Properties

Label 70.2.c.a.29.4
Level $70$
Weight $2$
Character 70.29
Analytic conductor $0.559$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.558952814149\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.4
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 70.29
Dual form 70.2.c.a.29.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(-0.224745 - 2.22474i) q^{5} -2.44949 q^{6} +1.00000i q^{7} -1.00000i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(-0.224745 - 2.22474i) q^{5} -2.44949 q^{6} +1.00000i q^{7} -1.00000i q^{8} -3.00000 q^{9} +(2.22474 - 0.224745i) q^{10} +4.89898 q^{11} -2.44949i q^{12} -0.449490i q^{13} -1.00000 q^{14} +(5.44949 - 0.550510i) q^{15} +1.00000 q^{16} -2.00000i q^{17} -3.00000i q^{18} -6.44949 q^{19} +(0.224745 + 2.22474i) q^{20} -2.44949 q^{21} +4.89898i q^{22} -6.89898i q^{23} +2.44949 q^{24} +(-4.89898 + 1.00000i) q^{25} +0.449490 q^{26} -1.00000i q^{28} +2.89898 q^{29} +(0.550510 + 5.44949i) q^{30} -0.898979 q^{31} +1.00000i q^{32} +12.0000i q^{33} +2.00000 q^{34} +(2.22474 - 0.224745i) q^{35} +3.00000 q^{36} -2.00000i q^{37} -6.44949i q^{38} +1.10102 q^{39} +(-2.22474 + 0.224745i) q^{40} -10.8990 q^{41} -2.44949i q^{42} +8.89898i q^{43} -4.89898 q^{44} +(0.674235 + 6.67423i) q^{45} +6.89898 q^{46} +0.898979i q^{47} +2.44949i q^{48} -1.00000 q^{49} +(-1.00000 - 4.89898i) q^{50} +4.89898 q^{51} +0.449490i q^{52} -1.10102i q^{53} +(-1.10102 - 10.8990i) q^{55} +1.00000 q^{56} -15.7980i q^{57} +2.89898i q^{58} +6.44949 q^{59} +(-5.44949 + 0.550510i) q^{60} +8.44949 q^{61} -0.898979i q^{62} -3.00000i q^{63} -1.00000 q^{64} +(-1.00000 + 0.101021i) q^{65} -12.0000 q^{66} +8.00000i q^{67} +2.00000i q^{68} +16.8990 q^{69} +(0.224745 + 2.22474i) q^{70} -10.8990 q^{71} +3.00000i q^{72} -6.89898i q^{73} +2.00000 q^{74} +(-2.44949 - 12.0000i) q^{75} +6.44949 q^{76} +4.89898i q^{77} +1.10102i q^{78} +2.89898 q^{79} +(-0.224745 - 2.22474i) q^{80} -9.00000 q^{81} -10.8990i q^{82} +2.44949i q^{83} +2.44949 q^{84} +(-4.44949 + 0.449490i) q^{85} -8.89898 q^{86} +7.10102i q^{87} -4.89898i q^{88} +10.0000 q^{89} +(-6.67423 + 0.674235i) q^{90} +0.449490 q^{91} +6.89898i q^{92} -2.20204i q^{93} -0.898979 q^{94} +(1.44949 + 14.3485i) q^{95} -2.44949 q^{96} +3.79796i q^{97} -1.00000i q^{98} -14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 4 q^{5} - 12 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{4} + 4 q^{5} - 12 q^{9} + 4 q^{10} - 4 q^{14} + 12 q^{15} + 4 q^{16} - 16 q^{19} - 4 q^{20} - 8 q^{26} - 8 q^{29} + 12 q^{30} + 16 q^{31} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 24 q^{39} - 4 q^{40} - 24 q^{41} - 12 q^{45} + 8 q^{46} - 4 q^{49} - 4 q^{50} - 24 q^{55} + 4 q^{56} + 16 q^{59} - 12 q^{60} + 24 q^{61} - 4 q^{64} - 4 q^{65} - 48 q^{66} + 48 q^{69} - 4 q^{70} - 24 q^{71} + 8 q^{74} + 16 q^{76} - 8 q^{79} + 4 q^{80} - 36 q^{81} - 8 q^{85} - 16 q^{86} + 40 q^{89} - 12 q^{90} - 8 q^{91} + 16 q^{94} - 4 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(1\) \(-1\)

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
\(3\) 2.44949i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(4\) −1.00000 −0.500000
\(5\) −0.224745 2.22474i −0.100509 0.994936i
\(6\) −2.44949 −1.00000
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) −3.00000 −1.00000
\(10\) 2.22474 0.224745i 0.703526 0.0710706i
\(11\) 4.89898 1.47710 0.738549 0.674200i \(-0.235511\pi\)
0.738549 + 0.674200i \(0.235511\pi\)
\(12\) 2.44949i 0.707107i
\(13\) 0.449490i 0.124666i −0.998055 0.0623330i \(-0.980146\pi\)
0.998055 0.0623330i \(-0.0198541\pi\)
\(14\) −1.00000 −0.267261
\(15\) 5.44949 0.550510i 1.40705 0.142141i
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 3.00000i 0.707107i
\(19\) −6.44949 −1.47961 −0.739807 0.672819i \(-0.765083\pi\)
−0.739807 + 0.672819i \(0.765083\pi\)
\(20\) 0.224745 + 2.22474i 0.0502545 + 0.497468i
\(21\) −2.44949 −0.534522
\(22\) 4.89898i 1.04447i
\(23\) 6.89898i 1.43854i −0.694732 0.719268i \(-0.744477\pi\)
0.694732 0.719268i \(-0.255523\pi\)
\(24\) 2.44949 0.500000
\(25\) −4.89898 + 1.00000i −0.979796 + 0.200000i
\(26\) 0.449490 0.0881522
\(27\) 0 0
\(28\) 1.00000i 0.188982i
\(29\) 2.89898 0.538327 0.269163 0.963095i \(-0.413253\pi\)
0.269163 + 0.963095i \(0.413253\pi\)
\(30\) 0.550510 + 5.44949i 0.100509 + 0.994936i
\(31\) −0.898979 −0.161461 −0.0807307 0.996736i \(-0.525725\pi\)
−0.0807307 + 0.996736i \(0.525725\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 12.0000i 2.08893i
\(34\) 2.00000 0.342997
\(35\) 2.22474 0.224745i 0.376051 0.0379888i
\(36\) 3.00000 0.500000
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 6.44949i 1.04625i
\(39\) 1.10102 0.176304
\(40\) −2.22474 + 0.224745i −0.351763 + 0.0355353i
\(41\) −10.8990 −1.70213 −0.851067 0.525057i \(-0.824044\pi\)
−0.851067 + 0.525057i \(0.824044\pi\)
\(42\) 2.44949i 0.377964i
\(43\) 8.89898i 1.35708i 0.734563 + 0.678541i \(0.237387\pi\)
−0.734563 + 0.678541i \(0.762613\pi\)
\(44\) −4.89898 −0.738549
\(45\) 0.674235 + 6.67423i 0.100509 + 0.994936i
\(46\) 6.89898 1.01720
\(47\) 0.898979i 0.131130i 0.997848 + 0.0655648i \(0.0208849\pi\)
−0.997848 + 0.0655648i \(0.979115\pi\)
\(48\) 2.44949i 0.353553i
\(49\) −1.00000 −0.142857
\(50\) −1.00000 4.89898i −0.141421 0.692820i
\(51\) 4.89898 0.685994
\(52\) 0.449490i 0.0623330i
\(53\) 1.10102i 0.151237i −0.997137 0.0756184i \(-0.975907\pi\)
0.997137 0.0756184i \(-0.0240931\pi\)
\(54\) 0 0
\(55\) −1.10102 10.8990i −0.148462 1.46962i
\(56\) 1.00000 0.133631
\(57\) 15.7980i 2.09249i
\(58\) 2.89898i 0.380655i
\(59\) 6.44949 0.839652 0.419826 0.907605i \(-0.362091\pi\)
0.419826 + 0.907605i \(0.362091\pi\)
\(60\) −5.44949 + 0.550510i −0.703526 + 0.0710706i
\(61\) 8.44949 1.08185 0.540923 0.841072i \(-0.318075\pi\)
0.540923 + 0.841072i \(0.318075\pi\)
\(62\) 0.898979i 0.114171i
\(63\) 3.00000i 0.377964i
\(64\) −1.00000 −0.125000
\(65\) −1.00000 + 0.101021i −0.124035 + 0.0125301i
\(66\) −12.0000 −1.47710
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 16.8990 2.03440
\(70\) 0.224745 + 2.22474i 0.0268622 + 0.265908i
\(71\) −10.8990 −1.29347 −0.646735 0.762714i \(-0.723866\pi\)
−0.646735 + 0.762714i \(0.723866\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 6.89898i 0.807464i −0.914877 0.403732i \(-0.867713\pi\)
0.914877 0.403732i \(-0.132287\pi\)
\(74\) 2.00000 0.232495
\(75\) −2.44949 12.0000i −0.282843 1.38564i
\(76\) 6.44949 0.739807
\(77\) 4.89898i 0.558291i
\(78\) 1.10102i 0.124666i
\(79\) 2.89898 0.326161 0.163080 0.986613i \(-0.447857\pi\)
0.163080 + 0.986613i \(0.447857\pi\)
\(80\) −0.224745 2.22474i −0.0251272 0.248734i
\(81\) −9.00000 −1.00000
\(82\) 10.8990i 1.20359i
\(83\) 2.44949i 0.268866i 0.990923 + 0.134433i \(0.0429214\pi\)
−0.990923 + 0.134433i \(0.957079\pi\)
\(84\) 2.44949 0.267261
\(85\) −4.44949 + 0.449490i −0.482615 + 0.0487540i
\(86\) −8.89898 −0.959602
\(87\) 7.10102i 0.761309i
\(88\) 4.89898i 0.522233i
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −6.67423 + 0.674235i −0.703526 + 0.0710706i
\(91\) 0.449490 0.0471193
\(92\) 6.89898i 0.719268i
\(93\) 2.20204i 0.228341i
\(94\) −0.898979 −0.0927227
\(95\) 1.44949 + 14.3485i 0.148715 + 1.47212i
\(96\) −2.44949 −0.250000
\(97\) 3.79796i 0.385624i 0.981236 + 0.192812i \(0.0617608\pi\)
−0.981236 + 0.192812i \(0.938239\pi\)
\(98\) 1.00000i 0.101015i
\(99\) −14.6969 −1.47710
\(100\) 4.89898 1.00000i 0.489898 0.100000i
\(101\) 8.44949 0.840756 0.420378 0.907349i \(-0.361898\pi\)
0.420378 + 0.907349i \(0.361898\pi\)
\(102\) 4.89898i 0.485071i
\(103\) 3.10102i 0.305553i 0.988261 + 0.152776i \(0.0488214\pi\)
−0.988261 + 0.152776i \(0.951179\pi\)
\(104\) −0.449490 −0.0440761
\(105\) 0.550510 + 5.44949i 0.0537243 + 0.531816i
\(106\) 1.10102 0.106941
\(107\) 8.00000i 0.773389i 0.922208 + 0.386695i \(0.126383\pi\)
−0.922208 + 0.386695i \(0.873617\pi\)
\(108\) 0 0
\(109\) 2.89898 0.277672 0.138836 0.990315i \(-0.455664\pi\)
0.138836 + 0.990315i \(0.455664\pi\)
\(110\) 10.8990 1.10102i 1.03918 0.104978i
\(111\) 4.89898 0.464991
\(112\) 1.00000i 0.0944911i
\(113\) 0.202041i 0.0190064i 0.999955 + 0.00950321i \(0.00302501\pi\)
−0.999955 + 0.00950321i \(0.996975\pi\)
\(114\) 15.7980 1.47961
\(115\) −15.3485 + 1.55051i −1.43125 + 0.144586i
\(116\) −2.89898 −0.269163
\(117\) 1.34847i 0.124666i
\(118\) 6.44949i 0.593724i
\(119\) 2.00000 0.183340
\(120\) −0.550510 5.44949i −0.0502545 0.497468i
\(121\) 13.0000 1.18182
\(122\) 8.44949i 0.764981i
\(123\) 26.6969i 2.40718i
\(124\) 0.898979 0.0807307
\(125\) 3.32577 + 10.6742i 0.297465 + 0.954733i
\(126\) 3.00000 0.267261
\(127\) 5.10102i 0.452642i 0.974053 + 0.226321i \(0.0726699\pi\)
−0.974053 + 0.226321i \(0.927330\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −21.7980 −1.91920
\(130\) −0.101021 1.00000i −0.00886009 0.0877058i
\(131\) −1.55051 −0.135469 −0.0677344 0.997703i \(-0.521577\pi\)
−0.0677344 + 0.997703i \(0.521577\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 6.44949i 0.559242i
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) 17.7980i 1.52058i −0.649582 0.760291i \(-0.725056\pi\)
0.649582 0.760291i \(-0.274944\pi\)
\(138\) 16.8990i 1.43854i
\(139\) −6.44949 −0.547039 −0.273519 0.961867i \(-0.588188\pi\)
−0.273519 + 0.961867i \(0.588188\pi\)
\(140\) −2.22474 + 0.224745i −0.188025 + 0.0189944i
\(141\) −2.20204 −0.185445
\(142\) 10.8990i 0.914622i
\(143\) 2.20204i 0.184144i
\(144\) −3.00000 −0.250000
\(145\) −0.651531 6.44949i −0.0541067 0.535601i
\(146\) 6.89898 0.570964
\(147\) 2.44949i 0.202031i
\(148\) 2.00000i 0.164399i
\(149\) −15.7980 −1.29422 −0.647110 0.762397i \(-0.724022\pi\)
−0.647110 + 0.762397i \(0.724022\pi\)
\(150\) 12.0000 2.44949i 0.979796 0.200000i
\(151\) −19.5959 −1.59469 −0.797347 0.603522i \(-0.793764\pi\)
−0.797347 + 0.603522i \(0.793764\pi\)
\(152\) 6.44949i 0.523123i
\(153\) 6.00000i 0.485071i
\(154\) −4.89898 −0.394771
\(155\) 0.202041 + 2.00000i 0.0162283 + 0.160644i
\(156\) −1.10102 −0.0881522
\(157\) 8.44949i 0.674343i −0.941443 0.337171i \(-0.890530\pi\)
0.941443 0.337171i \(-0.109470\pi\)
\(158\) 2.89898i 0.230630i
\(159\) 2.69694 0.213881
\(160\) 2.22474 0.224745i 0.175882 0.0177676i
\(161\) 6.89898 0.543716
\(162\) 9.00000i 0.707107i
\(163\) 16.8990i 1.32363i −0.749667 0.661815i \(-0.769786\pi\)
0.749667 0.661815i \(-0.230214\pi\)
\(164\) 10.8990 0.851067
\(165\) 26.6969 2.69694i 2.07835 0.209956i
\(166\) −2.44949 −0.190117
\(167\) 4.89898i 0.379094i −0.981872 0.189547i \(-0.939298\pi\)
0.981872 0.189547i \(-0.0607020\pi\)
\(168\) 2.44949i 0.188982i
\(169\) 12.7980 0.984458
\(170\) −0.449490 4.44949i −0.0344743 0.341260i
\(171\) 19.3485 1.47961
\(172\) 8.89898i 0.678541i
\(173\) 18.2474i 1.38733i 0.720299 + 0.693664i \(0.244005\pi\)
−0.720299 + 0.693664i \(0.755995\pi\)
\(174\) −7.10102 −0.538327
\(175\) −1.00000 4.89898i −0.0755929 0.370328i
\(176\) 4.89898 0.369274
\(177\) 15.7980i 1.18745i
\(178\) 10.0000i 0.749532i
\(179\) 5.79796 0.433360 0.216680 0.976243i \(-0.430477\pi\)
0.216680 + 0.976243i \(0.430477\pi\)
\(180\) −0.674235 6.67423i −0.0502545 0.497468i
\(181\) 14.2474 1.05900 0.529502 0.848309i \(-0.322379\pi\)
0.529502 + 0.848309i \(0.322379\pi\)
\(182\) 0.449490i 0.0333184i
\(183\) 20.6969i 1.52996i
\(184\) −6.89898 −0.508600
\(185\) −4.44949 + 0.449490i −0.327133 + 0.0330471i
\(186\) 2.20204 0.161461
\(187\) 9.79796i 0.716498i
\(188\) 0.898979i 0.0655648i
\(189\) 0 0
\(190\) −14.3485 + 1.44949i −1.04095 + 0.105157i
\(191\) −16.6969 −1.20815 −0.604074 0.796928i \(-0.706457\pi\)
−0.604074 + 0.796928i \(0.706457\pi\)
\(192\) 2.44949i 0.176777i
\(193\) 17.5959i 1.26658i 0.773914 + 0.633291i \(0.218296\pi\)
−0.773914 + 0.633291i \(0.781704\pi\)
\(194\) −3.79796 −0.272678
\(195\) −0.247449 2.44949i −0.0177202 0.175412i
\(196\) 1.00000 0.0714286
\(197\) 9.10102i 0.648421i −0.945985 0.324210i \(-0.894901\pi\)
0.945985 0.324210i \(-0.105099\pi\)
\(198\) 14.6969i 1.04447i
\(199\) −7.10102 −0.503378 −0.251689 0.967808i \(-0.580986\pi\)
−0.251689 + 0.967808i \(0.580986\pi\)
\(200\) 1.00000 + 4.89898i 0.0707107 + 0.346410i
\(201\) −19.5959 −1.38219
\(202\) 8.44949i 0.594504i
\(203\) 2.89898i 0.203468i
\(204\) −4.89898 −0.342997
\(205\) 2.44949 + 24.2474i 0.171080 + 1.69352i
\(206\) −3.10102 −0.216058
\(207\) 20.6969i 1.43854i
\(208\) 0.449490i 0.0311665i
\(209\) −31.5959 −2.18554
\(210\) −5.44949 + 0.550510i −0.376051 + 0.0379888i
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 1.10102i 0.0756184i
\(213\) 26.6969i 1.82924i
\(214\) −8.00000 −0.546869
\(215\) 19.7980 2.00000i 1.35021 0.136399i
\(216\) 0 0
\(217\) 0.898979i 0.0610267i
\(218\) 2.89898i 0.196344i
\(219\) 16.8990 1.14193
\(220\) 1.10102 + 10.8990i 0.0742308 + 0.734809i
\(221\) −0.898979 −0.0604719
\(222\) 4.89898i 0.328798i
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 14.6969 3.00000i 0.979796 0.200000i
\(226\) −0.202041 −0.0134396
\(227\) 7.34847i 0.487735i 0.969809 + 0.243868i \(0.0784162\pi\)
−0.969809 + 0.243868i \(0.921584\pi\)
\(228\) 15.7980i 1.04625i
\(229\) −15.1464 −1.00090 −0.500452 0.865764i \(-0.666833\pi\)
−0.500452 + 0.865764i \(0.666833\pi\)
\(230\) −1.55051 15.3485i −0.102238 1.01205i
\(231\) −12.0000 −0.789542
\(232\) 2.89898i 0.190327i
\(233\) 10.2020i 0.668358i 0.942510 + 0.334179i \(0.108459\pi\)
−0.942510 + 0.334179i \(0.891541\pi\)
\(234\) −1.34847 −0.0881522
\(235\) 2.00000 0.202041i 0.130466 0.0131797i
\(236\) −6.44949 −0.419826
\(237\) 7.10102i 0.461261i
\(238\) 2.00000i 0.129641i
\(239\) 25.7980 1.66873 0.834366 0.551211i \(-0.185834\pi\)
0.834366 + 0.551211i \(0.185834\pi\)
\(240\) 5.44949 0.550510i 0.351763 0.0355353i
\(241\) 20.6969 1.33321 0.666604 0.745412i \(-0.267747\pi\)
0.666604 + 0.745412i \(0.267747\pi\)
\(242\) 13.0000i 0.835672i
\(243\) 22.0454i 1.41421i
\(244\) −8.44949 −0.540923
\(245\) 0.224745 + 2.22474i 0.0143584 + 0.142134i
\(246\) 26.6969 1.70213
\(247\) 2.89898i 0.184458i
\(248\) 0.898979i 0.0570853i
\(249\) −6.00000 −0.380235
\(250\) −10.6742 + 3.32577i −0.675098 + 0.210340i
\(251\) −1.55051 −0.0978673 −0.0489337 0.998802i \(-0.515582\pi\)
−0.0489337 + 0.998802i \(0.515582\pi\)
\(252\) 3.00000i 0.188982i
\(253\) 33.7980i 2.12486i
\(254\) −5.10102 −0.320066
\(255\) −1.10102 10.8990i −0.0689486 0.682521i
\(256\) 1.00000 0.0625000
\(257\) 20.6969i 1.29104i −0.763744 0.645520i \(-0.776641\pi\)
0.763744 0.645520i \(-0.223359\pi\)
\(258\) 21.7980i 1.35708i
\(259\) 2.00000 0.124274
\(260\) 1.00000 0.101021i 0.0620174 0.00626503i
\(261\) −8.69694 −0.538327
\(262\) 1.55051i 0.0957908i
\(263\) 9.79796i 0.604168i −0.953281 0.302084i \(-0.902318\pi\)
0.953281 0.302084i \(-0.0976823\pi\)
\(264\) 12.0000 0.738549
\(265\) −2.44949 + 0.247449i −0.150471 + 0.0152007i
\(266\) 6.44949 0.395444
\(267\) 24.4949i 1.49906i
\(268\) 8.00000i 0.488678i
\(269\) 15.1464 0.923494 0.461747 0.887012i \(-0.347223\pi\)
0.461747 + 0.887012i \(0.347223\pi\)
\(270\) 0 0
\(271\) 12.0000 0.728948 0.364474 0.931214i \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 1.10102i 0.0666368i
\(274\) 17.7980 1.07521
\(275\) −24.0000 + 4.89898i −1.44725 + 0.295420i
\(276\) −16.8990 −1.01720
\(277\) 5.10102i 0.306491i 0.988188 + 0.153245i \(0.0489725\pi\)
−0.988188 + 0.153245i \(0.951028\pi\)
\(278\) 6.44949i 0.386815i
\(279\) 2.69694 0.161461
\(280\) −0.224745 2.22474i −0.0134311 0.132954i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 2.20204i 0.131130i
\(283\) 28.2474i 1.67914i 0.543254 + 0.839568i \(0.317192\pi\)
−0.543254 + 0.839568i \(0.682808\pi\)
\(284\) 10.8990 0.646735
\(285\) −35.1464 + 3.55051i −2.08189 + 0.210314i
\(286\) 2.20204 0.130209
\(287\) 10.8990i 0.643346i
\(288\) 3.00000i 0.176777i
\(289\) 13.0000 0.764706
\(290\) 6.44949 0.651531i 0.378727 0.0382592i
\(291\) −9.30306 −0.545355
\(292\) 6.89898i 0.403732i
\(293\) 6.24745i 0.364980i −0.983208 0.182490i \(-0.941584\pi\)
0.983208 0.182490i \(-0.0584157\pi\)
\(294\) 2.44949 0.142857
\(295\) −1.44949 14.3485i −0.0843926 0.835400i
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 15.7980i 0.915151i
\(299\) −3.10102 −0.179337
\(300\) 2.44949 + 12.0000i 0.141421 + 0.692820i
\(301\) −8.89898 −0.512929
\(302\) 19.5959i 1.12762i
\(303\) 20.6969i 1.18901i
\(304\) −6.44949 −0.369904
\(305\) −1.89898 18.7980i −0.108735 1.07637i
\(306\) −6.00000 −0.342997
\(307\) 4.24745i 0.242415i −0.992627 0.121207i \(-0.961323\pi\)
0.992627 0.121207i \(-0.0386766\pi\)
\(308\) 4.89898i 0.279145i
\(309\) −7.59592 −0.432117
\(310\) −2.00000 + 0.202041i −0.113592 + 0.0114752i
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 1.10102i 0.0623330i
\(313\) 17.5959i 0.994580i 0.867584 + 0.497290i \(0.165672\pi\)
−0.867584 + 0.497290i \(0.834328\pi\)
\(314\) 8.44949 0.476832
\(315\) −6.67423 + 0.674235i −0.376051 + 0.0379888i
\(316\) −2.89898 −0.163080
\(317\) 26.4949i 1.48810i −0.668123 0.744051i \(-0.732902\pi\)
0.668123 0.744051i \(-0.267098\pi\)
\(318\) 2.69694i 0.151237i
\(319\) 14.2020 0.795162
\(320\) 0.224745 + 2.22474i 0.0125636 + 0.124367i
\(321\) −19.5959 −1.09374
\(322\) 6.89898i 0.384465i
\(323\) 12.8990i 0.717718i
\(324\) 9.00000 0.500000
\(325\) 0.449490 + 2.20204i 0.0249332 + 0.122147i
\(326\) 16.8990 0.935948
\(327\) 7.10102i 0.392687i
\(328\) 10.8990i 0.601795i
\(329\) −0.898979 −0.0495623
\(330\) 2.69694 + 26.6969i 0.148462 + 1.46962i
\(331\) 10.6969 0.587957 0.293978 0.955812i \(-0.405021\pi\)
0.293978 + 0.955812i \(0.405021\pi\)
\(332\) 2.44949i 0.134433i
\(333\) 6.00000i 0.328798i
\(334\) 4.89898 0.268060
\(335\) 17.7980 1.79796i 0.972406 0.0982330i
\(336\) −2.44949 −0.133631
\(337\) 29.5959i 1.61219i 0.591785 + 0.806096i \(0.298424\pi\)
−0.591785 + 0.806096i \(0.701576\pi\)
\(338\) 12.7980i 0.696117i
\(339\) −0.494897 −0.0268791
\(340\) 4.44949 0.449490i 0.241307 0.0243770i
\(341\) −4.40408 −0.238494
\(342\) 19.3485i 1.04625i
\(343\) 1.00000i 0.0539949i
\(344\) 8.89898 0.479801
\(345\) −3.79796 37.5959i −0.204475 2.02410i
\(346\) −18.2474 −0.980989
\(347\) 19.1010i 1.02540i −0.858569 0.512698i \(-0.828646\pi\)
0.858569 0.512698i \(-0.171354\pi\)
\(348\) 7.10102i 0.380655i
\(349\) 3.55051 0.190054 0.0950272 0.995475i \(-0.469706\pi\)
0.0950272 + 0.995475i \(0.469706\pi\)
\(350\) 4.89898 1.00000i 0.261861 0.0534522i
\(351\) 0 0
\(352\) 4.89898i 0.261116i
\(353\) 13.1010i 0.697297i 0.937254 + 0.348648i \(0.113359\pi\)
−0.937254 + 0.348648i \(0.886641\pi\)
\(354\) −15.7980 −0.839652
\(355\) 2.44949 + 24.2474i 0.130005 + 1.28692i
\(356\) −10.0000 −0.529999
\(357\) 4.89898i 0.259281i
\(358\) 5.79796i 0.306432i
\(359\) −11.5959 −0.612009 −0.306005 0.952030i \(-0.598992\pi\)
−0.306005 + 0.952030i \(0.598992\pi\)
\(360\) 6.67423 0.674235i 0.351763 0.0355353i
\(361\) 22.5959 1.18926
\(362\) 14.2474i 0.748829i
\(363\) 31.8434i 1.67134i
\(364\) −0.449490 −0.0235597
\(365\) −15.3485 + 1.55051i −0.803376 + 0.0811574i
\(366\) −20.6969 −1.08185
\(367\) 32.0000i 1.67039i −0.549957 0.835193i \(-0.685356\pi\)
0.549957 0.835193i \(-0.314644\pi\)
\(368\) 6.89898i 0.359634i
\(369\) 32.6969 1.70213
\(370\) −0.449490 4.44949i −0.0233679 0.231318i
\(371\) 1.10102 0.0571621
\(372\) 2.20204i 0.114171i
\(373\) 24.6969i 1.27876i 0.768891 + 0.639380i \(0.220809\pi\)
−0.768891 + 0.639380i \(0.779191\pi\)
\(374\) 9.79796 0.506640
\(375\) −26.1464 + 8.14643i −1.35020 + 0.420680i
\(376\) 0.898979 0.0463613
\(377\) 1.30306i 0.0671111i
\(378\) 0 0
\(379\) −1.30306 −0.0669338 −0.0334669 0.999440i \(-0.510655\pi\)
−0.0334669 + 0.999440i \(0.510655\pi\)
\(380\) −1.44949 14.3485i −0.0743573 0.736061i
\(381\) −12.4949 −0.640133
\(382\) 16.6969i 0.854290i
\(383\) 16.8990i 0.863498i −0.901994 0.431749i \(-0.857897\pi\)
0.901994 0.431749i \(-0.142103\pi\)
\(384\) 2.44949 0.125000
\(385\) 10.8990 1.10102i 0.555463 0.0561132i
\(386\) −17.5959 −0.895609
\(387\) 26.6969i 1.35708i
\(388\) 3.79796i 0.192812i
\(389\) −22.8990 −1.16102 −0.580512 0.814252i \(-0.697148\pi\)
−0.580512 + 0.814252i \(0.697148\pi\)
\(390\) 2.44949 0.247449i 0.124035 0.0125301i
\(391\) −13.7980 −0.697793
\(392\) 1.00000i 0.0505076i
\(393\) 3.79796i 0.191582i
\(394\) 9.10102 0.458503
\(395\) −0.651531 6.44949i −0.0327821 0.324509i
\(396\) 14.6969 0.738549
\(397\) 17.3485i 0.870695i 0.900263 + 0.435347i \(0.143374\pi\)
−0.900263 + 0.435347i \(0.856626\pi\)
\(398\) 7.10102i 0.355942i
\(399\) 15.7980 0.790887
\(400\) −4.89898 + 1.00000i −0.244949 + 0.0500000i
\(401\) 29.3939 1.46786 0.733930 0.679225i \(-0.237684\pi\)
0.733930 + 0.679225i \(0.237684\pi\)
\(402\) 19.5959i 0.977356i
\(403\) 0.404082i 0.0201288i
\(404\) −8.44949 −0.420378
\(405\) 2.02270 + 20.0227i 0.100509 + 0.994936i
\(406\) −2.89898 −0.143874
\(407\) 9.79796i 0.485667i
\(408\) 4.89898i 0.242536i
\(409\) 14.4949 0.716727 0.358363 0.933582i \(-0.383335\pi\)
0.358363 + 0.933582i \(0.383335\pi\)
\(410\) −24.2474 + 2.44949i −1.19750 + 0.120972i
\(411\) 43.5959 2.15043
\(412\) 3.10102i 0.152776i
\(413\) 6.44949i 0.317359i
\(414\) −20.6969 −1.01720
\(415\) 5.44949 0.550510i 0.267505 0.0270235i
\(416\) 0.449490 0.0220380
\(417\) 15.7980i 0.773629i
\(418\) 31.5959i 1.54541i
\(419\) 6.44949 0.315078 0.157539 0.987513i \(-0.449644\pi\)
0.157539 + 0.987513i \(0.449644\pi\)
\(420\) −0.550510 5.44949i −0.0268622 0.265908i
\(421\) −23.7980 −1.15984 −0.579921 0.814673i \(-0.696917\pi\)
−0.579921 + 0.814673i \(0.696917\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 2.69694i 0.131130i
\(424\) −1.10102 −0.0534703
\(425\) 2.00000 + 9.79796i 0.0970143 + 0.475271i
\(426\) 26.6969 1.29347
\(427\) 8.44949i 0.408899i
\(428\) 8.00000i 0.386695i
\(429\) 5.39388 0.260419
\(430\) 2.00000 + 19.7980i 0.0964486 + 0.954742i
\(431\) 17.7980 0.857298 0.428649 0.903471i \(-0.358990\pi\)
0.428649 + 0.903471i \(0.358990\pi\)
\(432\) 0 0
\(433\) 19.7980i 0.951429i −0.879600 0.475715i \(-0.842190\pi\)
0.879600 0.475715i \(-0.157810\pi\)
\(434\) 0.898979 0.0431524
\(435\) 15.7980 1.59592i 0.757454 0.0765184i
\(436\) −2.89898 −0.138836
\(437\) 44.4949i 2.12848i
\(438\) 16.8990i 0.807464i
\(439\) −37.3939 −1.78471 −0.892356 0.451332i \(-0.850949\pi\)
−0.892356 + 0.451332i \(0.850949\pi\)
\(440\) −10.8990 + 1.10102i −0.519588 + 0.0524891i
\(441\) 3.00000 0.142857
\(442\) 0.898979i 0.0427601i
\(443\) 9.79796i 0.465515i −0.972535 0.232758i \(-0.925225\pi\)
0.972535 0.232758i \(-0.0747749\pi\)
\(444\) −4.89898 −0.232495
\(445\) −2.24745 22.2474i −0.106539 1.05463i
\(446\) 4.00000 0.189405
\(447\) 38.6969i 1.83030i
\(448\) 1.00000i 0.0472456i
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 3.00000 + 14.6969i 0.141421 + 0.692820i
\(451\) −53.3939 −2.51422
\(452\) 0.202041i 0.00950321i
\(453\) 48.0000i 2.25524i
\(454\) −7.34847 −0.344881
\(455\) −0.101021 1.00000i −0.00473591 0.0468807i
\(456\) −15.7980 −0.739807
\(457\) 9.59592i 0.448878i 0.974488 + 0.224439i \(0.0720550\pi\)
−0.974488 + 0.224439i \(0.927945\pi\)
\(458\) 15.1464i 0.707746i
\(459\) 0 0
\(460\) 15.3485 1.55051i 0.715626 0.0722929i
\(461\) 2.65153 0.123494 0.0617470 0.998092i \(-0.480333\pi\)
0.0617470 + 0.998092i \(0.480333\pi\)
\(462\) 12.0000i 0.558291i
\(463\) 35.5959i 1.65428i −0.561994 0.827141i \(-0.689966\pi\)
0.561994 0.827141i \(-0.310034\pi\)
\(464\) 2.89898 0.134582
\(465\) −4.89898 + 0.494897i −0.227185 + 0.0229503i
\(466\) −10.2020 −0.472600
\(467\) 5.55051i 0.256847i −0.991719 0.128423i \(-0.959008\pi\)
0.991719 0.128423i \(-0.0409917\pi\)
\(468\) 1.34847i 0.0623330i
\(469\) −8.00000 −0.369406
\(470\) 0.202041 + 2.00000i 0.00931946 + 0.0922531i
\(471\) 20.6969 0.953665
\(472\) 6.44949i 0.296862i
\(473\) 43.5959i 2.00454i
\(474\) −7.10102 −0.326161
\(475\) 31.5959 6.44949i 1.44972 0.295923i
\(476\) −2.00000 −0.0916698
\(477\) 3.30306i 0.151237i
\(478\) 25.7980i 1.17997i
\(479\) −38.6969 −1.76811 −0.884054 0.467385i \(-0.845196\pi\)
−0.884054 + 0.467385i \(0.845196\pi\)
\(480\) 0.550510 + 5.44949i 0.0251272 + 0.248734i
\(481\) −0.898979 −0.0409899
\(482\) 20.6969i 0.942720i
\(483\) 16.8990i 0.768930i
\(484\) −13.0000 −0.590909
\(485\) 8.44949 0.853572i 0.383672 0.0387587i
\(486\) 22.0454 1.00000
\(487\) 36.6969i 1.66290i 0.555602 + 0.831449i \(0.312488\pi\)
−0.555602 + 0.831449i \(0.687512\pi\)
\(488\) 8.44949i 0.382490i
\(489\) 41.3939 1.87190
\(490\) −2.22474 + 0.224745i −0.100504 + 0.0101529i
\(491\) −19.5959 −0.884351 −0.442176 0.896928i \(-0.645793\pi\)
−0.442176 + 0.896928i \(0.645793\pi\)
\(492\) 26.6969i 1.20359i
\(493\) 5.79796i 0.261127i
\(494\) −2.89898 −0.130431
\(495\) 3.30306 + 32.6969i 0.148462 + 1.46962i
\(496\) −0.898979 −0.0403654
\(497\) 10.8990i 0.488886i
\(498\) 6.00000i 0.268866i
\(499\) −25.7980 −1.15488 −0.577438 0.816435i \(-0.695947\pi\)
−0.577438 + 0.816435i \(0.695947\pi\)
\(500\) −3.32577 10.6742i −0.148733 0.477366i
\(501\) 12.0000 0.536120
\(502\) 1.55051i 0.0692027i
\(503\) 4.00000i 0.178351i −0.996016 0.0891756i \(-0.971577\pi\)
0.996016 0.0891756i \(-0.0284232\pi\)
\(504\) −3.00000 −0.133631
\(505\) −1.89898 18.7980i −0.0845035 0.836498i
\(506\) 33.7980 1.50250
\(507\) 31.3485i 1.39223i
\(508\) 5.10102i 0.226321i
\(509\) 36.4495 1.61560 0.807798 0.589460i \(-0.200659\pi\)
0.807798 + 0.589460i \(0.200659\pi\)
\(510\) 10.8990 1.10102i 0.482615 0.0487540i
\(511\) 6.89898 0.305193
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 20.6969 0.912903
\(515\) 6.89898 0.696938i 0.304005 0.0307108i
\(516\) 21.7980 0.959602
\(517\) 4.40408i 0.193691i
\(518\) 2.00000i 0.0878750i
\(519\) −44.6969 −1.96198
\(520\) 0.101021 + 1.00000i 0.00443004 + 0.0438529i
\(521\) 3.30306 0.144710 0.0723549 0.997379i \(-0.476949\pi\)
0.0723549 + 0.997379i \(0.476949\pi\)
\(522\) 8.69694i 0.380655i
\(523\) 1.14643i 0.0501298i 0.999686 + 0.0250649i \(0.00797924\pi\)
−0.999686 + 0.0250649i \(0.992021\pi\)
\(524\) 1.55051 0.0677344
\(525\) 12.0000 2.44949i 0.523723 0.106904i
\(526\) 9.79796 0.427211
\(527\) 1.79796i 0.0783203i
\(528\) 12.0000i 0.522233i
\(529\) −24.5959 −1.06939
\(530\) −0.247449 2.44949i −0.0107485 0.106399i
\(531\) −19.3485 −0.839652
\(532\) 6.44949i 0.279621i
\(533\) 4.89898i 0.212198i
\(534\) −24.4949 −1.06000
\(535\) 17.7980 1.79796i 0.769473 0.0777325i
\(536\) 8.00000 0.345547
\(537\) 14.2020i 0.612863i
\(538\) 15.1464i 0.653009i
\(539\) −4.89898 −0.211014
\(540\) 0 0
\(541\) −29.5959 −1.27243 −0.636214 0.771513i \(-0.719500\pi\)
−0.636214 + 0.771513i \(0.719500\pi\)
\(542\) 12.0000i 0.515444i
\(543\) 34.8990i 1.49766i
\(544\) 2.00000 0.0857493
\(545\) −0.651531 6.44949i −0.0279085 0.276266i
\(546\) −1.10102 −0.0471193
\(547\) 10.6969i 0.457368i −0.973501 0.228684i \(-0.926558\pi\)
0.973501 0.228684i \(-0.0734423\pi\)
\(548\) 17.7980i 0.760291i
\(549\) −25.3485 −1.08185
\(550\) −4.89898 24.0000i −0.208893 1.02336i
\(551\) −18.6969 −0.796516
\(552\) 16.8990i 0.719268i
\(553\) 2.89898i 0.123277i
\(554\) −5.10102 −0.216722
\(555\) −1.10102 10.8990i −0.0467357 0.462636i
\(556\) 6.44949 0.273519
\(557\) 16.6969i 0.707472i 0.935345 + 0.353736i \(0.115089\pi\)
−0.935345 + 0.353736i \(0.884911\pi\)
\(558\) 2.69694i 0.114171i
\(559\) 4.00000 0.169182
\(560\) 2.22474 0.224745i 0.0940126 0.00949720i
\(561\) 24.0000 1.01328
\(562\) 18.0000i 0.759284i
\(563\) 14.0454i 0.591943i 0.955197 + 0.295972i \(0.0956434\pi\)
−0.955197 + 0.295972i \(0.904357\pi\)
\(564\) 2.20204 0.0927227
\(565\) 0.449490 0.0454077i 0.0189102 0.00191032i
\(566\) −28.2474 −1.18733
\(567\) 9.00000i 0.377964i
\(568\) 10.8990i 0.457311i
\(569\) −14.2020 −0.595381 −0.297690 0.954663i \(-0.596216\pi\)
−0.297690 + 0.954663i \(0.596216\pi\)
\(570\) −3.55051 35.1464i −0.148715 1.47212i
\(571\) −20.8990 −0.874595 −0.437298 0.899317i \(-0.644064\pi\)
−0.437298 + 0.899317i \(0.644064\pi\)
\(572\) 2.20204i 0.0920720i
\(573\) 40.8990i 1.70858i
\(574\) 10.8990 0.454915
\(575\) 6.89898 + 33.7980i 0.287707 + 1.40947i
\(576\) 3.00000 0.125000
\(577\) 46.4949i 1.93561i −0.251705 0.967804i \(-0.580991\pi\)
0.251705 0.967804i \(-0.419009\pi\)
\(578\) 13.0000i 0.540729i
\(579\) −43.1010 −1.79122
\(580\) 0.651531 + 6.44949i 0.0270533 + 0.267800i
\(581\) −2.44949 −0.101622
\(582\) 9.30306i 0.385624i
\(583\) 5.39388i 0.223392i
\(584\) −6.89898 −0.285482
\(585\) 3.00000 0.303062i 0.124035 0.0125301i
\(586\) 6.24745 0.258080
\(587\) 33.1464i 1.36810i 0.729435 + 0.684050i \(0.239783\pi\)
−0.729435 + 0.684050i \(0.760217\pi\)
\(588\) 2.44949i 0.101015i
\(589\) 5.79796 0.238901
\(590\) 14.3485 1.44949i 0.590717 0.0596745i
\(591\) 22.2929 0.917006
\(592\) 2.00000i 0.0821995i
\(593\) 1.10102i 0.0452135i −0.999744 0.0226067i \(-0.992803\pi\)
0.999744 0.0226067i \(-0.00719656\pi\)
\(594\) 0 0
\(595\) −0.449490 4.44949i −0.0184273 0.182411i
\(596\) 15.7980 0.647110
\(597\) 17.3939i 0.711884i
\(598\) 3.10102i 0.126810i
\(599\) 22.8990 0.935627 0.467813 0.883827i \(-0.345042\pi\)
0.467813 + 0.883827i \(0.345042\pi\)
\(600\) −12.0000 + 2.44949i −0.489898 + 0.100000i
\(601\) 19.3939 0.791093 0.395546 0.918446i \(-0.370555\pi\)
0.395546 + 0.918446i \(0.370555\pi\)
\(602\) 8.89898i 0.362695i
\(603\) 24.0000i 0.977356i
\(604\) 19.5959 0.797347
\(605\) −2.92168 28.9217i −0.118783 1.17583i
\(606\) −20.6969 −0.840756
\(607\) 25.3939i 1.03071i 0.856978 + 0.515353i \(0.172339\pi\)
−0.856978 + 0.515353i \(0.827661\pi\)
\(608\) 6.44949i 0.261561i
\(609\) −7.10102 −0.287748
\(610\) 18.7980 1.89898i 0.761107 0.0768874i
\(611\) 0.404082 0.0163474
\(612\) 6.00000i 0.242536i
\(613\) 8.20204i 0.331277i −0.986187 0.165639i \(-0.947031\pi\)
0.986187 0.165639i \(-0.0529685\pi\)
\(614\) 4.24745 0.171413
\(615\) −59.3939 + 6.00000i −2.39499 + 0.241943i
\(616\) 4.89898 0.197386
\(617\) 9.59592i 0.386317i 0.981168 + 0.193159i \(0.0618732\pi\)
−0.981168 + 0.193159i \(0.938127\pi\)
\(618\) 7.59592i 0.305553i
\(619\) 46.4495 1.86696 0.933481 0.358626i \(-0.116755\pi\)
0.933481 + 0.358626i \(0.116755\pi\)
\(620\) −0.202041 2.00000i −0.00811416 0.0803219i
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) 10.0000i 0.400642i
\(624\) 1.10102 0.0440761
\(625\) 23.0000 9.79796i 0.920000 0.391918i
\(626\) −17.5959 −0.703274
\(627\) 77.3939i 3.09081i
\(628\) 8.44949i 0.337171i
\(629\) −4.00000 −0.159490
\(630\) −0.674235 6.67423i −0.0268622 0.265908i
\(631\) 6.49490 0.258558 0.129279 0.991608i \(-0.458734\pi\)
0.129279 + 0.991608i \(0.458734\pi\)
\(632\) 2.89898i 0.115315i
\(633\) 29.3939i 1.16830i
\(634\) 26.4949 1.05225
\(635\) 11.3485 1.14643i 0.450350 0.0454946i
\(636\) −2.69694 −0.106941
\(637\) 0.449490i 0.0178094i
\(638\) 14.2020i 0.562264i
\(639\) 32.6969 1.29347
\(640\) −2.22474 + 0.224745i −0.0879408 + 0.00888382i
\(641\) 6.20204 0.244966 0.122483 0.992471i \(-0.460914\pi\)
0.122483 + 0.992471i \(0.460914\pi\)
\(642\) 19.5959i 0.773389i
\(643\) 9.14643i 0.360700i −0.983603 0.180350i \(-0.942277\pi\)
0.983603 0.180350i \(-0.0577230\pi\)
\(644\) −6.89898 −0.271858
\(645\) 4.89898 + 48.4949i 0.192897 + 1.90948i
\(646\) −12.8990 −0.507504
\(647\) 22.2929i 0.876423i −0.898872 0.438211i \(-0.855612\pi\)
0.898872 0.438211i \(-0.144388\pi\)
\(648\) 9.00000i 0.353553i
\(649\) 31.5959 1.24025
\(650\) −2.20204 + 0.449490i −0.0863712 + 0.0176304i
\(651\) 2.20204 0.0863048
\(652\) 16.8990i 0.661815i
\(653\) 39.7980i 1.55741i −0.627387 0.778707i \(-0.715876\pi\)
0.627387 0.778707i \(-0.284124\pi\)
\(654\) −7.10102 −0.277672
\(655\) 0.348469 + 3.44949i 0.0136158 + 0.134783i
\(656\) −10.8990 −0.425534
\(657\) 20.6969i 0.807464i
\(658\) 0.898979i 0.0350459i
\(659\) −7.10102 −0.276616 −0.138308 0.990389i \(-0.544166\pi\)
−0.138308 + 0.990389i \(0.544166\pi\)
\(660\) −26.6969 + 2.69694i −1.03918 + 0.104978i
\(661\) 12.9444 0.503478 0.251739 0.967795i \(-0.418997\pi\)
0.251739 + 0.967795i \(0.418997\pi\)
\(662\) 10.6969i 0.415748i
\(663\) 2.20204i 0.0855202i
\(664\) 2.44949 0.0950586
\(665\) −14.3485 + 1.44949i −0.556410 + 0.0562088i
\(666\) −6.00000 −0.232495
\(667\) 20.0000i 0.774403i
\(668\) 4.89898i 0.189547i
\(669\) 9.79796 0.378811
\(670\) 1.79796 + 17.7980i 0.0694612 + 0.687595i
\(671\) 41.3939 1.59799
\(672\) 2.44949i 0.0944911i
\(673\) 1.79796i 0.0693062i 0.999399 + 0.0346531i \(0.0110326\pi\)
−0.999399 + 0.0346531i \(0.988967\pi\)
\(674\) −29.5959 −1.13999
\(675\) 0 0
\(676\) −12.7980 −0.492229
\(677\) 31.5505i 1.21258i 0.795242 + 0.606292i \(0.207344\pi\)
−0.795242 + 0.606292i \(0.792656\pi\)
\(678\) 0.494897i 0.0190064i
\(679\) −3.79796 −0.145752
\(680\) 0.449490 + 4.44949i 0.0172371 + 0.170630i
\(681\) −18.0000 −0.689761
\(682\) 4.40408i 0.168641i
\(683\) 35.5959i 1.36204i −0.732265 0.681020i \(-0.761537\pi\)
0.732265 0.681020i \(-0.238463\pi\)
\(684\) −19.3485 −0.739807
\(685\) −39.5959 + 4.00000i −1.51288 + 0.152832i
\(686\) 1.00000 0.0381802
\(687\) 37.1010i 1.41549i
\(688\) 8.89898i 0.339270i
\(689\) −0.494897 −0.0188541
\(690\) 37.5959 3.79796i 1.43125 0.144586i
\(691\) −13.1464 −0.500114 −0.250057 0.968231i \(-0.580449\pi\)
−0.250057 + 0.968231i \(0.580449\pi\)
\(692\) 18.2474i 0.693664i
\(693\) 14.6969i 0.558291i
\(694\) 19.1010 0.725065
\(695\) 1.44949 + 14.3485i 0.0549823 + 0.544268i
\(696\) 7.10102 0.269163
\(697\) 21.7980i 0.825657i
\(698\) 3.55051i 0.134389i
\(699\) −24.9898 −0.945201
\(700\) 1.00000 + 4.89898i 0.0377964 + 0.185164i
\(701\) 40.6969 1.53710 0.768551 0.639788i \(-0.220978\pi\)
0.768551 + 0.639788i \(0.220978\pi\)
\(702\) 0 0
\(703\) 12.8990i 0.486494i
\(704\) −4.89898 −0.184637
\(705\) 0.494897 + 4.89898i 0.0186389 + 0.184506i
\(706\) −13.1010 −0.493063
\(707\) 8.44949i 0.317776i
\(708\) 15.7980i 0.593724i
\(709\) −40.2929 −1.51323 −0.756615 0.653861i \(-0.773148\pi\)
−0.756615 + 0.653861i \(0.773148\pi\)
\(710\) −24.2474 + 2.44949i −0.909991 + 0.0919277i
\(711\) −8.69694 −0.326161
\(712\) 10.0000i 0.374766i
\(713\) 6.20204i 0.232268i
\(714\) −4.89898 −0.183340
\(715\) −4.89898 + 0.494897i −0.183211 + 0.0185081i
\(716\) −5.79796 −0.216680
\(717\) 63.1918i 2.35994i
\(718\) 11.5959i 0.432756i
\(719\) −44.4949 −1.65938 −0.829690 0.558225i \(-0.811483\pi\)
−0.829690 + 0.558225i \(0.811483\pi\)
\(720\) 0.674235 + 6.67423i 0.0251272 + 0.248734i
\(721\) −3.10102 −0.115488
\(722\) 22.5959i 0.840933i
\(723\) 50.6969i 1.88544i
\(724\) −14.2474 −0.529502
\(725\) −14.2020 + 2.89898i −0.527451 + 0.107665i
\(726\) −31.8434 −1.18182
\(727\) 6.69694i 0.248376i 0.992259 + 0.124188i \(0.0396325\pi\)
−0.992259 + 0.124188i \(0.960367\pi\)
\(728\) 0.449490i 0.0166592i
\(729\) 27.0000 1.00000
\(730\) −1.55051 15.3485i −0.0573870 0.568072i
\(731\) 17.7980 0.658281
\(732\) 20.6969i 0.764981i
\(733\) 43.6413i 1.61193i −0.591964 0.805965i \(-0.701647\pi\)
0.591964 0.805965i \(-0.298353\pi\)
\(734\) 32.0000 1.18114
\(735\) −5.44949 + 0.550510i −0.201007 + 0.0203059i
\(736\) 6.89898 0.254300
\(737\) 39.1918i 1.44365i
\(738\) 32.6969i 1.20359i
\(739\) 44.4949 1.63677 0.818386 0.574669i \(-0.194869\pi\)
0.818386 + 0.574669i \(0.194869\pi\)
\(740\) 4.44949 0.449490i 0.163566 0.0165236i
\(741\) −7.10102 −0.260863
\(742\) 1.10102i 0.0404197i
\(743\) 15.3031i 0.561415i −0.959793 0.280707i \(-0.909431\pi\)
0.959793 0.280707i \(-0.0905691\pi\)
\(744\) −2.20204 −0.0807307
\(745\) 3.55051 + 35.1464i 0.130081 + 1.28767i
\(746\) −24.6969 −0.904219
\(747\) 7.34847i 0.268866i
\(748\) 9.79796i 0.358249i
\(749\) −8.00000 −0.292314
\(750\) −8.14643 26.1464i −0.297465 0.954733i
\(751\) −22.2020 −0.810164 −0.405082 0.914280i \(-0.632757\pi\)
−0.405082 + 0.914280i \(0.632757\pi\)
\(752\) 0.898979i 0.0327824i
\(753\) 3.79796i 0.138405i
\(754\) 1.30306 0.0474547
\(755\) 4.40408 + 43.5959i 0.160281 + 1.58662i
\(756\) 0 0
\(757\) 32.2020i 1.17040i 0.810888 + 0.585202i \(0.198985\pi\)
−0.810888 + 0.585202i \(0.801015\pi\)
\(758\) 1.30306i 0.0473293i
\(759\) 82.7878 3.00501
\(760\) 14.3485 1.44949i 0.520474 0.0525785i
\(761\) −30.8990 −1.12009 −0.560044 0.828463i \(-0.689216\pi\)
−0.560044 + 0.828463i \(0.689216\pi\)
\(762\) 12.4949i 0.452642i
\(763\) 2.89898i 0.104950i
\(764\) 16.6969 0.604074
\(765\) 13.3485 1.34847i 0.482615 0.0487540i
\(766\) 16.8990 0.610585
\(767\) 2.89898i 0.104676i
\(768\) 2.44949i 0.0883883i
\(769\) 11.3031 0.407599 0.203799 0.979013i \(-0.434671\pi\)
0.203799 + 0.979013i \(0.434671\pi\)
\(770\) 1.10102 + 10.8990i 0.0396780 + 0.392772i
\(771\) 50.6969 1.82581
\(772\) 17.5959i 0.633291i
\(773\) 13.3485i 0.480111i −0.970759 0.240056i \(-0.922834\pi\)
0.970759 0.240056i \(-0.0771657\pi\)
\(774\) 26.6969 0.959602
\(775\) 4.40408 0.898979i 0.158199 0.0322923i
\(776\) 3.79796 0.136339
\(777\) 4.89898i 0.175750i
\(778\) 22.8990i 0.820968i
\(779\) 70.2929 2.51850
\(780\) 0.247449 + 2.44949i 0.00886009 + 0.0877058i
\(781\) −53.3939 −1.91058
\(782\) 13.7980i 0.493414i
\(783\) 0 0
\(784\) −1.00000 −0.0357143
\(785\) −18.7980 + 1.89898i −0.670928 + 0.0677775i
\(786\) 3.79796 0.135469
\(787\) 45.5505i 1.62370i −0.583866 0.811850i \(-0.698461\pi\)
0.583866 0.811850i \(-0.301539\pi\)
\(788\)