Properties

Label 722.2.c.m.429.2
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.324000000.2
Defining polynomial: \(x^{8} + 5 x^{6} + 20 x^{4} + 25 x^{2} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 429.2
Root \(0.587785 - 1.01807i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.m.653.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.642040 + 1.11205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84786 + 3.20059i) q^{5} +(-0.642040 - 1.11205i) q^{6} -0.442463 q^{7} +1.00000 q^{8} +(0.675571 + 1.17012i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.642040 + 1.11205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84786 + 3.20059i) q^{5} +(-0.642040 - 1.11205i) q^{6} -0.442463 q^{7} +1.00000 q^{8} +(0.675571 + 1.17012i) q^{9} +(-1.84786 - 3.20059i) q^{10} -4.02967 q^{11} +1.28408 q^{12} +(-2.44575 - 4.23616i) q^{13} +(0.221232 - 0.383185i) q^{14} +(-2.37280 - 4.10980i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.133446 + 0.231136i) q^{17} -1.35114 q^{18} +3.69572 q^{20} +(0.284079 - 0.492039i) q^{21} +(2.01484 - 3.48980i) q^{22} +(4.60465 + 7.97549i) q^{23} +(-0.642040 + 1.11205i) q^{24} +(-4.32916 - 7.49833i) q^{25} +4.89149 q^{26} -5.58721 q^{27} +(0.221232 + 0.383185i) q^{28} +(0.111791 + 0.193627i) q^{29} +4.74559 q^{30} +3.47985 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.58721 - 4.48118i) q^{33} +(-0.133446 - 0.231136i) q^{34} +(0.817610 - 1.41614i) q^{35} +(0.675571 - 1.17012i) q^{36} +1.44903 q^{37} +6.28106 q^{39} +(-1.84786 + 3.20059i) q^{40} +(3.93236 - 6.81105i) q^{41} +(0.284079 + 0.492039i) q^{42} +(2.81761 - 4.88024i) q^{43} +(2.01484 + 3.48980i) q^{44} -4.99344 q^{45} -9.20930 q^{46} +(-1.09934 - 1.90411i) q^{47} +(-0.642040 - 1.11205i) q^{48} -6.80423 q^{49} +8.65833 q^{50} +(-0.171356 - 0.296797i) q^{51} +(-2.44575 + 4.23616i) q^{52} +(-4.97120 - 8.61038i) q^{53} +(2.79360 - 4.83866i) q^{54} +(7.44627 - 12.8973i) q^{55} -0.442463 q^{56} -0.223582 q^{58} +(1.75476 - 3.03934i) q^{59} +(-2.37280 + 4.10980i) q^{60} +(-2.03977 - 3.53299i) q^{61} +(-1.73993 + 3.01364i) q^{62} +(-0.298915 - 0.517736i) q^{63} +1.00000 q^{64} +18.0776 q^{65} +(2.58721 + 4.48118i) q^{66} +(-0.0738814 - 0.127966i) q^{67} +0.266893 q^{68} -11.8255 q^{69} +(0.817610 + 1.41614i) q^{70} +(-5.73456 + 9.93255i) q^{71} +(0.675571 + 1.17012i) q^{72} +(-0.711130 + 1.23171i) q^{73} +(-0.724514 + 1.25490i) q^{74} +11.1180 q^{75} +1.78298 q^{77} +(-3.14053 + 5.43956i) q^{78} +(-5.10169 + 8.83638i) q^{79} +(-1.84786 - 3.20059i) q^{80} +(1.56050 - 2.70286i) q^{81} +(3.93236 + 6.81105i) q^{82} -3.28878 q^{83} -0.568158 q^{84} +(-0.493181 - 0.854214i) q^{85} +(2.81761 + 4.88024i) q^{86} -0.287096 q^{87} -4.02967 q^{88} +(2.98037 + 5.16216i) q^{89} +(2.49672 - 4.32444i) q^{90} +(1.08215 + 1.87434i) q^{91} +(4.60465 - 7.97549i) q^{92} +(-2.23420 + 3.86975i) q^{93} +2.19868 q^{94} +1.28408 q^{96} +(-2.04238 + 3.53750i) q^{97} +(3.40211 - 5.89263i) q^{98} +(-2.72233 - 4.71521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 2q^{6} - 4q^{7} + 8q^{8} - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 2q^{6} - 4q^{7} + 8q^{8} - 4q^{9} + 2q^{10} + 4q^{11} + 4q^{12} - 18q^{13} + 2q^{14} - 4q^{15} - 4q^{16} - 6q^{17} + 8q^{18} - 4q^{20} - 4q^{21} - 2q^{22} + 10q^{23} - 2q^{24} - 6q^{25} + 36q^{26} - 8q^{27} + 2q^{28} + 2q^{29} + 8q^{30} + 52q^{31} - 4q^{32} - 16q^{33} - 6q^{34} - 6q^{35} - 4q^{36} + 8q^{37} - 12q^{39} + 2q^{40} + 12q^{41} - 4q^{42} + 10q^{43} - 2q^{44} - 44q^{45} - 20q^{46} + 12q^{47} - 2q^{48} - 24q^{49} + 12q^{50} + 2q^{51} - 18q^{52} - 8q^{53} + 4q^{54} + 26q^{55} - 4q^{56} - 4q^{58} + 8q^{59} - 4q^{60} - 26q^{62} + 22q^{63} + 8q^{64} - 8q^{65} - 16q^{66} - 10q^{67} + 12q^{68} - 40q^{69} - 6q^{70} - 4q^{72} + 14q^{73} - 4q^{74} + 16q^{75} + 8q^{77} + 6q^{78} - 22q^{79} + 2q^{80} + 4q^{81} + 12q^{82} - 24q^{83} + 8q^{84} + 18q^{85} + 10q^{86} - 52q^{87} + 4q^{88} + 16q^{89} + 22q^{90} + 4q^{91} + 10q^{92} - 8q^{93} - 24q^{94} + 4q^{96} - 28q^{97} + 12q^{98} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.642040 + 1.11205i −0.370682 + 0.642040i −0.989671 0.143360i \(-0.954209\pi\)
0.618989 + 0.785400i \(0.287543\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.84786 + 3.20059i −0.826388 + 1.43135i 0.0744667 + 0.997224i \(0.476275\pi\)
−0.900854 + 0.434122i \(0.857059\pi\)
\(6\) −0.642040 1.11205i −0.262112 0.453990i
\(7\) −0.442463 −0.167235 −0.0836177 0.996498i \(-0.526647\pi\)
−0.0836177 + 0.996498i \(0.526647\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.675571 + 1.17012i 0.225190 + 0.390041i
\(10\) −1.84786 3.20059i −0.584344 1.01211i
\(11\) −4.02967 −1.21499 −0.607496 0.794323i \(-0.707826\pi\)
−0.607496 + 0.794323i \(0.707826\pi\)
\(12\) 1.28408 0.370682
\(13\) −2.44575 4.23616i −0.678328 1.17490i −0.975484 0.220069i \(-0.929372\pi\)
0.297156 0.954829i \(-0.403962\pi\)
\(14\) 0.221232 0.383185i 0.0591267 0.102410i
\(15\) −2.37280 4.10980i −0.612653 1.06115i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.133446 + 0.231136i −0.0323655 + 0.0560587i −0.881754 0.471709i \(-0.843637\pi\)
0.849389 + 0.527767i \(0.176971\pi\)
\(18\) −1.35114 −0.318467
\(19\) 0 0
\(20\) 3.69572 0.826388
\(21\) 0.284079 0.492039i 0.0619911 0.107372i
\(22\) 2.01484 3.48980i 0.429565 0.744028i
\(23\) 4.60465 + 7.97549i 0.960136 + 1.66300i 0.722151 + 0.691735i \(0.243153\pi\)
0.237985 + 0.971269i \(0.423513\pi\)
\(24\) −0.642040 + 1.11205i −0.131056 + 0.226995i
\(25\) −4.32916 7.49833i −0.865833 1.49967i
\(26\) 4.89149 0.959300
\(27\) −5.58721 −1.07526
\(28\) 0.221232 + 0.383185i 0.0418089 + 0.0724151i
\(29\) 0.111791 + 0.193627i 0.0207590 + 0.0359557i 0.876218 0.481914i \(-0.160058\pi\)
−0.855459 + 0.517870i \(0.826725\pi\)
\(30\) 4.74559 0.866423
\(31\) 3.47985 0.625000 0.312500 0.949918i \(-0.398834\pi\)
0.312500 + 0.949918i \(0.398834\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 2.58721 4.48118i 0.450375 0.780073i
\(34\) −0.133446 0.231136i −0.0228859 0.0396395i
\(35\) 0.817610 1.41614i 0.138201 0.239372i
\(36\) 0.675571 1.17012i 0.112595 0.195020i
\(37\) 1.44903 0.238219 0.119109 0.992881i \(-0.461996\pi\)
0.119109 + 0.992881i \(0.461996\pi\)
\(38\) 0 0
\(39\) 6.28106 1.00577
\(40\) −1.84786 + 3.20059i −0.292172 + 0.506057i
\(41\) 3.93236 6.81105i 0.614132 1.06371i −0.376404 0.926455i \(-0.622840\pi\)
0.990536 0.137252i \(-0.0438270\pi\)
\(42\) 0.284079 + 0.492039i 0.0438343 + 0.0759233i
\(43\) 2.81761 4.88024i 0.429682 0.744230i −0.567163 0.823605i \(-0.691959\pi\)
0.996845 + 0.0793752i \(0.0252925\pi\)
\(44\) 2.01484 + 3.48980i 0.303748 + 0.526107i
\(45\) −4.99344 −0.744377
\(46\) −9.20930 −1.35784
\(47\) −1.09934 1.90411i −0.160355 0.277743i 0.774641 0.632401i \(-0.217931\pi\)
−0.934996 + 0.354658i \(0.884597\pi\)
\(48\) −0.642040 1.11205i −0.0926704 0.160510i
\(49\) −6.80423 −0.972032
\(50\) 8.65833 1.22447
\(51\) −0.171356 0.296797i −0.0239946 0.0415599i
\(52\) −2.44575 + 4.23616i −0.339164 + 0.587449i
\(53\) −4.97120 8.61038i −0.682847 1.18273i −0.974108 0.226083i \(-0.927408\pi\)
0.291261 0.956644i \(-0.405925\pi\)
\(54\) 2.79360 4.83866i 0.380161 0.658459i
\(55\) 7.44627 12.8973i 1.00405 1.73907i
\(56\) −0.442463 −0.0591267
\(57\) 0 0
\(58\) −0.223582 −0.0293577
\(59\) 1.75476 3.03934i 0.228451 0.395688i −0.728898 0.684622i \(-0.759967\pi\)
0.957349 + 0.288934i \(0.0933007\pi\)
\(60\) −2.37280 + 4.10980i −0.306327 + 0.530573i
\(61\) −2.03977 3.53299i −0.261166 0.452353i 0.705386 0.708824i \(-0.250774\pi\)
−0.966552 + 0.256470i \(0.917440\pi\)
\(62\) −1.73993 + 3.01364i −0.220971 + 0.382733i
\(63\) −0.298915 0.517736i −0.0376598 0.0652287i
\(64\) 1.00000 0.125000
\(65\) 18.0776 2.24225
\(66\) 2.58721 + 4.48118i 0.318463 + 0.551595i
\(67\) −0.0738814 0.127966i −0.00902605 0.0156336i 0.861477 0.507796i \(-0.169540\pi\)
−0.870503 + 0.492163i \(0.836206\pi\)
\(68\) 0.266893 0.0323655
\(69\) −11.8255 −1.42362
\(70\) 0.817610 + 1.41614i 0.0977231 + 0.169261i
\(71\) −5.73456 + 9.93255i −0.680567 + 1.17878i 0.294241 + 0.955731i \(0.404933\pi\)
−0.974808 + 0.223045i \(0.928400\pi\)
\(72\) 0.675571 + 1.17012i 0.0796167 + 0.137900i
\(73\) −0.711130 + 1.23171i −0.0832315 + 0.144161i −0.904636 0.426185i \(-0.859857\pi\)
0.821405 + 0.570346i \(0.193191\pi\)
\(74\) −0.724514 + 1.25490i −0.0842230 + 0.145879i
\(75\) 11.1180 1.28379
\(76\) 0 0
\(77\) 1.78298 0.203190
\(78\) −3.14053 + 5.43956i −0.355595 + 0.615909i
\(79\) −5.10169 + 8.83638i −0.573985 + 0.994171i 0.422166 + 0.906518i \(0.361270\pi\)
−0.996151 + 0.0876525i \(0.972063\pi\)
\(80\) −1.84786 3.20059i −0.206597 0.357836i
\(81\) 1.56050 2.70286i 0.173389 0.300318i
\(82\) 3.93236 + 6.81105i 0.434257 + 0.752155i
\(83\) −3.28878 −0.360990 −0.180495 0.983576i \(-0.557770\pi\)
−0.180495 + 0.983576i \(0.557770\pi\)
\(84\) −0.568158 −0.0619911
\(85\) −0.493181 0.854214i −0.0534929 0.0926525i
\(86\) 2.81761 + 4.88024i 0.303831 + 0.526250i
\(87\) −0.287096 −0.0307800
\(88\) −4.02967 −0.429565
\(89\) 2.98037 + 5.16216i 0.315919 + 0.547188i 0.979632 0.200799i \(-0.0643539\pi\)
−0.663714 + 0.747987i \(0.731021\pi\)
\(90\) 2.49672 4.32444i 0.263177 0.455836i
\(91\) 1.08215 + 1.87434i 0.113440 + 0.196485i
\(92\) 4.60465 7.97549i 0.480068 0.831502i
\(93\) −2.23420 + 3.86975i −0.231676 + 0.401275i
\(94\) 2.19868 0.226776
\(95\) 0 0
\(96\) 1.28408 0.131056
\(97\) −2.04238 + 3.53750i −0.207372 + 0.359179i −0.950886 0.309541i \(-0.899824\pi\)
0.743514 + 0.668721i \(0.233158\pi\)
\(98\) 3.40211 5.89263i 0.343665 0.595246i
\(99\) −2.72233 4.71521i −0.273604 0.473896i
\(100\) −4.32916 + 7.49833i −0.432916 + 0.749833i
\(101\) −0.212639 0.368301i −0.0211583 0.0366473i 0.855252 0.518212i \(-0.173402\pi\)
−0.876411 + 0.481564i \(0.840069\pi\)
\(102\) 0.342712 0.0339335
\(103\) −4.53618 −0.446963 −0.223482 0.974708i \(-0.571742\pi\)
−0.223482 + 0.974708i \(0.571742\pi\)
\(104\) −2.44575 4.23616i −0.239825 0.415389i
\(105\) 1.04988 + 1.81844i 0.102457 + 0.177461i
\(106\) 9.94241 0.965692
\(107\) −3.17151 −0.306602 −0.153301 0.988180i \(-0.548990\pi\)
−0.153301 + 0.988180i \(0.548990\pi\)
\(108\) 2.79360 + 4.83866i 0.268815 + 0.465601i
\(109\) 3.39056 5.87262i 0.324757 0.562495i −0.656706 0.754146i \(-0.728051\pi\)
0.981463 + 0.191651i \(0.0613843\pi\)
\(110\) 7.44627 + 12.8973i 0.709974 + 1.22971i
\(111\) −0.930333 + 1.61138i −0.0883033 + 0.152946i
\(112\) 0.221232 0.383185i 0.0209044 0.0362075i
\(113\) −10.0444 −0.944893 −0.472447 0.881359i \(-0.656629\pi\)
−0.472447 + 0.881359i \(0.656629\pi\)
\(114\) 0 0
\(115\) −34.0350 −3.17378
\(116\) 0.111791 0.193627i 0.0103795 0.0179778i
\(117\) 3.30455 5.72364i 0.305506 0.529151i
\(118\) 1.75476 + 3.03934i 0.161539 + 0.279794i
\(119\) 0.0590452 0.102269i 0.00541266 0.00937501i
\(120\) −2.37280 4.10980i −0.216606 0.375172i
\(121\) 5.23826 0.476205
\(122\) 4.07955 0.369345
\(123\) 5.04946 + 8.74593i 0.455295 + 0.788594i
\(124\) −1.73993 3.01364i −0.156250 0.270633i
\(125\) 13.5201 1.20928
\(126\) 0.597831 0.0532590
\(127\) −7.04029 12.1941i −0.624725 1.08206i −0.988594 0.150605i \(-0.951878\pi\)
0.363869 0.931450i \(-0.381456\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 3.61803 + 6.26662i 0.318550 + 0.551745i
\(130\) −9.03879 + 15.6556i −0.792754 + 1.37309i
\(131\) −7.92075 + 13.7191i −0.692039 + 1.19865i 0.279129 + 0.960254i \(0.409954\pi\)
−0.971169 + 0.238394i \(0.923379\pi\)
\(132\) −5.17442 −0.450375
\(133\) 0 0
\(134\) 0.147763 0.0127648
\(135\) 10.3244 17.8823i 0.888581 1.53907i
\(136\) −0.133446 + 0.231136i −0.0114429 + 0.0198198i
\(137\) −1.10372 1.91169i −0.0942970 0.163327i 0.815018 0.579436i \(-0.196727\pi\)
−0.909315 + 0.416108i \(0.863394\pi\)
\(138\) 5.91273 10.2412i 0.503325 0.871785i
\(139\) 8.53222 + 14.7782i 0.723694 + 1.25347i 0.959510 + 0.281676i \(0.0908904\pi\)
−0.235816 + 0.971798i \(0.575776\pi\)
\(140\) −1.63522 −0.138201
\(141\) 2.82328 0.237763
\(142\) −5.73456 9.93255i −0.481234 0.833521i
\(143\) 9.85555 + 17.0703i 0.824163 + 1.42749i
\(144\) −1.35114 −0.112595
\(145\) −0.826294 −0.0686200
\(146\) −0.711130 1.23171i −0.0588535 0.101937i
\(147\) 4.36858 7.56661i 0.360315 0.624083i
\(148\) −0.724514 1.25490i −0.0595547 0.103152i
\(149\) −6.77288 + 11.7310i −0.554856 + 0.961039i 0.443059 + 0.896493i \(0.353893\pi\)
−0.997915 + 0.0645462i \(0.979440\pi\)
\(150\) −5.55899 + 9.62845i −0.453890 + 0.786160i
\(151\) −9.15317 −0.744875 −0.372437 0.928057i \(-0.621478\pi\)
−0.372437 + 0.928057i \(0.621478\pi\)
\(152\) 0 0
\(153\) −0.360610 −0.0291536
\(154\) −0.891491 + 1.54411i −0.0718384 + 0.124428i
\(155\) −6.43028 + 11.1376i −0.516492 + 0.894591i
\(156\) −3.14053 5.43956i −0.251444 0.435513i
\(157\) 8.19514 14.1944i 0.654043 1.13284i −0.328089 0.944647i \(-0.606405\pi\)
0.982133 0.188190i \(-0.0602620\pi\)
\(158\) −5.10169 8.83638i −0.405869 0.702985i
\(159\) 12.7668 1.01248
\(160\) 3.69572 0.292172
\(161\) −2.03739 3.52886i −0.160569 0.278113i
\(162\) 1.56050 + 2.70286i 0.122604 + 0.212357i
\(163\) −13.7722 −1.07873 −0.539363 0.842073i \(-0.681335\pi\)
−0.539363 + 0.842073i \(0.681335\pi\)
\(164\) −7.86472 −0.614132
\(165\) 9.56159 + 16.5612i 0.744369 + 1.28929i
\(166\) 1.64439 2.84817i 0.127629 0.221061i
\(167\) 5.16640 + 8.94847i 0.399788 + 0.692453i 0.993700 0.112077i \(-0.0357504\pi\)
−0.593911 + 0.804530i \(0.702417\pi\)
\(168\) 0.284079 0.492039i 0.0219172 0.0379617i
\(169\) −5.46334 + 9.46279i −0.420257 + 0.727907i
\(170\) 0.986361 0.0756504
\(171\) 0 0
\(172\) −5.63522 −0.429682
\(173\) 4.90601 8.49745i 0.372997 0.646049i −0.617028 0.786941i \(-0.711664\pi\)
0.990025 + 0.140892i \(0.0449969\pi\)
\(174\) 0.143548 0.248633i 0.0108824 0.0188488i
\(175\) 1.91550 + 3.31774i 0.144798 + 0.250797i
\(176\) 2.01484 3.48980i 0.151874 0.263053i
\(177\) 2.25325 + 3.90275i 0.169365 + 0.293349i
\(178\) −5.96075 −0.446777
\(179\) −8.79830 −0.657616 −0.328808 0.944397i \(-0.606647\pi\)
−0.328808 + 0.944397i \(0.606647\pi\)
\(180\) 2.49672 + 4.32444i 0.186094 + 0.322325i
\(181\) −7.26388 12.5814i −0.539920 0.935168i −0.998908 0.0467258i \(-0.985121\pi\)
0.458988 0.888442i \(-0.348212\pi\)
\(182\) −2.16431 −0.160429
\(183\) 5.23846 0.387238
\(184\) 4.60465 + 7.97549i 0.339459 + 0.587961i
\(185\) −2.67760 + 4.63774i −0.196861 + 0.340973i
\(186\) −2.23420 3.86975i −0.163820 0.283744i
\(187\) 0.537746 0.931403i 0.0393239 0.0681109i
\(188\) −1.09934 + 1.90411i −0.0801776 + 0.138872i
\(189\) 2.47214 0.179821
\(190\) 0 0
\(191\) 12.7302 0.921122 0.460561 0.887628i \(-0.347648\pi\)
0.460561 + 0.887628i \(0.347648\pi\)
\(192\) −0.642040 + 1.11205i −0.0463352 + 0.0802549i
\(193\) −8.73903 + 15.1364i −0.629049 + 1.08954i 0.358694 + 0.933455i \(0.383222\pi\)
−0.987743 + 0.156090i \(0.950111\pi\)
\(194\) −2.04238 3.53750i −0.146634 0.253978i
\(195\) −11.6065 + 20.1031i −0.831160 + 1.43961i
\(196\) 3.40211 + 5.89263i 0.243008 + 0.420902i
\(197\) −24.5113 −1.74636 −0.873178 0.487401i \(-0.837945\pi\)
−0.873178 + 0.487401i \(0.837945\pi\)
\(198\) 5.44466 0.386935
\(199\) −8.23305 14.2601i −0.583625 1.01087i −0.995045 0.0994230i \(-0.968300\pi\)
0.411420 0.911446i \(-0.365033\pi\)
\(200\) −4.32916 7.49833i −0.306118 0.530212i
\(201\) 0.189739 0.0133832
\(202\) 0.425277 0.0299224
\(203\) −0.0494633 0.0856730i −0.00347165 0.00601307i
\(204\) −0.171356 + 0.296797i −0.0119973 + 0.0207799i
\(205\) 14.5329 + 25.1717i 1.01502 + 1.75807i
\(206\) 2.26809 3.92845i 0.158025 0.273708i
\(207\) −6.22153 + 10.7760i −0.432426 + 0.748984i
\(208\) 4.89149 0.339164
\(209\) 0 0
\(210\) −2.09975 −0.144897
\(211\) −13.7402 + 23.7988i −0.945916 + 1.63837i −0.192010 + 0.981393i \(0.561501\pi\)
−0.753906 + 0.656982i \(0.771833\pi\)
\(212\) −4.97120 + 8.61038i −0.341424 + 0.591363i
\(213\) −7.36363 12.7542i −0.504547 0.873902i
\(214\) 1.58576 2.74661i 0.108400 0.187754i
\(215\) 10.4131 + 18.0360i 0.710167 + 1.23005i
\(216\) −5.58721 −0.380161
\(217\) −1.53971 −0.104522
\(218\) 3.39056 + 5.87262i 0.229638 + 0.397744i
\(219\) −0.913147 1.58162i −0.0617048 0.106876i
\(220\) −14.8925 −1.00405
\(221\) 1.30550 0.0878178
\(222\) −0.930333 1.61138i −0.0624399 0.108149i
\(223\) −10.1853 + 17.6414i −0.682058 + 1.18136i 0.292294 + 0.956329i \(0.405581\pi\)
−0.974352 + 0.225030i \(0.927752\pi\)
\(224\) 0.221232 + 0.383185i 0.0147817 + 0.0256026i
\(225\) 5.84931 10.1313i 0.389954 0.675420i
\(226\) 5.02218 8.69866i 0.334070 0.578626i
\(227\) −22.1493 −1.47010 −0.735051 0.678011i \(-0.762842\pi\)
−0.735051 + 0.678011i \(0.762842\pi\)
\(228\) 0 0
\(229\) 12.7148 0.840216 0.420108 0.907474i \(-0.361992\pi\)
0.420108 + 0.907474i \(0.361992\pi\)
\(230\) 17.0175 29.4752i 1.12210 1.94353i
\(231\) −1.14475 + 1.98276i −0.0753187 + 0.130456i
\(232\) 0.111791 + 0.193627i 0.00733942 + 0.0127123i
\(233\) 4.34088 7.51863i 0.284381 0.492562i −0.688078 0.725637i \(-0.741545\pi\)
0.972459 + 0.233075i \(0.0748787\pi\)
\(234\) 3.30455 + 5.72364i 0.216025 + 0.374166i
\(235\) 8.12569 0.530062
\(236\) −3.50953 −0.228451
\(237\) −6.55097 11.3466i −0.425531 0.737042i
\(238\) 0.0590452 + 0.102269i 0.00382733 + 0.00662913i
\(239\) 21.8749 1.41497 0.707485 0.706728i \(-0.249830\pi\)
0.707485 + 0.706728i \(0.249830\pi\)
\(240\) 4.74559 0.306327
\(241\) 9.48160 + 16.4226i 0.610764 + 1.05787i 0.991112 + 0.133031i \(0.0424709\pi\)
−0.380348 + 0.924843i \(0.624196\pi\)
\(242\) −2.61913 + 4.53647i −0.168364 + 0.291615i
\(243\) −6.37701 11.0453i −0.409085 0.708557i
\(244\) −2.03977 + 3.53299i −0.130583 + 0.226177i
\(245\) 12.5732 21.7775i 0.803275 1.39131i
\(246\) −10.0989 −0.643884
\(247\) 0 0
\(248\) 3.47985 0.220971
\(249\) 2.11153 3.65727i 0.133813 0.231770i
\(250\) −6.76007 + 11.7088i −0.427545 + 0.740529i
\(251\) −1.45138 2.51386i −0.0916102 0.158673i 0.816579 0.577234i \(-0.195868\pi\)
−0.908189 + 0.418561i \(0.862535\pi\)
\(252\) −0.298915 + 0.517736i −0.0188299 + 0.0326143i
\(253\) −18.5552 32.1386i −1.16656 2.02054i
\(254\) 14.0806 0.883495
\(255\) 1.26657 0.0793154
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −11.4525 19.8363i −0.714388 1.23736i −0.963195 0.268803i \(-0.913372\pi\)
0.248807 0.968553i \(-0.419961\pi\)
\(258\) −7.23607 −0.450498
\(259\) −0.641142 −0.0398386
\(260\) −9.03879 15.6556i −0.560562 0.970921i
\(261\) −0.151045 + 0.261618i −0.00934946 + 0.0161937i
\(262\) −7.92075 13.7191i −0.489346 0.847572i
\(263\) 2.53118 4.38413i 0.156079 0.270337i −0.777372 0.629041i \(-0.783448\pi\)
0.933452 + 0.358704i \(0.116781\pi\)
\(264\) 2.58721 4.48118i 0.159232 0.275797i
\(265\) 36.7443 2.25719
\(266\) 0 0
\(267\) −7.65407 −0.468421
\(268\) −0.0738814 + 0.127966i −0.00451303 + 0.00781679i
\(269\) 10.3710 17.9630i 0.632329 1.09523i −0.354745 0.934963i \(-0.615432\pi\)
0.987074 0.160263i \(-0.0512342\pi\)
\(270\) 10.3244 + 17.8823i 0.628321 + 1.08828i
\(271\) −3.14735 + 5.45137i −0.191188 + 0.331147i −0.945644 0.325203i \(-0.894567\pi\)
0.754456 + 0.656350i \(0.227901\pi\)
\(272\) −0.133446 0.231136i −0.00809138 0.0140147i
\(273\) −2.77914 −0.168201
\(274\) 2.20744 0.133356
\(275\) 17.4451 + 30.2158i 1.05198 + 1.82208i
\(276\) 5.91273 + 10.2412i 0.355905 + 0.616445i
\(277\) 7.17608 0.431169 0.215584 0.976485i \(-0.430834\pi\)
0.215584 + 0.976485i \(0.430834\pi\)
\(278\) −17.0644 −1.02346
\(279\) 2.35089 + 4.07185i 0.140744 + 0.243776i
\(280\) 0.817610 1.41614i 0.0488615 0.0846307i
\(281\) −1.38696 2.40228i −0.0827388 0.143308i 0.821687 0.569940i \(-0.193033\pi\)
−0.904425 + 0.426632i \(0.859700\pi\)
\(282\) −1.41164 + 2.44503i −0.0840618 + 0.145599i
\(283\) −3.87431 + 6.71049i −0.230304 + 0.398897i −0.957897 0.287111i \(-0.907305\pi\)
0.727594 + 0.686008i \(0.240639\pi\)
\(284\) 11.4691 0.680567
\(285\) 0 0
\(286\) −19.7111 −1.16554
\(287\) −1.73993 + 3.01364i −0.102705 + 0.177890i
\(288\) 0.675571 1.17012i 0.0398084 0.0689501i
\(289\) 8.46438 + 14.6607i 0.497905 + 0.862397i
\(290\) 0.413147 0.715592i 0.0242608 0.0420210i
\(291\) −2.62258 4.54243i −0.153738 0.266282i
\(292\) 1.42226 0.0832315
\(293\) −0.782870 −0.0457358 −0.0228679 0.999738i \(-0.507280\pi\)
−0.0228679 + 0.999738i \(0.507280\pi\)
\(294\) 4.36858 + 7.56661i 0.254781 + 0.441293i
\(295\) 6.48511 + 11.2325i 0.377578 + 0.653983i
\(296\) 1.44903 0.0842230
\(297\) 22.5146 1.30643
\(298\) −6.77288 11.7310i −0.392342 0.679557i
\(299\) 22.5236 39.0120i 1.30257 2.25612i
\(300\) −5.55899 9.62845i −0.320948 0.555899i
\(301\) −1.24669 + 2.15933i −0.0718580 + 0.124462i
\(302\) 4.57659 7.92688i 0.263353 0.456141i
\(303\) 0.546090 0.0313720
\(304\) 0 0
\(305\) 15.0769 0.863298
\(306\) 0.180305 0.312297i 0.0103074 0.0178529i
\(307\) 14.0844 24.3949i 0.803839 1.39229i −0.113234 0.993568i \(-0.536121\pi\)
0.917072 0.398721i \(-0.130546\pi\)
\(308\) −0.891491 1.54411i −0.0507974 0.0879837i
\(309\) 2.91241 5.04444i 0.165681 0.286968i
\(310\) −6.43028 11.1376i −0.365215 0.632571i
\(311\) 3.86827 0.219350 0.109675 0.993968i \(-0.465019\pi\)
0.109675 + 0.993968i \(0.465019\pi\)
\(312\) 6.28106 0.355595
\(313\) −15.1939 26.3166i −0.858809 1.48750i −0.873065 0.487603i \(-0.837871\pi\)
0.0142562 0.999898i \(-0.495462\pi\)
\(314\) 8.19514 + 14.1944i 0.462479 + 0.801036i
\(315\) 2.20941 0.124486
\(316\) 10.2034 0.573985
\(317\) −2.66402 4.61421i −0.149626 0.259160i 0.781463 0.623951i \(-0.214474\pi\)
−0.931089 + 0.364791i \(0.881140\pi\)
\(318\) −6.38342 + 11.0564i −0.357964 + 0.620012i
\(319\) −0.450480 0.780255i −0.0252221 0.0436859i
\(320\) −1.84786 + 3.20059i −0.103298 + 0.178918i
\(321\) 2.03624 3.52687i 0.113652 0.196850i
\(322\) 4.07478 0.227079
\(323\) 0 0
\(324\) −3.12099 −0.173389
\(325\) −21.1761 + 36.6780i −1.17464 + 2.03453i
\(326\) 6.88612 11.9271i 0.381387 0.660582i
\(327\) 4.35375 + 7.54091i 0.240763 + 0.417013i
\(328\) 3.93236 6.81105i 0.217128 0.376077i
\(329\) 0.486417 + 0.842500i 0.0268171 + 0.0464485i
\(330\) −19.1232 −1.05270
\(331\) −20.5480 −1.12942 −0.564711 0.825289i \(-0.691012\pi\)
−0.564711 + 0.825289i \(0.691012\pi\)
\(332\) 1.64439 + 2.84817i 0.0902476 + 0.156313i
\(333\) 0.978921 + 1.69554i 0.0536445 + 0.0929150i
\(334\) −10.3328 −0.565386
\(335\) 0.546090 0.0298361
\(336\) 0.284079 + 0.492039i 0.0154978 + 0.0268429i
\(337\) −6.64121 + 11.5029i −0.361770 + 0.626603i −0.988252 0.152832i \(-0.951161\pi\)
0.626483 + 0.779435i \(0.284494\pi\)
\(338\) −5.46334 9.46279i −0.297167 0.514708i
\(339\) 6.44887 11.1698i 0.350255 0.606659i
\(340\) −0.493181 + 0.854214i −0.0267465 + 0.0463262i
\(341\) −14.0227 −0.759370
\(342\) 0 0
\(343\) 6.10787 0.329794
\(344\) 2.81761 4.88024i 0.151915 0.263125i
\(345\) 21.8518 37.8484i 1.17646 2.03769i
\(346\) 4.90601 + 8.49745i 0.263749 + 0.456826i
\(347\) −15.0712 + 26.1040i −0.809062 + 1.40134i 0.104452 + 0.994530i \(0.466691\pi\)
−0.913514 + 0.406807i \(0.866642\pi\)
\(348\) 0.143548 + 0.248633i 0.00769499 + 0.0133281i
\(349\) 35.0653 1.87700 0.938501 0.345277i \(-0.112215\pi\)
0.938501 + 0.345277i \(0.112215\pi\)
\(350\) −3.83099 −0.204775
\(351\) 13.6649 + 23.6683i 0.729378 + 1.26332i
\(352\) 2.01484 + 3.48980i 0.107391 + 0.186007i
\(353\) 13.5411 0.720718 0.360359 0.932814i \(-0.382654\pi\)
0.360359 + 0.932814i \(0.382654\pi\)
\(354\) −4.50651 −0.239518
\(355\) −21.1933 36.7079i −1.12482 1.94825i
\(356\) 2.98037 5.16216i 0.157959 0.273594i
\(357\) 0.0758187 + 0.131322i 0.00401275 + 0.00695029i
\(358\) 4.39915 7.61955i 0.232502 0.402706i
\(359\) 11.7536 20.3579i 0.620332 1.07445i −0.369092 0.929393i \(-0.620331\pi\)
0.989424 0.145053i \(-0.0463354\pi\)
\(360\) −4.99344 −0.263177
\(361\) 0 0
\(362\) 14.5278 0.763562
\(363\) −3.36317 + 5.82518i −0.176521 + 0.305743i
\(364\) 1.08215 1.87434i 0.0567202 0.0982423i
\(365\) −2.62814 4.55206i −0.137563 0.238266i
\(366\) −2.61923 + 4.53664i −0.136909 + 0.237134i
\(367\) 6.34644 + 10.9924i 0.331282 + 0.573796i 0.982763 0.184868i \(-0.0591857\pi\)
−0.651482 + 0.758664i \(0.725852\pi\)
\(368\) −9.20930 −0.480068
\(369\) 10.6264 0.553186
\(370\) −2.67760 4.63774i −0.139202 0.241104i
\(371\) 2.19958 + 3.80978i 0.114196 + 0.197794i
\(372\) 4.46841 0.231676
\(373\) 2.64950 0.137186 0.0685930 0.997645i \(-0.478149\pi\)
0.0685930 + 0.997645i \(0.478149\pi\)
\(374\) 0.537746 + 0.931403i 0.0278062 + 0.0481617i
\(375\) −8.68047 + 15.0350i −0.448257 + 0.776405i
\(376\) −1.09934 1.90411i −0.0566941 0.0981970i
\(377\) 0.546824 0.947126i 0.0281629 0.0487795i
\(378\) −1.23607 + 2.14093i −0.0635765 + 0.110118i
\(379\) 18.1672 0.933187 0.466593 0.884472i \(-0.345481\pi\)
0.466593 + 0.884472i \(0.345481\pi\)
\(380\) 0 0
\(381\) 18.0806 0.926297
\(382\) −6.36508 + 11.0246i −0.325666 + 0.564070i
\(383\) −11.5042 + 19.9258i −0.587835 + 1.01816i 0.406680 + 0.913570i \(0.366686\pi\)
−0.994515 + 0.104590i \(0.966647\pi\)
\(384\) −0.642040 1.11205i −0.0327639 0.0567488i
\(385\) −3.29470 + 5.70659i −0.167913 + 0.290835i
\(386\) −8.73903 15.1364i −0.444805 0.770425i
\(387\) 7.61398 0.387040
\(388\) 4.08476 0.207372
\(389\) 8.28531 + 14.3506i 0.420082 + 0.727603i 0.995947 0.0899414i \(-0.0286680\pi\)
−0.575865 + 0.817545i \(0.695335\pi\)
\(390\) −11.6065 20.1031i −0.587719 1.01796i
\(391\) −2.45790 −0.124301
\(392\) −6.80423 −0.343665
\(393\) −10.1709 17.6165i −0.513053 0.888633i
\(394\) 12.2556 21.2274i 0.617430 1.06942i
\(395\) −18.8544 32.6568i −0.948668 1.64314i
\(396\) −2.72233 + 4.71521i −0.136802 + 0.236948i
\(397\) 8.89741 15.4108i 0.446548 0.773444i −0.551610 0.834102i \(-0.685986\pi\)
0.998159 + 0.0606575i \(0.0193197\pi\)
\(398\) 16.4661 0.825371
\(399\) 0 0
\(400\) 8.65833 0.432916
\(401\) −15.3107 + 26.5190i −0.764582 + 1.32429i 0.175886 + 0.984411i \(0.443721\pi\)
−0.940468 + 0.339884i \(0.889612\pi\)
\(402\) −0.0948696 + 0.164319i −0.00473167 + 0.00819549i
\(403\) −8.51084 14.7412i −0.423955 0.734311i
\(404\) −0.212639 + 0.368301i −0.0105792 + 0.0183237i
\(405\) 5.76716 + 9.98901i 0.286572 + 0.496358i
\(406\) 0.0989267 0.00490965
\(407\) −5.83911 −0.289434
\(408\) −0.171356 0.296797i −0.00848338 0.0146936i
\(409\) −4.57164 7.91831i −0.226053 0.391535i 0.730582 0.682825i \(-0.239249\pi\)
−0.956635 + 0.291290i \(0.905916\pi\)
\(410\) −29.0658 −1.43546
\(411\) 2.83452 0.139817
\(412\) 2.26809 + 3.92845i 0.111741 + 0.193541i
\(413\) −0.776418 + 1.34480i −0.0382051 + 0.0661731i
\(414\) −6.22153 10.7760i −0.305772 0.529612i
\(415\) 6.07720 10.5260i 0.298318 0.516702i
\(416\) −2.44575 + 4.23616i −0.119913 + 0.207695i
\(417\) −21.9121 −1.07304
\(418\) 0 0
\(419\) 12.6157 0.616315 0.308158 0.951335i \(-0.400288\pi\)
0.308158 + 0.951335i \(0.400288\pi\)
\(420\) 1.04988 1.81844i 0.0512287 0.0887307i
\(421\) −16.6277 + 28.8000i −0.810383 + 1.40362i 0.102213 + 0.994762i \(0.467408\pi\)
−0.912596 + 0.408862i \(0.865926\pi\)
\(422\) −13.7402 23.7988i −0.668864 1.15851i
\(423\) 1.48536 2.57272i 0.0722208 0.125090i
\(424\) −4.97120 8.61038i −0.241423 0.418157i
\(425\) 2.31085 0.112093
\(426\) 14.7273 0.713538
\(427\) 0.902526 + 1.56322i 0.0436763 + 0.0756495i
\(428\) 1.58576 + 2.74661i 0.0766504 + 0.132762i
\(429\) −25.3106 −1.22201
\(430\) −20.8262 −1.00433
\(431\) 11.4957 + 19.9112i 0.553730 + 0.959088i 0.998001 + 0.0631958i \(0.0201293\pi\)
−0.444271 + 0.895892i \(0.646537\pi\)
\(432\) 2.79360 4.83866i 0.134407 0.232800i
\(433\) −17.3546 30.0591i −0.834010 1.44455i −0.894834 0.446399i \(-0.852706\pi\)
0.0608241 0.998148i \(-0.480627\pi\)
\(434\) 0.769854 1.33343i 0.0369542 0.0640065i
\(435\) 0.530514 0.918877i 0.0254362 0.0440568i
\(436\) −6.78112 −0.324757
\(437\) 0 0
\(438\) 1.82629 0.0872637
\(439\) 18.2409 31.5942i 0.870591 1.50791i 0.00920482 0.999958i \(-0.497070\pi\)
0.861386 0.507950i \(-0.169597\pi\)
\(440\) 7.44627 12.8973i 0.354987 0.614855i
\(441\) −4.59673 7.96178i −0.218892 0.379132i
\(442\) −0.652752 + 1.13060i −0.0310483 + 0.0537772i
\(443\) −5.87915 10.1830i −0.279327 0.483808i 0.691891 0.722002i \(-0.256778\pi\)
−0.971218 + 0.238194i \(0.923445\pi\)
\(444\) 1.86067 0.0883033
\(445\) −22.0292 −1.04429
\(446\) −10.1853 17.6414i −0.482288 0.835347i
\(447\) −8.69691 15.0635i −0.411350 0.712479i
\(448\) −0.442463 −0.0209044
\(449\) −8.69102 −0.410154 −0.205077 0.978746i \(-0.565745\pi\)
−0.205077 + 0.978746i \(0.565745\pi\)
\(450\) 5.84931 + 10.1313i 0.275739 + 0.477594i
\(451\) −15.8461 + 27.4463i −0.746165 + 1.29240i
\(452\) 5.02218 + 8.69866i 0.236223 + 0.409151i
\(453\) 5.87670 10.1787i 0.276111 0.478239i
\(454\) 11.0747 19.1819i 0.519760 0.900250i
\(455\) −7.99866 −0.374983
\(456\) 0 0
\(457\) −13.0286 −0.609454 −0.304727 0.952440i \(-0.598565\pi\)
−0.304727 + 0.952440i \(0.598565\pi\)
\(458\) −6.35738 + 11.0113i −0.297061 + 0.514525i
\(459\) 0.745593 1.29141i 0.0348013 0.0602777i
\(460\) 17.0175 + 29.4752i 0.793444 + 1.37429i
\(461\) −4.52130 + 7.83112i −0.210578 + 0.364732i −0.951896 0.306423i \(-0.900868\pi\)
0.741318 + 0.671154i \(0.234201\pi\)
\(462\) −1.14475 1.98276i −0.0532584 0.0922462i
\(463\) −17.7205 −0.823542 −0.411771 0.911287i \(-0.635090\pi\)
−0.411771 + 0.911287i \(0.635090\pi\)
\(464\) −0.223582 −0.0103795
\(465\) −8.25698 14.3015i −0.382908 0.663217i
\(466\) 4.34088 + 7.51863i 0.201087 + 0.348294i
\(467\) −7.87772 −0.364537 −0.182269 0.983249i \(-0.558344\pi\)
−0.182269 + 0.983249i \(0.558344\pi\)
\(468\) −6.60909 −0.305506
\(469\) 0.0326898 + 0.0566205i 0.00150948 + 0.00261449i
\(470\) −4.06285 + 7.03706i −0.187405 + 0.324595i
\(471\) 10.5232 + 18.2267i 0.484884 + 0.839844i
\(472\) 1.75476 3.03934i 0.0807695 0.139897i
\(473\) −11.3540 + 19.6658i −0.522060 + 0.904234i
\(474\) 13.1019 0.601792
\(475\) 0 0
\(476\) −0.118090 −0.00541266
\(477\) 6.71680 11.6338i 0.307541 0.532677i
\(478\) −10.9375 + 18.9442i −0.500267 + 0.866489i
\(479\) 15.0899 + 26.1365i 0.689476 + 1.19421i 0.972008 + 0.234949i \(0.0754924\pi\)
−0.282532 + 0.959258i \(0.591174\pi\)
\(480\) −2.37280 + 4.10980i −0.108303 + 0.187586i
\(481\) −3.54395 6.13831i −0.161590 0.279883i
\(482\) −18.9632 −0.863751
\(483\) 5.23234 0.238080
\(484\) −2.61913 4.53647i −0.119051 0.206203i
\(485\) −7.54806 13.0736i −0.342740 0.593642i
\(486\) 12.7540 0.578534
\(487\) 35.7699 1.62089 0.810445 0.585814i \(-0.199225\pi\)
0.810445 + 0.585814i \(0.199225\pi\)
\(488\) −2.03977 3.53299i −0.0923362 0.159931i
\(489\) 8.84233 15.3154i 0.399864 0.692585i
\(490\) 12.5732 + 21.7775i 0.568001 + 0.983807i
\(491\) 9.13632 15.8246i 0.412316 0.714153i −0.582826 0.812597i \(-0.698053\pi\)
0.995143 + 0.0984441i \(0.0313866\pi\)
\(492\) 5.04946 8.74593i 0.227647 0.394297i
\(493\) −0.0596724 −0.00268751
\(494\) 0 0
\(495\) 20.1219 0.904413
\(496\) −1.73993 + 3.01364i −0.0781250 + 0.135316i
\(497\) 2.53733 4.39479i 0.113815 0.197133i
\(498\) 2.11153 + 3.65727i 0.0946197 + 0.163886i
\(499\) −8.84899 + 15.3269i −0.396135 + 0.686126i −0.993245 0.116033i \(-0.962982\pi\)
0.597110 + 0.802159i \(0.296316\pi\)
\(500\) −6.76007 11.7088i −0.302320 0.523633i
\(501\) −13.2681 −0.592777
\(502\) 2.90276 0.129556
\(503\) 5.09512 + 8.82501i 0.227180 + 0.393488i 0.956971 0.290182i \(-0.0937160\pi\)
−0.729791 + 0.683670i \(0.760383\pi\)
\(504\) −0.298915 0.517736i −0.0133147 0.0230618i
\(505\) 1.57171 0.0699400
\(506\) 37.1105 1.64976
\(507\) −7.01537 12.1510i −0.311563 0.539644i
\(508\) −7.04029 + 12.1941i −0.312363 + 0.541028i
\(509\) 4.21811 + 7.30598i 0.186964 + 0.323832i 0.944237 0.329268i \(-0.106802\pi\)
−0.757272 + 0.653099i \(0.773468\pi\)
\(510\) −0.633283 + 1.09688i −0.0280422 + 0.0485706i
\(511\) 0.314649 0.544988i 0.0139193 0.0241089i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 22.9050 1.01030
\(515\) 8.38222 14.5184i 0.369365 0.639759i
\(516\) 3.61803 6.26662i 0.159275 0.275873i
\(517\) 4.42998 + 7.67295i 0.194830 + 0.337456i
\(518\) 0.320571 0.555245i 0.0140851 0.0243961i
\(519\) 6.29970 + 10.9114i 0.276526 + 0.478957i
\(520\) 18.0776 0.792754
\(521\) 8.96365 0.392705 0.196352 0.980533i \(-0.437090\pi\)
0.196352 + 0.980533i \(0.437090\pi\)
\(522\) −0.151045 0.261618i −0.00661107 0.0114507i
\(523\) 1.06997 + 1.85324i 0.0467864 + 0.0810364i 0.888470 0.458934i \(-0.151769\pi\)
−0.841684 + 0.539971i \(0.818435\pi\)
\(524\) 15.8415 0.692039
\(525\) −4.91930 −0.214696
\(526\) 2.53118 + 4.38413i 0.110365 + 0.191157i
\(527\) −0.464374 + 0.804320i −0.0202285 + 0.0350367i
\(528\) 2.58721 + 4.48118i 0.112594 + 0.195018i
\(529\) −30.9056 + 53.5301i −1.34372 + 2.32739i
\(530\) −18.3722 + 31.8215i −0.798036 + 1.38224i
\(531\) 4.74186 0.205779
\(532\) 0 0
\(533\) −38.4702 −1.66633
\(534\) 3.82703 6.62862i 0.165612 0.286848i
\(535\) 5.86051 10.1507i 0.253372 0.438853i
\(536\) −0.0738814 0.127966i −0.00319119 0.00552731i
\(537\) 5.64886 9.78411i 0.243766 0.422216i
\(538\) 10.3710 + 17.9630i 0.447124 + 0.774442i
\(539\) 27.4188 1.18101
\(540\) −20.6487 −0.888581
\(541\) 5.85577 + 10.1425i 0.251759 + 0.436060i 0.964010 0.265865i \(-0.0856575\pi\)
−0.712251 + 0.701925i \(0.752324\pi\)
\(542\) −3.14735 5.45137i −0.135190 0.234156i
\(543\) 18.6548 0.800553
\(544\) 0.266893 0.0114429
\(545\) 12.5305 + 21.7035i 0.536750 + 0.929678i
\(546\) 1.38957 2.40681i 0.0594681 0.103002i
\(547\) 12.4948 + 21.6417i 0.534240 + 0.925332i 0.999200 + 0.0399995i \(0.0127356\pi\)
−0.464959 + 0.885332i \(0.653931\pi\)
\(548\) −1.10372 + 1.91169i −0.0471485 + 0.0816636i
\(549\) 2.75602 4.77357i 0.117624 0.203731i
\(550\) −34.8902 −1.48772
\(551\) 0 0
\(552\) −11.8255 −0.503325
\(553\) 2.25731 3.90978i 0.0959906 0.166261i
\(554\) −3.58804 + 6.21467i −0.152441 + 0.264036i
\(555\) −3.43825 5.95522i −0.145946 0.252785i
\(556\) 8.53222 14.7782i 0.361847 0.626737i
\(557\) −4.59783 7.96368i −0.194816 0.337432i 0.752024 0.659136i \(-0.229078\pi\)
−0.946840 + 0.321704i \(0.895744\pi\)
\(558\) −4.70177 −0.199042
\(559\) −27.5646 −1.16586
\(560\) 0.817610 + 1.41614i 0.0345503 + 0.0598429i
\(561\) 0.690508 + 1.19599i 0.0291533 + 0.0504949i
\(562\) 2.77391 0.117010
\(563\) 19.7224 0.831202 0.415601 0.909547i \(-0.363571\pi\)
0.415601 + 0.909547i \(0.363571\pi\)
\(564\) −1.41164 2.44503i −0.0594407 0.102954i
\(565\) 18.5605 32.1478i 0.780848 1.35247i
\(566\) −3.87431 6.71049i −0.162849 0.282063i
\(567\) −0.690463 + 1.19592i −0.0289967 + 0.0502238i
\(568\) −5.73456 + 9.93255i −0.240617 + 0.416760i
\(569\) 22.1469 0.928446 0.464223 0.885718i \(-0.346334\pi\)
0.464223 + 0.885718i \(0.346334\pi\)
\(570\) 0 0
\(571\) −3.02145 −0.126444 −0.0632218 0.998000i \(-0.520138\pi\)
−0.0632218 + 0.998000i \(0.520138\pi\)
\(572\) 9.85555 17.0703i 0.412081 0.713746i
\(573\) −8.17327 + 14.1565i −0.341443 + 0.591397i
\(574\) −1.73993 3.01364i −0.0726231 0.125787i
\(575\) 39.8686 69.0544i 1.66263 2.87977i
\(576\) 0.675571 + 1.17012i 0.0281488 + 0.0487551i
\(577\) 2.30938 0.0961407 0.0480704 0.998844i \(-0.484693\pi\)
0.0480704 + 0.998844i \(0.484693\pi\)
\(578\) −16.9288 −0.704144
\(579\) −11.2216 19.4364i −0.466354 0.807749i
\(580\) 0.413147 + 0.715592i 0.0171550 + 0.0297133i
\(581\) 1.45516 0.0603704
\(582\) 5.24515 0.217419
\(583\) 20.0323 + 34.6970i 0.829654 + 1.43700i
\(584\) −0.711130 + 1.23171i −0.0294268 + 0.0509687i
\(585\) 12.2127 + 21.1530i 0.504932 + 0.874568i
\(586\) 0.391435 0.677985i 0.0161700 0.0280073i
\(587\) −14.0445 + 24.3258i −0.579679 + 1.00403i 0.415837 + 0.909439i \(0.363489\pi\)
−0.995516 + 0.0945942i \(0.969845\pi\)
\(588\) −8.73716 −0.360315
\(589\) 0 0
\(590\) −12.9702 −0.533975
\(591\) 15.7372 27.2576i 0.647342 1.12123i
\(592\) −0.724514 + 1.25490i −0.0297773 + 0.0515759i
\(593\) 6.04695 + 10.4736i 0.248318 + 0.430100i 0.963059 0.269289i \(-0.0867887\pi\)
−0.714741 + 0.699389i \(0.753455\pi\)
\(594\) −11.2573 + 19.4982i −0.461893 + 0.800022i
\(595\) 0.218214 + 0.377958i 0.00894592 + 0.0154948i
\(596\) 13.5458 0.554856
\(597\) 21.1438 0.865357
\(598\) 22.5236 + 39.0120i 0.921059 + 1.59532i
\(599\) −9.75126 16.8897i −0.398426 0.690094i 0.595106 0.803647i \(-0.297110\pi\)
−0.993532 + 0.113554i \(0.963777\pi\)
\(600\) 11.1180 0.453890
\(601\) −38.9632 −1.58934 −0.794671 0.607040i \(-0.792357\pi\)
−0.794671 + 0.607040i \(0.792357\pi\)
\(602\) −1.24669 2.15933i −0.0508113 0.0880077i
\(603\) 0.0998242 0.172901i 0.00406516 0.00704106i
\(604\) 4.57659 + 7.92688i 0.186219 + 0.322540i
\(605\) −9.67957 + 16.7655i −0.393530 + 0.681614i
\(606\) −0.273045 + 0.472928i −0.0110917 + 0.0192114i
\(607\) 8.46029 0.343393 0.171696 0.985150i \(-0.445075\pi\)
0.171696 + 0.985150i \(0.445075\pi\)
\(608\) 0 0
\(609\) 0.127030 0.00514750
\(610\) −7.53843 + 13.0569i −0.305222 + 0.528660i
\(611\) −5.37741 + 9.31394i −0.217547 + 0.376802i
\(612\) 0.180305 + 0.312297i 0.00728840 + 0.0126239i
\(613\) 1.45746 2.52440i 0.0588664 0.101960i −0.835090 0.550113i \(-0.814585\pi\)
0.893957 + 0.448153i \(0.147918\pi\)
\(614\) 14.0844 + 24.3949i 0.568400 + 0.984497i
\(615\) −37.3228 −1.50500
\(616\) 1.78298 0.0718384
\(617\) 1.50953 + 2.61457i 0.0607712 + 0.105259i 0.894810 0.446446i \(-0.147311\pi\)
−0.834039 + 0.551705i \(0.813977\pi\)
\(618\) 2.91241 + 5.04444i 0.117154 + 0.202917i
\(619\) −3.92813 −0.157885 −0.0789423 0.996879i \(-0.525154\pi\)
−0.0789423 + 0.996879i \(0.525154\pi\)
\(620\) 12.8606 0.516492
\(621\) −25.7271 44.5607i −1.03239 1.78816i
\(622\) −1.93414 + 3.35002i −0.0775518 + 0.134324i
\(623\) −1.31871 2.28407i −0.0528328 0.0915092i
\(624\) −3.14053 + 5.43956i −0.125722 + 0.217757i
\(625\) −3.33750 + 5.78072i −0.133500 + 0.231229i
\(626\) 30.3878 1.21454
\(627\) 0 0
\(628\) −16.3903 −0.654043
\(629\) −0.193368 + 0.334923i −0.00771007 + 0.0133542i
\(630\) −1.10471 + 1.91341i −0.0440126 + 0.0762320i
\(631\) −5.06836 8.77865i −0.201768 0.349473i 0.747330 0.664453i \(-0.231335\pi\)
−0.949098 + 0.314980i \(0.898002\pi\)
\(632\) −5.10169 + 8.83638i −0.202934 + 0.351493i
\(633\) −17.6435 30.5595i −0.701268 1.21463i
\(634\) 5.32803 0.211603
\(635\) 52.0379 2.06506
\(636\) −6.38342 11.0564i −0.253119 0.438415i
\(637\) 16.6414 + 28.8238i 0.659357 + 1.14204i
\(638\) 0.900961 0.0356694
\(639\) −15.4964 −0.613028
\(640\) −1.84786 3.20059i −0.0730430 0.126514i
\(641\) −4.14015 + 7.17096i −0.163526 + 0.283236i −0.936131 0.351652i \(-0.885620\pi\)
0.772605 + 0.634887i \(0.218954\pi\)
\(642\) 2.03624 + 3.52687i 0.0803639 + 0.139194i
\(643\) −18.4270 + 31.9166i −0.726691 + 1.25867i 0.231583 + 0.972815i \(0.425610\pi\)
−0.958274 + 0.285851i \(0.907724\pi\)
\(644\) −2.03739 + 3.52886i −0.0802844 + 0.139057i
\(645\) −26.7425 −1.05298
\(646\) 0 0
\(647\) −20.1901 −0.793753 −0.396876 0.917872i \(-0.629906\pi\)
−0.396876 + 0.917872i \(0.629906\pi\)
\(648\) 1.56050 2.70286i 0.0613021 0.106178i
\(649\) −7.07112 + 12.2475i −0.277566 + 0.480758i
\(650\) −21.1761 36.6780i −0.830594 1.43863i
\(651\) 0.988553 1.71222i 0.0387445 0.0671074i
\(652\) 6.88612 + 11.9271i 0.269681 + 0.467102i
\(653\) −22.0387 −0.862443 −0.431221 0.902246i \(-0.641917\pi\)
−0.431221 + 0.902246i \(0.641917\pi\)
\(654\) −8.70749 −0.340490
\(655\) −29.2729 50.7021i −1.14379 1.98109i
\(656\) 3.93236 + 6.81105i 0.153533 + 0.265927i
\(657\) −1.92167 −0.0749716
\(658\) −0.972835 −0.0379251
\(659\) 13.6108 + 23.5746i 0.530202 + 0.918336i 0.999379 + 0.0352322i \(0.0112171\pi\)
−0.469178 + 0.883104i \(0.655450\pi\)
\(660\) 9.56159 16.5612i 0.372185 0.644643i
\(661\) 4.45412 + 7.71477i 0.173245 + 0.300070i 0.939553 0.342404i \(-0.111241\pi\)
−0.766307 + 0.642474i \(0.777908\pi\)
\(662\) 10.2740 17.7951i 0.399311 0.691627i
\(663\) −0.838186 + 1.45178i −0.0325524 + 0.0563825i
\(664\) −3.28878 −0.127629
\(665\) 0 0
\(666\) −1.95784 −0.0758648
\(667\) −1.02951 + 1.78317i −0.0398630 + 0.0690447i
\(668\) 5.16640 8.94847i 0.199894 0.346227i
\(669\) −13.0787 22.6530i −0.505653 0.875816i
\(670\) −0.273045 + 0.472928i −0.0105486 + 0.0182708i
\(671\) 8.21962 + 14.2368i 0.317315 + 0.549606i
\(672\) −0.568158 −0.0219172
\(673\) 35.7010 1.37617 0.688087 0.725629i \(-0.258451\pi\)
0.688087 + 0.725629i \(0.258451\pi\)
\(674\) −6.64121 11.5029i −0.255810 0.443076i
\(675\) 24.1879 + 41.8947i 0.930994 + 1.61253i
\(676\) 10.9267 0.420257
\(677\) −27.3849 −1.05249 −0.526243 0.850334i \(-0.676400\pi\)
−0.526243 + 0.850334i \(0.676400\pi\)
\(678\) 6.44887 + 11.1698i 0.247667 + 0.428972i
\(679\) 0.903678 1.56522i 0.0346800 0.0600675i
\(680\) −0.493181 0.854214i −0.0189126 0.0327576i
\(681\) 14.2207 24.6311i 0.544940 0.943864i
\(682\) 7.01133 12.1440i 0.268478 0.465017i
\(683\) −38.1521 −1.45985 −0.729925 0.683528i \(-0.760445\pi\)
−0.729925 + 0.683528i \(0.760445\pi\)
\(684\) 0 0
\(685\) 8.15806 0.311703
\(686\) −3.05393 + 5.28957i −0.116600 + 0.201957i
\(687\) −8.16338 + 14.1394i −0.311453 + 0.539452i
\(688\) 2.81761 + 4.88024i 0.107420 + 0.186058i
\(689\) −24.3166 + 42.1176i −0.926389 + 1.60455i
\(690\) 21.8518 + 37.8484i 0.831884 + 1.44086i
\(691\) −28.2058 −1.07300 −0.536499 0.843901i \(-0.680254\pi\)
−0.536499 + 0.843901i \(0.680254\pi\)
\(692\) −9.81201 −0.372997
\(693\) 1.20453 + 2.08631i 0.0457563 + 0.0792523i
\(694\) −15.0712 26.1040i −0.572094 0.990895i
\(695\) −63.0654 −2.39221
\(696\) −0.287096 −0.0108824
\(697\) 1.04952 + 1.81782i 0.0397534 + 0.0688549i
\(698\) −17.5326 + 30.3674i −0.663620 + 1.14942i
\(699\) 5.57404 + 9.65451i 0.210829 + 0.365167i
\(700\) 1.91550 3.31774i 0.0723990 0.125399i
\(701\) −21.3074 + 36.9055i −0.804769 + 1.39390i 0.111678 + 0.993744i \(0.464378\pi\)
−0.916447 + 0.400157i \(0.868956\pi\)
\(702\) −27.3298 −1.03150
\(703\) 0 0
\(704\) −4.02967 −0.151874
\(705\) −5.21702 + 9.03614i −0.196484 + 0.340321i
\(706\) −6.77053 + 11.7269i −0.254812 + 0.441348i
\(707\) 0.0940849 + 0.162960i 0.00353843 + 0.00612873i
\(708\) 2.25325 3.90275i 0.0846825 0.146674i
\(709\) 11.3446 + 19.6494i 0.426055 + 0.737949i 0.996518 0.0833743i \(-0.0265697\pi\)
−0.570463 + 0.821323i \(0.693236\pi\)
\(710\) 42.3866 1.59074
\(711\) −13.7862 −0.517023
\(712\) 2.98037 + 5.16216i 0.111694 + 0.193460i
\(713\) 16.0235 + 27.7535i 0.600085 + 1.03938i
\(714\) −0.151637 −0.00567489
\(715\) −72.8467 −2.72431
\(716\) 4.39915 + 7.61955i 0.164404 + 0.284756i
\(717\) −14.0446 + 24.3259i −0.524503 + 0.908467i
\(718\) 11.7536 + 20.3579i 0.438641 + 0.759748i
\(719\) 18.9162 32.7638i 0.705456 1.22188i −0.261071 0.965320i \(-0.584076\pi\)
0.966527 0.256565i \(-0.0825909\pi\)
\(720\) 2.49672 4.32444i 0.0930472 0.161162i
\(721\) 2.00709 0.0747481
\(722\) 0 0
\(723\) −24.3503 −0.905596
\(724\) −7.26388 + 12.5814i −0.269960 + 0.467584i
\(725\) 0.967921 1.67649i 0.0359477 0.0622632i
\(726\) −3.36317 5.82518i −0.124819 0.216193i
\(727\) 9.77015 16.9224i 0.362355 0.627617i −0.625993 0.779829i \(-0.715306\pi\)
0.988348 + 0.152212i \(0.0486395\pi\)
\(728\) 1.08215 + 1.87434i 0.0401073 + 0.0694678i
\(729\) 25.7402 0.953339
\(730\) 5.25627 0.194543
\(731\) 0.752000 + 1.30250i 0.0278137 + 0.0481748i
\(732\) −2.61923 4.53664i −0.0968096 0.167679i
\(733\) 35.1101 1.29682 0.648410 0.761291i \(-0.275434\pi\)
0.648410 + 0.761291i \(0.275434\pi\)
\(734\) −12.6929 −0.468503
\(735\) 16.1450 + 27.9640i 0.595519 + 1.03147i
\(736\) 4.60465 7.97549i 0.169730 0.293980i
\(737\) 0.297718 + 0.515663i 0.0109666 + 0.0189947i
\(738\) −5.31318 + 9.20269i −0.195581 + 0.338756i
\(739\) 8.13874 14.0967i 0.299388 0.518556i −0.676608 0.736344i \(-0.736551\pi\)
0.975996 + 0.217788i \(0.0698841\pi\)
\(740\) 5.35520 0.196861
\(741\) 0 0
\(742\) −4.39915 −0.161498
\(743\) −16.6543 + 28.8460i −0.610986 + 1.05826i 0.380089 + 0.924950i \(0.375893\pi\)
−0.991075 + 0.133309i \(0.957440\pi\)
\(744\) −2.23420 + 3.86975i −0.0819099 + 0.141872i
\(745\) −25.0307 43.3544i −0.917052 1.58838i
\(746\) −1.32475 + 2.29454i −0.0485026 + 0.0840089i
\(747\) −2.22180 3.84827i −0.0812915 0.140801i
\(748\) −1.07549 −0.0393239
\(749\) 1.40328 0.0512747
\(750\) −8.68047 15.0350i −0.316966 0.549001i
\(751\) −9.62995 16.6796i −0.351402 0.608646i 0.635093 0.772435i \(-0.280962\pi\)
−0.986495 + 0.163789i \(0.947628\pi\)
\(752\) 2.19868 0.0801776
\(753\) 3.72737 0.135833
\(754\) 0.546824 + 0.947126i 0.0199141 + 0.0344923i
\(755\) 16.9138 29.2955i 0.615555 1.06617i
\(756\) −1.23607 2.14093i −0.0449554 0.0778650i
\(757\) 11.9727 20.7373i 0.435156 0.753712i −0.562153 0.827033i \(-0.690027\pi\)
0.997308 + 0.0733218i \(0.0233600\pi\)
\(758\) −9.08361 + 15.7333i −0.329931 + 0.571458i
\(759\) 47.6528 1.72969
\(760\) 0 0
\(761\) −44.7968 −1.62388 −0.811941 0.583739i \(-0.801589\pi\)
−0.811941 + 0.583739i \(0.801589\pi\)
\(762\) −9.04029 + 15.6582i −0.327495 + 0.567238i
\(763\) −1.50020 + 2.59842i −0.0543108 + 0.0940691i
\(764\) −6.36508 11.0246i −0.230281 0.398858i
\(765\) 0.666356 1.15416i 0.0240922 0.0417289i
\(766\) −11.5042 19.9258i −0.415662 0.719948i
\(767\) −17.1668 −0.619858
\(768\) 1.28408 0.0463352
\(769\) 15.8684 + 27.4848i 0.572228 + 0.991128i 0.996337 + 0.0855164i \(0.0272540\pi\)
−0.424109 + 0.905611i \(0.639413\pi\)
\(770\) −3.29470 5.70659i −0.118733 0.205651i
\(771\) 29.4119 1.05924
\(772\) 17.4781 0.629049
\(773\) 11.1153 + 19.2523i 0.399791 + 0.692458i 0.993700 0.112074i \(-0.0357494\pi\)
−0.593909 + 0.804532i \(0.702416\pi\)
\(774\) −3.80699 + 6.59390i −0.136839 + 0.237013i
\(775\) −15.0649 26.0931i −0.541146 0.937292i
\(776\) −2.04238 + 3.53750i −0.0733171 + 0.126989i
\(777\) 0.411638 0.712979i 0.0147674 0.0255780i
\(778\) −16.5706 −0.594086
\(779\) 0 0
\(780\) 23.2130 0.831