Properties

Label 798.2.j.l.457.4
Level $798$
Weight $2$
Character 798.457
Analytic conductor $6.372$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37206208130\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.856615824.2
Defining polynomial: \(x^{8} + 11 x^{6} + 36 x^{4} + 32 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 457.4
Root \(0.385731i\) of defining polynomial
Character \(\chi\) \(=\) 798.457
Dual form 798.2.j.l.571.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.73065 - 2.99758i) q^{5} +1.00000 q^{6} +(-2.36975 - 1.17656i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.73065 - 2.99758i) q^{5} +1.00000 q^{6} +(-2.36975 - 1.17656i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.73065 - 2.99758i) q^{10} +(-0.139098 - 0.240925i) q^{11} +(0.500000 - 0.866025i) q^{12} +6.92261 q^{13} +(-2.20380 + 1.46399i) q^{14} +3.46130 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.89876 - 5.02079i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -3.46130 q^{20} +(-0.165947 - 2.64054i) q^{21} -0.278197 q^{22} +(-1.54617 + 2.67804i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.49031 - 6.04539i) q^{25} +(3.46130 - 5.99515i) q^{26} -1.00000 q^{27} +(0.165947 + 2.64054i) q^{28} -8.55364 q^{29} +(1.73065 - 2.99758i) q^{30} +(-3.67480 - 6.36493i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.139098 - 0.240925i) q^{33} -5.79751 q^{34} +(-7.62803 + 5.06730i) q^{35} +1.00000 q^{36} +(2.62056 - 4.53894i) q^{37} +(0.500000 + 0.866025i) q^{38} +(3.46130 + 5.99515i) q^{39} +(-1.73065 + 2.99758i) q^{40} +8.88553 q^{41} +(-2.36975 - 1.17656i) q^{42} +10.3705 q^{43} +(-0.139098 + 0.240925i) q^{44} +(1.73065 + 2.99758i) q^{45} +(1.54617 + 2.67804i) q^{46} +(0.896599 - 1.55296i) q^{47} -1.00000 q^{48} +(4.23143 + 5.57629i) q^{49} -6.98062 q^{50} +(2.89876 - 5.02079i) q^{51} +(-3.46130 - 5.99515i) q^{52} +(-4.19411 - 7.26442i) q^{53} +(-0.500000 + 0.866025i) q^{54} -0.962923 q^{55} +(2.36975 + 1.17656i) q^{56} -1.00000 q^{57} +(-4.27682 + 7.40767i) q^{58} +(3.89738 + 6.75046i) q^{59} +(-1.73065 - 2.99758i) q^{60} +(-4.56470 + 7.90630i) q^{61} -7.34959 q^{62} +(2.20380 - 1.46399i) q^{63} +1.00000 q^{64} +(11.9806 - 20.7510i) q^{65} +(-0.139098 - 0.240925i) q^{66} +(6.86891 + 11.8973i) q^{67} +(-2.89876 + 5.02079i) q^{68} -3.09233 q^{69} +(0.574394 + 9.13972i) q^{70} +0.684727 q^{71} +(0.500000 - 0.866025i) q^{72} +(0.962682 + 1.66741i) q^{73} +(-2.62056 - 4.53894i) q^{74} +(3.49031 - 6.04539i) q^{75} +1.00000 q^{76} +(0.0461660 + 0.734590i) q^{77} +6.92261 q^{78} +(-0.703803 + 1.21902i) q^{79} +(1.73065 + 2.99758i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.44277 - 7.69509i) q^{82} -0.146030 q^{83} +(-2.20380 + 1.46399i) q^{84} -20.0670 q^{85} +(5.18526 - 8.98114i) q^{86} +(-4.27682 - 7.40767i) q^{87} +(0.139098 + 0.240925i) q^{88} +(6.85037 - 11.8652i) q^{89} +3.46130 q^{90} +(-16.4048 - 8.14484i) q^{91} +3.09233 q^{92} +(3.67480 - 6.36493i) q^{93} +(-0.896599 - 1.55296i) q^{94} +(1.73065 + 2.99758i) q^{95} +(-0.500000 + 0.866025i) q^{96} +4.09233 q^{97} +(6.94492 - 0.876382i) q^{98} +0.278197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} + 4q^{3} - 4q^{4} + 8q^{6} - 2q^{7} - 8q^{8} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{2} + 4q^{3} - 4q^{4} + 8q^{6} - 2q^{7} - 8q^{8} - 4q^{9} + 2q^{11} + 4q^{12} - q^{14} - 4q^{16} - 10q^{17} + 4q^{18} - 4q^{19} - q^{21} + 4q^{22} + 5q^{23} - 4q^{24} - 4q^{25} - 8q^{27} + q^{28} - 6q^{29} - 9q^{31} + 4q^{32} - 2q^{33} - 20q^{34} - 9q^{35} + 8q^{36} + 14q^{37} + 4q^{38} + 8q^{41} - 2q^{42} + 42q^{43} + 2q^{44} - 5q^{46} - 7q^{47} - 8q^{48} - 4q^{49} - 8q^{50} + 10q^{51} + 7q^{53} - 4q^{54} + 2q^{56} - 8q^{57} - 3q^{58} - 7q^{59} - 23q^{61} - 18q^{62} + q^{63} + 8q^{64} + 48q^{65} + 2q^{66} - 6q^{67} - 10q^{68} + 10q^{69} + 15q^{70} + 4q^{71} + 4q^{72} + 5q^{73} - 14q^{74} + 4q^{75} + 8q^{76} - 17q^{77} + 11q^{79} - 4q^{81} + 4q^{82} + 28q^{83} - q^{84} + 12q^{85} + 21q^{86} - 3q^{87} - 2q^{88} - 10q^{89} - 48q^{91} - 10q^{92} + 9q^{93} + 7q^{94} - 4q^{96} - 2q^{97} + 25q^{98} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/798\mathbb{Z}\right)^\times\).

\(n\) \(115\) \(211\) \(533\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.73065 2.99758i 0.773971 1.34056i −0.161400 0.986889i \(-0.551601\pi\)
0.935371 0.353668i \(-0.115066\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.36975 1.17656i −0.895681 0.444696i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.73065 2.99758i −0.547280 0.947917i
\(11\) −0.139098 0.240925i −0.0419397 0.0726418i 0.844294 0.535881i \(-0.180020\pi\)
−0.886233 + 0.463239i \(0.846687\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 6.92261 1.91999 0.959993 0.280025i \(-0.0903427\pi\)
0.959993 + 0.280025i \(0.0903427\pi\)
\(14\) −2.20380 + 1.46399i −0.588991 + 0.391267i
\(15\) 3.46130 0.893705
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.89876 5.02079i −0.703052 1.21772i −0.967390 0.253291i \(-0.918487\pi\)
0.264338 0.964430i \(-0.414846\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i
\(20\) −3.46130 −0.773971
\(21\) −0.165947 2.64054i −0.0362127 0.576213i
\(22\) −0.278197 −0.0593118
\(23\) −1.54617 + 2.67804i −0.322398 + 0.558410i −0.980982 0.194097i \(-0.937822\pi\)
0.658584 + 0.752507i \(0.271156\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −3.49031 6.04539i −0.698062 1.20908i
\(26\) 3.46130 5.99515i 0.678817 1.17575i
\(27\) −1.00000 −0.192450
\(28\) 0.165947 + 2.64054i 0.0313611 + 0.499016i
\(29\) −8.55364 −1.58837 −0.794185 0.607676i \(-0.792102\pi\)
−0.794185 + 0.607676i \(0.792102\pi\)
\(30\) 1.73065 2.99758i 0.315972 0.547280i
\(31\) −3.67480 6.36493i −0.660013 1.14318i −0.980612 0.195961i \(-0.937218\pi\)
0.320599 0.947215i \(-0.396116\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.139098 0.240925i 0.0242139 0.0419397i
\(34\) −5.79751 −0.994265
\(35\) −7.62803 + 5.06730i −1.28937 + 0.856530i
\(36\) 1.00000 0.166667
\(37\) 2.62056 4.53894i 0.430817 0.746198i −0.566126 0.824318i \(-0.691559\pi\)
0.996944 + 0.0781207i \(0.0248920\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) 3.46130 + 5.99515i 0.554252 + 0.959993i
\(40\) −1.73065 + 2.99758i −0.273640 + 0.473958i
\(41\) 8.88553 1.38769 0.693843 0.720126i \(-0.255916\pi\)
0.693843 + 0.720126i \(0.255916\pi\)
\(42\) −2.36975 1.17656i −0.365660 0.181547i
\(43\) 10.3705 1.58149 0.790745 0.612145i \(-0.209693\pi\)
0.790745 + 0.612145i \(0.209693\pi\)
\(44\) −0.139098 + 0.240925i −0.0209699 + 0.0363209i
\(45\) 1.73065 + 2.99758i 0.257990 + 0.446852i
\(46\) 1.54617 + 2.67804i 0.227970 + 0.394855i
\(47\) 0.896599 1.55296i 0.130782 0.226522i −0.793196 0.608966i \(-0.791584\pi\)
0.923978 + 0.382445i \(0.124918\pi\)
\(48\) −1.00000 −0.144338
\(49\) 4.23143 + 5.57629i 0.604490 + 0.796613i
\(50\) −6.98062 −0.987209
\(51\) 2.89876 5.02079i 0.405907 0.703052i
\(52\) −3.46130 5.99515i −0.479996 0.831378i
\(53\) −4.19411 7.26442i −0.576106 0.997844i −0.995921 0.0902346i \(-0.971238\pi\)
0.419815 0.907610i \(-0.362095\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −0.962923 −0.129841
\(56\) 2.36975 + 1.17656i 0.316671 + 0.157224i
\(57\) −1.00000 −0.132453
\(58\) −4.27682 + 7.40767i −0.561574 + 0.972674i
\(59\) 3.89738 + 6.75046i 0.507395 + 0.878835i 0.999963 + 0.00856059i \(0.00272495\pi\)
−0.492568 + 0.870274i \(0.663942\pi\)
\(60\) −1.73065 2.99758i −0.223426 0.386985i
\(61\) −4.56470 + 7.90630i −0.584450 + 1.01230i 0.410493 + 0.911864i \(0.365357\pi\)
−0.994944 + 0.100434i \(0.967977\pi\)
\(62\) −7.34959 −0.933399
\(63\) 2.20380 1.46399i 0.277653 0.184445i
\(64\) 1.00000 0.125000
\(65\) 11.9806 20.7510i 1.48601 2.57385i
\(66\) −0.139098 0.240925i −0.0171218 0.0296559i
\(67\) 6.86891 + 11.8973i 0.839171 + 1.45349i 0.890589 + 0.454809i \(0.150293\pi\)
−0.0514182 + 0.998677i \(0.516374\pi\)
\(68\) −2.89876 + 5.02079i −0.351526 + 0.608861i
\(69\) −3.09233 −0.372273
\(70\) 0.574394 + 9.13972i 0.0686532 + 1.09241i
\(71\) 0.684727 0.0812621 0.0406311 0.999174i \(-0.487063\pi\)
0.0406311 + 0.999174i \(0.487063\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 0.962682 + 1.66741i 0.112673 + 0.195156i 0.916847 0.399238i \(-0.130725\pi\)
−0.804174 + 0.594394i \(0.797392\pi\)
\(74\) −2.62056 4.53894i −0.304634 0.527641i
\(75\) 3.49031 6.04539i 0.403026 0.698062i
\(76\) 1.00000 0.114708
\(77\) 0.0461660 + 0.734590i 0.00526111 + 0.0837143i
\(78\) 6.92261 0.783831
\(79\) −0.703803 + 1.21902i −0.0791840 + 0.137151i −0.902898 0.429855i \(-0.858565\pi\)
0.823714 + 0.567005i \(0.191898\pi\)
\(80\) 1.73065 + 2.99758i 0.193493 + 0.335139i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.44277 7.69509i 0.490621 0.849781i
\(83\) −0.146030 −0.0160289 −0.00801443 0.999968i \(-0.502551\pi\)
−0.00801443 + 0.999968i \(0.502551\pi\)
\(84\) −2.20380 + 1.46399i −0.240455 + 0.159734i
\(85\) −20.0670 −2.17657
\(86\) 5.18526 8.98114i 0.559141 0.968461i
\(87\) −4.27682 7.40767i −0.458523 0.794185i
\(88\) 0.139098 + 0.240925i 0.0148279 + 0.0256827i
\(89\) 6.85037 11.8652i 0.726138 1.25771i −0.232366 0.972628i \(-0.574647\pi\)
0.958504 0.285079i \(-0.0920199\pi\)
\(90\) 3.46130 0.364853
\(91\) −16.4048 8.14484i −1.71970 0.853811i
\(92\) 3.09233 0.322398
\(93\) 3.67480 6.36493i 0.381059 0.660013i
\(94\) −0.896599 1.55296i −0.0924771 0.160175i
\(95\) 1.73065 + 2.99758i 0.177561 + 0.307545i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 4.09233 0.415513 0.207757 0.978181i \(-0.433384\pi\)
0.207757 + 0.978181i \(0.433384\pi\)
\(98\) 6.94492 0.876382i 0.701543 0.0885279i
\(99\) 0.278197 0.0279598
\(100\) −3.49031 + 6.04539i −0.349031 + 0.604539i
\(101\) 1.22849 + 2.12781i 0.122240 + 0.211725i 0.920651 0.390388i \(-0.127659\pi\)
−0.798411 + 0.602113i \(0.794326\pi\)
\(102\) −2.89876 5.02079i −0.287020 0.497133i
\(103\) −8.67342 + 15.0228i −0.854617 + 1.48024i 0.0223826 + 0.999749i \(0.492875\pi\)
−0.877000 + 0.480491i \(0.840459\pi\)
\(104\) −6.92261 −0.678817
\(105\) −8.20242 4.07242i −0.800475 0.397427i
\(106\) −8.38823 −0.814737
\(107\) 5.73896 9.94017i 0.554806 0.960953i −0.443112 0.896466i \(-0.646126\pi\)
0.997919 0.0644867i \(-0.0205410\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 9.34068 + 16.1785i 0.894675 + 1.54962i 0.834206 + 0.551452i \(0.185926\pi\)
0.0604685 + 0.998170i \(0.480741\pi\)
\(110\) −0.481462 + 0.833916i −0.0459056 + 0.0795108i
\(111\) 5.24112 0.497465
\(112\) 2.20380 1.46399i 0.208240 0.138334i
\(113\) 3.29913 0.310356 0.155178 0.987886i \(-0.450405\pi\)
0.155178 + 0.987886i \(0.450405\pi\)
\(114\) −0.500000 + 0.866025i −0.0468293 + 0.0811107i
\(115\) 5.35175 + 9.26950i 0.499053 + 0.864386i
\(116\) 4.27682 + 7.40767i 0.397093 + 0.687784i
\(117\) −3.46130 + 5.99515i −0.319998 + 0.554252i
\(118\) 7.79476 0.717565
\(119\) 0.962082 + 15.3086i 0.0881939 + 1.40334i
\(120\) −3.46130 −0.315972
\(121\) 5.46130 9.45925i 0.496482 0.859932i
\(122\) 4.56470 + 7.90630i 0.413269 + 0.715803i
\(123\) 4.44277 + 7.69509i 0.400591 + 0.693843i
\(124\) −3.67480 + 6.36493i −0.330006 + 0.571588i
\(125\) −6.85553 −0.613177
\(126\) −0.165947 2.64054i −0.0147838 0.235238i
\(127\) −3.45699 −0.306758 −0.153379 0.988167i \(-0.549016\pi\)
−0.153379 + 0.988167i \(0.549016\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 5.18526 + 8.98114i 0.456537 + 0.790745i
\(130\) −11.9806 20.7510i −1.05077 1.81999i
\(131\) −9.24781 + 16.0177i −0.807985 + 1.39947i 0.106272 + 0.994337i \(0.466108\pi\)
−0.914257 + 0.405134i \(0.867225\pi\)
\(132\) −0.278197 −0.0242139
\(133\) 2.20380 1.46399i 0.191094 0.126944i
\(134\) 13.7378 1.18677
\(135\) −1.73065 + 2.99758i −0.148951 + 0.257990i
\(136\) 2.89876 + 5.02079i 0.248566 + 0.430530i
\(137\) 6.08402 + 10.5378i 0.519793 + 0.900308i 0.999735 + 0.0230078i \(0.00732427\pi\)
−0.479942 + 0.877300i \(0.659342\pi\)
\(138\) −1.54617 + 2.67804i −0.131618 + 0.227970i
\(139\) −2.91829 −0.247526 −0.123763 0.992312i \(-0.539496\pi\)
−0.123763 + 0.992312i \(0.539496\pi\)
\(140\) 8.20242 + 4.07242i 0.693231 + 0.344182i
\(141\) 1.79320 0.151015
\(142\) 0.342363 0.592991i 0.0287305 0.0497627i
\(143\) −0.962923 1.66783i −0.0805237 0.139471i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −14.8034 + 25.6402i −1.22935 + 2.12930i
\(146\) 1.92536 0.159344
\(147\) −2.71349 + 6.45267i −0.223805 + 0.532207i
\(148\) −5.24112 −0.430817
\(149\) 2.08246 3.60693i 0.170602 0.295491i −0.768028 0.640416i \(-0.778762\pi\)
0.938631 + 0.344924i \(0.112095\pi\)
\(150\) −3.49031 6.04539i −0.284983 0.493604i
\(151\) −9.63772 16.6930i −0.784306 1.35846i −0.929413 0.369043i \(-0.879686\pi\)
0.145106 0.989416i \(-0.453648\pi\)
\(152\) 0.500000 0.866025i 0.0405554 0.0702439i
\(153\) 5.79751 0.468701
\(154\) 0.659257 + 0.327314i 0.0531244 + 0.0263757i
\(155\) −25.4392 −2.04332
\(156\) 3.46130 5.99515i 0.277126 0.479996i
\(157\) 10.7284 + 18.5822i 0.856222 + 1.48302i 0.875507 + 0.483206i \(0.160528\pi\)
−0.0192847 + 0.999814i \(0.506139\pi\)
\(158\) 0.703803 + 1.21902i 0.0559915 + 0.0969802i
\(159\) 4.19411 7.26442i 0.332615 0.576106i
\(160\) 3.46130 0.273640
\(161\) 6.81489 4.52713i 0.537089 0.356788i
\(162\) −1.00000 −0.0785674
\(163\) −7.97231 + 13.8084i −0.624439 + 1.08156i 0.364209 + 0.931317i \(0.381339\pi\)
−0.988649 + 0.150244i \(0.951994\pi\)
\(164\) −4.44277 7.69509i −0.346922 0.600886i
\(165\) −0.481462 0.833916i −0.0374817 0.0649203i
\(166\) −0.0730150 + 0.126466i −0.00566706 + 0.00981564i
\(167\) 17.6073 1.36250 0.681248 0.732053i \(-0.261437\pi\)
0.681248 + 0.732053i \(0.261437\pi\)
\(168\) 0.165947 + 2.64054i 0.0128031 + 0.203722i
\(169\) 34.9225 2.68634
\(170\) −10.0335 + 17.3785i −0.769533 + 1.33287i
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) −5.18526 8.98114i −0.395373 0.684806i
\(173\) −5.00531 + 8.66945i −0.380547 + 0.659126i −0.991140 0.132818i \(-0.957598\pi\)
0.610594 + 0.791944i \(0.290931\pi\)
\(174\) −8.55364 −0.648449
\(175\) 1.15842 + 18.4326i 0.0875680 + 1.39338i
\(176\) 0.278197 0.0209699
\(177\) −3.89738 + 6.75046i −0.292945 + 0.507395i
\(178\) −6.85037 11.8652i −0.513457 0.889334i
\(179\) −3.12941 5.42029i −0.233903 0.405132i 0.725050 0.688696i \(-0.241816\pi\)
−0.958953 + 0.283564i \(0.908483\pi\)
\(180\) 1.73065 2.99758i 0.128995 0.223426i
\(181\) −4.25019 −0.315914 −0.157957 0.987446i \(-0.550491\pi\)
−0.157957 + 0.987446i \(0.550491\pi\)
\(182\) −15.2561 + 10.1346i −1.13085 + 0.751226i
\(183\) −9.12941 −0.674865
\(184\) 1.54617 2.67804i 0.113985 0.197428i
\(185\) −9.07055 15.7107i −0.666880 1.15507i
\(186\) −3.67480 6.36493i −0.269449 0.466700i
\(187\) −0.806425 + 1.39677i −0.0589716 + 0.102142i
\(188\) −1.79320 −0.130782
\(189\) 2.36975 + 1.17656i 0.172374 + 0.0855819i
\(190\) 3.46130 0.251109
\(191\) 5.47393 9.48112i 0.396080 0.686030i −0.597159 0.802123i \(-0.703704\pi\)
0.993238 + 0.116093i \(0.0370371\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −10.6449 18.4376i −0.766240 1.32717i −0.939588 0.342306i \(-0.888792\pi\)
0.173348 0.984861i \(-0.444541\pi\)
\(194\) 2.04617 3.54406i 0.146906 0.254449i
\(195\) 23.9612 1.71590
\(196\) 2.71349 6.45267i 0.193821 0.460905i
\(197\) −6.63103 −0.472441 −0.236221 0.971699i \(-0.575909\pi\)
−0.236221 + 0.971699i \(0.575909\pi\)
\(198\) 0.139098 0.240925i 0.00988529 0.0171218i
\(199\) 3.93523 + 6.81602i 0.278961 + 0.483175i 0.971127 0.238564i \(-0.0766766\pi\)
−0.692166 + 0.721739i \(0.743343\pi\)
\(200\) 3.49031 + 6.04539i 0.246802 + 0.427474i
\(201\) −6.86891 + 11.8973i −0.484495 + 0.839171i
\(202\) 2.45699 0.172873
\(203\) 20.2700 + 10.0638i 1.42267 + 0.706343i
\(204\) −5.79751 −0.405907
\(205\) 15.3778 26.6351i 1.07403 1.86027i
\(206\) 8.67342 + 15.0228i 0.604306 + 1.04669i
\(207\) −1.54617 2.67804i −0.107466 0.186137i
\(208\) −3.46130 + 5.99515i −0.239998 + 0.415689i
\(209\) 0.278197 0.0192433
\(210\) −7.62803 + 5.06730i −0.526384 + 0.349677i
\(211\) 14.9123 1.02660 0.513302 0.858208i \(-0.328422\pi\)
0.513302 + 0.858208i \(0.328422\pi\)
\(212\) −4.19411 + 7.26442i −0.288053 + 0.498922i
\(213\) 0.342363 + 0.592991i 0.0234583 + 0.0406311i
\(214\) −5.73896 9.94017i −0.392307 0.679496i
\(215\) 17.9478 31.0865i 1.22403 2.12008i
\(216\) 1.00000 0.0680414
\(217\) 1.21965 + 19.4069i 0.0827949 + 1.31743i
\(218\) 18.6814 1.26526
\(219\) −0.962682 + 1.66741i −0.0650520 + 0.112673i
\(220\) 0.481462 + 0.833916i 0.0324601 + 0.0562226i
\(221\) −20.0670 34.7570i −1.34985 2.33801i
\(222\) 2.62056 4.53894i 0.175880 0.304634i
\(223\) 3.92861 0.263079 0.131539 0.991311i \(-0.458008\pi\)
0.131539 + 0.991311i \(0.458008\pi\)
\(224\) −0.165947 2.64054i −0.0110878 0.176429i
\(225\) 6.98062 0.465375
\(226\) 1.64957 2.85713i 0.109728 0.190054i
\(227\) 3.51985 + 6.09657i 0.233621 + 0.404643i 0.958871 0.283842i \(-0.0916092\pi\)
−0.725250 + 0.688486i \(0.758276\pi\)
\(228\) 0.500000 + 0.866025i 0.0331133 + 0.0573539i
\(229\) −2.94199 + 5.09567i −0.194412 + 0.336731i −0.946708 0.322094i \(-0.895613\pi\)
0.752296 + 0.658826i \(0.228947\pi\)
\(230\) 10.7035 0.705768
\(231\) −0.613091 + 0.407276i −0.0403384 + 0.0267968i
\(232\) 8.55364 0.561574
\(233\) −1.40329 + 2.43057i −0.0919326 + 0.159232i −0.908324 0.418267i \(-0.862638\pi\)
0.816392 + 0.577499i \(0.195971\pi\)
\(234\) 3.46130 + 5.99515i 0.226272 + 0.391915i
\(235\) −3.10340 5.37525i −0.202444 0.350643i
\(236\) 3.89738 6.75046i 0.253698 0.439417i
\(237\) −1.40761 −0.0914338
\(238\) 13.7387 + 6.82110i 0.890545 + 0.442146i
\(239\) −12.4016 −0.802193 −0.401097 0.916036i \(-0.631371\pi\)
−0.401097 + 0.916036i \(0.631371\pi\)
\(240\) −1.73065 + 2.99758i −0.111713 + 0.193493i
\(241\) 7.59824 + 13.1605i 0.489446 + 0.847745i 0.999926 0.0121442i \(-0.00386573\pi\)
−0.510480 + 0.859889i \(0.670532\pi\)
\(242\) −5.46130 9.45925i −0.351066 0.608064i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 9.12941 0.584450
\(245\) 24.0385 3.03342i 1.53576 0.193798i
\(246\) 8.88553 0.566521
\(247\) −3.46130 + 5.99515i −0.220237 + 0.381462i
\(248\) 3.67480 + 6.36493i 0.233350 + 0.404174i
\(249\) −0.0730150 0.126466i −0.00462714 0.00801443i
\(250\) −3.42776 + 5.93706i −0.216791 + 0.375493i
\(251\) 5.91198 0.373161 0.186581 0.982440i \(-0.440259\pi\)
0.186581 + 0.982440i \(0.440259\pi\)
\(252\) −2.36975 1.17656i −0.149280 0.0741161i
\(253\) 0.860277 0.0540851
\(254\) −1.72849 + 2.99384i −0.108455 + 0.187850i
\(255\) −10.0335 17.3785i −0.628321 1.08828i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.702424 + 1.21663i −0.0438160 + 0.0758915i −0.887102 0.461574i \(-0.847285\pi\)
0.843286 + 0.537466i \(0.180618\pi\)
\(258\) 10.3705 0.645641
\(259\) −11.5504 + 7.67292i −0.717707 + 0.476772i
\(260\) −23.9612 −1.48601
\(261\) 4.27682 7.40767i 0.264728 0.458523i
\(262\) 9.24781 + 16.0177i 0.571332 + 0.989575i
\(263\) 5.38907 + 9.33414i 0.332304 + 0.575568i 0.982963 0.183802i \(-0.0588406\pi\)
−0.650659 + 0.759370i \(0.725507\pi\)
\(264\) −0.139098 + 0.240925i −0.00856091 + 0.0148279i
\(265\) −29.0342 −1.78356
\(266\) −0.165947 2.64054i −0.0101749 0.161902i
\(267\) 13.7007 0.838472
\(268\) 6.86891 11.8973i 0.419585 0.726743i
\(269\) −11.2231 19.4390i −0.684286 1.18522i −0.973661 0.228002i \(-0.926781\pi\)
0.289375 0.957216i \(-0.406553\pi\)
\(270\) 1.73065 + 2.99758i 0.105324 + 0.182427i
\(271\) 1.13826 1.97152i 0.0691442 0.119761i −0.829381 0.558684i \(-0.811306\pi\)
0.898525 + 0.438923i \(0.144640\pi\)
\(272\) 5.79751 0.351526
\(273\) −1.14879 18.2794i −0.0695278 1.10632i
\(274\) 12.1680 0.735098
\(275\) −0.970993 + 1.68181i −0.0585531 + 0.101417i
\(276\) 1.54617 + 2.67804i 0.0930683 + 0.161199i
\(277\) −13.7260 23.7742i −0.824717 1.42845i −0.902135 0.431454i \(-0.858001\pi\)
0.0774178 0.996999i \(-0.475332\pi\)
\(278\) −1.45915 + 2.52731i −0.0875137 + 0.151578i
\(279\) 7.34959 0.440009
\(280\) 7.62803 5.06730i 0.455862 0.302829i
\(281\) 8.14279 0.485758 0.242879 0.970057i \(-0.421908\pi\)
0.242879 + 0.970057i \(0.421908\pi\)
\(282\) 0.896599 1.55296i 0.0533917 0.0924771i
\(283\) 4.09293 + 7.08917i 0.243300 + 0.421407i 0.961652 0.274272i \(-0.0884369\pi\)
−0.718353 + 0.695679i \(0.755104\pi\)
\(284\) −0.342363 0.592991i −0.0203155 0.0351875i
\(285\) −1.73065 + 2.99758i −0.102515 + 0.177561i
\(286\) −1.92585 −0.113878
\(287\) −21.0565 10.4543i −1.24293 0.617099i
\(288\) −1.00000 −0.0589256
\(289\) −8.30558 + 14.3857i −0.488564 + 0.846217i
\(290\) 14.8034 + 25.6402i 0.869283 + 1.50564i
\(291\) 2.04617 + 3.54406i 0.119948 + 0.207757i
\(292\) 0.962682 1.66741i 0.0563367 0.0975781i
\(293\) −19.3421 −1.12998 −0.564988 0.825099i \(-0.691119\pi\)
−0.564988 + 0.825099i \(0.691119\pi\)
\(294\) 4.23143 + 5.57629i 0.246782 + 0.325216i
\(295\) 26.9800 1.57084
\(296\) −2.62056 + 4.53894i −0.152317 + 0.263821i
\(297\) 0.139098 + 0.240925i 0.00807131 + 0.0139799i
\(298\) −2.08246 3.60693i −0.120634 0.208944i
\(299\) −10.7035 + 18.5390i −0.618999 + 1.07214i
\(300\) −6.98062 −0.403026
\(301\) −24.5756 12.2015i −1.41651 0.703283i
\(302\) −19.2754 −1.10918
\(303\) −1.22849 + 2.12781i −0.0705751 + 0.122240i
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) 15.7998 + 27.3661i 0.904695 + 1.56698i
\(306\) 2.89876 5.02079i 0.165711 0.287020i
\(307\) −11.7007 −0.667797 −0.333898 0.942609i \(-0.608364\pi\)
−0.333898 + 0.942609i \(0.608364\pi\)
\(308\) 0.613091 0.407276i 0.0349341 0.0232067i
\(309\) −17.3468 −0.986827
\(310\) −12.7196 + 22.0310i −0.722424 + 1.25127i
\(311\) −6.92776 11.9992i −0.392837 0.680414i 0.599985 0.800011i \(-0.295173\pi\)
−0.992823 + 0.119597i \(0.961840\pi\)
\(312\) −3.46130 5.99515i −0.195958 0.339409i
\(313\) 0.985994 1.70779i 0.0557317 0.0965301i −0.836814 0.547488i \(-0.815584\pi\)
0.892545 + 0.450958i \(0.148918\pi\)
\(314\) 21.4569 1.21088
\(315\) −0.574394 9.13972i −0.0323634 0.514965i
\(316\) 1.40761 0.0791840
\(317\) −9.95023 + 17.2343i −0.558861 + 0.967975i 0.438731 + 0.898618i \(0.355428\pi\)
−0.997592 + 0.0693570i \(0.977905\pi\)
\(318\) −4.19411 7.26442i −0.235194 0.407368i
\(319\) 1.18980 + 2.06079i 0.0666158 + 0.115382i
\(320\) 1.73065 2.99758i 0.0967464 0.167570i
\(321\) 11.4779 0.640635
\(322\) −0.513164 8.16543i −0.0285975 0.455042i
\(323\) 5.79751 0.322582
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −24.1620 41.8499i −1.34027 2.32141i
\(326\) 7.97231 + 13.8084i 0.441545 + 0.764779i
\(327\) −9.34068 + 16.1785i −0.516541 + 0.894675i
\(328\) −8.88553 −0.490621
\(329\) −3.95185 + 2.62522i −0.217873 + 0.144733i
\(330\) −0.962923 −0.0530072
\(331\) 2.33381 4.04228i 0.128278 0.222184i −0.794732 0.606961i \(-0.792388\pi\)
0.923009 + 0.384777i \(0.125722\pi\)
\(332\) 0.0730150 + 0.126466i 0.00400722 + 0.00694070i
\(333\) 2.62056 + 4.53894i 0.143606 + 0.248733i
\(334\) 8.80367 15.2484i 0.481715 0.834355i
\(335\) 47.5508 2.59798
\(336\) 2.36975 + 1.17656i 0.129280 + 0.0641864i
\(337\) −11.4639 −0.624480 −0.312240 0.950003i \(-0.601079\pi\)
−0.312240 + 0.950003i \(0.601079\pi\)
\(338\) 17.4612 30.2438i 0.949766 1.64504i
\(339\) 1.64957 + 2.85713i 0.0895922 + 0.155178i
\(340\) 10.0335 + 17.3785i 0.544142 + 0.942481i
\(341\) −1.02232 + 1.77070i −0.0553615 + 0.0958890i
\(342\) −1.00000 −0.0540738
\(343\) −3.46661 18.1929i −0.187180 0.982326i
\(344\) −10.3705 −0.559141
\(345\) −5.35175 + 9.26950i −0.288129 + 0.499053i
\(346\) 5.00531 + 8.66945i 0.269087 + 0.466073i
\(347\) −3.92129 6.79187i −0.210506 0.364607i 0.741367 0.671100i \(-0.234178\pi\)
−0.951873 + 0.306493i \(0.900844\pi\)
\(348\) −4.27682 + 7.40767i −0.229261 + 0.397093i
\(349\) 21.2991 1.14012 0.570058 0.821604i \(-0.306921\pi\)
0.570058 + 0.821604i \(0.306921\pi\)
\(350\) 16.5423 + 8.21309i 0.884224 + 0.439008i
\(351\) −6.92261 −0.369501
\(352\) 0.139098 0.240925i 0.00741397 0.0128414i
\(353\) −4.35850 7.54915i −0.231980 0.401801i 0.726411 0.687261i \(-0.241187\pi\)
−0.958391 + 0.285460i \(0.907854\pi\)
\(354\) 3.89738 + 6.75046i 0.207143 + 0.358783i
\(355\) 1.18502 2.05252i 0.0628945 0.108936i
\(356\) −13.7007 −0.726138
\(357\) −12.7766 + 8.48748i −0.676208 + 0.449205i
\(358\) −6.25882 −0.330789
\(359\) −0.585642 + 1.01436i −0.0309090 + 0.0535359i −0.881066 0.472993i \(-0.843174\pi\)
0.850157 + 0.526529i \(0.176507\pi\)
\(360\) −1.73065 2.99758i −0.0912134 0.157986i
\(361\) −0.500000 0.866025i −0.0263158 0.0455803i
\(362\) −2.12509 + 3.68077i −0.111692 + 0.193457i
\(363\) 10.9226 0.573288
\(364\) 1.14879 + 18.2794i 0.0602129 + 0.958103i
\(365\) 6.66427 0.348824
\(366\) −4.56470 + 7.90630i −0.238601 + 0.413269i
\(367\) −2.50647 4.34134i −0.130837 0.226616i 0.793163 0.609010i \(-0.208433\pi\)
−0.923999 + 0.382394i \(0.875100\pi\)
\(368\) −1.54617 2.67804i −0.0805995 0.139602i
\(369\) −4.44277 + 7.69509i −0.231281 + 0.400591i
\(370\) −18.1411 −0.943111
\(371\) 1.39200 + 22.1495i 0.0722692 + 1.14994i
\(372\) −7.34959 −0.381059
\(373\) −0.932921 + 1.61587i −0.0483048 + 0.0836664i −0.889167 0.457583i \(-0.848715\pi\)
0.840862 + 0.541250i \(0.182049\pi\)
\(374\) 0.806425 + 1.39677i 0.0416992 + 0.0722252i
\(375\) −3.42776 5.93706i −0.177009 0.306589i
\(376\) −0.896599 + 1.55296i −0.0462386 + 0.0800875i
\(377\) −59.2135 −3.04965
\(378\) 2.20380 1.46399i 0.113351 0.0752993i
\(379\) −11.8065 −0.606457 −0.303228 0.952918i \(-0.598065\pi\)
−0.303228 + 0.952918i \(0.598065\pi\)
\(380\) 1.73065 2.99758i 0.0887806 0.153772i
\(381\) −1.72849 2.99384i −0.0885534 0.153379i
\(382\) −5.47393 9.48112i −0.280071 0.485097i
\(383\) −2.76320 + 4.78600i −0.141193 + 0.244553i −0.927946 0.372715i \(-0.878427\pi\)
0.786753 + 0.617268i \(0.211760\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.28189 + 1.13293i 0.116296 + 0.0577396i
\(386\) −21.2899 −1.08363
\(387\) −5.18526 + 8.98114i −0.263582 + 0.456537i
\(388\) −2.04617 3.54406i −0.103878 0.179923i
\(389\) −0.632104 1.09484i −0.0320490 0.0555104i 0.849556 0.527498i \(-0.176870\pi\)
−0.881605 + 0.471988i \(0.843537\pi\)
\(390\) 11.9806 20.7510i 0.606662 1.05077i
\(391\) 17.9278 0.906650
\(392\) −4.23143 5.57629i −0.213720 0.281645i
\(393\) −18.4956 −0.932981
\(394\) −3.31551 + 5.74264i −0.167033 + 0.289310i
\(395\) 2.43607 + 4.21940i 0.122572 + 0.212301i
\(396\) −0.139098 0.240925i −0.00698996 0.0121070i
\(397\) 0.702424 1.21663i 0.0352536 0.0610611i −0.847860 0.530220i \(-0.822109\pi\)
0.883114 + 0.469159i \(0.155443\pi\)
\(398\) 7.87047 0.394511
\(399\) 2.36975 + 1.17656i 0.118636 + 0.0589015i
\(400\) 6.98062 0.349031
\(401\) 2.38559 4.13197i 0.119131 0.206341i −0.800293 0.599610i \(-0.795323\pi\)
0.919423 + 0.393269i \(0.128656\pi\)
\(402\) 6.86891 + 11.8973i 0.342590 + 0.593383i
\(403\) −25.4392 44.0619i −1.26722 2.19488i
\(404\) 1.22849 2.12781i 0.0611198 0.105863i
\(405\) −3.46130 −0.171994
\(406\) 18.8505 12.5224i 0.935536 0.621476i
\(407\) −1.45806 −0.0722735
\(408\) −2.89876 + 5.02079i −0.143510 + 0.248566i
\(409\) 9.04448 + 15.6655i 0.447221 + 0.774609i 0.998204 0.0599071i \(-0.0190804\pi\)
−0.550983 + 0.834516i \(0.685747\pi\)
\(410\) −15.3778 26.6351i −0.759453 1.31541i
\(411\) −6.08402 + 10.5378i −0.300103 + 0.519793i
\(412\) 17.3468 0.854617
\(413\) −1.29352 20.5824i −0.0636499 1.01279i
\(414\) −3.09233 −0.151980
\(415\) −0.252727 + 0.437736i −0.0124059 + 0.0214876i
\(416\) 3.46130 + 5.99515i 0.169704 + 0.293937i
\(417\) −1.45915 2.52731i −0.0714547 0.123763i
\(418\) 0.139098 0.240925i 0.00680353 0.0117841i
\(419\) 2.70518 0.132157 0.0660784 0.997814i \(-0.478951\pi\)
0.0660784 + 0.997814i \(0.478951\pi\)
\(420\) 0.574394 + 9.13972i 0.0280276 + 0.445972i
\(421\) 6.14064 0.299276 0.149638 0.988741i \(-0.452189\pi\)
0.149638 + 0.988741i \(0.452189\pi\)
\(422\) 7.45615 12.9144i 0.362960 0.628664i
\(423\) 0.896599 + 1.55296i 0.0435941 + 0.0755073i
\(424\) 4.19411 + 7.26442i 0.203684 + 0.352791i
\(425\) −20.2351 + 35.0483i −0.981548 + 1.70009i
\(426\) 0.684727 0.0331751
\(427\) 20.1194 13.3653i 0.973647 0.646793i
\(428\) −11.4779 −0.554806
\(429\) 0.962923 1.66783i 0.0464904 0.0805237i
\(430\) −17.9478 31.0865i −0.865518 1.49912i
\(431\) −10.6383 18.4260i −0.512427 0.887549i −0.999896 0.0144092i \(-0.995413\pi\)
0.487469 0.873140i \(-0.337920\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −9.42099 −0.452744 −0.226372 0.974041i \(-0.572686\pi\)
−0.226372 + 0.974041i \(0.572686\pi\)
\(434\) 17.4167 + 8.64721i 0.836028 + 0.415079i
\(435\) −29.6067 −1.41953
\(436\) 9.34068 16.1785i 0.447337 0.774811i
\(437\) −1.54617 2.67804i −0.0739632 0.128108i
\(438\) 0.962682 + 1.66741i 0.0459987 + 0.0796722i
\(439\) −6.29620 + 10.9053i −0.300501 + 0.520483i −0.976250 0.216649i \(-0.930487\pi\)
0.675748 + 0.737132i \(0.263821\pi\)
\(440\) 0.962923 0.0459056
\(441\) −6.94492 + 0.876382i −0.330711 + 0.0417325i
\(442\) −40.1339 −1.90898
\(443\) 11.6473 20.1738i 0.553382 0.958486i −0.444645 0.895707i \(-0.646670\pi\)
0.998027 0.0627792i \(-0.0199964\pi\)
\(444\) −2.62056 4.53894i −0.124366 0.215409i
\(445\) −23.7112 41.0690i −1.12402 1.94686i
\(446\) 1.96430 3.40227i 0.0930124 0.161102i
\(447\) 4.16493 0.196994
\(448\) −2.36975 1.17656i −0.111960 0.0555871i
\(449\) −0.486074 −0.0229393 −0.0114696 0.999934i \(-0.503651\pi\)
−0.0114696 + 0.999934i \(0.503651\pi\)
\(450\) 3.49031 6.04539i 0.164535 0.284983i
\(451\) −1.23596 2.14075i −0.0581992 0.100804i
\(452\) −1.64957 2.85713i −0.0775891 0.134388i
\(453\) 9.63772 16.6930i 0.452820 0.784306i
\(454\) 7.03971 0.330390
\(455\) −52.8058 + 35.0789i −2.47558 + 1.64452i
\(456\) 1.00000 0.0468293
\(457\) −7.22987 + 12.5225i −0.338199 + 0.585778i −0.984094 0.177648i \(-0.943151\pi\)
0.645895 + 0.763426i \(0.276484\pi\)
\(458\) 2.94199 + 5.09567i 0.137470 + 0.238105i
\(459\) 2.89876 + 5.02079i 0.135302 + 0.234351i
\(460\) 5.35175 9.26950i 0.249527 0.432193i
\(461\) 18.0188 0.839218 0.419609 0.907705i \(-0.362167\pi\)
0.419609 + 0.907705i \(0.362167\pi\)
\(462\) 0.0461660 + 0.734590i 0.00214784 + 0.0341762i
\(463\) 23.3408 1.08474 0.542370 0.840140i \(-0.317527\pi\)
0.542370 + 0.840140i \(0.317527\pi\)
\(464\) 4.27682 7.40767i 0.198546 0.343892i
\(465\) −12.7196 22.0310i −0.589857 1.02166i
\(466\) 1.40329 + 2.43057i 0.0650061 + 0.112594i
\(467\) 4.07439 7.05706i 0.188540 0.326562i −0.756223 0.654314i \(-0.772958\pi\)
0.944764 + 0.327752i \(0.106291\pi\)
\(468\) 6.92261 0.319998
\(469\) −2.27975 36.2753i −0.105269 1.67504i
\(470\) −6.20680 −0.286298
\(471\) −10.7284 + 18.5822i −0.494340 + 0.856222i
\(472\) −3.89738 6.75046i −0.179391 0.310715i
\(473\) −1.44252 2.49852i −0.0663273 0.114882i
\(474\) −0.703803 + 1.21902i −0.0323267 + 0.0559915i
\(475\) 6.98062 0.320293
\(476\) 12.7766 8.48748i 0.585613 0.389023i
\(477\) 8.38823 0.384070
\(478\) −6.20080 + 10.7401i −0.283618 + 0.491241i
\(479\) −13.5813 23.5235i −0.620547 1.07482i −0.989384 0.145324i \(-0.953577\pi\)
0.368837 0.929494i \(-0.379756\pi\)
\(480\) 1.73065 + 2.99758i 0.0789931 + 0.136820i
\(481\) 18.1411 31.4213i 0.827163 1.43269i
\(482\) 15.1965 0.692181
\(483\) 7.32805 + 3.63830i 0.333438 + 0.165549i
\(484\) −10.9226 −0.496482
\(485\) 7.08240 12.2671i 0.321595 0.557019i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 5.97117 + 10.3424i 0.270580 + 0.468658i 0.969010 0.247020i \(-0.0794513\pi\)
−0.698431 + 0.715678i \(0.746118\pi\)
\(488\) 4.56470 7.90630i 0.206634 0.357901i
\(489\) −15.9446 −0.721041
\(490\) 9.39222 22.3346i 0.424297 1.00898i
\(491\) −7.00863 −0.316295 −0.158148 0.987415i \(-0.550552\pi\)
−0.158148 + 0.987415i \(0.550552\pi\)
\(492\) 4.44277 7.69509i 0.200295 0.346922i
\(493\) 24.7949 + 42.9460i 1.11671 + 1.93419i
\(494\) 3.46130 + 5.99515i 0.155731 + 0.269735i
\(495\) 0.481462 0.833916i 0.0216401 0.0374817i
\(496\) 7.34959 0.330006
\(497\) −1.62263 0.805620i −0.0727850 0.0361370i
\(498\) −0.146030 −0.00654376
\(499\) 4.56302 7.90339i 0.204269 0.353804i −0.745631 0.666359i \(-0.767852\pi\)
0.949900 + 0.312555i \(0.101185\pi\)
\(500\) 3.42776 + 5.93706i 0.153294 + 0.265513i
\(501\) 8.80367 + 15.2484i 0.393319 + 0.681248i
\(502\) 2.95599 5.11993i 0.131932 0.228514i
\(503\) −24.1190 −1.07541 −0.537706 0.843133i \(-0.680709\pi\)
−0.537706 + 0.843133i \(0.680709\pi\)
\(504\) −2.20380 + 1.46399i −0.0981652 + 0.0652111i
\(505\) 8.50438 0.378440
\(506\) 0.430138 0.745022i 0.0191220 0.0331203i
\(507\) 17.4612 + 30.2438i 0.775481 + 1.34317i
\(508\) 1.72849 + 2.99384i 0.0766895 + 0.132830i
\(509\) 18.7531 32.4813i 0.831215 1.43971i −0.0658607 0.997829i \(-0.520979\pi\)
0.897075 0.441877i \(-0.145687\pi\)
\(510\) −20.0670 −0.888580
\(511\) −0.319509 5.08401i −0.0141343 0.224903i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 0.866025i 0.0220755 0.0382360i
\(514\) 0.702424 + 1.21663i 0.0309826 + 0.0536634i
\(515\) 30.0213 + 51.9985i 1.32290 + 2.29133i
\(516\) 5.18526 8.98114i 0.228269 0.395373i
\(517\) −0.498862 −0.0219399
\(518\) 0.869750 + 13.8394i 0.0382146 + 0.608068i
\(519\) −10.0106 −0.439418
\(520\) −11.9806 + 20.7510i −0.525385 + 0.909993i
\(521\) −21.1025 36.5506i −0.924516 1.60131i −0.792338 0.610083i \(-0.791136\pi\)
−0.132179 0.991226i \(-0.542197\pi\)
\(522\) −4.27682 7.40767i −0.187191 0.324225i
\(523\) −9.54692 + 16.5358i −0.417458 + 0.723058i −0.995683 0.0928192i \(-0.970412\pi\)
0.578225 + 0.815877i \(0.303745\pi\)
\(524\) 18.4956 0.807985
\(525\) −15.3839 + 10.2195i −0.671409 + 0.446017i
\(526\) 10.7781 0.469949
\(527\) −21.3047 + 36.9008i −0.928046 + 1.60742i
\(528\) 0.139098 + 0.240925i 0.00605348 + 0.0104849i
\(529\) 6.71874 + 11.6372i 0.292119 + 0.505965i
\(530\) −14.5171 + 25.1443i −0.630582 + 1.09220i
\(531\) −7.79476 −0.338264
\(532\) −2.36975 1.17656i −0.102742 0.0510102i
\(533\) 61.5110 2.66434
\(534\) 6.85037 11.8652i 0.296445 0.513457i
\(535\) −19.8643 34.4060i −0.858808 1.48750i
\(536\) −6.86891 11.8973i −0.296692 0.513885i
\(537\) 3.12941 5.42029i 0.135044 0.233903i
\(538\) −22.4462 −0.967726
\(539\) 0.754885 1.79511i 0.0325152 0.0773210i
\(540\) 3.46130 0.148951
\(541\) −0.393062 + 0.680803i −0.0168991 + 0.0292700i −0.874351 0.485294i \(-0.838713\pi\)
0.857452 + 0.514564i \(0.172046\pi\)
\(542\) −1.13826 1.97152i −0.0488923 0.0846840i
\(543\) −2.12509 3.68077i −0.0911965 0.157957i
\(544\) 2.89876 5.02079i 0.124283 0.215265i
\(545\) 64.6619 2.76981
\(546\) −16.4048 8.14484i −0.702063 0.348567i
\(547\) 0.670738 0.0286787 0.0143394 0.999897i \(-0.495435\pi\)
0.0143394 + 0.999897i \(0.495435\pi\)
\(548\) 6.08402 10.5378i 0.259897 0.450154i
\(549\) −4.56470 7.90630i −0.194817 0.337433i
\(550\) 0.970993 + 1.68181i 0.0414033 + 0.0717126i
\(551\) 4.27682 7.40767i 0.182199 0.315577i
\(552\) 3.09233 0.131618
\(553\) 3.10208 2.06071i 0.131914 0.0876305i
\(554\) −27.4521 −1.16633
\(555\) 9.07055 15.7107i 0.385024 0.666880i
\(556\) 1.45915 + 2.52731i 0.0618815 + 0.107182i
\(557\) −3.07649 5.32864i −0.130355 0.225782i 0.793458 0.608624i \(-0.208278\pi\)
−0.923813 + 0.382843i \(0.874945\pi\)
\(558\) 3.67480 6.36493i 0.155567 0.269449i
\(559\) 71.7911 3.03644
\(560\) −0.574394 9.13972i −0.0242726 0.386224i
\(561\) −1.61285 −0.0680946
\(562\) 4.07139 7.05186i 0.171741 0.297465i
\(563\) 11.8377 + 20.5035i 0.498899 + 0.864118i 0.999999 0.00127111i \(-0.000404608\pi\)
−0.501100 + 0.865389i \(0.667071\pi\)
\(564\) −0.896599 1.55296i −0.0377536 0.0653912i
\(565\) 5.70965 9.88941i 0.240207 0.416050i
\(566\) 8.18586 0.344078
\(567\) 0.165947 + 2.64054i 0.00696913 + 0.110892i
\(568\) −0.684727 −0.0287305
\(569\) −18.3345 + 31.7563i −0.768623 + 1.33129i 0.169686 + 0.985498i \(0.445725\pi\)
−0.938309 + 0.345797i \(0.887609\pi\)
\(570\) 1.73065 + 2.99758i 0.0724890 + 0.125555i
\(571\) 8.86399 + 15.3529i 0.370947 + 0.642498i 0.989711 0.143078i \(-0.0457000\pi\)
−0.618765 + 0.785576i \(0.712367\pi\)
\(572\) −0.962923 + 1.66783i −0.0402619 + 0.0697356i
\(573\) 10.9479 0.457353
\(574\) −19.5820 + 13.0083i −0.817335 + 0.542955i
\(575\) 21.5864 0.900215
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 0.616028 + 1.06699i 0.0256456 + 0.0444194i 0.878563 0.477626i \(-0.158503\pi\)
−0.852918 + 0.522045i \(0.825169\pi\)
\(578\) 8.30558 + 14.3857i 0.345467 + 0.598366i
\(579\) 10.6449 18.4376i 0.442389 0.766240i
\(580\) 29.6067 1.22935
\(581\) 0.346054 + 0.171812i 0.0143568 + 0.00712798i
\(582\) 4.09233 0.169633
\(583\) −1.16679 + 2.02094i −0.0483235 + 0.0836987i
\(584\) −0.962682 1.66741i −0.0398361 0.0689981i
\(585\) 11.9806 + 20.7510i 0.495338 + 0.857950i
\(586\) −9.67104 + 16.7507i −0.399507 + 0.691967i
\(587\) −10.0714 −0.415691 −0.207845 0.978162i \(-0.566645\pi\)
−0.207845 + 0.978162i \(0.566645\pi\)
\(588\) 6.94492 0.876382i 0.286404 0.0361414i
\(589\) 7.34959 0.302835
\(590\) 13.4900 23.3654i 0.555375 0.961937i
\(591\) −3.31551 5.74264i −0.136382 0.236221i
\(592\) 2.62056 + 4.53894i 0.107704 + 0.186549i
\(593\) −14.1317 + 24.4769i −0.580320 + 1.00514i 0.415121 + 0.909766i \(0.363739\pi\)
−0.995441 + 0.0953778i \(0.969594\pi\)
\(594\) 0.278197 0.0114146
\(595\) 47.5537 + 23.6099i 1.94951 + 0.967912i
\(596\) −4.16493 −0.170602
\(597\) −3.93523 + 6.81602i −0.161058 + 0.278961i
\(598\) 10.7035 + 18.5390i 0.437699 + 0.758116i
\(599\) −2.13988 3.70638i −0.0874330 0.151438i 0.818992 0.573804i \(-0.194533\pi\)
−0.906425 + 0.422366i \(0.861200\pi\)
\(600\) −3.49031 + 6.04539i −0.142491 + 0.246802i
\(601\) −47.6366 −1.94314 −0.971569 0.236757i \(-0.923915\pi\)
−0.971569 + 0.236757i \(0.923915\pi\)
\(602\) −22.8546 + 15.1823i −0.931484 + 0.618785i
\(603\) −13.7378 −0.559447
\(604\) −9.63772 + 16.6930i −0.392153 + 0.679229i
\(605\) −18.9032 32.7413i −0.768525 1.33113i
\(606\) 1.22849 + 2.12781i 0.0499041 + 0.0864365i
\(607\) 10.3465 17.9207i 0.419953 0.727379i −0.575982 0.817463i \(-0.695380\pi\)
0.995934 + 0.0900833i \(0.0287133\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 1.41945 + 22.5862i 0.0575191 + 0.915240i
\(610\) 31.5997 1.27943
\(611\) 6.20680 10.7505i 0.251100 0.434919i
\(612\) −2.89876 5.02079i −0.117175 0.202954i
\(613\) −0.836989 1.44971i −0.0338057 0.0585532i 0.848628 0.528991i \(-0.177429\pi\)
−0.882433 + 0.470438i \(0.844096\pi\)
\(614\) −5.85037 + 10.1331i −0.236102 + 0.408940i
\(615\) 30.7555 1.24018
\(616\) −0.0461660 0.734590i −0.00186008 0.0295975i
\(617\) −13.5252 −0.544504 −0.272252 0.962226i \(-0.587768\pi\)
−0.272252 + 0.962226i \(0.587768\pi\)
\(618\) −8.67342 + 15.0228i −0.348896 + 0.604306i
\(619\) −22.5780 39.1062i −0.907485 1.57181i −0.817547 0.575862i \(-0.804666\pi\)
−0.0899383 0.995947i \(-0.528667\pi\)
\(620\) 12.7196 + 22.0310i 0.510831 + 0.884785i
\(621\) 1.54617 2.67804i 0.0620455 0.107466i
\(622\) −13.8555 −0.555556
\(623\) −30.1937 + 20.0577i −1.20969 + 0.803594i
\(624\) −6.92261 −0.277126
\(625\) 5.58702 9.67700i 0.223481 0.387080i
\(626\) −0.985994 1.70779i −0.0394083 0.0682571i
\(627\) 0.139098 + 0.240925i 0.00555505 + 0.00962164i
\(628\) 10.7284 18.5822i 0.428111 0.741510i
\(629\) −30.3855 −1.21155
\(630\) −8.20242 4.07242i −0.326792 0.162249i
\(631\) −3.01542 −0.120042 −0.0600210 0.998197i \(-0.519117\pi\)
−0.0600210 + 0.998197i \(0.519117\pi\)
\(632\) 0.703803 1.21902i 0.0279958 0.0484901i
\(633\) 7.45615 + 12.9144i 0.296355 + 0.513302i
\(634\) 9.95023 + 17.2343i 0.395174 + 0.684462i
\(635\) −5.98284 + 10.3626i −0.237422 + 0.411227i
\(636\) −8.38823 −0.332615
\(637\) 29.2925 + 38.6025i 1.16061 + 1.52948i
\(638\) 2.37959 0.0942090
\(639\) −0.342363 + 0.592991i −0.0135437 + 0.0234583i
\(640\) −1.73065 2.99758i −0.0684100 0.118490i
\(641\) −7.99808 13.8531i −0.315905 0.547164i 0.663724 0.747977i \(-0.268975\pi\)
−0.979630 + 0.200813i \(0.935642\pi\)
\(642\) 5.73896 9.94017i 0.226499 0.392307i
\(643\) −20.9315 −0.825460 −0.412730 0.910854i \(-0.635425\pi\)
−0.412730 + 0.910854i \(0.635425\pi\)
\(644\) −7.32805 3.63830i −0.288766 0.143369i
\(645\) 35.8955 1.41339
\(646\) 2.89876 5.02079i 0.114050 0.197541i
\(647\) −21.7099 37.6026i −0.853504 1.47831i −0.878026 0.478613i \(-0.841140\pi\)
0.0245220 0.999699i \(-0.492194\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 1.08424 1.87796i 0.0425601 0.0737162i
\(650\) −48.3241 −1.89543
\(651\) −16.1970 + 10.7597i −0.634812 + 0.421706i
\(652\) 15.9446 0.624439
\(653\) 3.03110 5.25002i 0.118616 0.205449i −0.800603 0.599195i \(-0.795488\pi\)
0.919220 + 0.393745i \(0.128821\pi\)
\(654\) 9.34068 + 16.1785i 0.365250 + 0.632631i
\(655\) 32.0095 + 55.4420i 1.25071 + 2.16630i
\(656\) −4.44277 + 7.69509i −0.173461 + 0.300443i
\(657\) −1.92536 −0.0751156
\(658\) 0.297576 + 4.73501i 0.0116007 + 0.184590i
\(659\) −0.570382 −0.0222189 −0.0111095 0.999938i \(-0.503536\pi\)
−0.0111095 + 0.999938i \(0.503536\pi\)
\(660\) −0.481462 + 0.833916i −0.0187409 + 0.0324601i
\(661\) 8.81981 + 15.2764i 0.343051 + 0.594181i 0.984998 0.172568i \(-0.0552064\pi\)
−0.641947 + 0.766749i \(0.721873\pi\)
\(662\) −2.33381 4.04228i −0.0907062 0.157108i
\(663\) 20.0670 34.7570i 0.779336 1.34985i
\(664\) 0.146030 0.00566706
\(665\) −0.574394 9.13972i −0.0222740 0.354423i
\(666\) 5.24112 0.203089
\(667\) 13.2253 22.9070i 0.512087 0.886961i
\(668\) −8.80367 15.2484i −0.340624 0.589978i
\(669\) 1.96430 + 3.40227i 0.0759443 + 0.131539i
\(670\) 23.7754 41.1802i 0.918523 1.59093i
\(671\) 2.53977 0.0980468
\(672\) 2.20380 1.46399i 0.0850135 0.0564745i
\(673\) −39.1296 −1.50833 −0.754167 0.656682i \(-0.771959\pi\)
−0.754167 + 0.656682i \(0.771959\pi\)
\(674\) −5.73197 + 9.92806i −0.220787 + 0.382415i
\(675\) 3.49031 + 6.04539i 0.134342 + 0.232687i
\(676\) −17.4612 30.2438i −0.671586 1.16322i
\(677\) −17.7074 + 30.6702i −0.680552 + 1.17875i 0.294261 + 0.955725i \(0.404927\pi\)
−0.974813 + 0.223025i \(0.928407\pi\)
\(678\) 3.29913 0.126702
\(679\) −9.69780 4.81486i −0.372168 0.184777i
\(680\) 20.0670 0.769533
\(681\) −3.51985 + 6.09657i −0.134881 + 0.233621i
\(682\) 1.02232 + 1.77070i 0.0391465 + 0.0678038i
\(683\) 18.1449 + 31.4279i 0.694295 + 1.20255i 0.970418 + 0.241431i \(0.0776169\pi\)
−0.276123 + 0.961122i \(0.589050\pi\)
\(684\) −0.500000 + 0.866025i −0.0191180 + 0.0331133i
\(685\) 42.1173 1.60922
\(686\) −17.4888 6.09429i −0.667727 0.232681i
\(687\) −5.88397 −0.224488
\(688\) −5.18526 + 8.98114i −0.197686 + 0.342403i
\(689\) −29.0342 50.2887i −1.10611 1.91585i
\(690\) 5.35175 + 9.26950i 0.203738 + 0.352884i
\(691\) −16.8574 + 29.1978i −0.641284 + 1.11074i 0.343862 + 0.939020i \(0.388265\pi\)
−0.985146 + 0.171717i \(0.945069\pi\)
\(692\) 10.0106 0.380547
\(693\) −0.659257 0.327314i −0.0250431 0.0124336i
\(694\) −7.84258 −0.297700
\(695\) −5.05054 + 8.74780i −0.191578 + 0.331823i
\(696\) 4.27682 + 7.40767i 0.162112 + 0.280787i
\(697\) −25.7570 44.6124i −0.975616 1.68982i
\(698\) 10.6496 18.4456i 0.403092 0.698176i
\(699\) −2.80658 −0.106155
\(700\) 15.3839 10.2195i 0.581457 0.386262i
\(701\) 12.6976 0.479583 0.239791 0.970824i \(-0.422921\pi\)
0.239791 + 0.970824i \(0.422921\pi\)
\(702\) −3.46130 + 5.99515i −0.130638 + 0.226272i
\(703\) 2.62056 + 4.53894i 0.0988363 + 0.171189i
\(704\) −0.139098 0.240925i −0.00524247 0.00908022i
\(705\) 3.10340 5.37525i 0.116881 0.202444i
\(706\) −8.71701 −0.328069
\(707\) −0.407731 6.48778i −0.0153343 0.243998i
\(708\) 7.79476 0.292945
\(709\) 10.6396 18.4283i 0.399578 0.692089i −0.594096 0.804394i \(-0.702490\pi\)
0.993674 + 0.112305i \(0.0358235\pi\)
\(710\) −1.18502 2.05252i −0.0444731 0.0770297i
\(711\) −0.703803 1.21902i −0.0263947 0.0457169i
\(712\) −6.85037 + 11.8652i −0.256728 + 0.444667i
\(713\) 22.7274 0.851147
\(714\) 0.962082 + 15.3086i 0.0360050 + 0.572909i
\(715\) −6.66594 −0.249292
\(716\) −3.12941 + 5.42029i −0.116951 + 0.202566i
\(717\) −6.20080 10.7401i −0.231573 0.401097i
\(718\) 0.585642 + 1.01436i 0.0218559 + 0.0378556i
\(719\) −24.1116 + 41.7625i −0.899210 + 1.55748i −0.0707049 + 0.997497i \(0.522525\pi\)
−0.828506 + 0.559981i \(0.810808\pi\)
\(720\) −3.46130 −0.128995
\(721\) 38.2290 25.3955i 1.42372 0.945778i
\(722\) −1.00000 −0.0372161
\(723\) −7.59824 + 13.1605i −0.282582 + 0.489446i
\(724\) 2.12509 + 3.68077i 0.0789784 + 0.136795i
\(725\) 29.8548 + 51.7101i 1.10878 + 1.92046i
\(726\) 5.46130 9.45925i 0.202688 0.351066i
\(727\) 49.2945 1.82823 0.914116 0.405452i \(-0.132886\pi\)
0.914116 + 0.405452i \(0.132886\pi\)
\(728\) 16.4048 + 8.14484i 0.608004 + 0.301868i
\(729\) 1.00000 0.0370370
\(730\) 3.33214 5.77143i 0.123328 0.213610i
\(731\) −30.0616 52.0683i −1.11187 1.92582i
\(732\) 4.56470 + 7.90630i 0.168716 + 0.292225i
\(733\) 0.462145 0.800458i 0.0170697 0.0295656i −0.857364 0.514710i \(-0.827900\pi\)
0.874434 + 0.485144i \(0.161233\pi\)
\(734\) −5.01295 −0.185031
\(735\) 14.6463 + 19.3012i 0.540236 + 0.711936i
\(736\) −3.09233 −0.113985
\(737\) 1.91091 3.30979i 0.0703892 0.121918i
\(738\) 4.44277 + 7.69509i 0.163540 + 0.283260i
\(739\) −1.17588 2.03668i −0.0432554 0.0749205i 0.843587 0.536992i \(-0.180440\pi\)
−0.886843 + 0.462072i \(0.847106\pi\)
\(740\) −9.07055 + 15.7107i −0.333440 + 0.577535i
\(741\) −6.92261 −0.254308
\(742\) 19.8780 + 9.86922i 0.729744 + 0.362310i
\(743\) −50.4616 −1.85126 −0.925628 0.378433i \(-0.876463\pi\)
−0.925628 + 0.378433i \(0.876463\pi\)
\(744\) −3.67480 + 6.36493i −0.134725 + 0.233350i
\(745\) −7.20804 12.4847i −0.264082 0.457404i
\(746\) 0.932921 + 1.61587i 0.0341567 + 0.0591611i
\(747\) 0.0730150 0.126466i 0.00267148 0.00462714i
\(748\) 1.61285 0.0589716
\(749\) −25.2951 + 16.8035i −0.924262 + 0.613987i
\(750\) −6.85553 −0.250328
\(751\) 3.11141 5.38912i 0.113537 0.196652i −0.803657 0.595093i \(-0.797115\pi\)
0.917194 + 0.398441i \(0.130449\pi\)
\(752\) 0.896599 + 1.55296i 0.0326956 + 0.0566304i
\(753\) 2.95599 + 5.11993i 0.107722 + 0.186581i
\(754\) −29.6067 + 51.2804i −1.07821 + 1.86752i
\(755\) −66.7181 −2.42812
\(756\) −0.165947 2.64054i −0.00603545 0.0960356i
\(757\) 19.9762 0.726047 0.363023 0.931780i \(-0.381745\pi\)
0.363023 + 0.931780i \(0.381745\pi\)
\(758\) −5.90323 + 10.2247i −0.214415 + 0.371377i
\(759\) 0.430138 + 0.745022i 0.0156130 + 0.0270426i
\(760\) −1.73065 2.99758i −0.0627773 0.108734i
\(761\) −7.65272 + 13.2549i −0.277411 + 0.480490i −0.970741 0.240131i \(-0.922810\pi\)
0.693330 + 0.720621i \(0.256143\pi\)
\(762\) −3.45699 −0.125233
\(763\) −3.10012 49.3289i −0.112232 1.78583i
\(764\) −10.9479 −0.396080
\(765\) 10.0335 17.3785i 0.362761 0.628321i
\(766\) 2.76320 + 4.78600i 0.0998383 + 0.172925i
\(767\) 26.9800 + 46.7308i 0.974192 + 1.68735i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −18.0461 −0.650761 −0.325380 0.945583i \(-0.605492\pi\)
−0.325380 + 0.945583i \(0.605492\pi\)
\(770\) 2.12209 1.40971i 0.0764749 0.0508023i
\(771\) −1.40485 −0.0505943
\(772\) −10.6449 + 18.4376i −0.383120 + 0.663583i
\(773\) 20.1390 + 34.8818i 0.724351 + 1.25461i 0.959241 + 0.282590i \(0.0911937\pi\)
−0.234890 + 0.972022i \(0.575473\pi\)
\(774\) 5.18526 + 8.98114i 0.186380 + 0.322820i
\(775\) −25.6524 + 44.4312i −0.921460 + 1.59602i
\(776\) −4.09233 −0.146906
\(777\) −12.4201 6.16647i −0.445570 0.221221i