Properties

Label 441.2.f.g.148.5
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 148.5
Root \(0.474636 - 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.g.295.5

$q$-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 −0.952423 0.304781i \(-0.901417\pi\)
0.740159 + 0.672432i \(0.234750\pi\)
\(6\) 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 \(0.411755\pi\)
−0.969804 + 0.243885i \(0.921578\pi\)
\(14\) 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 \(-0.128591\pi\)
0.919503 + 0.393083i \(0.128591\pi\)
\(18\) −3.38874 + 3.80987i −0.798733 + 0.897994i
\(19\) 4.46122 1.02347 0.511737 0.859142i \(-0.329002\pi\)
0.511737 + 0.859142i \(0.329002\pi\)
\(20\) −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 \(0.350334\pi\)
−0.998574 + 0.0533826i \(0.983000\pi\)
\(32\) −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 −0.904269 0.426964i \(-0.859583\pi\)
0.821896 + 0.569638i \(0.192917\pi\)
\(42\) 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 \(-0.983082\pi\)
0.453286 0.891365i \(-0.350251\pi\)
\(48\) 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 \(-0.595769\pi\)
0.975297 0.220896i \(-0.0708981\pi\)
\(60\) −0.148327 + 1.45370i −0.0191489 + 0.187672i
\(61\) 5.82644 + 10.0917i 0.745999 + 1.29211i 0.949726 + 0.313081i \(0.101361\pi\)
−0.203727 + 0.979028i \(0.565305\pi\)
\(62\) −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 \(-0.584076\pi\)
−0.261073 + 0.965319i \(0.584076\pi\)
\(74\) −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 0.666840 0.745201i \(-0.267647\pi\)
−0.978783 + 0.204900i \(0.934313\pi\)
\(84\) 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 \(-0.514237\pi\)
−0.0447134 + 0.999000i \(0.514237\pi\)
\(90\) −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 0.766513 0.642229i \(-0.221990\pi\)
−0.939443 + 0.342705i \(0.888657\pi\)
\(98\) 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 0.522701 0.852516i \(-0.324924\pi\)
−0.999651 + 0.0264143i \(0.991591\pi\)
\(102\) 2.26578 22.2061i 0.224346 2.19874i
\(103\) −5.82644 + 10.0917i −0.574096 + 0.994364i 0.422043 + 0.906576i \(0.361313\pi\)
−0.996139 + 0.0877882i \(0.972020\pi\)
\(104\) −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 −0.683984 0.729497i \(-0.739754\pi\)
0.973755 + 0.227600i \(0.0730877\pi\)
\(132\) 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 −0.616671 0.787221i \(-0.711519\pi\)
0.990089 + 0.140442i \(0.0448523\pi\)
\(140\) 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 −0.548501 0.836150i \(-0.684801\pi\)
0.998378 + 0.0569405i \(0.0181345\pi\)
\(158\) −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 −0.780595 0.625037i \(-0.785084\pi\)
0.931595 + 0.363497i \(0.118417\pi\)
\(168\) 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 \(0.0431961\pi\)
−0.378240 + 0.925708i \(0.623471\pi\)
\(174\) −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 \(-0.658983\pi\)
−0.478952 + 0.877841i \(0.658983\pi\)
\(182\) 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 \(-0.596538\pi\)
−0.298654 + 0.954361i \(0.596538\pi\)
\(200\) 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 \(-0.922105\pi\)
0.275283 0.961363i \(-0.411228\pi\)
\(224\) 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 0.639421 0.768857i \(-0.279174\pi\)
−0.985560 + 0.169326i \(0.945841\pi\)
\(228\) 6.26509 2.81223i 0.414916 0.186245i
\(229\) 7.52961 13.0417i 0.497570 0.861817i −0.502426 0.864620i \(-0.667559\pi\)
0.999996 + 0.00280316i \(0.000892274\pi\)
\(230\) 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 0.984308 0.176458i \(-0.0564640\pi\)
−0.644971 + 0.764207i \(0.723131\pi\)
\(242\) 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 \(-0.219683\pi\)
0.771148 + 0.636656i \(0.219683\pi\)
\(252\) 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 −0.796723 0.604345i \(-0.793435\pi\)
0.921739 + 0.387810i \(0.126768\pi\)
\(258\) −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 \(-0.357198\pi\)
0.433727 + 0.901044i \(0.357198\pi\)
\(270\) −2.51788 + 7.99647i −0.153233 + 0.486650i
\(271\) 5.39874 0.327950 0.163975 0.986464i \(-0.447568\pi\)
0.163975 + 0.986464i \(0.447568\pi\)
\(272\) 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 \(0.562193\pi\)
−0.752476 + 0.658620i \(0.771141\pi\)
\(284\) −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 \(-0.536517\pi\)
0.917568 0.397578i \(-0.130149\pi\)
\(294\) 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 \(-0.638967\pi\)
−0.422841 + 0.906204i \(0.638967\pi\)
\(308\) 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 \(-0.525059\pi\)
0.902665 0.430343i \(-0.141608\pi\)
\(312\) 14.9814 6.72477i 0.848156 0.380715i
\(313\) −12.2390 21.1986i −0.691790 1.19822i −0.971251 0.238058i \(-0.923489\pi\)
0.279461 0.960157i \(-0.409844\pi\)
\(314\) 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 0.802022 0.597294i \(-0.203757\pi\)
−0.918283 + 0.395925i \(0.870424\pi\)
\(350\) 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 \(0.0730747\pi\)
−0.289809 + 0.957084i \(0.593592\pi\)
\(354\) −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 0.826466 0.562986i \(-0.190348\pi\)
−0.900794 + 0.434248i \(0.857014\pi\)
\(368\) −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 −0.989345 0.145590i \(-0.953492\pi\)
0.620757 + 0.784003i \(0.286825\pi\)
\(384\) 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 \(-0.395175\pi\)
0.323397 + 0.946263i \(0.395175\pi\)
\(398\) −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 −0.769437 0.638723i \(-0.779463\pi\)
0.937869 + 0.346990i \(0.112796\pi\)
\(410\) 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 −0.964130 0.265431i \(-0.914486\pi\)
0.711935 + 0.702246i \(0.247819\pi\)
\(420\) 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 \(-0.557590\pi\)
−0.179938 + 0.983678i \(0.557590\pi\)
\(434\) 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 0.892048 0.451941i \(-0.149268\pi\)
−0.837417 + 0.546565i \(0.815935\pi\)
\(440\) −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 \(-0.990806\pi\)
0.474780 0.880105i \(-0.342528\pi\)
\(462\) 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 \(-0.654153\pi\)
−0.465577 + 0.885007i \(0.654153\pi\)
\(468\) 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 0.735495 0.677530i \(-0.236950\pi\)
−0.954506 + 0.298192i \(0.903616\pi\)
\(480\) −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 \(-0.616163\pi\)
−0.356892 + 0.934146i \(0.616163\pi\)
\(504\) 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 \(0.409552\pi\)
−0.971469 + 0.237167i \(0.923781\pi\)
\(510\) 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 \(-0.651889\pi\)
−0.459270 + 0.888297i \(0.651889\pi\)
\(522\) 27.3516 + 5.64030i 1.19715 + 0.246869i
\(523\) −43.5642 −1.90493 −0.952465 0.304647i \(-0.901462\pi\)
−0.952465 + 0.304647i \(0.901462\pi\)
\(524\) 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 \(0.414089\pi\)
−0.967990 + 0.250989i \(0.919244\pi\)
\(564\) −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 \(-0.229608\pi\)
0.750925 + 0.660387i \(0.229608\pi\)
\(578\) 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 0.876705 0.481028i \(-0.159737\pi\)
−0.854935 + 0.518735i \(0.826403\pi\)
\(588\) 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 \(-0.399857\pi\)
0.309445 + 0.950917i \(0.399857\pi\)
\(594\) 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 0.991834 0.127534i \(-0.0407064\pi\)
−0.606365 + 0.795186i \(0.707373\pi\)
\(602\) 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 \(0.370513\pi\)
−0.993186 + 0.116538i \(0.962820\pi\)
\(608\) −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 0.514303 0.857609i \(-0.328051\pi\)
−0.999862 + 0.0165947i \(0.994717\pi\)
\(620\) 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 −0.576809 0.816879i \(-0.695702\pi\)
0.995842 + 0.0910922i \(0.0290358\pi\)
\(644\) 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 \(-0.608097\pi\)
−0.333108 + 0.942889i \(0.608097\pi\)
\(648\) −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 \(-0.599075\pi\)
0.977539 0.210754i \(-0.0675918\pi\)
\(662\) 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 0.774939 0.632037i \(-0.217781\pi\)
−0.934829 + 0.355098i \(0.884447\pi\)
\(678\) 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 \(0.0684159\pi\)
−0.303786 + 0.952740i \(0.598251\pi\)
\(692\) −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 \(-0.661233\pi\)
−0.485145 + 0.874434i \(0.661233\pi\)
\(720\) −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 0.853026 0.521868i \(-0.174765\pi\)
−0.878464 + 0.477809i \(0.841431\pi\)
\(728\) 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 −0.873320 0.487148i \(-0.838037\pi\)
0.858542 + 0.512743i \(0.171371\pi\)
\(734\) 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 −0.958629 0.284658i \(-0.908120\pi\)
0.725835 + 0.687868i \(0.241453\pi\)
\(762\) 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 −0.838055 0.545586i \(-0.816307\pi\)
0.891519 + 0.452984i \(0.149641\pi\)
\(770\) 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 \(-0.387301\pi\)
0.346705 + 0.937974i \(0.387301\pi\)
\(774\) 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