Properties

Label 819.2.bm.f.550.2
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: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
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 550.2
Root \(0.874681 + 1.11128i\) of defining polynomial
Character \(\chi\) \(=\) 819.550
Dual form 819.2.bm.f.478.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.34523i q^{2} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.44601 + 1.00849i) q^{7} -2.94654i q^{8} +O(q^{10})\) \(q-1.34523i q^{2} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.44601 + 1.00849i) q^{7} -2.94654i q^{8} +(2.39973 + 4.15646i) q^{10} +(1.10736 - 0.639336i) q^{11} +(3.57420 + 0.474474i) q^{13} +(1.35664 + 3.29043i) q^{14} -3.58303 q^{16} +7.73920 q^{17} +(0.817422 + 0.471939i) q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} +1.64727 q^{23} +(3.86451 - 6.69354i) q^{25} +(0.638275 - 4.80810i) q^{26} +(-0.465638 + 0.191982i) q^{28} +(2.02242 - 3.50293i) q^{29} +(4.46193 + 2.57610i) q^{31} -1.07309i q^{32} -10.4110i q^{34} +(5.75861 - 7.47941i) q^{35} +1.05608i q^{37} +(0.634865 - 1.09962i) q^{38} +(5.25629 + 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(0.210805 - 0.121708i) q^{44} -2.21596i q^{46} +(-0.774415 + 0.447109i) q^{47} +(4.96591 - 4.93353i) q^{49} +(-9.00432 - 5.19865i) q^{50} +(0.680407 + 0.0903239i) q^{52} +(-0.0399961 + 0.0692754i) q^{53} +(-2.28101 + 3.95082i) q^{55} +(2.97154 + 7.20726i) q^{56} +(-4.71224 - 2.72061i) q^{58} +11.1847i q^{59} +(3.81196 - 6.60251i) q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(-11.8899 + 4.90994i) q^{65} +(5.47418 - 3.16052i) q^{67} +1.47328 q^{68} +(-10.0615 - 7.74664i) q^{70} +(-9.89346 + 5.71199i) q^{71} +(0.658617 + 0.380253i) q^{73} +1.42067 q^{74} +(0.155610 + 0.0898413i) q^{76} +(-2.06386 + 2.68058i) q^{77} +(1.42765 + 2.47277i) q^{79} +(11.0708 - 6.39172i) q^{80} +(2.82418 - 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(4.46270 - 2.57654i) q^{86} +(-1.88383 - 3.26289i) q^{88} -7.57626i q^{89} +(-9.22101 + 2.44396i) q^{91} +0.313586 q^{92} +(0.601462 + 1.04176i) q^{94} -3.36755 q^{95} +(-0.414443 + 0.239279i) q^{97} +(-6.63671 - 6.68028i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 8q^{4} + 3q^{5} - 3q^{7} + O(q^{10}) \) \( 12q - 8q^{4} + 3q^{5} - 3q^{7} + 12q^{10} - 12q^{11} - 2q^{13} - 4q^{14} + 16q^{16} + 34q^{17} + 9q^{19} + 3q^{20} - 15q^{22} + 6q^{23} - 5q^{25} + 6q^{26} - 9q^{28} + q^{29} + 18q^{31} + 6q^{35} - 19q^{38} - q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 15q^{47} - 3q^{49} - 18q^{50} - 7q^{52} + 8q^{53} - 15q^{55} - 27q^{56} - 24q^{58} + 5q^{61} - 41q^{62} + 2q^{64} - 21q^{65} + 15q^{67} - 22q^{68} + 3q^{70} - 30q^{71} + 42q^{73} - 66q^{74} - 45q^{76} + 19q^{77} - 35q^{79} + 63q^{80} + 5q^{82} - 21q^{85} + 57q^{86} - 14q^{88} - 7q^{91} + 66q^{92} + q^{94} + 4q^{95} - 3q^{97} + 18q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.34523i 0.951219i −0.879657 0.475609i \(-0.842228\pi\)
0.879657 0.475609i \(-0.157772\pi\)
\(3\) 0 0
\(4\) 0.190366 0.0951832
\(5\) −3.08979 + 1.78389i −1.38179 + 0.797779i −0.992372 0.123280i \(-0.960659\pi\)
−0.389422 + 0.921059i \(0.627325\pi\)
\(6\) 0 0
\(7\) −2.44601 + 1.00849i −0.924504 + 0.381172i
\(8\) 2.94654i 1.04176i
\(9\) 0 0
\(10\) 2.39973 + 4.15646i 0.758862 + 1.31439i
\(11\) 1.10736 0.639336i 0.333882 0.192767i −0.323681 0.946166i \(-0.604920\pi\)
0.657563 + 0.753399i \(0.271587\pi\)
\(12\) 0 0
\(13\) 3.57420 + 0.474474i 0.991304 + 0.131595i
\(14\) 1.35664 + 3.29043i 0.362578 + 0.879406i
\(15\) 0 0
\(16\) −3.58303 −0.895757
\(17\) 7.73920 1.87703 0.938515 0.345238i \(-0.112202\pi\)
0.938515 + 0.345238i \(0.112202\pi\)
\(18\) 0 0
\(19\) 0.817422 + 0.471939i 0.187530 + 0.108270i 0.590826 0.806799i \(-0.298802\pi\)
−0.403296 + 0.915070i \(0.632135\pi\)
\(20\) −0.588191 + 0.339592i −0.131524 + 0.0759352i
\(21\) 0 0
\(22\) −0.860052 1.48965i −0.183364 0.317595i
\(23\) 1.64727 0.343481 0.171740 0.985142i \(-0.445061\pi\)
0.171740 + 0.985142i \(0.445061\pi\)
\(24\) 0 0
\(25\) 3.86451 6.69354i 0.772903 1.33871i
\(26\) 0.638275 4.80810i 0.125176 0.942946i
\(27\) 0 0
\(28\) −0.465638 + 0.191982i −0.0879973 + 0.0362812i
\(29\) 2.02242 3.50293i 0.375554 0.650478i −0.614856 0.788639i \(-0.710786\pi\)
0.990410 + 0.138161i \(0.0441192\pi\)
\(30\) 0 0
\(31\) 4.46193 + 2.57610i 0.801387 + 0.462681i 0.843956 0.536413i \(-0.180221\pi\)
−0.0425691 + 0.999094i \(0.513554\pi\)
\(32\) 1.07309i 0.189698i
\(33\) 0 0
\(34\) 10.4110i 1.78547i
\(35\) 5.75861 7.47941i 0.973383 1.26425i
\(36\) 0 0
\(37\) 1.05608i 0.173619i 0.996225 + 0.0868094i \(0.0276671\pi\)
−0.996225 + 0.0868094i \(0.972333\pi\)
\(38\) 0.634865 1.09962i 0.102989 0.178382i
\(39\) 0 0
\(40\) 5.25629 + 9.10417i 0.831093 + 1.43950i
\(41\) 3.63629 + 2.09941i 0.567893 + 0.327873i 0.756307 0.654217i \(-0.227002\pi\)
−0.188415 + 0.982090i \(0.560335\pi\)
\(42\) 0 0
\(43\) 1.91532 + 3.31744i 0.292084 + 0.505904i 0.974302 0.225244i \(-0.0723180\pi\)
−0.682218 + 0.731148i \(0.738985\pi\)
\(44\) 0.210805 0.121708i 0.0317800 0.0183482i
\(45\) 0 0
\(46\) 2.21596i 0.326725i
\(47\) −0.774415 + 0.447109i −0.112960 + 0.0652175i −0.555416 0.831573i \(-0.687441\pi\)
0.442456 + 0.896790i \(0.354107\pi\)
\(48\) 0 0
\(49\) 4.96591 4.93353i 0.709416 0.704790i
\(50\) −9.00432 5.19865i −1.27340 0.735200i
\(51\) 0 0
\(52\) 0.680407 + 0.0903239i 0.0943554 + 0.0125257i
\(53\) −0.0399961 + 0.0692754i −0.00549389 + 0.00951570i −0.868759 0.495235i \(-0.835082\pi\)
0.863265 + 0.504750i \(0.168415\pi\)
\(54\) 0 0
\(55\) −2.28101 + 3.95082i −0.307571 + 0.532729i
\(56\) 2.97154 + 7.20726i 0.397089 + 0.963110i
\(57\) 0 0
\(58\) −4.71224 2.72061i −0.618747 0.357234i
\(59\) 11.1847i 1.45613i 0.685509 + 0.728064i \(0.259580\pi\)
−0.685509 + 0.728064i \(0.740420\pi\)
\(60\) 0 0
\(61\) 3.81196 6.60251i 0.488072 0.845365i −0.511834 0.859084i \(-0.671034\pi\)
0.999906 + 0.0137195i \(0.00436719\pi\)
\(62\) 3.46543 6.00231i 0.440111 0.762294i
\(63\) 0 0
\(64\) −8.60961 −1.07620
\(65\) −11.8899 + 4.90994i −1.47476 + 0.609003i
\(66\) 0 0
\(67\) 5.47418 3.16052i 0.668777 0.386119i −0.126836 0.991924i \(-0.540482\pi\)
0.795613 + 0.605805i \(0.207149\pi\)
\(68\) 1.47328 0.178662
\(69\) 0 0
\(70\) −10.0615 7.74664i −1.20258 0.925900i
\(71\) −9.89346 + 5.71199i −1.17414 + 0.677889i −0.954651 0.297727i \(-0.903772\pi\)
−0.219487 + 0.975616i \(0.570438\pi\)
\(72\) 0 0
\(73\) 0.658617 + 0.380253i 0.0770853 + 0.0445052i 0.538047 0.842915i \(-0.319162\pi\)
−0.460962 + 0.887420i \(0.652496\pi\)
\(74\) 1.42067 0.165149
\(75\) 0 0
\(76\) 0.155610 + 0.0898413i 0.0178497 + 0.0103055i
\(77\) −2.06386 + 2.68058i −0.235198 + 0.305481i
\(78\) 0 0
\(79\) 1.42765 + 2.47277i 0.160624 + 0.278208i 0.935093 0.354404i \(-0.115316\pi\)
−0.774469 + 0.632612i \(0.781983\pi\)
\(80\) 11.0708 6.39172i 1.23775 0.714616i
\(81\) 0 0
\(82\) 2.82418 4.89163i 0.311879 0.540190i
\(83\) 2.32483i 0.255183i 0.991827 + 0.127591i \(0.0407246\pi\)
−0.991827 + 0.127591i \(0.959275\pi\)
\(84\) 0 0
\(85\) −23.9125 + 13.8059i −2.59367 + 1.49746i
\(86\) 4.46270 2.57654i 0.481226 0.277836i
\(87\) 0 0
\(88\) −1.88383 3.26289i −0.200817 0.347825i
\(89\) 7.57626i 0.803082i −0.915841 0.401541i \(-0.868475\pi\)
0.915841 0.401541i \(-0.131525\pi\)
\(90\) 0 0
\(91\) −9.22101 + 2.44396i −0.966625 + 0.256196i
\(92\) 0.313586 0.0326936
\(93\) 0 0
\(94\) 0.601462 + 1.04176i 0.0620361 + 0.107450i
\(95\) −3.36755 −0.345503
\(96\) 0 0
\(97\) −0.414443 + 0.239279i −0.0420803 + 0.0242951i −0.520893 0.853622i \(-0.674401\pi\)
0.478812 + 0.877917i \(0.341067\pi\)
\(98\) −6.63671 6.68028i −0.670409 0.674810i
\(99\) 0 0
\(100\) 0.735674 1.27422i 0.0735674 0.127422i
\(101\) −1.43918 2.49273i −0.143204 0.248036i 0.785498 0.618865i \(-0.212407\pi\)
−0.928701 + 0.370829i \(0.879074\pi\)
\(102\) 0 0
\(103\) −5.66755 9.81649i −0.558441 0.967248i −0.997627 0.0688516i \(-0.978066\pi\)
0.439186 0.898396i \(-0.355267\pi\)
\(104\) 1.39806 10.5315i 0.137091 1.03270i
\(105\) 0 0
\(106\) 0.0931910 + 0.0538039i 0.00905151 + 0.00522589i
\(107\) 6.57206 0.635345 0.317673 0.948200i \(-0.397099\pi\)
0.317673 + 0.948200i \(0.397099\pi\)
\(108\) 0 0
\(109\) −5.05684 2.91957i −0.484358 0.279644i 0.237873 0.971296i \(-0.423550\pi\)
−0.722231 + 0.691652i \(0.756883\pi\)
\(110\) 5.31475 + 3.06847i 0.506741 + 0.292567i
\(111\) 0 0
\(112\) 8.76412 3.61343i 0.828131 0.341437i
\(113\) 3.26617 + 5.65717i 0.307255 + 0.532181i 0.977761 0.209723i \(-0.0672562\pi\)
−0.670506 + 0.741904i \(0.733923\pi\)
\(114\) 0 0
\(115\) −5.08973 + 2.93855i −0.474619 + 0.274022i
\(116\) 0.385001 0.666841i 0.0357464 0.0619146i
\(117\) 0 0
\(118\) 15.0460 1.38510
\(119\) −18.9301 + 7.80487i −1.73532 + 0.715471i
\(120\) 0 0
\(121\) −4.68250 + 8.11033i −0.425682 + 0.737302i
\(122\) −8.88187 5.12795i −0.804127 0.464263i
\(123\) 0 0
\(124\) 0.849402 + 0.490402i 0.0762786 + 0.0440394i
\(125\) 9.73656i 0.870865i
\(126\) 0 0
\(127\) 7.35818 12.7447i 0.652932 1.13091i −0.329475 0.944164i \(-0.606872\pi\)
0.982408 0.186748i \(-0.0597948\pi\)
\(128\) 9.43568i 0.834005i
\(129\) 0 0
\(130\) 6.60498 + 15.9946i 0.579295 + 1.40282i
\(131\) 5.59335 + 9.68796i 0.488693 + 0.846441i 0.999915 0.0130074i \(-0.00414049\pi\)
−0.511222 + 0.859448i \(0.670807\pi\)
\(132\) 0 0
\(133\) −2.47537 0.330008i −0.214641 0.0286153i
\(134\) −4.25161 7.36400i −0.367283 0.636153i
\(135\) 0 0
\(136\) 22.8038i 1.95541i
\(137\) 17.6308i 1.50630i −0.657848 0.753151i \(-0.728533\pi\)
0.657848 0.753151i \(-0.271467\pi\)
\(138\) 0 0
\(139\) 2.92855 + 5.07240i 0.248396 + 0.430235i 0.963081 0.269212i \(-0.0867631\pi\)
−0.714685 + 0.699447i \(0.753430\pi\)
\(140\) 1.09625 1.42383i 0.0926497 0.120335i
\(141\) 0 0
\(142\) 7.68392 + 13.3089i 0.644820 + 1.11686i
\(143\) 4.26128 1.75970i 0.356346 0.147153i
\(144\) 0 0
\(145\) 14.4311i 1.19844i
\(146\) 0.511526 0.885989i 0.0423342 0.0733250i
\(147\) 0 0
\(148\) 0.201043i 0.0165256i
\(149\) −9.07505 5.23948i −0.743457 0.429235i 0.0798677 0.996805i \(-0.474550\pi\)
−0.823325 + 0.567570i \(0.807884\pi\)
\(150\) 0 0
\(151\) −4.08249 2.35703i −0.332229 0.191812i 0.324602 0.945851i \(-0.394770\pi\)
−0.656830 + 0.754039i \(0.728103\pi\)
\(152\) 1.39059 2.40857i 0.112791 0.195361i
\(153\) 0 0
\(154\) 3.60599 + 2.77635i 0.290579 + 0.223725i
\(155\) −18.3819 −1.47647
\(156\) 0 0
\(157\) −4.50105 + 7.79604i −0.359223 + 0.622192i −0.987831 0.155530i \(-0.950291\pi\)
0.628608 + 0.777722i \(0.283625\pi\)
\(158\) 3.32643 1.92052i 0.264637 0.152788i
\(159\) 0 0
\(160\) 1.91428 + 3.31563i 0.151337 + 0.262123i
\(161\) −4.02925 + 1.66125i −0.317549 + 0.130925i
\(162\) 0 0
\(163\) 10.4203 + 6.01619i 0.816185 + 0.471224i 0.849099 0.528234i \(-0.177146\pi\)
−0.0329144 + 0.999458i \(0.510479\pi\)
\(164\) 0.692227 + 0.399657i 0.0540538 + 0.0312080i
\(165\) 0 0
\(166\) 3.12742 0.242735
\(167\) 16.8199 + 9.71099i 1.30157 + 0.751459i 0.980672 0.195657i \(-0.0626838\pi\)
0.320893 + 0.947116i \(0.396017\pi\)
\(168\) 0 0
\(169\) 12.5497 + 3.39173i 0.965365 + 0.260902i
\(170\) 18.5720 + 32.1677i 1.42441 + 2.46715i
\(171\) 0 0
\(172\) 0.364613 + 0.631528i 0.0278015 + 0.0481536i
\(173\) −7.18976 + 12.4530i −0.546627 + 0.946786i 0.451875 + 0.892081i \(0.350755\pi\)
−0.998503 + 0.0547049i \(0.982578\pi\)
\(174\) 0 0
\(175\) −2.70230 + 20.2697i −0.204275 + 1.53225i
\(176\) −3.96771 + 2.29076i −0.299077 + 0.172672i
\(177\) 0 0
\(178\) −10.1918 −0.763907
\(179\) −2.71303 4.69911i −0.202781 0.351228i 0.746642 0.665226i \(-0.231665\pi\)
−0.949424 + 0.313998i \(0.898331\pi\)
\(180\) 0 0
\(181\) −15.4902 −1.15138 −0.575688 0.817669i \(-0.695266\pi\)
−0.575688 + 0.817669i \(0.695266\pi\)
\(182\) 3.28768 + 12.4043i 0.243699 + 0.919471i
\(183\) 0 0
\(184\) 4.85376i 0.357824i
\(185\) −1.88393 3.26307i −0.138509 0.239905i
\(186\) 0 0
\(187\) 8.57010 4.94795i 0.626707 0.361830i
\(188\) −0.147423 + 0.0851144i −0.0107519 + 0.00620761i
\(189\) 0 0
\(190\) 4.53011i 0.328649i
\(191\) 2.37311 4.11035i 0.171712 0.297414i −0.767306 0.641281i \(-0.778403\pi\)
0.939019 + 0.343866i \(0.111737\pi\)
\(192\) 0 0
\(193\) 18.2204 10.5196i 1.31154 0.757215i 0.329185 0.944266i \(-0.393226\pi\)
0.982350 + 0.187050i \(0.0598928\pi\)
\(194\) 0.321884 + 0.557519i 0.0231099 + 0.0400276i
\(195\) 0 0
\(196\) 0.945343 0.939178i 0.0675245 0.0670842i
\(197\) −5.03342 2.90604i −0.358616 0.207047i 0.309857 0.950783i \(-0.399719\pi\)
−0.668474 + 0.743736i \(0.733052\pi\)
\(198\) 0 0
\(199\) −10.6182 −0.752703 −0.376352 0.926477i \(-0.622821\pi\)
−0.376352 + 0.926477i \(0.622821\pi\)
\(200\) −19.7228 11.3869i −1.39461 0.805178i
\(201\) 0 0
\(202\) −3.35329 + 1.93602i −0.235936 + 0.136218i
\(203\) −1.41420 + 10.6078i −0.0992571 + 0.744520i
\(204\) 0 0
\(205\) −14.9805 −1.04628
\(206\) −13.2054 + 7.62414i −0.920064 + 0.531199i
\(207\) 0 0
\(208\) −12.8064 1.70005i −0.887967 0.117877i
\(209\) 1.20691 0.0834837
\(210\) 0 0
\(211\) 2.33275 4.04043i 0.160593 0.278155i −0.774489 0.632588i \(-0.781993\pi\)
0.935081 + 0.354433i \(0.115326\pi\)
\(212\) −0.00761392 + 0.0131877i −0.000522926 + 0.000905735i
\(213\) 0 0
\(214\) 8.84091i 0.604352i
\(215\) −11.8359 6.83344i −0.807200 0.466037i
\(216\) 0 0
\(217\) −13.5119 1.80136i −0.917246 0.122284i
\(218\) −3.92748 + 6.80260i −0.266003 + 0.460730i
\(219\) 0 0
\(220\) −0.434227 + 0.752104i −0.0292756 + 0.0507068i
\(221\) 27.6614 + 3.67205i 1.86071 + 0.247009i
\(222\) 0 0
\(223\) 20.9798 + 12.1127i 1.40491 + 0.811126i 0.994891 0.100950i \(-0.0321883\pi\)
0.410020 + 0.912076i \(0.365522\pi\)
\(224\) 1.08220 + 2.62480i 0.0723075 + 0.175377i
\(225\) 0 0
\(226\) 7.61017 4.39373i 0.506221 0.292267i
\(227\) 15.3753i 1.02049i −0.860028 0.510247i \(-0.829554\pi\)
0.860028 0.510247i \(-0.170446\pi\)
\(228\) 0 0
\(229\) −14.1608 + 8.17573i −0.935771 + 0.540268i −0.888632 0.458621i \(-0.848344\pi\)
−0.0471389 + 0.998888i \(0.515010\pi\)
\(230\) 3.95302 + 6.84683i 0.260654 + 0.451467i
\(231\) 0 0
\(232\) −10.3215 5.95913i −0.677641 0.391236i
\(233\) 14.5554 + 25.2106i 0.953554 + 1.65160i 0.737643 + 0.675191i \(0.235939\pi\)
0.215911 + 0.976413i \(0.430728\pi\)
\(234\) 0 0
\(235\) 1.59518 2.76294i 0.104058 0.180234i
\(236\) 2.12920i 0.138599i
\(237\) 0 0
\(238\) 10.4993 + 25.4653i 0.680570 + 1.65067i
\(239\) 8.65409i 0.559787i −0.960031 0.279893i \(-0.909701\pi\)
0.960031 0.279893i \(-0.0902991\pi\)
\(240\) 0 0
\(241\) 18.1982i 1.17225i −0.810222 0.586124i \(-0.800653\pi\)
0.810222 0.586124i \(-0.199347\pi\)
\(242\) 10.9102 + 6.29902i 0.701336 + 0.404916i
\(243\) 0 0
\(244\) 0.725669 1.25690i 0.0464562 0.0804645i
\(245\) −6.54274 + 24.1022i −0.418000 + 1.53983i
\(246\) 0 0
\(247\) 2.69770 + 2.07465i 0.171651 + 0.132007i
\(248\) 7.59057 13.1473i 0.482002 0.834851i
\(249\) 0 0
\(250\) 13.0979 0.828383
\(251\) −7.93598 13.7455i −0.500915 0.867610i −0.999999 0.00105678i \(-0.999664\pi\)
0.499085 0.866553i \(-0.333670\pi\)
\(252\) 0 0
\(253\) 1.82413 1.05316i 0.114682 0.0662117i
\(254\) −17.1446 9.89841i −1.07574 0.621082i
\(255\) 0 0
\(256\) −4.52609 −0.282880
\(257\) −24.3267 −1.51746 −0.758730 0.651406i \(-0.774180\pi\)
−0.758730 + 0.651406i \(0.774180\pi\)
\(258\) 0 0
\(259\) −1.06504 2.58319i −0.0661786 0.160511i
\(260\) −2.26344 + 0.934688i −0.140372 + 0.0579669i
\(261\) 0 0
\(262\) 13.0325 7.52432i 0.805150 0.464854i
\(263\) 7.71727 + 13.3667i 0.475867 + 0.824226i 0.999618 0.0276456i \(-0.00880099\pi\)
−0.523751 + 0.851872i \(0.675468\pi\)
\(264\) 0 0
\(265\) 0.285395i 0.0175317i
\(266\) −0.443935 + 3.32993i −0.0272194 + 0.204171i
\(267\) 0 0
\(268\) 1.04210 0.601656i 0.0636563 0.0367520i
\(269\) 13.0407 0.795106 0.397553 0.917579i \(-0.369859\pi\)
0.397553 + 0.917579i \(0.369859\pi\)
\(270\) 0 0
\(271\) 26.9706i 1.63835i 0.573544 + 0.819174i \(0.305568\pi\)
−0.573544 + 0.819174i \(0.694432\pi\)
\(272\) −27.7298 −1.68136
\(273\) 0 0
\(274\) −23.7174 −1.43282
\(275\) 9.88289i 0.595961i
\(276\) 0 0
\(277\) −12.7015 −0.763156 −0.381578 0.924337i \(-0.624619\pi\)
−0.381578 + 0.924337i \(0.624619\pi\)
\(278\) 6.82352 3.93956i 0.409248 0.236279i
\(279\) 0 0
\(280\) −22.0384 16.9680i −1.31704 1.01403i
\(281\) 26.7216i 1.59408i −0.603930 0.797038i \(-0.706399\pi\)
0.603930 0.797038i \(-0.293601\pi\)
\(282\) 0 0
\(283\) 7.37113 + 12.7672i 0.438168 + 0.758929i 0.997548 0.0699819i \(-0.0222941\pi\)
−0.559380 + 0.828911i \(0.688961\pi\)
\(284\) −1.88338 + 1.08737i −0.111758 + 0.0645236i
\(285\) 0 0
\(286\) −2.36719 5.73238i −0.139975 0.338963i
\(287\) −11.0116 1.46803i −0.649995 0.0866553i
\(288\) 0 0
\(289\) 42.8952 2.52324
\(290\) 19.4131 1.13997
\(291\) 0 0
\(292\) 0.125379 + 0.0723874i 0.00733723 + 0.00423615i
\(293\) 10.0312 5.79153i 0.586030 0.338345i −0.177496 0.984121i \(-0.556800\pi\)
0.763526 + 0.645777i \(0.223466\pi\)
\(294\) 0 0
\(295\) −19.9523 34.5584i −1.16167 2.01207i
\(296\) 3.11179 0.180869
\(297\) 0 0
\(298\) −7.04829 + 12.2080i −0.408297 + 0.707190i
\(299\) 5.88768 + 0.781589i 0.340493 + 0.0452005i
\(300\) 0 0
\(301\) −8.03048 6.18290i −0.462869 0.356376i
\(302\) −3.17074 + 5.49188i −0.182455 + 0.316022i
\(303\) 0 0
\(304\) −2.92885 1.69097i −0.167981 0.0969838i
\(305\) 27.2004i 1.55749i
\(306\) 0 0
\(307\) 29.3335i 1.67415i 0.547086 + 0.837076i \(0.315737\pi\)
−0.547086 + 0.837076i \(0.684263\pi\)
\(308\) −0.392889 + 0.510293i −0.0223869 + 0.0290766i
\(309\) 0 0
\(310\) 24.7278i 1.40444i
\(311\) 0.0753271 0.130470i 0.00427141 0.00739830i −0.863882 0.503695i \(-0.831974\pi\)
0.868153 + 0.496296i \(0.165307\pi\)
\(312\) 0 0
\(313\) 5.26057 + 9.11157i 0.297345 + 0.515016i 0.975528 0.219877i \(-0.0705656\pi\)
−0.678183 + 0.734893i \(0.737232\pi\)
\(314\) 10.4874 + 6.05493i 0.591841 + 0.341699i
\(315\) 0 0
\(316\) 0.271777 + 0.470732i 0.0152887 + 0.0264808i
\(317\) −1.30489 + 0.753380i −0.0732901 + 0.0423140i −0.536197 0.844093i \(-0.680140\pi\)
0.462907 + 0.886407i \(0.346806\pi\)
\(318\) 0 0
\(319\) 5.17202i 0.289578i
\(320\) 26.6018 15.3586i 1.48709 0.858571i
\(321\) 0 0
\(322\) 2.23476 + 5.42025i 0.124538 + 0.302059i
\(323\) 6.32619 + 3.65243i 0.351999 + 0.203227i
\(324\) 0 0
\(325\) 16.9884 22.0904i 0.942349 1.22535i
\(326\) 8.09314 14.0177i 0.448237 0.776370i
\(327\) 0 0
\(328\) 6.18600 10.7145i 0.341565 0.591607i
\(329\) 1.44332 1.87462i 0.0795729 0.103351i
\(330\) 0 0
\(331\) −21.8679 12.6254i −1.20197 0.693957i −0.240976 0.970531i \(-0.577467\pi\)
−0.960993 + 0.276574i \(0.910801\pi\)
\(332\) 0.442569i 0.0242891i
\(333\) 0 0
\(334\) 13.0635 22.6266i 0.714802 1.23807i
\(335\) −11.2760 + 19.5306i −0.616075 + 1.06707i
\(336\) 0 0
\(337\) 32.1811 1.75302 0.876509 0.481386i \(-0.159866\pi\)
0.876509 + 0.481386i \(0.159866\pi\)
\(338\) 4.56264 16.8823i 0.248175 0.918273i
\(339\) 0 0
\(340\) −4.55213 + 2.62817i −0.246874 + 0.142533i
\(341\) 6.58797 0.356759
\(342\) 0 0
\(343\) −7.17127 + 17.0755i −0.387212 + 0.921991i
\(344\) 9.77495 5.64357i 0.527030 0.304281i
\(345\) 0 0
\(346\) 16.7521 + 9.67185i 0.900600 + 0.519962i
\(347\) −24.7638 −1.32939 −0.664695 0.747115i \(-0.731438\pi\)
−0.664695 + 0.747115i \(0.731438\pi\)
\(348\) 0 0
\(349\) −10.0075 5.77782i −0.535688 0.309280i 0.207642 0.978205i \(-0.433421\pi\)
−0.743330 + 0.668925i \(0.766755\pi\)
\(350\) 27.2674 + 3.63520i 1.45750 + 0.194310i
\(351\) 0 0
\(352\) −0.686067 1.18830i −0.0365675 0.0633368i
\(353\) 17.3971 10.0442i 0.925953 0.534599i 0.0404237 0.999183i \(-0.487129\pi\)
0.885529 + 0.464583i \(0.153796\pi\)
\(354\) 0 0
\(355\) 20.3791 35.2977i 1.08161 1.87340i
\(356\) 1.44227i 0.0764399i
\(357\) 0 0
\(358\) −6.32136 + 3.64964i −0.334094 + 0.192890i
\(359\) −13.0346 + 7.52551i −0.687938 + 0.397181i −0.802839 0.596196i \(-0.796678\pi\)
0.114901 + 0.993377i \(0.463345\pi\)
\(360\) 0 0
\(361\) −9.05455 15.6829i −0.476555 0.825418i
\(362\) 20.8378i 1.09521i
\(363\) 0 0
\(364\) −1.75537 + 0.465248i −0.0920064 + 0.0243856i
\(365\) −2.71331 −0.142021
\(366\) 0 0
\(367\) −4.50178 7.79731i −0.234991 0.407016i 0.724279 0.689507i \(-0.242173\pi\)
−0.959270 + 0.282491i \(0.908839\pi\)
\(368\) −5.90223 −0.307675
\(369\) 0 0
\(370\) −4.38956 + 2.53431i −0.228202 + 0.131753i
\(371\) 0.0279677 0.209784i 0.00145201 0.0108914i
\(372\) 0 0
\(373\) 8.06953 13.9768i 0.417824 0.723693i −0.577896 0.816110i \(-0.696126\pi\)
0.995720 + 0.0924174i \(0.0294594\pi\)
\(374\) −6.65611 11.5287i −0.344179 0.596136i
\(375\) 0 0
\(376\) 1.31742 + 2.28184i 0.0679409 + 0.117677i
\(377\) 8.89057 11.5606i 0.457888 0.595400i
\(378\) 0 0
\(379\) −13.5668 7.83277i −0.696878 0.402342i 0.109306 0.994008i \(-0.465137\pi\)
−0.806183 + 0.591666i \(0.798471\pi\)
\(380\) −0.641068 −0.0328861
\(381\) 0 0
\(382\) −5.52935 3.19237i −0.282906 0.163336i
\(383\) −21.3327 12.3164i −1.09005 0.629339i −0.156459 0.987685i \(-0.550008\pi\)
−0.933589 + 0.358345i \(0.883341\pi\)
\(384\) 0 0
\(385\) 1.59502 11.9641i 0.0812896 0.609747i
\(386\) −14.1512 24.5106i −0.720277 1.24756i
\(387\) 0 0
\(388\) −0.0788960 + 0.0455506i −0.00400534 + 0.00231248i
\(389\) 9.42834 16.3304i 0.478036 0.827982i −0.521647 0.853161i \(-0.674682\pi\)
0.999683 + 0.0251791i \(0.00801560\pi\)
\(390\) 0 0
\(391\) 12.7486 0.644724
\(392\) −14.5368 14.6323i −0.734221 0.739040i
\(393\) 0 0
\(394\) −3.90929 + 6.77108i −0.196947 + 0.341122i
\(395\) −8.82229 5.09355i −0.443897 0.256284i
\(396\) 0 0
\(397\) −12.5600 7.25149i −0.630366 0.363942i 0.150528 0.988606i \(-0.451903\pi\)
−0.780894 + 0.624664i \(0.785236\pi\)
\(398\) 14.2839i 0.715985i
\(399\) 0 0
\(400\) −13.8467 + 23.9831i −0.692333 + 1.19916i
\(401\) 20.9889i 1.04814i −0.851676 0.524069i \(-0.824413\pi\)
0.851676 0.524069i \(-0.175587\pi\)
\(402\) 0 0
\(403\) 14.7255 + 11.3245i 0.733531 + 0.564116i
\(404\) −0.273971 0.474532i −0.0136306 0.0236089i
\(405\) 0 0
\(406\) 14.2699 + 1.90241i 0.708201 + 0.0944152i
\(407\) 0.675191 + 1.16947i 0.0334680 + 0.0579683i
\(408\) 0 0
\(409\) 21.4276i 1.05953i 0.848146 + 0.529763i \(0.177719\pi\)
−0.848146 + 0.529763i \(0.822281\pi\)
\(410\) 20.1521i 0.995242i
\(411\) 0 0
\(412\) −1.07891 1.86873i −0.0531542 0.0920657i
\(413\) −11.2796 27.3580i −0.555035 1.34620i
\(414\) 0 0
\(415\) −4.14723 7.18321i −0.203580 0.352610i
\(416\) 0.509155 3.83545i 0.0249634 0.188048i
\(417\) 0 0
\(418\) 1.62357i 0.0794113i
\(419\) 3.98203 6.89708i 0.194535 0.336944i −0.752213 0.658920i \(-0.771014\pi\)
0.946748 + 0.321976i \(0.104347\pi\)
\(420\) 0 0
\(421\) 2.81786i 0.137334i −0.997640 0.0686670i \(-0.978125\pi\)
0.997640 0.0686670i \(-0.0218746\pi\)
\(422\) −5.43530 3.13807i −0.264586 0.152759i
\(423\) 0 0
\(424\) 0.204122 + 0.117850i 0.00991306 + 0.00572331i
\(425\) 29.9082 51.8026i 1.45076 2.51279i
\(426\) 0 0
\(427\) −2.66555 + 19.9941i −0.128995 + 0.967582i
\(428\) 1.25110 0.0604742
\(429\) 0 0
\(430\) −9.19253 + 15.9219i −0.443303 + 0.767823i
\(431\) −4.96775 + 2.86813i −0.239288 + 0.138153i −0.614849 0.788645i \(-0.710783\pi\)
0.375561 + 0.926797i \(0.377450\pi\)
\(432\) 0 0
\(433\) −12.2628 21.2398i −0.589314 1.02072i −0.994322 0.106409i \(-0.966065\pi\)
0.405009 0.914313i \(-0.367268\pi\)
\(434\) −2.42324 + 18.1765i −0.116319 + 0.872502i
\(435\) 0 0
\(436\) −0.962653 0.555788i −0.0461027 0.0266174i
\(437\) 1.34652 + 0.777413i 0.0644128 + 0.0371887i
\(438\) 0 0
\(439\) −36.6423 −1.74884 −0.874420 0.485169i \(-0.838758\pi\)
−0.874420 + 0.485169i \(0.838758\pi\)
\(440\) 11.6412 + 6.72108i 0.554975 + 0.320415i
\(441\) 0 0
\(442\) 4.93973 37.2108i 0.234959 1.76994i
\(443\) 13.5467 + 23.4635i 0.643622 + 1.11479i 0.984618 + 0.174721i \(0.0559022\pi\)
−0.340996 + 0.940065i \(0.610764\pi\)
\(444\) 0 0
\(445\) 13.5152 + 23.4090i 0.640682 + 1.10969i
\(446\) 16.2943 28.2226i 0.771558 1.33638i
\(447\) 0 0
\(448\) 21.0592 8.68267i 0.994953 0.410218i
\(449\) −23.7571 + 13.7162i −1.12117 + 0.647307i −0.941699 0.336456i \(-0.890772\pi\)
−0.179470 + 0.983764i \(0.557438\pi\)
\(450\) 0 0
\(451\) 5.36892 0.252812
\(452\) 0.621768 + 1.07693i 0.0292455 + 0.0506547i
\(453\) 0 0
\(454\) −20.6832 −0.970712
\(455\) 24.1312 24.0006i 1.13129 1.12516i
\(456\) 0 0
\(457\) 39.6639i 1.85540i −0.373327 0.927700i \(-0.621783\pi\)
0.373327 0.927700i \(-0.378217\pi\)
\(458\) 10.9982 + 19.0495i 0.513913 + 0.890123i
\(459\) 0 0
\(460\) −0.968913 + 0.559402i −0.0451758 + 0.0260823i
\(461\) 4.23988 2.44790i 0.197471 0.114010i −0.398004 0.917384i \(-0.630297\pi\)
0.595475 + 0.803374i \(0.296964\pi\)
\(462\) 0 0
\(463\) 4.71193i 0.218982i 0.993988 + 0.109491i \(0.0349221\pi\)
−0.993988 + 0.109491i \(0.965078\pi\)
\(464\) −7.24638 + 12.5511i −0.336405 + 0.582670i
\(465\) 0 0
\(466\) 33.9140 19.5803i 1.57104 0.907038i
\(467\) −16.0081 27.7268i −0.740765 1.28304i −0.952147 0.305639i \(-0.901130\pi\)
0.211383 0.977403i \(-0.432203\pi\)
\(468\) 0 0
\(469\) −10.2025 + 13.2513i −0.471110 + 0.611887i
\(470\) −3.71678 2.14588i −0.171442 0.0989822i
\(471\) 0 0
\(472\) 32.9563 1.51693
\(473\) 4.24191 + 2.44907i 0.195043 + 0.112608i
\(474\) 0 0
\(475\) 6.31788 3.64763i 0.289884 0.167365i
\(476\) −3.60366 + 1.48578i −0.165174 + 0.0681008i
\(477\) 0 0
\(478\) −11.6417 −0.532480
\(479\) −15.6097 + 9.01224i −0.713224 + 0.411780i −0.812254 0.583305i \(-0.801759\pi\)
0.0990298 + 0.995084i \(0.468426\pi\)
\(480\) 0 0
\(481\) −0.501083 + 3.77464i −0.0228474 + 0.172109i
\(482\) −24.4807 −1.11506
\(483\) 0 0
\(484\) −0.891390 + 1.54393i −0.0405177 + 0.0701788i
\(485\) 0.853693 1.47864i 0.0387642 0.0671416i
\(486\) 0 0
\(487\) 17.6004i 0.797550i 0.917049 + 0.398775i \(0.130565\pi\)
−0.917049 + 0.398775i \(0.869435\pi\)
\(488\) −19.4545 11.2321i −0.880666 0.508453i
\(489\) 0 0
\(490\) 32.4229 + 8.80146i 1.46472 + 0.397609i
\(491\) −1.93180 + 3.34598i −0.0871810 + 0.151002i −0.906318 0.422595i \(-0.861119\pi\)
0.819138 + 0.573597i \(0.194453\pi\)
\(492\) 0 0
\(493\) 15.6519 27.1099i 0.704926 1.22097i
\(494\) 2.79087 3.62902i 0.125567 0.163277i
\(495\) 0 0
\(496\) −15.9872 9.23023i −0.717848 0.414450i
\(497\) 18.4390 23.9490i 0.827103 1.07426i
\(498\) 0 0
\(499\) −10.9528 + 6.32363i −0.490317 + 0.283084i −0.724706 0.689058i \(-0.758024\pi\)
0.234389 + 0.972143i \(0.424691\pi\)
\(500\) 1.85351i 0.0828917i
\(501\) 0 0
\(502\) −18.4908 + 10.6757i −0.825287 + 0.476480i
\(503\) 11.0180 + 19.0837i 0.491268 + 0.850902i 0.999949 0.0100533i \(-0.00320011\pi\)
−0.508681 + 0.860955i \(0.669867\pi\)
\(504\) 0 0
\(505\) 8.89351 + 5.13467i 0.395756 + 0.228490i
\(506\) −1.41674 2.45387i −0.0629818 0.109088i
\(507\) 0 0
\(508\) 1.40075 2.42617i 0.0621482 0.107644i
\(509\) 15.6702i 0.694568i 0.937760 + 0.347284i \(0.112896\pi\)
−0.937760 + 0.347284i \(0.887104\pi\)
\(510\) 0 0
\(511\) −1.99446 0.265895i −0.0882299 0.0117625i
\(512\) 24.9600i 1.10309i
\(513\) 0 0
\(514\) 32.7249i 1.44344i
\(515\) 35.0230 + 20.2206i 1.54330 + 0.891025i
\(516\) 0 0
\(517\) −0.571705 + 0.990222i −0.0251436 + 0.0435499i
\(518\) −3.47497 + 1.43272i −0.152681 + 0.0629503i
\(519\) 0 0
\(520\) 14.4673 + 35.0341i 0.634435 + 1.53635i
\(521\) −12.6207 + 21.8598i −0.552925 + 0.957694i 0.445137 + 0.895463i \(0.353155\pi\)
−0.998062 + 0.0622317i \(0.980178\pi\)
\(522\) 0 0
\(523\) −13.2477 −0.579279 −0.289640 0.957136i \(-0.593535\pi\)
−0.289640 + 0.957136i \(0.593535\pi\)
\(524\) 1.06479 + 1.84426i 0.0465154 + 0.0805670i
\(525\) 0 0
\(526\) 17.9812 10.3815i 0.784019 0.452654i
\(527\) 34.5318 + 19.9369i 1.50423 + 0.868466i
\(528\) 0 0
\(529\) −20.2865 −0.882021
\(530\) −0.383920 −0.0166764
\(531\) 0 0
\(532\) −0.471226 0.0628224i −0.0204303 0.00272370i
\(533\) 12.0007 + 9.22903i 0.519807 + 0.399754i
\(534\) 0 0
\(535\) −20.3063 + 11.7238i −0.877916 + 0.506865i
\(536\) −9.31258 16.1299i −0.402242 0.696704i
\(537\) 0 0
\(538\) 17.5427i 0.756320i
\(539\) 2.34488 8.63809i 0.101001 0.372069i
\(540\) 0 0
\(541\) −12.4737 + 7.20170i −0.536287 + 0.309625i −0.743573 0.668655i \(-0.766870\pi\)
0.207286 + 0.978280i \(0.433537\pi\)
\(542\) 36.2816 1.55843
\(543\) 0 0
\(544\) 8.30488i 0.356069i
\(545\) 20.8328 0.892377
\(546\) 0 0
\(547\) 2.00679 0.0858042 0.0429021 0.999079i \(-0.486340\pi\)
0.0429021 + 0.999079i \(0.486340\pi\)
\(548\) 3.35631i 0.143375i
\(549\) 0 0
\(550\) −13.2947 −0.566889
\(551\) 3.30634 1.90892i 0.140855 0.0813226i
\(552\) 0 0
\(553\) −5.98581 4.60864i −0.254542 0.195979i
\(554\) 17.0863i 0.725928i
\(555\) 0 0
\(556\) 0.557497 + 0.965614i 0.0236432 + 0.0409512i
\(557\) 7.42977 4.28958i 0.314810 0.181755i −0.334267 0.942478i \(-0.608489\pi\)
0.649077 + 0.760723i \(0.275155\pi\)
\(558\) 0 0
\(559\) 5.27170 + 12.7659i 0.222969 + 0.539942i
\(560\) −20.6333 + 26.7989i −0.871915 + 1.13246i
\(561\) 0 0
\(562\) −35.9466 −1.51631
\(563\) −12.7744 −0.538375 −0.269188 0.963088i \(-0.586755\pi\)
−0.269188 + 0.963088i \(0.586755\pi\)
\(564\) 0 0
\(565\) −20.1835 11.6530i −0.849126 0.490243i
\(566\) 17.1747 9.91583i 0.721908 0.416794i
\(567\) 0 0
\(568\) 16.8306 + 29.1515i 0.706196 + 1.22317i
\(569\) −5.79116 −0.242778 −0.121389 0.992605i \(-0.538735\pi\)
−0.121389 + 0.992605i \(0.538735\pi\)
\(570\) 0 0
\(571\) −22.0666 + 38.2204i −0.923458 + 1.59948i −0.129435 + 0.991588i \(0.541316\pi\)
−0.794023 + 0.607888i \(0.792017\pi\)
\(572\) 0.811204 0.334987i 0.0339182 0.0140065i
\(573\) 0 0
\(574\) −1.97484 + 14.8131i −0.0824281 + 0.618287i
\(575\) 6.36592 11.0261i 0.265477 0.459820i
\(576\) 0 0
\(577\) 10.3343 + 5.96649i 0.430221 + 0.248388i 0.699441 0.714691i \(-0.253432\pi\)
−0.269220 + 0.963079i \(0.586766\pi\)
\(578\) 57.7037i 2.40016i
\(579\) 0 0
\(580\) 2.74719i 0.114071i
\(581\) −2.34455 5.68654i −0.0972685 0.235918i
\(582\) 0 0
\(583\) 0.102284i 0.00423617i
\(584\) 1.12043 1.94064i 0.0463637 0.0803043i
\(585\) 0 0
\(586\) −7.79091 13.4943i −0.321840 0.557443i
\(587\) −17.6250 10.1758i −0.727462 0.420000i 0.0900312 0.995939i \(-0.471303\pi\)
−0.817493 + 0.575939i \(0.804637\pi\)
\(588\) 0 0
\(589\) 2.43152 + 4.21152i 0.100189 + 0.173533i
\(590\) −46.4889 + 26.8404i −1.91392 + 1.10500i
\(591\) 0 0
\(592\) 3.78397i 0.155520i
\(593\) −15.7443 + 9.09000i −0.646543 + 0.373282i −0.787130 0.616787i \(-0.788434\pi\)
0.140588 + 0.990068i \(0.455101\pi\)
\(594\) 0 0
\(595\) 44.5670 57.8846i 1.82707 2.37304i
\(596\) −1.72759 0.997422i −0.0707646 0.0408560i
\(597\) 0 0
\(598\) 1.05141 7.92026i 0.0429955 0.323884i
\(599\) −19.1341 + 33.1412i −0.781797 + 1.35411i 0.149096 + 0.988823i \(0.452364\pi\)
−0.930894 + 0.365290i \(0.880970\pi\)
\(600\) 0 0
\(601\) 13.4360 23.2718i 0.548064 0.949275i −0.450343 0.892856i \(-0.648698\pi\)
0.998407 0.0564195i \(-0.0179684\pi\)
\(602\) −8.31740 + 10.8028i −0.338992 + 0.440290i
\(603\) 0 0
\(604\) −0.777170 0.448699i −0.0316226 0.0182573i
\(605\) 33.4122i 1.35840i
\(606\) 0 0
\(607\) 4.70105 8.14245i 0.190810 0.330492i −0.754709 0.656059i \(-0.772222\pi\)
0.945519 + 0.325568i \(0.105555\pi\)
\(608\) 0.506435 0.877171i 0.0205386 0.0355740i
\(609\) 0 0
\(610\) 36.5908 1.48152
\(611\) −2.98005 + 1.23061i −0.120560 + 0.0497853i
\(612\) 0 0
\(613\) 11.5089 6.64469i 0.464842 0.268376i −0.249236 0.968443i \(-0.580180\pi\)
0.714078 + 0.700066i \(0.246846\pi\)
\(614\) 39.4602 1.59248
\(615\) 0 0
\(616\) 7.89843 + 6.08123i 0.318237 + 0.245020i
\(617\) 9.72211 5.61306i 0.391397 0.225973i −0.291368 0.956611i \(-0.594110\pi\)
0.682765 + 0.730638i \(0.260777\pi\)
\(618\) 0 0
\(619\) −8.04109 4.64253i −0.323199 0.186599i 0.329619 0.944114i \(-0.393080\pi\)
−0.652817 + 0.757515i \(0.726413\pi\)
\(620\) −3.49929 −0.140535
\(621\) 0 0
\(622\) −0.175512 0.101332i −0.00703740 0.00406304i
\(623\) 7.64055 + 18.5316i 0.306112 + 0.742453i
\(624\) 0 0
\(625\) 1.95363 + 3.38379i 0.0781452 + 0.135351i
\(626\) 12.2571 7.07665i 0.489893 0.282840i
\(627\) 0 0
\(628\) −0.856848 + 1.48410i −0.0341920 + 0.0592222i
\(629\) 8.17322i 0.325888i
\(630\) 0 0
\(631\) 9.00894 5.20132i 0.358640 0.207061i −0.309844 0.950787i \(-0.600277\pi\)
0.668484 + 0.743726i \(0.266943\pi\)
\(632\) 7.28611 4.20664i 0.289826 0.167331i
\(633\) 0 0
\(634\) 1.01347 + 1.75538i 0.0402499 + 0.0697149i
\(635\) 52.5046i 2.08358i
\(636\) 0 0
\(637\) 20.0900 15.2772i 0.795994 0.605305i
\(638\) −6.95754 −0.275452
\(639\) 0 0
\(640\) −16.8322 29.1542i −0.665351 1.15242i
\(641\) 14.8591 0.586899 0.293449 0.955975i \(-0.405197\pi\)
0.293449 + 0.955975i \(0.405197\pi\)
\(642\) 0 0
\(643\) 1.98945 1.14861i 0.0784563 0.0452968i −0.460259 0.887785i \(-0.652243\pi\)
0.538715 + 0.842488i \(0.318910\pi\)
\(644\) −0.767033 + 0.316247i −0.0302254 + 0.0124619i
\(645\) 0 0
\(646\) 4.91334 8.51016i 0.193313 0.334828i
\(647\) −3.99932 6.92703i −0.157230 0.272330i 0.776639 0.629946i \(-0.216923\pi\)
−0.933869 + 0.357616i \(0.883590\pi\)
\(648\) 0 0
\(649\) 7.15081 + 12.3856i 0.280694 + 0.486176i
\(650\) −29.7166 22.8533i −1.16558 0.896380i
\(651\) 0 0
\(652\) 1.98368 + 1.14528i 0.0776871 + 0.0448526i
\(653\) −3.98444 −0.155923 −0.0779615 0.996956i \(-0.524841\pi\)
−0.0779615 + 0.996956i \(0.524841\pi\)
\(654\) 0 0
\(655\) −34.5645 19.9558i −1.35055 0.779738i
\(656\) −13.0289 7.52225i −0.508694 0.293695i
\(657\) 0 0
\(658\) −2.52178 1.94159i −0.0983094 0.0756912i
\(659\) −13.7501 23.8159i −0.535629 0.927737i −0.999133 0.0416417i \(-0.986741\pi\)
0.463504 0.886095i \(-0.346592\pi\)
\(660\) 0 0
\(661\) 6.05023 3.49310i 0.235327 0.135866i −0.377700 0.925928i \(-0.623285\pi\)
0.613027 + 0.790062i \(0.289952\pi\)
\(662\) −16.9841 + 29.4173i −0.660105 + 1.14333i
\(663\) 0 0
\(664\) 6.85019 0.265839
\(665\) 8.23704 3.39612i 0.319419 0.131696i
\(666\) 0 0
\(667\) 3.33148 5.77029i 0.128995 0.223427i
\(668\) 3.20195 + 1.84865i 0.123887 + 0.0715263i
\(669\) 0 0
\(670\) 26.2731 + 15.1688i 1.01502 + 0.586022i
\(671\) 9.74849i 0.376336i
\(672\) 0 0
\(673\) 2.72783 4.72474i 0.105150 0.182125i −0.808649 0.588291i \(-0.799801\pi\)
0.913800 + 0.406166i \(0.133134\pi\)
\(674\) 43.2909i 1.66750i
\(675\) 0 0
\(676\) 2.38905 + 0.645671i 0.0918866 + 0.0248335i
\(677\) 16.8961 + 29.2649i 0.649371 + 1.12474i 0.983273 + 0.182135i \(0.0583009\pi\)
−0.333903 + 0.942607i \(0.608366\pi\)
\(678\) 0 0
\(679\) 0.772421 1.00324i 0.0296428 0.0385007i
\(680\) 40.6795 + 70.4590i 1.55999 + 2.70198i
\(681\) 0 0
\(682\) 8.86231i 0.339355i
\(683\) 12.2988i 0.470602i −0.971923 0.235301i \(-0.924392\pi\)
0.971923 0.235301i \(-0.0756076\pi\)
\(684\) 0 0
\(685\) 31.4514 + 54.4754i 1.20170 + 2.08140i
\(686\) 22.9704 + 9.64698i 0.877015 + 0.368323i
\(687\) 0 0
\(688\) −6.86265 11.8865i −0.261636 0.453167i
\(689\) −0.175823 + 0.228627i −0.00669834 + 0.00870998i
\(690\) 0 0
\(691\) 11.0897i 0.421871i 0.977500 + 0.210935i \(0.0676509\pi\)
−0.977500 + 0.210935i \(0.932349\pi\)
\(692\) −1.36869 + 2.37064i −0.0520297 + 0.0901181i
\(693\) 0 0
\(694\) 33.3129i 1.26454i
\(695\) −18.0972 10.4484i −0.686465 0.396331i
\(696\) 0 0
\(697\) 28.1419 + 16.2478i 1.06595 + 0.615428i
\(698\) −7.77247 + 13.4623i −0.294193 + 0.509556i
\(699\) 0 0
\(700\) −0.514427 + 3.85868i −0.0194435 + 0.145844i
\(701\) −10.6470 −0.402133 −0.201066 0.979578i \(-0.564441\pi\)
−0.201066 + 0.979578i \(0.564441\pi\)
\(702\) 0 0
\(703\) −0.498406 + 0.863265i −0.0187977 + 0.0325587i
\(704\) −9.53396 + 5.50443i −0.359325 + 0.207456i
\(705\) 0 0
\(706\) −13.5117 23.4030i −0.508521 0.880784i
\(707\) 6.03413 + 4.64585i 0.226937 + 0.174725i
\(708\) 0 0
\(709\) 35.2532 + 20.3535i 1.32396 + 0.764391i 0.984358 0.176178i \(-0.0563733\pi\)
0.339605 + 0.940568i \(0.389707\pi\)
\(710\) −47.4833 27.4145i −1.78202 1.02885i
\(711\) 0 0
\(712\) −22.3237 −0.836618
\(713\) 7.35003 + 4.24354i 0.275261 + 0.158922i
\(714\) 0 0
\(715\) −10.0273 + 13.0387i −0.375001 + 0.487621i
\(716\) −0.516470 0.894552i −0.0193014 0.0334310i
\(717\) 0 0
\(718\) 10.1235 + 17.5344i 0.377806 + 0.654380i
\(719\) 4.88769 8.46572i 0.182280 0.315718i −0.760377 0.649482i \(-0.774986\pi\)
0.942657 + 0.333764i \(0.108319\pi\)
\(720\) 0 0
\(721\) 23.7627 + 18.2956i 0.884968 + 0.681363i
\(722\) −21.0971 + 12.1804i −0.785153 + 0.453308i
\(723\) 0 0
\(724\) −2.94881 −0.109592
\(725\) −15.6313 27.0743i −0.580533 1.00551i
\(726\) 0 0
\(727\) −12.2091 −0.452811 −0.226406 0.974033i \(-0.572697\pi\)
−0.226406 + 0.974033i \(0.572697\pi\)
\(728\) 7.20122 + 27.1701i 0.266895 + 1.00699i
\(729\) 0 0
\(730\) 3.65002i 0.135093i
\(731\) 14.8231 + 25.6743i 0.548251 + 0.949598i
\(732\) 0 0
\(733\) −19.3256 + 11.1577i −0.713809 + 0.412118i −0.812470 0.583003i \(-0.801877\pi\)
0.0986608 + 0.995121i \(0.468544\pi\)
\(734\) −10.4891 + 6.05591i −0.387161 + 0.223528i
\(735\) 0 0
\(736\) 1.76768i 0.0651576i
\(737\) 4.04126 6.99968i 0.148862 0.257836i
\(738\) 0 0
\(739\) −36.6960 + 21.1865i −1.34989 + 0.779357i −0.988233 0.152956i \(-0.951121\pi\)
−0.361653 + 0.932313i \(0.617787\pi\)
\(740\) −0.358637 0.621178i −0.0131838 0.0228350i
\(741\) 0 0
\(742\) −0.282206 0.0376229i −0.0103601 0.00138118i
\(743\) 26.8296 + 15.4901i 0.984282 + 0.568276i 0.903560 0.428461i \(-0.140944\pi\)
0.0807220 + 0.996737i \(0.474277\pi\)
\(744\) 0 0
\(745\) 37.3866 1.36974
\(746\) −18.8020 10.8553i −0.688390 0.397442i
\(747\) 0 0
\(748\) 1.63146 0.941923i 0.0596520 0.0344401i
\(749\) −16.0753 + 6.62783i −0.587379 + 0.242176i
\(750\) 0 0
\(751\) −22.5660 −0.823444 −0.411722 0.911309i \(-0.635073\pi\)
−0.411722 + 0.911309i \(0.635073\pi\)
\(752\) 2.77475 1.60200i 0.101185 0.0584190i
\(753\) 0 0
\(754\) −15.5516 11.9598i −0.566356 0.435551i
\(755\) 16.8187 0.612095
\(756\) 0 0
\(757\) −16.1404 + 27.9560i −0.586633 + 1.01608i 0.408037 + 0.912965i \(0.366213\pi\)
−0.994670 + 0.103112i \(0.967120\pi\)
\(758\) −10.5368 + 18.2504i −0.382716 + 0.662883i
\(759\) 0 0
\(760\) 9.92260i 0.359931i
\(761\) 25.7657 + 14.8758i 0.934006 + 0.539249i 0.888076 0.459696i \(-0.152042\pi\)
0.0459296 + 0.998945i \(0.485375\pi\)
\(762\) 0 0
\(763\) 15.3134 + 2.04154i 0.554383 + 0.0739086i
\(764\) 0.451761 0.782473i 0.0163441 0.0283089i
\(765\) 0 0
\(766\) −16.5684 + 28.6972i −0.598639 + 1.03687i
\(767\) −5.30687 + 39.9764i −0.191620 + 1.44347i
\(768\) 0 0
\(769\) −36.2090 20.9053i −1.30573 0.753863i −0.324349 0.945938i \(-0.605145\pi\)
−0.981380 + 0.192075i \(0.938478\pi\)
\(770\) −16.0944 2.14566i −0.580003 0.0773242i
\(771\) 0 0
\(772\) 3.46856 2.00257i 0.124836 0.0720742i
\(773\) 41.4336i 1.49026i 0.666917 + 0.745132i \(0.267613\pi\)
−0.666917 + 0.745132i \(0.732387\pi\)
\(774\) 0 0
\(775\) 34.4864 19.9107i 1.23879 0.715215i
\(776\) 0.705044 + 1.22117i 0.0253096 + 0.0438375i
\(777\) 0 0
\(778\) −21.9680 12.6832i −0.787592 0.454716i
\(779\) 1.98159 + 3.43221i 0.0709978 + 0.122972i
\(780\) 0 0
\(781\) −7.30376 + 12.6505i −0.261349 + 0.452670i
\(782\) 17.1497i 0.613273i
\(783\) 0 0
\(784\) −17.7930 + 17.6770i −0.635464 + 0.631320i
\(785\) 32.1175i 1.14632i
\(786\) 0 0
\(787\) 23.8627i 0.850612i −0.905050 0.425306i \(-0.860167\pi\)
0.905050 0.425306i \(-0.139833\pi\)
\(788\) −0.958193 0.553213i −0.0341342