Properties

Label 690.2.i.f.47.2
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.2
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.51580 + 0.838057i) q^{3} -1.00000i q^{4} +(-2.23509 - 0.0661068i) q^{5} +(0.479239 - 1.66443i) q^{6} +(2.39575 + 2.39575i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.59532 - 2.54066i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.51580 + 0.838057i) q^{3} -1.00000i q^{4} +(-2.23509 - 0.0661068i) q^{5} +(0.479239 - 1.66443i) q^{6} +(2.39575 + 2.39575i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.59532 - 2.54066i) q^{9} +(1.62719 - 1.53370i) q^{10} +3.77229i q^{11} +(0.838057 + 1.51580i) q^{12} +(3.87255 - 3.87255i) q^{13} -3.38810 q^{14} +(3.44336 - 1.77293i) q^{15} -1.00000 q^{16} +(2.58226 - 2.58226i) q^{17} +(0.668456 + 2.92458i) q^{18} +6.80541i q^{19} +(-0.0661068 + 2.23509i) q^{20} +(-5.63926 - 1.62371i) q^{21} +(-2.66741 - 2.66741i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.66443 - 0.479239i) q^{24} +(4.99126 + 0.295509i) q^{25} +5.47661i q^{26} +(-0.288974 + 5.18811i) q^{27} +(2.39575 - 2.39575i) q^{28} -6.48520 q^{29} +(-1.18117 + 3.68847i) q^{30} -7.09492 q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.16139 - 5.71805i) q^{33} +3.65187i q^{34} +(-5.19634 - 5.51309i) q^{35} +(-2.54066 - 1.59532i) q^{36} +(4.68887 + 4.68887i) q^{37} +(-4.81215 - 4.81215i) q^{38} +(-2.62461 + 9.11544i) q^{39} +(-1.53370 - 1.62719i) q^{40} +8.03681i q^{41} +(5.13569 - 2.83942i) q^{42} +(-2.86760 + 2.86760i) q^{43} +3.77229 q^{44} +(-3.73364 + 5.57314i) q^{45} +1.00000 q^{46} +(-3.40424 + 3.40424i) q^{47} +(1.51580 - 0.838057i) q^{48} +4.47922i q^{49} +(-3.73831 + 3.32040i) q^{50} +(-1.75012 + 6.07829i) q^{51} +(-3.87255 - 3.87255i) q^{52} +(1.15188 + 1.15188i) q^{53} +(-3.46421 - 3.87288i) q^{54} +(0.249374 - 8.43140i) q^{55} +3.38810i q^{56} +(-5.70332 - 10.3157i) q^{57} +(4.58573 - 4.58573i) q^{58} -0.993207 q^{59} +(-1.77293 - 3.44336i) q^{60} -11.6640 q^{61} +(5.01686 - 5.01686i) q^{62} +(9.90877 - 2.26480i) q^{63} +1.00000i q^{64} +(-8.91150 + 8.39950i) q^{65} +(6.27871 + 1.80783i) q^{66} +(1.09345 + 1.09345i) q^{67} +(-2.58226 - 2.58226i) q^{68} +(1.66443 + 0.479239i) q^{69} +(7.57271 + 0.223976i) q^{70} -9.26157i q^{71} +(2.92458 - 0.668456i) q^{72} +(2.14788 - 2.14788i) q^{73} -6.63106 q^{74} +(-7.81342 + 3.73503i) q^{75} +6.80541 q^{76} +(-9.03745 + 9.03745i) q^{77} +(-4.58971 - 8.30147i) q^{78} +4.59709i q^{79} +(2.23509 + 0.0661068i) q^{80} +(-3.90991 - 8.10633i) q^{81} +(-5.68288 - 5.68288i) q^{82} +(5.20343 + 5.20343i) q^{83} +(-1.62371 + 5.63926i) q^{84} +(-5.94230 + 5.60089i) q^{85} -4.05539i q^{86} +(9.83029 - 5.43497i) q^{87} +(-2.66741 + 2.66741i) q^{88} +9.56617 q^{89} +(-1.30072 - 6.58089i) q^{90} +18.5553 q^{91} +(-0.707107 + 0.707107i) q^{92} +(10.7545 - 5.94594i) q^{93} -4.81432i q^{94} +(0.449884 - 15.2107i) q^{95} +(-0.479239 + 1.66443i) q^{96} +(-10.5684 - 10.5684i) q^{97} +(-3.16729 - 3.16729i) q^{98} +(9.58410 + 6.01801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.51580 + 0.838057i −0.875150 + 0.483853i
\(4\) 1.00000i 0.500000i
\(5\) −2.23509 0.0661068i −0.999563 0.0295639i
\(6\) 0.479239 1.66443i 0.195649 0.679501i
\(7\) 2.39575 + 2.39575i 0.905508 + 0.905508i 0.995906 0.0903979i \(-0.0288139\pi\)
−0.0903979 + 0.995906i \(0.528814\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.59532 2.54066i 0.531773 0.846887i
\(10\) 1.62719 1.53370i 0.514563 0.485000i
\(11\) 3.77229i 1.13739i 0.822549 + 0.568694i \(0.192551\pi\)
−0.822549 + 0.568694i \(0.807449\pi\)
\(12\) 0.838057 + 1.51580i 0.241926 + 0.437575i
\(13\) 3.87255 3.87255i 1.07405 1.07405i 0.0770227 0.997029i \(-0.475459\pi\)
0.997029 0.0770227i \(-0.0245414\pi\)
\(14\) −3.38810 −0.905508
\(15\) 3.44336 1.77293i 0.889072 0.457768i
\(16\) −1.00000 −0.250000
\(17\) 2.58226 2.58226i 0.626291 0.626291i −0.320842 0.947133i \(-0.603966\pi\)
0.947133 + 0.320842i \(0.103966\pi\)
\(18\) 0.668456 + 2.92458i 0.157557 + 0.689330i
\(19\) 6.80541i 1.56127i 0.624988 + 0.780634i \(0.285104\pi\)
−0.624988 + 0.780634i \(0.714896\pi\)
\(20\) −0.0661068 + 2.23509i −0.0147819 + 0.499781i
\(21\) −5.63926 1.62371i −1.23059 0.354323i
\(22\) −2.66741 2.66741i −0.568694 0.568694i
\(23\) −0.707107 0.707107i −0.147442 0.147442i
\(24\) −1.66443 0.479239i −0.339751 0.0978243i
\(25\) 4.99126 + 0.295509i 0.998252 + 0.0591019i
\(26\) 5.47661i 1.07405i
\(27\) −0.288974 + 5.18811i −0.0556131 + 0.998452i
\(28\) 2.39575 2.39575i 0.452754 0.452754i
\(29\) −6.48520 −1.20427 −0.602136 0.798394i \(-0.705683\pi\)
−0.602136 + 0.798394i \(0.705683\pi\)
\(30\) −1.18117 + 3.68847i −0.215652 + 0.673420i
\(31\) −7.09492 −1.27428 −0.637142 0.770746i \(-0.719884\pi\)
−0.637142 + 0.770746i \(0.719884\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −3.16139 5.71805i −0.550328 0.995384i
\(34\) 3.65187i 0.626291i
\(35\) −5.19634 5.51309i −0.878342 0.931882i
\(36\) −2.54066 1.59532i −0.423443 0.265887i
\(37\) 4.68887 + 4.68887i 0.770846 + 0.770846i 0.978254 0.207409i \(-0.0665030\pi\)
−0.207409 + 0.978254i \(0.566503\pi\)
\(38\) −4.81215 4.81215i −0.780634 0.780634i
\(39\) −2.62461 + 9.11544i −0.420273 + 1.45964i
\(40\) −1.53370 1.62719i −0.242500 0.257282i
\(41\) 8.03681i 1.25514i 0.778561 + 0.627569i \(0.215950\pi\)
−0.778561 + 0.627569i \(0.784050\pi\)
\(42\) 5.13569 2.83942i 0.792455 0.438132i
\(43\) −2.86760 + 2.86760i −0.437304 + 0.437304i −0.891104 0.453799i \(-0.850068\pi\)
0.453799 + 0.891104i \(0.350068\pi\)
\(44\) 3.77229 0.568694
\(45\) −3.73364 + 5.57314i −0.556578 + 0.830795i
\(46\) 1.00000 0.147442
\(47\) −3.40424 + 3.40424i −0.496559 + 0.496559i −0.910365 0.413806i \(-0.864199\pi\)
0.413806 + 0.910365i \(0.364199\pi\)
\(48\) 1.51580 0.838057i 0.218787 0.120963i
\(49\) 4.47922i 0.639889i
\(50\) −3.73831 + 3.32040i −0.528677 + 0.469575i
\(51\) −1.75012 + 6.07829i −0.245066 + 0.851131i
\(52\) −3.87255 3.87255i −0.537026 0.537026i
\(53\) 1.15188 + 1.15188i 0.158223 + 0.158223i 0.781779 0.623556i \(-0.214313\pi\)
−0.623556 + 0.781779i \(0.714313\pi\)
\(54\) −3.46421 3.87288i −0.471420 0.527033i
\(55\) 0.249374 8.43140i 0.0336256 1.13689i
\(56\) 3.38810i 0.452754i
\(57\) −5.70332 10.3157i −0.755424 1.36634i
\(58\) 4.58573 4.58573i 0.602136 0.602136i
\(59\) −0.993207 −0.129304 −0.0646522 0.997908i \(-0.520594\pi\)
−0.0646522 + 0.997908i \(0.520594\pi\)
\(60\) −1.77293 3.44336i −0.228884 0.444536i
\(61\) −11.6640 −1.49343 −0.746713 0.665146i \(-0.768369\pi\)
−0.746713 + 0.665146i \(0.768369\pi\)
\(62\) 5.01686 5.01686i 0.637142 0.637142i
\(63\) 9.90877 2.26480i 1.24839 0.285337i
\(64\) 1.00000i 0.125000i
\(65\) −8.91150 + 8.39950i −1.10534 + 1.04183i
\(66\) 6.27871 + 1.80783i 0.772856 + 0.222528i
\(67\) 1.09345 + 1.09345i 0.133587 + 0.133587i 0.770738 0.637152i \(-0.219888\pi\)
−0.637152 + 0.770738i \(0.719888\pi\)
\(68\) −2.58226 2.58226i −0.313145 0.313145i
\(69\) 1.66443 + 0.479239i 0.200374 + 0.0576936i
\(70\) 7.57271 + 0.223976i 0.905112 + 0.0267703i
\(71\) 9.26157i 1.09915i −0.835446 0.549573i \(-0.814790\pi\)
0.835446 0.549573i \(-0.185210\pi\)
\(72\) 2.92458 0.668456i 0.344665 0.0787783i
\(73\) 2.14788 2.14788i 0.251390 0.251390i −0.570150 0.821540i \(-0.693115\pi\)
0.821540 + 0.570150i \(0.193115\pi\)
\(74\) −6.63106 −0.770846
\(75\) −7.81342 + 3.73503i −0.902216 + 0.431284i
\(76\) 6.80541 0.780634
\(77\) −9.03745 + 9.03745i −1.02991 + 1.02991i
\(78\) −4.58971 8.30147i −0.519683 0.939956i
\(79\) 4.59709i 0.517213i 0.965983 + 0.258607i \(0.0832633\pi\)
−0.965983 + 0.258607i \(0.916737\pi\)
\(80\) 2.23509 + 0.0661068i 0.249891 + 0.00739096i
\(81\) −3.90991 8.10633i −0.434434 0.900704i
\(82\) −5.68288 5.68288i −0.627569 0.627569i
\(83\) 5.20343 + 5.20343i 0.571151 + 0.571151i 0.932450 0.361299i \(-0.117667\pi\)
−0.361299 + 0.932450i \(0.617667\pi\)
\(84\) −1.62371 + 5.63926i −0.177161 + 0.615293i
\(85\) −5.94230 + 5.60089i −0.644533 + 0.607502i
\(86\) 4.05539i 0.437304i
\(87\) 9.83029 5.43497i 1.05392 0.582690i
\(88\) −2.66741 + 2.66741i −0.284347 + 0.284347i
\(89\) 9.56617 1.01401 0.507006 0.861943i \(-0.330752\pi\)
0.507006 + 0.861943i \(0.330752\pi\)
\(90\) −1.30072 6.58089i −0.137108 0.693687i
\(91\) 18.5553 1.94512
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) 10.7545 5.94594i 1.11519 0.616566i
\(94\) 4.81432i 0.496559i
\(95\) 0.449884 15.2107i 0.0461571 1.56059i
\(96\) −0.479239 + 1.66443i −0.0489121 + 0.169875i
\(97\) −10.5684 10.5684i −1.07306 1.07306i −0.997111 0.0759519i \(-0.975800\pi\)
−0.0759519 0.997111i \(-0.524200\pi\)
\(98\) −3.16729 3.16729i −0.319944 0.319944i
\(99\) 9.58410 + 6.01801i 0.963238 + 0.604833i
\(100\) 0.295509 4.99126i 0.0295509 0.499126i
\(101\) 3.09956i 0.308418i −0.988038 0.154209i \(-0.950717\pi\)
0.988038 0.154209i \(-0.0492829\pi\)
\(102\) −3.06048 5.53552i −0.303032 0.548098i
\(103\) −4.89445 + 4.89445i −0.482264 + 0.482264i −0.905854 0.423590i \(-0.860770\pi\)
0.423590 + 0.905854i \(0.360770\pi\)
\(104\) 5.47661 0.537026
\(105\) 12.4969 + 4.00193i 1.21957 + 0.390549i
\(106\) −1.62900 −0.158223
\(107\) −7.11744 + 7.11744i −0.688069 + 0.688069i −0.961805 0.273736i \(-0.911741\pi\)
0.273736 + 0.961805i \(0.411741\pi\)
\(108\) 5.18811 + 0.288974i 0.499226 + 0.0278065i
\(109\) 18.1228i 1.73584i 0.496700 + 0.867922i \(0.334545\pi\)
−0.496700 + 0.867922i \(0.665455\pi\)
\(110\) 5.78557 + 6.13824i 0.551632 + 0.585258i
\(111\) −11.0369 3.17786i −1.04758 0.301630i
\(112\) −2.39575 2.39575i −0.226377 0.226377i
\(113\) 14.5951 + 14.5951i 1.37299 + 1.37299i 0.855978 + 0.517012i \(0.172956\pi\)
0.517012 + 0.855978i \(0.327044\pi\)
\(114\) 11.3271 + 3.26142i 1.06088 + 0.305460i
\(115\) 1.53370 + 1.62719i 0.143019 + 0.151736i
\(116\) 6.48520i 0.602136i
\(117\) −3.66087 16.0168i −0.338448 1.48075i
\(118\) 0.702303 0.702303i 0.0646522 0.0646522i
\(119\) 12.3729 1.13422
\(120\) 3.68847 + 1.18117i 0.336710 + 0.107826i
\(121\) −3.23015 −0.293650
\(122\) 8.24772 8.24772i 0.746713 0.746713i
\(123\) −6.73531 12.1822i −0.607302 1.09843i
\(124\) 7.09492i 0.637142i
\(125\) −11.1364 0.990446i −0.996068 0.0885882i
\(126\) −5.40511 + 8.60801i −0.481525 + 0.766862i
\(127\) 4.72572 + 4.72572i 0.419339 + 0.419339i 0.884976 0.465637i \(-0.154175\pi\)
−0.465637 + 0.884976i \(0.654175\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 1.94350 6.74992i 0.171116 0.594298i
\(130\) 0.362041 12.2407i 0.0317531 1.07358i
\(131\) 9.59773i 0.838558i 0.907858 + 0.419279i \(0.137717\pi\)
−0.907858 + 0.419279i \(0.862283\pi\)
\(132\) −5.71805 + 3.16139i −0.497692 + 0.275164i
\(133\) −16.3041 + 16.3041i −1.41374 + 1.41374i
\(134\) −1.54638 −0.133587
\(135\) 0.988853 11.5768i 0.0851069 0.996372i
\(136\) 3.65187 0.313145
\(137\) −5.29519 + 5.29519i −0.452399 + 0.452399i −0.896150 0.443751i \(-0.853647\pi\)
0.443751 + 0.896150i \(0.353647\pi\)
\(138\) −1.51580 + 0.838057i −0.129034 + 0.0713402i
\(139\) 12.6513i 1.07307i −0.843879 0.536533i \(-0.819734\pi\)
0.843879 0.536533i \(-0.180266\pi\)
\(140\) −5.51309 + 5.19634i −0.465941 + 0.439171i
\(141\) 2.30721 8.01310i 0.194302 0.674825i
\(142\) 6.54892 + 6.54892i 0.549573 + 0.549573i
\(143\) 14.6084 + 14.6084i 1.22161 + 1.22161i
\(144\) −1.59532 + 2.54066i −0.132943 + 0.211722i
\(145\) 14.4950 + 0.428716i 1.20375 + 0.0356029i
\(146\) 3.03756i 0.251390i
\(147\) −3.75384 6.78962i −0.309612 0.559998i
\(148\) 4.68887 4.68887i 0.385423 0.385423i
\(149\) 13.7580 1.12710 0.563551 0.826081i \(-0.309435\pi\)
0.563551 + 0.826081i \(0.309435\pi\)
\(150\) 2.88386 8.16599i 0.235466 0.666750i
\(151\) −1.62442 −0.132194 −0.0660969 0.997813i \(-0.521055\pi\)
−0.0660969 + 0.997813i \(0.521055\pi\)
\(152\) −4.81215 + 4.81215i −0.390317 + 0.390317i
\(153\) −2.44112 10.6802i −0.197353 0.863442i
\(154\) 12.7809i 1.02991i
\(155\) 15.8578 + 0.469022i 1.27373 + 0.0376728i
\(156\) 9.11544 + 2.62461i 0.729819 + 0.210137i
\(157\) −12.9821 12.9821i −1.03608 1.03608i −0.999324 0.0367599i \(-0.988296\pi\)
−0.0367599 0.999324i \(-0.511704\pi\)
\(158\) −3.25064 3.25064i −0.258607 0.258607i
\(159\) −2.71137 0.780682i −0.215025 0.0619121i
\(160\) −1.62719 + 1.53370i −0.128641 + 0.121250i
\(161\) 3.38810i 0.267020i
\(162\) 8.49676 + 2.96732i 0.667569 + 0.233135i
\(163\) −5.71990 + 5.71990i −0.448017 + 0.448017i −0.894695 0.446678i \(-0.852607\pi\)
0.446678 + 0.894695i \(0.352607\pi\)
\(164\) 8.03681 0.627569
\(165\) 6.68800 + 12.9893i 0.520660 + 1.01122i
\(166\) −7.35876 −0.571151
\(167\) 9.01194 9.01194i 0.697365 0.697365i −0.266476 0.963841i \(-0.585859\pi\)
0.963841 + 0.266476i \(0.0858595\pi\)
\(168\) −2.83942 5.13569i −0.219066 0.396227i
\(169\) 16.9933i 1.30718i
\(170\) 0.241414 8.16227i 0.0185156 0.626017i
\(171\) 17.2902 + 10.8568i 1.32222 + 0.830241i
\(172\) 2.86760 + 2.86760i 0.218652 + 0.218652i
\(173\) 14.7185 + 14.7185i 1.11903 + 1.11903i 0.991884 + 0.127145i \(0.0405814\pi\)
0.127145 + 0.991884i \(0.459419\pi\)
\(174\) −3.10796 + 10.7942i −0.235614 + 0.818304i
\(175\) 11.2498 + 12.6658i 0.850408 + 0.957442i
\(176\) 3.77229i 0.284347i
\(177\) 1.50551 0.832364i 0.113161 0.0625643i
\(178\) −6.76430 + 6.76430i −0.507006 + 0.507006i
\(179\) 6.08838 0.455067 0.227533 0.973770i \(-0.426934\pi\)
0.227533 + 0.973770i \(0.426934\pi\)
\(180\) 5.57314 + 3.73364i 0.415398 + 0.278289i
\(181\) −11.1245 −0.826878 −0.413439 0.910532i \(-0.635673\pi\)
−0.413439 + 0.910532i \(0.635673\pi\)
\(182\) −13.1206 + 13.1206i −0.972562 + 0.972562i
\(183\) 17.6804 9.77513i 1.30697 0.722598i
\(184\) 1.00000i 0.0737210i
\(185\) −10.1701 10.7900i −0.747719 0.793298i
\(186\) −3.40016 + 11.8090i −0.249312 + 0.865878i
\(187\) 9.74104 + 9.74104i 0.712335 + 0.712335i
\(188\) 3.40424 + 3.40424i 0.248280 + 0.248280i
\(189\) −13.1217 + 11.7371i −0.954465 + 0.853748i
\(190\) 10.4375 + 11.0737i 0.757214 + 0.803371i
\(191\) 5.61428i 0.406235i 0.979154 + 0.203118i \(0.0651074\pi\)
−0.979154 + 0.203118i \(0.934893\pi\)
\(192\) −0.838057 1.51580i −0.0604816 0.109394i
\(193\) 9.77402 9.77402i 0.703549 0.703549i −0.261621 0.965171i \(-0.584257\pi\)
0.965171 + 0.261621i \(0.0842572\pi\)
\(194\) 14.9460 1.07306
\(195\) 6.46883 20.2003i 0.463242 1.44658i
\(196\) 4.47922 0.319944
\(197\) 1.13050 1.13050i 0.0805446 0.0805446i −0.665687 0.746231i \(-0.731861\pi\)
0.746231 + 0.665687i \(0.231861\pi\)
\(198\) −11.0324 + 2.52161i −0.784035 + 0.179203i
\(199\) 4.63646i 0.328670i 0.986405 + 0.164335i \(0.0525478\pi\)
−0.986405 + 0.164335i \(0.947452\pi\)
\(200\) 3.32040 + 3.73831i 0.234788 + 0.264338i
\(201\) −2.57384 0.741085i −0.181545 0.0522721i
\(202\) 2.19172 + 2.19172i 0.154209 + 0.154209i
\(203\) −15.5369 15.5369i −1.09048 1.09048i
\(204\) 6.07829 + 1.75012i 0.425565 + 0.122533i
\(205\) 0.531288 17.9630i 0.0371068 1.25459i
\(206\) 6.92180i 0.482264i
\(207\) −2.92458 + 0.668456i −0.203272 + 0.0464609i
\(208\) −3.87255 + 3.87255i −0.268513 + 0.268513i
\(209\) −25.6720 −1.77577
\(210\) −11.6664 + 6.00686i −0.805061 + 0.414513i
\(211\) −8.96557 −0.617215 −0.308608 0.951189i \(-0.599863\pi\)
−0.308608 + 0.951189i \(0.599863\pi\)
\(212\) 1.15188 1.15188i 0.0791114 0.0791114i
\(213\) 7.76173 + 14.0387i 0.531825 + 0.961918i
\(214\) 10.0656i 0.688069i
\(215\) 6.59891 6.21977i 0.450042 0.424185i
\(216\) −3.87288 + 3.46421i −0.263516 + 0.235710i
\(217\) −16.9976 16.9976i −1.15387 1.15387i
\(218\) −12.8147 12.8147i −0.867922 0.867922i
\(219\) −1.45572 + 5.05580i −0.0983681 + 0.341639i
\(220\) −8.43140 0.249374i −0.568445 0.0168128i
\(221\) 19.9999i 1.34534i
\(222\) 10.0514 5.55721i 0.674605 0.372976i
\(223\) 15.5814 15.5814i 1.04341 1.04341i 0.0443938 0.999014i \(-0.485864\pi\)
0.999014 0.0443938i \(-0.0141356\pi\)
\(224\) 3.38810 0.226377
\(225\) 8.71345 12.2097i 0.580896 0.813977i
\(226\) −20.6406 −1.37299
\(227\) 17.4824 17.4824i 1.16035 1.16035i 0.175945 0.984400i \(-0.443702\pi\)
0.984400 0.175945i \(-0.0562982\pi\)
\(228\) −10.3157 + 5.70332i −0.683172 + 0.377712i
\(229\) 9.74724i 0.644116i 0.946720 + 0.322058i \(0.104375\pi\)
−0.946720 + 0.322058i \(0.895625\pi\)
\(230\) −2.23509 0.0661068i −0.147378 0.00435895i
\(231\) 6.12510 21.2729i 0.403002 1.39965i
\(232\) −4.58573 4.58573i −0.301068 0.301068i
\(233\) −6.27349 6.27349i −0.410990 0.410990i 0.471093 0.882083i \(-0.343860\pi\)
−0.882083 + 0.471093i \(0.843860\pi\)
\(234\) 13.9142 + 8.73695i 0.909600 + 0.571152i
\(235\) 7.83382 7.38374i 0.511022 0.481662i
\(236\) 0.993207i 0.0646522i
\(237\) −3.85263 6.96829i −0.250255 0.452639i
\(238\) −8.74897 + 8.74897i −0.567111 + 0.567111i
\(239\) −23.7283 −1.53486 −0.767428 0.641135i \(-0.778464\pi\)
−0.767428 + 0.641135i \(0.778464\pi\)
\(240\) −3.44336 + 1.77293i −0.222268 + 0.114442i
\(241\) 6.12180 0.394340 0.197170 0.980369i \(-0.436825\pi\)
0.197170 + 0.980369i \(0.436825\pi\)
\(242\) 2.28406 2.28406i 0.146825 0.146825i
\(243\) 12.7202 + 9.01088i 0.816002 + 0.578048i
\(244\) 11.6640i 0.746713i
\(245\) 0.296107 10.0115i 0.0189176 0.639609i
\(246\) 13.3767 + 3.85155i 0.852868 + 0.245566i
\(247\) 26.3543 + 26.3543i 1.67688 + 1.67688i
\(248\) −5.01686 5.01686i −0.318571 0.318571i
\(249\) −12.2481 3.52661i −0.776195 0.223490i
\(250\) 8.57496 7.17426i 0.542328 0.453740i
\(251\) 14.4578i 0.912566i 0.889835 + 0.456283i \(0.150820\pi\)
−0.889835 + 0.456283i \(0.849180\pi\)
\(252\) −2.26480 9.90877i −0.142669 0.624194i
\(253\) 2.66741 2.66741i 0.167699 0.167699i
\(254\) −6.68317 −0.419339
\(255\) 4.31349 13.4698i 0.270121 0.843514i
\(256\) 1.00000 0.0625000
\(257\) −18.8018 + 18.8018i −1.17282 + 1.17282i −0.191288 + 0.981534i \(0.561267\pi\)
−0.981534 + 0.191288i \(0.938733\pi\)
\(258\) 3.39865 + 6.14718i 0.211591 + 0.382707i
\(259\) 22.4667i 1.39601i
\(260\) 8.39950 + 8.91150i 0.520915 + 0.552668i
\(261\) −10.3460 + 16.4767i −0.640400 + 1.01988i
\(262\) −6.78662 6.78662i −0.419279 0.419279i
\(263\) −9.69602 9.69602i −0.597882 0.597882i 0.341866 0.939749i \(-0.388941\pi\)
−0.939749 + 0.341866i \(0.888941\pi\)
\(264\) 1.80783 6.27871i 0.111264 0.386428i
\(265\) −2.49841 2.65070i −0.153476 0.162831i
\(266\) 23.0574i 1.41374i
\(267\) −14.5004 + 8.01700i −0.887412 + 0.490632i
\(268\) 1.09345 1.09345i 0.0667934 0.0667934i
\(269\) −4.30558 −0.262516 −0.131258 0.991348i \(-0.541902\pi\)
−0.131258 + 0.991348i \(0.541902\pi\)
\(270\) 7.48681 + 8.88525i 0.455632 + 0.540739i
\(271\) −8.66444 −0.526327 −0.263164 0.964751i \(-0.584766\pi\)
−0.263164 + 0.964751i \(0.584766\pi\)
\(272\) −2.58226 + 2.58226i −0.156573 + 0.156573i
\(273\) −28.1262 + 15.5504i −1.70228 + 0.941154i
\(274\) 7.48853i 0.452399i
\(275\) −1.11475 + 18.8285i −0.0672217 + 1.13540i
\(276\) 0.479239 1.66443i 0.0288468 0.100187i
\(277\) 20.8795 + 20.8795i 1.25453 + 1.25453i 0.953668 + 0.300862i \(0.0972743\pi\)
0.300862 + 0.953668i \(0.402726\pi\)
\(278\) 8.94580 + 8.94580i 0.536533 + 0.536533i
\(279\) −11.3187 + 18.0258i −0.677631 + 1.07917i
\(280\) 0.223976 7.57271i 0.0133852 0.452556i
\(281\) 21.9320i 1.30835i −0.756341 0.654177i \(-0.773015\pi\)
0.756341 0.654177i \(-0.226985\pi\)
\(282\) 4.03467 + 7.29756i 0.240261 + 0.434564i
\(283\) −1.56401 + 1.56401i −0.0929709 + 0.0929709i −0.752063 0.659092i \(-0.770941\pi\)
0.659092 + 0.752063i \(0.270941\pi\)
\(284\) −9.26157 −0.549573
\(285\) 12.0655 + 23.4335i 0.714699 + 1.38808i
\(286\) −20.6594 −1.22161
\(287\) −19.2542 + 19.2542i −1.13654 + 1.13654i
\(288\) −0.668456 2.92458i −0.0393891 0.172333i
\(289\) 3.66383i 0.215519i
\(290\) −10.5527 + 9.94637i −0.619674 + 0.584071i
\(291\) 24.8767 + 7.16273i 1.45830 + 0.419887i
\(292\) −2.14788 2.14788i −0.125695 0.125695i
\(293\) −6.39663 6.39663i −0.373695 0.373695i 0.495126 0.868821i \(-0.335122\pi\)
−0.868821 + 0.495126i \(0.835122\pi\)
\(294\) 7.45535 + 2.14662i 0.434805 + 0.125193i
\(295\) 2.21991 + 0.0656577i 0.129248 + 0.00382274i
\(296\) 6.63106i 0.385423i
\(297\) −19.5710 1.09009i −1.13563 0.0632536i
\(298\) −9.72840 + 9.72840i −0.563551 + 0.563551i
\(299\) −5.47661 −0.316721
\(300\) 3.73503 + 7.81342i 0.215642 + 0.451108i
\(301\) −13.7401 −0.791965
\(302\) 1.14864 1.14864i 0.0660969 0.0660969i
\(303\) 2.59761 + 4.69832i 0.149229 + 0.269912i
\(304\) 6.80541i 0.390317i
\(305\) 26.0702 + 0.771072i 1.49277 + 0.0441514i
\(306\) 9.27817 + 5.82591i 0.530397 + 0.333045i
\(307\) −17.5324 17.5324i −1.00063 1.00063i −1.00000 0.000625972i \(-0.999801\pi\)
−0.000625972 1.00000i \(-0.500199\pi\)
\(308\) 9.03745 + 9.03745i 0.514957 + 0.514957i
\(309\) 3.31719 11.5208i 0.188709 0.655398i
\(310\) −11.5448 + 10.8815i −0.655700 + 0.618027i
\(311\) 1.02922i 0.0583619i −0.999574 0.0291810i \(-0.990710\pi\)
0.999574 0.0291810i \(-0.00928991\pi\)
\(312\) −8.30147 + 4.58971i −0.469978 + 0.259841i
\(313\) −5.15305 + 5.15305i −0.291268 + 0.291268i −0.837581 0.546313i \(-0.816031\pi\)
0.546313 + 0.837581i \(0.316031\pi\)
\(314\) 18.3595 1.03608
\(315\) −22.2967 + 4.40699i −1.25628 + 0.248306i
\(316\) 4.59709 0.258607
\(317\) −2.15191 + 2.15191i −0.120863 + 0.120863i −0.764951 0.644088i \(-0.777237\pi\)
0.644088 + 0.764951i \(0.277237\pi\)
\(318\) 2.46925 1.36520i 0.138469 0.0765565i
\(319\) 24.4640i 1.36972i
\(320\) 0.0661068 2.23509i 0.00369548 0.124945i
\(321\) 4.82382 16.7535i 0.269239 0.935087i
\(322\) 2.39575 + 2.39575i 0.133510 + 0.133510i
\(323\) 17.5734 + 17.5734i 0.977808 + 0.977808i
\(324\) −8.10633 + 3.90991i −0.450352 + 0.217217i
\(325\) 20.4733 18.1845i 1.13565 1.00870i
\(326\) 8.08915i 0.448017i
\(327\) −15.1879 27.4705i −0.839893 1.51912i
\(328\) −5.68288 + 5.68288i −0.313785 + 0.313785i
\(329\) −16.3114 −0.899276
\(330\) −13.9140 4.45572i −0.765939 0.245280i
\(331\) −10.0289 −0.551239 −0.275619 0.961267i \(-0.588883\pi\)
−0.275619 + 0.961267i \(0.588883\pi\)
\(332\) 5.20343 5.20343i 0.285575 0.285575i
\(333\) 19.3931 4.43257i 1.06273 0.242904i
\(334\) 12.7448i 0.697365i
\(335\) −2.37169 2.51626i −0.129579 0.137478i
\(336\) 5.63926 + 1.62371i 0.307647 + 0.0885806i
\(337\) 17.9924 + 17.9924i 0.980107 + 0.980107i 0.999806 0.0196990i \(-0.00627080\pi\)
−0.0196990 + 0.999806i \(0.506271\pi\)
\(338\) 12.0161 + 12.0161i 0.653588 + 0.653588i
\(339\) −34.3548 9.89176i −1.86590 0.537247i
\(340\) 5.60089 + 5.94230i 0.303751 + 0.322266i
\(341\) 26.7641i 1.44936i
\(342\) −19.9030 + 4.54912i −1.07623 + 0.245988i
\(343\) 6.03915 6.03915i 0.326084 0.326084i
\(344\) −4.05539 −0.218652
\(345\) −3.68847 1.18117i −0.198581 0.0635922i
\(346\) −20.8151 −1.11903
\(347\) 16.7568 16.7568i 0.899551 0.899551i −0.0958454 0.995396i \(-0.530555\pi\)
0.995396 + 0.0958454i \(0.0305554\pi\)
\(348\) −5.43497 9.83029i −0.291345 0.526959i
\(349\) 13.6323i 0.729723i −0.931062 0.364861i \(-0.881116\pi\)
0.931062 0.364861i \(-0.118884\pi\)
\(350\) −16.9109 1.00122i −0.903925 0.0535172i
\(351\) 18.9722 + 21.2103i 1.01266 + 1.13212i
\(352\) 2.66741 + 2.66741i 0.142173 + 0.142173i
\(353\) −4.64603 4.64603i −0.247283 0.247283i 0.572571 0.819855i \(-0.305946\pi\)
−0.819855 + 0.572571i \(0.805946\pi\)
\(354\) −0.475983 + 1.65312i −0.0252982 + 0.0878625i
\(355\) −0.612253 + 20.7005i −0.0324950 + 1.09867i
\(356\) 9.56617i 0.507006i
\(357\) −18.7549 + 10.3692i −0.992614 + 0.548796i
\(358\) −4.30513 + 4.30513i −0.227533 + 0.227533i
\(359\) 34.5145 1.82160 0.910802 0.412845i \(-0.135465\pi\)
0.910802 + 0.412845i \(0.135465\pi\)
\(360\) −6.58089 + 1.30072i −0.346843 + 0.0685542i
\(361\) −27.3136 −1.43756
\(362\) 7.86622 7.86622i 0.413439 0.413439i
\(363\) 4.89628 2.70705i 0.256988 0.142083i
\(364\) 18.5553i 0.972562i
\(365\) −4.94269 + 4.65871i −0.258712 + 0.243848i
\(366\) −5.58986 + 19.4140i −0.292187 + 1.01478i
\(367\) 8.38016 + 8.38016i 0.437441 + 0.437441i 0.891150 0.453709i \(-0.149899\pi\)
−0.453709 + 0.891150i \(0.649899\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) 20.4188 + 12.8213i 1.06296 + 0.667450i
\(370\) 14.8210 + 0.438358i 0.770509 + 0.0227892i
\(371\) 5.51923i 0.286544i
\(372\) −5.94594 10.7545i −0.308283 0.557595i
\(373\) 7.63967 7.63967i 0.395567 0.395567i −0.481099 0.876666i \(-0.659762\pi\)
0.876666 + 0.481099i \(0.159762\pi\)
\(374\) −13.7759 −0.712335
\(375\) 17.7106 7.83160i 0.914572 0.404422i
\(376\) −4.81432 −0.248280
\(377\) −25.1143 + 25.1143i −1.29345 + 1.29345i
\(378\) 0.979073 17.5778i 0.0503581 0.904106i
\(379\) 1.05138i 0.0540060i 0.999635 + 0.0270030i \(0.00859636\pi\)
−0.999635 + 0.0270030i \(0.991404\pi\)
\(380\) −15.2107 0.449884i −0.780293 0.0230786i
\(381\) −11.1237 3.20284i −0.569883 0.164086i
\(382\) −3.96990 3.96990i −0.203118 0.203118i
\(383\) −16.4304 16.4304i −0.839554 0.839554i 0.149246 0.988800i \(-0.452315\pi\)
−0.988800 + 0.149246i \(0.952315\pi\)
\(384\) 1.66443 + 0.479239i 0.0849376 + 0.0244561i
\(385\) 20.7970 19.6021i 1.05991 0.999015i
\(386\) 13.8225i 0.703549i
\(387\) 2.71085 + 11.8603i 0.137800 + 0.602894i
\(388\) −10.5684 + 10.5684i −0.536532 + 0.536532i
\(389\) 4.44285 0.225261 0.112631 0.993637i \(-0.464072\pi\)
0.112631 + 0.993637i \(0.464072\pi\)
\(390\) 9.70964 + 18.8579i 0.491667 + 0.954909i
\(391\) −3.65187 −0.184683
\(392\) −3.16729 + 3.16729i −0.159972 + 0.159972i
\(393\) −8.04345 14.5483i −0.405738 0.733863i
\(394\) 1.59876i 0.0805446i
\(395\) 0.303899 10.2749i 0.0152908 0.516987i
\(396\) 6.01801 9.58410i 0.302416 0.481619i
\(397\) 2.78289 + 2.78289i 0.139669 + 0.139669i 0.773485 0.633815i \(-0.218512\pi\)
−0.633815 + 0.773485i \(0.718512\pi\)
\(398\) −3.27847 3.27847i −0.164335 0.164335i
\(399\) 11.0500 38.3775i 0.553192 1.92128i
\(400\) −4.99126 0.295509i −0.249563 0.0147755i
\(401\) 1.11565i 0.0557131i 0.999612 + 0.0278565i \(0.00886816\pi\)
−0.999612 + 0.0278565i \(0.991132\pi\)
\(402\) 2.34401 1.29595i 0.116908 0.0646363i
\(403\) −27.4754 + 27.4754i −1.36865 + 1.36865i
\(404\) −3.09956 −0.154209
\(405\) 8.20311 + 18.3769i 0.407616 + 0.913154i
\(406\) 21.9725 1.09048
\(407\) −17.6878 + 17.6878i −0.876750 + 0.876750i
\(408\) −5.53552 + 3.06048i −0.274049 + 0.151516i
\(409\) 15.3832i 0.760653i 0.924852 + 0.380326i \(0.124188\pi\)
−0.924852 + 0.380326i \(0.875812\pi\)
\(410\) 12.3261 + 13.0774i 0.608742 + 0.645849i
\(411\) 3.58880 12.4641i 0.177022 0.614811i
\(412\) 4.89445 + 4.89445i 0.241132 + 0.241132i
\(413\) −2.37947 2.37947i −0.117086 0.117086i
\(414\) 1.59532 2.54066i 0.0784057 0.124867i
\(415\) −11.2862 11.9741i −0.554016 0.587786i
\(416\) 5.47661i 0.268513i
\(417\) 10.6025 + 19.1768i 0.519206 + 0.939094i
\(418\) 18.1528 18.1528i 0.887883 0.887883i
\(419\) −3.29476 −0.160960 −0.0804798 0.996756i \(-0.525645\pi\)
−0.0804798 + 0.996756i \(0.525645\pi\)
\(420\) 4.00193 12.4969i 0.195274 0.609787i
\(421\) 26.2854 1.28107 0.640537 0.767927i \(-0.278712\pi\)
0.640537 + 0.767927i \(0.278712\pi\)
\(422\) 6.33962 6.33962i 0.308608 0.308608i
\(423\) 3.21816 + 14.0799i 0.156472 + 0.684586i
\(424\) 1.62900i 0.0791114i
\(425\) 13.6518 12.1257i 0.662211 0.588181i
\(426\) −15.4152 4.43851i −0.746871 0.215046i
\(427\) −27.9441 27.9441i −1.35231 1.35231i
\(428\) 7.11744 + 7.11744i 0.344035 + 0.344035i
\(429\) −34.3861 9.90077i −1.66018 0.478014i
\(430\) −0.268089 + 9.06417i −0.0129284 + 0.437113i
\(431\) 12.3440i 0.594591i −0.954786 0.297296i \(-0.903915\pi\)
0.954786 0.297296i \(-0.0960847\pi\)
\(432\) 0.288974 5.18811i 0.0139033 0.249613i
\(433\) 4.20594 4.20594i 0.202124 0.202124i −0.598785 0.800910i \(-0.704350\pi\)
0.800910 + 0.598785i \(0.204350\pi\)
\(434\) 24.0383 1.15387
\(435\) −22.3309 + 11.4978i −1.07068 + 0.551277i
\(436\) 18.1228 0.867922
\(437\) 4.81215 4.81215i 0.230196 0.230196i
\(438\) −2.54565 4.60434i −0.121636 0.220004i
\(439\) 23.3960i 1.11663i −0.829629 0.558315i \(-0.811448\pi\)
0.829629 0.558315i \(-0.188552\pi\)
\(440\) 6.13824 5.78557i 0.292629 0.275816i
\(441\) 11.3802 + 7.14579i 0.541913 + 0.340276i
\(442\) 14.1421 + 14.1421i 0.672669 + 0.672669i
\(443\) −1.58931 1.58931i −0.0755103 0.0755103i 0.668343 0.743853i \(-0.267004\pi\)
−0.743853 + 0.668343i \(0.767004\pi\)
\(444\) −3.17786 + 11.0369i −0.150815 + 0.523790i
\(445\) −21.3813 0.632389i −1.01357 0.0299781i
\(446\) 22.0354i 1.04341i
\(447\) −20.8545 + 11.5300i −0.986383 + 0.545351i
\(448\) −2.39575 + 2.39575i −0.113188 + 0.113188i
\(449\) 22.0511 1.04066 0.520328 0.853966i \(-0.325810\pi\)
0.520328 + 0.853966i \(0.325810\pi\)
\(450\) 2.47220 + 14.7949i 0.116540 + 0.697437i
\(451\) −30.3172 −1.42758
\(452\) 14.5951 14.5951i 0.686495 0.686495i
\(453\) 2.46231 1.36136i 0.115689 0.0639623i
\(454\) 24.7238i 1.16035i
\(455\) −41.4728 1.22663i −1.94427 0.0575054i
\(456\) 3.26142 11.3271i 0.152730 0.530442i
\(457\) 26.3823 + 26.3823i 1.23411 + 1.23411i 0.962370 + 0.271741i \(0.0875993\pi\)
0.271741 + 0.962370i \(0.412401\pi\)
\(458\) −6.89234 6.89234i −0.322058 0.322058i
\(459\) 12.6509 + 14.1433i 0.590492 + 0.660152i
\(460\) 1.62719 1.53370i 0.0758682 0.0715093i
\(461\) 12.2104i 0.568695i 0.958721 + 0.284348i \(0.0917770\pi\)
−0.958721 + 0.284348i \(0.908223\pi\)
\(462\) 10.7111 + 19.3733i 0.498326 + 0.901328i
\(463\) 12.7159 12.7159i 0.590959 0.590959i −0.346931 0.937891i \(-0.612776\pi\)
0.937891 + 0.346931i \(0.112776\pi\)
\(464\) 6.48520 0.301068
\(465\) −24.4303 + 12.5788i −1.13293 + 0.583327i
\(466\) 8.87206 0.410990
\(467\) 13.8067 13.8067i 0.638896 0.638896i −0.311387 0.950283i \(-0.600793\pi\)
0.950283 + 0.311387i \(0.100793\pi\)
\(468\) −16.0168 + 3.66087i −0.740376 + 0.169224i
\(469\) 5.23929i 0.241928i
\(470\) −0.318259 + 10.7604i −0.0146802 + 0.496342i
\(471\) 30.5580 + 8.79857i 1.40804 + 0.405417i
\(472\) −0.702303 0.702303i −0.0323261 0.0323261i
\(473\) −10.8174 10.8174i −0.497385 0.497385i
\(474\) 7.65154 + 2.20311i 0.351447 + 0.101192i
\(475\) −2.01106 + 33.9676i −0.0922739 + 1.55854i
\(476\) 12.3729i 0.567111i
\(477\) 4.76415 1.08892i 0.218136 0.0498581i
\(478\) 16.7784 16.7784i 0.767428 0.767428i
\(479\) 12.4597 0.569300 0.284650 0.958632i \(-0.408123\pi\)
0.284650 + 0.958632i \(0.408123\pi\)
\(480\) 1.18117 3.68847i 0.0539129 0.168355i
\(481\) 36.3158 1.65586
\(482\) −4.32877 + 4.32877i −0.197170 + 0.197170i
\(483\) 2.83942 + 5.13569i 0.129198 + 0.233682i
\(484\) 3.23015i 0.146825i
\(485\) 22.9228 + 24.3201i 1.04087 + 1.10432i
\(486\) −15.3662 + 2.62290i −0.697025 + 0.118977i
\(487\) −1.80667 1.80667i −0.0818682 0.0818682i 0.664987 0.746855i \(-0.268437\pi\)
−0.746855 + 0.664987i \(0.768437\pi\)
\(488\) −8.24772 8.24772i −0.373357 0.373357i
\(489\) 3.87664 13.4638i 0.175308 0.608856i
\(490\) 6.86980 + 7.28855i 0.310346 + 0.329263i
\(491\) 28.0135i 1.26423i 0.774874 + 0.632116i \(0.217813\pi\)
−0.774874 + 0.632116i \(0.782187\pi\)
\(492\) −12.1822 + 6.73531i −0.549217 + 0.303651i
\(493\) −16.7465 + 16.7465i −0.754224 + 0.754224i
\(494\) −37.2706 −1.67688
\(495\) −21.0235 14.0844i −0.944936 0.633045i
\(496\) 7.09492 0.318571
\(497\) 22.1884 22.1884i 0.995286 0.995286i
\(498\) 11.1544 6.16706i 0.499842 0.276353i
\(499\) 26.7176i 1.19605i 0.801479 + 0.598023i \(0.204047\pi\)
−0.801479 + 0.598023i \(0.795953\pi\)
\(500\) −0.990446 + 11.1364i −0.0442941 + 0.498034i
\(501\) −6.10781 + 21.2129i −0.272877 + 0.947720i
\(502\) −10.2232 10.2232i −0.456283 0.456283i
\(503\) −26.3520 26.3520i −1.17498 1.17498i −0.981007 0.193973i \(-0.937863\pi\)
−0.193973 0.981007i \(-0.562137\pi\)
\(504\) 8.60801 + 5.40511i 0.383431 + 0.240763i
\(505\) −0.204902 + 6.92780i −0.00911802 + 0.308283i
\(506\) 3.77229i 0.167699i
\(507\) 14.2413 + 25.7585i 0.632480 + 1.14397i
\(508\) 4.72572 4.72572i 0.209670 0.209670i
\(509\) 9.42990 0.417973 0.208986 0.977919i \(-0.432984\pi\)
0.208986 + 0.977919i \(0.432984\pi\)
\(510\) 6.47451 + 12.5747i 0.286696 + 0.556817i
\(511\) 10.2915 0.455271
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −35.3072 1.96659i −1.55885 0.0868270i
\(514\) 26.5897i 1.17282i
\(515\) 11.2631 10.6160i 0.496311 0.467796i
\(516\) −6.74992 1.94350i −0.297149 0.0855580i
\(517\) −12.8418 12.8418i −0.564780 0.564780i
\(518\) −15.8864 15.8864i −0.698007 0.698007i
\(519\) −34.6454 9.97543i −1.52076 0.437873i
\(520\) −12.2407 0.362041i −0.536791 0.0158766i
\(521\) 13.8604i 0.607237i −0.952794 0.303618i \(-0.901805\pi\)
0.952794 0.303618i \(-0.0981948\pi\)
\(522\) −4.33507 18.9665i −0.189741 0.830141i
\(523\) 14.8570 14.8570i 0.649650 0.649650i −0.303259 0.952908i \(-0.598075\pi\)
0.952908 + 0.303259i \(0.0980746\pi\)
\(524\) 9.59773 0.419279
\(525\) −27.6672 9.77081i −1.20749 0.426433i
\(526\) 13.7122 0.597882
\(527\) −18.3209 + 18.3209i −0.798073 + 0.798073i
\(528\) 3.16139 + 5.71805i 0.137582 + 0.248846i
\(529\) 1.00000i 0.0434783i
\(530\) 3.64097 + 0.107688i 0.158154 + 0.00467768i
\(531\) −1.58448 + 2.52340i −0.0687607 + 0.109506i
\(532\) 16.3041 + 16.3041i 0.706870 + 0.706870i
\(533\) 31.1229 + 31.1229i 1.34808 + 1.34808i
\(534\) 4.58448 15.9222i 0.198390 0.689022i
\(535\) 16.3786 15.4376i 0.708110 0.667426i
\(536\) 1.54638i 0.0667934i
\(537\) −9.22879 + 5.10241i −0.398251 + 0.220185i
\(538\) 3.04451 3.04451i 0.131258 0.131258i
\(539\) −16.8969 −0.727801
\(540\) −11.5768 0.988853i −0.498186 0.0425534i
\(541\) −19.6739 −0.845846 −0.422923 0.906166i \(-0.638996\pi\)
−0.422923 + 0.906166i \(0.638996\pi\)
\(542\) 6.12669 6.12669i 0.263164 0.263164i
\(543\) 16.8626 9.32297i 0.723642 0.400087i
\(544\) 3.65187i 0.156573i
\(545\) 1.19804 40.5060i 0.0513183 1.73509i
\(546\) 8.89243 30.8840i 0.380561 1.32171i
\(547\) 20.3990 + 20.3990i 0.872198 + 0.872198i 0.992712 0.120514i \(-0.0384543\pi\)
−0.120514 + 0.992712i \(0.538454\pi\)
\(548\) 5.29519 + 5.29519i 0.226199 + 0.226199i
\(549\) −18.6079 + 29.6343i −0.794165 + 1.26476i
\(550\) −12.5255 14.1020i −0.534089 0.601311i
\(551\) 44.1345i 1.88019i
\(552\) 0.838057 + 1.51580i 0.0356701 + 0.0645169i
\(553\) −11.0135 + 11.0135i −0.468341 + 0.468341i
\(554\) −29.5281 −1.25453
\(555\) 24.4585 + 7.83243i 1.03821 + 0.332468i
\(556\) −12.6513 −0.536533
\(557\) 3.65261 3.65261i 0.154766 0.154766i −0.625477 0.780243i \(-0.715096\pi\)
0.780243 + 0.625477i \(0.215096\pi\)
\(558\) −4.74264 20.7496i −0.200772 0.878403i
\(559\) 22.2098i 0.939375i
\(560\) 5.19634 + 5.51309i 0.219585 + 0.232971i
\(561\) −22.9291 6.60195i −0.968065 0.278735i
\(562\) 15.5083 + 15.5083i 0.654177 + 0.654177i
\(563\) −26.8125 26.8125i −1.13001 1.13001i −0.990175 0.139836i \(-0.955342\pi\)
−0.139836 0.990175i \(-0.544658\pi\)
\(564\) −8.01310 2.30721i −0.337412 0.0971511i
\(565\) −31.6565 33.5862i −1.33180 1.41298i
\(566\) 2.21185i 0.0929709i
\(567\) 10.0536 28.7879i 0.422211 1.20898i
\(568\) 6.54892 6.54892i 0.274787 0.274787i
\(569\) 35.3739 1.48295 0.741475 0.670980i \(-0.234126\pi\)
0.741475 + 0.670980i \(0.234126\pi\)
\(570\) −25.1016 8.03837i −1.05139 0.336690i
\(571\) −33.8705 −1.41744 −0.708718 0.705492i \(-0.750726\pi\)
−0.708718 + 0.705492i \(0.750726\pi\)
\(572\) 14.6084 14.6084i 0.610807 0.610807i
\(573\) −4.70509 8.51015i −0.196558 0.355516i
\(574\) 27.2295i 1.13654i
\(575\) −3.32040 3.73831i −0.138470 0.155898i
\(576\) 2.54066 + 1.59532i 0.105861 + 0.0664717i
\(577\) 25.3921 + 25.3921i 1.05709 + 1.05709i 0.998269 + 0.0588185i \(0.0187333\pi\)
0.0588185 + 0.998269i \(0.481267\pi\)
\(578\) −2.59072 2.59072i −0.107760 0.107760i
\(579\) −6.62430 + 23.0067i −0.275297 + 0.956125i
\(580\) 0.428716 14.4950i 0.0178015 0.601873i
\(581\) 24.9322i 1.03436i
\(582\) −22.6553 + 12.5256i −0.939091 + 0.519204i
\(583\) −4.34522 + 4.34522i −0.179961 + 0.179961i
\(584\) 3.03756 0.125695
\(585\) 7.12357 + 36.0410i 0.294523 + 1.49011i
\(586\) 9.04621 0.373695
\(587\) 31.7362 31.7362i 1.30989 1.30989i 0.388402 0.921490i \(-0.373027\pi\)
0.921490 0.388402i \(-0.126973\pi\)
\(588\) −6.78962 + 3.75384i −0.279999 + 0.154806i
\(589\) 48.2838i 1.98950i
\(590\) −1.61614 + 1.52328i −0.0665354 + 0.0627126i
\(591\) −0.766190 + 2.66103i −0.0315169 + 0.109460i
\(592\) −4.68887 4.68887i −0.192711 0.192711i
\(593\) 21.4857 + 21.4857i 0.882314 + 0.882314i 0.993769 0.111456i \(-0.0355513\pi\)
−0.111456 + 0.993769i \(0.535551\pi\)
\(594\) 14.6096 13.0680i 0.599440 0.536187i
\(595\) −27.6546 0.817933i −1.13373 0.0335320i
\(596\) 13.7580i 0.563551i
\(597\) −3.88562 7.02796i −0.159028 0.287635i
\(598\) 3.87255 3.87255i 0.158360 0.158360i
\(599\) 28.3661 1.15901 0.579504 0.814969i \(-0.303246\pi\)
0.579504 + 0.814969i \(0.303246\pi\)
\(600\) −8.16599 2.88386i −0.333375 0.117733i
\(601\) 40.0727 1.63460 0.817300 0.576213i \(-0.195470\pi\)
0.817300 + 0.576213i \(0.195470\pi\)
\(602\) 9.71571 9.71571i 0.395983 0.395983i
\(603\) 4.52251 1.03369i 0.184171 0.0420950i
\(604\) 1.62442i 0.0660969i
\(605\) 7.21969 + 0.213535i 0.293522 + 0.00868144i
\(606\) −5.15900 1.48543i −0.209570 0.0603415i
\(607\) −1.59716 1.59716i −0.0648268 0.0648268i 0.673950 0.738777i \(-0.264596\pi\)
−0.738777 + 0.673950i \(0.764596\pi\)
\(608\) 4.81215 + 4.81215i 0.195159 + 0.195159i
\(609\) 36.5717 + 10.5301i 1.48196 + 0.426701i
\(610\) −18.9796 + 17.8892i −0.768463 + 0.724311i
\(611\) 26.3662i 1.06666i
\(612\) −10.6802 + 2.44112i −0.431721 + 0.0986763i
\(613\) 12.0113 12.0113i 0.485130 0.485130i −0.421636 0.906765i \(-0.638544\pi\)
0.906765 + 0.421636i \(0.138544\pi\)
\(614\) 24.7945 1.00063
\(615\) 14.2487 + 27.6736i 0.574563 + 1.11591i
\(616\) −12.7809 −0.514957
\(617\) −20.3489 + 20.3489i −0.819214 + 0.819214i −0.985994 0.166780i \(-0.946663\pi\)
0.166780 + 0.985994i \(0.446663\pi\)
\(618\) 5.80086 + 10.4921i 0.233345 + 0.422053i
\(619\) 11.4711i 0.461063i −0.973065 0.230531i \(-0.925954\pi\)
0.973065 0.230531i \(-0.0740464\pi\)
\(620\) 0.469022 15.8578i 0.0188364 0.636864i
\(621\) 3.87288 3.46421i 0.155413 0.139014i
\(622\) 0.727771 + 0.727771i 0.0291810 + 0.0291810i
\(623\) 22.9181 + 22.9181i 0.918196 + 0.918196i
\(624\) 2.62461 9.11544i 0.105068 0.364910i
\(625\) 24.8253 + 2.94993i 0.993014 + 0.117997i
\(626\) 7.28751i 0.291268i
\(627\) 38.9137 21.5146i 1.55406 0.859209i
\(628\) −12.9821 + 12.9821i −0.518042 + 0.518042i
\(629\) 24.2158 0.965547
\(630\) 12.6499 18.8824i 0.503986 0.752292i
\(631\) 1.12832 0.0449177 0.0224588 0.999748i \(-0.492851\pi\)
0.0224588 + 0.999748i \(0.492851\pi\)
\(632\) −3.25064 + 3.25064i −0.129303 + 0.129303i
\(633\) 13.5900 7.51366i 0.540156 0.298641i
\(634\) 3.04326i 0.120863i
\(635\) −10.2500 10.8748i −0.406759 0.431553i
\(636\) −0.780682 + 2.71137i −0.0309561 + 0.107513i
\(637\) 17.3460 + 17.3460i 0.687274 + 0.687274i
\(638\) 17.2987 + 17.2987i 0.684862 + 0.684862i
\(639\) −23.5305 14.7752i −0.930852 0.584497i
\(640\) 1.53370 + 1.62719i 0.0606249 + 0.0643204i
\(641\) 31.3115i 1.23673i 0.785892 + 0.618364i \(0.212204\pi\)
−0.785892 + 0.618364i \(0.787796\pi\)
\(642\) 8.43553 + 15.2574i 0.332924 + 0.602163i
\(643\) 5.97111 5.97111i 0.235478 0.235478i −0.579497 0.814974i \(-0.696751\pi\)
0.814974 + 0.579497i \(0.196751\pi\)
\(644\) −3.38810 −0.133510
\(645\) −4.79012 + 14.9582i −0.188611 + 0.588979i
\(646\) −24.8525 −0.977808
\(647\) −10.0814 + 10.0814i −0.396340 + 0.396340i −0.876940 0.480600i \(-0.840419\pi\)
0.480600 + 0.876940i \(0.340419\pi\)
\(648\) 2.96732 8.49676i 0.116567 0.333784i
\(649\) 3.74666i 0.147069i
\(650\) −1.61839 + 27.3352i −0.0634785 + 1.07217i
\(651\) 40.0101 + 11.5201i 1.56812 + 0.451508i
\(652\) 5.71990 + 5.71990i 0.224008 + 0.224008i
\(653\) −14.5180 14.5180i −0.568134 0.568134i 0.363472 0.931605i \(-0.381591\pi\)
−0.931605 + 0.363472i \(0.881591\pi\)
\(654\) 30.1641 + 8.68513i 1.17951 + 0.339615i
\(655\) 0.634475 21.4518i 0.0247910 0.838191i
\(656\) 8.03681i 0.313785i
\(657\) −2.03047 8.88357i −0.0792163 0.346581i
\(658\) 11.5339 11.5339i 0.449638 0.449638i
\(659\) 20.3327 0.792048 0.396024 0.918240i \(-0.370390\pi\)
0.396024 + 0.918240i \(0.370390\pi\)
\(660\) 12.9893 6.68800i 0.505609 0.260330i
\(661\) −31.1622 −1.21207 −0.606035 0.795438i \(-0.707241\pi\)
−0.606035 + 0.795438i \(0.707241\pi\)
\(662\) 7.09151 7.09151i 0.275619 0.275619i
\(663\) 16.7610 + 30.3159i 0.650945 + 1.17737i
\(664\) 7.35876i 0.285575i
\(665\) 37.5188 35.3632i 1.45492 1.37133i
\(666\) −10.5787 + 16.8473i −0.409915 + 0.652819i
\(667\) 4.58573 + 4.58573i 0.177560 + 0.177560i
\(668\) −9.01194 9.01194i −0.348682 0.348682i
\(669\) −10.5602 + 36.6764i −0.408282 + 1.41799i
\(670\) 3.45630 + 0.102226i 0.133528 + 0.00394934i
\(671\) 44.0001i 1.69860i
\(672\) −5.13569 + 2.83942i −0.198114 + 0.109533i
\(673\) 32.7647 32.7647i 1.26299 1.26299i 0.313348 0.949638i \(-0.398549\pi\)
0.949638 0.313348i \(-0.101451\pi\)
\(674\) −25.4451 −0.980107
\(675\) −2.97548 + 25.8098i −0.114526 + 0.993420i
\(676\) −16.9933 −0.653588
\(677\) 10.4956 10.4956i 0.403380 0.403380i −0.476043 0.879422i \(-0.657929\pi\)
0.879422 + 0.476043i \(0.157929\pi\)
\(678\) 31.2870 17.2980i 1.20157 0.664325i
\(679\) 50.6387i 1.94333i
\(680\) −8.16227 0.241414i −0.313009 0.00925779i
\(681\) −11.8486 + 41.1510i −0.454040 + 1.57691i
\(682\) 18.9250 + 18.9250i 0.724678 + 0.724678i
\(683\) −2.34519 2.34519i −0.0897362 0.0897362i 0.660814 0.750550i \(-0.270211\pi\)
−0.750550 + 0.660814i \(0.770211\pi\)
\(684\) 10.8568 17.2902i 0.415121 0.661109i
\(685\) 12.1853 11.4852i 0.465575 0.438826i
\(686\) 8.54065i 0.326084i
\(687\) −8.16874 14.7749i −0.311657 0.563698i
\(688\) 2.86760 2.86760i 0.109326 0.109326i
\(689\) 8.92143 0.339879
\(690\) 3.44336 1.77293i 0.131086 0.0674942i
\(691\) 49.5125 1.88355 0.941773 0.336250i \(-0.109159\pi\)
0.941773 + 0.336250i \(0.109159\pi\)
\(692\) 14.7185 14.7185i 0.559515 0.559515i
\(693\) 8.54346 + 37.3787i 0.324539 + 1.41990i
\(694\) 23.6977i 0.899551i
\(695\) −0.836335 + 28.2767i −0.0317240 + 1.07260i
\(696\) 10.7942 + 3.10796i 0.409152 + 0.117807i
\(697\) 20.7532 + 20.7532i 0.786082 + 0.786082i
\(698\) 9.63952 + 9.63952i 0.364861 + 0.364861i
\(699\) 14.7669 + 4.25184i 0.558536 + 0.160819i
\(700\) 12.6658 11.2498i 0.478721 0.425204i
\(701\) 43.6716i 1.64945i −0.565532 0.824726i \(-0.691329\pi\)
0.565532 0.824726i \(-0.308671\pi\)
\(702\) −28.4133 1.58260i −1.07239 0.0597314i
\(703\) −31.9097 + 31.9097i −1.20350 + 1.20350i
\(704\) −3.77229 −0.142173
\(705\) −5.68654 + 17.7575i −0.214168 + 0.668786i
\(706\) 6.57049 0.247283
\(707\) 7.42577 7.42577i 0.279275 0.279275i
\(708\) −0.832364 1.50551i −0.0312822 0.0565804i
\(709\) 17.3686i 0.652292i −0.945319 0.326146i \(-0.894250\pi\)
0.945319 0.326146i \(-0.105750\pi\)
\(710\) −14.2045 15.0704i −0.533085 0.565581i
\(711\) 11.6796 + 7.33384i 0.438021 + 0.275040i
\(712\) 6.76430 + 6.76430i 0.253503 + 0.253503i
\(713\) 5.01686 + 5.01686i 0.187883 + 0.187883i
\(714\) 5.92958 20.5938i 0.221909 0.770705i
\(715\) −31.6853 33.6167i −1.18496 1.25719i
\(716\) 6.08838i 0.227533i
\(717\) 35.9674 19.8857i 1.34323 0.742644i
\(718\) −24.4054 + 24.4054i −0.910802 + 0.910802i
\(719\) −13.0073 −0.485089 −0.242545 0.970140i \(-0.577982\pi\)
−0.242545 + 0.970140i \(0.577982\pi\)
\(720\) 3.73364 5.57314i 0.139145 0.207699i
\(721\) −23.4517 −0.873388
\(722\) 19.3136 19.3136i 0.718779 0.718779i
\(723\) −9.27945 + 5.13042i −0.345106 + 0.190802i
\(724\) 11.1245i 0.413439i
\(725\) −32.3693 1.91644i −1.20217 0.0711747i
\(726\) −1.54802 + 5.37637i −0.0574523 + 0.199536i
\(727\) 3.34014 + 3.34014i 0.123879 + 0.123879i 0.766328 0.642449i \(-0.222082\pi\)
−0.642449 + 0.766328i \(0.722082\pi\)
\(728\) 13.1206 + 13.1206i 0.486281 + 0.486281i
\(729\) −26.8330 2.99846i −0.993814 0.111054i
\(730\) 0.200803 6.78921i 0.00743206 0.251280i
\(731\) 14.8098i 0.547760i
\(732\) −9.77513 17.6804i −0.361299 0.653486i
\(733\) 21.3827 21.3827i 0.789788 0.789788i −0.191671 0.981459i \(-0.561391\pi\)
0.981459 + 0.191671i \(0.0613906\pi\)
\(734\) −11.8513 −0.437441
\(735\) 7.94134 + 15.4236i 0.292921 + 0.568907i
\(736\) −1.00000 −0.0368605
\(737\) −4.12483 + 4.12483i −0.151940 + 0.151940i
\(738\) −23.5043 + 5.37225i −0.865205 + 0.197755i
\(739\) 27.3440i 1.00587i −0.864326 0.502933i \(-0.832254\pi\)
0.864326 0.502933i \(-0.167746\pi\)
\(740\) −10.7900 + 10.1701i −0.396649 + 0.373860i
\(741\) −62.0343 17.8615i −2.27889 0.656159i
\(742\) −3.90268 3.90268i −0.143272 0.143272i
\(743\) 24.1777 + 24.1777i 0.886995 + 0.886995i 0.994233 0.107238i \(-0.0342007\pi\)
−0.107238 + 0.994233i \(0.534201\pi\)
\(744\) 11.8090 + 3.40016i 0.432939 + 0.124656i
\(745\) −30.7505 0.909500i −1.12661 0.0333215i
\(746\) 10.8041i 0.395567i
\(747\) 21.5213 4.91901i 0.787423 0.179977i
\(748\) 9.74104 9.74104i 0.356168 0.356168i
\(749\) −34.1032 −1.24610
\(750\) −6.98552 + 18.0611i −0.255075 + 0.659497i
\(751\) 34.8097 1.27022 0.635112 0.772420i \(-0.280954\pi\)
0.635112 + 0.772420i \(0.280954\pi\)
\(752\) 3.40424 3.40424i 0.124140 0.124140i
\(753\) −12.1164 21.9151i −0.441548 0.798632i
\(754\) 35.5169i 1.29345i
\(755\) 3.63074 + 0.107385i 0.132136 + 0.00390816i
\(756\) 11.7371 + 13.1217i 0.426874 + 0.477232i
\(757\) −18.4573 18.4573i −0.670841 0.670841i 0.287069 0.957910i \(-0.407319\pi\)
−0.957910 + 0.287069i \(0.907319\pi\)
\(758\) −0.743441 0.743441i −0.0270030 0.0270030i
\(759\) −1.80783 + 6.27871i −0.0656200 + 0.227903i
\(760\) 11.0737 10.4375i 0.401686 0.378607i
\(761\) 4.20612i 0.152472i −0.997090 0.0762358i \(-0.975710\pi\)
0.997090 0.0762358i \(-0.0242902\pi\)
\(762\) 10.1304 5.60088i 0.366985 0.202898i
\(763\) −43.4176 + 43.4176i −1.57182 + 1.57182i
\(764\) 5.61428 0.203118
\(765\) 4.75008 + 24.0326i 0.171740 + 0.868899i
\(766\) 23.2361 0.839554
\(767\) −3.84624 + 3.84624i −0.138880 + 0.138880i
\(768\) −1.51580 + 0.838057i −0.0546968 + 0.0302408i
\(769\) 32.2378i 1.16253i −0.813716 0.581263i \(-0.802559\pi\)
0.813716 0.581263i \(-0.197441\pi\)
\(770\) −0.844904 + 28.5664i −0.0304482 + 1.02946i
\(771\) 12.7428 44.2567i 0.458922 1.59387i
\(772\) −9.77402 9.77402i −0.351775 0.351775i
\(773\) 0.232058 + 0.232058i 0.00834653 + 0.00834653i 0.711268 0.702921i \(-0.248121\pi\)
−0.702921 + 0.711268i \(0.748121\pi\)
\(774\) −10.3034 6.46965i −0.370347 0.232547i
\(775\) −35.4126 2.09661i −1.27206 0.0753126i
\(776\) 14.9460i 0.536532i
\(777\) −18.8284 34.0551i −0.675465 1.22172i
\(778\) −3.14157 +