Properties

Label 819.2.fm.e.370.6
Level $819$
Weight $2$
Character 819.370
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
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.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 370.6
Character \(\chi\) \(=\) 819.370
Dual form 819.2.fm.e.622.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.281068 + 1.04896i) q^{2} +(0.710736 - 0.410344i) q^{4} +(1.02734 + 1.02734i) q^{5} +(2.23270 - 1.41953i) q^{7} +(2.16598 + 2.16598i) q^{8} +O(q^{10})\) \(q+(0.281068 + 1.04896i) q^{2} +(0.710736 - 0.410344i) q^{4} +(1.02734 + 1.02734i) q^{5} +(2.23270 - 1.41953i) q^{7} +(2.16598 + 2.16598i) q^{8} +(-0.788887 + 1.36639i) q^{10} +(-0.972198 + 0.260500i) q^{11} +(-3.05530 + 1.91446i) q^{13} +(2.11656 + 1.94303i) q^{14} +(-0.842549 + 1.45934i) q^{16} +(2.37035 + 4.10557i) q^{17} +(0.391878 - 1.46251i) q^{19} +(1.15173 + 0.308606i) q^{20} +(-0.546507 - 0.946578i) q^{22} +(0.337046 + 0.194594i) q^{23} -2.88914i q^{25} +(-2.86693 - 2.66679i) q^{26} +(1.00437 - 1.92508i) q^{28} +(4.30065 - 7.44895i) q^{29} +(2.92542 + 2.92542i) q^{31} +(4.14997 + 1.11198i) q^{32} +(-3.64034 + 3.64034i) q^{34} +(3.75209 + 0.835406i) q^{35} +(9.77690 - 2.61971i) q^{37} +1.64425 q^{38} +4.45041i q^{40} +(-8.64616 + 2.31673i) q^{41} +(-8.28885 + 4.78557i) q^{43} +(-0.584082 + 0.584082i) q^{44} +(-0.109388 + 0.408241i) q^{46} +(-4.78928 + 4.78928i) q^{47} +(2.96989 - 6.33875i) q^{49} +(3.03058 - 0.812042i) q^{50} +(-1.38592 + 2.61440i) q^{52} -12.7329 q^{53} +(-1.26640 - 0.731158i) q^{55} +(7.91065 + 1.76131i) q^{56} +(9.02241 + 2.41755i) q^{58} +(-0.889636 - 0.238377i) q^{59} +(8.36449 - 4.82924i) q^{61} +(-2.24640 + 3.89088i) q^{62} +8.03588i q^{64} +(-5.10564 - 1.17203i) q^{65} +(1.71328 + 6.39405i) q^{67} +(3.36939 + 1.94532i) q^{68} +(0.178284 + 4.17059i) q^{70} +(2.56663 + 0.687727i) q^{71} +(-2.46596 + 2.46596i) q^{73} +(5.49594 + 9.51925i) q^{74} +(-0.321609 - 1.20026i) q^{76} +(-1.80084 + 1.96168i) q^{77} +7.06532 q^{79} +(-2.36483 + 0.633653i) q^{80} +(-4.86031 - 8.41830i) q^{82} +(-2.43414 - 2.43414i) q^{83} +(-1.78266 + 6.65299i) q^{85} +(-7.34959 - 7.34959i) q^{86} +(-2.67000 - 1.54152i) q^{88} +(-2.79345 - 10.4253i) q^{89} +(-4.10393 + 8.61149i) q^{91} +0.319401 q^{92} +(-6.36986 - 3.67764i) q^{94} +(1.90509 - 1.09990i) q^{95} +(3.55710 - 13.2753i) q^{97} +(7.48383 + 1.33367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.281068 + 1.04896i 0.198745 + 0.741726i 0.991266 + 0.131881i \(0.0421016\pi\)
−0.792521 + 0.609845i \(0.791232\pi\)
\(3\) 0 0
\(4\) 0.710736 0.410344i 0.355368 0.205172i
\(5\) 1.02734 + 1.02734i 0.459441 + 0.459441i 0.898472 0.439031i \(-0.144678\pi\)
−0.439031 + 0.898472i \(0.644678\pi\)
\(6\) 0 0
\(7\) 2.23270 1.41953i 0.843881 0.536531i
\(8\) 2.16598 + 2.16598i 0.765790 + 0.765790i
\(9\) 0 0
\(10\) −0.788887 + 1.36639i −0.249468 + 0.432091i
\(11\) −0.972198 + 0.260500i −0.293129 + 0.0785436i −0.402387 0.915470i \(-0.631819\pi\)
0.109258 + 0.994013i \(0.465153\pi\)
\(12\) 0 0
\(13\) −3.05530 + 1.91446i −0.847387 + 0.530975i
\(14\) 2.11656 + 1.94303i 0.565676 + 0.519295i
\(15\) 0 0
\(16\) −0.842549 + 1.45934i −0.210637 + 0.364834i
\(17\) 2.37035 + 4.10557i 0.574895 + 0.995747i 0.996053 + 0.0887595i \(0.0282903\pi\)
−0.421159 + 0.906987i \(0.638376\pi\)
\(18\) 0 0
\(19\) 0.391878 1.46251i 0.0899030 0.335522i −0.906294 0.422647i \(-0.861101\pi\)
0.996197 + 0.0871243i \(0.0277677\pi\)
\(20\) 1.15173 + 0.308606i 0.257535 + 0.0690064i
\(21\) 0 0
\(22\) −0.546507 0.946578i −0.116516 0.201811i
\(23\) 0.337046 + 0.194594i 0.0702790 + 0.0405756i 0.534728 0.845024i \(-0.320414\pi\)
−0.464449 + 0.885600i \(0.653748\pi\)
\(24\) 0 0
\(25\) 2.88914i 0.577827i
\(26\) −2.86693 2.66679i −0.562252 0.523000i
\(27\) 0 0
\(28\) 1.00437 1.92508i 0.189807 0.363806i
\(29\) 4.30065 7.44895i 0.798611 1.38324i −0.121909 0.992541i \(-0.538902\pi\)
0.920521 0.390694i \(-0.127765\pi\)
\(30\) 0 0
\(31\) 2.92542 + 2.92542i 0.525420 + 0.525420i 0.919203 0.393783i \(-0.128834\pi\)
−0.393783 + 0.919203i \(0.628834\pi\)
\(32\) 4.14997 + 1.11198i 0.733618 + 0.196572i
\(33\) 0 0
\(34\) −3.64034 + 3.64034i −0.624313 + 0.624313i
\(35\) 3.75209 + 0.835406i 0.634218 + 0.141209i
\(36\) 0 0
\(37\) 9.77690 2.61971i 1.60731 0.430678i 0.660072 0.751202i \(-0.270526\pi\)
0.947240 + 0.320524i \(0.103859\pi\)
\(38\) 1.64425 0.266733
\(39\) 0 0
\(40\) 4.45041i 0.703671i
\(41\) −8.64616 + 2.31673i −1.35030 + 0.361813i −0.860247 0.509878i \(-0.829690\pi\)
−0.490056 + 0.871691i \(0.663024\pi\)
\(42\) 0 0
\(43\) −8.28885 + 4.78557i −1.26404 + 0.729792i −0.973853 0.227179i \(-0.927050\pi\)
−0.290184 + 0.956971i \(0.593717\pi\)
\(44\) −0.584082 + 0.584082i −0.0880537 + 0.0880537i
\(45\) 0 0
\(46\) −0.109388 + 0.408241i −0.0161284 + 0.0601919i
\(47\) −4.78928 + 4.78928i −0.698588 + 0.698588i −0.964106 0.265518i \(-0.914457\pi\)
0.265518 + 0.964106i \(0.414457\pi\)
\(48\) 0 0
\(49\) 2.96989 6.33875i 0.424269 0.905536i
\(50\) 3.03058 0.812042i 0.428589 0.114840i
\(51\) 0 0
\(52\) −1.38592 + 2.61440i −0.192193 + 0.362552i
\(53\) −12.7329 −1.74900 −0.874498 0.485029i \(-0.838809\pi\)
−0.874498 + 0.485029i \(0.838809\pi\)
\(54\) 0 0
\(55\) −1.26640 0.731158i −0.170762 0.0985893i
\(56\) 7.91065 + 1.76131i 1.05710 + 0.235365i
\(57\) 0 0
\(58\) 9.02241 + 2.41755i 1.18470 + 0.317440i
\(59\) −0.889636 0.238377i −0.115821 0.0310341i 0.200443 0.979705i \(-0.435762\pi\)
−0.316264 + 0.948671i \(0.602428\pi\)
\(60\) 0 0
\(61\) 8.36449 4.82924i 1.07096 0.618321i 0.142519 0.989792i \(-0.454480\pi\)
0.928445 + 0.371471i \(0.121146\pi\)
\(62\) −2.24640 + 3.89088i −0.285293 + 0.494142i
\(63\) 0 0
\(64\) 8.03588i 1.00449i
\(65\) −5.10564 1.17203i −0.633277 0.145373i
\(66\) 0 0
\(67\) 1.71328 + 6.39405i 0.209311 + 0.781158i 0.988092 + 0.153863i \(0.0491713\pi\)
−0.778782 + 0.627295i \(0.784162\pi\)
\(68\) 3.36939 + 1.94532i 0.408598 + 0.235904i
\(69\) 0 0
\(70\) 0.178284 + 4.17059i 0.0213090 + 0.498481i
\(71\) 2.56663 + 0.687727i 0.304603 + 0.0816182i 0.407883 0.913034i \(-0.366267\pi\)
−0.103280 + 0.994652i \(0.532934\pi\)
\(72\) 0 0
\(73\) −2.46596 + 2.46596i −0.288619 + 0.288619i −0.836534 0.547915i \(-0.815422\pi\)
0.547915 + 0.836534i \(0.315422\pi\)
\(74\) 5.49594 + 9.51925i 0.638890 + 1.10659i
\(75\) 0 0
\(76\) −0.321609 1.20026i −0.0368911 0.137680i
\(77\) −1.80084 + 1.96168i −0.205225 + 0.223554i
\(78\) 0 0
\(79\) 7.06532 0.794911 0.397455 0.917622i \(-0.369893\pi\)
0.397455 + 0.917622i \(0.369893\pi\)
\(80\) −2.36483 + 0.633653i −0.264396 + 0.0708446i
\(81\) 0 0
\(82\) −4.86031 8.41830i −0.536731 0.929646i
\(83\) −2.43414 2.43414i −0.267181 0.267181i 0.560782 0.827963i \(-0.310501\pi\)
−0.827963 + 0.560782i \(0.810501\pi\)
\(84\) 0 0
\(85\) −1.78266 + 6.65299i −0.193357 + 0.721618i
\(86\) −7.34959 7.34959i −0.792526 0.792526i
\(87\) 0 0
\(88\) −2.67000 1.54152i −0.284623 0.164327i
\(89\) −2.79345 10.4253i −0.296105 1.10508i −0.940336 0.340248i \(-0.889489\pi\)
0.644231 0.764831i \(-0.277178\pi\)
\(90\) 0 0
\(91\) −4.10393 + 8.61149i −0.430209 + 0.902729i
\(92\) 0.319401 0.0332999
\(93\) 0 0
\(94\) −6.36986 3.67764i −0.657001 0.379320i
\(95\) 1.90509 1.09990i 0.195458 0.112848i
\(96\) 0 0
\(97\) 3.55710 13.2753i 0.361169 1.34790i −0.511372 0.859359i \(-0.670863\pi\)
0.872541 0.488541i \(-0.162471\pi\)
\(98\) 7.48383 + 1.33367i 0.755981 + 0.134721i
\(99\) 0 0
\(100\) −1.18554 2.05341i −0.118554 0.205341i
\(101\) −1.97748 + 3.42510i −0.196767 + 0.340810i −0.947478 0.319820i \(-0.896378\pi\)
0.750711 + 0.660630i \(0.229711\pi\)
\(102\) 0 0
\(103\) −12.7709 −1.25835 −0.629176 0.777263i \(-0.716607\pi\)
−0.629176 + 0.777263i \(0.716607\pi\)
\(104\) −10.7644 2.47103i −1.05554 0.242305i
\(105\) 0 0
\(106\) −3.57880 13.3563i −0.347604 1.29728i
\(107\) −1.79997 + 3.11764i −0.174010 + 0.301394i −0.939818 0.341675i \(-0.889006\pi\)
0.765808 + 0.643069i \(0.222339\pi\)
\(108\) 0 0
\(109\) −0.0623175 + 0.0623175i −0.00596893 + 0.00596893i −0.710085 0.704116i \(-0.751343\pi\)
0.704116 + 0.710085i \(0.251343\pi\)
\(110\) 0.411010 1.53391i 0.0391882 0.146252i
\(111\) 0 0
\(112\) 0.190411 + 4.45428i 0.0179922 + 0.420890i
\(113\) 1.09268 + 1.89259i 0.102791 + 0.178039i 0.912834 0.408332i \(-0.133889\pi\)
−0.810042 + 0.586371i \(0.800556\pi\)
\(114\) 0 0
\(115\) 0.146347 + 0.546176i 0.0136470 + 0.0509312i
\(116\) 7.05898i 0.655410i
\(117\) 0 0
\(118\) 1.00019i 0.0920751i
\(119\) 11.1202 + 5.80172i 1.01939 + 0.531843i
\(120\) 0 0
\(121\) −8.64897 + 4.99349i −0.786270 + 0.453953i
\(122\) 7.41666 + 7.41666i 0.671473 + 0.671473i
\(123\) 0 0
\(124\) 3.27962 + 0.878773i 0.294519 + 0.0789161i
\(125\) 8.10484 8.10484i 0.724919 0.724919i
\(126\) 0 0
\(127\) −12.3666 7.13987i −1.09736 0.633561i −0.161834 0.986818i \(-0.551741\pi\)
−0.935526 + 0.353257i \(0.885074\pi\)
\(128\) −0.129367 + 0.0346639i −0.0114346 + 0.00306389i
\(129\) 0 0
\(130\) −0.205617 5.68503i −0.0180338 0.498610i
\(131\) 17.8888i 1.56295i −0.623934 0.781477i \(-0.714467\pi\)
0.623934 0.781477i \(-0.285533\pi\)
\(132\) 0 0
\(133\) −1.20112 3.82162i −0.104151 0.331377i
\(134\) −6.22555 + 3.59432i −0.537805 + 0.310502i
\(135\) 0 0
\(136\) −3.75845 + 14.0267i −0.322284 + 1.20278i
\(137\) 0.654988 2.44445i 0.0559594 0.208843i −0.932285 0.361724i \(-0.882188\pi\)
0.988245 + 0.152881i \(0.0488550\pi\)
\(138\) 0 0
\(139\) −8.86338 + 5.11727i −0.751782 + 0.434041i −0.826337 0.563176i \(-0.809579\pi\)
0.0745556 + 0.997217i \(0.476246\pi\)
\(140\) 3.00955 0.945892i 0.254353 0.0799424i
\(141\) 0 0
\(142\) 2.88559i 0.242153i
\(143\) 2.47164 2.65714i 0.206689 0.222201i
\(144\) 0 0
\(145\) 12.0709 3.23438i 1.00243 0.268601i
\(146\) −3.27979 1.89359i −0.271437 0.156714i
\(147\) 0 0
\(148\) 5.87381 5.87381i 0.482825 0.482825i
\(149\) −8.14575 2.18265i −0.667326 0.178809i −0.0907761 0.995871i \(-0.528935\pi\)
−0.576550 + 0.817062i \(0.695601\pi\)
\(150\) 0 0
\(151\) −0.453678 0.453678i −0.0369198 0.0369198i 0.688406 0.725326i \(-0.258311\pi\)
−0.725326 + 0.688406i \(0.758311\pi\)
\(152\) 4.01656 2.31896i 0.325786 0.188093i
\(153\) 0 0
\(154\) −2.56388 1.33764i −0.206603 0.107790i
\(155\) 6.01081i 0.482800i
\(156\) 0 0
\(157\) 8.10530i 0.646874i 0.946250 + 0.323437i \(0.104838\pi\)
−0.946250 + 0.323437i \(0.895162\pi\)
\(158\) 1.98583 + 7.41123i 0.157984 + 0.589606i
\(159\) 0 0
\(160\) 3.12105 + 5.40583i 0.246741 + 0.427368i
\(161\) 1.02875 0.0439771i 0.0810771 0.00346588i
\(162\) 0 0
\(163\) 3.55525 13.2684i 0.278469 1.03926i −0.675012 0.737807i \(-0.735862\pi\)
0.953481 0.301453i \(-0.0974717\pi\)
\(164\) −5.19448 + 5.19448i −0.405621 + 0.405621i
\(165\) 0 0
\(166\) 1.86915 3.23746i 0.145074 0.251276i
\(167\) −5.75214 21.4673i −0.445114 1.66119i −0.715636 0.698473i \(-0.753863\pi\)
0.270523 0.962714i \(-0.412804\pi\)
\(168\) 0 0
\(169\) 5.66969 11.6985i 0.436130 0.899884i
\(170\) −7.47975 −0.573671
\(171\) 0 0
\(172\) −3.92745 + 6.80255i −0.299466 + 0.518690i
\(173\) 6.33728 + 10.9765i 0.481815 + 0.834527i 0.999782 0.0208728i \(-0.00664451\pi\)
−0.517967 + 0.855400i \(0.673311\pi\)
\(174\) 0 0
\(175\) −4.10121 6.45057i −0.310022 0.487617i
\(176\) 0.438968 1.63825i 0.0330884 0.123488i
\(177\) 0 0
\(178\) 10.1505 5.86042i 0.760816 0.439257i
\(179\) −9.48849 5.47818i −0.709203 0.409459i 0.101563 0.994829i \(-0.467616\pi\)
−0.810766 + 0.585370i \(0.800949\pi\)
\(180\) 0 0
\(181\) −4.38394 −0.325856 −0.162928 0.986638i \(-0.552094\pi\)
−0.162928 + 0.986638i \(0.552094\pi\)
\(182\) −10.1866 1.88445i −0.755079 0.139684i
\(183\) 0 0
\(184\) 0.308549 + 1.15152i 0.0227466 + 0.0848913i
\(185\) 12.7356 + 7.35288i 0.936338 + 0.540595i
\(186\) 0 0
\(187\) −3.37395 3.37395i −0.246728 0.246728i
\(188\) −1.43866 + 5.36916i −0.104925 + 0.391586i
\(189\) 0 0
\(190\) 1.68921 + 1.68921i 0.122548 + 0.122548i
\(191\) 4.92507 + 8.53047i 0.356366 + 0.617243i 0.987351 0.158552i \(-0.0506824\pi\)
−0.630985 + 0.775795i \(0.717349\pi\)
\(192\) 0 0
\(193\) 12.2874 3.29240i 0.884465 0.236992i 0.212133 0.977241i \(-0.431959\pi\)
0.672333 + 0.740249i \(0.265292\pi\)
\(194\) 14.9250 1.07155
\(195\) 0 0
\(196\) −0.490261 5.72385i −0.0350187 0.408847i
\(197\) 0.404048 + 1.50793i 0.0287873 + 0.107436i 0.978825 0.204701i \(-0.0656221\pi\)
−0.950037 + 0.312136i \(0.898955\pi\)
\(198\) 0 0
\(199\) −5.84499 10.1238i −0.414340 0.717659i 0.581019 0.813890i \(-0.302654\pi\)
−0.995359 + 0.0962317i \(0.969321\pi\)
\(200\) 6.25781 6.25781i 0.442494 0.442494i
\(201\) 0 0
\(202\) −4.14860 1.11161i −0.291894 0.0782128i
\(203\) −0.971923 22.7362i −0.0682156 1.59577i
\(204\) 0 0
\(205\) −11.2626 6.50249i −0.786617 0.454153i
\(206\) −3.58948 13.3961i −0.250091 0.933351i
\(207\) 0 0
\(208\) −0.219604 6.07174i −0.0152268 0.420999i
\(209\) 1.52393i 0.105413i
\(210\) 0 0
\(211\) −11.0809 + 19.1926i −0.762838 + 1.32127i 0.178544 + 0.983932i \(0.442861\pi\)
−0.941382 + 0.337343i \(0.890472\pi\)
\(212\) −9.04972 + 5.22486i −0.621537 + 0.358845i
\(213\) 0 0
\(214\) −3.77619 1.01183i −0.258135 0.0691670i
\(215\) −13.4319 3.59907i −0.916048 0.245454i
\(216\) 0 0
\(217\) 10.6843 + 2.37887i 0.725296 + 0.161488i
\(218\) −0.0828838 0.0478530i −0.00561360 0.00324101i
\(219\) 0 0
\(220\) −1.20010 −0.0809110
\(221\) −15.1021 8.00580i −1.01588 0.538528i
\(222\) 0 0
\(223\) 13.2842 3.55949i 0.889575 0.238361i 0.215041 0.976605i \(-0.431011\pi\)
0.674534 + 0.738244i \(0.264345\pi\)
\(224\) 10.8441 3.40828i 0.724553 0.227725i
\(225\) 0 0
\(226\) −1.67813 + 1.67813i −0.111627 + 0.111627i
\(227\) −1.04021 + 3.88213i −0.0690413 + 0.257666i −0.991816 0.127674i \(-0.959249\pi\)
0.922775 + 0.385339i \(0.125916\pi\)
\(228\) 0 0
\(229\) −1.36272 + 1.36272i −0.0900509 + 0.0900509i −0.750697 0.660646i \(-0.770282\pi\)
0.660646 + 0.750697i \(0.270282\pi\)
\(230\) −0.531783 + 0.307025i −0.0350647 + 0.0202446i
\(231\) 0 0
\(232\) 25.4494 6.81915i 1.67084 0.447699i
\(233\) 1.13013i 0.0740376i −0.999315 0.0370188i \(-0.988214\pi\)
0.999315 0.0370188i \(-0.0117861\pi\)
\(234\) 0 0
\(235\) −9.84046 −0.641921
\(236\) −0.730113 + 0.195633i −0.0475263 + 0.0127346i
\(237\) 0 0
\(238\) −2.96022 + 13.2953i −0.191883 + 0.861809i
\(239\) −3.62833 + 3.62833i −0.234697 + 0.234697i −0.814650 0.579953i \(-0.803071\pi\)
0.579953 + 0.814650i \(0.303071\pi\)
\(240\) 0 0
\(241\) 9.46780 + 2.53689i 0.609875 + 0.163415i 0.550521 0.834822i \(-0.314429\pi\)
0.0593540 + 0.998237i \(0.481096\pi\)
\(242\) −7.66890 7.66890i −0.492976 0.492976i
\(243\) 0 0
\(244\) 3.96330 6.86463i 0.253724 0.439463i
\(245\) 9.56316 3.46098i 0.610968 0.221114i
\(246\) 0 0
\(247\) 1.60261 + 5.21863i 0.101972 + 0.332054i
\(248\) 12.6728i 0.804723i
\(249\) 0 0
\(250\) 10.7797 + 6.22363i 0.681765 + 0.393617i
\(251\) −14.1820 24.5639i −0.895158 1.55046i −0.833610 0.552354i \(-0.813730\pi\)
−0.0615480 0.998104i \(-0.519604\pi\)
\(252\) 0 0
\(253\) −0.378367 0.101383i −0.0237878 0.00637391i
\(254\) 4.01357 14.9789i 0.251834 0.939857i
\(255\) 0 0
\(256\) 7.96316 + 13.7926i 0.497698 + 0.862037i
\(257\) −3.32083 + 5.75185i −0.207148 + 0.358790i −0.950815 0.309760i \(-0.899751\pi\)
0.743667 + 0.668550i \(0.233085\pi\)
\(258\) 0 0
\(259\) 18.1101 19.7276i 1.12531 1.22581i
\(260\) −4.10970 + 1.26206i −0.254873 + 0.0782698i
\(261\) 0 0
\(262\) 18.7646 5.02797i 1.15928 0.310629i
\(263\) 6.24723 10.8205i 0.385221 0.667222i −0.606579 0.795023i \(-0.707459\pi\)
0.991800 + 0.127801i \(0.0407920\pi\)
\(264\) 0 0
\(265\) −13.0810 13.0810i −0.803561 0.803561i
\(266\) 3.67113 2.33406i 0.225091 0.143111i
\(267\) 0 0
\(268\) 3.84145 + 3.84145i 0.234654 + 0.234654i
\(269\) 7.27737 4.20159i 0.443709 0.256176i −0.261460 0.965214i \(-0.584204\pi\)
0.705170 + 0.709038i \(0.250871\pi\)
\(270\) 0 0
\(271\) −0.0939748 0.350719i −0.00570857 0.0213047i 0.963013 0.269456i \(-0.0868438\pi\)
−0.968721 + 0.248151i \(0.920177\pi\)
\(272\) −7.98855 −0.484377
\(273\) 0 0
\(274\) 2.74822 0.166026
\(275\) 0.752619 + 2.80881i 0.0453846 + 0.169378i
\(276\) 0 0
\(277\) 13.5251 7.80875i 0.812647 0.469182i −0.0352270 0.999379i \(-0.511215\pi\)
0.847874 + 0.530197i \(0.177882\pi\)
\(278\) −7.85901 7.85901i −0.471352 0.471352i
\(279\) 0 0
\(280\) 6.31747 + 9.93642i 0.377541 + 0.593814i
\(281\) 0.848694 + 0.848694i 0.0506289 + 0.0506289i 0.731968 0.681339i \(-0.238602\pi\)
−0.681339 + 0.731968i \(0.738602\pi\)
\(282\) 0 0
\(283\) −11.9723 + 20.7366i −0.711678 + 1.23266i 0.252549 + 0.967584i \(0.418731\pi\)
−0.964227 + 0.265078i \(0.914602\pi\)
\(284\) 2.10640 0.564409i 0.124992 0.0334915i
\(285\) 0 0
\(286\) 3.48193 + 1.84581i 0.205891 + 0.109145i
\(287\) −16.0156 + 17.4460i −0.945371 + 1.02981i
\(288\) 0 0
\(289\) −2.73713 + 4.74084i −0.161007 + 0.278873i
\(290\) 6.78546 + 11.7528i 0.398456 + 0.690146i
\(291\) 0 0
\(292\) −0.740755 + 2.76454i −0.0433494 + 0.161782i
\(293\) −18.6502 4.99730i −1.08956 0.291946i −0.331051 0.943613i \(-0.607403\pi\)
−0.758505 + 0.651667i \(0.774070\pi\)
\(294\) 0 0
\(295\) −0.669066 1.15886i −0.0389545 0.0674712i
\(296\) 26.8508 + 15.5023i 1.56067 + 0.901055i
\(297\) 0 0
\(298\) 9.15803i 0.530510i
\(299\) −1.40232 + 0.0507193i −0.0810982 + 0.00293317i
\(300\) 0 0
\(301\) −11.7133 + 22.4510i −0.675141 + 1.29405i
\(302\) 0.348375 0.603403i 0.0200467 0.0347220i
\(303\) 0 0
\(304\) 1.80412 + 1.80412i 0.103473 + 0.103473i
\(305\) 13.5545 + 3.63191i 0.776127 + 0.207963i
\(306\) 0 0
\(307\) −17.1942 + 17.1942i −0.981322 + 0.981322i −0.999829 0.0185063i \(-0.994109\pi\)
0.0185063 + 0.999829i \(0.494109\pi\)
\(308\) −0.474959 + 2.13320i −0.0270633 + 0.121550i
\(309\) 0 0
\(310\) −6.30509 + 1.68944i −0.358105 + 0.0959539i
\(311\) 14.0638 0.797487 0.398744 0.917062i \(-0.369446\pi\)
0.398744 + 0.917062i \(0.369446\pi\)
\(312\) 0 0
\(313\) 18.8063i 1.06300i 0.847060 + 0.531498i \(0.178371\pi\)
−0.847060 + 0.531498i \(0.821629\pi\)
\(314\) −8.50213 + 2.27814i −0.479803 + 0.128563i
\(315\) 0 0
\(316\) 5.02158 2.89921i 0.282486 0.163093i
\(317\) 1.67207 1.67207i 0.0939128 0.0939128i −0.658590 0.752502i \(-0.728847\pi\)
0.752502 + 0.658590i \(0.228847\pi\)
\(318\) 0 0
\(319\) −2.24064 + 8.36218i −0.125452 + 0.468192i
\(320\) −8.25560 + 8.25560i −0.461502 + 0.461502i
\(321\) 0 0
\(322\) 0.335279 + 1.06676i 0.0186844 + 0.0594482i
\(323\) 6.93332 1.85778i 0.385780 0.103369i
\(324\) 0 0
\(325\) 5.53113 + 8.82717i 0.306812 + 0.489643i
\(326\) 14.9172 0.826190
\(327\) 0 0
\(328\) −23.7454 13.7094i −1.31112 0.756976i
\(329\) −3.89450 + 17.4915i −0.214711 + 0.964339i
\(330\) 0 0
\(331\) −33.2290 8.90368i −1.82643 0.489391i −0.828886 0.559418i \(-0.811025\pi\)
−0.997545 + 0.0700274i \(0.977691\pi\)
\(332\) −2.72886 0.731196i −0.149766 0.0401296i
\(333\) 0 0
\(334\) 20.9015 12.0675i 1.14368 0.660304i
\(335\) −4.80875 + 8.32901i −0.262730 + 0.455062i
\(336\) 0 0
\(337\) 3.43766i 0.187261i −0.995607 0.0936305i \(-0.970153\pi\)
0.995607 0.0936305i \(-0.0298472\pi\)
\(338\) 13.8648 + 2.65921i 0.754145 + 0.144642i
\(339\) 0 0
\(340\) 1.46301 + 5.46002i 0.0793428 + 0.296111i
\(341\) −3.60616 2.08201i −0.195284 0.112747i
\(342\) 0 0
\(343\) −2.36717 18.3684i −0.127815 0.991798i
\(344\) −28.3189 7.58803i −1.52685 0.409119i
\(345\) 0 0
\(346\) −9.73268 + 9.73268i −0.523232 + 0.523232i
\(347\) 9.46705 + 16.3974i 0.508218 + 0.880259i 0.999955 + 0.00951518i \(0.00302882\pi\)
−0.491737 + 0.870744i \(0.663638\pi\)
\(348\) 0 0
\(349\) −8.44404 31.5136i −0.451999 1.68688i −0.696764 0.717300i \(-0.745377\pi\)
0.244765 0.969582i \(-0.421289\pi\)
\(350\) 5.61366 6.11504i 0.300063 0.326863i
\(351\) 0 0
\(352\) −4.32426 −0.230484
\(353\) 31.7685 8.51233i 1.69086 0.453066i 0.720251 0.693713i \(-0.244026\pi\)
0.970613 + 0.240647i \(0.0773597\pi\)
\(354\) 0 0
\(355\) 1.93028 + 3.34334i 0.102449 + 0.177446i
\(356\) −6.26336 6.26336i −0.331957 0.331957i
\(357\) 0 0
\(358\) 3.07948 11.4928i 0.162756 0.607412i
\(359\) 1.45164 + 1.45164i 0.0766146 + 0.0766146i 0.744376 0.667761i \(-0.232747\pi\)
−0.667761 + 0.744376i \(0.732747\pi\)
\(360\) 0 0
\(361\) 14.4691 + 8.35375i 0.761533 + 0.439671i
\(362\) −1.23218 4.59857i −0.0647622 0.241696i
\(363\) 0 0
\(364\) 0.616856 + 7.80452i 0.0323320 + 0.409068i
\(365\) −5.06677 −0.265207
\(366\) 0 0
\(367\) −0.400843 0.231427i −0.0209238 0.0120804i 0.489502 0.872002i \(-0.337179\pi\)
−0.510425 + 0.859922i \(0.670512\pi\)
\(368\) −0.567956 + 0.327909i −0.0296067 + 0.0170935i
\(369\) 0 0
\(370\) −4.13331 + 15.4257i −0.214881 + 0.801946i
\(371\) −28.4287 + 18.0747i −1.47594 + 0.938390i
\(372\) 0 0
\(373\) 5.17460 + 8.96266i 0.267930 + 0.464069i 0.968327 0.249685i \(-0.0803269\pi\)
−0.700397 + 0.713754i \(0.746994\pi\)
\(374\) 2.59083 4.48744i 0.133968 0.232040i
\(375\) 0 0
\(376\) −20.7470 −1.06994
\(377\) 1.12093 + 30.9922i 0.0577309 + 1.59618i
\(378\) 0 0
\(379\) 3.99214 + 14.8989i 0.205062 + 0.765303i 0.989431 + 0.145007i \(0.0463206\pi\)
−0.784368 + 0.620295i \(0.787013\pi\)
\(380\) 0.902677 1.56348i 0.0463064 0.0802050i
\(381\) 0 0
\(382\) −7.56383 + 7.56383i −0.386999 + 0.386999i
\(383\) −8.40301 + 31.3605i −0.429374 + 1.60245i 0.324808 + 0.945780i \(0.394700\pi\)
−0.754182 + 0.656665i \(0.771966\pi\)
\(384\) 0 0
\(385\) −3.86539 + 0.165238i −0.196999 + 0.00842128i
\(386\) 6.90717 + 11.9636i 0.351566 + 0.608930i
\(387\) 0 0
\(388\) −2.91927 10.8948i −0.148203 0.553102i
\(389\) 37.3829i 1.89539i 0.319179 + 0.947694i \(0.396593\pi\)
−0.319179 + 0.947694i \(0.603407\pi\)
\(390\) 0 0
\(391\) 1.84502i 0.0933068i
\(392\) 20.1623 7.29690i 1.01835 0.368549i
\(393\) 0 0
\(394\) −1.46819 + 0.847660i −0.0739664 + 0.0427045i
\(395\) 7.25850 + 7.25850i 0.365215 + 0.365215i
\(396\) 0 0
\(397\) −34.9889 9.37524i −1.75604 0.470530i −0.770142 0.637873i \(-0.779815\pi\)
−0.985899 + 0.167343i \(0.946481\pi\)
\(398\) 8.97663 8.97663i 0.449958 0.449958i
\(399\) 0 0
\(400\) 4.21622 + 2.43424i 0.210811 + 0.121712i
\(401\) 33.6403 9.01390i 1.67992 0.450133i 0.712161 0.702016i \(-0.247716\pi\)
0.967758 + 0.251883i \(0.0810498\pi\)
\(402\) 0 0
\(403\) −14.5386 3.33743i −0.724220 0.166249i
\(404\) 3.24579i 0.161484i
\(405\) 0 0
\(406\) 23.5761 7.40990i 1.17006 0.367747i
\(407\) −8.82265 + 5.09376i −0.437323 + 0.252488i
\(408\) 0 0
\(409\) 2.97572 11.1055i 0.147140 0.549134i −0.852511 0.522709i \(-0.824921\pi\)
0.999651 0.0264241i \(-0.00841204\pi\)
\(410\) 3.65528 13.6417i 0.180521 0.673715i
\(411\) 0 0
\(412\) −9.07672 + 5.24044i −0.447178 + 0.258178i
\(413\) −2.32467 + 0.730638i −0.114390 + 0.0359523i
\(414\) 0 0
\(415\) 5.00138i 0.245508i
\(416\) −14.8082 + 4.54751i −0.726034 + 0.222960i
\(417\) 0 0
\(418\) −1.59854 + 0.428328i −0.0781872 + 0.0209502i
\(419\) −25.3323 14.6256i −1.23756 0.714507i −0.268967 0.963149i \(-0.586682\pi\)
−0.968595 + 0.248642i \(0.920016\pi\)
\(420\) 0 0
\(421\) −8.84750 + 8.84750i −0.431201 + 0.431201i −0.889037 0.457836i \(-0.848625\pi\)
0.457836 + 0.889037i \(0.348625\pi\)
\(422\) −23.2467 6.22894i −1.13163 0.303220i
\(423\) 0 0
\(424\) −27.5792 27.5792i −1.33936 1.33936i
\(425\) 11.8615 6.84826i 0.575369 0.332190i
\(426\) 0 0
\(427\) 11.8202 22.6559i 0.572017 1.09639i
\(428\) 2.95443i 0.142808i
\(429\) 0 0
\(430\) 15.1011i 0.728239i
\(431\) 3.91058 + 14.5945i 0.188366 + 0.702992i 0.993885 + 0.110422i \(0.0352201\pi\)
−0.805519 + 0.592570i \(0.798113\pi\)
\(432\) 0 0
\(433\) 16.6099 + 28.7692i 0.798222 + 1.38256i 0.920773 + 0.390100i \(0.127559\pi\)
−0.122550 + 0.992462i \(0.539107\pi\)
\(434\) 0.507674 + 11.8760i 0.0243691 + 0.570066i
\(435\) 0 0
\(436\) −0.0187197 + 0.0698628i −0.000896511 + 0.00334582i
\(437\) 0.416676 0.416676i 0.0199323 0.0199323i
\(438\) 0 0
\(439\) −3.12262 + 5.40854i −0.149035 + 0.258135i −0.930871 0.365348i \(-0.880950\pi\)
0.781836 + 0.623484i \(0.214283\pi\)
\(440\) −1.15933 4.32668i −0.0552689 0.206266i
\(441\) 0 0
\(442\) 4.15304 18.0916i 0.197540 0.860530i
\(443\) 17.0915 0.812043 0.406022 0.913863i \(-0.366916\pi\)
0.406022 + 0.913863i \(0.366916\pi\)
\(444\) 0 0
\(445\) 7.84051 13.5802i 0.371676 0.643762i
\(446\) 7.46751 + 12.9341i 0.353597 + 0.612448i
\(447\) 0 0
\(448\) 11.4072 + 17.9417i 0.538937 + 0.847666i
\(449\) 9.60577 35.8492i 0.453324 1.69183i −0.239644 0.970861i \(-0.577031\pi\)
0.692968 0.720968i \(-0.256303\pi\)
\(450\) 0 0
\(451\) 7.80227 4.50464i 0.367395 0.212115i
\(452\) 1.55322 + 0.896753i 0.0730574 + 0.0421797i
\(453\) 0 0
\(454\) −4.36456 −0.204839
\(455\) −13.0631 + 4.63080i −0.612407 + 0.217095i
\(456\) 0 0
\(457\) 2.07001 + 7.72540i 0.0968312 + 0.361379i 0.997291 0.0735609i \(-0.0234363\pi\)
−0.900460 + 0.434940i \(0.856770\pi\)
\(458\) −1.81245 1.04642i −0.0846902 0.0488959i
\(459\) 0 0
\(460\) 0.328134 + 0.328134i 0.0152993 + 0.0152993i
\(461\) −2.87961 + 10.7469i −0.134117 + 0.500531i 0.865883 + 0.500247i \(0.166757\pi\)
−1.00000 0.000284720i \(0.999909\pi\)
\(462\) 0 0
\(463\) 24.2312 + 24.2312i 1.12612 + 1.12612i 0.990803 + 0.135316i \(0.0432049\pi\)
0.135316 + 0.990803i \(0.456795\pi\)
\(464\) 7.24702 + 12.5522i 0.336435 + 0.582722i
\(465\) 0 0
\(466\) 1.18546 0.317644i 0.0549156 0.0147146i
\(467\) −10.5574 −0.488538 −0.244269 0.969707i \(-0.578548\pi\)
−0.244269 + 0.969707i \(0.578548\pi\)
\(468\) 0 0
\(469\) 12.9018 + 11.8439i 0.595748 + 0.546902i
\(470\) −2.76583 10.3222i −0.127578 0.476129i
\(471\) 0 0
\(472\) −1.41061 2.44325i −0.0649287 0.112460i
\(473\) 6.81176 6.81176i 0.313205 0.313205i
\(474\) 0 0
\(475\) −4.22539 1.13219i −0.193874 0.0519484i
\(476\) 10.2843 0.439630i 0.471378 0.0201504i
\(477\) 0 0
\(478\) −4.82578 2.78616i −0.220726 0.127436i
\(479\) −2.28082 8.51215i −0.104214 0.388930i 0.894041 0.447985i \(-0.147858\pi\)
−0.998255 + 0.0590545i \(0.981191\pi\)
\(480\) 0 0
\(481\) −24.8560 + 26.7215i −1.13334 + 1.21839i
\(482\) 10.6444i 0.484838i
\(483\) 0 0
\(484\) −4.09809 + 7.09810i −0.186277 + 0.322641i
\(485\) 17.2926 9.98389i 0.785217 0.453345i
\(486\) 0 0
\(487\) 19.8298 + 5.31338i 0.898574 + 0.240772i 0.678404 0.734689i \(-0.262672\pi\)
0.220170 + 0.975461i \(0.429339\pi\)
\(488\) 28.5774 + 7.65728i 1.29364 + 0.346629i
\(489\) 0 0
\(490\) 6.31832 + 9.05859i 0.285432 + 0.409225i
\(491\) 2.72329 + 1.57229i 0.122900 + 0.0709565i 0.560190 0.828364i \(-0.310728\pi\)
−0.437290 + 0.899321i \(0.644062\pi\)
\(492\) 0 0
\(493\) 40.7762 1.83647
\(494\) −5.02369 + 3.14786i −0.226026 + 0.141629i
\(495\) 0 0
\(496\) −6.73398 + 1.80436i −0.302364 + 0.0810183i
\(497\) 6.70676 2.10792i 0.300840 0.0945530i
\(498\) 0 0
\(499\) −10.7019 + 10.7019i −0.479082 + 0.479082i −0.904838 0.425756i \(-0.860008\pi\)
0.425756 + 0.904838i \(0.360008\pi\)
\(500\) 2.43463 9.08617i 0.108880 0.406346i
\(501\) 0 0
\(502\) 21.7804 21.7804i 0.972107 0.972107i
\(503\) 22.4889 12.9840i 1.00273 0.578926i 0.0936745 0.995603i \(-0.470139\pi\)
0.909055 + 0.416677i \(0.136805\pi\)
\(504\) 0 0
\(505\) −5.55031 + 1.48720i −0.246985 + 0.0661795i
\(506\) 0.425387i 0.0189108i
\(507\) 0 0
\(508\) −11.7192 −0.519955
\(509\) −31.8249 + 8.52745i −1.41061 + 0.377973i −0.882144 0.470980i \(-0.843900\pi\)
−0.528469 + 0.848952i \(0.677234\pi\)
\(510\) 0 0
\(511\) −2.00525 + 9.00624i −0.0887069 + 0.398412i
\(512\) −12.4191 + 12.4191i −0.548851 + 0.548851i
\(513\) 0 0
\(514\) −6.96683 1.86676i −0.307294 0.0823391i
\(515\) −13.1201 13.1201i −0.578139 0.578139i
\(516\) 0 0
\(517\) 3.40852 5.90373i 0.149907 0.259646i
\(518\) 25.7836 + 13.4520i 1.13287 + 0.591046i
\(519\) 0 0
\(520\) −8.52012 13.5973i −0.373632 0.596282i
\(521\) 26.4544i 1.15899i 0.814976 + 0.579495i \(0.196750\pi\)
−0.814976 + 0.579495i \(0.803250\pi\)
\(522\) 0 0
\(523\) 9.23888 + 5.33407i 0.403988 + 0.233243i 0.688203 0.725518i \(-0.258400\pi\)
−0.284215 + 0.958761i \(0.591733\pi\)
\(524\) −7.34057 12.7142i −0.320674 0.555424i
\(525\) 0 0
\(526\) 13.1062 + 3.51179i 0.571456 + 0.153121i
\(527\) −5.07623 + 18.9448i −0.221124 + 0.825247i
\(528\) 0 0
\(529\) −11.4243 19.7874i −0.496707 0.860322i
\(530\) 10.0448 17.3981i 0.436318 0.755726i
\(531\) 0 0
\(532\) −2.42186 2.22329i −0.105001 0.0963919i
\(533\) 21.9813 23.6310i 0.952116 1.02357i
\(534\) 0 0
\(535\) −5.05207 + 1.35370i −0.218420 + 0.0585255i
\(536\) −10.1385 + 17.5603i −0.437915 + 0.758490i
\(537\) 0 0
\(538\) 6.45273 + 6.45273i 0.278197 + 0.278197i
\(539\) −1.23608 + 6.93618i −0.0532415 + 0.298762i
\(540\) 0 0
\(541\) 3.42225 + 3.42225i 0.147134 + 0.147134i 0.776836 0.629702i \(-0.216823\pi\)
−0.629702 + 0.776836i \(0.716823\pi\)
\(542\) 0.341476 0.197151i 0.0146677 0.00846838i
\(543\) 0 0
\(544\) 5.27157 + 19.6738i 0.226017 + 0.843506i
\(545\) −0.128043 −0.00548475
\(546\) 0 0
\(547\) −19.6406 −0.839770 −0.419885 0.907577i \(-0.637930\pi\)
−0.419885 + 0.907577i \(0.637930\pi\)
\(548\) −0.537540 2.00613i −0.0229626 0.0856975i
\(549\) 0 0
\(550\) −2.73479 + 1.57893i −0.116612 + 0.0673259i
\(551\) −9.20882 9.20882i −0.392309 0.392309i
\(552\) 0 0
\(553\) 15.7747 10.0294i 0.670810 0.426494i
\(554\) 11.9925 + 11.9925i 0.509514 + 0.509514i
\(555\) 0 0
\(556\) −4.19968 + 7.27406i −0.178106 + 0.308489i
\(557\) 34.1973 9.16315i 1.44899 0.388255i 0.553316 0.832971i \(-0.313362\pi\)
0.895672 + 0.444716i \(0.146695\pi\)
\(558\) 0 0
\(559\) 16.1631 30.4900i 0.683627 1.28959i
\(560\) −4.38045 + 4.77169i −0.185108 + 0.201641i
\(561\) 0 0
\(562\) −0.651705 + 1.12879i −0.0274905 + 0.0476149i
\(563\) 15.9428 + 27.6137i 0.671908 + 1.16378i 0.977362 + 0.211572i \(0.0678583\pi\)
−0.305455 + 0.952207i \(0.598808\pi\)
\(564\) 0 0
\(565\) −0.821772 + 3.06689i −0.0345722 + 0.129025i
\(566\) −25.1168 6.73003i −1.05574 0.282884i
\(567\) 0 0
\(568\) 4.06967 + 7.04888i 0.170760 + 0.295764i
\(569\) −23.6253 13.6401i −0.990426 0.571823i −0.0850245 0.996379i \(-0.527097\pi\)
−0.905402 + 0.424556i \(0.860430\pi\)
\(570\) 0 0
\(571\) 33.0144i 1.38161i 0.723042 + 0.690804i \(0.242743\pi\)
−0.723042 + 0.690804i \(0.757257\pi\)
\(572\) 0.666344 2.90275i 0.0278612 0.121370i
\(573\) 0 0
\(574\) −22.8016 11.8962i −0.951721 0.496537i
\(575\) 0.562208 0.973772i 0.0234457 0.0406091i
\(576\) 0 0
\(577\) 18.3031 + 18.3031i 0.761967 + 0.761967i 0.976678 0.214711i \(-0.0688808\pi\)
−0.214711 + 0.976678i \(0.568881\pi\)
\(578\) −5.74226 1.53863i −0.238847 0.0639988i
\(579\) 0 0
\(580\) 7.25199 7.25199i 0.301123 0.301123i
\(581\) −8.89002 1.97937i −0.368820 0.0821181i
\(582\) 0 0
\(583\) 12.3789 3.31691i 0.512681 0.137373i
\(584\) −10.6824 −0.442042
\(585\) 0 0
\(586\) 20.9678i 0.866174i
\(587\) 30.3048 8.12014i 1.25081 0.335154i 0.428162 0.903702i \(-0.359161\pi\)
0.822650 + 0.568548i \(0.192495\pi\)
\(588\) 0 0
\(589\) 5.42485 3.13204i 0.223527 0.129053i
\(590\) 1.02754 1.02754i 0.0423031 0.0423031i
\(591\) 0 0
\(592\) −4.41447 + 16.4750i −0.181434 + 0.677120i
\(593\) −14.5568 + 14.5568i −0.597777 + 0.597777i −0.939721 0.341943i \(-0.888915\pi\)
0.341943 + 0.939721i \(0.388915\pi\)
\(594\) 0 0
\(595\) 5.46395 + 17.3846i 0.224000 + 0.712701i
\(596\) −6.68512 + 1.79127i −0.273833 + 0.0733733i
\(597\) 0 0
\(598\) −0.447349 1.45672i −0.0182934 0.0595696i
\(599\) −17.9695 −0.734214 −0.367107 0.930179i \(-0.619652\pi\)
−0.367107 + 0.930179i \(0.619652\pi\)
\(600\) 0 0
\(601\) 15.4598 + 8.92570i 0.630617 + 0.364087i 0.780991 0.624542i \(-0.214714\pi\)
−0.150374 + 0.988629i \(0.548048\pi\)
\(602\) −26.8423 5.97648i −1.09401 0.243583i
\(603\) 0 0
\(604\) −0.508609 0.136281i −0.0206950 0.00554521i
\(605\) −14.0155 3.75543i −0.569810 0.152680i
\(606\) 0 0
\(607\) −22.2125 + 12.8244i −0.901578 + 0.520526i −0.877712 0.479189i \(-0.840931\pi\)
−0.0238664 + 0.999715i \(0.507598\pi\)
\(608\) 3.25256 5.63361i 0.131909 0.228473i
\(609\) 0 0
\(610\) 15.2389i 0.617005i
\(611\) 5.46380 23.8015i 0.221042 0.962907i
\(612\) 0 0
\(613\) 0.916231 + 3.41942i 0.0370062 + 0.138109i 0.981957 0.189102i \(-0.0605578\pi\)
−0.944951 + 0.327211i \(0.893891\pi\)
\(614\) −22.8687 13.2032i −0.922905 0.532839i
\(615\) 0 0
\(616\) −8.14954 + 0.348376i −0.328354 + 0.0140365i
\(617\) 5.87829 + 1.57508i 0.236651 + 0.0634105i 0.375195 0.926946i \(-0.377576\pi\)
−0.138544 + 0.990356i \(0.544242\pi\)
\(618\) 0 0
\(619\) 34.1674 34.1674i 1.37331 1.37331i 0.517810 0.855496i \(-0.326747\pi\)
0.855496 0.517810i \(-0.173253\pi\)
\(620\) 2.46650 + 4.27210i 0.0990569 + 0.171572i
\(621\) 0 0
\(622\) 3.95289 + 14.7524i 0.158496 + 0.591517i
\(623\) −21.0359 19.3112i −0.842786 0.773685i
\(624\) 0 0
\(625\) 2.20722 0.0882889
\(626\) −19.7270 + 5.28584i −0.788451 + 0.211265i
\(627\) 0 0
\(628\) 3.32596 + 5.76073i 0.132720 + 0.229878i
\(629\) 33.9301 + 33.9301i 1.35288 + 1.35288i
\(630\) 0 0
\(631\) 2.80135 10.4548i 0.111520 0.416199i −0.887483 0.460841i \(-0.847548\pi\)
0.999003 + 0.0446417i \(0.0142146\pi\)
\(632\) 15.3033 + 15.3033i 0.608734 + 0.608734i
\(633\) 0 0
\(634\) 2.22390 + 1.28397i 0.0883222 + 0.0509928i
\(635\) −5.36966 20.0398i −0.213088 0.795257i
\(636\) 0 0
\(637\) 3.06139 + 25.0525i 0.121297 + 0.992616i
\(638\) −9.40135 −0.372203
\(639\) 0 0
\(640\) −0.168516 0.0972930i −0.00666120 0.00384584i
\(641\) −26.3470 + 15.2114i −1.04064 + 0.600815i −0.920015 0.391883i \(-0.871824\pi\)
−0.120627 + 0.992698i \(0.538490\pi\)
\(642\) 0 0
\(643\) 5.55469 20.7304i 0.219056 0.817527i −0.765644 0.643265i \(-0.777579\pi\)
0.984699 0.174262i \(-0.0557539\pi\)
\(644\) 0.713127 0.453399i 0.0281011 0.0178664i
\(645\) 0 0
\(646\) 3.89746 + 6.75060i 0.153344 + 0.265599i
\(647\) 3.76958 6.52911i 0.148198 0.256686i −0.782364 0.622822i \(-0.785986\pi\)
0.930561 + 0.366136i \(0.119319\pi\)
\(648\) 0 0
\(649\) 0.927000 0.0363879
\(650\) −7.70471 + 8.28296i −0.302204 + 0.324884i
\(651\) 0 0
\(652\) −2.91775 10.8892i −0.114268 0.426454i
\(653\) 11.4217 19.7830i 0.446966 0.774167i −0.551221 0.834359i \(-0.685838\pi\)
0.998187 + 0.0601918i \(0.0191712\pi\)
\(654\) 0 0
\(655\) 18.3779 18.3779i 0.718086 0.718086i
\(656\) 3.90392 14.5696i 0.152422 0.568848i
\(657\) 0 0
\(658\) −19.4425 + 0.831126i −0.757947 + 0.0324007i
\(659\) −13.0916 22.6753i −0.509975 0.883303i −0.999933 0.0115568i \(-0.996321\pi\)
0.489958 0.871746i \(-0.337012\pi\)
\(660\) 0 0
\(661\) −4.50623 16.8175i −0.175272 0.654124i −0.996505 0.0835312i \(-0.973380\pi\)
0.821233 0.570593i \(-0.193287\pi\)
\(662\) 37.3584i 1.45197i
\(663\) 0 0
\(664\) 10.5446i 0.409209i
\(665\) 2.69215 5.16008i 0.104397 0.200099i
\(666\) 0 0
\(667\) 2.89904 1.67376i 0.112251 0.0648083i
\(668\) −12.8972 12.8972i −0.499008 0.499008i
\(669\) 0 0
\(670\) −10.0884 2.70317i −0.389748 0.104433i
\(671\) −6.87393 + 6.87393i −0.265365 + 0.265365i
\(672\) 0 0
\(673\) 13.2813 + 7.66796i 0.511957 + 0.295578i 0.733638 0.679541i \(-0.237821\pi\)
−0.221681 + 0.975119i \(0.571154\pi\)
\(674\) 3.60596 0.966213i 0.138896 0.0372172i
\(675\) 0 0
\(676\) −0.770743 10.6411i −0.0296440 0.409271i
\(677\) 4.31369i 0.165789i −0.996558 0.0828943i \(-0.973584\pi\)
0.996558 0.0828943i \(-0.0264164\pi\)
\(678\) 0 0
\(679\) −10.9027 34.6891i −0.418406 1.33124i
\(680\) −18.2714 + 10.5490i −0.700678 + 0.404537i
\(681\) 0 0
\(682\) 1.17037 4.36789i 0.0448159 0.167255i
\(683\) 2.11067 7.87714i 0.0807627 0.301410i −0.913715 0.406355i \(-0.866800\pi\)
0.994478 + 0.104944i \(0.0334664\pi\)
\(684\) 0 0
\(685\) 3.18418 1.83839i 0.121661 0.0702412i
\(686\) 18.6023 7.64581i 0.710239 0.291918i
\(687\) 0 0
\(688\) 16.1283i 0.614886i
\(689\) 38.9028 24.3766i 1.48208 0.928674i
\(690\) 0 0
\(691\) −8.79665 + 2.35706i −0.334640 + 0.0896666i −0.422227 0.906490i \(-0.638751\pi\)
0.0875862 + 0.996157i \(0.472085\pi\)
\(692\) 9.00827 + 5.20093i 0.342443 + 0.197710i
\(693\) 0 0
\(694\) −14.5393 + 14.5393i −0.551905 + 0.551905i
\(695\) −14.3629 3.84853i −0.544816 0.145983i
\(696\) 0 0
\(697\) −30.0059 30.0059i −1.13656 1.13656i
\(698\) 30.6831 17.7149i 1.16137 0.670518i
\(699\) 0 0
\(700\) −5.56182 2.90175i −0.210217 0.109676i
\(701\) 42.0549i 1.58839i 0.607663 + 0.794195i \(0.292107\pi\)
−0.607663 + 0.794195i \(0.707893\pi\)
\(702\) 0 0
\(703\) 15.3254i 0.578009i
\(704\) −2.09335 7.81247i −0.0788959 0.294444i
\(705\) 0 0
\(706\) 17.8582 + 30.9312i 0.672101 + 1.16411i
\(707\) 0.446900 + 10.4543i 0.0168074 + 0.393175i
\(708\) 0 0
\(709\) 4.70279 17.5510i 0.176617 0.659143i −0.819654 0.572859i \(-0.805834\pi\)
0.996271 0.0862837i \(-0.0274991\pi\)
\(710\) −2.96449 + 2.96449i −0.111255 + 0.111255i
\(711\) 0 0
\(712\) 16.5304 28.6315i 0.619504 1.07301i
\(713\) 0.416733 + 1.55527i 0.0156068 + 0.0582453i
\(714\) 0 0
\(715\) 5.26901 0.190570i 0.197050 0.00712693i
\(716\) −8.99175 −0.336038
\(717\) 0 0
\(718\) −1.11470 + 1.93072i −0.0416003 + 0.0720538i
\(719\) 22.3307 + 38.6778i 0.832793 + 1.44244i 0.895815 + 0.444427i \(0.146593\pi\)
−0.0630222 + 0.998012i \(0.520074\pi\)
\(720\) 0 0
\(721\) −28.5135 + 18.1286i −1.06190 + 0.675144i
\(722\) −4.69594 + 17.5255i −0.174765 + 0.652231i
\(723\) 0 0
\(724\) −3.11583 + 1.79892i −0.115799 + 0.0668565i
\(725\) −21.5210 12.4252i −0.799271 0.461459i
\(726\) 0 0
\(727\) 21.6855 0.804272 0.402136 0.915580i \(-0.368268\pi\)
0.402136 + 0.915580i \(0.368268\pi\)
\(728\) −27.5413 + 9.76327i −1.02075 + 0.361851i
\(729\) 0 0
\(730\) −1.42410 5.31483i −0.0527085 0.196711i
\(731\) −39.2949 22.6869i −1.45338 0.839107i
\(732\) 0 0
\(733\) 36.4440 + 36.4440i 1.34609 + 1.34609i 0.889865 + 0.456223i \(0.150798\pi\)
0.456223 + 0.889865i \(0.349202\pi\)
\(734\) 0.130093 0.485514i 0.00480183 0.0179207i
\(735\) 0 0
\(736\) 1.18235 + 1.18235i 0.0435819 + 0.0435819i
\(737\) −3.33130 5.76998i −0.122710 0.212540i
\(738\) 0 0
\(739\) −6.28312 + 1.68356i −0.231128 + 0.0619307i −0.372524 0.928022i \(-0.621508\pi\)
0.141396 + 0.989953i \(0.454841\pi\)
\(740\) 12.0688 0.443659
\(741\) 0 0
\(742\) −26.9500 24.7403i −0.989364 0.908246i
\(743\) −6.75798 25.2211i −0.247926 0.925273i −0.971890 0.235435i \(-0.924348\pi\)
0.723964 0.689838i \(-0.242318\pi\)
\(744\) 0 0
\(745\) −6.12615 10.6108i −0.224445 0.388750i
\(746\) −7.94705 + 7.94705i −0.290962 + 0.290962i
\(747\) 0 0
\(748\) −3.78247 1.01351i −0.138301 0.0370576i
\(749\) 0.406783 + 9.51586i 0.0148635 + 0.347702i
\(750\) 0 0
\(751\) 31.8018 + 18.3608i 1.16046 + 0.669993i 0.951415 0.307912i \(-0.0996303\pi\)
0.209048 + 0.977905i \(0.432964\pi\)
\(752\) −2.95397 11.0244i −0.107720 0.402017i
\(753\) 0 0
\(754\) −32.1945 + 9.88671i −1.17245 + 0.360053i
\(755\) 0.932165i 0.0339250i
\(756\) 0 0
\(757\) 25.3385 43.8875i 0.920943 1.59512i 0.122984 0.992409i \(-0.460754\pi\)
0.797959 0.602711i \(-0.205913\pi\)
\(758\) −14.5062 + 8.37517i −0.526890 + 0.304200i
\(759\) 0 0
\(760\) 6.50876 + 1.74402i 0.236097 + 0.0632621i
\(761\) 25.8358 + 6.92269i 0.936548 + 0.250947i 0.694645 0.719353i \(-0.255562\pi\)
0.241903 + 0.970300i \(0.422228\pi\)
\(762\) 0 0
\(763\) −0.0506748 + 0.227597i −0.00183455 + 0.00823958i
\(764\) 7.00085 + 4.04194i 0.253282 + 0.146232i
\(765\) 0 0
\(766\) −35.2576 −1.27391
\(767\) 3.17447 0.974858i 0.114623 0.0352001i
\(768\) 0 0
\(769\) 22.6180 6.06047i 0.815626 0.218546i 0.173193 0.984888i \(-0.444592\pi\)
0.642433 + 0.766342i \(0.277925\pi\)
\(770\) −1.25976 4.00820i −0.0453988 0.144445i
\(771\) 0 0
\(772\) 7.38208 7.38208i 0.265687 0.265687i
\(773\) 3.07578 11.4790i 0.110628 0.412869i −0.888295 0.459274i \(-0.848110\pi\)
0.998923 + 0.0464045i \(0.0147763\pi\)
\(774\) 0 0
\(775\) 8.45192 8.45192i 0.303602 0.303602i
\(776\) 36.4586 21.0494i 1.30879 0.755628i
\(777\) 0 0
\(778\) −39.2131 + 10.5071i −1.40586 + 0.376699i
\(779\) 13.5530i 0.485585i
\(780\) 0 0
\(781\) −2.67443 −0.0956986
\(782\) −1.93535 + 0.518576i −0.0692080 + 0.0185442i
\(783\) 0 0
\(784\) 6.74810 + 9.67477i 0.241004 + 0.345528i
\(785\) −8.32692 + 8.32692i −0.297201 + 0.297201i
\(786\) 0 0
\(787\) −1.37868 0.369415i −0.0491445 0.0131682i 0.234163 0.972197i \(-0.424765\pi\)
−0.283308 + 0.959029i \(0.591432\pi\)
\(788\) 0.905941 + 0.905941i