Properties

Label 1950.2.bc.g.901.2
Level $1950$
Weight $2$
Character 1950.901
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.bc (of order \(6\), degree \(2\), 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 901.2
Root \(-1.70006 - 1.70006i\) of defining polynomial
Character \(\chi\) \(=\) 1950.901
Dual form 1950.2.bc.g.751.2

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 3.15637 1.82233i 1.19299 0.688776i 0.234010 0.972234i \(-0.424815\pi\)
0.958985 + 0.283458i \(0.0914817\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −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 \(0.747581\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.24376 2.82233i 0.622307 0.782773i
\(14\) −3.64466 −0.974076
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 5.46699 3.15637i 1.25421 0.724120i 0.282270 0.959335i \(-0.408913\pi\)
0.971943 + 0.235215i \(0.0755793\pi\)
\(20\) 0 0
\(21\) 3.64466i 0.795330i
\(22\) 0.834038 + 1.44460i 0.177817 + 0.307989i
\(23\) −0.622266 + 1.07780i −0.129752 + 0.224736i −0.923580 0.383405i \(-0.874751\pi\)
0.793829 + 0.608141i \(0.208085\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 0 0
\(26\) −3.35432 + 1.32233i −0.657836 + 0.259330i
\(27\) −1.00000 −0.192450
\(28\) 3.15637 + 1.82233i 0.596497 + 0.344388i
\(29\) −5.02239 + 8.69904i −0.932635 + 1.61537i −0.153837 + 0.988096i \(0.549163\pi\)
−0.778798 + 0.627275i \(0.784170\pi\)
\(30\) 0 0
\(31\) 4.21957i 0.757857i −0.925426 0.378928i \(-0.876293\pi\)
0.925426 0.378928i \(-0.123707\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −1.44460 + 0.834038i −0.251472 + 0.145187i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −8.54267 4.93211i −1.40441 0.810835i −0.409566 0.912281i \(-0.634320\pi\)
−0.994841 + 0.101446i \(0.967653\pi\)
\(38\) −6.31274 −1.02406
\(39\) −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 \(0.408334\pi\)
\(42\) −1.82233 + 3.15637i −0.281192 + 0.487038i
\(43\) 3.78643 + 6.55829i 0.577425 + 1.00013i 0.995773 + 0.0918433i \(0.0292759\pi\)
−0.418348 + 0.908287i \(0.637391\pi\)
\(44\) 1.66808i 0.251472i
\(45\) 0 0
\(46\) 1.07780 0.622266i 0.158912 0.0917482i
\(47\) 6.82522i 0.995560i −0.867303 0.497780i \(-0.834149\pi\)
0.867303 0.497780i \(-0.165851\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 3.14177 5.44171i 0.448825 0.777387i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 3.56609 + 0.531987i 0.494528 + 0.0737734i
\(53\) 0.848634 0.116569 0.0582844 0.998300i \(-0.481437\pi\)
0.0582844 + 0.998300i \(0.481437\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −1.82233 3.15637i −0.243519 0.421787i
\(57\) 6.31274i 0.836142i
\(58\) 8.69904 5.02239i 1.14224 0.659473i
\(59\) 5.29034 3.05438i 0.688744 0.397646i −0.114397 0.993435i \(-0.536494\pi\)
0.803141 + 0.595789i \(0.203160\pi\)
\(60\) 0 0
\(61\) −3.73205 6.46410i −0.477840 0.827643i 0.521837 0.853045i \(-0.325247\pi\)
−0.999677 + 0.0254017i \(0.991914\pi\)
\(62\) −2.10978 + 3.65425i −0.267943 + 0.464091i
\(63\) −3.15637 1.82233i −0.397665 0.229592i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 1.66808 0.205326
\(67\) −12.7768 7.37671i −1.56094 0.901209i −0.997162 0.0752814i \(-0.976014\pi\)
−0.563777 0.825927i \(-0.690652\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 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 \(0.400138\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 12.2175i 1.42995i 0.699149 + 0.714976i \(0.253563\pi\)
−0.699149 + 0.714976i \(0.746437\pi\)
\(74\) 4.93211 + 8.54267i 0.573347 + 0.993065i
\(75\) 0 0
\(76\) 5.46699 + 3.15637i 0.627107 + 0.362060i
\(77\) −6.07957 −0.692831
\(78\) −0.531987 + 3.56609i −0.0602357 + 0.403780i
\(79\) 9.93398 1.11766 0.558830 0.829282i \(-0.311250\pi\)
0.558830 + 0.829282i \(0.311250\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.64466 8.04479i −0.512917 0.888398i
\(83\) 7.95317i 0.872974i 0.899711 + 0.436487i \(0.143777\pi\)
−0.899711 + 0.436487i \(0.856223\pi\)
\(84\) 3.15637 1.82233i 0.344388 0.198832i
\(85\) 0 0
\(86\) 7.57286i 0.816603i
\(87\) 5.02239 + 8.69904i 0.538457 + 0.932635i
\(88\) −0.834038 + 1.44460i −0.0889087 + 0.153994i
\(89\) 5.15425 + 2.97581i 0.546350 + 0.315435i 0.747648 0.664095i \(-0.231183\pi\)
−0.201299 + 0.979530i \(0.564516\pi\)
\(90\) 0 0
\(91\) 1.93891 12.9972i 0.203253 1.36247i
\(92\) −1.24453 −0.129752
\(93\) −3.65425 2.10978i −0.378928 0.218774i
\(94\) −3.41261 + 5.91081i −0.351984 + 0.609654i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 2.38453 1.37671i 0.242113 0.139784i −0.374035 0.927415i \(-0.622026\pi\)
0.616147 + 0.787631i \(0.288693\pi\)
\(98\) −5.44171 + 3.14177i −0.549696 + 0.317367i
\(99\) 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 \(0.0811351\pi\)
\(102\) 3.46410 + 2.00000i 0.342997 + 0.198030i
\(103\) 7.51248 0.740227 0.370113 0.928987i \(-0.379319\pi\)
0.370113 + 0.928987i \(0.379319\pi\)
\(104\) −2.82233 2.24376i −0.276752 0.220019i
\(105\) 0 0
\(106\) −0.734939 0.424317i −0.0713835 0.0412133i
\(107\) 8.46410 14.6603i 0.818256 1.41726i −0.0887109 0.996057i \(-0.528275\pi\)
0.906966 0.421203i \(-0.138392\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 0.663848i 0.0635851i −0.999494 0.0317926i \(-0.989878\pi\)
0.999494 0.0317926i \(-0.0101216\pi\)
\(110\) 0 0
\(111\) −8.54267 + 4.93211i −0.810835 + 0.468136i
\(112\) 3.64466i 0.344388i
\(113\) −8.93500 15.4759i −0.840534 1.45585i −0.889444 0.457045i \(-0.848908\pi\)
0.0489094 0.998803i \(-0.484425\pi\)
\(114\) −3.15637 + 5.46699i −0.295621 + 0.512030i
\(115\) 0 0
\(116\) −10.0448 −0.932635
\(117\) −3.56609 0.531987i −0.329685 0.0491823i
\(118\) −6.10876 −0.562357
\(119\) −12.6255 7.28932i −1.15738 0.668211i
\(120\) 0 0
\(121\) −4.10876 7.11658i −0.373524 0.646962i
\(122\) 7.46410i 0.675768i
\(123\) 8.04479 4.64466i 0.725374 0.418795i
\(124\) 3.65425 2.10978i 0.328162 0.189464i
\(125\) 0 0
\(126\) 1.82233 + 3.15637i 0.162346 + 0.281192i
\(127\) −7.22034 + 12.5060i −0.640702 + 1.10973i 0.344575 + 0.938759i \(0.388023\pi\)
−0.985276 + 0.170969i \(0.945310\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 7.57286 0.666753
\(130\) 0 0
\(131\) −10.8892 −0.951393 −0.475697 0.879609i \(-0.657804\pi\)
−0.475697 + 0.879609i \(0.657804\pi\)
\(132\) −1.44460 0.834038i −0.125736 0.0725937i
\(133\) 11.5039 19.9253i 0.997513 1.72774i
\(134\) 7.37671 + 12.7768i 0.637251 + 1.10375i
\(135\) 0 0
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) −6.09419 + 3.51848i −0.520662 + 0.300604i −0.737205 0.675669i \(-0.763855\pi\)
0.216544 + 0.976273i \(0.430522\pi\)
\(138\) 1.24453i 0.105942i
\(139\) −5.82233 10.0846i −0.493844 0.855362i 0.506131 0.862456i \(-0.331075\pi\)
−0.999975 + 0.00709431i \(0.997742\pi\)
\(140\) 0 0
\(141\) −5.91081 3.41261i −0.497780 0.287394i
\(142\) 3.51093 0.294631
\(143\) −5.59526 + 2.20575i −0.467899 + 0.184454i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 6.10876 10.5807i 0.505565 0.875664i
\(147\) −3.14177 5.44171i −0.259129 0.448825i
\(148\) 9.86423i 0.810835i
\(149\) −0.669099 + 0.386305i −0.0548147 + 0.0316473i −0.527157 0.849768i \(-0.676742\pi\)
0.472342 + 0.881415i \(0.343409\pi\)
\(150\) 0 0
\(151\) 9.77838i 0.795754i 0.917439 + 0.397877i \(0.130253\pi\)
−0.917439 + 0.397877i \(0.869747\pi\)
\(152\) −3.15637 5.46699i −0.256015 0.443431i
\(153\) −2.00000 + 3.46410i −0.161690 + 0.280056i
\(154\) 5.26506 + 3.03978i 0.424271 + 0.244953i
\(155\) 0 0
\(156\) 2.24376 2.82233i 0.179644 0.225967i
\(157\) 12.0135 0.958786 0.479393 0.877600i \(-0.340857\pi\)
0.479393 + 0.877600i \(0.340857\pi\)
\(158\) −8.60308 4.96699i −0.684424 0.395152i
\(159\) 0.424317 0.734939i 0.0336505 0.0582844i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) 8.73960 5.04581i 0.684538 0.395218i −0.117025 0.993129i \(-0.537336\pi\)
0.801563 + 0.597911i \(0.204002\pi\)
\(164\) 9.28932i 0.725374i
\(165\) 0 0
\(166\) 3.97658 6.88764i 0.308643 0.534585i
\(167\) 6.83902 + 3.94851i 0.529219 + 0.305545i 0.740698 0.671838i \(-0.234495\pi\)
−0.211479 + 0.977382i \(0.567828\pi\)
\(168\) −3.64466 −0.281192
\(169\) −2.93109 12.6653i −0.225469 0.974250i
\(170\) 0 0
\(171\) −5.46699 3.15637i −0.418071 0.241373i
\(172\) −3.78643 + 6.55829i −0.288713 + 0.500065i
\(173\) 0.220343 + 0.381645i 0.0167523 + 0.0290159i 0.874280 0.485422i \(-0.161334\pi\)
−0.857528 + 0.514438i \(0.828001\pi\)
\(174\) 10.0448i 0.761493i
\(175\) 0 0
\(176\) 1.44460 0.834038i 0.108891 0.0628680i
\(177\) 6.10876i 0.459163i
\(178\) −2.97581 5.15425i −0.223046 0.386328i
\(179\) −9.81842 + 17.0060i −0.733863 + 1.27109i 0.221357 + 0.975193i \(0.428951\pi\)
−0.955220 + 0.295895i \(0.904382\pi\)
\(180\) 0 0
\(181\) 6.21752 0.462145 0.231072 0.972937i \(-0.425777\pi\)
0.231072 + 0.972937i \(0.425777\pi\)
\(182\) −8.17774 + 10.2864i −0.606174 + 0.762481i
\(183\) −7.46410 −0.551762
\(184\) 1.07780 + 0.622266i 0.0794562 + 0.0458741i
\(185\) 0 0
\(186\) 2.10978 + 3.65425i 0.154697 + 0.267943i
\(187\) 6.67230i 0.487927i
\(188\) 5.91081 3.41261i 0.431090 0.248890i
\(189\) −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 \(-0.358695\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −7.03901 4.06397i −0.506679 0.292531i 0.224788 0.974408i \(-0.427831\pi\)
−0.731468 + 0.681876i \(0.761164\pi\)
\(194\) −2.75342 −0.197684
\(195\) 0 0
\(196\) 6.28354 0.448825
\(197\) −0.771835 0.445619i −0.0549910 0.0317491i 0.472252 0.881463i \(-0.343441\pi\)
−0.527243 + 0.849714i \(0.676774\pi\)
\(198\) 0.834038 1.44460i 0.0592725 0.102663i
\(199\) 0.180558 + 0.312736i 0.0127994 + 0.0221692i 0.872354 0.488874i \(-0.162592\pi\)
−0.859555 + 0.511044i \(0.829259\pi\)
\(200\) 0 0
\(201\) −12.7768 + 7.37671i −0.901209 + 0.520313i
\(202\) −4.62124 + 2.66808i −0.325150 + 0.187725i
\(203\) 36.6098i 2.56951i
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) 0 0
\(206\) −6.50600 3.75624i −0.453295 0.261710i
\(207\) 1.24453 0.0865010
\(208\) 1.32233 + 3.35432i 0.0916871 + 0.232580i
\(209\) −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 \(0.191095\pi\)
\(212\) 0.424317 + 0.734939i 0.0291422 + 0.0504758i
\(213\) 3.51093i 0.240565i
\(214\) −14.6603 + 8.46410i −1.00215 + 0.578594i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −7.68945 13.3185i −0.521994 0.904119i
\(218\) −0.331924 + 0.574909i −0.0224807 + 0.0389378i
\(219\) 10.5807 + 6.10876i 0.714976 + 0.412792i
\(220\) 0 0
\(221\) −14.2644 2.12795i −0.959524 0.143141i
\(222\) 9.86423 0.662044
\(223\) −5.26872 3.04190i −0.352820 0.203701i 0.313107 0.949718i \(-0.398630\pi\)
−0.665927 + 0.746017i \(0.731964\pi\)
\(224\) 1.82233 3.15637i 0.121760 0.210894i
\(225\) 0 0
\(226\) 17.8700i 1.18869i
\(227\) 13.2679 7.66025i 0.880625 0.508429i 0.00976038 0.999952i \(-0.496893\pi\)
0.870864 + 0.491523i \(0.163560\pi\)
\(228\) 5.46699 3.15637i 0.362060 0.209036i
\(229\) 22.2644i 1.47127i 0.677378 + 0.735635i \(0.263116\pi\)
−0.677378 + 0.735635i \(0.736884\pi\)
\(230\) 0 0
\(231\) −3.03978 + 5.26506i −0.200003 + 0.346416i
\(232\) 8.69904 + 5.02239i 0.571120 + 0.329736i
\(233\) −10.8366 −0.709928 −0.354964 0.934880i \(-0.615507\pi\)
−0.354964 + 0.934880i \(0.615507\pi\)
\(234\) 2.82233 + 2.24376i 0.184501 + 0.146679i
\(235\) 0 0
\(236\) 5.29034 + 3.05438i 0.344372 + 0.198823i
\(237\) 4.96699 8.60308i 0.322641 0.558830i
\(238\) 7.28932 + 12.6255i 0.472496 + 0.818388i
\(239\) 16.4975i 1.06714i −0.845757 0.533568i \(-0.820851\pi\)
0.845757 0.533568i \(-0.179149\pi\)
\(240\) 0 0
\(241\) 3.81428 2.20218i 0.245700 0.141855i −0.372094 0.928195i \(-0.621360\pi\)
0.617794 + 0.786340i \(0.288027\pi\)
\(242\) 8.21752i 0.528242i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 3.73205 6.46410i 0.238920 0.413822i
\(245\) 0 0
\(246\) −9.28932 −0.592265
\(247\) 3.35830 22.5118i 0.213683 1.43239i
\(248\) −4.21957 −0.267943
\(249\) 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 \(0.710292\pi\)
\(252\) 3.64466i 0.229592i
\(253\) 1.79785 1.03799i 0.113030 0.0652577i
\(254\) 12.5060 7.22034i 0.784696 0.453045i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.73103 + 16.8546i −0.607005 + 1.05136i 0.384726 + 0.923031i \(0.374296\pi\)
−0.991731 + 0.128333i \(0.959038\pi\)
\(258\) −6.55829 3.78643i −0.408301 0.235733i
\(259\) −35.9518 −2.23393
\(260\) 0 0
\(261\) 10.0448 0.621757
\(262\) 9.43032 + 5.44460i 0.582607 + 0.336368i
\(263\) 1.01739 1.76217i 0.0627350 0.108660i −0.832952 0.553345i \(-0.813351\pi\)
0.895687 + 0.444685i \(0.146684\pi\)
\(264\) 0.834038 + 1.44460i 0.0513315 + 0.0889087i
\(265\) 0 0
\(266\) −19.9253 + 11.5039i −1.22170 + 0.705349i
\(267\) 5.15425 2.97581i 0.315435 0.182117i
\(268\) 14.7534i 0.901209i
\(269\) −10.2644 17.7784i −0.625829 1.08397i −0.988380 0.152003i \(-0.951428\pi\)
0.362551 0.931964i \(-0.381906\pi\)
\(270\) 0 0
\(271\) 22.1184 + 12.7700i 1.34359 + 0.775725i 0.987333 0.158662i \(-0.0507179\pi\)
0.356261 + 0.934386i \(0.384051\pi\)
\(272\) 4.00000 0.242536
\(273\) −10.2864 8.17774i −0.622563 0.494939i
\(274\) 7.03696 0.425119
\(275\) 0 0
\(276\) −0.622266 + 1.07780i −0.0374560 + 0.0648758i
\(277\) −9.03019 15.6407i −0.542572 0.939762i −0.998755 0.0498760i \(-0.984117\pi\)
0.456184 0.889886i \(-0.349216\pi\)
\(278\) 11.6447i 0.698400i
\(279\) −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 \(-0.206043\pi\)
\(282\) 3.41261 + 5.91081i 0.203218 + 0.351984i
\(283\) −4.34575 + 7.52705i −0.258328 + 0.447437i −0.965794 0.259310i \(-0.916505\pi\)
0.707466 + 0.706747i \(0.249838\pi\)
\(284\) −3.04056 1.75547i −0.180424 0.104168i
\(285\) 0 0
\(286\) 5.94851 + 0.887395i 0.351743 + 0.0524728i
\(287\) 33.8564 1.99848
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 2.75342i 0.161408i
\(292\) −10.5807 + 6.10876i −0.619188 + 0.357488i
\(293\) −6.53667 + 3.77395i −0.381876 + 0.220476i −0.678634 0.734476i \(-0.737428\pi\)
0.296758 + 0.954953i \(0.404095\pi\)
\(294\) 6.28354i 0.366464i
\(295\) 0 0
\(296\) −4.93211 + 8.54267i −0.286673 + 0.496533i
\(297\) 1.44460 + 0.834038i 0.0838240 + 0.0483958i
\(298\) 0.772609 0.0447560
\(299\) 1.64568 + 4.17456i 0.0951723 + 0.241421i
\(300\) 0 0
\(301\) 23.9027 + 13.8003i 1.37773 + 0.795433i
\(302\) 4.88919 8.46833i 0.281341 0.487298i
\(303\) −2.66808 4.62124i −0.153277 0.265483i
\(304\) 6.31274i 0.362060i
\(305\) 0 0
\(306\) 3.46410 2.00000i 0.198030 0.114332i
\(307\) 26.0427i 1.48634i 0.669104 + 0.743169i \(0.266678\pi\)
−0.669104 + 0.743169i \(0.733322\pi\)
\(308\) −3.03978 5.26506i −0.173208 0.300005i
\(309\) 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 \(0.244347\pi\)
\(312\) −3.35432 + 1.32233i −0.189901 + 0.0748622i
\(313\) 31.4600 1.77822 0.889112 0.457689i \(-0.151323\pi\)
0.889112 + 0.457689i \(0.151323\pi\)
\(314\) −10.4040 6.00677i −0.587134 0.338982i
\(315\) 0 0
\(316\) 4.96699 + 8.60308i 0.279415 + 0.483961i
\(317\) 24.7093i 1.38781i −0.720066 0.693905i \(-0.755889\pi\)
0.720066 0.693905i \(-0.244111\pi\)
\(318\) −0.734939 + 0.424317i −0.0412133 + 0.0237945i
\(319\) 14.5107 8.37773i 0.812441 0.469063i
\(320\) 0 0
\(321\) −8.46410 14.6603i −0.472420 0.818256i
\(322\) 2.26795 3.92820i 0.126388 0.218910i
\(323\) −21.8680 12.6255i −1.21677 0.702500i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −10.0916 −0.558923
\(327\) −0.574909 0.331924i −0.0317926 0.0183554i
\(328\) 4.64466 8.04479i 0.256458 0.444199i
\(329\) −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 \(0.382549\pi\)
\(332\) −6.88764 + 3.97658i −0.378009 + 0.218243i
\(333\) 9.86423i 0.540556i
\(334\) −3.94851 6.83902i −0.216053 0.374214i
\(335\) 0 0
\(336\) 3.15637 + 1.82233i 0.172194 + 0.0994162i
\(337\) −21.7868 −1.18680 −0.593402 0.804906i \(-0.702216\pi\)
−0.593402 + 0.804906i \(0.702216\pi\)
\(338\) −3.79423 + 12.4340i −0.206379 + 0.676319i
\(339\) −17.8700 −0.970565
\(340\) 0 0
\(341\) −3.51928 + 6.09557i −0.190580 + 0.330094i
\(342\) 3.15637 + 5.46699i 0.170677 + 0.295621i
\(343\) 2.61124i 0.140994i
\(344\) 6.55829 3.78643i 0.353599 0.204151i
\(345\) 0 0
\(346\) 0.440685i 0.0236914i
\(347\) 4.84081 + 8.38453i 0.259868 + 0.450105i 0.966206 0.257769i \(-0.0829875\pi\)
−0.706338 + 0.707875i \(0.749654\pi\)
\(348\) −5.02239 + 8.69904i −0.269229 + 0.466318i
\(349\) 16.7321 + 9.66025i 0.895646 + 0.517102i 0.875785 0.482701i \(-0.160344\pi\)
0.0198610 + 0.999803i \(0.493678\pi\)
\(350\) 0 0
\(351\) −2.24376 + 2.82233i −0.119763 + 0.150645i
\(352\) −1.66808 −0.0889087
\(353\) 19.8970 + 11.4875i 1.05901 + 0.611419i 0.925158 0.379583i \(-0.123932\pi\)
0.133851 + 0.991002i \(0.457266\pi\)
\(354\) −3.05438 + 5.29034i −0.162338 + 0.281179i
\(355\) 0 0
\(356\) 5.95162i 0.315435i
\(357\) −12.6255 + 7.28932i −0.668211 + 0.385792i
\(358\) 17.0060 9.81842i 0.898795 0.518920i
\(359\) 2.21752i 0.117036i 0.998286 + 0.0585182i \(0.0186376\pi\)
−0.998286 + 0.0585182i \(0.981362\pi\)
\(360\) 0 0
\(361\) 10.4253 18.0572i 0.548701 0.950378i
\(362\) −5.38453 3.10876i −0.283005 0.163393i
\(363\) −8.21752 −0.431308
\(364\) 12.2253 4.81944i 0.640782 0.252607i
\(365\) 0 0
\(366\) 6.46410 + 3.73205i 0.337884 + 0.195077i
\(367\) −3.04056 + 5.26640i −0.158716 + 0.274904i −0.934406 0.356210i \(-0.884069\pi\)
0.775690 + 0.631114i \(0.217402\pi\)
\(368\) −0.622266 1.07780i −0.0324379 0.0561841i
\(369\) 9.28932i 0.483583i
\(370\) 0 0
\(371\) 2.67860 1.54649i 0.139066 0.0802898i
\(372\) 4.21957i 0.218774i
\(373\) 7.83904 + 13.5776i 0.405890 + 0.703022i 0.994425 0.105450i \(-0.0336282\pi\)
−0.588535 + 0.808472i \(0.700295\pi\)
\(374\) 3.33615 5.77838i 0.172508 0.298793i
\(375\) 0 0
\(376\) −6.82522 −0.351984
\(377\) 13.2825 + 33.6934i 0.684085 + 1.73530i
\(378\) 3.64466 0.187461
\(379\) 26.6013 + 15.3583i 1.36642 + 0.788903i 0.990469 0.137737i \(-0.0439829\pi\)
0.375951 + 0.926640i \(0.377316\pi\)
\(380\) 0 0
\(381\) 7.22034 + 12.5060i 0.369909 + 0.640702i
\(382\) 15.6816i 0.802342i
\(383\) −17.3741 + 10.0310i −0.887777 + 0.512558i −0.873215 0.487336i \(-0.837969\pi\)
−0.0145623 + 0.999894i \(0.504635\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 0 0
\(386\) 4.06397 + 7.03901i 0.206851 + 0.358276i
\(387\) 3.78643 6.55829i 0.192475 0.333377i
\(388\) 2.38453 + 1.37671i 0.121056 + 0.0698919i
\(389\) 27.0314 1.37055 0.685273 0.728287i \(-0.259683\pi\)
0.685273 + 0.728287i \(0.259683\pi\)
\(390\) 0 0
\(391\) 4.97813 0.251755
\(392\) −5.44171 3.14177i −0.274848 0.158683i
\(393\) −5.44460 + 9.43032i −0.274644 + 0.475697i
\(394\) 0.445619 + 0.771835i 0.0224500 + 0.0388845i
\(395\) 0 0
\(396\) −1.44460 + 0.834038i −0.0725937 + 0.0419120i
\(397\) 3.23571 1.86814i 0.162396 0.0937592i −0.416600 0.909090i \(-0.636778\pi\)
0.578995 + 0.815331i \(0.303445\pi\)
\(398\) 0.361116i 0.0181011i
\(399\) −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 \(0.419225\pi\)
\(402\) 14.7534 0.735834
\(403\) −11.9090 9.46770i −0.593230 0.471620i
\(404\) 5.33615 0.265483
\(405\) 0 0
\(406\) 18.3049 31.7050i 0.908458 1.57349i
\(407\) 8.22714 + 14.2498i 0.407804 + 0.706338i
\(408\) 4.00000i 0.198030i
\(409\) 23.7122 13.6902i 1.17249 0.676938i 0.218225 0.975898i \(-0.429973\pi\)
0.954265 + 0.298961i \(0.0966399\pi\)
\(410\) 0 0
\(411\) 7.03696i 0.347108i
\(412\) 3.75624 + 6.50600i 0.185057 + 0.320528i
\(413\) 11.1322 19.2815i 0.547779 0.948780i
\(414\) −1.07780 0.622266i −0.0529708 0.0305827i
\(415\) 0 0
\(416\) 0.531987 3.56609i 0.0260828 0.174842i
\(417\) −11.6447 −0.570241
\(418\) 9.11935 + 5.26506i 0.446042 + 0.257523i
\(419\) 6.58068 11.3981i 0.321487 0.556833i −0.659308 0.751873i \(-0.729151\pi\)
0.980795 + 0.195041i \(0.0624839\pi\)
\(420\) 0 0
\(421\) 1.29341i 0.0630370i 0.999503 + 0.0315185i \(0.0100343\pi\)
−0.999503 + 0.0315185i \(0.989966\pi\)
\(422\) 1.92898 1.11370i 0.0939011 0.0542138i
\(423\) −5.91081 + 3.41261i −0.287394 + 0.165927i
\(424\) 0.848634i 0.0412133i
\(425\) 0 0
\(426\) 1.75547 3.04056i 0.0850527 0.147316i
\(427\) −23.5595 13.6021i −1.14012 0.658250i
\(428\) 16.9282 0.818256
\(429\) −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 \(0.572316\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 1.03901 + 1.79962i 0.0499317 + 0.0864842i 0.889911 0.456134i \(-0.150766\pi\)
−0.839979 + 0.542618i \(0.817433\pi\)
\(434\) 15.3789i 0.738210i
\(435\) 0 0
\(436\) 0.574909 0.331924i 0.0275332 0.0158963i
\(437\) 7.85641i 0.375823i
\(438\) −6.10876 10.5807i −0.291888 0.505565i
\(439\) −1.19820 + 2.07534i −0.0571869 + 0.0990506i −0.893202 0.449656i \(-0.851546\pi\)
0.836015 + 0.548707i \(0.184880\pi\)
\(440\) 0 0
\(441\) −6.28354 −0.299216
\(442\) 11.2893 + 8.97504i 0.536978 + 0.426899i
\(443\) −21.9959 −1.04506 −0.522529 0.852622i \(-0.675011\pi\)
−0.522529 + 0.852622i \(0.675011\pi\)
\(444\) −8.54267 4.93211i −0.405417 0.234068i
\(445\) 0 0
\(446\) 3.04190 + 5.26872i 0.144038 + 0.249481i
\(447\) 0.772609i 0.0365432i
\(448\) −3.15637 + 1.82233i −0.149124 + 0.0860970i
\(449\) 25.3098 14.6126i 1.19445 0.689613i 0.235134 0.971963i \(-0.424447\pi\)
0.959312 + 0.282350i \(0.0911138\pi\)
\(450\) 0 0
\(451\) −7.74765 13.4193i −0.364822 0.631891i
\(452\) 8.93500 15.4759i 0.420267 0.727924i
\(453\) 8.46833 + 4.88919i 0.397877 + 0.229714i
\(454\) −15.3205 −0.719027
\(455\) 0 0
\(456\) −6.31274 −0.295621
\(457\) 34.3321 + 19.8216i 1.60599 + 0.927216i 0.990256 + 0.139259i \(0.0444721\pi\)
0.615730 + 0.787957i \(0.288861\pi\)
\(458\) 11.1322 19.2815i 0.520172 0.900965i
\(459\) 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 \(0.206383\pi\)
\(462\) 5.26506 3.03978i 0.244953 0.141424i
\(463\) 32.2175i 1.49728i 0.662979 + 0.748638i \(0.269292\pi\)
−0.662979 + 0.748638i \(0.730708\pi\)
\(464\) −5.02239 8.69904i −0.233159 0.403843i
\(465\) 0 0
\(466\) 9.38476 + 5.41829i 0.434740 + 0.250998i
\(467\) 6.88137 0.318432 0.159216 0.987244i \(-0.449103\pi\)
0.159216 + 0.987244i \(0.449103\pi\)
\(468\) −1.32233 3.35432i −0.0611247 0.155053i
\(469\) −53.7712 −2.48292
\(470\) 0 0
\(471\) 6.00677 10.4040i 0.276778 0.479393i
\(472\) −3.05438 5.29034i −0.140589 0.243508i
\(473\) 12.6321i 0.580825i
\(474\) −8.60308 + 4.96699i −0.395152 + 0.228141i
\(475\) 0 0
\(476\) 14.5786i 0.668211i
\(477\) −0.424317 0.734939i −0.0194281 0.0336505i
\(478\) −8.24876 + 14.2873i −0.377290 + 0.653485i
\(479\) −16.4293 9.48547i −0.750675 0.433402i 0.0752629 0.997164i \(-0.476020\pi\)
−0.825938 + 0.563761i \(0.809354\pi\)
\(480\) 0 0
\(481\) −33.0878 + 13.0438i −1.50867 + 0.594744i
\(482\) −4.40435 −0.200613
\(483\) 3.92820 + 2.26795i 0.178739 + 0.103195i
\(484\) 4.10876 7.11658i 0.186762 0.323481i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −1.65948 + 0.958101i −0.0751982 + 0.0434157i −0.537128 0.843501i \(-0.680491\pi\)
0.461929 + 0.886917i \(0.347157\pi\)
\(488\) −6.46410 + 3.73205i −0.292616 + 0.168942i
\(489\) 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 \(0.892346\pi\)
\(492\) 8.04479 + 4.64466i 0.362687 + 0.209397i
\(493\) 40.1791 1.80958
\(494\) −14.1643 + 17.8166i −0.637280 + 0.801608i
\(495\) 0 0
\(496\) 3.65425 + 2.10978i 0.164081 + 0.0947321i
\(497\) −6.39808 + 11.0818i −0.286993 + 0.497087i
\(498\) −3.97658 6.88764i −0.178195 0.308643i
\(499\) 1.82522i 0.0817080i 0.999165 + 0.0408540i \(0.0130078\pi\)
−0.999165 + 0.0408540i \(0.986992\pi\)
\(500\) 0 0
\(501\) 6.83902 3.94851i 0.305545 0.176406i
\(502\) 11.9453i 0.533147i
\(503\) −9.99923 17.3192i −0.445843 0.772224i 0.552267 0.833667i \(-0.313763\pi\)
−0.998111 + 0.0614437i \(0.980430\pi\)
\(504\) −1.82233 + 3.15637i −0.0811730 + 0.140596i
\(505\) 0 0
\(506\) −2.07598 −0.0922884
\(507\) −12.4340 3.79423i −0.552212 0.168508i
\(508\) −14.4407 −0.640702
\(509\) 5.10196 + 2.94562i 0.226141 + 0.130562i 0.608790 0.793331i \(-0.291655\pi\)
−0.382650 + 0.923893i \(0.624988\pi\)
\(510\) 0 0
\(511\) 22.2644 + 38.5630i 0.984917 + 1.70593i
\(512\) 1.00000i 0.0441942i
\(513\) −5.46699 + 3.15637i −0.241373 + 0.139357i
\(514\) 16.8546 9.73103i 0.743426 0.429217i
\(515\) 0 0
\(516\) 3.78643 + 6.55829i 0.166688 + 0.288713i
\(517\) −5.69249 + 9.85968i −0.250355 + 0.433628i
\(518\) 31.1351 + 17.9759i 1.36800 + 0.789815i
\(519\) 0.440685 0.0193439
\(520\) 0 0
\(521\) 32.0370 1.40356 0.701782 0.712391i \(-0.252388\pi\)
0.701782 + 0.712391i \(0.252388\pi\)
\(522\) −8.69904 5.02239i −0.380747 0.219824i
\(523\) 19.3593 33.5313i 0.846523 1.46622i −0.0377693 0.999286i \(-0.512025\pi\)
0.884292 0.466934i \(-0.154641\pi\)
\(524\) −5.44460 9.43032i −0.237848 0.411965i
\(525\) 0 0
\(526\) −1.76217 + 1.01739i −0.0768344 + 0.0443604i
\(527\) −14.6170 + 8.43914i −0.636727 + 0.367615i
\(528\) 1.66808i 0.0725937i
\(529\) 10.7256 + 18.5772i 0.466329 + 0.807706i
\(530\) 0 0
\(531\) −5.29034 3.05438i −0.229581 0.132549i
\(532\) 23.0078 0.997513
\(533\) 31.1593 12.2835i 1.34966 0.532059i
\(534\) −5.95162 −0.257552
\(535\) 0 0
\(536\) −7.37671 + 12.7768i −0.318625 + 0.551875i
\(537\) 9.81842 + 17.0060i 0.423696 + 0.733863i
\(538\) 20.5287i 0.885056i
\(539\) −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 \(0.811535\pi\)
\(542\) −12.7700 22.1184i −0.548520 0.950065i
\(543\) 3.10876 5.38453i 0.133410 0.231072i
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) 0 0
\(546\) 4.81944 + 12.2253i 0.206253 + 0.523196i
\(547\) 17.7596 0.759348 0.379674 0.925120i \(-0.376036\pi\)
0.379674 + 0.925120i \(0.376036\pi\)
\(548\) −6.09419 3.51848i −0.260331 0.150302i
\(549\) −3.73205 + 6.46410i −0.159280 + 0.275881i
\(550\) 0 0
\(551\) 63.4101i 2.70136i
\(552\) 1.07780 0.622266i 0.0458741 0.0264854i
\(553\) 31.3553 18.1030i 1.33336 0.769817i
\(554\) 18.0604i 0.767312i
\(555\) 0 0
\(556\) 5.82233 10.0846i 0.246922 0.427681i
\(557\) 22.7074 + 13.1101i 0.962142 + 0.555493i 0.896832 0.442372i \(-0.145863\pi\)
0.0653102 + 0.997865i \(0.479196\pi\)
\(558\) 4.21957 0.178629
\(559\) 27.0055 + 4.02867i 1.14221 + 0.170394i
\(560\) 0 0
\(561\) 5.77838 + 3.33615i 0.243964 + 0.140852i
\(562\) −10.1088 + 17.5089i −0.426412 + 0.738568i
\(563\) 12.9964 + 22.5104i 0.547733 + 0.948702i 0.998429 + 0.0560243i \(0.0178424\pi\)
−0.450696 + 0.892677i \(0.648824\pi\)
\(564\) 6.82522i 0.287394i
\(565\) 0 0
\(566\) 7.52705 4.34575i 0.316386 0.182665i
\(567\) 3.64466i 0.153061i
\(568\) 1.75547 + 3.04056i 0.0736578 + 0.127579i
\(569\) −12.7349 + 22.0576i −0.533876 + 0.924701i 0.465340 + 0.885132i \(0.345932\pi\)
−0.999217 + 0.0395693i \(0.987401\pi\)
\(570\) 0 0
\(571\) −8.44491 −0.353409 −0.176704 0.984264i \(-0.556544\pi\)
−0.176704 + 0.984264i \(0.556544\pi\)
\(572\) −4.70786 3.74276i −0.196846 0.156493i
\(573\) −15.6816 −0.655109
\(574\) −29.3205 16.9282i −1.22381 0.706570i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 35.4216i 1.47462i 0.675554 + 0.737311i \(0.263905\pi\)
−0.675554 + 0.737311i \(0.736095\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) −7.03901 + 4.06397i −0.292531 + 0.168893i
\(580\) 0 0
\(581\) 14.4933 + 25.1031i 0.601283 + 1.04145i
\(582\) −1.37671 + 2.38453i −0.0570665 + 0.0988420i
\(583\) −1.22593 0.707793i −0.0507730 0.0293138i
\(584\) 12.2175 0.505565
\(585\) 0 0
\(586\) 7.54790 0.311801
\(587\) −23.7108 13.6894i −0.978650 0.565024i −0.0767878 0.997047i \(-0.524466\pi\)
−0.901862 + 0.432024i \(0.857800\pi\)
\(588\) 3.14177 5.44171i 0.129564 0.224412i
\(589\) −13.3185 23.0683i −0.548780 0.950514i
\(590\) 0 0
\(591\) −0.771835 + 0.445619i −0.0317491 + 0.0183303i
\(592\) 8.54267 4.93211i 0.351102 0.202709i
\(593\) 12.0619i 0.495324i −0.968846 0.247662i \(-0.920338\pi\)
0.968846 0.247662i \(-0.0796623\pi\)
\(594\) −0.834038 1.44460i −0.0342210 0.0592725i
\(595\) 0 0
\(596\) −0.669099 0.386305i −0.0274074 0.0158237i
\(597\) 0.361116 0.0147795
\(598\) 0.662076 4.43811i 0.0270743 0.181488i
\(599\) −28.6129 −1.16909 −0.584546 0.811360i \(-0.698727\pi\)
−0.584546 + 0.811360i \(0.698727\pi\)
\(600\) 0 0
\(601\) 9.58380 16.5996i 0.390931 0.677113i −0.601641 0.798766i \(-0.705486\pi\)
0.992573 + 0.121654i \(0.0388197\pi\)
\(602\) −13.8003 23.9027i −0.562456 0.974203i
\(603\) 14.7534i 0.600806i
\(604\) −8.46833 + 4.88919i −0.344571 + 0.198938i
\(605\) 0 0
\(606\) 5.33615i 0.216766i
\(607\) 9.46910 + 16.4010i 0.384339 + 0.665695i 0.991677 0.128749i \(-0.0410960\pi\)
−0.607338 + 0.794443i \(0.707763\pi\)
\(608\) 3.15637 5.46699i 0.128008 0.221716i
\(609\) 31.7050 + 18.3049i 1.28475 + 0.741753i
\(610\) 0 0
\(611\) −19.2630 15.3141i −0.779298 0.619544i
\(612\) −4.00000 −0.161690
\(613\) 15.5620 + 8.98472i 0.628543 + 0.362890i 0.780188 0.625546i \(-0.215124\pi\)
−0.151645 + 0.988435i \(0.548457\pi\)
\(614\) 13.0214 22.5537i 0.525500 0.910192i
\(615\) 0 0
\(616\) 6.07957i 0.244953i
\(617\) 15.6015 9.00755i 0.628094 0.362630i −0.151920 0.988393i \(-0.548545\pi\)
0.780014 + 0.625763i \(0.215212\pi\)
\(618\) −6.50600 + 3.75624i −0.261710 + 0.151098i
\(619\) 25.0505i 1.00687i 0.864035 + 0.503433i \(0.167930\pi\)
−0.864035 + 0.503433i \(0.832070\pi\)
\(620\) 0 0
\(621\) 0.622266 1.07780i 0.0249707 0.0432505i
\(622\) −21.9788 12.6894i −0.881268 0.508800i
\(623\) 21.6916 0.869057
\(624\) 3.56609 + 0.531987i 0.142758 + 0.0212965i
\(625\) 0 0
\(626\) −27.2452 15.7300i −1.08894 0.628697i
\(627\) −5.26506 + 9.11935i −0.210266 + 0.364192i
\(628\) 6.00677 + 10.4040i 0.239696 + 0.415166i
\(629\) 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 \(0.342314\pi\)
\(632\) 9.93398i 0.395152i
\(633\) 1.11370 + 1.92898i 0.0442654 + 0.0766700i
\(634\) −12.3546 + 21.3989i −0.490665 + 0.849857i
\(635\) 0 0
\(636\) 0.848634 0.0336505
\(637\) −8.30892 21.0770i −0.329211 0.835101i
\(638\) −16.7555 −0.663355
\(639\) 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 \(0.804252\pi\)
\(642\) 16.9282i 0.668103i
\(643\) −41.6468 + 24.0448i −1.64239 + 0.948234i −0.662408 + 0.749143i \(0.730465\pi\)
−0.979981 + 0.199091i \(0.936201\pi\)
\(644\) −3.92820 + 2.26795i −0.154793 + 0.0893697i
\(645\) 0 0
\(646\) 12.6255 + 21.8680i 0.496743 + 0.860383i
\(647\) −1.87282 + 3.24383i −0.0736283 + 0.127528i −0.900489 0.434879i \(-0.856791\pi\)
0.826861 + 0.562407i \(0.190125\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −10.1899 −0.399988
\(650\) 0 0
\(651\) −15.3789 −0.602746
\(652\) 8.73960 + 5.04581i 0.342269 + 0.197609i
\(653\) 21.1450 36.6241i 0.827466 1.43321i −0.0725541 0.997364i \(-0.523115\pi\)
0.900020 0.435849i \(-0.143552\pi\)
\(654\) 0.331924 + 0.574909i 0.0129793 + 0.0224807i
\(655\) 0 0
\(656\) −8.04479 + 4.64466i −0.314096 + 0.181343i
\(657\) 10.5807 6.10876i 0.412792 0.238325i
\(658\) 24.8756i 0.969752i
\(659\) 14.5875 + 25.2663i 0.568248 + 0.984234i 0.996739 + 0.0806881i \(0.0257118\pi\)
−0.428492 + 0.903546i \(0.640955\pi\)
\(660\) 0 0
\(661\) −38.5089 22.2331i −1.49782 0.864768i −0.497825 0.867277i \(-0.665868\pi\)
−0.999997 + 0.00250931i \(0.999201\pi\)
\(662\) 5.60360 0.217790
\(663\) −8.97504 + 11.2893i −0.348562 + 0.438441i
\(664\) 7.95317 0.308643
\(665\) 0 0
\(666\) 4.93211 8.54267i 0.191116 0.331022i
\(667\) −6.25053 10.8262i −0.242022 0.419194i
\(668\) 7.89701i 0.305545i
\(669\) −5.26872 + 3.04190i −0.203701 + 0.117607i
\(670\) 0 0
\(671\) 12.4507i 0.480654i
\(672\) −1.82233 3.15637i −0.0702979 0.121760i
\(673\) −3.95317 + 6.84709i −0.152383 + 0.263936i −0.932103 0.362193i \(-0.882028\pi\)
0.779720 + 0.626129i \(0.215362\pi\)
\(674\) 18.8680 + 10.8934i 0.726767 + 0.419599i
\(675\) 0 0
\(676\) 9.50289 8.87103i 0.365496 0.341193i
\(677\) 7.05615 0.271190 0.135595 0.990764i \(-0.456705\pi\)
0.135595 + 0.990764i \(0.456705\pi\)
\(678\) 15.4759 + 8.93500i 0.594347 + 0.343147i
\(679\) 5.01764 8.69081i 0.192559 0.333523i
\(680\) 0 0
\(681\) 15.3205i 0.587083i
\(682\) 6.09557 3.51928i 0.233412 0.134760i
\(683\) 5.15559 2.97658i 0.197273 0.113896i −0.398110 0.917338i \(-0.630334\pi\)
0.595383 + 0.803442i \(0.297000\pi\)
\(684\) 6.31274i 0.241373i
\(685\) 0 0
\(686\) 1.30562 2.26140i 0.0498488 0.0863406i
\(687\) 19.2815 + 11.1322i 0.735635 + 0.424719i
\(688\) −7.57286 −0.288713
\(689\) 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 \(0.550530\pi\)
\(692\) −0.220343 + 0.381645i −0.00837617 + 0.0145080i
\(693\) 3.03978 + 5.26506i 0.115472 + 0.200003i
\(694\) 9.68162i 0.367509i
\(695\) 0 0
\(696\) 8.69904 5.02239i 0.329736 0.190373i
\(697\) 37.1573i 1.40743i
\(698\) −9.66025 16.7321i −0.365646 0.633317i
\(699\) −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 \(0.681113\pi\)
\(702\) 3.35432 1.32233i 0.126601 0.0499081i
\(703\) −62.2703 −2.34857
\(704\) 1.44460 + 0.834038i 0.0544453 + 0.0314340i
\(705\) 0 0
\(706\) −11.4875 19.8970i −0.432338 0.748832i
\(707\) 19.4485i 0.731435i
\(708\) 5.29034 3.05438i 0.198823 0.114791i
\(709\) −20.0853 + 11.5963i −0.754321 + 0.435507i −0.827253 0.561830i \(-0.810098\pi\)
0.0729321 + 0.997337i \(0.476764\pi\)
\(710\) 0 0
\(711\) −4.96699 8.60308i −0.186277 0.322641i
\(712\) 2.97581 5.15425i 0.111523 0.193164i
\(713\) 4.54784 + 2.62570i 0.170318 + 0.0983331i
\(714\) 14.5786 0.545592
\(715\) 0 0
\(716\) −19.6368 −0.733863
\(717\) −14.2873 8.24876i −0.533568 0.308056i
\(718\) 1.10876 1.92043i 0.0413786 0.0716698i
\(719\) 5.85641 + 10.1436i 0.218407 + 0.378292i 0.954321 0.298783i \(-0.0965806\pi\)
−0.735914 + 0.677075i \(0.763247\pi\)
\(720\) 0 0
\(721\) 23.7122 13.6902i 0.883087 0.509850i
\(722\) −18.0572 + 10.4253i −0.672019 + 0.387990i
\(723\) 4.40435i 0.163800i
\(724\) 3.10876 + 5.38453i 0.115536 + 0.200115i
\(725\) 0 0
\(726\) 7.11658 + 4.10876i 0.264121 + 0.152490i
\(727\) −3.82677 −0.141927 −0.0709634 0.997479i \(-0.522607\pi\)
−0.0709634 + 0.997479i \(0.522607\pi\)
\(728\) −12.9972 1.93891i −0.481708 0.0718609i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 15.1457 26.2332i 0.560185 0.970269i
\(732\) −3.73205 6.46410i −0.137941 0.238920i
\(733\) 12.9340i 0.477727i −0.971053 0.238864i \(-0.923225\pi\)
0.971053 0.238864i \(-0.0767749\pi\)
\(734\) 5.26640 3.04056i 0.194386 0.112229i
\(735\) 0 0
\(736\) 1.24453i 0.0458741i
\(737\) 12.3049 + 21.3127i 0.453257 + 0.785065i
\(738\) −4.64466 + 8.04479i −0.170972 + 0.296133i
\(739\) −30.6107 17.6731i −1.12603 0.650115i −0.183098 0.983095i \(-0.558612\pi\)
−0.942934 + 0.332980i \(0.891946\pi\)
\(740\) 0 0
\(741\) −17.8166 14.1643i −0.654510 0.520337i
\(742\) −3.09298 −0.113547
\(743\) 32.1255 + 18.5477i 1.17857 + 0.680448i 0.955684 0.294396i \(-0.0951185\pi\)
0.222887 + 0.974844i \(0.428452\pi\)
\(744\) −2.10978 + 3.65425i −0.0773484 + 0.133971i
\(745\) 0 0
\(746\) 15.6781i 0.574015i
\(747\) 6.88764 3.97658i 0.252006 0.145496i
\(748\) −5.77838 + 3.33615i −0.211279 + 0.121982i
\(749\) 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 \(0.223052\pi\)
\(752\) 5.91081 + 3.41261i 0.215545 + 0.124445i
\(753\) 11.9453 0.435313
\(754\) 5.34370 35.8206i 0.194606 1.30451i
\(755\) 0 0
\(756\) −3.15637 1.82233i −0.114796 0.0662775i
\(757\) −21.8443 + 37.8354i −0.793943 + 1.37515i 0.129565 + 0.991571i \(0.458642\pi\)
−0.923508 + 0.383579i \(0.874691\pi\)
\(758\) −15.3583 26.6013i −0.557838 0.966204i
\(759\) 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 \(0.0760040\pi\)
\(762\) 14.4407i 0.523131i
\(763\) −1.20975 2.09535i −0.0437959 0.0758567i
\(764\) 7.84081 13.5807i 0.283671 0.491332i
\(765\) 0 0
\(766\) 20.0619 0.724867
\(767\) 3.24978 21.7844i 0.117343 0.786589i
\(768\) −1.00000 −0.0360844
\(769\) −15.2064 8.77941i −0.548356 0.316594i 0.200103 0.979775i \(-0.435872\pi\)
−0.748459 + 0.663181i \(0.769206\pi\)
\(770\) 0 0
\(771\) 9.73103 + 16.8546i 0.350454 + 0.607005i
\(772\) 8.12795i 0.292531i
\(773\) −11.1174 + 6.41861i −0.399864 + 0.230861i −0.686425 0.727201i \(-0.740821\pi\)
0.286562 + 0.958062i \(0.407488\pi\)
\(774\) −6.55829 + 3.78643i −0.235733 + 0.136100i
\(775\) 0 0
\(776\) −1.37671 2.38453i −0.0494210 0.0855997i
\(777\) −17.9759 + 31.1351i −0.644881 + 1.11697i
\(778\) −23.4099 13.5157i −0.839284 0.484561i
\(779\) 58.6410 2.10103
\(780\) 0 0
\(781\) 5.85651 0.209562
\(782\) −4.31119 2.48907i −0.154168 0.0890088i
\(783\) 5.02239 8.69904i 0.179486 0.310878i
\(784\) 3.14177 + 5.44171i 0.112206 + 0.194347i
\(785\) 0