Properties

Label 1950.2.y.j.199.3
Level $1950$
Weight $2$
Character 1950.199
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.3
Root \(1.33404 + 1.33404i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.j.49.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-1.82233 - 3.15637i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-1.82233 - 3.15637i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.44460 - 0.834038i) q^{11} -1.00000i q^{12} +(2.82233 + 2.24376i) q^{13} +3.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} -1.00000 q^{18} +(-5.46699 + 3.15637i) q^{19} -3.64466i q^{21} +(1.44460 - 0.834038i) q^{22} +(-1.07780 - 0.622266i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.35432 + 1.32233i) q^{26} +1.00000i q^{27} +(-1.82233 + 3.15637i) q^{28} +(5.02239 - 8.69904i) q^{29} -4.21957i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.834038 - 1.44460i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-4.93211 + 8.54267i) q^{37} -6.31274i q^{38} +(1.32233 + 3.35432i) q^{39} +(8.04479 + 4.64466i) q^{41} +(3.15637 + 1.82233i) q^{42} +(-6.55829 + 3.78643i) q^{43} +1.66808i q^{44} +(1.07780 - 0.622266i) q^{46} -6.82522 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-3.14177 + 5.44171i) q^{49} -4.00000 q^{51} +(0.531987 - 3.56609i) q^{52} +0.848634i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.82233 - 3.15637i) q^{56} -6.31274 q^{57} +(5.02239 + 8.69904i) q^{58} +(-5.29034 + 3.05438i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(3.65425 + 2.10978i) q^{62} +(1.82233 - 3.15637i) q^{63} +1.00000 q^{64} +1.66808 q^{66} +(-7.37671 + 12.7768i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-0.622266 - 1.07780i) q^{69} +(-3.04056 + 1.75547i) q^{71} +(0.500000 + 0.866025i) q^{72} -12.2175 q^{73} +(-4.93211 - 8.54267i) q^{74} +(5.46699 + 3.15637i) q^{76} +6.07957i q^{77} +(-3.56609 - 0.531987i) q^{78} -9.93398 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-8.04479 + 4.64466i) q^{82} -7.95317 q^{83} +(-3.15637 + 1.82233i) q^{84} -7.57286i q^{86} +(8.69904 - 5.02239i) q^{87} +(-1.44460 - 0.834038i) q^{88} +(-5.15425 - 2.97581i) q^{89} +(1.93891 - 12.9972i) q^{91} +1.24453i q^{92} +(2.10978 - 3.65425i) q^{93} +(3.41261 - 5.91081i) q^{94} -1.00000i q^{96} +(-1.37671 - 2.38453i) q^{97} +(-3.14177 - 5.44171i) q^{98} -1.66808i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + 6q^{11} + 6q^{13} - 4q^{14} - 4q^{16} - 8q^{18} + 6q^{19} - 6q^{22} + 6q^{23} - 12q^{26} + 2q^{28} + 8q^{29} - 4q^{32} + 2q^{33} + 4q^{36} - 10q^{37} - 6q^{39} - 48q^{43} - 6q^{46} - 16q^{47} - 14q^{49} - 32q^{51} + 6q^{52} + 2q^{56} + 8q^{58} - 24q^{59} - 16q^{61} + 30q^{62} - 2q^{63} + 8q^{64} - 4q^{66} - 12q^{67} - 4q^{69} - 12q^{71} + 4q^{72} + 24q^{73} - 10q^{74} - 6q^{76} - 6q^{78} + 20q^{79} - 4q^{81} - 32q^{83} + 6q^{87} + 6q^{88} - 42q^{89} - 10q^{91} + 4q^{93} + 8q^{94} + 36q^{97} - 14q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) −1.82233 3.15637i −0.688776 1.19299i −0.972234 0.234010i \(-0.924815\pi\)
0.283458 0.958985i \(-0.408518\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.44460 0.834038i −0.435562 0.251472i 0.266151 0.963931i \(-0.414248\pi\)
−0.701713 + 0.712459i \(0.747581\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.82233 + 2.24376i 0.782773 + 0.622307i
\(14\) 3.64466 0.974076
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.46410 + 2.00000i −0.840168 + 0.485071i −0.857321 0.514782i \(-0.827873\pi\)
0.0171533 + 0.999853i \(0.494540\pi\)
\(18\) −1.00000 −0.235702
\(19\) −5.46699 + 3.15637i −1.25421 + 0.724120i −0.971943 0.235215i \(-0.924421\pi\)
−0.282270 + 0.959335i \(0.591087\pi\)
\(20\) 0 0
\(21\) 3.64466i 0.795330i
\(22\) 1.44460 0.834038i 0.307989 0.177817i
\(23\) −1.07780 0.622266i −0.224736 0.129752i 0.383405 0.923580i \(-0.374751\pi\)
−0.608141 + 0.793829i \(0.708085\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −3.35432 + 1.32233i −0.657836 + 0.259330i
\(27\) 1.00000i 0.192450i
\(28\) −1.82233 + 3.15637i −0.344388 + 0.596497i
\(29\) 5.02239 8.69904i 0.932635 1.61537i 0.153837 0.988096i \(-0.450837\pi\)
0.778798 0.627275i \(-0.215830\pi\)
\(30\) 0 0
\(31\) 4.21957i 0.757857i −0.925426 0.378928i \(-0.876293\pi\)
0.925426 0.378928i \(-0.123707\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.834038 1.44460i −0.145187 0.251472i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −4.93211 + 8.54267i −0.810835 + 1.40441i 0.101446 + 0.994841i \(0.467653\pi\)
−0.912281 + 0.409566i \(0.865680\pi\)
\(38\) 6.31274i 1.02406i
\(39\) 1.32233 + 3.35432i 0.211742 + 0.537121i
\(40\) 0 0
\(41\) 8.04479 + 4.64466i 1.25638 + 0.725374i 0.972370 0.233446i \(-0.0750002\pi\)
0.284015 + 0.958820i \(0.408334\pi\)
\(42\) 3.15637 + 1.82233i 0.487038 + 0.281192i
\(43\) −6.55829 + 3.78643i −1.00013 + 0.577425i −0.908287 0.418348i \(-0.862609\pi\)
−0.0918433 + 0.995773i \(0.529276\pi\)
\(44\) 1.66808i 0.251472i
\(45\) 0 0
\(46\) 1.07780 0.622266i 0.158912 0.0917482i
\(47\) −6.82522 −0.995560 −0.497780 0.867303i \(-0.665851\pi\)
−0.497780 + 0.867303i \(0.665851\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) −3.14177 + 5.44171i −0.448825 + 0.777387i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 0.531987 3.56609i 0.0737734 0.494528i
\(53\) 0.848634i 0.116569i 0.998300 + 0.0582844i \(0.0185630\pi\)
−0.998300 + 0.0582844i \(0.981437\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0 0
\(56\) −1.82233 3.15637i −0.243519 0.421787i
\(57\) −6.31274 −0.836142
\(58\) 5.02239 + 8.69904i 0.659473 + 1.14224i
\(59\) −5.29034 + 3.05438i −0.688744 + 0.397646i −0.803141 0.595789i \(-0.796840\pi\)
0.114397 + 0.993435i \(0.463506\pi\)
\(60\) 0 0
\(61\) −3.73205 6.46410i −0.477840 0.827643i 0.521837 0.853045i \(-0.325247\pi\)
−0.999677 + 0.0254017i \(0.991914\pi\)
\(62\) 3.65425 + 2.10978i 0.464091 + 0.267943i
\(63\) 1.82233 3.15637i 0.229592 0.397665i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.66808 0.205326
\(67\) −7.37671 + 12.7768i −0.901209 + 1.56094i −0.0752814 + 0.997162i \(0.523986\pi\)
−0.825927 + 0.563777i \(0.809348\pi\)
\(68\) 3.46410 + 2.00000i 0.420084 + 0.242536i
\(69\) −0.622266 1.07780i −0.0749121 0.129752i
\(70\) 0 0
\(71\) −3.04056 + 1.75547i −0.360848 + 0.208336i −0.669453 0.742855i \(-0.733471\pi\)
0.308605 + 0.951190i \(0.400138\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −12.2175 −1.42995 −0.714976 0.699149i \(-0.753563\pi\)
−0.714976 + 0.699149i \(0.753563\pi\)
\(74\) −4.93211 8.54267i −0.573347 0.993065i
\(75\) 0 0
\(76\) 5.46699 + 3.15637i 0.627107 + 0.362060i
\(77\) 6.07957i 0.692831i
\(78\) −3.56609 0.531987i −0.403780 0.0602357i
\(79\) −9.93398 −1.11766 −0.558830 0.829282i \(-0.688750\pi\)
−0.558830 + 0.829282i \(0.688750\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −8.04479 + 4.64466i −0.888398 + 0.512917i
\(83\) −7.95317 −0.872974 −0.436487 0.899711i \(-0.643777\pi\)
−0.436487 + 0.899711i \(0.643777\pi\)
\(84\) −3.15637 + 1.82233i −0.344388 + 0.198832i
\(85\) 0 0
\(86\) 7.57286i 0.816603i
\(87\) 8.69904 5.02239i 0.932635 0.538457i
\(88\) −1.44460 0.834038i −0.153994 0.0889087i
\(89\) −5.15425 2.97581i −0.546350 0.315435i 0.201299 0.979530i \(-0.435484\pi\)
−0.747648 + 0.664095i \(0.768817\pi\)
\(90\) 0 0
\(91\) 1.93891 12.9972i 0.203253 1.36247i
\(92\) 1.24453i 0.129752i
\(93\) 2.10978 3.65425i 0.218774 0.378928i
\(94\) 3.41261 5.91081i 0.351984 0.609654i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −1.37671 2.38453i −0.139784 0.242113i 0.787631 0.616147i \(-0.211307\pi\)
−0.927415 + 0.374035i \(0.877974\pi\)
\(98\) −3.14177 5.44171i −0.317367 0.549696i
\(99\) 1.66808i 0.167648i
\(100\) 0 0
\(101\) 2.66808 4.62124i 0.265483 0.459831i −0.702207 0.711973i \(-0.747802\pi\)
0.967690 + 0.252142i \(0.0811351\pi\)
\(102\) 2.00000 3.46410i 0.198030 0.342997i
\(103\) 7.51248i 0.740227i 0.928987 + 0.370113i \(0.120681\pi\)
−0.928987 + 0.370113i \(0.879319\pi\)
\(104\) 2.82233 + 2.24376i 0.276752 + 0.220019i
\(105\) 0 0
\(106\) −0.734939 0.424317i −0.0713835 0.0412133i
\(107\) −14.6603 8.46410i −1.41726 0.818256i −0.421203 0.906966i \(-0.638392\pi\)
−0.996057 + 0.0887109i \(0.971725\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 0.663848i 0.0635851i 0.999494 + 0.0317926i \(0.0101216\pi\)
−0.999494 + 0.0317926i \(0.989878\pi\)
\(110\) 0 0
\(111\) −8.54267 + 4.93211i −0.810835 + 0.468136i
\(112\) 3.64466 0.344388
\(113\) 15.4759 8.93500i 1.45585 0.840534i 0.457045 0.889444i \(-0.348908\pi\)
0.998803 + 0.0489094i \(0.0155745\pi\)
\(114\) 3.15637 5.46699i 0.295621 0.512030i
\(115\) 0 0
\(116\) −10.0448 −0.932635
\(117\) −0.531987 + 3.56609i −0.0491823 + 0.329685i
\(118\) 6.10876i 0.562357i
\(119\) 12.6255 + 7.28932i 1.15738 + 0.668211i
\(120\) 0 0
\(121\) −4.10876 7.11658i −0.373524 0.646962i
\(122\) 7.46410 0.675768
\(123\) 4.64466 + 8.04479i 0.418795 + 0.725374i
\(124\) −3.65425 + 2.10978i −0.328162 + 0.189464i
\(125\) 0 0
\(126\) 1.82233 + 3.15637i 0.162346 + 0.281192i
\(127\) 12.5060 + 7.22034i 1.10973 + 0.640702i 0.938759 0.344575i \(-0.111977\pi\)
0.170969 + 0.985276i \(0.445310\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −7.57286 −0.666753
\(130\) 0 0
\(131\) −10.8892 −0.951393 −0.475697 0.879609i \(-0.657804\pi\)
−0.475697 + 0.879609i \(0.657804\pi\)
\(132\) −0.834038 + 1.44460i −0.0725937 + 0.125736i
\(133\) 19.9253 + 11.5039i 1.72774 + 0.997513i
\(134\) −7.37671 12.7768i −0.637251 1.10375i
\(135\) 0 0
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) 3.51848 + 6.09419i 0.300604 + 0.520662i 0.976273 0.216544i \(-0.0694783\pi\)
−0.675669 + 0.737205i \(0.736145\pi\)
\(138\) 1.24453 0.105942
\(139\) 5.82233 + 10.0846i 0.493844 + 0.855362i 0.999975 0.00709431i \(-0.00225821\pi\)
−0.506131 + 0.862456i \(0.668925\pi\)
\(140\) 0 0
\(141\) −5.91081 3.41261i −0.497780 0.287394i
\(142\) 3.51093i 0.294631i
\(143\) −2.20575 5.59526i −0.184454 0.467899i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 6.10876 10.5807i 0.505565 0.875664i
\(147\) −5.44171 + 3.14177i −0.448825 + 0.259129i
\(148\) 9.86423 0.810835
\(149\) 0.669099 0.386305i 0.0548147 0.0316473i −0.472342 0.881415i \(-0.656591\pi\)
0.527157 + 0.849768i \(0.323258\pi\)
\(150\) 0 0
\(151\) 9.77838i 0.795754i 0.917439 + 0.397877i \(0.130253\pi\)
−0.917439 + 0.397877i \(0.869747\pi\)
\(152\) −5.46699 + 3.15637i −0.443431 + 0.256015i
\(153\) −3.46410 2.00000i −0.280056 0.161690i
\(154\) −5.26506 3.03978i −0.424271 0.244953i
\(155\) 0 0
\(156\) 2.24376 2.82233i 0.179644 0.225967i
\(157\) 12.0135i 0.958786i −0.877600 0.479393i \(-0.840857\pi\)
0.877600 0.479393i \(-0.159143\pi\)
\(158\) 4.96699 8.60308i 0.395152 0.684424i
\(159\) −0.424317 + 0.734939i −0.0336505 + 0.0582844i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 5.04581 + 8.73960i 0.395218 + 0.684538i 0.993129 0.117025i \(-0.0373356\pi\)
−0.597911 + 0.801563i \(0.704002\pi\)
\(164\) 9.28932i 0.725374i
\(165\) 0 0
\(166\) 3.97658 6.88764i 0.308643 0.534585i
\(167\) 3.94851 6.83902i 0.305545 0.529219i −0.671838 0.740698i \(-0.734495\pi\)
0.977382 + 0.211479i \(0.0678281\pi\)
\(168\) 3.64466i 0.281192i
\(169\) 2.93109 + 12.6653i 0.225469 + 0.974250i
\(170\) 0 0
\(171\) −5.46699 3.15637i −0.418071 0.241373i
\(172\) 6.55829 + 3.78643i 0.500065 + 0.288713i
\(173\) −0.381645 + 0.220343i −0.0290159 + 0.0167523i −0.514438 0.857528i \(-0.671999\pi\)
0.485422 + 0.874280i \(0.338666\pi\)
\(174\) 10.0448i 0.761493i
\(175\) 0 0
\(176\) 1.44460 0.834038i 0.108891 0.0628680i
\(177\) −6.10876 −0.459163
\(178\) 5.15425 2.97581i 0.386328 0.223046i
\(179\) 9.81842 17.0060i 0.733863 1.27109i −0.221357 0.975193i \(-0.571049\pi\)
0.955220 0.295895i \(-0.0956180\pi\)
\(180\) 0 0
\(181\) 6.21752 0.462145 0.231072 0.972937i \(-0.425777\pi\)
0.231072 + 0.972937i \(0.425777\pi\)
\(182\) 10.2864 + 8.17774i 0.762481 + 0.606174i
\(183\) 7.46410i 0.551762i
\(184\) −1.07780 0.622266i −0.0794562 0.0458741i
\(185\) 0 0
\(186\) 2.10978 + 3.65425i 0.154697 + 0.267943i
\(187\) 6.67230 0.487927
\(188\) 3.41261 + 5.91081i 0.248890 + 0.431090i
\(189\) 3.15637 1.82233i 0.229592 0.132555i
\(190\) 0 0
\(191\) −7.84081 13.5807i −0.567341 0.982664i −0.996828 0.0795905i \(-0.974639\pi\)
0.429486 0.903073i \(-0.358695\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 4.06397 7.03901i 0.292531 0.506679i −0.681876 0.731468i \(-0.738836\pi\)
0.974408 + 0.224788i \(0.0721691\pi\)
\(194\) 2.75342 0.197684
\(195\) 0 0
\(196\) 6.28354 0.448825
\(197\) −0.445619 + 0.771835i −0.0317491 + 0.0549910i −0.881463 0.472252i \(-0.843441\pi\)
0.849714 + 0.527243i \(0.176774\pi\)
\(198\) 1.44460 + 0.834038i 0.102663 + 0.0592725i
\(199\) −0.180558 0.312736i −0.0127994 0.0221692i 0.859555 0.511044i \(-0.170741\pi\)
−0.872354 + 0.488874i \(0.837408\pi\)
\(200\) 0 0
\(201\) −12.7768 + 7.37671i −0.901209 + 0.520313i
\(202\) 2.66808 + 4.62124i 0.187725 + 0.325150i
\(203\) −36.6098 −2.56951
\(204\) 2.00000 + 3.46410i 0.140028 + 0.242536i
\(205\) 0 0
\(206\) −6.50600 3.75624i −0.453295 0.261710i
\(207\) 1.24453i 0.0865010i
\(208\) −3.35432 + 1.32233i −0.232580 + 0.0916871i
\(209\) 10.5301 0.728384
\(210\) 0 0
\(211\) −1.11370 + 1.92898i −0.0766700 + 0.132796i −0.901811 0.432130i \(-0.857762\pi\)
0.825141 + 0.564926i \(0.191095\pi\)
\(212\) 0.734939 0.424317i 0.0504758 0.0291422i
\(213\) −3.51093 −0.240565
\(214\) 14.6603 8.46410i 1.00215 0.578594i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −13.3185 + 7.68945i −0.904119 + 0.521994i
\(218\) −0.574909 0.331924i −0.0389378 0.0224807i
\(219\) −10.5807 6.10876i −0.714976 0.412792i
\(220\) 0 0
\(221\) −14.2644 2.12795i −0.959524 0.143141i
\(222\) 9.86423i 0.662044i
\(223\) 3.04190 5.26872i 0.203701 0.352820i −0.746017 0.665927i \(-0.768036\pi\)
0.949718 + 0.313107i \(0.101370\pi\)
\(224\) −1.82233 + 3.15637i −0.121760 + 0.210894i
\(225\) 0 0
\(226\) 17.8700i 1.18869i
\(227\) −7.66025 13.2679i −0.508429 0.880625i −0.999952 0.00976038i \(-0.996893\pi\)
0.491523 0.870864i \(-0.336440\pi\)
\(228\) 3.15637 + 5.46699i 0.209036 + 0.362060i
\(229\) 22.2644i 1.47127i −0.677378 0.735635i \(-0.736884\pi\)
0.677378 0.735635i \(-0.263116\pi\)
\(230\) 0 0
\(231\) −3.03978 + 5.26506i −0.200003 + 0.346416i
\(232\) 5.02239 8.69904i 0.329736 0.571120i
\(233\) 10.8366i 0.709928i −0.934880 0.354964i \(-0.884493\pi\)
0.934880 0.354964i \(-0.115507\pi\)
\(234\) −2.82233 2.24376i −0.184501 0.146679i
\(235\) 0 0
\(236\) 5.29034 + 3.05438i 0.344372 + 0.198823i
\(237\) −8.60308 4.96699i −0.558830 0.322641i
\(238\) −12.6255 + 7.28932i −0.818388 + 0.472496i
\(239\) 16.4975i 1.06714i 0.845757 + 0.533568i \(0.179149\pi\)
−0.845757 + 0.533568i \(0.820851\pi\)
\(240\) 0 0
\(241\) 3.81428 2.20218i 0.245700 0.141855i −0.372094 0.928195i \(-0.621360\pi\)
0.617794 + 0.786340i \(0.288027\pi\)
\(242\) 8.21752 0.528242
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −3.73205 + 6.46410i −0.238920 + 0.413822i
\(245\) 0 0
\(246\) −9.28932 −0.592265
\(247\) −22.5118 3.35830i −1.43239 0.213683i
\(248\) 4.21957i 0.267943i
\(249\) −6.88764 3.97658i −0.436487 0.252006i
\(250\) 0 0
\(251\) 5.97267 + 10.3450i 0.376992 + 0.652969i 0.990623 0.136624i \(-0.0436252\pi\)
−0.613631 + 0.789593i \(0.710292\pi\)
\(252\) −3.64466 −0.229592
\(253\) 1.03799 + 1.79785i 0.0652577 + 0.113030i
\(254\) −12.5060 + 7.22034i −0.784696 + 0.453045i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 16.8546 + 9.73103i 1.05136 + 0.607005i 0.923031 0.384726i \(-0.125704\pi\)
0.128333 + 0.991731i \(0.459038\pi\)
\(258\) 3.78643 6.55829i 0.235733 0.408301i
\(259\) 35.9518 2.23393
\(260\) 0 0
\(261\) 10.0448 0.621757
\(262\) 5.44460 9.43032i 0.336368 0.582607i
\(263\) 1.76217 + 1.01739i 0.108660 + 0.0627350i 0.553345 0.832952i \(-0.313351\pi\)
−0.444685 + 0.895687i \(0.646684\pi\)
\(264\) −0.834038 1.44460i −0.0513315 0.0889087i
\(265\) 0 0
\(266\) −19.9253 + 11.5039i −1.22170 + 0.705349i
\(267\) −2.97581 5.15425i −0.182117 0.315435i
\(268\) 14.7534 0.901209
\(269\) 10.2644 + 17.7784i 0.625829 + 1.08397i 0.988380 + 0.152003i \(0.0485725\pi\)
−0.362551 + 0.931964i \(0.618094\pi\)
\(270\) 0 0
\(271\) 22.1184 + 12.7700i 1.34359 + 0.775725i 0.987333 0.158662i \(-0.0507179\pi\)
0.356261 + 0.934386i \(0.384051\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 8.17774 10.2864i 0.494939 0.622563i
\(274\) −7.03696 −0.425119
\(275\) 0 0
\(276\) −0.622266 + 1.07780i −0.0374560 + 0.0648758i
\(277\) −15.6407 + 9.03019i −0.939762 + 0.542572i −0.889886 0.456184i \(-0.849216\pi\)
−0.0498760 + 0.998755i \(0.515883\pi\)
\(278\) −11.6447 −0.698400
\(279\) 3.65425 2.10978i 0.218774 0.126309i
\(280\) 0 0
\(281\) 20.2175i 1.20608i −0.797712 0.603038i \(-0.793957\pi\)
0.797712 0.603038i \(-0.206043\pi\)
\(282\) 5.91081 3.41261i 0.351984 0.203218i
\(283\) −7.52705 4.34575i −0.447437 0.258328i 0.259310 0.965794i \(-0.416505\pi\)
−0.706747 + 0.707466i \(0.749838\pi\)
\(284\) 3.04056 + 1.75547i 0.180424 + 0.104168i
\(285\) 0 0
\(286\) 5.94851 + 0.887395i 0.351743 + 0.0524728i
\(287\) 33.8564i 1.99848i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 2.75342i 0.161408i
\(292\) 6.10876 + 10.5807i 0.357488 + 0.619188i
\(293\) −3.77395 6.53667i −0.220476 0.381876i 0.734476 0.678634i \(-0.237428\pi\)
−0.954953 + 0.296758i \(0.904095\pi\)
\(294\) 6.28354i 0.366464i
\(295\) 0 0
\(296\) −4.93211 + 8.54267i −0.286673 + 0.496533i
\(297\) 0.834038 1.44460i 0.0483958 0.0838240i
\(298\) 0.772609i 0.0447560i
\(299\) −1.64568 4.17456i −0.0951723 0.241421i
\(300\) 0 0
\(301\) 23.9027 + 13.8003i 1.37773 + 0.795433i
\(302\) −8.46833 4.88919i −0.487298 0.281341i
\(303\) 4.62124 2.66808i 0.265483 0.153277i
\(304\) 6.31274i 0.362060i
\(305\) 0 0
\(306\) 3.46410 2.00000i 0.198030 0.114332i
\(307\) 26.0427 1.48634 0.743169 0.669104i \(-0.233322\pi\)
0.743169 + 0.669104i \(0.233322\pi\)
\(308\) 5.26506 3.03978i 0.300005 0.173208i
\(309\) −3.75624 + 6.50600i −0.213685 + 0.370113i
\(310\) 0 0
\(311\) 25.3789 1.43910 0.719552 0.694438i \(-0.244347\pi\)
0.719552 + 0.694438i \(0.244347\pi\)
\(312\) 1.32233 + 3.35432i 0.0748622 + 0.189901i
\(313\) 31.4600i 1.77822i 0.457689 + 0.889112i \(0.348677\pi\)
−0.457689 + 0.889112i \(0.651323\pi\)
\(314\) 10.4040 + 6.00677i 0.587134 + 0.338982i
\(315\) 0 0
\(316\) 4.96699 + 8.60308i 0.279415 + 0.483961i
\(317\) −24.7093 −1.38781 −0.693905 0.720066i \(-0.744111\pi\)
−0.693905 + 0.720066i \(0.744111\pi\)
\(318\) −0.424317 0.734939i −0.0237945 0.0412133i
\(319\) −14.5107 + 8.37773i −0.812441 + 0.469063i
\(320\) 0 0
\(321\) −8.46410 14.6603i −0.472420 0.818256i
\(322\) −3.92820 2.26795i −0.218910 0.126388i
\(323\) 12.6255 21.8680i 0.702500 1.21677i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −10.0916 −0.558923
\(327\) −0.331924 + 0.574909i −0.0183554 + 0.0317926i
\(328\) 8.04479 + 4.64466i 0.444199 + 0.256458i
\(329\) 12.4378 + 21.5429i 0.685718 + 1.18770i
\(330\) 0 0
\(331\) −4.85286 + 2.80180i −0.266737 + 0.154001i −0.627404 0.778694i \(-0.715883\pi\)
0.360667 + 0.932695i \(0.382549\pi\)
\(332\) 3.97658 + 6.88764i 0.218243 + 0.378009i
\(333\) −9.86423 −0.540556
\(334\) 3.94851 + 6.83902i 0.216053 + 0.374214i
\(335\) 0 0
\(336\) 3.15637 + 1.82233i 0.172194 + 0.0994162i
\(337\) 21.7868i 1.18680i 0.804906 + 0.593402i \(0.202216\pi\)
−0.804906 + 0.593402i \(0.797784\pi\)
\(338\) −12.4340 3.79423i −0.676319 0.206379i
\(339\) 17.8700 0.970565
\(340\) 0 0
\(341\) −3.51928 + 6.09557i −0.190580 + 0.330094i
\(342\) 5.46699 3.15637i 0.295621 0.170677i
\(343\) −2.61124 −0.140994
\(344\) −6.55829 + 3.78643i −0.353599 + 0.204151i
\(345\) 0 0
\(346\) 0.440685i 0.0236914i
\(347\) 8.38453 4.84081i 0.450105 0.259868i −0.257769 0.966206i \(-0.582987\pi\)
0.707875 + 0.706338i \(0.249654\pi\)
\(348\) −8.69904 5.02239i −0.466318 0.269229i
\(349\) −16.7321 9.66025i −0.895646 0.517102i −0.0198610 0.999803i \(-0.506322\pi\)
−0.875785 + 0.482701i \(0.839656\pi\)
\(350\) 0 0
\(351\) −2.24376 + 2.82233i −0.119763 + 0.150645i
\(352\) 1.66808i 0.0889087i
\(353\) −11.4875 + 19.8970i −0.611419 + 1.05901i 0.379583 + 0.925158i \(0.376068\pi\)
−0.991002 + 0.133851i \(0.957266\pi\)
\(354\) 3.05438 5.29034i 0.162338 0.281179i
\(355\) 0 0
\(356\) 5.95162i 0.315435i
\(357\) 7.28932 + 12.6255i 0.385792 + 0.668211i
\(358\) 9.81842 + 17.0060i 0.518920 + 0.898795i
\(359\) 2.21752i 0.117036i −0.998286 0.0585182i \(-0.981362\pi\)
0.998286 0.0585182i \(-0.0186376\pi\)
\(360\) 0 0
\(361\) 10.4253 18.0572i 0.548701 0.950378i
\(362\) −3.10876 + 5.38453i −0.163393 + 0.283005i
\(363\) 8.21752i 0.431308i
\(364\) −12.2253 + 4.81944i −0.640782 + 0.252607i
\(365\) 0 0
\(366\) 6.46410 + 3.73205i 0.337884 + 0.195077i
\(367\) 5.26640 + 3.04056i 0.274904 + 0.158716i 0.631114 0.775690i \(-0.282598\pi\)
−0.356210 + 0.934406i \(0.615931\pi\)
\(368\) 1.07780 0.622266i 0.0561841 0.0324379i
\(369\) 9.28932i 0.483583i
\(370\) 0 0
\(371\) 2.67860 1.54649i 0.139066 0.0802898i
\(372\) −4.21957 −0.218774
\(373\) −13.5776 + 7.83904i −0.703022 + 0.405890i −0.808472 0.588535i \(-0.799705\pi\)
0.105450 + 0.994425i \(0.466372\pi\)
\(374\) −3.33615 + 5.77838i −0.172508 + 0.298793i
\(375\) 0 0
\(376\) −6.82522 −0.351984
\(377\) 33.6934 13.2825i 1.73530 0.684085i
\(378\) 3.64466i 0.187461i
\(379\) −26.6013 15.3583i −1.36642 0.788903i −0.375951 0.926640i \(-0.622684\pi\)
−0.990469 + 0.137737i \(0.956017\pi\)
\(380\) 0 0
\(381\) 7.22034 + 12.5060i 0.369909 + 0.640702i
\(382\) 15.6816 0.802342
\(383\) −10.0310 17.3741i −0.512558 0.887777i −0.999894 0.0145623i \(-0.995365\pi\)
0.487336 0.873215i \(-0.337969\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 4.06397 + 7.03901i 0.206851 + 0.358276i
\(387\) −6.55829 3.78643i −0.333377 0.192475i
\(388\) −1.37671 + 2.38453i −0.0698919 + 0.121056i
\(389\) −27.0314 −1.37055 −0.685273 0.728287i \(-0.740317\pi\)
−0.685273 + 0.728287i \(0.740317\pi\)
\(390\) 0 0
\(391\) 4.97813 0.251755
\(392\) −3.14177 + 5.44171i −0.158683 + 0.274848i
\(393\) −9.43032 5.44460i −0.475697 0.274644i
\(394\) −0.445619 0.771835i −0.0224500 0.0388845i
\(395\) 0 0
\(396\) −1.44460 + 0.834038i −0.0725937 + 0.0419120i
\(397\) −1.86814 3.23571i −0.0937592 0.162396i 0.815331 0.578995i \(-0.196555\pi\)
−0.909090 + 0.416600i \(0.863222\pi\)
\(398\) 0.361116 0.0181011
\(399\) 11.5039 + 19.9253i 0.575915 + 0.997513i
\(400\) 0 0
\(401\) 24.3276 + 14.0456i 1.21486 + 0.701402i 0.963815 0.266573i \(-0.0858912\pi\)
0.251049 + 0.967974i \(0.419225\pi\)
\(402\) 14.7534i 0.735834i
\(403\) 9.46770 11.9090i 0.471620 0.593230i
\(404\) −5.33615 −0.265483
\(405\) 0 0
\(406\) 18.3049 31.7050i 0.908458 1.57349i
\(407\) 14.2498 8.22714i 0.706338 0.407804i
\(408\) −4.00000 −0.198030
\(409\) −23.7122 + 13.6902i −1.17249 + 0.676938i −0.954265 0.298961i \(-0.903360\pi\)
−0.218225 + 0.975898i \(0.570027\pi\)
\(410\) 0 0
\(411\) 7.03696i 0.347108i
\(412\) 6.50600 3.75624i 0.320528 0.185057i
\(413\) 19.2815 + 11.1322i 0.948780 + 0.547779i
\(414\) 1.07780 + 0.622266i 0.0529708 + 0.0305827i
\(415\) 0 0
\(416\) 0.531987 3.56609i 0.0260828 0.174842i
\(417\) 11.6447i 0.570241i
\(418\) −5.26506 + 9.11935i −0.257523 + 0.446042i
\(419\) −6.58068 + 11.3981i −0.321487 + 0.556833i −0.980795 0.195041i \(-0.937516\pi\)
0.659308 + 0.751873i \(0.270849\pi\)
\(420\) 0 0
\(421\) 1.29341i 0.0630370i 0.999503 + 0.0315185i \(0.0100343\pi\)
−0.999503 + 0.0315185i \(0.989966\pi\)
\(422\) −1.11370 1.92898i −0.0542138 0.0939011i
\(423\) −3.41261 5.91081i −0.165927 0.287394i
\(424\) 0.848634i 0.0412133i
\(425\) 0 0
\(426\) 1.75547 3.04056i 0.0850527 0.147316i
\(427\) −13.6021 + 23.5595i −0.658250 + 1.14012i
\(428\) 16.9282i 0.818256i
\(429\) 0.887395 5.94851i 0.0428439 0.287197i
\(430\) 0 0
\(431\) 10.5031 + 6.06397i 0.505917 + 0.292091i 0.731154 0.682213i \(-0.238982\pi\)
−0.225237 + 0.974304i \(0.572316\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) −1.79962 + 1.03901i −0.0864842 + 0.0499317i −0.542618 0.839979i \(-0.682567\pi\)
0.456134 + 0.889911i \(0.349234\pi\)
\(434\) 15.3789i 0.738210i
\(435\) 0 0
\(436\) 0.574909 0.331924i 0.0275332 0.0158963i
\(437\) 7.85641 0.375823
\(438\) 10.5807 6.10876i 0.505565 0.291888i
\(439\) 1.19820 2.07534i 0.0571869 0.0990506i −0.836015 0.548707i \(-0.815120\pi\)
0.893202 + 0.449656i \(0.148454\pi\)
\(440\) 0 0
\(441\) −6.28354 −0.299216
\(442\) 8.97504 11.2893i 0.426899 0.536978i
\(443\) 21.9959i 1.04506i −0.852622 0.522529i \(-0.824989\pi\)
0.852622 0.522529i \(-0.175011\pi\)
\(444\) 8.54267 + 4.93211i 0.405417 + 0.234068i
\(445\) 0 0
\(446\) 3.04190 + 5.26872i 0.144038 + 0.249481i
\(447\) 0.772609 0.0365432
\(448\) −1.82233 3.15637i −0.0860970 0.149124i
\(449\) −25.3098 + 14.6126i −1.19445 + 0.689613i −0.959312 0.282350i \(-0.908886\pi\)
−0.235134 + 0.971963i \(0.575553\pi\)
\(450\) 0 0
\(451\) −7.74765 13.4193i −0.364822 0.631891i
\(452\) −15.4759 8.93500i −0.727924 0.420267i
\(453\) −4.88919 + 8.46833i −0.229714 + 0.397877i
\(454\) 15.3205 0.719027
\(455\) 0 0
\(456\) −6.31274 −0.295621
\(457\) 19.8216 34.3321i 0.927216 1.60599i 0.139259 0.990256i \(-0.455528\pi\)
0.787957 0.615730i \(-0.211139\pi\)
\(458\) 19.2815 + 11.1322i 0.900965 + 0.520172i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) 14.4417 8.33792i 0.672617 0.388336i −0.124450 0.992226i \(-0.539717\pi\)
0.797068 + 0.603890i \(0.206383\pi\)
\(462\) −3.03978 5.26506i −0.141424 0.244953i
\(463\) −32.2175 −1.49728 −0.748638 0.662979i \(-0.769292\pi\)
−0.748638 + 0.662979i \(0.769292\pi\)
\(464\) 5.02239 + 8.69904i 0.233159 + 0.403843i
\(465\) 0 0
\(466\) 9.38476 + 5.41829i 0.434740 + 0.250998i
\(467\) 6.88137i 0.318432i −0.987244 0.159216i \(-0.949103\pi\)
0.987244 0.159216i \(-0.0508966\pi\)
\(468\) 3.35432 1.32233i 0.155053 0.0611247i
\(469\) 53.7712 2.48292
\(470\) 0 0
\(471\) 6.00677 10.4040i 0.276778 0.479393i
\(472\) −5.29034 + 3.05438i −0.243508 + 0.140589i
\(473\) 12.6321 0.580825
\(474\) 8.60308 4.96699i 0.395152 0.228141i
\(475\) 0 0
\(476\) 14.5786i 0.668211i
\(477\) −0.734939 + 0.424317i −0.0336505 + 0.0194281i
\(478\) −14.2873 8.24876i −0.653485 0.377290i
\(479\) 16.4293 + 9.48547i 0.750675 + 0.433402i 0.825938 0.563761i \(-0.190646\pi\)
−0.0752629 + 0.997164i \(0.523980\pi\)
\(480\) 0 0
\(481\) −33.0878 + 13.0438i −1.50867 + 0.594744i
\(482\) 4.40435i 0.200613i
\(483\) −2.26795 + 3.92820i −0.103195 + 0.178739i
\(484\) −4.10876 + 7.11658i −0.186762 + 0.323481i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 0.958101 + 1.65948i 0.0434157 + 0.0751982i 0.886917 0.461929i \(-0.152843\pi\)
−0.843501 + 0.537128i \(0.819509\pi\)
\(488\) −3.73205 6.46410i −0.168942 0.292616i
\(489\) 10.0916i 0.456359i
\(490\) 0 0
\(491\) −16.8187 + 29.1309i −0.759019 + 1.31466i 0.184332 + 0.982864i \(0.440988\pi\)
−0.943351 + 0.331795i \(0.892346\pi\)
\(492\) 4.64466 8.04479i 0.209397 0.362687i
\(493\) 40.1791i 1.80958i
\(494\) 14.1643 17.8166i 0.637280 0.801608i
\(495\) 0 0
\(496\) 3.65425 + 2.10978i 0.164081 + 0.0947321i
\(497\) 11.0818 + 6.39808i 0.497087 + 0.286993i
\(498\) 6.88764 3.97658i 0.308643 0.178195i
\(499\) 1.82522i 0.0817080i −0.999165 0.0408540i \(-0.986992\pi\)
0.999165 0.0408540i \(-0.0130078\pi\)
\(500\) 0 0
\(501\) 6.83902 3.94851i 0.305545 0.176406i
\(502\) −11.9453 −0.533147
\(503\) 17.3192 9.99923i 0.772224 0.445843i −0.0614437 0.998111i \(-0.519570\pi\)
0.833667 + 0.552267i \(0.186237\pi\)
\(504\) 1.82233 3.15637i 0.0811730 0.140596i
\(505\) 0 0
\(506\) −2.07598 −0.0922884
\(507\) −3.79423 + 12.4340i −0.168508 + 0.552212i
\(508\) 14.4407i 0.640702i
\(509\) −5.10196 2.94562i −0.226141 0.130562i 0.382650 0.923893i \(-0.375012\pi\)
−0.608790 + 0.793331i \(0.708345\pi\)
\(510\) 0 0
\(511\) 22.2644 + 38.5630i 0.984917 + 1.70593i
\(512\) 1.00000 0.0441942
\(513\) −3.15637 5.46699i −0.139357 0.241373i
\(514\) −16.8546 + 9.73103i −0.743426 + 0.429217i
\(515\) 0 0
\(516\) 3.78643 + 6.55829i 0.166688 + 0.288713i
\(517\) 9.85968 + 5.69249i 0.433628 + 0.250355i
\(518\) −17.9759 + 31.1351i −0.789815 + 1.36800i
\(519\) −0.440685 −0.0193439
\(520\) 0 0
\(521\) 32.0370 1.40356 0.701782 0.712391i \(-0.252388\pi\)
0.701782 + 0.712391i \(0.252388\pi\)
\(522\) −5.02239 + 8.69904i −0.219824 + 0.380747i
\(523\) 33.5313 + 19.3593i 1.46622 + 0.846523i 0.999286 0.0377693i \(-0.0120252\pi\)
0.466934 + 0.884292i \(0.345359\pi\)
\(524\) 5.44460 + 9.43032i 0.237848 + 0.411965i
\(525\) 0 0
\(526\) −1.76217 + 1.01739i −0.0768344 + 0.0443604i
\(527\) 8.43914 + 14.6170i 0.367615 + 0.636727i
\(528\) 1.66808 0.0725937
\(529\) −10.7256 18.5772i −0.466329 0.807706i
\(530\) 0 0
\(531\) −5.29034 3.05438i −0.229581 0.132549i
\(532\) 23.0078i 0.997513i
\(533\) 12.2835 + 31.1593i 0.532059 + 1.34966i
\(534\) 5.95162 0.257552
\(535\) 0 0
\(536\) −7.37671 + 12.7768i −0.318625 + 0.551875i
\(537\) 17.0060 9.81842i 0.733863 0.423696i
\(538\) −20.5287 −0.885056
\(539\) 9.07718 5.24071i 0.390982 0.225734i
\(540\) 0 0
\(541\) 25.9616i 1.11618i 0.829781 + 0.558089i \(0.188465\pi\)
−0.829781 + 0.558089i \(0.811535\pi\)
\(542\) −22.1184 + 12.7700i −0.950065 + 0.548520i
\(543\) 5.38453 + 3.10876i 0.231072 + 0.133410i
\(544\) 3.46410 + 2.00000i 0.148522 + 0.0857493i
\(545\) 0 0
\(546\) 4.81944 + 12.2253i 0.206253 + 0.523196i
\(547\) 17.7596i 0.759348i −0.925120 0.379674i \(-0.876036\pi\)
0.925120 0.379674i \(-0.123964\pi\)
\(548\) 3.51848 6.09419i 0.150302 0.260331i
\(549\) 3.73205 6.46410i 0.159280 0.275881i
\(550\) 0 0
\(551\) 63.4101i 2.70136i
\(552\) −0.622266 1.07780i −0.0264854 0.0458741i
\(553\) 18.1030 + 31.3553i 0.769817 + 1.33336i
\(554\) 18.0604i 0.767312i
\(555\) 0 0
\(556\) 5.82233 10.0846i 0.246922 0.427681i
\(557\) 13.1101 22.7074i 0.555493 0.962142i −0.442372 0.896832i \(-0.645863\pi\)
0.997865 0.0653102i \(-0.0208037\pi\)
\(558\) 4.21957i 0.178629i
\(559\) −27.0055 4.02867i −1.14221 0.170394i
\(560\) 0 0
\(561\) 5.77838 + 3.33615i 0.243964 + 0.140852i
\(562\) 17.5089 + 10.1088i 0.738568 + 0.426412i
\(563\) −22.5104 + 12.9964i −0.948702 + 0.547733i −0.892677 0.450696i \(-0.851176\pi\)
−0.0560243 + 0.998429i \(0.517842\pi\)
\(564\) 6.82522i 0.287394i
\(565\) 0 0
\(566\) 7.52705 4.34575i 0.316386 0.182665i
\(567\) 3.64466 0.153061
\(568\) −3.04056 + 1.75547i −0.127579 + 0.0736578i
\(569\) 12.7349 22.0576i 0.533876 0.924701i −0.465340 0.885132i \(-0.654068\pi\)
0.999217 0.0395693i \(-0.0125986\pi\)
\(570\) 0 0
\(571\) −8.44491 −0.353409 −0.176704 0.984264i \(-0.556544\pi\)
−0.176704 + 0.984264i \(0.556544\pi\)
\(572\) −3.74276 + 4.70786i −0.156493 + 0.196846i
\(573\) 15.6816i 0.655109i
\(574\) 29.3205 + 16.9282i 1.22381 + 0.706570i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 35.4216 1.47462 0.737311 0.675554i \(-0.236095\pi\)
0.737311 + 0.675554i \(0.236095\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 7.03901 4.06397i 0.292531 0.168893i
\(580\) 0 0
\(581\) 14.4933 + 25.1031i 0.601283 + 1.04145i
\(582\) 2.38453 + 1.37671i 0.0988420 + 0.0570665i
\(583\) 0.707793 1.22593i 0.0293138 0.0507730i
\(584\) −12.2175 −0.505565
\(585\) 0 0
\(586\) 7.54790 0.311801
\(587\) −13.6894 + 23.7108i −0.565024 + 0.978650i 0.432024 + 0.901862i \(0.357800\pi\)
−0.997047 + 0.0767878i \(0.975534\pi\)
\(588\) 5.44171 + 3.14177i 0.224412 + 0.129564i
\(589\) 13.3185 + 23.0683i 0.548780 + 0.950514i
\(590\) 0 0
\(591\) −0.771835 + 0.445619i −0.0317491 + 0.0183303i
\(592\) −4.93211 8.54267i −0.202709 0.351102i
\(593\) 12.0619 0.495324 0.247662 0.968846i \(-0.420338\pi\)
0.247662 + 0.968846i \(0.420338\pi\)
\(594\) 0.834038 + 1.44460i 0.0342210 + 0.0592725i
\(595\) 0 0
\(596\) −0.669099 0.386305i −0.0274074 0.0158237i
\(597\) 0.361116i 0.0147795i
\(598\) 4.43811 + 0.662076i 0.181488 + 0.0270743i
\(599\) 28.6129 1.16909 0.584546 0.811360i \(-0.301273\pi\)
0.584546 + 0.811360i \(0.301273\pi\)
\(600\) 0 0
\(601\) 9.58380 16.5996i 0.390931 0.677113i −0.601641 0.798766i \(-0.705486\pi\)
0.992573 + 0.121654i \(0.0388197\pi\)
\(602\) −23.9027 + 13.8003i −0.974203 + 0.562456i
\(603\) −14.7534 −0.600806
\(604\) 8.46833 4.88919i 0.344571 0.198938i
\(605\) 0 0
\(606\) 5.33615i 0.216766i
\(607\) 16.4010 9.46910i 0.665695 0.384339i −0.128749 0.991677i \(-0.541096\pi\)
0.794443 + 0.607338i \(0.207763\pi\)
\(608\) 5.46699 + 3.15637i 0.221716 + 0.128008i
\(609\) −31.7050 18.3049i −1.28475 0.741753i
\(610\) 0 0
\(611\) −19.2630 15.3141i −0.779298 0.619544i
\(612\) 4.00000i 0.161690i
\(613\) −8.98472 + 15.5620i −0.362890 + 0.628543i −0.988435 0.151645i \(-0.951543\pi\)
0.625546 + 0.780188i \(0.284876\pi\)
\(614\) −13.0214 + 22.5537i −0.525500 + 0.910192i
\(615\) 0 0
\(616\) 6.07957i 0.244953i
\(617\) −9.00755 15.6015i −0.362630 0.628094i 0.625763 0.780014i \(-0.284788\pi\)
−0.988393 + 0.151920i \(0.951455\pi\)
\(618\) −3.75624 6.50600i −0.151098 0.261710i
\(619\) 25.0505i 1.00687i −0.864035 0.503433i \(-0.832070\pi\)
0.864035 0.503433i \(-0.167930\pi\)
\(620\) 0 0
\(621\) 0.622266 1.07780i 0.0249707 0.0432505i
\(622\) −12.6894 + 21.9788i −0.508800 + 0.881268i
\(623\) 21.6916i 0.869057i
\(624\) −3.56609 0.531987i −0.142758 0.0212965i
\(625\) 0 0
\(626\) −27.2452 15.7300i −1.08894 0.628697i
\(627\) 9.11935 + 5.26506i 0.364192 + 0.210266i
\(628\) −10.4040 + 6.00677i −0.415166 + 0.239696i
\(629\) 39.4569i 1.57325i
\(630\) 0 0
\(631\) −1.22739 + 0.708634i −0.0488617 + 0.0282103i −0.524232 0.851576i \(-0.675647\pi\)
0.475370 + 0.879786i \(0.342314\pi\)
\(632\) −9.93398 −0.395152
\(633\) −1.92898 + 1.11370i −0.0766700 + 0.0442654i
\(634\) 12.3546 21.3989i 0.490665 0.849857i
\(635\) 0 0
\(636\) 0.848634 0.0336505
\(637\) −21.0770 + 8.30892i −0.835101 + 0.329211i
\(638\) 16.7555i 0.663355i
\(639\) −3.04056 1.75547i −0.120283 0.0694452i
\(640\) 0 0
\(641\) 2.30985 + 4.00077i 0.0912335 + 0.158021i 0.908030 0.418904i \(-0.137586\pi\)
−0.816797 + 0.576925i \(0.804252\pi\)
\(642\) 16.9282 0.668103
\(643\) −24.0448 41.6468i −0.948234 1.64239i −0.749143 0.662408i \(-0.769535\pi\)
−0.199091 0.979981i \(-0.563799\pi\)
\(644\) 3.92820 2.26795i 0.154793 0.0893697i
\(645\) 0 0
\(646\) 12.6255 + 21.8680i 0.496743 + 0.860383i
\(647\) 3.24383 + 1.87282i 0.127528 + 0.0736283i 0.562407 0.826861i \(-0.309875\pi\)
−0.434879 + 0.900489i \(0.643209\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 10.1899 0.399988
\(650\) 0 0
\(651\) −15.3789 −0.602746
\(652\) 5.04581 8.73960i 0.197609 0.342269i
\(653\) 36.6241 + 21.1450i 1.43321 + 0.827466i 0.997364 0.0725541i \(-0.0231150\pi\)
0.435849 + 0.900020i \(0.356448\pi\)
\(654\) −0.331924 0.574909i −0.0129793 0.0224807i
\(655\) 0 0
\(656\) −8.04479 + 4.64466i −0.314096 + 0.181343i
\(657\) −6.10876 10.5807i −0.238325 0.412792i
\(658\) −24.8756 −0.969752
\(659\) −14.5875 25.2663i −0.568248 0.984234i −0.996739 0.0806881i \(-0.974288\pi\)
0.428492 0.903546i \(-0.359045\pi\)
\(660\) 0 0
\(661\) −38.5089 22.2331i −1.49782 0.864768i −0.497825 0.867277i \(-0.665868\pi\)
−0.999997 + 0.00250931i \(0.999201\pi\)
\(662\) 5.60360i 0.217790i
\(663\) −11.2893 8.97504i −0.438441 0.348562i
\(664\) −7.95317 −0.308643
\(665\) 0 0
\(666\) 4.93211 8.54267i 0.191116 0.331022i
\(667\) −10.8262 + 6.25053i −0.419194 + 0.242022i
\(668\) −7.89701 −0.305545
\(669\) 5.26872 3.04190i 0.203701 0.117607i
\(670\) 0 0
\(671\) 12.4507i 0.480654i
\(672\) −3.15637 + 1.82233i −0.121760 + 0.0702979i
\(673\) −6.84709 3.95317i −0.263936 0.152383i 0.362193 0.932103i \(-0.382028\pi\)
−0.626129 + 0.779720i \(0.715362\pi\)
\(674\) −18.8680 10.8934i −0.726767 0.419599i
\(675\) 0 0
\(676\) 9.50289 8.87103i 0.365496 0.341193i
\(677\) 7.05615i 0.271190i −0.990764 0.135595i \(-0.956705\pi\)
0.990764 0.135595i \(-0.0432946\pi\)
\(678\) −8.93500 + 15.4759i −0.343147 + 0.594347i
\(679\) −5.01764 + 8.69081i −0.192559 + 0.333523i
\(680\) 0 0
\(681\) 15.3205i 0.587083i
\(682\) −3.51928 6.09557i −0.134760 0.233412i
\(683\) 2.97658 + 5.15559i 0.113896 + 0.197273i 0.917338 0.398110i \(-0.130334\pi\)
−0.803442 + 0.595383i \(0.797000\pi\)
\(684\) 6.31274i 0.241373i
\(685\) 0 0
\(686\) 1.30562 2.26140i 0.0498488 0.0863406i
\(687\) 11.1322 19.2815i 0.424719 0.735635i
\(688\) 7.57286i 0.288713i
\(689\) −1.90413 + 2.39513i −0.0725416 + 0.0912470i
\(690\) 0 0
\(691\) 16.2458 + 9.37953i 0.618020 + 0.356814i 0.776098 0.630613i \(-0.217196\pi\)
−0.158078 + 0.987427i \(0.550530\pi\)
\(692\) 0.381645 + 0.220343i 0.0145080 + 0.00837617i
\(693\) −5.26506 + 3.03978i −0.200003 + 0.115472i
\(694\) 9.68162i 0.367509i
\(695\) 0 0
\(696\) 8.69904 5.02239i 0.329736 0.190373i
\(697\) −37.1573 −1.40743
\(698\) 16.7321 9.66025i 0.633317 0.365646i
\(699\) 5.41829 9.38476i 0.204939 0.354964i
\(700\) 0 0
\(701\) −28.5298 −1.07755 −0.538777 0.842448i \(-0.681113\pi\)
−0.538777 + 0.842448i \(0.681113\pi\)
\(702\) −1.32233 3.35432i −0.0499081 0.126601i
\(703\) 62.2703i 2.34857i
\(704\) −1.44460 0.834038i −0.0544453 0.0314340i
\(705\) 0 0
\(706\) −11.4875 19.8970i −0.432338 0.748832i
\(707\) −19.4485 −0.731435
\(708\) 3.05438 + 5.29034i 0.114791 + 0.198823i
\(709\) 20.0853 11.5963i 0.754321 0.435507i −0.0729321 0.997337i \(-0.523236\pi\)
0.827253 + 0.561830i \(0.189902\pi\)
\(710\) 0 0
\(711\) −4.96699 8.60308i −0.186277 0.322641i
\(712\) −5.15425 2.97581i −0.193164 0.111523i
\(713\) −2.62570 + 4.54784i −0.0983331 + 0.170318i
\(714\) −14.5786 −0.545592
\(715\) 0 0
\(716\) −19.6368 −0.733863
\(717\) −8.24876 + 14.2873i −0.308056 + 0.533568i
\(718\) 1.92043 + 1.10876i 0.0716698 + 0.0413786i
\(719\) −5.85641 10.1436i −0.218407 0.378292i 0.735914 0.677075i \(-0.236753\pi\)
−0.954321 + 0.298783i \(0.903419\pi\)
\(720\) 0 0
\(721\) 23.7122 13.6902i 0.883087 0.509850i
\(722\) 10.4253 + 18.0572i 0.387990 + 0.672019i
\(723\) 4.40435 0.163800
\(724\) −3.10876 5.38453i −0.115536 0.200115i
\(725\) 0 0
\(726\) 7.11658 + 4.10876i 0.264121 + 0.152490i
\(727\) 3.82677i 0.141927i 0.997479 + 0.0709634i \(0.0226074\pi\)
−0.997479 + 0.0709634i \(0.977393\pi\)
\(728\) 1.93891 12.9972i 0.0718609 0.481708i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 15.1457 26.2332i 0.560185 0.970269i
\(732\) −6.46410 + 3.73205i −0.238920 + 0.137941i
\(733\) 12.9340 0.477727 0.238864 0.971053i \(-0.423225\pi\)
0.238864 + 0.971053i \(0.423225\pi\)
\(734\) −5.26640 + 3.04056i −0.194386 + 0.112229i
\(735\) 0 0
\(736\) 1.24453i 0.0458741i
\(737\) 21.3127 12.3049i 0.785065 0.453257i
\(738\) −8.04479 4.64466i −0.296133 0.170972i
\(739\) 30.6107 + 17.6731i 1.12603 + 0.650115i 0.942934 0.332980i \(-0.108054\pi\)
0.183098 + 0.983095i \(0.441388\pi\)
\(740\) 0 0
\(741\) −17.8166 14.1643i −0.654510 0.520337i
\(742\) 3.09298i 0.113547i
\(743\) −18.5477 + 32.1255i −0.680448 + 1.17857i 0.294396 + 0.955684i \(0.404882\pi\)
−0.974844 + 0.222887i \(0.928452\pi\)
\(744\) 2.10978 3.65425i 0.0773484 0.133971i
\(745\) 0 0
\(746\) 15.6781i 0.574015i
\(747\) −3.97658 6.88764i −0.145496 0.252006i
\(748\) −3.33615 5.77838i −0.121982 0.211279i
\(749\) 61.6975i 2.25438i
\(750\) 0 0
\(751\) −4.82904 + 8.36414i −0.176214 + 0.305212i −0.940581 0.339570i \(-0.889718\pi\)
0.764367 + 0.644782i \(0.223052\pi\)
\(752\) 3.41261 5.91081i 0.124445 0.215545i
\(753\) 11.9453i 0.435313i
\(754\) −5.34370 + 35.8206i −0.194606 + 1.30451i
\(755\) 0 0
\(756\) −3.15637 1.82233i −0.114796 0.0662775i
\(757\) 37.8354 + 21.8443i 1.37515 + 0.793943i 0.991571 0.129565i \(-0.0413580\pi\)
0.383579 + 0.923508i \(0.374691\pi\)
\(758\) 26.6013 15.3583i 0.966204 0.557838i
\(759\) 2.07598i 0.0753531i
\(760\) 0 0
\(761\) 34.5550 19.9503i 1.25262 0.723200i 0.280990 0.959711i \(-0.409337\pi\)
0.971629 + 0.236511i \(0.0760040\pi\)
\(762\) −14.4407 −0.523131
\(763\) 2.09535 1.20975i 0.0758567 0.0437959i
\(764\) −7.84081 + 13.5807i −0.283671 + 0.491332i
\(765\) 0 0
\(766\) 20.0619 0.724867
\(767\) −21.7844 3.24978i −0.786589 0.117343i
\(768\) 1.00000i 0.0360844i
\(769\) 15.2064 + 8.77941i 0.548356 + 0.316594i 0.748459 0.663181i \(-0.230794\pi\)
−0.200103 + 0.979775i \(0.564128\pi\)
\(770\) 0 0
\(771\) 9.73103 + 16.8546i 0.350454 + 0.607005i
\(772\) −8.12795 −0.292531
\(773\) −6.41861 11.1174i −0.230861 0.399864i 0.727201 0.686425i \(-0.240821\pi\)
−0.958062 + 0.286562i \(0.907488\pi\)
\(774\) 6.55829 3.78643i 0.235733 0.136100i
\(775\) 0 0
\(776\) −1.37671 2.38453i −0.0494210 0.0855997i
\(777\) 31.1351 + 17.9759i 1.11697 + 0.644881i
\(778\) 13.5157 23.4099i 0.484561 0.839284i
\(779\) −58.6410 −2.10103
\(780\) 0 0
\(781\) 5.85651 0.209562
\(782\) −2.48907 + 4.31119i −0.0890088 + 0.154168i
\(783\) 8.69904 + 5.02239i 0.310878 + 0.179486i
\(784\) −3.14177 5.44171i −0.112206 0.194347i