Properties

Label 690.2.e.a.551.7
Level $690$
Weight $2$
Character 690.551
Analytic conductor $5.510$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} - 198 x^{7} + 405 x^{6} - 108 x^{5} + 1215 x^{4} - 2916 x^{3} + 2187 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 551.7
Root \(-0.462710 - 1.66910i\) of defining polynomial
Character \(\chi\) \(=\) 690.551
Dual form 690.2.e.a.551.15

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(1.66910 - 0.462710i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.462710 - 1.66910i) q^{6} +2.82123i q^{7} +1.00000i q^{8} +(2.57180 - 1.54462i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(1.66910 - 0.462710i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.462710 - 1.66910i) q^{6} +2.82123i q^{7} +1.00000i q^{8} +(2.57180 - 1.54462i) q^{9} +1.00000i q^{10} +0.0884736 q^{11} +(-1.66910 + 0.462710i) q^{12} +5.38812 q^{13} +2.82123 q^{14} +(-1.66910 + 0.462710i) q^{15} +1.00000 q^{16} +2.84233 q^{17} +(-1.54462 - 2.57180i) q^{18} -5.08924i q^{19} +1.00000 q^{20} +(1.30541 + 4.70893i) q^{21} -0.0884736i q^{22} +(4.45994 - 1.76321i) q^{23} +(0.462710 + 1.66910i) q^{24} +1.00000 q^{25} -5.38812i q^{26} +(3.57789 - 3.76812i) q^{27} -2.82123i q^{28} -1.48542i q^{29} +(0.462710 + 1.66910i) q^{30} -5.56059 q^{31} -1.00000i q^{32} +(0.147671 - 0.0409376i) q^{33} -2.84233i q^{34} -2.82123i q^{35} +(-2.57180 + 1.54462i) q^{36} +6.20488i q^{37} -5.08924 q^{38} +(8.99332 - 2.49313i) q^{39} -1.00000i q^{40} +0.519960i q^{41} +(4.70893 - 1.30541i) q^{42} -0.907222i q^{43} -0.0884736 q^{44} +(-2.57180 + 1.54462i) q^{45} +(-1.76321 - 4.45994i) q^{46} +0.0243495i q^{47} +(1.66910 - 0.462710i) q^{48} -0.959358 q^{49} -1.00000i q^{50} +(4.74413 - 1.31517i) q^{51} -5.38812 q^{52} -10.2028 q^{53} +(-3.76812 - 3.57789i) q^{54} -0.0884736 q^{55} -2.82123 q^{56} +(-2.35484 - 8.49445i) q^{57} -1.48542 q^{58} +8.85335i q^{59} +(1.66910 - 0.462710i) q^{60} +10.4775i q^{61} +5.56059i q^{62} +(4.35773 + 7.25565i) q^{63} -1.00000 q^{64} -5.38812 q^{65} +(-0.0409376 - 0.147671i) q^{66} -3.80095i q^{67} -2.84233 q^{68} +(6.62825 - 5.00663i) q^{69} -2.82123 q^{70} +10.9253i q^{71} +(1.54462 + 2.57180i) q^{72} -5.85816 q^{73} +6.20488 q^{74} +(1.66910 - 0.462710i) q^{75} +5.08924i q^{76} +0.249605i q^{77} +(-2.49313 - 8.99332i) q^{78} -9.17572i q^{79} -1.00000 q^{80} +(4.22831 - 7.94490i) q^{81} +0.519960 q^{82} -7.55626 q^{83} +(-1.30541 - 4.70893i) q^{84} -2.84233 q^{85} -0.907222 q^{86} +(-0.687318 - 2.47932i) q^{87} +0.0884736i q^{88} +12.3408 q^{89} +(1.54462 + 2.57180i) q^{90} +15.2011i q^{91} +(-4.45994 + 1.76321i) q^{92} +(-9.28119 + 2.57294i) q^{93} +0.0243495 q^{94} +5.08924i q^{95} +(-0.462710 - 1.66910i) q^{96} -7.83418i q^{97} +0.959358i q^{98} +(0.227536 - 0.136658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} - 12q^{11} - 12q^{14} + 16q^{16} + 8q^{18} + 16q^{20} - 4q^{21} + 4q^{23} - 2q^{24} + 16q^{25} + 24q^{27} - 2q^{30} + 4q^{31} - 28q^{33} - 2q^{36} - 16q^{38} - 8q^{39} + 12q^{44} - 2q^{45} - 4q^{46} - 4q^{49} - 2q^{51} - 8q^{53} - 26q^{54} + 12q^{55} + 12q^{56} + 28q^{57} - 8q^{58} - 16q^{64} + 10q^{66} + 30q^{69} + 12q^{70} - 8q^{72} - 16q^{73} - 24q^{74} - 12q^{78} - 16q^{80} + 22q^{81} - 16q^{82} - 40q^{83} + 4q^{84} - 40q^{86} + 20q^{87} + 80q^{89} - 8q^{90} - 4q^{92} - 4q^{93} - 24q^{94} + 2q^{96} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.66910 0.462710i 0.963656 0.267145i
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.462710 1.66910i −0.188900 0.681408i
\(7\) 2.82123i 1.06633i 0.846013 + 0.533163i \(0.178997\pi\)
−0.846013 + 0.533163i \(0.821003\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.57180 1.54462i 0.857267 0.514873i
\(10\) 1.00000i 0.316228i
\(11\) 0.0884736 0.0266758 0.0133379 0.999911i \(-0.495754\pi\)
0.0133379 + 0.999911i \(0.495754\pi\)
\(12\) −1.66910 + 0.462710i −0.481828 + 0.133573i
\(13\) 5.38812 1.49440 0.747198 0.664602i \(-0.231399\pi\)
0.747198 + 0.664602i \(0.231399\pi\)
\(14\) 2.82123 0.754006
\(15\) −1.66910 + 0.462710i −0.430960 + 0.119471i
\(16\) 1.00000 0.250000
\(17\) 2.84233 0.689365 0.344683 0.938719i \(-0.387987\pi\)
0.344683 + 0.938719i \(0.387987\pi\)
\(18\) −1.54462 2.57180i −0.364070 0.606179i
\(19\) 5.08924i 1.16755i −0.811915 0.583775i \(-0.801575\pi\)
0.811915 0.583775i \(-0.198425\pi\)
\(20\) 1.00000 0.223607
\(21\) 1.30541 + 4.70893i 0.284864 + 1.02757i
\(22\) 0.0884736i 0.0188626i
\(23\) 4.45994 1.76321i 0.929963 0.367654i
\(24\) 0.462710 + 1.66910i 0.0944502 + 0.340704i
\(25\) 1.00000 0.200000
\(26\) 5.38812i 1.05670i
\(27\) 3.57789 3.76812i 0.688564 0.725175i
\(28\) 2.82123i 0.533163i
\(29\) 1.48542i 0.275836i −0.990444 0.137918i \(-0.955959\pi\)
0.990444 0.137918i \(-0.0440410\pi\)
\(30\) 0.462710 + 1.66910i 0.0844788 + 0.304735i
\(31\) −5.56059 −0.998712 −0.499356 0.866397i \(-0.666430\pi\)
−0.499356 + 0.866397i \(0.666430\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.147671 0.0409376i 0.0257063 0.00712631i
\(34\) 2.84233i 0.487455i
\(35\) 2.82123i 0.476875i
\(36\) −2.57180 + 1.54462i −0.428633 + 0.257436i
\(37\) 6.20488i 1.02008i 0.860152 + 0.510038i \(0.170369\pi\)
−0.860152 + 0.510038i \(0.829631\pi\)
\(38\) −5.08924 −0.825583
\(39\) 8.99332 2.49313i 1.44008 0.399221i
\(40\) 1.00000i 0.158114i
\(41\) 0.519960i 0.0812040i 0.999175 + 0.0406020i \(0.0129276\pi\)
−0.999175 + 0.0406020i \(0.987072\pi\)
\(42\) 4.70893 1.30541i 0.726603 0.201429i
\(43\) 0.907222i 0.138350i −0.997605 0.0691750i \(-0.977963\pi\)
0.997605 0.0691750i \(-0.0220367\pi\)
\(44\) −0.0884736 −0.0133379
\(45\) −2.57180 + 1.54462i −0.383381 + 0.230258i
\(46\) −1.76321 4.45994i −0.259971 0.657583i
\(47\) 0.0243495i 0.00355174i 0.999998 + 0.00177587i \(0.000565277\pi\)
−0.999998 + 0.00177587i \(0.999435\pi\)
\(48\) 1.66910 0.462710i 0.240914 0.0667864i
\(49\) −0.959358 −0.137051
\(50\) 1.00000i 0.141421i
\(51\) 4.74413 1.31517i 0.664311 0.184161i
\(52\) −5.38812 −0.747198
\(53\) −10.2028 −1.40147 −0.700733 0.713424i \(-0.747143\pi\)
−0.700733 + 0.713424i \(0.747143\pi\)
\(54\) −3.76812 3.57789i −0.512776 0.486889i
\(55\) −0.0884736 −0.0119298
\(56\) −2.82123 −0.377003
\(57\) −2.35484 8.49445i −0.311906 1.12512i
\(58\) −1.48542 −0.195045
\(59\) 8.85335i 1.15261i 0.817235 + 0.576304i \(0.195506\pi\)
−0.817235 + 0.576304i \(0.804494\pi\)
\(60\) 1.66910 0.462710i 0.215480 0.0597355i
\(61\) 10.4775i 1.34150i 0.741682 + 0.670751i \(0.234028\pi\)
−0.741682 + 0.670751i \(0.765972\pi\)
\(62\) 5.56059i 0.706196i
\(63\) 4.35773 + 7.25565i 0.549022 + 0.914126i
\(64\) −1.00000 −0.125000
\(65\) −5.38812 −0.668314
\(66\) −0.0409376 0.147671i −0.00503907 0.0181771i
\(67\) 3.80095i 0.464360i −0.972673 0.232180i \(-0.925414\pi\)
0.972673 0.232180i \(-0.0745859\pi\)
\(68\) −2.84233 −0.344683
\(69\) 6.62825 5.00663i 0.797947 0.602728i
\(70\) −2.82123 −0.337202
\(71\) 10.9253i 1.29659i 0.761389 + 0.648295i \(0.224518\pi\)
−0.761389 + 0.648295i \(0.775482\pi\)
\(72\) 1.54462 + 2.57180i 0.182035 + 0.303090i
\(73\) −5.85816 −0.685646 −0.342823 0.939400i \(-0.611383\pi\)
−0.342823 + 0.939400i \(0.611383\pi\)
\(74\) 6.20488 0.721302
\(75\) 1.66910 0.462710i 0.192731 0.0534291i
\(76\) 5.08924i 0.583775i
\(77\) 0.249605i 0.0284451i
\(78\) −2.49313 8.99332i −0.282292 1.01829i
\(79\) 9.17572i 1.03235i −0.856483 0.516175i \(-0.827356\pi\)
0.856483 0.516175i \(-0.172644\pi\)
\(80\) −1.00000 −0.111803
\(81\) 4.22831 7.94490i 0.469812 0.882766i
\(82\) 0.519960 0.0574199
\(83\) −7.55626 −0.829407 −0.414703 0.909957i \(-0.636115\pi\)
−0.414703 + 0.909957i \(0.636115\pi\)
\(84\) −1.30541 4.70893i −0.142432 0.513786i
\(85\) −2.84233 −0.308293
\(86\) −0.907222 −0.0978283
\(87\) −0.687318 2.47932i −0.0736883 0.265811i
\(88\) 0.0884736i 0.00943131i
\(89\) 12.3408 1.30813 0.654063 0.756440i \(-0.273063\pi\)
0.654063 + 0.756440i \(0.273063\pi\)
\(90\) 1.54462 + 2.57180i 0.162817 + 0.271091i
\(91\) 15.2011i 1.59351i
\(92\) −4.45994 + 1.76321i −0.464981 + 0.183827i
\(93\) −9.28119 + 2.57294i −0.962415 + 0.266801i
\(94\) 0.0243495 0.00251146
\(95\) 5.08924i 0.522145i
\(96\) −0.462710 1.66910i −0.0472251 0.170352i
\(97\) 7.83418i 0.795440i −0.917507 0.397720i \(-0.869802\pi\)
0.917507 0.397720i \(-0.130198\pi\)
\(98\) 0.959358i 0.0969098i
\(99\) 0.227536 0.136658i 0.0228683 0.0137346i
\(100\) −1.00000 −0.100000
\(101\) 11.3714i 1.13149i 0.824579 + 0.565747i \(0.191412\pi\)
−0.824579 + 0.565747i \(0.808588\pi\)
\(102\) −1.31517 4.74413i −0.130221 0.469739i
\(103\) 15.3014i 1.50770i −0.657049 0.753848i \(-0.728195\pi\)
0.657049 0.753848i \(-0.271805\pi\)
\(104\) 5.38812i 0.528349i
\(105\) −1.30541 4.70893i −0.127395 0.459544i
\(106\) 10.2028i 0.990986i
\(107\) −2.15054 −0.207901 −0.103950 0.994582i \(-0.533148\pi\)
−0.103950 + 0.994582i \(0.533148\pi\)
\(108\) −3.57789 + 3.76812i −0.344282 + 0.362588i
\(109\) 9.04331i 0.866192i −0.901348 0.433096i \(-0.857421\pi\)
0.901348 0.433096i \(-0.142579\pi\)
\(110\) 0.0884736i 0.00843562i
\(111\) 2.87106 + 10.3566i 0.272509 + 0.983002i
\(112\) 2.82123i 0.266582i
\(113\) 5.46926 0.514505 0.257252 0.966344i \(-0.417183\pi\)
0.257252 + 0.966344i \(0.417183\pi\)
\(114\) −8.49445 + 2.35484i −0.795578 + 0.220551i
\(115\) −4.45994 + 1.76321i −0.415892 + 0.164420i
\(116\) 1.48542i 0.137918i
\(117\) 13.8572 8.32259i 1.28110 0.769424i
\(118\) 8.85335 0.815017
\(119\) 8.01886i 0.735088i
\(120\) −0.462710 1.66910i −0.0422394 0.152367i
\(121\) −10.9922 −0.999288
\(122\) 10.4775 0.948585
\(123\) 0.240590 + 0.867865i 0.0216933 + 0.0782528i
\(124\) 5.56059 0.499356
\(125\) −1.00000 −0.0894427
\(126\) 7.25565 4.35773i 0.646384 0.388217i
\(127\) −1.22410 −0.108621 −0.0543105 0.998524i \(-0.517296\pi\)
−0.0543105 + 0.998524i \(0.517296\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −0.419780 1.51425i −0.0369596 0.133322i
\(130\) 5.38812i 0.472569i
\(131\) 17.3758i 1.51813i −0.651014 0.759066i \(-0.725656\pi\)
0.651014 0.759066i \(-0.274344\pi\)
\(132\) −0.147671 + 0.0409376i −0.0128531 + 0.00356316i
\(133\) 14.3579 1.24499
\(134\) −3.80095 −0.328352
\(135\) −3.57789 + 3.76812i −0.307935 + 0.324308i
\(136\) 2.84233i 0.243727i
\(137\) −18.2067 −1.55550 −0.777751 0.628573i \(-0.783639\pi\)
−0.777751 + 0.628573i \(0.783639\pi\)
\(138\) −5.00663 6.62825i −0.426193 0.564234i
\(139\) −7.87519 −0.667965 −0.333982 0.942579i \(-0.608393\pi\)
−0.333982 + 0.942579i \(0.608393\pi\)
\(140\) 2.82123i 0.238438i
\(141\) 0.0112667 + 0.0406418i 0.000948831 + 0.00342265i
\(142\) 10.9253 0.916828
\(143\) 0.476706 0.0398642
\(144\) 2.57180 1.54462i 0.214317 0.128718i
\(145\) 1.48542i 0.123357i
\(146\) 5.85816i 0.484825i
\(147\) −1.60127 + 0.443904i −0.132070 + 0.0366126i
\(148\) 6.20488i 0.510038i
\(149\) −7.85015 −0.643110 −0.321555 0.946891i \(-0.604205\pi\)
−0.321555 + 0.946891i \(0.604205\pi\)
\(150\) −0.462710 1.66910i −0.0377801 0.136282i
\(151\) 8.89534 0.723892 0.361946 0.932199i \(-0.382112\pi\)
0.361946 + 0.932199i \(0.382112\pi\)
\(152\) 5.08924 0.412792
\(153\) 7.30989 4.39031i 0.590970 0.354935i
\(154\) 0.249605 0.0201137
\(155\) 5.56059 0.446637
\(156\) −8.99332 + 2.49313i −0.720042 + 0.199611i
\(157\) 13.4878i 1.07644i −0.842803 0.538222i \(-0.819096\pi\)
0.842803 0.538222i \(-0.180904\pi\)
\(158\) −9.17572 −0.729981
\(159\) −17.0295 + 4.72094i −1.35053 + 0.374395i
\(160\) 1.00000i 0.0790569i
\(161\) 4.97442 + 12.5825i 0.392039 + 0.991643i
\(162\) −7.94490 4.22831i −0.624210 0.332207i
\(163\) −7.19796 −0.563788 −0.281894 0.959446i \(-0.590963\pi\)
−0.281894 + 0.959446i \(0.590963\pi\)
\(164\) 0.519960i 0.0406020i
\(165\) −0.147671 + 0.0409376i −0.0114962 + 0.00318698i
\(166\) 7.55626i 0.586479i
\(167\) 15.7105i 1.21572i 0.794045 + 0.607859i \(0.207971\pi\)
−0.794045 + 0.607859i \(0.792029\pi\)
\(168\) −4.70893 + 1.30541i −0.363301 + 0.100715i
\(169\) 16.0318 1.23322
\(170\) 2.84233i 0.217996i
\(171\) −7.86093 13.0885i −0.601140 1.00090i
\(172\) 0.907222i 0.0691750i
\(173\) 0.427486i 0.0325012i −0.999868 0.0162506i \(-0.994827\pi\)
0.999868 0.0162506i \(-0.00517295\pi\)
\(174\) −2.47932 + 0.687318i −0.187957 + 0.0521055i
\(175\) 2.82123i 0.213265i
\(176\) 0.0884736 0.00666895
\(177\) 4.09653 + 14.7771i 0.307914 + 1.11072i
\(178\) 12.3408i 0.924984i
\(179\) 12.9141i 0.965244i 0.875829 + 0.482622i \(0.160316\pi\)
−0.875829 + 0.482622i \(0.839684\pi\)
\(180\) 2.57180 1.54462i 0.191691 0.115129i
\(181\) 24.7502i 1.83967i 0.392308 + 0.919834i \(0.371677\pi\)
−0.392308 + 0.919834i \(0.628323\pi\)
\(182\) 15.2011 1.12678
\(183\) 4.84802 + 17.4880i 0.358376 + 1.29275i
\(184\) 1.76321 + 4.45994i 0.129985 + 0.328791i
\(185\) 6.20488i 0.456192i
\(186\) 2.57294 + 9.28119i 0.188657 + 0.680530i
\(187\) 0.251471 0.0183894
\(188\) 0.0243495i 0.00177587i
\(189\) 10.6307 + 10.0940i 0.773273 + 0.734234i
\(190\) 5.08924 0.369212
\(191\) −15.4356 −1.11688 −0.558441 0.829544i \(-0.688600\pi\)
−0.558441 + 0.829544i \(0.688600\pi\)
\(192\) −1.66910 + 0.462710i −0.120457 + 0.0333932i
\(193\) 3.49474 0.251557 0.125779 0.992058i \(-0.459857\pi\)
0.125779 + 0.992058i \(0.459857\pi\)
\(194\) −7.83418 −0.562461
\(195\) −8.99332 + 2.49313i −0.644025 + 0.178537i
\(196\) 0.959358 0.0685256
\(197\) 15.4600i 1.10148i 0.834677 + 0.550739i \(0.185654\pi\)
−0.834677 + 0.550739i \(0.814346\pi\)
\(198\) −0.136658 0.227536i −0.00971185 0.0161703i
\(199\) 1.10416i 0.0782715i 0.999234 + 0.0391357i \(0.0124605\pi\)
−0.999234 + 0.0391357i \(0.987540\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −1.75874 6.34417i −0.124052 0.447483i
\(202\) 11.3714 0.800087
\(203\) 4.19072 0.294131
\(204\) −4.74413 + 1.31517i −0.332156 + 0.0920804i
\(205\) 0.519960i 0.0363155i
\(206\) −15.3014 −1.06610
\(207\) 8.74660 11.4235i 0.607931 0.793990i
\(208\) 5.38812 0.373599
\(209\) 0.450263i 0.0311453i
\(210\) −4.70893 + 1.30541i −0.324947 + 0.0900820i
\(211\) −27.0611 −1.86297 −0.931483 0.363785i \(-0.881484\pi\)
−0.931483 + 0.363785i \(0.881484\pi\)
\(212\) 10.2028 0.700733
\(213\) 5.05523 + 18.2354i 0.346378 + 1.24947i
\(214\) 2.15054i 0.147008i
\(215\) 0.907222i 0.0618720i
\(216\) 3.76812 + 3.57789i 0.256388 + 0.243444i
\(217\) 15.6877i 1.06495i
\(218\) −9.04331 −0.612490
\(219\) −9.77787 + 2.71063i −0.660727 + 0.183167i
\(220\) 0.0884736 0.00596489
\(221\) 15.3148 1.03018
\(222\) 10.3566 2.87106i 0.695088 0.192693i
\(223\) −9.23318 −0.618299 −0.309150 0.951013i \(-0.600044\pi\)
−0.309150 + 0.951013i \(0.600044\pi\)
\(224\) 2.82123 0.188502
\(225\) 2.57180 1.54462i 0.171453 0.102975i
\(226\) 5.46926i 0.363810i
\(227\) −14.7794 −0.980945 −0.490473 0.871457i \(-0.663176\pi\)
−0.490473 + 0.871457i \(0.663176\pi\)
\(228\) 2.35484 + 8.49445i 0.155953 + 0.562559i
\(229\) 26.9323i 1.77974i 0.456216 + 0.889869i \(0.349204\pi\)
−0.456216 + 0.889869i \(0.650796\pi\)
\(230\) 1.76321 + 4.45994i 0.116263 + 0.294080i
\(231\) 0.115494 + 0.416615i 0.00759897 + 0.0274113i
\(232\) 1.48542 0.0975226
\(233\) 18.5217i 1.21340i 0.794932 + 0.606698i \(0.207506\pi\)
−0.794932 + 0.606698i \(0.792494\pi\)
\(234\) −8.32259 13.8572i −0.544065 0.905871i
\(235\) 0.0243495i 0.00158839i
\(236\) 8.85335i 0.576304i
\(237\) −4.24569 15.3152i −0.275787 0.994830i
\(238\) 8.01886 0.519786
\(239\) 23.2974i 1.50698i −0.657457 0.753492i \(-0.728368\pi\)
0.657457 0.753492i \(-0.271632\pi\)
\(240\) −1.66910 + 0.462710i −0.107740 + 0.0298678i
\(241\) 10.7446i 0.692122i 0.938212 + 0.346061i \(0.112481\pi\)
−0.938212 + 0.346061i \(0.887519\pi\)
\(242\) 10.9922i 0.706604i
\(243\) 3.38130 15.2173i 0.216910 0.976192i
\(244\) 10.4775i 0.670751i
\(245\) 0.959358 0.0612911
\(246\) 0.867865 0.240590i 0.0553331 0.0153395i
\(247\) 27.4214i 1.74478i
\(248\) 5.56059i 0.353098i
\(249\) −12.6122 + 3.49635i −0.799263 + 0.221572i
\(250\) 1.00000i 0.0632456i
\(251\) −10.1577 −0.641147 −0.320573 0.947224i \(-0.603876\pi\)
−0.320573 + 0.947224i \(0.603876\pi\)
\(252\) −4.35773 7.25565i −0.274511 0.457063i
\(253\) 0.394587 0.155997i 0.0248075 0.00980747i
\(254\) 1.22410i 0.0768067i
\(255\) −4.74413 + 1.31517i −0.297089 + 0.0823592i
\(256\) 1.00000 0.0625000
\(257\) 14.7723i 0.921468i −0.887538 0.460734i \(-0.847586\pi\)
0.887538 0.460734i \(-0.152414\pi\)
\(258\) −1.51425 + 0.419780i −0.0942728 + 0.0261344i
\(259\) −17.5054 −1.08773
\(260\) 5.38812 0.334157
\(261\) −2.29441 3.82020i −0.142020 0.236465i
\(262\) −17.3758 −1.07348
\(263\) 24.0408 1.48242 0.741209 0.671275i \(-0.234253\pi\)
0.741209 + 0.671275i \(0.234253\pi\)
\(264\) 0.0409376 + 0.147671i 0.00251953 + 0.00908854i
\(265\) 10.2028 0.626754
\(266\) 14.3579i 0.880341i
\(267\) 20.5981 5.71022i 1.26058 0.349460i
\(268\) 3.80095i 0.232180i
\(269\) 4.74366i 0.289226i 0.989488 + 0.144613i \(0.0461937\pi\)
−0.989488 + 0.144613i \(0.953806\pi\)
\(270\) 3.76812 + 3.57789i 0.229321 + 0.217743i
\(271\) −0.303443 −0.0184329 −0.00921643 0.999958i \(-0.502934\pi\)
−0.00921643 + 0.999958i \(0.502934\pi\)
\(272\) 2.84233 0.172341
\(273\) 7.03372 + 25.3723i 0.425700 + 1.53560i
\(274\) 18.2067i 1.09991i
\(275\) 0.0884736 0.00533516
\(276\) −6.62825 + 5.00663i −0.398973 + 0.301364i
\(277\) 23.1558 1.39129 0.695647 0.718383i \(-0.255118\pi\)
0.695647 + 0.718383i \(0.255118\pi\)
\(278\) 7.87519i 0.472322i
\(279\) −14.3007 + 8.58899i −0.856162 + 0.514210i
\(280\) 2.82123 0.168601
\(281\) 1.79749 0.107229 0.0536146 0.998562i \(-0.482926\pi\)
0.0536146 + 0.998562i \(0.482926\pi\)
\(282\) 0.0406418 0.0112667i 0.00242018 0.000670925i
\(283\) 25.5875i 1.52102i −0.649328 0.760509i \(-0.724950\pi\)
0.649328 0.760509i \(-0.275050\pi\)
\(284\) 10.9253i 0.648295i
\(285\) 2.35484 + 8.49445i 0.139489 + 0.503168i
\(286\) 0.476706i 0.0281882i
\(287\) −1.46693 −0.0865900
\(288\) −1.54462 2.57180i −0.0910175 0.151545i
\(289\) −8.92119 −0.524776
\(290\) 1.48542 0.0872269
\(291\) −3.62495 13.0760i −0.212498 0.766531i
\(292\) 5.85816 0.342823
\(293\) −24.0774 −1.40662 −0.703308 0.710885i \(-0.748295\pi\)
−0.703308 + 0.710885i \(0.748295\pi\)
\(294\) 0.443904 + 1.60127i 0.0258890 + 0.0933877i
\(295\) 8.85335i 0.515462i
\(296\) −6.20488 −0.360651
\(297\) 0.316548 0.333379i 0.0183680 0.0193446i
\(298\) 7.85015i 0.454747i
\(299\) 24.0307 9.50038i 1.38973 0.549421i
\(300\) −1.66910 + 0.462710i −0.0963656 + 0.0267145i
\(301\) 2.55949 0.147526
\(302\) 8.89534i 0.511869i
\(303\) 5.26164 + 18.9800i 0.302273 + 1.09037i
\(304\) 5.08924i 0.291888i
\(305\) 10.4775i 0.599938i
\(306\) −4.39031 7.30989i −0.250977 0.417879i
\(307\) −18.5284 −1.05747 −0.528735 0.848787i \(-0.677333\pi\)
−0.528735 + 0.848787i \(0.677333\pi\)
\(308\) 0.249605i 0.0142225i
\(309\) −7.08013 25.5397i −0.402774 1.45290i
\(310\) 5.56059i 0.315820i
\(311\) 29.6815i 1.68308i −0.540193 0.841541i \(-0.681649\pi\)
0.540193 0.841541i \(-0.318351\pi\)
\(312\) 2.49313 + 8.99332i 0.141146 + 0.509146i
\(313\) 8.20686i 0.463879i −0.972730 0.231939i \(-0.925493\pi\)
0.972730 0.231939i \(-0.0745071\pi\)
\(314\) −13.4878 −0.761161
\(315\) −4.35773 7.25565i −0.245530 0.408809i
\(316\) 9.17572i 0.516175i
\(317\) 30.8326i 1.73173i −0.500274 0.865867i \(-0.666768\pi\)
0.500274 0.865867i \(-0.333232\pi\)
\(318\) 4.72094 + 17.0295i 0.264737 + 0.954970i
\(319\) 0.131420i 0.00735813i
\(320\) 1.00000 0.0559017
\(321\) −3.58947 + 0.995077i −0.200345 + 0.0555398i
\(322\) 12.5825 4.97442i 0.701198 0.277214i
\(323\) 14.4653i 0.804869i
\(324\) −4.22831 + 7.94490i −0.234906 + 0.441383i
\(325\) 5.38812 0.298879
\(326\) 7.19796i 0.398658i
\(327\) −4.18443 15.0942i −0.231399 0.834711i
\(328\) −0.519960 −0.0287100
\(329\) −0.0686956 −0.00378731
\(330\) 0.0409376 + 0.147671i 0.00225354 + 0.00812904i
\(331\) −18.1025 −0.995004 −0.497502 0.867463i \(-0.665749\pi\)
−0.497502 + 0.867463i \(0.665749\pi\)
\(332\) 7.55626 0.414703
\(333\) 9.58417 + 15.9577i 0.525209 + 0.874477i
\(334\) 15.7105 0.859642
\(335\) 3.80095i 0.207668i
\(336\) 1.30541 + 4.70893i 0.0712160 + 0.256893i
\(337\) 19.1719i 1.04436i 0.852835 + 0.522181i \(0.174882\pi\)
−0.852835 + 0.522181i \(0.825118\pi\)
\(338\) 16.0318i 0.872017i
\(339\) 9.12875 2.53068i 0.495806 0.137448i
\(340\) 2.84233 0.154147
\(341\) −0.491965 −0.0266414
\(342\) −13.0885 + 7.86093i −0.707745 + 0.425070i
\(343\) 17.0421i 0.920185i
\(344\) 0.907222 0.0489141
\(345\) −6.62825 + 5.00663i −0.356853 + 0.269548i
\(346\) −0.427486 −0.0229818
\(347\) 24.7654i 1.32947i −0.747077 0.664737i \(-0.768543\pi\)
0.747077 0.664737i \(-0.231457\pi\)
\(348\) 0.687318 + 2.47932i 0.0368441 + 0.132905i
\(349\) 29.5558 1.58209 0.791043 0.611760i \(-0.209538\pi\)
0.791043 + 0.611760i \(0.209538\pi\)
\(350\) 2.82123 0.150801
\(351\) 19.2781 20.3031i 1.02899 1.08370i
\(352\) 0.0884736i 0.00471566i
\(353\) 28.0481i 1.49285i −0.665469 0.746425i \(-0.731769\pi\)
0.665469 0.746425i \(-0.268231\pi\)
\(354\) 14.7771 4.09653i 0.785396 0.217728i
\(355\) 10.9253i 0.579853i
\(356\) −12.3408 −0.654063
\(357\) 3.71040 + 13.3843i 0.196375 + 0.708372i
\(358\) 12.9141 0.682531
\(359\) 11.9019 0.628160 0.314080 0.949396i \(-0.398304\pi\)
0.314080 + 0.949396i \(0.398304\pi\)
\(360\) −1.54462 2.57180i −0.0814085 0.135546i
\(361\) −6.90033 −0.363175
\(362\) 24.7502 1.30084
\(363\) −18.3471 + 5.08618i −0.962970 + 0.266955i
\(364\) 15.2011i 0.796757i
\(365\) 5.85816 0.306630
\(366\) 17.4880 4.84802i 0.914110 0.253410i
\(367\) 31.6802i 1.65369i 0.562427 + 0.826847i \(0.309868\pi\)
−0.562427 + 0.826847i \(0.690132\pi\)
\(368\) 4.45994 1.76321i 0.232491 0.0919136i
\(369\) 0.803139 + 1.33723i 0.0418097 + 0.0696135i
\(370\) −6.20488 −0.322576
\(371\) 28.7845i 1.49442i
\(372\) 9.28119 2.57294i 0.481207 0.133401i
\(373\) 8.32570i 0.431088i −0.976494 0.215544i \(-0.930847\pi\)
0.976494 0.215544i \(-0.0691525\pi\)
\(374\) 0.251471i 0.0130032i
\(375\) −1.66910 + 0.462710i −0.0861920 + 0.0238942i
\(376\) −0.0243495 −0.00125573
\(377\) 8.00363i 0.412208i
\(378\) 10.0940 10.6307i 0.519182 0.546787i
\(379\) 9.50248i 0.488110i 0.969761 + 0.244055i \(0.0784777\pi\)
−0.969761 + 0.244055i \(0.921522\pi\)
\(380\) 5.08924i 0.261072i
\(381\) −2.04314 + 0.566402i −0.104673 + 0.0290176i
\(382\) 15.4356i 0.789755i
\(383\) 37.1871 1.90017 0.950087 0.311985i \(-0.100994\pi\)
0.950087 + 0.311985i \(0.100994\pi\)
\(384\) 0.462710 + 1.66910i 0.0236125 + 0.0851760i
\(385\) 0.249605i 0.0127210i
\(386\) 3.49474i 0.177878i
\(387\) −1.40131 2.33319i −0.0712327 0.118603i
\(388\) 7.83418i 0.397720i
\(389\) 18.6520 0.945696 0.472848 0.881144i \(-0.343226\pi\)
0.472848 + 0.881144i \(0.343226\pi\)
\(390\) 2.49313 + 8.99332i 0.126245 + 0.455394i
\(391\) 12.6766 5.01161i 0.641084 0.253448i
\(392\) 0.959358i 0.0484549i
\(393\) −8.03996 29.0020i −0.405562 1.46296i
\(394\) 15.4600 0.778863
\(395\) 9.17572i 0.461681i
\(396\) −0.227536 + 0.136658i −0.0114341 + 0.00686732i
\(397\) 2.78953 0.140003 0.0700013 0.997547i \(-0.477700\pi\)
0.0700013 + 0.997547i \(0.477700\pi\)
\(398\) 1.10416 0.0553463
\(399\) 23.9648 6.64355i 1.19974 0.332593i
\(400\) 1.00000 0.0500000
\(401\) 34.5221 1.72395 0.861976 0.506949i \(-0.169227\pi\)
0.861976 + 0.506949i \(0.169227\pi\)
\(402\) −6.34417 + 1.75874i −0.316419 + 0.0877178i
\(403\) −29.9611 −1.49247
\(404\) 11.3714i 0.565747i
\(405\) −4.22831 + 7.94490i −0.210106 + 0.394785i
\(406\) 4.19072i 0.207982i
\(407\) 0.548968i 0.0272113i
\(408\) 1.31517 + 4.74413i 0.0651107 + 0.234869i
\(409\) −13.4130 −0.663233 −0.331616 0.943414i \(-0.607594\pi\)
−0.331616 + 0.943414i \(0.607594\pi\)
\(410\) −0.519960 −0.0256790
\(411\) −30.3888 + 8.42440i −1.49897 + 0.415545i
\(412\) 15.3014i 0.753848i
\(413\) −24.9774 −1.22906
\(414\) −11.4235 8.74660i −0.561436 0.429872i
\(415\) 7.55626 0.370922
\(416\) 5.38812i 0.264174i
\(417\) −13.1445 + 3.64392i −0.643688 + 0.178444i
\(418\) −0.450263 −0.0220231
\(419\) 39.6632 1.93767 0.968837 0.247698i \(-0.0796741\pi\)
0.968837 + 0.247698i \(0.0796741\pi\)
\(420\) 1.30541 + 4.70893i 0.0636976 + 0.229772i
\(421\) 8.88923i 0.433234i −0.976257 0.216617i \(-0.930498\pi\)
0.976257 0.216617i \(-0.0695024\pi\)
\(422\) 27.0611i 1.31732i
\(423\) 0.0376107 + 0.0626220i 0.00182869 + 0.00304479i
\(424\) 10.2028i 0.495493i
\(425\) 2.84233 0.137873
\(426\) 18.2354 5.05523i 0.883507 0.244926i
\(427\) −29.5594 −1.43048
\(428\) 2.15054 0.103950
\(429\) 0.795671 0.220577i 0.0384154 0.0106495i
\(430\) 0.907222 0.0437501
\(431\) −40.0125 −1.92733 −0.963666 0.267110i \(-0.913931\pi\)
−0.963666 + 0.267110i \(0.913931\pi\)
\(432\) 3.57789 3.76812i 0.172141 0.181294i
\(433\) 24.6079i 1.18258i −0.806459 0.591289i \(-0.798619\pi\)
0.806459 0.591289i \(-0.201381\pi\)
\(434\) −15.6877 −0.753035
\(435\) 0.687318 + 2.47932i 0.0329544 + 0.118874i
\(436\) 9.04331i 0.433096i
\(437\) −8.97339 22.6977i −0.429255 1.08578i
\(438\) 2.71063 + 9.77787i 0.129519 + 0.467205i
\(439\) −28.9558 −1.38199 −0.690993 0.722861i \(-0.742827\pi\)
−0.690993 + 0.722861i \(0.742827\pi\)
\(440\) 0.0884736i 0.00421781i
\(441\) −2.46728 + 1.48184i −0.117489 + 0.0705639i
\(442\) 15.3148i 0.728450i
\(443\) 3.91361i 0.185941i 0.995669 + 0.0929706i \(0.0296362\pi\)
−0.995669 + 0.0929706i \(0.970364\pi\)
\(444\) −2.87106 10.3566i −0.136254 0.491501i
\(445\) −12.3408 −0.585011
\(446\) 9.23318i 0.437204i
\(447\) −13.1027 + 3.63234i −0.619737 + 0.171804i
\(448\) 2.82123i 0.133291i
\(449\) 16.9735i 0.801029i 0.916290 + 0.400514i \(0.131169\pi\)
−0.916290 + 0.400514i \(0.868831\pi\)
\(450\) −1.54462 2.57180i −0.0728140 0.121236i
\(451\) 0.0460027i 0.00216618i
\(452\) −5.46926 −0.257252
\(453\) 14.8472 4.11596i 0.697583 0.193385i
\(454\) 14.7794i 0.693633i
\(455\) 15.2011i 0.712641i
\(456\) 8.49445 2.35484i 0.397789 0.110275i
\(457\) 16.4848i 0.771129i 0.922681 + 0.385564i \(0.125993\pi\)
−0.922681 + 0.385564i \(0.874007\pi\)
\(458\) 26.9323 1.25846
\(459\) 10.1695 10.7102i 0.474672 0.499911i
\(460\) 4.45994 1.76321i 0.207946 0.0822100i
\(461\) 42.6536i 1.98657i 0.115674 + 0.993287i \(0.463097\pi\)
−0.115674 + 0.993287i \(0.536903\pi\)
\(462\) 0.416615 0.115494i 0.0193827 0.00537329i
\(463\) 9.52088 0.442473 0.221236 0.975220i \(-0.428991\pi\)
0.221236 + 0.975220i \(0.428991\pi\)
\(464\) 1.48542i 0.0689589i
\(465\) 9.28119 2.57294i 0.430405 0.119317i
\(466\) 18.5217 0.858001
\(467\) −18.2551 −0.844744 −0.422372 0.906423i \(-0.638802\pi\)
−0.422372 + 0.906423i \(0.638802\pi\)
\(468\) −13.8572 + 8.32259i −0.640548 + 0.384712i
\(469\) 10.7234 0.495159
\(470\) −0.0243495 −0.00112316
\(471\) −6.24094 22.5125i −0.287567 1.03732i
\(472\) −8.85335 −0.407509
\(473\) 0.0802652i 0.00369060i
\(474\) −15.3152 + 4.24569i −0.703451 + 0.195011i
\(475\) 5.08924i 0.233510i
\(476\) 8.01886i 0.367544i
\(477\) −26.2396 + 15.7595i −1.20143 + 0.721576i
\(478\) −23.2974 −1.06560
\(479\) −6.28781 −0.287298 −0.143649 0.989629i \(-0.545884\pi\)
−0.143649 + 0.989629i \(0.545884\pi\)
\(480\) 0.462710 + 1.66910i 0.0211197 + 0.0761837i
\(481\) 33.4326i 1.52440i
\(482\) 10.7446 0.489404
\(483\) 14.1249 + 18.6998i 0.642704 + 0.850872i
\(484\) 10.9922 0.499644
\(485\) 7.83418i 0.355732i
\(486\) −15.2173 3.38130i −0.690272 0.153379i
\(487\) −2.55380 −0.115724 −0.0578618 0.998325i \(-0.518428\pi\)
−0.0578618 + 0.998325i \(0.518428\pi\)
\(488\) −10.4775 −0.474293
\(489\) −12.0141 + 3.33057i −0.543298 + 0.150613i
\(490\) 0.959358i 0.0433394i
\(491\) 16.8062i 0.758452i 0.925304 + 0.379226i \(0.123810\pi\)
−0.925304 + 0.379226i \(0.876190\pi\)
\(492\) −0.240590 0.867865i −0.0108466 0.0391264i
\(493\) 4.22205i 0.190152i
\(494\) −27.4214 −1.23375
\(495\) −0.227536 + 0.136658i −0.0102270 + 0.00614232i
\(496\) −5.56059 −0.249678
\(497\) −30.8227 −1.38259
\(498\) 3.49635 + 12.6122i 0.156675 + 0.565164i
\(499\) −9.17252 −0.410619 −0.205309 0.978697i \(-0.565820\pi\)
−0.205309 + 0.978697i \(0.565820\pi\)
\(500\) 1.00000 0.0447214
\(501\) 7.26941 + 26.2225i 0.324773 + 1.17153i
\(502\) 10.1577i 0.453359i
\(503\) −5.33773 −0.237997 −0.118999 0.992894i \(-0.537968\pi\)
−0.118999 + 0.992894i \(0.537968\pi\)
\(504\) −7.25565 + 4.35773i −0.323192 + 0.194109i
\(505\) 11.3714i 0.506019i
\(506\) −0.155997 0.394587i −0.00693493 0.0175415i
\(507\) 26.7588 7.41809i 1.18840 0.329449i
\(508\) 1.22410 0.0543105
\(509\) 4.91462i 0.217837i −0.994051 0.108918i \(-0.965261\pi\)
0.994051 0.108918i \(-0.0347387\pi\)
\(510\) 1.31517 + 4.74413i 0.0582368 + 0.210074i
\(511\) 16.5272i 0.731122i
\(512\) 1.00000i 0.0441942i
\(513\) −19.1769 18.2087i −0.846679 0.803934i
\(514\) −14.7723 −0.651576
\(515\) 15.3014i 0.674262i
\(516\) 0.419780 + 1.51425i 0.0184798 + 0.0666610i
\(517\) 0.00215429i 9.47454e-5i
\(518\) 17.5054i 0.769144i
\(519\) −0.197802 0.713518i −0.00868255 0.0313200i
\(520\) 5.38812i 0.236285i
\(521\) 39.5006 1.73055 0.865276 0.501296i \(-0.167143\pi\)
0.865276 + 0.501296i \(0.167143\pi\)
\(522\) −3.82020 + 2.29441i −0.167206 + 0.100424i
\(523\) 9.23575i 0.403851i −0.979401 0.201926i \(-0.935280\pi\)
0.979401 0.201926i \(-0.0647199\pi\)
\(524\) 17.3758i 0.759066i
\(525\) 1.30541 + 4.70893i 0.0569728 + 0.205514i
\(526\) 24.0408i 1.04823i
\(527\) −15.8050 −0.688477
\(528\) 0.147671 0.0409376i 0.00642657 0.00178158i
\(529\) 16.7822 15.7276i 0.729661 0.683810i
\(530\) 10.2028i 0.443182i
\(531\) 13.6751 + 22.7691i 0.593447 + 0.988093i
\(532\) −14.3579 −0.622495
\(533\) 2.80160i 0.121351i
\(534\) −5.71022 20.5981i −0.247105 0.891367i
\(535\) 2.15054 0.0929761
\(536\) 3.80095 0.164176
\(537\) 5.97547 + 21.5549i 0.257861 + 0.930164i
\(538\) 4.74366 0.204514
\(539\) −0.0848778 −0.00365595
\(540\) 3.57789 3.76812i 0.153968 0.162154i
\(541\) 36.8369 1.58374 0.791870 0.610689i \(-0.209108\pi\)
0.791870 + 0.610689i \(0.209108\pi\)
\(542\) 0.303443i 0.0130340i
\(543\) 11.4522 + 41.3106i 0.491459 + 1.77281i
\(544\) 2.84233i 0.121864i
\(545\) 9.04331i 0.387373i
\(546\) 25.3723 7.03372i 1.08583 0.301015i
\(547\) 5.76966 0.246693 0.123347 0.992364i \(-0.460637\pi\)
0.123347 + 0.992364i \(0.460637\pi\)
\(548\) 18.2067 0.777751
\(549\) 16.1837 + 26.9460i 0.690703 + 1.15003i
\(550\) 0.0884736i 0.00377253i
\(551\) −7.55966 −0.322052
\(552\) 5.00663 + 6.62825i 0.213096 + 0.282117i
\(553\) 25.8868 1.10082
\(554\) 23.1558i 0.983794i
\(555\) −2.87106 10.3566i −0.121870 0.439612i
\(556\) 7.87519 0.333982
\(557\) −7.85492 −0.332823 −0.166412 0.986056i \(-0.553218\pi\)
−0.166412 + 0.986056i \(0.553218\pi\)
\(558\) 8.58899 + 14.3007i 0.363601 + 0.605398i
\(559\) 4.88822i 0.206750i
\(560\) 2.82123i 0.119219i
\(561\) 0.419730 0.116358i 0.0177210 0.00491263i
\(562\) 1.79749i 0.0758226i
\(563\) 9.90300 0.417362 0.208681 0.977984i \(-0.433083\pi\)
0.208681 + 0.977984i \(0.433083\pi\)
\(564\) −0.0112667 0.0406418i −0.000474415 0.00171133i
\(565\) −5.46926 −0.230094
\(566\) −25.5875 −1.07552
\(567\) 22.4144 + 11.9290i 0.941317 + 0.500973i
\(568\) −10.9253 −0.458414
\(569\) −7.04866 −0.295495 −0.147748 0.989025i \(-0.547202\pi\)
−0.147748 + 0.989025i \(0.547202\pi\)
\(570\) 8.49445 2.35484i 0.355793 0.0986333i
\(571\) 31.1060i 1.30175i −0.759186 0.650874i \(-0.774403\pi\)
0.759186 0.650874i \(-0.225597\pi\)
\(572\) −0.476706 −0.0199321
\(573\) −25.7636 + 7.14221i −1.07629 + 0.298370i
\(574\) 1.46693i 0.0612284i
\(575\) 4.45994 1.76321i 0.185993 0.0735309i
\(576\) −2.57180 + 1.54462i −0.107158 + 0.0643591i
\(577\) 8.95481 0.372794 0.186397 0.982475i \(-0.440319\pi\)
0.186397 + 0.982475i \(0.440319\pi\)
\(578\) 8.92119i 0.371072i
\(579\) 5.83308 1.61705i 0.242415 0.0672023i
\(580\) 1.48542i 0.0616787i
\(581\) 21.3180i 0.884418i
\(582\) −13.0760 + 3.62495i −0.542019 + 0.150259i
\(583\) −0.902680 −0.0373852
\(584\) 5.85816i 0.242412i
\(585\) −13.8572 + 8.32259i −0.572923 + 0.344097i
\(586\) 24.0774i 0.994628i
\(587\) 13.8103i 0.570014i 0.958525 + 0.285007i \(0.0919959\pi\)
−0.958525 + 0.285007i \(0.908004\pi\)
\(588\) 1.60127 0.443904i 0.0660351 0.0183063i
\(589\) 28.2992i 1.16605i
\(590\) −8.85335 −0.364487
\(591\) 7.15348 + 25.8043i 0.294255 + 1.06145i
\(592\) 6.20488i 0.255019i
\(593\) 2.50124i 0.102714i 0.998680 + 0.0513568i \(0.0163546\pi\)
−0.998680 + 0.0513568i \(0.983645\pi\)
\(594\) −0.333379 0.316548i −0.0136787 0.0129881i
\(595\) 8.01886i 0.328741i
\(596\) 7.85015 0.321555
\(597\) 0.510903 + 1.84295i 0.0209099 + 0.0754268i
\(598\) −9.50038 24.0307i −0.388499 0.982689i
\(599\) 0.571210i 0.0233390i 0.999932 + 0.0116695i \(0.00371460\pi\)
−0.999932 + 0.0116695i \(0.996285\pi\)
\(600\) 0.462710 + 1.66910i 0.0188900 + 0.0681408i
\(601\) −16.9300 −0.690588 −0.345294 0.938494i \(-0.612221\pi\)
−0.345294 + 0.938494i \(0.612221\pi\)
\(602\) 2.55949i 0.104317i
\(603\) −5.87102 9.77529i −0.239086 0.398080i
\(604\) −8.89534 −0.361946
\(605\) 10.9922 0.446895
\(606\) 18.9800 5.26164i 0.771009 0.213740i
\(607\) 1.41388 0.0573878 0.0286939 0.999588i \(-0.490865\pi\)
0.0286939 + 0.999588i \(0.490865\pi\)
\(608\) −5.08924 −0.206396
\(609\) 6.99473 1.93909i 0.283441 0.0785757i
\(610\) −10.4775 −0.424220
\(611\) 0.131198i 0.00530770i
\(612\) −7.30989 + 4.39031i −0.295485 + 0.177468i
\(613\) 3.59479i 0.145192i −0.997361 0.0725961i \(-0.976872\pi\)
0.997361 0.0725961i \(-0.0231284\pi\)
\(614\) 18.5284i 0.747744i
\(615\) −0.240590 0.867865i −0.00970153 0.0349957i
\(616\) −0.249605 −0.0100569
\(617\) 5.75072 0.231515 0.115758 0.993277i \(-0.463070\pi\)
0.115758 + 0.993277i \(0.463070\pi\)
\(618\) −25.5397 + 7.08013i −1.02736 + 0.284804i
\(619\) 37.6313i 1.51253i 0.654265 + 0.756265i \(0.272978\pi\)
−0.654265 + 0.756265i \(0.727022\pi\)
\(620\) −5.56059 −0.223319
\(621\) 9.31318 23.1142i 0.373725 0.927539i
\(622\) −29.6815 −1.19012
\(623\) 34.8164i 1.39489i
\(624\) 8.99332 2.49313i 0.360021 0.0998053i
\(625\) 1.00000 0.0400000
\(626\) −8.20686 −0.328012
\(627\) −0.208341 0.751534i −0.00832034 0.0300134i
\(628\) 13.4878i 0.538222i
\(629\) 17.6363i 0.703205i
\(630\) −7.25565 + 4.35773i −0.289072 + 0.173616i
\(631\) 18.9775i 0.755482i −0.925911 0.377741i \(-0.876701\pi\)
0.925911 0.377741i \(-0.123299\pi\)
\(632\) 9.17572 0.364991
\(633\) −45.1678 + 12.5214i −1.79526 + 0.497683i
\(634\) −30.8326 −1.22452
\(635\) 1.22410 0.0485768
\(636\) 17.0295 4.72094i 0.675265 0.187198i
\(637\) −5.16914 −0.204809
\(638\) −0.131420 −0.00520299
\(639\) 16.8754 + 28.0976i 0.667579 + 1.11152i
\(640\) 1.00000i 0.0395285i
\(641\) 39.5864 1.56357 0.781785 0.623548i \(-0.214309\pi\)
0.781785 + 0.623548i \(0.214309\pi\)
\(642\) 0.995077 + 3.58947i 0.0392725 + 0.141665i
\(643\) 8.50938i 0.335577i 0.985823 + 0.167789i \(0.0536626\pi\)
−0.985823 + 0.167789i \(0.946337\pi\)
\(644\) −4.97442 12.5825i −0.196020 0.495822i
\(645\) 0.419780 + 1.51425i 0.0165288 + 0.0596234i
\(646\) −14.4653 −0.569128
\(647\) 18.9221i 0.743903i −0.928252 0.371951i \(-0.878689\pi\)
0.928252 0.371951i \(-0.121311\pi\)
\(648\) 7.94490 + 4.22831i 0.312105 + 0.166104i
\(649\) 0.783288i 0.0307467i
\(650\) 5.38812i 0.211339i
\(651\) −7.25886 26.1844i −0.284497 1.02625i
\(652\) 7.19796 0.281894
\(653\) 10.9104i 0.426956i −0.976948 0.213478i \(-0.931521\pi\)
0.976948 0.213478i \(-0.0684791\pi\)
\(654\) −15.0942 + 4.18443i −0.590230 + 0.163624i
\(655\) 17.3758i 0.678929i
\(656\) 0.519960i 0.0203010i
\(657\) −15.0660 + 9.04863i −0.587781 + 0.353021i
\(658\) 0.0686956i 0.00267803i
\(659\) −9.42907 −0.367304 −0.183652 0.982991i \(-0.558792\pi\)
−0.183652 + 0.982991i \(0.558792\pi\)
\(660\) 0.147671 0.0409376i 0.00574810 0.00159349i
\(661\) 10.2837i 0.399991i −0.979797 0.199995i \(-0.935907\pi\)
0.979797 0.199995i \(-0.0640927\pi\)
\(662\) 18.1025i 0.703574i
\(663\) 25.5619 7.08630i 0.992744 0.275209i
\(664\) 7.55626i 0.293240i
\(665\) −14.3579 −0.556776
\(666\) 15.9577 9.58417i 0.618348 0.371379i
\(667\) −2.61911 6.62489i −0.101412 0.256517i
\(668\) 15.7105i 0.607859i
\(669\) −15.4111 + 4.27228i −0.595828 + 0.165176i
\(670\) 3.80095 0.146844
\(671\) 0.926979i 0.0357856i
\(672\) 4.70893 1.30541i 0.181651 0.0503573i
\(673\) 34.9603 1.34762 0.673811 0.738904i \(-0.264656\pi\)
0.673811 + 0.738904i \(0.264656\pi\)
\(674\) 19.1719 0.738476
\(675\) 3.57789 3.76812i 0.137713 0.145035i
\(676\) −16.0318 −0.616609
\(677\) 20.1189 0.773231 0.386615 0.922241i \(-0.373644\pi\)
0.386615 + 0.922241i \(0.373644\pi\)
\(678\) −2.53068 9.12875i −0.0971902 0.350588i
\(679\) 22.1020 0.848198
\(680\) 2.84233i 0.108998i
\(681\) −24.6684 + 6.83858i −0.945294 + 0.262055i
\(682\) 0.491965i 0.0188383i
\(683\) 16.5961i 0.635030i −0.948253 0.317515i \(-0.897152\pi\)
0.948253 0.317515i \(-0.102848\pi\)
\(684\) 7.86093 + 13.0885i 0.300570 + 0.500451i
\(685\) 18.2067 0.695641
\(686\) 17.0421 0.650669
\(687\) 12.4618 + 44.9528i 0.475449 + 1.71506i
\(688\) 0.907222i 0.0345875i
\(689\) −54.9740 −2.09434
\(690\) 5.00663 + 6.62825i 0.190599 + 0.252333i
\(691\) −44.3960 −1.68890 −0.844452 0.535630i \(-0.820074\pi\)
−0.844452 + 0.535630i \(0.820074\pi\)
\(692\) 0.427486i 0.0162506i
\(693\) 0.385544 + 0.641933i 0.0146456 + 0.0243850i
\(694\) −24.7654 −0.940081
\(695\) 7.87519 0.298723
\(696\) 2.47932 0.687318i 0.0939783 0.0260527i
\(697\) 1.47789i 0.0559792i
\(698\) 29.5558i 1.11870i
\(699\) 8.57017 + 30.9146i 0.324153 + 1.16930i
\(700\) 2.82123i 0.106633i
\(701\) 4.03643 0.152454 0.0762269 0.997090i \(-0.475713\pi\)
0.0762269 + 0.997090i \(0.475713\pi\)
\(702\) −20.3031 19.2781i −0.766291 0.727604i
\(703\) 31.5781 1.19099
\(704\) −0.0884736 −0.00333447
\(705\) −0.0112667 0.0406418i −0.000424330 0.00153066i
\(706\) −28.0481 −1.05560
\(707\) −32.0813 −1.20654
\(708\) −4.09653 14.7771i −0.153957 0.555359i
\(709\) 32.9635i 1.23797i −0.785402 0.618986i \(-0.787544\pi\)
0.785402 0.618986i \(-0.212456\pi\)
\(710\) −10.9253 −0.410018
\(711\) −14.1730 23.5981i −0.531528 0.884998i
\(712\) 12.3408i 0.462492i
\(713\) −24.7999 + 9.80448i −0.928764 + 0.367181i
\(714\) 13.3843 3.71040i 0.500895 0.138858i
\(715\) −0.476706 −0.0178278
\(716\) 12.9141i 0.482622i
\(717\) −10.7799 38.8857i −0.402584 1.45221i
\(718\) 11.9019i 0.444177i
\(719\) 9.37917i 0.349784i −0.984588 0.174892i \(-0.944042\pi\)
0.984588 0.174892i \(-0.0559576\pi\)
\(720\) −2.57180 + 1.54462i −0.0958453 + 0.0575645i
\(721\) 43.1690 1.60770
\(722\) 6.90033i 0.256804i
\(723\) 4.97164 + 17.9339i 0.184897 + 0.666968i
\(724\) 24.7502i 0.919834i
\(725\) 1.48542i 0.0551671i
\(726\) 5.08618 + 18.3471i 0.188766 + 0.680923i
\(727\) 37.6346i 1.39579i 0.716199 + 0.697896i \(0.245880\pi\)
−0.716199 + 0.697896i \(0.754120\pi\)
\(728\) −15.2011 −0.563392
\(729\) −1.39747 26.9638i −0.0517583 0.998660i
\(730\) 5.85816i 0.216820i
\(731\) 2.57862i 0.0953737i
\(732\) −4.84802 17.4880i −0.179188 0.646374i
\(733\) 48.8726i 1.80515i −0.430533 0.902575i \(-0.641674\pi\)
0.430533 0.902575i \(-0.358326\pi\)
\(734\) 31.6802 1.16934
\(735\) 1.60127 0.443904i 0.0590636 0.0163737i
\(736\) −1.76321 4.45994i −0.0649927 0.164396i
\(737\) 0.336284i 0.0123872i
\(738\) 1.33723 0.803139i 0.0492242 0.0295640i
\(739\) −4.24348 −0.156099 −0.0780495 0.996949i \(-0.524869\pi\)
−0.0780495 + 0.996949i \(0.524869\pi\)
\(740\) 6.20488i 0.228096i
\(741\) −12.6882 45.7691i −0.466111 1.68137i
\(742\) −28.7845 −1.05671
\(743\) −13.3090 −0.488261 −0.244130 0.969742i \(-0.578502\pi\)
−0.244130 + 0.969742i \(0.578502\pi\)
\(744\) −2.57294 9.28119i −0.0943285 0.340265i
\(745\) 7.85015 0.287607
\(746\) −8.32570 −0.304826
\(747\) −19.4332 + 11.6715i −0.711023 + 0.427039i
\(748\) −0.251471 −0.00919468
\(749\) 6.06718i 0.221690i
\(750\) 0.462710 + 1.66910i 0.0168958 + 0.0609470i
\(751\) 36.2427i 1.32251i 0.750159 + 0.661257i \(0.229977\pi\)
−0.750159 + 0.661257i \(0.770023\pi\)
\(752\) 0.0243495i 0.000887934i
\(753\) −16.9542 + 4.70005i −0.617845 + 0.171279i
\(754\) −8.00363 −0.291475
\(755\) −8.89534 −0.323735
\(756\) −10.6307 10.0940i −0.386637 0.367117i
\(757\) 38.6987i 1.40653i 0.710929 + 0.703264i \(0.248275\pi\)
−0.710929 + 0.703264i \(0.751725\pi\)
\(758\) 9.50248 0.345146
\(759\) 0.586424 0.442955i 0.0212859 0.0160782i
\(760\) −5.08924 −0.184606
\(761\) 33.2491i 1.20528i −0.798014 0.602639i \(-0.794116\pi\)
0.798014 0.602639i \(-0.205884\pi\)
\(762\) 0.566402 + 2.04314i 0.0205186 + 0.0740153i
\(763\) 25.5133 0.923643
\(764\) 15.4356 0.558441
\(765\) −7.30989 + 4.39031i −0.264290 + 0.158732i
\(766\) 37.1871i 1.34363i
\(767\) 47.7029i 1.72245i
\(768\) 1.66910 0.462710i 0.0602285 0.0166966i
\(769\) 5.52635i 0.199285i 0.995023 + 0.0996426i \(0.0317700\pi\)
−0.995023 + 0.0996426i \(0.968230\pi\)
\(770\) −0.249605 −0.00899512
\(771\) −6.83526 24.6564i −0.246166 0.887978i
\(772\) −3.49474 −0.125779
\(773\) 13.0486 0.469327 0.234663 0.972077i \(-0.424601\pi\)
0.234663 + 0.972077i \(0.424601\pi\)
\(774\) −2.33319 + 1.40131i −0.0838649 + 0.0503691i
\(775\) −5.56059 −0.199742
\(776\) 7.83418 0.281230
\(777\) −29.2183 + 8.09992i −1.04820 + 0.290583i
\(778\) 18.6520i 0.668708i
\(779\) 2.64620 0.0948098
\(780\) 8.99332 2.49313i 0.322013 0.0892685i
\(781\) 0.966597i 0.0345876i
\(782\) −5.01161 12.6766i −0.179215 0.453315i
\(783\) −5.59724 5.31466i −0.200029 0.189931i
\(784\) −0.959358 −0.0342628