Properties

Label 819.2.bm.f.550.1
Level $819$
Weight $2$
Character 819.550
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 550.1
Root \(1.21245 - 0.727987i\) of defining polynomial
Character \(\chi\) \(=\) 819.550
Dual form 819.2.bm.f.478.6

$q$-expansion

\(f(q)\) \(=\) \(q-2.30327i q^{2} -3.30504 q^{4} +(-0.733776 + 0.423646i) q^{5} +(-0.357777 - 2.62145i) q^{7} +3.00585i q^{8} +O(q^{10})\) \(q-2.30327i q^{2} -3.30504 q^{4} +(-0.733776 + 0.423646i) q^{5} +(-0.357777 - 2.62145i) q^{7} +3.00585i q^{8} +(0.975769 + 1.69008i) q^{10} +(-1.30198 + 0.751701i) q^{11} +(-2.92329 + 2.11054i) q^{13} +(-6.03790 + 0.824057i) q^{14} +0.313194 q^{16} +2.07140 q^{17} +(0.0410731 + 0.0237136i) q^{19} +(2.42516 - 1.40016i) q^{20} +(1.73137 + 2.99882i) q^{22} -7.81870 q^{23} +(-2.14105 + 3.70840i) q^{25} +(4.86115 + 6.73311i) q^{26} +(1.18247 + 8.66399i) q^{28} +(0.679854 - 1.17754i) q^{29} +(-6.80787 - 3.93052i) q^{31} +5.29033i q^{32} -4.77099i q^{34} +(1.37309 + 1.77199i) q^{35} -6.70219i q^{37} +(0.0546187 - 0.0946024i) q^{38} +(-1.27341 - 2.20562i) q^{40} +(8.67622 + 5.00922i) q^{41} +(4.63283 + 8.02430i) q^{43} +(4.30311 - 2.48440i) q^{44} +18.0086i q^{46} +(0.311781 - 0.180007i) q^{47} +(-6.74399 + 1.87579i) q^{49} +(8.54144 + 4.93141i) q^{50} +(9.66157 - 6.97543i) q^{52} +(1.35591 - 2.34850i) q^{53} +(0.636910 - 1.10316i) q^{55} +(7.87968 - 1.07542i) q^{56} +(-2.71219 - 1.56588i) q^{58} +1.64120i q^{59} +(-2.26097 + 3.91612i) q^{61} +(-9.05305 + 15.6803i) q^{62} +12.8114 q^{64} +(1.25091 - 2.78711i) q^{65} +(-1.76900 + 1.02133i) q^{67} -6.84606 q^{68} +(4.08136 - 3.16260i) q^{70} +(-12.3096 + 7.10697i) q^{71} +(5.85563 + 3.38075i) q^{73} -15.4369 q^{74} +(-0.135748 - 0.0783743i) q^{76} +(2.43637 + 3.14414i) q^{77} +(-5.82952 - 10.0970i) q^{79} +(-0.229814 + 0.132683i) q^{80} +(11.5376 - 19.9837i) q^{82} -11.5362i q^{83} +(-1.51994 + 0.877541i) q^{85} +(18.4821 - 10.6706i) q^{86} +(-2.25950 - 3.91357i) q^{88} -17.5112i q^{89} +(6.57857 + 6.90814i) q^{91} +25.8411 q^{92} +(-0.414604 - 0.718115i) q^{94} -0.0401846 q^{95} +(0.369125 - 0.213115i) q^{97} +(4.32044 + 15.5332i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30327i 1.62866i −0.580405 0.814328i \(-0.697106\pi\)
0.580405 0.814328i \(-0.302894\pi\)
\(3\) 0 0
\(4\) −3.30504 −1.65252
\(5\) −0.733776 + 0.423646i −0.328155 + 0.189460i −0.655022 0.755610i \(-0.727340\pi\)
0.326867 + 0.945070i \(0.394007\pi\)
\(6\) 0 0
\(7\) −0.357777 2.62145i −0.135227 0.990815i
\(8\) 3.00585i 1.06273i
\(9\) 0 0
\(10\) 0.975769 + 1.69008i 0.308565 + 0.534451i
\(11\) −1.30198 + 0.751701i −0.392563 + 0.226646i −0.683270 0.730166i \(-0.739443\pi\)
0.290707 + 0.956812i \(0.406110\pi\)
\(12\) 0 0
\(13\) −2.92329 + 2.11054i −0.810774 + 0.585360i
\(14\) −6.03790 + 0.824057i −1.61370 + 0.220238i
\(15\) 0 0
\(16\) 0.313194 0.0782985
\(17\) 2.07140 0.502389 0.251194 0.967937i \(-0.419177\pi\)
0.251194 + 0.967937i \(0.419177\pi\)
\(18\) 0 0
\(19\) 0.0410731 + 0.0237136i 0.00942282 + 0.00544027i 0.504704 0.863292i \(-0.331602\pi\)
−0.495281 + 0.868733i \(0.664935\pi\)
\(20\) 2.42516 1.40016i 0.542282 0.313086i
\(21\) 0 0
\(22\) 1.73137 + 2.99882i 0.369129 + 0.639350i
\(23\) −7.81870 −1.63031 −0.815156 0.579241i \(-0.803349\pi\)
−0.815156 + 0.579241i \(0.803349\pi\)
\(24\) 0 0
\(25\) −2.14105 + 3.70840i −0.428210 + 0.741681i
\(26\) 4.86115 + 6.73311i 0.953349 + 1.32047i
\(27\) 0 0
\(28\) 1.18247 + 8.66399i 0.223465 + 1.63734i
\(29\) 0.679854 1.17754i 0.126246 0.218664i −0.795973 0.605331i \(-0.793041\pi\)
0.922219 + 0.386668i \(0.126374\pi\)
\(30\) 0 0
\(31\) −6.80787 3.93052i −1.22273 0.705943i −0.257230 0.966350i \(-0.582810\pi\)
−0.965499 + 0.260407i \(0.916143\pi\)
\(32\) 5.29033i 0.935206i
\(33\) 0 0
\(34\) 4.77099i 0.818218i
\(35\) 1.37309 + 1.77199i 0.232095 + 0.299520i
\(36\) 0 0
\(37\) 6.70219i 1.10183i −0.834560 0.550917i \(-0.814278\pi\)
0.834560 0.550917i \(-0.185722\pi\)
\(38\) 0.0546187 0.0946024i 0.00886032 0.0153465i
\(39\) 0 0
\(40\) −1.27341 2.20562i −0.201345 0.348739i
\(41\) 8.67622 + 5.00922i 1.35500 + 0.782309i 0.988945 0.148285i \(-0.0473754\pi\)
0.366054 + 0.930594i \(0.380709\pi\)
\(42\) 0 0
\(43\) 4.63283 + 8.02430i 0.706500 + 1.22369i 0.966147 + 0.257991i \(0.0830604\pi\)
−0.259647 + 0.965704i \(0.583606\pi\)
\(44\) 4.30311 2.48440i 0.648718 0.374537i
\(45\) 0 0
\(46\) 18.0086i 2.65522i
\(47\) 0.311781 0.180007i 0.0454779 0.0262567i −0.477089 0.878855i \(-0.658308\pi\)
0.522567 + 0.852598i \(0.324975\pi\)
\(48\) 0 0
\(49\) −6.74399 + 1.87579i −0.963427 + 0.267970i
\(50\) 8.54144 + 4.93141i 1.20794 + 0.697406i
\(51\) 0 0
\(52\) 9.66157 6.97543i 1.33982 0.967318i
\(53\) 1.35591 2.34850i 0.186248 0.322591i −0.757748 0.652547i \(-0.773701\pi\)
0.943996 + 0.329956i \(0.107034\pi\)
\(54\) 0 0
\(55\) 0.636910 1.10316i 0.0858809 0.148750i
\(56\) 7.87968 1.07542i 1.05297 0.143710i
\(57\) 0 0
\(58\) −2.71219 1.56588i −0.356128 0.205611i
\(59\) 1.64120i 0.213666i 0.994277 + 0.106833i \(0.0340709\pi\)
−0.994277 + 0.106833i \(0.965929\pi\)
\(60\) 0 0
\(61\) −2.26097 + 3.91612i −0.289488 + 0.501407i −0.973688 0.227887i \(-0.926818\pi\)
0.684200 + 0.729295i \(0.260152\pi\)
\(62\) −9.05305 + 15.6803i −1.14974 + 1.99140i
\(63\) 0 0
\(64\) 12.8114 1.60143
\(65\) 1.25091 2.78711i 0.155157 0.345698i
\(66\) 0 0
\(67\) −1.76900 + 1.02133i −0.216117 + 0.124775i −0.604151 0.796870i \(-0.706488\pi\)
0.388034 + 0.921645i \(0.373154\pi\)
\(68\) −6.84606 −0.830206
\(69\) 0 0
\(70\) 4.08136 3.16260i 0.487815 0.378003i
\(71\) −12.3096 + 7.10697i −1.46088 + 0.843442i −0.999052 0.0435255i \(-0.986141\pi\)
−0.461832 + 0.886967i \(0.652808\pi\)
\(72\) 0 0
\(73\) 5.85563 + 3.38075i 0.685349 + 0.395687i 0.801867 0.597502i \(-0.203840\pi\)
−0.116518 + 0.993189i \(0.537173\pi\)
\(74\) −15.4369 −1.79451
\(75\) 0 0
\(76\) −0.135748 0.0783743i −0.0155714 0.00899015i
\(77\) 2.43637 + 3.14414i 0.277650 + 0.358308i
\(78\) 0 0
\(79\) −5.82952 10.0970i −0.655873 1.13600i −0.981674 0.190567i \(-0.938967\pi\)
0.325801 0.945438i \(-0.394366\pi\)
\(80\) −0.229814 + 0.132683i −0.0256940 + 0.0148344i
\(81\) 0 0
\(82\) 11.5376 19.9837i 1.27411 2.20683i
\(83\) 11.5362i 1.26627i −0.774043 0.633133i \(-0.781768\pi\)
0.774043 0.633133i \(-0.218232\pi\)
\(84\) 0 0
\(85\) −1.51994 + 0.877541i −0.164861 + 0.0951826i
\(86\) 18.4821 10.6706i 1.99298 1.15065i
\(87\) 0 0
\(88\) −2.25950 3.91357i −0.240863 0.417188i
\(89\) 17.5112i 1.85619i −0.372350 0.928093i \(-0.621448\pi\)
0.372350 0.928093i \(-0.378552\pi\)
\(90\) 0 0
\(91\) 6.57857 + 6.90814i 0.689622 + 0.724170i
\(92\) 25.8411 2.69412
\(93\) 0 0
\(94\) −0.414604 0.718115i −0.0427631 0.0740679i
\(95\) −0.0401846 −0.00412286
\(96\) 0 0
\(97\) 0.369125 0.213115i 0.0374790 0.0216385i −0.481143 0.876642i \(-0.659778\pi\)
0.518622 + 0.855003i \(0.326445\pi\)
\(98\) 4.32044 + 15.5332i 0.436431 + 1.56909i
\(99\) 0 0
\(100\) 7.07624 12.2564i 0.707624 1.22564i
\(101\) −4.83499 8.37444i −0.481099 0.833288i 0.518666 0.854977i \(-0.326429\pi\)
−0.999765 + 0.0216891i \(0.993096\pi\)
\(102\) 0 0
\(103\) −4.98912 8.64140i −0.491592 0.851463i 0.508361 0.861144i \(-0.330252\pi\)
−0.999953 + 0.00968129i \(0.996918\pi\)
\(104\) −6.34397 8.78695i −0.622078 0.861631i
\(105\) 0 0
\(106\) −5.40922 3.12301i −0.525390 0.303334i
\(107\) −9.86223 −0.953417 −0.476709 0.879061i \(-0.658170\pi\)
−0.476709 + 0.879061i \(0.658170\pi\)
\(108\) 0 0
\(109\) −10.0507 5.80275i −0.962679 0.555803i −0.0656822 0.997841i \(-0.520922\pi\)
−0.896996 + 0.442038i \(0.854256\pi\)
\(110\) −2.54087 1.46697i −0.242263 0.139870i
\(111\) 0 0
\(112\) −0.112054 0.821022i −0.0105881 0.0775793i
\(113\) −1.73879 3.01167i −0.163572 0.283314i 0.772576 0.634923i \(-0.218968\pi\)
−0.936147 + 0.351609i \(0.885635\pi\)
\(114\) 0 0
\(115\) 5.73718 3.31236i 0.534994 0.308879i
\(116\) −2.24694 + 3.89182i −0.208623 + 0.361346i
\(117\) 0 0
\(118\) 3.78011 0.347987
\(119\) −0.741100 5.43007i −0.0679366 0.497774i
\(120\) 0 0
\(121\) −4.36989 + 7.56887i −0.397263 + 0.688079i
\(122\) 9.01986 + 5.20762i 0.816620 + 0.471476i
\(123\) 0 0
\(124\) 22.5003 + 12.9905i 2.02058 + 1.16658i
\(125\) 7.86464i 0.703435i
\(126\) 0 0
\(127\) −7.84992 + 13.5965i −0.696567 + 1.20649i 0.273082 + 0.961991i \(0.411957\pi\)
−0.969649 + 0.244499i \(0.921376\pi\)
\(128\) 18.9275i 1.67297i
\(129\) 0 0
\(130\) −6.41945 2.88119i −0.563023 0.252697i
\(131\) −1.27259 2.20418i −0.111186 0.192580i 0.805063 0.593190i \(-0.202132\pi\)
−0.916249 + 0.400610i \(0.868798\pi\)
\(132\) 0 0
\(133\) 0.0474689 0.116155i 0.00411608 0.0100719i
\(134\) 2.35240 + 4.07447i 0.203216 + 0.351981i
\(135\) 0 0
\(136\) 6.22632i 0.533902i
\(137\) 1.86472i 0.159314i −0.996822 0.0796571i \(-0.974617\pi\)
0.996822 0.0796571i \(-0.0253825\pi\)
\(138\) 0 0
\(139\) −7.80462 13.5180i −0.661979 1.14658i −0.980095 0.198530i \(-0.936383\pi\)
0.318116 0.948052i \(-0.396950\pi\)
\(140\) −4.53813 5.85648i −0.383542 0.494963i
\(141\) 0 0
\(142\) 16.3692 + 28.3524i 1.37368 + 2.37928i
\(143\) 2.21957 4.94533i 0.185610 0.413550i
\(144\) 0 0
\(145\) 1.15207i 0.0956741i
\(146\) 7.78676 13.4871i 0.644437 1.11620i
\(147\) 0 0
\(148\) 22.1510i 1.82080i
\(149\) −5.51106 3.18181i −0.451484 0.260664i 0.256973 0.966419i \(-0.417275\pi\)
−0.708457 + 0.705754i \(0.750608\pi\)
\(150\) 0 0
\(151\) 0.575122 + 0.332047i 0.0468028 + 0.0270216i 0.523219 0.852198i \(-0.324731\pi\)
−0.476416 + 0.879220i \(0.658064\pi\)
\(152\) −0.0712794 + 0.123460i −0.00578152 + 0.0100139i
\(153\) 0 0
\(154\) 7.24180 5.61160i 0.583561 0.452196i
\(155\) 6.66060 0.534992
\(156\) 0 0
\(157\) 8.28798 14.3552i 0.661453 1.14567i −0.318781 0.947828i \(-0.603273\pi\)
0.980234 0.197842i \(-0.0633933\pi\)
\(158\) −23.2562 + 13.4269i −1.85016 + 1.06819i
\(159\) 0 0
\(160\) −2.24122 3.88191i −0.177184 0.306892i
\(161\) 2.79735 + 20.4963i 0.220462 + 1.61534i
\(162\) 0 0
\(163\) 7.83863 + 4.52563i 0.613969 + 0.354475i 0.774517 0.632553i \(-0.217993\pi\)
−0.160548 + 0.987028i \(0.551326\pi\)
\(164\) −28.6752 16.5557i −2.23916 1.29278i
\(165\) 0 0
\(166\) −26.5710 −2.06231
\(167\) 2.30156 + 1.32880i 0.178100 + 0.102826i 0.586400 0.810022i \(-0.300545\pi\)
−0.408300 + 0.912848i \(0.633878\pi\)
\(168\) 0 0
\(169\) 4.09120 12.3395i 0.314708 0.949189i
\(170\) 2.02121 + 3.50084i 0.155020 + 0.268502i
\(171\) 0 0
\(172\) −15.3117 26.5206i −1.16750 2.02218i
\(173\) −9.79352 + 16.9629i −0.744588 + 1.28966i 0.205799 + 0.978594i \(0.434021\pi\)
−0.950387 + 0.311070i \(0.899313\pi\)
\(174\) 0 0
\(175\) 10.4874 + 4.28587i 0.792774 + 0.323981i
\(176\) −0.407774 + 0.235428i −0.0307371 + 0.0177461i
\(177\) 0 0
\(178\) −40.3330 −3.02309
\(179\) 1.44666 + 2.50569i 0.108129 + 0.187284i 0.915012 0.403426i \(-0.132181\pi\)
−0.806884 + 0.590711i \(0.798848\pi\)
\(180\) 0 0
\(181\) −1.36804 −0.101686 −0.0508429 0.998707i \(-0.516191\pi\)
−0.0508429 + 0.998707i \(0.516191\pi\)
\(182\) 15.9113 15.1522i 1.17942 1.12316i
\(183\) 0 0
\(184\) 23.5018i 1.73258i
\(185\) 2.83936 + 4.91791i 0.208754 + 0.361572i
\(186\) 0 0
\(187\) −2.69693 + 1.55707i −0.197219 + 0.113865i
\(188\) −1.03045 + 0.594929i −0.0751531 + 0.0433897i
\(189\) 0 0
\(190\) 0.0925559i 0.00671471i
\(191\) −0.756625 + 1.31051i −0.0547475 + 0.0948254i −0.892100 0.451837i \(-0.850769\pi\)
0.837353 + 0.546663i \(0.184102\pi\)
\(192\) 0 0
\(193\) −6.02229 + 3.47697i −0.433494 + 0.250278i −0.700834 0.713324i \(-0.747189\pi\)
0.267340 + 0.963602i \(0.413855\pi\)
\(194\) −0.490860 0.850194i −0.0352417 0.0610404i
\(195\) 0 0
\(196\) 22.2891 6.19955i 1.59208 0.442825i
\(197\) 13.4037 + 7.73860i 0.954971 + 0.551353i 0.894622 0.446825i \(-0.147445\pi\)
0.0603494 + 0.998177i \(0.480779\pi\)
\(198\) 0 0
\(199\) −6.61529 −0.468945 −0.234473 0.972123i \(-0.575336\pi\)
−0.234473 + 0.972123i \(0.575336\pi\)
\(200\) −11.1469 6.43566i −0.788205 0.455070i
\(201\) 0 0
\(202\) −19.2886 + 11.1363i −1.35714 + 0.783545i
\(203\) −3.33010 1.36090i −0.233727 0.0955168i
\(204\) 0 0
\(205\) −8.48854 −0.592865
\(206\) −19.9035 + 11.4913i −1.38674 + 0.800634i
\(207\) 0 0
\(208\) −0.915555 + 0.661010i −0.0634823 + 0.0458328i
\(209\) −0.0713021 −0.00493207
\(210\) 0 0
\(211\) 4.04714 7.00986i 0.278617 0.482578i −0.692424 0.721490i \(-0.743457\pi\)
0.971041 + 0.238912i \(0.0767907\pi\)
\(212\) −4.48132 + 7.76187i −0.307778 + 0.533088i
\(213\) 0 0
\(214\) 22.7153i 1.55279i
\(215\) −6.79892 3.92536i −0.463683 0.267707i
\(216\) 0 0
\(217\) −7.86797 + 19.2527i −0.534113 + 1.30696i
\(218\) −13.3653 + 23.1493i −0.905211 + 1.56787i
\(219\) 0 0
\(220\) −2.10501 + 3.64599i −0.141920 + 0.245812i
\(221\) −6.05530 + 4.37178i −0.407323 + 0.294078i
\(222\) 0 0
\(223\) 13.9067 + 8.02903i 0.931261 + 0.537664i 0.887210 0.461366i \(-0.152640\pi\)
0.0440506 + 0.999029i \(0.485974\pi\)
\(224\) 13.8683 1.89276i 0.926616 0.126465i
\(225\) 0 0
\(226\) −6.93668 + 4.00490i −0.461421 + 0.266402i
\(227\) 1.29581i 0.0860057i −0.999075 0.0430029i \(-0.986308\pi\)
0.999075 0.0430029i \(-0.0136925\pi\)
\(228\) 0 0
\(229\) 18.0285 10.4088i 1.19136 0.687831i 0.232743 0.972538i \(-0.425230\pi\)
0.958614 + 0.284707i \(0.0918965\pi\)
\(230\) −7.62925 13.2142i −0.503058 0.871322i
\(231\) 0 0
\(232\) 3.53951 + 2.04354i 0.232380 + 0.134165i
\(233\) 6.65213 + 11.5218i 0.435796 + 0.754820i 0.997360 0.0726127i \(-0.0231337\pi\)
−0.561565 + 0.827433i \(0.689800\pi\)
\(234\) 0 0
\(235\) −0.152518 + 0.264169i −0.00994920 + 0.0172325i
\(236\) 5.42421i 0.353086i
\(237\) 0 0
\(238\) −12.5069 + 1.70695i −0.810702 + 0.110645i
\(239\) 13.3652i 0.864525i −0.901748 0.432263i \(-0.857715\pi\)
0.901748 0.432263i \(-0.142285\pi\)
\(240\) 0 0
\(241\) 0.834153i 0.0537325i 0.999639 + 0.0268663i \(0.00855282\pi\)
−0.999639 + 0.0268663i \(0.991447\pi\)
\(242\) 17.4331 + 10.0650i 1.12064 + 0.647004i
\(243\) 0 0
\(244\) 7.47259 12.9429i 0.478384 0.828585i
\(245\) 4.15391 4.23347i 0.265383 0.270467i
\(246\) 0 0
\(247\) −0.170117 + 0.0173651i −0.0108243 + 0.00110491i
\(248\) 11.8146 20.4634i 0.750225 1.29943i
\(249\) 0 0
\(250\) −18.1144 −1.14565
\(251\) −13.6360 23.6183i −0.860699 1.49078i −0.871255 0.490831i \(-0.836693\pi\)
0.0105555 0.999944i \(-0.496640\pi\)
\(252\) 0 0
\(253\) 10.1798 5.87733i 0.640000 0.369504i
\(254\) 31.3163 + 18.0804i 1.96496 + 1.13447i
\(255\) 0 0
\(256\) −17.9721 −1.12326
\(257\) 6.55188 0.408695 0.204348 0.978898i \(-0.434493\pi\)
0.204348 + 0.978898i \(0.434493\pi\)
\(258\) 0 0
\(259\) −17.5695 + 2.39789i −1.09171 + 0.148998i
\(260\) −4.13432 + 9.21148i −0.256399 + 0.571272i
\(261\) 0 0
\(262\) −5.07682 + 2.93110i −0.313647 + 0.181084i
\(263\) −11.2945 19.5627i −0.696450 1.20629i −0.969689 0.244341i \(-0.921428\pi\)
0.273239 0.961946i \(-0.411905\pi\)
\(264\) 0 0
\(265\) 2.29770i 0.141146i
\(266\) −0.267537 0.109334i −0.0164037 0.00670367i
\(267\) 0 0
\(268\) 5.84660 3.37553i 0.357138 0.206194i
\(269\) −16.0013 −0.975617 −0.487808 0.872951i \(-0.662203\pi\)
−0.487808 + 0.872951i \(0.662203\pi\)
\(270\) 0 0
\(271\) 8.75935i 0.532093i −0.963960 0.266046i \(-0.914283\pi\)
0.963960 0.266046i \(-0.0857174\pi\)
\(272\) 0.648750 0.0393363
\(273\) 0 0
\(274\) −4.29496 −0.259468
\(275\) 6.43771i 0.388209i
\(276\) 0 0
\(277\) 19.9183 1.19677 0.598387 0.801208i \(-0.295809\pi\)
0.598387 + 0.801208i \(0.295809\pi\)
\(278\) −31.1355 + 17.9761i −1.86739 + 1.07814i
\(279\) 0 0
\(280\) −5.32632 + 4.12731i −0.318308 + 0.246654i
\(281\) 14.0234i 0.836566i 0.908317 + 0.418283i \(0.137368\pi\)
−0.908317 + 0.418283i \(0.862632\pi\)
\(282\) 0 0
\(283\) 0.506295 + 0.876929i 0.0300961 + 0.0521280i 0.880681 0.473710i \(-0.157085\pi\)
−0.850585 + 0.525838i \(0.823752\pi\)
\(284\) 40.6838 23.4888i 2.41414 1.39380i
\(285\) 0 0
\(286\) −11.3904 5.11227i −0.673530 0.302295i
\(287\) 10.0273 24.5365i 0.591890 1.44834i
\(288\) 0 0
\(289\) −12.7093 −0.747606
\(290\) 2.65352 0.155820
\(291\) 0 0
\(292\) −19.3531 11.1735i −1.13255 0.653879i
\(293\) 0.172543 0.0996176i 0.0100801 0.00581972i −0.494952 0.868921i \(-0.664814\pi\)
0.505032 + 0.863101i \(0.331481\pi\)
\(294\) 0 0
\(295\) −0.695286 1.20427i −0.0404811 0.0701153i
\(296\) 20.1458 1.17095
\(297\) 0 0
\(298\) −7.32857 + 12.6935i −0.424532 + 0.735312i
\(299\) 22.8563 16.5017i 1.32181 0.954319i
\(300\) 0 0
\(301\) 19.3778 15.0156i 1.11692 0.865487i
\(302\) 0.764792 1.32466i 0.0440088 0.0762256i
\(303\) 0 0
\(304\) 0.0128639 + 0.00742695i 0.000737793 + 0.000425965i
\(305\) 3.83140i 0.219386i
\(306\) 0 0
\(307\) 27.2004i 1.55241i −0.630482 0.776204i \(-0.717143\pi\)
0.630482 0.776204i \(-0.282857\pi\)
\(308\) −8.05228 10.3915i −0.458821 0.592111i
\(309\) 0 0
\(310\) 15.3411i 0.871318i
\(311\) −13.5505 + 23.4701i −0.768376 + 1.33087i 0.170067 + 0.985432i \(0.445602\pi\)
−0.938443 + 0.345434i \(0.887732\pi\)
\(312\) 0 0
\(313\) 11.0392 + 19.1205i 0.623975 + 1.08076i 0.988738 + 0.149656i \(0.0478165\pi\)
−0.364763 + 0.931100i \(0.618850\pi\)
\(314\) −33.0639 19.0894i −1.86590 1.07728i
\(315\) 0 0
\(316\) 19.2668 + 33.3711i 1.08384 + 1.87727i
\(317\) 6.12126 3.53411i 0.343804 0.198496i −0.318149 0.948041i \(-0.603061\pi\)
0.661953 + 0.749545i \(0.269728\pi\)
\(318\) 0 0
\(319\) 2.04419i 0.114453i
\(320\) −9.40071 + 5.42750i −0.525516 + 0.303407i
\(321\) 0 0
\(322\) 47.2085 6.44305i 2.63083 0.359057i
\(323\) 0.0850789 + 0.0491204i 0.00473392 + 0.00273313i
\(324\) 0 0
\(325\) −1.56786 15.3595i −0.0869690 0.851992i
\(326\) 10.4237 18.0544i 0.577318 0.999943i
\(327\) 0 0
\(328\) −15.0569 + 26.0794i −0.831381 + 1.43999i
\(329\) −0.583427 0.752916i −0.0321654 0.0415096i
\(330\) 0 0
\(331\) 5.70588 + 3.29429i 0.313623 + 0.181071i 0.648547 0.761175i \(-0.275377\pi\)
−0.334923 + 0.942245i \(0.608710\pi\)
\(332\) 38.1277i 2.09253i
\(333\) 0 0
\(334\) 3.06059 5.30110i 0.167468 0.290063i
\(335\) 0.865365 1.49886i 0.0472799 0.0818912i
\(336\) 0 0
\(337\) −4.22290 −0.230036 −0.115018 0.993363i \(-0.536693\pi\)
−0.115018 + 0.993363i \(0.536693\pi\)
\(338\) −28.4210 9.42313i −1.54590 0.512551i
\(339\) 0 0
\(340\) 5.02347 2.90030i 0.272436 0.157291i
\(341\) 11.8183 0.639998
\(342\) 0 0
\(343\) 7.33014 + 17.0079i 0.395790 + 0.918341i
\(344\) −24.1198 + 13.9256i −1.30045 + 0.750817i
\(345\) 0 0
\(346\) 39.0700 + 22.5571i 2.10042 + 1.21268i
\(347\) 9.09478 0.488233 0.244117 0.969746i \(-0.421502\pi\)
0.244117 + 0.969746i \(0.421502\pi\)
\(348\) 0 0
\(349\) 7.98521 + 4.61026i 0.427439 + 0.246782i 0.698255 0.715849i \(-0.253960\pi\)
−0.270816 + 0.962631i \(0.587294\pi\)
\(350\) 9.87149 24.1553i 0.527653 1.29116i
\(351\) 0 0
\(352\) −3.97674 6.88792i −0.211961 0.367127i
\(353\) −1.86584 + 1.07724i −0.0993087 + 0.0573359i −0.548832 0.835933i \(-0.684927\pi\)
0.449523 + 0.893269i \(0.351594\pi\)
\(354\) 0 0
\(355\) 6.02167 10.4298i 0.319597 0.553559i
\(356\) 57.8752i 3.06738i
\(357\) 0 0
\(358\) 5.77128 3.33205i 0.305021 0.176104i
\(359\) 7.41107 4.27878i 0.391141 0.225825i −0.291513 0.956567i \(-0.594159\pi\)
0.682654 + 0.730741i \(0.260825\pi\)
\(360\) 0 0
\(361\) −9.49888 16.4525i −0.499941 0.865923i
\(362\) 3.15096i 0.165611i
\(363\) 0 0
\(364\) −21.7424 22.8317i −1.13961 1.19670i
\(365\) −5.72896 −0.299867
\(366\) 0 0
\(367\) −1.14912 1.99033i −0.0599833 0.103894i 0.834474 0.551047i \(-0.185771\pi\)
−0.894458 + 0.447153i \(0.852438\pi\)
\(368\) −2.44877 −0.127651
\(369\) 0 0
\(370\) 11.3273 6.53979i 0.588876 0.339988i
\(371\) −6.64158 2.71420i −0.344814 0.140914i
\(372\) 0 0
\(373\) −5.88418 + 10.1917i −0.304672 + 0.527707i −0.977188 0.212375i \(-0.931880\pi\)
0.672517 + 0.740082i \(0.265213\pi\)
\(374\) 3.58636 + 6.21175i 0.185446 + 0.321202i
\(375\) 0 0
\(376\) 0.541073 + 0.937166i 0.0279037 + 0.0483307i
\(377\) 0.497847 + 4.87715i 0.0256404 + 0.251186i
\(378\) 0 0
\(379\) −6.92034 3.99546i −0.355474 0.205233i 0.311619 0.950207i \(-0.399129\pi\)
−0.667094 + 0.744974i \(0.732462\pi\)
\(380\) 0.132812 0.00681310
\(381\) 0 0
\(382\) 3.01846 + 1.74271i 0.154438 + 0.0891647i
\(383\) 24.4605 + 14.1223i 1.24988 + 0.721616i 0.971084 0.238736i \(-0.0767331\pi\)
0.278791 + 0.960352i \(0.410066\pi\)
\(384\) 0 0
\(385\) −3.11975 1.27494i −0.158997 0.0649770i
\(386\) 8.00839 + 13.8709i 0.407616 + 0.706012i
\(387\) 0 0
\(388\) −1.21997 + 0.704352i −0.0619347 + 0.0357580i
\(389\) −3.84043 + 6.65182i −0.194717 + 0.337261i −0.946808 0.321799i \(-0.895712\pi\)
0.752090 + 0.659060i \(0.229046\pi\)
\(390\) 0 0
\(391\) −16.1957 −0.819050
\(392\) −5.63834 20.2714i −0.284779 1.02386i
\(393\) 0 0
\(394\) 17.8241 30.8722i 0.897964 1.55532i
\(395\) 8.55513 + 4.93931i 0.430455 + 0.248524i
\(396\) 0 0
\(397\) 6.45433 + 3.72641i 0.323933 + 0.187023i 0.653144 0.757233i \(-0.273449\pi\)
−0.329211 + 0.944256i \(0.606783\pi\)
\(398\) 15.2368i 0.763750i
\(399\) 0 0
\(400\) −0.670563 + 1.16145i −0.0335282 + 0.0580725i
\(401\) 18.1982i 0.908777i 0.890804 + 0.454389i \(0.150142\pi\)
−0.890804 + 0.454389i \(0.849858\pi\)
\(402\) 0 0
\(403\) 28.1969 2.87826i 1.40459 0.143376i
\(404\) 15.9798 + 27.6778i 0.795025 + 1.37702i
\(405\) 0 0
\(406\) −3.13453 + 7.67011i −0.155564 + 0.380661i
\(407\) 5.03804 + 8.72615i 0.249727 + 0.432539i
\(408\) 0 0
\(409\) 29.2825i 1.44793i 0.689838 + 0.723964i \(0.257682\pi\)
−0.689838 + 0.723964i \(0.742318\pi\)
\(410\) 19.5514i 0.965573i
\(411\) 0 0
\(412\) 16.4892 + 28.5602i 0.812365 + 1.40706i
\(413\) 4.30231 0.587183i 0.211703 0.0288934i
\(414\) 0 0
\(415\) 4.88728 + 8.46502i 0.239907 + 0.415531i
\(416\) −11.1655 15.4651i −0.547432 0.758241i
\(417\) 0 0
\(418\) 0.164228i 0.00803264i
\(419\) −10.3697 + 17.9608i −0.506591 + 0.877441i 0.493380 + 0.869814i \(0.335761\pi\)
−0.999971 + 0.00762733i \(0.997572\pi\)
\(420\) 0 0
\(421\) 24.8696i 1.21207i −0.795437 0.606036i \(-0.792759\pi\)
0.795437 0.606036i \(-0.207241\pi\)
\(422\) −16.1456 9.32165i −0.785954 0.453771i
\(423\) 0 0
\(424\) 7.05923 + 4.07565i 0.342826 + 0.197931i
\(425\) −4.43497 + 7.68159i −0.215128 + 0.372612i
\(426\) 0 0
\(427\) 11.0748 + 4.52592i 0.535948 + 0.219025i
\(428\) 32.5950 1.57554
\(429\) 0 0
\(430\) −9.04115 + 15.6597i −0.436003 + 0.755179i
\(431\) 18.3327 10.5844i 0.883055 0.509832i 0.0113906 0.999935i \(-0.496374\pi\)
0.871665 + 0.490103i \(0.163041\pi\)
\(432\) 0 0
\(433\) −11.7148 20.2906i −0.562977 0.975105i −0.997235 0.0743163i \(-0.976323\pi\)
0.434258 0.900789i \(-0.357011\pi\)
\(434\) 44.3442 + 18.1220i 2.12859 + 0.869885i
\(435\) 0 0
\(436\) 33.2178 + 19.1783i 1.59084 + 0.918474i
\(437\) −0.321139 0.185409i −0.0153621 0.00886934i
\(438\) 0 0
\(439\) 12.0384 0.574561 0.287280 0.957847i \(-0.407249\pi\)
0.287280 + 0.957847i \(0.407249\pi\)
\(440\) 3.31593 + 1.91445i 0.158081 + 0.0912680i
\(441\) 0 0
\(442\) 10.0694 + 13.9470i 0.478952 + 0.663390i
\(443\) 7.86656 + 13.6253i 0.373752 + 0.647357i 0.990139 0.140086i \(-0.0447379\pi\)
−0.616388 + 0.787443i \(0.711405\pi\)
\(444\) 0 0
\(445\) 7.41855 + 12.8493i 0.351673 + 0.609116i
\(446\) 18.4930 32.0308i 0.875669 1.51670i
\(447\) 0 0
\(448\) −4.58363 33.5845i −0.216556 1.58672i
\(449\) −22.5177 + 13.0006i −1.06268 + 0.613536i −0.926171 0.377104i \(-0.876920\pi\)
−0.136504 + 0.990640i \(0.543587\pi\)
\(450\) 0 0
\(451\) −15.0617 −0.709230
\(452\) 5.74676 + 9.95369i 0.270305 + 0.468182i
\(453\) 0 0
\(454\) −2.98459 −0.140074
\(455\) −7.75380 2.28204i −0.363504 0.106984i
\(456\) 0 0
\(457\) 30.7958i 1.44057i 0.693679 + 0.720284i \(0.255989\pi\)
−0.693679 + 0.720284i \(0.744011\pi\)
\(458\) −23.9742 41.5245i −1.12024 1.94031i
\(459\) 0 0
\(460\) −18.9616 + 10.9475i −0.884088 + 0.510429i
\(461\) 29.5278 17.0479i 1.37525 0.794000i 0.383665 0.923472i \(-0.374662\pi\)
0.991583 + 0.129472i \(0.0413284\pi\)
\(462\) 0 0
\(463\) 1.69184i 0.0786263i 0.999227 + 0.0393131i \(0.0125170\pi\)
−0.999227 + 0.0393131i \(0.987483\pi\)
\(464\) 0.212926 0.368799i 0.00988485 0.0171211i
\(465\) 0 0
\(466\) 26.5378 15.3216i 1.22934 0.709761i
\(467\) −14.1762 24.5539i −0.655996 1.13622i −0.981643 0.190727i \(-0.938916\pi\)
0.325647 0.945491i \(-0.394418\pi\)
\(468\) 0 0
\(469\) 3.31027 + 4.27192i 0.152854 + 0.197259i
\(470\) 0.608453 + 0.351290i 0.0280658 + 0.0162038i
\(471\) 0 0
\(472\) −4.93318 −0.227068
\(473\) −12.0637 6.96501i −0.554692 0.320251i
\(474\) 0 0
\(475\) −0.175879 + 0.101544i −0.00806989 + 0.00465915i
\(476\) 2.44936 + 17.9466i 0.112266 + 0.822581i
\(477\) 0 0
\(478\) −30.7837 −1.40801
\(479\) −5.44077 + 3.14123i −0.248595 + 0.143526i −0.619121 0.785296i \(-0.712511\pi\)
0.370526 + 0.928822i \(0.379178\pi\)
\(480\) 0 0
\(481\) 14.1453 + 19.5924i 0.644969 + 0.893338i
\(482\) 1.92128 0.0875117
\(483\) 0 0
\(484\) 14.4427 25.0154i 0.656484 1.13706i
\(485\) −0.180570 + 0.312757i −0.00819927 + 0.0142016i
\(486\) 0 0
\(487\) 13.0176i 0.589883i 0.955515 + 0.294942i \(0.0953002\pi\)
−0.955515 + 0.294942i \(0.904700\pi\)
\(488\) −11.7712 6.79613i −0.532859 0.307647i
\(489\) 0 0
\(490\) −9.75082 9.56756i −0.440497 0.432218i
\(491\) 6.17616 10.6974i 0.278726 0.482768i −0.692342 0.721569i \(-0.743421\pi\)
0.971068 + 0.238801i \(0.0767544\pi\)
\(492\) 0 0
\(493\) 1.40825 2.43916i 0.0634244 0.109854i
\(494\) 0.0399964 + 0.391825i 0.00179952 + 0.0176290i
\(495\) 0 0
\(496\) −2.13218 1.23102i −0.0957378 0.0552743i
\(497\) 23.0347 + 29.7264i 1.03325 + 1.33341i
\(498\) 0 0
\(499\) 7.92708 4.57670i 0.354865 0.204881i −0.311961 0.950095i \(-0.600986\pi\)
0.666826 + 0.745214i \(0.267652\pi\)
\(500\) 25.9929i 1.16244i
\(501\) 0 0
\(502\) −54.3993 + 31.4074i −2.42796 + 1.40178i
\(503\) 11.2519 + 19.4888i 0.501696 + 0.868963i 0.999998 + 0.00195935i \(0.000623680\pi\)
−0.498302 + 0.867003i \(0.666043\pi\)
\(504\) 0 0
\(505\) 7.09559 + 4.09664i 0.315750 + 0.182298i
\(506\) −13.5370 23.4469i −0.601795 1.04234i
\(507\) 0 0
\(508\) 25.9443 44.9368i 1.15109 1.99375i
\(509\) 38.6606i 1.71360i 0.515649 + 0.856800i \(0.327551\pi\)
−0.515649 + 0.856800i \(0.672449\pi\)
\(510\) 0 0
\(511\) 6.76745 16.5598i 0.299374 0.732562i
\(512\) 3.53972i 0.156435i
\(513\) 0 0
\(514\) 15.0907i 0.665623i
\(515\) 7.32179 + 4.22724i 0.322637 + 0.186274i
\(516\) 0 0
\(517\) −0.270623 + 0.468732i −0.0119020 + 0.0206148i
\(518\) 5.52298 + 40.4671i 0.242666 + 1.77802i
\(519\) 0 0
\(520\) 8.37761 + 3.76006i 0.367383 + 0.164889i
\(521\) 20.1176 34.8446i 0.881366 1.52657i 0.0315430 0.999502i \(-0.489958\pi\)
0.849823 0.527068i \(-0.176709\pi\)
\(522\) 0 0
\(523\) −0.732146 −0.0320145 −0.0160073 0.999872i \(-0.505095\pi\)
−0.0160073 + 0.999872i \(0.505095\pi\)
\(524\) 4.20594 + 7.28491i 0.183737 + 0.318243i
\(525\) 0 0
\(526\) −45.0581 + 26.0143i −1.96463 + 1.13428i
\(527\) −14.1018 8.14169i −0.614285 0.354658i
\(528\) 0 0
\(529\) 38.1321 1.65792
\(530\) 5.29221 0.229879
\(531\) 0 0
\(532\) −0.156887 + 0.383898i −0.00680189 + 0.0166441i
\(533\) −35.9353 + 3.66817i −1.55653 + 0.158886i
\(534\) 0 0
\(535\) 7.23667 4.17809i 0.312868 0.180635i
\(536\) −3.06996 5.31733i −0.132602 0.229674i
\(537\) 0 0
\(538\) 36.8553i 1.58894i
\(539\) 7.37054 7.51171i 0.317472 0.323552i
\(540\) 0 0
\(541\) −20.4847 + 11.8268i −0.880705 + 0.508476i −0.870891 0.491476i \(-0.836457\pi\)
−0.00981448 + 0.999952i \(0.503124\pi\)
\(542\) −20.1751 −0.866595
\(543\) 0 0
\(544\) 10.9584i 0.469837i
\(545\) 9.83325 0.421210
\(546\) 0 0
\(547\) −12.9472 −0.553582 −0.276791 0.960930i \(-0.589271\pi\)
−0.276791 + 0.960930i \(0.589271\pi\)
\(548\) 6.16298i 0.263270i
\(549\) 0 0
\(550\) −14.8278 −0.632258
\(551\) 0.0558475 0.0322436i 0.00237918 0.00137362i
\(552\) 0 0
\(553\) −24.3832 + 18.8943i −1.03688 + 0.803467i
\(554\) 45.8771i 1.94913i
\(555\) 0 0
\(556\) 25.7946 + 44.6775i 1.09393 + 1.89475i
\(557\) −5.54845 + 3.20340i −0.235096 + 0.135732i −0.612921 0.790145i \(-0.710005\pi\)
0.377825 + 0.925877i \(0.376672\pi\)
\(558\) 0 0
\(559\) −30.4787 13.6795i −1.28911 0.578582i
\(560\) 0.430045 + 0.554975i 0.0181727 + 0.0234520i
\(561\) 0 0
\(562\) 32.2996 1.36248
\(563\) 7.32084 0.308537 0.154268 0.988029i \(-0.450698\pi\)
0.154268 + 0.988029i \(0.450698\pi\)
\(564\) 0 0
\(565\) 2.55176 + 1.47326i 0.107354 + 0.0619806i
\(566\) 2.01980 1.16613i 0.0848986 0.0490162i
\(567\) 0 0
\(568\) −21.3625 37.0009i −0.896349 1.55252i
\(569\) −4.31743 −0.180996 −0.0904981 0.995897i \(-0.528846\pi\)
−0.0904981 + 0.995897i \(0.528846\pi\)
\(570\) 0 0
\(571\) 17.0847 29.5916i 0.714974 1.23837i −0.247996 0.968761i \(-0.579772\pi\)
0.962970 0.269610i \(-0.0868946\pi\)
\(572\) −7.33577 + 16.3445i −0.306724 + 0.683398i
\(573\) 0 0
\(574\) −56.5140 23.0954i −2.35885 0.963985i
\(575\) 16.7402 28.9949i 0.698115 1.20917i
\(576\) 0 0
\(577\) −5.50494 3.17828i −0.229174 0.132314i 0.381017 0.924568i \(-0.375574\pi\)
−0.610191 + 0.792254i \(0.708907\pi\)
\(578\) 29.2729i 1.21759i
\(579\) 0 0
\(580\) 3.80763i 0.158103i
\(581\) −30.2417 + 4.12740i −1.25464 + 0.171234i
\(582\) 0 0
\(583\) 4.07695i 0.168850i
\(584\) −10.1620 + 17.6011i −0.420507 + 0.728339i
\(585\) 0 0
\(586\) −0.229446 0.397412i −0.00947832 0.0164169i
\(587\) −27.2036 15.7060i −1.12281 0.648256i −0.180695 0.983539i \(-0.557835\pi\)
−0.942118 + 0.335283i \(0.891168\pi\)
\(588\) 0 0
\(589\) −0.186414 0.322878i −0.00768104 0.0133040i
\(590\) −2.77376 + 1.60143i −0.114194 + 0.0659298i
\(591\) 0 0
\(592\) 2.09909i 0.0862719i
\(593\) −0.409641 + 0.236506i −0.0168219 + 0.00971215i −0.508387 0.861128i \(-0.669758\pi\)
0.491565 + 0.870841i \(0.336425\pi\)
\(594\) 0 0
\(595\) 2.84423 + 3.67049i 0.116602 + 0.150476i
\(596\) 18.2143 + 10.5160i 0.746086 + 0.430753i
\(597\) 0 0
\(598\) −38.0079 52.6442i −1.55426 2.15278i
\(599\) −4.81348 + 8.33719i −0.196673 + 0.340648i −0.947448 0.319910i \(-0.896347\pi\)
0.750774 + 0.660559i \(0.229680\pi\)
\(600\) 0 0
\(601\) 20.5399 35.5762i 0.837842 1.45118i −0.0538542 0.998549i \(-0.517151\pi\)
0.891696 0.452635i \(-0.149516\pi\)
\(602\) −34.5850 44.6322i −1.40958 1.81907i
\(603\) 0 0
\(604\) −1.90080 1.09743i −0.0773424 0.0446537i
\(605\) 7.40514i 0.301062i
\(606\) 0 0
\(607\) −9.54289 + 16.5288i −0.387334 + 0.670882i −0.992090 0.125529i \(-0.959937\pi\)
0.604756 + 0.796411i \(0.293271\pi\)
\(608\) −0.125453 + 0.217290i −0.00508777 + 0.00881228i
\(609\) 0 0
\(610\) −8.82474 −0.357303
\(611\) −0.531513 + 1.18424i −0.0215027 + 0.0479092i
\(612\) 0 0
\(613\) −32.9131 + 19.0024i −1.32935 + 0.767500i −0.985199 0.171415i \(-0.945166\pi\)
−0.344149 + 0.938915i \(0.611833\pi\)
\(614\) −62.6498 −2.52834
\(615\) 0 0
\(616\) −9.45082 + 7.32335i −0.380784 + 0.295066i
\(617\) −7.20117 + 4.15759i −0.289908 + 0.167378i −0.637900 0.770119i \(-0.720197\pi\)
0.347992 + 0.937497i \(0.386864\pi\)
\(618\) 0 0
\(619\) −38.5146 22.2364i −1.54803 0.893756i −0.998292 0.0584199i \(-0.981394\pi\)
−0.549739 0.835336i \(-0.685273\pi\)
\(620\) −22.0135 −0.884085
\(621\) 0 0
\(622\) 54.0579 + 31.2103i 2.16752 + 1.25142i
\(623\) −45.9048 + 6.26512i −1.83914 + 0.251007i
\(624\) 0 0
\(625\) −7.37342 12.7711i −0.294937 0.510845i
\(626\) 44.0397 25.4263i 1.76018 1.01624i
\(627\) 0 0
\(628\) −27.3921 + 47.4445i −1.09306 + 1.89324i
\(629\) 13.8829i 0.553549i
\(630\) 0 0
\(631\) −10.1779 + 5.87622i −0.405177 + 0.233929i −0.688715 0.725032i \(-0.741825\pi\)
0.283539 + 0.958961i \(0.408492\pi\)
\(632\) 30.3501 17.5227i 1.20726 0.697014i
\(633\) 0 0
\(634\) −8.14001 14.0989i −0.323281 0.559939i
\(635\) 13.3023i 0.527887i
\(636\) 0 0
\(637\) 15.7557 19.7170i 0.624263 0.781215i
\(638\) 4.70831 0.186404
\(639\) 0 0
\(640\) 8.01854 + 13.8885i 0.316961 + 0.548992i
\(641\) 10.4868 0.414205 0.207102 0.978319i \(-0.433597\pi\)
0.207102 + 0.978319i \(0.433597\pi\)
\(642\) 0 0
\(643\) 27.0912 15.6411i 1.06837 0.616825i 0.140635 0.990061i \(-0.455085\pi\)
0.927736 + 0.373237i \(0.121752\pi\)
\(644\) −9.24536 67.7411i −0.364318 2.66937i
\(645\) 0 0
\(646\) 0.113137 0.195959i 0.00445133 0.00770992i
\(647\) 13.4337 + 23.2679i 0.528135 + 0.914757i 0.999462 + 0.0327983i \(0.0104419\pi\)
−0.471327 + 0.881959i \(0.656225\pi\)
\(648\) 0 0
\(649\) −1.23369 2.13681i −0.0484265 0.0838772i
\(650\) −35.3770 + 3.61119i −1.38760 + 0.141643i
\(651\) 0 0
\(652\) −25.9070 14.9574i −1.01459 0.585776i
\(653\) 4.14161 0.162074 0.0810369 0.996711i \(-0.474177\pi\)
0.0810369 + 0.996711i \(0.474177\pi\)
\(654\) 0 0
\(655\) 1.86759 + 1.07825i 0.0729726 + 0.0421308i
\(656\) 2.71734 + 1.56886i 0.106094 + 0.0612536i
\(657\) 0 0
\(658\) −1.73417 + 1.34379i −0.0676048 + 0.0523863i
\(659\) 10.7276 + 18.5807i 0.417887 + 0.723801i 0.995727 0.0923492i \(-0.0294376\pi\)
−0.577840 + 0.816150i \(0.696104\pi\)
\(660\) 0 0
\(661\) −36.7084 + 21.1936i −1.42779 + 0.824335i −0.996946 0.0780909i \(-0.975118\pi\)
−0.430844 + 0.902426i \(0.641784\pi\)
\(662\) 7.58763 13.1422i 0.294902 0.510785i
\(663\) 0 0
\(664\) 34.6762 1.34570
\(665\) 0.0143772 + 0.105342i 0.000557522 + 0.00408499i
\(666\) 0 0
\(667\) −5.31558 + 9.20685i −0.205820 + 0.356491i
\(668\) −7.60673 4.39175i −0.294313 0.169922i
\(669\) 0 0
\(670\) −3.45226 1.99317i −0.133373 0.0770027i
\(671\) 6.79830i 0.262445i
\(672\) 0 0
\(673\) −14.7928 + 25.6219i −0.570220 + 0.987650i 0.426323 + 0.904571i \(0.359809\pi\)
−0.996543 + 0.0830790i \(0.973525\pi\)
\(674\) 9.72645i 0.374649i
\(675\) 0 0
\(676\) −13.5216 + 40.7823i −0.520061 + 1.56855i
\(677\) 16.0830 + 27.8565i 0.618118 + 1.07061i 0.989829 + 0.142263i \(0.0454380\pi\)
−0.371711 + 0.928349i \(0.621229\pi\)
\(678\) 0 0
\(679\) −0.690734 0.891396i −0.0265079 0.0342086i
\(680\) −2.63775 4.56872i −0.101153 0.175202i
\(681\) 0 0
\(682\) 27.2207i 1.04234i
\(683\) 8.60236i 0.329160i −0.986364 0.164580i \(-0.947373\pi\)
0.986364 0.164580i \(-0.0526269\pi\)
\(684\) 0 0
\(685\) 0.789983 + 1.36829i 0.0301837 + 0.0522797i
\(686\) 39.1738 16.8833i 1.49566 0.644606i
\(687\) 0 0
\(688\) 1.45097 + 2.51316i 0.0553179 + 0.0958134i
\(689\) 0.992909 + 9.72704i 0.0378268 + 0.370571i
\(690\) 0 0
\(691\) 20.4420i 0.777651i 0.921311 + 0.388826i \(0.127119\pi\)
−0.921311 + 0.388826i \(0.872881\pi\)
\(692\) 32.3680 56.0629i 1.23044 2.13119i
\(693\) 0 0
\(694\) 20.9477i 0.795164i
\(695\) 11.4537 + 6.61279i 0.434463 + 0.250837i
\(696\) 0 0
\(697\) 17.9719 + 10.3761i 0.680736 + 0.393023i
\(698\) 10.6187 18.3921i 0.401922 0.696150i
\(699\) 0 0
\(700\) −34.6613 14.1649i −1.31007 0.535385i
\(701\) 25.1373 0.949422 0.474711 0.880142i \(-0.342553\pi\)
0.474711 + 0.880142i \(0.342553\pi\)
\(702\) 0 0
\(703\) 0.158933 0.275280i 0.00599427 0.0103824i
\(704\) −16.6803 + 9.63036i −0.628661 + 0.362958i
\(705\) 0 0
\(706\) 2.48118 + 4.29753i 0.0933804 + 0.161740i
\(707\) −20.2233 + 15.6709i −0.760576 + 0.589363i
\(708\) 0 0
\(709\) −25.5416 14.7464i −0.959234 0.553814i −0.0632970 0.997995i \(-0.520162\pi\)
−0.895937 + 0.444181i \(0.853495\pi\)
\(710\) −24.0227 13.8695i −0.901556 0.520514i
\(711\) 0 0
\(712\) 52.6360 1.97262
\(713\) 53.2287 + 30.7316i 1.99343 + 1.15091i
\(714\) 0 0
\(715\) 0.466399 + 4.56908i 0.0174423 + 0.170874i
\(716\) −4.78127 8.28140i −0.178684 0.309491i
\(717\) 0 0
\(718\) −9.85518 17.0697i −0.367792 0.637034i
\(719\) 4.16576 7.21531i 0.155357 0.269086i −0.777832 0.628472i \(-0.783681\pi\)
0.933189 + 0.359386i \(0.117014\pi\)
\(720\) 0 0
\(721\) −20.8680 + 16.1704i −0.777165 + 0.602218i
\(722\) −37.8946 + 21.8784i −1.41029 + 0.814231i
\(723\) 0 0
\(724\) 4.52143 0.168038
\(725\) 2.91120 + 5.04235i 0.108119 + 0.187268i
\(726\) 0 0
\(727\) 9.66141 0.358322 0.179161 0.983820i \(-0.442662\pi\)
0.179161 + 0.983820i \(0.442662\pi\)
\(728\) −20.7648 + 19.7742i −0.769595 + 0.732880i
\(729\) 0 0
\(730\) 13.1953i 0.488381i
\(731\) 9.59645 + 16.6215i 0.354938 + 0.614770i
\(732\) 0 0
\(733\) −12.1398 + 7.00894i −0.448395 + 0.258881i −0.707152 0.707061i \(-0.750020\pi\)
0.258757 + 0.965942i \(0.416687\pi\)
\(734\) −4.58425 + 2.64672i −0.169208 + 0.0976921i
\(735\) 0 0
\(736\) 41.3635i 1.52468i
\(737\) 1.53547 2.65951i 0.0565598 0.0979644i
\(738\) 0 0
\(739\) 33.6145 19.4073i 1.23653 0.713910i 0.268146 0.963378i \(-0.413589\pi\)
0.968383 + 0.249468i \(0.0802559\pi\)
\(740\) −9.38417 16.2539i −0.344969 0.597504i
\(741\) 0 0
\(742\) −6.25153 + 15.2973i −0.229501 + 0.561583i
\(743\) −29.7863 17.1971i −1.09275 0.630901i −0.158445 0.987368i \(-0.550648\pi\)
−0.934308 + 0.356467i \(0.883981\pi\)
\(744\) 0 0
\(745\) 5.39185 0.197542
\(746\) 23.4742 + 13.5528i 0.859452 + 0.496205i
\(747\) 0 0
\(748\) 8.91346 5.14619i 0.325908 0.188163i
\(749\) 3.52848 + 25.8533i 0.128928 + 0.944660i
\(750\) 0 0
\(751\) −48.1470 −1.75691 −0.878454 0.477827i \(-0.841425\pi\)
−0.878454 + 0.477827i \(0.841425\pi\)
\(752\) 0.0976479 0.0563770i 0.00356085 0.00205586i
\(753\) 0 0
\(754\) 11.2334 1.14667i 0.409096 0.0417594i
\(755\) −0.562681 −0.0204781
\(756\) 0 0
\(757\) 3.45319 5.98110i 0.125508 0.217387i −0.796423 0.604740i \(-0.793277\pi\)
0.921931 + 0.387353i \(0.126611\pi\)
\(758\) −9.20262 + 15.9394i −0.334254 + 0.578945i
\(759\) 0 0
\(760\) 0.120789i 0.00438147i
\(761\) 27.6895 + 15.9865i 1.00374 + 0.579511i 0.909353 0.416025i \(-0.136577\pi\)
0.0943888 + 0.995535i \(0.469910\pi\)
\(762\) 0 0
\(763\) −11.6157 + 28.4234i −0.420517 + 1.02900i
\(764\) 2.50067 4.33129i 0.0904712 0.156701i
\(765\) 0 0
\(766\) 32.5274 56.3391i 1.17526 2.03562i
\(767\) −3.46382 4.79769i −0.125071 0.173234i
\(768\) 0 0
\(769\) 12.4665 + 7.19752i 0.449553 + 0.259549i 0.707641 0.706572i \(-0.249759\pi\)
−0.258089 + 0.966121i \(0.583093\pi\)
\(770\) −2.93653 + 7.18562i −0.105825 + 0.258952i
\(771\) 0 0
\(772\) 19.9039 11.4915i 0.716357 0.413589i
\(773\) 37.2771i 1.34076i −0.742016 0.670382i \(-0.766130\pi\)
0.742016 0.670382i \(-0.233870\pi\)
\(774\) 0 0
\(775\) 29.1520 16.8309i 1.04717 0.604583i
\(776\) 0.640590 + 1.10953i 0.0229958 + 0.0398300i
\(777\) 0 0
\(778\) 15.3209 + 8.84553i 0.549281 + 0.317128i
\(779\) 0.237573 + 0.411489i 0.00851194 + 0.0147431i
\(780\) 0 0
\(781\) 10.6846 18.5063i 0.382326 0.662208i
\(782\) 37.3029i 1.33395i
\(783\) 0 0
\(784\) −2.11218 + 0.587486i −0.0754349 + 0.0209816i
\(785\) 14.0447i 0.501276i
\(786\) 0 0
\(787\)