Properties

Label 390.2.bb.c.361.3
Level $390$
Weight $2$
Character 390.361
Analytic conductor $3.114$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.3
Root \(1.33404 + 1.33404i\) of defining polynomial
Character \(\chi\) \(=\) 390.361
Dual form 390.2.bb.c.121.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.44460 + 0.834038i) q^{11} -1.00000 q^{12} +(-2.24376 - 2.82233i) q^{13} -3.64466 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(5.46699 + 3.15637i) q^{19} +(-0.866025 - 0.500000i) q^{20} +3.64466i q^{21} +(-0.834038 + 1.44460i) q^{22} +(0.622266 + 1.07780i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-3.35432 - 1.32233i) q^{26} +1.00000 q^{27} +(-3.15637 + 1.82233i) q^{28} +(-5.02239 - 8.69904i) q^{29} +(-0.500000 + 0.866025i) q^{30} +4.21957i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.44460 + 0.834038i) q^{33} -4.00000i q^{34} +(-1.82233 + 3.15637i) q^{35} +(0.500000 + 0.866025i) q^{36} +(8.54267 - 4.93211i) q^{37} +6.31274 q^{38} +(-1.32233 + 3.35432i) q^{39} -1.00000 q^{40} +(8.04479 - 4.64466i) q^{41} +(1.82233 + 3.15637i) q^{42} +(-3.78643 + 6.55829i) q^{43} +1.66808i q^{44} +(0.866025 + 0.500000i) q^{45} +(1.07780 + 0.622266i) q^{46} -6.82522i q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.14177 + 5.44171i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +(-3.56609 + 0.531987i) q^{52} -0.848634 q^{53} +(0.866025 - 0.500000i) q^{54} +(0.834038 + 1.44460i) q^{55} +(-1.82233 + 3.15637i) q^{56} -6.31274i q^{57} +(-8.69904 - 5.02239i) q^{58} +(5.29034 + 3.05438i) q^{59} +1.00000i q^{60} +(-3.73205 + 6.46410i) q^{61} +(2.10978 + 3.65425i) q^{62} +(3.15637 - 1.82233i) q^{63} -1.00000 q^{64} +(-2.82233 + 2.24376i) q^{65} +1.66808 q^{66} +(12.7768 - 7.37671i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(0.622266 - 1.07780i) q^{69} +3.64466i q^{70} +(-3.04056 - 1.75547i) q^{71} +(0.866025 + 0.500000i) q^{72} +12.2175i q^{73} +(4.93211 - 8.54267i) q^{74} +(0.500000 + 0.866025i) q^{75} +(5.46699 - 3.15637i) q^{76} +6.07957 q^{77} +(0.531987 + 3.56609i) q^{78} +9.93398 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.64466 - 8.04479i) q^{82} +7.95317i q^{83} +(3.15637 + 1.82233i) q^{84} +(-3.46410 - 2.00000i) q^{85} +7.57286i q^{86} +(-5.02239 + 8.69904i) q^{87} +(0.834038 + 1.44460i) q^{88} +(5.15425 - 2.97581i) q^{89} +1.00000 q^{90} +(1.93891 + 12.9972i) q^{91} +1.24453 q^{92} +(3.65425 - 2.10978i) q^{93} +(-3.41261 - 5.91081i) q^{94} +(3.15637 - 5.46699i) q^{95} +1.00000i q^{96} +(-2.38453 - 1.37671i) q^{97} +(5.44171 + 3.14177i) q^{98} -1.66808i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{3} + 4q^{4} - 4q^{9} - 4q^{10} + 6q^{11} - 8q^{12} - 12q^{13} + 4q^{14} - 4q^{16} + 16q^{17} - 6q^{19} + 2q^{22} + 4q^{23} - 8q^{25} - 12q^{26} + 8q^{27} - 8q^{29} - 4q^{30} - 6q^{33} + 2q^{35} + 4q^{36} + 30q^{37} + 6q^{39} - 8q^{40} - 2q^{42} + 14q^{43} - 6q^{46} - 4q^{48} + 14q^{49} - 32q^{51} - 6q^{52} + 16q^{53} - 2q^{55} + 2q^{56} - 6q^{58} + 24q^{59} - 16q^{61} + 4q^{62} - 8q^{64} - 6q^{65} - 4q^{66} + 24q^{67} - 16q^{68} + 4q^{69} - 12q^{71} + 10q^{74} + 4q^{75} - 6q^{76} + 16q^{77} + 6q^{78} - 20q^{79} - 4q^{81} + 4q^{82} - 8q^{87} - 2q^{88} + 42q^{89} + 8q^{90} - 10q^{91} + 8q^{92} + 30q^{93} - 8q^{94} - 24q^{97} + 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −3.15637 1.82233i −1.19299 0.688776i −0.234010 0.972234i \(-0.575185\pi\)
−0.958985 + 0.283458i \(0.908518\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −1.44460 + 0.834038i −0.435562 + 0.251472i −0.701713 0.712459i \(-0.747581\pi\)
0.266151 + 0.963931i \(0.414248\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.24376 2.82233i −0.622307 0.782773i
\(14\) −3.64466 −0.974076
\(15\) −0.866025 + 0.500000i −0.223607 + 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 5.46699 + 3.15637i 1.25421 + 0.724120i 0.971943 0.235215i \(-0.0755793\pi\)
0.282270 + 0.959335i \(0.408913\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 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 \(-0.125249\pi\)
−0.793829 + 0.608141i \(0.791915\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) −1.00000 −0.200000
\(26\) −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 −0.778798 0.627275i \(-0.784170\pi\)
−0.153837 0.988096i \(-0.549163\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 4.21957i 0.757857i 0.925426 + 0.378928i \(0.123707\pi\)
−0.925426 + 0.378928i \(0.876293\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 1.44460 + 0.834038i 0.251472 + 0.145187i
\(34\) 4.00000i 0.685994i
\(35\) −1.82233 + 3.15637i −0.308030 + 0.533524i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 8.54267 4.93211i 1.40441 0.810835i 0.409566 0.912281i \(-0.365680\pi\)
0.994841 + 0.101446i \(0.0323469\pi\)
\(38\) 6.31274 1.02406
\(39\) −1.32233 + 3.35432i −0.211742 + 0.537121i
\(40\) −1.00000 −0.158114
\(41\) 8.04479 4.64466i 1.25638 0.725374i 0.284015 0.958820i \(-0.408334\pi\)
0.972370 + 0.233446i \(0.0750002\pi\)
\(42\) 1.82233 + 3.15637i 0.281192 + 0.487038i
\(43\) −3.78643 + 6.55829i −0.577425 + 1.00013i 0.418348 + 0.908287i \(0.362609\pi\)
−0.995773 + 0.0918433i \(0.970724\pi\)
\(44\) 1.66808i 0.251472i
\(45\) 0.866025 + 0.500000i 0.129099 + 0.0745356i
\(46\) 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
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) −4.00000 −0.560112
\(52\) −3.56609 + 0.531987i −0.494528 + 0.0737734i
\(53\) −0.848634 −0.116569 −0.0582844 0.998300i \(-0.518563\pi\)
−0.0582844 + 0.998300i \(0.518563\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0.834038 + 1.44460i 0.112462 + 0.194789i
\(56\) −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 0.803141 0.595789i \(-0.203160\pi\)
−0.114397 + 0.993435i \(0.536494\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −3.73205 + 6.46410i −0.477840 + 0.827643i −0.999677 0.0254017i \(-0.991914\pi\)
0.521837 + 0.853045i \(0.325247\pi\)
\(62\) 2.10978 + 3.65425i 0.267943 + 0.464091i
\(63\) 3.15637 1.82233i 0.397665 0.229592i
\(64\) −1.00000 −0.125000
\(65\) −2.82233 + 2.24376i −0.350067 + 0.278304i
\(66\) 1.66808 0.205326
\(67\) 12.7768 7.37671i 1.56094 0.901209i 0.563777 0.825927i \(-0.309348\pi\)
0.997162 0.0752814i \(-0.0239855\pi\)
\(68\) −2.00000 3.46410i −0.242536 0.420084i
\(69\) 0.622266 1.07780i 0.0749121 0.129752i
\(70\) 3.64466i 0.435620i
\(71\) −3.04056 1.75547i −0.360848 0.208336i 0.308605 0.951190i \(-0.400138\pi\)
−0.669453 + 0.742855i \(0.733471\pi\)
\(72\) 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
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 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 \(0.311250\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) −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
\(85\) −3.46410 2.00000i −0.375735 0.216930i
\(86\) 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 −0.201299 0.979530i \(-0.564516\pi\)
0.747648 + 0.664095i \(0.231183\pi\)
\(90\) 1.00000 0.105409
\(91\) 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
\(95\) 3.15637 5.46699i 0.323837 0.560901i
\(96\) 1.00000i 0.102062i
\(97\) −2.38453 1.37671i −0.242113 0.139784i 0.374035 0.927415i \(-0.377974\pi\)
−0.616147 + 0.787631i \(0.711307\pi\)
\(98\) 5.44171 + 3.14177i 0.549696 + 0.317367i
\(99\) 1.66808i 0.167648i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 2.66808 + 4.62124i 0.265483 + 0.459831i 0.967690 0.252142i \(-0.0811351\pi\)
−0.702207 + 0.711973i \(0.747802\pi\)
\(102\) −3.46410 + 2.00000i −0.342997 + 0.198030i
\(103\) −7.51248 −0.740227 −0.370113 0.928987i \(-0.620681\pi\)
−0.370113 + 0.928987i \(0.620681\pi\)
\(104\) −2.82233 + 2.24376i −0.276752 + 0.220019i
\(105\) 3.64466 0.355682
\(106\) −0.734939 + 0.424317i −0.0713835 + 0.0412133i
\(107\) −8.46410 14.6603i −0.818256 1.41726i −0.906966 0.421203i \(-0.861608\pi\)
0.0887109 0.996057i \(-0.471725\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 0.663848i 0.0635851i 0.999494 + 0.0317926i \(0.0101216\pi\)
−0.999494 + 0.0317926i \(0.989878\pi\)
\(110\) 1.44460 + 0.834038i 0.137737 + 0.0795224i
\(111\) −8.54267 4.93211i −0.810835 0.468136i
\(112\) 3.64466i 0.344388i
\(113\) 8.93500 15.4759i 0.840534 1.45585i −0.0489094 0.998803i \(-0.515575\pi\)
0.889444 0.457045i \(-0.151092\pi\)
\(114\) −3.15637 5.46699i −0.295621 0.512030i
\(115\) 1.07780 0.622266i 0.100505 0.0580266i
\(116\) −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
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) −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
\(125\) 1.00000i 0.0894427i
\(126\) 1.82233 3.15637i 0.162346 0.281192i
\(127\) 7.22034 + 12.5060i 0.640702 + 1.10973i 0.985276 + 0.170969i \(0.0546898\pi\)
−0.344575 + 0.938759i \(0.611977\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 7.57286 0.666753
\(130\) −1.32233 + 3.35432i −0.115976 + 0.294193i
\(131\) −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
\(135\) 1.00000i 0.0860663i
\(136\) −3.46410 2.00000i −0.297044 0.171499i
\(137\) 6.09419 + 3.51848i 0.520662 + 0.300604i 0.737205 0.675669i \(-0.236145\pi\)
−0.216544 + 0.976273i \(0.569478\pi\)
\(138\) 1.24453i 0.105942i
\(139\) −5.82233 + 10.0846i −0.493844 + 0.855362i −0.999975 0.00709431i \(-0.997742\pi\)
0.506131 + 0.862456i \(0.331075\pi\)
\(140\) 1.82233 + 3.15637i 0.154015 + 0.266762i
\(141\) −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
\(145\) −8.69904 + 5.02239i −0.722416 + 0.417087i
\(146\) 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 0.472342 0.881415i \(-0.343409\pi\)
−0.527157 + 0.849768i \(0.676742\pi\)
\(150\) 0.866025 + 0.500000i 0.0707107 + 0.0408248i
\(151\) 9.77838i 0.795754i −0.917439 0.397877i \(-0.869747\pi\)
0.917439 0.397877i \(-0.130253\pi\)
\(152\) 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
\(155\) 4.21957 0.338924
\(156\) 2.24376 + 2.82233i 0.179644 + 0.225967i
\(157\) −12.0135 −0.958786 −0.479393 0.877600i \(-0.659143\pi\)
−0.479393 + 0.877600i \(0.659143\pi\)
\(158\) 8.60308 4.96699i 0.684424 0.395152i
\(159\) 0.424317 + 0.734939i 0.0336505 + 0.0582844i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 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 \(-0.462664\pi\)
−0.801563 + 0.597911i \(0.795998\pi\)
\(164\) 9.28932i 0.725374i
\(165\) 0.834038 1.44460i 0.0649298 0.112462i
\(166\) 3.97658 + 6.88764i 0.308643 + 0.534585i
\(167\) −6.83902 + 3.94851i −0.529219 + 0.305545i −0.740698 0.671838i \(-0.765505\pi\)
0.211479 + 0.977382i \(0.432172\pi\)
\(168\) 3.64466 0.281192
\(169\) −2.93109 + 12.6653i −0.225469 + 0.974250i
\(170\) −4.00000 −0.306786
\(171\) −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 \(-0.838666\pi\)
0.857528 + 0.514438i \(0.171999\pi\)
\(174\) 10.0448i 0.761493i
\(175\) 3.15637 + 1.82233i 0.238599 + 0.137755i
\(176\) 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 −0.955220 0.295895i \(-0.904382\pi\)
0.221357 0.975193i \(-0.428951\pi\)
\(180\) 0.866025 0.500000i 0.0645497 0.0372678i
\(181\) 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
\(185\) −4.93211 8.54267i −0.362616 0.628070i
\(186\) 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
\(190\) 6.31274i 0.457974i
\(191\) −7.84081 + 13.5807i −0.567341 + 0.982664i 0.429486 + 0.903073i \(0.358695\pi\)
−0.996828 + 0.0795905i \(0.974639\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 7.03901 4.06397i 0.506679 0.292531i −0.224788 0.974408i \(-0.572169\pi\)
0.731468 + 0.681876i \(0.238836\pi\)
\(194\) −2.75342 −0.197684
\(195\) 3.35432 + 1.32233i 0.240208 + 0.0946940i
\(196\) 6.28354 0.448825
\(197\) 0.771835 0.445619i 0.0549910 0.0317491i −0.472252 0.881463i \(-0.656559\pi\)
0.527243 + 0.849714i \(0.323226\pi\)
\(198\) −0.834038 1.44460i −0.0592725 0.102663i
\(199\) 0.180558 0.312736i 0.0127994 0.0221692i −0.859555 0.511044i \(-0.829259\pi\)
0.872354 + 0.488874i \(0.162592\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −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
\(205\) −4.64466 8.04479i −0.324397 0.561872i
\(206\) −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
\(210\) 3.15637 1.82233i 0.217810 0.125753i
\(211\) −1.11370 1.92898i −0.0766700 0.132796i 0.825141 0.564926i \(-0.191095\pi\)
−0.901811 + 0.432130i \(0.857762\pi\)
\(212\) −0.424317 + 0.734939i −0.0291422 + 0.0504758i
\(213\) 3.51093i 0.240565i
\(214\) −14.6603 8.46410i −1.00215 0.578594i
\(215\) 6.55829 + 3.78643i 0.447272 + 0.258232i
\(216\) 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
\(220\) 1.66808 0.112462
\(221\) −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 \(-0.601370\pi\)
0.665927 + 0.746017i \(0.268036\pi\)
\(224\) 1.82233 + 3.15637i 0.121760 + 0.210894i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 17.8700i 1.18869i
\(227\) −13.2679 7.66025i −0.880625 0.508429i −0.00976038 0.999952i \(-0.503107\pi\)
−0.870864 + 0.491523i \(0.836440\pi\)
\(228\) −5.46699 3.15637i −0.362060 0.209036i
\(229\) 22.2644i 1.47127i −0.677378 0.735635i \(-0.736884\pi\)
0.677378 0.735635i \(-0.263116\pi\)
\(230\) 0.622266 1.07780i 0.0410310 0.0710678i
\(231\) −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 \(-0.384493\pi\)
0.354964 + 0.934880i \(0.384493\pi\)
\(234\) 2.82233 2.24376i 0.184501 0.146679i
\(235\) −6.82522 −0.445228
\(236\) 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 \(0.179149\pi\)
−0.845757 + 0.533568i \(0.820851\pi\)
\(240\) 0.866025 + 0.500000i 0.0559017 + 0.0322749i
\(241\) 3.81428 + 2.20218i 0.245700 + 0.141855i 0.617794 0.786340i \(-0.288027\pi\)
−0.372094 + 0.928195i \(0.621360\pi\)
\(242\) 8.21752i 0.528242i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 3.73205 + 6.46410i 0.238920 + 0.413822i
\(245\) 5.44171 3.14177i 0.347658 0.200720i
\(246\) −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
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 5.97267 10.3450i 0.376992 0.652969i −0.613631 0.789593i \(-0.710292\pi\)
0.990623 + 0.136624i \(0.0436252\pi\)
\(252\) 3.64466i 0.229592i
\(253\) −1.79785 1.03799i −0.113030 0.0652577i
\(254\) 12.5060 + 7.22034i 0.784696 + 0.453045i
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 9.73103 + 16.8546i 0.607005 + 1.05136i 0.991731 + 0.128333i \(0.0409625\pi\)
−0.384726 + 0.923031i \(0.625704\pi\)
\(258\) 6.55829 3.78643i 0.408301 0.235733i
\(259\) −35.9518 −2.23393
\(260\) 0.531987 + 3.56609i 0.0329925 + 0.221159i
\(261\) 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 \(-0.186649\pi\)
−0.895687 + 0.444685i \(0.853316\pi\)
\(264\) 0.834038 1.44460i 0.0513315 0.0889087i
\(265\) 0.848634i 0.0521312i
\(266\) −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 0.362551 + 0.931964i \(0.381906\pi\)
−0.988380 + 0.152003i \(0.951428\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 22.1184 12.7700i 1.34359 0.775725i 0.356261 0.934386i \(-0.384051\pi\)
0.987333 + 0.158662i \(0.0507179\pi\)
\(272\) −4.00000 −0.242536
\(273\) 10.2864 8.17774i 0.622563 0.494939i
\(274\) 7.03696 0.425119
\(275\) 1.44460 0.834038i 0.0871124 0.0502944i
\(276\) −0.622266 1.07780i −0.0374560 0.0648758i
\(277\) 9.03019 15.6407i 0.542572 0.939762i −0.456184 0.889886i \(-0.650784\pi\)
0.998755 0.0498760i \(-0.0158826\pi\)
\(278\) 11.6447i 0.698400i
\(279\) −3.65425 2.10978i −0.218774 0.126309i
\(280\) 3.15637 + 1.82233i 0.188629 + 0.108905i
\(281\) 20.2175i 1.20608i 0.797712 + 0.603038i \(0.206043\pi\)
−0.797712 + 0.603038i \(0.793957\pi\)
\(282\) −3.41261 + 5.91081i −0.203218 + 0.351984i
\(283\) 4.34575 + 7.52705i 0.258328 + 0.447437i 0.965794 0.259310i \(-0.0834952\pi\)
−0.707466 + 0.706747i \(0.750162\pi\)
\(284\) −3.04056 + 1.75547i −0.180424 + 0.104168i
\(285\) −6.31274 −0.373934
\(286\) 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
\(290\) −5.02239 + 8.69904i −0.294925 + 0.510825i
\(291\) 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 \(-0.262572\pi\)
−0.296758 + 0.954953i \(0.595905\pi\)
\(294\) 6.28354i 0.366464i
\(295\) 3.05438 5.29034i 0.177833 0.308016i
\(296\) −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
\(300\) 1.00000 0.0577350
\(301\) 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
\(305\) 6.46410 + 3.73205i 0.370133 + 0.213697i
\(306\) 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
\(310\) 3.65425 2.10978i 0.207548 0.119828i
\(311\) 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 \(-0.848677\pi\)
−0.889112 + 0.457689i \(0.848677\pi\)
\(314\) −10.4040 + 6.00677i −0.587134 + 0.338982i
\(315\) −1.82233 3.15637i −0.102677 0.177841i
\(316\) 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
\(320\) 1.00000i 0.0559017i
\(321\) −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
\(325\) 2.24376 + 2.82233i 0.124461 + 0.156555i
\(326\) −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
\(330\) 1.66808i 0.0918246i
\(331\) −4.85286 2.80180i −0.266737 0.154001i 0.360667 0.932695i \(-0.382549\pi\)
−0.627404 + 0.778694i \(0.715883\pi\)
\(332\) 6.88764 + 3.97658i 0.378009 + 0.218243i
\(333\) 9.86423i 0.540556i
\(334\) −3.94851 + 6.83902i −0.216053 + 0.374214i
\(335\) −7.37671 12.7768i −0.403033 0.698073i
\(336\) 3.15637 1.82233i 0.172194 0.0994162i
\(337\) 21.7868 1.18680 0.593402 0.804906i \(-0.297784\pi\)
0.593402 + 0.804906i \(0.297784\pi\)
\(338\) 3.79423 + 12.4340i 0.206379 + 0.676319i
\(339\) −17.8700 −0.970565
\(340\) −3.46410 + 2.00000i −0.187867 + 0.108465i
\(341\) −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
\(345\) −1.07780 0.622266i −0.0580266 0.0335017i
\(346\) 0.440685i 0.0236914i
\(347\) −4.84081 + 8.38453i −0.259868 + 0.450105i −0.966206 0.257769i \(-0.917013\pi\)
0.706338 + 0.707875i \(0.250346\pi\)
\(348\) 5.02239 + 8.69904i 0.269229 + 0.466318i
\(349\) 16.7321 9.66025i 0.895646 0.517102i 0.0198610 0.999803i \(-0.493678\pi\)
0.875785 + 0.482701i \(0.160344\pi\)
\(350\) 3.64466 0.194815
\(351\) −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 \(-0.876068\pi\)
−0.133851 + 0.991002i \(0.542734\pi\)
\(354\) −3.05438 5.29034i −0.162338 0.281179i
\(355\) −1.75547 + 3.04056i −0.0931705 + 0.161376i
\(356\) 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 \(-0.981362\pi\)
0.998286 0.0585182i \(-0.0186376\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 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
\(365\) 12.2175 0.639494
\(366\) 6.46410 3.73205i 0.337884 0.195077i
\(367\) 3.04056 + 5.26640i 0.158716 + 0.274904i 0.934406 0.356210i \(-0.115931\pi\)
−0.775690 + 0.631114i \(0.782598\pi\)
\(368\) 0.622266 1.07780i 0.0324379 0.0561841i
\(369\) 9.28932i 0.483583i
\(370\) −8.54267 4.93211i −0.444112 0.256408i
\(371\) 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 \(-0.966372\pi\)
0.588535 + 0.808472i \(0.299705\pi\)
\(374\) 3.33615 + 5.77838i 0.172508 + 0.298793i
\(375\) 0.866025 0.500000i 0.0447214 0.0258199i
\(376\) −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 0.375951 0.926640i \(-0.377316\pi\)
0.990469 + 0.137737i \(0.0439829\pi\)
\(380\) −3.15637 5.46699i −0.161918 0.280451i
\(381\) 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 \(-0.162031\pi\)
0.0145623 + 0.999894i \(0.495365\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 6.07957i 0.309844i
\(386\) 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 \(0.259683\pi\)
\(390\) 3.56609 0.531987i 0.180576 0.0269382i
\(391\) 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
\(395\) 9.93398i 0.499833i
\(396\) −1.44460 0.834038i −0.0725937 0.0419120i
\(397\) −3.23571 1.86814i −0.162396 0.0937592i 0.416600 0.909090i \(-0.363222\pi\)
−0.578995 + 0.815331i \(0.696555\pi\)
\(398\) 0.361116i 0.0181011i
\(399\) −11.5039 + 19.9253i −0.575915 + 0.997513i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 24.3276 14.0456i 1.21486 0.701402i 0.251049 0.967974i \(-0.419225\pi\)
0.963815 + 0.266573i \(0.0858912\pi\)
\(402\) −14.7534 −0.735834
\(403\) 11.9090 9.46770i 0.593230 0.471620i
\(404\) 5.33615 0.265483
\(405\) −0.866025 + 0.500000i −0.0430331 + 0.0248452i
\(406\) 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 0.954265 0.298961i \(-0.0966399\pi\)
0.218225 + 0.975898i \(0.429973\pi\)
\(410\) −8.04479 4.64466i −0.397304 0.229383i
\(411\) 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
\(415\) 7.95317 0.390406
\(416\) 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 0.980795 0.195041i \(-0.0624839\pi\)
−0.659308 + 0.751873i \(0.729151\pi\)
\(420\) 1.82233 3.15637i 0.0889206 0.154015i
\(421\) 1.29341i 0.0630370i −0.999503 0.0315185i \(-0.989966\pi\)
0.999503 0.0315185i \(-0.0100343\pi\)
\(422\) −1.92898 1.11370i −0.0939011 0.0542138i
\(423\) 5.91081 + 3.41261i 0.287394 + 0.165927i
\(424\) 0.848634i 0.0412133i
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 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
\(430\) 7.57286 0.365196
\(431\) 10.5031 6.06397i 0.505917 0.292091i −0.225237 0.974304i \(-0.572316\pi\)
0.731154 + 0.682213i \(0.238982\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −1.03901 + 1.79962i −0.0499317 + 0.0864842i −0.889911 0.456134i \(-0.849234\pi\)
0.839979 + 0.542618i \(0.182567\pi\)
\(434\) 15.3789i 0.738210i
\(435\) 8.69904 + 5.02239i 0.417087 + 0.240805i
\(436\) 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 0.836015 0.548707i \(-0.184880\pi\)
−0.893202 + 0.449656i \(0.851546\pi\)
\(440\) 1.44460 0.834038i 0.0688684 0.0397612i
\(441\) −6.28354 −0.299216
\(442\) −11.2893 + 8.97504i −0.536978 + 0.426899i
\(443\) 21.9959 1.04506 0.522529 0.852622i \(-0.324989\pi\)
0.522529 + 0.852622i \(0.324989\pi\)
\(444\) −8.54267 + 4.93211i −0.405417 + 0.234068i
\(445\) −2.97581 5.15425i −0.141067 0.244335i
\(446\) 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 0.959312 0.282350i \(-0.0911138\pi\)
0.235134 + 0.971963i \(0.424447\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −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
\(455\) 12.9972 1.93891i 0.609317 0.0908976i
\(456\) −6.31274 −0.295621
\(457\) −34.3321 + 19.8216i −1.60599 + 0.927216i −0.615730 + 0.787957i \(0.711139\pi\)
−0.990256 + 0.139259i \(0.955528\pi\)
\(458\) −11.1322 19.2815i −0.520172 0.900965i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 1.24453i 0.0580266i
\(461\) 14.4417 + 8.33792i 0.672617 + 0.388336i 0.797068 0.603890i \(-0.206383\pi\)
−0.124450 + 0.992226i \(0.539717\pi\)
\(462\) −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
\(465\) −2.10978 3.65425i −0.0978389 0.169462i
\(466\) 9.38476 5.41829i 0.434740 0.250998i
\(467\) −6.88137 −0.318432 −0.159216 0.987244i \(-0.550897\pi\)
−0.159216 + 0.987244i \(0.550897\pi\)
\(468\) 1.32233 3.35432i 0.0611247 0.155053i
\(469\) −53.7712 −2.48292
\(470\) −5.91081 + 3.41261i −0.272645 + 0.157412i
\(471\) 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
\(475\) −5.46699 3.15637i −0.250843 0.144824i
\(476\) 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 −0.825938 0.563761i \(-0.809354\pi\)
0.0752629 + 0.997164i \(0.476020\pi\)
\(480\) 1.00000 0.0456435
\(481\) −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
\(485\) −1.37671 + 2.38453i −0.0625132 + 0.108276i
\(486\) 1.00000i 0.0453609i
\(487\) 1.65948 + 0.958101i 0.0751982 + 0.0434157i 0.537128 0.843501i \(-0.319509\pi\)
−0.461929 + 0.886917i \(0.652843\pi\)
\(488\) 6.46410 + 3.73205i 0.292616 + 0.168942i
\(489\) 10.0916i 0.456359i
\(490\) 3.14177 5.44171i 0.141931 0.245831i
\(491\) −16.8187 29.1309i −0.759019 1.31466i −0.943351 0.331795i \(-0.892346\pi\)
0.184332 0.982864i \(-0.440988\pi\)
\(492\) −8.04479 + 4.64466i −0.362687 + 0.209397i
\(493\) −40.1791 −1.80958
\(494\) −14.1643 17.8166i −0.637280 0.801608i
\(495\) −1.66808 −0.0749744
\(496\) 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 \(-0.986992\pi\)
0.999165 0.0408540i \(-0.0130078\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 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 \(-0.686237\pi\)
0.998111 + 0.0614437i \(0.0195705\pi\)
\(504\) −1.82233 3.15637i −0.0811730 0.140596i
\(505\) 4.62124 2.66808i 0.205643 0.118728i
\(506\) −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 −0.382650 0.923893i \(-0.624988\pi\)
0.608790 + 0.793331i \(0.291655\pi\)
\(510\) 2.00000 + 3.46410i 0.0885615 + 0.153393i
\(511\) 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
\(515\) 7.51248i 0.331040i
\(516\) 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
\(520\) 2.24376 + 2.82233i 0.0983953 + 0.123767i
\(521\) 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 −0.884292 0.466934i \(-0.845359\pi\)
0.0377693 0.999286i \(-0.487975\pi\)
\(524\) −5.44460 + 9.43032i −0.237848 + 0.411965i
\(525\) 3.64466i 0.159066i
\(526\) −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
\(530\) 0.424317 + 0.734939i 0.0184312 + 0.0319237i
\(531\) −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
\(535\) −14.6603 + 8.46410i −0.633818 + 0.365935i
\(536\) −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
\(540\) −0.866025 0.500000i −0.0372678 0.0215166i
\(541\) 25.9616i 1.11618i −0.829781 0.558089i \(-0.811535\pi\)
0.829781 0.558089i \(-0.188465\pi\)
\(542\) 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
\(545\) 0.663848 0.0284361
\(546\) 4.81944 12.2253i 0.206253 0.523196i
\(547\) −17.7596 −0.759348 −0.379674 0.925120i \(-0.623964\pi\)
−0.379674 + 0.925120i \(0.623964\pi\)
\(548\) 6.09419 3.51848i 0.260331 0.150302i
\(549\) −3.73205 6.46410i −0.159280 0.275881i
\(550\) 0.834038 1.44460i 0.0355635 0.0615978i
\(551\) 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
\(555\) −4.93211 + 8.54267i −0.209357 + 0.362616i
\(556\) 5.82233 + 10.0846i 0.246922 + 0.427681i
\(557\) −22.7074 + 13.1101i −0.962142 + 0.555493i −0.896832 0.442372i \(-0.854137\pi\)
−0.0653102 + 0.997865i \(0.520804\pi\)
\(558\) −4.21957 −0.178629
\(559\) 27.0055 4.02867i 1.14221 0.170394i
\(560\) 3.64466 0.154015
\(561\) 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 0.450696 + 0.892677i \(0.351176\pi\)
−0.998429 + 0.0560243i \(0.982158\pi\)
\(564\) 6.82522i 0.287394i
\(565\) −15.4759 8.93500i −0.651075 0.375898i
\(566\) 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 −0.999217 0.0395693i \(-0.987401\pi\)
0.465340 0.885132i \(-0.345932\pi\)
\(570\) −5.46699 + 3.15637i −0.228987 + 0.132206i
\(571\) −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
\(575\) −0.622266 1.07780i −0.0259503 0.0449472i
\(576\) 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
\(580\) 10.0448i 0.417087i
\(581\) 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
\(585\) −0.531987 3.56609i −0.0219950 0.147440i
\(586\) 7.54790 0.311801
\(587\) 23.7108 13.6894i 0.978650 0.565024i 0.0767878 0.997047i \(-0.475534\pi\)
0.901862 + 0.432024i \(0.142200\pi\)
\(588\) −3.14177 5.44171i −0.129564 0.224412i
\(589\) −13.3185 + 23.0683i −0.548780 + 0.950514i
\(590\) 6.10876i 0.251494i
\(591\) −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
\(595\) 7.28932 + 12.6255i 0.298833 + 0.517594i
\(596\) −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 \(0.698727\pi\)
\(600\) 0.866025 0.500000i 0.0353553 0.0204124i
\(601\) 9.58380 + 16.5996i 0.390931 + 0.677113i 0.992573 0.121654i \(-0.0388197\pi\)
−0.601641 + 0.798766i \(0.705486\pi\)
\(602\) 13.8003 23.9027i 0.562456 0.974203i
\(603\) 14.7534i 0.600806i
\(604\) −8.46833 4.88919i −0.344571 0.198938i
\(605\) 7.11658 + 4.10876i 0.289330 + 0.167045i
\(606\) 5.33615i 0.216766i
\(607\) −9.46910 + 16.4010i −0.384339 + 0.665695i −0.991677 0.128749i \(-0.958904\pi\)
0.607338 + 0.794443i \(0.292237\pi\)
\(608\) −3.15637 5.46699i −0.128008 0.221716i
\(609\) 31.7050 18.3049i 1.28475 0.741753i
\(610\) 7.46410 0.302213
\(611\) −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 \(-0.784876\pi\)
0.151645 + 0.988435i \(0.451543\pi\)
\(614\) 13.0214 + 22.5537i 0.525500 + 0.910192i
\(615\) −4.64466 + 8.04479i −0.187291 + 0.324397i
\(616\) 6.07957i 0.244953i
\(617\) −15.6015 9.00755i −0.628094 0.362630i 0.151920 0.988393i \(-0.451455\pi\)
−0.780014 + 0.625763i \(0.784788\pi\)
\(618\) 6.50600 + 3.75624i 0.261710 + 0.151098i
\(619\) 25.0505i 1.00687i −0.864035 0.503433i \(-0.832070\pi\)
0.864035 0.503433i \(-0.167930\pi\)
\(620\) 2.10978 3.65425i 0.0847310 0.146758i
\(621\) 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
\(625\) 1.00000 0.0400000
\(626\) −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
\(630\) −3.15637 1.82233i −0.125753 0.0726034i
\(631\) −1.22739 0.708634i −0.0488617 0.0282103i 0.475370 0.879786i \(-0.342314\pi\)
−0.524232 + 0.851576i \(0.675647\pi\)
\(632\) 9.93398i 0.395152i
\(633\) −1.11370 + 1.92898i −0.0442654 + 0.0766700i
\(634\) −12.3546 21.3989i −0.490665 0.849857i
\(635\) 12.5060 7.22034i 0.496285 0.286531i
\(636\) 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
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 2.30985 4.00077i 0.0912335 0.158021i −0.816797 0.576925i \(-0.804252\pi\)
0.908030 + 0.418904i \(0.137586\pi\)
\(642\) 16.9282i 0.668103i
\(643\) 41.6468 + 24.0448i 1.64239 + 0.948234i 0.979981 + 0.199091i \(0.0637988\pi\)
0.662408 + 0.749143i \(0.269535\pi\)
\(644\) −3.92820 2.26795i −0.154793 0.0893697i
\(645\) 7.57286i 0.298181i
\(646\) 12.6255 21.8680i 0.496743 0.860383i
\(647\) 1.87282 + 3.24383i 0.0736283 + 0.127528i 0.900489 0.434879i \(-0.143209\pi\)
−0.826861 + 0.562407i \(0.809875\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −10.1899 −0.399988
\(650\) 3.35432 + 1.32233i 0.131567 + 0.0518660i
\(651\) −15.3789 −0.602746
\(652\) −8.73960 + 5.04581i −0.342269 + 0.197609i
\(653\) −21.1450 36.6241i −0.827466 1.43321i −0.900020 0.435849i \(-0.856448\pi\)
0.0725541 0.997364i \(-0.476885\pi\)
\(654\) 0.331924 0.574909i 0.0129793 0.0224807i
\(655\) 10.8892i 0.425476i
\(656\) −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 −0.428492 0.903546i \(-0.640955\pi\)
0.996739 0.0806881i \(-0.0257118\pi\)
\(660\) −0.834038 1.44460i −0.0324649 0.0562308i
\(661\) −38.5089 + 22.2331i −1.49782 + 0.864768i −0.999997 0.00250931i \(-0.999201\pi\)
−0.497825 + 0.867277i \(0.665868\pi\)
\(662\) −5.60360 −0.217790
\(663\) 8.97504 + 11.2893i 0.348562 + 0.438441i
\(664\) 7.95317 0.308643
\(665\) −19.9253 + 11.5039i −0.772671 + 0.446102i
\(666\) 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
\(670\) −12.7768 7.37671i −0.493612 0.284987i
\(671\) 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 \(-0.117972\pi\)
−0.779720 + 0.626129i \(0.784638\pi\)
\(674\) 18.8680 10.8934i 0.726767 0.419599i
\(675\) −1.00000 −0.0384900
\(676\) 9.50289 + 8.87103i 0.365496 + 0.341193i
\(677\) −7.05615 −0.271190 −0.135595 0.990764i \(-0.543295\pi\)
−0.135595 + 0.990764i \(0.543295\pi\)
\(678\) −15.4759 + 8.93500i −0.594347 + 0.343147i
\(679\) 5.01764 + 8.69081i 0.192559 + 0.333523i
\(680\) −2.00000 + 3.46410i −0.0766965 + 0.132842i
\(681\) 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 \(-0.369666\pi\)
−0.595383 + 0.803442i \(0.703000\pi\)
\(684\) 6.31274i 0.241373i
\(685\) 3.51848 6.09419i 0.134434 0.232847i
\(686\) 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
\(690\) −1.24453 −0.0473786
\(691\) 16.2458 9.37953i 0.618020 0.356814i −0.158078 0.987427i \(-0.550530\pi\)
0.776098 + 0.630613i \(0.217196\pi\)
\(692\) 0.220343 + 0.381645i 0.00837617 + 0.0145080i
\(693\) −3.03978 + 5.26506i −0.115472 + 0.200003i
\(694\) 9.68162i 0.367509i
\(695\) 10.0846 + 5.82233i 0.382530 + 0.220854i
\(696\) 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
\(700\) 3.15637 1.82233i 0.119299 0.0688776i
\(701\) −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
\(705\) 3.41261 + 5.91081i 0.128526 + 0.222614i
\(706\) −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 0.0729321 0.997337i \(-0.476764\pi\)
−0.827253 + 0.561830i \(0.810098\pi\)
\(710\) 3.51093i 0.131763i
\(711\) −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
\(715\) 2.20575 5.59526i 0.0824902 0.209251i
\(716\) −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 −0.735914 0.677075i \(-0.763247\pi\)
0.954321 + 0.298783i \(0.0965806\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 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
\(725\) 5.02239 + 8.69904i 0.186527 + 0.323074i
\(726\) 7.11658 4.10876i 0.264121 0.152490i
\(727\) 3.82677 0.141927 0.0709634 0.997479i \(-0.477393\pi\)
0.0709634 + 0.997479i \(0.477393\pi\)
\(728\) 12.9972 1.93891i 0.481708 0.0718609i
\(729\) 1.00000 0.0370370
\(730\) 10.5807 6.10876i 0.391609 0.226095i
\(731\) 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
\(735\) −5.44171 3.14177i −0.200720 0.115886i
\(736\) 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 −0.942934 0.332980i \(-0.891946\pi\)
−0.183098 + 0.983095i \(0.558612\pi\)
\(740\) −9.86423 −0.362616
\(741\) −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 \(-0.904882\pi\)
−0.222887 + 0.974844i \(0.571548\pi\)
\(744\) −2.10978 3.65425i −0.0773484 0.133971i
\(745\) −0.386305 + 0.669099i −0.0141531 + 0.0245139i
\(746\) 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
\(750\) 0.500000 0.866025i 0.0182574 0.0316228i
\(751\) −4.82904 8.36414i −0.176214 0.305212i 0.764367 0.644782i \(-0.223052\pi\)
−0.940581 + 0.339570i \(0.889718\pi\)
\(752\) −5.91081 + 3.41261i −0.215545 + 0.124445i
\(753\) −11.9453 −0.435313
\(754\) 5.34370 + 35.8206i 0.194606 + 1.30451i
\(755\) −9.77838 −0.355872
\(756\) −3.15637 + 1.82233i −0.114796 + 0.0662775i
\(757\) 21.8443 + 37.8354i 0.793943 + 1.37515i 0.923508 + 0.383579i \(0.125309\pi\)
−0.129565 + 0.991571i \(0.541358\pi\)
\(758\) 15.3583 26.6013i 0.557838 0.966204i
\(759\) 2.07598i 0.0753531i
\(760\) −5.46699 3.15637i −0.198309 0.114493i
\(761\) 34.5550 + 19.9503i 1.25262 + 0.723200i 0.971629 0.236511i \(-0.0760040\pi\)
0.280990 + 0.959711i \(0.409337\pi\)
\(762\) 14.4407i 0.523131i
\(763\) 1.20975 2.09535i 0.0437959 0.0758567i
\(764\) 7.84081 + 13.5807i 0.283671 + 0.491332i
\(765\) 3.46410 2.00000i 0.125245 0.0723102i
\(766\) 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 −0.748459 0.663181i \(-0.769206\pi\)
0.200103 + 0.979775i \(0.435872\pi\)
\(770\) −3.03978 5.26506i −0.109546 0.189740i
\(771\) 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 \(-0.259179\pi\)
−0.286562 + 0.958062i \(0.592512\pi\)
\(774\) −6.55829 3.78643i −0.235733 0.136100i
\(775\) 4.21957i 0.151571i
\(776\)