Properties

Label 65.2.l.a.4.2
Level $65$
Weight $2$
Character 65.4
Analytic conductor $0.519$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.49787136.1
Defining polynomial: \(x^{8} + 3 x^{6} + 5 x^{4} + 12 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.2
Root \(-0.228425 + 1.39564i\) of defining polynomial
Character \(\chi\) \(=\) 65.4
Dual form 65.2.l.a.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.228425 + 0.395644i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.895644 + 1.55130i) q^{4} +(2.18890 - 0.456850i) q^{5} +(0.395644 - 0.228425i) q^{6} +(0.866025 + 1.50000i) q^{7} -1.73205 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.228425 + 0.395644i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.895644 + 1.55130i) q^{4} +(2.18890 - 0.456850i) q^{5} +(0.395644 - 0.228425i) q^{6} +(0.866025 + 1.50000i) q^{7} -1.73205 q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.319250 + 0.970381i) q^{10} +(-2.29129 - 1.32288i) q^{11} -1.79129i q^{12} +(-3.46410 - 1.00000i) q^{13} -0.791288 q^{14} +(-2.12407 - 0.698807i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(3.96863 - 2.29129i) q^{17} +0.913701 q^{18} +(-1.50000 + 0.866025i) q^{19} +(2.66919 + 2.98647i) q^{20} -1.73205i q^{21} +(1.04678 - 0.604356i) q^{22} +(-3.96863 - 2.29129i) q^{23} +(1.50000 + 0.866025i) q^{24} +(4.58258 - 2.00000i) q^{25} +(1.18693 - 1.14213i) q^{26} +5.00000i q^{27} +(-1.55130 + 2.68693i) q^{28} +(2.29129 - 3.96863i) q^{29} +(0.761669 - 0.680750i) q^{30} +6.20520i q^{31} +(-2.36965 - 4.10436i) q^{32} +(1.32288 + 2.29129i) q^{33} +2.09355i q^{34} +(2.58092 + 2.88771i) q^{35} +(1.79129 - 3.10260i) q^{36} +(-3.96863 + 6.87386i) q^{37} -0.791288i q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.79129 + 0.791288i) q^{40} +(2.29129 + 1.32288i) q^{41} +(0.685275 + 0.395644i) q^{42} +(9.16478 - 5.29129i) q^{43} -4.73930i q^{44} +(-2.98019 - 3.33444i) q^{45} +(1.81307 - 1.04678i) q^{46} -1.82740 q^{47} +(2.41733 - 1.39564i) q^{48} +(2.00000 - 3.46410i) q^{49} +(-0.255488 + 2.26992i) q^{50} -4.58258 q^{51} +(-1.55130 - 6.26951i) q^{52} +7.58258i q^{53} +(-1.97822 - 1.14213i) q^{54} +(-5.61976 - 1.84887i) q^{55} +(-1.50000 - 2.59808i) q^{56} +1.73205 q^{57} +(1.04678 + 1.81307i) q^{58} +(-12.0826 + 6.97588i) q^{59} +(-0.818350 - 3.92095i) q^{60} +(0.708712 + 1.22753i) q^{61} +(-2.45505 - 1.41742i) q^{62} +(1.73205 - 3.00000i) q^{63} -3.41742 q^{64} +(-8.03943 - 0.606325i) q^{65} -1.20871 q^{66} +(0.504525 - 0.873864i) q^{67} +(7.10895 + 4.10436i) q^{68} +(2.29129 + 3.96863i) q^{69} +(-1.73205 + 0.361500i) q^{70} +(6.08258 - 3.51178i) q^{71} +(1.73205 + 3.00000i) q^{72} +(-1.81307 - 3.14033i) q^{74} +(-4.96863 - 0.559237i) q^{75} +(-2.68693 - 1.55130i) q^{76} -4.58258i q^{77} +(-1.59898 + 0.395644i) q^{78} +6.00000 q^{79} +(-1.95057 + 5.92889i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.04678 + 0.604356i) q^{82} +6.01450 q^{83} +(2.68693 - 1.55130i) q^{84} +(7.64016 - 6.82847i) q^{85} +4.83465i q^{86} +(-3.96863 + 2.29129i) q^{87} +(3.96863 + 2.29129i) q^{88} +(8.29129 + 4.78698i) q^{89} +(2.00000 - 0.417424i) q^{90} +(-1.50000 - 6.06218i) q^{91} -8.20871i q^{92} +(3.10260 - 5.37386i) q^{93} +(0.417424 - 0.723000i) q^{94} +(-2.88771 + 2.58092i) q^{95} +4.73930i q^{96} +(5.70068 + 9.87386i) q^{97} +(0.913701 + 1.58258i) q^{98} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{4} - 6q^{6} - 8q^{9} + O(q^{10}) \) \( 8q - 2q^{4} - 6q^{6} - 8q^{9} - 4q^{10} + 12q^{14} - 6q^{15} - 2q^{16} - 12q^{19} + 24q^{20} + 12q^{24} - 18q^{26} - 10q^{30} + 6q^{35} - 4q^{36} + 20q^{39} - 12q^{40} + 12q^{45} + 42q^{46} + 16q^{49} - 12q^{50} + 30q^{54} - 14q^{55} - 12q^{56} - 60q^{59} + 24q^{61} - 64q^{64} - 24q^{65} - 28q^{66} + 12q^{71} - 42q^{74} - 8q^{75} + 6q^{76} + 48q^{79} + 18q^{80} - 4q^{81} - 6q^{84} + 42q^{85} + 48q^{89} + 16q^{90} - 12q^{91} + 40q^{94} - 6q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.228425 + 0.395644i −0.161521 + 0.279763i −0.935414 0.353553i \(-0.884973\pi\)
0.773893 + 0.633316i \(0.218307\pi\)
\(3\) −0.866025 0.500000i −0.500000 0.288675i 0.228714 0.973494i \(-0.426548\pi\)
−0.728714 + 0.684819i \(0.759881\pi\)
\(4\) 0.895644 + 1.55130i 0.447822 + 0.775650i
\(5\) 2.18890 0.456850i 0.978906 0.204310i
\(6\) 0.395644 0.228425i 0.161521 0.0932542i
\(7\) 0.866025 + 1.50000i 0.327327 + 0.566947i 0.981981 0.188982i \(-0.0605189\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) −1.73205 −0.612372
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) −0.319250 + 0.970381i −0.100956 + 0.306862i
\(11\) −2.29129 1.32288i −0.690849 0.398862i 0.113081 0.993586i \(-0.463928\pi\)
−0.803930 + 0.594724i \(0.797261\pi\)
\(12\) 1.79129i 0.517100i
\(13\) −3.46410 1.00000i −0.960769 0.277350i
\(14\) −0.791288 −0.211481
\(15\) −2.12407 0.698807i −0.548432 0.180431i
\(16\) −1.39564 + 2.41733i −0.348911 + 0.604332i
\(17\) 3.96863 2.29129i 0.962533 0.555719i 0.0655816 0.997847i \(-0.479110\pi\)
0.896952 + 0.442128i \(0.145776\pi\)
\(18\) 0.913701 0.215361
\(19\) −1.50000 + 0.866025i −0.344124 + 0.198680i −0.662094 0.749421i \(-0.730332\pi\)
0.317970 + 0.948101i \(0.396999\pi\)
\(20\) 2.66919 + 2.98647i 0.596849 + 0.667795i
\(21\) 1.73205i 0.377964i
\(22\) 1.04678 0.604356i 0.223173 0.128849i
\(23\) −3.96863 2.29129i −0.827516 0.477767i 0.0254855 0.999675i \(-0.491887\pi\)
−0.853001 + 0.521909i \(0.825220\pi\)
\(24\) 1.50000 + 0.866025i 0.306186 + 0.176777i
\(25\) 4.58258 2.00000i 0.916515 0.400000i
\(26\) 1.18693 1.14213i 0.232776 0.223989i
\(27\) 5.00000i 0.962250i
\(28\) −1.55130 + 2.68693i −0.293168 + 0.507782i
\(29\) 2.29129 3.96863i 0.425481 0.736956i −0.570984 0.820961i \(-0.693438\pi\)
0.996465 + 0.0840058i \(0.0267714\pi\)
\(30\) 0.761669 0.680750i 0.139061 0.124287i
\(31\) 6.20520i 1.11449i 0.830349 + 0.557244i \(0.188141\pi\)
−0.830349 + 0.557244i \(0.811859\pi\)
\(32\) −2.36965 4.10436i −0.418899 0.725555i
\(33\) 1.32288 + 2.29129i 0.230283 + 0.398862i
\(34\) 2.09355i 0.359041i
\(35\) 2.58092 + 2.88771i 0.436255 + 0.488112i
\(36\) 1.79129 3.10260i 0.298548 0.517100i
\(37\) −3.96863 + 6.87386i −0.652438 + 1.13006i 0.330091 + 0.943949i \(0.392920\pi\)
−0.982529 + 0.186107i \(0.940413\pi\)
\(38\) 0.791288i 0.128364i
\(39\) 2.50000 + 2.59808i 0.400320 + 0.416025i
\(40\) −3.79129 + 0.791288i −0.599455 + 0.125114i
\(41\) 2.29129 + 1.32288i 0.357839 + 0.206598i 0.668132 0.744042i \(-0.267094\pi\)
−0.310293 + 0.950641i \(0.600427\pi\)
\(42\) 0.685275 + 0.395644i 0.105740 + 0.0610492i
\(43\) 9.16478 5.29129i 1.39762 0.806914i 0.403473 0.914991i \(-0.367803\pi\)
0.994142 + 0.108078i \(0.0344695\pi\)
\(44\) 4.73930i 0.714477i
\(45\) −2.98019 3.33444i −0.444260 0.497069i
\(46\) 1.81307 1.04678i 0.267322 0.154339i
\(47\) −1.82740 −0.266554 −0.133277 0.991079i \(-0.542550\pi\)
−0.133277 + 0.991079i \(0.542550\pi\)
\(48\) 2.41733 1.39564i 0.348911 0.201444i
\(49\) 2.00000 3.46410i 0.285714 0.494872i
\(50\) −0.255488 + 2.26992i −0.0361314 + 0.321015i
\(51\) −4.58258 −0.641689
\(52\) −1.55130 6.26951i −0.215127 0.869424i
\(53\) 7.58258i 1.04155i 0.853695 + 0.520773i \(0.174356\pi\)
−0.853695 + 0.520773i \(0.825644\pi\)
\(54\) −1.97822 1.14213i −0.269202 0.155424i
\(55\) −5.61976 1.84887i −0.757768 0.249301i
\(56\) −1.50000 2.59808i −0.200446 0.347183i
\(57\) 1.73205 0.229416
\(58\) 1.04678 + 1.81307i 0.137448 + 0.238068i
\(59\) −12.0826 + 6.97588i −1.57302 + 0.908182i −0.577221 + 0.816588i \(0.695863\pi\)
−0.995796 + 0.0915940i \(0.970804\pi\)
\(60\) −0.818350 3.92095i −0.105649 0.506193i
\(61\) 0.708712 + 1.22753i 0.0907413 + 0.157169i 0.907823 0.419353i \(-0.137743\pi\)
−0.817082 + 0.576522i \(0.804410\pi\)
\(62\) −2.45505 1.41742i −0.311792 0.180013i
\(63\) 1.73205 3.00000i 0.218218 0.377964i
\(64\) −3.41742 −0.427178
\(65\) −8.03943 0.606325i −0.997168 0.0752054i
\(66\) −1.20871 −0.148782
\(67\) 0.504525 0.873864i 0.0616376 0.106759i −0.833560 0.552429i \(-0.813701\pi\)
0.895198 + 0.445670i \(0.147034\pi\)
\(68\) 7.10895 + 4.10436i 0.862087 + 0.497726i
\(69\) 2.29129 + 3.96863i 0.275839 + 0.477767i
\(70\) −1.73205 + 0.361500i −0.207020 + 0.0432075i
\(71\) 6.08258 3.51178i 0.721869 0.416771i −0.0935712 0.995613i \(-0.529828\pi\)
0.815440 + 0.578841i \(0.196495\pi\)
\(72\) 1.73205 + 3.00000i 0.204124 + 0.353553i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −1.81307 3.14033i −0.210765 0.365056i
\(75\) −4.96863 0.559237i −0.573728 0.0645751i
\(76\) −2.68693 1.55130i −0.308212 0.177946i
\(77\) 4.58258i 0.522233i
\(78\) −1.59898 + 0.395644i −0.181048 + 0.0447979i
\(79\) 6.00000 0.675053 0.337526 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) −1.95057 + 5.92889i −0.218080 + 0.662870i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.04678 + 0.604356i −0.115597 + 0.0667400i
\(83\) 6.01450 0.660177 0.330089 0.943950i \(-0.392921\pi\)
0.330089 + 0.943950i \(0.392921\pi\)
\(84\) 2.68693 1.55130i 0.293168 0.169261i
\(85\) 7.64016 6.82847i 0.828691 0.740652i
\(86\) 4.83465i 0.521334i
\(87\) −3.96863 + 2.29129i −0.425481 + 0.245652i
\(88\) 3.96863 + 2.29129i 0.423057 + 0.244252i
\(89\) 8.29129 + 4.78698i 0.878875 + 0.507419i 0.870287 0.492545i \(-0.163933\pi\)
0.00858752 + 0.999963i \(0.497266\pi\)
\(90\) 2.00000 0.417424i 0.210819 0.0440004i
\(91\) −1.50000 6.06218i −0.157243 0.635489i
\(92\) 8.20871i 0.855817i
\(93\) 3.10260 5.37386i 0.321725 0.557244i
\(94\) 0.417424 0.723000i 0.0430540 0.0745718i
\(95\) −2.88771 + 2.58092i −0.296273 + 0.264797i
\(96\) 4.73930i 0.483703i
\(97\) 5.70068 + 9.87386i 0.578816 + 1.00254i 0.995615 + 0.0935404i \(0.0298184\pi\)
−0.416799 + 0.908999i \(0.636848\pi\)
\(98\) 0.913701 + 1.58258i 0.0922977 + 0.159864i
\(99\) 5.29150i 0.531816i
\(100\) 7.20696 + 5.31767i 0.720696 + 0.531767i
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 1.04678 1.81307i 0.103646 0.179521i
\(103\) 3.16515i 0.311872i 0.987767 + 0.155936i \(0.0498393\pi\)
−0.987767 + 0.155936i \(0.950161\pi\)
\(104\) 6.00000 + 1.73205i 0.588348 + 0.169842i
\(105\) −0.791288 3.79129i −0.0772218 0.369992i
\(106\) −3.00000 1.73205i −0.291386 0.168232i
\(107\) −9.16478 5.29129i −0.885993 0.511528i −0.0133631 0.999911i \(-0.504254\pi\)
−0.872630 + 0.488383i \(0.837587\pi\)
\(108\) −7.75650 + 4.47822i −0.746370 + 0.430917i
\(109\) 13.1334i 1.25795i −0.777425 0.628976i \(-0.783474\pi\)
0.777425 0.628976i \(-0.216526\pi\)
\(110\) 2.01519 1.80110i 0.192141 0.171728i
\(111\) 6.87386 3.96863i 0.652438 0.376685i
\(112\) −4.83465 −0.456832
\(113\) −6.42368 + 3.70871i −0.604289 + 0.348886i −0.770727 0.637166i \(-0.780107\pi\)
0.166438 + 0.986052i \(0.446773\pi\)
\(114\) −0.395644 + 0.685275i −0.0370554 + 0.0641819i
\(115\) −9.73371 3.20233i −0.907673 0.298619i
\(116\) 8.20871 0.762160
\(117\) 1.73205 + 7.00000i 0.160128 + 0.647150i
\(118\) 6.37386i 0.586762i
\(119\) 6.87386 + 3.96863i 0.630126 + 0.363803i
\(120\) 3.67900 + 1.21037i 0.335845 + 0.110491i
\(121\) −2.00000 3.46410i −0.181818 0.314918i
\(122\) −0.647551 −0.0586265
\(123\) −1.32288 2.29129i −0.119280 0.206598i
\(124\) −9.62614 + 5.55765i −0.864453 + 0.499092i
\(125\) 9.11710 6.47135i 0.815459 0.578815i
\(126\) 0.791288 + 1.37055i 0.0704935 + 0.122098i
\(127\) 15.3700 + 8.87386i 1.36387 + 0.787428i 0.990136 0.140110i \(-0.0447455\pi\)
0.373729 + 0.927538i \(0.378079\pi\)
\(128\) 5.51993 9.56080i 0.487897 0.845063i
\(129\) −10.5826 −0.931744
\(130\) 2.07630 3.04225i 0.182103 0.266823i
\(131\) −7.58258 −0.662493 −0.331246 0.943544i \(-0.607469\pi\)
−0.331246 + 0.943544i \(0.607469\pi\)
\(132\) −2.36965 + 4.10436i −0.206252 + 0.357238i
\(133\) −2.59808 1.50000i −0.225282 0.130066i
\(134\) 0.230493 + 0.399225i 0.0199115 + 0.0344878i
\(135\) 2.28425 + 10.9445i 0.196597 + 0.941953i
\(136\) −6.87386 + 3.96863i −0.589429 + 0.340307i
\(137\) −5.24383 9.08258i −0.448010 0.775977i 0.550246 0.835003i \(-0.314534\pi\)
−0.998256 + 0.0590258i \(0.981201\pi\)
\(138\) −2.09355 −0.178215
\(139\) −10.8739 18.8341i −0.922309 1.59749i −0.795833 0.605517i \(-0.792967\pi\)
−0.126476 0.991970i \(-0.540367\pi\)
\(140\) −2.16812 + 6.59014i −0.183239 + 0.556968i
\(141\) 1.58258 + 0.913701i 0.133277 + 0.0769475i
\(142\) 3.20871i 0.269269i
\(143\) 6.61438 + 6.87386i 0.553122 + 0.574821i
\(144\) 5.58258 0.465215
\(145\) 3.20233 9.73371i 0.265939 0.808340i
\(146\) 0 0
\(147\) −3.46410 + 2.00000i −0.285714 + 0.164957i
\(148\) −14.2179 −1.16870
\(149\) −14.4564 + 8.34643i −1.18432 + 0.683766i −0.957009 0.290057i \(-0.906326\pi\)
−0.227308 + 0.973823i \(0.572992\pi\)
\(150\) 1.35622 1.83806i 0.110735 0.150077i
\(151\) 9.66930i 0.786877i −0.919351 0.393438i \(-0.871285\pi\)
0.919351 0.393438i \(-0.128715\pi\)
\(152\) 2.59808 1.50000i 0.210732 0.121666i
\(153\) −7.93725 4.58258i −0.641689 0.370479i
\(154\) 1.81307 + 1.04678i 0.146101 + 0.0843516i
\(155\) 2.83485 + 13.5826i 0.227701 + 1.09098i
\(156\) −1.79129 + 6.20520i −0.143418 + 0.496814i
\(157\) 9.16515i 0.731459i −0.930721 0.365729i \(-0.880820\pi\)
0.930721 0.365729i \(-0.119180\pi\)
\(158\) −1.37055 + 2.37386i −0.109035 + 0.188854i
\(159\) 3.79129 6.56670i 0.300669 0.520773i
\(160\) −7.06201 7.90145i −0.558301 0.624665i
\(161\) 7.93725i 0.625543i
\(162\) −0.228425 0.395644i −0.0179468 0.0310847i
\(163\) −10.5353 18.2477i −0.825191 1.42927i −0.901773 0.432209i \(-0.857734\pi\)
0.0765827 0.997063i \(-0.475599\pi\)
\(164\) 4.73930i 0.370077i
\(165\) 3.94242 + 4.41105i 0.306917 + 0.343399i
\(166\) −1.37386 + 2.37960i −0.106632 + 0.184693i
\(167\) 4.78698 8.29129i 0.370427 0.641599i −0.619204 0.785230i \(-0.712545\pi\)
0.989631 + 0.143631i \(0.0458779\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 11.0000 + 6.92820i 0.846154 + 0.532939i
\(170\) 0.956439 + 4.58258i 0.0733555 + 0.351468i
\(171\) 3.00000 + 1.73205i 0.229416 + 0.132453i
\(172\) 16.4168 + 9.47822i 1.25177 + 0.722707i
\(173\) −14.3609 + 8.29129i −1.09184 + 0.630375i −0.934066 0.357100i \(-0.883766\pi\)
−0.157775 + 0.987475i \(0.550432\pi\)
\(174\) 2.09355i 0.158712i
\(175\) 6.96863 + 5.14181i 0.526779 + 0.388685i
\(176\) 6.39564 3.69253i 0.482090 0.278335i
\(177\) 13.9518 1.04868
\(178\) −3.78788 + 2.18693i −0.283913 + 0.163917i
\(179\) 9.08258 15.7315i 0.678864 1.17583i −0.296460 0.955045i \(-0.595806\pi\)
0.975323 0.220781i \(-0.0708606\pi\)
\(180\) 2.50353 7.60964i 0.186602 0.567189i
\(181\) 8.74773 0.650213 0.325107 0.945677i \(-0.394600\pi\)
0.325107 + 0.945677i \(0.394600\pi\)
\(182\) 2.74110 + 0.791288i 0.203184 + 0.0586542i
\(183\) 1.41742i 0.104779i
\(184\) 6.87386 + 3.96863i 0.506748 + 0.292571i
\(185\) −5.54661 + 16.8593i −0.407795 + 1.23952i
\(186\) 1.41742 + 2.45505i 0.103931 + 0.180013i
\(187\) −12.1244 −0.886621
\(188\) −1.63670 2.83485i −0.119369 0.206753i
\(189\) −7.50000 + 4.33013i −0.545545 + 0.314970i
\(190\) −0.361500 1.73205i −0.0262260 0.125656i
\(191\) 8.29129 + 14.3609i 0.599937 + 1.03912i 0.992830 + 0.119536i \(0.0381408\pi\)
−0.392893 + 0.919584i \(0.628526\pi\)
\(192\) 2.95958 + 1.70871i 0.213589 + 0.123316i
\(193\) −7.43273 + 12.8739i −0.535020 + 0.926681i 0.464143 + 0.885760i \(0.346362\pi\)
−0.999162 + 0.0409206i \(0.986971\pi\)
\(194\) −5.20871 −0.373964
\(195\) 6.65918 + 4.54481i 0.476874 + 0.325460i
\(196\) 7.16515 0.511797
\(197\) 7.33738 12.7087i 0.522767 0.905458i −0.476882 0.878967i \(-0.658233\pi\)
0.999649 0.0264912i \(-0.00843339\pi\)
\(198\) −2.09355 1.20871i −0.148782 0.0858994i
\(199\) 5.29129 + 9.16478i 0.375089 + 0.649674i 0.990340 0.138657i \(-0.0442787\pi\)
−0.615251 + 0.788331i \(0.710945\pi\)
\(200\) −7.93725 + 3.46410i −0.561249 + 0.244949i
\(201\) −0.873864 + 0.504525i −0.0616376 + 0.0355865i
\(202\) −2.05583 3.56080i −0.144647 0.250537i
\(203\) 7.93725 0.557086
\(204\) −4.10436 7.10895i −0.287362 0.497726i
\(205\) 5.61976 + 1.84887i 0.392501 + 0.129131i
\(206\) −1.25227 0.723000i −0.0872500 0.0503738i
\(207\) 9.16515i 0.637022i
\(208\) 7.25198 6.97822i 0.502834 0.483852i
\(209\) 4.58258 0.316983
\(210\) 1.68075 + 0.552957i 0.115983 + 0.0381577i
\(211\) 0.0825757 0.143025i 0.00568475 0.00984627i −0.863169 0.504915i \(-0.831524\pi\)
0.868854 + 0.495069i \(0.164857\pi\)
\(212\) −11.7629 + 6.79129i −0.807876 + 0.466428i
\(213\) −7.02355 −0.481246
\(214\) 4.18693 2.41733i 0.286213 0.165245i
\(215\) 17.6435 15.7690i 1.20327 1.07544i
\(216\) 8.66025i 0.589256i
\(217\) −9.30780 + 5.37386i −0.631855 + 0.364802i
\(218\) 5.19615 + 3.00000i 0.351928 + 0.203186i
\(219\) 0 0
\(220\) −2.16515 10.3739i −0.145974 0.699406i
\(221\) −16.0390 + 3.96863i −1.07890 + 0.266959i
\(222\) 3.62614i 0.243370i
\(223\) 4.33013 7.50000i 0.289967 0.502237i −0.683835 0.729637i \(-0.739689\pi\)
0.973801 + 0.227400i \(0.0730224\pi\)
\(224\) 4.10436 7.10895i 0.274234 0.474987i
\(225\) −8.04668 5.93725i −0.536445 0.395817i
\(226\) 3.38865i 0.225410i
\(227\) −0.409175 0.708712i −0.0271579 0.0470389i 0.852127 0.523335i \(-0.175312\pi\)
−0.879285 + 0.476296i \(0.841979\pi\)
\(228\) 1.55130 + 2.68693i 0.102737 + 0.177946i
\(229\) 26.2668i 1.73576i 0.496774 + 0.867880i \(0.334518\pi\)
−0.496774 + 0.867880i \(0.665482\pi\)
\(230\) 3.49041 3.11959i 0.230151 0.205700i
\(231\) −2.29129 + 3.96863i −0.150756 + 0.261116i
\(232\) −3.96863 + 6.87386i −0.260553 + 0.451291i
\(233\) 2.83485i 0.185717i 0.995679 + 0.0928586i \(0.0296004\pi\)
−0.995679 + 0.0928586i \(0.970400\pi\)
\(234\) −3.16515 0.913701i −0.206912 0.0597305i
\(235\) −4.00000 + 0.834849i −0.260931 + 0.0544595i
\(236\) −21.6434 12.4958i −1.40886 0.813408i
\(237\) −5.19615 3.00000i −0.337526 0.194871i
\(238\) −3.14033 + 1.81307i −0.203557 + 0.117524i
\(239\) 0.190700i 0.0123354i 0.999981 + 0.00616769i \(0.00196325\pi\)
−0.999981 + 0.00616769i \(0.998037\pi\)
\(240\) 4.65369 4.15928i 0.300394 0.268481i
\(241\) −1.50000 + 0.866025i −0.0966235 + 0.0557856i −0.547533 0.836784i \(-0.684433\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 1.82740 0.117470
\(243\) 13.8564 8.00000i 0.888889 0.513200i
\(244\) −1.26951 + 2.19885i −0.0812719 + 0.140767i
\(245\) 2.79523 8.49628i 0.178580 0.542807i
\(246\) 1.20871 0.0770647
\(247\) 6.06218 1.50000i 0.385727 0.0954427i
\(248\) 10.7477i 0.682481i
\(249\) −5.20871 3.00725i −0.330089 0.190577i
\(250\) 0.477776 + 5.08535i 0.0302172 + 0.321626i
\(251\) 0.0825757 + 0.143025i 0.00521213 + 0.00902768i 0.868620 0.495479i \(-0.165008\pi\)
−0.863408 + 0.504507i \(0.831674\pi\)
\(252\) 6.20520 0.390891
\(253\) 6.06218 + 10.5000i 0.381126 + 0.660129i
\(254\) −7.02178 + 4.05403i −0.440586 + 0.254372i
\(255\) −10.0308 + 2.09355i −0.628153 + 0.131103i
\(256\) −0.895644 1.55130i −0.0559777 0.0969563i
\(257\) −15.7315 9.08258i −0.981303 0.566556i −0.0786397 0.996903i \(-0.525058\pi\)
−0.902663 + 0.430348i \(0.858391\pi\)
\(258\) 2.41733 4.18693i 0.150496 0.260667i
\(259\) −13.7477 −0.854242
\(260\) −6.25987 13.0146i −0.388221 0.807132i
\(261\) −9.16515 −0.567309
\(262\) 1.73205 3.00000i 0.107006 0.185341i
\(263\) −7.79423 4.50000i −0.480613 0.277482i 0.240059 0.970758i \(-0.422833\pi\)
−0.720672 + 0.693276i \(0.756167\pi\)
\(264\) −2.29129 3.96863i −0.141019 0.244252i
\(265\) 3.46410 + 16.5975i 0.212798 + 1.01958i
\(266\) 1.18693 0.685275i 0.0727755 0.0420169i
\(267\) −4.78698 8.29129i −0.292958 0.507419i
\(268\) 1.80750 0.110411
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) −4.85191 1.59625i −0.295278 0.0971447i
\(271\) 7.50000 + 4.33013i 0.455593 + 0.263036i 0.710189 0.704011i \(-0.248609\pi\)
−0.254597 + 0.967047i \(0.581943\pi\)
\(272\) 12.7913i 0.775586i
\(273\) −1.73205 + 6.00000i −0.104828 + 0.363137i
\(274\) 4.79129 0.289452
\(275\) −13.1458 1.47960i −0.792719 0.0892234i
\(276\) −4.10436 + 7.10895i −0.247053 + 0.427909i
\(277\) 6.42368 3.70871i 0.385961 0.222835i −0.294447 0.955668i \(-0.595136\pi\)
0.680409 + 0.732833i \(0.261802\pi\)
\(278\) 9.93545 0.595889
\(279\) 10.7477 6.20520i 0.643450 0.371496i
\(280\) −4.47028 5.00166i −0.267151 0.298906i
\(281\) 3.65480i 0.218027i 0.994040 + 0.109014i \(0.0347692\pi\)
−0.994040 + 0.109014i \(0.965231\pi\)
\(282\) −0.723000 + 0.417424i −0.0430540 + 0.0248573i
\(283\) 24.0302 + 13.8739i 1.42845 + 0.824716i 0.996998 0.0774209i \(-0.0246685\pi\)
0.431451 + 0.902136i \(0.358002\pi\)
\(284\) 10.8956 + 6.29060i 0.646538 + 0.373279i
\(285\) 3.79129 0.791288i 0.224577 0.0468718i
\(286\) −4.23049 + 1.04678i −0.250154 + 0.0618971i
\(287\) 4.58258i 0.270501i
\(288\) −4.73930 + 8.20871i −0.279266 + 0.483703i
\(289\) 2.00000 3.46410i 0.117647 0.203771i
\(290\) 3.11959 + 3.49041i 0.183189 + 0.204964i
\(291\) 11.4014i 0.668359i
\(292\) 0 0
\(293\) 9.06943 + 15.7087i 0.529842 + 0.917713i 0.999394 + 0.0348081i \(0.0110820\pi\)
−0.469552 + 0.882905i \(0.655585\pi\)
\(294\) 1.82740i 0.106576i
\(295\) −23.2606 + 20.7894i −1.35429 + 1.21041i
\(296\) 6.87386 11.9059i 0.399535 0.692015i
\(297\) 6.61438 11.4564i 0.383805 0.664770i
\(298\) 7.62614i 0.441770i
\(299\) 11.4564 + 11.9059i 0.662543 + 0.688535i
\(300\) −3.58258 8.20871i −0.206840 0.473930i
\(301\) 15.8739 + 9.16478i 0.914954 + 0.528249i
\(302\) 3.82560 + 2.20871i 0.220139 + 0.127097i
\(303\) 7.79423 4.50000i 0.447767 0.258518i
\(304\) 4.83465i 0.277286i
\(305\) 2.11210 + 2.36316i 0.120938 + 0.135314i
\(306\) 3.62614 2.09355i 0.207292 0.119680i
\(307\) −24.2487 −1.38395 −0.691974 0.721923i \(-0.743259\pi\)
−0.691974 + 0.721923i \(0.743259\pi\)
\(308\) 7.10895 4.10436i 0.405070 0.233867i
\(309\) 1.58258 2.74110i 0.0900296 0.155936i
\(310\) −6.02141 1.98101i −0.341993 0.112514i
\(311\) 7.58258 0.429968 0.214984 0.976618i \(-0.431030\pi\)
0.214984 + 0.976618i \(0.431030\pi\)
\(312\) −4.33013 4.50000i −0.245145 0.254762i
\(313\) 3.25227i 0.183829i −0.995767 0.0919147i \(-0.970701\pi\)
0.995767 0.0919147i \(-0.0292987\pi\)
\(314\) 3.62614 + 2.09355i 0.204635 + 0.118146i
\(315\) 2.42074 7.35799i 0.136393 0.414576i
\(316\) 5.37386 + 9.30780i 0.302303 + 0.523605i
\(317\) 0.190700 0.0107108 0.00535540 0.999986i \(-0.498295\pi\)
0.00535540 + 0.999986i \(0.498295\pi\)
\(318\) 1.73205 + 3.00000i 0.0971286 + 0.168232i
\(319\) −10.5000 + 6.06218i −0.587887 + 0.339417i
\(320\) −7.48040 + 1.56125i −0.418167 + 0.0872766i
\(321\) 5.29129 + 9.16478i 0.295331 + 0.511528i
\(322\) 3.14033 + 1.81307i 0.175004 + 0.101038i
\(323\) −3.96863 + 6.87386i −0.220820 + 0.382472i
\(324\) −1.79129 −0.0995160
\(325\) −17.8745 + 2.34563i −0.991499 + 0.130112i
\(326\) 9.62614 0.533142
\(327\) −6.56670 + 11.3739i −0.363140 + 0.628976i
\(328\) −3.96863 2.29129i −0.219131 0.126515i
\(329\) −1.58258 2.74110i −0.0872502 0.151122i
\(330\) −2.64575 + 0.552200i −0.145644 + 0.0303976i
\(331\) −3.87386 + 2.23658i −0.212927 + 0.122933i −0.602671 0.797990i \(-0.705897\pi\)
0.389744 + 0.920923i \(0.372563\pi\)
\(332\) 5.38685 + 9.33030i 0.295642 + 0.512067i
\(333\) 15.8745 0.869918
\(334\) 2.18693 + 3.78788i 0.119664 + 0.207263i
\(335\) 0.705131 2.14329i 0.0385254 0.117101i
\(336\) 4.18693 + 2.41733i 0.228416 + 0.131876i
\(337\) 30.7477i 1.67494i −0.546487 0.837468i \(-0.684035\pi\)
0.546487 0.837468i \(-0.315965\pi\)
\(338\) −5.25378 + 2.76951i −0.285768 + 0.150641i
\(339\) 7.41742 0.402859
\(340\) 17.4359 + 5.73630i 0.945593 + 0.311095i
\(341\) 8.20871 14.2179i 0.444527 0.769943i
\(342\) −1.37055 + 0.791288i −0.0741109 + 0.0427879i
\(343\) 19.0526 1.02874
\(344\) −15.8739 + 9.16478i −0.855861 + 0.494132i
\(345\) 6.82847 + 7.64016i 0.367633 + 0.411332i
\(346\) 7.57575i 0.407275i
\(347\) 18.4726 10.6652i 0.991660 0.572535i 0.0858901 0.996305i \(-0.472627\pi\)
0.905770 + 0.423769i \(0.139293\pi\)
\(348\) −7.10895 4.10436i −0.381080 0.220017i
\(349\) 2.12614 + 1.22753i 0.113809 + 0.0657079i 0.555824 0.831300i \(-0.312403\pi\)
−0.442015 + 0.897008i \(0.645736\pi\)
\(350\) −3.62614 + 1.58258i −0.193825 + 0.0845922i
\(351\) 5.00000 17.3205i 0.266880 0.924500i
\(352\) 12.5390i 0.668332i
\(353\) −3.41643 + 5.91742i −0.181838 + 0.314953i −0.942506 0.334188i \(-0.891538\pi\)
0.760668 + 0.649141i \(0.224871\pi\)
\(354\) −3.18693 + 5.51993i −0.169384 + 0.293381i
\(355\) 11.7098 10.4658i 0.621492 0.555465i
\(356\) 17.1497i 0.908933i
\(357\) −3.96863 6.87386i −0.210042 0.363803i
\(358\) 4.14938 + 7.18693i 0.219301 + 0.379841i
\(359\) 19.5293i 1.03072i −0.856975 0.515359i \(-0.827659\pi\)
0.856975 0.515359i \(-0.172341\pi\)
\(360\) 5.16184 + 5.77542i 0.272053 + 0.304391i
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) −1.99820 + 3.46099i −0.105023 + 0.181905i
\(363\) 4.00000i 0.209946i
\(364\) 8.06080 7.75650i 0.422500 0.406551i
\(365\) 0 0
\(366\) 0.560795 + 0.323775i 0.0293132 + 0.0169240i
\(367\) −1.51358 0.873864i −0.0790080 0.0456153i 0.459976 0.887932i \(-0.347858\pi\)
−0.538984 + 0.842316i \(0.681192\pi\)
\(368\) 11.0776 6.39564i 0.577459 0.333396i
\(369\) 5.29150i 0.275465i
\(370\) −5.40329 6.04556i −0.280903 0.314294i
\(371\) −11.3739 + 6.56670i −0.590502 + 0.340926i
\(372\) 11.1153 0.576302
\(373\) −11.2583 + 6.50000i −0.582934 + 0.336557i −0.762299 0.647225i \(-0.775929\pi\)
0.179364 + 0.983783i \(0.442596\pi\)
\(374\) 2.76951 4.79693i 0.143208 0.248043i
\(375\) −11.1313 + 1.04580i −0.574819 + 0.0540051i
\(376\) 3.16515 0.163230
\(377\) −11.9059 + 11.4564i −0.613184 + 0.590037i
\(378\) 3.95644i 0.203497i
\(379\) −9.24773 5.33918i −0.475024 0.274255i 0.243317 0.969947i \(-0.421765\pi\)
−0.718340 + 0.695692i \(0.755098\pi\)
\(380\) −6.59014 2.16812i −0.338067 0.111222i
\(381\) −8.87386 15.3700i −0.454622 0.787428i
\(382\) −7.57575 −0.387609
\(383\) −11.8105 20.4564i −0.603490 1.04528i −0.992288 0.123952i \(-0.960443\pi\)
0.388798 0.921323i \(-0.372890\pi\)
\(384\) −9.56080 + 5.51993i −0.487897 + 0.281688i
\(385\) −2.09355 10.0308i −0.106697 0.511217i
\(386\) −3.39564 5.88143i −0.172834 0.299357i
\(387\) −18.3296 10.5826i −0.931744 0.537943i
\(388\) −10.2116 + 17.6869i −0.518413 + 0.897918i
\(389\) 3.16515 0.160480 0.0802398 0.996776i \(-0.474431\pi\)
0.0802398 + 0.996776i \(0.474431\pi\)
\(390\) −3.31925 + 1.59652i −0.168077 + 0.0808428i
\(391\) −21.0000 −1.06202
\(392\) −3.46410 + 6.00000i −0.174964 + 0.303046i
\(393\) 6.56670 + 3.79129i 0.331246 + 0.191245i
\(394\) 3.35208 + 5.80598i 0.168876 + 0.292501i
\(395\) 13.1334 2.74110i 0.660813 0.137920i
\(396\) −8.20871 + 4.73930i −0.412503 + 0.238159i
\(397\) 10.1738 + 17.6216i 0.510610 + 0.884402i 0.999924 + 0.0122949i \(0.00391368\pi\)
−0.489315 + 0.872107i \(0.662753\pi\)
\(398\) −4.83465 −0.242339
\(399\) 1.50000 + 2.59808i 0.0750939 + 0.130066i
\(400\) −1.56099 + 13.8689i −0.0780496 + 0.693443i
\(401\) −25.8303 14.9131i −1.28990 0.744726i −0.311267 0.950323i \(-0.600753\pi\)
−0.978637 + 0.205596i \(0.934087\pi\)
\(402\) 0.460985i 0.0229918i
\(403\) 6.20520 21.4955i 0.309103 1.07076i
\(404\) −16.1216 −0.802079
\(405\) −0.698807 + 2.12407i −0.0347240 + 0.105546i
\(406\) −1.81307 + 3.14033i −0.0899811 + 0.155852i
\(407\) 18.1865 10.5000i 0.901473 0.520466i
\(408\) 7.93725 0.392953
\(409\) 7.50000 4.33013i 0.370851 0.214111i −0.302979 0.952997i \(-0.597981\pi\)
0.673830 + 0.738886i \(0.264648\pi\)
\(410\) −2.01519 + 1.80110i −0.0995230 + 0.0889498i
\(411\) 10.4877i 0.517318i
\(412\) −4.91010 + 2.83485i −0.241903 + 0.139663i
\(413\) −20.9276 12.0826i −1.02978 0.594545i
\(414\) −3.62614 2.09355i −0.178215 0.102892i
\(415\) 13.1652 2.74773i 0.646252 0.134881i
\(416\) 4.10436 + 16.5876i 0.201233 + 0.813272i
\(417\) 21.7477i 1.06499i
\(418\) −1.04678 + 1.81307i −0.0511995 + 0.0886801i
\(419\) −2.91742 + 5.05313i −0.142526 + 0.246861i −0.928447 0.371465i \(-0.878856\pi\)
0.785922 + 0.618326i \(0.212189\pi\)
\(420\) 5.17272 4.62317i 0.252403 0.225588i
\(421\) 5.48220i 0.267186i 0.991036 + 0.133593i \(0.0426515\pi\)
−0.991036 + 0.133593i \(0.957348\pi\)
\(422\) 0.0377247 + 0.0653411i 0.00183641 + 0.00318076i
\(423\) 1.82740 + 3.16515i 0.0888513 + 0.153895i
\(424\) 13.1334i 0.637815i
\(425\) 13.6040 18.4373i 0.659889 0.894338i
\(426\) 1.60436 2.77883i 0.0777313 0.134635i
\(427\) −1.22753 + 2.12614i −0.0594041 + 0.102891i
\(428\) 18.9564i 0.916294i
\(429\) −2.29129 9.26013i −0.110624 0.447083i
\(430\) 2.20871 + 10.5826i 0.106514 + 0.510337i
\(431\) 7.33485 + 4.23478i 0.353307 + 0.203982i 0.666141 0.745826i \(-0.267945\pi\)
−0.312834 + 0.949808i \(0.601278\pi\)
\(432\) −12.0866 6.97822i −0.581518 0.335740i
\(433\) 8.44178 4.87386i 0.405686 0.234223i −0.283248 0.959047i \(-0.591412\pi\)
0.688934 + 0.724824i \(0.258079\pi\)
\(434\) 4.91010i 0.235692i
\(435\) −7.64016 + 6.82847i −0.366317 + 0.327400i
\(436\) 20.3739 11.7629i 0.975731 0.563339i
\(437\) 7.93725 0.379690
\(438\) 0 0
\(439\) −7.24773 + 12.5534i −0.345915 + 0.599143i −0.985520 0.169562i \(-0.945765\pi\)
0.639604 + 0.768704i \(0.279098\pi\)
\(440\) 9.73371 + 3.20233i 0.464036 + 0.152665i
\(441\) −8.00000 −0.380952
\(442\) 2.09355 7.25227i 0.0995801 0.344955i
\(443\) 19.9129i 0.946089i 0.881038 + 0.473045i \(0.156845\pi\)
−0.881038 + 0.473045i \(0.843155\pi\)
\(444\) 12.3131 + 7.10895i 0.584352 + 0.337376i
\(445\) 20.3357 + 6.69034i 0.964007 + 0.317153i
\(446\) 1.97822 + 3.42638i 0.0936714 + 0.162244i
\(447\) 16.6929 0.789545
\(448\) −2.95958 5.12614i −0.139827 0.242187i
\(449\) 9.54356 5.50998i 0.450388 0.260032i −0.257606 0.966250i \(-0.582934\pi\)
0.707994 + 0.706218i \(0.249600\pi\)
\(450\) 4.18710 1.82740i 0.197382 0.0861445i
\(451\) −3.50000 6.06218i −0.164809 0.285457i
\(452\) −11.5067 6.64337i −0.541228 0.312478i
\(453\) −4.83465 + 8.37386i −0.227152 + 0.393438i
\(454\) 0.373864 0.0175463
\(455\) −6.05286 12.5842i −0.283762 0.589958i
\(456\) −3.00000 −0.140488
\(457\) −0.866025 + 1.50000i −0.0405110 + 0.0701670i −0.885570 0.464506i \(-0.846232\pi\)
0.845059 + 0.534673i \(0.179565\pi\)
\(458\) −10.3923 6.00000i −0.485601 0.280362i
\(459\) 11.4564 + 19.8431i 0.534741 + 0.926198i
\(460\) −3.75015 17.9681i −0.174852 0.837765i
\(461\) 31.0390 17.9204i 1.44563 0.834635i 0.447414 0.894327i \(-0.352345\pi\)
0.998217 + 0.0596914i \(0.0190117\pi\)
\(462\) −1.04678 1.81307i −0.0487004 0.0843516i
\(463\) −39.4002 −1.83108 −0.915542 0.402223i \(-0.868238\pi\)
−0.915542 + 0.402223i \(0.868238\pi\)
\(464\) 6.39564 + 11.0776i 0.296910 + 0.514264i
\(465\) 4.33624 13.1803i 0.201088 0.611221i
\(466\) −1.12159 0.647551i −0.0519567 0.0299972i
\(467\) 24.3303i 1.12587i 0.826500 + 0.562936i \(0.190328\pi\)
−0.826500 + 0.562936i \(0.809672\pi\)
\(468\) −9.30780 + 8.95644i −0.430253 + 0.414012i
\(469\) 1.74773 0.0807025
\(470\) 0.583398 1.77328i 0.0269101 0.0817951i
\(471\) −4.58258 + 7.93725i −0.211154 + 0.365729i
\(472\) 20.9276 12.0826i 0.963272 0.556146i
\(473\) −27.9989 −1.28739
\(474\) 2.37386 1.37055i 0.109035 0.0629515i
\(475\) −5.14181 + 6.96863i −0.235923 + 0.319743i
\(476\) 14.2179i 0.651677i
\(477\) 13.1334 7.58258i 0.601337 0.347182i
\(478\) −0.0754495 0.0435608i −0.00345098 0.00199242i
\(479\) 4.03901 + 2.33193i 0.184547 + 0.106548i 0.589427 0.807821i \(-0.299353\pi\)
−0.404880 + 0.914370i \(0.632687\pi\)
\(480\) 2.16515 + 10.3739i 0.0988252 + 0.473500i
\(481\) 20.6216 19.8431i 0.940264 0.904769i
\(482\) 0.791288i 0.0360422i
\(483\) −3.96863 + 6.87386i −0.180579 + 0.312772i
\(484\) 3.58258 6.20520i 0.162844 0.282055i
\(485\) 16.9891 + 19.0086i 0.771435 + 0.863134i
\(486\) 7.30960i 0.331570i
\(487\) −5.33918 9.24773i −0.241941 0.419055i 0.719326 0.694673i \(-0.244451\pi\)
−0.961267 + 0.275618i \(0.911117\pi\)
\(488\) −1.22753 2.12614i −0.0555675 0.0962457i
\(489\) 21.0707i 0.952848i
\(490\) 2.72300 + 3.04668i 0.123013 + 0.137635i
\(491\) −9.70871 + 16.8160i −0.438148 + 0.758895i −0.997547 0.0700041i \(-0.977699\pi\)
0.559399 + 0.828899i \(0.311032\pi\)
\(492\) 2.36965 4.10436i 0.106832 0.185039i
\(493\) 21.0000i 0.945792i
\(494\) −0.791288 + 2.74110i −0.0356017 + 0.123328i
\(495\) 2.41742 + 11.5826i 0.108655 + 0.520598i
\(496\) −15.0000 8.66025i −0.673520 0.388857i
\(497\) 10.5353 + 6.08258i 0.472574 + 0.272841i
\(498\) 2.37960 1.37386i 0.106632 0.0615643i
\(499\) 0.723000i 0.0323659i 0.999869 + 0.0161830i \(0.00515142\pi\)
−0.999869 + 0.0161830i \(0.994849\pi\)
\(500\) 18.2047 + 8.34734i 0.814139 + 0.373305i
\(501\) −8.29129 + 4.78698i −0.370427 + 0.213866i
\(502\) −0.0754495 −0.00336747
\(503\) 0.143025 0.0825757i 0.00637718 0.00368187i −0.496808 0.867860i \(-0.665495\pi\)
0.503185 + 0.864179i \(0.332161\pi\)
\(504\) −3.00000 + 5.19615i −0.133631 + 0.231455i
\(505\) −6.28926 + 19.1166i −0.279868 + 0.850678i
\(506\) −5.53901 −0.246239
\(507\) −6.06218 11.5000i −0.269231 0.510733i
\(508\) 31.7913i 1.41051i
\(509\) −7.33485 4.23478i −0.325111 0.187703i 0.328557 0.944484i \(-0.393438\pi\)
−0.653669 + 0.756781i \(0.726771\pi\)
\(510\) 1.46299 4.44685i 0.0647822 0.196910i
\(511\) 0 0
\(512\) 22.8981 1.01196
\(513\) −4.33013 7.50000i −0.191180 0.331133i
\(514\) 7.18693 4.14938i 0.317002 0.183021i
\(515\) 1.44600 + 6.92820i 0.0637184 + 0.305293i
\(516\) −9.47822 16.4168i −0.417255 0.722707i
\(517\) 4.18710 + 2.41742i 0.184149 + 0.106318i
\(518\) 3.14033 5.43920i 0.137978 0.238985i
\(519\) 16.5826 0.727894
\(520\) 13.9247 + 1.05019i 0.610638 + 0.0460537i
\(521\) 27.4955 1.20460 0.602299 0.798271i \(-0.294252\pi\)
0.602299 + 0.798271i \(0.294252\pi\)
\(522\) 2.09355 3.62614i 0.0916322 0.158712i
\(523\) −0.143025 0.0825757i −0.00625406 0.00361078i 0.496870 0.867825i \(-0.334483\pi\)
−0.503124 + 0.864214i \(0.667816\pi\)
\(524\) −6.79129 11.7629i −0.296679 0.513863i
\(525\) −3.46410 7.93725i −0.151186 0.346410i
\(526\) 3.56080 2.05583i 0.155258 0.0896383i
\(527\) 14.2179 + 24.6261i 0.619342 + 1.07273i
\(528\) −7.38505 −0.321393
\(529\) −1.00000 1.73205i −0.0434783 0.0753066i
\(530\) −7.35799 2.42074i −0.319611 0.105150i
\(531\) 24.1652 + 13.9518i 1.04868 + 0.605455i
\(532\) 5.37386i 0.232987i
\(533\) −6.61438 6.87386i −0.286501 0.297740i
\(534\) 4.37386 0.189276
\(535\) −22.4781 7.39517i −0.971814 0.319721i
\(536\) −0.873864 + 1.51358i −0.0377452 + 0.0653765i
\(537\) −15.7315 + 9.08258i −0.678864 + 0.391942i
\(538\) 6.85275 0.295443
\(539\) −9.16515 + 5.29150i −0.394771 + 0.227921i
\(540\) −14.9323 + 13.3459i −0.642586 + 0.574318i
\(541\) 10.3923i 0.446800i −0.974727 0.223400i \(-0.928284\pi\)
0.974727 0.223400i \(-0.0717156\pi\)
\(542\) −3.42638 + 1.97822i −0.147175 + 0.0849718i
\(543\) −7.57575 4.37386i −0.325107 0.187700i
\(544\) −18.8085 10.8591i −0.806409 0.465580i
\(545\) −6.00000 28.7477i −0.257012 1.23142i
\(546\) −1.97822 2.05583i −0.0846600 0.0879812i
\(547\) 28.7477i 1.22916i −0.788853 0.614582i \(-0.789325\pi\)
0.788853 0.614582i \(-0.210675\pi\)
\(548\) 9.39320 16.2695i 0.401258 0.694999i
\(549\) 1.41742 2.45505i 0.0604942 0.104779i
\(550\) 3.58822 4.86306i 0.153002 0.207362i
\(551\) 7.93725i 0.338138i
\(552\) −3.96863 6.87386i −0.168916 0.292571i
\(553\) 5.19615 + 9.00000i 0.220963 + 0.382719i
\(554\) 3.38865i 0.143970i
\(555\) 13.2331 11.8273i 0.561715 0.502039i
\(556\) 19.4782 33.7373i 0.826061 1.43078i
\(557\) −3.87328 + 6.70871i −0.164116 + 0.284257i −0.936341 0.351092i \(-0.885810\pi\)
0.772225 + 0.635349i \(0.219144\pi\)
\(558\) 5.66970i 0.240017i
\(559\) −37.0390 + 9.16478i −1.56658 + 0.387629i
\(560\) −10.5826 + 2.20871i −0.447195 + 0.0933351i
\(561\) 10.5000 + 6.06218i 0.443310 + 0.255945i
\(562\) −1.44600 0.834849i −0.0609958 0.0352160i
\(563\) −7.79423 + 4.50000i −0.328488 + 0.189652i −0.655169 0.755482i \(-0.727403\pi\)
0.326682 + 0.945134i \(0.394069\pi\)
\(564\) 3.27340i 0.137835i
\(565\) −12.3665 + 11.0527i −0.520261 + 0.464989i
\(566\) −10.9782 + 6.33828i −0.461449 + 0.266418i
\(567\) −1.73205 −0.0727393
\(568\) −10.5353 + 6.08258i −0.442053 + 0.255219i
\(569\) 3.87386 6.70973i 0.162401 0.281286i −0.773328 0.634006i \(-0.781410\pi\)
0.935729 + 0.352719i \(0.114743\pi\)
\(570\) −0.552957 + 1.68075i −0.0231608 + 0.0703989i
\(571\) −35.0780 −1.46797 −0.733985 0.679166i \(-0.762342\pi\)
−0.733985 + 0.679166i \(0.762342\pi\)
\(572\) −4.73930 + 16.4174i −0.198160 + 0.686447i
\(573\) 16.5826i 0.692747i
\(574\) −1.81307 1.04678i −0.0756760 0.0436916i
\(575\) −22.7691 2.56275i −0.949537 0.106874i
\(576\) 3.41742 + 5.91915i 0.142393 + 0.246631i
\(577\) 6.92820 0.288425 0.144212 0.989547i \(-0.453935\pi\)
0.144212 + 0.989547i \(0.453935\pi\)
\(578\) 0.913701 + 1.58258i 0.0380049 + 0.0658265i
\(579\) 12.8739 7.43273i 0.535020 0.308894i
\(580\) 17.9681 3.75015i 0.746083 0.155717i
\(581\) 5.20871 + 9.02175i 0.216094 + 0.374285i
\(582\) 4.51088 + 2.60436i 0.186982 + 0.107954i
\(583\) 10.0308 17.3739i 0.415433 0.719552i
\(584\) 0 0
\(585\) 6.98924 + 14.5310i 0.288969 + 0.600784i
\(586\) −8.28674 −0.342322
\(587\) −19.7478 + 34.2042i −0.815078 + 1.41176i 0.0941934 + 0.995554i \(0.469973\pi\)
−0.909272 + 0.416203i \(0.863361\pi\)
\(588\) −6.20520 3.58258i −0.255898 0.147743i
\(589\) −5.37386 9.30780i −0.221426 0.383521i
\(590\) −2.91190 13.9518i −0.119881 0.574385i
\(591\) −12.7087 + 7.33738i −0.522767 + 0.301819i
\(592\) −11.0776 19.1869i −0.455286 0.788578i
\(593\) 21.1660 0.869184 0.434592 0.900627i \(-0.356893\pi\)
0.434592 + 0.900627i \(0.356893\pi\)
\(594\) 3.02178 + 5.23388i 0.123985 + 0.214749i
\(595\) 16.8593 + 5.54661i 0.691163 + 0.227389i
\(596\) −25.8956 14.9509i −1.06073 0.612411i
\(597\) 10.5826i 0.433116i
\(598\) −7.32743 + 1.81307i −0.299641 + 0.0741419i
\(599\) −15.4955 −0.633127 −0.316564 0.948571i \(-0.602529\pi\)
−0.316564 + 0.948571i \(0.602529\pi\)
\(600\) 8.60591 + 0.968627i 0.351335 + 0.0395440i
\(601\) −8.45644 + 14.6470i −0.344945 + 0.597463i −0.985344 0.170580i \(-0.945436\pi\)
0.640398 + 0.768043i \(0.278769\pi\)
\(602\) −7.25198 + 4.18693i −0.295569 + 0.170647i
\(603\) −2.01810 −0.0821834
\(604\) 15.0000 8.66025i 0.610341 0.352381i
\(605\) −5.96038 6.66888i −0.242324 0.271128i
\(606\) 4.11165i 0.167024i
\(607\) −6.70973 + 3.87386i −0.272339 + 0.157235i −0.629950 0.776635i \(-0.716925\pi\)
0.357611 + 0.933871i \(0.383591\pi\)
\(608\) 7.10895 + 4.10436i 0.288306 + 0.166454i
\(609\) −6.87386 3.96863i −0.278543 0.160817i
\(610\) −1.41742 + 0.295834i −0.0573898 + 0.0119780i
\(611\) 6.33030 + 1.82740i 0.256097 + 0.0739287i
\(612\) 16.4174i 0.663635i
\(613\) 2.95958 5.12614i 0.119536 0.207043i −0.800048 0.599936i \(-0.795193\pi\)
0.919584 + 0.392894i \(0.128526\pi\)
\(614\) 5.53901 9.59386i 0.223536 0.387176i
\(615\) −3.94242 4.41105i −0.158974 0.177871i
\(616\) 7.93725i 0.319801i
\(617\) 6.97588 + 12.0826i 0.280838 + 0.486426i 0.971591 0.236664i \(-0.0760542\pi\)
−0.690753 + 0.723091i \(0.742721\pi\)
\(618\) 0.723000 + 1.25227i 0.0290833 + 0.0503738i
\(619\) 29.7309i 1.19499i −0.801874 0.597493i \(-0.796164\pi\)
0.801874 0.597493i \(-0.203836\pi\)
\(620\) −18.5316 + 16.5629i −0.744249 + 0.665180i
\(621\) 11.4564 19.8431i 0.459731 0.796278i
\(622\) −1.73205 + 3.00000i −0.0694489 + 0.120289i
\(623\) 16.5826i 0.664367i
\(624\) −9.76951 + 2.41733i −0.391093 + 0.0967705i
\(625\) 17.0000 18.3303i 0.680000 0.733212i
\(626\) 1.28674 + 0.742901i 0.0514286 + 0.0296923i
\(627\) −3.96863 2.29129i −0.158492 0.0915052i
\(628\) 14.2179 8.20871i 0.567356 0.327563i
\(629\) 36.3731i 1.45029i
\(630\) 2.35819 + 2.63850i 0.0939524 + 0.105120i
\(631\) −5.12614 + 2.95958i −0.204068 + 0.117819i −0.598552 0.801084i \(-0.704257\pi\)
0.394483 + 0.918903i \(0.370924\pi\)
\(632\) −10.3923 −0.413384
\(633\) −0.143025 + 0.0825757i −0.00568475 + 0.00328209i
\(634\) −0.0435608 + 0.0754495i −0.00173002 + 0.00299648i
\(635\) 37.6974 + 12.4022i 1.49598 + 0.492167i
\(636\) 13.5826 0.538584
\(637\) −10.3923 + 10.0000i −0.411758 + 0.396214i
\(638\) 5.53901i 0.219292i
\(639\) −12.1652 7.02355i −0.481246 0.277847i
\(640\) 7.71472 23.4494i 0.304951 0.926920i
\(641\) −9.08258 15.7315i −0.358740 0.621356i 0.629010 0.777397i \(-0.283460\pi\)
−0.987751 + 0.156041i \(0.950127\pi\)
\(642\) −4.83465 −0.190809
\(643\) 10.8968 + 18.8739i 0.429729 + 0.744313i 0.996849 0.0793227i \(-0.0252757\pi\)
−0.567120 + 0.823635i \(0.691942\pi\)
\(644\) 12.3131 7.10895i 0.485203 0.280132i
\(645\) −23.1642 + 4.83465i −0.912090 + 0.190364i
\(646\) −1.81307 3.14033i −0.0713342 0.123554i
\(647\) 23.3827 + 13.5000i 0.919268 + 0.530740i 0.883402 0.468617i \(-0.155247\pi\)
0.0358667 + 0.999357i \(0.488581\pi\)
\(648\) 0.866025 1.50000i 0.0340207 0.0589256i
\(649\) 36.9129 1.44896
\(650\) 3.15495 7.60774i 0.123747 0.298400i
\(651\) 10.7477 0.421237
\(652\) 18.8718 32.6869i 0.739077 1.28012i
\(653\) 37.0882 + 21.4129i 1.45137 + 0.837951i 0.998560 0.0536545i \(-0.0170870\pi\)
0.452814 + 0.891605i \(0.350420\pi\)
\(654\) −3.00000 5.19615i −0.117309 0.203186i
\(655\) −16.5975 + 3.46410i −0.648518 + 0.135354i
\(656\) −6.39564 + 3.69253i −0.249708 + 0.144169i
\(657\) 0 0
\(658\) 1.44600 0.0563710
\(659\) 15.2477 + 26.4098i 0.593967 + 1.02878i 0.993692 + 0.112146i \(0.0357724\pi\)
−0.399725 + 0.916635i \(0.630894\pi\)
\(660\) −3.31186 + 10.0666i −0.128914 + 0.391842i
\(661\) 15.8739 + 9.16478i 0.617422 + 0.356469i 0.775865 0.630900i \(-0.217314\pi\)
−0.158443 + 0.987368i \(0.550647\pi\)
\(662\) 2.04356i 0.0794252i
\(663\) 15.8745 + 4.58258i 0.616515 + 0.177972i
\(664\) −10.4174 −0.404274
\(665\) −6.37221 2.09642i −0.247104 0.0812957i
\(666\) −3.62614 + 6.28065i −0.140510 + 0.243370i
\(667\) −18.1865 + 10.5000i −0.704185 + 0.406562i
\(668\) 17.1497 0.663542
\(669\) −7.50000 + 4.33013i −0.289967 + 0.167412i
\(670\) 0.686911 + 0.768563i 0.0265377 + 0.0296922i
\(671\) 3.75015i 0.144773i
\(672\) −7.10895 + 4.10436i −0.274234 + 0.158329i
\(673\) 20.9276 + 12.0826i 0.806701 + 0.465749i 0.845809 0.533486i \(-0.179118\pi\)
−0.0391079 + 0.999235i \(0.512452\pi\)
\(674\) 12.1652 + 7.02355i 0.468584 + 0.270537i
\(675\) 10.0000 + 22.9129i 0.384900 + 0.881917i
\(676\) −0.895644 + 23.2695i −0.0344478 + 0.894981i
\(677\) 2.83485i 0.108952i 0.998515 + 0.0544760i \(0.0173489\pi\)
−0.998515 + 0.0544760i \(0.982651\pi\)
\(678\) −1.69433 + 2.93466i −0.0650702 + 0.112705i
\(679\) −9.87386 + 17.1020i −0.378924 + 0.656316i
\(680\) −13.2331 + 11.8273i −0.507468 + 0.453555i
\(681\) 0.818350i 0.0313593i
\(682\) 3.75015 + 6.49545i 0.143601 + 0.248724i
\(683\) −16.5498 28.6652i −0.633262 1.09684i −0.986881 0.161452i \(-0.948382\pi\)
0.353619 0.935390i \(-0.384951\pi\)
\(684\) 6.20520i 0.237262i
\(685\) −15.6276 17.4852i −0.597100 0.668076i
\(686\) −4.35208 + 7.53803i −0.166163 + 0.287803i
\(687\) 13.1334 22.7477i 0.501071 0.867880i
\(688\) 29.5390i 1.12616i
\(689\) 7.58258 26.2668i 0.288873 1.00069i
\(690\) −4.58258 + 0.956439i −0.174456 + 0.0364110i
\(691\) 17.1261 + 9.88778i 0.651509 + 0.376149i 0.789034 0.614349i \(-0.210581\pi\)
−0.137525 + 0.990498i \(0.543915\pi\)
\(692\) −25.7246 14.8521i −0.977901 0.564591i
\(693\) −7.93725 + 4.58258i −0.301511 + 0.174078i
\(694\) 9.74475i 0.369906i
\(695\) −32.4062 36.2582i −1.22924 1.37535i
\(696\) 6.87386 3.96863i 0.260553 0.150430i
\(697\) 12.1244 0.459243
\(698\) −0.971326 + 0.560795i −0.0367652 + 0.0212264i
\(699\) 1.41742 2.45505i 0.0536119 0.0928586i
\(700\) −1.73509 + 15.4157i −0.0655802 + 0.582658i
\(701\) −21.1652 −0.799397 −0.399698 0.916647i \(-0.630885\pi\)
−0.399698 + 0.916647i \(0.630885\pi\)
\(702\) 5.71063 + 5.93466i 0.215534 + 0.223989i
\(703\) 13.7477i 0.518505i
\(704\) 7.83030 + 4.52083i 0.295116 + 0.170385i
\(705\) 3.88153 + 1.27700i 0.146187 + 0.0480946i
\(706\) −1.56080 2.70338i −0.0587413 0.101743i
\(707\) −15.5885 −0.586264
\(708\) 12.4958 + 21.6434i 0.469621 + 0.813408i
\(709\) 31.5000 18.1865i 1.18301 0.683010i 0.226299 0.974058i \(-0.427337\pi\)
0.956708 + 0.291048i \(0.0940040\pi\)
\(710\) 1.46590 + 7.02355i 0.0550143 + 0.263589i
\(711\) −6.00000 10.3923i −0.225018 0.389742i
\(712\) −14.3609 8.29129i −0.538199 0.310729i
\(713\) 14.2179 24.6261i 0.532465 0.922256i
\(714\) 3.62614 0.135705
\(715\) 17.6185 + 12.0244i 0.658896 + 0.449688i
\(716\) 32.5390 1.21604
\(717\) 0.0953502 0.165151i 0.00356092 0.00616769i
\(718\) 7.72665 + 4.46099i 0.288356 + 0.166482i
\(719\) −12.2477 21.2137i −0.456763 0.791137i 0.542025 0.840363i \(-0.317658\pi\)
−0.998788 + 0.0492257i \(0.984325\pi\)
\(720\) 12.2197 2.55040i 0.455402 0.0950478i
\(721\) −4.74773 + 2.74110i −0.176815 + 0.102084i
\(722\) −3.65480 6.33030i −0.136018 0.235589i
\(723\) 1.73205 0.0644157
\(724\) 7.83485 + 13.5704i 0.291180 + 0.504338i
\(725\) 2.56275 22.7691i 0.0951780 0.845623i
\(726\) −1.58258 0.913701i −0.0587349 0.0339106i
\(727\) 15.2523i 0.565675i 0.959168 + 0.282838i \(0.0912758\pi\)
−0.959168 + 0.282838i \(0.908724\pi\)
\(728\) 2.59808 + 10.5000i 0.0962911 + 0.389156i
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 24.2477 41.9983i 0.896835 1.55336i
\(732\) 2.19885 1.26951i 0.0812719 0.0469223i
\(733\) −22.8027 −0.842237 −0.421119 0.907006i \(-0.638362\pi\)
−0.421119 + 0.907006i \(0.638362\pi\)
\(734\) 0.691478 0.399225i 0.0255229 0.0147357i
\(735\) −6.66888 + 5.96038i −0.245985 + 0.219852i
\(736\) 21.7182i 0.800544i
\(737\) −2.31203 + 1.33485i −0.0851646 + 0.0491698i
\(738\) 2.09355 + 1.20871i 0.0770647 + 0.0444933i
\(739\) −14.7523 8.51723i −0.542671 0.313311i 0.203490 0.979077i \(-0.434772\pi\)
−0.746161 + 0.665766i \(0.768105\pi\)
\(740\) −31.1216 + 6.49545i −1.14405 + 0.238778i
\(741\) −6.00000 1.73205i −0.220416 0.0636285i
\(742\) 6.00000i 0.220267i
\(743\) −2.86423 + 4.96099i −0.105078 + 0.182001i −0.913770 0.406232i \(-0.866843\pi\)
0.808692 + 0.588232i \(0.200176\pi\)
\(744\) −5.37386 + 9.30780i −0.197015 + 0.341241i
\(745\) −27.8306 + 24.8739i −1.01964 + 0.911310i
\(746\) 5.93905i 0.217444i
\(747\) −6.01450 10.4174i −0.220059 0.381154i
\(748\) −10.8591 18.8085i −0.397048 0.687708i
\(749\) 18.3296i 0.669748i
\(750\) 2.12891 4.64293i 0.0777367 0.169536i
\(751\) −5.87386 + 10.1738i −0.214340 + 0.371248i −0.953068 0.302755i \(-0.902093\pi\)
0.738728 + 0.674004i \(0.235427\pi\)
\(752\) 2.55040 4.41742i 0.0930036 0.161087i
\(753\) 0.165151i 0.00601845i
\(754\) −1.81307 7.32743i −0.0660281 0.266849i
\(755\) −4.41742 21.1652i −0.160767 0.770279i
\(756\) −13.4347 7.75650i −0.488614 0.282101i
\(757\) 8.44178 + 4.87386i 0.306822 + 0.177144i 0.645503 0.763757i \(-0.276648\pi\)
−0.338682 + 0.940901i \(0.609981\pi\)
\(758\) 4.22483 2.43920i 0.153453 0.0885959i
\(759\) 12.1244i 0.440086i
\(760\) 5.00166 4.47028i 0.181429 0.162154i
\(761\) −30.7087 + 17.7297i −1.11319 + 0.642701i −0.939654 0.342127i \(-0.888853\pi\)
−0.173536 + 0.984827i \(0.555519\pi\)
\(762\) 8.10805 0.293724
\(763\) 19.7001 11.3739i 0.713192 0.411762i
\(764\) −14.8521 + 25.7246i −0.537330 + 0.930682i
\(765\) −19.4674 6.40467i −0.703846 0.231561i
\(766\) 10.7913 0.389905
\(767\) 48.8311 12.0826i 1.76319 0.436277i
\(768\) 1.79129i 0.0646375i
\(769\) −13.5000 7.79423i −0.486822 0.281067i 0.236433 0.971648i \(-0.424022\pi\)
−0.723255 + 0.690581i \(0.757355\pi\)
\(770\) 4.44685 + 1.46299i 0.160253 + 0.0527224i
\(771\) 9.08258 + 15.7315i 0.327101 + 0.566556i
\(772\) −26.6283 −0.958374
\(773\) 12.0767 + 20.9174i 0.434368 + 0.752347i 0.997244 0.0741940i \(-0.0236384\pi\)
−0.562876 + 0.826541i \(0.690305\pi\)
\(774\) 8.37386 4.83465i 0.300992 0.173778i
\(775\) 12.4104 + 28.4358i 0.445795 + 1.02144i