 + 0.636649i
\(499\) −12.8125 + 22.1919i −0.573566 + 0.993446i 0.422630 + 0.906302i \(0.361107\pi\)
−0.996196 + 0.0871432i \(0.972226\pi\)
\(500\) 31.8867 55.2293i 1.42601 2.46993i
\(501\) 5.40741 + 1.19622i 0.241585 + 0.0534430i
\(502\) 30.9329 + 53.5774i 1.38060 + 2.39127i
\(503\) 5.79692 0.258472 0.129236 0.991614i \(-0.458748\pi\)
0.129236 + 0.991614i \(0.458748\pi\)
\(504\) 0 0
\(505\) −15.6066 −0.694483
\(506\) 0.521598 + 0.903434i 0.0231878 + 0.0401625i
\(507\) 3.38974 3.70262i 0.150543 0.164439i
\(508\) 22.4920 38.9573i 0.997921 1.72845i
\(509\) 12.5697 21.7714i 0.557144 0.965002i −0.440589 0.897709i \(-0.645230\pi\)
0.997733 0.0672931i \(-0.0214363\pi\)
\(510\) −6.29174 19.9233i −0.278603 0.882218i
\(511\) 0 0
\(512\) −23.9940 −1.06039
\(513\) −2.58204 1.97568i −0.114000 0.0872286i
\(514\) −65.9475 −2.90882
\(515\) 8.77113 + 15.1920i 0.386502 + 0.669441i
\(516\) −17.5366 55.5311i −0.772007 2.44462i
\(517\) −7.51771 + 13.0211i −0.330629 + 0.572665i
\(518\) 0 0
\(519\) −13.3770 + 14.6118i −0.587186 + 0.641386i
\(520\) 23.0808 + 39.9771i 1.01216 + 1.75311i
\(521\) −7.29656 −0.319668 −0.159834 0.987144i \(-0.551096\pi\)
−0.159834 + 0.987144i \(0.551096\pi\)
\(522\) −3.26218 36.9007i −0.142782 1.61510i
\(523\) −16.7727 −0.733421 −0.366710 0.930335i \(-0.619516\pi\)
−0.366710 + 0.930335i \(0.619516\pi\)
\(524\) −32.1580 55.6993i −1.40483 2.43324i
\(525\) 0 0
\(526\) −11.6908 + 20.2490i −0.509741 + 0.882898i
\(527\) −10.4041 + 18.0204i −0.453208 + 0.784979i
\(528\) −32.1933 7.12174i −1.40103 0.309934i
\(529\) 11.4594 + 19.8483i 0.498236 + 0.862970i
\(530\) −12.0042 −0.521431
\(531\) 1.20855 + 13.6707i 0.0524468 + 0.593260i
\(532\) 0 0
\(533\) −15.9339 27.5982i −0.690172 1.19541i
\(534\) 8.21535 8.97366i 0.355513 0.388328i
\(535\) 1.52635 2.64372i 0.0659900 0.114298i
\(536\) −11.6234 + 20.1322i −0.502053 + 0.869581i
\(537\) −0.572991 1.81442i −0.0247264 0.0782980i
\(538\) 20.6774 + 35.8143i 0.891466 + 1.54406i
\(539\) 0 0
\(540\) 5.72007 43.9107i 0.246153 1.88962i
\(541\) −5.29816 −0.227786 −0.113893 0.993493i \(-0.536332\pi\)
−0.113893 + 0.993493i \(0.536332\pi\)
\(542\) 6.35097 + 11.0002i 0.272798 + 0.472499i
\(543\) 1.66393 + 5.26898i 0.0714062 + 0.226113i
\(544\) −28.0202 + 48.5324i −1.20136 + 2.08081i
\(545\) 14.7589 25.5631i 0.632200 1.09500i
\(546\) 0 0
\(547\) 16.4325 + 28.4619i 0.702603 + 1.21694i 0.967550 + 0.252681i \(0.0813123\pi\)
−0.264947 + 0.964263i \(0.585354\pi\)
\(548\) 88.9084 3.79798
\(549\) 1.04727 + 0.487190i 0.0446962 + 0.0207928i
\(550\) −9.09416 −0.387776
\(551\) −1.42280 2.46436i −0.0606133 0.104985i
\(552\) 4.41062 + 0.975709i 0.187729 + 0.0415290i
\(553\) 0 0
\(554\) −22.2515 + 38.5408i −0.945376 + 1.63744i
\(555\) 21.5232 + 4.76132i 0.913610 + 0.202107i
\(556\) −21.2256 36.7638i −0.900166 1.55913i
\(557\) −18.8160 −0.797258 −0.398629 0.917112i \(-0.630514\pi\)
−0.398629 + 0.917112i \(0.630514\pi\)
\(558\) −49.5441 + 34.7583i −2.09737 + 1.47144i
\(559\) 19.8923 0.841354
\(560\) 0 0
\(561\) −4.41776 + 4.82554i −0.186518 + 0.203734i
\(562\) −4.77054 + 8.26282i −0.201233 + 0.348546i
\(563\) 13.8325 23.9586i 0.582970 1.00973i −0.412155 0.911114i \(-0.635224\pi\)
0.995125 0.0986197i \(-0.0314427\pi\)
\(564\) 31.2351 + 98.9083i 1.31523 + 4.16479i
\(565\) 2.52773 + 4.37816i 0.106343 + 0.184191i
\(566\) 70.7856 2.97534
\(567\) 0 0
\(568\) 13.2942 0.557812
\(569\) 20.0916 + 34.7996i 0.842282 + 1.45888i 0.887961 + 0.459920i \(0.152122\pi\)
−0.0456782 + 0.998956i \(0.514545\pi\)
\(570\) −1.40569 4.45124i −0.0588780 0.186442i
\(571\) 3.40565 5.89875i 0.142522 0.246855i −0.785924 0.618323i \(-0.787812\pi\)
0.928446 + 0.371468i \(0.121146\pi\)
\(572\) 11.5142 19.9431i 0.481431 0.833863i
\(573\) −4.52409 + 4.94169i −0.188997 + 0.206442i
\(574\) 0 0
\(575\) 0.707427 0.0295017
\(576\) −64.1075 + 44.9755i −2.67115 + 1.87398i
\(577\) 36.4222 1.51628 0.758138 0.652094i \(-0.226109\pi\)
0.758138 + 0.652094i \(0.226109\pi\)
\(578\) −12.4312 21.5315i −0.517071 0.895593i
\(579\) −6.99441 1.54729i −0.290678 0.0643031i
\(580\) 19.3787 33.5649i 0.804658 1.39371i
\(581\) 0 0
\(582\) −66.3930 14.6873i −2.75208 0.608810i
\(583\) 1.87947 + 3.25534i 0.0778397 + 0.134822i
\(584\) −4.28590 −0.177352
\(585\) 13.7148 + 6.38015i 0.567037 + 0.263787i
\(586\) 51.2721 2.11803
\(587\) −5.57943 9.66385i −0.230288 0.398870i 0.727605 0.685996i \(-0.240633\pi\)
−0.957893 + 0.287126i \(0.907300\pi\)
\(588\) 0 0
\(589\) −2.32446 + 4.02609i −0.0957779 + 0.165892i
\(590\) −9.85220 + 17.0645i −0.405609 + 0.702535i
\(591\) 0.463831 + 1.46876i 0.0190795 + 0.0604166i
\(592\) −56.6145 98.0593i −2.32684 4.03021i
\(593\) −19.8085 −0.813439 −0.406720 0.913553i \(-0.633327\pi\)
−0.406720 + 0.913553i \(0.633327\pi\)
\(594\) −17.5701 + 7.30586i −0.720911 + 0.299763i
\(595\) 0 0
\(596\) 36.7133 + 63.5893i 1.50384 + 2.60472i
\(597\) 3.29845 + 10.4448i 0.134997 + 0.427477i
\(598\) −1.22914 + 2.12893i −0.0502633 + 0.0870586i
\(599\) 9.06600 15.7028i 0.370427 0.641598i −0.619204 0.785230i \(-0.712545\pi\)
0.989631 + 0.143632i \(0.0458781\pi\)
\(600\) −26.5913 + 29.0458i −1.08558 + 1.18579i
\(601\) 12.3285 + 21.3536i 0.502889 + 0.871030i 0.999994 + 0.00333942i \(0.00106297\pi\)
−0.497105 + 0.867690i \(0.665604\pi\)
\(602\) 0 0
\(603\) 0.670802 + 7.58788i 0.0273172 + 0.309003i
\(604\) 20.9486 0.852387
\(605\) 7.28223 + 12.6132i 0.296065 + 0.512799i
\(606\) 45.1724 + 9.99295i 1.83500 + 0.405936i
\(607\) 8.63876 14.9628i 0.350637 0.607320i −0.635725 0.771916i \(-0.719299\pi\)
0.986361 + 0.164596i \(0.0526319\pi\)
\(608\) −6.26024 + 10.8431i −0.253886 + 0.439744i
\(609\) 0 0
\(610\) 0.829179 + 1.43618i 0.0335725 + 0.0581492i
\(611\) −35.4308 −1.43338
\(612\) 3.97445 + 44.9577i 0.160658 + 1.81731i
\(613\) 19.5566 0.789882 0.394941 0.918707i \(-0.370765\pi\)
0.394941 + 0.918707i \(0.370765\pi\)
\(614\) 29.3787 + 50.8855i 1.18563 + 2.05357i
\(615\) −18.6034 + 20.3206i −0.750161 + 0.819404i
\(616\) 0 0
\(617\) 10.8723 18.8314i 0.437702 0.758122i −0.559810 0.828621i \(-0.689126\pi\)
0.997512 + 0.0704988i \(0.0224591\pi\)
\(618\) −15.6601 49.5888i −0.629940 1.99475i
\(619\) 16.9024 + 29.2758i 0.679366 + 1.17670i 0.975172 + 0.221448i \(0.0710782\pi\)
−0.295807 + 0.955248i \(0.595588\pi\)
\(620\) −63.3190 −2.54295
\(621\) 1.36677 0.568317i 0.0548464 0.0228058i
\(622\) 12.2031 0.489300
\(623\) 0 0
\(624\) −23.3977 74.0906i −0.936658 2.96600i
\(625\) 3.20808 5.55655i 0.128323 0.222262i
\(626\) −11.6778 + 20.2266i −0.466740 + 0.808418i
\(627\) −0.987011 + 1.07812i −0.0394174 + 0.0430558i
\(628\) −0.790623 1.36940i −0.0315493 0.0546450i
\(629\) −22.4674 −0.895832
\(630\) 0 0
\(631\) −23.6410 −0.941134 −0.470567 0.882364i \(-0.655951\pi\)
−0.470567 + 0.882364i \(0.655951\pi\)
\(632\) −71.9258 124.579i −2.86105 4.95549i
\(633\) −19.3229 4.27458i −0.768018 0.169899i
\(634\) −10.9454 + 18.9581i −0.434699 + 0.752921i
\(635\) 6.64213 11.5045i 0.263585 0.456542i
\(636\) 25.3192 + 5.60107i 1.00397 + 0.222097i
\(637\) 0 0
\(638\) −16.6547 −0.659365
\(639\) 3.56615 2.50188i 0.141075 0.0989728i
\(640\) −48.9458 −1.93475
\(641\) −7.95901 13.7854i −0.314362 0.544491i 0.664940 0.746897i \(-0.268457\pi\)
−0.979302 + 0.202406i \(0.935124\pi\)
\(642\) −6.11074 + 6.67479i −0.241172 + 0.263433i
\(643\) 13.2527 22.9544i 0.522636 0.905231i −0.477017 0.878894i \(-0.658282\pi\)
0.999653 0.0263376i \(-0.00838450\pi\)
\(644\) 0 0
\(645\) −5.17875 16.3989i −0.203913 0.645707i
\(646\) 2.37883 + 4.12026i 0.0935938 + 0.162109i
\(647\) −0.0160392 −0.000630565 −0.000315282 1.00000i \(-0.500100\pi\)
−0.000315282 1.00000i \(0.500100\pi\)
\(648\) −28.0408 + 77.4794i −1.10155 + 3.04368i
\(649\) 6.17012 0.242198
\(650\) −10.7152 18.5592i −0.420283 0.727951i
\(651\) 0 0
\(652\) −28.7644 + 49.8214i −1.12650 + 1.95115i
\(653\) 16.6440 28.8282i 0.651328 1.12813i −0.331473 0.943465i \(-0.607545\pi\)
0.982801 0.184669i \(-0.0591212\pi\)
\(654\) −59.0870 + 64.5410i −2.31048 + 2.52375i
\(655\) −9.49661 16.4486i −0.371063 0.642700i
\(656\) 141.514 5.52520
\(657\) −1.14969 + 0.806577i −0.0448535 + 0.0314676i
\(658\) 0 0
\(659\) 19.4156 + 33.6288i 0.756324 + 1.30999i 0.944713 + 0.327897i \(0.106340\pi\)
−0.188389 + 0.982094i \(0.560327\pi\)
\(660\) −19.4384 4.30012i −0.756639 0.167382i
\(661\) 2.65322 4.59551i 0.103198 0.178745i −0.809802 0.586703i \(-0.800426\pi\)
0.913001 + 0.407958i \(0.133759\pi\)
\(662\) −31.0917 + 53.8525i −1.20842 + 2.09304i
\(663\) −15.0531 3.33001i −0.584613 0.129327i
\(664\) −64.0264 110.897i −2.48471 4.30364i
\(665\) 0 0
\(666\) −59.2492 27.5628i −2.29586 1.06804i
\(667\) 1.29555 0.0501640
\(668\) −8.58826 14.8753i −0.332290 0.575543i
\(669\) −19.5542 + 21.3592i −0.756010 + 0.825793i
\(670\) −5.46842 + 9.47158i −0.211263 + 0.365919i
\(671\) 0.259644 0.449717i 0.0100235 0.0173611i
\(672\) 0 0
\(673\) −3.03565 5.25789i −0.117016 0.202677i 0.801568 0.597903i \(-0.203999\pi\)
−0.918584 + 0.395227i \(0.870666\pi\)
\(674\) −37.0285 −1.42628
\(675\) −1.66686 + 12.7958i −0.0641574 + 0.492510i
\(676\) −15.5693 −0.598819
\(677\) −17.3925 30.1247i −0.668449 1.15779i −0.978338 0.207014i \(-0.933625\pi\)
0.309889 0.950773i \(-0.399708\pi\)
\(678\) −4.51304 14.2909i −0.173322 0.548838i
\(679\) 0 0
\(680\) −20.3373 + 35.2253i −0.779901 + 1.35083i
\(681\) 19.9647 21.8075i 0.765049 0.835666i
\(682\) 13.6046 + 23.5638i 0.520946 + 0.902305i
\(683\) 19.4241 0.743243 0.371622 0.928384i \(-0.378802\pi\)
0.371622 + 0.928384i \(0.378802\pi\)
\(684\) 0.887968 + 10.0444i 0.0339523 + 0.384057i
\(685\) 26.2556 1.00318
\(686\) 0 0
\(687\) −33.4672 7.40354i −1.27685 0.282463i
\(688\) −44.1676 + 76.5006i −1.68387 + 2.91656i
\(689\) −4.42895 + 7.67117i −0.168730 + 0.292248i
\(690\) 2.07506 + 0.459040i 0.0789961 + 0.0174754i
\(691\) −3.31837 5.74759i −0.126237 0.218649i 0.795979 0.605324i \(-0.206957\pi\)
−0.922216 + 0.386676i \(0.873623\pi\)
\(692\) 61.4416 2.33566
\(693\) 0 0
\(694\) 7.67197 0.291224
\(695\) −6.26814 10.8567i −0.237764 0.411820i
\(696\) −48.6982 + 53.1933i −1.84590 + 2.01629i
\(697\) 14.0399 24.3178i 0.531799 0.921103i
\(698\) −4.91987 + 8.52147i −0.186220 + 0.322542i
\(699\) −3.09385 9.79690i −0.117020 0.370553i
\(700\) 0 0
\(701\) −13.9153 −0.525574 −0.262787 0.964854i \(-0.584642\pi\)
−0.262787 + 0.964854i \(0.584642\pi\)
\(702\) −35.6116 27.2487i −1.34407 1.02844i
\(703\) −5.01963 −0.189319
\(704\) 17.6036 + 30.4904i 0.663462 + 1.14915i
\(705\) 9.22406 + 29.2087i 0.347398 + 1.10006i
\(706\) 3.73876 6.47571i 0.140710 0.243717i
\(707\) 0 0
\(708\) 28.7423 31.3954i 1.08020 1.17991i
\(709\) −17.0778 29.5796i −0.641370 1.11089i −0.985127 0.171827i \(-0.945033\pi\)
0.343757 0.939059i \(-0.388300\pi\)
\(710\) 6.25450 0.234727
\(711\) −42.7389 19.8822i −1.60283 0.745642i
\(712\) −23.6852 −0.887642
\(713\) −1.05829 1.83301i −0.0396332 0.0686467i
\(714\) 0 0
\(715\) 3.40025 5.88941i 0.127162 0.220251i
\(716\) −2.95068 + 5.11072i −0.110272 + 0.190997i
\(717\) 33.9169 + 7.50303i 1.26665 + 0.280206i
\(718\) −22.8092 39.5066i −0.851231 1.47437i
\(719\) 44.2900 1.65174 0.825870 0.563861i \(-0.190684\pi\)
0.825870 + 0.563861i \(0.190684\pi\)
\(720\) −54.9879 + 38.5775i −2.04928 + 1.43770i
\(721\) 0 0
\(722\) −25.2623 43.7556i −0.940165 1.62841i
\(723\) 34.2554 37.4173i 1.27397 1.39156i
\(724\) 8.56860 14.8413i 0.318450 0.551571i
\(725\) −5.64705 + 9.78099i −0.209726 + 0.363257i
\(726\) −13.0018 41.1711i −0.482541 1.52800i
\(727\) −14.1247 24.4647i −0.523857 0.907346i −0.999614 0.0277700i \(-0.991159\pi\)
0.475758 0.879576i \(-0.342174\pi\)
\(728\) 0 0
\(729\) 7.05919 + 26.0608i 0.261451 + 0.965217i
\(730\) −2.01638 −0.0746295
\(731\) 8.76391 + 15.1795i 0.324145 + 0.561435i
\(732\) −1.07879 3.41606i −0.0398731 0.126261i
\(733\) −12.5084 + 21.6653i −0.462010 + 0.800225i −0.999061 0.0433249i \(-0.986205\pi\)
0.537051 + 0.843550i \(0.319538\pi\)
\(734\) 32.4919 56.2776i 1.19930 2.07724i
\(735\) 0 0
\(736\) −2.85018 4.93666i −0.105059 0.181968i
\(737\) 3.42470 0.126150
\(738\) 66.8579 46.9050i 2.46107 1.72660i
\(739\) 32.0230 1.17798 0.588992 0.808139i \(-0.299525\pi\)
0.588992 + 0.808139i \(0.299525\pi\)
\(740\) −34.1840 59.2084i −1.25663 2.17655i
\(741\) −3.36314 0.743987i −0.123548 0.0273311i
\(742\) 0 0
\(743\) 19.4031 33.6072i 0.711833 1.23293i −0.252336 0.967640i \(-0.581199\pi\)
0.964169 0.265290i \(-0.0854678\pi\)
\(744\) 115.040 + 25.4489i 4.21757 + 0.933003i
\(745\) 10.8418 + 18.7786i 0.397214 + 0.687995i
\(746\) 52.0236 1.90472
\(747\) −38.0450 17.6986i −1.39200 0.647559i
\(748\) 20.2911 0.741915
\(749\) 0 0
\(750\) −37.6987 + 41.1785i −1.37656 + 1.50363i
\(751\) −10.8495 + 18.7920i −0.395905 + 0.685728i −0.993216 0.116282i \(-0.962903\pi\)
0.597311 + 0.802010i \(0.296236\pi\)
\(752\) 78.6685 136.258i 2.86874 4.96881i
\(753\) −11.8847 37.6337i −0.433102 1.37145i
\(754\) −19.6233 33.9885i −0.714638 1.23779i
\(755\) 6.18635 0.225144
\(756\) 0 0
\(757\) 33.5242 1.21846 0.609229 0.792995i \(-0.291479\pi\)
0.609229 + 0.792995i \(0.291479\pi\)
\(758\) 13.6802 + 23.6949i 0.496889 + 0.860637i
\(759\) −0.200402 0.634589i −0.00727414 0.0230341i
\(760\) −4.54374 + 7.86999i −0.164819 + 0.285475i
\(761\) −6.66048 + 11.5363i −0.241442 + 0.418190i −0.961125 0.276113i \(-0.910954\pi\)
0.719683 + 0.694303i \(0.244287\pi\)
\(762\) −26.5917 + 29.0462i −0.963315 + 1.05223i
\(763\) 0 0
\(764\) 20.7795 0.751775
\(765\) 1.17370 + 13.2765i 0.0424352 + 0.480012i
\(766\) −54.6923 −1.97611
\(767\) 7.26992 + 12.5919i 0.262502 + 0.454666i
\(768\) 53.3802 + 11.8087i 1.92619 + 0.426109i
\(769\) −27.3568 + 47.3833i −0.986510 + 1.70869i −0.351488 + 0.936192i \(0.614324\pi\)
−0.635022 + 0.772494i \(0.719009\pi\)
\(770\) 0 0
\(771\) 41.0765 + 9.08686i 1.47933 + 0.327255i
\(772\) 11.1088 + 19.2410i 0.399814 + 0.692498i
\(773\) −2.36042 −0.0848983 −0.0424491 0.999099i \(-0.513516\pi\)
−0.0424491 + 0.999099i \(0.513516\pi\)
\(774\) 4.48934 + 50.7818i 0.161366 + 1.82532i
\(775\) 18.4515 0.662796
\(776\) 66.1892 + 114.643i 2.37606 + 4.11545i
\(777\) 0 0
\(778\) 18.1842 31.4960i 0.651936 1.12919i
\(779\) 3.13678 5.43306i 0.112387 0.194660i
\(780\) −14.1276 44.7361i −0.505849 1.60181i
\(781\) −0.979248 1.69611i −0.0350403 0.0606915i
\(782\) −2.16608 −0.0774589
\(783\) −3.05261 + 23.4337i −0.109092 + 0.837452i
\(784\)