Properties

Label 690.2.i.f.47.11
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 47.11
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.838057 + 1.51580i) q^{3} -1.00000i q^{4} +(2.23509 + 0.0661068i) q^{5} +(0.479239 + 1.66443i) q^{6} +(2.39575 + 2.39575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.59532 - 2.54066i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.838057 + 1.51580i) 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} +(1.51580 + 0.838057i) q^{12} +(3.87255 - 3.87255i) q^{13} +3.38810 q^{14} +(-1.97334 + 3.33256i) q^{15} -1.00000 q^{16} +(-2.58226 + 2.58226i) q^{17} +(-2.92458 - 0.668456i) 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} +(5.18811 - 0.288974i) q^{27} +(2.39575 - 2.39575i) q^{28} +6.48520 q^{29} +(0.961112 + 3.75183i) q^{30} -7.09492 q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.71805 + 3.16139i) 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} +(-2.83942 + 5.13569i) q^{42} +(-2.86760 + 2.86760i) q^{43} -3.77229 q^{44} +(-3.39773 - 5.78407i) q^{45} +1.00000 q^{46} +(3.40424 - 3.40424i) q^{47} +(0.838057 - 1.51580i) 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} +(-10.3157 - 5.70332i) q^{57} +(4.58573 - 4.58573i) q^{58} +0.993207 q^{59} +(3.33256 + 1.97334i) q^{60} -11.6640 q^{61} +(-5.01686 + 5.01686i) q^{62} +(2.26480 - 9.90877i) 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} +(-0.668456 + 2.92458i) q^{72} +(2.14788 - 2.14788i) q^{73} +6.63106 q^{74} +(-4.63090 + 7.31812i) q^{75} +6.80541 q^{76} +(9.03745 - 9.03745i) q^{77} +(8.30147 + 4.58971i) 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} +(-5.43497 + 9.83029i) q^{87} +(-2.66741 + 2.66741i) q^{88} -9.56617 q^{89} +(-6.49251 - 1.68739i) q^{90} +18.5553 q^{91} +(0.707107 - 0.707107i) q^{92} +(5.94594 - 10.7545i) 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
\(3\) −0.838057 + 1.51580i −0.483853 + 0.875150i
\(4\) 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 \(-0.807449\pi\)
0.822549 0.568694i \(-0.192551\pi\)
\(12\) 1.51580 + 0.838057i 0.437575 + 0.241926i
\(13\) 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
\(15\) −1.97334 + 3.33256i −0.509514 + 0.860462i
\(16\) −1.00000 −0.250000
\(17\) −2.58226 + 2.58226i −0.626291 + 0.626291i −0.947133 0.320842i \(-0.896034\pi\)
0.320842 + 0.947133i \(0.396034\pi\)
\(18\) −2.92458 0.668456i −0.689330 0.157557i
\(19\) 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
\(27\) 5.18811 0.288974i 0.998452 0.0556131i
\(28\) 2.39575 2.39575i 0.452754 0.452754i
\(29\) 6.48520 1.20427 0.602136 0.798394i \(-0.294317\pi\)
0.602136 + 0.798394i \(0.294317\pi\)
\(30\) 0.961112 + 3.75183i 0.175474 + 0.684988i
\(31\) −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
\(33\) 5.71805 + 3.16139i 0.995384 + 0.550328i
\(34\) 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 \(-0.784050\pi\)
0.778561 0.627569i \(-0.215950\pi\)
\(42\) −2.83942 + 5.13569i −0.438132 + 0.792455i
\(43\) −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
\(45\) −3.39773 5.78407i −0.506504 0.862238i
\(46\) 1.00000 0.147442
\(47\) 3.40424 3.40424i 0.496559 0.496559i −0.413806 0.910365i \(-0.635801\pi\)
0.910365 + 0.413806i \(0.135801\pi\)
\(48\) 0.838057 1.51580i 0.120963 0.218787i
\(49\) 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 0.623556 0.781779i \(-0.285687\pi\)
−0.781779 + 0.623556i \(0.785687\pi\)
\(54\) 3.46421 3.87288i 0.471420 0.527033i
\(55\) 0.249374 8.43140i 0.0336256 1.13689i
\(56\) 3.38810i 0.452754i
\(57\) −10.3157 5.70332i −1.36634 0.755424i
\(58\) 4.58573 4.58573i 0.602136 0.602136i
\(59\) 0.993207 0.129304 0.0646522 0.997908i \(-0.479406\pi\)
0.0646522 + 0.997908i \(0.479406\pi\)
\(60\) 3.33256 + 1.97334i 0.430231 + 0.254757i
\(61\) −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
\(63\) 2.26480 9.90877i 0.285337 1.24839i
\(64\) 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 \(0.185210\pi\)
−0.835446 + 0.549573i \(0.814790\pi\)
\(72\) −0.668456 + 2.92458i −0.0787783 + 0.344665i
\(73\) 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
\(75\) −4.63090 + 7.31812i −0.534730 + 0.845023i
\(76\) 6.80541 0.780634
\(77\) 9.03745 9.03745i 1.02991 1.02991i
\(78\) 8.30147 + 4.58971i 0.939956 + 0.519683i
\(79\) 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 0.361299 0.932450i \(-0.382333\pi\)
−0.932450 + 0.361299i \(0.882333\pi\)
\(84\) 1.62371 + 5.63926i 0.177161 + 0.615293i
\(85\) −5.94230 + 5.60089i −0.644533 + 0.607502i
\(86\) 4.05539i 0.437304i
\(87\) −5.43497 + 9.83029i −0.582690 + 1.05392i
\(88\) −2.66741 + 2.66741i −0.284347 + 0.284347i
\(89\) −9.56617 −1.01401 −0.507006 0.861943i \(-0.669248\pi\)
−0.507006 + 0.861943i \(0.669248\pi\)
\(90\) −6.49251 1.68739i −0.684371 0.177867i
\(91\) 18.5553 1.94512
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) 5.94594 10.7545i 0.616566 1.11519i
\(94\) 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 \(0.0492829\pi\)
−0.988038 + 0.154209i \(0.950717\pi\)
\(102\) −5.53552 3.06048i −0.548098 0.303032i
\(103\) −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
\(105\) −12.7116 + 3.25635i −1.24052 + 0.317787i
\(106\) −1.62900 −0.158223
\(107\) 7.11744 7.11744i 0.688069 0.688069i −0.273736 0.961805i \(-0.588259\pi\)
0.961805 + 0.273736i \(0.0882594\pi\)
\(108\) −0.288974 5.18811i −0.0278065 0.499226i
\(109\) 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 \(-0.827044\pi\)
−0.517012 0.855978i \(-0.672956\pi\)
\(114\) −11.3271 + 3.26142i −1.06088 + 0.305460i
\(115\) 1.53370 + 1.62719i 0.143019 + 0.151736i
\(116\) 6.48520i 0.602136i
\(117\) −16.0168 3.66087i −1.48075 0.338448i
\(118\) 0.702303 0.702303i 0.0646522 0.0646522i
\(119\) −12.3729 −1.13422
\(120\) 3.75183 0.961112i 0.342494 0.0877372i
\(121\) −3.23015 −0.293650
\(122\) −8.24772 + 8.24772i −0.746713 + 0.746713i
\(123\) 12.1822 + 6.73531i 1.09843 + 0.607302i
\(124\) 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 \(-0.862283\pi\)
0.907858 0.419279i \(-0.137717\pi\)
\(132\) 3.16139 5.71805i 0.275164 0.497692i
\(133\) −16.3041 + 16.3041i −1.41374 + 1.41374i
\(134\) 1.54638 0.133587
\(135\) 11.6150 0.302914i 0.999660 0.0260707i
\(136\) 3.65187 0.313145
\(137\) 5.29519 5.29519i 0.452399 0.452399i −0.443751 0.896150i \(-0.646353\pi\)
0.896150 + 0.443751i \(0.146353\pi\)
\(138\) −0.838057 + 1.51580i −0.0713402 + 0.129034i
\(139\) 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
\(147\) −6.78962 3.75384i −0.559998 0.309612i
\(148\) 4.68887 4.68887i 0.385423 0.385423i
\(149\) −13.7580 −1.12710 −0.563551 0.826081i \(-0.690565\pi\)
−0.563551 + 0.826081i \(0.690565\pi\)
\(150\) 1.90015 + 8.44923i 0.155147 + 0.689876i
\(151\) −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
\(153\) 10.6802 + 2.44112i 0.863442 + 0.197353i
\(154\) 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
\(162\) 2.96732 + 8.49676i 0.233135 + 0.667569i
\(163\) −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
\(165\) 12.5714 + 7.44400i 0.978679 + 0.579515i
\(166\) −7.35876 −0.571151
\(167\) −9.01194 + 9.01194i −0.697365 + 0.697365i −0.963841 0.266476i \(-0.914141\pi\)
0.266476 + 0.963841i \(0.414141\pi\)
\(168\) 5.13569 + 2.83942i 0.396227 + 0.219066i
\(169\) 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 \(-0.959419\pi\)
−0.127145 0.991884i \(-0.540581\pi\)
\(174\) 3.10796 + 10.7942i 0.235614 + 0.818304i
\(175\) 11.2498 + 12.6658i 0.850408 + 0.957442i
\(176\) 3.77229i 0.284347i
\(177\) −0.832364 + 1.50551i −0.0625643 + 0.113161i
\(178\) −6.76430 + 6.76430i −0.507006 + 0.507006i
\(179\) −6.08838 −0.455067 −0.227533 0.973770i \(-0.573066\pi\)
−0.227533 + 0.973770i \(0.573066\pi\)
\(180\) −5.78407 + 3.39773i −0.431119 + 0.253252i
\(181\) −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
\(183\) 9.77513 17.6804i 0.722598 1.30697i
\(184\) 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 \(-0.934893\pi\)
0.979154 0.203118i \(-0.0651074\pi\)
\(192\) −1.51580 0.838057i −0.109394 0.0604816i
\(193\) 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
\(195\) 5.26364 + 20.5473i 0.376937 + 1.47143i
\(196\) 4.47922 0.319944
\(197\) −1.13050 + 1.13050i −0.0805446 + 0.0805446i −0.746231 0.665687i \(-0.768139\pi\)
0.665687 + 0.746231i \(0.268139\pi\)
\(198\) −2.52161 + 11.0324i −0.179203 + 0.784035i
\(199\) 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
\(207\) 0.668456 2.92458i 0.0464609 0.203272i
\(208\) −3.87255 + 3.87255i −0.268513 + 0.268513i
\(209\) 25.6720 1.77577
\(210\) −6.68587 + 11.2910i −0.461369 + 0.779155i
\(211\) −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
\(213\) −14.0387 7.76173i −0.961918 0.531825i
\(214\) 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
\(222\) −5.55721 + 10.0514i −0.372976 + 0.674605i
\(223\) 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
\(225\) −7.21187 13.1525i −0.480791 0.876835i
\(226\) −20.6406 −1.37299
\(227\) −17.4824 + 17.4824i −1.16035 + 1.16035i −0.175945 + 0.984400i \(0.556298\pi\)
−0.984400 + 0.175945i \(0.943702\pi\)
\(228\) −5.70332 + 10.3157i −0.377712 + 0.683172i
\(229\) 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 0.882083 0.471093i \(-0.156140\pi\)
−0.471093 + 0.882083i \(0.656140\pi\)
\(234\) −13.9142 + 8.73695i −0.909600 + 0.571152i
\(235\) 7.83382 7.38374i 0.511022 0.481662i
\(236\) 0.993207i 0.0646522i
\(237\) −6.96829 3.85263i −0.452639 0.250255i
\(238\) −8.74897 + 8.74897i −0.567111 + 0.567111i
\(239\) 23.7283 1.53486 0.767428 0.641135i \(-0.221536\pi\)
0.767428 + 0.641135i \(0.221536\pi\)
\(240\) 1.97334 3.33256i 0.127378 0.215116i
\(241\) 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
\(243\) −9.01088 12.7202i −0.578048 0.816002i
\(244\) 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 \(-0.849180\pi\)
0.889835 0.456283i \(-0.150820\pi\)
\(252\) −9.90877 2.26480i −0.624194 0.142669i
\(253\) 2.66741 2.66741i 0.167699 0.167699i
\(254\) 6.68317 0.419339
\(255\) −3.50986 13.7012i −0.219796 0.858004i
\(256\) 1.00000 0.0625000
\(257\) 18.8018 18.8018i 1.17282 1.17282i 0.191288 0.981534i \(-0.438733\pi\)
0.981534 0.191288i \(-0.0612665\pi\)
\(258\) −6.14718 3.39865i −0.382707 0.211591i
\(259\) 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 0.939749 0.341866i \(-0.111059\pi\)
−0.341866 + 0.939749i \(0.611059\pi\)
\(264\) −1.80783 6.27871i −0.111264 0.386428i
\(265\) −2.49841 2.65070i −0.153476 0.162831i
\(266\) 23.0574i 1.41374i
\(267\) 8.01700 14.5004i 0.490632 0.887412i
\(268\) 1.09345 1.09345i 0.0667934 0.0667934i
\(269\) 4.30558 0.262516 0.131258 0.991348i \(-0.458098\pi\)
0.131258 + 0.991348i \(0.458098\pi\)
\(270\) 7.99885 8.42724i 0.486795 0.512865i
\(271\) −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
\(273\) −15.5504 + 28.1262i −0.941154 + 1.70228i
\(274\) 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 \(0.226985\pi\)
−0.756341 + 0.654177i \(0.773015\pi\)
\(282\) 7.29756 + 4.03467i 0.434564 + 0.240261i
\(283\) −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
\(285\) −22.6794 13.4294i −1.34341 0.795488i
\(286\) −20.6594 −1.22161
\(287\) 19.2542 19.2542i 1.13654 1.13654i
\(288\) 2.92458 + 0.668456i 0.172333 + 0.0393891i
\(289\) 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 0.868821 0.495126i \(-0.164878\pi\)
−0.495126 + 0.868821i \(0.664878\pi\)
\(294\) −7.45535 + 2.14662i −0.434805 + 0.125193i
\(295\) 2.21991 + 0.0656577i 0.129248 + 0.00382274i
\(296\) 6.63106i 0.385423i
\(297\) −1.09009 19.5710i −0.0632536 1.13563i
\(298\) −9.72840 + 9.72840i −0.563551 + 0.563551i
\(299\) 5.47661 0.316721
\(300\) 7.31812 + 4.63090i 0.422512 + 0.267365i
\(301\) −13.7401 −0.791965
\(302\) −1.14864 + 1.14864i −0.0660969 + 0.0660969i
\(303\) −4.69832 2.59761i −0.269912 0.149229i
\(304\) 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 \(0.00928991\pi\)
−0.999574 + 0.0291810i \(0.990710\pi\)
\(312\) 4.58971 8.30147i 0.259841 0.469978i
\(313\) −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
\(315\) 5.71706 21.9973i 0.322120 1.23941i
\(316\) 4.59709 0.258607
\(317\) 2.15191 2.15191i 0.120863 0.120863i −0.644088 0.764951i \(-0.722763\pi\)
0.764951 + 0.644088i \(0.222763\pi\)
\(318\) 1.36520 2.46925i 0.0765565 0.138469i
\(319\) 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
\(327\) −27.4705 15.1879i −1.51912 0.839893i
\(328\) −5.68288 + 5.68288i −0.313785 + 0.313785i
\(329\) 16.3114 0.899276
\(330\) 14.1530 3.62559i 0.779097 0.199582i
\(331\) −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
\(333\) 4.43257 19.3931i 0.242904 1.06273i
\(334\) 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
\(342\) 4.54912 19.9030i 0.245988 1.07623i
\(343\) 6.03915 6.03915i 0.326084 0.326084i
\(344\) 4.05539 0.218652
\(345\) −3.75183 + 0.961112i −0.201992 + 0.0517446i
\(346\) −20.8151 −1.11903
\(347\) −16.7568 + 16.7568i −0.899551 + 0.899551i −0.995396 0.0958454i \(-0.969445\pi\)
0.0958454 + 0.995396i \(0.469445\pi\)
\(348\) 9.83029 + 5.43497i 0.526959 + 0.291345i
\(349\) 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 0.819855 0.572571i \(-0.194054\pi\)
−0.572571 + 0.819855i \(0.694054\pi\)
\(354\) 0.475983 + 1.65312i 0.0252982 + 0.0878625i
\(355\) −0.612253 + 20.7005i −0.0324950 + 1.09867i
\(356\) 9.56617i 0.507006i
\(357\) 10.3692 18.7549i 0.548796 0.992614i
\(358\) −4.30513 + 4.30513i −0.227533 + 0.227533i
\(359\) −34.5145 −1.82160 −0.910802 0.412845i \(-0.864535\pi\)
−0.910802 + 0.412845i \(0.864535\pi\)
\(360\) −1.68739 + 6.49251i −0.0889335 + 0.342185i
\(361\) −27.3136 −1.43756
\(362\) −7.86622 + 7.86622i −0.413439 + 0.413439i
\(363\) 2.70705 4.89628i 0.142083 0.256988i
\(364\) 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
\(372\) −10.7545 5.94594i −0.557595 0.308283i
\(373\) 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
\(375\) −10.8342 + 16.0505i −0.559478 + 0.828845i
\(376\) −4.81432 −0.248280
\(377\) 25.1143 25.1143i 1.29345 1.29345i
\(378\) 17.5778 0.979073i 0.904106 0.0503581i
\(379\) 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 0.988800 0.149246i \(-0.0476845\pi\)
−0.149246 + 0.988800i \(0.547685\pi\)
\(384\) −1.66443 + 0.479239i −0.0849376 + 0.0244561i
\(385\) 20.7970 19.6021i 1.05991 0.999015i
\(386\) 13.8225i 0.703549i
\(387\) 11.8603 + 2.71085i 0.602894 + 0.137800i
\(388\) −10.5684 + 10.5684i −0.536532 + 0.536532i
\(389\) −4.44285 −0.225261 −0.112631 0.993637i \(-0.535928\pi\)
−0.112631 + 0.993637i \(0.535928\pi\)
\(390\) 18.2511 + 10.8072i 0.924181 + 0.547244i
\(391\) −3.65187 −0.184683
\(392\) 3.16729 3.16729i 0.159972 0.159972i
\(393\) 14.5483 + 8.04345i 0.733863 + 0.405738i
\(394\) 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 \(-0.991132\pi\)
0.999612 0.0278565i \(-0.00886816\pi\)
\(402\) −1.29595 + 2.34401i −0.0646363 + 0.116908i
\(403\) −27.4754 + 27.4754i −1.36865 + 1.36865i
\(404\) 3.09956 0.154209
\(405\) −9.27488 + 17.8599i −0.460872 + 0.887466i
\(406\) 21.9725 1.09048
\(407\) 17.6878 17.6878i 0.876750 0.876750i
\(408\) −3.06048 + 5.53552i −0.151516 + 0.274049i
\(409\) 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
\(417\) 19.1768 + 10.6025i 0.939094 + 0.519206i
\(418\) 18.1528 18.1528i 0.887883 0.887883i
\(419\) 3.29476 0.160960 0.0804798 0.996756i \(-0.474355\pi\)
0.0804798 + 0.996756i \(0.474355\pi\)
\(420\) 3.25635 + 12.7116i 0.158893 + 0.620262i
\(421\) 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
\(423\) −14.0799 3.21816i −0.684586 0.156472i
\(424\) 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 \(0.0960847\pi\)
−0.954786 + 0.297296i \(0.903915\pi\)
\(432\) −5.18811 + 0.288974i −0.249613 + 0.0139033i
\(433\) 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
\(435\) −12.7975 + 21.6123i −0.613593 + 1.03623i
\(436\) 18.1228 0.867922
\(437\) −4.81215 + 4.81215i −0.230196 + 0.230196i
\(438\) 4.60434 + 2.54565i 0.220004 + 0.121636i
\(439\) 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 0.743853 0.668343i \(-0.232996\pi\)
−0.668343 + 0.743853i \(0.732996\pi\)
\(444\) 3.17786 + 11.0369i 0.150815 + 0.523790i
\(445\) −21.3813 0.632389i −1.01357 0.0299781i
\(446\) 22.0354i 1.04341i
\(447\) 11.5300 20.8545i 0.545351 0.986383i
\(448\) −2.39575 + 2.39575i −0.113188 + 0.113188i
\(449\) −22.0511 −1.04066 −0.520328 0.853966i \(-0.674190\pi\)
−0.520328 + 0.853966i \(0.674190\pi\)
\(450\) −14.3998 4.20068i −0.678813 0.198022i
\(451\) −30.3172 −1.42758
\(452\) −14.5951 + 14.5951i −0.686495 + 0.686495i
\(453\) 1.36136 2.46231i 0.0639623 0.115689i
\(454\) 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 \(-0.908223\pi\)
0.958721 0.284348i \(-0.0917770\pi\)
\(462\) 19.3733 + 10.7111i 0.901328 + 0.498326i
\(463\) 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
\(465\) 14.0007 23.6442i 0.649266 1.09647i
\(466\) 8.87206 0.410990
\(467\) −13.8067 + 13.8067i −0.638896 + 0.638896i −0.950283 0.311387i \(-0.899207\pi\)
0.311387 + 0.950283i \(0.399207\pi\)
\(468\) −3.66087 + 16.0168i −0.169224 + 0.740376i
\(469\) 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
\(477\) −1.08892 + 4.76415i −0.0498581 + 0.218136i
\(478\) 16.7784 16.7784i 0.767428 0.767428i
\(479\) −12.4597 −0.569300 −0.284650 0.958632i \(-0.591877\pi\)
−0.284650 + 0.958632i \(0.591877\pi\)
\(480\) −0.961112 3.75183i −0.0438686 0.171247i
\(481\) 36.3158 1.65586
\(482\) 4.32877 4.32877i 0.197170 0.197170i
\(483\) −5.13569 2.83942i −0.233682 0.129198i
\(484\) 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 \(-0.782187\pi\)
0.774874 0.632116i \(-0.217813\pi\)
\(492\) 6.73531 12.1822i 0.303651 0.549217i
\(493\) −16.7465 + 16.7465i −0.754224 + 0.754224i
\(494\) 37.2706 1.67688
\(495\) −21.8192 + 12.8172i −0.980698 + 0.576091i
\(496\) 7.09492 0.318571
\(497\) −22.1884 + 22.1884i −0.995286 + 0.995286i
\(498\) 6.16706 11.1544i 0.276353 0.499842i
\(499\) 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 \(0.0621374\pi\)
0.193973 + 0.981007i \(0.437863\pi\)
\(504\) −8.60801 + 5.40511i −0.383431 + 0.240763i
\(505\) −0.204902 + 6.92780i −0.00911802 + 0.308283i
\(506\) 3.77229i 0.167699i
\(507\) 25.7585 + 14.2413i 1.14397 + 0.632480i
\(508\) 4.72572 4.72572i 0.209670 0.209670i
\(509\) −9.42990 −0.417973 −0.208986 0.977919i \(-0.567016\pi\)
−0.208986 + 0.977919i \(0.567016\pi\)
\(510\) −12.1701 7.20638i −0.538900 0.319104i
\(511\) 10.2915 0.455271
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 1.96659 + 35.3072i 0.0868270 + 1.55885i
\(514\) 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 \(0.0981948\pi\)
−0.952794 + 0.303618i \(0.901805\pi\)
\(522\) −18.9665 4.33507i −0.830141 0.189741i
\(523\) 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
\(525\) −28.6268 + 6.43790i −1.24938 + 0.280973i
\(526\) 13.7122 0.597882
\(527\) 18.3209 18.3209i 0.798073 0.798073i
\(528\) −5.71805 3.16139i −0.248846 0.137582i
\(529\) 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
\(537\) 5.10241 9.22879i 0.220185 0.398251i
\(538\) 3.04451 3.04451i 0.131258 0.131258i
\(539\) 16.8969 0.727801
\(540\) −0.302914 11.6150i −0.0130353 0.499830i
\(541\) −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
\(543\) 9.32297 16.8626i 0.400087 0.723642i
\(544\) 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
\(552\) 1.51580 + 0.838057i 0.0645169 + 0.0356701i
\(553\) −11.0135 + 11.0135i −0.468341 + 0.468341i
\(554\) 29.5281 1.25453
\(555\) −24.8787 + 6.37320i −1.05604 + 0.270527i
\(556\) −12.6513 −0.536533
\(557\) −3.65261 + 3.65261i −0.154766 + 0.154766i −0.780243 0.625477i \(-0.784904\pi\)
0.625477 + 0.780243i \(0.284904\pi\)
\(558\) 20.7496 + 4.74264i 0.878403 + 0.200772i
\(559\) 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 \(0.0446576\pi\)
0.139836 + 0.990175i \(0.455342\pi\)
\(564\) 8.01310 2.30721i 0.337412 0.0971511i
\(565\) −31.6565 33.5862i −1.33180 1.41298i
\(566\) 2.21185i 0.0929709i
\(567\) −28.7879 + 10.0536i −1.20898 + 0.422211i
\(568\) 6.54892 6.54892i 0.274787 0.274787i
\(569\) −35.3739 −1.48295 −0.741475 0.670980i \(-0.765874\pi\)
−0.741475 + 0.670980i \(0.765874\pi\)
\(570\) −25.5328 + 6.54076i −1.06945 + 0.273962i
\(571\) −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
\(573\) 8.51015 + 4.70509i 0.355516 + 0.196558i
\(574\) 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
\(582\) 12.5256 22.6553i 0.519204 0.939091i
\(583\) −4.34522 + 4.34522i −0.179961 + 0.179961i
\(584\) −3.03756 −0.125695
\(585\) −35.5570 9.24120i −1.47010 0.382077i
\(586\) 9.04621 0.373695
\(587\) −31.7362 + 31.7362i −1.30989 + 1.30989i −0.388402 + 0.921490i \(0.626973\pi\)
−0.921490 + 0.388402i \(0.873027\pi\)
\(588\) −3.75384 + 6.78962i −0.154806 + 0.279999i
\(589\) 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 0.111456 0.993769i \(-0.464449\pi\)
−0.993769 + 0.111456i \(0.964449\pi\)
\(594\) −14.6096 13.0680i −0.599440 0.536187i
\(595\) −27.6546 0.817933i −1.13373 0.0335320i
\(596\) 13.7580i 0.563551i
\(597\) −7.02796 3.88562i −0.287635 0.159028i
\(598\) 3.87255 3.87255i 0.158360 0.158360i
\(599\) −28.3661 −1.15901 −0.579504 0.814969i \(-0.696754\pi\)
−0.579504 + 0.814969i \(0.696754\pi\)
\(600\) 8.44923 1.90015i 0.344938 0.0775734i
\(601\) 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
\(603\) 1.03369 4.52251i 0.0420950 0.184171i
\(604\) 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
\(612\) 2.44112 10.6802i 0.0986763 0.431721i
\(613\) 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
\(615\) 26.7831 + 15.8593i 1.08000 + 0.639511i
\(616\) −12.7809 −0.514957
\(617\) 20.3489 20.3489i 0.819214 0.819214i −0.166780 0.985994i \(-0.553337\pi\)
0.985994 + 0.166780i \(0.0533370\pi\)
\(618\) −10.4921 5.80086i −0.422053 0.233345i
\(619\) 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
\(627\) −21.5146 + 38.9137i −0.859209 + 1.55406i
\(628\) −12.9821 + 12.9821i −0.518042 + 0.518042i
\(629\) −24.2158 −0.965547
\(630\) −11.5119 19.5970i −0.458643 0.780763i
\(631\) 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
\(633\) 7.51366 13.5900i 0.298641 0.540156i
\(634\) 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 \(-0.787796\pi\)
0.785892 0.618364i \(-0.212204\pi\)
\(642\) 15.2574 + 8.43553i 0.602163 + 0.332924i
\(643\) 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
\(645\) −3.89769 15.2152i −0.153471 0.599097i
\(646\) −24.8525 −0.977808
\(647\) 10.0814 10.0814i 0.396340 0.396340i −0.480600 0.876940i \(-0.659581\pi\)
0.876940 + 0.480600i \(0.159581\pi\)
\(648\) 8.49676 2.96732i 0.333784 0.116567i
\(649\) 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 0.931605 0.363472i \(-0.118409\pi\)
−0.363472 + 0.931605i \(0.618409\pi\)
\(654\) −30.1641 + 8.68513i −1.17951 + 0.339615i
\(655\) 0.634475 21.4518i 0.0247910 0.838191i
\(656\) 8.03681i 0.313785i
\(657\) −8.88357 2.03047i −0.346581 0.0792163i
\(658\) 11.5339 11.5339i 0.449638 0.449638i
\(659\) −20.3327 −0.792048 −0.396024 0.918240i \(-0.629610\pi\)
−0.396024 + 0.918240i \(0.629610\pi\)
\(660\) 7.44400 12.5714i 0.289757 0.489340i
\(661\) −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
\(663\) −30.3159 16.7610i −1.17737 0.650945i
\(664\) 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
\(672\) 2.83942 5.13569i 0.109533 0.198114i
\(673\) 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
\(675\) 25.9806 + 0.0907905i 0.999994 + 0.00349453i
\(676\) −16.9933 −0.653588
\(677\) −10.4956 + 10.4956i −0.403380 + 0.403380i −0.879422 0.476043i \(-0.842071\pi\)
0.476043 + 0.879422i \(0.342071\pi\)
\(678\) 17.2980 31.2870i 0.664325 1.20157i
\(679\) 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 0.750550 0.660814i \(-0.229789\pi\)
−0.660814 + 0.750550i \(0.729789\pi\)
\(684\) −10.8568 17.2902i −0.415121 0.661109i
\(685\) 12.1853 11.4852i 0.465575 0.438826i
\(686\) 8.54065i 0.326084i
\(687\) −14.7749 8.16874i −0.563698 0.311657i
\(688\) 2.86760 2.86760i 0.109326 0.109326i
\(689\) −8.92143 −0.339879
\(690\) −1.97334 + 3.33256i −0.0751237 + 0.126868i
\(691\) 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
\(693\) −37.3787 8.54346i −1.41990 0.324539i
\(694\) 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 \(0.308671\pi\)
−0.565532 + 0.824726i \(0.691329\pi\)
\(702\) −1.58260 28.4133i −0.0597314 1.07239i
\(703\) −31.9097 + 31.9097i −1.20350 + 1.20350i
\(704\) 3.77229 0.142173
\(705\) 4.62710 + 18.0625i 0.174267 + 0.680274i
\(706\) 6.57049 0.247283
\(707\) −7.42577 + 7.42577i −0.279275 + 0.279275i
\(708\) 1.50551 + 0.832364i 0.0565804 + 0.0312822i
\(709\) 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
\(717\) −19.8857 + 35.9674i −0.742644 + 1.34323i
\(718\) −24.4054 + 24.4054i −0.910802 + 0.910802i
\(719\) 13.0073 0.485089 0.242545 0.970140i \(-0.422018\pi\)
0.242545 + 0.970140i \(0.422018\pi\)
\(720\) 3.39773 + 5.78407i 0.126626 + 0.215559i
\(721\) −23.4517 −0.873388
\(722\) −19.3136 + 19.3136i −0.718779 + 0.718779i
\(723\) −5.13042 + 9.27945i −0.190802 + 0.345106i
\(724\) 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
\(732\) −17.6804 9.77513i −0.653486 0.361299i
\(733\) 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
\(735\) −14.9273 8.83902i −0.550600 0.326032i
\(736\) −1.00000 −0.0368605
\(737\) 4.12483 4.12483i 0.151940 0.151940i
\(738\) −5.37225 + 23.5043i −0.197755 + 0.865205i
\(739\) 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 0.107238 0.994233i \(-0.465799\pi\)
−0.994233 + 0.107238i \(0.965799\pi\)
\(744\) −11.8090 + 3.40016i −0.432939 + 0.124656i
\(745\) −30.7505 0.909500i −1.12661 0.0333215i
\(746\) 10.8041i 0.395567i
\(747\) −4.91901 + 21.5213i −0.179977 + 0.787423i
\(748\) 9.74104 9.74104i 0.356168 0.356168i
\(749\) 34.1032 1.24610
\(750\) 3.68846 + 19.0104i 0.134684 + 0.694162i
\(751\) 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
\(753\) 21.9151 + 12.1164i 0.798632 + 0.441548i
\(754\) 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 \(0.0242902\pi\)
−0.997090 + 0.0762358i \(0.975710\pi\)
\(762\) −5.60088 + 10.1304i −0.202898 + 0.366985i
\(763\) −43.4176 + 43.4176i −1.57182 + 1.57182i
\(764\) −5.61428 −0.203118
\(765\) 23.7098 + 6.16215i 0.857230 + 0.222793i
\(766\) 23.2361 0.839554
\(767\) 3.84624 3.84624i 0.138880 0.138880i
\(768\) −0.838057 + 1.51580i −0.0302408 + 0.0546968i
\(769\) 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 0.702921 0.711268i \(-0.251879\pi\)
−0.711268 + 0.702921i \(0.751879\pi\)
\(774\) 10.3034 6.46965i 0.370347 0.232547i
\(775\) −35.4126 2.09661i −1.27206 0.0753126i
\(776\) 14.9460i 0.536532i
\(777\) −34.0551 18.8284i −1.22172 0.675465i