Properties

Label 405.2.r.a.152.11
Level $405$
Weight $2$
Character 405.152
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 152.11
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.08817 + 0.761943i) q^{2} +(-0.0804885 - 0.221140i) q^{4} +(-1.23426 + 1.86457i) q^{5} +(0.827388 + 1.77434i) q^{7} +(0.768546 - 2.86825i) q^{8} +O(q^{10})\) \(q+(1.08817 + 0.761943i) q^{2} +(-0.0804885 - 0.221140i) q^{4} +(-1.23426 + 1.86457i) q^{5} +(0.827388 + 1.77434i) q^{7} +(0.768546 - 2.86825i) q^{8} +(-2.76377 + 1.08853i) q^{10} +(2.76562 + 3.29594i) q^{11} +(2.90740 + 4.15220i) q^{13} +(-0.451609 + 2.56120i) q^{14} +(2.66120 - 2.23301i) q^{16} +(0.828434 + 3.09176i) q^{17} +(-0.776109 + 0.448087i) q^{19} +(0.511675 + 0.122868i) q^{20} +(0.498142 + 5.69379i) q^{22} +(-5.07230 - 2.36525i) q^{23} +(-1.95322 - 4.60271i) q^{25} +6.73356i q^{26} +(0.325783 - 0.325783i) q^{28} +(-1.14702 - 6.50507i) q^{29} +(2.27652 - 0.828586i) q^{31} +(-1.31900 + 0.115398i) q^{32} +(-1.45427 + 3.99557i) q^{34} +(-4.32959 - 0.647269i) q^{35} +(6.96604 - 1.86654i) q^{37} +(-1.18595 - 0.103757i) q^{38} +(4.39947 + 4.97316i) q^{40} +(-8.33680 - 1.47000i) q^{41} +(0.112459 - 1.28541i) q^{43} +(0.506265 - 0.876877i) q^{44} +(-3.71732 - 6.43859i) q^{46} +(7.46943 - 3.48305i) q^{47} +(2.03580 - 2.42617i) q^{49} +(1.38157 - 6.49676i) q^{50} +(0.684206 - 0.977148i) q^{52} +(0.947342 + 0.947342i) q^{53} +(-9.55899 + 1.08866i) q^{55} +(5.72514 - 1.00950i) q^{56} +(3.70835 - 7.95258i) q^{58} +(3.72879 + 3.12883i) q^{59} +(-7.90101 - 2.87573i) q^{61} +(3.10857 + 0.832940i) q^{62} +(-7.54029 - 4.35339i) q^{64} +(-11.3305 + 0.296169i) q^{65} +(-7.90560 + 5.53556i) q^{67} +(0.617033 - 0.432051i) q^{68} +(-4.21814 - 4.00324i) q^{70} +(-4.92123 - 2.84127i) q^{71} +(4.93694 + 1.32285i) q^{73} +(9.00242 + 3.27661i) q^{74} +(0.161558 + 0.135563i) q^{76} +(-3.55988 + 7.63418i) q^{77} +(-0.410612 + 0.0724019i) q^{79} +(0.879000 + 7.71810i) q^{80} +(-7.95178 - 7.95178i) q^{82} +(5.31732 - 7.59392i) q^{83} +(-6.78729 - 2.27135i) q^{85} +(1.10179 - 1.31306i) q^{86} +(11.5791 - 5.39942i) q^{88} +(0.974450 + 1.68780i) q^{89} +(-4.96186 + 8.59420i) q^{91} +(-0.114791 + 1.31207i) q^{92} +(10.7819 + 1.90114i) q^{94} +(0.122429 - 2.00016i) q^{95} +(13.4552 + 1.17718i) q^{97} +(4.06390 - 1.08892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08817 + 0.761943i 0.769451 + 0.538775i 0.891105 0.453797i \(-0.149931\pi\)
−0.121654 + 0.992573i \(0.538820\pi\)
\(3\) 0 0
\(4\) −0.0804885 0.221140i −0.0402443 0.110570i
\(5\) −1.23426 + 1.86457i −0.551976 + 0.833860i
\(6\) 0 0
\(7\) 0.827388 + 1.77434i 0.312723 + 0.670638i 0.998356 0.0573098i \(-0.0182523\pi\)
−0.685633 + 0.727947i \(0.740474\pi\)
\(8\) 0.768546 2.86825i 0.271722 1.01408i
\(9\) 0 0
\(10\) −2.76377 + 1.08853i −0.873982 + 0.344223i
\(11\) 2.76562 + 3.29594i 0.833867 + 0.993764i 0.999971 + 0.00765542i \(0.00243682\pi\)
−0.166104 + 0.986108i \(0.553119\pi\)
\(12\) 0 0
\(13\) 2.90740 + 4.15220i 0.806368 + 1.15161i 0.985814 + 0.167844i \(0.0536806\pi\)
−0.179446 + 0.983768i \(0.557431\pi\)
\(14\) −0.451609 + 2.56120i −0.120698 + 0.684510i
\(15\) 0 0
\(16\) 2.66120 2.23301i 0.665301 0.558253i
\(17\) 0.828434 + 3.09176i 0.200925 + 0.749861i 0.990653 + 0.136405i \(0.0435547\pi\)
−0.789729 + 0.613456i \(0.789779\pi\)
\(18\) 0 0
\(19\) −0.776109 + 0.448087i −0.178052 + 0.102798i −0.586377 0.810038i \(-0.699446\pi\)
0.408325 + 0.912836i \(0.366113\pi\)
\(20\) 0.511675 + 0.122868i 0.114414 + 0.0274740i
\(21\) 0 0
\(22\) 0.498142 + 5.69379i 0.106204 + 1.21392i
\(23\) −5.07230 2.36525i −1.05765 0.493189i −0.185607 0.982624i \(-0.559425\pi\)
−0.872040 + 0.489435i \(0.837203\pi\)
\(24\) 0 0
\(25\) −1.95322 4.60271i −0.390645 0.920541i
\(26\) 6.73356i 1.32056i
\(27\) 0 0
\(28\) 0.325783 0.325783i 0.0615672 0.0615672i
\(29\) −1.14702 6.50507i −0.212996 1.20796i −0.884350 0.466825i \(-0.845398\pi\)
0.671354 0.741137i \(-0.265713\pi\)
\(30\) 0 0
\(31\) 2.27652 0.828586i 0.408875 0.148818i −0.129390 0.991594i \(-0.541302\pi\)
0.538266 + 0.842775i \(0.319080\pi\)
\(32\) −1.31900 + 0.115398i −0.233169 + 0.0203996i
\(33\) 0 0
\(34\) −1.45427 + 3.99557i −0.249405 + 0.685235i
\(35\) −4.32959 0.647269i −0.731834 0.109408i
\(36\) 0 0
\(37\) 6.96604 1.86654i 1.14521 0.306858i 0.364166 0.931334i \(-0.381354\pi\)
0.781044 + 0.624476i \(0.214688\pi\)
\(38\) −1.18595 0.103757i −0.192387 0.0168317i
\(39\) 0 0
\(40\) 4.39947 + 4.97316i 0.695617 + 0.786326i
\(41\) −8.33680 1.47000i −1.30199 0.229576i −0.520697 0.853742i \(-0.674328\pi\)
−0.781292 + 0.624166i \(0.785439\pi\)
\(42\) 0 0
\(43\) 0.112459 1.28541i 0.0171499 0.196024i −0.982787 0.184745i \(-0.940854\pi\)
0.999936 0.0112790i \(-0.00359030\pi\)
\(44\) 0.506265 0.876877i 0.0763223 0.132194i
\(45\) 0 0
\(46\) −3.71732 6.43859i −0.548090 0.949319i
\(47\) 7.46943 3.48305i 1.08953 0.508055i 0.207013 0.978338i \(-0.433626\pi\)
0.882516 + 0.470283i \(0.155848\pi\)
\(48\) 0 0
\(49\) 2.03580 2.42617i 0.290829 0.346596i
\(50\) 1.38157 6.49676i 0.195383 0.918781i
\(51\) 0 0
\(52\) 0.684206 0.977148i 0.0948823 0.135506i
\(53\) 0.947342 + 0.947342i 0.130127 + 0.130127i 0.769171 0.639043i \(-0.220670\pi\)
−0.639043 + 0.769171i \(0.720670\pi\)
\(54\) 0 0
\(55\) −9.55899 + 1.08866i −1.28893 + 0.146794i
\(56\) 5.72514 1.00950i 0.765054 0.134900i
\(57\) 0 0
\(58\) 3.70835 7.95258i 0.486930 1.04422i
\(59\) 3.72879 + 3.12883i 0.485447 + 0.407339i 0.852391 0.522904i \(-0.175151\pi\)
−0.366944 + 0.930243i \(0.619596\pi\)
\(60\) 0 0
\(61\) −7.90101 2.87573i −1.01162 0.368200i −0.217566 0.976046i \(-0.569812\pi\)
−0.794055 + 0.607846i \(0.792034\pi\)
\(62\) 3.10857 + 0.832940i 0.394789 + 0.105783i
\(63\) 0 0
\(64\) −7.54029 4.35339i −0.942536 0.544173i
\(65\) −11.3305 + 0.296169i −1.40538 + 0.0367352i
\(66\) 0 0
\(67\) −7.90560 + 5.53556i −0.965822 + 0.676276i −0.946217 0.323532i \(-0.895130\pi\)
−0.0196049 + 0.999808i \(0.506241\pi\)
\(68\) 0.617033 0.432051i 0.0748262 0.0523939i
\(69\) 0 0
\(70\) −4.21814 4.00324i −0.504164 0.478478i
\(71\) −4.92123 2.84127i −0.584043 0.337197i 0.178696 0.983904i \(-0.442812\pi\)
−0.762738 + 0.646707i \(0.776146\pi\)
\(72\) 0 0
\(73\) 4.93694 + 1.32285i 0.577825 + 0.154828i 0.535883 0.844292i \(-0.319979\pi\)
0.0419419 + 0.999120i \(0.486646\pi\)
\(74\) 9.00242 + 3.27661i 1.04651 + 0.380898i
\(75\) 0 0
\(76\) 0.161558 + 0.135563i 0.0185320 + 0.0155502i
\(77\) −3.55988 + 7.63418i −0.405686 + 0.869996i
\(78\) 0 0
\(79\) −0.410612 + 0.0724019i −0.0461974 + 0.00814585i −0.196699 0.980464i \(-0.563022\pi\)
0.150502 + 0.988610i \(0.451911\pi\)
\(80\) 0.879000 + 7.71810i 0.0982752 + 0.862910i
\(81\) 0 0
\(82\) −7.95178 7.95178i −0.878127 0.878127i
\(83\) 5.31732 7.59392i 0.583652 0.833541i −0.413378 0.910560i \(-0.635651\pi\)
0.997030 + 0.0770185i \(0.0245401\pi\)
\(84\) 0 0
\(85\) −6.78729 2.27135i −0.736185 0.246362i
\(86\) 1.10179 1.31306i 0.118809 0.141591i
\(87\) 0 0
\(88\) 11.5791 5.39942i 1.23434 0.575580i
\(89\) 0.974450 + 1.68780i 0.103292 + 0.178906i 0.913039 0.407872i \(-0.133729\pi\)
−0.809747 + 0.586779i \(0.800396\pi\)
\(90\) 0 0
\(91\) −4.96186 + 8.59420i −0.520144 + 0.900917i
\(92\) −0.114791 + 1.31207i −0.0119678 + 0.136792i
\(93\) 0 0
\(94\) 10.7819 + 1.90114i 1.11207 + 0.196087i
\(95\) 0.122429 2.00016i 0.0125610 0.205212i
\(96\) 0 0
\(97\) 13.4552 + 1.17718i 1.36617 + 0.119524i 0.746524 0.665359i \(-0.231721\pi\)
0.619644 + 0.784883i \(0.287277\pi\)
\(98\) 4.06390 1.08892i 0.410516 0.109997i
\(99\) 0 0
\(100\) −0.860633 + 0.802402i −0.0860633 + 0.0802402i
\(101\) 1.45521 3.99814i 0.144798 0.397830i −0.845999 0.533185i \(-0.820995\pi\)
0.990797 + 0.135354i \(0.0432173\pi\)
\(102\) 0 0
\(103\) −13.3028 + 1.16385i −1.31077 + 0.114677i −0.721022 0.692912i \(-0.756327\pi\)
−0.589745 + 0.807589i \(0.700772\pi\)
\(104\) 14.1440 5.14800i 1.38694 0.504803i
\(105\) 0 0
\(106\) 0.309046 + 1.75269i 0.0300172 + 0.170236i
\(107\) 10.2616 10.2616i 0.992026 0.992026i −0.00794276 0.999968i \(-0.502528\pi\)
0.999968 + 0.00794276i \(0.00252829\pi\)
\(108\) 0 0
\(109\) 14.3459i 1.37409i 0.726615 + 0.687045i \(0.241092\pi\)
−0.726615 + 0.687045i \(0.758908\pi\)
\(110\) −11.2313 6.09877i −1.07086 0.581495i
\(111\) 0 0
\(112\) 6.16397 + 2.87431i 0.582441 + 0.271597i
\(113\) −1.18867 13.5865i −0.111821 1.27811i −0.820116 0.572198i \(-0.806091\pi\)
0.708295 0.705916i \(-0.249465\pi\)
\(114\) 0 0
\(115\) 10.6707 6.53832i 0.995046 0.609701i
\(116\) −1.34621 + 0.777236i −0.124993 + 0.0721646i
\(117\) 0 0
\(118\) 1.67356 + 6.24582i 0.154064 + 0.574974i
\(119\) −4.80039 + 4.02801i −0.440051 + 0.369247i
\(120\) 0 0
\(121\) −1.30443 + 7.39778i −0.118584 + 0.672525i
\(122\) −6.40648 9.14940i −0.580016 0.828348i
\(123\) 0 0
\(124\) −0.366468 0.436739i −0.0329098 0.0392204i
\(125\) 10.9928 + 2.03900i 0.983229 + 0.182374i
\(126\) 0 0
\(127\) 0.931838 3.47767i 0.0826872 0.308593i −0.912179 0.409792i \(-0.865601\pi\)
0.994866 + 0.101199i \(0.0322679\pi\)
\(128\) −3.76894 8.08251i −0.333130 0.714400i
\(129\) 0 0
\(130\) −12.5552 8.31094i −1.10116 0.728918i
\(131\) −0.189922 0.521807i −0.0165936 0.0455905i 0.931119 0.364715i \(-0.118833\pi\)
−0.947713 + 0.319124i \(0.896611\pi\)
\(132\) 0 0
\(133\) −1.43720 1.00634i −0.124621 0.0872607i
\(134\) −12.8204 −1.10751
\(135\) 0 0
\(136\) 9.50463 0.815015
\(137\) 4.95031 + 3.46624i 0.422934 + 0.296141i 0.765601 0.643315i \(-0.222442\pi\)
−0.342668 + 0.939457i \(0.611330\pi\)
\(138\) 0 0
\(139\) −6.33390 17.4022i −0.537234 1.47604i −0.850295 0.526306i \(-0.823577\pi\)
0.313061 0.949733i \(-0.398646\pi\)
\(140\) 0.205345 + 1.00954i 0.0173548 + 0.0853221i
\(141\) 0 0
\(142\) −3.19024 6.84148i −0.267719 0.574125i
\(143\) −5.64463 + 21.0660i −0.472027 + 1.76163i
\(144\) 0 0
\(145\) 13.5449 + 5.89023i 1.12484 + 0.489157i
\(146\) 4.36428 + 5.20115i 0.361190 + 0.430450i
\(147\) 0 0
\(148\) −0.973455 1.39024i −0.0800175 0.114277i
\(149\) −1.50609 + 8.54145i −0.123384 + 0.699743i 0.858871 + 0.512192i \(0.171166\pi\)
−0.982255 + 0.187551i \(0.939945\pi\)
\(150\) 0 0
\(151\) −12.2052 + 10.2414i −0.993244 + 0.833431i −0.986034 0.166543i \(-0.946740\pi\)
−0.00721007 + 0.999974i \(0.502295\pi\)
\(152\) 0.688750 + 2.57045i 0.0558650 + 0.208491i
\(153\) 0 0
\(154\) −9.69056 + 5.59485i −0.780887 + 0.450846i
\(155\) −1.26486 + 5.26742i −0.101596 + 0.423089i
\(156\) 0 0
\(157\) 1.15698 + 13.2243i 0.0923367 + 1.05541i 0.891112 + 0.453784i \(0.149926\pi\)
−0.798775 + 0.601630i \(0.794518\pi\)
\(158\) −0.501981 0.234077i −0.0399354 0.0186222i
\(159\) 0 0
\(160\) 1.41282 2.60180i 0.111693 0.205690i
\(161\) 10.9570i 0.863530i
\(162\) 0 0
\(163\) 5.24760 5.24760i 0.411024 0.411024i −0.471071 0.882095i \(-0.656133\pi\)
0.882095 + 0.471071i \(0.156133\pi\)
\(164\) 0.345940 + 1.96192i 0.0270133 + 0.153200i
\(165\) 0 0
\(166\) 11.5723 4.21196i 0.898183 0.326912i
\(167\) −8.20120 + 0.717512i −0.634628 + 0.0555227i −0.399930 0.916546i \(-0.630966\pi\)
−0.234698 + 0.972068i \(0.575410\pi\)
\(168\) 0 0
\(169\) −4.34150 + 11.9282i −0.333962 + 0.917553i
\(170\) −5.65507 7.64314i −0.433724 0.586202i
\(171\) 0 0
\(172\) −0.293309 + 0.0785918i −0.0223646 + 0.00599257i
\(173\) 7.74393 + 0.677506i 0.588760 + 0.0515098i 0.377643 0.925951i \(-0.376735\pi\)
0.211116 + 0.977461i \(0.432290\pi\)
\(174\) 0 0
\(175\) 6.55069 7.27391i 0.495186 0.549856i
\(176\) 14.7198 + 2.59549i 1.10954 + 0.195643i
\(177\) 0 0
\(178\) −0.225641 + 2.57908i −0.0169125 + 0.193310i
\(179\) −2.19929 + 3.80928i −0.164382 + 0.284719i −0.936436 0.350839i \(-0.885896\pi\)
0.772053 + 0.635558i \(0.219230\pi\)
\(180\) 0 0
\(181\) −2.85830 4.95072i −0.212456 0.367984i 0.740027 0.672577i \(-0.234813\pi\)
−0.952483 + 0.304593i \(0.901479\pi\)
\(182\) −11.9476 + 5.57127i −0.885617 + 0.412970i
\(183\) 0 0
\(184\) −10.6824 + 12.7308i −0.787519 + 0.938529i
\(185\) −5.11758 + 15.2924i −0.376252 + 1.12432i
\(186\) 0 0
\(187\) −7.89911 + 11.2811i −0.577640 + 0.824956i
\(188\) −1.37145 1.37145i −0.100023 0.100023i
\(189\) 0 0
\(190\) 1.65723 2.08323i 0.120228 0.151133i
\(191\) −14.2067 + 2.50503i −1.02796 + 0.181258i −0.662104 0.749412i \(-0.730336\pi\)
−0.365860 + 0.930670i \(0.619225\pi\)
\(192\) 0 0
\(193\) 7.33254 15.7247i 0.527808 1.13189i −0.443981 0.896036i \(-0.646434\pi\)
0.971789 0.235852i \(-0.0757879\pi\)
\(194\) 13.7446 + 11.5331i 0.986802 + 0.828025i
\(195\) 0 0
\(196\) −0.700384 0.254919i −0.0500274 0.0182085i
\(197\) 13.1476 + 3.52289i 0.936727 + 0.250995i 0.694721 0.719280i \(-0.255528\pi\)
0.242006 + 0.970275i \(0.422195\pi\)
\(198\) 0 0
\(199\) −7.78555 4.49499i −0.551903 0.318641i 0.197986 0.980205i \(-0.436560\pi\)
−0.749889 + 0.661564i \(0.769893\pi\)
\(200\) −14.7029 + 2.06495i −1.03965 + 0.146014i
\(201\) 0 0
\(202\) 4.62987 3.24187i 0.325756 0.228097i
\(203\) 10.5932 7.41743i 0.743496 0.520601i
\(204\) 0 0
\(205\) 13.0307 13.7302i 0.910101 0.958956i
\(206\) −15.3625 8.86955i −1.07036 0.617971i
\(207\) 0 0
\(208\) 17.0091 + 4.55757i 1.17937 + 0.316011i
\(209\) −3.62329 1.31877i −0.250628 0.0912212i
\(210\) 0 0
\(211\) −14.3607 12.0500i −0.988631 0.829559i −0.00326162 0.999995i \(-0.501038\pi\)
−0.985369 + 0.170435i \(0.945483\pi\)
\(212\) 0.133245 0.285746i 0.00915134 0.0196251i
\(213\) 0 0
\(214\) 18.9851 3.34758i 1.29779 0.228836i
\(215\) 2.25794 + 1.79622i 0.153990 + 0.122501i
\(216\) 0 0
\(217\) 3.35376 + 3.35376i 0.227668 + 0.227668i
\(218\) −10.9308 + 15.6108i −0.740326 + 1.05729i
\(219\) 0 0
\(220\) 1.01014 + 2.02626i 0.0681033 + 0.136610i
\(221\) −10.4290 + 12.4288i −0.701530 + 0.836051i
\(222\) 0 0
\(223\) −15.0323 + 7.00968i −1.00664 + 0.469403i −0.854775 0.518999i \(-0.826305\pi\)
−0.151862 + 0.988402i \(0.548527\pi\)
\(224\) −1.29608 2.24488i −0.0865981 0.149992i
\(225\) 0 0
\(226\) 9.05870 15.6901i 0.602576 1.04369i
\(227\) 1.57696 18.0248i 0.104667 1.19634i −0.744281 0.667867i \(-0.767207\pi\)
0.848947 0.528478i \(-0.177237\pi\)
\(228\) 0 0
\(229\) 18.7074 + 3.29862i 1.23622 + 0.217979i 0.753294 0.657684i \(-0.228464\pi\)
0.482924 + 0.875662i \(0.339575\pi\)
\(230\) 16.5933 + 1.01567i 1.09413 + 0.0669714i
\(231\) 0 0
\(232\) −19.5397 1.70951i −1.28285 0.112235i
\(233\) 7.30551 1.95750i 0.478600 0.128240i −0.0114509 0.999934i \(-0.503645\pi\)
0.490050 + 0.871694i \(0.336978\pi\)
\(234\) 0 0
\(235\) −2.72480 + 18.2262i −0.177747 + 1.18895i
\(236\) 0.391785 1.07642i 0.0255031 0.0700691i
\(237\) 0 0
\(238\) −8.29275 + 0.725521i −0.537539 + 0.0470286i
\(239\) −11.7518 + 4.27731i −0.760162 + 0.276676i −0.692875 0.721057i \(-0.743656\pi\)
−0.0672867 + 0.997734i \(0.521434\pi\)
\(240\) 0 0
\(241\) 2.97320 + 16.8619i 0.191521 + 1.08617i 0.917287 + 0.398227i \(0.130374\pi\)
−0.725766 + 0.687942i \(0.758514\pi\)
\(242\) −7.05612 + 7.05612i −0.453585 + 0.453585i
\(243\) 0 0
\(244\) 1.97870i 0.126673i
\(245\) 2.01106 + 6.79041i 0.128482 + 0.433823i
\(246\) 0 0
\(247\) −4.11700 1.91979i −0.261958 0.122153i
\(248\) −0.626983 7.16645i −0.0398134 0.455070i
\(249\) 0 0
\(250\) 10.4085 + 10.5947i 0.658288 + 0.670067i
\(251\) −4.66370 + 2.69259i −0.294370 + 0.169955i −0.639911 0.768449i \(-0.721029\pi\)
0.345541 + 0.938404i \(0.387696\pi\)
\(252\) 0 0
\(253\) −6.23233 23.2594i −0.391823 1.46231i
\(254\) 3.66378 3.07428i 0.229886 0.192897i
\(255\) 0 0
\(256\) −0.966651 + 5.48215i −0.0604157 + 0.342634i
\(257\) 7.03325 + 10.0445i 0.438722 + 0.626560i 0.976240 0.216692i \(-0.0695268\pi\)
−0.537518 + 0.843252i \(0.680638\pi\)
\(258\) 0 0
\(259\) 9.07550 + 10.8158i 0.563924 + 0.672059i
\(260\) 0.977472 + 2.48180i 0.0606203 + 0.153915i
\(261\) 0 0
\(262\) 0.190920 0.712524i 0.0117951 0.0440199i
\(263\) 5.75913 + 12.3505i 0.355123 + 0.761563i 0.999996 0.00272594i \(-0.000867694\pi\)
−0.644873 + 0.764289i \(0.723090\pi\)
\(264\) 0 0
\(265\) −2.93565 + 0.597121i −0.180335 + 0.0366808i
\(266\) −0.797143 2.19013i −0.0488760 0.134286i
\(267\) 0 0
\(268\) 1.86045 + 1.30270i 0.113645 + 0.0795749i
\(269\) −12.3342 −0.752028 −0.376014 0.926614i \(-0.622706\pi\)
−0.376014 + 0.926614i \(0.622706\pi\)
\(270\) 0 0
\(271\) 19.7578 1.20020 0.600099 0.799926i \(-0.295128\pi\)
0.600099 + 0.799926i \(0.295128\pi\)
\(272\) 9.10856 + 6.37789i 0.552288 + 0.386716i
\(273\) 0 0
\(274\) 2.74569 + 7.54371i 0.165873 + 0.455732i
\(275\) 9.76837 19.1671i 0.589055 1.15582i
\(276\) 0 0
\(277\) −0.856962 1.83776i −0.0514898 0.110420i 0.878880 0.477044i \(-0.158292\pi\)
−0.930370 + 0.366623i \(0.880514\pi\)
\(278\) 6.36718 23.7626i 0.381878 1.42519i
\(279\) 0 0
\(280\) −5.18402 + 11.9209i −0.309804 + 0.712410i
\(281\) 16.8041 + 20.0263i 1.00245 + 1.19467i 0.980822 + 0.194903i \(0.0624393\pi\)
0.0216244 + 0.999766i \(0.493116\pi\)
\(282\) 0 0
\(283\) 1.33019 + 1.89971i 0.0790717 + 0.112926i 0.856740 0.515749i \(-0.172486\pi\)
−0.777668 + 0.628675i \(0.783597\pi\)
\(284\) −0.232218 + 1.31697i −0.0137796 + 0.0781480i
\(285\) 0 0
\(286\) −22.1934 + 18.6225i −1.31232 + 1.10117i
\(287\) −4.28949 16.0086i −0.253200 0.944956i
\(288\) 0 0
\(289\) 5.84978 3.37737i 0.344105 0.198669i
\(290\) 10.2511 + 16.7300i 0.601963 + 0.982418i
\(291\) 0 0
\(292\) −0.104832 1.19823i −0.00613480 0.0701211i
\(293\) 10.9251 + 5.09445i 0.638250 + 0.297621i 0.714677 0.699454i \(-0.246574\pi\)
−0.0764274 + 0.997075i \(0.524351\pi\)
\(294\) 0 0
\(295\) −10.4362 + 3.09081i −0.607619 + 0.179954i
\(296\) 21.4149i 1.24471i
\(297\) 0 0
\(298\) −8.14698 + 8.14698i −0.471942 + 0.471942i
\(299\) −4.92621 27.9379i −0.284890 1.61569i
\(300\) 0 0
\(301\) 2.37381 0.863996i 0.136824 0.0497999i
\(302\) −21.0846 + 1.84467i −1.21328 + 0.106149i
\(303\) 0 0
\(304\) −1.06480 + 2.92551i −0.0610704 + 0.167790i
\(305\) 15.1139 11.1826i 0.865418 0.640313i
\(306\) 0 0
\(307\) 22.6984 6.08202i 1.29547 0.347119i 0.455732 0.890117i \(-0.349378\pi\)
0.839734 + 0.542998i \(0.182711\pi\)
\(308\) 1.97476 + 0.172769i 0.112522 + 0.00984441i
\(309\) 0 0
\(310\) −5.38985 + 4.76809i −0.306123 + 0.270809i
\(311\) −3.91683 0.690642i −0.222103 0.0391627i 0.0614891 0.998108i \(-0.480415\pi\)
−0.283592 + 0.958945i \(0.591526\pi\)
\(312\) 0 0
\(313\) −0.0797089 + 0.911077i −0.00450541 + 0.0514971i −0.998115 0.0613781i \(-0.980450\pi\)
0.993609 + 0.112875i \(0.0360060\pi\)
\(314\) −8.81718 + 15.2718i −0.497582 + 0.861838i
\(315\) 0 0
\(316\) 0.0490605 + 0.0849753i 0.00275987 + 0.00478023i
\(317\) −23.8990 + 11.1443i −1.34230 + 0.625924i −0.955158 0.296096i \(-0.904315\pi\)
−0.387141 + 0.922021i \(0.626537\pi\)
\(318\) 0 0
\(319\) 18.2681 21.7711i 1.02282 1.21895i
\(320\) 17.4238 8.68618i 0.974021 0.485572i
\(321\) 0 0
\(322\) 8.34859 11.9230i 0.465249 0.664444i
\(323\) −2.02833 2.02833i −0.112859 0.112859i
\(324\) 0 0
\(325\) 13.4325 21.4921i 0.745103 1.19217i
\(326\) 9.70865 1.71190i 0.537712 0.0948132i
\(327\) 0 0
\(328\) −10.6235 + 22.7823i −0.586587 + 1.25794i
\(329\) 12.3602 + 10.3715i 0.681442 + 0.571798i
\(330\) 0 0
\(331\) −12.0746 4.39481i −0.663682 0.241561i −0.0118569 0.999930i \(-0.503774\pi\)
−0.651825 + 0.758369i \(0.725996\pi\)
\(332\) −2.10731 0.564651i −0.115653 0.0309893i
\(333\) 0 0
\(334\) −9.47099 5.46808i −0.518229 0.299200i
\(335\) −0.563892 21.5728i −0.0308087 1.17865i
\(336\) 0 0
\(337\) −6.96283 + 4.87543i −0.379290 + 0.265581i −0.747638 0.664106i \(-0.768812\pi\)
0.368349 + 0.929688i \(0.379923\pi\)
\(338\) −13.8129 + 9.67189i −0.751322 + 0.526081i
\(339\) 0 0
\(340\) 0.0440119 + 1.68376i 0.00238688 + 0.0913148i
\(341\) 9.02697 + 5.21173i 0.488838 + 0.282231i
\(342\) 0 0
\(343\) 19.2267 + 5.15177i 1.03814 + 0.278169i
\(344\) −3.60046 1.31046i −0.194124 0.0706553i
\(345\) 0 0
\(346\) 7.91047 + 6.63767i 0.425270 + 0.356844i
\(347\) 2.22359 4.76851i 0.119369 0.255987i −0.837540 0.546376i \(-0.816007\pi\)
0.956909 + 0.290389i \(0.0937847\pi\)
\(348\) 0 0
\(349\) −20.3047 + 3.58026i −1.08688 + 0.191647i −0.688258 0.725466i \(-0.741624\pi\)
−0.398627 + 0.917113i \(0.630513\pi\)
\(350\) 12.6706 2.92398i 0.677270 0.156293i
\(351\) 0 0
\(352\) −4.02821 4.02821i −0.214704 0.214704i
\(353\) −16.5268 + 23.6027i −0.879631 + 1.25624i 0.0859911 + 0.996296i \(0.472594\pi\)
−0.965623 + 0.259948i \(0.916295\pi\)
\(354\) 0 0
\(355\) 11.3718 5.66911i 0.603553 0.300885i
\(356\) 0.294808 0.351339i 0.0156248 0.0186209i
\(357\) 0 0
\(358\) −5.29565 + 2.46940i −0.279884 + 0.130512i
\(359\) −8.91393 15.4394i −0.470459 0.814860i 0.528970 0.848641i \(-0.322578\pi\)
−0.999429 + 0.0337810i \(0.989245\pi\)
\(360\) 0 0
\(361\) −9.09844 + 15.7590i −0.478865 + 0.829419i
\(362\) 0.661859 7.56508i 0.0347865 0.397612i
\(363\) 0 0
\(364\) 2.29990 + 0.405534i 0.120547 + 0.0212558i
\(365\) −8.55998 + 7.57252i −0.448050 + 0.396364i
\(366\) 0 0
\(367\) −21.8448 1.91117i −1.14029 0.0997623i −0.498674 0.866790i \(-0.666179\pi\)
−0.641614 + 0.767028i \(0.721735\pi\)
\(368\) −18.7800 + 5.03210i −0.978978 + 0.262316i
\(369\) 0 0
\(370\) −17.2208 + 12.7414i −0.895264 + 0.662396i
\(371\) −0.897087 + 2.46473i −0.0465744 + 0.127962i
\(372\) 0 0
\(373\) −17.1932 + 1.50421i −0.890228 + 0.0778848i −0.523086 0.852280i \(-0.675219\pi\)
−0.367142 + 0.930165i \(0.619664\pi\)
\(374\) −17.1911 + 6.25706i −0.888932 + 0.323545i
\(375\) 0 0
\(376\) −4.24967 24.1011i −0.219160 1.24292i
\(377\) 23.6755 23.6755i 1.21935 1.21935i
\(378\) 0 0
\(379\) 27.1687i 1.39556i −0.716312 0.697780i \(-0.754171\pi\)
0.716312 0.697780i \(-0.245829\pi\)
\(380\) −0.452170 + 0.133916i −0.0231959 + 0.00686974i
\(381\) 0 0
\(382\) −17.3680 8.09883i −0.888624 0.414372i
\(383\) 0.640436 + 7.32022i 0.0327248 + 0.374046i 0.994844 + 0.101417i \(0.0323376\pi\)
−0.962119 + 0.272629i \(0.912107\pi\)
\(384\) 0 0
\(385\) −9.84065 16.0602i −0.501526 0.818502i
\(386\) 19.9604 11.5241i 1.01596 0.586562i
\(387\) 0 0
\(388\) −0.822667 3.07024i −0.0417646 0.155868i
\(389\) 23.9421 20.0898i 1.21391 1.01859i 0.214792 0.976660i \(-0.431093\pi\)
0.999120 0.0419334i \(-0.0133517\pi\)
\(390\) 0 0
\(391\) 3.11072 17.6418i 0.157316 0.892182i
\(392\) −5.39427 7.70382i −0.272452 0.389102i
\(393\) 0 0
\(394\) 11.6225 + 13.8512i 0.585535 + 0.697814i
\(395\) 0.371802 0.854976i 0.0187074 0.0430185i
\(396\) 0 0
\(397\) 4.26857 15.9305i 0.214234 0.799531i −0.772201 0.635378i \(-0.780844\pi\)
0.986435 0.164153i \(-0.0524890\pi\)
\(398\) −5.04706 10.8234i −0.252986 0.542530i
\(399\) 0 0
\(400\) −15.4758 7.88716i −0.773792 0.394358i
\(401\) 0.517022 + 1.42051i 0.0258188 + 0.0709367i 0.951932 0.306308i \(-0.0990938\pi\)
−0.926114 + 0.377245i \(0.876872\pi\)
\(402\) 0 0
\(403\) 10.0592 + 7.04354i 0.501085 + 0.350864i
\(404\) −1.00128 −0.0498155
\(405\) 0 0
\(406\) 17.1788 0.852571
\(407\) 25.4175 + 17.7975i 1.25990 + 0.882189i
\(408\) 0 0
\(409\) −8.02778 22.0561i −0.396948 1.09061i −0.963763 0.266760i \(-0.914047\pi\)
0.566815 0.823845i \(-0.308175\pi\)
\(410\) 24.6412 5.01210i 1.21694 0.247530i
\(411\) 0 0
\(412\) 1.32810 + 2.84812i 0.0654308 + 0.140317i
\(413\) −2.46645 + 9.20490i −0.121366 + 0.452944i
\(414\) 0 0
\(415\) 7.59644 + 19.2873i 0.372895 + 0.946779i
\(416\) −4.31402 5.14125i −0.211512 0.252070i
\(417\) 0 0
\(418\) −2.93792 4.19579i −0.143698 0.205223i
\(419\) 2.76242 15.6665i 0.134953 0.765357i −0.839939 0.542680i \(-0.817409\pi\)
0.974892 0.222677i \(-0.0714794\pi\)
\(420\) 0 0
\(421\) 27.8051 23.3312i 1.35514 1.13709i 0.377685 0.925934i \(-0.376720\pi\)
0.977452 0.211160i \(-0.0677241\pi\)
\(422\) −6.44539 24.0545i −0.313756 1.17096i
\(423\) 0 0
\(424\) 3.44529 1.98914i 0.167318 0.0966012i
\(425\) 12.6123 9.85193i 0.611788 0.477889i
\(426\) 0 0
\(427\) −1.43468 16.3984i −0.0694289 0.793576i
\(428\) −3.09519 1.44331i −0.149612 0.0697652i
\(429\) 0 0
\(430\) 1.08840 + 3.67501i 0.0524873 + 0.177225i
\(431\) 10.7570i 0.518146i 0.965858 + 0.259073i \(0.0834169\pi\)
−0.965858 + 0.259073i \(0.916583\pi\)
\(432\) 0 0
\(433\) −25.8369 + 25.8369i −1.24164 + 1.24164i −0.282321 + 0.959320i \(0.591104\pi\)
−0.959320 + 0.282321i \(0.908896\pi\)
\(434\) 1.09408 + 6.20483i 0.0525175 + 0.297842i
\(435\) 0 0
\(436\) 3.17246 1.15468i 0.151933 0.0552992i
\(437\) 4.99649 0.437136i 0.239015 0.0209111i
\(438\) 0 0
\(439\) 4.76440 13.0901i 0.227393 0.624756i −0.772556 0.634947i \(-0.781022\pi\)
0.999948 + 0.0101913i \(0.00324405\pi\)
\(440\) −4.22398 + 28.2543i −0.201371 + 1.34697i
\(441\) 0 0
\(442\) −20.8185 + 5.57831i −0.990237 + 0.265333i
\(443\) 11.3601 + 0.993879i 0.539734 + 0.0472206i 0.353764 0.935335i \(-0.384902\pi\)
0.185970 + 0.982555i \(0.440457\pi\)
\(444\) 0 0
\(445\) −4.34973 0.266246i −0.206197 0.0126213i
\(446\) −21.6986 3.82606i −1.02746 0.181169i
\(447\) 0 0
\(448\) 1.48564 16.9810i 0.0701900 0.802276i
\(449\) −0.807925 + 1.39937i −0.0381283 + 0.0660402i −0.884460 0.466616i \(-0.845473\pi\)
0.846332 + 0.532657i \(0.178806\pi\)
\(450\) 0 0
\(451\) −18.2114 31.5431i −0.857541 1.48530i
\(452\) −2.90886 + 1.35642i −0.136821 + 0.0638008i
\(453\) 0 0
\(454\) 15.4498 18.4124i 0.725097 0.864137i
\(455\) −9.90025 19.8592i −0.464131 0.931012i
\(456\) 0 0
\(457\) −3.17737 + 4.53775i −0.148631 + 0.212267i −0.886563 0.462608i \(-0.846914\pi\)
0.737932 + 0.674875i \(0.235803\pi\)
\(458\) 17.8434 + 17.8434i 0.833768 + 0.833768i
\(459\) 0 0
\(460\) −2.30475 1.83346i −0.107460 0.0854855i
\(461\) −14.9666 + 2.63902i −0.697065 + 0.122911i −0.510942 0.859615i \(-0.670703\pi\)
−0.186123 + 0.982527i \(0.559592\pi\)
\(462\) 0 0
\(463\) −13.9696 + 29.9580i −0.649224 + 1.39226i 0.255727 + 0.966749i \(0.417685\pi\)
−0.904951 + 0.425516i \(0.860093\pi\)
\(464\) −17.5784 14.7500i −0.816056 0.684752i
\(465\) 0 0
\(466\) 9.44112 + 3.43629i 0.437352 + 0.159183i
\(467\) −21.9378 5.87822i −1.01516 0.272012i −0.287377 0.957818i \(-0.592783\pi\)
−0.727784 + 0.685806i \(0.759450\pi\)
\(468\) 0 0
\(469\) −16.3630 9.44716i −0.755571 0.436229i
\(470\) −16.8524 + 17.7571i −0.777343 + 0.819072i
\(471\) 0 0
\(472\) 11.8400 8.29047i 0.544981 0.381600i
\(473\) 4.54767 3.18431i 0.209102 0.146415i
\(474\) 0 0
\(475\) 3.57833 + 2.69699i 0.164185 + 0.123746i
\(476\) 1.27713 + 0.737352i 0.0585372 + 0.0337965i
\(477\) 0 0
\(478\) −16.0470 4.29979i −0.733974 0.196668i
\(479\) −21.4594 7.81060i −0.980507 0.356875i −0.198470 0.980107i \(-0.563597\pi\)
−0.782037 + 0.623232i \(0.785819\pi\)
\(480\) 0 0
\(481\) 28.0033 + 23.4976i 1.27684 + 1.07140i
\(482\) −9.61245 + 20.6140i −0.437835 + 0.938941i
\(483\) 0 0
\(484\) 1.74094 0.306975i 0.0791336 0.0139534i
\(485\) −18.8021 + 23.6352i −0.853758 + 1.07322i
\(486\) 0 0
\(487\) 13.1004 + 13.1004i 0.593634 + 0.593634i 0.938611 0.344977i \(-0.112113\pi\)
−0.344977 + 0.938611i \(0.612113\pi\)
\(488\) −14.3206 + 20.4520i −0.648264 + 0.925817i
\(489\) 0 0
\(490\) −2.98553 + 8.92142i −0.134873 + 0.403029i
\(491\) 5.95862 7.10121i 0.268909 0.320473i −0.614644 0.788805i \(-0.710700\pi\)
0.883553 + 0.468332i \(0.155145\pi\)
\(492\) 0 0
\(493\) 19.1619 8.93533i 0.863007 0.402427i
\(494\) −3.01722 5.22597i −0.135751 0.235128i
\(495\) 0 0
\(496\) 4.20804 7.28854i 0.188947 0.327265i
\(497\) 0.969617 11.0828i 0.0434933 0.497131i
\(498\) 0 0
\(499\) −20.3482 3.58794i −0.910911 0.160618i −0.301494 0.953468i \(-0.597485\pi\)
−0.609417 + 0.792850i \(0.708596\pi\)
\(500\) −0.433892 2.59508i −0.0194042 0.116055i
\(501\) 0 0
\(502\) −7.12650 0.623488i −0.318071 0.0278276i
\(503\) −4.53760 + 1.21585i −0.202322 + 0.0542119i −0.358557 0.933508i \(-0.616731\pi\)
0.156235 + 0.987720i \(0.450064\pi\)
\(504\) 0 0
\(505\) 5.65871 + 7.64806i 0.251809 + 0.340334i
\(506\) 10.9405 30.0588i 0.486365 1.33628i
\(507\) 0 0
\(508\) −0.844055 + 0.0738452i −0.0374489 + 0.00327635i
\(509\) 30.3526 11.0475i 1.34536 0.489670i 0.433862 0.900979i \(-0.357151\pi\)
0.911496 + 0.411309i \(0.134928\pi\)
\(510\) 0 0
\(511\) 1.73758 + 9.85432i 0.0768661 + 0.435929i
\(512\) −17.8410 + 17.8410i −0.788469 + 0.788469i
\(513\) 0 0
\(514\) 16.2891i 0.718480i
\(515\) 14.2490 26.2405i 0.627887 1.15630i
\(516\) 0 0
\(517\) 32.1376 + 14.9860i 1.41341 + 0.659083i
\(518\) 1.63467 + 18.6844i 0.0718234 + 0.820945i
\(519\) 0 0
\(520\) −7.85854 + 32.7264i −0.344620 + 1.43515i
\(521\) 2.29310 1.32392i 0.100463 0.0580021i −0.448927 0.893568i \(-0.648194\pi\)
0.549390 + 0.835566i \(0.314860\pi\)
\(522\) 0 0
\(523\) 3.37351 + 12.5901i 0.147513 + 0.550527i 0.999631 + 0.0271764i \(0.00865159\pi\)
−0.852117 + 0.523351i \(0.824682\pi\)
\(524\) −0.100106 + 0.0839990i −0.00437316 + 0.00366951i
\(525\) 0 0
\(526\) −3.14347 + 17.8275i −0.137062 + 0.777317i
\(527\) 4.44773 + 6.35202i 0.193746 + 0.276698i
\(528\) 0 0
\(529\) 5.34967 + 6.37549i 0.232594 + 0.277195i
\(530\) −3.64945 1.58703i −0.158522 0.0689361i
\(531\) 0 0
\(532\) −0.106864 + 0.398822i −0.00463314 + 0.0172911i
\(533\) −18.1347 38.8899i −0.785499 1.68451i
\(534\) 0 0
\(535\) 6.46800 + 31.7989i 0.279636 + 1.37478i
\(536\) 9.80156 + 26.9296i 0.423363 + 1.16318i
\(537\) 0 0
\(538\) −13.4217 9.39794i −0.578649 0.405174i
\(539\) 13.6268 0.586947
\(540\) 0 0
\(541\) −42.0435 −1.80759 −0.903796 0.427963i \(-0.859231\pi\)
−0.903796 + 0.427963i \(0.859231\pi\)
\(542\) 21.4998 + 15.0543i 0.923494 + 0.646637i
\(543\) 0 0
\(544\) −1.44949 3.98243i −0.0621463 0.170745i
\(545\) −26.7489 17.7065i −1.14580 0.758465i
\(546\) 0 0
\(547\) −9.73975 20.8870i −0.416442 0.893062i −0.996893 0.0787671i \(-0.974902\pi\)
0.580451 0.814295i \(-0.302876\pi\)
\(548\) 0.368084 1.37371i 0.0157238 0.0586818i
\(549\) 0 0
\(550\) 25.2338 13.4140i 1.07597 0.571977i
\(551\) 3.80505 + 4.53468i 0.162101 + 0.193184i
\(552\) 0 0
\(553\) −0.468201 0.668660i −0.0199099 0.0284343i
\(554\) 0.467751 2.65275i 0.0198728 0.112704i
\(555\) 0 0
\(556\) −3.33853 + 2.80136i −0.141585 + 0.118804i
\(557\) 9.19419 + 34.3132i 0.389570 + 1.45390i 0.830835 + 0.556519i \(0.187863\pi\)
−0.441265 + 0.897377i \(0.645470\pi\)
\(558\) 0 0
\(559\) 5.66426 3.27026i 0.239572 0.138317i
\(560\) −12.9673 + 7.94551i −0.547967 + 0.335759i
\(561\) 0 0
\(562\) 3.02674 + 34.5957i 0.127675 + 1.45933i
\(563\) 4.24073 + 1.97748i 0.178725 + 0.0833410i 0.509922 0.860221i \(-0.329674\pi\)
−0.331196 + 0.943562i \(0.607452\pi\)
\(564\) 0 0
\(565\) 26.8001 + 14.5529i 1.12749 + 0.612246i
\(566\) 3.08073i 0.129493i
\(567\) 0 0
\(568\) −11.9317 + 11.9317i −0.500642 + 0.500642i
\(569\) −1.37633 7.80556i −0.0576988 0.327226i 0.942272 0.334848i \(-0.108685\pi\)
−0.999971 + 0.00762185i \(0.997574\pi\)
\(570\) 0 0
\(571\) 4.65824 1.69546i 0.194941 0.0709528i −0.242705 0.970100i \(-0.578035\pi\)
0.437646 + 0.899147i \(0.355812\pi\)
\(572\) 5.11288 0.447319i 0.213780 0.0187033i
\(573\) 0 0
\(574\) 7.52995 20.6884i 0.314294 0.863516i
\(575\) −0.979225 + 27.9662i −0.0408365 + 1.16627i
\(576\) 0 0
\(577\) 22.0266 5.90200i 0.916977 0.245703i 0.230684 0.973029i \(-0.425904\pi\)
0.686293 + 0.727325i \(0.259237\pi\)
\(578\) 8.93890 + 0.782053i 0.371809 + 0.0325291i
\(579\) 0 0
\(580\) 0.212362 3.46941i 0.00881784 0.144060i
\(581\) 17.8737 + 3.15161i 0.741526 + 0.130751i
\(582\) 0 0
\(583\) −0.502393 + 5.74237i −0.0208070 + 0.237825i
\(584\) 7.58853 13.1437i 0.314015 0.543891i
\(585\) 0 0
\(586\) 8.00664 + 13.8679i 0.330751 + 0.572878i
\(587\) −33.9155 + 15.8151i −1.39984 + 0.652758i −0.968405 0.249384i \(-0.919772\pi\)
−0.431439 + 0.902142i \(0.641994\pi\)
\(588\) 0 0
\(589\) −1.39555 + 1.66315i −0.0575026 + 0.0685290i
\(590\) −13.7114 4.58847i −0.564488 0.188904i
\(591\) 0 0
\(592\) 14.3700 20.5225i 0.590604 0.843470i
\(593\) 5.46266 + 5.46266i 0.224324 + 0.224324i 0.810317 0.585992i \(-0.199295\pi\)
−0.585992 + 0.810317i \(0.699295\pi\)
\(594\) 0 0
\(595\) −1.58558 13.9222i −0.0650024 0.570756i
\(596\) 2.01008 0.354432i 0.0823362 0.0145181i
\(597\) 0 0
\(598\) 15.9266 34.1546i 0.651286 1.39669i
\(599\) 1.79656 + 1.50749i 0.0734055 + 0.0615946i 0.678752 0.734367i \(-0.262521\pi\)
−0.605347 + 0.795962i \(0.706965\pi\)
\(600\) 0 0
\(601\) 38.1639 + 13.8905i 1.55674 + 0.566607i 0.969987 0.243159i \(-0.0781836\pi\)
0.586753 + 0.809766i \(0.300406\pi\)
\(602\) 3.24142 + 0.868536i 0.132110 + 0.0353989i
\(603\) 0 0
\(604\) 3.24716 + 1.87475i 0.132125 + 0.0762824i
\(605\) −12.1837 11.5629i −0.495336 0.470101i
\(606\) 0 0
\(607\) −1.53527 + 1.07501i −0.0623147 + 0.0436332i −0.604319 0.796743i \(-0.706555\pi\)
0.542004 + 0.840376i \(0.317666\pi\)
\(608\) 0.971981 0.680588i 0.0394190 0.0276015i
\(609\) 0 0
\(610\) 24.9669 0.652611i 1.01088 0.0264234i
\(611\) 36.1789 + 20.8879i 1.46364 + 0.845035i
\(612\) 0 0
\(613\) −17.5910 4.71349i −0.710494 0.190376i −0.114568 0.993415i \(-0.536548\pi\)
−0.595926 + 0.803039i \(0.703215\pi\)
\(614\) 29.3338 + 10.6766i 1.18382 + 0.430874i
\(615\) 0 0
\(616\) 19.1608 + 16.0778i 0.772012 + 0.647795i
\(617\) 7.87526 16.8885i 0.317046 0.679907i −0.681611 0.731715i \(-0.738720\pi\)
0.998657 + 0.0518073i \(0.0164982\pi\)
\(618\) 0 0
\(619\) −28.0130 + 4.93945i −1.12594 + 0.198533i −0.705447 0.708763i \(-0.749254\pi\)
−0.420492 + 0.907296i \(0.638142\pi\)
\(620\) 1.26665 0.144256i 0.0508697 0.00579345i
\(621\) 0 0
\(622\) −3.73594 3.73594i −0.149797 0.149797i
\(623\) −2.18848 + 3.12547i −0.0876795 + 0.125219i
\(624\) 0 0
\(625\) −17.3698 + 17.9802i −0.694793 + 0.719210i
\(626\) −0.780926 + 0.930671i −0.0312121 + 0.0371971i
\(627\) 0 0
\(628\) 2.83130 1.32026i 0.112981 0.0526840i
\(629\) 11.5418 + 19.9910i 0.460202 + 0.797093i
\(630\) 0 0
\(631\) −16.2016 + 28.0619i −0.644974 + 1.11713i 0.339333 + 0.940666i \(0.389799\pi\)
−0.984307 + 0.176462i \(0.943535\pi\)
\(632\) −0.107907 + 1.23338i −0.00429231 + 0.0490613i
\(633\) 0 0
\(634\) −34.4974 6.08282i −1.37007 0.241580i
\(635\) 5.33422 + 6.02981i 0.211682 + 0.239286i
\(636\) 0 0
\(637\) 15.9928 + 1.39919i 0.633659 + 0.0554380i
\(638\) 36.4671 9.77134i 1.44375 0.386851i
\(639\) 0 0
\(640\) 19.7222 + 2.94845i 0.779589 + 0.116548i
\(641\) 7.10695 19.5262i 0.280708 0.771238i −0.716571 0.697514i \(-0.754289\pi\)
0.997279 0.0737239i \(-0.0234884\pi\)
\(642\) 0 0
\(643\) 39.3334 3.44122i 1.55116 0.135709i 0.720880 0.693060i \(-0.243738\pi\)
0.830277 + 0.557351i \(0.188182\pi\)
\(644\) −2.42303 + 0.881910i −0.0954807 + 0.0347521i
\(645\) 0 0
\(646\) −0.661691 3.75263i −0.0260339 0.147645i
\(647\) −27.7872 + 27.7872i −1.09243 + 1.09243i −0.0971593 + 0.995269i \(0.530976\pi\)
−0.995269 + 0.0971593i \(0.969024\pi\)
\(648\) 0 0
\(649\) 20.9430i 0.822086i
\(650\) 30.9926 13.1522i 1.21563 0.515870i
\(651\) 0 0
\(652\) −1.58283 0.738085i −0.0619884 0.0289056i
\(653\) 1.47726 + 16.8852i 0.0578098 + 0.660770i 0.968719 + 0.248162i \(0.0798264\pi\)
−0.910909 + 0.412608i \(0.864618\pi\)
\(654\) 0 0
\(655\) 1.20736 + 0.289921i 0.0471754 + 0.0113281i
\(656\) −25.4684 + 14.7042i −0.994375 + 0.574103i
\(657\) 0 0
\(658\) 5.54754 + 20.7037i 0.216266 + 0.807115i
\(659\) −36.7210 + 30.8125i −1.43045 + 1.20029i −0.484997 + 0.874516i \(0.661179\pi\)
−0.945449 + 0.325770i \(0.894376\pi\)
\(660\) 0 0
\(661\) −0.726513 + 4.12026i −0.0282581 + 0.160259i −0.995671 0.0929427i \(-0.970373\pi\)
0.967413 + 0.253202i \(0.0814838\pi\)
\(662\) −9.79064 13.9825i −0.380524 0.543445i
\(663\) 0 0
\(664\) −17.6947 21.0877i −0.686687 0.818361i
\(665\) 3.65026 1.43768i 0.141551 0.0557508i
\(666\) 0 0
\(667\) −9.56811 + 35.7087i −0.370479 + 1.38264i
\(668\) 0.818774 + 1.75587i 0.0316793 + 0.0679365i
\(669\) 0 0
\(670\) 15.8237 23.9045i 0.611321 0.923511i
\(671\) −12.3730 33.9945i −0.477653 1.31234i
\(672\) 0 0
\(673\) −19.5570 13.6940i −0.753867 0.527863i 0.132311 0.991208i \(-0.457760\pi\)
−0.886178 + 0.463345i \(0.846649\pi\)
\(674\) −11.2915 −0.434933
\(675\) 0 0
\(676\) 2.98725 0.114894
\(677\) 18.1236 + 12.6903i 0.696547 + 0.487727i 0.867427 0.497565i \(-0.165772\pi\)
−0.170880 + 0.985292i \(0.554661\pi\)
\(678\) 0 0
\(679\) 9.04396 + 24.8481i 0.347075 + 0.953581i
\(680\) −11.7311 + 17.7220i −0.449869 + 0.679608i
\(681\) 0 0
\(682\) 5.85182 + 12.5493i 0.224078 + 0.480537i
\(683\) −6.53337 + 24.3829i −0.249993 + 0.932985i 0.720815 + 0.693127i \(0.243768\pi\)
−0.970808 + 0.239858i \(0.922899\pi\)
\(684\) 0 0
\(685\) −12.5730 + 4.95195i −0.480389 + 0.189204i
\(686\) 16.9965 + 20.2556i 0.648929 + 0.773363i
\(687\) 0 0
\(688\) −2.57107 3.67187i −0.0980212 0.139989i
\(689\) −1.17925 + 6.68785i −0.0449258 + 0.254787i
\(690\) 0 0
\(691\) 25.5999 21.4808i 0.973865 0.817170i −0.00928734 0.999957i \(-0.502956\pi\)
0.983153 + 0.182787i \(0.0585118\pi\)
\(692\) −0.473473 1.76703i −0.0179988 0.0671723i
\(693\) 0 0
\(694\) 6.05298 3.49469i 0.229768 0.132657i
\(695\) 40.2653 + 9.66884i 1.52735 + 0.366760i
\(696\) 0 0
\(697\) −2.36159 26.9931i −0.0894517 1.02244i
\(698\) −24.8229 11.5751i −0.939559 0.438124i
\(699\) 0 0
\(700\) −2.13581 0.863157i −0.0807261 0.0326243i
\(701\) 12.4042i 0.468499i −0.972177 0.234249i \(-0.924737\pi\)
0.972177 0.234249i \(-0.0752632\pi\)
\(702\) 0 0
\(703\) −4.57003 + 4.57003i −0.172362 + 0.172362i
\(704\) −6.50508 36.8922i −0.245170 1.39043i
\(705\) 0 0
\(706\) −35.9678 + 13.0912i −1.35367 + 0.492694i
\(707\) 8.29809 0.725989i 0.312082 0.0273036i
\(708\) 0 0
\(709\) −4.29127 + 11.7902i −0.161162 + 0.442789i −0.993821 0.110998i \(-0.964595\pi\)
0.832659 + 0.553786i \(0.186818\pi\)
\(710\) 16.6940 + 2.49573i 0.626514 + 0.0936631i
\(711\) 0 0
\(712\) 5.58994 1.49782i 0.209492 0.0561332i
\(713\) −13.5070 1.18171i −0.505842 0.0442554i
\(714\) 0 0
\(715\) −32.3121 36.5257i −1.20840 1.36598i
\(716\) 1.01940 + 0.179748i 0.0380969 + 0.00671750i
\(717\) 0 0
\(718\) 2.06408 23.5926i 0.0770308 0.880466i
\(719\) −9.10268 + 15.7663i −0.339473 + 0.587984i −0.984334 0.176316i \(-0.943582\pi\)
0.644861 + 0.764300i \(0.276915\pi\)
\(720\) 0 0
\(721\) −13.0717 22.6408i −0.486815 0.843188i
\(722\) −21.9081 + 10.2159i −0.815334 + 0.380196i
\(723\) 0 0
\(724\) −0.864744 + 1.03056i −0.0321380 + 0.0383005i
\(725\) −27.7006 + 17.9853i −1.02877 + 0.667956i
\(726\) 0 0
\(727\) −5.64377 + 8.06014i −0.209316 + 0.298934i −0.910058 0.414480i \(-0.863963\pi\)
0.700742 + 0.713414i \(0.252852\pi\)
\(728\) 20.8369 + 20.8369i 0.772267 + 0.772267i
\(729\) 0 0
\(730\) −15.0845 + 1.71795i −0.558304 + 0.0635841i
\(731\) 4.06735 0.717184i 0.150436 0.0265260i
\(732\) 0 0
\(733\) −15.6224 + 33.5024i −0.577027 + 1.23744i 0.373740 + 0.927533i \(0.378075\pi\)
−0.950767 + 0.309905i \(0.899703\pi\)
\(734\) −22.3146 18.7242i −0.823646 0.691121i
\(735\) 0 0
\(736\) 6.96332 + 2.53444i 0.256671 + 0.0934207i
\(737\) −40.1088 10.7471i −1.47743 0.395875i
\(738\) 0 0
\(739\) −7.02338 4.05495i −0.258359 0.149164i 0.365227 0.930919i \(-0.380991\pi\)
−0.623586 + 0.781755i \(0.714325\pi\)
\(740\) 3.79368 0.0991631i 0.139459 0.00364531i
\(741\) 0 0
\(742\) −2.85416 + 1.99851i −0.104780 + 0.0733675i
\(743\) −25.5056 + 17.8592i −0.935709 + 0.655190i −0.938674 0.344805i \(-0.887945\pi\)
0.00296531 + 0.999996i \(0.499056\pi\)
\(744\) 0 0
\(745\) −14.0672 13.3505i −0.515383 0.489126i
\(746\) −19.8552 11.4634i −0.726949 0.419704i
\(747\) 0 0
\(748\) 3.13050 + 0.838814i 0.114462 + 0.0306701i
\(749\) 26.6979 + 9.71724i 0.975519 + 0.355060i
\(750\) 0 0
\(751\) −13.4156 11.2570i −0.489541 0.410774i 0.364321 0.931273i \(-0.381301\pi\)
−0.853862 + 0.520500i \(0.825746\pi\)
\(752\) 12.1000 25.9484i 0.441240 0.946243i
\(753\) 0 0
\(754\) 43.8023 7.72353i 1.59519 0.281274i
\(755\) −4.03140 35.3979i −0.146718 1.28826i
\(756\) 0 0
\(757\) −20.1777 20.1777i −0.733371 0.733371i 0.237915 0.971286i \(-0.423536\pi\)
−0.971286 + 0.237915i \(0.923536\pi\)
\(758\) 20.7010 29.5641i 0.751893 1.07381i
\(759\) 0 0
\(760\) −5.64287 1.88837i −0.204688 0.0684985i
\(761\) −23.7584 + 28.3141i −0.861240 + 1.02639i 0.138113 + 0.990416i \(0.455896\pi\)
−0.999353 + 0.0359689i \(0.988548\pi\)
\(762\) 0 0
\(763\) −25.4545 + 11.8696i −0.921516 + 0.429710i
\(764\) 1.69744 + 2.94006i 0.0614113 + 0.106368i
\(765\) 0 0
\(766\) −4.88069 + 8.45360i −0.176346 + 0.305441i
\(767\) −2.15042 + 24.5794i −0.0776472 + 0.887512i
\(768\) 0 0
\(769\) 8.53754 + 1.50540i 0.307872 + 0.0542861i 0.325450 0.945559i \(-0.394484\pi\)
−0.0175779 + 0.999845i \(0.505595\pi\)
\(770\) 1.52866 24.9742i 0.0550891 0.900007i
\(771\) 0 0
\(772\) −4.06755 0.355865i −0.146394 0.0128078i
\(773\) −11.3983 + 3.05417i −0.409969 + 0.109851i −0.457908 0.889000i \(-0.651401\pi\)
0.0479396 + 0.998850i \(0.484734\pi\)
\(774\) 0 0
\(775\) −8.26030 8.85975i −0.296719 0.318252i
\(776\) 13.7174 37.6882i 0.492425 1.35293i
\(777\) 0 0
\(778\) 41.3603 3.61856i 1.48284 0.129732i
\(779\) 7.12895 2.59472i 0.255421 0.0929657i
\(780\) 0 0
\(781\) −4.24560 24.0780i −0.151919 0.861578i
\(782\) 16.8270 16.8270i 0.601733 0.601733i
\(783\) 0 0
\(784\) 11.0025i 0.392947i
\(785\) −26.0856 14.1649i −0.931035 0.505567i
\(786\) 0 0
\(787\) 17.0214