Properties

Label 819.2.fm.e.748.8
Level $819$
Weight $2$
Character 819.748
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 748.8
Character \(\chi\) \(=\) 819.748
Dual form 819.2.fm.e.496.8

$q$-expansion

\(f(q)\) \(=\) \(q+(2.16866 - 0.581092i) q^{2} +(2.63339 - 1.52039i) q^{4} +(-1.87790 + 1.87790i) q^{5} +(1.25762 + 2.32774i) q^{7} +(1.65230 - 1.65230i) q^{8} +O(q^{10})\) \(q+(2.16866 - 0.581092i) q^{2} +(2.63339 - 1.52039i) q^{4} +(-1.87790 + 1.87790i) q^{5} +(1.25762 + 2.32774i) q^{7} +(1.65230 - 1.65230i) q^{8} +(-2.98130 + 5.16377i) q^{10} +(1.20979 + 4.51499i) q^{11} +(1.52548 - 3.26694i) q^{13} +(4.07999 + 4.31730i) q^{14} +(-0.417624 + 0.723346i) q^{16} +(2.18729 + 3.78849i) q^{17} +(0.194491 + 0.0521138i) q^{19} +(-2.09010 + 7.80037i) q^{20} +(5.24724 + 9.08849i) q^{22} +(-7.20237 - 4.15829i) q^{23} -2.05302i q^{25} +(1.40986 - 7.97134i) q^{26} +(6.85087 + 4.21777i) q^{28} +(5.20380 - 9.01325i) q^{29} +(6.75799 - 6.75799i) q^{31} +(-1.69492 + 6.32554i) q^{32} +(6.94495 + 6.94495i) q^{34} +(-6.73296 - 2.00958i) q^{35} +(1.22755 + 4.58128i) q^{37} +0.452070 q^{38} +6.20572i q^{40} +(0.136339 + 0.508825i) q^{41} +(2.49507 - 1.44053i) q^{43} +(10.0504 + 10.0504i) q^{44} +(-18.0359 - 4.83270i) q^{46} +(0.928461 + 0.928461i) q^{47} +(-3.83677 + 5.85484i) q^{49} +(-1.19299 - 4.45231i) q^{50} +(-0.949833 - 10.9224i) q^{52} -1.95082 q^{53} +(-10.7506 - 6.20683i) q^{55} +(5.92410 + 1.76816i) q^{56} +(6.04777 - 22.5706i) q^{58} +(1.76081 - 6.57142i) q^{59} +(-2.13306 + 1.23152i) q^{61} +(10.7288 - 18.5828i) q^{62} +13.0324i q^{64} +(3.27029 + 8.99969i) q^{65} +(-1.40878 + 0.377482i) q^{67} +(11.5199 + 6.65104i) q^{68} +(-15.7693 - 0.445637i) q^{70} +(1.44014 - 5.37468i) q^{71} +(-8.75032 - 8.75032i) q^{73} +(5.32429 + 9.22194i) q^{74} +(0.591404 - 0.158466i) q^{76} +(-8.98827 + 8.49422i) q^{77} -4.46495 q^{79} +(-0.574115 - 2.14263i) q^{80} +(0.591348 + 1.02425i) q^{82} +(-5.42187 + 5.42187i) q^{83} +(-11.2219 - 3.00690i) q^{85} +(4.57389 - 4.57389i) q^{86} +(9.45905 + 5.46119i) q^{88} +(15.0461 - 4.03159i) q^{89} +(9.52308 - 0.557652i) q^{91} -25.2888 q^{92} +(2.55304 + 1.47400i) q^{94} +(-0.463100 + 0.267371i) q^{95} +(2.84925 + 0.763454i) q^{97} +(-4.91847 + 14.9267i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.16866 0.581092i 1.53348 0.410894i 0.609326 0.792920i \(-0.291440\pi\)
0.924152 + 0.382026i \(0.124774\pi\)
\(3\) 0 0
\(4\) 2.63339 1.52039i 1.31669 0.760193i
\(5\) −1.87790 + 1.87790i −0.839823 + 0.839823i −0.988835 0.149013i \(-0.952390\pi\)
0.149013 + 0.988835i \(0.452390\pi\)
\(6\) 0 0
\(7\) 1.25762 + 2.32774i 0.475337 + 0.879804i
\(8\) 1.65230 1.65230i 0.584177 0.584177i
\(9\) 0 0
\(10\) −2.98130 + 5.16377i −0.942771 + 1.63293i
\(11\) 1.20979 + 4.51499i 0.364764 + 1.36132i 0.867740 + 0.497019i \(0.165572\pi\)
−0.502975 + 0.864301i \(0.667761\pi\)
\(12\) 0 0
\(13\) 1.52548 3.26694i 0.423092 0.906087i
\(14\) 4.07999 + 4.31730i 1.09042 + 1.15385i
\(15\) 0 0
\(16\) −0.417624 + 0.723346i −0.104406 + 0.180836i
\(17\) 2.18729 + 3.78849i 0.530495 + 0.918845i 0.999367 + 0.0355783i \(0.0113273\pi\)
−0.468872 + 0.883266i \(0.655339\pi\)
\(18\) 0 0
\(19\) 0.194491 + 0.0521138i 0.0446194 + 0.0119557i 0.281060 0.959690i \(-0.409314\pi\)
−0.236440 + 0.971646i \(0.575981\pi\)
\(20\) −2.09010 + 7.80037i −0.467361 + 1.74422i
\(21\) 0 0
\(22\) 5.24724 + 9.08849i 1.11872 + 1.93767i
\(23\) −7.20237 4.15829i −1.50180 0.867064i −0.999998 0.00208060i \(-0.999338\pi\)
−0.501801 0.864983i \(-0.667329\pi\)
\(24\) 0 0
\(25\) 2.05302i 0.410604i
\(26\) 1.40986 7.97134i 0.276497 1.56331i
\(27\) 0 0
\(28\) 6.85087 + 4.21777i 1.29469 + 0.797084i
\(29\) 5.20380 9.01325i 0.966322 1.67372i 0.260300 0.965528i \(-0.416179\pi\)
0.706022 0.708190i \(-0.250488\pi\)
\(30\) 0 0
\(31\) 6.75799 6.75799i 1.21377 1.21377i 0.243995 0.969777i \(-0.421542\pi\)
0.969777 0.243995i \(-0.0784579\pi\)
\(32\) −1.69492 + 6.32554i −0.299623 + 1.11821i
\(33\) 0 0
\(34\) 6.94495 + 6.94495i 1.19105 + 1.19105i
\(35\) −6.73296 2.00958i −1.13808 0.339681i
\(36\) 0 0
\(37\) 1.22755 + 4.58128i 0.201808 + 0.753158i 0.990399 + 0.138240i \(0.0441444\pi\)
−0.788591 + 0.614919i \(0.789189\pi\)
\(38\) 0.452070 0.0733354
\(39\) 0 0
\(40\) 6.20572i 0.981210i
\(41\) 0.136339 + 0.508825i 0.0212926 + 0.0794651i 0.975755 0.218867i \(-0.0702362\pi\)
−0.954462 + 0.298333i \(0.903570\pi\)
\(42\) 0 0
\(43\) 2.49507 1.44053i 0.380494 0.219678i −0.297539 0.954710i \(-0.596166\pi\)
0.678033 + 0.735031i \(0.262832\pi\)
\(44\) 10.0504 + 10.0504i 1.51515 + 1.51515i
\(45\) 0 0
\(46\) −18.0359 4.83270i −2.65925 0.712543i
\(47\) 0.928461 + 0.928461i 0.135430 + 0.135430i 0.771572 0.636142i \(-0.219471\pi\)
−0.636142 + 0.771572i \(0.719471\pi\)
\(48\) 0 0
\(49\) −3.83677 + 5.85484i −0.548110 + 0.836406i
\(50\) −1.19299 4.45231i −0.168715 0.629651i
\(51\) 0 0
\(52\) −0.949833 10.9224i −0.131718 1.51467i
\(53\) −1.95082 −0.267966 −0.133983 0.990984i \(-0.542777\pi\)
−0.133983 + 0.990984i \(0.542777\pi\)
\(54\) 0 0
\(55\) −10.7506 6.20683i −1.44960 0.836929i
\(56\) 5.92410 + 1.76816i 0.791642 + 0.236281i
\(57\) 0 0
\(58\) 6.04777 22.5706i 0.794111 2.96366i
\(59\) 1.76081 6.57142i 0.229237 0.855526i −0.751425 0.659819i \(-0.770633\pi\)
0.980662 0.195707i \(-0.0627002\pi\)
\(60\) 0 0
\(61\) −2.13306 + 1.23152i −0.273111 + 0.157681i −0.630300 0.776351i \(-0.717068\pi\)
0.357190 + 0.934032i \(0.383735\pi\)
\(62\) 10.7288 18.5828i 1.36256 2.36002i
\(63\) 0 0
\(64\) 13.0324i 1.62905i
\(65\) 3.27029 + 8.99969i 0.405630 + 1.11627i
\(66\) 0 0
\(67\) −1.40878 + 0.377482i −0.172110 + 0.0461168i −0.343845 0.939026i \(-0.611729\pi\)
0.171735 + 0.985143i \(0.445063\pi\)
\(68\) 11.5199 + 6.65104i 1.39700 + 0.806558i
\(69\) 0 0
\(70\) −15.7693 0.445637i −1.88479 0.0532638i
\(71\) 1.44014 5.37468i 0.170913 0.637857i −0.826299 0.563232i \(-0.809558\pi\)
0.997212 0.0746244i \(-0.0237758\pi\)
\(72\) 0 0
\(73\) −8.75032 8.75032i −1.02415 1.02415i −0.999701 0.0244465i \(-0.992218\pi\)
−0.0244465 0.999701i \(-0.507782\pi\)
\(74\) 5.32429 + 9.22194i 0.618936 + 1.07203i
\(75\) 0 0
\(76\) 0.591404 0.158466i 0.0678387 0.0181773i
\(77\) −8.98827 + 8.49422i −1.02431 + 0.968006i
\(78\) 0 0
\(79\) −4.46495 −0.502346 −0.251173 0.967942i \(-0.580816\pi\)
−0.251173 + 0.967942i \(0.580816\pi\)
\(80\) −0.574115 2.14263i −0.0641880 0.239553i
\(81\) 0 0
\(82\) 0.591348 + 1.02425i 0.0653035 + 0.113109i
\(83\) −5.42187 + 5.42187i −0.595128 + 0.595128i −0.939012 0.343884i \(-0.888257\pi\)
0.343884 + 0.939012i \(0.388257\pi\)
\(84\) 0 0
\(85\) −11.2219 3.00690i −1.21719 0.326145i
\(86\) 4.57389 4.57389i 0.493215 0.493215i
\(87\) 0 0
\(88\) 9.45905 + 5.46119i 1.00834 + 0.582164i
\(89\) 15.0461 4.03159i 1.59488 0.427347i 0.651390 0.758743i \(-0.274186\pi\)
0.943492 + 0.331396i \(0.107520\pi\)
\(90\) 0 0
\(91\) 9.52308 0.557652i 0.998290 0.0584578i
\(92\) −25.2888 −2.63654
\(93\) 0 0
\(94\) 2.55304 + 1.47400i 0.263326 + 0.152031i
\(95\) −0.463100 + 0.267371i −0.0475131 + 0.0274317i
\(96\) 0 0
\(97\) 2.84925 + 0.763454i 0.289297 + 0.0775170i 0.400549 0.916275i \(-0.368819\pi\)
−0.111252 + 0.993792i \(0.535486\pi\)
\(98\) −4.91847 + 14.9267i −0.496841 + 1.50782i
\(99\) 0 0
\(100\) −3.12138 5.40639i −0.312138 0.540639i
\(101\) 0.316767 0.548657i 0.0315195 0.0545934i −0.849835 0.527048i \(-0.823299\pi\)
0.881355 + 0.472455i \(0.156632\pi\)
\(102\) 0 0
\(103\) −1.95716 −0.192845 −0.0964223 0.995341i \(-0.530740\pi\)
−0.0964223 + 0.995341i \(0.530740\pi\)
\(104\) −2.87742 7.91853i −0.282154 0.776475i
\(105\) 0 0
\(106\) −4.23068 + 1.13361i −0.410920 + 0.110106i
\(107\) 3.59988 6.23517i 0.348013 0.602777i −0.637883 0.770133i \(-0.720190\pi\)
0.985896 + 0.167357i \(0.0535231\pi\)
\(108\) 0 0
\(109\) −2.42207 2.42207i −0.231992 0.231992i 0.581531 0.813524i \(-0.302454\pi\)
−0.813524 + 0.581531i \(0.802454\pi\)
\(110\) −26.9211 7.21348i −2.56682 0.687778i
\(111\) 0 0
\(112\) −2.20898 0.0624252i −0.208729 0.00589863i
\(113\) −0.379755 0.657754i −0.0357243 0.0618763i 0.847610 0.530619i \(-0.178040\pi\)
−0.883335 + 0.468743i \(0.844707\pi\)
\(114\) 0 0
\(115\) 21.3342 5.71648i 1.98942 0.533065i
\(116\) 31.6471i 2.93836i
\(117\) 0 0
\(118\) 15.2744i 1.40612i
\(119\) −6.06786 + 9.85594i −0.556239 + 0.903492i
\(120\) 0 0
\(121\) −9.39523 + 5.42434i −0.854112 + 0.493122i
\(122\) −3.91027 + 3.91027i −0.354019 + 0.354019i
\(123\) 0 0
\(124\) 7.52164 28.0712i 0.675464 2.52086i
\(125\) −5.53414 5.53414i −0.494988 0.494988i
\(126\) 0 0
\(127\) −1.04032 0.600626i −0.0923131 0.0532970i 0.453133 0.891443i \(-0.350306\pi\)
−0.545446 + 0.838146i \(0.683640\pi\)
\(128\) 4.18317 + 15.6118i 0.369743 + 1.37990i
\(129\) 0 0
\(130\) 12.3218 + 17.6170i 1.08069 + 1.54511i
\(131\) 3.03417i 0.265097i −0.991177 0.132548i \(-0.957684\pi\)
0.991177 0.132548i \(-0.0423160\pi\)
\(132\) 0 0
\(133\) 0.123289 + 0.518266i 0.0106905 + 0.0449393i
\(134\) −2.83582 + 1.63726i −0.244978 + 0.141438i
\(135\) 0 0
\(136\) 9.87379 + 2.64567i 0.846671 + 0.226865i
\(137\) 11.2793 + 3.02227i 0.963654 + 0.258210i 0.706146 0.708066i \(-0.250432\pi\)
0.257508 + 0.966276i \(0.417099\pi\)
\(138\) 0 0
\(139\) −5.80746 + 3.35294i −0.492582 + 0.284393i −0.725645 0.688069i \(-0.758459\pi\)
0.233063 + 0.972462i \(0.425125\pi\)
\(140\) −20.7858 + 4.94470i −1.75672 + 0.417903i
\(141\) 0 0
\(142\) 12.4927i 1.04837i
\(143\) 16.5957 + 2.93522i 1.38780 + 0.245455i
\(144\) 0 0
\(145\) 7.15376 + 26.6982i 0.594087 + 2.21716i
\(146\) −24.0612 13.8918i −1.99132 1.14969i
\(147\) 0 0
\(148\) 10.1979 + 10.1979i 0.838265 + 0.838265i
\(149\) 1.23932 4.62521i 0.101529 0.378912i −0.896399 0.443248i \(-0.853826\pi\)
0.997928 + 0.0643356i \(0.0204928\pi\)
\(150\) 0 0
\(151\) −7.66300 + 7.66300i −0.623606 + 0.623606i −0.946452 0.322845i \(-0.895361\pi\)
0.322845 + 0.946452i \(0.395361\pi\)
\(152\) 0.407466 0.235251i 0.0330499 0.0190814i
\(153\) 0 0
\(154\) −14.5566 + 23.6441i −1.17301 + 1.90530i
\(155\) 25.3817i 2.03870i
\(156\) 0 0
\(157\) 8.00601i 0.638949i 0.947595 + 0.319475i \(0.103506\pi\)
−0.947595 + 0.319475i \(0.896494\pi\)
\(158\) −9.68297 + 2.59455i −0.770336 + 0.206411i
\(159\) 0 0
\(160\) −8.69584 15.0616i −0.687467 1.19073i
\(161\) 0.621570 21.9948i 0.0489865 1.73344i
\(162\) 0 0
\(163\) 18.3794 + 4.92475i 1.43959 + 0.385736i 0.892389 0.451266i \(-0.149028\pi\)
0.547199 + 0.837003i \(0.315694\pi\)
\(164\) 1.13264 + 1.13264i 0.0884447 + 0.0884447i
\(165\) 0 0
\(166\) −8.60761 + 14.9088i −0.668080 + 1.15715i
\(167\) 10.5127 2.81688i 0.813500 0.217977i 0.171997 0.985097i \(-0.444978\pi\)
0.641503 + 0.767121i \(0.278311\pi\)
\(168\) 0 0
\(169\) −8.34582 9.96731i −0.641986 0.766716i
\(170\) −26.0839 −2.00054
\(171\) 0 0
\(172\) 4.38032 7.58693i 0.333996 0.578498i
\(173\) 4.07283 + 7.05435i 0.309651 + 0.536332i 0.978286 0.207259i \(-0.0664543\pi\)
−0.668635 + 0.743591i \(0.733121\pi\)
\(174\) 0 0
\(175\) 4.77890 2.58192i 0.361251 0.195175i
\(176\) −3.77113 1.01047i −0.284260 0.0761672i
\(177\) 0 0
\(178\) 30.2872 17.4863i 2.27012 1.31065i
\(179\) −10.2340 5.90863i −0.764928 0.441631i 0.0661342 0.997811i \(-0.478933\pi\)
−0.831062 + 0.556179i \(0.812267\pi\)
\(180\) 0 0
\(181\) 10.4995 0.780423 0.390212 0.920725i \(-0.372402\pi\)
0.390212 + 0.920725i \(0.372402\pi\)
\(182\) 20.3283 6.74314i 1.50683 0.499835i
\(183\) 0 0
\(184\) −18.7712 + 5.02974i −1.38383 + 0.370797i
\(185\) −10.9084 6.29797i −0.802002 0.463036i
\(186\) 0 0
\(187\) −14.4588 + 14.4588i −1.05734 + 1.05734i
\(188\) 3.85661 + 1.03338i 0.281272 + 0.0753667i
\(189\) 0 0
\(190\) −0.848942 + 0.848942i −0.0615887 + 0.0615887i
\(191\) 6.67464 + 11.5608i 0.482960 + 0.836511i 0.999809 0.0195655i \(-0.00622830\pi\)
−0.516849 + 0.856077i \(0.672895\pi\)
\(192\) 0 0
\(193\) −2.08783 7.79189i −0.150285 0.560872i −0.999463 0.0327652i \(-0.989569\pi\)
0.849178 0.528107i \(-0.177098\pi\)
\(194\) 6.62270 0.475482
\(195\) 0 0
\(196\) −1.20208 + 21.2514i −0.0858631 + 1.51796i
\(197\) 12.2629 3.28585i 0.873699 0.234107i 0.206012 0.978549i \(-0.433951\pi\)
0.667686 + 0.744443i \(0.267285\pi\)
\(198\) 0 0
\(199\) −10.8366 18.7696i −0.768188 1.33054i −0.938544 0.345158i \(-0.887825\pi\)
0.170356 0.985383i \(-0.445508\pi\)
\(200\) −3.39221 3.39221i −0.239865 0.239865i
\(201\) 0 0
\(202\) 0.368142 1.37392i 0.0259024 0.0966689i
\(203\) 27.5249 + 0.777849i 1.93187 + 0.0545943i
\(204\) 0 0
\(205\) −1.21155 0.699491i −0.0846186 0.0488546i
\(206\) −4.24442 + 1.13729i −0.295723 + 0.0792387i
\(207\) 0 0
\(208\) 1.72605 + 2.46780i 0.119680 + 0.171111i
\(209\) 0.941173i 0.0651023i
\(210\) 0 0
\(211\) 6.50914 11.2742i 0.448108 0.776145i −0.550155 0.835062i \(-0.685431\pi\)
0.998263 + 0.0589170i \(0.0187647\pi\)
\(212\) −5.13727 + 2.96601i −0.352829 + 0.203706i
\(213\) 0 0
\(214\) 4.18372 15.6138i 0.285993 1.06734i
\(215\) −1.98032 + 7.39066i −0.135057 + 0.504039i
\(216\) 0 0
\(217\) 24.2299 + 7.23187i 1.64483 + 0.490931i
\(218\) −6.66011 3.84521i −0.451079 0.260431i
\(219\) 0 0
\(220\) −37.7471 −2.54491
\(221\) 15.7135 1.36647i 1.05700 0.0919186i
\(222\) 0 0
\(223\) −4.38178 16.3530i −0.293426 1.09508i −0.942460 0.334320i \(-0.891493\pi\)
0.649034 0.760759i \(-0.275173\pi\)
\(224\) −16.8558 + 4.00980i −1.12623 + 0.267916i
\(225\) 0 0
\(226\) −1.20578 1.20578i −0.0802070 0.0802070i
\(227\) −18.2910 4.90106i −1.21402 0.325295i −0.405679 0.914015i \(-0.632965\pi\)
−0.808336 + 0.588721i \(0.799632\pi\)
\(228\) 0 0
\(229\) 0.181433 + 0.181433i 0.0119894 + 0.0119894i 0.713076 0.701087i \(-0.247301\pi\)
−0.701087 + 0.713076i \(0.747301\pi\)
\(230\) 42.9449 24.7943i 2.83170 1.63488i
\(231\) 0 0
\(232\) −6.29435 23.4909i −0.413245 1.54225i
\(233\) 11.3848i 0.745842i −0.927863 0.372921i \(-0.878356\pi\)
0.927863 0.372921i \(-0.121644\pi\)
\(234\) 0 0
\(235\) −3.48711 −0.227474
\(236\) −5.35421 19.9822i −0.348529 1.30073i
\(237\) 0 0
\(238\) −7.43194 + 24.9002i −0.481741 + 1.61404i
\(239\) 12.2181 + 12.2181i 0.790322 + 0.790322i 0.981546 0.191224i \(-0.0612458\pi\)
−0.191224 + 0.981546i \(0.561246\pi\)
\(240\) 0 0
\(241\) −7.89185 + 29.4528i −0.508359 + 1.89722i −0.0721047 + 0.997397i \(0.522972\pi\)
−0.436254 + 0.899824i \(0.643695\pi\)
\(242\) −17.2231 + 17.2231i −1.10714 + 1.10714i
\(243\) 0 0
\(244\) −3.74479 + 6.48616i −0.239735 + 0.415234i
\(245\) −3.78973 18.1999i −0.242117 1.16275i
\(246\) 0 0
\(247\) 0.466946 0.555894i 0.0297111 0.0353707i
\(248\) 22.3325i 1.41811i
\(249\) 0 0
\(250\) −15.2175 8.78584i −0.962441 0.555666i
\(251\) −5.46171 9.45996i −0.344740 0.597107i 0.640566 0.767903i \(-0.278700\pi\)
−0.985307 + 0.170795i \(0.945366\pi\)
\(252\) 0 0
\(253\) 10.0613 37.5493i 0.632548 2.36070i
\(254\) −2.60511 0.698038i −0.163459 0.0437988i
\(255\) 0 0
\(256\) 5.11138 + 8.85317i 0.319461 + 0.553323i
\(257\) −14.2035 + 24.6012i −0.885991 + 1.53458i −0.0414174 + 0.999142i \(0.513187\pi\)
−0.844574 + 0.535439i \(0.820146\pi\)
\(258\) 0 0
\(259\) −9.12025 + 8.61895i −0.566705 + 0.535555i
\(260\) 22.2949 + 18.7276i 1.38267 + 1.16143i
\(261\) 0 0
\(262\) −1.76313 6.58009i −0.108927 0.406520i
\(263\) −10.8579 + 18.8064i −0.669526 + 1.15965i 0.308510 + 0.951221i \(0.400170\pi\)
−0.978037 + 0.208433i \(0.933164\pi\)
\(264\) 0 0
\(265\) 3.66345 3.66345i 0.225044 0.225044i
\(266\) 0.568533 + 1.05230i 0.0348590 + 0.0645208i
\(267\) 0 0
\(268\) −3.13595 + 3.13595i −0.191559 + 0.191559i
\(269\) 10.7149 6.18625i 0.653298 0.377182i −0.136420 0.990651i \(-0.543560\pi\)
0.789719 + 0.613469i \(0.210226\pi\)
\(270\) 0 0
\(271\) 7.64449 2.04834i 0.464370 0.124427i −0.0190456 0.999819i \(-0.506063\pi\)
0.483415 + 0.875391i \(0.339396\pi\)
\(272\) −3.65385 −0.221547
\(273\) 0 0
\(274\) 26.2172 1.58384
\(275\) 9.26935 2.48371i 0.558963 0.149774i
\(276\) 0 0
\(277\) 9.70888 5.60543i 0.583350 0.336797i −0.179113 0.983828i \(-0.557323\pi\)
0.762464 + 0.647031i \(0.223990\pi\)
\(278\) −10.6461 + 10.6461i −0.638509 + 0.638509i
\(279\) 0 0
\(280\) −14.4453 + 7.80445i −0.863272 + 0.466405i
\(281\) 15.1948 15.1948i 0.906448 0.906448i −0.0895355 0.995984i \(-0.528538\pi\)
0.995984 + 0.0895355i \(0.0285383\pi\)
\(282\) 0 0
\(283\) −7.64747 + 13.2458i −0.454595 + 0.787382i −0.998665 0.0516583i \(-0.983549\pi\)
0.544070 + 0.839040i \(0.316883\pi\)
\(284\) −4.37914 16.3432i −0.259854 0.969789i
\(285\) 0 0
\(286\) 37.6961 3.27812i 2.22902 0.193839i
\(287\) −1.01295 + 0.957272i −0.0597926 + 0.0565060i
\(288\) 0 0
\(289\) −1.06845 + 1.85062i −0.0628502 + 0.108860i
\(290\) 31.0282 + 53.7424i 1.82204 + 3.15586i
\(291\) 0 0
\(292\) −36.3468 9.73911i −2.12704 0.569938i
\(293\) 5.44000 20.3023i 0.317808 1.18608i −0.603539 0.797334i \(-0.706243\pi\)
0.921347 0.388742i \(-0.127090\pi\)
\(294\) 0 0
\(295\) 9.03385 + 15.6471i 0.525971 + 0.911009i
\(296\) 9.59795 + 5.54138i 0.557869 + 0.322086i
\(297\) 0 0
\(298\) 10.7507i 0.622771i
\(299\) −24.5720 + 17.1863i −1.42103 + 0.993912i
\(300\) 0 0
\(301\) 6.49103 + 3.99624i 0.374137 + 0.230339i
\(302\) −12.1656 + 21.0714i −0.700050 + 1.21252i
\(303\) 0 0
\(304\) −0.118921 + 0.118921i −0.00682057 + 0.00682057i
\(305\) 1.69300 6.31836i 0.0969409 0.361788i
\(306\) 0 0
\(307\) 12.7905 + 12.7905i 0.729995 + 0.729995i 0.970618 0.240624i \(-0.0773520\pi\)
−0.240624 + 0.970618i \(0.577352\pi\)
\(308\) −10.7551 + 36.0342i −0.612828 + 2.05324i
\(309\) 0 0
\(310\) 14.7491 + 55.0443i 0.837692 + 3.12631i
\(311\) −19.5517 −1.10868 −0.554338 0.832292i \(-0.687028\pi\)
−0.554338 + 0.832292i \(0.687028\pi\)
\(312\) 0 0
\(313\) 13.2495i 0.748904i 0.927246 + 0.374452i \(0.122169\pi\)
−0.927246 + 0.374452i \(0.877831\pi\)
\(314\) 4.65223 + 17.3624i 0.262540 + 0.979814i
\(315\) 0 0
\(316\) −11.7579 + 6.78845i −0.661435 + 0.381880i
\(317\) −17.8861 17.8861i −1.00458 1.00458i −0.999989 0.00459262i \(-0.998538\pi\)
−0.00459262 0.999989i \(-0.501462\pi\)
\(318\) 0 0
\(319\) 46.9902 + 12.5910i 2.63094 + 0.704959i
\(320\) −24.4735 24.4735i −1.36811 1.36811i
\(321\) 0 0
\(322\) −11.4330 48.0606i −0.637139 2.67831i
\(323\) 0.227976 + 0.850818i 0.0126849 + 0.0473408i
\(324\) 0 0
\(325\) −6.70709 3.13184i −0.372043 0.173723i
\(326\) 42.7206 2.36607
\(327\) 0 0
\(328\) 1.06601 + 0.615459i 0.0588603 + 0.0339830i
\(329\) −0.993565 + 3.32887i −0.0547770 + 0.183527i
\(330\) 0 0
\(331\) −3.51837 + 13.1307i −0.193387 + 0.721731i 0.799291 + 0.600944i \(0.205208\pi\)
−0.992678 + 0.120787i \(0.961458\pi\)
\(332\) −6.03454 + 22.5212i −0.331189 + 1.23601i
\(333\) 0 0
\(334\) 21.1617 12.2177i 1.15792 0.668524i
\(335\) 1.93668 3.35443i 0.105812 0.183272i
\(336\) 0 0
\(337\) 1.75678i 0.0956980i −0.998855 0.0478490i \(-0.984763\pi\)
0.998855 0.0478490i \(-0.0152366\pi\)
\(338\) −23.8912 16.7661i −1.29951 0.911954i
\(339\) 0 0
\(340\) −34.1233 + 9.14331i −1.85060 + 0.495866i
\(341\) 38.6880 + 22.3365i 2.09507 + 1.20959i
\(342\) 0 0
\(343\) −18.4538 1.56784i −0.996410 0.0846554i
\(344\) 1.74242 6.50279i 0.0939449 0.350607i
\(345\) 0 0
\(346\) 12.9318 + 12.9318i 0.695219 + 0.695219i
\(347\) −5.43920 9.42098i −0.291992 0.505744i 0.682289 0.731083i \(-0.260985\pi\)
−0.974281 + 0.225338i \(0.927651\pi\)
\(348\) 0 0
\(349\) 11.9450 3.20064i 0.639399 0.171326i 0.0754676 0.997148i \(-0.475955\pi\)
0.563931 + 0.825822i \(0.309288\pi\)
\(350\) 8.86349 8.37630i 0.473774 0.447732i
\(351\) 0 0
\(352\) −30.6102 −1.63153
\(353\) 4.55715 + 17.0075i 0.242552 + 0.905218i 0.974598 + 0.223962i \(0.0718992\pi\)
−0.732045 + 0.681256i \(0.761434\pi\)
\(354\) 0 0
\(355\) 7.38867 + 12.7975i 0.392150 + 0.679223i
\(356\) 33.4926 33.4926i 1.77510 1.77510i
\(357\) 0 0
\(358\) −25.6277 6.86691i −1.35446 0.362927i
\(359\) −11.4993 + 11.4993i −0.606911 + 0.606911i −0.942137 0.335227i \(-0.891187\pi\)
0.335227 + 0.942137i \(0.391187\pi\)
\(360\) 0 0
\(361\) −16.4194 9.47973i −0.864177 0.498933i
\(362\) 22.7699 6.10119i 1.19676 0.320671i
\(363\) 0 0
\(364\) 24.2301 15.9473i 1.27000 0.835864i
\(365\) 32.8645 1.72020
\(366\) 0 0
\(367\) 11.3884 + 6.57510i 0.594470 + 0.343217i 0.766863 0.641811i \(-0.221817\pi\)
−0.172393 + 0.985028i \(0.555150\pi\)
\(368\) 6.01577 3.47320i 0.313594 0.181053i
\(369\) 0 0
\(370\) −27.3164 7.31940i −1.42011 0.380518i
\(371\) −2.45340 4.54102i −0.127374 0.235758i
\(372\) 0 0
\(373\) 4.81532 + 8.34037i 0.249328 + 0.431848i 0.963339 0.268286i \(-0.0864571\pi\)
−0.714012 + 0.700134i \(0.753124\pi\)
\(374\) −22.9545 + 39.7583i −1.18695 + 2.05585i
\(375\) 0 0
\(376\) 3.06819 0.158230
\(377\) −21.5075 30.7500i −1.10769 1.58371i
\(378\) 0 0
\(379\) −32.1516 + 8.61500i −1.65152 + 0.442523i −0.960037 0.279872i \(-0.909708\pi\)
−0.691481 + 0.722395i \(0.743041\pi\)
\(380\) −0.813014 + 1.40818i −0.0417068 + 0.0722382i
\(381\) 0 0
\(382\) 21.1930 + 21.1930i 1.08433 + 1.08433i
\(383\) −3.73221 1.00004i −0.190707 0.0510998i 0.162201 0.986758i \(-0.448141\pi\)
−0.352908 + 0.935658i \(0.614807\pi\)
\(384\) 0 0
\(385\) 0.927780 32.8304i 0.0472840 1.67319i
\(386\) −9.05560 15.6848i −0.460918 0.798334i
\(387\) 0 0
\(388\) 8.66392 2.32149i 0.439844 0.117856i
\(389\) 12.5816i 0.637911i −0.947770 0.318955i \(-0.896668\pi\)
0.947770 0.318955i \(-0.103332\pi\)
\(390\) 0 0
\(391\) 36.3815i 1.83989i
\(392\) 3.33446 + 16.0135i 0.168416 + 0.808802i
\(393\) 0 0
\(394\) 24.6848 14.2518i 1.24360 0.717995i
\(395\) 8.38473 8.38473i 0.421881 0.421881i
\(396\) 0 0
\(397\) 6.87160 25.6452i 0.344876 1.28709i −0.547882 0.836556i \(-0.684566\pi\)
0.892757 0.450538i \(-0.148768\pi\)
\(398\) −34.4079 34.4079i −1.72471 1.72471i
\(399\) 0 0
\(400\) 1.48504 + 0.857390i 0.0742521 + 0.0428695i
\(401\) 3.89519 + 14.5370i 0.194517 + 0.725946i 0.992391 + 0.123123i \(0.0392908\pi\)
−0.797875 + 0.602823i \(0.794043\pi\)
\(402\) 0 0
\(403\) −11.7688 32.3872i −0.586245 1.61332i
\(404\) 1.92643i 0.0958437i
\(405\) 0 0
\(406\) 60.1443 14.3076i 2.98491 0.710075i
\(407\) −19.1994 + 11.0848i −0.951676 + 0.549451i
\(408\) 0 0
\(409\) −23.9970 6.42996i −1.18657 0.317941i −0.389042 0.921220i \(-0.627194\pi\)
−0.797531 + 0.603279i \(0.793861\pi\)
\(410\) −3.03392 0.812937i −0.149835 0.0401481i
\(411\) 0 0
\(412\) −5.15395 + 2.97564i −0.253917 + 0.146599i
\(413\) 17.5110 4.16566i 0.861660 0.204979i
\(414\) 0 0
\(415\) 20.3635i 0.999603i
\(416\) 18.0796 + 15.1867i 0.886426 + 0.744590i
\(417\) 0 0
\(418\) 0.546908 + 2.04109i 0.0267501 + 0.0998329i
\(419\) 15.5289 + 8.96562i 0.758637 + 0.437999i 0.828806 0.559536i \(-0.189021\pi\)
−0.0701691 + 0.997535i \(0.522354\pi\)
\(420\) 0 0
\(421\) 0.833811 + 0.833811i 0.0406375 + 0.0406375i 0.727134 0.686496i \(-0.240852\pi\)
−0.686496 + 0.727134i \(0.740852\pi\)
\(422\) 7.56482 28.2323i 0.368250 1.37433i
\(423\) 0 0
\(424\) −3.22335 + 3.22335i −0.156540 + 0.156540i
\(425\) 7.77785 4.49054i 0.377281 0.217823i
\(426\) 0 0
\(427\) −5.54926 3.41643i −0.268547 0.165333i
\(428\) 21.8928i 1.05823i
\(429\) 0 0
\(430\) 17.1786i 0.828426i
\(431\) −13.4572 + 3.60584i −0.648209 + 0.173687i −0.567919 0.823085i \(-0.692251\pi\)
−0.0802899 + 0.996772i \(0.525585\pi\)
\(432\) 0 0
\(433\) 0.380141 + 0.658423i 0.0182684 + 0.0316418i 0.875015 0.484096i \(-0.160851\pi\)
−0.856747 + 0.515737i \(0.827518\pi\)
\(434\) 56.7488 + 1.60371i 2.72403 + 0.0769806i
\(435\) 0 0
\(436\) −10.0607 2.69577i −0.481822 0.129104i
\(437\) −1.18410 1.18410i −0.0566430 0.0566430i
\(438\) 0 0
\(439\) −15.9560 + 27.6366i −0.761539 + 1.31902i 0.180518 + 0.983572i \(0.442223\pi\)
−0.942057 + 0.335453i \(0.891111\pi\)
\(440\) −28.0187 + 7.50759i −1.33574 + 0.357910i
\(441\) 0 0
\(442\) 33.2832 12.0944i 1.58312 0.575270i
\(443\) −13.9082 −0.660799 −0.330399 0.943841i \(-0.607183\pi\)
−0.330399 + 0.943841i \(0.607183\pi\)
\(444\) 0 0
\(445\) −20.6841 + 35.8260i −0.980522 + 1.69831i
\(446\) −19.0052 32.9180i −0.899923 1.55871i
\(447\) 0 0
\(448\) −30.3361 + 16.3898i −1.43324 + 0.774347i
\(449\) −37.3413 10.0056i −1.76224 0.472192i −0.775075 0.631869i \(-0.782288\pi\)
−0.987169 + 0.159677i \(0.948955\pi\)
\(450\) 0 0
\(451\) −2.13240 + 1.23114i −0.100411 + 0.0579721i
\(452\) −2.00008 1.15475i −0.0940759 0.0543148i
\(453\) 0 0
\(454\) −42.5150 −1.99533
\(455\) −16.8362 + 18.9306i −0.789292 + 0.887481i
\(456\) 0 0
\(457\) −11.2913 + 3.02549i −0.528183 + 0.141526i −0.513049 0.858359i \(-0.671484\pi\)
−0.0151341 + 0.999885i \(0.504818\pi\)
\(458\) 0.498897 + 0.288038i 0.0233119 + 0.0134591i
\(459\) 0 0
\(460\) 47.4899 47.4899i 2.21423 2.21423i
\(461\) 33.0727 + 8.86180i 1.54035 + 0.412735i 0.926379 0.376594i \(-0.122905\pi\)
0.613971 + 0.789329i \(0.289571\pi\)
\(462\) 0 0
\(463\) −18.1263 + 18.1263i −0.842399 + 0.842399i −0.989170 0.146772i \(-0.953112\pi\)
0.146772 + 0.989170i \(0.453112\pi\)
\(464\) 4.34646 + 7.52830i 0.201780 + 0.349492i
\(465\) 0 0
\(466\) −6.61561 24.6898i −0.306462 1.14373i
\(467\) −20.4427 −0.945975 −0.472988 0.881069i \(-0.656824\pi\)
−0.472988 + 0.881069i \(0.656824\pi\)
\(468\) 0 0
\(469\) −2.65040 2.80455i −0.122384 0.129502i
\(470\) −7.56238 + 2.02633i −0.348826 + 0.0934678i
\(471\) 0 0
\(472\) −7.94858 13.7673i −0.365863 0.633694i
\(473\) 9.52246 + 9.52246i 0.437843 + 0.437843i
\(474\) 0 0
\(475\) 0.106991 0.399295i 0.00490907 0.0183209i
\(476\) −0.994179 + 35.1800i −0.0455681 + 1.61247i
\(477\) 0 0
\(478\) 33.5967 + 19.3971i 1.53668 + 0.887202i
\(479\) −11.4241 + 3.06108i −0.521980 + 0.139864i −0.510182 0.860066i \(-0.670422\pi\)
−0.0117979 + 0.999930i \(0.503755\pi\)
\(480\) 0 0
\(481\) 16.8394 + 2.97832i 0.767810 + 0.135800i
\(482\) 68.4591i 3.11823i
\(483\) 0 0
\(484\) −16.4942 + 28.5688i −0.749736 + 1.29858i
\(485\) −6.78430 + 3.91692i −0.308059 + 0.177858i
\(486\) 0 0
\(487\) 0.0483236 0.180346i 0.00218975 0.00817226i −0.964822 0.262903i \(-0.915320\pi\)
0.967012 + 0.254731i \(0.0819868\pi\)
\(488\) −1.48961 + 5.55931i −0.0674316 + 0.251658i
\(489\) 0 0
\(490\) −18.7945 37.2673i −0.849047 1.68356i
\(491\) 2.43785 + 1.40749i 0.110019 + 0.0635193i 0.554000 0.832517i \(-0.313101\pi\)
−0.443981 + 0.896036i \(0.646434\pi\)
\(492\) 0 0
\(493\) 45.5288 2.05052
\(494\) 0.689624 1.47689i 0.0310276 0.0664482i
\(495\) 0 0
\(496\) 2.06607 + 7.71067i 0.0927691 + 0.346219i
\(497\) 14.3220 3.40704i 0.642430 0.152826i
\(498\) 0 0
\(499\) 1.80207 + 1.80207i 0.0806719 + 0.0806719i 0.746291 0.665619i \(-0.231833\pi\)
−0.665619 + 0.746291i \(0.731833\pi\)
\(500\) −22.9875 6.15949i −1.02803 0.275461i
\(501\) 0 0
\(502\) −17.3417 17.3417i −0.773999 0.773999i
\(503\) 6.33177 3.65565i 0.282320 0.162997i −0.352153 0.935942i \(-0.614550\pi\)
0.634473 + 0.772945i \(0.281217\pi\)
\(504\) 0 0
\(505\) 0.435466 + 1.62518i 0.0193780 + 0.0723196i
\(506\) 87.2783i 3.87999i
\(507\) 0 0
\(508\) −3.65274 −0.162064
\(509\) 6.75398 + 25.2062i 0.299365 + 1.11724i 0.937689 + 0.347477i \(0.112961\pi\)
−0.638324 + 0.769768i \(0.720372\pi\)
\(510\) 0 0
\(511\) 9.36390 31.3731i 0.414234 1.38786i
\(512\) −6.62788 6.62788i −0.292914 0.292914i
\(513\) 0 0
\(514\) −16.5071 + 61.6053i −0.728097 + 2.71729i
\(515\) 3.67535 3.67535i 0.161955 0.161955i
\(516\) 0 0
\(517\) −3.06875 + 5.31523i −0.134963 + 0.233763i
\(518\) −14.7704 + 23.9913i −0.648973 + 1.05412i
\(519\) 0 0
\(520\) 20.2737 + 9.46670i 0.889061 + 0.415142i
\(521\) 5.50223i 0.241057i 0.992710 + 0.120529i \(0.0384589\pi\)
−0.992710 + 0.120529i \(0.961541\pi\)
\(522\) 0 0
\(523\) 35.0507 + 20.2365i 1.53266 + 0.884882i 0.999238 + 0.0390336i \(0.0124279\pi\)
0.533423 + 0.845849i \(0.320905\pi\)
\(524\) −4.61311 7.99014i −0.201525 0.349051i
\(525\) 0 0
\(526\) −12.6189 + 47.0943i −0.550209 + 2.05341i
\(527\) 40.3843 + 10.8209i 1.75917 + 0.471367i
\(528\) 0 0
\(529\) 23.0828 + 39.9806i 1.00360 + 1.73829i
\(530\) 5.81600 10.0736i 0.252631 0.437569i
\(531\) 0 0
\(532\) 1.11263 + 1.17735i 0.0482387 + 0.0510444i
\(533\) 1.87028 + 0.330790i 0.0810110 + 0.0143281i
\(534\) 0 0
\(535\) 4.94882 + 18.4692i 0.213956 + 0.798495i
\(536\) −1.70402 + 2.95145i −0.0736024 + 0.127483i
\(537\) 0 0
\(538\) 19.6422 19.6422i 0.846836 0.846836i
\(539\) −31.0762 10.2399i −1.33855 0.441062i
\(540\) 0 0
\(541\) 25.7367 25.7367i 1.10651 1.10651i 0.112900 0.993606i \(-0.463986\pi\)
0.993606 0.112900i \(-0.0360139\pi\)
\(542\) 15.3881 8.88430i 0.660974 0.381613i
\(543\) 0 0
\(544\) −27.6716 + 7.41457i −1.18641 + 0.317897i
\(545\) 9.09682 0.389665
\(546\) 0 0
\(547\) 31.3852 1.34193 0.670967 0.741487i \(-0.265879\pi\)
0.670967 + 0.741487i \(0.265879\pi\)
\(548\) 34.2977 9.19005i 1.46513 0.392579i
\(549\) 0 0
\(550\) 18.6588 10.7727i 0.795616 0.459349i
\(551\) 1.48181 1.48181i 0.0631272 0.0631272i
\(552\) 0 0
\(553\) −5.61522 10.3933i −0.238783 0.441966i
\(554\) 17.7980 17.7980i 0.756166 0.756166i
\(555\) 0 0
\(556\) −10.1955 + 17.6592i −0.432387 + 0.748916i
\(557\) 0.169733 + 0.633453i 0.00719183 + 0.0268403i 0.969429 0.245374i \(-0.0789107\pi\)
−0.962237 + 0.272214i \(0.912244\pi\)
\(558\) 0 0
\(559\) −0.899944 10.3487i −0.0380636 0.437705i
\(560\) 4.26547 4.03101i 0.180249 0.170341i
\(561\) 0 0
\(562\) 24.1229 41.7821i 1.01756 1.76247i
\(563\) −12.5830 21.7944i −0.530309 0.918523i −0.999375 0.0353593i \(-0.988742\pi\)
0.469065 0.883164i \(-0.344591\pi\)
\(564\) 0 0
\(565\) 1.94834 + 0.522056i 0.0819672 + 0.0219630i
\(566\) −8.88777 + 33.1696i −0.373581 + 1.39422i
\(567\) 0 0
\(568\) −6.50104 11.2601i −0.272778 0.472465i
\(569\) 3.46005 + 1.99766i 0.145053 + 0.0837463i 0.570770 0.821110i \(-0.306645\pi\)
−0.425717 + 0.904856i \(0.639978\pi\)
\(570\) 0 0
\(571\) 17.9370i 0.750640i −0.926895 0.375320i \(-0.877533\pi\)
0.926895 0.375320i \(-0.122467\pi\)
\(572\) 48.1656 17.5023i 2.01390 0.731808i
\(573\) 0 0
\(574\) −1.64049 + 2.66462i −0.0684726 + 0.111219i
\(575\) −8.53705 + 14.7866i −0.356020 + 0.616644i
\(576\) 0 0
\(577\) −29.6210 + 29.6210i −1.23314 + 1.23314i −0.270389 + 0.962751i \(0.587152\pi\)
−0.962751 + 0.270389i \(0.912848\pi\)
\(578\) −1.24174 + 4.63424i −0.0516496 + 0.192759i
\(579\) 0 0
\(580\) 59.4302 + 59.4302i 2.46770 + 2.46770i
\(581\) −19.4394 5.80206i −0.806482 0.240710i
\(582\) 0 0
\(583\) −2.36008 8.80794i −0.0977446 0.364788i
\(584\) −28.9163 −1.19657
\(585\) 0 0
\(586\) 47.1901i 1.94941i
\(587\) −0.571868 2.13424i −0.0236035 0.0880895i 0.953119 0.302595i \(-0.0978528\pi\)
−0.976723 + 0.214505i \(0.931186\pi\)
\(588\) 0 0
\(589\) 1.66656 0.962187i 0.0686693 0.0396462i
\(590\) 28.6838 + 28.6838i 1.18089 + 1.18089i
\(591\) 0 0
\(592\) −3.82651 1.02531i −0.157268 0.0421400i
\(593\) 1.48928 + 1.48928i 0.0611573 + 0.0611573i 0.737024 0.675867i \(-0.236230\pi\)
−0.675867 + 0.737024i \(0.736230\pi\)
\(594\) 0 0
\(595\) −7.11364 29.9033i −0.291631 1.22592i
\(596\) −3.76850 14.0642i −0.154364 0.576093i
\(597\) 0 0
\(598\) −43.3015 + 51.5500i −1.77073 + 2.10804i
\(599\) −13.9002 −0.567945 −0.283973 0.958832i \(-0.591653\pi\)
−0.283973 + 0.958832i \(0.591653\pi\)
\(600\) 0 0
\(601\) 8.59776 + 4.96392i 0.350710 + 0.202482i 0.664998 0.746845i \(-0.268432\pi\)
−0.314288 + 0.949328i \(0.601766\pi\)
\(602\) 16.3991 + 4.89461i 0.668375 + 0.199489i
\(603\) 0 0
\(604\) −8.52892 + 31.8304i −0.347037 + 1.29516i
\(605\) 7.45694 27.8297i 0.303168 1.13144i
\(606\) 0 0
\(607\) −26.6015 + 15.3584i −1.07972 + 0.623378i −0.930821 0.365475i \(-0.880907\pi\)
−0.148900 + 0.988852i \(0.547573\pi\)
\(608\) −0.659297 + 1.14194i −0.0267380 + 0.0463116i
\(609\) 0 0
\(610\) 14.6862i 0.594626i
\(611\) 4.44958 1.61688i 0.180011 0.0654119i
\(612\) 0 0
\(613\) 9.42794 2.52621i 0.380791 0.102033i −0.0633459 0.997992i \(-0.520177\pi\)
0.444137 + 0.895959i \(0.353510\pi\)
\(614\) 35.1709 + 20.3059i 1.41938 + 0.819480i
\(615\) 0 0
\(616\) −0.816322 + 28.8863i −0.0328906 + 1.16386i
\(617\) −6.69956 + 25.0031i −0.269714 + 1.00659i 0.689587 + 0.724203i \(0.257792\pi\)
−0.959301 + 0.282384i \(0.908875\pi\)
\(618\) 0 0
\(619\) −25.5525 25.5525i −1.02704 1.02704i −0.999624 0.0274172i \(-0.991272\pi\)
−0.0274172 0.999624i \(-0.508728\pi\)
\(620\) 38.5899 + 66.8397i 1.54981 + 2.68435i
\(621\) 0 0
\(622\) −42.4011 + 11.3613i −1.70013 + 0.455548i
\(623\) 28.3068 + 29.9532i 1.13409 + 1.20005i
\(624\) 0 0
\(625\) 31.0502 1.24201
\(626\) 7.69915 + 28.7336i 0.307720 + 1.14843i
\(627\) 0 0
\(628\) 12.1722 + 21.0829i 0.485725 + 0.841300i
\(629\) −14.6712 + 14.6712i −0.584977 + 0.584977i
\(630\) 0 0
\(631\) 9.92759 + 2.66009i 0.395211 + 0.105897i 0.450951 0.892549i \(-0.351085\pi\)
−0.0557396 + 0.998445i \(0.517752\pi\)
\(632\) −7.37744 + 7.37744i −0.293459 + 0.293459i
\(633\) 0 0
\(634\) −49.1823 28.3954i −1.95328 1.12773i
\(635\) 3.08153 0.825692i 0.122287 0.0327666i
\(636\) 0 0
\(637\) 13.2745 + 21.4660i 0.525955 + 0.850512i
\(638\) 109.222 4.32416
\(639\) 0 0
\(640\) −37.1730 21.4618i −1.46939 0.848353i
\(641\) 26.2509 15.1559i 1.03685 0.598624i 0.117908 0.993025i \(-0.462381\pi\)
0.918939 + 0.394401i \(0.129048\pi\)
\(642\) 0 0
\(643\) −35.0393 9.38876i −1.38182 0.370256i −0.510035 0.860153i \(-0.670368\pi\)
−0.871780 + 0.489897i \(0.837034\pi\)
\(644\) −31.8038 58.8659i −1.25325 2.31964i
\(645\) 0 0
\(646\) 0.988806 + 1.71266i 0.0389041 + 0.0673838i
\(647\) −9.62979 + 16.6793i −0.378586 + 0.655730i −0.990857 0.134918i \(-0.956923\pi\)
0.612271 + 0.790648i \(0.290256\pi\)
\(648\) 0 0
\(649\) 31.8001 1.24826
\(650\) −16.3653 2.89447i −0.641901 0.113531i
\(651\) 0 0
\(652\) 55.8877 14.9751i 2.18873 0.586468i
\(653\) 0.0312823 0.0541825i 0.00122417 0.00212033i −0.865413 0.501060i \(-0.832944\pi\)
0.866637 + 0.498939i \(0.166277\pi\)
\(654\) 0 0
\(655\) 5.69787 + 5.69787i 0.222634 + 0.222634i
\(656\) −0.424995 0.113877i −0.0165933 0.00444615i
\(657\) 0 0
\(658\) −0.220329 + 7.79655i −0.00858932 + 0.303941i
\(659\) −3.09067 5.35320i −0.120395 0.208531i 0.799528 0.600628i \(-0.205083\pi\)
−0.919924 + 0.392098i \(0.871750\pi\)
\(660\) 0 0
\(661\) 6.90812 1.85103i 0.268695 0.0719965i −0.121956 0.992536i \(-0.538917\pi\)
0.390651 + 0.920539i \(0.372250\pi\)
\(662\) 30.5207i 1.18622i
\(663\) 0 0
\(664\) 17.9171i 0.695320i
\(665\) −1.20478 0.741726i −0.0467192 0.0287629i
\(666\) 0 0
\(667\) −74.9594 + 43.2778i −2.90244 + 1.67572i
\(668\) 23.4013 23.4013i 0.905425 0.905425i
\(669\) 0 0
\(670\) 2.25078 8.40001i 0.0869551 0.324521i
\(671\) −8.14087 8.14087i −0.314275 0.314275i
\(672\) 0 0
\(673\) −4.05354 2.34031i −0.156253 0.0902125i 0.419835 0.907600i \(-0.362088\pi\)
−0.576088 + 0.817388i \(0.695421\pi\)
\(674\) −1.02085 3.80987i −0.0393217 0.146751i
\(675\) 0 0
\(676\) −37.1319 13.5589i −1.42815 0.521497i
\(677\) 31.1590i 1.19754i −0.800922 0.598769i \(-0.795657\pi\)
0.800922 0.598769i \(-0.204343\pi\)
\(678\) 0 0
\(679\) 1.80615 + 7.59246i 0.0693139 + 0.291372i
\(680\) −23.5103 + 13.5737i −0.901579 + 0.520527i
\(681\) 0 0
\(682\) 96.8808 + 25.9591i 3.70976 + 0.994026i
\(683\) −41.3109 11.0692i −1.58072 0.423552i −0.641570 0.767064i \(-0.721717\pi\)
−0.939148 + 0.343512i \(0.888383\pi\)
\(684\) 0 0
\(685\) −26.8569 + 15.5058i −1.02615 + 0.592447i
\(686\) −40.9311 + 7.32322i −1.56276 + 0.279602i
\(687\) 0 0
\(688\) 2.40640i 0.0917430i
\(689\) −2.97595 + 6.37323i −0.113374 + 0.242801i
\(690\) 0 0
\(691\) −4.65384 17.3684i −0.177040 0.660724i −0.996195 0.0871512i \(-0.972224\pi\)
0.819155 0.573573i \(-0.194443\pi\)
\(692\) 21.4507 + 12.3845i 0.815432 + 0.470790i
\(693\) 0 0
\(694\) −17.2703 17.2703i −0.655570 0.655570i
\(695\) 4.60935 17.2023i 0.174843 0.652521i
\(696\) 0 0
\(697\) −1.62947 + 1.62947i −0.0617205 + 0.0617205i
\(698\) 24.0447 13.8822i 0.910106 0.525450i
\(699\) 0 0
\(700\) 8.65917 14.0650i 0.327286 0.531606i
\(701\) 34.0110i 1.28458i 0.766462 + 0.642290i \(0.222015\pi\)
−0.766462 + 0.642290i \(0.777985\pi\)
\(702\) 0 0
\(703\) 0.954993i 0.0360182i
\(704\) −58.8411 + 15.7664i −2.21766 + 0.594219i
\(705\) 0 0
\(706\) 19.7658 + 34.2354i 0.743897 + 1.28847i
\(707\) 1.67551 + 0.0473495i 0.0630139 + 0.00178076i
\(708\) 0 0
\(709\) −2.70932 0.725960i −0.101751 0.0272640i 0.207584 0.978217i \(-0.433440\pi\)
−0.309335 + 0.950953i \(0.600106\pi\)
\(710\) 23.4601 + 23.4601i 0.880441 + 0.880441i
\(711\) 0 0
\(712\) 18.1993 31.5221i 0.682047 1.18134i
\(713\) −76.7753 + 20.5719i −2.87526 + 0.770423i
\(714\) 0 0
\(715\) −36.6771 + 25.6530i −1.37165 + 0.959369i
\(716\) −35.9336 −1.34290
\(717\) 0 0
\(718\) −18.2560 + 31.6203i −0.681308 + 1.18006i
\(719\) −10.7719 18.6575i −0.401725 0.695809i 0.592209 0.805784i \(-0.298256\pi\)
−0.993934 + 0.109976i \(0.964923\pi\)
\(720\) 0 0
\(721\) −2.46137 4.55576i −0.0916661 0.169665i
\(722\) −41.1167 11.0172i −1.53021 0.410017i
\(723\) 0 0
\(724\) 27.6493 15.9633i 1.02758 0.593272i
\(725\) −18.5044 10.6835i −0.687235 0.396775i
\(726\) 0 0
\(727\) −25.2656 −0.937048 −0.468524 0.883451i \(-0.655214\pi\)
−0.468524 + 0.883451i \(0.655214\pi\)
\(728\) 14.8136 16.6564i 0.549028 0.617328i
\(729\) 0 0
\(730\) 71.2720 19.0973i 2.63789 0.706822i
\(731\) 10.9149 + 6.30170i 0.403701 + 0.233077i
\(732\) 0 0
\(733\) 22.8545 22.8545i 0.844152 0.844152i −0.145244 0.989396i \(-0.546397\pi\)
0.989396 + 0.145244i \(0.0463967\pi\)
\(734\) 28.5184 + 7.64147i 1.05263 + 0.282052i
\(735\) 0 0
\(736\) 38.5109 38.5109i 1.41953 1.41953i
\(737\) −3.40865 5.90396i −0.125559 0.217475i
\(738\) 0 0
\(739\) 3.35655 + 12.5268i 0.123473 + 0.460806i 0.999781 0.0209450i \(-0.00666750\pi\)
−0.876308 + 0.481751i \(0.840001\pi\)
\(740\) −38.3014 −1.40799
\(741\) 0 0
\(742\) −7.95935 8.42229i −0.292197 0.309192i
\(743\) −31.0606 + 8.32266i −1.13950 + 0.305329i −0.778751 0.627333i \(-0.784146\pi\)
−0.360751 + 0.932662i \(0.617480\pi\)
\(744\) 0 0
\(745\) 6.35837 + 11.0130i 0.232953 + 0.403486i
\(746\) 15.2893 + 15.2893i 0.559782 + 0.559782i
\(747\) 0 0
\(748\) −16.0927 + 60.0587i −0.588407 + 2.19596i
\(749\) 19.0412 + 0.538099i 0.695749 + 0.0196617i
\(750\) 0 0
\(751\) −13.1305 7.58091i −0.479140 0.276631i 0.240918 0.970545i \(-0.422551\pi\)
−0.720058 + 0.693914i \(0.755885\pi\)
\(752\) −1.05935 + 0.283851i −0.0386304 + 0.0103510i
\(753\) 0 0
\(754\) −64.5111 54.1887i −2.34935 1.97344i
\(755\) 28.7807i 1.04744i
\(756\) 0 0
\(757\) −17.8529 + 30.9221i −0.648875 + 1.12388i 0.334517 + 0.942390i \(0.391427\pi\)
−0.983392 + 0.181494i \(0.941907\pi\)
\(758\) −64.7200 + 37.3661i −2.35074 + 1.35720i
\(759\) 0 0
\(760\) −0.323404 + 1.20696i −0.0117311 + 0.0437810i
\(761\) −0.802382 + 2.99453i −0.0290863 + 0.108552i −0.978943 0.204134i \(-0.934562\pi\)
0.949857 + 0.312686i \(0.101229\pi\)
\(762\) 0 0
\(763\) 2.59191 8.68401i 0.0938334 0.314382i
\(764\) 35.1538 + 20.2961i 1.27182 + 0.734286i
\(765\) 0 0
\(766\) −8.67503 −0.313442
\(767\) −18.7824 15.7770i −0.678192 0.569675i
\(768\) 0 0
\(769\) −8.07284 30.1282i −0.291114 1.08645i −0.944255 0.329216i \(-0.893216\pi\)
0.653141 0.757237i \(-0.273451\pi\)
\(770\) −17.0654 71.7372i −0.614995 2.58523i
\(771\) 0 0
\(772\) −17.3447 17.3447i −0.624251 0.624251i
\(773\) 5.18000 + 1.38798i 0.186312 + 0.0499220i 0.350768 0.936462i \(-0.385920\pi\)
−0.164457 + 0.986384i \(0.552587\pi\)
\(774\) 0 0
\(775\) −13.8743 13.8743i −0.498379 0.498379i
\(776\) 5.96928 3.44636i 0.214284 0.123717i
\(777\) 0 0
\(778\) −7.31105 27.2852i −0.262114 0.978222i
\(779\) 0.106067i 0.00380026i
\(780\) 0 0
\(781\) 26.0089 0.930670
\(782\) −21.1410 78.8993i −0.756001 2.82143i
\(783\) 0 0
\(784\) −2.63275 5.22044i −0.0940267 0.186444i
\(785\) −15.0345 15.0345i −0.536604 0.536604i
\(786\) 0 0
\(787\) 3.63938 13.5824i 0.129730 0.484159i −0.870234 0.492638i \(-0.836033\pi\)
0.999964 + 0.00847973i \(0.00269922\pi\)
\(788\) 27.2973 27.2973i 0.9724