Properties

Label 735.2.q.e.214.3
Level $735$
Weight $2$
Character 735.214
Analytic conductor $5.869$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 214.3
Root \(-0.147520 + 0.550552i\) of defining polynomial
Character \(\chi\) \(=\) 735.214
Dual form 735.2.q.e.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.167954 + 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-0.710109 + 2.12032i) q^{5} -0.193937 q^{6} -0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.167954 + 0.0969683i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.981194 + 1.69948i) q^{4} +(-0.710109 + 2.12032i) q^{5} -0.193937 q^{6} -0.768452i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0863379 - 0.424974i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-1.69948 + 0.981194i) q^{12} +1.35026i q^{13} +(-1.67513 + 1.48119i) q^{15} +(-1.88787 - 3.26989i) q^{16} +(-2.90141 - 1.67513i) q^{17} +(-0.167954 - 0.0969683i) q^{18} +(2.67513 + 4.63346i) q^{19} +(-2.90668 - 3.28726i) q^{20} -0.387873i q^{22} +(4.29755 - 2.48119i) q^{23} +(0.384226 - 0.665499i) q^{24} +(-3.99149 - 3.01131i) q^{25} +(-0.130933 - 0.226782i) q^{26} +1.00000i q^{27} -7.92478 q^{29} +(0.137716 - 0.411207i) q^{30} +(-2.28726 + 3.96165i) q^{31} +(1.96515 + 1.13458i) q^{32} +(-1.73205 + 1.00000i) q^{33} +0.649738 q^{34} -1.96239 q^{36} +(0.671816 - 0.387873i) q^{37} +(-0.898598 - 0.518806i) q^{38} +(-0.675131 + 1.16936i) q^{39} +(1.62936 + 0.545685i) q^{40} +3.73813 q^{41} -12.6253i q^{43} +(-1.96239 - 3.39896i) q^{44} +(-2.19130 + 0.445186i) q^{45} +(-0.481194 + 0.833453i) q^{46} +(-8.59511 + 4.96239i) q^{47} -3.77575i q^{48} +(0.962389 + 0.118714i) q^{50} +(-1.67513 - 2.90141i) q^{51} +(-2.29474 - 1.32487i) q^{52} +(-7.42575 - 4.28726i) q^{53} +(-0.0969683 - 0.167954i) q^{54} +(-2.96239 - 3.35026i) q^{55} +5.35026i q^{57} +(1.33100 - 0.768452i) q^{58} +(-4.31265 + 7.46973i) q^{59} +(-0.873629 - 4.30019i) q^{60} +(4.35026 + 7.53487i) q^{61} -0.887166i q^{62} +7.11142 q^{64} +(-2.86298 - 0.958833i) q^{65} +(0.193937 - 0.335908i) q^{66} +(8.59511 + 4.96239i) q^{67} +(5.69370 - 3.28726i) q^{68} +4.96239 q^{69} +2.00000 q^{71} +(0.665499 - 0.384226i) q^{72} +(8.09756 + 4.67513i) q^{73} +(-0.0752228 + 0.130290i) q^{74} +(-1.95108 - 4.60362i) q^{75} -10.4993 q^{76} -0.261865i q^{78} +(5.35026 + 9.26693i) q^{79} +(8.27380 - 1.68091i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.627835 + 0.362481i) q^{82} +3.22425i q^{83} +(5.61213 - 4.96239i) q^{85} +(1.22425 + 2.12047i) q^{86} +(-6.86306 - 3.96239i) q^{87} +(1.33100 + 0.768452i) q^{88} +(0.518806 + 0.898598i) q^{89} +(0.324869 - 0.287258i) q^{90} +9.73813i q^{92} +(-3.96165 + 2.28726i) q^{93} +(0.962389 - 1.66691i) q^{94} +(-11.7240 + 2.38186i) q^{95} +(1.13458 + 1.96515i) q^{96} +18.4993i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.167954 + 0.0969683i −0.118761 + 0.0685669i −0.558204 0.829704i \(-0.688509\pi\)
0.439443 + 0.898271i \(0.355176\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −0.981194 + 1.69948i −0.490597 + 0.849739i
\(5\) −0.710109 + 2.12032i −0.317570 + 0.948235i
\(6\) −0.193937 −0.0791743
\(7\) 0 0
\(8\) 0.768452i 0.271689i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −0.0863379 0.424974i −0.0273025 0.134389i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) −1.69948 + 0.981194i −0.490597 + 0.283246i
\(13\) 1.35026i 0.374495i 0.982313 + 0.187248i \(0.0599567\pi\)
−0.982313 + 0.187248i \(0.940043\pi\)
\(14\) 0 0
\(15\) −1.67513 + 1.48119i −0.432517 + 0.382443i
\(16\) −1.88787 3.26989i −0.471968 0.817473i
\(17\) −2.90141 1.67513i −0.703696 0.406279i 0.105027 0.994469i \(-0.466507\pi\)
−0.808722 + 0.588190i \(0.799841\pi\)
\(18\) −0.167954 0.0969683i −0.0395871 0.0228556i
\(19\) 2.67513 + 4.63346i 0.613717 + 1.06299i 0.990608 + 0.136732i \(0.0436598\pi\)
−0.376891 + 0.926258i \(0.623007\pi\)
\(20\) −2.90668 3.28726i −0.649953 0.735053i
\(21\) 0 0
\(22\) 0.387873i 0.0826948i
\(23\) 4.29755 2.48119i 0.896102 0.517365i 0.0201686 0.999797i \(-0.493580\pi\)
0.875934 + 0.482432i \(0.160246\pi\)
\(24\) 0.384226 0.665499i 0.0784298 0.135844i
\(25\) −3.99149 3.01131i −0.798298 0.602262i
\(26\) −0.130933 0.226782i −0.0256780 0.0444756i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −7.92478 −1.47159 −0.735797 0.677202i \(-0.763192\pi\)
−0.735797 + 0.677202i \(0.763192\pi\)
\(30\) 0.137716 0.411207i 0.0251434 0.0750758i
\(31\) −2.28726 + 3.96165i −0.410804 + 0.711533i −0.994978 0.100096i \(-0.968085\pi\)
0.584174 + 0.811628i \(0.301418\pi\)
\(32\) 1.96515 + 1.13458i 0.347393 + 0.200567i
\(33\) −1.73205 + 1.00000i −0.301511 + 0.174078i
\(34\) 0.649738 0.111429
\(35\) 0 0
\(36\) −1.96239 −0.327065
\(37\) 0.671816 0.387873i 0.110446 0.0637660i −0.443760 0.896146i \(-0.646356\pi\)
0.554205 + 0.832380i \(0.313022\pi\)
\(38\) −0.898598 0.518806i −0.145772 0.0841614i
\(39\) −0.675131 + 1.16936i −0.108107 + 0.187248i
\(40\) 1.62936 + 0.545685i 0.257625 + 0.0862803i
\(41\) 3.73813 0.583799 0.291899 0.956449i \(-0.405713\pi\)
0.291899 + 0.956449i \(0.405713\pi\)
\(42\) 0 0
\(43\) 12.6253i 1.92534i −0.270677 0.962670i \(-0.587248\pi\)
0.270677 0.962670i \(-0.412752\pi\)
\(44\) −1.96239 3.39896i −0.295841 0.512412i
\(45\) −2.19130 + 0.445186i −0.326660 + 0.0663645i
\(46\) −0.481194 + 0.833453i −0.0709482 + 0.122886i
\(47\) −8.59511 + 4.96239i −1.25373 + 0.723839i −0.971847 0.235611i \(-0.924291\pi\)
−0.281878 + 0.959450i \(0.590957\pi\)
\(48\) 3.77575i 0.544982i
\(49\) 0 0
\(50\) 0.962389 + 0.118714i 0.136102 + 0.0167887i
\(51\) −1.67513 2.90141i −0.234565 0.406279i
\(52\) −2.29474 1.32487i −0.318223 0.183726i
\(53\) −7.42575 4.28726i −1.02000 0.588900i −0.105900 0.994377i \(-0.533772\pi\)
−0.914105 + 0.405477i \(0.867106\pi\)
\(54\) −0.0969683 0.167954i −0.0131957 0.0228556i
\(55\) −2.96239 3.35026i −0.399448 0.451749i
\(56\) 0 0
\(57\) 5.35026i 0.708659i
\(58\) 1.33100 0.768452i 0.174769 0.100903i
\(59\) −4.31265 + 7.46973i −0.561459 + 0.972476i 0.435910 + 0.899990i \(0.356427\pi\)
−0.997369 + 0.0724858i \(0.976907\pi\)
\(60\) −0.873629 4.30019i −0.112785 0.555152i
\(61\) 4.35026 + 7.53487i 0.556994 + 0.964742i 0.997745 + 0.0671126i \(0.0213787\pi\)
−0.440751 + 0.897629i \(0.645288\pi\)
\(62\) 0.887166i 0.112670i
\(63\) 0 0
\(64\) 7.11142 0.888927
\(65\) −2.86298 0.958833i −0.355109 0.118929i
\(66\) 0.193937 0.335908i 0.0238719 0.0413474i
\(67\) 8.59511 + 4.96239i 1.05006 + 0.606252i 0.922666 0.385600i \(-0.126006\pi\)
0.127394 + 0.991852i \(0.459339\pi\)
\(68\) 5.69370 3.28726i 0.690462 0.398639i
\(69\) 4.96239 0.597401
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0.665499 0.384226i 0.0784298 0.0452815i
\(73\) 8.09756 + 4.67513i 0.947748 + 0.547183i 0.892381 0.451283i \(-0.149034\pi\)
0.0553675 + 0.998466i \(0.482367\pi\)
\(74\) −0.0752228 + 0.130290i −0.00874447 + 0.0151459i
\(75\) −1.95108 4.60362i −0.225291 0.531580i
\(76\) −10.4993 −1.20435
\(77\) 0 0
\(78\) 0.261865i 0.0296504i
\(79\) 5.35026 + 9.26693i 0.601951 + 1.04261i 0.992525 + 0.122039i \(0.0389433\pi\)
−0.390574 + 0.920572i \(0.627723\pi\)
\(80\) 8.27380 1.68091i 0.925039 0.187932i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −0.627835 + 0.362481i −0.0693327 + 0.0400293i
\(83\) 3.22425i 0.353908i 0.984219 + 0.176954i \(0.0566244\pi\)
−0.984219 + 0.176954i \(0.943376\pi\)
\(84\) 0 0
\(85\) 5.61213 4.96239i 0.608721 0.538247i
\(86\) 1.22425 + 2.12047i 0.132015 + 0.228656i
\(87\) −6.86306 3.96239i −0.735797 0.424813i
\(88\) 1.33100 + 0.768452i 0.141885 + 0.0819173i
\(89\) 0.518806 + 0.898598i 0.0549933 + 0.0952512i 0.892212 0.451618i \(-0.149153\pi\)
−0.837218 + 0.546869i \(0.815820\pi\)
\(90\) 0.324869 0.287258i 0.0342442 0.0302796i
\(91\) 0 0
\(92\) 9.73813i 1.01527i
\(93\) −3.96165 + 2.28726i −0.410804 + 0.237178i
\(94\) 0.962389 1.66691i 0.0992628 0.171928i
\(95\) −11.7240 + 2.38186i −1.20286 + 0.244374i
\(96\) 1.13458 + 1.96515i 0.115798 + 0.200567i
\(97\) 18.4993i 1.87832i 0.343482 + 0.939159i \(0.388394\pi\)
−0.343482 + 0.939159i \(0.611606\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 9.03409 3.82877i 0.903409 0.382877i
\(101\) 8.83146 15.2965i 0.878763 1.52206i 0.0260630 0.999660i \(-0.491703\pi\)
0.852700 0.522401i \(-0.174964\pi\)
\(102\) 0.562690 + 0.324869i 0.0557146 + 0.0321668i
\(103\) 5.80282 3.35026i 0.571769 0.330111i −0.186086 0.982533i \(-0.559580\pi\)
0.757856 + 0.652422i \(0.226247\pi\)
\(104\) 1.03761 0.101746
\(105\) 0 0
\(106\) 1.66291 0.161516
\(107\) −11.8976 + 6.86907i −1.15018 + 0.664058i −0.948932 0.315482i \(-0.897834\pi\)
−0.201250 + 0.979540i \(0.564500\pi\)
\(108\) −1.69948 0.981194i −0.163532 0.0944155i
\(109\) −1.38787 + 2.40387i −0.132934 + 0.230249i −0.924806 0.380438i \(-0.875773\pi\)
0.791872 + 0.610687i \(0.209107\pi\)
\(110\) 0.822414 + 0.275432i 0.0784141 + 0.0262614i
\(111\) 0.775746 0.0736306
\(112\) 0 0
\(113\) 12.0508i 1.13364i 0.823841 + 0.566821i \(0.191827\pi\)
−0.823841 + 0.566821i \(0.808173\pi\)
\(114\) −0.518806 0.898598i −0.0485906 0.0841614i
\(115\) 2.20919 + 10.8741i 0.206008 + 1.01401i
\(116\) 7.77575 13.4680i 0.721960 1.25047i
\(117\) −1.16936 + 0.675131i −0.108107 + 0.0624159i
\(118\) 1.67276i 0.153990i
\(119\) 0 0
\(120\) 1.13823 + 1.28726i 0.103905 + 0.117510i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −1.46129 0.843675i −0.132299 0.0763827i
\(123\) 3.23732 + 1.86907i 0.291899 + 0.168528i
\(124\) −4.48849 7.77429i −0.403078 0.698152i
\(125\) 9.21933 6.32487i 0.824602 0.565713i
\(126\) 0 0
\(127\) 2.70052i 0.239633i −0.992796 0.119816i \(-0.961769\pi\)
0.992796 0.119816i \(-0.0382306\pi\)
\(128\) −5.12469 + 2.95874i −0.452963 + 0.261518i
\(129\) 6.31265 10.9338i 0.555798 0.962670i
\(130\) 0.573826 0.116579i 0.0503279 0.0102246i
\(131\) −10.3127 17.8620i −0.901020 1.56061i −0.826172 0.563418i \(-0.809486\pi\)
−0.0748486 0.997195i \(-0.523847\pi\)
\(132\) 3.92478i 0.341608i
\(133\) 0 0
\(134\) −1.92478 −0.166275
\(135\) −2.12032 0.710109i −0.182488 0.0611164i
\(136\) −1.28726 + 2.22960i −0.110381 + 0.191186i
\(137\) 19.4850 + 11.2496i 1.66471 + 0.961122i 0.970418 + 0.241431i \(0.0776168\pi\)
0.694294 + 0.719691i \(0.255717\pi\)
\(138\) −0.833453 + 0.481194i −0.0709482 + 0.0409620i
\(139\) 3.27504 0.277785 0.138893 0.990307i \(-0.455646\pi\)
0.138893 + 0.990307i \(0.455646\pi\)
\(140\) 0 0
\(141\) −9.92478 −0.835817
\(142\) −0.335908 + 0.193937i −0.0281888 + 0.0162748i
\(143\) −2.33872 1.35026i −0.195574 0.112915i
\(144\) 1.88787 3.26989i 0.157323 0.272491i
\(145\) 5.62745 16.8030i 0.467335 1.39542i
\(146\) −1.81336 −0.150075
\(147\) 0 0
\(148\) 1.52232i 0.125134i
\(149\) −2.22425 3.85252i −0.182218 0.315611i 0.760418 0.649434i \(-0.224994\pi\)
−0.942636 + 0.333824i \(0.891661\pi\)
\(150\) 0.774096 + 0.584003i 0.0632047 + 0.0476837i
\(151\) −0.649738 + 1.12538i −0.0528749 + 0.0915821i −0.891251 0.453510i \(-0.850172\pi\)
0.838376 + 0.545092i \(0.183505\pi\)
\(152\) 3.56059 2.05571i 0.288802 0.166740i
\(153\) 3.35026i 0.270853i
\(154\) 0 0
\(155\) −6.77575 7.66291i −0.544241 0.615500i
\(156\) −1.32487 2.29474i −0.106074 0.183726i
\(157\) −2.29474 1.32487i −0.183140 0.105736i 0.405627 0.914039i \(-0.367053\pi\)
−0.588767 + 0.808303i \(0.700387\pi\)
\(158\) −1.79720 1.03761i −0.142977 0.0825479i
\(159\) −4.28726 7.42575i −0.340002 0.588900i
\(160\) −3.80114 + 3.36107i −0.300506 + 0.265716i
\(161\) 0 0
\(162\) 0.193937i 0.0152371i
\(163\) 4.58948 2.64974i 0.359476 0.207544i −0.309375 0.950940i \(-0.600120\pi\)
0.668851 + 0.743397i \(0.266786\pi\)
\(164\) −3.66784 + 6.35288i −0.286410 + 0.496077i
\(165\) −0.890373 4.38261i −0.0693154 0.341185i
\(166\) −0.312650 0.541526i −0.0242664 0.0420306i
\(167\) 14.5501i 1.12592i 0.826485 + 0.562959i \(0.190337\pi\)
−0.826485 + 0.562959i \(0.809663\pi\)
\(168\) 0 0
\(169\) 11.1768 0.859753
\(170\) −0.461385 + 1.37765i −0.0353866 + 0.105661i
\(171\) −2.67513 + 4.63346i −0.204572 + 0.354330i
\(172\) 21.4564 + 12.3879i 1.63604 + 0.944566i
\(173\) −3.89650 + 2.24965i −0.296246 + 0.171037i −0.640755 0.767745i \(-0.721379\pi\)
0.344509 + 0.938783i \(0.388045\pi\)
\(174\) 1.53690 0.116512
\(175\) 0 0
\(176\) 7.55149 0.569215
\(177\) −7.46973 + 4.31265i −0.561459 + 0.324159i
\(178\) −0.174271 0.100615i −0.0130622 0.00754144i
\(179\) 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i \(-0.711416\pi\)
0.990134 + 0.140122i \(0.0447496\pi\)
\(180\) 1.39351 4.16089i 0.103866 0.310134i
\(181\) 10.6253 0.789772 0.394886 0.918730i \(-0.370784\pi\)
0.394886 + 0.918730i \(0.370784\pi\)
\(182\) 0 0
\(183\) 8.70052i 0.643161i
\(184\) −1.90668 3.30246i −0.140562 0.243461i
\(185\) 0.345352 + 1.69990i 0.0253908 + 0.124979i
\(186\) 0.443583 0.768308i 0.0325251 0.0563351i
\(187\) 5.80282 3.35026i 0.424344 0.244995i
\(188\) 19.4763i 1.42045i
\(189\) 0 0
\(190\) 1.73813 1.53690i 0.126098 0.111499i
\(191\) 6.92478 + 11.9941i 0.501059 + 0.867860i 0.999999 + 0.00122360i \(0.000389484\pi\)
−0.498940 + 0.866637i \(0.666277\pi\)
\(192\) 6.15867 + 3.55571i 0.444464 + 0.256611i
\(193\) −13.2726 7.66291i −0.955379 0.551588i −0.0606314 0.998160i \(-0.519311\pi\)
−0.894748 + 0.446572i \(0.852645\pi\)
\(194\) −1.79384 3.10703i −0.128791 0.223072i
\(195\) −2.00000 2.26187i −0.143223 0.161976i
\(196\) 0 0
\(197\) 0.574515i 0.0409325i 0.999791 + 0.0204663i \(0.00651507\pi\)
−0.999791 + 0.0204663i \(0.993485\pi\)
\(198\) 0.335908 0.193937i 0.0238719 0.0137825i
\(199\) −0.100615 + 0.174271i −0.00713244 + 0.0123537i −0.869570 0.493810i \(-0.835604\pi\)
0.862437 + 0.506164i \(0.168937\pi\)
\(200\) −2.31405 + 3.06727i −0.163628 + 0.216889i
\(201\) 4.96239 + 8.59511i 0.350020 + 0.606252i
\(202\) 3.42548i 0.241016i
\(203\) 0 0
\(204\) 6.57452 0.460308
\(205\) −2.65448 + 7.92603i −0.185397 + 0.553578i
\(206\) −0.649738 + 1.12538i −0.0452694 + 0.0784089i
\(207\) 4.29755 + 2.48119i 0.298701 + 0.172455i
\(208\) 4.41521 2.54912i 0.306140 0.176750i
\(209\) −10.7005 −0.740171
\(210\) 0 0
\(211\) 6.44851 0.443934 0.221967 0.975054i \(-0.428752\pi\)
0.221967 + 0.975054i \(0.428752\pi\)
\(212\) 14.5722 8.41327i 1.00082 0.577825i
\(213\) 1.73205 + 1.00000i 0.118678 + 0.0685189i
\(214\) 1.33216 2.30737i 0.0910648 0.157729i
\(215\) 26.7696 + 8.96534i 1.82567 + 0.611431i
\(216\) 0.768452 0.0522865
\(217\) 0 0
\(218\) 0.538319i 0.0364595i
\(219\) 4.67513 + 8.09756i 0.315916 + 0.547183i
\(220\) 8.60038 1.74726i 0.579837 0.117800i
\(221\) 2.26187 3.91767i 0.152150 0.263531i
\(222\) −0.130290 + 0.0752228i −0.00874447 + 0.00504862i
\(223\) 1.55149i 0.103896i 0.998650 + 0.0519478i \(0.0165429\pi\)
−0.998650 + 0.0519478i \(0.983457\pi\)
\(224\) 0 0
\(225\) 0.612127 4.96239i 0.0408085 0.330826i
\(226\) −1.16854 2.02398i −0.0777304 0.134633i
\(227\) −11.3874 6.57452i −0.755808 0.436366i 0.0719807 0.997406i \(-0.477068\pi\)
−0.827789 + 0.561040i \(0.810401\pi\)
\(228\) −9.09265 5.24965i −0.602176 0.347666i
\(229\) 1.38787 + 2.40387i 0.0917132 + 0.158852i 0.908232 0.418467i \(-0.137432\pi\)
−0.816519 + 0.577319i \(0.804099\pi\)
\(230\) −1.42548 1.61213i −0.0939937 0.106300i
\(231\) 0 0
\(232\) 6.08981i 0.399816i
\(233\) −0.0439813 + 0.0253926i −0.00288131 + 0.00166353i −0.501440 0.865192i \(-0.667196\pi\)
0.498559 + 0.866856i \(0.333863\pi\)
\(234\) 0.130933 0.226782i 0.00855933 0.0148252i
\(235\) −4.41838 21.7482i −0.288223 1.41870i
\(236\) −8.46310 14.6585i −0.550901 0.954188i
\(237\) 10.7005i 0.695074i
\(238\) 0 0
\(239\) −5.84955 −0.378376 −0.189188 0.981941i \(-0.560586\pi\)
−0.189188 + 0.981941i \(0.560586\pi\)
\(240\) 8.00578 + 2.68119i 0.516771 + 0.173070i
\(241\) 0.0376114 0.0651448i 0.00242276 0.00419635i −0.864811 0.502097i \(-0.832562\pi\)
0.867234 + 0.497900i \(0.165895\pi\)
\(242\) −1.17568 0.678778i −0.0755754 0.0436335i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −17.0738 −1.09304
\(245\) 0 0
\(246\) −0.724961 −0.0462218
\(247\) −6.25639 + 3.61213i −0.398084 + 0.229834i
\(248\) 3.04434 + 1.75765i 0.193315 + 0.111611i
\(249\) −1.61213 + 2.79229i −0.102164 + 0.176954i
\(250\) −0.935111 + 1.95627i −0.0591416 + 0.123725i
\(251\) 19.2243 1.21342 0.606712 0.794922i \(-0.292488\pi\)
0.606712 + 0.794922i \(0.292488\pi\)
\(252\) 0 0
\(253\) 9.92478i 0.623965i
\(254\) 0.261865 + 0.453564i 0.0164309 + 0.0284591i
\(255\) 7.34144 1.49149i 0.459739 0.0934008i
\(256\) −6.53761 + 11.3235i −0.408601 + 0.707717i
\(257\) −6.36551 + 3.67513i −0.397070 + 0.229248i −0.685219 0.728337i \(-0.740293\pi\)
0.288149 + 0.957586i \(0.406960\pi\)
\(258\) 2.44851i 0.152437i
\(259\) 0 0
\(260\) 4.43866 3.92478i 0.275274 0.243404i
\(261\) −3.96239 6.86306i −0.245266 0.424813i
\(262\) 3.46410 + 2.00000i 0.214013 + 0.123560i
\(263\) 11.2258 + 6.48119i 0.692210 + 0.399648i 0.804439 0.594035i \(-0.202466\pi\)
−0.112229 + 0.993682i \(0.535799\pi\)
\(264\) 0.768452 + 1.33100i 0.0472950 + 0.0819173i
\(265\) 14.3634 12.7005i 0.882339 0.780187i
\(266\) 0 0
\(267\) 1.03761i 0.0635008i
\(268\) −16.8669 + 9.73813i −1.03031 + 0.594851i
\(269\) 2.05571 3.56059i 0.125339 0.217093i −0.796527 0.604604i \(-0.793332\pi\)
0.921865 + 0.387510i \(0.126665\pi\)
\(270\) 0.424974 0.0863379i 0.0258631 0.00525436i
\(271\) 8.21203 + 14.2237i 0.498846 + 0.864026i 0.999999 0.00133248i \(-0.000424141\pi\)
−0.501154 + 0.865358i \(0.667091\pi\)
\(272\) 12.6497i 0.767003i
\(273\) 0 0
\(274\) −4.36344 −0.263605
\(275\) 9.20724 3.90215i 0.555217 0.235309i
\(276\) −4.86907 + 8.43347i −0.293083 + 0.507635i
\(277\) −9.59020 5.53690i −0.576219 0.332680i 0.183410 0.983036i \(-0.441286\pi\)
−0.759629 + 0.650356i \(0.774620\pi\)
\(278\) −0.550056 + 0.317575i −0.0329902 + 0.0190469i
\(279\) −4.57452 −0.273869
\(280\) 0 0
\(281\) 14.3733 0.857438 0.428719 0.903438i \(-0.358965\pi\)
0.428719 + 0.903438i \(0.358965\pi\)
\(282\) 1.66691 0.962389i 0.0992628 0.0573094i
\(283\) −0.995090 0.574515i −0.0591520 0.0341514i 0.470132 0.882596i \(-0.344206\pi\)
−0.529284 + 0.848445i \(0.677540\pi\)
\(284\) −1.96239 + 3.39896i −0.116446 + 0.201691i
\(285\) −11.3443 3.79927i −0.671976 0.225049i
\(286\) 0.523730 0.0309688
\(287\) 0 0
\(288\) 2.26916i 0.133711i
\(289\) −2.88787 5.00194i −0.169875 0.294232i
\(290\) 0.684209 + 3.36782i 0.0401781 + 0.197765i
\(291\) −9.24965 + 16.0209i −0.542224 + 0.939159i
\(292\) −15.8906 + 9.17442i −0.929925 + 0.536893i
\(293\) 0.649738i 0.0379581i 0.999820 + 0.0189791i \(0.00604158\pi\)
−0.999820 + 0.0189791i \(0.993958\pi\)
\(294\) 0 0
\(295\) −12.7757 14.4485i −0.743833 0.841225i
\(296\) −0.298062 0.516258i −0.0173245 0.0300069i
\(297\) −1.73205 1.00000i −0.100504 0.0580259i
\(298\) 0.747145 + 0.431364i 0.0432809 + 0.0249883i
\(299\) 3.35026 + 5.80282i 0.193751 + 0.335586i
\(300\) 9.73813 + 1.20123i 0.562231 + 0.0693531i
\(301\) 0 0
\(302\) 0.252016i 0.0145019i
\(303\) 15.2965 8.83146i 0.878763 0.507354i
\(304\) 10.1006 17.4948i 0.579310 1.00339i
\(305\) −19.0655 + 3.87336i −1.09169 + 0.221788i
\(306\) 0.324869 + 0.562690i 0.0185715 + 0.0321668i
\(307\) 24.1016i 1.37555i −0.725924 0.687775i \(-0.758588\pi\)
0.725924 0.687775i \(-0.241412\pi\)
\(308\) 0 0
\(309\) 6.70052 0.381179
\(310\) 1.88107 + 0.629984i 0.106838 + 0.0357807i
\(311\) −4.12601 + 7.14646i −0.233964 + 0.405238i −0.958971 0.283503i \(-0.908503\pi\)
0.725007 + 0.688742i \(0.241837\pi\)
\(312\) 0.898598 + 0.518806i 0.0508731 + 0.0293716i
\(313\) −12.9053 + 7.45088i −0.729451 + 0.421148i −0.818221 0.574904i \(-0.805040\pi\)
0.0887706 + 0.996052i \(0.471706\pi\)
\(314\) 0.513881 0.0290000
\(315\) 0 0
\(316\) −20.9986 −1.18126
\(317\) −8.76938 + 5.06300i −0.492537 + 0.284367i −0.725627 0.688089i \(-0.758450\pi\)
0.233089 + 0.972455i \(0.425117\pi\)
\(318\) 1.44012 + 0.831456i 0.0807582 + 0.0466257i
\(319\) 7.92478 13.7261i 0.443702 0.768515i
\(320\) −5.04988 + 15.0785i −0.282297 + 0.842912i
\(321\) −13.7381 −0.766788
\(322\) 0 0
\(323\) 17.9248i 0.997361i
\(324\) −0.981194 1.69948i −0.0545108 0.0944155i
\(325\) 4.06606 5.38956i 0.225544 0.298959i
\(326\) −0.513881 + 0.890068i −0.0284612 + 0.0492963i
\(327\) −2.40387 + 1.38787i −0.132934 + 0.0767496i
\(328\) 2.87258i 0.158612i
\(329\) 0 0
\(330\) 0.574515 + 0.649738i 0.0316260 + 0.0357669i
\(331\) −13.9248 24.1184i −0.765375 1.32567i −0.940048 0.341042i \(-0.889220\pi\)
0.174673 0.984626i \(-0.444113\pi\)
\(332\) −5.47955 3.16362i −0.300729 0.173626i
\(333\) 0.671816 + 0.387873i 0.0368153 + 0.0212553i
\(334\) −1.41090 2.44374i −0.0772008 0.133716i
\(335\) −16.6253 + 14.7005i −0.908337 + 0.803175i
\(336\) 0 0
\(337\) 3.84955i 0.209699i 0.994488 + 0.104849i \(0.0334360\pi\)
−0.994488 + 0.104849i \(0.966564\pi\)
\(338\) −1.87719 + 1.08379i −0.102106 + 0.0589506i
\(339\) −6.02539 + 10.4363i −0.327254 + 0.566821i
\(340\) 2.92689 + 14.4068i 0.158733 + 0.781316i
\(341\) −4.57452 7.92329i −0.247724 0.429070i
\(342\) 1.03761i 0.0561076i
\(343\) 0 0
\(344\) −9.70194 −0.523093
\(345\) −3.52384 + 10.5218i −0.189717 + 0.566477i
\(346\) 0.436289 0.755674i 0.0234550 0.0406253i
\(347\) 8.30318 + 4.79384i 0.445738 + 0.257347i 0.706029 0.708183i \(-0.250485\pi\)
−0.260290 + 0.965530i \(0.583818\pi\)
\(348\) 13.4680 7.77575i 0.721960 0.416824i
\(349\) 15.1490 0.810909 0.405455 0.914115i \(-0.367113\pi\)
0.405455 + 0.914115i \(0.367113\pi\)
\(350\) 0 0
\(351\) −1.35026 −0.0720716
\(352\) −3.93030 + 2.26916i −0.209486 + 0.120947i
\(353\) 17.6226 + 10.1744i 0.937957 + 0.541530i 0.889319 0.457287i \(-0.151179\pi\)
0.0486379 + 0.998816i \(0.484512\pi\)
\(354\) 0.836381 1.44865i 0.0444531 0.0769951i
\(355\) −1.42022 + 4.24063i −0.0753773 + 0.225070i
\(356\) −2.03620 −0.107918
\(357\) 0 0
\(358\) 1.93937i 0.102499i
\(359\) −15.7005 27.1941i −0.828642 1.43525i −0.899104 0.437735i \(-0.855781\pi\)
0.0704619 0.997514i \(-0.477553\pi\)
\(360\) 0.342104 + 1.68391i 0.0180305 + 0.0887499i
\(361\) −4.81265 + 8.33575i −0.253297 + 0.438724i
\(362\) −1.78456 + 1.03032i −0.0937945 + 0.0541523i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) −15.6629 + 13.8496i −0.819834 + 0.724919i
\(366\) −0.843675 1.46129i −0.0440996 0.0763827i
\(367\) −25.4621 14.7005i −1.32911 0.767361i −0.343947 0.938989i \(-0.611764\pi\)
−0.985162 + 0.171628i \(0.945097\pi\)
\(368\) −16.2265 9.36836i −0.845864 0.488360i
\(369\) 1.86907 + 3.23732i 0.0972998 + 0.168528i
\(370\) −0.222839 0.252016i −0.0115849 0.0131017i
\(371\) 0 0
\(372\) 8.97698i 0.465435i
\(373\) 13.8564 8.00000i 0.717458 0.414224i −0.0963587 0.995347i \(-0.530720\pi\)
0.813816 + 0.581122i \(0.197386\pi\)
\(374\) −0.649738 + 1.12538i −0.0335972 + 0.0581920i
\(375\) 11.1466 0.867833i 0.575608 0.0448147i
\(376\) 3.81336 + 6.60493i 0.196659 + 0.340623i
\(377\) 10.7005i 0.551105i
\(378\) 0 0
\(379\) −10.7005 −0.549649 −0.274824 0.961494i \(-0.588620\pi\)
−0.274824 + 0.961494i \(0.588620\pi\)
\(380\) 7.45564 22.2618i 0.382466 1.14201i
\(381\) 1.35026 2.33872i 0.0691760 0.119816i
\(382\) −2.32609 1.34297i −0.119013 0.0687122i
\(383\) −14.5282 + 8.38787i −0.742357 + 0.428600i −0.822926 0.568149i \(-0.807660\pi\)
0.0805684 + 0.996749i \(0.474326\pi\)
\(384\) −5.91748 −0.301975
\(385\) 0 0
\(386\) 2.97224 0.151283
\(387\) 10.9338 6.31265i 0.555798 0.320890i
\(388\) −31.4391 18.1514i −1.59608 0.921498i
\(389\) −14.6629 + 25.3969i −0.743439 + 1.28767i 0.207481 + 0.978239i \(0.433473\pi\)
−0.950920 + 0.309435i \(0.899860\pi\)
\(390\) 0.555237 + 0.185953i 0.0281155 + 0.00941608i
\(391\) −16.6253 −0.840778
\(392\) 0 0
\(393\) 20.6253i 1.04041i
\(394\) −0.0557098 0.0964922i −0.00280662 0.00486121i
\(395\) −23.4481 + 4.76373i −1.17980 + 0.239689i
\(396\) 1.96239 3.39896i 0.0986137 0.170804i
\(397\) −15.8906 + 9.17442i −0.797525 + 0.460451i −0.842605 0.538532i \(-0.818979\pi\)
0.0450802 + 0.998983i \(0.485646\pi\)
\(398\) 0.0390260i 0.00195620i
\(399\) 0 0
\(400\) −2.31124 + 18.7367i −0.115562 + 0.936836i
\(401\) 18.6629 + 32.3251i 0.931981 + 1.61424i 0.779930 + 0.625866i \(0.215254\pi\)
0.152051 + 0.988373i \(0.451412\pi\)
\(402\) −1.66691 0.962389i −0.0831377 0.0479996i
\(403\) −5.34926 3.08840i −0.266466 0.153844i
\(404\) 17.3307 + 30.0177i 0.862237 + 1.49344i
\(405\) −1.48119 1.67513i −0.0736011 0.0832379i
\(406\) 0 0
\(407\) 1.55149i 0.0769046i
\(408\) −2.22960 + 1.28726i −0.110381 + 0.0637288i
\(409\) −11.1866 + 19.3758i −0.553144 + 0.958073i 0.444901 + 0.895580i \(0.353239\pi\)
−0.998045 + 0.0624938i \(0.980095\pi\)
\(410\) −0.322743 1.58861i −0.0159391 0.0784558i
\(411\) 11.2496 + 19.4850i 0.554904 + 0.961122i
\(412\) 13.1490i 0.647806i
\(413\) 0 0
\(414\) −0.962389 −0.0472988
\(415\) −6.83644 2.28957i −0.335588 0.112391i
\(416\) −1.53198 + 2.65347i −0.0751115 + 0.130097i
\(417\) 2.83627 + 1.63752i 0.138893 + 0.0801897i
\(418\) 1.79720 1.03761i 0.0879037 0.0507512i
\(419\) −23.4763 −1.14689 −0.573445 0.819244i \(-0.694394\pi\)
−0.573445 + 0.819244i \(0.694394\pi\)
\(420\) 0 0
\(421\) −25.2243 −1.22935 −0.614677 0.788779i \(-0.710714\pi\)
−0.614677 + 0.788779i \(0.710714\pi\)
\(422\) −1.08305 + 0.625301i −0.0527222 + 0.0304392i
\(423\) −8.59511 4.96239i −0.417909 0.241280i
\(424\) −3.29455 + 5.70633i −0.159998 + 0.277124i
\(425\) 6.53662 + 15.4233i 0.317073 + 0.748141i
\(426\) −0.387873 −0.0187925
\(427\) 0 0
\(428\) 26.9596i 1.30314i
\(429\) −1.35026 2.33872i −0.0651913 0.112915i
\(430\) −5.36542 + 1.09004i −0.258744 + 0.0525665i
\(431\) 9.70052 16.8018i 0.467258 0.809314i −0.532042 0.846718i \(-0.678575\pi\)
0.999300 + 0.0374035i \(0.0119087\pi\)
\(432\) 3.26989 1.88787i 0.157323 0.0908303i
\(433\) 6.49929i 0.312336i 0.987731 + 0.156168i \(0.0499141\pi\)
−0.987731 + 0.156168i \(0.950086\pi\)
\(434\) 0 0
\(435\) 13.2750 11.7381i 0.636489 0.562800i
\(436\) −2.72355 4.71732i −0.130434 0.225919i
\(437\) 22.9930 + 13.2750i 1.09991 + 0.635031i
\(438\) −1.57041 0.906679i −0.0750373 0.0433228i
\(439\) −7.32487 12.6870i −0.349597 0.605520i 0.636581 0.771210i \(-0.280348\pi\)
−0.986178 + 0.165690i \(0.947015\pi\)
\(440\) −2.57452 + 2.27645i −0.122735 + 0.108526i
\(441\) 0 0
\(442\) 0.877317i 0.0417297i
\(443\) 16.5750 9.56959i 0.787503 0.454665i −0.0515798 0.998669i \(-0.516426\pi\)
0.839083 + 0.544004i \(0.183092\pi\)
\(444\) −0.761158 + 1.31836i −0.0361230 + 0.0625668i
\(445\) −2.27372 + 0.461931i −0.107785 + 0.0218976i
\(446\) −0.150446 0.260579i −0.00712380 0.0123388i
\(447\) 4.44851i 0.210407i
\(448\) 0 0
\(449\) 32.8021 1.54803 0.774013 0.633169i \(-0.218246\pi\)
0.774013 + 0.633169i \(0.218246\pi\)
\(450\) 0.378385 + 0.892810i 0.0178372 + 0.0420875i
\(451\) −3.73813 + 6.47464i −0.176022 + 0.304879i
\(452\) −20.4800 11.8242i −0.963300 0.556162i
\(453\) −1.12538 + 0.649738i −0.0528749 + 0.0305274i
\(454\) 2.55008 0.119681
\(455\) 0 0
\(456\) 4.11142 0.192535
\(457\) 16.1951 9.35026i 0.757576 0.437387i −0.0708487 0.997487i \(-0.522571\pi\)
0.828425 + 0.560100i \(0.189237\pi\)
\(458\) −0.466198 0.269159i −0.0217840 0.0125770i
\(459\) 1.67513 2.90141i 0.0781884 0.135426i
\(460\) −20.6479 6.91513i −0.962715 0.322420i
\(461\) −6.96239 −0.324271 −0.162135 0.986769i \(-0.551838\pi\)
−0.162135 + 0.986769i \(0.551838\pi\)
\(462\) 0 0
\(463\) 5.29948i 0.246288i 0.992389 + 0.123144i \(0.0392976\pi\)
−0.992389 + 0.123144i \(0.960702\pi\)
\(464\) 14.9610 + 25.9132i 0.694546 + 1.20299i
\(465\) −2.03651 10.0241i −0.0944410 0.464859i
\(466\) 0.00492456 0.00852958i 0.000228126 0.000395125i
\(467\) 11.3874 6.57452i 0.526946 0.304232i −0.212826 0.977090i \(-0.568267\pi\)
0.739772 + 0.672858i \(0.234933\pi\)
\(468\) 2.64974i 0.122484i
\(469\) 0 0
\(470\) 2.85097 + 3.22425i 0.131505 + 0.148724i
\(471\) −1.32487 2.29474i −0.0610467 0.105736i
\(472\) 5.74013 + 3.31406i 0.264211 + 0.152542i
\(473\) 21.8677 + 12.6253i 1.00548 + 0.580512i
\(474\) −1.03761 1.79720i −0.0476591 0.0825479i
\(475\) 3.27504 26.5501i 0.150269 1.21820i
\(476\) 0 0
\(477\) 8.57452i 0.392600i
\(478\) 0.982456 0.567221i 0.0449365 0.0259441i
\(479\) 2.57452 4.45919i 0.117633 0.203746i −0.801196 0.598401i \(-0.795803\pi\)
0.918829 + 0.394656i \(0.129136\pi\)
\(480\) −4.97242 + 1.01020i −0.226959 + 0.0461091i
\(481\) 0.523730 + 0.907127i 0.0238800 + 0.0413614i
\(482\) 0.0145884i 0.000664486i
\(483\) 0 0
\(484\) −13.7367 −0.624396
\(485\) −39.2244 13.1365i −1.78109 0.596498i
\(486\) 0.0969683 0.167954i 0.00439857 0.00761855i
\(487\) −19.2057 11.0884i −0.870292 0.502463i −0.00284661 0.999996i \(-0.500906\pi\)
−0.867445 + 0.497533i \(0.834239\pi\)
\(488\) 5.79019 3.34297i 0.262110 0.151329i
\(489\) 5.29948 0.239651
\(490\) 0 0
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) −6.35288 + 3.66784i −0.286410 + 0.165359i
\(493\) 22.9930 + 13.2750i 1.03555 + 0.597878i
\(494\) 0.700523 1.21334i 0.0315180 0.0545908i
\(495\) 1.42022 4.24063i 0.0638340 0.190602i
\(496\) 17.2722 0.775545
\(497\) 0 0
\(498\) 0.625301i 0.0280204i
\(499\) −3.27504 5.67253i −0.146611 0.253937i 0.783362 0.621566i \(-0.213503\pi\)
−0.929973 + 0.367628i \(0.880170\pi\)
\(500\) 1.70303 + 21.8740i 0.0761616 + 0.978234i
\(501\) −7.27504 + 12.6007i −0.325025 + 0.562959i
\(502\) −3.22879 + 1.86414i −0.144108 + 0.0832008i
\(503\) 8.77575i 0.391291i 0.980675 + 0.195646i \(0.0626802\pi\)
−0.980675 + 0.195646i \(0.937320\pi\)
\(504\) 0 0
\(505\) 26.1622 + 29.5877i 1.16420 + 1.31663i
\(506\) −0.962389 1.66691i −0.0427834 0.0741030i
\(507\) 9.67939 + 5.58840i 0.429877 + 0.248189i
\(508\) 4.58948 + 2.64974i 0.203625 + 0.117563i
\(509\) 6.56959 + 11.3789i 0.291192 + 0.504359i 0.974092 0.226153i \(-0.0726148\pi\)
−0.682900 + 0.730512i \(0.739281\pi\)
\(510\) −1.08840 + 0.962389i −0.0481950 + 0.0426153i
\(511\) 0 0
\(512\) 14.3707i 0.635103i
\(513\) −4.63346 + 2.67513i −0.204572 + 0.118110i
\(514\) 0.712742 1.23451i 0.0314377 0.0544517i
\(515\) 2.98298 + 14.6829i 0.131446 + 0.647005i
\(516\) 12.3879 + 21.4564i 0.545346 + 0.944566i
\(517\) 19.8496i 0.872982i
\(518\) 0 0
\(519\) −4.49929 −0.197497
\(520\) −0.736817 + 2.20007i −0.0323116 + 0.0964793i
\(521\) 18.8315 32.6170i 0.825021 1.42898i −0.0768821 0.997040i \(-0.524497\pi\)
0.901903 0.431938i \(-0.142170\pi\)
\(522\) 1.33100 + 0.768452i 0.0582562 + 0.0336342i
\(523\) −3.46410 + 2.00000i −0.151475 + 0.0874539i −0.573822 0.818980i \(-0.694540\pi\)
0.422347 + 0.906434i \(0.361206\pi\)
\(524\) 40.4749 1.76815
\(525\) 0 0
\(526\) −2.51388 −0.109610
\(527\) 13.2726 7.66291i 0.578161 0.333802i
\(528\) 6.53978 + 3.77575i 0.284608 + 0.164318i
\(529\) 0.812650 1.40755i 0.0353326 0.0611979i
\(530\) −1.18085 + 3.52590i −0.0512928 + 0.153155i
\(531\) −8.62530 −0.374306
\(532\) 0 0
\(533\) 5.04746i 0.218630i
\(534\) −0.100615 0.174271i −0.00435405 0.00754144i
\(535\) −6.11603 30.1044i −0.264419 1.30153i
\(536\) 3.81336 6.60493i 0.164712 0.285289i
\(537\) 8.66025 5.00000i 0.373718 0.215766i
\(538\) 0.797355i 0.0343764i
\(539\) 0 0
\(540\) 3.28726 2.90668i 0.141461 0.125084i
\(541\) 11.2374 + 19.4638i 0.483135 + 0.836814i 0.999812 0.0193660i \(-0.00616479\pi\)
−0.516678 + 0.856180i \(0.672831\pi\)
\(542\) −2.75849 1.59261i −0.118487 0.0684086i
\(543\) 9.20178 + 5.31265i 0.394886 + 0.227988i
\(544\) −3.80114 6.58377i −0.162972 0.282277i
\(545\) −4.11142 4.64974i −0.176114 0.199173i
\(546\) 0 0
\(547\) 25.9248i 1.10846i 0.832362 + 0.554232i \(0.186988\pi\)
−0.832362 + 0.554232i \(0.813012\pi\)
\(548\) −38.2371 + 22.0762i −1.63341 + 0.943048i
\(549\) −4.35026 + 7.53487i −0.185665 + 0.321581i
\(550\) −1.16801 + 1.54819i −0.0498040 + 0.0660151i
\(551\) −21.1998 36.7192i −0.903143 1.56429i
\(552\) 3.81336i 0.162307i
\(553\) 0 0
\(554\) 2.14762 0.0912435
\(555\) −0.550864 + 1.64483i −0.0233829 + 0.0698191i
\(556\) −3.21345 + 5.56586i −0.136281 + 0.236045i
\(557\) −24.7039 14.2628i −1.04674 0.604335i −0.125004 0.992156i \(-0.539895\pi\)
−0.921735 + 0.387821i \(0.873228\pi\)
\(558\) 0.768308 0.443583i 0.0325251 0.0187784i
\(559\) 17.0475 0.721031
\(560\) 0 0
\(561\) 6.70052 0.282896
\(562\) −2.41405 + 1.39375i −0.101831 + 0.0587919i
\(563\) 10.0690 + 5.81336i 0.424359 + 0.245004i 0.696941 0.717129i \(-0.254544\pi\)
−0.272582 + 0.962133i \(0.587877\pi\)
\(564\) 9.73813 16.8669i 0.410049 0.710226i
\(565\) −25.5515 8.55737i −1.07496 0.360011i
\(566\) 0.222839 0.00936663
\(567\) 0 0
\(568\) 1.53690i 0.0644871i
\(569\) 4.66291 + 8.07640i 0.195479 + 0.338580i 0.947058 0.321064i \(-0.104040\pi\)
−0.751578 + 0.659644i \(0.770707\pi\)
\(570\) 2.27372 0.461931i 0.0952357 0.0193481i
\(571\) 9.84955 17.0599i 0.412191 0.713936i −0.582938 0.812517i \(-0.698097\pi\)
0.995129 + 0.0985808i \(0.0314303\pi\)
\(572\) 4.58948 2.64974i 0.191896 0.110791i
\(573\) 13.8496i 0.578573i
\(574\) 0 0
\(575\) −24.6253 3.03761i −1.02695 0.126677i
\(576\) 3.55571 + 6.15867i 0.148155 + 0.256611i
\(577\) 28.4033 + 16.3987i 1.18245 + 0.682686i 0.956579 0.291472i \(-0.0941451\pi\)
0.225867 + 0.974158i \(0.427478\pi\)
\(578\) 0.970060 + 0.560064i 0.0403492 + 0.0232956i
\(579\) −7.66291 13.2726i −0.318460 0.551588i
\(580\) 23.0348 + 26.0508i 0.956467 + 1.08170i
\(581\) 0 0
\(582\) 3.58769i 0.148715i
\(583\) 14.8515 8.57452i 0.615086 0.355120i
\(584\) 3.59261 6.22259i 0.148663 0.257493i
\(585\) −0.601118 2.95883i −0.0248532 0.122333i
\(586\) −0.0630040 0.109126i −0.00260267 0.00450796i
\(587\) 18.8218i 0.776859i −0.921479 0.388429i \(-0.873018\pi\)
0.921479 0.388429i \(-0.126982\pi\)
\(588\) 0 0
\(589\) −24.4749 −1.00847
\(590\) 3.54678 + 1.18784i 0.146019 + 0.0489027i
\(591\) −0.287258 + 0.497545i −0.0118162 + 0.0204663i
\(592\) −2.53661 1.46451i −0.104254 0.0601910i
\(593\) 29.2283 16.8749i 1.20026 0.692971i 0.239648 0.970860i \(-0.422968\pi\)
0.960613 + 0.277889i \(0.0896347\pi\)
\(594\) 0.387873 0.0159146
\(595\) 0 0
\(596\) 8.72970 0.357582
\(597\) −0.174271 + 0.100615i −0.00713244 + 0.00411791i
\(598\) −1.12538 0.649738i −0.0460202 0.0265698i
\(599\) −10.1490 + 17.5786i −0.414678 + 0.718244i −0.995395 0.0958622i \(-0.969439\pi\)
0.580716 + 0.814106i \(0.302773\pi\)
\(600\) −3.53766 + 1.49931i −0.144424 + 0.0612090i
\(601\) −13.8496 −0.564935 −0.282468 0.959277i \(-0.591153\pi\)
−0.282468 + 0.959277i \(0.591153\pi\)
\(602\) 0 0
\(603\) 9.92478i 0.404168i
\(604\) −1.27504 2.20843i −0.0518806 0.0898598i
\(605\) −15.3391 + 3.11631i −0.623624 + 0.126696i
\(606\) −1.71274 + 2.96656i −0.0695754 + 0.120508i
\(607\) 21.8677 12.6253i 0.887581 0.512445i 0.0144305 0.999896i \(-0.495406\pi\)
0.873150 + 0.487451i \(0.162073\pi\)
\(608\) 12.1406i 0.492366i
\(609\) 0 0
\(610\) 2.82653 2.49929i 0.114443 0.101193i
\(611\) −6.70052 11.6056i −0.271074 0.469514i
\(612\) 5.69370 + 3.28726i 0.230154 + 0.132880i
\(613\) 7.92329 + 4.57452i 0.320019 + 0.184763i 0.651401 0.758734i \(-0.274182\pi\)
−0.331382 + 0.943497i \(0.607515\pi\)
\(614\) 2.33709 + 4.04796i 0.0943172 + 0.163362i
\(615\) −6.26187 + 5.53690i −0.252503 + 0.223270i
\(616\) 0 0
\(617\) 15.9492i 0.642091i −0.947064 0.321046i \(-0.895966\pi\)
0.947064 0.321046i \(-0.104034\pi\)
\(618\) −1.12538 + 0.649738i −0.0452694 + 0.0261363i
\(619\) 5.58673 9.67651i 0.224550 0.388932i −0.731634 0.681697i \(-0.761242\pi\)
0.956184 + 0.292765i \(0.0945755\pi\)
\(620\) 19.6713 3.99643i 0.790018 0.160500i
\(621\) 2.48119 + 4.29755i 0.0995669 + 0.172455i
\(622\) 1.60037i 0.0641689i
\(623\) 0 0
\(624\) 5.09825 0.204093
\(625\) 6.86400 + 24.0392i 0.274560 + 0.961570i
\(626\) 1.44500 2.50281i 0.0577537 0.100032i
\(627\) −9.26693 5.35026i −0.370085 0.213669i
\(628\) 4.50317 2.59991i 0.179696 0.103748i
\(629\) −2.59895 −0.103627
\(630\) 0 0
\(631\) −14.5501 −0.579229 −0.289615 0.957143i \(-0.593527\pi\)
−0.289615 + 0.957143i \(0.593527\pi\)
\(632\) 7.12119 4.11142i 0.283266 0.163543i
\(633\) 5.58457 + 3.22425i 0.221967 + 0.128153i
\(634\) 0.981902 1.70070i 0.0389963 0.0675436i
\(635\) 5.72597 + 1.91767i 0.227228 + 0.0761002i
\(636\) 16.8265 0.667215
\(637\) 0 0
\(638\) 3.07381i 0.121693i
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) −2.63438 12.9670i −0.104133 0.512566i
\(641\) 19.3634 33.5385i 0.764810 1.32469i −0.175537 0.984473i \(-0.556166\pi\)
0.940347 0.340217i \(-0.110500\pi\)
\(642\) 2.30737 1.33216i 0.0910648 0.0525763i
\(643\) 11.9511i 0.471306i −0.971837 0.235653i \(-0.924277\pi\)
0.971837 0.235653i \(-0.0757229\pi\)
\(644\) 0 0
\(645\) 18.7005 + 21.1490i 0.736332 + 0.832742i
\(646\) 1.73813 + 3.01054i 0.0683860 + 0.118448i
\(647\) −12.6007 7.27504i −0.495386 0.286011i 0.231420 0.972854i \(-0.425663\pi\)
−0.726806 + 0.686843i \(0.758996\pi\)
\(648\) 0.665499 + 0.384226i 0.0261433 + 0.0150938i
\(649\) −8.62530 14.9395i −0.338573 0.586425i
\(650\) −0.160295 + 1.29948i −0.00628727 + 0.0509697i
\(651\) 0 0
\(652\) 10.3996i 0.407281i
\(653\) 43.2801 24.9878i 1.69368 0.977847i 0.742181 0.670199i \(-0.233791\pi\)
0.951500 0.307648i \(-0.0995420\pi\)
\(654\) 0.269159 0.466198i 0.0105250 0.0182298i
\(655\) 45.1963 9.18210i 1.76596 0.358775i
\(656\) −7.05712 12.2233i −0.275534 0.477240i
\(657\) 9.35026i 0.364788i
\(658\) 0 0
\(659\) 16.9525 0.660377 0.330189 0.943915i \(-0.392888\pi\)
0.330189 + 0.943915i \(0.392888\pi\)
\(660\) 8.32177 + 2.78702i 0.323925 + 0.108485i
\(661\) 7.82653 13.5560i 0.304417 0.527265i −0.672715 0.739902i \(-0.734872\pi\)
0.977131 + 0.212637i \(0.0682051\pi\)
\(662\) 4.67744 + 2.70052i 0.181794 + 0.104959i
\(663\) 3.91767 2.26187i 0.152150 0.0878436i
\(664\) 2.47768 0.0961528
\(665\) 0 0
\(666\) −0.150446 −0.00582965
\(667\) −34.0572 + 19.6629i −1.31870 + 0.761351i
\(668\) −24.7275 14.2765i −0.956737 0.552373i
\(669\) −0.775746 + 1.34363i −0.0299921 + 0.0519478i
\(670\) 1.36680 4.08114i 0.0528041 0.157668i
\(671\) −17.4010 −0.671760
\(672\) 0 0
\(673\) 26.0263i 1.00324i 0.865088 + 0.501621i \(0.167263\pi\)
−0.865088 + 0.501621i \(0.832737\pi\)
\(674\) −0.373285 0.646548i −0.0143784 0.0249041i
\(675\) 3.01131 3.99149i 0.115905 0.153633i
\(676\) −10.9666 + 18.9947i −0.421793 + 0.730566i
\(677\) 30.7022 17.7259i 1.17998 0.681262i 0.223971 0.974596i \(-0.428098\pi\)
0.956010 + 0.293334i \(0.0947647\pi\)
\(678\) 2.33709i 0.0897553i
\(679\) 0 0
\(680\) −3.81336 4.31265i −0.146236 0.165383i
\(681\) −6.57452 11.3874i −0.251936 0.436366i
\(682\) 1.53662 + 0.887166i 0.0588401 + 0.0339713i
\(683\) 20.4927 + 11.8315i 0.784131 + 0.452718i 0.837892 0.545836i \(-0.183788\pi\)
−0.0537615 + 0.998554i \(0.517121\pi\)
\(684\) −5.24965 9.09265i −0.200725 0.347666i
\(685\) −37.6893 + 33.3258i −1.44003 + 1.27331i
\(686\) 0 0
\(687\) 2.77575i 0.105901i
\(688\) −41.2834 + 23.8350i −1.57391 + 0.908700i
\(689\) 5.78892 10.0267i 0.220540 0.381987i
\(690\) −0.428442 2.10889i −0.0163105 0.0802839i
\(691\) 0.287258 + 0.497545i 0.0109278 + 0.0189275i 0.871438 0.490506i \(-0.163188\pi\)
−0.860510 + 0.509434i \(0.829855\pi\)
\(692\) 8.82936i 0.335642i
\(693\) 0 0
\(694\) −1.85940 −0.0705820
\(695\) −2.32563 + 6.94412i −0.0882163 + 0.263406i
\(696\) −3.04491 + 5.27393i −0.115417 + 0.199908i
\(697\) −10.8459 6.26187i −0.410817 0.237185i
\(698\) −2.54434 + 1.46898i −0.0963047 + 0.0556015i
\(699\) −0.0507852 −0.00192087
\(700\) 0 0
\(701\) 42.7269 1.61377 0.806886 0.590707i \(-0.201151\pi\)
0.806886 + 0.590707i \(0.201151\pi\)
\(702\) 0.226782 0.130933i 0.00855933 0.00494173i
\(703\) 3.59439 + 2.07522i 0.135565 + 0.0782685i
\(704\) −7.11142 + 12.3173i −0.268022 + 0.464227i
\(705\) 7.04767 21.0437i 0.265431 0.792551i
\(706\) −3.94639 −0.148524
\(707\) 0 0
\(708\) 16.9262i 0.636125i
\(709\) 13.6253 + 23.5997i 0.511709 + 0.886306i 0.999908 + 0.0135735i \(0.00432070\pi\)
−0.488199 + 0.872732i \(0.662346\pi\)
\(710\) −0.172676 0.849948i −0.00648041 0.0318980i
\(711\) −5.35026 + 9.26693i −0.200650 + 0.347537i
\(712\) 0.690529 0.398677i 0.0258787 0.0149411i
\(713\) 22.7005i 0.850141i
\(714\) 0 0
\(715\) 4.52373 4.00000i 0.169178 0.149592i
\(716\) 9.81194 + 16.9948i 0.366690 + 0.635125i
\(717\) −5.06586 2.92478i −0.189188 0.109228i
\(718\) 5.27393 + 3.04491i 0.196821 + 0.113635i
\(719\) −5.35026 9.26693i −0.199531 0.345598i 0.748845 0.662745i \(-0.230609\pi\)
−0.948376 + 0.317147i \(0.897275\pi\)
\(720\) 5.59261 + 6.32487i 0.208424 + 0.235714i
\(721\) 0 0
\(722\) 1.86670i 0.0694713i
\(723\) 0.0651448 0.0376114i 0.00242276 0.00139878i
\(724\) −10.4255 + 18.0575i −0.387460 + 0.671101i
\(725\) 31.6317 + 23.8640i 1.17477 + 0.886286i
\(726\) −0.678778 1.17568i −0.0251918 0.0436335i
\(727\) 39.9511i 1.48171i −0.671668 0.740853i \(-0.734422\pi\)
0.671668 0.740853i \(-0.265578\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 1.28768 3.84489i 0.0476592 0.142306i
\(731\) −21.1490 + 36.6312i −0.782225 + 1.35485i
\(732\) −14.7864 8.53690i −0.546519 0.315533i
\(733\) −26.2829 + 15.1744i −0.970780 + 0.560480i −0.899474 0.436974i \(-0.856050\pi\)
−0.0713061 + 0.997454i \(0.522717\pi\)
\(734\) 5.70194 0.210462
\(735\) 0 0
\(736\) 11.2605 0.415066
\(737\) −17.1902 + 9.92478i −0.633210 + 0.365584i
\(738\) −0.627835 0.362481i −0.0231109 0.0133431i
\(739\) 18.6253 32.2600i 0.685143 1.18670i −0.288249 0.957555i \(-0.593073\pi\)
0.973392 0.229147i \(-0.0735935\pi\)
\(740\) −3.22779 1.08101i −0.118656 0.0397387i
\(741\) −7.22425 −0.265390
\(742\) 0 0
\(743\) 26.3634i 0.967181i 0.875294 + 0.483590i \(0.160668\pi\)
−0.875294 + 0.483590i \(0.839332\pi\)
\(744\) 1.75765 + 3.04434i 0.0644385 + 0.111611i
\(745\) 9.74803 1.98042i 0.357140 0.0725568i
\(746\) −1.55149 + 2.68726i −0.0568042 + 0.0983877i
\(747\) −2.79229 + 1.61213i −0.102164 + 0.0589846i
\(748\) 13.1490i 0.480776i
\(749\) 0 0
\(750\) −1.78797 + 1.22662i −0.0652873 + 0.0447900i
\(751\) −25.3258 43.8656i −0.924152 1.60068i −0.792919 0.609328i \(-0.791439\pi\)
−0.131234 0.991351i \(-0.541894\pi\)
\(752\) 32.4530 + 18.7367i 1.18344 + 0.683258i
\(753\) 16.6487 + 9.61213i 0.606712 + 0.350285i
\(754\) 1.03761 + 1.79720i 0.0377876 + 0.0654500i
\(755\) −1.92478 2.17679i −0.0700498 0.0792216i
\(756\) 0 0
\(757\) 38.9525i 1.41575i −0.706336 0.707877i \(-0.749653\pi\)
0.706336 0.707877i \(-0.250347\pi\)
\(758\) 1.79720 1.03761i 0.0652771 0.0376877i
\(759\) −4.96239 + 8.59511i −0.180123 + 0.311983i
\(760\) 1.83035 + 9.00937i 0.0663937 + 0.326804i
\(761\) −24.1065 41.7537i −0.873860 1.51357i −0.857972 0.513696i \(-0.828276\pi\)
−0.0158873 0.999874i \(-0.505057\pi\)
\(762\) 0.523730i 0.0189727i
\(763\) 0 0
\(764\) −27.1782 −0.983273
\(765\) 7.10362 + 2.37905i 0.256832 + 0.0860147i
\(766\) 1.62672 2.81755i 0.0587756 0.101802i
\(767\) −10.0861 5.82321i −0.364188 0.210264i
\(768\) −11.3235 + 6.53761i −0.408601 + 0.235906i
\(769\) −4.44851 −0.160417 −0.0802086 0.996778i \(-0.525559\pi\)
−0.0802086 + 0.996778i \(0.525559\pi\)
\(770\) 0 0
\(771\) −7.35026 −0.264713
\(772\) 26.0459 15.0376i 0.937413 0.541215i
\(773\) −34.0360 19.6507i −1.22419 0.706786i −0.258381 0.966043i \(-0.583189\pi\)
−0.965808 + 0.259257i \(0.916522\pi\)
\(774\) −1.22425 + 2.12047i −0.0440049 + 0.0762187i
\(775\) 21.0593 8.92523i 0.756473 0.320604i
\(776\) 14.2158 0.510318
\(777\) 0 0
\(778\) 5.68735