Properties

Label 585.2.bu.c.316.2
Level $585$
Weight $2$
Character 585.316
Analytic conductor $4.671$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bu (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.2
Root \(1.40994 - 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 585.316
Dual form 585.2.bu.c.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.05628 - 0.609843i) q^{2} +(-0.256182 - 0.443720i) q^{4} -1.00000i q^{5} +(3.11786 - 1.80010i) q^{7} +3.06430i q^{8} +O(q^{10})\) \(q+(-1.05628 - 0.609843i) q^{2} +(-0.256182 - 0.443720i) q^{4} -1.00000i q^{5} +(3.11786 - 1.80010i) q^{7} +3.06430i q^{8} +(-0.609843 + 1.05628i) q^{10} +(4.65213 + 2.68591i) q^{11} +(1.81988 + 3.11256i) q^{13} -4.39111 q^{14} +(1.35638 - 2.34932i) q^{16} +(0.565928 + 0.980215i) q^{17} +(-1.96410 + 1.13397i) q^{19} +(-0.443720 + 0.256182i) q^{20} +(-3.27597 - 5.67414i) q^{22} +(1.94644 - 3.37133i) q^{23} -1.00000 q^{25} +(-0.0241312 - 4.39758i) q^{26} +(-1.59748 - 0.922305i) q^{28} +(-0.0123639 + 0.0214150i) q^{29} -5.46410i q^{31} +(2.44209 - 1.40994i) q^{32} -1.38051i q^{34} +(-1.80010 - 3.11786i) q^{35} +(7.53794 + 4.35203i) q^{37} +2.76619 q^{38} +3.06430 q^{40} +(-3.23205 - 1.86603i) q^{41} +(-0.565928 - 0.980215i) q^{43} -2.75232i q^{44} +(-4.11196 + 2.37404i) q^{46} -2.58535i q^{47} +(2.98070 - 5.16273i) q^{49} +(1.05628 + 0.609843i) q^{50} +(0.914884 - 1.60490i) q^{52} +4.43937 q^{53} +(2.68591 - 4.65213i) q^{55} +(5.51603 + 9.55405i) q^{56} +(0.0261196 - 0.0150801i) q^{58} +(0.148458 - 0.0857123i) q^{59} +(-1.68012 - 2.91005i) q^{61} +(-3.33225 + 5.77162i) q^{62} -8.86488 q^{64} +(3.11256 - 1.81988i) q^{65} +(5.54239 + 3.19990i) q^{67} +(0.289961 - 0.502227i) q^{68} +4.39111i q^{70} +(-9.35076 + 5.39866i) q^{71} -4.70308i q^{73} +(-5.30812 - 9.19393i) q^{74} +(1.00633 + 0.581008i) q^{76} +19.3396 q^{77} -11.9826 q^{79} +(-2.34932 - 1.35638i) q^{80} +(2.27597 + 3.94209i) q^{82} -12.1286i q^{83} +(0.980215 - 0.565928i) q^{85} +1.38051i q^{86} +(-8.23042 + 14.2555i) q^{88} +(-13.9898 - 8.07702i) q^{89} +(11.2771 + 6.42856i) q^{91} -1.99457 q^{92} +(-1.57666 + 2.73086i) q^{94} +(1.13397 + 1.96410i) q^{95} +(-10.5379 + 6.08408i) q^{97} +(-6.29692 + 3.63553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} - 6 q^{7} + O(q^{10}) \) \( 8 q + 2 q^{4} - 6 q^{7} - 2 q^{10} - 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} - 12 q^{20} - 12 q^{22} + 10 q^{23} - 8 q^{25} - 10 q^{26} - 18 q^{28} + 8 q^{29} - 6 q^{32} - 10 q^{35} + 6 q^{37} + 16 q^{38} - 12 q^{40} - 12 q^{41} - 2 q^{43} - 42 q^{46} + 12 q^{49} - 6 q^{52} + 24 q^{53} - 12 q^{56} + 36 q^{58} + 12 q^{59} - 28 q^{61} - 4 q^{62} - 8 q^{64} + 8 q^{65} + 6 q^{67} + 14 q^{68} - 10 q^{74} + 54 q^{76} + 36 q^{77} - 16 q^{79} + 4 q^{82} + 18 q^{85} - 18 q^{88} - 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 16 q^{95} - 30 q^{97} - 72 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.05628 0.609843i −0.746903 0.431224i 0.0776710 0.996979i \(-0.475252\pi\)
−0.824574 + 0.565755i \(0.808585\pi\)
\(3\) 0 0
\(4\) −0.256182 0.443720i −0.128091 0.221860i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 3.11786 1.80010i 1.17844 0.680373i 0.222787 0.974867i \(-0.428484\pi\)
0.955653 + 0.294494i \(0.0951511\pi\)
\(8\) 3.06430i 1.08339i
\(9\) 0 0
\(10\) −0.609843 + 1.05628i −0.192849 + 0.334025i
\(11\) 4.65213 + 2.68591i 1.40267 + 0.809832i 0.994666 0.103149i \(-0.0328917\pi\)
0.408004 + 0.912980i \(0.366225\pi\)
\(12\) 0 0
\(13\) 1.81988 + 3.11256i 0.504745 + 0.863269i
\(14\) −4.39111 −1.17357
\(15\) 0 0
\(16\) 1.35638 2.34932i 0.339094 0.587329i
\(17\) 0.565928 + 0.980215i 0.137258 + 0.237737i 0.926458 0.376399i \(-0.122838\pi\)
−0.789200 + 0.614136i \(0.789505\pi\)
\(18\) 0 0
\(19\) −1.96410 + 1.13397i −0.450596 + 0.260152i −0.708082 0.706130i \(-0.750439\pi\)
0.257486 + 0.966282i \(0.417106\pi\)
\(20\) −0.443720 + 0.256182i −0.0992188 + 0.0572840i
\(21\) 0 0
\(22\) −3.27597 5.67414i −0.698438 1.20973i
\(23\) 1.94644 3.37133i 0.405860 0.702970i −0.588561 0.808453i \(-0.700305\pi\)
0.994421 + 0.105483i \(0.0336387\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −0.0241312 4.39758i −0.00473251 0.862436i
\(27\) 0 0
\(28\) −1.59748 0.922305i −0.301895 0.174299i
\(29\) −0.0123639 + 0.0214150i −0.00229593 + 0.00397666i −0.867171 0.498010i \(-0.834064\pi\)
0.864875 + 0.501987i \(0.167397\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i −0.871334 0.490691i \(-0.836744\pi\)
0.871334 0.490691i \(-0.163256\pi\)
\(32\) 2.44209 1.40994i 0.431705 0.249245i
\(33\) 0 0
\(34\) 1.38051i 0.236755i
\(35\) −1.80010 3.11786i −0.304272 0.527015i
\(36\) 0 0
\(37\) 7.53794 + 4.35203i 1.23923 + 0.715470i 0.968937 0.247309i \(-0.0795462\pi\)
0.270293 + 0.962778i \(0.412879\pi\)
\(38\) 2.76619 0.448735
\(39\) 0 0
\(40\) 3.06430 0.484508
\(41\) −3.23205 1.86603i −0.504762 0.291424i 0.225916 0.974147i \(-0.427462\pi\)
−0.730678 + 0.682723i \(0.760796\pi\)
\(42\) 0 0
\(43\) −0.565928 0.980215i −0.0863031 0.149481i 0.819643 0.572875i \(-0.194172\pi\)
−0.905946 + 0.423394i \(0.860839\pi\)
\(44\) 2.75232i 0.414929i
\(45\) 0 0
\(46\) −4.11196 + 2.37404i −0.606276 + 0.350034i
\(47\) 2.58535i 0.377113i −0.982062 0.188556i \(-0.939619\pi\)
0.982062 0.188556i \(-0.0603808\pi\)
\(48\) 0 0
\(49\) 2.98070 5.16273i 0.425815 0.737533i
\(50\) 1.05628 + 0.609843i 0.149381 + 0.0862449i
\(51\) 0 0
\(52\) 0.914884 1.60490i 0.126872 0.222560i
\(53\) 4.43937 0.609795 0.304897 0.952385i \(-0.401378\pi\)
0.304897 + 0.952385i \(0.401378\pi\)
\(54\) 0 0
\(55\) 2.68591 4.65213i 0.362168 0.627293i
\(56\) 5.51603 + 9.55405i 0.737111 + 1.27671i
\(57\) 0 0
\(58\) 0.0261196 0.0150801i 0.00342967 0.00198012i
\(59\) 0.148458 0.0857123i 0.0193276 0.0111588i −0.490305 0.871551i \(-0.663115\pi\)
0.509633 + 0.860392i \(0.329781\pi\)
\(60\) 0 0
\(61\) −1.68012 2.91005i −0.215117 0.372594i 0.738192 0.674591i \(-0.235680\pi\)
−0.953309 + 0.301997i \(0.902347\pi\)
\(62\) −3.33225 + 5.77162i −0.423196 + 0.732997i
\(63\) 0 0
\(64\) −8.86488 −1.10811
\(65\) 3.11256 1.81988i 0.386066 0.225729i
\(66\) 0 0
\(67\) 5.54239 + 3.19990i 0.677111 + 0.390930i 0.798766 0.601642i \(-0.205487\pi\)
−0.121655 + 0.992572i \(0.538820\pi\)
\(68\) 0.289961 0.502227i 0.0351629 0.0609040i
\(69\) 0 0
\(70\) 4.39111i 0.524838i
\(71\) −9.35076 + 5.39866i −1.10973 + 0.640703i −0.938760 0.344573i \(-0.888024\pi\)
−0.170971 + 0.985276i \(0.554691\pi\)
\(72\) 0 0
\(73\) 4.70308i 0.550454i −0.961379 0.275227i \(-0.911247\pi\)
0.961379 0.275227i \(-0.0887531\pi\)
\(74\) −5.30812 9.19393i −0.617056 1.06877i
\(75\) 0 0
\(76\) 1.00633 + 0.581008i 0.115435 + 0.0666462i
\(77\) 19.3396 2.20395
\(78\) 0 0
\(79\) −11.9826 −1.34815 −0.674075 0.738663i \(-0.735457\pi\)
−0.674075 + 0.738663i \(0.735457\pi\)
\(80\) −2.34932 1.35638i −0.262661 0.151648i
\(81\) 0 0
\(82\) 2.27597 + 3.94209i 0.251338 + 0.435331i
\(83\) 12.1286i 1.33129i −0.746270 0.665643i \(-0.768157\pi\)
0.746270 0.665643i \(-0.231843\pi\)
\(84\) 0 0
\(85\) 0.980215 0.565928i 0.106319 0.0613835i
\(86\) 1.38051i 0.148864i
\(87\) 0 0
\(88\) −8.23042 + 14.2555i −0.877366 + 1.51964i
\(89\) −13.9898 8.07702i −1.48292 0.856162i −0.483105 0.875562i \(-0.660491\pi\)
−0.999812 + 0.0194001i \(0.993824\pi\)
\(90\) 0 0
\(91\) 11.2771 + 6.42856i 1.18216 + 0.673896i
\(92\) −1.99457 −0.207948
\(93\) 0 0
\(94\) −1.57666 + 2.73086i −0.162620 + 0.281666i
\(95\) 1.13397 + 1.96410i 0.116343 + 0.201513i
\(96\) 0 0
\(97\) −10.5379 + 6.08408i −1.06997 + 0.617745i −0.928172 0.372151i \(-0.878620\pi\)
−0.141794 + 0.989896i \(0.545287\pi\)
\(98\) −6.29692 + 3.63553i −0.636085 + 0.367244i
\(99\) 0 0
\(100\) 0.256182 + 0.443720i 0.0256182 + 0.0443720i
\(101\) 2.02721 3.51122i 0.201714 0.349380i −0.747366 0.664412i \(-0.768682\pi\)
0.949081 + 0.315032i \(0.102015\pi\)
\(102\) 0 0
\(103\) 17.9035 1.76408 0.882041 0.471173i \(-0.156169\pi\)
0.882041 + 0.471173i \(0.156169\pi\)
\(104\) −9.53781 + 5.57666i −0.935259 + 0.546837i
\(105\) 0 0
\(106\) −4.68922 2.70732i −0.455457 0.262958i
\(107\) −4.56593 + 7.90842i −0.441405 + 0.764536i −0.997794 0.0663862i \(-0.978853\pi\)
0.556389 + 0.830922i \(0.312186\pi\)
\(108\) 0 0
\(109\) 7.37605i 0.706498i −0.935529 0.353249i \(-0.885077\pi\)
0.935529 0.353249i \(-0.114923\pi\)
\(110\) −5.67414 + 3.27597i −0.541008 + 0.312351i
\(111\) 0 0
\(112\) 9.76645i 0.922843i
\(113\) 3.53794 + 6.12789i 0.332821 + 0.576463i 0.983064 0.183263i \(-0.0586661\pi\)
−0.650243 + 0.759727i \(0.725333\pi\)
\(114\) 0 0
\(115\) −3.37133 1.94644i −0.314378 0.181506i
\(116\) 0.0126697 0.00117635
\(117\) 0 0
\(118\) −0.209084 −0.0192478
\(119\) 3.52897 + 2.03745i 0.323500 + 0.186773i
\(120\) 0 0
\(121\) 8.92820 + 15.4641i 0.811655 + 1.40583i
\(122\) 4.09843i 0.371055i
\(123\) 0 0
\(124\) −2.42453 + 1.39980i −0.217729 + 0.125706i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −5.71806 + 9.90396i −0.507395 + 0.878835i 0.492568 + 0.870274i \(0.336058\pi\)
−0.999963 + 0.00856072i \(0.997275\pi\)
\(128\) 4.47962 + 2.58631i 0.395946 + 0.228600i
\(129\) 0 0
\(130\) −4.39758 + 0.0241312i −0.385693 + 0.00211644i
\(131\) 10.5680 0.923328 0.461664 0.887055i \(-0.347253\pi\)
0.461664 + 0.887055i \(0.347253\pi\)
\(132\) 0 0
\(133\) −4.08253 + 7.07115i −0.354000 + 0.613146i
\(134\) −3.90288 6.75998i −0.337157 0.583974i
\(135\) 0 0
\(136\) −3.00367 + 1.73417i −0.257563 + 0.148704i
\(137\) −3.27940 + 1.89336i −0.280178 + 0.161761i −0.633504 0.773739i \(-0.718384\pi\)
0.353326 + 0.935500i \(0.385051\pi\)
\(138\) 0 0
\(139\) −1.00693 1.74406i −0.0854068 0.147929i 0.820158 0.572138i \(-0.193886\pi\)
−0.905564 + 0.424209i \(0.860552\pi\)
\(140\) −0.922305 + 1.59748i −0.0779490 + 0.135012i
\(141\) 0 0
\(142\) 13.1694 1.10515
\(143\) 0.106280 + 19.3681i 0.00888757 + 1.61964i
\(144\) 0 0
\(145\) 0.0214150 + 0.0123639i 0.00177842 + 0.00102677i
\(146\) −2.86814 + 4.96777i −0.237369 + 0.411136i
\(147\) 0 0
\(148\) 4.45965i 0.366581i
\(149\) −4.77855 + 2.75890i −0.391474 + 0.226018i −0.682799 0.730607i \(-0.739237\pi\)
0.291324 + 0.956624i \(0.405904\pi\)
\(150\) 0 0
\(151\) 4.88961i 0.397911i −0.980009 0.198956i \(-0.936245\pi\)
0.980009 0.198956i \(-0.0637549\pi\)
\(152\) −3.47484 6.01859i −0.281846 0.488172i
\(153\) 0 0
\(154\) −20.4280 11.7941i −1.64614 0.950397i
\(155\) −5.46410 −0.438887
\(156\) 0 0
\(157\) 10.0405 0.801323 0.400661 0.916226i \(-0.368780\pi\)
0.400661 + 0.916226i \(0.368780\pi\)
\(158\) 12.6570 + 7.30752i 1.00694 + 0.581355i
\(159\) 0 0
\(160\) −1.40994 2.44209i −0.111466 0.193064i
\(161\) 14.0151i 1.10454i
\(162\) 0 0
\(163\) 5.87273 3.39062i 0.459988 0.265574i −0.252051 0.967714i \(-0.581105\pi\)
0.712039 + 0.702140i \(0.247772\pi\)
\(164\) 1.91217i 0.149315i
\(165\) 0 0
\(166\) −7.39654 + 12.8112i −0.574083 + 0.994341i
\(167\) 9.08444 + 5.24490i 0.702975 + 0.405863i 0.808455 0.588559i \(-0.200304\pi\)
−0.105479 + 0.994421i \(0.533638\pi\)
\(168\) 0 0
\(169\) −6.37605 + 11.3290i −0.490466 + 0.871460i
\(170\) −1.38051 −0.105880
\(171\) 0 0
\(172\) −0.289961 + 0.502227i −0.0221093 + 0.0382944i
\(173\) 2.22923 + 3.86113i 0.169485 + 0.293557i 0.938239 0.345988i \(-0.112456\pi\)
−0.768754 + 0.639545i \(0.779123\pi\)
\(174\) 0 0
\(175\) −3.11786 + 1.80010i −0.235688 + 0.136075i
\(176\) 12.6201 7.28621i 0.951275 0.549219i
\(177\) 0 0
\(178\) 9.85143 + 17.0632i 0.738396 + 1.27894i
\(179\) −9.31564 + 16.1352i −0.696284 + 1.20600i 0.273462 + 0.961883i \(0.411831\pi\)
−0.969746 + 0.244116i \(0.921502\pi\)
\(180\) 0 0
\(181\) −18.0900 −1.34462 −0.672310 0.740270i \(-0.734698\pi\)
−0.672310 + 0.740270i \(0.734698\pi\)
\(182\) −7.99131 13.6676i −0.592355 1.01311i
\(183\) 0 0
\(184\) 10.3307 + 5.96446i 0.761593 + 0.439706i
\(185\) 4.35203 7.53794i 0.319968 0.554200i
\(186\) 0 0
\(187\) 6.08012i 0.444622i
\(188\) −1.14717 + 0.662321i −0.0836662 + 0.0483047i
\(189\) 0 0
\(190\) 2.76619i 0.200680i
\(191\) 13.6682 + 23.6740i 0.988994 + 1.71299i 0.622632 + 0.782515i \(0.286063\pi\)
0.366361 + 0.930473i \(0.380603\pi\)
\(192\) 0 0
\(193\) −18.8511 10.8837i −1.35693 0.783425i −0.367723 0.929935i \(-0.619863\pi\)
−0.989209 + 0.146510i \(0.953196\pi\)
\(194\) 14.8413 1.06555
\(195\) 0 0
\(196\) −3.05441 −0.218172
\(197\) 1.46940 + 0.848360i 0.104691 + 0.0604432i 0.551431 0.834220i \(-0.314082\pi\)
−0.446741 + 0.894664i \(0.647415\pi\)
\(198\) 0 0
\(199\) 12.6627 + 21.9325i 0.897637 + 1.55475i 0.830506 + 0.557009i \(0.188051\pi\)
0.0671309 + 0.997744i \(0.478615\pi\)
\(200\) 3.06430i 0.216679i
\(201\) 0 0
\(202\) −4.28259 + 2.47256i −0.301322 + 0.173968i
\(203\) 0.0890252i 0.00624834i
\(204\) 0 0
\(205\) −1.86603 + 3.23205i −0.130329 + 0.225736i
\(206\) −18.9111 10.9183i −1.31760 0.760715i
\(207\) 0 0
\(208\) 9.78083 0.0536711i 0.678179 0.00372142i
\(209\) −12.1830 −0.842716
\(210\) 0 0
\(211\) 0.167753 0.290558i 0.0115486 0.0200028i −0.860193 0.509968i \(-0.829657\pi\)
0.871742 + 0.489965i \(0.162991\pi\)
\(212\) −1.13729 1.96984i −0.0781092 0.135289i
\(213\) 0 0
\(214\) 9.64579 5.56900i 0.659373 0.380689i
\(215\) −0.980215 + 0.565928i −0.0668501 + 0.0385959i
\(216\) 0 0
\(217\) −9.83592 17.0363i −0.667706 1.15650i
\(218\) −4.49824 + 7.79118i −0.304659 + 0.527685i
\(219\) 0 0
\(220\) −2.75232 −0.185562
\(221\) −2.02106 + 3.54536i −0.135951 + 0.238487i
\(222\) 0 0
\(223\) −10.6493 6.14838i −0.713130 0.411726i 0.0990887 0.995079i \(-0.468407\pi\)
−0.812219 + 0.583353i \(0.801741\pi\)
\(224\) 5.07606 8.79200i 0.339159 0.587440i
\(225\) 0 0
\(226\) 8.63036i 0.574083i
\(227\) −6.60974 + 3.81613i −0.438704 + 0.253286i −0.703048 0.711143i \(-0.748178\pi\)
0.264344 + 0.964428i \(0.414845\pi\)
\(228\) 0 0
\(229\) 14.4008i 0.951631i −0.879545 0.475815i \(-0.842153\pi\)
0.879545 0.475815i \(-0.157847\pi\)
\(230\) 2.37404 + 4.11196i 0.156540 + 0.271135i
\(231\) 0 0
\(232\) −0.0656218 0.0378868i −0.00430828 0.00248739i
\(233\) 9.49617 0.622115 0.311057 0.950391i \(-0.399317\pi\)
0.311057 + 0.950391i \(0.399317\pi\)
\(234\) 0 0
\(235\) −2.58535 −0.168650
\(236\) −0.0760645 0.0439159i −0.00495138 0.00285868i
\(237\) 0 0
\(238\) −2.48505 4.30423i −0.161082 0.279002i
\(239\) 19.9143i 1.28815i −0.764962 0.644076i \(-0.777242\pi\)
0.764962 0.644076i \(-0.222758\pi\)
\(240\) 0 0
\(241\) 20.1493 11.6332i 1.29793 0.749360i 0.317883 0.948130i \(-0.397028\pi\)
0.980046 + 0.198770i \(0.0636947\pi\)
\(242\) 21.7792i 1.40002i
\(243\) 0 0
\(244\) −0.860832 + 1.49100i −0.0551091 + 0.0954518i
\(245\) −5.16273 2.98070i −0.329835 0.190430i
\(246\) 0 0
\(247\) −7.10400 4.04968i −0.452017 0.257675i
\(248\) 16.7436 1.06322
\(249\) 0 0
\(250\) 0.609843 1.05628i 0.0385699 0.0668050i
\(251\) −5.92008 10.2539i −0.373672 0.647219i 0.616455 0.787390i \(-0.288568\pi\)
−0.990127 + 0.140171i \(0.955235\pi\)
\(252\) 0 0
\(253\) 18.1101 10.4559i 1.13858 0.657357i
\(254\) 12.0797 6.97424i 0.757950 0.437603i
\(255\) 0 0
\(256\) 5.71040 + 9.89070i 0.356900 + 0.618169i
\(257\) 2.77501 4.80646i 0.173100 0.299819i −0.766402 0.642361i \(-0.777955\pi\)
0.939502 + 0.342543i \(0.111288\pi\)
\(258\) 0 0
\(259\) 31.3363 1.94714
\(260\) −1.60490 0.914884i −0.0995317 0.0567387i
\(261\) 0 0
\(262\) −11.1627 6.44481i −0.689636 0.398161i
\(263\) 3.42983 5.94065i 0.211493 0.366316i −0.740689 0.671848i \(-0.765501\pi\)
0.952182 + 0.305532i \(0.0988342\pi\)
\(264\) 0 0
\(265\) 4.43937i 0.272709i
\(266\) 8.62459 4.97941i 0.528807 0.305307i
\(267\) 0 0
\(268\) 3.27903i 0.200299i
\(269\) −0.710994 1.23148i −0.0433501 0.0750845i 0.843536 0.537072i \(-0.180470\pi\)
−0.886886 + 0.461988i \(0.847136\pi\)
\(270\) 0 0
\(271\) 8.63381 + 4.98473i 0.524467 + 0.302801i 0.738760 0.673968i \(-0.235412\pi\)
−0.214294 + 0.976769i \(0.568745\pi\)
\(272\) 3.07045 0.186173
\(273\) 0 0
\(274\) 4.61862 0.279021
\(275\) −4.65213 2.68591i −0.280534 0.161966i
\(276\) 0 0
\(277\) −8.76187 15.1760i −0.526449 0.911837i −0.999525 0.0308154i \(-0.990190\pi\)
0.473076 0.881022i \(-0.343144\pi\)
\(278\) 2.45628i 0.147318i
\(279\) 0 0
\(280\) 9.55405 5.51603i 0.570964 0.329646i
\(281\) 10.7352i 0.640406i −0.947349 0.320203i \(-0.896249\pi\)
0.947349 0.320203i \(-0.103751\pi\)
\(282\) 0 0
\(283\) 0.659192 1.14175i 0.0391849 0.0678702i −0.845768 0.533551i \(-0.820857\pi\)
0.884953 + 0.465681i \(0.154191\pi\)
\(284\) 4.79099 + 2.76608i 0.284293 + 0.164137i
\(285\) 0 0
\(286\) 11.6992 20.5229i 0.691790 1.21355i
\(287\) −13.4361 −0.793109
\(288\) 0 0
\(289\) 7.85945 13.6130i 0.462321 0.800763i
\(290\) −0.0150801 0.0261196i −0.000885536 0.00153379i
\(291\) 0 0
\(292\) −2.08685 + 1.20485i −0.122124 + 0.0705082i
\(293\) −16.2316 + 9.37133i −0.948261 + 0.547479i −0.892540 0.450968i \(-0.851079\pi\)
−0.0557207 + 0.998446i \(0.517746\pi\)
\(294\) 0 0
\(295\) −0.0857123 0.148458i −0.00499036 0.00864356i
\(296\) −13.3359 + 23.0985i −0.775134 + 1.34257i
\(297\) 0 0
\(298\) 6.72998 0.389857
\(299\) 14.0357 0.0770194i 0.811708 0.00445415i
\(300\) 0 0
\(301\) −3.52897 2.03745i −0.203406 0.117437i
\(302\) −2.98190 + 5.16480i −0.171589 + 0.297201i
\(303\) 0 0
\(304\) 6.15239i 0.352864i
\(305\) −2.91005 + 1.68012i −0.166629 + 0.0962032i
\(306\) 0 0
\(307\) 14.3043i 0.816387i 0.912895 + 0.408194i \(0.133841\pi\)
−0.912895 + 0.408194i \(0.866159\pi\)
\(308\) −4.95445 8.58137i −0.282306 0.488969i
\(309\) 0 0
\(310\) 5.77162 + 3.33225i 0.327806 + 0.189259i
\(311\) 2.76102 0.156563 0.0782815 0.996931i \(-0.475057\pi\)
0.0782815 + 0.996931i \(0.475057\pi\)
\(312\) 0 0
\(313\) −16.3858 −0.926179 −0.463090 0.886311i \(-0.653259\pi\)
−0.463090 + 0.886311i \(0.653259\pi\)
\(314\) −10.6056 6.12316i −0.598510 0.345550i
\(315\) 0 0
\(316\) 3.06973 + 5.31693i 0.172686 + 0.299101i
\(317\) 1.78575i 0.100297i 0.998742 + 0.0501487i \(0.0159695\pi\)
−0.998742 + 0.0501487i \(0.984030\pi\)
\(318\) 0 0
\(319\) −0.115037 + 0.0664168i −0.00644085 + 0.00371863i
\(320\) 8.86488i 0.495562i
\(321\) 0 0
\(322\) −8.54702 + 14.8039i −0.476307 + 0.824987i
\(323\) −2.22308 1.28349i −0.123695 0.0714156i
\(324\) 0 0
\(325\) −1.81988 3.11256i −0.100949 0.172654i
\(326\) −8.27099 −0.458088
\(327\) 0 0
\(328\) 5.71806 9.90396i 0.315727 0.546855i
\(329\) −4.65389 8.06077i −0.256577 0.444405i
\(330\) 0 0
\(331\) −6.25652 + 3.61220i −0.343889 + 0.198545i −0.661991 0.749512i \(-0.730288\pi\)
0.318101 + 0.948057i \(0.396955\pi\)
\(332\) −5.38170 + 3.10713i −0.295359 + 0.170526i
\(333\) 0 0
\(334\) −6.39714 11.0802i −0.350036 0.606280i
\(335\) 3.19990 5.54239i 0.174829 0.302813i
\(336\) 0 0
\(337\) 4.36219 0.237624 0.118812 0.992917i \(-0.462091\pi\)
0.118812 + 0.992917i \(0.462091\pi\)
\(338\) 13.6438 8.07818i 0.742125 0.439395i
\(339\) 0 0
\(340\) −0.502227 0.289961i −0.0272371 0.0157253i
\(341\) 14.6761 25.4197i 0.794754 1.37655i
\(342\) 0 0
\(343\) 3.73913i 0.201894i
\(344\) 3.00367 1.73417i 0.161947 0.0935002i
\(345\) 0 0
\(346\) 5.43792i 0.292344i
\(347\) −13.3536 23.1291i −0.716858 1.24163i −0.962239 0.272207i \(-0.912246\pi\)
0.245381 0.969427i \(-0.421087\pi\)
\(348\) 0 0
\(349\) −20.4131 11.7855i −1.09269 0.630865i −0.158399 0.987375i \(-0.550633\pi\)
−0.934292 + 0.356510i \(0.883967\pi\)
\(350\) 4.39111 0.234715
\(351\) 0 0
\(352\) 15.1479 0.807385
\(353\) −4.96862 2.86863i −0.264453 0.152682i 0.361911 0.932213i \(-0.382124\pi\)
−0.626364 + 0.779531i \(0.715458\pi\)
\(354\) 0 0
\(355\) 5.39866 + 9.35076i 0.286531 + 0.496287i
\(356\) 8.27675i 0.438667i
\(357\) 0 0
\(358\) 19.6799 11.3622i 1.04011 0.600509i
\(359\) 24.7583i 1.30669i 0.757059 + 0.653347i \(0.226636\pi\)
−0.757059 + 0.653347i \(0.773364\pi\)
\(360\) 0 0
\(361\) −6.92820 + 12.0000i −0.364642 + 0.631579i
\(362\) 19.1081 + 11.0321i 1.00430 + 0.579833i
\(363\) 0 0
\(364\) −0.0364951 6.65074i −0.00191286 0.348593i
\(365\) −4.70308 −0.246171
\(366\) 0 0
\(367\) −13.0268 + 22.5630i −0.679992 + 1.17778i 0.294991 + 0.955500i \(0.404683\pi\)
−0.974983 + 0.222280i \(0.928650\pi\)
\(368\) −5.28021 9.14558i −0.275250 0.476747i
\(369\) 0 0
\(370\) −9.19393 + 5.30812i −0.477969 + 0.275956i
\(371\) 13.8413 7.99131i 0.718607 0.414888i
\(372\) 0 0
\(373\) −6.60224 11.4354i −0.341851 0.592103i 0.642926 0.765929i \(-0.277720\pi\)
−0.984776 + 0.173826i \(0.944387\pi\)
\(374\) 3.70792 6.42231i 0.191732 0.332089i
\(375\) 0 0
\(376\) 7.92229 0.408561
\(377\) −0.0891563 0.000489234i −0.00459178 2.51968e-5i
\(378\) 0 0
\(379\) 22.5147 + 12.9989i 1.15650 + 0.667707i 0.950463 0.310837i \(-0.100609\pi\)
0.206039 + 0.978544i \(0.433943\pi\)
\(380\) 0.581008 1.00633i 0.0298051 0.0516239i
\(381\) 0 0
\(382\) 33.3418i 1.70591i
\(383\) −8.31401 + 4.80010i −0.424826 + 0.245274i −0.697140 0.716935i \(-0.745544\pi\)
0.272314 + 0.962208i \(0.412211\pi\)
\(384\) 0 0
\(385\) 19.3396i 0.985637i
\(386\) 13.2747 + 22.9924i 0.675664 + 1.17028i
\(387\) 0 0
\(388\) 5.39926 + 3.11726i 0.274106 + 0.158255i
\(389\) 5.63129 0.285518 0.142759 0.989758i \(-0.454403\pi\)
0.142759 + 0.989758i \(0.454403\pi\)
\(390\) 0 0
\(391\) 4.40617 0.222829
\(392\) 15.8201 + 9.13376i 0.799038 + 0.461325i
\(393\) 0 0
\(394\) −1.03473 1.79221i −0.0521291 0.0902903i
\(395\) 11.9826i 0.602911i
\(396\) 0 0
\(397\) −14.5196 + 8.38291i −0.728719 + 0.420726i −0.817953 0.575285i \(-0.804891\pi\)
0.0892344 + 0.996011i \(0.471558\pi\)
\(398\) 30.8891i 1.54833i
\(399\) 0 0
\(400\) −1.35638 + 2.34932i −0.0678189 + 0.117466i
\(401\) −12.0187 6.93902i −0.600187 0.346518i 0.168928 0.985628i \(-0.445969\pi\)
−0.769115 + 0.639110i \(0.779303\pi\)
\(402\) 0 0
\(403\) 17.0073 9.94402i 0.847196 0.495347i
\(404\) −2.07733 −0.103351
\(405\) 0 0
\(406\) 0.0542914 0.0940355i 0.00269444 0.00466690i
\(407\) 23.3783 + 40.4924i 1.15882 + 2.00713i
\(408\) 0 0
\(409\) −25.4829 + 14.7125i −1.26005 + 0.727489i −0.973083 0.230453i \(-0.925979\pi\)
−0.286964 + 0.957941i \(0.592646\pi\)
\(410\) 3.94209 2.27597i 0.194686 0.112402i
\(411\) 0 0
\(412\) −4.58655 7.94413i −0.225963 0.391379i
\(413\) 0.308581 0.534478i 0.0151843 0.0262999i
\(414\) 0 0
\(415\) −12.1286 −0.595369
\(416\) 8.83284 + 5.03522i 0.433066 + 0.246872i
\(417\) 0 0
\(418\) 12.8687 + 7.42973i 0.629427 + 0.363400i
\(419\) 3.48397 6.03440i 0.170203 0.294800i −0.768288 0.640104i \(-0.778891\pi\)
0.938491 + 0.345305i \(0.112224\pi\)
\(420\) 0 0
\(421\) 7.12125i 0.347069i −0.984828 0.173534i \(-0.944481\pi\)
0.984828 0.173534i \(-0.0555188\pi\)
\(422\) −0.354389 + 0.204607i −0.0172514 + 0.00996010i
\(423\) 0 0
\(424\) 13.6036i 0.660647i
\(425\) −0.565928 0.980215i −0.0274515 0.0475474i
\(426\) 0 0
\(427\) −10.4767 6.04875i −0.507005 0.292720i
\(428\) 4.67883 0.226160
\(429\) 0 0
\(430\) 1.38051 0.0665740
\(431\) −26.1664 15.1072i −1.26039 0.727687i −0.287241 0.957858i \(-0.592738\pi\)
−0.973150 + 0.230171i \(0.926071\pi\)
\(432\) 0 0
\(433\) 0.600065 + 1.03934i 0.0288373 + 0.0499476i 0.880084 0.474818i \(-0.157486\pi\)
−0.851247 + 0.524766i \(0.824153\pi\)
\(434\) 23.9935i 1.15172i
\(435\) 0 0
\(436\) −3.27290 + 1.88961i −0.156744 + 0.0904960i
\(437\) 8.82884i 0.422341i
\(438\) 0 0
\(439\) −8.27705 + 14.3363i −0.395042 + 0.684233i −0.993107 0.117215i \(-0.962603\pi\)
0.598064 + 0.801448i \(0.295937\pi\)
\(440\) 14.2555 + 8.23042i 0.679605 + 0.392370i
\(441\) 0 0
\(442\) 4.29692 2.51236i 0.204383 0.119501i
\(443\) −4.55949 −0.216628 −0.108314 0.994117i \(-0.534545\pi\)
−0.108314 + 0.994117i \(0.534545\pi\)
\(444\) 0 0
\(445\) −8.07702 + 13.9898i −0.382887 + 0.663180i
\(446\) 7.49910 + 12.9888i 0.355093 + 0.615038i
\(447\) 0 0
\(448\) −27.6395 + 15.9577i −1.30584 + 0.753929i
\(449\) −11.9963 + 6.92608i −0.566142 + 0.326862i −0.755607 0.655025i \(-0.772658\pi\)
0.189465 + 0.981887i \(0.439325\pi\)
\(450\) 0 0
\(451\) −10.0239 17.3620i −0.472009 0.817544i
\(452\) 1.81271 3.13971i 0.0852628 0.147680i
\(453\) 0 0
\(454\) 9.30897 0.436892
\(455\) 6.42856 11.2771i 0.301376 0.528676i
\(456\) 0 0
\(457\) 34.7402 + 20.0573i 1.62508 + 0.938240i 0.985532 + 0.169489i \(0.0542117\pi\)
0.639548 + 0.768751i \(0.279122\pi\)
\(458\) −8.78222 + 15.2113i −0.410366 + 0.710775i
\(459\) 0 0
\(460\) 1.99457i 0.0929972i
\(461\) −6.52897 + 3.76950i −0.304084 + 0.175563i −0.644276 0.764793i \(-0.722841\pi\)
0.340192 + 0.940356i \(0.389508\pi\)
\(462\) 0 0
\(463\) 23.3031i 1.08299i 0.840705 + 0.541494i \(0.182141\pi\)
−0.840705 + 0.541494i \(0.817859\pi\)
\(464\) 0.0335403 + 0.0580936i 0.00155707 + 0.00269693i
\(465\) 0 0
\(466\) −10.0306 5.79118i −0.464659 0.268271i
\(467\) −22.6297 −1.04718 −0.523589 0.851971i \(-0.675407\pi\)
−0.523589 + 0.851971i \(0.675407\pi\)
\(468\) 0 0
\(469\) 23.0405 1.06391
\(470\) 2.73086 + 1.57666i 0.125965 + 0.0727260i
\(471\) 0 0
\(472\) 0.262648 + 0.454919i 0.0120893 + 0.0209394i
\(473\) 6.08012i 0.279564i
\(474\) 0 0
\(475\) 1.96410 1.13397i 0.0901192 0.0520303i
\(476\) 2.08783i 0.0956956i
\(477\) 0 0
\(478\) −12.1446 + 21.0351i −0.555482 + 0.962124i
\(479\) 17.8789 + 10.3224i 0.816910 + 0.471643i 0.849350 0.527831i \(-0.176994\pi\)
−0.0324399 + 0.999474i \(0.510328\pi\)
\(480\) 0 0
\(481\) 0.172207 + 31.3825i 0.00785198 + 1.43092i
\(482\) −28.3777 −1.29257
\(483\) 0 0
\(484\) 4.57449 7.92325i 0.207931 0.360148i
\(485\) 6.08408 + 10.5379i 0.276264 + 0.478503i
\(486\) 0 0
\(487\) −2.62929 + 1.51802i −0.119145 + 0.0687882i −0.558388 0.829580i \(-0.688580\pi\)
0.439243 + 0.898368i \(0.355247\pi\)
\(488\) 8.91725 5.14838i 0.403665 0.233056i
\(489\) 0 0
\(490\) 3.63553 + 6.29692i 0.164236 + 0.284466i
\(491\) −5.33401 + 9.23877i −0.240720 + 0.416940i −0.960920 0.276827i \(-0.910717\pi\)
0.720199 + 0.693767i \(0.244050\pi\)
\(492\) 0 0
\(493\) −0.0279884 −0.00126053
\(494\) 5.03414 + 8.60992i 0.226497 + 0.387379i
\(495\) 0 0
\(496\) −12.8369 7.41139i −0.576394 0.332781i
\(497\) −19.4362 + 33.6646i −0.871835 + 1.51006i
\(498\) 0 0
\(499\) 33.9143i 1.51821i −0.650966 0.759107i \(-0.725636\pi\)
0.650966 0.759107i \(-0.274364\pi\)
\(500\) 0.443720 0.256182i 0.0198438 0.0114568i
\(501\) 0 0
\(502\) 14.4413i 0.644546i
\(503\) −6.31380 10.9358i −0.281518 0.487604i 0.690241 0.723580i \(-0.257505\pi\)
−0.971759 + 0.235976i \(0.924171\pi\)
\(504\) 0 0
\(505\) −3.51122 2.02721i −0.156247 0.0902095i
\(506\) −25.5058 −1.13387
\(507\) 0 0
\(508\) 5.85945 0.259971
\(509\) 20.9168 + 12.0763i 0.927120 + 0.535273i 0.885899 0.463877i \(-0.153542\pi\)
0.0412201 + 0.999150i \(0.486876\pi\)
\(510\) 0 0
\(511\) −8.46601 14.6636i −0.374514 0.648678i
\(512\) 24.2750i 1.07281i
\(513\) 0 0
\(514\) −5.86238 + 3.38465i −0.258578 + 0.149290i
\(515\) 17.9035i 0.788921i
\(516\) 0 0
\(517\) 6.94402 12.0274i 0.305398 0.528964i
\(518\) −33.0999 19.1103i −1.45433 0.839656i
\(519\) 0 0
\(520\) 5.57666 + 9.53781i 0.244553 + 0.418261i
\(521\) 24.7521 1.08441 0.542205 0.840246i \(-0.317590\pi\)
0.542205 + 0.840246i \(0.317590\pi\)
\(522\) 0 0
\(523\) −18.5163 + 32.0712i −0.809662 + 1.40238i 0.103436 + 0.994636i \(0.467016\pi\)
−0.913098 + 0.407739i \(0.866317\pi\)
\(524\) −2.70732 4.68922i −0.118270 0.204850i
\(525\) 0 0
\(526\) −7.24573 + 4.18332i −0.315929 + 0.182402i
\(527\) 5.35600 3.09229i 0.233311 0.134702i
\(528\) 0 0
\(529\) 3.92277 + 6.79444i 0.170555 + 0.295410i
\(530\) −2.70732 + 4.68922i −0.117599 + 0.203687i
\(531\) 0 0
\(532\) 4.18348 0.181377
\(533\) −0.0738376 13.4559i −0.00319826 0.582840i
\(534\) 0 0
\(535\) 7.90842 + 4.56593i 0.341911 + 0.197402i
\(536\) −9.80545 + 16.9835i −0.423531 + 0.733577i
\(537\) 0 0
\(538\) 1.73438i 0.0747744i
\(539\) 27.7332 16.0118i 1.19456 0.689677i
\(540\) 0 0
\(541\) 8.38144i 0.360346i −0.983635 0.180173i \(-0.942334\pi\)
0.983635 0.180173i \(-0.0576658\pi\)
\(542\) −6.07981 10.5305i −0.261150 0.452326i
\(543\) 0 0
\(544\) 2.76409 + 1.59585i 0.118509 + 0.0684215i
\(545\) −7.37605 −0.315955
\(546\) 0 0
\(547\) −22.7842 −0.974181 −0.487091 0.873351i \(-0.661942\pi\)
−0.487091 + 0.873351i \(0.661942\pi\)
\(548\) 1.68025 + 0.970090i 0.0717765 + 0.0414402i
\(549\) 0 0
\(550\) 3.27597 + 5.67414i 0.139688 + 0.241946i
\(551\) 0.0560816i 0.00238915i
\(552\) 0 0
\(553\) −37.3601 + 21.5699i −1.58871 + 0.917245i
\(554\) 21.3735i 0.908071i
\(555\) 0 0
\(556\) −0.515915 + 0.893592i −0.0218797 + 0.0378967i
\(557\) −24.3810 14.0764i −1.03306 0.596435i −0.115197 0.993343i \(-0.536750\pi\)
−0.917858 + 0.396908i \(0.870083\pi\)
\(558\) 0 0
\(559\) 2.02106 3.54536i 0.0854816 0.149953i
\(560\) −9.76645 −0.412708
\(561\) 0 0
\(562\) −6.54676 + 11.3393i −0.276159 + 0.478321i
\(563\) 9.06514 + 15.7013i 0.382050 + 0.661731i 0.991355 0.131206i \(-0.0418848\pi\)
−0.609305 + 0.792936i \(0.708551\pi\)
\(564\) 0 0
\(565\) 6.12789 3.53794i 0.257802 0.148842i
\(566\) −1.39258 + 0.804007i −0.0585346 + 0.0337950i
\(567\) 0 0
\(568\) −16.5431 28.6535i −0.694133 1.20227i
\(569\) −20.2992 + 35.1593i −0.850988 + 1.47395i 0.0293292 + 0.999570i \(0.490663\pi\)
−0.880317 + 0.474385i \(0.842670\pi\)
\(570\) 0 0
\(571\) −24.7159 −1.03433 −0.517164 0.855886i \(-0.673012\pi\)
−0.517164 + 0.855886i \(0.673012\pi\)
\(572\) 8.56677 5.00891i 0.358195 0.209433i
\(573\) 0 0
\(574\) 14.1923 + 8.19393i 0.592375 + 0.342008i
\(575\) −1.94644 + 3.37133i −0.0811720 + 0.140594i
\(576\) 0 0
\(577\) 23.0691i 0.960379i −0.877165 0.480189i \(-0.840568\pi\)
0.877165 0.480189i \(-0.159432\pi\)
\(578\) −16.6036 + 9.58607i −0.690617 + 0.398728i
\(579\) 0 0
\(580\) 0.0126697i 0.000526079i
\(581\) −21.8327 37.8153i −0.905771 1.56884i
\(582\) 0 0
\(583\) 20.6525 + 11.9237i 0.855341 + 0.493831i
\(584\) 14.4116 0.596358
\(585\) 0 0
\(586\) 22.8602 0.944345
\(587\) 17.6256 + 10.1762i 0.727487 + 0.420015i 0.817502 0.575926i \(-0.195358\pi\)
−0.0900152 + 0.995940i \(0.528692\pi\)
\(588\) 0 0
\(589\) 6.19615 + 10.7321i 0.255308 + 0.442206i
\(590\) 0.209084i 0.00860786i
\(591\) 0 0
\(592\) 20.4486 11.8060i 0.840432 0.485223i
\(593\) 10.3834i 0.426395i −0.977009 0.213198i \(-0.931612\pi\)
0.977009 0.213198i \(-0.0683878\pi\)
\(594\) 0 0
\(595\) 2.03745 3.52897i 0.0835273 0.144674i
\(596\) 2.44836 + 1.41356i 0.100289 + 0.0579017i
\(597\) 0 0
\(598\) −14.8726 8.47825i −0.608187 0.346701i
\(599\) 31.5965 1.29100 0.645499 0.763761i \(-0.276649\pi\)
0.645499 + 0.763761i \(0.276649\pi\)
\(600\) 0 0
\(601\) 21.9423 38.0051i 0.895044 1.55026i 0.0612928 0.998120i \(-0.480478\pi\)
0.833751 0.552141i \(-0.186189\pi\)
\(602\) 2.48505 + 4.30423i 0.101283 + 0.175428i
\(603\) 0 0
\(604\) −2.16962 + 1.25263i −0.0882806 + 0.0509688i
\(605\) 15.4641 8.92820i 0.628705 0.362983i
\(606\) 0 0
\(607\) −1.08770 1.88395i −0.0441484 0.0764673i 0.843107 0.537746i \(-0.180724\pi\)
−0.887255 + 0.461279i \(0.847391\pi\)
\(608\) −3.19768 + 5.53854i −0.129683 + 0.224617i
\(609\) 0 0
\(610\) 4.09843 0.165941
\(611\) 8.04707 4.70504i 0.325550 0.190346i
\(612\) 0 0
\(613\) −12.7843 7.38100i −0.516352 0.298116i 0.219089 0.975705i \(-0.429691\pi\)
−0.735441 + 0.677589i \(0.763025\pi\)
\(614\) 8.72336 15.1093i 0.352046 0.609762i
\(615\) 0 0
\(616\) 59.2622i 2.38774i
\(617\) −17.5779 + 10.1486i −0.707659 + 0.408567i −0.810194 0.586162i \(-0.800638\pi\)
0.102535 + 0.994729i \(0.467305\pi\)
\(618\) 0 0
\(619\) 9.94207i 0.399605i 0.979836 + 0.199803i \(0.0640301\pi\)
−0.979836 + 0.199803i \(0.935970\pi\)
\(620\) 1.39980 + 2.42453i 0.0562175 + 0.0973716i
\(621\) 0 0
\(622\) −2.91641 1.68379i −0.116937 0.0675138i
\(623\) −58.1577 −2.33004
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 17.3080 + 9.99276i 0.691766 + 0.399391i
\(627\) 0 0
\(628\) −2.57221 4.45519i −0.102642 0.177782i
\(629\) 9.85174i 0.392815i
\(630\) 0 0
\(631\) 0.843006 0.486710i 0.0335596 0.0193756i −0.483126 0.875551i \(-0.660499\pi\)
0.516686 + 0.856175i \(0.327165\pi\)
\(632\) 36.7183i 1.46058i
\(633\) 0 0
\(634\) 1.08903 1.88625i 0.0432507 0.0749124i
\(635\) 9.90396 + 5.71806i 0.393027 + 0.226914i
\(636\) 0 0
\(637\) 21.4938 0.117945i 0.851617 0.00467314i
\(638\) 0.162015 0.00641425
\(639\) 0 0
\(640\) 2.58631 4.47962i 0.102233 0.177072i
\(641\) 6.31047 + 10.9301i 0.249249 + 0.431711i 0.963318 0.268364i \(-0.0864830\pi\)
−0.714069 + 0.700075i \(0.753150\pi\)
\(642\) 0 0
\(643\) −8.62599 + 4.98022i −0.340176 + 0.196401i −0.660350 0.750958i \(-0.729592\pi\)
0.320174 + 0.947359i \(0.396259\pi\)
\(644\) −6.21878 + 3.59042i −0.245054 + 0.141482i
\(645\) 0 0
\(646\) 1.56546 + 2.71146i 0.0615923 + 0.106681i
\(647\) 18.1381 31.4162i 0.713084 1.23510i −0.250610 0.968088i \(-0.580631\pi\)
0.963694 0.267009i \(-0.0860354\pi\)
\(648\) 0 0
\(649\) 0.920861 0.0361470
\(650\) 0.0241312 + 4.39758i 0.000946502 + 0.172487i
\(651\) 0 0
\(652\) −3.00898 1.73723i −0.117841 0.0680353i
\(653\) 6.87769 11.9125i 0.269145 0.466172i −0.699497 0.714636i \(-0.746592\pi\)
0.968641 + 0.248464i \(0.0799257\pi\)
\(654\) 0 0
\(655\) 10.5680i 0.412925i
\(656\) −8.76776 + 5.06207i −0.342324 + 0.197641i
\(657\) 0 0
\(658\) 11.3526i 0.442570i
\(659\) −1.29092 2.23593i −0.0502869 0.0870995i 0.839786 0.542917i \(-0.182680\pi\)
−0.890073 + 0.455818i \(0.849347\pi\)
\(660\) 0 0
\(661\) −21.5437 12.4382i −0.837951 0.483791i 0.0186163 0.999827i \(-0.494074\pi\)
−0.856567 + 0.516036i \(0.827407\pi\)
\(662\) 8.81151 0.342469
\(663\) 0 0
\(664\) 37.1656 1.44231
\(665\) 7.07115 + 4.08253i 0.274207 + 0.158314i
\(666\) 0 0
\(667\) 0.0481312 + 0.0833657i 0.00186365 + 0.00322793i
\(668\) 5.37460i 0.207949i
\(669\) 0 0
\(670\) −6.75998 + 3.90288i −0.261161 + 0.150781i
\(671\) 18.0506i 0.696834i
\(672\) 0 0
\(673\) 21.6611 37.5181i 0.834974 1.44622i −0.0590774 0.998253i \(-0.518816\pi\)
0.894052 0.447964i \(-0.147851\pi\)
\(674\) −4.60770 2.66025i −0.177482 0.102469i
\(675\) 0 0
\(676\) 6.66033 0.0730977i 0.256167 0.00281145i
\(677\) 41.3625 1.58969 0.794845 0.606813i \(-0.207552\pi\)
0.794845 + 0.606813i \(0.207552\pi\)
\(678\) 0 0
\(679\) −21.9039 + 37.9386i −0.840594 + 1.45595i
\(680\) 1.73417 + 3.00367i 0.0665024 + 0.115186i
\(681\) 0 0
\(682\) −31.0041 + 17.9002i −1.18721 + 0.685435i
\(683\) −2.27495 + 1.31344i −0.0870484 + 0.0502574i −0.542892 0.839802i \(-0.682671\pi\)
0.455844 + 0.890060i \(0.349338\pi\)
\(684\) 0 0
\(685\) 1.89336 + 3.27940i 0.0723416 + 0.125299i
\(686\) 2.28028 3.94957i 0.0870617 0.150795i
\(687\) 0 0
\(688\) −3.07045 −0.117060
\(689\) 8.07914 + 13.8178i 0.307791 + 0.526417i
\(690\) 0 0
\(691\) −13.2288 7.63765i −0.503247 0.290550i 0.226806 0.973940i \(-0.427172\pi\)
−0.730053 + 0.683390i \(0.760505\pi\)
\(692\) 1.14218 1.97831i 0.0434190 0.0752039i
\(693\) 0 0
\(694\) 32.5744i 1.23651i
\(695\) −1.74406 + 1.00693i −0.0661558 + 0.0381951i
\(696\) 0 0
\(697\) 4.22414i 0.160001i
\(698\) 14.3747 + 24.8976i 0.544089 + 0.942390i
\(699\) 0 0
\(700\) 1.59748 + 0.922305i 0.0603790 + 0.0348599i
\(701\) −48.1947 −1.82029 −0.910144 0.414292i \(-0.864029\pi\)
−0.910144 + 0.414292i \(0.864029\pi\)
\(702\) 0 0
\(703\) −19.7404 −0.744522
\(704\) −41.2406 23.8103i −1.55431 0.897383i
\(705\) 0 0
\(706\) 3.49884 + 6.06016i 0.131680 + 0.228077i
\(707\) 14.5967i 0.548964i
\(708\) 0 0
\(709\) −33.6624 + 19.4350i −1.26422 + 0.729896i −0.973887 0.227031i \(-0.927098\pi\)
−0.290329 + 0.956927i \(0.593765\pi\)
\(710\) 13.1694i 0.494237i
\(711\) 0 0
\(712\) 24.7504 42.8689i 0.927560 1.60658i
\(713\) −18.4213 10.6355i −0.689882 0.398304i
\(714\) 0 0
\(715\) 19.3681 0.106280i 0.724325 0.00397464i
\(716\) 9.54600 0.356751
\(717\) 0 0
\(718\) 15.0987 26.1517i 0.563478 0.975973i
\(719\) −3.30830 5.73015i −0.123379 0.213698i 0.797719 0.603029i \(-0.206040\pi\)
−0.921098 + 0.389331i \(0.872706\pi\)
\(720\) 0 0
\(721\) 55.8205 32.2280i 2.07887 1.20023i
\(722\) 14.6362 8.45024i 0.544705 0.314485i
\(723\) 0 0
\(724\) 4.63433 + 8.02690i 0.172234 + 0.298317i
\(725\) 0.0123639 0.0214150i 0.000459185 0.000795332i
\(726\) 0 0
\(727\) 18.3735 0.681435 0.340717 0.940166i \(-0.389330\pi\)
0.340717 + 0.940166i \(0.389330\pi\)
\(728\) −19.6990 + 34.5562i −0.730094 + 1.28074i
\(729\) 0 0
\(730\) 4.96777 + 2.86814i 0.183866 + 0.106155i
\(731\) 0.640548 1.10946i 0.0236915 0.0410349i
\(732\) 0 0
\(733\) 0.791131i 0.0292211i −0.999893 0.0146105i \(-0.995349\pi\)
0.999893 0.0146105i \(-0.00465084\pi\)
\(734\) 27.5198 15.8886i 1.01578 0.586458i
\(735\) 0 0
\(736\) 10.9774i 0.404634i
\(737\) 17.1893 + 29.7727i 0.633175 + 1.09669i
\(738\) 0 0
\(739\) −27.0073 15.5926i −0.993478 0.573585i −0.0871658 0.996194i \(-0.527781\pi\)
−0.906312 + 0.422609i \(0.861114\pi\)
\(740\) −4.45965 −0.163940
\(741\) 0 0
\(742\) −19.4938 −0.715639
\(743\) −4.81773 2.78152i −0.176745 0.102044i 0.409017 0.912527i \(-0.365872\pi\)
−0.585763 + 0.810483i \(0.699205\pi\)
\(744\) 0 0
\(745\) 2.75890 + 4.77855i 0.101078 + 0.175073i
\(746\) 16.1053i 0.589658i
\(747\) 0 0
\(748\) 2.69787 1.55762i 0.0986439 0.0569521i
\(749\) 32.8765i 1.20128i
\(750\) 0 0
\(751\) −17.6048 + 30.4925i −0.642410 + 1.11269i 0.342483 + 0.939524i \(0.388732\pi\)
−0.984893 + 0.173163i \(0.944601\pi\)
\(752\) −6.07381 3.50672i −0.221489 0.127877i
\(753\) 0 0
\(754\) 0.0944723 + 0.0538546i 0.00344048 + 0.00196127i
\(755\) −4.88961 −0.177951
\(756\) 0 0
\(757\) −25.0223 + 43.3399i −0.909451 + 1.57522i −0.0946237 + 0.995513i \(0.530165\pi\)
−0.814828 + 0.579703i \(0.803169\pi\)
\(758\) −15.8545 27.4609i −0.575863 0.997424i
\(759\) 0 0
\(760\) −6.01859 + 3.47484i −0.218317 + 0.126046i
\(761\) −38.8161 + 22.4105i −1.40708 + 0.812379i −0.995106 0.0988165i \(-0.968494\pi\)
−0.411975 + 0.911195i \(0.635161\pi\)
\(762\) 0 0
\(763\) −13.2776 22.9975i −0.480682 0.832566i
\(764\) 7.00307 12.1297i 0.253362 0.438836i
\(765\) 0 0
\(766\) 11.7092 0.423072
\(767\) 0.536961 + 0.306098i 0.0193885 + 0.0110526i
\(768\) 0 0
\(769\) −34.0897 19.6817i −1.22930 0.709739i −0.262420 0.964954i \(-0.584521\pi\)
−0.966884 + 0.255215i \(0.917854\pi\)
\(770\) −11.7941 + 20.4280i −0.425031 + 0.736175i
\(771\) 0 0
\(772\) 11.1528i 0.401399i
\(773\) 42.2452 24.3902i 1.51945 0.877256i 0.519715 0.854340i \(-0.326038\pi\)
0.999737 0.0229167i \(-0.00729525\pi\)
\(774\) 0 0
\(775\) 5.46410i 0.196276i
\(776\) −18.6434 32.2914i −0.669260 1.15919i
\(777\) 0 0
\(778\) −5.94822 3.43420i −0.213254 0.123122i
\(779\) 8.46410 0.303258
\(780\) 0 0
\(781\) −58.0013 −2.07545
\(782\) −4.65415 2.68707i −0.166432 0.0960895i
\(783\) 0 0
\(784\) −8.08592 14.0052i −0.288783 0.500187i
\(785\) 10.0405i 0.358363i
\(786\) 0 0
\(787\) 34.5204 19.9304i 1.23052 0.710442i 0.263382 0.964692i \(-0.415162\pi\)
0.967139 + 0.254250i \(0.0818286\pi\)
\(788\) 0.869338i 0.0309689i
\(789\) 0