Properties

Label 735.2.q.e.214.1
Level $735$
Weight $2$
Character 735.214
Analytic conductor $5.869$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.89539436150784.1
Defining polynomial: \(x^{12} - 2 x^{11} + 2 x^{10} - 8 x^{9} + 4 x^{8} + 16 x^{7} - 8 x^{6} + 20 x^{5} + 20 x^{4} - 24 x^{3} + 8 x^{2} - 8 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 214.1
Root \(0.312819 - 1.16746i\) of defining polynomial
Character \(\chi\) \(=\) 735.214
Dual form 735.2.q.e.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.34630 + 1.35464i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.67009 - 4.62473i) q^{4} +(-1.55199 - 1.60976i) q^{5} -2.70928 q^{6} +9.04945i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-2.34630 + 1.35464i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.67009 - 4.62473i) q^{4} +(-1.55199 - 1.60976i) q^{5} -2.70928 q^{6} +9.04945i q^{8} +(0.500000 + 0.866025i) q^{9} +(5.82208 + 1.67458i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(4.62473 - 2.67009i) q^{12} -0.921622i q^{13} +(-0.539189 - 2.17009i) q^{15} +(-6.91855 - 11.9833i) q^{16} +(-0.933903 - 0.539189i) q^{17} +(-2.34630 - 1.35464i) q^{18} +(1.53919 + 2.66595i) q^{19} +(-11.5886 + 2.87936i) q^{20} -5.41855i q^{22} +(-2.02665 + 1.17009i) q^{23} +(-4.52472 + 7.83705i) q^{24} +(-0.182626 + 4.99666i) q^{25} +(1.24846 + 2.16240i) q^{26} +1.00000i q^{27} +6.68035 q^{29} +(4.20478 + 4.36127i) q^{30} +(3.87936 - 6.71925i) q^{31} +(16.7919 + 9.69481i) q^{32} +(-1.73205 + 1.00000i) q^{33} +2.92162 q^{34} +5.34017 q^{36} +(9.38521 - 5.41855i) q^{37} +(-7.22280 - 4.17009i) q^{38} +(0.460811 - 0.798148i) q^{39} +(14.5674 - 14.0447i) q^{40} +6.49693 q^{41} +6.52359i q^{43} +(5.34017 + 9.24945i) q^{44} +(0.618092 - 2.14894i) q^{45} +(3.17009 - 5.49075i) q^{46} +(4.05330 - 2.34017i) q^{47} -13.8371i q^{48} +(-6.34017 - 11.9711i) q^{50} +(-0.539189 - 0.933903i) q^{51} +(-4.26225 - 2.46081i) q^{52} +(3.25515 + 1.87936i) q^{53} +(-1.35464 - 2.34630i) q^{54} +(4.34017 - 1.07838i) q^{55} +3.07838i q^{57} +(-15.6741 + 9.04945i) q^{58} +(5.26180 - 9.11370i) q^{59} +(-11.4757 - 3.30072i) q^{60} +(2.07838 + 3.59986i) q^{61} +21.0205i q^{62} -24.8576 q^{64} +(-1.48359 + 1.43035i) q^{65} +(2.70928 - 4.69260i) q^{66} +(-4.05330 - 2.34017i) q^{67} +(-4.98720 + 2.87936i) q^{68} -2.34017 q^{69} +2.00000 q^{71} +(-7.83705 + 4.52472i) q^{72} +(6.13005 + 3.53919i) q^{73} +(-14.6803 + 25.4271i) q^{74} +(-2.65649 + 4.23592i) q^{75} +16.4391 q^{76} +2.49693i q^{78} +(3.07838 + 5.33191i) q^{79} +(-8.55260 + 29.7352i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-15.2438 + 8.80098i) q^{82} -6.83710i q^{83} +(0.581449 + 2.34017i) q^{85} +(-8.83710 - 15.3063i) q^{86} +(5.78535 + 3.34017i) q^{87} +(-15.6741 - 9.04945i) q^{88} +(4.17009 + 7.22280i) q^{89} +(1.46081 + 5.87936i) q^{90} +12.4969i q^{92} +(6.71925 - 3.87936i) q^{93} +(-6.34017 + 10.9815i) q^{94} +(1.90272 - 6.61526i) q^{95} +(9.69481 + 16.7919i) q^{96} -8.43907i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + O(q^{10}) \) \( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34630 + 1.35464i −1.65909 + 0.957873i −0.685948 + 0.727651i \(0.740612\pi\)
−0.973138 + 0.230222i \(0.926055\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 2.67009 4.62473i 1.33504 2.31236i
\(5\) −1.55199 1.60976i −0.694073 0.719905i
\(6\) −2.70928 −1.10606
\(7\) 0 0
\(8\) 9.04945i 3.19946i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 5.82208 + 1.67458i 1.84110 + 0.529549i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 4.62473 2.67009i 1.33504 0.770788i
\(13\) 0.921622i 0.255612i −0.991799 0.127806i \(-0.959207\pi\)
0.991799 0.127806i \(-0.0407935\pi\)
\(14\) 0 0
\(15\) −0.539189 2.17009i −0.139218 0.560314i
\(16\) −6.91855 11.9833i −1.72964 2.99582i
\(17\) −0.933903 0.539189i −0.226505 0.130773i 0.382454 0.923975i \(-0.375079\pi\)
−0.608959 + 0.793202i \(0.708412\pi\)
\(18\) −2.34630 1.35464i −0.553029 0.319291i
\(19\) 1.53919 + 2.66595i 0.353114 + 0.611612i 0.986793 0.161984i \(-0.0517894\pi\)
−0.633679 + 0.773596i \(0.718456\pi\)
\(20\) −11.5886 + 2.87936i −2.59130 + 0.643845i
\(21\) 0 0
\(22\) 5.41855i 1.15524i
\(23\) −2.02665 + 1.17009i −0.422586 + 0.243980i −0.696183 0.717864i \(-0.745120\pi\)
0.273597 + 0.961844i \(0.411786\pi\)
\(24\) −4.52472 + 7.83705i −0.923605 + 1.59973i
\(25\) −0.182626 + 4.99666i −0.0365252 + 0.999333i
\(26\) 1.24846 + 2.16240i 0.244844 + 0.424082i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 6.68035 1.24051 0.620255 0.784401i \(-0.287029\pi\)
0.620255 + 0.784401i \(0.287029\pi\)
\(30\) 4.20478 + 4.36127i 0.767684 + 0.796256i
\(31\) 3.87936 6.71925i 0.696754 1.20681i −0.272832 0.962062i \(-0.587960\pi\)
0.969586 0.244752i \(-0.0787064\pi\)
\(32\) 16.7919 + 9.69481i 2.96842 + 1.71382i
\(33\) −1.73205 + 1.00000i −0.301511 + 0.174078i
\(34\) 2.92162 0.501054
\(35\) 0 0
\(36\) 5.34017 0.890029
\(37\) 9.38521 5.41855i 1.54292 0.890804i 0.544265 0.838913i \(-0.316808\pi\)
0.998653 0.0518912i \(-0.0165249\pi\)
\(38\) −7.22280 4.17009i −1.17169 0.676477i
\(39\) 0.460811 0.798148i 0.0737888 0.127806i
\(40\) 14.5674 14.0447i 2.30331 2.22066i
\(41\) 6.49693 1.01465 0.507325 0.861755i \(-0.330634\pi\)
0.507325 + 0.861755i \(0.330634\pi\)
\(42\) 0 0
\(43\) 6.52359i 0.994838i 0.867510 + 0.497419i \(0.165719\pi\)
−0.867510 + 0.497419i \(0.834281\pi\)
\(44\) 5.34017 + 9.24945i 0.805061 + 1.39441i
\(45\) 0.618092 2.14894i 0.0921397 0.320346i
\(46\) 3.17009 5.49075i 0.467404 0.809567i
\(47\) 4.05330 2.34017i 0.591234 0.341349i −0.174351 0.984684i \(-0.555783\pi\)
0.765585 + 0.643334i \(0.222449\pi\)
\(48\) 13.8371i 1.99721i
\(49\) 0 0
\(50\) −6.34017 11.9711i −0.896636 1.69297i
\(51\) −0.539189 0.933903i −0.0755015 0.130773i
\(52\) −4.26225 2.46081i −0.591068 0.341253i
\(53\) 3.25515 + 1.87936i 0.447129 + 0.258150i 0.706617 0.707596i \(-0.250220\pi\)
−0.259488 + 0.965746i \(0.583554\pi\)
\(54\) −1.35464 2.34630i −0.184343 0.319291i
\(55\) 4.34017 1.07838i 0.585229 0.145408i
\(56\) 0 0
\(57\) 3.07838i 0.407741i
\(58\) −15.6741 + 9.04945i −2.05811 + 1.18825i
\(59\) 5.26180 9.11370i 0.685027 1.18650i −0.288401 0.957510i \(-0.593124\pi\)
0.973428 0.228992i \(-0.0735431\pi\)
\(60\) −11.4757 3.30072i −1.48151 0.426121i
\(61\) 2.07838 + 3.59986i 0.266109 + 0.460914i 0.967854 0.251514i \(-0.0809286\pi\)
−0.701745 + 0.712429i \(0.747595\pi\)
\(62\) 21.0205i 2.66961i
\(63\) 0 0
\(64\) −24.8576 −3.10720
\(65\) −1.48359 + 1.43035i −0.184016 + 0.177413i
\(66\) 2.70928 4.69260i 0.333489 0.577619i
\(67\) −4.05330 2.34017i −0.495189 0.285898i 0.231535 0.972826i \(-0.425625\pi\)
−0.726725 + 0.686929i \(0.758958\pi\)
\(68\) −4.98720 + 2.87936i −0.604787 + 0.349174i
\(69\) −2.34017 −0.281724
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −7.83705 + 4.52472i −0.923605 + 0.533244i
\(73\) 6.13005 + 3.53919i 0.717469 + 0.414231i 0.813820 0.581117i \(-0.197384\pi\)
−0.0963516 + 0.995347i \(0.530717\pi\)
\(74\) −14.6803 + 25.4271i −1.70656 + 2.95584i
\(75\) −2.65649 + 4.23592i −0.306745 + 0.489122i
\(76\) 16.4391 1.88569
\(77\) 0 0
\(78\) 2.49693i 0.282721i
\(79\) 3.07838 + 5.33191i 0.346345 + 0.599886i 0.985597 0.169111i \(-0.0540895\pi\)
−0.639253 + 0.768997i \(0.720756\pi\)
\(80\) −8.55260 + 29.7352i −0.956210 + 3.32449i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −15.2438 + 8.80098i −1.68339 + 0.971906i
\(83\) 6.83710i 0.750469i −0.926930 0.375235i \(-0.877562\pi\)
0.926930 0.375235i \(-0.122438\pi\)
\(84\) 0 0
\(85\) 0.581449 + 2.34017i 0.0630670 + 0.253827i
\(86\) −8.83710 15.3063i −0.952929 1.65052i
\(87\) 5.78535 + 3.34017i 0.620255 + 0.358104i
\(88\) −15.6741 9.04945i −1.67087 0.964674i
\(89\) 4.17009 + 7.22280i 0.442028 + 0.765615i 0.997840 0.0656928i \(-0.0209257\pi\)
−0.555812 + 0.831308i \(0.687592\pi\)
\(90\) 1.46081 + 5.87936i 0.153983 + 0.619739i
\(91\) 0 0
\(92\) 12.4969i 1.30289i
\(93\) 6.71925 3.87936i 0.696754 0.402271i
\(94\) −6.34017 + 10.9815i −0.653939 + 1.13266i
\(95\) 1.90272 6.61526i 0.195215 0.678712i
\(96\) 9.69481 + 16.7919i 0.989472 + 1.71382i
\(97\) 8.43907i 0.856858i −0.903576 0.428429i \(-0.859067\pi\)
0.903576 0.428429i \(-0.140933\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 22.6206 + 14.1861i 2.26206 + 1.41861i
\(101\) 2.90829 5.03731i 0.289386 0.501231i −0.684277 0.729222i \(-0.739882\pi\)
0.973663 + 0.227991i \(0.0732156\pi\)
\(102\) 2.53020 + 1.46081i 0.250527 + 0.144642i
\(103\) 1.86781 1.07838i 0.184040 0.106256i −0.405149 0.914251i \(-0.632780\pi\)
0.589190 + 0.807995i \(0.299447\pi\)
\(104\) 8.34017 0.817821
\(105\) 0 0
\(106\) −10.1834 −0.989101
\(107\) −14.2868 + 8.24846i −1.38115 + 0.797409i −0.992296 0.123889i \(-0.960463\pi\)
−0.388857 + 0.921298i \(0.627130\pi\)
\(108\) 4.62473 + 2.67009i 0.445014 + 0.256929i
\(109\) −6.41855 + 11.1173i −0.614786 + 1.06484i 0.375636 + 0.926767i \(0.377424\pi\)
−0.990422 + 0.138073i \(0.955909\pi\)
\(110\) −8.72254 + 8.40956i −0.831662 + 0.801820i
\(111\) 10.8371 1.02861
\(112\) 0 0
\(113\) 5.23513i 0.492480i 0.969209 + 0.246240i \(0.0791951\pi\)
−0.969209 + 0.246240i \(0.920805\pi\)
\(114\) −4.17009 7.22280i −0.390564 0.676477i
\(115\) 5.02890 + 1.44644i 0.468948 + 0.134881i
\(116\) 17.8371 30.8948i 1.65613 2.86851i
\(117\) 0.798148 0.460811i 0.0737888 0.0426020i
\(118\) 28.5113i 2.62468i
\(119\) 0 0
\(120\) 19.6381 4.87936i 1.79270 0.445423i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −9.75300 5.63090i −0.882995 0.509798i
\(123\) 5.62651 + 3.24846i 0.507325 + 0.292904i
\(124\) −20.7165 35.8820i −1.86039 3.22230i
\(125\) 8.32684 7.46081i 0.744775 0.667315i
\(126\) 0 0
\(127\) 1.84324i 0.163562i 0.996650 + 0.0817808i \(0.0260607\pi\)
−0.996650 + 0.0817808i \(0.973939\pi\)
\(128\) 24.7397 14.2834i 2.18670 1.26249i
\(129\) −3.26180 + 5.64960i −0.287185 + 0.497419i
\(130\) 1.54333 5.36576i 0.135359 0.470608i
\(131\) −0.738205 1.27861i −0.0644973 0.111713i 0.831974 0.554815i \(-0.187211\pi\)
−0.896471 + 0.443103i \(0.853878\pi\)
\(132\) 10.6803i 0.929605i
\(133\) 0 0
\(134\) 12.6803 1.09542
\(135\) 1.60976 1.55199i 0.138546 0.133574i
\(136\) 4.87936 8.45130i 0.418402 0.724693i
\(137\) −3.84435 2.21953i −0.328445 0.189628i 0.326706 0.945126i \(-0.394061\pi\)
−0.655150 + 0.755498i \(0.727395\pi\)
\(138\) 5.49075 3.17009i 0.467404 0.269856i
\(139\) −13.6020 −1.15370 −0.576852 0.816849i \(-0.695719\pi\)
−0.576852 + 0.816849i \(0.695719\pi\)
\(140\) 0 0
\(141\) 4.68035 0.394156
\(142\) −4.69260 + 2.70928i −0.393794 + 0.227357i
\(143\) 1.59630 + 0.921622i 0.133489 + 0.0770699i
\(144\) 6.91855 11.9833i 0.576546 0.998607i
\(145\) −10.3679 10.7537i −0.861004 0.893048i
\(146\) −19.1773 −1.58712
\(147\) 0 0
\(148\) 57.8720i 4.75705i
\(149\) 7.83710 + 13.5743i 0.642040 + 1.11205i 0.984977 + 0.172688i \(0.0552452\pi\)
−0.342936 + 0.939359i \(0.611421\pi\)
\(150\) 0.494784 13.5373i 0.0403990 1.10532i
\(151\) −2.92162 + 5.06040i −0.237758 + 0.411809i −0.960071 0.279757i \(-0.909746\pi\)
0.722312 + 0.691567i \(0.243079\pi\)
\(152\) −24.1254 + 13.9288i −1.95683 + 1.12978i
\(153\) 1.07838i 0.0871817i
\(154\) 0 0
\(155\) −16.8371 + 4.18342i −1.35239 + 0.336020i
\(156\) −2.46081 4.26225i −0.197023 0.341253i
\(157\) −4.26225 2.46081i −0.340165 0.196394i 0.320180 0.947357i \(-0.396257\pi\)
−0.660345 + 0.750963i \(0.729590\pi\)
\(158\) −14.4456 8.34017i −1.14923 0.663509i
\(159\) 1.87936 + 3.25515i 0.149043 + 0.258150i
\(160\) −10.4547 42.0772i −0.826514 3.32649i
\(161\) 0 0
\(162\) 2.70928i 0.212861i
\(163\) 8.52450 4.92162i 0.667690 0.385491i −0.127511 0.991837i \(-0.540699\pi\)
0.795201 + 0.606346i \(0.207365\pi\)
\(164\) 17.3474 30.0465i 1.35460 2.34624i
\(165\) 4.29789 + 1.23618i 0.334590 + 0.0962368i
\(166\) 9.26180 + 16.0419i 0.718855 + 1.24509i
\(167\) 19.2039i 1.48605i −0.669266 0.743023i \(-0.733391\pi\)
0.669266 0.743023i \(-0.266609\pi\)
\(168\) 0 0
\(169\) 12.1506 0.934662
\(170\) −4.53434 4.70310i −0.347768 0.360711i
\(171\) −1.53919 + 2.66595i −0.117705 + 0.203871i
\(172\) 30.1698 + 17.4186i 2.30043 + 1.32815i
\(173\) 19.4328 11.2195i 1.47745 0.853005i 0.477773 0.878483i \(-0.341444\pi\)
0.999675 + 0.0254777i \(0.00811068\pi\)
\(174\) −18.0989 −1.37207
\(175\) 0 0
\(176\) 27.6742 2.08602
\(177\) 9.11370 5.26180i 0.685027 0.395501i
\(178\) −19.5686 11.2979i −1.46673 0.846814i
\(179\) 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i \(-0.711416\pi\)
0.990134 + 0.140122i \(0.0447496\pi\)
\(180\) −8.28792 8.59637i −0.617745 0.640736i
\(181\) −8.52359 −0.633553 −0.316777 0.948500i \(-0.602601\pi\)
−0.316777 + 0.948500i \(0.602601\pi\)
\(182\) 0 0
\(183\) 4.15676i 0.307276i
\(184\) −10.5886 18.3401i −0.780605 1.35205i
\(185\) −23.2883 6.69833i −1.71219 0.492471i
\(186\) −10.5103 + 18.2043i −0.770650 + 1.33480i
\(187\) 1.86781 1.07838i 0.136587 0.0788588i
\(188\) 24.9939i 1.82286i
\(189\) 0 0
\(190\) 4.49693 + 18.0989i 0.326241 + 1.31303i
\(191\) −7.68035 13.3027i −0.555730 0.962553i −0.997846 0.0655953i \(-0.979105\pi\)
0.442116 0.896958i \(-0.354228\pi\)
\(192\) −21.5273 12.4288i −1.55360 0.896972i
\(193\) 7.24589 + 4.18342i 0.521571 + 0.301129i 0.737577 0.675263i \(-0.235970\pi\)
−0.216006 + 0.976392i \(0.569303\pi\)
\(194\) 11.4319 + 19.8006i 0.820761 + 1.42160i
\(195\) −2.00000 + 0.496928i −0.143223 + 0.0355858i
\(196\) 0 0
\(197\) 11.7587i 0.837774i −0.908038 0.418887i \(-0.862420\pi\)
0.908038 0.418887i \(-0.137580\pi\)
\(198\) 4.69260 2.70928i 0.333489 0.192540i
\(199\) −11.2979 + 19.5686i −0.800888 + 1.38718i 0.118145 + 0.992996i \(0.462305\pi\)
−0.919032 + 0.394182i \(0.871028\pi\)
\(200\) −45.2170 1.65267i −3.19733 0.116861i
\(201\) −2.34017 4.05330i −0.165063 0.285898i
\(202\) 15.7587i 1.10878i
\(203\) 0 0
\(204\) −5.75872 −0.403191
\(205\) −10.0832 10.4585i −0.704241 0.730451i
\(206\) −2.92162 + 5.06040i −0.203559 + 0.352575i
\(207\) −2.02665 1.17009i −0.140862 0.0813266i
\(208\) −11.0441 + 6.37629i −0.765768 + 0.442116i
\(209\) −6.15676 −0.425872
\(210\) 0 0
\(211\) −13.6742 −0.941371 −0.470685 0.882301i \(-0.655993\pi\)
−0.470685 + 0.882301i \(0.655993\pi\)
\(212\) 17.3831 10.0361i 1.19387 0.689283i
\(213\) 1.73205 + 1.00000i 0.118678 + 0.0685189i
\(214\) 22.3474 38.7068i 1.52763 2.64594i
\(215\) 10.5014 10.1246i 0.716189 0.690490i
\(216\) −9.04945 −0.615737
\(217\) 0 0
\(218\) 34.7792i 2.35555i
\(219\) 3.53919 + 6.13005i 0.239156 + 0.414231i
\(220\) 6.60144 22.9515i 0.445069 1.54739i
\(221\) −0.496928 + 0.860705i −0.0334270 + 0.0578973i
\(222\) −25.4271 + 14.6803i −1.70656 + 0.985280i
\(223\) 21.6742i 1.45141i 0.688005 + 0.725706i \(0.258487\pi\)
−0.688005 + 0.725706i \(0.741513\pi\)
\(224\) 0 0
\(225\) −4.41855 + 2.34017i −0.294570 + 0.156012i
\(226\) −7.09171 12.2832i −0.471733 0.817066i
\(227\) 9.97440 + 5.75872i 0.662024 + 0.382220i 0.793048 0.609159i \(-0.208493\pi\)
−0.131024 + 0.991379i \(0.541826\pi\)
\(228\) 14.2367 + 8.21953i 0.942845 + 0.544352i
\(229\) 6.41855 + 11.1173i 0.424150 + 0.734649i 0.996341 0.0854716i \(-0.0272397\pi\)
−0.572191 + 0.820121i \(0.693906\pi\)
\(230\) −13.7587 + 3.41855i −0.907223 + 0.225413i
\(231\) 0 0
\(232\) 60.4534i 3.96896i
\(233\) 5.85855 3.38243i 0.383806 0.221591i −0.295667 0.955291i \(-0.595542\pi\)
0.679473 + 0.733701i \(0.262208\pi\)
\(234\) −1.24846 + 2.16240i −0.0816147 + 0.141361i
\(235\) −10.0578 2.89288i −0.656099 0.188711i
\(236\) −28.0989 48.6687i −1.82908 3.16806i
\(237\) 6.15676i 0.399924i
\(238\) 0 0
\(239\) 23.3607 1.51108 0.755539 0.655104i \(-0.227375\pi\)
0.755539 + 0.655104i \(0.227375\pi\)
\(240\) −22.2744 + 21.4751i −1.43780 + 1.38621i
\(241\) 7.34017 12.7136i 0.472822 0.818952i −0.526694 0.850055i \(-0.676569\pi\)
0.999516 + 0.0311030i \(0.00990199\pi\)
\(242\) −16.4241 9.48246i −1.05578 0.609556i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 22.1978 1.42107
\(245\) 0 0
\(246\) −17.6020 −1.12226
\(247\) 2.45700 1.41855i 0.156335 0.0902602i
\(248\) 60.8055 + 35.1061i 3.86115 + 2.22924i
\(249\) 3.41855 5.92110i 0.216642 0.375235i
\(250\) −9.43058 + 28.7852i −0.596443 + 1.82053i
\(251\) 9.16290 0.578357 0.289179 0.957275i \(-0.406618\pi\)
0.289179 + 0.957275i \(0.406618\pi\)
\(252\) 0 0
\(253\) 4.68035i 0.294251i
\(254\) −2.49693 4.32481i −0.156671 0.271363i
\(255\) −0.666537 + 2.31737i −0.0417401 + 0.145120i
\(256\) −13.8402 + 23.9719i −0.865011 + 1.49824i
\(257\) −4.39800 + 2.53919i −0.274340 + 0.158390i −0.630858 0.775898i \(-0.717297\pi\)
0.356518 + 0.934288i \(0.383964\pi\)
\(258\) 17.6742i 1.10035i
\(259\) 0 0
\(260\) 2.65368 + 10.6803i 0.164574 + 0.662367i
\(261\) 3.34017 + 5.78535i 0.206752 + 0.358104i
\(262\) 3.46410 + 2.00000i 0.214013 + 0.123560i
\(263\) 4.90155 + 2.82991i 0.302243 + 0.174500i 0.643450 0.765488i \(-0.277502\pi\)
−0.341207 + 0.939988i \(0.610836\pi\)
\(264\) −9.04945 15.6741i −0.556955 0.964674i
\(265\) −2.02666 8.15676i −0.124497 0.501066i
\(266\) 0 0
\(267\) 8.34017i 0.510410i
\(268\) −21.6453 + 12.4969i −1.32220 + 0.763371i
\(269\) −13.9288 + 24.1254i −0.849255 + 1.47095i 0.0326200 + 0.999468i \(0.489615\pi\)
−0.881875 + 0.471484i \(0.843718\pi\)
\(270\) −1.67458 + 5.82208i −0.101912 + 0.354321i
\(271\) −12.5597 21.7541i −0.762948 1.32146i −0.941325 0.337502i \(-0.890418\pi\)
0.178377 0.983962i \(-0.442915\pi\)
\(272\) 14.9216i 0.904756i
\(273\) 0 0
\(274\) 12.0267 0.726557
\(275\) −8.47185 5.31298i −0.510872 0.320385i
\(276\) −6.24846 + 10.8227i −0.376113 + 0.651447i
\(277\) 24.4200 + 14.0989i 1.46726 + 0.847121i 0.999328 0.0366462i \(-0.0116675\pi\)
0.467928 + 0.883767i \(0.345001\pi\)
\(278\) 31.9143 18.4257i 1.91409 1.10510i
\(279\) 7.75872 0.464503
\(280\) 0 0
\(281\) −20.3545 −1.21425 −0.607125 0.794606i \(-0.707677\pi\)
−0.607125 + 0.794606i \(0.707677\pi\)
\(282\) −10.9815 + 6.34017i −0.653939 + 0.377552i
\(283\) 20.3667 + 11.7587i 1.21068 + 0.698984i 0.962906 0.269836i \(-0.0869694\pi\)
0.247769 + 0.968819i \(0.420303\pi\)
\(284\) 5.34017 9.24945i 0.316881 0.548854i
\(285\) 4.95544 4.77763i 0.293535 0.283002i
\(286\) −4.99386 −0.295293
\(287\) 0 0
\(288\) 19.3896i 1.14254i
\(289\) −7.91855 13.7153i −0.465797 0.806784i
\(290\) 38.8935 + 11.1868i 2.28391 + 0.656911i
\(291\) 4.21953 7.30845i 0.247354 0.428429i
\(292\) 32.7356 18.8999i 1.91570 1.10603i
\(293\) 2.92162i 0.170683i 0.996352 + 0.0853415i \(0.0271981\pi\)
−0.996352 + 0.0853415i \(0.972802\pi\)
\(294\) 0 0
\(295\) −22.8371 + 5.67420i −1.32963 + 0.330365i
\(296\) 49.0349 + 84.9309i 2.85010 + 4.93651i
\(297\) −1.73205 1.00000i −0.100504 0.0580259i
\(298\) −36.7764 21.2329i −2.13040 1.22999i
\(299\) 1.07838 + 1.86781i 0.0623642 + 0.108018i
\(300\) 12.4969 + 23.5958i 0.721511 + 1.36231i
\(301\) 0 0
\(302\) 15.8310i 0.910969i
\(303\) 5.03731 2.90829i 0.289386 0.167077i
\(304\) 21.2979 36.8891i 1.22152 2.11573i
\(305\) 2.56926 8.93264i 0.147115 0.511481i
\(306\) 1.46081 + 2.53020i 0.0835090 + 0.144642i
\(307\) 10.4703i 0.597570i −0.954321 0.298785i \(-0.903419\pi\)
0.954321 0.298785i \(-0.0965813\pi\)
\(308\) 0 0
\(309\) 2.15676 0.122694
\(310\) 33.8379 32.6237i 1.92186 1.85290i
\(311\) −11.9155 + 20.6382i −0.675665 + 1.17029i 0.300609 + 0.953747i \(0.402810\pi\)
−0.976274 + 0.216538i \(0.930523\pi\)
\(312\) 7.22280 + 4.17009i 0.408911 + 0.236085i
\(313\) −28.3646 + 16.3763i −1.60326 + 0.925643i −0.612431 + 0.790524i \(0.709808\pi\)
−0.990829 + 0.135118i \(0.956859\pi\)
\(314\) 13.3340 0.752483
\(315\) 0 0
\(316\) 32.8781 1.84954
\(317\) −15.5153 + 8.95774i −0.871424 + 0.503117i −0.867821 0.496877i \(-0.834480\pi\)
−0.00360269 + 0.999994i \(0.501147\pi\)
\(318\) −8.81910 5.09171i −0.494550 0.285529i
\(319\) −6.68035 + 11.5707i −0.374028 + 0.647835i
\(320\) 38.5789 + 40.0147i 2.15663 + 2.23689i
\(321\) −16.4969 −0.920769
\(322\) 0 0
\(323\) 3.31965i 0.184710i
\(324\) 2.67009 + 4.62473i 0.148338 + 0.256929i
\(325\) 4.60504 + 0.168312i 0.255441 + 0.00933629i
\(326\) −13.3340 + 23.0952i −0.738504 + 1.27913i
\(327\) −11.1173 + 6.41855i −0.614786 + 0.354947i
\(328\) 58.7936i 3.24633i
\(329\) 0 0
\(330\) −11.7587 + 2.92162i −0.647296 + 0.160830i
\(331\) 0.680346 + 1.17839i 0.0373952 + 0.0647704i 0.884117 0.467265i \(-0.154761\pi\)
−0.846722 + 0.532035i \(0.821427\pi\)
\(332\) −31.6197 18.2557i −1.73536 1.00191i
\(333\) 9.38521 + 5.41855i 0.514306 + 0.296935i
\(334\) 26.0144 + 45.0582i 1.42344 + 2.46548i
\(335\) 2.52359 + 10.1568i 0.137878 + 0.554923i
\(336\) 0 0
\(337\) 25.3607i 1.38148i −0.723101 0.690742i \(-0.757284\pi\)
0.723101 0.690742i \(-0.242716\pi\)
\(338\) −28.5090 + 16.4597i −1.55069 + 0.895288i
\(339\) −2.61757 + 4.53376i −0.142167 + 0.246240i
\(340\) 12.3752 + 3.55942i 0.671138 + 0.193037i
\(341\) 7.75872 + 13.4385i 0.420158 + 0.727736i
\(342\) 8.34017i 0.450985i
\(343\) 0 0
\(344\) −59.0349 −3.18295
\(345\) 3.63194 + 3.76711i 0.195537 + 0.202814i
\(346\) −30.3968 + 52.6488i −1.63414 + 2.83042i
\(347\) −14.6044 8.43188i −0.784008 0.452647i 0.0538410 0.998550i \(-0.482854\pi\)
−0.837849 + 0.545902i \(0.816187\pi\)
\(348\) 30.8948 17.8371i 1.65613 0.956169i
\(349\) −9.51745 −0.509457 −0.254729 0.967013i \(-0.581986\pi\)
−0.254729 + 0.967013i \(0.581986\pi\)
\(350\) 0 0
\(351\) 0.921622 0.0491926
\(352\) −33.5838 + 19.3896i −1.79002 + 1.03347i
\(353\) −31.0035 17.8999i −1.65015 0.952715i −0.977008 0.213201i \(-0.931611\pi\)
−0.673142 0.739514i \(-0.735056\pi\)
\(354\) −14.2557 + 24.6915i −0.757679 + 1.31234i
\(355\) −3.10399 3.21951i −0.164743 0.170874i
\(356\) 44.5380 2.36051
\(357\) 0 0
\(358\) 27.0928i 1.43190i
\(359\) −11.1568 19.3241i −0.588831 1.01989i −0.994386 0.105815i \(-0.966255\pi\)
0.405555 0.914071i \(-0.367078\pi\)
\(360\) 19.4468 + 5.59339i 1.02493 + 0.294798i
\(361\) 4.76180 8.24767i 0.250621 0.434088i
\(362\) 19.9989 11.5464i 1.05112 0.606864i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) −3.81658 15.3607i −0.199769 0.804015i
\(366\) −5.63090 9.75300i −0.294332 0.509798i
\(367\) −17.5920 10.1568i −0.918296 0.530178i −0.0352048 0.999380i \(-0.511208\pi\)
−0.883091 + 0.469202i \(0.844542\pi\)
\(368\) 28.0430 + 16.1906i 1.46184 + 0.843994i
\(369\) 3.24846 + 5.62651i 0.169108 + 0.292904i
\(370\) 63.7152 15.8310i 3.31240 0.823012i
\(371\) 0 0
\(372\) 41.4329i 2.14820i
\(373\) 13.8564 8.00000i 0.717458 0.414224i −0.0963587 0.995347i \(-0.530720\pi\)
0.813816 + 0.581122i \(0.197386\pi\)
\(374\) −2.92162 + 5.06040i −0.151073 + 0.261667i
\(375\) 10.9417 2.29783i 0.565025 0.118659i
\(376\) 21.1773 + 36.6801i 1.09213 + 1.89163i
\(377\) 6.15676i 0.317089i
\(378\) 0 0
\(379\) −6.15676 −0.316251 −0.158126 0.987419i \(-0.550545\pi\)
−0.158126 + 0.987419i \(0.550545\pi\)
\(380\) −25.5133 26.4629i −1.30881 1.35752i
\(381\) −0.921622 + 1.59630i −0.0472161 + 0.0817808i
\(382\) 36.0408 + 20.8082i 1.84401 + 1.06464i
\(383\) −23.2416 + 13.4186i −1.18759 + 0.685656i −0.957758 0.287574i \(-0.907151\pi\)
−0.229833 + 0.973230i \(0.573818\pi\)
\(384\) 28.5669 1.45780
\(385\) 0 0
\(386\) −22.6681 −1.15377
\(387\) −5.64960 + 3.26180i −0.287185 + 0.165806i
\(388\) −39.0284 22.5330i −1.98137 1.14394i
\(389\) −2.81658 + 4.87846i −0.142806 + 0.247348i −0.928552 0.371201i \(-0.878946\pi\)
0.785746 + 0.618549i \(0.212279\pi\)
\(390\) 4.01944 3.87522i 0.203532 0.196229i
\(391\) 2.52359 0.127623
\(392\) 0 0
\(393\) 1.47641i 0.0744750i
\(394\) 15.9288 + 27.5895i 0.802482 + 1.38994i
\(395\) 3.80544 13.2305i 0.191473 0.665700i
\(396\) −5.34017 + 9.24945i −0.268354 + 0.464802i
\(397\) 32.7356 18.8999i 1.64295 0.948558i 0.663173 0.748466i \(-0.269209\pi\)
0.979777 0.200092i \(-0.0641241\pi\)
\(398\) 61.2183i 3.06860i
\(399\) 0 0
\(400\) 61.1399 32.3812i 3.05700 1.61906i
\(401\) 6.81658 + 11.8067i 0.340404 + 0.589597i 0.984508 0.175341i \(-0.0561029\pi\)
−0.644104 + 0.764938i \(0.722770\pi\)
\(402\) 10.9815 + 6.34017i 0.547708 + 0.316219i
\(403\) −6.19261 3.57531i −0.308476 0.178099i
\(404\) −15.5308 26.9001i −0.772685 1.33833i
\(405\) 2.17009 0.539189i 0.107832 0.0267925i
\(406\) 0 0
\(407\) 21.6742i 1.07435i
\(408\) 8.45130 4.87936i 0.418402 0.241564i
\(409\) 6.17727 10.6994i 0.305447 0.529049i −0.671914 0.740629i \(-0.734528\pi\)
0.977361 + 0.211580i \(0.0678609\pi\)
\(410\) 37.8257 + 10.8796i 1.86808 + 0.537307i
\(411\) −2.21953 3.84435i −0.109482 0.189628i
\(412\) 11.5174i 0.567424i
\(413\) 0 0
\(414\) 6.34017 0.311603
\(415\) −11.0061 + 10.6111i −0.540266 + 0.520881i
\(416\) 8.93495 15.4758i 0.438072 0.758763i
\(417\) −11.7797 6.80098i −0.576852 0.333046i
\(418\) 14.4456 8.34017i 0.706558 0.407931i
\(419\) −28.9939 −1.41644 −0.708221 0.705991i \(-0.750502\pi\)
−0.708221 + 0.705991i \(0.750502\pi\)
\(420\) 0 0
\(421\) −15.1629 −0.738994 −0.369497 0.929232i \(-0.620470\pi\)
−0.369497 + 0.929232i \(0.620470\pi\)
\(422\) 32.0838 18.5236i 1.56181 0.901714i
\(423\) 4.05330 + 2.34017i 0.197078 + 0.113783i
\(424\) −17.0072 + 29.4573i −0.825942 + 1.43057i
\(425\) 2.86470 4.56793i 0.138958 0.221577i
\(426\) −5.41855 −0.262530
\(427\) 0 0
\(428\) 88.0965i 4.25830i
\(429\) 0.921622 + 1.59630i 0.0444963 + 0.0770699i
\(430\) −10.9243 + 37.9809i −0.526816 + 1.83160i
\(431\) 5.15676 8.93176i 0.248392 0.430228i −0.714688 0.699444i \(-0.753431\pi\)
0.963080 + 0.269216i \(0.0867645\pi\)
\(432\) 11.9833 6.91855i 0.576546 0.332869i
\(433\) 20.4391i 0.982239i −0.871092 0.491120i \(-0.836588\pi\)
0.871092 0.491120i \(-0.163412\pi\)
\(434\) 0 0
\(435\) −3.60197 14.4969i −0.172701 0.695075i
\(436\) 34.2762 + 59.3681i 1.64153 + 2.84321i
\(437\) −6.23879 3.60197i −0.298442 0.172306i
\(438\) −16.6080 9.58864i −0.793561 0.458163i
\(439\) −8.46081 14.6546i −0.403812 0.699424i 0.590370 0.807133i \(-0.298982\pi\)
−0.994182 + 0.107709i \(0.965649\pi\)
\(440\) 9.75872 + 39.2762i 0.465229 + 1.87242i
\(441\) 0 0
\(442\) 2.69263i 0.128075i
\(443\) 11.0942 6.40522i 0.527100 0.304321i −0.212735 0.977110i \(-0.568237\pi\)
0.739835 + 0.672789i \(0.234904\pi\)
\(444\) 28.9360 50.1186i 1.37324 2.37852i
\(445\) 5.15499 17.9226i 0.244370 0.849611i
\(446\) −29.3607 50.8542i −1.39027 2.40802i
\(447\) 15.6742i 0.741364i
\(448\) 0 0
\(449\) 14.6270 0.690292 0.345146 0.938549i \(-0.387829\pi\)
0.345146 + 0.938549i \(0.387829\pi\)
\(450\) 7.19716 11.4763i 0.339278 0.540997i
\(451\) −6.49693 + 11.2530i −0.305928 + 0.529884i
\(452\) 24.2111 + 13.9783i 1.13879 + 0.657482i
\(453\) −5.06040 + 2.92162i −0.237758 + 0.137270i
\(454\) −31.2039 −1.46447
\(455\) 0 0
\(456\) −27.8576 −1.30455
\(457\) 12.2601 7.07838i 0.573504 0.331113i −0.185044 0.982730i \(-0.559243\pi\)
0.758548 + 0.651618i \(0.225909\pi\)
\(458\) −30.1197 17.3896i −1.40740 0.812564i
\(459\) 0.539189 0.933903i 0.0251672 0.0435908i
\(460\) 20.1170 19.3952i 0.937960 0.904304i
\(461\) 0.340173 0.0158434 0.00792172 0.999969i \(-0.497478\pi\)
0.00792172 + 0.999969i \(0.497478\pi\)
\(462\) 0 0
\(463\) 9.84324i 0.457454i 0.973491 + 0.228727i \(0.0734564\pi\)
−0.973491 + 0.228727i \(0.926544\pi\)
\(464\) −46.2183 80.0525i −2.14563 3.71634i
\(465\) −16.6731 4.79560i −0.773195 0.222391i
\(466\) −9.16394 + 15.8724i −0.424511 + 0.735275i
\(467\) −9.97440 + 5.75872i −0.461560 + 0.266482i −0.712700 0.701469i \(-0.752528\pi\)
0.251140 + 0.967951i \(0.419195\pi\)
\(468\) 4.92162i 0.227502i
\(469\) 0 0
\(470\) 27.5174 6.83710i 1.26929 0.315372i
\(471\) −2.46081 4.26225i −0.113388 0.196394i
\(472\) 82.4739 + 47.6163i 3.79617 + 2.19172i
\(473\) −11.2992 6.52359i −0.519537 0.299955i
\(474\) −8.34017 14.4456i −0.383077 0.663509i
\(475\) −13.6020 + 7.20394i −0.624101 + 0.330539i
\(476\) 0 0
\(477\) 3.75872i 0.172100i
\(478\) −54.8112 + 31.6453i −2.50701 + 1.44742i
\(479\) −9.75872 + 16.9026i −0.445887 + 0.772300i −0.998114 0.0613946i \(-0.980445\pi\)
0.552226 + 0.833694i \(0.313779\pi\)
\(480\) 11.9846 41.6672i 0.547018 1.90184i
\(481\) −4.99386 8.64961i −0.227700 0.394388i
\(482\) 39.7731i 1.81162i
\(483\) 0 0
\(484\) 37.3812 1.69915
\(485\) −13.5848 + 13.0974i −0.616856 + 0.594722i
\(486\) 1.35464 2.34630i 0.0614476 0.106430i
\(487\) −20.0490 11.5753i −0.908508 0.524527i −0.0285570 0.999592i \(-0.509091\pi\)
−0.879951 + 0.475065i \(0.842425\pi\)
\(488\) −32.5767 + 18.8082i −1.47468 + 0.851406i
\(489\) 9.84324 0.445127
\(490\) 0 0
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) 30.0465 17.3474i 1.35460 0.782079i
\(493\) −6.23879 3.60197i −0.280981 0.162224i
\(494\) −3.84324 + 6.65669i −0.172916 + 0.299499i
\(495\) 3.10399 + 3.21951i 0.139514 + 0.144706i
\(496\) −107.358 −4.82053
\(497\) 0 0
\(498\) 18.5236i 0.830062i
\(499\) 13.6020 + 23.5593i 0.608908 + 1.05466i 0.991421 + 0.130709i \(0.0417254\pi\)
−0.382513 + 0.923950i \(0.624941\pi\)
\(500\) −12.2708 58.4304i −0.548768 2.61309i
\(501\) 9.60197 16.6311i 0.428984 0.743023i
\(502\) −21.4989 + 12.4124i −0.959544 + 0.553993i
\(503\) 18.8371i 0.839905i 0.907546 + 0.419952i \(0.137953\pi\)
−0.907546 + 0.419952i \(0.862047\pi\)
\(504\) 0 0
\(505\) −12.6225 + 3.13624i −0.561693 + 0.139561i
\(506\) 6.34017 + 10.9815i 0.281855 + 0.488187i
\(507\) 10.5227 + 6.07531i 0.467331 + 0.269814i
\(508\) 8.52450 + 4.92162i 0.378214 + 0.218362i
\(509\) 3.40522 + 5.89801i 0.150934 + 0.261425i 0.931571 0.363560i \(-0.118439\pi\)
−0.780637 + 0.624984i \(0.785105\pi\)
\(510\) −1.57531 6.34017i −0.0697557 0.280748i
\(511\) 0 0
\(512\) 17.8599i 0.789303i
\(513\) −2.66595 + 1.53919i −0.117705 + 0.0679568i
\(514\) 6.87936 11.9154i 0.303436 0.525566i
\(515\) −4.63475 1.33307i −0.204231 0.0587422i
\(516\) 17.4186 + 30.1698i 0.766809 + 1.32815i
\(517\) 9.36069i 0.411683i
\(518\) 0 0
\(519\) 22.4391 0.984966
\(520\) −12.9439 13.4256i −0.567628 0.588753i
\(521\) 12.9083 22.3578i 0.565523 0.979514i −0.431478 0.902123i \(-0.642008\pi\)
0.997001 0.0773904i \(-0.0246588\pi\)
\(522\) −15.6741 9.04945i −0.686037 0.396084i
\(523\) −3.46410 + 2.00000i −0.151475 + 0.0874539i −0.573822 0.818980i \(-0.694540\pi\)
0.422347 + 0.906434i \(0.361206\pi\)
\(524\) −7.88428 −0.344426
\(525\) 0 0
\(526\) −15.3340 −0.668595
\(527\) −7.24589 + 4.18342i −0.315636 + 0.182233i
\(528\) 23.9666 + 13.8371i 1.04301 + 0.602183i
\(529\) −8.76180 + 15.1759i −0.380948 + 0.659821i
\(530\) 15.8046 + 16.3928i 0.686508 + 0.712058i
\(531\) 10.5236 0.456685
\(532\) 0 0
\(533\) 5.98771i 0.259357i
\(534\) −11.2979 19.5686i −0.488908 0.846814i
\(535\) 35.4510 + 10.1966i 1.53268 + 0.440838i
\(536\) 21.1773 36.6801i 0.914719 1.58434i
\(537\) 8.66025 5.00000i 0.373718 0.215766i
\(538\) 75.4740i 3.25391i
\(539\) 0 0
\(540\) −2.87936 11.5886i −0.123908 0.498696i
\(541\) −12.9421 22.4164i −0.556426 0.963758i −0.997791 0.0664306i \(-0.978839\pi\)
0.441365 0.897328i \(-0.354494\pi\)
\(542\) 58.9377 + 34.0277i 2.53159 + 1.46162i
\(543\) −7.38165 4.26180i −0.316777 0.182891i
\(544\) −10.4547 18.1080i −0.448240 0.776375i
\(545\) 27.8576 6.92162i 1.19329 0.296490i
\(546\) 0 0
\(547\) 11.3197i 0.483993i 0.970277 + 0.241997i \(0.0778023\pi\)
−0.970277 + 0.241997i \(0.922198\pi\)
\(548\) −20.5295 + 11.8527i −0.876976 + 0.506322i
\(549\) −2.07838 + 3.59986i −0.0887030 + 0.153638i
\(550\) 27.0747 + 0.989569i 1.15447 + 0.0421954i
\(551\) 10.2823 + 17.8095i 0.438041 + 0.758710i
\(552\) 21.1773i 0.901365i
\(553\) 0 0
\(554\) −76.3956 −3.24574
\(555\) −16.8191 17.4451i −0.713932 0.740503i
\(556\) −36.3184 + 62.9054i −1.54024 + 2.66778i
\(557\) 23.0788 + 13.3246i 0.977882 + 0.564580i 0.901630 0.432508i \(-0.142371\pi\)
0.0762519 + 0.997089i \(0.475705\pi\)
\(558\) −18.2043 + 10.5103i −0.770650 + 0.444935i
\(559\) 6.01229 0.254293
\(560\) 0 0
\(561\) 2.15676 0.0910583
\(562\) 47.7579 27.5730i 2.01455 1.16310i
\(563\) 40.1442 + 23.1773i 1.69188 + 0.976806i 0.953002 + 0.302963i \(0.0979758\pi\)
0.738875 + 0.673843i \(0.235358\pi\)
\(564\) 12.4969 21.6453i 0.526216 0.911432i
\(565\) 8.42728 8.12490i 0.354539 0.341817i
\(566\) −63.7152 −2.67815
\(567\) 0 0
\(568\) 18.0989i 0.759413i
\(569\) −7.18342 12.4420i −0.301145 0.521598i 0.675251 0.737588i \(-0.264035\pi\)
−0.976395 + 0.215990i \(0.930702\pi\)
\(570\) −5.15499 + 17.9226i −0.215919 + 0.750694i
\(571\) −19.3607 + 33.5337i −0.810220 + 1.40334i 0.102490 + 0.994734i \(0.467319\pi\)
−0.912710 + 0.408608i \(0.866014\pi\)
\(572\) 8.52450 4.92162i 0.356427 0.205783i
\(573\) 15.3607i 0.641702i
\(574\) 0 0
\(575\) −5.47641 10.3402i −0.228382 0.431215i
\(576\) −12.4288 21.5273i −0.517867 0.896972i
\(577\) −37.6496 21.7370i −1.56737 0.904922i −0.996474 0.0839011i \(-0.973262\pi\)
−0.570898 0.821021i \(-0.693405\pi\)
\(578\) 37.1586 + 21.4535i 1.54559 + 0.892349i
\(579\) 4.18342 + 7.24589i 0.173857 + 0.301129i
\(580\) −77.4161 + 19.2351i −3.21453 + 0.798695i
\(581\) 0 0
\(582\) 22.8638i 0.947733i
\(583\) −6.51030 + 3.75872i −0.269629 + 0.155670i
\(584\) −32.0277 + 55.4736i −1.32532 + 2.29551i
\(585\) −1.98052 0.569647i −0.0818842 0.0235520i
\(586\) −3.95774 6.85501i −0.163493 0.283178i
\(587\) 36.0288i 1.48707i 0.668699 + 0.743533i \(0.266851\pi\)
−0.668699 + 0.743533i \(0.733149\pi\)
\(588\) 0 0
\(589\) 23.8843 0.984135
\(590\) 45.8962 44.2494i 1.88952 1.82172i
\(591\) 5.87936 10.1834i 0.241845 0.418887i
\(592\) −129.864 74.9770i −5.33738 3.08154i
\(593\) −27.2679 + 15.7431i −1.11976 + 0.646493i −0.941339 0.337462i \(-0.890432\pi\)
−0.178419 + 0.983955i \(0.557098\pi\)
\(594\) 5.41855 0.222326
\(595\) 0 0
\(596\) 83.7030 3.42861
\(597\) −19.5686 + 11.2979i −0.800888 + 0.462393i
\(598\) −5.06040 2.92162i −0.206935 0.119474i
\(599\) 14.5174 25.1450i 0.593167 1.02740i −0.400636 0.916237i \(-0.631211\pi\)
0.993803 0.111158i \(-0.0354559\pi\)
\(600\) −38.3328 24.0398i −1.56493 0.981420i
\(601\) 15.3607 0.626576 0.313288 0.949658i \(-0.398570\pi\)
0.313288 + 0.949658i \(0.398570\pi\)
\(602\) 0 0
\(603\) 4.68035i 0.190598i
\(604\) 15.6020 + 27.0234i 0.634835 + 1.09957i
\(605\) 4.32664 15.0426i 0.175903 0.611569i
\(606\) −7.87936 + 13.6475i −0.320077 + 0.554390i
\(607\) −11.2992 + 6.52359i −0.458620 + 0.264784i −0.711464 0.702723i \(-0.751967\pi\)
0.252844 + 0.967507i \(0.418634\pi\)
\(608\) 59.6886i 2.42069i
\(609\) 0 0
\(610\) 6.07223 + 24.4391i 0.245858 + 0.989509i
\(611\) −2.15676 3.73561i −0.0872530 0.151127i
\(612\) −4.98720 2.87936i −0.201596 0.116391i
\(613\) −13.4385 7.75872i −0.542776 0.313372i 0.203427 0.979090i \(-0.434792\pi\)
−0.746203 + 0.665718i \(0.768125\pi\)
\(614\) 14.1834 + 24.5664i 0.572396 + 0.991419i
\(615\) −3.50307 14.0989i −0.141257 0.568522i
\(616\) 0 0
\(617\) 22.7649i 0.916479i −0.888829 0.458240i \(-0.848480\pi\)
0.888829 0.458240i \(-0.151520\pi\)
\(618\) −5.06040 + 2.92162i −0.203559 + 0.117525i
\(619\) 3.96388 6.86565i 0.159322 0.275954i −0.775302 0.631590i \(-0.782403\pi\)
0.934624 + 0.355637i \(0.115736\pi\)
\(620\) −25.6094 + 89.0371i −1.02850 + 3.57581i
\(621\) −1.17009 2.02665i −0.0469540 0.0813266i
\(622\) 64.5646i 2.58881i
\(623\) 0 0
\(624\) −12.7526 −0.510512
\(625\) −24.9333 1.82504i −0.997332 0.0730017i
\(626\) 44.3679 76.8474i 1.77330 3.07144i
\(627\) −5.33191 3.07838i −0.212936 0.122939i
\(628\) −22.7612 + 13.1412i −0.908269 + 0.524389i
\(629\) −11.6865 −0.465971
\(630\) 0 0
\(631\) 19.2039 0.764497 0.382248 0.924060i \(-0.375150\pi\)
0.382248 + 0.924060i \(0.375150\pi\)
\(632\) −48.2508 + 27.8576i −1.91931 + 1.10812i
\(633\) −11.8422 6.83710i −0.470685 0.271750i
\(634\) 24.2690 42.0351i 0.963844 1.66943i
\(635\) 2.96717 2.86071i 0.117749 0.113524i
\(636\) 20.0722 0.795916
\(637\) 0 0
\(638\) 36.1978i 1.43308i
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) −61.3887 17.6570i −2.42660 0.697953i
\(641\) 2.97334 5.14997i 0.117440 0.203412i −0.801313 0.598246i \(-0.795865\pi\)
0.918752 + 0.394834i \(0.129198\pi\)
\(642\) 38.7068 22.3474i 1.52763 0.881980i
\(643\) 30.8904i 1.21820i 0.793094 + 0.609100i \(0.208469\pi\)
−0.793094 + 0.609100i \(0.791531\pi\)
\(644\) 0 0
\(645\) 14.1568 3.51745i 0.557422 0.138499i
\(646\) 4.49693 + 7.78891i 0.176929 + 0.306451i
\(647\) 16.6311 + 9.60197i 0.653836 + 0.377492i 0.789924 0.613204i \(-0.210120\pi\)
−0.136088 + 0.990697i \(0.543453\pi\)
\(648\) −7.83705 4.52472i −0.307868 0.177748i
\(649\) 10.5236 + 18.2274i 0.413087 + 0.715488i
\(650\) −11.0328 + 5.84324i −0.432742 + 0.229191i
\(651\) 0 0
\(652\) 52.5646i 2.05859i
\(653\) 24.7292 14.2774i 0.967727 0.558718i 0.0691846 0.997604i \(-0.477960\pi\)
0.898543 + 0.438886i \(0.144627\pi\)
\(654\) 17.3896 30.1197i 0.679988 1.17777i
\(655\) −0.912557 + 3.17272i −0.0356565 + 0.123969i
\(656\) −44.9493 77.8545i −1.75498 3.03971i
\(657\) 7.07838i 0.276154i
\(658\) 0 0
\(659\) 27.9877 1.09025 0.545123 0.838356i \(-0.316483\pi\)
0.545123 + 0.838356i \(0.316483\pi\)
\(660\) 17.1927 16.5758i 0.669227 0.645214i
\(661\) 11.0722 19.1777i 0.430660 0.745925i −0.566270 0.824220i \(-0.691614\pi\)
0.996930 + 0.0782946i \(0.0249475\pi\)
\(662\) −3.19259 1.84324i −0.124084 0.0716397i
\(663\) −0.860705 + 0.496928i −0.0334270 + 0.0192991i
\(664\) 61.8720 2.40110
\(665\) 0 0
\(666\) −29.3607 −1.13770
\(667\) −13.5387 + 7.81658i −0.524221 + 0.302659i
\(668\) −88.8129 51.2762i −3.43628 1.98393i
\(669\) −10.8371 + 18.7704i −0.418987 + 0.725706i
\(670\) −19.6798 20.4123i −0.760298 0.788594i
\(671\) −8.31351 −0.320940
\(672\) 0 0
\(673\) 2.21008i 0.0851923i −0.999092 0.0425962i \(-0.986437\pi\)
0.999092 0.0425962i \(-0.0135629\pi\)
\(674\) 34.3545 + 59.5038i 1.32329 + 2.29200i
\(675\) −4.99666 0.182626i −0.192322 0.00702928i
\(676\) 32.4432 56.1932i 1.24781 2.16128i
\(677\) 16.9296 9.77432i 0.650658 0.375658i −0.138050 0.990425i \(-0.544084\pi\)
0.788708 + 0.614768i \(0.210750\pi\)
\(678\) 14.1834i 0.544711i
\(679\) 0 0
\(680\) −21.1773 + 5.26180i −0.812111 + 0.201781i
\(681\) 5.75872 + 9.97440i 0.220675 + 0.382220i
\(682\) −36.4086 21.0205i −1.39416 0.804917i
\(683\) 10.2335 + 5.90829i 0.391572 + 0.226074i 0.682841 0.730567i \(-0.260744\pi\)
−0.291269 + 0.956641i \(0.594077\pi\)
\(684\) 8.21953 + 14.2367i 0.314282 + 0.544352i
\(685\) 2.39350 + 9.63317i 0.0914508 + 0.368064i
\(686\) 0 0
\(687\) 12.8371i 0.489766i
\(688\) 78.1740 45.1338i 2.98036 1.72071i
\(689\) 1.73206 3.00002i 0.0659863 0.114292i
\(690\) −13.6247 3.91881i −0.518683 0.149187i
\(691\) −5.87936 10.1834i −0.223661 0.387393i 0.732256 0.681030i \(-0.238468\pi\)
−0.955917 + 0.293637i \(0.905134\pi\)
\(692\) 119.829i 4.55520i
\(693\) 0 0
\(694\) 45.6886 1.73431
\(695\) 21.1102 + 21.8958i 0.800755 + 0.830557i
\(696\) −30.2267 + 52.3542i −1.14574 + 1.98448i
\(697\) −6.06750 3.50307i −0.229823 0.132688i
\(698\) 22.3308 12.8927i 0.845233 0.487996i
\(699\) 6.76487 0.255871
\(700\) 0 0
\(701\) 9.94668 0.375681 0.187840 0.982200i \(-0.439851\pi\)
0.187840 + 0.982200i \(0.439851\pi\)
\(702\) −2.16240 + 1.24846i −0.0816147 + 0.0471202i
\(703\) 28.8912 + 16.6803i 1.08965 + 0.629111i
\(704\) 24.8576 43.0547i 0.936857 1.62268i
\(705\) −7.26387 7.53421i −0.273573 0.283755i
\(706\) 96.9914 3.65032
\(707\) 0 0
\(708\) 56.1978i 2.11204i
\(709\) −5.52359 9.56714i −0.207443 0.359301i 0.743465 0.668774i \(-0.233181\pi\)
−0.950908 + 0.309473i \(0.899847\pi\)
\(710\) 11.6442 + 3.34916i 0.436998 + 0.125692i
\(711\) −3.07838 + 5.33191i −0.115448 + 0.199962i
\(712\) −65.3624 + 37.7370i −2.44956 + 1.41425i
\(713\) 18.1568i 0.679976i
\(714\) 0 0
\(715\) −0.993857 4.00000i −0.0371681 0.149592i
\(716\) −26.7009 46.2473i −0.997858 1.72834i
\(717\) 20.2310 + 11.6803i 0.755539 + 0.436211i
\(718\) 52.3542 + 30.2267i 1.95384 + 1.12805i
\(719\) −3.07838 5.33191i −0.114804 0.198847i 0.802897 0.596117i \(-0.203291\pi\)
−0.917701 + 0.397271i \(0.869957\pi\)
\(720\) −30.0277 + 7.46081i −1.11907 + 0.278048i
\(721\) 0 0
\(722\) 25.8020i 0.960252i
\(723\) 12.7136 7.34017i 0.472822 0.272984i
\(724\) −22.7587 + 39.4193i −0.845821 + 1.46501i
\(725\) −1.22001 + 33.3794i −0.0453099 + 1.23968i
\(726\) −9.48246 16.4241i −0.351927 0.609556i
\(727\) 2.89043i 0.107200i 0.998562 + 0.0536000i \(0.0170696\pi\)
−0.998562 + 0.0536000i \(0.982930\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 29.7630 + 30.8707i 1.10158 + 1.14258i
\(731\) 3.51745 6.09240i 0.130097 0.225335i
\(732\) 19.2239 + 11.0989i 0.710534 + 0.410227i
\(733\) 22.3432 12.8999i 0.825267 0.476468i −0.0269626 0.999636i \(-0.508583\pi\)
0.852229 + 0.523168i \(0.175250\pi\)
\(734\) 55.0349 2.03138
\(735\) 0 0
\(736\) −45.3751 −1.67255
\(737\) 8.10660 4.68035i 0.298610 0.172403i
\(738\) −15.2438 8.80098i −0.561130 0.323969i
\(739\) −0.523590 + 0.906885i −0.0192606 + 0.0333603i −0.875495 0.483227i \(-0.839465\pi\)
0.856234 + 0.516587i \(0.172798\pi\)
\(740\) −93.1598 + 89.8170i −3.42462 + 3.30174i
\(741\) 2.83710 0.104224
\(742\) 0 0
\(743\) 9.97334i 0.365886i 0.983123 + 0.182943i \(0.0585624\pi\)
−0.983123 + 0.182943i \(0.941438\pi\)
\(744\) 35.1061 + 60.8055i 1.28705 + 2.22924i
\(745\) 9.68810 33.6830i 0.354944 1.23405i
\(746\) −21.6742 + 37.5408i −0.793549 + 1.37447i
\(747\) 5.92110 3.41855i 0.216642 0.125078i
\(748\) 11.5174i 0.421120i
\(749\) 0 0
\(750\) −22.5597 + 20.2134i −0.823764 + 0.738089i
\(751\) −1.63317 2.82872i −0.0595950 0.103222i 0.834689 0.550722i \(-0.185648\pi\)
−0.894284 + 0.447501i \(0.852314\pi\)
\(752\) −56.0859 32.3812i −2.04524 1.18082i
\(753\) 7.93530 + 4.58145i 0.289179 + 0.166957i
\(754\) 8.34017 + 14.4456i 0.303731 + 0.526078i
\(755\) 12.6803 3.15061i 0.461485 0.114663i
\(756\) 0 0
\(757\) 49.9877i 1.81683i −0.418065 0.908417i \(-0.637292\pi\)
0.418065 0.908417i \(-0.362708\pi\)
\(758\) 14.4456 8.34017i 0.524688 0.302929i
\(759\) 2.34017 4.05330i 0.0849429 0.147125i
\(760\) 59.8645 + 17.2186i 2.17151 + 0.624583i
\(761\) −1.30632 2.26262i −0.0473542 0.0820198i 0.841377 0.540449i \(-0.181746\pi\)
−0.888731 + 0.458429i \(0.848412\pi\)
\(762\) 4.99386i 0.180908i
\(763\) 0 0
\(764\) −82.0288 −2.96770
\(765\) −1.73592 + 1.67364i −0.0627625 + 0.0605104i
\(766\) 36.3545 62.9679i 1.31354 2.27512i
\(767\) −8.39939 4.84939i −0.303284 0.175101i
\(768\) −23.9719 + 13.8402i −0.865011 + 0.499414i
\(769\) 15.6742 0.565226 0.282613 0.959234i \(-0.408799\pi\)
0.282613 + 0.959234i \(0.408799\pi\)
\(770\) 0 0
\(771\) −5.07838 −0.182893
\(772\) 38.6943 22.3402i 1.39264 0.804040i
\(773\) 5.03338 + 2.90602i 0.181038 + 0.104522i 0.587780 0.809021i \(-0.300002\pi\)
−0.406742 + 0.913543i \(0.633335\pi\)
\(774\) 8.83710 15.3063i 0.317643 0.550174i
\(775\) 32.8654 + 20.6110i 1.18056 + 0.740368i
\(776\) 76.3689 2.74148
\(777\) 0 0
\(778\) 15.2618i 0.547162i
\(779\) 10.0000 + 17.3205i 0.358287 + 0.620572i
\(780\) −3.04202 + 10.5763i −0.108922 + 0.378692i