Properties

Label 70.2.c.a.29.2
Level $70$
Weight $2$
Character 70.29
Analytic conductor $0.559$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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 29.2
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 70.29
Dual form 70.2.c.a.29.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(2.22474 - 0.224745i) q^{5} +2.44949 q^{6} -1.00000i q^{7} +1.00000i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(2.22474 - 0.224745i) q^{5} +2.44949 q^{6} -1.00000i q^{7} +1.00000i q^{8} -3.00000 q^{9} +(-0.224745 - 2.22474i) q^{10} -4.89898 q^{11} -2.44949i q^{12} -4.44949i q^{13} -1.00000 q^{14} +(0.550510 + 5.44949i) q^{15} +1.00000 q^{16} +2.00000i q^{17} +3.00000i q^{18} -1.55051 q^{19} +(-2.22474 + 0.224745i) q^{20} +2.44949 q^{21} +4.89898i q^{22} -2.89898i q^{23} -2.44949 q^{24} +(4.89898 - 1.00000i) q^{25} -4.44949 q^{26} +1.00000i q^{28} -6.89898 q^{29} +(5.44949 - 0.550510i) q^{30} +8.89898 q^{31} -1.00000i q^{32} -12.0000i q^{33} +2.00000 q^{34} +(-0.224745 - 2.22474i) q^{35} +3.00000 q^{36} +2.00000i q^{37} +1.55051i q^{38} +10.8990 q^{39} +(0.224745 + 2.22474i) q^{40} -1.10102 q^{41} -2.44949i q^{42} +0.898979i q^{43} +4.89898 q^{44} +(-6.67423 + 0.674235i) q^{45} -2.89898 q^{46} +8.89898i q^{47} +2.44949i q^{48} -1.00000 q^{49} +(-1.00000 - 4.89898i) q^{50} -4.89898 q^{51} +4.44949i q^{52} +10.8990i q^{53} +(-10.8990 + 1.10102i) q^{55} +1.00000 q^{56} -3.79796i q^{57} +6.89898i q^{58} +1.55051 q^{59} +(-0.550510 - 5.44949i) q^{60} +3.55051 q^{61} -8.89898i q^{62} +3.00000i q^{63} -1.00000 q^{64} +(-1.00000 - 9.89898i) q^{65} -12.0000 q^{66} -8.00000i q^{67} -2.00000i q^{68} +7.10102 q^{69} +(-2.22474 + 0.224745i) q^{70} -1.10102 q^{71} -3.00000i q^{72} -2.89898i q^{73} +2.00000 q^{74} +(2.44949 + 12.0000i) q^{75} +1.55051 q^{76} +4.89898i q^{77} -10.8990i q^{78} -6.89898 q^{79} +(2.22474 - 0.224745i) q^{80} -9.00000 q^{81} +1.10102i q^{82} +2.44949i q^{83} -2.44949 q^{84} +(0.449490 + 4.44949i) q^{85} +0.898979 q^{86} -16.8990i q^{87} -4.89898i q^{88} +10.0000 q^{89} +(0.674235 + 6.67423i) q^{90} -4.44949 q^{91} +2.89898i q^{92} +21.7980i q^{93} +8.89898 q^{94} +(-3.44949 + 0.348469i) q^{95} +2.44949 q^{96} +15.7980i q^{97} +1.00000i q^{98} +14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + 4q^{5} - 12q^{9} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{5} - 12q^{9} + 4q^{10} - 4q^{14} + 12q^{15} + 4q^{16} - 16q^{19} - 4q^{20} - 8q^{26} - 8q^{29} + 12q^{30} + 16q^{31} + 8q^{34} + 4q^{35} + 12q^{36} + 24q^{39} - 4q^{40} - 24q^{41} - 12q^{45} + 8q^{46} - 4q^{49} - 4q^{50} - 24q^{55} + 4q^{56} + 16q^{59} - 12q^{60} + 24q^{61} - 4q^{64} - 4q^{65} - 48q^{66} + 48q^{69} - 4q^{70} - 24q^{71} + 8q^{74} + 16q^{76} - 8q^{79} + 4q^{80} - 36q^{81} - 8q^{85} - 16q^{86} + 40q^{89} - 12q^{90} - 8q^{91} + 16q^{94} - 4q^{95} + O(q^{100}) \)

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
\(5\) 2.22474 0.224745i 0.994936 0.100509i
\(6\) 2.44949 1.00000
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) −3.00000 −1.00000
\(10\) −0.224745 2.22474i −0.0710706 0.703526i
\(11\) −4.89898 −1.47710 −0.738549 0.674200i \(-0.764489\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 2.44949i 0.707107i
\(13\) 4.44949i 1.23407i −0.786937 0.617033i \(-0.788334\pi\)
0.786937 0.617033i \(-0.211666\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0.550510 + 5.44949i 0.142141 + 1.40705i
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 3.00000i 0.707107i
\(19\) −1.55051 −0.355711 −0.177856 0.984057i \(-0.556916\pi\)
−0.177856 + 0.984057i \(0.556916\pi\)
\(20\) −2.22474 + 0.224745i −0.497468 + 0.0502545i
\(21\) 2.44949 0.534522
\(22\) 4.89898i 1.04447i
\(23\) 2.89898i 0.604479i −0.953232 0.302240i \(-0.902266\pi\)
0.953232 0.302240i \(-0.0977342\pi\)
\(24\) −2.44949 −0.500000
\(25\) 4.89898 1.00000i 0.979796 0.200000i
\(26\) −4.44949 −0.872617
\(27\) 0 0
\(28\) 1.00000i 0.188982i
\(29\) −6.89898 −1.28111 −0.640554 0.767913i \(-0.721295\pi\)
−0.640554 + 0.767913i \(0.721295\pi\)
\(30\) 5.44949 0.550510i 0.994936 0.100509i
\(31\) 8.89898 1.59830 0.799152 0.601129i \(-0.205282\pi\)
0.799152 + 0.601129i \(0.205282\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 12.0000i 2.08893i
\(34\) 2.00000 0.342997
\(35\) −0.224745 2.22474i −0.0379888 0.376051i
\(36\) 3.00000 0.500000
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 1.55051i 0.251526i
\(39\) 10.8990 1.74523
\(40\) 0.224745 + 2.22474i 0.0355353 + 0.351763i
\(41\) −1.10102 −0.171951 −0.0859753 0.996297i \(-0.527401\pi\)
−0.0859753 + 0.996297i \(0.527401\pi\)
\(42\) 2.44949i 0.377964i
\(43\) 0.898979i 0.137093i 0.997648 + 0.0685465i \(0.0218362\pi\)
−0.997648 + 0.0685465i \(0.978164\pi\)
\(44\) 4.89898 0.738549
\(45\) −6.67423 + 0.674235i −0.994936 + 0.100509i
\(46\) −2.89898 −0.427431
\(47\) 8.89898i 1.29805i 0.760767 + 0.649025i \(0.224823\pi\)
−0.760767 + 0.649025i \(0.775177\pi\)
\(48\) 2.44949i 0.353553i
\(49\) −1.00000 −0.142857
\(50\) −1.00000 4.89898i −0.141421 0.692820i
\(51\) −4.89898 −0.685994
\(52\) 4.44949i 0.617033i
\(53\) 10.8990i 1.49709i 0.663084 + 0.748545i \(0.269247\pi\)
−0.663084 + 0.748545i \(0.730753\pi\)
\(54\) 0 0
\(55\) −10.8990 + 1.10102i −1.46962 + 0.148462i
\(56\) 1.00000 0.133631
\(57\) 3.79796i 0.503052i
\(58\) 6.89898i 0.905880i
\(59\) 1.55051 0.201859 0.100930 0.994894i \(-0.467818\pi\)
0.100930 + 0.994894i \(0.467818\pi\)
\(60\) −0.550510 5.44949i −0.0710706 0.703526i
\(61\) 3.55051 0.454596 0.227298 0.973825i \(-0.427011\pi\)
0.227298 + 0.973825i \(0.427011\pi\)
\(62\) 8.89898i 1.13017i
\(63\) 3.00000i 0.377964i
\(64\) −1.00000 −0.125000
\(65\) −1.00000 9.89898i −0.124035 1.22782i
\(66\) −12.0000 −1.47710
\(67\) 8.00000i 0.977356i −0.872464 0.488678i \(-0.837479\pi\)
0.872464 0.488678i \(-0.162521\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 7.10102 0.854862
\(70\) −2.22474 + 0.224745i −0.265908 + 0.0268622i
\(71\) −1.10102 −0.130667 −0.0653335 0.997863i \(-0.520811\pi\)
−0.0653335 + 0.997863i \(0.520811\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 2.89898i 0.339300i −0.985504 0.169650i \(-0.945736\pi\)
0.985504 0.169650i \(-0.0542637\pi\)
\(74\) 2.00000 0.232495
\(75\) 2.44949 + 12.0000i 0.282843 + 1.38564i
\(76\) 1.55051 0.177856
\(77\) 4.89898i 0.558291i
\(78\) 10.8990i 1.23407i
\(79\) −6.89898 −0.776196 −0.388098 0.921618i \(-0.626868\pi\)
−0.388098 + 0.921618i \(0.626868\pi\)
\(80\) 2.22474 0.224745i 0.248734 0.0251272i
\(81\) −9.00000 −1.00000
\(82\) 1.10102i 0.121587i
\(83\) 2.44949i 0.268866i 0.990923 + 0.134433i \(0.0429214\pi\)
−0.990923 + 0.134433i \(0.957079\pi\)
\(84\) −2.44949 −0.267261
\(85\) 0.449490 + 4.44949i 0.0487540 + 0.482615i
\(86\) 0.898979 0.0969395
\(87\) 16.8990i 1.81176i
\(88\) 4.89898i 0.522233i
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0.674235 + 6.67423i 0.0710706 + 0.703526i
\(91\) −4.44949 −0.466433
\(92\) 2.89898i 0.302240i
\(93\) 21.7980i 2.26034i
\(94\) 8.89898 0.917860
\(95\) −3.44949 + 0.348469i −0.353910 + 0.0357522i
\(96\) 2.44949 0.250000
\(97\) 15.7980i 1.60404i 0.597297 + 0.802020i \(0.296241\pi\)
−0.597297 + 0.802020i \(0.703759\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 14.6969 1.47710
\(100\) −4.89898 + 1.00000i −0.489898 + 0.100000i
\(101\) 3.55051 0.353289 0.176644 0.984275i \(-0.443476\pi\)
0.176644 + 0.984275i \(0.443476\pi\)
\(102\) 4.89898i 0.485071i
\(103\) 12.8990i 1.27097i −0.772111 0.635487i \(-0.780799\pi\)
0.772111 0.635487i \(-0.219201\pi\)
\(104\) 4.44949 0.436308
\(105\) 5.44949 0.550510i 0.531816 0.0537243i
\(106\) 10.8990 1.05860
\(107\) 8.00000i 0.773389i −0.922208 0.386695i \(-0.873617\pi\)
0.922208 0.386695i \(-0.126383\pi\)
\(108\) 0 0
\(109\) −6.89898 −0.660802 −0.330401 0.943841i \(-0.607184\pi\)
−0.330401 + 0.943841i \(0.607184\pi\)
\(110\) 1.10102 + 10.8990i 0.104978 + 1.03918i
\(111\) −4.89898 −0.464991
\(112\) 1.00000i 0.0944911i
\(113\) 19.7980i 1.86244i −0.364464 0.931218i \(-0.618748\pi\)
0.364464 0.931218i \(-0.381252\pi\)
\(114\) −3.79796 −0.355711
\(115\) −0.651531 6.44949i −0.0607556 0.601418i
\(116\) 6.89898 0.640554
\(117\) 13.3485i 1.23407i
\(118\) 1.55051i 0.142736i
\(119\) 2.00000 0.183340
\(120\) −5.44949 + 0.550510i −0.497468 + 0.0502545i
\(121\) 13.0000 1.18182
\(122\) 3.55051i 0.321448i
\(123\) 2.69694i 0.243175i
\(124\) −8.89898 −0.799152
\(125\) 10.6742 3.32577i 0.954733 0.297465i
\(126\) 3.00000 0.267261
\(127\) 14.8990i 1.32207i −0.750355 0.661035i \(-0.770117\pi\)
0.750355 0.661035i \(-0.229883\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −2.20204 −0.193879
\(130\) −9.89898 + 1.00000i −0.868198 + 0.0877058i
\(131\) −6.44949 −0.563495 −0.281747 0.959489i \(-0.590914\pi\)
−0.281747 + 0.959489i \(0.590914\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 1.55051i 0.134446i
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) 1.79796i 0.153610i −0.997046 0.0768050i \(-0.975528\pi\)
0.997046 0.0768050i \(-0.0244719\pi\)
\(138\) 7.10102i 0.604479i
\(139\) −1.55051 −0.131513 −0.0657563 0.997836i \(-0.520946\pi\)
−0.0657563 + 0.997836i \(0.520946\pi\)
\(140\) 0.224745 + 2.22474i 0.0189944 + 0.188025i
\(141\) −21.7980 −1.83572
\(142\) 1.10102i 0.0923956i
\(143\) 21.7980i 1.82284i
\(144\) −3.00000 −0.250000
\(145\) −15.3485 + 1.55051i −1.27462 + 0.128763i
\(146\) −2.89898 −0.239921
\(147\) 2.44949i 0.202031i
\(148\) 2.00000i 0.164399i
\(149\) 3.79796 0.311141 0.155570 0.987825i \(-0.450278\pi\)
0.155570 + 0.987825i \(0.450278\pi\)
\(150\) 12.0000 2.44949i 0.979796 0.200000i
\(151\) 19.5959 1.59469 0.797347 0.603522i \(-0.206236\pi\)
0.797347 + 0.603522i \(0.206236\pi\)
\(152\) 1.55051i 0.125763i
\(153\) 6.00000i 0.485071i
\(154\) 4.89898 0.394771
\(155\) 19.7980 2.00000i 1.59021 0.160644i
\(156\) −10.8990 −0.872617
\(157\) 3.55051i 0.283362i 0.989912 + 0.141681i \(0.0452507\pi\)
−0.989912 + 0.141681i \(0.954749\pi\)
\(158\) 6.89898i 0.548853i
\(159\) −26.6969 −2.11720
\(160\) −0.224745 2.22474i −0.0177676 0.175882i
\(161\) −2.89898 −0.228472
\(162\) 9.00000i 0.707107i
\(163\) 7.10102i 0.556195i 0.960553 + 0.278097i \(0.0897038\pi\)
−0.960553 + 0.278097i \(0.910296\pi\)
\(164\) 1.10102 0.0859753
\(165\) −2.69694 26.6969i −0.209956 2.07835i
\(166\) 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
\(169\) −6.79796 −0.522920
\(170\) 4.44949 0.449490i 0.341260 0.0344743i
\(171\) 4.65153 0.355711
\(172\) 0.898979i 0.0685465i
\(173\) 6.24745i 0.474985i 0.971389 + 0.237492i \(0.0763255\pi\)
−0.971389 + 0.237492i \(0.923675\pi\)
\(174\) −16.8990 −1.28111
\(175\) −1.00000 4.89898i −0.0755929 0.370328i
\(176\) −4.89898 −0.369274
\(177\) 3.79796i 0.285472i
\(178\) 10.0000i 0.749532i
\(179\) −13.7980 −1.03131 −0.515654 0.856797i \(-0.672451\pi\)
−0.515654 + 0.856797i \(0.672451\pi\)
\(180\) 6.67423 0.674235i 0.497468 0.0502545i
\(181\) −10.2474 −0.761687 −0.380843 0.924640i \(-0.624366\pi\)
−0.380843 + 0.924640i \(0.624366\pi\)
\(182\) 4.44949i 0.329818i
\(183\) 8.69694i 0.642896i
\(184\) 2.89898 0.213716
\(185\) 0.449490 + 4.44949i 0.0330471 + 0.327133i
\(186\) 21.7980 1.59830
\(187\) 9.79796i 0.716498i
\(188\) 8.89898i 0.649025i
\(189\) 0 0
\(190\) 0.348469 + 3.44949i 0.0252806 + 0.250252i
\(191\) 12.6969 0.918718 0.459359 0.888251i \(-0.348079\pi\)
0.459359 + 0.888251i \(0.348079\pi\)
\(192\) 2.44949i 0.176777i
\(193\) 21.5959i 1.55451i 0.629187 + 0.777254i \(0.283388\pi\)
−0.629187 + 0.777254i \(0.716612\pi\)
\(194\) 15.7980 1.13423
\(195\) 24.2474 2.44949i 1.73640 0.175412i
\(196\) 1.00000 0.0714286
\(197\) 18.8990i 1.34650i 0.739417 + 0.673248i \(0.235101\pi\)
−0.739417 + 0.673248i \(0.764899\pi\)
\(198\) 14.6969i 1.04447i
\(199\) −16.8990 −1.19794 −0.598968 0.800773i \(-0.704423\pi\)
−0.598968 + 0.800773i \(0.704423\pi\)
\(200\) 1.00000 + 4.89898i 0.0707107 + 0.346410i
\(201\) 19.5959 1.38219
\(202\) 3.55051i 0.249813i
\(203\) 6.89898i 0.484213i
\(204\) 4.89898 0.342997
\(205\) −2.44949 + 0.247449i −0.171080 + 0.0172826i
\(206\) −12.8990 −0.898714
\(207\) 8.69694i 0.604479i
\(208\) 4.44949i 0.308517i
\(209\) 7.59592 0.525421
\(210\) −0.550510 5.44949i −0.0379888 0.376051i
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 10.8990i 0.748545i
\(213\) 2.69694i 0.184791i
\(214\) −8.00000 −0.546869
\(215\) 0.202041 + 2.00000i 0.0137791 + 0.136399i
\(216\) 0 0
\(217\) 8.89898i 0.604102i
\(218\) 6.89898i 0.467258i
\(219\) 7.10102 0.479842
\(220\) 10.8990 1.10102i 0.734809 0.0742308i
\(221\) 8.89898 0.598610
\(222\) 4.89898i 0.328798i
\(223\) 4.00000i 0.267860i 0.990991 + 0.133930i \(0.0427597\pi\)
−0.990991 + 0.133930i \(0.957240\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −14.6969 + 3.00000i −0.979796 + 0.200000i
\(226\) −19.7980 −1.31694
\(227\) 7.34847i 0.487735i 0.969809 + 0.243868i \(0.0784162\pi\)
−0.969809 + 0.243868i \(0.921584\pi\)
\(228\) 3.79796i 0.251526i
\(229\) 19.1464 1.26523 0.632616 0.774466i \(-0.281981\pi\)
0.632616 + 0.774466i \(0.281981\pi\)
\(230\) −6.44949 + 0.651531i −0.425267 + 0.0429607i
\(231\) −12.0000 −0.789542
\(232\) 6.89898i 0.452940i
\(233\) 29.7980i 1.95213i −0.217481 0.976065i \(-0.569784\pi\)
0.217481 0.976065i \(-0.430216\pi\)
\(234\) 13.3485 0.872617
\(235\) 2.00000 + 19.7980i 0.130466 + 1.29148i
\(236\) −1.55051 −0.100930
\(237\) 16.8990i 1.09771i
\(238\) 2.00000i 0.129641i
\(239\) 6.20204 0.401177 0.200588 0.979676i \(-0.435715\pi\)
0.200588 + 0.979676i \(0.435715\pi\)
\(240\) 0.550510 + 5.44949i 0.0355353 + 0.351763i
\(241\) −8.69694 −0.560219 −0.280110 0.959968i \(-0.590371\pi\)
−0.280110 + 0.959968i \(0.590371\pi\)
\(242\) 13.0000i 0.835672i
\(243\) 22.0454i 1.41421i
\(244\) −3.55051 −0.227298
\(245\) −2.22474 + 0.224745i −0.142134 + 0.0143584i
\(246\) −2.69694 −0.171951
\(247\) 6.89898i 0.438972i
\(248\) 8.89898i 0.565086i
\(249\) −6.00000 −0.380235
\(250\) −3.32577 10.6742i −0.210340 0.675098i
\(251\) −6.44949 −0.407088 −0.203544 0.979066i \(-0.565246\pi\)
−0.203544 + 0.979066i \(0.565246\pi\)
\(252\) 3.00000i 0.188982i
\(253\) 14.2020i 0.892875i
\(254\) −14.8990 −0.934845
\(255\) −10.8990 + 1.10102i −0.682521 + 0.0689486i
\(256\) 1.00000 0.0625000
\(257\) 8.69694i 0.542500i −0.962509 0.271250i \(-0.912563\pi\)
0.962509 0.271250i \(-0.0874370\pi\)
\(258\) 2.20204i 0.137093i
\(259\) 2.00000 0.124274
\(260\) 1.00000 + 9.89898i 0.0620174 + 0.613909i
\(261\) 20.6969 1.28111
\(262\) 6.44949i 0.398451i
\(263\) 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 + 24.2474i 0.150471 + 1.48951i
\(266\) 1.55051 0.0950679
\(267\) 24.4949i 1.49906i
\(268\) 8.00000i 0.488678i
\(269\) −19.1464 −1.16738 −0.583689 0.811977i \(-0.698391\pi\)
−0.583689 + 0.811977i \(0.698391\pi\)
\(270\) 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
\(273\) 10.8990i 0.659636i
\(274\) −1.79796 −0.108619
\(275\) −24.0000 + 4.89898i −1.44725 + 0.295420i
\(276\) −7.10102 −0.427431
\(277\) 14.8990i 0.895193i −0.894236 0.447596i \(-0.852280\pi\)
0.894236 0.447596i \(-0.147720\pi\)
\(278\) 1.55051i 0.0929934i
\(279\) −26.6969 −1.59830
\(280\) 2.22474 0.224745i 0.132954 0.0134311i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 21.7980i 1.29805i
\(283\) 3.75255i 0.223066i −0.993761 0.111533i \(-0.964424\pi\)
0.993761 0.111533i \(-0.0355761\pi\)
\(284\) 1.10102 0.0653335
\(285\) −0.853572 8.44949i −0.0505612 0.500505i
\(286\) 21.7980 1.28894
\(287\) 1.10102i 0.0649912i
\(288\) 3.00000i 0.176777i
\(289\) 13.0000 0.764706
\(290\) 1.55051 + 15.3485i 0.0910491 + 0.901293i
\(291\) −38.6969 −2.26845
\(292\) 2.89898i 0.169650i
\(293\) 18.2474i 1.06603i −0.846107 0.533014i \(-0.821059\pi\)
0.846107 0.533014i \(-0.178941\pi\)
\(294\) −2.44949 −0.142857
\(295\) 3.44949 0.348469i 0.200837 0.0202887i
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 3.79796i 0.220010i
\(299\) −12.8990 −0.745967
\(300\) −2.44949 12.0000i −0.141421 0.692820i
\(301\) 0.898979 0.0518163
\(302\) 19.5959i 1.12762i
\(303\) 8.69694i 0.499626i
\(304\) −1.55051 −0.0889279
\(305\) 7.89898 0.797959i 0.452294 0.0456910i
\(306\) −6.00000 −0.342997
\(307\) 20.2474i 1.15558i −0.816184 0.577791i \(-0.803915\pi\)
0.816184 0.577791i \(-0.196085\pi\)
\(308\) 4.89898i 0.279145i
\(309\) 31.5959 1.79743
\(310\) −2.00000 19.7980i −0.113592 1.12445i
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 10.8990i 0.617033i
\(313\) 21.5959i 1.22067i 0.792142 + 0.610337i \(0.208966\pi\)
−0.792142 + 0.610337i \(0.791034\pi\)
\(314\) 3.55051 0.200367
\(315\) 0.674235 + 6.67423i 0.0379888 + 0.376051i
\(316\) 6.89898 0.388098
\(317\) 22.4949i 1.26344i −0.775197 0.631720i \(-0.782349\pi\)
0.775197 0.631720i \(-0.217651\pi\)
\(318\) 26.6969i 1.49709i
\(319\) 33.7980 1.89232
\(320\) −2.22474 + 0.224745i −0.124367 + 0.0125636i
\(321\) 19.5959 1.09374
\(322\) 2.89898i 0.161554i
\(323\) 3.10102i 0.172545i
\(324\) 9.00000 0.500000
\(325\) −4.44949 21.7980i −0.246813 1.20913i
\(326\) 7.10102 0.393289
\(327\) 16.8990i 0.934516i
\(328\) 1.10102i 0.0607937i
\(329\) 8.89898 0.490617
\(330\) −26.6969 + 2.69694i −1.46962 + 0.148462i
\(331\) −18.6969 −1.02768 −0.513838 0.857887i \(-0.671777\pi\)
−0.513838 + 0.857887i \(0.671777\pi\)
\(332\) 2.44949i 0.134433i
\(333\) 6.00000i 0.328798i
\(334\) −4.89898 −0.268060
\(335\) −1.79796 17.7980i −0.0982330 0.972406i
\(336\) 2.44949 0.133631
\(337\) 9.59592i 0.522723i 0.965241 + 0.261361i \(0.0841715\pi\)
−0.965241 + 0.261361i \(0.915829\pi\)
\(338\) 6.79796i 0.369760i
\(339\) 48.4949 2.63388
\(340\) −0.449490 4.44949i −0.0243770 0.241307i
\(341\) −43.5959 −2.36085
\(342\) 4.65153i 0.251526i
\(343\) 1.00000i 0.0539949i
\(344\) −0.898979 −0.0484697
\(345\) 15.7980 1.59592i 0.850534 0.0859213i
\(346\) 6.24745 0.335865
\(347\) 28.8990i 1.55138i 0.631115 + 0.775689i \(0.282598\pi\)
−0.631115 + 0.775689i \(0.717402\pi\)
\(348\) 16.8990i 0.905880i
\(349\) 8.44949 0.452291 0.226145 0.974094i \(-0.427388\pi\)
0.226145 + 0.974094i \(0.427388\pi\)
\(350\) −4.89898 + 1.00000i −0.261861 + 0.0534522i
\(351\) 0 0
\(352\) 4.89898i 0.261116i
\(353\) 22.8990i 1.21879i −0.792867 0.609395i \(-0.791412\pi\)
0.792867 0.609395i \(-0.208588\pi\)
\(354\) 3.79796 0.201859
\(355\) −2.44949 + 0.247449i −0.130005 + 0.0131332i
\(356\) −10.0000 −0.529999
\(357\) 4.89898i 0.259281i
\(358\) 13.7980i 0.729245i
\(359\) 27.5959 1.45646 0.728228 0.685334i \(-0.240344\pi\)
0.728228 + 0.685334i \(0.240344\pi\)
\(360\) −0.674235 6.67423i −0.0355353 0.351763i
\(361\) −16.5959 −0.873469
\(362\) 10.2474i 0.538594i
\(363\) 31.8434i 1.67134i
\(364\) 4.44949 0.233217
\(365\) −0.651531 6.44949i −0.0341027 0.337582i
\(366\) 8.69694 0.454596
\(367\) 32.0000i 1.67039i 0.549957 + 0.835193i \(0.314644\pi\)
−0.549957 + 0.835193i \(0.685356\pi\)
\(368\) 2.89898i 0.151120i
\(369\) 3.30306 0.171951
\(370\) 4.44949 0.449490i 0.231318 0.0233679i
\(371\) 10.8990 0.565847
\(372\) 21.7980i 1.13017i
\(373\) 4.69694i 0.243198i 0.992579 + 0.121599i \(0.0388022\pi\)
−0.992579 + 0.121599i \(0.961198\pi\)
\(374\) −9.79796 −0.506640
\(375\) 8.14643 + 26.1464i 0.420680 + 1.35020i
\(376\) −8.89898 −0.458930
\(377\) 30.6969i 1.58097i
\(378\) 0 0
\(379\) −30.6969 −1.57680 −0.788398 0.615166i \(-0.789089\pi\)
−0.788398 + 0.615166i \(0.789089\pi\)
\(380\) 3.44949 0.348469i 0.176955 0.0178761i
\(381\) 36.4949 1.86969
\(382\) 12.6969i 0.649632i
\(383\) 7.10102i 0.362845i 0.983405 + 0.181423i \(0.0580702\pi\)
−0.983405 + 0.181423i \(0.941930\pi\)
\(384\) −2.44949 −0.125000
\(385\) 1.10102 + 10.8990i 0.0561132 + 0.555463i
\(386\) 21.5959 1.09920
\(387\) 2.69694i 0.137093i
\(388\) 15.7980i 0.802020i
\(389\) −13.1010 −0.664248 −0.332124 0.943236i \(-0.607765\pi\)
−0.332124 + 0.943236i \(0.607765\pi\)
\(390\) −2.44949 24.2474i −0.124035 1.22782i
\(391\) 5.79796 0.293215
\(392\) 1.00000i 0.0505076i
\(393\) 15.7980i 0.796902i
\(394\) 18.8990 0.952117
\(395\) −15.3485 + 1.55051i −0.772265 + 0.0780146i
\(396\) −14.6969 −0.738549
\(397\) 2.65153i 0.133077i −0.997784 0.0665383i \(-0.978805\pi\)
0.997784 0.0665383i \(-0.0211954\pi\)
\(398\) 16.8990i 0.847069i
\(399\) −3.79796 −0.190136
\(400\) 4.89898 1.00000i 0.244949 0.0500000i
\(401\) −29.3939 −1.46786 −0.733930 0.679225i \(-0.762316\pi\)
−0.733930 + 0.679225i \(0.762316\pi\)
\(402\) 19.5959i 0.977356i
\(403\) 39.5959i 1.97241i
\(404\) −3.55051 −0.176644
\(405\) −20.0227 + 2.02270i −0.994936 + 0.100509i
\(406\) 6.89898 0.342391
\(407\) 9.79796i 0.485667i
\(408\) 4.89898i 0.242536i
\(409\) −34.4949 −1.70566 −0.852831 0.522186i \(-0.825117\pi\)
−0.852831 + 0.522186i \(0.825117\pi\)
\(410\) 0.247449 + 2.44949i 0.0122206 + 0.120972i
\(411\) 4.40408 0.217237
\(412\) 12.8990i 0.635487i
\(413\) 1.55051i 0.0762956i
\(414\) 8.69694 0.427431
\(415\) 0.550510 + 5.44949i 0.0270235 + 0.267505i
\(416\) −4.44949 −0.218154
\(417\) 3.79796i 0.185987i
\(418\) 7.59592i 0.371528i
\(419\) 1.55051 0.0757474 0.0378737 0.999283i \(-0.487942\pi\)
0.0378737 + 0.999283i \(0.487942\pi\)
\(420\) −5.44949 + 0.550510i −0.265908 + 0.0268622i
\(421\) −4.20204 −0.204795 −0.102397 0.994744i \(-0.532651\pi\)
−0.102397 + 0.994744i \(0.532651\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 26.6969i 1.29805i
\(424\) −10.8990 −0.529301
\(425\) 2.00000 + 9.79796i 0.0970143 + 0.475271i
\(426\) −2.69694 −0.130667
\(427\) 3.55051i 0.171821i
\(428\) 8.00000i 0.386695i
\(429\) −53.3939 −2.57788
\(430\) 2.00000 0.202041i 0.0964486 0.00974328i
\(431\) −1.79796 −0.0866046 −0.0433023 0.999062i \(-0.513788\pi\)
−0.0433023 + 0.999062i \(0.513788\pi\)
\(432\) 0 0
\(433\) 0.202041i 0.00970947i 0.999988 + 0.00485474i \(0.00154532\pi\)
−0.999988 + 0.00485474i \(0.998455\pi\)
\(434\) −8.89898 −0.427165
\(435\) −3.79796 37.5959i −0.182098 1.80259i
\(436\) 6.89898 0.330401
\(437\) 4.49490i 0.215020i
\(438\) 7.10102i 0.339300i
\(439\) 21.3939 1.02107 0.510537 0.859856i \(-0.329447\pi\)
0.510537 + 0.859856i \(0.329447\pi\)
\(440\) −1.10102 10.8990i −0.0524891 0.519588i
\(441\) 3.00000 0.142857
\(442\) 8.89898i 0.423281i
\(443\) 9.79796i 0.465515i −0.972535 0.232758i \(-0.925225\pi\)
0.972535 0.232758i \(-0.0747749\pi\)
\(444\) 4.89898 0.232495
\(445\) 22.2474 2.24745i 1.05463 0.106539i
\(446\) 4.00000 0.189405
\(447\) 9.30306i 0.440020i
\(448\) 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
\(451\) 5.39388 0.253988
\(452\) 19.7980i 0.931218i
\(453\) 48.0000i 2.25524i
\(454\) 7.34847 0.344881
\(455\) −9.89898 + 1.00000i −0.464071 + 0.0468807i
\(456\) 3.79796 0.177856
\(457\) 29.5959i 1.38444i 0.721687 + 0.692219i \(0.243367\pi\)
−0.721687 + 0.692219i \(0.756633\pi\)
\(458\) 19.1464i 0.894654i
\(459\) 0 0
\(460\) 0.651531 + 6.44949i 0.0303778 + 0.300709i
\(461\) 17.3485 0.807999 0.403999 0.914759i \(-0.367620\pi\)
0.403999 + 0.914759i \(0.367620\pi\)
\(462\) 12.0000i 0.558291i
\(463\) 3.59592i 0.167116i −0.996503 0.0835582i \(-0.973372\pi\)
0.996503 0.0835582i \(-0.0266285\pi\)
\(464\) −6.89898 −0.320277
\(465\) 4.89898 + 48.4949i 0.227185 + 2.24890i
\(466\) −29.7980 −1.38036
\(467\) 10.4495i 0.483545i 0.970333 + 0.241772i \(0.0777287\pi\)
−0.970333 + 0.241772i \(0.922271\pi\)
\(468\) 13.3485i 0.617033i
\(469\) −8.00000 −0.369406
\(470\) 19.7980 2.00000i 0.913212 0.0922531i
\(471\) −8.69694 −0.400734
\(472\) 1.55051i 0.0713680i
\(473\) 4.40408i 0.202500i
\(474\) −16.8990 −0.776196
\(475\) −7.59592 + 1.55051i −0.348525 + 0.0711423i
\(476\) −2.00000 −0.0916698
\(477\) 32.6969i 1.49709i
\(478\) 6.20204i 0.283675i
\(479\) −9.30306 −0.425068 −0.212534 0.977154i \(-0.568172\pi\)
−0.212534 + 0.977154i \(0.568172\pi\)
\(480\) 5.44949 0.550510i 0.248734 0.0251272i
\(481\) 8.89898 0.405759
\(482\) 8.69694i 0.396135i
\(483\) 7.10102i 0.323108i
\(484\) −13.0000 −0.590909
\(485\) 3.55051 + 35.1464i 0.161220 + 1.59592i
\(486\) −22.0454 −1.00000
\(487\) 7.30306i 0.330933i −0.986215 0.165467i \(-0.947087\pi\)
0.986215 0.165467i \(-0.0529130\pi\)
\(488\) 3.55051i 0.160724i
\(489\) −17.3939 −0.786578
\(490\) 0.224745 + 2.22474i 0.0101529 + 0.100504i
\(491\) 19.5959 0.884351 0.442176 0.896928i \(-0.354207\pi\)
0.442176 + 0.896928i \(0.354207\pi\)
\(492\) 2.69694i 0.121587i
\(493\) 13.7980i 0.621429i
\(494\) 6.89898 0.310400
\(495\) 32.6969 3.30306i 1.46962 0.148462i
\(496\) 8.89898 0.399576
\(497\) 1.10102i 0.0493875i
\(498\) 6.00000i 0.268866i
\(499\) −6.20204 −0.277641 −0.138821 0.990318i \(-0.544331\pi\)
−0.138821 + 0.990318i \(0.544331\pi\)
\(500\) −10.6742 + 3.32577i −0.477366 + 0.148733i
\(501\) 12.0000 0.536120
\(502\) 6.44949i 0.287855i
\(503\) 4.00000i 0.178351i 0.996016 + 0.0891756i \(0.0284232\pi\)
−0.996016 + 0.0891756i \(0.971577\pi\)
\(504\) −3.00000 −0.133631
\(505\) 7.89898 0.797959i 0.351500 0.0355087i
\(506\) 14.2020 0.631358
\(507\) 16.6515i 0.739520i
\(508\) 14.8990i 0.661035i
\(509\) 31.5505 1.39845 0.699226 0.714901i \(-0.253528\pi\)
0.699226 + 0.714901i \(0.253528\pi\)
\(510\) 1.10102 + 10.8990i 0.0487540 + 0.482615i
\(511\) −2.89898 −0.128243
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −8.69694 −0.383606
\(515\) −2.89898 28.6969i −0.127744 1.26454i
\(516\) 2.20204 0.0969395
\(517\) 43.5959i 1.91735i
\(518\) 2.00000i 0.0878750i
\(519\) −15.3031 −0.671730
\(520\) 9.89898 1.00000i 0.434099 0.0438529i
\(521\) 32.6969 1.43248 0.716239 0.697855i \(-0.245862\pi\)
0.716239 + 0.697855i \(0.245862\pi\)
\(522\) 20.6969i 0.905880i
\(523\) 33.1464i 1.44939i 0.689069 + 0.724696i \(0.258020\pi\)
−0.689069 + 0.724696i \(0.741980\pi\)
\(524\) 6.44949 0.281747
\(525\) 12.0000 2.44949i 0.523723 0.106904i
\(526\) −9.79796 −0.427211
\(527\) 17.7980i 0.775291i
\(528\) 12.0000i 0.522233i
\(529\) 14.5959 0.634605
\(530\) 24.2474 2.44949i 1.05324 0.106399i
\(531\) −4.65153 −0.201859
\(532\) 1.55051i 0.0672231i
\(533\) 4.89898i 0.212198i
\(534\) 24.4949 1.06000
\(535\) −1.79796 17.7980i −0.0777325 0.769473i
\(536\) 8.00000 0.345547
\(537\) 33.7980i 1.45849i
\(538\) 19.1464i 0.825461i
\(539\) 4.89898 0.211014
\(540\) 0 0
\(541\) 9.59592 0.412561 0.206280 0.978493i \(-0.433864\pi\)
0.206280 + 0.978493i \(0.433864\pi\)
\(542\) 12.0000i 0.515444i
\(543\) 25.1010i 1.07719i
\(544\) 2.00000 0.0857493
\(545\) −15.3485 + 1.55051i −0.657456 + 0.0664166i
\(546\) −10.8990 −0.466433
\(547\) 18.6969i 0.799423i −0.916641 0.399712i \(-0.869110\pi\)
0.916641 0.399712i \(-0.130890\pi\)
\(548\) 1.79796i 0.0768050i
\(549\) −10.6515 −0.454596
\(550\) 4.89898 + 24.0000i 0.208893 + 1.02336i
\(551\) 10.6969 0.455705
\(552\) 7.10102i 0.302240i
\(553\) 6.89898i 0.293374i
\(554\) −14.8990 −0.632997
\(555\) −10.8990 + 1.10102i −0.462636 + 0.0467357i
\(556\) 1.55051 0.0657563
\(557\) 12.6969i 0.537987i 0.963142 + 0.268993i \(0.0866909\pi\)
−0.963142 + 0.268993i \(0.913309\pi\)
\(558\) 26.6969i 1.13017i
\(559\) 4.00000 0.169182
\(560\) −0.224745 2.22474i −0.00949720 0.0940126i
\(561\) 24.0000 1.01328
\(562\) 18.0000i 0.759284i
\(563\) 30.0454i 1.26626i 0.774044 + 0.633131i \(0.218231\pi\)
−0.774044 + 0.633131i \(0.781769\pi\)
\(564\) 21.7980 0.917860
\(565\) −4.44949 44.0454i −0.187191 1.85300i
\(566\) −3.75255 −0.157731
\(567\) 9.00000i 0.377964i
\(568\) 1.10102i 0.0461978i
\(569\) −33.7980 −1.41688 −0.708442 0.705769i \(-0.750602\pi\)
−0.708442 + 0.705769i \(0.750602\pi\)
\(570\) −8.44949 + 0.853572i −0.353910 + 0.0357522i
\(571\) −11.1010 −0.464563 −0.232282 0.972649i \(-0.574619\pi\)
−0.232282 + 0.972649i \(0.574619\pi\)
\(572\) 21.7980i 0.911418i
\(573\) 31.1010i 1.29926i
\(574\) 1.10102 0.0459557
\(575\) −2.89898 14.2020i −0.120896 0.592266i
\(576\) 3.00000 0.125000
\(577\) 2.49490i 0.103864i −0.998651 0.0519320i \(-0.983462\pi\)
0.998651 0.0519320i \(-0.0165379\pi\)
\(578\) 13.0000i 0.540729i
\(579\) −52.8990 −2.19841
\(580\) 15.3485 1.55051i 0.637310 0.0643814i
\(581\) 2.44949 0.101622
\(582\) 38.6969i 1.60404i
\(583\) 53.3939i 2.21135i
\(584\) 2.89898 0.119961
\(585\) 3.00000 + 29.6969i 0.124035 + 1.22782i
\(586\) −18.2474 −0.753795
\(587\) 1.14643i 0.0473182i 0.999720 + 0.0236591i \(0.00753162\pi\)
−0.999720 + 0.0236591i \(0.992468\pi\)
\(588\) 2.44949i 0.101015i
\(589\) −13.7980 −0.568535
\(590\) −0.348469 3.44949i −0.0143463 0.142013i
\(591\) −46.2929 −1.90423
\(592\) 2.00000i 0.0821995i
\(593\) 10.8990i 0.447567i 0.974639 + 0.223784i \(0.0718409\pi\)
−0.974639 + 0.223784i \(0.928159\pi\)
\(594\) 0 0
\(595\) 4.44949 0.449490i 0.182411 0.0184273i
\(596\) −3.79796 −0.155570
\(597\) 41.3939i 1.69414i
\(598\) 12.8990i 0.527478i
\(599\) 13.1010 0.535293 0.267647 0.963517i \(-0.413754\pi\)
0.267647 + 0.963517i \(0.413754\pi\)
\(600\) −12.0000 + 2.44949i −0.489898 + 0.100000i
\(601\) −39.3939 −1.60691 −0.803455 0.595366i \(-0.797007\pi\)
−0.803455 + 0.595366i \(0.797007\pi\)
\(602\) 0.898979i 0.0366397i
\(603\) 24.0000i 0.977356i
\(604\) −19.5959 −0.797347
\(605\) 28.9217 2.92168i 1.17583 0.118783i
\(606\) 8.69694 0.353289
\(607\) 33.3939i 1.35542i 0.735331 + 0.677708i \(0.237027\pi\)
−0.735331 + 0.677708i \(0.762973\pi\)
\(608\) 1.55051i 0.0628815i
\(609\) −16.8990 −0.684781
\(610\) −0.797959 7.89898i −0.0323084 0.319820i
\(611\) 39.5959 1.60188
\(612\) 6.00000i 0.242536i
\(613\) 27.7980i 1.12275i 0.827562 + 0.561374i \(0.189727\pi\)
−0.827562 + 0.561374i \(0.810273\pi\)
\(614\) −20.2474 −0.817121
\(615\) −0.606123 6.00000i −0.0244412 0.241943i
\(616\) −4.89898 −0.197386
\(617\) 29.5959i 1.19149i 0.803175 + 0.595743i \(0.203142\pi\)
−0.803175 + 0.595743i \(0.796858\pi\)
\(618\) 31.5959i 1.27097i
\(619\) 41.5505 1.67006 0.835028 0.550207i \(-0.185451\pi\)
0.835028 + 0.550207i \(0.185451\pi\)
\(620\) −19.7980 + 2.00000i −0.795105 + 0.0803219i
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) 10.0000i 0.400642i
\(624\) 10.8990 0.436308
\(625\) 23.0000 9.79796i 0.920000 0.391918i
\(626\) 21.5959 0.863146
\(627\) 18.6061i 0.743057i
\(628\) 3.55051i 0.141681i
\(629\) −4.00000 −0.159490
\(630\) 6.67423 0.674235i 0.265908 0.0268622i
\(631\) −42.4949 −1.69170 −0.845848 0.533425i \(-0.820905\pi\)
−0.845848 + 0.533425i \(0.820905\pi\)
\(632\) 6.89898i 0.274427i
\(633\) 29.3939i 1.16830i
\(634\) −22.4949 −0.893387
\(635\) −3.34847 33.1464i −0.132880 1.31538i
\(636\) 26.6969 1.05860
\(637\) 4.44949i 0.176295i
\(638\) 33.7980i 1.33807i
\(639\) 3.30306 0.130667
\(640\) 0.224745 + 2.22474i 0.00888382 + 0.0879408i
\(641\) 25.7980 1.01896 0.509479 0.860483i \(-0.329838\pi\)
0.509479 + 0.860483i \(0.329838\pi\)
\(642\) 19.5959i 0.773389i
\(643\) 25.1464i 0.991678i −0.868414 0.495839i \(-0.834861\pi\)
0.868414 0.495839i \(-0.165139\pi\)
\(644\) 2.89898 0.114236
\(645\) −4.89898 + 0.494897i −0.192897 + 0.0194866i
\(646\) −3.10102 −0.122008
\(647\) 46.2929i 1.81996i −0.414652 0.909980i \(-0.636097\pi\)
0.414652 0.909980i \(-0.363903\pi\)
\(648\) 9.00000i 0.353553i
\(649\) −7.59592 −0.298166
\(650\) −21.7980 + 4.44949i −0.854986 + 0.174523i
\(651\) 21.7980 0.854329
\(652\) 7.10102i 0.278097i
\(653\) 20.2020i 0.790567i 0.918559 + 0.395283i \(0.129354\pi\)
−0.918559 + 0.395283i \(0.870646\pi\)
\(654\) −16.8990 −0.660802
\(655\) −14.3485 + 1.44949i −0.560641 + 0.0566363i
\(656\) −1.10102 −0.0429876
\(657\) 8.69694i 0.339300i
\(658\) 8.89898i 0.346918i
\(659\) −16.8990 −0.658291 −0.329145 0.944279i \(-0.606761\pi\)
−0.329145 + 0.944279i \(0.606761\pi\)
\(660\) 2.69694 + 26.6969i 0.104978 + 1.03918i
\(661\) −40.9444 −1.59255 −0.796276 0.604933i \(-0.793200\pi\)
−0.796276 + 0.604933i \(0.793200\pi\)
\(662\) 18.6969i 0.726677i
\(663\) 21.7980i 0.846563i
\(664\) −2.44949 −0.0950586
\(665\) 0.348469 + 3.44949i 0.0135131 + 0.133765i
\(666\) −6.00000 −0.232495
\(667\) 20.0000i 0.774403i
\(668\) 4.89898i 0.189547i
\(669\) −9.79796 −0.378811
\(670\) −17.7980 + 1.79796i −0.687595 + 0.0694612i
\(671\) −17.3939 −0.671483
\(672\) 2.44949i 0.0944911i
\(673\) 17.7980i 0.686061i 0.939324 + 0.343030i \(0.111453\pi\)
−0.939324 + 0.343030i \(0.888547\pi\)
\(674\) 9.59592 0.369621
\(675\) 0 0
\(676\) 6.79796 0.261460
\(677\) 36.4495i 1.40087i −0.713717 0.700434i \(-0.752990\pi\)
0.713717 0.700434i \(-0.247010\pi\)
\(678\) 48.4949i 1.86244i
\(679\) 15.7980 0.606270
\(680\) −4.44949 + 0.449490i −0.170630 + 0.0172371i
\(681\) −18.0000 −0.689761
\(682\) 43.5959i 1.66937i
\(683\) 3.59592i 0.137594i −0.997631 0.0687970i \(-0.978084\pi\)
0.997631 0.0687970i \(-0.0219161\pi\)
\(684\) −4.65153 −0.177856
\(685\) −0.404082 4.00000i −0.0154392 0.152832i
\(686\) 1.00000 0.0381802
\(687\) 46.8990i 1.78931i
\(688\) 0.898979i 0.0342733i
\(689\) 48.4949 1.84751
\(690\) −1.59592 15.7980i −0.0607556 0.601418i
\(691\) 21.1464 0.804448 0.402224 0.915541i \(-0.368237\pi\)
0.402224 + 0.915541i \(0.368237\pi\)
\(692\) 6.24745i 0.237492i
\(693\) 14.6969i 0.558291i
\(694\) 28.8990 1.09699
\(695\) −3.44949 + 0.348469i −0.130847 + 0.0132182i
\(696\) 16.8990 0.640554
\(697\) 2.20204i 0.0834083i
\(698\) 8.44949i 0.319818i
\(699\) 72.9898 2.76073
\(700\) 1.00000 + 4.89898i 0.0377964 + 0.185164i
\(701\) 11.3031 0.426911 0.213455 0.976953i \(-0.431528\pi\)
0.213455 + 0.976953i \(0.431528\pi\)
\(702\) 0 0
\(703\) 3.10102i 0.116957i
\(704\) 4.89898 0.184637
\(705\) −48.4949 + 4.89898i −1.82642 + 0.184506i
\(706\) −22.8990 −0.861814
\(707\) 3.55051i 0.133531i
\(708\) 3.79796i 0.142736i
\(709\) 28.2929 1.06256 0.531280 0.847196i \(-0.321711\pi\)
0.531280 + 0.847196i \(0.321711\pi\)
\(710\) 0.247449 + 2.44949i 0.00928658 + 0.0919277i
\(711\) 20.6969 0.776196
\(712\) 10.0000i 0.374766i
\(713\) 25.7980i 0.966141i
\(714\) 4.89898 0.183340
\(715\) 4.89898 + 48.4949i 0.183211 + 1.81361i
\(716\) 13.7980 0.515654
\(717\) 15.1918i 0.567350i
\(718\) 27.5959i 1.02987i
\(719\) 4.49490 0.167631 0.0838157 0.996481i \(-0.473289\pi\)
0.0838157 + 0.996481i \(0.473289\pi\)
\(720\) −6.67423 + 0.674235i −0.248734 + 0.0251272i
\(721\) −12.8990 −0.480383
\(722\) 16.5959i 0.617636i
\(723\) 21.3031i 0.792269i
\(724\) 10.2474 0.380843
\(725\) −33.7980 + 6.89898i −1.25522 + 0.256222i
\(726\) 31.8434 1.18182
\(727\) 22.6969i 0.841783i 0.907111 + 0.420891i \(0.138283\pi\)
−0.907111 + 0.420891i \(0.861717\pi\)
\(728\) 4.44949i 0.164909i
\(729\) 27.0000 1.00000
\(730\) −6.44949 + 0.651531i −0.238706 + 0.0241142i
\(731\) −1.79796 −0.0664999
\(732\) 8.69694i 0.321448i
\(733\) 39.6413i 1.46419i −0.681205 0.732093i \(-0.738544\pi\)
0.681205 0.732093i \(-0.261456\pi\)
\(734\) 32.0000 1.18114
\(735\) −0.550510 5.44949i −0.0203059 0.201007i
\(736\) −2.89898 −0.106858
\(737\) 39.1918i 1.44365i
\(738\) 3.30306i 0.121587i
\(739\) −4.49490 −0.165347 −0.0826737 0.996577i \(-0.526346\pi\)
−0.0826737 + 0.996577i \(0.526346\pi\)
\(740\) −0.449490 4.44949i −0.0165236 0.163566i
\(741\) −16.8990 −0.620800
\(742\) 10.8990i 0.400114i
\(743\) 44.6969i 1.63977i 0.572527 + 0.819886i \(0.305963\pi\)
−0.572527 + 0.819886i \(0.694037\pi\)
\(744\) −21.7980 −0.799152
\(745\) 8.44949 0.853572i 0.309565 0.0312725i
\(746\) 4.69694 0.171967
\(747\) 7.34847i 0.268866i
\(748\) 9.79796i 0.358249i
\(749\) −8.00000 −0.292314
\(750\) 26.1464 8.14643i 0.954733 0.297465i
\(751\) −41.7980 −1.52523 −0.762615 0.646853i \(-0.776085\pi\)
−0.762615 + 0.646853i \(0.776085\pi\)
\(752\) 8.89898i 0.324512i
\(753\) 15.7980i 0.575710i
\(754\) 30.6969 1.11792
\(755\) 43.5959 4.40408i 1.58662 0.160281i
\(756\) 0 0
\(757\) 51.7980i 1.88263i −0.337531 0.941314i \(-0.609592\pi\)
0.337531 0.941314i \(-0.390408\pi\)
\(758\) 30.6969i 1.11496i
\(759\) −34.7878 −1.26272
\(760\) −0.348469 3.44949i −0.0126403 0.125126i
\(761\) −21.1010 −0.764911 −0.382456 0.923974i \(-0.624922\pi\)
−0.382456 + 0.923974i \(0.624922\pi\)
\(762\) 36.4949i 1.32207i
\(763\) 6.89898i 0.249760i
\(764\) −12.6969 −0.459359
\(765\) −1.34847 13.3485i −0.0487540 0.482615i
\(766\) 7.10102 0.256570
\(767\) 6.89898i 0.249108i
\(768\) 2.44949i 0.0883883i
\(769\) 40.6969 1.46757 0.733785 0.679382i \(-0.237752\pi\)
0.733785 + 0.679382i \(0.237752\pi\)
\(770\) 10.8990 1.10102i 0.392772 0.0396780i
\(771\) 21.3031 0.767211
\(772\) 21.5959i 0.777254i
\(773\) 1.34847i 0.0485011i −0.999706 0.0242505i \(-0.992280\pi\)
0.999706 0.0242505i \(-0.00771994\pi\)
\(774\) −2.69694 −0.0969395
\(775\) 43.5959 8.89898i 1.56601 0.319661i
\(776\) −15.7980 −0.567114
\(777\) 4.89898i 0.175750i
\(778\) 13.1010i 0.469694i
\(779\) 1.70714 0.0611648
\(780\) −24.2474 + 2.44949i −0.868198 + 0.0877058i
\(781\) 5.39388 0.193008
\(782\) 5.79796i 0.207335i
\(783\) 0 0
\(784\) −1.00000 −0.0357143
\(785\) 0.797959 + 7.89898i 0.0284804 + 0.281927i
\(786\) −15.7980 −0.563495
\(787\) 50.4495i 1.79833i 0.437610 + 0.899165i \(0.355825\pi\)
−0.437610 + 0.899165i \(0.644175\pi\)
\(788\) 18.8990i