Properties

Label 441.2.f.h.148.12
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 148.12
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.h.295.12

$q$-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 −0.632343 0.774688i \(-0.717907\pi\)
0.987071 + 0.160281i \(0.0512400\pi\)
\(6\) −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 −0.556991 0.830518i \(-0.688044\pi\)
0.997746 + 0.0671096i \(0.0213777\pi\)
\(14\) 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 \(-0.389703\pi\)
0.339615 + 0.940565i \(0.389703\pi\)
\(18\) −7.38536 3.43568i −1.74075 0.809799i
\(19\) 0.625693 0.143544 0.0717719 0.997421i \(-0.477135\pi\)
0.0717719 + 0.997421i \(0.477135\pi\)
\(20\) 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 \(0.399190\pi\)
−0.978673 + 0.205423i \(0.934143\pi\)
\(32\) 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 \(-0.547050\pi\)
0.930219 0.367004i \(-0.119616\pi\)
\(42\) 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 \(-0.864485\pi\)
0.0977106 0.995215i \(-0.468848\pi\)
\(48\) 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 −0.975629 0.219425i \(-0.929582\pi\)
0.677842 + 0.735207i \(0.262915\pi\)
\(60\) −9.96715 + 10.8872i −1.28675 + 1.40553i
\(61\) 0.192507 + 0.333432i 0.0246480 + 0.0426916i 0.878086 0.478502i \(-0.158820\pi\)
−0.853438 + 0.521194i \(0.825487\pi\)
\(62\) −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 \(-0.508721\pi\)
−0.0273955 + 0.999625i \(0.508721\pi\)
\(74\) 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 \(-0.888106\pi\)
0.171225 0.985232i \(-0.445228\pi\)
\(84\) 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 \(-0.543783\pi\)
−0.137114 + 0.990555i \(0.543783\pi\)
\(90\) −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 \(0.0957089\pi\)
−0.221079 + 0.975256i \(0.570958\pi\)
\(98\) 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 0.510479 0.859890i \(-0.329468\pi\)
−0.999926 + 0.0121430i \(0.996135\pi\)
\(102\) −8.89326 + 9.71414i −0.880564 + 0.961844i
\(103\) −5.52897 + 9.57646i −0.544786 + 0.943597i 0.453834 + 0.891086i \(0.350056\pi\)
−0.998620 + 0.0525110i \(0.983278\pi\)
\(104\) −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 \(-0.658137\pi\)
0.999641 0.0267937i \(-0.00852971\pi\)
\(132\) −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 −0.648375 0.761321i \(-0.724551\pi\)
0.983511 + 0.180849i \(0.0578845\pi\)
\(140\) 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 −0.860093 0.510138i \(-0.829594\pi\)
0.871839 + 0.489793i \(0.162928\pi\)
\(158\) −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 −0.797516 0.603298i \(-0.793853\pi\)
0.921229 + 0.389020i \(0.127186\pi\)
\(168\) 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 0.997278 0.0737284i \(-0.0234898\pi\)
−0.562490 + 0.826804i \(0.690156\pi\)
\(174\) −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 \(-0.462172\pi\)
0.118560 + 0.992947i \(0.462172\pi\)
\(182\) 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 \(-0.428042\pi\)
0.224143 + 0.974556i \(0.428042\pi\)
\(200\) −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 \(0.0224538\pi\)
−0.437717 + 0.899113i \(0.644213\pi\)
\(224\) 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 \(-0.974968\pi\)
0.430421 0.902628i \(-0.358365\pi\)
\(228\) −5.68432 1.25747i −0.376453 0.0832783i
\(229\) −9.89471 + 17.1381i −0.653861 + 1.13252i 0.328317 + 0.944567i \(0.393518\pi\)
−0.982178 + 0.187953i \(0.939815\pi\)
\(230\) 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 \(-0.774346\pi\)
−0.184256 0.982878i \(-0.558988\pi\)
\(242\) 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 \(-0.755448\pi\)
−0.719106 + 0.694901i \(0.755448\pi\)
\(252\) 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 \(-0.559730\pi\)
0.944097 0.329668i \(-0.106937\pi\)
\(258\) 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 \(-0.653706\pi\)
−0.464332 + 0.885661i \(0.653706\pi\)
\(270\) −17.7748 13.6006i −1.08174 0.827707i
\(271\) −4.67820 −0.284181 −0.142090 0.989854i \(-0.545382\pi\)
−0.142090 + 0.989854i \(0.545382\pi\)
\(272\) −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 \(0.448853\pi\)
−0.934865 + 0.355002i \(0.884480\pi\)
\(284\) 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 \(0.352650\pi\)
−0.998159 + 0.0606487i \(0.980683\pi\)
\(294\) 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 \(-0.711875\pi\)
−0.617551 + 0.786531i \(0.711875\pi\)
\(308\) 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 −0.922680 0.385567i \(-0.874006\pi\)
0.795251 + 0.606281i \(0.207339\pi\)
\(312\) −49.2103 10.8862i −2.78598 0.616309i
\(313\) −4.30102 7.44958i −0.243108 0.421075i 0.718490 0.695537i \(-0.244834\pi\)
−0.961598 + 0.274462i \(0.911500\pi\)
\(314\) 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 0.813444 0.581643i \(-0.197590\pi\)
−0.910440 + 0.413642i \(0.864256\pi\)
\(350\) 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 0.900342 0.435184i \(-0.143317\pi\)
−0.827051 + 0.562127i \(0.809983\pi\)
\(354\) −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 \(0.0480999\pi\)
−0.363934 + 0.931425i \(0.618567\pi\)
\(368\) −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 \(-0.661258\pi\)
0.999856 0.0169915i \(-0.00540883\pi\)
\(384\) −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 \(-0.649300\pi\)
−0.452031 + 0.892002i \(0.649300\pi\)
\(398\) 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 −0.700000 0.714142i \(-0.746817\pi\)
0.968466 + 0.249147i \(0.0801502\pi\)
\(410\) 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 −0.872009 0.489489i \(-0.837183\pi\)
0.859915 + 0.510438i \(0.170517\pi\)
\(420\) 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 \(-0.797476\pi\)
−0.804330 + 0.594183i \(0.797476\pi\)
\(434\) 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 0.500498 0.865738i \(-0.333150\pi\)
−1.00000 0.000574559i \(0.999817\pi\)
\(440\) −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 0.993397 0.114731i \(-0.0366005\pi\)
−0.596058 + 0.802941i \(0.703267\pi\)
\(462\) 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 \(-0.560697\pi\)
−0.189531 + 0.981875i \(0.560697\pi\)
\(468\) −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 \(0.0317747\pi\)
−0.411205 + 0.911543i \(0.634892\pi\)
\(480\) 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 \(-0.541252\pi\)
−0.129236 + 0.991614i \(0.541252\pi\)
\(504\) 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 \(0.354770\pi\)
−0.997733 + 0.0672931i \(0.978564\pi\)
\(510\) 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 \(-0.448904\pi\)
0.159834 + 0.987144i \(0.448904\pi\)
\(522\) −3.26218 36.9007i −0.142782 1.61510i
\(523\) 16.7727 0.733421 0.366710 0.930335i \(-0.380484\pi\)
0.366710 + 0.930335i \(0.380484\pi\)
\(524\) 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 \(0.364776\pi\)
−0.995125 + 0.0986197i \(0.968557\pi\)
\(564\) 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 \(-0.773891\pi\)
−0.758138 + 0.652094i \(0.773891\pi\)
\(578\) −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 0.957893 0.287126i \(-0.0927000\pi\)
−0.727605 + 0.685996i \(0.759367\pi\)
\(588\) 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 \(-0.366673\pi\)
0.406720 + 0.913553i \(0.366673\pi\)
\(594\) 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 \(-0.998937\pi\)
0.497105 0.867690i \(-0.334396\pi\)
\(602\) 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 −0.986361 0.164596i \(-0.947368\pi\)
0.635725 + 0.771916i \(0.280701\pi\)
\(608\) 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 \(-0.928922\pi\)
0.295807 0.955248i \(-0.404412\pi\)
\(620\) −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 \(0.341718\pi\)
−0.999653 + 0.0263376i \(0.991616\pi\)
\(644\) 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 \(-0.499900\pi\)
0.000315282 1.00000i \(0.499900\pi\)
\(648\) −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 −0.913001 0.407958i \(-0.866241\pi\)
0.809802 + 0.586703i \(0.199574\pi\)
\(662\) −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 \(0.0663747\pi\)
−0.309889 + 0.950773i \(0.600292\pi\)
\(678\) 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 0.922216 0.386676i \(-0.126377\pi\)
−0.795979 + 0.605324i \(0.793043\pi\)
\(692\) −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 \(-0.809316\pi\)
−0.825870 + 0.563861i \(0.809316\pi\)
\(720\) 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 \(0.00884060\pi\)
−0.475758 + 0.879576i \(0.657826\pi\)
\(728\) 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 −0.537051 0.843550i \(-0.680462\pi\)
0.999061 + 0.0433249i \(0.0137951\pi\)
\(734\) −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 −0.719683 0.694303i \(-0.755713\pi\)
0.961125 + 0.276113i \(0.0890462\pi\)
\(762\) 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 \(-0.385676\pi\)
0.635022 0.772494i \(-0.280991\pi\)
\(770\) 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 \(-0.486484\pi\)
0.0424491 + 0.999099i \(0.486484\pi\)
\(774\) 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
\(784\) 0