Properties

Label 507.2.e.g.22.2
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.2
Root \(1.28078 - 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.g.484.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.28078 - 2.21837i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} -0.561553 q^{5} +(1.28078 + 2.21837i) q^{6} +(-1.78078 - 3.08440i) q^{7} -6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.28078 - 2.21837i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} -0.561553 q^{5} +(1.28078 + 2.21837i) q^{6} +(-1.78078 - 3.08440i) q^{7} -6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.719224 + 1.24573i) q^{10} +(-1.00000 + 1.73205i) q^{11} +4.56155 q^{12} -9.12311 q^{14} +(0.280776 - 0.486319i) q^{15} +(-3.84233 + 6.65511i) q^{16} +(-1.28078 - 2.21837i) q^{17} -2.56155 q^{18} +(-0.561553 - 0.972638i) q^{19} +(1.28078 + 2.21837i) q^{20} +3.56155 q^{21} +(2.56155 + 4.43674i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(3.28078 - 5.68247i) q^{24} -4.68466 q^{25} +1.00000 q^{27} +(-8.12311 + 14.0696i) q^{28} +(2.84233 - 4.92306i) q^{29} +(-0.719224 - 1.24573i) q^{30} +1.56155 q^{31} +(3.28078 + 5.68247i) q^{32} +(-1.00000 - 1.73205i) q^{33} -6.56155 q^{34} +(1.00000 + 1.73205i) q^{35} +(-2.28078 + 3.95042i) q^{36} +(1.71922 - 2.97778i) q^{37} -2.87689 q^{38} +3.68466 q^{40} +(1.28078 - 2.21837i) q^{41} +(4.56155 - 7.90084i) q^{42} +(-0.219224 - 0.379706i) q^{43} +9.12311 q^{44} +(0.280776 + 0.486319i) q^{45} +(2.56155 + 4.43674i) q^{46} +8.24621 q^{47} +(-3.84233 - 6.65511i) q^{48} +(-2.84233 + 4.92306i) q^{49} +(-6.00000 + 10.3923i) q^{50} +2.56155 q^{51} +11.6847 q^{53} +(1.28078 - 2.21837i) q^{54} +(0.561553 - 0.972638i) q^{55} +(11.6847 + 20.2384i) q^{56} +1.12311 q^{57} +(-7.28078 - 12.6107i) q^{58} +(-5.56155 - 9.63289i) q^{59} -2.56155 q^{60} +(-6.06155 - 10.4989i) q^{61} +(2.00000 - 3.46410i) q^{62} +(-1.78078 + 3.08440i) q^{63} +1.43845 q^{64} -5.12311 q^{66} +(0.219224 - 0.379706i) q^{67} +(-5.84233 + 10.1192i) q^{68} +(-1.00000 - 1.73205i) q^{69} +5.12311 q^{70} +(7.00000 + 12.1244i) q^{71} +(3.28078 + 5.68247i) q^{72} +1.87689 q^{73} +(-4.40388 - 7.62775i) q^{74} +(2.34233 - 4.05703i) q^{75} +(-2.56155 + 4.43674i) q^{76} +7.12311 q^{77} +9.56155 q^{79} +(2.15767 - 3.73720i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.28078 - 5.68247i) q^{82} +9.12311 q^{83} +(-8.12311 - 14.0696i) q^{84} +(0.719224 + 1.24573i) q^{85} -1.12311 q^{86} +(2.84233 + 4.92306i) q^{87} +(6.56155 - 11.3649i) q^{88} +(6.56155 - 11.3649i) q^{89} +1.43845 q^{90} +9.12311 q^{92} +(-0.780776 + 1.35234i) q^{93} +(10.5616 - 18.2931i) q^{94} +(0.315342 + 0.546188i) q^{95} -6.56155 q^{96} +(-2.21922 - 3.84381i) q^{97} +(7.28078 + 12.6107i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} - 2q^{3} - 5q^{4} + 6q^{5} + q^{6} - 3q^{7} - 18q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + q^{2} - 2q^{3} - 5q^{4} + 6q^{5} + q^{6} - 3q^{7} - 18q^{8} - 2q^{9} - 7q^{10} - 4q^{11} + 10q^{12} - 20q^{14} - 3q^{15} - 3q^{16} - q^{17} - 2q^{18} + 6q^{19} + q^{20} + 6q^{21} + 2q^{22} - 4q^{23} + 9q^{24} + 6q^{25} + 4q^{27} - 16q^{28} - q^{29} - 7q^{30} - 2q^{31} + 9q^{32} - 4q^{33} - 18q^{34} + 4q^{35} - 5q^{36} + 11q^{37} - 28q^{38} - 10q^{40} + q^{41} + 10q^{42} - 5q^{43} + 20q^{44} - 3q^{45} + 2q^{46} - 3q^{48} + q^{49} - 24q^{50} + 2q^{51} + 22q^{53} + q^{54} - 6q^{55} + 22q^{56} - 12q^{57} - 25q^{58} - 14q^{59} - 2q^{60} - 16q^{61} + 8q^{62} - 3q^{63} + 14q^{64} - 4q^{66} + 5q^{67} - 11q^{68} - 4q^{69} + 4q^{70} + 28q^{71} + 9q^{72} + 24q^{73} + 3q^{74} - 3q^{75} - 2q^{76} + 12q^{77} + 30q^{79} + 21q^{80} - 2q^{81} - 9q^{82} + 20q^{83} - 16q^{84} + 7q^{85} + 12q^{86} - q^{87} + 18q^{88} + 18q^{89} + 14q^{90} + 20q^{92} + q^{93} + 34q^{94} + 26q^{95} - 18q^{96} - 13q^{97} + 25q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28078 2.21837i 0.905646 1.56862i 0.0855975 0.996330i \(-0.472720\pi\)
0.820048 0.572295i \(-0.193947\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −2.28078 3.95042i −1.14039 1.97521i
\(5\) −0.561553 −0.251134 −0.125567 0.992085i \(-0.540075\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 1.28078 + 2.21837i 0.522875 + 0.905646i
\(7\) −1.78078 3.08440i −0.673070 1.16579i −0.977029 0.213107i \(-0.931642\pi\)
0.303959 0.952685i \(-0.401692\pi\)
\(8\) −6.56155 −2.31986
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.719224 + 1.24573i −0.227438 + 0.393935i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 4.56155 1.31681
\(13\) 0 0
\(14\) −9.12311 −2.43825
\(15\) 0.280776 0.486319i 0.0724962 0.125567i
\(16\) −3.84233 + 6.65511i −0.960582 + 1.66378i
\(17\) −1.28078 2.21837i −0.310634 0.538034i 0.667866 0.744282i \(-0.267208\pi\)
−0.978500 + 0.206248i \(0.933875\pi\)
\(18\) −2.56155 −0.603764
\(19\) −0.561553 0.972638i −0.128829 0.223138i 0.794394 0.607403i \(-0.207789\pi\)
−0.923223 + 0.384264i \(0.874455\pi\)
\(20\) 1.28078 + 2.21837i 0.286390 + 0.496043i
\(21\) 3.56155 0.777195
\(22\) 2.56155 + 4.43674i 0.546125 + 0.945916i
\(23\) −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i \(-0.900196\pi\)
0.742732 + 0.669588i \(0.233529\pi\)
\(24\) 3.28078 5.68247i 0.669686 1.15993i
\(25\) −4.68466 −0.936932
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −8.12311 + 14.0696i −1.53512 + 2.65891i
\(29\) 2.84233 4.92306i 0.527807 0.914189i −0.471667 0.881777i \(-0.656348\pi\)
0.999475 0.0324124i \(-0.0103190\pi\)
\(30\) −0.719224 1.24573i −0.131312 0.227438i
\(31\) 1.56155 0.280463 0.140232 0.990119i \(-0.455215\pi\)
0.140232 + 0.990119i \(0.455215\pi\)
\(32\) 3.28078 + 5.68247i 0.579965 + 1.00453i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) −6.56155 −1.12530
\(35\) 1.00000 + 1.73205i 0.169031 + 0.292770i
\(36\) −2.28078 + 3.95042i −0.380129 + 0.658403i
\(37\) 1.71922 2.97778i 0.282639 0.489544i −0.689395 0.724385i \(-0.742124\pi\)
0.972034 + 0.234841i \(0.0754570\pi\)
\(38\) −2.87689 −0.466694
\(39\) 0 0
\(40\) 3.68466 0.582596
\(41\) 1.28078 2.21837i 0.200024 0.346451i −0.748512 0.663121i \(-0.769231\pi\)
0.948536 + 0.316670i \(0.102565\pi\)
\(42\) 4.56155 7.90084i 0.703863 1.21913i
\(43\) −0.219224 0.379706i −0.0334313 0.0579047i 0.848826 0.528673i \(-0.177310\pi\)
−0.882257 + 0.470768i \(0.843977\pi\)
\(44\) 9.12311 1.37536
\(45\) 0.280776 + 0.486319i 0.0418557 + 0.0724962i
\(46\) 2.56155 + 4.43674i 0.377680 + 0.654162i
\(47\) 8.24621 1.20283 0.601417 0.798935i \(-0.294603\pi\)
0.601417 + 0.798935i \(0.294603\pi\)
\(48\) −3.84233 6.65511i −0.554592 0.960582i
\(49\) −2.84233 + 4.92306i −0.406047 + 0.703294i
\(50\) −6.00000 + 10.3923i −0.848528 + 1.46969i
\(51\) 2.56155 0.358689
\(52\) 0 0
\(53\) 11.6847 1.60501 0.802506 0.596645i \(-0.203500\pi\)
0.802506 + 0.596645i \(0.203500\pi\)
\(54\) 1.28078 2.21837i 0.174292 0.301882i
\(55\) 0.561553 0.972638i 0.0757198 0.131150i
\(56\) 11.6847 + 20.2384i 1.56143 + 2.70447i
\(57\) 1.12311 0.148759
\(58\) −7.28078 12.6107i −0.956013 1.65586i
\(59\) −5.56155 9.63289i −0.724053 1.25410i −0.959363 0.282175i \(-0.908944\pi\)
0.235310 0.971920i \(-0.424389\pi\)
\(60\) −2.56155 −0.330695
\(61\) −6.06155 10.4989i −0.776102 1.34425i −0.934173 0.356821i \(-0.883861\pi\)
0.158071 0.987428i \(-0.449473\pi\)
\(62\) 2.00000 3.46410i 0.254000 0.439941i
\(63\) −1.78078 + 3.08440i −0.224357 + 0.388597i
\(64\) 1.43845 0.179806
\(65\) 0 0
\(66\) −5.12311 −0.630611
\(67\) 0.219224 0.379706i 0.0267824 0.0463885i −0.852324 0.523015i \(-0.824807\pi\)
0.879106 + 0.476626i \(0.158141\pi\)
\(68\) −5.84233 + 10.1192i −0.708486 + 1.22713i
\(69\) −1.00000 1.73205i −0.120386 0.208514i
\(70\) 5.12311 0.612328
\(71\) 7.00000 + 12.1244i 0.830747 + 1.43890i 0.897447 + 0.441123i \(0.145420\pi\)
−0.0666994 + 0.997773i \(0.521247\pi\)
\(72\) 3.28078 + 5.68247i 0.386643 + 0.669686i
\(73\) 1.87689 0.219674 0.109837 0.993950i \(-0.464967\pi\)
0.109837 + 0.993950i \(0.464967\pi\)
\(74\) −4.40388 7.62775i −0.511941 0.886708i
\(75\) 2.34233 4.05703i 0.270469 0.468466i
\(76\) −2.56155 + 4.43674i −0.293830 + 0.508929i
\(77\) 7.12311 0.811753
\(78\) 0 0
\(79\) 9.56155 1.07576 0.537879 0.843022i \(-0.319226\pi\)
0.537879 + 0.843022i \(0.319226\pi\)
\(80\) 2.15767 3.73720i 0.241235 0.417831i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.28078 5.68247i −0.362301 0.627524i
\(83\) 9.12311 1.00139 0.500695 0.865624i \(-0.333078\pi\)
0.500695 + 0.865624i \(0.333078\pi\)
\(84\) −8.12311 14.0696i −0.886303 1.53512i
\(85\) 0.719224 + 1.24573i 0.0780108 + 0.135119i
\(86\) −1.12311 −0.121108
\(87\) 2.84233 + 4.92306i 0.304730 + 0.527807i
\(88\) 6.56155 11.3649i 0.699464 1.21151i
\(89\) 6.56155 11.3649i 0.695523 1.20468i −0.274481 0.961593i \(-0.588506\pi\)
0.970004 0.243089i \(-0.0781607\pi\)
\(90\) 1.43845 0.151626
\(91\) 0 0
\(92\) 9.12311 0.951150
\(93\) −0.780776 + 1.35234i −0.0809627 + 0.140232i
\(94\) 10.5616 18.2931i 1.08934 1.88679i
\(95\) 0.315342 + 0.546188i 0.0323534 + 0.0560377i
\(96\) −6.56155 −0.669686
\(97\) −2.21922 3.84381i −0.225328 0.390280i 0.731090 0.682281i \(-0.239012\pi\)
−0.956418 + 0.292002i \(0.905679\pi\)
\(98\) 7.28078 + 12.6107i 0.735469 + 1.27387i
\(99\) 2.00000 0.201008
\(100\) 10.6847 + 18.5064i 1.06847 + 1.85064i
\(101\) 1.71922 2.97778i 0.171069 0.296300i −0.767725 0.640780i \(-0.778611\pi\)
0.938794 + 0.344479i \(0.111945\pi\)
\(102\) 3.28078 5.68247i 0.324845 0.562649i
\(103\) −7.56155 −0.745062 −0.372531 0.928020i \(-0.621510\pi\)
−0.372531 + 0.928020i \(0.621510\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 14.9654 25.9209i 1.45357 2.51766i
\(107\) −4.12311 + 7.14143i −0.398596 + 0.690388i −0.993553 0.113369i \(-0.963836\pi\)
0.594957 + 0.803757i \(0.297169\pi\)
\(108\) −2.28078 3.95042i −0.219468 0.380129i
\(109\) −17.8078 −1.70567 −0.852837 0.522177i \(-0.825120\pi\)
−0.852837 + 0.522177i \(0.825120\pi\)
\(110\) −1.43845 2.49146i −0.137151 0.237552i
\(111\) 1.71922 + 2.97778i 0.163181 + 0.282639i
\(112\) 27.3693 2.58616
\(113\) 7.40388 + 12.8239i 0.696499 + 1.20637i 0.969673 + 0.244406i \(0.0785931\pi\)
−0.273174 + 0.961965i \(0.588074\pi\)
\(114\) 1.43845 2.49146i 0.134723 0.233347i
\(115\) 0.561553 0.972638i 0.0523651 0.0906990i
\(116\) −25.9309 −2.40762
\(117\) 0 0
\(118\) −28.4924 −2.62294
\(119\) −4.56155 + 7.90084i −0.418157 + 0.724269i
\(120\) −1.84233 + 3.19101i −0.168181 + 0.291298i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −31.0540 −2.81149
\(123\) 1.28078 + 2.21837i 0.115484 + 0.200024i
\(124\) −3.56155 6.16879i −0.319837 0.553974i
\(125\) 5.43845 0.486430
\(126\) 4.56155 + 7.90084i 0.406375 + 0.703863i
\(127\) −4.78078 + 8.28055i −0.424225 + 0.734780i −0.996348 0.0853884i \(-0.972787\pi\)
0.572122 + 0.820168i \(0.306120\pi\)
\(128\) −4.71922 + 8.17394i −0.417124 + 0.722481i
\(129\) 0.438447 0.0386031
\(130\) 0 0
\(131\) −17.3693 −1.51756 −0.758782 0.651345i \(-0.774205\pi\)
−0.758782 + 0.651345i \(0.774205\pi\)
\(132\) −4.56155 + 7.90084i −0.397032 + 0.687680i
\(133\) −2.00000 + 3.46410i −0.173422 + 0.300376i
\(134\) −0.561553 0.972638i −0.0485108 0.0840231i
\(135\) −0.561553 −0.0483308
\(136\) 8.40388 + 14.5560i 0.720627 + 1.24816i
\(137\) −0.719224 1.24573i −0.0614474 0.106430i 0.833665 0.552270i \(-0.186238\pi\)
−0.895113 + 0.445840i \(0.852905\pi\)
\(138\) −5.12311 −0.436108
\(139\) −5.46543 9.46641i −0.463572 0.802930i 0.535564 0.844495i \(-0.320099\pi\)
−0.999136 + 0.0415643i \(0.986766\pi\)
\(140\) 4.56155 7.90084i 0.385522 0.667743i
\(141\) −4.12311 + 7.14143i −0.347228 + 0.601417i
\(142\) 35.8617 3.00945
\(143\) 0 0
\(144\) 7.68466 0.640388
\(145\) −1.59612 + 2.76456i −0.132550 + 0.229584i
\(146\) 2.40388 4.16365i 0.198947 0.344586i
\(147\) −2.84233 4.92306i −0.234431 0.406047i
\(148\) −15.6847 −1.28927
\(149\) −3.28078 5.68247i −0.268772 0.465526i 0.699773 0.714365i \(-0.253284\pi\)
−0.968545 + 0.248839i \(0.919951\pi\)
\(150\) −6.00000 10.3923i −0.489898 0.848528i
\(151\) −15.3693 −1.25074 −0.625369 0.780329i \(-0.715051\pi\)
−0.625369 + 0.780329i \(0.715051\pi\)
\(152\) 3.68466 + 6.38202i 0.298865 + 0.517650i
\(153\) −1.28078 + 2.21837i −0.103545 + 0.179345i
\(154\) 9.12311 15.8017i 0.735161 1.27334i
\(155\) −0.876894 −0.0704339
\(156\) 0 0
\(157\) −4.36932 −0.348709 −0.174355 0.984683i \(-0.555784\pi\)
−0.174355 + 0.984683i \(0.555784\pi\)
\(158\) 12.2462 21.2111i 0.974256 1.68746i
\(159\) −5.84233 + 10.1192i −0.463327 + 0.802506i
\(160\) −1.84233 3.19101i −0.145649 0.252271i
\(161\) 7.12311 0.561379
\(162\) 1.28078 + 2.21837i 0.100627 + 0.174292i
\(163\) 7.90388 + 13.6899i 0.619080 + 1.07228i 0.989654 + 0.143475i \(0.0458276\pi\)
−0.370574 + 0.928803i \(0.620839\pi\)
\(164\) −11.6847 −0.912419
\(165\) 0.561553 + 0.972638i 0.0437168 + 0.0757198i
\(166\) 11.6847 20.2384i 0.906905 1.57081i
\(167\) −3.12311 + 5.40938i −0.241673 + 0.418590i −0.961191 0.275884i \(-0.911030\pi\)
0.719518 + 0.694474i \(0.244363\pi\)
\(168\) −23.3693 −1.80298
\(169\) 0 0
\(170\) 3.68466 0.282600
\(171\) −0.561553 + 0.972638i −0.0429430 + 0.0743795i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −1.87689 3.25088i −0.142698 0.247160i 0.785814 0.618463i \(-0.212244\pi\)
−0.928512 + 0.371303i \(0.878911\pi\)
\(174\) 14.5616 1.10391
\(175\) 8.34233 + 14.4493i 0.630621 + 1.09227i
\(176\) −7.68466 13.3102i −0.579253 1.00330i
\(177\) 11.1231 0.836064
\(178\) −16.8078 29.1119i −1.25980 2.18203i
\(179\) 6.56155 11.3649i 0.490433 0.849456i −0.509506 0.860467i \(-0.670172\pi\)
0.999939 + 0.0110115i \(0.00350513\pi\)
\(180\) 1.28078 2.21837i 0.0954634 0.165348i
\(181\) 9.68466 0.719855 0.359927 0.932980i \(-0.382801\pi\)
0.359927 + 0.932980i \(0.382801\pi\)
\(182\) 0 0
\(183\) 12.1231 0.896166
\(184\) 6.56155 11.3649i 0.483724 0.837835i
\(185\) −0.965435 + 1.67218i −0.0709802 + 0.122941i
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) 5.12311 0.374639
\(188\) −18.8078 32.5760i −1.37170 2.37585i
\(189\) −1.78078 3.08440i −0.129532 0.224357i
\(190\) 1.61553 0.117203
\(191\) 0.438447 + 0.759413i 0.0317249 + 0.0549492i 0.881452 0.472274i \(-0.156567\pi\)
−0.849727 + 0.527223i \(0.823233\pi\)
\(192\) −0.719224 + 1.24573i −0.0519055 + 0.0899029i
\(193\) 9.74621 16.8809i 0.701548 1.21512i −0.266375 0.963869i \(-0.585826\pi\)
0.967923 0.251247i \(-0.0808406\pi\)
\(194\) −11.3693 −0.816269
\(195\) 0 0
\(196\) 25.9309 1.85220
\(197\) −5.68466 + 9.84612i −0.405015 + 0.701507i −0.994323 0.106402i \(-0.966067\pi\)
0.589308 + 0.807908i \(0.299400\pi\)
\(198\) 2.56155 4.43674i 0.182042 0.315305i
\(199\) 11.5885 + 20.0719i 0.821490 + 1.42286i 0.904573 + 0.426320i \(0.140190\pi\)
−0.0830828 + 0.996543i \(0.526477\pi\)
\(200\) 30.7386 2.17355
\(201\) 0.219224 + 0.379706i 0.0154628 + 0.0267824i
\(202\) −4.40388 7.62775i −0.309856 0.536686i
\(203\) −20.2462 −1.42101
\(204\) −5.84233 10.1192i −0.409045 0.708486i
\(205\) −0.719224 + 1.24573i −0.0502328 + 0.0870057i
\(206\) −9.68466 + 16.7743i −0.674762 + 1.16872i
\(207\) 2.00000 0.139010
\(208\) 0 0
\(209\) 2.24621 0.155374
\(210\) −2.56155 + 4.43674i −0.176764 + 0.306164i
\(211\) −3.65767 + 6.33527i −0.251804 + 0.436138i −0.964023 0.265820i \(-0.914357\pi\)
0.712218 + 0.701958i \(0.247691\pi\)
\(212\) −26.6501 46.1593i −1.83034 3.17023i
\(213\) −14.0000 −0.959264
\(214\) 10.5616 + 18.2931i 0.721973 + 1.25049i
\(215\) 0.123106 + 0.213225i 0.00839573 + 0.0145418i
\(216\) −6.56155 −0.446457
\(217\) −2.78078 4.81645i −0.188771 0.326962i
\(218\) −22.8078 + 39.5042i −1.54474 + 2.67556i
\(219\) −0.938447 + 1.62544i −0.0634144 + 0.109837i
\(220\) −5.12311 −0.345400
\(221\) 0 0
\(222\) 8.80776 0.591138
\(223\) 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i \(-0.747017\pi\)
0.968309 + 0.249756i \(0.0803503\pi\)
\(224\) 11.6847 20.2384i 0.780714 1.35224i
\(225\) 2.34233 + 4.05703i 0.156155 + 0.270469i
\(226\) 37.9309 2.52312
\(227\) −0.561553 0.972638i −0.0372716 0.0645563i 0.846788 0.531931i \(-0.178533\pi\)
−0.884059 + 0.467374i \(0.845200\pi\)
\(228\) −2.56155 4.43674i −0.169643 0.293830i
\(229\) −0.246211 −0.0162701 −0.00813505 0.999967i \(-0.502589\pi\)
−0.00813505 + 0.999967i \(0.502589\pi\)
\(230\) −1.43845 2.49146i −0.0948484 0.164282i
\(231\) −3.56155 + 6.16879i −0.234333 + 0.405877i
\(232\) −18.6501 + 32.3029i −1.22444 + 2.12079i
\(233\) 26.0000 1.70332 0.851658 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) 0 0
\(235\) −4.63068 −0.302072
\(236\) −25.3693 + 43.9409i −1.65140 + 2.86031i
\(237\) −4.78078 + 8.28055i −0.310545 + 0.537879i
\(238\) 11.6847 + 20.2384i 0.757404 + 1.31186i
\(239\) 0.630683 0.0407955 0.0203977 0.999792i \(-0.493507\pi\)
0.0203977 + 0.999792i \(0.493507\pi\)
\(240\) 2.15767 + 3.73720i 0.139277 + 0.241235i
\(241\) 1.40388 + 2.43160i 0.0904320 + 0.156633i 0.907693 0.419635i \(-0.137842\pi\)
−0.817261 + 0.576268i \(0.804509\pi\)
\(242\) 17.9309 1.15264
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −27.6501 + 47.8914i −1.77012 + 3.06593i
\(245\) 1.59612 2.76456i 0.101972 0.176621i
\(246\) 6.56155 0.418349
\(247\) 0 0
\(248\) −10.2462 −0.650635
\(249\) −4.56155 + 7.90084i −0.289077 + 0.500695i
\(250\) 6.96543 12.0645i 0.440533 0.763025i
\(251\) 15.3693 + 26.6204i 0.970103 + 1.68027i 0.695231 + 0.718786i \(0.255302\pi\)
0.274871 + 0.961481i \(0.411365\pi\)
\(252\) 16.2462 1.02342
\(253\) −2.00000 3.46410i −0.125739 0.217786i
\(254\) 12.2462 + 21.2111i 0.768396 + 1.33090i
\(255\) −1.43845 −0.0900791
\(256\) 13.5270 + 23.4294i 0.845437 + 1.46434i
\(257\) 8.08854 14.0098i 0.504549 0.873905i −0.495437 0.868644i \(-0.664992\pi\)
0.999986 0.00526106i \(-0.00167466\pi\)
\(258\) 0.561553 0.972638i 0.0349608 0.0605538i
\(259\) −12.2462 −0.760943
\(260\) 0 0
\(261\) −5.68466 −0.351872
\(262\) −22.2462 + 38.5316i −1.37438 + 2.38049i
\(263\) 7.68466 13.3102i 0.473856 0.820743i −0.525696 0.850673i \(-0.676195\pi\)
0.999552 + 0.0299295i \(0.00952826\pi\)
\(264\) 6.56155 + 11.3649i 0.403836 + 0.699464i
\(265\) −6.56155 −0.403073
\(266\) 5.12311 + 8.87348i 0.314118 + 0.544068i
\(267\) 6.56155 + 11.3649i 0.401561 + 0.695523i
\(268\) −2.00000 −0.122169
\(269\) −1.68466 2.91791i −0.102715 0.177908i 0.810087 0.586310i \(-0.199420\pi\)
−0.912803 + 0.408401i \(0.866086\pi\)
\(270\) −0.719224 + 1.24573i −0.0437706 + 0.0758128i
\(271\) −0.534565 + 0.925894i −0.0324725 + 0.0562441i −0.881805 0.471614i \(-0.843671\pi\)
0.849332 + 0.527858i \(0.177005\pi\)
\(272\) 19.6847 1.19356
\(273\) 0 0
\(274\) −3.68466 −0.222598
\(275\) 4.68466 8.11407i 0.282496 0.489297i
\(276\) −4.56155 + 7.90084i −0.274573 + 0.475575i
\(277\) −8.84233 15.3154i −0.531284 0.920211i −0.999333 0.0365086i \(-0.988376\pi\)
0.468049 0.883702i \(-0.344957\pi\)
\(278\) −28.0000 −1.67933
\(279\) −0.780776 1.35234i −0.0467439 0.0809627i
\(280\) −6.56155 11.3649i −0.392128 0.679185i
\(281\) 2.80776 0.167497 0.0837486 0.996487i \(-0.473311\pi\)
0.0837486 + 0.996487i \(0.473311\pi\)
\(282\) 10.5616 + 18.2931i 0.628931 + 1.08934i
\(283\) 0.657671 1.13912i 0.0390945 0.0677136i −0.845816 0.533475i \(-0.820886\pi\)
0.884911 + 0.465761i \(0.154219\pi\)
\(284\) 31.9309 55.3059i 1.89475 3.28180i
\(285\) −0.630683 −0.0373584
\(286\) 0 0
\(287\) −9.12311 −0.538520
\(288\) 3.28078 5.68247i 0.193322 0.334843i
\(289\) 5.21922 9.03996i 0.307013 0.531762i
\(290\) 4.08854 + 7.08156i 0.240087 + 0.415844i
\(291\) 4.43845 0.260186
\(292\) −4.28078 7.41452i −0.250513 0.433902i
\(293\) 12.2808 + 21.2709i 0.717451 + 1.24266i 0.962007 + 0.273026i \(0.0880244\pi\)
−0.244556 + 0.969635i \(0.578642\pi\)
\(294\) −14.5616 −0.849247
\(295\) 3.12311 + 5.40938i 0.181834 + 0.314946i
\(296\) −11.2808 + 19.5389i −0.655682 + 1.13567i
\(297\) −1.00000 + 1.73205i −0.0580259 + 0.100504i
\(298\) −16.8078 −0.973648
\(299\) 0 0
\(300\) −21.3693 −1.23376
\(301\) −0.780776 + 1.35234i −0.0450032 + 0.0779478i
\(302\) −19.6847 + 34.0948i −1.13272 + 1.96194i
\(303\) 1.71922 + 2.97778i 0.0987668 + 0.171069i
\(304\) 8.63068 0.495004
\(305\) 3.40388 + 5.89570i 0.194906 + 0.337587i
\(306\) 3.28078 + 5.68247i 0.187550 + 0.324845i
\(307\) −10.1922 −0.581702 −0.290851 0.956768i \(-0.593938\pi\)
−0.290851 + 0.956768i \(0.593938\pi\)
\(308\) −16.2462 28.1393i −0.925714 1.60338i
\(309\) 3.78078 6.54850i 0.215081 0.372531i
\(310\) −1.12311 + 1.94528i −0.0637881 + 0.110484i
\(311\) −10.8769 −0.616772 −0.308386 0.951261i \(-0.599789\pi\)
−0.308386 + 0.951261i \(0.599789\pi\)
\(312\) 0 0
\(313\) −1.31534 −0.0743475 −0.0371738 0.999309i \(-0.511835\pi\)
−0.0371738 + 0.999309i \(0.511835\pi\)
\(314\) −5.59612 + 9.69276i −0.315807 + 0.546994i
\(315\) 1.00000 1.73205i 0.0563436 0.0975900i
\(316\) −21.8078 37.7722i −1.22678 2.12485i
\(317\) 23.0540 1.29484 0.647420 0.762133i \(-0.275848\pi\)
0.647420 + 0.762133i \(0.275848\pi\)
\(318\) 14.9654 + 25.9209i 0.839220 + 1.45357i
\(319\) 5.68466 + 9.84612i 0.318280 + 0.551277i
\(320\) −0.807764 −0.0451554
\(321\) −4.12311 7.14143i −0.230129 0.398596i
\(322\) 9.12311 15.8017i 0.508411 0.880593i
\(323\) −1.43845 + 2.49146i −0.0800373 + 0.138629i
\(324\) 4.56155 0.253420
\(325\) 0 0
\(326\) 40.4924 2.24267
\(327\) 8.90388 15.4220i 0.492386 0.852837i
\(328\) −8.40388 + 14.5560i −0.464027 + 0.803718i
\(329\) −14.6847 25.4346i −0.809591 1.40225i
\(330\) 2.87689 0.158368
\(331\) −11.9039 20.6181i −0.654297 1.13327i −0.982070 0.188518i \(-0.939631\pi\)
0.327773 0.944756i \(-0.393702\pi\)
\(332\) −20.8078 36.0401i −1.14197 1.97796i
\(333\) −3.43845 −0.188426
\(334\) 8.00000 + 13.8564i 0.437741 + 0.758189i
\(335\) −0.123106 + 0.213225i −0.00672598 + 0.0116497i
\(336\) −13.6847 + 23.7025i −0.746559 + 1.29308i
\(337\) 2.12311 0.115653 0.0578265 0.998327i \(-0.481583\pi\)
0.0578265 + 0.998327i \(0.481583\pi\)
\(338\) 0 0
\(339\) −14.8078 −0.804247
\(340\) 3.28078 5.68247i 0.177925 0.308175i
\(341\) −1.56155 + 2.70469i −0.0845628 + 0.146467i
\(342\) 1.43845 + 2.49146i 0.0777823 + 0.134723i
\(343\) −4.68466 −0.252948
\(344\) 1.43845 + 2.49146i 0.0775559 + 0.134331i
\(345\) 0.561553 + 0.972638i 0.0302330 + 0.0523651i
\(346\) −9.61553 −0.516934
\(347\) 6.80776 + 11.7914i 0.365460 + 0.632995i 0.988850 0.148916i \(-0.0475784\pi\)
−0.623390 + 0.781911i \(0.714245\pi\)
\(348\) 12.9654 22.4568i 0.695020 1.20381i
\(349\) −6.90388 + 11.9579i −0.369556 + 0.640090i −0.989496 0.144559i \(-0.953824\pi\)
0.619940 + 0.784649i \(0.287157\pi\)
\(350\) 42.7386 2.28448
\(351\) 0 0
\(352\) −13.1231 −0.699464
\(353\) 8.84233 15.3154i 0.470630 0.815155i −0.528806 0.848743i \(-0.677360\pi\)
0.999436 + 0.0335881i \(0.0106934\pi\)
\(354\) 14.2462 24.6752i 0.757178 1.31147i
\(355\) −3.93087 6.80847i −0.208629 0.361356i
\(356\) −59.8617 −3.17267
\(357\) −4.56155 7.90084i −0.241423 0.418157i
\(358\) −16.8078 29.1119i −0.888318 1.53861i
\(359\) −15.3693 −0.811162 −0.405581 0.914059i \(-0.632931\pi\)
−0.405581 + 0.914059i \(0.632931\pi\)
\(360\) −1.84233 3.19101i −0.0970993 0.168181i
\(361\) 8.86932 15.3621i 0.466806 0.808532i
\(362\) 12.4039 21.4842i 0.651934 1.12918i
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) −1.05398 −0.0551676
\(366\) 15.5270 26.8935i 0.811609 1.40575i
\(367\) −10.0270 + 17.3673i −0.523404 + 0.906563i 0.476224 + 0.879324i \(0.342005\pi\)
−0.999629 + 0.0272394i \(0.991328\pi\)
\(368\) −7.68466 13.3102i −0.400591 0.693843i
\(369\) −2.56155 −0.133349
\(370\) 2.47301 + 4.28338i 0.128566 + 0.222682i
\(371\) −20.8078 36.0401i −1.08029 1.87111i
\(372\) 7.12311 0.369316
\(373\) −1.81534 3.14426i −0.0939948 0.162804i 0.815194 0.579188i \(-0.196630\pi\)
−0.909189 + 0.416384i \(0.863297\pi\)
\(374\) 6.56155 11.3649i 0.339290 0.587667i
\(375\) −2.71922 + 4.70983i −0.140420 + 0.243215i
\(376\) −54.1080 −2.79040
\(377\) 0 0
\(378\) −9.12311 −0.469242
\(379\) 5.65767 9.79937i 0.290615 0.503360i −0.683340 0.730100i \(-0.739473\pi\)
0.973955 + 0.226740i \(0.0728068\pi\)
\(380\) 1.43845 2.49146i 0.0737908 0.127809i
\(381\) −4.78078 8.28055i −0.244927 0.424225i
\(382\) 2.24621 0.114926
\(383\) 13.3693 + 23.1563i 0.683140 + 1.18323i 0.974017 + 0.226473i \(0.0727195\pi\)
−0.290877 + 0.956760i \(0.593947\pi\)
\(384\) −4.71922 8.17394i −0.240827 0.417124i
\(385\) −4.00000 −0.203859
\(386\) −24.9654 43.2414i −1.27071 2.20093i
\(387\) −0.219224 + 0.379706i −0.0111438 + 0.0193016i
\(388\) −10.1231 + 17.5337i −0.513923 + 0.890140i
\(389\) −3.05398 −0.154843 −0.0774213 0.996998i \(-0.524669\pi\)
−0.0774213 + 0.996998i \(0.524669\pi\)
\(390\) 0 0
\(391\) 5.12311 0.259087
\(392\) 18.6501 32.3029i 0.941972 1.63154i
\(393\) 8.68466 15.0423i 0.438083 0.758782i
\(394\) 14.5616 + 25.2213i 0.733600 + 1.27063i
\(395\) −5.36932 −0.270160
\(396\) −4.56155 7.90084i −0.229227 0.397032i
\(397\) −6.02699 10.4390i −0.302486 0.523921i 0.674213 0.738537i \(-0.264483\pi\)
−0.976698 + 0.214617i \(0.931150\pi\)
\(398\) 59.3693 2.97591
\(399\) −2.00000 3.46410i −0.100125 0.173422i
\(400\) 18.0000 31.1769i 0.900000 1.55885i
\(401\) 9.28078 16.0748i 0.463460 0.802736i −0.535671 0.844427i \(-0.679941\pi\)
0.999131 + 0.0416909i \(0.0132745\pi\)
\(402\) 1.12311 0.0560154
\(403\) 0 0
\(404\) −15.6847 −0.780341
\(405\) 0.280776 0.486319i 0.0139519 0.0241654i
\(406\) −25.9309 + 44.9136i −1.28693 + 2.22902i
\(407\) 3.43845 + 5.95557i 0.170437 + 0.295206i
\(408\) −16.8078 −0.832108
\(409\) −9.18466 15.9083i −0.454152 0.786615i 0.544487 0.838769i \(-0.316724\pi\)
−0.998639 + 0.0521548i \(0.983391\pi\)
\(410\) 1.84233 + 3.19101i 0.0909862 + 0.157593i
\(411\) 1.43845 0.0709534
\(412\) 17.2462 + 29.8713i 0.849660 + 1.47165i
\(413\) −19.8078 + 34.3081i −0.974676 + 1.68819i
\(414\) 2.56155 4.43674i 0.125893 0.218054i
\(415\) −5.12311 −0.251483
\(416\) 0 0
\(417\) 10.9309 0.535287
\(418\) 2.87689 4.98293i 0.140714 0.243723i
\(419\) 8.87689 15.3752i 0.433665 0.751129i −0.563521 0.826102i \(-0.690554\pi\)
0.997186 + 0.0749725i \(0.0238869\pi\)
\(420\) 4.56155 + 7.90084i 0.222581 + 0.385522i
\(421\) −14.7538 −0.719056 −0.359528 0.933134i \(-0.617062\pi\)
−0.359528 + 0.933134i \(0.617062\pi\)
\(422\) 9.36932 + 16.2281i 0.456091 + 0.789973i
\(423\) −4.12311 7.14143i −0.200472 0.347228i
\(424\) −76.6695 −3.72340
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) −17.9309 + 31.0572i −0.868753 + 1.50473i
\(427\) −21.5885 + 37.3924i −1.04474 + 1.80955i
\(428\) 37.6155 1.81822
\(429\) 0 0
\(430\) 0.630683 0.0304142
\(431\) −1.43845 + 2.49146i −0.0692876 + 0.120010i −0.898588 0.438794i \(-0.855406\pi\)
0.829300 + 0.558803i \(0.188739\pi\)
\(432\) −3.84233 + 6.65511i −0.184864 + 0.320194i
\(433\) −12.6231 21.8639i −0.606628 1.05071i −0.991792 0.127862i \(-0.959189\pi\)
0.385164 0.922848i \(-0.374145\pi\)
\(434\) −14.2462 −0.683840
\(435\) −1.59612 2.76456i −0.0765280 0.132550i
\(436\) 40.6155 + 70.3482i 1.94513 + 3.36907i
\(437\) 2.24621 0.107451
\(438\) 2.40388 + 4.16365i 0.114862 + 0.198947i
\(439\) 0.657671 1.13912i 0.0313889 0.0543672i −0.849904 0.526937i \(-0.823340\pi\)
0.881293 + 0.472570i \(0.156674\pi\)
\(440\) −3.68466 + 6.38202i −0.175659 + 0.304251i
\(441\) 5.68466 0.270698
\(442\) 0 0
\(443\) 14.7386 0.700254 0.350127 0.936702i \(-0.386138\pi\)
0.350127 + 0.936702i \(0.386138\pi\)
\(444\) 7.84233 13.5833i 0.372180 0.644635i
\(445\) −3.68466 + 6.38202i −0.174670 + 0.302537i
\(446\) −10.2462 17.7470i −0.485172 0.840343i
\(447\) 6.56155 0.310351
\(448\) −2.56155 4.43674i −0.121022 0.209616i
\(449\) 4.12311 + 7.14143i 0.194581 + 0.337025i 0.946763 0.321931i \(-0.104332\pi\)
−0.752182 + 0.658956i \(0.770998\pi\)
\(450\) 12.0000 0.565685
\(451\) 2.56155 + 4.43674i 0.120619 + 0.208918i
\(452\) 33.7732 58.4969i 1.58856 2.75146i
\(453\) 7.68466 13.3102i 0.361057 0.625369i
\(454\) −2.87689 −0.135019
\(455\) 0 0
\(456\) −7.36932 −0.345100
\(457\) −14.3078 + 24.7818i −0.669289 + 1.15924i 0.308814 + 0.951122i \(0.400068\pi\)
−0.978103 + 0.208120i \(0.933265\pi\)
\(458\) −0.315342 + 0.546188i −0.0147349 + 0.0255217i
\(459\) −1.28078 2.21837i −0.0597815 0.103545i
\(460\) −5.12311 −0.238866
\(461\) −18.4039 31.8765i −0.857154 1.48463i −0.874632 0.484787i \(-0.838897\pi\)
0.0174778 0.999847i \(-0.494436\pi\)
\(462\) 9.12311 + 15.8017i 0.424445 + 0.735161i
\(463\) 26.6847 1.24014 0.620071 0.784546i \(-0.287104\pi\)
0.620071 + 0.784546i \(0.287104\pi\)
\(464\) 21.8423 + 37.8320i 1.01400 + 1.75631i
\(465\) 0.438447 0.759413i 0.0203325 0.0352169i
\(466\) 33.3002 57.6776i 1.54260 2.67186i
\(467\) −26.0000 −1.20314 −0.601568 0.798821i \(-0.705457\pi\)
−0.601568 + 0.798821i \(0.705457\pi\)
\(468\) 0 0
\(469\) −1.56155 −0.0721058
\(470\) −5.93087 + 10.2726i −0.273571 + 0.473838i
\(471\) 2.18466 3.78394i 0.100664 0.174355i
\(472\) 36.4924 + 63.2067i 1.67970 + 2.90933i
\(473\) 0.876894 0.0403196
\(474\) 12.2462 + 21.2111i 0.562487 + 0.974256i
\(475\) 2.63068 + 4.55648i 0.120704 + 0.209065i
\(476\) 41.6155 1.90744
\(477\) −5.84233 10.1192i −0.267502 0.463327i
\(478\) 0.807764 1.39909i 0.0369463 0.0639928i
\(479\) −3.12311 + 5.40938i −0.142698 + 0.247161i −0.928512 0.371303i \(-0.878911\pi\)
0.785814 + 0.618463i \(0.212245\pi\)
\(480\) 3.68466 0.168181
\(481\) 0 0
\(482\) 7.19224 0.327597
\(483\) −3.56155 + 6.16879i −0.162056 + 0.280690i
\(484\) 15.9654 27.6529i 0.725702 1.25695i
\(485\) 1.24621 + 2.15850i 0.0565875 + 0.0980125i
\(486\) −2.56155 −0.116194
\(487\) −0.561553 0.972638i −0.0254464 0.0440744i 0.853022 0.521875i \(-0.174767\pi\)
−0.878468 + 0.477801i \(0.841434\pi\)
\(488\) 39.7732 + 68.8892i 1.80045 + 3.11847i
\(489\) −15.8078 −0.714852
\(490\) −4.08854 7.08156i −0.184701 0.319912i
\(491\) 9.87689 17.1073i 0.445738 0.772041i −0.552365 0.833602i \(-0.686275\pi\)
0.998103 + 0.0615613i \(0.0196080\pi\)
\(492\) 5.84233 10.1192i 0.263393 0.456209i
\(493\) −14.5616 −0.655819
\(494\) 0 0
\(495\) −1.12311 −0.0504798
\(496\) −6.00000 + 10.3923i −0.269408 + 0.466628i
\(497\) 24.9309 43.1815i 1.11830 1.93696i
\(498\) 11.6847 + 20.2384i 0.523602 + 0.906905i
\(499\) 28.4924 1.27550 0.637748 0.770245i \(-0.279866\pi\)
0.637748 + 0.770245i \(0.279866\pi\)
\(500\) −12.4039 21.4842i −0.554718 0.960801i
\(501\) −3.12311 5.40938i −0.139530 0.241673i
\(502\) 78.7386 3.51428
\(503\) 5.87689 + 10.1791i 0.262038 + 0.453863i 0.966783 0.255597i \(-0.0822722\pi\)
−0.704746 + 0.709460i \(0.748939\pi\)
\(504\) 11.6847 20.2384i 0.520476 0.901491i
\(505\) −0.965435 + 1.67218i −0.0429613 + 0.0744111i
\(506\) −10.2462 −0.455500
\(507\) 0 0
\(508\) 43.6155 1.93513
\(509\) 3.40388 5.89570i 0.150874 0.261322i −0.780675 0.624938i \(-0.785124\pi\)
0.931549 + 0.363615i \(0.118458\pi\)
\(510\) −1.84233 + 3.19101i −0.0815797 + 0.141300i
\(511\) −3.34233 5.78908i −0.147856 0.256094i
\(512\) 50.4233 2.22842
\(513\) −0.561553 0.972638i −0.0247932 0.0429430i
\(514\) −20.7192 35.8867i −0.913886 1.58290i
\(515\) 4.24621 0.187110
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) −8.24621 + 14.2829i −0.362668 + 0.628159i
\(518\) −15.6847 + 27.1666i −0.689144 + 1.19363i
\(519\) 3.75379 0.164773
\(520\) 0 0
\(521\) −37.9309 −1.66178 −0.830891 0.556436i \(-0.812169\pi\)
−0.830891 + 0.556436i \(0.812169\pi\)
\(522\) −7.28078 + 12.6107i −0.318671 + 0.551954i
\(523\) 11.9309 20.6649i 0.521701 0.903612i −0.477981 0.878370i \(-0.658631\pi\)
0.999681 0.0252415i \(-0.00803549\pi\)
\(524\) 39.6155 + 68.6161i 1.73061 + 2.99751i
\(525\) −16.6847 −0.728178
\(526\) −19.6847 34.0948i −0.858292 1.48661i
\(527\) −2.00000 3.46410i −0.0871214 0.150899i
\(528\) 15.3693 0.668864
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) −8.40388 + 14.5560i −0.365041 + 0.632270i
\(531\) −5.56155 + 9.63289i −0.241351 + 0.418032i
\(532\) 18.2462 0.791074
\(533\) 0 0
\(534\) 33.6155 1.45469
\(535\) 2.31534 4.01029i 0.100101 0.173380i
\(536\) −1.43845 + 2.49146i −0.0621315 + 0.107615i
\(537\) 6.56155 + 11.3649i 0.283152 + 0.490433i
\(538\) −8.63068 −0.372095
\(539\) −5.68466 9.84612i −0.244856 0.424102i
\(540\) 1.28078 + 2.21837i 0.0551158 + 0.0954634i
\(541\) 29.7386 1.27856 0.639282 0.768972i \(-0.279232\pi\)
0.639282 + 0.768972i \(0.279232\pi\)
\(542\) 1.36932 + 2.37173i 0.0588172 + 0.101874i
\(543\) −4.84233 + 8.38716i −0.207804 + 0.359927i
\(544\) 8.40388 14.5560i 0.360313 0.624081i
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) −24.9309 −1.06597 −0.532984 0.846126i \(-0.678929\pi\)
−0.532984 + 0.846126i \(0.678929\pi\)
\(548\) −3.28078 + 5.68247i −0.140148 + 0.242743i
\(549\) −6.06155 + 10.4989i −0.258701 + 0.448083i
\(550\) −12.0000 20.7846i −0.511682 0.886259i
\(551\) −6.38447 −0.271988
\(552\) 6.56155 + 11.3649i 0.279278 + 0.483724i
\(553\) −17.0270 29.4916i −0.724061 1.25411i
\(554\) −45.3002 −1.92462
\(555\) −0.965435 1.67218i −0.0409804 0.0709802i
\(556\) −24.9309 + 43.1815i −1.05730 + 1.83130i
\(557\) −7.03457 + 12.1842i −0.298064 + 0.516262i −0.975693 0.219142i \(-0.929674\pi\)
0.677629 + 0.735404i \(0.263008\pi\)
\(558\) −4.00000 −0.169334
\(559\) 0 0
\(560\) −15.3693 −0.649472
\(561\) −2.56155 + 4.43674i −0.108149 + 0.187319i
\(562\) 3.59612 6.22866i 0.151693 0.262740i
\(563\) −0.684658 1.18586i −0.0288549 0.0499782i 0.851237 0.524781i \(-0.175853\pi\)
−0.880092 + 0.474803i \(0.842519\pi\)
\(564\) 37.6155 1.58390
\(565\) −4.15767 7.20130i −0.174915 0.302961i
\(566\) −1.68466 2.91791i −0.0708115 0.122649i
\(567\) 3.56155 0.149571
\(568\) −45.9309 79.5546i −1.92722 3.33804i
\(569\) −20.3693 + 35.2807i −0.853926 + 1.47904i 0.0237115 + 0.999719i \(0.492452\pi\)
−0.877638 + 0.479325i \(0.840882\pi\)
\(570\) −0.807764 + 1.39909i −0.0338335 + 0.0586014i
\(571\) 19.3693 0.810581 0.405290 0.914188i \(-0.367170\pi\)
0.405290 + 0.914188i \(0.367170\pi\)
\(572\) 0 0
\(573\) −0.876894 −0.0366328
\(574\) −11.6847 + 20.2384i −0.487708 + 0.844735i
\(575\) 4.68466 8.11407i 0.195364 0.338380i
\(576\) −0.719224 1.24573i −0.0299676 0.0519055i
\(577\) 29.6847 1.23579 0.617894 0.786261i \(-0.287986\pi\)
0.617894 + 0.786261i \(0.287986\pi\)
\(578\) −13.3693 23.1563i −0.556090 0.963177i
\(579\) 9.74621 + 16.8809i 0.405039 + 0.701548i
\(580\) 14.5616 0.604636
\(581\) −16.2462 28.1393i −0.674006 1.16741i
\(582\) 5.68466 9.84612i 0.235637 0.408135i
\(583\) −11.6847 + 20.2384i −0.483929 + 0.838190i
\(584\) −12.3153 −0.509612
\(585\) 0 0
\(586\) 62.9157 2.59902
\(587\) 7.31534 12.6705i 0.301936 0.522969i −0.674638 0.738149i \(-0.735700\pi\)
0.976575 + 0.215179i \(0.0690336\pi\)
\(588\) −12.9654 + 22.4568i −0.534686 + 0.926102i
\(589\) −0.876894 1.51883i −0.0361318 0.0625821i
\(590\) 16.0000 0.658710
\(591\) −5.68466 9.84612i −0.233836 0.405015i
\(592\) 13.2116 + 22.8832i 0.542995 + 0.940495i
\(593\) −44.4233 −1.82425 −0.912123 0.409917i \(-0.865558\pi\)
−0.912123 + 0.409917i \(0.865558\pi\)
\(594\) 2.56155 + 4.43674i 0.105102 + 0.182042i
\(595\) 2.56155 4.43674i 0.105013 0.181889i
\(596\) −14.9654 + 25.9209i −0.613008 + 1.06176i
\(597\) −23.1771 −0.948575
\(598\) 0 0
\(599\) −0.384472 −0.0157091 −0.00785455 0.999969i \(-0.502500\pi\)
−0.00785455 + 0.999969i \(0.502500\pi\)
\(600\) −15.3693 + 26.6204i −0.627450 + 1.08677i
\(601\) 17.9654 31.1170i 0.732825 1.26929i −0.222846 0.974854i \(-0.571535\pi\)
0.955671 0.294437i \(-0.0951321\pi\)
\(602\) 2.00000 + 3.46410i 0.0815139 + 0.141186i
\(603\) −0.438447 −0.0178549
\(604\) 35.0540 + 60.7153i 1.42633 + 2.47047i
\(605\) −1.96543 3.40423i −0.0799063 0.138402i
\(606\) 8.80776 0.357791
\(607\) 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i \(-0.0614000\pi\)
−0.656744 + 0.754114i \(0.728067\pi\)
\(608\) 3.68466 6.38202i 0.149433 0.258825i
\(609\) 10.1231 17.5337i 0.410209 0.710503i
\(610\) 17.4384 0.706062
\(611\) 0 0
\(612\) 11.6847 0.472324
\(613\) 11.4309 19.7988i 0.461688 0.799668i −0.537357 0.843355i \(-0.680577\pi\)
0.999045 + 0.0436871i \(0.0139105\pi\)
\(614\) −13.0540 + 22.6101i −0.526816 + 0.912471i
\(615\) −0.719224 1.24573i −0.0290019 0.0502328i
\(616\) −46.7386 −1.88315
\(617\) −5.40388 9.35980i −0.217552 0.376811i 0.736507 0.676430i \(-0.236474\pi\)
−0.954059 + 0.299619i \(0.903141\pi\)
\(618\) −9.68466 16.7743i −0.389574 0.674762i
\(619\) 24.3002 0.976707 0.488353 0.872646i \(-0.337598\pi\)
0.488353 + 0.872646i \(0.337598\pi\)
\(620\) 2.00000 + 3.46410i 0.0803219 + 0.139122i
\(621\) −1.00000 + 1.73205i −0.0401286 + 0.0695048i
\(622\) −13.9309 + 24.1290i −0.558577 + 0.967484i
\(623\) −46.7386 −1.87254
\(624\) 0 0
\(625\) 20.3693 0.814773
\(626\) −1.68466 + 2.91791i −0.0673325 + 0.116623i
\(627\) −1.12311 + 1.94528i −0.0448525 + 0.0776868i
\(628\) 9.96543 + 17.2606i 0.397664 + 0.688774i
\(629\) −8.80776 −0.351189
\(630\) −2.56155 4.43674i −0.102055 0.176764i
\(631\) −7.21922 12.5041i −0.287393 0.497779i 0.685794 0.727796i \(-0.259455\pi\)
−0.973187 + 0.230017i \(0.926122\pi\)
\(632\) −62.7386 −2.49561
\(633\) −3.65767 6.33527i −0.145379 0.251804i
\(634\) 29.5270 51.1422i 1.17267 2.03112i
\(635\) 2.68466 4.64996i 0.106537 0.184528i
\(636\) 53.3002 2.11349
\(637\) 0 0
\(638\) 29.1231 1.15299
\(639\) 7.00000 12.1244i 0.276916 0.479632i
\(640\) 2.65009 4.59010i 0.104754 0.181439i
\(641\) −13.0885 22.6700i −0.516966 0.895412i −0.999806 0.0197030i \(-0.993728\pi\)
0.482840 0.875709i \(-0.339605\pi\)
\(642\) −21.1231 −0.833662
\(643\) 19.2732 + 33.3822i 0.760061 + 1.31646i 0.942819 + 0.333306i \(0.108164\pi\)
−0.182758 + 0.983158i \(0.558502\pi\)
\(644\) −16.2462 28.1393i −0.640190 1.10884i
\(645\) −0.246211 −0.00969456
\(646\) 3.68466 + 6.38202i 0.144971 + 0.251097i
\(647\) 23.8078 41.2363i 0.935980 1.62116i 0.163102 0.986609i \(-0.447850\pi\)
0.772877 0.634555i \(-0.218817\pi\)
\(648\) 3.28078 5.68247i 0.128881 0.223229i
\(649\) 22.2462 0.873240
\(650\) 0 0
\(651\) 5.56155 0.217974
\(652\) 36.0540 62.4473i 1.41198 2.44563i
\(653\) −7.43845 + 12.8838i −0.291089 + 0.504181i −0.974068 0.226258i \(-0.927351\pi\)
0.682979 + 0.730438i \(0.260684\pi\)
\(654\) −22.8078 39.5042i −0.891854 1.54474i
\(655\) 9.75379 0.381112
\(656\) 9.84233 + 17.0474i 0.384278 + 0.665590i
\(657\) −0.938447 1.62544i −0.0366123 0.0634144i
\(658\) −75.2311 −2.93281
\(659\) −7.12311 12.3376i −0.277477 0.480604i 0.693280 0.720668i \(-0.256165\pi\)
−0.970757 + 0.240064i \(0.922831\pi\)
\(660\) 2.56155 4.43674i 0.0997083 0.172700i
\(661\) 15.1847 26.3006i 0.590615 1.02297i −0.403535 0.914964i \(-0.632219\pi\)
0.994150 0.108011i \(-0.0344480\pi\)
\(662\) −60.9848 −2.37024
\(663\) 0 0
\(664\) −59.8617 −2.32309
\(665\) 1.12311 1.94528i 0.0435522 0.0754346i
\(666\) −4.40388 + 7.62775i −0.170647 + 0.295569i
\(667\) 5.68466 + 9.84612i 0.220111 + 0.381243i
\(668\) 28.4924 1.10240
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 0.315342 + 0.546188i 0.0121827 + 0.0211011i
\(671\) 24.2462 0.936015
\(672\) 11.6847 + 20.2384i 0.450745 + 0.780714i
\(673\) 3.37689 5.84895i 0.130170 0.225461i −0.793572 0.608476i \(-0.791781\pi\)
0.923742 + 0.383016i \(0.125114\pi\)
\(674\) 2.71922 4.70983i 0.104741 0.181416i
\(675\) −4.68466 −0.180313
\(676\) 0 0
\(677\) 25.6155 0.984485 0.492242 0.870458i \(-0.336177\pi\)
0.492242 + 0.870458i \(0.336177\pi\)
\(678\) −18.9654 + 32.8491i −0.728363 + 1.26156i
\(679\) −7.90388 + 13.6899i −0.303323 + 0.525371i
\(680\) −4.71922 8.17394i −0.180974 0.313456i
\(681\) 1.12311 0.0430375
\(682\) 4.00000 + 6.92820i 0.153168 + 0.265295i
\(683\) 18.0540 + 31.2704i 0.690816 + 1.19653i 0.971571 + 0.236749i \(0.0760819\pi\)
−0.280755 + 0.959780i \(0.590585\pi\)
\(684\) 5.12311 0.195887
\(685\) 0.403882 + 0.699544i 0.0154315 + 0.0267282i
\(686\) −6.00000 + 10.3923i −0.229081 + 0.396780i
\(687\) 0.123106 0.213225i 0.00469677 0.00813505i
\(688\) 3.36932 0.128454
\(689\) 0 0
\(690\) 2.87689 0.109521
\(691\) 1.15009 1.99202i 0.0437516 0.0757800i −0.843320 0.537411i \(-0.819402\pi\)
0.887072 + 0.461631i \(0.152736\pi\)
\(692\) −8.56155 + 14.8290i −0.325461 + 0.563716i
\(693\) −3.56155 6.16879i −0.135292 0.234333i
\(694\) 34.8769 1.32391
\(695\) 3.06913 + 5.31589i 0.116419 + 0.201643i
\(696\) −18.6501 32.3029i −0.706930 1.22444i
\(697\) −6.56155 −0.248537
\(698\) 17.6847 + 30.6307i 0.669374 + 1.15939i
\(699\) −13.0000 + 22.5167i −0.491705 + 0.851658i
\(700\) 38.0540 65.9114i 1.43831 2.49122i
\(701\) 19.3693 0.731569 0.365785 0.930700i \(-0.380801\pi\)
0.365785 + 0.930700i \(0.380801\pi\)
\(702\) 0 0
\(703\) −3.86174 −0.145648
\(704\) −1.43845 + 2.49146i −0.0542135 + 0.0939006i
\(705\) 2.31534 4.01029i 0.0872008 0.151036i
\(706\) −22.6501 39.2311i −0.852448 1.47648i
\(707\) −12.2462 −0.460566
\(708\) −25.3693 43.9409i −0.953437 1.65140i
\(709\) 12.7462 + 22.0771i 0.478694 + 0.829122i 0.999702 0.0244297i \(-0.00777700\pi\)
−0.521008 + 0.853552i \(0.674444\pi\)
\(710\) −20.1383 −0.755775
\(711\) −4.78078 8.28055i −0.179293 0.310545i
\(712\) −43.0540 + 74.5717i −1.61352 + 2.79469i
\(713\) −1.56155 + 2.70469i −0.0584806 + 0.101291i
\(714\) −23.3693 −0.874575
\(715\) 0 0
\(716\) −59.8617 −2.23714
\(717\) −0.315342 + 0.546188i −0.0117766 + 0.0203977i
\(718\) −19.6847 + 34.0948i −0.734625 + 1.27241i
\(719\) −0.684658 1.18586i −0.0255335 0.0442252i 0.852976 0.521950i \(-0.174795\pi\)
−0.878510 + 0.477724i \(0.841462\pi\)
\(720\) −4.31534 −0.160823
\(721\) 13.4654 + 23.3228i 0.501479 + 0.868587i
\(722\) −22.7192 39.3508i −0.845522 1.46449i
\(723\) −2.80776 −0.104422
\(724\) −22.0885 38.2585i −0.820914 1.42187i
\(725\) −13.3153 + 23.0628i −0.494519 + 0.856533i
\(726\) −8.96543 + 15.5286i −0.332738 + 0.576320i
\(727\) 39.6695 1.47126 0.735630 0.677383i \(-0.236886\pi\)
0.735630 + 0.677383i \(0.236886\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.34991 + 2.33811i −0.0499623 + 0.0865372i
\(731\) −0.561553 + 0.972638i −0.0207698 + 0.0359743i
\(732\) −27.6501 47.8914i −1.02198 1.77012i
\(733\) −53.4924 −1.97579 −0.987894 0.155131i \(-0.950420\pi\)
−0.987894 + 0.155131i \(0.950420\pi\)
\(734\) 25.6847 + 44.4871i 0.948038 + 1.64205i
\(735\) 1.59612 + 2.76456i 0.0588737 + 0.101972i
\(736\) −13.1231 −0.483724
\(737\) 0.438447 + 0.759413i 0.0161504 + 0.0279733i
\(738\) −3.28078 + 5.68247i −0.120767 + 0.209175i
\(739\) −3.12311 + 5.40938i −0.114885 + 0.198987i −0.917734 0.397196i \(-0.869983\pi\)
0.802849 + 0.596183i \(0.203317\pi\)
\(740\) 8.80776 0.323780
\(741\) 0 0
\(742\) −106.600 −3.91342
\(743\) −18.6847 + 32.3628i −0.685474 + 1.18728i 0.287814 + 0.957686i \(0.407071\pi\)
−0.973288 + 0.229589i \(0.926262\pi\)
\(744\) 5.12311 8.87348i 0.187822 0.325318i
\(745\) 1.84233 + 3.19101i 0.0674977 + 0.116909i
\(746\) −9.30019 −0.340504
\(747\) −4.56155 7.90084i −0.166898 0.289077i
\(748\) −11.6847 20.2384i −0.427233 0.739990i
\(749\) 29.3693 1.07313
\(750\) 6.96543 + 12.0645i 0.254342 + 0.440533i
\(751\) 15.0540 26.0743i 0.549327 0.951463i −0.448993 0.893535i \(-0.648217\pi\)
0.998321 0.0579278i \(-0.0184493\pi\)
\(752\) −31.6847 + 54.8794i −1.15542 + 2.00125i
\(753\) −30.7386 −1.12018
\(754\) 0 0
\(755\) 8.63068 0.314103
\(756\) −8.12311 + 14.0696i −0.295434 + 0.511708i
\(757\) −15.0000 + 25.9808i −0.545184 + 0.944287i 0.453411 + 0.891302i \(0.350207\pi\)
−0.998595 + 0.0529853i \(0.983126\pi\)
\(758\) −14.4924 25.1016i −0.526388 0.911732i
\(759\) 4.00000 0.145191
\(760\) −2.06913 3.58384i −0.0750552 0.129999i
\(761\) −7.68466 13.3102i −0.278569 0.482495i 0.692461 0.721456i \(-0.256527\pi\)
−0.971029 + 0.238961i \(0.923193\pi\)
\(762\) −24.4924 −0.887267
\(763\) 31.7116 + 54.9262i 1.14804 + 1.98846i
\(764\) 2.00000 3.46410i 0.0723575 0.125327i
\(765\) 0.719224 1.24573i 0.0260036 0.0450395i
\(766\) 68.4924 2.47473
\(767\) 0 0
\(768\) −27.0540 −0.976226
\(769\) −9.00000 + 15.5885i −0.324548 + 0.562134i −0.981421 0.191867i \(-0.938546\pi\)
0.656873 + 0.754002i \(0.271879\pi\)
\(770\) −5.12311 + 8.87348i −0.184624 + 0.319778i
\(771\) 8.08854 + 14.0098i 0.291302 + 0.504549i
\(772\) −88.9157 −3.20015
\(773\) −3.87689 6.71498i −0.139442 0.241521i 0.787843 0.615876i \(-0.211198\pi\)
−0.927286 + 0.374355i \(0.877864\pi\)
\(774\) 0.561553 + 0.972638i 0.0201846 + 0.0349608i
\(775\) −7.31534 −0.262775
\(776\) 14.5616 + 25.2213i 0.522729 + 0.905394i
\(777\) 6.12311 10.6055i 0.219665 0.380471i
\(778\) −3.91146 + 6.77485i −0.140233 + 0.242890i
\(779\) −2.87689 −0.103075