Properties

Label 507.2.e.g.484.2
Level $507$
Weight $2$
Character 507.484
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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 484.2
Root \(1.28078 + 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.g.22.2

$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28078 + 2.21837i 0.905646 + 1.56862i 0.820048 + 0.572295i \(0.193947\pi\)
0.0855975 + 0.996330i \(0.472720\pi\)
\(3\) −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 0.303959 + 0.952685i \(0.401692\pi\)
−0.977029 + 0.213107i \(0.931642\pi\)
\(8\) −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 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 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 −0.978500 0.206248i \(-0.933875\pi\)
0.667866 + 0.744282i \(0.267208\pi\)
\(18\) −2.56155 −0.603764
\(19\) −0.561553 + 0.972638i −0.128829 + 0.223138i −0.923223 0.384264i \(-0.874455\pi\)
0.794394 + 0.607403i \(0.207789\pi\)
\(20\) 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 0.742732 0.669588i \(-0.233529\pi\)
−0.951247 + 0.308431i \(0.900196\pi\)
\(24\) 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 0.999475 + 0.0324124i \(0.0103190\pi\)
−0.471667 + 0.881777i \(0.656348\pi\)
\(30\) −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 0.972034 0.234841i \(-0.0754570\pi\)
−0.689395 + 0.724385i \(0.742124\pi\)
\(38\) −2.87689 −0.466694
\(39\) 0 0
\(40\) 3.68466 0.582596
\(41\) 1.28078 + 2.21837i 0.200024 + 0.346451i 0.948536 0.316670i \(-0.102565\pi\)
−0.748512 + 0.663121i \(0.769231\pi\)
\(42\) 4.56155 + 7.90084i 0.703863 + 1.21913i
\(43\) −0.219224 + 0.379706i −0.0334313 + 0.0579047i −0.882257 0.470768i \(-0.843977\pi\)
0.848826 + 0.528673i \(0.177310\pi\)
\(44\) 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 0.235310 + 0.971920i \(0.424389\pi\)
−0.959363 + 0.282175i \(0.908944\pi\)
\(60\) −2.56155 −0.330695
\(61\) −6.06155 + 10.4989i −0.776102 + 1.34425i 0.158071 + 0.987428i \(0.449473\pi\)
−0.934173 + 0.356821i \(0.883861\pi\)
\(62\) 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 0.879106 0.476626i \(-0.158141\pi\)
−0.852324 + 0.523015i \(0.824807\pi\)
\(68\) −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 −0.0666994 0.997773i \(-0.521247\pi\)
0.897447 0.441123i \(-0.145420\pi\)
\(72\) 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 0.970004 + 0.243089i \(0.0781607\pi\)
−0.274481 + 0.961593i \(0.588506\pi\)
\(90\) 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 −0.956418 0.292002i \(-0.905679\pi\)
0.731090 + 0.682281i \(0.239012\pi\)
\(98\) 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 0.938794 0.344479i \(-0.111945\pi\)
−0.767725 + 0.640780i \(0.778611\pi\)
\(102\) 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 0.594957 0.803757i \(-0.297169\pi\)
−0.993553 + 0.113369i \(0.963836\pi\)
\(108\) −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 −0.273174 0.961965i \(-0.588074\pi\)
0.969673 0.244406i \(-0.0785931\pi\)
\(114\) 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 0.572122 0.820168i \(-0.306120\pi\)
−0.996348 + 0.0853884i \(0.972787\pi\)
\(128\) −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 −0.895113 0.445840i \(-0.852905\pi\)
0.833665 + 0.552270i \(0.186238\pi\)
\(138\) −5.12311 −0.436108
\(139\) −5.46543 + 9.46641i −0.463572 + 0.802930i −0.999136 0.0415643i \(-0.986766\pi\)
0.535564 + 0.844495i \(0.320099\pi\)
\(140\) 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 −0.968545 0.248839i \(-0.919951\pi\)
0.699773 + 0.714365i \(0.253284\pi\)
\(150\) −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 −0.370574 0.928803i \(-0.620839\pi\)
0.989654 0.143475i \(-0.0458276\pi\)
\(164\) −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 0.719518 0.694474i \(-0.244363\pi\)
−0.961191 + 0.275884i \(0.911030\pi\)
\(168\) −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 −0.928512 0.371303i \(-0.878911\pi\)
0.785814 + 0.618463i \(0.212244\pi\)
\(174\) 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 0.999939 0.0110115i \(-0.00350513\pi\)
−0.509506 + 0.860467i \(0.670172\pi\)
\(180\) 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 −0.849727 0.527223i \(-0.823233\pi\)
0.881452 + 0.472274i \(0.156567\pi\)
\(192\) −0.719224 1.24573i −0.0519055 0.0899029i
\(193\) 9.74621 + 16.8809i 0.701548 + 1.21512i 0.967923 + 0.251247i \(0.0808406\pi\)
−0.266375 + 0.963869i \(0.585826\pi\)
\(194\) −11.3693 −0.816269
\(195\) 0 0
\(196\) 25.9309 1.85220
\(197\) −5.68466 9.84612i −0.405015 0.701507i 0.589308 0.807908i \(-0.299400\pi\)
−0.994323 + 0.106402i \(0.966067\pi\)
\(198\) 2.56155 + 4.43674i 0.182042 + 0.315305i
\(199\) 11.5885 20.0719i 0.821490 1.42286i −0.0830828 0.996543i \(-0.526477\pi\)
0.904573 0.426320i \(-0.140190\pi\)
\(200\) 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 0.712218 0.701958i \(-0.247691\pi\)
−0.964023 + 0.265820i \(0.914357\pi\)
\(212\) −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 0.968309 0.249756i \(-0.0803503\pi\)
−0.700449 + 0.713702i \(0.747017\pi\)
\(224\) 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 −0.884059 0.467374i \(-0.845200\pi\)
0.846788 + 0.531931i \(0.178533\pi\)
\(228\) −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 −0.817261 0.576268i \(-0.804509\pi\)
0.907693 + 0.419635i \(0.137842\pi\)
\(242\) 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 0.274871 0.961481i \(-0.411365\pi\)
0.695231 0.718786i \(-0.255302\pi\)
\(252\) 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 0.999986 + 0.00526106i \(0.00167466\pi\)
−0.495437 + 0.868644i \(0.664992\pi\)
\(258\) 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 0.999552 0.0299295i \(-0.00952826\pi\)
−0.525696 + 0.850673i \(0.676195\pi\)
\(264\) 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 −0.912803 0.408401i \(-0.866086\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(270\) −0.719224 1.24573i −0.0437706 0.0758128i
\(271\) −0.534565 0.925894i −0.0324725 0.0562441i 0.849332 0.527858i \(-0.177005\pi\)
−0.881805 + 0.471614i \(0.843671\pi\)
\(272\) 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 0.468049 + 0.883702i \(0.344957\pi\)
−0.999333 + 0.0365086i \(0.988376\pi\)
\(278\) −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 0.884911 0.465761i \(-0.154219\pi\)
−0.845816 + 0.533475i \(0.820886\pi\)
\(284\) 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 −0.244556 0.969635i \(-0.578642\pi\)
0.962007 0.273026i \(-0.0880244\pi\)
\(294\) −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 0.327773 + 0.944756i \(0.393702\pi\)
−0.982070 + 0.188518i \(0.939631\pi\)
\(332\) −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 −0.623390 0.781911i \(-0.714245\pi\)
0.988850 + 0.148916i \(0.0475784\pi\)
\(348\) 12.9654 + 22.4568i 0.695020 + 1.20381i
\(349\) −6.90388 11.9579i −0.369556 0.640090i 0.619940 0.784649i \(-0.287157\pi\)
−0.989496 + 0.144559i \(0.953824\pi\)
\(350\) 42.7386 2.28448
\(351\) 0 0
\(352\) −13.1231 −0.699464
\(353\) 8.84233 + 15.3154i 0.470630 + 0.815155i 0.999436 0.0335881i \(-0.0106934\pi\)
−0.528806 + 0.848743i \(0.677360\pi\)
\(354\) 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 −0.999629 0.0272394i \(-0.991328\pi\)
0.476224 0.879324i \(-0.342005\pi\)
\(368\) −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 −0.909189 0.416384i \(-0.863297\pi\)
0.815194 + 0.579188i \(0.196630\pi\)
\(374\) 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 0.973955 0.226740i \(-0.0728068\pi\)
−0.683340 + 0.730100i \(0.739473\pi\)
\(380\) 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 −0.290877 0.956760i \(-0.593947\pi\)
0.974017 0.226473i \(-0.0727195\pi\)
\(384\) −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 −0.976698 0.214617i \(-0.931150\pi\)
0.674213 + 0.738537i \(0.264483\pi\)
\(398\) 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 0.999131 0.0416909i \(-0.0132745\pi\)
−0.535671 + 0.844427i \(0.679941\pi\)
\(402\) 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 −0.998639 0.0521548i \(-0.983391\pi\)
0.544487 + 0.838769i \(0.316724\pi\)
\(410\) 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 0.997186 0.0749725i \(-0.0238869\pi\)
−0.563521 + 0.826102i \(0.690554\pi\)
\(420\) 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 0.829300 0.558803i \(-0.188739\pi\)
−0.898588 + 0.438794i \(0.855406\pi\)
\(432\) −3.84233 6.65511i −0.184864 0.320194i
\(433\) −12.6231 + 21.8639i −0.606628 + 1.05071i 0.385164 + 0.922848i \(0.374145\pi\)
−0.991792 + 0.127862i \(0.959189\pi\)
\(434\) −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 0.881293 0.472570i \(-0.156674\pi\)
−0.849904 + 0.526937i \(0.823340\pi\)
\(440\) −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 −0.752182 0.658956i \(-0.770998\pi\)
0.946763 + 0.321931i \(0.104332\pi\)
\(450\) 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 −0.978103 0.208120i \(-0.933265\pi\)
0.308814 0.951122i \(-0.400068\pi\)
\(458\) −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 0.0174778 + 0.999847i \(0.494436\pi\)
−0.874632 + 0.484787i \(0.838897\pi\)
\(462\) 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 0.785814 0.618463i \(-0.212245\pi\)
−0.928512 + 0.371303i \(0.878911\pi\)
\(480\) 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 −0.878468 0.477801i \(-0.841434\pi\)
0.853022 + 0.521875i \(0.174767\pi\)
\(488\) 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 0.998103 0.0615613i \(-0.0196080\pi\)
−0.552365 + 0.833602i \(0.686275\pi\)
\(492\) 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 −0.704746 0.709460i \(-0.748939\pi\)
0.966783 + 0.255597i \(0.0822722\pi\)
\(504\) 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 0.931549 0.363615i \(-0.118458\pi\)
−0.780675 + 0.624938i \(0.785124\pi\)
\(510\) −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 0.999681 + 0.0252415i \(0.00803549\pi\)
−0.477981 + 0.878370i \(0.658631\pi\)
\(524\) 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 0.677629 0.735404i \(-0.263008\pi\)
−0.975693 + 0.219142i \(0.929674\pi\)
\(558\) −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 −0.880092 0.474803i \(-0.842519\pi\)
0.851237 + 0.524781i \(0.175853\pi\)
\(564\) 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 −0.877638 0.479325i \(-0.840882\pi\)
0.0237115 0.999719i \(-0.492452\pi\)
\(570\) −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 0.976575 0.215179i \(-0.0690336\pi\)
−0.674638 + 0.738149i \(0.735700\pi\)
\(588\) −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 0.955671 + 0.294437i \(0.0951321\pi\)
−0.222846 + 0.974854i \(0.571535\pi\)
\(602\) 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 −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) 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 0.999045 0.0436871i \(-0.0139105\pi\)
−0.537357 + 0.843355i \(0.680577\pi\)
\(614\) −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 −0.954059 0.299619i \(-0.903141\pi\)
0.736507 + 0.676430i \(0.236474\pi\)
\(618\) −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 −0.973187 0.230017i \(-0.926122\pi\)
0.685794 + 0.727796i \(0.259455\pi\)
\(632\) −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 0.482840 + 0.875709i \(0.339605\pi\)
−0.999806 + 0.0197030i \(0.993728\pi\)
\(642\) −21.1231 −0.833662
\(643\) 19.2732 33.3822i 0.760061 1.31646i −0.182758 0.983158i \(-0.558502\pi\)
0.942819 0.333306i \(-0.108164\pi\)
\(644\) −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 0.772877 + 0.634555i \(0.218817\pi\)
0.163102 + 0.986609i \(0.447850\pi\)
\(648\) 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 0.682979 0.730438i \(-0.260684\pi\)
−0.974068 + 0.226258i \(0.927351\pi\)
\(654\) −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 −0.970757 0.240064i \(-0.922831\pi\)
0.693280 + 0.720668i \(0.256165\pi\)
\(660\) 2.56155 + 4.43674i 0.0997083 + 0.172700i
\(661\) 15.1847 + 26.3006i 0.590615 + 1.02297i 0.994150 + 0.108011i \(0.0344480\pi\)
−0.403535 + 0.914964i \(0.632219\pi\)
\(662\) −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 0.923742 0.383016i \(-0.125114\pi\)
−0.793572 + 0.608476i \(0.791781\pi\)
\(674\) 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 −0.280755 0.959780i \(-0.590585\pi\)
0.971571 0.236749i \(-0.0760819\pi\)
\(684\) 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 0.887072 0.461631i \(-0.152736\pi\)
−0.843320 + 0.537411i \(0.819402\pi\)
\(692\) −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 −0.521008 0.853552i \(-0.674444\pi\)
0.999702 + 0.0244297i \(0.00777700\pi\)
\(710\) −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 −0.878510 0.477724i \(-0.841462\pi\)
0.852976 + 0.521950i \(0.174795\pi\)
\(720\) −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 0.802849 0.596183i \(-0.203317\pi\)
−0.917734 + 0.397196i \(0.869983\pi\)
\(740\) 8.80776 0.323780
\(741\) 0 0
\(742\) −106.600 −3.91342
\(743\) −18.6847 32.3628i −0.685474 1.18728i −0.973288 0.229589i \(-0.926262\pi\)
0.287814 0.957686i \(-0.407071\pi\)
\(744\) 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 0.998321 + 0.0579278i \(0.0184493\pi\)
−0.448993 + 0.893535i \(0.648217\pi\)
\(752\) −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 −0.998595 0.0529853i \(-0.983126\pi\)
0.453411 0.891302i \(-0.350207\pi\)
\(758\) −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 −0.971029 0.238961i \(-0.923193\pi\)
0.692461 + 0.721456i \(0.256527\pi\)
\(762\) −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 0.656873 0.754002i \(-0.271879\pi\)
−0.981421 + 0.191867i \(0.938546\pi\)
\(770\) −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 −0.927286 0.374355i \(-0.877864\pi\)
0.787843 + 0.615876i \(0.211198\pi\)
\(774\) 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