Properties

Label 804.2.c.b.671.12
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(128\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.12
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.37515 + 0.330103i) q^{2} +(0.355099 - 1.69526i) q^{3} +(1.78206 - 0.907880i) q^{4} -0.0453328i q^{5} +(0.0712965 + 2.44845i) q^{6} -2.82199i q^{7} +(-2.15091 + 1.83673i) q^{8} +(-2.74781 - 1.20397i) q^{9} +O(q^{10})\) \(q+(-1.37515 + 0.330103i) q^{2} +(0.355099 - 1.69526i) q^{3} +(1.78206 - 0.907880i) q^{4} -0.0453328i q^{5} +(0.0712965 + 2.44845i) q^{6} -2.82199i q^{7} +(-2.15091 + 1.83673i) q^{8} +(-2.74781 - 1.20397i) q^{9} +(0.0149645 + 0.0623394i) q^{10} +3.33857 q^{11} +(-0.906284 - 3.34345i) q^{12} -5.31881 q^{13} +(0.931548 + 3.88066i) q^{14} +(-0.0768509 - 0.0160976i) q^{15} +(2.35151 - 3.23580i) q^{16} -0.0462961i q^{17} +(4.17608 + 0.748576i) q^{18} -3.00472i q^{19} +(-0.0411568 - 0.0807860i) q^{20} +(-4.78401 - 1.00209i) q^{21} +(-4.59103 + 1.10207i) q^{22} -8.74554 q^{23} +(2.34996 + 4.29857i) q^{24} +4.99794 q^{25} +(7.31415 - 1.75575i) q^{26} +(-3.01678 + 4.23072i) q^{27} +(-2.56203 - 5.02897i) q^{28} -3.33779i q^{29} +(0.110995 - 0.00323207i) q^{30} -1.84815i q^{31} +(-2.16552 + 5.22595i) q^{32} +(1.18552 - 5.65975i) q^{33} +(0.0152825 + 0.0636640i) q^{34} -0.127929 q^{35} +(-5.98983 + 0.349132i) q^{36} +0.528333 q^{37} +(0.991868 + 4.13194i) q^{38} +(-1.88870 + 9.01677i) q^{39} +(0.0832644 + 0.0975068i) q^{40} +4.07375i q^{41} +(6.90952 - 0.201198i) q^{42} -0.346936i q^{43} +(5.94955 - 3.03102i) q^{44} +(-0.0545793 + 0.124566i) q^{45} +(12.0264 - 2.88693i) q^{46} -0.457301 q^{47} +(-4.65051 - 5.13544i) q^{48} -0.963647 q^{49} +(-6.87291 + 1.64984i) q^{50} +(-0.0784839 - 0.0164397i) q^{51} +(-9.47846 + 4.82884i) q^{52} +2.89403i q^{53} +(2.75195 - 6.81372i) q^{54} -0.151347i q^{55} +(5.18325 + 6.06985i) q^{56} +(-5.09379 - 1.06697i) q^{57} +(1.10182 + 4.58996i) q^{58} -0.226764 q^{59} +(-0.151568 + 0.0410844i) q^{60} -6.11785 q^{61} +(0.610078 + 2.54147i) q^{62} +(-3.39759 + 7.75430i) q^{63} +(1.25281 - 7.90129i) q^{64} +0.241117i q^{65} +(0.238029 + 8.17433i) q^{66} +1.00000i q^{67} +(-0.0420313 - 0.0825027i) q^{68} +(-3.10553 + 14.8260i) q^{69} +(0.175921 - 0.0422297i) q^{70} -7.18463 q^{71} +(8.12166 - 2.45737i) q^{72} -5.00203 q^{73} +(-0.726537 + 0.174404i) q^{74} +(1.77476 - 8.47281i) q^{75} +(-2.72793 - 5.35461i) q^{76} -9.42143i q^{77} +(-0.379213 - 13.0229i) q^{78} -15.3051i q^{79} +(-0.146688 - 0.106600i) q^{80} +(6.10092 + 6.61656i) q^{81} +(-1.34476 - 5.60201i) q^{82} -14.2834 q^{83} +(-9.43519 + 2.55753i) q^{84} -0.00209873 q^{85} +(0.114525 + 0.477088i) q^{86} +(-5.65843 - 1.18525i) q^{87} +(-7.18096 + 6.13207i) q^{88} +0.699578i q^{89} +(0.0339351 - 0.189313i) q^{90} +15.0097i q^{91} +(-15.5851 + 7.93990i) q^{92} +(-3.13309 - 0.656274i) q^{93} +(0.628857 - 0.150956i) q^{94} -0.136213 q^{95} +(8.09036 + 5.52685i) q^{96} +2.90757 q^{97} +(1.32516 - 0.318103i) q^{98} +(-9.17376 - 4.01954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} - 4q^{10} + 4q^{12} - 8q^{13} - 4q^{16} + 18q^{18} - 8q^{21} - 8q^{22} - 24q^{24} - 136q^{25} + 14q^{30} - 32q^{33} + 34q^{36} - 48q^{37} + 16q^{40} - 28q^{42} - 16q^{45} - 28q^{46} - 22q^{48} - 152q^{49} + 8q^{52} - 16q^{54} - 32q^{57} - 20q^{58} - 14q^{60} + 8q^{61} + 16q^{64} + 14q^{66} + 56q^{69} - 4q^{70} - 8q^{72} - 48q^{73} - 36q^{76} + 40q^{78} + 44q^{81} + 60q^{82} + 46q^{84} + 64q^{85} - 28q^{88} - 14q^{90} + 32q^{93} - 8q^{96} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37515 + 0.330103i −0.972377 + 0.233418i
\(3\) 0.355099 1.69526i 0.205016 0.978759i
\(4\) 1.78206 0.907880i 0.891032 0.453940i
\(5\) 0.0453328i 0.0202735i −0.999949 0.0101367i \(-0.996773\pi\)
0.999949 0.0101367i \(-0.00322668\pi\)
\(6\) 0.0712965 + 2.44845i 0.0291067 + 0.999576i
\(7\) 2.82199i 1.06661i −0.845922 0.533307i \(-0.820949\pi\)
0.845922 0.533307i \(-0.179051\pi\)
\(8\) −2.15091 + 1.83673i −0.760461 + 0.649384i
\(9\) −2.74781 1.20397i −0.915937 0.401323i
\(10\) 0.0149645 + 0.0623394i 0.00473219 + 0.0197134i
\(11\) 3.33857 1.00662 0.503309 0.864107i \(-0.332116\pi\)
0.503309 + 0.864107i \(0.332116\pi\)
\(12\) −0.906284 3.34345i −0.261622 0.965171i
\(13\) −5.31881 −1.47517 −0.737586 0.675253i \(-0.764035\pi\)
−0.737586 + 0.675253i \(0.764035\pi\)
\(14\) 0.931548 + 3.88066i 0.248967 + 1.03715i
\(15\) −0.0768509 0.0160976i −0.0198428 0.00415639i
\(16\) 2.35151 3.23580i 0.587877 0.808951i
\(17\) 0.0462961i 0.0112285i −0.999984 0.00561423i \(-0.998213\pi\)
0.999984 0.00561423i \(-0.00178707\pi\)
\(18\) 4.17608 + 0.748576i 0.984311 + 0.176441i
\(19\) 3.00472i 0.689331i −0.938726 0.344666i \(-0.887992\pi\)
0.938726 0.344666i \(-0.112008\pi\)
\(20\) −0.0411568 0.0807860i −0.00920294 0.0180643i
\(21\) −4.78401 1.00209i −1.04396 0.218673i
\(22\) −4.59103 + 1.10207i −0.978811 + 0.234963i
\(23\) −8.74554 −1.82357 −0.911786 0.410666i \(-0.865296\pi\)
−0.911786 + 0.410666i \(0.865296\pi\)
\(24\) 2.34996 + 4.29857i 0.479683 + 0.877442i
\(25\) 4.99794 0.999589
\(26\) 7.31415 1.75575i 1.43442 0.344332i
\(27\) −3.01678 + 4.23072i −0.580580 + 0.814203i
\(28\) −2.56203 5.02897i −0.484179 0.950387i
\(29\) 3.33779i 0.619813i −0.950767 0.309906i \(-0.899702\pi\)
0.950767 0.309906i \(-0.100298\pi\)
\(30\) 0.110995 0.00323207i 0.0202649 0.000590093i
\(31\) 1.84815i 0.331937i −0.986131 0.165968i \(-0.946925\pi\)
0.986131 0.165968i \(-0.0530750\pi\)
\(32\) −2.16552 + 5.22595i −0.382814 + 0.923825i
\(33\) 1.18552 5.65975i 0.206373 0.985235i
\(34\) 0.0152825 + 0.0636640i 0.00262092 + 0.0109183i
\(35\) −0.127929 −0.0216239
\(36\) −5.98983 + 0.349132i −0.998306 + 0.0581887i
\(37\) 0.528333 0.0868575 0.0434287 0.999057i \(-0.486172\pi\)
0.0434287 + 0.999057i \(0.486172\pi\)
\(38\) 0.991868 + 4.13194i 0.160902 + 0.670289i
\(39\) −1.88870 + 9.01677i −0.302435 + 1.44384i
\(40\) 0.0832644 + 0.0975068i 0.0131653 + 0.0154172i
\(41\) 4.07375i 0.636213i 0.948055 + 0.318107i \(0.103047\pi\)
−0.948055 + 0.318107i \(0.896953\pi\)
\(42\) 6.90952 0.201198i 1.06616 0.0310456i
\(43\) 0.346936i 0.0529073i −0.999650 0.0264536i \(-0.991579\pi\)
0.999650 0.0264536i \(-0.00842143\pi\)
\(44\) 5.94955 3.03102i 0.896929 0.456944i
\(45\) −0.0545793 + 0.124566i −0.00813621 + 0.0185692i
\(46\) 12.0264 2.88693i 1.77320 0.425654i
\(47\) −0.457301 −0.0667042 −0.0333521 0.999444i \(-0.510618\pi\)
−0.0333521 + 0.999444i \(0.510618\pi\)
\(48\) −4.65051 5.13544i −0.671243 0.741237i
\(49\) −0.963647 −0.137664
\(50\) −6.87291 + 1.64984i −0.971977 + 0.233322i
\(51\) −0.0784839 0.0164397i −0.0109899 0.00230202i
\(52\) −9.47846 + 4.82884i −1.31443 + 0.669640i
\(53\) 2.89403i 0.397526i 0.980048 + 0.198763i \(0.0636924\pi\)
−0.980048 + 0.198763i \(0.936308\pi\)
\(54\) 2.75195 6.81372i 0.374493 0.927230i
\(55\) 0.151347i 0.0204076i
\(56\) 5.18325 + 6.06985i 0.692641 + 0.811118i
\(57\) −5.09379 1.06697i −0.674689 0.141324i
\(58\) 1.10182 + 4.58996i 0.144675 + 0.602691i
\(59\) −0.226764 −0.0295222 −0.0147611 0.999891i \(-0.504699\pi\)
−0.0147611 + 0.999891i \(0.504699\pi\)
\(60\) −0.151568 + 0.0410844i −0.0195673 + 0.00530398i
\(61\) −6.11785 −0.783310 −0.391655 0.920112i \(-0.628097\pi\)
−0.391655 + 0.920112i \(0.628097\pi\)
\(62\) 0.610078 + 2.54147i 0.0774800 + 0.322767i
\(63\) −3.39759 + 7.75430i −0.428056 + 0.976950i
\(64\) 1.25281 7.90129i 0.156602 0.987662i
\(65\) 0.241117i 0.0299069i
\(66\) 0.238029 + 8.17433i 0.0292993 + 1.00619i
\(67\) 1.00000i 0.122169i
\(68\) −0.0420313 0.0825027i −0.00509705 0.0100049i
\(69\) −3.10553 + 14.8260i −0.373862 + 1.78484i
\(70\) 0.175921 0.0422297i 0.0210266 0.00504741i
\(71\) −7.18463 −0.852659 −0.426329 0.904568i \(-0.640194\pi\)
−0.426329 + 0.904568i \(0.640194\pi\)
\(72\) 8.12166 2.45737i 0.957147 0.289604i
\(73\) −5.00203 −0.585443 −0.292722 0.956198i \(-0.594561\pi\)
−0.292722 + 0.956198i \(0.594561\pi\)
\(74\) −0.726537 + 0.174404i −0.0844582 + 0.0202741i
\(75\) 1.77476 8.47281i 0.204932 0.978356i
\(76\) −2.72793 5.35461i −0.312915 0.614216i
\(77\) 9.42143i 1.07367i
\(78\) −0.379213 13.0229i −0.0429374 1.47455i
\(79\) 15.3051i 1.72196i −0.508640 0.860979i \(-0.669852\pi\)
0.508640 0.860979i \(-0.330148\pi\)
\(80\) −0.146688 0.106600i −0.0164002 0.0119183i
\(81\) 6.10092 + 6.61656i 0.677880 + 0.735173i
\(82\) −1.34476 5.60201i −0.148504 0.618639i
\(83\) −14.2834 −1.56781 −0.783904 0.620881i \(-0.786775\pi\)
−0.783904 + 0.620881i \(0.786775\pi\)
\(84\) −9.43519 + 2.55753i −1.02946 + 0.279049i
\(85\) −0.00209873 −0.000227640
\(86\) 0.114525 + 0.477088i 0.0123495 + 0.0514458i
\(87\) −5.65843 1.18525i −0.606647 0.127072i
\(88\) −7.18096 + 6.13207i −0.765493 + 0.653681i
\(89\) 0.699578i 0.0741551i 0.999312 + 0.0370776i \(0.0118049\pi\)
−0.999312 + 0.0370776i \(0.988195\pi\)
\(90\) 0.0339351 0.189313i 0.00357707 0.0199554i
\(91\) 15.0097i 1.57344i
\(92\) −15.5851 + 7.93990i −1.62486 + 0.827792i
\(93\) −3.13309 0.656274i −0.324886 0.0680524i
\(94\) 0.628857 0.150956i 0.0648616 0.0155700i
\(95\) −0.136213 −0.0139751
\(96\) 8.09036 + 5.52685i 0.825719 + 0.564082i
\(97\) 2.90757 0.295219 0.147610 0.989046i \(-0.452842\pi\)
0.147610 + 0.989046i \(0.452842\pi\)
\(98\) 1.32516 0.318103i 0.133861 0.0321332i
\(99\) −9.17376 4.01954i −0.921998 0.403979i
\(100\) 8.90666 4.53754i 0.890666 0.453754i
\(101\) 18.8879i 1.87941i −0.341982 0.939706i \(-0.611098\pi\)
0.341982 0.939706i \(-0.388902\pi\)
\(102\) 0.113354 0.00330075i 0.0112237 0.000326823i
\(103\) 14.3849i 1.41739i 0.705516 + 0.708694i \(0.250715\pi\)
−0.705516 + 0.708694i \(0.749285\pi\)
\(104\) 11.4403 9.76924i 1.12181 0.957953i
\(105\) −0.0454274 + 0.216873i −0.00443326 + 0.0211646i
\(106\) −0.955328 3.97972i −0.0927897 0.386545i
\(107\) −0.659701 −0.0637757 −0.0318878 0.999491i \(-0.510152\pi\)
−0.0318878 + 0.999491i \(0.510152\pi\)
\(108\) −1.53511 + 10.2783i −0.147716 + 0.989030i
\(109\) 11.4114 1.09301 0.546505 0.837456i \(-0.315958\pi\)
0.546505 + 0.837456i \(0.315958\pi\)
\(110\) 0.0499600 + 0.208124i 0.00476350 + 0.0198439i
\(111\) 0.187610 0.895662i 0.0178072 0.0850125i
\(112\) −9.13141 6.63594i −0.862837 0.627037i
\(113\) 9.58855i 0.902015i −0.892520 0.451007i \(-0.851065\pi\)
0.892520 0.451007i \(-0.148935\pi\)
\(114\) 7.35692 0.214226i 0.689039 0.0200641i
\(115\) 0.396460i 0.0369701i
\(116\) −3.03032 5.94816i −0.281358 0.552273i
\(117\) 14.6151 + 6.40368i 1.35116 + 0.592021i
\(118\) 0.311834 0.0748555i 0.0287067 0.00689101i
\(119\) −0.130647 −0.0119764
\(120\) 0.194866 0.106530i 0.0177888 0.00972483i
\(121\) 0.146066 0.0132787
\(122\) 8.41295 2.01952i 0.761673 0.182839i
\(123\) 6.90607 + 1.44658i 0.622699 + 0.130434i
\(124\) −1.67789 3.29351i −0.150679 0.295766i
\(125\) 0.453235i 0.0405386i
\(126\) 2.11248 11.7849i 0.188194 1.04988i
\(127\) 6.92851i 0.614806i −0.951579 0.307403i \(-0.900540\pi\)
0.951579 0.307403i \(-0.0994600\pi\)
\(128\) 0.885434 + 11.2790i 0.0782620 + 0.996933i
\(129\) −0.588147 0.123197i −0.0517834 0.0108469i
\(130\) −0.0795933 0.331571i −0.00698080 0.0290807i
\(131\) 0.832599 0.0727445 0.0363723 0.999338i \(-0.488420\pi\)
0.0363723 + 0.999338i \(0.488420\pi\)
\(132\) −3.02570 11.1623i −0.263353 0.971557i
\(133\) −8.47931 −0.735250
\(134\) −0.330103 1.37515i −0.0285165 0.118795i
\(135\) 0.191791 + 0.136759i 0.0165067 + 0.0117704i
\(136\) 0.0850337 + 0.0995787i 0.00729158 + 0.00853880i
\(137\) 4.92259i 0.420565i −0.977641 0.210282i \(-0.932562\pi\)
0.977641 0.210282i \(-0.0674384\pi\)
\(138\) −0.623527 21.4130i −0.0530781 1.82280i
\(139\) 6.30934i 0.535151i −0.963537 0.267576i \(-0.913777\pi\)
0.963537 0.267576i \(-0.0862225\pi\)
\(140\) −0.227978 + 0.116144i −0.0192676 + 0.00981598i
\(141\) −0.162387 + 0.775244i −0.0136755 + 0.0652873i
\(142\) 9.87993 2.37167i 0.829105 0.199026i
\(143\) −17.7572 −1.48493
\(144\) −10.3573 + 6.06023i −0.863108 + 0.505019i
\(145\) −0.151312 −0.0125658
\(146\) 6.87853 1.65118i 0.569271 0.136653i
\(147\) −0.342190 + 1.63363i −0.0282233 + 0.134740i
\(148\) 0.941524 0.479663i 0.0773928 0.0394281i
\(149\) 17.5015i 1.43378i −0.697187 0.716889i \(-0.745565\pi\)
0.697187 0.716889i \(-0.254435\pi\)
\(150\) 0.356336 + 12.2372i 0.0290947 + 0.999165i
\(151\) 14.7325i 1.19891i −0.800408 0.599455i \(-0.795384\pi\)
0.800408 0.599455i \(-0.204616\pi\)
\(152\) 5.51888 + 6.46289i 0.447640 + 0.524209i
\(153\) −0.0557391 + 0.127213i −0.00450624 + 0.0102846i
\(154\) 3.11004 + 12.9559i 0.250614 + 1.04401i
\(155\) −0.0837817 −0.00672951
\(156\) 4.82035 + 17.7832i 0.385937 + 1.42379i
\(157\) 12.3226 0.983451 0.491726 0.870750i \(-0.336366\pi\)
0.491726 + 0.870750i \(0.336366\pi\)
\(158\) 5.05226 + 21.0468i 0.401936 + 1.67439i
\(159\) 4.90614 + 1.02767i 0.389082 + 0.0814993i
\(160\) 0.236907 + 0.0981693i 0.0187291 + 0.00776096i
\(161\) 24.6799i 1.94505i
\(162\) −10.5738 7.08481i −0.830757 0.556636i
\(163\) 21.0635i 1.64982i 0.565261 + 0.824912i \(0.308775\pi\)
−0.565261 + 0.824912i \(0.691225\pi\)
\(164\) 3.69848 + 7.25969i 0.288803 + 0.566887i
\(165\) −0.256572 0.0537431i −0.0199741 0.00418390i
\(166\) 19.6418 4.71500i 1.52450 0.365955i
\(167\) 21.7501 1.68308 0.841538 0.540198i \(-0.181651\pi\)
0.841538 + 0.540198i \(0.181651\pi\)
\(168\) 12.1305 6.63156i 0.935891 0.511636i
\(169\) 15.2898 1.17614
\(170\) 0.00288607 0.000692798i 0.000221351 5.31352e-5i
\(171\) −3.61760 + 8.25641i −0.276644 + 0.631384i
\(172\) −0.314976 0.618262i −0.0240167 0.0471421i
\(173\) 25.8893i 1.96833i 0.177259 + 0.984164i \(0.443277\pi\)
−0.177259 + 0.984164i \(0.556723\pi\)
\(174\) 8.17243 0.237973i 0.619550 0.0180407i
\(175\) 14.1042i 1.06617i
\(176\) 7.85067 10.8030i 0.591767 0.814304i
\(177\) −0.0805237 + 0.384424i −0.00605253 + 0.0288951i
\(178\) −0.230933 0.962023i −0.0173091 0.0721067i
\(179\) 1.87615 0.140230 0.0701149 0.997539i \(-0.477663\pi\)
0.0701149 + 0.997539i \(0.477663\pi\)
\(180\) 0.0158272 + 0.271536i 0.00117969 + 0.0202391i
\(181\) 10.8705 0.808001 0.404000 0.914759i \(-0.367619\pi\)
0.404000 + 0.914759i \(0.367619\pi\)
\(182\) −4.95473 20.6405i −0.367269 1.52998i
\(183\) −2.17244 + 10.3713i −0.160591 + 0.766672i
\(184\) 18.8109 16.0632i 1.38675 1.18420i
\(185\) 0.0239508i 0.00176090i
\(186\) 4.52510 0.131766i 0.331796 0.00966158i
\(187\) 0.154563i 0.0113028i
\(188\) −0.814940 + 0.415175i −0.0594356 + 0.0302797i
\(189\) 11.9391 + 8.51334i 0.868440 + 0.619255i
\(190\) 0.187313 0.0449642i 0.0135891 0.00326204i
\(191\) −4.00209 −0.289581 −0.144791 0.989462i \(-0.546251\pi\)
−0.144791 + 0.989462i \(0.546251\pi\)
\(192\) −12.9499 4.92959i −0.934577 0.355762i
\(193\) 19.1089 1.37549 0.687743 0.725954i \(-0.258602\pi\)
0.687743 + 0.725954i \(0.258602\pi\)
\(194\) −3.99834 + 0.959798i −0.287064 + 0.0689094i
\(195\) 0.408756 + 0.0856203i 0.0292716 + 0.00613139i
\(196\) −1.71728 + 0.874876i −0.122663 + 0.0624911i
\(197\) 3.18758i 0.227105i −0.993532 0.113553i \(-0.963777\pi\)
0.993532 0.113553i \(-0.0362231\pi\)
\(198\) 13.9421 + 2.49918i 0.990825 + 0.177609i
\(199\) 17.5383i 1.24326i 0.783313 + 0.621628i \(0.213528\pi\)
−0.783313 + 0.621628i \(0.786472\pi\)
\(200\) −10.7501 + 9.17990i −0.760148 + 0.649117i
\(201\) 1.69526 + 0.355099i 0.119574 + 0.0250467i
\(202\) 6.23494 + 25.9736i 0.438689 + 1.82750i
\(203\) −9.41923 −0.661101
\(204\) −0.154789 + 0.0419574i −0.0108374 + 0.00293761i
\(205\) 0.184675 0.0128982
\(206\) −4.74850 19.7814i −0.330844 1.37824i
\(207\) 24.0311 + 10.5294i 1.67028 + 0.731841i
\(208\) −12.5072 + 17.2106i −0.867220 + 1.19334i
\(209\) 10.0315i 0.693893i
\(210\) −0.00912089 0.313228i −0.000629401 0.0216148i
\(211\) 3.20034i 0.220321i −0.993914 0.110160i \(-0.964864\pi\)
0.993914 0.110160i \(-0.0351364\pi\)
\(212\) 2.62744 + 5.15735i 0.180453 + 0.354208i
\(213\) −2.55125 + 12.1798i −0.174809 + 0.834547i
\(214\) 0.907186 0.217769i 0.0620140 0.0148864i
\(215\) −0.0157276 −0.00107261
\(216\) −1.28189 14.6409i −0.0872214 0.996189i
\(217\) −5.21545 −0.354048
\(218\) −15.6923 + 3.76692i −1.06282 + 0.255128i
\(219\) −1.77621 + 8.47974i −0.120025 + 0.573008i
\(220\) −0.137405 0.269710i −0.00926384 0.0181838i
\(221\) 0.246240i 0.0165639i
\(222\) 0.0376683 + 1.29360i 0.00252813 + 0.0868207i
\(223\) 23.6656i 1.58476i −0.610026 0.792382i \(-0.708841\pi\)
0.610026 0.792382i \(-0.291159\pi\)
\(224\) 14.7476 + 6.11109i 0.985365 + 0.408314i
\(225\) −13.7334 6.01737i −0.915560 0.401158i
\(226\) 3.16521 + 13.1857i 0.210546 + 0.877098i
\(227\) 25.7062 1.70618 0.853091 0.521762i \(-0.174725\pi\)
0.853091 + 0.521762i \(0.174725\pi\)
\(228\) −10.0461 + 2.72313i −0.665322 + 0.180344i
\(229\) −11.9383 −0.788906 −0.394453 0.918916i \(-0.629066\pi\)
−0.394453 + 0.918916i \(0.629066\pi\)
\(230\) −0.130873 0.545191i −0.00862948 0.0359489i
\(231\) −15.9718 3.34554i −1.05087 0.220120i
\(232\) 6.13064 + 7.17929i 0.402496 + 0.471344i
\(233\) 17.8239i 1.16769i −0.811867 0.583843i \(-0.801548\pi\)
0.811867 0.583843i \(-0.198452\pi\)
\(234\) −22.2118 3.98153i −1.45203 0.260281i
\(235\) 0.0207308i 0.00135233i
\(236\) −0.404108 + 0.205875i −0.0263052 + 0.0134013i
\(237\) −25.9461 5.43482i −1.68538 0.353030i
\(238\) 0.179659 0.0431270i 0.0116456 0.00279551i
\(239\) 22.2718 1.44064 0.720320 0.693642i \(-0.243995\pi\)
0.720320 + 0.693642i \(0.243995\pi\)
\(240\) −0.232804 + 0.210821i −0.0150274 + 0.0136084i
\(241\) 19.3681 1.24761 0.623804 0.781580i \(-0.285586\pi\)
0.623804 + 0.781580i \(0.285586\pi\)
\(242\) −0.200863 + 0.0482169i −0.0129119 + 0.00309950i
\(243\) 13.3832 7.99311i 0.858533 0.512758i
\(244\) −10.9024 + 5.55428i −0.697955 + 0.355576i
\(245\) 0.0436848i 0.00279092i
\(246\) −9.97439 + 0.290445i −0.635944 + 0.0185181i
\(247\) 15.9816i 1.01688i
\(248\) 3.39455 + 3.97519i 0.215554 + 0.252425i
\(249\) −5.07202 + 24.2141i −0.321426 + 1.53451i
\(250\) 0.149614 + 0.623265i 0.00946243 + 0.0394188i
\(251\) −12.1468 −0.766701 −0.383350 0.923603i \(-0.625230\pi\)
−0.383350 + 0.923603i \(0.625230\pi\)
\(252\) 0.985249 + 16.9033i 0.0620649 + 1.06481i
\(253\) −29.1976 −1.83564
\(254\) 2.28712 + 9.52773i 0.143507 + 0.597823i
\(255\) −0.000745258 0.00355790i −4.66699e−5 0.000222804i
\(256\) −4.94083 15.2180i −0.308802 0.951126i
\(257\) 22.4036i 1.39750i −0.715367 0.698748i \(-0.753741\pi\)
0.715367 0.698748i \(-0.246259\pi\)
\(258\) 0.849456 0.0247353i 0.0528848 0.00153996i
\(259\) 1.49095i 0.0926433i
\(260\) 0.218905 + 0.429686i 0.0135759 + 0.0266480i
\(261\) −4.01860 + 9.17162i −0.248745 + 0.567709i
\(262\) −1.14495 + 0.274843i −0.0707351 + 0.0169799i
\(263\) 26.2457 1.61838 0.809189 0.587548i \(-0.199907\pi\)
0.809189 + 0.587548i \(0.199907\pi\)
\(264\) 7.84550 + 14.3511i 0.482857 + 0.883248i
\(265\) 0.131195 0.00805923
\(266\) 11.6603 2.79904i 0.714940 0.171620i
\(267\) 1.18597 + 0.248419i 0.0725800 + 0.0152030i
\(268\) 0.907880 + 1.78206i 0.0554576 + 0.108857i
\(269\) 16.0941i 0.981276i 0.871364 + 0.490638i \(0.163236\pi\)
−0.871364 + 0.490638i \(0.836764\pi\)
\(270\) −0.308885 0.124754i −0.0187982 0.00759227i
\(271\) 13.4888i 0.819383i −0.912224 0.409692i \(-0.865636\pi\)
0.912224 0.409692i \(-0.134364\pi\)
\(272\) −0.149805 0.108866i −0.00908327 0.00660095i
\(273\) 25.4453 + 5.32991i 1.54002 + 0.322581i
\(274\) 1.62496 + 6.76928i 0.0981674 + 0.408947i
\(275\) 16.6860 1.00620
\(276\) 7.92594 + 29.2403i 0.477086 + 1.76006i
\(277\) −13.5911 −0.816609 −0.408304 0.912846i \(-0.633880\pi\)
−0.408304 + 0.912846i \(0.633880\pi\)
\(278\) 2.08273 + 8.67628i 0.124914 + 0.520369i
\(279\) −2.22511 + 5.07835i −0.133214 + 0.304033i
\(280\) 0.275163 0.234971i 0.0164442 0.0140422i
\(281\) 14.2655i 0.851007i −0.904957 0.425504i \(-0.860097\pi\)
0.904957 0.425504i \(-0.139903\pi\)
\(282\) −0.0326040 1.11968i −0.00194154 0.0666760i
\(283\) 2.05619i 0.122228i −0.998131 0.0611138i \(-0.980535\pi\)
0.998131 0.0611138i \(-0.0194653\pi\)
\(284\) −12.8035 + 6.52278i −0.759746 + 0.387056i
\(285\) −0.0483689 + 0.230916i −0.00286513 + 0.0136783i
\(286\) 24.4188 5.86171i 1.44392 0.346610i
\(287\) 11.4961 0.678594
\(288\) 12.2423 11.7527i 0.721386 0.692534i
\(289\) 16.9979 0.999874
\(290\) 0.208076 0.0499484i 0.0122186 0.00293307i
\(291\) 1.03248 4.92909i 0.0605248 0.288948i
\(292\) −8.91394 + 4.54124i −0.521649 + 0.265756i
\(293\) 30.5801i 1.78651i −0.449554 0.893253i \(-0.648417\pi\)
0.449554 0.893253i \(-0.351583\pi\)
\(294\) −0.0687047 2.35944i −0.00400694 0.137606i
\(295\) 0.0102799i 0.000598517i
\(296\) −1.13640 + 0.970408i −0.0660517 + 0.0564038i
\(297\) −10.0718 + 14.1246i −0.584422 + 0.819591i
\(298\) 5.77729 + 24.0671i 0.334669 + 1.39417i
\(299\) 46.5159 2.69008
\(300\) −4.52956 16.7104i −0.261514 0.964774i
\(301\) −0.979051 −0.0564316
\(302\) 4.86322 + 20.2593i 0.279847 + 1.16579i
\(303\) −32.0198 6.70706i −1.83949 0.385310i
\(304\) −9.72270 7.06563i −0.557635 0.405242i
\(305\) 0.277339i 0.0158804i
\(306\) 0.0346562 0.193336i 0.00198116 0.0110523i
\(307\) 17.9892i 1.02670i 0.858181 + 0.513348i \(0.171595\pi\)
−0.858181 + 0.513348i \(0.828405\pi\)
\(308\) −8.55353 16.7896i −0.487383 0.956676i
\(309\) 24.3862 + 5.10807i 1.38728 + 0.290588i
\(310\) 0.115212 0.0276566i 0.00654361 0.00157079i
\(311\) −26.8825 −1.52436 −0.762182 0.647363i \(-0.775872\pi\)
−0.762182 + 0.647363i \(0.775872\pi\)
\(312\) −12.4990 22.8633i −0.707615 1.29438i
\(313\) −14.6195 −0.826344 −0.413172 0.910653i \(-0.635579\pi\)
−0.413172 + 0.910653i \(0.635579\pi\)
\(314\) −16.9454 + 4.06773i −0.956285 + 0.229555i
\(315\) 0.351524 + 0.154022i 0.0198062 + 0.00867818i
\(316\) −13.8952 27.2747i −0.781666 1.53432i
\(317\) 16.4279i 0.922683i −0.887223 0.461341i \(-0.847368\pi\)
0.887223 0.461341i \(-0.152632\pi\)
\(318\) −7.08590 + 0.206335i −0.397358 + 0.0115707i
\(319\) 11.1435i 0.623914i
\(320\) −0.358188 0.0567936i −0.0200233 0.00317486i
\(321\) −0.234259 + 1.11836i −0.0130751 + 0.0624210i
\(322\) −8.14689 33.9385i −0.454008 1.89132i
\(323\) −0.139107 −0.00774013
\(324\) 16.8793 + 6.25222i 0.937737 + 0.347346i
\(325\) −26.5831 −1.47457
\(326\) −6.95313 28.9655i −0.385098 1.60425i
\(327\) 4.05216 19.3452i 0.224085 1.06979i
\(328\) −7.48240 8.76227i −0.413147 0.483815i
\(329\) 1.29050i 0.0711476i
\(330\) 0.370566 0.0107905i 0.0203990 0.000593998i
\(331\) 18.0323i 0.991146i 0.868566 + 0.495573i \(0.165042\pi\)
−0.868566 + 0.495573i \(0.834958\pi\)
\(332\) −25.4540 + 12.9676i −1.39697 + 0.711691i
\(333\) −1.45176 0.636097i −0.0795559 0.0348579i
\(334\) −29.9097 + 7.17978i −1.63658 + 0.392860i
\(335\) 0.0453328 0.00247680
\(336\) −14.4922 + 13.1237i −0.790614 + 0.715957i
\(337\) 21.9123 1.19364 0.596821 0.802375i \(-0.296430\pi\)
0.596821 + 0.802375i \(0.296430\pi\)
\(338\) −21.0257 + 5.04719i −1.14365 + 0.274531i
\(339\) −16.2551 3.40488i −0.882855 0.184928i
\(340\) −0.00374008 + 0.00190540i −0.000202834 + 0.000103335i
\(341\) 6.17017i 0.334133i
\(342\) 2.24926 12.5480i 0.121626 0.678516i
\(343\) 17.0345i 0.919779i
\(344\) 0.637229 + 0.746228i 0.0343571 + 0.0402339i
\(345\) 0.672103 + 0.140782i 0.0361848 + 0.00757947i
\(346\) −8.54614 35.6016i −0.459443 1.91396i
\(347\) −8.77121 −0.470863 −0.235432 0.971891i \(-0.575650\pi\)
−0.235432 + 0.971891i \(0.575650\pi\)
\(348\) −11.1597 + 3.02499i −0.598225 + 0.162156i
\(349\) −24.2036 −1.29559 −0.647794 0.761815i \(-0.724308\pi\)
−0.647794 + 0.761815i \(0.724308\pi\)
\(350\) 4.65582 + 19.3953i 0.248864 + 1.03672i
\(351\) 16.0457 22.5024i 0.856456 1.20109i
\(352\) −7.22975 + 17.4472i −0.385347 + 0.929939i
\(353\) 30.4426i 1.62030i −0.586225 0.810148i \(-0.699387\pi\)
0.586225 0.810148i \(-0.300613\pi\)
\(354\) −0.0161675 0.555221i −0.000859293 0.0295097i
\(355\) 0.325700i 0.0172863i
\(356\) 0.635133 + 1.24669i 0.0336620 + 0.0660746i
\(357\) −0.0463927 + 0.221481i −0.00245536 + 0.0117220i
\(358\) −2.57998 + 0.619322i −0.136356 + 0.0327322i
\(359\) 17.3593 0.916188 0.458094 0.888904i \(-0.348532\pi\)
0.458094 + 0.888904i \(0.348532\pi\)
\(360\) −0.111400 0.368178i −0.00587127 0.0194047i
\(361\) 9.97163 0.524823
\(362\) −14.9486 + 3.58840i −0.785681 + 0.188602i
\(363\) 0.0518679 0.247620i 0.00272236 0.0129967i
\(364\) 13.6270 + 26.7482i 0.714247 + 1.40198i
\(365\) 0.226756i 0.0118690i
\(366\) −0.436182 14.9793i −0.0227996 0.782978i
\(367\) 20.2091i 1.05491i −0.849584 0.527453i \(-0.823147\pi\)
0.849584 0.527453i \(-0.176853\pi\)
\(368\) −20.5652 + 28.2988i −1.07203 + 1.47518i
\(369\) 4.90467 11.1939i 0.255327 0.582731i
\(370\) 0.00790624 + 0.0329360i 0.000411026 + 0.00171226i
\(371\) 8.16694 0.424007
\(372\) −6.17918 + 1.67494i −0.320376 + 0.0868418i
\(373\) −9.05088 −0.468637 −0.234318 0.972160i \(-0.575286\pi\)
−0.234318 + 0.972160i \(0.575286\pi\)
\(374\) 0.0510217 + 0.212547i 0.00263827 + 0.0109905i
\(375\) −0.768351 0.160943i −0.0396775 0.00831107i
\(376\) 0.983613 0.839941i 0.0507260 0.0433166i
\(377\) 17.7531i 0.914331i
\(378\) −19.2283 7.76599i −0.988996 0.399439i
\(379\) 21.7509i 1.11727i −0.829415 0.558634i \(-0.811326\pi\)
0.829415 0.558634i \(-0.188674\pi\)
\(380\) −0.242740 + 0.123665i −0.0124523 + 0.00634387i
\(381\) −11.7456 2.46031i −0.601747 0.126045i
\(382\) 5.50347 1.32110i 0.281582 0.0675934i
\(383\) 14.9683 0.764845 0.382423 0.923987i \(-0.375090\pi\)
0.382423 + 0.923987i \(0.375090\pi\)
\(384\) 19.4353 + 2.50412i 0.991802 + 0.127788i
\(385\) −0.427100 −0.0217670
\(386\) −26.2775 + 6.30789i −1.33749 + 0.321063i
\(387\) −0.417700 + 0.953314i −0.0212329 + 0.0484597i
\(388\) 5.18148 2.63973i 0.263050 0.134012i
\(389\) 26.1553i 1.32613i 0.748564 + 0.663063i \(0.230744\pi\)
−0.748564 + 0.663063i \(0.769256\pi\)
\(390\) −0.590363 + 0.0171908i −0.0298942 + 0.000870490i
\(391\) 0.404885i 0.0204759i
\(392\) 2.07272 1.76996i 0.104688 0.0893966i
\(393\) 0.295655 1.41147i 0.0149138 0.0711993i
\(394\) 1.05223 + 4.38339i 0.0530105 + 0.220832i
\(395\) −0.693823 −0.0349100
\(396\) −19.9975 + 1.16560i −1.00491 + 0.0585738i
\(397\) −21.6228 −1.08522 −0.542610 0.839985i \(-0.682564\pi\)
−0.542610 + 0.839985i \(0.682564\pi\)
\(398\) −5.78944 24.1177i −0.290198 1.20891i
\(399\) −3.01099 + 14.3746i −0.150738 + 0.719632i
\(400\) 11.7527 16.1724i 0.587635 0.808618i
\(401\) 30.4479i 1.52050i −0.649633 0.760248i \(-0.725077\pi\)
0.649633 0.760248i \(-0.274923\pi\)
\(402\) −2.44845 + 0.0712965i −0.122118 + 0.00355595i
\(403\) 9.82994i 0.489664i
\(404\) −17.1479 33.6594i −0.853141 1.67462i
\(405\) 0.299947 0.276572i 0.0149045 0.0137430i
\(406\) 12.9528 3.10932i 0.642839 0.154313i
\(407\) 1.76388 0.0874322
\(408\) 0.199007 0.108794i 0.00985232 0.00538610i
\(409\) −9.38435 −0.464026 −0.232013 0.972713i \(-0.574531\pi\)
−0.232013 + 0.972713i \(0.574531\pi\)
\(410\) −0.253955 + 0.0609617i −0.0125420 + 0.00301068i
\(411\) −8.34506 1.74800i −0.411631 0.0862227i
\(412\) 13.0598 + 25.6349i 0.643410 + 1.26294i
\(413\) 0.639927i 0.0314888i
\(414\) −36.5221 6.54670i −1.79496 0.321753i
\(415\) 0.647508i 0.0317849i
\(416\) 11.5180 27.7958i 0.564717 1.36280i
\(417\) −10.6960 2.24044i −0.523784 0.109715i
\(418\) 3.31142 + 13.7948i 0.161967 + 0.674725i
\(419\) 14.5317 0.709920 0.354960 0.934881i \(-0.384494\pi\)
0.354960 + 0.934881i \(0.384494\pi\)
\(420\) 0.115940 + 0.427724i 0.00565729 + 0.0208708i
\(421\) 7.75853 0.378127 0.189064 0.981965i \(-0.439455\pi\)
0.189064 + 0.981965i \(0.439455\pi\)
\(422\) 1.05644 + 4.40095i 0.0514268 + 0.214235i
\(423\) 1.25658 + 0.550576i 0.0610969 + 0.0267699i
\(424\) −5.31557 6.22480i −0.258147 0.302303i
\(425\) 0.231385i 0.0112238i
\(426\) −0.512239 17.5912i −0.0248181 0.852297i
\(427\) 17.2645i 0.835489i
\(428\) −1.17563 + 0.598929i −0.0568262 + 0.0289503i
\(429\) −6.30557 + 30.1031i −0.304436 + 1.45339i
\(430\) 0.0216278 0.00519172i 0.00104298 0.000250367i
\(431\) −24.2429 −1.16774 −0.583869 0.811848i \(-0.698462\pi\)
−0.583869 + 0.811848i \(0.698462\pi\)
\(432\) 6.59580 + 19.7103i 0.317340 + 0.948312i
\(433\) 30.8720 1.48361 0.741806 0.670614i \(-0.233969\pi\)
0.741806 + 0.670614i \(0.233969\pi\)
\(434\) 7.17202 1.72164i 0.344268 0.0826412i
\(435\) −0.0537306 + 0.256513i −0.00257618 + 0.0122988i
\(436\) 20.3358 10.3602i 0.973907 0.496161i
\(437\) 26.2779i 1.25704i
\(438\) −0.356627 12.2472i −0.0170403 0.585195i
\(439\) 36.8150i 1.75708i 0.477665 + 0.878542i \(0.341483\pi\)
−0.477665 + 0.878542i \(0.658517\pi\)
\(440\) 0.277984 + 0.325533i 0.0132524 + 0.0155192i
\(441\) 2.64792 + 1.16020i 0.126091 + 0.0552477i
\(442\) −0.0812846 0.338617i −0.00386631 0.0161064i
\(443\) −20.0252 −0.951425 −0.475712 0.879601i \(-0.657810\pi\)
−0.475712 + 0.879601i \(0.657810\pi\)
\(444\) −0.478820 1.76646i −0.0227238 0.0838323i
\(445\) 0.0317139 0.00150338
\(446\) 7.81207 + 32.5436i 0.369912 + 1.54099i
\(447\) −29.6696 6.21476i −1.40332 0.293948i
\(448\) −22.2974 3.53543i −1.05345 0.167034i
\(449\) 19.0841i 0.900634i 0.892869 + 0.450317i \(0.148689\pi\)
−0.892869 + 0.450317i \(0.851311\pi\)
\(450\) 20.8718 + 3.74134i 0.983907 + 0.176369i
\(451\) 13.6005i 0.640424i
\(452\) −8.70526 17.0874i −0.409461 0.803724i
\(453\) −24.9753 5.23148i −1.17344 0.245796i
\(454\) −35.3499 + 8.48570i −1.65905 + 0.398253i
\(455\) 0.680430 0.0318991
\(456\) 12.9160 7.06097i 0.604848 0.330660i
\(457\) −14.3677 −0.672092 −0.336046 0.941846i \(-0.609090\pi\)
−0.336046 + 0.941846i \(0.609090\pi\)
\(458\) 16.4170 3.94087i 0.767114 0.184145i
\(459\) 0.195866 + 0.139665i 0.00914224 + 0.00651902i
\(460\) 0.359938 + 0.706517i 0.0167822 + 0.0329415i
\(461\) 24.9347i 1.16132i 0.814145 + 0.580661i \(0.197206\pi\)
−0.814145 + 0.580661i \(0.802794\pi\)
\(462\) 23.0679 0.671715i 1.07322 0.0312510i
\(463\) 15.6605i 0.727807i −0.931437 0.363904i \(-0.881444\pi\)
0.931437 0.363904i \(-0.118556\pi\)
\(464\) −10.8004 7.84885i −0.501398 0.364374i
\(465\) −0.0297508 + 0.142032i −0.00137966 + 0.00658656i
\(466\) 5.88373 + 24.5106i 0.272559 + 1.13543i
\(467\) −0.0672601 −0.00311243 −0.00155621 0.999999i \(-0.500495\pi\)
−0.00155621 + 0.999999i \(0.500495\pi\)
\(468\) 31.8588 1.85697i 1.47267 0.0858384i
\(469\) 2.82199 0.130308
\(470\) −0.00684328 0.0285079i −0.000315657 0.00131497i
\(471\) 4.37574 20.8900i 0.201624 0.962561i
\(472\) 0.487749 0.416506i 0.0224505 0.0191712i
\(473\) 1.15827i 0.0532574i
\(474\) 37.4738 1.09120i 1.72123 0.0501205i
\(475\) 15.0174i 0.689048i
\(476\) −0.232822 + 0.118612i −0.0106714 + 0.00543658i
\(477\) 3.48433 7.95225i 0.159536 0.364109i
\(478\) −30.6270 + 7.35197i −1.40085 + 0.336271i
\(479\) 10.4537 0.477640 0.238820 0.971064i \(-0.423239\pi\)
0.238820 + 0.971064i \(0.423239\pi\)
\(480\) 0.250548 0.366759i 0.0114359 0.0167402i
\(481\) −2.81011 −0.128130
\(482\) −26.6340 + 6.39346i −1.21315 + 0.291214i
\(483\) 41.8388 + 8.76379i 1.90373 + 0.398766i
\(484\) 0.260299 0.132611i 0.0118318 0.00602776i
\(485\) 0.131808i 0.00598511i
\(486\) −15.7653 + 15.4095i −0.715131 + 0.698991i
\(487\) 23.8327i 1.07996i −0.841677 0.539982i \(-0.818431\pi\)
0.841677 0.539982i \(-0.181569\pi\)
\(488\) 13.1589 11.2369i 0.595677 0.508669i
\(489\) 35.7082 + 7.47964i 1.61478 + 0.338241i
\(490\) −0.0144205 0.0600731i −0.000651451 0.00271383i
\(491\) −29.4130 −1.32739 −0.663694 0.748004i \(-0.731012\pi\)
−0.663694 + 0.748004i \(0.731012\pi\)
\(492\) 13.6204 3.69198i 0.614054 0.166447i
\(493\) −0.154527 −0.00695954
\(494\) −5.27556 21.9770i −0.237359 0.988793i
\(495\) −0.182217 + 0.415873i −0.00819005 + 0.0186921i
\(496\) −5.98023 4.34593i −0.268520 0.195138i
\(497\) 20.2750i 0.909457i
\(498\) −1.01836 34.9723i −0.0456337 1.56714i
\(499\) 39.5774i 1.77173i 0.463946 + 0.885864i \(0.346433\pi\)
−0.463946 + 0.885864i \(0.653567\pi\)
\(500\) −0.411483 0.807694i −0.0184021 0.0361212i
\(501\) 7.72344 36.8721i 0.345058 1.64732i
\(502\) 16.7037 4.00970i 0.745522 0.178962i
\(503\) −6.34209 −0.282780 −0.141390 0.989954i \(-0.545157\pi\)
−0.141390 + 0.989954i \(0.545157\pi\)
\(504\) −6.93468 22.9193i −0.308895 1.02091i
\(505\) −0.856240 −0.0381022
\(506\) 40.1511 9.63822i 1.78493 0.428471i
\(507\) 5.42937 25.9201i 0.241127 1.15115i
\(508\) −6.29026 12.3471i −0.279085 0.547812i
\(509\) 27.5700i 1.22202i 0.791623 + 0.611009i \(0.209236\pi\)
−0.791623 + 0.611009i \(0.790764\pi\)
\(510\) −0.000149632 0.00513865i −6.62584e−6 0.000227543i
\(511\) 14.1157i 0.624441i
\(512\) 11.8179 + 19.2960i 0.522282 + 0.852773i
\(513\) 12.7122 + 9.06460i 0.561255 + 0.400212i
\(514\) 7.39548 + 30.8082i 0.326201 + 1.35889i
\(515\) 0.652109 0.0287354
\(516\) −1.15996 + 0.314423i −0.0510645 + 0.0138417i
\(517\) −1.52673 −0.0671456
\(518\) 0.492168 + 2.05028i 0.0216246 + 0.0900842i
\(519\) 43.8891 + 9.19326i 1.92652 + 0.403539i
\(520\) −0.442867 0.518620i −0.0194210 0.0227430i
\(521\) 27.0474i 1.18497i 0.805581 + 0.592485i \(0.201853\pi\)
−0.805581 + 0.592485i \(0.798147\pi\)
\(522\) 2.49859 13.9389i 0.109360 0.610089i
\(523\) 5.32931i 0.233035i −0.993189 0.116517i \(-0.962827\pi\)
0.993189 0.116517i \(-0.0371730\pi\)
\(524\) 1.48375 0.755901i 0.0648177 0.0330217i
\(525\) −23.9102 5.00837i −1.04353 0.218583i
\(526\) −36.0917 + 8.66378i −1.57367 + 0.377759i
\(527\) −0.0855620 −0.00372714
\(528\) −15.5261 17.1450i −0.675685 0.746142i
\(529\) 53.4845 2.32541
\(530\) −0.180412 + 0.0433077i −0.00783660 + 0.00188117i
\(531\) 0.623105 + 0.273017i 0.0270405 + 0.0118479i
\(532\) −15.1107 + 7.69820i −0.655131 + 0.333759i
\(533\) 21.6675i 0.938525i
\(534\) −1.71288 + 0.0498775i −0.0741237 + 0.00215841i
\(535\) 0.0299061i 0.00129295i
\(536\) −1.83673 2.15091i −0.0793348 0.0929051i
\(537\) 0.666218 3.18056i 0.0287494 0.137251i
\(538\) −5.31271 22.1318i −0.229047 0.954170i
\(539\) −3.21721 −0.138575
\(540\) 0.465944 + 0.0695910i 0.0200511 + 0.00299472i
\(541\) −18.5591 −0.797920 −0.398960 0.916968i \(-0.630629\pi\)
−0.398960 + 0.916968i \(0.630629\pi\)
\(542\) 4.45267 + 18.5490i 0.191259 + 0.796749i
\(543\) 3.86012 18.4284i 0.165653 0.790838i
\(544\) 0.241941 + 0.100255i 0.0103731 + 0.00429841i
\(545\) 0.517309i 0.0221591i
\(546\) −36.7504 + 1.07014i −1.57277 + 0.0457976i
\(547\) 16.1107i 0.688845i −0.938815 0.344423i \(-0.888075\pi\)
0.938815 0.344423i \(-0.111925\pi\)
\(548\) −4.46912 8.77236i −0.190911 0.374737i
\(549\) 16.8107 + 7.36570i 0.717463 + 0.314360i
\(550\) −22.9457 + 5.50810i −0.978409 + 0.234866i
\(551\) −10.0292 −0.427256
\(552\) −20.5516 37.5933i −0.874736 1.60008i
\(553\) −43.1909 −1.83666
\(554\) 18.6897 4.48645i 0.794051 0.190611i
\(555\) −0.0406029 0.00850491i −0.00172350 0.000361014i
\(556\) −5.72813 11.2437i −0.242927 0.476837i
\(557\) 0.882960i 0.0374122i −0.999825 0.0187061i \(-0.994045\pi\)
0.999825 0.0187061i \(-0.00595469\pi\)
\(558\) 1.38348 7.71800i 0.0585673 0.326729i
\(559\) 1.84529i 0.0780473i
\(560\) −0.300826 + 0.413953i −0.0127122 + 0.0174927i
\(561\) −0.262024 0.0548851i −0.0110627 0.00231725i
\(562\) 4.70908 + 19.6172i 0.198640 + 0.827500i
\(563\) 4.74187 0.199846 0.0999230 0.994995i \(-0.468140\pi\)
0.0999230 + 0.994995i \(0.468140\pi\)
\(564\) 0.414445 + 1.52896i 0.0174513 + 0.0643810i
\(565\) −0.434676 −0.0182870
\(566\) 0.678753 + 2.82756i 0.0285301 + 0.118851i
\(567\) 18.6719 17.2167i 0.784145 0.723035i
\(568\) 15.4535 13.1963i 0.648414 0.553702i
\(569\) 29.6251i 1.24195i 0.783830 + 0.620975i \(0.213263\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(570\) −0.00971149 0.333510i −0.000406770 0.0139692i
\(571\) 7.09982i 0.297118i 0.988904 + 0.148559i \(0.0474635\pi\)
−0.988904 + 0.148559i \(0.952536\pi\)
\(572\) −31.6445 + 16.1214i −1.32312 + 0.674072i
\(573\) −1.42114 + 6.78458i −0.0593689 + 0.283430i
\(574\) −15.8088 + 3.79490i −0.659849 + 0.158396i
\(575\) −43.7097 −1.82282
\(576\) −12.9554 + 20.2029i −0.539809 + 0.841788i
\(577\) −45.0273 −1.87451 −0.937256 0.348641i \(-0.886643\pi\)
−0.937256 + 0.348641i \(0.886643\pi\)
\(578\) −23.3746 + 5.61104i −0.972254 + 0.233388i
\(579\) 6.78553 32.3945i 0.281997 1.34627i
\(580\) −0.269647 + 0.137373i −0.0111965 + 0.00570410i
\(581\) 40.3077i 1.67225i
\(582\) 0.207300 + 7.11905i 0.00859285 + 0.295094i
\(583\) 9.66194i 0.400157i
\(584\) 10.7589 9.18740i 0.445207 0.380177i
\(585\) 0.290297 0.662543i 0.0120023 0.0273928i
\(586\) 10.0946 + 42.0521i 0.417003 + 1.73716i
\(587\) 34.7911 1.43598 0.717990 0.696053i \(-0.245062\pi\)
0.717990 + 0.696053i \(0.245062\pi\)
\(588\) 0.873338 + 3.22190i 0.0360158 + 0.132869i
\(589\) −5.55317 −0.228814
\(590\) −0.00339341 0.0141363i −0.000139705 0.000581984i
\(591\) −5.40377 1.13190i −0.222281 0.0465603i
\(592\) 1.24238 1.70958i 0.0510615 0.0702634i
\(593\) 22.8534i 0.938475i 0.883072 + 0.469237i \(0.155471\pi\)
−0.883072 + 0.469237i \(0.844529\pi\)
\(594\) 9.18759 22.7481i 0.376971 0.933366i
\(595\) 0.00592261i 0.000242803i
\(596\) −15.8893 31.1888i −0.650850 1.27754i
\(597\) 29.7319 + 6.22782i 1.21685 + 0.254888i
\(598\) −63.9662 + 15.3550i −2.61577 + 0.627914i
\(599\) 27.3056 1.11568 0.557838 0.829950i \(-0.311631\pi\)
0.557838 + 0.829950i \(0.311631\pi\)
\(600\) 11.7450 + 21.4840i 0.479486 + 0.877081i
\(601\) 35.2624 1.43838 0.719192 0.694812i \(-0.244512\pi\)
0.719192 + 0.694812i \(0.244512\pi\)
\(602\) 1.34634 0.323188i 0.0548727 0.0131721i
\(603\) 1.20397 2.74781i 0.0490294 0.111899i
\(604\) −13.3753 26.2542i −0.544234 1.06827i
\(605\) 0.00662160i 0.000269206i
\(606\) 46.2460 1.34664i 1.87862 0.0547035i
\(607\) 23.8874i 0.969560i 0.874636 + 0.484780i \(0.161100\pi\)
−0.874636 + 0.484780i \(0.838900\pi\)
\(608\) 15.7025 + 6.50680i 0.636822 + 0.263886i
\(609\) −3.34476 + 15.9680i −0.135536 + 0.647058i
\(610\) −0.0915505 0.381383i −0.00370677 0.0154417i
\(611\) 2.43230 0.0984003
\(612\) 0.0161635 + 0.277306i 0.000653370 + 0.0112094i
\(613\) −32.2630 −1.30309 −0.651545 0.758610i \(-0.725879\pi\)
−0.651545 + 0.758610i \(0.725879\pi\)
\(614\) −5.93827 24.7377i −0.239649 0.998334i
\(615\) 0.0655778 0.313072i 0.00264435 0.0126243i
\(616\) 17.3047 + 20.2646i 0.697225 + 0.816485i
\(617\) 42.1094i 1.69526i −0.530587 0.847630i \(-0.678029\pi\)
0.530587 0.847630i \(-0.321971\pi\)
\(618\) −35.2208 + 1.02560i −1.41679 + 0.0412555i
\(619\) 8.85623i 0.355962i 0.984034 + 0.177981i \(0.0569566\pi\)
−0.984034 + 0.177981i \(0.943043\pi\)
\(620\) −0.149304 + 0.0760637i −0.00599621 + 0.00305479i
\(621\) 26.3834 37.0000i 1.05873 1.48476i
\(622\) 36.9673 8.87397i 1.48226 0.355814i
\(623\) 1.97420 0.0790948
\(624\) 24.7352 + 27.3145i 0.990200 + 1.09345i
\(625\) 24.9692 0.998767
\(626\) 20.1040 4.82594i 0.803518 0.192884i
\(627\) −17.0060 3.56217i −0.679153 0.142259i
\(628\) 21.9597 11.1875i 0.876287 0.446428i
\(629\) 0.0244598i 0.000975275i
\(630\) −0.534241 0.0957645i −0.0212847 0.00381535i
\(631\) 45.1892i 1.79895i 0.436970 + 0.899476i \(0.356051\pi\)
−0.436970 + 0.899476i \(0.643949\pi\)
\(632\) 28.1114 + 32.9199i 1.11821 + 1.30948i
\(633\) −5.42541 1.13644i −0.215641 0.0451694i
\(634\) 5.42290 + 22.5908i 0.215371 + 0.897195i
\(635\) −0.314089 −0.0124642
\(636\) 9.67605 2.62282i 0.383680 0.104001i
\(637\) 5.12546 0.203078
\(638\) 3.67849 + 15.3239i 0.145633 + 0.606680i
\(639\) 19.7420 + 8.65007i 0.780981 + 0.342191i
\(640\) 0.511309 0.0401392i 0.0202113 0.00158664i
\(641\) 15.8749i 0.627021i −0.949585 0.313510i \(-0.898495\pi\)
0.949585 0.313510i \(-0.101505\pi\)
\(642\) −0.0470344 1.61525i −0.00185630 0.0637487i
\(643\) 11.1940i 0.441449i −0.975336 0.220725i \(-0.929158\pi\)
0.975336 0.220725i \(-0.0708422\pi\)
\(644\) 22.4064 + 43.9811i 0.882934 + 1.73310i
\(645\) −0.00558485 + 0.0266624i −0.000219903 + 0.00104983i
\(646\) 0.191293 0.0459196i 0.00752632 0.00180668i
\(647\) 9.10556 0.357977 0.178988 0.983851i \(-0.442718\pi\)
0.178988 + 0.983851i \(0.442718\pi\)
\(648\) −25.2754 3.02584i −0.992910 0.118866i
\(649\) −0.757069 −0.0297176
\(650\) 36.5557 8.77516i 1.43383 0.344190i
\(651\) −1.85200 + 8.84155i −0.0725856 + 0.346528i
\(652\) 19.1232 + 37.5366i 0.748921 + 1.47005i
\(653\) 23.2914i 0.911461i −0.890118 0.455731i \(-0.849378\pi\)
0.890118 0.455731i \(-0.150622\pi\)
\(654\) 0.813591 + 27.9402i 0.0318139 + 1.09255i
\(655\) 0.0377441i 0.00147478i
\(656\) 13.1819 + 9.57946i 0.514665 + 0.374015i
\(657\) 13.7446 + 6.02229i 0.536229 + 0.234952i
\(658\) −0.425998 1.77463i −0.0166071 0.0691823i
\(659\) −31.9785 −1.24571 −0.622853 0.782339i \(-0.714026\pi\)
−0.622853 + 0.782339i \(0.714026\pi\)
\(660\) −0.506021 + 0.137163i −0.0196968 + 0.00533908i
\(661\) 0.528143 0.0205424 0.0102712 0.999947i \(-0.496731\pi\)
0.0102712 + 0.999947i \(0.496731\pi\)
\(662\) −5.95252 24.7971i −0.231351 0.963767i
\(663\) 0.417441 + 0.0874396i 0.0162121 + 0.00339587i
\(664\) 30.7223 26.2348i 1.19226 1.01811i
\(665\) 0.384391i 0.0149061i
\(666\) 2.20636 + 0.395498i 0.0854948 + 0.0153252i
\(667\) 29.1908i 1.13027i
\(668\) 38.7601 19.7465i 1.49967 0.764016i
\(669\) −40.1193 8.40361i −1.55110 0.324902i
\(670\) −0.0623394 + 0.0149645i −0.00240838 + 0.000578129i
\(671\) −20.4249 −0.788494
\(672\) 15.5967 22.8309i 0.601657 0.880723i
\(673\) 14.1935 0.547121 0.273561 0.961855i \(-0.411799\pi\)
0.273561 + 0.961855i \(0.411799\pi\)
\(674\) −30.1327 + 7.23333i −1.16067 + 0.278617i
\(675\) −15.0777 + 21.1449i −0.580342 + 0.813868i
\(676\) 27.2473 13.8813i 1.04797 0.533895i
\(677\) 5.83261i 0.224165i −0.993699 0.112083i \(-0.964248\pi\)
0.993699 0.112083i \(-0.0357521\pi\)
\(678\) 23.4771 0.683631i 0.901633 0.0262547i
\(679\) 8.20515i 0.314885i
\(680\) 0.00451418 0.00385482i 0.000173111 0.000147825i
\(681\) 9.12825 43.5787i 0.349795 1.66994i
\(682\) 2.03679 + 8.48489i 0.0779927 + 0.324903i
\(683\) 20.2308 0.774110 0.387055 0.922057i \(-0.373492\pi\)
0.387055 + 0.922057i \(0.373492\pi\)
\(684\) 1.04905 + 17.9978i 0.0401113 + 0.688163i
\(685\) −0.223155 −0.00852630
\(686\) 5.62315 + 23.4250i 0.214693 + 0.894372i
\(687\) −4.23928 + 20.2385i −0.161739 + 0.772149i
\(688\) −1.12262 0.815822i −0.0427994 0.0311029i
\(689\) 15.3928i 0.586420i
\(690\) −0.970714 + 0.0282662i −0.0369544 + 0.00107608i
\(691\) 27.2492i 1.03661i −0.855196 0.518305i \(-0.826563\pi\)
0.855196 0.518305i \(-0.173437\pi\)
\(692\) 23.5044 + 46.1364i 0.893503 + 1.75384i
\(693\) −11.3431 + 25.8883i −0.430889 + 0.983415i
\(694\) 12.0617 2.89540i 0.457856 0.109908i
\(695\) −0.286020 −0.0108494
\(696\) 14.3477 7.84367i 0.543850 0.297314i
\(697\) 0.188599 0.00714370
\(698\) 33.2835 7.98967i 1.25980 0.302413i
\(699\) −30.2162 6.32926i −1.14288 0.239395i
\(700\) −12.8049 25.1345i −0.483980 0.949996i
\(701\) 1.36934i 0.0517193i 0.999666 + 0.0258596i \(0.00823230\pi\)
−0.999666 + 0.0258596i \(0.991768\pi\)
\(702\) −14.6371 + 36.2409i −0.552442 + 1.36782i
\(703\) 1.58750i 0.0598735i
\(704\) 4.18261 26.3790i 0.157638 0.994198i
\(705\) 0.0351440 + 0.00736147i 0.00132360 + 0.000277249i
\(706\) 10.0492 + 41.8631i 0.378206 + 1.57554i
\(707\) −53.3014 −2.00461
\(708\) 0.205513 + 0.758175i 0.00772364 + 0.0284939i
\(709\) −9.08190 −0.341078 −0.170539 0.985351i \(-0.554551\pi\)
−0.170539 + 0.985351i \(0.554551\pi\)
\(710\) −0.107514 0.447885i −0.00403494 0.0168088i
\(711\) −18.4269 + 42.0555i −0.691061 + 1.57720i
\(712\) −1.28494 1.50473i −0.0481551 0.0563921i
\(713\) 16.1630i 0.605310i
\(714\) −0.00931470 0.319884i −0.000348594 0.0119713i
\(715\) 0.804986i 0.0301048i
\(716\) 3.34342 1.70332i 0.124949 0.0636560i
\(717\) 7.90868 37.7564i 0.295355 1.41004i
\(718\) −23.8716 + 5.73035i −0.890880 + 0.213855i
\(719\) −3.80251 −0.141810 −0.0709048 0.997483i \(-0.522589\pi\)
−0.0709048 + 0.997483i \(0.522589\pi\)
\(720\) 0.274727 + 0.469526i 0.0102385 + 0.0174982i
\(721\) 40.5942 1.51181
\(722\) −13.7125 + 3.29166i −0.510325 + 0.122503i
\(723\) 6.87759 32.8340i 0.255780 1.22111i
\(724\) 19.3720 9.86915i 0.719955 0.366784i
\(725\) 16.6821i 0.619558i
\(726\) 0.0104140 + 0.357636i 0.000386500 + 0.0132731i
\(727\) 7.17785i 0.266212i 0.991102 + 0.133106i \(0.0424950\pi\)
−0.991102 + 0.133106i \(0.957505\pi\)
\(728\) −27.5687 32.2844i −1.02177 1.19654i
\(729\) −8.79803 25.5264i −0.325853 0.945420i
\(730\) −0.0748528 0.311823i −0.00277043 0.0115411i
\(731\) −0.0160618 −0.000594067
\(732\) 5.54451 + 20.4547i 0.204931 + 0.756028i
\(733\) −2.44611 −0.0903492 −0.0451746 0.998979i \(-0.514384\pi\)
−0.0451746 + 0.998979i \(0.514384\pi\)
\(734\) 6.67107 + 27.7905i 0.246234 + 1.02576i
\(735\) 0.0740571 + 0.0155124i 0.00273164 + 0.000572185i
\(736\) 18.9387 45.7037i 0.698088 1.68466i
\(737\) 3.33857i 0.122978i
\(738\) −3.04951 + 17.0123i −0.112254 + 0.626232i
\(739\) 49.4937i 1.82065i −0.413890 0.910327i \(-0.635830\pi\)
0.413890 0.910327i \(-0.364170\pi\)
\(740\) −0.0217445 0.0426819i −0.000799344 0.00156902i
\(741\) 27.0929 + 5.67503i 0.995283 + 0.208478i
\(742\) −11.2308 + 2.69593i −0.412294 + 0.0989707i
\(743\) −47.0335 −1.72549 −0.862746 0.505638i \(-0.831257\pi\)
−0.862746 + 0.505638i \(0.831257\pi\)
\(744\) 7.94438 4.34306i 0.291255 0.159224i
\(745\) −0.793392 −0.0290676
\(746\) 12.4463 2.98772i 0.455691 0.109388i
\(747\) 39.2481 + 17.1968i 1.43601 + 0.629198i
\(748\) −0.140325 0.275441i −0.00513078 0.0100711i
\(749\) 1.86167i 0.0680240i
\(750\) 1.10972 0.0323141i 0.0405214 0.00117994i
\(751\) 43.9718i 1.60455i 0.596952 + 0.802277i \(0.296378\pi\)
−0.596952 + 0.802277i \(0.703622\pi\)
\(752\) −1.07535 + 1.47974i −0.0392139 + 0.0539604i
\(753\) −4.31332 + 20.5920i −0.157186 + 0.750415i
\(754\) −5.86035 24.4131i −0.213421 0.889074i
\(755\) −0.667864 −0.0243061
\(756\) 29.0053 + 4.33208i 1.05491 + 0.157556i
\(757\) 18.1609 0.660068 0.330034 0.943969i \(-0.392940\pi\)
0.330034 + 0.943969i \(0.392940\pi\)
\(758\) 7.18002 + 29.9107i 0.260790 + 1.08640i
\(759\) −10.3680 + 49.4975i −0.376336 + 1.79665i
\(760\) 0.292981 0.250186i 0.0106275 0.00907522i
\(761\) 33.2514i 1.20536i −0.797982 0.602681i \(-0.794099\pi\)
0.797982 0.602681i \(-0.205901\pi\)
\(762\) 16.9641 0.493979i 0.614546 0.0178950i