Properties

Label 570.2.q.a.349.3
Level $570$
Weight $2$
Character 570.349
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.3
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 570.349
Dual form 570.2.q.a.49.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917738 + 2.03906i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000i q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917738 + 2.03906i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000i q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.81431 + 1.30701i) q^{10} +2.00000 q^{11} -1.00000i q^{12} +(1.25529 + 0.724745i) q^{13} +(1.50000 + 2.59808i) q^{14} +(1.81431 + 1.30701i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.24264 + 2.44949i) q^{17} -1.00000i q^{18} +(1.00000 - 4.24264i) q^{19} +(2.22474 + 0.224745i) q^{20} +(1.50000 + 2.59808i) q^{21} +(1.73205 - 1.00000i) q^{22} +(2.12132 + 1.22474i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.31552 + 3.74264i) q^{25} +1.44949 q^{26} -1.00000i q^{27} +(2.59808 + 1.50000i) q^{28} +(2.67423 - 4.63191i) q^{29} +(2.22474 + 0.224745i) q^{30} +1.89898 q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.73205 - 1.00000i) q^{33} +(-2.44949 + 4.24264i) q^{34} +(-6.11717 + 2.75321i) q^{35} +(-0.500000 - 0.866025i) q^{36} -9.44949i q^{37} +(-1.25529 - 4.17423i) q^{38} +1.44949 q^{39} +(2.03906 - 0.917738i) q^{40} +(1.22474 + 2.12132i) q^{41} +(2.59808 + 1.50000i) q^{42} +(-4.71940 + 2.72474i) q^{43} +(1.00000 - 1.73205i) q^{44} +(2.22474 + 0.224745i) q^{45} +2.44949 q^{46} +(-7.31747 - 4.22474i) q^{47} +(-0.866025 - 0.500000i) q^{48} -2.00000 q^{49} +(-1.00000 + 4.89898i) q^{50} +(-2.44949 + 4.24264i) q^{51} +(1.25529 - 0.724745i) q^{52} +(-11.1708 - 6.44949i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.83548 + 4.07812i) q^{55} +3.00000 q^{56} +(-1.25529 - 4.17423i) q^{57} -5.34847i q^{58} +(-3.89898 - 6.75323i) q^{59} +(2.03906 - 0.917738i) q^{60} +(5.17423 - 8.96204i) q^{61} +(1.64456 - 0.949490i) q^{62} +(2.59808 + 1.50000i) q^{63} -1.00000 q^{64} +(-0.325765 + 3.22474i) q^{65} +(1.00000 - 1.73205i) q^{66} +(2.98735 + 1.72474i) q^{67} +4.89898i q^{68} +2.44949 q^{69} +(-3.92102 + 5.44294i) q^{70} +(4.22474 + 7.31747i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(1.81954 - 1.05051i) q^{73} +(-4.72474 - 8.18350i) q^{74} +(-1.00000 + 4.89898i) q^{75} +(-3.17423 - 2.98735i) q^{76} +6.00000i q^{77} +(1.25529 - 0.724745i) q^{78} +(-1.39898 - 2.42310i) q^{79} +(1.30701 - 1.81431i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.12132 + 1.22474i) q^{82} +13.3485i q^{83} +3.00000 q^{84} +(-8.88828 - 6.40300i) q^{85} +(-2.72474 + 4.71940i) q^{86} -5.34847i q^{87} -2.00000i q^{88} +(-8.22474 + 14.2457i) q^{89} +(2.03906 - 0.917738i) q^{90} +(-2.17423 + 3.76588i) q^{91} +(2.12132 - 1.22474i) q^{92} +(1.64456 - 0.949490i) q^{93} -8.44949 q^{94} +(9.56873 - 1.85457i) q^{95} -1.00000 q^{96} +(9.26382 - 5.34847i) q^{97} +(-1.73205 + 1.00000i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + 4q^{5} + 4q^{6} + 4q^{9} + O(q^{10}) \) \( 8q + 4q^{4} + 4q^{5} + 4q^{6} + 4q^{9} + 4q^{10} + 16q^{11} + 12q^{14} + 4q^{15} - 4q^{16} + 8q^{19} + 8q^{20} + 12q^{21} - 4q^{24} - 8q^{26} - 8q^{29} + 8q^{30} - 24q^{31} + 12q^{35} - 4q^{36} - 8q^{39} - 4q^{40} + 8q^{44} + 8q^{45} - 16q^{49} - 8q^{50} - 4q^{54} + 8q^{55} + 24q^{56} + 8q^{59} - 4q^{60} + 12q^{61} - 8q^{64} - 32q^{65} + 8q^{66} - 12q^{70} + 24q^{71} - 28q^{74} - 8q^{75} + 4q^{76} + 28q^{79} + 4q^{80} - 4q^{81} + 24q^{84} + 24q^{85} - 12q^{86} - 56q^{89} - 4q^{90} + 12q^{91} - 48q^{94} + 40q^{95} - 8q^{96} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.917738 + 2.03906i 0.410425 + 0.911894i
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 3.00000i 1.13389i 0.823754 + 0.566947i \(0.191875\pi\)
−0.823754 + 0.566947i \(0.808125\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.81431 + 1.30701i 0.573736 + 0.413312i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.25529 + 0.724745i 0.348156 + 0.201008i 0.663873 0.747845i \(-0.268912\pi\)
−0.315717 + 0.948853i \(0.602245\pi\)
\(14\) 1.50000 + 2.59808i 0.400892 + 0.694365i
\(15\) 1.81431 + 1.30701i 0.468454 + 0.337468i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −4.24264 + 2.44949i −1.02899 + 0.594089i −0.916696 0.399586i \(-0.869154\pi\)
−0.112296 + 0.993675i \(0.535820\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000 4.24264i 0.229416 0.973329i
\(20\) 2.22474 + 0.224745i 0.497468 + 0.0502545i
\(21\) 1.50000 + 2.59808i 0.327327 + 0.566947i
\(22\) 1.73205 1.00000i 0.369274 0.213201i
\(23\) 2.12132 + 1.22474i 0.442326 + 0.255377i 0.704584 0.709621i \(-0.251134\pi\)
−0.262258 + 0.964998i \(0.584467\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −3.31552 + 3.74264i −0.663103 + 0.748528i
\(26\) 1.44949 0.284268
\(27\) 1.00000i 0.192450i
\(28\) 2.59808 + 1.50000i 0.490990 + 0.283473i
\(29\) 2.67423 4.63191i 0.496593 0.860124i −0.503399 0.864054i \(-0.667918\pi\)
0.999992 + 0.00392972i \(0.00125087\pi\)
\(30\) 2.22474 + 0.224745i 0.406181 + 0.0410326i
\(31\) 1.89898 0.341067 0.170533 0.985352i \(-0.445451\pi\)
0.170533 + 0.985352i \(0.445451\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 1.73205 1.00000i 0.301511 0.174078i
\(34\) −2.44949 + 4.24264i −0.420084 + 0.727607i
\(35\) −6.11717 + 2.75321i −1.03399 + 0.465378i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 9.44949i 1.55349i −0.629817 0.776743i \(-0.716870\pi\)
0.629817 0.776743i \(-0.283130\pi\)
\(38\) −1.25529 4.17423i −0.203636 0.677150i
\(39\) 1.44949 0.232104
\(40\) 2.03906 0.917738i 0.322403 0.145107i
\(41\) 1.22474 + 2.12132i 0.191273 + 0.331295i 0.945672 0.325121i \(-0.105405\pi\)
−0.754399 + 0.656416i \(0.772072\pi\)
\(42\) 2.59808 + 1.50000i 0.400892 + 0.231455i
\(43\) −4.71940 + 2.72474i −0.719701 + 0.415520i −0.814643 0.579963i \(-0.803067\pi\)
0.0949415 + 0.995483i \(0.469734\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) 2.22474 + 0.224745i 0.331645 + 0.0335030i
\(46\) 2.44949 0.361158
\(47\) −7.31747 4.22474i −1.06736 0.616242i −0.139903 0.990165i \(-0.544679\pi\)
−0.927460 + 0.373923i \(0.878012\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) −2.00000 −0.285714
\(50\) −1.00000 + 4.89898i −0.141421 + 0.692820i
\(51\) −2.44949 + 4.24264i −0.342997 + 0.594089i
\(52\) 1.25529 0.724745i 0.174078 0.100504i
\(53\) −11.1708 6.44949i −1.53443 0.885906i −0.999150 0.0412333i \(-0.986871\pi\)
−0.535284 0.844672i \(-0.679795\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 1.83548 + 4.07812i 0.247495 + 0.549893i
\(56\) 3.00000 0.400892
\(57\) −1.25529 4.17423i −0.166268 0.552891i
\(58\) 5.34847i 0.702288i
\(59\) −3.89898 6.75323i −0.507604 0.879196i −0.999961 0.00880259i \(-0.997198\pi\)
0.492357 0.870393i \(-0.336135\pi\)
\(60\) 2.03906 0.917738i 0.263241 0.118479i
\(61\) 5.17423 8.96204i 0.662493 1.14747i −0.317466 0.948270i \(-0.602832\pi\)
0.979959 0.199202i \(-0.0638348\pi\)
\(62\) 1.64456 0.949490i 0.208860 0.120585i
\(63\) 2.59808 + 1.50000i 0.327327 + 0.188982i
\(64\) −1.00000 −0.125000
\(65\) −0.325765 + 3.22474i −0.0404062 + 0.399980i
\(66\) 1.00000 1.73205i 0.123091 0.213201i
\(67\) 2.98735 + 1.72474i 0.364962 + 0.210711i 0.671255 0.741226i \(-0.265755\pi\)
−0.306293 + 0.951937i \(0.599089\pi\)
\(68\) 4.89898i 0.594089i
\(69\) 2.44949 0.294884
\(70\) −3.92102 + 5.44294i −0.468652 + 0.650556i
\(71\) 4.22474 + 7.31747i 0.501385 + 0.868424i 0.999999 + 0.00159997i \(0.000509286\pi\)
−0.498614 + 0.866824i \(0.666157\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 1.81954 1.05051i 0.212961 0.122953i −0.389726 0.920931i \(-0.627430\pi\)
0.602687 + 0.797978i \(0.294097\pi\)
\(74\) −4.72474 8.18350i −0.549240 0.951312i
\(75\) −1.00000 + 4.89898i −0.115470 + 0.565685i
\(76\) −3.17423 2.98735i −0.364110 0.342672i
\(77\) 6.00000i 0.683763i
\(78\) 1.25529 0.724745i 0.142134 0.0820612i
\(79\) −1.39898 2.42310i −0.157397 0.272620i 0.776532 0.630078i \(-0.216977\pi\)
−0.933929 + 0.357457i \(0.883644\pi\)
\(80\) 1.30701 1.81431i 0.146128 0.202846i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.12132 + 1.22474i 0.234261 + 0.135250i
\(83\) 13.3485i 1.46518i 0.680668 + 0.732592i \(0.261690\pi\)
−0.680668 + 0.732592i \(0.738310\pi\)
\(84\) 3.00000 0.327327
\(85\) −8.88828 6.40300i −0.964070 0.694503i
\(86\) −2.72474 + 4.71940i −0.293817 + 0.508906i
\(87\) 5.34847i 0.573416i
\(88\) 2.00000i 0.213201i
\(89\) −8.22474 + 14.2457i −0.871821 + 1.51004i −0.0117104 + 0.999931i \(0.503728\pi\)
−0.860111 + 0.510107i \(0.829606\pi\)
\(90\) 2.03906 0.917738i 0.214936 0.0967380i
\(91\) −2.17423 + 3.76588i −0.227922 + 0.394772i
\(92\) 2.12132 1.22474i 0.221163 0.127688i
\(93\) 1.64456 0.949490i 0.170533 0.0984575i
\(94\) −8.44949 −0.871498
\(95\) 9.56873 1.85457i 0.981731 0.190275i
\(96\) −1.00000 −0.102062
\(97\) 9.26382 5.34847i 0.940598 0.543055i 0.0504506 0.998727i \(-0.483934\pi\)
0.890148 + 0.455672i \(0.150601\pi\)
\(98\) −1.73205 + 1.00000i −0.174964 + 0.101015i
\(99\) 1.00000 1.73205i 0.100504 0.174078i
\(100\) 1.58346 + 4.74264i 0.158346 + 0.474264i
\(101\) −7.89898 + 13.6814i −0.785978 + 1.36135i 0.142435 + 0.989804i \(0.454507\pi\)
−0.928413 + 0.371549i \(0.878827\pi\)
\(102\) 4.89898i 0.485071i
\(103\) 0.101021i 0.00995385i −0.999988 0.00497692i \(-0.998416\pi\)
0.999988 0.00497692i \(-0.00158421\pi\)
\(104\) 0.724745 1.25529i 0.0710671 0.123092i
\(105\) −3.92102 + 5.44294i −0.382653 + 0.531176i
\(106\) −12.8990 −1.25286
\(107\) 5.55051i 0.536588i 0.963337 + 0.268294i \(0.0864599\pi\)
−0.963337 + 0.268294i \(0.913540\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 3.62863 + 2.61401i 0.345976 + 0.249236i
\(111\) −4.72474 8.18350i −0.448453 0.776743i
\(112\) 2.59808 1.50000i 0.245495 0.141737i
\(113\) 5.10102i 0.479864i 0.970790 + 0.239932i \(0.0771251\pi\)
−0.970790 + 0.239932i \(0.922875\pi\)
\(114\) −3.17423 2.98735i −0.297294 0.279791i
\(115\) −0.550510 + 5.44949i −0.0513353 + 0.508168i
\(116\) −2.67423 4.63191i −0.248296 0.430062i
\(117\) 1.25529 0.724745i 0.116052 0.0670027i
\(118\) −6.75323 3.89898i −0.621685 0.358930i
\(119\) −7.34847 12.7279i −0.673633 1.16677i
\(120\) 1.30701 1.81431i 0.119313 0.165623i
\(121\) −7.00000 −0.636364
\(122\) 10.3485i 0.936906i
\(123\) 2.12132 + 1.22474i 0.191273 + 0.110432i
\(124\) 0.949490 1.64456i 0.0852667 0.147686i
\(125\) −10.6742 3.32577i −0.954733 0.297465i
\(126\) 3.00000 0.267261
\(127\) 10.9959 + 6.34847i 0.975726 + 0.563336i 0.900977 0.433867i \(-0.142851\pi\)
0.0747488 + 0.997202i \(0.476185\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −2.72474 + 4.71940i −0.239900 + 0.415520i
\(130\) 1.33025 + 2.95559i 0.116671 + 0.259223i
\(131\) 5.89898 + 10.2173i 0.515396 + 0.892692i 0.999840 + 0.0178702i \(0.00568857\pi\)
−0.484444 + 0.874822i \(0.660978\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 12.7279 + 3.00000i 1.10365 + 0.260133i
\(134\) 3.44949 0.297991
\(135\) 2.03906 0.917738i 0.175494 0.0789863i
\(136\) 2.44949 + 4.24264i 0.210042 + 0.363803i
\(137\) −9.43879 5.44949i −0.806411 0.465581i 0.0392973 0.999228i \(-0.487488\pi\)
−0.845708 + 0.533646i \(0.820821\pi\)
\(138\) 2.12132 1.22474i 0.180579 0.104257i
\(139\) 5.72474 9.91555i 0.485567 0.841026i −0.514296 0.857613i \(-0.671947\pi\)
0.999862 + 0.0165869i \(0.00528002\pi\)
\(140\) −0.674235 + 6.67423i −0.0569832 + 0.564076i
\(141\) −8.44949 −0.711575
\(142\) 7.31747 + 4.22474i 0.614069 + 0.354533i
\(143\) 2.51059 + 1.44949i 0.209946 + 0.121212i
\(144\) −1.00000 −0.0833333
\(145\) 11.8990 + 1.20204i 0.988156 + 0.0998241i
\(146\) 1.05051 1.81954i 0.0869408 0.150586i
\(147\) −1.73205 + 1.00000i −0.142857 + 0.0824786i
\(148\) −8.18350 4.72474i −0.672679 0.388372i
\(149\) −7.89898 13.6814i −0.647110 1.12083i −0.983810 0.179215i \(-0.942644\pi\)
0.336700 0.941612i \(-0.390689\pi\)
\(150\) 1.58346 + 4.74264i 0.129289 + 0.387235i
\(151\) 0.202041 0.0164419 0.00822093 0.999966i \(-0.497383\pi\)
0.00822093 + 0.999966i \(0.497383\pi\)
\(152\) −4.24264 1.00000i −0.344124 0.0811107i
\(153\) 4.89898i 0.396059i
\(154\) 3.00000 + 5.19615i 0.241747 + 0.418718i
\(155\) 1.74277 + 3.87213i 0.139982 + 0.311017i
\(156\) 0.724745 1.25529i 0.0580260 0.100504i
\(157\) 0.476756 0.275255i 0.0380493 0.0219678i −0.480855 0.876800i \(-0.659674\pi\)
0.518904 + 0.854833i \(0.326340\pi\)
\(158\) −2.42310 1.39898i −0.192772 0.111297i
\(159\) −12.8990 −1.02296
\(160\) 0.224745 2.22474i 0.0177676 0.175882i
\(161\) −3.67423 + 6.36396i −0.289570 + 0.501550i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) 8.34847i 0.653903i 0.945041 + 0.326951i \(0.106021\pi\)
−0.945041 + 0.326951i \(0.893979\pi\)
\(164\) 2.44949 0.191273
\(165\) 3.62863 + 2.61401i 0.282488 + 0.203501i
\(166\) 6.67423 + 11.5601i 0.518021 + 0.897239i
\(167\) −3.28913 1.89898i −0.254520 0.146947i 0.367312 0.930098i \(-0.380278\pi\)
−0.621832 + 0.783150i \(0.713611\pi\)
\(168\) 2.59808 1.50000i 0.200446 0.115728i
\(169\) −5.44949 9.43879i −0.419192 0.726061i
\(170\) −10.8990 1.10102i −0.835914 0.0844444i
\(171\) −3.17423 2.98735i −0.242740 0.228448i
\(172\) 5.44949i 0.415520i
\(173\) −0.389270 + 0.224745i −0.0295956 + 0.0170870i −0.514725 0.857355i \(-0.672106\pi\)
0.485129 + 0.874442i \(0.338773\pi\)
\(174\) −2.67423 4.63191i −0.202733 0.351144i
\(175\) −11.2279 9.94655i −0.848751 0.751888i
\(176\) −1.00000 1.73205i −0.0753778 0.130558i
\(177\) −6.75323 3.89898i −0.507604 0.293065i
\(178\) 16.4495i 1.23294i
\(179\) −6.24745 −0.466956 −0.233478 0.972362i \(-0.575011\pi\)
−0.233478 + 0.972362i \(0.575011\pi\)
\(180\) 1.30701 1.81431i 0.0974186 0.135231i
\(181\) 10.4495 18.0990i 0.776704 1.34529i −0.157127 0.987578i \(-0.550223\pi\)
0.933832 0.357713i \(-0.116443\pi\)
\(182\) 4.34847i 0.322330i
\(183\) 10.3485i 0.764981i
\(184\) 1.22474 2.12132i 0.0902894 0.156386i
\(185\) 19.2681 8.67215i 1.41662 0.637589i
\(186\) 0.949490 1.64456i 0.0696200 0.120585i
\(187\) −8.48528 + 4.89898i −0.620505 + 0.358249i
\(188\) −7.31747 + 4.22474i −0.533682 + 0.308121i
\(189\) 3.00000 0.218218
\(190\) 7.35948 6.39047i 0.533912 0.463614i
\(191\) 14.6969 1.06343 0.531717 0.846922i \(-0.321547\pi\)
0.531717 + 0.846922i \(0.321547\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 10.3048 5.94949i 0.741757 0.428254i −0.0809508 0.996718i \(-0.525796\pi\)
0.822708 + 0.568464i \(0.192462\pi\)
\(194\) 5.34847 9.26382i 0.383998 0.665104i
\(195\) 1.33025 + 2.95559i 0.0952613 + 0.211654i
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) 12.6969i 0.904619i −0.891861 0.452310i \(-0.850600\pi\)
0.891861 0.452310i \(-0.149400\pi\)
\(198\) 2.00000i 0.142134i
\(199\) −8.94949 + 15.5010i −0.634413 + 1.09883i 0.352227 + 0.935915i \(0.385425\pi\)
−0.986639 + 0.162920i \(0.947909\pi\)
\(200\) 3.74264 + 3.31552i 0.264645 + 0.234442i
\(201\) 3.44949 0.243308
\(202\) 15.7980i 1.11154i
\(203\) 13.8957 + 8.02270i 0.975289 + 0.563083i
\(204\) 2.44949 + 4.24264i 0.171499 + 0.297044i
\(205\) −3.20150 + 4.44414i −0.223603 + 0.310392i
\(206\) −0.0505103 0.0874863i −0.00351922 0.00609546i
\(207\) 2.12132 1.22474i 0.147442 0.0851257i
\(208\) 1.44949i 0.100504i
\(209\) 2.00000 8.48528i 0.138343 0.586939i
\(210\) −0.674235 + 6.67423i −0.0465266 + 0.460566i
\(211\) 6.17423 + 10.6941i 0.425052 + 0.736211i 0.996425 0.0844788i \(-0.0269225\pi\)
−0.571373 + 0.820690i \(0.693589\pi\)
\(212\) −11.1708 + 6.44949i −0.767217 + 0.442953i
\(213\) 7.31747 + 4.22474i 0.501385 + 0.289475i
\(214\) 2.77526 + 4.80688i 0.189713 + 0.328592i
\(215\) −9.88708 7.12252i −0.674293 0.485752i
\(216\) −1.00000 −0.0680414
\(217\) 5.69694i 0.386733i
\(218\) −12.1244 7.00000i −0.821165 0.474100i
\(219\) 1.05051 1.81954i 0.0709869 0.122953i
\(220\) 4.44949 + 0.449490i 0.299985 + 0.0303046i
\(221\) −7.10102 −0.477666
\(222\) −8.18350 4.72474i −0.549240 0.317104i
\(223\) −13.5939 + 7.84847i −0.910318 + 0.525572i −0.880533 0.473984i \(-0.842815\pi\)
−0.0297846 + 0.999556i \(0.509482\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) 1.58346 + 4.74264i 0.105564 + 0.316176i
\(226\) 2.55051 + 4.41761i 0.169657 + 0.293855i
\(227\) 1.34847i 0.0895010i 0.998998 + 0.0447505i \(0.0142493\pi\)
−0.998998 + 0.0447505i \(0.985751\pi\)
\(228\) −4.24264 1.00000i −0.280976 0.0662266i
\(229\) 17.0454 1.12639 0.563196 0.826323i \(-0.309572\pi\)
0.563196 + 0.826323i \(0.309572\pi\)
\(230\) 2.24799 + 4.99465i 0.148228 + 0.329338i
\(231\) 3.00000 + 5.19615i 0.197386 + 0.341882i
\(232\) −4.63191 2.67423i −0.304100 0.175572i
\(233\) 25.4165 14.6742i 1.66509 0.961341i 0.694866 0.719140i \(-0.255464\pi\)
0.970226 0.242201i \(-0.0778695\pi\)
\(234\) 0.724745 1.25529i 0.0473781 0.0820612i
\(235\) 1.89898 18.7980i 0.123876 1.22624i
\(236\) −7.79796 −0.507604
\(237\) −2.42310 1.39898i −0.157397 0.0908735i
\(238\) −12.7279 7.34847i −0.825029 0.476331i
\(239\) −23.3485 −1.51029 −0.755143 0.655560i \(-0.772433\pi\)
−0.755143 + 0.655560i \(0.772433\pi\)
\(240\) 0.224745 2.22474i 0.0145072 0.143607i
\(241\) −5.50000 + 9.52628i −0.354286 + 0.613642i −0.986996 0.160748i \(-0.948609\pi\)
0.632709 + 0.774389i \(0.281943\pi\)
\(242\) −6.06218 + 3.50000i −0.389692 + 0.224989i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −5.17423 8.96204i −0.331246 0.573736i
\(245\) −1.83548 4.07812i −0.117264 0.260541i
\(246\) 2.44949 0.156174
\(247\) 4.33013 4.60102i 0.275519 0.292756i
\(248\) 1.89898i 0.120585i
\(249\) 6.67423 + 11.5601i 0.422962 + 0.732592i
\(250\) −10.9070 + 2.45692i −0.689822 + 0.155389i
\(251\) −4.34847 + 7.53177i −0.274473 + 0.475401i −0.970002 0.243097i \(-0.921837\pi\)
0.695529 + 0.718498i \(0.255170\pi\)
\(252\) 2.59808 1.50000i 0.163663 0.0944911i
\(253\) 4.24264 + 2.44949i 0.266733 + 0.153998i
\(254\) 12.6969 0.796677
\(255\) −10.8990 1.10102i −0.682521 0.0689486i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.92104 4.57321i −0.494101 0.285269i 0.232173 0.972674i \(-0.425416\pi\)
−0.726274 + 0.687405i \(0.758750\pi\)
\(258\) 5.44949i 0.339270i
\(259\) 28.3485 1.76149
\(260\) 2.62983 + 1.89449i 0.163095 + 0.117492i
\(261\) −2.67423 4.63191i −0.165531 0.286708i
\(262\) 10.2173 + 5.89898i 0.631229 + 0.364440i
\(263\) 12.1244 7.00000i 0.747620 0.431638i −0.0772134 0.997015i \(-0.524602\pi\)
0.824833 + 0.565376i \(0.191269\pi\)
\(264\) −1.00000 1.73205i −0.0615457 0.106600i
\(265\) 2.89898 28.6969i 0.178083 1.76284i
\(266\) 12.5227 3.76588i 0.767816 0.230901i
\(267\) 16.4495i 1.00669i
\(268\) 2.98735 1.72474i 0.182481 0.105356i
\(269\) 11.2474 + 19.4812i 0.685769 + 1.18779i 0.973194 + 0.229984i \(0.0738673\pi\)
−0.287425 + 0.957803i \(0.592799\pi\)
\(270\) 1.30701 1.81431i 0.0795419 0.110416i
\(271\) 7.44949 + 12.9029i 0.452524 + 0.783795i 0.998542 0.0539785i \(-0.0171903\pi\)
−0.546018 + 0.837774i \(0.683857\pi\)
\(272\) 4.24264 + 2.44949i 0.257248 + 0.148522i
\(273\) 4.34847i 0.263181i
\(274\) −10.8990 −0.658431
\(275\) −6.63103 + 7.48528i −0.399866 + 0.451379i
\(276\) 1.22474 2.12132i 0.0737210 0.127688i
\(277\) 16.4949i 0.991082i 0.868584 + 0.495541i \(0.165030\pi\)
−0.868584 + 0.495541i \(0.834970\pi\)
\(278\) 11.4495i 0.686695i
\(279\) 0.949490 1.64456i 0.0568445 0.0984575i
\(280\) 2.75321 + 6.11717i 0.164536 + 0.365571i
\(281\) 10.7753 18.6633i 0.642798 1.11336i −0.342008 0.939697i \(-0.611107\pi\)
0.984805 0.173661i \(-0.0555598\pi\)
\(282\) −7.31747 + 4.22474i −0.435749 + 0.251580i
\(283\) 0.778539 0.449490i 0.0462793 0.0267194i −0.476682 0.879076i \(-0.658161\pi\)
0.522961 + 0.852357i \(0.324827\pi\)
\(284\) 8.44949 0.501385
\(285\) 7.35948 6.39047i 0.435938 0.378539i
\(286\) 2.89898 0.171420
\(287\) −6.36396 + 3.67423i −0.375653 + 0.216883i
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 3.50000 6.06218i 0.205882 0.356599i
\(290\) 10.9058 4.90849i 0.640413 0.288237i
\(291\) 5.34847 9.26382i 0.313533 0.543055i
\(292\) 2.10102i 0.122953i
\(293\) 9.10102i 0.531687i −0.964016 0.265844i \(-0.914350\pi\)
0.964016 0.265844i \(-0.0856505\pi\)
\(294\) −1.00000 + 1.73205i −0.0583212 + 0.101015i
\(295\) 10.1920 14.1479i 0.593401 0.823725i
\(296\) −9.44949 −0.549240
\(297\) 2.00000i 0.116052i
\(298\) −13.6814 7.89898i −0.792544 0.457576i
\(299\) 1.77526 + 3.07483i 0.102666 + 0.177822i
\(300\) 3.74264 + 3.31552i 0.216081 + 0.191421i
\(301\) −8.17423 14.1582i −0.471155 0.816064i
\(302\) 0.174973 0.101021i 0.0100685 0.00581308i
\(303\) 15.7980i 0.907569i
\(304\) −4.17423 + 1.25529i −0.239409 + 0.0719961i
\(305\) 23.0227 + 2.32577i 1.31828 + 0.133173i
\(306\) 2.44949 + 4.24264i 0.140028 + 0.242536i
\(307\) 18.8776 10.8990i 1.07740 0.622038i 0.147207 0.989106i \(-0.452972\pi\)
0.930194 + 0.367068i \(0.119638\pi\)
\(308\) 5.19615 + 3.00000i 0.296078 + 0.170941i
\(309\) −0.0505103 0.0874863i −0.00287343 0.00497692i
\(310\) 3.44534 + 2.48198i 0.195682 + 0.140967i
\(311\) 1.10102 0.0624331 0.0312166 0.999513i \(-0.490062\pi\)
0.0312166 + 0.999513i \(0.490062\pi\)
\(312\) 1.44949i 0.0820612i
\(313\) −21.5631 12.4495i −1.21882 0.703687i −0.254155 0.967163i \(-0.581797\pi\)
−0.964666 + 0.263477i \(0.915131\pi\)
\(314\) 0.275255 0.476756i 0.0155335 0.0269049i
\(315\) −0.674235 + 6.67423i −0.0379888 + 0.376051i
\(316\) −2.79796 −0.157397
\(317\) 15.8028 + 9.12372i 0.887571 + 0.512439i 0.873147 0.487457i \(-0.162075\pi\)
0.0144239 + 0.999896i \(0.495409\pi\)
\(318\) −11.1708 + 6.44949i −0.626430 + 0.361669i
\(319\) 5.34847 9.26382i 0.299457 0.518674i
\(320\) −0.917738 2.03906i −0.0513031 0.113987i
\(321\) 2.77526 + 4.80688i 0.154900 + 0.268294i
\(322\) 7.34847i 0.409514i
\(323\) 6.14966 + 20.4495i 0.342176 + 1.13784i
\(324\) −1.00000 −0.0555556
\(325\) −6.87441 + 2.29522i −0.381324 + 0.127316i
\(326\) 4.17423 + 7.22999i 0.231189 + 0.400432i
\(327\) −12.1244 7.00000i −0.670478 0.387101i
\(328\) 2.12132 1.22474i 0.117130 0.0676252i
\(329\) 12.6742 21.9524i 0.698753 1.21028i
\(330\) 4.44949 + 0.449490i 0.244936 + 0.0247436i
\(331\) −1.24745 −0.0685660 −0.0342830 0.999412i \(-0.510915\pi\)
−0.0342830 + 0.999412i \(0.510915\pi\)
\(332\) 11.5601 + 6.67423i 0.634444 + 0.366296i
\(333\) −8.18350 4.72474i −0.448453 0.258914i
\(334\) −3.79796 −0.207815
\(335\) −0.775255 + 7.67423i −0.0423567 + 0.419288i
\(336\) 1.50000 2.59808i 0.0818317 0.141737i
\(337\) −12.0369 + 6.94949i −0.655690 + 0.378563i −0.790633 0.612291i \(-0.790248\pi\)
0.134943 + 0.990853i \(0.456915\pi\)
\(338\) −9.43879 5.44949i −0.513403 0.296413i
\(339\) 2.55051 + 4.41761i 0.138525 + 0.239932i
\(340\) −9.98930 + 4.49598i −0.541746 + 0.243829i
\(341\) 3.79796 0.205671
\(342\) −4.24264 1.00000i −0.229416 0.0540738i
\(343\) 15.0000i 0.809924i
\(344\) 2.72474 + 4.71940i 0.146908 + 0.254453i
\(345\) 2.24799 + 4.99465i 0.121028 + 0.268903i
\(346\) −0.224745 + 0.389270i −0.0120824 + 0.0209273i
\(347\) 17.7491 10.2474i 0.952822 0.550112i 0.0588654 0.998266i \(-0.481252\pi\)
0.893956 + 0.448154i \(0.147918\pi\)
\(348\) −4.63191 2.67423i −0.248296 0.143354i
\(349\) 31.4495 1.68345 0.841726 0.539904i \(-0.181540\pi\)
0.841726 + 0.539904i \(0.181540\pi\)
\(350\) −14.6969 3.00000i −0.785584 0.160357i
\(351\) 0.724745 1.25529i 0.0386840 0.0670027i
\(352\) −1.73205 1.00000i −0.0923186 0.0533002i
\(353\) 13.1464i 0.699714i 0.936803 + 0.349857i \(0.113770\pi\)
−0.936803 + 0.349857i \(0.886230\pi\)
\(354\) −7.79796 −0.414457
\(355\) −11.0435 + 15.3300i −0.586130 + 0.813633i
\(356\) 8.22474 + 14.2457i 0.435911 + 0.755019i
\(357\) −12.7279 7.34847i −0.673633 0.388922i
\(358\) −5.41045 + 3.12372i −0.285951 + 0.165094i
\(359\) 2.12372 + 3.67840i 0.112086 + 0.194138i 0.916611 0.399780i \(-0.130913\pi\)
−0.804525 + 0.593918i \(0.797580\pi\)
\(360\) 0.224745 2.22474i 0.0118451 0.117254i
\(361\) −17.0000 8.48528i −0.894737 0.446594i
\(362\) 20.8990i 1.09843i
\(363\) −6.06218 + 3.50000i −0.318182 + 0.183702i
\(364\) 2.17423 + 3.76588i 0.113961 + 0.197386i
\(365\) 3.81191 + 2.74605i 0.199524 + 0.143735i
\(366\) −5.17423 8.96204i −0.270462 0.468453i
\(367\) 19.5686 + 11.2980i 1.02147 + 0.589749i 0.914531 0.404516i \(-0.132560\pi\)
0.106944 + 0.994265i \(0.465893\pi\)
\(368\) 2.44949i 0.127688i
\(369\) 2.44949 0.127515
\(370\) 12.3506 17.1443i 0.642075 0.891291i
\(371\) 19.3485 33.5125i 1.00452 1.73988i
\(372\) 1.89898i 0.0984575i
\(373\) 34.8990i 1.80700i −0.428587 0.903500i \(-0.640989\pi\)
0.428587 0.903500i \(-0.359011\pi\)
\(374\) −4.89898 + 8.48528i −0.253320 + 0.438763i
\(375\) −10.9070 + 2.45692i −0.563237 + 0.126875i
\(376\) −4.22474 + 7.31747i −0.217875 + 0.377370i
\(377\) 6.71391 3.87628i 0.345784 0.199638i
\(378\) 2.59808 1.50000i 0.133631 0.0771517i
\(379\) −33.2474 −1.70781 −0.853903 0.520432i \(-0.825771\pi\)
−0.853903 + 0.520432i \(0.825771\pi\)
\(380\) 3.17826 9.21405i 0.163041 0.472671i
\(381\) 12.6969 0.650484
\(382\) 12.7279 7.34847i 0.651217 0.375980i
\(383\) 11.5601 6.67423i 0.590694 0.341037i −0.174678 0.984626i \(-0.555888\pi\)
0.765372 + 0.643588i \(0.222555\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) −12.2343 + 5.50643i −0.623520 + 0.280633i
\(386\) 5.94949 10.3048i 0.302821 0.524501i
\(387\) 5.44949i 0.277013i
\(388\) 10.6969i 0.543055i
\(389\) −5.12372 + 8.87455i −0.259783 + 0.449958i −0.966184 0.257855i \(-0.916984\pi\)
0.706401 + 0.707812i \(0.250318\pi\)
\(390\) 2.62983 + 1.89449i 0.133167 + 0.0959314i
\(391\) −12.0000 −0.606866
\(392\) 2.00000i 0.101015i
\(393\) 10.2173 + 5.89898i 0.515396 + 0.297564i
\(394\) −6.34847 10.9959i −0.319831 0.553964i
\(395\) 3.65695 5.07637i 0.184001 0.255420i
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) −13.2047 + 7.62372i −0.662724 + 0.382624i −0.793314 0.608813i \(-0.791646\pi\)
0.130590 + 0.991436i \(0.458313\pi\)
\(398\) 17.8990i 0.897195i
\(399\) 12.5227 3.76588i 0.626919 0.188530i
\(400\) 4.89898 + 1.00000i 0.244949 + 0.0500000i
\(401\) 18.1464 + 31.4305i 0.906189 + 1.56957i 0.819313 + 0.573347i \(0.194355\pi\)
0.0868767 + 0.996219i \(0.472311\pi\)
\(402\) 2.98735 1.72474i 0.148995 0.0860225i
\(403\) 2.38378 + 1.37628i 0.118745 + 0.0685572i
\(404\) 7.89898 + 13.6814i 0.392989 + 0.680677i
\(405\) 1.30701 1.81431i 0.0649457 0.0901539i
\(406\) 16.0454 0.796320
\(407\) 18.8990i 0.936788i
\(408\) 4.24264 + 2.44949i 0.210042 + 0.121268i
\(409\) −10.4495 + 18.0990i −0.516694 + 0.894940i 0.483118 + 0.875555i \(0.339504\pi\)
−0.999812 + 0.0193851i \(0.993829\pi\)
\(410\) −0.550510 + 5.44949i −0.0271878 + 0.269131i
\(411\) −10.8990 −0.537607
\(412\) −0.0874863 0.0505103i −0.00431014 0.00248846i
\(413\) 20.2597 11.6969i 0.996914 0.575569i
\(414\) 1.22474 2.12132i 0.0601929 0.104257i
\(415\) −27.2183 + 12.2504i −1.33609 + 0.601348i
\(416\) −0.724745 1.25529i −0.0355335 0.0615459i
\(417\) 11.4495i 0.560684i
\(418\) −2.51059 8.34847i −0.122797 0.408337i
\(419\) −18.0454 −0.881576 −0.440788 0.897611i \(-0.645301\pi\)
−0.440788 + 0.897611i \(0.645301\pi\)
\(420\) 2.75321 + 6.11717i 0.134343 + 0.298488i
\(421\) −8.79796 15.2385i −0.428786 0.742680i 0.567979 0.823043i \(-0.307725\pi\)
−0.996766 + 0.0803632i \(0.974392\pi\)
\(422\) 10.6941 + 6.17423i 0.520580 + 0.300557i
\(423\) −7.31747 + 4.22474i −0.355788 + 0.205414i
\(424\) −6.44949 + 11.1708i −0.313215 + 0.542504i
\(425\) 4.89898 24.0000i 0.237635 1.16417i
\(426\) 8.44949 0.409379
\(427\) 26.8861 + 15.5227i 1.30111 + 0.751196i
\(428\) 4.80688 + 2.77526i 0.232349 + 0.134147i
\(429\) 2.89898 0.139964
\(430\) −12.1237 1.22474i −0.584658 0.0590624i
\(431\) −2.87628 + 4.98186i −0.138545 + 0.239968i −0.926946 0.375194i \(-0.877576\pi\)
0.788401 + 0.615162i \(0.210909\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 0.691053 + 0.398979i 0.0332099 + 0.0191737i 0.516513 0.856279i \(-0.327230\pi\)
−0.483303 + 0.875453i \(0.660563\pi\)
\(434\) 2.84847 + 4.93369i 0.136731 + 0.236825i
\(435\) 10.9058 4.90849i 0.522895 0.235344i
\(436\) −14.0000 −0.670478
\(437\) 7.31747 7.77526i 0.350042 0.371941i
\(438\) 2.10102i 0.100391i
\(439\) 15.7474 + 27.2754i 0.751585 + 1.30178i 0.947054 + 0.321073i \(0.104044\pi\)
−0.195470 + 0.980710i \(0.562623\pi\)
\(440\) 4.07812 1.83548i 0.194417 0.0875029i
\(441\) −1.00000 + 1.73205i −0.0476190 + 0.0824786i
\(442\) −6.14966 + 3.55051i −0.292510 + 0.168881i
\(443\) −8.48528 4.89898i −0.403148 0.232758i 0.284693 0.958619i \(-0.408108\pi\)
−0.687841 + 0.725861i \(0.741442\pi\)
\(444\) −9.44949 −0.448453
\(445\) −36.5959 3.69694i −1.73481 0.175252i
\(446\) −7.84847 + 13.5939i −0.371636 + 0.643692i
\(447\) −13.6814 7.89898i −0.647110 0.373609i
\(448\) 3.00000i 0.141737i
\(449\) −18.6969 −0.882363 −0.441182 0.897418i \(-0.645441\pi\)
−0.441182 + 0.897418i \(0.645441\pi\)
\(450\) 3.74264 + 3.31552i 0.176430 + 0.156295i
\(451\) 2.44949 + 4.24264i 0.115342 + 0.199778i
\(452\) 4.41761 + 2.55051i 0.207787 + 0.119966i
\(453\) 0.174973 0.101021i 0.00822093 0.00474636i
\(454\) 0.674235 + 1.16781i 0.0316434 + 0.0548080i
\(455\) −9.67423 0.977296i −0.453535 0.0458164i
\(456\) −4.17423 + 1.25529i −0.195476 + 0.0587846i
\(457\) 23.8990i 1.11795i 0.829185 + 0.558974i \(0.188805\pi\)
−0.829185 + 0.558974i \(0.811195\pi\)
\(458\) 14.7618 8.52270i 0.689772 0.398240i
\(459\) 2.44949 + 4.24264i 0.114332 + 0.198030i
\(460\) 4.44414 + 3.20150i 0.207209 + 0.149271i
\(461\) −0.123724 0.214297i −0.00576242 0.00998080i 0.863130 0.504982i \(-0.168501\pi\)
−0.868892 + 0.495001i \(0.835168\pi\)
\(462\) 5.19615 + 3.00000i 0.241747 + 0.139573i
\(463\) 29.2929i 1.36135i −0.732583 0.680677i \(-0.761686\pi\)
0.732583 0.680677i \(-0.238314\pi\)
\(464\) −5.34847 −0.248296
\(465\) 3.44534 + 2.48198i 0.159774 + 0.115099i
\(466\) 14.6742 25.4165i 0.679771 1.17740i
\(467\) 8.44949i 0.390996i 0.980704 + 0.195498i \(0.0626323\pi\)
−0.980704 + 0.195498i \(0.937368\pi\)
\(468\) 1.44949i 0.0670027i
\(469\) −5.17423 + 8.96204i −0.238924 + 0.413828i
\(470\) −7.75442 17.2290i −0.357684 0.794714i
\(471\) 0.275255 0.476756i 0.0126831 0.0219678i
\(472\) −6.75323 + 3.89898i −0.310843 + 0.179465i
\(473\) −9.43879 + 5.44949i −0.433996 + 0.250568i
\(474\) −2.79796 −0.128515
\(475\) 12.5632 + 17.8092i 0.576438 + 0.817141i
\(476\) −14.6969 −0.673633
\(477\) −11.1708 + 6.44949i −0.511478 + 0.295302i
\(478\) −20.2204 + 11.6742i −0.924858 + 0.533967i
\(479\) −0.348469 + 0.603566i −0.0159220 + 0.0275777i −0.873877 0.486148i \(-0.838402\pi\)
0.857955 + 0.513725i \(0.171735\pi\)
\(480\) −0.917738 2.03906i −0.0418888 0.0930698i
\(481\) 6.84847 11.8619i 0.312263 0.540856i
\(482\) 11.0000i 0.501036i
\(483\) 7.34847i 0.334367i
\(484\) −3.50000 + 6.06218i −0.159091 + 0.275554i
\(485\) 19.4076 + 13.9810i 0.881254 + 0.634843i
\(486\) −1.00000 −0.0453609
\(487\) 25.1010i 1.13744i 0.822533 + 0.568718i \(0.192560\pi\)
−0.822533 + 0.568718i \(0.807440\pi\)
\(488\) −8.96204 5.17423i −0.405692 0.234227i
\(489\) 4.17423 + 7.22999i 0.188765 + 0.326951i
\(490\) −3.62863 2.61401i −0.163925 0.118089i
\(491\) −17.0227 29.4842i −0.768224 1.33060i −0.938525 0.345211i \(-0.887807\pi\)
0.170301 0.985392i \(-0.445526\pi\)
\(492\) 2.12132 1.22474i 0.0956365 0.0552158i
\(493\) 26.2020i 1.18008i
\(494\) 1.44949 6.14966i 0.0652156 0.276686i
\(495\) 4.44949 + 0.449490i 0.199990 + 0.0202031i
\(496\) −0.949490 1.64456i −0.0426333 0.0738431i
\(497\) −21.9524 + 12.6742i −0.984701 + 0.568517i
\(498\) 11.5601 + 6.67423i 0.518021 + 0.299080i
\(499\) 15.4217 + 26.7111i 0.690369 + 1.19575i 0.971717 + 0.236149i \(0.0758853\pi\)
−0.281348 + 0.959606i \(0.590781\pi\)
\(500\) −8.21731 + 7.58128i −0.367489 + 0.339045i
\(501\) −3.79796 −0.169680
\(502\) 8.69694i 0.388163i
\(503\) 11.9494 + 6.89898i 0.532797 + 0.307610i 0.742155 0.670229i \(-0.233804\pi\)
−0.209358 + 0.977839i \(0.567137\pi\)
\(504\) 1.50000 2.59808i 0.0668153 0.115728i
\(505\) −35.1464 3.55051i −1.56400 0.157996i
\(506\) 4.89898 0.217786
\(507\) −9.43879 5.44949i −0.419192 0.242020i
\(508\) 10.9959 6.34847i 0.487863 0.281668i
\(509\) −4.77526 + 8.27098i −0.211659 + 0.366605i −0.952234 0.305369i \(-0.901220\pi\)
0.740575 + 0.671974i \(0.234553\pi\)
\(510\) −9.98930 + 4.49598i −0.442334 + 0.199085i
\(511\) 3.15153 + 5.45861i 0.139416 + 0.241475i
\(512\) 1.00000i 0.0441942i
\(513\) −4.24264 1.00000i −0.187317 0.0441511i
\(514\) −9.14643 −0.403432
\(515\) 0.205987 0.0927103i 0.00907686 0.00408531i
\(516\) 2.72474 + 4.71940i 0.119950 + 0.207760i
\(517\) −14.6349 8.44949i −0.643644 0.371608i
\(518\) 24.5505 14.1742i 1.07869 0.622780i
\(519\) −0.224745 + 0.389270i −0.00986520 + 0.0170870i
\(520\) 3.22474 + 0.325765i 0.141414 + 0.0142858i
\(521\) −6.24745 −0.273706 −0.136853 0.990591i \(-0.543699\pi\)
−0.136853 + 0.990591i \(0.543699\pi\)
\(522\) −4.63191 2.67423i −0.202733 0.117048i
\(523\) 1.43027 + 0.825765i 0.0625412 + 0.0361082i 0.530945 0.847407i \(-0.321837\pi\)
−0.468403 + 0.883515i \(0.655171\pi\)
\(524\) 11.7980 0.515396
\(525\) −14.6969 3.00000i −0.641427 0.130931i
\(526\) 7.00000 12.1244i 0.305215 0.528647i
\(527\) −8.05669 + 4.65153i −0.350955 + 0.202624i
\(528\) −1.73205 1.00000i −0.0753778 0.0435194i
\(529\) −8.50000 14.7224i −0.369565 0.640106i
\(530\) −11.8379 26.3018i −0.514205 1.14248i
\(531\) −7.79796 −0.338403
\(532\) 8.96204 9.52270i 0.388554 0.412862i
\(533\) 3.55051i 0.153790i
\(534\) 8.22474 + 14.2457i 0.355920 + 0.616471i
\(535\) −11.3178 + 5.09391i −0.489312 + 0.220229i
\(536\) 1.72474 2.98735i 0.0744976 0.129034i
\(537\) −5.41045 + 3.12372i −0.233478 + 0.134799i
\(538\) 19.4812 + 11.2474i 0.839892 + 0.484912i
\(539\) −4.00000 −0.172292
\(540\) 0.224745 2.22474i 0.00967148 0.0957378i
\(541\) −0.174235 + 0.301783i −0.00749093 + 0.0129747i −0.869747 0.493499i \(-0.835718\pi\)
0.862256 + 0.506473i \(0.169051\pi\)
\(542\) 12.9029 + 7.44949i 0.554227 + 0.319983i
\(543\) 20.8990i 0.896861i
\(544\) 4.89898 0.210042
\(545\) 18.2981 25.4004i 0.783805 1.08803i
\(546\) 2.17423 + 3.76588i 0.0930487 + 0.161165i
\(547\) 17.4473 + 10.0732i 0.745993 + 0.430700i 0.824244 0.566234i \(-0.191600\pi\)
−0.0782510 + 0.996934i \(0.524934\pi\)
\(548\) −9.43879 + 5.44949i −0.403205 + 0.232791i
\(549\) −5.17423 8.96204i −0.220831 0.382490i
\(550\) −2.00000 + 9.79796i −0.0852803 + 0.417786i
\(551\) −16.9773 15.9777i −0.723257 0.680674i
\(552\) 2.44949i 0.104257i
\(553\) 7.26931 4.19694i 0.309123 0.178472i
\(554\) 8.24745 + 14.2850i 0.350401 + 0.606912i
\(555\) 12.3506 17.1443i 0.524252 0.727736i
\(556\) −5.72474 9.91555i −0.242783 0.420513i
\(557\) −31.8198 18.3712i −1.34825 0.778412i −0.360247 0.932857i \(-0.617308\pi\)
−0.988001 + 0.154445i \(0.950641\pi\)
\(558\) 1.89898i 0.0803902i
\(559\) −7.89898 −0.334091
\(560\) 5.44294 + 3.92102i 0.230006 + 0.165693i
\(561\) −4.89898 + 8.48528i −0.206835 + 0.358249i
\(562\) 21.5505i 0.909053i
\(563\) 13.5959i 0.573000i 0.958080 + 0.286500i \(0.0924918\pi\)
−0.958080 + 0.286500i \(0.907508\pi\)
\(564\) −4.22474 + 7.31747i −0.177894 + 0.308121i
\(565\) −10.4013 + 4.68140i −0.437585 + 0.196948i
\(566\) 0.449490 0.778539i 0.0188935 0.0327244i
\(567\) 2.59808 1.50000i 0.109109 0.0629941i
\(568\) 7.31747 4.22474i 0.307034 0.177266i
\(569\) 23.1010 0.968445 0.484223 0.874945i \(-0.339102\pi\)
0.484223 + 0.874945i \(0.339102\pi\)
\(570\) 3.17826 9.21405i 0.133123 0.385934i
\(571\) −25.4495 −1.06503 −0.532514 0.846421i \(-0.678753\pi\)
−0.532514 + 0.846421i \(0.678753\pi\)
\(572\) 2.51059 1.44949i 0.104973 0.0606062i
\(573\) 12.7279 7.34847i 0.531717 0.306987i
\(574\) −3.67423 + 6.36396i −0.153360 + 0.265627i
\(575\) −11.6170 + 3.87868i −0.484464 + 0.161752i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 22.0000i 0.915872i 0.888985 + 0.457936i \(0.151411\pi\)
−0.888985 + 0.457936i \(0.848589\pi\)
\(578\) 7.00000i 0.291162i
\(579\) 5.94949 10.3048i 0.247252 0.428254i
\(580\) 6.99049 9.70380i 0.290264 0.402928i
\(581\) −40.0454 −1.66136
\(582\) 10.6969i 0.443402i
\(583\) −22.3417 12.8990i −0.925298 0.534221i
\(584\) −1.05051 1.81954i −0.0434704 0.0752930i
\(585\) 2.62983 + 1.89449i 0.108730 + 0.0783277i
\(586\) −4.55051 7.88171i −0.187980 0.325591i
\(587\) 31.4305 18.1464i 1.29728 0.748983i 0.317344 0.948310i \(-0.397209\pi\)
0.979933 + 0.199327i \(0.0638757\pi\)
\(588\) 2.00000i 0.0824786i
\(589\) 1.89898 8.05669i 0.0782461 0.331970i
\(590\) 1.75255 17.3485i 0.0721514 0.714225i
\(591\) −6.34847 10.9959i −0.261141 0.452310i
\(592\) −8.18350 + 4.72474i −0.336340 + 0.194186i
\(593\) −13.1172 7.57321i −0.538658 0.310995i 0.205877 0.978578i \(-0.433995\pi\)
−0.744535 + 0.667583i \(0.767329\pi\)
\(594\) −1.00000 1.73205i −0.0410305 0.0710669i
\(595\) 19.2090 26.6648i 0.787492 1.09315i
\(596\) −15.7980 −0.647110
\(597\) 17.8990i 0.732556i
\(598\) 3.07483 + 1.77526i 0.125739 + 0.0725956i
\(599\) −2.87628 + 4.98186i −0.117521 + 0.203553i −0.918785 0.394759i \(-0.870828\pi\)
0.801263 + 0.598312i \(0.204162\pi\)
\(600\) 4.89898 + 1.00000i 0.200000 + 0.0408248i
\(601\) −15.0000 −0.611863 −0.305931 0.952054i \(-0.598968\pi\)
−0.305931 + 0.952054i \(0.598968\pi\)
\(602\) −14.1582 8.17423i −0.577045 0.333157i
\(603\) 2.98735 1.72474i 0.121654 0.0702370i
\(604\) 0.101021 0.174973i 0.00411047 0.00711954i
\(605\) −6.42416 14.2734i −0.261179 0.580296i
\(606\) 7.89898 + 13.6814i 0.320874 + 0.555770i
\(607\) 27.0000i 1.09590i −0.836512 0.547948i \(-0.815409\pi\)
0.836512 0.547948i \(-0.184591\pi\)
\(608\) −2.98735 + 3.17423i −0.121153 + 0.128732i
\(609\) 16.0454 0.650193
\(610\) 21.1011 9.49718i 0.854360 0.384530i
\(611\) −6.12372 10.6066i −0.247739 0.429097i
\(612\) 4.24264 + 2.44949i 0.171499 + 0.0990148i
\(613\) −18.2740 + 10.5505i −0.738081 + 0.426131i −0.821371 0.570394i \(-0.806790\pi\)
0.0832904 + 0.996525i \(0.473457\pi\)
\(614\) 10.8990 18.8776i 0.439847 0.761837i
\(615\) −0.550510 + 5.44949i −0.0221987 + 0.219745i
\(616\) 6.00000 0.241747
\(617\) −38.9230 22.4722i −1.56698 0.904696i −0.996518 0.0833723i \(-0.973431\pi\)
−0.570462 0.821324i \(-0.693236\pi\)
\(618\) −0.0874863 0.0505103i −0.00351922 0.00203182i
\(619\) −33.0454 −1.32821 −0.664104 0.747641i \(-0.731187\pi\)
−0.664104 + 0.747641i \(0.731187\pi\)
\(620\) 4.22474 + 0.426786i 0.169670 + 0.0171401i
\(621\) 1.22474 2.12132i 0.0491473 0.0851257i
\(622\) 0.953512 0.550510i 0.0382323 0.0220735i
\(623\) −42.7370 24.6742i −1.71222 0.988552i
\(624\) −0.724745 1.25529i −0.0290130 0.0502520i
\(625\) −3.01472 24.8176i −0.120589 0.992703i
\(626\) −24.8990 −0.995163
\(627\) −2.51059 8.34847i −0.100263 0.333406i
\(628\) 0.550510i 0.0219678i
\(629\) 23.1464 + 40.0908i 0.922909 + 1.59852i
\(630\) 2.75321 + 6.11717i 0.109691 + 0.243714i
\(631\) −16.0505 + 27.8003i −0.638961 + 1.10671i 0.346700 + 0.937976i \(0.387302\pi\)
−0.985661 + 0.168737i \(0.946031\pi\)
\(632\) −2.42310 + 1.39898i −0.0963859 + 0.0556484i
\(633\) 10.6941 + 6.17423i 0.425052 + 0.245404i
\(634\) 18.2474 0.724699
\(635\) −2.85357 + 28.2474i −0.113241 + 1.12097i
\(636\) −6.44949 + 11.1708i −0.255739 + 0.442953i
\(637\) −2.51059 1.44949i −0.0994732 0.0574309i
\(638\) 10.6969i 0.423496i
\(639\) 8.44949 0.334257
\(640\) −1.81431 1.30701i −0.0717170 0.0516640i
\(641\) 8.87628 + 15.3742i 0.350592 + 0.607243i 0.986353 0.164643i \(-0.0526471\pi\)
−0.635761 + 0.771886i \(0.719314\pi\)
\(642\) 4.80688 + 2.77526i 0.189713 + 0.109531i
\(643\) 18.7508 10.8258i 0.739458 0.426927i −0.0824140 0.996598i \(-0.526263\pi\)
0.821872 + 0.569672i \(0.192930\pi\)
\(644\) 3.67423 + 6.36396i 0.144785 + 0.250775i
\(645\) −12.1237 1.22474i −0.477371 0.0482243i
\(646\) 15.5505 + 14.6349i 0.611827 + 0.575804i
\(647\) 31.8434i 1.25189i −0.779866 0.625946i \(-0.784713\pi\)
0.779866 0.625946i \(-0.215287\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −7.79796 13.5065i −0.306097 0.530175i
\(650\) −4.80581 + 5.42492i −0.188499 + 0.212783i
\(651\) 2.84847 + 4.93369i 0.111640 + 0.193367i
\(652\) 7.22999 + 4.17423i 0.283148 + 0.163476i
\(653\) 2.44949i 0.0958559i 0.998851 + 0.0479280i \(0.0152618\pi\)
−0.998851 + 0.0479280i \(0.984738\pi\)
\(654\) −14.0000 −0.547443
\(655\) −15.4200 + 21.4052i −0.602510 + 0.836370i
\(656\) 1.22474 2.12132i 0.0478183 0.0828236i
\(657\) 2.10102i 0.0819686i
\(658\) 25.3485i 0.988186i
\(659\) −14.3485 + 24.8523i −0.558937 + 0.968107i 0.438649 + 0.898659i \(0.355457\pi\)
−0.997586 + 0.0694486i \(0.977876\pi\)
\(660\) 4.07812 1.83548i 0.158740 0.0714458i
\(661\) −1.44949 + 2.51059i −0.0563786 + 0.0976506i −0.892837 0.450379i \(-0.851289\pi\)
0.836459 + 0.548030i \(0.184622\pi\)
\(662\) −1.08032 + 0.623724i −0.0419879 + 0.0242417i
\(663\) −6.14966 + 3.55051i −0.238833 + 0.137890i
\(664\) 13.3485 0.518021
\(665\) 5.56372 + 28.7062i 0.215752 + 1.11318i
\(666\) −9.44949 −0.366160
\(667\) 11.3458 6.55051i 0.439312 0.253637i
\(668\) −3.28913 + 1.89898i −0.127260 + 0.0734737i
\(669\) −7.84847 + 13.5939i −0.303439 + 0.525572i
\(670\) 3.16573 + 7.03371i 0.122303 + 0.271736i
\(671\) 10.3485 17.9241i 0.399498 0.691951i
\(672\) 3.00000i 0.115728i
\(673\) 39.6969i 1.53020i 0.643909 + 0.765102i \(0.277312\pi\)
−0.643909 + 0.765102i \(0.722688\pi\)
\(674\) −6.94949 + 12.0369i −0.267684 + 0.463643i
\(675\) 3.74264 + 3.31552i 0.144054 + 0.127614i
\(676\) −10.8990 −0.419192
\(677\) 41.1464i 1.58139i 0.612213 + 0.790693i \(0.290279\pi\)
−0.612213 + 0.790693i \(0.709721\pi\)
\(678\) 4.41761 + 2.55051i 0.169657 + 0.0979518i
\(679\) 16.0454 + 27.7915i 0.615766 + 1.06654i
\(680\) −6.40300 + 8.88828i −0.245544 + 0.340850i
\(681\) 0.674235 + 1.16781i 0.0258367 + 0.0447505i
\(682\) 3.28913 1.89898i 0.125947 0.0727157i
\(683\) 39.1918i 1.49963i 0.661645 + 0.749817i \(0.269858\pi\)
−0.661645 + 0.749817i \(0.730142\pi\)
\(684\) −4.17423 + 1.25529i −0.159606 + 0.0479974i
\(685\) 2.44949 24.2474i 0.0935902 0.926447i
\(686\) 7.50000 + 12.9904i 0.286351 + 0.495975i
\(687\) 14.7618 8.52270i 0.563196 0.325161i
\(688\) 4.71940 + 2.72474i 0.179925 + 0.103880i
\(689\) −9.34847 16.1920i −0.356148 0.616867i
\(690\) 4.44414 + 3.20150i 0.169186 + 0.121879i
\(691\) 39.5959 1.50630 0.753150 0.657849i \(-0.228534\pi\)
0.753150 + 0.657849i \(0.228534\pi\)
\(692\) 0.449490i 0.0170870i
\(693\) 5.19615 + 3.00000i 0.197386 + 0.113961i
\(694\) 10.2474 17.7491i 0.388988 0.673747i
\(695\) 25.4722 + 2.57321i 0.966215 + 0.0976076i
\(696\) −5.34847 −0.202733
\(697\) −10.3923 6.00000i −0.393637 0.227266i
\(698\) 27.2361 15.7247i 1.03090 0.595190i
\(699\) 14.6742 25.4165i 0.555031 0.961341i
\(700\) −14.2279 + 4.75039i −0.537765 + 0.179548i
\(701\) 18.8990 + 32.7340i 0.713805 + 1.23635i 0.963419 + 0.268000i \(0.0863629\pi\)
−0.249614 + 0.968345i \(0.580304\pi\)
\(702\) 1.44949i 0.0547075i
\(703\) −40.0908 9.44949i −1.51205 0.356394i
\(704\) −2.00000 −0.0753778
\(705\) −7.75442 17.2290i −0.292048 0.648882i
\(706\) 6.57321 + 11.3851i 0.247386 + 0.428485i
\(707\) −41.0443 23.6969i −1.54363 0.891215i
\(708\) −6.75323 + 3.89898i −0.253802 + 0.146533i
\(709\) −8.37628 + 14.5081i −0.314578 + 0.544864i −0.979348 0.202184i \(-0.935196\pi\)
0.664770 + 0.747048i \(0.268530\pi\)
\(710\) −1.89898 + 18.7980i −0.0712674 + 0.705475i
\(711\) −2.79796 −0.104932
\(712\) 14.2457 + 8.22474i 0.533879 + 0.308235i
\(713\) 4.02834 + 2.32577i 0.150863 + 0.0871006i
\(714\) −14.6969 −0.550019
\(715\) −0.651531 + 6.44949i −0.0243659 + 0.241197i
\(716\) −3.12372 + 5.41045i −0.116739 + 0.202198i
\(717\) −20.2204 + 11.6742i −0.755143 + 0.435982i
\(718\) 3.67840 + 2.12372i 0.137277 + 0.0792567i
\(719\) 19.2247 + 33.2982i 0.716962 + 1.24181i 0.962198 + 0.272351i \(0.0878012\pi\)
−0.245236 + 0.969463i \(0.578865\pi\)
\(720\) −0.917738 2.03906i −0.0342021 0.0759912i
\(721\) 0.303062 0.0112866
\(722\) −18.9651 + 1.15153i −0.705807 + 0.0428555i
\(723\) 11.0000i 0.409094i
\(724\) −10.4495 18.0990i −0.388352 0.672646i
\(725\) 8.46911 + 25.3659i 0.314535 + 0.942065i
\(726\) −3.50000 + 6.06218i −0.129897 + 0.224989i
\(727\) 6.23715 3.60102i 0.231323 0.133554i −0.379859 0.925044i \(-0.624028\pi\)
0.611182 + 0.791490i \(0.290694\pi\)
\(728\) 3.76588 + 2.17423i 0.139573 + 0.0805825i
\(729\) −1.00000 −0.0370370
\(730\) 4.67423 + 0.472194i 0.173001 + 0.0174767i
\(731\) 13.3485 23.1202i 0.493711 0.855132i
\(732\) −8.96204 5.17423i −0.331246 0.191245i
\(733\) 1.30306i 0.0481297i −0.999710 0.0240648i \(-0.992339\pi\)
0.999710 0.0240648i \(-0.00766082\pi\)
\(734\) 22.5959 0.834031
\(735\) −3.62863 2.61401i −0.133844 0.0964194i
\(736\) −1.22474 2.12132i −0.0451447 0.0781929i
\(737\) 5.97469 + 3.44949i 0.220081 + 0.127064i
\(738\) 2.12132 1.22474i 0.0780869 0.0450835i
\(739\) 18.1742 + 31.4787i 0.668550 + 1.15796i 0.978310 + 0.207148i \(0.0664181\pi\)
−0.309760 + 0.950815i \(0.600249\pi\)
\(740\) 2.12372 21.0227i 0.0780697 0.772810i
\(741\) 1.44949 6.14966i 0.0532483 0.225914i
\(742\) 38.6969i 1.42061i
\(743\) −39.8372 + 23.0000i −1.46148 + 0.843788i −0.999080 0.0428813i \(-0.986346\pi\)
−0.462404 + 0.886669i \(0.653013\pi\)
\(744\) −0.949490 1.64456i −0.0348100 0.0602927i
\(745\) 20.6480 28.6624i 0.756486 1.05011i
\(746\) −17.4495 30.2234i −0.638871 1.10656i
\(747\) 11.5601 + 6.67423i 0.422962 + 0.244197i
\(748\) 9.79796i 0.358249i
\(749\) −16.6515 −0.608434
\(750\) −8.21731 + 7.58128i −0.300054 + 0.276829i
\(751\) 24.8485 43.0388i 0.906734 1.57051i 0.0881603 0.996106i \(-0.471901\pi\)
0.818573 0.574402i \(-0.194765\pi\)
\(752\) 8.44949i 0.308121i
\(753\) 8.69694i 0.316934i
\(754\) 3.87628 6.71391i 0.141166 0.244506i
\(755\) 0.185421 + 0.411973i 0.00674815 + 0.0149932i
\(756\) 1.50000 2.59808i 0.0545545 0.0944911i
\(757\) 2.03383 1.17423i 0.0739210 0.0426783i −0.462584 0.886575i \(-0.653078\pi\)
0.536505 + 0.843897i \(0.319744\pi\)
\(758\) −28.7931 + 16.6237i −1.04581 + 0.603801i
\(759\) 4.89898 0.177822
\(760\) −1.85457 9.56873i −0.0672724 0.347094i
\(761\) 25.1010 0.909911 0.454956 0.890514i \(-0.349655\pi\)
0.454956 + 0.890514i \(0.349655\pi\)
\(762\) 10.9959 6.34847i 0.398338 0.229981i
\(763\) 36.3731 21.0000i 1.31679 0.760251i
\(764\) 7.34847 12.7279i 0.265858 0.460480i
\(765\) −9.98930 + 4.49598i −0.361164 + 0.162552i
\(766\) 6.67423 11.5601i 0.241150 0.417684i
\(767\) 11.3031i 0.408130i
\(768\) 1.00000i 0.0360844i
\(769\) −19.2980 + 33.4250i −0.695902 + 1.20534i 0.273973 + 0.961737i \(0.411662\pi\)
−0.969876 + 0.243601i \(0.921671\pi\)
\(770\) −7.84204 + 10.8859i −0.282608 + 0.392300i
\(771\) −9.14643 −0.329401
\(772\) 11.8990i 0.428254i
\(773\) 25.2022 + 14.5505i 0.906461 + 0.523345i 0.879291 0.476285i \(-0.158017\pi\)
0.0271702 + 0.999631i \(0.491350\pi\)
\(774\) 2.72474 + 4.71940i 0.0979389 + 0.169635i
\(775\) −6.29610 + 7.10720i