Properties

Label 441.2.f.g.148.6
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.6
Root \(-0.474636 + 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.g.295.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.849814 + 1.47192i) q^{2} +(1.40434 + 1.01381i) q^{3} +(-0.444368 + 0.769668i) q^{4} +(0.474636 - 0.822093i) q^{5} +(-0.298820 + 2.92864i) q^{6} +1.88874 q^{8} +(0.944368 + 2.84748i) q^{9} +O(q^{10})\) \(q+(0.849814 + 1.47192i) q^{2} +(1.40434 + 1.01381i) q^{3} +(-0.444368 + 0.769668i) q^{4} +(0.474636 - 0.822093i) q^{5} +(-0.298820 + 2.92864i) q^{6} +1.88874 q^{8} +(0.944368 + 2.84748i) q^{9} +1.61341 q^{10} +(0.294182 + 0.509538i) q^{11} +(-1.40434 + 0.630373i) q^{12} +(2.50987 - 4.34722i) q^{13} +(1.50000 - 0.673310i) q^{15} +(2.49381 + 4.31941i) q^{16} -7.58242 q^{17} +(-3.38874 + 3.80987i) q^{18} -4.46122 q^{19} +(0.421826 + 0.730623i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-1.23855 + 2.14523i) q^{23} +(2.65244 + 1.91482i) q^{24} +(2.04944 + 3.54974i) q^{25} +8.53169 q^{26} +(-1.56060 + 4.95626i) q^{27} +(-2.73855 - 4.74331i) q^{29} +(2.26578 + 1.63569i) q^{30} +(3.03731 - 5.26078i) q^{31} +(-2.34981 + 4.07000i) q^{32} +(-0.103443 + 1.01381i) q^{33} +(-6.44364 - 11.1607i) q^{34} +(-2.61126 - 0.538481i) q^{36} -6.98762 q^{37} +(-3.79121 - 6.56657i) q^{38} +(7.93199 - 3.56046i) q^{39} +(0.896461 - 1.55272i) q^{40} +(0.527445 - 0.913562i) q^{41} +(-3.49381 - 6.05146i) q^{43} -0.522900 q^{44} +(2.78913 + 0.575159i) q^{45} -4.21015 q^{46} +(3.73840 + 6.47510i) q^{47} +(-0.876899 + 8.59419i) q^{48} +(-3.48329 + 6.03323i) q^{50} +(-10.6483 - 7.68715i) q^{51} +(2.23061 + 3.86353i) q^{52} +6.92216 q^{53} +(-8.62145 + 1.91482i) q^{54} +0.558517 q^{55} +(-6.26509 - 4.52284i) q^{57} +(4.65452 - 8.06186i) q^{58} +(-5.21512 + 9.03284i) q^{59} +(-0.148327 + 1.45370i) q^{60} +(-5.82644 - 10.0917i) q^{61} +10.3246 q^{62} +1.98762 q^{64} +(-2.38255 - 4.12669i) q^{65} +(-1.58016 + 0.709292i) q^{66} +(5.93199 - 10.2745i) q^{67} +(3.36938 - 5.83594i) q^{68} +(-3.91421 + 1.75699i) q^{69} +4.30037 q^{71} +(1.78366 + 5.37815i) q^{72} +4.46122 q^{73} +(-5.93818 - 10.2852i) q^{74} +(-0.720646 + 7.06281i) q^{75} +(1.98242 - 3.43366i) q^{76} +(11.9814 + 8.64953i) q^{78} +(0.666896 + 1.15510i) q^{79} +4.73460 q^{80} +(-7.21634 + 5.37815i) q^{81} +1.79292 q^{82} +(2.84194 + 4.92238i) q^{83} +(-3.59888 + 6.23345i) q^{85} +(5.93818 - 10.2852i) q^{86} +(0.962957 - 9.43762i) q^{87} +(0.555632 + 0.962383i) q^{88} +0.843651 q^{89} +(1.52365 + 4.59415i) q^{90} +(-1.10074 - 1.90654i) q^{92} +(9.59888 - 4.30868i) q^{93} +(-6.35389 + 11.0053i) q^{94} +(-2.11745 + 3.66754i) q^{95} +(-7.42616 + 3.33341i) q^{96} +(1.70317 + 2.94997i) q^{97} +(-1.17309 + 1.31887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} + 12q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} + 12q^{9} - 8q^{11} + 18q^{15} - 6q^{16} - 42q^{18} - 6q^{22} - 4q^{23} - 12q^{25} - 22q^{29} - 48q^{30} - 16q^{32} - 30q^{36} - 12q^{37} + 24q^{39} - 6q^{43} - 28q^{44} + 24q^{46} - 56q^{50} - 18q^{51} + 56q^{53} - 6q^{57} - 18q^{58} + 108q^{60} - 48q^{64} + 6q^{65} + 76q^{71} + 60q^{72} - 36q^{74} + 36q^{78} + 6q^{79} - 48q^{81} + 30q^{85} + 36q^{86} + 6q^{88} - 62q^{92} + 42q^{93} - 60q^{95} - 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.849814 + 1.47192i 0.600909 + 1.04081i 0.992684 + 0.120744i \(0.0385280\pi\)
−0.391774 + 0.920061i \(0.628139\pi\)
\(3\) 1.40434 + 1.01381i 0.810799 + 0.585325i
\(4\) −0.444368 + 0.769668i −0.222184 + 0.384834i
\(5\) 0.474636 0.822093i 0.212263 0.367651i −0.740159 0.672432i \(-0.765250\pi\)
0.952423 + 0.304781i \(0.0985832\pi\)
\(6\) −0.298820 + 2.92864i −0.121993 + 1.19561i
\(7\) 0 0
\(8\) 1.88874 0.667769
\(9\) 0.944368 + 2.84748i 0.314789 + 0.949162i
\(10\) 1.61341 0.510204
\(11\) 0.294182 + 0.509538i 0.0886992 + 0.153632i 0.906962 0.421213i \(-0.138396\pi\)
−0.818262 + 0.574845i \(0.805062\pi\)
\(12\) −1.40434 + 0.630373i −0.405399 + 0.181973i
\(13\) 2.50987 4.34722i 0.696112 1.20570i −0.273692 0.961817i \(-0.588245\pi\)
0.969804 0.243885i \(-0.0784218\pi\)
\(14\) 0 0
\(15\) 1.50000 0.673310i 0.387298 0.173848i
\(16\) 2.49381 + 4.31941i 0.623453 + 1.07985i
\(17\) −7.58242 −1.83901 −0.919503 0.393083i \(-0.871409\pi\)
−0.919503 + 0.393083i \(0.871409\pi\)
\(18\) −3.38874 + 3.80987i −0.798733 + 0.897994i
\(19\) −4.46122 −1.02347 −0.511737 0.859142i \(-0.670998\pi\)
−0.511737 + 0.859142i \(0.670998\pi\)
\(20\) 0.421826 + 0.730623i 0.0943231 + 0.163372i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) −1.23855 + 2.14523i −0.258256 + 0.447312i −0.965775 0.259382i \(-0.916481\pi\)
0.707519 + 0.706694i \(0.249814\pi\)
\(24\) 2.65244 + 1.91482i 0.541426 + 0.390862i
\(25\) 2.04944 + 3.54974i 0.409888 + 0.709948i
\(26\) 8.53169 1.67320
\(27\) −1.56060 + 4.95626i −0.300337 + 0.953833i
\(28\) 0 0
\(29\) −2.73855 4.74331i −0.508536 0.880810i −0.999951 0.00988468i \(-0.996854\pi\)
0.491415 0.870925i \(-0.336480\pi\)
\(30\) 2.26578 + 1.63569i 0.413673 + 0.298635i
\(31\) 3.03731 5.26078i 0.545518 0.944865i −0.453056 0.891482i \(-0.649666\pi\)
0.998574 0.0533826i \(-0.0170003\pi\)
\(32\) −2.34981 + 4.07000i −0.415392 + 0.719481i
\(33\) −0.103443 + 1.01381i −0.0180072 + 0.176482i
\(34\) −6.44364 11.1607i −1.10508 1.91405i
\(35\) 0 0
\(36\) −2.61126 0.538481i −0.435211 0.0897469i
\(37\) −6.98762 −1.14876 −0.574379 0.818590i \(-0.694756\pi\)
−0.574379 + 0.818590i \(0.694756\pi\)
\(38\) −3.79121 6.56657i −0.615015 1.06524i
\(39\) 7.93199 3.56046i 1.27013 0.570130i
\(40\) 0.896461 1.55272i 0.141743 0.245506i
\(41\) 0.527445 0.913562i 0.0823731 0.142674i −0.821896 0.569638i \(-0.807083\pi\)
0.904269 + 0.426964i \(0.140417\pi\)
\(42\) 0 0
\(43\) −3.49381 6.05146i −0.532801 0.922838i −0.999266 0.0382990i \(-0.987806\pi\)
0.466465 0.884540i \(-0.345527\pi\)
\(44\) −0.522900 −0.0788302
\(45\) 2.78913 + 0.575159i 0.415779 + 0.0857397i
\(46\) −4.21015 −0.620753
\(47\) 3.73840 + 6.47510i 0.545301 + 0.944490i 0.998588 + 0.0531249i \(0.0169181\pi\)
−0.453286 + 0.891365i \(0.649749\pi\)
\(48\) −0.876899 + 8.59419i −0.126569 + 1.24046i
\(49\) 0 0
\(50\) −3.48329 + 6.03323i −0.492612 + 0.853228i
\(51\) −10.6483 7.68715i −1.49106 1.07642i
\(52\) 2.23061 + 3.86353i 0.309330 + 0.535775i
\(53\) 6.92216 0.950831 0.475416 0.879761i \(-0.342298\pi\)
0.475416 + 0.879761i \(0.342298\pi\)
\(54\) −8.62145 + 1.91482i −1.17323 + 0.260575i
\(55\) 0.558517 0.0753104
\(56\) 0 0
\(57\) −6.26509 4.52284i −0.829832 0.599065i
\(58\) 4.65452 8.06186i 0.611168 1.05857i
\(59\) −5.21512 + 9.03284i −0.678950 + 1.17598i 0.296347 + 0.955080i \(0.404231\pi\)
−0.975297 + 0.220896i \(0.929102\pi\)
\(60\) −0.148327 + 1.45370i −0.0191489 + 0.187672i
\(61\) −5.82644 10.0917i −0.745999 1.29211i −0.949726 0.313081i \(-0.898639\pi\)
0.203727 0.979028i \(-0.434695\pi\)
\(62\) 10.3246 1.31123
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) −2.38255 4.12669i −0.295518 0.511853i
\(66\) −1.58016 + 0.709292i −0.194504 + 0.0873078i
\(67\) 5.93199 10.2745i 0.724708 1.25523i −0.234387 0.972143i \(-0.575308\pi\)
0.959094 0.283087i \(-0.0913585\pi\)
\(68\) 3.36938 5.83594i 0.408598 0.707712i
\(69\) −3.91421 + 1.75699i −0.471216 + 0.211516i
\(70\) 0 0
\(71\) 4.30037 0.510360 0.255180 0.966894i \(-0.417865\pi\)
0.255180 + 0.966894i \(0.417865\pi\)
\(72\) 1.78366 + 5.37815i 0.210207 + 0.633821i
\(73\) 4.46122 0.522146 0.261073 0.965319i \(-0.415924\pi\)
0.261073 + 0.965319i \(0.415924\pi\)
\(74\) −5.93818 10.2852i −0.690299 1.19563i
\(75\) −0.720646 + 7.06281i −0.0832130 + 0.815543i
\(76\) 1.98242 3.43366i 0.227400 0.393868i
\(77\) 0 0
\(78\) 11.9814 + 8.64953i 1.35663 + 0.979367i
\(79\) 0.666896 + 1.15510i 0.0750317 + 0.129959i 0.901100 0.433611i \(-0.142761\pi\)
−0.826068 + 0.563570i \(0.809428\pi\)
\(80\) 4.73460 0.529345
\(81\) −7.21634 + 5.37815i −0.801815 + 0.597572i
\(82\) 1.79292 0.197995
\(83\) 2.84194 + 4.92238i 0.311943 + 0.540301i 0.978783 0.204900i \(-0.0656868\pi\)
−0.666840 + 0.745201i \(0.732353\pi\)
\(84\) 0 0
\(85\) −3.59888 + 6.23345i −0.390354 + 0.676113i
\(86\) 5.93818 10.2852i 0.640330 1.10908i
\(87\) 0.962957 9.43762i 0.103240 1.01182i
\(88\) 0.555632 + 0.962383i 0.0592306 + 0.102590i
\(89\) 0.843651 0.0894269 0.0447134 0.999000i \(-0.485763\pi\)
0.0447134 + 0.999000i \(0.485763\pi\)
\(90\) 1.52365 + 4.59415i 0.160607 + 0.484266i
\(91\) 0 0
\(92\) −1.10074 1.90654i −0.114760 0.198771i
\(93\) 9.59888 4.30868i 0.995358 0.446790i
\(94\) −6.35389 + 11.0053i −0.655353 + 1.13511i
\(95\) −2.11745 + 3.66754i −0.217246 + 0.376281i
\(96\) −7.42616 + 3.33341i −0.757930 + 0.340215i
\(97\) 1.70317 + 2.94997i 0.172930 + 0.299524i 0.939443 0.342705i \(-0.111343\pi\)
−0.766513 + 0.642229i \(0.778010\pi\)
\(98\) 0 0
\(99\) −1.17309 + 1.31887i −0.117900 + 0.132551i
\(100\) −3.64283 −0.364283
\(101\) 4.79329 + 8.30222i 0.476950 + 0.826102i 0.999651 0.0264143i \(-0.00840890\pi\)
−0.522701 + 0.852516i \(0.675076\pi\)
\(102\) 2.26578 22.2061i 0.224346 2.19874i
\(103\) 5.82644 10.0917i 0.574096 0.994364i −0.422043 0.906576i \(-0.638687\pi\)
0.996139 0.0877882i \(-0.0279799\pi\)
\(104\) 4.74048 8.21075i 0.464842 0.805130i
\(105\) 0 0
\(106\) 5.88255 + 10.1889i 0.571363 + 0.989630i
\(107\) −3.79851 −0.367216 −0.183608 0.983000i \(-0.558778\pi\)
−0.183608 + 0.983000i \(0.558778\pi\)
\(108\) −3.12120 3.40355i −0.300337 0.327506i
\(109\) −12.8640 −1.23215 −0.616073 0.787689i \(-0.711277\pi\)
−0.616073 + 0.787689i \(0.711277\pi\)
\(110\) 0.474636 + 0.822093i 0.0452547 + 0.0783835i
\(111\) −9.81303 7.08414i −0.931411 0.672397i
\(112\) 0 0
\(113\) −4.51052 + 7.81245i −0.424314 + 0.734934i −0.996356 0.0852908i \(-0.972818\pi\)
0.572042 + 0.820224i \(0.306151\pi\)
\(114\) 1.33310 13.0653i 0.124857 1.22368i
\(115\) 1.17572 + 2.03641i 0.109636 + 0.189896i
\(116\) 4.86769 0.451954
\(117\) 14.7489 + 3.04144i 1.36353 + 0.281181i
\(118\) −17.7275 −1.63195
\(119\) 0 0
\(120\) 2.83310 1.27171i 0.258626 0.116090i
\(121\) 5.32691 9.22649i 0.484265 0.838771i
\(122\) 9.90278 17.1521i 0.896556 1.55288i
\(123\) 1.66690 0.748226i 0.150299 0.0674652i
\(124\) 2.69937 + 4.67545i 0.242411 + 0.419867i
\(125\) 8.63731 0.772544
\(126\) 0 0
\(127\) 6.43268 0.570808 0.285404 0.958407i \(-0.407872\pi\)
0.285404 + 0.958407i \(0.407872\pi\)
\(128\) 6.38874 + 11.0656i 0.564690 + 0.978071i
\(129\) 1.22853 12.0404i 0.108166 1.06010i
\(130\) 4.04944 7.01384i 0.355160 0.615154i
\(131\) −3.31657 + 5.74447i −0.289770 + 0.501897i −0.973755 0.227600i \(-0.926912\pi\)
0.683984 + 0.729497i \(0.260246\pi\)
\(132\) −0.734332 0.530123i −0.0639154 0.0461413i
\(133\) 0 0
\(134\) 20.1643 1.74193
\(135\) 3.33379 + 3.63537i 0.286927 + 0.312883i
\(136\) −14.3212 −1.22803
\(137\) −7.01671 12.1533i −0.599478 1.03833i −0.992898 0.118968i \(-0.962042\pi\)
0.393420 0.919359i \(-0.371292\pi\)
\(138\) −5.91250 4.26830i −0.503305 0.363342i
\(139\) −4.40254 + 7.62541i −0.373418 + 0.646779i −0.990089 0.140442i \(-0.955148\pi\)
0.616671 + 0.787221i \(0.288481\pi\)
\(140\) 0 0
\(141\) −1.31453 + 12.8833i −0.110704 + 1.08497i
\(142\) 3.65452 + 6.32981i 0.306680 + 0.531186i
\(143\) 2.95343 0.246978
\(144\) −9.94437 + 11.1802i −0.828697 + 0.931683i
\(145\) −5.19925 −0.431774
\(146\) 3.79121 + 6.56657i 0.313763 + 0.543453i
\(147\) 0 0
\(148\) 3.10507 5.37815i 0.255236 0.442081i
\(149\) 2.18292 3.78092i 0.178832 0.309745i −0.762649 0.646813i \(-0.776102\pi\)
0.941481 + 0.337067i \(0.109435\pi\)
\(150\) −11.0083 + 4.94134i −0.898825 + 0.403459i
\(151\) 6.32691 + 10.9585i 0.514877 + 0.891793i 0.999851 + 0.0172645i \(0.00549573\pi\)
−0.484974 + 0.874529i \(0.661171\pi\)
\(152\) −8.42607 −0.683444
\(153\) −7.16059 21.5908i −0.578899 1.74551i
\(154\) 0 0
\(155\) −2.88323 4.99391i −0.231587 0.401120i
\(156\) −0.784350 + 7.68715i −0.0627983 + 0.615465i
\(157\) −5.63694 + 9.76347i −0.449877 + 0.779210i −0.998378 0.0569405i \(-0.981865\pi\)
0.548501 + 0.836150i \(0.315199\pi\)
\(158\) −1.13348 + 1.96324i −0.0901745 + 0.156187i
\(159\) 9.72109 + 7.01777i 0.770933 + 0.556545i
\(160\) 2.23061 + 3.86353i 0.176345 + 0.305439i
\(161\) 0 0
\(162\) −14.0488 6.05146i −1.10377 0.475447i
\(163\) −1.66621 −0.130507 −0.0652537 0.997869i \(-0.520786\pi\)
−0.0652537 + 0.997869i \(0.520786\pi\)
\(164\) 0.468760 + 0.811916i 0.0366040 + 0.0634000i
\(165\) 0.784350 + 0.566231i 0.0610616 + 0.0440811i
\(166\) −4.83024 + 8.36622i −0.374899 + 0.649344i
\(167\) −1.95135 + 3.37984i −0.151000 + 0.261540i −0.931595 0.363497i \(-0.881583\pi\)
0.780595 + 0.625037i \(0.214916\pi\)
\(168\) 0 0
\(169\) −6.09888 10.5636i −0.469145 0.812583i
\(170\) −12.2335 −0.938269
\(171\) −4.21303 12.7033i −0.322179 0.971442i
\(172\) 6.21015 0.473519
\(173\) −8.05705 13.9552i −0.612566 1.06100i −0.990806 0.135288i \(-0.956804\pi\)
0.378240 0.925708i \(-0.376529\pi\)
\(174\) 14.7098 6.60282i 1.11514 0.500559i
\(175\) 0 0
\(176\) −1.46727 + 2.54138i −0.110599 + 0.191564i
\(177\) −16.4814 + 7.39808i −1.23882 + 0.556074i
\(178\) 0.716947 + 1.24179i 0.0537374 + 0.0930760i
\(179\) 14.2880 1.06793 0.533967 0.845505i \(-0.320701\pi\)
0.533967 + 0.845505i \(0.320701\pi\)
\(180\) −1.68208 + 1.89112i −0.125375 + 0.140956i
\(181\) 12.8873 0.957905 0.478952 0.877841i \(-0.341017\pi\)
0.478952 + 0.877841i \(0.341017\pi\)
\(182\) 0 0
\(183\) 2.04875 20.0791i 0.151448 1.48429i
\(184\) −2.33929 + 4.05178i −0.172455 + 0.298701i
\(185\) −3.31657 + 5.74447i −0.243839 + 0.422342i
\(186\) 14.4993 + 10.4672i 1.06314 + 0.767494i
\(187\) −2.23061 3.86353i −0.163118 0.282529i
\(188\) −6.64490 −0.484629
\(189\) 0 0
\(190\) −7.19777 −0.522181
\(191\) 1.08217 + 1.87438i 0.0783034 + 0.135625i 0.902518 0.430652i \(-0.141716\pi\)
−0.824215 + 0.566277i \(0.808383\pi\)
\(192\) 2.79130 + 2.01507i 0.201445 + 0.145425i
\(193\) −5.21565 + 9.03377i −0.375431 + 0.650265i −0.990391 0.138293i \(-0.955839\pi\)
0.614961 + 0.788558i \(0.289172\pi\)
\(194\) −2.89475 + 5.01385i −0.207831 + 0.359973i
\(195\) 0.837775 8.21075i 0.0599943 0.587984i
\(196\) 0 0
\(197\) −18.7848 −1.33836 −0.669179 0.743101i \(-0.733354\pi\)
−0.669179 + 0.743101i \(0.733354\pi\)
\(198\) −2.93818 0.605896i −0.208807 0.0430591i
\(199\) 8.42607 0.597308 0.298654 0.954361i \(-0.403462\pi\)
0.298654 + 0.954361i \(0.403462\pi\)
\(200\) 3.87085 + 6.70452i 0.273711 + 0.474081i
\(201\) 18.7470 8.41502i 1.32231 0.593550i
\(202\) −8.14681 + 14.1107i −0.573208 + 0.992825i
\(203\) 0 0
\(204\) 10.6483 4.77975i 0.745532 0.334650i
\(205\) −0.500689 0.867218i −0.0349696 0.0605692i
\(206\) 19.8056 1.37992
\(207\) −7.27816 1.50086i −0.505867 0.104317i
\(208\) 25.0365 1.73597
\(209\) −1.31241 2.27316i −0.0907814 0.157238i
\(210\) 0 0
\(211\) −5.61126 + 9.71899i −0.386295 + 0.669083i −0.991948 0.126646i \(-0.959579\pi\)
0.605653 + 0.795729i \(0.292912\pi\)
\(212\) −3.07598 + 5.32776i −0.211259 + 0.365912i
\(213\) 6.03920 + 4.35977i 0.413799 + 0.298727i
\(214\) −3.22803 5.59111i −0.220664 0.382200i
\(215\) −6.63315 −0.452377
\(216\) −2.94756 + 9.36107i −0.200556 + 0.636940i
\(217\) 0 0
\(218\) −10.9320 18.9348i −0.740408 1.28242i
\(219\) 6.26509 + 4.52284i 0.423356 + 0.305625i
\(220\) −0.248187 + 0.429872i −0.0167328 + 0.0289820i
\(221\) −19.0309 + 32.9624i −1.28016 + 2.21729i
\(222\) 2.08804 20.4642i 0.140140 1.37347i
\(223\) 10.3774 + 17.9742i 0.694923 + 1.20364i 0.970206 + 0.242279i \(0.0778951\pi\)
−0.275283 + 0.961363i \(0.588772\pi\)
\(224\) 0 0
\(225\) −8.17240 + 9.18801i −0.544826 + 0.612534i
\(226\) −15.3324 −1.01990
\(227\) 5.21512 + 9.03284i 0.346139 + 0.599531i 0.985560 0.169326i \(-0.0541591\pi\)
−0.639421 + 0.768857i \(0.720826\pi\)
\(228\) 6.26509 2.81223i 0.414916 0.186245i
\(229\) −7.52961 + 13.0417i −0.497570 + 0.861817i −0.999996 0.00280316i \(-0.999108\pi\)
0.502426 + 0.864620i \(0.332441\pi\)
\(230\) −1.99829 + 3.46113i −0.131763 + 0.228220i
\(231\) 0 0
\(232\) −5.17240 8.95886i −0.339585 0.588178i
\(233\) 4.38688 0.287394 0.143697 0.989622i \(-0.454101\pi\)
0.143697 + 0.989622i \(0.454101\pi\)
\(234\) 8.05705 + 24.2939i 0.526706 + 1.58814i
\(235\) 7.09751 0.462990
\(236\) −4.63486 8.02781i −0.301704 0.522566i
\(237\) −0.234501 + 2.29826i −0.0152325 + 0.149288i
\(238\) 0 0
\(239\) 4.77561 8.27160i 0.308909 0.535046i −0.669215 0.743069i \(-0.733370\pi\)
0.978124 + 0.208023i \(0.0667029\pi\)
\(240\) 6.64902 + 4.80000i 0.429192 + 0.309839i
\(241\) −5.26792 9.12431i −0.339337 0.587749i 0.644971 0.764207i \(-0.276869\pi\)
−0.984308 + 0.176458i \(0.943536\pi\)
\(242\) 18.1075 1.16400
\(243\) −15.5867 + 0.236756i −0.999885 + 0.0151879i
\(244\) 10.3563 0.662996
\(245\) 0 0
\(246\) 2.51788 + 1.81769i 0.160534 + 0.115892i
\(247\) −11.1971 + 19.3939i −0.712453 + 1.23401i
\(248\) 5.73668 9.93623i 0.364280 0.630951i
\(249\) −0.999311 + 9.79391i −0.0633288 + 0.620664i
\(250\) 7.34011 + 12.7134i 0.464229 + 0.804068i
\(251\) −24.4346 −1.54230 −0.771148 0.636656i \(-0.780317\pi\)
−0.771148 + 0.636656i \(0.780317\pi\)
\(252\) 0 0
\(253\) −1.45744 −0.0916282
\(254\) 5.46658 + 9.46839i 0.343004 + 0.594100i
\(255\) −11.3736 + 5.10532i −0.712244 + 0.319707i
\(256\) −8.87085 + 15.3648i −0.554428 + 0.960298i
\(257\) −2.00416 + 3.47131i −0.125016 + 0.216534i −0.921739 0.387810i \(-0.873232\pi\)
0.796723 + 0.604345i \(0.206565\pi\)
\(258\) 18.7665 8.42380i 1.16835 0.524443i
\(259\) 0 0
\(260\) 4.23491 0.262638
\(261\) 10.9203 12.2774i 0.675949 0.759952i
\(262\) −11.2739 −0.696503
\(263\) −8.84362 15.3176i −0.545321 0.944524i −0.998587 0.0531485i \(-0.983074\pi\)
0.453265 0.891376i \(-0.350259\pi\)
\(264\) −0.195377 + 1.91482i −0.0120246 + 0.117849i
\(265\) 3.28550 5.69066i 0.201827 0.349574i
\(266\) 0 0
\(267\) 1.18478 + 0.855304i 0.0725072 + 0.0523438i
\(268\) 5.27197 + 9.13132i 0.322037 + 0.557784i
\(269\) −14.2273 −0.867455 −0.433727 0.901044i \(-0.642802\pi\)
−0.433727 + 0.901044i \(0.642802\pi\)
\(270\) −2.51788 + 7.99647i −0.153233 + 0.486650i
\(271\) −5.39874 −0.327950 −0.163975 0.986464i \(-0.552432\pi\)
−0.163975 + 0.986464i \(0.552432\pi\)
\(272\) −18.9091 32.7515i −1.14653 1.98585i
\(273\) 0 0
\(274\) 11.9258 20.6561i 0.720464 1.24788i
\(275\) −1.20582 + 2.08854i −0.0727136 + 0.125944i
\(276\) 0.387055 3.79339i 0.0232980 0.228335i
\(277\) −3.83310 6.63913i −0.230309 0.398907i 0.727590 0.686012i \(-0.240640\pi\)
−0.957899 + 0.287105i \(0.907307\pi\)
\(278\) −14.9653 −0.897562
\(279\) 17.8483 + 3.68059i 1.06855 + 0.220351i
\(280\) 0 0
\(281\) 11.3312 + 19.6263i 0.675965 + 1.17081i 0.976186 + 0.216936i \(0.0696065\pi\)
−0.300220 + 0.953870i \(0.597060\pi\)
\(282\) −20.0803 + 9.01352i −1.19577 + 0.536747i
\(283\) 15.9246 27.5822i 0.946619 1.63959i 0.194144 0.980973i \(-0.437807\pi\)
0.752476 0.658620i \(-0.228859\pi\)
\(284\) −1.91095 + 3.30986i −0.113394 + 0.196404i
\(285\) −6.69183 + 3.00379i −0.396390 + 0.177929i
\(286\) 2.50987 + 4.34722i 0.148412 + 0.257057i
\(287\) 0 0
\(288\) −13.8083 2.84748i −0.813664 0.167790i
\(289\) 40.4930 2.38194
\(290\) −4.41840 7.65289i −0.259457 0.449393i
\(291\) −0.598884 + 5.86946i −0.0351072 + 0.344074i
\(292\) −1.98242 + 3.43366i −0.116013 + 0.200940i
\(293\) −13.7468 + 23.8102i −0.803097 + 1.39100i 0.114472 + 0.993427i \(0.463483\pi\)
−0.917568 + 0.397578i \(0.869851\pi\)
\(294\) 0 0
\(295\) 4.95056 + 8.57462i 0.288233 + 0.499234i
\(296\) −13.1978 −0.767105
\(297\) −2.98450 + 0.662859i −0.173179 + 0.0384630i
\(298\) 7.42030 0.429846
\(299\) 6.21720 + 10.7685i 0.359550 + 0.622758i
\(300\) −5.11578 3.69314i −0.295360 0.213224i
\(301\) 0 0
\(302\) −10.7534 + 18.6254i −0.618789 + 1.07177i
\(303\) −1.68547 + 16.5187i −0.0968275 + 0.948973i
\(304\) −11.1254 19.2698i −0.638088 1.10520i
\(305\) −11.0617 −0.633394
\(306\) 25.6948 28.8880i 1.46887 1.65142i
\(307\) 14.8176 0.845683 0.422841 0.906204i \(-0.361033\pi\)
0.422841 + 0.906204i \(0.361033\pi\)
\(308\) 0 0
\(309\) 18.4134 8.26530i 1.04750 0.470196i
\(310\) 4.90043 8.48779i 0.278326 0.482074i
\(311\) −14.5318 + 25.1698i −0.824021 + 1.42725i 0.0786442 + 0.996903i \(0.474941\pi\)
−0.902665 + 0.430343i \(0.858392\pi\)
\(312\) 14.9814 6.72477i 0.848156 0.380715i
\(313\) 12.2390 + 21.1986i 0.691790 + 1.19822i 0.971251 + 0.238058i \(0.0765110\pi\)
−0.279461 + 0.960157i \(0.590156\pi\)
\(314\) −19.1614 −1.08134
\(315\) 0 0
\(316\) −1.18539 −0.0666834
\(317\) 3.69344 + 6.39722i 0.207444 + 0.359304i 0.950909 0.309472i \(-0.100152\pi\)
−0.743465 + 0.668775i \(0.766819\pi\)
\(318\) −2.06848 + 20.2725i −0.115995 + 1.13682i
\(319\) 1.61126 2.79079i 0.0902135 0.156254i
\(320\) 0.943395 1.63401i 0.0527374 0.0913438i
\(321\) −5.33442 3.85098i −0.297738 0.214941i
\(322\) 0 0
\(323\) 33.8268 1.88218
\(324\) −0.932677 7.94406i −0.0518154 0.441337i
\(325\) 20.5753 1.14131
\(326\) −1.41597 2.45253i −0.0784231 0.135833i
\(327\) −18.0655 13.0417i −0.999022 0.721206i
\(328\) 0.996205 1.72548i 0.0550062 0.0952736i
\(329\) 0 0
\(330\) −0.166896 + 1.63569i −0.00918734 + 0.0900419i
\(331\) −10.0309 17.3740i −0.551347 0.954960i −0.998178 0.0603420i \(-0.980781\pi\)
0.446831 0.894618i \(-0.352552\pi\)
\(332\) −5.05146 −0.277235
\(333\) −6.59888 19.8971i −0.361617 1.09036i
\(334\) −6.63315 −0.362950
\(335\) −5.63106 9.75329i −0.307658 0.532879i
\(336\) 0 0
\(337\) −3.20327 + 5.54823i −0.174493 + 0.302231i −0.939986 0.341214i \(-0.889162\pi\)
0.765493 + 0.643445i \(0.222495\pi\)
\(338\) 10.3658 17.9542i 0.563827 0.976577i
\(339\) −14.2547 + 6.39855i −0.774208 + 0.347522i
\(340\) −3.19846 5.53989i −0.173461 0.300443i
\(341\) 3.57409 0.193548
\(342\) 15.1179 16.9967i 0.817482 0.919074i
\(343\) 0 0
\(344\) −6.59888 11.4296i −0.355788 0.616243i
\(345\) −0.413419 + 4.05178i −0.0222577 + 0.218140i
\(346\) 13.6940 23.7187i 0.736194 1.27512i
\(347\) 14.5963 25.2816i 0.783572 1.35719i −0.146276 0.989244i \(-0.546729\pi\)
0.929848 0.367943i \(-0.119938\pi\)
\(348\) 6.83592 + 4.93493i 0.366444 + 0.264540i
\(349\) 2.17192 + 3.76188i 0.116260 + 0.201369i 0.918283 0.395925i \(-0.129576\pi\)
−0.802022 + 0.597294i \(0.796243\pi\)
\(350\) 0 0
\(351\) 17.6291 + 19.2238i 0.940970 + 1.02609i
\(352\) −2.76509 −0.147380
\(353\) −12.8503 22.2574i −0.683955 1.18464i −0.973764 0.227560i \(-0.926925\pi\)
0.289809 0.957084i \(-0.406408\pi\)
\(354\) −24.8955 17.9724i −1.32318 0.955221i
\(355\) 2.04111 3.53530i 0.108331 0.187635i
\(356\) −0.374892 + 0.649331i −0.0198692 + 0.0344145i
\(357\) 0 0
\(358\) 12.1421 + 21.0308i 0.641732 + 1.11151i
\(359\) 20.6872 1.09183 0.545916 0.837840i \(-0.316182\pi\)
0.545916 + 0.837840i \(0.316182\pi\)
\(360\) 5.26792 + 1.08632i 0.277644 + 0.0572543i
\(361\) 0.902493 0.0474996
\(362\) 10.9518 + 18.9691i 0.575614 + 0.996992i
\(363\) 16.8348 7.55667i 0.883595 0.396622i
\(364\) 0 0
\(365\) 2.11745 3.66754i 0.110833 0.191968i
\(366\) 31.2960 14.0479i 1.63587 0.734297i
\(367\) 1.42391 + 2.46628i 0.0743273 + 0.128739i 0.900794 0.434248i \(-0.142986\pi\)
−0.826466 + 0.562986i \(0.809652\pi\)
\(368\) −12.3548 −0.644040
\(369\) 3.09946 + 0.639154i 0.161351 + 0.0332730i
\(370\) −11.2739 −0.586101
\(371\) 0 0
\(372\) −0.949180 + 9.30259i −0.0492127 + 0.482317i
\(373\) −10.7163 + 18.5612i −0.554871 + 0.961065i 0.443043 + 0.896501i \(0.353899\pi\)
−0.997914 + 0.0645641i \(0.979434\pi\)
\(374\) 3.79121 6.56657i 0.196039 0.339549i
\(375\) 12.1298 + 8.75661i 0.626378 + 0.452189i
\(376\) 7.06085 + 12.2297i 0.364135 + 0.630701i
\(377\) −27.4936 −1.41599
\(378\) 0 0
\(379\) 27.0494 1.38943 0.694716 0.719284i \(-0.255530\pi\)
0.694716 + 0.719284i \(0.255530\pi\)
\(380\) −1.88186 3.25947i −0.0965372 0.167207i
\(381\) 9.03370 + 6.52153i 0.462810 + 0.334108i
\(382\) −1.83929 + 3.18575i −0.0941064 + 0.162997i
\(383\) 7.21340 12.4940i 0.368588 0.638412i −0.620757 0.784003i \(-0.713175\pi\)
0.989345 + 0.145590i \(0.0465081\pi\)
\(384\) −2.24647 + 22.0169i −0.114640 + 1.12355i
\(385\) 0 0
\(386\) −17.7293 −0.902399
\(387\) 13.9320 15.6634i 0.708203 0.796214i
\(388\) −3.02733 −0.153689
\(389\) 3.05377 + 5.28929i 0.154832 + 0.268178i 0.932998 0.359882i \(-0.117183\pi\)
−0.778166 + 0.628059i \(0.783850\pi\)
\(390\) 12.7975 5.74447i 0.648028 0.290883i
\(391\) 9.39120 16.2660i 0.474933 0.822609i
\(392\) 0 0
\(393\) −10.4814 + 4.70484i −0.528718 + 0.237328i
\(394\) −15.9635 27.6497i −0.804232 1.39297i
\(395\) 1.26613 0.0637059
\(396\) −0.493810 1.48895i −0.0248149 0.0748226i
\(397\) −12.8873 −0.646794 −0.323397 0.946263i \(-0.604825\pi\)
−0.323397 + 0.946263i \(0.604825\pi\)
\(398\) 7.16059 + 12.4025i 0.358928 + 0.621682i
\(399\) 0 0
\(400\) −10.2218 + 17.7047i −0.511092 + 0.885237i
\(401\) −4.19530 + 7.26647i −0.209503 + 0.362870i −0.951558 0.307469i \(-0.900518\pi\)
0.742055 + 0.670339i \(0.233851\pi\)
\(402\) 28.3177 + 20.4429i 1.41236 + 1.01960i
\(403\) −15.2465 26.4078i −0.759483 1.31546i
\(404\) −8.51994 −0.423883
\(405\) 0.996205 + 8.48516i 0.0495018 + 0.421631i
\(406\) 0 0
\(407\) −2.05563 3.56046i −0.101894 0.176485i
\(408\) −20.1119 14.5190i −0.995686 0.718797i
\(409\) −3.40633 + 5.89994i −0.168432 + 0.291733i −0.937869 0.346990i \(-0.887204\pi\)
0.769437 + 0.638723i \(0.220537\pi\)
\(410\) 0.850985 1.47395i 0.0420271 0.0727931i
\(411\) 2.46729 24.1810i 0.121702 1.19276i
\(412\) 5.17817 + 8.96885i 0.255110 + 0.441864i
\(413\) 0 0
\(414\) −3.97593 11.9883i −0.195406 0.589194i
\(415\) 5.39554 0.264857
\(416\) 11.7955 + 20.4303i 0.578320 + 1.00168i
\(417\) −13.9134 + 6.24536i −0.681343 + 0.305837i
\(418\) 2.23061 3.86353i 0.109103 0.188971i
\(419\) 5.16231 8.94137i 0.252195 0.436815i −0.711935 0.702246i \(-0.752181\pi\)
0.964130 + 0.265431i \(0.0855142\pi\)
\(420\) 0 0
\(421\) −1.56801 2.71588i −0.0764202 0.132364i 0.825283 0.564720i \(-0.191016\pi\)
−0.901703 + 0.432356i \(0.857682\pi\)
\(422\) −19.0741 −0.928514
\(423\) −14.9073 + 16.7599i −0.724818 + 0.814894i
\(424\) 13.0741 0.634936
\(425\) −15.5397 26.9156i −0.753787 1.30560i
\(426\) −1.28504 + 12.5942i −0.0622603 + 0.610192i
\(427\) 0 0
\(428\) 1.68794 2.92359i 0.0815895 0.141317i
\(429\) 4.14764 + 2.99423i 0.200250 + 0.144563i
\(430\) −5.63694 9.76347i −0.271837 0.470836i
\(431\) 31.8726 1.53525 0.767625 0.640899i \(-0.221438\pi\)
0.767625 + 0.640899i \(0.221438\pi\)
\(432\) −25.2999 + 5.61912i −1.21724 + 0.270350i
\(433\) 7.48855 0.359877 0.179938 0.983678i \(-0.442410\pi\)
0.179938 + 0.983678i \(0.442410\pi\)
\(434\) 0 0
\(435\) −7.30154 5.27107i −0.350082 0.252728i
\(436\) 5.71634 9.90099i 0.273763 0.474171i
\(437\) 5.52544 9.57035i 0.264318 0.457812i
\(438\) −1.33310 + 13.0653i −0.0636982 + 0.624284i
\(439\) −1.14465 1.98259i −0.0546311 0.0946238i 0.837417 0.546565i \(-0.184065\pi\)
−0.892048 + 0.451941i \(0.850732\pi\)
\(440\) 1.05489 0.0502900
\(441\) 0 0
\(442\) −64.6908 −3.07703
\(443\) −18.6749 32.3458i −0.887270 1.53680i −0.843090 0.537773i \(-0.819266\pi\)
−0.0441800 0.999024i \(-0.514067\pi\)
\(444\) 9.81303 4.40481i 0.465706 0.209043i
\(445\) 0.400427 0.693560i 0.0189821 0.0328779i
\(446\) −17.6378 + 30.5495i −0.835172 + 1.44656i
\(447\) 6.89872 3.09665i 0.326298 0.146467i
\(448\) 0 0
\(449\) −6.20286 −0.292731 −0.146366 0.989231i \(-0.546758\pi\)
−0.146366 + 0.989231i \(0.546758\pi\)
\(450\) −20.4691 4.22102i −0.964920 0.198981i
\(451\) 0.620660 0.0292257
\(452\) −4.00866 6.94320i −0.188552 0.326581i
\(453\) −2.22473 + 21.8039i −0.104527 + 1.02444i
\(454\) −8.86376 + 15.3525i −0.415997 + 0.720527i
\(455\) 0 0
\(456\) −11.8331 8.54245i −0.554136 0.400037i
\(457\) −10.0858 17.4691i −0.471795 0.817172i 0.527685 0.849440i \(-0.323060\pi\)
−0.999479 + 0.0322682i \(0.989727\pi\)
\(458\) −25.5951 −1.19598
\(459\) 11.8331 37.5804i 0.552322 1.75410i
\(460\) −2.08981 −0.0974378
\(461\) 11.2680 + 19.5168i 0.524803 + 0.908986i 0.999583 + 0.0288813i \(0.00919447\pi\)
−0.474780 + 0.880105i \(0.657472\pi\)
\(462\) 0 0
\(463\) 13.8145 23.9275i 0.642016 1.11200i −0.342966 0.939348i \(-0.611432\pi\)
0.984982 0.172656i \(-0.0552350\pi\)
\(464\) 13.6588 23.6578i 0.634096 1.09829i
\(465\) 1.01383 9.93623i 0.0470154 0.460782i
\(466\) 3.72803 + 6.45714i 0.172698 + 0.299121i
\(467\) 20.1224 0.931155 0.465577 0.885007i \(-0.345847\pi\)
0.465577 + 0.885007i \(0.345847\pi\)
\(468\) −8.89483 + 10.0002i −0.411164 + 0.462261i
\(469\) 0 0
\(470\) 6.03156 + 10.4470i 0.278215 + 0.481883i
\(471\) −17.8145 + 7.99647i −0.820850 + 0.368458i
\(472\) −9.84997 + 17.0607i −0.453382 + 0.785280i
\(473\) 2.05563 3.56046i 0.0945181 0.163710i
\(474\) −3.58215 + 1.60793i −0.164533 + 0.0738547i
\(475\) −9.14301 15.8362i −0.419510 0.726613i
\(476\) 0 0
\(477\) 6.53706 + 19.7107i 0.299312 + 0.902493i
\(478\) 16.2335 0.742504
\(479\) 4.79329 + 8.30222i 0.219011 + 0.379338i 0.954506 0.298192i \(-0.0963836\pi\)
−0.735495 + 0.677530i \(0.763050\pi\)
\(480\) −0.784350 + 7.68715i −0.0358005 + 0.350869i
\(481\) −17.5380 + 30.3767i −0.799664 + 1.38506i
\(482\) 8.95351 15.5079i 0.407821 0.706367i
\(483\) 0 0
\(484\) 4.73422 + 8.19991i 0.215192 + 0.372723i
\(485\) 3.23353 0.146827
\(486\) −13.5942 22.7411i −0.616648 1.03156i
\(487\) 13.0741 0.592445 0.296223 0.955119i \(-0.404273\pi\)
0.296223 + 0.955119i \(0.404273\pi\)
\(488\) −11.0046 19.0605i −0.498155 0.862830i
\(489\) −2.33993 1.68922i −0.105815 0.0763893i
\(490\) 0 0
\(491\) −7.67054 + 13.2858i −0.346167 + 0.599578i −0.985565 0.169298i \(-0.945850\pi\)
0.639398 + 0.768876i \(0.279183\pi\)
\(492\) −0.164830 + 1.61544i −0.00743112 + 0.0728298i
\(493\) 20.7648 + 35.9657i 0.935201 + 1.61982i
\(494\) −38.0617 −1.71248
\(495\) 0.527445 + 1.59037i 0.0237069 + 0.0714817i
\(496\) 30.2979 1.36042
\(497\) 0 0
\(498\) −15.2651 + 6.85210i −0.684045 + 0.307050i
\(499\) −2.43268 + 4.21352i −0.108902 + 0.188623i −0.915326 0.402715i \(-0.868067\pi\)
0.806424 + 0.591338i \(0.201400\pi\)
\(500\) −3.83814 + 6.64786i −0.171647 + 0.297301i
\(501\) −6.16690 + 2.76816i −0.275517 + 0.123672i
\(502\) −20.7648 35.9657i −0.926780 1.60523i
\(503\) 16.0085 0.713783 0.356892 0.934146i \(-0.383837\pi\)
0.356892 + 0.934146i \(0.383837\pi\)
\(504\) 0 0
\(505\) 9.10026 0.404956
\(506\) −1.23855 2.14523i −0.0550603 0.0953672i
\(507\) 2.14455 21.0180i 0.0952429 0.933443i
\(508\) −2.85848 + 4.95102i −0.126824 + 0.219666i
\(509\) 15.5925 27.0071i 0.691127 1.19707i −0.280342 0.959900i \(-0.590448\pi\)
0.971469 0.237167i \(-0.0762188\pi\)
\(510\) −17.1801 12.4025i −0.760747 0.549192i
\(511\) 0 0
\(512\) −4.59937 −0.203265
\(513\) 6.96217 22.1110i 0.307387 0.976224i
\(514\) −6.81266 −0.300494
\(515\) −5.53087 9.57975i −0.243719 0.422134i
\(516\) 8.72119 + 6.29593i 0.383929 + 0.277163i
\(517\) −2.19954 + 3.80971i −0.0967356 + 0.167551i
\(518\) 0 0
\(519\) 2.83310 27.7663i 0.124359 1.21880i
\(520\) −4.50000 7.79423i −0.197338 0.341800i
\(521\) 20.9661 0.918541 0.459270 0.888297i \(-0.348111\pi\)
0.459270 + 0.888297i \(0.348111\pi\)
\(522\) 27.3516 + 5.64030i 1.19715 + 0.246869i
\(523\) 43.5642 1.90493 0.952465 0.304647i \(-0.0985383\pi\)
0.952465 + 0.304647i \(0.0985383\pi\)
\(524\) −2.94756 5.10532i −0.128765 0.223027i
\(525\) 0 0
\(526\) 15.0309 26.0342i 0.655377 1.13515i
\(527\) −23.0302 + 39.8894i −1.00321 + 1.73761i
\(528\) −4.63704 + 2.08144i −0.201801 + 0.0905832i
\(529\) 8.43199 + 14.6046i 0.366608 + 0.634984i
\(530\) 11.1683 0.485118
\(531\) −30.6459 6.31963i −1.32992 0.274249i
\(532\) 0 0
\(533\) −2.64764 4.58584i −0.114682 0.198635i
\(534\) −0.252100 + 2.47075i −0.0109094 + 0.106920i
\(535\) −1.80291 + 3.12273i −0.0779466 + 0.135007i
\(536\) 11.2040 19.4058i 0.483937 0.838204i
\(537\) 20.0653 + 14.4853i 0.865880 + 0.625089i
\(538\) −12.0906 20.9415i −0.521262 0.902852i
\(539\) 0 0
\(540\) −4.27946 + 0.950469i −0.184159 + 0.0409017i
\(541\) 9.86535 0.424145 0.212072 0.977254i \(-0.431979\pi\)
0.212072 + 0.977254i \(0.431979\pi\)
\(542\) −4.58793 7.94652i −0.197068 0.341332i
\(543\) 18.0982 + 13.0653i 0.776668 + 0.560686i
\(544\) 17.8173 30.8604i 0.763909 1.32313i
\(545\) −6.10570 + 10.5754i −0.261539 + 0.453000i
\(546\) 0 0
\(547\) −0.284350 0.492509i −0.0121579 0.0210582i 0.859882 0.510492i \(-0.170537\pi\)
−0.872040 + 0.489434i \(0.837203\pi\)
\(548\) 12.4720 0.532778
\(549\) 23.2336 26.1210i 0.991587 1.11482i
\(550\) −4.09888 −0.174777
\(551\) 12.2173 + 21.1609i 0.520473 + 0.901487i
\(552\) −7.39292 + 3.31848i −0.314663 + 0.141244i
\(553\) 0 0
\(554\) 6.51485 11.2841i 0.276789 0.479413i
\(555\) −10.4814 + 4.70484i −0.444912 + 0.199709i
\(556\) −3.91269 6.77698i −0.165935 0.287408i
\(557\) −2.58699 −0.109614 −0.0548071 0.998497i \(-0.517454\pi\)
−0.0548071 + 0.998497i \(0.517454\pi\)
\(558\) 9.75023 + 29.3992i 0.412760 + 1.24457i
\(559\) −35.0760 −1.48356
\(560\) 0 0
\(561\) 0.784350 7.68715i 0.0331153 0.324552i
\(562\) −19.2589 + 33.3574i −0.812388 + 1.40710i
\(563\) 16.6416 28.8240i 0.701358 1.21479i −0.266632 0.963798i \(-0.585911\pi\)
0.967990 0.250989i \(-0.0807558\pi\)
\(564\) −9.33173 6.73668i −0.392937 0.283665i
\(565\) 4.28171 + 7.41613i 0.180133 + 0.311999i
\(566\) 54.1318 2.27533
\(567\) 0 0
\(568\) 8.12227 0.340803
\(569\) 2.67673 + 4.63623i 0.112214 + 0.194361i 0.916663 0.399662i \(-0.130872\pi\)
−0.804448 + 0.594022i \(0.797539\pi\)
\(570\) −10.1081 7.29719i −0.423384 0.305646i
\(571\) −2.45056 + 4.24449i −0.102553 + 0.177626i −0.912736 0.408551i \(-0.866034\pi\)
0.810183 + 0.586177i \(0.199368\pi\)
\(572\) −1.31241 + 2.27316i −0.0548747 + 0.0950457i
\(573\) −0.380525 + 3.72940i −0.0158967 + 0.155798i
\(574\) 0 0
\(575\) −10.1533 −0.423424
\(576\) 1.87704 + 5.65972i 0.0782102 + 0.235822i
\(577\) −36.0757 −1.50185 −0.750925 0.660387i \(-0.770392\pi\)
−0.750925 + 0.660387i \(0.770392\pi\)
\(578\) 34.4116 + 59.6026i 1.43133 + 2.47914i
\(579\) −16.4831 + 7.39884i −0.685015 + 0.307485i
\(580\) 2.31038 4.00170i 0.0959333 0.166161i
\(581\) 0 0
\(582\) −9.14833 + 4.10644i −0.379210 + 0.170217i
\(583\) 2.03637 + 3.52710i 0.0843380 + 0.146078i
\(584\) 8.42607 0.348673
\(585\) 9.50069 10.6814i 0.392805 0.441621i
\(586\) −46.7289 −1.93035
\(587\) −0.527445 0.913562i −0.0217700 0.0377068i 0.854935 0.518735i \(-0.173597\pi\)
−0.876705 + 0.481028i \(0.840263\pi\)
\(588\) 0 0
\(589\) −13.5501 + 23.4695i −0.558323 + 0.967045i
\(590\) −8.41411 + 14.5737i −0.346403 + 0.599988i
\(591\) −26.3803 19.0442i −1.08514 0.783375i
\(592\) −17.4258 30.1824i −0.716196 1.24049i
\(593\) −15.0710 −0.618890 −0.309445 0.950917i \(-0.600143\pi\)
−0.309445 + 0.950917i \(0.600143\pi\)
\(594\) −3.51195 3.82965i −0.144097 0.157132i
\(595\) 0 0
\(596\) 1.94004 + 3.36024i 0.0794670 + 0.137641i
\(597\) 11.8331 + 8.54245i 0.484297 + 0.349619i
\(598\) −10.5669 + 18.3024i −0.432114 + 0.748443i
\(599\) −21.0283 + 36.4221i −0.859194 + 1.48817i 0.0135047 + 0.999909i \(0.495701\pi\)
−0.872699 + 0.488259i \(0.837632\pi\)
\(600\) −1.36111 + 13.3398i −0.0555671 + 0.544594i
\(601\) −9.44989 16.3677i −0.385469 0.667652i 0.606365 0.795186i \(-0.292627\pi\)
−0.991834 + 0.127534i \(0.959294\pi\)
\(602\) 0 0
\(603\) 34.8585 + 7.18833i 1.41955 + 0.292732i
\(604\) −11.2459 −0.457590
\(605\) −5.05669 8.75844i −0.205583 0.356081i
\(606\) −25.7465 + 11.5569i −1.04588 + 0.469468i
\(607\) 14.7213 25.4980i 0.597518 1.03493i −0.395668 0.918393i \(-0.629487\pi\)
0.993186 0.116538i \(-0.0371796\pi\)
\(608\) 10.4830 18.1572i 0.425143 0.736370i
\(609\) 0 0
\(610\) −9.40043 16.2820i −0.380612 0.659240i
\(611\) 37.5316 1.51836
\(612\) 19.7997 + 4.08299i 0.800355 + 0.165045i
\(613\) −11.6676 −0.471249 −0.235625 0.971844i \(-0.575714\pi\)
−0.235625 + 0.971844i \(0.575714\pi\)
\(614\) 12.5922 + 21.8103i 0.508179 + 0.880191i
\(615\) 0.176057 1.72548i 0.00709932 0.0695780i
\(616\) 0 0
\(617\) 16.4054 28.4151i 0.660458 1.14395i −0.320037 0.947405i \(-0.603695\pi\)
0.980495 0.196542i \(-0.0629713\pi\)
\(618\) 27.8138 + 20.0791i 1.11884 + 0.807701i
\(619\) 12.0806 + 20.9242i 0.485560 + 0.841014i 0.999862 0.0165947i \(-0.00528250\pi\)
−0.514303 + 0.857609i \(0.671949\pi\)
\(620\) 5.12487 0.205820
\(621\) −8.69945 9.48642i −0.349097 0.380677i
\(622\) −49.3972 −1.98065
\(623\) 0 0
\(624\) 35.1599 + 25.3824i 1.40752 + 1.01611i
\(625\) −6.14764 + 10.6480i −0.245906 + 0.425921i
\(626\) −20.8018 + 36.0297i −0.831406 + 1.44004i
\(627\) 0.461483 4.52284i 0.0184299 0.180625i
\(628\) −5.00975 8.67714i −0.199911 0.346256i
\(629\) 52.9830 2.11257
\(630\) 0 0
\(631\) −11.1003 −0.441894 −0.220947 0.975286i \(-0.570915\pi\)
−0.220947 + 0.975286i \(0.570915\pi\)
\(632\) 1.25959 + 2.18168i 0.0501038 + 0.0867824i
\(633\) −17.7334 + 7.96005i −0.704839 + 0.316383i
\(634\) −6.27747 + 10.8729i −0.249310 + 0.431818i
\(635\) 3.05318 5.28826i 0.121162 0.209858i
\(636\) −9.72109 + 4.36354i −0.385466 + 0.173026i
\(637\) 0 0
\(638\) 5.47710 0.216840
\(639\) 4.06113 + 12.2452i 0.160656 + 0.484414i
\(640\) 12.1293 0.479452
\(641\) −3.65019 6.32231i −0.144174 0.249716i 0.784891 0.619634i \(-0.212719\pi\)
−0.929064 + 0.369918i \(0.879386\pi\)
\(642\) 1.13507 11.1245i 0.0447978 0.439048i
\(643\) −10.6256 + 18.4041i −0.419033 + 0.725787i −0.995842 0.0910922i \(-0.970964\pi\)
0.576809 + 0.816879i \(0.304298\pi\)
\(644\) 0 0
\(645\) −9.31522 6.72477i −0.366787 0.264787i
\(646\) 28.7465 + 49.7904i 1.13102 + 1.95898i
\(647\) 16.9460 0.666216 0.333108 0.942889i \(-0.391903\pi\)
0.333108 + 0.942889i \(0.391903\pi\)
\(648\) −13.6298 + 10.1579i −0.535427 + 0.399040i
\(649\) −6.13677 −0.240889
\(650\) 17.4852 + 30.2853i 0.685826 + 1.18789i
\(651\) 0 0
\(652\) 0.740409 1.28243i 0.0289967 0.0502237i
\(653\) 1.86652 3.23292i 0.0730427 0.126514i −0.827191 0.561921i \(-0.810062\pi\)
0.900233 + 0.435408i \(0.143396\pi\)
\(654\) 3.84402 37.6739i 0.150313 1.47317i
\(655\) 3.14833 + 5.45306i 0.123015 + 0.213069i
\(656\) 5.26140 0.205423
\(657\) 4.21303 + 12.7033i 0.164366 + 0.495601i
\(658\) 0 0
\(659\) 11.7992 + 20.4368i 0.459632 + 0.796105i 0.998941 0.0460022i \(-0.0146481\pi\)
−0.539310 + 0.842107i \(0.681315\pi\)
\(660\) −0.784350 + 0.352074i −0.0305308 + 0.0137045i
\(661\) −17.2588 + 29.8930i −0.671288 + 1.16270i 0.306252 + 0.951951i \(0.400925\pi\)
−0.977539 + 0.210754i \(0.932408\pi\)
\(662\) 17.0488 29.5293i 0.662619 1.14769i
\(663\) −60.1436 + 26.9969i −2.33579 + 1.04847i
\(664\) 5.36767 + 9.29708i 0.208306 + 0.360796i
\(665\) 0 0
\(666\) 23.6792 26.6219i 0.917550 1.03158i
\(667\) 13.5673 0.525329
\(668\) −1.73424 3.00379i −0.0670996 0.116220i
\(669\) −3.64902 + 35.7628i −0.141079 + 1.38267i
\(670\) 9.57072 16.5770i 0.369749 0.640424i
\(671\) 3.42807 5.93759i 0.132339 0.229218i
\(672\) 0 0
\(673\) 12.2287 + 21.1808i 0.471382 + 0.816458i 0.999464 0.0327353i \(-0.0104218\pi\)
−0.528082 + 0.849194i \(0.677088\pi\)
\(674\) −10.8887 −0.419418
\(675\) −20.7918 + 4.61786i −0.800276 + 0.177741i
\(676\) 10.8406 0.416946
\(677\) 4.16022 + 7.20572i 0.159890 + 0.276938i 0.934829 0.355098i \(-0.115553\pi\)
−0.774939 + 0.632037i \(0.782219\pi\)
\(678\) −21.5320 15.5442i −0.826931 0.596971i
\(679\) 0 0
\(680\) −6.79734 + 11.7733i −0.260666 + 0.451487i
\(681\) −1.83379 + 17.9724i −0.0702711 + 0.688703i
\(682\) 3.03731 + 5.26078i 0.116305 + 0.201446i
\(683\) −42.4624 −1.62478 −0.812389 0.583116i \(-0.801833\pi\)
−0.812389 + 0.583116i \(0.801833\pi\)
\(684\) 11.6494 + 2.40228i 0.445427 + 0.0918536i
\(685\) −13.3215 −0.508989
\(686\) 0 0
\(687\) −23.7960 + 10.6814i −0.907873 + 0.407520i
\(688\) 17.4258 30.1824i 0.664352 1.15069i
\(689\) 17.3737 30.0921i 0.661885 1.14642i
\(690\) −6.31522 + 2.83474i −0.240416 + 0.107917i
\(691\) −17.6964 30.6511i −0.673204 1.16602i −0.976990 0.213284i \(-0.931584\pi\)
0.303786 0.952740i \(-0.401749\pi\)
\(692\) 14.3212 0.544410
\(693\) 0 0
\(694\) 49.6167 1.88342
\(695\) 4.17920 + 7.23859i 0.158526 + 0.274575i
\(696\) 1.81877 17.8252i 0.0689404 0.675661i
\(697\) −3.99931 + 6.92701i −0.151485 + 0.262379i
\(698\) −3.69146 + 6.39380i −0.139724 + 0.242009i
\(699\) 6.16069 + 4.44747i 0.233019 + 0.168219i
\(700\) 0 0
\(701\) −7.00372 −0.264527 −0.132263 0.991215i \(-0.542224\pi\)
−0.132263 + 0.991215i \(0.542224\pi\)
\(702\) −13.3145 + 42.2853i −0.502525 + 1.59596i
\(703\) 31.1733 1.17572
\(704\) 0.584722 + 1.01277i 0.0220375 + 0.0381701i
\(705\) 9.96735 + 7.19554i 0.375392 + 0.271000i
\(706\) 21.8408 37.8294i 0.821989 1.42373i
\(707\) 0 0
\(708\) 1.62976 15.9727i 0.0612500 0.600291i
\(709\) 1.11126 + 1.92477i 0.0417344 + 0.0722861i 0.886138 0.463421i \(-0.153378\pi\)
−0.844404 + 0.535707i \(0.820045\pi\)
\(710\) 6.93825 0.260388
\(711\) −2.65933 + 2.98981i −0.0997326 + 0.112127i
\(712\) 1.59343 0.0597165
\(713\) 7.52373 + 13.0315i 0.281766 + 0.488033i
\(714\) 0 0
\(715\) 1.40180 2.42800i 0.0524245 0.0908019i
\(716\) −6.34913 + 10.9970i −0.237278 + 0.410977i
\(717\) 15.0925 6.77461i 0.563638 0.253002i
\(718\) 17.5803 + 30.4500i 0.656092 + 1.13638i
\(719\) 26.0175 0.970291 0.485145 0.874434i \(-0.338767\pi\)
0.485145 + 0.874434i \(0.338767\pi\)
\(720\) 4.47121 + 13.4817i 0.166632 + 0.502434i
\(721\) 0 0
\(722\) 0.766951 + 1.32840i 0.0285430 + 0.0494379i
\(723\) 1.85236 18.1544i 0.0688901 0.675168i
\(724\) −5.72670 + 9.91893i −0.212831 + 0.368634i
\(725\) 11.2250 19.4423i 0.416886 0.722068i
\(726\) 25.4292 + 18.3577i 0.943767 + 0.681317i
\(727\) 0.685875 + 1.18797i 0.0254377 + 0.0440594i 0.878464 0.477809i \(-0.158569\pi\)
−0.853026 + 0.521868i \(0.825235\pi\)
\(728\) 0 0
\(729\) −22.1291 15.4695i −0.819595 0.572943i
\(730\) 7.19777 0.266401
\(731\) 26.4915 + 45.8847i 0.979824 + 1.69711i
\(732\) 14.5439 + 10.4994i 0.537557 + 0.388068i
\(733\) 0.400087 0.692971i 0.0147776 0.0255955i −0.858542 0.512743i \(-0.828629\pi\)
0.873320 + 0.487148i \(0.161963\pi\)
\(734\) −2.42011 + 4.19176i −0.0893280 + 0.154721i
\(735\) 0 0
\(736\) −5.82072 10.0818i −0.214555 0.371620i
\(737\) 6.98034 0.257124
\(738\) 1.69318 + 5.10532i 0.0623268 + 0.187929i
\(739\) 5.37093 0.197573 0.0987865 0.995109i \(-0.468504\pi\)
0.0987865 + 0.995109i \(0.468504\pi\)
\(740\) −2.94756 5.10532i −0.108354 0.187675i
\(741\) −35.3864 + 15.8840i −1.29995 + 0.583513i
\(742\) 0 0
\(743\) 6.63162 11.4863i 0.243290 0.421391i −0.718359 0.695672i \(-0.755107\pi\)
0.961650 + 0.274281i \(0.0884399\pi\)
\(744\) 18.1298 8.13797i 0.664669 0.298352i
\(745\) −2.07218 3.58912i −0.0759188 0.131495i
\(746\) −36.4276 −1.33371
\(747\) −11.3326 + 12.7409i −0.414637 + 0.466166i
\(748\) 3.96485 0.144969
\(749\) 0 0
\(750\) −2.58100 + 25.2955i −0.0942449 + 0.923662i
\(751\) −2.77816 + 4.81191i −0.101377 + 0.175589i −0.912252 0.409629i \(-0.865658\pi\)
0.810875 + 0.585219i \(0.198991\pi\)
\(752\) −18.6457 + 32.2953i −0.679939 + 1.17769i
\(753\) −34.3145 24.7721i −1.25049 0.902744i
\(754\) −23.3645 40.4684i −0.850883 1.47377i
\(755\) 12.0119 0.437158
\(756\) 0 0
\(757\) −13.3942 −0.486819 −0.243410 0.969924i \(-0.578266\pi\)
−0.243410 + 0.969924i \(0.578266\pi\)
\(758\) 22.9869 + 39.8145i 0.834923 + 1.44613i
\(759\) −2.04674 1.47757i −0.0742921 0.0536323i
\(760\) −3.99931 + 6.92701i −0.145070 + 0.251269i
\(761\) 6.42191 11.1231i 0.232794 0.403211i −0.725835 0.687868i \(-0.758547\pi\)
0.958629 + 0.284658i \(0.0918799\pi\)
\(762\) −1.92221 + 18.8390i −0.0696345 + 0.682464i
\(763\) 0 0
\(764\) −1.92353 −0.0695910
\(765\) −21.1483 4.36110i −0.764619 0.157676i
\(766\) 24.5202 0.885951
\(767\) 26.1785 + 45.3425i 0.945251 + 1.63722i
\(768\) −28.0347 + 12.5841i −1.01162 + 0.454088i
\(769\) −1.48259 + 2.56793i −0.0534636 + 0.0926018i −0.891519 0.452984i \(-0.850359\pi\)
0.838055 + 0.545586i \(0.183693\pi\)
\(770\) 0 0
\(771\) −6.33379 + 2.84307i −0.228106 + 0.102391i
\(772\) −4.63533 8.02864i −0.166829 0.288957i
\(773\) −19.2788 −0.693409 −0.346705 0.937974i \(-0.612699\pi\)
−0.346705 + 0.937974i \(0.612699\pi\)
\(774\) 34.8948 + 7.19583i 1.25427 + 0.258649i
\(775\) 24.8992 0.894406
\(776\) 3.21683 + 5.57171i 0.115477 + 0.200013i
\(777\) 0 0
\(778\) −5.19028 + 8.98983i −0.186080 + 0.322301i
\(779\) −2.35305 + 4.07560i −0.0843068 + 0.146024i
\(780\) 5.94727 + 4.29340i 0.212946 + 0.153728i
\(781\) 1.26509 + 2.19120i 0.0452685 + 0.0784074i