Properties

Label 735.2.q.e.214.6
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: \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) Copy content Toggle raw display
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 214.6
Root \(-1.16746 - 0.312819i\) of defining polynomial
Character \(\chi\) \(=\) 735.214
Dual form 735.2.q.e.79.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.34630 - 1.35464i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.67009 - 4.62473i) q^{4} +(-0.618092 - 2.14894i) q^{5} -2.70928 q^{6} -9.04945i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(2.34630 - 1.35464i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.67009 - 4.62473i) q^{4} +(-0.618092 - 2.14894i) q^{5} -2.70928 q^{6} -9.04945i q^{8} +(0.500000 + 0.866025i) q^{9} +(-4.36127 - 4.20478i) 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} +(-4.23592 + 2.65649i) q^{25} +(1.24846 + 2.16240i) q^{26} -1.00000i q^{27} +6.68035 q^{29} +(1.67458 + 5.82208i) 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} +(-19.4468 + 5.59339i) q^{40} +6.49693 q^{41} -6.52359i q^{43} +(5.34017 + 9.24945i) q^{44} +(1.55199 - 1.60976i) 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} +(8.59637 + 8.28792i) q^{60} +(2.07838 + 3.59986i) q^{61} -21.0205i q^{62} -24.8576 q^{64} +(1.98052 - 0.569647i) 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} +(4.99666 - 0.182626i) q^{75} +16.4391 q^{76} -2.49693i q^{78} +(3.07838 + 5.33191i) q^{79} +(-21.4751 + 22.2744i) 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} +(4.77763 - 4.95544i) q^{95} +(9.69481 + 16.7919i) q^{96} +8.43907i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(-0.259388\pi\)
0.973138 0.230222i \(-0.0739454\pi\)
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 2.67009 4.62473i 1.33504 2.31236i
\(5\) −0.618092 2.14894i −0.276419 0.961037i
\(6\) −2.70928 −1.10606
\(7\) 0 0
\(8\) 9.04945i 3.19946i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −4.36127 4.20478i −1.37916 1.32967i
\(11\) −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 \(0.0407935\pi\)
−0.991799 + 0.127806i \(0.959207\pi\)
\(14\) 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 0.608959 0.793202i \(-0.291588\pi\)
−0.382454 + 0.923975i \(0.624921\pi\)
\(18\) 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 −0.273597 0.961844i \(-0.588214\pi\)
0.696183 + 0.717864i \(0.254880\pi\)
\(24\) −4.52472 + 7.83705i −0.923605 + 1.59973i
\(25\) −4.23592 + 2.65649i −0.847185 + 0.531298i
\(26\) 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 \(0.287029\pi\)
\(30\) 1.67458 + 5.82208i 0.305735 + 1.06296i
\(31\) 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 \(0.683192\pi\)
−0.998653 + 0.0518912i \(0.983475\pi\)
\(38\) 7.22280 + 4.17009i 1.17169 + 0.676477i
\(39\) 0.460811 0.798148i 0.0737888 0.127806i
\(40\) −19.4468 + 5.59339i −3.07480 + 0.884393i
\(41\) 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 \(-0.834281\pi\)
0.867510 0.497419i \(-0.165719\pi\)
\(44\) 5.34017 + 9.24945i 0.805061 + 1.39441i
\(45\) 1.55199 1.60976i 0.231358 0.239968i
\(46\) 3.17009 5.49075i 0.467404 0.809567i
\(47\) −4.05330 + 2.34017i −0.591234 + 0.341349i −0.765585 0.643334i \(-0.777551\pi\)
0.174351 + 0.984684i \(0.444217\pi\)
\(48\) 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 0.259488 0.965746i \(-0.416446\pi\)
−0.706617 + 0.707596i \(0.749780\pi\)
\(54\) −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 \(-0.0735431\pi\)
\(60\) 8.59637 + 8.28792i 1.10979 + 1.06997i
\(61\) 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
\(65\) 1.98052 0.569647i 0.245653 0.0706561i
\(66\) 2.70928 4.69260i 0.333489 0.577619i
\(67\) 4.05330 + 2.34017i 0.495189 + 0.285898i 0.726725 0.686929i \(-0.241042\pi\)
−0.231535 + 0.972826i \(0.574375\pi\)
\(68\) 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 0.0963516 0.995347i \(-0.469283\pi\)
−0.813820 + 0.581117i \(0.802616\pi\)
\(74\) −14.6803 + 25.4271i −1.70656 + 2.95584i
\(75\) 4.99666 0.182626i 0.576965 0.0210878i
\(76\) 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 \(0.720756\pi\)
\(80\) −21.4751 + 22.2744i −2.40099 + 2.49035i
\(81\) −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 \(0.122438\pi\)
−0.926930 + 0.375235i \(0.877562\pi\)
\(84\) 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
\(95\) 4.77763 4.95544i 0.490174 0.508417i
\(96\) 9.69481 + 16.7919i 0.989472 + 1.71382i
\(97\) 8.43907i 0.856858i 0.903576 + 0.428429i \(0.140933\pi\)
−0.903576 + 0.428429i \(0.859067\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0.975255 + 26.6830i 0.0975255 + 2.66830i
\(101\) 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 −0.589190 0.807995i \(-0.700553\pi\)
0.405149 + 0.914251i \(0.367220\pi\)
\(104\) 8.34017 0.817821
\(105\) 0 0
\(106\) −10.1834 −0.989101
\(107\) 14.2868 8.24846i 1.38115 0.797409i 0.388857 0.921298i \(-0.372870\pi\)
0.992296 + 0.123889i \(0.0395367\pi\)
\(108\) −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 \(0.955909\pi\)
\(110\) 11.6442 3.34916i 1.11023 0.319330i
\(111\) 10.8371 1.02861
\(112\) 0 0
\(113\) 5.23513i 0.492480i −0.969209 0.246240i \(-0.920805\pi\)
0.969209 0.246240i \(-0.0791951\pi\)
\(114\) −4.17009 7.22280i −0.390564 0.676477i
\(115\) −3.76711 3.63194i −0.351284 0.338680i
\(116\) 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 \(-0.973939\pi\)
0.996650 0.0817808i \(-0.0260607\pi\)
\(128\) −24.7397 + 14.2834i −2.18670 + 1.26249i
\(129\) −3.26180 + 5.64960i −0.287185 + 0.497419i
\(130\) 3.87522 4.01944i 0.339879 0.352529i
\(131\) −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
\(135\) −2.14894 + 0.618092i −0.184952 + 0.0531969i
\(136\) 4.87936 8.45130i 0.418402 0.724693i
\(137\) 3.84435 + 2.21953i 0.328445 + 0.189628i 0.655150 0.755498i \(-0.272605\pi\)
−0.326706 + 0.945126i \(0.605939\pi\)
\(138\) −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
\(145\) −4.12907 14.3557i −0.342900 1.19218i
\(146\) −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 \(0.611421\pi\)
\(150\) 11.4763 7.19716i 0.937035 0.587646i
\(151\) −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 0.660345 0.750963i \(-0.270410\pi\)
−0.320180 + 0.947357i \(0.603743\pi\)
\(158\) 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 −0.795201 0.606346i \(-0.792635\pi\)
0.127511 + 0.991837i \(0.459301\pi\)
\(164\) 17.3474 30.0465i 1.35460 2.34624i
\(165\) −3.21951 3.10399i −0.250639 0.241645i
\(166\) 9.26180 + 16.0419i 0.718855 + 1.24509i
\(167\) 19.2039i 1.48605i 0.669266 + 0.743023i \(0.266609\pi\)
−0.669266 + 0.743023i \(0.733391\pi\)
\(168\) 0 0
\(169\) 12.1506 0.934662
\(170\) −1.80583 6.27840i −0.138501 0.481532i
\(171\) −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 −0.999675 0.0254777i \(-0.991889\pi\)
−0.477773 + 0.878483i \(0.658556\pi\)
\(174\) −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 \(0.0447496\pi\)
\(180\) −3.30072 11.4757i −0.246021 0.855351i
\(181\) −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
\(185\) 17.4451 + 16.8191i 1.28259 + 1.23657i
\(186\) −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 0.216006 0.976392i \(-0.430697\pi\)
−0.737577 + 0.675263i \(0.764030\pi\)
\(194\) 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 \(0.137580\pi\)
−0.908038 + 0.418887i \(0.862420\pi\)
\(198\) −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 \(0.871028\pi\)
\(200\) 24.0398 + 38.3328i 1.69987 + 2.71054i
\(201\) −2.34017 4.05330i −0.165063 0.285898i
\(202\) 15.7587i 1.10878i
\(203\) 0 0
\(204\) −5.75872 −0.403191
\(205\) −4.01570 13.9615i −0.280469 0.975116i
\(206\) −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
\(215\) −14.0188 + 4.03218i −0.956077 + 0.274992i
\(216\) −9.04945 −0.615737
\(217\) 0 0
\(218\) 34.7792i 2.35555i
\(219\) 3.53919 + 6.13005i 0.239156 + 0.414231i
\(220\) 16.5758 17.1927i 1.11754 1.15913i
\(221\) −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 \(-0.741513\pi\)
0.688005 0.725706i \(-0.258487\pi\)
\(224\) 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 0.131024 0.991379i \(-0.458174\pi\)
−0.793048 + 0.609159i \(0.791507\pi\)
\(228\) −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 −0.679473 0.733701i \(-0.737792\pi\)
0.295667 + 0.955291i \(0.404458\pi\)
\(234\) −1.24846 + 2.16240i −0.0816147 + 0.141361i
\(235\) 7.53421 + 7.26387i 0.491478 + 0.473843i
\(236\) −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 \(0.227375\pi\)
\(240\) 29.7352 8.55260i 1.91940 0.552068i
\(241\) 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
\(250\) 29.6440 + 6.22546i 1.87485 + 0.393732i
\(251\) 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
\(255\) −1.67364 + 1.73592i −0.104807 + 0.108708i
\(256\) −13.8402 + 23.9719i −0.865011 + 1.49824i
\(257\) 4.39800 2.53919i 0.274340 0.158390i −0.356518 0.934288i \(-0.616036\pi\)
0.630858 + 0.775898i \(0.282703\pi\)
\(258\) 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 0.341207 0.939988i \(-0.389164\pi\)
−0.643450 + 0.765488i \(0.722498\pi\)
\(264\) −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 \(0.843718\pi\)
\(270\) −4.20478 + 4.36127i −0.255895 + 0.265419i
\(271\) −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
\(275\) −0.365252 9.99333i −0.0220255 0.602620i
\(276\) −6.24846 + 10.8227i −0.376113 + 0.651447i
\(277\) −24.4200 14.0989i −1.46726 0.847121i −0.467928 0.883767i \(-0.654999\pi\)
−0.999328 + 0.0366462i \(0.988333\pi\)
\(278\) −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 −0.247769 0.968819i \(-0.579697\pi\)
−0.962906 + 0.269836i \(0.913031\pi\)
\(284\) 5.34017 9.24945i 0.316881 0.548854i
\(285\) −6.61526 + 1.90272i −0.391854 + 0.112707i
\(286\) −4.99386 −0.295293
\(287\) 0 0
\(288\) 19.3896i 1.14254i
\(289\) −7.91855 13.7153i −0.465797 0.806784i
\(290\) −29.1348 28.0894i −1.71085 1.64947i
\(291\) 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 \(-0.972802\pi\)
0.996352 0.0853415i \(-0.0271981\pi\)
\(294\) 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
\(305\) 6.45126 6.69136i 0.369398 0.383146i
\(306\) 1.46081 + 2.53020i 0.0835090 + 0.144642i
\(307\) 10.4703i 0.597570i 0.954321 + 0.298785i \(0.0965813\pi\)
−0.954321 + 0.298785i \(0.903419\pi\)
\(308\) 0 0
\(309\) 2.15676 0.122694
\(310\) −45.1719 + 12.9926i −2.56559 + 0.737931i
\(311\) −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 \(-0.290192\pi\)
0.990829 0.135118i \(-0.0431415\pi\)
\(314\) 13.3340 0.752483
\(315\) 0 0
\(316\) 32.8781 1.84954
\(317\) 15.5153 8.95774i 0.871424 0.503117i 0.00360269 0.999994i \(-0.498853\pi\)
0.867821 + 0.496877i \(0.165520\pi\)
\(318\) 8.81910 + 5.09171i 0.494550 + 0.285529i
\(319\) −6.68035 + 11.5707i −0.374028 + 0.647835i
\(320\) 15.3643 + 53.4176i 0.858890 + 2.98614i
\(321\) −16.4969 −0.920769
\(322\) 0 0
\(323\) 3.31965i 0.184710i
\(324\) 2.67009 + 4.62473i 0.148338 + 0.256929i
\(325\) −2.44828 3.90392i −0.135806 0.216551i
\(326\) −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 \(0.242716\pi\)
−0.723101 + 0.690742i \(0.757284\pi\)
\(338\) 28.5090 16.4597i 1.55069 0.895288i
\(339\) −2.61757 + 4.53376i −0.142167 + 0.246240i
\(340\) −9.27014 8.93751i −0.502744 0.484704i
\(341\) 7.75872 + 13.4385i 0.420158 + 0.727736i
\(342\) 8.34017i 0.450985i
\(343\) 0 0
\(344\) −59.0349 −3.18295
\(345\) 1.44644 + 5.02890i 0.0778738 + 0.270747i
\(346\) −30.3968 + 52.6488i −1.63414 + 2.83042i
\(347\) 14.6044 + 8.43188i 0.784008 + 0.452647i 0.837849 0.545902i \(-0.183813\pi\)
−0.0538410 + 0.998550i \(0.517146\pi\)
\(348\) −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 \(0.0683889\pi\)
0.673142 + 0.739514i \(0.264944\pi\)
\(354\) −14.2557 + 24.6915i −0.757679 + 1.31234i
\(355\) −1.23618 4.29789i −0.0656098 0.228108i
\(356\) 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 \(-0.367078\pi\)
\(360\) −14.5674 14.0447i −0.767769 0.740220i
\(361\) 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 0.883091 0.469202i \(-0.155458\pi\)
0.0352048 + 0.999380i \(0.488792\pi\)
\(368\) −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 −0.813816 0.581122i \(-0.802614\pi\)
0.0963587 + 0.995347i \(0.469280\pi\)
\(374\) −2.92162 + 5.06040i −0.151073 + 0.261667i
\(375\) −3.48085 10.6247i −0.179750 0.548656i
\(376\) 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 \(0.550545\pi\)
\(380\) −10.1609 35.3266i −0.521241 1.81222i
\(381\) −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 0.229833 0.973230i \(-0.426182\pi\)
0.957758 + 0.287574i \(0.0928488\pi\)
\(384\) 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 \(0.212279\pi\)
\(390\) −5.36576 + 1.54333i −0.271706 + 0.0781496i
\(391\) 2.52359 0.127623
\(392\) 0 0
\(393\) 1.47641i 0.0744750i
\(394\) 15.9288 + 27.5895i 0.802482 + 1.38994i
\(395\) 9.55525 9.91087i 0.480777 0.498670i
\(396\) −5.34017 + 9.24945i −0.268354 + 0.464802i
\(397\) −32.7356 + 18.8999i −1.64295 + 0.948558i −0.663173 + 0.748466i \(0.730791\pi\)
−0.979777 + 0.200092i \(0.935876\pi\)
\(398\) 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 \(0.0678609\pi\)
\(410\) −28.3349 27.3182i −1.39936 1.34915i
\(411\) −2.21953 3.84435i −0.109482 0.189628i
\(412\) 11.5174i 0.567424i
\(413\) 0 0
\(414\) 6.34017 0.311603
\(415\) 14.6926 4.22596i 0.721229 0.207444i
\(416\) 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
\(425\) −5.38829 + 0.196940i −0.261370 + 0.00955299i
\(426\) −5.41855 −0.262530
\(427\) 0 0
\(428\) 88.0965i 4.25830i
\(429\) 0.921622 + 1.59630i 0.0444963 + 0.0770699i
\(430\) −27.4303 + 28.4511i −1.32280 + 1.37204i
\(431\) 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 \(0.163412\pi\)
−0.871092 + 0.491120i \(0.836588\pi\)
\(434\) 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 −0.739835 0.672789i \(-0.765096\pi\)
0.212735 + 0.977110i \(0.431763\pi\)
\(444\) 28.9360 50.1186i 1.37324 2.37852i
\(445\) 12.9439 13.4256i 0.613600 0.636436i
\(446\) −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 \(0.387829\pi\)
\(450\) −13.5373 + 0.494784i −0.638156 + 0.0233244i
\(451\) −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 −0.758548 0.651618i \(-0.774091\pi\)
0.185044 + 0.982730i \(0.440757\pi\)
\(458\) 30.1197 + 17.3896i 1.40740 + 0.812564i
\(459\) 0.539189 0.933903i 0.0251672 0.0435908i
\(460\) −26.8552 + 7.72425i −1.25213 + 0.360145i
\(461\) 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 \(-0.926544\pi\)
0.973491 0.228727i \(-0.0734564\pi\)
\(464\) −46.2183 80.0525i −2.14563 3.71634i
\(465\) 12.4896 + 12.0415i 0.579194 + 0.558411i
\(466\) −9.16394 + 15.8724i −0.424511 + 0.735275i
\(467\) 9.97440 5.75872i 0.461560 0.266482i −0.251140 0.967951i \(-0.580805\pi\)
0.712700 + 0.701469i \(0.247472\pi\)
\(468\) 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 \(0.313779\pi\)
\(480\) 30.0926 31.2126i 1.37353 1.42465i
\(481\) −4.99386 8.64961i −0.227700 0.394388i
\(482\) 39.7731i 1.81162i
\(483\) 0 0
\(484\) 37.3812 1.69915
\(485\) 18.1351 5.21612i 0.823472 0.236852i
\(486\) 1.35464 2.34630i 0.0614476 0.106430i
\(487\) 20.0490 + 11.5753i 0.908508 + 0.524527i 0.879951 0.475065i \(-0.157575\pi\)
0.0285570 + 0.999592i \(0.490909\pi\)
\(488\) 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
\(495\) 1.23618 + 4.29789i 0.0555623 + 0.193176i
\(496\) −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 \(0.624941\pi\)
\(500\) 56.7376 18.5883i 2.53738 0.831296i
\(501\) 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 \(-0.862047\pi\)
0.907546 0.419952i \(-0.137953\pi\)
\(504\) 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
\(515\) 3.47185 + 3.34727i 0.152988 + 0.147498i
\(516\) 17.4186 + 30.1698i 0.766809 + 1.32815i
\(517\) 9.36069i 0.411683i
\(518\) 0 0
\(519\) 22.4391 0.984966
\(520\) −5.15499 17.9226i −0.226061 0.785957i
\(521\) 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 −0.422347 0.906434i \(-0.638794\pi\)
0.573822 + 0.818980i \(0.305460\pi\)
\(524\) −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
\(530\) 6.29429 + 21.8836i 0.273406 + 0.950563i
\(531\) 10.5236 0.456685
\(532\) 0 0
\(533\) 5.98771i 0.259357i
\(534\) −11.2979 19.5686i −0.488908 0.846814i
\(535\) −26.5560 25.6031i −1.14812 1.10692i
\(536\) 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 \(-0.922198\pi\)
0.970277 0.241997i \(-0.0778023\pi\)
\(548\) 20.5295 11.8527i 0.876976 0.506322i
\(549\) −2.07838 + 3.59986i −0.0887030 + 0.153638i
\(550\) −14.3943 22.9526i −0.613776 0.978701i
\(551\) 10.2823 + 17.8095i 0.438041 + 0.758710i
\(552\) 21.1773i 0.901365i
\(553\) 0 0
\(554\) −76.3956 −3.24574
\(555\) −6.69833 23.2883i −0.284328 0.988535i
\(556\) −36.3184 + 62.9054i −1.54024 + 2.66778i
\(557\) −23.0788 13.3246i −0.977882 0.564580i −0.0762519 0.997089i \(-0.524295\pi\)
−0.901630 + 0.432508i \(0.857629\pi\)
\(558\) 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 \(-0.902024\pi\)
−0.738875 0.673843i \(-0.764642\pi\)
\(564\) 12.4969 21.6453i 0.526216 0.911432i
\(565\) −11.2500 + 3.23579i −0.473292 + 0.136131i
\(566\) −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 \(0.930702\pi\)
\(570\) −12.9439 + 13.4256i −0.542160 + 0.562338i
\(571\) −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 \(0.0267380\pi\)
0.570898 + 0.821021i \(0.306595\pi\)
\(578\) −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
\(585\) 1.48359 + 1.43035i 0.0613388 + 0.0591378i
\(586\) −3.95774 6.85501i −0.163493 0.283178i
\(587\) 36.0288i 1.48707i −0.668699 0.743533i \(-0.733149\pi\)
0.668699 0.743533i \(-0.266851\pi\)
\(588\) 0 0
\(589\) 23.8843 0.984135
\(590\) −61.2692 + 17.6226i −2.52241 + 0.725511i
\(591\) 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 0.178419 0.983955i \(-0.442902\pi\)
0.941339 + 0.337462i \(0.109568\pi\)
\(594\) 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 \(-0.0354559\pi\)
\(600\) −1.65267 45.2170i −0.0674698 1.84598i
\(601\) 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
\(605\) 10.8640 11.2683i 0.441683 0.458121i
\(606\) −7.87936 + 13.6475i −0.320077 + 0.554390i
\(607\) 11.2992 6.52359i 0.458620 0.264784i −0.252844 0.967507i \(-0.581366\pi\)
0.711464 + 0.702723i \(0.248033\pi\)
\(608\) 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 0.746203 0.665718i \(-0.231875\pi\)
−0.203427 + 0.979090i \(0.565208\pi\)
\(614\) 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 \(0.151520\pi\)
−0.888829 + 0.458240i \(0.848480\pi\)
\(618\) 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 \(0.115736\pi\)
\(620\) −64.3037 + 66.6969i −2.58250 + 2.67861i
\(621\) −1.17009 2.02665i −0.0469540 0.0813266i
\(622\) 64.5646i 2.58881i
\(623\) 0 0
\(624\) −12.7526 −0.510512
\(625\) 10.8861 22.5054i 0.435445 0.900216i
\(626\) 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
\(635\) −3.96103 + 1.13929i −0.157189 + 0.0452115i
\(636\) 20.0722 0.795916
\(637\) 0 0
\(638\) 36.1978i 1.43308i
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) 45.9857 + 44.3357i 1.81775 + 1.75252i
\(641\) 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 \(-0.791531\pi\)
0.793094 0.609100i \(-0.208469\pi\)
\(644\) 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 0.136088 0.990697i \(-0.456547\pi\)
−0.789924 + 0.613204i \(0.789880\pi\)
\(648\) 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 −0.898543 0.438886i \(-0.855373\pi\)
−0.0691846 + 0.997604i \(0.522040\pi\)
\(654\) 17.3896 30.1197i 0.679988 1.17777i
\(655\) −2.29138 + 2.37666i −0.0895316 + 0.0928637i
\(656\) −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 \(0.316483\pi\)
\(660\) −22.9515 + 6.60144i −0.893385 + 0.256961i
\(661\) 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
\(670\) −7.83762 27.2494i −0.302794 1.05273i
\(671\) −8.31351 −0.320940
\(672\) 0 0
\(673\) 2.21008i 0.0851923i 0.999092 + 0.0425962i \(0.0135629\pi\)
−0.999092 + 0.0425962i \(0.986437\pi\)
\(674\) 34.3545 + 59.5038i 1.32329 + 2.29200i
\(675\) 2.65649 + 4.23592i 0.102248 + 0.163041i
\(676\) 32.4432 56.1932i 1.24781 2.16128i
\(677\) −16.9296 + 9.77432i −0.650658 + 0.375658i −0.788708 0.614768i \(-0.789250\pi\)
0.138050 + 0.990425i \(0.455916\pi\)
\(678\) 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 0.291269 0.956641i \(-0.405923\pi\)
−0.682841 + 0.730567i \(0.739256\pi\)
\(684\) 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
\(690\) 10.2061 + 9.83991i 0.388541 + 0.374599i
\(691\) −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
\(695\) 8.40727 + 29.2299i 0.318906 + 1.10875i
\(696\) −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
\(705\) −2.89288 10.0578i −0.108952 0.378799i
\(706\) 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 \(0.899847\pi\)
\(710\) −8.72254 8.40956i −0.327351 0.315605i
\(711\) −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
\(725\) −28.2974 + 17.7463i −1.05094 + 0.659080i
\(726\) −9.48246 16.4241i −0.351927 0.609556i
\(727\) 2.89043i 0.107200i −0.998562 0.0536000i \(-0.982930\pi\)
0.998562 0.0536000i \(-0.0170696\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 11.8533 + 41.2109i 0.438711 + 1.52528i
\(731\) 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 −0.852229 0.523168i \(-0.824750\pi\)
0.0269626 + 0.999636i \(0.491417\pi\)
\(734\) 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 \(0.172798\pi\)
\(740\) 124.364 35.7702i 4.57170 1.31494i
\(741\) 2.83710 0.104224
\(742\) 0 0
\(743\) 9.97334i 0.365886i −0.983123 0.182943i \(-0.941438\pi\)
0.983123 0.182943i \(-0.0585624\pi\)
\(744\) 35.1061 + 60.8055i 1.28705 + 2.22924i
\(745\) 24.3263 25.2316i 0.891246 0.924416i
\(746\) −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 \(0.362708\pi\)
−0.418065 + 0.908417i \(0.637292\pi\)
\(758\) −14.4456 + 8.34017i −0.524688 + 0.302929i
\(759\) 2.34017 4.05330i 0.0849429 0.147125i
\(760\) −44.8440 43.2349i −1.62666 1.56829i
\(761\) −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
\(765\) 2.31737 0.666537i 0.0837848 0.0240987i
\(766\) 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 0.406742 0.913543i \(-0.366665\pi\)
−0.587780 + 0.809021i \(0.699998\pi\)
\(774\) 8.83710 15.3063i 0.317643 0.550174i
\(775\) 1.41695 + 38.7677i 0.0508982 + 1.39258i
\(776\) 76.3689 2.74148
\(777\) 0 0
\(778\) 15.2618i 0.547162i
\(779\) 10.0000