Properties

Label 325.2.m.c.49.3
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 49.3
Root \(1.40994 - 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 325.49
Dual form 325.2.m.c.199.3

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9} - 8 q^{13} - 4 q^{14} - 2 q^{16} - 18 q^{17} + 40 q^{18} - 12 q^{19} - 6 q^{22} - 6 q^{23} + 12 q^{24} + 10 q^{26} - 8 q^{28} + 8 q^{29} + 4 q^{32} + 18 q^{33} + 20 q^{36} + 2 q^{37} + 12 q^{41} + 42 q^{42} + 18 q^{43} - 42 q^{46} + 16 q^{47} + 6 q^{48} - 12 q^{49} - 8 q^{51} - 16 q^{52} - 18 q^{54} + 12 q^{56} + 28 q^{57} - 22 q^{58} + 12 q^{59} - 28 q^{61} - 12 q^{62} + 4 q^{63} + 8 q^{64} + 12 q^{66} + 30 q^{67} - 12 q^{68} + 16 q^{69} - 12 q^{72} + 16 q^{73} - 10 q^{74} + 54 q^{76} - 18 q^{78} + 16 q^{79} + 8 q^{81} + 6 q^{82} - 24 q^{83} + 30 q^{84} - 54 q^{87} - 42 q^{88} - 24 q^{89} + 28 q^{91} - 8 q^{93} - 32 q^{94} + 2 q^{97} - 24 q^{98} + O(q^{100}) \)

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 0.996979 0.0776710i \(-0.0247484\pi\)
−0.565755 + 0.824574i \(0.691415\pi\)
\(3\) −2.01978 + 1.16612i −1.16612 + 0.673262i −0.952764 0.303712i \(-0.901774\pi\)
−0.213359 + 0.976974i \(0.568441\pi\)
\(4\) 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 \(0.404849\pi\)
−0.974867 + 0.222787i \(0.928484\pi\)
\(8\) 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 0.376399 0.926458i \(-0.377162\pi\)
−0.614136 + 0.789200i \(0.710495\pi\)
\(18\) 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 −0.808453 0.588561i \(-0.799695\pi\)
0.105483 + 0.994421i \(0.466361\pi\)
\(24\) −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 \(0.0871205\pi\)
−0.247309 + 0.968937i \(0.579546\pi\)
\(38\) 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 0.572875 0.819643i \(-0.305828\pi\)
−0.423394 + 0.905946i \(0.639161\pi\)
\(44\) 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 \(-0.439619\pi\)
0.188556 + 0.982062i \(0.439619\pi\)
\(48\) −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 \(0.0986222\pi\)
−0.952385 + 0.304897i \(0.901378\pi\)
\(54\) 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 0.992572 0.121655i \(-0.0388200\pi\)
−0.601642 + 0.798766i \(0.705487\pi\)
\(68\) −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 \(-0.411247\pi\)
0.275227 + 0.961379i \(0.411247\pi\)
\(74\) −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 \(-0.731843\pi\)
−0.665643 + 0.746270i \(0.731843\pi\)
\(84\) −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 \(-0.621380\pi\)
0.989896 0.141794i \(-0.0452869\pi\)
\(98\) 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 \(-0.656169\pi\)
0.471173 0.882041i \(-0.343831\pi\)
\(104\) −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 −0.830922 0.556389i \(-0.812186\pi\)
0.0663862 + 0.997794i \(0.478853\pi\)
\(108\) −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 0.759727 0.650243i \(-0.225333\pi\)
−0.183263 + 0.983064i \(0.558666\pi\)
\(114\) −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 0.00856072 0.999963i \(-0.497275\pi\)
0.870274 + 0.492568i \(0.163942\pi\)
\(128\) 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 −0.935500 0.353326i \(-0.885051\pi\)
0.773739 + 0.633504i \(0.218384\pi\)
\(138\) 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 \(0.131220\pi\)
−0.916226 + 0.400661i \(0.868780\pi\)
\(158\) 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 −0.702140 0.712039i \(-0.747772\pi\)
0.967714 + 0.252051i \(0.0811052\pi\)
\(164\) 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 0.588559 0.808455i \(-0.299696\pi\)
−0.994421 + 0.105479i \(0.966362\pi\)
\(168\) 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 0.639545 0.768754i \(-0.279123\pi\)
−0.345988 + 0.938239i \(0.612456\pi\)
\(174\) 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 \(0.119863\pi\)
−0.146510 + 0.989209i \(0.546804\pi\)
\(194\) 14.8413 1.06555
\(195\) 0 0
\(196\) −3.05441 −0.218172
\(197\) −0.848360 1.46940i −0.0604432 0.104691i 0.834220 0.551431i \(-0.185918\pi\)
−0.894664 + 0.446741i \(0.852585\pi\)
\(198\) −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 0.995079 0.0990887i \(-0.0315928\pi\)
−0.583353 + 0.812219i \(0.698259\pi\)
\(224\) 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 −0.964428 0.264344i \(-0.914845\pi\)
0.711143 + 0.703048i \(0.248178\pi\)
\(228\) −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 \(0.100683\pi\)
−0.950391 + 0.311057i \(0.899317\pi\)
\(234\) −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 −0.342543 0.939502i \(-0.611288\pi\)
0.642361 + 0.766402i \(0.277955\pi\)
\(258\) −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 −0.671848 0.740689i \(-0.734499\pi\)
0.305532 + 0.952182i \(0.401166\pi\)
\(264\) 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 −0.0308154 0.999525i \(-0.509810\pi\)
−0.881022 + 0.473076i \(0.843144\pi\)
\(278\) 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 −0.465681 0.884953i \(-0.654191\pi\)
0.533551 + 0.845768i \(0.320857\pi\)
\(284\) 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 \(-0.648921\pi\)
0.998446 0.0557207i \(-0.0177456\pi\)
\(294\) 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 \(-0.366159\pi\)
0.408194 + 0.912895i \(0.366159\pi\)
\(308\) −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 \(0.153259\pi\)
−0.886311 + 0.463090i \(0.846741\pi\)
\(314\) −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 \(-0.515970\pi\)
−0.0501487 + 0.998742i \(0.515970\pi\)
\(318\) 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 \(0.0379085\pi\)
−0.992917 + 0.118812i \(0.962091\pi\)
\(338\) −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 0.969427 0.245381i \(-0.0789130\pi\)
0.272207 + 0.962239i \(0.412246\pi\)
\(348\) 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 0.779531 0.626364i \(-0.215458\pi\)
−0.932213 + 0.361911i \(0.882124\pi\)
\(354\) −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 0.222280 0.974983i \(-0.428650\pi\)
0.955500 + 0.294991i \(0.0953167\pi\)
\(368\) −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 0.765929 0.642926i \(-0.222280\pi\)
−0.173826 + 0.984776i \(0.555613\pi\)
\(374\) 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 −0.716935 0.697140i \(-0.754456\pi\)
0.962208 + 0.272314i \(0.0877889\pi\)
\(384\) −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 −0.575285 0.817953i \(-0.695109\pi\)
0.996011 + 0.0892344i \(0.0284420\pi\)
\(398\) −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 0.474818 0.880084i \(-0.342514\pi\)
−0.524766 + 0.851247i \(0.675847\pi\)
\(434\) 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 \(-0.965455\pi\)
0.994117 0.108314i \(-0.0345452\pi\)
\(444\) −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 \(0.220878\pi\)
0.169489 + 0.985532i \(0.445788\pi\)
\(458\) 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 \(-0.682141\pi\)
−0.541494 + 0.840705i \(0.682141\pi\)
\(464\) 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 \(0.175407\pi\)
−0.851971 + 0.523589i \(0.824593\pi\)
\(468\) −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 −0.829580 0.558388i \(-0.811420\pi\)
0.898368 + 0.439243i \(0.144753\pi\)
\(488\) −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 0.235976 0.971759i \(-0.424171\pi\)
−0.723580 + 0.690241i \(0.757505\pi\)
\(504\) 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 −0.994636 0.103436i \(-0.967016\pi\)
−0.407739 + 0.913098i \(0.633683\pi\)
\(524\) −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 \(-0.838058\pi\)
0.873351 0.487091i \(-0.161942\pi\)
\(548\) 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 \(0.0367499\pi\)
−0.396908 + 0.917858i \(0.629917\pi\)
\(558\) 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 0.792936 0.609305i \(-0.208551\pi\)
−0.131206 + 0.991355i \(0.541885\pi\)
\(564\) 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 \(-0.659432\pi\)
−0.480189 + 0.877165i \(0.659432\pi\)
\(578\) 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 0.575926 0.817502i \(-0.304642\pi\)
−0.995940 + 0.0900152i \(0.971308\pi\)
\(588\) 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 \(-0.568388\pi\)
−0.213198 + 0.977009i \(0.568388\pi\)
\(594\) −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 0.461279 0.887255i \(-0.347391\pi\)
−0.537746 + 0.843107i \(0.680724\pi\)
\(608\) 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 0.975705 0.219089i \(-0.0703085\pi\)
−0.677589 + 0.735441i \(0.736975\pi\)
\(614\) 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 −0.994729 0.102535i \(-0.967305\pi\)
0.586162 + 0.810194i \(0.300638\pi\)
\(618\) −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 −0.947359 0.320174i \(-0.896259\pi\)
0.750958 + 0.660350i \(0.229592\pi\)
\(644\) −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 0.267009 0.963694i \(-0.413965\pi\)
0.968088 + 0.250610i \(0.0806313\pi\)
\(648\) 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 −0.714636 0.699497i \(-0.753408\pi\)
0.248464 + 0.968641i \(0.420074\pi\)
\(654\) −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 0.447964 0.894052i \(-0.352149\pi\)
0.998253 + 0.0590774i \(0.0188159\pi\)
\(674\) −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 \(-0.707552\pi\)
0.606813 0.794845i \(-0.292448\pi\)
\(678\) −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 −0.839802 0.542892i \(-0.817329\pi\)
0.890060 + 0.455844i \(0.150662\pi\)
\(684\) 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 \(0.110670\pi\)
−0.940166 + 0.340717i \(0.889330\pi\)
\(728\) 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 \(-0.495349\pi\)
0.0146105 + 0.999893i \(0.495349\pi\)
\(734\) 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 0.810483 0.585763i \(-0.199205\pi\)
−0.912527 + 0.409017i \(0.865872\pi\)
\(744\) −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 \(-0.303169\pi\)
0.995513 0.0946237i \(-0.0301648\pi\)
\(758\) −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 \(0.507295\pi\)
−0.854340 + 0.519715i \(0.826038\pi\)
\(774\) 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 +