Properties

Label 798.2.j.l.571.3
Level $798$
Weight $2$
Character 798.571
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 571.3
Root \(2.06288i\) of defining polynomial
Character \(\chi\) \(=\) 798.571
Dual form 798.2.j.l.457.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.574618 + 0.995268i) q^{5} +1.00000 q^{6} +(0.00953166 - 2.64573i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.574618 + 0.995268i) q^{5} +1.00000 q^{6} +(0.00953166 - 2.64573i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.574618 + 0.995268i) q^{10} +(1.08415 - 1.87780i) q^{11} +(0.500000 + 0.866025i) q^{12} +2.29847 q^{13} +(2.29604 - 1.31461i) q^{14} +1.14924 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.49840 - 4.32735i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} -1.14924 q^{20} +(-2.28651 - 1.33112i) q^{21} +2.16830 q^{22} +(3.45783 + 5.98914i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.83963 - 3.18633i) q^{25} +(1.14924 + 1.99054i) q^{26} -1.00000 q^{27} +(2.28651 + 1.33112i) q^{28} +3.76643 q^{29} +(0.574618 + 0.995268i) q^{30} +(-2.19283 + 3.79808i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.08415 - 1.87780i) q^{33} +4.99679 q^{34} +(2.63869 - 1.51080i) q^{35} +1.00000 q^{36} +(-0.330096 - 0.571742i) q^{37} +(0.500000 - 0.866025i) q^{38} +(1.14924 - 1.99054i) q^{39} +(-0.574618 - 0.995268i) q^{40} +0.806583 q^{41} +(0.00953166 - 2.64573i) q^{42} -2.08397 q^{43} +(1.08415 + 1.87780i) q^{44} +(0.574618 - 0.995268i) q^{45} +(-3.45783 + 5.98914i) q^{46} +(1.86113 + 3.22356i) q^{47} -1.00000 q^{48} +(-6.99982 - 0.0504365i) q^{49} +3.67925 q^{50} +(-2.49840 - 4.32735i) q^{51} +(-1.14924 + 1.99054i) q^{52} +(5.63567 - 9.76126i) q^{53} +(-0.500000 - 0.866025i) q^{54} +2.49189 q^{55} +(-0.00953166 + 2.64573i) q^{56} -1.00000 q^{57} +(1.88322 + 3.26183i) q^{58} +(-5.21331 + 9.02972i) q^{59} +(-0.574618 + 0.995268i) q^{60} +(-1.28811 - 2.23107i) q^{61} -4.38565 q^{62} +(-2.29604 + 1.31461i) q^{63} +1.00000 q^{64} +(1.32075 + 2.28760i) q^{65} +(1.08415 - 1.87780i) q^{66} +(-4.44284 + 7.69523i) q^{67} +(2.49840 + 4.32735i) q^{68} +6.91567 q^{69} +(2.62774 + 1.52977i) q^{70} -0.323591 q^{71} +(0.500000 + 0.866025i) q^{72} +(2.36415 - 4.09483i) q^{73} +(0.330096 - 0.571742i) q^{74} +(-1.83963 - 3.18633i) q^{75} +1.00000 q^{76} +(-4.95783 - 2.88627i) q^{77} +2.29847 q^{78} +(3.79604 + 6.57493i) q^{79} +(0.574618 - 0.995268i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.403292 + 0.698521i) q^{82} +3.17435 q^{83} +(2.29604 - 1.31461i) q^{84} +5.74250 q^{85} +(-1.04198 - 1.80477i) q^{86} +(1.88322 - 3.26183i) q^{87} +(-1.08415 + 1.87780i) q^{88} +(-6.18879 - 10.7193i) q^{89} +1.14924 q^{90} +(0.0219083 - 6.08115i) q^{91} -6.91567 q^{92} +(2.19283 + 3.79808i) q^{93} +(-1.86113 + 3.22356i) q^{94} +(0.574618 - 0.995268i) q^{95} +(-0.500000 - 0.866025i) q^{96} -5.91567 q^{97} +(-3.45623 - 6.08724i) q^{98} -2.16830 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 \(\left(\mathbb{Z}/798\mathbb{Z}\right)^\times\).

\(n\) \(115\) \(211\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(5\) 0.574618 + 0.995268i 0.256977 + 0.445098i 0.965431 0.260660i \(-0.0839401\pi\)
−0.708453 + 0.705758i \(0.750607\pi\)
\(6\) 1.00000 0.408248
\(7\) 0.00953166 2.64573i 0.00360263 0.999994i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.574618 + 0.995268i −0.181710 + 0.314732i
\(11\) 1.08415 1.87780i 0.326884 0.566179i −0.655008 0.755622i \(-0.727335\pi\)
0.981892 + 0.189443i \(0.0606682\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 2.29847 0.637482 0.318741 0.947842i \(-0.396740\pi\)
0.318741 + 0.947842i \(0.396740\pi\)
\(14\) 2.29604 1.31461i 0.613642 0.351345i
\(15\) 1.14924 0.296732
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.49840 4.32735i 0.605950 1.04954i −0.385951 0.922519i \(-0.626126\pi\)
0.991901 0.127017i \(-0.0405402\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −0.500000 0.866025i −0.114708 0.198680i
\(20\) −1.14924 −0.256977
\(21\) −2.28651 1.33112i −0.498957 0.290475i
\(22\) 2.16830 0.462283
\(23\) 3.45783 + 5.98914i 0.721008 + 1.24882i 0.960596 + 0.277948i \(0.0896544\pi\)
−0.239588 + 0.970875i \(0.577012\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 1.83963 3.18633i 0.367925 0.637266i
\(26\) 1.14924 + 1.99054i 0.225384 + 0.390376i
\(27\) −1.00000 −0.192450
\(28\) 2.28651 + 1.33112i 0.432109 + 0.251558i
\(29\) 3.76643 0.699409 0.349704 0.936860i \(-0.386282\pi\)
0.349704 + 0.936860i \(0.386282\pi\)
\(30\) 0.574618 + 0.995268i 0.104911 + 0.181710i
\(31\) −2.19283 + 3.79808i −0.393843 + 0.682156i −0.992953 0.118511i \(-0.962188\pi\)
0.599110 + 0.800667i \(0.295521\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.08415 1.87780i −0.188726 0.326884i
\(34\) 4.99679 0.856943
\(35\) 2.63869 1.51080i 0.446020 0.255372i
\(36\) 1.00000 0.166667
\(37\) −0.330096 0.571742i −0.0542674 0.0939938i 0.837616 0.546260i \(-0.183949\pi\)
−0.891883 + 0.452266i \(0.850616\pi\)
\(38\) 0.500000 0.866025i 0.0811107 0.140488i
\(39\) 1.14924 1.99054i 0.184025 0.318741i
\(40\) −0.574618 0.995268i −0.0908552 0.157366i
\(41\) 0.806583 0.125967 0.0629836 0.998015i \(-0.479938\pi\)
0.0629836 + 0.998015i \(0.479938\pi\)
\(42\) 0.00953166 2.64573i 0.00147077 0.408246i
\(43\) −2.08397 −0.317802 −0.158901 0.987295i \(-0.550795\pi\)
−0.158901 + 0.987295i \(0.550795\pi\)
\(44\) 1.08415 + 1.87780i 0.163442 + 0.283089i
\(45\) 0.574618 0.995268i 0.0856591 0.148366i
\(46\) −3.45783 + 5.98914i −0.509830 + 0.883051i
\(47\) 1.86113 + 3.22356i 0.271473 + 0.470205i 0.969239 0.246120i \(-0.0791559\pi\)
−0.697766 + 0.716326i \(0.745823\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.99982 0.0504365i −0.999974 0.00720521i
\(50\) 3.67925 0.520325
\(51\) −2.49840 4.32735i −0.349845 0.605950i
\(52\) −1.14924 + 1.99054i −0.159370 + 0.276038i
\(53\) 5.63567 9.76126i 0.774118 1.34081i −0.161170 0.986927i \(-0.551527\pi\)
0.935289 0.353886i \(-0.115140\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 2.49189 0.336006
\(56\) −0.00953166 + 2.64573i −0.00127372 + 0.353551i
\(57\) −1.00000 −0.132453
\(58\) 1.88322 + 3.26183i 0.247278 + 0.428299i
\(59\) −5.21331 + 9.02972i −0.678715 + 1.17557i 0.296653 + 0.954985i \(0.404130\pi\)
−0.975368 + 0.220584i \(0.929204\pi\)
\(60\) −0.574618 + 0.995268i −0.0741829 + 0.128489i
\(61\) −1.28811 2.23107i −0.164926 0.285660i 0.771703 0.635983i \(-0.219405\pi\)
−0.936629 + 0.350323i \(0.886072\pi\)
\(62\) −4.38565 −0.556978
\(63\) −2.29604 + 1.31461i −0.289274 + 0.165626i
\(64\) 1.00000 0.125000
\(65\) 1.32075 + 2.28760i 0.163818 + 0.283742i
\(66\) 1.08415 1.87780i 0.133450 0.231142i
\(67\) −4.44284 + 7.69523i −0.542779 + 0.940121i 0.455964 + 0.889998i \(0.349295\pi\)
−0.998743 + 0.0501231i \(0.984039\pi\)
\(68\) 2.49840 + 4.32735i 0.302975 + 0.524768i
\(69\) 6.91567 0.832549
\(70\) 2.62774 + 1.52977i 0.314075 + 0.182843i
\(71\) −0.323591 −0.0384031 −0.0192016 0.999816i \(-0.506112\pi\)
−0.0192016 + 0.999816i \(0.506112\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 2.36415 4.09483i 0.276703 0.479264i −0.693860 0.720110i \(-0.744091\pi\)
0.970563 + 0.240846i \(0.0774248\pi\)
\(74\) 0.330096 0.571742i 0.0383728 0.0664637i
\(75\) −1.83963 3.18633i −0.212422 0.367925i
\(76\) 1.00000 0.114708
\(77\) −4.95783 2.88627i −0.564998 0.328921i
\(78\) 2.29847 0.260251
\(79\) 3.79604 + 6.57493i 0.427088 + 0.739738i 0.996613 0.0822363i \(-0.0262062\pi\)
−0.569525 + 0.821974i \(0.692873\pi\)
\(80\) 0.574618 0.995268i 0.0642443 0.111274i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0.403292 + 0.698521i 0.0445361 + 0.0771388i
\(83\) 3.17435 0.348431 0.174215 0.984708i \(-0.444261\pi\)
0.174215 + 0.984708i \(0.444261\pi\)
\(84\) 2.29604 1.31461i 0.250518 0.143436i
\(85\) 5.74250 0.622861
\(86\) −1.04198 1.80477i −0.112360 0.194613i
\(87\) 1.88322 3.26183i 0.201902 0.349704i
\(88\) −1.08415 + 1.87780i −0.115571 + 0.200174i
\(89\) −6.18879 10.7193i −0.656010 1.13624i −0.981640 0.190745i \(-0.938910\pi\)
0.325630 0.945497i \(-0.394424\pi\)
\(90\) 1.14924 0.121140
\(91\) 0.0219083 6.08115i 0.00229661 0.637478i
\(92\) −6.91567 −0.721008
\(93\) 2.19283 + 3.79808i 0.227385 + 0.393843i
\(94\) −1.86113 + 3.22356i −0.191960 + 0.332485i
\(95\) 0.574618 0.995268i 0.0589546 0.102112i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) −5.91567 −0.600645 −0.300323 0.953838i \(-0.597094\pi\)
−0.300323 + 0.953838i \(0.597094\pi\)
\(98\) −3.45623 6.08724i −0.349132 0.614904i
\(99\) −2.16830 −0.217922
\(100\) 1.83963 + 3.18633i 0.183963 + 0.318633i
\(101\) 6.43414 11.1443i 0.640221 1.10890i −0.345162 0.938543i \(-0.612176\pi\)
0.985383 0.170352i \(-0.0544905\pi\)
\(102\) 2.49840 4.32735i 0.247378 0.428471i
\(103\) −3.47791 6.02392i −0.342689 0.593554i 0.642242 0.766502i \(-0.278004\pi\)
−0.984931 + 0.172947i \(0.944671\pi\)
\(104\) −2.29847 −0.225384
\(105\) 0.0109541 3.04058i 0.00106901 0.296730i
\(106\) 11.2713 1.09477
\(107\) 6.19933 + 10.7376i 0.599312 + 1.03804i 0.992923 + 0.118762i \(0.0378924\pi\)
−0.393611 + 0.919277i \(0.628774\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −9.02841 + 15.6377i −0.864765 + 1.49782i 0.00251502 + 0.999997i \(0.499199\pi\)
−0.867280 + 0.497820i \(0.834134\pi\)
\(110\) 1.24595 + 2.15804i 0.118796 + 0.205761i
\(111\) −0.660191 −0.0626626
\(112\) −2.29604 + 1.31461i −0.216955 + 0.124219i
\(113\) −8.63792 −0.812587 −0.406294 0.913743i \(-0.633179\pi\)
−0.406294 + 0.913743i \(0.633179\pi\)
\(114\) −0.500000 0.866025i −0.0468293 0.0811107i
\(115\) −3.97387 + 6.88295i −0.370565 + 0.641838i
\(116\) −1.88322 + 3.26183i −0.174852 + 0.302853i
\(117\) −1.14924 1.99054i −0.106247 0.184025i
\(118\) −10.4266 −0.959848
\(119\) −11.4252 6.65134i −1.04735 0.609727i
\(120\) −1.14924 −0.104911
\(121\) 3.14924 + 5.45464i 0.286294 + 0.495876i
\(122\) 1.28811 2.23107i 0.116620 0.201992i
\(123\) 0.403292 0.698521i 0.0363636 0.0629836i
\(124\) −2.19283 3.79808i −0.196922 0.341078i
\(125\) 9.97452 0.892148
\(126\) −2.28651 1.33112i −0.203698 0.118586i
\(127\) −13.8683 −1.23061 −0.615305 0.788289i \(-0.710967\pi\)
−0.615305 + 0.788289i \(0.710967\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −1.04198 + 1.80477i −0.0917416 + 0.158901i
\(130\) −1.32075 + 2.28760i −0.115837 + 0.200636i
\(131\) −6.10565 10.5753i −0.533453 0.923968i −0.999237 0.0390690i \(-0.987561\pi\)
0.465784 0.884899i \(-0.345773\pi\)
\(132\) 2.16830 0.188726
\(133\) −2.29604 + 1.31461i −0.199092 + 0.113991i
\(134\) −8.88568 −0.767606
\(135\) −0.574618 0.995268i −0.0494553 0.0856591i
\(136\) −2.49840 + 4.32735i −0.214236 + 0.371067i
\(137\) −5.54038 + 9.59622i −0.473347 + 0.819860i −0.999535 0.0305079i \(-0.990288\pi\)
0.526188 + 0.850368i \(0.323621\pi\)
\(138\) 3.45783 + 5.98914i 0.294350 + 0.509830i
\(139\) −11.0175 −0.934494 −0.467247 0.884127i \(-0.654754\pi\)
−0.467247 + 0.884127i \(0.654754\pi\)
\(140\) −0.0109541 + 3.04058i −0.000925793 + 0.256976i
\(141\) 3.72225 0.313470
\(142\) −0.161795 0.280238i −0.0135776 0.0235170i
\(143\) 2.49189 4.31608i 0.208382 0.360929i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 2.16426 + 3.74861i 0.179732 + 0.311305i
\(146\) 4.72830 0.391317
\(147\) −3.54359 + 6.03680i −0.292270 + 0.497907i
\(148\) 0.660191 0.0542674
\(149\) 10.6085 + 18.3744i 0.869082 + 1.50529i 0.862936 + 0.505312i \(0.168623\pi\)
0.00614520 + 0.999981i \(0.498044\pi\)
\(150\) 1.83963 3.18633i 0.150205 0.260163i
\(151\) −4.70093 + 8.14226i −0.382557 + 0.662608i −0.991427 0.130662i \(-0.958290\pi\)
0.608870 + 0.793270i \(0.291623\pi\)
\(152\) 0.500000 + 0.866025i 0.0405554 + 0.0702439i
\(153\) −4.99679 −0.403967
\(154\) 0.0206675 5.73675i 0.00166543 0.462280i
\(155\) −5.04015 −0.404835
\(156\) 1.14924 + 1.99054i 0.0920126 + 0.159370i
\(157\) −3.07361 + 5.32364i −0.245300 + 0.424873i −0.962216 0.272287i \(-0.912220\pi\)
0.716916 + 0.697160i \(0.245553\pi\)
\(158\) −3.79604 + 6.57493i −0.301997 + 0.523074i
\(159\) −5.63567 9.76126i −0.446937 0.774118i
\(160\) 1.14924 0.0908552
\(161\) 15.8786 9.09142i 1.25141 0.716505i
\(162\) −1.00000 −0.0785674
\(163\) 4.30397 + 7.45469i 0.337113 + 0.583896i 0.983888 0.178784i \(-0.0572163\pi\)
−0.646776 + 0.762680i \(0.723883\pi\)
\(164\) −0.403292 + 0.698521i −0.0314918 + 0.0545454i
\(165\) 1.24595 2.15804i 0.0969967 0.168003i
\(166\) 1.58718 + 2.74907i 0.123189 + 0.213369i
\(167\) 11.9749 0.926644 0.463322 0.886190i \(-0.346657\pi\)
0.463322 + 0.886190i \(0.346657\pi\)
\(168\) 2.28651 + 1.33112i 0.176408 + 0.102698i
\(169\) −7.71702 −0.593617
\(170\) 2.87125 + 4.97315i 0.220215 + 0.381423i
\(171\) −0.500000 + 0.866025i −0.0382360 + 0.0662266i
\(172\) 1.04198 1.80477i 0.0794506 0.137612i
\(173\) −4.05092 7.01641i −0.307986 0.533448i 0.669936 0.742419i \(-0.266322\pi\)
−0.977922 + 0.208972i \(0.932988\pi\)
\(174\) 3.76643 0.285532
\(175\) −8.41264 4.89754i −0.635936 0.370219i
\(176\) −2.16830 −0.163442
\(177\) 5.21331 + 9.02972i 0.391856 + 0.678715i
\(178\) 6.18879 10.7193i 0.463869 0.803445i
\(179\) 3.42378 5.93016i 0.255905 0.443241i −0.709236 0.704971i \(-0.750960\pi\)
0.965141 + 0.261731i \(0.0842932\pi\)
\(180\) 0.574618 + 0.995268i 0.0428295 + 0.0741829i
\(181\) −16.5905 −1.23316 −0.616582 0.787291i \(-0.711483\pi\)
−0.616582 + 0.787291i \(0.711483\pi\)
\(182\) 5.27739 3.02160i 0.391186 0.223976i
\(183\) −2.57622 −0.190440
\(184\) −3.45783 5.98914i −0.254915 0.441526i
\(185\) 0.379358 0.657067i 0.0278910 0.0483086i
\(186\) −2.19283 + 3.79808i −0.160786 + 0.278489i
\(187\) −5.41727 9.38299i −0.396150 0.686152i
\(188\) −3.72225 −0.271473
\(189\) −0.00953166 + 2.64573i −0.000693326 + 0.192449i
\(190\) 1.14924 0.0833744
\(191\) −7.94509 13.7613i −0.574887 0.995733i −0.996054 0.0887501i \(-0.971713\pi\)
0.421167 0.906983i \(-0.361621\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −3.24838 + 5.62636i −0.233824 + 0.404994i −0.958930 0.283642i \(-0.908457\pi\)
0.725107 + 0.688637i \(0.241790\pi\)
\(194\) −2.95783 5.12312i −0.212360 0.367819i
\(195\) 2.64149 0.189161
\(196\) 3.54359 6.03680i 0.253113 0.431200i
\(197\) 1.06491 0.0758713 0.0379357 0.999280i \(-0.487922\pi\)
0.0379357 + 0.999280i \(0.487922\pi\)
\(198\) −1.08415 1.87780i −0.0770472 0.133450i
\(199\) −11.7959 + 20.4310i −0.836186 + 1.44832i 0.0568749 + 0.998381i \(0.481886\pi\)
−0.893061 + 0.449936i \(0.851447\pi\)
\(200\) −1.83963 + 3.18633i −0.130081 + 0.225307i
\(201\) 4.44284 + 7.69523i 0.313374 + 0.542779i
\(202\) 12.8683 0.905409
\(203\) 0.0359003 9.96498i 0.00251971 0.699404i
\(204\) 4.99679 0.349845
\(205\) 0.463478 + 0.802767i 0.0323707 + 0.0560677i
\(206\) 3.47791 6.02392i 0.242317 0.419706i
\(207\) 3.45783 5.98914i 0.240336 0.416274i
\(208\) −1.14924 1.99054i −0.0796852 0.138019i
\(209\) −2.16830 −0.149984
\(210\) 2.63869 1.51080i 0.182087 0.104255i
\(211\) 17.8699 1.23022 0.615109 0.788442i \(-0.289112\pi\)
0.615109 + 0.788442i \(0.289112\pi\)
\(212\) 5.63567 + 9.76126i 0.387059 + 0.670406i
\(213\) −0.161795 + 0.280238i −0.0110860 + 0.0192016i
\(214\) −6.19933 + 10.7376i −0.423777 + 0.734004i
\(215\) −1.19749 2.07411i −0.0816679 0.141453i
\(216\) 1.00000 0.0680414
\(217\) 10.0278 + 5.83783i 0.680733 + 0.396298i
\(218\) −18.0568 −1.22296
\(219\) −2.36415 4.09483i −0.159755 0.276703i
\(220\) −1.24595 + 2.15804i −0.0840016 + 0.145495i
\(221\) 5.74250 9.94630i 0.386282 0.669060i
\(222\) −0.330096 0.571742i −0.0221546 0.0383728i
\(223\) 4.44605 0.297729 0.148865 0.988858i \(-0.452438\pi\)
0.148865 + 0.988858i \(0.452438\pi\)
\(224\) −2.28651 1.33112i −0.152774 0.0889393i
\(225\) −3.67925 −0.245284
\(226\) −4.31896 7.48066i −0.287293 0.497606i
\(227\) −10.0469 + 17.4017i −0.666835 + 1.15499i 0.311949 + 0.950099i \(0.399018\pi\)
−0.978784 + 0.204894i \(0.934315\pi\)
\(228\) 0.500000 0.866025i 0.0331133 0.0573539i
\(229\) −8.97773 15.5499i −0.593265 1.02757i −0.993789 0.111279i \(-0.964505\pi\)
0.400524 0.916286i \(-0.368828\pi\)
\(230\) −7.94774 −0.524059
\(231\) −4.97850 + 2.85047i −0.327561 + 0.187547i
\(232\) −3.76643 −0.247278
\(233\) −5.12697 8.88016i −0.335879 0.581759i 0.647775 0.761832i \(-0.275700\pi\)
−0.983653 + 0.180073i \(0.942367\pi\)
\(234\) 1.14924 1.99054i 0.0751280 0.130125i
\(235\) −2.13887 + 3.70464i −0.139525 + 0.241664i
\(236\) −5.21331 9.02972i −0.339358 0.587785i
\(237\) 7.59208 0.493158
\(238\) 0.0476277 13.2202i 0.00308724 0.856937i
\(239\) 1.73965 0.112529 0.0562644 0.998416i \(-0.482081\pi\)
0.0562644 + 0.998416i \(0.482081\pi\)
\(240\) −0.574618 0.995268i −0.0370915 0.0642443i
\(241\) 10.4246 18.0560i 0.671508 1.16309i −0.305968 0.952042i \(-0.598980\pi\)
0.977476 0.211044i \(-0.0676865\pi\)
\(242\) −3.14924 + 5.45464i −0.202441 + 0.350637i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 2.57622 0.164926
\(245\) −3.97203 6.99568i −0.253764 0.446938i
\(246\) 0.806583 0.0514259
\(247\) −1.14924 1.99054i −0.0731242 0.126655i
\(248\) 2.19283 3.79808i 0.139245 0.241179i
\(249\) 1.58718 2.74907i 0.100583 0.174215i
\(250\) 4.98726 + 8.63819i 0.315422 + 0.546327i
\(251\) 3.19663 0.201769 0.100885 0.994898i \(-0.467833\pi\)
0.100885 + 0.994898i \(0.467833\pi\)
\(252\) 0.00953166 2.64573i 0.000600438 0.166666i
\(253\) 14.9952 0.942743
\(254\) −6.93414 12.0103i −0.435087 0.753592i
\(255\) 2.87125 4.97315i 0.179805 0.311431i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.51095 + 13.0094i 0.468520 + 0.811501i 0.999353 0.0359757i \(-0.0114539\pi\)
−0.530832 + 0.847477i \(0.678121\pi\)
\(258\) −2.08397 −0.129742
\(259\) −1.51582 + 0.867895i −0.0941887 + 0.0539284i
\(260\) −2.64149 −0.163818
\(261\) −1.88322 3.26183i −0.116568 0.201902i
\(262\) 6.10565 10.5753i 0.377208 0.653344i
\(263\) −5.33802 + 9.24573i −0.329157 + 0.570116i −0.982345 0.187080i \(-0.940098\pi\)
0.653188 + 0.757196i \(0.273431\pi\)
\(264\) 1.08415 + 1.87780i 0.0667248 + 0.115571i
\(265\) 12.9534 0.795723
\(266\) −2.28651 1.33112i −0.140195 0.0816163i
\(267\) −12.3776 −0.757495
\(268\) −4.44284 7.69523i −0.271390 0.470061i
\(269\) 1.62453 2.81377i 0.0990494 0.171559i −0.812242 0.583321i \(-0.801753\pi\)
0.911291 + 0.411762i \(0.135086\pi\)
\(270\) 0.574618 0.995268i 0.0349702 0.0605701i
\(271\) −9.01746 15.6187i −0.547772 0.948768i −0.998427 0.0560702i \(-0.982143\pi\)
0.450655 0.892698i \(-0.351190\pi\)
\(272\) −4.99679 −0.302975
\(273\) −5.25548 3.05955i −0.318076 0.185172i
\(274\) −11.0808 −0.669413
\(275\) −3.98886 6.90892i −0.240538 0.416623i
\(276\) −3.45783 + 5.98914i −0.208137 + 0.360504i
\(277\) −11.1420 + 19.2984i −0.669455 + 1.15953i 0.308601 + 0.951192i \(0.400139\pi\)
−0.978057 + 0.208339i \(0.933194\pi\)
\(278\) −5.50876 9.54145i −0.330393 0.572258i
\(279\) 4.38565 0.262562
\(280\) −2.63869 + 1.51080i −0.157692 + 0.0902876i
\(281\) 7.10790 0.424022 0.212011 0.977267i \(-0.431999\pi\)
0.212011 + 0.977267i \(0.431999\pi\)
\(282\) 1.86113 + 3.22356i 0.110828 + 0.191960i
\(283\) 7.87368 13.6376i 0.468042 0.810672i −0.531291 0.847189i \(-0.678293\pi\)
0.999333 + 0.0365169i \(0.0116263\pi\)
\(284\) 0.161795 0.280238i 0.00960078 0.0166290i
\(285\) −0.574618 0.995268i −0.0340375 0.0589546i
\(286\) 4.98378 0.294697
\(287\) 0.00768807 2.13400i 0.000453813 0.125966i
\(288\) −1.00000 −0.0589256
\(289\) −3.98396 6.90043i −0.234351 0.405907i
\(290\) −2.16426 + 3.74861i −0.127090 + 0.220126i
\(291\) −2.95783 + 5.12312i −0.173391 + 0.300323i
\(292\) 2.36415 + 4.09483i 0.138352 + 0.239632i
\(293\) 22.0139 1.28607 0.643034 0.765837i \(-0.277675\pi\)
0.643034 + 0.765837i \(0.277675\pi\)
\(294\) −6.99982 0.0504365i −0.408238 0.00294151i
\(295\) −11.9827 −0.697657
\(296\) 0.330096 + 0.571742i 0.0191864 + 0.0332318i
\(297\) −1.08415 + 1.87780i −0.0629088 + 0.108961i
\(298\) −10.6085 + 18.3744i −0.614534 + 1.06440i
\(299\) 7.94774 + 13.7659i 0.459630 + 0.796102i
\(300\) 3.67925 0.212422
\(301\) −0.0198637 + 5.51363i −0.00114492 + 0.317800i
\(302\) −9.40187 −0.541017
\(303\) −6.43414 11.1443i −0.369632 0.640221i
\(304\) −0.500000 + 0.866025i −0.0286770 + 0.0496700i
\(305\) 1.48035 2.56403i 0.0847643 0.146816i
\(306\) −2.49840 4.32735i −0.142824 0.247378i
\(307\) 14.3776 0.820571 0.410286 0.911957i \(-0.365429\pi\)
0.410286 + 0.911957i \(0.365429\pi\)
\(308\) 4.97850 2.85047i 0.283676 0.162421i
\(309\) −6.95582 −0.395703
\(310\) −2.52008 4.36490i −0.143131 0.247910i
\(311\) 1.48726 2.57601i 0.0843348 0.146072i −0.820773 0.571255i \(-0.806457\pi\)
0.905108 + 0.425183i \(0.139790\pi\)
\(312\) −1.14924 + 1.99054i −0.0650627 + 0.112692i
\(313\) 8.37942 + 14.5136i 0.473633 + 0.820356i 0.999544 0.0301834i \(-0.00960914\pi\)
−0.525912 + 0.850539i \(0.676276\pi\)
\(314\) −6.14721 −0.346907
\(315\) −2.62774 1.52977i −0.148056 0.0861930i
\(316\) −7.59208 −0.427088
\(317\) 1.40531 + 2.43406i 0.0789298 + 0.136710i 0.902788 0.430085i \(-0.141516\pi\)
−0.823859 + 0.566795i \(0.808183\pi\)
\(318\) 5.63567 9.76126i 0.316032 0.547384i
\(319\) 4.08338 7.07262i 0.228625 0.395990i
\(320\) 0.574618 + 0.995268i 0.0321221 + 0.0556372i
\(321\) 12.3987 0.692026
\(322\) 15.8127 + 9.20560i 0.881209 + 0.513008i
\(323\) −4.99679 −0.278029
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 4.22834 7.32369i 0.234546 0.406245i
\(326\) −4.30397 + 7.45469i −0.238375 + 0.412877i
\(327\) 9.02841 + 15.6377i 0.499272 + 0.864765i
\(328\) −0.806583 −0.0445361
\(329\) 8.54643 4.89332i 0.471180 0.269777i
\(330\) 2.49189 0.137174
\(331\) 5.06954 + 8.78069i 0.278647 + 0.482631i 0.971049 0.238882i \(-0.0767808\pi\)
−0.692402 + 0.721512i \(0.743447\pi\)
\(332\) −1.58718 + 2.74907i −0.0871076 + 0.150875i
\(333\) −0.330096 + 0.571742i −0.0180891 + 0.0313313i
\(334\) 5.98744 + 10.3706i 0.327618 + 0.567451i
\(335\) −10.2118 −0.557928
\(336\) −0.00953166 + 2.64573i −0.000519994 + 0.144337i
\(337\) 21.4364 1.16772 0.583858 0.811856i \(-0.301542\pi\)
0.583858 + 0.811856i \(0.301542\pi\)
\(338\) −3.85851 6.68313i −0.209875 0.363515i
\(339\) −4.31896 + 7.48066i −0.234574 + 0.406294i
\(340\) −2.87125 + 4.97315i −0.155715 + 0.269707i
\(341\) 4.75470 + 8.23539i 0.257482 + 0.445971i
\(342\) −1.00000 −0.0540738
\(343\) −0.200161 + 18.5192i −0.0108077 + 0.999942i
\(344\) 2.08397 0.112360
\(345\) 3.97387 + 6.88295i 0.213946 + 0.370565i
\(346\) 4.05092 7.01641i 0.217779 0.377204i
\(347\) −14.5913 + 25.2729i −0.783302 + 1.35672i 0.146706 + 0.989180i \(0.453133\pi\)
−0.930008 + 0.367539i \(0.880200\pi\)
\(348\) 1.88322 + 3.26183i 0.100951 + 0.174852i
\(349\) 9.36208 0.501141 0.250570 0.968098i \(-0.419382\pi\)
0.250570 + 0.968098i \(0.419382\pi\)
\(350\) 0.0350694 9.73433i 0.00187454 0.520322i
\(351\) −2.29847 −0.122683
\(352\) −1.08415 1.87780i −0.0577854 0.100087i
\(353\) −16.7997 + 29.0980i −0.894159 + 1.54873i −0.0593161 + 0.998239i \(0.518892\pi\)
−0.834843 + 0.550489i \(0.814441\pi\)
\(354\) −5.21331 + 9.02972i −0.277084 + 0.479924i
\(355\) −0.185941 0.322059i −0.00986873 0.0170931i
\(356\) 12.3776 0.656010
\(357\) −11.4728 + 6.56884i −0.607206 + 0.347660i
\(358\) 6.84755 0.361905
\(359\) 12.1815 + 21.0990i 0.642915 + 1.11356i 0.984779 + 0.173812i \(0.0556087\pi\)
−0.341863 + 0.939750i \(0.611058\pi\)
\(360\) −0.574618 + 0.995268i −0.0302851 + 0.0524553i
\(361\) −0.500000 + 0.866025i −0.0263158 + 0.0455803i
\(362\) −8.29527 14.3678i −0.435989 0.755156i
\(363\) 6.29847 0.330584
\(364\) 5.25548 + 3.05955i 0.275462 + 0.160364i
\(365\) 5.43394 0.284426
\(366\) −1.28811 2.23107i −0.0673307 0.116620i
\(367\) 16.5786 28.7149i 0.865394 1.49891i −0.00126140 0.999999i \(-0.500402\pi\)
0.866655 0.498907i \(-0.166265\pi\)
\(368\) 3.45783 5.98914i 0.180252 0.312206i
\(369\) −0.403292 0.698521i −0.0209945 0.0363636i
\(370\) 0.758716 0.0394438
\(371\) −25.7720 15.0035i −1.33801 0.778944i
\(372\) −4.38565 −0.227385
\(373\) 11.2730 + 19.5254i 0.583693 + 1.01099i 0.995037 + 0.0995064i \(0.0317264\pi\)
−0.411343 + 0.911480i \(0.634940\pi\)
\(374\) 5.41727 9.38299i 0.280120 0.485183i
\(375\) 4.98726 8.63819i 0.257541 0.446074i
\(376\) −1.86113 3.22356i −0.0959802 0.166243i
\(377\) 8.65704 0.445860
\(378\) −2.29604 + 1.31461i −0.118095 + 0.0676164i
\(379\) 18.7616 0.963717 0.481858 0.876249i \(-0.339962\pi\)
0.481858 + 0.876249i \(0.339962\pi\)
\(380\) 0.574618 + 0.995268i 0.0294773 + 0.0510562i
\(381\) −6.93414 + 12.0103i −0.355247 + 0.615305i
\(382\) 7.94509 13.7613i 0.406506 0.704090i
\(383\) 4.05885 + 7.03014i 0.207398 + 0.359223i 0.950894 0.309517i \(-0.100167\pi\)
−0.743496 + 0.668740i \(0.766834\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0.0237518 6.59288i 0.00121051 0.336004i
\(386\) −6.49676 −0.330676
\(387\) 1.04198 + 1.80477i 0.0529670 + 0.0917416i
\(388\) 2.95783 5.12312i 0.150161 0.260087i
\(389\) 17.5017 30.3138i 0.887371 1.53697i 0.0443993 0.999014i \(-0.485863\pi\)
0.842972 0.537958i \(-0.180804\pi\)
\(390\) 1.32075 + 2.28760i 0.0668786 + 0.115837i
\(391\) 34.5562 1.74758
\(392\) 6.99982 + 0.0504365i 0.353544 + 0.00254743i
\(393\) −12.2113 −0.615978
\(394\) 0.532453 + 0.922235i 0.0268246 + 0.0464615i
\(395\) −4.36255 + 7.55615i −0.219504 + 0.380191i
\(396\) 1.08415 1.87780i 0.0544806 0.0943632i
\(397\) −7.51095 13.0094i −0.376964 0.652921i 0.613655 0.789574i \(-0.289699\pi\)
−0.990619 + 0.136654i \(0.956365\pi\)
\(398\) −23.5917 −1.18255
\(399\) −0.00953166 + 2.64573i −0.000477180 + 0.132452i
\(400\) −3.67925 −0.183963
\(401\) 13.3143 + 23.0611i 0.664886 + 1.15162i 0.979316 + 0.202336i \(0.0648532\pi\)
−0.314430 + 0.949281i \(0.601814\pi\)
\(402\) −4.44284 + 7.69523i −0.221589 + 0.383803i
\(403\) −5.04015 + 8.72980i −0.251068 + 0.434862i
\(404\) 6.43414 + 11.1443i 0.320110 + 0.554448i
\(405\) −1.14924 −0.0571060
\(406\) 8.64787 4.95140i 0.429187 0.245734i
\(407\) −1.43149 −0.0709565
\(408\) 2.49840 + 4.32735i 0.123689 + 0.214236i
\(409\) −13.8245 + 23.9447i −0.683575 + 1.18399i 0.290307 + 0.956934i \(0.406243\pi\)
−0.973882 + 0.227053i \(0.927091\pi\)
\(410\) −0.463478 + 0.802767i −0.0228895 + 0.0396458i
\(411\) 5.54038 + 9.59622i 0.273287 + 0.473347i
\(412\) 6.95582 0.342689
\(413\) 23.8405 + 13.8791i 1.17312 + 0.682946i
\(414\) 6.91567 0.339887
\(415\) 1.82404 + 3.15933i 0.0895387 + 0.155086i
\(416\) 1.14924 1.99054i 0.0563460 0.0975941i
\(417\) −5.50876 + 9.54145i −0.269765 + 0.467247i
\(418\) −1.08415 1.87780i −0.0530275 0.0918464i
\(419\) 1.91888 0.0937433 0.0468716 0.998901i \(-0.485075\pi\)
0.0468716 + 0.998901i \(0.485075\pi\)
\(420\) 2.62774 + 1.52977i 0.128221 + 0.0746453i
\(421\) 25.9815 1.26626 0.633130 0.774046i \(-0.281770\pi\)
0.633130 + 0.774046i \(0.281770\pi\)
\(422\) 8.93497 + 15.4758i 0.434948 + 0.753351i
\(423\) 1.86113 3.22356i 0.0904910 0.156735i
\(424\) −5.63567 + 9.76126i −0.273692 + 0.474049i
\(425\) −9.19223 15.9214i −0.445889 0.772302i
\(426\) −0.323591 −0.0156780
\(427\) −5.91511 + 3.38673i −0.286252 + 0.163896i
\(428\) −12.3987 −0.599312
\(429\) −2.49189 4.31608i −0.120310 0.208382i
\(430\) 1.19749 2.07411i 0.0577479 0.100022i
\(431\) −0.482541 + 0.835785i −0.0232432 + 0.0402584i −0.877413 0.479736i \(-0.840733\pi\)
0.854170 + 0.519994i \(0.174066\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −5.93960 −0.285439 −0.142720 0.989763i \(-0.545585\pi\)
−0.142720 + 0.989763i \(0.545585\pi\)
\(434\) −0.0418025 + 11.6033i −0.00200658 + 0.556975i
\(435\) 4.32852 0.207537
\(436\) −9.02841 15.6377i −0.432383 0.748909i
\(437\) 3.45783 5.98914i 0.165411 0.286500i
\(438\) 2.36415 4.09483i 0.112964 0.195659i
\(439\) −10.7960 18.6993i −0.515267 0.892468i −0.999843 0.0177192i \(-0.994359\pi\)
0.484576 0.874749i \(-0.338974\pi\)
\(440\) −2.49189 −0.118796
\(441\) 3.45623 + 6.08724i 0.164582 + 0.289869i
\(442\) 11.4850 0.546286
\(443\) −6.96718 12.0675i −0.331021 0.573345i 0.651691 0.758484i \(-0.274060\pi\)
−0.982712 + 0.185139i \(0.940726\pi\)
\(444\) 0.330096 0.571742i 0.0156656 0.0271337i
\(445\) 7.11238 12.3190i 0.337159 0.583977i
\(446\) 2.22302 + 3.85039i 0.105263 + 0.182321i
\(447\) 21.2170 1.00353
\(448\) 0.00953166 2.64573i 0.000450328 0.124999i
\(449\) 14.3273 0.676149 0.338074 0.941119i \(-0.390224\pi\)
0.338074 + 0.941119i \(0.390224\pi\)
\(450\) −1.83963 3.18633i −0.0867209 0.150205i
\(451\) 0.874457 1.51460i 0.0411766 0.0713199i
\(452\) 4.31896 7.48066i 0.203147 0.351861i
\(453\) 4.70093 + 8.14226i 0.220869 + 0.382557i
\(454\) −20.0938 −0.943047
\(455\) 6.06497 3.47254i 0.284330 0.162795i
\(456\) 1.00000 0.0468293
\(457\) −16.1491 27.9710i −0.755421 1.30843i −0.945165 0.326594i \(-0.894099\pi\)
0.189744 0.981834i \(-0.439234\pi\)
\(458\) 8.97773 15.5499i 0.419502 0.726598i
\(459\) −2.49840 + 4.32735i −0.116615 + 0.201983i
\(460\) −3.97387 6.88295i −0.185283 0.320919i
\(461\) 0.375849 0.0175050 0.00875252 0.999962i \(-0.497214\pi\)
0.00875252 + 0.999962i \(0.497214\pi\)
\(462\) −4.95783 2.88627i −0.230659 0.134282i
\(463\) 7.80824 0.362880 0.181440 0.983402i \(-0.441924\pi\)
0.181440 + 0.983402i \(0.441924\pi\)
\(464\) −1.88322 3.26183i −0.0874261 0.151426i
\(465\) −2.52008 + 4.36490i −0.116866 + 0.202417i
\(466\) 5.12697 8.88016i 0.237502 0.411366i
\(467\) 6.12774 + 10.6136i 0.283558 + 0.491137i 0.972258 0.233909i \(-0.0751518\pi\)
−0.688701 + 0.725046i \(0.741819\pi\)
\(468\) 2.29847 0.106247
\(469\) 20.3172 + 11.8279i 0.938160 + 0.546163i
\(470\) −4.27775 −0.197318
\(471\) 3.07361 + 5.32364i 0.141624 + 0.245300i
\(472\) 5.21331 9.02972i 0.239962 0.415627i
\(473\) −2.25933 + 3.91328i −0.103884 + 0.179933i
\(474\) 3.79604 + 6.57493i 0.174358 + 0.301997i
\(475\) −3.67925 −0.168816
\(476\) 11.4728 6.56884i 0.525856 0.301082i
\(477\) −11.2713 −0.516079
\(478\) 0.869826 + 1.50658i 0.0397849 + 0.0689095i
\(479\) −13.5375 + 23.4477i −0.618546 + 1.07135i 0.371206 + 0.928551i \(0.378945\pi\)
−0.989751 + 0.142802i \(0.954389\pi\)
\(480\) 0.574618 0.995268i 0.0262276 0.0454276i
\(481\) −0.758716 1.31413i −0.0345945 0.0599194i
\(482\) 20.8492 0.949656
\(483\) 0.0659178 18.2970i 0.00299936 0.832543i
\(484\) −6.29847 −0.286294
\(485\) −3.39925 5.88768i −0.154352 0.267346i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −14.8749 + 25.7641i −0.674047 + 1.16748i 0.302699 + 0.953086i \(0.402112\pi\)
−0.976746 + 0.214398i \(0.931221\pi\)
\(488\) 1.28811 + 2.23107i 0.0583101 + 0.100996i
\(489\) 8.60793 0.389264
\(490\) 4.07242 6.93772i 0.183973 0.313414i
\(491\) 18.4381 0.832099 0.416050 0.909342i \(-0.363414\pi\)
0.416050 + 0.909342i \(0.363414\pi\)
\(492\) 0.403292 + 0.698521i 0.0181818 + 0.0314918i
\(493\) 9.41004 16.2987i 0.423807 0.734055i
\(494\) 1.14924 1.99054i 0.0517066 0.0895585i
\(495\) −1.24595 2.15804i −0.0560011 0.0969967i
\(496\) 4.38565 0.196922
\(497\) −0.00308435 + 0.856135i −0.000138352 + 0.0384029i
\(498\) 3.17435 0.142246
\(499\) −16.5785 28.7148i −0.742156 1.28545i −0.951512 0.307612i \(-0.900470\pi\)
0.209356 0.977840i \(-0.432863\pi\)
\(500\) −4.98726 + 8.63819i −0.223037 + 0.386311i
\(501\) 5.98744 10.3706i 0.267499 0.463322i
\(502\) 1.59831 + 2.76836i 0.0713362 + 0.123558i
\(503\) 12.8678 0.573747 0.286873 0.957968i \(-0.407384\pi\)
0.286873 + 0.957968i \(0.407384\pi\)
\(504\) 2.29604 1.31461i 0.102274 0.0585575i
\(505\) 14.7887 0.658089
\(506\) 7.49762 + 12.9863i 0.333310 + 0.577310i
\(507\) −3.85851 + 6.68313i −0.171362 + 0.296808i
\(508\) 6.93414 12.0103i 0.307653 0.532870i
\(509\) −4.35117 7.53645i −0.192862 0.334047i 0.753335 0.657637i \(-0.228444\pi\)
−0.946198 + 0.323589i \(0.895110\pi\)
\(510\) 5.74250 0.254282
\(511\) −10.8113 6.29395i −0.478264 0.278428i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 + 0.866025i 0.0220755 + 0.0382360i
\(514\) −7.51095 + 13.0094i −0.331294 + 0.573818i
\(515\) 3.99694 6.92291i 0.176126 0.305060i
\(516\) −1.04198 1.80477i −0.0458708 0.0794506i
\(517\) 8.07096 0.354960
\(518\) −1.50953 0.878795i −0.0663250 0.0386120i
\(519\) −8.10185 −0.355632
\(520\) −1.32075 2.28760i −0.0579185 0.100318i
\(521\) −18.8983 + 32.7328i −0.827948 + 1.43405i 0.0716971 + 0.997426i \(0.477159\pi\)
−0.899645 + 0.436622i \(0.856175\pi\)
\(522\) 1.88322 3.26183i 0.0824261 0.142766i
\(523\) −21.1682 36.6644i −0.925620 1.60322i −0.790561 0.612383i \(-0.790211\pi\)
−0.135058 0.990838i \(-0.543122\pi\)
\(524\) 12.2113 0.533453
\(525\) −8.44771 + 4.83679i −0.368688 + 0.211095i
\(526\) −10.6760 −0.465498
\(527\) 10.9571 + 18.9782i 0.477298 + 0.826705i
\(528\) −1.08415 + 1.87780i −0.0471816 + 0.0817209i
\(529\) −12.4132 + 21.5004i −0.539706 + 0.934798i
\(530\) 6.47672 + 11.2180i 0.281331 + 0.487279i
\(531\) 10.4266 0.452477
\(532\) 0.00953166 2.64573i 0.000413250 0.114707i
\(533\) 1.85391 0.0803018
\(534\) −6.18879 10.7193i −0.267815 0.463869i
\(535\) −7.12450 + 12.3400i −0.308019 + 0.533505i
\(536\) 4.44284 7.69523i 0.191901 0.332383i
\(537\) −3.42378 5.93016i −0.147747 0.255905i
\(538\) 3.24906 0.140077
\(539\) −7.68356 + 13.0896i −0.330955 + 0.563809i
\(540\) 1.14924 0.0494553
\(541\) −4.00573 6.93813i −0.172220 0.298294i 0.766976 0.641676i \(-0.221761\pi\)
−0.939196 + 0.343382i \(0.888427\pi\)
\(542\) 9.01746 15.6187i 0.387333 0.670880i
\(543\) −8.29527 + 14.3678i −0.355984 + 0.616582i
\(544\) −2.49840 4.32735i −0.107118 0.185534i
\(545\) −20.7516 −0.888900
\(546\) 0.0219083 6.08115i 0.000937587 0.260249i
\(547\) −34.1587 −1.46052 −0.730260 0.683170i \(-0.760601\pi\)
−0.730260 + 0.683170i \(0.760601\pi\)
\(548\) −5.54038 9.59622i −0.236673 0.409930i
\(549\) −1.28811 + 2.23107i −0.0549753 + 0.0952199i
\(550\) 3.98886 6.90892i 0.170086 0.294597i
\(551\) −1.88322 3.26183i −0.0802277 0.138958i
\(552\) −6.91567 −0.294350
\(553\) 17.4317 9.98064i 0.741271 0.424420i
\(554\) −22.2839 −0.946753
\(555\) −0.379358 0.657067i −0.0161029 0.0278910i
\(556\) 5.50876 9.54145i 0.233623 0.404648i
\(557\) 20.2395 35.0559i 0.857576 1.48537i −0.0166578 0.999861i \(-0.505303\pi\)
0.874234 0.485505i \(-0.161364\pi\)
\(558\) 2.19283 + 3.79808i 0.0928297 + 0.160786i
\(559\) −4.78995 −0.202593
\(560\) −2.62774 1.52977i −0.111042 0.0646448i
\(561\) −10.8345 −0.457435
\(562\) 3.55395 + 6.15562i 0.149914 + 0.259659i
\(563\) −9.10220 + 15.7655i −0.383612 + 0.664436i −0.991576 0.129529i \(-0.958653\pi\)
0.607964 + 0.793965i \(0.291987\pi\)
\(564\) −1.86113 + 3.22356i −0.0783675 + 0.135737i
\(565\) −4.96351 8.59705i −0.208816 0.361681i
\(566\) 15.7474 0.661911
\(567\) 2.28651 + 1.33112i 0.0960243 + 0.0559019i
\(568\) 0.323591 0.0135776
\(569\) 8.01265 + 13.8783i 0.335908 + 0.581809i 0.983659 0.180043i \(-0.0576237\pi\)
−0.647751 + 0.761852i \(0.724290\pi\)
\(570\) 0.574618 0.995268i 0.0240681 0.0416872i
\(571\) −3.51315 + 6.08495i −0.147021 + 0.254647i −0.930125 0.367243i \(-0.880302\pi\)
0.783104 + 0.621890i \(0.213635\pi\)
\(572\) 2.49189 + 4.31608i 0.104191 + 0.180464i
\(573\) −15.8902 −0.663822
\(574\) 1.85195 1.06034i 0.0772987 0.0442579i
\(575\) 25.4445 1.06111
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −11.4555 + 19.8414i −0.476897 + 0.826010i −0.999649 0.0264748i \(-0.991572\pi\)
0.522753 + 0.852484i \(0.324905\pi\)
\(578\) 3.98396 6.90043i 0.165711 0.287020i
\(579\) 3.24838 + 5.62636i 0.134998 + 0.233824i
\(580\) −4.32852 −0.179732
\(581\) 0.0302568 8.39850i 0.00125527 0.348428i
\(582\) −5.91567 −0.245212
\(583\) −12.2198 21.1653i −0.506093 0.876579i
\(584\) −2.36415 + 4.09483i −0.0978293 + 0.169445i
\(585\) 1.32075 2.28760i 0.0546061 0.0945806i
\(586\) 11.0070 + 19.0646i 0.454694 + 0.787553i
\(587\) −9.55395 −0.394334 −0.197167 0.980370i \(-0.563174\pi\)
−0.197167 + 0.980370i \(0.563174\pi\)
\(588\) −3.45623 6.08724i −0.142533 0.251033i
\(589\) 4.38565 0.180708
\(590\) −5.99133 10.3773i −0.246659 0.427226i
\(591\) 0.532453 0.922235i 0.0219022 0.0379357i
\(592\) −0.330096 + 0.571742i −0.0135668 + 0.0234985i
\(593\) −4.05336 7.02062i −0.166452 0.288302i 0.770718 0.637176i \(-0.219898\pi\)
−0.937170 + 0.348874i \(0.886564\pi\)
\(594\) −2.16830 −0.0889664
\(595\) 0.0547355 15.1931i 0.00224394 0.622857i
\(596\) −21.2170 −0.869082
\(597\) 11.7959 + 20.4310i 0.482772 + 0.836186i
\(598\) −7.94774 + 13.7659i −0.325007 + 0.562929i
\(599\) 9.15859 15.8631i 0.374210 0.648150i −0.615999 0.787747i \(-0.711247\pi\)
0.990208 + 0.139597i \(0.0445807\pi\)
\(600\) 1.83963 + 3.18633i 0.0751025 + 0.130081i
\(601\) 15.5629 0.634824 0.317412 0.948288i \(-0.397186\pi\)
0.317412 + 0.948288i \(0.397186\pi\)
\(602\) −4.78487 + 2.73961i −0.195017 + 0.111658i
\(603\) 8.88568 0.361853
\(604\) −4.70093 8.14226i −0.191278 0.331304i
\(605\) −3.61922 + 6.26867i −0.147142 + 0.254858i
\(606\) 6.43414 11.1443i 0.261369 0.452705i
\(607\) −14.1959 24.5880i −0.576193 0.997996i −0.995911 0.0903411i \(-0.971204\pi\)
0.419718 0.907655i \(-0.362129\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −8.61197 5.01358i −0.348975 0.203160i
\(610\) 2.96069 0.119875
\(611\) 4.27775 + 7.40928i 0.173059 + 0.299747i
\(612\) 2.49840 4.32735i 0.100992 0.174923i
\(613\) 17.7205 30.6927i 0.715723 1.23967i −0.246957 0.969026i \(-0.579431\pi\)
0.962680 0.270642i \(-0.0872360\pi\)
\(614\) 7.18879 + 12.4513i 0.290116 + 0.502495i
\(615\) 0.926955 0.0373784
\(616\) 4.95783 + 2.88627i 0.199757 + 0.116291i
\(617\) 27.6964 1.11502 0.557508 0.830172i \(-0.311758\pi\)
0.557508 + 0.830172i \(0.311758\pi\)
\(618\) −3.47791 6.02392i −0.139902 0.242317i
\(619\) 13.1957 22.8556i 0.530380 0.918645i −0.468992 0.883203i \(-0.655383\pi\)
0.999372 0.0354425i \(-0.0112841\pi\)
\(620\) 2.52008 4.36490i 0.101209 0.175299i
\(621\) −3.45783 5.98914i −0.138758 0.240336i
\(622\) 2.97452 0.119267
\(623\) −28.4194 + 16.2717i −1.13860 + 0.651912i
\(624\) −2.29847 −0.0920126
\(625\) −3.46659 6.00431i −0.138664 0.240173i
\(626\) −8.37942 + 14.5136i −0.334909 + 0.580079i
\(627\) −1.08415 + 1.87780i −0.0432968 + 0.0749922i
\(628\) −3.07361 5.32364i −0.122650 0.212436i
\(629\) −3.29884 −0.131533
\(630\) 0.0109541 3.04058i 0.000436423 0.121139i
\(631\) 21.3293 0.849105 0.424553 0.905403i \(-0.360431\pi\)
0.424553 + 0.905403i \(0.360431\pi\)
\(632\) −3.79604 6.57493i −0.150998 0.261537i
\(633\) 8.93497 15.4758i 0.355133 0.615109i
\(634\) −1.40531 + 2.43406i −0.0558118 + 0.0966689i
\(635\) −7.96897 13.8027i −0.316239 0.547742i
\(636\) 11.2713 0.446937
\(637\) −16.0889 0.115927i −0.637465 0.00459319i
\(638\) 8.16675 0.323325
\(639\) 0.161795 + 0.280238i 0.00640052 + 0.0110860i
\(640\) −0.574618 + 0.995268i −0.0227138 + 0.0393414i
\(641\) −9.50348 + 16.4605i −0.375365 + 0.650151i −0.990382 0.138363i \(-0.955816\pi\)
0.615017 + 0.788514i \(0.289149\pi\)
\(642\) 6.19933 + 10.7376i 0.244668 + 0.423777i
\(643\) 3.46630 0.136697 0.0683487 0.997661i \(-0.478227\pi\)
0.0683487 + 0.997661i \(0.478227\pi\)
\(644\) −0.0659178 + 18.2970i −0.00259752 + 0.721004i
\(645\) −2.39497 −0.0943020
\(646\) −2.49840 4.32735i −0.0982981 0.170257i
\(647\) −6.18045 + 10.7049i −0.242979 + 0.420851i −0.961561 0.274590i \(-0.911458\pi\)
0.718583 + 0.695441i \(0.244791\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 11.3040 + 19.5791i 0.443722 + 0.768549i
\(650\) 8.45667 0.331698
\(651\) 10.0696 5.76543i 0.394660 0.225965i
\(652\) −8.60793 −0.337113
\(653\) −25.3561 43.9181i −0.992262 1.71865i −0.603658 0.797244i \(-0.706291\pi\)
−0.388605 0.921405i \(-0.627043\pi\)
\(654\) −9.02841 + 15.6377i −0.353039 + 0.611481i
\(655\) 7.01684 12.1535i 0.274171 0.474877i
\(656\) −0.403292 0.698521i −0.0157459 0.0272727i
\(657\) −4.72830 −0.184469
\(658\) 8.51095 + 4.95477i 0.331792 + 0.193157i
\(659\) −29.4985 −1.14910 −0.574549 0.818470i \(-0.694822\pi\)
−0.574549 + 0.818470i \(0.694822\pi\)
\(660\) 1.24595 + 2.15804i 0.0484984 + 0.0840016i
\(661\) 18.9490 32.8205i 0.737029 1.27657i −0.216799 0.976216i \(-0.569562\pi\)
0.953827 0.300355i \(-0.0971051\pi\)
\(662\) −5.06954 + 8.78069i −0.197033 + 0.341271i
\(663\) −5.74250 9.94630i −0.223020 0.386282i
\(664\) −3.17435 −0.123189
\(665\) −2.62774 1.52977i −0.101899 0.0593221i
\(666\) −0.660191 −0.0255819
\(667\) 13.0237 + 22.5577i 0.504279 + 0.873438i
\(668\) −5.98744 + 10.3706i −0.231661 + 0.401249i
\(669\) 2.22302 3.85039i 0.0859471 0.148865i
\(670\) −5.10588 8.84364i −0.197257 0.341660i
\(671\) −5.58602 −0.215646
\(672\) −2.29604 + 1.31461i −0.0885716 + 0.0507123i
\(673\) −0.234048 −0.00902187 −0.00451094 0.999990i \(-0.501436\pi\)
−0.00451094 + 0.999990i \(0.501436\pi\)
\(674\) 10.7182 + 18.5645i 0.412850 + 0.715077i
\(675\) −1.83963 + 3.18633i −0.0708073 + 0.122642i
\(676\) 3.85851 6.68313i 0.148404 0.257044i
\(677\) 5.61173 + 9.71981i 0.215676 + 0.373562i 0.953482 0.301451i \(-0.0974710\pi\)
−0.737805 + 0.675014i \(0.764138\pi\)
\(678\) −8.63792 −0.331737
\(679\) −0.0563861 + 15.6513i −0.00216390 + 0.600641i
\(680\) −5.74250 −0.220215
\(681\) 10.0469 + 17.4017i 0.384997 + 0.666835i
\(682\) −4.75470 + 8.23539i −0.182067 + 0.315349i
\(683\) −8.25937 + 14.3056i −0.316036 + 0.547390i −0.979657 0.200679i \(-0.935685\pi\)
0.663621 + 0.748069i \(0.269019\pi\)
\(684\) −0.500000 0.866025i −0.0191180 0.0331133i
\(685\) −12.7344 −0.486557
\(686\) −16.1382 + 9.08624i −0.616158 + 0.346914i
\(687\) −17.9555 −0.685043
\(688\) 1.04198 + 1.80477i 0.0397253 + 0.0688062i
\(689\) 12.9534 22.4360i 0.493486 0.854744i
\(690\) −3.97387 + 6.88295i −0.151283 + 0.262029i
\(691\) −20.7288 35.9033i −0.788559 1.36582i −0.926850 0.375433i \(-0.877494\pi\)
0.138291 0.990392i \(-0.455839\pi\)
\(692\) 8.10185 0.307986
\(693\) −0.0206675 + 5.73675i −0.000785093 + 0.217921i
\(694\) −29.1826 −1.10776
\(695\) −6.33087 10.9654i −0.240144 0.415941i
\(696\) −1.88322 + 3.26183i −0.0713831 + 0.123639i
\(697\) 2.01516 3.49037i 0.0763298 0.132207i
\(698\) 4.68104 + 8.10780i 0.177180 + 0.306885i
\(699\) −10.2539 −0.387839
\(700\) 8.44771 4.83679i 0.319293 0.182814i
\(701\) 26.9202 1.01676 0.508380 0.861133i \(-0.330244\pi\)
0.508380 + 0.861133i \(0.330244\pi\)
\(702\) −1.14924 1.99054i −0.0433752 0.0751280i
\(703\) −0.330096 + 0.571742i −0.0124498 + 0.0215637i
\(704\) 1.08415 1.87780i 0.0408604 0.0707724i
\(705\) 2.13887 + 3.70464i 0.0805547 + 0.139525i
\(706\) −33.5994 −1.26453
\(707\) −29.4234 17.1292i −1.10658 0.644212i
\(708\) −10.4266 −0.391856
\(709\) −14.8103 25.6522i −0.556212 0.963388i −0.997808 0.0661736i \(-0.978921\pi\)
0.441596 0.897214i \(-0.354412\pi\)
\(710\) 0.185941 0.322059i 0.00697825 0.0120867i
\(711\) 3.79604 6.57493i 0.142363 0.246579i
\(712\) 6.18879 + 10.7193i 0.231935 + 0.401722i
\(713\) −30.3297 −1.13586
\(714\) −11.4252 6.65134i −0.427577 0.248920i
\(715\) 5.72755 0.214198
\(716\) 3.42378 + 5.93016i 0.127953 + 0.221620i
\(717\) 0.869826 1.50658i 0.0324843 0.0562644i
\(718\) −12.1815 + 21.0990i −0.454610 + 0.787407i
\(719\) 13.2519 + 22.9530i 0.494213 + 0.856001i 0.999978 0.00666979i \(-0.00212307\pi\)
−0.505765 + 0.862671i \(0.668790\pi\)
\(720\) −1.14924 −0.0428295
\(721\) −15.9708 + 9.14421i −0.594785 + 0.340548i
\(722\) −1.00000 −0.0372161
\(723\) −10.4246 18.0560i −0.387695 0.671508i
\(724\) 8.29527 14.3678i 0.308291 0.533976i
\(725\) 6.92883 12.0011i 0.257330 0.445709i
\(726\) 3.14924 + 5.45464i 0.116879 + 0.202441i
\(727\) 27.4510 1.01810 0.509051 0.860736i \(-0.329996\pi\)
0.509051 + 0.860736i \(0.329996\pi\)
\(728\) −0.0219083 + 6.08115i −0.000811974 + 0.225382i
\(729\) 1.00000 0.0370370
\(730\) 2.71697 + 4.70593i 0.100560 + 0.174174i
\(731\) −5.20658 + 9.01806i −0.192572 + 0.333545i
\(732\) 1.28811 2.23107i 0.0476100 0.0824629i
\(733\) 7.08255 + 12.2673i 0.261600 + 0.453104i 0.966667 0.256036i \(-0.0824166\pi\)
−0.705067 + 0.709140i \(0.749083\pi\)
\(734\) 33.1571 1.22385
\(735\) −8.04445 0.0579634i −0.296724 0.00213801i
\(736\) 6.91567 0.254915
\(737\) 9.63341 + 16.6856i 0.354851 + 0.614621i
\(738\) 0.403292 0.698521i 0.0148454 0.0257129i
\(739\) −3.77009 + 6.52999i −0.138685 + 0.240210i −0.926999 0.375063i \(-0.877621\pi\)
0.788314 + 0.615273i \(0.210954\pi\)
\(740\) 0.379358 + 0.657067i 0.0139455 + 0.0241543i
\(741\) −2.29847 −0.0844365
\(742\) 0.107434 29.8209i 0.00394404 1.09476i
\(743\) −53.8226 −1.97456 −0.987279 0.158997i \(-0.949174\pi\)
−0.987279 + 0.158997i \(0.949174\pi\)
\(744\) −2.19283 3.79808i −0.0803929 0.139245i
\(745\) −12.1917 + 21.1166i −0.446668 + 0.773652i
\(746\) −11.2730 + 19.5254i −0.412734 + 0.714876i
\(747\) −1.58718 2.74907i −0.0580718 0.100583i
\(748\) 10.8345 0.396150
\(749\) 28.4678 16.2994i 1.04019 0.595568i
\(750\) 9.97452 0.364218
\(751\) −10.3881 17.9927i −0.379068 0.656565i 0.611859 0.790967i \(-0.290422\pi\)
−0.990927 + 0.134402i \(0.957089\pi\)
\(752\) 1.86113 3.22356i 0.0678683 0.117551i
\(753\) 1.59831 2.76836i 0.0582458 0.100885i
\(754\) 4.32852 + 7.49722i 0.157635 + 0.273033i
\(755\) −10.8050 −0.393233
\(756\) −2.28651 1.33112i −0.0831595 0.0484124i
\(757\) −15.9757 −0.580647 −0.290323 0.956929i \(-0.593763\pi\)
−0.290323 + 0.956929i \(0.593763\pi\)
\(758\) 9.38078 + 16.2480i 0.340725 + 0.590154i
\(759\) 7.49762 12.9863i 0.272146 0.471371i
\(760\) −0.574618 + 0.995268i −0.0208436 + 0.0361022i
\(761\) −7.09149 12.2828i −0.257066 0.445252i 0.708388 0.705823i \(-0.249422\pi\)
−0.965455 + 0.260571i \(0.916089\pi\)
\(762\) −13.8683 −0.502395
\(763\) 41.2871 + 24.0358i 1.49469 + 0.870156i
\(764\) 15.8902 0.574887
\(765\) −2.87125 4.97315i −0.103810 0.179805i
\(766\) −4.05885 + 7.03014i −0.146652 + 0.254009i
\(767\) −11.9827 + 20.7546i −0.432669 + 0.749404i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −39.7426 −1.43316 −0.716578 0.697507i \(-0.754292\pi\)
−0.716578 + 0.697507i \(0.754292\pi\)
\(770\) 5.72148 3.27587i 0.206188 0.118054i
\(771\) 15.0219 0.541001
\(772\) −3.24838 5.62636i −0.116912 0.202497i
\(773\) −0.0918959 + 0.159168i −0.00330527 + 0.00572489i −0.867673 0.497135i \(-0.834385\pi\)
0.864368 + 0.502860i \(0.167719\pi\)
\(774\) −1.04198 + 1.80477i −0.0374533 + 0.0648711i
\(775\) 8.06796 + 13.9741i 0.289810 + 0.501965i
\(776\) 5.91567 0.212360
\(777\) −0.00629271 + 1.74669i