Properties

Label 475.2.l.a.351.1
Level $475$
Weight $2$
Character 475.351
Analytic conductor $3.793$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.l (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 351.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 475.351
Dual form 475.2.l.a.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.233956 + 1.32683i) q^{2} +(2.20574 - 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(2.97178 + 2.49362i) q^{6} +(0.173648 - 0.300767i) q^{7} +(1.47178 + 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +O(q^{10})\) \(q+(0.233956 + 1.32683i) q^{2} +(2.20574 - 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(2.97178 + 2.49362i) q^{6} +(0.173648 - 0.300767i) q^{7} +(1.47178 + 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +(1.11334 + 1.92836i) q^{11} +(0.266044 - 0.460802i) q^{12} +(-1.97178 - 1.65452i) q^{13} +(0.439693 + 0.160035i) q^{14} +(-2.75490 + 2.31164i) q^{16} +(-0.0812519 - 0.460802i) q^{17} +7.12836 q^{18} +(-4.29813 - 0.725293i) q^{19} +(-0.173648 - 0.984808i) q^{21} +(-2.29813 + 1.92836i) q^{22} +(-2.53209 + 0.921605i) q^{23} +(7.96451 + 2.89884i) q^{24} +(1.73396 - 3.00330i) q^{26} +(-3.29813 - 5.71253i) q^{27} +(0.0111444 - 0.0632028i) q^{28} +(-1.19459 + 6.77487i) q^{29} +(3.55303 - 6.15403i) q^{31} +(0.798133 + 0.669713i) q^{32} +(6.02481 + 2.19285i) q^{33} +(0.592396 - 0.215615i) q^{34} +(-0.169778 - 0.962858i) q^{36} -4.94356 q^{37} +(-0.0432332 - 5.87257i) q^{38} -7.41147 q^{39} +(1.89646 - 1.59132i) q^{41} +(1.26604 - 0.460802i) q^{42} +(3.66637 + 1.33445i) q^{43} +(0.315207 + 0.264490i) q^{44} +(-1.81521 - 3.14403i) q^{46} +(1.26604 - 7.18009i) q^{47} +(-1.79813 + 10.1977i) q^{48} +(3.43969 + 5.95772i) q^{49} +(-1.03209 - 0.866025i) q^{51} +(-0.446967 - 0.162683i) q^{52} +(-2.66637 + 0.970481i) q^{53} +(6.80793 - 5.71253i) q^{54} +1.02229 q^{56} +(-10.8229 + 6.35532i) q^{57} -9.26857 q^{58} +(-1.09492 - 6.20961i) q^{59} +(-8.57785 + 3.12208i) q^{61} +(8.99660 + 3.27449i) q^{62} +(-1.40760 - 1.18112i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-1.50000 + 8.50692i) q^{66} +(-1.33275 + 7.55839i) q^{67} +(-0.0432332 - 0.0748822i) q^{68} +(-3.87939 + 6.71929i) q^{69} +(8.74422 + 3.18264i) q^{71} +(14.6348 - 5.32661i) q^{72} +(-1.06418 + 0.892951i) q^{73} +(-1.15657 - 6.55926i) q^{74} +(-0.792204 + 0.145708i) q^{76} +0.773318 q^{77} +(-1.73396 - 9.83375i) q^{78} +(-9.07398 + 7.61397i) q^{79} +(-2.93242 - 1.06731i) q^{81} +(2.55509 + 2.14398i) q^{82} +(-7.41534 + 12.8438i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(-0.912818 + 5.17685i) q^{86} +(9.90420 + 17.1546i) q^{87} +(-3.27719 + 5.67626i) q^{88} +(-7.88326 - 6.61484i) q^{89} +(-0.840022 + 0.305743i) q^{91} +(-0.381445 + 0.320070i) q^{92} +(-3.55303 - 20.1503i) q^{93} +9.82295 q^{94} +3.00000 q^{96} +(-1.64156 - 9.30975i) q^{97} +(-7.10014 + 5.95772i) q^{98} +(11.0706 - 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} + O(q^{10}) \) \( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{13} - 3 q^{14} - 18 q^{16} - 3 q^{17} + 6 q^{18} - 12 q^{19} - 6 q^{23} + 15 q^{24} + 15 q^{26} - 6 q^{27} - 6 q^{28} - 3 q^{29} + 9 q^{31} - 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} + 21 q^{41} + 3 q^{42} + 3 q^{43} + 9 q^{44} - 18 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 3 q^{51} - 15 q^{52} + 3 q^{53} + 30 q^{54} - 6 q^{56} - 24 q^{57} - 36 q^{58} + 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{63} - 12 q^{64} - 9 q^{66} + 30 q^{67} + 15 q^{68} - 12 q^{69} - 6 q^{71} + 12 q^{72} + 12 q^{73} + 15 q^{74} + 36 q^{76} + 18 q^{77} - 15 q^{78} - 39 q^{79} + 6 q^{81} + 54 q^{82} + 3 q^{84} + 24 q^{86} + 21 q^{87} - 9 q^{88} - 12 q^{89} + 15 q^{91} - 42 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 9 q^{98} + 9 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.233956 + 1.32683i 0.165432 + 0.938209i 0.948618 + 0.316423i \(0.102482\pi\)
−0.783187 + 0.621786i \(0.786407\pi\)
\(3\) 2.20574 1.85083i 1.27348 1.06858i 0.279375 0.960182i \(-0.409873\pi\)
0.994108 0.108397i \(-0.0345718\pi\)
\(4\) 0.173648 0.0632028i 0.0868241 0.0316014i
\(5\) 0 0
\(6\) 2.97178 + 2.49362i 1.21322 + 1.01802i
\(7\) 0.173648 0.300767i 0.0656328 0.113679i −0.831342 0.555762i \(-0.812427\pi\)
0.896975 + 0.442082i \(0.145760\pi\)
\(8\) 1.47178 + 2.54920i 0.520353 + 0.901278i
\(9\) 0.918748 5.21048i 0.306249 1.73683i
\(10\) 0 0
\(11\) 1.11334 + 1.92836i 0.335685 + 0.581423i 0.983616 0.180276i \(-0.0576989\pi\)
−0.647931 + 0.761699i \(0.724366\pi\)
\(12\) 0.266044 0.460802i 0.0768004 0.133022i
\(13\) −1.97178 1.65452i −0.546874 0.458882i 0.327007 0.945022i \(-0.393960\pi\)
−0.873881 + 0.486140i \(0.838404\pi\)
\(14\) 0.439693 + 0.160035i 0.117513 + 0.0427712i
\(15\) 0 0
\(16\) −2.75490 + 2.31164i −0.688725 + 0.577909i
\(17\) −0.0812519 0.460802i −0.0197065 0.111761i 0.973368 0.229249i \(-0.0736270\pi\)
−0.993074 + 0.117488i \(0.962516\pi\)
\(18\) 7.12836 1.68017
\(19\) −4.29813 0.725293i −0.986059 0.166394i
\(20\) 0 0
\(21\) −0.173648 0.984808i −0.0378931 0.214903i
\(22\) −2.29813 + 1.92836i −0.489964 + 0.411128i
\(23\) −2.53209 + 0.921605i −0.527977 + 0.192168i −0.592235 0.805765i \(-0.701754\pi\)
0.0642578 + 0.997933i \(0.479532\pi\)
\(24\) 7.96451 + 2.89884i 1.62575 + 0.591724i
\(25\) 0 0
\(26\) 1.73396 3.00330i 0.340057 0.588995i
\(27\) −3.29813 5.71253i −0.634726 1.09938i
\(28\) 0.0111444 0.0632028i 0.00210608 0.0119442i
\(29\) −1.19459 + 6.77487i −0.221830 + 1.25806i 0.646822 + 0.762641i \(0.276097\pi\)
−0.868653 + 0.495421i \(0.835014\pi\)
\(30\) 0 0
\(31\) 3.55303 6.15403i 0.638144 1.10530i −0.347696 0.937607i \(-0.613036\pi\)
0.985840 0.167690i \(-0.0536307\pi\)
\(32\) 0.798133 + 0.669713i 0.141091 + 0.118390i
\(33\) 6.02481 + 2.19285i 1.04879 + 0.381727i
\(34\) 0.592396 0.215615i 0.101595 0.0369776i
\(35\) 0 0
\(36\) −0.169778 0.962858i −0.0282963 0.160476i
\(37\) −4.94356 −0.812717 −0.406358 0.913714i \(-0.633202\pi\)
−0.406358 + 0.913714i \(0.633202\pi\)
\(38\) −0.0432332 5.87257i −0.00701336 0.952657i
\(39\) −7.41147 −1.18679
\(40\) 0 0
\(41\) 1.89646 1.59132i 0.296177 0.248522i −0.482574 0.875855i \(-0.660298\pi\)
0.778751 + 0.627333i \(0.215854\pi\)
\(42\) 1.26604 0.460802i 0.195355 0.0711034i
\(43\) 3.66637 + 1.33445i 0.559117 + 0.203502i 0.606093 0.795394i \(-0.292736\pi\)
−0.0469757 + 0.998896i \(0.514958\pi\)
\(44\) 0.315207 + 0.264490i 0.0475193 + 0.0398734i
\(45\) 0 0
\(46\) −1.81521 3.14403i −0.267638 0.463562i
\(47\) 1.26604 7.18009i 0.184672 1.04732i −0.741705 0.670726i \(-0.765983\pi\)
0.926377 0.376598i \(-0.122906\pi\)
\(48\) −1.79813 + 10.1977i −0.259538 + 1.47191i
\(49\) 3.43969 + 5.95772i 0.491385 + 0.851103i
\(50\) 0 0
\(51\) −1.03209 0.866025i −0.144521 0.121268i
\(52\) −0.446967 0.162683i −0.0619831 0.0225600i
\(53\) −2.66637 + 0.970481i −0.366255 + 0.133306i −0.518590 0.855023i \(-0.673543\pi\)
0.152335 + 0.988329i \(0.451321\pi\)
\(54\) 6.80793 5.71253i 0.926442 0.777377i
\(55\) 0 0
\(56\) 1.02229 0.136609
\(57\) −10.8229 + 6.35532i −1.43353 + 0.841783i
\(58\) −9.26857 −1.21702
\(59\) −1.09492 6.20961i −0.142547 0.808423i −0.969304 0.245864i \(-0.920928\pi\)
0.826757 0.562559i \(-0.190183\pi\)
\(60\) 0 0
\(61\) −8.57785 + 3.12208i −1.09828 + 0.399742i −0.826682 0.562669i \(-0.809775\pi\)
−0.271599 + 0.962411i \(0.587552\pi\)
\(62\) 8.99660 + 3.27449i 1.14257 + 0.415861i
\(63\) −1.40760 1.18112i −0.177341 0.148807i
\(64\) −4.29813 + 7.44459i −0.537267 + 0.930573i
\(65\) 0 0
\(66\) −1.50000 + 8.50692i −0.184637 + 1.04713i
\(67\) −1.33275 + 7.55839i −0.162821 + 0.923405i 0.788461 + 0.615084i \(0.210878\pi\)
−0.951283 + 0.308320i \(0.900233\pi\)
\(68\) −0.0432332 0.0748822i −0.00524280 0.00908080i
\(69\) −3.87939 + 6.71929i −0.467023 + 0.808908i
\(70\) 0 0
\(71\) 8.74422 + 3.18264i 1.03775 + 0.377709i 0.804026 0.594594i \(-0.202687\pi\)
0.233722 + 0.972303i \(0.424909\pi\)
\(72\) 14.6348 5.32661i 1.72472 0.627748i
\(73\) −1.06418 + 0.892951i −0.124553 + 0.104512i −0.702936 0.711253i \(-0.748128\pi\)
0.578384 + 0.815765i \(0.303684\pi\)
\(74\) −1.15657 6.55926i −0.134449 0.762498i
\(75\) 0 0
\(76\) −0.792204 + 0.145708i −0.0908720 + 0.0167139i
\(77\) 0.773318 0.0881278
\(78\) −1.73396 9.83375i −0.196332 1.11345i
\(79\) −9.07398 + 7.61397i −1.02090 + 0.856639i −0.989741 0.142876i \(-0.954365\pi\)
−0.0311616 + 0.999514i \(0.509921\pi\)
\(80\) 0 0
\(81\) −2.93242 1.06731i −0.325824 0.118590i
\(82\) 2.55509 + 2.14398i 0.282163 + 0.236763i
\(83\) −7.41534 + 12.8438i −0.813940 + 1.40979i 0.0961469 + 0.995367i \(0.469348\pi\)
−0.910087 + 0.414418i \(0.863985\pi\)
\(84\) −0.0923963 0.160035i −0.0100813 0.0174613i
\(85\) 0 0
\(86\) −0.912818 + 5.17685i −0.0984317 + 0.558234i
\(87\) 9.90420 + 17.1546i 1.06184 + 1.83916i
\(88\) −3.27719 + 5.67626i −0.349349 + 0.605091i
\(89\) −7.88326 6.61484i −0.835623 0.701171i 0.120951 0.992658i \(-0.461406\pi\)
−0.956575 + 0.291487i \(0.905850\pi\)
\(90\) 0 0
\(91\) −0.840022 + 0.305743i −0.0880583 + 0.0320506i
\(92\) −0.381445 + 0.320070i −0.0397684 + 0.0333696i
\(93\) −3.55303 20.1503i −0.368432 2.08948i
\(94\) 9.82295 1.01316
\(95\) 0 0
\(96\) 3.00000 0.306186
\(97\) −1.64156 9.30975i −0.166675 0.945261i −0.947320 0.320287i \(-0.896221\pi\)
0.780645 0.624974i \(-0.214891\pi\)
\(98\) −7.10014 + 5.95772i −0.717222 + 0.601821i
\(99\) 11.0706 4.02936i 1.11263 0.404966i
\(100\) 0 0
\(101\) −7.08512 5.94512i −0.704996 0.591562i 0.218194 0.975905i \(-0.429983\pi\)
−0.923190 + 0.384343i \(0.874428\pi\)
\(102\) 0.907604 1.57202i 0.0898662 0.155653i
\(103\) −2.75490 4.77163i −0.271448 0.470162i 0.697785 0.716308i \(-0.254169\pi\)
−0.969233 + 0.246145i \(0.920836\pi\)
\(104\) 1.31567 7.46156i 0.129012 0.731666i
\(105\) 0 0
\(106\) −1.91147 3.31077i −0.185659 0.321570i
\(107\) 5.11721 8.86327i 0.494699 0.856845i −0.505282 0.862954i \(-0.668611\pi\)
0.999981 + 0.00610974i \(0.00194480\pi\)
\(108\) −0.933763 0.783520i −0.0898514 0.0753943i
\(109\) 1.71301 + 0.623485i 0.164077 + 0.0597190i 0.422753 0.906245i \(-0.361064\pi\)
−0.258676 + 0.965964i \(0.583286\pi\)
\(110\) 0 0
\(111\) −10.9042 + 9.14971i −1.03498 + 0.868452i
\(112\) 0.216881 + 1.23000i 0.0204934 + 0.116224i
\(113\) 17.6878 1.66393 0.831963 0.554830i \(-0.187217\pi\)
0.831963 + 0.554830i \(0.187217\pi\)
\(114\) −10.9645 12.8733i −1.02692 1.20570i
\(115\) 0 0
\(116\) 0.220752 + 1.25195i 0.0204963 + 0.116240i
\(117\) −10.4324 + 8.75384i −0.964477 + 0.809293i
\(118\) 7.98293 2.90555i 0.734888 0.267477i
\(119\) −0.152704 0.0555796i −0.0139983 0.00509497i
\(120\) 0 0
\(121\) 3.02094 5.23243i 0.274631 0.475675i
\(122\) −6.14930 10.6509i −0.556731 0.964287i
\(123\) 1.23783 7.02006i 0.111611 0.632977i
\(124\) 0.228026 1.29320i 0.0204773 0.116133i
\(125\) 0 0
\(126\) 1.23783 2.14398i 0.110274 0.191001i
\(127\) −8.88919 7.45891i −0.788788 0.661871i 0.156657 0.987653i \(-0.449928\pi\)
−0.945445 + 0.325782i \(0.894373\pi\)
\(128\) −8.92514 3.24849i −0.788879 0.287128i
\(129\) 10.5569 3.84240i 0.929484 0.338304i
\(130\) 0 0
\(131\) 0.320422 + 1.81720i 0.0279954 + 0.158770i 0.995601 0.0936982i \(-0.0298689\pi\)
−0.967605 + 0.252468i \(0.918758\pi\)
\(132\) 1.18479 0.103123
\(133\) −0.964508 + 1.16679i −0.0836334 + 0.101174i
\(134\) −10.3405 −0.893282
\(135\) 0 0
\(136\) 1.05509 0.885328i 0.0904735 0.0759162i
\(137\) 0.240352 0.0874810i 0.0205347 0.00747401i −0.331732 0.943374i \(-0.607633\pi\)
0.352267 + 0.935900i \(0.385411\pi\)
\(138\) −9.82295 3.57526i −0.836185 0.304346i
\(139\) 3.26604 + 2.74054i 0.277022 + 0.232449i 0.770704 0.637193i \(-0.219905\pi\)
−0.493682 + 0.869643i \(0.664349\pi\)
\(140\) 0 0
\(141\) −10.4966 18.1806i −0.883973 1.53109i
\(142\) −2.17705 + 12.3467i −0.182694 + 1.03611i
\(143\) 0.995252 5.64436i 0.0832272 0.472005i
\(144\) 9.51367 + 16.4782i 0.792806 + 1.37318i
\(145\) 0 0
\(146\) −1.43376 1.20307i −0.118659 0.0995668i
\(147\) 18.6138 + 6.77487i 1.53524 + 0.558782i
\(148\) −0.858441 + 0.312447i −0.0705634 + 0.0256830i
\(149\) 12.6853 10.6442i 1.03922 0.872007i 0.0472981 0.998881i \(-0.484939\pi\)
0.991919 + 0.126874i \(0.0404945\pi\)
\(150\) 0 0
\(151\) −4.36184 −0.354962 −0.177481 0.984124i \(-0.556795\pi\)
−0.177481 + 0.984124i \(0.556795\pi\)
\(152\) −4.47700 12.0243i −0.363132 0.975298i
\(153\) −2.47565 −0.200145
\(154\) 0.180922 + 1.02606i 0.0145791 + 0.0826823i
\(155\) 0 0
\(156\) −1.28699 + 0.468426i −0.103042 + 0.0375041i
\(157\) −9.03849 3.28974i −0.721350 0.262550i −0.0448510 0.998994i \(-0.514281\pi\)
−0.676499 + 0.736444i \(0.736504\pi\)
\(158\) −12.2253 10.2583i −0.972596 0.816105i
\(159\) −4.08512 + 7.07564i −0.323971 + 0.561135i
\(160\) 0 0
\(161\) −0.162504 + 0.921605i −0.0128071 + 0.0726326i
\(162\) 0.730085 4.14052i 0.0573609 0.325310i
\(163\) 4.17752 + 7.23567i 0.327209 + 0.566742i 0.981957 0.189105i \(-0.0605587\pi\)
−0.654748 + 0.755847i \(0.727225\pi\)
\(164\) 0.228741 0.396191i 0.0178617 0.0309373i
\(165\) 0 0
\(166\) −18.7763 6.83402i −1.45732 0.530423i
\(167\) 3.79174 1.38008i 0.293413 0.106794i −0.191120 0.981567i \(-0.561212\pi\)
0.484533 + 0.874773i \(0.338990\pi\)
\(168\) 2.25490 1.89209i 0.173969 0.145978i
\(169\) −1.10694 6.27779i −0.0851496 0.482907i
\(170\) 0 0
\(171\) −7.72803 + 21.7290i −0.590977 + 1.66166i
\(172\) 0.721000 0.0549758
\(173\) 3.49794 + 19.8378i 0.265943 + 1.50824i 0.766335 + 0.642441i \(0.222078\pi\)
−0.500391 + 0.865799i \(0.666811\pi\)
\(174\) −20.4440 + 17.1546i −1.54986 + 1.30049i
\(175\) 0 0
\(176\) −7.52481 2.73881i −0.567204 0.206445i
\(177\) −13.9081 11.6703i −1.04539 0.877190i
\(178\) 6.93242 12.0073i 0.519607 0.899985i
\(179\) 5.75624 + 9.97011i 0.430242 + 0.745201i 0.996894 0.0787564i \(-0.0250949\pi\)
−0.566652 + 0.823957i \(0.691762\pi\)
\(180\) 0 0
\(181\) 1.48246 8.40744i 0.110190 0.624920i −0.878829 0.477136i \(-0.841675\pi\)
0.989020 0.147784i \(-0.0472141\pi\)
\(182\) −0.602196 1.04303i −0.0446378 0.0773149i
\(183\) −13.1420 + 22.7627i −0.971487 + 1.68266i
\(184\) −6.07604 5.09840i −0.447931 0.375859i
\(185\) 0 0
\(186\) 25.9047 9.42853i 1.89942 0.691333i
\(187\) 0.798133 0.669713i 0.0583653 0.0489743i
\(188\) −0.233956 1.32683i −0.0170630 0.0967689i
\(189\) −2.29086 −0.166635
\(190\) 0 0
\(191\) 18.3354 1.32671 0.663353 0.748307i \(-0.269133\pi\)
0.663353 + 0.748307i \(0.269133\pi\)
\(192\) 4.29813 + 24.3759i 0.310191 + 1.75918i
\(193\) −0.228026 + 0.191336i −0.0164137 + 0.0137727i −0.650958 0.759114i \(-0.725632\pi\)
0.634544 + 0.772887i \(0.281188\pi\)
\(194\) 11.9684 4.35613i 0.859279 0.312752i
\(195\) 0 0
\(196\) 0.973841 + 0.817150i 0.0695601 + 0.0583678i
\(197\) 6.57057 11.3806i 0.468134 0.810832i −0.531203 0.847245i \(-0.678260\pi\)
0.999337 + 0.0364128i \(0.0115931\pi\)
\(198\) 7.93629 + 13.7461i 0.564008 + 0.976890i
\(199\) −0.0445774 + 0.252811i −0.00316001 + 0.0179213i −0.986347 0.164680i \(-0.947341\pi\)
0.983187 + 0.182602i \(0.0584519\pi\)
\(200\) 0 0
\(201\) 11.0496 + 19.1385i 0.779381 + 1.34993i
\(202\) 6.23055 10.7916i 0.438380 0.759297i
\(203\) 1.83022 + 1.53574i 0.128456 + 0.107788i
\(204\) −0.233956 0.0851529i −0.0163802 0.00596189i
\(205\) 0 0
\(206\) 5.68660 4.77163i 0.396204 0.332455i
\(207\) 2.47565 + 14.0401i 0.172070 + 0.975856i
\(208\) 9.25671 0.641837
\(209\) −3.38666 9.09586i −0.234260 0.629174i
\(210\) 0 0
\(211\) 0.425145 + 2.41112i 0.0292682 + 0.165988i 0.995938 0.0900364i \(-0.0286983\pi\)
−0.966670 + 0.256024i \(0.917587\pi\)
\(212\) −0.401674 + 0.337044i −0.0275871 + 0.0231483i
\(213\) 25.1780 9.16404i 1.72517 0.627909i
\(214\) 12.9572 + 4.71605i 0.885738 + 0.322382i
\(215\) 0 0
\(216\) 9.70826 16.8152i 0.660564 1.14413i
\(217\) −1.23396 2.13727i −0.0837664 0.145088i
\(218\) −0.426489 + 2.41874i −0.0288855 + 0.163818i
\(219\) −0.694593 + 3.93923i −0.0469362 + 0.266189i
\(220\) 0 0
\(221\) −0.602196 + 1.04303i −0.0405081 + 0.0701621i
\(222\) −14.6912 12.3274i −0.986008 0.827359i
\(223\) −7.99660 2.91052i −0.535492 0.194903i 0.0600971 0.998193i \(-0.480859\pi\)
−0.595589 + 0.803289i \(0.703081\pi\)
\(224\) 0.340022 0.123758i 0.0227187 0.00826893i
\(225\) 0 0
\(226\) 4.13816 + 23.4686i 0.275266 + 1.56111i
\(227\) 14.1506 0.939211 0.469606 0.882876i \(-0.344396\pi\)
0.469606 + 0.882876i \(0.344396\pi\)
\(228\) −1.47771 + 1.78763i −0.0978638 + 0.118389i
\(229\) −20.5330 −1.35686 −0.678430 0.734665i \(-0.737339\pi\)
−0.678430 + 0.734665i \(0.737339\pi\)
\(230\) 0 0
\(231\) 1.70574 1.43128i 0.112229 0.0941715i
\(232\) −19.0287 + 6.92588i −1.24929 + 0.454706i
\(233\) 16.5865 + 6.03698i 1.08662 + 0.395496i 0.822366 0.568959i \(-0.192654\pi\)
0.264249 + 0.964454i \(0.414876\pi\)
\(234\) −14.0556 11.7940i −0.918841 0.770999i
\(235\) 0 0
\(236\) −0.582596 1.00909i −0.0379238 0.0656859i
\(237\) −5.92262 + 33.5888i −0.384715 + 2.18183i
\(238\) 0.0380187 0.215615i 0.00246438 0.0139762i
\(239\) −1.17617 2.03719i −0.0760804 0.131775i 0.825475 0.564438i \(-0.190907\pi\)
−0.901556 + 0.432663i \(0.857574\pi\)
\(240\) 0 0
\(241\) 10.5719 + 8.87089i 0.680997 + 0.571424i 0.916298 0.400498i \(-0.131163\pi\)
−0.235300 + 0.971923i \(0.575607\pi\)
\(242\) 7.64930 + 2.78412i 0.491716 + 0.178970i
\(243\) 10.1518 3.69496i 0.651240 0.237032i
\(244\) −1.29220 + 1.08429i −0.0827249 + 0.0694144i
\(245\) 0 0
\(246\) 9.60401 0.612329
\(247\) 7.27497 + 8.54147i 0.462895 + 0.543481i
\(248\) 20.9172 1.32824
\(249\) 7.41534 + 42.0545i 0.469928 + 2.66510i
\(250\) 0 0
\(251\) 3.91400 1.42458i 0.247050 0.0899187i −0.215528 0.976498i \(-0.569147\pi\)
0.462577 + 0.886579i \(0.346925\pi\)
\(252\) −0.319078 0.116135i −0.0201000 0.00731581i
\(253\) −4.59627 3.85673i −0.288965 0.242470i
\(254\) 7.81702 13.5395i 0.490483 0.849542i
\(255\) 0 0
\(256\) −0.763356 + 4.32921i −0.0477098 + 0.270575i
\(257\) −0.115867 + 0.657115i −0.00722759 + 0.0409897i −0.988208 0.153116i \(-0.951069\pi\)
0.980981 + 0.194105i \(0.0621804\pi\)
\(258\) 7.56805 + 13.1082i 0.471166 + 0.816084i
\(259\) −0.858441 + 1.48686i −0.0533409 + 0.0923892i
\(260\) 0 0
\(261\) 34.2028 + 12.4488i 2.11710 + 0.770561i
\(262\) −2.33615 + 0.850290i −0.144328 + 0.0525311i
\(263\) −8.73261 + 7.32753i −0.538476 + 0.451835i −0.871016 0.491254i \(-0.836539\pi\)
0.332540 + 0.943089i \(0.392094\pi\)
\(264\) 3.27719 + 18.5859i 0.201697 + 1.14388i
\(265\) 0 0
\(266\) −1.77379 1.00676i −0.108758 0.0617283i
\(267\) −29.6313 −1.81341
\(268\) 0.246282 + 1.39673i 0.0150441 + 0.0853191i
\(269\) 14.8537 12.4637i 0.905646 0.759927i −0.0656400 0.997843i \(-0.520909\pi\)
0.971286 + 0.237916i \(0.0764644\pi\)
\(270\) 0 0
\(271\) 12.5865 + 4.58110i 0.764573 + 0.278282i 0.694725 0.719276i \(-0.255526\pi\)
0.0698486 + 0.997558i \(0.477748\pi\)
\(272\) 1.28905 + 1.08164i 0.0781600 + 0.0655841i
\(273\) −1.28699 + 2.22913i −0.0778921 + 0.134913i
\(274\) 0.172304 + 0.298439i 0.0104093 + 0.0180294i
\(275\) 0 0
\(276\) −0.248970 + 1.41198i −0.0149863 + 0.0849913i
\(277\) 8.87346 + 15.3693i 0.533154 + 0.923450i 0.999250 + 0.0387161i \(0.0123268\pi\)
−0.466096 + 0.884734i \(0.654340\pi\)
\(278\) −2.87211 + 4.97464i −0.172258 + 0.298359i
\(279\) −28.8011 24.1670i −1.72428 1.44684i
\(280\) 0 0
\(281\) −17.1766 + 6.25179i −1.02467 + 0.372950i −0.799050 0.601265i \(-0.794664\pi\)
−0.225622 + 0.974215i \(0.572442\pi\)
\(282\) 21.6668 18.1806i 1.29024 1.08264i
\(283\) −1.33497 7.57099i −0.0793557 0.450049i −0.998432 0.0559700i \(-0.982175\pi\)
0.919077 0.394079i \(-0.128936\pi\)
\(284\) 1.71957 0.102038
\(285\) 0 0
\(286\) 7.72193 0.456608
\(287\) −0.149300 0.846723i −0.00881290 0.0499805i
\(288\) 4.22281 3.54336i 0.248832 0.208794i
\(289\) 15.7690 5.73946i 0.927590 0.337615i
\(290\) 0 0
\(291\) −20.8516 17.4966i −1.22234 1.02567i
\(292\) −0.128356 + 0.222318i −0.00751144 + 0.0130102i
\(293\) −5.25150 9.09586i −0.306796 0.531386i 0.670864 0.741581i \(-0.265924\pi\)
−0.977660 + 0.210195i \(0.932590\pi\)
\(294\) −4.63429 + 26.2823i −0.270277 + 1.53282i
\(295\) 0 0
\(296\) −7.27584 12.6021i −0.422900 0.732484i
\(297\) 7.34389 12.7200i 0.426136 0.738089i
\(298\) 17.0908 + 14.3409i 0.990044 + 0.830745i
\(299\) 6.51754 + 2.37219i 0.376919 + 0.137187i
\(300\) 0 0
\(301\) 1.03802 0.871001i 0.0598304 0.0502037i
\(302\) −1.02048 5.78742i −0.0587219 0.333028i
\(303\) −26.6313 −1.52993
\(304\) 13.5175 7.93761i 0.775284 0.455253i
\(305\) 0 0
\(306\) −0.579193 3.28476i −0.0331102 0.187777i
\(307\) 8.95929 7.51774i 0.511334 0.429060i −0.350264 0.936651i \(-0.613908\pi\)
0.861598 + 0.507591i \(0.169464\pi\)
\(308\) 0.134285 0.0488759i 0.00765162 0.00278496i
\(309\) −14.9081 5.42609i −0.848091 0.308680i
\(310\) 0 0
\(311\) −7.98293 + 13.8268i −0.452670 + 0.784048i −0.998551 0.0538151i \(-0.982862\pi\)
0.545881 + 0.837863i \(0.316195\pi\)
\(312\) −10.9081 18.8933i −0.617548 1.06962i
\(313\) 4.62402 26.2241i 0.261365 1.48227i −0.517825 0.855487i \(-0.673258\pi\)
0.779190 0.626788i \(-0.215631\pi\)
\(314\) 2.25031 12.7622i 0.126993 0.720211i
\(315\) 0 0
\(316\) −1.09446 + 1.89565i −0.0615679 + 0.106639i
\(317\) −22.6229 18.9829i −1.27063 1.06618i −0.994465 0.105073i \(-0.966492\pi\)
−0.276164 0.961111i \(-0.589063\pi\)
\(318\) −10.3439 3.76487i −0.580057 0.211123i
\(319\) −14.3944 + 5.23913i −0.805932 + 0.293335i
\(320\) 0 0
\(321\) −5.11721 29.0211i −0.285615 1.61980i
\(322\) −1.26083 −0.0702633
\(323\) 0.0150147 + 2.03952i 0.000835443 + 0.113482i
\(324\) −0.576666 −0.0320370
\(325\) 0 0
\(326\) −8.62314 + 7.23567i −0.477592 + 0.400747i
\(327\) 4.93242 1.79525i 0.272763 0.0992777i
\(328\) 6.84776 + 2.49238i 0.378104 + 0.137619i
\(329\) −1.93969 1.62760i −0.106939 0.0897322i
\(330\) 0 0
\(331\) −13.8327 23.9590i −0.760317 1.31691i −0.942687 0.333677i \(-0.891710\pi\)
0.182371 0.983230i \(-0.441623\pi\)
\(332\) −0.475900 + 2.69896i −0.0261184 + 0.148125i
\(333\) −4.54189 + 25.7583i −0.248894 + 1.41155i
\(334\) 2.71823 + 4.70810i 0.148735 + 0.257616i
\(335\) 0 0
\(336\) 2.75490 + 2.31164i 0.150292 + 0.126110i
\(337\) 16.7827 + 6.10841i 0.914212 + 0.332746i 0.755934 0.654648i \(-0.227183\pi\)
0.158279 + 0.987394i \(0.449406\pi\)
\(338\) 8.07057 2.93745i 0.438981 0.159776i
\(339\) 39.0146 32.7371i 2.11898 1.77804i
\(340\) 0 0
\(341\) 15.8229 0.856861
\(342\) −30.6386 5.17015i −1.65675 0.279569i
\(343\) 4.82026 0.260270
\(344\) 1.99432 + 11.3103i 0.107526 + 0.609813i
\(345\) 0 0
\(346\) −25.5030 + 9.28233i −1.37105 + 0.499021i
\(347\) −5.45084 1.98394i −0.292616 0.106504i 0.191541 0.981485i \(-0.438652\pi\)
−0.484157 + 0.874981i \(0.660874\pi\)
\(348\) 2.80406 + 2.35289i 0.150314 + 0.126128i
\(349\) −2.68614 + 4.65253i −0.143786 + 0.249044i −0.928919 0.370282i \(-0.879261\pi\)
0.785134 + 0.619326i \(0.212594\pi\)
\(350\) 0 0
\(351\) −2.94831 + 16.7207i −0.157369 + 0.892485i
\(352\) −0.402856 + 2.28471i −0.0214723 + 0.121775i
\(353\) −12.6172 21.8537i −0.671546 1.16315i −0.977466 0.211095i \(-0.932297\pi\)
0.305919 0.952057i \(-0.401036\pi\)
\(354\) 12.2306 21.1839i 0.650047 1.12591i
\(355\) 0 0
\(356\) −1.78699 0.650411i −0.0947102 0.0344717i
\(357\) −0.439693 + 0.160035i −0.0232710 + 0.00846995i
\(358\) −11.8819 + 9.97011i −0.627979 + 0.526937i
\(359\) 1.16116 + 6.58526i 0.0612837 + 0.347557i 0.999996 + 0.00285518i \(0.000908833\pi\)
−0.938712 + 0.344702i \(0.887980\pi\)
\(360\) 0 0
\(361\) 17.9479 + 6.23481i 0.944626 + 0.328148i
\(362\) 11.5021 0.604535
\(363\) −3.02094 17.1326i −0.158558 0.899230i
\(364\) −0.126545 + 0.106183i −0.00663274 + 0.00556553i
\(365\) 0 0
\(366\) −33.2768 12.1118i −1.73941 0.633092i
\(367\) −6.21941 5.21870i −0.324650 0.272414i 0.465865 0.884856i \(-0.345743\pi\)
−0.790516 + 0.612441i \(0.790188\pi\)
\(368\) 4.84524 8.39220i 0.252575 0.437473i
\(369\) −6.54916 11.3435i −0.340936 0.590518i
\(370\) 0 0
\(371\) −0.171122 + 0.970481i −0.00888421 + 0.0503849i
\(372\) −1.89053 3.27449i −0.0980194 0.169775i
\(373\) 17.4488 30.2222i 0.903463 1.56484i 0.0804968 0.996755i \(-0.474349\pi\)
0.822967 0.568090i \(-0.192317\pi\)
\(374\) 1.07532 + 0.902302i 0.0556036 + 0.0466569i
\(375\) 0 0
\(376\) 20.1668 7.34013i 1.04003 0.378538i
\(377\) 13.5646 11.3821i 0.698615 0.586207i
\(378\) −0.535959 3.03958i −0.0275668 0.156339i
\(379\) 1.70140 0.0873950 0.0436975 0.999045i \(-0.486086\pi\)
0.0436975 + 0.999045i \(0.486086\pi\)
\(380\) 0 0
\(381\) −33.4124 −1.71177
\(382\) 4.28968 + 24.3280i 0.219479 + 1.24473i
\(383\) −2.24969 + 1.88771i −0.114954 + 0.0964575i −0.698453 0.715656i \(-0.746128\pi\)
0.583499 + 0.812114i \(0.301683\pi\)
\(384\) −25.6989 + 9.35365i −1.31144 + 0.477326i
\(385\) 0 0
\(386\) −0.307218 0.257787i −0.0156370 0.0131210i
\(387\) 10.3216 17.8775i 0.524677 0.908767i
\(388\) −0.873455 1.51287i −0.0443430 0.0768043i
\(389\) −4.26604 + 24.1939i −0.216297 + 1.22668i 0.662344 + 0.749199i \(0.269562\pi\)
−0.878642 + 0.477482i \(0.841550\pi\)
\(390\) 0 0
\(391\) 0.630415 + 1.09191i 0.0318815 + 0.0552203i
\(392\) −10.1250 + 17.5369i −0.511387 + 0.885749i
\(393\) 4.07011 + 3.41523i 0.205310 + 0.172275i
\(394\) 16.6373 + 6.05547i 0.838174 + 0.305070i
\(395\) 0 0
\(396\) 1.66772 1.39938i 0.0838060 0.0703216i
\(397\) 5.52822 + 31.3521i 0.277453 + 1.57352i 0.731059 + 0.682314i \(0.239026\pi\)
−0.453606 + 0.891202i \(0.649863\pi\)
\(398\) −0.345866 −0.0173367
\(399\) 0.0320889 + 4.35878i 0.00160645 + 0.218212i
\(400\) 0 0
\(401\) −0.0150147 0.0851529i −0.000749801 0.00425233i 0.984431 0.175774i \(-0.0562428\pi\)
−0.985180 + 0.171522i \(0.945132\pi\)
\(402\) −22.8084 + 19.1385i −1.13758 + 0.954543i
\(403\) −17.1878 + 6.25584i −0.856185 + 0.311626i
\(404\) −1.60607 0.584561i −0.0799048 0.0290830i
\(405\) 0 0
\(406\) −1.60947 + 2.78768i −0.0798767 + 0.138350i
\(407\) −5.50387 9.53298i −0.272817 0.472532i
\(408\) 0.688663 3.90560i 0.0340939 0.193356i
\(409\) 3.47400 19.7021i 0.171778 0.974204i −0.770019 0.638021i \(-0.779753\pi\)
0.941797 0.336182i \(-0.109136\pi\)
\(410\) 0 0
\(411\) 0.368241 0.637812i 0.0181640 0.0314609i
\(412\) −0.779963 0.654467i −0.0384260 0.0322433i
\(413\) −2.05778 0.748971i −0.101257 0.0368545i
\(414\) −18.0496 + 6.56953i −0.887091 + 0.322875i
\(415\) 0 0
\(416\) −0.465690 2.64106i −0.0228323 0.129488i
\(417\) 12.2763 0.601174
\(418\) 11.2763 6.62154i 0.551542 0.323870i
\(419\) 25.4097 1.24135 0.620673 0.784070i \(-0.286859\pi\)
0.620673 + 0.784070i \(0.286859\pi\)
\(420\) 0 0
\(421\) 3.34730 2.80872i 0.163137 0.136888i −0.557565 0.830134i \(-0.688264\pi\)
0.720702 + 0.693245i \(0.243820\pi\)
\(422\) −3.09967 + 1.12819i −0.150890 + 0.0549193i
\(423\) −36.2486 13.1934i −1.76247 0.641485i
\(424\) −6.39827 5.36879i −0.310727 0.260731i
\(425\) 0 0
\(426\) 18.0496 + 31.2629i 0.874507 + 1.51469i
\(427\) −0.550507 + 3.12208i −0.0266409 + 0.151088i
\(428\) 0.328411 1.86251i 0.0158744 0.0900279i
\(429\) −8.25150 14.2920i −0.398386 0.690025i
\(430\) 0 0
\(431\) −29.3444 24.6228i −1.41347 1.18604i −0.954732 0.297468i \(-0.903858\pi\)
−0.458736 0.888572i \(-0.651698\pi\)
\(432\) 22.2913 + 8.11338i 1.07249 + 0.390355i
\(433\) −17.0376 + 6.20118i −0.818775 + 0.298010i −0.717244 0.696823i \(-0.754597\pi\)
−0.101532 + 0.994832i \(0.532374\pi\)
\(434\) 2.54710 2.13727i 0.122265 0.102592i
\(435\) 0 0
\(436\) 0.336867 0.0161330
\(437\) 11.5517 2.12467i 0.552592 0.101637i
\(438\) −5.38919 −0.257505
\(439\) −1.05762 5.99806i −0.0504774 0.286272i 0.949112 0.314940i \(-0.101984\pi\)
−0.999589 + 0.0286685i \(0.990873\pi\)
\(440\) 0 0
\(441\) 34.2028 12.4488i 1.62870 0.592800i
\(442\) −1.52481 0.554987i −0.0725280 0.0263981i
\(443\) 22.8995 + 19.2149i 1.08799 + 0.912928i 0.996559 0.0828833i \(-0.0264129\pi\)
0.0914266 + 0.995812i \(0.470857\pi\)
\(444\) −1.31521 + 2.27801i −0.0624170 + 0.108109i
\(445\) 0 0
\(446\) 1.99092 11.2910i 0.0942726 0.534646i
\(447\) 8.27972 46.9566i 0.391617 2.22097i
\(448\) 1.49273 + 2.58548i 0.0705247 + 0.122152i
\(449\) 5.62495 9.74270i 0.265458 0.459787i −0.702226 0.711955i \(-0.747810\pi\)
0.967683 + 0.252168i \(0.0811435\pi\)
\(450\) 0 0
\(451\) 5.18004 + 1.88538i 0.243919 + 0.0887792i
\(452\) 3.07145 1.11792i 0.144469 0.0525824i
\(453\) −9.62108 + 8.07305i −0.452038 + 0.379305i
\(454\) 3.31062 + 18.7755i 0.155375 + 0.881176i
\(455\) 0 0
\(456\) −32.1300 18.2362i −1.50463 0.853989i
\(457\) 23.3901 1.09414 0.547072 0.837086i \(-0.315742\pi\)
0.547072 + 0.837086i \(0.315742\pi\)
\(458\) −4.80381 27.2438i −0.224468 1.27302i
\(459\) −2.36437 + 1.98394i −0.110359 + 0.0926025i
\(460\) 0 0
\(461\) 34.4149 + 12.5260i 1.60286 + 0.583395i 0.980011 0.198945i \(-0.0637514\pi\)
0.622853 + 0.782339i \(0.285974\pi\)
\(462\) 2.29813 + 1.92836i 0.106919 + 0.0897156i
\(463\) −21.4932 + 37.2273i −0.998873 + 1.73010i −0.458340 + 0.888777i \(0.651556\pi\)
−0.540534 + 0.841322i \(0.681778\pi\)
\(464\) −12.3701 21.4256i −0.574265 0.994657i
\(465\) 0 0
\(466\) −4.12954 + 23.4198i −0.191297 + 1.08490i
\(467\) 12.7981 + 22.1670i 0.592227 + 1.02577i 0.993932 + 0.109998i \(0.0350845\pi\)
−0.401705 + 0.915769i \(0.631582\pi\)
\(468\) −1.25830 + 2.17945i −0.0581651 + 0.100745i
\(469\) 2.04189 + 1.71335i 0.0942857 + 0.0791151i
\(470\) 0 0
\(471\) −26.0253 + 9.47243i −1.19918 + 0.436466i
\(472\) 14.2181 11.9304i 0.654439 0.549140i
\(473\) 1.50862 + 8.55580i 0.0693663 + 0.393396i
\(474\) −45.9522 −2.11066
\(475\) 0 0
\(476\) −0.0300295 −0.00137640
\(477\) 2.60694 + 14.7847i 0.119364 + 0.676946i
\(478\) 2.42783 2.03719i 0.111046 0.0931791i
\(479\) −35.8739 + 13.0570i −1.63912 + 0.596591i −0.986885 0.161424i \(-0.948391\pi\)
−0.652236 + 0.758016i \(0.726169\pi\)
\(480\) 0 0
\(481\) 9.74763 + 8.17923i 0.444453 + 0.372941i
\(482\) −9.29679 + 16.1025i −0.423457 + 0.733449i
\(483\) 1.34730 + 2.33359i 0.0613041 + 0.106182i
\(484\) 0.193877 1.09953i 0.00881261 0.0499788i
\(485\) 0 0
\(486\) 7.27766 + 12.6053i 0.330121 + 0.571787i
\(487\) 3.88191 6.72367i 0.175906 0.304678i −0.764568 0.644543i \(-0.777048\pi\)
0.940475 + 0.339864i \(0.110381\pi\)
\(488\) −20.5835 17.2716i −0.931773 0.781850i
\(489\) 22.6065 + 8.22811i 1.02230 + 0.372088i
\(490\) 0 0
\(491\) −28.1313 + 23.6050i −1.26955 + 1.06528i −0.274954 + 0.961457i \(0.588663\pi\)
−0.994596 + 0.103822i \(0.966893\pi\)
\(492\) −0.228741 1.29725i −0.0103124 0.0584848i
\(493\) 3.21894 0.144974
\(494\) −9.63104 + 11.6510i −0.433321 + 0.524201i
\(495\) 0 0
\(496\) 4.43763 + 25.1671i 0.199256 + 1.13003i
\(497\) 2.47565 2.07732i 0.111048 0.0931805i
\(498\) −54.0642 + 19.6778i −2.42268 + 0.881782i
\(499\) −4.62923 1.68490i −0.207233 0.0754266i 0.236318 0.971676i \(-0.424059\pi\)
−0.443551 + 0.896249i \(0.646281\pi\)
\(500\) 0 0
\(501\) 5.80928 10.0620i 0.259539 0.449535i
\(502\) 2.80587 + 4.85992i 0.125232 + 0.216909i
\(503\) −5.72163 + 32.4490i −0.255115 + 1.44683i 0.540663 + 0.841239i \(0.318173\pi\)
−0.795778 + 0.605589i \(0.792938\pi\)
\(504\) 0.939226 5.32661i 0.0418364 0.237266i
\(505\) 0 0
\(506\) 4.04189 7.00076i 0.179684 0.311222i
\(507\) −14.0608 11.7984i −0.624461 0.523985i
\(508\) −2.01501 0.733405i −0.0894018 0.0325396i
\(509\) 34.7075 12.6325i 1.53839 0.559926i 0.572728 0.819746i \(-0.305885\pi\)
0.965657 + 0.259819i \(0.0836630\pi\)
\(510\) 0 0
\(511\) 0.0837781 + 0.475129i 0.00370613 + 0.0210185i
\(512\) −24.9186 −1.10126
\(513\) 10.0326 + 26.9453i 0.442948 + 1.18967i
\(514\) −0.898986 −0.0396526
\(515\) 0 0
\(516\) 1.59034 1.33445i 0.0700107 0.0587459i
\(517\) 15.2554 5.55250i 0.670930 0.244199i
\(518\) −2.17365 0.791143i −0.0955046 0.0347608i
\(519\) 44.4320 + 37.2829i 1.95035 + 1.63654i
\(520\) 0 0
\(521\) −4.64590 8.04693i −0.203540 0.352542i 0.746126 0.665804i \(-0.231912\pi\)
−0.949667 + 0.313262i \(0.898578\pi\)
\(522\) −8.51548 + 48.2937i −0.372713 + 2.11376i
\(523\) 4.93423 27.9834i 0.215759 1.22363i −0.663826 0.747887i \(-0.731068\pi\)
0.879585 0.475742i \(-0.157820\pi\)
\(524\) 0.170493 + 0.295303i 0.00744802 + 0.0129004i
\(525\) 0 0
\(526\) −11.7654 9.87236i −0.512996 0.430455i
\(527\) −3.12449 1.13722i −0.136105 0.0495381i
\(528\) −21.6668 + 7.88609i −0.942928 + 0.343198i
\(529\) −12.0569 + 10.1169i −0.524213 + 0.439867i
\(530\) 0 0
\(531\) −33.3610 −1.44775
\(532\) −0.0937404 + 0.263571i −0.00406416 + 0.0114273i
\(533\) −6.37227 −0.276014
\(534\) −6.93242 39.3157i −0.299995 1.70136i
\(535\) 0 0
\(536\) −21.2294 + 7.72686i −0.916969 + 0.333749i
\(537\) 31.1498 + 11.3376i 1.34421 + 0.489253i
\(538\) 20.0123 + 16.7923i 0.862793 + 0.723969i
\(539\) −7.65910 + 13.2660i −0.329901 + 0.571405i
\(540\) 0 0
\(541\) 2.60220 14.7578i 0.111877 0.634487i −0.876372 0.481635i \(-0.840043\pi\)
0.988249 0.152852i \(-0.0488458\pi\)
\(542\) −3.13366 + 17.7718i −0.134602 + 0.763366i
\(543\) −12.2909 21.2884i −0.527451 0.913572i
\(544\) 0.243756 0.422197i 0.0104509 0.0181016i
\(545\) 0 0
\(546\) −3.25877 1.18610i −0.139463 0.0507602i
\(547\) −3.65270 + 1.32948i −0.156178 + 0.0568443i −0.418926 0.908020i \(-0.637593\pi\)
0.262748 + 0.964864i \(0.415371\pi\)
\(548\) 0.0362077 0.0303818i 0.00154672 0.00129785i
\(549\) 8.38666 + 47.5631i 0.357934 + 2.02994i
\(550\) 0 0
\(551\) 10.0483 28.2529i 0.428071 1.20361i
\(552\) −22.8384 −0.972068
\(553\) 0.714355 + 4.05131i 0.0303775 + 0.172279i
\(554\) −18.3164 + 15.3693i −0.778189 + 0.652978i
\(555\) 0 0
\(556\) 0.740352 + 0.269466i 0.0313979 + 0.0114279i
\(557\) −10.1152 8.48762i −0.428593 0.359632i 0.402828 0.915276i \(-0.368027\pi\)
−0.831420 + 0.555644i \(0.812472\pi\)
\(558\) 25.3273 43.8681i 1.07219 1.85709i
\(559\) −5.02141 8.69734i −0.212383 0.367858i
\(560\) 0 0
\(561\) 0.520945 2.95442i 0.0219943 0.124736i
\(562\) −12.3136 21.3278i −0.519418 0.899659i
\(563\) 5.35638 9.27752i 0.225745 0.391001i −0.730798 0.682594i \(-0.760852\pi\)
0.956543 + 0.291593i \(0.0941852\pi\)
\(564\) −2.97178 2.49362i −0.125135 0.105000i
\(565\) 0 0
\(566\) 9.73308 3.54255i 0.409112 0.148905i
\(567\) −0.830222 + 0.696639i −0.0348661 + 0.0292561i
\(568\) 4.75641 + 26.9749i 0.199574 + 1.13184i
\(569\) −13.4706 −0.564717 −0.282358 0.959309i \(-0.591117\pi\)
−0.282358 + 0.959309i \(0.591117\pi\)
\(570\) 0 0
\(571\) 12.6655 0.530035 0.265017 0.964244i \(-0.414622\pi\)
0.265017 + 0.964244i \(0.414622\pi\)
\(572\) −0.183915 1.04303i −0.00768988 0.0436115i
\(573\) 40.4432 33.9358i 1.68954 1.41769i
\(574\) 1.08853 0.396191i 0.0454342 0.0165367i
\(575\) 0 0
\(576\) 34.8410 + 29.2350i 1.45171 + 1.21813i
\(577\) −5.27719 + 9.14036i −0.219692 + 0.380518i −0.954714 0.297526i \(-0.903839\pi\)
0.735022 + 0.678044i \(0.237172\pi\)
\(578\) 11.3045 + 19.5800i 0.470206 + 0.814421i
\(579\) −0.148833 + 0.844075i −0.00618530 + 0.0350786i
\(580\) 0 0
\(581\) 2.57532 + 4.46059i 0.106842 + 0.185056i
\(582\) 18.3366 31.7600i 0.760077 1.31649i
\(583\) −4.84002 4.06126i −0.200453 0.168200i
\(584\) −3.84255 1.39857i −0.159006 0.0578734i
\(585\) 0 0
\(586\) 10.8400 9.09586i 0.447797 0.375746i
\(587\) 3.32619 + 18.8638i 0.137287 + 0.778591i 0.973240 + 0.229791i \(0.0738041\pi\)
−0.835954 + 0.548800i \(0.815085\pi\)
\(588\) 3.66044 0.150954
\(589\) −19.7349 + 23.8739i −0.813162 + 0.983706i
\(590\) 0 0
\(591\) −6.57057 37.2636i −0.270277 1.53282i
\(592\) 13.6190 11.4277i 0.559738 0.469676i
\(593\) −8.17024 + 2.97373i −0.335512 + 0.122116i −0.504282 0.863539i \(-0.668243\pi\)
0.168770 + 0.985655i \(0.446020\pi\)
\(594\) 18.5954 + 6.76817i 0.762978 + 0.277701i
\(595\) 0 0
\(596\) 1.53003 2.65009i 0.0626724 0.108552i
\(597\) 0.369585 + 0.640140i 0.0151261 + 0.0261992i
\(598\) −1.62267 + 9.20264i −0.0663561 + 0.376324i
\(599\) 3.44373 19.5303i 0.140707 0.797988i −0.830008 0.557752i \(-0.811664\pi\)
0.970715 0.240236i \(-0.0772248\pi\)
\(600\) 0 0
\(601\) 16.8807 29.2383i 0.688579 1.19265i −0.283718 0.958908i \(-0.591568\pi\)
0.972298 0.233747i \(-0.0750986\pi\)
\(602\) 1.39852 + 1.17350i 0.0569994 + 0.0478282i
\(603\) 38.1584 + 13.8885i 1.55393 + 0.565584i
\(604\) −0.757426 + 0.275681i −0.0308192 + 0.0112173i
\(605\) 0 0
\(606\) −6.23055 35.3352i −0.253099 1.43540i
\(607\) −35.2850 −1.43217 −0.716087 0.698011i \(-0.754068\pi\)
−0.716087 + 0.698011i \(0.754068\pi\)
\(608\) −2.94475 3.45740i −0.119425 0.140216i
\(609\) 6.87939 0.278767
\(610\) 0 0
\(611\) −14.3760 + 12.0629i −0.581590 + 0.488012i
\(612\) −0.429892 + 0.156468i −0.0173774 + 0.00632485i
\(613\) 17.3405 + 6.31142i 0.700376 + 0.254916i 0.667571 0.744546i \(-0.267334\pi\)
0.0328044 + 0.999462i \(0.489556\pi\)
\(614\) 12.0708 + 10.1286i 0.487139 + 0.408758i
\(615\) 0 0
\(616\) 1.13816 + 1.97134i 0.0458576 + 0.0794277i
\(617\) 6.19671 35.1433i 0.249470 1.41482i −0.560408 0.828217i \(-0.689356\pi\)
0.809878 0.586598i \(-0.199533\pi\)
\(618\) 3.71167 21.0499i 0.149305 0.846752i
\(619\) −1.82976 3.16923i −0.0735441 0.127382i 0.826908 0.562337i \(-0.190098\pi\)
−0.900452 + 0.434955i \(0.856764\pi\)
\(620\) 0 0
\(621\) 13.6159 + 11.4251i 0.546386 + 0.458472i
\(622\) −20.2135 7.35710i −0.810487 0.294993i
\(623\) −3.35844 + 1.22237i −0.134553 + 0.0489733i
\(624\) 20.4179 17.1326i 0.817369 0.685854i
\(625\) 0 0
\(626\) 35.8767 1.43392
\(627\) −24.3050 13.7949i −0.970648 0.550917i
\(628\) −1.77744 −0.0709275
\(629\) 0.401674 + 2.27801i 0.0160158 + 0.0908301i
\(630\) 0 0
\(631\) 0.745977 0.271514i 0.0296969 0.0108088i −0.327129 0.944980i \(-0.606081\pi\)
0.356826 + 0.934171i \(0.383859\pi\)
\(632\) −32.7645 11.9253i −1.30330 0.474362i
\(633\) 5.40033 + 4.53141i 0.214644 + 0.180108i
\(634\) 19.8942 34.4578i 0.790101 1.36850i
\(635\) 0 0
\(636\) −0.262174 + 1.48686i −0.0103959 + 0.0589579i
\(637\) 3.07486 17.4384i 0.121830 0.690933i
\(638\) −10.3191 17.8732i −0.408536 0.707605i
\(639\) 24.6168 42.6375i 0.973826 1.68672i
\(640\) 0 0
\(641\) −27.6104 10.0494i −1.09055 0.396926i −0.266723 0.963773i \(-0.585941\pi\)
−0.823823 + 0.566847i \(0.808163\pi\)
\(642\) 37.3089 13.5793i 1.47246 0.535933i
\(643\) −17.0168 + 14.2788i −0.671078 + 0.563101i −0.913384 0.407098i \(-0.866541\pi\)
0.242306 + 0.970200i \(0.422096\pi\)
\(644\) 0.0300295 + 0.170306i 0.00118333 + 0.00671099i
\(645\) 0 0
\(646\) −2.70258 + 0.497079i −0.106332 + 0.0195573i
\(647\) −11.2591 −0.442640 −0.221320 0.975201i \(-0.571037\pi\)
−0.221320 + 0.975201i \(0.571037\pi\)
\(648\) −1.59508 9.04617i −0.0626608 0.355367i
\(649\) 10.7554 9.02482i 0.422185 0.354255i
\(650\) 0 0
\(651\) −6.67752 2.43042i −0.261713 0.0952556i
\(652\) 1.18273 + 0.992431i 0.0463194 + 0.0388666i
\(653\) 13.5000 23.3827i 0.528296 0.915035i −0.471160 0.882048i \(-0.656165\pi\)
0.999456 0.0329874i \(-0.0105021\pi\)
\(654\) 3.53596 + 6.12446i 0.138267 + 0.239485i
\(655\) 0 0
\(656\) −1.54601 + 8.76785i −0.0603615 + 0.342327i
\(657\) 3.67499 + 6.36527i 0.143375 + 0.248333i
\(658\) 1.70574 2.95442i 0.0664966 0.115175i
\(659\) 21.4691 + 18.0147i 0.836317 + 0.701753i 0.956732 0.290970i \(-0.0939781\pi\)
−0.120415 + 0.992724i \(0.538423\pi\)
\(660\) 0 0
\(661\) −10.6823 + 3.88803i −0.415492 + 0.151227i −0.541303 0.840827i \(-0.682069\pi\)
0.125811 + 0.992054i \(0.459847\pi\)
\(662\) 28.5533 23.9590i 1.10975 0.931194i
\(663\) 0.602196 + 3.41523i 0.0233874 + 0.132636i
\(664\) −43.6551 −1.69415
\(665\) 0 0
\(666\) −35.2395 −1.36550
\(667\) −3.21894 18.2555i −0.124638 0.706857i
\(668\) 0.571203 0.479297i 0.0221005 0.0185445i
\(669\) −23.0253 + 8.38052i −0.890209 + 0.324010i
\(670\) 0 0
\(671\) −15.5706 13.0653i −0.601095 0.504379i
\(672\) 0.520945 0.902302i 0.0200959 0.0348071i
\(673\) −8.28359 14.3476i −0.319309 0.553059i 0.661035 0.750355i \(-0.270117\pi\)
−0.980344 + 0.197296i \(0.936784\pi\)
\(674\) −4.17840 + 23.6969i −0.160946 + 0.912769i
\(675\) 0 0
\(676\) −0.588993 1.02017i −0.0226536 0.0392371i
\(677\) −4.52481 + 7.83721i −0.173903 + 0.301208i −0.939781 0.341777i \(-0.888971\pi\)
0.765878 + 0.642986i \(0.222305\pi\)
\(678\) 52.5642 + 44.1066i 2.01872 + 1.69390i
\(679\) −3.08512 1.12289i −0.118396 0.0430927i
\(680\) 0 0
\(681\) 31.2126 26.1905i 1.19607 1.00362i
\(682\) 3.70187 + 20.9943i 0.141752 + 0.803914i
\(683\) −8.73143 −0.334099 −0.167049 0.985949i \(-0.553424\pi\)
−0.167049 + 0.985949i \(0.553424\pi\)
\(684\) 0.0313737 + 4.26163i 0.00119960 + 0.162947i
\(685\) 0 0
\(686\) 1.12773 + 6.39566i 0.0430568 + 0.244187i
\(687\) −45.2904 + 38.0032i −1.72794 + 1.44991i
\(688\) −13.1853 + 4.79904i −0.502683 + 0.182962i
\(689\) 6.86319 + 2.49800i 0.261467 + 0.0951661i
\(690\) 0 0
\(691\) −17.3601 + 30.0686i −0.660409 + 1.14386i 0.320099 + 0.947384i \(0.396284\pi\)
−0.980508 + 0.196478i \(0.937050\pi\)
\(692\) 1.86122 + 3.22372i 0.0707528 + 0.122547i
\(693\) 0.710485 4.02936i 0.0269891 0.153063i
\(694\) 1.35710 7.69648i 0.0515147 0.292154i
\(695\) 0 0
\(696\) −29.1536 + 50.4956i −1.10507 + 1.91403i
\(697\) −0.887374 0.744596i −0.0336117 0.0282036i
\(698\) −6.80154 2.47556i −0.257442 0.0937012i
\(699\) 47.7588 17.3828i 1.80640 0.657478i
\(700\) 0 0
\(701\) 6.84436 + 38.8163i 0.258508 + 1.46607i 0.786905 + 0.617074i \(0.211682\pi\)
−0.528397 + 0.848997i \(0.677207\pi\)
\(702\) −22.8753 −0.863371
\(703\) 21.2481 + 3.58553i 0.801387 + 0.135231i
\(704\) −19.1411 −0.721409
\(705\) 0 0
\(706\) 26.0442 21.8537i 0.980185 0.822473i
\(707\) −3.01842 + 1.09861i −0.113519 + 0.0413176i
\(708\) −3.15270 1.14749i −0.118486 0.0431253i
\(709\) −31.5009 26.4324i −1.18304 0.992690i −0.999954 0.00959399i \(-0.996946\pi\)
−0.183088 0.983096i \(-0.558609\pi\)
\(710\) 0 0
\(711\) 31.3357 + 54.2751i 1.17518 + 2.03548i
\(712\) 5.26011 29.8316i 0.197131 1.11799i
\(713\) −3.32501 + 18.8571i −0.124523 + 0.706202i
\(714\) −0.315207 0.545955i −0.0117963 0.0204319i
\(715\) 0 0
\(716\) 1.62970 + 1.36748i 0.0609047 + 0.0511051i
\(717\) −6.36484 2.31661i −0.237699 0.0865154i
\(718\) −8.46585 + 3.08132i −0.315943 + 0.114994i
\(719\) −32.4768 + 27.2513i −1.21118 + 1.01630i −0.211943 + 0.977282i \(0.567979\pi\)
−0.999238 + 0.0390200i \(0.987576\pi\)
\(720\) 0 0
\(721\) −1.91353 −0.0712637
\(722\) −4.07351 + 25.2724i −0.151600 + 0.940543i
\(723\) 39.7374 1.47785
\(724\) −0.273947 1.55363i −0.0101812 0.0577403i
\(725\) 0 0
\(726\) 22.0253 8.01655i 0.817435 0.297522i
\(727\) 48.5411 + 17.6675i 1.80029 + 0.655251i 0.998324 + 0.0578805i \(0.0184342\pi\)
0.801965 + 0.597371i \(0.203788\pi\)
\(728\) −2.01573 1.69140i −0.0747079 0.0626874i
\(729\) 20.2344 35.0470i 0.749423 1.29804i
\(730\) 0 0
\(731\) 0.317018 1.79790i 0.0117254 0.0664978i
\(732\) −0.843426 + 4.78331i −0.0311739 + 0.176796i
\(733\) −11.4581 19.8460i −0.423215 0.733030i 0.573037 0.819530i \(-0.305765\pi\)
−0.996252 + 0.0864997i \(0.972432\pi\)
\(734\) 5.46926 9.47303i 0.201874 0.349656i
\(735\) 0 0
\(736\) −2.63816 0.960210i −0.0972437 0.0353938i
\(737\) −16.0591 + 5.84504i −0.591545 + 0.215305i
\(738\) 13.5186 11.3435i 0.497628 0.417559i
\(739\) 4.88413 + 27.6993i 0.179666 + 1.01894i 0.932619 + 0.360862i \(0.117517\pi\)
−0.752954 + 0.658074i \(0.771372\pi\)
\(740\) 0 0
\(741\) 31.8555 + 5.37549i 1.17024 + 0.197474i
\(742\) −1.32770 −0.0487413
\(743\) −1.06489 6.03931i −0.0390671 0.221561i 0.959024 0.283326i \(-0.0914380\pi\)
−0.998091 + 0.0617657i \(0.980327\pi\)
\(744\) 46.1377 38.7142i 1.69149 1.41933i
\(745\) 0 0
\(746\) 44.1819 + 16.0809i 1.61761 + 0.588763i
\(747\) 60.1093 + 50.4377i 2.19928 + 1.84542i
\(748\) 0.0962667 0.166739i 0.00351986 0.00609657i
\(749\) −1.77719 3.07818i −0.0649371 0.112474i
\(750\) 0 0
\(751\) 0.979522 5.55515i 0.0357433 0.202710i −0.961707 0.274081i \(-0.911626\pi\)
0.997450 + 0.0713710i \(0.0227374\pi\)
\(752\) 13.1099 + 22.7071i 0.478070 + 0.828042i
\(753\) 5.99660 10.3864i 0.218528 0.378502i
\(754\) 18.2756 + 15.3350i 0.665558 + 0.558469i
\(755\) 0 0
\(756\) −0.397804 + 0.144789i −0.0144680 + 0.00526591i
\(757\) −12.0207 + 10.0866i −0.436900 + 0.366602i −0.834548 0.550936i \(-0.814271\pi\)
0.397648 + 0.917538i \(0.369827\pi\)
\(758\) 0.398052 + 2.25746i 0.0144579 + 0.0819948i
\(759\) −17.2763 −0.627090
\(760\) 0 0
\(761\) 4.86484 0.176350 0.0881751 0.996105i \(-0.471896\pi\)
0.0881751 + 0.996105i \(0.471896\pi\)
\(762\) −7.81702 44.3325i −0.283181 1.60600i
\(763\) 0.484985 0.406951i 0.0175576 0.0147326i
\(764\) 3.18392 1.15885i 0.115190 0.0419257i
\(765\) 0 0
\(766\) −3.03099 2.54331i −0.109514 0.0918934i
\(767\) −8.11499 + 14.0556i −0.293015 + 0.507517i
\(768\) 6.32888 + 10.9619i 0.228374 + 0.395555i
\(769\) 3.91266 22.1898i 0.141094 0.800184i −0.829327 0.558764i \(-0.811276\pi\)
0.970421 0.241420i \(-0.0776131\pi\)
\(770\) 0 0
\(771\) 0.960637 + 1.66387i 0.0345965 + 0.0599229i
\(772\) −0.0275033 + 0.0476371i −0.000989864 + 0.00171450i
\(773\) 20.2481 + 16.9902i 0.728273 + 0.611094i 0.929660 0.368418i \(-0.120100\pi\)
−0.201387 + 0.979512i \(0.564545\pi\)
\(774\) 26.1352 + 9.51244i 0.939411 + 0.341918i
\(775\) 0 0
\(776\) 21.3164 17.8866i 0.765214 0.642091i
\(777\) 0.858441 + 4.86846i 0.0307964 + 0.174655i
\(778\) −33.0993 −1.18667
\(779\) −9.30541 + 5.46421i −0.333401 + 0.195776i
\(780\) 0 0