Properties

Label 405.2.r.a.197.6
Level $405$
Weight $2$
Character 405.197
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 197.6
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.03978 + 0.0909691i) q^{2} +(-0.896746 + 0.158121i) q^{4} +(-2.23373 - 0.102160i) q^{5} +(-0.567627 + 0.397456i) q^{7} +(2.93441 - 0.786273i) q^{8} +O(q^{10})\) \(q+(-1.03978 + 0.0909691i) q^{2} +(-0.896746 + 0.158121i) q^{4} +(-2.23373 - 0.102160i) q^{5} +(-0.567627 + 0.397456i) q^{7} +(2.93441 - 0.786273i) q^{8} +(2.33189 - 0.0969768i) q^{10} +(-0.597632 - 1.64198i) q^{11} +(-0.0630233 + 0.720360i) q^{13} +(0.554051 - 0.464904i) q^{14} +(-1.26829 + 0.461619i) q^{16} +(2.95614 + 0.792096i) q^{17} +(3.38781 + 1.95596i) q^{19} +(2.01925 - 0.261588i) q^{20} +(0.770776 + 1.65293i) q^{22} +(4.63055 - 6.61310i) q^{23} +(4.97913 + 0.456395i) q^{25} -0.754750i q^{26} +(0.446171 - 0.446171i) q^{28} +(5.68683 + 4.77181i) q^{29} +(0.764639 + 4.33648i) q^{31} +(-4.22984 + 1.97241i) q^{32} +(-3.14580 - 0.554689i) q^{34} +(1.30853 - 0.829823i) q^{35} +(2.86540 - 10.6938i) q^{37} +(-3.70052 - 1.72558i) q^{38} +(-6.63502 + 1.45655i) q^{40} +(-2.71443 - 3.23493i) q^{41} +(2.74095 - 5.87799i) q^{43} +(0.795555 + 1.37794i) q^{44} +(-4.21317 + 7.29742i) q^{46} +(2.32838 + 3.32527i) q^{47} +(-2.22991 + 6.12663i) q^{49} +(-5.21872 - 0.0216046i) q^{50} +(-0.0573878 - 0.655945i) q^{52} +(5.90884 + 5.90884i) q^{53} +(1.16721 + 3.72880i) q^{55} +(-1.35314 + 1.61261i) q^{56} +(-6.34714 - 4.44432i) q^{58} +(-2.63750 - 0.959971i) q^{59} +(1.13591 - 6.44205i) q^{61} +(-1.18954 - 4.43943i) q^{62} +(6.55640 - 3.78534i) q^{64} +(0.214369 - 1.60265i) q^{65} +(11.1831 + 0.978397i) q^{67} +(-2.77616 - 0.242882i) q^{68} +(-1.28510 + 0.981870i) q^{70} +(-5.58689 + 3.22559i) q^{71} +(-2.16667 - 8.08612i) q^{73} +(-2.00658 + 11.3799i) q^{74} +(-3.34729 - 1.21831i) q^{76} +(0.991847 + 0.694499i) q^{77} +(-1.04738 + 1.24822i) q^{79} +(2.88018 - 0.901566i) q^{80} +(3.11669 + 3.11669i) q^{82} +(-0.156261 - 1.78607i) q^{83} +(-6.52232 - 2.07133i) q^{85} +(-2.31528 + 6.36117i) q^{86} +(-3.04474 - 4.34834i) q^{88} +(-2.78132 + 4.81739i) q^{89} +(-0.250538 - 0.433944i) q^{91} +(-3.10676 + 6.66246i) q^{92} +(-2.72350 - 3.24574i) q^{94} +(-7.36765 - 4.71518i) q^{95} +(-4.20036 - 1.95866i) q^{97} +(1.76129 - 6.57321i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03978 + 0.0909691i −0.735236 + 0.0643248i −0.448622 0.893721i \(-0.648085\pi\)
−0.286614 + 0.958046i \(0.592530\pi\)
\(3\) 0 0
\(4\) −0.896746 + 0.158121i −0.448373 + 0.0790603i
\(5\) −2.23373 0.102160i −0.998956 0.0456872i
\(6\) 0 0
\(7\) −0.567627 + 0.397456i −0.214543 + 0.150224i −0.675908 0.736986i \(-0.736249\pi\)
0.461366 + 0.887210i \(0.347360\pi\)
\(8\) 2.93441 0.786273i 1.03747 0.277990i
\(9\) 0 0
\(10\) 2.33189 0.0969768i 0.737407 0.0306668i
\(11\) −0.597632 1.64198i −0.180193 0.495076i 0.816406 0.577478i \(-0.195963\pi\)
−0.996599 + 0.0824022i \(0.973741\pi\)
\(12\) 0 0
\(13\) −0.0630233 + 0.720360i −0.0174795 + 0.199792i 0.982434 + 0.186612i \(0.0597508\pi\)
−0.999913 + 0.0131795i \(0.995805\pi\)
\(14\) 0.554051 0.464904i 0.148076 0.124251i
\(15\) 0 0
\(16\) −1.26829 + 0.461619i −0.317072 + 0.115405i
\(17\) 2.95614 + 0.792096i 0.716970 + 0.192112i 0.598819 0.800884i \(-0.295637\pi\)
0.118151 + 0.992996i \(0.462303\pi\)
\(18\) 0 0
\(19\) 3.38781 + 1.95596i 0.777218 + 0.448727i 0.835443 0.549576i \(-0.185211\pi\)
−0.0582254 + 0.998303i \(0.518544\pi\)
\(20\) 2.01925 0.261588i 0.451517 0.0584928i
\(21\) 0 0
\(22\) 0.770776 + 1.65293i 0.164330 + 0.352407i
\(23\) 4.63055 6.61310i 0.965535 1.37893i 0.0404446 0.999182i \(-0.487123\pi\)
0.925091 0.379746i \(-0.123989\pi\)
\(24\) 0 0
\(25\) 4.97913 + 0.456395i 0.995825 + 0.0912790i
\(26\) 0.754750i 0.148019i
\(27\) 0 0
\(28\) 0.446171 0.446171i 0.0843184 0.0843184i
\(29\) 5.68683 + 4.77181i 1.05602 + 0.886103i 0.993713 0.111954i \(-0.0357109\pi\)
0.0623035 + 0.998057i \(0.480155\pi\)
\(30\) 0 0
\(31\) 0.764639 + 4.33648i 0.137333 + 0.778855i 0.973207 + 0.229933i \(0.0738506\pi\)
−0.835873 + 0.548922i \(0.815038\pi\)
\(32\) −4.22984 + 1.97241i −0.747738 + 0.348676i
\(33\) 0 0
\(34\) −3.14580 0.554689i −0.539500 0.0951284i
\(35\) 1.30853 0.829823i 0.221182 0.140266i
\(36\) 0 0
\(37\) 2.86540 10.6938i 0.471069 1.75805i −0.164870 0.986315i \(-0.552720\pi\)
0.635939 0.771739i \(-0.280613\pi\)
\(38\) −3.70052 1.72558i −0.600303 0.279926i
\(39\) 0 0
\(40\) −6.63502 + 1.45655i −1.04909 + 0.230300i
\(41\) −2.71443 3.23493i −0.423923 0.505212i 0.511236 0.859441i \(-0.329188\pi\)
−0.935159 + 0.354229i \(0.884743\pi\)
\(42\) 0 0
\(43\) 2.74095 5.87799i 0.417991 0.896385i −0.578733 0.815517i \(-0.696453\pi\)
0.996725 0.0808685i \(-0.0257694\pi\)
\(44\) 0.795555 + 1.37794i 0.119934 + 0.207733i
\(45\) 0 0
\(46\) −4.21317 + 7.29742i −0.621197 + 1.07595i
\(47\) 2.32838 + 3.32527i 0.339628 + 0.485040i 0.952243 0.305342i \(-0.0987709\pi\)
−0.612614 + 0.790382i \(0.709882\pi\)
\(48\) 0 0
\(49\) −2.22991 + 6.12663i −0.318559 + 0.875234i
\(50\) −5.21872 0.0216046i −0.738038 0.00305535i
\(51\) 0 0
\(52\) −0.0573878 0.655945i −0.00795825 0.0909632i
\(53\) 5.90884 + 5.90884i 0.811642 + 0.811642i 0.984880 0.173238i \(-0.0554230\pi\)
−0.173238 + 0.984880i \(0.555423\pi\)
\(54\) 0 0
\(55\) 1.16721 + 3.72880i 0.157386 + 0.502791i
\(56\) −1.35314 + 1.61261i −0.180821 + 0.215494i
\(57\) 0 0
\(58\) −6.34714 4.44432i −0.833420 0.583567i
\(59\) −2.63750 0.959971i −0.343373 0.124978i 0.164577 0.986364i \(-0.447374\pi\)
−0.507950 + 0.861387i \(0.669596\pi\)
\(60\) 0 0
\(61\) 1.13591 6.44205i 0.145438 0.824820i −0.821576 0.570098i \(-0.806905\pi\)
0.967014 0.254722i \(-0.0819838\pi\)
\(62\) −1.18954 4.43943i −0.151072 0.563808i
\(63\) 0 0
\(64\) 6.55640 3.78534i 0.819551 0.473168i
\(65\) 0.214369 1.60265i 0.0265892 0.198785i
\(66\) 0 0
\(67\) 11.1831 + 0.978397i 1.36624 + 0.119530i 0.746556 0.665323i \(-0.231706\pi\)
0.619682 + 0.784853i \(0.287262\pi\)
\(68\) −2.77616 0.242882i −0.336659 0.0294538i
\(69\) 0 0
\(70\) −1.28510 + 0.981870i −0.153598 + 0.117356i
\(71\) −5.58689 + 3.22559i −0.663042 + 0.382807i −0.793435 0.608655i \(-0.791709\pi\)
0.130393 + 0.991462i \(0.458376\pi\)
\(72\) 0 0
\(73\) −2.16667 8.08612i −0.253589 0.946409i −0.968870 0.247571i \(-0.920368\pi\)
0.715280 0.698838i \(-0.246299\pi\)
\(74\) −2.00658 + 11.3799i −0.233261 + 1.32289i
\(75\) 0 0
\(76\) −3.34729 1.21831i −0.383960 0.139750i
\(77\) 0.991847 + 0.694499i 0.113032 + 0.0791455i
\(78\) 0 0
\(79\) −1.04738 + 1.24822i −0.117840 + 0.140436i −0.821739 0.569863i \(-0.806996\pi\)
0.703899 + 0.710300i \(0.251441\pi\)
\(80\) 2.88018 0.901566i 0.322013 0.100798i
\(81\) 0 0
\(82\) 3.11669 + 3.11669i 0.344181 + 0.344181i
\(83\) −0.156261 1.78607i −0.0171518 0.196046i −0.999936 0.0112903i \(-0.996406\pi\)
0.982784 0.184756i \(-0.0591494\pi\)
\(84\) 0 0
\(85\) −6.52232 2.07133i −0.707444 0.224667i
\(86\) −2.31528 + 6.36117i −0.249663 + 0.685942i
\(87\) 0 0
\(88\) −3.04474 4.34834i −0.324571 0.463535i
\(89\) −2.78132 + 4.81739i −0.294820 + 0.510643i −0.974943 0.222455i \(-0.928593\pi\)
0.680123 + 0.733098i \(0.261926\pi\)
\(90\) 0 0
\(91\) −0.250538 0.433944i −0.0262635 0.0454897i
\(92\) −3.10676 + 6.66246i −0.323902 + 0.694610i
\(93\) 0 0
\(94\) −2.72350 3.24574i −0.280907 0.334772i
\(95\) −7.36765 4.71518i −0.755905 0.483767i
\(96\) 0 0
\(97\) −4.20036 1.95866i −0.426482 0.198872i 0.197513 0.980300i \(-0.436714\pi\)
−0.623995 + 0.781429i \(0.714491\pi\)
\(98\) 1.76129 6.57321i 0.177917 0.663995i
\(99\) 0 0
\(100\) −4.53718 + 0.378032i −0.453718 + 0.0378032i
\(101\) −11.1359 1.96356i −1.10806 0.195381i −0.410469 0.911875i \(-0.634635\pi\)
−0.697594 + 0.716493i \(0.745746\pi\)
\(102\) 0 0
\(103\) −4.47475 + 2.08661i −0.440911 + 0.205600i −0.630380 0.776287i \(-0.717101\pi\)
0.189470 + 0.981887i \(0.439323\pi\)
\(104\) 0.381463 + 2.16339i 0.0374055 + 0.212137i
\(105\) 0 0
\(106\) −6.68142 5.60638i −0.648957 0.544540i
\(107\) 11.1511 11.1511i 1.07801 1.07801i 0.0813251 0.996688i \(-0.474085\pi\)
0.996688 0.0813251i \(-0.0259152\pi\)
\(108\) 0 0
\(109\) 20.3152i 1.94584i 0.231133 + 0.972922i \(0.425757\pi\)
−0.231133 + 0.972922i \(0.574243\pi\)
\(110\) −1.55284 3.77096i −0.148058 0.359546i
\(111\) 0 0
\(112\) 0.536441 0.766117i 0.0506889 0.0723912i
\(113\) −0.0516106 0.110679i −0.00485512 0.0104118i 0.903865 0.427817i \(-0.140717\pi\)
−0.908720 + 0.417405i \(0.862940\pi\)
\(114\) 0 0
\(115\) −11.0190 + 14.2989i −1.02753 + 1.33338i
\(116\) −5.85416 3.37990i −0.543545 0.313816i
\(117\) 0 0
\(118\) 2.82975 + 0.758229i 0.260500 + 0.0698006i
\(119\) −1.99281 + 0.725323i −0.182681 + 0.0664903i
\(120\) 0 0
\(121\) 6.08755 5.10806i 0.553414 0.464369i
\(122\) −0.595068 + 6.80165i −0.0538749 + 0.615793i
\(123\) 0 0
\(124\) −1.37137 3.76782i −0.123153 0.338360i
\(125\) −11.0754 1.52813i −0.990615 0.136680i
\(126\) 0 0
\(127\) −16.0361 + 4.29687i −1.42298 + 0.381286i −0.886539 0.462654i \(-0.846897\pi\)
−0.536439 + 0.843939i \(0.680231\pi\)
\(128\) 1.17328 0.821539i 0.103704 0.0726144i
\(129\) 0 0
\(130\) −0.0771050 + 1.68591i −0.00676256 + 0.147864i
\(131\) 22.1825 3.91138i 1.93810 0.341739i 0.938109 0.346341i \(-0.112576\pi\)
0.999989 + 0.00460251i \(0.00146503\pi\)
\(132\) 0 0
\(133\) −2.70042 + 0.236256i −0.234156 + 0.0204860i
\(134\) −11.7170 −1.01220
\(135\) 0 0
\(136\) 9.29735 0.797241
\(137\) −5.19392 + 0.454409i −0.443747 + 0.0388228i −0.306840 0.951761i \(-0.599272\pi\)
−0.136907 + 0.990584i \(0.543716\pi\)
\(138\) 0 0
\(139\) 12.7974 2.25653i 1.08546 0.191396i 0.397833 0.917458i \(-0.369762\pi\)
0.687630 + 0.726061i \(0.258651\pi\)
\(140\) −1.04221 + 0.951046i −0.0880826 + 0.0803781i
\(141\) 0 0
\(142\) 5.51571 3.86214i 0.462868 0.324104i
\(143\) 1.22048 0.327027i 0.102062 0.0273474i
\(144\) 0 0
\(145\) −12.2154 11.2399i −1.01443 0.933425i
\(146\) 2.98845 + 8.21069i 0.247326 + 0.679522i
\(147\) 0 0
\(148\) −0.878625 + 10.0427i −0.0722225 + 0.825507i
\(149\) 8.70742 7.30639i 0.713340 0.598563i −0.212194 0.977227i \(-0.568061\pi\)
0.925534 + 0.378664i \(0.123617\pi\)
\(150\) 0 0
\(151\) −8.54652 + 3.11068i −0.695506 + 0.253143i −0.665491 0.746406i \(-0.731778\pi\)
−0.0300149 + 0.999549i \(0.509555\pi\)
\(152\) 11.4792 + 3.07583i 0.931083 + 0.249483i
\(153\) 0 0
\(154\) −1.09448 0.631900i −0.0881959 0.0509199i
\(155\) −1.26498 9.76466i −0.101606 0.784316i
\(156\) 0 0
\(157\) 1.41498 + 3.03444i 0.112928 + 0.242175i 0.954646 0.297742i \(-0.0962335\pi\)
−0.841718 + 0.539917i \(0.818456\pi\)
\(158\) 0.975501 1.39316i 0.0776067 0.110834i
\(159\) 0 0
\(160\) 9.64984 3.97371i 0.762887 0.314150i
\(161\) 5.59421i 0.440886i
\(162\) 0 0
\(163\) 9.97670 9.97670i 0.781435 0.781435i −0.198638 0.980073i \(-0.563652\pi\)
0.980073 + 0.198638i \(0.0636517\pi\)
\(164\) 2.94567 + 2.47171i 0.230018 + 0.193008i
\(165\) 0 0
\(166\) 0.324953 + 1.84290i 0.0252213 + 0.143037i
\(167\) 12.6150 5.88249i 0.976182 0.455201i 0.131995 0.991250i \(-0.457862\pi\)
0.844187 + 0.536049i \(0.180084\pi\)
\(168\) 0 0
\(169\) 12.2876 + 2.16663i 0.945196 + 0.166664i
\(170\) 6.97021 + 1.56040i 0.534590 + 0.119677i
\(171\) 0 0
\(172\) −1.52851 + 5.70447i −0.116548 + 0.434962i
\(173\) 2.81939 + 1.31470i 0.214354 + 0.0999551i 0.526830 0.849971i \(-0.323380\pi\)
−0.312476 + 0.949926i \(0.601158\pi\)
\(174\) 0 0
\(175\) −3.00768 + 1.71992i −0.227359 + 0.130014i
\(176\) 1.51594 + 1.80663i 0.114268 + 0.136180i
\(177\) 0 0
\(178\) 2.45373 5.26205i 0.183915 0.394407i
\(179\) −2.53650 4.39334i −0.189587 0.328374i 0.755526 0.655119i \(-0.227381\pi\)
−0.945113 + 0.326745i \(0.894048\pi\)
\(180\) 0 0
\(181\) −4.66805 + 8.08530i −0.346974 + 0.600976i −0.985710 0.168449i \(-0.946124\pi\)
0.638737 + 0.769425i \(0.279457\pi\)
\(182\) 0.299980 + 0.428416i 0.0222360 + 0.0317563i
\(183\) 0 0
\(184\) 8.38822 23.0464i 0.618388 1.69901i
\(185\) −7.49302 + 23.5944i −0.550898 + 1.73470i
\(186\) 0 0
\(187\) −0.466079 5.32731i −0.0340831 0.389572i
\(188\) −2.61375 2.61375i −0.190628 0.190628i
\(189\) 0 0
\(190\) 8.08968 + 4.23253i 0.586887 + 0.307060i
\(191\) −0.729528 + 0.869417i −0.0527868 + 0.0629088i −0.791792 0.610791i \(-0.790852\pi\)
0.739005 + 0.673700i \(0.235296\pi\)
\(192\) 0 0
\(193\) 11.2910 + 7.90607i 0.812746 + 0.569091i 0.904393 0.426701i \(-0.140324\pi\)
−0.0916467 + 0.995792i \(0.529213\pi\)
\(194\) 4.54563 + 1.65447i 0.326357 + 0.118784i
\(195\) 0 0
\(196\) 1.03092 5.84663i 0.0736371 0.417617i
\(197\) −0.517983 1.93314i −0.0369048 0.137730i 0.945015 0.327026i \(-0.106046\pi\)
−0.981920 + 0.189295i \(0.939380\pi\)
\(198\) 0 0
\(199\) 16.0030 9.23931i 1.13442 0.654957i 0.189377 0.981905i \(-0.439353\pi\)
0.945043 + 0.326947i \(0.106020\pi\)
\(200\) 14.9697 2.57570i 1.05851 0.182130i
\(201\) 0 0
\(202\) 11.7575 + 1.02865i 0.827256 + 0.0723755i
\(203\) −5.12458 0.448343i −0.359675 0.0314675i
\(204\) 0 0
\(205\) 5.73284 + 7.50329i 0.400399 + 0.524052i
\(206\) 4.46295 2.57668i 0.310948 0.179526i
\(207\) 0 0
\(208\) −0.252600 0.942717i −0.0175147 0.0653656i
\(209\) 1.18697 6.73167i 0.0821047 0.465639i
\(210\) 0 0
\(211\) 15.7638 + 5.73754i 1.08522 + 0.394989i 0.821849 0.569705i \(-0.192943\pi\)
0.263374 + 0.964694i \(0.415165\pi\)
\(212\) −6.23304 4.36442i −0.428087 0.299750i
\(213\) 0 0
\(214\) −10.5803 + 12.6091i −0.723251 + 0.861937i
\(215\) −6.72305 + 12.8498i −0.458508 + 0.876352i
\(216\) 0 0
\(217\) −2.15759 2.15759i −0.146467 0.146467i
\(218\) −1.84806 21.1234i −0.125166 1.43066i
\(219\) 0 0
\(220\) −1.63629 3.15923i −0.110318 0.212995i
\(221\) −0.756900 + 2.07957i −0.0509146 + 0.139887i
\(222\) 0 0
\(223\) 11.5264 + 16.4615i 0.771868 + 1.10234i 0.991921 + 0.126854i \(0.0404879\pi\)
−0.220054 + 0.975488i \(0.570623\pi\)
\(224\) 1.61703 2.80077i 0.108042 0.187134i
\(225\) 0 0
\(226\) 0.0637321 + 0.110387i 0.00423940 + 0.00734285i
\(227\) −1.96975 + 4.22414i −0.130737 + 0.280366i −0.960769 0.277349i \(-0.910544\pi\)
0.830032 + 0.557715i \(0.188322\pi\)
\(228\) 0 0
\(229\) −15.6103 18.6036i −1.03156 1.22936i −0.972935 0.231080i \(-0.925774\pi\)
−0.0586205 0.998280i \(-0.518670\pi\)
\(230\) 10.1566 15.8701i 0.669706 1.04644i
\(231\) 0 0
\(232\) 20.4394 + 9.53106i 1.34191 + 0.625745i
\(233\) −1.83322 + 6.84167i −0.120098 + 0.448213i −0.999618 0.0276501i \(-0.991198\pi\)
0.879519 + 0.475863i \(0.157864\pi\)
\(234\) 0 0
\(235\) −4.86126 7.66562i −0.317114 0.500050i
\(236\) 2.51696 + 0.443808i 0.163840 + 0.0288894i
\(237\) 0 0
\(238\) 2.00610 0.935462i 0.130036 0.0606370i
\(239\) −2.01666 11.4370i −0.130447 0.739799i −0.977923 0.208966i \(-0.932990\pi\)
0.847476 0.530833i \(-0.178121\pi\)
\(240\) 0 0
\(241\) 8.02324 + 6.73230i 0.516822 + 0.433665i 0.863522 0.504311i \(-0.168253\pi\)
−0.346700 + 0.937976i \(0.612698\pi\)
\(242\) −5.86505 + 5.86505i −0.377020 + 0.377020i
\(243\) 0 0
\(244\) 5.95649i 0.381325i
\(245\) 5.60692 13.4575i 0.358213 0.859766i
\(246\) 0 0
\(247\) −1.62250 + 2.31717i −0.103237 + 0.147438i
\(248\) 5.65342 + 12.1238i 0.358993 + 0.769862i
\(249\) 0 0
\(250\) 11.6550 + 0.581402i 0.737128 + 0.0367711i
\(251\) 9.75413 + 5.63155i 0.615675 + 0.355460i 0.775183 0.631736i \(-0.217657\pi\)
−0.159508 + 0.987197i \(0.550991\pi\)
\(252\) 0 0
\(253\) −13.6259 3.65106i −0.856656 0.229540i
\(254\) 16.2832 5.92660i 1.02170 0.371868i
\(255\) 0 0
\(256\) −12.7442 + 10.6936i −0.796511 + 0.668352i
\(257\) −1.72895 + 19.7620i −0.107849 + 1.23272i 0.728701 + 0.684832i \(0.240124\pi\)
−0.836551 + 0.547890i \(0.815431\pi\)
\(258\) 0 0
\(259\) 2.62385 + 7.20897i 0.163038 + 0.447944i
\(260\) 0.0611778 + 1.47107i 0.00379408 + 0.0912318i
\(261\) 0 0
\(262\) −22.7092 + 6.08491i −1.40298 + 0.375927i
\(263\) 13.8257 9.68085i 0.852529 0.596947i −0.0635351 0.997980i \(-0.520237\pi\)
0.916064 + 0.401033i \(0.131349\pi\)
\(264\) 0 0
\(265\) −12.5951 13.8024i −0.773713 0.847876i
\(266\) 2.78635 0.491310i 0.170842 0.0301241i
\(267\) 0 0
\(268\) −10.1831 + 0.890909i −0.622034 + 0.0544209i
\(269\) −30.5994 −1.86568 −0.932838 0.360296i \(-0.882676\pi\)
−0.932838 + 0.360296i \(0.882676\pi\)
\(270\) 0 0
\(271\) −5.21670 −0.316892 −0.158446 0.987368i \(-0.550648\pi\)
−0.158446 + 0.987368i \(0.550648\pi\)
\(272\) −4.11489 + 0.360006i −0.249502 + 0.0218286i
\(273\) 0 0
\(274\) 5.35921 0.944973i 0.323761 0.0570879i
\(275\) −2.22629 8.44838i −0.134251 0.509457i
\(276\) 0 0
\(277\) −9.56033 + 6.69422i −0.574425 + 0.402216i −0.824377 0.566042i \(-0.808474\pi\)
0.249952 + 0.968258i \(0.419585\pi\)
\(278\) −13.1012 + 3.51047i −0.785760 + 0.210544i
\(279\) 0 0
\(280\) 3.18730 3.46390i 0.190478 0.207008i
\(281\) −4.68215 12.8641i −0.279313 0.767407i −0.997441 0.0714958i \(-0.977223\pi\)
0.718127 0.695912i \(-0.244999\pi\)
\(282\) 0 0
\(283\) 0.773481 8.84093i 0.0459787 0.525539i −0.937925 0.346838i \(-0.887255\pi\)
0.983904 0.178700i \(-0.0571892\pi\)
\(284\) 4.49999 3.77594i 0.267025 0.224061i
\(285\) 0 0
\(286\) −1.23928 + 0.451062i −0.0732804 + 0.0266719i
\(287\) 2.82653 + 0.757366i 0.166845 + 0.0447059i
\(288\) 0 0
\(289\) −6.61106 3.81690i −0.388886 0.224524i
\(290\) 13.7238 + 10.5758i 0.805889 + 0.621035i
\(291\) 0 0
\(292\) 3.22153 + 6.90860i 0.188526 + 0.404295i
\(293\) −6.47833 + 9.25201i −0.378468 + 0.540508i −0.962521 0.271207i \(-0.912577\pi\)
0.584053 + 0.811716i \(0.301466\pi\)
\(294\) 0 0
\(295\) 5.79340 + 2.41377i 0.337305 + 0.140535i
\(296\) 33.6331i 1.95488i
\(297\) 0 0
\(298\) −8.38915 + 8.38915i −0.485971 + 0.485971i
\(299\) 4.47198 + 3.75244i 0.258621 + 0.217009i
\(300\) 0 0
\(301\) 0.780408 + 4.42591i 0.0449820 + 0.255105i
\(302\) 8.60353 4.01189i 0.495078 0.230858i
\(303\) 0 0
\(304\) −5.19963 0.916835i −0.298219 0.0525841i
\(305\) −3.19543 + 14.2738i −0.182970 + 0.817314i
\(306\) 0 0
\(307\) 2.20847 8.24213i 0.126044 0.470403i −0.873831 0.486230i \(-0.838372\pi\)
0.999875 + 0.0158274i \(0.00503823\pi\)
\(308\) −0.999250 0.465958i −0.0569376 0.0265504i
\(309\) 0 0
\(310\) 2.20359 + 10.0380i 0.125155 + 0.570122i
\(311\) 9.40563 + 11.2092i 0.533344 + 0.635615i 0.963682 0.267053i \(-0.0860500\pi\)
−0.430338 + 0.902668i \(0.641606\pi\)
\(312\) 0 0
\(313\) −3.94117 + 8.45186i −0.222768 + 0.477727i −0.985648 0.168812i \(-0.946007\pi\)
0.762880 + 0.646540i \(0.223785\pi\)
\(314\) −1.74731 3.02644i −0.0986067 0.170792i
\(315\) 0 0
\(316\) 0.741868 1.28495i 0.0417333 0.0722843i
\(317\) −13.5519 19.3542i −0.761152 1.08704i −0.993436 0.114390i \(-0.963509\pi\)
0.232283 0.972648i \(-0.425380\pi\)
\(318\) 0 0
\(319\) 4.43659 12.1894i 0.248402 0.682478i
\(320\) −15.0320 + 7.78564i −0.840312 + 0.435231i
\(321\) 0 0
\(322\) −0.508900 5.81676i −0.0283599 0.324155i
\(323\) 8.46556 + 8.46556i 0.471036 + 0.471036i
\(324\) 0 0
\(325\) −0.642570 + 3.55800i −0.0356434 + 0.197362i
\(326\) −9.46601 + 11.2812i −0.524274 + 0.624805i
\(327\) 0 0
\(328\) −10.5088 7.35834i −0.580252 0.406297i
\(329\) −2.64330 0.962081i −0.145730 0.0530413i
\(330\) 0 0
\(331\) 4.01625 22.7773i 0.220753 1.25195i −0.649886 0.760032i \(-0.725183\pi\)
0.870639 0.491922i \(-0.163705\pi\)
\(332\) 0.422540 + 1.57694i 0.0231899 + 0.0865458i
\(333\) 0 0
\(334\) −12.5818 + 7.26408i −0.688443 + 0.397473i
\(335\) −24.8802 3.32794i −1.35935 0.181825i
\(336\) 0 0
\(337\) −12.4168 1.08633i −0.676384 0.0591760i −0.256212 0.966621i \(-0.582475\pi\)
−0.420172 + 0.907445i \(0.638030\pi\)
\(338\) −12.9735 1.13503i −0.705663 0.0617375i
\(339\) 0 0
\(340\) 6.17638 + 0.826146i 0.334961 + 0.0448040i
\(341\) 6.66344 3.84714i 0.360846 0.208334i
\(342\) 0 0
\(343\) −2.42474 9.04926i −0.130924 0.488614i
\(344\) 3.42137 19.4036i 0.184468 1.04617i
\(345\) 0 0
\(346\) −3.05115 1.11053i −0.164031 0.0597023i
\(347\) −9.36840 6.55983i −0.502922 0.352150i 0.294421 0.955676i \(-0.404873\pi\)
−0.797343 + 0.603526i \(0.793762\pi\)
\(348\) 0 0
\(349\) −15.6113 + 18.6048i −0.835652 + 0.995891i 0.164303 + 0.986410i \(0.447462\pi\)
−0.999955 + 0.00948135i \(0.996982\pi\)
\(350\) 2.97087 2.06195i 0.158800 0.110216i
\(351\) 0 0
\(352\) 5.76654 + 5.76654i 0.307358 + 0.307358i
\(353\) 2.92059 + 33.3825i 0.155447 + 1.77677i 0.528472 + 0.848951i \(0.322765\pi\)
−0.373024 + 0.927822i \(0.621679\pi\)
\(354\) 0 0
\(355\) 12.8091 6.63436i 0.679839 0.352115i
\(356\) 1.73241 4.75976i 0.0918177 0.252267i
\(357\) 0 0
\(358\) 3.03706 + 4.33737i 0.160514 + 0.229237i
\(359\) −9.34241 + 16.1815i −0.493073 + 0.854028i −0.999968 0.00797981i \(-0.997460\pi\)
0.506895 + 0.862008i \(0.330793\pi\)
\(360\) 0 0
\(361\) −1.84847 3.20165i −0.0972881 0.168508i
\(362\) 4.11824 8.83159i 0.216450 0.464178i
\(363\) 0 0
\(364\) 0.293285 + 0.349523i 0.0153723 + 0.0183200i
\(365\) 4.01368 + 18.2836i 0.210086 + 0.957006i
\(366\) 0 0
\(367\) −6.45312 3.00914i −0.336850 0.157076i 0.246831 0.969058i \(-0.420611\pi\)
−0.583682 + 0.811983i \(0.698388\pi\)
\(368\) −2.82013 + 10.5249i −0.147009 + 0.548647i
\(369\) 0 0
\(370\) 5.64474 25.2147i 0.293456 1.31085i
\(371\) −5.70252 1.00551i −0.296060 0.0522034i
\(372\) 0 0
\(373\) −9.36399 + 4.36650i −0.484849 + 0.226089i −0.649643 0.760239i \(-0.725082\pi\)
0.164794 + 0.986328i \(0.447304\pi\)
\(374\) 0.969241 + 5.49684i 0.0501183 + 0.284235i
\(375\) 0 0
\(376\) 9.44698 + 7.92696i 0.487191 + 0.408802i
\(377\) −3.79582 + 3.79582i −0.195495 + 0.195495i
\(378\) 0 0
\(379\) 5.45309i 0.280106i −0.990144 0.140053i \(-0.955273\pi\)
0.990144 0.140053i \(-0.0447273\pi\)
\(380\) 7.35248 + 3.06334i 0.377174 + 0.157146i
\(381\) 0 0
\(382\) 0.679459 0.970368i 0.0347641 0.0496483i
\(383\) 1.88914 + 4.05128i 0.0965307 + 0.207011i 0.948643 0.316348i \(-0.102457\pi\)
−0.852113 + 0.523359i \(0.824679\pi\)
\(384\) 0 0
\(385\) −2.14457 1.65265i −0.109298 0.0842270i
\(386\) −12.4594 7.19344i −0.634167 0.366137i
\(387\) 0 0
\(388\) 4.07636 + 1.09226i 0.206946 + 0.0554510i
\(389\) 9.10172 3.31276i 0.461476 0.167963i −0.100811 0.994906i \(-0.532144\pi\)
0.562287 + 0.826942i \(0.309922\pi\)
\(390\) 0 0
\(391\) 18.9268 15.8814i 0.957168 0.803159i
\(392\) −1.72627 + 19.7314i −0.0871899 + 0.996586i
\(393\) 0 0
\(394\) 0.714445 + 1.96292i 0.0359932 + 0.0988906i
\(395\) 2.46710 2.68120i 0.124133 0.134906i
\(396\) 0 0
\(397\) −0.981728 + 0.263053i −0.0492715 + 0.0132023i −0.283371 0.959010i \(-0.591453\pi\)
0.234099 + 0.972213i \(0.424786\pi\)
\(398\) −15.7991 + 11.0626i −0.791936 + 0.554520i
\(399\) 0 0
\(400\) −6.52565 + 1.71962i −0.326282 + 0.0859810i
\(401\) −8.07342 + 1.42356i −0.403168 + 0.0710893i −0.371555 0.928411i \(-0.621175\pi\)
−0.0316124 + 0.999500i \(0.510064\pi\)
\(402\) 0 0
\(403\) −3.17202 + 0.277515i −0.158009 + 0.0138240i
\(404\) 10.2965 0.512272
\(405\) 0 0
\(406\) 5.36923 0.266470
\(407\) −19.2715 + 1.68604i −0.955253 + 0.0835738i
\(408\) 0 0
\(409\) −28.0740 + 4.95021i −1.38817 + 0.244772i −0.817274 0.576249i \(-0.804516\pi\)
−0.570897 + 0.821021i \(0.693405\pi\)
\(410\) −6.64346 7.28026i −0.328097 0.359547i
\(411\) 0 0
\(412\) 3.68278 2.57871i 0.181438 0.127044i
\(413\) 1.87866 0.503386i 0.0924429 0.0247700i
\(414\) 0 0
\(415\) 0.166580 + 4.00556i 0.00817710 + 0.196625i
\(416\) −1.15426 3.17132i −0.0565925 0.155487i
\(417\) 0 0
\(418\) −0.621820 + 7.10744i −0.0304142 + 0.347636i
\(419\) 19.6956 16.5265i 0.962192 0.807375i −0.0191165 0.999817i \(-0.506085\pi\)
0.981308 + 0.192443i \(0.0616409\pi\)
\(420\) 0 0
\(421\) −12.0396 + 4.38206i −0.586775 + 0.213569i −0.618310 0.785934i \(-0.712182\pi\)
0.0315356 + 0.999503i \(0.489960\pi\)
\(422\) −16.9128 4.53177i −0.823303 0.220603i
\(423\) 0 0
\(424\) 21.9849 + 12.6930i 1.06768 + 0.616427i
\(425\) 14.3575 + 5.29312i 0.696441 + 0.256754i
\(426\) 0 0
\(427\) 1.91566 + 4.10815i 0.0927054 + 0.198807i
\(428\) −8.23645 + 11.7629i −0.398124 + 0.568580i
\(429\) 0 0
\(430\) 5.82156 13.9726i 0.280741 0.673819i
\(431\) 5.16823i 0.248945i 0.992223 + 0.124473i \(0.0397239\pi\)
−0.992223 + 0.124473i \(0.960276\pi\)
\(432\) 0 0
\(433\) −2.74947 + 2.74947i −0.132131 + 0.132131i −0.770079 0.637948i \(-0.779783\pi\)
0.637948 + 0.770079i \(0.279783\pi\)
\(434\) 2.43970 + 2.04715i 0.117109 + 0.0982663i
\(435\) 0 0
\(436\) −3.21225 18.2176i −0.153839 0.872464i
\(437\) 28.6224 13.3468i 1.36919 0.638465i
\(438\) 0 0
\(439\) −31.6512 5.58095i −1.51063 0.266364i −0.643886 0.765122i \(-0.722679\pi\)
−0.866742 + 0.498757i \(0.833790\pi\)
\(440\) 6.35692 + 10.0241i 0.303054 + 0.477880i
\(441\) 0 0
\(442\) 0.597834 2.23115i 0.0284361 0.106125i
\(443\) −13.9035 6.48333i −0.660577 0.308032i 0.0632661 0.997997i \(-0.479848\pi\)
−0.723843 + 0.689965i \(0.757626\pi\)
\(444\) 0 0
\(445\) 6.70488 10.4766i 0.317842 0.496640i
\(446\) −13.4825 16.0678i −0.638413 0.760831i
\(447\) 0 0
\(448\) −2.21708 + 4.75455i −0.104747 + 0.224631i
\(449\) 1.37821 + 2.38713i 0.0650416 + 0.112655i 0.896712 0.442614i \(-0.145949\pi\)
−0.831671 + 0.555269i \(0.812615\pi\)
\(450\) 0 0
\(451\) −3.68947 + 6.39034i −0.173730 + 0.300910i
\(452\) 0.0637823 + 0.0910905i 0.00300007 + 0.00428454i
\(453\) 0 0
\(454\) 1.66384 4.57137i 0.0780879 0.214545i
\(455\) 0.515303 + 0.994911i 0.0241578 + 0.0466421i
\(456\) 0 0
\(457\) −2.98806 34.1536i −0.139775 1.59764i −0.665111 0.746745i \(-0.731616\pi\)
0.525335 0.850895i \(-0.323940\pi\)
\(458\) 17.9236 + 17.9236i 0.837515 + 0.837515i
\(459\) 0 0
\(460\) 7.62030 14.5648i 0.355298 0.679086i
\(461\) 1.95614 2.33124i 0.0911067 0.108577i −0.718565 0.695460i \(-0.755201\pi\)
0.809672 + 0.586883i \(0.199645\pi\)
\(462\) 0 0
\(463\) 22.0633 + 15.4489i 1.02537 + 0.717970i 0.960031 0.279894i \(-0.0902992\pi\)
0.0653361 + 0.997863i \(0.479188\pi\)
\(464\) −9.41529 3.42689i −0.437094 0.159089i
\(465\) 0 0
\(466\) 1.28377 7.28061i 0.0594694 0.337268i
\(467\) −4.45355 16.6209i −0.206086 0.769122i −0.989116 0.147138i \(-0.952994\pi\)
0.783030 0.621983i \(-0.213673\pi\)
\(468\) 0 0
\(469\) −6.73671 + 3.88944i −0.311073 + 0.179598i
\(470\) 5.75198 + 7.52834i 0.265319 + 0.347257i
\(471\) 0 0
\(472\) −8.49431 0.743156i −0.390982 0.0342065i
\(473\) −11.2896 0.987714i −0.519098 0.0454152i
\(474\) 0 0
\(475\) 15.9757 + 11.2851i 0.733014 + 0.517797i
\(476\) 1.67236 0.965535i 0.0766523 0.0442552i
\(477\) 0 0
\(478\) 3.13729 + 11.7085i 0.143497 + 0.535536i
\(479\) −6.03903 + 34.2490i −0.275930 + 1.56488i 0.460061 + 0.887888i \(0.347828\pi\)
−0.735991 + 0.676991i \(0.763283\pi\)
\(480\) 0 0
\(481\) 7.52282 + 2.73808i 0.343011 + 0.124846i
\(482\) −8.95484 6.27025i −0.407882 0.285602i
\(483\) 0 0
\(484\) −4.65130 + 5.54320i −0.211423 + 0.251964i
\(485\) 9.18238 + 4.80423i 0.416951 + 0.218149i
\(486\) 0 0
\(487\) −10.1713 10.1713i −0.460908 0.460908i 0.438045 0.898953i \(-0.355671\pi\)
−0.898953 + 0.438045i \(0.855671\pi\)
\(488\) −1.73199 19.7968i −0.0784036 0.896157i
\(489\) 0 0
\(490\) −4.60576 + 14.5029i −0.208067 + 0.655173i
\(491\) −10.0702 + 27.6677i −0.454462 + 1.24863i 0.475091 + 0.879937i \(0.342415\pi\)
−0.929553 + 0.368688i \(0.879807\pi\)
\(492\) 0 0
\(493\) 13.0313 + 18.6107i 0.586902 + 0.838183i
\(494\) 1.47626 2.55695i 0.0664199 0.115043i
\(495\) 0 0
\(496\) −2.97158 5.14694i −0.133428 0.231104i
\(497\) 1.88923 4.05148i 0.0847438 0.181734i
\(498\) 0 0
\(499\) 11.3613 + 13.5399i 0.508604 + 0.606130i 0.957847 0.287279i \(-0.0927507\pi\)
−0.449243 + 0.893410i \(0.648306\pi\)
\(500\) 10.1735 0.380905i 0.454971 0.0170346i
\(501\) 0 0
\(502\) −10.6545 4.96826i −0.475532 0.221744i
\(503\) 3.36375 12.5537i 0.149982 0.559742i −0.849501 0.527588i \(-0.823097\pi\)
0.999483 0.0321541i \(-0.0102367\pi\)
\(504\) 0 0
\(505\) 24.6740 + 5.52370i 1.09798 + 0.245802i
\(506\) 14.5001 + 2.55677i 0.644610 + 0.113662i
\(507\) 0 0
\(508\) 13.7009 6.38885i 0.607880 0.283459i
\(509\) 0.0644329 + 0.365417i 0.00285594 + 0.0161968i 0.986202 0.165544i \(-0.0529380\pi\)
−0.983346 + 0.181741i \(0.941827\pi\)
\(510\) 0 0
\(511\) 4.44374 + 3.72874i 0.196579 + 0.164950i
\(512\) 10.2528 10.2528i 0.453113 0.453113i
\(513\) 0 0
\(514\) 20.7055i 0.913279i
\(515\) 10.2086 4.20379i 0.449843 0.185241i
\(516\) 0 0
\(517\) 4.06851 5.81043i 0.178933 0.255542i
\(518\) −3.38403 7.25707i −0.148686 0.318857i
\(519\) 0 0
\(520\) −0.631076 4.87140i −0.0276745 0.213625i
\(521\) 2.40696 + 1.38966i 0.105451 + 0.0608820i 0.551798 0.833978i \(-0.313942\pi\)
−0.446347 + 0.894860i \(0.647275\pi\)
\(522\) 0 0
\(523\) 14.6842 + 3.93462i 0.642096 + 0.172049i 0.565153 0.824986i \(-0.308817\pi\)
0.0769434 + 0.997035i \(0.475484\pi\)
\(524\) −19.2736 + 7.01503i −0.841973 + 0.306453i
\(525\) 0 0
\(526\) −13.4950 + 11.3237i −0.588411 + 0.493736i
\(527\) −1.17453 + 13.4249i −0.0511633 + 0.584799i
\(528\) 0 0
\(529\) −14.4247 39.6316i −0.627162 1.72311i
\(530\) 14.3518 + 13.2057i 0.623401 + 0.573620i
\(531\) 0 0
\(532\) 2.38424 0.638854i 0.103370 0.0276978i
\(533\) 2.50139 1.75149i 0.108347 0.0758655i
\(534\) 0 0
\(535\) −26.0477 + 23.7693i −1.12614 + 1.02764i
\(536\) 33.5852 5.92198i 1.45066 0.255790i
\(537\) 0 0
\(538\) 31.8166 2.78359i 1.37171 0.120009i
\(539\) 11.3925 0.490709
\(540\) 0 0
\(541\) −16.6575 −0.716163 −0.358081 0.933690i \(-0.616569\pi\)
−0.358081 + 0.933690i \(0.616569\pi\)
\(542\) 5.42423 0.474558i 0.232990 0.0203840i
\(543\) 0 0
\(544\) −14.0664 + 2.48028i −0.603090 + 0.106341i
\(545\) 2.07540 45.3788i 0.0889002 1.94381i
\(546\) 0 0
\(547\) 0.317541 0.222344i 0.0135771 0.00950676i −0.566768 0.823877i \(-0.691806\pi\)
0.580345 + 0.814371i \(0.302918\pi\)
\(548\) 4.58578 1.22876i 0.195895 0.0524899i
\(549\) 0 0
\(550\) 3.08340 + 8.58195i 0.131477 + 0.365935i
\(551\) 9.93246 + 27.2892i 0.423137 + 1.16256i
\(552\) 0 0
\(553\) 0.0984086 1.12482i 0.00418476 0.0478320i
\(554\) 9.33168 7.83021i 0.396465 0.332674i
\(555\) 0 0
\(556\) −11.1192 + 4.04707i −0.471561 + 0.171634i
\(557\) −12.2853 3.29185i −0.520546 0.139480i −0.0110271 0.999939i \(-0.503510\pi\)
−0.509519 + 0.860459i \(0.670177\pi\)
\(558\) 0 0
\(559\) 4.06152 + 2.34492i 0.171784 + 0.0991797i
\(560\) −1.27653 + 1.65650i −0.0539433 + 0.0699998i
\(561\) 0 0
\(562\) 6.03864 + 12.9499i 0.254725 + 0.546259i
\(563\) 16.7779 23.9613i 0.707102 1.00985i −0.291478 0.956578i \(-0.594147\pi\)
0.998580 0.0532691i \(-0.0169641\pi\)
\(564\) 0 0
\(565\) 0.103977 + 0.252500i 0.00437436 + 0.0106228i
\(566\) 9.26299i 0.389353i
\(567\) 0 0
\(568\) −13.8580 + 13.8580i −0.581470 + 0.581470i
\(569\) 3.92124 + 3.29031i 0.164387 + 0.137937i 0.721270 0.692654i \(-0.243559\pi\)
−0.556884 + 0.830591i \(0.688003\pi\)
\(570\) 0 0
\(571\) 1.16063 + 6.58228i 0.0485710 + 0.275460i 0.999415 0.0342116i \(-0.0108920\pi\)
−0.950844 + 0.309671i \(0.899781\pi\)
\(572\) −1.04275 + 0.486243i −0.0435997 + 0.0203309i
\(573\) 0 0
\(574\) −3.00787 0.530368i −0.125546 0.0221372i
\(575\) 26.0743 30.8141i 1.08737 1.28504i
\(576\) 0 0
\(577\) −11.9622 + 44.6435i −0.497992 + 1.85853i 0.0145873 + 0.999894i \(0.495357\pi\)
−0.512580 + 0.858640i \(0.671310\pi\)
\(578\) 7.22128 + 3.36734i 0.300366 + 0.140063i
\(579\) 0 0
\(580\) 12.7313 + 8.14786i 0.528640 + 0.338321i
\(581\) 0.798581 + 0.951712i 0.0331307 + 0.0394837i
\(582\) 0 0
\(583\) 6.17089 13.2335i 0.255572 0.548076i
\(584\) −12.7158 22.0244i −0.526183 0.911376i
\(585\) 0 0
\(586\) 5.89440 10.2094i 0.243495 0.421746i
\(587\) −1.01832 1.45431i −0.0420306 0.0600260i 0.797587 0.603204i \(-0.206110\pi\)
−0.839617 + 0.543178i \(0.817221\pi\)
\(588\) 0 0
\(589\) −5.89151 + 16.1868i −0.242755 + 0.666965i
\(590\) −6.24344 1.98277i −0.257039 0.0816293i
\(591\) 0 0
\(592\) 1.30232 + 14.8856i 0.0535250 + 0.611794i
\(593\) −27.8118 27.8118i −1.14209 1.14209i −0.988066 0.154028i \(-0.950775\pi\)
−0.154028 0.988066i \(-0.549225\pi\)
\(594\) 0 0
\(595\) 4.52550 1.41659i 0.185528 0.0580747i
\(596\) −6.65306 + 7.92880i −0.272520 + 0.324776i
\(597\) 0 0
\(598\) −4.99124 3.49490i −0.204107 0.142917i
\(599\) −37.7245 13.7306i −1.54138 0.561017i −0.575005 0.818150i \(-0.695000\pi\)
−0.966376 + 0.257133i \(0.917222\pi\)
\(600\) 0 0
\(601\) 3.13840 17.7988i 0.128018 0.726027i −0.851451 0.524434i \(-0.824277\pi\)
0.979469 0.201593i \(-0.0646119\pi\)
\(602\) −1.21407 4.53099i −0.0494820 0.184669i
\(603\) 0 0
\(604\) 7.17219 4.14087i 0.291832 0.168490i
\(605\) −14.1198 + 10.7881i −0.574052 + 0.438601i
\(606\) 0 0
\(607\) −14.2779 1.24916i −0.579522 0.0507016i −0.206374 0.978473i \(-0.566166\pi\)
−0.373149 + 0.927772i \(0.621722\pi\)
\(608\) −18.1879 1.59123i −0.737616 0.0645330i
\(609\) 0 0
\(610\) 2.02408 15.1323i 0.0819525 0.612688i
\(611\) −2.54213 + 1.46770i −0.102844 + 0.0593767i
\(612\) 0 0
\(613\) 7.34062 + 27.3956i 0.296485 + 1.10650i 0.940031 + 0.341090i \(0.110796\pi\)
−0.643546 + 0.765408i \(0.722537\pi\)
\(614\) −1.54655 + 8.77091i −0.0624136 + 0.353965i
\(615\) 0 0
\(616\) 3.45655 + 1.25808i 0.139269 + 0.0506896i
\(617\) −19.2569 13.4838i −0.775255 0.542839i 0.117666 0.993053i \(-0.462459\pi\)
−0.892921 + 0.450214i \(0.851348\pi\)
\(618\) 0 0
\(619\) 5.35313 6.37961i 0.215160 0.256418i −0.647659 0.761930i \(-0.724252\pi\)
0.862820 + 0.505512i \(0.168696\pi\)
\(620\) 2.67836 + 8.55640i 0.107566 + 0.343633i
\(621\) 0 0
\(622\) −10.7995 10.7995i −0.433020 0.433020i
\(623\) −0.335951 3.83994i −0.0134596 0.153844i
\(624\) 0 0
\(625\) 24.5834 + 4.54490i 0.983336 + 0.181796i
\(626\) 3.32909 9.14661i 0.133057 0.365572i
\(627\) 0 0
\(628\) −1.74869 2.49739i −0.0697803 0.0996566i
\(629\) 16.9411 29.3428i 0.675485 1.16997i
\(630\) 0 0
\(631\) 10.7788 + 18.6694i 0.429097 + 0.743218i 0.996793 0.0800204i \(-0.0254985\pi\)
−0.567696 + 0.823238i \(0.692165\pi\)
\(632\) −2.09201 + 4.48633i −0.0832158 + 0.178457i
\(633\) 0 0
\(634\) 15.8517 + 18.8913i 0.629550 + 0.750269i
\(635\) 36.2594 7.95982i 1.43891 0.315876i
\(636\) 0 0
\(637\) −4.27285 1.99246i −0.169296 0.0789442i
\(638\) −3.50422 + 13.0779i −0.138734 + 0.517761i
\(639\) 0 0
\(640\) −2.70472 + 1.71524i −0.106913 + 0.0678007i
\(641\) 4.89330 + 0.862821i 0.193274 + 0.0340794i 0.269447 0.963015i \(-0.413159\pi\)
−0.0761733 + 0.997095i \(0.524270\pi\)
\(642\) 0 0
\(643\) −20.7326 + 9.66776i −0.817613 + 0.381259i −0.785989 0.618241i \(-0.787846\pi\)
−0.0316243 + 0.999500i \(0.510068\pi\)
\(644\) −0.884560 5.01659i −0.0348566 0.197681i
\(645\) 0 0
\(646\) −9.57243 8.03223i −0.376622 0.316024i
\(647\) 8.15287 8.15287i 0.320522 0.320522i −0.528445 0.848967i \(-0.677225\pi\)
0.848967 + 0.528445i \(0.177225\pi\)
\(648\) 0 0
\(649\) 4.90443i 0.192516i
\(650\) 0.344464 3.75799i 0.0135110 0.147401i
\(651\) 0 0
\(652\) −7.36905 + 10.5241i −0.288594 + 0.412155i
\(653\) 15.6937 + 33.6553i 0.614142 + 1.31703i 0.929767 + 0.368148i \(0.120008\pi\)
−0.315625 + 0.948884i \(0.602214\pi\)
\(654\) 0 0
\(655\) −49.9495 + 6.47082i −1.95169 + 0.252836i
\(656\) 4.93599 + 2.84980i 0.192718 + 0.111266i
\(657\) 0 0
\(658\) 2.83597 + 0.759896i 0.110558 + 0.0296238i
\(659\) −17.4051 + 6.33493i −0.678005 + 0.246774i −0.657991 0.753026i \(-0.728593\pi\)
−0.0200144 + 0.999800i \(0.506371\pi\)
\(660\) 0 0
\(661\) 32.6452 27.3925i 1.26975 1.06545i 0.275178 0.961393i \(-0.411263\pi\)
0.994572 0.104053i \(-0.0331813\pi\)
\(662\) −2.10399 + 24.0488i −0.0817740 + 0.934682i
\(663\) 0 0
\(664\) −1.86287 5.11819i −0.0722933 0.198624i
\(665\) 6.05616 0.251859i 0.234848 0.00976668i
\(666\) 0 0
\(667\) 57.8896 15.5115i 2.24149 0.600607i
\(668\) −10.3824 + 7.26980i −0.401705 + 0.281277i
\(669\) 0 0
\(670\) 26.1727 + 1.19701i 1.01114 + 0.0462444i
\(671\) −11.2566 + 1.98484i −0.434555 + 0.0766238i
\(672\) 0 0
\(673\) 9.45392 0.827111i 0.364422 0.0318828i 0.0965254 0.995331i \(-0.469227\pi\)
0.267896 + 0.963448i \(0.413672\pi\)
\(674\) 13.0095 0.501109
\(675\) 0 0
\(676\) −11.3614 −0.436977
\(677\) 10.7923 0.944208i 0.414783 0.0362888i 0.122146 0.992512i \(-0.461023\pi\)
0.292638 + 0.956223i \(0.405467\pi\)
\(678\) 0 0
\(679\) 3.16272 0.557672i 0.121374 0.0214015i
\(680\) −20.7678 0.949814i −0.796408 0.0364237i
\(681\) 0 0
\(682\) −6.57855 + 4.60635i −0.251906 + 0.176386i
\(683\) 2.18859 0.586431i 0.0837441 0.0224392i −0.216704 0.976237i \(-0.569531\pi\)
0.300448 + 0.953798i \(0.402864\pi\)
\(684\) 0 0
\(685\) 11.6483 0.484420i 0.445057 0.0185087i
\(686\) 3.34440 + 9.18868i 0.127690 + 0.350825i
\(687\) 0 0
\(688\) −0.762924 + 8.72026i −0.0290862 + 0.332457i
\(689\) −4.62889 + 3.88410i −0.176347 + 0.147972i
\(690\) 0 0
\(691\) 7.28698 2.65224i 0.277210 0.100896i −0.199674 0.979862i \(-0.563988\pi\)
0.476884 + 0.878966i \(0.341766\pi\)
\(692\) −2.73616 0.733152i −0.104013 0.0278703i
\(693\) 0 0
\(694\) 10.3378 + 5.96855i 0.392419 + 0.226563i
\(695\) −28.8165 + 3.73311i −1.09307 + 0.141605i
\(696\) 0 0
\(697\) −5.46187 11.7130i −0.206883 0.443662i
\(698\) 14.5398 20.7650i 0.550341 0.785969i
\(699\) 0 0
\(700\) 2.42517 2.01791i 0.0916629 0.0762699i
\(701\) 3.06270i 0.115677i −0.998326 0.0578383i \(-0.981579\pi\)
0.998326 0.0578383i \(-0.0184208\pi\)
\(702\) 0 0
\(703\) 30.6241 30.6241i 1.15501 1.15501i
\(704\) −10.1338 8.50324i −0.381931 0.320478i
\(705\) 0 0
\(706\) −6.07355 34.4448i −0.228581 1.29635i
\(707\) 7.10146 3.31146i 0.267078 0.124540i
\(708\) 0 0
\(709\) 45.6222 + 8.04442i 1.71338 + 0.302114i 0.942335 0.334671i \(-0.108625\pi\)
0.771041 + 0.636785i \(0.219736\pi\)
\(710\) −12.7152 + 8.06351i −0.477192 + 0.302618i
\(711\) 0 0
\(712\) −4.37376 + 16.3231i −0.163914 + 0.611734i
\(713\) 32.2183 + 15.0236i 1.20658 + 0.562640i
\(714\) 0 0
\(715\) −2.75964 + 0.605807i −0.103205 + 0.0226559i
\(716\) 2.96927 + 3.53864i 0.110967 + 0.132245i
\(717\) 0 0
\(718\) 8.24204 17.6751i 0.307590 0.659629i
\(719\) 25.2485 + 43.7317i 0.941610 + 1.63092i 0.762400 + 0.647106i \(0.224021\pi\)
0.179211 + 0.983811i \(0.442646\pi\)
\(720\) 0 0
\(721\) 1.71065 2.96294i 0.0637080 0.110346i
\(722\) 2.21326 + 3.16086i 0.0823690 + 0.117635i
\(723\) 0 0
\(724\) 2.90761 7.98858i 0.108060 0.296893i
\(725\) 26.1376 + 26.3549i 0.970726 + 0.978796i
\(726\) 0 0
\(727\) −0.922993 10.5499i −0.0342319 0.391273i −0.993912 0.110178i \(-0.964858\pi\)
0.959680 0.281095i \(-0.0906976\pi\)
\(728\) −1.07638 1.07638i −0.0398933 0.0398933i
\(729\) 0 0
\(730\) −5.83659 18.6458i −0.216022 0.690112i
\(731\) 12.7586 15.2051i 0.471893 0.562380i
\(732\) 0 0
\(733\) −23.8946 16.7312i −0.882569 0.617981i 0.0419494 0.999120i \(-0.486643\pi\)
−0.924518 + 0.381139i \(0.875532\pi\)
\(734\) 6.98357 + 2.54181i 0.257768 + 0.0938200i
\(735\) 0 0
\(736\) −6.54274 + 37.1057i −0.241169 + 1.36774i
\(737\) −5.07689 18.9472i −0.187010 0.697929i
\(738\) 0 0
\(739\) 5.54415 3.20092i 0.203945 0.117748i −0.394549 0.918875i \(-0.629099\pi\)
0.598494 + 0.801127i \(0.295766\pi\)
\(740\) 2.98858 22.3430i 0.109862 0.821346i
\(741\) 0 0
\(742\) 6.02085 + 0.526756i 0.221032 + 0.0193378i
\(743\) −29.7334 2.60134i −1.09081 0.0954338i −0.472473 0.881345i \(-0.656639\pi\)
−0.618339 + 0.785911i \(0.712194\pi\)
\(744\) 0 0
\(745\) −20.1965 + 15.4310i −0.739941 + 0.565347i
\(746\) 9.33928 5.39204i 0.341935 0.197416i
\(747\) 0 0
\(748\) 1.26031 + 4.70355i 0.0460816 + 0.171979i
\(749\) −1.89758 + 10.7617i −0.0693359 + 0.393224i
\(750\) 0 0
\(751\) −9.53000 3.46864i −0.347755 0.126572i 0.162237 0.986752i \(-0.448129\pi\)
−0.509991 + 0.860180i \(0.670351\pi\)
\(752\) −4.48806 3.14257i −0.163663 0.114598i
\(753\) 0 0
\(754\) 3.60152 4.29213i 0.131160 0.156310i
\(755\) 19.4084 6.07531i 0.706345 0.221103i
\(756\) 0 0
\(757\) 6.39851 + 6.39851i 0.232558 + 0.232558i 0.813760 0.581202i \(-0.197417\pi\)
−0.581202 + 0.813760i \(0.697417\pi\)
\(758\) 0.496062 + 5.67002i 0.0180178 + 0.205944i
\(759\) 0 0
\(760\) −25.3271 8.04329i −0.918712 0.291761i
\(761\) −9.16585 + 25.1830i −0.332262 + 0.912882i 0.655260 + 0.755403i \(0.272559\pi\)
−0.987522 + 0.157479i \(0.949663\pi\)
\(762\) 0 0
\(763\) −8.07441 11.5315i −0.292313 0.417467i
\(764\) 0.516728 0.895000i 0.0186946 0.0323800i
\(765\) 0 0
\(766\) −2.33284 4.04059i −0.0842888 0.145993i
\(767\) 0.857749 1.83945i 0.0309715 0.0664186i
\(768\) 0 0
\(769\) −8.41448 10.0280i −0.303434 0.361619i 0.592684 0.805435i \(-0.298068\pi\)
−0.896117 + 0.443817i \(0.853624\pi\)
\(770\) 2.38023 + 1.52331i 0.0857774 + 0.0548962i
\(771\) 0 0
\(772\) −11.3753 5.30439i −0.409406 0.190909i
\(773\) 3.35520 12.5218i 0.120678 0.450377i −0.878971 0.476876i \(-0.841769\pi\)
0.999649 + 0.0264987i \(0.00843577\pi\)
\(774\) 0 0
\(775\) 1.82808 + 21.9409i 0.0656667 + 0.788139i
\(776\) −13.8656 2.44488i −0.497747 0.0877662i
\(777\) 0 0
\(778\) −9.16244 + 4.27252i −0.328489 + 0.153177i
\(779\) −2.86861 16.2687i −0.102778 0.582886i
\(780\) 0 0
\(781\) 8.63526 + 7.24584i 0.308994 + 0.259277i
\(782\) −18.2350 + 18.2350i −0.652082 + 0.652082i
\(783\) 0 0
\(784\) 8.79971i 0.314275i
\(785\) −2.85070 6.92269i −0.101746 0.247081i
\(786\) 0 0
\(787\)