Properties

Label 750.2.l.c.107.5
Level $750$
Weight $2$
Character 750.107
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 107.5
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.c.743.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.891007 - 0.453990i) q^{2} +(1.31434 + 1.12805i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.454984 + 2.96530i) q^{9} +O(q^{10})\) \(q+(-0.891007 - 0.453990i) q^{2} +(1.31434 + 1.12805i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(-1.51403 - 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.454984 + 2.96530i) q^{9} +(-5.62798 + 1.82864i) q^{11} +(-0.140065 + 1.72638i) q^{12} +(-0.479621 - 0.941310i) q^{13} +(0.661655 + 2.03636i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-5.68203 + 0.899945i) q^{17} +(0.940823 - 2.84866i) q^{18} +(-3.16950 + 4.36244i) q^{19} +(-0.282042 - 3.69786i) q^{21} +(5.84476 + 0.925718i) q^{22} +(0.702799 - 1.37932i) q^{23} +(0.908558 - 1.47463i) q^{24} +1.05646i q^{26} +(-2.74701 + 4.41066i) q^{27} +(0.334951 - 2.11480i) q^{28} +(-3.67723 + 2.67167i) q^{29} +(8.62475 + 6.26624i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-9.45990 - 3.94521i) q^{33} +(5.47129 + 1.77773i) q^{34} +(-2.13154 + 2.11105i) q^{36} +(-0.197006 + 0.100380i) q^{37} +(4.80455 - 2.44804i) q^{38} +(0.431463 - 1.77824i) q^{39} +(1.54235 + 0.501139i) q^{41} +(-1.42749 + 3.42286i) q^{42} +(1.33532 - 1.33532i) q^{43} +(-4.78745 - 3.47829i) q^{44} +(-1.25240 + 0.909919i) q^{46} +(0.752458 - 4.75083i) q^{47} +(-1.47900 + 0.901424i) q^{48} -2.41543i q^{49} +(-8.48331 - 5.22681i) q^{51} +(0.479621 - 0.941310i) q^{52} +(-5.99683 - 0.949805i) q^{53} +(4.45000 - 2.68281i) q^{54} +(-1.25854 + 1.73224i) q^{56} +(-9.08688 + 2.15837i) q^{57} +(4.48935 - 0.711043i) q^{58} +(-2.24119 + 6.89769i) q^{59} +(-1.30934 - 4.02973i) q^{61} +(-4.83989 - 9.49882i) q^{62} +(3.80069 - 5.17841i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(6.63774 + 7.80992i) q^{66} +(-0.202800 - 1.28043i) q^{67} +(-4.06788 - 4.06788i) q^{68} +(2.47967 - 1.02010i) q^{69} +(2.39892 + 3.30183i) q^{71} +(2.85761 - 0.913257i) q^{72} +(-0.278530 - 0.141918i) q^{73} +0.221105 q^{74} -5.39228 q^{76} +(11.2895 + 5.75231i) q^{77} +(-1.19174 + 1.38854i) q^{78} +(-0.555462 - 0.764528i) q^{79} +(-8.58598 + 2.69833i) q^{81} +(-1.14673 - 1.14673i) q^{82} +(1.18337 + 7.47149i) q^{83} +(2.82585 - 2.40172i) q^{84} +(-1.79600 + 0.583556i) q^{86} +(-7.84692 - 0.636640i) q^{87} +(2.68654 + 5.27263i) q^{88} +(-2.67429 - 8.23061i) q^{89} +(-0.699010 + 2.15133i) q^{91} +(1.52899 - 0.242168i) q^{92} +(4.26719 + 17.9652i) q^{93} +(-2.82728 + 3.89142i) q^{94} +(1.72703 - 0.131724i) q^{96} +(11.9156 + 1.88725i) q^{97} +(-1.09658 + 2.15217i) q^{98} +(-7.98311 - 15.8566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + 4q^{3} + 4q^{7} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{7} + 16q^{12} + 20q^{16} - 8q^{18} + 40q^{19} + 4q^{22} - 56q^{27} + 4q^{28} - 96q^{33} + 40q^{34} - 64q^{37} + 40q^{39} - 4q^{42} - 24q^{43} + 16q^{48} - 64q^{57} + 20q^{58} + 4q^{63} - 104q^{67} - 140q^{69} + 8q^{72} - 60q^{73} - 60q^{78} - 80q^{79} - 40q^{81} + 96q^{82} - 60q^{84} + 80q^{87} + 24q^{88} + 12q^{93} - 12q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.891007 0.453990i −0.630037 0.321020i
\(3\) 1.31434 + 1.12805i 0.758835 + 0.651283i
\(4\) 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 \(-0.382604\pi\)
−0.932756 + 0.360507i \(0.882604\pi\)
\(8\) −0.156434 0.987688i −0.0553079 0.349201i
\(9\) 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 \(0.750778\pi\)
\(12\) −0.140065 + 1.72638i −0.0404334 + 0.498362i
\(13\) −0.479621 0.941310i −0.133023 0.261072i 0.814881 0.579628i \(-0.196802\pi\)
−0.947904 + 0.318556i \(0.896802\pi\)
\(14\) 0.661655 + 2.03636i 0.176835 + 0.544241i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −5.68203 + 0.899945i −1.37809 + 0.218269i −0.801125 0.598497i \(-0.795765\pi\)
−0.576969 + 0.816766i \(0.695765\pi\)
\(18\) 0.940823 2.84866i 0.221754 0.671435i
\(19\) −3.16950 + 4.36244i −0.727133 + 1.00081i 0.272123 + 0.962262i \(0.412274\pi\)
−0.999257 + 0.0385508i \(0.987726\pi\)
\(20\) 0 0
\(21\) −0.282042 3.69786i −0.0615467 0.806939i
\(22\) 5.84476 + 0.925718i 1.24611 + 0.197364i
\(23\) 0.702799 1.37932i 0.146544 0.287608i −0.806054 0.591843i \(-0.798401\pi\)
0.952597 + 0.304235i \(0.0984007\pi\)
\(24\) 0.908558 1.47463i 0.185459 0.301007i
\(25\) 0 0
\(26\) 1.05646i 0.207188i
\(27\) −2.74701 + 4.41066i −0.528663 + 0.848832i
\(28\) 0.334951 2.11480i 0.0632998 0.399659i
\(29\) −3.67723 + 2.67167i −0.682845 + 0.496116i −0.874300 0.485386i \(-0.838679\pi\)
0.191455 + 0.981501i \(0.438679\pi\)
\(30\) 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
\(33\) −9.45990 3.94521i −1.64676 0.686774i
\(34\) 5.47129 + 1.77773i 0.938319 + 0.304878i
\(35\) 0 0
\(36\) −2.13154 + 2.11105i −0.355257 + 0.351841i
\(37\) −0.197006 + 0.100380i −0.0323876 + 0.0165023i −0.470109 0.882608i \(-0.655786\pi\)
0.437722 + 0.899111i \(0.355786\pi\)
\(38\) 4.80455 2.44804i 0.779402 0.397125i
\(39\) 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 \(0.559582\pi\)
\(42\) −1.42749 + 3.42286i −0.220267 + 0.528159i
\(43\) 1.33532 1.33532i 0.203634 0.203634i −0.597921 0.801555i \(-0.704006\pi\)
0.801555 + 0.597921i \(0.204006\pi\)
\(44\) −4.78745 3.47829i −0.721735 0.524371i
\(45\) 0 0
\(46\) −1.25240 + 0.909919i −0.184656 + 0.134160i
\(47\) 0.752458 4.75083i 0.109757 0.692980i −0.870039 0.492983i \(-0.835907\pi\)
0.979796 0.199998i \(-0.0640935\pi\)
\(48\) −1.47900 + 0.901424i −0.213475 + 0.130109i
\(49\) 2.41543i 0.345062i
\(50\) 0 0
\(51\) −8.48331 5.22681i −1.18790 0.731899i
\(52\) 0.479621 0.941310i 0.0665115 0.130536i
\(53\) −5.99683 0.949805i −0.823728 0.130466i −0.269680 0.962950i \(-0.586918\pi\)
−0.554049 + 0.832484i \(0.686918\pi\)
\(54\) 4.45000 2.68281i 0.605569 0.365084i
\(55\) 0 0
\(56\) −1.25854 + 1.73224i −0.168180 + 0.231480i
\(57\) −9.08688 + 2.15837i −1.20359 + 0.285883i
\(58\) 4.48935 0.711043i 0.589480 0.0933645i
\(59\) −2.24119 + 6.89769i −0.291779 + 0.898002i 0.692506 + 0.721412i \(0.256507\pi\)
−0.984285 + 0.176590i \(0.943493\pi\)
\(60\) 0 0
\(61\) −1.30934 4.02973i −0.167644 0.515954i 0.831578 0.555408i \(-0.187438\pi\)
−0.999221 + 0.0394543i \(0.987438\pi\)
\(62\) −4.83989 9.49882i −0.614667 1.20635i
\(63\) 3.80069 5.17841i 0.478842 0.652418i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) 6.63774 + 7.80992i 0.817050 + 0.961334i
\(67\) −0.202800 1.28043i −0.0247759 0.156429i 0.972199 0.234158i \(-0.0752332\pi\)
−0.996975 + 0.0777287i \(0.975233\pi\)
\(68\) −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 \(0.722138\pi\)
\(72\) 2.85761 0.913257i 0.336773 0.107628i
\(73\) −0.278530 0.141918i −0.0325994 0.0166102i 0.437615 0.899163i \(-0.355823\pi\)
−0.470214 + 0.882552i \(0.655823\pi\)
\(74\) 0.221105 0.0257030
\(75\) 0 0
\(76\) −5.39228 −0.618537
\(77\) 11.2895 + 5.75231i 1.28656 + 0.655537i
\(78\) −1.19174 + 1.38854i −0.134938 + 0.157222i
\(79\) −0.555462 0.764528i −0.0624944 0.0860162i 0.776626 0.629962i \(-0.216930\pi\)
−0.839120 + 0.543946i \(0.816930\pi\)
\(80\) 0 0
\(81\) −8.58598 + 2.69833i −0.953998 + 0.299814i
\(82\) −1.14673 1.14673i −0.126635 0.126635i
\(83\) 1.18337 + 7.47149i 0.129891 + 0.820102i 0.963493 + 0.267735i \(0.0862752\pi\)
−0.833601 + 0.552367i \(0.813725\pi\)
\(84\) 2.82585 2.40172i 0.308325 0.262050i
\(85\) 0 0
\(86\) −1.79600 + 0.583556i −0.193668 + 0.0629264i
\(87\) −7.84692 0.636640i −0.841278 0.0682550i
\(88\) 2.68654 + 5.27263i 0.286386 + 0.562064i
\(89\) −2.67429 8.23061i −0.283474 0.872443i −0.986852 0.161627i \(-0.948326\pi\)
0.703378 0.710816i \(-0.251674\pi\)
\(90\) 0 0
\(91\) −0.699010 + 2.15133i −0.0732762 + 0.225521i
\(92\) 1.52899 0.242168i 0.159408 0.0252477i
\(93\) 4.26719 + 17.9652i 0.442487 + 1.86290i
\(94\) −2.82728 + 3.89142i −0.291612 + 0.401369i
\(95\) 0 0
\(96\) 1.72703 0.131724i 0.176265 0.0134440i
\(97\) 11.9156 + 1.88725i 1.20985 + 0.191621i 0.728584 0.684956i \(-0.240179\pi\)
0.481262 + 0.876577i \(0.340179\pi\)
\(98\) −1.09658 + 2.15217i −0.110772 + 0.217402i
\(99\) −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 \(0.995086\pi\)
\(102\) 5.18576 + 8.50846i 0.513467 + 0.842463i
\(103\) −1.38199 + 8.72553i −0.136171 + 0.859752i 0.821147 + 0.570717i \(0.193335\pi\)
−0.957318 + 0.289035i \(0.906665\pi\)
\(104\) −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 −0.880077 0.474831i \(-0.842509\pi\)
0.474831 + 0.880077i \(0.342509\pi\)
\(108\) −5.18295 + 0.370140i −0.498730 + 0.0356167i
\(109\) −1.79521 0.583300i −0.171950 0.0558700i 0.221777 0.975098i \(-0.428814\pi\)
−0.393727 + 0.919227i \(0.628814\pi\)
\(110\) 0 0
\(111\) −0.372167 0.0903007i −0.0353245 0.00857096i
\(112\) 1.90779 0.972066i 0.180269 0.0918516i
\(113\) −7.55774 + 3.85086i −0.710972 + 0.362258i −0.771779 0.635891i \(-0.780633\pi\)
0.0608066 + 0.998150i \(0.480633\pi\)
\(114\) 9.07635 + 2.20224i 0.850078 + 0.206258i
\(115\) 0 0
\(116\) −4.32285 1.40458i −0.401366 0.130412i
\(117\) 2.57304 1.85050i 0.237878 0.171079i
\(118\) 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
\(122\) −0.662830 + 4.18494i −0.0600098 + 0.378887i
\(123\) 1.46186 + 2.39852i 0.131811 + 0.216267i
\(124\) 10.6608i 0.957366i
\(125\) 0 0
\(126\) −5.73738 + 2.88852i −0.511127 + 0.257330i
\(127\) −4.74807 + 9.31862i −0.421323 + 0.826894i 0.578613 + 0.815602i \(0.303594\pi\)
−0.999936 + 0.0112913i \(0.996406\pi\)
\(128\) 0.987688 + 0.156434i 0.0873001 + 0.0138270i
\(129\) 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 \(-0.125372\pi\)
\(132\) −2.36864 9.97216i −0.206164 0.867965i
\(133\) 11.4036 1.80615i 0.988816 0.156613i
\(134\) −0.400605 + 1.23294i −0.0346070 + 0.106510i
\(135\) 0 0
\(136\) 1.77773 + 5.47129i 0.152439 + 0.469159i
\(137\) 5.44330 + 10.6831i 0.465053 + 0.912717i 0.997791 + 0.0664369i \(0.0211631\pi\)
−0.532738 + 0.846280i \(0.678837\pi\)
\(138\) −2.67251 0.216828i −0.227500 0.0184576i
\(139\) −22.1318 + 7.19107i −1.87720 + 0.609939i −0.888747 + 0.458399i \(0.848423\pi\)
−0.988451 + 0.151540i \(0.951577\pi\)
\(140\) 0 0
\(141\) 6.34819 5.39540i 0.534614 0.454375i
\(142\) −0.638455 4.03104i −0.0535779 0.338278i
\(143\) 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
\(147\) 2.72474 3.17470i 0.224733 0.261845i
\(148\) −0.197006 0.100380i −0.0161938 0.00825116i
\(149\) 14.7140 1.20542 0.602711 0.797960i \(-0.294087\pi\)
0.602711 + 0.797960i \(0.294087\pi\)
\(150\) 0 0
\(151\) −8.54879 −0.695691 −0.347845 0.937552i \(-0.613087\pi\)
−0.347845 + 0.937552i \(0.613087\pi\)
\(152\) 4.80455 + 2.44804i 0.389701 + 0.198562i
\(153\) −5.25384 16.4394i −0.424748 1.32905i
\(154\) −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 −0.788446 0.615104i \(-0.789114\pi\)
−0.615104 0.788446i \(-0.710886\pi\)
\(158\) 0.147832 + 0.933375i 0.0117609 + 0.0742553i
\(159\) −6.81045 8.01312i −0.540104 0.635482i
\(160\) 0 0
\(161\) −3.15239 + 1.02427i −0.248443 + 0.0807240i
\(162\) 8.87518 + 1.49373i 0.697300 + 0.117358i
\(163\) −0.912200 1.79029i −0.0714490 0.140227i 0.852519 0.522696i \(-0.175074\pi\)
−0.923968 + 0.382469i \(0.875074\pi\)
\(164\) 0.501139 + 1.54235i 0.0391324 + 0.120437i
\(165\) 0 0
\(166\) 2.33760 7.19438i 0.181433 0.558392i
\(167\) 14.6571 2.32146i 1.13420 0.179640i 0.439021 0.898477i \(-0.355325\pi\)
0.695179 + 0.718837i \(0.255325\pi\)
\(168\) −3.60821 + 0.857043i −0.278379 + 0.0661223i
\(169\) 6.98518 9.61428i 0.537322 0.739560i
\(170\) 0 0
\(171\) −14.3780 7.41367i −1.09951 0.566937i
\(172\) 1.86518 + 0.295415i 0.142218 + 0.0225252i
\(173\) −2.27656 + 4.46800i −0.173084 + 0.339696i −0.961210 0.275818i \(-0.911051\pi\)
0.788126 + 0.615514i \(0.211051\pi\)
\(174\) 6.70263 + 4.12968i 0.508125 + 0.313070i
\(175\) 0 0
\(176\) 5.91761i 0.446057i
\(177\) −10.7267 + 6.53772i −0.806265 + 0.491405i
\(178\) −1.35381 + 8.54762i −0.101472 + 0.640672i
\(179\) 2.56353 1.86252i 0.191607 0.139211i −0.487846 0.872930i \(-0.662217\pi\)
0.679453 + 0.733719i \(0.262217\pi\)
\(180\) 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
\(183\) 2.82484 6.77345i 0.208818 0.500707i
\(184\) −1.47228 0.478373i −0.108538 0.0352661i
\(185\) 0 0
\(186\) 4.35392 17.9443i 0.319245 1.31574i
\(187\) 30.3327 15.4553i 2.21815 1.13020i
\(188\) 4.28579 2.18372i 0.312573 0.159264i
\(189\) 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 \(0.325163\pi\)
\(192\) −1.59860 0.666690i −0.115369 0.0481142i
\(193\) 7.00922 7.00922i 0.504535 0.504535i −0.408309 0.912844i \(-0.633881\pi\)
0.912844 + 0.408309i \(0.133881\pi\)
\(194\) −9.76009 7.09112i −0.700734 0.509113i
\(195\) 0 0
\(196\) 1.95413 1.41976i 0.139580 0.101411i
\(197\) 1.59685 10.0821i 0.113771 0.718320i −0.863186 0.504885i \(-0.831535\pi\)
0.976957 0.213435i \(-0.0684652\pi\)
\(198\) −0.0857583 + 17.7526i −0.00609458 + 1.26162i
\(199\) 15.1147i 1.07146i 0.844391 + 0.535728i \(0.179963\pi\)
−0.844391 + 0.535728i \(0.820037\pi\)
\(200\) 0 0
\(201\) 1.17784 1.91169i 0.0830786 0.134840i
\(202\) 0.140865 0.276463i 0.00991123 0.0194519i
\(203\) 9.61241 + 1.52246i 0.674659 + 0.106856i
\(204\) −0.757790 9.93538i −0.0530559 0.695616i
\(205\) 0 0
\(206\) 5.19267 7.14709i 0.361790 0.497962i
\(207\) 4.40986 + 1.45644i 0.306506 + 0.101229i
\(208\) 1.04345 0.165266i 0.0723503 0.0114592i
\(209\) 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 \(0.943652\pi\)
\(212\) −2.75644 5.40982i −0.189313 0.371548i
\(213\) −0.571647 + 7.04585i −0.0391686 + 0.482774i
\(214\) 5.63809 1.83193i 0.385412 0.125228i
\(215\) 0 0
\(216\) 4.78608 + 2.02321i 0.325652 + 0.137662i
\(217\) −3.57084 22.5454i −0.242404 1.53048i
\(218\) 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
\(222\) 0.290608 + 0.249419i 0.0195043 + 0.0167399i
\(223\) 11.9279 + 6.07755i 0.798748 + 0.406983i 0.805205 0.592996i \(-0.202055\pi\)
−0.00645660 + 0.999979i \(0.502055\pi\)
\(224\) −2.14116 −0.143062
\(225\) 0 0
\(226\) 8.48225 0.564231
\(227\) −0.762629 0.388579i −0.0506175 0.0257909i 0.428499 0.903542i \(-0.359043\pi\)
−0.479116 + 0.877752i \(0.659043\pi\)
\(228\) −7.08729 6.08278i −0.469367 0.402842i
\(229\) 9.72545 + 13.3859i 0.642676 + 0.884567i 0.998755 0.0498887i \(-0.0158867\pi\)
−0.356079 + 0.934456i \(0.615887\pi\)
\(230\) 0 0
\(231\) 8.34939 + 20.2957i 0.549350 + 1.33536i
\(232\) 3.21402 + 3.21402i 0.211011 + 0.211011i
\(233\) −0.852656 5.38346i −0.0558593 0.352682i −0.999749 0.0224200i \(-0.992863\pi\)
0.943889 0.330262i \(-0.107137\pi\)
\(234\) −3.13271 + 0.480671i −0.204792 + 0.0314225i
\(235\) 0 0
\(236\) −6.89769 + 2.24119i −0.449001 + 0.145889i
\(237\) 0.132363 1.63144i 0.00859790 0.105974i
\(238\) −5.59216 10.9752i −0.362486 0.711418i
\(239\) −2.69306 8.28837i −0.174199 0.536130i 0.825397 0.564553i \(-0.190951\pi\)
−0.999596 + 0.0284230i \(0.990951\pi\)
\(240\) 0 0
\(241\) −7.85699 + 24.1813i −0.506113 + 1.55766i 0.292779 + 0.956180i \(0.405420\pi\)
−0.798892 + 0.601475i \(0.794580\pi\)
\(242\) −23.7224 + 3.75726i −1.52494 + 0.241526i
\(243\) −14.3288 6.13893i −0.919191 0.393813i
\(244\) 2.49051 3.42789i 0.159439 0.219448i
\(245\) 0 0
\(246\) −0.213620 2.80077i −0.0136199 0.178570i
\(247\) 5.62657 + 0.891162i 0.358010 + 0.0567033i
\(248\) 4.83989 9.49882i 0.307333 0.603176i
\(249\) −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 \(0.768131\pi\)
\(252\) 6.42341 + 0.0310298i 0.404637 + 0.00195469i
\(253\) −1.43306 + 9.04796i −0.0900954 + 0.568840i
\(254\) 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 −0.972526 0.232792i \(-0.925214\pi\)
0.232792 + 0.972526i \(0.425214\pi\)
\(258\) −3.01884 1.25900i −0.187945 0.0783816i
\(259\) 0.450251 + 0.146295i 0.0279772 + 0.00909035i
\(260\) 0 0
\(261\) −9.59537 9.68852i −0.593938 0.599704i
\(262\) −17.4029 + 8.86724i −1.07516 + 0.547820i
\(263\) −20.2720 + 10.3291i −1.25002 + 0.636919i −0.948572 0.316562i \(-0.897471\pi\)
−0.301453 + 0.953481i \(0.597471\pi\)
\(264\) −2.41679 + 9.96060i −0.148743 + 0.613033i
\(265\) 0 0
\(266\) −10.9806 3.56783i −0.673266 0.218757i
\(267\) 5.76965 13.8346i 0.353097 0.846662i
\(268\) 0.916684 0.916684i 0.0559954 0.0559954i
\(269\) 8.37684 + 6.08613i 0.510745 + 0.371078i 0.813106 0.582115i \(-0.197775\pi\)
−0.302361 + 0.953193i \(0.597775\pi\)
\(270\) 0 0
\(271\) −0.517312 + 0.375849i −0.0314245 + 0.0228312i −0.603387 0.797449i \(-0.706182\pi\)
0.571962 + 0.820280i \(0.306182\pi\)
\(272\) 0.899945 5.68203i 0.0545672 0.344524i
\(273\) −3.34556 + 2.03906i −0.202482 + 0.123410i
\(274\) 11.9899i 0.724336i
\(275\) 0 0
\(276\) 2.28279 + 1.40649i 0.137408 + 0.0846608i
\(277\) −13.7839 + 27.0524i −0.828193 + 1.62542i −0.0488650 + 0.998805i \(0.515560\pi\)
−0.779328 + 0.626616i \(0.784440\pi\)
\(278\) 22.9843 + 3.64035i 1.37851 + 0.218334i
\(279\) −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 \(-0.0242890\pi\)
\(282\) −8.10574 + 1.92532i −0.482690 + 0.114651i
\(283\) 3.41737 0.541258i 0.203142 0.0321745i −0.0540343 0.998539i \(-0.517208\pi\)
0.257176 + 0.966365i \(0.417208\pi\)
\(284\) −1.26119 + 3.88154i −0.0748378 + 0.230327i
\(285\) 0 0
\(286\) −1.93188 5.94572i −0.114235 0.351578i
\(287\) −1.57642 3.09390i −0.0930531 0.182627i
\(288\) 2.41850 + 1.77506i 0.142512 + 0.104596i
\(289\) 15.3076 4.97374i 0.900446 0.292573i
\(290\) 0 0
\(291\) 13.5323 + 15.9219i 0.793275 + 0.933361i
\(292\) −0.0489016 0.308752i −0.00286175 0.0180684i
\(293\) −12.2527 12.2527i −0.715808 0.715808i 0.251936 0.967744i \(-0.418933\pi\)
−0.967744 + 0.251936i \(0.918933\pi\)
\(294\) −3.86905 + 1.59167i −0.225647 + 0.0928283i
\(295\) 0 0
\(296\) 0.129962 + 0.178878i 0.00755391 + 0.0103971i
\(297\) 7.39463 29.8464i 0.429080 1.73187i
\(298\) −13.1103 6.68004i −0.759460 0.386964i
\(299\) −1.63544 −0.0945802
\(300\) 0 0
\(301\) −4.04342 −0.233059
\(302\) 7.61703 + 3.88107i 0.438311 + 0.223330i
\(303\) −0.350015 + 0.407816i −0.0201078 + 0.0234284i
\(304\) −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 \(-0.0126167\pi\)
−0.0396263 + 0.999215i \(0.512617\pi\)
\(308\) 1.98211 + 12.5146i 0.112941 + 0.713083i
\(309\) −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 \(0.329206\pi\)
\(312\) −1.82384 0.147973i −0.103255 0.00837732i
\(313\) −9.44284 18.5326i −0.533741 1.04753i −0.987679 0.156492i \(-0.949981\pi\)
0.453939 0.891033i \(-0.350019\pi\)
\(314\) 7.68555 + 23.6537i 0.433721 + 1.33486i
\(315\) 0 0
\(316\) 0.292024 0.898757i 0.0164276 0.0505590i
\(317\) −0.214085 + 0.0339077i −0.0120242 + 0.00190445i −0.162444 0.986718i \(-0.551938\pi\)
0.150419 + 0.988622i \(0.451938\pi\)
\(318\) 2.43027 + 10.2316i 0.136283 + 0.573761i
\(319\) 15.8099 21.7604i 0.885183 1.21835i
\(320\) 0 0
\(321\) −10.2383 + 0.780892i −0.571445 + 0.0435852i
\(322\) 3.27381 + 0.518520i 0.182442 + 0.0288960i
\(323\) 14.0832 27.6399i 0.783612 1.53793i
\(324\) −7.22970 5.36017i −0.401650 0.297787i
\(325\) 0 0
\(326\) 2.00929i 0.111284i
\(327\) −1.70153 2.79176i −0.0940947 0.154384i
\(328\) 0.253693 1.60175i 0.0140078 0.0884421i
\(329\) −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
\(333\) −0.387290 0.538511i −0.0212234 0.0295102i
\(334\) −14.1135 4.58575i −0.772255 0.250921i
\(335\) 0 0
\(336\) 3.60403 + 0.874463i 0.196616 + 0.0477058i
\(337\) −6.01777 + 3.06621i −0.327809 + 0.167027i −0.610147 0.792288i \(-0.708890\pi\)
0.282339 + 0.959315i \(0.408890\pi\)
\(338\) −10.5886 + 5.39518i −0.575946 + 0.293459i
\(339\) −14.2774 3.46420i −0.775443 0.188150i
\(340\) 0 0
\(341\) −59.9987 19.4947i −3.24911 1.05570i
\(342\) 9.44517 + 13.1331i 0.510736 + 0.710157i
\(343\) −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
\(347\) −0.716076 + 4.52113i −0.0384410 + 0.242707i −0.999425 0.0338958i \(-0.989209\pi\)
0.960984 + 0.276603i \(0.0892086\pi\)
\(348\) −4.09725 6.72250i −0.219636 0.360364i
\(349\) 9.78119i 0.523575i 0.965126 + 0.261787i \(0.0843120\pi\)
−0.965126 + 0.261787i \(0.915688\pi\)
\(350\) 0 0
\(351\) 5.46932 + 0.470345i 0.291931 + 0.0251052i
\(352\) −2.68654 + 5.27263i −0.143193 + 0.281032i
\(353\) 10.7063 + 1.69571i 0.569840 + 0.0902538i 0.434704 0.900573i \(-0.356853\pi\)
0.135136 + 0.990827i \(0.456853\pi\)
\(354\) 12.5256 0.955350i 0.665727 0.0507763i
\(355\) 0 0
\(356\) 5.08679 7.00137i 0.269600 0.371072i
\(357\) 4.93044 + 20.7575i 0.260947 + 1.09860i
\(358\) −3.12969 + 0.495694i −0.165409 + 0.0261982i
\(359\) −6.51044 + 20.0371i −0.343608 + 1.05752i 0.618717 + 0.785614i \(0.287653\pi\)
−0.962325 + 0.271902i \(0.912347\pi\)
\(360\) 0 0
\(361\) −3.11386 9.58347i −0.163887 0.504393i
\(362\) 2.83323 + 5.56052i 0.148911 + 0.292254i
\(363\) 41.4644 + 3.36411i 2.17632 + 0.176570i
\(364\) −2.15133 + 0.699010i −0.112760 + 0.0366381i
\(365\) 0 0
\(366\) −5.59203 + 4.75273i −0.292300 + 0.248429i
\(367\) 4.22522 + 26.6770i 0.220555 + 1.39253i 0.810809 + 0.585311i \(0.199028\pi\)
−0.590254 + 0.807218i \(0.700972\pi\)
\(368\) 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
\(372\) −12.0259 + 14.0119i −0.623516 + 0.726483i
\(373\) −23.8387 12.1464i −1.23432 0.628917i −0.289711 0.957114i \(-0.593559\pi\)
−0.944609 + 0.328197i \(0.893559\pi\)
\(374\) −34.0432 −1.76033
\(375\) 0 0
\(376\) −4.81005 −0.248060
\(377\) 4.27854 + 2.18003i 0.220356 + 0.112277i
\(378\) −10.7993 2.67559i −0.555455 0.137617i
\(379\) −9.28018 12.7731i −0.476691 0.656109i 0.501174 0.865347i \(-0.332902\pi\)
−0.977865 + 0.209238i \(0.932902\pi\)
\(380\) 0 0
\(381\) −16.7525 + 6.89175i −0.858257 + 0.353075i
\(382\) −14.8555 14.8555i −0.760073 0.760073i
\(383\) 2.49780 + 15.7705i 0.127632 + 0.805836i 0.965584 + 0.260092i \(0.0837529\pi\)
−0.837952 + 0.545744i \(0.816247\pi\)
\(384\) 1.12169 + 1.31977i 0.0572411 + 0.0673495i
\(385\) 0 0
\(386\) −9.42739 + 3.06314i −0.479841 + 0.155910i
\(387\) 4.56717 + 3.35207i 0.232162 + 0.170395i
\(388\) 5.47700 + 10.7492i 0.278053 + 0.545709i
\(389\) −3.56490 10.9716i −0.180748 0.556284i 0.819102 0.573648i \(-0.194472\pi\)
−0.999849 + 0.0173647i \(0.994472\pi\)
\(390\) 0 0
\(391\) −2.75201 + 8.46982i −0.139175 + 0.428337i
\(392\) −2.38569 + 0.377857i −0.120496 + 0.0190847i
\(393\) 32.9143 7.81799i 1.66031 0.394365i
\(394\) −5.99998 + 8.25827i −0.302275 + 0.416046i
\(395\) 0 0
\(396\) 8.13594 15.7788i 0.408846 0.792913i
\(397\) −20.6866 3.27643i −1.03823 0.164439i −0.386030 0.922486i \(-0.626154\pi\)
−0.652200 + 0.758047i \(0.726154\pi\)
\(398\) 6.86195 13.4673i 0.343958 0.675057i
\(399\) 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 \(0.791080\pi\)
\(402\) −1.91735 + 1.16859i −0.0956289 + 0.0582842i
\(403\) 1.76187 11.1240i 0.0877648 0.554125i
\(404\) −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
\(408\) −3.83537 + 9.19652i −0.189879 + 0.455296i
\(409\) 9.31361 + 3.02618i 0.460528 + 0.149635i 0.530087 0.847943i \(-0.322159\pi\)
−0.0695588 + 0.997578i \(0.522159\pi\)
\(410\) 0 0
\(411\) −4.89675 + 20.1816i −0.241539 + 0.995483i
\(412\) −7.87141 + 4.01069i −0.387797 + 0.197592i
\(413\) 13.8365 7.05006i 0.680851 0.346911i
\(414\) −3.26800 3.29973i −0.160614 0.162173i
\(415\) 0 0
\(416\) −1.00475 0.326463i −0.0492619 0.0160062i
\(417\) −37.2007 15.5144i −1.82173 0.759744i
\(418\) −22.5634 + 22.5634i −1.10361 + 1.10361i
\(419\) 20.8723 + 15.1646i 1.01968 + 0.740840i 0.966217 0.257730i \(-0.0829745\pi\)
0.0534618 + 0.998570i \(0.482974\pi\)
\(420\) 0 0
\(421\) −31.8859 + 23.1664i −1.55402 + 1.12906i −0.613316 + 0.789837i \(0.710165\pi\)
−0.940705 + 0.339225i \(0.889835\pi\)
\(422\) −0.621291 + 3.92268i −0.0302440 + 0.190953i
\(423\) 14.4300 + 0.0697075i 0.701610 + 0.00338930i
\(424\) 6.07158i 0.294862i
\(425\) 0 0
\(426\) 3.70809 6.01838i 0.179658 0.291591i
\(427\) −4.11875 + 8.08350i −0.199320 + 0.391188i
\(428\) −5.85525 0.927381i −0.283024 0.0448267i
\(429\) 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 \(0.247296\pi\)
\(432\) −3.34591 3.97553i −0.160980 0.191273i
\(433\) −16.5283 + 2.61783i −0.794299 + 0.125805i −0.540380 0.841421i \(-0.681720\pi\)
−0.253919 + 0.967225i \(0.581720\pi\)
\(434\) −7.05375 + 21.7092i −0.338591 + 1.04208i
\(435\) 0 0
\(436\) −0.583300 1.79521i −0.0279350 0.0859752i
\(437\) 3.78968 + 7.43768i 0.181285 + 0.355792i
\(438\) −0.0437846 + 0.539668i −0.00209211 + 0.0257863i
\(439\) 19.1311 6.21606i 0.913076 0.296676i 0.185453 0.982653i \(-0.440625\pi\)
0.727623 + 0.685977i \(0.240625\pi\)
\(440\) 0 0
\(441\) 7.16248 1.09898i 0.341070 0.0523326i
\(442\) −0.950753 6.00282i −0.0452227 0.285525i
\(443\) −17.1571 17.1571i −0.815159 0.815159i 0.170243 0.985402i \(-0.445545\pi\)
−0.985402 + 0.170243i \(0.945545\pi\)
\(444\) −0.145699 0.354167i −0.00691459 0.0168080i
\(445\) 0 0
\(446\) −7.86865 10.8303i −0.372591 0.512828i
\(447\) 19.3393 + 16.5983i 0.914716 + 0.785071i
\(448\) 1.90779 + 0.972066i 0.0901345 + 0.0459258i
\(449\) −15.9242 −0.751511 −0.375755 0.926719i \(-0.622617\pi\)
−0.375755 + 0.926719i \(0.622617\pi\)
\(450\) 0 0
\(451\) −9.59671 −0.451891
\(452\) −7.55774 3.85086i −0.355486 0.181129i
\(453\) −11.2360 9.64350i −0.527914 0.453091i
\(454\) 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 \(-0.225733\pi\)
−0.651198 + 0.758908i \(0.725733\pi\)
\(458\) −2.58835 16.3422i −0.120946 0.763621i
\(459\) 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 \(0.325822\pi\)
\(462\) 1.77471 21.8742i 0.0825668 1.01768i
\(463\) 10.4958 + 20.5992i 0.487783 + 0.957328i 0.995406 + 0.0957485i \(0.0305245\pi\)
−0.507623 + 0.861580i \(0.669476\pi\)
\(464\) −1.40458 4.32285i −0.0652059 0.200683i
\(465\) 0 0
\(466\) −1.68432 + 5.18379i −0.0780245 + 0.240135i
\(467\) 4.58995 0.726976i 0.212397 0.0336405i −0.0493288 0.998783i \(-0.515708\pi\)
0.261726 + 0.965142i \(0.415708\pi\)
\(468\) 3.00948 + 0.993939i 0.139113 + 0.0459448i
\(469\) −1.63156 + 2.24565i −0.0753383 + 0.103694i
\(470\) 0 0
\(471\) −3.27611 42.9530i −0.150955 1.97917i
\(472\) 7.16336 + 1.13457i 0.329721 + 0.0522226i
\(473\) −5.07333 + 9.95697i −0.233272 + 0.457822i
\(474\) −0.858596 + 1.39353i −0.0394366 + 0.0640072i
\(475\) 0 0
\(476\) 12.3178i 0.564585i
\(477\) 0.0879897 18.2145i 0.00402877 0.833986i
\(478\) −1.36331 + 8.60761i −0.0623564 + 0.393703i
\(479\) −12.7801 + 9.28530i −0.583939 + 0.424256i −0.840142 0.542367i \(-0.817528\pi\)
0.256203 + 0.966623i \(0.417528\pi\)
\(480\) 0 0
\(481\) 0.188977 + 0.137300i 0.00861660 + 0.00626032i
\(482\) 17.9787 17.9787i 0.818908 0.818908i
\(483\) −5.29875 2.20982i −0.241101 0.100550i
\(484\) 22.8426 + 7.42201i 1.03830 + 0.337364i
\(485\) 0 0
\(486\) 9.98001 + 11.9750i 0.452702 + 0.543195i
\(487\) −0.120793 + 0.0615473i −0.00547367 + 0.00278898i −0.456725 0.889608i \(-0.650978\pi\)
0.451252 + 0.892397i \(0.350978\pi\)
\(488\) −3.77529 + 1.92361i −0.170899 + 0.0870776i
\(489\) 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 \(0.534178\pi\)
\(492\) −1.08119 + 2.59248i −0.0487436 + 0.116878i
\(493\) 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
\(497\) 1.36703 8.63111i 0.0613198 0.387158i
\(498\) 11.1881 6.81893i 0.501349 0.305564i
\(499\) 27.5900i 1.23510i −0.786532 0.617549i \(-0.788126\pi\)
0.786532 0.617549i \(-0.211874\pi\)
\(500\) 0 0
\(501\) 21.8831 + 13.4828i 0.977667 + 0.602368i
\(502\) 9.57626 18.7945i 0.427409 0.838838i
\(503\) 10.8159 + 1.71307i 0.482257 + 0.0763820i 0.392829 0.919611i \(-0.371496\pi\)
0.0894274 + 0.995993i \(0.471496\pi\)
\(504\) −5.70921 2.94381i −0.254308 0.131128i
\(505\) 0 0
\(506\) 5.38455 7.41120i 0.239372 0.329468i
\(507\) 20.0263 4.75677i 0.889401 0.211256i
\(508\) −10.3298 + 1.63607i −0.458309 + 0.0725891i
\(509\) 2.83257 8.71775i 0.125551 0.386407i −0.868450 0.495777i \(-0.834883\pi\)
0.994001 + 0.109370i \(0.0348833\pi\)
\(510\) 0 0
\(511\) 0.206834 + 0.636570i 0.00914980 + 0.0281602i
\(512\) 0.453990 + 0.891007i 0.0200637 + 0.0393773i
\(513\) −10.5346 25.9633i −0.465114 1.14631i
\(514\) 15.9501 5.18250i 0.703529 0.228590i
\(515\) 0 0
\(516\) 2.11823 + 2.49230i 0.0932500 + 0.109717i
\(517\) 4.45276 + 28.1136i 0.195832 + 1.23643i
\(518\) −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 \(0.633652\pi\)
\(522\) 4.15104 + 12.9887i 0.181686 + 0.568502i
\(523\) −32.1380 16.3751i −1.40530 0.716035i −0.423488 0.905902i \(-0.639194\pi\)
−0.981810 + 0.189867i \(0.939194\pi\)
\(524\) 19.5318 0.853250
\(525\) 0 0
\(526\) 22.7518 0.992025
\(527\) −54.6453 27.8432i −2.38039 1.21287i
\(528\) 6.67539 7.77776i 0.290509 0.338484i
\(529\) 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
\(533\) −0.268016 1.69218i −0.0116090 0.0732966i
\(534\) −11.4216 + 9.70732i −0.494259 + 0.420077i
\(535\) 0 0
\(536\) −1.23294 + 0.400605i −0.0532548 + 0.0173035i
\(537\) 5.47038 + 0.443825i 0.236064 + 0.0191525i
\(538\) −4.70077 9.22579i −0.202665 0.397752i
\(539\) 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 \(-0.166280\pi\)
\(542\) 0.631560 0.100029i 0.0271278 0.00429663i
\(543\) −2.49797 10.5166i −0.107198 0.451312i
\(544\) −3.38144 + 4.65416i −0.144978 + 0.199545i
\(545\) 0 0
\(546\) 3.90663 0.297966i 0.167188 0.0127518i
\(547\) −22.3156 3.53445i −0.954148 0.151122i −0.340098 0.940390i \(-0.610460\pi\)
−0.614049 + 0.789268i \(0.710460\pi\)
\(548\) −5.44330 + 10.6831i −0.232526 + 0.456359i
\(549\) 11.3536 5.71604i 0.484561 0.243955i
\(550\) 0 0
\(551\) 24.5096i 1.04414i
\(552\) −1.39545 2.28956i −0.0593942 0.0974500i
\(553\) −0.316532 + 1.99850i −0.0134603 + 0.0849851i
\(554\) 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 −0.622943 0.782267i \(-0.714063\pi\)
0.782267 + 0.622943i \(0.214063\pi\)
\(558\) 25.9647 18.6735i 1.09918 0.790513i
\(559\) −1.89740 0.616502i −0.0802513 0.0260752i
\(560\) 0 0
\(561\) 57.3019 + 13.9034i 2.41929 + 0.587003i
\(562\) −19.3495 + 9.85907i −0.816210 + 0.415880i
\(563\) −21.6061 + 11.0089i −0.910590 + 0.463969i −0.845539 0.533913i \(-0.820721\pi\)
−0.0650508 + 0.997882i \(0.520721\pi\)
\(564\) 8.09634 + 1.96445i 0.340918 + 0.0827185i
\(565\) 0 0
\(566\) −3.29063 1.06919i −0.138315 0.0449414i
\(567\) 17.0848 + 8.91407i 0.717493 + 0.374356i
\(568\) 2.88591 2.88591i 0.121090 0.121090i
\(569\) −24.5934 17.8681i −1.03101 0.749071i −0.0624977 0.998045i \(-0.519907\pi\)
−0.968510 + 0.248974i \(0.919907\pi\)
\(570\) 0 0
\(571\) 4.57335 3.32274i 0.191389 0.139052i −0.487964 0.872864i \(-0.662260\pi\)
0.679353 + 0.733811i \(0.262260\pi\)
\(572\) −0.977982 + 6.17473i −0.0408915 + 0.258179i
\(573\) 18.9379 + 31.0720i 0.791141 + 1.29805i
\(574\) 3.47236i 0.144934i
\(575\) 0 0
\(576\) −1.34904 2.67957i −0.0562101 0.111649i
\(577\) 11.6678 22.8994i 0.485739 0.953316i −0.509919 0.860223i \(-0.670324\pi\)
0.995657 0.0930933i \(-0.0296755\pi\)
\(578\) −15.8972 2.51787i −0.661236 0.104729i
\(579\) 17.1193 1.30572i 0.711454 0.0542639i
\(580\) 0 0
\(581\) 9.52039 13.1037i 0.394972 0.543633i
\(582\) −4.82891 20.3301i −0.200165 0.842708i
\(583\) 35.4869 5.62058i 1.46972 0.232781i
\(584\) −0.0965991 + 0.297301i −0.00399730 + 0.0123024i
\(585\) 0 0
\(586\) 5.35461 + 16.4798i 0.221197 + 0.680773i
\(587\) −6.56280 12.8802i −0.270876 0.531623i 0.714995 0.699129i \(-0.246429\pi\)
−0.985871 + 0.167506i \(0.946429\pi\)
\(588\) 4.16995 + 0.338318i 0.171966 + 0.0139520i
\(589\) −54.6723 + 17.7641i −2.25273 + 0.731957i
\(590\) 0 0
\(591\) 13.4720 11.4500i 0.554163 0.470990i
\(592\) −0.0345885 0.218383i −0.00142158 0.00897549i
\(593\) −27.1124 27.1124i −1.11337 1.11337i −0.992691 0.120680i \(-0.961492\pi\)
−0.120680 0.992691i \(-0.538508\pi\)
\(594\) −20.1387 + 23.2363i −0.826299 + 0.953396i
\(595\) 0 0
\(596\) 8.64870 + 11.9039i 0.354265 + 0.487603i
\(597\) −17.0503 + 19.8659i −0.697821 + 0.813058i
\(598\) 1.45719 + 0.742476i 0.0595890 + 0.0303621i
\(599\) 22.2597 0.909506 0.454753 0.890618i \(-0.349728\pi\)
0.454753 + 0.890618i \(0.349728\pi\)
\(600\) 0 0
\(601\) −0.661317 −0.0269757 −0.0134878 0.999909i \(-0.504293\pi\)
−0.0134878 + 0.999909i \(0.504293\pi\)
\(602\) 3.60272 + 1.83568i 0.146836 + 0.0748165i
\(603\) 3.70457 1.18393i 0.150862 0.0482135i
\(604\) −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 −0.999705 0.0242876i \(-0.992268\pi\)
−0.0242876 0.999705i \(-0.507732\pi\)
\(608\) 0.843538 + 5.32589i 0.0342100 + 0.215993i
\(609\) 10.9166 + 12.8444i 0.442362 + 0.520480i
\(610\) 0 0
\(611\) −4.83290 + 1.57031i −0.195518 + 0.0635278i
\(612\) 10.2117 13.9133i 0.412782 0.562412i
\(613\) 11.3412 + 22.2583i 0.458065 + 0.899003i 0.998345 + 0.0575173i \(0.0183184\pi\)
−0.540280 + 0.841485i \(0.681682\pi\)
\(614\) −7.34770 22.6139i −0.296529 0.912623i
\(615\) 0 0
\(616\) 3.91542 12.0504i 0.157757 0.485525i
\(617\) 30.7946 4.87738i 1.23974 0.196356i 0.498081 0.867131i \(-0.334038\pi\)
0.741661 + 0.670775i \(0.234038\pi\)
\(618\) 14.8873 3.53610i 0.598853 0.142243i
\(619\) −2.12975 + 2.93135i −0.0856019 + 0.117821i −0.849670 0.527314i \(-0.823199\pi\)
0.764068 + 0.645135i \(0.223199\pi\)
\(620\) 0 0
\(621\) 4.15311 + 6.88882i 0.166659 + 0.276439i
\(622\) −7.68404 1.21703i −0.308102 0.0487985i
\(623\) −8.41243 + 16.5103i −0.337037 + 0.661472i
\(624\) 1.55788 + 0.959853i 0.0623651 + 0.0384249i
\(625\) 0 0
\(626\) 20.7996i 0.831321i
\(627\) 47.1939 28.7639i 1.88474 1.14872i
\(628\) 3.89068 24.5648i 0.155255 0.980241i
\(629\) 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
\(633\) 2.64781 6.34896i 0.105241 0.252349i
\(634\) 0.206145 + 0.0669805i 0.00818706 + 0.00266014i
\(635\) 0 0
\(636\) 2.47967 10.2198i 0.0983253 0.405240i
\(637\) −2.27367 + 1.15849i −0.0900861 + 0.0459012i
\(638\) −23.9657 + 12.2112i −0.948813 + 0.483444i
\(639\) −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 \(0.987253\pi\)
\(642\) 9.47689 + 3.95230i 0.374023 + 0.155985i
\(643\) −17.9186 + 17.9186i −0.706639 + 0.706639i −0.965827 0.259188i \(-0.916545\pi\)
0.259188 + 0.965827i \(0.416545\pi\)
\(644\) −2.68158 1.94828i −0.105669 0.0767731i
\(645\) 0 0
\(646\) −25.0965 + 18.2337i −0.987409 + 0.717395i
\(647\) −1.11876 + 7.06356i −0.0439829 + 0.277697i −0.999871 0.0160323i \(-0.994897\pi\)
0.955889 + 0.293730i \(0.0948965\pi\)
\(648\) 4.00825 + 8.05816i 0.157459 + 0.316554i
\(649\) 42.9184i 1.68469i
\(650\) 0 0
\(651\) 20.7391 33.6604i 0.812831 1.31926i
\(652\) 0.912200 1.79029i 0.0357245 0.0701133i
\(653\) 22.9855 + 3.64054i 0.899490 + 0.142465i 0.589021 0.808118i \(-0.299514\pi\)
0.310470 + 0.950583i \(0.399514\pi\)
\(654\) 0.248642 + 3.25995i 0.00972269 + 0.127474i
\(655\) 0 0
\(656\) −0.953223 + 1.31200i −0.0372171 + 0.0512250i
\(657\) 0.294102 0.890494i 0.0114740 0.0347415i
\(658\) 10.1723 1.61113i 0.396557 0.0628085i
\(659\) 1.14382 3.52031i 0.0445568 0.137132i −0.926303 0.376779i \(-0.877032\pi\)
0.970860 + 0.239647i \(0.0770317\pi\)
\(660\) 0 0
\(661\) −11.4157 35.1339i −0.444019 1.36655i −0.883556 0.468326i \(-0.844857\pi\)
0.439537 0.898224i \(-0.355143\pi\)
\(662\) −3.26336 6.40470i −0.126834 0.248926i
\(663\) −0.851267 + 10.4923i −0.0330605 + 0.407488i
\(664\) 7.19438 2.33760i 0.279196 0.0907163i
\(665\) 0 0
\(666\) 0.100599 + 0.655643i 0.00389815 + 0.0254056i
\(667\) 1.10073 + 6.94972i 0.0426203 + 0.269094i
\(668\) 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
\(672\) −2.81421 2.41535i −0.108561 0.0931740i
\(673\) 1.06415 + 0.542210i 0.0410198 + 0.0209006i 0.474380 0.880320i \(-0.342672\pi\)
−0.433360 + 0.901221i \(0.642672\pi\)
\(674\) 6.75390 0.260151
\(675\) 0 0
\(676\) 11.8839 0.457073
\(677\) 30.6338 + 15.6087i 1.17735 + 0.599892i 0.929470 0.368898i \(-0.120265\pi\)
0.247884 + 0.968790i \(0.420265\pi\)
\(678\) 11.1486 + 9.56844i 0.428158 + 0.367474i
\(679\) −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
\(683\) 7.05008 + 44.5125i 0.269764 + 1.70322i 0.635169 + 0.772373i \(0.280930\pi\)
−0.365405 + 0.930849i \(0.619070\pi\)
\(684\) −2.45340 15.9897i −0.0938081 0.611382i
\(685\) 0 0
\(686\) 19.1733 6.22977i 0.732038 0.237854i
\(687\) −2.31751 + 28.5645i −0.0884185 + 1.08980i
\(688\) 0.857327 + 1.68260i 0.0326853 + 0.0641485i
\(689\) 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 \(0.0783746\pi\)
\(692\) −4.95282 + 0.784450i −0.188278 + 0.0298203i
\(693\) −11.9207 + 36.0941i −0.452832 + 1.37110i
\(694\) 2.69058 3.70326i 0.102133 0.140574i
\(695\) 0 0
\(696\) 0.598727 + 7.84991i 0.0226947 + 0.297550i
\(697\) −9.21466 1.45946i −0.349030 0.0552809i
\(698\) 4.44057 8.71510i 0.168078 0.329871i
\(699\) 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 \(-0.120781\pi\)
\(702\) −4.65967 2.90210i −0.175868 0.109533i
\(703\) 0.186511 1.17758i 0.00703438 0.0444133i
\(704\) 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
\(708\) −11.5941 4.83527i −0.435733 0.181721i
\(709\) 22.4237 + 7.28590i 0.842140 + 0.273628i 0.698150 0.715951i \(-0.254007\pi\)
0.143990 + 0.989579i \(0.454007\pi\)
\(710\) 0 0
\(711\) 2.01433 1.99496i 0.0755432 0.0748168i
\(712\) −7.71092 + 3.92891i −0.288979 + 0.147242i
\(713\) 14.7046 7.49238i 0.550692 0.280592i
\(714\) 5.03066 20.7335i 0.188268 0.775930i
\(715\) 0 0
\(716\) 3.01361 + 0.979183i 0.112624 + 0.0365938i
\(717\) 5.81015 13.9317i 0.216984 0.520287i
\(718\) 14.8975 14.8975i 0.555969 0.555969i
\(719\) −30.2210 21.9569i −1.12705 0.818853i −0.141791 0.989897i \(-0.545286\pi\)
−0.985263 + 0.171044i \(0.945286\pi\)
\(720\) 0 0
\(721\) 15.3031 11.1183i 0.569916 0.414068i
\(722\) −1.57634 + 9.95259i −0.0586651 + 0.370397i
\(723\) −37.6046 + 22.9194i −1.39853 + 0.852381i
\(724\) 6.24071i 0.231934i
\(725\) 0 0
\(726\) −35.4178 21.8219i −1.31448 0.809886i
\(727\) 19.2896 37.8579i 0.715411 1.40407i −0.190964 0.981597i \(-0.561161\pi\)
0.906374 0.422476i \(-0.138839\pi\)
\(728\) 2.23419 + 0.353862i 0.0828047 + 0.0131150i
\(729\) −11.9078 24.2323i −0.441031 0.897492i
\(730\) 0 0
\(731\) −6.38561 + 8.78903i −0.236180 + 0.325074i
\(732\) 7.14023 1.69599i 0.263911 0.0626855i
\(733\) −44.0735 + 6.98056i −1.62789 + 0.257833i −0.902559 0.430565i \(-0.858314\pi\)
−0.725333 + 0.688398i \(0.758314\pi\)
\(734\) 8.34641 25.6876i 0.308072 0.948147i
\(735\) 0 0
\(736\) −0.478373 1.47228i −0.0176331 0.0542690i
\(737\) 3.48279 + 6.83537i 0.128290 + 0.251784i
\(738\) 2.87865 3.92214i 0.105965 0.144376i
\(739\) 8.01855 2.60538i 0.294967 0.0958406i −0.157795 0.987472i \(-0.550439\pi\)
0.452762 + 0.891631i \(0.350439\pi\)
\(740\) 0 0
\(741\) 6.38996 + 7.51837i 0.234741 + 0.276194i
\(742\) −2.03368 12.8402i −0.0746589 0.471378i
\(743\) 24.9192 + 24.9192i 0.914196 + 0.914196i 0.996599 0.0824029i \(-0.0262594\pi\)
−0.0824029 + 0.996599i \(0.526259\pi\)
\(744\) 17.0765 7.02502i 0.626053 0.257550i
\(745\) 0 0
\(746\) 15.7261 + 21.6451i 0.575772 + 0.792482i
\(747\) −21.6168 + 6.90844i −0.790916 + 0.252767i
\(748\) 30.3327 + 15.4553i 1.10907 + 0.565101i
\(749\) 12.6933 0.463804
\(750\) 0 0
\(751\) −8.40064 −0.306544 −0.153272 0.988184i \(-0.548981\pi\)
−0.153272 + 0.988184i \(0.548981\pi\)
\(752\) 4.28579 + 2.18372i 0.156287 + 0.0796320i
\(753\) −23.7946 + 27.7241i −0.867125 + 1.01032i
\(754\) −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 \(-0.204208\pi\)
−0.598429 + 0.801176i \(0.704208\pi\)
\(758\) 2.46985 + 15.5940i 0.0897089 + 0.566400i
\(759\) −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 \(0.435991\pi\)
\(762\) 18.0554 + 1.46488i 0.654077 + 0.0530669i
\(763\) 1.83487 + 3.60114i 0.0664268 + 0.130370i
\(764\) 6.49209 + 19.9806i 0.234875 + 0.722872i
\(765\) 0 0
\(766\) 4.93411 15.1856i 0.178276 0.548679i
\(767\) 7.56779 1.19862i 0.273257 0.0432796i
\(768\) −0.400270 1.68517i −0.0144435 0.0608082i
\(769\) 2.22958 3.06876i 0.0804008 0.110662i −0.766922 0.641740i \(-0.778213\pi\)
0.847323 + 0.531078i \(0.178213\pi\)
\(770\) 0 0
\(771\) −28.9640 + 2.20914i −1.04311 + 0.0795601i
\(772\) 9.79050 + 1.55066i 0.352368 + 0.0558096i
\(773\) 15.4685 30.3587i 0.556364 1.09193i −0.425960 0.904742i \(-0.640064\pi\)
0.982325 0.187185i \(-0.0599363\pi\)
\(774\) −2.54757 5.06017i −0.0915704 0.181884i
\(775\) 0 0
\(776\) 12.0641i 0.433077i
\(777\) 0.426754 + 0.700189i 0.0153097 + 0.0251192i
\(778\) −1.80467 + 11.3942i −0.0647005 + 0.408503i
\(779\) −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