Properties

Label 325.2.m.b.49.2
Level $325$
Weight $2$
Character 325.49
Analytic conductor $2.595$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.59513806569\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.2
Root \(1.40994 - 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 325.49
Dual form 325.2.m.b.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.609843 - 1.05628i) q^{2} +(2.01978 - 1.16612i) q^{3} +(0.256182 - 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(1.21969 - 2.11256i) q^{9} +O(q^{10})\) \(q+(-0.609843 - 1.05628i) q^{2} +(2.01978 - 1.16612i) q^{3} +(0.256182 - 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(1.21969 - 2.11256i) q^{9} +(-4.65213 + 2.68591i) q^{11} -1.19496i q^{12} +(3.11256 + 1.81988i) q^{13} -4.39111 q^{14} +(1.35638 + 2.34932i) q^{16} +(0.980215 + 0.565928i) q^{17} -2.97527 q^{18} +(1.96410 + 1.13397i) q^{19} -8.39654i q^{21} +(5.67414 + 3.27597i) q^{22} +(3.37133 - 1.94644i) q^{23} +(-6.18922 + 3.57335i) q^{24} +(0.0241312 - 4.39758i) q^{26} +1.30752i q^{27} +(-0.922305 - 1.59748i) q^{28} +(-0.0123639 - 0.0214150i) q^{29} +5.46410i q^{31} +(-1.40994 + 2.44209i) q^{32} +(-6.26420 + 10.8499i) q^{33} -1.38051i q^{34} +(-0.624924 - 1.08240i) q^{36} +(-4.35203 - 7.53794i) q^{37} -2.76619i q^{38} +(8.40891 + 0.0461428i) q^{39} +(3.23205 - 1.86603i) q^{41} +(-8.86910 + 5.12058i) q^{42} +(-0.980215 - 0.565928i) q^{43} +2.75232i q^{44} +(-4.11196 - 2.37404i) q^{46} -2.58535 q^{47} +(5.47918 + 3.16341i) q^{48} +(-2.98070 - 5.16273i) q^{49} +2.63977 q^{51} +(1.60490 - 0.914884i) q^{52} -4.43937i q^{53} +(1.38111 - 0.797382i) q^{54} +(-5.51603 + 9.55405i) q^{56} +5.28942 q^{57} +(-0.0150801 + 0.0261196i) q^{58} +(0.148458 + 0.0857123i) q^{59} +(-1.68012 + 2.91005i) q^{61} +(5.77162 - 3.33225i) q^{62} +(-4.39111 - 7.60563i) q^{63} +8.86488 q^{64} +15.2807 q^{66} +(-3.19990 - 5.54239i) q^{67} +(0.502227 - 0.289961i) q^{68} +(4.53957 - 7.86276i) q^{69} +(9.35076 + 5.39866i) q^{71} +(-3.73748 + 6.47351i) q^{72} -4.70308 q^{73} +(-5.30812 + 9.19393i) q^{74} +(1.00633 - 0.581008i) q^{76} +19.3396i q^{77} +(-5.07938 - 8.91030i) q^{78} +11.9826 q^{79} +(5.18379 + 8.97859i) q^{81} +(-3.94209 - 2.27597i) q^{82} +12.1286 q^{83} +(-3.72572 - 2.15104i) q^{84} +1.38051i q^{86} +(-0.0499450 - 0.0288357i) q^{87} +(14.2555 - 8.23042i) q^{88} +(-13.9898 + 8.07702i) q^{89} +(11.2771 - 6.42856i) q^{91} -1.99457i q^{92} +(6.37182 + 11.0363i) q^{93} +(1.57666 + 2.73086i) q^{94} +6.57666i q^{96} +(-6.08408 + 10.5379i) q^{97} +(-3.63553 + 6.29692i) q^{98} +13.1039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} + 6q^{3} - 2q^{4} - 18q^{6} + 10q^{7} + 12q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 2q^{2} + 6q^{3} - 2q^{4} - 18q^{6} + 10q^{7} + 12q^{8} + 4q^{9} + 8q^{13} - 4q^{14} - 2q^{16} + 18q^{17} - 40q^{18} - 12q^{19} + 6q^{22} + 6q^{23} + 12q^{24} + 10q^{26} + 8q^{28} + 8q^{29} - 4q^{32} - 18q^{33} + 20q^{36} - 2q^{37} + 12q^{41} - 42q^{42} - 18q^{43} - 42q^{46} - 16q^{47} - 6q^{48} - 12q^{49} - 8q^{51} + 16q^{52} - 18q^{54} + 12q^{56} - 28q^{57} + 22q^{58} + 12q^{59} - 28q^{61} + 12q^{62} - 4q^{63} + 8q^{64} + 12q^{66} - 30q^{67} + 12q^{68} + 16q^{69} + 12q^{72} - 16q^{73} - 10q^{74} + 54q^{76} + 18q^{78} + 16q^{79} + 8q^{81} - 6q^{82} + 24q^{83} + 30q^{84} + 54q^{87} + 42q^{88} - 24q^{89} + 28q^{91} + 8q^{93} - 32q^{94} - 2q^{97} + 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.609843 1.05628i −0.431224 0.746903i 0.565755 0.824574i \(-0.308585\pi\)
−0.996979 + 0.0776710i \(0.975252\pi\)
\(3\) 2.01978 1.16612i 1.16612 0.673262i 0.213359 0.976974i \(-0.431559\pi\)
0.952764 + 0.303712i \(0.0982261\pi\)
\(4\) 0.256182 0.443720i 0.128091 0.221860i
\(5\) 0 0
\(6\) −2.46350 1.42231i −1.00572 0.580654i
\(7\) 1.80010 3.11786i 0.680373 1.17844i −0.294494 0.955653i \(-0.595151\pi\)
0.974867 0.222787i \(-0.0715156\pi\)
\(8\) −3.06430 −1.08339
\(9\) 1.21969 2.11256i 0.406562 0.704187i
\(10\) 0 0
\(11\) −4.65213 + 2.68591i −1.40267 + 0.809832i −0.994666 0.103149i \(-0.967108\pi\)
−0.408004 + 0.912980i \(0.633775\pi\)
\(12\) 1.19496i 0.344955i
\(13\) 3.11256 + 1.81988i 0.863269 + 0.504745i
\(14\) −4.39111 −1.17357
\(15\) 0 0
\(16\) 1.35638 + 2.34932i 0.339094 + 0.587329i
\(17\) 0.980215 + 0.565928i 0.237737 + 0.137258i 0.614136 0.789200i \(-0.289505\pi\)
−0.376399 + 0.926458i \(0.622838\pi\)
\(18\) −2.97527 −0.701278
\(19\) 1.96410 + 1.13397i 0.450596 + 0.260152i 0.708082 0.706130i \(-0.249561\pi\)
−0.257486 + 0.966282i \(0.582894\pi\)
\(20\) 0 0
\(21\) 8.39654i 1.83228i
\(22\) 5.67414 + 3.27597i 1.20973 + 0.698438i
\(23\) 3.37133 1.94644i 0.702970 0.405860i −0.105483 0.994421i \(-0.533639\pi\)
0.808453 + 0.588561i \(0.200305\pi\)
\(24\) −6.18922 + 3.57335i −1.26337 + 0.729407i
\(25\) 0 0
\(26\) 0.0241312 4.39758i 0.00473251 0.862436i
\(27\) 1.30752i 0.251632i
\(28\) −0.922305 1.59748i −0.174299 0.301895i
\(29\) −0.0123639 0.0214150i −0.00229593 0.00397666i 0.864875 0.501987i \(-0.167397\pi\)
−0.867171 + 0.498010i \(0.834064\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i 0.871334 + 0.490691i \(0.163256\pi\)
−0.871334 + 0.490691i \(0.836744\pi\)
\(32\) −1.40994 + 2.44209i −0.249245 + 0.431705i
\(33\) −6.26420 + 10.8499i −1.09046 + 1.88873i
\(34\) 1.38051i 0.236755i
\(35\) 0 0
\(36\) −0.624924 1.08240i −0.104154 0.180400i
\(37\) −4.35203 7.53794i −0.715470 1.23923i −0.962778 0.270293i \(-0.912879\pi\)
0.247309 0.968937i \(-0.420454\pi\)
\(38\) 2.76619i 0.448735i
\(39\) 8.40891 + 0.0461428i 1.34650 + 0.00738877i
\(40\) 0 0
\(41\) 3.23205 1.86603i 0.504762 0.291424i −0.225916 0.974147i \(-0.572538\pi\)
0.730678 + 0.682723i \(0.239204\pi\)
\(42\) −8.86910 + 5.12058i −1.36853 + 0.790122i
\(43\) −0.980215 0.565928i −0.149481 0.0863031i 0.423394 0.905946i \(-0.360839\pi\)
−0.572875 + 0.819643i \(0.694172\pi\)
\(44\) 2.75232i 0.414929i
\(45\) 0 0
\(46\) −4.11196 2.37404i −0.606276 0.350034i
\(47\) −2.58535 −0.377113 −0.188556 0.982062i \(-0.560381\pi\)
−0.188556 + 0.982062i \(0.560381\pi\)
\(48\) 5.47918 + 3.16341i 0.790852 + 0.456598i
\(49\) −2.98070 5.16273i −0.425815 0.737533i
\(50\) 0 0
\(51\) 2.63977 0.369641
\(52\) 1.60490 0.914884i 0.222560 0.126872i
\(53\) 4.43937i 0.609795i −0.952385 0.304897i \(-0.901378\pi\)
0.952385 0.304897i \(-0.0986222\pi\)
\(54\) 1.38111 0.797382i 0.187945 0.108510i
\(55\) 0 0
\(56\) −5.51603 + 9.55405i −0.737111 + 1.27671i
\(57\) 5.28942 0.700600
\(58\) −0.0150801 + 0.0261196i −0.00198012 + 0.00342967i
\(59\) 0.148458 + 0.0857123i 0.0193276 + 0.0111588i 0.509633 0.860392i \(-0.329781\pi\)
−0.490305 + 0.871551i \(0.663115\pi\)
\(60\) 0 0
\(61\) −1.68012 + 2.91005i −0.215117 + 0.372594i −0.953309 0.301997i \(-0.902347\pi\)
0.738192 + 0.674591i \(0.235680\pi\)
\(62\) 5.77162 3.33225i 0.732997 0.423196i
\(63\) −4.39111 7.60563i −0.553228 0.958219i
\(64\) 8.86488 1.10811
\(65\) 0 0
\(66\) 15.2807 1.88093
\(67\) −3.19990 5.54239i −0.390930 0.677111i 0.601642 0.798766i \(-0.294513\pi\)
−0.992572 + 0.121655i \(0.961180\pi\)
\(68\) 0.502227 0.289961i 0.0609040 0.0351629i
\(69\) 4.53957 7.86276i 0.546500 0.946566i
\(70\) 0 0
\(71\) 9.35076 + 5.39866i 1.10973 + 0.640703i 0.938760 0.344573i \(-0.111976\pi\)
0.170971 + 0.985276i \(0.445309\pi\)
\(72\) −3.73748 + 6.47351i −0.440467 + 0.762911i
\(73\) −4.70308 −0.550454 −0.275227 0.961379i \(-0.588753\pi\)
−0.275227 + 0.961379i \(0.588753\pi\)
\(74\) −5.30812 + 9.19393i −0.617056 + 1.06877i
\(75\) 0 0
\(76\) 1.00633 0.581008i 0.115435 0.0666462i
\(77\) 19.3396i 2.20395i
\(78\) −5.07938 8.91030i −0.575126 1.00889i
\(79\) 11.9826 1.34815 0.674075 0.738663i \(-0.264543\pi\)
0.674075 + 0.738663i \(0.264543\pi\)
\(80\) 0 0
\(81\) 5.18379 + 8.97859i 0.575976 + 0.997621i
\(82\) −3.94209 2.27597i −0.435331 0.251338i
\(83\) 12.1286 1.33129 0.665643 0.746270i \(-0.268157\pi\)
0.665643 + 0.746270i \(0.268157\pi\)
\(84\) −3.72572 2.15104i −0.406509 0.234698i
\(85\) 0 0
\(86\) 1.38051i 0.148864i
\(87\) −0.0499450 0.0288357i −0.00535466 0.00309152i
\(88\) 14.2555 8.23042i 1.51964 0.877366i
\(89\) −13.9898 + 8.07702i −1.48292 + 0.856162i −0.999812 0.0194001i \(-0.993824\pi\)
−0.483105 + 0.875562i \(0.660491\pi\)
\(90\) 0 0
\(91\) 11.2771 6.42856i 1.18216 0.673896i
\(92\) 1.99457i 0.207948i
\(93\) 6.37182 + 11.0363i 0.660727 + 1.14441i
\(94\) 1.57666 + 2.73086i 0.162620 + 0.281666i
\(95\) 0 0
\(96\) 6.57666i 0.671228i
\(97\) −6.08408 + 10.5379i −0.617745 + 1.06997i 0.372151 + 0.928172i \(0.378620\pi\)
−0.989896 + 0.141794i \(0.954713\pi\)
\(98\) −3.63553 + 6.29692i −0.367244 + 0.636085i
\(99\) 13.1039i 1.31699i
\(100\) 0 0
\(101\) −2.02721 3.51122i −0.201714 0.349380i 0.747366 0.664412i \(-0.231318\pi\)
−0.949081 + 0.315032i \(0.897985\pi\)
\(102\) −1.60984 2.78833i −0.159398 0.276086i
\(103\) 17.9035i 1.76408i 0.471173 + 0.882041i \(0.343831\pi\)
−0.471173 + 0.882041i \(0.656169\pi\)
\(104\) −9.53781 5.57666i −0.935259 0.546837i
\(105\) 0 0
\(106\) −4.68922 + 2.70732i −0.455457 + 0.262958i
\(107\) 7.90842 4.56593i 0.764536 0.441405i −0.0663862 0.997794i \(-0.521147\pi\)
0.830922 + 0.556389i \(0.187814\pi\)
\(108\) 0.580172 + 0.334963i 0.0558271 + 0.0322318i
\(109\) 7.37605i 0.706498i −0.935529 0.353249i \(-0.885077\pi\)
0.935529 0.353249i \(-0.114923\pi\)
\(110\) 0 0
\(111\) −17.5803 10.1500i −1.66865 0.963396i
\(112\) 9.76645 0.922843
\(113\) −6.12789 3.53794i −0.576463 0.332821i 0.183263 0.983064i \(-0.441334\pi\)
−0.759727 + 0.650243i \(0.774667\pi\)
\(114\) −3.22572 5.58710i −0.302116 0.523280i
\(115\) 0 0
\(116\) −0.0126697 −0.00117635
\(117\) 7.64096 4.35578i 0.706407 0.402692i
\(118\) 0.209084i 0.0192478i
\(119\) 3.52897 2.03745i 0.323500 0.186773i
\(120\) 0 0
\(121\) 8.92820 15.4641i 0.811655 1.40583i
\(122\) 4.09843 0.371055
\(123\) 4.35203 7.53794i 0.392409 0.679673i
\(124\) 2.42453 + 1.39980i 0.217729 + 0.125706i
\(125\) 0 0
\(126\) −5.35578 + 9.27648i −0.477131 + 0.826415i
\(127\) −9.90396 + 5.71806i −0.878835 + 0.507395i −0.870274 0.492568i \(-0.836058\pi\)
−0.00856072 + 0.999963i \(0.502725\pi\)
\(128\) −2.58631 4.47962i −0.228600 0.395946i
\(129\) −2.63977 −0.232418
\(130\) 0 0
\(131\) −10.5680 −0.923328 −0.461664 0.887055i \(-0.652747\pi\)
−0.461664 + 0.887055i \(0.652747\pi\)
\(132\) 3.20955 + 5.55910i 0.279355 + 0.483858i
\(133\) 7.07115 4.08253i 0.613146 0.354000i
\(134\) −3.90288 + 6.75998i −0.337157 + 0.583974i
\(135\) 0 0
\(136\) −3.00367 1.73417i −0.257563 0.148704i
\(137\) 1.89336 3.27940i 0.161761 0.280178i −0.773739 0.633504i \(-0.781616\pi\)
0.935500 + 0.353326i \(0.114949\pi\)
\(138\) −11.0737 −0.942656
\(139\) 1.00693 1.74406i 0.0854068 0.147929i −0.820158 0.572138i \(-0.806114\pi\)
0.905564 + 0.424209i \(0.139448\pi\)
\(140\) 0 0
\(141\) −5.22186 + 3.01484i −0.439760 + 0.253895i
\(142\) 13.1694i 1.10515i
\(143\) −19.3681 0.106280i −1.61964 0.00888757i
\(144\) 6.61742 0.551452
\(145\) 0 0
\(146\) 2.86814 + 4.96777i 0.237369 + 0.411136i
\(147\) −12.0408 6.95174i −0.993105 0.573370i
\(148\) −4.45965 −0.366581
\(149\) −4.77855 2.75890i −0.391474 0.226018i 0.291324 0.956624i \(-0.405904\pi\)
−0.682799 + 0.730607i \(0.739237\pi\)
\(150\) 0 0
\(151\) 4.88961i 0.397911i 0.980009 + 0.198956i \(0.0637549\pi\)
−0.980009 + 0.198956i \(0.936245\pi\)
\(152\) −6.01859 3.47484i −0.488172 0.281846i
\(153\) 2.39111 1.38051i 0.193310 0.111608i
\(154\) 20.4280 11.7941i 1.64614 0.950397i
\(155\) 0 0
\(156\) 2.17469 3.71938i 0.174114 0.297789i
\(157\) 10.0405i 0.801323i −0.916226 0.400661i \(-0.868780\pi\)
0.916226 0.400661i \(-0.131220\pi\)
\(158\) −7.30752 12.6570i −0.581355 1.00694i
\(159\) −5.17686 8.96658i −0.410551 0.711096i
\(160\) 0 0
\(161\) 14.0151i 1.10454i
\(162\) 6.32260 10.9511i 0.496750 0.860397i
\(163\) −3.39062 + 5.87273i −0.265574 + 0.459988i −0.967714 0.252051i \(-0.918895\pi\)
0.702140 + 0.712039i \(0.252228\pi\)
\(164\) 1.91217i 0.149315i
\(165\) 0 0
\(166\) −7.39654 12.8112i −0.574083 0.994341i
\(167\) 5.24490 + 9.08444i 0.405863 + 0.702975i 0.994421 0.105479i \(-0.0336377\pi\)
−0.588559 + 0.808455i \(0.700304\pi\)
\(168\) 25.7295i 1.98507i
\(169\) 6.37605 + 11.3290i 0.490466 + 0.871460i
\(170\) 0 0
\(171\) 4.79118 2.76619i 0.366391 0.211536i
\(172\) −0.502227 + 0.289961i −0.0382944 + 0.0221093i
\(173\) −3.86113 2.22923i −0.293557 0.169485i 0.345988 0.938239i \(-0.387544\pi\)
−0.639545 + 0.768754i \(0.720877\pi\)
\(174\) 0.0703412i 0.00533255i
\(175\) 0 0
\(176\) −12.6201 7.28621i −0.951275 0.549219i
\(177\) 0.399804 0.0300511
\(178\) 17.0632 + 9.85143i 1.27894 + 0.738396i
\(179\) −9.31564 16.1352i −0.696284 1.20600i −0.969746 0.244116i \(-0.921502\pi\)
0.273462 0.961883i \(-0.411831\pi\)
\(180\) 0 0
\(181\) −18.0900 −1.34462 −0.672310 0.740270i \(-0.734698\pi\)
−0.672310 + 0.740270i \(0.734698\pi\)
\(182\) −13.6676 7.99131i −1.01311 0.592355i
\(183\) 7.83690i 0.579320i
\(184\) −10.3307 + 5.96446i −0.761593 + 0.439706i
\(185\) 0 0
\(186\) 7.77162 13.4608i 0.569843 0.986997i
\(187\) −6.08012 −0.444622
\(188\) −0.662321 + 1.14717i −0.0483047 + 0.0836662i
\(189\) 4.07666 + 2.35366i 0.296533 + 0.171204i
\(190\) 0 0
\(191\) −13.6682 + 23.6740i −0.988994 + 1.71299i −0.366361 + 0.930473i \(0.619397\pi\)
−0.622632 + 0.782515i \(0.713937\pi\)
\(192\) 17.9052 10.3375i 1.29219 0.746048i
\(193\) −10.8837 18.8511i −0.783425 1.35693i −0.929935 0.367723i \(-0.880137\pi\)
0.146510 0.989209i \(-0.453196\pi\)
\(194\) 14.8413 1.06555
\(195\) 0 0
\(196\) −3.05441 −0.218172
\(197\) 0.848360 + 1.46940i 0.0604432 + 0.104691i 0.894664 0.446741i \(-0.147415\pi\)
−0.834220 + 0.551431i \(0.814082\pi\)
\(198\) 13.8413 7.99131i 0.983662 0.567917i
\(199\) −12.6627 + 21.9325i −0.897637 + 1.55475i −0.0671309 + 0.997744i \(0.521385\pi\)
−0.830506 + 0.557009i \(0.811949\pi\)
\(200\) 0 0
\(201\) −12.9262 7.46296i −0.911746 0.526397i
\(202\) −2.47256 + 4.28259i −0.173968 + 0.301322i
\(203\) −0.0890252 −0.00624834
\(204\) 0.676260 1.17132i 0.0473477 0.0820086i
\(205\) 0 0
\(206\) 18.9111 10.9183i 1.31760 0.760715i
\(207\) 9.49617i 0.660030i
\(208\) −0.0536711 + 9.78083i −0.00372142 + 0.678179i
\(209\) −12.1830 −0.842716
\(210\) 0 0
\(211\) 0.167753 + 0.290558i 0.0115486 + 0.0200028i 0.871742 0.489965i \(-0.162991\pi\)
−0.860193 + 0.509968i \(0.829657\pi\)
\(212\) −1.96984 1.13729i −0.135289 0.0781092i
\(213\) 25.1820 1.72544
\(214\) −9.64579 5.56900i −0.659373 0.380689i
\(215\) 0 0
\(216\) 4.00663i 0.272616i
\(217\) 17.0363 + 9.83592i 1.15650 + 0.667706i
\(218\) −7.79118 + 4.49824i −0.527685 + 0.304659i
\(219\) −9.49922 + 5.48438i −0.641898 + 0.370600i
\(220\) 0 0
\(221\) 2.02106 + 3.54536i 0.135951 + 0.238487i
\(222\) 24.7597i 1.66176i
\(223\) −6.14838 10.6493i −0.411726 0.713130i 0.583353 0.812219i \(-0.301741\pi\)
−0.995079 + 0.0990887i \(0.968407\pi\)
\(224\) 5.07606 + 8.79200i 0.339159 + 0.587440i
\(225\) 0 0
\(226\) 8.63036i 0.574083i
\(227\) 3.81613 6.60974i 0.253286 0.438704i −0.711143 0.703048i \(-0.751822\pi\)
0.964428 + 0.264344i \(0.0851554\pi\)
\(228\) 1.35505 2.34702i 0.0897406 0.155435i
\(229\) 14.4008i 0.951631i −0.879545 0.475815i \(-0.842153\pi\)
0.879545 0.475815i \(-0.157847\pi\)
\(230\) 0 0
\(231\) 22.5523 + 39.0618i 1.48384 + 2.57008i
\(232\) 0.0378868 + 0.0656218i 0.00248739 + 0.00430828i
\(233\) 9.49617i 0.622115i −0.950391 0.311057i \(-0.899317\pi\)
0.950391 0.311057i \(-0.100683\pi\)
\(234\) −9.26071 5.41465i −0.605392 0.353966i
\(235\) 0 0
\(236\) 0.0760645 0.0439159i 0.00495138 0.00285868i
\(237\) 24.2023 13.9732i 1.57211 0.907657i
\(238\) −4.30423 2.48505i −0.279002 0.161082i
\(239\) 19.9143i 1.28815i 0.764962 + 0.644076i \(0.222758\pi\)
−0.764962 + 0.644076i \(0.777242\pi\)
\(240\) 0 0
\(241\) 20.1493 + 11.6332i 1.29793 + 0.749360i 0.980046 0.198770i \(-0.0636947\pi\)
0.317883 + 0.948130i \(0.397028\pi\)
\(242\) −21.7792 −1.40002
\(243\) 17.5432 + 10.1286i 1.12540 + 0.649750i
\(244\) 0.860832 + 1.49100i 0.0551091 + 0.0954518i
\(245\) 0 0
\(246\) −10.6162 −0.676866
\(247\) 4.04968 + 7.10400i 0.257675 + 0.452017i
\(248\) 16.7436i 1.06322i
\(249\) 24.4972 14.1434i 1.55244 0.896304i
\(250\) 0 0
\(251\) 5.92008 10.2539i 0.373672 0.647219i −0.616455 0.787390i \(-0.711432\pi\)
0.990127 + 0.140171i \(0.0447652\pi\)
\(252\) −4.49969 −0.283454
\(253\) −10.4559 + 18.1101i −0.657357 + 1.13858i
\(254\) 12.0797 + 6.97424i 0.757950 + 0.437603i
\(255\) 0 0
\(256\) 5.71040 9.89070i 0.356900 0.618169i
\(257\) −4.80646 + 2.77501i −0.299819 + 0.173100i −0.642361 0.766402i \(-0.722045\pi\)
0.342543 + 0.939502i \(0.388712\pi\)
\(258\) 1.60984 + 2.78833i 0.100224 + 0.173594i
\(259\) −31.3363 −1.94714
\(260\) 0 0
\(261\) −0.0603205 −0.00373375
\(262\) 6.44481 + 11.1627i 0.398161 + 0.689636i
\(263\) 5.94065 3.42983i 0.366316 0.211493i −0.305532 0.952182i \(-0.598834\pi\)
0.671848 + 0.740689i \(0.265501\pi\)
\(264\) 19.1954 33.2474i 1.18139 2.04623i
\(265\) 0 0
\(266\) −8.62459 4.97941i −0.528807 0.305307i
\(267\) −18.8376 + 32.6277i −1.15284 + 1.99678i
\(268\) −3.27903 −0.200299
\(269\) −0.710994 + 1.23148i −0.0433501 + 0.0750845i −0.886886 0.461988i \(-0.847136\pi\)
0.843536 + 0.537072i \(0.180470\pi\)
\(270\) 0 0
\(271\) 8.63381 4.98473i 0.524467 0.302801i −0.214294 0.976769i \(-0.568745\pi\)
0.738760 + 0.673968i \(0.235412\pi\)
\(272\) 3.07045i 0.186173i
\(273\) 15.2807 26.1347i 0.924831 1.58175i
\(274\) −4.61862 −0.279021
\(275\) 0 0
\(276\) −2.32591 4.02860i −0.140003 0.242493i
\(277\) 15.1760 + 8.76187i 0.911837 + 0.526449i 0.881022 0.473076i \(-0.156856\pi\)
0.0308154 + 0.999525i \(0.490190\pi\)
\(278\) −2.45628 −0.147318
\(279\) 11.5432 + 6.66449i 0.691076 + 0.398993i
\(280\) 0 0
\(281\) 10.7352i 0.640406i −0.947349 0.320203i \(-0.896249\pi\)
0.947349 0.320203i \(-0.103751\pi\)
\(282\) 6.36903 + 3.67716i 0.379270 + 0.218972i
\(283\) −1.14175 + 0.659192i −0.0678702 + 0.0391849i −0.533551 0.845768i \(-0.679143\pi\)
0.465681 + 0.884953i \(0.345809\pi\)
\(284\) 4.79099 2.76608i 0.284293 0.164137i
\(285\) 0 0
\(286\) 11.6992 + 20.5229i 0.691790 + 1.21355i
\(287\) 13.4361i 0.793109i
\(288\) 3.43937 + 5.95717i 0.202667 + 0.351030i
\(289\) −7.85945 13.6130i −0.462321 0.800763i
\(290\) 0 0
\(291\) 28.3792i 1.66362i
\(292\) −1.20485 + 2.08685i −0.0705082 + 0.122124i
\(293\) −9.37133 + 16.2316i −0.547479 + 0.948261i 0.450968 + 0.892540i \(0.351079\pi\)
−0.998446 + 0.0557207i \(0.982254\pi\)
\(294\) 16.9579i 0.989004i
\(295\) 0 0
\(296\) 13.3359 + 23.0985i 0.775134 + 1.34257i
\(297\) −3.51187 6.08275i −0.203780 0.352957i
\(298\) 6.72998i 0.389857i
\(299\) 14.0357 + 0.0770194i 0.811708 + 0.00445415i
\(300\) 0 0
\(301\) −3.52897 + 2.03745i −0.203406 + 0.117437i
\(302\) 5.16480 2.98190i 0.297201 0.171589i
\(303\) −8.18904 4.72794i −0.470448 0.271613i
\(304\) 6.15239i 0.352864i
\(305\) 0 0
\(306\) −2.91641 1.68379i −0.166720 0.0962558i
\(307\) −14.3043 −0.816387 −0.408194 0.912895i \(-0.633841\pi\)
−0.408194 + 0.912895i \(0.633841\pi\)
\(308\) 8.58137 + 4.95445i 0.488969 + 0.282306i
\(309\) 20.8777 + 36.1612i 1.18769 + 2.05714i
\(310\) 0 0
\(311\) −2.76102 −0.156563 −0.0782815 0.996931i \(-0.524943\pi\)
−0.0782815 + 0.996931i \(0.524943\pi\)
\(312\) −25.7674 0.141395i −1.45879 0.00800494i
\(313\) 16.3858i 0.926179i −0.886311 0.463090i \(-0.846741\pi\)
0.886311 0.463090i \(-0.153259\pi\)
\(314\) −10.6056 + 6.12316i −0.598510 + 0.345550i
\(315\) 0 0
\(316\) 3.06973 5.31693i 0.172686 0.299101i
\(317\) 1.78575 0.100297 0.0501487 0.998742i \(-0.484030\pi\)
0.0501487 + 0.998742i \(0.484030\pi\)
\(318\) −6.31414 + 10.9364i −0.354080 + 0.613284i
\(319\) 0.115037 + 0.0664168i 0.00644085 + 0.00371863i
\(320\) 0 0
\(321\) 10.6489 18.4444i 0.594362 1.02946i
\(322\) −14.8039 + 8.54702i −0.824987 + 0.476307i
\(323\) 1.28349 + 2.22308i 0.0714156 + 0.123695i
\(324\) 5.31197 0.295110
\(325\) 0 0
\(326\) 8.27099 0.458088
\(327\) −8.60139 14.8980i −0.475658 0.823864i
\(328\) −9.90396 + 5.71806i −0.546855 + 0.315727i
\(329\) −4.65389 + 8.06077i −0.256577 + 0.444405i
\(330\) 0 0
\(331\) −6.25652 3.61220i −0.343889 0.198545i 0.318101 0.948057i \(-0.396955\pi\)
−0.661991 + 0.749512i \(0.730288\pi\)
\(332\) 3.10713 5.38170i 0.170526 0.295359i
\(333\) −21.2325 −1.16353
\(334\) 6.39714 11.0802i 0.350036 0.606280i
\(335\) 0 0
\(336\) 19.7261 11.3889i 1.07615 0.621315i
\(337\) 4.36219i 0.237624i −0.992917 0.118812i \(-0.962091\pi\)
0.992917 0.118812i \(-0.0379085\pi\)
\(338\) 8.07818 13.6438i 0.439395 0.742125i
\(339\) −16.5027 −0.896303
\(340\) 0 0
\(341\) −14.6761 25.4197i −0.794754 1.37655i
\(342\) −5.84374 3.37388i −0.315993 0.182439i
\(343\) 3.73913 0.201894
\(344\) 3.00367 + 1.73417i 0.161947 + 0.0935002i
\(345\) 0 0
\(346\) 5.43792i 0.292344i
\(347\) −23.1291 13.3536i −1.24163 0.716858i −0.272207 0.962239i \(-0.587754\pi\)
−0.969427 + 0.245381i \(0.921087\pi\)
\(348\) −0.0255900 + 0.0147744i −0.00137177 + 0.000791991i
\(349\) 20.4131 11.7855i 1.09269 0.630865i 0.158399 0.987375i \(-0.449367\pi\)
0.934292 + 0.356510i \(0.116033\pi\)
\(350\) 0 0
\(351\) −2.37953 + 4.06973i −0.127010 + 0.217226i
\(352\) 15.1479i 0.807385i
\(353\) 2.86863 + 4.96862i 0.152682 + 0.264453i 0.932213 0.361911i \(-0.117876\pi\)
−0.779531 + 0.626364i \(0.784542\pi\)
\(354\) −0.243818 0.422305i −0.0129588 0.0224453i
\(355\) 0 0
\(356\) 8.27675i 0.438667i
\(357\) 4.75184 8.23042i 0.251494 0.435600i
\(358\) −11.3622 + 19.6799i −0.600509 + 1.04011i
\(359\) 24.7583i 1.30669i −0.757059 0.653347i \(-0.773364\pi\)
0.757059 0.653347i \(-0.226636\pi\)
\(360\) 0 0
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 11.0321 + 19.1081i 0.579833 + 1.00430i
\(363\) 41.6455i 2.18582i
\(364\) 0.0364951 6.65074i 0.00191286 0.348593i
\(365\) 0 0
\(366\) 8.27796 4.77928i 0.432696 0.249817i
\(367\) −22.5630 + 13.0268i −1.17778 + 0.679992i −0.955500 0.294991i \(-0.904683\pi\)
−0.222280 + 0.974983i \(0.571350\pi\)
\(368\) 9.14558 + 5.28021i 0.476747 + 0.275250i
\(369\) 9.10387i 0.473928i
\(370\) 0 0
\(371\) −13.8413 7.99131i −0.718607 0.414888i
\(372\) 6.52938 0.338532
\(373\) −11.4354 6.60224i −0.592103 0.341851i 0.173826 0.984776i \(-0.444387\pi\)
−0.765929 + 0.642926i \(0.777720\pi\)
\(374\) 3.70792 + 6.42231i 0.191732 + 0.332089i
\(375\) 0 0
\(376\) 7.92229 0.408561
\(377\) 0.000489234 0.0891563i 2.51968e−5 0.00459178i
\(378\) 5.74146i 0.295309i
\(379\) −22.5147 + 12.9989i −1.15650 + 0.667707i −0.950463 0.310837i \(-0.899391\pi\)
−0.206039 + 0.978544i \(0.566057\pi\)
\(380\) 0 0
\(381\) −13.3359 + 23.0985i −0.683220 + 1.18337i
\(382\) 33.3418 1.70591
\(383\) −4.80010 + 8.31401i −0.245274 + 0.424826i −0.962208 0.272314i \(-0.912211\pi\)
0.716935 + 0.697140i \(0.245544\pi\)
\(384\) −10.4476 6.03191i −0.533151 0.307815i
\(385\) 0 0
\(386\) −13.2747 + 22.9924i −0.675664 + 1.17028i
\(387\) −2.39111 + 1.38051i −0.121547 + 0.0701752i
\(388\) 3.11726 + 5.39926i 0.158255 + 0.274106i
\(389\) 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
\(392\) 9.13376 + 15.8201i 0.461325 + 0.799038i
\(393\) −21.3450 + 12.3236i −1.07671 + 0.621641i
\(394\) 1.03473 1.79221i 0.0521291 0.0902903i
\(395\) 0 0
\(396\) 5.81445 + 3.35697i 0.292187 + 0.168694i
\(397\) −8.38291 + 14.5196i −0.420726 + 0.728719i −0.996011 0.0892344i \(-0.971558\pi\)
0.575285 + 0.817953i \(0.304891\pi\)
\(398\) 30.8891 1.54833
\(399\) 9.52147 16.4917i 0.476670 0.825616i
\(400\) 0 0
\(401\) 12.0187 6.93902i 0.600187 0.346518i −0.168928 0.985628i \(-0.554031\pi\)
0.769115 + 0.639110i \(0.220697\pi\)
\(402\) 18.2050i 0.907980i
\(403\) −9.94402 + 17.0073i −0.495347 + 0.847196i
\(404\) −2.07733 −0.103351
\(405\) 0 0
\(406\) 0.0542914 + 0.0940355i 0.00269444 + 0.00466690i
\(407\) 40.4924 + 23.3783i 2.00713 + 1.15882i
\(408\) −8.08903 −0.400466
\(409\) 25.4829 + 14.7125i 1.26005 + 0.727489i 0.973083 0.230453i \(-0.0740208\pi\)
0.286964 + 0.957941i \(0.407354\pi\)
\(410\) 0 0
\(411\) 8.83157i 0.435629i
\(412\) 7.94413 + 4.58655i 0.391379 + 0.225963i
\(413\) 0.534478 0.308581i 0.0262999 0.0151843i
\(414\) −10.0306 + 5.79118i −0.492978 + 0.284621i
\(415\) 0 0
\(416\) −8.83284 + 5.03522i −0.433066 + 0.246872i
\(417\) 4.69683i 0.230005i
\(418\) 7.42973 + 12.8687i 0.363400 + 0.629427i
\(419\) 3.48397 + 6.03440i 0.170203 + 0.294800i 0.938491 0.345305i \(-0.112224\pi\)
−0.768288 + 0.640104i \(0.778891\pi\)
\(420\) 0 0
\(421\) 7.12125i 0.347069i 0.984828 + 0.173534i \(0.0555188\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(422\) 0.204607 0.354389i 0.00996010 0.0172514i
\(423\) −3.15332 + 5.46171i −0.153320 + 0.265558i
\(424\) 13.6036i 0.660647i
\(425\) 0 0
\(426\) −15.3571 26.5993i −0.744054 1.28874i
\(427\) 6.04875 + 10.4767i 0.292720 + 0.507005i
\(428\) 4.67883i 0.226160i
\(429\) −39.2433 + 22.3709i −1.89468 + 1.08008i
\(430\) 0 0
\(431\) 26.1664 15.1072i 1.26039 0.727687i 0.287241 0.957858i \(-0.407262\pi\)
0.973150 + 0.230171i \(0.0739286\pi\)
\(432\) −3.07177 + 1.77349i −0.147791 + 0.0853270i
\(433\) 1.03934 + 0.600065i 0.0499476 + 0.0288373i 0.524766 0.851247i \(-0.324153\pi\)
−0.474818 + 0.880084i \(0.657486\pi\)
\(434\) 23.9935i 1.15172i
\(435\) 0 0
\(436\) −3.27290 1.88961i −0.156744 0.0904960i
\(437\) 8.82884 0.422341
\(438\) 11.5861 + 6.68922i 0.553604 + 0.319623i
\(439\) 8.27705 + 14.3363i 0.395042 + 0.684233i 0.993107 0.117215i \(-0.0373966\pi\)
−0.598064 + 0.801448i \(0.704063\pi\)
\(440\) 0 0
\(441\) −14.5421 −0.692481
\(442\) 2.51236 4.29692i 0.119501 0.204383i
\(443\) 4.55949i 0.216628i 0.994117 + 0.108314i \(0.0345452\pi\)
−0.994117 + 0.108314i \(0.965455\pi\)
\(444\) −9.00753 + 5.20050i −0.427478 + 0.246805i
\(445\) 0 0
\(446\) −7.49910 + 12.9888i −0.355093 + 0.615038i
\(447\) −12.8689 −0.608676
\(448\) 15.9577 27.6395i 0.753929 1.30584i
\(449\) −11.9963 6.92608i −0.566142 0.326862i 0.189465 0.981887i \(-0.439325\pi\)
−0.755607 + 0.655025i \(0.772658\pi\)
\(450\) 0 0
\(451\) −10.0239 + 17.3620i −0.472009 + 0.817544i
\(452\) −3.13971 + 1.81271i −0.147680 + 0.0852628i
\(453\) 5.70189 + 9.87596i 0.267898 + 0.464013i
\(454\) −9.30897 −0.436892
\(455\) 0 0
\(456\) −16.2083 −0.759025
\(457\) −20.0573 34.7402i −0.938240 1.62508i −0.768751 0.639548i \(-0.779122\pi\)
−0.169489 0.985532i \(-0.554212\pi\)
\(458\) −15.2113 + 8.78222i −0.710775 + 0.410366i
\(459\) −0.739961 + 1.28165i −0.0345384 + 0.0598223i
\(460\) 0 0
\(461\) 6.52897 + 3.76950i 0.304084 + 0.175563i 0.644276 0.764793i \(-0.277159\pi\)
−0.340192 + 0.940356i \(0.610492\pi\)
\(462\) 27.5068 47.6432i 1.27973 2.21656i
\(463\) 23.3031 1.08299 0.541494 0.840705i \(-0.317859\pi\)
0.541494 + 0.840705i \(0.317859\pi\)
\(464\) 0.0335403 0.0580936i 0.00155707 0.00269693i
\(465\) 0 0
\(466\) −10.0306 + 5.79118i −0.464659 + 0.268271i
\(467\) 22.6297i 1.04718i −0.851971 0.523589i \(-0.824593\pi\)
0.851971 0.523589i \(-0.175407\pi\)
\(468\) 0.0247279 4.50632i 0.00114305 0.208305i
\(469\) −23.0405 −1.06391
\(470\) 0 0
\(471\) −11.7085 20.2797i −0.539500 0.934441i
\(472\) −0.454919 0.262648i −0.0209394 0.0120893i
\(473\) 6.08012 0.279564
\(474\) −29.5192 17.0429i −1.35586 0.782808i
\(475\) 0 0
\(476\) 2.08783i 0.0956956i
\(477\) −9.37844 5.41465i −0.429409 0.247920i
\(478\) 21.0351 12.1446i 0.962124 0.555482i
\(479\) 17.8789 10.3224i 0.816910 0.471643i −0.0324399 0.999474i \(-0.510328\pi\)
0.849350 + 0.527831i \(0.176994\pi\)
\(480\) 0 0
\(481\) 0.172207 31.3825i 0.00785198 1.43092i
\(482\) 28.3777i 1.29257i
\(483\) −16.3433 28.3075i −0.743648 1.28804i
\(484\) −4.57449 7.92325i −0.207931 0.360148i
\(485\) 0 0
\(486\) 24.7074i 1.12075i
\(487\) −1.51802 + 2.62929i −0.0687882 + 0.119145i −0.898368 0.439243i \(-0.855247\pi\)
0.829580 + 0.558388i \(0.188580\pi\)
\(488\) 5.14838 8.91725i 0.233056 0.403665i
\(489\) 15.8155i 0.715203i
\(490\) 0 0
\(491\) 5.33401 + 9.23877i 0.240720 + 0.416940i 0.960920 0.276827i \(-0.0892830\pi\)
−0.720199 + 0.693767i \(0.755950\pi\)
\(492\) −2.22982 3.86217i −0.100528 0.174120i
\(493\) 0.0279884i 0.00126053i
\(494\) 5.03414 8.60992i 0.226497 0.387379i
\(495\) 0 0
\(496\) −12.8369 + 7.41139i −0.576394 + 0.332781i
\(497\) 33.6646 19.4362i 1.51006 0.871835i
\(498\) −29.8789 17.2506i −1.33890 0.773016i
\(499\) 33.9143i 1.51821i −0.650966 0.759107i \(-0.725636\pi\)
0.650966 0.759107i \(-0.274364\pi\)
\(500\) 0 0
\(501\) 21.1872 + 12.2324i 0.946572 + 0.546504i
\(502\) −14.4413 −0.644546
\(503\) 10.9358 + 6.31380i 0.487604 + 0.281518i 0.723580 0.690241i \(-0.242495\pi\)
−0.235976 + 0.971759i \(0.575829\pi\)
\(504\) 13.4557 + 23.3059i 0.599363 + 1.03813i
\(505\) 0 0
\(506\) 25.5058 1.13387
\(507\) 26.0893 + 15.4468i 1.15866 + 0.686019i
\(508\) 5.85945i 0.259971i
\(509\) 20.9168 12.0763i 0.927120 0.535273i 0.0412201 0.999150i \(-0.486876\pi\)
0.885899 + 0.463877i \(0.153542\pi\)
\(510\) 0 0
\(511\) −8.46601 + 14.6636i −0.374514 + 0.648678i
\(512\) −24.2750 −1.07281
\(513\) −1.48269 + 2.56810i −0.0654625 + 0.113384i
\(514\) 5.86238 + 3.38465i 0.258578 + 0.149290i
\(515\) 0 0
\(516\) −0.676260 + 1.17132i −0.0297707 + 0.0515644i
\(517\) 12.0274 6.94402i 0.528964 0.305398i
\(518\) 19.1103 + 33.0999i 0.839656 + 1.45433i
\(519\) −10.3982 −0.456431
\(520\) 0 0
\(521\) −24.7521 −1.08441 −0.542205 0.840246i \(-0.682410\pi\)
−0.542205 + 0.840246i \(0.682410\pi\)
\(522\) 0.0367861 + 0.0637154i 0.00161008 + 0.00278875i
\(523\) 32.0712 18.5163i 1.40238 0.809662i 0.407739 0.913098i \(-0.366317\pi\)
0.994636 + 0.103436i \(0.0329838\pi\)
\(524\) −2.70732 + 4.68922i −0.118270 + 0.204850i
\(525\) 0 0
\(526\) −7.24573 4.18332i −0.315929 0.182402i
\(527\) −3.09229 + 5.35600i −0.134702 + 0.233311i
\(528\) −33.9865 −1.47907
\(529\) −3.92277 + 6.79444i −0.170555 + 0.295410i
\(530\) 0 0
\(531\) 0.362145 0.209084i 0.0157157 0.00907348i
\(532\) 4.18348i 0.181377i
\(533\) 13.4559 + 0.0738376i 0.582840 + 0.00319826i
\(534\) 45.9519 1.98854
\(535\) 0 0
\(536\) 9.80545 + 16.9835i 0.423531 + 0.733577i
\(537\) −37.6312 21.7264i −1.62391 0.937562i
\(538\) 1.73438 0.0747744
\(539\) 27.7332 + 16.0118i 1.19456 + 0.689677i
\(540\) 0 0
\(541\) 8.38144i 0.360346i 0.983635 + 0.180173i \(0.0576658\pi\)
−0.983635 + 0.180173i \(0.942334\pi\)
\(542\) −10.5305 6.07981i −0.452326 0.261150i
\(543\) −36.5379 + 21.0952i −1.56799 + 0.905281i
\(544\) −2.76409 + 1.59585i −0.118509 + 0.0684215i
\(545\) 0 0
\(546\) −36.9245 0.202618i −1.58022 0.00867126i
\(547\) 22.7842i 0.974181i 0.873351 + 0.487091i \(0.161942\pi\)
−0.873351 + 0.487091i \(0.838058\pi\)
\(548\) −0.970090 1.68025i −0.0414402 0.0717765i
\(549\) 4.09843 + 7.09870i 0.174917 + 0.302965i
\(550\) 0 0
\(551\) 0.0560816i 0.00238915i
\(552\) −13.9106 + 24.0938i −0.592074 + 1.02550i
\(553\) 21.5699 37.3601i 0.917245 1.58871i
\(554\) 21.3735i 0.908071i
\(555\) 0 0
\(556\) −0.515915 0.893592i −0.0218797 0.0378967i
\(557\) −14.0764 24.3810i −0.596435 1.03306i −0.993343 0.115197i \(-0.963250\pi\)
0.396908 0.917858i \(-0.370083\pi\)
\(558\) 16.2572i 0.688222i
\(559\) −2.02106 3.54536i −0.0854816 0.149953i
\(560\) 0 0
\(561\) −12.2805 + 7.09017i −0.518484 + 0.299347i
\(562\) −11.3393 + 6.54676i −0.478321 + 0.276159i
\(563\) −15.7013 9.06514i −0.661731 0.382050i 0.131206 0.991355i \(-0.458115\pi\)
−0.792936 + 0.609305i \(0.791449\pi\)
\(564\) 3.08939i 0.130087i
\(565\) 0 0
\(566\) 1.39258 + 0.804007i 0.0585346 + 0.0337950i
\(567\) 37.3253 1.56752
\(568\) −28.6535 16.5431i −1.20227 0.694133i
\(569\) −20.2992 35.1593i −0.850988 1.47395i −0.880317 0.474385i \(-0.842670\pi\)
0.0293292 0.999570i \(-0.490663\pi\)
\(570\) 0 0
\(571\) −24.7159 −1.03433 −0.517164 0.855886i \(-0.673012\pi\)
−0.517164 + 0.855886i \(0.673012\pi\)
\(572\) −5.00891 + 8.56677i −0.209433 + 0.358195i
\(573\) 63.7551i 2.66341i
\(574\) −14.1923 + 8.19393i −0.592375 + 0.342008i
\(575\) 0 0
\(576\) 10.8124 18.7276i 0.450516 0.780317i
\(577\) 23.0691 0.960379 0.480189 0.877165i \(-0.340568\pi\)
0.480189 + 0.877165i \(0.340568\pi\)
\(578\) −9.58607 + 16.6036i −0.398728 + 0.690617i
\(579\) −43.9654 25.3834i −1.82714 1.05490i
\(580\) 0 0
\(581\) 21.8327 37.8153i 0.905771 1.56884i
\(582\) 29.9763 17.3068i 1.24256 0.717392i
\(583\) 11.9237 + 20.6525i 0.493831 + 0.855341i
\(584\) 14.4116 0.596358
\(585\) 0 0
\(586\) 22.8602 0.944345
\(587\) 10.1762 + 17.6256i 0.420015 + 0.727487i 0.995940 0.0900152i \(-0.0286916\pi\)
−0.575926 + 0.817502i \(0.695358\pi\)
\(588\) −6.16925 + 3.56182i −0.254416 + 0.146887i
\(589\) −6.19615 + 10.7321i −0.255308 + 0.442206i
\(590\) 0 0
\(591\) 3.42701 + 1.97859i 0.140968 + 0.0813881i
\(592\) 11.8060 20.4486i 0.485223 0.840432i
\(593\) 10.3834 0.426395 0.213198 0.977009i \(-0.431612\pi\)
0.213198 + 0.977009i \(0.431612\pi\)
\(594\) −4.28339 + 7.41904i −0.175750 + 0.304407i
\(595\) 0 0
\(596\) −2.44836 + 1.41356i −0.100289 + 0.0579017i
\(597\) 59.0652i 2.41738i
\(598\) −8.47825 14.8726i −0.346701 0.608187i
\(599\) 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 0.833751 + 0.552141i \(0.186189\pi\)
0.0612928 + 0.998120i \(0.480478\pi\)
\(602\) 4.30423 + 2.48505i 0.175428 + 0.101283i
\(603\) −15.6115 −0.635750
\(604\) 2.16962 + 1.25263i 0.0882806 + 0.0509688i
\(605\) 0 0
\(606\) 11.5332i 0.468505i
\(607\) 1.88395 + 1.08770i 0.0764673 + 0.0441484i 0.537746 0.843107i \(-0.319276\pi\)
−0.461279 + 0.887255i \(0.652609\pi\)
\(608\) −5.53854 + 3.19768i −0.224617 + 0.129683i
\(609\) −0.179812 + 0.103814i −0.00728634 + 0.00420677i
\(610\) 0 0
\(611\) −8.04707 4.70504i −0.325550 0.190346i
\(612\) 1.41465i 0.0571837i
\(613\) −7.38100 12.7843i −0.298116 0.516352i 0.677589 0.735441i \(-0.263025\pi\)
−0.975705 + 0.219089i \(0.929691\pi\)
\(614\) 8.72336 + 15.1093i 0.352046 + 0.609762i
\(615\) 0 0
\(616\) 59.2622i 2.38774i
\(617\) 10.1486 17.5779i 0.408567 0.707659i −0.586162 0.810194i \(-0.699362\pi\)
0.994729 + 0.102535i \(0.0326953\pi\)
\(618\) 25.4642 44.1053i 1.02432 1.77418i
\(619\) 9.94207i 0.399605i 0.979836 + 0.199803i \(0.0640301\pi\)
−0.979836 + 0.199803i \(0.935970\pi\)
\(620\) 0 0
\(621\) 2.54500 + 4.40807i 0.102127 + 0.176890i
\(622\) 1.68379 + 2.91641i 0.0675138 + 0.116937i
\(623\) 58.1577i 2.33004i
\(624\) 11.2973 + 19.8178i 0.452252 + 0.793345i
\(625\) 0 0
\(626\) −17.3080 + 9.99276i −0.691766 + 0.399391i
\(627\) −24.6070 + 14.2069i −0.982711 + 0.567368i
\(628\) −4.45519 2.57221i −0.177782 0.102642i
\(629\) 9.85174i 0.392815i
\(630\) 0 0
\(631\) 0.843006 + 0.486710i 0.0335596 + 0.0193756i 0.516686 0.856175i \(-0.327165\pi\)
−0.483126 + 0.875551i \(0.660499\pi\)
\(632\) −36.7183 −1.46058
\(633\) 0.677652 + 0.391243i 0.0269342 + 0.0155505i
\(634\) −1.08903 1.88625i −0.0432507 0.0749124i
\(635\) 0 0
\(636\) −5.30487 −0.210352
\(637\) 0.117945 21.4938i 0.00467314 0.851617i
\(638\) 0.162015i 0.00641425i
\(639\) 22.8100 13.1694i 0.902350 0.520972i
\(640\) 0 0
\(641\) −6.31047 + 10.9301i −0.249249 + 0.431711i −0.963318 0.268364i \(-0.913517\pi\)
0.714069 + 0.700075i \(0.246850\pi\)
\(642\) −25.9766 −1.02521
\(643\) 4.98022 8.62599i 0.196401 0.340176i −0.750958 0.660350i \(-0.770408\pi\)
0.947359 + 0.320174i \(0.103741\pi\)
\(644\) −6.21878 3.59042i −0.245054 0.141482i
\(645\) 0 0
\(646\) 1.56546 2.71146i 0.0615923 0.106681i
\(647\) −31.4162 + 18.1381i −1.23510 + 0.713084i −0.968088 0.250610i \(-0.919369\pi\)
−0.267009 + 0.963694i \(0.586035\pi\)
\(648\) −15.8847 27.5131i −0.624009 1.08081i
\(649\) −0.920861 −0.0361470
\(650\) 0 0
\(651\) 45.8796 1.79816
\(652\) 1.73723 + 3.00898i 0.0680353 + 0.117841i
\(653\) 11.9125 6.87769i 0.466172 0.269145i −0.248464 0.968641i \(-0.579926\pi\)
0.714636 + 0.699497i \(0.246592\pi\)
\(654\) −10.4910 + 18.1709i −0.410231 + 0.710540i
\(655\) 0 0
\(656\) 8.76776 + 5.06207i 0.342324 + 0.197641i
\(657\) −5.73629 + 9.93555i −0.223794 + 0.387623i
\(658\) 11.3526 0.442570
\(659\) −1.29092 + 2.23593i −0.0502869 + 0.0870995i −0.890073 0.455818i \(-0.849347\pi\)
0.839786 + 0.542917i \(0.182680\pi\)
\(660\) 0 0
\(661\) −21.5437 + 12.4382i −0.837951 + 0.483791i −0.856567 0.516036i \(-0.827407\pi\)
0.0186163 + 0.999827i \(0.494074\pi\)
\(662\) 8.81151i 0.342469i
\(663\) 8.21643 + 4.80406i 0.319100 + 0.186574i
\(664\) −37.1656 −1.44231
\(665\) 0 0
\(666\) 12.9485 + 22.4274i 0.501743 + 0.869045i
\(667\) −0.0833657 0.0481312i −0.00322793 0.00186365i
\(668\) 5.37460 0.207949
\(669\) −24.8368 14.3395i −0.960246 0.554398i
\(670\) 0 0
\(671\) 18.0506i 0.696834i
\(672\) 20.5051 + 11.8386i 0.791002 + 0.456685i
\(673\) −37.5181 + 21.6611i −1.44622 + 0.834974i −0.998253 0.0590774i \(-0.981184\pi\)
−0.447964 + 0.894052i \(0.647851\pi\)
\(674\) −4.60770 + 2.66025i −0.177482 + 0.102469i
\(675\) 0 0
\(676\) 6.66033 + 0.0730977i 0.256167 + 0.00281145i
\(677\) 41.3625i 1.58969i 0.606813 + 0.794845i \(0.292448\pi\)
−0.606813 + 0.794845i \(0.707552\pi\)
\(678\) 10.0641 + 17.4315i 0.386508 + 0.669451i
\(679\) 21.9039 + 37.9386i 0.840594 + 1.45595i
\(680\) 0 0
\(681\) 17.8003i 0.682110i
\(682\) −17.9002 + 31.0041i −0.685435 + 1.18721i
\(683\) −1.31344 + 2.27495i −0.0502574 + 0.0870484i −0.890060 0.455844i \(-0.849338\pi\)
0.839802 + 0.542892i \(0.182671\pi\)
\(684\) 2.83459i 0.108383i
\(685\) 0 0
\(686\) −2.28028 3.94957i −0.0870617 0.150795i
\(687\) −16.7931 29.0865i −0.640696 1.10972i
\(688\) 3.07045i 0.117060i
\(689\) 8.07914 13.8178i 0.307791 0.526417i
\(690\) 0 0
\(691\) −13.2288 + 7.63765i −0.503247 + 0.290550i −0.730053 0.683390i \(-0.760505\pi\)
0.226806 + 0.973940i \(0.427172\pi\)
\(692\) −1.97831 + 1.14218i −0.0752039 + 0.0434190i
\(693\) 40.8560 + 23.5882i 1.55199 + 0.896043i
\(694\) 32.5744i 1.23651i
\(695\) 0 0
\(696\) 0.153046 + 0.0883613i 0.00580120 + 0.00334933i
\(697\) 4.22414 0.160001
\(698\) −24.8976 14.3747i −0.942390 0.544089i
\(699\) −11.0737 19.1802i −0.418846 0.725463i
\(700\) 0 0
\(701\) 48.1947 1.82029 0.910144 0.414292i \(-0.135971\pi\)
0.910144 + 0.414292i \(0.135971\pi\)
\(702\) 5.74991 + 0.0315519i 0.217017 + 0.00119085i
\(703\) 19.7404i 0.744522i
\(704\) −41.2406 + 23.8103i −1.55431 + 0.897383i
\(705\) 0 0
\(706\) 3.49884 6.06016i 0.131680 0.228077i
\(707\) −14.5967 −0.548964
\(708\) 0.102423 0.177401i 0.00384928 0.00666715i
\(709\) 33.6624 + 19.4350i 1.26422 + 0.729896i 0.973887 0.227031i \(-0.0729019\pi\)
0.290329 + 0.956927i \(0.406235\pi\)
\(710\) 0 0
\(711\) 14.6150 25.3140i 0.548107 0.949349i
\(712\) 42.8689 24.7504i 1.60658 0.927560i
\(713\) 10.6355 + 18.4213i 0.398304 + 0.689882i
\(714\) −11.5915 −0.433801
\(715\) 0 0
\(716\) −9.54600 −0.356751
\(717\) 23.2226 + 40.2227i 0.867263 + 1.50214i
\(718\) −26.1517 + 15.0987i −0.975973 + 0.563478i
\(719\) −3.30830 + 5.73015i −0.123379 + 0.213698i −0.921098 0.389331i \(-0.872706\pi\)
0.797719 + 0.603029i \(0.206040\pi\)
\(720\) 0 0
\(721\) 55.8205 + 32.2280i 2.07887 + 1.20023i
\(722\) −8.45024 + 14.6362i −0.314485 + 0.544705i
\(723\) 54.2629 2.01806
\(724\) −4.63433 + 8.02690i −0.172234 + 0.298317i
\(725\) 0 0
\(726\) −43.9893 + 25.3973i −1.63260 + 0.942581i
\(727\) 18.3735i 0.681435i −0.940166 0.340717i \(-0.889330\pi\)
0.940166 0.340717i \(-0.110670\pi\)
\(728\) −34.5562 + 19.6990i −1.28074 + 0.730094i
\(729\) 16.1420 0.597853
\(730\) 0 0
\(731\) −0.640548 1.10946i −0.0236915 0.0410349i
\(732\) 3.47739 + 2.00767i 0.128528 + 0.0742057i
\(733\) −0.791131 −0.0292211 −0.0146105 0.999893i \(-0.504651\pi\)
−0.0146105 + 0.999893i \(0.504651\pi\)
\(734\) 27.5198 + 15.8886i 1.01578 + 0.586458i
\(735\) 0 0
\(736\) 10.9774i 0.404634i
\(737\) 29.7727 + 17.1893i 1.09669 + 0.633175i
\(738\) −9.61623 + 5.55193i −0.353978 + 0.204369i
\(739\) 27.0073 15.5926i 0.993478 0.573585i 0.0871658 0.996194i \(-0.472219\pi\)
0.906312 + 0.422609i \(0.138886\pi\)
\(740\) 0 0
\(741\) 16.4636 + 9.62612i 0.604806 + 0.353624i
\(742\) 19.4938i 0.715639i
\(743\) 2.78152 + 4.81773i 0.102044 + 0.176745i 0.912527 0.409017i \(-0.134128\pi\)
−0.810483 + 0.585763i \(0.800795\pi\)
\(744\) −19.5251 33.8185i −0.715826 1.23985i
\(745\) 0 0
\(746\) 16.1053i 0.589658i
\(747\) 14.7931 25.6224i 0.541251 0.937474i
\(748\) −1.55762 + 2.69787i −0.0569521 + 0.0986439i
\(749\) 32.8765i 1.20128i
\(750\) 0 0
\(751\) −17.6048 30.4925i −0.642410 1.11269i −0.984893 0.173163i \(-0.944601\pi\)
0.342483 0.939524i \(-0.388732\pi\)
\(752\) −3.50672 6.07381i −0.127877 0.221489i
\(753\) 27.6142i 1.00632i
\(754\) −0.0944723 + 0.0538546i −0.00344048 + 0.00196127i
\(755\) 0 0
\(756\) 2.08873 1.20593i 0.0759665 0.0438593i
\(757\) −43.3399 + 25.0223i −1.57522 + 0.909451i −0.579703 + 0.814828i \(0.696831\pi\)
−0.995513 + 0.0946237i \(0.969835\pi\)
\(758\) 27.4609 + 15.8545i 0.997424 + 0.575863i
\(759\) 48.7715i 1.77029i
\(760\) 0 0
\(761\) 38.8161 + 22.4105i 1.40708 + 0.812379i 0.995106 0.0988165i \(-0.0315057\pi\)
0.411975 + 0.911195i \(0.364839\pi\)
\(762\) 32.5313 1.17848
\(763\) −22.9975 13.2776i −0.832566 0.480682i
\(764\) 7.00307 + 12.1297i 0.253362 + 0.438836i
\(765\) 0 0
\(766\) 11.7092 0.423072
\(767\) 0.306098 + 0.536961i 0.0110526 + 0.0193885i
\(768\) 26.6361i 0.961148i
\(769\) 34.0897 19.6817i 1.22930 0.709739i 0.262420 0.964954i \(-0.415479\pi\)
0.966884 + 0.255215i \(0.0821461\pi\)
\(770\) 0 0
\(771\) −6.47201 + 11.2099i −0.233084 + 0.403713i
\(772\) −11.1528 −0.401399
\(773\) 24.3902 42.2452i 0.877256 1.51945i 0.0229167 0.999737i \(-0.492705\pi\)
0.854340 0.519715i \(-0.173962\pi\)
\(774\) 2.91641 + 1.68379i 0.104828 + 0.0605225i
\(775\) 0 0
\(776\) 18.6434 32.2914i 0.669260 1.15919i
\(777\) −63.2926 + 36.5420i −2.27061 + 1.31094i
\(778\) −3.43420 5.94822i −0.123122 0.213254i
\(779\) 8.46410 0.303258
\(780\) 0 0
\(781\) −58.0013 −2.07545
\(782\) −2.68707 4.65415i −0.0960895 0.166432i
\(783\) 0.0280005