Properties

Label 750.2.l.b.143.10
Level $750$
Weight $2$
Character 750.143
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 143.10
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.b.257.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.453990 - 0.891007i) q^{2} +(1.12805 - 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(1.51403 - 1.51403i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +O(q^{10})\) \(q+(0.453990 - 0.891007i) q^{2} +(1.12805 - 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(1.51403 - 1.51403i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +(-5.62798 + 1.82864i) q^{11} +(-1.72638 - 0.140065i) q^{12} +(-0.941310 + 0.479621i) q^{13} +(-0.661655 - 2.03636i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.899945 - 5.68203i) q^{17} +(-2.84866 - 0.940823i) q^{18} +(3.16950 - 4.36244i) q^{19} +(-0.282042 - 3.69786i) q^{21} +(-0.925718 + 5.84476i) q^{22} +(-1.37932 - 0.702799i) q^{23} +(-0.908558 + 1.47463i) q^{24} +1.05646i q^{26} +(-4.41066 - 2.74701i) q^{27} +(-2.11480 - 0.334951i) q^{28} +(3.67723 - 2.67167i) q^{29} +(8.62475 + 6.26624i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.94521 + 9.45990i) q^{33} +(-5.47129 - 1.77773i) q^{34} +(-2.13154 + 2.11105i) q^{36} +(-0.100380 - 0.197006i) q^{37} +(-2.44804 - 4.80455i) q^{38} +(-0.431463 + 1.77824i) q^{39} +(1.54235 + 0.501139i) q^{41} +(-3.42286 - 1.42749i) q^{42} +(-1.33532 - 1.33532i) q^{43} +(4.78745 + 3.47829i) q^{44} +(-1.25240 + 0.909919i) q^{46} +(4.75083 + 0.752458i) q^{47} +(0.901424 + 1.47900i) q^{48} +2.41543i q^{49} +(-8.48331 - 5.22681i) q^{51} +(0.941310 + 0.479621i) q^{52} +(-0.949805 + 5.99683i) q^{53} +(-4.45000 + 2.68281i) q^{54} +(-1.25854 + 1.73224i) q^{56} +(-2.15837 - 9.08688i) q^{57} +(-0.711043 - 4.48935i) q^{58} +(2.24119 - 6.89769i) q^{59} +(-1.30934 - 4.02973i) q^{61} +(9.49882 - 4.83989i) q^{62} +(-5.17841 - 3.80069i) q^{63} +(0.951057 - 0.309017i) q^{64} +(6.63774 + 7.80992i) q^{66} +(1.28043 - 0.202800i) q^{67} +(-4.06788 + 4.06788i) q^{68} +(-2.47967 + 1.02010i) q^{69} +(2.39892 + 3.30183i) q^{71} +(0.913257 + 2.85761i) q^{72} +(-0.141918 + 0.278530i) q^{73} -0.221105 q^{74} -5.39228 q^{76} +(-5.75231 + 11.2895i) q^{77} +(1.38854 + 1.19174i) q^{78} +(0.555462 + 0.764528i) q^{79} +(-8.58598 + 2.69833i) q^{81} +(1.14673 - 1.14673i) q^{82} +(7.47149 - 1.18337i) q^{83} +(-2.82585 + 2.40172i) q^{84} +(-1.79600 + 0.583556i) q^{86} +(0.636640 - 7.84692i) q^{87} +(5.27263 - 2.68654i) q^{88} +(2.67429 + 8.23061i) q^{89} +(-0.699010 + 2.15133i) q^{91} +(0.242168 + 1.52899i) q^{92} +(17.9652 - 4.26719i) q^{93} +(2.82728 - 3.89142i) q^{94} +(1.72703 - 0.131724i) q^{96} +(-1.88725 + 11.9156i) q^{97} +(2.15217 + 1.09658i) q^{98} +(7.98311 + 15.8566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{3} - 4q^{7} + O(q^{10}) \) \( 80q - 4q^{3} - 4q^{7} + 4q^{12} + 20q^{16} + 8q^{18} - 40q^{19} + 36q^{22} - 4q^{27} + 16q^{28} - 4q^{33} - 40q^{34} + 24q^{37} - 40q^{39} + 4q^{42} + 24q^{43} + 4q^{48} + 64q^{57} - 20q^{58} - 64q^{63} - 96q^{67} + 140q^{69} - 8q^{72} - 100q^{73} - 100q^{78} + 80q^{79} - 40q^{81} - 96q^{82} + 60q^{84} - 80q^{87} - 4q^{88} - 12q^{93} + 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.453990 0.891007i 0.321020 0.630037i
\(3\) 1.12805 1.31434i 0.651283 0.758835i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) −0.658960 1.60180i −0.269019 0.653933i
\(7\) 1.51403 1.51403i 0.572249 0.572249i −0.360507 0.932756i \(-0.617396\pi\)
0.932756 + 0.360507i \(0.117396\pi\)
\(8\) −0.987688 + 0.156434i −0.349201 + 0.0553079i
\(9\) −0.454984 2.96530i −0.151661 0.988433i
\(10\) 0 0
\(11\) −5.62798 + 1.82864i −1.69690 + 0.551357i −0.988068 0.154020i \(-0.950778\pi\)
−0.708833 + 0.705376i \(0.750778\pi\)
\(12\) −1.72638 0.140065i −0.498362 0.0404334i
\(13\) −0.941310 + 0.479621i −0.261072 + 0.133023i −0.579628 0.814881i \(-0.696802\pi\)
0.318556 + 0.947904i \(0.396802\pi\)
\(14\) −0.661655 2.03636i −0.176835 0.544241i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −0.899945 5.68203i −0.218269 1.37809i −0.816766 0.576969i \(-0.804235\pi\)
0.598497 0.801125i \(-0.295765\pi\)
\(18\) −2.84866 0.940823i −0.671435 0.221754i
\(19\) 3.16950 4.36244i 0.727133 1.00081i −0.272123 0.962262i \(-0.587726\pi\)
0.999257 0.0385508i \(-0.0122742\pi\)
\(20\) 0 0
\(21\) −0.282042 3.69786i −0.0615467 0.806939i
\(22\) −0.925718 + 5.84476i −0.197364 + 1.24611i
\(23\) −1.37932 0.702799i −0.287608 0.146544i 0.304235 0.952597i \(-0.401599\pi\)
−0.591843 + 0.806054i \(0.701599\pi\)
\(24\) −0.908558 + 1.47463i −0.185459 + 0.301007i
\(25\) 0 0
\(26\) 1.05646i 0.207188i
\(27\) −4.41066 2.74701i −0.848832 0.528663i
\(28\) −2.11480 0.334951i −0.399659 0.0632998i
\(29\) 3.67723 2.67167i 0.682845 0.496116i −0.191455 0.981501i \(-0.561321\pi\)
0.874300 + 0.485386i \(0.161321\pi\)
\(30\) 0 0
\(31\) 8.62475 + 6.26624i 1.54905 + 1.12545i 0.944324 + 0.329017i \(0.106718\pi\)
0.604726 + 0.796433i \(0.293282\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −3.94521 + 9.45990i −0.686774 + 1.64676i
\(34\) −5.47129 1.77773i −0.938319 0.304878i
\(35\) 0 0
\(36\) −2.13154 + 2.11105i −0.355257 + 0.351841i
\(37\) −0.100380 0.197006i −0.0165023 0.0323876i 0.882608 0.470109i \(-0.155786\pi\)
−0.899111 + 0.437722i \(0.855786\pi\)
\(38\) −2.44804 4.80455i −0.397125 0.779402i
\(39\) −0.431463 + 1.77824i −0.0690894 + 0.284747i
\(40\) 0 0
\(41\) 1.54235 + 0.501139i 0.240874 + 0.0782648i 0.426966 0.904268i \(-0.359582\pi\)
−0.186092 + 0.982532i \(0.559582\pi\)
\(42\) −3.42286 1.42749i −0.528159 0.220267i
\(43\) −1.33532 1.33532i −0.203634 0.203634i 0.597921 0.801555i \(-0.295994\pi\)
−0.801555 + 0.597921i \(0.795994\pi\)
\(44\) 4.78745 + 3.47829i 0.721735 + 0.524371i
\(45\) 0 0
\(46\) −1.25240 + 0.909919i −0.184656 + 0.134160i
\(47\) 4.75083 + 0.752458i 0.692980 + 0.109757i 0.492983 0.870039i \(-0.335907\pi\)
0.199998 + 0.979796i \(0.435907\pi\)
\(48\) 0.901424 + 1.47900i 0.130109 + 0.213475i
\(49\) 2.41543i 0.345062i
\(50\) 0 0
\(51\) −8.48331 5.22681i −1.18790 0.731899i
\(52\) 0.941310 + 0.479621i 0.130536 + 0.0665115i
\(53\) −0.949805 + 5.99683i −0.130466 + 0.823728i 0.832484 + 0.554049i \(0.186918\pi\)
−0.962950 + 0.269680i \(0.913082\pi\)
\(54\) −4.45000 + 2.68281i −0.605569 + 0.365084i
\(55\) 0 0
\(56\) −1.25854 + 1.73224i −0.168180 + 0.231480i
\(57\) −2.15837 9.08688i −0.285883 1.20359i
\(58\) −0.711043 4.48935i −0.0933645 0.589480i
\(59\) 2.24119 6.89769i 0.291779 0.898002i −0.692506 0.721412i \(-0.743493\pi\)
0.984285 0.176590i \(-0.0565066\pi\)
\(60\) 0 0
\(61\) −1.30934 4.02973i −0.167644 0.515954i 0.831578 0.555408i \(-0.187438\pi\)
−0.999221 + 0.0394543i \(0.987438\pi\)
\(62\) 9.49882 4.83989i 1.20635 0.614667i
\(63\) −5.17841 3.80069i −0.652418 0.478842i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) 6.63774 + 7.80992i 0.817050 + 0.961334i
\(67\) 1.28043 0.202800i 0.156429 0.0247759i −0.0777287 0.996975i \(-0.524767\pi\)
0.234158 + 0.972199i \(0.424767\pi\)
\(68\) −4.06788 + 4.06788i −0.493303 + 0.493303i
\(69\) −2.47967 + 1.02010i −0.298517 + 0.122806i
\(70\) 0 0
\(71\) 2.39892 + 3.30183i 0.284700 + 0.391856i 0.927283 0.374360i \(-0.122138\pi\)
−0.642584 + 0.766215i \(0.722138\pi\)
\(72\) 0.913257 + 2.85761i 0.107628 + 0.336773i
\(73\) −0.141918 + 0.278530i −0.0166102 + 0.0325994i −0.899163 0.437615i \(-0.855823\pi\)
0.882552 + 0.470214i \(0.155823\pi\)
\(74\) −0.221105 −0.0257030
\(75\) 0 0
\(76\) −5.39228 −0.618537
\(77\) −5.75231 + 11.2895i −0.655537 + 1.28656i
\(78\) 1.38854 + 1.19174i 0.157222 + 0.134938i
\(79\) 0.555462 + 0.764528i 0.0624944 + 0.0860162i 0.839120 0.543946i \(-0.183070\pi\)
−0.776626 + 0.629962i \(0.783070\pi\)
\(80\) 0 0
\(81\) −8.58598 + 2.69833i −0.953998 + 0.299814i
\(82\) 1.14673 1.14673i 0.126635 0.126635i
\(83\) 7.47149 1.18337i 0.820102 0.129891i 0.267735 0.963493i \(-0.413725\pi\)
0.552367 + 0.833601i \(0.313725\pi\)
\(84\) −2.82585 + 2.40172i −0.308325 + 0.262050i
\(85\) 0 0
\(86\) −1.79600 + 0.583556i −0.193668 + 0.0629264i
\(87\) 0.636640 7.84692i 0.0682550 0.841278i
\(88\) 5.27263 2.68654i 0.562064 0.286386i
\(89\) 2.67429 + 8.23061i 0.283474 + 0.872443i 0.986852 + 0.161627i \(0.0516741\pi\)
−0.703378 + 0.710816i \(0.748326\pi\)
\(90\) 0 0
\(91\) −0.699010 + 2.15133i −0.0732762 + 0.225521i
\(92\) 0.242168 + 1.52899i 0.0252477 + 0.159408i
\(93\) 17.9652 4.26719i 1.86290 0.442487i
\(94\) 2.82728 3.89142i 0.291612 0.401369i
\(95\) 0 0
\(96\) 1.72703 0.131724i 0.176265 0.0134440i
\(97\) −1.88725 + 11.9156i −0.191621 + 1.20985i 0.684956 + 0.728584i \(0.259821\pi\)
−0.876577 + 0.481262i \(0.840179\pi\)
\(98\) 2.15217 + 1.09658i 0.217402 + 0.110772i
\(99\) 7.98311 + 15.8566i 0.802333 + 1.59365i
\(100\) 0 0
\(101\) 0.310282i 0.0308742i 0.999881 + 0.0154371i \(0.00491398\pi\)
−0.999881 + 0.0154371i \(0.995086\pi\)
\(102\) −8.50846 + 5.18576i −0.842463 + 0.513467i
\(103\) 8.72553 + 1.38199i 0.859752 + 0.136171i 0.570717 0.821147i \(-0.306665\pi\)
0.289035 + 0.957318i \(0.406665\pi\)
\(104\) 0.854692 0.620970i 0.0838094 0.0608911i
\(105\) 0 0
\(106\) 4.91201 + 3.56879i 0.477097 + 0.346631i
\(107\) −4.19190 4.19190i −0.405246 0.405246i 0.474831 0.880077i \(-0.342509\pi\)
−0.880077 + 0.474831i \(0.842509\pi\)
\(108\) 0.370140 + 5.18295i 0.0356167 + 0.498730i
\(109\) 1.79521 + 0.583300i 0.171950 + 0.0558700i 0.393727 0.919227i \(-0.371186\pi\)
−0.221777 + 0.975098i \(0.571186\pi\)
\(110\) 0 0
\(111\) −0.372167 0.0903007i −0.0353245 0.00857096i
\(112\) 0.972066 + 1.90779i 0.0918516 + 0.180269i
\(113\) 3.85086 + 7.55774i 0.362258 + 0.710972i 0.998150 0.0608066i \(-0.0193673\pi\)
−0.635891 + 0.771779i \(0.719367\pi\)
\(114\) −9.07635 2.20224i −0.850078 0.206258i
\(115\) 0 0
\(116\) −4.32285 1.40458i −0.401366 0.130412i
\(117\) 1.85050 + 2.57304i 0.171079 + 0.237878i
\(118\) −5.12840 5.12840i −0.472108 0.472108i
\(119\) −9.96530 7.24021i −0.913517 0.663709i
\(120\) 0 0
\(121\) 19.4311 14.1175i 1.76646 1.28341i
\(122\) −4.18494 0.662830i −0.378887 0.0600098i
\(123\) 2.39852 1.46186i 0.216267 0.131811i
\(124\) 10.6608i 0.957366i
\(125\) 0 0
\(126\) −5.73738 + 2.88852i −0.511127 + 0.257330i
\(127\) −9.31862 4.74807i −0.826894 0.421323i −0.0112913 0.999936i \(-0.503594\pi\)
−0.815602 + 0.578613i \(0.803594\pi\)
\(128\) 0.156434 0.987688i 0.0138270 0.0873001i
\(129\) −3.26138 + 0.248751i −0.287148 + 0.0219013i
\(130\) 0 0
\(131\) 11.4805 15.8015i 1.00306 1.38059i 0.0796236 0.996825i \(-0.474628\pi\)
0.923432 0.383762i \(-0.125372\pi\)
\(132\) 9.97216 2.36864i 0.867965 0.206164i
\(133\) −1.80615 11.4036i −0.156613 0.988816i
\(134\) 0.400605 1.23294i 0.0346070 0.106510i
\(135\) 0 0
\(136\) 1.77773 + 5.47129i 0.152439 + 0.469159i
\(137\) −10.6831 + 5.44330i −0.912717 + 0.465053i −0.846280 0.532738i \(-0.821163\pi\)
−0.0664369 + 0.997791i \(0.521163\pi\)
\(138\) −0.216828 + 2.67251i −0.0184576 + 0.227500i
\(139\) 22.1318 7.19107i 1.87720 0.609939i 0.888747 0.458399i \(-0.151577\pi\)
0.988451 0.151540i \(-0.0484232\pi\)
\(140\) 0 0
\(141\) 6.34819 5.39540i 0.534614 0.454375i
\(142\) 4.03104 0.638455i 0.338278 0.0535779i
\(143\) 4.42062 4.42062i 0.369671 0.369671i
\(144\) 2.96076 + 0.483612i 0.246730 + 0.0403010i
\(145\) 0 0
\(146\) 0.183742 + 0.252900i 0.0152066 + 0.0209301i
\(147\) 3.17470 + 2.72474i 0.261845 + 0.224733i
\(148\) −0.100380 + 0.197006i −0.00825116 + 0.0161938i
\(149\) −14.7140 −1.20542 −0.602711 0.797960i \(-0.705913\pi\)
−0.602711 + 0.797960i \(0.705913\pi\)
\(150\) 0 0
\(151\) −8.54879 −0.695691 −0.347845 0.937552i \(-0.613087\pi\)
−0.347845 + 0.937552i \(0.613087\pi\)
\(152\) −2.44804 + 4.80455i −0.198562 + 0.389701i
\(153\) −16.4394 + 5.25384i −1.32905 + 0.424748i
\(154\) 7.44757 + 10.2507i 0.600142 + 0.826025i
\(155\) 0 0
\(156\) 1.69224 0.696163i 0.135487 0.0557377i
\(157\) 17.5864 17.5864i 1.40355 1.40355i 0.615104 0.788446i \(-0.289114\pi\)
0.788446 0.615104i \(-0.210886\pi\)
\(158\) 0.933375 0.147832i 0.0742553 0.0117609i
\(159\) 6.81045 + 8.01312i 0.540104 + 0.635482i
\(160\) 0 0
\(161\) −3.15239 + 1.02427i −0.248443 + 0.0807240i
\(162\) −1.49373 + 8.87518i −0.117358 + 0.697300i
\(163\) −1.79029 + 0.912200i −0.140227 + 0.0714490i −0.522696 0.852519i \(-0.675074\pi\)
0.382469 + 0.923968i \(0.375074\pi\)
\(164\) −0.501139 1.54235i −0.0391324 0.120437i
\(165\) 0 0
\(166\) 2.33760 7.19438i 0.181433 0.558392i
\(167\) 2.32146 + 14.6571i 0.179640 + 1.13420i 0.898477 + 0.439021i \(0.144675\pi\)
−0.718837 + 0.695179i \(0.755325\pi\)
\(168\) 0.857043 + 3.60821i 0.0661223 + 0.278379i
\(169\) −6.98518 + 9.61428i −0.537322 + 0.739560i
\(170\) 0 0
\(171\) −14.3780 7.41367i −1.09951 0.566937i
\(172\) −0.295415 + 1.86518i −0.0225252 + 0.142218i
\(173\) 4.46800 + 2.27656i 0.339696 + 0.173084i 0.615514 0.788126i \(-0.288949\pi\)
−0.275818 + 0.961210i \(0.588949\pi\)
\(174\) −6.70263 4.12968i −0.508125 0.313070i
\(175\) 0 0
\(176\) 5.91761i 0.446057i
\(177\) −6.53772 10.7267i −0.491405 0.806265i
\(178\) 8.54762 + 1.35381i 0.640672 + 0.101472i
\(179\) −2.56353 + 1.86252i −0.191607 + 0.139211i −0.679453 0.733719i \(-0.737783\pi\)
0.487846 + 0.872930i \(0.337783\pi\)
\(180\) 0 0
\(181\) −5.04884 3.66820i −0.375278 0.272655i 0.384118 0.923284i \(-0.374505\pi\)
−0.759396 + 0.650629i \(0.774505\pi\)
\(182\) 1.59951 + 1.59951i 0.118563 + 0.118563i
\(183\) −6.77345 2.82484i −0.500707 0.208818i
\(184\) 1.47228 + 0.478373i 0.108538 + 0.0352661i
\(185\) 0 0
\(186\) 4.35392 17.9443i 0.319245 1.31574i
\(187\) 15.4553 + 30.3327i 1.13020 + 2.21815i
\(188\) −2.18372 4.28579i −0.159264 0.312573i
\(189\) −10.8369 + 2.51881i −0.788270 + 0.183216i
\(190\) 0 0
\(191\) 19.9806 + 6.49209i 1.44574 + 0.469751i 0.923683 0.383157i \(-0.125163\pi\)
0.522062 + 0.852908i \(0.325163\pi\)
\(192\) 0.666690 1.59860i 0.0481142 0.115369i
\(193\) −7.00922 7.00922i −0.504535 0.504535i 0.408309 0.912844i \(-0.366119\pi\)
−0.912844 + 0.408309i \(0.866119\pi\)
\(194\) 9.76009 + 7.09112i 0.700734 + 0.509113i
\(195\) 0 0
\(196\) 1.95413 1.41976i 0.139580 0.101411i
\(197\) 10.0821 + 1.59685i 0.718320 + 0.113771i 0.504885 0.863186i \(-0.331535\pi\)
0.213435 + 0.976957i \(0.431535\pi\)
\(198\) 17.7526 + 0.0857583i 1.26162 + 0.00609458i
\(199\) 15.1147i 1.07146i −0.844391 0.535728i \(-0.820037\pi\)
0.844391 0.535728i \(-0.179963\pi\)
\(200\) 0 0
\(201\) 1.17784 1.91169i 0.0830786 0.134840i
\(202\) 0.276463 + 0.140865i 0.0194519 + 0.00991123i
\(203\) 1.52246 9.61241i 0.106856 0.674659i
\(204\) 0.757790 + 9.93538i 0.0530559 + 0.695616i
\(205\) 0 0
\(206\) 5.19267 7.14709i 0.361790 0.497962i
\(207\) −1.45644 + 4.40986i −0.101229 + 0.306506i
\(208\) −0.165266 1.04345i −0.0114592 0.0723503i
\(209\) −9.86055 + 30.3476i −0.682068 + 2.09919i
\(210\) 0 0
\(211\) −1.22728 3.77719i −0.0844897 0.260033i 0.899883 0.436132i \(-0.143652\pi\)
−0.984372 + 0.176099i \(0.943652\pi\)
\(212\) 5.40982 2.75644i 0.371548 0.189313i
\(213\) 7.04585 + 0.571647i 0.482774 + 0.0391686i
\(214\) −5.63809 + 1.83193i −0.385412 + 0.125228i
\(215\) 0 0
\(216\) 4.78608 + 2.02321i 0.325652 + 0.137662i
\(217\) 22.5454 3.57084i 1.53048 0.242404i
\(218\) 1.33473 1.33473i 0.0903996 0.0903996i
\(219\) 0.205992 + 0.500725i 0.0139196 + 0.0338359i
\(220\) 0 0
\(221\) 3.57235 + 4.91692i 0.240302 + 0.330748i
\(222\) −0.249419 + 0.290608i −0.0167399 + 0.0195043i
\(223\) 6.07755 11.9279i 0.406983 0.798748i −0.592996 0.805205i \(-0.702055\pi\)
0.999979 + 0.00645660i \(0.00205521\pi\)
\(224\) 2.14116 0.143062
\(225\) 0 0
\(226\) 8.48225 0.564231
\(227\) 0.388579 0.762629i 0.0257909 0.0506175i −0.877752 0.479116i \(-0.840957\pi\)
0.903542 + 0.428499i \(0.140957\pi\)
\(228\) −6.08278 + 7.08729i −0.402842 + 0.469367i
\(229\) −9.72545 13.3859i −0.642676 0.884567i 0.356079 0.934456i \(-0.384113\pi\)
−0.998755 + 0.0498887i \(0.984113\pi\)
\(230\) 0 0
\(231\) 8.34939 + 20.2957i 0.549350 + 1.33536i
\(232\) −3.21402 + 3.21402i −0.211011 + 0.211011i
\(233\) −5.38346 + 0.852656i −0.352682 + 0.0558593i −0.330262 0.943889i \(-0.607137\pi\)
−0.0224200 + 0.999749i \(0.507137\pi\)
\(234\) 3.13271 0.480671i 0.204792 0.0314225i
\(235\) 0 0
\(236\) −6.89769 + 2.24119i −0.449001 + 0.145889i
\(237\) 1.63144 + 0.132363i 0.105974 + 0.00859790i
\(238\) −10.9752 + 5.59216i −0.711418 + 0.362486i
\(239\) 2.69306 + 8.28837i 0.174199 + 0.536130i 0.999596 0.0284230i \(-0.00904853\pi\)
−0.825397 + 0.564553i \(0.809049\pi\)
\(240\) 0 0
\(241\) −7.85699 + 24.1813i −0.506113 + 1.55766i 0.292779 + 0.956180i \(0.405420\pi\)
−0.798892 + 0.601475i \(0.794580\pi\)
\(242\) −3.75726 23.7224i −0.241526 1.52494i
\(243\) −6.13893 + 14.3288i −0.393813 + 0.919191i
\(244\) −2.49051 + 3.42789i −0.159439 + 0.219448i
\(245\) 0 0
\(246\) −0.213620 2.80077i −0.0136199 0.178570i
\(247\) −0.891162 + 5.62657i −0.0567033 + 0.358010i
\(248\) −9.49882 4.83989i −0.603176 0.307333i
\(249\) 6.87290 11.1550i 0.435552 0.706918i
\(250\) 0 0
\(251\) 21.0935i 1.33141i 0.746215 + 0.665706i \(0.231869\pi\)
−0.746215 + 0.665706i \(0.768131\pi\)
\(252\) −0.0310298 + 6.42341i −0.00195469 + 0.404637i
\(253\) 9.04796 + 1.43306i 0.568840 + 0.0900954i
\(254\) −8.46113 + 6.14737i −0.530898 + 0.385720i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −11.8588 11.8588i −0.739734 0.739734i 0.232792 0.972526i \(-0.425214\pi\)
−0.972526 + 0.232792i \(0.925214\pi\)
\(258\) −1.25900 + 3.01884i −0.0783816 + 0.187945i
\(259\) −0.450251 0.146295i −0.0279772 0.00909035i
\(260\) 0 0
\(261\) −9.59537 9.68852i −0.593938 0.599704i
\(262\) −8.86724 17.4029i −0.547820 1.07516i
\(263\) 10.3291 + 20.2720i 0.636919 + 1.25002i 0.953481 + 0.301453i \(0.0974715\pi\)
−0.316562 + 0.948572i \(0.602529\pi\)
\(264\) 2.41679 9.96060i 0.148743 0.613033i
\(265\) 0 0
\(266\) −10.9806 3.56783i −0.673266 0.218757i
\(267\) 13.8346 + 5.76965i 0.846662 + 0.353097i
\(268\) −0.916684 0.916684i −0.0559954 0.0559954i
\(269\) −8.37684 6.08613i −0.510745 0.371078i 0.302361 0.953193i \(-0.402225\pi\)
−0.813106 + 0.582115i \(0.802225\pi\)
\(270\) 0 0
\(271\) −0.517312 + 0.375849i −0.0314245 + 0.0228312i −0.603387 0.797449i \(-0.706182\pi\)
0.571962 + 0.820280i \(0.306182\pi\)
\(272\) 5.68203 + 0.899945i 0.344524 + 0.0545672i
\(273\) 2.03906 + 3.34556i 0.123410 + 0.202482i
\(274\) 11.9899i 0.724336i
\(275\) 0 0
\(276\) 2.28279 + 1.40649i 0.137408 + 0.0846608i
\(277\) −27.0524 13.7839i −1.62542 0.828193i −0.998805 0.0488650i \(-0.984440\pi\)
−0.626616 0.779328i \(-0.715560\pi\)
\(278\) 3.64035 22.9843i 0.218334 1.37851i
\(279\) 14.6572 28.4260i 0.877501 1.70182i
\(280\) 0 0
\(281\) 12.7646 17.5690i 0.761473 1.04808i −0.235617 0.971846i \(-0.575711\pi\)
0.997090 0.0762322i \(-0.0242890\pi\)
\(282\) −1.92532 8.10574i −0.114651 0.482690i
\(283\) −0.541258 3.41737i −0.0321745 0.203142i 0.966365 0.257176i \(-0.0827920\pi\)
−0.998539 + 0.0540343i \(0.982792\pi\)
\(284\) 1.26119 3.88154i 0.0748378 0.230327i
\(285\) 0 0
\(286\) −1.93188 5.94572i −0.114235 0.351578i
\(287\) 3.09390 1.57642i 0.182627 0.0930531i
\(288\) 1.77506 2.41850i 0.104596 0.142512i
\(289\) −15.3076 + 4.97374i −0.900446 + 0.292573i
\(290\) 0 0
\(291\) 13.5323 + 15.9219i 0.793275 + 0.933361i
\(292\) 0.308752 0.0489016i 0.0180684 0.00286175i
\(293\) −12.2527 + 12.2527i −0.715808 + 0.715808i −0.967744 0.251936i \(-0.918933\pi\)
0.251936 + 0.967744i \(0.418933\pi\)
\(294\) 3.86905 1.59167i 0.225647 0.0928283i
\(295\) 0 0
\(296\) 0.129962 + 0.178878i 0.00755391 + 0.0103971i
\(297\) 29.8464 + 7.39463i 1.73187 + 0.429080i
\(298\) −6.68004 + 13.1103i −0.386964 + 0.759460i
\(299\) 1.63544 0.0945802
\(300\) 0 0
\(301\) −4.04342 −0.233059
\(302\) −3.88107 + 7.61703i −0.223330 + 0.438311i
\(303\) 0.407816 + 0.350015i 0.0234284 + 0.0201078i
\(304\) 3.16950 + 4.36244i 0.181783 + 0.250203i
\(305\) 0 0
\(306\) −2.78215 + 17.0328i −0.159045 + 0.973703i
\(307\) −16.8133 + 16.8133i −0.959588 + 0.959588i −0.999215 0.0396263i \(-0.987383\pi\)
0.0396263 + 0.999215i \(0.487383\pi\)
\(308\) 12.5146 1.98211i 0.713083 0.112941i
\(309\) 11.6593 9.90936i 0.663273 0.563724i
\(310\) 0 0
\(311\) 7.39905 2.40410i 0.419562 0.136324i −0.0916250 0.995794i \(-0.529206\pi\)
0.511187 + 0.859470i \(0.329206\pi\)
\(312\) 0.147973 1.82384i 0.00837732 0.103255i
\(313\) −18.5326 + 9.44284i −1.04753 + 0.533741i −0.891033 0.453939i \(-0.850019\pi\)
−0.156492 + 0.987679i \(0.550019\pi\)
\(314\) −7.68555 23.6537i −0.433721 1.33486i
\(315\) 0 0
\(316\) 0.292024 0.898757i 0.0164276 0.0505590i
\(317\) −0.0339077 0.214085i −0.00190445 0.0120242i 0.986718 0.162444i \(-0.0519376\pi\)
−0.988622 + 0.150419i \(0.951938\pi\)
\(318\) 10.2316 2.43027i 0.573761 0.136283i
\(319\) −15.8099 + 21.7604i −0.885183 + 1.21835i
\(320\) 0 0
\(321\) −10.2383 + 0.780892i −0.571445 + 0.0435852i
\(322\) −0.518520 + 3.27381i −0.0288960 + 0.182442i
\(323\) −27.6399 14.0832i −1.53793 0.783612i
\(324\) 7.22970 + 5.36017i 0.401650 + 0.297787i
\(325\) 0 0
\(326\) 2.00929i 0.111284i
\(327\) 2.79176 1.70153i 0.154384 0.0940947i
\(328\) −1.60175 0.253693i −0.0884421 0.0140078i
\(329\) 8.33214 6.05366i 0.459366 0.333749i
\(330\) 0 0
\(331\) 5.81535 + 4.22510i 0.319640 + 0.232232i 0.736022 0.676958i \(-0.236702\pi\)
−0.416382 + 0.909190i \(0.636702\pi\)
\(332\) −5.34899 5.34899i −0.293564 0.293564i
\(333\) −0.538511 + 0.387290i −0.0295102 + 0.0212234i
\(334\) 14.1135 + 4.58575i 0.772255 + 0.250921i
\(335\) 0 0
\(336\) 3.60403 + 0.874463i 0.196616 + 0.0477058i
\(337\) −3.06621 6.01777i −0.167027 0.327809i 0.792288 0.610147i \(-0.208890\pi\)
−0.959315 + 0.282339i \(0.908890\pi\)
\(338\) 5.39518 + 10.5886i 0.293459 + 0.575946i
\(339\) 14.2774 + 3.46420i 0.775443 + 0.188150i
\(340\) 0 0
\(341\) −59.9987 19.4947i −3.24911 1.05570i
\(342\) −13.1331 + 9.44517i −0.710157 + 0.510736i
\(343\) 14.2552 + 14.2552i 0.769710 + 0.769710i
\(344\) 1.52777 + 1.10999i 0.0823718 + 0.0598466i
\(345\) 0 0
\(346\) 4.05686 2.94748i 0.218098 0.158458i
\(347\) −4.52113 0.716076i −0.242707 0.0384410i 0.0338958 0.999425i \(-0.489209\pi\)
−0.276603 + 0.960984i \(0.589209\pi\)
\(348\) −6.72250 + 4.09725i −0.360364 + 0.219636i
\(349\) 9.78119i 0.523575i −0.965126 0.261787i \(-0.915688\pi\)
0.965126 0.261787i \(-0.0843120\pi\)
\(350\) 0 0
\(351\) 5.46932 + 0.470345i 0.291931 + 0.0251052i
\(352\) −5.27263 2.68654i −0.281032 0.143193i
\(353\) 1.69571 10.7063i 0.0902538 0.569840i −0.900573 0.434704i \(-0.856853\pi\)
0.990827 0.135136i \(-0.0431471\pi\)
\(354\) −12.5256 + 0.955350i −0.665727 + 0.0507763i
\(355\) 0 0
\(356\) 5.08679 7.00137i 0.269600 0.371072i
\(357\) −20.7575 + 4.93044i −1.09860 + 0.260947i
\(358\) 0.495694 + 3.12969i 0.0261982 + 0.165409i
\(359\) 6.51044 20.0371i 0.343608 1.05752i −0.618717 0.785614i \(-0.712347\pi\)
0.962325 0.271902i \(-0.0876527\pi\)
\(360\) 0 0
\(361\) −3.11386 9.58347i −0.163887 0.504393i
\(362\) −5.56052 + 2.83323i −0.292254 + 0.148911i
\(363\) 3.36411 41.4644i 0.176570 2.17632i
\(364\) 2.15133 0.699010i 0.112760 0.0366381i
\(365\) 0 0
\(366\) −5.59203 + 4.75273i −0.292300 + 0.248429i
\(367\) −26.6770 + 4.22522i −1.39253 + 0.220555i −0.807218 0.590254i \(-0.799028\pi\)
−0.585311 + 0.810809i \(0.699028\pi\)
\(368\) 1.09463 1.09463i 0.0570618 0.0570618i
\(369\) 0.784283 4.80153i 0.0408281 0.249958i
\(370\) 0 0
\(371\) 7.64135 + 10.5174i 0.396719 + 0.546037i
\(372\) −14.0119 12.0259i −0.726483 0.623516i
\(373\) −12.1464 + 23.8387i −0.628917 + 1.23432i 0.328197 + 0.944609i \(0.393559\pi\)
−0.957114 + 0.289711i \(0.906441\pi\)
\(374\) 34.0432 1.76033
\(375\) 0 0
\(376\) −4.81005 −0.248060
\(377\) −2.18003 + 4.27854i −0.112277 + 0.220356i
\(378\) −2.67559 + 10.7993i −0.137617 + 0.555455i
\(379\) 9.28018 + 12.7731i 0.476691 + 0.656109i 0.977865 0.209238i \(-0.0670983\pi\)
−0.501174 + 0.865347i \(0.667098\pi\)
\(380\) 0 0
\(381\) −16.7525 + 6.89175i −0.858257 + 0.353075i
\(382\) 14.8555 14.8555i 0.760073 0.760073i
\(383\) 15.7705 2.49780i 0.805836 0.127632i 0.260092 0.965584i \(-0.416247\pi\)
0.545744 + 0.837952i \(0.316247\pi\)
\(384\) −1.12169 1.31977i −0.0572411 0.0673495i
\(385\) 0 0
\(386\) −9.42739 + 3.06314i −0.479841 + 0.155910i
\(387\) −3.35207 + 4.56717i −0.170395 + 0.232162i
\(388\) 10.7492 5.47700i 0.545709 0.278053i
\(389\) 3.56490 + 10.9716i 0.180748 + 0.556284i 0.999849 0.0173647i \(-0.00552762\pi\)
−0.819102 + 0.573648i \(0.805528\pi\)
\(390\) 0 0
\(391\) −2.75201 + 8.46982i −0.139175 + 0.428337i
\(392\) −0.377857 2.38569i −0.0190847 0.120496i
\(393\) −7.81799 32.9143i −0.394365 1.66031i
\(394\) 5.99998 8.25827i 0.302275 0.416046i
\(395\) 0 0
\(396\) 8.13594 15.7788i 0.408846 0.792913i
\(397\) 3.27643 20.6866i 0.164439 1.03823i −0.758047 0.652200i \(-0.773846\pi\)
0.922486 0.386030i \(-0.126154\pi\)
\(398\) −13.4673 6.86195i −0.675057 0.343958i
\(399\) −17.0256 10.4900i −0.852348 0.525155i
\(400\) 0 0
\(401\) 24.4394i 1.22045i 0.792229 + 0.610223i \(0.208920\pi\)
−0.792229 + 0.610223i \(0.791080\pi\)
\(402\) −1.16859 1.91735i −0.0582842 0.0956289i
\(403\) −11.1240 1.76187i −0.554125 0.0877648i
\(404\) 0.251023 0.182379i 0.0124889 0.00907370i
\(405\) 0 0
\(406\) −7.87354 5.72046i −0.390757 0.283902i
\(407\) 0.925189 + 0.925189i 0.0458599 + 0.0458599i
\(408\) 9.19652 + 3.83537i 0.455296 + 0.189879i
\(409\) −9.31361 3.02618i −0.460528 0.149635i 0.0695588 0.997578i \(-0.477841\pi\)
−0.530087 + 0.847943i \(0.677841\pi\)
\(410\) 0 0
\(411\) −4.89675 + 20.1816i −0.241539 + 0.995483i
\(412\) −4.01069 7.87141i −0.197592 0.387797i
\(413\) −7.05006 13.8365i −0.346911 0.680851i
\(414\) 3.26800 + 3.29973i 0.160614 + 0.162173i
\(415\) 0 0
\(416\) −1.00475 0.326463i −0.0492619 0.0160062i
\(417\) 15.5144 37.2007i 0.759744 1.82173i
\(418\) 22.5634 + 22.5634i 1.10361 + 1.10361i
\(419\) −20.8723 15.1646i −1.01968 0.740840i −0.0534618 0.998570i \(-0.517026\pi\)
−0.966217 + 0.257730i \(0.917026\pi\)
\(420\) 0 0
\(421\) −31.8859 + 23.1664i −1.55402 + 1.12906i −0.613316 + 0.789837i \(0.710165\pi\)
−0.940705 + 0.339225i \(0.889835\pi\)
\(422\) −3.92268 0.621291i −0.190953 0.0302440i
\(423\) 0.0697075 14.4300i 0.00338930 0.701610i
\(424\) 6.07158i 0.294862i
\(425\) 0 0
\(426\) 3.70809 6.01838i 0.179658 0.291591i
\(427\) −8.08350 4.11875i −0.391188 0.199320i
\(428\) −0.927381 + 5.85525i −0.0448267 + 0.283024i
\(429\) −0.823500 10.7969i −0.0397590 0.521280i
\(430\) 0 0
\(431\) −3.61295 + 4.97279i −0.174030 + 0.239531i −0.887118 0.461543i \(-0.847296\pi\)
0.713088 + 0.701074i \(0.247296\pi\)
\(432\) 3.97553 3.34591i 0.191273 0.160980i
\(433\) 2.61783 + 16.5283i 0.125805 + 0.794299i 0.967225 + 0.253919i \(0.0817197\pi\)
−0.841421 + 0.540380i \(0.818280\pi\)
\(434\) 7.05375 21.7092i 0.338591 1.04208i
\(435\) 0 0
\(436\) −0.583300 1.79521i −0.0279350 0.0859752i
\(437\) −7.43768 + 3.78968i −0.355792 + 0.181285i
\(438\) 0.539668 + 0.0437846i 0.0257863 + 0.00209211i
\(439\) −19.1311 + 6.21606i −0.913076 + 0.296676i −0.727623 0.685977i \(-0.759375\pi\)
−0.185453 + 0.982653i \(0.559375\pi\)
\(440\) 0 0
\(441\) 7.16248 1.09898i 0.341070 0.0523326i
\(442\) 6.00282 0.950753i 0.285525 0.0452227i
\(443\) −17.1571 + 17.1571i −0.815159 + 0.815159i −0.985402 0.170243i \(-0.945545\pi\)
0.170243 + 0.985402i \(0.445545\pi\)
\(444\) 0.145699 + 0.354167i 0.00691459 + 0.0168080i
\(445\) 0 0
\(446\) −7.86865 10.8303i −0.372591 0.512828i
\(447\) −16.5983 + 19.3393i −0.785071 + 0.914716i
\(448\) 0.972066 1.90779i 0.0459258 0.0901345i
\(449\) 15.9242 0.751511 0.375755 0.926719i \(-0.377383\pi\)
0.375755 + 0.926719i \(0.377383\pi\)
\(450\) 0 0
\(451\) −9.59671 −0.451891
\(452\) 3.85086 7.55774i 0.181129 0.355486i
\(453\) −9.64350 + 11.2360i −0.453091 + 0.527914i
\(454\) −0.503096 0.692453i −0.0236115 0.0324984i
\(455\) 0 0
\(456\) 3.55330 + 8.63736i 0.166398 + 0.404482i
\(457\) −2.30257 + 2.30257i −0.107710 + 0.107710i −0.758908 0.651198i \(-0.774267\pi\)
0.651198 + 0.758908i \(0.274267\pi\)
\(458\) −16.3422 + 2.58835i −0.763621 + 0.120946i
\(459\) −11.6393 + 27.5337i −0.543274 + 1.28516i
\(460\) 0 0
\(461\) 9.43135 3.06443i 0.439262 0.142725i −0.0810333 0.996711i \(-0.525822\pi\)
0.520295 + 0.853987i \(0.325822\pi\)
\(462\) 21.8742 + 1.77471i 1.01768 + 0.0825668i
\(463\) 20.5992 10.4958i 0.957328 0.487783i 0.0957485 0.995406i \(-0.469476\pi\)
0.861580 + 0.507623i \(0.169476\pi\)
\(464\) 1.40458 + 4.32285i 0.0652059 + 0.200683i
\(465\) 0 0
\(466\) −1.68432 + 5.18379i −0.0780245 + 0.240135i
\(467\) 0.726976 + 4.58995i 0.0336405 + 0.212397i 0.998783 0.0493288i \(-0.0157082\pi\)
−0.965142 + 0.261726i \(0.915708\pi\)
\(468\) 0.993939 3.00948i 0.0459448 0.139113i
\(469\) 1.63156 2.24565i 0.0753383 0.103694i
\(470\) 0 0
\(471\) −3.27611 42.9530i −0.150955 1.97917i
\(472\) −1.13457 + 7.16336i −0.0522226 + 0.329721i
\(473\) 9.95697 + 5.07333i 0.457822 + 0.233272i
\(474\) 0.858596 1.39353i 0.0394366 0.0640072i
\(475\) 0 0
\(476\) 12.3178i 0.564585i
\(477\) 18.2145 + 0.0879897i 0.833986 + 0.00402877i
\(478\) 8.60761 + 1.36331i 0.393703 + 0.0623564i
\(479\) 12.7801 9.28530i 0.583939 0.424256i −0.256203 0.966623i \(-0.582472\pi\)
0.840142 + 0.542367i \(0.182472\pi\)
\(480\) 0 0
\(481\) 0.188977 + 0.137300i 0.00861660 + 0.00626032i
\(482\) 17.9787 + 17.9787i 0.818908 + 0.818908i
\(483\) −2.20982 + 5.29875i −0.100550 + 0.241101i
\(484\) −22.8426 7.42201i −1.03830 0.337364i
\(485\) 0 0
\(486\) 9.98001 + 11.9750i 0.452702 + 0.543195i
\(487\) −0.0615473 0.120793i −0.00278898 0.00547367i 0.889608 0.456725i \(-0.150978\pi\)
−0.892397 + 0.451252i \(0.850978\pi\)
\(488\) 1.92361 + 3.77529i 0.0870776 + 0.170899i
\(489\) −0.820608 + 3.38207i −0.0371092 + 0.152942i
\(490\) 0 0
\(491\) 8.65368 + 2.81175i 0.390535 + 0.126893i 0.497701 0.867349i \(-0.334178\pi\)
−0.107166 + 0.994241i \(0.534178\pi\)
\(492\) −2.59248 1.08119i −0.116878 0.0487436i
\(493\) −18.4898 18.4898i −0.832738 0.832738i
\(494\) 4.60873 + 3.34844i 0.207357 + 0.150654i
\(495\) 0 0
\(496\) −8.62475 + 6.26624i −0.387263 + 0.281363i
\(497\) 8.63111 + 1.36703i 0.387158 + 0.0613198i
\(498\) −6.81893 11.1881i −0.305564 0.501349i
\(499\) 27.5900i 1.23510i 0.786532 + 0.617549i \(0.211874\pi\)
−0.786532 + 0.617549i \(0.788126\pi\)
\(500\) 0 0
\(501\) 21.8831 + 13.4828i 0.977667 + 0.602368i
\(502\) 18.7945 + 9.57626i 0.838838 + 0.427409i
\(503\) 1.71307 10.8159i 0.0763820 0.482257i −0.919611 0.392829i \(-0.871496\pi\)
0.995993 0.0894274i \(-0.0285037\pi\)
\(504\) 5.70921 + 2.94381i 0.254308 + 0.131128i
\(505\) 0 0
\(506\) 5.38455 7.41120i 0.239372 0.329468i
\(507\) 4.75677 + 20.0263i 0.211256 + 0.889401i
\(508\) 1.63607 + 10.3298i 0.0725891 + 0.458309i
\(509\) −2.83257 + 8.71775i −0.125551 + 0.386407i −0.994001 0.109370i \(-0.965117\pi\)
0.868450 + 0.495777i \(0.165117\pi\)
\(510\) 0 0
\(511\) 0.206834 + 0.636570i 0.00914980 + 0.0281602i
\(512\) −0.891007 + 0.453990i −0.0393773 + 0.0200637i
\(513\) −25.9633 + 10.5346i −1.14631 + 0.465114i
\(514\) −15.9501 + 5.18250i −0.703529 + 0.228590i
\(515\) 0 0
\(516\) 2.11823 + 2.49230i 0.0932500 + 0.109717i
\(517\) −28.1136 + 4.45276i −1.23643 + 0.195832i
\(518\) −0.334760 + 0.334760i −0.0147085 + 0.0147085i
\(519\) 8.03233 3.30439i 0.352580 0.145047i
\(520\) 0 0
\(521\) 13.3932 + 18.4342i 0.586767 + 0.807615i 0.994417 0.105523i \(-0.0336517\pi\)
−0.407650 + 0.913138i \(0.633652\pi\)
\(522\) −12.9887 + 4.15104i −0.568502 + 0.181686i
\(523\) −16.3751 + 32.1380i −0.716035 + 1.40530i 0.189867 + 0.981810i \(0.439194\pi\)
−0.905902 + 0.423488i \(0.860806\pi\)
\(524\) −19.5318 −0.853250
\(525\) 0 0
\(526\) 22.7518 0.992025
\(527\) 27.8432 54.6453i 1.21287 2.38039i
\(528\) −7.77776 6.67539i −0.338484 0.290509i
\(529\) −12.1105 16.6686i −0.526542 0.724723i
\(530\) 0 0
\(531\) −21.4734 3.50747i −0.931866 0.152211i
\(532\) −8.16406 + 8.16406i −0.353957 + 0.353957i
\(533\) −1.69218 + 0.268016i −0.0732966 + 0.0116090i
\(534\) 11.4216 9.70732i 0.494259 0.420077i
\(535\) 0 0
\(536\) −1.23294 + 0.400605i −0.0532548 + 0.0173035i
\(537\) −0.443825 + 5.47038i −0.0191525 + 0.236064i
\(538\) −9.22579 + 4.70077i −0.397752 + 0.202665i
\(539\) −4.41696 13.5940i −0.190252 0.585536i
\(540\) 0 0
\(541\) 10.6711 32.8422i 0.458786 1.41200i −0.407847 0.913050i \(-0.633720\pi\)
0.866633 0.498947i \(-0.166280\pi\)
\(542\) 0.100029 + 0.631560i 0.00429663 + 0.0271278i
\(543\) −10.5166 + 2.49797i −0.451312 + 0.107198i
\(544\) 3.38144 4.65416i 0.144978 0.199545i
\(545\) 0 0
\(546\) 3.90663 0.297966i 0.167188 0.0127518i
\(547\) 3.53445 22.3156i 0.151122 0.954148i −0.789268 0.614049i \(-0.789540\pi\)
0.940390 0.340098i \(-0.110460\pi\)
\(548\) 10.6831 + 5.44330i 0.456359 + 0.232526i
\(549\) −11.3536 + 5.71604i −0.484561 + 0.243955i
\(550\) 0 0
\(551\) 24.5096i 1.04414i
\(552\) 2.28956 1.39545i 0.0974500 0.0593942i
\(553\) 1.99850 + 0.316532i 0.0849851 + 0.0134603i
\(554\) −24.5631 + 17.8461i −1.04358 + 0.758209i
\(555\) 0 0
\(556\) −18.8265 13.6782i −0.798420 0.580086i
\(557\) 3.76017 + 3.76017i 0.159323 + 0.159323i 0.782267 0.622943i \(-0.214063\pi\)
−0.622943 + 0.782267i \(0.714063\pi\)
\(558\) −18.6735 25.9647i −0.790513 1.09918i
\(559\) 1.89740 + 0.616502i 0.0802513 + 0.0260752i
\(560\) 0 0
\(561\) 57.3019 + 13.9034i 2.41929 + 0.587003i
\(562\) −9.85907 19.3495i −0.415880 0.816210i
\(563\) 11.0089 + 21.6061i 0.463969 + 0.910590i 0.997882 + 0.0650508i \(0.0207209\pi\)
−0.533913 + 0.845539i \(0.679279\pi\)
\(564\) −8.09634 1.96445i −0.340918 0.0827185i
\(565\) 0 0
\(566\) −3.29063 1.06919i −0.138315 0.0449414i
\(567\) −8.91407 + 17.0848i −0.374356 + 0.717493i
\(568\) −2.88591 2.88591i −0.121090 0.121090i
\(569\) 24.5934 + 17.8681i 1.03101 + 0.749071i 0.968510 0.248974i \(-0.0800934\pi\)
0.0624977 + 0.998045i \(0.480093\pi\)
\(570\) 0 0
\(571\) 4.57335 3.32274i 0.191389 0.139052i −0.487964 0.872864i \(-0.662260\pi\)
0.679353 + 0.733811i \(0.262260\pi\)
\(572\) −6.17473 0.977982i −0.258179 0.0408915i
\(573\) 31.0720 18.9379i 1.29805 0.791141i
\(574\) 3.47236i 0.144934i
\(575\) 0 0
\(576\) −1.34904 2.67957i −0.0562101 0.111649i
\(577\) 22.8994 + 11.6678i 0.953316 + 0.485739i 0.860223 0.509919i \(-0.170324\pi\)
0.0930933 + 0.995657i \(0.470324\pi\)
\(578\) −2.51787 + 15.8972i −0.104729 + 0.661236i
\(579\) −17.1193 + 1.30572i −0.711454 + 0.0542639i
\(580\) 0 0
\(581\) 9.52039 13.1037i 0.394972 0.543633i
\(582\) 20.3301 4.82891i 0.842708 0.200165i
\(583\) −5.62058 35.4869i −0.232781 1.46972i
\(584\) 0.0965991 0.297301i 0.00399730 0.0123024i
\(585\) 0 0
\(586\) 5.35461 + 16.4798i 0.221197 + 0.680773i
\(587\) 12.8802 6.56280i 0.531623 0.270876i −0.167506 0.985871i \(-0.553571\pi\)
0.699129 + 0.714995i \(0.253571\pi\)
\(588\) 0.338318 4.16995i 0.0139520 0.171966i
\(589\) 54.6723 17.7641i 2.25273 0.731957i
\(590\) 0 0
\(591\) 13.4720 11.4500i 0.554163 0.470990i
\(592\) 0.218383 0.0345885i 0.00897549 0.00142158i
\(593\) −27.1124 + 27.1124i −1.11337 + 1.11337i −0.120680 + 0.992691i \(0.538508\pi\)
−0.992691 + 0.120680i \(0.961492\pi\)
\(594\) 20.1387 23.2363i 0.826299 0.953396i
\(595\) 0 0
\(596\) 8.64870 + 11.9039i 0.354265 + 0.487603i
\(597\) −19.8659 17.0503i −0.813058 0.697821i
\(598\) 0.742476 1.45719i 0.0303621 0.0595890i
\(599\) −22.2597 −0.909506 −0.454753 0.890618i \(-0.650272\pi\)
−0.454753 + 0.890618i \(0.650272\pi\)
\(600\) 0 0
\(601\) −0.661317 −0.0269757 −0.0134878 0.999909i \(-0.504293\pi\)
−0.0134878 + 0.999909i \(0.504293\pi\)
\(602\) −1.83568 + 3.60272i −0.0748165 + 0.146836i
\(603\) −1.18393 3.70457i −0.0482135 0.150862i
\(604\) 5.02485 + 6.91612i 0.204458 + 0.281413i
\(605\) 0 0
\(606\) 0.497011 0.204463i 0.0201897 0.00830576i
\(607\) 25.2285 25.2285i 1.02399 1.02399i 0.0242876 0.999705i \(-0.492268\pi\)
0.999705 0.0242876i \(-0.00773174\pi\)
\(608\) 5.32589 0.843538i 0.215993 0.0342100i
\(609\) −10.9166 12.8444i −0.442362 0.520480i
\(610\) 0 0
\(611\) −4.83290 + 1.57031i −0.195518 + 0.0635278i
\(612\) 13.9133 + 10.2117i 0.562412 + 0.412782i
\(613\) 22.2583 11.3412i 0.899003 0.458065i 0.0575173 0.998345i \(-0.481682\pi\)
0.841485 + 0.540280i \(0.181682\pi\)
\(614\) 7.34770 + 22.6139i 0.296529 + 0.912623i
\(615\) 0 0
\(616\) 3.91542 12.0504i 0.157757 0.485525i
\(617\) 4.87738 + 30.7946i 0.196356 + 1.23974i 0.867131 + 0.498081i \(0.165962\pi\)
−0.670775 + 0.741661i \(0.734038\pi\)
\(618\) −3.53610 14.8873i −0.142243 0.598853i
\(619\) 2.12975 2.93135i 0.0856019 0.117821i −0.764068 0.645135i \(-0.776801\pi\)
0.849670 + 0.527314i \(0.176801\pi\)
\(620\) 0 0
\(621\) 4.15311 + 6.88882i 0.166659 + 0.276439i
\(622\) 1.21703 7.68404i 0.0487985 0.308102i
\(623\) 16.5103 + 8.41243i 0.661472 + 0.337037i
\(624\) −1.55788 0.959853i −0.0623651 0.0384249i
\(625\) 0 0
\(626\) 20.7996i 0.831321i
\(627\) 28.7639 + 47.1939i 1.14872 + 1.88474i
\(628\) −24.5648 3.89068i −0.980241 0.155255i
\(629\) −1.02906 + 0.747655i −0.0410312 + 0.0298109i
\(630\) 0 0
\(631\) 4.12680 + 2.99829i 0.164285 + 0.119360i 0.666890 0.745156i \(-0.267625\pi\)
−0.502605 + 0.864516i \(0.667625\pi\)
\(632\) −0.668222 0.668222i −0.0265805 0.0265805i
\(633\) −6.34896 2.64781i −0.252349 0.105241i
\(634\) −0.206145 0.0669805i −0.00818706 0.00266014i
\(635\) 0 0
\(636\) 2.47967 10.2198i 0.0983253 0.405240i
\(637\) −1.15849 2.27367i −0.0459012 0.0900861i
\(638\) 12.2112 + 23.9657i 0.483444 + 0.948813i
\(639\) 8.69945 8.61580i 0.344145 0.340836i
\(640\) 0 0
\(641\) −45.1681 14.6760i −1.78403 0.579668i −0.784836 0.619703i \(-0.787253\pi\)
−0.999198 + 0.0400355i \(0.987253\pi\)
\(642\) −3.95230 + 9.47689i −0.155985 + 0.374023i
\(643\) 17.9186 + 17.9186i 0.706639 + 0.706639i 0.965827 0.259188i \(-0.0834550\pi\)
−0.259188 + 0.965827i \(0.583455\pi\)
\(644\) 2.68158 + 1.94828i 0.105669 + 0.0767731i
\(645\) 0 0
\(646\) −25.0965 + 18.2337i −0.987409 + 0.717395i
\(647\) −7.06356 1.11876i −0.277697 0.0439829i 0.0160323 0.999871i \(-0.494897\pi\)
−0.293730 + 0.955889i \(0.594897\pi\)
\(648\) 8.05816 4.00825i 0.316554 0.157459i
\(649\) 42.9184i 1.68469i
\(650\) 0 0
\(651\) 20.7391 33.6604i 0.812831 1.31926i
\(652\) 1.79029 + 0.912200i 0.0701133 + 0.0357245i
\(653\) 3.64054 22.9855i 0.142465 0.899490i −0.808118 0.589021i \(-0.799514\pi\)
0.950583 0.310470i \(-0.100486\pi\)
\(654\) −0.248642 3.25995i −0.00972269 0.127474i
\(655\) 0 0
\(656\) −0.953223 + 1.31200i −0.0372171 + 0.0512250i
\(657\) 0.890494 + 0.294102i 0.0347415 + 0.0114740i
\(658\) −1.61113 10.1723i −0.0628085 0.396557i
\(659\) −1.14382 + 3.52031i −0.0445568 + 0.137132i −0.970860 0.239647i \(-0.922968\pi\)
0.926303 + 0.376779i \(0.122968\pi\)
\(660\) 0 0
\(661\) −11.4157 35.1339i −0.444019 1.36655i −0.883556 0.468326i \(-0.844857\pi\)
0.439537 0.898224i \(-0.355143\pi\)
\(662\) 6.40470 3.26336i 0.248926 0.126834i
\(663\) 10.4923 + 0.851267i 0.407488 + 0.0330605i
\(664\) −7.19438 + 2.33760i −0.279196 + 0.0907163i
\(665\) 0 0
\(666\) 0.100599 + 0.655643i 0.00389815 + 0.0254056i
\(667\) −6.94972 + 1.10073i −0.269094 + 0.0426203i
\(668\) 10.4933 10.4933i 0.405999 0.405999i
\(669\) −8.82147 21.4432i −0.341058 0.829044i
\(670\) 0 0
\(671\) 14.7379 + 20.2849i 0.568949 + 0.783092i
\(672\) 2.41535 2.81421i 0.0931740 0.108561i
\(673\) 0.542210 1.06415i 0.0209006 0.0410198i −0.880320 0.474380i \(-0.842672\pi\)
0.901221 + 0.433360i \(0.142672\pi\)
\(674\) −6.75390 −0.260151
\(675\) 0 0
\(676\) 11.8839 0.457073
\(677\) −15.6087 + 30.6338i −0.599892 + 1.17735i 0.368898 + 0.929470i \(0.379735\pi\)
−0.968790 + 0.247884i \(0.920265\pi\)
\(678\) 9.56844 11.1486i 0.367474 0.428158i
\(679\) 15.1832 + 20.8979i 0.582679 + 0.801988i
\(680\) 0 0
\(681\) −0.564016 1.37101i −0.0216132 0.0525373i
\(682\) −44.6088 + 44.6088i −1.70816 + 1.70816i
\(683\) 44.5125 7.05008i 1.70322 0.269764i 0.772373 0.635169i \(-0.219070\pi\)
0.930849 + 0.365405i \(0.119070\pi\)
\(684\) 2.45340 + 15.9897i 0.0938081 + 0.611382i
\(685\) 0 0
\(686\) 19.1733 6.22977i 0.732038 0.237854i
\(687\) −28.5645 2.31751i −1.08980 0.0884185i
\(688\) 1.68260 0.857327i 0.0641485 0.0326853i
\(689\) −1.98215 6.10043i −0.0755138 0.232408i
\(690\) 0 0
\(691\) 1.10289 3.39434i 0.0419558 0.129127i −0.927885 0.372867i \(-0.878375\pi\)
0.969840 + 0.243741i \(0.0783746\pi\)
\(692\) −0.784450 4.95282i −0.0298203 0.188278i
\(693\) 36.0941 + 11.9207i 1.37110 + 0.452832i
\(694\) −2.69058 + 3.70326i −0.102133 + 0.140574i
\(695\) 0 0
\(696\) 0.598727 + 7.84991i 0.0226947 + 0.297550i
\(697\) 1.45946 9.21466i 0.0552809 0.349030i
\(698\) −8.71510 4.44057i −0.329871 0.168078i
\(699\) −4.95215 + 8.03754i −0.187308 + 0.304008i
\(700\) 0 0
\(701\) 19.6139i 0.740807i −0.928871 0.370403i \(-0.879219\pi\)
0.928871 0.370403i \(-0.120781\pi\)
\(702\) 2.90210 4.65967i 0.109533 0.175868i
\(703\) −1.17758 0.186511i −0.0444133 0.00703438i
\(704\) −4.78745 + 3.47829i −0.180434 + 0.131093i
\(705\) 0 0
\(706\) −8.76956 6.37146i −0.330047 0.239793i
\(707\) 0.469776 + 0.469776i 0.0176677 + 0.0176677i
\(708\) −4.83527 + 11.5941i −0.181721 + 0.435733i
\(709\) −22.4237 7.28590i −0.842140 0.273628i −0.143990 0.989579i \(-0.545993\pi\)
−0.698150 + 0.715951i \(0.745993\pi\)
\(710\) 0 0
\(711\) 2.01433 1.99496i 0.0755432 0.0748168i
\(712\) −3.92891 7.71092i −0.147242 0.288979i
\(713\) −7.49238 14.7046i −0.280592 0.550692i
\(714\) −5.03066 + 20.7335i −0.188268 + 0.775930i
\(715\) 0 0
\(716\) 3.01361 + 0.979183i 0.112624 + 0.0365938i
\(717\) 13.9317 + 5.81015i 0.520287 + 0.216984i
\(718\) −14.8975 14.8975i −0.555969 0.555969i
\(719\) 30.2210 + 21.9569i 1.12705 + 0.818853i 0.985263 0.171044i \(-0.0547140\pi\)
0.141791 + 0.989897i \(0.454714\pi\)
\(720\) 0 0
\(721\) 15.3031 11.1183i 0.569916 0.414068i
\(722\) −9.95259 1.57634i −0.370397 0.0586651i
\(723\) 22.9194 + 37.6046i 0.852381 + 1.39853i
\(724\) 6.24071i 0.231934i
\(725\) 0 0
\(726\) −35.4178 21.8219i −1.31448 0.809886i
\(727\) 37.8579 + 19.2896i 1.40407 + 0.715411i 0.981597 0.190964i \(-0.0611612\pi\)
0.422476 + 0.906374i \(0.361161\pi\)
\(728\) 0.353862 2.23419i 0.0131150 0.0828047i
\(729\) 11.9078 + 24.2323i 0.441031 + 0.897492i
\(730\) 0 0
\(731\) −6.38561 + 8.78903i −0.236180 + 0.325074i
\(732\) 1.69599 + 7.14023i 0.0626855 + 0.263911i
\(733\) 6.98056 + 44.0735i 0.257833 + 1.62789i 0.688398 + 0.725333i \(0.258314\pi\)
−0.430565 + 0.902559i \(0.641686\pi\)
\(734\) −8.34641 + 25.6876i −0.308072 + 0.948147i
\(735\) 0 0
\(736\) −0.478373 1.47228i −0.0176331 0.0542690i
\(737\) −6.83537 + 3.48279i −0.251784 + 0.128290i
\(738\) −3.92214 2.87865i −0.144376 0.105965i
\(739\) −8.01855 + 2.60538i −0.294967 + 0.0958406i −0.452762 0.891631i \(-0.649561\pi\)
0.157795 + 0.987472i \(0.449561\pi\)
\(740\) 0 0
\(741\) 6.38996 + 7.51837i 0.234741 + 0.276194i
\(742\) 12.8402 2.03368i 0.471378 0.0746589i
\(743\) 24.9192 24.9192i 0.914196 0.914196i −0.0824029 0.996599i \(-0.526259\pi\)
0.996599 + 0.0824029i \(0.0262594\pi\)
\(744\) −17.0765 + 7.02502i −0.626053 + 0.257550i
\(745\) 0 0
\(746\) 15.7261 + 21.6451i 0.575772 + 0.792482i
\(747\) −6.90844 21.6168i −0.252767 0.790916i
\(748\) 15.4553 30.3327i 0.565101 1.10907i
\(749\) −12.6933 −0.463804
\(750\) 0 0
\(751\) −8.40064 −0.306544 −0.153272 0.988184i \(-0.548981\pi\)
−0.153272 + 0.988184i \(0.548981\pi\)
\(752\) −2.18372 + 4.28579i −0.0796320 + 0.156287i
\(753\) 27.7241 + 23.7946i 1.01032 + 0.867125i
\(754\) 2.82250 + 3.88484i 0.102789 + 0.141477i
\(755\) 0 0
\(756\) 8.40754 + 7.28674i 0.305779 + 0.265016i
\(757\) −5.57829 + 5.57829i −0.202746 + 0.202746i −0.801176 0.598429i \(-0.795792\pi\)
0.598429 + 0.801176i \(0.295792\pi\)
\(758\) 15.5940 2.46985i 0.566400 0.0897089i
\(759\) 12.0901 10.2755i 0.438843 0.372978i
\(760\) 0 0
\(761\) −5.92036 + 1.92364i −0.214613 + 0.0697320i −0.414350 0.910118i \(-0.635991\pi\)
0.199737 + 0.979849i \(0.435991\pi\)
\(762\) −1.46488 + 18.0554i −0.0530669 + 0.654077i
\(763\) 3.60114 1.83487i 0.130370 0.0664268i
\(764\) −6.49209 19.9806i −0.234875 0.722872i
\(765\) 0 0
\(766\) 4.93411 15.1856i 0.178276 0.548679i
\(767\) 1.19862 + 7.56779i 0.0432796 + 0.273257i
\(768\) −1.68517 + 0.400270i −0.0608082 + 0.0144435i
\(769\) −2.22958 + 3.06876i −0.0804008 + 0.110662i −0.847323 0.531078i \(-0.821787\pi\)
0.766922 + 0.641740i \(0.221787\pi\)
\(770\) 0 0
\(771\) −28.9640 + 2.20914i −1.04311 + 0.0795601i
\(772\) −1.55066 + 9.79050i −0.0558096 + 0.352368i
\(773\) −30.3587 15.4685i −1.09193 0.556364i −0.187185 0.982325i \(-0.559936\pi\)
−0.904742 + 0.425960i \(0.859936\pi\)
\(774\) 2.54757 + 5.06017i 0.0915704 + 0.181884i
\(775\) 0 0
\(776\) 12.0641i 0.433077i
\(777\) −0.700189 + 0.426754i −0.0251192 + 0.0153097i
\(778\) 11.3942 + 1.80467i 0.408503 + 0.0647005i
\(779\) 7.07466 5.14004i 0.253476 0.184161i
\(780\) 0 0
\(781\) −19.5390 14.1959i −0.699159 0.507969i
\(782\) 6.29727 + 6.29727i 0.225190 + 0.225190i
\(783\)