Properties

Label 819.2.bm.f.478.6
Level $819$
Weight $2$
Character 819.478
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 478.6
Root \(1.21245 + 0.727987i\) of defining polynomial
Character \(\chi\) \(=\) 819.478
Dual form 819.2.bm.f.550.1

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30327i 1.62866i 0.580405 + 0.814328i \(0.302894\pi\)
−0.580405 + 0.814328i \(0.697106\pi\)
\(3\) 0 0
\(4\) −3.30504 −1.65252
\(5\) −0.733776 0.423646i −0.328155 0.189460i 0.326867 0.945070i \(-0.394007\pi\)
−0.655022 + 0.755610i \(0.727340\pi\)
\(6\) 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 0.290707 0.956812i \(-0.406110\pi\)
−0.683270 + 0.730166i \(0.739443\pi\)
\(12\) 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 −0.495281 0.868733i \(-0.664935\pi\)
0.504704 + 0.863292i \(0.331602\pi\)
\(20\) 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 0.922219 0.386668i \(-0.126374\pi\)
−0.795973 + 0.605331i \(0.793041\pi\)
\(30\) 0 0
\(31\) −6.80787 + 3.93052i −1.22273 + 0.705943i −0.965499 0.260407i \(-0.916143\pi\)
−0.257230 + 0.966350i \(0.582810\pi\)
\(32\) 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 \(0.185722\pi\)
−0.834560 + 0.550917i \(0.814278\pi\)
\(38\) 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 0.366054 0.930594i \(-0.380709\pi\)
0.988945 + 0.148285i \(0.0473754\pi\)
\(42\) 0 0
\(43\) 4.63283 8.02430i 0.706500 1.22369i −0.259647 0.965704i \(-0.583606\pi\)
0.966147 0.257991i \(-0.0830604\pi\)
\(44\) 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 0.522567 0.852598i \(-0.324975\pi\)
−0.477089 + 0.878855i \(0.658308\pi\)
\(48\) 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 0.943996 0.329956i \(-0.107034\pi\)
−0.757748 + 0.652547i \(0.773701\pi\)
\(54\) 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 \(-0.965929\pi\)
0.994277 0.106833i \(-0.0340709\pi\)
\(60\) 0 0
\(61\) −2.26097 3.91612i −0.289488 0.501407i 0.684200 0.729295i \(-0.260152\pi\)
−0.973688 + 0.227887i \(0.926818\pi\)
\(62\) −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 0.388034 0.921645i \(-0.373154\pi\)
−0.604151 + 0.796870i \(0.706488\pi\)
\(68\) −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 −0.461832 0.886967i \(-0.652808\pi\)
−0.999052 + 0.0435255i \(0.986141\pi\)
\(72\) 0 0
\(73\) 5.85563 3.38075i 0.685349 0.395687i −0.116518 0.993189i \(-0.537173\pi\)
0.801867 + 0.597502i \(0.203840\pi\)
\(74\) −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 0.325801 + 0.945438i \(0.394366\pi\)
−0.981674 + 0.190567i \(0.938967\pi\)
\(80\) −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 \(0.218232\pi\)
−0.774043 + 0.633133i \(0.781768\pi\)
\(84\) 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 \(0.378552\pi\)
−0.372350 + 0.928093i \(0.621448\pi\)
\(90\) 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 0.518622 0.855003i \(-0.326445\pi\)
−0.481143 + 0.876642i \(0.659778\pi\)
\(98\) 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 −0.999765 0.0216891i \(-0.993096\pi\)
0.518666 + 0.854977i \(0.326429\pi\)
\(102\) 0 0
\(103\) −4.98912 + 8.64140i −0.491592 + 0.851463i −0.999953 0.00968129i \(-0.996918\pi\)
0.508361 + 0.861144i \(0.330252\pi\)
\(104\) −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 −0.896996 0.442038i \(-0.854256\pi\)
−0.0656822 + 0.997841i \(0.520922\pi\)
\(110\) −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 −0.936147 0.351609i \(-0.885635\pi\)
0.772576 + 0.634923i \(0.218968\pi\)
\(114\) 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 −0.969649 0.244499i \(-0.921376\pi\)
0.273082 0.961991i \(-0.411957\pi\)
\(128\) 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 −0.916249 0.400610i \(-0.868798\pi\)
0.805063 + 0.593190i \(0.202132\pi\)
\(132\) 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 \(0.0253825\pi\)
−0.996822 + 0.0796571i \(0.974617\pi\)
\(138\) 0 0
\(139\) −7.80462 + 13.5180i −0.661979 + 1.14658i 0.318116 + 0.948052i \(0.396950\pi\)
−0.980095 + 0.198530i \(0.936383\pi\)
\(140\) −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 −0.708457 0.705754i \(-0.750608\pi\)
0.256973 + 0.966419i \(0.417275\pi\)
\(150\) 0 0
\(151\) 0.575122 0.332047i 0.0468028 0.0270216i −0.476416 0.879220i \(-0.658064\pi\)
0.523219 + 0.852198i \(0.324731\pi\)
\(152\) −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 0.980234 + 0.197842i \(0.0633933\pi\)
−0.318781 + 0.947828i \(0.603273\pi\)
\(158\) −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 −0.160548 0.987028i \(-0.551326\pi\)
0.774517 + 0.632553i \(0.217993\pi\)
\(164\) −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 −0.408300 0.912848i \(-0.633878\pi\)
0.586400 + 0.810022i \(0.300545\pi\)
\(168\) 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 −0.950387 0.311070i \(-0.899313\pi\)
0.205799 0.978594i \(-0.434021\pi\)
\(174\) 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 −0.806884 0.590711i \(-0.798848\pi\)
0.915012 + 0.403426i \(0.132181\pi\)
\(180\) 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 0.837353 0.546663i \(-0.184102\pi\)
−0.892100 + 0.451837i \(0.850769\pi\)
\(192\) 0 0
\(193\) −6.02229 3.47697i −0.433494 0.250278i 0.267340 0.963602i \(-0.413855\pi\)
−0.700834 + 0.713324i \(0.747189\pi\)
\(194\) −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 0.0603494 0.998177i \(-0.480779\pi\)
0.894622 + 0.446825i \(0.147445\pi\)
\(198\) 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 0.971041 0.238912i \(-0.0767907\pi\)
−0.692424 + 0.721490i \(0.743457\pi\)
\(212\) −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 0.0440506 0.999029i \(-0.485974\pi\)
0.887210 + 0.461366i \(0.152640\pi\)
\(224\) 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 \(0.0136925\pi\)
−0.999075 + 0.0430029i \(0.986308\pi\)
\(228\) 0 0
\(229\) 18.0285 + 10.4088i 1.19136 + 0.687831i 0.958614 0.284707i \(-0.0918965\pi\)
0.232743 + 0.972538i \(0.425230\pi\)
\(230\) −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 −0.561565 0.827433i \(-0.689800\pi\)
0.997360 + 0.0726127i \(0.0231337\pi\)
\(234\) 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 \(0.142285\pi\)
−0.901748 + 0.432263i \(0.857715\pi\)
\(240\) 0 0
\(241\) 0.834153i 0.0537325i −0.999639 0.0268663i \(-0.991447\pi\)
0.999639 0.0268663i \(-0.00855282\pi\)
\(242\) 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 0.0105555 + 0.999944i \(0.496640\pi\)
−0.871255 + 0.490831i \(0.836693\pi\)
\(252\) 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 0.273239 + 0.961946i \(0.411905\pi\)
−0.969689 + 0.244341i \(0.921428\pi\)
\(264\) 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 \(0.0857174\pi\)
−0.963960 + 0.266046i \(0.914283\pi\)
\(272\) 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 \(-0.862632\pi\)
0.908317 0.418283i \(-0.137368\pi\)
\(282\) 0 0
\(283\) 0.506295 0.876929i 0.0300961 0.0521280i −0.850585 0.525838i \(-0.823752\pi\)
0.880681 + 0.473710i \(0.157085\pi\)
\(284\) 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 0.505032 0.863101i \(-0.331481\pi\)
−0.494952 + 0.868921i \(0.664814\pi\)
\(294\) 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 \(0.282857\pi\)
−0.630482 + 0.776204i \(0.717143\pi\)
\(308\) −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 −0.938443 0.345434i \(-0.887732\pi\)
0.170067 0.985432i \(-0.445602\pi\)
\(312\) 0 0
\(313\) 11.0392 19.1205i 0.623975 1.08076i −0.364763 0.931100i \(-0.618850\pi\)
0.988738 0.149656i \(-0.0478165\pi\)
\(314\) −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 0.661953 0.749545i \(-0.269728\pi\)
−0.318149 + 0.948041i \(0.603061\pi\)
\(318\) 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 −0.334923 0.942245i \(-0.608710\pi\)
0.648547 + 0.761175i \(0.275377\pi\)
\(332\) 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 −0.270816 0.962631i \(-0.587294\pi\)
0.698255 + 0.715849i \(0.253960\pi\)
\(350\) 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 0.449523 0.893269i \(-0.351594\pi\)
−0.548832 + 0.835933i \(0.684927\pi\)
\(354\) 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 0.682654 0.730741i \(-0.260825\pi\)
−0.291513 + 0.956567i \(0.594159\pi\)
\(360\) 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 −0.894458 0.447153i \(-0.852438\pi\)
0.834474 + 0.551047i \(0.185771\pi\)
\(368\) −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 0.672517 0.740082i \(-0.265213\pi\)
−0.977188 + 0.212375i \(0.931880\pi\)
\(374\) 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 −0.667094 0.744974i \(-0.732462\pi\)
0.311619 + 0.950207i \(0.399129\pi\)
\(380\) 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 0.278791 0.960352i \(-0.410066\pi\)
0.971084 + 0.238736i \(0.0767331\pi\)
\(384\) 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 0.752090 0.659060i \(-0.229046\pi\)
−0.946808 + 0.321799i \(0.895712\pi\)
\(390\) 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 −0.329211 0.944256i \(-0.606783\pi\)
0.653144 + 0.757233i \(0.273449\pi\)
\(398\) 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 \(-0.849858\pi\)
0.890804 0.454389i \(-0.150142\pi\)
\(402\) 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 \(-0.742318\pi\)
0.689838 0.723964i \(-0.257682\pi\)
\(410\) 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 −0.999971 0.00762733i \(-0.997572\pi\)
0.493380 0.869814i \(-0.335761\pi\)
\(420\) 0 0
\(421\) 24.8696i 1.21207i 0.795437 + 0.606036i \(0.207241\pi\)
−0.795437 + 0.606036i \(0.792759\pi\)
\(422\) −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 0.871665 0.490103i \(-0.163041\pi\)
0.0113906 + 0.999935i \(0.496374\pi\)
\(432\) 0 0
\(433\) −11.7148 + 20.2906i −0.562977 + 0.975105i 0.434258 + 0.900789i \(0.357011\pi\)
−0.997235 + 0.0743163i \(0.976323\pi\)
\(434\) 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 −0.616388 0.787443i \(-0.711405\pi\)
0.990139 + 0.140086i \(0.0447379\pi\)
\(444\) 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 −0.136504 0.990640i \(-0.543587\pi\)
−0.926171 + 0.377104i \(0.876920\pi\)
\(450\) 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 \(-0.744011\pi\)
0.693679 0.720284i \(-0.255989\pi\)
\(458\) −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 0.991583 0.129472i \(-0.0413284\pi\)
0.383665 + 0.923472i \(0.374662\pi\)
\(462\) 0 0
\(463\) 1.69184i 0.0786263i −0.999227 0.0393131i \(-0.987483\pi\)
0.999227 0.0393131i \(-0.0125170\pi\)
\(464\) 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 0.325647 + 0.945491i \(0.394418\pi\)
−0.981643 + 0.190727i \(0.938916\pi\)
\(468\) 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 0.370526 0.928822i \(-0.379178\pi\)
−0.619121 + 0.785296i \(0.712511\pi\)
\(480\) 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 \(-0.904700\pi\)
0.955515 0.294942i \(-0.0953002\pi\)
\(488\) −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 0.971068 0.238801i \(-0.0767544\pi\)
−0.692342 + 0.721569i \(0.743421\pi\)
\(492\) 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 0.666826 0.745214i \(-0.267652\pi\)
−0.311961 + 0.950095i \(0.600986\pi\)
\(500\) 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 −0.498302 0.867003i \(-0.666043\pi\)
0.999998 0.00195935i \(-0.000623680\pi\)
\(504\) 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 \(-0.672449\pi\)
0.515649 0.856800i \(-0.327551\pi\)
\(510\) 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 0.849823 + 0.527068i \(0.176709\pi\)
0.0315430 + 0.999502i \(0.489958\pi\)
\(522\) 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 −0.00981448 0.999952i \(-0.503124\pi\)
−0.870891 + 0.491476i \(0.836457\pi\)
\(542\) −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 0.377825 0.925877i \(-0.376672\pi\)
−0.612921 + 0.790145i \(0.710005\pi\)
\(558\) 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 0.962970 + 0.269610i \(0.0868946\pi\)
−0.247996 + 0.968761i \(0.579772\pi\)
\(572\) −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 −0.610191 0.792254i \(-0.708907\pi\)
0.381017 + 0.924568i \(0.375574\pi\)
\(578\) 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 −0.942118 0.335283i \(-0.891168\pi\)
−0.180695 + 0.983539i \(0.557835\pi\)
\(588\) 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 0.491565 0.870841i \(-0.336425\pi\)
−0.508387 + 0.861128i \(0.669758\pi\)
\(594\) 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 0.750774 0.660559i \(-0.229680\pi\)
−0.947448 + 0.319910i \(0.896347\pi\)
\(600\) 0 0
\(601\) 20.5399 + 35.5762i 0.837842 + 1.45118i 0.891696 + 0.452635i \(0.149516\pi\)
−0.0538542 + 0.998549i \(0.517151\pi\)
\(602\) −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 0.604756 0.796411i \(-0.293271\pi\)
−0.992090 + 0.125529i \(0.959937\pi\)
\(608\) −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 −0.344149 0.938915i \(-0.611833\pi\)
−0.985199 + 0.171415i \(0.945166\pi\)
\(614\) −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 0.347992 0.937497i \(-0.386864\pi\)
−0.637900 + 0.770119i \(0.720197\pi\)
\(618\) 0 0
\(619\) −38.5146 + 22.2364i −1.54803 + 0.893756i −0.549739 + 0.835336i \(0.685273\pi\)
−0.998292 + 0.0584199i \(0.981394\pi\)
\(620\) −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 0.283539 0.958961i \(-0.408492\pi\)
−0.688715 + 0.725032i \(0.741825\pi\)
\(632\) 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 0.927736 0.373237i \(-0.121752\pi\)
0.140635 + 0.990061i \(0.455085\pi\)
\(644\) −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 −0.471327 0.881959i \(-0.656225\pi\)
0.999462 0.0327983i \(-0.0104419\pi\)
\(648\) 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 −0.577840 0.816150i \(-0.696104\pi\)
0.995727 + 0.0923492i \(0.0294376\pi\)
\(660\) 0 0
\(661\) −36.7084 21.1936i −1.42779 0.824335i −0.430844 0.902426i \(-0.641784\pi\)
−0.996946 + 0.0780909i \(0.975118\pi\)
\(662\) 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 −0.996543 0.0830790i \(-0.973525\pi\)
0.426323 0.904571i \(-0.359809\pi\)
\(674\) 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 −0.371711 0.928349i \(-0.621229\pi\)
0.989829 0.142263i \(-0.0454380\pi\)
\(678\) 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 \(0.0526269\pi\)
−0.986364 + 0.164580i \(0.947373\pi\)
\(684\) 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 \(-0.872881\pi\)
0.921311 0.388826i \(-0.127119\pi\)
\(692\) 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 −0.895937 0.444181i \(-0.853495\pi\)
−0.0632970 + 0.997995i \(0.520162\pi\)
\(710\) −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 0.933189 0.359386i \(-0.117014\pi\)
−0.777832 + 0.628472i \(0.783681\pi\)
\(720\) 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 0.258757 0.965942i \(-0.416687\pi\)
−0.707152 + 0.707061i \(0.750020\pi\)
\(734\) −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 0.968383 0.249468i \(-0.0802559\pi\)
0.268146 + 0.963378i \(0.413589\pi\)
\(740\) −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 −0.934308 0.356467i \(-0.883981\pi\)
−0.158445 + 0.987368i \(0.550648\pi\)
\(744\) 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 0.921931 0.387353i \(-0.126611\pi\)
−0.796423 + 0.604740i \(0.793277\pi\)
\(758\) −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 0.0943888 0.995535i \(-0.469910\pi\)
0.909353 + 0.416025i \(0.136577\pi\)
\(762\) 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 −0.258089 0.966121i \(-0.583093\pi\)
0.707641 + 0.706572i \(0.249759\pi\)
\(770\) −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 \(0.233870\pi\)
−0.742016 + 0.670382i \(0.766130\pi\)
\(774\) 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